THE LIBRARY 
 
 OF 
 
 THE UNIVERSITY 
 OF CALIFORNIA 
 
 PRESENTED BY 
 
 PROF. CHARLES A. KOFOID AND 
 MRS. PRUDENCE W. KOFOID 
 
y 
 
y, del. 
 
 WATERSPOUT OBSERVED OFF THE COAST OF SOUTHERN SICILY IN AUGUST, 1876. 
 
 Frontispiece. 
 
A POPULAR TREATISE 
 
 ON THE 
 
 WINDS 
 
 COMPRISING THE 
 
 GENERAL MOTIONS OF THE ATMOSPHERE, 
 
 MONSOONS, CYCLONES, TORNADOES, 
 
 WATERSPOUTS, HAIL-STORMS, 
 
 ETC. ETC. 
 
 BY 
 
 WILLIAM ^ER^EL, M.A., PH.D., 
 
 LATE PROFESSOR AND ASSISTANT IN THE SIGNAL SERVICE, MEMBER OF THE NATIONAL 
 
 ACADEMY OF SCIENCES AND OF OTHER HOME AND FOREIGN 
 
 SCIENTIFIC SOCIETIES. 
 
 Eontron 
 MACMILLAN AND CO, 
 
 1890 
 
 /7 
 
FERRIS BROS., 
 
 Printers, 
 
 326 Pearl Street, 
 
 New York. 
 
QcKl 
 
 PREFACE. 
 
 SINCE the middle of the present century great advances 
 have been made in meteorology, especially in the study of the 
 mechanics of the atmosphere. Before this epoch little was 
 known even with regard to the general motions of the atmos- 
 phere, the true theories of cyclones, tornadoes, water-spouts, 
 hail-storms, cloud-bursts, etc., were entirely unknown, and the 
 observed phenomena were mostly regarded as mysteries. Al- 
 though there are still some things which require more study 
 and further explanation, yet these subjects have now become 
 much clearer and better understood ; and so great has the 
 change been, that the recent advances are often called the " new 
 meteorology." 
 
 During this period of advancement the writer has had pub- 
 lished a number of meteorological papers in an endeavor to ad- 
 vance our knowledge in the subjects mentioned above. The 
 first of these, entitled " An Essay on the Winds and the Cur- 
 rents of the Ocean," was published in the Nashville Journal of 
 Medicine and Surgery in the year 1856. The writer's attention 
 was first directed to this subject by reading Maury's Physical 
 Geography of the Sea, from which he learned that the pressure 
 of the atmosphere is less both at the poles and at the equator 
 of the earth than it is over two belts extending around the 
 globe about the parallels of 30 north and south of the equator. 
 An attempt to account for this phenomenon, which was then 
 inexplicable upon any known principles, resulted in the essay 
 named above. This essay was mostly of a popular character, 
 and only a very imperfect, though at the time important, first 
 step, which subsequently led to further researches, and the dis- 
 covery of the effect of the earth's rotation in the dynamics of 
 the atmosphere, which has served to clear up many of the 
 
 iii 
 
 M37345O 
 
IV PREFACE. 
 
 mysteries of the older meteorology. This, essay was subse- 
 quently republished by the Signal Service in Professional Paper 
 of the Signal Service, No. XII. 
 
 In the year 1858 this subject was again taken up by the 
 writer, but treated in a very mathematical manner, and the re- 
 sults were given in a paper entitled " The Motions of Fluids and 
 Solids relative to the Earth's Surface," which was published in 
 a series of parts in Runkle's Mathematical Monthly, and subse- 
 quently republished by the Signal Service in Professional Paper 
 of the Signal Service, No. VIII, with extensive notes, giving the 
 mathematical processes in detail, by Professor Frank Waldo, 
 then in the Signal Service. 
 
 This subject was taken up a second time by the writer a 
 number of years afterward, but still treated in a very mathe- 
 matical manner, and the researches so extended as to embrace 
 cyclones, tornadoes, water-spouts, hail-storms, cloud-bursts, etc. 
 This resulted in his " Meteorological Researches for the Use 
 of the Coast Pilot," published in three parts in the Reports of 
 the Superintendent of the Coast and Geodetic Survey for the 
 years 1875, 1878, and 1881. 
 
 In his " Recent Advances in Meteorology," published as the 
 second part of the Chief Signal Officer's Report for 1885, the 
 writer went over the same ground again, but adopted mathe- 
 matical methods somewhat simplified and gave further exten- 
 sions of the more popular parts of the subjects. 
 
 Although these papers have been pretty widely distributed 
 as Government publications, yet they have fallen into the hands 
 of comparatively few of the large number of readers who are 
 interested in the important subjects of which they treat, and 
 they are also too mathematical, for the most part, for many 
 readers. On account of the great and pretty general interest 
 which has been taken of late years in meteorological subjects, 
 there are now many who wish to obtain at least a general, 
 if not a thorough, knowledge of the most important princi- 
 ples of these subjects, but who, either from lack of ability or 
 time and inclination to take hold of difficult reading, are de- 
 sirous of having some more popular presentation of them,. 
 
PREFACE. V 
 
 and the desire has often been expressed that the writer 
 would undertake such a presentation of these subjects, treated 
 mostly in a mathematical way in the papers referred to. To 
 comply with this desire, so far as the nature of the subjects 
 treated will admit, is the object of the present work. 
 
 From the nature of the subjects, however, little can be 
 done where even the simpler operations of mathematics are en- 
 tirely discarded, and the results of such a method of treatment 
 would be very unsatisfactory to a large class of readers who 
 have some knowledge of the simpler principles and operations 
 of mathematics, so that these have been used in the work ; but 
 all that could well be done has been done in the way of mere 
 verbal explanations and illustrations of the subjects. It is there- 
 fore thought that the work can be read with profit by those 
 who are deficient in even the elementary principles of mathe- 
 matics. 
 
 In the present more popular presentation of the subjects 
 treated in the works referred to above, of course the methods are 
 very different, and the whole matter is very much expanded, so- 
 that all has been rewritten except a few pages in the chapter on 
 Tornadoes, which have been copied with little or no change 
 from my " Recent Advances in Meteorology." In the mathe- 
 matical treatment of the subjects, where this has been intro- 
 duced, no claim is made to elegance of methods, and sometimes 
 simple arithmetical methods are used instead of algebraic 
 methods and the calculus, such as almost any one well versed 
 in the higher methods of analysis frequently adopts in the first 
 discovery of important principles and results, or which he may 
 use as a check of results obtained in a more mathematical way, 
 the principal object being to give some insight into the sub- 
 jects, though in a homely way, to readers who have little facil- 
 ity ia the use of mathematics. 
 
 The subject-matter contained in the following pages^ is 
 mostly an expansion of a series of forty lectures delivered by 
 the writer before a class of army officers of the Signal Service 
 during the months of February and March, 1886, in which the 
 manner of presentation of the matter was somewhat the same 
 
VI PREFA CE. 
 
 as that adopted here. This was necessary, since the members 
 of the class had no time for reading and study, and so for en- 
 tering into the matter more thoroughly, for all their time not 
 given to the hearing of the lectures had to be given to their 
 daily work in the service. 
 
 A thorough knowledge of the principles contained in the 
 following work, it is thought, will be of great advantage to all 
 who are desirous of understanding the observed phenomena 
 and sequences of the weather, and of forming rules for weather 
 prediction, and especially to the seaman on the ocean in the 
 management of his vessel. For although no attempt has been 
 made to lay down detailed rules to be followed in the various 
 cases, yet the principles are given and explained by which each 
 one with a knowledge of them can intelligently form his own 
 rule in any case, which is generally much better than to blindly 
 follow rules which can rarely be given so as to cover all cases 
 without exceptions. 
 
 So much interest is now being taken in meteorology that its 
 principles must soon be taught to a considerable extent in our 
 colleges and universities, and it must form a part of any course 
 in Physics where a separate chair is not assigned to it. It is 
 therefore thought that lecturers on meteorological subjects be- 
 fore college classes, or any general and larger audiences, will 
 find much in the following work which can be advantageously 
 and conveniently used. 
 
 The author is indebted to the courtesy of the Chief Signal 
 Officer for permission to copy from the publications of the Sig- 
 nal Service a few of the illustrations contained in the following' 
 pages. 
 
 He is also indebted to the kindness of his friend Professor 
 Frank Waldo for the full and well-arranged index to this work. 
 
 WM. FERREL. 
 
 KANSAS CITY, Mo., April, 1889. 
 
CONTENTS. 
 
 CHAPTER I. 
 
 THE CONSTITUTION AND NATURE OF THE ATMOSPHERE. 
 
 SECTION 
 
 I Composition of the Atmosphere, I 
 
 2-3 Boyle and Mariotte's Law, 2 
 
 4 The Law of Charles and Gay-Lussac, 3 
 
 5-8 Arrangement of the Constituents, 4 
 
 9-13 Pressure of the Atmosphere, 9 
 
 14-16 Aqueous Vapor of the Atmosphere, 16 
 
 17-27 Dynamical Heating and Cooling of the Air 20 
 
 28-31 Stable and Unstable Equilibrium, 34 
 
 32 Relation between Changes of Altitude and Density, 39 
 
 33 The Viscosity of the Air, 40 
 
 CHAPTER II. 
 
 THE MOTIONS OF BODIES RELATIVE TO THE EARTH'S SURFACE. 
 
 34 Introduction, 42 
 
 35-40 Centrifugal Force, 42 
 
 41-43 The Principle of the Preservation of Areas, 54 
 
 44-46 Centrifugal Force in Motions on the Earth's Surface, ...... 59 
 
 47-49 The Principle of Equal Areas in Motions on the Earth's Surface, . 65 
 
 50-51 Resultants of the Two Forces and Motions, ........ 71 
 
 52 Where the Centre of Force is not the Pole, ..,,.*.. 75 
 
 53-60 The Deflecting Force of the Earth's Rotation, 77 
 
 CHAPTER HI. 
 THE GENERAL CIRCULATION OF THE ATMOSPHERE. 
 
 61-67 Introduction, 89 
 
 68-69 Distribution of Temperature over the Earth's Surface, .... 98 
 
 70 Distribution of Aqueous Vapor, 101 
 
 71-73 General Circulation without Rotation of the Earth, 102 
 
 74-82 General Circulation with Rotation of the Earth, 106 
 
 83-89 Comparisons with Observations, 121 
 
 v 
 
VI CONTENTS. 
 
 SECTION PAGE 
 
 90-96 Effect of the General Motions upon Atmospheric Pressure, . . . 133 
 97-99 East Velocities deduced from ^Pressure and jTemperature Gra- 
 dients, 145 
 
 100-103 Surface Winds, Calms, and Calm-belts 149 
 
 104 Summary and Graphic Representation of the Motions and Pres- 
 sures, ., . '. 154 
 
 105-109 Annual Oscillations of the Calm-belts, 156 
 
 CHAPTER IV. 
 CLIMATIC INFLUENCES OF THE GENERAL CIRCULATION. 
 
 no On the Relative Climates of the Lower and Higher~Latitudes, . . 163 
 
 TH-I2O Wet and Dry Zones, 164 
 
 1 21-122 Relative Temperatures of East and West Sides of the Continents, . 179 
 
 123-128 In Connection with Mountain Ranges, 183 
 
 CHAPTER V. 
 MONSOONS, AND LAND- AND SEA-BREEZES. 
 
 129-136 Introduction, 193 
 
 137-145 The Monsoons of Asia and the Indian Ocean 200 
 
 146-147 The Monsoons of Africa, 212 
 
 148-149 The Monsoons of North America, 214 
 
 150 The Monsoons of South America, 217 
 
 151-152 Land- and Sea-breezes, 219 
 
 153-154 Mountain and Valley Winds, 223 
 
 CHAPTER VI. 
 
 CYCLONES. 
 
 155 Introduction, 226 
 
 156-165 Vertical Circulation, 227 
 
 166-172 Gyratory Motion of Cyclones, 241 
 
 I 73~ I 74 Atmospheric Pressure in Cyclones, 251 
 
 I 75~ I 76 Resultant Motions, 255 
 
 177 Surface Calms, 257 
 
 178 Graphic Representation of Motions and Pressures, 258 
 
 179-183 Comparisons with Observation, 261 
 
 184 Gradual Enlargement of Cyclones, 273 
 
 185-191 Progressive Motion of Cyclones, 275 
 
 192-193 Veering and Backing of the Wind and Changes of Pressure and 
 
 i. Temperature, 287 
 
 194 Cyclone of August 2, 1837, at St. Thomas 292 
 
CONTENTS. vii 
 
 SECTION PAGE 
 
 195 Manilla Typhoon of November 5, 1882 295 
 
 196 Cyclone of Cienfuegos on September 5, 1882, 297 
 
 197-199 Rain and Cloud Areas in Cyclones, . . . 298 
 
 200-205 Resultants of Cyclonic and Progressive Motions 303 
 
 206-207 The Eye of the Storm, 311 
 
 208-209 Secondary Cyclones, . . . 315 
 
 210-212 Stationary Cyclones 318 
 
 213-216 Cold Waves and Northers, 322 
 
 217 Pamperos, 329 
 
 218 The Mistral and the Bora, 331 
 
 219-220 The Foehn and the Chinooks, 332 
 
 221 The Sirocco, 336 
 
 222-226 Cyclones with a Cold Centre, 337 
 
 227-228 Areas of High Barometric Pressure, 342 
 
 CHAPTER VII. 
 TORNADOES. 
 
 229 Introduction, 347 
 
 230-231 The Conditions of a Tornado 348 
 
 232-237 Gyratory Velocity and its Effect on Pressure, . . . ." . . . 353 
 
 238-243 The Energy of a Tornado, 362 
 
 244-258 Force of the Wind and Supporting Power of Ascend ing Currents, . 371 
 
 259-261 Resultants of Gyratory and Progressive Motions 395 
 
 262 Rainfall in Tornadoes, 399 
 
 263-271 Waterspouts 401 
 
 272-276 Hail-storms, 420 
 
 277-281 Cloud-bursts, 429 
 
 282-283 Fair-weather Whirlwinds and White Squalls 434 
 
 284-292 Where Tornadoes are most likely to Occur, 437 
 
 293-294 Sand-spouts and Dust- whirlwinds, 443 
 
 295 Blasts of Wind and Oscillations of the Wind- vane, 446 
 
 296 " Pumping " of the Barometer, . . 448 
 
 CHAPTER VIII. 
 
 THUNDERSTORMS. 
 
 297 Introduction, 450 
 
 298-302 Observed Phenomena, 450 
 
 303-309 The Theory 459 
 
 310-311 Relation between Thunder-storms and Cyclones 467 
 
 312 Annual and Diurnal Inequalities 470 
 
 APPENDIX 473 
 
 INDEX 481 
 
THE WINDS. 
 
 CHAPTER I. 
 THE CONSTITUTION AND NATURE OF THE ATMOSPHERE. 
 
 COMPOSITION OF THE ATMOSPHERE. 
 
 1. THE gaseous envelope surrounding the earth called air, 
 and regarded as a whole, the Atmosphere, is composed of the 
 two principal gases in its constitution, oxygen and nitrogen, 
 together with a small amount of carbonic acid and traces of 
 other gases. These constitute what is called dry air. When 
 composed of oxygen and nitrogen only, it is said to be dry and 
 pure. In addition to the constituents of dry air the atmosphere 
 contains also a variable amount of aqueous vapor, which, in a 
 warm climate, may amount to one-twentieth part, or more, of 
 the whole. The proportions of dry air, neglecting the slight 
 and mostly unmeasurable traces of the other constituents, may 
 be put as follows : Oxygen, 20.95 ; nitrogen, 79.02 ; and car- 
 bonic acid, 0.03 parts, in 100 by volume. 1 * 
 
 The constituents of the atmosphere are not chemically com- 
 bined, but exist together as a mechanical mixture. If the at- 
 mosphere were perfectly at rest each constituent would assume 
 the same status and distribution as it would if the others were 
 not present. Each one, therefore, would form an atmosphere 
 of itself, independent of, and unaffected by, the others. This 
 arrangement of the constituents is called Daltons law. But as 
 perfect quiet for a long time is a condition of this arrangement, 
 on account of the almost continual agitations of the atmosphere, 
 this law is never satisfied. 
 
 * For the references see the Appendix. 
 
2 CONSTITUTION AND NA TURE OF THE A TMOSPHERE. 
 
 BOYLE AND MARIOTTE'S LAW. 
 
 2. Gases are extremely elastic, so that a given amount of 
 any one of them may be compressed into a space almost infi- 
 nitely small ; and if the pressure is sufficiently removed, it ex- 
 pands into a space almost infinitely great. The space which a 
 given amount of gas occupies under varying pressures and tem- 
 peratures is its volume ; and the space which a unit mass, as 
 one gram or one grain, occupies under an assumed standard 
 pressure and temperature is called the specific volume. The 
 standard pressure is that of the mercurial column of the barom- 
 eter 76o mm in height at the temperature of o C., and subject 
 to the action of the force of gravity at sea-level on the paral- 
 lel of 45; and the standard temperature is that of melting ice. 
 
 If we let P represent the pressure and Fthe volume of any 
 given amount of gas at any temperature, then, however much 
 the pressure may vary, the temperature remaining the same, we 
 have sensibly the product PV equal to a constant. The law 
 represented by this expression is called Boyle and Mariottes 
 law, from the names of its two independent discoverers, of 
 whom Boyle seems to have been the first. 
 
 If we let P represent the standard pressure, as defined 
 above, and F the specific volume of the gas, we have, what- 
 ever may be the pressure, 
 
 PV P V 
 
 * o * o > 
 
 in which Fis the volume of unit mass at standard temperature 
 of oC. when subject to the pressure P. 
 
 According to Boyle and Mariotte's law, whatever the tem- 
 perature of the gas, if P is doubled Fis reduced to one half, or 
 if P is diminished to one half Fis then doubled, and so for 
 any other ratios, either integral or fractional ; and, consequently, 
 if P is infinitely great, F becomes infinitely small, and vice versa. 
 
 The elastic or expansive force of a gas, which in a static 
 state of the gas is exactly equal to the pressure, arises, according 
 to the kinetic theory of gases, from the action of the atoms 
 or molecules upon one another and upon the sides of the con- 
 taining vessel in their numerous contacts in flying x -with very 
 
THE LAW OF CHARLES AND GAY-LUSSAC. 3 
 
 great and differing velocities in* all directions. The molecules 
 of different gases at the same temperature have, on the average, 
 different velocities ; and as the forces are as the squares of the 
 velocities, different gases have different elastic forces and vol- 
 umes under the same conditions of pressure and temperature. 
 
 3. The law of Boyle and Mariotte is not strictly true for 
 any of the gases, or for the atmosphere regarded as a simple 
 gas ; and this is especially the case where the pressure is either 
 extremely great or extremely small. According to Regnault's 
 experiments, the product PV in the case of the atmosphere de- 
 creases with increase of pressure up to the pressure of about 
 65 atmospheres, after which it increases, and for very great 
 pressures it becomes much greater than it is in the case of the 
 ordinary pressure of the atmosphere at the earth's surface. 
 According to the experiments of Mendeleef 2 of St. Peters- 
 burg, the atmosphere conforms to Boyle's law at a pressure 
 of about 650 millimeters of mercury ; but for smaller pressures 
 the product PV diminishes, and at very low pressures the air 
 seems to almost entirely lose its elasticity and become an ex- 
 ceedingly rare liquid. 
 
 THE LAW OF CHARLES AND GAY-LUSSAC. 
 
 4. The elastic force of a gas and of the atmosphere is in- 
 creased with increase of temperature. It is found from ex- 
 periment that its volume increases the -^^ part of what it is at 
 the temperature of melting ice for each degree Centigrade of 
 increase of temperature. This is the law of Charles and Gay- 
 Lussac, so called from its discoverers, of whom Charles is thought 
 to have been the first. By this law the volume of unit mass of 
 gas under the standard pressure P and temperature r be- 
 comes V (i H-^-g-r). We therefore have, as an expression of 
 both the laws of Boyle and Charles combined, 
 
 in which V, for any given pressure P, is the volume of unit mass 
 for the temperature ^ 
 
4 CONSTITUTION AND NATURE OF THE ATMOSPHERE. 
 
 By the law of Charles, as represented in the last member of 
 this equation, a gas would lose all of its elastic force when 
 cooled down to 273 below the zero of the Centigrade scale, 
 since with t = 273 the second member of this expression 
 would vanish. As the elastic force depends upon temperature, 
 or by the kinetic theory of heat, upon the velocities of the 
 molecules in their impacts upon one another, where elasticity 
 ceases temperature also must cease, and hence at 273 below 
 the ordinary zero there cannot be any temperature. This 
 point, therefore, is called the absolute zero, and the temperature 
 reckoned from this point is called the absolute temperature. 
 
 If we put T for the absolute temperature, the preceding 
 expression of the combined laws of Boyle and Charles in a 
 function of T becomes 
 
 in which R = -^^ P F . From this it seems that the pressure,, 
 if the volume remains constant, and conversely the volume, 
 if the pressure remains constant, is proportional to the absolute 
 temperature. Since different gases under the same temperature 
 have different elastic forces, and consequently have different 
 specific volumes, it follows that F differs in different gases, and 
 consequently the value of R in the expression above. 
 
 Since the pressure, and consequently the elastic force, in a 
 static condition of the gas, is proportional to T when the volume 
 is constant, and the elastic force depends upon and is propor- 
 tional to the square of the velocities of the atoms or molecules, 
 it follows that in the increase of velocities with the increase of 
 temperature the mean square of the velocities is as the absolute 
 temperature. 
 
 The law of Charles, as that of Boyle, is not strictly correct 
 in all cases, but the deviations from the law within the range of 
 experiments are extremely small. 
 
 ARRANGEMENT OF THE CONSTITUENTS. 
 
 5. If each of the several constituents of the atmosphere 
 formed an atmosphere of itself around the globe, the arrange- 
 
ARRANGEMENT OF THE CONSTITUENTS. 5 
 
 merits of the particles with regard to altitude would be different 
 in the several gases, so that the densities would not decrease 
 with increase of altitude in the same ratio. Since different 
 gases have different elastic forces, the same weight of each 
 under the same pressure occupies different spaces, or, in other 
 words, has different volumes ; and in order to have the same 
 weights in a given space it is necessary for the gases to be sub- 
 ject to different pressures. As the density under the same 
 pressure must be inversely as the volume where the tempera- 
 ture remains the same, the greater the elastic force of a gas the 
 less its density. Hence the greater the elastic force of a gas 
 forming an atmosphere around the globe, the higher it would 
 be necessary to ascend to get above a certain part of it, as one 
 half or any other proportion, and the more the whole mass 
 would be expanded upward, where it is subject to the pressure 
 only arising from the action of the force of gravitation upon its 
 own mass. 
 
 In the case of a gaseous atmosphere surrounding the earth 
 in a state of static equilibrium, the pressure at any altitude 
 depends upon, and is very nearly proportional to, the mass 
 of gas above that altitude, since the force of gravity of unit 
 mass differs but little at the different altitudes in the atmos- 
 phere. Hence the density, since by Boyle's law it is as the 
 pressure, decreases with increase of altitude ; for the greater 
 the altitude, the less the pressure of the part above that alti- 
 tude. The greater the altitude, therefore, the greater must be 
 the increase of altitude required to cause a given ratio of de- 
 crease of pressure of the whole, and of the density at the earth's 
 surface. For instance, at the altitude where the pressure is 
 reduced to one half of what it is at the earth's surface, it 
 would be necessary to ascend twice as far to arrive where the 
 pressure and density are diminished, say the -j-J^ part of what 
 they are at the earth's surface, as it would at the earth's 
 surface. If, therefore, Boyle's law held for infinitely small 
 pressures, there would be no exterior limit to such a gaseous 
 atmosphere, though it would become extremely rare at no 
 very great altitude. But if, as may be the case according to 
 
6 CONSTITUTION AND NA TURE OF THE A TMOSPHERE. 
 
 the experiments of Mendeleef, 3, a gas under a very low- 
 pressure loses its elastic force and becomes a very rare liquid,, 
 then there must be a limit to such an atmosphere, but the 
 density at this limit must be very small. 
 
 6. According to Dalton's law, deduced from experiments,, 
 and being also in accordance with the kinetic theory of gases r 
 each constituent of our atmosphere in a perfectly quiet state 
 would form a separate and independent atmosphere, with 
 exactly the same arrangement of its parts, and the same rela- 
 tion of the densities of these parts with reference to altitude, as 
 if the other constituents were not present. The constituents,, 
 therefore, with the greatest elastic forces and least densities 
 under the same pressure would be expanded upward the most, 
 so that whatever might be the relative densities of the inde- 
 pendent gaseous atmospheres at the earth's surface, the densi- 
 ties of the more elastic gases would decrease with the increase 
 of elevation at a less rate than those of the gases of less 
 elastic force. For instance, if an atmosphere of hydrogen 
 existed with one of nitrogen, the density of the latter under 
 the same pressure and temperature being fourteen times 
 greater, and consequently its elastic force as many times less, 
 if the densities of both gases at the earth's surface were the 
 same, at only a small altitude the density of the hydrogen 
 would be much greater than that of the nitrogen, since it 
 decreases with increase of altitude at a much less rate, and at 
 an altitude where the nitrogen would sensibly vanish the 
 density of the hydrogen would be diminished by only a small 
 part ; and if at the earth's surface the density of the hydrogen 
 were very small in comparison with that of the nitrogen, yet 
 at only a very moderate altitude it would be the predominating 
 constituent. 
 
 7. The density of a gas, in relation to that of dry and pure 
 air of the same temperature and subject to the same pressure, 
 is called its relative density. The relative densities of oxygen, 
 nitrogen, and carbonic acid gas are respectively 1.1056, 0.9714, 
 and 1.52. The densities and consequently the elastic forces 
 of the two principal constituents of our atmosphere being so 
 
ARRANGEMENT OF THE CONSTITUENTS. 7 
 
 nearly the same, the relations between the densities of the two 
 at the earth's surface and up at considerable altitudes, from 
 what has been shown, would not be very different if the two 
 existed together in accordance with Dalton's law. For 
 instance, the ratios by volume of the two constituents, oxygen 
 and nitrogen, at the earth's surface being as 20.95 to 79.02, re- 
 spectively, I, there would be very nearly the same ratio up at 
 a considerable altitude, the proportion of oxygen to that of 
 nitrogen decreasing very slowly. The density of carbonic acid 
 gas being much greater, and consequently its elastic force 
 much less, its density decreases with increase of altitude at a 
 much more rapid rate than that of oxygen and nitrogen, and 
 consequently in the upper part of the atmosphere the propor- 
 tion of this gas relative to that of the two others would be 
 much less by Dalton's law than it is at the earth's surface ; but 
 this, we have seen, I, forms only a very small part of our 
 atmosphere. This compound atmosphere, therefore, can be 
 regarded as a simple gas ; for although the several gases "of 
 which it is composed would not have, if it were in a quiescent 
 state, quite the same ratios between them at the earth's surface 
 and in the higher altitudes, yet on account of the continued 
 agitation of the atmosphere in its general circulation and by 
 storms, these relations are so nearly the same at different 
 altitudes, that analyses of air at sea-level and on the tops of 
 the highest mountains, and of samples obtained from very 
 high altitudes in balloon ascensions, show no sensible differ- 
 ences in the proportions of oxygen and nitrogen. And as the 
 rate of expansion with increase of temperature is sensibly the 
 same for all gases, the laws of both Boyle and Charles can, 
 therefore, be applied with sensibly the same accuracy as in the 
 case of any simple gas. 
 
 8. According to Boyle's law, the atmosphere with constant 
 temperature would occupy precisely the same volume, however 
 much its mass were increased or diminished. If the mass 
 were doubled or diminished to one half, the pressure, and con- 
 sequently the density, would be changed in the same ratios, and 
 so for any other proportions ; and hence the volume would, in 
 
8 CONSTITUTION AND NA TURE OF THE A TMOSPHERE. 
 
 all cases, be the same. The densities at the same altitudes, 
 however much the whole mass of the atmosphere were 
 increased or diminished, would have the same ratios to the 
 densities at the surface, and it would in all cases be necessary 
 to ascend to th*e same altitude to get above any given propor- 
 tion of the whole. If, therefore, the atmosphere were of uni- 
 form temperature at all altitudes and the part above any given 
 level, as that of the top of Dike's Peak, were considered by 
 itself, it would form an atmosphere exactly similar to the 
 whole, but the pressures and densities at equal altitudes above 
 the base would be less, and in the same proportion as the mass 
 of atmosphere above that level is less than that of the whole. 
 Since the densities at different altitudes in an atmosphere 
 of uniform* temperature decrease in the same ratio as the pres- 
 sures in ascending vertically, and these, as the amounts of 
 atmosphere remaining above, it follows that, at all altitudes, it 
 is necessary to ascend through the same vertical distance, in 
 order to get above a given proportion of the whole existing above 
 the level of the starting point. For instance, if it is necessary 
 to ascend from sea-level to the altitude of Pike's Peak to get 
 above two fifths of the whole atmosphere, then it is necessary 
 to ascend just as much higher to get above two fifths of what 
 still remains above that level, and so on. Again, if it is neces- 
 sary to ascend vertically a given distance to get above one 
 tenth of the atmosphere, then it is necessary to ascend the 
 same distance to get above one tenth of what is left ; and so on, 
 ad infinitum. After the first ascent there would be nine 
 tenths of the whole mass left above, and consequently the 
 pressure and density would be diminished to nine tenths ; after 
 the second ascent, to nine tenths of nine tenths of what they 
 were at the earth's surface ; and after the third ascent, in the 
 ratio of the third power of nine tenths, or in the ratio of 1000 
 to 729, and so on. Hence if different altitudes are taken in 
 arithmetical progression, the corresponding pressures and den- 
 sities diminish in geometrical progression. And this is true 
 whether we start on the earth's surface or at any level above 
 
PRESSURE OF THE ATMOSPHERE. 9 
 
 It, since, as we have seen, the part above that level forms an 
 atmosphere precisely similar to the whole. 
 
 Where the temperature diminishes with increase of altitude, 
 as in the real case of nature, the rate of increase of pressure and 
 of density with increase of altitude, relatively to the whole, be- 
 comes greater above than below, and it is not necessary at any 
 given level to ascend through so great distances, to get above 
 a given proportion of the whole above that level, as it is at the 
 earth's surface. 
 
 PRESSURE OF THE ATMOSPHERE. 
 
 9. The pressure of a body arises from the action of a force 
 upon that body when it is not free to move, and this pressure 
 is measured by the product of the mass of the body into the 
 velocity which would be generated in any assumed unit of time, 
 as one second, if the body were free to move in the direction in 
 which the force acts. The latter factor is called the acceleration. 
 In the case of the atmosphere the force is that of gravity acting 
 in a direction normal to the earth's surface ; and the accelera- 
 tion of this force, usually denoted by g, at the sea-level on the 
 parallel of 45, if the unit of time is one second, is 9.8o6 m or 
 32.17 feet. The atmosphere being subject to the action of the 
 force of gravity, it presses upon the earth's surface at any given 
 place and upon itself at any level above the surface very nearly 
 in proportion to the mass of air above. Since the force of 
 gravity is not precisely the same at all latitudes and altitudes, 
 being about -^ part greater at the poles than at the equator, 
 and diminishing a little with increase of altitude, the same mass 
 of air does not press with quite equal force at all latitudes and 
 altitudes. 
 
 If the surface upon which the atmosphere presses is that of 
 a liquid, and any part of it is entirely relieved of this pressure, 
 as in the case of a barometer tube or a suction pump, the liquid 
 rises until the pressure of the vertical column is exactly equal 
 to that of a column of atmosphere of the same base extending 
 up to its top. Since the volumes of different liquids are inversely 
 
10 CONSTITUTION AND NA TURE OF THE A TMOSPHERE. 
 
 as the densities, the greater the density the less in proportion: 
 is the volume, and consequently the height to which the liquid- 
 has to ascend, to counterpoise the pressure of the atmosphere. 
 
 10. For any given standard temperature, as that of melting 
 ice, the height of the liquid column, either of mercury or of 
 water, becomes a measure of the atmospheric pressure, provided 
 this column and the atmosphere are both acted upon by the same 
 intensity of the force of gravity, that is, force per unit mass. 
 This latter provision becomes necessary as well as that of equal- 
 ity of temperature, since the pressure is measured by the prod- 
 uct of the mass into the acceleration, and the latter, being as 
 the intensity of force, varies slightly with a change of both 
 latitude and altitude. A true measure must be independent of 
 both temperature and locality. 
 
 Since the density of mercury at the standard temperature 
 of melting ice is 13.596 times greater than that of water at the 
 standard temperature of 4 C, which is that of its maximum 
 density, the column of water has to rise 13.596 times higher 
 than that of mercury, both being taken at their standard tem- 
 peratures, in order to counterpoise the pressure of the atmos- 
 phere. Where the atmospheric pressure, as it usually is, is 
 indicated by the height of the mercurial column as observed in 
 the barometer tube, it is called the barometric pressure. 
 
 When the height of the mercurial column is observed under 
 different temperatures and subject to different forces of gravity, 
 there must be a reduction, for the reason just given, to some 
 standard temperature and force. The assumed standard tem- 
 perature is that of melting ice or zero of the Centigrade scale, 
 and the reduction to this standard is called the reduction to 
 freezing. 
 
 Since also the pressure of the same mass of mercury is 
 different on different parallels of latitude, and at different alti- 
 tudes, as has been stated, the observations of the barometer 
 must be reduced to the height at which the mercurial column 
 would stand if placed on the parallel of 45 and at sea-level. 
 This is called the reduction to standard gravity. 
 
 The average barometric pressure for all seasons and for all. 
 
PRESSURE OF THE ATMOSPHERE. II 
 
 parts of the earth's surface is found from observation to be 
 about 760 millimeters (29.92 inches). This is therefore assumed 
 as the pressure of an atmosphere, and in cases of very great 
 pressures is assumed as the unit of pressure, the pressure being- 
 said to be equal to a certain number of atmospheres. It is also 
 the standard pressure, or value of P in 4, in giving the abso- 
 lute and relative densities of gases. 
 
 The reductions of the observed heights of the mercurial col- 
 umn at sea-level, which may be assumed to be sensibly the 
 reduction of 76o mm , to the parallel of 45, is given for each 
 degree of latitude in Table I of the Appendix. For the par- 
 allels from o to 45 the reductions are negative and for the 
 rest positive, as indicated by the signs placed over the first and 
 last columns of the table. 
 
 At the poles the pressure of the mercurial column is greater 
 than on the parallel of 45, and hence the height at which it must 
 stand in order to counterpoise the pressure of the atmosphere 
 is less than it would be if subject to the standard force of 
 gravity of the parallel of 45, and so it must be increased in 
 order to reduce it to this standard. At the equator the reverse 
 is true, and hence the reduction there is negative. Between 
 the parallels of 45 and the poles, therefore, the reductions are 
 positive, but between this parallel and the equator, negative. 
 
 For pressures at different altitudes above the earth's surface 
 where they are less than 7o"o mm the reductions given in the table 
 must be decreased in proportion. For instance, on the top of 
 Pike's Peak where the barometric pressure is only about three 
 fifths of that at the sea-level, the proper reduction would be 
 only about three fifths of that given in the table. 
 
 The forces of gravity are very nearly inversely as the 
 squares of the distances from the earth's surface. Hence at 
 any given altitude above the earth's surface the pressure of the 
 measuring column is less than it would be at the earth's surface. 
 There must be, therefore, a negative reduction applied for the 
 same reason as there is at the equator, where the pressure of the 
 mercurial column is less than it is on the parallel of 45. This re- 
 duction in millimeters is given by the expression 0.000003 &P, 
 
12 CONSTITUTION AND NATURE OF THE ATMOSPHERE. 
 
 in which h is the altitude of the station in meters and P the 
 observed barometric pressure in millimeters. The exact nu- 
 merical coefficient by the law above is 0.00000314, but this 
 is diminished a little for the effect of the increase of gravity at 
 the top by the attraction of the mountain mass. This, however, 
 is found to have scarcely any sensible influence. 3 In English 
 inches the expression above is 0.0000232 kP t in which h must 
 be expressed in feet and P in inches. The reductions for any 
 given altitude are very readily obtained from these simple 
 expressions. 
 
 11. Since force or pressure is measured by the product of 
 the mass into the acceleration, pressure is proportional to, and 
 becomes a measure of, mass where the acceleration is the same 
 for both the measuring and the measured mass, as in the case 
 of ordinary weighing, by counterpoising the one against the 
 other, both having the same position upon the earth with regard 
 to latitude and altitude. Two masses which have the same 
 pressures, or, in other words, exactly counterpoise each other 
 where they are suspended at equal distances from the fulcrum 
 on the beam of the balance, are said to have the same weight. 
 The weight of a body, therefore, is proportional to the mass, 
 and not to its pressure under the varying positions which it may 
 have with regard to the earth and other attracting bodies, and 
 is therefore a measure of mass, and not of pressure. 
 
 Any mass which weighs as much as a cubic centimeter of 
 pure water at the standard temperature of 4 C., which is that 
 of its maximum density, is called a gram. But if this is used 
 as a unit of pressure instead of one of mass, as it sometimes is, 
 this unit must be understood to be the pressure of a gram sub- 
 ject to the standard force of gravity as already defined, since 
 the pressure of the same mass differs in different localities. 
 The pressure of the atmosphere in grams, as thus defined, on a 
 square centimeter of the earth's surface is equal to the height in 
 centimeters of a column of pure water of the temperature of 
 4 C. and subject to the standard force of gravity, which would 
 exactly counterpoise it, as in the case of the mercurial column 
 in a barometer ; for the pressure would be that of a column of 
 
PRESSURE OF THE ATMOSPHERE. 1$ 
 
 water of that height and having a base of one square centimeter,, 
 and consequently the pressure in grams would be equal to the 
 number of centimeters in the height of the column. Or, since 
 the density of mercury at o C. is 13.596 times greater than that 
 of water at the temperature of maximum density, it is equal 
 to the height in centimeters of the mercurial column in the 
 barometer when reduced to freezing and to standard gravity 
 multiplied into 13.596. Hence the pressure in grams of a 
 standard atmosphere of a barometric pressure of 760, or 
 76, upon each square centimeter of the earth's surface, is 
 76 X 13.5961033.3. This upon a square meter is 10333 kilo- 
 grams. 
 
 As a centimeter is equal to 0.3937 of an inch, and a gram is 
 equal to 0.00220462 of a pound avoirdupois, the pressure of 
 such an atmosphere in pounds avoirdupois upon a square inch 
 is 1033.3 multiplied into 0.00220462 and divided by 0.3937*, 
 Avhich gives 14.696. 
 
 12. The density of air relative to that of pure water of the 
 standard temperature of 4 C. is called its absolute density. 
 But as air is very elastic, and its elasticity depends upon both 
 the pressure to which it is subject and its temperature, the 
 density is a very indefinite thing unless it is given for some 
 standard pressure and temperature. The density of pure and 
 dry air under the standard barometric pressure of 76o mm , and 
 standard temperature of o C., deduced from Regnault's experi- 
 ments, is 0.00129278. If the density of such an atmosphere 
 were the same at all altitudes as at the earth's surface, it would 
 of course have a definite limit, and the height of such an atmos- 
 phere in centimeters, neglecting the very slight diminution of 
 gravity with increase of altitude, would be 1033. 3 cm divided by 
 0.00129278, or 7993 meters; for 1033. 3 cm is the height of a column 
 of pure water at the temperature of 4 C., which, being subject 
 to the action of the force of standard gravity, counterpoises a 
 column of air of the same base and of barometric pressure of 
 76o mm which extends to the top of the atmosphere ; and the 
 height of a column of air of uniform density must be to that of 
 the column of water of the same pressure inversely as the 
 
14 CONSTITUTION AND NATURE OF THE ATMOSPHERE. 
 
 densities, that of water here being unity. This is called the 
 .height of a homogeneous atmosphere. 
 
 If the mass of the atmosphere were increased or decreased 
 in any given ratio, the pressure and density at the earth's sur- 
 face would be increased or decreased in precisely the same ratio, 
 and consequently the height of the corresponding homogeneous 
 atmosphere would in all cases be the same. This may also be 
 inferred from what has been stated in 8. For any other 
 temperatures above o C. the corresponding heights of the 
 homogeneous atmospheres would be -pfa part greater for each 
 -degree Centigrade of increase of temperature, and hence for 
 different temperatures they would be as the absolute temper- 
 matures. With the usual amount of carbonic acid gas in the air 
 the height of a homogeneous atmosphere is a very little less 
 than in the case of a pure atmosphere of the same mass. 
 
 In hypothetical atmospheres of the different kinds of gases 
 it is evident that the heights of the corresponding homogeneous 
 atmospheres, whatever their masses, are proportionally greater 
 for gases of greater than for those of less elastic force ; for the 
 <eflect of an increase of elastic force is the same whether this 
 arises from an original greater velocity imparted to the molecules, 
 or from an increase of this velocity and of elasticity by means of 
 an increase of temperature. As in a static atmosphere the elastic 
 force and pressure are equal and the densities for different kinds 
 of atmospheres of the same mass are inversely as the elastic 
 forces, it follows that the heights of homogeneous atmospheres 
 of different elastic forces are inversely as their relative densities. 
 Hence the height of a homogeneous atmosphere of pure and dry 
 air being 7993 meters, that of a hydrogen atmosphere with a 
 relative density of only 0.0692 would be 7993/0.0692 = 115,506 
 meters. 
 
 13. The pressure of the atmosphere at any given altitude 
 can be computed from a well-known formula where the tem- 
 perature at different altitudes is known. This, for the aver- 
 age conditions of the atmosphere for all places and at all alti- 
 tudes, decreases about 0.4 C. for each 100 meters of increase 
 of altitude. Assuming that it decreases at this rate, and that 
 
PRESSURE OF THE ATMOSPHERE. 
 
 the temperature at the earth's surface is 20, the temperatures 
 at the different altitudes given in the second column of the fol- 
 lowing table will be those of the first column, and the baro- 
 metric pressures at the several altitudes as given in the last 
 column : 
 
 Temperatures 
 C. 
 
 ALTITUDES IN 
 
 Pressures in 
 Millimeters. 
 
 Kilometers. 
 
 Miles. 
 
 + 20 
 
 
 
 0.00 
 
 7 60 
 
 + 10 
 
 2-5 
 
 1.56 
 
 565 
 
 o 
 
 5-o 
 
 3." 
 
 416 
 
 IO 
 
 7-5 
 
 4.66 
 
 301 
 
 20 
 
 IO.O 
 
 6.21 
 
 217 
 
 30 
 
 12.5 
 
 7-77 
 
 153 
 
 40 
 
 15.0 
 
 9-32 
 
 108 
 
 50 
 
 17.5 
 
 10.87 
 
 75 
 
 60 
 
 20. o 
 
 12.42 
 
 5i 
 
 80 
 
 25.0 
 
 15-53 
 
 27 
 
 100 
 
 30.0 
 
 18.63 
 
 9 
 
 I2O 
 
 35-o 
 
 21.74 
 
 3 
 
 - 140 
 
 40.0 
 
 24.85 
 
 i 
 
 The pressures are computed from a formula based upon 
 ^Boyle's law, which, we have seen, 3, may not hold accurately 
 up to the altitude of 40 kilometers, where the atmosphere, by 
 this law, becomes extremely rare ; but up to the altitude of 30 
 kilometers, and higher, the deviations from the law are ex- 
 tremely small. But if there is any certain evidence that the at- 
 mosphere extends to the height of 45 miles, as is usually said, 
 and with a density sufficiently great to indicate its existence 
 there by means of reflected light, there must be very great 
 deviations from this law at low pressures. With a higher tem- 
 perature the atmosphere would be expanded upward more, and 
 consequently the pressures would not decrease so rapidly with 
 increase of altitude if our assumed temperatures in the upper 
 part of the atmosphere in the preceding table were greater, but 
 JIG probable error in these assumed temperatures would affect 
 the results much in the last column of the table. 
 
 The following table contains a few of the observed pressures 
 
1 6 CONSTITUTION AND NATURE OF THE ATMOSPHERE. 
 
 of the atmosphere at different altitudes in different parts of the 
 earth : 
 
 PLACES. 
 
 ALTITUDES IN 
 
 Pressures in 
 Millimeters. 
 
 Meters. 
 
 Feet. 
 
 Level of the Ocean . 
 
 
 408 
 1,200 
 1,916 
 
 2,479 
 2,674 
 3,320 
 4.308 
 6,100 
 11,280 
 
 O 
 
 1,339 
 3-937 
 6,285 
 8,130 
 
 8,773 
 10,893 
 
 14,134 
 20,014 
 37,ooo 
 
 760 
 726 
 660 
 600 
 565 
 555 
 5io 
 
 45i 
 360 
 180 
 
 Geneva Observatory ............ 
 
 
 
 Summit of the Great St Bernard . 
 
 The Summit of the Faulhorn (Bravais) 
 
 
 Pike's Peak 
 
 On the Chimborazo (Humboldt and Bonpland). 
 Glaisher's highest balloon ascent 
 
 
 These pressures are annual means in some cases, deduced 
 from a series of years of observations, but mostly they have 
 been obtained from one, or at most only a few, observations 
 under different conditions of temperature and pressure at the 
 surface, and some of the altitudes were only approximately 
 known. 
 
 Table VI, Appendix, contains the height, in meters, of a 
 column of dry air, corresponding to a millimeter of the barome- 
 ter at different temperatures and under different barometric 
 pressures. This will be found useful in the course of this work, 
 and is of great practical value for various purposes. For in- 
 stance, in balloon ascents and in the ascent of high mountains, 
 with the observed barometric pressure and temperature as ar- 
 guments, the table indicates the amount of ascent or descent 
 corresponding to each change of one millimeter in the baro- 
 metric pressure. 
 
 AQUEOUS VAPOR OF THE ATMOSPHERE. 
 
 14. If the atmosphere had the same temperature at all alti- 
 tudes, and were in a perfectly quiet state, the aqueous vapor 
 contained in it would form an independent atmosphere around 
 the globe of the same nature as that of oxygen or nitrogen, 6, 
 and it would be distributed through the other elements in ac- 
 
AQUEOUS VAPOR OF THE ATMOSPHERE. I/ 
 
 cordance with Dalton's law, and so it w r ould exist at all altitudes 
 in the same proportions as if the dry atmosphere were not pres- 
 ent, and the densities would be such as are given by the laws 
 of Boyle and of Charles, just as in the case of the other gases.* 
 But on account of its less relative density than that of the at- 
 mosphere, 0.622, it would be expanded upward more, so that it 
 would be necessary to ascend higher than in the atmosphere, in 
 the ratio of I to 0.622, before getting above the half or any 
 other proportion of it, and it would exist in greater proportions 
 in comparison with the other constituents, oxygen and nitrogen, 
 in the higher altitudes than at and near the earth's surface. But 
 it so happens that the prevailing temperatures of the atmos- 
 phere are those at which aqueous vapor of considerable ten- 
 sion is condensed into liquid, and as the temperature decreases 
 with increase of altitude, the vapor tension at the different al- 
 titudes is not determined, as in the case of the other constitu- 
 ents of the atmosphere, by the laws of Boyle and of Charles, but 
 by the temperatures alone which exist at these altitudes, and 
 hence by a law which is very different. It is found from ex- 
 periment that to any given temperature there corresponds a 
 certain maximum vapor tension, which is the same whether the 
 vapor exists alone or forms a constituent of the atmosphere, 
 and if by any means the tension is increased above this, a part 
 of the vapor is at once condensed and the tension reduced to 
 the maximum corresponding to the existing temperature. 
 
 15. The maximum vapor tensions corresponding to the given 
 temperatures, which include mostly those within the range of 
 ordinary observation, are given in Table II. They have been 
 deduced from Regnault's experiments by the International Bu- 
 reau of Weights and Measures. The table will be convenient 
 for reference in studying the relations between the vapor 
 tension and the temperature, and the relations between the ab- 
 solute maximum tension which can exist in the air at any given 
 altitude and temperature and that which could exist by the laws 
 of Boyle and of Charles. 
 
 If the temperature at the earth's surface were 25, 
 and the same at all altitudes, and the vapor tension 2 
 
1 8 CONSTITUTION AND NATURE OF THE ATMOSPHERE. 
 
 then, in a quiet state of the atmosphere, its distribution 
 with regard to altitude would be according to Dalton's 
 law, or such as would take place if the vapor were an in- 
 dependent atmosphere, in accordance with the laws of Boyle 
 and of Charles. But since the temperature of the atmosphere 
 decreases usually with increase of altitude, and at such a 
 rate that the maximum tension corresponding to it decreases 
 more rapidly than it would by the laws of Boyle and of Charles, 
 the maximum tension is that of Table II corresponding to the 
 existing temperature, and is usually less than what would be 
 given by Dalton's law. It is seen from the table that at any al- 
 titude where the temperature is at the zero of the Centigrade 
 scale the maximum vapor tension which can exist there is only 
 4.569 mm ; whatever may be the tension at and near the earth's 
 surface, where a warmer temperature prevails. By the laws of 
 Boyle and of Charles, if the vapor tension were 2O mm at the 
 earth's surface, at the altitude of 5 kilometers (3.1 miles) it 
 would be about i3 mm ; but if at that altitude there was the tem- 
 perature of o C., it is seen from the table that the maximum 
 tension which could exist there would be only about one third 
 of that. 
 
 As the vapor rises or is diffused upward to altitudes where 
 the temperature is less than that which, by the table, corre- 
 sponds to its tension, the vapor is condensed and the tension 
 reduced to the maximum corresponding to the temperature as 
 determined by the table. When the air contains as much vapor 
 as, at the given temperature, can exist in it, it is said to be sat- 
 urated, and the temperature of unsaturated air at which, as it 
 cools, the vapor begins to condense is called the dew-point. 
 Where the vapor tension of the atmosphere is known from hy- 
 grometrical observations of any kind, this point is readily de- 
 termined from Table II, it being the temperature in the first 
 column to which corresponds the observed tension ; for at this 
 temperature the air is saturated, and if it cools still lower, con- 
 densation takes place. For instance, if the observed vapor ten- 
 sion is I7.363 mm , then the air, whatever its initial temperature, 
 has to cool down to 20 C. before condensation takes place, and 
 
AQUEOUS VAPOR OF THE ATMOSPHERE. 1 9 
 
 this is the dew-point belonging to this assumed hygrometric state 
 of the atmosphere. 
 
 The observed vapor tension of the atmosphere in comparison 
 with the tension of saturation at the observed temperature is 
 called the relative humidity. For instance, if, in the example 
 above, the temperature of the air were 30 C., then the tension of 
 saturation, by the table, would be 3i.5i mm , and hence the relative 
 humidity equal 17.363 : 31.51 = 0.55, or 55 per cent. 
 
 16. The amount of aqueous vapor in the atmosphere is very 
 variable, both at different places on the earth's surface and at dif- 
 ferent altitudes, at the same time, and in the same locality at dif- 
 ferent times. The mere diffusion of aqueous vapor through 
 the atmosphere, as that of any one gas through another, takes 
 place slowly ; so that, as the water of the ocean and of moist land 
 surfaces is evaporated, it penetrates through the lower strata of 
 the air very slowly, and remains mostly near the earth's surface, 
 unless there is an ascending current to carry it upward, and when 
 the air is calm it may be nearly or quite saturated at the earth's 
 surface, while it is comparatively dry at only small altitudes 
 above it. On account also of the slow rate of diffusion, and the 
 absence, often, of rapid convective currents, the vapor generally 
 abounds more over water surfaces and damp places, and less 
 over the interior and dry parts of the continents. Since, also, 
 the temperature of the air is almost always much less in the 
 upper than the lower strata of the atmosphere, the absolute 
 amount of vapor which can exist in the upper strata, as we 
 have seen in 14, is small even when the air is completely sat- 
 urated, and it generally falls much belo\^ this. For the same 
 reason the amount of vapor in high polar latitudes, where the 
 temperature is generally very low, is small in comparison with 
 that in the lower and much warmer latitudes. The aqueous 
 vapor is, therefore, very irregularly distributed, in general, both 
 with regard to the earth's surface and also altitude, and not at all 
 as it would be as an independent atmosphere existing alone, or as 
 it would in a quiet atmosphere in \vhich it would have time to 
 be equally diffused laterally to all places, and upward, so as 
 to satisfy Dalton's law, in case the temperature at all places 
 
20 CONSTITUTION AND NA TURE OF THE A TMOSPHERE. 
 
 and altitudes were so great that no condensation would take 
 place. 
 
 Since the temperature of the atmosphere is very change- 
 able, and the absolute amount of vapor which can exist in it, 
 by the table, depends very much upon the temperature, the 
 actual amount found in it must also be very different at differ- 
 ent times in the same locality, so that it is very variable both 
 with regard to space and time. 
 
 DYNAMICAL HEATING AND COOLING OF THE AIR. 
 
 17. It is well known that if air or any gas is suddenly com- 
 pressed there is an increase of its temperature, and the contrary 
 if the pressure is removed and it is allowed to suddenly expand. 
 The former is seen in the sudden compression of air in a con- 
 densing syringe or in a pneumatic tinder-box, in which light 
 and dry substances may be ignited from the increased tempera- 
 ture, and the latter, in the rarefaction of air in the receiver of 
 an air-pump, by which it is soon so cooled that the aqueous 
 vapor contained in it is condensed. 
 
 The action of a force F through the space s is called work. 
 If the force is constant through the whole space, the product, 
 Fs, of the force into the space is the measure of the work. 
 Where the force varies, the amount of work can only be ob- 
 tained by integrating the products of each element of the 
 spaces into the force corresponding to it. Work usually con- 
 sists in moving bodies in opposition to the force of gravity, or 
 in overcoming inertfa in the case of the acceleration of the 
 motions of bodies, or in overcoming frictional or other resist- 
 ances to motion, by the application of some force. 
 
 If a body is raised vertically through the space s by the 
 application of any kind of force, a certain amount of work has 
 been done to place it in this position. The force which has 
 been overcome is the force of gravity, equal gm, where ^rep- 
 resents the acceleration of the force of gravity and m the mass 
 of the body. The force applied is equal to that overcome, and. 
 so the amount of work done is gsm. 
 
DYNAMICAL HEATING AND COOLING OF THE AIR. 21 
 
 18. The capacity for doing work is called energy. The 
 elevated body now, acted upon by the force of gravity, if it has 
 .space to move through, has the power of overcoming inertia, 
 or resistance of any kind to its motion. It consequently has 
 energy, and this is usually called potential energy, sometimes 
 .energy of position, and is exactly equal to the amount of energy 
 spent, of whatever kind, in raising it to its position. If the 
 body in falling is not obstructed in its motion by some resist- 
 ing medium or frictional resistance, this potential energy is all 
 :spent in overcoming the inertia of the body in producing ac- 
 celerated motion. Letting v represent the velocity of motion 
 corresponding to the space s passed over, we have by the well- 
 known relations between the space and velocity in the case of 
 falling bodies, gs = \v*, and so the amount of energy spent in 
 producing this velocity or the momentum mv, is gsm = \v*m. 
 But this body in motion now has the capacity of overcoming 
 other forces or resistances, and consequently has energy, called 
 .kinetic energy, formerly vis viva or living force, and the meas- 
 ure of this energy is equal to that of the work gsm spent in 
 producing it, and consequently equal to ^m. The kinetic 
 energy is therefore proportional to the square of the velocity. 
 
 It is well known that heat is produced by the concussion of 
 inelastic bodies. If the body, of mass in, after having acquired 
 in any way the velocity v, should be brought to rest by contact 
 with another body, as in the case of completely inelastic bodies, 
 it would then have lost all of its kinetic energy. This kind of 
 energy is thus transformed into heat, which is a well-known 
 agent in doing many kinds of work, and is called thermal energy. 
 If the velocity v is produced by potential energy, then this is 
 directly transformed into kinetic energy, and thus indirectly 
 into thermal energy. 
 
 If a falling body or a body descending in any way from a 
 higher to a lower level, is retarded by the action of a resisting 
 medium or by friction, then the potential energy is spent par- 
 tially in giving momentum or kinetic energy to the body and 
 to certain parts of the fluid, and partly in causing heat. But 
 as soon as the body is brought to rest, and likewise all parts of 
 
22 CONSTITUTION AND NATURE OF THE ATMOSPHERE. 
 
 the fluid in the case of a resisting medium, then all the kinetic, 
 energy generated at first, is likewise transformed into heat, and 
 the whole amount is proportional to the amount of potential 
 energy of the body spent in descending to a lower level. This 
 heat is contained partly in the body acted upon, and partly in 
 the resisting medium or body offering the frictional resistance. 
 
 19. We have seen that a given amount of potential energy 
 can be transformed into a corresponding amount of kinetic 
 energy. Conversely, this kinetic energy can be transformed 
 back again into potential energy, as, for instance, where the 
 whole momentum acquired is used up in causing the body to 
 ascend against the force of gravity, in which case the body as- 
 cends exactly to the height from which it had fallen in generat- 
 ing the kinetic energy, and so the same amount of potential 
 energy is reproduced which was spent in producing the kinetic 
 energy. But there must not be any resisting medium or fric- 
 tional resistance affecting either the descending or ascending^ 
 motion of the body. In like manner the heat generated by a 
 given amount of kinetic energy can be used to reproduce this 
 energy, and if it could be applied without loss it would give 
 rise to exactly the same amount of kinetic energy as was spent 
 in producing it. Hence each of these three kinds of energy 
 can be transformed, either directly or indirectly, into each of 
 the others; and the amount of energy in each case, if it could 
 be applied in doing work without loss, would do the same 
 amount of work. The same is true with regard to other kinds 
 of energy which might be named. In fact, work is simply the 
 creation of energy of some kind at the expense of another, or 
 the transformation of one kind of energy into another. In this 
 way, at the expense of either heat or kinetic energy, the work of 
 raising a body against the force of gravity is performed, or, in 
 other words, potential energy is produced. The same, in doing 
 the work of overcoming frictional resistances to motion, gener- 
 ates as much heat as is spent, though it may be so scattered as. 
 not to be perceptible. 
 
 In the compression of air a certain amount of work is done 
 at the expense of some kind of energy. This is transformed 
 
DYNAMICAL HEATING AN.D COOLING OF THE AIR. 2$ 
 
 for the most part directly into heat, the amount of kinetic 
 energy in the motion of the air in being compressed, and which 
 is transformed into heat energy as soon as all motion ceases, 
 being very small. If heat energy were the agent used in the 
 compression, and it could be applied without loss, the heat of 
 the compressed air would be increased by the amount of heat 
 expended in the compression. The whole amount of energy, 
 therefore, remains the same, and is not diminished in doing 
 work. This principle is called the conservation of energy. 
 
 20. If the whole potential energy of a raised body, subject 
 to the action of the force of gravity, is spent in falling, by 
 means of some mechanical contrivance, in agitating a given 
 amount of water, and so heating it by means of friction, the 
 amount of heat generated is the equivalent of the potential en- 
 ergy spent, and so of the work required to raise the body. In 
 this way we can compare the work with the heat produced by 
 its equivalent potential energy, and hence get an equivalent ex- 
 pression of one in terms of the other, whatever the units used 
 in the measure of each. The raising of one kilogram, subject 
 to the force of standard gravity, through one meter, called a 
 kilogram-meter, is taken as the unit of work. The unit of heat 
 is the amount of heat required to raise the temperature of a 
 unit mass of pure water from o to i C. The unit of water 
 which is usually assumed in the unit of work is the kilogram, 
 and so the heat unit in this case is the amount of heat required 
 to raise the temperature of a kilogram of pure water from o 
 to i C. According to the most recent experiments, 4 the 
 height to which a unit of heat is capable of raising one kilo- 
 gram, subject to the force of standard gravity, may be put at 
 430 meters, the equivalent of which would be the raising of 430 
 kilograms through one meter. Hence the capacity of such a 
 heat unit for doing work is 430 kilogram-meters. This is called 
 the mechanical equivalent of heat. The amount of heat, there- 
 fore, required to do one unit of work, called the equivalent oj 
 work, is the reciprocal of this number, or -%-$ of a unit of 
 heat. 
 
 21. If heat is applied to any given portion of air which is 
 
24 CONSTITUTION AND NATURE OF THE ATMOSPHERE. 
 
 free to expand, a part of this heat is consumed in the work of 
 expansion and the balance only goes toward heating the air. 
 Taking a simple case, if we have a cubic meter of pure and dry 
 air at the standard temperature of o C, and under the stan- 
 dard pressure of one atmosphere, and free to expand in one 
 direction only, the heat which raises this cubic meter of air 
 through one degree of temperature, we have seen in 4, ex- 
 pands it in this one direction -^^ part of one meter. The resist- 
 ance to the expansive force in the expansion is the pressure of 
 a standard atmosphere on a square meter of surface, which is 
 10,333 kilograms ( n). The space through which this resist- 
 ance is overcome being ^ of a meter, the amount of work 
 done in the expansion in kilogram-meters is 10333 X -%%-% = 
 
 37-85- 
 
 If the cubic meter of air should expand equally in each of 
 the directions normal to its six surfaces, then the space through 
 which each surface of the cube would move, for the same ex- 
 pansion of volume, would be only \ as much, but the amount of 
 surface moved and force overcome would be six times as much, 
 and so the amount of work done would be precisely the same. 
 Moreover, whatever may be the figure of the volume of air 
 equal to that of one cubic meter, and the amount of surface, 
 and the amount of displacement of this surface in the various 
 directions perpendicular to the surface, the same amount of 
 work is done in the same expansion of volume ; for the work 
 done is proportional to the sum of all the elements of surface 
 multiplied into the space through which they move in the ex- 
 pansion, and the pressure or resisting force being the same on 
 all sides, the amount of work done is the same in all cases for 
 the same expansion of volume. 
 
 22. The same masses of different bodies at the same tem- 
 perature require different amounts of heat to raise their temper- 
 atures through one degree. By the definition of a heat unit, 
 20, it requires one unit of heat to raise the temperature of a 
 kilogram of pure water from o to i C. ; but it is found from 
 experiment that to raise the temperature of a kilogram of pure 
 and dry air, under constant pressure, from o to i C., only 
 
DYNAMICAL HEATING AND COOLING OF THE AIR. 2$ 
 
 0.2375 of a unit of heat is required. This is called the specific 
 heat of air. 
 
 According to the results obtained by the International Bu- 
 reau of Weights and Measures from the experiments of Reg- 
 nault, a cubic meter of pure dry air of standard pressure and 
 temperature weighs 1.29278 kilograms. Multiplying this into 
 the specific heat of air, we get 1.29278 X 0.2375 = 0.30703 of a 
 heat unit as the amount required to increase the temperature of 
 the air by one degree, and so to expand the cubic meter of air 
 ^ o_ p ar t of its volume, since it expands so much for each degree 
 of increase of temperature. But we have just seen that in this 
 expansion the amount of work done is 37.85 kilogram-meters. 
 Dividing this therefore by 0.30703, we get 123.28 kilogram- 
 Tneters as the amount of work done by a unit of heat in expand- 
 ing the cubic meter of air the ^fg- part of its volume. 
 
 If the cubic meter of air, of whatever figure, were subject 
 to any other than the standard barometric pressure of 76o mm , 
 then the work corresponding to any given amount of expan- 
 sion of the volume would be in proportion to the pressure, and 
 consequently to the density, where the temperature is constant. 
 But the amount of heat required to raise the temperature of a 
 given volume of air through one degree is likewise in proportion 
 to the density. Hence the same amount of heat is required to 
 be applied to the cubic meter of air to do a certain amount of 
 work of expansion, whatever the pressure and density may be. 
 
 Where the cubic meter of air has temperatures differing from 
 that of o, the amounts of expansion, and consequently of 
 work done, by the heat which raises its temperature by a given 
 quantity, are inversely as the absolute temperatures, being a 
 constant part of the volume when reduced to the temperature 
 of o. But the amounts of heating by a given quantity of heat 
 are directly as the absolute temperatures, being inversely as the 
 densities. The same quantity of heat, therefore, applied to the 
 cubic meter of air at all temperatures does the same work of 
 expansion. 
 
 Again, if a unit or any other quantity of heat is applied to 
 any other volume than a cubic meter under the same circum- 
 
26 CONSTITUTION AND NATURE OF THE ATMOSPHERE. 
 
 stances, there is the same work of expansion done, for the 
 greater the volume, of whatever figure, the greater the surface, 
 but the less in proportion is the heating and the space through 
 which this surface is moved, by the application of the same 
 amount of heat. 
 
 From what has been shown, it now follows that the amount 
 of work of expansion done by a given quantity of heat is the 
 same whatever the pressure, temperature, and volume may be 
 to which it is applied, and in all cases the amount of work done 
 by a unit of heat is 123.28 kilogram-meters. But the whole 
 work equivalent of this heat unit is 430 kilogram-meters, and 
 therefore the part of the heat used in doing the work of expan- 
 sion is to the whole as 123.28 to 430, or as 0.2867 to unity. Of 
 a unit of heat, therefore, applied to any given volume of air,. 
 0.2867 of a unit is used in doing work, and the balance, 0.7133 
 of a unit, goes toward heating the air. 
 
 23. Where the air is not allowed to expand there is no work 
 done at the expense of the heat supplied, and the whole goes 
 toward heating the air. The increase of temperature, there- 
 fore, given to air by a certain amount of heat communicated to 
 it where it is not allowed to expand, is to that in the case of 
 expansion under constant pressure in the ratio of unity to 
 0.7133, or as 1.402 to unity. Conversely, the heat required to 
 raise the temperature of a given quantity of air through one 
 degree under constant volume is to that required in the case of 
 expansion under constant pressure as unity to 1.402. The 
 specific heat of air, therefore, under the latter conditions being 
 0.2375, in the case of constant volume it is 0.2375/1.402 = 
 0.1694. 
 
 We have seen that of the heat communicated to air under 
 constant pressure which raises its temperature one degree, the 
 part 0.2867 is used in doing the work of expansion. Conse- 
 quently, if no heat is communicated, and the same work of 
 expansion is done in the air's coming under different pressures, 
 this work is done at the expense of the heat already in the air, 
 and hence it is cooled o.2867 by this expansion. 
 
 24. In order to obtain the heating effect of compression, or 
 
DYNAMICAL HEATING AND COOLING OF THE AIR. 2JT 
 
 the cooling effect of expansion, we must compute the amount 
 of work spent in compression, or of work done in expansion, 
 and then the equivalent of this work in heat units is equal to 
 the number of kilogram-meters of work divided by 430. Each 
 one of these heat units produced by the expenditure of work 
 in compression would raise the temperature of a kilogram of 
 water one degree, but as the specific heat of air under constant 
 volume, in which case no heat is spent in doing work, is 0.1694, 
 the temperature of a kilogram of air would be raised in the 
 ratio of unity to 0.1694, or to 5.9 by each unit of heat pro- 
 duced by the work of compression. Each unit of work, there- 
 fore, would heat a kilogram of air the -^ of 5.9, or o.oi37. 
 On the contrary, for each unit of work done in expansion at the: 
 expense of the heat in a kilogram of air, it is cooled by the 
 same amount. 
 
 In the compression or expansion of confined air the work 
 expended in the one case, or done in the other, is not propor- 
 tional to the amount of contraction or expansion of the volume, 
 since the force, or resistance overcome, is constantly changing, 
 becoming continually greater in case of compression, and less 
 in that of expansion, so that the amount of work can be com- 
 puted accurately only by means of a logarithmic formula. 
 Under the special case, however, where heat is communicated 
 to, or taken away from, air under constant pressure, the force 
 is constant, and the work done in the expansion, or spent in 
 compression, is proportional to the change of volume. 
 
 25. We now come to the subject of the cooling or heating^ 
 of air in ascending or descending currents. The amount of 
 expansion of air under constant pressure corresponding to an 
 increase of temperature of i is ^-$ of the volume at the tem- 
 perature of o C. Hence wehn the volume of air in coming 
 under less pressure expands so rapidly that there is no time for 
 it to gain or lose heat by radiation or conduction, it loses o.2867 
 of temperature for each expansion of ^iy of its volume at the 
 temperature of o C., and consequently this expansion must be 
 increased in the ratio of unity to 0.2867, or to y^Vy part of its: 
 volume in order to cool one degree. 
 
28 CONSTITUTION AND NA TURE OF THE A TMOSPHERE. 
 
 It has been shown, n, that the height of a homogeneous 
 atmosphere, at the temperature of o C., reckoned from the 
 earth's surface or any other level, is 7993 meters. If, therefore, 
 air of this temperature ascends one meter, the pressure is 
 diminished, and the volume increased, the T-^- part. Hence, 
 dividing ^g^y by T -^V3> we get 102.1 meters for the height to 
 which the air must ascend to cool one degree. This gives a 
 rate of cooling of air in its ascent of o.98 very nearly for each 
 100 meters of ascent. 
 
 For other temperatures than that of o C., the masses of 
 air left below in ascending one meter, and consequently the 
 diminutions of pressure, are inversely as the absolute tem- 
 peratures, and consequently the amounts of expansion of 
 volume at those temperatures are in the same proportion. But 
 the volumes for different temperatures are directly as the abso- 
 lute temperatures. The air therefore in ascending one meter, 
 whatever its temperature, is expanded the Y^g- part of its 
 volume at the temperature of o C., and hence is cooled by the 
 same amount as in the case of air of the temperature of o C. 
 For all temperatures of the air, therefore, it has to ascend 
 through 102.1 meters to cool i, and hence cools o.98 for each 
 100 meters of ascent. 
 
 In the case of air descending vertically we have compression 
 instead of expansion, and consequently a heating instead of a 
 cooling, and at the same rate. Since the cooling in the one 
 case depends upon expansion, and the heating in the other 
 upon compression, it is not necessary that the ascent or descent 
 should be vertical, but only that the air should come under dif- 
 ferent pressures, and consequently arrive at different levels, and 
 the rate of cooling or heating is o.98 for each 100 meters of 
 change of level, whatever be the directions of ascent or 
 descent. 
 
 26. Where the ascending air is saturated with aqueous 
 vapor, the cooling arising from the expansion continually 
 diminishes the capacity of the air for moisture, for by Table II 
 the lower the temperature the less the amount of vapor which 
 can exist in the air. Hence, as the saturated air ascends and 
 
DYNAMICAL HEATING AND COOLING OF THE AIR. 2$ 
 
 cools, the aqueous vapor is condensed, and the latent heat 
 gradually given out, as condensation takes place, raises the tem- 
 perature of the air above what it would otherwise be, and thus 
 causes the rate of cooling of the ascending saturated air to be 
 much less than in the case of dry or unsaturated air. 
 
 The number of heat units required to evaporate one unit by 
 weight of water is 606.5 0.6957, in which T is the temperature 
 above that of melting ice. Hence it decreases with increase of 
 temperature, and in the case of boiling water, in which r = 100, 
 it becomes 536. This means that at the boiling temperature 
 the heat which is used in the transformation of water into vapor 
 would heat 536 units of water at the zero temperature by one 
 degree. Condensation being the reverse of evaporation, where 
 the vapor in the air is gradually condensed in ascending, each 
 unit by weight of vapor condensed gives out a certain amount 
 of heat, varying a little by the preceding expression with the 
 temperature. 
 
 From an inspection of Table II it is seen that the colder 
 the air the less is its capacity for moisture, and also the less is 
 this decreased by a given decrease of temperature. For in- 
 stance, at the temperature of 30 the vapor tension of saturation 
 by the table is 23.5i7 mm , and in the ascent of the air and cool- 
 ing down to 25 the tension is diminished to I7.363 mm by con- 
 densation. But when saturated air has a temperature of only 
 5 the vapor tension is6.5O7 mm ; and in ascending and cooling 
 down to o the tension is reduced by condensation to 4.569 mm , 
 and so is decreased by i.938 mm only, and consequently there is 
 in this case a much less amount of vapor condensed than in the 
 other for the same decrease of temperature. Since, therefore, 
 the rate of decrease of temperature with increase of altitude in 
 the case of no condensation is the same at all altitudes and for 
 all temperatures, and the amount of condensation and of latent 
 heat given out for the same amount of cooling is much less for 
 the lower than for the higher temperatures, in the ascent of 
 saturated air at very low temperatures, such as generally prevail 
 in the winter season, and at all seasons in high altitudes, the 
 rate of cooling with increase of altitude in ascending air is 
 
30 CONSTITUTION AND NA TURE OF THE A TMOSPHERE. 
 
 much greater than it is in the summer season, since in the 
 former the latent heat given out is much less and the rate be- 
 comes more nearly that of ascending dry or unsaturated air, 
 namely, about one degree for each 100 meters. 
 
 The rate of cooling in ascending saturated air also depends 
 upon the density of the air and consequently upon the altitude. 
 At high altitudes the rate of condensation in ascending satu- 
 rated air, for the same temperatures, is the same as at low alti- 
 tudes for equal volumes, and consequently the rate with which 
 heat is given out as the air ascends is the same in both cases ; 
 but at high altitudes, where the density is less, the same amount 
 of latent heat given out in condensation gives rise to a greater 
 increase of temperature, the heating being inversely as the 
 density; and hence at these altitudes, at the same temperatures, 
 the rate of decrease of temperature in ascending air is less, 
 since the same volumes of air there are heated more by the 
 same amount of condensation. In the higher altitudes, how- 
 ever, the temperature is usually much less, and on this account 
 the rate of decrease of temperature above is not nearly so much 
 diminished as it would be if the temperature there were the 
 same as at lower altitudes. 
 
 After the saturated air has ascended to an altitude where it 
 has cooled down to the temperature of o, the vapor is then 
 condensed into snow, and by this an additional amount of latent 
 heat is given out equal to that of liquefaction, which is 79.25 
 .heat units for each unit of weight of liquid, and so is about one 
 seventh of that given out in the condensation of the vapor into 
 rain. This diminishes a little the rate of cooling above the 
 plane of incipient freezing. 
 
 Where there are rain-drops and fine cloud-particles carried 
 up above this plane, as there always are more or less in ascend- 
 ing currents, the rate of cooling is still further diminished by the 
 latent heat given out in freezing, until all are completely frozen, 
 and this rate may even be sensibly suspended for some little 
 distance above this plane, where the water particles carried up 
 are very fine, and so thoroughly diffused through the air that the 
 Jieat given out is almost instantly communicated to all parts, 
 
DYNAMICAL HEATIXG A. YD COOLIXG OF THE AIR. 31 
 
 for until the drops and fine particles are completely frozen they 
 must remain at the temperature of o. 
 
 In descending currents of air, even if it is saturated at the 
 start, the rate with which it becomes heated with decrease of 
 altitude is in all cases the same as that of dry air about one 
 degree for each 100 meters; for if it is saturated it at once be- 
 comes unsaturated as it descends and becomes warmer, and 
 consequently there is no condensation, and the rate is in no 
 way affected by latent heat becoming sensible, as in the case 
 of ascending saturated air. Where the saturated air is cloud- 
 ed, the clouds consisting of very small droplets of condensed 
 vapor, these, after the air in descending becomes unsaturated, 
 are gradually evaporated, and the heat of evaporation taken 
 from the air causes the rate of increase of temperature in 
 descending to be a little less than that of unsaturated and clear 
 air, until the cloud particles are all evaporated and the air 
 becomes clear. 
 
 27. The theoretical formula for computing the rates of 
 -decrease of temperature of saturated ascending air with increase 
 of altitude, for the different conditions with regard to temper- 
 ature and altitude, is too complex to be investigated here, but 
 these rates are given in Table III of the Appendix correspond- 
 ing to the temperatures at the heads of the columns, and the 
 pressures in the first, and the approximate altitudes in the last, 
 column of the table. 5 
 
 It has been explained in 26 that the rate of decrease must 
 be greater for the same pressures and altitudes in the case of 
 low than in those of high temperatures, and also, that for the 
 same temperatures the rates must be greater near the earth's 
 surface than at considerable altitudes. It is seen from an in- 
 spection of the computed rates in the table that this is the 
 case ; for at the earth's surface for a temperature of 10 this 
 rate is twice as great as it is for a temperature of 30, and the 
 rates also for the same temperature, are much less above than 
 at the earth's surface. 
 
 From Table III we readily compute the temperature of 
 rapidly ascending saturated air at any given altitude when it is 
 
32 CONSTITUTION AND NATURE OF THE ATMOSPHERE. 
 
 known at the earth's surface or any other lower level. For 
 instance, suppose the temperature at the earth's surface is 30, 
 and the temperature of the ascending current is required at the 
 altitude of 4000 meters (2.5 miles nearly). It is seen from the 
 table that the rate of decrease at the earth's surface at that 
 temperature is o.37 per 100 meters, and that this is very nearly 
 the rate at all altitudes in its ascent, since the air as it ascends 
 gradually becomes cooler. It can therefore be assumed to be 
 the same in getting approximate values of the rate of decrease 
 of temperature at the altitude of 4000 meters. The temper- 
 ature, therefore, at the altitude of 4000 meters is decreased 
 approximately o.37 X 40 I4.8, and hence the approximate 
 temperature at that altitude is 30 14. 8 = 15. 2. Corre- 
 sponding to this temperature and the altitude 4000 meters the 
 table gives a rate of decrease of o.39. Taking the average of 
 this rate and that at the earth's surface, which is o.38, we get 
 a more correct decrease of temperature at the height of 4000 
 meters, 0.38 X 40 15. 2, which being deducted from the sur- 
 face temperature, 30, we get 14. 8 for the temperature at that 
 altitude. 
 
 Where the air at the earth's surface or any of the lower 
 strata of the atmosphere is not saturated with aqueous vapor, 
 but only becomes so after having ascended to a certain alti- 
 tude, the rate of decrease before arriving at this altitude is 
 o.98 per 100 meters of ascent. This altitude is where the air 
 in ascending becomes cooled down to the dew-point which it 
 has after having reached that altitude, which is lower than the 
 dew-point of the lower level from which it has ascended, since 
 the vapor tension of the lower level is decreased from expan- 
 sion, and this in the ratio of the decrease of air-pressure. The 
 vapor tension at the lower level being given, the dew-point of 
 the level of incipient condensation is that temperature of 
 Table II corresponding to this tension diminished in the ratio 
 of the pressures of the two levels. The ratio between these 
 pressures, and also the amount of cooling of the air in ascend- 
 ing, depend upon the height of ascent, and this for the plane 
 of incipient condensation is determined by the condition that 
 
DYNAMICAL HEATING- AND COOLING OF THE AIR. 33 
 
 the air in ascending must be cooled, at the rate of o.98 for 
 each 100 meters, down to the new dew-point. The altitude 
 which satisfies this condition, where the temperature of the 
 air T, and the depression of the dew-point T d are given, 
 cannot be determined directly, but only by approximations. 
 These altitudes, so determined, corresponding to the air tem- 
 peratures at the heads of the columns and the depressions of 
 the dew-point in the first column, are given in Table IV. 
 
 It is seen that these altitudes are nearly independent of the 
 air temperatures, being only a little less for freezing tempera- 
 tures than for high summer temperatures. They are also- 
 entirely independent of the air-pressure, so that the lower 
 level may be either sea-level or of any high plateau, or high 
 level in the open air above the earth's surface. 
 
 It is also seen that if the depression of the dew-point,. 
 T d, is multiplied into 125, we have approximately the alti- 
 tudes in the table, especially for the lower altitudes. A 
 convenient rule, therefore, for determining the altitude approxi- 
 mately in meters, is to add one fourth part to the depression 
 of the dew-point in Centigrade degrees and multiply by 100. 
 For instance, if the difference between the air temperature and 
 the dew-point were 10, then the air would have to ascend 
 about 1250 meters before it would become saturated, and con- 
 densation would take place, and only after this altitude would 
 be reached would the rate of decrease of temperature be as. 
 given in Table III, and the amount of decrease of temperature 
 through the remaining difference of altitude be obtained as. 
 in the preceding example. 
 
 It must be understood that the rate of cooling which has. 
 been given for ascending dry or unsaturated air, as likewise the 
 rates given in Table III, are applicable in the case only in which 
 the ascent of air is so rapid that it does not have time to be 
 sensibly affected in other ways than by expansion and the latent 
 heat of condensation. 
 
 The observed rate of decrease of temperature with increase 
 of elevation in the lower part of the atmosphere has been found 
 to be o p .6o for each 100 meters on the average for all localities 
 
34 CONSTITUTION AND NATURE OF THE ATMOSPHERE. 
 
 and seasons of the year, but this rate varies considerably in dif- 
 ferent places, and is thought to be in general a little greater in 
 the lower than in the higher latitudes, and it is also consider- 
 ably greater in summer than in winter. In the latter season, 
 and especially at night in the lower strata of the atmosphere in 
 the interior of the continents, it not only becomes very small, 
 but may even be reversed, so that there is an increase instead 
 of a decrease with increase of altitude. 
 
 The following table, given by Dr. Hann, contains the rates of 
 decrease of temperature in summer as deduced from Glaisher's 
 observations during balloon ascensions : 
 
 DIMINUTION OF TEMPERATURE PER IOO METERS IN CELSIUS 
 
 DEGREES. 
 
 WEATHER. 
 
 Altitudes in thousands of English feet. 
 
 0-1 
 
 1-2 
 
 2-3 
 
 3-4 
 
 4-5 
 
 5-io 
 
 10-15 
 
 15-20 
 
 Clear. 
 Cloudy. 
 
 0.98 
 
 0.86 
 
 0.71 
 0-73 
 
 0.55 
 0.73 
 
 0.55 
 0.56 
 
 0.55 
 0-55 
 
 0.46 
 0.45 
 
 0-39 
 0.40 
 
 0.30 
 
 0.25 
 
 STABLE AND UNSTABLE EQUILIBRIUM. 
 
 28. If, when a portion of the atmosphere in a state of static 
 equilibrium receives, from any slight temporary cause of 
 disturbance, an upward or a downward motion, the changed 
 conditions arising from such a movement tend to bring it back 
 again to its original position, it is said to be in a state of stable 
 equilibrium, since, immediately after such disturbance, the part 
 disturbed is brought back and soon settles in its original posi- 
 tion. But if, after any such disturbance, the changed condition 
 tends to continue the motion and to increase the velocity of the 
 air disturbed in the direction in which it was started, either up- 
 ward or downward, the atmosphere is then said to be in a state 
 of unstable equilibrium, since although in static equilibrium as 
 long as it is not disturbed, yet the slightest disturbance intro- 
 duces an initial change in the conditions, which tends to con- 
 
STABLE AND UNSTABLE EQUILIBRIUM. 35 
 
 tinue the motion, until by a complete inversion of the strata of 
 the atmosphere, or from some other cause, the conditions are so 
 changed that the state of stable equilibrium is brought about. 
 
 It is well known that if any portion of a fluid, or a solid im- 
 mersed in a fluid, has a less density than the surrounding part 
 of the fluid at the same level, it tends to rise up, and if not hin- 
 dered, continues to rise until it comes to the top ; but if, on 
 the other hand, it has a greater density, it sinks down to the 
 bottom. So if, when any portion of the atmosphere receives 
 .an upward motion, its density becomes greater, or a downward 
 motion, less, than that of the surrounding air at the same level, 
 it at once comes back to its former position after the tempo- 
 rary cause of disturbance ceases ; but if, in rising up, the den- 
 sity becomes less, or in sinking down, greater, than that of the 
 surrounding parts of the same level, the tendency is to continue 
 on in the direction in which it is started. In the former case it 
 is in a state of stable, and in the latter of unstable, equilibrium. 
 But since a difference of density in these cases depends mostly, 
 if not entirely, upon a difference of temperature of the ascend- 
 ing or descending air and that of the surrounding part of the 
 atmosphere at the same level, the state of stable or unstable 
 equilibrium depends very much upon the relation between 
 the rate of decrease of temperature with increase of altitude in 
 the surrounding undisturbed part of the atmosphere and that of 
 the ascending or descending current. 
 
 29. We have seen that the temperature of rapidly ascending 
 unsaturated air decreases very nearly one degree for each 100 
 meters of ascent. If, therefore, the temperature of the sur- 
 rounding undisturbed part of the atmosphere decreases with in- 
 crease of altitude at a rate less than this, then as the air, started 
 by some slight temporary impulse, ascends, its temperature be- 
 comes less, and consequently its density greater, than that of 
 the surrounding undisturbed air at the same level ; and hence 
 the motion is soon arrested and reversed, and the air after a few 
 oscillations is brought by friction to a state of rest in its origi- 
 nal position. For instance, let us suppose that the arrange- 
 ment of temperature with regard to altitude, of a dry or unsatu- 
 
36 CONSTITUTION AND NATURE OF THE ATMOSPHERE. 
 
 rated and undisturbed atmosphere to be represented in the 
 third column of the following table, in which the first column 
 contains the altitudes, and the second the temperatures of the 
 ascending current of air at the altitudes in the first column : 
 
 Meters. 
 
 
 
 
 3000 
 
 
 
 6 
 
 -6 
 
 2500 
 
 5 
 
 10 
 
 o 
 
 2OOO 
 
 IO 
 
 14 
 
 6 
 
 1500 
 
 15 
 
 18 
 
 12 
 
 1000 
 
 20 
 
 22 
 
 18 
 
 5OO 
 
 25 
 
 26 
 
 24 
 
 ooo 
 
 30 
 
 30 
 
 30 
 
 The temperature of the ascending column is here supposed 
 to decrease exactly i for each 100 meters. It is readily seen 
 that with the arrangement of temperature in the third column 
 a slight upward motion of air at any place would cause its tem- 
 perature at all altitudes to be a little less and consequently its 
 density a little greater than that of the surrounding undisturbed 
 air at the same levels, and this would continue to increase as the 
 air ascends, until the temperatures would finally be as in the 
 second column of the preceding table, if the ascent were "to con- 
 tinue. But this increased pressure of the whole column having 
 an ascending motion would soon bring it back. It would then 
 descend a little lower than its original undisturbed position, 
 and in so doing it is readily seen that the temperature then 
 would be greater and the density less than that of the sur- 
 rounding undisturbed air, and the further it descended below 
 this position, the more so, and hence the downward motion 
 would soon be stopped and reversed, and after a few oscilla- 
 tions it would be brought to rest by friction in its first position. 
 And this would be the case whatever the direction, upward or 
 downward, of the first impulse. Hence with this vertical dis- 
 tribution of the temperature, the atmosphere is in the state of 
 stable equilibrium. 
 
 But if we suppose the temperature to decrease with increase 
 of altitude at the rate of i.2 for each 100 meters, instead of 
 o.8 as in the preceding case, we shall have the vertical dis- 
 
STABLE AND UNSTABLE EQUILIBRIUM. 37 
 
 tribution of temperature as given in the fourth column of the 
 preceding table. It is readily seen that now a slight upward 
 motion would cause all parts receiving such a motion to have a 
 little greater temperature and less density than those of the 
 surrounding undisturbed parts, and the greater the disturbance 
 the less the density relative to that of the surrounding air at 
 the same levels. Hence there would be no tendency to fall 
 back again, but to continue on, and the further the displace- 
 ment the greater this tendency until a regular ascending cur- 
 rent would be established, in which the temperatures at differ- 
 ent altitudes would be as represented in the second column 
 of the preceding table. The difference of temperature, then, 
 between the ascending air and the surrounding quiet air would 
 increase one degree for each 500 meters, so that at the altitude 
 of 1500 meters it would be 3, at 3000 meters 6, and so on; 
 and consequently there would be a strong tendency to rush up 
 to the top of the atmosphere, at least if the same vertical 
 decrease of temperature in the undisturbed atmosphere should 
 extend all the way up. If the initial motion were downward, 
 the temperature would become less and the density greater 
 than in the surrounding air at the same level, and hence, being 
 once started, the tendency would be to continue. In this case, 
 however, the down-rushing air could not escape so readily on 
 account of the friction of the earth's surface in its lateral escape 
 at the surface. Without some initial disturbance, however, 
 either upward or downward, the atmosphere would remain at 
 rest. With the vertical distribution of temperature, therefore, 
 given in the last column of the table, if the air should receive a 
 start, either upward or downward, the tendency would be to 
 continue on, and hence with this distribution the atmosphere 
 is in the state of unstable equilibrium. 
 
 If the vertical temperature gradient in the undisturbed 
 atmosphere is such that the temperature decreases i for each 
 100 meters of increase of altitude, then the atmosphere is said 
 to be in the indifferent state of equilibrium. 
 
 30. Again, let us imagine a portion of air confined within a 
 balloon of very fine silk, the weight of which would be insensible 
 
38 CONSTITUTION AND NATURE OF THE ATMOSPHERE. 
 
 in comparison with the weight of the confined air. If the 
 decrease of the temperature of the air with increase of altitude 
 were i.2 for each 100 meters, then the air in the balloon in its 
 ascent, its initial temperature being supposed to be the same as 
 that of the surrounding air, would become o.2 warmer than 
 the surrounding air for each 100 meters of ascent, or one degree 
 for each 500 meters, and after having ascended 2000 meters 
 would be 4 warmer than that of the surrounding air; so that 
 the higher it would ascend, the stronger would be the tendency 
 to continue on. But if the balloon were at some altitude above 
 the earth's surface and started downward in the same condition 
 of the air, the air contained within would become one degree 
 colder for each 500 meters of descent, and consequently heavier 
 than the surrounding air, and so, being once started, the ten- 
 dency would be to go on. Supposing the silk to have no weight, 
 and the initial temperature of the air within and without to be 
 the same, there would be no tendency to move either up or 
 down until once started by some initial impulse. This would, 
 therefore, be a state of unstable equilibrium for unsaturated 
 air. 
 
 If the rate of decrease of temperature in the air with increase 
 of altitude were only o.8 for each 100 meters, then, it is readily 
 seen, the air in the ascending balloon would become o.2 colder 
 than the surrounding air for each 100 meters of ascent, and o. 2 
 warmer for each 100 meters of descent : so that in the former 
 case it would become heavier than the surrounding air, and soon- 
 cease to ascend, and then fall back again ; and in the latter it 
 would become lighter, and soon cease to fall, and would run up 
 again to the position which it left. This would therefore be a 
 state of stable equilibrium for unsaturated air. 
 
 It will be readily understood from the preceding illustrations 
 that if an unsaturated atmosphere has a temperature which 
 decreases with increase of altitude at a rate which is less than 
 one degree (accurately o.98) for each 100 meters, it is in the 
 stable state ; but if this rate is greater than one degree for each 
 IOO meters, it is in the unstable state. 
 
 31. If the ascending air is saturated with aqueous vapor, it 
 
CHANGES OF ALTITUDE AND DENSITY. 39 
 
 is seen from Table III that the rate of decrease of temperature 
 with increase of altitude required to produce the state of un- 
 stable equilibrium is much less, and this is especially the case 
 in the summer season, and in all seasons at great altitudes. 
 For instance, in the example given in 27, the average rate of 
 decrease is o.38 for each 100 meters, and the rate is very 
 nearly constant at all altitudes. If, therefore, the rate of de- 
 crease in the quiet air were only a little greater than this, the 
 air would be in the unstable state, whereas in the case of dry 
 or unsaturated air the rate would have to be more than twice 
 as great. But with a temperature of 10 the rate of decrease 
 in ascending air is about twice as great, and so the rate of 
 decrease in the undisturbed and quiet air would have to be 
 greater than this is, to give rise to the unstable state, but still 
 considerably less than in the case of dry or unsaturated air. 
 
 In the case of saturated air the initial motion of disturbance 
 must be upward, since when it is downward the air becomes 
 warmer, and so at once unsaturated, so that the tendency to a 
 continued downward motion can only take place, although the 
 air at first may be completely saturated, when the rate of 
 increase or decrease with change of altitude in the undisturbed 
 surrounding air is greater than o.98 for each 100 meters. 
 
 RELATION BETWEEN CHANGES OF ALTITUDE AND DENSITY. 
 
 32. In a quiet atmosphere at the temperature of o C., the 
 pressure, and consequently the density, is decreased by the 
 7 0*03 part for each meter of increase of altitude, for in an ascent 
 through a vertical distance of one meter this part of the mass 
 is left below ; and this is true for all pressures and altitudes, if 
 the temperature is the same, since the height of a homogeneous 
 atmosphere is the same, whatever the mass and pressure. But 
 we have seen that the volume of the air at all temperatures is 
 increased, and consequently its density decreased, by the -^^ 
 part of that at the temperature of o C., for each degree of 
 increase of temperature. Dividing, therefore, ^-^3 by -^, we 
 get -fffj = o.O348 for the decrease of temperature for each 
 
40 CONSTITUTION AND NA TURK OF THE A TMOSPHERE. 
 
 meter of increase of altitude required to give the same density 
 at all altitudes. 
 
 For other and higher temperatures it would be necessary to 
 ascend through a vertical distance of more than one meter in 
 the ratio of the absolute temperatures, in order to diminish the 
 density ^Vs" P art ; and hence the decrease of temperature in 
 this case would be o.O348 for a change of altitude greater in 
 the same proportion, and the rate of decrease required would 
 be inversely as the absolute temperature. 
 
 THE VISCOSITY OF THE AIR. 
 
 33. That property of the atmosphere, or of any gas by which 
 one stratum cannot move with greater velocity over another 
 without receiving resistance from it, is called viscosity. By the 
 kinetic theory of gases this arises from the continual inter- 
 change of molecules between the strata. Those of the more 
 slowly moving stratum, coming in contact with those of the 
 contiguous stratum moving with greater velocity, tend to 
 diminish its velocity, while those of the more rapidly moving 
 stratum, coming in contact with those of the other, tend to 
 accelerate its motion, so that there is a tendency in these 
 contacts to equalize the velocities of the two, but leaving the 
 whole amount of momentum in the two strata unchanged, 
 when there is simply a mutual action between the two. The 
 measure of viscosity is the amount of force required per square 
 unit of surface to overcome the mutual action of two strata 
 of unity of thickness upon each other, and having a relative 
 velocity of unity. This mutual action between the two, usually 
 called friction or frictional resistance, is proportional to the 
 relative velocities of the strata, and, according to the deduction 
 of Maxwell from the kinetic theory of gases, is independent of 
 density and pressure where the temperature remains the same. 
 
 When the whole atmosphere from bottom to top moves in 
 the same horizontal direction with velocities increasing with 
 increase of altitude, the lower stratum in contact with the 
 earth's surface is retarded by the contacts of its molecules with 
 
THE VISCOSITY OF THE AIR. 41 
 
 the asperities of that surface, but the motions of each successive 
 stratum above is acted upon by the more slowly moving stratum 
 below and retarded in its motion, unless there is some constantly 
 acting force to overcome the effect of this frictional resistance, 
 and maintain a constant relative velocity between the two 
 strata. If there are three successive strata, of which the relative 
 velocity between the first and second is the same as that be- 
 tween the second and third, then the actions of the first and 
 third upon the intermediate one are precisely the same, but in 
 contrary directions. 
 
 Since an increase of temperature increases the velocities of 
 the interchanging motions of the molecules between the strata, 
 the viscosity of the atmosphere is increased by increase of tem- 
 perature. Experiment makes it about as the three-fourths 
 power of the absolute temperature.' 
 
CHAPTER II. 
 
 THE MOTIONS OF BODIES RELATIVE TO THE EARTH'S 
 
 SURFACE. 
 
 34. THE motion of a body relative to the earth's surface,, 
 called relative motion, whether this body is set in motion by a 
 single impulse, or is continually acted upon by some force 
 other than that of gravity, is very different upon the earth with 
 a rotation upon its axis from what it would be if the earth were 
 at rest. If the earth were at rest, and spherical, as it would 
 have to be in this case, a body set in motion in any direction 
 upon its surface, supposed to be perfectly smooth and without 
 friction, would continue to move uniformly with its initial 
 velocity in a great circle of the sphere. But where the earth 
 has a motion of rotation upon its axis, we shall see that this is- 
 far from being so, except in the case where the initial motion 
 is in the line of the equator. If, also, the earth were at rest, a 
 body projected vertically upward would fall back to the point 
 where it started, but in the case of the earth with a rotation 
 upon its axis, it falls to the earth a little west of this point, and 
 projectiles generally, started in any direction relative to the 
 earth's surface, would have different relative motions in the two 
 cases. In considering, therefore, the relative motions of bodies 
 on the earth's surface, it is very important to take into account 
 the influence of the earth's rotation upon such motions, and to 
 not regard these as being the same as the absolute motion in 
 case of no rotation. 
 
 CENTRIFUGAL FORCE. 
 
 35. In determining the influence of the earth's rotation 
 upon relative motions upon and near its surface, the centrifugal 
 force arising from the earth's rotation comes in as an impor- 
 
 42- 
 
CENTRIFUGAL FORCE. 
 
 43 
 
 tant consideration. It is necessary, therefore, to understand at 
 the start, the nature and law of this force. If a free body in 
 space has a motion in any direction and is not acted upon by 
 any force, or affected by any kind of resistance, frictional or 
 otherwise, it continues to move on with uniform velocity in 
 this direction. If, therefore, a body at a, Fig. i, has, under 
 these conditions, a motion in the direction of the line ad, tan- 
 gent to the circle aegh, of which o is the centre, and has a 
 velocity which will carry it to b in a unit of time, as one second, 
 then, at the end of this unit of time, it will have departed from 
 
 the circumference, and have increased its distance from the 
 centre o, by the space eb. Drawing now the line cf tangent 
 to the circle at e, it will perhaps be evident to most readers, 
 without a rigorous demonstration, that the angle dcf at the 
 intersection of the two tangents to the circle at a and at e is 
 equal to the angle aoe, since at the start as the movable radius 
 oe changes its direction with regard to oa, the tangent at e must 
 change its direction with reference to that of ad at the same 
 rate. In the case of very small angles between two lines form- 
 ing an angle as cd and cf, the rates at which a body moving : 
 along one of them with a given velocity departs in different 
 
44 MOTIONS OF BODIES RELATIVE TO EARTH'S SURFACE. 
 
 cases from the other are sensibly proportional to the angles 
 between them. The body then, in moving from a towards d 
 with a given uniform velocity, will, at the ends of different 
 units of time, if the unit is very small, and this is entirely arbi- 
 trary, depart from the line cf and from the centre of the circle 
 with velocities which are proportional to the angle dcf at the 
 ends of these units of time, and consequently proportional to 
 the angle aob which is proportional to the time ; for while the 
 angle aob is small it is proportional to ab, which, since the body 
 moves with uniform velocity, is proportional to the time. The 
 law of departure, then, for very small arcs, is that the rate or 
 velocity of departure of the body from the circumference of 
 the circle and from the centre, is proportional to the time 
 elapsed. 
 
 If a body is free and is acted upon by any constant force, 
 as that of gravity, its motion is accelerated in proportion to the 
 time, the increase of velocity in a unit of time being called the 
 acceleration. For instance, a body near the earth's surface, 
 acted upon by the force of gravity, acquires a velocity of about 
 32 feet per second at the end of the first second, 64 feet at the 
 end of the second second, and so on ; the velocity continuing 
 to be increased in proportion to the time. Now we have seen 
 above that in the motion of a body in the direction of a tangent 
 to the circumference of a circle the law of departure from the 
 circumference and from the centre of the circle is precisely the 
 same as that of a falling body, or of any body acted upon by a 
 given uniform force, the velocities acquired in both cases being 
 in proportion to the time. The tendency, therefore, of a body 
 at a to depart from the centre is exactly similar to the action 
 of any force in a given direction in causing a body to move 
 from its initial position. And if a body at a, with a motion in 
 the direction of ad, is constrained to move in the circumference 
 of the circle toward e, as in a groove, or in consequence of 
 being attached to the centre o by a cord, corresponding to the 
 radius of the circle, the pressure against the side of the groove 
 in the one case, and the tension of the cord in the other, are the 
 same as the pressure which would arise from the action of any 
 
CENTRIFUGAL FORCE. 45 
 
 force on a body of the same mass if it were such as to cause an 
 acceleration in the body, if free to move, equal to that of the 
 rate of departure of the moving body from the centre of the 
 circle. This tendency of a body, in gyrating around a centre, 
 to recede from the centre, and, when not free to depart, to 
 cause pressure in the direction of the radius from the centre, is 
 called centrifugal force. It must be understood, however, that 
 this so-called force is not a real force, such as arises from any 
 attracting or propelling force in a given direction, but simply 
 that the gyrating body, if free, would at any given instant be 
 carried away from the centre by its inertia in the varying direc- 
 tion of the radius, in the same manner as it would be moved in 
 a given direction by the action of a constant and real force in 
 this direction. The centrifugal force depends simply upon the 
 inertia of the body, and being always at right angles to the 
 direction of the gyratory motion, it does not increase velocity 
 and momentum, as a real force does, but tends simply to drive 
 a body away from the centre of curvature, and to cause pressure 
 in that direction. 
 
 36. The effect of centrifugal force with reference to the 
 varying distance of the body along a radius of constantly vary- 
 ing direction being similar to that of a real force with reference 
 to the motion of the body along a fixed direction, we obtain an 
 expression of this force in the same manner, namely, by multi- 
 plying the mass of the body into its rate of departure from the 
 centre at the end of a unit of time, corresponding to what is 
 called acceleration in the case of a real force. In the case of 
 the centrifugal force, however, it must be understood that the 
 unit of time, which is entirely arbitrary, must be so small that 
 the body describes only a very small, strictly infinitely small,, 
 arc in comparison with the whole circumference of a circle 
 during this time. 
 
 In a falling body, if the unit of time is one second, the 
 velocity at the beginning of the first unit is o, and at the end 
 of it 32 feet ; and as the velocity increases in proportion to the 
 time, the average velocity is 16 feet. Consequently the space 
 fallen through during the first second is 16 feet, one half the 
 
46 MOTIONS OF BODIES RELATIVE TO EARTH'S SURFACE. 
 
 velocity acquired at the end of the second. If now, in Fig. i, 
 -we suppose ab to be the space passed over by the body in a 
 unit of time, this unit being such that ab is very small in com- 
 parison with the radius ao, or the whole circumference of the 
 circle, though it is necessarily very much exaggerated as repre- 
 sented in the figure, then be is the space over which the body 
 passed during this unit of time in the varying direction of the 
 radius from the centre, or the space by which the distance of 
 the body from the centre is increased. Consequently, from what 
 has just been stated in the case of a falling body, 2be is the 
 acceleration of the centrifugal force. Putting, therefore, as 
 usual, m for the mass of the body, we have 2be X m for the ex- 
 pression of the centrifugal force. 
 
 But it is desirable to have an expression of this force in 
 terms of the gyratory velocity of the body around the centre 
 of gyration, and the distance of the body from the centre. The 
 gyratory velocity of a body is its velocity, or that component 
 of its velocity, which is at right angles to the radius of gyration. 
 If the body at a, Fig. I, has a velocity which would carry it to 
 b in a unit of time, then the distance ab, sensibly equal to the 
 arc ae, is its gyratory velocity at the point a. The gyratory 
 velocity a'b' of any point a' in the radius ao, at the distance of 
 unity from the centre o, expressed in terms of this unit, is called 
 the gyratory velocity in terms of the radius, since this would be 
 the real gyratory velocity if the radius were made the measur- 
 ing unit. It is the ratio between the gyratory velocity and the 
 radius, since it is the gyratory velocity divided by the radius, 
 and so expressed it is often called simply angular velocity, since 
 it is proportional to the rate of change of the angle at the 
 centre. The real gyratory velocity, therefore, is equal to the 
 gyratory velocity in terms of the radius multiplied into the 
 radius. Denoting the gyratory velocity ab, Fig. I, by w, the 
 radius ao by r, and the gyratory velocity in terms of the radius 
 by n, we evidently have ab = ao x n, or w = rn. 
 
 We have in the figure, as has been shown, the angle bee 
 equal the angle aob ; and hence be is evidently as many times 
 greater than ce as ab is greater than ao, and as ab or w is equal 
 
CENTRIFUGAL FORCE. 47 
 
 to rn, be is equal to ce X n, and so 2be is equal to 2ce X n. But 
 <r^ is equal to ac or one half of ab, where all are very small, as 
 here supposed, and consequently 2ce is equal to ab or w, and 
 hence we have 2ce = w = rn. Putting rn for 2ce in the preced- 
 ing expression of 2be, we have 2be = rn X n = rn*, and the pre- 
 ceding expression of the centrifugal force, 2be x m, becomes 
 rn*m. Or putting F c for the centrifugal force, we have* 
 
 77 9 W * 
 
 F c = rtfni m. 
 r 
 
 The last form of this expression is obtained from the first one 
 by putting rn* = rn X n, and then for rn and n their equals w 
 and w/r. From the last form of expression it is seen that the 
 centrifugal force is directly as the square of the gyratory veloc- 
 ity and inversely as the distance of the body from the centre 
 of gyration. 
 
 In obtaining the preceding results it was assumed that the 
 unit of time is very small (strictly it should be infinitely small), 
 but the expressions thus obtained are applicable to any other 
 unit. For velocity expresses simply the relation between an 
 infinitely small portion of space passed over by the body at any 
 instant of time and the corresponding infinitely small portion 
 of time, and this can be expressed by using either large or 
 small units of time, it being understood that the space passed 
 over during the unit of time is that which would result from a 
 continuance of the rate of motion or relation between the 
 infinitely small portions of space and time at any instant 
 through the whole unit of time, however large it may be. 
 
 * Joining e and^- in the figure, and considering the arc ac a straight line, and 
 be a continuation of the line ge, as we may when they are very small, we have 
 by the well-known proportions of similar triangles eg : ae : : ae : be ; or putting 
 
 fib = ae, as we can where these quantities are very small, we have be = . ' 
 
 -w> C Z 
 
 or 2be = , since where ae is very small we have sensibly eg = ag= 2r. Hence, 
 
 multiplying this expression of the acceleration ibe into the mas m, we get the 
 expression of the centrifugal force above. 
 
48 MOTIONS OF BODIES RELATIVE TO EARTH'S SURFACE.. 
 
 37. If the body is forced to move in an irregular curve, as 
 in a groove, which is not the circumference of a circle, there is 
 always some circle the circumference of which coincides sensibly 
 with a very small portion of this irregular curve at any point 
 where the body may be moving, and the radius of this circle is 
 called the radius of curvature. Since the preceding expression 
 of centrifugal force is deduced from the consideration of only 
 a very small portion of the circumference of the circle, strictly 
 only an infinitely small part, and is dependent simply upon the 
 curvature at that point, it is evident that it is applicable to any 
 point of an irregular curve, if we use for r in the expression the 
 radius of curvature of that point of the curve. Hence, the 
 velocity remaining the same, the centrifugal force is inversely 
 as the radius of curvature. 
 
 As an expression of the ratio between the centrifugal force 
 and that of gravity, where both forces act upon the same or 
 equal masses, we get from the preceding expression, by divid- 
 ing by gm, the force of gravity, 
 
 gm 9.806^ 
 
 in which the units are the second of time and the meter. If 
 the English foot is used as the unit of length instead of the 
 meter, then 32.2 instead of 9.806 must be used as the numerical 
 coefficient of r in the denominator of the expression. 
 
 As an example of the practical application of this relation, 
 let us suppose that the body has a velocity on a horizontal 
 plane of 20 meters per second (45 miles per hour nearly*), and 
 that it is constrained to move in a curve with a radius of curva- 
 ture at any given point of 1000 meters. We then have for the 
 ratio of the centrifugal force to that of gravity at that point 
 20 2 : (1000 X 9.806) = 0.0408. If, therefore, the moving body 
 were that of a railroad car, with a velocity of 20 meters per 
 second, on a part of the road having a radius of curvature of 
 
 *To reduce meters per second to miles per hour, multiply by 2.237, and vice 
 versa. 
 
CENTRIFUGAL FORCE. 49 
 
 1000 meters, the lateral pressure ofi the side of the rails, in a 
 direction from the centre of curvature, would be about the -^ 
 part of the vertical pressure of the car. 
 
 38. If the body is entirely free, and is not constrained to 
 move in a given path, but is acted upon by some centripetal 
 force which is exactly equal to the centrifugal force, it in this 
 case moves concentrically around the centre of the forces in the 
 circumference of a circle. Such a force may be found in the 
 one component of the force of gravity where the body gyrates 
 horizontally upon a surface having a descending gradient on all 
 sides from the exterior part toward the centre of gyration. 
 The measure of such a gradient is the ratio between the change 
 of level in a given horizontal distance, and this distance. For 
 instance, if the change of level is one meter in the distance of 
 1000 meters, the gradient is o.ooi, or one in one thousand, what 
 ever the unit of measure. If the body in moving rises to a 
 higher level, it is called an ascending gradient, and vice versa. 
 
 The ratio expressing the gradient is also that between the 
 component of gravity, acting in any direction along the inclined 
 surface, and the whole force of gravity. If de in Fig. 2 is the 
 change of level in the horizontal distance ad, if we denote the 
 ratio expressing the gradient by e we shall have e = de : ad. 
 If now we let the vertical line ce represent the force of gravity, 
 and cb is drawn perpendicular to the inclined surface, then, by 
 the principle of the resolution of forces, the whole force of 
 gravity represented by ce is equivalent to two other forces^ 
 called components, one of which is represented by the line cb 
 and acts in the direction from c to b, and the other by the line 
 be and acts in the direction from b to e\ these components and: 
 the whole force being to one another as the sides of the triangle 
 representing them. Denoting the component of the force of 
 gravity represented by be by f t that of the whole force, as we 
 have seen in 9, being represented by gm, we have sensibly, put- 
 ting be = ec, f : gm = be : be. But the angles at a and c being 
 equal, as is pretty evident without rigorous demonstration, the 
 lines forming the angles must separate from each other 4n pro- 
 portion to the distances from the angles, and hence we have 
 
50 MOTIONS OF BODIES RELATIVE TO EARTH'S SURFACE. 
 
 de : ad = be : be. These ratios are also derived more directly 
 from the well-known geometrical relations of similar triangles. 
 Putting the ratios above, which are both equal to the ratio 
 be : be, equal to each other, we get fi gm = de : ad', or represent- 
 ing, as above, this latter ratio be e, we get f \gm-=.e y orf=. 
 egm. Strictly, this expression of f here is the horizontal com- 
 ponent of the force down the slope, but in putting be = ec 
 
 Fig. 2. 
 
 above we neglect the very small difference between the two 
 where the gradients are so small. 
 
 Where the gradient is very small, as it usually is, the centrif- 
 ugal force in the direction of the slope is sensibly the same as 
 in a horizontal direction ; and so, in order that the centrifugal 
 and centripetal forces on the slope may be exactly equal, the 
 gyratory velocity must be such as to satisfy the condition 
 
 w* 
 eg= = rn\ 
 
 as is readily seen by comparing the expression of the centrip- 
 etal force above, with that of the centrifugal force F c in 36. 
 Since g may be regarded as constant, it is seen from this ex- 
 pression that the gradient of the slope which satisfies this con- 
 dition varies directly as the square of the gyratory velocity and 
 inversely as the distance r of the body from the centre of gyra- 
 tion. With the same value ofj w it is seen that the gradient 
 very near the centre, where r is small, would be very steep, and 
 consequently this expression would not hold there, since it has 
 
CENTRIFUGAL FORCE. $1 
 
 been assumed above that the gradient is so small that the 
 horizontal and inclined distances do not differ sensibly. 
 
 From what precedes, if the railroad car, in the example 
 which we have just had, were to move around upon a surface 
 declining at all points toward the centre of curvature, or, what 
 would be the same, if the outer rail were a little above the level 
 of the inner one, then the centrifugal and centripetal tendencies 
 would exactly counteract each other, and there would be no 
 lateral pressure against the rails, if the gradient between the 
 two rails were determined by the preceding expression. In the 
 example above, the outer rail would have to be higher than the 
 inner one by the ^5- part of the width between them. Since 
 the required gradient differs with different velocities, the best 
 that can be done is to adapt the gradient to an average velocity, 
 or rather, to an average of the squares of the usual varying 
 velocities. 
 
 Upon the same principle, the gradient between the two 
 banks of a river, flowing in a channel around a centre of curva- 
 ture, can be determined. If the velocity were 2 meters per 
 second (4.5 miles per hour), and the radius of curvature 1000 
 meters, then the value of the gradient e from the preceding ex- 
 pression would be 2 2 : (1000 X 9.806) .000408 ; and hence the 
 -level of the water on the opposite side from the centre of curva- 
 ture would be higher than on the other side the ^Vo- part, 
 nearly, of the width of the river, if all parts had the same veloc- 
 ity and the same radius of curvature. 
 
 39. If a body, as at a, Fig. I, is at rest relative to the sur- 
 iace, with a descending gradient from all sides toward the 
 centre 0, and the whole sub-stratum of the surface gyrates 
 around this centre with a velocity w at the distance r from the 
 centre, it is evident that the centrifugal force F c and the coun- 
 teracting component of gravity / along the descending gradient, 
 are precisely the same as if the body gyrated with the same 
 .angular velocity around the centre of gyration, and moves with- 
 out friction over the surface, since the absolute motion of the 
 body is the same in both cases. In order, therefore, that the 
 ibody may remain at rest upon such a revolving surface and not 
 
52 MOTIONS OF BODIES RELATIVE TO EARTH'S SURFACE. 
 
 move either from or toward the centre, the condition of the ex- 
 pression in 38 must be satisfied. It is seen from this expres- 
 sion, since n is constant with the same angular velocity of 
 gyration, that the gradient e must be proportional to r, and 
 consequently vanish at the centre where r vanishes and increase 
 as the distance r increases. Such a gradient would be found 
 in a concave surface corresponding to a small segment of a 
 spherical shell, a section of which, aob, in which o is the centre, 
 is represented in Fig. 3. 
 
 If the whole gyrating stratum were covered by a fluid, con- 
 fined within a given area by a circular rim, as in the case of a 
 very shallow basin of water revolving horizontally around its, 
 centre, then all parts of the surface of the fluid in static equilib- 
 rium and at rest relatively to the basin, must have a gradient 
 
 d 
 
 Fig. 3. 
 
 satisfying the preceding condition, and be such as that repre- 
 sented in Fig. 3, in which a body at rest upon any part of it 
 would not move either toward or from the centre. 
 
 40. If we now suppose the concave surface of the revolving 
 solid stratum, abed, Fig. 3, to be the same as that which a liquid 
 at rest relative to the solid would assume, and that a body 
 placed upon this surface has a gyratory velocity v, either in the 
 same or the contrary direction, the surface gyrating with the 
 velocity GJ at the distance r of this body from the centre of 
 gyration, then the absolute gyratory velocity of the body at the 
 distance of r is GJ -|- v, the latter being negative when the body 
 gyrates in the contrary way to that of the solid. Hence, in 
 order to obtain now an expression of the centrifugal force F c , 
 we must put in the expression of F c in 36, oo-\- ^instead of w~ 
 But since the square of the sum or difference of two quantities, 
 or of numbers representing them, is equal to the square of the 
 
CENTRIFUGAL FORCE. 53 
 
 first, plus or minus twice the product of the first into the sec- 
 ond, plus the square of the second, as any one not familiar with 
 algebraical operations can easily verify in special numerical 
 cases, we shall now have for the expression of the centrifugal 
 force 
 
 ,-, (GO + Vf 60' + 2GOV + V* 
 
 F c = ^ ! J -m = ! 3 m. 
 
 The first term of this expression <&*m/r is the part of the 
 centrifugal force which exactly counteracts the tendency of the 
 body to slide down the slope toward the centre of concavity 
 and of gyration, since we have assumed that the gradient of the 
 surface is such as to satisfy the condition of 38, and conse- 
 quently such as a liquid surface would assume where all parts 
 have the same angular velocity of gyration. The second part 
 of this expression, containing both GO and v as factors, depends 
 upon both GO and v, and vanishes if either GO or v is equal to o. 
 If v is the velocity of gyration in the same direction as that of 
 GO, then the effect of this term is positive, and the part of the 
 force represented by it tends to drive the body away from the 
 centre of the slope, being so much force in addition to that 
 which is just sufficient to support the body upon the slope and 
 to keep it from sliding down toward the centre. But if v is 
 negative, that is, contrary to the direction of GO, then the cen- 
 trifugal force is diminished, and is not sufficient to counteract 
 the tendency of the body to slide down the inclined surface 
 toward the centre. The effect of this term, therefore, is to 
 deflect the body on the concave surface, away from the centre 
 when v is positive, but toward the centre when negative, and 
 in both cases to the right of the direction of the relative mo- 
 tion. The last term in the expression of F c , depending upon 
 7' 2 , is simply the centrifugal force belonging to the relative gyra- 
 tory velocity, in case the solid surface had no gyratory velocity 
 oo. Consequently the effect of this part of the force is always 
 to drive the body from the centre, whether v is positive or 
 negative. 
 
54 MOTIONS OF BODIES RELATIVE TO EARTH'S SURFACE. 
 
 On a gyrating surface, therefore, in which the condition of 
 38 is satisfied, namely, that the body when at rest has no ten- 
 dency to move either toward or from the centre, the gradient 
 and the gyratory velocity being such that these two tendencies 
 exactly counteract each other, we then have for the expression 
 of the effective centrifugal force 
 
 m. 
 
 THE PRINCIPLE OF THE PRESERVATION OF AREAS. 
 
 41. If a body has a gyratory motion around any given 
 centre, and is also acted upon by a force in a direction either 
 toward or from that centre, the variable line connecting the body 
 with the centre, called the radius vector, always sweeps over 
 
 equal areas in equal times. Thus,, 
 if a body at# in the annexed figure 
 has a gyratory component of velo- 
 city from left to right around the 
 centre at o, and is at the same 
 time acted upon by a centripetal 
 force of any kind, so as to cause 
 it to move, in successive equal in- 
 tervals of time, to the points b, 
 c, and d, then the areas aob, boc, 
 cod, etc., are equal. This was 
 demonstrated by Newton, and is a 
 firmly established principle in me- 
 chanics. This equality of areas,, 
 of course, holds for each area, in 
 any part of the path of the body, 
 swept over by the radius vector 
 in an infinitely small portion of time, and these areas are 
 equal to one half of the product of the radius vector into- 
 the component of motion in this infinitely small portion of time 
 which is perpendicular to the radius vector, called the gyratory 
 
 Fig. 4. 
 
THE PRINCIPLE OF THE PRESERVATION OF AREAS. 55 
 
 component of motion. It also holds where the body recedes 
 from the centre in consequence of either the centrifugal force 
 arising from the gyratory component of motion, or any real 
 force acting in a direction from the centre. 
 
 The velocity of a body of variable motion at any point is 
 the space it would pass over in a unit of time, as one second, 
 if the rate of motion which it has at that point should con- 
 tinue through that time, and not the space which it actually 
 passes over in a unit of time with varying velocity. The gyra- 
 tory component of velocity is that part of its actual velocity in 
 the path described, resolved in a direction perpendicular to the 
 radius vector. For instance, if the body at d in the figure 
 above has a rate of motion which, if unchanged, would carry 
 it to e in the direction of the tangent in a unit of time, then if 
 this velocity de is resolved into the two components ei and di, 
 the former is called the gyratory and the latter the centripetal 
 velocity. As the velocities depend upon the rate of motions 
 at any given point, and not upon the actual motion in a unit of 
 time, and the areas swept over in infinitely small portions of 
 time are equal to half the product of the radii vectores into the 
 gyratory components of motion, and these areas are all equal, 
 it is evident that the gyratory velocities of the body in different 
 parts of its orbit are inversely as the radii vectores. Putting, 
 therefore, as heretofore, w for the gyratory velocity and r for 
 the radius vector, or variable radius, we have for all parts of 
 the path of motion 
 
 rw = c, 
 
 In which c is a constant. This is the expression of the law of 
 equal areas in this case. Hence the nearer the body comes to 
 the centre the greater is the gyratory velocity, and vice versa. 
 
 A familiar example of this law is observed in twirling a small 
 body attached to the end of a string around the end of a stick, 
 and, after the gyratory motion has been established, allowing 
 the string to wind up around it. The string acts as a force, 
 continually drawing the body closer to the axis or centre of 
 
56 MOTIONS OF BODIES RELATIVE TO EARTH'S SURFACE. 
 
 gyration, and as this is done the gyratory velocity increases, 
 and when the string becomes very short the velocity becomes 
 very great. Just the reverse takes place if the motion is such 
 as to unwind the string, and to allow the body to recede to 
 greater distances from the centre of gyration. As the dis- 
 tance increases, the gyratory velocity becomes less ; and when 
 the distance becomes very great, the gyratory velocity becomes 
 very small. 
 
 A more perfect exemplification of this law is found in the 
 motions of the planets and comets in their orbits around the 
 sun. In this case the law of the centripetal attractive force is 
 such as to cause elliptical orbits ; but the law holds, whatever 
 may be the law of this force and the path of the body. At 
 aphelion, where the planet or comet is at its greatest distance, 
 the gyratory velocity is least ; but as it comes nearer to the 
 sun in moving around to its perihelion, the gyratory velocity 
 increases in accordance with the law above, except so far as it 
 may be slightly affected by the perturbations of the other 
 planets. In the case of comets with very eccentric elliptical 
 orbits, the radius vector at perihelion becomes very small, and 
 the corresponding gyratory velocity enormous. 
 
 42. As the body is drawn or forced toward the centre of 
 gyration, the gyratory velocity, if the body is free, is increased, 
 just as in the case of a force acting upon a body in the 
 direction of its motion, and the amount of acceleration in a 
 unit of time, multiplied into its mass, in the former case as in 
 the latter, is the measure of the force causing the acceleration. 
 If the body is constrained to move in a given path, not directly 
 toward the centre, or is retarded by frictional or other resist- 
 ances, a part of this force may be spent in causing pressure 
 and overcoming the resistance of the friction, and the balance 
 only, in causing acceleration in the direction of motion. 
 
 According to the preceding expression of the law of equal 
 areas, rw = c, if r is decreased by the action of any kind of cen- 
 tripetal force by the \/m part of r in a very, strictly infinitely, 
 small portion of time, m being a very large or infinitely great 
 number, then w is increased by the same part, that is, by 
 
THE PRINCIPLE OF THE PRESERVATION OF AREAS. $? 
 
 i/m part of w, or w/m. If we now suppose that r continues 
 to decrease by the same rate during a unit of time, and we call 
 this rate, or centripetal velocity of the body, x, then r is 
 changing at the rate of the xj ' r part of it in a unit of time; 
 and consequently w, if it increased uniformly, would increase 
 the x/r part of w or xw/r in a unit of time. Now the in- 
 crease of velocity in a unit of time is called the acceleration, 
 and the acceleration multiplied into the mass m is the measure 
 of the force which causes the acceleration. And this force 
 acting in the direction of the gyratory velocity w, and so at 
 right angles to the radius, may be called the gyratory force. 
 Putting, therefore, F g for this force, we have 
 
 xw 
 
 
 
 r 
 
 The gyratory force, therefore, is directly as the product of 
 the gyratory velocity w into the centripetal velocity x, and in- 
 versely as the distance r of the body from the centre. If r, 
 therefore, could become infinitely small, the gyratory force 
 would become infinitely great. By comparing this expression 
 with that of the centrifugal force F e , 36, it is seen that they 
 are both equal where x and w are equal, that is, where the 
 velocity of the body toward the centre is equal to the gyratory 
 velocity. 
 
 43. If we suppose that a horizontal plane has a gyratory 
 motion around the centre o in Fig. 5 (p. 58) with a velocity 
 ab at the distance of a from the centre, the line AB being sup- 
 posed to be fixed in space, and also that a body at a, while 
 acted upon by a centripetal force toward o, also has a gyratory 
 velocity relative to the plane equal to be, then the absolute 
 gyratory velocity is ac. Denoting now, as in 40, by GJ 
 the gyratory velocity ab of the plane at the distance of oa or 
 r, and by v the gyratory velocity be relative to the plane, then 
 the absolute gyratory velocity ac of the body is GO -f v, and 
 Whence in this case, in order to get the gyratory force F ft we 
 
58 MOTIONS OF BODIES RELATIVE TO EARTH'S SURFACE.. 
 
 must put co + v for w in the preceding expression, and we thus- 
 get 
 
 r, XGO . XV N X 
 
 r. = in A m-=. GO-T-V) m. 
 
 r r J r 
 
 But the gyratory velocity, reckoned from the line ob instead 
 of the fixed line AB in space, is greater by the difference. 
 
 between ab and a'b' , supposing the body to move with uniform 
 velocity toward the centre by the distance aa! in a unit of time. 
 Now in a unit of time under these conditions ab is greater than 
 a'b' by the x/r part of c, or xco/r. Hence if the gyratory veloci- 
 ty is reckoned from the line ob instead of the fixed line AB, we 
 must add xco/r to the acceleration where the gyratory velocity 
 is reckoned from the gyrating line ob fixed relatively to the 
 plane, but not in space. With this additional term added to 
 the acceleration in the previous case, we get for the relative 
 gyratory force 
 
 ~ 2XG>) . XV . X 
 
 Fg. = m -\ m = (2Go + v) m. 
 
 r r } r 
 
CENTRIFUGAL FORCE OX THE EARTH'S SURFACE. 59 
 
 By comparing this expression with the last expression of the? 
 centrifugal force F e in 40, it is seen that they are the same if 
 x and v are equal, that is, if the centripetal velocity is equal to- 
 the relative gyratory velocity. From this it is to be understood 
 that, if a body has a gyratory velocity relative to a gyrating 
 surface around the same centre, in which the condition of 40- 
 is satisfied, and the gyrating body is drawn in toward the centre 
 by a centripetal force of any kind, with a given velocity, there 
 results a gyratory force which tends to overcome resistances to> 
 gyratory motion on the surface, or the inertia of the body, 
 when there are no frictional or other resistances, and to cause 
 accelerated gyratory velocity, and that this force is exactly 
 equal to that which tends to drive the body away from the 
 centre when the gyratory velocity is equal to the centripetal 
 velocity in the other case. If the force is centrifugal instead 
 of centripetal, then the direction of the gyratory force is re- 
 versed, and the relative greater velocity is diminished and may 
 be even overcome and reversed as the distance of the body 
 from the centre is increased ; just as has been shown, 40, in 
 the other case when the gyratory velocity v is negative, or in 
 the contrary direction, the deflecting force tends to draw the 
 body from the direction of motion toward instead of from the 
 centre. 
 
 If the body is not free to gyrate relatively to the gyrating 
 surface, but is constrained to move either directly towards or 
 from the centre, as in a groove, then the gyratory force causes 
 pressure against the one side or the other, according as the 
 body is forced toward or from the centre. 
 
 CENTRIFUGAL FORCE IN MOTIONS ON THE EARTH'S SURFACE.. 
 
 44. With the preceding preliminary results with regard to- 
 centrifugal force in general, 3540, we are now prepared to 
 investigate the effect of the centrifugal force arising from the 
 earth's rotation on its axis, upon the motions of bodies upon; 
 its surface. Let PCE, Fig. 6 (p. 60), represent one quadrant of a. 
 
*5O MOTIONS OF BODIES RELATIVE TO EARTH'S SURFACE. 
 
 meridional section of the earth turning on its axis, of which P 
 is the pole, C the centre, and E the point in the equator inter- 
 sected by this plane, and let a be a body at rest on the earth's 
 surface, subject to the action of the centrifugal force arising 
 from the earth's rotation and the consequent gyration of the 
 body around the point e as a centre in the semi-axis PC. The 
 amount of this force is given by the expression of F, in 36, 
 and it is in the direction of the line ab in the plane of gyration, 
 and the body would be driven away in this direction if this 
 centrifugal force were not counteracted by the stronger force 
 
 A 
 
 of the earth's attraction. Let us now suppose that the centrifu- 
 gal force is represented by the line ab, and that this is resolved 
 into two component forces in the directions of ad and ac, the 
 former parallel and the latter perpendicular to the earth's sur- 
 face, which together are equivalent to the force represented by 
 ab. If the points c and d are determined by perpendiculars 
 drawn to these lines from the point b, thus completing the 
 parallelogram of forces, it is well known that the original or 
 resultant force, and the two components in the directions of 
 ad and ac, are respectively proportional to the lines ab, ad, 
 and ac. 
 
 The component of the centrifugal force acting in the direc- 
 tion of ad, and represented by this line, tends to drive the body 
 
CENTRIFUGAL FORCE ON THE EARTH'S SURFACE. 6*. 
 
 on the earth's surface from the pole toward the equator, and if 
 the surface were perfectly smooth and without friction, would 
 do so on a spherical globe ; but this tendency is exactly counter- 
 acted by the tendency to slide down the ellipsoidal surface of 
 the earth toward the pole P. The ellipticity of the rotating" 
 earth is necessarily such that these two tendencies or forces are 
 exactly balanced, and just as in the case of the concave gyrat- 
 ing surface in 39, the concavity, and gradient of the slope at 
 each point, are such that the tendency to slide down toward 
 the centre is exactly counteracted by the centrifugal force. In 
 fact the earth's surface of either hemisphere, referred to a 
 spherical surface, or even one everywhere normal to the direc- 
 tion of the earth's attraction, is a concave surface, lower at the 
 pole than at the equator. A body, therefore, at rest upon the 
 ellipsoidal surface has no tendency to move, either toward the 
 equator on account of one component of the centrifugal force, 
 or toward the pole on account of the earth's ellipticity. 
 
 The other component of the centrifugal force, acting in the 
 direction of, and represented by, ac, tends simply to counteract 
 a comparatively small part of the force of the earth's attraction, 
 thus causing the force of gravity to be a little less than that of 
 the earth's attraction. 
 
 45. The centrifugal force of the earth's rotation acting in 
 the plane of gyration is, by the first form of the expression o 
 F c in 36, 
 
 F c rn*m, 
 
 in which r corresponds to ae in the figure, and in which n is the 
 gyratory velocity of the earth's rotation in terms of the radius. 
 This being a constant, this force is proportional to r, and this 
 latter is proportional to the cosine of the latitude if we neglect, 
 as we may in researches of this kind, quantities of the order of 
 the earth's ellipticity.* Putting, therefore, / for the latitude 
 
 * Neglecting such quantities, the line ao, Fig. 6, can always be taken as the 
 mean radius r ', and may be supposed to be drawn to the centre C instead of 0, 
 and so perpendicular to the surface at a. Then the angle aCE = CaE is the 
 latitude of the body at a, and we consequently have r \r = I : cos /, or r = r 
 cos /. And as r is constant, we have r = cos / when r is taken as unity. 
 
'62 MOTIONS OF BODIES RELATIVE TO EARTH'S SURFACE. 
 
 and r' for the mean radius of the earth, we have r =. r' cos /, 
 and hence the preceding expression becomes 
 
 F c = r'ri* cos/ m. 
 
 The cosines for each fifth degree of latitude are given in 
 Table V, to which those who are not familiar with such func- 
 tions can refer, and from which it is seen that they are great- 
 est at the equator and vanish at the poles. The horizontal 
 component of the centrifugal force, represented by ad in the 
 figure, varies on the different latitudes in comparison with the 
 whole, as the sines of the latitudes. These also are given in 
 Table V, from which it is seen that this component, in com- 
 parison with the whole, is greatest at the pole and vanishes at 
 the equator. But as the whole varies as the cosines of the lati- 
 tudes, the horizontal component varies as the product of the 
 cosine into the sine. Putting, therefore, F h for the horizontal 
 component of the centrifugal force, we have 
 
 F h r'n* cos/ sin/ m. 
 
 This component, therefore, vanishes both at the equator and 
 the pole, and is a maximum on the parallel of 45*. 
 
 Since the earth performs a complete sidereal revolution on 
 its axis in 2$h. 56m. 45., or 86,164 seconds, any part of the 
 earth, at the distance of unity from the axis, moves through the 
 space 27t = 6.2832 such units in this time. Hence the space 
 moved through in one second, in terms of the radius, is 
 6.2832/86164 = 0.00007292, which is the value of n above. The 
 equatorial radius of the earth being 6,378,190 meters, we get 
 for the acceleration of the centrifugal force at the equator, in 
 meters, or, in other words, the force for unity of mass, r'n* = 
 6,378,190 X (o.oooo7292) 2 = 0.033913. Comparing this with 
 
 * By a well-known transformation we can put cos /sin 1= -J sin 2/. On the 
 parallel of 45 we have 2/ = 90, and hence the maximum is on that parallel as 
 stated. 
 
CENTRIFUGAL FORCE ON THE EARTH'S SURFACE. 63 
 
 the acceleration of the force of standard gravity, which is 
 9.806 m., we get 0.033913 : 9.806 = 1/289, ver y nearly. 
 
 The velocity of rotation of any point on the earth's surface 
 is rn = r'n cos /, since n is simply the ratio between this velocity 
 aijd the radius of gyration r. These values, and also the values 
 of r, corrected for the effect of the earth's eccentricity, are 
 given for each degree of latitude in Table V. 
 
 Since the centrifugal force is as the square of n, if the gyra- 
 tory velocity of rotation were seventeen times greater, the cen- 
 trifugal force at the equator would be very nearly equal to that 
 of the earth's attraction, since the square of 17 is equal to 289, 
 and then a body at the equator would have little or no pressure 
 upon the earth's surface ; and if the rotary velocity were still a 
 little more increased, the body would fly off into space, not, 
 however, in the direction of a tangent, as is often said, but in 
 an elliptic orbit, which would bring it back again to the earth's 
 surface. 
 
 46. If a body at a, Fig. 6, has, in addition to the gyratory 
 east velocity due to the earth's rotation, also an easterly* 
 velocity relative to the earth's surface, called relative velocity, 
 the absolute east velocity is then increased by the east com- 
 ponent of this velocity, and the centrifugal force in the plane 
 of gyration is increased in proportion to the square of the 
 absolute east velocity. The centrifugal force is then given by 
 the first form of the expression of F e , in 40, using for GO and r, 
 for any given latitude, the values in Table V. But the hori- 
 zontal component of this force, the part which tends to drive 
 the body from the pole toward the equator, we have seen, is to 
 the whole as the sine of the latitude to unity; and hence in 
 order to obtain the expression for the horizontal component 
 F h in this more general case, in which the body has an east or 
 
 * In this work east or eastern is used in an exact sense, so that an east 
 or eastern direction means one exactly toward the east, while easterly is used 
 more vaguely to indicate directions varying considerably from an exact eastern 
 direction, but having a large east component. An east wind is one coming ex- 
 actly from the east, while an easterly one may have a considerable north or 
 south component of motion. So for all other points of the compass. 
 
64 MOTIONS OF BODIES RELATIVE TO EARTH'S SURFACED 
 
 west relative velocity v in addition to that of the earth's rota- 
 tion, we must multiply the expression of F c , in 40, into sin /, 
 and we thus get 
 
 ft/ + 200V + V* . 
 
 F = ! sin / m. 
 
 The first term in this expression (oo*/r) sin lm rn* sin Im 
 = r'n* cos / sin Im, putting r r' cos / to obtain the last form, 
 is the part of the horizontal component of the centrifugal force, 
 as shown in the last section, which is exactly counteracted by 
 the tendency of the body to slide down the elliptical surface 
 toward the pole, so that in the case of a body resting upon such 
 a surface, and having an easterly relative velocity with an east 
 component v, the force which tends to drive it toward the 
 equator is expressed by the last two terms above ; so that we 
 get in this case, putting F v for the force deflecting to the right 
 or south of the direction of motion of the east component of 
 velocity v, 
 
 i> 
 F v =. (200 -f- v) sin / m. 
 
 This is the same as would be obtained by multiplying the last 
 expression of F c , in 40, into sin /. 
 
 If the relative velocity is westerly, then the west component 
 v is negative ; and the absolute velocity of gyration, and conse- 
 quently the centrifugal force and its horizontal component, are 
 less than in the case in which the body is at rest on the earth's 
 surface, and in which case v = o. This force, therefore, in this 
 case, is not sufficient to counteract completely the tendency of 
 the body to move on the ellipsoidal surface toward the pole, 
 and there is a residual part of this tendency or force left, equal 
 to the preceding expression where v is, negative, and the body 
 consequently tends to move toward the pole. If, therefore, the 
 body has a relative motion with an east component of motion, 
 ' it is deflected toward the equator ; but if it has a relative motion 
 
THE PRINCIPLE OF EQUAL AREAS. 65 
 
 with a west component of motion, it is deflected toward the 
 pole ; and consequently in both cases to the right of the direc- 
 tion of the east or west component of motion in the northern 
 hemisphere, and the contrary in the southern, where sin / is 
 negative. 
 
 If the earth had no rotation on its axis and the body had an 
 east or west component of velocity z>, we should still have the 
 last term in the preceding expression of F h , depending upon ^ 2 , 
 which is independent of GO, the earth's gyratory velocity, and is 
 the same as if the body had an absolute east or west velocity 
 equal to v upon the earth without rotation on its axis. This 
 part of the force, however, is generally very small in all ordinary 
 cases of relative motions on the earth's surface, since the 
 velocities of these are generally very small, in comparison with 
 the velocities of the earth's rotation, as given in Table V, ex- 
 cept very near the poles. For instance, on the parallel of 45, 
 where GO = 329 meters per second, if v had one tenth of this 
 value, say 33 meters (about 74 miles per hour), it is seen from 
 a comparison of the two terms in the preceding expression of 
 F v , that the latter, which is independent of GO, would be only 
 -fa part of the other depending on GO. If the relative gyratory 
 velocity were west and equal to twice the east velocity of the 
 earth's rotation, then, it is seen, the whole deflecting force F v 
 would vanish, since then v would be equal to 200, and be 
 negative. 
 
 THE PRINCIPLE OF EQUAL AREAS IN MOTIONS ON THE 
 
 EARTH'S SURFACE. 
 
 47. If a free body upon the spheroidal surface of the earth, 
 supposed to be perfectly smooth and without friction, has an 
 absolute gyratory velocity around the earth's axis, and is also 
 acted upon by a force in the plane of the meridian in a direction 
 either directly toward or from the pole, then, as the body ap- 
 proaches or recedes from" the axis, the principle of equal areas 
 explained in 41 holds in this case also, just as it does where 
 
66 MOTIONS OF BODIES RELATIVE TO EARTH'S SURFACE. 
 
 the body is forced directly toward or from the centre of gyra- 
 tion, provided we consider the motions of the body, and the 
 areas swept over by the radius, as projected upon a plane per- 
 pendicular to the axis of the earth's rotation. 
 
 Since the perfectly smooth surface of the earth without 
 friction can have no effect upon the absolute motions of the 
 body in space, they are entirely independent of the earth's rota- 
 tion, and are the same as if the earth were at rest. If the body 
 on the parallel of a, Fig. 6, has an absolute gyratory velocity 
 along that parallel, either the same as, or greater or less than, 
 that of the earth's surface, and is forced toward the pole until 
 it arrives at the parallel of a', and the radius becomes a ' e' in- 
 stead of ae, the effect upon the absolute gyratory velocity around 
 the earth's axis is the same as if the body had been forced di- 
 rectly in the same plane from a to z, and the absolute gyratory 
 velocities on the two parallels are inversely as the distances from 
 the axis. For the force acting along the earth's surface in the 
 plane of the meridian may be resolved into two components, the 
 one in a direction parallel to the earth's axis, and the other perpen- 
 dicular to it, so that the former has no effect upon the gyratory 
 velocity, and the latter only is a central force, directed toward 
 the earth's axis and the centre of gyration. The absolute 
 gyratory velocity, therefore, is determined by the equation of 
 41, rw = c, where the value of c is known. If the values of 
 r and w are known for any given latitude, and are denoted by 
 r' and w' respectively, then we have r'w' = c, and the preced- 
 ing equation becomes 
 
 rw = r(cj -\-v) = r'w' , 
 
 putting, as heretofore, for w the sum of its two components &> 
 and v, the former being the gyratory velocity of the earth's 
 surface and the latter that of the body relative to the earth's 
 surface. From this expression, with the values of r' and w' 
 corresponding to any given latitude I', the value of w, and also 
 of v, are known for any latitude /. For since the values of r 
 
THE PRINCIPLE OF EQUAL AREAS. 6? 
 
 or different latitudes are as the cosines of these latitudes, by 
 dividing each term of the preceding equation by r, we get 
 
 in which GO' and v' are the values of GO and v corresponding to 
 / = /'. The values of the cosines and also of GO' are given in 
 Table V. 
 
 48. The following important applications may be made of 
 the preceding principle by means of this expression. If a body 
 on the equator having no relative east or west velocity were 
 forced toward the pole, the value of cos /' in this case being 
 unity, we should have, by means of the values of GO and cos / 
 in Table V, on the parallel of 45, where cos / is equal to 0.707, 
 for the value of w, 465/0.707 = 658 meters per second ; on the 
 parallel of 60, where cos /=o.5, the value of w would be 
 465/0.5 = 930 meters per second ; on the parallel of 80, where 
 cos 7=0.174, we should have 2^ = 465/0.174 = 2674 meters 
 per second. Also, for points much nearer the pole it is seen 
 that w would be still very much greater. 
 
 But these are the velocities reckoned from a fixed plane in 
 space and not from a given meridian on the earth's surface. 
 To obtain, therefore, the relative east velocities, or values of v, 
 we must subtract from these the values of GO in Table V, which 
 are the absolute east or gyratory velocities of the earth's sur- 
 face. Hence, deducting these from the absolute velocities 
 above, we get, on the parallel of 45, ^=658 329 = 329 
 meters per second ; on the parallel of 60, v = 930 232 = 698 
 meters per second; and on the parallel of 80, v = 2674 8 1 
 = 2593 meters per second. 
 
 If the body before leaving the equator had an east or west 
 relative velocity, then the absolute velocity here, w' , would be 
 greater or less by this amount, and so the absolute velocities on 
 the several parallels above, from which the values of GO have to 
 be deducted in order to obtain the relative values v, would all 
 .be greater or less in the same proportion. 
 
68 MOTIONS OF BODIES RELATIVE TO EARTH'S SURFACED 
 
 If the initial position of the body were that of some par- 
 allel between the equator and the pole without any initial 
 relative motion, then, if forced toward the pole, it would 
 gradually acquire an east component of relative velocity, which, 
 near the pole, would be enormously great, but if forced from 
 the pole, it would gradually acquire a west component of 
 velocity relative to the earth's surface. Thus a body without 
 any relative east or west velocity on the parallel of 30, where 
 the absolute east or gyratory velocity of the earth's surface is- 
 403 meters per second, on arriving at the parallel of 60 would 
 have this velocity increased inversely as the cosines of the 
 latitudes, that is, as 0.500 to 0.866, and hence would be 698 
 meters per second, and deducting from this the value of GO, in 
 Table V, for this parallel we should have a relative east veloc- 
 ity v = 698 232 = 466 meters per second. But if the body 
 were forced directly toward the equator, on arriving there its 
 absolute east velocity would be decreased inversely as the 
 cosine of 30 degrees to unity or as I to 0.866, and hence would 
 be 349 meters per second. Deducting this from the absolute 
 easterly velocity of the earth at the equator, we get for the 
 relative west component of the velocity of the body at the 
 equator 465 349 = 1 16 meters per second. 
 
 If the initial relative west component of velocity were 
 exactly equal to the absolute east or gyratory velocity, either 
 at the equator or any parallel of latitude, then the initial abso- 
 lute gyratory velocity w' would be o, and the body then would 
 move in space directly toward or from the pole, and its relative 
 west velocities, at all latitudes, would be those of the absolute 
 east velocities of the earth's surface. 
 
 The preceding results, obtained from the principle of 41, 
 differ very much from those obtained from the principle 
 adopted by Hadley, about the year i/35> m explaining the 
 trade-winds, namely, that a body, being forced directly toward 
 or from the pole, tends to keep its initial absolute gyratory 
 velocity. He says: 7 " A particle of air drawn from the tropics, 
 where it is supposed to have no motion east or west, toward the 
 equator acquires a westward velocity on account of the parallels- 
 
THE PRINCIPLE OF EQUAL AREAS. 69 
 
 continually enlarging. The increase of the parallels from the 
 tropics to the equator is in the ratio of 917 to 1000, and hence 
 the westward motion in an hour is 83 miles at the equator, 
 which is decreased by the effect of the earth's surface to what is 
 observed." But from what has been shown above, the velocity 
 of a body having an absolute east velocity of 917 miles per hour 
 at the tropics, as here supposed, would be decreased at the 
 equator in the ratio of unity to the cosine of the latitude at 
 the tropics, or as I to 0.917. Hence, instead of still having an 
 absolute east velocity of 917 miles per hour, it would have a 
 velocity of only 917 x 0.917 = 841 miles per hour. This being 
 deducted from 1000, the supposed absolute east velocity of the 
 earth's surface at the equator, we have 159 miles for the rela- 
 tive west velocity there, instead of 83 miles as given above. 
 
 According to this erroneous principle, in order to obtain the 
 relative east components of velocity of the body at the several 
 latitudes, in moving from the equator to the pole in the pre- 
 ceding example, it would be necessary to subtract the absolute 
 east velocities of the several parallels, as given in Table V, 
 from that of the equator, and we should thus get in meters per 
 second, at the parallel of 45, v = 465 329 = 136; at the 
 parallel of 60, v = 465 232 = 233 ; and at the parallel of 80, 
 v= 465 81 = 384. 
 
 These differ very much from the velocities obtained above 
 upon the correct principle, which is that of equality of areas in 
 the case of central forces. 
 
 49. The gyratory force F g in this case that is, the tendency 
 of the body, when free, to acquire an east component of ve- 
 locity relative to the earth's surface, and when not free, to 
 cause pressure and to overcome resistances to such relative 
 motion is the same as in the case of any gyrating surface 
 where the body is forced toward the centre with the velocity 
 of ;tr, and is given by the last expression of F g in 43. But 
 this may be given in a function of the polar component of 
 velocity of the body in moving on the earth's surface instead 
 of a function of x, which is the velocity, in this case, with 
 which it approaches the earth's axis. From Fig. 6 it is seen 
 
70 MOTIONS OF BODIES RELATIVE TO EARTH'S SURFACED 
 
 that by similar triangles we have aa! : ai= aC \ Ce = i : sin / r 
 neglecting quantities of the order of the earth's eccentricity,. 
 and supposing aa' to be so small as not to deviate sensibly 
 from a straight line. If we let this represent the polar com- 
 ponent of velocity of the body on the earth's surface and 
 denote it by u, then ai^x is the component of this velocity 
 perpendicular to the earth's axis. We therefore have u : x 
 I : sin /, or ;r = u sin /. Putting this expression of x for x in 
 the last expression of F g in 43, we get 
 
 F u = (200 -f- v) sin / m, 
 
 in which, in analogy with the expression of F v in 46, F u is 
 put, instead of F f , for the force deflecting to the right or east 
 of the direction of motion of the polar component of velocity^. 
 
 By comparing this expression with that of F v in 46, it is 
 seen that they are very similar ; in this a polar component of 
 velocity u gives rise to a force deflecting to the right of the 
 direction of this component, and in the other an east com- 
 ponent of velocity v gives rise to a force also deflecting to the 
 right of the direction of this component. And it is also seen 
 that these forces are precisely equal if u and v are equal. 
 When the directions of motion are reversed and u and v become 
 negative, of course the deflecting forces are reversed in their 
 directions of action, but the deflecting force is still toward 
 the right of the directions of these components. This must 
 be understood of the northern hemisphere where sin / is 
 positive. In the southern hemisphere, where sin / is negative, 
 of course the deflecting forces are reversed in the directions of 
 their actions, and are always to the left of the directions of the 
 components, whether these are north or south, or east or west. 
 
 We have by definition in 45, n = oo/r ; and if, by analogy, 
 we put v = v/r , we shall have v equal to the relative gyratory- 
 velocity of the body around the earth's axis in terms of the 
 radius, as n is the absolute gyratory velocity, in the same 
 terms, of a body fixed on the earth's surface. Substituting n 
 
RESULTANTS OF THE TWO FORCES AND MOTIONS. 71 
 
 and v for their equivalents in the preceding expressions of F u 
 and F, , we get 
 
 F u = (2n -\-v)u sin / m ; 
 
 F v = (2n -}- v)v sin / w. 
 
 RESULTANTS OF THE TWO FORCES AND MOTIONS. 
 
 50. Where the motion of a body upon the earth's surface 
 is such as to change both its longitude and latitude at the same 
 time, both of the preceding forces are called into play at the 
 same time, and they give rise to one resultant force in a certain 
 determinate direction. If, in Fig. 7, we let AB represent the 
 
 Fig. 7. 
 
 velocity u and direction of the polar component of motion, and 
 AC, at right angles to AB, the east component of velocity; 
 then AD, the diagonal of the parallelogram, which we shall 
 denote by s, represents the resultant velocity. But the forces 
 arising from the component velocities, which act in directions 
 toward the right and at right angles to the directions of mo- 
 tion, and consequently at right angles to each other, may be 
 
72 MOTIONS OF BODIES RELATIVE TO EARTH'S SURFACE* 
 
 icpresented by the lines AB' and AC ', drawn perpendicular to, 
 and to the right of, the directions of motion, and from what is 
 shown in the preceding expressions of F u and F vy they are 
 proportional to the velocities u and v respectively. Complet- 
 ing the parallelogram, the diagonal AD' then represents the 
 resultant of the two forces, both in magnitude and direction, 
 and as the forces represented by AB' and AC' have been 
 denoted by F u and F v respectively, we may let F s denote, by 
 analogy, the resultant force represented by AD', since it 
 depends upon the resultant velocity s, just as the others do 
 upon the component velocities u and v. Now by a well-known 
 theorem we have the diagonal of a parallelogram equal to the 
 square root of the sum of the squares of two contiguous sides. 
 Hence we have 
 
 s= iV+y, and F s = 
 
 If we now square both members of the last two equations 
 of 49 and take the square roots of their sums, we get, by 
 putting s and F s for their equivalents above, 
 
 F s = (2n -f- v)s sin / m. 
 
 Since, by the construction of the figure and the relations of 
 the homologous sides of similar triangles, we have AB : AC 
 (= BD) = AB' : AC(=B'D'\ and so the angle BAD equal the 
 angle B'AD', by adding* the angle CAD to both, we have the 
 angle BAC equal the angle DAD' , and hence the latter is a 
 right angle. The direction, therefore, of the resultant of the 
 two deflecting components is at right angles to the direction of 
 the resultant motions, of which the velocity is represented by 
 the line AD or s. As the components of velocity?/ and v may 
 have any value, either positive or negative, the resultant motion 
 with velocity s may have any direction, and the resultant 
 deflecting force will always be at right angles to, and to the 
 right of, this direction in the northern hemisphere, where sin / 
 is positive, but to the left in the southern hemisphere, where 
 sin / is negative, and where, consequently, the resultant force 
 
RESULTANTS OF THE TWO FORCES AND MOTIONS. 73 
 
 F s is reversed in direction. This deflecting force, however, is 
 not a real force, but is of the same nature as centrifugal force, 
 35; and as it always acts, as we have just seen, in a direction 
 at right angles to the direction of motion, its tendency is to 
 continually change direction only, and not to increase or 
 decrease velocity and momentum. But this change of direc- 
 tion must not be understood to be a change of absolute direc- 
 tion in space, for this would require a real force, but simply a 
 change of direction relative to the earth's surface. 
 
 51. In obtaining the preceding expression of F t , the only 
 condition with regard to any real force to which the body may 
 be subject was that it shall act only in the plane of the meridian, 
 and so one component of the force be a central force, directed 
 toward the earth's axis. The initial values of u and z>, and so 
 of s, are entirely arbitrary, and the value of the latter is only 
 changed subsequently by the action of the real force acting 
 upon the body, in a direction either toward or from the pole. 
 We consequently have no relation between the force and the 
 value of s, and the value of the preceding expression at any 
 time depends simply upon that of s, and in no way upon the 
 force acting upon the body by which the value of s is changed. 
 The preceding expression of F s , therefore, holds when the force 
 is infinitely small, and so when it entirely vanishes and the 
 value of s and the direction of motion depend upon an in- 
 stantaneous impulse. This expression, therefore, holds wher- 
 ever the body has a motion in any direction relative to the 
 earth's surface, in whatever way this motion may have been 
 produced. If a body, therefore, were set in motion upon the 
 spheroidal surface of the earth, supposed to be perfectly smooth 
 and without friction, it would continue to move on forever with 
 its initial velocity, but with continually changing direction 
 relative to the earth's surface, and its path would vary very 
 much with different initial velocities. It is seen from the 
 expression of F s that the deflecting force, for the same value 
 of s, would differ with different directions of motion, since 
 v = v/r is a function of v, which is the east component of s, 
 and so changes with different directions, and even becomes 
 
74 MOTIONS OF BODIES RELATIVE TO EARTH'S SURFACE* 
 
 negative when v becomes a west component, as it may in 
 many cases even where the initial direction is east. It is also 
 seen that this force varies with latitude, so that if the initial; 
 velocity given were great, the body might be carried from a 
 high latitude down to a very low one, when sin / and conse- 
 quently the whole expression would be small, or it might 
 even be carried across the equator into the opposite hemi- 
 sphere, where the deflecting force would be changed from the 
 right-hand to the left-hand side of the direction, or the contrary, 
 according to the hemisphere from which it passes. 
 
 In case the earth had no rotation around its axis, n in the 
 preceding expression of F t would vanish, and it would then be 
 the expression of the deflecting force due simply to the cen- 
 trifugal force of the motion of the body. But it must be here 
 borne in mind that these so-called forces, as they have beerr 
 defined and used, are not real forces, but simply tendencies to 
 cause departures from the parallels and meridians. If the 
 initial motion is in the direction of the meridian, then v, and 
 consequently v = v/r, vanishes, and so the expression of F 3 van- 
 ishes, and consequently there is no tendency of the body to 
 depart to either side of the meridian. But if the initial motion* 
 is in the direction of a parallel of latitude, then we have s v, 
 and the expression then simply becomes that of the horizontal" 
 component of the centrifugal force of the body in its motion along 
 the parallel, and F s is then the force with which the body tends- 
 to depart from this parallel, and of the lateral pressure of the 
 body in a direction from the pole toward the equator if the 
 body were constrained to move in a groove on a given parallel. 
 Since in this case s becomes the same as v, the expression has 
 the same sign and the force the same direction of action,, 
 whether the initial motion is east or west. At the equator, 
 where sin /=o, this force vanishes, as in the case where the 
 initial motion is in the direction of the meridian, and the body- 
 moves in the great circle of the equator. 
 
WHERE THE CENTRE OF FORCE IS NOT THE POLE. 75; 
 
 WHERE THE CENTRE OF FORCE IS NOT THE POLE. 
 
 52. In what precedes, it has been supposed that the body is 
 not acted upon by any real force tending to move it out of the 
 plane of the meridian. We come now to consider the case in 
 which there is some force tending to drive the body either 
 toward or from some point on the earth's surface which is not 
 one of the poles, and for the sake of simplicity we shall here 
 limit the case to a portion of the earth's surface around this 
 centre which is not so great that it cannot be regarded, without 
 material error, as a plane surface. Let us, by way of introduc- 
 tion to what is to follow, consider first the case of a limited 
 area around the north pole. In this case if the area does not 
 extend, say, more than ten degrees from the pole, then we can 
 regard sin / for this whole area as being equal to unity, without 
 any material error arising from such an assumption ; and then 
 we get from the expressions of F H and F v , 49, by putting 
 sin / = i , 
 
 F u = (211 -\- v)u . m ; 
 F v = (2n -f- v)v . m. 
 
 We have here the case of the gyrating concave disk of 
 39, the concavity being that arising from the spheroidicity of 
 the earth's surface, and being such that the tendency of a body 
 at rest to slide down toward the pole is exactly counteracted by 
 the centrifugal force due to the earth's rotation. 
 
 The value of n in this case is that of the earth's rotation on 
 its axis. If the centre of the area considered were on the 
 equator, there would be no gyratory motion of this area around 
 the centre, though of course the centre and the whole area 
 would gyrate around the earth's axis, but not around any axis 
 in the plane of the equator. In this case, therefore, we have 
 n = o. It is reasonable to suppose, therefore, that the value of 
 n is the greatest at the pole, and decreases with decrease of 
 latitude, according to some function of the latitude, from the- 
 
76 MOTIONS OF BODIES RELATIVE TO EARTH'S SURFACE. 
 
 pole to the equator. This function, it is well known, is the 
 sine of the latitude. Assuming this here without attempting to 
 demonstrate it, if we put ri for the gyratory velocity in terms 
 of the radius around any point on the parallel of latitude /, we 
 shall have 
 
 ri = n sin /. 
 
 Putting n' or n sin / instead of n in the preceding expres- 
 sions, they become 
 
 F H = (2n sin /-)- r)u . m, 
 F v = (2n sin l-\- v)v . m, 
 
 in which u is the velocity toward the centre and v is the gyra- 
 tory velocity around that centre, and v = v/r t in which r is the 
 distance from the centre. The first of these is the expression 
 of the gyratory force, and corresponds to the last expression of 
 F s in 43 ; and the second is the expression of force from the 
 centre, and corresponds to the last expression of F e in 40, since 
 n sin / = n' is the angular gyratory velocity around the centre 
 :in this case. 
 
 The resultant of these, taken as in 50, is 
 
 F s = (2n sin l-\-v)s . m. 
 
 As in the preceding case, this expression varies with different 
 directions of motion of velocity s, since v = v/r varies as v 
 varies, and this being one of the components of s changes with 
 change of direction for the same value .of s, and may even be- 
 come negative as in the case in which the relative gyratory 
 velocity is in a direction contrary to that of the area under con- 
 sideration, depending upon the earth's rotation. 
 
 As is usual in the case of a central force, the value of 
 r = v/r may become very great in comparison with 2.n or 
 2n sin /; for not only does the value of v become very great 
 near the centre, but r becomes very small, and so for both 
 reasons v becomes large near the centre. In such cases the 
 motion of the body becomes mostly a rapid gyration around 
 the centre, and the deflecting force is almost entirely the cen- 
 
THE DEFLECTING FORCE OF THE EARTH'S ROTATION. 77 
 
 trifugal force arising from the relative gyratory velocity of the 
 body, the part depending upon n in such cases being very small 
 in comparison with that depending upon v v/r. 
 
 THE DEFLECTING FORCE OF THE EARTH'S ROTATION. 
 
 53. We have seen from what precedes that wherever a body 
 upon the earth's surface has a motion relative to that surface, 
 however produced, there is a deflecting force, depending in 
 part upon the earth's rotation, and partly upon the velocity 
 and direction of motion relative to the earth's surface, and en- 
 tirely independent of any real forces, by which the body is con- 
 tinually acted upon in a direction at right angles to the direc- 
 tion of motion and deflected from its course, and that this, in- 
 the case of central forces, may become very great near the cen- 
 tre of force, where the value of r, the distance from the centre, 
 is small. In all straight-lined motions on the earth's surface,, 
 the value of r in the expression of v v/r becomes infinite, and 
 so the value of v in the preceding expression of F s vanishes,, 
 and the whole deflecting force depends upon the earth's rota- 
 tion. In the case also in which the body is not acted upon by a 
 local force but is subject only to a force acting in the plane of the 
 meridian, the value of v in the expression of F s , 50, is very small 
 in comparison with 2n, unless it should be very near the pole, 
 where r, in the expression of v = v/r, is the distance from the 
 earth's axis. It is seen from Table V that the value of 2oo on the 
 parallel of 45 is 658 meters per second ; so for a relative easterly 
 velocity v of any body of only 20 meters per second (45 miles 
 per hour), the ratio of v to 2u sin / in the expression of F t is as 
 20 to 658, since v = v/r and 2n sin /= 2(&/r. For any ordinary 
 velocity, therefore, on the earth's surface where the body is 
 not subject to the action of a strong local central force, the 
 whole deflecting force depends mostly upon the influence of 
 the earth's rotation, and is almost entirely independent of the 
 centrifugal force arising from the relative motion on the 
 earth's surface, which would exist in case the earth had no> 
 rotation on its axis. 
 
78 MOTIONS OF BODIES RELATIVE TO EARTH'S SURFACE. 
 
 For the part of the deflecting force depending only upon the 
 -earth's rotation, we obtain either from the expression of F s in 
 50, or the last one in 52, by neglecting the part independent 
 of n, 
 
 F s = 2ns sin / m. 
 
 In the northern hemisphere this force acts in a direction at 
 Tight angles to the direction of motion, and to the right; but 
 in the southern hemisphere, where sin / is negative, the direc- 
 tion is reversed, and consequently at right angles to the left. 
 It is seen from the preceding expression that this force, for any 
 given mass, depends simply upon the sine of the latitude and 
 the velocity s of the relative motion and is entirely independ- 
 ent of the direction of this motion. Hence, if a body moves in 
 any direction upon the earth's surface, there is a deflecting force 
 arising from the earths rotation, which deflects it to the right in the 
 northern hemisphere, but to the left in the southern hemisphere* 
 
 54. This important part of the subject may be viewed in a 
 different manner, and one by which it may perhaps be more 
 readily understood by many readers, than by the preceding 
 method of considering the matter. If a body at a, Fig. 8, has 
 
 m 
 
 Fig. 8. 
 
 a motion with uniform velocity in the direction from m to n, or 
 the contrary, in the line mn, which is continually and uniformly 
 changing its direction from right to left of the direction of mo- 
 tion, it is readily seen that as the line changes its direction, the 
 body by virtue of its inertia has a tendency to continue on in 
 the same direction, and to depart from the gyrating line to the 
 
 * This important proposition was first demonstrated by the present writer in 
 the year 1859 in a paper on "The Motions of Fluids and Solids on the Earth's 
 Surface," published in Runkle's Mathematical Monthly. This part of that paper 
 appeared in the May number of the Monthly. The whole paper has since been 
 republished by the Signal Service (Professional Paper No. VIII), with extensive 
 notes by Professor Frank Waldo. 
 
-THE DEFLECTING FORCE OF THE EARTH'S ROTATION. 79 
 
 right, just as it would from a line fixed in space if there was a 
 constant real force acting on the body, at right angles to the 
 direction of motion. If the body moved in the contrary way 
 from n towards ;;/, the tendency would be to depart on the 
 other side, but still to the right of the direction of motion, 
 where the line gyrates from right to left, looking in the direc- 
 tion of motion. It is also evident that if the line is changing 
 its direction from left to right, the body tends to depart from 
 this line to the left-hand side. But if the body were not free 
 to move in a fixed direction in space, but were compelled to 
 move in the line continually and uniformly changing its direc- 
 tion, as in a groove, then, instead of departing to the right- or the 
 left-hand side, as the case may be, it would press against the 
 .side with a force sensibly equal to a real force which, during 
 a very small interval of time, would cause the body to depart 
 from a fixed line in space at the same rate. It is readily seen 
 that this rate of departure at any instant of time must be pro- 
 portional to the velocity s in the direction of motion, and the 
 rate of change of direction, or the gyratory velocity of the line 
 in terms of the radius. Denoting this latter by n' t it is, there- 
 fore, proportional to n' s, and consequently the lateral pressure, 
 where the body is constrained to move in a straight line with 
 changing direction in space, is in the same proportion. 
 
 Some general idea of this deflecting force may be formed 
 from the experience of any one in walking over a narrow draw- 
 bridge while it is turning around its central pivot. If there were 
 no railings, the tendency would be, if not guarded against, to 
 run off on the one side or the other, according to the direction 
 of gyration ; and where there are railings, to press against that 
 side. And this tendency would evidently be in proportion to 
 the velocity of transit across the bridge and the angular veloc- 
 ity of its gyration. Of precisely the same nature is the deflect- 
 ing force of the earth's rotation; for every horizontal line, fixed 
 relatively to the earth's surface, except at the equator, is con- 
 tinually changing its direction with reference to a direction 
 fixed in space; and so a body, set in motion in any direction 
 relative to the earth's surface, tends, if free, to depart from 
 
80 MOTIONS OF BODIES RELATIVE TO EARTH'S SURFACED 
 
 this direction, and if constrained to move as in a groove in this 
 direction, to press toward one side or the other, as the case 
 may be. 
 
 55. The absolute amount of deflecting force may be de- 
 duced in the following manner : If a body at a, Fig. 8, has, at 
 any instant of time, a motion in the direction from m toward n 
 in the line mn with the velocity s, and this line at the same 
 time is changing its direction or gyrating around the point a, 
 whatever other motion the whole line may have, with a gyra- 
 tory velocity n 1 in terms of the radius, then if ab represents s,. 
 and the angle nan' the change of direction in a unit of time, 
 this unit, which is entirely arbitrary, being taken so small that 
 this angle is very small and ab is sensibly equal to ac, be being 
 perpendicular to m'n' and measuring the nearest distance of 
 the point b from m'n', the body at the end of this unit of time 
 is departing from the line m'n' by the space be in a unit of time 
 by virtue of its velocity s in the direction of mn. But this 
 perpendicular at the distance of unity from a is n', and there- 
 fore the body in moving through the space s in a unit of time 
 departs from the line m'n' , supposed to remain fixed for the 
 time, by the space n's. If we now suppose that when the body 
 arrives at b it remains stationary for the time, then the line 
 m'n', by virtue of its change of direction, or gyratory velocity 
 n' around the point a at the distance of unity, is departing from 
 the body at b, which is at the distance s from a, at the rate of 
 ns. Therefore by virtue of both the motions of the body in its 
 direction mn, fixed in space, and also of the uniform change of 
 direction of the line m'n', the body at the end of the unit of 
 time is departing from the line of varying direction in space at 
 the rate of 2n's in a unit of time. It is therefore departing 
 from it at the same rate that a body moving in a direction fixed 
 in space would be drawn out of the line of this direction by a 
 force acting in a direction at right angles to the direction of 
 motion, if the acceleration of this force were 2n's. The lateral 
 pressure, therefore, of a body of the mass m, if constrained to 
 move in the line of varying direction, is 2n's . m. In case of a 
 straight line on the earth's surface, at any given parallel /, we 
 
THE DEFLECTING FORCE OF THE EARTH'S ROTATION. 8 1 
 
 have seen that the value of ri is n sin /. Denoting, therefore, 
 as before, this deflecting force of a body, of velocity j, by F s , 
 and putting n sin / for n' ', we have, as in 53, 
 
 F t = 2ns sin/, m. 
 
 In the southern hemisphere the line m'n' would gyrate, with 
 reference to the line mn fixed in space, from left to right ; and 
 so in this hemisphere the deflecting force, or tendency to de- 
 part from the line m'n' , is to the left-hand side. 
 
 56. If the body in motion were a stratum of liquid, as the 
 water of a wide river, moving with a velocity s in any uniform 
 direction, then the deflecting force at right angles to this direc- 
 tion would cause an ascending gradient of the surface and of 
 all strata of equal pressure in that direction, and this, as ex- 
 plained in the case of the gradient arising from centrifugal 
 force, 38, would be 
 
 F s 2ns sin / 
 
 sn 
 
 putting for n and g their numerical values in 45 in obtaining 
 the last form of this expression. 
 
 The value of e being the change of level in the distance of 
 unity, which in this expression is the meter, for a distance of r 
 meters the change of level is re. If a river one mile in width 
 (1609 m.) has a velocity of 2 meters per second (4.5 miles per 
 hour) in any uniform direction on the parallel of 45, then the 
 surface of the right-hand side in the northern hemisphere stands 
 higher than the other by 
 
 re 0.00001487 X 1609 X 2 X 0.707 = 0.034^ =1.3 inches, 
 
 in which 0.707 is sin 45, taken from Table V or any table of 
 natural sines. 
 
 The values of e/s have been computed from the formula 
 above, for each fifth parallel of latitude, and given in Table V, 
 from which the values of re can be more conveniently obtained. 
 Thus from the table we get for the parallel of 45, e/s equal to- 
 
82 MOTIONS OF BODIES RELATIVE TO EARTH'S SURFACE. 
 
 0.00001052 ; and so in the example above, we have, as just ob- 
 tained, 
 
 re = 2 X 1609 X 0.00001052 = o.034 m . 
 
 The value of e above, since it is the ratio between the de- 
 flecting force and that of gravity, expresses also the ratio be- 
 tween the lateral pressure, due to the earth's rotation, of a body 
 moving in any uniform direction with velocity s, and the verti- 
 cal pressure of the body. Multiplying, therefore, the value of 
 e/s in the table by s, we get this ratio. Hence if a railroad car 
 on the parallel of 40 moves with a velocity of 20 meters per 
 second (45 miles per hour), we get 
 
 e = 0.00000956 X 20 = 0.0001912. 
 
 The lateral pressure is therefore about 1/5230 part of the ver- 
 tical pressure of the car. If the road had a curvature of radius 
 r, then the pressure arising from the centrifugal force, as given 
 in 37, would have to be added, in the northern hemisphere, 
 if the motion of the car was from right to left around the cen- 
 tre of curvature, but subtracted if the contrary way, in order to 
 obtain the pressure to the right of the direction of motion. 
 It is to be understood of course that the two rails of the road 
 are on the same level. 
 
 For intermediate latitudes of the five-degree intervals of 
 the table the value of e/s is readily obtained by interpolation 
 with sufficient accuracy by using only the first differences. Thus, 
 if the value of e is required, for the latitude of 52, correspond- 
 ing to a wind velocity of 1 5 meters per second, we readily ob- 
 tain from the table, by adding 2/5 of 80 to 0.00001139, e/s = 
 0.00001171. Hence we have 
 
 e 0.00001171 X 15 = 0.0001756. 
 
 57. The value of e, for any given velocity s, is the difference 
 -of level of the surface of any inelastic fluid, or of a stratum of 
 equal pressure in the case of the atmosphere, between two 
 
THE DEFLECTING FORCE OF THE EARTH'S ROTATION. 83 
 
 stations at the distance of unity. Or, e is the height of the 
 column of the fluid, subject to the force of gravity, which ex- 
 actly counterpoises a horizontal column of a unit in length and 
 of the same base, subject to the action of the deflecting force 
 causing the gradient. The height of this column is a measure 
 of the difference of pressure on a horizontal surface at the dis- 
 tance of unity, and the vertical pressure of such a column of 
 unit base would express the difference of pressure on such a 
 base in kilograms or pounds of pressure according to the meas- 
 ure adopted. In the case of the atmosphere, however, the 
 gradient is usually measured by the height of the mercurial col- 
 umn which exactly counterpoises the lateral pressure on the 
 same base, 10, and this is called the barometric gradient. But 
 in expressing this gradient we do not use the meter as the 
 unit of length, but use the millimeter in the vertical height 
 of the mercury and one degree of a great circle, or 1 1 1,1 11 me- 
 ters, as the unit of horizontal distance. The height, also, of 
 the mercurial column is less than that of the air column of 
 standard pressure and temperature, in the ratio of the density 
 of such an air column to that of mercury, or as I to 10,517. 
 In order, therefore, to obtain the barometric gradient, which 
 we shall denote by G, from the preceding general expression 
 of e, it is necessary to multiply this expression by 1000, on ac- 
 count of a change of the unit of the vertical column from the 
 meter to the millimeter, and also by 111,111 on account of the 
 change of the unit of horizontal distance, and to divide by 10,517 
 on account of the height of the mercurial column being less 
 than that of the counterpoising air column in the ratio of I to 
 10,517. We then get 
 
 G l = O.I57U sin /. 
 
 But it must be understood that this is only for air of standard 
 pressure and temperature. For any other it must be increased 
 or diminished directly as the pressure of the air and inversely as 
 the absolute temperature, since the density of the air by the laws 
 of Boyle and of Charles, 4, changes in these ratios. Putting, 
 .therefore, as heretofore, P for the standard pressure P, and T^ 
 
84 MOTIONS OF BODIES RELATIVE TO EARTH'S SURFACE.. 
 
 for the standard absolute temperature T, we obtain the fol- 
 lowing more general expression : 
 
 P T 
 sin l-'- 
 
 But this expression holds only in the case of straight-lined 
 winds with little or no friction, where the direction of gradient 
 is at right angles to that of the wind. 
 
 The preceding less general expression of G^ gives values at 
 the earth's surface and for all ordinary temperatures, which are 
 sufficiently accurate for most purposes, and these are given in 
 Table V for unit of velocity. For other velocities it is only 
 necessary to multiply the tabular numbers into the velocity.. 
 Thus on the parallel of 40, for a wind of 15 meters per second, 
 we get in millimeters 
 
 G = o.ioio X 15 = 1.51. 
 
 By reversing the preceding expressions, the value of s, the 
 velocity of the wind, may be found corresponding to any given 
 gradient. By the preceding example, if there is an observed 
 gradient of 1.5 mm., the corresponding wind velocity in a direc- 
 tion at right angles to that of the gradient must be about 15 
 meters per second. 
 
 All the preceding gradients depend upon n, and so upon the 
 earth's rotation, and would vanish if the earth were at rest. In 
 addition to these there may be gradients depending upon the 
 centrifugal force when the wind blows in circuits, and these 
 may be very great if the radius of curvature is small and the 
 velocity large. 
 
 In order to obtain the gradient G in the case of centrifugal 
 force in connection with that of the earth's rotation, we must 
 use the expression of F s , 52, instead of the preceding one of 
 F t . We thus get, by multiplying by 1000, by 1 1 1,1 1 1, and divid- 
 ing by 10,517, 
 
 272 sin /+ v ill ill in 
 G ' = 
 
 9.806 10517 
 
THE DEFLECTING FORCE OF THE EARTH'S ROTATION. 8$ 
 
 By neglecting v, the part depending upon the centrifugal force, 
 and giving n its value 0.00007292, we get the first of the two pre- 
 ceding expressions of G, in the case of standard temperature 
 and pressure. The general expression of this, for any pressure 
 P and absolute temperature T, becomes 
 
 P T 
 (zn sin7+*)^r- ~. 
 
 in which v = v/r. 
 
 The relation of the part of the gradient, whether the linear 
 gradient e or the barometric gradient G, depending upon the 
 curvature of the path, to that depending upon the earth's rota- 
 tion is given by the relation between v = v/r and 2n sin / 
 in the expressions of the deflecting forces in 52. Thus, 
 if a body on the parallel of 45 moves with a velocity of 20 
 meters per second, and has a radius of curvature of 400 
 kilometers (400000 meters, or 250 miles nearly) we have 
 w/r = 20/400000 = 0.00005, while the value of 2n sin /, from 
 Table V, is 0.000103 ; and therefore the tabular gradient must 
 be increased in the ratio of the sum of these quantities to the 
 latter, or nearly one half, for the effect of curvature and its 
 consequent centrifugal force. 
 
 58. If a body has a motion of uniform velocity in any direc- 
 tion, however produced, over the earth's surface, supposed to 
 be entirely smooth and without friction, and the velocity is such 
 that the range of motion in latitude is so small that sin / can 
 be regarded as a constant, then the lateral deflecting force is 
 constant, and the body is being continually deflected from its 
 course by equal angles in equal times, and so it describes a 
 circle. The radius r of this circle must be such that the cen- 
 trifugal force corresponding to the velocity s, or (s*/r)m, 36, in 
 a direction from the centre must be exactly equal to the de- 
 flecting force in the contrary direction. Hence, comparing this 
 -with the expression of F,, 55, we have s*/r = 2ns sin /, 
 or 
 
86 MOTIONS OF BODIES RELATIVE TO EARTH'S SURFACE, 
 
 r = 
 
 2n sin 
 
 Since sin / = o at the equator, r would be infinite there, and 
 consequently the body would move sensibly in a straight line 
 so long as it remained near the equator. But if, on the parallel 
 of 45, where sin / = 0.707, the body should receive a velocity s 
 in any direction of 5 meters per second, we should then have 
 
 r = 6857 X j~z = 48500 m. = 30 miles nearly. 
 
 This would give a range of less than one degree in latitude, 
 and consequently sin / would remain nearly constant. 
 
 59. The acceleration of the deflecting force F s , 55, is 
 2ns sin /. In the case of a falling body the space passed over 
 is given by the well-known expression %gf, in which g is the 
 acceleration of gravity, and t is the time. So in the case of this 
 deflecting force, putting 2ns sin / for g, and d for the departure 
 of the body from the tangent or initial direction, we get for a 
 very short range 
 
 d =. 0.00007292^ sin / . f. 
 
 If a rifle-ball on the parallel of 50 is discharged at a target 
 at the distance of one kilometer with a velocity of 500 meters 
 per second, we have in this case t = 2 seconds, and hence we 
 get for the departure d of the ball from the direction of initial 
 discharge relative to the earth's surface 
 
 ^ = 0.00007292 X 500 X 0.766 X2 2 = o.i I meter. 
 
 The ball, therefore, in the northern hemisphere, would deviate 
 to the right of the target about four inches. It would continue 
 on in the same direction in space, but by the time of its arrival 
 at the distance of the target this would have moved around 
 from right to left about four inches. This lateral deviation, 
 
THE DEFLECTING FORCE OF THE EARTH' S ROTATION. 87 
 
 however, would be very small in comparison with the vertical 
 deviation downward, due to gravity. The ratio between the 
 two is that of the corresponding forces, or of 2ns sin / to g. 
 This, in the preceding example, is 
 
 2 X 0.00007292 X 500 X 0.766/9.806 = 0.0057, 
 
 and hence the lateral deviation is only about i/i 80 of the vertical 
 one. If, however, the velocity s is increased, this ratio is in- 
 creased in the same proportion. 
 
 The preceding general expression of d is applicable where 
 the velocity of the projectile is variable, provided s represents 
 its mean velocity, just as in the case of a falling body the ex- 
 pression \g? would be applicable if g were variable, provided 
 we should use the mean of g for all the increments of time. 
 Letting, therefore, D represent the distance to which the pro- 
 jectile is cast, we can put D st, and then the expression of d 
 becomes 
 
 d = 0.00007292 sin IDt. 
 
 This is applicable to a projectile thrown high up in the air, and 
 describing approximately a parabolic curve, in which the hori- 
 zontal velocity varies. It is only necessary to know the time 
 and distance. If a cannon-ball were projected to the distance 
 of 5 kilometers in 10 seconds on the parallel of 40, we should 
 have for the lateral deviation 
 
 d 0.00007292 X 0.643 X 5000 X 10= 2.35 meters. 
 
 It is seen that the deviations due to the earth's rotation are 
 of little importance in gunnery ; but still it is interesting and 
 important to know of about what order these effects are in 
 ordinary cases. 
 
 60. In the case of a projectile thrown vertically upward, the 
 condition of rw = c, 41, must be satisfied, so that the higher 
 the projectile and the greater the value of r is, the less must be 
 the gyratory velocity w. The initial value of this at the earth's 
 surface for the different latitudes is that of GO in Table V, and 
 
88 MOTIONS OF BODIES RELATIVE TO EARTH'S SURFACE. 
 
 the initial value of r = r' cos / is the initial distance of the body 
 from the earth's axis. The approximate value of r' is 6370 
 kilometers. Hence we shall have rw = 637002 cos /, in which 
 r is the distance of the projectile from the earth's axis. If h is 
 the height of the projectile above the earth's surface, we have 
 r (6370+ Ji] cos /. Hence with this we get from the preced- 
 ing equation 
 
 63/0 
 
 in which h is expressed in kilometers, but w and GO may have 
 any unit of measure. 
 
 At the equator, where GO = 465 m., we have at the height of 
 10 kilometers 
 
 6370 
 W = 6380 X 4 5 = 4 4 ' 27 m * 
 
 Hence the absolute gyratory or east velocity per second at 
 the altitude of 10 kilometers would be 0.73 m. less than that 
 of the earth's surface, and hence there would be a west velocity 
 relative to the earth's surface of 0.73 meters per second, while 
 at lower altitudes the rate of gain of the absolute easterly 
 motion of the earth's surface upon that of the projectile would 
 be proportionally less. The projectile, therefore, after falling 
 back to the earth's surface, strikes it at a point west of the 
 point from which it was projected, since while at higher alti- 
 tudes its absolute easterly velocity was less than that of the 
 point of the earth's surface from which it started. The dis- 
 tance between the two points, of course, depends upon the 
 height to which the projectile ascends, and the time between 
 leaving and returning to the earth's surface. 
 
 For other latitudes, it is seen from the preceding expression, 
 iv is less in proportion to the values of G? in Table V, or in the 
 ratio of the cosines of the latitudes. 
 
CHAPTER III. 
 THE GENERAL CIRCULATION OF THE ATMOSPHERE. 
 
 INTRODUCTION. 
 
 61. THE motions of the atmosphere depend, either directly 
 or indirectly, upon differences of temperature. Without these 
 the aqueous vapor would be uniformly distributed in all parts, 
 there would be everywhere the same density, and a perfect 
 calm in the atmosphere would exist over all parts of the globe. 
 The great disturber of uniformity of temperature on the earth's 
 surface is the unequal distribution of the sun's radiated heat. 
 This gives rise not only to differences of temperature, but also 
 to differences in the amount of aqueous vapor, in the air, from 
 both of which causes the density of the atmosphere differs in 
 different places, and thus atmospheric currents are produced. 
 The forces, therefore, which overcome the inertia of the atmos- 
 phere when at rest and set it in motion, and which overcome 
 
 the frictional and other resistances and maintain this motion 
 
 
 
 depend upon solar heat energy. 
 
 Before entering upon the subject of the general circulation 
 of the atmosphere which, we have seen, is exceedingly elastic 
 and, so far as we know, has no definite superior limit or surface 
 it will be best to consider a few simpler cases of the motions 
 of inelastic fluids. 
 
 If any kind of liquid in a canal, or reservoir of any kind, or 
 the ocean covering the greater part of the earth, had the same 
 density in all parts and were at rest, the surface of the liquid 
 in this case would be everywhere perpendicular to the direction 
 of the force of gravity, and consequently coincide with, or be 
 parallel to, the spheroidal surface of the earth, and the pres- 
 sures in a horizontal direction on each side of any part of the 
 fluid would be exactly equal, so that it would have no ten- 
 
 89 
 
go THE GENERAL CIRCULATION OF THE ATMOSPHERE. 
 
 dency to move in any direction. But if, from any cause, the- 
 fluid is so disturbed that its surface is not a level surface, then 
 the pressure of the fluid beneath, at different points of the 
 same level, is different, and horizontal motion takes place in 
 the direction of least pressure. From the nature of a fluid the 
 pressure at any point is equal in all directions, and is not in the 
 direction, only, in which the force acts, as in the case of a 
 .solid. 
 
 62. If the fluid has the same density in all parts, but is so 
 disturbed, from some cause, from its state of static equilib- 
 rium, that its surface is not a level surface, then the fluid at all 
 depths has the same tendency to flow toward the lowest sur- 
 face level. Let ABCD, Fig. I, represent a part of a longi- 
 tudinal and vertical section of a canal, and abed that of a 
 cubic unit of the fluid a cubic centimeter or a cubic inch, for 
 instance ; then the pressure on each point of the vertical sides 
 
 of the cube is proportional to the depth of the point below 
 the surface, and the pressure on any one side is equal to the 
 sum of the pressures upon all the differential elements of the 
 surface. If we draw the line C ' D' parallel to CD, it will rep- 
 resent a line in a plane parallel to that of the surface, and 
 hence every point in this plane will be subject to the same 
 pressure. The differences of these pressures, therefore, upon 
 all the differential elements on the same level of the sides of 
 the cube in the directions of greatest and least pressure are 
 equal to the vertical pressure of a column of fluid of the same 
 infinitely small base and altitude de, since this is the differ- 
 ence of depth below the line of equal pressure CD' between 
 the corresponding differential elements of the two sides at the 
 same depth. The difference of pressure, therefore, upon the 
 
INTRODUCTION. 91: 
 
 two sides of the cube in the direction of greatest and least 
 pressure is equal to the vertical pressure of a stratum of fluid 
 of unit base and depth de. But the pressure of the whole cube 
 in the direction of the force of gravity is to that of the thin 
 stratum of the same base as their respective altitudes, that is, 
 as cd or ad to de. The force, therefore, which tends to move 
 the cube horizontally in the direction of least pressure, and 
 which is the difference of the pressures on the two sides, is to 
 the force of gravity of this cube as de to ad\ and hence we 
 have the force which tends to move a cube of unit mass hori- 
 zontally in the direction of least pressure equal to g(de/ad\ or 
 to g tan dae. But tan dae is the change of level in the hori- 
 zontal distance of unity, or gradient of the inclined surface, 
 which we have denoted by e 9 38. The horizontal force, 
 therefore, for unit mass, becomes, as in 38, ge^ and it is evi- 
 dent that this is the same for all depths, since the preceding 
 reasoning is entirely independent of the depth at which the 
 line CD' is drawn. 
 
 The horizontal force in this case being the same at all depths,, 
 the fluid at all depths in the canal has the same tendency to 
 move in the direction of least pressure, and in the case of no 
 resistances from the bottom or sides, all parts in the same ver- 
 tical line would acquire the same velocity of horizontal motion 
 in a given time, and this would be accelerated until the sur- 
 face gradient would vanish and become reversed, after which 
 the force arising from the reversed gradient would gradually- 
 overcome the momentum and stop motion in that direction, 
 and then cause a reverse motion. Thus an oscillatory motion 
 would be produced, which in the case of no friction would 
 never stop, but which in the case of friction is generally of 
 short duration. If the surface of this fluid and all isobaric 
 surfaces are perfectly horizontal, then de, Fig. I, vanishes, and 
 also the quotient e, and hence, also, the force ge at all depths. 
 There are, therefore, no forces then to give rise to and main- 
 tain motions, and the fluid remains at rest. 
 
 63. If different parts of the fluid of a canal or reservoir 
 have different densities, there can be no static equilibrium of. 
 
9 2 THE GENERAL CIRCULATION OF THE ATMOSPHERE. 
 
 the forces arising from gravity with any arrangement of the 
 fluid, as long as the differences of density remain, but the 
 forces give rise to, and maintain, a system of counter currents, 
 which, however, tend to equalize the differences of densities 
 unless they are being continually reproduced from some cause. 
 The differences of density are usually caused, either directly 
 or indirectly, by differences of temperature. Since heat ex- 
 pands all fluids, if different parts have different temperatures 
 they are expanded unequally ; and as density is inversely as 
 the volume of the same unit of mass, the more the fluid is 
 expanded by heat, the lighter any given volume of it becomes. 
 Let us consider here the simple case only of a canal or trough 
 of definite length and of uniform depth. If all parts have the 
 same temperature, and consequently the same density, we 
 have seen that if the surface is perfectly level, all the isobaric 
 -surfaces are level, and there is no tendency in any part of it to 
 flow in any direction, and the whole fluid remains at rest. If, 
 however, one end of the canal has a greater temperature than 
 the other, with such a distribution, let us suppose, that there 
 is a uniform temperature gradient from one end to the other, 
 and has also the same temperatures at all depths of the same 
 parts of the canal, then the fluid of the warmer end is expanded 
 more than that of the other end, and its surface and each 
 of the isobaric planes which were level before expansion are 
 raised up at one end so as to become inclined planes, and the 
 inclination is greater in proportion to the height of the plane 
 above the bottom. There is, consequently, a tendency in the 
 fluid to flow down the inclined planes toward the colder end ; 
 but this tendency is not the same at all depths, as in the pre- 
 vious case of a disturbance of level but not of density, but is 
 greatest at the top and gradually decreases downward, being 
 'in proportion to the height above, and vanishing at, the bot- 
 tom. The mere upward expansion of the fluid at the warmer 
 end, before any horizontal motion ensues, does not affect the 
 pressure at the bottom, and there is still a uniform pressure 
 there from one end to the other, and consequently no force 
 vthere to move the fluid in either direction. As the upper part 
 
IN TROD UCTIOiV. 
 
 93. 
 
 of the fluid, however, begins to flow, it fills up a little the other 
 end and raises its level and increases the pressure there on the 
 bottom, while the level at the warmer end is depressed a little 
 and the pressure at the bottom decreased ; so that there is 
 now at the bottom and in the lower strata a gradient of pres- 
 sure decreasing from the colder to the warmer end, and a 
 tendency in the fluid there to flow in that direction, and thus, 
 to give rise to a counter current in the lower strata. After 
 this has taken place the arrangement of the isobaric surfaces, 
 represented by the nearly horizontal lines, and the motions of 
 the fluid, are somewhat as represented in Fig. 2, according to 
 which these surfaces decline from the warmer to the colder 
 end of the canal in the upper strata of the fluid, and reversely 
 below, and in consequence of which the fluid flows in counter 
 directions above and below a given neutral intermediate plane 
 
 D 
 
 d 
 
 b ** 
 
 Fig. 2. 
 
 of equal pressure, ced, in which, being horizontal, there 1 is no- 
 pressure gradient, and consequently no tendency in the fluid 
 to move in either direction. In the upper strata the greatest 
 velocity is at the surface, and this gradually becomes smaller 
 with increase of depth below the surface until the neutral 
 plane is reached, when the velocity vanishes and changes di- 
 rection, and then increases with increase of depth below the 
 surface ; but in the case of friction between the fluid and the 
 bottom of the canal, this velocity at a certain depth before the 
 bottom is reached has its maximum, and then decreases again,, 
 and is least at the bottom. 
 
 64. In the motions of fluids the condition must be satisfied 
 that no more of the fluid shall pass into any given space than 
 flows out of it in a given time where there is no* change of 
 density, or more flow out than flows into it ; for in the former 
 
'94 THE GENERAL CIRCULATION OF THE ATMOSPHERE, 
 
 case the density would be necessarily increased, and in the lat- 
 ter diminished, or a partial vacuum produced. This is called 
 .the condition of continuity. In the counter motions of the canal 
 this condition must be fulfilled, and this, consequently, after 
 the regular motions are established and there is no further 
 change of surface level, requires that just as much fluid in the 
 counter currents must pass through any given vertical section 
 bef of the canal in the one direction as in the other. 
 
 The satisfying of the condition of continuity not only re- 
 quires counter horizontal motions in the canal, but likewise 
 vertical ones ; so that there must be a gradual settling down of 
 the fluid toward the bottom at the end toward which the cur- 
 rents in the upper strata run, and a rising up again toward the 
 surface at the other end. The vertical components of velocity, 
 .at least in a shallow canal, are extremely small in comparison 
 with those of the horizontal motions, and are not indicated in 
 Fig. 2. The counter vertical motions have likewise a neutral 
 plane, a vertical one, bef, somewhere in the middle part of 
 the canal, separating the part of the fluid which, at any time, 
 has a slight downward tendency from that on the other side 
 which is slowly rising toward the surface ; and with reference 
 to this plane the condition must likewise be satisfied that just 
 .as much of the fluid must slowly descend on the one side to- 
 ward the bottom, through any given horizontal section of the 
 >canal as that represented by de t as rises up on the other side 
 of it toward the surface, through the corresponding section ce 
 at the same depth. If the canal or trough, therefore, were 
 wedge-shaped, or had any shape which would make it narrower 
 toward the one end than the other, the vertical section divid- 
 ing the very slowly moving vertical counter currents, would 
 have to be nearer the wide end so that the horizontal sectional 
 .areas of these counter vertical currents might be equal, or 
 nearly so. 
 
 65. If there were no frictional resistances to the counter 
 motions, th$ tendency of the pressure gradients, in the one di- 
 rection above and the contrary below, would be to cause a 
 continued acceleration of these motions; but as there are al- 
 
INTRODUCTION 95 
 
 ways resistances of this kind, the motions are only accelerated 
 until the frictional resistances become equal to the forces caus- 
 ing'and maintaining the motions, after which the whole of the 
 forces is spent in overcoming the resistances, and there is no 
 further acceleration. 
 
 In case of friction between the horizontal strata, but none 
 between the fluid and the bottom of the canal, the velocities 
 of the counter horizontal currents must increase from the hor- 
 izontal neutral plane both toward the top and the bottom, 
 where they are, consequently, the greatest. The relative ve- 
 locities, however, between the strata must decrease from this 
 neutral plane both upward and downward, and be least at the 
 top and bottom. The forces arising from the pressure gra- 
 dients which cause the counter motions act on all the strata, 
 but most upon the upper and bottom strata, since here the 
 gradients are greatest. The action of the force upon the 
 first stratum increases the relative velocity between this stra- 
 tum and the next until the frictional resistance is equal to the 
 force. This force, by means of friction, is communicated to 
 the second stratum, so that the force overcoming the frictional 
 resistance between the second and third stratum is equal to 
 the sum of the forces acting upon the first two strata, and con- 
 sequently the relative velocity between the second and third is 
 greater than that between the first and second. So the force 
 overcoming the resistance between the third and fourth is 
 equal to the sum of the forces acting upon the first three 
 strata, and so on. The relative velocities between the strata 
 must therefore increase from the surface down to the neutral 
 plane where the forces vanish. But the sums of these forces 
 are not proportional to the depth, since the gradients and the 
 forces gradually decrease down to, and vanish at, the neutral 
 plane. The relative velocities, therefore, at and near this neu- 
 tral plane are greatest and vary very slowly near, and are least 
 at, the top. The same would be the case commencing at the 
 bottom, if there were no friction between the bottom of the 
 canal and the lower stratum, so that this would be as free to 
 move from the force acting upon it as the upper stratum, and 
 
96 THE GENERAL CIRCULATION OF THE ATMOSPHERE. 
 
 the actual velocities would be greatest and the relative veloci- 
 ties least at the bottom. 
 
 When the lower stratum suffers resistance from the bottom 
 the velocities of the strata near the bottom increase up to 
 some intermediate stratum between the bottom and the neu- 
 tral plane, and then decrease up to this plane, where they van- 
 ish and become reversed in direction. In this case the resist- 
 ances to the motions of the strata between the neutral plane 
 and the bottom, if there is the same amount of flow through 
 equal sectional areas, are much greater than they are in the 
 strata above this plane, since in the one case the flow is re- 
 sisted through friction both by the bottom of the canal and 
 the neutral stratum, while in the other it is resisted by the one 
 only, the neutral stratum. In order, therefore, that the condi- 
 tion of continuity may be satisfied in the case of friction on the 
 bottom, there must be either a greater force, or a greater ver- 
 tical sectional area for the fluid to pass through, or both, in the 
 lower current ; and both of these are brought about by an ele- 
 vation of the horizontal neutral plane, that is, by a greater fill- 
 ing up and raising up of the surface of the colder end of the 
 canal, which both makes the sectional area and the pressure 
 gradients of the lower one of the counter currents greater in 
 comparison with those of the upper one. There is then a 
 slower motion through a greater sectional area in the lower 
 current and a comparatively rapid one of smaller sectional area 
 in the upper one, and the velocity is especially much greater 
 near the surface. 
 
 66. The interchanging horizontal motions of the fluid be- 
 tween the two ends of the canal are oscillatory. The motion 
 of any particle of the fluid starting from its extreme position 
 in the warmer end and upper strata of the canal is first accel- 
 erated until the middle part is reached, after which it is gradu- 
 ally retarded until the particle is brought to rest in its extreme 
 position toward the other end, where, gradually settling down 
 toward the bottom, its motion is first accelerated again, and 
 after passing its middle position it is then gradually retarded, 
 and at the same time rises up into the upper strata whence it 
 
INTRODUCTION. 97 
 
 started. Thus a particle describes a very elongated elliptic 
 orbit, in which, especially in shallow and long canals, the trans- 
 verse axis is very small in comparison with the other. The 
 major axes also are very different for different particles, those 
 near the top and bottom passing nearly or quite to the ends of 
 the canal, while those near the central part and at medium 
 depth make only short excursions on either side of the neutral 
 vertical plane bef, Fig. 2. If, however, there are any ab- 
 normal disturbances, however small, besides that arising from 
 the regular temperature gradient, or any irregularities in the 
 bottom or sides of the canal, there is an interchanging and 
 mixing up of the particles, so that the same one does not con- 
 tinue in the same regular orbit. 
 
 67. In the case of the open ocean extending from the 
 equator to the pole, we can consider alone any part included 
 between two meridians meeting at the pole, and this half-lune 
 is similar to the wedge-shaped trough except that it does not 
 become narrow so rapidly near the equator, and only becomes 
 reduced to half its equatorial width on the parallel of 60, 
 which is two thirds of the distance from the equator to the 
 pole. If we suppose that there is a uniform temperature gra- 
 dient at all depths between the equator and the pole, the in- 
 terchanging motion for any such half-lune would be somewhat 
 as in the case of the wedge-shaped trough. There would be a 
 more rapid motion in the upper current of smaller sectional 
 area, and a comparatively slow one in the lower counter cur- 
 rent with large sectional area ; so that the neutral plane be- 
 tween the counter currents would be at no great depth below 
 the surface. The vertical section, also, between the parts hav- 
 ing a slow descent toward the bottom in the polar region and 
 those slowly rising toward the surface in the equatorial region 
 would not be on the parallel of 45, but somewhere near the 
 parallel of 30, so as to make the horizontal sectional areas of 
 both parts about equal. 
 
98 THE GENERAL CIRCULATION OF THE ATMOSPHERE. 
 
 DISTRIBUTION OF TEMPERATURE OVER THE EARTH'S SURFACE. 
 
 68. Since the motions of the atmosphere depend upon dif- 
 ferences of temperature, it is necessary to know at the outset, 
 in the investigation of these motions, the distribution of tem- 
 perature over the earth's surface, not only for the mean of the 
 year, but also for the different seasons of the year. Since all 
 parts of the earth's surface on the same parallels of latitude have 
 the same relation to the sun, upon which their temperatures and 
 the differences of temperature depend, if the whole surface 
 were either all land or all water, and perfectly homogeneous, 
 there would be the same temperature all around the globe on 
 the same latitude, and there would be, at all longitudes, the 
 same temperature gradient between the equator and the pole. 
 In the case of a wholly land surface, however, the differ- 
 ence of temperature between the equator and the pole, and 
 consequently the temperature gradient, would be much greater 
 than in the case of an earth entirely covered by the ocean. 
 For in the latter case, in consequence of the difference of 
 temperature of the water of the equatorial and the polar 
 regions, there are interchanging counter currents, as just ex- 
 plained, by which heat is conveyed from the former to the 
 latter region, the effect of which is to make the difference of 
 temperature between the two regions much less than it other- 
 wise would be, and consequently to diminish the temperature 
 gradient between the equator and the poles. In the case of 
 the earth, therefore, as really constituted, with continents and 
 oceans extending from the equator to the pole, or nearly so, 
 the temperature gradients between the equator and the pole 
 on the continents are somewhat as they would be in case of a 
 wholly land surface, while on the oceans they are somewhat as 
 on an earth entirely covered by the ocean, and consequently 
 the temperature gradients on the former are greater than on 
 the latter. For this reason the equatorial and tropical parts of 
 the continents are warmer than those of the ocean, while the 
 reverse is true in the higher latitudes, and hence there are 
 
'DISTRIBUTION OF TEMPERATURE OVER THE EARTH. 99 
 
 Differences of temperature on the same latitude in different 
 longitudes. 
 
 In the general circulation of the atmosphere all the second- 
 ary and abnormal irregularities are neglected, and only the 
 normal and principal temperature inequality, determined by 
 the averages of temperature of each latitude, taken all around 
 the globe, is considered. These averages of temperature are 
 called the normal temperatures of the latitude. These normals of 
 temperature, taken from " Meteorological Researches," Part I, 8 
 for the average of the year, and also for the two months of ex- 
 treme temperatures, are given for each tenth degree of latitude 
 in the following table : 
 
 LATITUDE. 
 
 JANUARY. 
 
 JULY. 
 
 MEAN OF THE YEAR. 
 
 C. 
 
 OF. 
 
 C. 
 
 F. 
 
 C. 
 
 r . 
 
 + 80 
 
 -31-9 
 
 -25.4 
 
 + 1.0 
 
 + 33.8 
 
 15-5 
 
 + 4-1 
 
 70 
 
 26.5 
 
 15.7 
 
 6.9 
 
 44.4 
 
 9.8 
 
 14.4 
 
 60 
 
 l6!g 
 
 -1.6 
 
 I3 -8 
 
 56.8 
 
 -1.6 
 
 29.1 
 
 50 
 
 -6.0 
 
 -f-21.2 ' 
 
 18.6 
 
 65.5 
 
 + 6.3 
 
 43-3 
 
 40 
 
 + 4-5 
 
 40.1 
 
 22.8 
 
 73-0 
 
 13-6 
 
 56-5 
 
 30 
 
 12.9 
 
 55-2 
 
 26.6 
 
 79-9 
 
 19.8 
 
 67.6 
 
 20 
 
 21.7 
 
 71.1 
 
 29.0 
 
 84.2 
 
 25.3 
 
 77-5 
 
 -f 10 
 
 25-9 
 
 78,6 
 
 28.4 
 
 83.1 
 
 27.2 
 
 81.0 
 
 O 
 
 27-3 
 
 Bi.l 
 
 26.1 
 
 79.0 
 
 26.7 
 
 80. i 
 
 10 
 
 27-9 
 
 82.2 
 
 24.0 
 
 75-2 
 
 25-9 
 
 78.6 
 
 20 
 
 26.6 
 
 79-9 
 
 20.8 
 
 69.4 
 
 23-7 
 
 74-7 
 
 30 
 
 23-0 
 
 73-4 
 
 15.6 
 
 60. i 
 
 19-3 
 
 66.7 
 
 40 
 
 17.6 
 
 63.7 
 
 II. I 
 
 52.0 
 
 14.4 
 
 57-9 
 
 50 
 
 ii. I 
 
 52.0 
 
 + 6.4 
 
 43-5 
 
 8.8 
 
 47-8 
 
 -60 
 
 + 3-6 
 
 + 38.5 
 
 0.0 
 
 + 32.0 
 
 + 1.8 
 
 + 35.2 
 
 It is seen from this table that, while the temperatures at 
 and near the equator are very nearly the same the year around, 
 in the higher latitudes of the northern hemisphere they vary 
 very much in the different seasons of the year, and that the 
 temperature gradients between the equator and the pole are 
 more than twice as great in midwinter as in midsummer. In 
 the southern hemisphere, however, these annual variations are 
 comparatively very small. This is because nearly all the land 
 lies in the northern hemisphere and the southern hemisphere 
 
IOO THE GENERAL CIRCULATION OF THE ATMOSPHERE.. 
 
 is mostly covered by the ocean, which equalizes somewhat the 
 extreme temperatures of the seasons. 
 
 On account of the interchange of equatorial and polar 
 waters in nearly every part of the southern hemisphere, while 
 this in the northern hemisphere takes place over a much 
 smaller part, since much less of it is covered by the ocean, the 
 normal temperatures of latitude for the average of the year in 
 the southern hemisphere are a little less in the lower, and a 
 little greater in the higher, latitudes than on the corresponding 
 latitudes of the northern hemisphere. This causes the maxi- 
 mum of temperature or thermal equator to fall a little north of 
 the equator. 
 
 The normals of latitude in the preceding table were ob- 
 tained from Buchan's isothermal charts. According to later 
 researches of Dr. Hann, 9 in which are used observations on 
 high southern latitudes more recent than any used by Buchan, 
 and the tabular means and normals of temperature given by 
 Herr Spitaler, deduced from Dr. Hann's recent isothermal 
 charts, the normals of temperature in these latitudes are 
 somewhat less than those given in the preceding table. Al- 
 though the disturbing forces which we are to consider in the 
 motions of the atmosphere do not depend upon the abso- 
 lute average temperature of the globe but upon differences 
 of temperature or temperature gradients, yet it may not be 
 amiss to state here, as a matter of general interest, that the 
 average temperature of the atmosphere at the earth's surface, 
 taken over the whole of the northern hemisphere, is 15. 3 
 (59. 5 F.), and that that of the southern hemisphere is sensibly 
 the same. 
 
 69. It must not be understood that the preceding normals 
 are those of the whole atmosphere extending to the top, but 
 simply those of the part in contact with the earth's surface, for 
 the temperature everywhere decreases with increase of altitude. 
 The rate of this decrease, on the average for all latitudes and all 
 seasons of the year, is, for the lower half of the atmosphere, 
 about o.65 for each 100 meters of ascent ; or, in English meas- 
 ures, o.36 for each 100 feet. This rate is supposed to be a little 
 
DISTRIBUTION OF AQUEOUS VAPOR. IOI 
 
 greater in the lower than in the higher latitudes, but the differ- 
 ence is small, and it is also greater in general in summer than in 
 winter, and by day than by night, and this is especially the case 
 on land and in the lower part of the atmosphere. The varia- 
 tion of temperature with altitude, however, so long as the 
 unstable state is not induced, is of little importance in the dy- 
 namics of the atmosphere, since the forces depend not upon 
 absolute temperatures, but upon the horizontal temperature 
 gradients, and these, so far as they pertain to the general circu- 
 lation, are very nearly the same at all altitudes. 
 
 DISTRIBUTION OF AQUEOUS VAPOR. 
 
 70. Since aqueous vapor under the same pressure is lighter 
 than air, its density being to that of air as 0.622 to I, the un- 
 equal distribution of this vapor in the atmosphere also gives 
 rise to small differences of normal pressure in different lati- 
 tudes, or, in other words, to pressure gradients between the 
 equatorial and polar regions, but these are small in comparison 
 with those arising from difference of temperature. It is seen 
 from Table II, Appendix, that the greatest vapor tension 
 which can exist in the atmosphere at the equator with a tem- 
 perature, say, of 26, is about 25 mm. ; while for the cold tem- 
 perature of the polar regions at a temperature of 15 the 
 tension of saturation is almost nothing. As the relative hu- 
 midity of the atmosphere at all places and all seasons of the 
 year is about 80 per cent, this gives 25 X 0.80 = 20 mm. for 
 the average vapor tension at the equator. This is the 1/38 
 part of 760 mm., the normal barometric pressure of the atmos- 
 phere. The density of the aqueous vapor being 0.622, the 
 density of the part of the atmosphere comprising the aqueous 
 vapor is diminished by I 0.622 =0.378, and this multiplied 
 into 1/38 gives a decrease of the density of the whole atmos- 
 phere equal to i/ioo part. This is equal to the diminution of 
 density arising from an increase of temperature of 2. 7. Hence 
 the effect of the average amount of aqueous vapor in the at- 
 mosphere at the equator on its density is about the same as 
 
102 THE GENERAL CIRCULATION OF THE ATMOSPHERE. 
 
 that of increasing its temperature 2. 7, or about the one-tenth 
 part. This is the proportion of increase of the numerical co- 
 efficient of temperature which Laplace introduced into his baro- 
 metric formula in order to take into account approximately 
 the effect of the average amount of aqueous vapor in the at- 
 mosphere. Although this proportion is very nearly correct 
 for equatorial temperatures at and near the earth's surface, yet 
 it becomes erroneous for temperatures at and below the zero* 
 of the Centigrade scale ; but at these temperatures the absolute 
 amount of vapor is so small that the erroneous proportion 
 gives rise to only very small errors. In all cases, therefore, we 
 may assume, that for the average or normal state of the atmos- 
 phere the modifying effect of the aqueous vapor is such as to 
 cause the atmosphere to expand its volume and diminish its 
 density about the 1/250 instead of the 1/273 part, for each 
 degree of increase of temperature. But this is the case in the 
 lower part only of the atmosphere. In the upper regions of 
 the atmosphere the proportion of vapor in the atmosphere is 
 less, both on account of the diminished temperature with in- 
 crease of altitude, and also because evaporation takes place at 
 the earth's surface and the vapor is very slowly diffused upward 
 to high altitudes. The decrease of density, therefore, from this 
 cause, at high altitudes, and the corresponding effect upon the 
 pressure gradients between the equator and the pole, are small 
 in comparison with those arising directly from differences of 
 temperature. Upon the whole, therefore, considering the 
 whole depth of the atmosphere, the effect of the aqueous 
 vapor is small, but even this depends indirectly upon difference 
 of temperature, since without this there would be no difference 
 in the amount of the vapor in the equatorial and the polar 
 regions. 
 
 GENERAL CIRCULATION WITHOUT ROTATION OF THE EARTH. 
 
 71. In treating the general circulation of the atmosphere, 
 it will be best to consider first, in a preliminary way, the more 
 simple case of circulation without rotation of the earth on its 
 
CIRCULATION WITHOUT ROTATION OF THE EARTH. 1 03 
 
 axis. For although this is not the real case of nature, yet the 
 results obtained in this case will be useful and necessary in 
 treating the more general and more complex case in which the 
 earth turns on its axis. Let PCE, Fig. 3, represent a quadrant 
 of a meridional section of the earth, and oaf, bb r , cc' , etc., repre- 
 sent infinitely thin strata of the atmosphere of equal pressure in 
 case all parts had the temperature of the pole P. In this case 
 these strata would all be horizontal or equidistant from the 
 earth's surface and from one another at the equator and at the 
 poles, neglecting quantities of the order of the earth's ellipticity, 
 which are of no importance here. But by the preceding table, 
 
 Fig. 3. 
 
 68, the temperature of the atmosphere at the earth's surface 
 is about 45 C. greater at the equator than at the poles; and 
 in the upper strata, we have reason to think, the difference is 
 nearly the same. The effect of increase of temperature being to 
 expand the air the 1/273 part of its volume at the temperature 
 of melting ice for each degree of its increase, the effect of an 
 increase of temperature of 45 at the equator is to expand the 
 air upward the 45/273 or 1/6 part nearly of its volume at this 
 temperature, but a little more than this part of its volume at 
 the temperature of the poles. The stratum aa' is accordingly 
 elevated at the equator about 1/6 of the altitude Ed of this 
 stratum above the earth's surface, that of bb' by 1/6 of Eb' , and 
 that of cc' by 1/6 of EC', and so on ; each successive stratum 
 
104 THE GENERAL CIRCULATION OF THE ATMOSPHERE. 
 
 being raised in proportion to its altitude above the earth's sur- 
 face, and the new positions of the strata, resulting from such 
 an increase of temperature as given in the preceding 1 table, and 
 consequently the upward expansions, are somewhat as repre- 
 sented by the dotted lines in the figure. 
 
 If this increase of the temperature of the equatorial over 
 that of the polar regions were made instantaneously, the first 
 effect of the expansion would be to cause gradients down 
 which the air of the upper strata would tend to flow from the 
 equator toward the poles, just as in the case of the canal, 62, 
 the upper strata have a tendency to flow from the warmer 
 toward the colder end ; and the greater the altitude above the 
 bottom or earth's surface, the greater is this tendency in both 
 cases. At the earth's surface, however, there would be no 
 tendency in the air to flow either from or toward the equator, 
 since the mere upward expansion would not affect the pressure 
 at the earth's surface, and thus give rise to a pressure gradient 
 acting in either direction. 
 
 The linear gradient e of any isobaric surface at the altitude 
 h, due to difference of temperatures, is equal to the difference 
 of upward expansion of a vertical column of air at each end of 
 a unit of length in the direction in which the gradient is 
 reckoned, whatever may be the assumed unit. Putting, there- 
 fore, r, and r 2 for the temperatures at the beginning and end of 
 the unit respectively, we shall have the upward expansion of 
 the former equal to -^^/ir l and that of the latter equal to 
 -s^hr^ , if 1i is the height of the column at the temperature of 
 o C., since the volume of air expands the -^-3 part of its 
 volume at o C., for each degree of increase of temperature. 
 Hence, putting AT: (variation of r) for the change of tempera- 
 ture in the distance of unity, or, in other words, for this tem- 
 perature gradient, we shall have 
 
 e = 
 
 72. The first effect of the motion in the upper strata of 
 the atmosphere from the equator toward the pole, as in the 
 case of the water flowing from the warmer toward the colder 
 
'CIRCULATION WITHOUT ROTATION OF THE EARTH. IO5 
 
 *end of the canal, would be to fill up a little, as it were, the 
 polar region with air from the equatorial, the effect of which is 
 to increase the pressure a little in the former and to decrease 
 it a little in the latter region, thus creating at the earth's 
 surface and in the lower strata a gradient of pressure decreas- 
 ing from the pole toward the equator, which would cause a 
 -counter current in the lower strata. The neutral plane where 
 there is no pressure gradient, and consequently no motion in 
 either direction, is now raised from the earth's surface up to 
 such an altitude that the counter-flows between the equator 
 and the pole, from the equator above and toward it below, 
 satisfy the condition of continuity, and this altitude must be 
 greater or less according to the relative amounts of friction in 
 the upper and lower strata. For reasons given in 65 in the 
 -case of the canal, this must be above half the mass of the 
 atmosphere. Since the upper part of the atmosphere has no 
 definite limit, but becomes more and more rare and extends to 
 a very high but unknown altitude, the isobaric surfaces of the 
 upper very rare part of the atmosphere have very steep gradi- 
 ents, which increase in proportion to the altitude above the 
 neutral plane. But the force with which a given volume of air 
 tends to slide down these gradients or press toward the pole is 
 as the density, and this, where the temperature remains the 
 same, is as the pressure. While the gradients, therefore, 
 increase with increase of altitude above the neutral plane in an 
 arithmetical progression, the forces for the same gradient de- 
 crease with increase of this altitude in a geometrical progression, 
 and so become small above, while, by the nature of gases, 33, 
 the frictional resistances for equal relative velocities between 
 the strata are the same for all densities, and so the same at all 
 .altitudes. Hence the relative velocities between the strata, in 
 the case of no rotation of the earth on its axis, would be very 
 small at great altitudes, and the absolute velocities nearly the 
 same at all high altitudes. 
 
 ' 73. The whole vertical circulation of the atmosphere in this 
 case would be similar to that of the water of the canal, 66, 
 the particles of air would have an oscillatory horizontal and 
 
IO6 THE GENERAL CIRCULATION OF THE ATMOSPHERE. 
 
 vertical motion, which in the upper strata of the equatorial! 
 region is first accelerated until the particle arrives at some 
 intermediate latitude, after which it is gradually retarded in its 
 further motion toward the pole and brought to rest at its polar 
 limit of range, meanwhile gradually settling down toward the 
 earth's surface, where the pressure gradient is reversed and the 
 reversed motion of the particle is again accelerated until it 
 arrives at some intermediate latitude of its range of oscillation,, 
 after which it is again retarded in its horizontal motion and 
 brought to rest, meanwhile rising up to higher altitudes, where 
 the force of the pressure gradient is again reversed, and it 
 commences again another circuit as before. The nearer the 
 particle is to the neutral planes, the shorter are the ranges of 
 oscillation, both horizontal and vertical, and the smaller the 
 elliptic circuit. On account of the narrowing of the spaces- 
 between the meridians in approaching the pole, the vertical 
 plane between the descending air in the higher latitudes and 
 ascending air in the lower ones, as in the case of the oceanic 
 circulation, cannot be half-way from the equator to the pole, 
 but must be about the parallel of 30. 
 
 In the case of no friction the motions would be continually 
 accelerated as long as any difference of temperature between 
 the equator and the pole remained, but of course a very rapid 
 and increasing interchange would tend to diminish and finally 
 to sensibly destroy this difference. In the case of friction the 
 motions would be accelerated until the frictional resistances 
 would be equal to the forces, after which a uniform horizontal 
 oscillatory motion would be maintained, the relation between 
 the gradients and the frictional resistances being such as to 
 leave a small residual force to alternately accelerate and retard, 
 the motions of the oscillations. 
 
 GENERAL CIRCULATION WITH ROTATION OF THE EARTH 
 ON ITS AXIS. 
 
 74. The general vertical circulation of the atmosphere 
 which would take place in case the earth had no rotation on its- 
 axis having just been explained, we come now to consider the 
 
CIRCULATION WITH EARTH ROTATING ON ITS AXIS. IO? 
 
 effect upon this circulation of the deflecting force arising from 
 the earth's rotation, explained in the preceding chapter, in the 
 real case of nature. In consequence of this force, 53, in 
 whatever direction any part of the atmosphere may be moving,, 
 it is continually deflected, if free, to the right of the direction. 
 of motion in the northern hemisphere and the contrary in the 
 southern ; and if not free, it presses in these directions and 
 causes atmospheric gradients, ascending in the directions of 
 pressure. Hence the vertical circulation due to the real forces 
 arising from difference of temperature between the equator and 
 the poles being once established, the air in the upper strata of. 
 the atmosphere in either hemisphere, in moving toward the. 
 pole, is deflected eastward, and in the counter current in the 
 lower strata the tendency is to counteract and destroy motion 
 toward the east and then to cause a west component of motion. 
 These contrary forces, acting toward the east above and the 
 west below, give rise to relative velocities between the strata,. 
 and maintain them by overcoming the friction between the. 
 strata, which otherwise would constantly tend to reduce and 
 to destroy these relative velocities, and to reduce the absolute 
 velocities above and below all to the same velocity on any given, 
 parallel of latitude. 
 
 In the case of no friction between the air and the earth's 
 surface, the east and west components of velocity arising from 
 the interchanging motions between the equatorial and polar 
 regions and the deflecting forces depending upon the earth's 
 rotation arising from them, would satisfy the expression 
 
 in which the value of c is the average value of rw for all the 
 particles of the air of the hemisphere, before interchanging 
 motion took place, the definitions of r and w being those of 
 47 ; or it is the average value of r n w , in which r and w are. 
 the values of r and w before motion commences and while 
 the air is at rest relative to the earth's surface, in which case w 
 is equal to rn. If each particle of air were entirely free, both 
 from the effect of friction of the earth's surface and the inter- 
 
IO8 THE GENERAL CIRCULATION OF THE ATMOSPHERE. 
 
 action of the particles upon each other, then its motions would 
 satisfy the equation rw = r w Q , and since in the interactions 
 between the particles action and reaction are equal, these can- 
 not affect the average value of rw for the whole hemisphere, 
 and it must remain the same at all times and be the same as 
 before motion commenced, that is, be the average value of r w 
 taken for the whole hemisphere. 
 
 In order to satisfy the preceding relation near the pole, 
 where r is small w must be very large ; and this here becomes 
 mostly an east velocity relative to the earth's surface, since 
 near the pole the part depending upon the earth's rotation, 
 rn, is small. 
 
 In consequence of friction between the lower stratum of 
 the atmosphere and the earth's surface, this stratum, with the 
 forces only being here considered, cannot have either an east- 
 erly or a westerly motion, since the rate of polar motion on 
 any given parallel, mass multiplied into velocity, in the upper 
 strata in which the 'air moves from the equator toward the 
 poles, is, on account of the condition of continuity, exactly 
 equal to that of equatorial motion in the lower strata, in which 
 the air moves from the poles toward the equator; and so the 
 whole force deflecting eastward above, arising from the earth's 
 rotation, is exactly equal to that deflecting westward below, 
 and these being in contrary directions, there is no force arising 
 directly from the interchanging motions and deflecting forces 
 to overcome the friction between the atmosphere and the 
 earth's surface. This force arises from the vertical motions, as 
 explained further on in 77. But whatever east or west com- 
 ponents of velocity may exist at the earth's surface, there are 
 the same relative velocities of these components all the way 
 up above, so that all the absolute east or west components 
 above are increased algebraically by the amount of velocity at 
 the surface. 
 
 75. The greater the absolute east components of velocity, 
 the greater also are the relative velocities and the friction 
 between the strata, so that for a given amount of interchanging 
 motion between the equatorial and polar regions there is a 
 
CIRCULATION WITH EARTH ROTATING ON ITS AXIS. IO9' 
 
 limit beyond which these absolute east components of velocity 
 cannot go, and this limit is where the frictional resistance 
 between the strata becomes equal to the forces which overcome 
 it and maintain the motions. But now with the establishment 
 of these east components of motion, increasing with increase 
 of altitude, there is called into play another [deflecting force 
 depending upon the earth's rotation, which interferes with and 
 diminishes the amount of interchanging motion between the 
 equatorial and the polar regions which would exist if the earth 
 had no rotation on its axis. For as in the case of a current of 
 air flowing from the equator toward the pole in the northern 
 hemisphere there is a force deflecting to the right or east, so in. 
 the case of the east component of motion there is also a force 
 deflecting toward the right or the equator. In the southern 
 hemisphere it is to the left, but still toward the equator. This 
 force is contrary to, and counteracts, that arising, as explained 
 in 71, from the temperature gradient between the equator 
 and the pole. The greater the east components of velocity in 
 the atmosphere above, the greater this force ; so that if certain 
 velocities were reached, this force would be exactly equal to 
 that depending upon the temperature gradient, and the inter- 
 changing motion between the equator and the poles could not 
 then be maintained, and without some motion of this sort 
 there would be no forces to overcome the friction and main- 
 tain the east components of motion. The limit, therefore, 
 beyond which the east components of velocity cannot go must 
 fall a little short of those velocities which would entirely de- 
 stroy the force which keeps up the interchanging motions ; but 
 the less the frictional resistance to the motions the more 
 nearly they can approach to this limit, and in the case of no 
 friction the east components of velocity which would satisfy all 
 the conditions of the problem would be those coming up to the 
 limit ; for in this case, the interchanging motions being once 
 established, there would be no need of any force to overcome 
 friction and to maintain them. 
 
 The general motions of the atmosphere and their relations- 
 to the forces producing them, in the case of an earth with ro- 
 
110 THE GENERAL CIRCULATION OF THE ATMOSPHERE. 
 
 tation on its axis, are similar to those of machinery run by a 
 steam-engine, and controlled by a governor. Without this the 
 whole force would be applied to overcome the friction and 
 doing the work, and great speed might be obtained, but with 
 the governor suitably adjusted there is a certain limit beyond 
 which the speed cannot go, however much the friction or work 
 of any kind may be diminished ; for when this is reached all the 
 force is cut off. As long, therefore, as there is any friction to 
 be overcome or work of any kind to be done, the speed must 
 fall a little short of this limit, and it can only reach this limit 
 when these vanish. So, in the general motions of the atmos- 
 phere in case of no rotation of the earth on its axis, we have 
 .seen, 73, the whole force of the temperature gradient is 
 brought to bear in overcoming the friction and maintaining the 
 interchanging motion between the equatorial and polar regions, 
 and so this might become very great. But in the case of the 
 earth with rotation on its axis, there are soon developed east 
 components of motion, which, by means of the consequent 
 deflecting forces, in a great measure counteract or cut off the 
 forces which give rise to and maintain the interchanging 
 motion, so that there is a limit beyond which the speed of this 
 motion cannot go ; for if this limit were reached, the motions 
 would give rise to east components of motion and deflecting 
 forces which would entirely counteract the forces arising from 
 the temperature gradients. 
 
 76. The limit beyond which the east components of 
 velocity cannot go may be determined by equating the ex- 
 pression of the horizontal force for unit of mass, ge, 62, with 
 that of F v , 49, which is the deflecting force acting in the direc- 
 tion from the poles toward the equator, depending upon the 
 east components of velocity v. We thus get 
 
 ge =. (2n -\- r)v sin /. 
 
 By neglecting v in comparison with 2, as we may without 
 any sensible error in the case of any real easterly motions 
 in the general circulation of the atmosphere, we get from the 
 preceding equation 
 
-CIRCULATION WITH EARTH ROTATING ON ITS AXIS. Ill 
 
 The same is deducible from the expression of e, 56, by chang- 
 ing s to Vj since this is simply the special case in the general 
 expression in which s becomes v. This limiting value of v can 
 be expressed in a function of the temperature gradient AT, 
 instead of that of e, the gradient of the isobaric surface, by 
 putting for e above its value in 71. We thus get 
 
 ghAt 
 = 
 
 
 X 2 sin / 
 
 using for^- and 2n their numerical values found in 45, in ob- 
 taining the last form of expression. 
 
 Strictly, the value of h in this expression is the height of the 
 isobaric surface if the atmosphere had the temperature of o C. ; 
 but as the average temperature up to a considerable altitude, 
 and for all latitudes, does not differ much from this tempera- 
 ture, this value of h in any case differs but little from the actual 
 height of this surface, and so the latter may be used for ap- 
 proximate results without much error. 
 
 If AT be assumed to be the change of temperature in one 
 degree of latitude, instead of one meter, then we must divide 
 this expression by 1 1 1,1 1 1, the number of meters in a degree, in 
 order to obtain the expression of v in terms of the temperature 
 gradient thus expressed. We thus get 
 
 hAT 
 
 V 0.00221 - . 
 
 sm / 
 
 Since sin / becomes small towards, and vanishes at, the 
 equator, and AT is supposed to do the same, the value of v be- 
 comes indeterminate at, and very uncertain near, the equator, 
 since, where sin / is very small, a small inaccuracy in AT* would 
 give rise to a large error in v* 
 
 * If the temperature r for each isobaric surface is a function of the latitude 
 of the form A -\- A\ cos 2/, in which A is the temperature on the parallel of 
 45 where cos2/=o, and A\ is the half difference of the temperatures at the 
 
112 THE GENERAL CIRCULATION OF THE ATMOSPHERE. 
 
 77. So far we have considered only the horizontal motions, 
 and their deflecting forces in the vertical circulation arising 
 from difference of temperature between the equator and the 
 poles, and have obtained the preceding results. 
 
 We come now to consider the vertical motions, or com- 
 ponents of motion, downward from the upper strata toward 
 the earth's surface in the higher latitudes, and the reverse in 
 the lower latitudes. As the air in the upper strata of the 
 higher latitudes with its large east component of velocity 
 above settles down toward the earth's surface where this com- 
 ponent is less, it gradually loses its momentum, and the effect 
 of this lost momentum transferred by means of friction from 
 one stratum to another until it reaches the earth's surface, is 
 spent in overcoming the friction between the lower stratum and 
 the earth's surface and maintaining a small east component of 
 velocity of the air at and near the surface. 
 
 In the passage of the air of the upper strata from the equa- 
 torial toward the polar regions, a part of the force deflecting 
 eastward is spent in overcoming the frictional resistance between 
 the strata with east components of velocity increasing with 
 increase of altitude, which, we have seen, is necessary to satisfy 
 the conditions, and the other part is spent in accumulating the 
 momentum of the east components of motion. In passing in 
 
 equator and the pole, then, by taking the differential of this expression and sub- 
 stituting the small variations of temperature and of latitude AT and Al, respec- 
 tively, for the corresponding differentials dr and dl, we have, since ^//has been 
 assumed to be equal to unity or one meter, 
 
 AT = 2,A l sin 2^=4^1 sin /cos /. 
 
 Substituting this expression of AT in the first of the preceding expressions of 
 
 v t we get 
 
 v 985.6/^1 cos /. 
 
 Since v here is proportional to cos /, and this to the distance of the air with 
 velocity v from the axis of rotation, the velocities which, at any given altitude 
 h, correspond to the limit of velocities which can be reached, are those which 
 have the same angular velocity with reference to the earth's axis. 
 
 The values of A\ corresponding to the mean of the year, and January and 
 July respectively, according to the table of 68, are approximately 22, 30, and 
 14, as deduced from the northern hemisphere. The temperature gradient, 
 therefore, is more than twice as great in January as in July. 
 
CIRCULATION WITH EARTH ROTATING ON ITS AXIS. 113 
 
 the lower strata from the polar toward the equatorial regions, 
 the reverse is the case, and part of the force now tending to 
 deflect westward is spent in overcoming the frictional resistances 
 to a west component of motion, whether arising from the strata 
 above having greater east components of velocity, or from the 
 earth's surface below, where, in the lower latitudes, there is a 
 west component of motion, and the balance is spent in over- 
 coming the momentum of the east component of motion in the 
 higher latitudes already acquired, or in giving rise in the lower 
 latitudes to the momentum of the west components of motion. 
 In the higher latitudes, therefore, where there is an east com- 
 ponent of motion at the earth's surface, the amount of east 
 momentum lost by any portion of air in its passage above from 
 any given latitude toward the pole until it returns below to the 
 same parallel, is the kinetic energy which it has contributed 
 toward overcoming the frictional resistance of the earth's surface 
 to the east component of motion at the surface between that 
 parallel and the pole ; and in the lower latitudes, where there 
 is a west component of motion at the earth's surface, the 
 amount of west momentum lost or east momentum gained, or, 
 considered algebraically, the amount of west momentum lost, 
 by any portion of air from the time it leaves any given parallel 
 of latitude in its passage toward the equator below until it 
 returns to the same parallel above, is the amount of kinetic 
 energy which it has contributed towards overcoming the fric- 
 tional resistance of the earth's surface to the west components 
 of motion between that parallel and the equator. 
 
 From the consideration, therefore, of the interchanging 
 horizontal and vertical motions and the change of east and 
 west momentum as the vertical motions take place, we see there 
 is a sort of torsional force arising from the effect of the earth's 
 rotation on the interchanging motions arising from the tem- 
 perature gradient, which tends to give rise to and maintain an 
 east component of motion of the atmosphere at the earth's 
 surface in the higher latitudes, and the reverse in the lower 
 latitudes. There are, however, the same relative velocities 
 between the successive strata, since the forces remain the 
 
114 THE GENERAL CIRCULATION OF THE ATMOSPHERE. 
 
 same which overcome the friction and keep up these relative 
 velocities, as if there were no such torsional force, or the fric- 
 tional resistance to east or west components of motion at the 
 earth's surface were infinitely great. Whatever velocities, 
 therefore, of this sort are given to the lower stratum of the 
 atmosphere, the same increase of velocity is also given to all 
 the strata up to the top of the atmosphere. If we therefore 
 put v for the value of v at the earth's surface, instead of the 
 expression of ^ in 76, we now get 
 
 Mr 
 
 V = ^o + 246.4- 
 
 sin /' 
 
 in which AT: is the change of temperature in the distance of 
 one meter. If At expresses the change in the distance of one 
 degree of latitude, then 0.00221 must be used instead of the 
 numerical coefficient 246.4. 
 
 According to this expression of v, the east components of 
 velocity in the higher latitudes where v is positive increase 
 from the earth's surface to the top of the atmosphere. In the 
 lower latitudes where v is negative or a west component the 
 west components of velocity above the earth's surface decrease 
 up to a certain altitude, where they vanish and change to east 
 components, and then these increase to the top of the atmos- 
 phere. It is evident that the higher the stratum the nearer to 
 the equator must be the parallel of latitude where the change 
 from west to east components of motion takes place until that 
 altitude is reached where there is no west component of 
 motion at any parallel. 
 
 78. It is seen from this expression that the differences 
 between the limiting east components of velocity at different 
 altitudes, and approximately, at least in the higher latitudes, 
 between the real velocities, are proportional to AT, and so to 
 the difference of temperature between the equator and the 
 poles. But the amount of east or positive momentum lost in 
 a given time while the air in the higher latitudes is descending 
 from higher to lower altitudes, and west or negative momen- 
 tum, in ascending in the lower latitudes from lower to higher 
 
CIRCULATION WITH EARTH ROTATING ON ITS AXIS. 115 
 
 altitudes, depend both upon the rate of change in the east 
 components of velocity with regard to change of altitude and 
 also upon the speed of the vertical circulation. This latter, if 
 we suppose the friction between the strata, moving with rela- 
 tive velocities, to be as these velocities, is, as likewise the 
 former, proportional to AT, the temperature gradient which 
 .gives rise to the forces overcoming the friction and maintaining 
 the circulation. The amount of east or west momentum lost 
 in a given time, and spent in overcoming friction between the 
 atmosphere and the earth's surface and giving value to v 9 is, 
 therefore, as the .square of AT, or as the square of the differ- 
 ence of temperature between the equator and the poles. If, 
 then, frictional and other resistance between the atmosphere 
 and the earth's surface were as the velocity, the value of v 9 
 would have to be as the square of AT, and so about four times 
 greater in winter than in summer. But it is probable that the 
 resistances at the earth's surface increase in a ratio which is 
 greater than the first power of the velocity, and if so the value 
 of v t would have to increase in a ratio which is less than that 
 of the square of At. But whatever may be the relation 
 between the frictional and other resistances and velocity, the 
 values of v 9 must be greater in winter than in summer. 
 
 The relative east velocities between the motions of the 
 upper strata and the earth's surface are likewise greater in 
 winter than in summer, on account of the value of At in the 
 expression of v in 77 being greater, and in the northern 
 hemisphere more than twice greater in January than in July. 
 There is, then, an annual inequality in the east and west com- 
 ponents of motion of the atmosphere, both at the earth's 
 surface and all altitudes above the surface, such that the east 
 components of velocity above are greater in January than in 
 July, and in the middle latitudes of the northern hemisphere, 
 more than twice as great, since the easterly velocities there at 
 the earth's surface are very small. 
 
 In the case of a stratum of air between two parallel and 
 vertical plates extending from the equator to the poles and 
 reaching to the top of the atmosphere, the horizontal inter- 
 
Il6 THE GENERAL CIRCULATION OF THE ATMOSPHERE. 
 
 changing motion between the equatorial and polar part of it. 
 arising from a vertical circulation would not give rise to any 
 force which would tend to turn the polar end toward the east 
 and the equatorial toward the west, if it were free to turn 
 around some vertical axis in its middle. For in this case there 
 would be no east momentum lost in the descent of the air in 
 the polar end, or west momentum, in its ascent at the equato- 
 rial end, and the deflecting force of the current of air moving 
 toward the pole above, and causing pressure against the east 
 side, at any latitude, would be exactly counteracted by that of 
 an equal amount of motion toward the equator below, and caus- 
 ing pressure against the west side. In this case no part of the 
 deflecting forces is spent in creating east momentum in lower 
 latitudes which is lost in higher latitudes, and vice versa, but it 
 is all spent in giving rise to lateral pressure. 
 
 79. There is still another effect in addition to the preced- 
 ing, though much smaller, depending upon the ascending and 
 descending components of motion in the vertical circulation, 
 which tends to give rise to and maintain an east component of 
 motion in the higher latitudes, and the contrary in the lower 
 ones. This is a necessary consequence of the principle of the 
 preservation of areas in the case of central and centrifugal 
 forces. As the air in the higher latitudes descends toward the 
 earth's surface it comes nearer to the earth's axis ; and so, if free, 
 must have a proportionally greater absolute gyratory velocity 
 around this axis, and consequently a greater relative velocity 
 with reference to the earth's surface. 
 
 If not entirely free, this tendency to acquire an increased 
 east component of velocity causes pressure in that direction, 
 which tends to overcome the resistances to motion, whether 
 frictional or otherwise, and through friction between the differ- 
 ent strata is communicated to the earth's surface. In the lower 
 latitudes where the air ascends the effect is the reverse, and 
 tends to overcome frictional resistances to motions from east 
 to west, and is likewise communicated through friction to the 
 earth's surface. In the preceding case of a vertical stratum of 
 air, free to turn around a vertical axis, these forces being in art 
 
CIRCULATION WITH EARTH ROTATING ON ITS AXIS. 1 1/ 
 
 east direction in the higher latitudes where the air descends, 
 and the contrary in the lower latitudes where it ascends, would 
 both tend to turn the vertical stratum horizontally around the 
 vertical axis. The formula for computing the absolute gyra- 
 tory velocity of a projectile or any free body, forced directly 
 upward, and consequently the loss of absolute velocity, and the 
 relative west velocity acquired at any given altitude, is given 
 in 60. By reversing this formula, the amount of relative east 
 velocity acquired in falling through a given space, if the body 
 is entirely free, can be likewise computed. On account, how- 
 ever, of the small depth in comparison with the earth's radius 
 of that part of the atmosphere having any considerable density, 
 these effects are very small for the atmosphere generally. 
 
 80. The relation between the amount of the east compo- 
 nents of velocity of the air at the earth's surface in the higher 
 latitudes, and that of the west components in the lower lati- 
 tudes, is determined by the condition that the sum of all the 
 forces of the air-particles of the higher latitudes acting in an 
 easterly direction upon the earth's surface through friction or 
 resistance of any kind, multiplied into their distances from the 
 axis of rotation, called moments of couple, must be exactly 
 equal to similar products in the lower latitudes, where there is 
 a west component of motion, and the forces by means of fric- 
 tional and other resistances act in the contrary direction. If 
 this condition were not satisfied there would be a residual un- 
 counteracted force acting in the one direction or the other 
 tending to change the velocity of rotation ; but this can only 
 arise from external forces which do not act in the direction of 
 the axis of rotation, and not from any central forces, or such 
 as act only in the planes of the meridians, and which conse- 
 quently have no gyratory components of force, for the actions 
 and reactions in the motions arising from such forces, being 
 exactly equal and in contrary directions, where the mass as a 
 whole remains at the same distance from the centre, cannot 
 affect the velocity of rotation. This principle was recognized 
 by Hadley in his theory of the trade-winds, for he states that 
 "all motions in any direction must have their counter-motions, 
 
Il8 THE GENERAL CIRCULATION OF THE ATMOSPHERE.. 
 
 else the effect upon the earth's surface would be to change the 
 earth's rotation upon its axis." 
 
 The forces exerted upon the earth's surface tending to turn 
 the earth on its axis are effective in proportion to the distance 
 from the axis at which these forces are applied. This is not 
 only in accordance with a well-established principle in mechan- 
 ics, but also with almost every one's experience. One man at 
 the end of a lever of a given length can turn a capstan which 
 would require two men of equal strength with levers of only 
 half the length. The forces, therefore, have to be multiplied 
 into the distances from the axis, and then the forces of equal 
 products have equal tendencies to turn the earth on its axis^ 
 If a given gyratory force were applied on the parallel of 6o r 
 where the distance from the axis is only half as great as at the 
 equator, its effectiveness in turning the earth on its axis would 
 be counteracted by half the amount of this force applied in 
 the contrary way at the equator, and it would require twice as 
 much of the former to counteract the latter. The east com- 
 ponents of velocity, therefore, in the higher latitudes, where 
 the distances from the axis are much less, must be much great- 
 er than the west components in the lower latitudes where, the 
 distances from the axis are much greater, if we suppose the 
 surface of the earth to be homogeneous, so that equal veloci- 
 ties meet with equal resistances and so exert equal forces upon- 
 the earth's surface, or else the east components of velocity 
 must comprise a much greater amount of air. The quantity 
 of air is equally divided by the parallel of 30, and therefore 
 the east components of the higher latitudes at the earth's sur- 
 face must be much greater than the west components in the 
 lower latitudes, or else the dividing parallel between the east 
 and west components of motion at the earth's surface must be 
 nearer the equator, on the average, than the parallel of 30. 
 
 81. The velocities of the east and west components at the 
 earth's surface depending upon the forces of momentum, as 
 explained in 77, depend very much upon the nature of that 
 surface. For the velocities increase until the resistances to 
 the motions are equal to the forces producing them, so that 
 
CIRCULATION WITH EARTH ROTATING ON ITS AXIS. 119 
 
 the smoother the surface, and the less the friction between the 
 air and that surface, the greater the velocities. If there were 
 no resistances from the earth's surface these velocities would 
 be very great somewhat as given in 48, but on account of the 
 smallness of the forces giving rise to them, and maintaining 
 them by overcoming the friction when they are once estab- 
 lished, these velocities are comparatively very small. Since 
 they depend upon the amount of resistance to the motion, 
 they must, in general, be greater on land than on the ocean on 
 the same latitudes, and since there is little land in the southern 
 hemisphere in comparison with that of the northern, they must 
 be much greater in the former than in the latter. The values 
 of v , therefore, in the expression of the limiting value of v, 
 77, are much greater on the several parallels of latitude of the 
 southern hemisphere than on corresponding parallels of the 
 northern hemisphere, especially for the higher latitudes, where, 
 in the southern hemisphere, the ocean extends entirely around 
 the globe. The east components of velocity, therefore, at all 
 altitudes in the higher latitudes, where v is positive, or at least 
 the limits of these velocities, must be greater in the southern 
 than in the northern hemisphere by the same amount that z> 
 is, since the relations between the east components of velocity 
 of the strata above the earth's surface remain the same what- 
 ever those velocities may be at the surface. 
 
 The whole system of atmospheric circulation is so complex 
 and the friction constant of the atmosphere and the resistances 
 from the earth's surface so uncertain, that it is impossible to 
 compute the values of v from the known forces ; and all that 
 can be obtained from theory is an indication that there must 
 be motions in certain directions, and that these must be greater 
 or less according to the variations of the forces at different 
 times and the resistances of the earth's surface at different 
 places. Even the values of V Q are very imperfectly known 
 from direct observation, though this indicates that there are 
 such values, positive in the higher and negative in the lower 
 latitudes. 
 
 82. We have seen that in the case of no frictional resist- 
 
120 THE GENERAL CIRCULATION OF THE ATMOSPHERE. 
 
 ances to the motions of the atmosphere the east components 
 of velocity of the different strata on any given parallel of lati- 
 tude come up to the limit as given by the expression of v 
 in 77, whatever the surface value V Q may be, and that in this 
 c.ase there is no necessity for any meridional interchanging 
 motion to overcome the friction of these east components of 
 motion. In the case of friction, therefore, the less the friction, 
 and the greater the deflecting force belonging to a given 
 amount of meridional motion, the less of this motion is re- 
 quited to overcome the friction of the east component of mo- 
 tion. The frictional resistance to the motions of the atmos- 
 phere, except near the earth's surface, are so small that a very 
 little interchanging motion between the equatorial and polar 
 regions is required to give force enough to overcome the re- 
 sistance to the east component of motion, especially in the 
 higher latitudes where sin / in the expression of this force, 
 49, is large. In the higher altitudes, therefore, where the east 
 components of velocity are great in comparison with the velocity 
 of the interchanging motion, the resultant direction must be very 
 nearly from west to east, being a little north of east in high 
 altitudes where the interchanging motion is toward the pole, 
 and a little south of east in the lower strata where it is from 
 the pole. 
 
 In the lower latitudes, however, where the deflecting forces 
 depending upon the earth's rotation are small in consequence of 
 the smallness of sin /, the relative velocities between the strata, 
 and the absolute east components of velocity in the strata above, 
 are less than in higher latitudes for the same interchanging 
 velocity, and so the resultant motion deviates more from an east 
 direction. The motions here, both in velocity and direction, 
 become more nearly such as they would be in the case of an 
 earth without rotation, in which case they would be in the 
 planes of the meridians and would become comparatively very 
 rapid. At the altitudes in these latitudes where the west com- 
 ponent of motion changes to an east component there is very 
 little motion in any direction, and so the direction is very un- 
 certain ; but at still lower altitudes, where there is a west com- 
 
COMPARISONS WITH OBSERVATIONS. 121 
 
 ^ponent of motion, this combined with the component of motion 
 toward the equator gives rise to the trade-winds in the lower 
 strata of these latitudes. 
 
 At the equator the deflecting forces giving rise to east 
 motions entirely vanish, and hence here there are no such 
 motions ; and as the horizontal interchanging motions also 
 vanish here, or at least at the thermal equator, on account of 
 the vanishing of the temperature gradient, there can be no 
 such motion here. Though there may be a westerly motion 
 at a considerable altitude above the earth's surface arising 
 from the unchecked momentum of the west component of mo- 
 tion acquired as the air moves in from both sides toward the 
 equator. 
 
 COMPARISONS WITH OBSERVATIONS. 
 
 83. The preceding theoretical deductions, so far made,, 
 with regard to the general circulation of the atmosphere, must 
 be understood to be those simply which depend upon the nor- 
 mal temperature gradient between the equator and the poles, 
 unaffected by abnormal local and temporary disturbances of 
 temperature. Hence in these comparisons the prevailing mo- 
 tions and directions of the air, observed at different times and 
 places, and not individual observations, made in one locality, 
 must be used. 
 
 With regard to the strong easterly currents of the upper 
 strata of the atmosphere in nearly all latitudes, as deduced 
 from theoretical considerations in the preceding pages, any one 
 of ordinary observing habits could scarcely live a week upon 
 the earth without discovering from the motions of the clouds, 
 and especially the very high cirrus clouds, that the general 
 tendency of the air above is easterly, even in the lower lati- 
 tudes where, in the lower strata, there is a west component of 
 motion, and that the velocities above in the middle and higher 
 latitudes are much greater than at and near the earth's surface. 
 Espy says : " I have found the true cirrus clouds to average 
 scarcely once a year from any eastern direction; and when they 
 
122 THE GENERAL CIRCULATION OF THE ATMOSPHERE. 
 
 do come from that direction, it is only when there is a storm' 
 of uncommon violence in the east." Mr. Ley also, in his nu- 
 merous observations of the cirrus clouds, almost universally 
 found them to have an easterly motion, from which they rarely 
 deviated. From these observations it is evident that the pre- 
 vailing normal currents in the regions of these clouds is easter- 
 ly, and with a velocity so great that abnormal temporary dis- 
 turbances of the atmosphere are rarely sufficient to reverse- 
 their directions. 
 
 At Toronto, Canada, the resultant directions of the clouds,. 
 as ascertained from a very long series of observations, are as- 
 
 follows : 
 
 \ 
 
 Spring. Summer. Autumn. Winter. 
 
 N. 83 W. N. 75 W. N. 8iW. N. 78 W. 
 
 Here, at all seasons of the year, the resultant directions of 
 cloud-motion are from a direction a little north of west, 
 indicating that the principal component of motion is an east 
 component in accordance with theory. The other component,, 
 being a southern one, indicates that the clouds observed were 
 mostly down in the lower strata of the atmosphere, below the 
 neutral plane, where the interchanging motion is from the pole. 
 toward the equator. 
 
 That there is a strong easterly current prevailing at great 
 altitudes in the atmosphere, deviating but little from an east 
 direction, even as near the equator as the parallel of 30, 
 which the great local and temporary disturbances to which 
 the atmosphere is subject scarcely ever reverses, or even 
 changes much in direction, is shown from the results of four 
 years' observations of the directions of the cirrus clouds at 
 Zi-ka-wei, 11 latitude 31 12' N., longitude 121 26' E. These- 
 give, for the four years, 
 
 Directions N. N.N.E. N.E. E.N.E. E. E.S.E. S.E. S S.E. 
 
 Frequency 13 i 6 15021 
 
 Directions S. S.S.W. S.W. W.S.W. W. W.N.W. N.W. N.N.W.. 
 
 Frequency 3 6 43 69 395 24 18 i 
 
 Here the direction of by far the greatest frequency is the: 
 
COMPARISONS WITH OBSERVATIONS. 123- 
 
 western one, comparatively few being even from the adjacent 
 directions given ; and as there are a few more motions from 
 W.S.W. than from W.N.W., and from S.W. than from N.W., 
 they indicate that the normal current has a small northern 
 component. The results, therefore, are strictly in accordance 
 with theory, 82, which requires that there should be a 
 motion toward the pole at high altitudes, with a velocity^ 
 small in comparison with that of the east component of 
 motion. 
 
 Even much nearer the equator, at Colonia Tover, Vene- 
 zuela, latitude 10 26', observations of the directions of the 
 clouds indicate that the principal component of motion above 
 is an eastern one, while in the lower strata the motions have 
 a west component, as required by theory. While the motions, 
 of the upper clouds were generally from some westerly point, 
 those of the lower ones were from some easterly direction. 12 
 
 84. The theoretical deductions of the preceding pages are 
 also confirmed by the observations of the directions in which, 
 the smoke and ashes of active volcanoes have been carried. 
 On the first of May, 1812, the island of Barbadoes was sud- 
 denly obscured by a shower of ashes from an eruptive volcano- 
 of St. Vincent, West Indies, more than a hundred miles to the, 
 westward. 13 Although the motion of the air here in the lower 
 strata has a western component, yet the ashes were carried up 
 to altitudes where the principal component of motion is toward 
 the east, and hence the ashes were drifted in that direction. 
 Also on the 2Oth of January, 1835, the volcano of Coseguina, 
 Central America, lying in the belt of the north-easterly trade- 
 winds, sent forth great quantities of lava and ashes, and the 
 latter were borne in a direction just contrary to that of the 
 surface winds, and lodged on the island of Jamaica, 800 miles 
 to the east-northeast. 13 In this case, also, the ashes were 
 carried up to altitudes where the prevailing direction of the 
 current of air was a little north of east, the northern component 
 arising from the general poleward motion of the air at all, 
 latitudes in the upper strata of the atmosphere. 
 
 With regard to the volcanic eruption of the island of! 
 
124 THE GENERAL CIRCULATION OF THE ATMOSPHERE. 
 
 Sumbawa, about 200 miles east of the eastern part of Java, 
 Lyellsays: 14 
 
 " On the side of Java the ashes were carried to the distance of 300, 
 and 217 miles toward Celebes, in sufficient quantities to darken the air. 
 The floating cinders to the westward of Sumatra formed on the I2th of 
 April a mass two feet thick and several miles in extent, through which 
 ships with difficulty forced their way. 
 
 " The darkness occasioned in day-time by the ashes in Java was so 
 profound, that nothing equal to it was ever witnessed in the darkest 
 night. Although the volcanic dust when it fell was an impalpable 
 powder, it was of considerable weight when compressed : a pint of it 
 weighed twelve ounces and three quarters. ' Some of the finest particles,' 
 says Mr. Crawford, ' were transported to the islands of Amboyna and 
 Banda, which last is about 800 miles east from the site of the volcano, 
 although the southeast monsoon was then at its height.' They must 
 have been projected, therefore, into the upper regions of the atmosphere, 
 where a counter current prevailed." 
 
 Notwithstanding this volcano was only a few degrees from 
 the equator, yet it seems the finer ashes were carried to so great 
 a distance eastward by the currents above, while the southeast 
 trade-wind below, strengthened by the southeast monsoon pre- 
 vailing at the time, carried the coarser particles in nearly the 
 contrary direction. 
 
 In the account of the volcanic eruptions of Krakatoa of the 
 latter part of May, 1883, it is stated: 15 
 
 " The volcano was ejecting, with a great noise, masses of pumice, 
 molten stone, and volumes of steam and smoke, part of which was 
 carried away westward by the monsoon wind/dropping all around and 
 close at hand its larger pieces, while a high rising cloud is especially 
 recorded as driving away eastward, having evidently encountered a cur- 
 rent in that direction in the upper air. Some of this dust-cloud was 
 carried far to the eastward, for Mr. Forbes relates that on the morning of 
 the 24th of May, when in the island of Timor, twelve hundred miles 
 distant, he observed on the veranda of his hut, situated high in the hills 
 behind Dilly, a sprinkling of small particles of grayish cinder, to which 
 his attention was more particularly drawn later on, and the next day by 
 their repeated falling on the page before him." 
 
 Here again, only a few degrees south of the equator, we 
 
COMPARISONS WITH OBSERVATIONS. 12$, 
 
 have evidence that while in the lower strata there was a current 
 which carried the coarser parts of the ejecta westward, there 
 was a strong upper current which carried the cloud of steam, 
 smoke, and finer ashes, which ascended to great altitudes, away 
 to the east. 
 
 85. The general easterly tendency of nearly the whole upper 
 part of the atmosphere is not only shown from observed cloud- 
 motions and the drift of the smoke and ashes of volcanoes, but 
 also from observations of the winds on all high peaks and 
 mountain ranges. Very strong and prevailing westerly winds, 
 have been observed on Mauna Loa in the Sandwich Islands, 
 on the tops of Pike's Peak and of Mount Washington, in all 
 the passes and on all the peaks of the Rocky Mountains and the 
 Andes, on the Peak of Teneriffe, the Himalayas of Asia, and 
 at every elevated position in either hemisphere all around the 
 globe, except at and near the equator, even in the trade-wind 
 zones, where, at the same time, there is a wind of considerable 
 strength from nearly the opposite direction. Leopold von 
 Buch says with regard to the Peak of TenerifTe : 13 " It is hard to 
 find any account of an ascent of the Peak in which the strong 
 west wind which has been met with on the summit has not been 
 mentioned. Humboldt ascended the Peak on the 2ist of June ; 
 when he reached the edge of the crater he could scarcely keep 
 his feet, such was the violence of the west wind." 
 
 The following are the relative frequencies of the winds on 
 Pike's Peak from the several directions, as given by 10 years of 
 observations of the Signal Service 1873-1883, inclusive : 16 
 
 Directions N. N.E. E. S.E. S. S.W. W. N.W. 
 
 Rel. Frequencies. . .8 13 2 2 4 36 17 18 
 
 From these results from the observations of direction mere- 
 ly, it is evident that at the top of the Peak the current, on the 
 average, is easterly, with a considerable polar component. The 
 latter is indicated by the relative frequency from the S.W. be- 
 ing twice as great as that from the N.W., though the contrary is. 
 indicated by the much greater relative frequency from the N.E.. 
 than from the S.E., but this should have much less weight. We- 
 
-126 THE GENERAL CIRCULATION OF THE ATMOSPHERE. 
 
 cannot infer, however, from the results of these observations 
 that Pike's Peak reaches up to where the general motion is to- 
 ward the pole, since the winds of this locality may be affected 
 by an abnormal local disturbance of some kind. 
 
 For the top of Mt. Washington, from three years' observa- 
 tions, Loomis found the resultant direction of the wind N. 76 
 W. This and the resultants from cloud observations at Toronto, 
 83, indicate that the general current at the top of Mt. Wash- 
 ington, and at the average altitudes of the clouds generally, has 
 -a south component of motion at these latitudes, as required 
 >y theory. 
 
 In the high latitudes of Asia it also appears that the direc- 
 tion of the wind on high mountain tops is easterly, and with a 
 south component of motion. " At Mt. Alibut, 200 miles west 
 -of Irkutsk, and over 7000 feet high, a very constant and strong 
 W.N.W. wind is observed." 20 
 
 86. While theory indicates that the whole upper part of 
 the atmosphere, except at and near the equator, must have an 
 easterly motion with velocity increasing with increase of alti- 
 tude, and the existence of such a motion is confirmed by all 
 -observations, it is evident from the Report of the Krakatoa 
 'Committee of the Royal Society that at very high altitudes at 
 -and near the equator there must have been, in the latter part 
 of August, 1883, a strong current from east to west of at least 
 70 miles per hour, by which the dust-particles causing the sun- 
 set glows and other phenomena were carried in this direction 
 around the globe. According to the observations, also, of the. 
 Hon. Ralph Abercromby in the equatorial regions in the months 
 >of December and May, there is likewise a westerly current here 
 at the altitudes of the cirrus clouds, though only a few degrees 
 south of the equator there seemed to be an east component of 
 motion. For such currents theory furnishes a slight force, 
 '60, arising from the ascent of air in the equatorial region, which 
 tends to give rise to a westerly current, which, if it were not 
 for friction, would be considerable at great altitudes. This 
 current, it is seen, if the motions were without friction, as in 
 the case of a projectile in a vacuum, would have a velocity of 
 
COMPARISONS WITH OBSERVATIONS. I2/ 
 
 only 0.73 m. per second at the altitude of 10 kilometers, and 
 a velocity of 70 miles per hour would require, by the formula, 
 an altitude of about 270 miles. This is not, therefore, an ade- 
 quate cause of itself for the existence of such currents. But 
 in addition to this there are the northeast and southeast trade- 
 \vinds, extending up to a considerable altitude, and coming in 
 obliquely from both sides toward the equator, or rather the 
 -doldrums a little north of the equator, and the deflecting force 
 Tvhich produces the western component of velocity is counter- 
 acted by friction, except at and near the earth's surface, only 
 after considerable westerly velocity is acquired ; for friction 
 can only be brought into play where there is a relative velocity 
 between different strata, and so the velocity must increase with 
 increase of altitude, and become large at high altitudes. 
 
 But, besides the preceding, there is another cause for westerly 
 currents at high altitudes in the equatorial regions during the 
 summer and winter seasons of the year. When both hemi- 
 spheres have about the same temperature there is little or no 
 interchange of air between them, and so, little or no current 
 -crossing the equatorial regions in either direction, either above 
 or below. But at other times, during the summer of the north- 
 ern hemisphere for instance, there is a current from the northern 
 to the southern hemisphere above, and the reverse below, and 
 it is readily seen that the current above, considered by itself 
 and not in connection with the interchanging motions between 
 . the equatorial and polar regions at a mean annual temperature, 
 in approaching the equator tends to acquire, by the deflecting 
 force of the earth's rotation, a western component of motion, 
 which continues to increase until the friction, which is small 
 here, exactly counteracts this tendency, and mostly after the 
 air passes the equator and the deflecting force changes to the 
 left of the direction of motion, is this western component grad- 
 ually decreased and at a short distance south of the equator 
 changed to an eastern component of motion, though the effect 
 of friction takes place in some measure before the air arrives 
 -at the equator, and while the deflecting force to the right, north 
 of the equator, is vanishing. As the friction above is small, 
 
128 THE GENERAL CIRCULATION OF THE ATMOSPHERE. 
 
 the velocity required above to give rise to friction enough to> 
 counteract the deflecting force, and to overcome the momentum 
 of the western component of motion, may be very great. 
 
 If there were no friction between the air and the earth's 
 surface, of course the contrary effect would be produced in the 
 lower part of the atmosphere where the interchanging motion 
 is from south to north, and there would be, then, an east com- 
 ponent of motion. But the great amount of friction at the 
 earth's surface prevents such a result, and so the western com- 
 ponent above is increased thereby, for the relative velocities 
 between the different strata must be such as to counteract the 
 deflecting forces in the one direction above and the contrary 
 below. Of course similar effects in the same directions, and 
 perhaps of the same magnitudes, are produced at the opposite- 
 season of the year, when the interchanging currents above and 
 below are reversed in direction. 
 
 At the time of the Krakatoa eruption the latter part of 
 August, the effect arising from this cause, in giving rise to a 
 westerly current at high altitudes, would be near its maximum, 
 and it is probable that if it had occurred at a time when the 
 two hemispheres had nearly the same temperature, the dust- 
 particles and their accompanying phenomena would not have 
 been transferred westwardly so rapidly. Observations, also, 
 upon the motions of the cirrus clouds at such a time would per- 
 haps not indicate so much of a western component of motion 
 as during the extremes of summer and winter. 
 
 At the time of the great Krakatoa eruptions the great mon- 
 soon influence, no doubt, played an important part ; for then 
 the doldrums and the place of meeting of northerly and south- 
 erly currents were transferred to the north of India, and the 
 great return current above toward the equator was powerfully 
 deflected toward the west, while the contrary took place below.. 
 This higher current, moving toward the south and west, carried 
 the higher dust-particles down toward Madagascar, while in 
 the lower or medium strata the current carried them toward 
 Japan, thus causing the apparent initial streams or branches in, 
 these directions. 
 
COMPARISONS WITH OBSERVATIONS. 12Q 
 
 87. We have seen, 77, that, according to theory, the at- 
 mosphere at the earth's surface has an easterly tendency in the 
 higher latitudes, and the contrary in the lower ones. It must 
 be evident to almost every one that in the middle and higher 
 latitudes winds with a principal west component are both the 
 strongest and most frequent, and that in the latitudes of the 
 trade-winds the west component, especially upon the great 
 oceans, is well marked, and without much variation. The few 
 observations which we have from the interior of North Africa 
 indicate that the prevailing winds are easterly and northeasterly. 
 This is also shown to be the case on the northwest coast of 
 Africa in the trade-wind latitudes by the sand and dust which 
 is blown out into the Atlantic Ocean by the prevailing winds 
 there. According to Mr. Laughton, 18 " The sand which these 
 winds raise in the desert is carried by them far out to sea. 
 During the summer it fills the air as far as the Canaries and to- 
 the height of the Peak of Teneriffe with an impalpable dust, 
 which has the effect of a thick haze ; and at all seasons of the 
 year ships, even at a considerable distance from the shore, find- 
 it covering their sails and decks." 
 
 Professor Piazzi Smyth, also, observed on the Peak of 
 Teneriffe " that the dust haze, which almost constantly filled 
 the atmosphere and rendered the view very indistinct, was in 
 the stratum of air moving from the eastward, that high over- 
 head the air was clear, and that when the westerly wind de- 
 scended to their level all traces of the dust haze in their im- 
 mediate neighborhood vanished." ] Of course these general 
 tendencies are very much changed frequently by the numerous 
 local and temporary disturbances, especially upon land, so that 
 the directions, temporarily, are often nearly or quite reversed 
 from that of the general tendency. 
 
 The average velocity of resultant motion of the air at the 
 earth's surface for the whole year at a great many stations in 
 all parts of the United States, according to the estimates of 
 Coffin, is about two miles per hour with a resultant direction a 
 little north of east. The east component of motion is, therefore, 
 very nearly the same. These estimates, however, are extremely 
 
130 THE GENERAL CIRCULATION OF THE ATMOSPHERE. 
 
 vague and uncertain, being based mostly upon the relative fre- 
 quency of the winds from the different principal points of the 
 compass. Unfortunately the numerous observations of the 
 Signal Service, as given in the Reports of the Chief Signal 
 Officer, are of little avail in determining such resultants, since 
 only the relative frequencies of direction from the different 
 points are given, and not the corresponding velocities. The 
 average hourly velocities, however, of motion in all directions 
 are obtainable from the whole number of miles passed over in 
 all directions by the air in the course of a month. From all 
 the data of this kind available in the United States, and from 
 similar data in Europe and Asia, Loomis 17 obtained the follow- 
 ing average velocities in miles per hour without regard to 
 direction : 
 
 Jan. Feb. Mar. April May June July Aug. Sept. Oct. Nov. Dec. Year. 
 
 United States (45 stations). 
 
 " 9.69 10.13 IO -97 10.13 8.88 7.95 7.28 6.91 7.97 8.90 9.83 9.75 9.5 
 Northern Europe (between parallels of 50 and 60). 
 
 11.23 11.54 I1[ -45 10.15 9-84 8.99 9.01 9.19 9.06 10.60 11.52 ii. 21 10.3 
 
 . Southern Asia, south of latitude 20 N. (34 stations). 
 4.87 4.79 4.91 5.34 6.67 8.46 8.37 7.42 6.44 4.63 4.37 4.71 6.5 
 
 Near the West India Islands (7 stations). 
 7.12 7.66 7.55 7.96 7.47 7.46 7.17 5.79 5.98 6.70 6.76 7.04 7.0 
 
 From these results alone we know nothing with regard to 
 the resultants ; but knowing that the general tendency of the 
 air in northern latitudes is easterly, it is reasonable to suppose 
 that the velocity of the east component of motion may be as 
 much as two or three miles per hour. 
 
 At the West India Islands the wind blows pretty steadily 
 in a direction nearly from the east, except when disturbed by 
 cyclones, so that we may regard the average velocity of the 
 west component as being at least five miles per hour. In 
 southern Asia, on account of the great monsoon disturbances, 
 little can be inferred from the results with regard to the veloc- 
 ity of this west component. 
 
 88. For theoretical reasons given in 81, the velocity of the 
 east component of motion at the earth's surface in the higher 
 
COMPARISONS WITH OBSERVATIONS. IJI 
 
 latitudes of the southern hemisphere should be much greater 
 than in the northern hemisphere. According to the universal 
 experience of navigators, the westerly winds of these latitudes 
 are nearly incessant, and very strong. With regard to the 
 westerly winds of the higher latitudes of both hemispheres, 
 and especially of the southern hemisphere, Mr. Laughton 
 says : ld 
 
 " In both hemispheres, to the north and south of the parallel of 35 
 or 40 a strong westerly wind blows with great constancy all around the 
 world. In the southern hemisphere more particularly it blows with a 
 persistency little less than that of the trade-winds, but with a strength 
 which, although fitful, is very much greater. From a fresh strong breeze 
 at rises frequently into a violent gale, and as such blows for days together ; 
 tthe mean direction being very nearly west, from which it seldom varies 
 more than a couple of points on either side. South of the Atlantic, 
 south of the Indian Ocean, south of Australia, in the higher latitudes of 
 the southern Pacific, and to the southward of Cape Horn, we find it still 
 the same a westerly gale, whose strength and constancy combined have 
 enabled Australian clippers to make passages which seem to border on 
 the fabulous." 
 
 With regard io the winds of the southern hemisphere it is 
 
 said: 19 
 
 " The trade-wind system of the southern hemisphere is narrower than 
 Tin the northern, extending from the equator to only about 30 and to 
 ;about 33 in winter. The system of westerly winds comprises a zone 
 bounded on the north by that of the equatorial winds just described, and 
 extends southerly in the winter season to latitudes varying from about 
 61 in the southern Indian Ocean to about 65 or 66 in the South Pa- 
 cific. Its southern limit in the summer season (their winter), which I 
 have ventured to draw in latitude 50, is as yet a matter of conjecture, 
 no observations having been made from which to determine it. 
 
 " Of all the reliable resultants delineated in the well-defined portions 
 of the system, amounting in the whole to over 250, every one in winter, 
 and all but seven in summer, are westerly, and most of them are within 
 a few degrees of the general mean, which is about N. 75 to 80 W." 
 
 89. With regard to the annual inequality in the easterly 
 ;and westerly motions of the atmosphere, as deduced from the- 
 ory, 78, we have but few observations having any bearing on 
 the subject, but these seem to indicate with some degree of 
 
132 THE GENERAL CIRCULATION OF THE ATMOSPHERE 
 
 certainty that there really is such an inequality. It is observed 1 
 upon the summits of Pike's Peak and Mt. Washington that 
 easterly winds prevail more in the summer than in winter.. 
 Supposing the magnitude of the abnormal disturbances which 
 entirely counteract and reverse the easterly motions so as to> 
 give rise to easterly winds to be the same at both seasons, it 
 then follows that the easterly motions are less and so more fre- 
 quently reversed in summer than in winter by these abnormal 
 disturbances. 
 
 Away up in the region of the cirrus clouds we have seen;, 
 83, that the easterly velocities are so great that they are 
 scarcely ever reversed there by abnormal disturbances, or even 
 at lower altitudes in winter, for these easterly velocities at this, 
 season are unusually great. That the easterly velocities of the 
 general motions of the upper strata are greater in winter than 
 in summer may be inferred from observations by the Rev. 
 Clement Ley upon the motions of the cirrus clouds. He says: 
 " I have found that in winter very local depressions, even when 
 deep, scarcely affect the directions of the cirrus currents in 
 their vicinity, the latter continuing to be governed by the 
 more general distribution of atmospheric pressures. Curiously 
 enough this is not the case in summer." This would seem to 
 indicate that the easterly velocities of the general progressive 
 motions of the upper strata are so much greater in winter than 
 in summer, that though they may be reversed by the abnormal 
 gyratory disturbances in the latter season, they cannot be in 
 the former. 
 
 On the earth's surface the velocities of resultant motions 
 are so small, and these may be affected so much by monsoon 
 influences, which have an annual period, that it is difficult to 
 ascertain from observation whether there is an annual inequal- 
 ity in the general motions of the atmosphere at the earth's sur- 
 face. In the estimates of the resultant motions at the earth's 
 surface for numerous stations in the United States, Coffin 
 found the velocities to be about twice as great in winter as in 
 summer, and in a direction, in general, a little to the north* of" 
 east. But this, being for only a comparatively small part of 
 
EFFECT OF MOTIONS O.V ATMOSPHERIC PRESSURE. 133 
 
 the belt of easterly motions around the globe in the northern 
 hemisphere, may be due to local circumstances of a monsoon 
 character, such as the greater surface flow of air into the Atlan- 
 tic Ocean in the winter than in the summer, since in the former 
 season its temperature is greater, and in the latter less, than 
 that of the continent. 
 
 It is seen from Professor Loomis's results, 87, that in both 
 the United States and in northern Europe there is an annual 
 inequality in the velocities taken without regard to direction, 
 and that, therefore, there is probably one in the velocities of 
 the resultants, but this is not entirely conclusive, since the ab- 
 normal disturbances of a gyratory character may be greater in 
 winter than in summer. 
 
 EFFECT OF THE GENERAL MOTIONS UPON ATMOSPHERIC 
 
 PRESSURE. 
 
 90. Having investigated the effect of the temperature 
 gradient in producing an interchanging motion between the 
 equatorial and polar regions, and then the effect of these, in 
 connection with the deflecting force of the earth's rotation, 
 in causing east and west components of motion, the next step 
 in order is to examine the effects of these latter motions, in 
 connection with this same deflecting force, in causing gradients 
 of atmospheric pressure, and so differences of pressure, between 
 different parallels of latitude. While the atmosphere, if it had 
 in all latitudes the same temperature, has no relative east or 
 west motion, but only the absolute motion of rotation in con- 
 nection with that of the earth's surface, the centrifugal force 
 of rotation is just sufficient to cause the same ellipticity in the 
 isobaric surfaces which the earth's surface has, and so to keep 
 these surfaces parallel with the earth's surface. But if the at- 
 mosphere has an absolute east component of motion at all 
 altitudes greater or less than that of the earth's surface, or, in 
 other words, has an east or west component of motion relative 
 to the earth's surface, then the atmospheric pressure at the 
 earth's surface is no longer the same on all parallels of lati- 
 
134 THE GENERAL CIRCULATION OF THE ATMOSPHERE. 
 
 tude, and the isobaric surfaces are no longer parallel with the 
 earth's surface, but pressure gradients with reference to this- 
 surface are produced in which the pressure either increases or 
 decreases in a direction from the pole toward the equator, ac- 
 cording as this component of motion is east or west. If the 
 atmosphere at all latitudes had a relative east or west motion 
 with a velocity on each parallel proportional to that of the 
 absolute east velocity of the earth's surface, then the ellipticity 
 of the isobaric surfaces would be increased or decreased just as- 
 much as that of the earth's surface would be if the angular 
 velocity of the earth's rotation were changed by the same 
 amount. 
 
 We have seen, 71, that the effect of the upward expansion 
 of the atmosphere due to the temperature gradient between; 
 the equator and the poles is to increase the ellipticities of the 
 isobaric surfaces, and that this increase is in proportion to the 
 altitudes of the strata, and therefore the east components of 
 velocity, represented by v, which would give rise to a deflect- 
 ing force sufficient to counteract the force arising from the 
 gradient of this increased ellipticity, 76, increases as the alti- 
 tude. But since these, by means of the deflecting forces, are 
 merely sufficient to keep the atmosphere, as it expands up- 
 ward, from flowing away toward the poles, they have no effect 
 upon the atmospheric pressure at the earth's surface. But if, 
 now, the atmosphere at the earth's surface has an east or west 
 component of motion of given velocity, that of all the strata 
 above is changed by this same amount, and so diminished 
 when the relative velocity at the surface is toward the west. 
 The change of pressure, therefore, or pressure gradient, at the 
 earth's surface depends only upon the east and w T est compo- 
 nents of velocity at the earth's surface, and entirely vanishes 
 where they vanish, whatever these velocities may be at altitudes 
 above the earth's surface. At these altitudes, however, there 
 are pressure gradients when there are no east or west compo- 
 nents of velocity and pressure gradients at the surface ; for 
 since the deflecting forces arising from the east or west com- 
 ponents of motion at different altitudes are just sufficient to> 
 
EFFECT OF MOTIONS ON ATMOSPHERIC PRESSURE. 135 
 
 counteract those of the temperature gradients, these remain 
 and, as we have seen, 71, increase with increase of altitude. 
 
 What precedes is based upon the hypothesis that there is 
 no interchanging motion of the atmosphere between the equa- 
 torial and polar regions or at least, if there is such a motion, 
 no sensible force or pressure gradient is required to overcome 
 the frictional resistances to this motion and to maintain it. 
 But we have seen that the east or west components of motion 
 where there is friction cannot be maintained without the other ; 
 and so wherever there is polar motion, as in the upper strata, 
 the east components of velocities must be a little less ; and 
 where there is equatorial motion, as in the lower strata mostly, 
 they must be greater, or if the components of motion are 
 toward the west, less, than those which would give rise to a 
 deflecting force which would exactly counteract that of the 
 temperature gradient. 
 
 91. The general expression of the barometric gradient G, 
 corresponding to any given velocity s in any direction, so far 
 as it depends upon the deflecting forces corresponding to this 
 velocity, is given in 57. In the special case now being con- 
 sidered, s becomes v, the east component of relative velocity 
 of the atmosphere, and we therefore have here 
 
 P T 
 
 G 0.1571*' sin l-p ~ . 
 *i * 
 
 By substituting for v its general expression, 77, in a func- 
 tion of the temperature gradient A-r and of the east component 
 of velocity at the earth's surface v , we get 
 
 p T 
 G o.i57i(V sin /+ 246.4/2/77-) ~- ~ - 
 
 *9 * 
 
 From this expression of the barometric gradient we arrive 
 at the same conclusion as in the preceding paragraph, namely, 
 that the pressure gradient at the earth's surface, so far as it 
 depends merely upon the east or west components of velocity 
 at the earth's surface, vanishes where they vanish. For at the 
 earth's surface we have h equal to o, and as P there is generally 
 
136 THE GENERAL CIRCULATION OF THE ATMOSPHERE. 
 
 very nearly the same as P , we always have in this special case, 
 very nearly, 
 
 T 
 G Q = 0.1571^ sin /-- 
 
 It will be remembered that G is the change of atmospheric 
 pressure in millimeters of mercury in the distance of one de- 
 gree of a great circle of the earth, in a direction at right angles 
 to the direction of motion, in case the rate of change should 
 continue the same through so great a range. From this ex- 
 pression we may infer that in the northern hemisphere and in 
 the higher latitudes, where z/ is positive, the atmospheric pres- 
 sure increases from the pole toward the equator to about the 
 parallel of 35 or 30, where V Q vanishes and changes sign ; but 
 between this parallel and the equator, where V Q is negative or 
 west, the pressure decreases. In the southern hemisphere the 
 gradient is reversed on account of the change of sign of sin /. 
 Hence immediately south of the equator, where V Q is negative, 
 we have increasing pressure to about the parallel of 30, where 
 ^ vanishes and changes sign, becoming positive again ; after 
 which the pressure decreases again to the pole, and very rapidly 
 in the middle latitudes where the positive values of v are very 
 large ( 88). At the equator, where sin /vanishes, the gradient 
 also vanishes, and there is here consequently a minimum pres- 
 sure. The pressure, therefore, in both hemispheres increases in 
 the higher and middle latitudes in going from the poles toward 
 the equator to about the parallel of 30 or 35 where there is a 
 maximum pressure, and then decreases to the equator where 
 there is a minimum. The gradients, however, in approaching 
 the equator from either side, are small on account of the 
 small value of sin / there, and consequently the equatorial de- 
 pression is small. There is then, or would be if they were not 
 interfered with by abnormal disturbances, a zone of high pres- 
 sure in each hemisphere around the globe with its maximum 
 near the parallel of 30, an equatorial zone of low pressure with 
 its minimum at the equator, and an area of low pressure around 
 each pole with its minimum at the pole. 
 
EFFECT OF MOTIONS ON ATMOSPHERIC PRESSURE. 137 
 
 It seems difficult for some to conceive how the equatorial 
 depression can be due to the westerly motion of the atmos- 
 phere, since this motion prevails at the earth's surface and in the 
 lower strata of the atmosphere only, while above the motion is 
 easterly. But it has been shown that in the case of no east or 
 west component of motion at the earth's surface the east com- 
 ponents are necessary to keep the air above from flowing away 
 from the equatorial region, and thus from diminishing the pres- 
 .sure there. If, then, the lower stratum next the earth's surface 
 has a west component of motion, we have seen that the veloci- 
 ties of all the strata above to the top of the atmosphere have 
 their velocities changed by the same amount, and the effect 
 upon the pressure at the earth's surface is precisely the same 
 as if there were no temperature gradient and no east compo- 
 nents of velocity above, and all the strata from bottom to top 
 should receive a west component of motion. 
 
 92. According to the preceding approximate general ex- 
 pression of G, it is seen that the pressure gradient at the earth's 
 surface, where h=o, is positive where v sin /is, and vanishes and 
 changes sign at the latitude where v does. The greatest pres- 
 sure, therefore, at the earth's surface is on this parallel, or nearly. 
 But at any altitude above the earth's surface the expression of 
 G vanishes at some latitude nearer the equator, since after v be- 
 comes negative, the term in the parenthesis depending upon h 
 being always positive in the northern hemisphere, and in either 
 of a contrary sign to that of v sin / in these latitudes, the ex- 
 pression only vanishes where the negative value of v sin / is 
 equal to the part in the parenthesis depending upon h, and 
 hence the greater h is, the nearer the equator is the latitude 
 where G vanishes and the pressure is a maximum. In order 
 to make G vanish, the following conditions must be satisfied : 
 
 2/ sin / + 246.4^ AT: = o. 
 
 The altitude on any given latitude where this condition is 
 satisfied of course depends upon the value of z/ , but for some 
 distance toward the equator from the parallel where v vanishes, 
 the term % sin / increases although sin / diminishes ; and hence 
 
138 THE GENERAL CIRCULATION OF THE ATMOSPHERE. 
 
 the greater the altitude the nearer the equator is the latitude- 
 where G vanishes and the maximum pressure occurs in going 
 horizontally toward the equator. The values of V Q , however,, 
 corresponding to the different latitudes or values of sin /, may 
 be so small that at and above a given altitude the second term 
 above may, for all latitudes, be greater than the negative value 
 of the first one, and then the expression is positive and does, 
 not vanish at all, except at the equator, where both sin / and 
 AT: vanish ; and therefore, above a given altitude and at all 
 higher altitudes, the maximum pressure, in going horizontally 
 toward the equator, is only reached at the equator, and at 
 these altitudes there is a continuous gradient of pressure in- 
 creasing from the 'pole to the equator. With no value of V Q on 
 any parallel, that is, with no east or west components of mo- 
 tion at the earth's surface, we have seen there would be no 
 pressure gradient at the earth's surface, so far as it depends 
 upon v and the deflecting forces, but at any altitude above the 
 surface there would be a gradient of increasing pressure from> 
 the pole to the equator, and this at great altitudes is so large,, 
 that the west component of motion of the atmosphere at the 
 earth's surface, and the consequent change of velocities by the 
 same amount at all altitudes, are not sufficient, by means of the 
 deflecting forces, to reverse this gradient except in the lower- 
 strata of the atmosphere up to a certain altitude. Above this 
 altitude, therefore, there is no barometric minimum at the 
 equator, but a maximum, arising from the gradual nearer 
 approach of the maxima on each side towards the equator as 
 the altitude increases. 
 
 It must be always borne in mind that the preceding rela- 
 tions are not strictly correct, but only approximately so, since 
 the value of v, 77, which has been used in obtaining the pre- 
 ceding expression of G is approximate only, being the true ex- 
 pression in the case of no friction, in which case there is no 
 necessity for an interchanging motion between the equator and 
 the poles, but is in all cases a limit beyond which the value of 
 v cannot go and of which it must fall a little short, and the: 
 greater the amount of friction to be overcome the more so. 
 
EFFECT OF MOTIONS ON ATMOSPHERIC PRESSURE. 139 
 
 93. From what precedes, there is, at the earth's surface, an 
 area of low pressure around each pole with its minimum at 
 the pole, a zone of high pressure hi each hemisphere with its 
 maximum about the parallel of 30, and an equatorial zone of 
 slightly diminished pressure with the minimum at the equator. 
 And this same arrangement exists in the lower strata of the at- 
 mosphere up to a considerable altitude, except that the polar 
 depressions are greater and the parallel of maximum pressure 
 comes nearer the equator as the altitude is increased, until at 
 a certain altitude the two maxima combine to form a maximum 
 pressure at the equator. Instead, then, of the isobaric surfaces 
 being elliptical, and having an increasing ellipticity in propor- 
 tion to the altitude, as represented in Fig. 3, they have, in 
 consequence of the east and west components of motion of the 
 atmosphere at the earth's surface, steeper gradients in the 
 higher and middle latitudes, a bulging up nearer the equator, 
 and in the lower strata a minimum altitude at the equator, as 
 represented in Fig. 4, in which the intersections of the line eo- 
 with the isobaric surfaces indi- 
 cate the latitudes, at the several 
 altitudes, where the pressures are 
 the greatest and where the east 
 components of velocity vanish, 
 change sign, and become west 
 components of velocity. The 
 actual form and position of the 
 line eo, since they depend upon the 
 west components of motion at 
 the earth's surface, and the tem- 
 perature gradient, are quite un- 
 certain toward the equator. 
 
 Before the exploring expeditions led by Captain Wilkes 
 and Sir James Ross it was pretty generally thought that the 
 barometric pressure at sea-level in all parts of the earth is 
 nearly or quite the same, and about 30 inches. From the 
 barometric observations of these expeditions it was first clearly 
 
140 THE GENERAL CIRCULATION OF THE ATMOSPHERE. 
 
 shown that this is by no means the case. Says Captain 
 Wilkes: 35 
 
 "The most remarkable phenomenon which our observations have 
 shown is the irregular outline of the atmosphere surrounding the earth 
 as indicated by the pressure upon the measured column at different parts 
 of the surface. Our barometrical observations show a depression within 
 the tropics, a bulging in the temperate zone, again undergoing a depres- 
 sion on advancing towards the arctic and antartic circles." 
 
 Says Sir James Ross: 36 
 
 " Our barometrical experiments appear to prove that the atmospheric 
 pressure is considerably less at the equator than near the tropics ; and to 
 the south of the tropic of Capricorn, where it is greatest, a gradual diminu- 
 tion occurs as the latitude is increased, as will be shown from the follow- 
 ing table, derived from hourly observations of the height of the column 
 of mercury between the 2oth of November, 1839, an d tne 3ist of July, 
 1843." 
 
 EXTRACT FROM ROSS'S TABLE. 
 
 Latitude. 
 
 Pressure, 
 Inches. 
 
 . Latitude. 
 
 Pressure, 
 Inches. 
 
 Latitude. 
 
 Pressure, 
 Inches. 
 
 Equator. 
 
 29.974 
 
 42 53' 
 
 29.950 
 
 55 52' 
 
 29.360 
 
 13 o'S. 
 
 30.016 
 
 45 o 
 
 29.664 
 
 60 o 
 
 29.114 
 
 22 17 
 
 30.085 
 
 49 8 
 
 29.467 
 
 66 o 
 
 29.078 
 
 34 43 
 
 30.023 
 
 5i 33 
 
 29.497 
 
 74 o 
 
 28.928 
 
 
 
 54 26 
 
 29-347 
 
 
 
 So strange and unaccountable did these phenomena appear 
 before the discovery of the deflecting force of the earth's rota- 
 tion, that Espy said : " Unless I have positive testimony to the 
 fact, I shall not believe that the barometer stands lower at the 
 level of the sea in the southern hemisphere than in the north- 
 ern, only in regions where great snows or rains prevail, and only 
 while they do prevail." This was upon the theory that great 
 barometric depressions are caused by a great quantity of 
 aqueous vapor in the atmosphere. 
 
 94. Since the whole vertical circulation and the east and 
 'west components of motion, and the deflecting forces arising 
 .from them, from which result the polar and equatorial depres- 
 
EFFECT OF MOTIONS ON ATMOSPHERIC PRESSURE. 141 
 
 sions and the zones of high pressure near the tropics, depend 
 upon the temperature gradients between the equator and the 
 poles, there must be greater polar depressions of the isobaric 
 surfaces and a greater bulging up in the middle and lower lati- 
 tudes in winter than in summer, since the temperature gradients 
 are much greater in the former season than in the latter, espe- 
 cially in the northern hemisphere, where they are more than 
 twice as great in January as in July. There must, then, be an 
 annual inequality of atmospheric pressure from this cause, such 
 that the pressure is greater in the winter than in the summer 
 of each hemisphere in the middle and lower latitudes, and the 
 reverse in the polar regions. 
 
 But for another reason, also, there is an annual oscillation 
 of pressure. During the winter of each hemisphere the atmos- 
 phere becomes much colder than it is in the other hemisphere, 
 and consequently its volume considerably less, so that the iso- 
 baric surfaces lie lower in the colder hemisphere than in the 
 other. There is, consequently, a pressure gradient above by 
 which the air of the higher strata flows from the warmer hemi- 
 sphere to the colder one and increases the mass and pressure of 
 the atmosphere there a little, and diminishes them by the same 
 amount in the warmer hemisphere, until there is a reverse gra- 
 dient formed in the lower strata which gives rise to a counter 
 flow of air below from the colder to the warmer hemisphere. 
 There is, in this way, an interchanging motion originated and 
 maintained between the two hemispheres, just as there is be- 
 tween the warm equatorial and cold polar region of each hemi- 
 sphere, as has been describee! in 72. But the interchange 
 between the two hemispheres is kept up with greater facility, 
 since there are no east components of motion at and near the 
 equator, where the temperature and pressure gradients in this 
 case and the velocity of flow are the greatest, to give rise to 
 counter deflecting forces, as there are in the middle latitudes 
 in the other case, but the whole temperature and pressure 
 gradients are brought to bear in maintaining the flow of air 
 above from the warmer to the colder hemisphere, and the con- 
 trary in the lower strata. 
 
I4 2 THE GENERAL CIRCULATION OF THE ATMOSPHERE. 
 
 As there is an annual inversion of the temperature conditions 
 which give rise to and maintain these interchanging motions 
 between the two hemispheres, so there is also one in the pres- 
 sure gradients at the earth's surface and in the lower strata, 
 .arising from the flow of air above from the warmer to the 
 colder hemisphere, and in the slight increase of pressure there 
 and corresponding diminution in the other hemisphere, to cause 
 this gradient. There is therefore a little more air, and conse- 
 quently a little greater pressure at the earth's surface, in each 
 hemisphere in winter than in summer, and this causes a slight 
 annual inequality of pressure, the pressure being the greatest 
 in each hemisphere in the midwinter of that hemisphere. The 
 greatest effect of this latter cause of the annual inequality is at 
 the poles, whereas in the other case the pressure is increased 
 an winter in the middle latitudes, but diminished in the polar 
 regions. It is the resultant of these two effects which is ob- 
 served. 
 
 95. An annual inequa'ity of pressure is observed on nearly 
 every part of the globe, but on account of various local disturb- 
 ances of pressure, this, as the temperature, is not the same at 
 all places on the same parallel. But by obtaining the normal 
 pressures of latitude, as those of temperature, by taking the 
 average of observed values all around the globe on each 
 parallel, we eliminate the effects of these local disturbances. In 
 this way the results given in the following table have been ob- 
 tained. 8 These results, however, must be regarded as being only 
 approximate, since the material on hand then, more than ten 
 years ago was insufficient for accurate results since there was 
 a great deficiency of observations over nearly all parts of the 
 great oceans. It is much to be regretted that the work has 
 not been repeated with the now much greater material on hand 
 for such a purpose. 
 
 In the following table are given for the earth's surface the 
 normal barometic pressure of latitude, P\ the barometric gra- 
 dient, G', and the annual variations, AP and AG, for each 
 fifth degree of latitude, so far as there were any available obser- 
 vations. 
 
EFFECT OF MOTIONS ON ATMOSPHERIC PRESSURE. 143 
 
 Latitude. 
 
 Annual Mean. 
 
 Annual Inequality. 
 
 P 
 
 G 
 
 " 
 
 AC 
 
 
 mm. 
 
 mm. 
 
 mm. 
 
 mm. 
 
 + 80 
 
 760.5 
 
 .... 
 
 0.06 
 
 .... 
 
 75 
 
 760.0 
 
 O.ig 
 
 + 0.19 
 
 + 0.04 
 
 70 
 
 758.6 
 
 0.14 
 
 0.36 
 
 0.05 
 
 65 
 
 758.2 
 
 + 0.01 
 
 0.63 
 
 O.O6 
 
 60 
 
 758.7 
 
 0.15 
 
 0.97 
 
 0.06 
 
 55 
 
 759-7 
 
 O.2O 
 
 .26 
 
 0.05 
 
 50 
 
 760.7 
 
 0.18 
 
 .41 
 
 0.03 
 
 45 
 
 761.5 
 
 0.15 
 
 53 
 
 0.02 
 
 40 
 
 762.0 
 
 + 0.07 
 
 .61 
 
 + 0.01 
 
 35 
 
 762.4 
 
 0.03 
 
 .66 
 
 O.OO 
 
 30 
 
 761.7 
 
 0.18 
 
 .66 
 
 0.01 
 
 25 
 
 760.4 
 
 0.25 
 
 .61 
 
 0.03 
 
 20 
 
 759-2 
 
 O.2I 
 
 .41 
 
 O.O6 
 
 15 
 
 758-3 
 
 0.13 
 
 -05 
 
 0.09 
 
 10 
 
 757-9 
 
 0.03 
 
 + 0.50 
 
 O.II 
 
 4-5 
 
 758.0 
 
 + O.OI 
 
 0.05 
 
 0.12 
 
 
 
 758.0 
 
 0.04 
 
 0.63 
 
 0.12 
 
 - 5 
 
 758.3 
 
 O.II 
 
 1.18 
 
 O.II 
 
 10 
 
 759- 1 
 
 O.2O 
 
 1.70 
 
 0.08 
 
 15 
 
 760.2 
 
 0.26 
 
 2.OO 
 
 0.06 
 
 20 
 
 761.7 
 
 0.29 
 
 2.22 
 
 O.O3 
 
 25 
 
 763.2 
 
 + 0.18 
 
 2.36 
 
 O.OO 
 
 30 
 
 763-5 
 
 0.08 
 
 2.22 
 
 + 0.03 
 
 35 
 
 762.4 
 
 0.30 
 
 1.85 
 
 0.06 
 
 40 
 
 760.5 
 
 0.51 
 
 I.4I 
 
 0.07 
 
 45 
 
 757-3 
 
 0.73 
 
 I.OO 
 
 0.09 
 
 50 
 
 753-2 
 
 0.91 
 
 0.50 
 
 O.IO 
 
 55 
 
 748.2 
 
 0.97 
 
 0.00 
 
 + 0.10 
 
 60 
 
 743-4 
 
 0.83 
 
 
 
 65 
 
 739-7 
 
 0.56 
 
 
 
 -70 
 
 738.0 
 
 
 
 
 From the preceding table it is seen that the mean normal 
 pressure of latitude is greatest in the northern hemisphere 
 about the parallel of 3-5, and in the southern hemisphere a 
 little nearer the equator, about the parallel of 30, and that 
 there is an equatorial depression and a polar one in each hemi- 
 sphere, in accordance with the theoretical deductions of 93. 
 The mean pressure gradient is greater in the southern than in 
 the northern hemisphere, and is especially large in the vicinity 
 of the parallel of 55 S., as it should be according to theory 
 -and the theoretical expression of G, 91, since the east and 
 west components of velocity, or values of v , are greater in the 
 
144 THE CENEKAL CIRCULATION OF THE ATMOSPHERE. 
 
 former than in the latter, and the east component is especially 
 large at and near the parallel of 55 ( 88). The pressure gra- 
 dients, being reckoned on the meridian from the north toward 
 the south pole, have contrary signs generally on corresponding 
 parallels of the two hemispheres. 
 
 96. The coefficients of the annual inequalities AP and AG 
 in the preceding table, added to the mean pressure and mean 
 pressure gradient for the year, give the mean pressure and 
 mean pressure gradient for January, and subtracted, those for 
 July. It is seen, therefore, that the pressures, by observation, 
 are greatest in each hemisphere during the winter of that 
 hemisphere, except very near each pole, as required by theory, 
 94. The annual inequality of pressure, by the theory, is the 
 result of two separate effects, which in the middle and lower 
 latitudes of each hemisphere are both in the same direction,, 
 tending to increase the pressure in the winter season of the 
 hemisphere. But the effect which arises from the bulging up 
 of the isobaric surfaces in the middle and lower latitudes, 
 and a corresponding depression in the polar latitudes, has a 
 contrary sign in the polar latitudes, and seems to be of such a 
 magnitude as to more than counteract the other effect, and hence 
 in these latitudes the annual inequality is reversed, and the baro- 
 metric pressure is less during the winter than the summer sea- 
 son. There is, consequently, a parallel very near the pole in 
 the northern hemisphere, but near the parallel of 55 m the 
 southern, where there is no annual inequality of barometric 
 pressure. 
 
 The annual inequality of pressure is greater in the southern 
 than in the northern hemisphere, and the maximum nearer the 
 equator, being in the southern hemisphere on the parallel of 
 25, while in the northern it is about the parallel 32. 5. This 
 arises from the greater amount of water surface and conse- 
 quently less amount of frictional resistance to the east and west 
 components of motion at the surface in the southern hemi- 
 sphere than in the other. For since, on this account, there is a 
 greater mean bulging up of the strata of equal pressure in the 
 middle and lower latitudes, and depression of them in the 
 
EAST VELOCITIES DEDUCED FROM PRESSURE GRADIENT. 145 
 
 polar latitudes, corresponding to the mean temperature gra- 
 dients of the year, in the southern than in the northern hemi- 
 sphere, the annual inequality of pressure corresponding to the 
 annual inequality of temperature must likewise be greater in 
 the former than in the latter, for the effect of the annual 
 reversion of the interchanging motions between the two 
 hemispheres, upon the east components of motion of the 
 atmosphere, and consequently upon the pressures, must be 
 the greater in the hemisphere which has the more water sur- 
 face. 
 
 EAST VELOCITIES DEDUCED FROM PRESSURE AND TEMPERA- 
 TURE GRADIENTS. 
 
 97. To any pressure gradient G at the earth's surface, or 
 any altitude above it, there is a corresponding velocity v of 
 east or west component of motion, 91, so that if one is known 
 the other may be approximately computed. We can more 
 easily obtain from observation the normal gradients of pressure 
 than the east or west component of wind velocity, and there- 
 fore this component can be more readily obtained from the ob- 
 served pressure gradients than directly from observation. For 
 instance, taking the parallel of 50 N. for an example, we find in 
 the preceding table the normal gradient of pressure at the 
 earth's surface is 0.18 mm. With this value of G and the value 
 of sin 50, Table V, we readily get from the special expression 
 of G in 91, v = 1.5 m. as the east component of velocity at 
 the earth's surface. Now from the temperature differences for 
 10 preceding and following the latitude of 50 for the mean 
 of the year, 68, we get approximately the gradient Ar = 
 (7-9 + 7-3)/ 20 = -76. This is for the distance of one degree, in> 
 which case the numerical coefficient 0.00221 must be used in 
 the expression of v in 77. With these values of v and AT 
 this expression gives for the altitude h 1000 meters, v = 
 1.5 + 2.2 = 3.7 m. for the value of the east component of mo- 
 tion, in meters per second, at the height of one kilometer. For 
 any other altitude the last term would be increased in propor- 
 tion. Thus, for an altitude of 5 kilometers we should have 
 
146 THE GENERAL CIRCULATION OF THE ATMOSPHERE. 
 
 <v 1.5 x 2.2 X 5 = 12.5 in meters per second. Multiplying 
 by 3.6, we get v = 45 in kilometers per hour. 
 
 98. Somewhat in the same manner, the following table of 
 values of v in kilometers per hour have been computed for the 
 mean of the year, and for January and July, for each fifth de- 
 gree of latitude, except near the equator and the poles, where 
 the formula and the data are too uncertain. The temperature 
 gradients, however, were obtained by another method, more 
 accurate than that used above. 8 
 
 Lcititu.de 
 
 
 
 V 
 
 
 
 
 
 Mean of the Year 
 
 
 January. 
 
 
 July. 
 
 
 
 km. 
 
 
 km. 
 
 
 km. 
 
 
 + 75 
 
 4.4 + 4.8 / 
 
 i 
 
 1.9 + 4.4 / 
 
 t 
 
 5-7 + 5-1 J 
 
 
 70 
 
 3-3 6.6 
 
 
 - LI 7.5 
 
 
 4-8 5-8 
 
 
 65 
 
 + 0.2 7-7 
 
 
 + 1.6 9.6 
 
 
 1.2 5.9 
 
 
 60 
 
 3.9 8.3 
 
 
 5-5 10.9 
 
 
 + 2.3 5-6 
 
 
 \ 55 
 
 5-5 8.5 
 
 
 7.0 ii. 6 
 
 
 4-o 5.4 
 
 
 50 
 
 5.4 8.6 
 
 
 6.4 12. I 
 
 
 4.4 5-i 
 
 
 45 
 
 4.9 8.8 
 
 
 5-5 126 
 
 
 4.1 5.0 
 
 
 40 
 
 + 2.6 9.0 
 
 
 + 2.8 12.9 
 
 
 + 2.4 4.8 
 
 
 1 35 
 
 -1.2 9.3 
 
 
 i.o 13.8 
 
 
 1.4 4.6 
 
 
 30 
 
 8.6 9.5 
 
 
 9.1 14.7 
 
 
 8.1 4.3 
 
 
 25 
 
 14-4 9-4 
 
 
 16.0 15.2 
 
 
 12.2 3.6 
 
 
 20 
 
 15-1 9- 
 
 
 2O. 2 15.6 
 
 
 ii. 7 2.4 
 
 
 + 15 
 
 12.5 5.6 
 
 
 21.8 10.5 
 
 
 3.8 0.6 
 
 
 
 
 
 
 
 
 
 15 
 
 25.0 8.2 
 
 
 18.7 4.9 
 
 
 31.0 ii. 7 
 
 
 2O 
 
 20.9 7.8 
 
 
 18.8 5.8 
 
 
 23.0 10.0 
 
 
 25 
 
 10.3 7.6 
 
 
 10.4 6.6 
 
 
 16.1 8.7 
 
 
 r 30 
 
 + 3-8 7-5 
 
 
 + 2.3 7.3 
 
 
 + 5-2 7-8 
 
 
 > 35 
 
 12.4 7.4 
 
 
 10. 7.8 
 
 
 14.4 7.1 
 
 
 40 
 
 18.7 7.4 
 
 
 16.0 8.2 
 
 
 21.4 6.7 
 
 
 45 
 
 24.0 7.4 
 
 
 21.0 8.6 
 
 
 27.0 6.4 
 
 
 50 
 
 27-5 7-5 
 
 
 24.5 8.9 
 
 
 30.5 6.1 
 
 
 55 
 
 27-3 7-5 
 
 
 + 24.6 + 9.1 
 
 
 30.0 5.9 
 
 
 60 
 
 + 21.9+7.5 
 
 
 
 
 
 
 By adding together the two parts of the value of v, the first 
 being v , the value of v at the earth's surface, where kQ, and 
 depending upon and deduced from the pressure gradient there, 
 and the second depending upon the altitude h r we get the east 
 component of velocity v in kilometers per hour at any given 
 altitude h in kilometers. But by reducing the first part to 
 
IE AST VELOCITIES DEDUCED FROM PRESSURE GRADIENT. 147 
 
 miles by multiplying by 0.62 we get the result in miles per hour 
 if the value of h is given in miles. For instance, on the paral- 
 lel of 50 N. and for altitude h = 5 kilometers, we have for the 
 mean of the year v 5.4 + 8.6 X 5 = 48.4 kilometers per 
 hour. This 'differs a little from the result of the preceding 
 computation with the temperature gradient deduced approxi- 
 mately from first differences merely where the intervals are ten 
 degrees of latitude. In like manner, by reducing the first part 
 to miles, we have i/= 3.3 + 8.6 X 5 = 46.3 miles per hour for 
 the east component of velocity at the altitude h = 5 miles. 
 
 In the same way we get, on this same parallel of latitude, 
 v = 4.0 + 12. i X 5 =64-$ miles per hour for the approximate 
 ast component of velocity of the air at the altitude of 5 miles 
 in January, and v = 2.8 -f- 5.1 X 5 = 28.3 miles per hour for 
 this velocity in July. Hence the east component of velocity at 
 considerable altitudes is more than twice as great in January 
 as in July on this latitude, and the same is true of the middle 
 and higher altitudes generally in the northern hemisphere, as 
 has already been deduced in a general way in 78. At and 
 near the earth's surface, however, where the value of v depends 
 mostly upon v , and especially in the lower latitudes where the 
 value of v is considerable and negative, the ratio between Jan- 
 uary and July is a little different, since it depends mostly or 
 entirely upon that of f for the two extremes of the seasons, in 
 which the uncertainty of friction corresponding to different 
 velocities comes in, so that this part, as deduced from the 
 barometric gradients of pressure, does not quite have the same 
 relations between the different seasons as the temperature 
 gradients. 
 
 In the lower latitudes, where there is a west component of 
 motion at the earth's surface, we have V Q negative, and so these 
 west components of velocity are diminished above by the 
 quantity, for the different altitudes, in the preceding table 
 depending upon h, so that at certain altitudes they become 
 reversed and become east components of velocity. Thus on 
 the parallel of 20 N. we have, for the mean of the year, v = 
 15.1 -4-Q.O/t. It is readily seen that in order to make v van- 
 
148 THE GENERAL CIRCULA TION OF THE A TMOSPHERE. 
 
 ish we must have h = 15.1/9.0= 1.7 km. nearly for the alti- 
 tude where v vanishes and changes sign, and where, consequent- 
 ly, there is no east or west component of motion of the air. It 
 is seen from the table that this altitude differs for different 
 parallels of latitude and the different seasons, of the year, being 
 very small at the parallel of 30 and gradually increasing toward 
 the equator, and being also, at and within the tropics, very 
 much greater in July than in January. 
 
 In the southern hemisphere on the parallel of 50 we have 
 for the mean of the year at the altitude of 5 kilometers, v = 
 27.5 -f- 7.5 X 5 = 65 kilometers for the east component of veloc- 
 ity of the air per hour. This is considerably greater than that 
 obtained above for the same latitude and altitude in the north- 
 ern hemisphere, due to the greater east component of velocity 
 at the earth's surface for reasons already explained. The differ- 
 ences between January and July, as given by this table, are 
 very small in comparison with those of the northern hemisphere 
 on account of the comparatively small differences, generally, in 
 the temperatures, as may be seen from the table of 68. 
 
 99. We have seen that the maximum atmospheric pressure, 
 92, in going at any altitude horizontally toward the equator, 
 occurs where v = o ; and hence the latitude of greatest pressure 
 at any given altitude is readily ascertained approximately from 
 a mere inspection of the preceding table, it being on the parallel 
 which makes the expression of v vanish at the given altitude. 
 Thus, in the northern hemisphere, for the mean of the year, at 
 the altitude of one kilometer, the latitude on which this condi- 
 tion is satisfied is a little below 30, while at the earth's surface 
 the greatest pressure is about 36. At greater altitudes this 
 latitude is still nearer the equator, but the exact latitude be- 
 comes more uncertain on account of the uncertainty of the 
 data, and the small changes of pressure with a given change of 
 latitude at these altitudes. Above a certain altitude, it is read- 
 ily seen, so far as the table extends, that the condition cannot 
 be satisfied, and hence east velocities prevail above this altitude. 
 
 From the applications which have been made of the pre- 
 ceding table, both to the east and west component of velocity 
 
SURFACE WINDS, CALMS, AND CALM-BELTS. 149 
 
 of the air and to the pressures, it is seen that this table is of 
 great importance in studying the general motions and pressures 
 of the atmosphere on different parallels of latitude and at dif- 
 ferent altitudes, and also their annual changes with the seasons 
 of the year, although the results are to be regarded as being 
 only approximate, and, near the equator, not at all accurate. 
 
 SURFACE WINDS, CALMS, AND CALM BELTS. 
 
 100. So far we have considered mostly the general circula- 
 tion of the great mass of the atmosphere generally, and deter- 
 mined the effect of this in connection with the deflecting forces 
 of the earth's rotation, upon the atmospheric pressures. We 
 come now to consider the reflex and secondary action of this 
 modified pressure in modifying the general circulation arising 
 directly from the temperature gradients between the equator 
 and the poles and the deflecting forces. It has been shown, 
 93, that in this modified pressure there is a zone of high pres- 
 sure in each hemisphere, with its maximum pressure near the 
 parallel of 30, and extending all around the globe. The effect 
 of this is to cause the air at the earth's surface to flow out from 
 beneath, on the one hand toward the equator, and on the other 
 toward the pole. In the former case the flow of air at the sur- 
 face, combining with the general flow in the lower strata from 
 the pole toward the equator, and acted upon by the deflecting 
 force of the earth's rotation, adds greatly to the strength of the 
 trade-winds. In the latter case, the flow being in a direction 
 contrary to that of the general flow of the lower strata from 
 the pole toward the equator, and being also a little stronger at 
 and near the earth's surface, there is a residual motion toward 
 the pole in the middle latitudes, which, also acted upon by the 
 deflecting force of the earth's rotation, inclines toward the east, 
 and gives rise to the gentle southwest winds in the northern 
 and northwest winds in the southern hemisphere in these lati- 
 tudes. 
 
 It must be borne in mind in this connection that we are not 
 here considering the actual circulation and other conditions of 
 
ISO THE GENERAL CIRCULATION OF THE ATMOSPHERE. 
 
 the atmosphere as disturbed from various abnormal causes, but 
 the case of an earth with a homogeneous surface, and with 
 uniform temperatures at all longitudes on the same latitudes. 
 To the results here obtained must still be added those depend- 
 ing upon the irregular and abnormal disturbances in order to 
 get the true results as observed. 
 
 The effect of these zones of high pressure, with their maxi- 
 ma in the lower part of the atmosphere nearer the equator as the 
 altitude is increased, is undoubtedly felt to a considerable alti- 
 tude, but mostly near the earth's surface. Above, where there 
 is little friction, the equatorial and polar motions arising from 
 pressure gradients, however produced, we have seen give rise 
 to east or west components of motion which, by means of the 
 deflecting forces of the earth's rotation, almost entirely coun- 
 teract the effect of the pressure gradients, and leave the veloci- 
 ties of the polar and equatorial motions very small in compari- 
 son with what they otherwise would be, except very near the 
 equator, where the deflecting forces are very small. But near 
 the earth's surface, where the friction is great, it requires 
 greater polar and equatorial components of motion to overcome 
 the friction and to keep up east and west components of velocity 
 which, by means of the deflecting forces arising from them,, 
 would materially interfere with the free outflow below. Besides,, 
 since this outflow of air below from beneath the high pressure 
 is confined mostly to a comparatively thin stratum at the 
 earth's surface, there is great resistance to this flow both from 
 friction between it and the earth's surface and from the strata 
 above, which have much less motion, and this in a somewhat 
 different direction, since the motion above is more nearly in an 
 east or west direction. It is therefore necessary to have com- 
 paratively small east or west components of velocity, so as to- 
 leave nearly the full force of the pressure gradient to overcome 
 the resistance to the polar and equatorial motions near the 
 earth's surface. For two reasons, therefore, it is necessary 
 here, and wherever there is much friction, that the polar and 
 equatorial components of motion shall be large in comparison 
 with the east and west ones. While therefore the motions o 
 
SURFACE WINDS, CALMS, AND CALM-BELTS. !$! 
 
 the air are nearly in a direction either east or west on each side 
 of the zone of high pressure at a small elevation above the 
 earth's surface, at and near the surface they deviate consider- 
 ably from these directions, and assume more nearly polar and 
 equatorial directions. Looking at the matter in a more general 
 way, all the conditions of the general atmospheric circulation, 
 in the case of no friction, are satisfied with east and west mo- 
 tions only ; for the initial motions may be such that the deflect- 
 ing forces of these motions exactly counteract the forces aris- 
 ing from the temperature and pressure gradients. But the 
 greater the friction and the less the deflecting forces of the 
 earth's rotation, the greater must be the equatorial and polar 
 motions in comparison with the others, and the greater the 
 deviation of the resultant from an east or west direction. As 
 the deflecting force of the earth's rotation becomes small on 
 the trade-wind parallels, the trade-winds have a smaller west 
 component of motion than they otherwise would have in com- 
 parison with the other component. 
 
 101. It is probable that the polar motion of the lower part 
 of the atmosphere in the middle latitudes does not extend, so 
 as to be sensible, beyond about the parallel of 60 in either 
 hemisphere. In the northern hemisphere there are too many 
 abnormal disturbances for the determination of this limit. In 
 the southern hemisphere, on account of the smooth-water sur- 
 face in the middle and polar latitudes, there are fewer disturb- 
 ances of this sort ; but here there is a great deficiency of obser- 
 vations : the few, however, which have been made indicate that 
 in the polar region south of the parallel of 60 or 65 there is an 
 equatorial component of motion. With regard to the winds of 
 this region Coffin says : 19 
 
 " Of the third system, comprising the southern polar winds, our 
 knowledge is confined to the months of winter and early spring (of the 
 northern hemisphere). Of the five resultants near the margin of the 
 zone, 60 to 65, all are from nearly a south point. Of the whole fifteen 
 within the zone only five tend toward, and two of them but slightly so, 
 while ten recede from it, generally at a large angle." 
 
 It seems, therefore, that in the polar regions of this 
 
152 THE GENERAL CIRCULATION OF THE ATMOSPHERE. 
 
 hemisphere the winds, upon the whole, have a component of 
 motion from the pole. 
 
 102. It has been shown, 78, that the east component of 
 velocity of the air at the earth's surface in the middle and 
 polar latitudes depends upon the rapidity of the vertical circu- 
 lation and the relative motions of the strata with reference to 
 one another at different altitudes. But these relative motions, 
 or differences of motion of different strata, depend upon the 
 deflecting forces of the earth's rotation ; and where these forces 
 are very weak, they do not nearly come up to the limit given 
 by the expression of v in 77, which gives the limit beyond 
 which the value of VV Q cannot go, and consequently to the 
 relative velocities between the strata having an east component 
 of velocity ^ at the earth's surface, and v at any altitude h. 
 
 The forces deflecting towards the east or west depend upon 
 the horizontal polar or equatorial velocity, as is seen from the 
 expression of F u , 49. But very near the poles the value of u 
 nearly vanishes, since the interchanging motion of any particle 
 of air between the equatorial and polar regions is oscillatory, 
 having its greatest velocity in the middle latitudes, which grad- 
 ually decreases both toward the equator and the poles, and 
 nearly vanishes just before it arrives at its greatest limit of 
 range. Near the po^e, therefore, there is not much difference 
 between the east components of velocity of the upper and 
 lower strata, and consequently little force to overcome the 
 friction at the earth's surface and keep up an east component 
 of velocity there. Since, therefore, this component of velocity 
 in the polar regions is small, and also the component of motion 
 from the poles, these must be regions in which there is very 
 nearly a calm, unless there is some abnormal disturbance. 
 
 At and near the equator the deflecting forces which cause 
 a difference in the east and west components of velocity at 
 different altitudes vanish, or nearly so, for two reasons : the 
 one, because as near the pole, and for the same reason, there is 
 little motion either toward or from the equator ; and the other, 
 because the deflecting forces here, with any given velocity u of 
 motion toward or from the equator, decrease as sin / de- 
 
SURFACE WINDS, CALMS, AND CALM-BELTS. 1 53 
 
 ^creases, and entirely vanishes at the equator. The relative 
 velocities between the strata, therefore, vanish at, and are very 
 small near, the equator ; and consequently the same is the case 
 with the force which overcomes the friction at the earth's sur- 
 face and maintains an east or west component of motion there. 
 And as there is no motion north or south between the systems 
 of winds of the two hemispheres where the trade-winds meet, 
 which is near the equator, there is here a belt of calms extending 
 around the globe, where not interfered with by abnormal dis- 
 turbances or forces not considered in the general circulation of 
 the atmosphere. 
 
 103. For reasons given in 80 there can be no east or west 
 'Component of motion at the earth's surface on the parallel of 
 maximum atmospheric pressure on the earth's surface, at or 
 near the parallel of 30. And as the air is pressed out at the 
 -earth's surface, toward the pole on the one side and the equa- 
 tor on the other, from beneath the zone of high pressure, there 
 is no sensible motion north or south in the middle part of this 
 .zone. There is then here, in each hemisphere, a belt of calms, 
 extending around the globe, and having its middle on this par- 
 allel of latitude, except so far as it is interfered with by abnor- 
 mal disturbances not here considered. 
 
 Since the deflecting forces arising from the much greater 
 east components of velocity in the southern hemisphere, both 
 at the earth's surface and at all altitudes, are much stronger 
 than the similar and opposing forces of the northern hemi- 
 sphere, the southern system of circulation encroaches some- 
 what upon the area of the other, causing all the calm-belts to 
 be a little further north than they otherwise would be, so that 
 the equatorial calm-belt is a little north of the equator, while 
 the tropical calm-belt of the northern hemisphere is a little fur- 
 ther from the equator than that of the southern hemisphere. 
 For the same reason there is, on the average of the year, a lit- 
 tle more air in the northern than in the southern hemisphere, 
 as may be seen from an inspection of the barometric pressures 
 in the second column of the table of 95, although the maxi- 
 mum about the parallel of 30 in the southern hemisphere is a 
 
154 THE GENERAL CIRCULATION OF THE ATMOSPHERE. 
 
 little greater than that of the northern, on account of a little 
 greater bulging up of the isobaric surfaces. 
 
 SUMMARY AND GRAPHIC REPRESENTATION OF THE MOTIONS 
 AND PRESSURES. 
 
 104. In the preceding part of this chapter it has been shown 
 that if all parts of the atmosphere had the same temperature 
 there would be a complete calm over all parts of the earth's 
 surface. But that in consequence of the difference of temper- 
 ature between the equatorial and polar regions of the globe, 
 and the consequent temperature gradient, there arise pressure 
 gradients and forces which give rise to and maintain a vertical, 
 circulation of the atmosphere with a motion of the air of the 
 upper strata of the atmosphere from the equator toward the 
 poles, and a counter current in the lower part from the poles 
 toward the equator, as represented by the arrows in the follow- 
 ing figure, and that this of course requires a gradual settling 
 down of the air from the higher to the lower strata in the mid- 
 dle and higher latitudes, and the reverse in the lower latitudes. 
 It has also been shown that in case the earth had no rotation 
 on its axis, this would be exclusively a vertical circulation in 
 the planes of the meridians without any east or west compo- 
 nents of motion in any part ; but that, in consequence of the 
 deflecting forces arising from the earth's rotation, the atmos- 
 phere at the earth's surface has also an east component of mo- 
 tion in the middle and higher latitudes, and the reverse in the 
 lower latitudes, and that the velocities of the east components 
 increase with increase of elevation, so that at great altitudes 
 they become very much greater than those at the earth's sur- 
 face ; wjiile those of the west components decrease with in- 
 crease of altitude up to a certain altitude, where they vanish 
 and change signs and become east velocities, now increasing 
 with increase of altitude to the top of the atmosphere. 
 
 It has been further shown that the deflecting forces arising 
 from the cast components of motion of each hemisphere from 
 the earth's surface to the top of the atmosphere, in the middle 
 
SUMMARY OF THE MOTIONS AND PRESSURES. 
 
 and higher latitudes and of the upper part of the atmosphere 
 in the lower latitudes, drives the atmosphere from the polar 
 regions toward the equator, while those arising from the west- 
 components of motion in the lower part of the atmosphere in 
 the lower latitudes, having a contrary effect, but small in com- 
 parison with the other on account of the weakness of these 
 forces near the equator, tend to drive the air a little from the 
 equator toward the poles. There is, therefore, a depression of 
 the isobaric surfaces at all altitudes in the polar regions, espe- 
 cially in the southern hemisphere, a much smaller depression- 
 in the equatorial regions, and a bulging up of the isobaric sur- 
 faces in the vicinity of the parallel of 30 in the lower part of 
 the atmosphere, the maximum being nearer the equator as the- 
 altitude increases, as represented in Fig. 4, but at high altitudes. 
 there is a minimum of barometric pressure at the poles and a. 
 maximum at the equator. 
 
 In the accompanying figure the solid arrows in the interior 
 part represent the resultant motions of the winds (longer ar- 
 
1156 THE GENERAL CIRCULATION- OF THE ATMOSPHERE. 
 
 rows indicating greater velocities), in case of an earth with a 
 homogeneous surface over both hemispheres, in which the mo- 
 tions would be symmetrical in both and the same at all longi- 
 tudes, and the equatorial and tropical calm-belts would be situ- 
 ated at equal distances from each pole. The dotted arrows 
 indicate the strong, almost eastern motion of the air at all lati- 
 tudes at some high altitude, as that of the cirrus clouds. 
 
 The outline of the outer part of the figure represents an 
 isobaric surface high up where the bulging up near the parallel 
 of 30 disappears and the maximum pressure at the same alti- 
 tude is transferred to the equator. For lower altitudes the 
 .isobaric surfaces have a bulging up at the parallel of 30, and 
 a slight depression at and near the equator. The arrows in this 
 part represent the polar and equatorial components of motion, 
 the former above and the latter below, except near the earth's 
 .surface on the polar sides of the tropical calm-belts, where 
 there is a polar component of motion arising from the air's be- 
 ing pressed out from under the belt of high pressure. This, 
 perhaps, does not extend beyond the polar circles, beyond 
 which there can be little motion in any direction, except from 
 abnormal disturbances. 
 
 For reasons given in 103, the actual mean positions of the 
 equatorial and tropical calm-belts are not precisely as here rep- 
 resented, but are all a little displaced toward the north pole, 
 and the polar depression of the isobaric surfaces is greater in 
 the southern than in the northern hemisphere. 
 
 ANNUAL OSCILLATION OF THE CALM-BELTS. 
 
 105. For the same reason that there is a semi-annual inver- 
 sion of the interchanging motions between the two hemispheres, 
 in the one direction in the spring and the contrary in the fall, 
 from which results an annual inequality of the atmospheric 
 pressure at the earth's surface, 94, there is also an annual 
 oscillation of the calm-belts. During the summer of the north- 
 ern hemisphere, while there is a flow of air below from the 
 
ANNUAL OSCILLATION OF THE CALM-BELTS. l$f 
 
 southern to the northern hemisphere and the contrary above, 
 the vertical circulation and interchanging motion of the south- 
 ern hemisphere, due to the difference of the mean temperatures 
 of the equatorial and polar regions, is strengthened while that 
 of the northern hemisphere is weakened. The consequence is 
 that the southern stronger system at this season encroaches 
 somewhat upon the territory of the other, causing the middle 
 of the equatorial calm-belt, which is the dividing line between 
 the two systems, to be a little north of its mean position ; and 
 as the tropical calm-belts are intermediate between the equa- 
 torial calnrubelt and the poles, and their positions must depend 
 somewhat upon the extension and the limits of the systems, 
 respectively to which they belong, the positions of these also 
 must be thrown further north, when that of the equatorial calm- 
 belt is. Of course just the reverse takes place during the 
 winter of the northern hemisphere. There is, therefore, an 
 annual oscillation of all the calm-belts, such that they have 
 their most northerly position in midsummer and the reverse in 
 midwinter of the northern hemisphere. 
 
 Or looking at the matter in a somewhat different way, we 
 have seen that the southern system of circulation, for the mean 
 of the year, especially the east components of motions, due to 
 the same temperature gradients, or nearly, between the equator 
 and the poles as in the northern hemisphere, is stronger than 
 that of the northern one on account of there being less frictional 
 resistance at the earth's surface to the former than to the latter, 
 and that in consequence of this the mean position of the equa- 
 torial calm-belt is a little north of the equator and both the 
 tropical calm-belts are a little farther north than they otherwise 
 would be, and so at unequal distances from the equator. Now 
 the effect is the same whether we diminish the resistance or 
 increase the forces. In the summer season, therefore, of the 
 northern hemisphere, when the forces are increased in the 
 southern and diminished in the northern hemisphere, we have 
 exactly the same effect as where the resistances are less in 
 the southern and greater in the northern hemisphere, namely,. 
 
158 THE GENERAL CIRCULATION OF THE ATMOSPHERE. 
 
 that all the calm-belts are thrown a little to the north of their 
 >mean positions, or positions which they otherwise would have ; 
 and the reverse in the winter season of the northern hemi- 
 sphere. 
 
 106. Since the equatorial calm-belt depends upon two 
 circumstances, the meeting below of the air currents belonging 
 to the two hemispherical systems of circulation, and the vanish- 
 ing of the forces which cause a westerly motion of the air, its 
 northern limit is better defined than the equatorial or southern 
 limit, and its range of oscillation is greater. In the summer 
 reason of the northern hemisphere, when the lower currents of 
 the two system meet at a greater distance north of the equator, 
 the forces on the north side of the belt which gives rise to the 
 west component of motion are very much stronger than those 
 on the equatorial side very near the equator, where these forces 
 almost entirely vanish. Over the whole space therefore be- 
 tween the calm-belt and the equator these forces sensibly vanish, 
 so that, although the southeast trade-winds blow beyond the 
 equator, yet they have here, and for a few degrees north of the 
 equator, no west component of motion, and become southerly 
 winds, and of little strength on account of their being so near 
 the place of meeting where all motion ceases. The winds, then, 
 between the equator and the calm-belt are weak, especially at 
 the season when this belt is near the equator, so that the 
 southern limit of the belt is then uncertain, and the southeast 
 trade-winds appear to vanish soon after passing the equator, 
 and even when the belt has its most northerly position these 
 winds are too weak to be observed far beyond the equator. 
 There is, therefore, an apparent widening of the calm-belt dur- 
 ing the summer season of the northern hemisphere. 
 
 107. The preceding theoretical deductions with regard to 
 the calm-belts are fully confirmed by observations of the trade 
 winds in both the great oceans of both hemispheres. 
 
 The following table of the northern limits, in different longi- 
 tudes, of the northeast trade-wind in the Atlantic Ocean was 
 given by Maury : l3 
 
ANNUAL OSCILLATION OF THE CALM-BELTS. 
 
 59 
 
 LONGITUDE AAr . 
 
 LATITUDE OF COMMENCEMENT OF N.E. TRADES IN 
 
 
 Winter. 
 
 Spring. 
 
 Summer. 
 
 Autumn. 
 
 70 
 
 28 
 
 28. 7 
 
 29 -3 
 
 29. o 
 
 65 
 
 26.3 
 
 28 .0 
 
 29 -3 
 
 28 .3 
 
 60 
 
 24 
 
 24 -3 
 
 27 -3 
 
 28 .3 
 
 55 
 
 22 
 
 22 .7 
 
 24 -7 
 
 25 .0 
 
 50 
 
 21 
 
 23 -7 
 
 28 .3 
 
 23 .7 
 
 45 
 
 23 
 
 24 -7 
 
 31 -3 
 
 28 . 7 
 
 40 
 
 27.7 
 
 29 -7 
 
 30 -7 
 
 29 -3 
 
 35 
 
 26 
 
 27 -3 
 
 30 .7 
 
 25 -7 
 
 30 
 
 24-3 
 
 28 .7 
 
 29 -7 
 
 26 .7 
 
 25 
 
 25-3 
 
 24 .7 
 
 3i -3 
 
 26 .3 
 
 20 
 
 24-3 
 
 28.3 
 
 28 .7 
 
 27 .0 
 
 15 
 
 29 
 
 31 .0 
 
 32 .0 
 
 3i -3 
 
 10 
 
 
 
 31 -3 
 
 34 -7 
 
 32 .0 
 
 The following tables were prepared by Woeikoff from the 
 " Pilot *Chart of the Atlantic Ocean," edited by the Meteoro- 
 logical Office in London : 20 
 
 MEAN POLAR LIMITS OF THE N.E. TRADE-WIND. 
 
 MONTHS. 
 
 MERIDIANS WEST. 
 
 65 
 
 60 
 
 55 
 
 50 
 
 45 
 
 40 
 
 35 
 
 30 
 
 25 
 
 20 
 
 17 
 
 Jan. to Mar.. 
 Apr. to June. 
 July to Sept. 
 Oct. to Dec. . 
 
 26 
 28.5 
 27 
 26 
 
 25 
 
 24.5 
 27 
 24 
 
 23- 5 
 
 23 
 
 26 .5 
 
 22 .5 
 
 23 
 25 
 26 
 22 
 
 24 -5 
 27 
 
 26 .5 
 
 22 .5 
 
 20 
 28 
 27-5 
 24-5 
 
 26. 5 
 
 28 
 27 -5 
 25 -5 
 
 25. 5 
 28 
 28 .5 
 
 25 -5 
 
 25. 5 
 28 .5 
 3i 
 26 .5 
 
 28. 5 
 32 
 31 -5 
 29 -5 
 
 30 
 33 
 32-5 
 3i 
 
 MEAN POLAR LIMITS OF THE S.E. TRADE-WIND. 
 
 MERIDIANS. 
 
 
 30 w. 
 
 25 W. 
 
 20 W. 
 
 15 W. 
 
 10 W. 
 
 sw. 
 
 o 
 
 SB. 
 
 10 E. 
 
 15 E. 
 
 Jan. to March 
 -April to June 
 
 19 -5 
 2= c 
 
 21 
 
 21 
 
 24 
 24 
 
 26. 5 
 
 2^ 
 
 28 
 25 
 
 29 
 
 27 
 
 30 
 
 28 5 
 
 3i. 5 
 
 32 
 
 32. 5 
 
 7-7 e 
 
 33 
 
 July to Sept 
 
 20 <; 
 
 22. 5 
 
 24 
 
 24 .5 
 
 27. 5 
 
 28.5 
 
 2Q. 5 
 
 2Q . 5 
 
 -JQ . *> 
 
 
 Oct to Dec 
 
 16 * 
 
 18 s 
 
 20 ^ 
 
 21 
 
 22 5 
 
 28 
 
 28 5 
 
 2Q 
 
 VQ 
 
 
 
 
 
 
 
 
 
 
 
 
 
l6o THE GENERAL CIRCULATION OF THE ATMOSPHERE. 
 
 EQUATORIAL LIMITS OF THE NORTHERN AND SOUTHERN: 
 
 TRADE-WINDS. 
 
 MONTHS. 
 
 MERIDIANS WEST. 
 
 40 
 
 35 
 
 3 
 
 25 
 
 20 
 
 *7 
 
 ( N. E .. 
 
 3 N. 
 i N. 
 1.5 N. 
 i S. 
 3-* N. 
 0.5 S. 
 8.5 N. 
 4 N. 
 11.5 N. 
 6 N. 
 6 N. 
 4-5 N. 
 
 i-5 N. 
 
 o .sN. 
 o 
 o -5S. 
 
 3 N. 
 o 
 
 9 N. 
 4 N. 
 
 12 N. 
 
 4 N. 
 6 N. 
 4 N. 
 
 2 N. 
 
 i N. 
 o.sN. 
 i S. 
 3-5 N. 
 
 2 N. 
 
 10 N. 
 3 N. 
 ii. 5N. 
 
 2 N. 
 
 6 N. 
 3-5N. 
 
 4- 5 N. 
 
 2 N. 
 
 2 .sN. 
 o .5 N. 
 5 -5N. 
 
 3 N. 
 
 12 N. 
 
 3 N. 
 ii N. 
 
 2 N. 
 
 6 N. 
 3 -5N. 
 
 6. 5 N. 
 
 3 N. 
 5 N. 
 o.sN. 
 8 .s N. 
 3 -5N. 
 14 N. 
 3 N. 
 
 12 N. 
 
 o N. 
 9 - 5 N. 
 4 N. 
 
 8 N. 
 3 N. 
 6 N. 
 i N. 
 
 Jan. ] s E 
 
 , N E .. 
 
 March |s E... :..::.. 
 
 ( N E 
 
 May ]s E 
 
 IN. E 
 
 J u] y \ s E 
 
 ( N E... 
 
 Sept. { 
 
 { N E . 
 
 NOV. If;!; 
 
 
 108. The first of the last three tables does not diffSr more 
 from the preceding one, given by Maury, than is to be expected 
 in determining a limit so ill-defined as that of the northern limit 
 of the northeast trade-wind, which is likewise the southern limit 
 of the northern tropical calm-belt. Either of these tables indi- 
 cates that there is an annual oscillation of this limit with a 
 range of about three degrees of latitude, and having its most 
 northerly position in midsummer. It is seen, also, that this 
 limit does not coincide with any parallel of latitude across the 
 Atlantic Ocean, but it has a more northerly position on each 
 side of the ocean than in the middle, the longitude of minimum 
 latitude being that of about 50 W. 
 
 There are observations that indicate that the northern limit 
 of this tropical calm-belt has a corresponding oscillation. When 
 this belt in the fall moves southward from its most northerly 
 position, it has been observed that the southwest winds are felt 
 first on the coast of Portugal, then at Madeira, and afterwards, 
 at Teneriffe and the Canaries. 
 
 The southern limit of the southeast trade-wind is not so well 
 determined from observation ; but according to the second of 
 the last three tables, this wind extends to about the same dis- 
 tance from the equator as the northeast trade-wind, and it has. 
 
ANNUAL OSCILLATION OF THE CALM-BELTS. l6l 
 
 also an annual oscillation corresponding to that of the northern 
 limit of the northeast trade-wind, having its most northerly 
 position about the same time, as required by theory, but this 
 oscillation is not so marked, the range being smaller. In this 
 case the limit lies nearest the equator on the west side of the 
 ocean, and is about ten degrees further towards the south on 
 the other side. 
 
 According to the last of the preceding tables, the equato- 
 rial limit of the northeast trade-wind, which is likewise the 
 northern limit of the equatorial calm-belt, has a range of annual 
 oscillation of about twelve degrees of latitude, from 20 to 40 
 W. longitude, with a position, at all seasons, a little more 
 northerly on the east than on the west side of the field of obser- 
 vation, the extreme northerly position here in summer being 
 about the parallel of 13 N. But the equatorial limit of the 
 southeast trade-wind, which is also the southern limit of the 
 equatorial calm-belt, has a much smaller range, for reasons 
 given in 102, it being only about five degrees on the west side 
 on the longitude of 40 W., and sensibly vanishing on the east 
 side of the ocean. The most southerly position, in March, is 
 about one degree south of the equator. 
 
 Since the northern limit of the equatorial calm-belt has a 
 much greater range of oscillation than the southern limit, 
 especially on the east side, it follows that this calm-belt is much 
 wider in summer than in winter, and especially so on the eastern 
 side of the ocean. 
 
 109. Kerhallet, according to Dove, 13 gave the following 
 table of the extent of the trade-winds in the Pacific Ocean, 
 compiled from the observations of 92 ships : 
 
 The irregularity in these numbers indicates that they are 
 not very accurate; but still they plainly show, as in the Atlantic 
 Ocean, that the limits of both the northeast and southeast 
 trade-winds have an oscillatory movement with a range, in the 
 equatorial limits at least, of several degrees of latitude, and 
 that the mean position of the equatorial calm-belt lies north of 
 the equator, and has a greater width in summer than in winter. 
 This greater width here, as in the Atlantic Ocean, it is seen 
 
1 62 THE GENERAL CIRCULATION OF THE ATMOSPHERE. 
 CONSIDERATIONS GENERALES SUR L'OCEAN PACIFIQUE, 1856. 
 
 MONTH. 
 
 POLAR LIMIT. 
 
 EQUATORIAL LIMIT. 
 
 Breadth 
 of 
 Calm-belt. 
 
 N.E. Trade, 
 Lat. N. 
 
 S.E. Trade, 
 Lat. S. 
 
 N.E. Trade, 
 Lat. N. 
 
 S.E. Trade, 
 Lat. N. 
 
 
 21 0' 
 28 28 
 29 o 
 30 o 
 25 5 
 27 4i 
 3i 43 
 29 30 
 24 20 
 26 6 
 
 25 9 
 24 o 
 
 33 25' 
 28 51 
 31 10 
 27 25 
 28 24 
 25 o 
 
 25 28 
 
 24 18 
 24 5i 
 23 27 
 28 39 
 
 22 30 
 
 6 30' 
 
 4 I 
 8 15 
 4 45 
 7 52 
 9 58 
 12 5 
 15 o 
 13 56 
 
 12 20 
 
 5 o' 
 
 2 
 
 5 50 
 
 2 O 
 
 3 36 
 
 2 30 
 
 5 4 
 
 2 30 
 
 8 n 
 3 32 
 
 1*56 
 
 3 30 
 
 2 I 
 * 2 25 
 
 2 45 
 4 16 
 7 28 
 
 7 i 
 12 30 
 
 5 45 
 8 48 
 
 3* 16 
 
 February 
 
 March 
 
 April 
 
 May 
 
 Jung , 
 
 Tulv . . 
 
 August 
 
 September 
 
 October 
 
 November . . . 
 
 December 
 
 5 12 
 
 
 from the table, is due to the greater range of oscillation of the 
 northern than of the southern limit of the belt. 
 
 We are not advised with regard to the part of the ocean 
 where the observations were mostly made, so that it is uncer- 
 tain whether these results are applicable to the belt generally 
 in this ocean, and whether the mean positions of the limits and 
 the range of oscillation may not differ considerably at different 
 longitudes. 
 
 It had formerly been supposed that the mean position of 
 these limits and of the central parts of the calm-belts in this 
 ocean were nearly symmetrically situated with regard to the 
 two hemispheres, the central line of the equatorial calm coin- 
 ciding with the equator. Kaemtz places the limits of the north- 
 east trade-wind at 23 and 2 N., and those of the southeast 
 trade-wind at 21 and 2 S. But the equatorial calm-belt in 
 this ocean, as in the Atlantic Ocean, doubtless lies a little north 
 of the equator. 
 
CHAPTER IV. 
 CLIMATIC INFLUENCES OF THE GENERAL CIRCULATION. 
 
 ON THE RELATIVE CLIMATES OF THE LOWER AND 
 HIGHER LATITUDES. 
 
 110. IN consequence of the interchange of equatorial and 
 polar waters, especially in the southern hemisphere, as ex- 
 plained in 68, the equatorial regions of the globe are colder, 
 and the polar regions warmer, than they otherwise would be. 
 A similar, but perhaps a much smaller, effect is produced by 
 the interchange of the warm air of the equatorial, and the cold 
 -air of the polar, regions in the general circulation of the atmos- 
 phere. Although the volume of air interchanged in a given 
 time is much greater than that of the water of the ocean, yet 
 the mass is probably less, since the mass of the whole atmos- 
 phere is only equal to that of an ocean covering the whole sur- 
 face of the earth of about 10 meters in depth, and as the 
 .specific heat of air is only 0.2375, the whole capacity of the 
 atmosphere for heat is only equal to that of an ocean of 2.5 
 meters in depth. If we suppose the ocean to have a uniform 
 depth of 5000 meters (3. 1 miles), the interchanging velocity in 
 the case of the atmosphere would have to be 2000 times as 
 great as that of the ocean to give rise to an equal transfer of 
 heat from the equatorial to the polar regions. The velocity of 
 interchange in the case of the atmosphere is, of course, much 
 the greater ; but it can scarcely be regarded as being 2000 times 
 as great as that of the ocean, for it must be remembered that 
 the motion of the atmosphere, except at the earth's surface, 
 and at all altitudes near the equator, is mostly easterly or 
 westerly, the polar and equatorial components of motion being 
 generally small in comparison with the east and west com- 
 ponents. It is probable, therefore, that the amount of heat 
 
 163 
 
164 CLIMATIC INFLUENCES OF THE GENERAL CIRCULATION. 
 
 transferred from the equatorial to the polar regions is less in' 
 the case of the atmosphere than in that of the ocean. But we 
 have reason to think that the difference of temperature be- 
 tween the equator and the polls is very much diminished by 
 the latter, and therefore the effect of the former in the same 
 direction must be at least quite sensible. 
 
 The relation between the hygrometric states of the atmos- 
 phere of the lower and higher latitudes is also affected by the 
 general vertical circulation. In the middle and higher latitudes- 
 there is a gradual settling down of the atmosphere toward the 
 earth's surface, where the temperature is higher than it is above ; 
 and so here the relative humidity gradually becomes less, and 
 being very small above it becomes still much less after having, 
 descended to the lower strata. In the lower latitudes, and. 
 especially near the equator, on the contrary, where there is a 
 gradual ascent of the air from the lower strata, where the tem- 
 perature is much greater, to the upper ones, where it is much, 
 less, the relative humidity is gradually increased, even, it may- 
 be, to complete saturation. Of course the absolute amount of 
 vapor in the higher latitudes, on account of the lowness of 
 temperature, is much less than in the lower latitudes, but if 
 there was the same relative humidity in both, the effect of the 
 vertical circulation would be to decrease that of the higher 
 latitudes and to increase that of the lower latitudes. 
 
 WET AND DRY ZONES. 
 
 111. As all the vapor of evaporation, or nearly, over both 
 trade-wind zones of about 20 in width, especially where the 
 trade-winds are regular, as on the ocean, is carried into the 
 comparatively narrow zone of the equatorial calm-belt before it 
 ascends to sufficient height to be condensed into rain, the 
 amount of rain falling in this belt is very large and the cloud 
 nearly continuous. The equatorial calm-belt, therefore, is also 
 a cloud- and rain-belt. The height to which the vapor of the 
 surface currents ascends before condensation and cloud-forma- 
 tion take place depends upon the amount of moisture in the- 
 
W 'ET AND DRY ZONES. 165 
 
 .air at the earth's surface, and so upon the difference between 
 the air temperature and that of the dew-point. The height at 
 'which condensation commences is given accurately by Table 
 IV, and is nearly, under all conditions, 125 meters for each 
 degree Centigrade of the depression of the dew-point below the 
 ,air temperature, as explained in 27. 
 
 The first vapor condensed is supported and carried farther 
 up by the ascending current in the form of cloud and small 
 particles of rain, and the more the stronger the current is. 
 Small particles are carried upward by the current, and the still 
 smaller ones more rapidly than the larger ones, and so the dif- 
 ferent sizes of the smaller drops, being carried up with different 
 velocities, come in contact and combine until they form drops 
 too large to be supported by the ascending current, and these 
 then fall as rain. The stronger the ascending current the 
 larger the drops. When there is no ascending current there is 
 no rain, though there may be fog and mist. 
 
 The daily amount of evaporation on the ocean within the 
 tropics is about one fourth of an inch per day. If then all this 
 amount of vapor over zones say 1000 miles in width on each 
 side 'is carried into the calm-belt say 300 miles in width, and is 
 there condensed and falls as rain, then the daily rainfall is 1.67 
 inches per day ; and if this belt were to remain stationary > it 
 would be, for the average of the width, about 60 feet per year. 
 But since the cloud- and rain-belt, as the calm-belt, oscillates 
 through a range generally more than twice as great as its width, 
 this amount of rain is distributed, in the course of the year, 
 over a zone more than three times as wide, and hence, in gen- 
 eral, less than one third of this amount falls in any one place 
 during the year. 
 
 The calm-belt, as it exists at any given time, is mostly nar- 
 rower than the belt on which rain falls ; for as the air in the 
 equatorial region generally, but mostly over the surface calm- 
 belt, ascends it gradually expands and diverges from the cen- 
 tral line of this belt to form the upper return current toward 
 the poles ; and before the vapor is all condensed, and while the 
 air is still ascending, it is carried out beyond the limits of the 
 
1 66 CLIMATIC INFLUENCES OF THE GENERAL CIRCULATION.. 
 
 calm-belt, so that considerable rain falls at some distance be- 
 yond these limits. 
 
 Of course neither the calm-belt nor the rain- and cloud-belt 
 has very definite limits, but these are much better defined over 
 the great oceans, where the trade-winds blow very steadily in 
 nearly the same direction and with the same force, than on the 
 continents, where regularity of outline is very much interfered 
 with by the various abnormal disturbances of uneven surfaces, 
 and mountain ranges, and likewise by the monsoons of the 
 Indian Ocean and others. The rain-belt is, however, clearly 
 traceable across the whole of Africa, wherever observations 
 have been made, as also across the American isthmus, but it 
 has greater width, and its limits are not so well defined. The 
 zone on which rain falls during the course of the year has been 
 given on a chart by WoeikofL 21 This, on the great oceans,, 
 lies mostly between i and 11 north latitude ; but on the west 
 coast of Africa it extends a little farther north, and on the east 
 coast of South America to about 5 south latitude. These 
 limits correspond pretty closely with the extreme northern 
 limit of the southeast trade-wind in January on the one hand, 
 and the extreme southern limit of the northeast trade-wind in 
 July on the other, as given in the tables of 107 and 109 ; 
 and so the rainy zone falls nearly within the range of oscillation 
 of the calm-belt. 
 
 112. Loomis" has given a chart of mean annual rainfall on 
 which the northern limit of the zone of 50 inches and upward 
 of mean annual rainfall, on the continent of Africa, lies mostly 
 between the parallels of 10 and 12 north latitude, but the 
 southern limit is more irregular and extends from a point near 
 the equator on the west coast to about 10 south on the east 
 coast of Africa. Beyond these limits, both north and south,, 
 there is a gradual shading off on the chart and diminution in 
 the amount of rainfall, so that although the rainy zone here 
 has no definite limits, yet the amount of rain falling a little 
 north of the equator, on the parallels of latitude corresponding 
 to those of the rain-belt on the oceans, as the result of the gen- 
 eral circulation of the atmosphere and meeting near the equa- 
 
WET AND DRY ZONES. 
 
 tor of the vapor-laden surface currents of the trade-winds is 
 unusually great, notwithstanding the amount of evaporation 
 over the land surface is much less than on the ocean, and this 
 vapor, on account of the inequalities of the land surface and 
 the frictional resistances, is not all carried so nearly into the 
 central line of the meeting of the trade-winds as on the smooth 
 ocean surface. 
 
 Farther east, over the islands of Sumatra, Java, Borneo, and 
 Celebes, and also over the Malayan peninsula, all lying on and 
 near the equator, the mean annual rainfall, according to the 
 chart, is still more abundant ; for they all fall within the zone 
 of 75 inches and over of rainfall, and at many individual sta- 
 tions the annual rainfall is over 150 inches, and even more 
 than 200 inches at Buitenzorg, Java, all going to show the ten- 
 dency to a concentration of rainfall in a zone at and near the 
 equator. The amount of rainfall here is much greater than 
 over the continent of Africa, because the amount of evapora- 
 tion over the warm ocean surface is greater ; but on account of 
 the monsoon influences, to be considered hereafter, this rain- 
 fall is scattered over a much wider zone than on the ocean 
 generally, and consequently the rainfall in the central parts of 
 the rainy zone is less, and the zone has no definite limits. 
 
 In the northern part of South America, a little north of the 
 equator, this chart does not indicate that there is a distinct and 
 well-defined rainy zone, as on the same parallels on the two 
 great oceans, because it is mostly obscured by the rainfalls over 
 a great part of South and Central America, arising from the 
 influence of the mountain chain of the Andes, to be explained 
 farther on. There is much evidence, however, to show that 
 here also there is, at least in many places, a distinct rain-belt, 
 oscillating with the seasons, and having, at any given time, 
 definite limits beyond which little or no rain falls. 
 
 The latent heat given out in the condensation of the great 
 amount of aqueous vapor carried into, and ascending in, the 
 calm-belt gives additional strength to the trade-winds. In con- 
 sequence of this heat the upper part of the air, above the plane 
 of incipient condensation, is not cooled by expansion down to 
 
1 68 CLIMATIC INFLUENCES OF THE GENERAL CIRCULATION. 
 
 the temperature of the air on each side, and hence the tendency 
 to ascend in this belt is very much stronger than that of the 
 air on each side, which simply ascends with sufficient rapidity 
 to supply the returning polar currents above, in the general 
 vertical interchange between the equatorial and polar regions, 
 which, we have seen, is small, the force arising from the differ- 
 ence of temperature between the equator and the poles being 
 almost entirely counteracted by the deflecting forces arising 
 from the earth's rotation. Hence there is a very rapid ascent 
 of air in this belt, which requires an increased equatorial com- 
 ponent of velocity in the trade-winds near the earth's surface to 
 supply it, and this adds greatly to their strength. This is en- 
 tirely a secondary matter, dependent upon the general vertical 
 circulation, for if it were not for this the air, with its aqueous 
 vapor, would not ascend at all, and hence no condensation 
 would take place. 
 
 113. The air within the rain-belt being almost entirely 
 calm, and also warm and nearly saturated with vapor, is always 
 extremely oppressive, such as is sometimes experienced for a 
 short time in other regions of the globe when the air is warm 
 and calm, and saturated, or nearly so, with aqueous vapor. A 
 graphic description of the kind of weather which is usually ex- 
 perienced under the cloud-ring of the equatorial calm-belt is 
 found, as cited by Maury, 23 in the journal of Commodore Sin- 
 clair, kept on board of the United States frigate Congress dur- 
 ing a cruise to South America in 1817-18. He crossed it in the 
 month of January, 1818, between the parallel of 4 north and 
 the equator, and between the meridians of 19 and 23 west. 
 He says of it : 
 
 "This is certainly one of the most unpleasant regions on our globe. 
 A dense, close atmosphere, except for a few hours after a thunder-storm, 
 during which time torrents of rain fall, when the air becomes a little 
 refreshed ; but a hot, glowing sun soon heats it again, and but for your 
 awnings, and the little air put in circulation by the continual flapping of 
 the ship's sails, it would be almost insufferable. No person who has not 
 crossed the region can form an adequate idea of its unpleasant effects. 
 You feel a degree of lassitude unconquerable, which not even sea-bathing, 
 which everywhere else proves so salutary and renovating, can dispel. 
 
WET AND DRY ZONES. 169 
 
 Except when in actual danger of shipwreck, I never spent twelve more 
 disagreeable days in the professional part of my life than in these calm 
 latitudes. 
 
 " I crossed the line on the I7th of January, at eight A.M., in longitude 
 21 20', and soon found I had surmounted all the difficulties consequent 
 to that event ; that the breeze continued to freshen and draw around to 
 the south-southeast, bringing with it a clear sky and most heavenly 
 temperature, renovating and refreshing beyond description. Nothing 
 was now to be seen but cheerful countenances, exchanging as by 
 enchantment from that sleepy sluggishness which had borne us all down 
 lor the last two weeks." 
 
 But notwithstanding the oppressive character of the weather 
 under the cloud-ring the temperature is not extremely high 
 much less so than on either side of it, and the disagreeable 
 -and oppressive character arises mostly from the calmness and 
 extreme dampness of the air. The great cloud-ring protects 
 the earth's surface from the almost vertical rays of the sun, 
 .and hence it is considerably cooler than on either side where 
 the sun's heat reaches the earth's surface unobstructed. Espy 
 found from examining the tables of Wilkes that in the rainy 
 belt of the equator the temperature of the air on the ocean is 
 about 6 F. lower than it is beyond the borders of the rains 
 .both north and south. On land the difference is much greater. 
 According to Humboldt, each side of the belt of rains in South 
 America is from 10 to 18 hotter than in the belt of rains. 
 This is caused, not only by the absence of the heating rays of 
 the sun in the rain-belt, but also by the cooling effect of the 
 drops of rain coming down from high and cold altitudes. 
 
 114. From the general circulation of the atmosphere and 
 meeting of the trade-winds near the equator, and the annual 
 oscillation and shifting of the parallels on which they meet, arise 
 peculiarities of climate within the zone of the range of oscilla- 
 tion of the calm- and rain-belt, such as are not to be found else- 
 where. Since the calm-belt with its daily torrents of rain oscil- 
 lates forth and back annually through a range, especially on the 
 great oceans, more than twice as great as its width, while just 
 outside of the limits of this narrow belt, with winds from dif- 
 ferent directions on the two sides, there is no rainfall at the 
 
170 CLIMATIC INFLUENCES OF THE GENERAL CIRCULATION.. 
 
 time, this is necessarily a zone of alternations of extremely wet: 
 and extremely dry seasons, and of winds which vary in direction 
 at different seasons of the year. The position of a place with, 
 regard to the mean position of the oscillating rain-belt may be 
 such that there is either a long rainy and a long dry season' 
 during the year, or two rainy seasons of shorter duration with 
 two intervening dry seasons. The latter takes place where the 
 station is situated at or near the mean position of the middle 
 of the rain-belt, and the range of oscillation is considerably 
 greater than the width of the belt, as it generally is, on the 
 oceans ; for then the middle of the belt, as it moves towards- 
 the north, is over the place of observation in April or May, and 
 again in October and November as it moves back southward, 
 and at these times there is a great abundance of rain. But in 
 July or August, when the rain-belt has its most northerly posi- 
 tion and its southern limit is north of the place, or in January 
 or February, when it has its most southerly position, and its 
 northern limit is south of the place, there is of course no rain- 
 fall. There are, consequently, in this case, two wet and two 
 very dry seasons in the course of the year. Or the width of 
 the rain-belt and the range of oscillation, especially on land, 
 may be such that there is no total cessation of rain during the 
 year, but simply two minima instead of the two dry seasons, 
 and so two maxima, one in the middle of each of the rainy sea- 
 sons. 
 
 If the place of observation is a little north of the mean posi- 
 tion of the rain-belt, so that its southern limit never moves 
 north of the place, then there is no intervening dry season when 
 the belt has its extreme northerly position, though there may 
 be a considerable diminution in the rate of rainfall in August or 
 September, when a minimum only occurs instead of a complete 
 cessation and a very dry season, but a long drought at the 
 opposite season of the year. On the other hand, if the place is 
 so far south of the mean position of the oscillating rain-belt 
 that the northern limit of the belt, in its extreme southerly 
 position, does not lie beyond it, then there is no complete ces- 
 sation of rain in January or February, but simply a minimum 
 
WET AND DRY ZONES. I?l 
 
 in the monthly rainfalls, preceded and followed by a maximum,, 
 while at the opposite season of the year there may be no rain 
 for several months. The position of the place also and the 
 width of the rain-belt may be such as to cause a rainy season 
 without a minimum in the middle, and in such cases the dry 
 season is much longer than the rainy season. 
 
 Since on the north side of the rain-belt the winds are gener- 
 ally from some point between north and east, and in the other 
 from some point between south and east, wherever the rain-belt,, 
 in its annual oscillations, passes entirely over a place, there is a 
 change of the winds from some point in the northeast to one in 
 the southeast quadrant, or the contrary, Since the calm-belt 
 is sometimes considerably north of the equator, the southeast 
 trade-winds, after passing the equator, in consequence of the 
 influence of the earth's rotation, then become southerly or even 
 southwesterly winds near the southern border of the calm-belt. 
 
 115. The preceding deductions from theoretical considera- 
 tions are verified by numerous observations of the monthly 
 rainfalls and prevailing directions of the wind at many places 
 near the equator, all around the globe. Since the oscillating 
 calm, and the accompanying rain-belt always follow each other 
 and occupy the same parallels, except that the latter is a little 
 the wider, the oscillations of the calm-belt can be more readily 
 traced from the observations of the monthly rainfalls than from 
 the direct observations of the winds and calms. 
 
 The following table of average monthly rainfalls on the 
 Congo and the southwest coast of Africa has been taken from 
 a work by Dr. A. v. Danckelman." 
 
 At Vivi, 5 40' S., 13 49' E., it is seen that there is a total 
 cessation of rain during June, July, and August, and very near- 
 ly so in September, while at the opposite season of the year 
 there is only a minimum with a maximum preceding in Novem- 
 ber and one following in April. The station being south of the 
 equator, during the summer of the northern hemisphere, when 
 the rain-belt has its most northerly position, the southern bor- 
 der of this belt was entirely north of the place, notwithstand- 
 ing it is wider at this land station than on the ocean and its, 
 
 o 
 
:-I7 2 CLIMATIC INFLUENCES OF THE GENERAL CIRCULATION. 
 
 MONTH. 
 
 MONTHLY RAINFALLS IN MILLIMETERS AT 
 
 Vivi. 
 
 Ponta da 
 Lenha. 
 
 Gabun. 
 
 Chinchoxo. 
 
 Loanda. 
 
 
 96 
 68 
 103 
 231 
 50 
 
 
 
 o 
 o 
 
 I 
 75 
 237 
 1 80 
 
 65 
 104 
 
 94 
 118 
 
 27 
 
 
 
 o 
 o 
 
 T 
 
 3 
 143 
 
 53 
 
 155 
 217 
 349 
 381 
 169 
 
 7 
 i 
 ii 
 40 
 288 
 
 423 
 224 
 
 311 
 1 2O 
 
 185 
 IO2 
 
 54 
 
 
 
 o 
 
 5 
 8 
 
 23 
 
 222 
 
 52 
 
 39 
 30 
 
 58 
 
 122 
 
 12 
 O 
 
 
 I 
 2 
 
 4 
 
 51 
 
 25 
 
 JFebruary . ... . . ... 
 
 March 
 
 April 
 
 May 
 
 Tune 
 
 July . 
 
 August . ... 
 
 September . .... 
 
 
 November 
 
 December 
 
 
 Year 
 
 1,041 
 
 608 
 
 2,265 
 
 1,082 
 
 344 
 
 
 limits not so well defined, and so no rain fell for several months. 
 The minimum in February, if there are no abnormal local dis- 
 turbances, indicates the middle of the rain-belt at this time is 
 .south of the station, and if so, it must have a more southerly 
 mean position or a wider range than on the Atlantic Ocean. 
 What has been stated here with regard to Vivi is also true of 
 , Ponta da Lenha. 
 
 At Gabun, o 30' N., 9 35' E., since it lies farther north, the 
 rainfall does not quite vanish in the summer of the northern 
 hemisphere, and the minimum of the opposite season is less 
 marked than at Vivi. The same is true with renard to Chin- 
 choxo, except that here there seems to be a total cessation of 
 rain during June and July, but the numbers expressing the 
 monthly rainfalls seem to be very irregular, and so are perhaps 
 not very reliable. 
 
 At Loanda, 8 49' S., 13 f E., there is much less rain than 
 at Vivi ; but there are two maxima and two minima, with an 
 intervening minimum in the winter of the northern hemisphere 
 and a total cessation of rain for several months at the opposite 
 .season of the year, as at Vivi. 
 
 At the island of St. Thomas, o 20' N., 6 43' E., and so of 
 .nearly the same latitude as Gabun, from the average of five or 
 
WET AND DRY ZONES. 173', 
 
 six years of observation, no rain fell in July ; in June, July,, 
 August, and September only 47 mm. of rain fell ; while the 
 amount for the whole year on the average was 1019 mm. The 
 greatest amount fell in March. 36 
 
 116. "In Nango, 13 N., 9 W., from Paris, the rainy season com- 
 mences the latter part of May, but the rain is then only seldom. It be- 
 comes more frequent in July. The rainfall then is very great. The- 
 temperature then sinks still more. The rain holds on in August, and is 
 as abundant as in July. The temperature is then a minimum. Septem- 
 ber brings a great change, but the rain is still frequent. The temperature- 
 rises again, and the air becomes more clear." 26 
 
 This place, being 9 north of the equator, is within the rain- 
 belt from June to September inclusive, and the rainfall during 
 the middle part of this period is abundant ; but during the 
 other eight months of the year, when the rain-belt has moved 
 southward, the northern limit of the belt is south of the place, 
 and hence there is no rain. 
 
 Observations on the upper Nile in the interior of Africa, 
 both of the winds and the rainfall, indicate clearly the exist- 
 ence of the calm- and rain-belt there. At Rubaga, o 20' N., 32^ 
 45' E., altitude 1300 meters, the mean probability of rain is as 
 follows : 
 
 Jan. Feb. Mar. April. May. June. July Aug. Sept. Oct. Nov. Dec. 
 43 42 4 2 ?o 51 60 29 46 52 74 67 47 
 
 There are, therefore, two maxima and two minima, as usual 
 at places near the equator ; but the numbers indicate that the 
 rain-belt here is wide and not well defined, and so, instead of 
 two rainy and two dry seasons, there are simply two maxima 
 and two minima of rainfall. 
 
 At Lado, 5 2' N., 31 50' E., the winds from April to Sep- 
 tember are mostly from S.W. and S. ; from October to March, 
 N. and N.E. The greatest rainfall is in August and Septem- 
 ber ; the least in December, January, and February." 
 
 These observations, as well as those of Rubaga, indicate 
 that the calm- and rain-belt here is but little north of the 
 equator, and that its width and range of oscillation are such 
 that the places are at all times comprised between its limits ; 
 
174 CLIMATIC INFLUENCES OF THE GENERAL CIRCULATION. 
 
 tout since there is more rain during the summer than the win- 
 ter of the northern hemisphere, the mean position of the mid- 
 >dle of the belt must be south of Lado. The winds, however, 
 indicate that the mean position cannot be far from Lado. 
 
 " At Nyassa Sea (south of the equator) there is no rain between May 
 -and October. The soil becomes dried out, and the grass becomes dry 
 -and assumes the appearance of wheat-fields in England in July." 
 
 During this dry season the rain-belt is north of the equator, 
 .and Nyassa Sea is left in the zone of the southeast trade-winds, 
 where there is no rain. 
 
 During Emin Effendi's travels in equatorial Africa, from 
 Nov. 29 to Dec. 1 8, 1877, from Mreili, 3 N., to Rubaga 
 (Mtesa's residence), rain fell nearly every day in great abun- 
 dance, and the whole country was flooded with water, and the 
 travellers had to wade through water often from two to three 
 feet deep." 
 
 The middle line of the rain-belt, therefore, at this time, 
 which is about the time of its mean position, must have been 
 .about two degrees north of the equator. 
 
 117. In the northern part of South America and the 
 Isthmus of Panama the middle line of the rain-belt seems to 
 oscillate between the equator and the parallel of 10 or 12 
 N, ; and so, in its mean position, is considerably north of the 
 equator. 
 
 At Guatemala, 14 38' N.,9O 31' W.; altitude 1480 m., from 
 three years of observations, 1880-1882, the average monthly 
 rainfall in millimeters is: 
 
 Jan. Feb. Mar. April. May. June. July. Aug. Sept. Oct. Nov. Dec. Year. 
 4 6 i 20 144 253 137 234 231 159 51 2 1242 
 
 Hence this place is fully within the limits of the rain-belt from 
 May to November, but during the rest of the year, while the 
 belt has a more southerly position, it is almost wholly north of 
 the northern limit of the belt, where it receives little or no rain. 
 "There is an indication of a slight minimum in July also, from 
 which it seems that the middle of the rain-belt passes a little 
 north of Guatemala at this time. 
 
WET AND DRY ZONES. 1/5 
 
 At Greytown, Nicaragua, lat. 10 55' N., according to Com- 
 mander A. V. Reed, " the dry season lasts till late in May, 
 when the rains set in and are of daily occurrence during June 
 and July, with considerable thunder and lightning. In August 
 and September, they have very pleasant weather, with less rain, 
 and the sea outside is usually smooth ; but in October and No- 
 vember again they have disagreeable weather and daily rains." 
 
 Here again, it seems, there are two maxima, one in June or 
 July and the other in October or November, with a minimum 
 in August or September, and a long dry season at the opposite 
 season of the year. This indicates that the mean position of 
 the middle of the rain-belt is considerably south of Greytown ; 
 for at any place in the middle of the belt in its mean position 
 the two maxima would occur at exactly opposite times of the 
 year, and there would be two intervening dry seasons of equal 
 length, in which there would probably be one or two months 
 with scarcely any rain. 
 
 From the report of Lieut. Frederick Collins of the survey 
 for an Interoceanic Canal in the State of Cauca, we learn that, 
 at the junction of the Napipi and Merindo rivers (about 5 
 N.), " as a rule, two well-marked dry seasons are experienced 
 here, with corresponding periods of rain. January, February, 
 and March are the months which constitute the dryest and 
 pleasantest season. In April the rains commence, and in May 
 and June they are very heavy. In July a second dry season 
 begins to set in, and August and September are generally 
 pleasant and comparatively dry. In October rains again com- 
 mence, and in November and December they are the heaviest." 
 
 Here the mean position of the middle of the rain-belt seems 
 to be a little south of the place, since the dry season of August 
 and September is not so marked and of as long duration as 
 that of January, February, and March. 
 
 On the Panama Interoceanic Ship Canal, 8. 5 N., "the year 
 is divided, as in other parts of the American isthmus and of 
 Central America, into two seasons, the rainy and the dry, the 
 former beginning in the latter part of May and lasting until 
 November, when it gives place to the latter, which lasts until 
 
1/6 CLIMATIC INFLUENCES OF THE GENERAL CIRCULATION.. 
 
 May comes around again. The annual rainfall is from 90 to 
 1 40 inches." 28 
 
 This place being a little farther north than the preceding 
 one, there are here only a wet and a dry season, the former 
 taking place while the belt is north of its mean position ; but, 
 as in other places considerably north of the equator, if we had 
 the monthly rainfalls, a minimum in August or September 
 would undoubtedly be observable. 
 
 The effect of the oscillation of the rain-belt near the equator 
 in producing a wet and a dry season seems to be felt in Mexico. 
 Humboldt says : 
 
 " There are only two seasons known in the equatorial region of Mex- 
 ico, even as far as the 28th degree of N. latitude : the rainy season, esta- 
 cion de las aguas, which begins in the month of June or July, and ends 
 in the month of September or October ; and the dry season, el estio, 
 which lasts eight months, from October to the end of May." 29 
 
 118. Although the rain falls every day in the rain-belt dur- 
 ing at least the middle part of the rainy season, yet it is not 
 continuous through both the day and night, but it takes place 
 mostly during the day. The abundant downpour of rain, at 
 least on land, seems to be of the nature of thunder showers in 
 all countries during very warm and damp weather, and to de- 
 pend upon the heating effects of the sun's rays in inducing a 
 state of unstable equilibrium, so that the aqueous vapor brought 
 in by the trade-winds into the calm-belt ascend and are con- 
 densed into rain, mostly while the atmosphere is in this state. 
 Tomlinson says : 30 
 
 "The atmospheric phenomena of such countries as lie under the calm- 
 belt are marked by a striking uniformity and regularity. For hours after 
 the rising of the sun the sky remains entirely free from clouds. About 
 noon a few clouds appear at the horizon, which, as they become more 
 vertical, rapidly increase in size and density; presently the thunder is- 
 heard, the wind blows in violent gusts, and at the same time there occurs 
 a heavy downpour of rain, which lasts for a few hours. The clouds 
 quickly disappear toward evening, and the sun sets in a deep-blue and 
 cloudless sky. It is rare for rain to fall during more than eight hours at 
 a time. The countries near the equator experience this kind of weather 
 nearly all the year, and what is called the rainy season differs from the 
 
WET AND DRY ZONES. 
 
 remainder of the year in the rain being rather more continuous and 
 
 plentiful." 
 
 This, or at least the latter part, seems to apply more espe- 
 cially to continents where the rainfall is more scattering and not 
 well defined, and not to the ocean, or even to the American 
 isthmus, where, we have seen, there are long seasons with little 
 or no rain. 
 
 Since the origination of the shower or daily rainfall de- 
 pends upon the unstable state, which is more readily induced 
 during the heat of the day, the rain commences at that time ; 
 but after an abundant fall of rain for several hours, some of 
 which descends from very high altitudes where the air and the 
 condensed vapor are very cold, the unstable state of the atmos- 
 phere toward evening is destroyed by the cooling effect of the 
 rain upon the lower strata of the atmosphere, and the rain 
 ceases until next day, when the unstable state is again induced. 
 
 119. The following contrasts of the wet and the dry sea- 
 sons on the Orinoco and the great Amazonian basin within 
 the range of oscillation of the rain-belt, and which is true of all 
 places within this range where the rain-belt is narrow and well 
 defined, and not much affected by the abnormal disturbances, 
 but is somewhat as it is on the ocean and on level countries 
 near the ocean, have been given, as cited by Maury, 23 by Hum- 
 boldt in his "Aspects of Nature:" 
 
 " When, under the vertical rays of the never-clouded sun, the carbon- 
 ized turfy covering falls into dust, the indurated soil cracks asunder as if 
 from the shock of an earthquake. If at such times two opposing cur- 
 rents of air, whose conflict produces a rotary motion, come in contact 
 with the soil, the plain assumes a strange and singular aspect. Like 
 conical-shaped clouds, the points of which descend to the earth, the sand 
 rises through the rarefied air on the electrically charged centre of the 
 whirling current, resembling the loud water-spout, dreaded by the ex- 
 perienced mariner. The lowering sky sheds a dim, almost straw-colored 
 light on the desolate plain. The horizon draws suddenly nearer, the 
 steppe seems to contract, and with it the heart of the wanderer. The 
 hot, dusty particles which fill the air increase its ^uffocating heat, and 
 the east wind, blowing over the long-heated soil, brings with it no re- 
 freshment, but rather a still more burning glow. The pools, which the 
 
1?8 CLIMATIC INFLUENCES OF THE GENERAL CIRCULATION'. 
 
 yellow, fading branches of the fan-palm had protected from evaporation, 
 now gradually disappear. As in the icy north the animals become torpid 
 with cold, so here, under the influence of the parching drought, the croc- 
 odile and the boa become motionless and fall asleep, deeply buried in 
 the mud. . . . 
 
 " The distant palm-bush, apparently raised by the influence of the con- 
 tact of unequally heated and therefore unequally dense strata of air, 
 hovers above the ground, from which it is separated by a narrow inter- 
 vening margin. Half concealed by the dense clouds of dust, restless with 
 the pain of thirst and hunger, the horses and cattle roam around, the 
 cattle lowing dismally, and the horses stretching out their long necks, 
 and snuffing the wind, if haply a moister current may betray the neigh- 
 borhood of a not wholly dried-up pool. . . . 
 
 " At length, after the long drought, the welcome season of the rain 
 arrives ; and then how suddenly is the scene changed ! . . . 
 
 " Hardly has the surface of the earth received the refreshing moisture 
 when the previously barren steppe begins to exhale sweet odors, and to 
 clothe itself with killingias, the many panicles of the paspulum, and a 
 variety of grasses. The herbaceous mimosas, with renewed sensibility 
 to the influence of light, unfold their drooping, slumbering leaves to 
 greet the rising sun; and the early song of birds and the opening blos- 
 soms of the water plants join to salute the morning." 
 
 120. We have seen that under the high pressure of the 
 tropical calm-belts there is a gradual settling down of the air to 
 supply the outward flow on each side at the earth's surface 
 from beneath this high pressure. The aqueous vapor in these 
 belts cannot rise up so as to be condensed, but, on the contrary, 
 it rather sinks down and is carried away by the surface cur- 
 rents ; on the one hand, by the trade-winds to the equatorial 
 calm-belt, and on the other, away toward the middle latitudes. 
 The tropical calm-belts are therefore dry belts. Over the 
 trade-wind latitudes, also, since the horizontal and compara- 
 tively strong surface currents hurry away the vapor which is 
 evaporated over the ocean and the land surface of these lati- 
 tudes to the equatorial calm-belt, where alone it rises up to 
 where it can be condensed, there is scarcely any rainfall. 
 There is, therefore, in each hemisphere, a wide zone, extending 
 from the zone of equatorial variable rains, over the trade-wind 
 latitud.es and comprising the tropical calm-belt, in which there 
 is little rain, especially on the oceans, where the general vertical 
 
'RELATIVE EAST AND WEST TEMPERATURES. 1/9 
 
 circulation is more regular. It is true there is considerable 
 rain in some places within these zones, but this is due to abnor- 
 mal disturbances of mountain ranges, and not to the general 
 circulation of the atmosphere, such as would exist if the whole 
 surface of the earth were homogeneous. 
 
 These zones are almost completely rainless on most parts 
 of the great oceans, but there is at least a strong tendency 
 toward this same condition on the continents, as is readily seen 
 from an inspection of Loomis's chart of Mean Annual Rainfall. 
 In the northern hemisphere between the parallels of 15 and 
 40, are the dry regions of California, Arizona, and Colorado in 
 North America, the great Sahara and Nubian deserts of North 
 Africa, and the dry region of Arabia and Persia in Asia. In 
 the southern hemisphere within the same parallels are the dry 
 regions of the southern part of the Argentine Republic and of 
 eastern Patagonia in South America, a large dry region in 
 South Africa, and one comprising the whole of the interior of 
 Australia. It must not be understood that these regions are 
 entirely rainless throughout the year, but simply that the 
 amount of rain is very scant, and small in comparison with 
 that of the middle latitudes of each hemisphere. Even in the 
 .great Sahara rain sometimes falls. 
 
 RELATIVE TEMPERATURES OF EAST AND WEST SIDES OF THE 
 
 CONTINENTS. 
 
 121. One of the principal climatic effects arising from the 
 general circulation of the atmosphere is the great difference of 
 temperatures observed on the same latitudes on the east and 
 west sides of the continents, especially in high latitudes, both 
 in the annual means of temperature and also in the extreme 
 temperatures of the seasons. It is a matter of observation, 
 which has been explained in 68, that the mean annual tem- 
 peratures of the oceans in the higher latitudes are greater, and 
 those of the lower latitudes less, than those of the same lati- 
 tudes on the continents ; and the differences would be still 
 greater if it were not for the equalizing tendency of the general 
 
ISO CLIMATIC INFLUENCES OF THE GENERAL CIRCULATION. 
 
 circulation around the globe, easterly in the higher, and the 
 contrary at the earth's surface in the lower, latitudes. The 
 effect, also, of this circulation is to cause the highest mean 
 annual temperatures of the oceans in the higher latitudes to be 
 on the east sides, near the continents, and the lowest mean 
 temperatures of the continents to be on the east sides of the 
 continents near to the adjacent oceans. Hence there are the 
 greatest contrasts between the east sides of the oceans and of the 
 continents. From a chart of isotherms for the mean tempera- 
 tures of the year it is seen that the mean annual temperature 
 of the Atlantic Ocean near the coast of Norway is 40 F., while 
 on the same latitude in the eastern part of Siberia it is only 
 about 10 F. There is also a difference of about 20 between 
 the mean annual temperatures of the British Isles and those of 
 the same latitudes on the eastern side of Asia. Likewise the 
 difference of mean annual temperatures between the North 
 Pacific Ocean, adjacent to Alaska in the neighborhood of the 
 Aleutian Islands, and those of corresponding latitudes of Hud- 
 son's Bay and Labrador, is about 15, but for latitudes a little 
 lower, some less. 
 
 Since the annual inequalities of temperature are very great 
 on the continents in comparison with those on the ocean, the 
 greatest contrasts of temperature are found in the winter season. 
 For since the mean annual temperatures on the ocean in the 
 higher latitudes are considerably above those of the same lati- 
 tude on the continent, and the range of annual oscillation is 
 small on the ocean, the mean midwinter temperatures scarcely 
 fall to the mean annual temperatures of the land ; and so the 
 differences of the temperatures on the ocean and on the conti- 
 nent, when the east sides are compared, are equal to the whole 
 differences between the annual mean and the midwinter tem- 
 peratures of the latter. Thus the mean temperature of the 
 ocean in January between Iceland and Norway, according to- 
 Buchan's charts, is about 35 F., while that of eastern Siberia is 
 40, a difference of about 75. Between the mean January 
 temperatures of the ocean west of the British Isles and those 
 of the same latitudes in the eastern part of Asia the difference 
 
 \ 
 
RELATIVE EAST AND WEST TEMPERATURES. l8l 
 
 is less, but still about 60. Between the eastern sides of the 
 North Pacific and the corresponding latitudes on the east side 
 of America the differences in January are nearly as great. 
 
 In midsummer the contrasts in the higher latitudes made 
 in a similar manner are much less and reversed, the oceans at 
 this season being colder than the continents. But still there 
 are considerable differences when we compare the eastern sides 
 of the oceans with those of the continents. The July mean 
 temperature midway between Iceland and Norway is about 10 
 less than on the same latitude in the eastern part of Asia, and 
 the difference between the Aleutian Islands and Labrador on 
 the same latitude is about the same. 
 
 On the lower latitudes, those of the trade-winds, the differ- 
 ences between the mean annual temperatures of the continents 
 and the oceans are considerable, those of the continents being 
 the higher. The differences in midsummer are still greater, 
 but in midwinter the temperatures are somewhat the same. 
 
 122. The characteristics of a continental climate in the 
 -middle and higher latitudes are great extremes in the annual 
 changes of temperature with the maxima and minima occurring 
 earlier in the season, a dry atmosphere, and a lower mean 
 annual temperature than the normal of the latitude ; while on 
 the ocean the range of annual oscillation is very small, the max- 
 ima and minima occur later in the season, and the mean annual 
 temperature is higher than on the continents on the same lati- 
 tudes. Now it is readily seen that the effect of the general 
 circulation from west to east around the globe in the middle 
 and higher latitudes is not only to throw the true continental 
 .and oceanic climates from the middle over toward the eastern 
 sides of the continents and oceans, but also to cause the west- 
 ern sides of the oceans to have a somewhat continental climate 
 and the western sides of the continents to have in some meas- 
 ure an oceanic climate, and consequently to cause a great 
 contrast of climates between the western and eastern sides of 
 the continents. Accordingly Europe, especially the western 
 side, has a mean temperature a little above the normal of lati- 
 tude, small annual inequalities with the maxima and minima 
 
1 82 CLIMATIC INFLUENCES OF THE GENERAL CIRCULATION 
 
 occurring later in the season, and a damper atmosphere ; while 
 on the eastern side of Asia, on the same latitudes, the mean, 
 annual temperature is a little below the normal of latitude, and 
 there are large annual inequalities of temperature with maxima 
 and minima occurring earlier in the season, and a much drier- 
 atmosphere. 
 
 The mean annual temperatures of Norway and Sweden, from 
 this cause, are about 20 F. higher than those of the eastern- 
 part of Siberia, and those of France about 15 higher than 
 those of the Chinese Empire on the same latitudes. Similar 
 differences of mean temperature are also found between the 
 western and eastern sides of North America. Again, while the 
 mean annual range of temperature in Norway and Sweden is 
 scarcely as much as 35 F., that of the eastern part of Asia orr 
 the same latitude is more than 90. The annual temperature 
 ranges, also, in Germany, are only about half as great as on the 
 same parallels of latitude in the Chinese Empire. Similar dif- 
 ferences are observed in the annual inequalities of temperature 
 between the west and east sides of North America, but not 
 nearly so great, because the continent is much narrower. The 
 epochs, also, of midwinter and midsummer occur about a half 
 month later on the west than on the east sides of the conti- 
 nents, the former corresponding more nearly with those of 
 oceanic, and the latter with those of continental, climates. 
 
 In the southern hemisphere the continents do not extend so 
 far into the higher latitudes, and the contrasts of climate be- 
 tween the two sides of the continents are comparatively small, 
 the tendency of the general circulation around the globe being 
 to reduce the temperatures and all the climatic features some- 
 what to those of the ocean, so that in the southern parts of 
 South America and of Africa there are only small annual tem- 
 perature ranges. 
 
 In the lower latitudes of both hemispheres the annual tem- 
 perature ranges of course are small, and consequently there is 
 but little difference in temperature between the two sides of 
 the continents, and the principal differences here are in the 
 mean annual temperatures, those of the ocean being consider- 
 
IN CONNECTION WITH MOUNTAIN RANGES. 183 
 
 ably lower, but in consequence here of the westerly motion of 
 the atmosphere at the earth's surface, the eastern sides of the 
 oceans and the western sides of the continents have higher 
 mean annual temperatures than the western sides of the oceans 
 and the eastern sides of the continents. For instance, the 
 easterly winds of the great Sahara, and North Africa generally, 
 must tend to drive the heat and the dryness westward toward 
 the Atlantic, so that the east side of the Atlantic here which 
 receives the sand and dust from the continent, 87, must have 
 a higher air temperature and a drier air than the west side. 
 
 IN CONNECTION WITH MOUNTAIN RANGES. 
 
 123. If the whole surface of the earth were that of the 
 ocean, or any smooth homogeneous surface, the calm-belts, the 
 rain-belt, and the dry zones would extend without interruption 
 entirely around the globe with the same regularity which is 
 observed upon the oceans, and everywhere the same climatic 
 conditions would exist on the same parallels of latitude. But 
 on account of the influence of mountain ranges in deflecting 
 the currents of the general circulation of the atmosphere, great 
 diversities of climate are found in different places on the same 
 parallels arising from this cause. The air of the lower strata of 
 the atmosphere in the trade-wind zone of the North Atlantic, 
 having a westerly motion, and impinging against the high table- 
 lands and mountain ranges of Mexico, is deflected around 
 toward the north over the southeastern States and up the 
 Mississippi Valley into the higher latitudes, where it combines 
 with the general easterly flow of these latitudes, and adds to its 
 strength. This completely breaks up the continuity of the 
 tropical calm-belt and dry zone, so that instead of a dry region 
 with scanty rainfall, such as is found in North Africa, Arabia, 
 Persia, Beloochistan, and Cabul, we have on the same parallels 
 in the southern and eastern United States a region of abundant 
 rainfall, and all the way up the Mississippi Valley and in the 
 interior of the continent there is much more rain than in the 
 interior of Asia. In consequence of this deflection, the trade- 
 
1 84 CLIMATIC INFLUENCES OF THE GENERAL CIRCULATION*. 
 
 winds of the Atlantic become nearly east winds in the vicinity 
 of the West India Islands, and farther on in the southeastern 
 States and the Mississippi Valley the winds are southeasterly 
 and then southerly, and the warm and moist air of the Gulf of 
 Mexico, being carried around into higher and cooler latitudes, 
 not only furnishes vapor for condensation into rain, but also 
 modifies somewhat the temperatures. There is, therefore, a 
 sufficiency of rain here on the parallels of the north tropical 
 dry zone for agricultural purposes as far as the looth meridian 
 west of Greenwich. 
 
 The easterly current across the Atlantic Ocean on the mid- 
 dle and higher parallels, strengthened a little by the deflected 
 current coming from the Gulf up the Mississippi Valley, 
 impinging against the inequalities of the coast of Europe, and 
 especially the interior mountain ranges, is partly deflected both 
 to the right and to the left, the one branch passing down 
 toward the Canaries and the northwest coast of Africa, joins 
 the general westerly flow in the trade-wind latitudes, while the 
 other curves around along the coast of Norway on to Spitz- 
 bergen and around to Greenland. 
 
 In consequence of these deflections there is a gyration of 
 air around a central region midway between America and the 
 eastern continent on the parallels of the zone of high pressure, 
 and also one around a central area in the vicinity of Iceland. 
 These gyrations are indicated by the arrows showing the pre- 
 vailing directions of the winds on Coffin's charts, 19 and also by 
 the charts of M. Brault, based upon many thousands of obser- 
 vations. From the former of these gyrations it results that the 
 northeast trade-winds adjacent to Africa seem to come from a 
 more northerly direction and from a higher latitude than they 
 do farther west, while on the west side of the ocean they 
 become easterly, and even southeasterly, winds. The former 
 also gives rise to the prevailing northwest winds in the part of 
 the Atlantic Ocean adjacent to Spain and Portugal and the 
 northwest coast of Africa, and the latter in part to the prevail- 
 ing southwest winds of the British Isles and the coast of Nor- 
 way, and the northeasterly winds of Greenland. 
 
IN CONNECTION WITH MOUNTAIN RANGES. 185 
 
 Where the general easterly current of the middle latitudes 
 impinges against the high lands of the interior of Asia, com- 
 prising the Kuenlun and Himalaya chains, the latter 1300 
 miles in length, with an average height of 18,000 feet, on the 
 south, and the Great and Little Altai Mountains on the north, 
 with the elevated and desert table-lands containing the Desert 
 of Gobi between them, they are again deflected, not around 
 and back, as on the west coast of Europe, but to each side, the 
 southern branch giving rise to prevailing northwesterly winds 
 over a large region, including southeast Europe and southwest 
 Russia. WoeikofT says: " There is a region comprising Hun- 
 gary, Transylvania, the Danubian Principalities, and southwest 
 Russia, in which the prevailing winds are northwest both win- 
 ter and summer." 20 These winds also prevail over Arabia and 
 Persia, and this deflection likewise affects the directions of the 
 regular monsoons of India, and its effect is felt even at the 
 equator south of Asia, where it gives rise to a strong west wind, 
 sometimes called the west monsoon of the line, where, otherwise, 
 there would be no wind with an east or west component of 
 motion. 
 
 124. In like manner, in the lower latitudes of the South 
 Atlantic Ocean the general westerly current of the lower part 
 of the atmosphere, on arriving at the continent of South 
 America, and especially at the high range of the Andes, with a 
 mean elevation of nearly 12,000 feet, is deflected around toward 
 the south over Brazil and on southeastward until it enters and 
 combines with the strong easterly current of the middle latitudes 
 of the South Atlantic. Instead, therefore, of the rainless zone, as 
 it exists on the ocean in the trade-wind and high-pressure lati- 
 tudes, extending across the continent of South America, or 
 there being a deficiency of rain, as in some other countries on 
 these latitudes, there is a sufficiency of rain over all Brazil and 
 the eastern side of South America, up nearly to the parallel 
 of 40 S. 
 
 The moisture for this rain is furnished by the deflected cur- 
 rents of warm and damp air from the trade-wind and rainy zone, 
 for the air of the trade-winds is damp, but the zones of trade- 
 
1 86 CLIMATIC INFLUENCES OF THE GENERAL CIRCULATION.. 
 
 winds on the oceans are rainless, because the conditions, which 
 are found on the uneven land surface, for producing ascending 
 currents and vapor condensation are wanting on the oceans. 
 On account of this deflection, instead of southeasterly winds, 
 as in the ocean on the same latitudes, the prevailing winds are 
 northeasterly and northerly over Brazil, just as in the southern 
 part of the United States and the Mississippi Valley they are 
 southeasterly and southerly, and the continuity of the tropical 
 calm-belt and rainless zone of this hemisphere is also interfered 
 with. 
 
 A small part also of the strong easterly current of the mid- 
 dle latitudes is deflected around toward the equator by the west 
 coast and the mountain ranges of South Africa, so that there 
 is, on the South Atlantic, as on the North Atlantic, a gyration 
 of air around a central area, midway between South America 
 and Africa, and on the parallels of the zone of high pressure. 
 This is also plainly indicated by the charts of both Coffin and 
 M. Brault. As a result of this gyration the southeast trade- 
 winds come apparently from a higher latitude and have a more- 
 southerly direction on the part of the ocean adjacent to Africa, 
 and gradually assume a direction more from the east on longi- 
 tudes farther west. The continent of Africa does not extend 
 far enough toward the south pole to cause a deflection the con- 
 trary way and a gyration of air in the higher latitudes of the 
 South Atlantic, as in those of the North Atlantic. 
 
 125. On the east coasts of China and of South Africa, and 
 in some measure on those of New Guinea and Australia, there 
 are similar deflections of the trade-winds by the highlands and 
 mountain ranges of these countries around toward the middle 
 and higher latitudes, where the deflected currents become a 
 part of the easterly currents of these latitudes. For this rea- 
 son the winds on the southeast of China and the adjacent sea, 
 comprising the Philippine and the Ladrone Islands, are more 
 from easterly and southeasterly directions and are damper tharv 
 they otherwise would be, and the rainfall is more abundant. 
 This effect, however, is much obscured here by the great dis- 
 turbing influence of the monsoons, which introduces great 
 
IN CONNECTION WITH MOUNTAIN RANGES. 1 87 
 
 annual changss and alterations in both the directions of the 
 winds and the amount of rainfall. East of New Guinea and 
 Australia the normal direction of the trade-winds is changed to 
 one more from the east and northeast, and on the east coast of 
 South Africa a similar but still greater effect is produced upon 
 the direction of the trade-wind. Consequently the calm-belts 
 and dry zones are very much broken up on all these eastern 
 coasts in the lower latitudes of both hemispheres, and great 
 climatic changes introduced. 
 
 The easterly current over the middle latitudes of the North- 
 Pacific, strengthened a little by the deflected current on the: 
 east coast of China, on arriving at the west coast of North 
 America, is likewise in part deflected by the coast and the 
 mountain ranges, a small part around northward by Alaska on 
 to Behrings Strait, but mostly around to the right along the 
 coast of California and on to the latitudes of the northeast 
 trades, where it becomes a part of the westerly current in the 
 direction of China. This latter deflection gives rise to a pre- 
 dominance of northwesterly and northerly winds along the 
 coast of California and the adjacent sea, and to a more north- 
 erly direction of the trade-winds west of Mexico for some dis- 
 tance westward, and to a breaking up of the continuity of the 
 calm-belt and the dry zone which would otherwise exist here 
 on those latitudes. 
 
 In the South Pacific Ocean the strong easterly current of 
 the middle latitudes impinges against the high mountain range 
 of the Andes, and a part of it is deflected around by the coasts 
 of Chili and Peru and over the adjacent ocean until it likewise 
 joins the general westerly current in the latitudes of the south- 
 east trade-winds. On this account these winds seem to extend 
 much farther south here and are more southerly than in the 
 trade-wind zone farther west, where the direction becomes 
 more from the east. Here, consequently, the deflected current 
 breaks through the belt of high pressure of these latitudes and 
 interferes with the continuity of the rainless zone of the tropi- 
 cal calm-belt and southeast trade-winds. 
 
 126. In consequence of the general circulation of the at- 
 
1 88 CLIMATIC INFLUENCES OF THE GENERAL CIRCULATION. 
 
 mosphere, both the temperature and the amount of rainfall are 
 often different on the two sides of a mountain range, especially 
 where the direction of this range is normal to the prevailing 
 direction of the wind. The current, in passing over the moun- 
 tain, carries the aqueous vapor up to a higher altitude where it 
 is cooled by the expansion of the ascending air and condensed, 
 just as in the case of a vertically ascending current in the equa- 
 torial rain-belt ; so that on the windward side of the mountain 
 there is an unusual amount of rainfall. This is especially the 
 case if the rain-producing currents pass to the mountain side 
 from the ocean, where the air is generally more nearly satu- 
 rated, and more especially if it passes from a warmer ocean 
 to a colder district, for then the air has greater capacity for 
 moisture, and is liable to be very nearly saturated before it 
 reaches the mountain side and begins to ascend. On the lee- 
 ward side the air descends to a lower level, and if it were even 
 .saturated with aqueous vapor in crossing the top of the range, 
 it soon becomes unsaturated, and consequently there is no 
 longer any condensation or rainfall, so far as it depends upon 
 the general current passing over the mountain, and there can 
 therefore be no rainfall on this side, unless it arises from other 
 local and temporary causes. 
 
 In the general circulation of the atmosphere, we have seen 
 that the average or resultant direction of the winds in the mid- 
 <dle and higher latitudes, at the earth's surface and in the lower 
 strata of the air, is nearly from west to east, and in the zones 
 of the trade-winds there is a large west component of motion. 
 Hence in the case of all high mountain ranges extending north 
 and south, or approximately so, especially in the case of coast 
 ranges, the west sides of these ranges, in the middle and higher 
 latitudes, should be the rainy sides, and the east sides the dry 
 sides, and the reverse in equatorial and tropical latitudes. 
 Hence in the northern part of California, in Oregon, Washing- 
 ton Territory, and Alaska, along the Pacific coast, there is an 
 abundant annual rainfall, of from 50 to 75 inches and more, as 
 may be seen from Loomis's rain chart, 22 caused by the coast 
 :ranges of mountains, the winds in this case coming directly 
 
IN CONNECTION WITH MOUNTAIN RANGES. 1 89* 
 
 from the ocean. After passing the coast ranges in these high 
 and cool latitudes the amount of aqueous vapor left in the air 
 is very much diminished, so that farther on there is but little 
 rainfall, and especially east of the main Rocky Mountain 
 range. There is, consequently, a large area east of this range, 
 extending to about the looth meridian west from Greenwich, 
 over which the amount of annual rainfall is small. Farther 
 east, over the United States and Canada, the vapor for pro- 
 ducing rain, as has been explained, comes mostly from the Gulf 
 of Mexico, and the causes of the ascending currents necessary 
 to give rise to condensation and rainfall depend mostly upon 
 the local and temporary disturbances of ordinary rain-storms, 
 and but little upon mountain ranges. 
 
 In western Europe, where the westerly winds from the 
 Atlantic Ocean first strike the continent, especially on the west 
 sides of the mountain ranges, even those near the ocean of 
 only moderate height, and on the west side of the Caucasus 
 Mountains on the east side of the Black Sea, over which the 
 winds pass before reaching them, there is mostly an abundant 
 annual rainfall ; while in the interior parts of Asia, especially in 
 Tartary and Mongolia, the amount of annual rainfall is scant, 
 the aqueous vapor having been mostly condensed and having 
 fallen in rain, in passing over the mountain ranges of Europe,, 
 and in ascending currents in ordinary rain-storms, before reach- 
 ing them. 
 
 On the west side of the Andes, south of the parallel of about 
 35, in Chili and Patagonia, the amount of rainfall is very great, 
 arising from the upward deflection of the moist and strong air 
 currents of these latitudes, coming directly from the ocean; 
 while on the east side of the range of the Andes here, there 
 is scarcely any rain. 
 
 27. In the trade-wind latitudes of both hemispheres, 
 where the air, on account of its west component of motion, is 
 deflected upward by the mountain ranges of Central America,, 
 and the Andes in South America, the rainfall is very great r 
 while on the opposite sides, especially in Peru, and on the 
 ocean adjacent, there is scarcely any rain, although it is said 
 
19 CLIMATIC INFLUENCES OF THE GENERAL CIRCULATION'. 
 
 that the air here is often nearly or quite saturated with aqueous 
 vapor, and that fogs and mists frequently occur. At the head- 
 waters of the Amazon on the east side of the very high range 
 of the Andes, and where the warm and very moist air currents 
 of the zone of the southern trade-winds strike, the amount of 
 annual rainfall is especially great, but this is increased by the 
 rainfall of the equatorial calm-belt, which oscillates here through 
 a considerable range of latitude, and so increases the annual 
 rainfall over the whole of this range. On the east coasts also 
 of South Africa, of Madagascar, and of Australia, within the 
 .zone of the southeast trade-winds, and which on the oceans is 
 a rainless zone, there are considerable rainfalls, while on the 
 west sides there are scant rainfalls, if not an almost entire 
 deficiency, and the latter is the case all the way through the 
 interior of Australia to the western coast. 
 
 The large annual rainfall on the eastern coast of China is 
 'due in part to the same cause, but mostly perhaps to the sum- 
 mer monsoon which draws the warm and moist air from the 
 adjacent ocean over the mountain ranges in toward the interior 
 of the continent. 
 
 On both sides of the Rocky Mountains and the Andes on 
 the parallels from 30 to 40, there is scarcely any rainfall, for 
 these being the parallels of little or no easterly or westerly mo- 
 tion of the atmosphere, there is no upward deflection of the 
 air on either side, and besides, being in the belt of high pres- 
 .-sure, there is a tendency in the air to settle down toward the 
 surface, and hence there is little rainfall. 
 
 28. Wherever, on account of the prevailing currents, there 
 is a wet and a dry side to the mountains, the dry side is the 
 warmer. The air in ascending on the wet side, until condensa- 
 tion takes place, cools at the same rate with increase of altitude, 
 as it is warmed on the other side in falling through the same 
 distance. But pfter condensation commences, as may be seen 
 from Table III, the rate of cooling of ascending air is much less, 
 especially where the temperature is high, as in the lower lati- 
 tudes; while on the other side, where the air descends from its 
 highest level to that where condensation commences, the rate 
 
IN CONNECTION WITH MOUNTAIN RANGES. IQI 
 
 is the same as that of dry air, except that it is diminished a 
 little by the evaporation of the cloud-particles immediately 
 after it first begins to descend. Suppose the height of the 
 range is 3000 meters, but that the condensation begins at the 
 altitude of 1000 meters. Then if the rate of cooling on the 
 average, while the air is ascending and condensation is taking 
 place, is o.5 C. for each 100 meters of ascent, the air is cooled 
 in this ascent 10, while in descending on the other side to the 
 same level of incipient condensation in ascending, the increase 
 of temperature is 20, or nearly, and so there is a gain of nearly 
 10 C. of temperature from the time the air left the level of in- 
 cipient condensation on the one side until it descended to the 
 same level on the other side. Since the rate of cooling below 
 this level as the air ascends, is exactly the same as that of 
 increase of temperature in descending on the other side through 
 the same distance, of course there is the same difference of 
 temperature at the earth's surface between the two sides, if the 
 surface on each side has the same level, as there is at the level 
 ot incipient condensation as the air ascends. The effect is that 
 of a temporary foe/in to be considered farther on, and is here 
 a permanent effect continuing through the year, with most 
 probably a considerable annual inequality, since the strength 
 of the general air currents upon which it depends is greater in 
 winter than in summer. Of course the full effect, as computed 
 above, is never reached, since the computation assumes that 
 the air is cooled and heated simply by expansion and compres- 
 sion ; but the temperature depends upon a balancing of the 
 rates of absorption and radiation, and the radiation of the 
 warm air on the one side is greater than that of the cold air on 
 the other side, and consequently the difference is a little less 
 than that of the computation. As the air flows away from the 
 base of the mountain range eastward, of course the tempera- 
 ture becomes less until it is reduced to that depending upon 
 the local conditions and independent of the foehn effect of the 
 ^distant mountain. 
 
 In accordance with what precedes, there is a belt close along 
 the eastern side of the Rocky Mountain range, with a mean 
 
IQ2 CLIMATIC INFLUENCES OF THE GENERAL CIRCULATION.. 
 
 temperature above that of the same latitude farther east, and 
 which is sensibly felt to a considerable distance over the plain, 
 and this is especially the case in the winter season. Accord- 
 ingly the coldest winds in winter at Denver and Cheyenne, and 
 other places similarly situated on the east side of the Rocky 
 Mountain range, are not the northerly or northwesterly winds, 
 but those from a northeasterly direction. It is also said that 
 the mean winter temperature at Georgetown, Colorado, close 
 to the base of the mountain, is milder than that of Denver, 
 some forty miles farther east, although the elevation of the 
 former is nearly 4000 feet greater. 
 
 A similar effect seems to be produced by the range of the 
 Andes in South America. According to Dr. Gould's isother 
 mal chart of the mean annual temperature of the southern part 
 of South America, 31 the temperature immediately east of the 
 range is several degrees of the Centigrade scale higher than 
 on the west side, and also considerably higher than that farther 
 east on the same parallels, at least north of the parallel of 40, 
 where the continent is wide, and the isotherms are well deter- 
 mined on the eastern side of the continent. 
 
CHAPTER V. 
 MONSOONS, AND LAND- AND SEA-BREEZES. 
 
 INTRODUCTION. 
 
 129. HAVING treated the general circulation of the atmos- 
 phere with its annual inequalities or changes with the seasons, 
 arising from the difference of temperature between the equa- 
 torial and polar regions and its annual variations, we come now 
 to consider the less general, but still often powerful, atmos- 
 pheric disturbances arising from differences of atmospheric tem- 
 perature between continents or islands and the surrounding 
 oceans, or between any region of the earth's surface, abnor- 
 mally heated or cooled, and the surrounding parts of that sur- 
 face. In the general circulation of the atmosphere the tem- 
 perature difference upon which it depends is permanent, though 
 subject to large annual inequalities ; but in these secondary and 
 less general disturbances there is little or no permanent tern 
 perature disturbance, independent of the annual and diurnal 
 changes and reverses, and so they are mostly of the latter charac- 
 ter, and these give rise to annual and diurnal alternations of 
 direction and velocity of motion. The former of these alter- 
 nations are called monsoons, and the latter land- and sea-breezes^ 
 
 It has been shown, 68, that in the lower latitudes the mean 
 annual temperature of the continents is greater than that of 
 the oceans on the same latitudes, and the reverse in the higher 
 latitudes. There is, consequently, a permanent difference of 
 temperature between the continents and the oceans in the equa- 
 torial regions, the mean temperatures of the former being the 
 greater, but this vanishes in the middle latitudes, and becomes, 
 reversed in the polar latitudes. This difference, however, at 
 most, is small in comparison with the great annual changes and 
 
 i93 
 
194 MONSOONS, AND LAND- AND SEA-BREEZES. 
 
 reversals of differences, except near the equator, where these 
 annual changes are small. These permanent differences of tem- 
 perature must give rise to corresponding permanent atmos- 
 pheric circulations, with motions of the lower part of the atmos- 
 phere from the colder to the warmer region, and the reverse 
 above, to which are superadded the usually greater disturbances 
 depending upon the annual variations of temperature. Mon- 
 soons are usually defined to be winds which blow six months 
 in one direction and the other six months in the contrary direc- 
 tion ; but this complete reversal takes place only where there is 
 no permanent atmospheric disturbance of any kind, such as that 
 of the general circulation with its various deflections by conti- 
 nents and mountain ranges, or from the permanent part of the 
 monsoon influence just referred to. The monsoons, therefore, 
 are generally not complete reversals of direction with interven- 
 ing intervals of little or no velocity, but the directions at the 
 different seasons may change less than a quadrant, and the 
 strength of the winds may vary considerably at different sea- 
 sons, but not entirely vanish. In fact, where there are strong 
 perennial winds, the monsoon influence may be such as to 
 merely change a little the strength and direction of these winds, 
 one way at one season of the year and the contrary way at the 
 opposite season. 
 
 130. The temperature differences or gradients upon which 
 the monsoons depend are not those of the absolute tempera- 
 tures, but the gradients of the differences between these and 
 the normal temperatures of latitude of summer and of winter. 
 From the temperature gradients of the latter or normal tem- 
 peratures of latitude arise the general atmospheric circulations 
 of the two hemispheres, so that these must not be again taken 
 in as a part of the monsoon influences ; but these latter must 
 depend upon differences or temperature gradients in the ab- 
 normals of temperature, that is, departures of temperature from 
 the normals of latitude, for without such departures we should 
 have no monsoon influences, but simply the undisturbed gen- 
 eral atmospheric circulation, with velocities a little greater in 
 winter than in summer, but no monsoon. For instance, the 
 
INTRODUCTION. IQ5 
 
 interior of a large continent may be much warmer than the 
 polar and much colder than the equatorial side, but still the 
 temperature gradients arising from such differences may not 
 form any part of the monsoon influence. But if there is an 
 increase or decrease from the interior outward of the departures 
 of actually existing temperatures from the normals of latitude, 
 then we have a temperature disturbance which gives rise to a 
 monsoon, or at least to a monsoon influence. 
 
 131. Land- and sea-breezes, at least of small islands, are sim- 
 ilar to monsoons, the latter being a regular alternation, more 
 or less complete, of the direction of the wind between summer 
 and winter, and the former between day and night ; but the 
 lengths of the periods of the alternations are very different. 
 Jn the case of continents the land- and sea-breezes are sensible 
 along the coasts only, where the temperature gradients are 
 greatest ; for the periods of alternation are so short that a com- 
 plete system of interchanging motions between the ocean and 
 the land, extending into the interior of the continent, cannot 
 be formed and reversed every day, and so the winds in this 
 case generally extend only a short distance either inland or out 
 on the ocean. In the case of a small island, however, where a 
 complete interchanging circulation can be inaugurated in a 
 short time, there is little difference between the land- and sea- 
 breezes and the monsoons of continents, except in their extent 
 .and in the periods of alternation. 
 
 132. The strength of the monsoon, or of the land- and sea- 
 breeze, depends very much upon the nature of the surface of 
 the continent. In the case of a perfectly flat continent with 
 no highlands or mountain ranges, there would, of course, be an 
 interchange of air between it and the ocean in case of differ- 
 ence of temperature, that of the lower part moving toward the 
 ^warmer region, and that of the upper part away from it ; but 
 the monsoon effects would be comparatively small, and would 
 not at all have the great strength of surface winds which is 
 usually observed. The interchange would be mostly in the 
 ;great mass of air above, and no strong motion would take place 
 .at the earth's surface. In this case, also, the land- and sea- 
 
196 MONSOONS, AND LAND- AND SEA-BREEZES. 
 
 breezes have but little strength, and are felt near the coasts 
 only, but they are very much increased in strength, and are felt 
 at a much greater distance, where there are hillsides and moun- 
 tain slopes near the coast. 
 
 In the annual and diurnal oscillations of temperature the 
 amplitudes are small on the ocean surface, and in the air at all 
 altitudes above it, and also in the great mass of air over the 
 continent except in a stratum next the earth's surface, of small 
 depth in comparison with that of the whole. The monsoon 
 effects, therefore, depend mostly upon the temperature differ- 
 ences between the continent and the ocean of only a compara- 
 tively thin stratum of the atmosphere next the earth's surface,, 
 of which the part over the continent is very much heated above, 
 or cooled below, that of the ocean. The temperature differ- 
 ences of such a stratum, over a perfectly level continent, even 
 if they were very great, would give rise to very little horizontal 
 disturbance of the atmosphere. If this stratum over the con- 
 tinent were greatly heated, it might give rise to the unstable 
 state, from which would result numerous, but very small, local 
 eruptions through the strata above, but no sensible monsoon-; 
 effects. On the other hand, if it were cooled down to a very- 
 low temperature, the increased density would tend mostly to^ 
 keep it next the earth's surface, and there would be scarcely 
 any tendency to flow away laterally toward the warmer ocean. 
 But if the surface of the continent is convex, or if it has high- 
 lands with long slopes, or the interior is in almost any way 
 considerably elevated above sea-level, the tendency in the case 
 of the summer monsoon to flow in from the ocean toward the 
 interior of the continent, or the reverse in that of the winter 
 monsoon, is very much increased. The same is true with re- 
 gard to land- and sea-breezes where there are mountain eleva- 
 tions near the coast. 
 
 133. The reason of this can, perhaps, be made clearer by 
 assuming an analogous case, but one which will be more easily 
 understood. If a perfectly level plain were covered with a 
 stratum of water, there would, of course, be some flow of water 
 in all directions from the interior outward ; but unless the depth. 
 
INTRODUCTION. 
 
 were considerable in comparison with the extent of the plain, 
 the current might not be perceptible except near the outer 
 part. But if the same depth of water were placed upon the 
 surface of a continent with an elevated interior having long 
 declining slopes from the interior outward, the rapidity of the 
 rush of water would be very great, and somewhat in propor- 
 tion to the steepness of these slopes. The case is somewhat 
 similar where there is a stratum of air next the earth's surface 
 abnormally cold and dense in comparison with the air above it 
 and over the ocean. If the earth's surface is flat there is little 
 tendency in this air to move in any direction, but if it rests 
 upon declining slopes, this tendency, as in the case of water, is 
 very much increased. Of course the absolute tendencies in 
 the case of water and the abnormally dense stratum of air are 
 very different, the former being due to the force of the whole 
 pressure of the fluid down an inclined plane, but the other 
 merely to the increased pressure arising from the diminished 
 temperature and increase of density. The relative tendencies, 
 however, for different surfaces are the same in both cases, and 
 .somewhat in proportion to the steepness of the declining sur- 
 face. 
 
 The very reverse of this is the case where the stratum of air 
 next the earth's surface is abnormally heated in comparison 
 with the temperature of the air above and around about. If 
 the excess of temperature in this case is the same as the defi- 
 ciency in the other, the tendency now to flow from all sides to- 
 ward the interior up the slopes is exactly equal to the tendency 
 to flow outward and down these slopes in the other case. There 
 being now a deficiency of pressure in the warm rarefied stratum, 
 where this rests upon an inclined surface, the greater pressure 
 of the heavier air everywhere else at the same level tends to 
 drive the lighter surface air up the slopes with the same 
 force with which it descends in the other case, both depending 
 upon the same difference of density between the stratum and 
 the air generally at the same levels. 
 
 The case of the warm and rarefied air ascending on the slopes 
 is somewhat similar to that of warm air ascending in a flue. If 
 
MONSOONS, AND LAND- AND SEA-BREEZES. 
 
 the flue is horizontal, although the air within is kept much 
 warmer than that of the flue, and the outside air generally, the 
 warmer air gradually, but very slowly, passes out of the flue 
 and allows other air to take its place ; but if it is only a little in- 
 clined, the air ascends the incline and escapes rapidly from the 
 higher end, and the more so the greater the differences of 
 temperature, the length of the tube, and the steepness of the 
 inclination. So the tendency of the warmer stratum of air to< 
 flow up an inclined surface increases with increasing differences. 
 of temperature, and increasing length and steepness of slope. 
 
 134. There is also another consideration in connection with 
 the subject of the monsoon influence of highlands. The ten- 
 dency of air to ascend or descend and to give rise to ascending 
 or descending currents depends upon differences of temperature 
 between the air and that of the surrounding regions at the same- 
 level. But it is a matter of observation that the temperature 
 of highlands, and especially of high plateaus, in summer, is. 
 nearly as great as that on plains near sea-level. The tempera- 
 ture, also, for the altitudes above the surface, at least to a con- 
 siderable height, must be much greater than that of the sur- 
 rounding air at the same levels, since the rate of decrease of 
 temperature with increase of altitude above the surface of the 
 plateau is somewhat the same as above any plain near sea-leveL 
 If a portion of air, therefore, either on a horizontal plane or a 
 slope near sea-level is only a little warmer than the surrounding 
 air on the same level, it tends to ascend and to give rise to an 
 ascending current ; but if air at the same temperature is high 
 up on some mountain side or plateau, this tendency is much 
 increased, because now the difference of temperature between 
 this air and the surrounding air at a distance on the same level 
 is much greater. 
 
 If a tall flue with a temperature only a little raised above the 
 surrounding temperatures at sea-level were elevated to the top 
 of a high mountain, where the surrounding air is much colder 
 and more dense, the draught of the flue would be very much in- 
 creased. So the wide column of air of higher temperature over 
 a high plateau and extending up to a considerable height above 
 
IN TROD UCTIOtV. 1 99 
 
 the surface has a much greater tendency to ascend than a simi- 
 lar one of the same temperature on a low plane near sea-level. 
 
 This effect, however, is felt mostly in the summer monsoon 
 influence, for in winter the temperature of the plateau is not so 
 much below surrounding temperatures as it is above them in 
 the summer. 
 
 135. In accordance with the preceding vie-w of the principal 
 cause of monsoons and land- and sea-breezes, it is seen from ob- 
 servation that all the great monsoons and the strongest land- 
 and sea-breezes are found the former in countries and on oceans 
 adjacent to high mountain ranges, and the latter along coasts 
 with high mountains in the background. Neither the heated 
 interior in summer of the Great Sahara of northern Africa nor 
 of Arabia and Persia, which is considered the warmest region 
 on the globe, causes, during this season of the year, any con- 
 siderable indraught of air. It is true that at this season the north- 
 westerly winds prevail a little more on the northwest coast of 
 Africa and the ocean adjacent, due, no doubt, to the influence 
 of the highly heated desert of the Sahara ; but over Arabia and 
 Persia the northwest winds continue to blow almost incessantly 
 during June and July, away from the heated interior toward 
 the Arabian Sea, though at times they are quite light. Even 
 at this season the tendency to flow in towards this heated dis- 
 trict is not sufficient to overcome the northwest wind of this 
 region arising from the deflection around the elevated regions 
 of Asia ( 123). The monsoon influence, therefore, of countries 
 mostly level without an elevated interior, however highly they 
 may become heated in summer or cooled in winter, is not very 
 great. 
 
 With regard to land- and sea-breezes Mr. Laughton says : 3a 
 
 " This seems to be sufficiently established by facts, that the sea-breeze 
 nowhere blows with any great strength, except where there are mountains in 
 the background ; and that these mountains are, during the afternoon, when 
 the sea-breeze has gotten well home to them, constantly enveloped in 
 mist or storm. The Blue Mountains of Jamaica afford the best illustra- 
 tion of this ; and it is on the coast of Jamaica, more especially of Port 
 Royal, that the sea-breeze has a force unknown anywhere else." 
 
20O MONSOONS, AND LAND- AND SEA-BREEZES. 
 
 In the same connection it is said : 
 
 ' " As a matter of geographical fact, the land-breeze has nowhere any- 
 noticeable strength unless there are mountains in the immediate neigh- 
 borhood." 
 
 136. In the case of the summer monsoon, where the interior 
 of the country is so elevated that the current ascends the slopes 
 to an altitude where condensation of the vapor takes place, 
 the latent heat of condensation adds much strength to the cur- 
 rent, just as in the case of the trade- winds, in which their 
 strength is increased by the latent heat of condensation in the 
 equatorial rain-belt. On this account the summer monsoon of 
 the North Indian Ocean is much stronger than the winter mon- 
 soon : so much so, that the southwest monsoon is often spoken 
 of as The Monsoon, the northeast monsoon being insignificant 
 in comparison with it. Notwithstanding the trade-wind is com- 
 bined with the monsoon effect, the resultant of both produces 
 in the Arabian Sea only a gentle and steady breeze during the 
 winter season ; whereas the southwest monsoon of the summer 
 is a steady gale of so great strength that it is impossible for 
 even steamers to force a passage from Bombay to the Gulf of 
 Aden in June and July. 
 
 In all cases, also, of extraordinarily strong sea-breezes, there 
 are high mountain elevations near the coast on which there is a 
 vast amount of condensation and precipitation of rain at the 
 time. 
 
 THE MONSOONS OF ASIA AND THE INDIAN OCEAN. 
 
 137. In no other part of the world are the conditions for a 
 powerful monsoon influence so favorable, and the strength of 
 the monsoons produced so great, as in India and the North 
 Indian Ocean. The Himalayas on the north with an east and 
 west extent of 1300 miles and an average height of 18,000 feet, 
 the parallel Kuenlun range still farther north, much greater in 
 extent but of less height, with the high plateaus of Thibet and 
 Cashmere between, and beyond these yet the vast and elevated 
 deserts of the interior of Asia between the Kuenlun and Altai 
 
THE MONSOONS OF ASIA AND THE INDIAN OCEAN. 2OI 
 
 ;ranges, together with the warmth and great capacity of the air 
 for moisture over India and the North Indian Ocean, for reasons 
 just given in the preceding pages, all combine to add strength 
 to the monsoons, especially those of the summer season. As 
 the sun in early summer approaches the northern tropic, the 
 air of the Himalayan southern slopes and the desert of Gobi 
 and the sunburned plains of Central Asia becomes warmed 
 up to a temperature much above that of the adjacent and sur- 
 rounding air at a distance on the same level, and so a powerful 
 centripetal and ascending tendency is induced, by which the air 
 is drawn in toward the centre of warmth and rarefaction from 
 all sides, but especially from the equatorial side, where the in- 
 fluence is felt even beyond the equator. For there is not only 
 the tendency of the heated stratum of air in contact with the 
 southern slopes to ascend, but the air over the whole of the 
 elevated part of Central Asia, not only near the surface, but up 
 to a considerable altitude, being warmer than that of the sur- 
 rounding regions on the same level, it has a strong tendency to 
 rise up and leave a partial vacuum into which air from all sides 
 flows to take the place of that which is continually ascending. 
 
 The warmth of the air, and consequently the monsoon 
 influence, is much increased in summer by the latent heat given 
 out in the condensation of the aqueous vapor in the almost 
 or quite saturated air at the beginning of its ascent, for, being 
 of high temperature over India and the adjacent ocean, its 
 capacity for moisture is very great, and this is condensed, not 
 only as it ascends the southern slopes to the general height 
 of the Himalayas, but still beyond in its further ascent over 
 the plateaus of Thibet and Cashmere, where the amount of 
 rain during the summer monsoon is often enormous. Although 
 there would, no doubt, be a considerable monsoon influence in 
 the case of perfectly dry air, yet the principal part of the 
 energy in the summer monsoons of India is probably in the 
 aqueous vapor of the air. Some idea of the difference of 
 temperature between the ascending air up the slopes of the 
 Himalayas and that over Thibet beyond, and the air of the 
 adjacent and surrounding regions at the same level, may be 
 
202 MONSOONS, AND LAND- AND SEA-BREEZES. 
 
 formed from an examination of Table III. From this it is seen- 
 that the average rate of decrease of temperature with increase 
 of elevation in ascending air, even up to great altitudes, would 
 be only about o.4 C. in each 100- meters, while we know that 
 the rate of decrease in air generally in the summer season, 
 especially in the lower part of it, is much greater, and conse- 
 quently the difference of temperature above, between the 
 ascending air and the surrounding air at the same level, must 
 be considerable. 
 
 138. During the month of April the weather is unsettled, 
 and the wind variable, without any prevailing direction. By 
 the middle of May the summer monsoon, with its accompany- 
 ing rains, is fairly set in, and soon after arrives nearly at its full 
 strength. The general direction of the wind on the Arabian 
 Sea is from the southwest, or rather from the west-southwest, 
 and is here called the Southwest Monsoon. The direction is 
 more from the west than it otherwise would be, both on account 
 of the deflected current around the highlands of Asia, 123, 
 and also on account of the deflecting force of the earth's rota- 
 tion, which, however, is not very strong here, so near the 
 equator. Further east, in the Bay of Bengal, the wind is more 
 southerly ; along the coast of China, and over the Chinese Sea, 
 it is from the southeast, and in Japan it is still more easterly. 
 Along the whole of the north coast of Siberia the wind blows 
 inland during the summer season, though not directly in towards 
 the interior, but rather from the northwest, the direction being 
 the resultant of the monsoon influence and the general easterly 
 tendency of the atmosphere in these latitudes. The prevailing 
 direction of the wind observed in the Vega expedition in 
 summer from North Cape to Yokohama was from the north- 
 west. The monsoon influence then is felt on the north side 
 of Asia ; but, as we would expect, it is comparatively weak, 
 because there are not many highlands and high mountains in 
 Siberia, and the effect arising from the condensation of aqueous 
 vapor is small. 
 
 The general tendency in the summer season is to flow in 
 from all sides toward the heated interior, with a slight deflec- 
 
THE MONSOONS OF ASIA AND THE INDIAN OCEAN. 20$. 
 
 tion to the right, on account of the influence of the earth's 
 rotation, and consequently to flow out above in all directions.. 
 In consequence, however, of the high range of the Himalayas, 
 little air from India passes over this range toward the north ;: 
 but it continues mostly to ascend after arriving at the top of 
 the slope, until it is immerged into the returning current above 
 toward the equator. It is said, however, that there is some air 
 passing through all the highest passes of the range, on toward 
 the interior of the continent. According to the experience of 
 Prjivalsky in his travels over the high plateau of Thibet in 
 June and July, there must be a great deal of air brought into- 
 this region at this season, which in ascending gives rise ta 
 much rain. It is said : "As to rain, it poured down every day, 
 sometimes several days without interruption. The amount of 
 vapor brought by the southwest monsoon, and deposited there, 
 is so great that, during the summer, northern Thibet becomes 
 an immense marsh." But this vapor comes in, most probably,, 
 from other directions, and not from the southwest monsoon 
 only, since southern Thibet, next the Himalayan range, is. 
 said to be comparatively dry. 
 
 In the Arabian Sea the monsoon influence in summer is in 
 the right direction and sufficiently strong to entirely overcome 
 and reverse the northeast trade-wind ; but in the Chinese Sea,, 
 and the vicinity of the Philippine Islands, the effect is such as 
 to change the northeast trade-wind to a southeast wind. Not 
 only is the regular trade-wind systems, then, of the North 
 Indian Ocean entirely broken up in the summer season, but 
 the monsoon influence draws air from the other side of the 
 equator, thus strengthening the southeast trade-winds there. 
 This is especially the case over all the equatorial region 
 between China and Australia, since, while the interior of Asia 
 during its summer is heated and the air rarefied, that of Aus- 
 tralia is cooled and its pressure increased, so that the tempera- 
 ture and pressure gradients between the two countries are due 
 to both causes. There is consequently no equatorial calm- 
 belt during the monsoon ; but the air is drawn from about the 
 parallel of 25 S. across the equator to the rarefied central part 
 
-204 MONSOONS, AND LAND- AND SEA-BREEZES. 
 
 of Asia not directly, but is deflected toward the west, south of 
 the equator, and then eastward, after crossing the equator to 
 the north side, by the deflecting force of the earth's rotation. 
 The region of greatest temperature, or, at least, of greatest 
 departure from the normals of latitude, upon which the mon- 
 soon depends, and lowest barometric pressure, is not now near 
 the equator, but in the interior of Asia, and the highest pres- 
 .sure is in the southern belt of high pressure, about the parallel 
 of 30 S., so that there is now a continuous gradient of pressure 
 decreasing from this belt across the equator into the interior of 
 -Asia. There is therefore, at this season of the year, an enor- 
 4nous disturbing influence, due to this monsoon, which entirely 
 breaks up the general circulation of the atmosphere and the 
 "tropical and equatorial calm-belts. 
 
 139. As in the case of the general motions of the atmos- 
 phere, so in that of monsoons wherever the vapor-laden 
 current strikes a range of hills or mountains, and is deflected 
 upward, there is a very large amount of rainfall during the 
 time. The current of the southwest monsoon, in its passage 
 from the Arabian Sea toward the southern slopes of the 
 Himalayas, first encounters the western Ghauts, a range of 
 ^mountains from 4000 to 6000 feet in height, near the Malabar 
 coast, where a great part of its vapor is condensed, and the 
 rainfall is immense. Passing on then with little precipitation 
 to the mighty Himalayas, it now in the ascent loses nearly all 
 of the remaining part of its vapor, which, falling on a small 
 area on account of the steepness of the slope, causes an 
 immense amount of rain to be precipitated, greater or less 
 according to the nature of the country and the height and 
 steepness of the mountain sides. 
 
 But the greatest rainfalls are experienced in the mountains 
 of Khasia, north of the head of the Bay of Bengal, where the 
 warm and moist air of the nearly equatorial winds blowing 
 across the bay is somewhat concentrated by the converging 
 coasts and highlands on the east and west before it commences 
 its ascent up the mountain slopes, and having previously lost 
 little or no vapor by condensation, as it does in the case of the 
 
THE MONSOONS OF ASIA AND THE INDIAN OCEAN. 
 
 southwest monsoon in passing over the western Ghauts, the 
 whole vapor is now condensed in the ascent of the Himalayan 
 slope. According to Dr. Hooker, as cited by Laughton : 18 
 
 " The climate of Khasia is remarkable for its excessive rainfall. At- 
 tention was first drawn to it by Mr. Yule, who stated that in the month 
 of August, 1841, 264 inches fell, or twenty-two feet; and that during five 
 successive days, thirty inches fell in every twenty-four hours. Dr. Thom- 
 son and I also recorded thirty inches in one day and night ; and during 
 the seven months of our stay upward of 500 inches fell ; so that the total 
 annual rainfall perhaps greatly exceeded 600 inches, or 50 feet, which has- 
 been registered in succeeding years. From April, 1849, to April, 1850, 502 
 inches fell. This unparalleled amount of rainfall is attributable to the: 
 abruptness of the mountains which face the Bay of Bengal, from which 
 they are separated by 200 miles of Jheels and Sunderbunds." 
 
 On account of the vast amount of precipitation during the 
 summer monsoon over India, and especially the slopes of the 
 Himalayas, the southwesterly monsoon of the Arabian Sea and 
 western India and the more southerly monsoon farther east, 
 is often called the Wet Monsoon. 
 
 140. The air which is drawn across the equator during the 
 summer monsoon from the southern hemisphere of course 
 simply strengthens the regular southeast trade-wind which ex- 
 ists when there is no disturbance from the monsoon influence ; 
 but at and a little north of the equator the wind becomes 
 southerly, and still farther north of the equator it is deflected 
 around by the influence of the earth's rotation into a north- 
 easterly direction, and becomes the southwest monsoon. This 
 is clearly shown by the following table given by Woeikoff, 33 of 
 percentages of the winds from the different directions as de- 
 duced from the observations on the ships of Holland, during the 
 months of June, July, and August : 
 
 Latitude. E. Long. N. N.E. E. S.E. S. S.W. W. N.W. Cairns 
 I0 15 S. 80 90 
 5 10 80 90 
 
 o5 75 85 
 
 o 5 N. 80 90 
 
 5 10 80 90 
 
 1015 8595 
 
 I 
 
 3 
 
 17 
 
 63 
 
 12 
 
 i 
 
 i 
 
 
 
 2 
 
 3 
 
 9 
 
 22 
 
 40 
 
 10 
 
 8 
 
 7 
 
 2 
 
 2 
 
 i 
 
 3 
 
 22 
 
 23 
 
 15 
 
 J2 
 
 14 
 
 5 
 
 5 
 
 i 
 
 
 
 
 
 5 
 
 18 
 
 43 
 
 24 
 
 7 
 
 2 
 
 
 
 i 
 
 I 
 
 3 
 
 9 
 
 57 
 
 23 
 
 2 
 
 3 
 
 
 
 
 
 
 
 2 
 
 10 
 
 64 
 
 13 
 
 3 
 
 9 
 
:206 MOiVSOOKS, AND LAND- AND SEA-BREEZES. 
 
 From this table it is seen that the southeast trade-wind 
 gradually changes around into the southwest monsoon, the ob- 
 served directions being mostly southeasterly south of the equa- 
 tor and southwesterly north of it, and there is apparently no 
 calm-belt at or near the equator. 
 
 141. Toward the end of October, or the beginning of No- 
 vember, the interior of Asia and the slopes of the Himalayan 
 range are cooled down to the mean temperatures of the year, 
 .and there has been an equalization of the air-pressure, and the 
 monsoon has subsided ; or rather, the pressures have changed 
 to the normal pressures for the mean temperature of the year, 
 and the winds to those of the corresponding general circula- 
 tion, with high pressure and calms near the two tropics, and 
 low pressure and calms near the equator. But now a reversion 
 of the summer conditions gradually takes place. During the 
 winter season of the northern hemisphere the interior of Asia, 
 and especially of Siberia, becomes cooled down by the radia- 
 tion of heat into space, through the now very dry air, to a very 
 low temperature, far below that of the normals of latitude for 
 the season, and the density of the air and the barometric pres- 
 sure are very much increased, instead of being diminished as in 
 the summer season. The effect is now a complete reversal of 
 all the motions between the central and surrounding regions, 
 and instead of a flowing in below from all sides toward the cen- 
 tral part, and a flowing out above in all directions, the flow is 
 outward below and inward above. The southern slope of the 
 Himalayas is now cooled by radiation far below the general 
 temperature of the air at the same levels at a distance from it, 
 and the stratum of air in contact becomes dense and heavy, and 
 consequently tends to flow down toward the lower levels of 
 India and the Indian Ocean. The monsoon is now completely 
 reversed, and instead of S.W., S., and S.E. winds around the 
 southern and eastern coasts of Asia, there are N.E., N., and 
 N.W. winds. 
 
 The wind over the Arabian Sea and India depending upon 
 the monsoon influence being mostly a northeast wind combines 
 with the regular trade-winds of these latitudes, and the result- 
 
THE MONSOONS OF ASIA AND THE INDIAN OCEAN. 2O/ 
 
 ant is a stronger wind than that which would arise from the 
 monsoon influence alone, but still not nearly so strong as that 
 of the southwest monsoon. It is called the Northeast Monsoon, 
 and the monsoons generally of the winter season of the region 
 south and east of Asia are often called the Winter Monsoons. 
 Since the air of these monsoons comes from the elevated dry 
 and cool interior of the continent into warmer regions of lower 
 level, it is very dry, especially that in India which comes down 
 from the Himalayas. Hence these monsoons are often called 
 the Dry Monsoons. 
 
 But when the northeasterly monsoon does not come di- 
 rectly from the elevated and dry interior of the continent, but 
 blows a long distance over the sea, on coming in contact with 
 mountain ranges, as in Ceylon, it gives rise to just as much 
 rain, or nearly so, as the southwest monsoon. The latter is 
 usually a little the stronger, and blowing from more southern 
 latitudes may have a little more vapor, and so for both reasons 
 give rise to a little more rain. 
 
 In the summer or wet monsoons we have the effect of the 
 latent heat of condensation in connection with that of the 
 heating from the sun's radiation, but in the winter and dry 
 monsoons we have simply the effect from greater cooling by 
 radiation, which is about equivalent only to that from the 
 greater heating in summer from solar radiation, so that the 
 effect is not nearly so great in the case of the winter monsoons 
 as in that of the summer monsoons in which much energy 
 arises from the latent heat of condensation of aqueous vapor. 
 Accordingly the northeast monsoon, though strengthened by 
 the regular northeast trade-wind, is not nearly so strong as the 
 southwest monsoon, as has been already stated in 136. 
 
 During the winter season the winds of Northern Siberia, 
 especially near the coast, are mostly southerly, blowing from 
 the colder continent toward the warmer polar sea, and hence in 
 a direction nearly the reverse of that of the polar winds of the 
 summer season. There is, therefore, a monsoon along this 
 coast with alternating winds of no great strength ; but these 
 are not exactly opposite in direction, but rather from the 
 
208 MONSOONS, AND LAND- AND SEA-BREEZES. 
 
 northwest in summer and the southwest in winter, owing to the- 
 general prevalence of westerly winds in these latitudes arising 
 from the general circulation of the atmosphere. 
 
 " In winter the whole coast of Norway has monsoon winds, blowing 
 from the land to the sea: they are N. and N.E. at Christiania ; S.E. at 
 Christiansund, Bosekop, and Hammerfest ; and S.W. at Vardoe. In sum- 
 mer the conditions are reversed. In northern Norway the winds are 
 variable in summer, and decidedly from the S. in winter." 20 
 
 142. On account of the great lowering of temperature in 
 Asia in winter below that of the normals of latitude, which, 
 considered alone, gives rise in the general circulation to a belt 
 of high pressure about the parallel of 35, and one of low pres- 
 sure at or near the equator, this regular system is now com- 
 pletely broken up, and the highest pressure is found in the in- 
 terior of Asia, and there is a gradient of decreasing pressure 
 thence to about the parallel of 12 south of the equator in the 
 Indian Ocean. The normal equatorial belt of low pressure and 
 calms is now transferred to this parallel, where the northerly 
 monsoon of Asia, crossing the equator, meets the regular 
 southeast trade-winds, and hence the belt of these trade-winds 
 is now confined within the limits of the parallels of 12 and 
 about 25 or 30 S. After the northeasterly and northerly 
 winds of the winter monsoon pass over the equator they are 
 deflected to the east by the force depending upon the earth's 
 rotation, which is towards the left in this hemisphere, so that 
 there is a belt between the equator and the parallel of 12 S., 
 where the prevailing direction of the wind is from the north- 
 west. This is called the Northwest Monsoon. Where this 
 monsoon meets the southeast trade-winds we have the condi- 
 tions of the equatorial calm-belt, a meeting of counter currents,, 
 calms, an ascending current over a belt of several degrees in 
 width, and consequently an abundance of condensation and of 
 rainfall over this belt. Espy says : 34 " The monsoon in the 
 Indian Ocean, which blows from the northwest during the sum- 
 mer, terminates in a belt of rains 6000 miles long." 
 
 On the western side of the southern Indian Ocean the north- 
 west monsoon is much modified by the whirl of atmosphere 
 
THE MONSOONS OF ASIA AND THE INDIAN OCEAN. 2(X) 
 
 deflected by the high table-lands and mountain ranges of the 
 east coast of Africa, 125, by which the direction of the wind 
 is changed and the monsoon is changed to what is called in 
 this region the Northern Monsoon. According to Espy, " the 
 northern monsoon, which blows into the northern end of the 
 Mozambique Channel in the southern summer, terminates 
 there in a great rain, and the southern trade, which blows into 
 the same channel at the same time, terminates there in the 
 same rain ; and the ship that is caught in that channel at that 
 season finds the wind dead against her at whichever end of it 
 she tries to escape." This rainy portion of the channel at this, 
 time is simply the western end of the general rainy belt of the 
 Indian Ocean explained above and referred to by Espy, but 
 moved here a little farther south than it is farther east, by 
 the atmospheric whirl referred to above. 
 
 143. There are monsoon influences arising from the annual 
 alternations of temperature in Australia similar to those of 
 Asia, but on account of its smaller extent and the absence of 
 very high plateaus and mountain ranges, these influences are 
 comparatively small. In Asia the monsoon influence, at least 
 at the extremes, is the predominating one, giving rise to at- 
 mospheric disturbances and velocities of air currents by far 
 greater than those of the general circulation of the atmos- 
 phere, so that the latter merely cause perturbations in the 
 regular annual alternations and inversions of the monsoon.. 
 In the case of Australia, however, the monsoon influence is the 
 weaker, and its effects merely cause perturbations in the gen- 
 eral circulation of the atmosphere. The continent lying mostly 
 within the belt of the southeast trade-winds, these in its vicin- 
 ity are considerably modified all around the coast of the north- 
 ern half of it, and also the prevailing westerly winds in the 
 region on, and adjacent to, the southern coast. 
 
 During the summer of the southern hemisphere, when the 
 earth is in perihelion, the whole land, exposed to an almost 
 vertical sun at midday, and lying mostly in the southern zone 
 of high pressure and dry air ( 120), becomes intensely heated, 
 far above the temperature of the surrounding ocean. Conse- 
 
2IO MONSOONS, AND LAND- AND SEA-BREEZES. 
 
 quently the tendency now is for the air below to flow in from 
 all sides toward the central part, and of course the contrary 
 above. In this flow, however, the currents are deflected a lit- 
 tle to the left by the force depending upon the earth's rotation, 
 but this force is small on the northern side on account of its 
 nearness to the equator. On the northeast side of Australia, 
 where the southeast trade-winds prevail, their directions are 
 now changed, so that they become easterly and northeasterly 
 winds, especially during the day. On the eastern side along 
 the coast of New South Wales, which is in the south tropical 
 calm-belt, where calms prevail when there is no monsoon or 
 other abnormal atmospheric disturbance, the wind blows from 
 the ocean toward the interior of the continent. Along the 
 southern and southwestern coast the westerly and northwest- 
 erly winds which prevail in these latitudes are a little changed 
 in direction by the monsoon influence and blow from a more 
 southerly direction. On the northwest coast, in the zone of 
 the regular southeast trade-winds, the monsoon influence is not 
 strong enough to reverse them, even in midsummer, so that 
 here the wind at all seasons blows from the land toward the 
 ocean, but with a strength a little diminished by the monsoon 
 influence. The effect of this is to bring the line of meeting 
 between the northwest monsoon and the southeast trade-winds 
 a little farther south than it is over the South Indian Ocean 
 generally, where this monsoon influence is not felt, so that in 
 the ocean adjacent to the north and northwest coast this line 
 is brought down several degrees south of the parallel of 12, and 
 passes over the northern extremity of the continent. 
 
 144. The climatic effect of the summer monsoon influence 
 in Australia, where it is not counteracted by the regular south- 
 east trade-winds, is to bring in cool and moist air from the 
 cooler ocean into the dry and heated interior, and so to modify 
 the intense heat along the coast and to increase the rainfall. 
 Accordingly on all sides from the north around by east to the 
 southwest side, where the wind blows from the ocean inland, 
 there is an abundance of rainfall, as may be seen from Loomis's 
 chart. 22 But for this influence, along the coast of New South 
 
THE MONSOONS OF ASIA AND THE INDIAN OCEAN. 211 
 
 "Wales, where otherwise calms would prevail, there would be 
 the same scant rainfall, or nearly so, as in the interior on the 
 same latitudes. This rainfall all along the eastern side is much 
 increased, though reduced to a much narrower strip, by the 
 succession of mountain ranges from 3000 to 5000 feet high 
 near the coast. 
 
 The abundance of rain on the northern extremity of Aus- 
 tralia in summer is -due to the line of the meeting of the south- 
 east trade-winds with the northwest monsoon, and the conse- 
 quent accompanying rain-belt, passing over it at this season ; 
 for it is simply the normal equatorial rain-belt brought down 
 to this parallel, mostly by the Asiatic monsoon influence, but 
 jin part also by that of Australia, as has been explained above. 
 
 Along the west and northwest coast of Australia there is 
 little rain, because here the regular southeast trade-winds pre- 
 vail at all seasons, bearing away the warm and dry air of the 
 interior toward the ocean; for if there were even mountain 
 ranges here to cause -upward deflections, the amount of moist- 
 ure in the air coming from the interior of the continent would 
 be too scant to give .rise to much rain. 
 
 145. During the winter of the southern hemisphere the 
 conditions are mostly reversed, and there is now a tendency of 
 the air to flow out below in all directions from the interior 
 "toward the ocean. The effect of this along the northeast coast, 
 where the southeasterly trade-winds blow, is to change them 
 somewhat to more southerly winds, which are found to prevail 
 here at this season. Further south, however, along the coast 
 of New South Wales, in the belt of calms and high pressure, 
 and where easterly winds prevail in summer, there are now 
 westerly winds, so that here there is a somewhat regular mon- 
 soon, but of no great strength. The monsoon effect upon the 
 prevailing westerly winds along the south and southwest coast 
 is to cause them to blow from a direction a little more from 
 the northwest. Along the whole of the northwest coast and 
 'Over the whole northern half of the continent there are, at this 
 season, the regular southeast trade-winds, but strengthened 
 somewhat by the monsoon influence. 
 
212 MONSOONS, AND LAND- AND SEA-BREEZES. 
 
 The climatic effect of the winter monsoon influence is to 
 increase the dryness and to diminish the amount of rainfall 
 over the whole of the interior, which, aside from this influence, 
 is a very dry region, from its lying mostly in the south tropical 
 zone of high pressure and in the zone of the trade-winds, in) 
 both of which there is, in general, little rainfall. 
 
 Since the mean temperature of land in tropical and equa- 
 torial latitudes, for reasons given in 68, is greater than that of 
 the ocean on the same latitudes, the strength of the winter 
 monsoon influence is less than that of the summer. For if we 
 suppose that, in the annual oscillation of temperature, this rises 
 in summer as far above the mean annual temperature as it falls 
 below in winter, then the difference between the land temper- 
 ature and that of the ocean must be greater in summer than in 
 winter, since the mean temperature of the land is higher than 
 that of the ocean, and hence the air-pressure is decreased more 
 below the annual mean of the ocean during the Australian.! 
 summer than it is raised above it in winter. 
 
 THE MONSOONS OF AFRICA. 
 
 146. For reasons given in the case of Australia, the mean an- 
 nual temperature of the whole of equatorial and tropical Africa. 
 is higher than that of the oceans on the same latitudes. Since- 
 the monsoon influence depends upon the range of the annual 
 oscillation of temperature, and this is not very great here, so 
 near the equator, this influence is not so great here as it other- 
 wise would be: in fact, there is little of the real monsoon influ- 
 ence, which would cause a reversion of directions at the two 
 seasons ; for the mean temperature of the land being consider- 
 ably greater than that of the ocean, it scarcely becomes lower 
 in general than that of the ocean in winter.. The consequence 
 is, that while there is a strong tendency in the air at the earth's-, 
 surface to flow in from the ocean in summer, or at the times of 
 highest temperature, there is little or no tendency to flow outr 
 when the temperature of the land is reduced to the lowest, 
 since it is then but little below the temperature of the adjacent. 
 
THE MONSOONS OF AFRICA. 
 
 ocean. Over the whole of the northern part of Africa, and 
 even over the Mediterranean Sea, the regular northeast trade- 
 wind prevails, with slight annual variations and strengthened a 
 little by the summer monsoon influence, throughout the whole 
 year ; but along the northwest coast of Africa, and to a con- 
 siderable distance over the adjacent part of the Atlantic, it 
 becomes northerly and even northwesterly in midsummer, the 
 air being drawn in towards the heated region of the Sahara. 
 At the same time in the Gulf of Guinea and to some distance 
 into the Atlantic, the regular southeast trade-wind is changed, 
 first to a southerly, and nearer the coast to a southwesterly 
 wind, called the Southwest Monsoon of Africa, which is really 
 not a monsoon, but simply a change in direction of the regular 
 trade-winds by the indraught of air toward the Sahara at this 
 season. But at the opposite season there is little reversing 
 action, since there is then but little difference between the tem- 
 perature of the land and that of the ocean, and so the south- 
 east trade-wind then has nearly its usual direction. 
 
 147. West of the Gulf of Guinea and the coast of Liberia, 
 and a little north of the equator, there is a wedge-shaped area 
 with its apex extending far west into the Atlantic Ocean, in 
 which calms and light variable winds usually prevail, and the 
 ^vvinds, especially in the summer season of the northern hemi- 
 sphere, sometimes blow directly in toward the interior of Africa. 
 This is caused by the nearly permanent difference of temper- 
 ature between the equatorial parts of the continent and the 
 ocean ; for the annual variations here are small, and conse- 
 quently there is very little real monsoon effect, or reversal of 
 the winds with the seasons. The tendency is to draw the air 
 in from the ocean toward the Sahara, and this entirely counter- 
 acts the regular northeasterly trade-winds in summer up to the 
 parallel of about 13, causing an apparent widening of the equa- 
 torial calm-belt in this region. During the winter of the north- 
 ern hemisphere, when the Sahara becomes cooled down some- 
 what and the region of greatest heat and rarefaction of the air 
 is transferred to South Africa, the northeasterly trade-winds 
 jblow again to a lower latitude, as in other parts, and there is 
 
214 MONSOONS, AND LAND- AND SEA-BREEZES. 
 
 now a considerable narrowing of this area. The tendency now 
 is to draw the air more toward South Africa, so that this area, 
 not only becomes narrower, but there is now often a northwest- 
 erly wind blowing from this region into the Gulf of Guinea. 
 
 There is a wide zone through Central Africa, comprising 
 the country of the Soudan, and lying mostly between the paral- 
 lels of 5 and 15 N. and extending eastward to the Abyssinian 
 mountains, in which there is apparently a somewhat regular- 
 monsoon, the winds changing with the seasons from a north- 
 easterly or northerly direction in the winter to a southerly di- 
 rection in the summer. During the winter the regular trade- 
 winds, which are always more northerly on land, where there is 
 more friction, than on the ocean, where there is less, blow down 
 to the parallel of about 5 N. But during the summer the 
 southeasterly trade-winds, becoming southerly winds at and 
 near the equator on account of there being here no deflecting 
 force from the earth's rotation, blow up to about the parallel 
 of 15 N., and hence between these parallels there is an annual 
 reversion of the directions of the winds from northerly winds, 
 or nearly so, in the winter, to southerly winds in the summer,, 
 of the northern hemisphere, and back again. This, however, 
 arises mostly from the general oscillation of the equatorial' 
 calm-belt all around the globe, depending upon varying tem- 
 perature conditions extending over the whole of each hemi- 
 sphere, as has been explained, but also in some measure upon 
 the annual transfer of the local more heated regions of Africa 
 from the northern to the southern hemisphere and back again. 
 The same is observed more or less in nearly all parts of the 
 zone over which the equatorial calm and rain-belt oscillates. 
 
 MONSOONS OF NORTH AMERICA. 
 
 148. On the continent of North America we have monsoon 
 influences similar to those of Asia, but not nearly so strong,, 
 because the extent of the continent, and consequently the an- 
 nual range of temperature, are not so great. They are, for the 
 most part, not sufficiently strong to completely overcome and! 
 
MONSOONS OF NORTH AMERICA. 21$ 
 
 reverse the current of the general circulation of the atmosphere, 
 and so to produce a real monsoon, but they cause great differ- 
 ences between the prevailing directions of the winter and sum- 
 mer winds. 
 
 In the summer the whole interior of the continent becomes 
 heated up to .a temperature much above that of the oceans on 
 the same latitudes on each side indeed above that of the Gulf 
 of Mexico and the Pacific Ocean on its southern and southwest- 
 ern borders. The consequence is that the air over the interior 
 of the continent becomes more rare than over the oceans, rises 
 up, and flows out in all directions above while the barometric 
 pressure is diminished, and the air from all sides, from the 
 Atlantic on the east, the Pacific Ocean on the west, the Gulf of 
 Mexico on the south, and the polar sea on the north, flows in 
 below to supply its place. On the east the tendency to flow in 
 is not strong enough to counteract the general easterly motion 
 of the air at the earth's surface in the middle latitudes, and to 
 cause a westerly current, but it simply retards the general east- 
 erly current and gives rise to a greater prevalence of easterly 
 winds along the Atlantic sea-coast during the summer season. 
 On the southern and southeastern coast, in connection with 
 the deflection referred to in 123, it causes the prevailing winds 
 to be southerly and southeasterly instead of northeasterly, 
 as they otherwise would be in these trade-wind latitudes. 
 It is precisely the same effect as is produced in the region 
 southeast of China ( 138). The monsoon influence in the 
 Mississippi valley and westward is much strengthened by the 
 gradual slope from this valley up to the high plateaus east of 
 the Rocky Mountain range, for reasons which have been al- 
 ready given ( 132); so that when this slope in summer be- 
 comes heated the surface air tends to flow up it toward the 
 mountain range, and causes winds, which otherwise would be 
 southerly ones, to become more southeasterly, and southwest- 
 erly winds to become southerly ones. 
 
 In winter the thermal conditions over the continent are 
 reversed. The interior of the continent is now the coldest 
 part, and it is especially colder than the surrounding oceans at 
 
2l6 MONSOONS, AND LAND- AND SEA-BREEZES. 
 
 that season. It has also very high plateaus and mountain 
 ranges. The air, therefore, of the lower strata, and especially 
 those next the earth's surface, now tends to flow out in all 
 directions to the warmer oceans and the Gulf of Mexico, and 
 especially to run down the long slope of plateau from the 
 Rocky Mountains into the Mississippi valley. The effect over 
 the whole of the United States east of the Rocky Mountains 
 is to cause the winds, which otherwise would be westerly 
 and southwesterly, to become generally northwesterly winds, 
 instead of southerly and southwesterly ones, as in summer. 
 There is not a complete monsoon effect, but simply a great 
 change between summer and winter in the prevailing direc- 
 tions of the winds. In Texas, however, and farther east along 
 the northern border of the Gulf, the effect is somewhat that of 
 a complete monsoon. In New England and farther south in 
 the Eastern States the monsoon effect is to cause the prevail- 
 ing winds to be from some point north of west, instead of souch 
 of west as in summer. 
 
 149. In summer Central America and Mexico have a much 
 higher temperature than that of the adjacent tropical sea on 
 the southwest, and having high mountain ranges and elevated 
 plateaus, there is consequently a strong tendency to draw in 
 air from the southwest at this season, which not only entirely 
 counteracts the regular trade-winds of these latitudes, but even 
 reverses them and causes southwest winds. The effect is to 
 cause in midsummer a large area here, extending far westward, 
 of calms and irregular and light winds, mostly southwesterly 
 ones, and an apparent widening of the equatorial calm-belt at 
 this season so as to make its northern limit reach up, along the 
 coast, nearly to the parallel of 20. The effect is similar to 
 that in the Atlantic west of the Gulf of Guinea and Liberia, 
 except that it here appears to be some greater, and causes a 
 true monsoon effect, since during the winter the regular north- 
 easterly trade-winds prevail, but strengthened by the reverse 
 thermal conditions of the winter season. On the eastern side 
 and over the western end of the Gulf of Mexico there is a 
 somewhat regular monsoon effect, the prevailing winds being 
 
MONSOONS OF SOUTH AMERICA. 2 1/ 
 
 -easterly, or blowing toward the land, during the summer, and 
 the reverse in winter. 
 
 Along the west coast of North America in the middle lati- 
 tudes there is a strong monsoon influence ; for the interior of 
 the continent becomes heated in summer to a much higher 
 temperature than that of the southwesterly ocean, and hence a 
 strong current is drawn in from this direction, at right angles 
 to the general trend of the coast, which, combining with the 
 general southwesterly winds of these latitudes in the general 
 circulation of the atmosphere, causes the strong and steady 
 westerly and southwesterly winds of this region during the 
 summer. Farther north, up toward Alaska, the summer mon- 
 soon effect is combined with the current caused by the deflec- 
 tion of the continent ( 123) as well as the general easterly cur- 
 rent of high latitudes, so that the winds here are generally 
 southerly, but still have somewhat of a monsoon character, 
 being southerly and southwesterly in summer, and easterly and 
 southeasterly during the winter. 
 
 All along the northern coast of America, as along that of 
 Siberia, the monsoon tendency is to draw the air from the 
 colder land to the warmer ocean in winter, and the reverse in 
 summer ; and these effects, combined with the general easterly 
 motion of the atmosphere in these latitudes, gives rise to pre- 
 vailing southwesterly winds in winter and northwesterly ones 
 in summer. The winter monsoon influence, however, is small 
 here much more so than in Siberia, for the ocean contains so 
 many large islands that it has rather a continental than an 
 oceanic winter temperature ; and besides, it has not the influ- 
 ence of a warm current such as the continuation of a part of 
 the Gulf Stream along the northern coast of Europe and Asia. 
 
 MONSOONS OF SOUTH AMERICA. 
 
 150. In South America we have conditions similar to those 
 of Australia, and the monsoon influences are well marked, being 
 stronger than those of Australia, both because the continent is 
 larger and the mountain ranges higher. Along the northeast- 
 
2l8 MONSOONS, AND LAND- AND SEA-BREEZES. 
 
 ern coast of South America, and in the whole Amazon valley,, 
 the indraught of air from the ocean toward the interior of the con- 
 tinent and the eastern slope of the Andes is so strong during 
 the summer of the southern hemisphere, that there is now a 
 continuous northeasterly wind from the region of the north- 
 easterly trade-winds, far into the interior, and the monsoon 
 effect appears as a continuation of these trade-winds across the 
 equator into the opposite hemisphere. But this is somewhat 
 of a perennial effect, though much greater during the summer 
 of the southern hemisphere than at the opposite season. For 
 the mean temperature of equatorial and tropical South Amer- 
 ica being considerably greater than that of the oceans, and the 
 annual thermal changes being small, there is perhaps scarcely 
 any time when the land is colder than the ocean, and when 
 there is a reverse monsoon effect. 
 
 The effect of the monsoon influence in summer over Brazil,, 
 which is mostly in the zone of the southeasterly trade-winds,, 
 together with that of the deflection by the continent, and espe- 
 cially the range of the Andes, is to change these winds into 
 northeasterly and northerly ones, which are the prevailing 
 winds here in the summer. The effect is similar to that in the 
 southern part of the United States and the Gulf of Mexico, by 
 which the winds here are changed from the regular northeast- 
 erly trade-winds to southeasterly and southerly winds in the 
 summer season. During the winter the winds are more vari- 
 able here, since the monsoon influence rather antagonizes the 
 easterly and northerly winds which arise from the deflection 
 of the continent and the Andes, but they are largely polar 
 and southwesterly winds, as in the corresponding part of the 
 United States they are polar and northwesterly winds. 
 
 On the coast of Chili and the adjacent part of the ocean 
 the prevailing winds are mostly southerly and southwesterly in 
 December, January, and February, the southern summer, but 
 northerly and northwesterly at the opposite season of the year. 
 This arises in part from the deflection of the strong westerly 
 winds of these latitudes by the lofty range of the Andes, and 
 in part from the monsoon effect, by which the air is drawn ia 
 
LAND- AND SEA-BREEZES. 2IC/ 
 
 toward the interior of the continent, and by which they are 
 strengthened but not much changed in direction. At the op- 
 posite season of the year this monsoon influence is in the con- 
 trary direction, and reverses the directions, giving rise to north- 
 erly and northeasterly winds, but of less strength. 
 
 Farther south toward the Cape northwesterly winds prevail 
 the whole year, arising in part from the deflection of the pre- 
 vailing westerly winds of the middle latitudes by the Andes 
 toward the south. The monsoon influence is also here per- 
 ceptible in causing these winds to be more northerly in winter 
 than in summer. 
 
 Along the coast of Peru and on the adjacent ocean, in the: 
 latitudes of the southeasterly trade-winds, the temperature of 
 the continent being greater than that of the oceans, there is a 
 tendency of the air the whole year to flow in toward the land, 
 but especially in December, January, and February, which, 
 however, is not strong enough to change the direction, even at 
 this season, of the southeasterly trade-winds so much as to 
 make them southwesterly winds, as in the Gulf of Guinea, but 
 it simply makes them a little more southerly than they other- 
 wise would be. 
 
 LAND- AND SEA-BREEZES. 
 
 151. Land- and sea-breezes are observed in all countries 
 wherever there is a diurnal alternation of the temperature of 
 the land, above that of the adjacent ocean during the day, and 
 below it during the night just as there are monsoons where 
 this temperature over a whole continent or large area of coun- 
 try is higher than that of the oceans or surrounding parts of 
 the country during the summer, and below it during the 
 winter. They are observed mostly in equatorial and tropical 
 latitudes, because here the diurnal range of temperature is 
 greatest, and consequently there are the greatest contrasts be- 
 tween land and ocean temperatures ; but they are also quite 
 common in middle latitudes, and likewise traces of them were 
 found by Scoresby in Greenland during calm and clear weather*. 
 These winds, for reasons already given ( 132), are light winds. 
 
22O MONSOONS, AND LAND- AND SEA-BREEZES. 
 
 except where there are high lands or mountain ranges near the 
 coast, and extend no great distance from the shore either inland 
 or out into the sea. They depend upon the thermal conditions 
 mostly in the vicinity near the coast, and but little upon those 
 at a great distance toward the interior of continents. They 
 are, therefore, where there are no other causes of disturbance, 
 in a direction perpendicular to the general trend of the coast 
 inward toward the land during the day, and the reverse at 
 night. 
 
 As weak monsoon influences, such as those of Australia, are 
 -often not sufficient to reverse the general currents of the at- 
 mosphere, such as the trade-winds and the general westerly 
 *and southwesterly winds of the middle latitudes, but merely to 
 cause annual oscillations in their strength and direction, so land- 
 and sea-breezes are entirely overwhelmed and not observable 
 where there are other strong prevailing currents, either of the 
 general circulation of the atmosphere, or of monsoons, or other 
 more local and temporary disturbances to be treated farther 
 on, or, if observable at all, it is merely their effect in causing 
 diurnal variations of strength and direction. For instance, if 
 there is a prevailing wind of considerable strength from the 
 ocean inland, the effect of the sea-breeze influence would be 
 superadded to this during the day and increase its strength, 
 while at night the contrary influence would not be sufficient to 
 entirely counteract and reverse [it and cause a wind from the 
 land toward the sea, but might diminish very much its strength. 
 Likewise, if the prevailing wind were in the direction of the 
 general trend of the coast, the effect of the land- and sea-breeze 
 influence would be to cause the wind to incline in toward the 
 land during the day and away from it during the night, more 
 or less according to the comparative strength of the disturbing 
 influence. The pure land- and sea-breezes are observed in 
 calm weather only, and of course mostly in clear weather, 
 when the changes of temperature between day and night are 
 the greatest. Along the coasts of India, therefore, and in all 
 monsoon regions, they are only observed for a few weeks at 
 the times of the reversals of the monsoon in spring and fall, 
 
LAND- AND SEA-BREEZES. 22 I 
 
 when calms prevail, unless there are prevailing winds from other 
 causes than those of the monsoons. 
 
 152. As the effect of the monsoon influence first begins to 
 be seen in the spring as the temperature of the continent first 
 rises above that of the oceans, is the greatest in midsummer, 
 and is reversed in the fall into the winter monsoon as the tem- 
 perature of the land falls below that of the ocean, and this has 
 its greatest strength in midwinter, so the pure sea-breeze is 
 first felt in the forenoon about 10 o'clock, when the tempera- 
 ture of the adjacent land becomes greater than that of the sea,. 
 is greatest at about 3 o'clock in the afternoon, during the 
 warmest part of the day, and is then reversed into a land- 
 breeze about 8 o'clock in the evening, when the temperature of 
 the land becomes greater than that of the ocean ; and this has 
 its greatest strength early in the morning, when the tempera- 
 ture is the lowest. 
 
 The effect of the land-wind upon the calm smooth ocean in 
 the forenoon is usually observed first near shore, and as the 
 strength of the breeze increases it extends gradually back from 
 the land into the ocean. But the reverse of this, according to 
 Dampier, is often observed. It no doubt depends upon local 
 circumstances. In the case of the true sea-breeze, depending 
 simply upon contrast of temperature between the level coast and 
 the ocean, the greatest thermal, and consequently the greatest 
 pressure, gradient is first caused at and near the coast, where 
 there is an abrupt change of temperature between land and 
 sea ; and therefore the interchange of air between sea and land 
 must first commence there, and gradually extend to greater dis- 
 tances, both inland and out into the sea, as the temperature 
 differences increase toward the middle of the day. In the case, 
 however, of the strong sea-winds experienced along coasts 
 where there are steep slopes from high lands and mountain 
 ranges near, it is reasonable to suppose that the interchange 
 may commence first between these slopes and the sea at a dis- 
 tance, and be gradually communicated to the air on the coast, 
 and so the effect would first be seen at a distance, and only 
 afterwards near the coast. 
 
'222 MONSOONS, AND LAND- AND SEA-BREEZES. 
 
 For the same reason that the summer monsoons are stronger 
 than the winter ones in equatorial and tropical latitudes ( 145), 
 are the sea-breezes here stronger than the land-breezes. Many 
 evidences of this fact might be cited here, and this has been 
 especially observed frequently along the coast of the Gulf of 
 Guinea by many others, as well as somewhat recently by Com- 
 mander Burke, R. N. He says: 37 
 
 " The winds that prevail along these coasts are already so well known 
 as to render much comment unnecessary, the usual sea- and land-breezes 
 being, with few exceptions, constant; the latter, however, are nowhere 
 very strong, and as a rule are not felt before midnight, nor do they last 
 later than 8 A.M. The sea-breeze commences at about 10 A.M., reaches 
 its maximum strength at 4 P.M., and then gradually falls light; but fre- 
 quently, and especially in the Gulf of Guinea, it maintains its full 
 strength until it suddenly drops and gives place to the land-breeze." 
 
 The strong land- and sea-winds along coasts with long slopes 
 from highlands and mountain ranges depend very much upon 
 the configuration of such coasts. Around high promontories 
 they are comparatively weak, because the area heated above 
 or cooled below the temperature of the sea is small, and the 
 effect is distributed around over a comparatively large area. 
 On the contrary in a narrow bay surrounded by high hills or 
 mountains the effect of the heated or cooled slopes all around 
 is concentrated upon a comparatively small space. The cooled 
 stratum of air at night in contact with the hill-sides flows in 
 irom all sides toward the bay with a concentrated effect at the 
 lower part of the bay, or at the common outlet of several val- 
 leys which come together, just as floods from the concentrated 
 water of heavy rains increase in volume and force as the 
 streams from all sides come into one large river in the valley. 
 Hence it is said, 18 " The land-breeze frequently comes off in 
 sharp, sometimes in dangerous, squalls ; and our Sailing Direc- 
 tions are full of cautions to navigators to look out for the first 
 squalls of the land-breeze : even when it does not come in 
 squalls, it comes quickly." 
 
 On the contrary, the sea-winds are strengthened in the 
 same proportion, for when the surfaces of the hill-sides are as 
 
MOUNTAIN AND VALLEY WINDS. 22$ 
 
 much heated above the temperature of the ocean and the 
 superincumbent air at the same levels above it, the air tends to 
 rush up the slopes and hill-side valleys with the same force as 
 it flows down when they are as much cooled below this tem- 
 perature, and the air which is drawn up at all sides over a com- 
 paratively large area is drawn up the bay and gives rise to 
 .a strong wind. 
 
 MOUNTAIN AND VALLEY WINDS. 
 
 153. On the slopes of mountain ranges and the plains near 
 the base, and especially in deep valleys extending from the 
 slopes into the country below, there are often strong winds, 
 toward and up the mountain side during the day, and the 
 reverse at night. This fact is well known to hunters and all 
 who are accustomed to encamp in the mountains at night; and 
 ;so the camp-fires are always placed below the tents on the 
 slope, that the smoke may be drawn away by the descending 
 current, instead of being blown toward them. Such currents 
 of course extend to some distance over the plain below, and 
 ^vhere the air is brought together by a number of ravines and 
 deep valleys into one common and somewhat contracted cur- 
 rent below, the force of the wind may be very great. Just the 
 reverse takes place during the day, for the air then rushes up 
 the mountain side from the plain below, and if this air is con- 
 centrated into narrow valleys, either near the base of the 
 mountain or up the side, the current becomes unusually 
 strong. 
 
 R. Strachey, Esq., of the Bengal Engineers, in the 2ist Vol. 
 Royal Geog. Soc., as given by Espy, says : 
 
 " The winds in the mountains of the Himalayas blow up the valley 
 during the day from 9 A.M. to 9 P,M., and down during the correspond- 
 ing hours of the night. At the debouches of the principal streams into 
 the plains these night-winds blow with great violence, particularly in 
 the winter. They diminish in force as we ascend the mountains, and at 
 great elevations and in the plains of western Thibet the nights are 
 almost perfectly calm. The diurnal winds, on the other hand, in the 
 latter country are terrific; and in travelling there we looked forward to 
 the afternoon, when the winds were at their height, with real dread." 
 
224 MONSOONS, AND LAND- AND SEA-BREEZES. 
 
 At the time of the total solar eclipse on the 2Qth of July,, 
 1878, the writer ascended about midday the eastern slope of 
 the mountain to the top of Gray's Peak in Colorado, where the 
 eclipse was total. The day was almost perfectly clear, and the 
 wind above, as indicated by the motion of a few specks of 
 cloud, was westerly. On the way up the mountain there was 
 a very strong current rushing directly up the mountain, such 
 that it was necessary to hold on to one's hat with one hand to 
 keep it from being blown away. This was met by the westerly 
 wind above and by a similar current up the west side, but of 
 less strength because the slope was not so long. On the crest 
 of the mountain, a few rods in width, there was a calm, for the 
 ascending currents from each side after meeting continued on 
 upward, which was indicated by some of the writer's note- 
 paper, on stepping down the east side a few rods, being caught 
 and carried vertically up to a considerable height, and after- 
 wards falling back again near the same spot. 
 
 On the descent, late in the afternoon, there was a perfect 
 calm, the mountain slope being now cooled down to about 
 the mean temperature of the day. During the night, especi- 
 ally in the latter part of it, there was, no doubt, a reverse 
 current down the mountain of about the same strength, and 
 continuing until about the middle of the forenoon. 
 
 These winds depend upon the same circumstances and are 
 explained upon precisely the same principles as the land- and 
 sea-breezes on mountain slopes along sea-coasts ; in fact, the 
 only difference is in the circumstance that in the one case there 
 is ocean and in the other a plain at the base of the slope. 
 
 154. A similar but much feebler effect is observed on long 
 declivities of open country with only a very small gradient, 
 such as that between the Mississippi valley and the Rocky 
 Mountains ; but in such cases it is generally somewhat masked 
 by other prevailing currents, so that there is not a complete 
 reversion of the wind, but a diurnal change of its direction.. 
 The writer has often observed in Missouri and Kansas during 
 clear warm weather, when the prevailing wind is generally 
 southerly or a little west of south, that in the morning when> 
 
MOUNTAIN AND VALLEY WINDS. 22$ 
 
 the surface air is cooled down and tends to flow down the in- 
 cline, the wind is southwesterly, but as the heat of the day 
 increases it gradually changes around toward the south, and 
 toward evening is from a southeasterly direction, the tendency 
 now being for the heated surface air to move gently up the 
 slope toward the mountains. But during the night, if no ab- 
 normal disturbance of any kind takes place, it always gets back 
 again to a southwesterly direction. 
 
CHAPTER VI. 
 CYCLONES. 
 
 155. IN preceding chapters we have considered the general 
 circulation of the atmosphere which would arise, upon an 
 earth with a homogeneous and smooth surface, from a regular 
 temperature gradient between the equator and the poles, with- 
 out regard to differences of temperature in different longitudes 
 on the same parallels of latitude. Such a gradient is deducible 
 from the normals of latitude given in the table of 68. This 
 gradient, it is seen, varies with the seasons of the year, being 
 greatest in winter and least in summer, and hence there is an 
 annual variation in the general motions of the atmosphere, 
 which has likewise been considered. But upon the earth's sur- 
 face as it actually exists there are mountain ranges and irregu- 
 lar distributions of land and water, and the effects of these in 
 disturbing the regularity of the general motions by means of 
 deflections and the differences in the frictional resistances on 
 different parts of the earth's surface, and especially between 
 the two hemispheres, have been pointed out. 
 
 The temperature gradient from which this general but dis- 
 turbed circulation of the atmosphere at any time arises, de- 
 pends upon the difference between the mean diurnal vertical 
 intensity of solar radiation upon the earth's surface between 
 the equatorial and polar regions, which, though variable, never 
 vanishes, and hence the general motions of the atmosphere are 
 variable, but never cease. The general circulation also consists 
 of two systems, which are similar, except so far as they are 
 disturbed on account of a non-homogeneity of the earth's 
 surface, each of which extends over a whole hemisphere. 
 
 226 
 
VERTICAL CIRCULATION. 22? 
 
 Subsequently .another class of temperature disturbances 
 ivere considered those arising from the abnormals of latitude 
 at any time, giving rise to monsoons and land- and sea-breezes. 
 These are fixed in locality, and extend mostly over large areas 
 of the earth's surface, but are subject to annual and diurnal 
 changes, and even to complete reversals with a cessation of 
 motion at the time of reversal, so far as it depends on the mon- 
 rsoon influence, and sensibly so for some little time immediately 
 before and after. 
 
 We come now to the consideration of another class of tem- 
 perature disturbances, which extend over a comparatively small 
 part of the earth's surface and are mostly neither fixed to any 
 given part of the earth's surface, nor do they continue gener- 
 .ally for a great length of time, and hence they are of a more 
 local and temporary character than the others. In these there 
 is a gyratory motion of the air around some central point, and 
 .hence they are called cyclones. 
 
 VERTICAL CIRCULATION. 
 
 156. If the air over any portion of the earth's surface is 
 warmer at all altitudes than that of the surrounding parts at 
 the same levels, it is lighter, and tends to rise up above its 
 original level, and flow out in all directions above. This de- 
 creases the pressure at the earth's surface over this area, but 
 increases it a little over the surrounding parts ; and thus there 
 arises a gradient of pressure decreasing from the exterior to- 
 ward the interior below, which causes a flow of air in from all 
 sides to supply the ascending current. There is thus a verti- 
 cal circulation and interchange of air between the interior and 
 exterior parts established, just as in the case of the general cir- 
 culation of the atmosphere ( 72), except that now the motion 
 is toward the central part below and from it above, while in the 
 general circulation it is toward the polar central region above 
 ^and from it below, the central region in this case being colder 
 instead of warmer than the surrounding parts. 
 
 It is not necessary, however, in order to have such a circu- 
 
228 CYCLONES. 
 
 lation, that all the strata of air from bottom to top shall be: 
 warmer in the interior than in the surrounding parts, but only 
 that there shall be such a disturbance of the equality of tem- 
 perature that the pressure of any part of the interior is less 
 than that of the exterior part ; for where this is the case the air 
 tends to rise up, and that of greater pressure at the same level 
 to flow in and takes its place, and thus the circulation is estab- 
 lished. In general the velocity of the ascending current in the 
 interior part is much greater, but over a smaller area, than 
 that of the descending current in the exterior surrounding part 
 over a much greater area, where it is simply a very gradual 
 settling down ; for since there is no definite limit, the tendency 
 is for the air above to flow out to still greater distances, and thus- 
 to press down and bring in the air below from greater distances. 
 
 On account of the non-homogeneity of the earth's surface, 
 comprising hills and valleys, land and water, and dry and 
 marshy areas, all with different radiating and absorbing powers, 
 and also on account of the frequent irregular and varying dis- 
 tribution of clouds, it must often happen that there are consid- 
 erable local departures of temperature from that of the sur- 
 rounding parts ; and if it should so happen, as it frequently 
 must, that this area is of a somewhat circular form, and the air 
 has a temperature higher than that of the surrounding part of 
 the atmosphere, then we have the conditions required to give 
 rise to a vertical circulation, with an ascending current in the 
 interior, as described above. But unless there is some source 
 of heat by which this interior higher temperature is kept up, 
 this circulation soon ceases, for the interchange of air between 
 the interior and exterior parts of the air comprised in the cir- 
 culation tends to continually reduce the difference of tempera- 
 ture upon which the circulation depends, and to bring all parts 
 to the same temperature. 
 
 157. It has been shown ( 29) that if any portion of the 
 atmosphere, when it is in the unstable state, receives, from any 
 slight temperature or other disturbance, an upward motion, it- 
 becomes warmer than the surrounding air at the same level ; and 
 the tendency then is for it to continue to rise as long as the. 
 
VERTICAL CIRCULATION. 22$ 
 
 air is in the unstable state, and thus to give rise to a vertical 
 circulation, and this must continue as long as the atmosphere 
 of the surrounding parts is in the unstable state. Let us con- 
 sider first the case of a dry atmosphere, and suppose, as in the 
 example previously given ( 29), that the vertical temperature 
 gradient is that of a decrease of i.2 for each 100 meters of in- 
 crease of altitude. In this case the air of the ascending current 
 becomes warmer than that of the comparatively slow descend- 
 ing; current on all sides at the same level at the rate of o.2 
 
 o 
 
 for each 100 meters of ascent ; and so the temperature dif- 
 ferences and the force by which the vertical circulation is 
 kept up increase at first until this circulation is fully estab- 
 lished and air has ascended from the earth's surface up to 
 the upper strata, after which it gradually decreases ; for the in- 
 terchange of air between the lower and upper strata tends to 
 reduce the temperature gradient of all of it to that of the in- 
 different state, which is i for each 100 meters of difference of 
 altitude, and the horizontal interchange tends to equalize the 
 temperatures between the interior and exterior parts of the cir- 
 culation, and when this equality takes place all force to keep 
 up the circulation vanishes. Of course the more the unstable 
 :state differs from the indifferent state, the greater the energy 
 which maintains the circulation, and the greater the rapidity 
 of this circulation. But in all cases there is probably such 
 an interchange and inversion of the air of the lower and upper 
 strata that the unstable state is soon broken up and the circu- 
 lation ceases. 
 
 In the case supposed above, of a regular and uniform verti- 
 cal temperature gradient at all altitudes, the differences of tem- 
 perature at the same levels between the ascending air and that 
 of the surrounding air would increase with increase of altitude ; 
 but such gradients are by no means uniform, but may so 
 change at different altitudes that the atmosphere may be in the 
 unstable state below and the stable state above, or vice versa. 
 In the first case the ascending air would first become warmer, 
 the differences then decrease, and finally the ascending air be- 
 come colder than that of the surrounding air at the same lev- 
 
230 CYCLONES. 
 
 els, but, still the vertical circulation would take place, thougb 
 its energy would be less, and it would not generally extend up 
 to the top of the atmosphere. 
 
 158. In the case of a moist atmosphere with the unstable 
 state for dry air, we have the same energy for originating and 
 maintaining a vertical calculation as in the case of dry air, with 
 the additional energy of all the latent heat of the aqueous 
 vapor set free in its condensation in the ascending current, and 
 this latter is a continuous source of energy as long as moist air 
 is being drawn in from all sides to supply this current. For in- 
 stance, suppose the air is saturated, and is in the unstable state 
 for dry air, then at the first upward start of the air it be- 
 comes warmer than the surrounding air and the tendency is to 
 continue on. As soon as the vertical circulation is fully estab^ 
 lished, the vertical gradient in this ascending current becomes 
 that given by Table III, which is greater or less according to> 
 the season of the year and the altitude. With a summer tem- 
 perature of 30 at the earth's surface, as may be seen from the 
 example given in 27, the rate of decrease of temperature is 
 only about o.37 for each 100 meters of ascent up to an alti- 
 tude of 4000 meters, and even up to much greater altitudes 
 the rate would vary but little from this. If the vertical gradi- 
 ent of unstable equilibrium were i.2, as assumed in the pre- 
 ceding case, we should have, after vertical circulation was first 
 fully established, a difference of temperature between the air 
 of the ascending current and that of the comparatively quiet 
 surrounding air of nearly o.83 for each 100 meters of altitude ; 
 for at this time the vertical temperature gradient of the very 
 slowly descending air over a very large area will not have 
 changed much. In the case of dry air it was only o.2 for the 
 same vertical temperature gradient; and so of the o.83 above, 
 o.63 is due to the heat of condensation of the vapor. 
 
 If the atmosphere were not completely saturated, but had 
 a depression of the dew-point air-temperature minus temper- 
 ature of the dew-point of 8, then by Table IV the air at the 
 earth's surface would have to ascend about 1000 meters before: 
 condensation would commence, and in this part of the ascent 
 
VERTICAL CIRCULATION. 23 1 
 
 the rate of the cooling would be i instead of o.37 for each 
 100 meters, after which the latter rate would take place. 
 Hence in this case the whole of the ascending column would 
 have a lower temperature than in the preceding case of com- 
 plete saturation, being, above the altitude of 1000 meters, equal 
 to 10 X (i.o o.37) 6. 3 less than in the case of complete 
 saturation, and hence the energy of the vertical circulation 
 would be much less in consequence of the lack of complete 
 saturation. 
 
 In the preceding examples we have assumed a uniform ver- 
 tical gradient which makes a dry atmosphere unstable. But 
 this is not necessary in the case of a moist atmosphere, in order 
 to produce a vertical circulation. In fact, in the case of com- 
 plete saturation it is only necessary that this gradient shall be 
 a little greater than that given by Table III, which in the last ex- 
 ample is o.37 for each 100 meters. If the gradient were o.8, a 
 little less than that of the indifferent state for dry air, then 
 each part of the air at all altitudes, in its initial ascent of 100 
 meters, would be o.8 o.37 = o.43 warmer than the sur- 
 rounding undisturbed air at the same levels ; and after vertical 
 circulation were fully established, and air had ascended from 
 the earth's surface up to high altitudes, the differences of tem- 
 perature would be o.43 for each 100 meters up to these alti- 
 tudes, and so in the upper strata of the air they would be very 
 great. If the vertical gradient were still less but a little 
 greater than o.37, these differences would be smaller, and the 
 force would be able to give rise to and maintain a compara- 
 tively feeble circulation only. 
 
 159. In the case in which the atmosphere is not completely 
 saturated, we have seen that in the first ascent of the air, until 
 it is cooled, at the rate of i for each 100 meters, down to the 
 dew-point, it becomes colder and heavier than the surrounding 
 air, unless the atmosphere is in the unstable state for dry air. 
 It may, therefore, happen that before the air rises up to the 
 altitude where condensation takes place the whole air-column 
 may be heavier than a similar one of the surrounding part of 
 the atmosphere. In this case there must be more than a mere 
 
232 
 
 CYCLONES. 
 
 initial and temporary impulse, or very slight temperature dis- 
 turbance merely, to start the vertical ascent of the air. The 
 initial temperature of the air before ascent commences must 
 be so much greater than that of the surrounding air, that it 
 does not become cooled down in its first ascent, before conden- 
 sation takes place, to a lower temperature, on the average for 
 the whole column, than that of the surrounding air. 
 
 This will be better understood by tracing the effects which 
 must follow in a few assumed cases. In the following table 
 the first column contains the altitudes of several successive 
 strata at equal intervals, and the column A the corresponding 
 temperatures of the air in its undisturbed state as it existed 
 very nearly on the average of Glaisher's balloon ascensions in 
 clear weather, as given in the table of 27, assuming that the 
 temperature at the earth's surface was 25 C.: 
 
 
 
 SATURATED 
 
 o 
 
 
 ,/ QO 
 
 
 Q 
 
 
 Altitudes 
 in 
 
 
 AIR. 
 
 4 
 
 
 
 
 = 4 
 
 
 Meters. 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 A 
 
 B 
 
 C 
 
 B' 
 
 C' 
 
 D 
 
 E 
 
 F 
 
 G 
 
 H 
 
 I 
 
 K 
 
 6000 
 
 -3.o 
 
 -4. 3 
 
 ~2-5 
 
 -60.5 
 
 -3 -5 
 
 -14 o 
 
 2O. 
 
 - 9- 3 
 
 -39- 5 
 
 -43-o 
 
 -47- 5 
 
 -60 
 
 5500 
 
 x -5 
 
 2 .7 
 
 + -3 
 
 -5 -o 
 
 o .7 
 
 12 
 
 18 .0 
 
 6 .y 
 
 38 -5 
 
 4t -5 
 
 42 .9 
 
 55 
 
 5000 
 
 .0 
 
 o .8 
 
 3 -o 
 
 3 -3 
 
 2 .0 
 
 10 4 
 
 15 .5 
 
 4 -5 
 
 37 -o 
 
 39 -5 
 
 38 -5 
 
 50 
 
 4500 
 
 | i . 7 
 
 +i -3 
 
 5 -5 
 
 i .4 
 
 4 -5 
 
 8 o 
 
 13 .0 
 
 - i .9 
 
 35 -o 
 
 36 .8 
 
 34 -o 
 
 45 
 
 4000 
 
 3 -6 
 
 3 -3 
 
 7 -8 
 
 o .6 
 
 4 -8 
 
 5 5 
 
 10 .0 
 
 + o .7 
 
 32 -5 
 
 33 -8 
 
 29 -7 
 
 40 
 
 3500 
 
 5 .6 
 
 5 -5 
 
 IO . I 
 
 +2 .8 
 
 8 .1 
 
 - 3 
 
 7 - 
 
 3 -2 
 
 29 -5 
 
 
 25 -4 
 
 35 
 
 3000 
 
 7 -8 
 
 8 .1 
 
 12 . 4 
 
 5 -3 
 
 10 .4 
 
 
 
 -3-5 
 
 5 -7 
 
 26 .0 
 
 26 !o 
 
 21 .3 
 
 30 
 
 2500 
 
 10 .3 
 
 10 .7 
 
 14 .6 
 
 7 -8 
 
 12 .6 
 
 + 3 
 
 o .0 
 
 8 .1 
 
 22 .0 
 
 21 .7 
 
 T 7 -3 
 
 25 
 
 2000 
 
 12 .8 
 
 13 -3 
 
 16 .7 
 
 10 .4 
 
 14 .7 
 
 6 . 
 
 + 4 -0 
 
 10 .4 
 
 18 .0 
 
 17 .4 
 
 13 .6 
 
 20 
 
 1500 
 
 15 '4 
 
 15 -9 
 
 18 .8 
 
 13 .0 
 
 16 .8 
 
 10 . 
 
 9 .0 
 
 12 .7 
 
 13 -8 
 
 13 -o 
 
 10 .0 
 
 15 
 
 IOOO 
 
 18 .8 
 
 19 .0 
 
 20 .9 
 
 16 .0 
 
 18 .9 
 
 14 
 
 15 .0 
 
 15 .0 
 
 9 -5 
 
 8 .4 
 
 6 .6 
 
 10 
 
 500 
 
 21 .0 
 
 23 -o 
 
 23 .0 
 
 20 .0 
 
 20 .0 
 
 19 .0 
 
 20 .0 
 
 20 .0 
 
 -5 -o 
 
 -5 -o 
 
 ~3 - 2 
 
 5 
 
 000 
 
 25 -o 
 
 25 .0 
 
 25 .0 
 
 25 .0 
 
 25 .0 
 
 25 .0 
 
 +25 .0 
 
 + 2 5 -o 
 
 o .0 
 
 o .0] o .0 
 
 
 
 The columns B and C in the case of saturated air represent 
 the first the temperatures which the air of each stratum would 
 have after ascending through 500 meters to the stratum above 
 as given in the preceding table ; and the second, the tempera- 
 tures at the different altitudes after the vertical circulation has 
 been fully established and the air has ascended from the earth's 
 surface high up into the upper strata, both being determined 
 by the rates of cooling of ascending air given in Table III. 
 By comparing B and A it is seen that, after this initial start, 
 the temperature of the ascending air is warmer than that of 
 the surrounding and sensibly undisturbed air up to the altitude 
 
VERTICAL CIRCULATION. 233 
 
 <of 3500 meters, so that up to that altitude the atmosphere is in 
 the unstable state, and the air being once started upward by 
 any slight impulse or temperature disturbance, the tendency is 
 to go on ; but above the altitude of 3500 meters with any 
 small initial ascent, it becomes colder and heavier than the sur- 
 rounding undisturbed air, and so is deflected off horizontally in 
 .all directions from the central part of the ascending air outward, 
 and a vertical circulation commences. As this progresses the 
 vertical gradient gradually approximates to that of a fully-estab- 
 lished current, and the temperatures become those of the col- 
 umn C. By comparing these temperatures with those of A, it 
 is seen that the temperatures of the ascending air are greater 
 than those of the undisturbed air at the same altitudes, even 
 far above the altitude of 6000 meters, and the tendency for it 
 to continue to ascend is then very strong. With the vertical 
 decrease of temperatures, therefore, of the column A, in the 
 case of completely saturated air, it would be possible for a cy- 
 clonic disturbance of the atmosphere to originate from a very 
 small initial disturbance, and after being fully established, to 
 have considerable violence. But as the air above in this case 
 in its initial ascent becomes colder and heavier than the sur- 
 rounding air, the vertical circulation may not extend very high 
 .before it is deflected off laterally; but it must extend higher 
 than the limit of the unstable state on account of the momen- 
 tum which it acquires below in its ascent. 
 
 If instead of a very small temperature or other disturbance 
 by which initial ascending currents are induced over a given 
 area, we suppose the temperature of the interior part of the air 
 over this area to be several degrees higher than that of the 
 surrounding undisturbed parts, then this number of degrees 
 must be added to columns B and C ; and then, it is seen, both 
 the initial force and that after the vertical circulation is fully 
 established are very much increased as long as this difference 
 of temperature between the central and surrounding parts re- 
 mains, and a vertical circulation might originate in this case if 
 the vertical temperature gradient were even considerably less 
 than that of column A. But as the vertical circulation contin- 
 
234 CYCLONES. 
 
 ues, this difference of temperature is gradually diminished by 
 the interchange of air between the central and exterior parts, 
 and likewise the general vertical temperature gradient of the 
 whole atmosphere for a long distance all around is gradually 
 brought to that of the indifferent state for saturated air, just 
 as in the case of dry air ( 157), and then the whole force van- 
 ishes. 
 
 160. With the same vertical temperature gradient of the 
 atmosphere generally over a large extent of the earth's surface, 
 represented by column A, let us consider the case in which 
 the air is not completely saturated, but in which there is a 
 given difference between the temperature of the air, r, and that 
 of the dew-point, d, or a depression of the dew-point, T d, at 
 all altitudes. In this case the air in its initial disturbance has 
 to rise at all altitudes, by Table IV, about 125 meters for each 
 degree Centigrade of r d before condensation and cloud for- 
 mation take place, and during this time the rate of cooling is 
 i for each 100 meters, the same as in dry air. If we take r d 
 = 4, then the air of each stratum in ascending through 500 
 meters is cooled down to the dew-point and condensation 
 commences, after which the rate of cooling is that given by 
 Table III, and consequently differs at different altitudes and, 
 temperatures. After the air of each stratum from any supposed 
 initial impulse has ascended to the one 500 meters above, the 
 temperatures become those of the column B', instead of those 
 of A, which represent the temperatures of the surrounding air 
 which has riot ascended. By comparing B' with A it is seen 
 that the ascending air has now become colder, and conse- 
 quently heavier than the surrounding undisturbed air, and has 
 no tendency to ascend higher, unless the ascent is maintained 
 by the initial starting force, but tends to fall back. It is there- 
 fore in the stable state for unsaturated air. If, however, this 
 initial force were continued until the ascending current and the 
 whole vertical circulation were fully established, then the tem- 
 peratures in such an ascending current would be those of C' as 
 determined from Table III, allowing a decrease of 5 between 
 the earth's surface and the plane of incipient condensation 500* 
 
VERTICAL CIRCULATION. 235, 
 
 meters above. It is seen that the temperatures now, from the 
 disengaged latent heat of condensation, are much greater than 
 those before the ascent commenced and those of the surround- 
 ing atmosphere generally. If, therefore, the initial temperature 
 disturbance is sufficient to inaugurate a complete vertical cir- 
 culation, there is then a tendency for it to continue until this 
 tendency vanishes, for reasons already given. If we suppose, 
 for reasons given in 1 56, that the temperature of the interior- 
 ascending air is 3 greater than that of the surrounding quiet air,, 
 we must add 3 to the temperatures of the columns B' and CV 
 and then, by comparing these with A, it is seen that not only the 
 tendency of the air to ascend is greatly increased when the 
 vertical circulation is fully established, but that there is this, 
 tendency as soon as the air of each stratum has ascended to 
 the plane of incipient condensation 500 meters above, and this 
 tendency after that continues to increase until the circulation 
 is fully established. 
 
 161. Let us now assume that the vertical distribution of 
 temperature in the atmosphere over a very large part of the 
 earth's surface is that represented by the column D in the 
 preceding table, and that the depression of the dew-point, t d, 
 at all altitudes is 8. The air of each very thin stratum in this 
 case has to ascend about 1000 meters before condensation of 
 aqueous vapor commences, and in doing so is cooled down 
 10. It then has the temperatures of the column E, and con- 
 sequently is now much colder and heavier than the surround- 
 ing undisturbed air, so that if by any temporary impulse it 
 had received such an upward motion, it would not now tend to 
 go on but to fall back, and so in all cases where the vertical 
 temperature gradient is not greater than that of the indifferent 
 state for dry air. But if the initial disturbing force arising from 
 a central higher temperature were sufficient to establish a com- 
 plete vertical circulation such as to have carried air from the 
 surface up to high altitudes, the distribution of vertical tem- 
 perature now in the ascending air would be as represented by 
 the column F, the whole ascending air having been warmed up- 
 by the setting free of the latent heat in condensation above its. 
 
2 36 CYCLONES. 
 
 original temperatures of the same altitudes, instead of being 
 cooled below them in the ascent through the first 1000 meters 
 before condensation commenced. The whole of the ascending 
 air now is consequently warmer than that of the surrounding 
 parts, and has a tendency to continue to rise up and to main- 
 tain the vertical circulation. Such a circulation, however, 
 could not originate from any slight disturbance of the atmos- 
 phere, as in the case of unstable equilibrium of either dry or 
 fully saturated air; but it would require that the ascending air, 
 ^before ascent, should have a higher initial temperature than 
 that of the surrounding air by about 4 or 5, in order that, 
 when it has ascended and cooled down to the dew-point, the 
 temperatures may be a little greater than that of the surround- 
 ing air, at least up to a considerable altitude, and not have 
 fallen below, and so stopped the further ascent ; for if 4 or 5 
 were added to the column E it would make the temperatures 
 greater than those of the column D up to a considerable alti- 
 tude, and so the air would continue to ascend and not fall back, 
 and an initial circulation would be established up to at least a 
 high altitude. This additional amount of temperature added 
 to the column F indicates by comparison with D that the force 
 by which the vertical circulation, when once established, is 
 maintained, would be much increased. It is therefore possible, 
 with the preceding assumed vertical temperature gradient and 
 hygrometric condition of the air, for a vertical circulation of 
 the air to originate and be maintained for some time, provided 
 that the initial temperature disturbance is considerable, and 
 not merely such as to give it a slight upward motion, as re- 
 quired in the cases of the unstable state of the atmosphere. 
 
 By comparing F with A instead of with D, it is seen that a 
 vertical circulation cannot be maintained with a depression of 
 the dew-point equal to 8 with the same condition of the at- 
 mosphere with regard to vertical temperature gradient as in the 
 case in which the depression of the dew-point is only 4 ; for 
 in this latter case the vertical circulation is kept up with the 
 vertical temperature gradient corresponding to A, since the 
 -temperatures of C ' which exist after complete circulation is 
 
VERTICAL CIRCULATION. 
 
 established are greater than those of A, while those of F, in the: 
 former case, when complete circulation is established are less 
 than those of A, though greater than those of D. Now the 
 longer the vertical circulation continues, the greater is the 
 depression of the dew-point, for as the moist air ascends and 
 loses its moisture by condensation, and the surrounding air 
 gradually descends, and the cold air of the upper strata with 
 comparatively little aqueous vapor comes down near the earth's 
 surface, the ascending current is supplied with air which is 
 gradually becoming drier, and consequently with air having a 
 lower depression of the dew-point. It follows, therefore, that a 
 vertical circulation which originates from and is maintained by 
 a given vertical temperature gradient gradually loses its force 
 and finally vanishes, because the supply of air to the ascending 
 current becomes gradually drier and its dew-point lower. 
 
 As the dew-point becomes lower and the plane of incipient 
 condensation and cloud-formation rises, all the strata in the; 
 ascending current below this are reduced to the indifferent 
 state for dry air, and the slowly descending air in the region 
 around is also slowly reduced to this state, so that in time the 
 whole atmosphere in and around the region of ascending air is. 
 reduced very nearly down to the indifferent state for dry air, 
 and would be entirely so, if, when the vapor is all nearly con- 
 densed, the energy were still sufficient to continue the circula- 
 tion and it were not broken up by abnormal disturbances be- 
 fore this state is reached. 
 
 162. Let us now consider still another temperature condi- 
 tion one belonging to the winter season with a temperature of 
 o at the earth's surface, and let us assume a vertical tempera- 
 ture gradient corresponding to the vertical distribution of tem- 
 perature represented by the column G in the preceding table, 
 and that the depression of the dew-point is 4. Proceeding 
 now as before, we get for the temperatures, after the air of the 
 different levels has ascended 500 meters, when condensation 
 commences, those contained in column H ; and after complete 
 vertical circulation is established, approximately those of the 
 column I, as accurately as they can be conveniently obtained. 
 
1238 CYCLONES. 
 
 from Table III by an extrapolation for the lower temperatures. 
 By comparing H with G it is seen that when condensation first 
 commences the ascending air at the higher altitudes is colder 
 than the surrounding air, if the ascent does not arise from an 
 initial higher temperature in the ascending air, and that unless 
 this temperature is several degrees greater the tendency is to 
 fall back after the initial ascent of 500 meters. At lower levels, 
 however, the temperature is greater and the tendency is to 
 continue on. If the initial upward motion arises from a single 
 momentary impulse, or only a very small difference of tempera- 
 ture of the ascending air before starting, a vertical circulation 
 at first will take place in the lower strata only, and gradually 
 extend to higher levels ; but it cannot extend to very high alti- 
 tudes, since if such were established we should have the tem- 
 peratures of the column I, whfch above the altitude of 5000 
 meters are less than those of the column G, and consequently 
 of the surrounding undisturbed air at the same levels. The 
 air, therefore, would be heavier and could not continue to as- 
 cend above that altitude, but would be deflected from the cen- 
 tral part outward in all directions and descend slowly in the 
 surrounding regions toward the earth's surface without disturb- 
 ing much the air above at high altitudes. 
 
 If the air in this case were saturated, the vertical circulation 
 would take place with a smaller vertical gradient, that is, with 
 smaller differences of temperature between the lower and higher 
 strata ; but, on the other hand, if the air were drier and the 
 depression of the dew-point were 8 instead of 4, this vertical 
 gradient would have to be larger, and the more so the drier 
 the air and the greater the depression, until in the case of per- 
 fectly dry air, in order to have a vertical circulation, it would 
 have to be greater than that of the indifferent state for dry air, 
 corresponding to the vertical distribution of temperature given 
 in the column K. 
 
 The relation between the radiation of dry air and its ab- 
 sorption of solar heat radiation is no doubt such that the un- 
 stable state would be induced in a dry atmosphere after a long 
 interval of perfect calm ; but in the real atmosphere of nature, 
 
VERTICAL CIRCULATION. 239 
 
 ^containing more or less of aqueous vapor, we have seen that this 
 state is induced with a much smaller vertical temperature gra- 
 dient, and before it approximates very nearly to that of the 
 indifferent state of dry air vertical circulations and reversions 
 take place, which tend to bring it back only partially to that of 
 the indifferent state of dry air. 
 
 163. In the first assumed cases in the preceding table, in 
 -which the air at all altitudes is supposed to be saturated, con- 
 densation takes place at once at all levels, as soon as an ascend- 
 ing current is from any cause induced, and the cloud or fog is 
 formed at all altitudes down to the earth's surface. In the 
 second case, with the same vertical gradient of temperature, 
 rbut with a depression of the dew-point of 4, incipient conden- 
 sation takes place at the altitude of 500 meters, and the base 
 -of the cloud is at that level ; but if the depression of the dew- 
 point were 8, the base of the cloud would be at the level of 
 1000 meters above the earth's surface, supposing in all cases 
 that air ascends from the surface. And in general the height 
 >of the base of the cloud is about 125 meters for each degree of 
 the depression of the dew-point, varying slightly with different 
 temperatures and altitudes as is seen from Table IV. The 
 -drier the air, therefore, the higher are the clouds where the 
 conditions are favorable to the production of ascending cur- 
 Brents. 
 
 Without ascending currents, therefore, there can be no 
 clouds ; and in all the region around that of the ascending air, 
 where there is a gradual descent of air to supply the indraught 
 of these currents, the air is clear ; for if even there were complete 
 saturation and cloud from a previous ascent of the air, as it 
 began to descend the air would at once become warmer and 
 unsaturated, and the cloud would soon disappear by evapora- 
 tion. Of course it must be understood here, as in all that im- 
 mediately precedes, that the air cools by expansion only. If 
 -the air is cooled in other ways, as by nocturnal radiation during 
 a clear night, or by passing from lower to higher latitudes, or 
 from a warmer to a colder surface, as from the ocean to the 
 land in the winter, or vice versa in summer, there may be cloud, 
 
240 CYCLONES. 
 
 called fog, at and near the earth's surface without any ascent 
 of air to higher altitudes to give rise to cooling by expansion. 
 
 164. In all of the assumed vertical temperature gradients 
 of the table of 159, represented by the columns A, D, and G, 
 and the assumed depressions of the dew-point, it is seen, by 
 comparing these columns with those of C, (7, F, and I, that 
 after the ascending current is fully established, its temperature 
 in all of these cases, up to 6000 meters, is greater than that of 
 the surrounding air. It is observed, however, that in the un- 
 disturbed atmosphere generally, the gradient becomes much 
 smaller at great altitudes, as is seen in the results obtained 
 from Glaisher's balloon ascents ( 27), and instead of the gradi- 
 ent being the same at all altitudes, it diminishes with increase 
 of altitude very nearly as the pressure does, and consequently 
 the vertical temperature gradients at very high altitudes be- 
 come small. They may be, and most probably are, such that 
 the temperature of the ascending air at high altitudes is less 
 and consequently the density greater than that of the surround- 
 ing air; and so, even with the momentum which it has acquired 
 in its ascent in the lower strata, it does not ascend to the top 
 of the atmosphere, or even to very high altitudes, but is mostly 
 or entirely deflected horizontally in all directions at a lower 
 level. In such a case the vertical circulation would scarcely, or 
 not at all, extend to high altitudes, but be confined mostly to> 
 the lower strata, and the air at very high altitudes be very little 
 disturbed, and this mostly or entirely by means of friction be- 
 tween it and the air currents below. 
 
 If the ascending current extends up to a given level only, 
 of course there is no condensation and cloud-formation above 
 that level, and the air remains clear and comparatively quiet 
 above, while below there may be a brisk ascending current and 
 great cloudiness. 
 
 165. We have seen in preceding sections, and especially in 
 the examples given in the table of 159, that the vertical tem- 
 perature gradient of the ascending air in a cyclone, and the 
 differences between it and that of the surrounding air, may be 
 and must generally be very irregular, so that there is not a 
 
GYRATORY MOTION OF CYCLONES. 
 
 uniform horizontal temperature gradient at all altitudes be- 
 tween the interior and the exterior part, as there is somewhat 
 between the equatorial and polar regions of each hemisphere, 
 the differences of temperature here on different parallels, and 
 consequently the horizontal temperature gradients, being 
 nearly the same at all altitudes. But still the greater tempera- 
 ture in the interior causes an upward expansion of the air and 
 greater vertical distances between the isobaric surfaces here 
 than in the exterior part where the temperature is less, just as 
 in the case of the general motions of the atmosphere these ver- 
 tical distances are greater in the equatorial than in the polar 
 regions, as explained in 71. The motions of each part of the 
 air between the interior and the exterior are very similar in the 
 two cases, except that they are reversed. In the general mo- 
 tions of the atmosphere the air moves toward the pole or cen- 
 tre above, descends gradually in the central part, that is, in the 
 polar and middle latitudes, moves from the central toward the 
 exterior part in the lower latitudes and ascends slowly in the 
 exterior or tropical regions ; but where the interior is the 
 warmer, the air moves toward the interior below, ascends in 
 the interior part, flows away above toward the exterior part, 
 where it descends very slowly toward the earth's surface, there 
 to commence again another circuit. All that is stated in the 
 former case with regard to neutral planes between the counter 
 horizontal and vertical currents, the satisfying of the condition 
 of continuity, and the explanations of the vertical circulation, 
 holds also in this in a general way. In this, however, there is 
 not that definiteness of outer limit which there is at the equa- 
 tor to each of the hemispheres in the general hemispheric cir- 
 culation. 
 
 GYRATORY MOTION OF CYCLONES. 
 
 1 66. We have seen that while the atmosphere is clear and 
 somewhat quiet, the tendency is for the upper strata to cool 
 down to so low a temperature in comparison with that of the 
 earth's surface and the lower strata, that the unstable state is, 
 
242 CYCLONES. 
 
 induced, if not for dry air, at least in the case of saturated air, 
 and that although the air without ascending currents is rarely, 
 and only near the earth's surface completely, saturated, yet if 
 there is only a slight local temperature disturbance a little ex- 
 cess of temperature over some central area above that of the 
 surrounding air a vertical circulation is started which contin- 
 ues until there is such an interchange and inversion of the air 
 of the upper and lower strata that the unstable state is de- 
 stroyed, and the stable state and comparative calmness and 
 clearness are again restored for a while, until broken up again, 
 in perhaps a short time, in a similar manner as before. If the 
 earth had no rotation on its axis the air in its vertical circula- 
 tion, in all such cases of local and temporary disturbances, 
 would move in the lower strata directly toward the central part 
 of the area of higher temperature and less pressure and out 
 from it above, as already described, and there would be no 
 gyratory motion around the centre. But in consequence of the 
 earth's rotation, where a body moves in any direction on the 
 earth's surface there is a force which deflects it to the right in 
 the northern hemisphere, and the contrary in the southern 
 ( 53)' I n the case of a central force acting upon the body, as 
 where air is forced in from all sides toward a centre by a pres- 
 sure gradient, this deflecting force is strengthened by the rela- 
 tive gyratory motion of the body itself, as is seen from the ex- 
 pression of F t , 52, in which the part depending upon n is due 
 to the earth's rotation, and that upon v to the gyratory mo- 
 tion ; and so very near the centre, where v = v/r becomes 
 very large, the deflecting force becomes much greater, with the 
 same velocity of the body s. The air therefore in the lower 
 strata, in being forced in from all sides toward the centre, runs 
 into a gyration around this centre, and this in the northern 
 hemisphere is from right to left, or contrary to the motion of 
 the hands of a watch. 
 
 This may be illustrated by means of the behavior of water 
 in a shallow basin, where it is allowed to run out through a 
 hole in the centre. If the basin is at rest, and the water in the 
 basin has no motion of any kind before the hole is opened, the 
 
GYRATORY MOTION OF CYCLONES. 243 
 
 water flows directly from all sides toward the centre, without 
 any gyratory motion. But if the basin, although the water 
 with reference to the basin is perfectly at rest, has the least 
 gyration around its centre, the water in approaching toward 
 the centre runs into a gyration around that centre, and the 
 gyratory velocity becomes very great near the centre. It is 
 somewhat the same where the air over a considerable area of 
 the earth's surface is forced from all sides toward the centre. 
 This area, we have seen, 52, gyrates, in consequence of the 
 earth's rotation, around its centre, with an angular velocity 
 proportional to the sine of the latitude ; and so the air, in run- 
 ning in from all sides toward the centre, runs into a gyration 
 around the centre, just as the water in the basin. The princi- 
 pal difference in the two cases is, that the water runs down 
 through the hole and disappears, while the air runs upward 
 over the central area, and flows away above. 
 
 167. In the flowing away of the air above in all directions 
 from the centre, it is deflected toward the right in the north- 
 ern hemisphere by the same force as in running in toward the 
 centre. The first effect is to counteract and overcome the gy- 
 ratory velocity acquired by the air in being forced toward the 
 centre, and after that it produces a gyratory motion in the con- 
 trary direction, that is, from left to right. Where the system 
 of vertical circulation and gyratory motions becomes fully es- 
 tablished, and the air which flows out above is drawn in again 
 toward the centre below, this gyratory motion from left to 
 right has first to be overcome by the deflecting force before a 
 gyratory motion from right to left begins to be generated. In 
 connection, therefore, with every vertical system of circulation 
 there is produced by the deflecting force of the earth's. rotation 
 two kinds of gyrations the one, mostly in the interior part, 
 from right to left in the northern hemisphere, and the other, 
 mostly in the exterior part, in the contrary direction. The in- 
 terior, and by far the most violent part, is called a cyclone, and 
 therefore the exterior and comparatively gentle part is prop- 
 erly called an anti-cyclone ; and the two always go together. 
 The gyrations of the former are properly called cyclonic gyr a- 
 
244 CYCLONES. 
 
 tions, and those of the other, anti-cyclone gyrations ; it being 
 understood that each of them is exactly reversed in the other 
 hemisphere. 
 
 The deflecting forces upon which the gyrations depend be- 
 ing greatest at the poles and diminishing as the sine of the lati- 
 tude toward, and vanishing at, the equator, of course the gy- 
 rations arising from any given temperature disturbance or ver- 
 tical circulation, all other circumstances being the same, are 
 most violent in the polar regions, less so with decrease of lati- 
 tude, and vanish at the equator, the motions there being di- 
 rectly toward and from the centre, the same as would be the 
 case everywhere on the earth's surface if the earth had no 
 rotation on its axis. 
 
 168. In the case of no friction between the air and the 
 earth's surface, and the initial state of the air being that of 
 relative rest, each particle of air, in being drawn in toward the 
 centre, would, after the system of motions had become fully 
 established, move in accordance with the principle of the 
 preservation of areas, 41, provided we consider the absolute 
 gyratory velocity, including both that depending upon the 
 earth's rotation and that which is relative to the earth's surface. 
 Hence, putting w for the absolute gyratory velocity, and r for 
 the distance from the centre, we must at all distances from the 
 centre have the relation, as in 42, 
 
 in which c is a constant equal to the average value of rw taken 
 while the air is yet at rest, and w has the value rn' t for the 
 whole mass of air brought into motion. As r diminishes w 
 must increase, and consequently near the centre it becomes 
 very great, and the value there of w consists mostly of the 
 gyratory velocity relative to the earth's surface, since the part 
 depending upon the earth's rotation decreases as r, and con- 
 sequently near the centre becomes very small. 
 
 If each particle of air, in being acted upon by the centripetal 
 force below, and centrifugal force above, arising from pressure 
 gradients, were entirely free, not only from the effect of the 
 
GYRATORY MOTION OF CYCLONES. 245 
 
 friction of the earth's surface, but likewise from the effect of 
 other particles acting upon it by contact and by friction, its 
 gyratory velocity would satisfy the preceding expression for 
 all values of r or distances from the centre, with the value of 
 the constant c =. r w , in which r and w were the values of r 
 and w before relative motion commenced. But since in the 
 interactions of the different parts of the air action and reaction 
 .are equal, these cannot affect the average of rw for the whole 
 mass, and this, therefore, must remain constant and equal to 
 its value before motion commenced, and therefore equal to the 
 average of r w for the whole mass. The gyratory velocity at 
 all altitudes is in this case the same at the same distances from 
 the centre, and there is consequently no friction then between 
 the strata arising from relative gyratory velocities. The whole 
 deflecting force is spent in either giving gyratory velocity and 
 momentum to the air, or in overcoming this where already 
 acquired. The air, therefore, has a cyclonic motion at all 
 -altitudes in the interior and an anti-cyclonic motion in the 
 exterior part, and the distance from the centre at which the 
 cyclonic changes to the anti-cyclonic motion is the same at 
 all altitudes. 
 
 By referring to 74 it will be seen that this result is very 
 rsimilar to that in the general motions of the atmosphere in the 
 case of no friction, the value of r being the distance from the 
 centre of gyration in this, while in the other it is the distance 
 from the earth's axis of rotation. 
 
 169. If the whole region of temperature disturbance and 
 vertical circulation, and the underlying portion of the earth's 
 surface, did not have a gyratory motion around the centre in 
 consequence of the earth's rotation, the vertical circulation 
 would have the full force due to the pressure gradients arising 
 from the differences of temperature between the interior and 
 the exterior, as in the case of the general motions of the 
 atmosphere if the earth had no rotation on its axis, and if 
 there was no friction there would be continued acceleration ; 
 but in case of friction the acceleration continues until the 
 friction becomes equal to the forces, after which the circulation 
 
246 CYCLONES. 
 
 is uniform so long as the disturbing forces are the same. But 
 where the whole gyrates around the centre, we have seen, the 
 deflecting forces tend to produce a cyclonic gyration in the 
 lower strata of the atmosphere, and an anti-cyclonic in the 
 upper strata ; but in the case of friction between the earth's 
 surface and the air, and between the different strata having 
 relative velocities, the forces are not entirely spent upon the 
 inertia of the air, as in the case of no friction ( 168), but partly 
 upon the inertia and partly in overcoming the friction. So far 
 as it is spent upon the inertia, the effect is to cause cyclonic 
 gyrations in the interior and anti-cyclonic gyrations in the 
 exterior, as in the case of no friction between the air and the 
 earth's surface, in which the whole force is spent upon the 
 inertia of the air ; but so far as it is spent upon the friction 
 between the different strata, the tendency is to maintain 
 counter gyrations in the lower and upper strata, cyclonic 
 below and anti-cyclonic above. The resultant effect is, there- 
 fore, in part the one and in part the other. Whatever the 
 gyratory velocity below may be, that above is less for the 
 cyclonic and greater for the anti-cyclonic at the same distances 
 from the center. The greater the altitude of the stratum, 
 therefore, the nearer the centre does the change take place 
 from the cyclonic to the anti-cyclonic gyrations. 
 
 By comparing these results with those obtained in a some- 
 what different manner with regard to a whole hemisphere in 
 the general circulation of the atmosphere, it will be seen that 
 they are very similar, except that in the general circulation of 
 a hemisphere the gyratory or east components of velocity are 
 greatest above, while in the cyclonic they are least above ; 
 and in the general circulation the distance from the pole at 
 which the easterly velocities vanish and change to westerly 
 ones increases with increase of altitude, while in cyclones the 
 distance from the centre at which the gyrations vanish and 
 change from the cyclonic to the anti-cyclonic decreases with 
 increase of altitude. This arises from the difference in the 
 distribution of temperature and of the horizontal temperature 
 gradients ; in the case of the hemisphere in the general circu- 
 
GYRATORY MOTION OF CYCLONES. 247 
 
 lation the polar or central region is the colder, and in the 
 cyclone the central part is the warmer, and consequently the 
 directions of the vertical circulations are reversed in the two 
 cases. 
 
 1 70. Although in the cyclones the gyratory velocities for 
 the whole system, considered algebraically, and regarding the 
 cyclonic as the positive ones, are less above than below, yet 
 there is a limit beyond which the difference cannot go, and 
 this depends upon the temperature gradients between the 
 interior and exterior parts. As soon as gyratory motions are 
 produced there arises another modifying force, the force 
 deflecting to the right of the direction of gyratory motion in 
 the northern hemisphere ( 52), and so from the centre in the 
 case of cyclonic, and toward it in that of the anti-cyclonic 
 gyrations. If the gyratory velocities, and consequently the 
 deflecting forces, were the same in the upper as in the lower 
 strata, they would not interfere with the vertical circulation 
 which is maintained by the gradients arising from differ- 
 ences of temperature, as explained in 63, and the vertical 
 circulation would be maintained by the full force of the 
 pressure gradients arising from the differences of temperature, 
 just as in the case of no gyrations whatever. But if these 
 deflecting forces are greater below than above, it interferes 
 with this vertical circulation, and the difference between the 
 gyratory velocities and the forces below and above may be 
 such as to entirely counteract the forces by which the vertical 
 circulation is maintained, just as forces of different strengths 
 applied in the same direction at the bottom and top of a 
 turning wheel, if the difference is great enough, and the 
 stronger force is applied in the direction which tends to stop 
 it, entirely counteracts the force by which the wheel is kept in 
 motion. 
 
 In the case of regular temperature gradients, an expression 
 of the differences of the velocities required for this might be 
 obtained in a function of the temperature gradient, as in the 
 case of the differences of the east components of velocity above 
 and below in the general circulation of the atmosphere ( 77). 
 
248 CYCLONES. 
 
 But however irregular the temperature disturbance and the 
 temperature gradients may be, the differences between the 
 gyratory velocities above and at or near the earth's surface 
 may be such as to entirely destroy vertical circulation. But 
 it is evident that the actual differences must fall short of this ; 
 for if the gyratory velocities were such as to entirely stop ver- 
 tical circulation there would then be no deflecting force in a 
 direction at right angles to that of the vertical circulation to 
 overcome the friction between the strata having different gyra- 
 tory velocities, and so this friction would tend to reduce the 
 velocities above and below to the same, and would at once so 
 decrease the differences between them that the vertical circula- 
 tion would not be entirely stopped ; but still its velocity would 
 be comparatively much smaller than in the case of no gyration 
 of the whole system around a centre, in which cases the verti- 
 cal circulation is not hindered by differences in the deflecting 
 forces below and above, but the vertical circulation is main- 
 tained by the full force of the pressure gradients arising from 
 the difference of temperature between the interior and the 
 exterior. These deflecting forces, therefore, act as a sort of 
 governor, as in the case of the general motions of the atmos- 
 phere ( 75). If the differences between the gyratory veloci- 
 ties below and above, and consequently between the deflecting 
 forces, are a little too great, the velocity of the vertical cir- 
 culation becomes too small, and the effect of this is to 
 diminish these differences, and vice versa. 
 
 Since the differences of the velocities above and at the 
 earth's surface, in order to counteract the vertical circulation, 
 must be such that the differences of the deflecting forces above 
 and at the earth's surface are adequate to counteract the forces 
 by which the vertical circulation is maintained, and these de- 
 flecting forces at the same distance from the centre are propor- 
 tional to the temperature gradient there between the interior 
 and exterior part of the cyclonic area, it is evident that the 
 greater the temperature gradients, the greater the gyratory 
 velocities above differ from those at or near the earth's surface, 
 and very nearly or quite in proportion, since the limits which 
 
GYRATORY MOTION OF CYCLONES. 249 
 
 they do not reach, but fall short of a very little, are in that 
 proportion. 
 
 But the deflecting forces, as seen from the expression of 
 F v , 52, for the same gyratory velocity z/, increase as r de- 
 creases, and near the centre very nearly inversely as r, so that 
 the relative velocities of the strata below and above, required 
 to counteract the effect of any given temperature gradient, 
 are smaller the nearer the centre. 
 
 171. The conditions of temperature and of temperature 
 gradients determine the relations between the gyratory velocities 
 above and those near the earth's surface, whatever the latter 
 may be. These depend upon the amount of frictional resist- 
 ance of the earth's surface to the gyrations and upon the forces 
 which overcome these resistances, and must be so adjusted 
 that the principle will be satisfied that all the resistances from 
 every differential element of the earth's surface, so far as the 
 gyrations extend, multiplied into the distances from the centre, 
 or, in other words, the sum of all the moments of couple must 
 be o, or else the tendency would be to turn the earth around 
 the axis the pole of which is the centre of the cyclone. But 
 this cannot arise from central forces alone, either centripetal 
 or centrifugal, such as arise from the temperature gradients, 
 and these are the only real forces concerned, the deflecting 
 forces, so called, being simply modifications of the directions of 
 motion as referred to the gyrating surface of the earth. 
 
 From the centripetal motion of the air in the lower part of 
 the atmosphere arises the deflecting force which gives rise to a 
 cyclonic motion, and from the centrifugal motion in the upper 
 strata, that which counteracts the cyclonic and tends to pro- 
 duce an anti-cyclonic gyration. Since there must be as much 
 motion toward the central part below as away from it above, 
 with a slight exception while the cyclone is forming or vanish- 
 ing, in order to satisfy the condition of continuity, these de- 
 flecting forces are exactly equal and contrary to each other, 
 and so, taken together, have no tendency to overcome the 
 friction between the air and the earth's surface in the cyclonic' 
 -and anti-cyclonic gyrations, but tend mostly, after the vertical 
 
250 CYCLONES. 
 
 and gyratory circulations are fully established, to overcome the- 
 friction between the strata of air having different gyratory 
 velocities, and in part to change the gyratory moments. Be- 
 fore that, of course, especially at first, the forces are mostly 
 spent in overcoming the inertia of the air in producing or de- 
 stroying these moments. As the air which moves in toward 
 the centre below has a greater gyratory velocity than it has at 
 the same distance from the centre in flowing out above, the 
 air, from the time it enters below within a given distance of the 
 centre until it passes out above beyond that distance, loses a 
 certain amount of kinetic energy corresponding to the differ- 
 ence of gyratory velocities at the times of entering within, and 
 passing without, this limit ; and this amount, meanwhile, has. 
 been spent upon the frictional resistance of the earth's surface 
 within the given distance from the centre. A part of the de- 
 flecting force above is spent in decreasing the gyratory velocity 
 there, and consequently only what is left counteracts, through 
 friction between the strata, the equal deflecting force in the 
 contrary way below, and the remainder not counteracted is left 
 to overcome the friction at the earth's surface, but this is equal 
 to that arising from the gradual loss of the kinetic energy. 
 
 We have just seen that the relative velocities of the gyra- 
 tions above and below decrease directly as the radial temper- 
 ature gradients, and also decrease with the decrease of r, the 
 distance from the centre, but not in proportion. But the 
 temperature gradient vanishes at the centre, and must be very 
 small for some distance near the centre. The amount of mo- 
 mentum lost, therefore, as the air ascends to higher altitudes, 
 and consequently the force upon which the gyratory velocity 
 at the earth's surface is maintained, is very small near the 
 centre, and consequently the gyratory velocity there is com- 
 paratively small, where there are frictional resistances to be 
 overcome, though where there are no such resistances they 
 become greater very nearly inversely as the distance from the 
 centre. 
 
 In the exterior part of the cyclonic system, where the gy- 
 rations at the earth's surface are anti-cyclonic, it is readily seen?. 
 
ATMOSPHERIC PRESSURE IN CYCLONE-S. 2$l 
 
 how the air in the upper strata, where it has a greater anti- 
 cyclonic gyratory velocity, in settling down gradually into the 
 lower strata in its vertical circulation, where the gyratory ve- 
 locity is less, gradually loses its momentum, and that this lost 
 momentum, by means of friction, is transferred to the surface, 
 where it becomes a force applied directly to overcoming the 
 frictional resistance to the anti-cyclonic gyrations. 
 
 172. The gyratory velocities at the earth's surface corre- 
 sponding to the frictional resistances which are equal to the 
 forces overcoming them, of course depend upon the nature of 
 the surface and the law of resistance with regard to different 
 velocities. For a homogeneous surface, however, whatever this 
 law, it is evident that the velocities of the cyclonic gyrations 
 must, upon the whole, be much greater than those of the anti- 
 cyclonic, in order to have the sums of the moments of couple 
 equal, since the former are much nearer the centre, unless the 
 cyclonic gyrations cover a much larger area. But this is not 
 the case, but rather the contrary ; for the whole cyclonic area 
 having no definite limit, the anti-cyclonic part is spread over a 
 much larger area, and therefore the gyratory velocities are very 
 small in comparison with those of the interior cyclonic part. 
 
 The less the amount of frictional resistance at the earth's 
 surface corresponding to any given gyratory velocity, the 
 greater the gyratory velocities, so that at sea, with a smooth 
 surface, the gyrations, with the same amount of energy spent, 
 are greater than on land. And in the case of no such fric- 
 tional resistances, as we have seen, they would become very 
 great near the centre, the principle of the preservation of areas 
 being satisfied in this case, and the whole deflecting force in 
 this case would act in overcoming the inertia of the air and 
 producing gyratory momentum as it proceeds toward the 
 centre in the cyclonic part, and in overcoming this momentum 
 as the air flows back from the centre. 
 
 ATMOSPHERIC PRESSURE IN CYCLONES. 
 
 173. Whatever the nature of the earth's surface and the 
 gyratory velocities there, it has been shown that the differences. 
 
252 CYCLONES. 
 
 between these velocities and those at any altitude above at the 
 same distance from the centre are the same in any case, so that 
 where the gyratory velocities at the earth's surface are greater 
 for any reason, all those at any altitudes above are increased 
 by the same amount. This however must be taken in an alge- 
 braic sense toward the outer limit of the cyclonic part at the 
 earth's surface, where the cyclonic gyrations below change to 
 the anti-cyclonic above ; that is, an increase of the cyclonic 
 velocities below diminishes the anti-cyclonic gyratory velocities 
 -above. If we imagine the resistances at the earth's surface to 
 be so great that there are sensibly no gyratory velocities there, 
 then the same differences will exist between these and the 
 gyratory velocities above, now all anti-cyclonic, and these are 
 .such as to approximate very nearly to that limit at which, by 
 means of the deflecting force toward the centre, the air, ex- 
 panded upward by a higher temperature in the interior than 
 the exterior part of the whole area of cyclonic disturbance, is 
 completely hindered from flowing away above from the interior 
 to the exterior part. It has been explained that the differ- 
 ences between the gyratory velocities below and above must fall 
 a little short of this limit so as to allow a little vertical circu- 
 lation, and consequently small gradient of decreasing pressure 
 toward the centre at the earth's surface to keep up this circu- 
 lation, as explained in 63. The pressure, therefore, at the 
 earth's surface is scarcely affected by the upward expansion of 
 air in the interior from a higher temperature, since the anti- 
 cyclonic gyrations almost entirely prevent its flowing away 
 above, and the consequent diminution of the pressure at the 
 earth's surface. 
 
 All the other conditions remaining the same, if we now 
 suppose that there are gyratory velocities at the earth's surface, 
 then all the velocities at all altitudes are changed by the same 
 ^amount, taken algebraically when the gyrations change with 
 change of altitude from positive to negative, that is, from cy- 
 clonic to anti-cyclonic, or the reverse. Hence the pressure 
 gradients change by the same amount proportionally at all alti- 
 tudes, and the pressure gradient at the earth's surface, depends 
 
ATMOSPHERIC PRESSURE IN CYCLONES. 2$$ 
 
 simply upon the gyratory velocity at the surface, with the ex- 
 ception of the small gradient referred to above, sufficient to 
 overcome the friction of the centripetal flow below. 
 
 The method of obtaining the barometric gradient corre- 
 sponding to any given gyratory velocity by means of Table V, 
 has been explained in 57. If, in connection with the gyratory 
 velocity, there is a component of velocity toward or from the 
 centre, then the gradient required to maintain this velocity, 
 must be added. 
 
 Since the barometric gradient is proportional to the hori- 
 zontal force which causes it, and this, as we have seen, depends 
 almost entirely upon the gyratory velocities, then it follows 
 from the expression of this force, F v in 52, that near the 
 centre of the cyclone, where r is small, and consequently v = v/r 
 is large, that this gradient is very steep in comparison with 
 what it is for the same gyratory velocity v at a distance from 
 the centre, where r is comparatively large. But v also is largest 
 somewhere near the centre, and consequently the gradients 
 here are comparatively very steep. 
 
 For instance, suppose on the parallel of 40 we had in the 
 anti-cyclonic part a gyratory velocity of 20 meters per second 
 at the distance of 2000 kilometers. From Table V we have 
 o.ioio X 20 = 2.02 for the gradient of pressure increasing to- 
 ward the centre. But this must be decreased by the centrifu- 
 gal force of curvature, since here the two forces are in con- 
 trary directions, in the ratio of v/r 20/2,000,000 = o.ooooi to 
 2 n sin / = 0.0000917, by Table V, or 1/9 very nearly. In the 
 cyclonic part, at the distance of 200 kilometers, the part of the 
 gradient of pressure increasing in a direction from the centre 
 due to the earth's rotation is the same as before, but now the 
 centrifugal force is 10 times as much as in the other case, and 
 is in the same direction as the other. We therefore have in this 
 case the gradient G 2.02 + 2.02 X 10/9 = 4.26. Still nearer 
 the centre, with the same gyratory velocity, the gradient, it is 
 readily seen, would be still much steeper. The gradient there- 
 fore, in the anti-cyclonic part, even in this case, is small in com- 
 parison with what it is near the centre, but the gyratory velocity 
 
:254 CYCLONES 
 
 in the anti-cyclonic part, we have seen, is also much smaller, 
 and so for both these reasons it is always comparatively small 
 here. 
 
 174. Since the deflecting forces of the cyclonic and the 
 anti-cyclonic gyrations are from the centre in the former, and 
 .toward it in the latter, the greatest pressure is at the distance 
 from the centre where they vanish and change from the one 
 to the other, at least so far as the pressure and pressure gra- 
 dients depend upon these forces. The difference of pressure 
 between the lowest at the centre and the highest where the 
 gyrations vanish, depends of course upon the summation of the 
 pressure gradients, and as these are comparatively sttep in the 
 cyclonic part, the difference between the highest pressure and 
 that at the centre is generally very much greater than that in 
 the anti-cyclonic part between the highest pressure and that of 
 the general undisturbed surrounding pressure. 
 
 What has just been stated with regard to pressures at the 
 earth's surface is true of those at any altitude above the sur- 
 face. For the atmosphere above any given level can be re- 
 garded as a separate atmosphere, and the gyratory velocities 
 of the general atmosphere at that level as those of the base of 
 the atmosphere above that level. At any given altitude, 
 therefore, the highest pressure in the plane of that altitude is 
 also, or very nearly, where the gyrations vanish and the cy- 
 clonic change into the anti-cyclonic. But the greater the alti- 
 tude the nearer the centre, as we have seen, does this change 
 take place, and the conditions maybe such that at considerable 
 .altitudes the gyrations may be anti-cyclonic at all distances from 
 the centre, and in this case there is no central area of low 
 pressure, but the greatest pressure is in the centre, and the 
 gyrations are all anti-cyclonic ; and considering the part of the 
 atmosphere above this level, we have here an anti-cyclone alone, 
 with no interior cyclone, while at lower levels, the gyrations 
 are partly cyclonic, and partly anti-cyclonic, the former increas- 
 ing and the latter decreasing in area, and the barometric de- 
 pression in the centre becoming deeper as the altitude is di- 
 minished, until we reach the earth's surface. 
 
RESULTANT MOTIONS. 
 
 All that area in a cyclone in which the barometric pressure 
 is below the usual average, say 30 inches or 760 mm., is called 
 an area of low pressure. It is evident that the depth of the 
 minimum pressure depends both upon the extent of the area 
 and the gradients at the different distances from the centre. 
 Where the gyratory velocity is very great near the centre, the 
 gradient depends almost entirely upon the centrifugal force, 
 especially in low latitudes, and as this becomes very great 
 where the radius is small, such cyclones, even if of small extent, 
 -may have a deeper minimum pressure than large cyclones. 
 
 RESULTANT MOTIONS. 
 
 175. Since the motions of the air in a cyclone consist of 
 both a vertical and gyratory circulation, the resultant at any 
 place depends upon both of these motions as rectangular 
 components, and hence the direction of motion, upon the rela- 
 tions of these components. In the lower part of the atmos- 
 phere the horizontal motion of the vertical circulation of the 
 air is mostly from the exterior toward the centre, and hence 
 here in both the cyclonic and anti-cyclonic parts of the system, 
 the resultant direction inclines from the tangent of gyratory 
 motion in toward the centre, and the angle between this tan- 
 gent and the resultant direction is called the inclination. But 
 in the upper part of the atmosphere, above the neutral plane, 
 where there is no interchanging motion between the interior 
 and the exterior of the area of cyclonic disturbance, the motion 
 is outward, and hence the resultant direction deviates toward 
 the exterior from the tangent, and the inclination in this case is 
 negative or outward. In the neutral plane, of course, there is 
 no inclination, and the only component of motion here is that 
 -of gyratory motion. 
 
 Since the horizontal component of the motion of the air, 
 in its vertical circulation, is gradually retarded as the air ap- 
 proaches the centre of the cyclone, and becomes o at the cen- 
 tre, and small even at a considerable distance from the centre, 
 while the gyratory component of motion here is usually large, 
 
256 CYCLONES. 
 
 the inclination of the resultant or cyclonic motion near the 
 centre is small in comparison with what it is in the outer part 
 of the area of violence and of the cyclone proper, and so much 
 more nearly circular. 
 
 At and near the earth's surface, just beyond the ring of 
 highest pressure, there is an exception to the inclination toward 
 the centre. In consequence of the anti-cyclonic gyratory mo- 
 tion being retarded here by the greater amount of friction, the 
 deflecting force toward the centre here is so much weakened 
 
 o 
 
 that it is not equal to that of the pressure gradient, and the 
 air, instead of flowing in toward the centre, is forced out in the 
 contrary direction from beneath the high pressure. Hence 
 here the resultant direction is anti-cyclonic and outward and 
 the inclination negative, as in the upper part of the atmos- 
 phere. 
 
 On the other side of the ring of highest pressure the ten- 
 dency, for the same reason, is for the air to be forced out from 
 beneath toward the centre, and consequently this force com- 
 bines with that of the general gradient near the surface arising 
 from differences of temperature, upon which the vertical circu- 
 lation depends, and so increases this component of motion 
 very much, and causes the inclination here to be much greater 
 than it otherwise would be, and also greater than that in the 
 higher strata immediately above. 
 
 On both sides of the ring of highest pressure the gyrations 
 are strengthened by the outflow of air beneath on each side, 
 for the deflecting force depending upon the earth's rotation aris- 
 ing from this outflow is in both cases in the right direction for 
 this. In fact, on the outside of this ring there could be no 
 anti-cyclonic gyration if it were not for this force. 
 
 176. We have seen that if it were not for the viscosity of 
 the air, the relative gyratory velocities below and above would 
 be such that all vertical circulation would be prevented, and 
 so in this case all the conditions of the problem would be sat- 
 isfied with a gyratory motion simply, whatever these may be 
 at the earth's surface. But with the least viscosity, the ten- 
 dency is to reduce these relativeve locities to o, unless there is 
 
SURFACE CALMS. 2$? 
 
 a little vertical circulation sufficient to give rise to deflecting 
 forces, in the one direction below and the contrary above, suf- 
 ficient to overcome the friction which tends to diminish these 
 relative velocities. The less the friction, therefore, due to vis- 
 cosity, between strata of air moving with different velocities, 
 the less of the vertical circulation is required. The less the 
 friction, therefore, the less the inclination of the resultant mo- 
 tion, this entirely vanishing where there is no friction. Hence 
 near the earth's surface, where there is much friction, there is a 
 larger inclination, while in the upper strata it is comparatively 
 small and the gyrations are more nearly circular. 
 
 It must not be understood, however, that this is true ii> 
 general for all parts of the system, but only at any given place ; 
 for the inclination depends upon the condition of continuity 
 and other conditions. For instance, near the centre there is a 
 tendency of the air to run into rapid gyrations, while the veloc 
 ity of the inflow of air toward a centre, or any barrier by which 
 it is stopped, must gradually become less and less and finally 
 vanish. Near the centre of a cyclone, therefore, the ratio be- 
 tween the radial and the gyratory velocity, and consequently 
 the inclination, is in general less than at greater distances. 
 
 SURFACE CALMS. 
 
 177. It has been shown ( 171), that near the centre of a 
 cyclone the force which tends to keep up a gyratory motion 
 becomes very small. There is, therefore, little or no motion 
 of that sort for some distance from the centre. But we have 
 just seen above that the motion to or from the centre also be- 
 comes small near, and vanishes at, the centre. However vio- 
 lent the gyrations of a cyclone, therefore, may be at some dis- 
 tance from the centre, at and near the centre there is always 
 sensibly a calm, extending to greater or less distances, accord- 
 ing to the dimensions of the cyclone and other circumstances. 
 
 Under the ring of highest pressure there is no gyratory 
 motion, for we have seen that the gyratory velocities must 
 necessarily vanish and change sign at some distance from the 
 
258 CYCLONES. 
 
 centre, and it has been shown that here is the place where 
 there is the highest pressure. And as the air also flows out 
 from beneath this highest pressure, on the one hand toward the 
 interior and on the other toward the exterior, it is evident that 
 there is here no radial motion. There being, therefore, neither 
 gyratory nor radial motion, there must be here a ring of calms. 
 But on account of the very small gyratory velocities ( 174) 
 and consequent pressure gradients at the earth's surface in the 
 anti-cyclone, as compared with those of the cyclone, and also 
 because here the radial velocity depends upon the differences 
 between two forces, the one arising from the temperature and 
 resulting pressure gradient, which tends to keep up the vertical 
 circulation, and the other arising from the tendency to flow out 
 from beneath the high pressure, the motions of the air at the 
 earth's surface in the anti-cyclone are very gentle, and generally 
 of about the same order as the various abnormal disturbances 
 and irregularities, so that they are not readily distinguished by 
 observation ; but that such anti-cyclonic and outward motions 
 do exist, and a corresponding pressure gradient, with a maxi- 
 mum pressure at some intervening distance between the centre 
 and exterior limit, is without doubt. 
 
 GRAPHIC REPRESENTATION OF MOTION AND PRESSURE. 
 
 178. In Fig. I is given a graphic representation of the re- 
 sultant motions and of the barometric pressures for both the 
 surface of the earth and for some level high up in the atmos- 
 phere and above the neutral plane, where the motions in the 
 vertical circulation are outward from the centre. The solid 
 circles represent isobars at the earth's surface and the solid 
 arrows the directions, and in some measure, by their different 
 lengths, the relative velocities of the. wind. The heavy circle 
 represents the circle of greatest barometric pressure at the 
 earth's surface, say 765 mm,, while the pressure of the outer 
 border is 760 mm., and the dividing line between the cyclonic 
 and anti-cyclonic gyrations. Within this limit the pressure 
 diminishes to the centre and the gyrations are cyclonic and 
 
GRAPHIC REPRESENTATION OF MOTION AND PRESSURE. 259 
 
 the direction -of the resultant of motion inclines in toward the 
 centre, but beyond that limit the gyrations are anti-cyclonic 
 and the direction of resultant motion inclines toward the outer 
 border of these gyrations. The heavy dotted circle represents 
 the circle of maximum pressure at some high level, and is much 
 nearer the centre than that at the earth's surface. It is also 
 
 Fig. I. 
 
 the dividing line between the cyclonic and anti-cyclonic gyra- 
 tions at that level. The dotted arrows indicate the directions, 
 .and in some measure the relative velocities, of the wind at this 
 level. The arrows in the cyclonic part represent the direction 
 of the wind as declining outward, because the plane here con- 
 sidered is supposed to be above the neutral plane, where the 
 radial component of motion is outward, but for any level be- 
 
26O CYCLONES. 
 
 low the neutral plane the inclination is still inward. The 
 arrows are shorter above in the cyclonic part and longer in the 
 anti-cyclonic part than they are at the earth's surface, since the 
 cyclonic gyratory velocities decrease and the anti-cylonic in- 
 crease with increase of altitude. 
 
 The upper part of the figure is a representation of a verti- 
 cal section of the air, very much exaggerated in altitude, in 
 which the solid curved line represents a section of an isobaric 
 surface near the earth's surface, say of 740 mm. barometric 
 pressure. The lowest part corresponds with the centre of the 
 cyclone and the highest part with the heavy circle in the lower 
 part of the figure, and the steepest gradients with the longest 
 solid arrows, since the greater the gyratory velocities at the 
 earth's surface the greater the gradients, though they are not 
 strictly proportional. The second dotted curved line from the 
 top represents a section of the isobaric surface of high altitudes, 
 in which the highest parts correspond with the heavy dotted 
 circle below, since the highest pressure at all altitudes is very 
 nearly where the cyclonic gyrations vanish and change to the 
 anti-cyclonic. The depression here is smaller because the 
 cyclonic area is smaller, and the gyratory velocities less, than 
 at the earth's surface. The upper dotted line belongs to an 
 isobaric surface still higher, where the gyrations are supposed 
 to be all anti-cyclonic, and here, consequently, the greatest 
 pressure is in the centre, as indicated by the curved line. 
 
 As the interior of the whole cyclonic system is warmer 
 than the exterior, and consequently the air less dense, the dis- 
 tances between the isobaric surfaces are necessarily greater in 
 the interior than the exterior part, and so, however much the 
 isobaric surface at or near the earth's surface may be depressed 
 by the cyclonic gyrations there, at a considerable altitude, if 
 the temperature difference is great enough, it must become 
 convex instead of concave. 
 
 The track of any given particle of air in a cyclone, resulting 
 from the vertical and gyratory circulation, is that of a large 
 converging and ascending spiral in the lower part, but of a 
 diverging and ascending spiral in the upper strata of the at- 
 
COMPARISONS WITH OBSERVATIONS. 26 1 
 
 mosphere, and the nearer the earth's surface the more nearly 
 horizontal is the motion, since the vertical component gradu- 
 ally decreases and vanishes at the surface. 
 
 The whole energy of the system by which the inertia of the 
 .air and the frictional resistances are overcome and the motions 
 maintained, is in the greater interior temperature and the tem- 
 perature gradients, by which the circulation is maintained. 
 This being kept up, the deflections and gyrations are merely the 
 result of the modifying influence of the earth's rotation, which 
 is not a real force, since it does not give rise to kinetic energy, 
 ; but merely to changes of direction. 
 
 It must be borne in mind that the preceding is a represen- 
 tation of the motions and pressures of a cyclone resulting from 
 perfectly regular conditions, in an amosphere otherwise undis- 
 turbed, and having a uniform temperature, except so far as it 
 is affected by the temperature disturbance arising from the 
 cyclonic conditions. Accordingly results so regular are not to 
 be found in nature, but generally only rough approximations 
 to them. 
 
 Since the wind inclines less and less toward the centre of the 
 cyclone below the neutral plane and declines from the centre 
 above it, the upper currents above this plane in a cyclone are 
 always from a direction, in the northern hemisphere, a little 
 to the right of that of the lower currents, when not affected by 
 abnormal circumstances. 
 
 COMPARISONS WITH OBSERVATIONS. 
 
 179. All the phenomena, as deduced from theoretical con- 
 siderations, have been confirmed by observation. Areas of 
 low pressure with encircling winds, properly called cyclonic 
 depressions, are constantly occurring in nearly all parts of the 
 world, and their delineations on the charts of the different 
 Weather Bureaus are familiar to many persons. A remarkable 
 example of this kind has been recently given by Mr. Harding 3 
 of the storm which swept across the British Islands on Decem- 
 ber 8th and Qth, 1886, and which was one of the most violent dis- 
 
262 
 
 CYCLONES. 
 
 turbance swhich had occurred for many years. The following* 
 figure is a copy of his chart given for 6 P.M. of the 8th so far 
 as observations were available. From this it is seen that the 
 barometric depression in the centre is more than two inches,, 
 and that the gradients, especially on the southeasterly side, are 
 very steep, indicating very strong winds. The arrows indicate 
 that the motion of the air is cyclonic around the lowest press- 
 ure with an inclination toward the centre. 
 
 On the southeasterly side the difference of the barometer 
 was I inch in 240 miles, giving a gradient of about 7 mm. The 
 
 greatest observed velocities were 
 over 70 miles per hour, giving 
 a gyratory velocity a little less 
 of about 30 m. per second, and 
 these most probably correspond^ 
 ed very nearly with the preced- 
 ing gradient. A straight-lined 
 wind on the parallel of 50 with 
 a velocity of 30 meters per sec- 
 ond, by Table V, would give a 
 gradient G 0.1204 X 30 = 3.6 
 mm., and consequently would 
 not nearly give the observed 
 gradient of 7 mm. But if we 
 suppose the gyration had a ra- 
 dius of curvature of 400 kilome- 
 
 Fig. 2. 
 
 ters, then, as explained in 173, this gradient is increased from 
 this cause by a quantity which is to it in the ratio of 30/400000 
 to 2 n sin /= .00009, by Table V, and so by a quantity equal 
 3.0 mm. The gradient, therefore, with this radius of curva- 
 ture becomes 6.6 mm., very nearly equal to the observed gradi- 
 ent. But to this a small unknown addition has to be made for 
 the pressure gradient resulting directly from the temperature 
 gradient. 
 
 180. The inclination of the winds at the. earth's surface in a 
 cyclone was observed by Redfield in the great cyclones which 
 originate within the tropics and progress northward and north- 
 
COMPARISONS WITH OBSERVATIONS. 263 
 
 eastward to the higher latitudes, but no estimates were made 
 of the average angle of inclination. 
 
 Soon after this Dr. Buys Ballot gave his law, of more general 
 application, namely, that winds always blow, in the northern 
 hemisphere, with high barometer to the right and low barom- 
 eter to the left of the direction in which they blow, but that 
 this direction inclines a little toward the area of low barometer. 
 Mr. Ley was the first to determine the average angle of incli- 
 nation in large cyclones from a large number of observations 
 made in the British Islands and the adjacent parts of the con- 
 tinent. 39 His results were, i, that the winds commonly incline 
 from the districts of higher toward those of lower pressure ; 2, 
 that this inclination is much greater at inland than at well 
 exposed sea-stations. The collective mean result for 15 sta- 
 tions was an angle of inclination of 20 31'. The mean for five 
 of the well exposed sea-stations was 12 49', while for five of 
 the most inland stations it was 28 53'. This is in accordance 
 with the theory, by which the angle is increased by increase of 
 friction at the earth's surface. He also obtained a much larger 
 inclination on the east than on the west side of the cyclones. 
 
 Subsequently Mr. Ley determined the relation between the 
 direction of both the under and upper currents of the air in 
 areas of low pressure from a much larger number of observations 
 in the British Islands, France, Spain, Switzerland, Austria, 
 Turkey, Russia, Denmark, Sweden and Norway. 40 
 
 His table of results is so important, not only for our present 
 purpose, for which only those results belonging to the surface 
 are needed, but likewise in comparisons further on ( 205), that 
 we shall give it here in full, though in a different form and dif- 
 ferent notation. The following table and accompanying figure, 
 taken from the Meteorological Researches, Part II, Coast Sur- 
 vey Report for 1878, give his numerical results. Each area 
 of low pressure was divided into 16 districts as represented in 
 Fig- 3- Considering for the present the results only of the sur- 
 face winds, we find that the average angle with the radius for 
 the exterior districts, denoted by the large letters, is 64. 6, and 
 for the interior districts, denoted by the smaller letters, 65. 9. 
 
264 
 
 CYCLONES. 
 
 
 SURFACE WINDS. 
 
 UPPER CURRENTS. 
 
 Districts. 
 
 No. of observations. 
 
 Mean angle with 
 radius. 
 
 No. of observations. 
 
 Mean angle with 
 radius. 
 
 A 
 
 198 
 
 62 
 
 51 
 
 5 
 
 B 
 
 407 
 
 52 
 
 173 
 
 163 
 
 C 
 
 5" 
 
 48 
 
 226 
 
 152 
 
 D 
 
 675 
 
 54 
 
 290 
 
 146 
 
 E 
 
 803 
 
 66 
 
 328 
 
 124 
 
 F 
 
 378 
 
 76 
 
 199 
 
 IOI 
 
 G 
 
 277 
 
 79 
 
 81 
 
 96 
 
 1 H 
 
 196 
 
 80 
 
 43 
 
 99 
 
 a 
 
 195 
 
 65 
 
 58 
 
 172 
 
 ! b 
 
 39i f 
 
 53 
 
 104 
 
 130 
 
 c 
 
 426 
 
 58 
 
 94 
 
 135 
 
 d 
 
 454 
 
 55 
 
 141 
 
 1 02 
 
 e 
 
 629 
 
 64 
 
 135 
 
 73 
 
 f 
 
 402 
 
 74 
 
 142 
 
 5i 
 
 g 
 
 250 
 
 77 
 
 83 
 
 90 
 
 h 
 
 204 
 
 81 
 
 46 
 
 1 06 
 
 This gives an average inclination of about 25, a little greater 
 than before. But he now has mostly inland stations and only 
 
 Fig. 3. 
 
 few coast stations in comparison, and so this is also a confirma- 
 tion of theory. 
 
 From the Weather Maps ofthe United States Signal Service 
 for the years 1872 and 1873 Professor Loomis obtained an aver- 
 age inclination of nearly 47, which is much greater than that 
 obtained by Mr. Ley for Europe. These two results, however, 
 are not inconsistent with each other. The difference may be 
 in a small measure due to difference of latitude, since theory 
 
COMPARISONS WITH OBSERVATIONS. 26$ 
 
 Tequires greater inclinations for lower than for higher latitudes, 
 but it is no doubt due mostly to the fact that Loomis took in 
 all observations within isobars of 29.9 inches, and hence many 
 cases of only very small velocities, while Mr. Ley took in cases 
 mostly of the more violent winds nearer the centres of the cy- 
 clones. The winds from the outer border of the cyclone proper, 
 where the motion of the air is more toward the centre and has 
 not yet assumed much gyratory velocity, of course, have a 
 greater inclination than those nearer the centre, where the gy- 
 ratory velocity is greatest, and where, it has been shown, the 
 inclination must be less ( 175). 
 
 In subsequent researches with a greater number of observa- 
 tions and measurements taken from the Signal Service Weather 
 Maps, Loomis 41 deduced an average inclination a few degrees 
 less than that given above. From this discussion it resulted 
 that the inclinations at smaller distances from the centre are 
 less than at greater distances. This is, again, in accordance 
 with theory. The inclinations ranged from about 37 for an 
 average distance of 250 kilometers to 44 at the average dis- 
 tance of 1,200 kilometers. 
 
 The average inclination which he obtained at the same time 
 for low barometric pressures from Hoffmeyer's charts of the 
 northern part of the North Atlantic ocean is considerably less 
 than in the preceding case, as it should be in the case of a water 
 surface, where the friction is less. The inclination in this case 
 likewise increased with increase of distance from the centre, 
 being 2^.4. at the distance of 278 kilometers, and 34.8 at the 
 distance of 1535 kilometers. For barometric pressures above 
 760 mm. the inclinations were still larger. 
 
 The late J. Allen Brown from the observations of Makers- 
 town, Dublin and Greenwich, 1843-1848, obtained the following 
 results: 54 
 
 Jan. Feb. Mar. April May June July Aug. Sept. Oct. Nov. Dec. Year 
 6 = 257 293 267 260 22 262 274 287 284 267 240 255 269 
 = 247 280 239 260 o 240 249 264 243 245 226 257 249 
 
 60 = 20 13 28 O 22 22 25 23 41 22 14 2 2O 
 
 in which, reckoned from N. around by E , 
 
 6 = the direction of the isobars. 
 <p = the direction of the wind. 
 
266 CYCLONES. 
 
 The deviation, therefore, of the direction of the wind from that 
 of the isobar is 20 to the left on the average of the year. 
 
 The following contains the average directions of the cirri, 
 ^ (day only), and the average directions of the surface winds 
 0, made day and night: 
 
 Jan. Feb. Mar. April May June July Aug. Sept. Oct. Nov. Dec. Year 
 iff = 279 303 301 242 291 263 269 267 274 276 236 308 277 
 
 <p =241 287 244 274 24 233 230 247 244 237 211 249 243 
 
 ip(f>= 38 16 57 32 94 30 39 20 30 39 25 59 34 
 
 These results indicate that for the average of the year the- 
 upper currents come from a direction 34 to the right of the 
 surface winds, and that they come from the right in the case of 
 each separate month except two. Supposing the winds to be. 
 mostly cyclonic, this confirms the theoretical deduction of 178. 
 
 Mr. Brown also stated that M. Quetelet observed the direc- 
 tions of the cloud motions (without distinction of species) at the 
 Brussels observatory during the years 1833 to 1846, and found 
 the resultant direction by Lambert's formula to be for the 14. 
 years tp = 257 50'. Also that by noting the difference of di- 
 rections of surface currents and different kinds of clouds, he ob- 
 tained from the averages of large numbers of observations, 
 
 Cirrus current Surface currents, orif)0=2g.6 
 
 Cirro-stratus current " =22 .8 
 
 Cumulus current =14 .5 
 
 This is likewise a confirmation of the deduction that high cur- 
 rents come from a direction to the right of the lower currents 
 and the higher the more so. 
 
 The observations of Padre Viftes 42 on the hurricanes of the 
 Antilles also show that there is an inclination of the winds to- 
 ward the centre, and that this is least nearest the centre. In all 
 these hurricanes it was observed that " the gyrating winds cease 
 to be circular at a long distance from the vortex, and are found 
 to deviate from the tangent to the circle with an inclination to- 
 ward the centre, forming a kind of large converging spiral." 
 This converging is likewise said to " vary, not only in different 
 hurricanes, but likewise in the same hurricane with different di- 
 rections and intensities of the wind, and with different distances. 
 
COMPARISONS WITH OBSERVATIONS. 26? 
 
 from the vortex." In the same connection it is also stated that 
 it is " especially small at no great distance from the vortex." 
 
 In more recent researches Hilderbrandsson 43 has deduced 
 from observations at Upsala, including those for both high and 
 low pressures, an average inclination of 40. 2, and for the aver- 
 age of the three maritime stations Waderobed, Utklippau, and 
 Landou, 32. 2. He likewise obtained for these three stations,, 
 as Ley did for the British Isles, 39 Hoffmeyer in Denmark, 44 
 and Spindler in Russia, 45 a larger angle of inclination on the- 
 east than on the west side of the cyclone. This angle also in- 
 creased with increase of distance from the centre, though the 
 differences near the centre were very small. 
 
 The following is the summary of the practical results ob- 
 tained by Captain Toynbee from a discussion of the observa- 
 tions of the North Atlantic Ocean during the great cyclone of 
 the 24th and 2$th of August, 1873 : 
 
 1. There is strong evidence that the wind in a hurricane 
 draws in towards its centre. 
 
 2. The indraught is probably greater in one quarter than 
 another. 
 
 3. The indraught is probably greater near the centre than- 
 farther from it. 
 
 The average inclination from all the observations was 29, 
 the average latitude being about the parallel of 50. 
 
 Piddington gives as an effect, and also a proof, of the in- 
 clination of the winds toward the centre, that ships are often 
 surrounded or have their decks covered, during the passage of 
 the calm centre of cyclones in the neighborhood of land, with 
 land and aquatic birds, butterflies, horseflies, etc. He says : 
 
 " They must be carried inwards by the incurving of the winds, and at 
 the centre are kept there because they cannot fly out of it, and when the 
 ship reaches it of course they make a last effort to reach her as a resting, 
 place." 
 
 181. From the deductions of theory confirmed and supple- 
 mented by numerous observations, it is evident that many of 
 the usual rules and sailing directions must be very much modi- 
 
:268 CYCLONES. 
 
 fied, especially in low latitudes. Although the horn-cards of 
 Piddington, and all rules based upon the strictly circular the- 
 ory of the winds, may be still used at sea in high latitudes 
 without great error, yet nearer the equator they must become 
 more erroneous, and almost entirely fail very near the equator. 
 It is beginning to be pretty generally acknowledged that in 
 sailing directions in a storm, some allowance should be made 
 for a certain small amount of inclining of the winds toward the 
 centre, but it seems to be thought that this should be the same 
 .at all latitudes and at all distances from the centre of the 
 storm. If in low latitudes the inclination of the winds accord- 
 ing to theory may be 60 or more, the usual rules for the deter- 
 mination of the direction of the dangerous centre of the storm 
 based upon the circular theory would lead to an error of five 
 or six points of the compass. Not only latitude, but distance 
 from the centre also, should be taken into account. While 
 the centre of a cyclone is yet at a considerable distance and 
 the winds have not yet a great gyratory velocity, they may, 
 even in high latitudes, have a considerable inclination toward 
 the centre, and nearer the equator they may be nearly radial; 
 but even in these latitudes, at places near the centre, where 
 the velocities are very great, the gyrations may become nearly 
 circular. 
 
 The preceding is confirmed by rules recently laid down by 
 Dr. Doberck from observations made in the China Sea and in 
 the Philippine Islands. He says: 49 
 
 " The whereabouts of the centre of a typhoon may, in the China Sea, 
 be ascertained by the rule : Stand with your back to the wind, and you 
 will have the centre on your left side, but between 2 and 4 points 
 in front of your left hand. There are, however, certain exceptions to 
 this rule. Thus there often blows a steady easterly gale along the 
 southern coast of China when a typhoon is crossing the China Sea, and 
 the gale blows often steady from northeast about the northern entrance 
 to the Formosa Straits when there is a typhoon in a more southern lati- 
 tude." 
 
 Again he says : " 
 
 " Further researches have shown that in the Philippine Islands and 
 .-along the Coast of China as far north as 24 latitude, when you stand 
 
COMPARISONS WITH OBSERVATIONS. 269 
 
 with your back to the wind in a typhoon, you will probably have the 
 centre nearly 4 points in front of your left hand ; but on the open sea far 
 from any shore you will generally have it about 3 points in front of your 
 left hand when your ship is in front of the centre of the typhoon, and 
 more than 3 points in front of your left hand behind the centre. Above 
 25 latitude the angle will probably be found to be between 2 and 3 
 points. It appears to be smaller the greater the distance from the near- 
 est shore and the greater the latitude. At some distance behind the 
 centre the wind blows generally straight towards it. 
 
 182. With regard to the ring of high pressure with its max- 
 imum corresponding to the heavy circle in Fig. I, there are 
 many observations which indicate that it really exists, and is; 
 sensible to observation in all well-developed cyclones. This 
 is not shown so clearly from observations made at the same 
 time over different parts of the cyclonic area, and presented in 
 synoptic charts, as from observations made at different times 
 at the same place while the whole system of motions and 
 pressures pass over ; though in the former case it is generally 
 observed that around an area of low pressure the barometer 
 stands a little higher than the general average. Before all 
 great storms it is frequently observed that the barometer- 
 stands unusually high, and the same soon after it has passed. 
 This was first noticed and remarked upon by Redfield. These 
 are the times when the ring of high pressure around the cy- 
 clone in its progressive motion passes over the place of obser- 
 vation. At Havana, Cuba, over which the tropical cyclones of 
 great violence frequently pass, the zone of high pressure is dis- 
 tinctly observed, both before and after the passage of the cen- 
 tral part of low pressure and great violence ; and the abnor- 
 mally high pressure which precedes is usually regarded as an 
 indication of the approach of a cyclone. The approach of the 
 hurricane of September, 1875, was indicated at Havana by a 
 sudden rise of the barometer while the cyclone was yet at the 
 Windward Islands, about 1200 miles distant. 48 Also, on the 
 1 3th of September, 1876, there was a great rise of the barome- 
 ter at Havana while a cyclone was causing great destruction 
 on the Island of Porto Rico. 42 
 
 Espy remarks, in his Fourth Meteorological Report, that 
 
-2/0 ;, CYCLONES. 
 
 41 A sudden rise of the barometer, especially in low latitudes, is 
 a proof that there is a storm in the neighborhood, and is one 
 of the first indications of an approaching storm." On the 1st 
 of September, 1845, at Fort Brooke, Florida, at the very time 
 there was a most violent hurricane approaching, and was 
 within 4 or 5 of the place, the barometer arose there that 
 morning 0.15 in., though it had been nearly stationary for 
 more than a month before. A great storm of rain reached 
 there that day ; and then in the afternoon the barometer fell 
 0.3 in. Espy considered it a fact fully established that without 
 .such a rise no storm of dangerous violence need be feared, but 
 that the converse of it was not true. The barometer rises where 
 the violent part of the storm passes by one side or the other. 
 
 We also have evidence of this ring of high barometer from 
 ^observations in the southern hemisphere. The gale observed 
 at Kerguelen by the exploring party of the Challenger " were 
 preceded by an unusually high barometer, which fell rapidly as 
 the storm began from the north ; as the wind shifted to the 
 west the barometer rose." 
 
 183. The observations of the upper currents of the air are 
 -more vague and uncertain. But even here the results of the 
 observations confirm the motions given in the preceding figure 
 for the upper strata of the atmosphere. From 620 observa- 
 tions of the motions of cirrus clouds, Mr. Ley 46 arrived at the 
 following general law showing the relation between the direc- 
 tion of the higher currents of the atmosphere and the distribu- 
 tion of pressure at the earth's surface : The higher currents of 
 the atmosphere, while moving commonly with the highest pressures, 
 in a general way, on the right of their course, yet manifest a dis- 
 tinct centrifugal tendency over the areas of low pressure, and a 
 centripetal over those of high. 
 
 This " centrifugal tendency over the areas of low pressure" 
 is represented by the dotted arrows within the dotted circle of 
 Fig. I, these observations having been made on the motions of 
 cirrus clouds which are always at high altitudes, where the 
 radial component of motion is outward, but yet generally not 
 so high that the gyrations are anti-cyclonic. 
 
COMPARISONS WITH OBSERVATIONS. 
 
 This keen observer of air currents and cloud motions, and 
 generally riot seeking a confirmation of any theoretical law, 
 has likewise observed air currents which corroborate in a re- 
 markable manner the counter-motions of the air at the earth's 
 surface and at high altitudes, as delineated in Fig. I between 
 -the heavy solid and dotted circles. He says : 
 
 " There occur at rare intervals in Western Europe depression systems, 
 which affect, but in a very singular way, the directions of the upper-cur- 
 :rents, reversing them so that they become, on all sides of the area, 
 nearly or quite in opposition to Ballot's law ; that is to say, there exists 
 -a direct (anti-cyclonic) upper current circulation above a retrograde 
 (cyclonic) circulation of the surface winds." 
 
 It is seen from the figure that within a certain belt the cur- 
 rents below and above are reversed. But this is only when 
 the upper currents are at very high altitudes, above the average 
 height of the cirrus clouds. This reversion of the currents is 
 therefore said to occur at only rare intervals ; that is, when the 
 cirrus clouds observed are unusually high. 
 
 The following figure, given by Hildebrandsson, represents 
 
 . Jfin. 
 
 Fig. 4. 
 
 the results of his observations of the cirrus clouds at Upsala 
 on the average for the year. The left-hand figure represents 
 the observations for barometric pressures less than 760 mm. 
 and corresponds with the interior part of Fig. I. The exterior 
 part, those of barometric pressures greater than 760 mm., and 
 corresponds with the exterior part of Fig. I beyond the isobar 
 of 760 mm. It is seen that the arrows incline out from low 
 toward high barometer, as in Fig. I ; but in no case do they 
 
2/2 CYCLONES. 
 
 indicate completely anti-cyclonic gyrations, as in Mr. Ley's rare 
 cases, the average altitude of the observations not being great 
 enough for that. 
 
 From an examination of 121 cases of high winds on Mount 
 Washington, by classifying them with reference to the direc- 
 tion of lowest pressure, Professor Loomis deduced the follow- 
 ing conclusions : 
 
 " i. High winds on Mount Washington circulate about a low centre 
 as they do near the level of the sea. 2. The motion of the winds is 
 nearly at right angles to the direction of low centre. 3. The low centre 
 at the height of Mount Washington lies behind the low centre at the sur- 
 face of the earth as much as 200 miles." 
 
 At the height only of Mount Washington we would expect 
 to find the winds blowing with reference to the centre of the 
 cyclone very nearly as at sea-level, since it is far below the 
 neutral plane where the radial component of motion is out- 
 ward from the centre, and especially lower than the altitude at 
 which the gyrations become anti-cyclonic. But as the motions 
 at the neutral plane become circular we would expect them to 
 deviate but little from a circular motion at the top of Mount 
 Washington, and so be nearly at right angles to the direction 
 of the low centre. The third deduction of Professor Loomis 
 is explained by the circumstance that the temperature of the 
 air is not symmetrical on all sides of the cyclone and is colder 
 on the west than the east side of the centre, as represented in 
 191, Fig. 5. Taking two points on each side in the line of 
 progressive motion of the centre where the pressures on the 
 earth's surface are equal, as we ascend on the colder side the 
 pressure decreases faster than on the east side on account of 
 the greater density of the air, and so after arriving at a given 
 altitude the pressure on the rear side is less than on the front 
 side. This throws the point of lowest pressure on the level 
 above a little behind that on the earth's surface. On the latter 
 the low centre is perhaps near the medium point between points 
 of equal pressure ; but above, it is near the medium point be- 
 tween equal pressures there, and so behind the middle point 
 or point of lowest pressure below. 
 
GRADUAL ENLARGEMENT OF CYCLONES. 2/3 
 
 GRADUAL ENLARGEMENT OF CYCLONES. 
 
 184. In the preceding consideration of cyclones it has been 
 supposed that the whole system of circulation has a definite 
 limit, and comprises at all times the same air, which, by means 
 of the vertical circulation, is being continually interchanged 
 between the interior and exterior parts within this limit. This, 
 however, is far from being the case in nature. As long as the 
 vertical circulation is maintained with increasing or at least 
 sufficient energy, the tendency of the cyclone is to extend 
 farther and farther from the centre, and so to continually ex- 
 tend the gyrations and the whole system of circulation over a 
 greater area. But unless the energy which sustains it increases, 
 likewise, it must reach a limit, for otherwise the temperature 
 gradient and the forces upon which the vertical circulation 
 depends become barely sufficient to overcome the frictional 
 resistances, when further enlargement must cease ; and then, 
 as the energy begins to fail, either through a diminution of the 
 supply of aqueous vapor or a change in the relative temper- 
 atures of the lower and upper strata by means of the inter- 
 change of air in the vertical circulation, the whole system of 
 circulation must gradually become w r eaker and finally entirely 
 subside. 
 
 It may be that cyclones mostly commence over a small 
 area and gradually enlarge, but this is not necessarily so. If the 
 atmosphere is in an unstable state, and the temperature con~ 
 ditions ( 156) are such that the initial upward motion takes, 
 place over a large area at once, then the vertical and gyratory 
 circulations begin at once over a large area and gradually grow 
 in strength until the frictional resistance from increase of veloc- 
 ity becomes equal to the force, when further increase in vio- 
 lence, as well as extent of limits, must cease. There is there- 
 fore a certain limit to the extent and violence of a 'cyclone 
 somewhat proportional to the amount of energy ; and if the 
 initial temperature conditions are such as to start it over a. 
 
274 CYCLONES. 
 
 small area only, it gradually increases in both extent and 
 violence until this limit is reached. 
 
 As the area is gradually enlarged and air from greater dis- 
 tances is brought in, there must be such an adjustment between 
 the cyclonic and anti-cyclonic gyrations as to satisfy the prin- 
 ciple of 171, and so the extent of both must increase together, 
 and also that of the ring of highest barometer. 
 
 The observed dimensions of the violent part of cyclones 
 are very different, especially in different latitudes. In the 
 Indian Ocean, and especially in the Bay of Bengal, and also in 
 the China Sea, they are said to be comparatively small, rang- 
 ing from 50 to 250 miles in diameter. According to Redfield 
 the cyclones in the lower latitudes of the western part of the 
 Atlantic Ocean are of about the same dimensions. 
 
 Piddington says : 54 
 
 " In the West Indies the researches of Mr. Redfield and Col. Reid 
 seem to show that though while approaching to, or within, the Islands 
 they are sometimes as small as 100 or 150 miles in diameter, they may, 
 and it would seem most frequently do, after reaching the Atlantic Ocean, 
 dilate considerably, and then often attain to 600 or even 1000 miles in 
 diameter, the wind blowing an excessively severe gale over all this area, 
 and toward its centre becoming of true hurricane violence, and the 
 whole vortex, so whirling, travels over thousands of miles of track." 
 
 He further says : 
 
 "The typhoons (cyclones) of the China Sea appear to vary from 60 
 or 80 miles to three or four degrees in diameter." 
 
 In the middle and higher latitudes, however, they are gen- 
 erally from 1000 to 1500 miles, and often much more, in 
 diameter. As a rule the diameters are much greater in the 
 higher than in the lower latitudes. But tropical cyclones are 
 observed at sea and those of high latitudes mostly on land, 
 and those observed at sea have perhaps mostly originated on 
 the continents, and the difference may lie in the places of 
 origin, those originating at sea being generally smaller. 
 
PROGRESSIVE MOTIONS OF CYCLONES. 2?$ 
 
 PROGRESSIVE MOTIONS OF CYCLONES. 
 
 185. Ordinary cyclones are never stationary, and the di- 
 rections in which their centres move and their velocities vary 
 not only in different latitudes and regions of the globe, but in 
 the same places at different times. In general their tendency 
 in lower latitudes is westerly, and in the middle and higher 
 latitudes easterly. There are several circumstances which con- 
 trol, to a greater or less extent, the progressive motions of 
 cyclones. The principal one of these is undoubtedly the gen- 
 eral motion of the atmosphere in which they exist, not at and 
 near the earth's surface merely, but at high altitudes where the 
 centre of energy is. This carries them along as a stream of water 
 carries along the small whirling eddies which are formed in it. 
 This idea was first suggested by the writer more than a quarter 
 of a century ago. 47 Tropical cyclones move westward, or at least 
 have a large west component, because the general motion of 
 the atmosphere there, up to a considerable altitude, is westerly, 
 while in the higher latitudes cyclones move in an easterly 
 direction with much greater velocities, because there the gen- 
 eral motion at all altitudes is easterly, and the velocity, espe- 
 cially at high altitudes, is comparatively great. The average 
 direction for the United States, as determined by Loomis 
 from an examination of the individual directions laid down on 
 the Weather Maps of the Signal Service for three years, com- 
 prising 485 cases, is N. 81 E., with an average velocity of 26 
 miles per hour. The monthly averages indicate an annual 
 inequality. For April to September, inclusive, it is N. 82.5 E. 
 23 miles, and for October to March, inclusive, N. 78. 5 E. 29 
 miles per hour. Hence the direction is more nearly toward the 
 east and the velocity greater in winter than in summer. 
 
 The rate of progress of cyclone centres over the North At- 
 lantic Ocean and over Europe seems to be much less, and the 
 annual inequality proportionally less. As the results of later 
 and more extended researches Loomis 17 gives, in miles per 
 hour, the following monthly rates of progressive motion of 
 -cyclone centres : 
 
2 7 6 
 
 CYCLONES. 
 
 Month. 
 
 United States. 
 
 Atlantic Ocean, 
 Middle Latitudes. 
 
 Europe. 
 
 
 33.8 
 
 17.4 
 
 17 A 
 
 
 34. 2 
 
 iq. i) 
 
 18 o 
 
 March . 
 
 31 c 
 
 IO.7 
 
 17 Z 
 
 
 27. 5 
 
 19.4 
 
 16 2 
 
 
 25 . 5 
 
 16.6 
 
 I/i 7 
 
 June . 
 
 24 A 
 
 17. K 
 
 I-- g 
 
 Tulv . 
 
 24.6 
 
 15.8 
 
 I A 2 
 
 August 
 
 22 6 
 
 16 } 
 
 
 September 
 
 24 7 
 
 17.2 
 
 17 ^ 
 
 
 27.6 
 
 18.7 
 
 IQ O 
 
 November . 
 
 2Q Q 
 
 20. o 
 
 18 6 
 
 December . . 
 
 33 A 
 
 18.3 
 
 17 Q 
 
 
 
 
 1 / y 
 
 Year 
 
 28.4 
 
 18.0 
 
 16.7 
 
 The values for the United States are the averages of 13 
 years, 1872-1884. Those for the Atlantic Ocean were obtained 
 from the monthly storm tracks published with the Interna- 
 tional Bulletin for a period of four years, 1879-1882. Those of 
 Europe, from the monthly charts of storm tracks published by 
 the Deutsche Seevvarte for five years, 1876-1880. The average 
 in the United States for the 6 winter months is 31.7 miles, 
 while for the summer it is 24.9 miles, the ratio being very 
 nearly as obtained above from the three years. 
 
 If the general motions of the atmosphere have a controlling 
 influence upon the progressive motions of cyclones, then we 
 would expect that these motions would not be only westerly in 
 lower latitudes and easterly in the higher latitudes, but also if 
 there is an annual inequality in the one there must also be 
 such in the other. According to the table of 98 the easterly 
 velocity in the middle latitudes is more than twice as great in 
 January as in July; but the averages for the winter half and 
 the summer half of the year would be nearly as 29 to 23 re- 
 spectively, the same as the ratio between the winter and sum- 
 mer velocities of the progressive motions of cyclones given 
 above. This velocity, however, is much greater than that of 
 the easterly motion of the atmosphere in the lower strata, even 
 up to & considerable altitude. But the energy of the cyclone, 
 as may be seen from 159, is mostly above, where the conden- 
 
PROGRESSIVE MOTIONS OF CYCLONES. 2// 
 
 Cation of the aqueous vapor occurs, and where the air temper- 
 ature in the cyclone differs most from that of the surrounding 
 atmosphere ; and so the progressive motion is controlled mostly 
 by that of the general motion of the atmosphere up at that 
 altitude. From the table of 98 it is seen that at the altitude 
 of 2.5 miles in the United States the east component of the 
 general motion is about 26 miles, the same as the easterly 
 velocity of the cyclones. 
 
 In the tropical latitudes, where by the table of 98 the 
 velocity of the west component of motion of the atmosphere 
 vanishes at no great altitude, especially in the winter season, 
 the westerly velocity of the progressive motion is comparatively 
 small, and must be controlled mostly by the lower part of the 
 -atmosphere. It is remarkable that this westerly progression 
 of tropical cyclones occurs almost exclusively at a season when 
 the westerly velocity of the atmosphere extends the highest up. 
 
 186. There seems to be a general tendency in cyclones 
 which originate in the lower latitudes to move toward the 
 poles, but observations are wanting to show that this is the case 
 everwhere without exceptions. Such a tendency may arise 
 from the deflecting force due to the earth's rotation being 
 greater for equal gyratory velocities on the polar than on the 
 equatorial sides of cyclones, this force being as the sine of the 
 latitude. Hence the tendency of the gyrating air on the polar 
 side to move toward the pole is greater than that of the air on 
 the equatorial side to move toward the equator, and so the 
 difference between these unbalanced counter forces tends to 
 draw the whole system toward the pole, since the condensation 
 of aqueous vapor and centre of energy are in the cyclonic part, 
 and so the whole system of gyration must follow it. It is evi- 
 dent that such a tendency must, for cyclones of the same ex- 
 tent, be greatest near the equator, where the sines of the lati- 
 tudes on the two sides differ most, and be comparatively small 
 in high latitudes, where the difference between the sines, even 
 for large differences of latitude, is small. 
 
 But the directions and velocities of progressive motion are 
 also much influenced by the irregularities and deflections of 
 
2/8 CYCLONES. 
 
 the general motions of the atmosphere, caused by the conti- 
 nents and mountain ranges, as explained in 123 and follow- 
 ing ones. Hence on the east coasts of the United States, of 
 China, and of South Africa, where mostly tropical cyclones 
 pass up into the higher latitudes, they simply drift in the 
 prevailing current, but are probably somewhat aided by the in- 
 fluence referred to above. On the eastern sides of the conti- 
 nents near the tropics, where the deflections and the general! 
 currents are mostly toward the equator, as west of Northwest 
 Africa and of Mexico, there is no well authenticated account 
 of cyclones having passed from lower to higher latitudes. We 
 have, however, a reliable account of a very violent and destruc- 
 tive cyclone passing in a direction from the equator toward the 
 pole in the Fiji Islands with a velocity of about ten miles per 
 hour, where there is no known cause for a general current of the 
 atmosphere toward the pole. 48 This occurred on the 3d and 4th 
 of March, 1886. Its track was traced not quite to the parallel 
 of 20 S., but here it seemed to be inclining around toward the 
 east, as if already feeling the influence of the easterly cur- 
 rents of more southerly latitudes. This cyclone was a charac- 
 teristic one of these latitudes, of small diameter, about 300 
 miles, minimum pressure of 27.63 in., and of extraordinarily 
 steep gradients, estimated at one inch of mercury in a distance 
 of 63 miles. 
 
 187. From the combined action of the two preceding prin- 
 ciples, namely, that cyclones have a tendency to move with 
 the general atmospheric current in which they exist, and that 
 they at the same time tend to move toward the poles, all cy- 
 clones which originate near the equator must first move in a 
 westerly direction and also toward the pole, after arriving at the 
 parallel of about 30, which is the dividing line between the 
 westerly and easterly motions of the strata which mostly con- 
 trol the progressive motion of the cyclone, the tendency must 
 be toward the pole only, but after arriving in still higher lat- 
 itudes, where the general motion of the atmosphere is easterly,. 
 the resultant motion must be northeasterly, and finally after 
 reaching still a higher latitude, where the polar tendency is. 
 
PROGRESSIVE MOTIONS OF CYCLONES. 279 
 
 small, it must -be still more toward the east, unless affected by 
 some of the other controlling influences. Hence the path of 
 such a cyclone is somewhat of the form of a parabola, with its 
 vertex at or near the tropical calm-belt, except that the equa- 
 torial branch of the parabola continues more on the same par- 
 allels of latitude than the polar branch. 
 
 Many cyclones of this sort originate during the latter part of 
 summer and the fall in the North Atlantic Ocean, apparently 
 near the equatorial limits of the trade-winds, which at first are 
 comparatively small ; but they seem to have great power of 
 continuance, for they usually run through the whole course of 
 their parabolic orbit, gradually expanding as they go, until, 
 after reaching high latitudes in the northern part of the Atlan- 
 tic, they have the usual dimensions of cyclones of these lati- 
 tudes. Being carried at first in a nearly west direction by the 
 westerly motion of the atmosphere in the trade-wind zone, un- 
 til they arrive in the neighborhood of the West India Islands 
 and the Gulf of Mexico, they then curve around toward the 
 north over the United States, or along the east coast and the 
 Gulf Stream, up into higher latitudes, aided here in their polar 
 movement, no doubt, by the deflected current referred to in 
 123. Here their progressive motions are controlled mostly by 
 the strong easterly tendency of the atmosphere in these lati- 
 tudes, and so their directions become more toward the east, 
 the same as those of cyclones having their origins in the higher 
 latitudes. 
 
 The rate of westerly progress of these cyclones is compara- 
 tively small while near the equator, and it becomes still smaller 
 while they are curving around into the higher latitudes ; but 
 after arriving into the middle and higher latitudes, where their 
 general direction is a little, north of east, they have the usual 
 velocities of progression of cyclones generally of these latitudes. 
 According to Loomis 17 the average direction and velocity of 
 forty of these cyclones while moving westerly was respectively 
 26 north of west and 17.4 miles per hour. In only two cases 
 was the direction south of west. Of course the farther west, 
 the more the directions inclined away from the equator. The 
 
280 CYCLONES. 
 
 average direction of these storms while moving eastwardly to 
 the parallel of 40 was E. 38. 5 N., and the hourly velocity in 
 this part of their course was 20.5 miles. In the first part of 
 this, however, the course was more northerly and gradually 
 changed around to a course only a little north of east. 
 
 The steady current of the northeast trade-winds is not fa- 
 vorable to the origination of cyclones, and therefore they seem 
 to originate at the northern limit of the calm-belt only, or at 
 least not so far within that the deflecting force depending upon 
 the earth's rotation is too small to produce gyrations ; for, we 
 have seen, this force becomes very small near and vanishes at 
 the equator. Hence, of the forty paths of cyclone centres ex- 
 amined by Loomis, no part of any one of them was found within 
 10 of the equator. If the conditions of a vertical circulation 
 were found at the equator, they would not give rise to any cy- 
 clone, and there would be little violence and no sensible baro- 
 metric depression in the centre. In all seasons of the year ex- 
 cept during the latter part of summer and the fall, the trade- 
 winds blow down to a latitude where the deflecting force of 
 the earth's rotation is too weak to give rise to cyclones, and as 
 they cannot originate within the zone of these winds, they can 
 generally originate at the time only in which these winds do 
 not extend down very near the equator. 
 
 188. The east coast of China, and the adjacent oceans, in- 
 cluding Japan, is also traversed by numerous cyclones of this 
 sort, originating in the same manner and mostly at the same 
 season of the year. These likewise curve around in a kind of 
 parabolic path with its vertex near the parallel of 30, until 
 they arrive in the higher latitudes and assume a direction nearly 
 east across the North Pacific Ocean. The rate of progress is 
 probably about the same as in the case of the tropical cyclones 
 of the North Atlantic Ocean and the United States. 
 
 In the Arabian Sea and Bay of Bengal there are similar 
 small cyclones originating near the equator, which first move 
 only a little north of west, and then gradually curve around 
 toward the north and are lost within the continent. But these 
 seem to be interfered with by the great Asiatic monsoon, so 
 
PROGRESSIVE MOTIONS OF CYCLONES. 28 1 
 
 that they originate mostly spring and fall at the times of the 
 changes of the monsoon, when there is a month or more of 
 comparatively calm weather. Consequently there is a tendency 
 toward two maxima in the monthly numbers of cyclone fre- 
 quency, as is seen in the following table. The average wester- 
 ly velocity of these cyclones, as obtained by Loomis 17 , is only 
 8.5 miles per hour. 
 
 On the eastern coast of Africa and the adjacent ocean, 
 including Madagascar, cyclones originating in the Indian Ocean 
 near the southern limit of the equatorial calm-belt, when 
 it has its most southern position in midwinter of the northern 
 hemisphere, being then forced down to the parallel of about 12 
 S. ( 142), pass around into middle latitudes of the southern 
 hemisphere, where their directions become more nearly east, 
 being controlled there by the strong general easterly currents 
 of the atmosphere in these latitudes. The forms of their paths 
 are very similar to those of the North Atlantic and North Pa- 
 cific Oceans, but their motions in them are comparatively very 
 slow, usually only 3 or 4 miles per hour. These being in the 
 opposite hemisphere, the time most favorable for their origina- 
 tion, and consequently the time of greatest frequency, is in 
 February intead of August. 
 
 The relative frequency of the occurrence of all the tropical 
 cyclones in the several months of the year may be seen in the 
 table on page 282. 
 
 In the South Atlantic Ocean the southeast trade-winds 
 often extend considerably beyond the equator, and at any sea- 
 son too near the equator for cyclones of this class to originate. 
 Hence on the east side of South America and on the adjacent 
 ocean there do not seem to be any cyclones which move around 
 in a parabolic orbit into the higher latitudes of the southern 
 hemisphere. 
 
 1 89. Although cyclones are carried along by the general 
 drift of the atmosphere, yet as the velocity of this is very dif- 
 ferent at different altitudes, varying circumstances of the 
 cyclone may cause great variations in the progressive velocity, 
 while that of the general drift remains the same. According 
 
282 CYCLONES. 
 
 THE YEARLY PERIODS OF CYCLONE FREQUENCY IN SEVERAL SEAS. 49 
 
 
 Arabian Sea. 
 
 Bay of Ben- 
 gal. 
 
 S. Indian 
 Ocean. 
 
 Java Sea. 
 
 China Sea. 
 
 Havana. 
 
 No. of years. 
 No. of cyclones. 
 
 Authority. 
 
 234 
 70 
 
 Chambers. 
 
 i39 
 "5 
 
 Blanfond. 
 
 40 
 53 
 
 Piddington, 
 Thorn and 
 Reid. 
 
 12 
 
 Piddington 
 and Thorn. 
 
 85 
 214 
 
 Schuck. 
 
 363 
 355 
 
 Poey. 
 
 Tan.., 
 
 6 
 
 2 
 
 17 
 
 2C 
 
 2 
 
 j 
 
 Feb 
 
 
 o 
 
 2C 
 
 42 
 
 o 
 
 2 
 
 Mar 
 
 
 2 
 
 IQ 
 
 8 
 
 2 
 
 
 April 
 
 iq 
 
 8 
 
 je 
 
 8 
 
 2 
 
 
 May.. 
 
 18 
 
 16 
 
 7 
 
 o 
 
 e 
 
 I 
 
 June . . 
 
 20 
 
 
 o 
 
 o 
 
 5" 
 
 
 July . 
 
 -i 
 
 
 o 
 
 o 
 
 IO 
 
 12 
 
 \ y 
 
 7 
 
 4" 
 
 o 
 
 o 
 
 IQ 
 
 27 
 
 Sept . . 
 
 
 
 2 
 
 o 
 
 27 
 
 2-3 
 
 Oct 
 
 6 
 
 27 
 
 2 
 
 o 
 
 16 
 
 1 7 
 
 Nov 
 
 14. 
 
 16 
 
 7 
 
 o 
 
 8 
 
 5' 
 
 Dec 
 
 
 8 
 
 6 
 
 17 
 
 
 2 
 
 
 
 
 
 
 
 
 as the central controlling power of the cyclone is at greater or 
 less altitudes must the progressive velocity be greater or less,, 
 so far as it depends upon the mere drift of atmosphere ; and 
 these variations depend very much upon the hygrometric state,, 
 as well as the unstability, of the atmosphere, as may be seen 
 from the table of 159. Taking the first example in which 
 the vertical temperature gradient is represented by the column 
 A, it is seen by comparing the column C in the case of sat- 
 uration with that of A, and then that of C ' in the case of r d 
 = 4, that the weight of the differences, and consequently the 
 power of the cyclone, is much lower in the former case than in 
 the latter. The more nearly, therefore, the air is saturated, 
 other circumstances remaining the same, the lower down is the 
 controlling power, and consequently the less must be the pro- 
 gressive easterly velocity of cyclones in the middle latitudes. 
 
 The annual inequalities in the velocities of the progressive 
 motions of cyclones, we have seen, is less than that of the 
 general easterly velocities of the wind ; and this may be caused 
 by the atmosphere's being more nearly saturated in winter 
 than in summer. It may also be the cause of the greater 
 velocity of progressive motion over the United States at ali ; 
 
PROGRESSIVE MOTIONS OF CYCLONES. 28$ 
 
 seasons than over the Atlantic Ocean and Europe, since the 
 climate of the United States is continental, and consequently 
 drier, than that of the Atlantic Ocean and of Europe, which, 
 for reasons given in 122, has somewhat of an oceanic climate. 
 Over the United States, therefore, the vapor has to ascend a 
 little higher generally before condensation takes place, and so 
 the seat of controlling energy is higher, and the progressive 
 velocities of cyclones greater, than on the Atlantic Ocean and 
 in Europe. 
 
 But the more unstable the state of the atmosphere is, the 
 higher is the central controlling power, as may be seen from 
 the same table of 1 59 ; and so the rate of progression also de- 
 pends upon this circumstance, and consequently it causes vari- 
 ations at different seasons and places. 
 
 190. As the energy of the cyclone is mostly in the aqueous 
 vapor condensed, and without this we rarely have the condi- 
 tions of more than an initial cyclonic action, the velocity and di- 
 rection of the progressive motion of a cyclone depends, to some 
 extent at least, upon the distribution of this vapor in the region 
 in which the cyclone exists : for the cyclone is likely to be 
 drawn somewhat in the direction in which there is the most 
 vapor, and to pass around those regions in which there is little 
 vapor. It is for this reason, perhaps, that the chain of lakes 
 between Canada and the United States seems to be a great 
 highway for cyclones. It is also very often observed that cy- 
 clones in the interior of the United States, especially in winter, 
 instead of pursuing their usual easterly direction, strike directly 
 across in a southeasterly direction to the Atlantic coast where 
 the air is warmer and the aqueous vapor more abundant, beingf 
 drawn in the direction from which they receive the most sus- 
 tenance, and then proceed along the coast toward Newfound- 
 land. In the winter season, also, cyclones which make their 
 first appearance on the Pacific coast of the United States, if 
 not too far north, instead of passing through the cold and dry 
 interior of the continent, follow the coast down into Lower 
 California and Mexico, and, crossing over into Texas and the 
 gulf region, then make their way up along the eastern coast of 
 
-284 CYCLONES. 
 
 the United States, as is usual with all tropical cyclones of that 
 region coming from the direction of the West India Islands, 
 thus seeming to skirt entirely around the interior of the con- 
 tinent on the warmer and moister side of the continent, be- 
 cause here more aqueous vapor is found for their support. 
 
 We have seen that there are two dry belts extending en- 
 tirely around the globe ( 120), except so far as they are broken 
 up by monsoons and the deflected atmospheric currents of 
 continents and mountain ranges ( 124, 125). It is doubtful 
 whether the polar tendency of tropical cyclones is in general 
 strong enough to carry them through the trade-wind zones 
 against the trade-winds, and whether the amount of vapor in 
 the dry belts is sufficient to sustain them in their passage through 
 them into higher latitudes, except on the eastern sides of the 
 continents, where the deflected atmospheric currents counter- 
 act and change the directions of the trade winds and carry 
 aqueous vapor with them for the support of the cyclone. 
 Hence the regions of these deflected currents on the east sides 
 of the United States and China, and of the southern part of 
 Africa, seem to be gaps in the dry belts through which alone, 
 or at least for the most part, tropical cyclones are able to pass 
 into the higher latitudes. We have had one notable example, 
 however ( 186), in which such a passage seems to have been 
 made, but this was a cyclone of unusual power and violence ; 
 and the passage was through a region where there are nu- 
 merous and very large islands. 
 
 191. In all which precedes upon this subject, as well as 
 upon the subject of cyclones in general, no account has been 
 taken of the effect of differences of temperature of the atmos- 
 phere upon the polar and equatorial sides of the cyclone, but 
 the whole region of atmosphere in which the cyclone exists is 
 supposed to be of uniform temperature, except within the cy- 
 clonic region. But in the real cases of nature, especially in the 
 middle latitudes and in the winter season, there is a great dif- 
 ference of temperature, where the cyclone is large, between 
 the polar and equatorial sides, which has nothing to do with 
 the temperature disturbance upon which the origination of the 
 
PROGRESSIVE MOTIONS OF CYCLOXES. 
 
 28 5 
 
 cyclone depends, but which give rise to large modifying influ- 
 ences after the cyclone has originated, which would not take 
 place in an atmosphere of uniform temperature on all sides 
 around the cyclone. 
 
 The following figure represents the action of a large cyclone, 
 say 1000 miles in diameter, in the middle latitudes, in winter, 
 at which time the difference of temperature on the two sides 
 may be as much as 20 C. On the southeasterly and easterly 
 sides the cyclonic currents, as represented by the arrows, carry 
 the warmer and moister air of lower latitudes to higher ones,. 
 
 Fig. 5. 
 
 and on the northwesterly and westerly sides, the colder and' 
 drier air of higher into lower latitudes. The difference of 
 temperatures between the west and east sides of the cyclones 
 is also increased by terrestrial radiation through the clear air 
 on the west side, which is the clearing-up side of the cyclone, 
 while on the other, clouds prevail which hinder this radiation. 
 The effect from both causes upon the isotherms, which we 
 may at first suppose to have extended nearly in an east and 
 west direction, is somewhat as shown by the figure. The tem- 
 perature gradient now is in the direction of the line a b instead 
 of from the pole toward the equator, and is steeper, the 
 isotherms being closer. Comparing now the temperatures on 
 the same latitudes in the lines c d and e f, as indicated by the 
 disturbed isotherms, it is seen there is a great difference and 
 
'286 CYCLONES. 
 
 ;a steep temperature gradient in an east and west direction, 
 where, before cyclonic disturbance, there was none. Not only 
 does the cold and dry air on the west side tend to press the 
 warmer and moister air on the east side still farther toward the 
 east, but the latter is continually forming a new centre of tem- 
 perature disturbance a little in advance, which becomes a new 
 cyclone centre, and so there is an apparent progressive motion 
 from the tendency to continually form a new cyclone a little in 
 .advance of the old one. Such an effect would evidently take 
 place in an atmosphere without any drifting progressive mo- 
 tion ; but this effect must be subordinate to, and much less 
 than, that of the progressive motion of the atmosphere ; for, if 
 it were not, since its action is always in a direction from west 
 to east, cyclones in the tropical latitudes would never move 
 westwardly. 
 
 The effect of a cyclone upon the isotherms, as represented in 
 the preceding figure, may be seen almost any time upon the 
 synoptic weather charts of the Signal Service, in cases of well- 
 developed cyclones ; but of course the observed effects are 
 never so regular as those of the preceding figure, since we 
 never have a perfectly regular cyclone, as assumed above, and 
 besides there are always other abnormal disturbances of tem- 
 perature combined with those of the cyclone. 
 
 The air on the east side of a cyclone, at least near the surface 
 of the earth, is very damp and oppressive, much more so than 
 it was while in the lower latitudes from which it has been 
 drawn ; for as it is carried up to higher latitudes over a surface 
 which becomes colder with increase of latitude, it of course 
 cools down some, though not nearly to the normal of the lati- 
 tude where the air remains undisturbed, and in this cooling it 
 becomes more nearly or quite saturated. Exactly the reverse 
 of this takes place on the west side. The air found there is 
 not only colder because it has been brought down from a 
 higher latitude, but it is much drier than it was in its original 
 position. 
 
VEERING OF THE WIND CHANGES OF TEMPERATURE. 287 
 
 VEERING AND BACKING OF THE WIND AND CHANGES OF 
 PRESSURE AND TEMPERATURE. 
 
 192. If a cyclone remained stationary without any pro- 
 gressive motion, there would be no veering of the wind, and 
 the only change would be a gradual increase and then decrease 
 in its velocity. The barometric depression, and the tempera- 
 ture of the interior, mostly in the upper strata, would be sub- 
 ject to similar changes, and these changes would have a period 
 coinciding with the time of duration of the cyclone. But 
 where the cyclone has a progressive motion these changes fol- 
 low in more rapid succession, and complete their period in the 
 time that the cyclone occupies in passing over the place of 
 observation. 
 
 Let the arrows of the following figure represent the direc- 
 
 Fig. 6. 
 
 tions and relative velocities of the wind in a cyclone, the 
 interior solid circle representing the line of highest barometric 
 pressure between the cyclonic and the anti-cyclonic gyrations. 
 If the cyclone passes centrally over the place, say from west to 
 ^ast, then while the place is in the outer or anti-cyclonic part, 
 HS at a, there is a very slight rise of the barometer and a very 
 gentle wind from a point west of north, if there are no abnor- 
 mal disturbances. Then comes the highest barometric pressure 
 and the calm connected with it, and when the point b of the 
 cyclone has reached the place of observation the direction of 
 
288 CYCLONES. 
 
 the wind is southeasterly, and the velocity continues to increase 
 with little change of direction, and the barometer to fall, until 
 the place of observation relative to the cyclone is at some 
 point c still nearer the centre, where the cyclonic motion is 
 most rapid. While the centre, and contiguous parts very near 
 on either side, are passing over the place of observation, there 
 is a calm, called the " dead calm," and the barometric pressure 
 is then the least. When the progressive motion has continued 
 a little longer, until the place of observation is at d y there has 
 been a complete change of the wind to the contrary direction, 
 and the barometer is now rising, which continues until the 
 opposite side of the ring of high pressure and of calm arrives. 
 If the direction of progressive motion is exactly from west to 
 east, the change in the direction of the wind at the centre is 
 from about S.S.E. to N.N.W., but if, as most usual in the mid- 
 dle latitudes of the northern hemisphere, the cyclone moves 
 toward the E.N.E., then the change, it is readily seen from 
 the figure, must be very nearly from S.E. to N.W. At the 
 time of this sudden change of direction near the centre there is 
 of course a great and sudden change in the character of the 
 air. On the east side, for reasons given in 191, it is warm, 
 damp, and oppressive, and this is suddenly changed to cold 
 and very dry air, using the terms warm arid cold here relatively 
 to the seasons. 
 
 Within the tropics, where the direction of progressive motion 
 in the northern hemisphere is W.N.W., the manner of veering 
 is readily seen by placing the figure with the line W.E. in that 
 direction. The directions of the arrows then indicate that the 
 change, when the centre passes over the place of observation, 
 is from a northerly to a southerly direction. The same may 
 be done for any other directions of progressive motion. When 
 the place of observation, in any case, is at e, the violence of the 
 wind has very much diminished and the height of the barome- 
 ter increased, and soon after follows the highest barometer 
 with its accompanying calm, after which the usual light varia- 
 ble winds, due to various abnormal disturbances, are observed, 
 the normal inversion of direction again in the anti-cyclonic 
 
VEERING OF THE WIND CHANGES OF TEMPERA TURE. 289 
 
 part being usually entirely obscured by these. If the area of 
 central calm is small and the gyrations are very rapid close up 
 to the centre, as in violent cyclones of moderate dimensions at 
 sea, then there is a very sudden change of a very strong wind 
 to the opposite direction. 
 
 If the north side of the cyclone passes eastwardly over any 
 place of observation in the northern hemisphere, so that the 
 place of observation occupies successively the places within 
 the cyclone m, n, and o, then it is seen that the change of the 
 more violent winds in the cyclone proper is from about E. at 
 m to N.E. at n and then to N. at o. In this case there is a 
 change of the wind through only about one quadrant, and this 
 in a direction contrary to the motion of the hands of a watch, 
 called backing; but if the south side of the cyclone passes in 
 the same direction, over the place of observation, so that this 
 occupies successively the places /;/', n' ', and o' in the cyclone, 
 then the change is from S. at m' to S.W. at n', and then to W. 
 at o', and the change in this case, through about one quadrant, 
 being in the direction of the hands of a watch, is called veering. 
 
 The direction in which the wind changes depends entirely 
 upon which side of the place of observation the centre of the 
 cyclone passes ; and the amount of change, upon the distance 
 of the path of this centre from the place of observation. If 
 the distance is small in comparison with the dimensions of the 
 cyclone, the change is through about two quadrants, but with 
 greater distances the amount of change is less. For other 
 directions of progressive motion, the veering or backing of the 
 wind is indicated in all cases by the arrows, when the line 
 W.E. is placed so as to coincide with these directions. 
 
 The winds at any given place are liable to change as fre- 
 quently, on the average, in one direction as the other, unless 
 the cyclones pass more frequently on the one side of the place 
 of observation than the other. In the middle latitudes of the 
 United States and of Europe cyclones pass more frequently 
 on the north side, so that in these latitudes the change is more 
 frequently in the same manner as the motion of the hands of a 
 watch. It was only for this reason Dove found a preponder- 
 
2QO CYCLONES. 
 
 ance of changes of this kind, in confirmation of his theory 
 with regard to the rotation of the winds. 
 
 For the southern hemisphere it is only necessary, in what 
 precedes, to change N. to S. and vice versa, in order to have 
 the successive changes in the veering and backing of the wind 
 in each case. 
 
 193. In what precedes with regard to the changing of the 
 directions of the winds, no account is taken of the effect of the 
 secondary conditions introduced by the action of the cyclone 
 itself, where there is a considerable difference of the general 
 temperature on the two sides, by which a steep temperature 
 and pressure gradient is introduced in an east and west direc- 
 tion between the lines cd and ef, as represented in Fig. 5. The 
 other component of the gradient in a north and south direction 
 remains much as it was at first before there was any cyclonic 
 disturbance, and has nothing to do with the cyclonic disturb- 
 ance, but simply with the general easterly motion of the atmos- 
 phere, and has already been considered in a previous chapter. 
 But the other component of the temperature gradient intro- 
 duced has to be here considered in connection with the cyclone. 
 The tendency of the cold dry air on the west side is to press 
 eastward below even beyond the centre of the cyclone, and as 
 cold and warm portions of air do not readily intermingle, but 
 tend to keep apart, there is often a long line, several hundred 
 miles in length, in the central, or perhaps rather easterly, part 
 of the cyclone, where there is a short but sharp temperature 
 and pressure gradient, and where, in the passage of a cyclone 
 eastward, there is a very sudden change of the wind around to 
 some westerly or northwesterly point, and there may even be 
 violent and simultaneous squalls, called line squalls, along this 
 whole line with a very sudden change of temperature. And 
 the general effect of this east and west temperature gradient 
 on the west side of the cyclone, beyond the line of sudden 
 transition from warm to cold air, is to give rise to a corre- 
 sponding pressure gradient, and so to cause the wind to be from 
 a direction more nearly west than it would be by a purely 
 cyclonic motion. It is on account of this increased pressure 
 
VEERING OF THE WIND CHANGES OF TEMPERATURE. 29 1 
 
 gradient on the west side, no doubt, that Loomis obtained a 
 greater inclination and velocity of the wind in the west than in 
 the east quadrant of a cyclone. His results fcr the several 
 quadrants were (Sill. Jour., July, 1874): 
 
 
 W. QUADRANT. 
 
 S. QUADRANT. 
 
 E. QUADRANT. 
 
 N. QUADRANT. 
 
 Inclination 
 "Velocity in miles 
 per hour 
 
 58 48' 
 IO. I 
 
 49 35' 
 8.8 
 
 32 6' 
 
 8-3 
 
 47 27' 
 7.6 
 
 
 
 
 
 
 The line of sudden transition from warm to cold air, and 
 likewise of the meeting of the southeasterly and north- 
 westerly winds, is a line of minimum pressure, and the low- 
 pressure area on both sides is sometimes called a " trough." 
 It is simply a great extension of the central area of low press- 
 ure and of calm of a regular cyclone, so that the winds, instead 
 of coming from all sides in toward and around the centre, come 
 in, not directly, but obliquely, toward the middle of the trough. 
 For this reason the isobars of cyclones in the middle latitudes 
 are not circular but somewhat elliptical, with the northerly 
 part of their longer axes corresponding to the trough, extend- 
 ing in a direction a little to the east of north, as was first dis- 
 covered by Espy, and now more fully proven by the researches 
 of Loomis. 17 He found from an actual measurement of the 
 greatest and least diameters of the isobars represented on the 
 Signal Service maps during a period of three years, that the 
 -average ratio of the longest diameter of the isobars to the 
 shortest was nearly as two to one. 
 
 Since the preceding secondary effect depends upon differ- 
 ences of general temperature in latitude, they occur principally 
 and most strikingly in the middle latitudes and in the winter 
 season, but they may occur at all latitudes and in all seasons 
 wherever conditions are such, whether of temperature or ter- 
 restrial radiation, as to cause a difference of temperature be- 
 tween the two sides ; for it must be remembered that slight 
 differences of temperature and small pressure gradients give 
 rise to violent winds where there are no deflecting forces arising 
 from the earth's rotation to counteract the forces of these 
 
CYCLONES. 
 
 gradients, as in the case of the interchanging motions in the 
 cases of the vertical circulations of the atmosphere and of 
 cyclones. In the lower latitudes, however, where the differ- 
 ence of temperature depending upon latitude is small, these 
 effects are very small, and hence it is said that in the tropical 
 cyclones there is an " absence of any marked squall or change 
 of weather during the passage of the trough in the tropics, 
 that is, at the moment when the barometer begins to turn 
 upward. 50 " 
 
 In the easterly progression of cyclones in the middle lati- 
 tudes, following one another in somewhat regular succession at 
 intervals of a few days, there is first encountered the southerly 
 winds on the easterly side of the trough, and then, in a few 
 days, the northerly winds on the west side, and this is frequently 
 repeated at short intervals. This seeming struggle, as re- 
 garded by Dove, between " equatorial and polar winds," now 
 so well understood, was formerly a great mystery to the meteor- 
 ologist. 
 
 CYCLONE OF AUGUST 2, 1837, AT ST. THOMAS. 
 
 194. As an example of some of the theoretical results 
 arrived at, we give (page 293) the observations of a cyclone at 
 St. Thomas, made by Hoskiaer, and copied here from Dove. 13 
 
 The normal barometric pressure here being about 29.9 
 inches, the whole low-pressure area, and the part of the cyclone 
 having any considerable violence, passed over the place of ob- 
 servation in about 24 hours. This, at the average rate of 15 
 miles per hour, at which cyclones progress here, would make 
 the diameter of this part 360 miles, and consequently, accord- 
 ing to Piddington ( 184), it was not one of the smallest kind. 
 With a barometric depression of nearly two inches in the cen- 
 tre, even with this area, the barometric gradients become very 
 large. Between 6 h. 30 m. and 7 h. 30 m. the change of baro- 
 metric pressure was 0.977 in., which, with the assumed rate of 
 progressive motion, would make a gradient of nearly one inch 
 in 15 miles. On the opposite or rear side at about the same 
 distance from the centre, the gradient is less, being only about 
 
CYCLONE OF AUGUST 2, 1837, AT ST. THOMAS. 293 
 
 MEAN 
 
 TIME. 
 
 BAROMETER. 
 
 DIRECTION OF THE WIND. 
 
 
 h. m. 
 
 Inches. 
 
 
 Aug. i 
 
 18 o 
 
 29.932 
 
 
 Aug. 2 
 
 2 IO 
 
 754 
 
 N.W." 
 
 
 
 3 20 
 
 .666 
 
 N. 
 
 
 
 3 45 
 
 .666 
 
 N. 
 
 Gale freshening. 
 
 
 4 45 
 
 .489 
 
 N. 
 
 
 
 5 40 
 
 443 
 
 N.E. 
 
 
 
 5 45 
 
 .310 
 
 N.E. = 
 
 
 
 "6 30 
 
 29.133 
 
 N.W. 
 
 
 
 6 35 
 
 28.911 
 
 N.W. 
 
 
 
 6 45 
 7 o 
 
 778 
 778 
 
 N.W. 
 N.W. 
 
 Hurricane. 
 
 
 7 10 
 
 .600 
 
 N.W. 
 
 
 
 7 22 
 
 .289 
 
 N.W. 
 
 
 
 7 30 
 
 .156 
 
 N.W. 
 
 
 
 7 35 
 
 .in 
 
 
 
 
 7 52 
 8 10 
 
 .067 
 .067 
 
 
 Dead calm. 
 
 
 8 20 
 
 .067 
 
 
 
 
 8 23 
 
 423 
 
 S.S.E.' 
 
 
 
 8 33 
 
 511 
 
 S.E. 
 
 
 
 8 38 
 
 .600 
 
 S.E. 
 
 
 
 8 45 
 
 .689 
 
 S.E. 
 
 
 
 8 50 
 
 778 
 
 S.E. 
 
 
 
 9 o 
 
 28.995 
 
 S.E. 
 
 
 
 vQ 10 
 
 29.133 
 
 S.E. 
 
 
 
 9 25 
 
 .222 
 
 S.E. 
 
 
 
 9 35 
 
 310 
 
 S.E. 
 
 Hurricane. 
 
 
 9 50 
 
 399 
 
 S.E. 
 
 
 
 IO IO 
 
 .489 
 
 S.E. 
 
 
 
 10 35 
 
 577 
 
 S.E. 
 
 
 
 II 10 
 
 599 
 
 S.E. 
 
 
 
 ii 30 
 
 .621 
 
 S.E. 
 
 
 
 14 45 
 
 -754 
 
 S.E. 
 
 
 
 20 
 
 .888 
 
 S.W. 
 
 
 
 2T 
 
 29.910 
 
 E. 
 
 
 O.8 in. in 15 miles. These gradients, therefore, are enormously 
 greater than the estimated gradient of the cyclone of the Fiji 
 Islands ( 186), although the minimum of the depression in 
 this latter case was much lower. But it is seen that the ba- 
 rometer, as usual in such storms, was irregular, being affected 
 by various irregular and abnormal disturbances, so that the 
 gradients at any given time can be only approximately deter- 
 mined. In the front part of the storm at 7 h., taking the aver- 
 age between 6 h. 30 m. and 7 h. 30 m., it was approximately one 
 inch in 15 miles or 21 mm. in the distance of 60 geographical 
 
294 CYCLONES. 
 
 miles. Assuming the exact centre of the cyclone to be at the 
 place of observation at 8 h. 10 m. and that the progressive ve- 
 locity was 15 miles per hour, the distance of that gradient from 
 the centre was about 17 miles, or 27 kilometers. Putting now 
 G t , 57, equal to 21 mm. and r 27.000 meters, and /= 18, 
 the value of v which satisfies the expression for a temperature 
 of 30 C. is 24 meters per second, or about 54 miles per hour 
 for the approximate gyratory component of velocity, and as 
 the inclination in such small and violent cyclones is small, even 
 in this latitude, this is not much less than the real velocity. 
 Of course this estimate is subject to all the uncertainties of 
 gradient and distance, where there are so many irregularities 
 in the barometer, and where the exact progressive velocity is 
 not known. 
 
 By comparing the value of v = v/r in the preceding com- 
 putation, with that of 2n sin / as deduced from Table V, it is 
 seen that the former is more than 14 times greater, and hence 
 the gradient here in this low latitude depends almost entirely 
 upon the centrifugal force of the gyrations, and very little upon 
 the earth's rotation. 
 
 As the progressive motions of cyclones in this vicinity are 
 in a direction only a little north of west, and this cyclone seems 
 to have passed very nearly centrally over the place of observa- 
 tion, by placing the line W.E. in Fig. 6 in that direction, andi 
 making allowance for a greater inclining in toward the centre 
 in this low latitude than that represented in the figure, which is 
 more adapted to the middle latitudes, it is seen that in the more 
 violent part of the front of the cyclone, as at the points e and d, 
 the wind is N.W., as represented in the preceding table of ob- 
 servations. Then comes the " dead calm" at the centre with 
 lowest pressure, which continues about 45 minutes, and so, with 
 a progressive velocity of 15 miles per hour, it must have been 
 about 12 miles in diameter; but of course there is no definite 
 limit, since the gyrations at first become merely perceptible, 
 and then gradually increase with distance from the centre, 
 though very rapidly, so that at only a short distance they be- 
 come extremely violent. At the points c and b in the rear 
 
MANILLA TYPHOON OF NOVEMBER 5, 1882. 
 
 295 
 
 part there is a complete change of direction to the S.E., as 
 shown in the preceding observations, which has taken place in 
 a short time, while the central calm passed over the place. 
 
 The observations, as given, were not commenced soon 
 enough, and continued long enough, to indicate the belt of 
 high pressure and the anti-cyclonic directions of the wind on the 
 outer border of the cyclonic region of disturbance, but these, 
 most probably, would have been masked by small abnormal 
 disturbances. 
 
 MANILLA TYPHOON OF NOVEMBER 5, 1882. 
 
 195. This cyclone has been investigated by Loomis, 17 and 
 the following table of observations of its central and more vio- 
 lent part is copied approximately from the curves of his dia- 
 gram. 
 
 TIME. 
 
 BAR. PRESSURE. 
 
 TEMPERATURE. 
 
 WIND. 
 
 Velocity. 
 
 Direction. 
 
 d. h. 
 
 mm. 
 
 
 m. 
 
 
 4 22 
 
 752 
 
 23 
 
 6 
 
 N.W. 
 
 23 
 
 52 
 
 23 
 
 10 
 
 N.W. 
 
 5 o 
 
 51 
 
 22 
 
 20 
 
 W. i N.W. 
 
 I 
 
 50 
 
 22 
 
 21 
 
 W.N.W. 
 
 2 
 
 48 
 
 22 
 
 30 
 
 W. i N.W. 
 
 3 
 
 47 
 
 21 
 
 33 
 
 W.N.W. 
 
 4 
 
 46 
 
 21 
 
 22 
 
 W.N.W. 
 
 5 
 
 46 
 
 21 
 
 34 
 
 W.N.W. 
 
 6 
 
 46 
 
 21 
 
 28 
 
 W.N.W. 
 
 7 
 
 45 
 
 21 
 
 29 
 
 W.N.W. 
 
 8 
 
 43 
 
 21 
 
 36 
 
 W.N.W. 
 
 9 
 
 37 
 
 21 
 
 44 
 
 W.N.W. 
 
 10 
 
 35 
 
 22 
 
 2 
 
 N.N.E. 
 
 ii 
 
 37 
 
 25 
 
 9 
 
 E. iS.E. 
 
 12 
 
 38 
 
 24 
 
 12 
 
 S-E. iE. 
 
 13 
 
 43 
 
 26 
 
 25 
 
 S.E. E. 
 
 14 
 
 45 
 
 27 
 
 28 
 
 E.S.E. 
 
 15 
 
 46 
 
 26 
 
 30 
 
 E. iS.E. 
 
 16 
 
 47 
 
 25 
 
 22 
 
 E.S.E. 
 
 17 
 
 48 
 
 25 
 
 16 
 
 E.S.E. 
 
 If 
 
 49 
 
 25 
 
 15 
 
 E.S.E. 
 
 19 
 
 50 
 
 25 
 
 14 
 
 E.S.E. 
 
 20 
 
 51 
 
 25 
 
 IO 
 
 E.S.E. 
 
 21 
 
 52 
 
 24 
 
 10 
 
 E. 
 
 22 
 
 52 
 
 24 
 
 12 
 
 E.S.E. 
 
296 
 
 CYCLONES, 
 
 The minimum pressure of this cyclone was not very low nor 
 the gradients very steep, except very near the centre, although 
 the velocities of the wind were considerable/ This is because 
 the cyclone was large for this latitude, and the distances mostly 
 were much greater than in the case of the St. Thomas cyclone. 
 It is seen from the expression of 4 , 57, that with larger val- 
 ues of r the value of G becomes smaller. The sudden rever- 
 sion of the direction of the wind is explained as in the pre- 
 ceding case. This cyclone, however, being a little nearer the 
 equator, the directions of the wind seem to have been more 
 nearly radial, as they should be, than in the preceding case, so 
 that the change is from W.N.W. to E.S.E. mostly, instead of 
 from N.W. to S.E., as in the case of the St. Thomas cyclone. 
 The duration of the central calm seems, as usual, to have been 
 short. 
 
 If we assume that 5 d. 10 h. was the exact time of the pas- 
 sage of the centre, and compare the several pressures and tem- 
 peratures for each hour preceding and following this passage, 
 we get the following results : 
 
 Hours 
 Before and 
 
 After. 
 
 PRESSURE. 
 
 TEMPERATURE. 
 
 WIND VELOCITY. 
 
 Before. 
 
 After. 
 
 Before. 
 
 After. 
 
 Before. 
 
 After. 
 
 
 mm. 
 
 mm. 
 
 
 
 
 
 I 
 
 737 
 
 737 
 
 21 
 
 25 
 
 44 
 
 9 
 
 2 
 
 43 
 
 38 
 
 21 
 
 24 
 
 36 
 
 12 
 
 3 
 
 45 
 
 43 
 
 21 
 
 26 
 
 29 
 
 25 
 
 ! 4 
 
 46 
 
 45 
 
 21 
 
 27 
 
 28 
 
 28 
 
 ; s 
 
 46 
 
 46 
 
 21 
 
 26 
 
 34 
 
 30 
 
 6 
 
 46 
 
 47 
 
 21 
 
 25 
 
 22 
 
 22 
 
 ! 7 
 
 47 
 
 48 
 
 21 
 
 25 
 
 33 
 
 16 
 
 8 
 
 48 
 
 49 
 
 22 
 
 25 
 
 30 
 
 15 
 
 9 
 
 50 
 
 50 
 
 22 
 
 25 
 
 21 
 
 14 
 
 10 
 
 5i 
 
 5i 
 
 22 
 
 25 
 
 20 
 
 10 
 
 ii 
 
 52 
 
 52 
 
 23 
 
 24 
 
 IO 
 
 IO 
 
 12 
 
 52 
 
 52 
 
 23 
 
 24 
 
 6 
 
 12 
 
 From this it is seen that the rear side of the cyclone is the 
 warmer side, and in the passage of the cyclone the transition is 
 from cold to warm, contrary to what occurs in the middle lati- 
 tudes, as illustrated by Fig. 5 and shown by observation ; and 
 the isotherms, if drawn, would curve down on the front side 
 
CYCLONE OF CIENFUEGOS ON SEPT. 5, 1882. 
 
 297 
 
 toward the equator instead of toward the pole. This is be- 
 cause the progressive motion is nearly in the contrary direc- 
 tion. The effect, however, is comparatively small, since in this 
 low latitude, even in November, the difference of temperature 
 due to difference of latitude on the two sides is small. The cor- 
 responding increase of pressure on the front side on account 
 of lower temperature seems to be only very faintly indicated 
 in the preceding table. In general the wind velocities in the 
 preceding table are greater on the front than the rear side, but 
 this is most probably due to the winter monsoon, which at this 
 season is already set in, and the direction in this region is 
 rather from the N.W., which tends to increase the velocity in 
 front a little and to decrease it a little in the rear. 
 
 CYCLONE OF CIENFUEGOS ON SEPT. 5, 1 882. 
 
 196. The following observations of this cyclone are taken 
 from the Report of the Chief Signal Officer for 1883, p. 759. 
 
 Time. 
 
 Barometer. 
 
 Temper- 
 ature. 
 
 Wind. 
 
 Force. 
 
 State of the Weather. 
 
 d. h. 
 
 Inches. 
 
 
 
 
 
 5 
 
 29.82 
 
 82 
 
 N. 
 
 2 
 
 Clouds between i and 2 quadrant. 
 
 2 
 
 29.76 
 
 80 
 
 N.W. 
 
 3 
 
 Heavy gusts of rain. 
 
 8 
 
 .66 
 
 80 
 
 N.W. 
 
 3 
 
 Do. 
 
 9 
 9 3^ 
 
 59 
 50 
 
 78 
 78 
 
 N.W. 
 W.N.W. 
 
 4 
 4 
 
 Hurricanes, gusts. 
 Violent gusts of wind and rain. 
 
 10 
 
 38 
 
 78 
 
 W.N.W. 
 
 4 
 
 Hurricane. 
 
 10 15 
 
 3 1 
 
 78 
 
 W. Yt N.W. 
 
 4 
 
 Gloomy and cloudy weather. 
 
 10 30 
 
 .27 
 
 78 
 
 w. 
 
 4 
 
 
 30 45 
 
 .22 
 
 78 
 
 w. 
 
 4 
 
 Greatest intensity. 
 
 II O 
 
 ii 30 
 
 .18 
 .13 
 
 78 
 
 78 
 
 W. J4S.W. 
 
 w.s!w. 
 
 4 
 4 
 
 Blowing with great force. 
 Do. 
 
 11 45 
 
 15 
 
 78 
 
 s.w. YI w. 
 
 4 
 
 Barometer rising. 
 
 12 
 
 .16 
 
 78 
 
 s.s.w. 
 
 4 
 
 I Gloomy appearance, rain in tor- 
 | rents. 
 
 12 30 
 
 .18 
 
 78 
 
 s.s.w. 
 
 4 
 
 Do. 
 
 I O 
 
 .27 
 
 78 
 
 s.s.w. 
 
 4 
 
 Do. 
 
 I 30 
 
 32 
 
 78 
 
 s. YA, s.w. 
 
 4 
 
 Do. 
 
 2 
 
 44 
 
 78 
 
 s. M s.w. 
 
 4 
 
 j Less wind gusts and of short du- 
 { ration. 
 
 2 30 
 
 .46 
 
 78 
 
 s. Y4 s.w. 
 
 4 
 
 
 3 o 
 
 .46 
 
 78 
 
 s. 
 
 4 
 
 Gusts diminishing. 
 
 3 30 
 4 o 
 
 49 
 
 78 
 78 
 
 s. 
 
 S.S.E. 
 
 
 Rapid gusts. 
 Heavy rain. 
 
 5 
 
 6O 
 
 78 
 
 S.S.E. 
 
 
 Do. 
 
 6 o 
 
 !66 
 
 78 
 
 S.E. 
 
 
 Rains and gusts. 
 
 7 o 
 
 .70 
 
 78 
 
 S.E. 
 
 
 Strong winds with lasting gusts. 
 
 8 o 
 
 .78 
 
 78 
 
 S.E. 
 
 
 * Do. 
 
 9 o 
 
 79 
 
 78 
 
 SE. 
 
 
 Heavy rain and strong wind. 
 
 10 O 
 
 .80 
 
 78 
 
 S.E. 
 
 3 
 
 Gusts at intervals. 
 
 This is an example in which the centre of the cyclone did 
 not pass over the place of observation, but on the north side. 
 
298 CYCLONES. 
 
 There is, accordingly, no dead calm and sudden change of the 
 wind to the opposite direction, but a gradual backing of the 
 wind from a N.W. wind in the front to a S.E. wind in the rear. 
 The explanation of this is readily seen by reference to the ac- 
 companying figure, in which the large arrow indicates the di- 
 rection of progression, and the parallel line with the small 
 arrows and the even hours of the time indicates the place of 
 observation at the several times with reference to the centre of 
 
 29-80 
 
 Fig. 7. 
 
 the cyclone. The calm centre passed north of the place of ob- 
 servation, and so when it was nearest, the place of observation 
 was at the distance of greatest violence. If the centre had 
 passed on the other side there would have been a gradual veer- 
 ing instead of backing of the wind. 
 
 RAIN AND CLOUD AREAS IN CYCLONES. 
 
 197. Since the air flows in from all sides of a cyclone 
 toward the central area, and consequently gradually ascends 
 there, this must be a region of cloud and rain, just as the equa- 
 torial belt is, where the air, coming in from both sides in the 
 lower strata, is deflected upward and becomes an ascending 
 current. The explanation of the formation of cloud and rain, 
 and the height to which the surface vapor has to ascend before 
 cloud-formation takes place, is the same in both cases, and has 
 been already given ( in). 
 
 The rain and cloud areas do not coincide with, nor are they 
 
RAIN AND CLOUD AREAS IN CYCLONES. 299, 
 
 even concentric with, the areas of low pressure and of ascending 
 currents ; for the ascending and partially condensed vapor and 
 the cloud may be, and generally is in the middle and higher 
 latitudes, carried eastward beyond the limits of the low press- 
 ure area, by the strong easterly currents above, into the anti- 
 cyclonic area before it falls as rain ; and hence the centre of 
 the area of cloud and rain falls considerably in advance of the 
 centre of low pressure and of cyclonic gyration in their easterly 
 progression. These areas, as those of low pressure, are ellip- 
 tical, and not circular as they would be in case of regular con- 
 ditions with no greater progressive motion of the atmosphere 
 above than below. 
 
 According to Loomis, 51 " the form of these rain areas is. 
 sometimes quite irregular, but generally it approximates to an 
 ellipse of which] the major axis is not quite double the minor 
 axis." The average distance of the centre of rainfall from the 
 centre of low pressure, north of latitude 36, was found to be^ 
 300 miles, but it sometimes exceeded 750 miles. The general 
 direction of the longer axis of the rain-area, and of the centre 
 of this area from that of the area of low pressure, is the same 
 as the direction of the progressive motion of cyclones. This 
 indicates that both the former and the latter depend mostly 
 upon the general motion of the atmosphere. The whole cy- 
 clone and storm area drifts with the average velocity of the 
 different strata, but the upper strata, in which the vapor con- 
 densation takes place mostly, have a greater average velocity, 
 and so the rain and the cloud are carried forward, and the rain 
 falls mostly in the front part of the cyclone in the direction in 
 which the general atmosphere and the whole cyclone are mov- 
 ing. Of course this is only approximately so, for we have seen 
 ( 189) that the direction of the progressive motion may be 
 affected considerably by other circumstances. The direction 
 and distance of the centre of rainfall from the centre of low 
 area indicates the location of greatest energy in the cyclone,, 
 and this, we have seen, does not depend entirely upon the mere 
 drifting of the upper strata of the atmosphere where the centre, 
 of energy is. 
 
3OO CYCLONES. 
 
 In general the cloud area, though somewhat concentric with 
 that of the rain area, is very much larger ; for it requires a con- 
 siderable depth of cloud to give rise to rainfall, and so the 
 outer parts of the cloud, arising mostly from the lateral expan- 
 sion of the air in its ascent, and not directly from the ascent of 
 air, are not of sufficient depth to furnish rain. In the easterly 
 progression of a cyclone, therefore, there is observed first merely 
 haziness, then a thin and light stratum of cloud, and then the 
 heavy, deep nimbus, from which rain falls. 
 
 Where the conditions of a cyclone are such that the vapor 
 of the air is carried by the ascending current in the interior to 
 very high altitudes, where there is a freezing temperature, the 
 fine cirrus clouds formed by the freezing of the vapor there are 
 ^carried eastward far in advance of the cyclone, by the swift- 
 moving easterly currents of these altitudes in the form of fine 
 filaments, which are often so distorted by the small whirling 
 motions which frequently exist in the atmosphere as to resem- 
 ble a horse's tail, and are called " mares' tails." These cirrus 
 ^clouds of various forms, coming from a westerly direction, 
 while the hazy border of the cloud has not yet made its 
 appearance, are generally precursors of a violent cyclone and 
 storm coming from that quarter, which may be expected in a 
 few days. 
 
 198. It has been shown ( 156) that the conditions of a 
 cyclone are not absolutely dependent upon the condensation 
 of aqueous vapor. There may, therefore, be considerable cy- 
 clonic action and barometric depression, with little or no rain- 
 fall. If the atmosphere were entirely void of vapor, but was 
 in the unstable state for dry air, from some slight determining 
 cause arising from a small local increase of temperature over a 
 considerable area, moderate vertical and cyclonic circulations 
 would ensue, and likewise barometrical depression in the cen- 
 tral part. Also where the temperature over a considerable 
 area is considerably above that of the surrounding air, as shown 
 in 159, it gives rise to cyclonic action of some degree of 
 strength, even where the vapor is not sufficient to produce 
 >clouds of sufficient depth and density to give rise to rainfall. 
 
RAIN AND CLOUD AREAS IN CYCLONES. 30 F 
 
 The energy of the cyclone is in the condensation and not in- 
 the rainfall, the latter being only an evidence of the former,, 
 but there may be considerable cloud-formation without rainfall. 
 In 101 cases of low barometer in which the depth of rain 
 did not amount to one eighth of an inch, Loomis 51 found that 
 more than one half showed a barometric pressure less than 
 29.70 inches ; more than one third were below 29.60 inches, 
 and nearly one fourth of the cases were below 29.50 inches. 
 He says : 
 
 "There seems to be no room for doubt that barometric minima some- 
 times form with very little rain, and continue without any considerable 
 rain for eight hours, and sometimes for twenty-four hours and longer. 
 These barometric minima seldom continue stationary for eight hours,, 
 but almost invariably travel to the eastward." 
 
 In general, areas of low barometer are areas of cloud and 
 rain but there is no proportionate relation between the depth 
 of rain, and of barometric depression, for the latter depends 
 very much upon the deflecting force of the earth's rotation, 
 and the extent of area, being the result of an integration of the 
 gradient through a distance from the centre, while the former 
 depends mostly upon the velocity of the ascending currents 
 and the amount of moisture in the air at any given place, and 
 not upon extent of area. Where considerable depressions are 
 observed with little or no rainfall, the cyclonic action and the 
 barometric gradients are generally small, but the depression is 
 considerable from the extent of area. 
 
 199. There is a characteristic difference between tropical 
 cyclones and those of the middle and higher latitudes. Aber- 
 cromby says : M 
 
 " Cirrus and halo appear all round a tropical cyclone, while they are- 
 never seen in the rear of a European storm ; and though the way in 
 which the rain seems to grow out of the air in front of the cyclone is the 
 same everywhere, the sky and clouds in the rear of a hurricane are much 
 softer and dirtier than in temperate cyclones. There is not that sharp 
 difference between the quality of clouds in front and rear which is so 
 striking in higher latitudes. Still greater is the absence of any marked 
 squall or change of weather during the passage of the trough in the 
 tropics, that is, at the moment when the barometer begins to turn,: 
 
302 CYCLONES. 
 
 upwards. Some who study hurricanes have scarcely noticed any change 
 then ; and all are agreed that the trough-phenomena are slight." 
 
 According to Padre Viftes" the approach of cyclones from 
 the E. or S.E. is always indicated at Havana by the appearance 
 of cirrus clouds while the vortex is 500 miles or more distant, 
 and while fair weather is yet prevailing. The same is also 
 observed as they pass off at a distance. This indicates that 
 the cirrus clouds are observed on all sides of the tropical cy- 
 clones, in accordance with what is stated above. Again, ac- 
 cording to Dr. Doberck, 52 at Hong Kong and in the China Sea 
 " there does not generally exist a fine-weather area behind the 
 cyclone, as the S. and particularly the S.W. winds blow there 
 very fresh, accompanied by overcast, damp and frequently wet 
 weather. Thunder-storms likewise follow after a typhoon, 
 especially along the coast of Southern China." 
 
 In the middle latitudes the general motion of the air is 
 easterly at all altitudes, but its velocity is much greater above 
 than below. Hence cirrus clouds and halos never appear in the 
 rear of cyclones in Europe, or anywhere in the middle latitudes. 
 Near the equator the general motion of the atmosphere is 
 westerly in the lower part, and at the season of the year in 
 which the tropical cyclones mostly appear, it is so up to a high 
 altitude, and above that altitude the velocity of easterly motion 
 is comparatively small. In this latitude, therefore, the air 
 .ascends more nearly vertically, and in the expansion of the air 
 in all directions as it comes under less pressure, the vapor of 
 the ascending current is diffused somewhat equally in all direc- 
 tions around the centre of the cyclone, so that there is here no 
 striking difference between the clouds in front and rear, and 
 at Havana the cirrus clouds are observed when the cyclone 
 centre is still 500 miles or more distant toward the east, and 
 while fair weather is still prevailing. 
 
 The reason the usual trough-phenomena observed in higher 
 latitudes in the passage of a cyclone over a place are not observed 
 in tropical cyclones is clear from what has been stated with 
 regard to the Manilla typhoon ( 195). In these there is no 
 'dose contact between warm and cold air of very different tern- 
 
RESULTANTS OF CYCLONIC AND PROGRESSIVE MOTIONS. 303 
 
 peratures and a sudden change from the former to the latter, 
 but, on the contrary, the change is from colder air to that which 
 is only a little warmer. 
 
 In the higher latitudes the west side is the clearing-up side 
 of the cyclone, because the strong easterly currents above, es- 
 pecially at high altitudes, carry all the vapor and cloud east- 
 ward, so that soon after the centre of the cyclone has passed a 
 place, the clouds mostly have passed it also, and clear weather 
 prevails. It is not so in tropical cyclones. Here the pro- 
 gressive motion is westerly, and although the atmospheric 
 currents below are also westerly up to a considerable altitude, 
 yet the westerly velocity decreases with increase of altitude, 
 .and becomes easterly above, so that the clouds are not driven 
 .ahead in advance of the cyclone, but there is enough of easterly 
 current above in the cloud region to carry the clouds eastward 
 to the rear of the cyclone, and consequently there is there 
 " overcast, damp and frequently wet, weather," instead of a 
 fine-weather area such as is observed in the rear of cyclones in 
 higher latitudes. 
 
 RESULTANTS OF CYCLONIC AND PROGRESSIVE MOTIONS. 
 
 200. Where the atmosphere in which a cyclone exists has 
 .a progressive motion in some direction, as it generally has, the 
 resultant of this and the cyclonic motion differs from the purely 
 cyclonic motion, and the effect of the progressive motion upon 
 the velocity and direction of the cyclonic motion is different on 
 different sides of the cyclone. 
 
 Let ab, Fig. 8, represent the velocity and direction of the 
 cyclonic motion on the several sides of the cyclone, with its 
 centre progressing a little north of east, as usual in the middle 
 latitudes, and as represented by the arrow, and also let be rep- 
 resent the velocity and direction of the wind at the earth's sur- 
 face, which may be assumed to be the same, or nearly, in all 
 parts of the cyclone, and to have very nearly the same direction 
 as that of the cyclone centre, but its velocity is generally much 
 less. It is seen from the figure that the resultants, represented 
 
304 CYCLONES. 
 
 by ac, indicate very different velocities and inclinations on the 
 different sides of the cyclone. On the side of the cyclone on 
 the right-hand side of the centre's path the velocity is changed 
 from ab to ac, and is, therefore, considerably increased, though 
 the direction is changed but little, since the directions of both 
 the cyclonic and progressive motions are nearly the same. On 
 the left hand, on the contrary, both the velocity and direction, 
 as represented by ac as compared with ab, are very much 
 
 Fig. 8. 
 
 changed, the former being decreased and the latter becoming 
 nearly radial in a direction toward the centre. On the front 
 side the direction only is very much changed, since nearly the 
 whole effect of the progressive motion of the air is upon the 
 direction of motion and not upon the velocity. The inclination 
 here, with the assumed relation between progressive and cy- 
 clonic velocity, is negative or outward. In the rear the effect 
 is an increase of both velocity of the wind and its inclination 
 toward the centre. 
 
 Of course the relations between the resultant velocities and 
 directions and those of the cyclonic, depend upon those be- 
 tween the two components. If the progressive velocity of the 
 air is small in comparison with the cyclonic, as is usually the 
 case on land, the cyclonic velocities and directions are not 
 much changed, but this is generally different at sea, where the 
 progressive velocity of the air is usually greater. The rela- 
 tions, as represented here in Fig. 8, are perhaps those which 
 usually occur at sea, where the progressive velocity may be 
 nearly as great as the cyclonic. 
 
RESULTANTS OF CYCLONIC AND PROGRESSIVE MOTIONS, 305 
 
 201. The progressive motion of the air in the region of the 
 West India Islands being comparatively large, its effect upon 
 both the velocities and directions is quite large. Here the 
 trade-winds become nearly east winds ( 123). Hence, the 
 winds whose cyclonic component of motion is from the north 
 or south suffer the greatest deviation from the original cy- 
 clonic direction, the inclination toward the centre being de- 
 creased where the wind is from the north and increased where 
 it is from the south. This will be better understood from Fig. 
 9, in which ab represents the cyclonic and be the progressive 
 
 Fig. 9. 
 
 component of the motion of the air at the earth's surface, the 
 inclination here in these low latitudes being assumed to be 
 about 45. The direction of progressive motion of the centres 
 of the cyclones here is about W.N.W., as represented by the 
 arrow in the figure. It is seen that in front of the storm the 
 inclination of the resultant ac is diminished and becomes 
 nearly at right angles to the radius, while in the rear it is in- 
 creased and becomes nearly radial, in consequence of the pro- 
 gressive motion of the air be. On the right-hand side the di- 
 rection of the progressive motion coincides nearly with that of 
 the cyclonic motion, and hence the direction is little changed, 
 but the velocity is greatly increased ; but on the left-hand side 
 
306 CYCLONES. 
 
 the direction and velocity are both much changed, the latter 
 being very small, since the cyclonic motion is somewhat coun- 
 teracted by the progressive motion. 
 
 These results are verified by observations of the hurricanes 
 of the Antilles of 1875 and 1876. In the hurricane of Septem- 
 ber, 1875, it is said, 42 "the winds of the anterior part of the 
 storm were approximately circular, or with a slight inclination 
 toward the centre in some cases." But from observations 
 made at numerous places " the winds of the second (S.E.) 
 quadrant, which remained at all these places when the vortex 
 was at a considerable distance, suffered a great deviation to- 
 ward the centre, and in some cases, likewise, the winds not far 
 from the vortex." This large deviation is represented by ac 
 in the rear part of the storm in the figure. The reason that 
 this great inclination occurred in some cases only near the vor- 
 tex, is that there the cyclonic component is large and has but 
 little inclination, the winds there, as we have seen ( 175), be- 
 coming nearly circular. Again, on the island of Porto Rico 
 " little deviation in the winds of the third and fourth (S.W. and 
 N.W.) quadrants was noted, some greater convergency in 
 those of the first (N.E.) quadrant, and a great inclination to- 
 ward the centre in those of the E. and S., especially as they 
 became at a great distance from the vortex." 
 
 Of the hurricane of the iQth of October, 1876, it is likewise 
 said, 42 
 
 "After its passage by Havana the winds, which in the posterior part 
 blew from west to south, suffered a great deviation toward the centre, 
 and that not only at a distance from the vortex, but even in its vicinity." 
 
 And 
 
 " The winds which prevailed from S.S.E. to S., and which, during the 
 passage of the vortex by Havana blew with force in the different towns 
 situated to the E.S.E. of Havana, suffered likeyise a very notable incli- 
 nation toward the centre. With respect to the winds which prevailed in 
 the first quadrant in the different localities of the anterior part of the 
 cyclone, there was observed in them likewise a notable convergency, 
 though in general in a less degree." 
 
 It is readily seen from a mere inspection of Fig. 9, why on 
 
RESULTANTS OF CYCLONIC AND PROGRESSIVE MOTIONS. 307 
 
 the Island of Porto Rico the winds had little deviation from 
 the tangent in the S.W. and N.W. quadrants, that is, in the 
 anterior parts of the cyclone, and why the inclinations in those 
 of the east and south quadrants were great, especially at a 
 great distance from the centre, where the inclination of the cy- 
 clonic component is large ( 175). 
 
 Also why the winds in the posterior of the cyclone of the 
 1 9th of October, after it had passed Havana, suffered a great 
 deviation toward the centre, and the winds in the region E.S.E. 
 of Havana, which prevailed from E.S.E. to S., suffered likewise 
 a very notable inclination. 
 
 202. From what precedes it is seen that the navigator, in 
 determining the direction of the centre of a cyclone from the 
 direction of the wind, should, in addition to considering lati- 
 tude, distance, from centre, and velocity ( 181), likewise con- 
 sider in what quadrant of the cyclone he is situated, since the 
 -direction of the centre with reference to that of the wind is so 
 different in different quadrants, especially where there is a 
 large progressive motion of the air, as in the trade-wind re- 
 gions. In the front part of the cyclone, where the mariner is 
 in the greatest danger, the direction of the centre is generally 
 more nearly at right angles to the direction of the wind, and 
 consequently the old rules of the circular theory are more 
 nearly correct here than on any other side of the storm ; while 
 in the rear the motions are more nearly radial in the direction 
 of the centre. This difference between the front and rear of 
 the cyclone is embraced in Dr. Doberck's rule for the Philip- 
 pine Islands ( 181). 
 
 It is seen from Figs. 8 and 9 that both in the middle and 
 tropical latitudes the velocity of cyclonic motion is increased 
 on the right-hand side of the path of the centre, and decreased 
 on the left-hand side, by the progressive motion of the air in 
 the neighborhood of the cyclone. The right-hand side, there- 
 fore, in the northern hemisphere has long been recognized as 
 the dangerous side of the cyclone. In the southern hemisphere 
 it is of course reversed. In endeavoring, therefore, to escape 
 the most dangerous part of the cyclone, care should be taken 
 "to avoid if possible this side. 
 
308 
 
 CYCLONES. 
 
 203. But the effects of the progressive motions of the air 
 at a considerable altitude above sea-level, on mountain tops 
 and in the regions of the clouds, especially the cirrus clouds, 
 are much greater than at the surface, because the velocities of 
 progressive motion are much greater. In fact up at the alti- 
 tude of the cirrus clouds the progressive component is usu- 
 ally the principal one, and the cyclonic merely causes considera- 
 ble perturbations in the strong easterly current of these re- 
 gions. This is seen from the results deduced from the obser- 
 vations of the cirrus clouds made at Zi-ka-wei, as given in 83. 
 From these it is seen that the motions are mostly from a west- 
 erly direction, the cyclonic component being merely sufficient, 
 for the most part, to cause deviations of one or two points from 
 this direction, and rarely sufficient to entirely reverse this 
 strong easterly current and give rise to a motion from an east- 
 erly direction. And this is in accordance with the estimates 
 made by Mr. Ley from his early observations on the motions 
 of the cirrus clouds. He states that the most elevated ones 
 not uncommonly traverse a distance of 120 miles in an hour. 
 This is, no doubt, when the great easterly motions of the air 
 in these regions coincide in direction with a great cyclonic mo- 
 tion, as in the S. or S.E. quadrant. On the other hand, he 
 states that calms are uncommon in this elevated stratum, and 
 that he observed only twice an actually motionless cirrus 
 cloud. 46 In these cases the observations, no doubt, were made 
 in the N. and N.W. octant of a cyclone region, where the cy- 
 clonic and progressive motions very nearly or quite counteract 
 each other. 
 
 204. Professor Loomis' discussion of observations of the 
 Signal Service, made on the top of Mount Washington at the 
 times of low barometer, gives the following velocities and in- 
 clination of the wind : 53 
 
 
 West 
 Quadrant. 
 
 South 
 Quadrant. 
 
 East 
 Quadrant. 
 
 North 
 Quadrant. 
 
 Velocity in miles 
 Inclination 
 
 49 
 55 7' 
 
 44 
 13 25' 
 
 -5^.44' 
 
 6 9 3 54' 
 
JRESULTANTS OF CYCLONIC AND PROGRESSIVE MOTIONS. 309 
 
 Fig. 10 is a copy of his graphic representation of the direc- 
 tions of the resultants. Comparing this with Fig. 8, which 
 may be regarded as a representation of the resultant motions 
 usually at the surface of the ocean, it is seen that the results 
 are somewhat similar, but the effect of the progressive motions 
 upon the directions of the cyclonic are more striking, the in- 
 clination in the front part of the cyclone being outward or 
 negative. But the resultant velocity deduced from these results 
 is from N. 65 W. 28 miles per hour, while in Fig. 8 the direc^ 
 tion of progressive motion was assumed to be from a point a 
 little S. of W. If we assume that the cyclonic velocity on the 
 average was 30 miles per hour and the inclination at this alti- 
 
 Fig. 10. Fig. II. 
 
 tude 10, the results of such an assumption with the progressive 
 velocity and the direction given above are represented by Fig. 
 ii. By comparing this with the preceding figure, it is seen 
 that the results are very nearly the same, and so are accounted 
 for by a cyclonic motion as assumed above. 
 
 In cyclonic motions at a considerable altitude the inclination 
 is outward and not inward, as represented in Fig. 8 ; and so for 
 the same velocities of progressive motion the inclination of 
 the resultant ac in front is greater and in the rear less above 
 than at the earth's surface. 
 
 205. We come now to the examination of the results ob- 
 tained by Mr. Ley from observations of the upper currents 
 already given in the table of 180. From a mere inspection of 
 
CYCLONES. 
 
 the angles given in this table for the several districts it is 
 readily seen that they result from a cyclonic motion with a. 
 considerable outward inclination, combined with a large pro- 
 gressive motion in the direction of the progress of the area 
 of depression, or nearly so, represented by the large arrow 
 in Fig. 3. Let A, B, C, etc., in Fig. 12 represent the cen- 
 tres of the several octants in Fig. 3, and let Aa, Ba, Ca y 
 etc., represent the velocities of cyclonic motion, having an 
 outward declination of about 30; and also ab represent the 
 velocity of progressive motion of the upper atmosphere in the 
 direction of the motion of the centre of low-pressure area, rep- 
 
 Fig. 12. 
 
 resented by the arrow, and let us also suppose that this lat- 
 ter velocity is very nearly equal to that of the cyclonic velocity 
 Aa, Ba, Ca, etc. The resultants will then be represented by 
 Ab, Bb, Cb, etc. It is readily seen that the effect of the pro- 
 gressive component is to increase the angles with the radius in 
 the front and to diminish them in the rear. The effect is 
 similar to that on Mt. Washington represented in Fig. 10. 
 It is seen that the largest angles with radius are in the dis- 
 tricts B, C, and D, and the smallest those of F, G, and H. By 
 a reference to the column of " Mean angles with radius" in 
 the table of 180, it is seen that this is very nearly the case, 
 there being two exceptions in the inner districts, in which the 
 maximum in front and the minimum in the rear seem to be a 
 little more toward the north and south sides respectively. In 
 
THE EYE OF THE STORM. 311 
 
 vague observations of this sort it cannot, of course, be expected 
 that any hypothesis would give a nice agreement with obser- 
 vation in quantitative results. 
 
 It is seen from Fig. 12 that the resultant velocity in the 
 octant A is very small, and consequently the average angle 
 from observation very uncertain. In fact, the progressive 
 velocity so nearly counteracts the cyclonic, that this must be 
 a district, on the average, of calms rather than of currents. 
 This is in accordance with the observations of Mr. Ley, who 
 with regard to this district remarks that " the upper current, 
 which had previously nearly coincided in direction with the 
 trajectory, presently changes, as a rule, to a nearly opposite 
 point, having just before become very slow. In the interval 
 the cirrus, when visible, which is rarely the case, is sometimes 
 stationary, sometimes moves towards, and sometimes from, 
 the centre of depression, these three instances being nearly 
 equally common, but calms and motions toward the centre 
 predominating." 40 
 
 THE EYE OF THE STORM. 
 
 206. In all parts of the world there appears to be in the 
 central part of most at least, if not all, cyclones a thinning 
 of the cloud-stratum and a partial, and sometimes complete, 
 clearing away of the clouds. This was observed by Dove at 
 Konigsberg as early as the year I82/. 13 He says: 
 
 " Whenever the equatorial current sets in suddenly and is as sud- 
 denly displaced again, at the precise time when the barometer is at its 
 lowest level, the showers which belong to the equatorial current are 
 separated from those produced by the intrusion of the polar current 
 into it by a short period of clear weather, to which I gave the* name of 
 'clear interval.' At the centre of a cyclone, when the barometer is 
 lowest, a similar fine moment is so frequently observed that sailors have 
 given it a special name, ' the eye of the storm.' Captain Salis describes 
 its occurrence in a cyclone experienced by the ship Paquebot des Mers du 
 Sud, in latitude 38 S., longitude 22 E., in these words : ' While there 
 was a dense bank of clouds all round us, the sky over our heads was 
 quite clear, so that we could see the stars, one of which, right over the 
 head of the foremast, was so bright that every one on board noticed it. 
 The barometer was 27.79 inches English.' " 
 
312 CYCLONES. 
 
 Dove here has in mind the old idea of a constant wrestling- 
 between equatorial and polar winds, and makes a distinction 
 between what he observed and what is seen in the central part 
 of tropical cyclones. But in fact he simply observed what oc- 
 curred in the passage of the centre of cyclones, modified how- 
 ever in high latitudes by the trough-phenomena ( 193). 
 
 The following quotation taken from an account of a cyclone 
 in the Arabian Sea, by Dr. Malcolmson, is given by Pid- 
 dington : 
 
 " During the height of the storm the rain fell in torrents, the lightning 
 darted in awful vividness from the intensely dark masses of clouds that 
 pressed down, as it were, on the troubled sea. In the zenith there was 
 'visible an obscure circle of imperfect light of ten or twelve degrees." 
 
 With regard to the cyclone of October, 1848, in the Bay of 
 Bengal Piddington further says : 
 
 "The superintendent of the light-house at False Point, Palmiras, 
 distinctly states that at the time of the passage of the centre, or for 
 about two hours of calm, the stars were seen very clear overhead, with a 
 thick bank of haze all round." 
 
 This feature of cyclones seems to belong mostly to tropical 
 latitudes. Abercromby &0 says : 
 
 " The tropical cyclone has a striking feature which is absent in our 
 latitudes : There is a patch of blue sky over the calm centre, which is 
 well known in hurricane countries as the ' eye of the storm,' or as a 
 ' bull's-eye/ " 
 
 From the fact that it was noticed by Dove, the phenome- 
 non does not seem to be entirely absent in higher latitudes, 
 though it is undoubtedly less distinctly manifested than in 
 tropical latitudes ; and the name is not so appropriate as it is 
 in the case of the small tropical cyclones in which the clear 
 patch seems to be small and often very distinct, and which 
 consequently gave origin to the name. 
 
 Every one perhaps has observed in ordinary rain-storms that 
 after it has rained for some time there is frequently a cessation 
 of rain at least, if not a partial clearing away of clouds, as 
 though the storm had all passed by ; but after a short time 
 
THE EYE OF THE STORM. 313 
 
 there is a thickening and a darkening of the clouds and a sec- 
 ond shower of rain. Indeed, of so frequent occurrence is it 
 that it is generally remarked that the latter is the " clearing-up 
 shower," as though it were a matter of course, and to be ex- 
 pected before the final clearing away. 
 
 207. The origin and explanation of these phenomena are 
 to be found in temperature conditions, such as assumed in the 
 table of 159, which give rise to a vertical circulation which 
 does not extend to the top of the atmosphere, often to a mod- 
 erate height only, and which, except so far as it acts upon the 
 upper part of the air by friction merely, gives rise to cyclonic 
 motion in the lower strata only. It was the opinion of Red- 
 field that our great revolving storms do not generally extend 
 to a greater altitude than a mile, and this is no doubt some- 
 times the case ; for the cirrus clouds sometimes seen through 
 an opening of the lower clouds, the eye of the storm, fre- 
 quently appear to be undisturbed by the storm beneath. But 
 at other times, we know, and this is frequently the case, the 
 highest cirrus clouds are brought into the whirl, and have a cy- 
 clonic motion. If the conditions are such in the upper part of 
 the atmosphere that the ascending current becomes colder in- 
 stead of warmer than the surrounding part of the atmosphere, 
 of course it ceases to ascend and is deflected off horizontally in 
 .all directions before reaching that level. As the gyratory mo- 
 tion depends upon the vertical circulation, this, at least at 
 first, extends up to this level only, but the strata above may be 
 acted upon more or less by friction. The air, charged with 
 .moisture, in its vertical circulation, in toward the centre below, 
 up in the interior to a given altitude, and outward above in 
 the middle strata, necessarily moves in a path somewhat ellip- 
 tical ; so that it is being deflected outward above and still 
 ascends until at a considerable distance from the centre ; and so 
 there is little condensation of vapor in the central part, and the 
 cloud stratum is thin, sometimes entirely wanting. And this 
 state is still further promoted by the gyratory motion, which is 
 confined mostly to the lower and middle strata, bringing the 
 .air down from above, it may be, down pretty low, into the' inte- 
 
CYCLONES. 
 
 rior central part, where it is carried out horizontally on alP 
 sides ; and the descending air in the interior above is of course 
 clear air. The effect under such conditions is a thinning of 
 the cloud and a scantiness of condensation and rainfall in the 
 centre, a ring of deeper and denser cloud at some distance 
 from the centre, which gradually shades off to the outer limit. 
 Where, however, the conditions give rise to a vertical or cy- 
 clonic circulation up to very high altitudes, this phenomenon 
 is perhaps never observed. 
 
 The tendency of the air in the interior of a cyclone to set- 
 tle down, and thus to either partially hinder the ascending cur- 
 rents and the cloud-formation, and so to cause a thinning of 
 the cloud, or to even cause a gently descending current and a 
 complete clearing off here, is no doubt caused often by the fall- 
 ing of a great amount of comparatively cold rain from the upper 
 strata, which, both from its weight, which is partially sustained 
 by the air in falling, and also from the cooling effect, increases* 
 the downward pressure in the centre. And this would espe- 
 cially be the case in tropical cyclones, where the air ascends: 
 more vertically and symmetrically on all sides, and the rain is; 
 not mostly carried away in front of the centre before it falls. 
 Hence the central partially or wholly clear space is mostly 
 observed in these cyclones. 
 
 In the regular progression of a cyclone in the middle lati- 
 tudes somewhat centrally over a place, the cloud and rain area 
 of the front part, extending far toward the east, first passes- 
 over, occupying a half-day, or a day and more, and then the 
 front part of the ring of dense cloud with a heavy shower of 
 rainfall. After this there are indications of a clearing up, and 
 even the sun may break through the cloud for an hour or two ; 
 but presently there is an apparent gathering and thickening of 
 the cloud and a second shower. This is at the time of the 
 passage of the rear side of the ring of denser cloud. After 
 this there is the final clearing up. 
 
 It is not to be supposed that this is a regular occurrence in* 
 every rain-storm, or that the cloud ring in the special cases of 
 favorable conditions is regularly formed on all sides, but simply 
 
SECONDARY CYCLOXES. 31$, 
 
 that in general the tendency is toward the formation of such a 
 ring. 
 
 SECONDARY CYCLONES. 
 
 208. It often happens that the conditions of a smaller 
 cyclone, such as described in 157, or even several of them, are 
 contained within the limits of a larger one. The isobars then, 
 which in a perfectly regular cyclone are circular, become very 
 irregular. The contained cyclone may be such as to give a sec- 
 ondary minimum pressure, or it may simply produce derange- 
 ments in the regularity of the isobars of the primary cyclone. 
 Where the isobars become crowded, and consequently the baro- 
 metric gradients steeper, the velocities are likewise greater ; for 
 in such places the motions of the primary and secondary cy- 
 clones are somewhat in the same direction. Where, however, 
 the isobars are farther apart, and the gradients consequently 
 smaller, the velocities are also smaller, since there the motions 
 are nearly in contrary directions, and partially or quite neutral- 
 ize each other. 
 
 Fig. 13 represents the effects of secondary cyclones con- 
 tained in a primary, upon the isobars and the directions of the 
 wind. In the one on the left the depression is not sufficient to 
 give rise to a secondary minimum of pressure, but merely to 
 cause considerable derangement of the isobars, crowding them 
 together on the one side* and widening them on the other, and' 
 changing somewhat the velocities and directions of the wind. 
 The one on the right being more violent and the depression 
 deeper, produces a secondary centre of low pressure, with 
 the wind blowing around it, but with much greater velocity on 
 the right side, where the directions of the currents of both the 
 larger and the smaller cyclone coincide, than on the other side 
 where the cyclonic motion of the smaller cyclone is but little 
 greater than that of the larger in the contrary direction. The 
 ring of high barometer of the large cyclone is increased in- 
 height in an irregular manner by those of the smaller ones fall- 
 ing upon it. There are usually many smaller secondaries of 
 this sort, which tend to distort the isobars, and to cause irregu- 
 
CYCLONES. 
 
 larities in the velocities and directions of the wind as the cy- 
 clone and its secondaries pass over any place of observation. 
 
 Secondary cyclones occur mostly in the southern and east- 
 ern quadrants of a cyclone, in which the air is warmer and 
 moister than in the other quadrants, and where consequently 
 -the conditions are more favorable for the origination and main- 
 
 Fig. 13. 
 
 'tenance of these smaller cyclones. They are rarely, if ever, 
 found in the other quadrants. 
 
 209. Of course each secondary cyclone gives rise to an area 
 of more dense cloud and more abundant rainfall within the 
 large one. The amount of rainfall, therefore, in a large cyclone 
 may be very unequally distributed, large amounts of rain fall- 
 ing in some places, while at others at no great distance off, lit- 
 tle or none falls. In fact, the larger cyclone may be such as 
 to give rise to cloudiness mostly, and to little or no rain, while 
 there are numerous small secondaries contained within it, 
 which cause heavy rainfalls over limited areas. In the pro- 
 gressive motion of a primary cyclone, with its numerous small 
 secondaries, each one of the latter, as it arrives at any place, 
 
SECONDARY CYCLONES. 317- 
 
 causes an increase in the density and darkness of the clouds, 
 with a shower of rain of longer or shorter duration, and greater 
 or less abundance, after which the general cloudiness, or per- 
 haps very moderate rainfall, prevails until a new secondary 
 arrives, when the same thing occurs again. Such weather is 
 called showery weather. After the whole of the large cyclone 
 has passed over, the showers cease and the weather for a while 
 becomes settled. 
 
 While all areas of low barometer, whether of primary or 
 secondary cyclones, are generally areas of more or less rainfall,. 
 or at least of cloudy weather, it is not to be supposed that 
 there may not be much cloudy weather and rain without any- 
 sensible barometric depression. The atmosphere over a large 
 area of the earth's surface may be nearly saturated with 
 aqueous vapor, and nearly or quite in a state of unstable equi- 
 librium, and yet the temperature conditions may not be such 
 as to give rise to a vertica.1 and a cyclonic circulation over an 
 area sufficiently large to cause a sensible depression in the 
 middle, and yet the vertical circulation and the ascension of 
 moist air may be sufficient to give rise to much rain. For it 
 must be remembered that a barometric depression depends, 
 not only upon gyratory circulation, but also upon extent of 
 area, and where the area is small, the barometric depression 
 becomes sensible only in the case of rapid gyrations, to which 
 the conditions may, or may not, give rise. When the atmos- 
 phere is in the condition described above there are often many 
 local rains, with little cyclonic action, and consequently little 
 wind, or damp, sultry weather may prevail with little or no rain. 
 But if, after a time, the temperature conditions become such 
 as to cause an initial inflowing of air over a large area toward 
 some central point, and a vertical and cyclonic circulation 
 over this area, this gives rise to a cyclone ot considerable ex 
 tent, and when this, by its usual progressive motion, has passed 
 away in a day or two, the damp drizzly weather is changed 
 and followed by fair weather. 
 
3 1 8 CYCLONES. 
 
 f 
 
 STATIONARY CYCLONES. 
 
 210. If, for some reason, there is a local and permanent 
 -cause of temperature disturbance between the central and 
 exterior part of any somewhat circular portion of the atmos- 
 phere, we have the conditions of a cyclone which is indepen- 
 dent of the state of unstable equilibrium, but which would be 
 aided and strengthened by such a state. The cause of the tem- 
 perature disturbance being fixed, of course the cyclone cannot 
 have a progressive motion. 
 
 The rough approximate conditions of such a cyclone are 
 found in the northern part of the North Atlantic Ocean, where 
 there is a large area over which the temperature is higher than 
 that of the surrounding parts, and this is especially the case in 
 the winter season. The central part of this area of higher 
 temperature is near Iceland, where the mean annual temper- 
 ature is about 16 F. above the normals of latitude for the 
 year, given in the table of 68. In January, however, the 
 temperature on the continents in these latitudes has become 
 very much less, while that of the ocean has changed but little, 
 so that at that time the abnormals of temperature are at least 
 twice as great, and likewise the difference between the temper- 
 ature of this area and that of the surrounding parts of the 
 atmosphere, so that now we have the conditions of a cyclone of 
 about twice as much energy as in the case of the average for 
 the year, or during the spring and fall. But in July the reverse 
 takes place ; there is then an equalizing somewhat of the tem- 
 peratures in all longitudes, and the abnormals of temperature 
 are very small. 
 
 Similar conditions are found in the northern part of the 
 North Pacific Ocean, but not so marked. The greatest abnor- 
 mal temperature for the mean of the year is only about 8 F., 
 and that for January a little more than twice as much. Hence 
 in the northern parts of both the Atlantic and Pacific Oceans 
 we have roughly the conditions of a permanent cyclone at all 
 seasons except the summer season, the effects of which upon 
 
STATIONARY CYCLONES. 319 
 
 the winds and the barometric pressures of these regions are 
 observed, especially during the winter season. 
 
 In the North Atlantic Ocean the cyclonic winds on the 
 southern side of this great and permanent cyclone in winter, 
 with its centre near Iceland, coinciding in direction with the 
 general westerly winds of these latitudes on the Atlantic Ocean, 
 produce unusually strong westerly winds at this season ; but 
 adjacent to Great Britain and the coast of Norway they come 
 more from a southwesterly direction, and then, curving around 
 toward the extreme northern part of the ocean, and on the 
 northern side of the cyclone, in Greenland and adjacent to it 
 on the ocean, the winds are from the N.E. This cyclonic 
 motion causes a barometric depression in the centre in winter 
 of about 10 mm. below the normal mean pressure of the lati- 
 tude. 
 
 In the summer season the temperature of that region is so 
 nearly the same as that of the surrounding regions, and of the 
 normal temperature of latitude, that there is no sensible cy- 
 clonic action or barometric depression, and the winds which 
 prevail there are the westerly winds of the general motions of 
 the atmosphere in these latitudes. 
 
 211. In the region of the cirrus clouds above the winter 
 cyclone of the lower strata of the atmosphere over the North 
 Atlantic Ocean, the motion of the air, in the exterior part at 
 least, is anti-cyclonic, and consequently over the British Isles 
 and Europe generally the winds have a considerable north 
 component, which, combined with the large east component 
 of the general motion of the atmosphere at high altitudes, 
 causes their directions to be from a point more to the N. of W. ; 
 while in the summer season, when there is little or no cyclonic 
 effect, the general westerly winds at high altitudes are not 
 sensibly disturbed. There is, therefore, an annual inequality 
 in the observed directions of the cirrus clouds over these re- 
 gions, the directions being, according to theory, from a point a 
 little more to the N. of W. in winter than in summer. This is 
 found to be the case from observation. Taking the averages 
 
3 20 
 
 CYCLONES, 
 
 of the angles $ for each month, given by the late J. A. Brown, 
 1 80, we get : 
 
 October April, i/> = 284 
 , May September, t/> = 268. 
 
 Hence it is seen that during the summer half of the year the 
 currents are almost exactly from the west, as they should be, 
 for if entirely undisturbed by the anti-cyclonic action they 
 should be from a point a little S. of W., since the motion of 
 the atmosphere above is slightly poleward. But during the 
 winter half year they are from a point 1 6 more toward the 
 north, because now there is a northerly component arising from 
 the anti-cyclone of the cirrus regions. 
 
 A similar result has been obtained from observations made 
 on the upper clouds at many places in Europe, by Dr. Hugo 
 Hildebrand Hildebrandsson. 66 His results are contained in 
 the following table : 
 
 ZONES. 
 
 WINTER. 
 
 SUMMER. 
 
 YEAR. 
 
 Below 760 mm. (minimum) 
 Above 760 mm. (maximum) 
 
 W. 7 42' N. 
 W. 42 12 N. 
 
 W. 11 30' S. 
 W. 23 24 N. 
 
 W. 2 2 4 ' S. 
 
 W. 31 o N. 
 
 Mean 
 
 W. 16 54 N. 
 
 W. 3 24 N. 
 
 W. 10 54 N 
 
 
 
 
 
 Taking the general mean, we find that the direction in win- 
 ter is from a westerly point 13 30' more toward the north in 
 winter than in summer, and that in the latter season it is very 
 nearly from the west, as it should be. Taking the results for 
 the two zones separately, it is seen that in each the difference 
 between winter and summer is very nearly the same, but that 
 for the average of the whole year the direction is from a 
 westerly point 33 24' farther north in the pressures above 760 
 mm. than in those below 760 mm. This is in accordance with 
 theory; for the low pressures are more in the interior of the great 
 cyclone, where the gyrations above, at least in the lower cloud- 
 region, may not only have little anti-cyclonic motion, but even 
 some cyclonic motion, and hence the directions should be from 
 a point farther south than in the outer border, in the zone of 
 
STATIONARY CYCLONES. 321 
 
 high pressures, where the great anti-cyclone above may extend 
 over all Europe. 
 
 Of course, the individual observations are affected by the 
 varying pressures of every transient cyclone passing along, but 
 in the averages of great numbers of observations the effects of 
 these are mostly eliminated, and we have left mostly that of 
 the great stationary cyclone only. 
 
 212. The conditions of an ordinary stationary cyclone are 
 found in summer on every island in the ocean ; for since the 
 annual range of temperature on land is much greater than that 
 of the ocean, the mean annual temperature on land and sea 
 being very nearly the same, the island in summer, especially in 
 high latitudes where the annual temperature changes are great, 
 becomes very much warmer than the surrounding ocean. And 
 this is not merely an incipient condition, such as is required 
 generally to originate a cyclone when the other conditions of 
 proper vertical temperature gradient and hygrometric state are 
 present, but it is continuous, especially during the day, and 
 keeps up the vertical and cyclonic circulations independently 
 of the other conditions. Of course this condition is confined 
 to the island, and so there is no progressive motion. The 
 cyclonic action, however, is of no great violence, for the tem- 
 perature differences and gradients are mostly in the lower strata 
 of the atmosphere, and in the great body of air in the upper 
 strata they are small. Their power, therefore, to give rise to a 
 vertical, and so to a cyclonic, circulation is small, but this is 
 very much increased where the interior of the island consists, 
 of highlands, as has been explained in 132 in the case of 
 monsoons. 
 
 Australia furnishes such conditions in some measure, but 
 the island comprises too great a range of latitude for a perfect 
 cyclone, which requires that the area shall be of smaller extent ; 
 and besides it is too near the equator for the influence of the 
 earth's rotation to be considerable, especially on its equatorial 
 side. The effect, therefore, arising from the temperature con- 
 ditions here has been treated as monsoonic and not cyclonic^ 
 
322 CYCLONES. 
 
 though some allowance has been made for the deflecting force 
 of the earth's rotation upon the directions of the winds. 
 
 During the summer season the great continents of Europe, 
 Asia and America are heated up considerably above the sur- 
 rounding regions, which give rise to vertical circulations, inward 
 below and outward above, giving rise to the summer monsoons, 
 and causing considerable barometric depressions in the interior, 
 especially in Asia, but the areas are of too great extent and 
 comprise too great a range of latitude for much cyclonic effect 
 to be produced, and the lower pressures in the interior are to be 
 attributed almost entirely to the differences of temperature, and 
 very little, if any, to cyclonic gyrations. The influence, how- 
 ever, of the deflecting force of the earth's rotation upon the 
 directions of the monsoon winds is no doubt considerable. 
 
 COLD WAVES AND NORTHERS. 
 
 213. It frequently happens in. the United States during the 
 winter season that there are large and progressive areas of in- 
 tense cold which originate mostly in the extreme Northwest 
 and progress easterly and southeasterly, frequently as far as the 
 Atlantic Ocean. On account of the great contrast between 
 the temperature of this air and that which it encounters, its 
 easterly progression causes very great and sudden changes of 
 temperature, and hence it is called a " cold wave." Those 
 down in Texas are generally called " Northers." 
 
 These cold waves have been investigated by Lieut. Wood- 
 ruff 5? of the Signal Service, for the years 1881-84. He finds 
 that they occur in winter only, and more in January than in any 
 other month ; that 86 per cent originate east of the Rocky 
 Mountains and 14 per cent come across these mountains, and 
 that by far the greatest number travel across the country from 
 Helena, Montana, to the Atlantic in 32 to 40 hours. He gives 
 instances of temperature changes of 40 to 50 F. in 24 hours. 
 
 These cold waves are closely connected with, and form a 
 part of, the cyclones which pass over the United States, and 
 an explanation of them has been already partially given in the 
 
COLD WAVES AND NORTHERS. 323 
 
 explanation of the trough-phenomena and weather sequences 
 in the passage of a cyclone over any given place ( 193). The 
 whole cold area, however, is not due entirely to the whirling of 
 colder air from higher to lower latitudes on the west side of the 
 cyclone, but also, in a great measure, to the increased terrestrial 
 radiation in winter through the clear air on the clearing-up side 
 of the cyclone, especially on the high plateaus east of the 
 Rocky Mountains. The easterly progressive motion of this 
 <:old air west of the Mississippi River is increased by the easterly 
 slope of this plateau, upon the same principles that winter mon- 
 soons and land winds are, in the case of high and sloping pla- 
 teaus in the interior of a country ; so that the cold stratum is 
 actually forced under a cyclone a little beyond the centre, but 
 cannot advance faster than the cyclone which it follows, and 
 upon which it in a great measure depends for its origination 
 and continuance. 
 
 214. That a cold wave is simply the rear part of a cyclone 
 with the degree of cold mpre than usually intensified by certain 
 favorable circumstances, is evident from the fact that we have 
 preceding and accompanying it the same sequences of tempera- 
 ture, wind, and pressure which are observed in high latitudes in 
 the passage of cyclones in the winter season, when the trough- 
 phenomena are developed. There are first southeasterly and 
 southerly winds, moist air, increasing cloudiness and rain, and 
 low pressure ; then follow a sudden change of the wind to the 
 north or northwest, a rapid increase of pressure, and a lower- 
 ing of the temperature. Lieut. Woodruff says: 57 
 
 " In studies upon the origin and movements of areas of high and low 
 barometer it has been shown generally that they move almost invariably 
 across the United States from west to east. The determination of the 
 movement of the area of low barometer largely determines the move- 
 ment of the following high. Now most of the areas of low barometer are 
 formed in the region east of the Rocky Mountains, and as these areas 
 move eastwardly the high moves in, and we have accompanying a cold 
 wave of more or less intensity. Even if the low area pursue an abnormal 
 track the circulation of the winds about the high and low is such as to 
 produce almost invariably a decided fall in temperature, if the low be 
 eastward of the high." 
 
324 CYCLONES. 
 
 In the general easterly progression of the atmosphere, and' 
 by the unusually high pressure in the Northwest of the United 
 States at the time of cold waves, it is possible that a thin 
 stratum of the lower very cold air travels entirely across to the 
 Eastern States; and this, when the temperature of the earth's 
 surface is very low, and especially when it is covered with snow, 
 which prevents the heat of the earth below from coming through 
 readily to warm up the air above, continues very cold all the 
 way. Under these conditions the flow of air from the north 
 or northwest may extend to a long distance before its tempera- 
 ture is much changed. The coldest winter weather is experi- 
 enced in the middle and southern latitudes of the United States, 
 when the whole country is covered with snow, and there is an 
 area of very high barometer and low temperature in the north- 
 ern part, or in British America. But whether the air in the 
 rear of a cyclone comes from the extreme Northwest, or directly 
 down from higher latitudes, we are not safe in predicting a 
 cold wave in the middle and southern latitudes, from the 
 occurrence of an area of very high barometer and low tempera- 
 ture in the North or Northwest, if the intervening surface of 
 the earth is warm and uncovered with snow, since the stratum 
 of cold air becomes warmed up before it travels very far. 
 
 The cold waves are said to not occur in summer, but even 
 in this season there are similar changes, but of course not so 
 marked, which give rise to agreeable changes from very warm 
 to cooler weather, and which may be called " Cool Waves." 
 
 As most of the areas of low barometer, or, in other words, 
 cyclones, originate in the region east of the Rocky Mountains, 
 so the cold waves, which are their rear parts, we have seen, 
 originate there also, and both progress across to the Atlantic 
 Ocean together. 
 
 Again Lieut. Woodruff says : 
 
 "It is observed that some of the severest 'northers' in Texas occur 
 when an area of low barometer appears near the coast, the winds at Gal- 
 veston and Indianola are easterly, and the temperature high; the 'low' 
 moves northeasterly, the winds back to northerly and northwesterly, and 
 the temperature falls more or less rapidly, according to the rapidity- 
 
COLD WAVES AND NORTHERS. 325 
 
 with which the low moves off. If the storm have considerable energy, 
 the ' norther' is severe and sudden." 
 
 Here again the cold wave or norther is the west side of a 
 cyclone, and the intensity of the former seems to depend upon 
 that of the latter. The northers of Texas are noted for the 
 greatness and suddenness of the changes from high to low tem- 
 peratures. The cyclone here which gives rise to the northers 
 being near the coast of the Gulf of Mexico, and the contrast 
 in winter between the temperature of the land and the Gulf 
 being very great, the warm air of the Gulf is carried northward 
 over the land on the east side of the cyclone, while the colder 
 air of higher latitudes is brought down on the west side, and 
 pressing under the cyclone, comes in contact with, and rather 
 meets, the southeasterly much warmer and moister air on the 
 other side ; and when this line of meeting, or trough of the 
 cyclone, passes over a place, there is a great and sudden change 
 of temperature. 
 
 215. An interesting and instructive paper on the northers 
 of Texas was read at the meeting of the American Association 
 for the Advancement of Science about 20 years ago by Solomon 
 Sias, 58 who seems to have resided in Texas for some time and 
 to have made many observations of them. The following ex- 
 tracts are taken from this paper and given here with the ex- 
 planations and comments following : 
 
 "The wind from whatever quarter blowing, usually S.S.E. or S.W., 
 either entirely dies away or very materially slackens, and is changed to 
 -a cold, piercing north wind. This is a norther. . . . Frequently, we 
 may say usually, the change is so sudden and marked that a person 
 standing in the open air feels it slap him with a chilling roughness, and 
 almost immediately the moisture is dried upon him which the preceding 
 warmth had produced. While riding over the prairies, uncomfortably 
 warm in the lightest clothing, I have repeatedly been struck by them, 
 and before I could wrap my blanket around me, been as uncomfortably 
 cold." 
 
 " Sometimes, instead of changing, the preceding wind dies entirely 
 ^away, and a dead, oppressive, suffocating calm ensues, to be broken in a 
 few hours by the wild bursts of the descending norther." 
 
 "They frequently commence faint as a summer's zephyr, again bend 
 the trees like reeds, and I have known the brick walls of our Institute to 
 
326 CYCLONES, 
 
 quiver at the first striking of the blast. . . . They die down in a few- 
 hours to a force of about two, hold at this rate perhaps a day or so, then, 
 fade entirely away." 
 
 "The wind in a norther is not always strictly from the north ; it fre- 
 quently veers for a few hours, to N.E. or N.W., or back and forth be- 
 tween these points, and I have known it to give way completely for an 
 hour or two to a southerly wind. This veering and changing, however, 
 seldom occurs in the early stages, or in a norther of a high degree." 
 
 " The total number of northers in a year varies from thirty-five to- 
 forty- eight ; the average is about forty-two or forty-three. We are told 
 they commence the last of September and end in May; but meteorolog- 
 ical observations show they commence earlier and end later; in fact,, 
 there is no month in which they may not occur." 
 
 "The thermometer frequently falls rapidly at their commencement,. 
 it is said, sometimes seventy degrees in fifteen minutes ; but I have 
 never witnessed such rapid or extreme falls. The greatest I have noted 
 is twenty degrees the first hour and fifteen the next, making thirty-five 
 degrees in two hours; and this is a very exceptional case." 
 
 " Usually the barometer commences falling from two to six days before 
 a norther sets in, and drops down slowly but pretty regularly until the 
 first stroke of the norther, when it rises rapidly. Frequently the fall is 
 more rapid just before the change; and I have often been led to the be- 
 lief that a norther was close at hand by this phenomenon, in the ab- 
 sence of othej usual indications, and I do not remember ever being dis- 
 appointed. And the almost invariable fact that it rises the moment one 
 begins has sometimes been my first and surest evidence that one is 
 blowing." 
 
 " The northers may be divided into two classes, the wet, or those 
 accompanied by rain, sleet, or snow; and the dry, in which the sky is 
 clear, or but partially covered with clouds. If the preceding wind has 
 been east or south, we usually look for a wet norther ; if it has been 
 directly south, the sky laden with clouds, and the norther does not 
 scatter them immediately, it may be wet; if the wind has been west of 
 south, it is usually a dry norther." 
 
 "The northers are mere surface winds. When the wind is ranging 
 from three to five, the clouds, and even down, are frequently seen float- 
 ing in the opposite direction. The gusts of wind sometimes seem to 
 actually roll along the ground." 
 
 As heralds of the approach and attendants during the 
 progress of a norther, Mr. Sias states : 
 
 "A warm, moist wind blows from some southerly quarter a few days ; 
 the thermometer rises; the barometer sinks slowly, then rapidly; the 
 
COLD WAVES AND NORTHERS. 327 
 
 wind materially slackens, veers to the west or gives way to a dead, op- 
 pressive calm ; and lastly, a peculiar dark cloud-like appearance forms 
 in the northwestern horizon, slowly rises, and when in a few hours it 
 reaches an angle of thirty or forty degees, the norther bursts upon us." 
 
 " The attendants are usually the immediate rise of the barometer and 
 falling of the thermometer ; sometimes a dash of rain, occasionally the 
 ozonic smell and curdling of the air; almost invariably the rapid disap- 
 pearance of the northern cloud-like formation; and frequently so great 
 a reduction of temperature that a frost or freezing occurs out of season." 
 
 216. From a mere reading of these extracts and those from 
 Lieut. Woodruff's paper, and comparing them with 193, it is 
 seen that in cold waves and northers we simply have the usual 
 trough-phenomena of cyclones in their passage over a place, 
 where these phenomena are well marked. These, we have 
 seen, occur mostly in winter, and in latitudes where cyclones 
 have an easterly progressive motion, and rarely in summer ; 
 and precisely the same is true of cold waves and northers. In 
 all there are, first, mostly southerly and southeasterly, warm 
 and damp winds, accompanied by a gradually falling barometer, 
 which toward the last becomes very rapid. Then comes the 
 dividing line between the warm southerly and southeasterly, 
 and the cold northwesterly winds, which, on account of the 
 great difference of temperature, do not readily mix, and so 
 there is a sudden passage from the one to the other. There is, 
 on this line, a very steep pressure gradient for a short distance, 
 which, however, soon passes over, and during this time the 
 squalls are often terrific ; after which there are, for several days, 
 the usual westerly winds of the rear of the cyclone. Some- 
 times, however, it seems that there is not this very sudden 
 change, but the central dead calm is observed for a short time. 
 This is, no doubt, when the centre of the cyclone passes over 
 the place, and when, for some reason, the trough-phenomena 
 are not so well developed as usual. 
 
 The northers, like cyclones, mayor may not be accompanied 
 by rain, that is, at any given place, though there is, perhaps, 
 always more or less rain somewhere. When the preceding 
 winds are west of south, as they are mostly when the track of 
 the cyclone is on the north side and the place is on the south 
 
328 CYCLONES. 
 
 side of the cyclone and out of the rain area, there is no rain, 
 and the norther is called a dry norther. On the other hand, 
 if the preceding winds are southeasterly, as they are when the 
 central part or the northern side of the cyclone passes over the 
 place, and this falls within the rain area, the norther is called a 
 wet norther. 
 
 The norther is said to be a mere surface wind, and the 
 clouds above are frequently seen floating in the opposite direc- 
 tion. A stratum of the cold air of no great depth is naturally 
 forced under the warmer and lighter air on the southeast side 
 of the cyclone, where the usual cyclonic motions, giving rise to 
 southerly and southeasterly winds, prevail. Besides, at the 
 dividing line, where the pressure gradient is very steep for a 
 little distance, and the air rushes out with great velocity, there 
 is a return current above at no great height. 
 
 At the line of meeting of the winds of nearly opposite 
 directions and great contrasts of temperature, the warm moist 
 winds are thrown up, and somewhat over the stratum of cold 
 air which they meet, and the cooling of this moist air, both by 
 ascent and by coming into contact with the cold air, causes the 
 usual " dark, cloud-like appearance which forms in the north- 
 western horizon/' and which is usually seen at some distance, 
 and for some time before the norther arrives, but which gen- 
 erally soon passes by. In high latitudes, where the colder air 
 is below the freezing-point, the mingling of the warm and 
 moist air with it gives rise not only to a very strong wind, but 
 also to a dense snow-storm, called a " blizzard," * in which per- 
 sons who are caught are sometimes unable to find their way 
 to a place of shelter and protection, and often perish. 
 
 Since cold waves, by the preceding explanation, depend 
 upon cyclonic gyration and a large temperature gradient in a 
 north and south direction, they should not only abound mostly 
 in winter when the gradient at any place is largest, but also in 
 countries where, at the same season, this gradient is greatest. 
 
 * This term is said to have had its origin amongst the Germans of Dakota, 
 who called a wind of this sort a blitzartig (lightning-like) wind, and finally a 
 blitzart simply, which was changed by the English settlers to blizzard. 
 
PAMPEROS. 329 
 
 In the Mississippi valley, between the warm Gulf of Mexico 
 .and the cold regions of the northern and northwestern part of 
 North America, the temperature gradient is very steep. And 
 as the changes depend upon the progressive motions of the 
 cyclones, these changes should be most sudden where the pro- 
 gressive motions are most rapid, as in the United States of 
 America. Hence here the cold waves are most numerous, 
 and the changes of temperature unusually great and sudden. 
 This seems to be the view taken of the matter by Dr. Hinrichs, 
 who says (Am. Met. Journal, Feb., 1888): 
 
 " In winter the great thermic gradient of the Mississippi valley is the 
 real cause of the sudden changes in our weather. In this thermic con- 
 trast between the north and the south we have the origin of our blizzards 
 and cold waves. This great difference in temperature makes it possible 
 for us to have a thunder-storm in winter, followed in a few hours by a 
 blizzard. The irregular changes of temperature from day to day are 
 accordingly much greater in the Mississippi valley than in Russia. Our 
 so-called cyclonic storms travel about twice as fast as those in Europe 
 and Russia." 
 
 PAMPEROS. 
 
 217. The pamperos of South America, cold southwest winds 
 from the Pampas, or plains, are the same as the cold waves 
 and northers of North America. This will be at once seen 
 from a few extracts from Dr. David Christison's paper on the 
 pamperos of Central Uruguay : 69 
 
 " The barometer fell pretty steadily from two to four and one half 
 days before the storms, the fall varying from 0.18 to 0.56 of an inch. In 
 two it began to rise some hours before the storm burst, and it may pos- 
 sibly have done so in all. In all it continued to rise for some days after 
 the pampero. 
 
 " The thermometer in all cases showed a marked tendency to rise for 
 some days before the pampero. Unless interrupted by the occurrence 
 of rain, thunder, or a temporary shifting of the wind to a cold southern 
 point, this rise seemed to go on pretty steadily, a few degrees being 
 added every day to the heat, in some instances for more than a week. 
 After the pampero the fall was rapid, but the temperature soon began to 
 rise again, particularly with a change of wind to the east. The coolness 
 produced by the pampero is one of their most striking characteristics. 
 
33O CYCLONES. 
 
 and although it occurs at all seasons, it is particularly welcome in hot. 
 weather. It happened in every one of the twelve cases under considera- 
 tion. Comparing the daily maxima before and after them, the average 
 fall of temperature was 13 F., the least being 4, and the greatest 24. 
 The greatest absolute fall was 44 in 14 hours ; in another instance it 
 was 33 in 6 hours. 
 
 " Thunder accompanied seven, and immediately preceded two others. 
 of the twelve. It also occurred within a few days before or after several 
 of them ; but three were not accompanied with thunder at all. 
 
 "Rain accompanied eight, immediately preceded two, and closely 
 followed another. In some instances it was very heavy, in others quite 
 trifling. There was also a good deal of rain within a few days before 
 them, and a small amount within the same period after them. Only one 
 was quite unconnected with rain. 
 
 " The wind before this class of pamperos almost invariably blew 
 moderately or gently for several days from easterly points, perhaps shift- 
 ing to the N. ; the change to S.W. sometimes takes place from the latter 
 quarter. Any deviation to other points seemed to be quite exceptional. 
 The change to S.W. was sometimes preceded by a calm ; but in most, 
 cases that I had the opportunity of watching closely, the east or north 
 wind continued to blow, although with diminished force, until the. 
 moment when the pampero supplanted it. For some time before this, 
 however, the clouds overhead were either motionless, or moving very 
 slowly from the N.W., more rarely from the N. or W. 
 
 " Perhaps the most striking characteristic of this class of pamperos 
 was the invariably sudden outburst of the wind at its full strength almost 
 from the first. Continuing to blow thus steadily from ten to thirty min- 
 utes only in one case for an hour it then either ceased entirely, or 
 more frequently continued with diminished force for a certain number 
 of hours. The force of these short outbursts varied from that of a strong 
 gale to a moderate puff of wind, but was always sufficient to mark them 
 off distinctly from the preceding or following wind. 
 
 " Sometimes the wind continued in the S.W. for only twelve hours, 
 but never more than three days, before returning to some easterly point. 
 In general it spent the greater part of the time in the S., changing to 
 that quarter soon after the pampero had blown itself out. But in some 
 cases it changed several times between S.W. and S. before reverting to 
 the east." 
 
 From these extracts it is evident that the sequence of phe- 
 nomena preceding and attending pamperos are the same as in 
 the case of cold waves and northers, except that in the direc- 
 tions of the winds, on account of their being in the opposite 
 
THE MISTRAL AND THE BORA. 331 
 
 hemisphere, we must put N. for S. and S. for N. There is first,, 
 for several days, the gradual falling of the barometer and in- 
 crease of temperature with damp winds from E. to N. ; then, 
 sometimes a short calm, but mostly a sudden change of the 
 wind to S.W., which is the pampero proper. This at first is 
 generally very strong, and then more moderate, and is accom- 
 panied by a rapid lowering of the temperature and increase of 
 barometric pressure. But the principal characteristic, as in. 
 cold waves and northers, is " the invariably sudden outburst 
 of the wind at its full strength, almost at the first." They were 
 usually preceded by several days of rain with thunder, as the 
 trough of a cyclone is, and also followed by some rain. 
 
 THE MISTRAL AND THE BORA. 
 
 218. Along the whole northern coast of the Mediterranean* 
 in winter, unusually cold northerly winds frequently prevail for 
 several days, called in the Rhone valley and the Gulf of Lyons 
 the Mistral, in the Adriatic a Bora, and in the Grecian Archi- 
 pelago a Tramontane negra, or Black Norther. These winds 
 are always connected with, and form part of, a cyclone, and 
 are the same as the northers of Texas. They prevail when- 
 ever there is a cyclone so situated in the Mediterranean that 
 the currents of the northwestern side of the cyclone bring the 
 comparatively very cold air from higher latitudes down to the 
 Mediterranean coast ; for along this coast in winter there is a 
 contrast between the land and sea temperature similar to that 
 between Texas and the Gulf of Mexico. But the mistral and 
 the bora are strengthened by the prevailing belt of high 
 pressure north of them in winter, extending from the Atlantic 
 over the Spanish peninsula, France and Austria, on toward the 
 interior of Asia, Woeikoff s " Great Axis of the Continent," " 
 which gives rise to a prevalence of northerly winds at all times 
 along the northern coast of the Mediterranean during the 
 winter. These winds, as those of the cold waves and northers 
 of North America, are also strengthened by any area of high- 
 pressure existing from any cause at the time to the north orr 
 
332 CYCLONES. 
 
 northwest of them, and which may be nearly or quite inde- 
 pendent of the cyclone. 
 
 These winds are especially cold after there has been high 
 pressure and very clear and cold weather over the mountain- 
 ous regions to the north, when the air, very cold from radia- 
 tion from the mountain sides, runs down and settles in the 
 valleys. When all the conditions favorable to the norther are 
 at hand, this very cold air is drawn down to the Mediterranean 
 -coast, and even on to much lower latitudes. " In the eastern 
 part of the Mediterranean, the northerly winds reach to the 
 African coast, continue over Egypt and the Nubian desert, 
 .and have even been felt on the Nile as far south as 8 or 9 
 
 :N." 18 
 
 Since these winds are always connected with a cyclone, they 
 last generally only a few days, until after the cyclone, in its 
 progressive motion, has passed away. There is here, however, 
 usually no sudden transition from very warm and moist to very 
 cold and dry air, as in the case of cold waves and northers, 
 ^since the direction of progressive motion is toward the 
 N.N.E., very nearly in the direction of the trough of the 
 cyclone, or line separating the warm winds on the south- 
 easterly side from the cold winds of the northwesterly side. 
 
 THE FOEHN AND THE CHINOOKS. 
 
 219. It sometimes happens that near the base of a high 
 mountain range for several days there are unusually warm and 
 dry winds coming from the direction of the mountain. These 
 are noted winds on both sides of the Alps, especially on the 
 north side, and are called there and elsewhere the Foehn ; but 
 in the northwest part of North America, east of the Rocky 
 Mountains, Chinooks. Although the true explanation of these 
 winds was given by Espy, yet it is only somewhat recently, 
 since the full explanation of them by Dr. Hann, that they 
 have been generally understood. They are connected with, 
 -and are a part of, cyclones, just as the northers of Texas and 
 :the Mediterranean. 
 
THE FOEHN AND THE CHI NOOKS. 333; 
 
 The effects of several permanent foehns, depending upon 
 the general motions of the atmosphere over mountain ranges, 
 have already been referred to and explained ( 128). In the 
 same manner temporary foehns are produced wherever there is 
 a cyclone so situated as to draw a current of air over a high 
 mountain range, and the effect is particularly marked where 
 this air is drawn from warmer latitudes and is very moist. 
 For then the air is warm at the beginning of the ascent, and 
 being very damp, it is seen from Table III that after having 
 ascended to only a very moderate altitude, its rate of cooling 
 with increase of altitude in its ascent is comparatively slow, so 
 that on arriving at the top it still has a high temperature for 
 the altitude. In its descent, now, it becomes warmed up i C. 
 for each 100 meters, and so on arriving at the base of the 
 mountain on the other side, as it is drawn in toward and 
 around the centre of the cyclone, it has a much warmer tem- 
 perature than that of the surrounding air, and than that which 
 usually prevails at the season. And having lost most of its 
 vapor in ascending to the top of the mountain, it of course 
 becomes a very dry wind after descending to the base of the 
 mountain on the other side, down perhaps to about the same 
 level as that from which it started. 
 
 Dr. Hann has shown that the foehn of Switzerland occurs 
 when there is a large cyclone of considerable intensity with its 
 central depression in the direction of the British Isles, or 
 beyond in the Atlantic Ocean, and high barometer S.E. of 
 the Alps, and the foehn on the south side of the Alps, when 
 the reverse is the case ; that is, when the low pressure is in 
 the Mediterranean S.E. of the Alps and high pressure in the 
 direction of the British Isles. He has given a graphic repre- 
 sentation of each, which may be regarded as typical cases the 
 one of the great foehn of January 31, 1885, south foehn in 
 Switzerland, and the other of the foehn of October 5, 1884, 
 north foehn, on the south side of the Alps. 60 In the case of 
 the south foehn, the wind is drawn across the Alps in the 
 southeast part of the great cyclone, and in the other from the 
 north side by the slight cyclonic action in this case of a cyclone 
 
:334 CYCLONES. 
 
 in the Mediterranean, but mostly forced across by the very high 
 pressure in the direction of the British Isles. The foehn on 
 the north side is generally the most marked, because of the 
 permanent cyclone in the winter season in the north Atlantic ; 
 for the depression of an ordinary progressive cyclone, added to 
 that of the southeastern side of the permanent one, frequently 
 causes a great depression on the eastern coast of Europ.e or the 
 contiguous part of the Atlantic. 
 
 220. The chinook winds of Virginia City, of our North- 
 west Territory, have been investigated by Professor Harring- 
 ton 61 from the bulletins of Weather Reports of the Signal 
 Service for several years. He shows that they are of the same 
 character as the foehns of Switzerland and other places, and 
 defines them to be " warm, dry, westerly or northerly winds 
 -occurring on the eastern slopes of the mountains of the North- 
 west, beginning at any hour of the day, and continuing from a 
 few hours to several days" Again he says: " The chinooks 
 occur when a cyclone is passing to the north of the place of obser- 
 vation" This condition is necessary in order that the westerly 
 wind of the southwesterly part of the cyclone may draw the 
 ;air across the main divide of the Rocky Mountains to the place 
 of observation on the east side. 
 
 The chinooks are felt, more or less, along the whole eastern 
 ^side of the Rocky Mountain range, from the southern part of 
 Colorado at least as far north as Peace River, in British 
 America, and to a considerable distance east of the range, the 
 area in which they are most marked including most of Wyo- 
 ming, much of Montana, and some of Dakota, and they are 
 perceptible as far east as Bismarck, about 500 miles east of the 
 main divide. "A marked effect of the chinooks is the ameli- 
 oration of the winter temperature caused by them. On the 
 arrival of the chinooks the winter appears to yield. The air 
 becomes mild, and to the residents of this naturally dry region 
 appears balmy and spring-like." 61 
 
 To the effect of the frequent occurrence of chinooks in this 
 region, but perhaps mostly to the more permanent foehn effect 
 of the westerly winds due to the general motions of the atmos- 
 
THE FOEHN AND THE CHI NOOKS. 335 
 
 phere, as explained in 128, is due the general mildness and 
 dryness of the winter in comparison with the greater seventy 
 and dampness experienced farther toward the east on the same 
 latitudes. So dry are these warm winds that they immediately 
 evaporate the melted snow, and it seems to pass directly and 
 very rapidly into vapor without wetting and softening that 
 which is left. They are consequently sometimes called " snow- 
 eaters." 
 
 With regard to the chinooks of British America, George 
 M. Dawson 62 of Ottawa, Canada, says : 
 
 "As experienced, the chinook is a strong westerly wind, becoming 
 almost a gale, which blows from the direction of the mountains out across 
 the adjacent plains. It is extremely dry, and, as compared with the 
 winter temperature, warm. Such winds occur at irregular intervals dur- 
 ing the winter, and are also not infrequent during the summer, but being 
 cool as compared with the average summer temperature, are in conse- 
 quence then not commonly recognized by the same name. When the 
 ground is covered with snow, the effect of the winds in its removal is 
 marvellous, as owing to the extremely desiccated condition of the air, the 
 snow may be said to vanish rather than to melt the moisture being 
 licked up as soon as it is produced." 
 
 Similar foehn-like winds are experienced in all parts of the 
 world, under different names, wherever a current of air is 
 drawn or forced over a high mountain range. They are more 
 marked in the winter season of high latitudes, because in this 
 case the vertical gradient of the undisturbed atmosphere is 
 small, so that .the temperature of the air, descending from a 
 high altitude and heated at the rate of i C. for each 100 
 meters, is much higher at the lower level than that of the sur- 
 rounding air, or the air generally over the region. In the 
 summer season during the day when the earth's surface is very 
 warm, and the decrease of temperature with increase of alti- 
 tude great, the foehn effect is small, and the conditions may 
 even be such as to give them a lower temperature than that of 
 the surface air generally. 
 
CYCLONES. 
 
 THE SIROCCO. 
 
 221. There is in Italy and the eastern part of the Mediter- 
 ranean still another warm wind which is connected with 
 cyclones, and is the counterpart of the Mistral and the Bora 
 the Sirocco. It is a very warm, and generally damp, south and 
 southeast wind on the eastern side of a cyclone, with its centre 
 westward of the place of observation. The very warm and dry 
 air from the Sahara and the northern coast of Africa is whirled 
 around toward the northeast and north, and in passing over the 
 sea it becomes a very damp as well as warm wind, and as such 
 mostly it is experienced in Sicily, Italy, and the eastern parts 
 generally of the Mediterranean and the adjacent coasts. 
 Although the temperature never rises above 95 F., yet on 
 account of the great dampness these winds are very oppressive, 
 and seem to be of a higher temperature. This is due to local 
 circumstances, to the existence of the highly heated Sahara 
 from which warm air is drawn, which in its passage over the 
 sea becomes nearly saturated with vapor ; but the same in some 
 measure is observed in nearly all parts of the world on the 
 eastern sides of cyclones, where much warmer and damper 
 winds than usual prevail. Like all phenomena of this kind 
 connected with and dependent upon cyclones, they continue 
 only a few days, until the cyclone has passed away. The dust 
 raised from the Sahara and carried northward by the sirocco 
 often falls over the countries north of the Mediterranean as 
 " blood rain" or as " red snow," the moisture and the sand fall- 
 ing together in the rain or snow. 
 
 As in the case of the Mistral and Bora, there is generally 
 no sudden transition from very warm and moist air to very 
 cold and dry air, as in the case of the northers of Texas, 
 since the direction of the storm's path here is nearly that of 
 the trough of the cyclone, which separates the winds of the 
 two characters. There is, however, always the same marked 
 contrast between the two sides of the storm, and the storm's 
 path may sometimes have such a direction as to give a con- 
 siderable change of air in the passage of the storm. 
 
CYCLONES' WITH A COLD CENTRE. 337 
 
 Dr. Harm 60 has given a graphic representation of the great 
 Sirocco storm of the 25th of February, 1879, m t* 16 Adriatic 
 Sea, and of its path, which lay over the northwestern part of 
 Italy, and extended in a direction N.N.E. 
 
 CYCLONES WITH A COLD CENTRE. 
 
 222. If for any reason the central part of any given portion 
 of the atmosphere of a somewhat circular form is maintained 
 in any way at a lower temperature than the surrounding parts, 
 and the temperature gradient on all sides is somewhat sym- 
 metrical, we have approximately the conditions which give rise 
 to a cyclone. In this case it is readily seen that there must be 
 a vertical circulation as in the ordinary cyclone, but that it is 
 reversed, out from the centre below, and in toward the centre 
 above, with a gradual settling down of the air in the interior 
 to supply the outward current beneath. This vertical circula- 
 tion, as in the case of the ordinary cyclone, gives rise to a 
 cyclonic motion in the interior and an anti-cyclonic in the ex- 
 terior part of the air under consideration, but in this case the 
 gyratory velocity is greatest above and is less at lower altitudes, 
 diminishing down to the earth's surface, where it is least. In 
 the anti-cyclonic part the reverse takes place, the gyratory 
 velocity being least above and greatest down near the earth's 
 surface. The distance from the centre at which the gyratory 
 velocity vanishes and changes sign, is greatest above and grad- 
 ually becomes less, with decrease of altitude down to the sur- 
 face, where it is nearest the centre. Consequently, contrary to 
 what takes place in an ordinary cyclone, the upper part of the 
 air, taken over the whole area, is mostly cyclonic, especially if 
 the friction at the earth's surface is but little, and there is con- 
 siderable gyratory velocity below in the cyclonic part ; for,. 
 whatever this is, there is always a certain difference between 
 the gyratory velocities above and below, greater or less accord- 
 ing to the amount of temperature gradient between the central 
 and exterior parts. If the atmosphere were in the unstable 
 state for dry air, and for any reason it should receive a down- 
 
338 CYCLONES. 
 
 ward motion over a given area, either from a lower temperature 
 or for any other reason, then this motion would continue, and 
 the central area would continue to be colder as long as this 
 unstable state continued, and during this time the vertical cir- 
 culation would give rise to and maintain a cyclone with a cold 
 centre, which would be a progressive one. But for reasons 
 given in 162, we have reason to think the atmosphere is 
 never reduced to this state, except through a stratum of incon- 
 siderable depth next the earth's surface. Hence we have no 
 progressive cyclones with a cold centre. 
 
 The cases in nature which give even rough approximations 
 to these conditions are few, and these are such as to give rise 
 to stationary cyclones only. An island, such as Iceland, in 
 winter, when the air over the whole island, and especially the 
 interior part, is much colder than that of the surrounding ocean, 
 furnishes approximate conditions which must give rise to con- 
 siderable cyclonic action of this sort, though it is all included 
 in the very much larger ordinary and stationary cyclone of the 
 North Atlantic in the winter season. 
 
 223. The conditions of a cyclone with a cold centre which 
 are the most nearly perfect are those furnished by each hemi- 
 sphere of the globe, as divided by the equator, in which the 
 pole is the cold centre and the temperature gradient from the 
 pole toward the equator is somewhat symmetrical in all direc- 
 tions from the centre. It is true, the deflecting force of the 
 earth's rotation is greatest at the centre and decreases with 
 increase of distance from the centre, and vanishes at the equa- 
 tor, and the curvature of the surface makes the conditions vary 
 considerably from those of a small portion of the earth's sur- 
 face, but still the general results are the same, and all the ex- 
 planations given with regard to the vertical circulation and the 
 east and west gyratory motions in the case of the general mo- 
 tions of the earth are applicable to the effects of cyclonic con- 
 ditions of this sort over a small area of the earth's surface. 
 The easterly motions in the higher latitudes and the westerly 
 ones in the lower latitudes, in the one case, correspond to the 
 cyclonic in the interior and the anti-cyclonic in the exterior 
 
Cr 'CLONES WITH A COLD CENTRE. 339 
 
 part, and the belt of high pressure near the tropics to that of 
 high pressure in the case of any cyclone with a cold centre. 
 
 Looking at the general circulation of the two hemispheres 
 of the globe as two cyclones of this sort, we see in another 
 light the cause of the annual shifting of the equatorial and 
 tropical calm-belts north and south, and why they are a little 
 nearer the north than the south pole. The tendency of the 
 two cyclones is to expand over a greater area, and the more so 
 the greater the internal energy upon which their actions de- 
 pend and the less the amount of friction at the earth's surface. 
 As the outer limit of each is common and the one tends to 
 encroach on the other, during the winter of the northern hemi- 
 sphere, when the temperature gradient between the equator 
 and the pole, and consequently the energy of the cyclone, is 
 greatest, while at the same time that of the southern cyclone 
 is least, the northern cyclone encroaches a little on the territory 
 of the southern one, and consequently becomes larger, while 
 the other becomes smaller. Hence at this season all these 
 calm-belts have a position a little farther south than their mean 
 position. During the summer of the northern hemisphere, on 
 the contrary, the energy of the northern cyclone is diminished 
 and that of the southern increased, and consequently the re- 
 verse takes place, and the calm-belts now have a position a 
 little north of their mean position. 
 
 The less, also, the frictional resistances to the gyratory mo- 
 tions of a cyclone, the greater is its tendency to spread and 
 encroach upon the territory of an opposing one, and hence the 
 southern cyclone, being mostly on an ocean surface, is one of 
 much greater violence with the same amount of energy, and 
 the depression at the south pole is much greater than that at 
 the north pole, and the tendency is to occupy a little more 
 territory than its opposing less violent cyclone, and so the mean 
 position of all the calm-belts is a little farther from the south 
 than the north pole. 
 
 224. The centre of a cyclone with a cold centre may, or 
 may not, have a minimum pressure, according to circumstances. 
 -A certain amount of temperature gradient, and of pressure gra- 
 
340 CYCLONES. 
 
 dient which is independent of the gyratory motion, as explained! 
 in 72 in the case of the general circulation of the atmosphere, 
 is necessary to overcome the friction in the lower strata and to 
 keep up the vertical circulation, upon which the cyclonic de- 
 pends ; and the pressure gradient, which depends upon the 
 temperature gradient and is independent of the gyrations, may 
 be such that the increase of pressure in the central part due to 
 this cause may be greater than the decrease of pressure arising 
 from the cyclonic gyrations, especially where surface friction is 
 great. For instance, in the southern hemispherical cyclone, 
 where this friction is comparatively small, the cyclonic gyra- 
 tions are comparatively large, and the effect is to diminish the 
 pressure there more than it is increased by the colder and 
 heavier air there. And this is also in some measure the case 
 in the northern hemispherical cyclone ; but with still a little 
 more of land surface, and with still greater mountain ranges, 
 the resistance to the gyratory motion might be such that the 
 decrease of pressure at the pole from this cause would not be 
 equal to its increase from the lower temperature and greater 
 density of the air. 
 
 Each of the great continents of Europe, Asia and of North 
 America furnish, in winter, only very roughly the conditions of 
 a stationary cyclone with a cold centre, as they do in summer 
 those of an ordinary cyclone, both because the areas are too 
 large and irregular, and also because the deflecting forces are 
 very different on the polar and equatorial sides, and conse- 
 quently not symmetrical in all directions. The surfaces also 
 are very uneven, and consequently the resistances to gyratory 
 motion great. There is, however, some motion of this sort, no 
 doubt, but it is not sufficient to reduce the pressure in the 
 central part as much as it is increased by the greater coldness 
 and density of the air in winter, for the effect of this is very 
 great, and so there is a maximum pressure in the interior of 
 these continents during the winter. The whole effect of the 
 unequal distribution of temperature, therefore, has been treated 
 in Chapter V, and regarded as a winter monsoon, some allow- 
 
CYCLONES WITH A COLD CENTRE. 341 
 
 ance, however, being made for the deflecting force of the earth's 
 rotation upon the directions of the monsoon winds. 
 
 225. Regarding the general motions of each hemisphere as 
 a cyclone, then all ordinary cyclones become secondaries, and 
 their effects upon the isobars and the general motions of the 
 atmosphere become similar to those of the secondaries of ordi- 
 nary cyclones, as stated in 208 and represented in Fig. 13. 
 If the depression of the cyclone is considerable, so that its 
 pressure gradient is greater than that of the gradient between 
 the equator and the pole where the cyclone exists, then the 
 cyclone gives rise to another minimum, just as in the case of 
 the great stationary winter cyclone of the North Atlantic, as 
 represented by the right-hand secondary minimum in Fig. 13; 
 .and the winds gyrate around this centre, but with a velocity 
 much greater on the equatorial than on the polar side, in the 
 middle and higher latitudes, and with a correspondingly steeper 
 gradient. In fact, we have here the resultant of two motions 
 in nearly the same direction, as explained in 202, and it be- 
 comes the dangerous side of the storm. In the northern hemi- 
 sphere the general gradients between the pole and the equator 
 at all times are so small that any cyclone of only a very mod- 
 erate barometric depression gives a minimum, but in the south- 
 ern hemisphere, on the middle latitudes, as in the region of 
 Cape Horn, where the general hemispherical gradients are very 
 steep, unless the cyclone has a considerable barometric depres- 
 sion of its own, it does not give a minimum, but simply causes 
 a derangement in the general isobars extending east and west 
 around the globe, making them closer on the equatorial side, 
 and the isobars on the other side do not inclose a minimum, 
 but are open, as represented in the left-hand secondary in Fig. 
 13. However, with a little greater cyclonic depression, there 
 is a minimum even here, as represented by the right-hand sec- 
 ondary in Fig. 13. 
 
 It is readily seen, therefore, that the minimum pressure in 
 an ordinary cyclone, as observed and laid down on synoptic 
 charts, being the resultant of two separate effects, is not the 
 place of the true centre, especially in the southern hemisphere, 
 
34 2 CYCLONES. 
 
 where the general gradient is steep. In fact, without a very 
 marked cyclonic depression, the cyclone centre would be inde- 
 terminate, since there is no minimum of pressure, or isobars, 
 inclosing an area of lower pressure. In tracing the paths of 
 cyclone centres, therefore, unless there is a marked cyclonic 
 depression, there is always considerable error from not taking 
 these considerations into account, and the error in the middle 
 latitudes of the southern hemisphere would generally be very 
 great. 
 
 226, The great permanent cyclone of the North Atlantic 
 in winter may be regarded as a secondary cyclone with refer- 
 ence to the great hemispherical cyclone in which it is situated,, 
 and as the ring of high pressure of the secondary on the equa- 
 torial side falls somewhat upon that of the primary, that is r 
 upon the tropical belt of high pressure around the globe, the 
 effect is similar to that represented in Fig. 13, in which the re- 
 sultant, where the two rings fall together, is a pressure consid- 
 erably higher than elsewhere in the ring of high pressure of the 
 primary. This is the explanation in part of the area of unusu- 
 ally high pressure in the Atlantic between Spain and the 
 United States. The other part arises from the gyration of 
 air around this region resulting from the deflections of the 
 coasts and mountain ranges, as explained in 123. The de- 
 flecting force arising from the earth's rotation being on all 
 sides to the right, and so in toward the centre of this region, 
 causes a little accumulation of atmosphere and increase of 
 pressure. 
 
 AREAS OF HIGH BAROMETRIC PRESSURE. 
 
 227. If only a single regular cyclone, without any other 
 abnormal disturbances, existed in any part of the globe, in 
 which the atmosphere in its normal condition had a uniform 
 barometric pressure at all places, we have seen, 174, that 
 there must necessarily be a ring of barometric pressure around 
 the central part of the area of low barometer, a little above the 
 normal mean pressure. But it has been shown that the press- 
 ure of the atmosphere, undisturbed by transient and progress- 
 
AREAS OF HIGH BAROMETRIC PRESSURE. 343 
 
 ive cyclones, is not of uniform pressure at all places on the 
 earth's surface, but is made to vary in different latitudes by the 
 general motions of the atmosphere, and both in latitude and 
 longitude by the stationary cyclones, and unequal distributions 
 of temperature between land and water, both in winter and 
 summer, giving rise to monsoons, if not regular and stationary 
 cyclones. If, therefore, the inequalities of pressure of regular 
 cyclones are superimposed upon all these other irregularities, a 
 chart of the resultant pressures does not give regular circular 
 isobars, and indicate a regular ring of high pressure around an 
 area of low pressure, but the former are very much distorted, 
 and the latter is broken up into areas of higher and lower press- 
 ure. The duration of the area of high pressure depends upon 
 that of the cyclone, and generally has an easterly progressive 
 motion, somewhat as that of the cyclone, but not necessarily 
 the same, since it depends upon many other irregularities upon 
 which it may be superimposed. 
 
 But two or more progressive cyclones may interfere with and 
 overlap one another, and then the irregularities thus produced, 
 together with other more permanent irregularities, may make 
 the barometric pressure very irregular and cause great distor- 
 tions in the isobars of the charts. Across the United States 
 there is generally a pretty regular series of cyclones passing 
 from west to east, at intervals of a few days, of which the part 
 of the ring of high barometer on the west side of the one 
 which precedes, falls somewhat upon that of the east side of 
 the one which follows, causing a sort of ridge of high pressure 
 between them ; and if this is still interfered with by other ir- 
 regularities, as it usually is, it may be an area of high barome- 
 ter of almost any form. 
 
 In forty-four cases of ridges or areas of high barometer 
 with an area of low barometer between, passing over the 
 United States, Loomis 63 found the average distance from the 
 centre of low barometer to that of the areas of high barometer 
 preceding and following to be about 1000 miles, and the aver- 
 age height of the barometer about 30.35 inches, the, normal 
 height being about 30 inches. This indicates that the average 
 
344 CYCLONES. 
 
 height of the rings of high barometer was about 0.2 inch above 
 the normal height, supposing that the highest parts of each did 
 not in general fall exactly together. 
 
 228, The areas of greatest high pressure do not generally 
 depend directly upon cyclones, but only indirectly, and di- 
 rectly upon low temperature. On the clearing-up side of a 
 cyclone which has passed ov^r any region, the air is clear and 
 the terrestrial radiation into space great, so that the air be- 
 comes unusually cold and dense, and consequently the baromet- 
 ric pressure greater than at surrounding places where the air is 
 warmer. Thus on the morning of the thirteenth of February, 
 1888, according to the Signal Service Charts, in the northwest- 
 ern part of the United States, the barometric pressure was be- 
 low 30 inches, the lowest 29.6 inches, with partially cloudy 
 weather, and temperature little below freezing. By the next 
 morning the low pressure and cloudy area had passed off to- 
 ward the east, fair and clear weather prevailed, the tempera- 
 ture over that region had fallen about 30 F., and the maximum 
 barometric pressure in Dakota was 30.9 inches. This increase 
 of pressure was evidently due mostly to the lowering of the 
 temperature by radiation into space through the now clear 
 atmosphere. By the morning of the I5th the region of highest 
 pressure, now 31.0 inches, had moved eastward to Lake Supe- 
 rior, the weather being still very clear and cold. After this it 
 still moved farther eastward but rapidly subsided. 
 
 The principal cause of the large areas of very high barom- 
 eter which frequently occur in the higher latitudes in winter 
 is undoubtedly found in the clearness of the atmosphere over 
 these areas and the intense coldness produced by the radiation 
 of heat at a time when little is received from solar radiation. 
 The density and pressure of the air are much increased from 
 this cause, and the areas are too large and irregular for this 
 temperature disturbance to give rise to a cyclone with a cold 
 centre, by the gyrations of which this pressure would be dimin- 
 ished in the central part, as it is in the great hemispherical cy- 
 clones, especially that of the southern hemisphere. If there 
 were no gyrations around the poles of the earth, the polar re- 
 
AREAS OF HIGH BAROMETRIC PRESSURE. 
 
 345 
 
 gions, instead of being areas of low pressure, as they are, would 
 be areas of very high pressure. 
 
 As there is a gradual settling down of the air in the regions 
 of unusually high pressure, they are clear areas, and since the 
 <lry atmosphere has comparatively little radiating power, the 
 cooling takes place mostly at the earth's surface, the contigu- 
 ous stratum being cooled mostly from contact with the earth's 
 surface, while the air at some distance above is becoming 
 warmed from gradually descending and coming under greater 
 pressure, an effect which is not felt near the earth's surface, 
 since the descending air does not reach it but is deflected lat- 
 erally and the air near the surface remains under the same 
 pressure. Hence the cooling is so much greater below than 
 at some height above the earth's surface, that the vertical 
 temperature gradient after a continuance for some time of high 
 barometric pressure becomes inverted, and the temperature is 
 higher above than below. A remarkable instance of this kind 
 occurred in France during two periods of January, 1880. The 
 following table shows the minimum temperature observed dur- 
 ing these periods at the several places named : 64 
 
 DATES. 
 
 Pare St. Maur, 
 Paris (altitude 
 46 ro.). 
 
 Poitiers (alti- 
 tude 117 m.). 
 
 Clermont (alti- 
 tude 407 m.). 
 
 Puy-de-D6me 
 (altitude 
 1,467 m.). 
 
 Pic du Midi 
 (altitude 
 2,366 m.). 
 
 4 
 
 - i.4 
 
 0-4 
 
 - 4 .o 
 
 -3-o 
 
 0.2 
 
 5 
 
 - i -5 
 
 o .6 
 
 6 .0 
 
 i .0 
 
 .0 
 
 6 
 
 i .1 
 
 -o .3 
 
 - 4 .0 
 
 2 .0 
 
 -3-5 
 
 7 
 
 i -5 
 
 .0 
 
 - i .4 
 
 I .0 
 
 -3-3 
 
 8 
 
 - 3 -5 
 
 -2 -3 
 
 - 7 .0 
 
 I .0 
 
 - 4 .0 
 
 9 
 
 2 .O 
 
 -3 -3 
 
 7 .0 
 
 2 .0 
 
 4.2 
 
 10 
 
 - 3 -4 
 
 -4 -4 
 
 7 .0 
 
 2 .0 
 
 -5-o 
 
 ii 
 
 - o .7 
 
 4 -2 
 
 - 8 .0 
 
 I .O 
 
 4-5 
 
 12 
 
 - 4 .8 
 
 -6 .1 
 
 12 .0 
 
 2 .0 
 
 5-2 
 
 13 
 
 - 7 -6 
 
 -5 -4 
 
 7 .0 
 
 .0 
 
 5-4 
 
 14 
 
 Wanting. 
 
 -3 -2 
 
 10 .0 
 
 -6 .0 
 
 - 4.8 
 
 25 
 
 7 -5 
 
 -8 .1 
 
 14 .0 
 
 -7 -o 
 
 10 .9 
 
 26 
 
 - 9 .8 
 
 -7 -i 
 
 10 .0 
 
 -5 -o 
 
 8 .0 
 
 27 
 
 9 .0 
 
 -6 .1 
 
 12 .O 
 
 2 .0 
 
 - 8 .2 
 
 28 
 
 -ii -5 
 
 -8 .0 
 
 14 .O 
 
 I .0 
 
 8 .2 
 
 2 9 
 
 II .0 
 
 -5 -9 
 
 - 5 -o 
 
 I .0 
 
 - 5 .8 
 
 30 
 
 - 5 -3 
 
 -o .4 
 
 4 .0 
 
 I .0 
 
 - 5 .2 
 
 3i 
 
 - 5 -4 
 
 i -7 
 
 - 4 .0 
 
 I .0 
 
 5-2 
 
346 CYCLONES. 
 
 The Puy-de-D6me is about ten kilometers from Clermont. 
 From this table it is seen that during the first and last parts of 
 the month the temperature at Paris, Poitiers, and Clermont 
 was generally lower than at the top of the Puy-de-D6me, and 
 frequently less than that on the top of the Pic du Midi. 
 
 According to the late Professor Plantamour : 
 
 " It happens every year that the temperature on St. Bernard at 
 several hours, or even during several days, of December is higher than 
 at Geneva. But during December of 1879, this anomaly lasted during a 
 longer period of time than usual. The average temperature of St. 
 Bernard was 8. 4 C. higher than at Geneva. Out of the 31 days of the 
 month, only during 14 days was it from o4 to 6. 2 C. lower than at 
 Geneva, while during the 17 days it exceeded this by 2 to i6.4." 
 
CHAPTER VII. 
 
 TORNADOES. 
 
 229. IN addition to the more general atmospheric disturb- 
 ances considered in the preceding chapters, comprising the 
 general circulation of the atmosphere, monsoons, and cyclones, 
 there is another and distinct class of disturbances, with their 
 attendant phenomena of waterspouts, hail, thunder, etc., which 
 are very local in character, and occupy at any one time only a 
 very small portion of the earth's surface in comparison with 
 that of a cyclone, but which, over this small area, are generally 
 characterized by far greater violence and destructiveness. 
 These smaller disturbances, though differing from one another 
 in many respects, are all somewhat similar in their general' 
 character, and all depend mostly upon the unstable state of 
 the atmosphere. They all have more or less gyratory motion, 
 and may therefore all be included under the general name of 
 Tornado, but in this more extended sense of the term it does 
 not include necessarily the popular idea of great violence. 
 
 Tornadoes differ from cyclones mostly in their extent. 
 Both have vertical and gyratory circulations; but while a 
 cyclone may extend over a circular area of one or two thousand 
 miles in diameter, a tornado rarely affects sensibly at any one 
 time such an area of one mile in diameter, and generally very 
 much less. To understand clearly the distinction between a 
 tornado and a cyclone, it is necessary to understand the differ- 
 ence in the conditions which give rise to them. A cyclone", 
 we have seen, requires, in addition to the state of unstable 
 equilibrium for saturated air, such a disturbance in the general 
 equality of temperature over a considerable area that there is 
 a central and somewhat circular area of higher or lower tem- 
 perature, from which arises a vertical, and consequently at. 
 
 347 
 
348 TORNADOES. 
 
 gyratory, circulation, and the initial extent of the cyclone 
 depends upon that of the initial temperature disturbance. 
 The tornado, we shall see, is independent of any such tem- 
 perature disturbance which determines the initial extent of the 
 atmospheric disturbance, but simply depends upon conditions 
 which give rise to very local disturbances merely. 
 
 THE CONDITIONS OF A TORNADO. 
 
 230. The principal condition of a tornado is the unstable 
 state of the atmosphere, from which, with any very slight dis- 
 turbance, arises a bursting up of the air of the lower strata of 
 the atmosphere through those above, over one or more small 
 spots, somewhat as the vapor of boiling water, which is gen- 
 erated mostly at the bottom of the containing vessel, bursts up 
 through the water above and comes to the surface. But this 
 initial start in the tornado having once taken place, the condi- 
 tion of unstable equilibrium tends to continue the initial 
 motions as long as this state continues, unless the whole 
 system is broken up by great abnormal disturbances and 
 irregularities of the earth's surface. The start being once 
 made, the interior part where the air ascends is kept warmer 
 than the surrounding parts, exactly in the manner explained in 
 the case of cyclones in 159, and illustrated in the table of that 
 section, and while the unstable state and this warmer central 
 part continue, a vertical circulation is maintained, the air ascend- 
 ing in the interior, flowing out in all directions above and in 
 from all directions below to supply the ascending current, just 
 as in the case of a cyclone ; but in this latter the vertical cir- 
 culation is of great extent horizontally in comparison with its 
 height, while in the tornado the reverse is the case, the vertical 
 >extent being generally much greater than the horizontal. 
 
 The vertical circulation is the initial stage in the formation 
 of a tornado, and so the tornado cannot originate without the 
 -condition of unstable equilibrium which gives rise to a vertical 
 circulation. It is not necessary, however, that this state shall 
 extend from the bottom to the top of the atmosphere, and 
 
THE COXDITIOXS OF A TORNADO. 349' 
 
 such a state, perhaps, never exists ; but if it does, rapidly 
 ascending air continues to become warmer than the surround- 
 ing air at the same level up to the highest strata, and the 
 difference of temperature there is the greatest. This condition 
 would, of course, give the strongest ascending current and 
 vertical circulation. The ascending current in this case has a 
 maximum velocity at some very high altitude, where the 
 pressure is the same as in the surrounding air at the same 
 altitude, the pressure below this level being less than that of 
 the surrounding air at the same level, on account of its greater 
 temperature and less density. Above this level the pressure is 
 greater than in the surrounding air, on account of the heaping 
 up of the atmosphere, the kinetic energy of the ascending 
 current being gradually changed to the potential energy of 
 increased pressure. But this heaping up of the atmosphere and 
 increase of pressure causes a lateral deflection of the ascending 
 currents in all directions in the upper strata of the atmosphere. 
 If the unstable state does not extend to, a very high alti- 
 tude, the difference of temperature between the ascending and 
 the surrounding air increases up to this level,, and then begins 
 to decrease, until at some higher altitude it vanishes, and then 
 above this it becomes colder than in the surrounding air. The 
 level at which the difference of temperature between the as- 
 cending and surrounding air vanishes is an isobaric as well as 
 an isothermic surface. The velocity of the ascending current 
 is increased up to this level ; above this the air is colder and 
 the pressure greater than in the surrounding air at the same 
 level, but this does not necessarily extend to the top of the 
 atmosphere. Below that level the temperature is greater and 
 the pressure less in the ascending current than in the surround- 
 ing air at the same level, and the greater the difference of 
 pressure, the greater the force by which the kinetic energy is 
 generated, and the whole kinetic energy at any level is the 
 equivalent of the sum of the differences of the forces from some 
 lower stratum of the earth's surface where the difference of 
 pressure and the ascending current begins. Above this level 
 the difference of temperature and of pressure is reversed, the-. 
 
'35 TORNADOES. 
 
 temperature of the ascending current being the less and the 
 pressure the greater, and the greater the difference of pressure 
 the greater the rate at which the kinetic energy of the ascend- 
 ing current is diminished. The condition of stability of the 
 air here may be such that the temperature is diminished and 
 the pressure increased at such a rate that the ascending veloc- 
 ity and kinetic energy are brought to naught before the top of 
 the atmosphere is reached, the increase of pressure being suffi- 
 cient to counteract the ascending velocity before the top or a 
 very high altitude is reached. In this case the increase of 
 pressure above deflects the air off laterally in all directions up 
 .as high as the ascending current reaches, and the vertical cir- 
 culation extends up to that altitude only as a direct effect of 
 the conditions ; but air of a higher altitude may be brought 
 into the circulation by friction. 
 
 In what precedes, a vertical circulation merely is considered, 
 and not the modifying effects of a gyratory circulation, which 
 depress, as will be seen, the isothermic and isobaric surfaces in 
 the interior of the gyrating portion of air; so that in this case 
 the relative temperatures and pressures on the same levels 
 become different. 
 
 Again, the air may be in the unstable state in the middle 
 strata, and in the stable state both above and below. It also 
 frequently happens that the unstable state exists above, but 
 near the earth's surface the stable state. This is especially the 
 case where the air is not completely saturated. For in this 
 case the unstable state near the earth's surface requires a de- 
 crease of temperature with increase of elevation in the sur- 
 rounding undisturbed air at a rate greater than i C. for each 
 100 meters, which is rarely found, at least to any considerable 
 altitude. In such a case the vertical circulation does not in- 
 clude the stable strata near the earth's surface, except as they 
 may be acted upon by means of friction. 
 
 From what precedes, therefore, the conditions of vertical 
 circulation, and consequently of a tornado, does not require 
 that the unstable state shall extend to all strata of the atmos- 
 phere from the earth's surface up to the top. 
 
THE CONDITIONS OF A TORNADO. 35 l 
 
 231. But in order that the vertical circulation may give 
 rise to a gyratory circulation and to much violence in a tornado, 
 another condition is necessary, namely, an initial gyratory 
 motion of the air around the central point where the first as- 
 cent of air takes place and toward which the air from all sides 
 is drawn. This may be illustrated by means of the behavior 
 of water which is allowed to run out of a basin through a hole 
 in the bottom. If the w r ater is entirely at rest with reference 
 to the basin, it flows directly in from all sides toward and out 
 at the hole without assuming any gyratory motion ; but if the 
 water is not entirely quiet, if there is only the least perceptible 
 disturbance, it is liable to run, in the one direction or the other, 
 into very rapid gyrations near the centre. The direction of 
 the gyration, from right to left or the contrary, depends upon 
 the predominance of the gyrations in the mass generally in the 
 one direction or the other, and does not require that the whole 
 mass shall have an initial gyration in one way. The case of the 
 tornado is similar ; but instead of running dow r n, the air of the 
 lower strata runs up through the strata above, where the first 
 ascent takes place, and flows away there in all directions. And 
 if there is no initial gyratory motion of the air, it runs directly 
 toward the centre from all sides, up in the central part and out 
 above, and thus a vertical circulation is inaugurated and main- 
 tained, but there is no gyratory motion or much violence. 
 But if there are initial gyrations of the air, however slight, at a 
 distance from the centre, the air as it approaches the centre 
 below runs into a gyration around that centre, and the direc- 
 tion of the gyration is determined upon the same principle as 
 in the case of the water in the basin. It is not necessary that 
 the initial motion of the air shall be that of an absolute gyra- 
 tion around this centre as a fixed point, but only that there 
 shall be a whirl in the atmosphere around some point at no 
 very great distance, such as to cause a relative gyratory motion 
 around this centre, just as every part of the atmosphere, except 
 at the equator, has a gyratory motion relative to any assumed 
 point, in consequence of the rotation of the earth on its axis, 
 though an absolute motion around the pole only. 
 
352 TORNADOES. 
 
 In a cyclone, we have seen, the gyratory motion arises from? 
 the absolute motion of the air and the earth's surface around 
 the centre of the cyclone, and not from initial gyrations which 
 the air has relative to the earth's surface. In a tornado, on 
 account of the smallness of its horizontal dimensions, this effect 
 is comparatively small. For instance, at the distance of 1000 
 meters from the centre of a tornado on the parallel of 45, the 
 absolute gyratory velocity relative to this centre, arising from 
 the earth's rotation, is 1000 X n sin 45 = 0.05 of a meter per 
 second, obtaining the value of n sin 45 from Table V, it being 
 one half of 2n sin / for that latitude. This is probably less 
 than the relative gyratory velocity which the air may have with 
 reference to the centre arising from the numerous whirls into 
 which the air is being continually thrown relatively to the 
 earth's surface ; but still it seems it must have something to do 
 with determining the direction of the gyratory motions in tor- 
 nadoes, since this is generally, if not always, the same as in 
 cyclones, and its effect may have been heretofore underesti- 
 mated. 
 
 Although the horizontal extent of the violent part of a tor- 
 nado is small, yet the air may be drawn in slowly from a much 
 greater distance than 1000 meters, and so at this distance it may 
 have sufficient gyratory velocity to determine its direction ; for, 
 as we shall see, a very small gyratory motion at this distance 
 suffices to give rise to a great gyratory velocity and much vio- 
 lence near the centre. 
 
 It is said that in making experiments to ascertain whether 
 the earth's rotation has any sensible effect in determining the 
 manner of gyrations jn the flowing of water through a hole in 
 the bottom of a large and shallow basin, it is impossible to 
 have the water so quiet that in running out it does not gener- 
 ally run into a gyration the one way or the other, but that 
 there is no observable preponderance of the gyrations in the 
 direction which would indicate that the earth's rotation has 
 any sensible influence upon the direction of the gyrations. 
 This is to be expected in so small an area ; but if the extent 
 
GYRATORY VELOCITY AND ITS EFFECT ON PRESSURE. 353 
 
 of tilt, basin were as large as the base of a tornado, the result 
 would probably be different. 
 
 GYRATORY VELOCITY AND ITS EFFECT ON PRESSURE. 
 
 232. In a cyclone the base is so great in comparison with 
 the height, that the whole mass of gyrating air maybe regarded 
 as a thin disk, and consequently a large amount of the forces 
 is spent in overcoming the frictional resistances at the earth's 
 surface ; and the gyratory velocities with regard to distance 
 from the centre do not at all follow the law which would hold 
 in the case of no friction. But in a tornado the height is so- 
 great in comparison with the base that it may be regarded as 
 a gyrating pillar of air, and hence the effect of frictional re- 
 sistance upon the gyratory velocities, except near the surface, 
 is small, and the law of the gyrations at all altitudes a little 
 above the earth's surface is somewhat the same as in the case 
 of no friction, and follows very nearly the law of a free body 
 in the case of central forces. The general expression of this 
 law has been given in 41, and is rw = c, in which r is the dis- 
 tance of the body from the centre, and w is the absolute gyra- 
 tory velocity of the body at that distance around that centre, 
 c being some constant quantity. Or if, for simplicity, we neg- 
 lect the small influence which the earth's rotation may have, it 
 becomes 
 
 rv = r'v' = c, 
 
 in which v is the gyratory velocity relative to the earth's sur- 
 face, and in which v' is the value of v at the distance of r' from 
 the centre. It must be understood here that v is simply the 
 gyratory component of a motion which may also have both a 
 horizontal and vertical component of motion. From this law 
 it is seen that the gyratory component of velocity v is inversely 
 as the distance r from the centre, and hence near the centre it 
 becomes enormously great. 
 
 After the vertical circulation in a tornado is fully estab- 
 lished and each particle of air has passed in toward the centre 
 and out several times, assuming that no part of the gyrating 
 
354 TORNADOES. 
 
 column of air is changed, although the initial gyratory veloci- 
 ties at the same distances may be very different at different 
 altitudes and at different distances from the centre, yet by the 
 mutual action of the particles upon one another by contact and 
 by friction, and from the tendency of each one to follow the 
 law of a free body with regard to gyratory velocities at differ- 
 ent distances, they all soon have approximately the same 
 gyratory velocities at the same distances from the centre, and 
 nearly follow the preceding law, which makes the gyratory 
 velocities inversely as the distance ; especially at a little distance 
 above the earth's surface where the effect of friction is small. 
 The value of c, then, does not depend upon the initial value of 
 v' at any assumed distance r', but upon the average of rv for 
 the whole mass of air brought into circulation. 
 233. From the preceding law we get 
 
 r'v' 
 
 so that for any assumed value of v' at the distance r' we know 
 the value of v corresponding to the distance r. 
 
 The centrifugal force of the gyratory velocity v at the dis- 
 tance r is, putting v for w, 36, since we assume here that they 
 are sensibly the same, 
 
 if r"v" 
 
 F c = m = 5 m, 
 
 by putting for v in the first form of expression its value 
 above to obtain the second form. 
 
 This expression may be obtained directly from that of F c 
 in 40 by neglecting GO in comparison with v, the former, as 
 has just been shown, being very small in tornadoes in compari- 
 son with v. 
 
 This force, which becomes very great near the centre where 
 r is small, causes a depression of the isobaric surfaces all around 
 the centre of gyration, which becomes very great near the 
 centre. In the figure following let the curved line beaf repre- 
 
'GYRATORY VELOCITY AND ITS EFFECT ON PRESSURE. 355 
 
 sent a vertical section of the isobaric surface brought down to 
 the surface of the earth DE at/, and let ed represent a vertical 
 column of air of unit base, which being entirely arbitrary, may 
 be infinitely small, and ad a similar horizontal prism or cylinder 
 of the same base or cross-section. Since the pressure of a 
 fluid is equal in all directions, in order that the air may be in 
 a state of static equilibrium, we must have the horizontal 
 pressure ad in the direction of d, arising from the centrifugal 
 force of the gyration, exactly equal to the vertical pressure of 
 *d at the base d arising from the force of gravity. These 
 spaces being supposed to be very small, the density in all parts 
 is sensibly the same, and using d to denote this density, we 
 
 Tiave ed X 8 and ad X & for the masses respectively of these 
 horizontal and vertical air columns. Since the vertical force is 
 equal to the acceleration of gravity multiplied into the mass, 
 the expression of this is gd X ed. And putting ad X 8 for m 
 in the preceding expression of the centrifugal force F et we get 
 (r'W/r 3 ) X ad for the expression of the latter in this case. 
 Equating these two expressions, we get 
 
 r'V 
 
 as a condition which must be satisfied in determining the curved 
 line beaf. 
 
356 TORNADOES. 
 
 Supposing the arc ae, Fig. i, to be very small, and putting,. 
 as in 38, e for the ratio between the lines ed and ad, we get 
 from the preceding equation 
 
 in which e is the gradient of the curve between the points a 
 and <?, supposed to be very near to each other. 
 
 This could have been deduced directly from the expression 
 of eg in 38 by substituting v for w, since the effect of the 
 earth's rotation here being supposed to be insensible, v becomes 
 sensibly equal to w t and then substituting for v the preceding 
 expression of it. For it is very evident that the gradient of a 
 surface upon which a body, acted upon by the force of gravity 
 and a horizontal centrifugal force, must be the same as that of 
 a liquid surface, or of an isobaric surface, where the liquid is 
 subject to the same forces. 
 
 It is seen from the preceding expression, since g, r f , and v' 
 are constants, that as r 3 increases, the gradient e of the curve 
 diminishes, and at an infinite distance from the centre C, Fig. I, 
 it must vanish, that is, the isobaric surface must become a 
 level surface. Also, near the centre, where r is very small, the 
 gradient becomes very steep, and the more so the nearer the 
 centre. 
 
 234. If we let Cx and Cy, Fig. I, represent the two rec- 
 tangular co-ordinates of any point a of the curve bcaf, then 
 Cy = xa is represented by r in the notation above, and denot- 
 ing the line Cx = ya, the depression of the curve at the point 
 a, by /, the equation of the curve or expression of /becomes* 
 
 * By the principles of the differential calculus, if we suppose the points a 
 and e in the curve, Fig. I, to be infinitely near to each other, the lines ed and 
 tf^/are represented by the differential expressions dl and dr respectively, and 
 the equation becomes 
 
 gdl = r ^v V~ 3 */r. 
 
 The integration of this gives the expression of / above. 
 
GYRATORY VELOCITY AND ITS EFFECT ON PRESSURE. 357 
 
 From this expression it is seen that neither one of / or r can 
 vanish unless the other becomes infinitely great, and conse- 
 quently the curve cannot cut either of the lines CB or Cc, in 
 Fig. i, produced, but simply approximates to them and touches 
 them at an infinite distance only, as a hyperbolic curve does its 
 assymptotes. 
 
 For any other isobaric surface which, before being depressed 
 by the centrifugal force, corresponded to the line A'B', either 
 below or above the other, it is evident that we must have a 
 similar curve, since v' is supposed to be the same at all alti- 
 tudes. If it is lower, it is brought down to the earth's surface 
 Tepresented by the line DE, at a point f farther from the 
 centre than /", but, if higher, at some point between c and f. 
 But however high the undisturbed isobaric surface may be, the 
 value of r at the earth's surface cannot vanish. Also, the verti- 
 cal distance mn, Fig. I, between the two isobaric surfaces, is 
 the same at all distances from the centre, and equal to the 
 vertical distance aa' or bb' . 
 
 It is seen from the preceding expression of / that it vanishes 
 only where the value of r is infinite, whatever the value of r'v'. 
 But the greater v' is at any distance r ', and in the ratio of its 
 square, the greater is the depression / at any given distance r 
 from the centre, until /becomes equal to the height Cc, Fig. i, 
 of the undisturbed isobaric surface AB; and the value of r cor- 
 responding to this value of / in the preceding expression is the 
 value of cfj or the distance from the centre, at which the iso- 
 baric surface meets the earth's surface. With this value of r 
 we get from the expression ot v, 233, where the value of v' 
 at the distance of r' is known, the value of v at the distance cf 
 from the centre. 
 
 If in the preceding expression of /we assume that at the 
 distance of 1000 meters from the centre of the tornado, as that 
 of D or E, Fig. i, the gyratory velocity v at all altitudes is 3 
 meters per second, then we have r'v' = 1000 X 3 = 3000, and 
 
 9,000,000 
 lr = 
 
358 TORNADOES. 
 
 If we now suppose that the height of any undisturbed isobaric 
 surface is 1000 meters, we then get, by putting / 1000, the 
 value of r = 21.4 m., for the distance cf, Fig. i, at which the 
 isobaric surface is brought down to the earth's surface. By 
 assuming any other value of / less than 1000 meters, we get the 
 value of r corresponding to it. For instance, if the depression,, 
 as at a in the figure, is ya = 300 meters, we then get xa or 
 r 39 meters nearly. In this way a sufficient number of 
 points can be determined to construct the curve. 
 
 At the distance of 21.4 meters from the centre, by the pre- 
 ceding relation of rv = r'v', we get in this case 
 
 3000 
 
 v = - = 140 meters per second 
 21.4 
 
 for the gyratory velocity at f t where the pressure is the same 
 as at b. 
 
 In the same manner we get for a depression of 500 meters,. 
 as at i in the figure, r = 30.3 m., and with this, from the rela- 
 tion of rv = r'v' 3000, we get v = 99 meters at the distance 
 of this point from the centre, and so at/ 7 at this distance from 
 the centre at the earth's surface, when the pressure is the same 
 as at b'. 
 
 The curved lines, Fig. I, represent the form of the isobaric 
 surfaces where v' is taken equal to 5 meters at the distance of 
 IOOO meters, and where the undisturbed isobaric surfaces AB 
 and A' B' are taken respectively at the heights of 1000 and 500 
 meters. 
 
 235. The gyratory velocity v at the earth's surface, in any 
 isobaric surface, as that represented by baef, Fig. i, is equal to 
 the velocity s acquired by a free body in falling through the 
 height BE of the undisturbed and level isobaric surface, repre- 
 sented by the line AB, and this is given by the expression 
 
 in which s is the velocity in meters per second, and h is the 
 height in meters through which the body falls. The demon- 
 
GYRATORY VELOCITY AND ITS EFFECT ON PRESSURE. 359 
 
 stration of this is too complex to be given here, but it may be 
 found in Recent Advances of Meteorology, p. 241. It is also 
 the theoretical velocity with which a homogeneous fluid issues 
 from a fountain at a level which is at the distance h below the 
 level of the head of the fountain. The value of v, therefore, 
 at/ Fig. i, is the velocity which a body would acquire in fall- 
 ing through the space BE\ at f, that acquired in falling 
 through the distance B'E, etc., no account being taken of the 
 effect of friction upon the value of v. 
 
 The difference of pressure between / and /' is the same as 
 that between i and f or that between b and b'\ and so the cen- 
 trifugal force of a horizontal prism or cylinder ff is exactly 
 equal to the force of gravity on the vertical prism or cylinder 
 if or bb' of the same cross-section. 
 
 The value of v is also equal to that acquired by air, at rest 
 under the higher pressure, in passing horizontally to a lower 
 pressure, as for instance of air in passing from E to /, Fig. i, 
 or to velocity arising in any way from such difference of press- 
 ure, and this, when the difference of pressure is not very great, 
 is given approximately by 
 
 P. T . 
 s* = 206.3 -p~AP, 
 
 * J o 
 
 in which, as before, s is the velocity in metres per second, P t 
 is the standard barometric pressure of 760 mm., P that where 
 the velocity is s, AP is the variation of pressure, and T and T 
 have their usual significations, being the absolute temperatures 
 corresponding respectively to P and P. To a given amount 
 of potential energy AP corresponds its equivalent in kinetic 
 energy, but the latter, \?m ( 18), is proportional to the mass 
 m, and consequently, for a given volume of air, is as the den- 
 sity. But this varies directly as the pressure and inversely as 
 the absolute temperature T, and therefore s* must vary in- 
 versely as the pressure and directly as the absolute tempera- 
 ture, as the expression above indicates. 
 
 By the preceding expression, if the pressure P at / Fig. i, 
 is known, and AP the difference between / and , or rather 
 
360 TORNADOES. 
 
 between that at /and at an infinite distance where v o, the 
 value of v at f is known, in case AP is not very large. Con- 
 versely, if v is known, the difference of pressure sensibly be- 
 tween E and /, or rather the whole amount of depression, can 
 be computed. At high altitudes where P is small and the air 
 rare, it is seen from the formula s* has to be proportionately 
 large, where AP is taken the same at all altitudes. 
 
 236. On account of the great depression of the isobaric 
 surfaces, as represented in Fig. I, the pressure near the centre 
 of tornadoes becomes very much diminished, and in their pas- 
 sage over a place there is sometimes a very sudden change of 
 pressure. Hence, we see the reason of the explosive effects 
 often observed during the passage of tornadoes. Corks fly 
 from empty bottles, cellar doors are burst open against the 
 force of a strong wind blowing against them on the outside, 
 the walls of houses are thrown outward on all sides, the whole 
 roof is suddenly raised up and blown away, or the sudden ex- 
 pansion of air under copper and tin covering rips it up and it 
 is rolled away. And in case the walls which inclose air are not 
 tight, but there are openings through which the air can escape, 
 towels and light articles of clothing which are carried along 
 with the escaping air have been found lodged in them. 
 
 " During the tornado of Dec. 22, 1884, in Clarendon County, S. C, a 
 lady, perceiving the approach of a storm, was in the act of closing a glazed 
 door, which extended down to the floor and opened on a piazza ; but be- 
 fore she could fasten it the house was enveloped by the tempest, the door 
 flew open, and she was dashed violently against the balustrade running 
 around the piazza, and received injuries and bruises which confined her 
 to bed for several weeks. In the same room there was a heavy pine 
 press, the door of which was locked. This door was burst open, torn 
 from its hinges, and, in the language of the narrator, ' shivered into 
 kindling splinters.' There was no damage done to the house, or at 
 least none mentioned."" 8 
 
 In the tornado at St. Cloud, Minnesota, a few years ago, 
 panels were torn from the doors, and with this exception the 
 buildings seem to have been untouched. In other places win- 
 dow panes were blown out and the sash untouched. 
 
 The normal air pressure is 14.69 pounds to a square inch. 
 
GYRATORY VELOCITY AND ITS EFFECT ON PRESSURE. 361 
 
 If, therefore, one-fourth of this pressure is suddenly taken off 
 from the outside of any inclosure containing air of the normal 
 tension, then the effective explosive force is 3.7 pounds to each 
 square inch of the interior surface, or 533 pounds to the square 
 foot. And when we consider the small diameter of a tornado 
 and its rapid progressive motion, it is readily seen how sud- 
 denly this explosive force is brought into play, not allowing 
 time for the gradual escape of air and diminution of tension, 
 even where the inclosure of the air is not very tight. 
 
 237. In all the preceding relations between gyratory veloc- 
 ity and pressure it has been assumed that there are no frictional 
 resistances between the air and the earth's surface, or between 
 contiguous portions of air with different gyratory velocities at 
 different distances from the centre, and that these velocities 
 follow the law of rv = c, as would be the case without friction 
 where the air is drawn in toward, or recedes from, the centre 
 on account of slight centripetal or centrifugal forces. In the 
 case of friction, however, the gyratory velocities can only be 
 maintained by means of a vertical circulation from which arise 
 deflecting forces which overcome the frictional resistances to 
 the gyrations. In the case of friction, therefore, we cannot 
 have a strictly gyratory velocity, as we could if there were no 
 friction to be overcome, but besides the gyratory velocity v, 
 also two other components of velocity, the one the velocity u, 
 of radial motion toward or from the centre, and the other the 
 velocity x, of vertical motion. Putting, therefore, s for the 
 velocity of the resultant motion, we have 
 
 / = x* + * + v\ 
 
 But in this case s is less than v in the preceding, where there is 
 the same difference of pressure between the points of initial 
 and final velocity, since in the case of friction a small part of 
 the force due to difference of pressure is spent in overcoming 
 the frictional resistance, and only the balance in producing 
 kinetic energy. So that although we have the additional com- 
 ponents of velocity x and u, yet v is so much diminished as to 
 
362 TORNADOES. 
 
 make the value of the resultant s less than v would be in the 
 case of no resistances with the same differences of pressure. 
 
 In the case of friction, therefore, in which it is necessary to< 
 have a vertical in connection with a gyratory circulation, the 
 motions in the interior and lower part of the tornado are in 
 toward and around the centre, while the air also ascends, but 
 in the upper part it is around and from the centre, the air still 
 ascending. But the gyratory velocity near the centre of the 
 tornado is usually so great in comparison with that of the* 
 radial and vertical motions that x* and u* do not add much to 
 the value of s* in the preceding expression, and so s does not 
 generally differ much from v. The case is similar to that of a 
 right-angled triangle in which one leg is considerably shorter 
 than the other and the square of the smaller one adds but lit- 
 tle to the sum of the squares, and so the hypothenuse does not 
 differ much in length from the longer leg. 
 
 Since in the case of friction a part of the forces arising from 
 differences of pressure goes toward overcoming the frictional 
 resistances, it is evident that the theoretical relations which have 1 
 been obtained between velocities and differences of pressure 
 upon the hypothesis of no friction, is not strictly applicable in 
 the usual cases where there is more or less friction, but often 
 considerable allowances must be made for its effect ; so that 
 the velocities corresponding to differences of pressure are 
 never quite so great as they would be in the case of no fric- 
 tion ; just as, in the case of fountains, the water does not issue 
 from the orifice with that velocity with which it would in case 
 of no friction, and so is not thrown vertically upward to the 
 height of the head of the fountain. The gyratory velocities 
 also, denoted by v, in the case of friction are less in the interior 
 than those given by the law rv = c, where c, depending upon 
 the initial gyrations of the air, is known. 
 
 THE ENERGY OF A TORNADO. 
 
 238. In case of friction, we have seen, a gyratory circula- 
 tion cannot be maintained without the vertical, nor the latter 
 
THE ENERGY OF A TORNADO. 36$ 
 
 without a supply of energy to overcome the frictional resistances, 
 to such a circulation. This is found in the supply of heat which 
 originates and maintains the vertical circulation by inducing 
 and keeping up the unstable state ; for as long as this state is 
 maintained, the central part of the tornado, where the air 
 ascends, is warmer than the surrounding air, from which arises 
 a force which maintains the vertical circulation. The latent 
 heat of the vapor given out in condensation as the air ascends 
 plays an important part, and is perhaps absolutely essential, 
 since in the case of dry air the unstable state could not be in* 
 duced up to a considerable altitude, and maintained sufficiently 
 long to give rise to a tornado, as it would require a vertical 
 gradient of temperature decreasing with the increase of altitude 
 at a rate greater than i C. for each 100 meters. In this case 
 the heat would have to be continually supplied to the lower 
 strata as fast as it would be diminished by the vertical inter- 
 change between the lower and upper strata, in order to keep 
 up the unstable state. 
 
 In the case of saturated ascending air, we have seen that 
 the unstable state is maintained with a vertical temperature 
 gradient which is only about half as great, and one which is. 
 readily induced in the atmosphere and easily maintained, and 
 so the supply of air nearly or quite saturated for the ascending 
 current is very important, since the latent heat furnished be- 
 comes available energy in maintaining the interior part of the 
 tornado warmer than the surrounding part with a much lower 
 temperature in the lower strata, and a smaller vertical gradient 
 of decreasing temperature. 
 
 Thermal energy is available in doing work of any kind, or 
 in producing kinetic energy, only where there are differences 
 of temperature, that is, temperature gradients. For instance, 
 if the whole atmosphere were heated up equally in the equa- 
 torial and the polar regions to a very high temperature, there 
 would be no general circulation of the atmosphere, and no 
 expenditure of thermal energy in producing motion and kinetic 
 energy and overcoming the resistances to motion. In the case 
 of a tornado it requires not only a vertical temperature gra- 
 
364 TORNADOES. 
 
 <Iient, but this must be such as to induce the unstable state. 
 In this case the effective force in maintaining an ascending 
 current and a vertical circulation depends upon the difference 
 of temperature, or temperature gradient, taken along an iso- 
 baric surface ; so that the greater this difference of temperature 
 between the interior and ascending air and the surrounding air, 
 the greater is this force. But this difference cannot be main- 
 tained unless the atmosphere is kept in the unstable state for 
 saturated air by the continual supply of heat to the lower strata 
 as it is drawn away by the ascending current. If, however, the 
 atmosphere is not merely unstable, but considerably beyond 
 the neutral condition, before the ascending current and vertical 
 -circulation set in, there is a considerable reserve of energy, 
 which suffices to maintain the motion, until the unstable state 
 is gradually reduced either to the neutral or the stable state. 
 And this latter state can be produced not only by the convec- 
 tion of heat in the ascending air currents, but also by the sup- 
 ply of air for the ascending current which is gradually becoming 
 -drier, since the drier the air the greater the difference of tem- 
 perature required between the lower and the upper strata, and 
 for the lower part, up to where the vapor in the ascending cur- 
 rent begins to condense, the gradient of decreasing temperature 
 has to be more than i C. for each 100 meters. As there is no 
 expenditure of energy until motion commences, so the more 
 rapid this motion, the greater the rate at which energy is 
 expended. 
 
 239. In the origination and first starting of a tornado, the 
 force which overcomes the inertia of the air and causes motion, 
 is the difference of pressure depending upon the difference of 
 temperature between the interior and exterior. This, in the 
 lower strata of the atmosphere, is a centripetal force, and as 
 the air is drawn in toward the centre the velocity is accelerated, 
 and where there is initial gyratory motion, the body is at the 
 same time deflected from its course ; but the velocity at any 
 time is the same as if the same force had acted during the same 
 time in a radial direction without any gyratory motion and de- 
 decting force, for the latter, we have seen, does not increase 
 
THE ENERGY OF A TORNADO. 365; 
 
 the kinetic energy, but simply changes the direction of motion. 
 After the vertical and gyratory circulations are fully established,, 
 the whole force arising from difference of pressure due to dif- 
 ference of temperature goes to overcome the frictional resist- 
 ances, and no part to creating motion and kinetic energy, and 
 the velocity of the vertical circulation is such that the resist- 
 ances are exactly equal to the forces. In the case of no friction, 
 no forces are needed to maintain ^the circulation after it is 
 once inaugurated, and so no difference of temperature between 
 the interior and the exterior and expenditure of heat energy, 
 but if there is such, it tends to continually accelerate the verti- 
 cal circulation. The kinetic energy of the gyratory velocity 
 has its exact equivalent in the potential energy of the differ- 
 ence of pressure caused by the centrifugal force of the gyra- 
 tions, and where there is friction and a necessity for a vertical 
 circulation, there must be a difference of temperature and a 
 corresponding difference of pressure arising from it, to over- 
 come the frictional resistances to this circulation. 
 
 In a cyclone, for reasons given in 232, the forces are mostly 
 spent in overcoming the resistances, while in a tornado they 
 are spent mostly upon the inertia of the air, and so the rela- 
 tions between gyratory velocities and distances from the centre 
 are nearly those given by the law of rv = c, and between these 
 velocities and differences of pressure, or pressure gradients, 
 those given in 233, determined upon the principle that the 
 difference of pressure is caused almost entirely by the centrifu- 
 gal force, which of course is only approximately so in the case 
 of friction, since a little force and difference of pressure, even 
 in the open air at some distance above the earth's surface, is 
 necessary to maintain the vertical circulation. 
 
 240. In a vertical circulation arising from the unstable 
 state, where there is no gyratory motion, the force which gives 
 rise to and maintains the ascending current depends upon the 
 difference of pressure in the column of ascending air and the 
 surrounding undisturbed air at the same levels ; and if we 
 assume that the force is spent mostly upon the inertia of the 
 air, and but little in overcoming the friction, we can determine 
 
.366 TORNAbOES. 
 
 -approximately the velocity of the ascending current from the 
 differences of temperature and pressure, where these are known. 
 At the earth's surface the vertical component of velocity is 
 nothing, and the pressure at the base of the ascending column, 
 if we neglect the friction of the current, is the same as at the 
 earth's surface in the surrounding parts. The differences of 
 temperature in the ascending current and the surrounding un- 
 disturbed air, in the case of tornadoes is the same as in the 
 case of cyclones between the columns A and C or C' in the 
 table of 159, or between D and F, or G and /. Of course 
 these differences depend very much upon the assumed vertical 
 gradient of temperature and the hygrometric state of the air, 
 as exemplified in the table, and there may be cases in nature 
 in which the temperature differences between a column of as- 
 cending air and one in the exterior undisturbed air are much 
 ^greater than those in the table under the assumed conditions. 
 The maximum differences, it is seen, are about 5 C. Let us 
 assume that the average difference of temperature, taken with 
 regard to mass and not volume, in the column of ascending air 
 and one in the surrounding undisturbed air, up to the altitude 
 where the pressure at the same level is equal, is 3 C., and that 
 the level of equal pressure is at the height where the barometric 
 pressure is equal to 380 mm. Supposing the mean tempera- 
 ture of the air column below the level of equal pressure to be 
 o C., then the difference of pressure of the column of ascend- 
 ing air below this level and of a similar column in the sur- 
 rounding undisturbed air, and the effective potential energy 
 in causing kinetic energy at the height of the column, is the 
 3/273 part of 380 mm., or 4.2 mm. With this value of A P in 
 the last expression of / in 235, putting P= 380 and T= T , 
 as it is very nearly by the table of 13, we get s = 42 m., nearly, 
 for the velocity per second due to the difference of pressure 
 between the two columns. Or by Table VI we have the value 
 of h for each millimeter of* barometric pressure at the pressure 
 of 380 mm. and at the temperature of o C. equal to 21.03 m - 
 and so for 4.2 mm. equal to 88.33 m., and with this value of // 
 multiplied into 2g= 19.61 m., we get by the first form of the 
 
THE ENERGY OF A TORNADO. 367 
 
 -expression of s* in 235, the same value of s as above by the 
 last form. This theoretical result is, of course, considerably 
 diminished by the effect of friction, which is not taken into the 
 account in the theory. 
 
 241. Where the atmosphere is in the unstable state all the 
 way up to the top, or even to very high altitudes only, the 
 level at which the pressures in the ascending air and at the 
 same level in the surrounding undisturbed air are the same, 
 where there is no depression in the interior from gyratory 
 motion, is very high, and the effective force in causing ascend- 
 ing velocity is great. But if the unstable state of the atmos- 
 phere does not extend very high, as is undoubtedly the case 
 often, the horizontal isobaric surface is not very high. The 
 unstable state may extend to so low a level only, that the 
 kinetic energy of the ascending current may be destroyed by 
 the pressure of the column of air before the current reaches 
 the top of the atmosphere. In that case the ascending current 
 is deflected off laterally in all directions below this level, and 
 the isobaric surfaces above that level are not affected directly 
 by the thermal conditions, though they are all, together with 
 those below, depressed by the gyratory motion of the tornado ; 
 but as the vertical circulation in this case depending upon 
 differences of temperature extends only up to a certain height, 
 the air above this can only be brought into the gyration by 
 the friction between it and the gyrating air below, and an 
 inverse vertical circulation induced indirectly in the air above. 
 For while the gyrations are more rapid below than above, the 
 tendency is to carry the comparatively little disturbed air 
 above out and around the centre, and to draw down that above 
 in the central part, just as has been explained in the case of 
 cyclones, where the vertical circulation from temperature dis- 
 turbances does not extend to the top of the atmosphere, and 
 the interior dry and clear air above is brought down into the 
 central part and causes the " eye" of the cyclonic storm. In 
 this way, if the duration of the tornado were long enough, and 
 the atmosphere were calm, or had the same general motion 
 above and below, the gyratory motion would always be induced 
 
368 TORNADOES. 
 
 from bottom to top, though with less force ; but the time of 
 duration being generally short, and the general easterly motion 
 above being mostly much greater than below, tornadoes of 
 this sort, in which the atmosphere above is not in the unstable 
 state, perhaps rarely extend with much violence to very high 
 altitudes in the atmosphere. They may, notwithstanding, 
 have great energy and violence, for the ascending air escapes 
 laterally on all sides above ; but of course tornadoes, in general, 
 are of the greatest violence, and the ascending currents most 
 rapid, where there are gyrations and a rarefied centre extend- 
 ing to great altitudes, just as the taller a flue, the greater the 
 draft with the same difference of temperature within and with- 
 out. 
 
 As in cyclones, as may be seen from the examples in the 
 table of 159, so in tornadoes, the greatest temperature dif- 
 ferences are not in the lower strata of the atmosphere, but up 
 at a certain altitude above ; or if the atmosphere is in the 
 unstable state all the way up, this difference increases to the 
 top. The conditions may even be such, especially if the air is- 
 not nearly saturated, that there is no difference of temperature 
 below between the interior and exterior part, or the interior 
 part up to some height may even be colder. In such cases the 
 energy is mostly at a considerable altitude, and the vertical 
 circulation and the gyrations are first originated there, and 
 gradually communicated to the strata below by friction and by 
 the relieving of the lower strata in the central part of a part of 
 the pressure from the air above, which finally gives rise to an 
 ascent of air from the stratum next the earth's surface and a 
 drawing of it in from all sides at the surface toward the centre. 
 
 242. If the gyratory velocity near the earth's surface in a 
 tornado were as great as it is above, there would not be, in 
 general, a very strong ascending current in the interior, for 
 although there might be an enormous difference of pressure, 
 yet the force arising from this difference of pressure with which 
 the air would tend to run in below toward the centre and up irt 
 the interior would be in a great measure counteracted by the 
 centrifugal force of the gyratory velocity below. When the 
 
THE ENERGY OF A TORNADO. 369 
 
 gyratory velocities are the same at all altitudes, the only force 
 by which it flows in below and up the interior is that due to dif- 
 ference of temperature between the central and exterior parts 
 of the isobaric surfaces, by which the vertical circulation is 
 maintained. But even this, we have ( seen ( 240), under 
 assumed not improbable conditions, may give rise to a con- 
 siderable ascensional velocity. This, however, is very greatly 
 increased in consequence of the great frictional resistance to 
 the rapid gyration of the air near the earth's surface, by 
 which the gyratory velocity and centrifugal force here, which 
 tend to prevent the air from rushing into the partial vacuum, 
 are much diminished. 
 
 In the assumed example of 234 the difference of pressure 
 between the points f and , Fig. I, is equal to the pressure 
 of the column of air bE, that is, equal to the pressure of a 
 column of air of 1000 meters in height and of the average 
 density between the earth's surface and that altitude, which, in 
 barometric measure at an ordinary medium temperature of 
 20 C., as may be readily determined by table VI, is about 
 84 mm., since I mm. of barometric pressure corresponds to- 
 about 12 meters of altitude. If we suppose the gyratory 
 velocity near the earth's surface beyond f, taking no account 
 of those between f and the centre, to be so diminished by 
 friction that the centrifugal force would be diminished one 
 third, the difference of barometric pressure between /"and E, 
 which would be effective in causing an inflow toward the 
 centre, in addition to that considered above due directly to* 
 temperature differences, would be 28 mm. This would give 
 rise to a very great ascensional velocity in the interior of the 
 tornado, not however near the earth'$ surface but at some 
 distance above, for the kinetic energy of the inrush of air from 
 all sides toward the centre would be changed to potential 
 energy in the form of increased pressure in the central part 
 of the tornado at the earth's surface, which would be equal to- 
 that at E if the whole centrifugal force at the earth's surface 
 were destroyed, and then this increased pressure would give 
 rise again to kinetic energy in a rapidly ascending current in. 
 
3/0 TORNADOES. 
 
 the interior, where the air is comparatively rare and the 
 pressure much diminished from the effect of the gyrations 
 above. 
 
 With the value of 4P=2& mm. or the corresponding 
 value of h taken from Table VI, either of the expressions of j 2 
 in 235, applied as in 240, gives for a temperature of 20 C., 
 s = 78.5 meters per second, or about 176 miles per hour. Com- 
 bined with this ascensional velocity would be the gyratory ve- 
 locity of the ascending air, which would be diminished by the 
 effect of friction near the earth's surface, for the ascending air 
 near the centre would consist mostly of the air entering near 
 the earth's surface. 
 
 243. The tornado being a column of rapidly gyrating air, of 
 great height generally in comparison with its diameter, and 
 with the air very much rarefied in its interior from the effect 
 of the rapid gyrations near the centre, may be likened to a tall 
 flue with heated and rarefied air in its interior. If the draft of 
 the flue is almost entirely cut off below, the ascending current 
 is feeble, but if the air below has free access, the velocity of 
 the ascending current- in the flue becomes very great, and in 
 proportion to the difference of temperature between the inte- 
 rior and exterior. So in a tornado, if the access of air were 
 almost entirely cut off from the lower central part by the cen- 
 trifugal force of the undiminished gyratory velocities near the 
 earth's surface, the ascending current in the interior would be 
 of no great violence, generally such perhaps as in the assumed 
 cases of 240 ; but with a somewhat free access of air below 
 into the rarefied interior, on account of a decrease by friction of 
 the gyratory velocity near the earth's surface, the velocity of 
 the uprush of air in tl^ interior becomes enormous. In this 
 case the centrifugal force of the gyrations in the open air a 
 little above the earth's surface, where there is little friction, 
 almost entirely excludes the access of air into the interior, and 
 serves very nearly the same purpose as the wall of the flue, 
 while the partial destruction of these gyrations near the earth's 
 surface by friction is similar to the letting on the draft of a flue 
 which had been almost entirely cut off. 
 
FORCE OF THE WIND. 3/1 
 
 With an increase of the force of the ascending current, and 
 of kinetic energy, there is a corresponding increase in the ex- 
 penditure of heat energy, for the more rapid the current the 
 faster is the condensation of aqueous vapor and the freeing of 
 .latent heat, and the faster is the heat of the lower strata con- 
 veyed to the upper ones by which the unstable state is de- 
 stroyed unless heat is constantly supplied to the lower strata. 
 The part which friction plays in this matter is the facilitating 
 the application- of the heat energy by allowing a more free and 
 rapid vertical circulation and vapor condensation. 
 
 FORCE OF THE WIND AND SUPPORTING POWER OF ASCEND- 
 ING CURRENTS. 
 
 244. In view of the enormous gyratory and ascensional 
 velocities in a tornado, it is interesting and important to know 
 the destructive force of the former and the supporting power 
 of the latter. These are both deducible from the first of the 
 expressions of s* in 235. According to this, when air with a 
 velocity of s impinges against a barrier at right angles to the 
 direction of motion, so that velocity in this direction is com- 
 pletely destroyed, or s = o, it gives rise to a force which sup- 
 ports a column of mercury of the height AP, determined by 
 this expression where P and T are known. But if instead of a 
 mercurial barometer we use one of pure water of standard 
 temperature, and denote the change in the height of the col- 
 umn corresponding to AP by Ap, we have Ap = 13.596 AP, the 
 pressure of mercury being so many times greater than water, 
 and we then get, if we express Ap in centimeters instead of 
 millimeters, 
 
 If we now consider the pressure on a unit of surface of one 
 square centimeter, then, since by definition a cubic centimeter 
 of pure .water of standard temperature is a gram, the pressure 
 of the column of water of the height Ap and unit base in 
 
3/2 TORNADOES. 
 
 grams, is dp, and the pressure upon a surface of which the- 
 area is A, is Adp, a gram of pressure being the gravitational 
 pressure of a gram. Putting/ for the pressure of air in mo- 
 tion upon a normal surface area of A, we have/ = A dp, and 
 with this the preceding expression gives 
 
 P T 
 
 The pressure, therefore, is as the square of the velocity and' 
 as the density of the air, this latter being directly as the press- 
 ure and inversely as the absolute temperature. Hence, at 
 high altitudes where P is much less than P , the pressure of 
 the wind for the same velocity is much less than near the sur- 
 face. This is for pure and dry air. For air with an average 
 amount of moisture in it, it is more accurately expressed by 
 
 .00659 P 
 
 - 
 
 The same formula in English measures, in which / is ex- 
 pressed in pounds avoirdupois, s in miles per hour, and A in 
 square feet, is 
 
 .002698 P 2 
 
 With this formula we get for the pressure of wind of the 
 velocity of 80 miles per hour upon a square foot at the earth's 
 surface, where P P , when the temperature r is 25C.,/ = 
 15.7 pounds. At the altitude where P= 380 mm., with the 
 same temperature, the pressure for the same velocity would 
 be only .half as much. With the temperature equal o C., in- 
 stead of 25 C., the pressure would be increased in the ratio of 
 10 to ii. 
 
 245. The preceding formulae express the pressure of the 
 wind arising from the momentum of the air, or the change of 
 kinetic into the potential energy of pressure. But this, as in 
 other cases where friction is not taken into account in the 
 theory, is considerably modified by the effect of friction ; and 
 in this case the effect is to increase the effect, and not, as is- 
 
FORCE OF THE WIND. 373 
 
 usually the case, to diminish it. What is usually called the 
 force of the wind upon any given object, as a plate of a given 
 area, is the difference of pressure on the two sides. On the one 
 side the pressure is increased, not only by the momentum of 
 the air, but likewise by the dragging effect through friction of 
 the air which passes by, upon the cone or pyramid of compara- 
 tively stationary air in front of the plate or barrier. On the 
 other side the effect, to the same amount, is to drag the air 
 away and to diminish the pressure of the air. Hence the theo- 
 retical difference of pressure, or effective force of the wind, is 
 increased by equal amounts by the effect of friction upon the 
 pressure of both sides. Accordingly the force of wind deter- 
 mined experimentally is found to be a little greater than the 
 theoretical pressure given by the formulae. 
 
 According to Hagen's empirical formula, determined from 
 very accurate experiments made a few years ago by means of 
 a whirling apparatus, the experimental pressure of the wind on 
 small plates, in grams, denoted here by/>', is 65 
 
 p' = (0.00707 + o.oooi 125^) Fv*, 
 
 in which u is the periphery and F the surface of the plate in 
 decimeters, and v is the velocity per second in decimeters. 
 The average barometric pressure in the experiments was 758mm., 
 but no account seems to have been taken of the temperature. 
 If we reduce this expression of/ to English measures and the 
 standard pressure, we get 
 
 p' = (0.00289 -f 0.000140 u) As\ 
 
 in which the notation is the same as in the preceding theoreti- 
 cal expression of/ in English measures. 
 
 Supposing Hagen's experiments to have been made at a 
 temperature of 15 C., a very comfortable working temperature, 
 and reducing, for comparison, the preceding theoretical expres- 
 sion of/ to this temperature, we get 
 
 / = 0.00255^*. 
 
374 TORNADOES. 
 
 The difference of these two expressions, 
 
 p' p (0.00034 -f- o.ooo 1 4042^) 
 
 is the effect of friction in increasing the theoretical value of/. 
 The plates used were small, ranging from about two to six; 
 inches square, and the velocities in the experiments were also* 
 small. Supposing the average size of the plates to be five 
 inches square, the value of u become 20 inches, equal ta 
 1. 667 feet. With this value of u we get for the experimental 
 expression representing the average for all the velocities and 
 for all the plates 
 
 p' p 0.0005 7 A /. 
 
 Hence it is seen that the theoretical coefficient is increased 
 about two-ninths by the effect of friction. 
 
 While Hagen's experimental formula may very nearly give 
 the true force of the wind for the average of the plates and 
 velocities used, it is obviously at fault with regard to the law of 
 variation with variations of u and s. By increasing the pe- 
 riphery of the plate, the force, per unit of surface, is increased 
 enormously by his law, and the part/' /, for very large plates, 
 in which u is large and the term depending upon it, becomes 
 the principal term, being very nearly as the cubes of the linear 
 dimensions of the plates, or as uA. For such a law there does 
 not seem to be any reason in theory ; and more numerous and 
 accurate experiments, made with plates of a larger range of 
 sizes, would undoubtedly give a different law. It is improb- 
 able, therefore, that the formula is applicable to plates of a size 
 much greater than those used in the experiments. Again, the 
 formula makes the part arising from friction to be as the 
 square of the velocity, which is not in accordance with either 
 theory or experiment. The theory of the viscosity of gases 
 would make it as the first power, and hence for high velocities 
 the force given by the formula must be too great even for 
 small plates. 
 
 From what precedes, it may be inferred that about one- 
 fourth or one-fifth part must be added to the theoretical 
 
FORCE OF THE WIND. 375 
 
 values of wind-pressures per square foot of normal surface given 
 by theory, to obtain the effective force of the wind in moving 
 objects, this force being increased by the diminution of the 
 ordinary pressure of the air on the other side opposite to that 
 on which the wind strikes. 
 
 246. The force with which the wind tends to move a spheri- 
 cal body is one-half of that with which it tends to move a body 
 with a normal surface exposed to the wind which is equal to the 
 maximum section of the sphere. The theoretical formula, 
 therefore, which gives the pressure p of the wind against a 
 globe, or the resistance of the air to a globe moving through 
 it, is 
 
 0.00135 
 
 : - 
 
 I + .004r 
 
 in which the notation is the same as in 243. But here, as in 
 the case of wind-pressure on plates, the theoretical pressure 
 and resistance are increased by friction and for the same 
 reasons. 
 
 From the two sets of experiments made at the request of 
 Newton, in St. Paul's Cathedral, at London, the one with 
 several hollow glass globes of about 5 inches in diameter, let 
 fall from an elevation of 220 feet, and the second one with sev- 
 eral bladders formed into spheres about 5 inches in diameter, 
 let fall from a height of 272 feet, the weights being known and 
 the times of descent being carefully noted, Loomis 66 obtained 
 from the first series, for the coefficient of resistance to a globe 
 5 inches in diameter, the velocity being in feet per second, 
 0.0013455, and from the second series, with the bladders, 
 0.0012693, in ounces Troy. The average is 0.0013074. Hence 
 the expression of the resistance to such a globe, or of the 
 pressure of the wind against such a globe, denoted here 
 is, in ounces Troy, 
 
 /= 0.0013074^', 
 
376 TORNADOES. 
 
 in which s is in feet per second. The reduction of this formula 
 to the units of measure of 244, that is, pounds avoirdupois, 
 miles, and hours, gives 
 
 p' = 0.00142 iAs\ 
 
 .But in these experiments, as in the case of Hagen's, no ac- 
 count seems to have been taken of the temperature, and so we 
 are at a loss to know what temperature to use in the preceding 
 theoretical expression of / in order to make a comparison of 
 the experimental coefficient with the theoretical. But assum- 
 ing in this case, as in the other, that the experiments were 
 made at a temperature of 15 C, and also that the barometric 
 pressure was 760 mm., then the preceding theoretical expres- 
 sion of/, for P =. P Q and T = 15, becomes 
 
 / = 0.001274^*. 
 We therefore get 
 
 p' p 0.000147^*. 
 
 Hence the theoretical coefficient is increased about one-ninth 
 part by the effect of friction in the case of spheres, according 
 to the preceding experiments. 
 
 But Loomis also determined another coefficient of resist- 
 ance from the results of experiments made by Hutton with a 
 whirling machine and a sphere of pasteboard 6f inches in 
 diameter, for velocities from 3 to 20 feet per second. This was 
 found to be one-fourth greater than the other. This great dif- 
 ference indicates that there is considerable uncertainty in such 
 experiments. Adding one-fourth part to the preceding experi- 
 mental coefficient, we get in this case 
 
 p' 0.001776^5*. 
 
 Combining this with the previous experimental expression, 
 giving the former one double weight, and supposing all the ex- 
 periments to have been made under the same pressure and 
 temperature, we get 
 
 p' = 
 
FORCE OF THE WIND. 377 
 
 Comparing this with the preceding theoretical expression re- 
 duced to the temperature of 15 C., we find that, with this com- 
 bination of the results of the three series of experiments, the 
 effect of friction increases the theoretical coefficient about two- 
 ninths, the same as in the case of the wind blowing normally 
 against a plate. We may, therefore, assume with considerable 
 probability that the theoretical coefficient 0.002698, in the case 
 of a plate, is increased two-ninths by the effect of friction, and 
 we therefore get for the whole wind pressure against a normal 
 plate 
 
 0.00330 
 - 
 
 and for the pressure against a sphere, or the resistance to a 
 sphere moving through the air with velocity s, 
 
 0.00165 P A ^ 
 i + 0.004T P 
 
 From the former of these the values of p' in Table VII have 
 been computed for the several velocities and barometric press- 
 ures given as arguments in the table, the temperatures used be- 
 ing those of the table of 13, corresponding to the pressures at 
 different altitudes. These temperatures may be regarded as 
 a sort of annual means in the middle latitudes, corresponding 
 to the altitudes of the given pressures. For extreme tem- 
 peratures, deviating considerably from these, slight corrections 
 would be necessary if great accuracy were required. 
 
 According to this table and the formula, the mechanical 
 force of the wind in tornadoes, upon surfaces exposed normally 
 to its direction must often be enormous. In the example of 
 234, although the gyratory velocity of the air at the distance 
 of looo meters is only 3 meters per second, yet by theory the 
 velocity at the distance of 21.4 meters is 140 meters per sec- 
 ond, or about 310 miles an hour. This by the preceding for- 
 mula and the table would give, at the earth's surface, for an 
 average temperature, an effective force in moving an object of 
 about 300 pounds for each square foot of normal surface ex- 
 
3/8 TORNADOES. 
 
 posed to the wind. But if the body were a sphere it would be- 
 only half as much for each square foot of area of maximum 
 section. 
 
 In the case of the velocity of the ascending current of 176 
 miles per hour near the earth's surface obtained upon the as- 
 sumptions of 242, Table VII gives a supporting power of 
 more than 90 pounds to the square foot. 
 
 247. Having now determined the force of an ascending 
 current of given velocity s against a sphere of given maximum 
 sectional area A, as in the last expression of p' , this becomes. 
 the supporting power of an ascending current in keeping such 
 a sphere from falling to the earth. The mass of a sphere of 
 pure water one foot in diameter, expressed in pounds avoirdu- 
 pois, is 62.43 X 0.5236 D a , in which D is the diameter of the 
 sphere in feet, 62.43 being the mass of a cubic foot of water, 
 and 0.5236 the ratio of a sphere to its circumscribing cube. 
 Hence the mass M of any sphere of diameter D and density p, 
 and likewise the force of gravity expressed in pounds, taking 
 no account of the slight variations of gravity at different lati- 
 tudes and altitudes, is M 32.69 D 3 p. 
 
 In the case of a body falling through the atmosphere, or 
 any other resisting medium, the velocity of the body is acceler- 
 ated until the resistance becomes equal to the force of gravity, 
 after which it continues uniform unless the force or the density 
 of the medium changes. But if the ascending current has the 
 same velocity as that with which the body would fall through 
 it after the velocity becomes uniform, the force/ 7 of the ascend- 
 ing current against the sphere, which is the resistance in the 
 case of the falling body,- is equal to the force of gravity, and 
 the body is supported. Hence, putting the preceding expres- 
 sion of/' equal to the force of gravity, M, we get 
 
 
 as the condition for determining the diameter of a sphere of 
 given density p which would be supported by an ascending cur- 
 
SUPPORTING POWER OF ASCENDING CURRENTS. 379* 
 
 rent of velocity s, under any given condition of pressure P and 
 temperature r. 
 
 Since A is the maximum section of the sphere, we have 
 A = O.7854/? 2 , 0.7854 being the ratio of the circle to its cir- 
 cumscribing square. With this value of A, the preceding equa- 
 tion gives 
 
 _ 0.0000396 P s^ 
 ~ I +0.0042- P p' 
 
 Having used the expression of p' instead of /, the theoretical 
 expression of the force of the wind, this expression takes into 
 account the effect of friction as heretofore determined. 
 
 For the diameter of a sphere of the density of water, which 
 is supported by an ascending current of 100 miles per hour near 
 the earth's surface, where P may be put equal to P 9 , assuming 
 that the temperature is o C., we get, very nearly, D = 0.4 of 
 a foot, or 4.8 inches. For a sphere of ice of density 0.92 at the 
 altitude where P = %P , it gives for the same ascending velocity 
 D = 0.215 of a foot, or 2.58 inches. 
 
 With the preceding expression the values of D in Table VII 
 have been computed, giving the diameters, in inches, of a sphere 
 of the density of water which would be supported by ascending 
 currents of air of the velocities s in the first column, at the alti- 
 tudes where the barometric pressures are as given at the heads 
 of the columns, the temperatures being assumed to be as in the 
 table of 13. For spheres of other densities, it is seen from 
 the formula the tabular numbers must be divided by the den- 
 sity as compared with water. 
 
 248. In the case of an ascending current of velocity j, a 
 body with a diameter of the value of D given by the preceding 
 formula, or by Table VII, would remain suspended in the air, 
 but if the ascending velocity were increased, the body would be 
 carried up at such a rate as to lef the relative ascending 
 velocity between the air and the booy equal to s. According 
 to the preceding example of a sphere of ice, a hailstone of the 
 diameter of 2.58 inches, up where the pressure in only 380 mm. 
 would be sustained in the air at the same level, by an ascend- 
 
380 TORNADOES. 
 
 ing current of 100 miles per hour, but if this current were in- 
 creased to no miles, then the hailstone would be carried up at 
 the rate of 10 miles per hour, as long as the pressure and 
 density were not sensibly changed, and it would continue to 
 ascend with decreasing velocity until the value of P in the pre- 
 ceding expression of D would be satisfied for D = 0.215 and 
 s = ioo. 
 
 The ascending velocity required to sustain a rain-drop in 
 the air is given by the preceding formula and Table VII. If 
 the rain-drop is o.i of an inch, then D = 0.0083 f a foot. 
 With this value of D the preceding formula is satisfied up at 
 the altitude where P 600 mm. and t = 10 C., with the value 
 of s = 16.6, which is a very gentle ascending current, but sufifi- 
 ciently strong to prevent the falling of ordinary rain-drops. 
 
 Mr. Dines has measured rain-drops as small as 0.0033 inch 
 in diameter. Drops of this size satisfy the formula up where 
 .P =. 600 mm. with a value of s =-3, and hence an ascending 
 velocity of 3 miles per hour would sustain such drops. Mr. 
 Dines 97 has also measured fog particles as small as 0.00062 
 inch, equal 0.0000517 of a foot. With this value of D the 
 formula at an altitude where P = 600 mm. gives s = 0.41. 
 The law of resistance as the square of the diameter and 
 velocity, as given by the expression of/ 7 , 246 (for A is as D 2 ) 
 may not hold very accurately for so small particles, but the 
 formula applied in these cases at least shows that exceedingly 
 small ascending velocities are sufficient to sustain even the 
 larger and measurable cloud and fog particles in the air, and 
 so there is no necessity to resort to the old and improbable 
 vesicular theory of cloud particles in order to account for the 
 floating of clouds in the air. For in the cyclone and cloud 
 areas we know there are always ascending currents, and in the 
 surrounding parts where there is no ascent of the air, or gen- 
 erally a slight descent, there is a clearing off from the descent 
 'of the cloud particles innfthe unsaturated air below, where they 
 are evaporated and converted back again into clear and trans- 
 parent vapor. Hence, as in the vertical circulations of the 
 atmosphere the slight ascending currents in some places give 
 
SUPPORTING POWER OF ASCENDING CURRENTS. 381 
 
 rise, first to haziness, and then to a clouded sky, so at others, 
 where there are very slowly descending currents, the sky which 
 previously was entirely overcast with clouds becomes, somewhat 
 all at once, clear from the vanishing, and not from the passing 
 over of the clouds. 
 
 The size of rain-drops in all cases is an indication, in some 
 measure, of the velocity of the ascending currents. Small rain- 
 drops indicate that the ascending current is so feeble that they 
 can fall, and are not carried up ; but where only very large 
 drops fall, the indication is that the ascending current is so 
 strong that all except the very large ones are either carried 
 upward, and in the case of a tornado outward above to where 
 the ascending currents are less, or else are sustained in the at- 
 mosphere until by the contact and blending with them of other 
 drops, they become large enough to fall. 
 
 249. Only a few of the many instances of observed force of 
 the wind and supporting power of ascending currents in tor- 
 nadoes can be given here, for the literature on this subject has 
 become immense. From the account of the tornado of April 
 1 6, 1875, at Walterborough, S. C., 69 the following facts are 
 taken : 
 
 The Academy and seven churches were totally destroyed,, 
 and of the whole number of ninety dwellings some sixty were 
 torn to pieces and strewn to the four winds of heaven. At 
 least 5000 trees in the village were scattered in every direction. 
 The roar of the wind was such that the tremendous crash was 
 heard by no one. One gentleman was looking from his piazza 
 and saw large trees fall in his yard, but heard no more sound 
 than if they had been feathers. 
 
 The greatest destruction was on the south side of the track. 
 A heavy piece of timber 6 by 6 inches and 40 feet long, weigh- 
 ing 600 pounds, was carried from the Episcopal church in a 
 direct line over the tops of houses to a distance of 440 yards in 
 a direction W. 10 N. The wind continued in its first direction 
 for a few seconds only, when it changed to the north with in- 
 creased fury. A large 4-horse lumber wagon, weighing 3,500 
 
382 TORNADOES. 
 
 dbs., was lifted over a 6-foot fence and carried 60 feet from its 
 -original position. 
 
 A chicken coop, box 4 by 4 feet, weight 75 Ibs., was 
 carried 4 miles. Hickory trees, 54 inches in circumference at 
 butt, weight 3000 pounds, were lifted out of the ground and 
 carried up a bank 10 feet high. A cart weighing 600 pounds 
 was carried up in the whirl, torn to pieces, and the tire of one 
 wheel found 1320 yards distant. Dead sheep were found with 
 wool off the hide. Geese plucked of feathers, as if picked by 
 hand. 
 
 From the account of the tornado of Aug. 9, 1878, at Wal- 
 lingford, Conn., 70 the following statements are gleaned : The 
 :great power of the wind at one place was illustrated by the 
 carrying of a large oak tree so far that its place of growth 
 could not be found. Persons witnessing it said that two cur- 
 rents of air seemed to unite at this point, where the valley 
 grew narrower. 
 
 The indraught reaching down Old Colony street was severe 
 enough to take large elm trees and wrench them off at some 
 distance from the ground. Along this street where the roots 
 of trees were strong and well planted, the limbs only were 
 affected, the appearance being that the force was exerted some 
 feet above the surface. A barn was carried bodily away and 
 no parts of it afterward recognized. Mr. Vasseur's house was 
 lifted up and the parlor floor arched upward. An elm tree, 
 measuring 9 feet in circumference, was broken off 9 or 10 feet 
 from the ground. 
 
 Pieces of timber and scantling were imbedded in apple trees 
 so far (fully 6 or 7 inches deep), that in efforts to pull them out 
 they were broken off. An iron rowboat, said to weigh about 
 80 or 85 pounds, was lifted from the water of the pond and car- 
 ried by the force of the wind 225 feet. A large apple tree, 
 weighing nearly 1500 pounds, was carried 20 feet due north. 
 
 The arching up of Mr. Vasseur's parlor floor was, no doubt, 
 caused by the expansion of the air beneath, from the sudden 
 removal of the surrounding pressure ( 236). 
 
 250. The following facts are taken from the account of the 
 
SUPPORTING POWER OF ASCENDING CURRENTS. 383 
 
 tornado at Mount Carmel, Illinois, June 4, 1877:" The houses 
 on the south side of the street were totally destroyed, and 
 bricks and other objects hurled with great force northward 
 against the buildings, somewhat damaged but left standing, on 
 the opposite side of the street. A brick moving at an angle of 
 15 or 20 with the horizon, entered the Harris house through 
 the weather-boarding, lath and plastering, crossed two rooms, 
 a distance of 27 feet, and lodged in a rear wall without break- 
 ing even the corners from the brick. From the large and cir- 
 cular aperture through which the brick entered it was thought 
 that it must have whirled rapidly in its transit. So great was 
 its velocity, that the laths were cut quite smoothly without 
 cracking the adjoining plastering. 
 
 Lewis Gott saw the tornado strike his house, his point of 
 observation being one square north. As he described it, the 
 house appeared to go up bodily and plunge into the cloud. 
 Only a very small portion of it was ever seen afterward to be 
 recognized. 
 
 Although many small objects were thrown outward by the 
 whirl of the tornado, yet the general tendency of trees and 
 prostrate buildings was inward toward the centre of the track, 
 this effect being more noticeable, however, on its southern than 
 on its northern side. 
 
 Objects were carried to great distances. A piece of tin roof 
 was carried 17 miles N.E. The spire, vane, and gilded ball of 
 the Methodist Church were found at the distance of 15 miles 
 N.E. A letter was carried by the wind 45 miles in the direc- 
 tion of N.N.E. A paper sack of flour was found nearly 5 miles 
 distant in Indiana. 
 
 The accompanying plate, copied from the Report of the 
 Chief Signal Officer for 1877, shows the destructive violence of 
 this tornado in a narrow path where it passed through Mount 
 Carmel. 
 
 251. The following extracts are taken from an account by 
 H. C. Hovey of the tornado at St. Cloud and Sauk Rapids, 
 Minn., which took place on April 14, i886. 76 
 
 " During the day a remarkably high temperature, for the season, had 
 
384 
 
 TORNADOES. 
 
SUPPORTING POWER OF ASCENDING CURRENTS. 385 
 
 prevailed, the mercury rising as high as 80, and the air was sultry and 
 oppressive. At 3 P.M. observers saw dark banks of struggling clouds 
 overhanging the ridge that in ancient times used to be the river limit, 
 and there were apprehensions of impending danger. Suddenly the clouds 
 began to revolve, while sharp points shot downward, until a whirling fun- 
 nel-shaped mass was formed above a basin amid the hills, that seems to 
 have furnished the cradle for the ensuing tornado. Its first condition 
 was undoubtedly that of a simple whirlwind, having a diameter of about 
 looo feet, which uprooted or twisted off nearly every tree in its circle, 
 overturned the monuments in the adjoining Masonic cemetery, and tore 
 up the boulders from the ground. Thence it moved slowly and majesti- 
 cally along at the rate of about 12 or 15 miles per hour, but with an in- 
 conceivably rapid rotary motion upon its vertical axis, confining itself 
 for some distance to a path hardly more than 150 feet wide. Hundreds 
 of people took timely warning and got out of the road of the moving 
 column of cloud, whose general trend was toward the northeast. Hav- 
 ing wrecked the Catholic Church on Calvary Hill, and also several farm- 
 houses, it entered a portion of the city of St. Cloud mainly occupied by 
 foreigners, whose frame cottages were strewn over the plain indiscrimi- 
 nately, leaving nothing but the cellars to mark the sites of the houses. 
 
 " I noticed but one exception to this general work of complete demo>- 
 lition, and that was a house that had been whirled about end for end and 
 left on its foundation as a wreck. Reaching the freight depot of the 
 Manitoba R. R. the wind tore to pieces, and overturned the long line of 
 freight cars, carried the trucks away, and even in places wrenched the 
 iron rails from the ties. 
 
 " The tornado struck the Mississippi River at a point opposite the 
 village of Sauk Rapids, and fishermen who were in full view of the cross- 
 ing aver that for a few moments the bed of the river was swept dry ; and 
 in corroboration of this remarkable statement they showed me a marshy 
 spot where no water had been before this event took place. Two spans 
 were torn away from the substantial wagon bridge below the rapids, one 
 span being hurled up stream and the other down it by the rotary motion 
 of the blast; and great blocks of granite being also torn bodily out from 
 the piers. The large flour mill near the bridge was levelled. The depot 
 of the Northern Pacific R. R. was demolished, and the central portion 
 of the village itself was attacked with the greatest violence. Being the 
 county seat, the court-house was located here, a substantial structure, of 
 which only the vault, six iron safes, and the calaboose were left the 
 latter turned upside down. A fine new school-house, costing $15,000, 
 was completely swept away. The Episcopal Church was so utterly re- 
 moved that the sole relic thus far found is a battered communion plate. 
 The floor of the skating-rink is all that is left of that structure. Stores,. 
 
386 TORNADOES. 
 
 hotels, a brewery, and four-fifths of the residences in the village were 
 scattered as rubbish along the hillsides, or borne away for miles through 
 the air. 
 
 "One of the saddest of the tragedies marking this wide disaster took 
 place at a farm-house in the country, about 16 miles north of Sauk Rapids, 
 where a wedding party of 30 persons were assembled. The ceremony 
 was just concluded, and the officiating clergyman was offering prayer 
 when the building was struck by the tornado. The bridegroom was killed 
 ouiright, as were also 15 others ; 7 more victims have since died, and only 
 one of the company escaped severe injury of some kind." 
 
 The number of killed at Sauk Rapids was 39, and about 100 
 injured more or less. 
 
 252. On the 2Qth and 3Oth of May, 1879, there were many 
 very destructive tornadoes in the States of Kansas, Nebraska, 
 Iowa, and Missouri, which were thoroughly investigated by 
 Sergeant (now Lieutenant) F. P. Finley of the Signal Service, 
 and the results given in a published report. 72 From this lengthy 
 report of 116 quarto pages, containing a great number and va- 
 riety of very important and astonishing facts in relation to tor- 
 nadoes, the following few are selected as examples of the great 
 force of the wind and its raising and supporting power in a 
 tornado, and in corroboration of the theoretical deductions in 
 preceding pages : 
 
 From the account of the Lee Summit tornado on the 
 western border of Missouri the following extracts are taken : 
 
 " Among several of the peculiar manifestations of the wind's force at 
 this place, I relate the following: 150 feet N.E. of the house and 10 feet 
 W. from the stable, a large gate was carried 200 feet to the S.E. and torn 
 to pieces without injuring the stable. A heavy lumber wagon, standing 
 behind the corn-crib and at a distance of 155 feet east of the house, was 
 lifted up bodily and carried to the S.E. over a corn-field a distance of 100 
 feet, without injury. Two window-panes were blown from a sash on the 
 W. side of the house and carried inside without breaking them, while two 
 out of the N. window were found broken. A large well-curb lying E. of 
 the house 15 feet was carried one-fourth mile to the S.E. and lodged in a 
 wheat-field. A heavy sulky cultivator, weighing about 600 pounds, was 
 carried free from the ground a distance of 86 yards to the S.S.E. and 
 broken by the fall. Another one standing near the corn-crib was partly 
 carried and partly rolled along a distance of about 60 rods to the S.E., and 
 
-SUPPORTING POWER OF ASCENDING CURRENTS. 387 
 
 then literally twisted to pieces and the debris scattered about over a field 
 of 12 acres, apparently in circles." 
 
 " The following will indicate some of the peculiar freaks of the storm : 
 A carpet upon the floor of the Jog part of the house, and securely tacked 
 about the edges, was taken up and carried out of the house without 
 being torn. A new sewing-machine was broken into forty or fifty pieces. 
 Five feather beds were torn into strips and the feathers scattered broad- 
 cast over the country. Several garments were carried four or five miles 
 to the N.E. An iron kettle, holding 15 gallons, was found broken into 
 six pieces* and scattered about in several directions. A lo-gallon keg 
 filled with vinegar was carried to the N.E. 40 rods. A large iron-bound 
 trunk, fitted with an extra heavy lock, was torn to pieces, and the lock 
 found a half mile to the N.E. sticking into a rail. Several photographs 
 ^which were known to have been securely placed in an album in the 
 trunk, were found over four miles to the N.E. A watch in the vest of 
 Mr. J. H. Warden, was blown 50 yards to the N.E. and found covered 
 ivith mud, but the vest was carried to the E. 20 yards. Several chickens 
 were carried to the N.E., from one-fourth to one-half mile and entirely 
 stripped of feathers. Two stoves were broken into small pieces, and one 
 standing near the middle of the house was uninjured. Heavy bed-quilts 
 were so filled with mud that when dry they were as stiff and hard as 
 boards. A lumber wagon was carried to the N.W. 10 rods, the box torn 
 to pieces, and nearly all the spokes taken out of the wheels. An iron- 
 beam plow, 25 feet W. of the house, was not moved or injured, and aseed- 
 drill and harrow near the barn were also untouched." 
 
 According to t Mr. Richardson's account, at Mr. Hutchins's, 
 
 "trees and broken timber could be seen jerked up into the vortex, 
 whirled around with terrible fury, and then thrown outward at the top." 
 
 253. The following instances of the great power and fury 
 of a tornado are taken from the account of the Irving tor- 
 nado : 72 
 
 " The houses of Edward Wentworth, Gavin Reed, Robert Reed, and 
 Wesley Cooper, situated in the bottom of a 'draw ' leading into Game 
 Fork Creek from Timber Creek, in an E.N.E. direction, were next 
 reached and fairly ground to pieces. Hardly a board 6 feet long was left 
 near the foundation of any of the buildings. The funnel as it passed the 
 high ' divide ' to the ' draw ' perceptibly widened at the bottom ; but 
 without bodily swooping downward at once, it drew the buildings up 
 into its vortex and then twisted them to pieces. The house of Robert 
 Reed, 16 by 24 feet, and one and a half stories high, was lifted up as 
 easily as a feather, and without at first cracking the timber. So quickly 
 
388 TORNADOES. 
 
 was it done, that before Mr. Reed, who was within, knew his danger, the 
 building had risen a height of 25 feet or more. The house being then 
 enveloped in darkness, and not knowing what had happened, he started 
 for the door, thinking it time to make good his escape, when, instead of 
 stepping out upon the ground, as he expected, he fell the above distance, 
 injuring himself severely." 
 
 After giving various other details with regard to this tor- 
 nado, it is further stated : 
 
 "Going back to the funnel cloud where we left it at its entrance 
 upon Game Fork Creek, we find that it followed the bed of the stream 
 very closely, hugging the eastern bluffs with such tenacity that it ripped 
 up nearly every tree along their sides and withered the tough prairie 
 grass. Persons who watched its progress along this portion of its track 
 stated that the demoniac fury of the cloud was appalling ; whirling with 
 most frightful rapidity, the intense black column would at times seem to 
 level the whole bluff as it disappeared from view within the huge rolling 
 mass of darkness. The eastern bank, covered with a luxuriant growth of 
 timber, would, as the cloud moved along, successively emerge from its 
 awful baptism swept clean to the soil. While this terrific manifestation 
 of force was going on along the stream, westward over the valley, a dis- 
 tance of 60 rods, only a gentle wind was experienced." 
 
 254. Of the Stockdale tornado, when it struck Mr. Con- 
 dray's house, it was said 
 
 "that the roof was carried to a perpendicular height of nearly 200 feet. 
 .... The roof was lifted as easily as if it had been a feather, shot up- 
 ward in the very centre of the cloud, and fairly ground to pieces, the 
 debris whirling in circles about the upper portion of the cloud, and finally 
 dropping to the ground one-fourth of a mile from the centre of the. 
 storm's path." 
 
 In the Delphos tornado, 72 
 
 "two new lumber wagons were carried, one 35 and the other 40 rods to 
 the N.W., and broken into pieces ; one of the wheels, nearly whole, was 
 found a distance of one mile N.W. of the barn ; the other wheels were 
 broken from the axles, divested of their spokes, and the large heavy iron 
 tires were bent into every shape. A log from the barn, 12 feet long and 
 10 inches in diameter, was carried 320 yards to the N.N.W. The front 
 iron axle of a top buggy (i inches in diameter) was found bent double, 
 the two ends crossing each other, and both wheels were torn off even to 
 the hubs." 
 
 It is also stated of the same tornado that heavy cast-iron 
 
SUPPORTING POWER OF ASCENDING CURRENTS. 389 
 
 wheels broken from a large harvester, and weighing 200 pounds 
 each, were carried half a mile. 
 
 In the Barnard tornado 
 
 "a large government wagon-box, covered with about 200 pounds of iron 
 in the way of fasten ings, .was carried away from near the corn-house, and 
 no portion of it afterward discovered. Two sulky cultivators, weighing 
 between 400 and 500 pounds each, were broken into pieces and portions 
 carried to the E. for a distance of -one-fourth of a mile." 
 
 The Gentry County tornado, in crossing the river at Green- 
 well ford, 4 miles S. of Albany, 
 
 "lifted the new iron bridge of 160 feet span and weighing 120 tons, from 
 the stone pier upon which it rested, carrying it into the bed of the river 
 without overturning it. The structure was strongly bolted to the abut- 
 ment at one end, while the other end rested on rollers at the opposite 
 abutment to allow for the expansion and contraction of the iron string- 
 gers." 
 
 255. The prostrating force of horizontal, and the raising and 
 supporting power of ascending, currents, as manifested in the 
 preceding extracts from the accounts of the observed phenom- 
 ena of tornadoes, are mostly explicable from the theoretical 
 deductions of the preceding pages. By the law of rv = c, 232, 
 we have seen that where there is a centripetal force and an 
 initial gyratory motion, even very small at a considerable dis- 
 tance from the centre, the velocity becomes enormously great 
 near the centre, and there is a great concentration of the 
 energy there. The assumed example of 234, in which we get 
 a theoretical velocity of 140 meters per second at the distance 
 of 21 meters from the centre, is not an improbable one, which 
 can rarely occur in nature, but there are probably cases which, 
 after making all due allowance for friction, may give much 
 greater velocities at that distance, and these are enormously 
 increased still nearer the centre. But with this velocity we 
 have seen, 246, the force exerted upon each square foot of 
 normal surface is about 300 pounds. The force of such a veloci- 
 ty, therefore, on the side of a large building, although it were 
 of great weight, is amply sufficient to overthrow it and carry it 
 along until it is broken to pieces and the parts scattered in 
 many directions. 
 
390 TORNADOES. 
 
 Such a force also is sufficient to move cars from the track 
 of a railroad, of which we have several instances in the preced- 
 ing extracts, and carry them to a considerable distance. 
 
 According to the preceding law, it is seen how the kinetic 
 energy of a tornado may be enormously great in the vortex of 
 a tornado, while at a very short distance there is scarcely any- 
 perceptible wind. Thus in the case of the Irving tornado* 
 ( 2 53) at a distance of only 60 rods from the vortex and place 
 of greatest devastation, only a gentle wind was experienced. 
 Hence the track of destructive violence of a tornado is always 
 narrow. According to Finley, 73 
 
 " The width of the path of destruction, supposed to measure the dis- 
 tance between the areas of sensible winds on the sides of the storm's. 
 centre, varied from 40 to 10,000 feet, the average being 1085 feet." 
 
 A wind with a velocity of 140 meters per second would of 
 course have much less force against a tree, even with foliage, 
 than against a solid barrier, since much of the air would pass 
 through the tree, and so would exert no force against it except 
 by friction upon the air which is obstructed and does not pass. 
 But making an allowance of one-half, we yet have an enormous 
 force against the top part of the tree, which acts with a lever- 
 age upon the stem in breaking it, and upon the roots of the 
 tree in overturning it. 
 
 But we have reason to think that the velocity of the air in 
 a tornado, especially very near its centre, is often much more 
 than 140 meters per second, and so by Table VII, the forces, 
 exerted against the obstructions are still much greater. 
 
 256. From the theoretical result of the example in 242 of 
 an ascending velocity of 176 miles per hour, which is based, 
 upon no unreasonable assumptions, but upon such as can by 
 no means be regarded as extreme ones, we have reason to 
 think that the velocity of the ascending current in the central 
 part of a tornado is often enormously great. Even the veloci- 
 ty of 176 miles per hour, gives a lifting and supporting force 
 near the earth's surface of more than 90 pounds to a square 
 foot ( 246). ^Extreme cases may even give forces several 
 times greater than this. 
 
SUPPORTING POWER OF ASCENDING CURRENTS. 39 1 
 
 The nearly horizontal and gyratory currents at a little dis- 
 tance from the centre near the earth's surface, where they are 
 more radial than at a small altitude above the earth's surface, 
 necessarily become largely ascending currents also as they ap- 
 proach the vortex of the tornado, and so, with the enormous 
 forces of so great velocities, readily carry large and heavy 
 bodies into the vortex and up in the interior of the tornado, 
 and support them at a considerable altitude above the earth's 
 surface, until, in the progressive motion of the tornado, they 
 have been carried to a great distance. As the altitude is in- 
 creased and the density of the air diminished, the formula and 
 Table VII show that the supporting power of the same veloc- 
 ity is diminished, and in proportion to the density. It may 
 happen, therefore, that the raising and supporting force of the 
 tornado may be such as to raise a body and support it at a 
 considerable altitude, but not be able to raise it up to where 
 the currents above are outward from the centre, and so it has 
 to remain at some distance above the earth's surface, within 
 the vortex of the tornado, where it is at the same time whirled 
 rapidly round and round the centre, until, from some increase 
 of the energy of the tornado, it is carried up and out above, 
 where the ascending current is not strong enough to prevent 
 its falling, or until for some reason the energy of the tornado 
 is so exhausted, and the velocity of the ascending current so 
 diminished, that it falls directly back in the interior and central 
 part. In either case the tornado may have progressed mean- 
 while to a long distance. Smaller and lighter bodies are of 
 course carried up at once to great altitudes, if the ascending 
 currents extend up so high, but these may be retained for a 
 considerable time in the central region of the tornado above, 
 where the motion is much more gyratory than radial, before 
 they get so far from the centre that the ascending currents do 
 not keep them from dropping down ; for the lighter bodies 
 have to be carried out to a much greater distance from the cen- 
 tre before they can fall. 
 
 257. There is not much difficulty, therefore, in accounting 
 for the sustaining in the air and the transportation of light,* 
 
392 TORNADOES. 
 
 and even heavy, bodies to a great distance. Take, for instance, 
 the heavy piece of timber 6 by 6 inches and 40 feet long, 
 weighing 600 pounds, which was carried from the Episcopal 
 Church over the tops of houses, 249. While it was horizontal 
 it offered a surface of 20 square feet to the wind. By Table 
 VII an ascending velocity of 100 miles per hour would raise 
 and support a weight of 600 pounds with a normal surface of 
 20 square feet exposed to the current, and this may be con- 
 sidered as no unusual velocity of the ascending air in a tor- 
 nado. The same velocity perhaps was sufficient to carry up 
 the cart weighing 600 pounds, as the amount of surface ex- 
 posed to the current was probably at least 20 square feet. 
 Also a much smaller velocity would raise and sustain the 
 chicken coop 4 by 4 feet, weight 75 pounds, while being car- 
 ried 4 miles. 
 
 No unusual velocity, likewise, was necessary to raise and 
 keep up in the air the tin roof at Mt. Carmel, 250, while it 
 was carried 17 miles N.E., or the spire, vane and gilded ball of 
 the Methodist Church while being carried 15 miles N.E., or a 
 paper sack of flour while being transported 5 miles. 
 
 In the same manner the lifting and carrying away of the 
 heavy lumber wagon at Lee's Summit, 252, or the well-curb, 
 or the cultivator weighing 600 Ibs., may be accounted for, for 
 we can assume as probable an ascending velocity of much more 
 than 100 miles per hour, if necessary. 
 
 The iron bridge weighing 1 20 tons, which was lifted by the 
 Gentry County tornado, 254, although of great weight, had 
 also a great amount of surface exposed to the ascending cur- 
 rent. If we suppose that there was a weight on the average 
 of 300 pounds to the square foot, then according to computa- 
 tions 247, and to Table VII, an ascending velocity of about 320 
 miles per hour would be necessary to lift it. This is perhaps 
 an extremely great velocity, but the weight of the bridge may 
 have been much less than that assumed above, and so the 
 ascending velocity required much less. 
 
 258. We now see how a body may be raised up and sus- 
 tained in the atmosphere when once up where there are rap- 
 
SUPPORTING POWER OF ASCENDING CURRENTS. 393 
 
 idly ascending currents, as in the case of the iron bridge above, 
 but it remains to explain how bodies close on the earth's 
 surface, where there cannot be such currents, are raised bodily 
 and vertically up into the air. Several examples of this sort 
 are given in the preceding extracts. The house of Lewis Gott 
 appeared to go up bodily and plunge into the cloud ( 250), and 
 in the Lincoln County tornado, Mr. Moore's house, 200 yards 
 west of the storm's centre, 12 by 30 feet and one and a half 
 stories high, " was lifted bodily and carried, with the entire fam- 
 ily in it, to the centre of the track, in a direction a little S. of 
 E., where it went to pieces." 72 The house also of Robert Reed 
 and of others was lifted up as easily as a feather ( 253), and 
 likewise the roof of Mr. Condray's house ( 254), in the Stock- 
 dale tornado. In the account of the Irving tornado it is also 
 stated," that 
 
 " the house of Mr. Morgan stood nearly in the storm's centre. The wind 
 first struck it on the E. side, lifting it bodily up to the W., off the foun- 
 dation, when it disappeared out of sight in the dark boiling mass of 
 whirling clouds. Mr. Morgan and family were in the cellar and saw the 
 house pass from over their heads in the manner above described." 
 
 In the rapid gyrations of the vortex of a tornado, where 
 there are numerous inequalities of the surface and substantial 
 building obstructions, the horizontal currents may be abruptly 
 deflected upward so as to give a strong vertical current very 
 near the earth's surface, by which objects may receive an up- 
 ward start, but there are cases in which buildings seem to be 
 drawn vertically upward into the vortex of the tornado from a 
 level surface where there are no inequalities and obstructions 
 of this sort. 
 
 Let us suppose that a tornado, by its rapid gyratory motion 
 in the open air above the earth's surface and down to very 
 near the surface, brings down the horizontal and disturbed iso- 
 baric surface AB in the figure following to the earth's surface, 
 DE, or nearly, in the form of the curved lines ae and bf, as ex- 
 plained in 233, but that near the earth's surface in the stra- 
 tum of air between the points e and /and the surface DE there 
 is little or no gyratory motion. This would be very much less 
 
394 
 
 TORNADOES. 
 
 here than above, on account of the friction of the earth's sur- 
 face, if even the tornado were stationary, but in its progressive 
 motion, carried along by the general progressive currents 
 above, the rapid whirl of the air above does not have time to 
 communicate such gyratory motion to the lower stratum of air, 
 which has less progressive motion, for the vortex above is being 
 continually brought over new portions of the stratum below. 
 
 Fig. 2. 
 
 Between the points e and/, say at the height of 1 50 feet above the 
 earth's surface, there may be nearly a vacuum, while at the earth's 
 surface, at c, the pressure and density are very nearly the same as 
 at D and E, since there is, at least at first, scarcely any gyratory 
 motion to counteract the horizontal communication of the press- 
 ure from D and E to c. Let us suppose that instead of a vacu- 
 um the barometric pressure between e, and/is 1 5 inches, while at 
 c it is 30 inches. There is then a decrease of barometric press- 
 ure between c and the central part of the vortex at the level 
 of e and /of 15 inches, in 150 feet, or one inch for each ten 
 feet, supposing the rate of decrease to be the same through the 
 whole vertical space of 150 feet. If now there is a cubical 
 body, of no very great weight or solidity, as a wooden house, 
 with a linear dimension of 20 feet, at the point c under the vor- 
 tex, and resting on or being very near the earth's surface, then 
 the height of this body being 20 feet, the upward pressure at 
 the bottom is nearly 15 pounds to the square inch, being the 
 ordinary air pressure at the earth's surface, while at the top, 
 since the barometric pressure is decreased two inches, or one 
 
GYRATORY AND PROGRESSIVE MOTIONS. 395 
 
 fifteenth of the whole at the earth's surface, the pressure to the 
 square inch is only 14 pounds. Hence the upward pressure on 
 the lower surface is one pound to the square inch greater than 
 the downward pressure on the upper surface, and the force 
 which tends to raise the whole body vertically upward into the 
 vortex at the level of e and/, is one pound to the square inch,, 
 or nearly 30 tons for the whole body with a superficial area at 
 the bottom and top of 403 square feet. This would be much 
 more than sufficient to raise vertically upward from the earth's 
 surface any wooden structure of those dimensions, and hence, 
 from this assumed example and estimated force, it is seen how 
 bodies upon and close to the earth's surface, where there can be 
 little, if any, ascending velocity of the air, get a start upward. 
 When once a little distance up, where the velocity of the as- 
 cending current in consequence of this rapid decrease of press- 
 ure is very great, bodies are raised and sustained by the force 
 of the current, as already explained. 
 
 RESULTANTS OF GYRATORY AND PROGRESSIVE MOTIONS. 
 
 259. According to Finley," of the 600 tornadoes upon which 
 he reported, " the rotary movement of the whirling cloud was 
 invariably from right to left, or the opposite movement of the 
 hands of a watch." This indicates either that the earth's rota- 
 tion on its axis, as in cyclones, must determine the direction, 
 or that the atmosphere has numerous whirls in this direction, 
 the results of previous cyclonic gyrations which have not been 
 brought entirely to rest. There is little doubt, however, that 
 the direction of gyratory motion is almost always, if not en- 
 tirely so, contrary to that of the hands of a watch, though 
 reports are not entirely wanting of their rotation the other way. 
 
 The direction of the progressive motion of tornadoes is 
 mostly northeasterly. 
 
 "Of the tornadoes the courses of which have been recorded, 310- 
 moved from S.W. to N.E.; 38 from N.W. to S.E. ; 16 from W.S.W. to 
 E.N.E.; 14 from W. to E.; 7 from S.S.W. to N.N.E. ; 5 from W.N.W. 
 to E.S.E. ; 3 from N.N.W. to S.S.E." "The velocity of progression of" 
 
396 TORNADOES. 
 
 'the storm cloud, as determined from the reports in 1 30 cases, varied from 
 12 to 60 miles, the average being 30.08 miles." 73 
 
 The direction of the general drift of the air is very nearly 
 that of the progressive motion of the tornado, and so mostly 
 from S.W. to N.E. The velocity of this is always consider- 
 able in comparison with, though generally much less than, the 
 gyratory velocity of the violent part of the tornado. On the 
 right hand, and mostly the southeast side, of the path of the 
 tornado, therefore, the two motions very nearly coincide in 
 direction, and so the velocity of the resultant of the two mo- 
 tions combined becomes much greater than on the left-hand 
 side where the progressive and gyratory motions are somewhat 
 in contrary directions, and where, consequently, the velocity of 
 'the resultant motion is very nearly the difference of the two 
 velocities. For this reason the most violent and destructive 
 part of the tornado is found on the right-hand side of the cen- 
 tral path, and the tornado, consequently, as the cyclone ( 202), 
 has its dangerous side. Consequently where a tornado passes 
 through a forest the fallen trees are found mostly on the right 
 hand side of the central track, and with their tops in a north- 
 easterly or north-northeasterly direction. The gyratory velo- 
 city, however, may be so great that the weaker trees at least 
 are overthrown on the other side, and then they are there 
 found lying mostly in a somewhat contrary direction. 
 
 260. On account of the general progressive motion of the 
 air, nearly in the direction of the motion of the tornado, the 
 absolute motion of the air in the front of the tornado is nearly 
 at right angles to the direction of the path, or perhaps gen- 
 erally inclines a little forward, the progressive motion counter- 
 acting, and even move, the inclining of the wind toward the 
 centre. But in the rear of the tornado, the progressive motion 
 increases the inclination toward the centre, and here trees are 
 overthrown and objects carried nearly toward the centre and 
 in the direction of the storm's path. The effect upon the 
 resultant direction is similar to that in cyclones, as explained 
 in 201 and represented in Fig. 9. Where the centre of a tor- 
 nado passes over a place in a northeasterly direction the trees 
 
GYRATORY AND PROGRESSIVE MOTIONS. 397 
 
 in front may be thrown toward the N. or N.W., but in the rear 
 toward the E., or still more around toward the N.E. in the direc- 
 tion of the storm's progress. In consequence of the progressive 
 motion in the rear of a tornado being more nearly in the direc- 
 tion of the gyratory motion, the winds in the rear are usually 
 stronger than in the front part, and so the stronger trees, which 
 are not overthrown in the former, may be prostrated in the 
 latter. 
 
 Where the right-hand side of a tornado passes over a place 
 the trees may be first thrown toward the N.W. or N., but 
 mostly by the south quadrant of the tornado toward the N.E., 
 for here the gyratory and progressive motions most nearly 
 coincide in directions, and consequently the resultant velocities 
 are the greatest : and this is the most dangerous part of a storm. 
 But if the left-hand side pass over a place, the trees may be 
 thrown successively toward the N.W., W., and S.W., and by 
 the western quadrant even toward the S. or S.E. Hence it is 
 stated with regard to the Gentry County tornado : 72 
 
 "The largest trees were twisted off near the ground, uprooted, or 
 broken off, and lay with their tops pointing in a circular direction from 
 right to left within the central part of greatest destruction. Those on 
 the S. (right-hand) side of the centre were pointing to the E. and N.E., 
 and even N.W. when very near the centre. On the N. side they were 
 pointing N.W., W., S.W./and S.E." 
 
 261. In the progression of a tornado in a northeasterly di- 
 rection, the trees first thrown down being those of the front 
 part, are thrown more from an easterly direction than those 
 afterward prostrated by the rear part, which are decidedly 
 from a westerly direction, because here the progressive and 
 gyratory motions are somewhat in the same direction. Those 
 from a more easterly direction, therefore, where they cross, 
 generally lie under those of a more westerly direction. This 
 accords with the observations of Dr. Anderson, 68 who says : 
 
 " The first area examined, tornado of April 23, 1883, was composed of 
 two distinct parts. The first was a long rectangular space of about half 
 a mile in length, from west-southwest to east-northeast, and a hundred 
 and fifty to two hundred yards in width. Within this space the trees- 
 were prostrated from southeast, south, southwest, and west, and inter- 
 
TORNADOES. 
 
 mediate points ; and wherever two were found lying across each other, 
 the one thrown from the direction the nearest to east, or farthest around 
 from west, was always at the bottom. Thus, those thrown from south 
 always lay on top of those from southeast, those from west were always 
 on top of all other directions. This order was without exception. The 
 rectangular area terminated at the east end in an irregularly circular area 
 of about eight hundred yards diameter, either east and west or north and 
 south. Bisecting this area both ways and dividing it into four quad- 
 rants, the southwest and southeast were found to correspond in all re- 
 spects with the rectangular area, except that in the southeast there was 
 a greater proportion of trees thrown down from east-southeast and 
 southeast than in the other sections ; and in the southwest quadrant, 
 near the centre, a tree thrown from the southwest was overlaid by one 
 from south, the single exception to the order noted above. In the north- 
 east quadrant the destruction was less than in either of the others, and 
 trees were thrown down from east, northeast, north, northwest, and 
 west. In the northwest quadrant the trees were thrown from north, 
 northwest, and west, chiefly from northwest, west-northwest, and west ; 
 and in the instances where they crossed each other, the order in relation 
 to the west was similar precisely to that of the other parts, progressing 
 irom east round by north to west, as, on the other side, the progression 
 was from east round by south to west ; so that in these, the northeast 
 and northwest quadrants, trees thrown from northeast lay under those 
 from north, those from north under those from northwest, while, as in 
 the south quadrants and the rectangular space, those from west were on 
 top of all." 
 
 The destruction and prostration of trees in the rectangular 
 ;area referred to was caused by the dangerous side while the 
 tornado had a progressive motion, the other side not having 
 .sufficient violence to prostrate the trees. But at the end of 
 this area the tornado seems to have remained nearly stationary 
 for short time, when the violence was nearly the same on 
 both sides, and during this time trees were prostrated on the 
 nor,th side, in the northeast and northwest quadrants. The 
 order of prostration in the rectangular strip, and in the south- 
 east and southwest quadrants while the tornado was stationary, 
 was the same from east around by south to the southwest, 
 while in the northeast and northwest quadrants, while the tor- 
 nado was stationary, the order was the reverse, from the east 
 round by north to west. 
 
RAINFALL IN TORNADOES. 399 
 
 On account of the right-hand side of a tornado, as already 
 -explained, being the more violent and destructive side, there is 
 generally a marked difference in the width of the destructive 
 parts of the two sides. With regard to this it is stated in the 
 account of the Lees Summit tornado : 73 
 
 " Mr. Bradley and his son, who had been engaged for several days in 
 putting up fences over the path of the storm, were struck with the 
 marked contrast in the comparative width of the E. and W. sides of the 
 -storm's track. For a distance of nearly four miles they had found that 
 the W. (left-hand) side averaged about 40 rods in width, the maximum 
 being 80 and the minimum 25 rods. On the E. (right-hand) side, over 
 the same distance, the average width was over a mile, the maximum be- 
 ing two miles and the minimum three fourths of a mile." 
 
 Finley also states with regard to the tornado tracks gener- 
 -ally : 72 
 
 " The left or W. side was always the narrowest, and, unless within the 
 limits of the path of greatest destruction, the force manifested was al- 
 ways the weakest on this side. I inquired repeatedly if any one experi- 
 enced strong inrushing currents on this side which were often mentioned 
 -as occurring on the opposite side, but always received a negative answer. 
 The W. side was generally from one third to one half as wide as the E. 
 :side or right-hand side." 
 
 In the tornado investigated by Dr. Anderson, while it had 
 a rapid progressive motion, the left-hand side of the destruc- 
 tive part seems to have been entirely wanting, so far as the 
 prostration of trees, at least, is concerned. 
 
 RAINFALL IN TORNADOES. 
 
 262. The rapid ascent of nearly saturated air in a tornado 
 must give rise generally to a great amount of rainfall. Some 
 idea of this may be formed from considering the amount of 
 aqueous vapor in the ascending air, drawn mostly from the 
 strata near the earth's surface, and its capacity for vapor, from 
 which the amount left in the air, after it has ascended up to 
 altitudes where it has become cooled down to a lower temper- 
 ature, becomes known. Suppose the air temperature near the 
 earth's surface is 25 C, but that the depression of the 
 
4OO TORNADOES. 
 
 point is 5. The tension of aqueous vapor in the air, in milli- 
 meters of mercury, is that of saturation at 20; and with this 
 as an argument Table n gives 17.36 mm. The density of 
 vapor being 0.622, this gives 17.36 X 0.622 = 10.80 mm. for the 
 height of a column of mercury equal to the weight of aqueous 
 vapor in a homogeneous atmosphere of saturated air at the 
 temperature of 20. Multiplying this by 13.6, the density of 
 mercury, we get 10.80 X 13.6= 146.7 mm. for the height of 
 a corresponding column of water. Dividing this by 7992,. 
 the height in meters of a homogeneous atmosphere, we get 
 0.0184 mm. for the depth of rain in each stratum of saturated 
 atmosphere of one meter in depth, and of the temperature of 
 20 if the vapor were all precipitated. If now we suppose that 
 the ascending velocity of the air at the base of the cloud where 
 condensation first commences to be 60 meters per second, then 
 the depth of rainfall, supposing the current to extend so high 
 that all the vapor is coudensed, and that the rain all falls di- 
 rectly back, would be 0.0184 X 60 = i.i mm. per second, or 
 0.066 m. (about 2.6 inches) per minute. With higher temper- 
 atures and higher degrees of saturation the rate of rainfall 
 would be considerably more. 
 
 The preceding calculation, however, upon the assumptions 
 made, gives us only a rough approximate idea of the possible 
 rate of rainfall, for the air, at least all of it, never ascends so 
 high that all the vapor is condensed ; but, on the contrary, as 
 has been explained in 241, the ascending current may be de- 
 flected off laterally on all sides at no very great altitude. The 
 vapor, therefore, which is carried up mostly by the more rapid 
 currents in the interior of the tornado after being condensed 
 into rain, is carried outward above by the outflowing currents 
 there, and falls mostly over the regions adjacent to the vio- 
 lent part of the tornado, and not directly back over the place 
 where it ascended as vapor. Besides, we have just seen that 
 where there is an ascending current of only moderate velocity, 
 small rain-drops cannot fall back, but are carried up to where 
 the current is outward, and then out where there is little or no. 
 ascending current, and where they are permitted to fall to the 
 
WATERSPOUTS. 
 
 401 
 
 earth. In fact, with an ascending velocity even very much less 
 than that assumed above, no ordinary rain-drops by Table VII 
 could fall directly back to the earth. 
 
 WATERSPOUTS. 
 
 263. As soon as the ascending and expanding air in a tor- 
 nado cools down to the dew-point corresponding to the di- 
 minished vapor tension as it gradually comes under less pres- 
 sure, condensation and cloud formation take place. Where 
 the air ascends vertically, we have seen, 27, this takes place 
 at an altitude which, in meters, is equal very nearly to the de- 
 pression of the dew-point at the earth's surface in centigrade 
 degrees multiplied by 125 or 125 (r d\ 
 
 But the rate of cooling does not necessarily depend upon 
 the ascent of vapor, but only on the amount of decrease of 
 pressure and of expansion, whether this takes place in the ascent 
 or horizontal motion of air, or in air without any motion. In 
 all cases, to a given amount of decrease of pressure and corre- 
 sponding increase of expansion there is a corresponding de- 
 crease of temperature. 
 
 If in the annexed figure we suppose that the horizontal iso- 
 baric surface in the undisturbed air, and represented by a hori- 
 
 Fig. 3. 
 
 zontal line ab, is brought down by tornadic action to the earth's 
 surface DE at / in the form of the line af, as explained in 
 233, then the air which ascends from the stratum next to 
 
4O2 TORNADOES. 
 
 the earth's surface, all supposed to have the same temperature 
 and dew-point, whether it ascends slowly and nearly vertically 
 at the outer border as at a and b, or more obliquely and rapidly 
 toward and up in the interior, wherever it arrives at the de- 
 pressed isobaric surface, represented by the curved line af or bf t 
 it has cooled down to the same temperature ; and if the height of 
 that isobaric surface before being depressed in the interior of 
 the tornado was 125 (r d], then condensation and cloud for- 
 mation take place as soon as the air ascends above or enters 
 within that surface up as high as aqueous vapor is carried by 
 the ascending current. But without and below this surface 
 there is no condensation and cloud formation, and the air re- 
 mains unclouded. The clouded portion of the air therefore 
 assumes the form of a tapering trunk, as outlined on the two 
 sides by the curved lines bf in the figure, and we have the 
 phenomenon called a waterspout. A waterspout, therefore, is 
 simply the cloud brought down to the earths surface by the rapid 
 gyratory motion of the tornado. As Espy with a few strokes 
 of the handle of an air-pump produced a cloud in the receiver 
 from the expansion and cooling of the moist air within, so na- 
 ture, by means of a whirl in the open atmosphere, produces a 
 cloud in the vortex of a tornado, from the expansion and cool- 
 ing of the air there, on account of the partial vacuum caused by 
 the centrifugal force of the gyrations. 
 
 We have seen, 242, that the air which ascends in the in- 
 terior of a tornado comes in below mostly near the earth's sur- 
 face especially that which ascends where the spout is formed, 
 and so it may be regarded as all having very nearly the same 
 temperature and depression of the dew-point. If the compara- 
 tively small amount of air coming in at the sides from the 
 higher strata of the atmosphere had the same depression of the 
 dew-point, it would have to enter some distance within the iso- 
 baric surface af, ^/"before condensation of the vapor would com- 
 mence, since having a less pressure before commencing to 
 ascend than at the earth's surface, it would have to, arrive when 
 the pressure is less than that of the isobaric surface of incipient 
 condensation for air ascending from the earth's surface, and so 
 
WATERSPOUTS. 403 
 
 the outline of the spout is determined by the latter. If, how- 
 ever, the air entering from the higher strata should have a much 
 less depression of the dew-point, its vapor might begin to be 
 condensed before entering within and above this surface, and 
 so affect the distinctness of outline of the spout ; but this can 
 scarcely, if ever, occur, since the further from the earth's sur- 
 face, generally, the drier the undisturbed quiet air. 
 
 The arrows in the figure represent approximately the air 
 currents coming in from the sides, and mostly near the earth's 
 surface, to supply the draught of the rapidly-ascending current in 
 the interior. It must be understood, however, that these repre- 
 sent merely the currents of the vertical circulation, and that in 
 a tornado there is, in connection with this, also a rapid gyra- 
 tory motion around the centre. The same system of circula- 
 tion somewhat takes place in all tornadoes, whether the tor- 
 nadic violence is sufficient to bring down the spout or not ; for, 
 as will be explained, a certain degree of violence is necessary 
 to bring the spout down to the earth's surface. At a consider- 
 able distance from the centre, beyond the limits represented by 
 the figure, the air on all sides descends, mostly very gently, and 
 at the same time is drawn in toward the interior. 
 
 264. The height of the spout depends upon the hygro- 
 metric state of the air, being 125 meters for each degree of the 
 depression of the dew-point at the earth's surface. The diame- 
 ter of the spout at any given distance / below the level of the 
 undisturbed isobaric surface AJ3, as at a or f t Fig. I, 233, de- 
 pends upon the amount of gyratory velocity or value of c = r'v', 
 as may be seen in 234 ; for the greater the value of c, the 
 greater is the value of r the distance of the isobaric surface 
 from the centre, and, in the case of a waterspout, the greater is 
 its radius. Since the spout is tapering down to the earth's sur- 
 face, the drier the air and the taller the spout the smaller its 
 diameter at the earth's surface for the same gyratory velocities. 
 For instance, with a small dew-point depression and rapid 
 gyratory motion we get a spout of the form of Fig. 4 in which 
 the cloud is low on the outer border of the tornado where the 
 isobaric surface, or surface of incipient condensation, is not de- 
 
404 
 
 TORNADOES. 
 
 pressed sensibly, and on account of the smallness of the de- 
 pression / and the largeness of the value of r'v', the value of r 
 is large, as is seen from the inspection of the equation of 234. 
 With the conditions there assumed of r'v' = 3000, and / = 500 
 meters, which corresponds to a depression of the dew-point of 
 4, we get for the radius of the spout at the earth's surface,. 
 
 Fig. 4. 
 
 Fig. 5. 
 
 r = 30 meters, and hence a short spout only 500 meters in 
 height with a diameter of 60 meters at the base. In a tornado 
 under such conditions even the cloud-rim is low, and the dense 
 cloud is brought down to the earth's surface over a considerable 
 area at any given instant, and everything is involved, for the 
 time, in great darkness. 
 
 On the other hand, if the air is very dry and the depression, 
 
WATERSPOUTS. 
 
 405 
 
 consequently, of the dew-point very great, we get a very tall 
 spout with small diameter, as represented in Fig. 5. If the de- 
 pression of the dew-point is 16 C, then the height of the spout 
 is 1 25 X 1 6 = 2000 meters ; and if in this case we put r'v' = 1000, 
 we get from the expression of /, 234, by putting / = 2000 
 meters, as above assumed, r = 5 meters nearly, or a diameter 
 of about 10 meters for the spout at the earth's surface. But 
 the value of r'v' cannot be taken so small, or that of / so great, 
 that r vanishes, so that in any case there must be at least a small 
 threadlike spout coming down to the ground according to the 
 theory, in which we take n'o account of friction. 
 
 265. In the preceding results from theory and formulae in 
 which no account is taken of friction, of course considerable 
 
 s f 
 
 Fig. 6. 
 
 allowance must be made for its effect, as has heretofore been 
 pointed out in similar cases. It has been shown that the greater 
 the initial gyratory velocity or value of r'v' = c, the greater 
 the diameter of the spout, all other circumstances being the 
 same. Consequently the effect of friction, which tends to di- 
 minish the gyratory velocity, is to make the diameter of the 
 spout smaller, and even to vanish where the gyratory velocity 
 is small ; and this is especially the case very near the earth's 
 surface where the amount of friction and decrease of gyratory 
 
406 
 
 TORNADOES. 
 
 velocity are comparatively great. For instance, if we had con- 
 ditions which would give a theoretical spout of the form out- 
 lined by the dotted curved lines bf, Fig. 6, the effect of friction 
 would diminish its diameter somewhat as represented in the 
 figure, and even prevent its coming entirely down to the earth's 
 surface. 
 
 With a still less gyratory velocity, other conditions remain- 
 ing the same, there would simply be a funnel-shaped cloud as 
 represented in Fig. 7, the gyrations in this case retarded by 
 friction, being merely sufficient to bring the cloud in the vortex 
 a little below the general level of the undisturbed base of the 
 
 Fig. 7. 
 
 cloud. It is in this form it first appears in a tornado, when it 
 is seen at all ; and as the energy of the tornado and the veloci- 
 ty of the gyrations increase, it may be brought either wholly 
 or only part of the way down to the earth's surface. Finally, 
 as the energy of the tornado becomes exhausted, and the 
 velocity of the gyrations diminishes, it is drawn up again ap- 
 parently into the cloud, its last appearance being again that of 
 the funnel-shaped cloud. 
 
 In tornadoes of large base with not fully developed and 
 rapid gyratory velocities in the vortex, instead of a completely 
 developed spout or a funnel-shaped cloud, a large basket- 
 shaped cloud is observed suspended from the level of the gen- 
 eral base of the clouds. The rapidity of the gyratory veloci- 
 ties in the vortex is not sufficient to bring the cloud down 
 with a sharp point as in the funnel-shaped cloud. 
 
 The action of a tornado is somewhat intermittent, now 
 
WA TERSPO UTS. 407 
 
 stronger and again weaker. This is observed frequently in the 
 greater manifestation of violence at some times than at others. 
 With regard to the tornado force in the S. C. tornadoes 
 of April, 1883, Dr. Anderson states: 68 
 
 " The tracks examined by me did not present continuous lines of de- 
 struction, but areas of destruction separated by intervals entirely or al- 
 most entirely exempt from destructive forces ; from which it is inferred 
 that, while the storm, in its common, ordinary features, pursued its way 
 steadily onward by bodily transference, the tornadic action was devel- 
 oped interruptedly, and progressed by successive transplantings." 
 
 That is to say, in the general progress of the tornado, the 
 unstable state and the vertical circulation continues nearly the 
 same, but the gyratory motion depends very much upon the 
 initial and slight whirl which the air near the earth's surface at 
 some distance from the centre may have, as it is drawn into 
 and up the vortex ; for while the whirling column above con- 
 sists somewhat of the same air drifting along, that near the 
 surface, not partaking of the same amount of progressive veloci- 
 ty, is being continually changed, and consequently the value 
 of c = r'v' , upon which the gyratory motion depends ( 232.) 
 According as the value of c is greater or less, for the new por- 
 tions of air drawn into the central part, is the gyratory velocity 
 and violence of the tornado greater or less. This intermittent 
 action in tornadoes is often indicated by the dropping down 
 and rising up of the spout where the gyratory violence of the 
 tornado is barely sufficient to develop a spout, and is an ex- 
 planation of this phenomenon ; for in that case a very little in- 
 crease or decrease in the rapidity of the gyrations brings the 
 spout in part or wholly to the earth's surface from the funnel 
 shape, or lets it up again. 
 
 Finley states, with regard to the Lee's Summit tornado, that 
 from a certain point "the funnel raised again, committing no 
 damage for a distance of 9! miles over an alternation of hill 
 and dale, when it struck a large elm-tree situated in a broad 
 valley with gently sloping sides." While passing over the un- 
 even surface of hill and dale, the gyratory violence, on account 
 of this unevenness, was not sufficient to keep the spout down 
 to the earth's surface, and so here it rose up. 
 
4O8 TORNADOES. 
 
 In the account of the Walterborough tornado, 69 it is stated 
 that "its path was continuous for 24 miles, then a gap of 25 
 miles where no damage was done, followed by a track f mile 
 in length/' 
 
 With increase of tornadic violence, the spout is brought 
 down to the earth, and the consequent increased destructive- 
 ness is attributed to the spout, whereas the latter is simply an 
 effect of the increase of the tornadic violence, and with a drier 
 air there might be no spout accompanying the same amount of 
 violence and destructiveness. 
 
 266. From what precedes, it is evident that waterspouts 
 may be of a great variety of forms, varying from that of a 
 cloud brought down over a large area of the earth's surface in 
 a tornado, where the air is nearly saturated with vapor and 
 the general base of the clouds very low, somewhat as repre- 
 sented in Fig. 4, to that which occurs when the air is very dry, 
 and when the tornadic action is barely able to bring the cloud 
 down from a great height into a slender spout of small diame- 
 ter, somewhat as represented in Fig. 5. Horner says that their 
 diameters range from 2 to 200 feet and their heights from 30 
 to 1 500 feet. Dr. Reye states that their diameters on land, at 
 base, are sometimes more than 1000 feet. Oersted puts the 
 usual height of watesprouts from 1500 feet to 2000 feet, but 
 states that in some rare cases they cannot be much less than 
 5000 or 6000 feet. On the I4th of August, 1847, Professor 
 Loomis observed a waterspout on Lake Erie, the height of 
 which, by a rough estimate, was a half a mile, and the diame- 
 ter about 10 rods at the base and 20 rods above. 74 
 
 Judge Williams, in speaking of the tornado of Lee's Sum- 
 mit, where he saw it, says : 72 " It seemed to be about the size 
 of a man's body where it touched the clouds above, and then 
 tapered down to the size of a mere rod." 
 
 The preceding symmetrical waterspouts, deduced from the- 
 ory upon certain assumed regular conditions, differ of course 
 very much in form from those usually observed in nature, 
 where these regular conditions are rarely found, even approxi- 
 mately. It is assumed in the theory that the progressive mo- 
 
WATERSPOUTS. 
 
 tion of the strata of the atmosphere at all heights to which the 
 tornado extends is the same, from which results a perfectly 
 straight and vertical spout. But this condition usually does 
 not exist, but the upper strata either move faster or slower 
 than the lower ones, and so in the former case the upper part 
 of the spout inclines forward and in the latter backward. 
 Sometimes the progressive motions of the atmosphere in the 
 different strata are not only very irregular at different alti- 
 tudes, on account of the great abnormal disturbances to which 
 the winds are subject, but likewise very changeable at different 
 times, so that in this case the spout may not only be bent and 
 sinuous, but subject to continual contortions and twistings. 
 Hence, the Rev. S. R. Reese describes the appearance of the 
 spout of the Lee's Summit tornado, as he saw it, 72 to be " that 
 of a funnel, at times elongated in a serpentine-like form of 
 heavy mould, hung up by the head and writhing in agony, its 
 tail curling and lashing as if actuated by the impulses of a liv- 
 ing body. It was above the ground and doing no damage, 
 though at times, in its violent contortions and struggles, it 
 would descend very near the ground." 
 
 Other irregularities arise, also, from unequal distributions of 
 temperature and of aqueous vapor in all portions of the air 
 around on all sides. The base of the cloud also, from which 
 the spout depends, does not have the smoothness and the uni- 
 formity on all sides shown in the preceding graphic representa- 
 tions of the results deduced from theory. For although the 
 surface of incipient condensation, as the air, charged with 
 vapor, ascends, may be somewhat regular, yet the cloud above 
 is at some distance from the vortex brought down below this 
 level in the form of scud clouds, which often gives it an irregu- 
 lar and jagged appearance. In fact, this regular base of in- 
 cipient condensation and the extreme upper wide part of the 
 spout or funnel is frequently concealed by such clouds, which 
 .are brought down and, before they are evaporated, are carried 
 into the vortex. For although the air is drawn into the vor- 
 tex below, at the earth's surface mostly, as has been explained, 
 yet it also seems to be drawn down also, at no great distance 
 
410 TORNADOES. 
 
 from the vortex, to supply the ascending current ; and so it 
 brings portions of the cloud above down, sometimes even near 
 to the earth's surface. Thus, in the Lee Summit tornado, 72 
 
 " The funnel is represented as reaching the ground, which under such 
 circumstances causes the narrowest part to be some distance above the 
 surface, but when it rises the lower portion tapers down to a very small 
 diameter. Dark masses of cloud shot downward on either side of the 
 funnel, entering it just above the ground, apparently thereafter rushing, 
 upward through the centre." 
 
 Espy says: 
 
 " Whenever low clouds appear under the rim of the hurricane cloud, 
 they always are seen in the form of scud moving rapidly toward the 
 centre of the great hurricane cloud, where they unite with its base and 
 ascend with the ascending current, where the barometer is very low." 
 
 267. Waterspouts, especially on land, frequently have the: 
 appearance of a widening at the bottom on the earth's surface. 
 On land, dust and a great many light substances are carried up 
 in the interior ; and as they are being collected from all sides 
 on the earth's surface by the inflowing currents, which are 
 here more nearly radial, toward the vortex below, they often 
 assume the form of a cone, which, in the first formation of the 
 spout, seems to rise up and meet the descending spout falling 
 apparently from the clouds, and thus the whole phenomenon 
 often assumes the form of an hour-glass. Of the great tornado* 
 of West Cambridge (now Arlington), August 22, 1851, it was 
 said : 
 
 " To some who watched it closely its form resembled a tall, wide- 
 spreading elm tree. To others it appeared like an inverted cone.. 
 Several represented it as a dense upright column, and a few as having 
 the shape of an hour-glass." 
 
 The several observers no doubt saw it at different times- 
 and under somewhat different circumstances in its progressive 
 motion over the inequalities of surface. It was only where the 
 earth contained a great amount of dust, or other light materials 
 on the surface, that the right cone at the base was observed,, 
 and where the whole assumed the form of an hour-glass. 
 
WATERSPOUTS. 
 
 411. 
 
 With regard to the Lee's Summit tornado, it was stated :" 
 
 " The small funnel cloud was seen reaching part way to the ground; 
 at the same time an inverted funnel of dust and light materials formed 
 over the earth beneath and reached up to it." 
 
 The graphic representation of it in Fig. 8 is given in the 
 account of it. 
 
 Sometimes the right and inverted cones do not come to- 
 gether, but a small space is left between the two vertices of the- 
 
 Fig. 8. 
 
 Fig. 9. 
 
 cones, pointing the one down and the other up toward each 
 other. From no accounts can it be inferred that in land torna- 
 does the lower part is composed of condensed vapor at least 
 the outer part of it, which causes the widening, but the true, 
 spout may reach through it to the earth's surface. 
 
412 
 
 TORNADOES. 
 
 There are often two or more spouts in close proximity. 
 The graphic representation in Fig. 9 of two spouts, brought 
 part of the way down to the earth, seen by Mrs. Kerr in the 
 Lee's Summit tornado, is given by Finley. Sometimes several 
 small spouts protrude from the lower base of the cloud in the 
 same vicinity, some to a greater and some to a less distance 
 down, sometimes not differing much in size ; at others there is 
 a larger and principal spout accompanied by one or more 
 smaller ones. The accompanying representation of a group of 
 little spouts or funnels, as seen by McLaren at one time in the 
 JDelphos tornado, is given by Finley. 
 
 Fig. 10, 
 
 As the tornado originates in air in the unstable state, it 
 often happens that there is about an equal tendency in the air 
 of the lower stratum to burst up through those above at several 
 places in the same vicinity at the same time. Each of these 
 gives rise to a separate and independent gyration in the atmos- 
 phere, and a small funnel where they are of sufficient violence ; 
 but generally, as they increase in dimensions and violence, 
 they interfere with one another and finally become united into 
 one. This seems to have been the case in the tornado of St. 
 Cloud and Sauk Rapids, in the formation of which it is stated 
 that as the clouds began to revolve sharp points suddenly shot 
 downward. As in cyclones there are generally smaller second- 
 ary ones included, complicating the resultant motions of the 
 *air and causing irregularities in the isobars, so in tornadoes 
 
WATERSPOUTS. 413 
 
 there are undoubtedly secondary whirls independent of the 
 main one, though not always accompanied by corresponding^ 
 funnel clouds visible above. This seems to be indicated by 
 side-or spur tracks sometimes observed in connection with the 
 main track, and by isolated spots at some distance from the 
 main track "with every tree uprooted and piled in confusion." 8 
 
 268. Waterspouts at sea are usually more regular and 
 better defined than those on land, and the whole area of 
 tornadic disturbance is generally smaller, so that the spouts 
 may be approached with safety within a very short distance, 
 and it is only the larger and more violent ones that seriously- 
 injure a ship running into them. The destructive gyratory 
 winds, even in the larger ones, extend only a short distance 
 from the centre, and at distances a little greater scarcely a 
 breeze sometimes is experienced. The reason of this is that, 
 the surface of the sea being smoother than that of the land,, 
 there is a more nearly perfect development of the gyrations,, 
 and a greater concentration of energy in the centre of the 
 vortex, although the whole amount of energy is generally 
 smaller on sea than on land, since this arises from the unstable 
 state, which is more liable to occur, and to a greater degree of 
 unstability, on land, where the surface of the earth becomes 
 much warmer than that of the ocean. The whole disturbance, 
 however, is simply a tornado it may be a very small one, with 
 the phenomenon of the waterspout developed in the same 
 way as in a tornado on land. 
 
 It was formerly supposed that the spout consisted of water 
 drawn up into the clouds from the sea, and that the real water- 
 spout was found on seas and lakes only, and hence the name. 
 It is true that a considerable amount of water may be drawn 
 up from the sea, but this is merely an incidental and secondary 
 matter and has nothing to do with the formation of the spout. 
 The amount of water drawn up is so small generally in com- 
 parison with the amount of rainfall, that the latter is never 
 observed to be sensibly affected by it at sea, but always appears 
 to consist of fresh water. 
 
 When we consider how houses, men, and various kinds of 
 
414 TORNADOES. 
 
 heavy bodies and debris are drawn up into the vortex of land 
 tornadoes and thrown out above in all directions, as explained 
 in 258, it is not surprising, but to be expected, that much 
 water and other things would be carried up in tornadoes at 
 sea. Here the very centre of the vortex may become nearly 
 a vacuum, and hence the tendency of the water from the sur- 
 rounding great pressure would be to rise up nearly 32 feet ; and 
 having risen so far, or at least to a considerable height, the 
 rapidly ascending currents would carry it farther, and, being 
 lashed and separated into drops, it would then be carried to 
 still great heights, as raindrops are in the interior of a tornado. 
 We have accounts of not only water, but of fish and frogs 
 being drawn up in the vortex of small tornadoes from ponds 
 and creeks, leaving, for the moment, the bottoms of the latter 
 dry, and afterwards scattering the fish and frogs over the neigh- 
 boring land. Tomlinson says : 30 
 
 " Showers of fish and frogs are by no means uncommon, especially in 
 India. One of these showers, which fell about 20 miles south of Cal- 
 'cutta, is thus noticed by an observer : ' About two o'clock P.M. of the 
 42oth inst. (Sept. 1839) we had a very smart shower of rain, and with it de- 
 scended a quantity of live fish, about three inches in length, and all of one 
 kind only. They fell in a straight line on the road from my house to the 
 tank, which is about 40 or 50 yards distant. Those which fell on the 
 hard ground were, as a matter of course, killed from the fall ; but those 
 which fell where there was grass sustained no injury, and I picked up a 
 large quantity of them, 'alive and kicking,' and let them go into my 
 tank. The most strange thing which ever struck me in connection with 
 this event, was, that the fish did not fall helter-skelter, everywhere, or here 
 and there, but they fell in a straight line, not more than a cubit in 
 breadth." 
 
 The following is taken from an account of a waterspout 
 given by Sidney B. J. Skirtchly, H. M. Geo. Survey: 75 
 
 " Duringthe summer of 1870, while in Deeping Fen, on a day when the 
 wind was blowing in gusts, carrying the dry powdery peat-dust in clouds 
 before it, I observed a whirling column of dust advancing toward me. 
 It was like those small pillars so frequently seen in streets of a town on 
 such a day, but it was considerably larger, being from 15 to 20 feet in 
 height. When it was first seen it was advancing from the far side of a 
 ground, as the uninclosed fields are called, toward me at the rate of 
 
WA TERSPO UTS. 4 1 5 
 
 :about six miles an hour, and was distant some 500 yards. It moved with 
 an unsteady, staggering motion, accompanied with a rushing noise. I 
 stayed to watch it across a dike about 15 feet wide, which ran directly 
 across its path. The smaller dikes it seemed to cross without affecting 
 them ; but on reaching the one in question, it whisked the water up into 
 a waterspout some ten feet high with a gurgling, hissing sound, and 
 steering directly across the dike burst, on reaching the opposite shore, 
 projecting a considerable quantity of water upon the land. This effort 
 seemed to spend its force, for the dust-column resumed on the opposite 
 land was but small in proportion, and after swaying about for a few 
 yards, -died away." 
 
 This was simply a whirlwind, as small tornadoes are gen- 
 erally called, in which the air was too dry and the energy too 
 small to develop the real waterspout of particles of condensed 
 vapor, yet it seems to have had considerable power in raising 
 up water from the dike. 
 
 In addition to the water carried up in the spout of a tornado 
 there is often also much spray about the base of the spout which 
 sometimes assumes the form somewhat of the sand and dust 
 cone in a land tornado, causing an apparent widening of the 
 spout at the base. 
 
 269. Small waterspouts observed on seas and lakes in clear, 
 calm, and hot weather usually arise from a state of unstable 
 equilibrium in the lower strata of the atmosphere. In such 
 cases the whirling of the air and the agitation of the water is 
 first observed below, and afterwards the formation of a cloud 
 above, and finally the complete spout, unless the atmosphere 
 is very dry. When, however, the air is very moist, near the 
 point of saturation, such spouts extend up to only a small 
 height, and are not accompanied by any rainfall, since they are 
 usually too small and continue too short a time to send up the 
 vapor to so great a height that it can be condensed and col- 
 lected into drops and fall as rain. 
 
 A number of such small spouts are often seen at one time 
 in the same vicinity. When the air is brought to the unstable 
 state it is liable to burst up through the strata above at several 
 places at nearly the same time, and then, if there is any whirl- 
 ing motion, even only very small and imperceptible, as in the 
 
41 6 TORNADOES. 
 
 case of the water in a basin, there is a concentration of this mo- 
 tion into rapid gyratory motions at the centre of each one of 
 these upbursts, which may continue to increase until a water- 
 spout is formed. 
 
 M. Defranc" has given an account of a great many water- 
 spouts of the class which occurs mostly in weather which is- 
 nearly clear and calm. He says : 
 
 " On the 23d of June, 1764, a waterspout was seen on the Seine, which 
 had its base on the river and reached up into the clouds. It was judged 
 to be about three feet in diameter where it touched the river. There 
 were some parts transparent, which allowed the ascension of the water 
 to be seen. It finally broke at about one third of its height. The lower 
 part fell in rain, the upper part was drawn up into the cloud in a second 
 of time and the phenomenon was followed by hail." 
 
 This seems to have been a tall spout notwithstanding the 
 smallness of the diameter. The air in the vicinity must have 
 been nearly calm, and in the unstable state up to a consider- 
 able altitude. Being a very tall, slender column with its base 
 upon the river, the friction was small, and so it approximated 
 to the theoretical case of no friction in which the least amount 
 of initial gyratory motion would bring down to the earth a fine 
 thread-like column of very much rarefied and cooled air, which 
 gives rise to a slender waterspout. At the time when the air in 
 the central column is not quite rarefied and cooled sufficiently 
 to condense the vapor, the least increase in gyratory velocity 
 brings it into this condition, and then the spout darts down 
 from the cloud above almost at once. Just the reverse of this 
 takes place in the case of a slender spout when the gyrations 
 are a little decreased from any cause, and this spout seems to 
 have been thus drawn up. The lower part which is said to 
 have fallen as rain was, no doubt, simply the water raised from 
 the river, as fish and frogs are said to be, and not rain. The 
 falling of hail indicates that the ascending currents extended 
 very high up into the upper and very cold strata of the atmos- 
 phere 
 
 Defranc also states : 
 
 "On May 17, 1763, Captain Cook saw six waterspouts on Queen Char- 
 lotte Sound. In one of them a bird was seen, and in arising was drawn in 
 
WA TERSPO UTS. 41 / 
 
 by force and turned around like a spit. Their first appearance was in- 
 dicated by a violent agitation and elevation of the water. When the tube 
 was first formed or became visible, its apparent diameter increased. It 
 then diminished and became invisible at its lower extremity." 
 
 The violent agitation and heaping up of the water before 
 the spouts appeared show that the gyrations and barometric 
 depressions in the centre existed before the spouts became visi- 
 ble, and that the spouts appeared only after the diminution of 
 tension and of temperature became sufficient to condense the 
 vapor. The fact of the bird's being drawn in and whirled around 
 shows that the air is really drawn in from ail sides and up in a 
 spiral in accordance with theory. 
 
 The frontispiece to the title-page is the view of a water- 
 spout as observed off the coast of Sicily, and sketched by Mr* 
 Morey in August, 1876. The following is his account of it : 
 
 " It formed during a comparatively calm and clear afternoon, with 
 the temperature of the atmosphere not much, if any, higher than usual 
 for that latitude and place. The wind was so light as to barely cause a 
 slight ripple on the surface of the sea, but sufficient to give the spout a 
 perceptible motion from east to west. Three little protuberances first 
 appeared under the cloud, the centre one rapidly elongating connected 
 with the water. The two on the sides increased and decreased in length, 
 bat never reached further down than one fifth the length of the main 
 spout. 
 
 "It lasted about twenty minutes, and disappeared shortly after the 
 breaking of the main column at a point which seemed the connection be- 
 tween the funnel and the water. 
 
 "No noise accompanied the break in addition to the noise resem- 
 bling a cataract, which lasted from the time the spout connected with the 
 water to the break up. No electrical phenomena were noticed at all. 
 
 " A rough estimate of the main column gave its height between 700 
 and 800 feet. 
 
 The stability of the formation during the twenty minutes of its dura- 
 tion was wonderful in the extreme." 
 
 Of the two partial spouts or funnel-shaped protuberances 
 on each side the one, according to the sketch, seems to have 
 caused a considerable agitation of the water beneath it. 
 
 270. Waterspouts of the class here considered are very often 
 seen along the eastern coast of the United States in the vicin* 
 
41 8 TORNADOES. 
 
 ity of the Gulf Stream, not only during the summer season, but 
 likewise in the winter. On the Little Bahama Bank as many as 
 fifteen have been seen at the same time. The following ac- 
 C0unt of them is given by an officer of H. M. Surveying Vessel 
 " Sparrow-Hawk," employed in the West Indies : 78 
 
 " I have noticed that the first movement which eventually produces a 
 waterspout is a whirlwind on the surface of the water, gradually increas- 
 ing in velocity of rotation and decreasing in diameter as it travels along 
 before the prevailing wind. The spray is lifted up to a height of from 
 five to ten feet, and then gradually melts away, assuming the appearance 
 of hot air, which is visible (still rotating) to a similar height above the 
 spray. A motion amongst the clouds soon becomes apparent, a tongue 
 is protruded, and the spout becomes visible from the top downwards. 
 
 "On one occasion a portion of a spout appeared for a moment in mid- 
 air above the disturbances on the surface of the water. 
 
 " Although these appearances are commonly called waterspouts, I have 
 been informed by men who have been caught in them that they contain 
 no water and should be properly called ' windspouts.' The small fore- 
 and-aft-rigged schooners that ply on the bank do not fear them, although 
 a prudent captain would probably shorten sail to one. I have been un- 
 able taJiear of an accident having occurred through a vessel being caught 
 in a waterspout. 
 
 They frequently cross the land, but no water falls ; they take up any 
 light articles, such as clothes spread out to dry, straw, etc., that happen 
 in their course, but have never been known to carry anything with them 
 to a distance." 
 
 It is seen from the preceding account of this class of spouts 
 that the whirlwind, and the consequent agitation of the water 
 beneath, first commence and gradually increase until the 
 strength of the gyratory motion becomes sufficient to bring 
 down the spout, and that this first appears above as a funnel 
 or short spout, and then becomes visible from the top down- 
 ward, the same as in the larger and more violent land torna- 
 does. It seems that there is no water carried up in these 
 small whirlwinds except some spray to a short distance ; but 
 in the larger ones, and especially the land tornadoes, some 
 water is evidently carried up when they pass over water. If 
 it were necessary to change the name, which, as in many other 
 things, was given before the thing was understood, it would be 
 
WA TERSPO UTS. 4 1 9 
 
 more appropriate to call them vapor-spouts, since they are evi- 
 dently composed of condensed vapor, and no amount of rotary 
 motion in dry air would produce such a phenomenon. 
 
 Where the atmosphere is clear and calm over a river or 
 small lake, as may frequently happen where it is surrounded 
 by highlands and forests, and the air is very nearly saturated 
 with vapor, very diminutive spouts of small altitude are some- 
 times seen. Under such conditions the air near the surface 
 of the water becomes heated, both by the direct and reflected 
 rays of the sun, and a stratum of air of small depth next to the 
 surface is brought to the unstable state, in which little whirl- 
 winds and ascending currents originate in the usual way. The 
 air, being nearly saturated, would have to ascend to only a 
 small altitude without any whirl before cloud formation would 
 take place, and this being so near the earth's surface, a slight 
 whirling of the air is able to bring the cloud down to the surface 
 of the water in the form of a little spout. 
 
 271. Such small spouts have been observed, under very 
 peculiar circumstances, to be hollow. M. Boue, 79 in the year 
 1850, observed three small waterspouts at the same time on 
 Lake Janina, from the top of a high mountain. The weather 
 was entirely clear, without clouds or wind, but very oppressive 
 and hot. The spouts seemed to rise up from the lake, and he 
 could look down into the top of them and see that they were 
 hollow in the middle. The same seems to exist in some 
 measure in large spouts both on sea and land, as is indicated 
 by the central part of the column appearing lighter than the 
 surrounding parts. 
 
 This hollowness, or less density of the condensed vapor, in 
 the middle, arises, no doubt, from the effect of the centrifugal 
 force of the very rapid gyratory velocity near the centre, in 
 driving the condensed vapor, as soon as formed, out from the 
 centre, and also from the fact that the central part is so rarefied 
 and cooled down that but little vapor, even before condensa- 
 tion, can approach near it, since it is mostly condensed before 
 arriving there ; just as in the vertical ascent up into the region 
 of freezing cold very little uncondensed vapor is left after 
 
420 TORNADOES. 
 
 having ascended to that altitude. The central part of a water- 
 spout corresponds in temperature, density, and capacity for 
 vapor with these high dry strata of the atmosphere in the 
 surrounding vicinity, as is understood from Fig. I, 233. 
 
 In fact there seems to be a slightly analogous phenomenon 
 even in cyclones, in which the clouds are frequently less dense, 
 and even entirely disappear sometimes, in the central part, 
 giving rise to what is called " the eye of the storm," though the 
 explanation is only in part the same. 
 
 HAIL-STORMS. 
 
 272. A hail-storm is simply a tornado in which the ascend- 
 ing currents are so strong, and reach so high up into the upper 
 strata of the atmosphere, that the rain-drops are carried up 
 into the cold regions above, and into the central part within the 
 isobaric and isothermic surface of the freezing-point, where 
 they are frozen into hail. In fact hail, as well as rain, is 
 almost a universal accompaniment of a tornado, and so, as the 
 latter, it is usually found in the S.E. quadrant of a cyclone 
 and at a considerable distance from the centre, as has been 
 shown to be the case in Russia by Klosovsky from observation 
 ( 3.11). Finley says, 72 in his account of the tornadoes of May 
 29 and 30, 1879: 
 
 " In referring to the several storm descriptions, it will be found that 
 rain and hail invariably preceded the tornado cloud from ten to thirty 
 minutes, nearly always attended by a southerly wind." 
 
 But this applies mostly to the more violent tornadoes, such 
 as were investigated by him, and not to every class of atmos- 
 pheric phenomena which we have included under the generic 
 name tornado. 
 
 It has been shown in 233 that every isobaric and isother- 
 mic surface, however high above the earth's surface, would in 
 a perfectly regular tornado, and in the case of no friction, be 
 brought down by the centrifugal force of the gyratory motion 
 to the earth's surface near the centre of the tornado, as 
 represented in Fig. i. The horizontal and isothermic surface. 
 
HAIL-STORMS. 
 
 421 
 
 therefore, high up in the air, which separates the strata of 
 freezing temperature above from those of a non-freezing tem- 
 perature below, would, in case of no friction, be brought down 
 by tornadic action to the earth's surface at c. The effect of 
 friction, however, prevents its bringing the freezing atmosphere 
 entirely down, or rather its so expanding and rarefying the air 
 
 Fig. II. 
 
 in the central part that the air in consequence is reduced to 
 the freezing temperature down to the earth's surface. But 
 still the air of freezing temperature is brought down in the central 
 part in the form of a funnel, considerably below the general 
 level of its base when undisturbed, just as it has been shown 
 the cloud region is, Fig. 7, and as is represented by a'c'b', Fig. 
 1 1, in which the unshaded part represents the unclouded air 
 below and beyond the surface of incipient condensation, here 
 
422 TORNADOES. 
 
 supposed to be brought entirely down to the earth's surface 
 A B ; the darker shaded portion, the part in which the vapor is 
 condensed to ordinary cloud ; and the lighter shading above, 
 the part where the vapor is converted directly to snow, and the 
 rain-drops, carried up by the ascending currents, to hail. The 
 height of the surface of incipient freezing, or temperature of 
 C, where the temperature of the air at the earth's surface is 
 given, may be ascertained in the same way as the temperature 
 at any given height, as explained in 27. 
 
 273. In a torrado the air at and near the earth's surface 
 is drawn in and ascends on all sides until it arrives at the 
 surface of incipient condensation, represented by the lower 
 line ab, brought down to the earth on each side of the centre 
 at /, at which surface, as has already been explained, cloud- 
 formation commences. In its further ascent and approach 
 toward the interior central part the vapor contained in it is 
 gradually condensed, and the temperature of the air reduced, 
 until it arrives at the surface of incipient freezing, either up at 
 the undisturbed level beyond the influence of tornadic action 
 as at a' or b', or where that surface is brought down below this 
 level near the centre in the region of c' . As the air, with the 
 uncondensed vapor yet remaining, enters above and within 
 this surface, the vapor left is gradually frozen to snow, and 
 the higher it ascends the more of it is so changed. This snow, 
 however, never falls to the earth in the summer season, but 
 melts soon after falling below the level of incipient freezing. 
 In the winter season, at times when this level is not very far 
 above the earth's surface, it reaches the surface as soft snow, 
 where there is no tornadic action and only gentle ascending 
 currents. 
 
 In the ascending current of a tornado, as in that of the 
 equatorial calm-belt or of a cyclone, the rain-drops are formed 
 down in the cloud region and carried upward until they be- 
 come too large to be supported by the current, and so fall to 
 the earth, as explained in in. In a tornado, however, the 
 ascending current is often so strong that the rain is supported 
 until, by the blending of the small drops by coming in contact, 
 
HAIL-STORMS. 423 
 
 very large drops are formed, and the strong ascending currents 
 often extend so high that these large drops are carried away 
 up into the region of freezing temperature, represented by the 
 upper lighter shading in the preceding figure. They are there 
 frozen, and after having been carried up and outward above to 
 a distance from the centre where the ascending current is not 
 strong enough, by the formula of 247, to keep them up, they 
 slowly descend, and, receiving additions of ice as they fall, as 
 long as their temperature remains below zero, from the rain 
 below, which is being either kept suspended in the air or being 
 carried farther up, they finally fall to the earth as solid hail- 
 stones. 
 
 274. But the origin of the hailstone is often not a rain- 
 drop, but a bunch of snow formed in the snow region, and 
 moistened by the rain carried up into this region before it has 
 had time to become frozen into hail. This moist snow is kept 
 up there until it freezes, and after that, while being kept up 
 there, and after it commences to fall, as long as its temperature 
 remains below zero it continues to receive a coating of ice 
 from the rain which is carried up past it and that through 
 which it falls. As it grows and is carried outward above 
 where the ascending current is weaker, it finally becomes too 
 heavy to be kept suspended in the air, and it falls to the earth 
 a hailstone, with a kernel of frozen snow in its centre. 
 
 In such a case we may imagine the soft ball of snow to 
 have originated in the snow region at m and then to have been 
 kept partially suspended and to have been carried up and out 
 slowly from the centre to a distance where it could drop down, 
 having become meanwhile reduced to a low temperature, and 
 that on its way down it received a coating of ice from the 
 small ascending rain-drops, or others with which it came in 
 contact during its fall, and that it finally reached the earth at n. 
 
 It often happens, however, that in falling very gently 
 where the ascending current at no great distance from the vor- 
 tex is not quite but nearly sufficient to keep it suspended, it 
 is drawn in again by the indrawing currents from all sides to- 
 ward the vortex, as the scud clouds under the rim of the tor- 
 
424 TORNADOES. 
 
 nado cloud, 266, where the ascending current is sufficient to 
 carry it up again into the snow region, where it receives a 
 coating of snow moistened by the small rain-drops carried up 
 into the snow-region before they freeze. This coating now 
 becomes frozen solid, and the whole mass, it may be, is re- 
 duced considerably below zero temperature before it is carried 
 out above, where it can gradually drop down again toward the 
 earth ; and in falling, even through the lower part of the snow- 
 region where there is little snow, but mostly rain-drops not yet 
 frozen, it receives another coating of solid ice ; for its temper- 
 ature having been reduced considerably below zero, it contin- 
 ues to freeze the rain coming in contact with it for a long dis- 
 tance after having passed down into the cloud region. But in 
 gently falling down it may be drawn in a second time toward 
 the centre and be carried up by the ascending current into the 
 snow-region and receive another coating of wet snow over the 
 last one of solid ice, and in falling receive another coating of 
 solid ice in the same manner as before. This process may be 
 repeated a number of times, in each of which the hailstone, 
 disregarding its gyratory motion all the while, describes a kind 
 of orbit, not returning into itself, somewhat as represented in 
 Fig. 11, until finally it is carried out above so far from the 
 centre, or the strength of the tornado becomes so much weak- 
 ened, that it is no longer carried in toward, and up in, the cen- 
 tral part, but falls to the earth a hailstone with a snow-kernel 
 and a number of alternating concentric coatings of solid ice and 
 frozen wet snow. 
 
 In this case we may suppose the small snowball to have 
 originated at p and to have been carried up and out, and then 
 to have fallen down and to have been drawn in toward the 
 centre several times, until finally it was carried out so far, and 
 had grown to be so heavy, that it was not brought in toward 
 the centre but dropped down to the earth at q, Fig. n. 
 
 Hail-storms occur mostly in the summer season. In the 
 winter season the plane of incipient freezing is so low that 
 there is little or no rain-cloud region in which large rain-drops 
 can be formed and in which, after having been frozen above, 
 
HA I L- STORMS. 4 2 5 
 
 they are increased in size in falling through. Winter hail, there- 
 fore, consists of only very small particles of frozen water. 
 
 275. A remarkable example of hailstones with concentric 
 coatings was observed at Northampton, Mass., June 20,1870, 
 an account of which has been given by Mr. Houry. 85 In this 
 case hailstones fell weighing over a half pound, and most of 
 them were formed of concentric layers, like the coats of an 
 onion. Mr. Houry states that in one of them he counted 
 thirteen layers, indicating, as he says, that it had passed 
 through as many strata of snowy and vaporous clouds. The 
 true explanation is, that it oscillated as many times between 
 the rain-cloud and the snow-cloud regions, or, in other words, 
 that it performed six or seven revolutions with the lower part 
 of its orbit in the rain-cloud, and the upper part in the snow- 
 cloud, in the manner represented in Fig. II. 
 
 In corroboration of the preceding theory of the formation 
 of hail, and as an exemplification of the motions of a hailstone, 
 as represented above, the following extract from a letter of 
 Mr. John Wise, the balloonist, written to the New York Trib- 
 une in Feb., 1857, w ^ tn reference to an ascent which he made 
 in a tornado, is given here, from which it is seen that he de- 
 scribed similar orbits with his balloon in the tornado cloud : 88 
 
 "This storm originated nearly over the town of Carlisle, Pennsyl- 
 vania, on the 1 7th of June, 1843. I entered it just as it was forming. 
 The nucleous cloud was just spreading out as I entered the vortex un- 
 suspectingly. I was hurled into it so quickly that I had no opportunity 
 of viewing the surroundings outside, and must therefore confine this 
 relation to its internal action. On entering it the motions of the air 
 swung the balloon to and fro, as around in a circle, and a dismal, howl- 
 ing noise accompanied the unpleasant and sickening motion, and in a 
 few minutes thereafter was heard the falling of heavy rain below, resem- 
 bling in sound a cataract. The color of the cloud internally was of a 
 milky hue, somewhat like a dense body of steam in the open air, and the 
 -cold was so sharp that my beard became bushy with hoar-frost. As 
 there were no electrical explosions in this storm during my incarcera- 
 tion, it might have been borne comfortably enough but for the seasick- 
 ness occasioned by the agitated air-storm. Still, I could hear and see, 
 and even smell, eveiything close by and around. Little pellets of snow 
 {with an icy nucleus when broken) were pattering profusely around me 
 
426 TORNADOES. 
 
 in promiscuous and confused disorder, and slight blasts of wind seemed 
 occasionally to penetrate this cloud laterally, notwithstanding there was 
 an upmoving column of wind all the while. This upmoving stream 
 would carry the balloon up to a point in the upper cloud, where its force 
 was expended by the outspreading of its vapor, whence the balloon 
 would be thrown outward, fall down some distance, then be drawn into- 
 the vortex, again to be carried upward to perform the same revolution, 
 until I had gone through the cold furnace seven or eight times ; and all 
 this time the smell of sulphur, or what is now termed ozone, was percep- 
 tible, and I was sweating profusely from some cause unknown to me, 
 unless it was from undue excitement. The last time of descent in this 
 cloud brought the balloon through its base, where, instead of pellets of 
 snow, there was encountered a drenching rain, with which I came into- 
 a clear field, and the storm passed on." 
 
 The "cold furnace" through which he passed seven or 
 eight times was most probably in and near the interior and 
 upper part of the vortex, in the vicinity of c' t Fig. 11, where 
 the snow-cloud and cold upper strata are brought down in the 
 form of the funnel-cloud in tornadoes, or, it may be, still lower 
 in the form of a waterspout, for it must be borne in mind that 
 the balloon could be carried into this snow-region, or at least 
 into a region of very low temperature, without ascending to 
 very high altitudes by being carried close into the centre where 
 this region is brought down. Low temperatures are reached 
 by going in toward the centre as well as by ascending to higher 
 altitudes. 
 
 The small pellets seem to have originated in small rain-drops- 
 which, being carried up into the snow-cloud, received a coating 
 of snow, but had not received a subsequent one of ice when they 
 struck his balloon. 
 
 The motions of the balloon in which M. H. Lecocq recently 
 ascended from Paris seem to have been similar, on entering 
 up through the base into a thunder-cloud, to those of Mr.. 
 Wise's balloon. According to the account : 91 
 
 " The balloon, influenced by electrical attraction, rose toward the 
 cloud, accompanied, or rather preceded, by the pieces of paper which the 
 balloonists had thrown from their basket. At 20 minutes of 8, and at 
 a height of iioo meters, the balloon entered a cloud-mass of greenish- 
 gray color, which immediately shut out from them all sight of the 
 
HAIL-STORMS. 
 
 earth. . . . The balloon constantly rotated and ascended and de- 
 scended without the interference of the balloonists ; and, what is a 
 very rare thing in a balloon, they felt almost constantly a very consider- 
 able wind, which shook the balloon and gave to the basket a swinging 
 motion of considerable amplitude." 
 
 The account further states : 
 
 " At certain times a sensation as of a current of cold air was very 
 perceptible. This was followed immediately by a rapid ascension, and 
 the expelled gas descended even to the basket. During one of these 
 ascents the balloon reached a height of 1600 meters, which was the 
 maximum." 
 
 The balloon was not drawn into the cloud by electrical 
 attraction, but carried up into it by the ascending currents, 
 which gave rise to the cloud, and with a velocity less than in 
 the case of the pieces of paper, because the latter had more, 
 surface exposed to the ascending currents, in proportion to 
 their mass, than the balloon. At the height of 1100 meters, 
 the vapor began to be condensed to form the base of the cloud. 
 The relative air-current in this case arose from the air's ascend- 
 ing and being drawn in obliquely toward the centre past the 
 balloon, which was acted upon by the force of gravity and the 
 centrifugal force of the gyrations. The balloon ascended 
 rapidly when drawn in near the centre where the ascending 
 current is rapid, and descended when carried out above to 
 where the ascending currents are weak. It was near the cold 
 centre where the sensation of a cold current was experienced, 
 and then the balloon ascended rapidly, because here the 
 ascending current is strong. 
 
 In this thunder-cloud there was no doubt considerable 
 tornadic action, as indicated by the observed constant rotation 
 and ascent and descent of the balloon, though not enough to 
 .give rise to either hail or a waterspout. 
 
 276. The shape of hailstones varies very much. Some are 
 like a disk or very oblate spheroid. If for any reason the hail- 
 stone becomes the least flattened, the ascending current which 
 keeps it suspended for a time in the air also keeps its shortest 
 diameter perpendicular to the current, and hence it then. 
 
.428 TORNADOES. 
 
 increases most on the edges. Others are of a pyramidal form, 
 or of an irregular oval shape with uneven surface. They also 
 appear sometimes to be fragments of large pieces of ice, broken 
 by collision with one another by the gyratory vortex of the 
 tornado. 
 
 In Iowa, in 1880, according to Dr. Hinrichs, 
 
 " Hailstones 12 inches in circumference have been measured in Sac 
 County. In Davis County a flattened disk of hail measured 4^ inches 
 in diameter, and was 2 inches thick. In Iowa County a group of ice 
 crystals fell, 2 inches in length, if inches wide, and I inch thick." 
 
 From the report on the tornadoes of May 29 and 30, iS/Q, 72 
 have been extracted the following notices of some very extraor- 
 dinary hail-falls : 
 
 In the Lee's Summit tornado, Mrs. Irwin stated that " hail 
 like ' large chunks of ice,' with very little rain, fell just after the 
 storm-cloud passed." 
 
 In the Delphos tornado, it is stated : 
 
 "On the farm of Mr. Peter Bock, in the adjoining township of 
 Fountain, about 4 miles W. of the storm's centre, and during the hail- 
 storm that preceded the tornado, masses of ice fell as large as a man's 
 head, breaking in pieces as they struck the earth. One measured 13 
 inches in circumference, another 15, and a hole made by one that fell 
 near the place of Mr. J. H. Kams measured 7 inches across one way 
 and 8 the other. This immense fragment of aerial ice broke into small 
 pieces, so that its exact size could not be determined." 
 
 It is also stated in the copy of a letter from Mr. Billingsley, 
 of Delphos, that several hailstones fell which measured 12 to 
 15 inches in circumference and I to 2 inches in diameter. 
 These must have been in the form of disks the thickness of 
 which was from I to 2 inches. 
 
 In the account of the Lincoln County tornado, it is stated : 
 
 " At first the hailstones were about the size of marbles, but they 
 rapidly increased in diameter until they were as large as hens' eggs and 
 very uniform in shape. After the precipitation had continued about 
 fifteen minutes, the wind ceased and the small hail nearly stopped, when 
 there commenced to fall perpendicularly large bodies of frozen snow and 
 ice, some round and smooth and as large as a pint bowl, others inclined 
 
CLOUD-BURSTS. 429- 
 
 to be flat, with scalloped edges, and others resembled rough sea-shells. 
 One of the latter, after being exposed an hour to the sun, measured 14 
 inches in circumference." 
 
 CLOUD-BURSTS. 
 
 277. Considering the strong ascending currents in tor- 
 nadoes, and their great supporting power, as deduced from 
 theory and exemplified in numerous cases of observation, it is 
 not to be wondered at if great accumulations of rain and hail 
 are sustained for a while by these currents at a considerable 
 altitude in the vortex of the tornado, and then, on account of 
 a sudden weakening or breaking up of the tornado for some 
 reason, a great amount of rain and hail should sometimes fall 
 to the earth in a short time. Such abundant and sudden pre- 
 cipitations are called cloud-bursts. If the velocity of the ascend- 
 ing current in the interior is not so great that the rain is all 
 carried up where the current is outward from the vortex, or 
 where this outward current and the centrifugal force of the 
 gyrations together are able to drive it out where it can fall 
 through the weaker ascending current, and yet is great 
 enough to prevent its falling back, then in the whole of the 
 lower part of the cloud in the central part of the tornado, even 
 up to an altitude of three miles or more, there may be a great 
 accumulation of rain, prevented by the ascending current from 
 falling, and also by the centripetal in-drawing current below a 
 given level from being carried out and dispersed. Of course, a 
 considerable part of the energy of the tornado is required to 
 support this mass, so that, as this increases, the strength of the 
 ascending current is weakened, until finally the whole mass 
 suddenly falls. Or the whole system may become weak and 
 break up from some other cause, when the same result follows. 
 This is especially liable to occur in mountainous regions ; for 
 if we suppose that a tornado thus heavily charged with rain is 
 moving toward the side of a mountain, its coming in contact 
 with it would interfere very much with the gyrations and 
 energy of the tornado, and tend to break up the whole system 
 almost at once, and let the whole accumulation of water drop 
 
-43 TORNADOES. 
 
 suddenly down. Hence cloud-bursts most frequently occur on 
 mountain-sides. 
 
 278. The water in cloud-bursts does not generally fall as 
 rain, but is poured down. Long before the ascending current is 
 so reduced as to allow it to fall in drops, the water seems to col- 
 lect together at certain places and to force its way downward, 
 through the ascending current, in a stream. This it would 
 naturally do, since we cannot suppose that it is ever evenly 
 distributed over any given place, or that the velocity of the 
 ascending current is exactly the same at all points in the 
 same vicinity. A considerable body of water having been col- 
 lected at certain points, it is there able to force its way down, 
 and it draws into its train much more from all sides on its way, 
 so that continuous streams of water are formed and kept up 
 for several minutes, during which an immense amount of water 
 falls on a number of small spots, while not even rain-drops fall 
 between on account of the strength of the ascending current, 
 through which water can only be poured down. Having col- 
 lected in large masses and once made an opening for itself at 
 one or more places, the velocity of the streams is gradually 
 accelerated, since the ascending current then is not able to sup- 
 port them, so that on reaching the earth the velocity may be- 
 come immensely great, and the streams strike with great force. 
 Each one of these descending streams may make a great hole 
 or basin in the ground ; and on a steep mountain-side, if the 
 stream continues for a short time only, it may give rise to a 
 mountain slide, or at least to a great ravine, and carry rocks 
 and trees with it down the mountain-side. 
 
 279. Immediately after the great tornado at Hollidaysburg, 
 Pa., on the iQth of June, 1838, Espy 34 visited the vicinity and 
 examined the sides of the ridges and mountains. He found a 
 great many holes eight or ten meters in diameter and one or 
 two in depth, according to the nature of the soil and depth of 
 the rock, and the sides often cut almost perpendicularly down 
 on the upper sides, but entirely washed out below, so as to 
 form the commencement of a ravine. Sometimes the current 
 descending through the atmosphere seemed to strike the earth 
 
CL UD-B URSTS. 431 
 
 with so great a force that it made a great hole or basin and 
 then rebounded so as not to strike the earth again on the 
 mountain-side for a considerable distance below. Several of 
 these holes were often found close together in the same vicin- 
 ity, indicating that the water was poured down at the same time 
 through several openings made in the current of ascending air 
 by the concentration of large bodies of water at these places. 
 
 With regard to a ridge a half-mile west of Hollidaysburg, 
 he says : 
 
 " On examining the northern side of this ridge, large masses of gravel 
 and rocks and trees and earth, to the number of 22, were found lying 
 at the base on the. plain below, having been washed down from the 
 side of the ridge by running water. The places from which these 
 masses started could easily be seen from the base, being only about 30 
 yards up the side. On going to the head of these washes, they were found 
 to be nearly round basins from i to 6 feet deep, without any drains lead- 
 ing into them from above. The old .leaves of last year's growth, and 
 -other light materials, were lying undisturbed above, within an inch of 
 the rim of these basins, which were generally cut down nearly perpen- 
 dicularly on the upper side, and washed out clean on the lower. The 
 greater part of these basins were nearly of the same diameter, about 20 
 feet, and the trees that stood in their places were all washed out. 
 Those below the basin were generally standing, and showed by the leaves 
 and grass drifted on their upper side how high the water was in running 
 down the side of the ridge ; on some it was as high as 3 feet. It proba- 
 bly, however, dashed up on the trees above its general level." 
 
 In an account of a remarkable storm which occurred at 
 Catskill, July 26, 1819, it is stated that " the rain at times de- 
 scended in very large drops, and at times in streams and 
 sheets." In the mountainous regions of the States and Terri- 
 tories of the United States immediately east of the Rocky 
 Mountain range, where tornadoes especially abound, the im- 
 mense amount of water which sometimes drops down suddenly 
 from the clouds and collects in the ravines, and the valleys into 
 which they lead, often cause great floods, which are especially 
 disastrous on account of their suddenness, which leaves little 
 or no time for escape. The following is a newspaper account 
 of cloud-bursts which occurred near Fort Keogh, Mont., a few 
 
43 2 TORNADOES. 
 
 years ago, and which are merely samples of similar occurrences, 
 which frequently take place in Montana and adjacent territories. 
 
 " Word has been received from Simmons' sheep corral, on the Amer- 
 ican fork of the Mussel shoal, that a cloud-burst there Monday evening 
 destroyed 800 head of sheep. The cloud exploded at the head of Dry 
 Run Creek and came pouring down in a solid wall 32 feet high, car- 
 rying off nearly the entire herd, and almost drowning a herder. The 
 carcasses of the animals are strewn along the river for a distance of 
 1 6 miles below the scene of the disaster. The upper Yellowstone 
 valley was visited yesterday by a terrific hail-storm, which rooted up and 
 destroyed every growing thing in a strip of country six miles wide. Near 
 Merill occurred a cloud hail-burst. For half an hour the hail was. 
 beyond description. There were drifts of hail 14 inches deep in some 
 places. There was little rain accompanying the hail simply one sheet 
 of hail came pouring down." 
 
 The Signal Service observer at Fort Elliott, Tex., reports: 93 
 
 " A thunder-storm began at 4.10 P.M. and ended at 7.40 P.M., moving 
 from southwest to northeast. Hail began at 5.18 P.M. and ended at 5.26 
 P.M., the hailstones being spheroidical in shape and about two inches in 
 diameter; formation, solid snow. The ' breaks ' (hills) at the foot of 
 the plains several miles northwest of station were absolutely white with 
 hailstones for three hours after the storm. This was observed by every- 
 body at the station ; on the morning of the 26th I walked down to the 
 Sweetwater Creek, three fourths of a mile distant, and saw great banks 
 of hailstones which had been washed down during the night. The bot- 
 toms along the Sweetwater were literally covered with banks of hail- 
 stones from six to eight feet in depth. It was estimated that there was 
 enough hail to cover ten acres to a depth of six feet. The hailstones 
 killed five horses which were out on the prairie on a ranch six miles 
 north of station. The Sweetwater Creek was higher than ever known 
 before, the freshet destroying nearly the entire post garden. The high 
 water is supposed to have been caused by a ' cloud-burst' at or near the 
 foot of the plains, where the Sweetwater has its source ; there was only 
 0.36 inch of rainfall at the station. On Sunday, May 27th, hailstones 
 were collected on the banks of the Sweetwater, which had been washed 
 down and lay in drifts 6 feet deep, actual measurement by the observer." 
 
 280. From these accounts and many other similar ones 
 which might be cited, it is evident that the water in such cases 
 does not fall as rain, but is poured down in streams ; and this 
 is especially evident from the observed effects of the Hollidays- 
 
CLOUD-BURSTS. 433 
 
 burg tornado, by which great holes and basins were made in the 
 ground, and the lightest materials on the margins of these on 
 the upper sides were not washed away; and the reason of this 
 evidently is that the accumulated water in the cloud is poured 
 down in streams through the ascending current of air, which at 
 the time is too strong to allow even the largest drops to fall as 
 rain. 
 
 It is seen from a reference to Table VII that a rain-drop of 
 0.2 inch in diameter at an altitude of one mile cannot fall 
 through an ascending current of air with a velocity of 25 miles 
 per hour; and those with still smaller diameters are carried up 
 to where the velocity and density are such that they are sup- 
 ported by the current, and begin to fall only after they become 
 so large, or the velocity of the ascending current becomes so 
 much diminished, that they are no longer supported in the air, 
 and fall as rain. Hence with an ascending velocity of 25 miles 
 per hour, no rain in drops of ordinary size of 0.2 inch or less can 
 fall directly back to the earth ; but in the case of a tornado it can 
 be carried out above, and fall at a distance from the centre, 
 provided the drops are not too large to be carried up above 
 the level which separates the lateral inflowing current -below 
 from the outflowing current above. The ascending velocity 
 may be such as to carry out above the smaller drops only, and 
 those with larger diameters are supported in the cloud in the 
 central part of the tornado until, by blending with one another, 
 they become much larger, or, in the case of very rapid ascend- 
 ing currents, until they collect into large masses which force 
 their way down in streams of water. 
 
 281. All that has been stated with regard to immense rain- 
 falls in cloud-bursts is applicable, with a few modifications, to 
 the sudden falls of immense quantities of hail. In this case, 
 however, the circumstances must be such that the out-turning 
 current is at a great altitude and the strength of the ascending 
 current is so great that, instead of the accumulation being 
 down very far below the region of freezing, it must be higher 
 up, but not necessarily in this region. For the hail-stones, 
 formed in the manner described, may fall directly back from 
 
434 TORNADOES. 
 
 above, or be carried out above and come around and be car- 
 ried up into this place where the ascending current is too 
 strong to allow them to fall, and not strong enough to carry 
 them up where the current above would carry them out where 
 they can fall, and so they remain there a considerable time 
 without much loss from melting even when collected below 
 the region of freezing temperature, until from some cause the 
 energy of the tornado becomes exhausted suddenly, or the 
 accumulation becomes too great to be supported, and having 
 once broken through in spots, it collects together into streams, 
 as rain does in a cloud-burst, and falls to the earth in a very 
 short time, leaving a great depth of hail over a short and very 
 narrow district of country. 
 
 If the collection of hail is up in the freezing-region, then, 
 by the continual freezing of the rain carried up from below and 
 coming in contact with the hail-stones, they grow until they 
 become so large, or until the velocity of the current is so much 
 diminished, that they can be no longer supported in the air. 
 This may not be until they become very large. Accordingly, 
 hail-stones of enormous size are sometimes observed, and even 
 great chunks of ice, seemingly formed by the freezing together 
 of the water and the hail-stones collected in the vortex of the 
 
 tornado ( 276). 
 
 
 
 FAIR-WEATHER WHIRLWINDS AND WHITE SQUALLS. 
 
 282. These are simply small tornadoes which occur during 
 fair weather whenever and wherever the proper conditions are 
 found, which are generally when there is an unusually rapid de- 
 crease of temperature with increase of altitude, or else a very 
 nearly saturated atmosphere. They are sometimes observed 
 on land, but mostly on lakes and at sea, and may be accom- 
 panied by a water-spout or not, according to the violence of the 
 gyratory motion and the amount of aqueous vapor in the at- 
 mosphere. At first a small cloud is formed in the clear sky, 
 which gradually increases from the condensation of vapor 
 rapidly carried up in the central part of the gyrating and 
 
FAIR-WEATHER WHIRLWINDS AND WHITE SQUALLS. 435 
 
 ascending air just as in the case of any other tornado. The 
 gyrations may sometimes continue to increase in violence 
 and extent, and the cloud to spread until it assumes the dimen- 
 sions of a tornado such as usually takes place in a cyclone ; but 
 it is mostly confined to only a very narrow streak, and its vio- 
 lence, although very great at the centre, is not felt at a short 
 distance away. Although the gyrations are violent very near 
 the centre, yet decreasing in velocity, at least a little above the 
 earth's surface where the friction is small, somewhat according 
 to the law expressed in 42, at a short distance from the centre 
 they are entirely harmless, and they may pass very near with- 
 out doing any injury. If, however, they pass directly over 
 houses on land or a ship at sea, their destructive effects may 
 be very great and sudden. 
 
 When these small tornadoes are accompanied by a water- 
 spout and are first seen at sea at a distance, they can generally 
 be avoided, or, if not, preparations can be made to guard 
 against danger; but where they are suddenly formed on the 
 spot and drop down, as it were, from above, they give no fore- 
 warning of approaching danger. A remarkable example of 
 this kind was related in the New York Herald of December 10, 
 1878. The British bark Bel Stuart, Captain Harper, on the 
 evening of November 14, 1878, 160 miles from Cape Sable, 
 
 " was struck by a white squall in a comparatively smooth sea and clear 
 ^ky. which swept her decks and created consternation on board. At 6 
 P.M. of the same day, all hands being on deck after supper, a strange 
 sighing of the wind was observed by the watch, and the sky became sud- 
 denly threatening without corresponding indication of the barometer, 
 which showed a rising tendency ; Captain Harper and his first officer were 
 on the deck at the time. All hands noticed the peculiar change in sea 
 and sky, and were discussing it, when, without a moment's notice, the sea 
 forward seemed to swell up to meet the lowering sky, and swept the bark 
 across her bows, carrying away her fore top-gallant-mast, jib, jib-boom, 
 foretop-mast stays, and the maintop-gallant-mast, with all their accom- 
 panying sails. In a moment, as it seemed, the bark, with all sail set, in a 
 fair wind, with a moderate sea, was left a comparative wreck to wallow 
 in the trough of the tremendous seas which had followed the spiral vol- 
 ume of water. Two minutes before the fatal catastrophe, Captain Har- 
 per says, there was no indication of the water-spout." 
 
TORNADOES. 
 
 It seems from this account that the bark ran into the spout 
 as it was being formed and before it became visible. The sigh- 
 ing of the wind was caused by the rapid gyrations of the air, 
 and the threatening sky by the incipient condensation of the 
 aqueous vapors carried up by the ascending current. The 
 barometer, before its very near approach, remained unaffected, 
 because, as we have seen, the barometric pressure is diminished 
 only at and very near the centre, and it was by this that the 
 uprising of the sea was caused which swept across the bark. 
 
 283. When we have the conditions of a water-spout in fair 
 weather with little moisture in the air, we have what are called 
 
 white squalls, or fair-weather whirl- 
 winds. In such cases the dew-point 
 is so low, and consequently the 
 cloud, when formed, is so high, that 
 the gyrations may not be able to 
 bring it down, in the form of a 
 spout, to the sea. But still the 
 gyrations and the rapidly ascending 
 current in the central part are there, 
 and the rising and boiling of the 
 sea below. High up in the air also, 
 directly over the boiling of the 
 sea, is a patch of white cloud, 
 formed by the condensation of the 
 vapor in the ascending current when 
 it arrives at the height at which it 
 begins to be condensed. This cloud 
 may eventually extend over a con- 
 siderable portion of the heavens, 
 but at first it is a small cloud in a 
 clear sky, as represented in Fig. 12, 
 and is white because of the great 
 amount of reflected light. It has 
 no doubt the funnel shape beneath, 
 but being high up, and the observer being generally near- 
 ly under it, this feature is hardly ever observed.. If the 
 
 Fig. 12. 
 
WHERE TORNADOES ARE MOST LIKELY TO OCCUR. 437 
 
 air be not too dry, it may be followed by a shower of 
 rain. 
 
 Peltier says : 
 
 " White squalls are very rare, but they are sometimes met with be- 
 tween the tropics, especially near elevated lands. They are generally 
 violent and of short duration. They often take place when the sky is 
 clear, and without any atmospheric circumstances giving notice of their 
 approach. The only thing which indicates their proximity is the boiling 
 of the sea, which is very much agitated by the violence of the winds. 
 Many of these squalls, which commence by a little cloud, or even with- 
 out any visible cloud, are soon accompanied by violent rains and thick 
 clouds." 
 
 On the west coast of Africa these little tornadoes or whirl- 
 winds are called bull's-eye squalls. According to Piddington, 
 the Portuguese describe such a squall as " first appearing like a 
 bright white spot at or near the zenith, in a perfectly clear sky 
 and fine weather, and which, rapidly descending, brings with it 
 a furious white squall or tornado." 
 
 From the preceding description it is evident that these 
 squalls differ but little in their nature from the small tornadoes 
 and water-spouts met with in higher latitudes, such as the one 
 which nearly wrecked the bark Bel Stuart, except that the at- 
 mosphere is usually too dry for the formation of a water-spout. 
 
 WHERE TORNADOES ARE MOST LIKELY TO OCCUR. 
 
 284. It has been shown that there are two principal condi- 
 tions upon which tornadoes depend, and that in the absence of 
 either of these they cannot take place. The one is the state 
 of unstable equilibrium of the air, and the other a gyratory 
 motion with reference to any assumed centre. It is not neces- 
 sary that the centre shall be stationary, but simply that the 
 motion of the air around it shall be such that, when it is drawn 
 in toward this centre, it shall run into a gyration around it. 
 When we have these two principal conditions, the other, that 
 that there shall be some slight initial disturbance to cause the 
 air to burst up at some point through the strata above, can 
 scarcely ever be wanting. The places and times, then, in which 
 
438 TORNADOES. 
 
 these two principal conditions are found are those in which 
 tornadoes are most likely to occur. Of these two, however,, 
 the unstable equilibrium is the most important, since it more 
 rarely occurs than the other, which is scarcely ever so entirely 
 absent as not to give at least some gyratory motion which be- 
 comes violent very near the centre. 
 
 285. With regard to fixed areas on the earth's surface 
 where the unstable state is most readily induced at all seasons 
 of the year, these are found where, in the general motions of 
 the atmosphere as deflected by continents and mountain 
 ranges, currents of air at the earth's surface which come from 
 a warmer latitude, or at sea from a much warmer continent, are 
 caused to flow under the cold upper strata where the normal 
 motion is nearly eastward, and where consequently the temper- 
 ature is the normal one, not affected by such motion as takes 
 place in the lower strata. One such place is found in the Mis- 
 sissippi Valley, and especially between the Mississippi and the 
 Rocky Mountain range, where the air currents of the lower 
 strata are from lower latitudes, comprising the Gulf of Mexico^ 
 curving around first northward and then more eastwardly under 
 the higher upper strata which pass over the top of the range 
 of the Rocky Mountains, and directly or nearly eastward with- 
 out having their temperatures changed from the normal tem- 
 perature of the latitude by such deflections.. And this is espe- 
 cially the case in the summer season, when the interior of the 
 continent is warmed up and the air of the lower strata is 
 drawn from lower latitudes far up into the higher latitudes on 
 the eastern side of the Rocky Mountains, and the isothermal 
 curve there is deflected very far toward the north. From this 
 cause the temperature of the lower strata of this region be- 
 comes unusually great relatively to that of the strata above ; 
 and if the complete unstable state is not induced from this 
 alone, it is readily brought about by the addition of any small 
 effect from some other cause, as from extremely warm weather 
 in which the earth's surface and the lower air strata become 
 abnormally heated. The great moisture of the air in these 
 southerly winds is also favorable to the induction of the un- 
 
WHERE TORNADOES ARE MOST LIKELY TO OCCUR. 439 
 
 stable state, since this state is more readily brought about in air 
 nearly or quite saturated. 
 
 286. The other condition of tornadoes, that of a relative 
 gyratory motion with regard to any point, is also found to an 
 unusual extent in this region, especially in the winter season. 
 For the southerly current curving around toward the east 
 causes a pressure toward the right, giving rise to the perma- 
 nent barometric gradient of increasing pressure toward the 
 central part of the permanent area of high pressure in the 
 Atlantic Ocean east of Florida ; and on account of this there is 
 a counter-current between this and the Rocky Mountains, flow- 
 ing down toward Texas, just as in the Atlantic Ocean the 
 Greenland current flows down to Florida between the Gulf 
 Stream and the coast of the United States. There is evidence 
 of such a current in this region in the averages of all seasons 
 since the resultant of these has a large southerly component, 
 and especially is this seen in the isotherms of the Mississippi 
 Valley extending in a somewhat northeasterly and southwest- 
 erly direction, so that the mean temperature of New Mexico 
 and the northern part of Texas is the same as that of places 
 east of the Mississippi from five to ten degrees farther north. 
 In the summer season this flow of cold air down toward the 
 Gulf is confined to a comparatively narrow belt close to the 
 mountain range; for then the warm currents from the Gulf are 
 drawn farther up toward the northwest. At this season the 
 northern part of Texas has the same mean temperature as 
 Minnesota, and the isotherms are nearly north and south in di- 
 rection, and the contrast between the temperature of the warm 
 southerly winds on the one side, and the colder northerly ones 
 on the other side, is similar to that of the cold wall between 
 the Gulf Stream and Greenland current in the Atlantic Ocean. 
 This tendency of the air, therefore, to flow in contrary direc- 
 tions gives the second condition of a tornado to a greater de- 
 g^ee in this region than in almost any other. Both of the two 
 principal conditions of tornadoes, therefore, are found in a pre- 
 eminent degree in the Mississippi Valley, and especially be- 
 tween the Mississippi and the Rocky Mountains. Hence there 
 
440 TORNADOES. 
 
 is perhaps no part of the world where they prevail more than 
 in this region, and especially in that part of it in the middle 
 latitudes west of the Mississippi River embracing Kansas and 
 Missouri. 
 
 Near the Rocky Mountain range, and some distance to the 
 east of it, the conditions are not so favorable, both on account 
 of the dryness and the lower temperature of the air. Hence 
 in this region large destructive tornadoes do not prevail much, 
 though small tornadoes with water-spouts are of frequent occur- 
 rence in the lower strata of the 4 atmosphere. 
 
 287. Another place on the globe where the normal condi- 
 tion of the atmosphere approximates to the unstable state is 
 on the west coast of Africa and extending a considerable dis- 
 tance westward over the ocean. Here the warm trade-winds 
 from the northern part of Africa run under the comparatively 
 very cold air of the upper strata, moving eastward over the 
 Atlantic, and thus causes a very rapid decrease of temperature 
 with increase of altitude, very nearly, if not quite equal to that 
 which produces the unstable state in unsaturated air. But the 
 excessive dryness of the air here, coming from the coast of 
 Africa, is a condition which is not favorable to the formation of 
 large tornadoes accompanied by water-spouts, but very small 
 tornadoes or whirlwinds without spouts, usually called white 
 squalls, are very frequently seen in this region and are here 
 called bull's-eye squalls. 
 
 288. For well-known reasons, the unstable state occurs 
 mostly in the cloud region, and hence the tornadic gyrations 
 usually commence there first, and are afterwards propagated 
 downward to the earth's surface. The unstable state, however, 
 is often produced in the lower, unsaturated strata of the atmos- 
 phere, even when very dry; and then if the other condition 
 of a tornado is present, small tornadoes at least may be 
 formed, even where this unstable state does not extend to the 
 upper strata, and thus tornadoes occur not only in cyclones, 
 but elsewhere and in clear weather. In such cases, however, 
 the effects do not reach very high into the atmosphere. 
 
 The unstable state in unsaturated air occurs mostly on very 
 
WHERE TORNADOES ARE MOST LIKELY TO OCCUR. 44* 
 
 dry and sandy soils, with little heat conductivity, when the 
 weather is very warm and the heat rays of the sun are un- 
 obstructed by any clouds above. The heat thus accumulates 
 in the surface strata of the soil and the lower strata of the 
 atmosphere, and thus is brought about the unstable state, at 
 least up to a low altitude, even in clear and dry weather. 
 
 The same is often found, also, in very calm weather over 
 the surface of seas and lakes. The surface of the water be- 
 comes heated, and also the lower strata of the atmosphere, by 
 heat rays passing directly down and by those reflected back 
 until the unstable is brought about. 
 
 289. The season of the year in which tornadoes mostly 
 occur is that in which the atmosphere in its normal state for 
 the season approaches most nearly the unstable state. This 
 seems to be in all parts of the world in the summer season, and 
 in the United States at least in the early part of summer, May 
 or June. Hence, although tornadoes occur at all seasons and 
 in every month of the year, yet, according to Finley's re- 
 searches, 73 " summer is the season of greatest frequency," and 
 " June is the month in which they occur most frequently." 
 The relative frequency of their occurrence in the United 
 States during the winter, spring, summer, and fall seasons was 
 found to be respectively as the numbers 35, 215, 240, and 86. 
 These numbers indicate a great difference between summer 
 and winter in the frequency of their occurrence, and also, since 
 the numbers for spring and summer do not differ much, that 
 the maximum occurs very early in the summer. 
 
 290. For the very same reason that tornadoes occur mostly 
 during the warmest season of the year and very rarely in the 
 winter season, they should occur during the warmest part of 
 the day and seldom at night. For during the day the surface 
 of the earth and the lower strata become very much warmed 
 up, and at night the reverse takes place from nocturnal cooling, 
 while the temperature at a moderate elevation is subject to 
 only a small diurnal variation. Hence, when the general state 
 of the atmosphere, aside from its diurnal variation, is very 
 mearly that of the unstable state, this state is frequently induced 
 
442 TORNADOES. 
 
 during the warmest part of the day by this diurnal and other, 
 abnormal variations, but very rarely at night. Accordingly 
 Finley found that " tornadoes are most frequent in the after- 
 noon between noon and 6 o'clock," and that " the hour during 
 which the greatest number of tornadoes occurred was from 
 5 to 6 P.M.," and that " the next hour was from 4 to 5 P.M." 
 
 The same is true with regard to small tornadoes and water- 
 spouts, as well as those which occur in cyclones. M. Defranc 77 
 remarks that he "never saw a water-spout before 10 o'clock in, 
 the morning nor after 5 o'clock in the evening," that " they 
 never appear during the night nor during the winter, and that 
 there are always two circumstances attending them : the first 
 is the presence of the sun during or a little before the phe- 
 nomenon ; the second is the absence of the wind, or only a 
 very feeble one, except in the space occupied by the water- 
 spout." 
 
 This refers mostly to small water-spouts on seas and lakes,, 
 depending upon the conditions referred to in a preceding 
 paragraph. 
 
 291. Tornadoes occur mostly in the summer season and 
 during the warmest part of the day, not only because the 
 vertical gradient of decreasing temperature is greatest at these 
 times, but also because a smaller gradient is required to induce 
 the unstable state then than during the coldest season of the 
 year and the coldest part of the day. By referring to Table 
 III, Appendix, it is seen that with a hot surface temperature 
 of the air during the warmest part of the day in the summer 
 season, say 35, the unstable state for saturated air is induced 
 with a vertical gradient of decreasing temperature of 0.35 for 
 each 100 meters, while, if the temperature were that of freez- 
 ing, the gradient would have to be 0.63 for each 100 meters, 
 and Jience nearly twice as great as in the former case. So 
 great a gradient as the latter is rarely if ever found in winter, 
 even during the warmest part of the day. 
 
 In the case of small fair-weather tornadoes and water- 
 spouts, such as are observed on seas and lakes, unless the 
 atmosphere is very near the point of saturation, the vertical 
 
SAND-SPOUTS AND DUST WHIRLWINDS. 445 
 
 temperature gradient required is very nearly that of dry air,, 
 which is never found in the winter season, and only during the 
 hottest part of the day in summer. Hence these are never 
 observed at night even in the summer season. 
 
 292. Where the unstable state has been very nearly induced 
 from some other cause, as a very hot surface temperature 
 during a warm, clear day, it may often be consummated by the 
 burning of dry brush on the earth's surface, or of a cane-brake,, 
 or by a large fire of any sort, and thus great whirlwinds, and 
 even showers of rain accompanied with thunder, may be pro- 
 duced. The vertical columns often visible in such cases are 
 composed of dark smoke brought in from all sides, and carried 
 up in the centre. These assume all the usual forms of water- 
 spouts, and of course often contain also condensed vapor in the 
 form of a water-spout, concealed by the smoke, else rain would 
 not be produced. 
 
 Mr. Olmsted " has given an interesting account of such 
 phenomena arising from the burning of a cane-brake on the 
 shores of the Black Warrior, in Alabama. Columns of smoke 
 of various forms were witnessed, which assumed the usual 
 forms of water-spouts, some extending up to only a moderate 
 height with a funnel shape at the top, while others were very 
 slender columns extending up 300 yards into the clouds of 
 smoke, and all were accompanied with a whirling motion of 
 the air and the smoke. Both Redfield 88 and Espy 34 have given 
 a number of statements made by eye witnesses of the effects 
 of great fires in producing whirlwinds, rain, and thunder, from 
 which it appears evident that they are at times followed by a 
 considerable amount of rain. And it was proposed by the 
 latter to try the experiment of producing artificial rains in time 
 of drought by burning great quantities of brush-wood, or by 
 means of prairie fires in the West when the grass is dry. 
 
 SAND-SPOUTS AND DUST WHIRLWINDS. 
 
 293. In very hot, dry climates, where there is a sandy soil,, 
 sand-spouts and dust whirlwinds are of frequent occurrence^ 
 
444 TORNADOES. 
 
 The dry air of such climates, especially over a sandy soil, is 
 often in a state of unstable equilibrium from the accumulation 
 of heat on the earth's surface, for a sandy, dry soil conducts it 
 very slowly down into the earth, and there are then generally 
 all the conditions of a whirlwind and a water-spout, except 
 the vapor in the air to condense, for the condition of an initial 
 whirl of the air can scarcely ever be wanting where there is not 
 a perfect calm. The gyrations of the air and the ascending 
 currents are the same as in a water-spout, but instead of 
 aqueous vapor, sand or dust collected and drawn in from the 
 vicinity is carried up. The inflowing and spiral currents from 
 all sides towards the vortex, up to a considerable height often, 
 keep it near the centre in the form of a column or pillar of 
 sand, if the whirlwind is well developed over a small area 
 only, with very rapid gyrations and a strong ascending current. 
 The height of the column depends upon the strength of the 
 ascending currents and the altitude at which they are turned 
 outward from the vortex ; for, as in cyclones and water-spouts, 
 where there is a flowing of the air in from all sides below, it 
 must flow out again above a certain altitude, depending upon 
 the different circumstances under which the whirlwind takes 
 place. Sand-spouts are frequently observed in Arabia, Persia, 
 and India, and also in Arizona and other places in the western 
 part of the United States, where the climate is very dry. In 
 the hot, dry climate of Australia, situated in the dry zone of 
 the southern hemisphere, these pillars of sand are said to be 
 often more than a half-mile in height. 
 
 Humboldt, in his " Aspects of Nature," refers to the sand- 
 spouts during the dry season on the Orinoco, South America, 
 and says that " like conical-shaped clouds, the points of which 
 descend to the earth, the sand rises through the rarefied air on 
 the electrically charged centre of the whirling current, resem- 
 bling the loud water-spout, dreaded by the experienced mar- 
 iner" ( 119). He seems to think, however, that electricity 
 has something to do with the phenomena. 
 
 Where the whirls take place over a considerable area, and 
 do not become concentrated into rapid gyrations near the 
 
SAND-SPOUTS AND DUST WHIRLWINDS. 44$ 
 
 centre, and the ascending currents do not extend up very high, 
 they give rise to dust whirlwinds, which often overtake caravans 
 and travellers in the deserts ; and if they produce no fatal 
 effects, they are at least very unpleasant and annoying. These 
 are very frequent in India and the Sahara, or Great Desert of 
 northern Africa, and in fact in all places in the warmer lati- 
 tudes where there is a dry, sandy soil. 
 
 When the air is nearly calm, the sand and a thin stratum of 
 atmosphere in contact with it become heated very much above 
 the ordinary temperature of the air a little above the surface. 
 The inflowing currents of the whirlwind from all sides collect 
 this warm surface stratum into the central part of the whirl- 
 wind and cause the whole interior to be of an extraordinarily 
 high temperature. The much-dreaded simoom, stripped of all 
 exaggerations, is most probably simply one of these dust whirl- 
 winds. 
 
 294. Sand-spouts, as well as water-spouts, have been. ob- 
 served to be hollow. Of a whirlwind observed at Schell City, 
 Mo., in the summer of 1879, ^ was sa ^ :H> 
 
 " There were no suface winds strong enough to bear dust along the 
 surface of the ground, but the dust carried up in the vortex was collected 
 only at the vortex of the whirl. The dust column was about two hun- 
 dred feet high, and perhaps about thirty or forty feet in diameter at the 
 top. The direction of rotation was the same as of storms in the northern 
 hemisphere. Leaving the road, the whirl passed out on the prairie, im- 
 mediately filling the air with hay, which was carried up in somewhat 
 wider spirals, the diameter of the cone thus filled with hay being about 
 one hundred and fifty feet at the top. It was then observed also that 
 the column was hollow. Standing nearly under it, the bottom of the 
 dust column appeared like an annulus of dust surrounding a circular 
 area of perfectly clear air. The area grew larger as the dust was raised 
 higher, being about fifteen or twenty feet wide when last observed." 
 
 The sand-spout and the dust whirlwind, where well devel- 
 oped and concentrated, are free from sand or dust in the centre, 
 for the same reason that the water-spout is free from cloud or 
 condensed vapor. The centrifugal force of the gyrations keeps 
 it off at a distance where this force is just equal to that of the 
 indrawing currents which tend to drive it in toward the vortex- 
 
446 TORNADOES. 
 
 BLASTS OF WIND AND OSCILLATIONS OF THE WIND-VANE. 
 
 295. The wind is often observed to blow in blasts, with an 
 oscillating vane and unsteady barometer. This arises from 
 the air running into numerous whirls, or gyrations, while it at 
 the same time has a progressive motion. As in a cyclone, 
 while passing over any place, the wind is first from one direc- 
 tion and then, in the course of a day or two, gradually veers 
 around to another, often to one in nearly a contrary direction, 
 so, in the passages of small whirlwinds, the vane in like manner 
 oscillates from one direction to another in a few minutes, the 
 manner and range of oscillation, as in the case of a cyclone, 
 depending upon which side of the vane the centre of the whirl 
 passes, and the distance from it. If the centre of the whirl 
 passes over the vane, then there is a very sudden oscillation of 
 the vane through a range of 180, or nearly, especially where 
 the diameter of the whirling air column is small. 
 
 As in a cyclone the velocity of the wind is the greatest on 
 the side called the dangerous side, on which the direction of 
 cyclonic motion coincides with that of the general progressive 
 motion, and is comparatively small, or may entirely vanish, on 
 the opposite side, so in one of these small whirls of air the 
 velocity on the one side is very much increased above the 
 average, which is that of the general progressive motion, while 
 on the other it is much diminished, and there may be almost a 
 calm. Wherever the air is in the unstable state these little 
 whirls are very numerous, and consequently, in their passage 
 over any place, they cause the wind to blow in blasts, and a 
 very frequent oscillation of the vane from side to side occurs, 
 sometimes from right to left, and at other times in the contrary 
 way. 
 
 These little whirls in the atmosphere are especially liable to 
 occur in connection with cyclones extending over a consider- 
 able area ; for in these, especially up in the cloud region, the 
 air is in the unstable state, and, on account of the gyrations of 
 the cyclone and the general agitation of the air, the sum of the 
 
OSCILLATIONS OF THE WIND-VANE. 447 
 
 moments of gyration, with regard to any point where there is a 
 rushing up of the air of the lower strata through those above, 
 can scarcely ever be o, and hence there are both of the two 
 principal conditions of such little whirlwinds. These may form 
 small secondary cyclones contained within the larger, or tor- 
 nadoes and water-spouts, or simply local whirlings in the 
 atmosphere of small extent and no great violence, but suffi- 
 cient to cause intermittences in the steadiness of the velocity 
 of the wind and oscillations in its general direction. Hence 
 there is generally great unsteadiness in the velocity and direc- 
 tion of the wind in a cyclone, and the greatest injuries usually 
 arise from the violence of the wind on the side of these sub- 
 sidiary whirls where the direction of motion coincides with that 
 of the gyratory motion of the cyclone. 
 
 These blasts and oscillations of the vane are generally ob- 
 served on the clearing-up side of a storm. As the central area 
 of a cyclone is warmer than the surrounding parts, and the 
 upper colder strata in middle and higher latitudes move east- 
 ward faster than the lower strata, the effect is to cause a more 
 rapid decrease of temperature with increase of altitude, and 
 hence to induce the unstable state which gives rise to these 
 whirls. As the air is comparatively dry on this side of the 
 storm, the small amount of vapor remaining is usually carried 
 up in the central part of the whirl to a considerable altitude 
 fcefore condensation takes place, and then it forms a patch of 
 -whitish fracto-cumulus cloud of greater or less extent, or even 
 .sometimes to a large dark cloud if the extent and duration of 
 the whirlwind are sufficiently great. As the condensed vapor 
 is carried up in the shape of a cumulus cloud to a considerable 
 height above its base, and the progressive velocity of the upper 
 strata is greater than that of the lower, the tops are blown 
 forward in the general direction of the currents, so that they 
 often appear of an oblong shape and indicate the general 
 direction of the currents at that altitude. Such clouds usually 
 appear for a while and gradually vanish by the re-evaporation 
 of the condensed vapor forming them. 
 
448 TORNADOES. 
 
 " PUMPING " OF THE BAROMETER. 
 
 296. In connection with frequent changes of the velocity, 
 and consequently force, of the wind, there is an unsteadiness of 
 barometrical column called " pumping," where the barometer 
 is placed on one side or the other of a barrier to the progress 
 of the air. This effect is given in millimeters of the barome- 
 ter by the formula of 235. According to this, where the 
 barometer is placed against a wall or post where the wind 
 blows normally against its surface with a velocity of 10 meters 
 per second, the height of the barometer is increased 0.5 
 mm. If the velocity is increased to 20 m. per second, it becomes 
 2.0 mm., and hence a change of 1.5 mm. with a change of 
 velocity from 10 m. to 20 m. per second. With a change, 
 however, from 20 m. to 30 m. per second the change in baro- 
 metric pressure would be 2.5 mm. Hence the same change of 
 velocity where the velocity is already great gives a much 
 greater effect upon the barometer than the same change in 
 velocity where the velocity as yet is small. Hence in cyclones 
 where the general velocity is great, small changes in velocity 
 produce a considerable effect on the barometer ; and it is in 
 cyclones, therefore, where this effect is mostly observed. 
 Much depends upon the position of the barometer. If placed 
 in the open air, little or no effect is observed, since there is 
 little obstruction to the wind. If placed where wind blows 
 obliquely against the face of the barrier, the value of AP in 
 the formula must be multiplied by cos 2 /', i being the angle 
 of incidence of the wind, and hence the effect is diminished 
 proportionally. On the lee side of a barrier there is a slight 
 depression of the barometer with the increase of velocity in 
 the blasts arising from the dragging away of the air on that 
 side through friction. A barometer placed in a tight room, of 
 course, cannot be much affected, and perhaps not sensibly in 
 any room with doors and windows closed, especially when the 
 blasts are sudden and of so short duration that there is not 
 time for the increase of pressure to be felt inside. 
 
"PUMPING" OF THE BAROMETER. 449 
 
 In the hurricanes of the Antilles, observation shows that 
 these small oscillations of the barometer are closely connected 
 with and dependent upon the blasts of the wind, and that 
 oscillations of the vane always accompany the blasts, showing 
 that the latter are due to small gyrations of the air. Padre 
 Vifles says : 
 
 " Under the influence of the blasts, the barometric column is so agi- 
 tated and so irregular that it renders the reading of it very difficult, 
 since it is scarcely possible to take an exact medium. The amplitude 
 of the oscillations is usually from four to eight tenths of a millimeter, 
 and sometimes more. The agitation is fitful and violent, just as the 
 impulses which the anemometer receives and the oscillations made by 
 the vane." 
 
CHAPTER VIII. 
 
 THUNDER-STORMS. 
 
 297. THE greater part of violent tornadoes are accompanied 
 by thunder, and so are properly called thunder-storms. Ac- 
 cording to Finley, " of 473 cases in which the atmospheric con- 
 (iitions preceding tornadoes were observed, 410 were reported 
 as violent thunder-storms." But usually in thunder-storms 
 there is little of either cyclonic or tornadic violence, and the 
 wind accompanying them, when strong, is more of the character 
 of a sudden and violent squall, though it often amounts to 
 nothing more than a gentle wind blowing out beneath the 
 thunder-cloud. 
 
 Much attention has been given of late years to the study of 
 thunder-storms, both in the principal countries of Europe, and 
 by the Signal Service and the New England Meteorological 
 Society of our country. The principal results obtained in 
 these studies, from very numerous observations by M. Fron in 
 France, Ferrari in Italy, Von Bezold in Bavaria, Assmann in 
 Germany, Mantel in Switzerland, Klossovsky in Russia, Elliot 
 in India, and Mohn in Norway, have been given briefly by 
 Professor W. M. Davis. 80 He has also given a report on the 
 thunder-storms in New England in the summer of 1885." To 
 these contributions on the subject the writer is indebted mainly 
 for the facts in what follows on this subject. 
 
 OBSERVED PHENOMENA. 
 
 298. Thunder-storms often appear to be small and imper- 
 fectly developed cyclones in which there is little or no sensible 
 gyratory motion or barometric depression. Klossovsky regards 
 them as small cyclones originating in certain segments near the 
 
 450 
 
OBSERVED PHENOMENA. 45 1 
 
 periphery of larger cyclones. According to Abercromby, 
 thunder-storms are always connected with secondary cyclones. 
 He says : 50 
 
 "As surely as we see a secondary on the charts in summer, so cer- 
 tainly will thunder-storms occur during the day, though we cannot say 
 in what portion of the small depression." 
 
 Again : 
 
 " As the secondary approaches any station, the wind draws more or 
 less in toward the centre, and recovers its former direction after the de- 
 pression has passed." 
 
 In central Germany also 
 
 " The wind in thunder-storms veers and backs with equal frequency ; 
 and not unfrequently reverses its course directly." 80 
 
 In one of the local thunder-storms of July 29, 1885, in New 
 England, there were indications of 
 
 " a tolerably distinct cyclonic motion of the winds within and around the 
 oval rain-area, implying that the thunder-storm area possessed a gentle, 
 spiral, rotary circulation on a small scale, as has been determined for 
 .storms of this kind in Europe." 81 
 
 In Italy it is said : 80 
 
 "The storms occur on the after-side of a small, faint area of low pres- 
 .sure ; and that the pressure rises as the maximum phase of the storm 
 approaches. . . . Sometimes the storms form at the end of a V-shaped 
 " sack' or enlargement on the side of a large area of low pressure." 
 
 And in Bavaria : 
 
 "On maps having the pressure shown from five to five milli- 
 meters, the areas of low pressure are but faintly indicated by curves in 
 the isobars ; with more detailed study, they appear in greater distinct- 
 ness and are generally seen to be extensions of larger low-pressure areas, 
 with gradients so faint that they cause no noticeable winds." 
 
 But the slight barometic depressions and cyclonic motions 
 over a considerable area are often, perhaps generally, not ob- 
 served, but a sudden change of temperature and pressure and 
 a corresponding sudden wind-squall generally from some north- 
 westerly direction. The sudden change of temperature is 
 usually 10 to 20 or 25 F., and the corresponding changes of 
 barometric pressure rarely amount to as much as O.I of an inch 
 
452 THUNDER-S TO RMS. 
 
 (2.5 mm.), and these changes take place mostly in about ten- 
 minutes. In India the change of temperature is said to be 
 only 10 to 12 F., while the change of pressure is from 0.8 to 
 0.15 of an inch, the greater part of which always occurs very 
 suddenly. The corresponding sudden increase of the wind 
 here often amounts to from 40 to 60 miles an hour. 
 In Italy, according to Ferrari, 90 
 
 "Before the thunder-storm, the pressure and the relative humidity fall 
 and the temperature rises in such a manner that the first two reach a 
 minimum and the last a maximum at the moment of commencement of 
 the thunder-storm; then the pressure and the relative humidity rise 
 rapidly and the temperature falls, and both of the first often reach a 
 maximum and the last a minimum by the end of the storm. The change 
 of temperature is exactly the reverse of that of the relative humidity and 
 of the pressure. The velocity of the wind, before the thunder-storm 
 small or very nearly nothing, increases rapidly with the commencement 
 of the storm, reaches its maximum at the end or shortly after, and then 
 rapidly falls again." 
 
 It should be observed here that the changes of temperature, 
 and the corresponding reverse changes of relative humidity, 
 necessarily take place from the changes of capacity of the air 
 for moisture with changes of temperature, and do not indicate 
 any corresponding changes in the absolute amount of moisture 
 in the air before and after the thunder-storm sets in. Although 
 the relative humidity is greater, yet it is most probable that 
 the absolute amount of vapor is less after than before the storm. 
 
 299. On the evening of June 7, 1885, barographic curves 
 were obtained at Ann Arbor (Michigan) of two thunder-storms 
 which passed over. These are described in the same words 
 which had been used to describe similar changes during thun- 
 der-storms observed at Berlin: 
 
 "Before the outburst of the thunder-storm, the curves sank slowly, 
 next rose steeply to a considerable height ; . . . the curve then main- 
 tained itself at a level for some time, throughout which the thunder- 
 shower or hail was wont to fall ; on the cessation of rain, the atmos- 
 pheric pressure sank steeply. . . ." 
 
 It is also stated in the same connection : 
 
 " Eye observations of the barometric height were also taken during the 
 first storm at Ann Arbor, and immediately after the beginning of the 
 
OBSERVED PHENOMENA. 453 
 
 rainfall the barometer was observed to rise 0.07 of an inch in about ten 
 minutes, then remained nearly stationary for about 20 minutes, when it 
 began to sink. Preceding this thunder-storm (which came up from the 
 west), the wind had been blowing pretty steadily from the west for an 
 hour or two at the rate of 12 miles per hour; but as the thunder-storm 
 approached, it fell to a velocity of about 5 miles and. coincident with the 
 rise of pressure, increased to a velocity of 24 miles per hour, which it 
 maintained for about 15 minutes, then in less than an hour decreased to 
 a velocity of about 3 miles, having shifted in direction from the west to 
 the east, but soon rose again to a velocity of 6 miles. The phenomena 
 connected with the second storm were very similar, except that the wind 
 fell from its highest velocity of about 30 miles to an almost calm within 
 ten minutes; but soon rose again to a velocity of nine miles from the S. 
 E., which continued for several hours. These changes of wind velocity 
 are in accordance with the supposition that there was an indraught of air 
 toward the cloud in front and rear of the storms, but that immediately 
 under the storm there was an outward movement in every direction, the 
 different effects at the earth's surface in front and rear of the storm being 
 due to the movement of the thunder-storm along the earth's surface." 8a 
 
 300. According to observation, thunder-storms often ap- 
 pear in groups, all progressing eastwardly, in parallel directions, 
 some abreast, and others following after. Hence there is often 
 a succession of such storms at the same place within a short 
 period of time, as, the same afternoon. Thus on July 29, 1885, 
 five separate storms were traced in the southern part of New 
 Hampshire and the eastern part of Massachusetts. Of the 
 last and most extensive of these it is said : 
 
 " It does not seem to have been a well-united storm, but consisted of 
 numerous loosely connected parts, from which showers of varying 
 strength fell." 81 
 
 On July 3 there was a group of thunder-storms in central 
 and southern Massachusetts and central and south New Hamp- 
 shire, of which no less than ten could be traced from the obser- 
 vations. There may have been a hundred different centres of 
 action around which rain and thunder occurred over progres- 
 sive areas, of greater or less extent and of various times of du- 
 ration, from which no reports were received. In such a thun- 
 der-storm area there may be such a blending of the different 
 storms that there are few places where rain does not fall and 
 
454 THUNDER-STORMS. 
 
 thunder is not heard, and so, from reports received from a lim- 
 ited number of stations, it may seem to be one homogeneous 
 storm area. But even the reports often indicate that this is 
 not the case, as is seen above in the extract from the report of 
 the storm of July 29, but that it consists of numerous loosely 
 connected parts. In all such cases the relation of each distinct 
 storm area to the general storm area is the same as that of 
 heavy showers to the general rain area on a larger scale, 209, 
 where the atmosphere over a large area is in the unstable state, 
 but in which the conditions have not been such as to give rise 
 to a cyclone. It is simply one of the numerous places where as- 
 cending currents are for some reason started more than at 
 other places, which give rise to rain and generally thunder, but 
 in which the condition is generally absent which gives rise to 
 rotary circulation. 
 
 The general form of the rain area at any given time in a 
 compact group of simultaneous storms, and even where it may 
 be regarded as one solid storm, is no doubt very different in 
 different cases, and in the same storm different at different 
 times. In the case of the storm in New England, July 21, 
 1885, the average form seems to have been that of the annexed 
 figure, as obtained from a composite portrait of the forms at 
 
 E 
 
 Fig. I. 
 
 different times. 81 This also seems to be the form, according 
 to Dr. Hinrichs, of the front convex part of the storms and 
 squalls of Iowa. \ 
 
OBSERVED PHENOMENA. 455 
 
 " In northeastern Iowa the storm-front has a tendency to bend up, so 
 as to make the squall below more nearly from the west. In a like man- 
 ner in southwestern Iowa its front bends westward and hence blows more 
 nearly from the north." 
 
 The convex front part of such storms generally seems to be 
 well determined where the rain area assumes a somewhat regu- 
 lar form of any kind ; but even this is often represented to be 
 quite irregular and ill-defined. 
 
 According to Ferrari, 90 as observed in Italy, 
 
 " Thunder-storm days generally exhibit two different types of storms : 
 in the one the thunder-storm activity is divided, and in the other one a 
 large thunder-storm is formed, usually accompanied by others of smaller 
 extent. In the first case small thunder-showers are formed here and 
 there which follow after and encroach upon one another; such appear 
 almost exclusively during the midday and afternoon hours, especially 
 between i and 4 P.M. In the second case a single thunder-storm ex- 
 tends over a large area in a certain interval of time, while the smaller 
 thunder-storms which appear on these days preserve their usual charac- 
 ter almost exclusively and prefer the afternoon hours. It is sure to hap- 
 pen that the more extended storm on such a day is composed of more 
 than one ; but at all events, even in this case, a thunder-storm takes place 
 wfyich we, on account of its character, call the ' principal storm.' Such 
 a principal storm is often the last to occur, and that which properly ends 
 the thunder-storm activity of the period ; in other cases it is, on the other 
 hand, followed by smaller thunder-storms." 
 
 301. The antecedent and following observed phenomena 
 are usually somewhat as follows, as deduced from a graphic 
 average by means of a composite portrait in the case of the 
 storm of July 9, 1885, in New England : 
 
 " An hour and a half or an hour before the storm, clouds are seen ris- 
 ing on the western horizon, while the winds are lightly southerly, and 
 the temperature high (85 95). Nearer the storm-front, the clouds are 
 seen to rise higher, and the temperature falls slightly, but the wind does 
 not change significantly. The first thunder is heard from thirty to sixty 
 minutes, and the clouds are recorded as reaching the zenith or passing 
 overhead from ten to thirty minutes before the rain. The sudden 
 change from gentle southerly wind to the northwest squall seldom comes 
 more than fifteen minutes before the rain, and is generally only five to 
 .seven minutes before it; with this change the temperature falls rapidly. 
 The squall seldom continues after the rain begins. The heaviest rain is 
 
456 THUNDER-STORMS. 
 
 marked close to the rain-beginning in many cases ; in others it falls from 
 seven to twenty-five minutes later. The loudest thunder runs from ten 
 to thirty minutes after the rain-front, and the lightning-strokes, as far as 
 reported, fall with one exception between thirteen and twenty-seven min- 
 utes after the rain-front. Already at twenty to twenty-five minutes after 
 the rain had begun, the western horizon is seen lighting up, and soon the 
 clouds begin to break away ; the rear edge is overhead in an hour to an 
 hour and a half, while the rain had ceased fifteen minutes sooner on the 
 average, its shortest duration being thirty and its longest ninety minutes. 
 During the rain the temperature stood fifteen to twenty-five degrees 
 lower than before the storm, and the winds were light and variable ; as 
 the storm passed over in the afternoon, an absolute rise of temperature 
 after its passage is seldom seen, and then is faint ; but a relative rise is 
 clearly found in the maintenance of an almost uniform temperature past 
 those hours when it ordinarily decreases most rapidly. Rainbows 
 make their appearance between an hour and an hour and a half after 
 the rain-beginning, and the last thunder is heard from one to two hours 
 after the storm began." 81 
 
 302. Although the rain-area, as represented in Fig. I, may 
 have considerable width, yet the energy and violence of the 
 storm is mostly around on the front and convex edge ; in fact 
 it 'seems from accounts that the whole storm often assumes the 
 form of a long extended and narrow band lying somewhat 
 transverse to the direction of general progressive motion, but 
 mostly, at least in New England, considerably inclined, as the 
 southeasterly side of Fig. I. In Italy, according to Ferrari, 90 
 from the few cases in which he could observe the beginning, 
 
 " the origin of a thunder-storm was a point. From this it spread out, 
 not on all sides, but only in one direction, as is represented in Fig. 5 [here 
 the following figure (2)]. I believe that this may generally be the way 
 in which the thunder-storm arises. At first, also, the form of the thun- 
 der-storm is that of the sector of a circle, out of which it gradually 
 passes into that of a band of a greater or less length." 
 
 On the 24th of June, 1888, the writer observed the first 
 formation of a thunder-storm almost vertically over Kansas 
 City, Mo. A little before II A.M. a circular dark cloud ap- 
 peared a little to the north and east of his point of observation, 
 while toward the west, and in nearly all directions, there were 
 visible spots of clear sky. The first thunder was heard in this 
 
OBSERVED PHENOMENA. 457 
 
 cloud nearly overhead. It continued to darken and to spread 
 at first in all directions, and soon there was an unusually heavy 
 shower of rain, which continued nearly an hour. Before it 
 ended the cloud seemed to cover the whole heavens evenly in 
 all directions, and the thunder was heard on all sides. The 
 upper clouds before and after the shower had a scarcely percep- 
 tible motion in a direction from W.S.W., and there was very 
 little surface wind. During the rain there was a wind blowing 
 out from the place where the cloud first formed toward the 
 
 W.S.W. The breaking and thinning out of the clouds first 
 took place in the west, and the thunder-cloud, as usual, passed 
 slowly away in an easterly direction. The origin of this 
 thunder-storm was evidently similar to those observed by 
 Ferrari, but whether it continued its progressive motion a long 
 distance and expanded laterally as it went, as represented in 
 Fig. 2, is not known. 
 In Bavaria, 80 
 
 "When lines are drawn so as to include the whole district over which 
 thunder is heard at a given time, the area thus occupied is found to be a 
 long, narrow band, at right angles to the storm's path. Storms are fre- 
 quently observed that stretch from the northern limits of Bavaria to the 
 Alps, about 200 miles, while their breadth (determined by audible thun- 
 der) is at highest 50 miles, generally about 25 miles, and often much 
 less. In such cases the whole length of the storm-band is not meas- 
 ured." 
 
 Of such storms in Iowa it is said : 
 
 " The storm-front is fierce in its power along a considerable distance ; 
 20 to 50 miles and more in its front along the earth are struck simulta- 
 neously. As the great storm -front sweeps on, it generally diminishes in 
 fury, but at times it can be traced for 350 miles from the northwest to 
 the southeast of our State." 
 
458 
 
 THUNDER-STORMS. 
 
 In Switzerland at least there seem to be thunder-storms, 
 which do not have the usual easterly progressive motion, but 
 sometimes the contrary. It is said : 
 
 " The storm occupies at first a small area, and then expands in nearly 
 all directions, its front lines being sharply bent, almost closed, curves." 
 
 But the front lines generally seem to be similar to those 
 represented in the preceding figure, and the great convexity 
 on the one side undoubtedly arises from the tendency to 
 spread faster in this direction than in any other, while in Italy 
 and most other places the directions of spreading are confined 
 within a small range of easterly directions, and there is a dying 
 out of the storm in other directions. 
 
 The accompanying plate is a sketch of a thunder-storm 
 
 THUNDER-STORM OBSERVED OFF THE COAST OF MAINE, JULY, 1883. 
 
 taken by Mr. Morey off the coast of Maine, in July, 1883. 
 The following is his account of it: 
 
 " The point of observation was about two miles out at sea. 
 
 "The storm occurred during a clear sultry afternoon, and moved 
 from a southwesterly to a northeasterly direction, accompanied by a 
 great display of electricity and a large amount of rain. 
 
 "The cumuli on the top of the cloud-bank were of almost snowy 
 
THE THEORY. 459 
 
 whiteness, growing rapidly darker to the almost black strata forming 
 the base. 
 
 " Previous to the disturbance the distant sky was perfectly clear except 
 in the southwest, where a few dun-colored cumuli seemed to rest on the 
 land. The wind was extremely light. These conditions remained after 
 the passage of the storm, with the exception that the cumuli in the south- 
 west had disappeared and the wind blew fresher from the northwest. 
 Duration of storm, 30 minutes." 
 
 THE THEORY. 
 
 303. The fundamental conditions of thunder-storms, as of 
 cyclones and tornadoes, are the state of unstable equilibrium, 
 at least for saturated if not for dry air, and a high relative hu- 
 midity. The less the latter, the more nearly must the state 
 of the air approximate to that of the unstable state of dry 
 air. From these conditions rapidly ascending currents and a 
 vertical circulation arise, just as in the case of cyclones and 
 tornadoes, and a condensation of aqueous vapor and a fall of 
 rain or hail takes place in the ascending current, accompanied 
 generally in summer by electrical phenomena. In what are 
 usually called thunder-storms, the conditions are nearly or 
 quite absent which give rise to a gyratory circulation over a 
 large area, such as takes place in the case of cyclones, and usu- 
 ally the conditions are wanting which give rise to small local 
 and violent tornadic gyrations, though, as we have seen, 297, 
 most tornadoes are thunder-storms. Since secondary cyclones, 
 tornadoes, and thunder-storms are dependent upon great hu- 
 midity and the unstable state of the atmosphere, it is reasona- 
 ble to suppose that they must be found to exist together often 
 in the same region having these conditions, and that there is a 
 running together and a blending of the several forms of the 
 storms without any distinct dividing line. Hence we find that 
 there are thunder-storms with more or less cyclonic motions 
 and local depressions, that they occur in regions where there 
 are secondary cyclones, and that tornadoes are frequently ob- 
 served in connection with thunder-storms. In order to the 
 latter, it is merely necessary that, in addition to the general 
 
460 
 
 THUNDER- S TO RMS. 
 
 conditions, there shall also be the condition, where the unsta- 
 ble air at any point bursts up through the strata above, which 
 gives rise to the violent tornadic gyrations also. 
 
 We have seen that the thunder-storms seem often to arise 
 at some given point and to enlarge and extend mostly in some 
 easterly direction, but when the air is in the unstable state it 
 is liable to burst up and to give rise almost simultaneously to 
 many ascending currents and centres of local thunder-showers, 
 which spread and eventually somewhat blend together so as to 
 form apparently only one thunder-storm, while in reality it is 
 composed of a number of loosely connected parts, as in the 
 -case of the thunder-storms of July 3, referred to in 300. 
 
 Where the ascending current of one of these points of 
 eruption is unusually strong and reaches to great altitudes, 
 though there may not be much violent tornadic action, it gives 
 rise to hail in the interior of the thunder-storm. Hence Ferrari 
 states 90 " that in the region passed over by thunder-storms the 
 hail extended in small strips in the direction of motion." 
 
 304. Let us consider first the case of a simple thunder- 
 
 a, 
 
 c 
 
 Fig. 3. 
 
 fforey.' 
 
 -storm under conditions which are homogeneous on all sides, 
 and in which the air has no progressive motion in any direc- 
 
THE THEORY. 
 
 461 
 
 tion. If the air is in the unstable state, and over a given cir- 
 cular area of diameter ab, Fig. 3, is a little warmer and lighter 
 than that of the surrounding parts, or for any reason receives 
 an upward motion, there is set up, in the manner heretofore 
 explained, a vertical circulation with an ascending current in 
 the interior over and around the centre c, and an incoming cur- 
 rent from all sides in the lower part of the air to supply the 
 ascending current, as indicated by the arrows in the figure ; 
 while above, the current is outward in all directions, and there 
 is a slow descent or settling down of the air on all sides. In 
 the interior ascending current the height of incipient condensa- 
 
 fe. 
 
 Vvw *ivv*>M 
 
 ' ,/ \ v y ' v /MO 
 
 ^x t v ^ ' ^ ~ y w 
 
 Fig. 4. 
 
 tion and of the base of the cloud depends upon the depression of 
 the dew-point of the air, and the aqueous vapor above that 
 height is condensed, falls as rain, and cools the air through 
 which it falls, as already explained, until its temperature is 
 lower than that of the surrounding air. This central cooled 
 air, being now heavier than the surrounding air, both on ac- 
 count of its greater density and the amount of falling rain 
 pressing on it, now gradually settles down and causes an out- 
 ward current in all directions from the centre c, Fig. 4. At c r , 
 Fig. 4, there is a maximum of pressure which decreases on all 
 
462 THUNDER- S TO RMS. 
 
 sides toward c, but at some point between c' and c, but much 
 nearer to c after the ring has expanded considerably, there is a 
 very steep part in both the temperature and pressure gradient, 
 exactly under the vertical between the warmer ascending cur- 
 rent on the one side, and the colder descending current on the 
 other, where most of the change of pressure takes place in 
 about ten minutes generally, and where the squall exists, which 
 encounters the inflowing current from all sides, and both. are 
 gradually retarded and deflected upward, and there is now a 
 ring of ascending air, the middle of which is at the distance of 
 c' from the centre. This ring of ascending air in turn becomes 
 cooled down and changed to a descending current in precisely 
 the same way as the first central ascending current was, and 
 another ring of ascending air with its middle at a greater dis- 
 tance from the centre is developed, and so on ; and this is con- 
 tinued as long as the air is in the unstable state. As the air 
 on the interior side of the ring is gradually cooled down and 
 changed to a descending current and flows under it, more of 
 the air on the other side is thrown up into an ascending cur- 
 rent, and the ring progresses and enlarges somewhat as a wave 
 of water flowing out from a central point. 
 
 In Switzerland, according to observation, 302, the condi- 
 tions of this case are sometimes nearly satisfied, since the 
 storms expand in nearly all directions and their front lines are 
 almost closed lines. In Switzerland, in summer, the velocity 
 of the general easterly progression of the air is small at all 
 altitudes, and on the north side of a cyclone there may be no 
 such motion; so that it may happen that the conditions of this 
 case may be nearly or quite satisfied here in some cases. 
 
 305. In what immediately precedes, the air is supposed to 
 be at rest on the earth's surface and homogeneous, or at least 
 symmetrical, on all sides of the centre, and the area is so small 
 at first that it is not thrown into any sensible gyration around 
 the centre. There is consequently no reason why it should 
 progress as a whole in any one direction rather than another, 
 and whatever changes occur must take place equally and sym- 
 metrically in all directions. But if one side, as the south side, 
 
THE THEORY. 463 
 
 is warmer and moister than the other, then the supply of 
 energy which keeps up the vertical circulation is strongest on 
 that side ; and although the tendency is still to spread in all 
 directions, yet it does so mostly on this side. 
 
 Again, if we suppose the whole system to be stationary, 
 but that there is a current of air in the lower stratum next the 
 earth's surface passing in any direction under it, as a southerly 
 or easterly surface wind, this brings the warm moist surface air 
 in below on the windward side, and carries the comparatively 
 -cool and dry air of the interior out to the other side, and there is, 
 consequently, an unequal distribution of energy on the two sides, 
 and a tendency in the ring to spread, and the whole system to 
 move mostly, if not entirely, in the direction from which the 
 wind and the energy come. We have a similar case if there 
 is a wind in a great conflagration, as in a city, where the burn- 
 ing material is distributed equally and symmetrically in all 
 directions. The fire extends mostly, if not entirely, in the di- 
 rection from which the wind comes, because on that side is the 
 supply of oxygen mostly to sustain the combustion, while on 
 the other side there is air which has passed through the flame 
 and has had its oxygen mostly burnt out. 
 
 We have a case similar to the preceding relatively, where 
 the whole atmosphere has a regular progressive motion, say 
 toward the east, but the part nearest the earth's surface is re- 
 tarded by frictional resistance of that surface. 
 
 The more slowly moving stratum next the earth is rela- 
 tively a wind blowing under the storm from the direction in 
 which the storm, drifting in the strata above, is progressing, 
 and consequently the effect is the same, and the tendency is 
 for the storm not only to spread in that direction relatively to 
 the air in which it exists, but even to subside and die out in 
 the rear, and so to not progress in that direction. The storm 
 then assumes the form of Fig. I. It not only drifts in an east- 
 erly direction with the general motions of the air, but it pro- 
 gresses also relatively to the air, mostly in this direction, and 
 it also spreads a little toward the south on account of the air 
 on that side being warmer and moister, and this is especially 
 
464 THUNDER STORMS. 
 
 the case where there is a southerly wind, as there usually is in 
 thunder-storms ; but it progresses or spreads but little if any 
 toward the north. For this reason we have the unsymmetrical 
 form of the storm with reference to the apex and axis of pro- 
 gression, as represented in Fig. I. The progress is mostly 
 toward the east, but also toward the south, and there is a grad- 
 ual dying out of the storm in the rear and on the north side, 
 leaving a much longer wing or branch extending back on the 
 south than on the north side, which is supported and kept up 
 by the greater energy on that side arising from warmer and 
 moister air, if not also from surface southerly winds, which 
 blow somewhat under the strata above, moving more in an 
 easterly direction. 
 
 306. Whatever the form which the thunder-storm may as- 
 sume, whether that of 304, in which there is an enlargement 
 and a spreading in nearly all directions without 'much progres- 
 sive motion in any direction, or that of 305, in which there is 
 an easterly progressive motion, and the rain and the storm 
 areas are of the form of Fig. I, or even more nearly a mere 
 narrow convex band progressing as a wave and increasing in 
 length as it goes, as represented in Fig. 2, there is a steep but 
 short pressure gradient around the front border of the rain area 
 as it progresses, which often gives rise to a sudden and violent 
 squall where it passes over any place, but usually only to a 
 gentle wind blowing out from under the thunder-cloud. This 
 pressure gradient has been attributed to the difference of tem- 
 perature within a short horizontal distance of the point c' r 
 Fig. 4, between the contiguous portions of air in which rain has 
 not yet commenced to fall and that in which rain is falling. 
 The rain having been produced by the condensation of vapor,, 
 at least in part, up in the high and cold strata, and then carried 
 by the ascending current still higher, much of it is cooled down 
 to a low temperature, and, it may be, even frozen into hail. In 
 falling slowly through the air it cools it to a temperature con- 
 siderably lower than that of the contiguous air through which 
 rain has not yet commenced to fall, and hence the great differ- 
 ence of temperature and of pressure within a short distance. 
 
THE THEORY. 46$ 
 
 The cooling of the air is also increased by the evaporation of 
 the rain in falling through the lower unsaturated air, and also 
 by the melting of the hail in the case of hail-fall. These seem 
 to have been the causes assigned by Dr. Koppen in his explana- 
 tion of the phenomena in the thunder-storm of August 9, 1881, 
 which passed over Germany, so far as the writer can learn in a 
 second-hand way from extracts from, and references to, his 
 paper on that subject, and they are, no doubt, the true causes. 
 
 307. A difference of i C. in the temperature of two con- 
 tiguous portions of the atmosphere extending to the top would 
 give a difference of barometric pressure of 2.8 mm. (o.n of an 
 inch), which may be considered as a somewhat extreme differ- 
 ence, as observed in thunder-storm squalls, though of course it 
 is undoubtedly much more in very destructive squalls, in which 
 observations cannot be made. This, by the formula of 235, 
 gives at the earth's surface, where we have P = P and T, say, 
 equal to T 9 + 30 = 303, s = 25 m. p. s., or about 56 miles 
 per hour, for the velocity of the wind in the squall arising from 
 this difference of pressure in case of no friction. Making con- 
 siderable allowance for this, which is always necessary in such 
 cases, we still have a destructive squall, and one which usually 
 corresponds to a difference of pressure of that order. In the 
 observation of Mr. Clayton, 299, the difference of pressure of 
 0.07 of an inch (1.78 mm.) by the same formula gives s = 19 
 m. p. s., or nearly 43 miles an hour. Making a very liberal al- 
 lowance for friction, we still have the greatest observed velocity 
 of 24 miles an hour, as obtained in his observations. 
 
 We see that a difference of temperature of i C. extending 
 to the top of the atmosphere would give rise to a difference of 
 pressure from which would result a destructive squall. But 
 thunder-storms and differences of temperature in contiguous 
 portions of the atmosphere do not reach to the top, perhaps 
 often not very far up. But say the observed difference at 
 the earth's surface is 6 C., and that it gradually and uniformly 
 diminishes with increase of altitude and vanishes at the alti- 
 tude which leaves one third of the atmosphere below it. The 
 effect upon the difference of pressure upon this suppositioa 
 
466 THUNDER-STORMS. 
 
 would be exactly equal to that of a difference of i C., extend- 
 ing up to the top. But the observed difference of temperature 
 in the air at the earth's surface before and after the shower is 
 often more than 6 C., and so it is reasonable to suppose that 
 the difference so extends up to the strata above as to give the 
 usual observed corresponding difference of pressure. 
 
 308. There is still another cause besides the lowering of 
 the temperature of the air which may very sensibly increase 
 the air pressure in the region of falling rain, and that is the 
 pressure of the rain contained in the air. This, in falling, soon 
 acquires a maximum velocity, after which the air pressure is 
 increased by the full statical pressure of the rain, since the 
 whole force of gravity then upon the rain is exerted by means 
 of friction upon the atmosphere. We cannot have generally 
 much idea of the amount of rain and hail which may be con- 
 tained in the air at any time, but we know from the amount 
 which often falls suddenly in cloud-bursts that it is some- 
 times very great. If there were at any one time rain and hail 
 falling with uniform velocity equivalent to a rainfall of 13.6 
 mm. in depth, it would increase the barometric pressure I mm., 
 and from this alone, by the formula of 235, would arise a 
 squall with a velocity of about 15 m. p. s., or 34 miles per 
 hour, making no allowance for friction. 
 
 As the falling rain, either from its cooling effect upon the 
 air or the direct effect of its own pressure, causes a pressure 
 gradient, and the maximum velocity of the squall is at the foot 
 of the gradient, where the pressure is the least, the squall 
 wind is felt a little before the arrival of the rain, since the mo- 
 mentum which the air has at the foot of the gradient carries it 
 to some distance beyond before it is counteracted and the cur- 
 rent deflected upward. Hence the beginning of the squall and 
 the sudden change of the wind from a southerly to a north- 
 westerly direction occurs in New England generally from five 
 to seven minutes, sometimes considerably more, before the 
 commencement of the rainfall ( 301), and on land in dry and 
 dusty weather it usually raises a great cloud of dust. 
 
 309. In the rear of the storm there is a pressure gradient, 
 
ItELA TION BE TWEEN THUNDER-STORMS AND CYCLONES. 467 
 
 but it is more gradual without any part which is abruptly 
 steep, and there is consequently a flowing out of the air behind 
 the storm, relatively to the storm itself, but no sudden squall 
 observed, and a wind in New England thunder-storms is some- 
 times observed to blow out from beneath in the rear. 
 
 When the whole atmosphere has a progressive motion 
 somewhat in the direction in which the squall blows in front, 
 the velocity of the squall as observed on the earth is the sum 
 of the velocity of progressive motion of the air and of the rela- 
 tive velocity with which the wind blows out from under the 
 .storm, and hence the observed wind for this reason alone 
 would be much stronger in front than in the rear. As there 
 is a gradual drawing in of the air from all sides toward the 
 storm, or at least toward the area of ascending air whatever the 
 form of this area, the air blowing out from under the storm en- 
 counters this and brings it to rest relatively to the storm at a 
 greater or less distance, and at a still greater distance relatively 
 to the earth, when the air has a progressive motion, and hence 
 sometimes a little before the storm arrives a calm is observed. 
 Sometimes the indrawing current is merely sufficient to reduce 
 the progressive velocity a little, as in the case of the observa- 
 tions at Ann Arbor, Michigan, where the velocity of the west 
 wind was merely reduced from 12 to 5 miles per hour and 
 there was no perfect calm ( 213). In this case there was a 
 blowing out behind, or a reversal of direction, with a very 
 small velocity. 
 
 RELATION BETWEEN THUNDER-STORMS AND CYCLONES. 
 
 310. We have seen that the origination of thunder-storms 
 requires an unstable state of the atmosphere. If, therefore, 
 this state is induced more readily in some parts of the cyclonic 
 area than in others, then there must be a preponderance of 
 thunder-storms in the former over those of the latter. But the 
 unstable state requires a vertical gradient of rapidly decreasing 
 temperature with increase of altitude, and this is brought about 
 by the passage of warm southerly currents in the lower strata 
 
468 THUNDER-STORMS. 
 
 of the atmosphere under colder northerly currents above, either 
 absolutely or merely relatively. By referring to Fig. I, 178,. 
 it is seen that this occurs in a cyclone in about the E. S. E. 
 octant, and in some measure in the adjacent octants on each 
 side of this octant, in which large north and south components 
 of the winds pass, the latter below under the former above. 
 By referring to the opposite side of the figure it is seen that 
 just the reverse of this takes place there, and that in the W. 
 N. W. octant the cold northerly winds below pass under the 
 southerly winds above, and that this is the case with regard to 
 large components of these winds in the adjacent octants on 
 each side. The tendency, then, of the cyclonic circulation 
 above and below is to produce an unstable state in the E. S. E. 
 octant, and also in some measure in the adjoining octants, but 
 just the reverse in the opposite octants. Of course the unsta- 
 ble state may be brought about anywhere without any cyclonic 
 influence, but this influence favors it in the E. S. E. and adja- 
 cent octants, and works against it in the opposite ones. 
 
 But there is also another consideration in this connection. 
 Thunder-storms occur most frequently in the warmer and mois- 
 ter atmosphere of the lower latitudes than in the cooler and 
 drier air of higher latitudes. Without, therefore, any of the 
 cyclonic influence just referred to, there would be a maximum 
 of thunder-storm occurrences in the southern part of a given 
 circular area of considerable extent, and a minimum in the 
 northern. The resultant maximum and minimum, therefore, 
 of the two, the maxima in the E. S. E. and the S, and the 
 minima in the opposite directions from the centre, would fall 
 somewhere between, and most likely nearest to those arising 
 from the cyclonic influence, and so the maximum of the re- 
 sultant would fall in the S. E. octant, and the minimum in the 
 opposite or N. W. octant. 
 
 Again it is seen from a reference to the same figure ( 178), 
 that in the interior of the cyclone the motion of the air below 
 and above is somewhat in the same direction, except that it 
 inclines in toward the centre a little, below, and out above, and 
 so there is little or no passing, relatively, of warmer, southerly^ 
 
RELA TION BETWEEN THUNDER-STORMS AND CYCLONES. 469 
 
 wind below under cooler, northerly winds above, or the reverse, 
 in any octant of the cyclone, and so the cyclonic influence 
 which tends to produce the unstable state or the reverse in 
 certain octants, is not found in the whole interior of the cy- 
 clone. Besides there is little tendency in this central region, 
 on account of its smallness, and so the little difference in lati- 
 tude between the northern and southern sides, toward a maxi- 
 mum frequency of occurrence on the south sides, or the reverse 
 on the other. 
 
 In the outer part also of the cyclone, beyond the isobar of 
 about 760 mm., the currents below are feeble, being under the 
 region of high pressure, and at and near the middle of the cir- 
 cular calm-belt of this high pressure, and the currents above 
 toward the outer border of the cyclone cannot be supposed to 
 be very strong ; so the cyclonic influence in this whole outer 
 part in inducing an unstable state in any octant, or the stable 
 state in the opposite, is very small. Besides this is a dry 
 region, and for this reason, also, thunder-storms should rarely 
 occur. 
 
 311. From what precedes, therefore, thunder-storm fre- 
 quency should be confined, not only to the S. E. octant 
 mostly, but also, in average cyclones, within the isobars of 
 about 750 and 760 mm. Let us now compare these theoreti- 
 cal deductions with results of observations. The latter, for 
 Russia, are contained in the following tables in percentages for 
 the whole year, given by Klossovsky 80 from very numerous ob- 
 servations : 
 
 Octant 
 
 N. 
 2-3 
 
 N.E. 
 12.6 
 9.4 
 
 E. 
 8.4 
 
 6.2 
 
 S.E. 
 41.4 
 46.9 
 
 S. 
 9-5 
 15-6 
 
 s.w. 
 19-3 
 
 15.6 
 
 W. 
 
 1.4 
 2.1 
 
 N.W. 
 5-1 
 4.2 
 
 Thunder-storms 
 Hail-storms .... 
 
 
 Pressure in millimeters 
 
 ,.{ 735 
 1740 
 
 740 
 
 745 
 0-3 
 
 4.6 
 
 745 
 75 
 
 5-8 
 
 750 
 
 755 
 
 37-5 
 <K.S 
 
 755 
 760 
 
 48.3 
 48.0 
 
 760 
 765 
 
 7-9 
 
 II. 2 
 
 765 
 770 
 O.I 
 
 Hail-storms. . 
 
 
 . 0.6 
 
 It is seen from the first of these tables that by far the 
 greatest relative frequency of thunder-storms is in the S.E. 
 octant, though there appears to be, for some reason, a slight 
 
470 THUNDER-STORMS. 
 
 secondary maximum in the S.W. octant. And! according to 
 the second table, nearly all occur at the distance from the 
 centre at which the barometric pressure ranges from 750 to 
 760 mm. These results accord with those deduced by Fron 
 from the observations of thunder-storms in France, who found 
 that they occur in the " dangerous" half of the depression 
 between the centre and border. As the storms move mostly 
 from S.W. to N.E. they consequently occur mostly in the S.E.. 
 octant. 
 
 Professor Hazen 83 of the Signal Service, from the study of 
 the thunder-storms which occurred in May, 1884, in the United : 
 States, likewise found that thunder-storms generally accompany- 
 an area of low pressure, and are found in the S.E. quadrant at 
 a distance of 400 to 500 miles from the centre. 
 
 It is seen that hail-storms and thunder-storms have about 
 the same relative percentages in the different octants and 
 average pressures or distances from the centres of the cyclones,, 
 and hence their relations to the cyclone centre are the same. 
 The same is true with regard to tornadoes generally and 
 thunder-storms. This is what we would expect from theo- 
 retical considerations, since all depend upon the same general; 
 conditions of humidity and instability of the atmosphere, and 
 tornadoes, including hail-storms, are usually found in the. 
 thunder-storm region, and simply require the additional local 
 condition which gives rise to tornadic gyrations and, in the 
 case of hail-storms, to ascending currents which extend to- 
 high altitudes. 
 
 ANNUAL AND DIURNAL INEQUALITIES. 
 
 312. As thunder-storms depend upon the unstable state,, 
 and this is brought about mainly by the heating up of the 
 earth's. surface and lower strata of the atmosphere, the condi- 
 tions which give rise to thunder-storms occur mostly during: 
 the warmest season of the year and the warmest part of the 
 day. Hence thunder-storms are experienced mostly in summer 
 and in the afternoon of the day. And where thunder-storms 
 
ANNUAL AND DIURNAL INEQUALITIES. 
 
 and line squalls progress over the country in connection with 
 cyclones they have been known to cease at night and com- 
 mence again the next day. 
 
 On the ocean, however, the reverse of this in some measure 
 takes place, and there seems to be a slight maximum during 
 the winter and the night. 
 
 According to Buchan, 84 of the 23 thunder-storms which 
 occurred at Stykkisholm in 14 years, only one occurred in any 
 of the six warm months of the year from April to September. 
 They occur also mostly during the night. These storms are 
 short-lived, being in almost every case restricted to one, or at 
 most only a few flashes of lightning and claps of thunder. 
 Taking also the northwest stations of Scotland alone, adjacent 
 to the ocean, the thunder-storm frequency is twice as great 
 during the hours immediately after midnight as during the 
 hours from noon to 4 P.M., and the storms occur here also 
 mostly in the winter. On the east coast the reverse takes 
 place, the diurnal maximum being in the warmer hours of the 
 afternoon, and very few storms occur during the winter. 
 
 Along the coast of Norway also, according to Mohn, there 
 seems to be a slight tendency to a winter maximum, not only 
 in storm frequency, but likewise in intensity, and according to 
 Scott, Valentia, Ireland, has a strong winter maximum of 
 thunder-storm frequency. 
 
 The reason of contrast between ocean and land in the times 
 of the diurnal and annual maxima of thunder-storm frequency 
 is that the unstable state of the atmosphere upon which these 
 storms depend is most readily induced on the former during 
 the colder part of the day and the year, and the reverse on 
 land. On the latter the diurnal and annual changes are great 
 on and near the earth's surface, in comparison with what they 
 are in the upper part of the atmosphere ; while on the ocean 
 the reverse is the case, the diurnal and annual changes being 
 very small below in comparison with what they are above, 
 where they are somewhat the same as over the continents. 
 The average state of the atmosphere, therefore, on the ocean 
 is more nearly that of the unstable state in the winter and 
 
47 2 THUNDER-STORMS. 
 
 during the coldest part of the night than at other times, while 
 ,the reverse is the case on the land. The unstable state is, 
 therefore, more readily brought about on the ocean at these 
 times, and hence there is the greatest frequency of thunder- 
 storms at night and during the winter. For well-known reasons 
 it is just the reverse of this on land. 
 
 But we have seen ( 122) that the western sides of the con- 
 tinents in middle and higher latitudes partake of an oceanic, 
 rather than of a continental, climate ; and hence nocturnal and 
 winter maxima occur, not only on the ocean, but likewise on 
 the western sides of the continents to some distance into the 
 interior. 
 
 The average state of the atmosphere on land is nearer to 
 the unstable state during the summer and the warmer part of 
 the day than it is on the ocean during the winter and the 
 colder part of the day ; and hence upon the whole there must 
 be more thunder-storms upon land than upon the ocean, and 
 to some extent on the eastern than on the western sides of the 
 continents in the middle and the higher latitudes. For this 
 reason thunder-storms and all small local storms depending 
 upon the unstable state of the atmosphere are of greater fre- 
 quency, on the average of the year, on land than on the ocean ; 
 and this is especially the case in the interiors of the continents, 
 while small parts of the western sides, for reasons already given, 
 are exceptions. 
 
APPENDIX. 
 
 CONTAINING THE TABLES AND A LIST OF THE 
 
 BOOKS AND PAPERS REFERRED TO 
 
 IN THE PRECEDING PAGES. 
 
 TABLE I. 
 
 Gravity Correction for a Barometric Pressure of 760 mm., for each Degree of 
 Latitude /, which is the Argument of the Table. 
 
 L 
 
 Correction. 
 
 4- 
 
 - 
 
 Correction. 
 
 i 
 
 
 mm. 
 
 Inches. 
 
 
 
 mm. 
 
 Inches. 
 
 
 
 
 .98 
 
 0.078 
 
 90 
 
 23 
 
 37 
 
 0.054 
 
 67 
 
 I 
 
 .98 
 
 .078 
 
 89 
 
 24 
 
 33 
 
 .052 
 
 66 
 
 2 
 
 97 
 
 .078 
 
 88 
 
 25 
 
 .27 
 
 .050 
 
 65 
 
 3 
 
 97 
 
 .078 
 
 87 
 
 26 
 
 .22 
 
 .048 
 
 64 
 
 4 
 
 .96 
 
 077 
 
 86 
 
 27 
 
 .16 
 
 .046 
 
 63 
 
 5 
 
 95 
 
 .077 
 
 85 
 
 28 
 
 .11 
 
 .044 
 
 62 
 
 6 
 
 94 
 
 .076 
 
 84 
 
 29 
 
 05 
 
 .041 
 
 61 
 
 7 
 
 .92 
 
 .076 
 
 83 
 
 30 
 
 0.99 
 
 039 
 
 60 
 
 8 
 
 .90 
 
 075 
 
 82 
 
 3i 
 
 0-93 
 
 037 
 
 59 
 
 9 
 
 .88 
 
 .074 
 
 81 
 
 32 
 
 0.87 
 
 034 
 
 58 
 
 10 
 
 .86 
 
 073 
 
 80 
 
 33 
 
 0.81 
 
 .032 
 
 57 
 
 ii 
 
 .84 
 
 .072 
 
 79 
 
 34 
 
 0.74 
 
 .029 
 
 56 
 
 12 
 
 .81 
 
 .071 
 
 78 
 
 35 
 
 0.68 
 
 .027 
 
 55 
 
 13 
 
 78 
 
 .070 
 
 77 
 
 36 
 
 0.61 
 
 .024 
 
 54 
 
 14 
 
 75 
 
 .069 
 
 76 
 
 37 
 
 o.55 
 
 .022 
 
 53 
 
 15 
 
 72 
 
 .067 
 
 75 
 
 38 
 
 0.48 
 
 .Olg 
 
 52 
 
 16 
 
 .68 
 
 .066 
 
 74 
 
 39 
 
 0.41 
 
 .016 
 
 51 
 
 17 
 
 .64 
 
 .065 
 
 73 
 
 40 
 
 0.34 
 
 .014 
 
 50 
 
 18 
 
 .60 
 
 .063 
 
 72 
 
 41 
 
 0.28 
 
 .Oil 
 
 49 
 
 19 
 
 56 
 
 .062 
 
 71 
 
 42 
 
 0.21 
 
 .008 
 
 48 
 
 20 
 
 52 
 
 .060 
 
 70 
 
 43 
 
 0.14 
 
 .005 
 
 47 
 
 21 
 
 47 
 
 .058 
 
 69 
 
 44 
 
 0.07 
 
 .003 
 
 46 
 
 22 
 
 .42 
 
 .056 
 
 68 
 
 45 
 
 0.00 
 
 .OOO 
 
 45 
 
 NOTE. The correction must be taken according to the sign placed under the 
 argument /. The corrections for smaller pressures, at some altitude above sea- 
 level, must be diminished in proportion to the pressures. 
 
 473 
 
474 
 
 APPENDIX. 
 
 TABLE II. 
 
 The Tension of Aqueous Vapor in Saturated Air at the Temperature T, used as 
 
 an Argument. 
 
 T 
 
 Tension. 
 
 T 
 
 Tension. 
 
 T 
 
 Tension. 
 
 r 
 
 Tension. 
 
 T 
 
 Tension. 
 
 F. 
 
 Inches. 
 
 o p 
 
 Inches. 
 
 F. 
 
 Inches. 
 
 o T7 
 
 Inches. 
 
 F. 
 
 Inches. 
 
 o 
 
 0.045 
 
 20 
 
 0.109 
 
 40 
 
 0.246 
 
 60' 
 
 0.517 
 
 80 
 
 .O2I 
 
 I 
 
 0.047 
 
 21 
 
 0.114 
 
 41 
 
 0.256 
 
 61 
 
 0.536 
 
 8l 
 
 055 
 
 2 
 
 0.049 
 
 22 
 
 0.119 
 
 42 
 
 0.266 
 
 62 
 
 0-555 
 
 82 
 
 .090 
 
 3 
 
 0.051 
 
 23 
 
 0.124 
 
 43 
 
 0.276 
 
 63 
 
 0-575 
 
 83 
 
 .126 
 
 4 
 
 0.054 
 
 24 
 
 0.129 
 
 44 
 
 0.287 
 
 64 
 
 0.595 
 
 84 
 
 .163 
 
 5 
 
 0.057 
 
 25 
 
 0.135 
 
 45 
 
 0.298 
 
 65 
 
 0.616 
 
 85 
 
 .201 
 
 6 
 
 0.059 
 
 26 
 
 0.141 
 
 46 
 
 0.310 
 
 66 
 
 0.638 
 
 86 
 
 239 
 
 7 
 
 0.062 
 
 27 
 
 0.147 
 
 47 
 
 0.322 
 
 67 
 
 0.660 
 
 87 
 
 .279 
 
 8 
 
 0.065 
 
 28 
 
 0.153 
 
 48 
 
 0-334 
 
 68 
 
 0.683 
 
 88 
 
 .320 
 
 9 
 
 0.068 
 
 29 
 
 0.159 
 
 49 
 
 0-347 
 
 69 
 
 0.707 
 
 89 
 
 363 
 
 10 
 
 0.071 
 
 30 
 
 0.166 
 
 50 
 
 0.360 
 
 70 
 
 0.732 
 
 90 
 
 .407 
 
 ii 
 
 0.075 
 
 31 
 
 0.173 
 
 51 
 
 0.374 
 
 71 
 
 0-757 
 
 91 
 
 452 
 
 12 
 
 0.078 
 
 32 
 
 0.180 
 
 52 
 
 0.388 
 
 72 
 
 0.783 
 
 92 
 
 .498 
 
 13 
 
 0.081 
 
 33 
 
 0.187 
 
 53 
 
 0.402 
 
 73 
 
 0.810 
 
 93 
 
 545 
 
 14 
 
 0.085 
 
 34 
 
 0.195 
 
 54 
 
 0.417 
 
 74 
 
 0.837 
 
 94 
 
 594 
 
 15 
 
 0.088 
 
 35 
 
 0.203 
 
 55 
 
 0.432 
 
 75 
 
 0.865 
 
 95 
 
 .644 
 
 16 
 
 0.092 
 
 36 
 
 0.2II 
 
 56 
 
 0.448 
 
 76 
 
 0.894 
 
 96 
 
 695 
 
 17 
 
 0.096 
 
 37 
 
 0.219 
 
 57 
 
 0.464 
 
 77 
 
 0.925 
 
 97 
 
 .748 
 
 18 
 
 O.IOO 
 
 38 
 
 0.228 
 
 58 
 
 0.481 
 
 78 
 
 0.956 
 
 98 
 
 .802 
 
 19 
 
 0.104 
 
 39 
 
 0.237 
 
 59 
 
 0.499 
 
 79 
 
 0.988 
 
 99 
 
 857 
 
 C. 
 
 mm. 
 
 C. 
 
 mm. 
 
 C. 
 
 mm. 
 
 c. 
 
 mm. 
 
 C 
 
 mm. 
 
 - 18 
 
 1. 12 
 
 7 
 
 2.72 
 
 + 4 
 
 6.07 
 
 + 15 
 
 12.67 
 
 + 26 
 
 24.96 
 
 17 
 
 1.22 
 
 6 
 
 2-93 
 
 5 
 
 6. 5 I 
 
 16 
 
 13-51 
 
 27 
 
 26.47 
 
 16 
 
 .32 
 
 5 
 
 3-16 
 
 6 
 
 6-97 
 
 17 
 
 14.40 
 
 28 
 
 28.07 
 
 15 
 
 44 
 
 4 
 
 3-41 
 
 7 
 
 7-47 
 
 18 
 
 15-33 
 
 29 
 
 29.74 
 
 34 
 
 56 
 
 3 
 
 3.67 
 
 8 
 
 7-99 
 
 19 
 
 16.32 
 
 30 
 
 3I-5I 
 
 13 
 
 .69 
 
 2 
 
 3-95 
 
 9 
 
 8-55 
 
 20 
 
 17.36 
 
 3i 
 
 33-37 
 
 12 
 
 .84 
 
 I 
 
 4 25 
 
 10 
 
 9.14 
 
 21 
 
 18.47 
 
 32 
 
 35.32 
 
 tfl 
 
 99 
 
 
 
 4-57 
 
 ii 
 
 9-77 
 
 22 
 
 19.63 
 
 33 
 
 37-37 
 
 10 
 
 2.15 
 
 + 1 
 
 4.91 
 
 12 
 
 10.43 
 
 23 
 
 20.86 
 
 34 
 
 39-52 
 
 9 
 
 2-33 
 
 2 
 
 5-27 
 
 13 
 
 11.14 
 
 24 
 
 22.15 
 
 35 
 
 41.78 
 
 - 8 
 
 2.51 
 
 + 3 
 
 5.66 
 
 + 14 
 
 11.88 
 
 + 25. 
 
 23-52 
 
 + 36 
 
 44.16 
 
APPENDIX. 
 TABLE III. 
 
 47$ 
 
 The Decrease in Temperature of Ascending. Air for each 100 Meters of Ascent 
 for the different Barometric Pressures P and Temperatures r, used as Argu- 
 ments. Also the Weight of Aqueous Vapor in a Kilogram of Saturated Air, 
 
 
 T 
 
 A l.itiitflA * 
 
 P. 
 
 -10 
 
 -5 
 
 
 
 5 
 
 10 
 
 15 
 
 20 
 
 25 
 
 3 o 
 
 Altitude.* 
 
 mm. 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 Meters. 
 
 760 
 
 0.74 
 
 0.68 
 
 0.64 
 
 0.58 
 
 o-53 
 
 0.48 
 
 0-43 
 
 0.40 
 
 0-37 
 
 
 
 700 
 
 73 
 
 .66 
 
 .63 
 
 57 
 
 51 
 
 .46 
 
 .42 
 
 38 
 
 .36 
 
 660 
 
 600 
 
 .70 
 
 63 
 
 .60 
 
 54 
 
 .48 
 
 .43 
 
 .40 
 
 36 
 
 
 1897 
 
 500 
 
 .66 
 
 .60 
 
 .56 
 
 -50 
 
 45 
 
 .40 
 
 37 
 
 
 
 3357 
 
 400 
 
 .62 
 
 55 
 
 51 
 
 .46 
 
 .41 
 
 37 
 
 
 
 
 5142 
 
 300 
 
 .56 
 
 .49 
 
 .46 
 
 .42 
 
 
 
 
 
 
 7550 
 
 200 
 
 .48 
 
 .41 
 
 39 
 
 
 
 
 
 
 
 10680 
 
 Weight of Aqueous Vapor in a Kilogram of Saturated Air. 
 
 mm. 
 
 gram. 
 
 gram. 
 
 gram. 
 
 gram. 
 
 gram. 
 
 gram. 
 
 gram. 
 
 gram. 
 
 gram. 
 
 
 760 
 
 1-7 
 
 2.6 
 
 3-8 
 
 5-4 
 
 7.6 
 
 10.5 
 
 14.4 
 
 19.5 
 
 26.3 
 
 
 
 600 
 
 2.2 
 
 3-2 
 
 4.6 
 
 6.8 
 
 9.6 
 
 13.3 
 
 I8. 3 
 
 24.8 
 
 
 1897 
 
 400 
 
 3-3 
 
 4.8 
 
 7.2 
 
 10.2 
 
 14.4 
 
 20.0 
 
 
 
 
 5142 
 
 200 
 
 6-5 
 
 6.7 
 
 
 
 
 
 
 
 
 10680 
 
 * Computed with the temperatures of 13. 
 
47 6 
 
 APPENDIX. 
 
 TABLE IV. 
 
 The Heights, in meters, of Incipient Condensation in ascending currents of Air, 
 for the Temperatures r, and the Depressions of the Dew-point, r d, in 
 Centigrade degrees, used as arguments. 
 
 J 
 
 AIR TEMPERATURES r. 
 
 
 35 
 
 30 
 
 25 
 
 20 
 
 15 
 
 10 
 
 5 
 
 
 
 -5 
 
 10 
 
 -15 
 
 1 
 
 128 
 
 127 
 
 127 
 
 126 
 
 126 
 
 125 
 
 125 
 
 125 
 
 125 
 
 125 
 
 125 
 
 2 
 
 255 
 
 254 
 
 253 
 
 252 
 
 251 
 
 250 
 
 250 
 
 250 
 
 250 
 
 250 
 
 250 
 
 3 
 
 382 
 
 380 
 
 379 
 
 377 
 
 376 
 
 375 
 
 375 
 
 375 
 
 395 
 
 375 
 
 375 
 
 4 
 
 509 
 
 506 
 
 505 
 
 502 
 
 50i 
 
 500 
 
 500 
 
 500 
 
 500 
 
 500 
 
 500 
 
 5 
 
 635 
 
 632 
 
 630 
 
 627 
 
 625 
 
 624 
 
 624 
 
 625 
 
 624 
 
 624 
 
 624 
 
 6 
 
 7 6l 
 
 758 
 
 755 
 
 75i 
 
 748 
 
 747 
 
 746 
 
 748 
 
 746 
 
 748 
 
 
 7 
 
 886 
 
 883 
 
 879 
 
 874 
 
 871 
 
 869 
 
 868 
 
 870 
 
 868 
 
 870 
 
 
 8 
 
 1012 
 
 1009 
 
 1003 
 
 997 
 
 993 
 
 991 
 
 99 
 
 991 
 
 990 
 
 992 
 
 
 9 
 
 H37 
 
 H33 
 
 1127 
 
 1120 
 
 IH5 
 
 1113 
 
 IIII 
 
 III2 
 
 III2 
 
 1114 
 
 
 10 
 
 1262 
 
 1257 
 
 1250 
 
 1242 
 
 1236 
 
 1234 
 
 1232 
 
 1232 
 
 1233 
 
 1235 
 
 
 ii 
 
 1387 
 
 1382 
 
 1374 
 
 1364 
 
 1357 
 
 1355 
 
 1352 
 
 1351 
 
 1352 
 
 
 
 12 
 
 I5H 
 
 1506 
 
 1497 
 
 1485 
 
 1478 
 
 1476 
 
 1472 
 
 1470 
 
 1470 
 
 
 
 13 
 
 1635 
 
 1630 
 
 1620 
 
 1606 
 
 1599 
 
 1596 
 
 1592 
 
 1589 
 
 1588 
 
 
 
 14 
 
 1759 
 
 1754 
 
 1743 
 
 1727 
 
 1720 
 
 1716 
 
 1711 
 
 1708 
 
 1705 
 
 
 
 15 
 
 1883 
 
 1877 
 
 1865 
 
 1848 
 
 1841 
 
 1836 
 
 1830 
 
 1826 
 
 1822 
 
 
 
 16 
 
 2005 
 
 1999 
 
 1985 
 
 1969 
 
 1962 
 
 1956 
 
 1950 
 
 1945 
 
 
 
 
 17 
 
 2127 
 
 2I2O 
 
 2105 
 
 2090 
 
 2083 
 
 2076 
 
 2070 
 
 2065 
 
 
 
 
 18 
 
 2249 
 
 2241 
 
 2225 
 
 2211 
 
 2203 
 
 2196 
 
 2190 
 
 2185 
 
 
 
 
 19 
 
 2371 
 
 2361 
 
 2344 
 
 2332 
 
 2323 
 
 2316 
 
 2310 
 
 2305 
 
 
 
 
 20 
 
 2493 
 
 2480 
 
 2463 
 
 2452 
 
 2443 
 
 2435 
 
 2430 
 
 2425 
 
 
 
 
 21 
 
 2614 
 
 2599 
 
 2582 
 
 2572 
 
 2563 
 
 2554 
 
 2548 
 
 
 
 
 
 22 
 
 2734 
 
 2718 
 
 2700 
 
 2691 
 
 2683 
 
 2672 
 
 2665 
 
 
 
 
 
 23 
 
 2854 
 
 2837 
 
 2819 
 
 28lO 
 
 2802 
 
 2790 
 
 2681 
 
 
 
 
 
 24 
 
 2974 
 
 2956 
 
 2938 
 
 2929 
 
 2921 
 
 2908 
 
 2795 
 
 
 
 
 
 25 
 
 3093 
 
 3075 
 
 3056 
 
 3048 
 
 3040 
 
 3025 
 
 3009 
 
 
 
 
 
 26 
 
 3214 
 
 3192 
 
 3 J 73 
 
 3165 
 
 3158 
 
 3i4i 
 
 
 
 
 
 
 27 
 
 3332 
 
 3309 
 
 3290 
 
 3282 
 
 3275 
 
 3256 
 
 
 
 
 
 
 28 
 
 3450 
 
 3426 
 
 3407 
 
 3399 
 
 3391 
 
 3371 
 
 
 
 
 
 
 29 
 
 3568 
 
 3543 
 
 3524 
 
 3515 
 
 3506 
 
 349 6 
 
 
 
 
 
 
 30 
 
 3685 
 
 3660 
 
 3640 
 
 3631 
 
 3621 
 
 3600 
 
 
 
 
 
 
 31 
 
 3801 
 
 3775 
 
 3757 
 
 3749 
 
 3737 
 
 
 
 
 
 
 
 32 
 
 39 1 ? 
 
 3891 
 
 3874 
 
 3867 
 
 3854 
 
 
 
 
 
 
 
 33 
 
 4032 
 
 4006 
 
 399 
 
 3984 
 
 397i 
 
 
 
 
 
 
 
 34 
 
 4M7 
 
 4120 
 
 4107 
 
 4101 
 
 4088 
 
 
 
 
 
 
 
 35 
 
 4261 
 
 4235 
 
 4223 
 
 4218 
 
 4205 
 
 
 
 
 
 
 
 36 
 
 4375 
 
 4349 
 
 4338 
 
 4333 
 
 
 
 
 
 
 
 
 37 
 
 4488 
 
 4462 
 
 4452 
 
 4448 
 
 
 
 
 
 
 
 
 38 
 
 4601 
 
 4576 
 
 4566 
 
 4562 
 
 
 
 
 
 
 
 
 39 
 
 4713 
 
 4690 
 
 4680 
 
 4686 
 
 
 
 
 
 
 
 
 40 
 
 4826 
 
 4804 
 
 4794 
 
 4790 
 
 
 
 
 
 
 
 
 41 
 
 4939 
 
 4918 
 
 4908 
 
 
 
 
 
 
 
 
 
 42 
 
 5053 
 
 5032 
 
 5022 
 
 
 
 
 
 
 
 
 
 43 
 
 5168 
 
 5146 
 
 5136 
 
 
 
 
 
 
 
 
 
 44 
 
 5284 
 
 5261 
 
 5250 
 
 
 
 
 
 
 
 
 
 45 
 
 5400 
 
 5376 
 
 5364 
 
 
 
 
 
 
 
 
 
 46 
 
 55i8 
 
 5492 
 
 
 
 
 
 
 
 
 
 
 47 
 
 5638 
 
 5609 
 
 
 
 
 
 
 
 
 
 
 48 
 
 5759 
 
 5727 
 
 
 
 
 
 
 
 
 
 
 49 
 
 5881 
 
 5846 
 
 
 
 
 
 
 
 
 
 
 50 
 
 6005 
 
 5966 
 
 
 
 
 
 
 
 
 
 
APPENDIX. 
 TABLE V. 
 
 477 
 
 Containing several functions defined and referred to in the preceding pages> 
 useful in facilitating the computations of many of the Formulae. The 
 functions are given for each Fifth Degree of the Latitude /, used as an 
 argument. 
 
 I 
 
 sin / 
 
 COS / 
 
 (0 
 
 in Meters. 
 
 e 
 s 
 
 2 n sin / 
 
 G 
 
 
 
 0.00000 
 
 I.OOOOO 
 
 465.0 
 
 0.00000000 
 
 o.ooooooo 
 
 o.oooo 
 
 5 
 
 .08716 
 
 0.99619 
 
 463.2 
 
 130 
 
 127 
 
 0.0137 
 
 10 
 
 .17365 
 
 .98481 
 
 458.0 
 
 258 
 
 253 
 
 .0273 
 
 15 
 
 .25882 
 
 96593 
 
 449.2 
 
 385 
 
 377 
 
 . 0406 
 
 20 
 
 .34202 
 
 .93969 
 
 436.9 
 
 509 
 
 499 
 
 .0537 
 
 25 
 
 .42262 
 
 .90631 
 
 421.5 
 
 629 
 
 616 
 
 .0664 
 
 30 
 
 .50000 
 
 .86603 
 
 402.7 
 
 744 
 
 729 
 
 .0785 
 
 35 
 
 .57358 
 
 .81915 
 
 380.7 
 
 853 
 
 837 
 
 .0901 
 
 40 
 
 .64279 
 
 .76604 
 
 356.3 
 
 956 
 
 937 
 
 .1010 
 
 45 
 
 .70711 
 
 .70711 
 
 328.8 
 
 1052 
 
 1031 
 
 .1111 
 
 50 
 
 .76604 
 
 .64279 
 
 298.9 
 
 "39 
 
 1117 
 
 .I2O4 
 
 55 
 
 .81915 
 
 .57358 
 
 266.7 
 
 1219 
 
 "95 
 
 .1287 
 
 60 
 
 .86603 
 
 .50000 
 
 232.5 
 
 1288 
 
 1263 
 
 .I36l 
 
 65 
 
 .90631 
 
 .42262 
 
 196.6 
 
 1348 
 
 1322 
 
 .1424 
 
 70 
 
 .93969 
 
 .34202 
 
 159.0 
 
 1398 
 
 1370 
 
 -1477 
 
 75 
 
 .96593 
 
 .25882 
 
 I2O.4 
 
 1437 
 
 1408 
 
 .1518 
 
 80 
 
 .98481 
 
 .17365 
 
 80.8 
 
 1465 
 
 1436 
 
 -1547 
 
 85 
 
 .99619 
 
 .08716 
 
 40.6 
 
 1481 
 
 1453 
 
 .1565 
 
 90 
 
 I.OOOOO 
 
 o.ooooo 
 
 oo.o 
 
 0.00001487 
 
 0.0001458 
 
 O.I57I 
 
478 
 
 APPENDIX. 
 
 TABLE VI. 
 
 Height in Meters AH oi a Column of Pure and Dry Air, corresponding to a 
 Millimeter of Barometric Pressure, at different Temperatures and Pressures, 
 
 7993 T_ 
 P ' To 
 
 Computed by the Formula AH ' = 
 
 Barometric 
 Pressure in 
 Millimeters. 
 
 TEMPERATURE BY THE CENTIGRADE SCALE. 
 
 10 
 
 -5 
 
 
 
 5 
 
 10 
 
 15 
 
 20 
 
 25 
 
 30 
 
 35 
 
 760 
 
 10.13 
 
 10.32 
 
 10.52 
 
 10.71 
 
 10.90 
 
 1 1. 1C 
 
 11.29 
 
 ii. 4 
 
 ii 6 
 
 11.87 
 
 750 
 
 10.27 
 
 10.46 
 
 10.66 
 
 10.85 
 
 11.05 
 
 11.24 
 
 11.44 
 
 11.63 
 
 ii. 8 
 
 12.02 
 
 740 
 
 10.40 
 
 10.60 
 
 10.80 
 
 II. OO 
 
 11.20 
 
 H.39 
 
 "59 
 
 11.79 
 
 11.99 
 
 12. 19 
 
 730 
 
 10.55 
 
 io.75 
 
 10.95 
 
 H.I5 
 
 n-35 
 
 H-55 
 
 H.75 
 
 11.93 
 
 12. I 
 
 12-35 
 
 720 
 
 10.70 
 
 10.90 
 
 II. 10 
 
 11-30 
 
 11.51 
 
 11.71 
 
 11.91 
 
 12.12 
 
 13.32 
 
 12.52 
 
 710 
 
 10.85 
 
 11.05 
 
 11.26 
 
 11.67 
 
 11.68 
 
 11.88 
 
 12.08 
 
 12.29 
 
 12.49 
 
 I2.7O 
 
 700 
 
 II. OO 
 
 II. 21 
 
 11.42 
 
 11.63 
 
 11.84 
 
 12.05 
 
 12.26 
 
 12.46 
 
 12.67 
 
 12.88 
 
 690 
 
 11.16 
 
 H-37 
 
 11.58 
 
 II.80 
 
 12.01 
 
 12.22 
 
 12.43 
 
 12.64 
 
 12. 80 
 
 13.07 
 
 680 
 
 11.32 
 
 11-54 
 
 -75 
 
 11.97 
 
 12. l8 
 
 12.40 
 
 12.61 
 
 12.83 
 
 13.05 
 
 13.26 
 
 670 
 
 11.49 
 
 11.71 
 
 H-93 
 
 12.15 
 
 12.37 
 
 12.58 
 
 12.80 
 
 13.02 
 
 13.24 
 
 13.46 
 
 660 
 
 11.67 
 
 11.89 
 
 12. II 
 
 12.33 
 
 12.55 
 
 12.78 
 
 13-00 
 
 13.22 
 
 13.44 
 
 13.66 
 
 650 
 
 11.85 
 
 12.07 
 
 12.30 
 
 12.52 
 
 12.75 
 
 I2. 9 7 
 
 13-20 
 
 13.42 
 
 13.65 
 
 13-87 
 
 640 
 
 12.03 
 
 12.26 
 
 12.49 
 
 12.72 
 
 12.96 
 
 I3-I8 
 
 13.40 
 
 13.63 
 
 13.86 
 
 14.09 
 
 630 
 
 12.22 
 
 12.45 
 
 12.69 
 
 12.92 
 
 13.15 
 
 13.38 
 
 13.61 
 
 13.85 
 
 14.08 
 
 I4.3I 
 
 620 
 
 12.42 
 
 12.66 
 
 12.89 
 
 13.13 
 
 13-36 
 
 13.60 
 
 13.84 
 
 14.07 
 
 14.31 
 
 14-54 
 
 610 
 
 12.62 
 
 12.86 
 
 13-10 
 
 13-34 
 
 13.58 
 
 13.82 
 
 14.06 
 
 14.30 
 
 14-54 
 
 14.78 
 
 -600 
 
 12.83 
 
 13 08 
 
 13.32 
 
 13-57 
 
 13.81 
 
 14.05 
 
 14.30 
 
 14.54 
 
 14.79 
 
 15-03 
 
 59 
 
 I3-05 
 
 I3-30 
 
 13-55 
 
 I3-80 
 
 14.04 
 
 14.29 
 
 14.54 
 
 14.79 
 
 15-Oij 
 
 15.28 
 
 580 
 
 13.28 
 
 13-53 
 
 13.78 
 
 14.03 
 
 14.28 
 
 14.54 
 
 14.79 
 
 15.04 
 
 15.30 
 
 15-54 
 
 570 
 
 I3-5I 
 
 13-77 
 
 14.02 
 
 14.28 
 
 14-54 
 
 14.79 
 
 15-05 
 
 15.31 
 
 15.56 
 
 15.82 
 
 560 
 
 13-75 
 
 14.01 
 
 14.27 
 
 14-53 
 
 14.80 
 
 15.06 
 
 15-32 
 
 15.58 
 
 15.84 
 
 16.10 
 
 :550 
 
 I4.OI 
 
 14.28 
 
 14-54 
 
 I4.8l 
 
 15.07 
 
 15-34 
 
 15.60 
 
 15.87 
 
 16.13 
 
 16.40 
 
 540 
 
 14.26 
 
 14-53 
 
 14.80 
 
 15.07 
 
 15.34 
 
 I5.6I 
 
 15.89 
 
 16.16 
 
 16.43 
 
 16.70 
 
 530 
 
 14-53 
 
 14.80 
 
 15.08 
 
 15.36 
 
 15.63 
 
 15.91 
 
 16.18 
 
 16.46 
 
 16.74 
 
 17. 01 
 
 520 
 
 I4.8l 
 
 15.09 
 
 15.37 
 
 15.65 
 
 15.93 
 
 16.21 
 
 16.50 
 
 16.78 
 
 17.06 
 
 17-34 
 
 510 
 
 15.10 
 
 15-39 
 
 15.67 
 
 15.96 
 
 16.25 
 
 16.53 
 
 16.82 
 
 17.11 
 
 17.39 
 
 17.68 
 
 500 
 
 15.40 
 
 15.69 
 
 15.99 
 
 16.28 
 
 16.57 
 
 16.86 
 
 17.16 
 
 17-45 
 
 17.74 
 
 18.04 
 
 .490 
 
 15-71 
 
 16.01 
 
 16.31 
 
 16.61 
 
 16.91 
 
 17.21 
 
 17-51 
 
 17.81 
 
 I8.IO 
 
 18.40 
 
 480 
 
 16.04 
 
 16.35 
 
 16.65 
 
 16.96 
 
 17.26 
 
 17.57 
 
 17.87 
 
 18.18 
 
 18.48 
 
 18.79 
 
 470 
 
 16.38 
 
 16.70 
 
 17.01 
 
 17.32 
 
 17.63 
 
 17.94 
 
 18.25 
 
 18.56 
 
 18.87 
 
 19.18 
 
 460 
 
 16.74 
 
 17.07 
 
 17.38 
 
 17.69 
 
 18.01 
 
 18.33 
 
 18.65 
 
 18.97 
 
 19.28 
 
 19.60 
 
 450 
 
 17.11 
 
 17.44 
 
 17.76 
 
 18.09 
 
 18.41 
 
 18.74 
 
 19.06 
 
 19-39 
 
 19.71 
 
 20.04 
 
 440 
 
 17.50 
 
 17-83 
 
 18.17 
 
 18.50 
 
 18.83 19-16 
 
 19.50 
 
 19.83 
 
 20. 16 
 
 20.50 
 
 430 
 
 17.91 
 
 18.25 
 
 18.59 
 
 18.93 
 
 19.27 19.61 
 
 19-95 
 
 2;. 29 
 
 20.63 
 
 20.97 
 
 420 
 
 18.33 
 
 18.68 
 
 19.03 
 
 19.38 
 
 19.73 20.07 
 
 20.42 
 
 20.77 
 
 21.12 
 
 21.47 
 
 410 
 
 18.78 
 
 19.14 
 
 19.50 
 
 19.85 
 
 20.21 
 
 20.57 
 
 20.92 
 
 21.28 
 
 21.64 
 
 21- V9 
 
 400 
 
 19.25 
 
 19.62 
 
 19.98 
 
 20.35 
 
 20.71 
 
 21. 08 
 
 21.45 
 
 21. 8l 
 
 22.18 
 
 22.54 
 
 390 
 
 19.74 
 
 20.12 
 
 2O.5O 
 
 20.87 
 
 2I.24i 21.62 
 
 22.00 
 
 22.37 
 
 22-75 
 
 23.12 
 
 380 
 
 20.26 
 
 20.65 
 
 21.03 
 
 21.42 
 
 21. 80 
 
 22.19 
 
 22.57 
 
 22.96 
 
 23-35 
 
 23.73 
 
 NOTE. The Barometric Pressures are the Barometer Readings corrected 
 for varying gravity, and, strictly, they, as well as the Temperatures, belong to 
 the middle of the column AH. The Carbonic Acid in the air makes AH a very 
 kittle less, and the Aqueous Vapor a little greater, than the values above. 
 
APPENDIX. 
 
 479 
 
 TABLE VII. 
 
 The approximate force of the Wind, /', upon a square foot of Normal Surface, 
 and the diameter D of a sphere of the density of water supported in the air 
 by an ascending current, for the several Velocities s and Barometric Pres- 
 sures P, used as arguments. 
 
 S| 
 
 BAROMETRIC PRESSURES P IN MILLIMETERS. 
 
 fcjL 
 
 760 
 
 700 
 
 600 
 
 500 
 
 400 
 
 II 
 
 r 
 
 D 
 
 f 
 
 D 
 
 P' 
 
 D 
 
 f 
 
 D 
 
 P' 
 
 D 
 
 
 pounds 
 
 inches. 
 
 pounds 
 
 inches. 
 
 pounds. 
 
 inches. 
 
 pounds. 
 
 inches. 
 
 pounds. 
 
 inches. 
 
 5 
 
 O.I 
 
 O.OI 
 
 O.I 
 
 O.OI 
 
 O.I 
 
 O.OI 
 
 0.0 
 
 O.OI 
 
 0.0 
 
 O.OI 
 
 10 
 
 0.3 
 
 0.04 
 
 0-3 
 
 0.04 
 
 0.2 
 
 O.O4 
 
 O.2 
 
 0.03 
 
 O.2 
 
 0.03 
 
 15 
 
 0-3 
 
 O. IO 
 
 0.6 
 
 O.IO 
 
 0.6 
 
 0.09 
 
 0-5 
 
 0.07 
 
 0. 4 
 
 0.06 
 
 20 
 
 1.2 
 
 0.18 
 
 i.i 
 
 0.17 
 
 I.O 
 
 0.15 
 
 0.8 
 
 0.12 
 
 0.7 
 
 O.IO 
 
 25 
 
 I.g 
 
 0.27 
 
 1.8 
 
 0.26 
 
 1-5 
 
 0.23 
 
 1-3 
 
 O.ig 
 
 I.I 
 
 0.16 
 
 30 
 
 2.7 
 
 0.40 
 
 2-5 
 
 0-37 
 
 2.2 
 
 0.32 
 
 
 0.27 
 
 1.6 
 
 0.22 
 
 35 
 
 3-7 
 
 o.54 
 
 3-5 
 
 0.50 
 
 3O 
 
 0.44 
 
 2.6 
 
 0-37 
 
 2.1 
 
 0.31 
 
 40 
 
 4.9 
 
 0.70 
 
 4-5 
 
 0.65 
 
 4.0 
 
 0-57 
 
 3-4 
 
 0.48 
 
 2.8 
 
 O.4O 
 
 45 
 
 6.2 
 
 0.89 
 
 5-7 
 
 0.83 
 
 5-O 
 
 0.72 
 
 4.2 
 
 0.62 
 
 3-5 
 
 0-51 
 
 50 
 
 7-6 
 
 I. IO 
 
 7- * 
 
 I. O2 
 
 6.2 
 
 0.99 
 
 5-3 
 
 0.76 
 
 4-3 
 
 0.63 
 
 55 
 
 9-2 
 
 1-33 
 
 8.6 
 
 1.24 
 
 7.1 
 
 I. II 
 
 6.4 
 
 0.88 
 
 5-2 
 
 0.75 
 
 60 
 
 II. O 
 
 1.58 
 
 10.2 
 
 1.47 
 
 8.9 
 
 1.28 
 
 7.6 
 
 .09 
 
 6.2 
 
 
 65 
 
 12.9 
 
 i 86 
 
 12. 
 
 1-73 
 
 10.4 
 
 1.51 
 
 8.9 
 
 .28 
 
 7.3 
 
 !o6 
 
 70 
 
 15-0 
 
 2-15 
 
 13-9 
 
 2.00 
 
 12. 1 
 
 1.74 
 
 10.3 
 
 .49 
 
 8-5 
 
 23 
 
 75 
 
 17.2 
 
 2.47 
 
 16.0 
 
 2.30 
 
 13-9 
 
 2.00 
 
 ii. 8 
 
 71 
 
 9.8 
 
 .41 
 
 80 
 
 19-5 
 
 2.81 
 
 18.2 
 
 2.62 
 
 I 5 .8 
 
 2.28 
 
 13-5 
 
 -94 
 
 n. i 
 
 .60 
 
 85 
 
 22. 
 
 3 17 
 
 20.5 
 
 2-95 
 
 I 7 .8 
 
 2-57 
 
 15-2 
 
 2.18 
 
 12.5 
 
 ,80 
 
 90 
 
 24.7 
 
 3.56 
 
 23-0 
 
 3-31 
 
 20. o 
 
 2.88 
 
 17.0 
 
 2-45 
 
 14.1 
 
 2.02 
 
 95 
 
 2 7 .6 
 
 3-97 
 
 25.6 
 
 3-70 
 
 22.4 
 
 3-22 
 
 19.0 
 
 2.74 
 
 15-7 
 
 2.26 
 
 100 
 
 30.5 
 
 4.40 
 
 28.4 
 
 4.09 
 
 24.7 
 
 3.56 
 
 21.0 
 
 3.03 
 
 17.4 
 
 2.50 
 
 These functions have been computed from the formulae of 246, 247, using 
 the temperatures given in 13, corresponding to the several barometric pres- 
 sures. For exceptionally great velocities, these functions can be obtained from 
 those above by taking them as the squares of the velocities. 
 
BOOKS AND PAPERS REFERRED TO. 
 
 1. Recent Advances in Meteorology; by W. Ferrel. Annual Report of 
 
 the Chief Signal Officer, Part II, 1885. 
 
 2. Mendeleefs Researches on Mariotte's Law. Nature, vol. xv. p. 455. 
 
 3. Meteorological Researches, Part III ; by W. Ferrel. Report of the 
 
 Superintendent of the Coast and Geodetic Survey for 1881. 
 
 4. On the Mechanical Equivalent of Heat; by Prof. Rowland. Proc. 
 
 Am. Academy of Arts and Sciences. See also Paper by F. Neesen 
 of Berlin, Annalen der Physik und der Chimie, and by G. A. 
 Liebig, Sillimans Journal, July 1883. 
 
 5. The Laws of the Variation of Temperature in Ascending and De- 
 
 scending Currents deducible therefrom ; by Dr. J. Hann. Trans- 
 lated by Professor Cleveland Abbe from Zeitsch. Oest. Gesell.fiir 
 Met. 1874, and published in the Smithsonian Report for 1877. See 
 also Recent Advances in Met., p. 46, in which very slight changes 
 are introduced. 
 
 6. The Effect of Temperature upon the Viscosity of Gases; by Pro- 
 
 fessor Silas W. Holman. Proc. Am. Academy of Arts and Sciences, 
 vol. xxi, 1885. 
 
 7. Concerning the Cause of the General Trade-winds ; by Geo. Hadley, 
 
 Esq. Phil. Trans., 1735. 
 
 8. Meteorological Researches, Part I ; by W. Ferrel. Report of the 
 
 Superintendent of the Coast Survey for 1875, Appendix No. 20. 
 
 9. Ueber die Temperatur der Siidlichen Hemisphere. Sitz. der k. 
 
 Akad der Wissensch., 1882. 
 
 10. Meteorological Researches, Part II; by W. Ferrel. Report of the 
 
 Superintendent of the Coast Survey for 1878, Appendix No. 10. 
 
 11. Zeitschrift der Oest. Gesellschaft fur Meteorologie, Band 17, Seitc 17. 
 
 12. Smithsonian Report for 1857. 
 
 13. The Law of Storms; by H. W. Dove; Translated by R. H. Scott, 
 
 M.A. ; p. 37. 
 
 14. Principles of Geology. 
 
 15. Proceedings of the Royal Geog. Society. Also Popular Science 
 
 Monthly, July 1884. 
 
 16. Report of Chief Signal Officer. 
 
 480 
 
APPENDIX. 481 
 
 17. Contributions to Meteorology ; by Elias Loomis. Memoirs of tht 
 
 National Academy of Sciences, vol. Ill, Part II, 1886. 
 
 18. Physical Geography in its Relation to the Prevailing Winds and 
 
 Currents. 
 
 19. Coffin ; Winds of the Globe, p. 284. 
 
 20. Analysis and Discussion of the Winds, Appendix to Coffin's Winds 
 
 of the Globe ; by A. Woeikof. 
 
 21. Die Atmospharische Circulation, Verbreitung des Luftdruckes der 
 
 Winde und der Regen auf der Oberflache der Erde. Petermann's 
 Mittheilungen, Ergdnzungsheft, No. 38. 
 
 22. Contributions to Meteorology. Eighteenth Paper. Silliman's Jour- 
 
 nal. vol. xxv, January 1883. 
 
 23. The Physical Geography of the Sea. 
 
 24. Ueber das Klima am Congo und an derS.W. Kiiste von Africa iiber- 
 
 haupt; by Dr. A. v. Danckelman. Oest. Zeitsch. fiir Meteorologie, 
 December 1885. Taken from his work entitled Mtmoire sur les 
 observations mettorologique faite a Vivi (Congo Inftrieur) et sur la 
 climatologie de la cote Sud-Ouest d'Afrique. 
 
 25. Zeitsch. der Oester. Gesellschaft fiir Meteorologie, B. 16, S. 354. 
 
 26. Zeitsch. der Oester. Gesellschaft fiir Meteorologie, B. 19, S. 496. 
 
 27. Petermann's Mittheilungen, B. 24, 1878. 
 
 28. Report of Commander E. P. Lull on the Panama Inter-oceanic Ship 
 
 Canal. 
 
 29. Selections from the Works of Humboldt ; by John Taylor. 
 
 30. The Rain-cloud and the Snow-storm ; by Charles Tomlinson, F.C.S. 
 
 31. Isotermas de la Mitad Austral de Sud-America. Officina Meteorolog. 
 
 Argent., Tomo III. 
 
 32. Quar. Journal Met. Soc., London, vol. I, p. 203. 
 
 33. Die Klimate der Erde. Von Dr. A. Woeikof. 
 
 34. Philosophy of Storms ; by James P. Espy, A.M. 
 
 35. United States Exploring Expedition. 
 
 36. Voyage to the Southern Seas, vol. n, p. 283. 
 
 37. Notes on the Meteorology and Physical Geography of the West 
 
 Coast of Africa, etc. ; by Commander Edmund George Burke, 
 R.N., F.M.S. Jour, of the Met. Soc., vol. IV, 1878. 
 
 38. The Storm and Low Barometer of December 8th and 9th, 1886; by 
 
 Charles Harding, F. R. Met. Soc. Quar. Jour. Roy. Met. Soc., vol. 
 XIII, July 1887. 
 
 39. Journal of the Scottish Meteorological Society, 1873, p. 66. Also 
 
 Quarterly Journal of the Meteorological Society, October 1877. 
 
 40. Quarterly Journal of the Met. Society, 1877, P- 437- 
 
 41. Contributions to Meteorology. Nineteenth Paper. Silliman's Jour- 
 
 nal, January 1878. 
 
482 APPENDIX. 
 
 42. Apuntes relatives a los huracanes de las Antillas en Setiembre y 
 
 Octobre de 1875 y 1876 ; by R. P. Benito Vines, S. J. 
 
 43. Sur la distribution des elements meteorologique autour des minima 
 
 et des maxima barometrique. Upsala, 1883. 
 
 44. Zeitschrift der Oest. Gesellschaft fur Meteorologie, October 1878. 
 
 45. Repertorium fur Meteorologie, Bd. vu, No. 5. 
 
 46. Laws of the Winds ; by Rev. Clement Ley. 1873. 
 
 47. Motions of Fluids and Solids relative to the Earth's Surface ; by W. 
 
 Ferrel. Runkles Math. Monthly, 1859. Reprinted by the Signal 
 Service, with notes by Frank Waldo, junior, Professor in the Signal 
 Service. 
 
 48. Hurricane in Fiji ; by Robert Langley Holmes, F. R. Met. Soc. 
 
 Quar. Jour. R. Met. Soc., January 1878. 
 
 49. Appendix to the Observations and Researches made at the Hong 
 
 Kong Observatory, in the year 1884; by Dr. W. Doberck. Met. 
 Zeitschrift, April 1886. 
 
 50. Weather. A Popular Exposition of Weather Changes from day to 
 
 day; by the Hon. Ralph Abercromby. London 1887. 
 
 51. Contributions to Meteorology. Seventh Paper. Sillimans Journal, 
 
 July 1877. 
 
 52. Observations and Researches made at the Hong Kong Observatory, 
 
 in the year 1886; by W. Doberck, Government Astronomer. 
 App. B. 
 
 53. Contributions to Meteorology. Second Paper. Silliman' s Journal, 
 
 January 1875. 
 
 54. Piddington's Sailor's Horn-book. Fifth Edition. 1869. 
 
 55. On the Mean Direction and Distribution of Lines of equal Barometric 
 
 Pressure, and their Relation to the Mean Direction and Force of 
 the Wind over the British Isles, etc. Proceedings R. Society, 
 vol. xxv. 
 
 56. The Mean Direction of Cirrus Clouds over Europe. Quar. Jour. 
 
 Met. Society, October 1885. 
 
 57. Cold Waves and their Progress ; by Lieut. Thomas M. Woodruff, 
 
 Signal Service Notes, No. 23. 
 
 58. The Northers of Texas ; by Solomon Sias. Proceedings of the Am. 
 
 Ass. for the Advancement of Science, vol. XIX, 1871. 
 
 59. On the Pamperos of Central Uruguay; by David Christison, M.D. 
 
 Jour. Scottish Met. Soc., 1880. 
 
 60. Atlas der Meteorologie (Berghaus' Physikalischer Atlas, Abtheilung 
 
 III); von Dr. Julius Hann. Gotha : Justus Perthes. 1887. 
 <6i. American Meteorological Journal; November 1886, and February 
 
 and March 1887. 
 62. Science, June 8, 1886, 
 
APPENDIX. 483 
 
 63. Contributions to Meteorology. Eighth Paper. Sillimans Journal^ 
 January 1878. 
 
 64. Annuaire de la Societe Meteorologique de France, 1880. 
 
 65. Messung des Widerstandes, den Planscheiben erfahren wenn sie in 
 
 normaler Richtung gegen ihre Ebenen durch die Luft bewegt 
 werden. 1874. 
 
 66. On the Resistance experienced by Bodies falling through the Atmos- 
 
 phere. Sillimaris Journal, second series, vol. XVIII, p. 67. 
 
 67. Symon's Meteorological Magazine, January 1880. 
 
 68. Tornado Force; by W. W. Anderson, M.D. Science, vol. X. 
 
 69. Report of Chief Signal Officer for 1875. 
 
 70. Report of Chief Signal Officer for 1878. Paper 43. 
 
 71. Report of Chief Signal Officer, 1877, p. 518. 
 
 72. Report of the Tornadoes of May 29 and 30, 1879, in Kansas, Nebraska, 
 
 Missouri, and Iowa, by Sergeant (now Lientenant) J.P.Finley, Signal 
 Corps, U. S. A. Professional Paper of the Signal Service, No. 4. 
 
 73. Report on the Character of Six Hundred Tornadoes. Professional 
 
 Paper of the Signal Service, No. 7. 
 
 74. Silliman's Journal, vol. IV, p. 362. 
 
 75. Waterspout in Fenland. Nature, vol. vi, p. 44; 1872. 
 
 76. Scientific American. Also Am. Met. Journal, vol. Ill, p. 227. 
 
 77. Journal de Physique, vol. LXXXVIII. 
 
 78. Nature; July 19, 1883. 
 
 79. Bulletin Soc. Geologique de France, t. vm, p. 274. 
 
 80. Foreign Studies of Thunder-storms. Am. Met. Journal ; March, 
 
 May, and June 1886. 
 
 81. Thunder-storms in New England in the summer of 1885. Proc. Am. 
 
 Academy of Arts and Sciences, Boston, vol. XXII, July 1886. 
 
 82. Pressure Changes during Thunder-storms. Am. Met. Jour., vol. II, 
 
 p. 287. 
 
 83. Thunder-storms of May 1884. Signal Service Notes, No. 20. 
 
 84. Diurnal Periods of Thunder-storms in Scotland. Jour. Scott. Met. 
 
 Soc., vol. v, 1880. 
 
 85. Silliman's Journal, vol. I, p. 403; 1870. 
 
 86. Espy's Fourth Meteorological Report. 
 
 87. Whirlwinds produced by the Burning of a Cane-brake. Silliman's 
 
 Jour., 2d series, vol. XI, p. 181. 
 
 88. Whirlwinds excited by Fires. Sillimans Jour., 2d series, vol. XXXVI. 
 
 89. Whirlwind observed at Schell City, Mo. Nature, Sept. n, 1879. 
 
 -90. Beitrage zur Gewitterkunde. Von Dr. Ciro Ferrari. Met. Zeit- 
 
 schrift, January 1888. 
 91. Science, July 20, 1888, p. 33. 
 .92. Monthly Weather Review of the Signal Service, May 1888. 
 
INDEX. 
 
 Abercromby. Observations of upper equatorial currents of air, 127 
 Phenomena attending the approach of cyclones, 301 
 Remarks on the eye of the storm, 312 
 Thunder-storms, 451 
 Acceleration, 9-44 
 Air (see also Atmosphere.) 
 Dry, i 
 
 Dry and pure, i 
 The density of, 13 
 
 Dynamical heating and cooling of the, 20 
 The expansion of, 24 
 The specific heat of, 25 
 Weight of dry, 25 
 
 Amount of work done by heating, 26 
 Heating effect of compressing, 27 
 Cooling effect of expanding, 27 
 
 Cooling and heating of, in ascending and descending currents, 27 
 Ascending and descending saturated, 30, 31 
 Rates of decrease of temperature of saturated ascending, for different 
 
 temperatures and altitudes, 31 
 
 Normal rate of cooling for ascending currents of, 33 
 Height at which ascending moist, becomes saturated, 33 
 Stable and unstable equilibrium, 34-39 
 Relation between altitude and density of, 39 
 The viscosity of the, 40 
 
 Effect of the general motions of the, upon atmospheric pressure, 133 
 Interchanging motions of the, between the two hemispheres, 141 
 Conditions of the, within the rain-belt, 167 
 
 Great tendency of heated currents of, on plateaus, to ascend, 198 
 Outflow of, from interior Asia in winter, 206 
 Anderson, Dr. Observation on direction of strong winds in tornadoes, 397 
 
 Observations on discontinuity of line of destruction in the tornado 
 of April, 1883, 399 
 
 485 
 
486 INDEX. 
 
 Aqueous Vapor of the atmosphere, 16 
 
 Distribution of, according to Dalton's law, 17 
 The maximum tension of, 17 
 Distribution of, 101, 102 
 Areas, The principle of the preservation of, 54-59 
 
 The principle of equal, in motions on the earth's surface, 65-70- 
 Application of the principle of equal, 67 
 
 Principle of the preservation of, applied to vertical currents, 116 
 Atmosphere, Constitution and nature of the, i 
 Composition of the, I 
 Arrangement of the constituents of the, 4 
 Pressure of the, 9 
 The height of a homogeneous, 14 
 Hypothetical, 14 
 
 Law of the heights of homogeneous, 15 
 Tables of pressures of the, at various heights, 15 
 The general circulation of the, 89-162 
 Superior limit of the, 89 
 
 General circulation of the, without rotation of the earth, 102-106 
 Neutral plane in the motions of the, 105 
 Vertical circulation of the, 105 
 
 General circulation of the, with rotation of the earth, 106-133 
 Principle of preservation of areas applied to vertical currents 
 
 of the, 116 
 
 Complexity of the circulation of the, 119 
 
 Observed circulation of the, compared with the theoretical, 121 
 Easterly currents of the upper strata of the, 121 
 Annual inequality in the easterly and westerly motions of the, 131 
 Effect of the general motions of the air upon the pressure of the, 
 
 133-145 
 
 Effect of the upward expansion ofjthe, on the isobaric surfaces, 134 
 General distribution of pressure of the, along a meridian, 136 
 Equatorial depression of pressure of the, 136 
 The greatest pressure of the, at the earth's surface, 136 
 Zones of high and low pressure of the, on the earth's surface, 139 
 Table showing decrease of pressure of the, from the tropics, 140 
 Annual inequality of pressure of the, due to differences in tem- 
 perature gradient, 141 
 
 Interchanging motions of the, between the two hemispheres, 142 
 Annual inversion of pressure gradients of the, 142 
 Annual mean pressure of the, and annual inequality for various 
 
 latitudes, 143 
 Comparison with theory of the observed pressure of the, and its. 
 
 inequalities, 144 
 
 Annual inequality of the pressure of the, greater in the northern 
 than in the southern hemisphere, 144 
 
INDEX. 487 
 
 Atmosphere, Study of the general motions and pressures of the, 148 
 
 Necessity for excess of polar and equatorial over east and west 
 
 motions of the, in case of much friction, 150 
 No east and west motion of the, at the earth's surface on the 
 
 parallel of maximum pressure, 153 
 Summary and graphic representation of the motions and pressure 
 
 of the, 154-156 
 
 Climatic influence of the general circulation of the, 163 
 Vertical circulation of the, in the calm-belt, 167 
 
 Balloon ascensions, 7 
 Barnard tornado, 389 
 
 Barometer, The reduction of the, to sea-level and for latitude, 10 
 " Pumping" of the, 448 
 Vines' remarks on pumping of the, 449 
 Barometric gradient, 83 
 
 Mathematical expressions for the, 83-85 
 Conditions for making the, vanish, 137 
 Vertical distribution of, 138 
 
 Barometric pressure, Zones of high and low, on the earth's surface, 139 
 Effect of the zones of high, 150 
 Areas of high, 342-346 
 Bora, The, 331 
 
 Boue. Observation of the hollow centre of water-spouts, 419 
 Boyle and Mariotte's Law, 2 
 
 Deviation from, 3 
 
 Brault's charts of wind directions, 184 
 
 Brown, J. Allen. Tables of inclination of winds in cyclones, 265 
 Buch, Leopold. Remarks on winds at Teneriffe, 126 
 Buchan, Isothermal charts of, 100 
 
 Reference to temperature charts of, 180 
 Winter thunder-storms at Stykkisholm, 471 
 Burke, Observations of sea-breezes on coast of Guinea by, 222 
 Buy-s Ballot's Law for direction of wind, 263 
 
 Calms and calm-belts, 149 
 
 Calms, Surface, in cyclones (see also under Cyclones), 257 
 
 Calm-belts and calms, 149 
 
 Annual oscillations of the, 156-162 
 Calm-belts, Mean position of the equatorial, a little north of the equator, 157 
 
 Causes of the equatorial, 158 
 
 Limits and oscillations of the equatorial, 159 
 
 Oscillations of the, of the Pacific Ocean, 162 
 
 Weather under the cloud-ring of the, 168 
 
 Calm-belts, Lower temperature in the, according to Espy, Wilkes, and Hum- 
 boldt, 169 
 
INDEX. 
 
 Peculiarities of climate within range of oscillation of rain-belt and, 
 
 169, 170 
 
 Regularity of atmospheric phenomena in the, 177 
 Centrifugal force, and gyratory velocity, 47 
 Ratio of, and gravity, 48 
 Mathematical expression for, 53, 54 
 in motions on the earth's surface, 60-65 
 of the earth's rotation, 61 
 Horizontal component of, 62 
 Acceleration of the, at the equator, 63 
 General expression for the horizontal component of, 64 
 Barometric gradients depending upon, 85 
 Charles and Gay-Lussac, Laws of, 3, 4 
 Charles, Deviation from the law of, 3 
 Chinook winds, Description of, 334 
 
 Investigation of, by Harrington, Dawson, 334, 335 
 Christison, Investigation of the pamperos of Uruguay by, 329 
 Clayton, Observations of pressure gradient in thunder-storms by, 465 
 Climate, Effect of the general circulation of the winds on the, of the higher 
 
 and lower latitudes, 163, 164 
 Characteristics of a continental, 181 
 
 Differences of the, on eastern and western coasts, 181, 182 
 Influence of mountain ranges on, 183-192 
 
 Clouds, Resultant directions of the motions of, at Toronto, Canada, 122 
 Directions and frequency of cirrus, at Zi-ka-wei, 122, 308 
 Motions of the, at Colonia Tover, Venezuela, 123 
 Remarks of Ley on the motions of cirrus, 121, 308 
 Height at which, are formed, 239 
 Formation and disappearance of, 239 
 Mares' tails, 300 
 Cloud-bursts, Account of, 429-434 
 
 in the Hollidaysburg, Pa., tornado, observed by Espy, 431 
 Accounts of, at Catskill, N. Y.; Ft. Keogh, Mont.; and Ft. Eliott, 
 
 Tex., 431, 432 
 
 Down-pour of water from, 430, 432 
 Coffin, Prof., Velocity of resultant motion, for the year, of the air in the U. S., 
 
 by, 129 
 
 Annual inequality of resultant wind velocities in U. S. , by, 133 
 Prevailing wind directions, by, 186 
 
 Collins, Lieut. Observations of rainfall at Nicaragua, 175 
 Cold-waves, Woodruff's investigation of, in U. S., 322 
 as trough phenomena of cyclones, 327 
 Explanation of, in Mississippi Valley, by Hinrichs, 329 
 Condensation, Latent heat given out in, 29 
 Continuity, The condition of, 94 
 
INDEX. 489 
 
 Curvature, Radius of, 48 
 Cyclones, 226 
 
 Definition and general causes of, 227 
 
 Vertical circi: ation in, 227-240 
 
 Sustaining power of the vertical circulation in, 230, 231 
 
 Vertical temperature gradients in, 229, 230 
 
 Stable and unstable atmosphere in, 229 
 
 A cause of the vanishing of the force of, 234 
 
 Ascending and descending currents in, due to the various temperature 
 gradients, 234-239 
 
 Dew-point in the vertical circulation of, 237 
 
 Vertical circulation in, with change of temperature gradient with 
 height, 240 
 
 Irregularity of temperature gradient in, 240 
 
 Undefined outer limit to, 241 
 
 Gyratory motion of, 241 
 
 Rotation of the earth on its axis the cause of the gyratory motion 
 in, 242 
 
 Gyratory motion of the air from right to left in, 242 
 
 Inflow of air below and outflow above in, 243 
 
 And. Definition of, 243 
 
 Application of the principle of the preservation of areas in, 244 
 
 Centrifugal and centripetal forces in, 244 
 
 Motion of limited, compared with the atmospheric motions of a 
 whole hemisphere, 246 
 
 Motions toward the centre in, 247 
 
 Conditions which might prevent vertical circulation in, 248 
 
 Momentum and inertia of the air in, 250 
 
 Law of decrease of the relative velocities of the gyrations above and 
 below in, 250 
 
 Relative gyratory velocities in, and anti-cyclones, 250 
 
 Atmospheric pressure in, 251 
 
 Effect of the upward expansion of the air on the pressure in, 252 
 
 Gyratory velocity and barometric gradient in, 252 
 
 The region of greatest pressure in, 254 
 
 Pressure distribution above the earth's surface in, 254 
 
 Resultant motions in, 255 
 
 Definition of the inclination in, 255 
 
 The ring of highest pressure in, 256 
 
 Effect of the viscosity of the air upon the gyratory and vertical circu- 
 lation in, 256 
 
 Ratio between the radial and gyratory velocities near the centre of, 257 
 
 Surface calms in, 257 
 
 Graphic representation of motions and pressures in, 258-261 
 
 Relative direction of upper and lower currents in, 261 
 
49 INDEX. 
 
 Cyclones, Comparison of the theory of, with observation, 261-271 
 
 Inclination of the wind at the earth's surface in, according to Redfield^ 
 Buys-Ballot, Ley, Loomis, Brown, Vines, Hildebrandsson, Hoff- 
 meyer, Spindler, Toynbee, and Piddington. 262-265 
 
 Inclination of winds in, according to Loomis, 264 
 
 Difference of inclination of winds in front and rear of, 265 
 
 preceded and followed by unusually high barometer, according to 
 Redfield and Espy, 269, 270 
 
 Upper currents of air in, according to Ley, Hildebrandson, and Loo- 
 mis, 270-271 
 
 Gradual enlargement of, 273, 274 
 
 Dimensions of the violent part of, according to Redfield, Piddington, 
 and Reid, 274 
 
 Progressive motion of, 275-286 
 
 Loomis' tables of the motions of centres of, in U. S. , Atlantic Ocean, 
 and Europe, 276 
 
 Polar tendency of, in lower latitudes, 277 
 
 Motions of, on east coasts of U. S., China, S. Africa, and at the Fiji 
 Islands, 278 
 
 Parabolic form of the path of, 279 
 
 Direction and velocity of westwardly moving, according to Loomis, 279 
 
 Paths of, in various quarters of the globe, 280 
 
 Table of annual period of frequency of, in several seas, 282 
 
 Cause of the more rapid progress of, in U. S. than in Europe, 283 
 
 Aqueous vapor in, 283 
 
 Effect of differences of temperature on polar and equatorial sides of,. 
 284, 285 
 
 Effect of, upon the isotherms, 285 
 
 , Veering and backing of the wind, and changes of pressure and tempera- 
 ture in, 287-292 
 
 Phenomena attending the passage of, 288 
 
 Changes of wind on the north and south side of, during the eastward 
 passage, 289 
 
 Backing and veering of the wind in, 289 
 
 Preponderance of veering winds in, in the middle latitudes of U. S. 
 and Europe, 289 
 
 Passage of, in the southern hemisphere, 290 
 
 Line squalls in, 290 
 
 Loomis' results of inclination and velocity of winds in the four quad- 
 rants of, 291 
 
 Ellipticity of the isobars in, 291 
 
 of Aug. 2, 1837, at St. Thomas, 292 
 
 Typhoon at Manilla, Nov. 5, 1882, 295 
 
 of Cienfuegos on Sept. 5, 1882, 297 
 
 Rain and cloud areas in, 298-303 
 
 Form and position of rain areas in, according to Loomis, 299 
 
INDEX. 491 
 
 Cyclones, Form and position of cloud areas in, 300 
 Cirrus clouds as precursors of, 300 
 with little rain according to Loomis, 301 
 Phenomena attending the approach of, according to Abercromby, 
 
 Vines, and Doberck, 301, 302 
 Phenomena after the passage of, 302 
 
 Relations between the progressive velocities of the air and, 304 
 v Dangerous side of, 307 
 
 Wind velocities and inclinations at Mt. Washington in, according to 
 
 Loomis, 308 
 The " eye of the storm" or "bull's-eye" in, as remarked on by Dove, 
 
 Captain Salis, Dr. Malcolmson, Abercromby, 311, 312 
 Secondary, 315-317 
 Occurrence of secondary, in the southern and eastern quadrants of 
 
 primary cyclones, 316 
 
 Showery weather produced by secondary, 317 
 Stationary, 318-322 
 
 Geographical positions of some stationary, 322 
 with cold centre, 337-342 
 Cause of, with cold centre, 337 
 The poles the centres of, with cold centre, 338 
 with cold centre may or may not have a minimum pressure at the 
 
 centre, 339 
 
 with cold centre in Europe, Asia, and N. America, 340 
 Difficulty of locating the centres of, 341 
 and tornadoes compared, 347 
 Relation between, and thunderstorms, 467-470 
 
 Octants of, containing least and greatest number of thunder-storms, 468 
 Cyclonic gyrations, 243 
 
 Anti-, gyrations, 244 
 
 gyrations caused by any given temperature disturbance are most violent 
 
 near the poles, and vanish at the equator, 244 
 Resultants of, and progressive motions, 303-311 
 
 Dalton's law, i 
 
 Arrangement of constituents according to, 6 
 Dampier. Remarks on land- and sea-breezes, 221 
 Danckelman. Table of rainfall on the Congo, 172 
 Davis. Thunder-storms in New England, 450 
 Dawson. On the Chinooks, 335 
 Defecting force of the earth's rotation, 77 
 
 Effect of the, of the earth's rotation on projectiles fired upward, 87; 
 Defranc. Description of small water-spouts, 416 
 
 Remarks on times of occurrence of water-spouts, 441 
 Delphos tornado, 388 
 Density, Relative, of gases, 6 
 
-49 2 INDEX. 
 
 Density, Relation between changes of altitude and, 39 
 Deviation of a rifle-ball due to the earth's rotation, 86 
 
 due to the earth's rotation of a projectile describing a parabolic curve, 87 
 Dew-point, 18, 401 
 Dines. Size of rain-drops, 380 
 Doberck. Observations of typhoons in China Sea and Philippine Isles, 268 
 
 Phenomena attending the approach of cyclones, 302 
 Dove. Tables of the Pacific trades, 161 
 
 Cylones, 289, 292 
 
 Cyclone of Aug. 2, 1837, at St. Thomas, 292 
 
 Remarks on eye of the storm, 311 
 
 Earth's rotation, Deflecting force of the, 77-88 
 
 Elementary proof of the effects of, 78 
 
 Illustration of the effects of, 79 
 
 Deduction of absolute amount of deflecting force due to, 
 
 80, 8 1 
 
 Numerical value of the effects of, on rivers, 81 
 Numerical computation of the effects of the, on railroad trains, 82 
 Effect of the, on tornadoes, 352 
 
 Effendi Emin. Rainfall observed in the travels of, from Mreili to Rubaga, 174 
 Elliot. Thunder-storms in India, 450 
 Energy, potential, kinetic, and thermal, 21 
 
 The conservation of, 23 
 Equilibrium, General principles of stable and unstable, 34 -36 
 
 Vertical distribution of temperature causing stable and unstable, 
 
 35, 36 
 
 Indifferent state of, 37 
 Espy. Easterly motion of the upper currents, 121 
 
 Remarks on low barometric pressure in the southern hemisphere, 140 
 Lower temperature in the calm-belt, 169 
 Remarks on the northwest monsoon, 208 
 Remarks on the northern monsoon, 209 
 Sudden rise of the barometer preceding storms, 270 
 Researches on the ellipticity of isobars in cyclones, 291 
 on the foehn, 332 
 Formation of a cloud, 402 
 Motions of the low clouds in a hurricane, 410 
 Observations of cloud-bursts, 430, 431 
 Whirlwinds produced by great fires, 443 
 Evaporation, Daily amount of, within the tropics, 164 
 
 Falling bodies, 45 
 
 Ferrari. Thunder-storms in Italy, 451, 455 
 
 Origin of thunder-storms, 456 
 Finley. Account of tornadoes of May 29 and 30, 1879, 386-389 
 
INDEX. 493; 
 
 Finley. Width of the path of destruction of tornadoes, 390 
 Direction of the rotary motion of tornadoes, 395 
 Velocity of progression of tornadoes, 395 
 Direction of progressive motion of tornadoes, 396 
 Intermittent action of the Lee's Summit tornado, 407. 
 Hail in tornadoes, 420 
 
 The times of greatest frequency of tornadoes, 441 
 Thunder-storms in tornadoes, 450 
 Fluids, Motions of inelastic, 90 
 Flow of, 90 
 Pressures in, 91 
 
 Motions in, of uniform density, 90 
 Motions in, of different densities, 91 
 Motion of, in canals of definite lengths, 92 
 Continuity in the motions of, 94 
 Frictional resistances in the motion of, 94 
 Oscillatory, interchanging horizontal motions of, 96 
 Orbit of particles of, moving in closed canals, 97 
 Motions of, in wedge-shaped canals, 94 
 Motions of, in the open ocean from equator to pole, 97 
 Foehn, 332-335 
 
 Explanation of, by Espy and Hahn, 332, 333 
 Force or pressure, 12 
 
 Centrifugal, 42-45 
 
 Formula for relative gyratory, 59 
 
 Mathematical expression for the deflecting, 64 
 
 Resultants of the two, and motions, 71 
 
 The deflecting, not a real force, 73 
 
 Mathematical expression for deflecting, 72 
 
 Deflecting, general remarks on, 73-74 
 
 Torsional, arising from the effects of the earth's rotation on motion* 
 
 caused by temperature gradients, 113 
 
 Motions due to the actions of a central, 242 [ 2 44 
 
 Centrifugal and centripetal, in cyclones arising from pressure gradients, 
 Freezing, The reduction to, 10 
 Plane of incipient, 30 
 
 Gases, Elasticity of, 2 
 
 Specific volume of, 2 
 
 The relation of pressure and volume in, 2 
 
 Kinetic theory of, 2 
 
 Relation of volume and temperature in, 3 
 
 at low pressure. Mendeleef's experiments, & 
 
 Relative density of, 6 
 Gay-Lussac and Charles' law, 3, 4 
 Gentry County tornado, 389 
 
494 INDEX. 
 
 Glaisher. Balloon ascents, 232 
 
 Gould, Dr. Isothermal charts of southern S. America, ic,2 
 'Gradient, Measure of the, 49 
 Ascending, 49 
 Relation between the, the gyratory velocity and distance from the 
 
 centre, 50 
 
 on a railway curve, 51 
 between the two banks of a river, 51 
 Linear, of an isobaric surface at various altitudes due to difference of 
 
 temperatures, 103 
 
 Change of, with change of altitude, 104 
 General expression of barometric, corresponding to any given velocity 
 
 in any direction, 135 
 
 Table of barometric, for various latitudes, 143 
 'Gravity, The force of, 9 
 
 The reduction to standard, 10 
 Ratio of centrifugal force and, 48 
 Gyratory velocity, 46 
 
 Equation for the absolute, 67 
 
 Its effect on pressure (see also under Tornadoes), 508-521 
 Gyratory motion, 52 
 
 in cyclones (see also under Cyclones), 241 
 
 Hadley's principle, 68 
 
 principle compared with the author's, 69 
 
 remarks on motions and counter- motions of the atmosphere, 117 
 Hagen, Experiments on wind, velocity, and pressure, 373 
 Hail, Theory of the formation of, 420-422 
 -storms, 420^-429 
 
 -stones, Shape of. Hinrichs, 428 
 
 -falls in Lee's Summit, Delphos, and Lincoln tornadoes, 428 
 Abnormal fall of, at Ft. Elliott, 432 
 Theory of the formation of chunks of, 434 
 Hann. Isothermal charts, 100 
 on the foehn, 333 
 
 Reference to description of the Sirocco, 337 
 
 Harding. Account of storm in the British Isles, Dec. 8 and 9, 1886, 261 
 Harrington on chinooks, 334 
 
 Hazen, Location of thunder-storms with reference to cyclonic areas, 470 
 Heat, The unit of, 23 
 
 The mechanical equivalent of, 23 
 
 Capacity of the atmosphere for, compared with that of the ocean, 163 
 Relative amounts of, transferred by atmospheric and oceanic circulation, 164 
 Latent, of condensation in the calm-belt strengthens the trade-winds, 167 
 Hildebrandsson. Observations on the inclination of winds in the front and rear 
 of cyclones, 267 
 
INDEX. 495 
 
 Hildebrandsson. Observations on the upper currents, 271 
 
 Direction of cirrus clouds over stationary cyclones, 320 
 Himalayas, Mountain winds in the, 223 
 Hinrichs. Shape of hailstones, 428 
 
 Observations of storm front by, 454 
 
 Hoffmeyer. Observations on inclination of winds in cyclones, 265 
 Hooker, Dr. Rainfall in Khasia, 205 
 Horner. Diameters of water-spouts, 408 
 Houry, Mr. Description of hailstones, 425 
 Humboldt. Lower temperature in the calm-belt, 169 
 
 Wet and dry seasons in equatorial Mexico, 176 
 
 Wet and dry seasons in S. America, 177 
 
 Sand spouts on the Orinoco, 444 
 Humidity, Relative, 19 
 
 Average relative, for the earth's surface, IO2 
 Hutton. Experiments on the resistance of air, 377 
 
 Irving tornado, 387 
 
 isobaric surfaces, General forms of the, 139 
 
 Isothermal charts, Hann's, Buchan's, 100 
 
 Dr. Gould's, of southern S. America, 192 
 
 Jamaica, Strongest sea-breezes at, 199 
 
 Kerhallet, Table of limits of Pacific trade-winds, 162 
 
 Khasia, India. Enormous rainfall in, 204 
 
 Klossovsky. Table of thunder-storms in Russia, 469 
 
 Koppen. Investigation of thunder-storm of Aug. 9, 1881, in Germany, 465 
 
 Krakatoa, Eruption of, 124 
 
 Land- and sea.-breezes (see also tinder Sea-breeze), 219 
 
 breeze often comes off with dangerous squalls, 222 
 
 Laplace. Increase of the temperature in the barometric formula of, 102 
 Laughton. Remarks on sand carried to sea from the African desert, 129 
 
 Remarks on westerly winds in both hemispheres, 132 
 Law, Boyle and Mariotte's, 2 
 
 Charles and Gay-Lussac, 3 
 
 of Boyle and Charles combined, expressed mathematically, 3 
 Lecoq. Balloon ascensions in a thunder-cloud, 426 
 Lee's Summit tornado, 386 
 Ley. Easterly motion of the upper currents, 121 
 
 Values for the average angle of inclination of the winds in cyclones, 203 
 Table showing directions of surface and upper currents in cyclones, 264 
 Cirrus cloud observations by, 308 
 
 Loomis. Average wind velocities for U. S. , Northern Europe, Southern Asia, 
 and West Indies, 130 
 
INDEX. 
 
 Loomis. Chart of mean annual rainfall, 166, 188 
 Inclination of the winds in cyclones, 255 
 Investigation of winds on Mt. Washington, 272 
 Table of movement of cyclone centres, 276 
 Results concerning direction and velocity of westwardly moving 
 
 cyclones, 279 
 Results of inclination and velocity of winds in the four quadrants of a 
 
 cyclone, 291 
 
 Researches on the ellipticity of isobars in cyclones, 291 
 Investigation of the Manilla typhoon of Nov. 5, 1882, 295 
 Form and position of rain areas in cyclones, 299 
 Cyclones with little rain, 300 
 Results of wind velocities and inclinations for the four quadrants at 
 
 Mt. Washington in the passage of cyclones, 308 
 Relation of high barometer to cyclones in the U. S., 343-354 
 Determination of the coefficient of resistance of air, 372-377 
 Diameter of water-spouts, 408 
 
 Malcolmson. Remarks on eye of the storm, 312 [*59 
 
 Maury. Table of northern limits of the N.E. trade-wind in the Atlantic Ocean, 
 
 Weather under the cloud-ring of the equatorial calm- belt, 168 
 Mendeleef. Experiments on Boyle's law, 3 
 
 Experiments on gases at low pressure, 6 
 Mistral, The, 331 
 Moisture, Capacity of air for, 28 
 
 The effect on, of cooling the air, 29 
 Moments of couple, 117 
 
 Monsoons and land- and sea-breezes, 192-225 
 Monsoon, Definition of, and character, 193 
 
 Dependence of, upon temperature differences or gradients, 194 
 
 Similarity of, and land- and sea-breezes on small islands, 195 
 
 Dependence of the strength of the, on the nature of the surface of 
 the continent, 195 
 
 Greatest, found adjacent to high mountain ranges, 196 
 
 Influence of hot, low, level countries not great in winter, 196 
 
 S. W. , of Indian Ocean, called the monsoon, 200 
 
 Great strength of the, in Arabian Sea, 201 
 
 Effect of, on the southern, eastern, and northern coasts of Asia, 203, 
 
 The wet, of western India, 205 
 
 Northeast, Winter, and Dry, 207 
 
 in Norway, 208 
 
 Comparative strength of N.E. and S.W., 207 
 
 winds of the northern Siberian coast, 207 
 
 Northwest, 208 
 
 Northern, 209 | 
 
 influence in Australia, 209, 210 
 
INDEX. 497 
 
 Monsoon, Climatic influence of the summer, in Australia, 210, 211 
 Climatic effect of the winter, in Australia, 212 
 of Africa, 212 
 
 The southwest, of Africa, 213 
 winds in central Africa, 214 
 of N. America, 214 
 
 influences in N. America in summer, 215 
 influences in N. America in winter, 216 
 influences in Central America and Mexico in summer, 216 
 influences on the west and northern coast of N. America, 217 
 of South America, 217 
 influences over Brazil, 218 
 
 influences in Chili, Peru, and at Cape Horn, 219 
 Motions of bodies relative to the earth's surface, 42 
 in a groove, 48-59 
 
 on the earth's surface, centrifugal force in, 60 
 The principles of equal areas in, on the earth's surface, 65 
 Relative, between the equator and the pole, 68 
 Resultants of the two forces and, 71 
 where the centre of force is not the pole, 75-77 
 Uniform, over the earth's surface without friction, 86 
 Frictional resistances in the, of fluids, 94 
 of a fluid in a wedge-shaped canal, 94 
 of a fluid in the open ocean from equator to pole, 97 
 Remarks on general, of the atmosphere and forces producing them, 109 
 Vertical, downward in the higher latitudes and upward in the lower 
 
 latitudes, 112 
 
 Annual inequality in the east and west components of, 115 
 Resultant direction of, for various altitudes and latitudes, 120 
 Gyratory in cyclones, 241 
 
 of water flowing out at the centre of a shallow basin, 242 
 Resultants of cyclonic and progressive, 303-311 
 Mount Washington, Winds at, 127 
 
 Washington, Annual equality of winds at, 130 f 
 Alibut (near Irkutsk), Winds at, 127 
 Carmel, 111., tornado, 383 
 Mountain ranges, Climatic influences of, 183, 184 
 
 Effect of, on adjacent temperatures and rainfall, 188 
 
 Newton. Experiments on resistance of the atmosphere to falling bodies, 375 
 Northers, Cold-waves and, in cyclones (see under Cyclones), 322-329 
 
 Extracts from an account of, in Texas, by Solomon Sias, 325-327 
 
 Wet and dry, 328 
 
 Cloud appearance preceding, 328 
 
 Ocean, Pilot chart of the Atlantic, 159 
 
498 INDEX. 
 
 Ocean, Table of the limits of the trade-winds in the Pacific, 162 
 Olmsted. Whirlwinds produced by great fires, 441 
 
 Pamperos, 329-331 
 
 Christison's investigation of the, of Central Uruguay, 329 
 Similarity of, and northers, 330 
 Panama, Wet and dry seasons at, 175 
 
 Piddington. Remarks on the results of the inclination of the winds in cyclones, 
 Remarks on dimensions of the violent part of cyclones, 274 [267 
 Remarks on the " eye of the storm," 312 
 Pike's Peak, Winds at, 125 
 
 Annual inequality of winds at, 126 
 
 Plantamour. Inversion of temperature at St. Bernard in winter, 346 
 Pressure, Standard, 2 
 
 Decrease of, in the vertical, 8 
 
 Barometric, 10 
 
 Unit of, 12 
 
 Observed, at various altitudes, 16 
 
 Lateral, of a railroad car, 49 
 
 Causes of change of barometric, or pressure gradient at the earth's 
 
 surface, 134 
 Area of low, 255 
 
 Relation of, and velocity of the air, 377 
 Prjivalsky. Observation of winds in Thibet, 203 
 
 Quetelet. Observations on upper and lower currents of air, 266 
 
 Radius vector, 54 
 
 Rain, Monthly probability of, at Rubaga, 173 
 Size of drops of, 380, 433 
 
 Size of drops of, an indication of velocity of ascending currents, 381 
 Rain-belt, Oscillation of the middle line of the, in South America and Isthmus of 
 
 Panama, 173 
 
 Rainy and dry seasons at Greytown, Nicaragua, observed by Commander Reed, 
 in equatorial Mexico, 176 [174 
 
 at Panama, 175 
 
 on the Orinoco and Amazon rivers, 177 
 
 Rainfall, Woeikoff's and Loo mis' charts of mean annual, 166 
 Table of average monthly, on the Congo, 172 
 Peculiarities of, at Vivi, Ponta da Leaha, Gabun, Loanda, St. Thomas, 
 
 Nango, 172, 173 
 at Lado, Nyassa Lake, 173 
 at Guatemala, 174 
 
 Regions of little, in eastern and western hemispheres, 179 
 west and east of Rocky Mts., according to Loomis' chart, 188 
 Distribution of, in Europe and Asia affected by mountains, 189 
 
INDEX. 499 
 
 Rainfall in South America, affected by the Andes, 189 
 on eastern coasts of Africa and China, 190 
 Effect of small easterly or westerly wind motion on the, of the Andes 
 
 and Rocky Mts. , from 30 to 40 latitude, 190 
 Greatest, in Khasia, 204 
 in tornadoes, 399-401 
 
 Pressure caused by, in thunder-storms, 465 
 Redfield. Observation of the inclination of surface winds in a cyclone, 262 
 
 Cyclones preceded and followed by unusually high barometer, first 
 
 observed by, 269 
 
 Whirlwinds produced by great fires, 443 
 
 Reese. Appearance of the spout of the Lee's Summit tornado, 409 
 Reed. Rainy and dry seasons at Greytown, Nicaragua, observed by, 175 
 Resultants of the two forces and motions, 71-74 
 Reye. Diameter of water-spouts, 408 
 
 Ross, Sir James. Table showing decrease of atmospheric pressure from the 
 tropics, 140 
 
 Sand-spouts and dust whirlwinds, 443-445 
 
 Formation of, and places where observed, 444 
 hollow on inside, 445 
 
 Scoresby. Observations on sea-breezes in Greenland, 219 
 Scott. Thunder storm frequency at Valencia, Ireland, 471 
 Sea and land breezes. Special treatment of, 219 
 Character of, 195 
 
 Dependence of the strength of, on the nature of the sur- 
 face of the land, 195, 196 
 
 Strongest, along coast with high mountains in the back- 
 ground, 222 
 
 observed mostly in equatorial and tropical latitudes, 219 
 Effect of strong prevailing winds on, 220 
 True, observed in calm weather only, 220 
 Initiatory action of, 221 
 
 Sea-breezes have greatest strength in Jamaica, 199 
 in Greenland, 219 
 
 Time of beginning, maximum and end of, 221 
 stronger than land-breezes in equatorial and tropical latitudes, 222 
 along the coast of Guinea observed by Com. Burke, 222 
 Sias, Solomon. Account of northers in Texas, 125-127 
 Simoom probably a dust whirlwind, 445 
 
 Sinclair, Commodore. ' Weather under the cloud-ling of the equatorial calm- 
 belt, 1 68 
 Sirocco, The, 336 
 
 Reference to description of the, by Hahn, 337 
 Skirtchly. Account of a water-spout, 414 
 Smyth, Prof. Piazzi. Remarks on dust haze at Teneriffe, 129 
 
500 INDEX. 
 
 Spitaler. Normals of temperature, 100 
 Squalls, White, 436 
 
 Bull's-eye, 437 
 
 St. Cloud and Sauk Rapid, Minn., tornado, 386 
 Stockdale tornado, 388 
 
 Strachey, R., Esq., Mountain winds in the Himalayas observed by, 223 
 Sunsets, Theory of the red, due to volcanic ashes, 126 
 
 Table of altitudes and corresponding temperatures and pressures, 15 
 
 of observed pressures at different altitudes indifferent parts of the earth, 16 
 of observed rates of diminution of temperature, 34 
 
 of mean annual barometric pressure gradients, and annual inequalities, 143 
 of mean easterly velocities for the year, January and July, for various lati- 
 tudes and altitudes, 146 
 by Maury, of northern limits of the N.E. trade-wind in the Atlantic 
 
 Ocean, 159 
 
 showing limits of the trade-winds, 159 
 of the limits of the Pacific trades, 162 
 Dr. Danckelman's, of rainfall on the Congo, 172 
 of vertical temperature distribution for saturated air compared with that of 
 
 undisturbed air, 232 
 
 by Ley, showing directions of surface and upper winds in cyclones, 264 
 of J. Allen Brown, of inclination of winds in cyclones, 265, 266 
 of movement of cyclone centres by Loomis, 276 
 of yearly periods of cyclone frequency in several seas, 282 
 Temperature, Standard, 2 
 
 The absolute zero of, 4 
 
 The absolute, 4 
 
 Table of diminution of, per hundred meters, 34 
 
 Vertical distribution of, causing stable equilibrium, 36 
 
 Distribution of, over the earth's surface, 98-101 
 
 Effect of the distribution of land and water on the, at the earth's 
 
 surface, 98 
 
 Normal, of the latitude, 99 
 Table of normal, for different latitudes, 99 
 Average, at the earth's surface for the northern and southern 
 
 hemispheres, 100 
 Average rate of decrease with altitude for all latitudes and the 
 
 year, 100 
 
 Difference of the, gradient in winter and summer, 141 
 conditions, annual inversion of, 142 
 
 Relative, of east and west sides of the continents, 179, 180 
 Annual ranges of, are small in lower latitudes, 182 
 Effects of mountains and moisture on, 189, 191 
 Abnormally high, just east of Rocky and Andes Mountains, 192 
 Summer, of high plateaus, 198 
 
INDEX. 501 
 
 Temperature, Inversion of the, with the altitude in winter, 345 
 
 Sudden changes of, in thunder-storms, 451, 452 
 Teneriffe, Westerly wind at, 126 
 
 Thermal equator or the maximum of temperature, 100 
 Thunder-storms, 450-472. 
 
 Observed phenomena of, 450-459 
 
 Relation of, and cyclones as observed by Klossovsky, Aber- 
 
 cromby, Von Bezold, Davis, Ferrari, 451 
 
 Sudden changes of temperature, pressure, and wind in, 452, 453 
 Groups of, 453 
 Rain areas in, 454 
 Composite portraiture of, 454 
 Types, Ferrari, 455 
 
 Antecedent and following phenomena of, 455, 456 
 Origin and form of, 456 
 The theory of, 459, 467 
 
 Cause and results of pressure gradients in, 464-466 
 Observation of pressure gradient in, by Clayton, 465 
 Relation between, and cyclones, 467-470 
 Table of, in Russia by Klossovsky, 469 
 Location of, with reference to cyclonic areas. Klossovsky, 
 
 Hazen, 469, 470 
 
 Annual and diurnal inequalities of, 470-472 
 Time of occurrence of, on land and sea, 471 
 Winter, at Stykkisholm according to Buchan, 471 
 frequency at Valencia, Ireland, according to Scott, 471 
 Greater frequency of, on land than on the ocean, 472 
 Tomlinson. Regularity of atmospheric phenomena in the calm-belt, 175 
 
 Account of showers of fish caused by water-spouts, 414 
 Tornadoes, 347 
 
 dependent on the unstable state of the atmosphere, 348 
 
 and cyclones compared, 347 
 
 The conditions giving rise to, 348-353 
 
 Vertical distribution of temperature and pressure in, 349, 350 
 
 Vertical circulation in, 349 
 
 Gyratory circulation in, 351 
 
 Initial gyratory motion of the air necessary for starting, 351 
 
 Smallness of the effect of the earth's rotation on the currents of, 352 
 
 Gyratory velocity and its effect on pressure, 353-362 
 
 Law of gyratory velocities at the same distances from the centre of, 
 
 356 
 
 Expression for the centrifugal force of the gyratory velocity in, 354 
 Isobaric surfaces and gradients in, 355 
 Gyratory velocity within, 358 
 Diminution of pressure in the centre of, and its effects, 360 
 
5O2 INDEX. 
 
 Tornadoes, Instances of the outbursting of confined air during the passage of the 
 centre of, 360 
 
 Computation of outward pressure caused by the passage of the centre 
 of, over confined air, 361 
 
 Friction in a gyratory circulation necessitates vertical currents in, 362 
 
 The energy of, 362-371 
 
 Maintenance of the unstable state in, 363 
 
 Thermal energy and temperature gradient in, 363, 364 
 
 Reduction of the unstable to the neutral or stable state in, 364 
 
 Cause of the first motion in, 365 
 
 Relation of the kinetic energy of the gyratory velocity and the poten- 
 tial energy due to pressure in, 366 
 
 Analogous phenomena in, to the eye of the cyclone storms, 367 
 
 The greater the altitude of the rarefied centre, the more violent the, 
 368 
 
 Relation of the height to the diameter of, 370 
 
 Force of the wind and supporting power of ascending currents in,. 
 
 371-395 
 
 Theoretical enormous pressures of wind in, 377 
 Support of rain and hail by ascending currents in, 379-380 
 of Walterborough, S. C., 381 
 of Wallingford, Conn., 382 
 of Mt. Carmel, 111., 383 
 
 - of St. Cloud and Sauk Rapids, Minn., 385, 386 
 of Lee's Summit, 386, 399, 407 
 of Irving, 387 
 
 of Stockdale and of Delphos, 388 
 of Barnard and of Gentry County, 389 
 Computation of the enormous velocities and pressures of wind in,. 
 
 389 
 
 Width of the path of destruction of, according to Finley, 390 
 Velocity and lifting force of the ascending current in, 390 
 Movement of bodies carried up in, 391 
 
 Explanation of the lifting power at the earth's surface of, 393-395 
 Resultants of gyratory and progressive motions in, 395-399 
 Direction of the rotary motion of. Finley, 395 
 Velocity and direction of progression of. Finley, 395 
 Dangerous side of, 396 
 
 Direction and relative strength of winds in front and rear of, 396, 397 
 Dr. Anderson's account of direction of strong winds in the, of April 
 
 23, 1883, 397 
 Difference in the width of the path of destruction on the two sides 
 
 of, 399 
 
 Rainfall in, 399-401 
 Cause of a cloud in the vortex of, 402 
 System of circulation in, 403 
 
INDEX. 503 
 
 Tornadoes as funnel-shaped and basket-shapea clouds, 406 
 
 Intermittent action of, 407 
 
 Discontinuity of line of destruction of the, of April, 1883, 407 
 
 Appearance of clouds in, 410 
 
 Appearance of the, of West Cambridge, 410 
 
 Plurality of. spouts in, 412 
 
 Hail-storms, 420-429 
 
 Movements of a balloon in a, observed by John Wise, 425 
 
 Fair-weather whirlwinds and white squalls, 434-437 
 
 Where they are most likely to occur, 437-443 
 
 Summer and afternoon the times of greatest frequency of, according 
 
 to Finley, 441 
 
 Toynbee. Results of observations on winds in cyclones, 267 
 Trade-winds. See under Winds. 
 
 Typhoons, Doberck's observations of, in China Sea and Philippine Islands, 268 
 Manilla, of Nov. 5, 1882, as investigated by Loomis, 295 
 
 Vapor, Aqueous, of the atmosphere, 16 
 
 The amount of aqueous, in the atmosphere, 19 
 
 tension, average, at the equator, 101 
 
 Effect of average amount of aqueous, on the density of the atmosphere 
 
 at the equator, 101 
 Distribution of aqueous, 101 
 
 Effect of the aqueous, in expanding the atmosphere, 103 
 Velocity, The gyratory, in terms of the radius, 46 
 Gyratory and centripetal, 55 
 
 Gyratory, increases with approach toward a centre. Examples, 55 
 East and west components of, 108 
 East component of, increasing with altitude, 109 
 Limits of the east components of, 1 10 
 Change from west to east components of, 114 
 Annual inequality in the east and west components of, 115 
 Of the east and west components depending much on the nature of the 
 
 surface, 118 
 
 Easterly, deduced from pressure and temperature gradients, 144 
 Mean easterly, for the year, January and July, for various latitudes and 
 
 altitudes, 146 
 
 Annual inequality of easterly, 147 
 
 Easterly component of, at various points on the earth, 148 
 Venezuela, Motions of the clouds at Colonia Tover in, 123 
 Vines, Padre. Observation on the inclination of winds, 266 
 
 Phenomena attending the approach of cyclones, 302 
 Remarks on pumping of the barometer, 642 
 
 Volcanic ashes carried eastward by upper air currents. Some examples of this, 
 123, 124 
 
504 INDEX. 
 
 Wallingford, Conn., tornado, 382 
 Walterborough, S. C., tornado, 381 
 Water-spouts, 401-420 
 
 Formation of, 401 
 
 Cause of the peculiar outline of, 402 
 
 System of circulation in, 403 
 
 The height of, 408 
 
 Diameters of, according to Horner, Reye, Loomis, and Judge 
 
 Williams, 408 
 
 Appearance of, on land, 410 
 at sea, 413 
 
 Account of, by Sydney Skirtchly, 414 
 Formation of small, on seas and lakes, and description by Defranc 
 
 and others, 415, 416 
 
 Observations of the hollow centre of, 419 
 West Indies, Steady winds from the east at, 130 
 Wilkes, Capt. , Irregular outline of the atmosphere surrounding the earth first 
 
 shown by, 140 
 
 Lower temperature in the calm-belt, 169 
 Winds, Relation of barometric gradient and velocity of, 85 
 Prevailing westerly, at elevated mountain peaks, 126 
 Directions and relative frequencies of, at Pike's Peak, 126 
 Westerly tendency of, near the earth's surface, 113, 129 
 in the interior of North Africa, 129 
 Average velocity of, for United States, Northern Europe, Southern Asia, 
 
 and West Indies, 130 
 
 Remarks of Mr. Laughton on westerly, in both hemispheres, 140 
 Surface, 149-154 
 of the polar regions in the northern hemisphere having a component 
 
 from the pole, 152 
 
 Components of, in northern and middle latitudes, 152 
 Components of, near the equator, 152 
 Consequences of deflection of, due to land barriers on various portions of 
 
 the earth, 183-185 
 
 Charts of, by Coffin and Brault, 186 
 Effect of the Himalaya mountains on, 186 
 Effect of the Andes on, 187 
 Effect of the African Mountains on, 186 
 
 Effect of the, on the Pacific and Indian Oceans on bordering lands, 186 
 Table of directions of, observed in summer on the Indian Ocean accord- 
 ing to Woeikoff , 205 
 on west coast of Africa, 213 
 Mountain and valley, 223 
 
 Mountain, in the Himalayas observed by Strachey, 223 
 Terrific diurnal, in western Thibet, 223 
 Mountain, on Grey's Peak, Colorado, 224 
 
INDEX. 505 
 
 Winds, Diurnal change in direction of T in Missouri and Kansas, 224 
 Definition of the force of, 373 
 
 Equation for converting velocities into pressures of, 377 
 Observed force of, in tornadoes, 381 
 Blasts of, and oscillations of the wind-vane, 446, 447 
 Effect of blasts of, on the barometer, 449 
 Wind-spouts, 418 ^ 
 
 Wind, trade, Table showing the northern limits of the northeast, in the Atlantic 
 
 Ocean, 158 
 
 Table of the mean polar limits of the northeast and southeast, 159 
 Table of the equatorial limits of the northern and southern, 160 
 Annual oscillation of the limits of the, 160 
 Remarks on limits and progress of the, 161 
 Table of limits of the, in the Pacific Ocean, 162 
 Williams, Judge. Diameter of spout in Lee Summit tornado, 408 
 Wise, John. Movements of a balloon in a tornado cloud observed by, 425 
 Woeikoff. Tables of trade-winds, 158 
 
 Chart of the zone on which rain falls in the course of the year, 166 
 Remarks on winds of south central Europe, 185 
 Table of wind directions observed in summer on Indian Ocean, 205 
 Woodruff. Investigation of cold waves in the United States, 323-325 
 Work, Definition, measure and unit of, 20-23 
 The equivalent of, 23 
 
 Zi-ka-wei, Directions and frequency of the cirrus clouds at, 122 
 

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