f / I IN MEMORIAM FLORIAN CAJORI ////v* N I //9 - r*?*S + t \ / A NEW TREATISE ON THE USE OF THE GLOBES, AND Practical Astronomy ; OR A COMPREHENSIVE VIEW OF THE SYSTEM OF THE WORLD. IN FOUR PARTS. I. An extensive collection of Astro- X or a star, at any given time, with noraical and other Definitions. the method of representing the II. Problems performed by the TER- spherical triangles on the globe, &c, RESTRIAL GLOBE, including 1 those >:IV. A comprehensive account of the relative to Geography, Navigation, A SOLAR SYSTEM, with the elemen- Dialling, See. with many new and {> tary principles, and most valuable important problems and investiga- > modern discoveries in Astronomy tions, particularly useful to the Na- X to the present time. The nature vigator and Practical Astronomer. and motion of COMETS, OF THE III. Problems performed by the CE- y FIXED STARS, ECLIPSES, THE LESTIAL GLOBE, including those >: THEORY OF THE TIDES, LAWS of finding the longitude at sea, new A OF MOTION, GRAVITY, &c. with methods of finding the latitude, i"> DIAGRAMS elucidating the de.- with only one altitude of the sun, V mnstrations. The whole serving as an introduction to the higher Astronomy and Natural Philosophy, is illustrated with a variety of important notes, useful remarks, Sec. and each problem with several examples. The necessary astronomical instruments are poiin-cQ uuv, iuul the muat usciui taDles are inserted in the work. DESIGNED FOR THE INSTRUCTION OF YOUTH, AND PARTICULARLY ADAPTED TO THE UNITED STATES. BY J. WALLACE, Jllcmber of the JVeiv^York Literary Institution, &c. Quid munus Reipublicce majus aut melitis afftrre posximus, quam si Jnventutem bene erudiamus ? CJCERO, NEW-YORK : Printed and published by SMITH 8c FORMAN, AT THE FRANKLIN JUVENILE BOOKSTORES 195 and 213 Greenwich-Stree f . 1812. M308234 DISTRICT OF NEW-YORK, ss. Be it remembered, That on the sixth day of January, in the thirty -sixth year ofthe Independence of the United Slates of America, JJMES W*IL- LJ1CE> of the said district, hath deposited in this office the title of a book, the right whereof he claims as Author, in the words and figures fol- lowing', to wit : c A new Treatise on the Use of the Globes, and Practical Astronomy ; or a comprehensive view of the System of the World. In four parts. I. An extensive collection of astronomical and other definitions. II. Problems performed by the Terrestrial Globe, including those relative to geography, navigation, dialling, &c. with many new and important problems and investigations, particularly useful to the navigator and practical astrono- mer. III. Problems performed by the Celestial Globe, including those of finding the longitude at sea, new methods of finding the latitude, with only one altitude of the sun, or a star, at any given time, with the method of re- presenting the spherical triangles on the globe, &c. IV. A comprehensive account of the Solar System, with the elementary principles, and most va- luable modern discoveries in Astronomy to the present time. The nature and motion of Comets, of the Fixed Stars, Eclipses, the theory of the Tides, Laws of Motion, Gravity, &c. with Diagrams elucidating the demonstrations. The whole serving as an introduction 'to the higher Astronomy and Natural Philosophy, is illustrated with a variety of important notes, useful remarks, &c. and each problem with several examples. The necessary astronomical instruments are pointed out, and the most useful tables are inserted in the work. Designed for the instruction of youth, and particularly adapted to the United States.' By J. Wallace, Member of the New-York Literary Insti- tution, &c. Qifid munus lleipublicx mqjus aut melius afferre possimus, quam si Juventutem bene erudiamus, &c. Cicero. In conformity to the act of the Congress of the United States, entitled * An act for the encouragement of learning, by securing the copies of Maps, Charts, and Books to the authors and proprietors of such copies, during the times therein mentioned.' And also, to an act, entitled * An act, supple- mentary to an act, entitled ' An act for the encouragement of learning, by securing the copies of Maps, Charts, and Books, to the authors and propri- etors of such copies, during the times therein mentioned, and extending the benefits thereof to the ails of designing, engraving, and etching historical and other prints.' CHARLES CLINTON, Clerk of the District of New-York. PREFACE. . MAN cannot but behold with gratitude and delight, the multi- plied benefits and amazing; objects which surround him on all sides, contributing equally to his wants and pleasure. This plea- sure, however, is greatly increased in proportion as the nature, utility, and number of these objects .ire known and understood ; and this knowledge is only attained from a cultivation of those no- ble powers with which the mind of man is gifted, and which so eminently distinguish him from the brute creation. The savage that ranges our forests in common with the brute ; that at the same fountain satisfies his thirst, and eats of nature's fare, whatever his tuste or appetite craves ; that seems no way dis- tinguished from the animals with which he associates, than by the figure of his species ; has still within him the seeds of those noble acquirements which exalt and dignify human nature. Yes, this same savage enjoying similar advantages with a Cicero, a Demost- henes, or a Newton, might become their rival ; but those seeds, from a \vantofr cultivation, must remain for ever buried in oblivion. Such is the picture of uncultivated man, whom, in his wild and savage state, the mines of Peru cannot enrich, or whose wants the most fertile regions of the earth cannot lessen In the midst of profusion he is indigent, and in the unequal conflict with those animals, whose master he was destined to be, must often be- come a prey to their superior strength and ferocity. It is evident, then, that an acquaintance with the elements of science is intimately connected with our necessities, no less than with our future progress, advancement, and eminence ; and that in proportion as we neglect the acquirement of this knowledge, we approximate to the state of th# rude, uncultivated savage It is well known, that Great-Britain and France respectively owe more to the successful cultivation and application of the sciences, than they do to the valour of their armies, or to the strength of their marine. Among all the branches of science within the compass of hu- man acquirements, there are few that unite greater importance and utility, than that which exhibits and explains the phenom- ena of the earth, our destined habitation, and more pleasure, than that which traces the evolutions of those immense orbs that decorate the heavens, and investigates the unerring laws by which they are regulated and governed : for there is nothing which so much excites our attention and curiosity, which unites in itself so much grandeur and magnificence, and which produces in the soul so much sublimity and admiration, as the contemplation of those prodigies which that immense vault surrounding the habitation of man exhibits to our view. And if there be some in whom this grand spectacle excites no emotion, it is because they are too much ab- sorbed in those artificial wants or necessities which they create to themselves ; -veluti fiecora, as Sallust suys, qua natura firona^ af quc vcnfri obedcntia finxlt \ iv PREFACE. It is in the heavens that the Creator has chiefly manifested his greatness and majesty It is here that the Sovereign Wisdom shines with the greatest lustre, and that the sublime ideas of order and harmony reign. In this immense host of celestial bodies all is prodigy and magnificence : all is regularity and proportion : all announce a power infinitely ferule in the production of beings, in- finitely wise in their arrangement and destination. But this magnificent spectacle is not thus exposed to our con- stant view, to be the object of an idle admiration, or a fruitless con- templation ; it is much more connected with the wants and ad- vantages ot the inhabitant of the earth. It is in the heavens that we have found the means of arresting time in the rapidity of its course : of regulating our seasons, and fixing those interesting epochs, from which the Historian and Chronologer date the most important events The form, the extent, the exact position of the different parts of the earth we inhabit, and its situation in the im- mense expanse, is attained only by the assistance of Astronomy. If we now traverse the ocean with so much security and skill, it is principally owing to this science which has furnished the means of ascertaining our place, at any time, in this trackless element. Thus by the interposition of the heavens the most distant nations hold their correspondence : extensive deserts, immense oceans, seas, and unknown countries are explored, and their riches transported to other countries destitute of these resources. In a word, it is to this science that Columbus owed the greatest discovery that human ingenuity has ever made, and that he has been able to add a new world to the old. It is not only in enlarging the sphere of human knowledge, and contributing to the wants and convenii ncies of man that Astronomy is useful ; it has also dissipated fflfe alarms occasioned by extraor- dinary celestial phenomena, and destroyed many of the errors aris- ing from our true relation with nature. Such are the obligations we have to this science ; such the benefits which it has conferred on society ; such the services it has rendered the human mind. This sublime science then, claims a right to our esteem and res- pect, and without doubt, there is not among human sciences another, more worthy to engage our attention, and better calculated to oc- cupy and amuse our leisure moments. It is no objection to it that it has often been made the unwilling 1 instrument of impiety in the hands of the impious, or of an absurd science in the hands of the Astrologer ; for the greatest benefits conferred on man are susceptible of abuse. To put a stop to these growing evils, Emperors have passed their edicts and enforceti their decrees, to expel those impious pretenders from cities that became the scenes of their folly and impiety, and some who de- served a better fate were unhappily involved in their number. The irreligious Philosopher and the impious of the day, will ascribe many of these unhappy occurrences to the religious prejudices and ignorance of those times; but with no more reason than those PREFACE v have, who charge this science with supporting impiety, though of all others the least calculated to afford it any support If history has any truth in it, history affirms that it was in houses dedicated in those days to piety and religion, that the most precious remains of science were preserved, and that it is from them they have been principally handed ddwn to the present time. To trace this science to its origin, and point out the various al- terations and improvements it has received, the long series of dis- coveries which it presents, and the illustrious authors who have contributed to them, would far exceed the limits of a preface. It will be sufficient to observe, that the origin of Astronomy coiri- nunces its date with that of Agriculture and of Society itself. There is still an immense difference between the first view of the heavens, and the view by which, at present, we comprehend the past and future state of the system of the world. It is, however, to the improvements in the past and present age, that we are principally indebted for this developement of the most important and curious discoveries in this system ; and such of those authors as have been most successful, and have particularly excelled in this respect, have been consulted in the following compendium. Their works have been also pointed out to direct the choice of the student, and exhi- bit their superior advantages and excellence. Among the inconveniencies attending our public places of edu- cation, it is no small one, that many of those works which are the standard of elegance and perfection, are inaccessible both to the Student and Master, in consequence of the difficulty of procuring them from Europe, and their too great expense to be introduced into Schools. To remedy, in some measure, this inconvenience, the author of the present work has^mdertaken to draw up an entire course of Mathematics and NaUmB Philosophy (if his avocations will suffer him to continue) principally for the use of the Students belonging to the New-York Literary Institution. And conceiving that this course, undertaken more from necessity than choice, would asssist him no less than others occupied in the education of youth, he has been induced, principally from this motive, to make this introduction public. The present treatise on the Use of the Globes and Practical As- tronomy is complete in itself, and detached from the contemplated course, the author having immediate and urgent necessity for its use ; and being a subject uniting extensive utility with pleasure and ornament, no pains have been spared, in calculating it for these im- portant objects, as far as his hurry in drawing it up would allow. Each problem is illustrated with several examples, and their de- monstration or calculation, cc. given in notes at the bottom, in or- der to make it more fully answer the end of an elementary trea- tise on practical astronomy, and to adapt it to academies and places of public education in general, where this branch of science is now considered as one of the most entertaining and necessary. vi PREFACE. Many new and important problems will be found in this, inaddi- ~tion to :hose f'ounn in oiher treatises; and which likewise are per- formed on the globes, by methods generally entirely new, and found .in no other treatise ; which cannot but render this work extremely tinte resting to those who are capable of relishing the beauties of science, and of appreciating its value. Many important Tables arr: inserted in the course of the work, as well as figures to illus- trate the demonstrations, &c. and it is no small recommendation to it that these figures were cut by the celebrated Dr. Anderson. There arc also given, besides a complete account of the Solar Sys- tem, the elements and laws of the planet's motions, their phe- nomena, their principles, Sec a full investigation of the nature and motion of Cornets, the doctrine of Eclipses, the Tides, the Gene- ral laws of Motion, Gravity, Sec enriched with many discoveries and late improvements from H^rschel, Vince, Maskelyne, La Lade, Laplace, Delambre, &c. The work bein>; printed close, and the notes (which are of con- siderable length) being in small type, this treatise must contain -more matter than any other of the size and nature in print; so that in one volume f moderate size, besides the Treatise on the Globes, an entire course of Astronomy is given, including both the calculations, and the geometrical and physical part ; and the au- thor does not believe that he has omitted any thing of importance, that has any particular relation to these subjects. The teacher will immediately perreive that the work is calcu- lated for three distinct classes of students. The first is, of those who are supposed to be unacquainted with the principles of Mathe- matics, and who may read the definitions and all the problems on the globes, contained in the ^ and 3d parts. The second class, who are supposed to have sorffi knowledge of Geometry and Trig- onometry, may read the notes on the definitions and problems on the g;obes, and perform the problems by calculation ; they may also read some select parts of the 4th part, particularly those rela- tive to the order and motion of the planets* in the solar system. The third class, supposed to be somewhat acquainted with the ele- ments of the Conic Sections, Algebra, and the first principles of Fluxions, may continue the 4th part This last class, by finishing the elements of Fluxions, will obtain any further knowledge in Physical Astronomy that may be necessary, being the most proper place for fully investigating this abstruse subject. The author in presenting this work to the public, is equally re- gardless of its censure or praise, as his object is neither emolu- ment nor celebrity. His whole aim in the undertaking 'vas to Jighten the burden of the Teacher and to improve the student If by comprising in a comparatively small compass ail that is useful and necessary either on the Globes or in Astronomy, he succeed in this, his object will be fully attained. Distance from the press and hurry in the execution^ have pro- duced some few errors, most of which are found in the errata at the end. CONTENTS. PART I. Containing the description of the Globes, Astronomical and other Definitions, t/ie method of calculating and adjusting the Calendar, table of Climates, a full description of all the Constellations, number of Stars, Clusters, Nebula, &c. as inserted on t/te neiv British Globes, ivith observations on their origin t the origin and nature of the Heathen worship, with some useful refections, &c. page 1 to 50. FART II. Or problems performed by the Terrestrial Globe, contains different methods of finding the latitudes and longitudes of places, of finding the hour of the day or night at any time, difference of times, hours, seasons, &?c. according to. the change of latitude or longitude, Antxci, Periceci, Antipodes, Sun's Ion" gitude, declination, rt. ascension, rising, setting, length of days and nights, &c. in every latitude, the manner of exhibiting these phenomena ivith the different seasons on the globe, their calculation, &c the equation of time with its investigation and tables, the method of finding morning and evening twilight in the different latitudes, -with observations, &c. method of finding the different climates, their breadth, 6?c. methods of finding the distance of places, with extensive tables of the lengths of a degree, &c. and the measures used in different countries, together with the late French measures, &c. Problems in Navigation, Dialling, &c. and many other particulars sv/wc/i itnll be seen by consulting this part, 50 to 192. PART III. Contains the methods of finding the right ascensions, declinations, latitudes and longitudes of the sun, stars, planets, &c. and the methods of making the ob- servations, application of pendulum clocks to this purpose, the manner of ad- justing them, &c. of finding- the rising and setting of the stars, or planets^ time of their passing the meridian, method of finding their distance, and from thence the longitude at sea, various methods of finding the latitude, of finding a meridian line, variation of the compass, moon's southing, &c. time of high water, with the necessary tables, Ac/ironical, Cosmical and HcUucal rising, set" ting, &c. of the stars, of describing the apparent paths of the planets or comets among the fixed stars, of the precession of the equinoxes, &c. 192 to 247. PART IV. CONTAINS Ch. I. Of the sun, his phenomena, &c. diameter, spots, rotary motion, distance, Kepler's laws, nature of the Centre of Gravity, atmosphere, &c. 250 to 257- Ch. II. Of JMercury, his phenomena, motions, diamet r, distance, magnitude^ methods of finding these, c#c. of describing a planet's orbit, of finding its nodes and inclination, of finding a planet's heliocentric and geocentric places, conjunctions of the inferior planets, phases of the planet s, &?c. 257 to 270. viii CONTENTS. Ch. HI. Of Venus, her motions, phenomena, &c. her spots, phases, her par ai- lax, &c. 270 to 280. Ch. IV. Of the earth and its satellite the moon, the earth's globular figure , measure of a degree on its surface, its diurnal motion, general refections on its cause, an idea of the universe, the earth's annual revolution, aberration f light, length of tJie sidereal year, of the solar or tropical year, the substance of Newton's discoveries relative to the planets' motions, theory of the earth or planets-' motions, &c. 280 to 320. Of the moon, her mean motions, plienomena, method of finding her apparent diameter, 6fc. Parallax of the moon and planets, moon's phases, atmosphere, mountains, fcfc. 320 to 346. Ch. V. Of Mars, his motions and pJienomena, &c. Theory of the planets' mo. tions, &c. 346 to 357. Ch. VI. Of the new planets Ceres, Pallas, Juno and Vesta, 357 to 359. Ch. VII. Of Jupiter, his motions and phenomena, &?c. 359 to 363. Of his Sat- ellites, their periodic times, distances, &c. ho-w found, their immersions and emersions, their rotary motion, their edipses, laws of their inequalities, their configurations, &c. 363 to 377. Ch. VIII Of Saturn, his motions, phenomena, &c. method of finding the oppo- sition oftJie superior planets, of Ids ring and its phenomena, his satellites and their periods, &c. 377 to 388. Ch. IX. Of Uranus or HerscJiel and his satellites, 388 to 392. Ch. X. Of the nature and motion of Comets, of their tails, table of their ele- ments, -with examples of the method of calculating them, &c. the names of the authors who have calcidated them, &c. 392 to 436. Ch. XI. Of the fixed stars, double stars, their phenomena, a full investigation of their aberration, the nature of the nebulous appearances in the heavens, their number, distance of the stars, &c. 436 to 448. Ch. XII. Of Solar and Lunar Eclipses, method of calculating them, &c. 448 to 458. Ch. XIII. Of the Tides, their phenomena, laws, method of calculating them, &fc. 458 to 463. Ch. XIV. Of the General Lavas of Motion, Forces, Gravity, &c. motion of bodies on inclined planes, in curves, &c. properties of the pendulum, masses and densities of the planets determined, forces of gravity at their surface, their perturbating forces, &c. 463 to 486, PRACTICAL ASTRONOMY, &c. IN THE DEFINITION AND USE OF THE GLOBES. ' PART I. DEFINITIONS, UV. 1. A GLOBE or SPHERE, is a round solid body, having every part of its surface equally distant from a point within it, called the centre. It is formed by the revolution of a semicircle round its diameter, which remains fixed. 2. The terrestrial globe* is an artificial representation of the earth, having the different countries, empires, kingdoms, chief towns, seas, rivers, Sec. truly represented on it, according to their relative situations on the real globe of the earth. * If a map of the world be accurately delineated on a spherical ball, its surface will represent the surface of the earth. For the highest hills are so inconsiderable with respect to the bulk of the earth, that they take off' no more from its spherical figure, than grains of sand do from the spherical figure of an artificial globe. The diameter of the earth is about 7964 miles. Chimborazo, one of the Andes, considered the highest mountain in the world, is about 20,282 feet or nearly 4 miles high. The radius or semi- diameter of the earth is about 3982 miles, and that of an 18 inch globe 9 inches : hence we have this proportion 3982m : 3986m :: 9 in. : 9.009 in. Now by taking the radius of the artificial gl<3be from this, the remainder .009 =s=Y^y= ==T *-j of an inch, nearly, which is the elevation of the highest peak of the Ancles on an 18 inch globe. That the globe of the earth is spherical, or nearly so, appears 1. From its casting- a spherical shadow on the modn, whatever be its position, when it is eclipsed. 2. From our seeing the further, the higher we are elevated on its surface. 3. From our first seeing the tops of mountains, the masts of vessels, Sec. when we advance towards them in any direction. 4. From its having been sailed round from east to west byseveraj. persons ; and that in whatever direction a ship sails, the stars are elevated above the horizon as many degrees as the vessel sails towards them, and those behind depressed in like manner. Thus in sailing from the equator towards the north pole one degree, the pole star is elevat- ed 1; in sailing 2, the pole is elevated 2, &c. so that if thsi-e were a star exactly in the pole, its height would always indicate the number of degrees a place is from the equator or its latitude. This phenomenon could not possibly take place unless the globe was round. 5. From the length of pendulums vibrating in the same time in different parts of the world, being 1 always as the force of gravity (Emerson's Tracts, part 1. prop. 27.) that is, as the distance from the earth's centre (Newton's Principia. b. 3, prop. 6.) But the increase of gravity or weight in passing from the equator to the poles is as the square of the sine of the lat. (Newton, b. 3, prop. 20.) so that the equator is something higher than the poles, the diameters being s* 2 DEFINITIONS, We. 3. A great circle of a sphere is any circle on its surface, whos? centre is the same as the centre of the sphere. Its plane divides the sphere into two equal segments called hemispheres. Note. The plane of a circle is the surface included -within its circumference. 4>. A lesser circle is that whose centre is different from the cen- tre of the sphere. I plane Avid* th globe into two unequal segments. 5. The axis of a sphere is the fixed straight line about whicfe the generating semicircle revolves. The axis of the earthy is an imaginary straight line passing through its centre, and upon which it is supposed to turn. The axis of the artificial globe is a line which passes through its centre from north to south, and is repre- sented by the wire on which it turns.* 6. The poles of a great circle of the sphere, are the two points equally distant from any part of the circumference of that circle. The poles of the earth are the extremities of its axis, at the earth's surface ; one of which is called the north or arctic pole : the other the south or antartic pole The celestial poles are the imaginary points in the heavens corresponding to the terrestrial poles, or the extremities of the earth's axis produced to the heavens.f 7. The diameter of a sphere is any straight line which passes through the centre, and is terminated both ways by the surface of the sphere. 8. The circumference \ of a sphere is any great circle described on its surface. 230 to 229 And the pendulum indicates not only this small difference, but even the difference made in the height of mountains ; for a pendulum that vibrates seconds in a valley, will not vibrate seconds exactly when carried to the top of a mountain. Now if the semi-diameter of the equator be 3982, the polar semi-diameter will be 3964.6. For 230 : 229 :: 3982 : 3964.6 nearly. Hence the radius or semidiameter of the earth at the pole, is shorter than the semidiameter at the equator by 17 miles nearly. But this difference is so imperceptible on the largest globes, that it is not thicker than the paper and paste on the surface. For suppose the diam- eter of a globe at the equator be 18 inches, then 230 : 229 :: 9 : || .the polar semidiameter ; therefore the difference is -y^ of an inch, the flatness of an 18 inch globe at each pole ; a difference less than the 23d part of an inch. Hence though the earth be not strictly speaking a globe, yet no other figure can give so exact an idea of its shape. And a lecturer who informs his hearers that it is in the form of a turnip or orange, gives a very false idea of its true figure. Though 7964 be generally assumed for 1.he earth's diameter, it is however probably something less. * The diurnal motion of the earth on its imaginary axis is from west to east, and is the cause of the apparent motion of the heavens from east to west. This phenomenon of the earth is not unlike that of a large vessel carried along the current of a river, in which the passengers imagine them- selves at rest, and that the banks and objects on shore, which are at resl^ are actually in motion. f The poles of the earth nre the same as those of the equator. The poles are 90 distant from the great circle to which they belong. t The circumference of every circle is divided into 360 equal parts called degrees, each degree into 60 equal parts called minutes, each minute into DEFINITIONS, er c . 3 9. The equator* is a great circle of the earth equidistant from the poles, which divides the globe into two equal hemispheres, northern and southern. 10. Latitude of a place f on the terrestrial globe, is its distance from the equator north or south. 60 equal parts called seconds, &c. The length of a degree is therefore differ- ent in different circles, and on the equator is 60 geographical or 69 English miles nearly. It varies in the respective parallels of latitude towards each pole, in the direct proportion of the cosine of the latitude, or which is the eame as the semidiameter of the respective circles. The utility of finding- Ike length of a degree, in order to determine tjie magnitude and figure of the earth is apparent, and may be rendered familiar to a learner thus ; sup- pose the latitude of New- York be 40 43', and that a person travels due north until the latitude be found 41 43', then he will have travelled a degree, and the distance between the two places will be its length. Mr. Richard Nor- wood in 1635 measured the distance between London and York, and found it equal 905751 feet London measure, and observing the difference of lati- tude to be 2 28' found that 1 degree was equal 367196 feet. M. Picard found by a trigonometrical survey, that the distance of the " Pavilion de Malvoisine" south of Paris, to the steeple of the cathedral of Amiens, re- duced to the meridian, was 78907 toises. He found also by astronomical observation, that the distance of these places was 1 22' 58 tf ; hence 1 22 r 58" : 78907 :: 1 : 57064 toises the length of a degree. The as- sumed distance (in the late French measures) from the equator to the north pole, established on the measure ofia degree of the meridian equally distant from both, is 30794580 feet, which divided by 90 gives 342162 feet or 57027 toises. Now as 5280 feet make a mile, therefore 367196-4-5280=69.54 (or 69) miles nearly, which multiplied by 360 produces 25034 the circum- ference of the earth ; but the circumference of a circle is to its diameter as 355 to 113 ; hence 355 : 113 :: 25034 : 7965 miles the earth's diameter according to Norwood's measure. Again ; as 811 French feet are equal to 864 English feet, or 107 to 114 nearly, hence 107 F.f. : 114 E.f. :: 342162 F.f. : 364546 English feet, which divided by 5280 gives 6.9.04 English miles, the length of a degree, according to the late French measure. Now 342162X360=123178320 French feet the circumference of the earth, and 811 : 864 :: 123178320 : 131228188 English feet =24853.82 miles the cir- cumference, and 355 : 113 :: 24853.82 : 7911.2, the diameter in English miles. According to Picard the circumference is 24871.5 miles, and diam- eter 7916.8 miles. It was Picard's measure that Sir Isaac Newton has fol- lowed in his principia, making the number of toises in a degree =57060 by taking the distance between Malvoisine and Amiens 1 22' 25". See his principia book, 3 prop. 19. * The equator, so called from its dividing the earth into two equal parts, is, when referred to the heavens, fermed the equinoctial, because when the sun appears in it, the days and nights are equal all over the world, viz. 12 hours each. This circle is also by mariners called the line. On this line is found the rt. ascension, oblique ascension, oblique descension, ascensional difference, longitude of places, semidiurnal and nocturnal arches, planetary hour, distinction between north and south latitude of places, difference o'f longitude, most exact and equal measure of time, &c. f Difference of latitude is the nearest distance between any two parallels of latitude shewing how far the one is to the north or south of the other, and difference of longitude is the nearest distance between any two meridians either east or west If the latitude be in the northern hemisphere, it is call- ed north latitude, if in the southern, south latitude. The greatest latitude that a place can have N, or S. is 90, and the greatest longitude E. or W, 4 DEFINITIONS, fcV. 11. Longitude of a place, is its distance from the first meridian, reckoned on the equator towards the east or west. 12. Parallels of latitude, are small circles drawn on the terres- trial globe, through every ten degrees of latitude parallel to the equator 'i3 The tropics* are two lesser circles parallel to the equator, at the distance of 23 28' from it ; the northern is called the tropic of Cancer, the southern the tropic of Capricorn. 14. The /War circles are two lesser circles, parallel to the equa- tor, at the distance of 66 32' from it, or 23 28' from each pole. 15. A zonef is a portion of the surface of the earth contained between two lesser circles, parallel to the equator ; they are^f e in number, one torrid, two temperate, and two frigid. 16. The torrid zone \ is the space contained between the two tropics, and is 46 56 ; broad. 17. ihe temperatt zones are the spaces between the tropics and polar circles, in both hemispheres. They are each 43 4' broad. 18. The frigid zones are the spaces included within the polar circles. 19. Amphiscii \\ are the inhabitants of the torrid zone, so called because they cast their shadows both north and south at different times of the year. 20. Heteroscii is a name given to the inhabitants of the tempe- rate zones, because they cast their shadows at noon only one way.1[ 2 1 . Periscii are those people who inhabit the frigid zones, be- cause their shadows, during a revolution of the earth on its axis, are directed towards every point of the compass. * So called from the Greek word trepo, to turn, because when the sun comes to either tropic s it begins to return again towards the other. f So called from zone or zona, a girdle, being extended round the globe in that form. It is similar to the term climate, for pointing out the situation of places on the earth, but less exact, as there are only five zones, whereas there are 60 climates, as will be seen in its proper place. $ This zone was called by the ancients Torrid, because they conceived that being exposed to the perpendicular or direct rays of the sun, the heat must be so great, and the country so barren and parched, as to render it entirely uninhabitable. But this idea has long since been refuted, The sun is perpendicular twice in the year to every part of this zone. These zones were called temperate by the ancients, because, meeting the sun's ra}^s obliquely, they enjoy a moderate degree of heat, the sun be- ing never perpendicular to my part of them. The breadth of the temperate zones increases a little every year, whilst that of the torrid and frigid zones decrease in the same proportion, owing to the animal decrease of the ob- liquity of the ecliptic. || When the sun is vertical or in the zenith, which happens twice a year, they are then called ascii, or shadowless, because at that time they have no shadow. 5f Thus the shadow of an inhabitant of the north temperate zone always falls to the north at noon, because the sun is then directly south ; and an in- habitant of the south temperate zone casts his shadow towards the south at noon, because the sun is due north at that time. These distinctions are however rather trifling. DEFINITIONS, &c. 5 22. The anted* are those who live under the same meridian, and in the same latitude, but on different sides of the equator. 23. Periceci f are those who live in the same latitude, but in op- posite longitudes. 24. Antipodes \ are those inhabitants of the earth, who live dia- metrically opposite to each other. 25. Meridians are great circles passing through the poles, and cutting the equator at right angles. * The antccci have the same hours, but contrary seasons of the year; thus when it is noon with one, it is noon with the other, Sec. But when it is sum- mer with one, it is winter with the other, &c. consequently the length of the days with one, is equal to the length of the nights with the other ; the sun when in the equinoctial rises and sets to the one at the same time that it rises ancl sets to the other, &c. Those who live at the equator have no antoeci. f The perioeci have their seasons of the year at the same time, and also their days and nights of the same length with each other ; but when it is noon with the one it is midnight with the other, and when the sun is in the equinoctial, he rises with one when he sets with the other. Those who live under the poles have no perioeci. Their difference of longitude is 180. t The antipodes have both their latitude and longitude different, and con- sequently both their seasons and hours ; so that when it is summer with one it is winter with the other ; when it is twelve o'clock in the day with one it is twelve at night with the other. They have like seasons, and the same length of days and nights, but at different times. When they stand, their feet are towards one another, and their heads opposite. Hence that part of the heavens which appears over the head of one, seems to be beneath or un- der the feet of the other ; and therefore, when we speak of up or do-tvn, we speak relatively and only with regard to ourselves ; for no point, either in the heavens, or on the surface of the earth is above or below, but only with res- pect to ourselves. Upon whatsoever part of the earth we stand, our feet is always nearly directed towards the centre, and our head towards the sky ; in the latter case we say up t in the former do-urn. $ These are so called from the Latin word meridies, midday, because when the sun is on any of these meridians, it is then noon or 12 o'clock, in all places under that meridian. Every place on the globe is supposed to have a meridian passing through it, though on most globes there are but 24, the deficiency being supplied by the brass meridian, which is therefore called the universal meridian. They are drawn through every 15 of the equinoc- tial, and are therefore sometimes called hour circles, the reason of which is evident; for if 360, the number of degrees in a circle, be divided by 24, the hours in one day, the quotient 15 will give the number of degrees corres ponding to each hour. Geographers assume one of these meridians as the first, commonly that which passes through the metropolis of their own coun- try, but the general practice is, to reckon longitude from the meridian oi' Greenwich observatory in England. The brazen meridian is divided into 360 equal parts, called degrees, these are again supposed to be divided into 60 equal parts, called minutes, and these into 60 equal parts, called seconds. &.C. to thirds, fourths, fifths, &c. On the globes, however, the degrees aiv seldom subdivided into fewer parts than quarters. In the upper semicircle of the brass meridian, the degrees are numbered from to 90 from the equa tor towards the poles, and are generally used in finding the latitude of places On the lower semicircle they are numbered from to 90, reckoning from t ! poles towards the equator, und are principally used in elevating either of the poles to the latitude, .c ^- 6 DEFINITIONS, Vc. 26. The brazen meridian (or universal meridian) is the brass circle in which the artificial globe turns. 27. Thejirst meridian is that from which geographers begin to count the longitude of places. 28. Hour circles,* or horary circles, are the same as the meri- dians ; they are supplied by the brass meridian, the hour circle and its index. 29. The hour circle or index, is a small circle of brass fixed to the north pole, and on which the hours of the day are marked. 30. The ecliptic t is that great circle in which the earth per- forms its annual motion round the sun, or in which the sun seems to move round the earth once bi a year. 31. Signs of the ecliptic are the 12 equal parts into which it is divided. The signs and the days on which the sun enters them are These circles are drawn through every 15 of longitude reckoning fr meridian, for the reason given above, but on Gary's globes they from any meridian, tor tne reason given above, but on Vary's globes tney are drawn through every 10, as on a map, though without answering any useful purpose. As 15 correspond to an hour, 4 minutes of time must correspond to each degree, 2 minutes to half a degree, 1 minute to one quarter of a de- gree, &c. (see Keil's astr. lect. 18.) On some globes the index, which points out the hours, has two rows of figures on it, others but one. On Bardin's new British globes, there is an hour circle at each pole numbered with two rows of figures. On Gary's there is but one hour circle placed under the brass meridian at the north pole, marked with only one row of figures, and is therefore more convenient, as it answers every purpose to which a circle of this kind can be applied, without that confusion generally arising from two rows of figures. On Adams' common globes there is but one index ; but on his improved globes the hours are counted by a brass wire with two indexes placed over the equator. On many of the globes fitted up by Jones, the hour circle is calculated to slide on the brass meridian, for the conveniency of pointing- out the bearings of places, &c. These circles are however of little consequence, as the equator and quadrant of altitude will answer every pur- pose to Xvhich they can be applied. f The ecliptic (so called, because the eclipses of the sun and moon can happen only in the plane of this circle) makes an angle of 23 28' with the equinoctional, one half being 1 in the northern hemisphere, and the other in the southern. The spring and autumn signs being- in the northern hemis- phere, are therefore called northern signs ; the other six, or the summer and winter signs, being in the southern, are for the same reason called southern sig?is. The spring and autumnal signs are likewise called ascending' signs, because when the sun is in any of these signs,his declination is increasing-; the summer and winter signs are called descending signs, because when the sun is in any of them, his declination is decreasing. Each of these signs is divided into 30, &c. and in whatever sign and degree the sun is, that point is called the sun's place. The day of the month corresponding to the sun's place is likewise commonly marked on this circle. The equinoctial point aries is that point from which the sun's place or longitude is reckoned, with- out any regard to the constellations themselves, which, on account of the precession of the equinoctial points, are now a whole sign advanced from west to east, or according to the order in which the signs are reckoned. Be- sides the sun's place or longitude, his apparent and annual motion, stars longitude, poetical rising and setting-, increase and decrease of days, culmi- nating- degree, eclipses of the sun and moon, distinction of north and south latitude of the stars, &c. arc dso found on this circle. DEFINITIONS, fcV. 7 as follows, according as they are represented on Gary's globes. The beginning of each day is to be taken. Sfiring signs. 9jP Aries, the ram, 21st of March. 8 Taunts, the bull, 20th of April. n Gemini, the twins, 21st of May. Autumnal signs. aQt libra, the balance, 23d of Sept. }\ Scorpio, the scorpion, 23d of Oct. $ Sagittarius,tbc archer, 22d of Nov. Summer signs. 25 Cancer, the crab, 21st of June. SI Leo, the lion, 23d of July, njj Virgo, the virgin, 23d of August. Winter signs. V? Capricornus, the goat, 22d of Dec. Zg Aquarius, the water-bearer, 20th of January. X Pisces,, the fishes, 18th of Feb. 32. The equinoctial points* are Aries and Libra, -where the eclip- tic cuts the equinoctial. 33. The solstitial points\ are Cancer and Capricorn. 34. The colures\ are the two meridians passing through the equinoctial and solstitial points. The one called the equinoctial, and the other the solstitial colure. 35. The horizon is a great circle,* which separates the visible half of the heavens from the invisible. It is distinguished into two kinds, the sensible and the rational. * The point aries is called the vernal equinox, and the point libra the autumnal equinox. When the sun is in either of these points, the days and nights are equal on every part of the globe. f When the sun is in or near these points, the variation in his meridian, or greatest altitude, is scarcely perceptible for several days, because the ecliptic, near these points, may be considered nearly parallel to the equinoe- tial, and hence in these points, the sun does not perceptibly vary his decli- nation for some days. When the sun enters the beginning of cancer, all the Inhabitants on the north side of the equator have their longest day % and those in the southern hemisphere their shortest. When he enters Capricorn, the inhabitants of the northern hemisphere have their shortest day, and those iit the southern their longest. The learner must notice, that when the sun en- ters cancer, all the inhabitants within the north polar circle have constant day, and those within the south polar circle constant night, but wh$n the sun enters Capricorn, the reverse happens. They are called solstice* from the circumstance of the sun's standing' still, or having no motion when he is in either of these points, hence said to be stationary (solis static.) $ These colures divide the ecliptic into four equal parts, and mark the four seasons of the year. In the time of Ifipparckus the equinoctial colure ies supposed to have passed through the middle of the constellation aries. Hipparchus was born at Nicsea, a town of Bythinia in Asia minoir, about 75 miles S. E. of Constantinople, now called Isnic ; he flourished between the 154th and 163d olympiads, or between 160 and 135 years before Christ. He foretold eclipses, and as Pliny remarks, was the first who dared to number the stars for posterity, and reduce them to a standard. He gave a catalogue of 1022 stars, and rendered many other important serviccs\o astronomy. Horizon takes its name from the Greek word orizon CfniensJ because it defines or bounds our view. The sensible horizon extends only a few miles ; thus at the height of 6 feet, the utmost extent of our view on the earth, or sea, would be 2.42 miles ; at 20 feet 4.4 geographical! miles, &c. In general, if h be the height of the eye above the surface of the sea, and d the diameter of the earth in feet, then ^d^Ti^h will nearly' shew the greatest extent to which a person can see, or the diameter of t he sensible horizon, the centre being- supposed at the eye. (Euclid, 36 prop , 3b.) This DEFINITIONS, &e. 36. The sensible or apparent horizon is that circle that termi- nates our view, where the sky, and the land or water, appear to meet. 37. The rational or real horizon, is an imaginary circle, whose plane passes through the centre of the earth, parallel to the plane of the sensible horizon. 38. The wooden horizon is that circular plane circumscribing the artificial globe, which represents the rational horizon on the real globe. 39. The cardinal points of the horizon, are the east, west, north and south points.* 40. The cardinal points in the heavens, are the zenith the nadir, and the points where the sun rises and sets 4 1 The cardinal points of the ecliptic are the equinoctial and solstitial points, which mark out the four seasons of the year ; and the cardinal signs are ^ Aries, 05 Cancer, =^ Libra, and itf Capricorn. 42. The Zenith is a point in the heavens exactly over our heads, and is the elevated pole of our horizon. determines the apparent rising, setting-, &c. of the sun, stars, planets, &c. The rational horizon determining their real rising, setting 1 , &c. The wooden horizon respecting the rational horizon on the real globe of the earth, is di- vided into several concentric circles. On Bardin's new British globes they are arranged in the following order : the 1st circle marked amplitude, is numbered from the east towards the north and south, from to 90, and from the west towards the north and south in the same manner. The 2d circle marked azimuth, is numbered from the north and south points of the horizon towards the east and west from to 90. The 3d circle repre- sents the 32 points of the compass. The degrees belonging to these may be found iai the circle of amplitude. The 4th circle contains the twelve stgnx of the Zodiac, The 5th, the degrees corresponding to each sign, each com- prehending 30. The 6th contains the day of the month corresponding- to each degree, &c. of the sun's place in the ecliptic. The 7th contains the equation of time, the sign -f- shews that the clock is faster than the dial by so many minutes, the sign that it is slower, and the number of minutes in the dif- ference is expressed opposite the corresponding- days of the month. The 8th circle contains the twelve calendar months of the year, &c. These cir- cles are in the same order on Gary's globes, except that of the equation of time, which is represented on a vacant part of the globe between the tro- pic's, nearly in the shape of the figure g. The days of the month being marked in the curve of the figure, and the time or equation on a small scale drawn through that point where the curve of the figure intersects, in a di- rection pa rallel to the equator. Though the rising and setting of the stars respect the rational horizon, and the place of observation reduced to the earth's centre, yet it holds true of the sensible horizon, the spectator being placed on the earth's surface, on account of the great distance of the fixt stars, the semidiameter of the earth being no i nore than a point at that immense distance. * The east is that point of the horizon where the sun rises when in the equinoctia I, and the -west is the point directly opposite on the plane of the horizon, < >r where the sun sets when the clays and nights are equal : the south is 9C ) distant from the east or west, and is that point towards which the sun appears at noon, to those situated in north latitude, and the north is that poi nt of the horizon directly opposite to the south. v DEFINITIONS, tff. 9 43. The nadir is a point in the heavens opposite to the zenith, or directly under our teet, and is the depressed pole of our horizon. 44. The mariners compass is a representation of the horizon, which is divided into 32 equal parts, and is so called from its being used to ascertain the course of a ship at sea. 45. The -variation of the comfiass* is the deviation of its point? from the corresponding points in the heavens, or the angle formec| between the true and magnetic meridian, and is reckoned towards the east or west. 46. Azimuth or -vertical circles are imaginary circles passing through the zenith and nadir, cutting the horizon at right angles.f 47. The azimuth of any object in the heavens is an arch of the horizon, contained between a vertical circle passing through the object, and the north or south points of the horizon. 48. The firime -vertical is that azimuth circle, which passes through the east and west points of the horizon. :$ 49. The altitude of any object in the heavens is an arch of a vertical circle, contained between the centre of the object and the horizon. 50. The zenith distance of any celestial object is an arch of a vertical circle, intercepted between the centre of the object and the zenith. 5 1 . The meridian altitude, or meridian zenith distance, is the altitude or zenith distance, when the object is on the meridian. 52. The/zo/ar distance of any celestial object, is an arch of the meridian, contained between the centre of that object and the pole of the equinoctial. 53. The quadrant cf altitude is a thin slip of brass, one edge of which is divided into degrees, &c. equal to those of the equator, arid is used to find the distances of places, &c. on the earth, and the distances, altitude, Sec. of bodies in the heavens,. 54. The amplitude of any object in the heavens, is an arch of the horizon contained between the centre of the object, when ris- ing or setting, and the east or west points of the horizon. Or it is the number of degrees which the sun or a star rises from the east and sets from the west. *. See the note to definition 54 and problems 49 and 50, part 2d. f- The altitudes of the heavenly bodies are measured on these circles t they may be represented by the quadrant of altitude screwed in the zenith of any place and moving- the other end along- the wooden horizon of the lobe. These circles are always at rig-lit angles to the horizon. \ This is always at right angles both with the brazen meridian and ho* rizon. In our summer the sun rises to the north of the east and sets to tha north of the west ; and in the winter it rises to the south of the east and sets to the south of the west. The amplitude and azimuth are in point of utility, much the same ; the amplitude shewing- the bearing- of any object when it rises or sets, from the east or west points of the horizon, and the- azimuth the bearing- of any object when it is above the horizon, cither from the north or south points thereof. They are generally useful in determining B 10 DEFINITIONS, &c. 55. Time* is that succession in the existence of beings, which' have a beginning and will have an end, and is measured by the mo- tion of some moving body. It is distinguished into years, months, weeks, days, hours, minutes, Sec. 56. Time is either absolute and relative, true and apparent, or mathematical and common. Absolute, true, and mathematical time, 6f itself and from its own nature flows equably, without regard to any thing external, and by another name is called duration ; rela- tive, apparent, and common time, is some sensible and external measure of duration, by means of motion, whether accurate or un- equal, and is commonly used instead of true time. 57. The equation of time\ is the difference between the abso- lute and relative time, or it is the difference of time shewn by a well regulated clock and a correct sun dial. 58. Apparent noon is the time when the sun comes to the meri- dian, viz. 12 o'clock, as shewn by a correct sun diai. the variation of the magnetic needle. For if th6 observed and true ampli- tudes be both north or both south, their difference will be the variation ; but if one be north and the other south, their sum will be the variation. In like manner if the true and observed azimuth, be both east or both west, their difference will be the variation ; if otherwise, their sum will be the variation. The variation is easterly, when the true bearing is to the right hand of the magnetic bearing, but westerly when to the left hand ; the observer being 1 supposed to look directly towards the point representing the magnetic bearing*. * What time is in itself, or what its physical essence is, no philosopher can fathom or define, but this we know, and it is the most important know- ledge for us, if reflected on, that it hurries us to that eternity in which time has no existence, and that every moment may be the last" momentum a quo tota peiidit ceternitas" If then it be necessary to consider time, as it re- gulates our seasons, is it not more necessary to consider it, as it relates to an immortal existence towards which it imperceptibly hurries us. Truths of this nature are better calculated to expand our ideas, and point out to us that state which has no termination or limits, and in which we are destined to enjoy a dignified existence, than those whose objects are as fleeting us time itself; for as soon as futurity begins to expand its extensive prospects, then we see the vanity of what the world sets such a value on, and learn to value those things alone which are immortal. f The equation of time arises from t\\r> principal causes, the sun's unequal motion in the ecliptic, describing the southern signs in less time than the northern, the difference amounting to about eight days ; and from the obliqui- ty of the plane of the ecliptic to that of the equator. For the space between two meridians, or hour lines on the ecliptic will not, in consequence, be al- ways the same as the space between the same meridians on the equator, the difference being sometimes greater, sometimes equal, and sometimes less ; but as the sun in consequence of this difference, takes sometimes less, sometimes more than 24 hours, in revolving from any meridian, until his return to the same again, it thence follows that the hours shewn by a well regulated clock, must be different from those shewn by a true sun dial, and hence the equation of time. If the sun performed its annual revolution in the plane of the equator, there would be no equation except what arises irom the difference in his annual motion, (see prob. 22, part 2d, Keil lect 25, Ferguson, chap. 13, or Mayor's tables, published by Nevil Maskehm-. and note to prob. 8.) DEFINITIONS, csV. 11 59. True or mean noon is the middle of the day, or 12 o'clock, ^ shewn by a well regulated clock, adjusted to go 24 hours in a mean solar day. 60. An hour is a certain determined part of the day, and is either equal or unequal. An equal hour is the 24th part of a mean natural day, as shewn by well regulated clocks, &c. unequal hours are those measured by the returns of the sun to the meridian, or those shewn by a correct dial. Hours are divided into 60 equal parts called minutes, a minute into 60 equal parts called seconds, a second into 60 equal parts called thirds, &c. 6 1 . A true solar day>* is the time from the sun's leaving the meridian of any place on any day, till it returns to the same me- ridian on the next day. Or it is the time elapsed from 1 2 o'clock at noon, on any day, to 12 o'clock at noon on the next day, as shewn by a correct sun dial. 62. A mean solar dayrf is the space of time consisting of 24 hours, as measured by a clock or time-piece. 63. The astronomical or natural day,\ is the time from noon to noon, as shewn by a correct dial, and also consists of 24 hours. * A true solar day is subject to a continual variation, arising from the ob- liquity of the ecliptic and the unequal motion of the earth in its orbit ; the duration thereof sometimes exceeds and sometimes falls short of 24 hours, as taken notice of in the note on the equation of time. The variation is the greatest about the 1st of November, when the solar day is 16' 15" less than 24 hours, as shewn by a well regulated clock. | There are in the course of a year as many mean solar days as there are true solar days, the clock being as much faster than the sun dial on some days of the year, as the sun dial is faster than the clock on others, as may be' seen by consulting the analemmaor the circle on which the equation of time is marked on the globes. Thus the clock is faster than the sun dial from the 24th of December to the 15th of April, and from the 16th of June to the 31st of August ; but from the 15th of April to the 16th of June, and from the 31st of August to the 24th of December, the sun dial is faster than the clock. When the clock is faster than the sun dial, the true solar day exceeds 24 hours ; and when the sun dial is faster than the clock, the true solar day is less than 24 hours ; but when the clock and sun dial agree, viz. about the 15th of April, 16th of June, 31st of August, and 24th of December the true solar day is exactly 24 hours. (See the table annexed to problem 21.) t This is called a natural day, being of the same length in all latitudes, It begins at noon, because the increase and decrease of days, terminated by the horizon are very unequal among themselves ; which inequality is like- wise augmented by the inconstancy of the horizontal refractions (see 183 Perguson's Astronomy) and therefore the astronomer takes noon, or the mo- ment when the sun's centre is on the meridian, for the beginning of the day. The hours are reckoned in numerical succession from 1 to 24. Navigators begin their computation at noon 24 hours before the commencement of the astronomical day, reckoning their hours froml to 12; the first 12 hours arc marked A. M. (ante meridiem} or forenoon, the second P. M. (post meri- diem } or afternoon. All the calculations in the nautical almanac are adapt- ed to astronomical time. The declination, 8cc. there calculated, is adapted to the beginning of the astronomical day, or to the end of the sea day; it being at the end of the sea day, that mariners want the declination, to determine: their latitudes. 12 DEFINITIONS, &v. 64. The artificial day, is the time elapsed between the sun's ris- ing and setting, and is variable according to the different latitudes of places. Night, is the time from sun setting to sun rising, and varies in like manner. 65. The civil day,* like the astronomical or natural day, consists 6f 24 hours, but begins differently, according to the customs of dif- ferent nations 66. A siderceal day, is the interval of time from the passage of any fixed star over the meridian, till it returns to it again ; or it is the time which the earth takes to revolve once round its axis, and consists of 23 hours, 56 minutes, 4> seconds. Note. Though -we suppose the earth to turn on its axis once in 24 fiours from H>est to east, yet its eocact revolution is as above, making about 366 revolutions in 365 days. But as the sun advances about 1 in its orbit daily,* which cor- responds to about 4? of time, the day is properly taken 24 hours, because the earth has to advance 1 more on its axis to have tJie sun over the same meridian as on the preceding day. * The ancient Babylonians, Persians, Syrians, and most of the eastern na- tions, began their day at sunrising, which custom is followed by the modern. Greeks. The ancient Greeks, Jews, &c. began their day at sunsetting, and this custom is observed by the modern Austrians, Bohemians, Silesians, Ital- ians, Chinese, &c. The Arabians beg-in their day at noon like the astrono- mers. The more ancient Jews, tog-ether with the ancient Egyptians, Ro- mans, &c. began their day at midnight, and this custom is followed by the 9nglish, French, Germans, Dutch, Spanish, Portuguese and Americans. The famous astronomers Hipparchus, Copernicus, and some others, began their day in like manner from midnight. Those wko begin their day at aim rising, have this advantage, that their hours tell them how much time is Already past since sun rising; and they who reckon their hours from sun setting, know how long it is to sun setting ; and hence they may proportion their journies and labours for that time. But both have this inconvenience, that their midday and midnight happen on different hours, according to the seasons