GIFT OF 
 MICHAEL REESE 
 
PHYSICS 
 
 OF THE 
 
 EARTH'S CKUST.' 
 
 BY 
 
 THE REV. OSMOND FISHER, M.A., F.G.S., 
 
 ** // 
 
 IECTOR OF HARLTON, HON. FELLOW OF KING'S COLLEGE, LONDON, AND LATE 
 FELLOW AND TUTOR OF JESUS COLLEGE, CAMBRIDGE. 
 
 Hontron : 
 
 MACMILLAN AND CO. 
 1881 
 
 [The Right of Translation and Reproduction is reserved.] 
 
PRINTED BY C. J. CLAY, M.A. 
 AT THE UNIVERSITY PRESS. 
 
PEEFACE. 
 
 FOR many years past I have been convinced that various 
 questions of Physical Geology might be answered negatively, 
 if not positively, by applying to them simple mathematical 
 reasoning, and quantitative treatment. My own views have, 
 in some respects, been greatly altered by the application of 
 this method ; and I confess that the present work contains 
 within itself evidence of the circumstance ; for not only will 
 it be found that the views now put forward differ in some 
 respects from those which I have previously published in con- 
 tributions to scientific periodicals; but the effect of the pro- 
 gressive application of the quantitative method may be traced 
 in the book itself; and the development of ideas, proposed 
 in the earlier chapters, will sometimes be found to have taken 
 an unexpected turn later on. This remark applies especially 
 to certain hypotheses, which at first presented themselves 
 in a favourable light, to account for compression and for the 
 formation of ocean basins. 
 
 It is extremely probable that, if these investigations are 
 carried further, some of the theories now offered as fairly 
 established, may turn out to be untenable. With a growing 
 science like Geology this is unavoidable. On a review of what 
 I have written, I feel how many difficulties have been left 
 unsolved, and some which have occurred to me not even 
 mentioned. Nevertheless I hope that this attempt will not 
 be without a certain value in advancing the study of the 
 Physics of the Earth's Crust. 
 
vi PREFACE. 
 
 The mathematical reader will perhaps be surprised by the 
 rough and ready mode of treatment adopted in some instances. 
 But when it is recollected that, for the most part, we can assign 
 only very hypothetical values for our symbols, it would be 
 affectation to seek close results, which would after all have 
 no greater value than those which claim to be only distant 
 approximations. 
 
 The course of the argument and the general conclusions, will 
 be found repeated in the Summary at Chapter XXII. But 
 it is hoped that a perusal of this may not be substituted for 
 reading the book. It is believed that the reasoning of the 
 several chapters will be found intelligible, even without wading 
 . through the calculations. 
 
 My thanks are due to the Councils of the Geological Society 
 of London, and of the Philosophical Society of Cambridge, for 
 permission to make free use of papers contributed by me to 
 their publications. I have similar acknowledgments to make 
 to the Proprietors of the Philosophical Magazine, the Geological 
 Magazine, and the Quarterly Journal of Science. My kind 
 friends, H. W. BRISTOW, Esq., F.R.S., Senior Director of the 
 Geological Survey, and A. F. GRIFFITH, Esq., B.A., of Lincoln's 
 Inn, Scholar of Christ's College, Cambridge, have rendered me 
 most valuable help in revising the proofs while they were 
 passing through the press. 
 
 OSMOND FISHER. 
 
 HARLTON RECTORY, 
 
 18 October, 1881. 
 
CONTENTS. 
 
 CHAPTER I. 
 
 ON UNDEEGEOUND TEMPEEATUEE. 
 
 The rise of temperature on descending into the earth The causes which have been 
 assigned for it Attempts to determine the law of increase by observation 
 Their results Deep bore-hole at Sperenberg and metJwds of observation used 
 there General effects of convection currents in a bore-hole Tabulated obser- 
 vations at Sperenberg Anomalous result supposed to be deducible therefrom 
 Anomaly explained General law of average rise of temperature not impaired 
 thereby Hot springs and volcanos prove that the rise of temperature con- 
 tinues, but do not inform us whether the laiv near the surface obtains unaltered 
 for all depths . . ]" , ... .... > . . . 1 
 
 CHAPTER II. 
 
 CONDITION OF INTEEIOE. 
 
 Little known about the condition of the interior of the earth Results of the mathe- 
 matical " Theory of the Earth" point to a former condition of fluidity 
 Determination of the mean and surface densities The question proposed 
 whether the fluid condition still partially exists more or less Connection be- 
 tween this question and that of the law of internal temperature Two modes 
 of attacking the question, (1) Precession, (2) the tides Opinions of Sir Wm. 
 Thomson, Hopkins, Delaunay, and others Possibility of a cooled crust resting 
 on an internal fluid layer . . ^ , ^ . .18 
 
 CHAPTER III. 
 
 INTEENAL DENSITIES AND PEESSUEES. 
 
 Speculations concerning tlw materials in successive couches Waltershausen's 
 theory His law of density open to correction His tables of densities and 
 pressures Fluid pressures within the earth calculated from Laplace's law of 
 density Fluid pressure at the centre . .' . . . .28 
 
viii CONTENTS. 
 
 CHAPTER IV. 
 LATEEAL PEESSUEE, ITS AMOUNT. 
 
 Generally received views regarding the contortion of rocks by lateral pressure 
 Calculation of the possible amount of such pressure at the surface Attempt to 
 estimate the same within the earth Mountain chains elevated by lateral 
 pressure The Himalayas ......... 34 
 
 CHAPTER V. 
 
 ELEVATIONS AND DEPEESSIONS. 
 
 Distinction between compression and contraction Definition of datum levels 
 General geometrical relation between the compression of a portion of the 
 earth's crust and the elevations and depressions referred to the upper datum 
 level resulting therefrom The same extended to the whole surface of the globe 
 Modification of this relation if the globe is supposed to be wholly solid 
 Average height of all the elevations above the datum level upon the supposi- 
 tion of solidity, expressed in terms of depth of sea and height of land, and 
 of areas of the same This average height of actual elevations estimated in 
 feet . . . .45 
 
 CHAPTER VI. 
 
 ELEVATIONS ON THE HYPOTHESIS OF SOLIDITY. 
 
 Any physical hypothesis regarding the condition of the interior of the earth may 
 be tested by comparing the average height of the elevations it would produce 
 with that which exists in nature Sir Wm. Thomson regards the earth as a 
 solid cooling by conduction Some of the results of his paper " On the Secular 
 Cooling of the Earth " His mathematical formula for expressing the law of 
 temperature in descending Calculation in general symbols of the average 
 height of the elevations which would be produced upon the supposition of the 
 earth cooling as a solid Numerical result obtained loith a value of the coeffi- 
 cient of contraction deduced from Mallet's experiments and Sir Wm. Thomson's 
 estimates of the melting temperature and conductivity The same with Mr 
 Mallet's estimate of the melting temperature of slag The corresponding age 
 of the earth Amount of radial contraction 57 
 
 CHAPTER VII. 
 
 HYPOTHESIS OF SOLIDITY FAILS. 
 
 Summary of results of Chap. VI. Grounds on which Physicists have restricted 
 geological time within certain limits Discrepancy between height of the 
 actual average elevations and of those which would be produced upon a 
 cooling solid globe Necessary alternative suppositions Captain Dutton's 
 
CONTENTS. ix 
 
 argument Ocean basins Opinions about them of Pratt, Mallet, Hopkins, 
 LeConte Radial contraction cannot explain them Stitt less oscillations of 
 surface Examples of oscillation N. Wales, Appalachians, New Zealand, 
 India, Colorado Plateau Gwyn Jeffreys on changes of level Babbage The 
 distribution of elevations in ranges requires a fluid substratum This sup- 
 position explains other surface movements The pressures under which any 
 part of the crust is in equilibrium The so-called " contractional hypothesis" 
 not to be abandoned Captain Dutton's objections to it considered . . 73 
 
 CHAPTER VIII. 
 FLUID SUBSTEATUM. 
 
 The extravasation of water-substance from beneath the crust suggested as a 
 cause of contraction of volume Igneo-aqueous fusion Dissolving power of 
 water when above the critical temperature Scrope LeConte Escape of 
 steam from volcanic vents Opinion that sea-water gains access to volcanic 
 foci Objections to this hypothesis Experiment of Daubree not in point 
 Views on cosmogony Dr Sterry Hunt's theory Objections to it Fails to 
 account for the facts A suggestion to explain the presence of water-substance 
 below the cooled crust . . . < '.. , . .87 
 
 CHAPTER IX. 
 
 CEUST NOT FLEXIBLE. 
 
 The "datum level" equation has served an important purpose Supposition of a 
 flexible crust Mode of determining the general character of the undulations 
 which a thin flexible crust would assume when resting upon a liquid 
 Mathematical investigation of the problem Certain negative conclusions 
 therefrom regarding the earth's crust Alternative assumption to which we 
 are led . . ... . . , 99 
 
 CHAPTER X. 
 
 ,. DISTUKBED TEACT. 
 
 Conditions of equilibrium of a disturbed portion of the earth's crust Probable 
 result of compression Part of the crust sheared upwards andpart downwards 
 These separated by a "neutral zone" Calculation of its position Confused 
 contortions in highly metamorphosed rocks explained Depth of neutral zone 
 Probable thickness of crust Prof. A. Favre's experiments on contortions 
 Inverted flexures Formation of a mountain chain and its elevation above 
 the ocean Subsequent effects of denudation and accumulation of additional 
 sediment Consequent tilting of tract Also general elevation from the same 
 cause Why areas of deposition are sinking areas Degree of tilting depends 
 upon width of tract and the existence of a mountain chain . ' ." . 114 
 
x CONTENTS. 
 
 CHAPTER XI. 
 
 THE EEVELATIONS OF THE PLUMB-LINE. 
 
 Mountains the "backbones" of continents They have "roots" TJiese are revealed 
 by the plumb-line Pratt's calculation of the attraction of the Himalayas 
 The actual attraction less than that calculated His attempted explanation of 
 the discrepancy Sir G. B. Airy's explanation more satisfactory Pratt's 
 reply shown to be inconclusive The result confii-ms the reasoning of the 
 preceding chapter The plumb-line reveals a greater density beneath 
 oceans 142 
 
 CHAPTER XII. 
 
 THE EEVELATIONS OF THE THEEMOMETEE. 
 
 Recapitulation of results of previous chapter Eoots of mountains should be 
 revealed by phenomena of underground temperature Conditions upon which 
 the mean rate of increase of temperature will depend Eate greater in plains 
 and less in mountains Dr Stapff His observations on temperature of rocks 
 in St Gothard tunnel His explanation of the smallness of the rate Why not 
 satisfactory Effect of convexity of mountain upon the rate The rate may 
 be considered uniform above The conclusion from the premises is that the 
 mountain has roots The rate may be regarded as nearly uniform throughout 
 General method of determining the thickness of the crust at the sea-level, 
 and the melting temperature, from the rates beneath the mountain and the 
 usual rate Application to St Gothard Thickness of crust at sea-level and 
 melting temperature deduced numerically from the data The like for Mont 
 Cenis Results confirmatory of previous conclusions Considerations about 
 the oceanic areas How the water is retained there The thickness of the 
 sub-oceanic crust and its density . 151 
 
 CHAPTER XIII. 
 
 AMOUNT OF COMPEESSION. 
 
 Our ideas respecting the sub-oceanic crust necessarily speculative Compression 
 possibly confined to continental areas Compression might arise from extrava- 
 sation of matter from beneath the crust, or from expansion of the crust 
 Amount of compression needs to be estimated afresh Datum-level equation 
 transformed to mean level Formula to express compression in terms of 
 inequalities Estimate of inequalities from Atlas (1) Contraction on sup- 
 position that Oceans are due to compression, (2) that they are due to denser 
 crust . ...... . .168 
 
CONTENTS. xi 
 
 CHAPTER XIV. 
 
 EXTKAVASATION OF *WATER WILL NOT ACCOUNT FOR 
 COMPKESSION. 
 
 Hypothesis that oceans consist of water that has been extravasated Density 
 of the water before extravasation Volume of interior which would need to 
 have contributed it Hypothesis shown to be inadequate to produce the entire 
 compression Disturbance of crust by change of ellipticity of spheroid 
 Inequalities do not appear connected with such a cause .... 180 
 
 CHAPTER XV. 
 COMPBESSION AND VOLCANIC ACTION. 
 
 Compression not being sufficiently accounted for by contraction of the globe, 
 alternative hypothesis that the cause of it is situated within the crust 
 Attraction of thickened crust not operative Intrusive dykes may afford a key 
 to the problem may be widened by fluid pressure Excess of horizontal over 
 vertical pressure so caused TJieir connection with volcanic vents Hypothesis 
 concerning the constitution of the magma mode of its elevation in a fissure 
 Pressure on the sides of the fissure Comparison of the work of compression 
 ivith that done against gravity Mineral veins Prof. Judd and Baron 
 Richthofen on the relation of volcanic energy to continental movements 
 Possible additional compression upon solidification of dykes Analogies of 
 earth's crust and ice Prof. Nordenskiold's theory of compression Analogy 
 of ice disturbed by skaters and earth's crust by sedimentation Corrugation 
 attributed to cracks opening from below, and a continental phenomenon 
 Views of American Geologists as set forth by Dr Sterry Hunt Their observed 
 facts agree with the present theory Effect of increased thickness of crust on 
 compressing force Whence the energy invoked Circulation of rock Sug- 
 gestion to explain diminished density of continental areas "Red clay" of 
 profound ocean . ...... . ... . . 185 
 
 CHAPTER XVI. 
 
 ON FAULTING. 
 
 Faulting due to contraction "Hade to the downthrow" Faults may die out 
 in the depths The fissure which gives rise to the fault Fissure will have 
 the same hade as the fault Course of fault in a straight line Fissures 
 which cause faults commence at the surface Faults of Utah described by 
 Captain Dutton Faulting superimposed on corrugation Extent of throw 
 of great faults Faults will not usually admit the fluid "magma If they 
 do so may give rise to fissure eruptions of igneous rock Application 
 of datum-level equation to faulting Faulting must depress the tract 
 affected General theoretical conclusion respecting the connection of fault- 
 ing and corrugation . , , . . . . . 208 
 
xii CONTENTS. 
 
 CHAPTER XVII. 
 
 . GEOLOGICAL MOVEMENTS EXPLAINED. 
 
 Recapitulation of the four suggested causes of compression Three of them 
 negatived The fourth possibly the true one The fact of compression certain, 
 and the duplex character of the corrugations most probable The conse- 
 quences of denudation followed out Elevation its correlative Fresh-water 
 strata covered by marine Movements most energetic near, but not confined to, 
 continents Degradation of mountains a law of nature Enormous thickness 
 of certain strata accounted for Raised sea beaches Two classes of elevatory 
 movements Drainage across dip Theories of compression compared . 217 
 
 CHAPTER XVIII. 
 
 ME MALLET'S THEOKY OF VOLCANIC ENERGY. 
 
 Early opinions regarding the seat of volcanic energy Hopkins' lava lakes 
 Mallet's theory Opposed to the results of the present work His mode of 
 estimating the temperature derivable from crushing rock His results pub- 
 lished in the "Phil. Trans." differ from those given in an earlier publica- 
 tion Latent heat of fusion Localization of heat from crushing not possible 
 More favourable hypothesis suggested and considered A pressure, the 
 greatest obtainable on the hypothesis, incapable of causing volcanic phe- 
 nomena , . 226 
 
 CHAPTER XIX. 
 
 THE VOLCANO IN EEUPTION. 
 
 Theories of volcanic eruption Scrope, Dutton, Mallet Local and temporary in- 
 crease of temperature not probable Richthof en's theory unsatisfactory Ex- 
 planation of phenomena on hypothesis of fluid substratum in igneo-aqueous 
 fusion Amount of water-substance beneath vent probably variable Mechanics 
 of an eruption Estimate of amount of water-substance in magma Eruption, 
 how brought to an end Evisceration of cone State of intermediate activity 
 Stromboli Unsympathetic craters Richthofen's difficulties met Renewal 
 of activity Comparison with Geyser 240 
 
CONTENTS. xiii 
 
 CHAPTER XX. 
 
 SEQUENCE OF VOLCANIC BOCKS. 
 
 Flow of matter melted off roots of mountains Force causing it considerable 
 Formation of lavas These will differ in different areas and at different 
 times Law of Bunsen Richthofen's "Natural System of Volcanic Rocks" 
 How explained by him Difficulty arising Captain Dutton's explanation 
 Prof. Judd on Richthofen's System Melting of roots of the mountains 
 affords an explanation of the sequence And of the variation of volcanic 
 products in adjacent regions . , . , ... * . . 249 
 
 CHAPTER XXI. 
 
 GEOGEAPHICAL DISTRIBUTION OF VOLCANOS. 
 
 The Linear arrangement of Volcanos accords with the doctrine of a thin crust 
 and fluid substratum Volcanic bands related to the boundaries of continents 
 Distinction between coastline and oceanic volcanos Darwin on coral islands 
 Platforms on which oceanic islands standtheir possible origin Great vol- 
 canic band of the Pacific coast Sinking and rising areas adjoining it 
 It follows nearly a great circle of the sphere and divides the land from the 
 water -hemisphere Is not equally active at every part Suggested cause of 
 local activity Other possible causes of the same Unknown cosmical causes 
 have operated Conclusion ......... 259 
 
 CHAPTER XXIL 
 
 SUMMAEY. 
 
 [The Roman numerals refer to the Chapters.] 
 
 I. On underground temperature II. Condition of interior III. Internal den* 
 sities and pressures IV. Lateral pressure, its amount V. Elevations and 
 depressions VI. Elevations on the hypothesis of solidity VII. Hypothesis 
 of solidity fails VIII. Fluid substratum IX. Crust not flexible X. Dis- 
 turbed tract XI. The revelations of the plumbline XII. The revelations 
 of the thermometer XIII. Amount of compression XTV. Extravasation of 
 water will not account for compression XV. Compression and volcanic 
 action XVI. On Faulting XVII. Geological movements explained 
 XVIII. Mr Mallet's theory of volcanic energy XIX. The volcano in 
 eruption XX. Sequence of volcanic rocks XXI. Geographical distribution 
 of volcanos . . _ , . ... . ; . . . 267 
 
xiv CONTENTS. 
 
 APPENDIX. 
 
 Mr G. H. Darwin " On the stresses caused by continents and mountains" his 
 argument for solidity met by Sir G. B. Airy's explanation M. Roche " On 
 the constitution of the interior of the earth" his theory, though in accord- 
 ance with Geology, requires fuller statement than is yet published . . 291 
 
 INDEX .,.:-. . 295 
 
 ERRATA. 
 
 Page 33, line 8, read 171-875. 
 
 46, 3, for "Z" read "Z (! + <?)". 
 
 75, 14, for "one" read "one or both". 
 
 ,, 180, 6, for "obtaining" read "obtained". 
 
 182, 4 from bottom, for 'V' read "<r". 
 
 219, ,, 2, of note, for "crust of" read "crest of". 
 
 ,, 244, ,, 5, for "lava" read "magma". 
 
 273, 17 (in some copies) for "mean" read "datum". 
 
 278, ,, 3 from bottom, for "not so deep as " read "deeper than 
 
w ou ll ^f/J 
 
 ^ OF THE ' \ 
 
 UNIVERSITY] 
 
 CHAPTER I. 
 
 ON UNDERGROUND TEMPERATURE. 
 
 The rise of temperature on descending into the earth The causes which have 
 been assigned for it Attempts to determine the law of increase by ob- 
 servation Their results Deep bore-hole at Sperenberg and methods of 
 observation used there General effects of convection currents in a bore-hole 
 Tabulated observations at Sperenberg Anomalous result supposed to be 
 deducible therefrom Anomaly explained-^General law of average rise of 
 temperature not impaired tJiereby Hot springs and volcanos prove that 
 the rise of temperature continues, but do not inform us whether the law near 
 the surface obtains unaltered for all depths. 
 
 THEKE is no fact more firmly established in terrestrial 
 physics than that the temperature of the rocks of the earth's 
 surface increases with increasing depth. Observations upon 
 this subject have been made in all parts of the world, and 
 the same result has been everywhere arrived at. Even in 
 the frozen soil of Yakoutzk, in Siberia, this increase of 
 temperature is found to prevail, although the ground is con- 
 gealed to the whole depth penetrated 1 . In all mining opera- 
 tions this gradual increase of temperature becomes a very 
 serious consideration, rendering human labour at great depths 
 a very severe trial to the constitution of the workman. And 
 
 1 The increase of temperature at Yakoutzk, although the soil is frozen even 
 beyond the depth reached, proves that this freezing is owing to the present 
 low mean temperature of the locality, and that it is not a residual effect of a 
 former glacial and still colder period; for if that were so the strata would be 
 now warmer above than below, whereas the reverse is in fact the case. 
 
 The average temperature for the year is -86, E. or 12-7, F. Prof. Milne, 
 in " Geol. Mag." N. S. Vol. iv. p. 518. 
 
 F 1 
 
ON UNDERGROUND TEMPERATURE. [CH. i. 
 
 indeed it is this circumstance, more than any other, which 
 fixes a practical limit to the depth at which mining operations 
 are possible. It is not the raising the minerals from profound 
 depths, for the resources of modern engineering are quite 
 competent to overcome any difficulty on that score ; it is not 
 keeping the mines clear of water, for they are less troubled 
 with its influx at great than at moderate depths ; but it is the 
 impossibility of furnishing the men with an atmosphere to 
 breathe in below the temperature of the blood. For when the 
 air has to be conveyed to long distances it acquires the tem- 
 perature of the rocks, and no means have been yet suggested 
 which could furnish it at the atmospheric temperature un- 
 affected or but slightly so by its long journey through the 
 subterranean passages. 
 
 This increase of temperature, though universal, is not every- 
 where the same. The average is about 1 degree Fahr. for 
 between 50 and 60 feet of descent.' Such is the result of very 
 numerous observations. Some of these have been made by 
 drilling holes in the rock in deep mines; others by lowering 
 thermometers in Artesian bore-holes. A Committee was ap- 
 pointed by the British Association to report upon the subject, 
 and their reports extend from the year 1869. Much informa- 
 tion upon the matter may also be gathered from the Reports of 
 the Parliamentary Commission upon the Coal Supply. 
 
 Unquestioned as is the fact, nevertheless the cause of this 
 increase of heat has formed the ground for much speculation. 
 The most obvious explanation of it is offered by the phenomena 
 of hot springs and volcanos. These show us that, in some 
 places at any rate, much higher temperatures exist at great 
 depths than have ever been reached by artificial perforations. 
 But these phenomena might be said to be local, while the 
 general slow increase of temperature we have been describing 
 exists more or less at every place. Are these phenomena 
 directly connected ? Are they indirectly connected ? Or, are 
 they altogether unconnected? Various answers have been re- 
 turned to these questions. 
 
 Among " practical men " engaged in mining operations an 
 opinion seems to have prevailed that the increase of temperature 
 
CH. i.] ON UNDERGROUND TEMPERATURE. 3 
 
 in deep mines is due to the pressure of the overlying strata or 
 "cover." We may unhesitatingly dismiss this hypothesis. 
 Pressure by itself cannot develop heat. Where motion is 
 destroyed as motion, there it is that it is converted into heat. 
 Thus the motion which is destroyed when a hammer strikes 
 upon an anvil will develop heat that can explode fulminating 
 powder, or heat a nail red-hot. So, also, the bearings of a 
 wheel become heated by friction, which gradually destroys its 
 motion. But though mountains rise on mountains, there will 
 be no heat produced unless motion of some kind is destroyed. 
 In deep coal-mines an effect called " creep " is caused by the 
 enormous pressure upon the sides of a passage, or upon the 
 pillars left to support the roof, causing the floor of the excava- 
 tion to swell up. In this case there is immense friction between 
 the particles of the rock, were it not for which the passage 
 would become instantaneously closed. It has been remarked 
 that considerable heat sometimes accompanies this creep, in 
 which, be it observed, we have not pressure alone, but motion 
 destroyed by friction and converted into heat. 
 
 Sir Humphry Davy ascribed the volcanic fires to the oxida- 
 tion of earthy and metallic bases, supposed by him to exist low 
 down in the interior of the earth. Since water is everywhere 
 present in the crust, if it be dissipated by the abstraction of its 
 oxygen when it encounters the bases, and by the blowing-off 
 from volcanic vents of the equivalent hydrogen, then its place 
 must be continuously supplied by the percolation downwards of 
 fresh accessions ; and thus a generally diffused increase of tem- 
 perature was supposed to arise, and to manifest- itself by its 
 escape towards the surface. 
 
 A very fascinating theory, which has met with support 
 among many scientific men, has of late years been promulgated 
 by Mr Mallet, who considers the heat of volcanic action to 
 be derived from the transformed work of crushing the rocks 
 of the earth's crust, owing to the contraction of its interior 
 through long- sustained cooling. The cause of evolution of the 
 volcanic heat under this theory is of the same kind as that 
 alluded to above, in the case of creeps ; while the ubiquitous 
 increase of temperature in descending into the earth is looked 
 
4 ON UNDERGROUND TEMPERATURE. [CH. i. 
 
 upon as chiefly a manifestation of the generally diffused heat of 
 the interior, by the escape of which the contraction in volume 
 is produced. Volcanic action, Mr Mallet tells us, is caused by 
 this contraction manifesting itself locally and paroxysmally. 
 
 In order to decide what theory best accounts for the phe- 
 nomena, it is obvious that the first step is to make sure of the 
 facts themselves. In other words What is the law regulating 
 this increase of heat? At what rate does the temperature 
 augment ? This might be supposed to be a point easily settled. 
 It might be supposed that nothing would be easier than to 
 insert thermometers into the rock at different depths in a mine, 
 and to read off their indications ; or to lower them into a bore- 
 hole for the same purpose. But there are many difficulties to 
 be overcome, and a host of disturbing causes present. The 
 rock, or the face of the coal in a mine, is affected by the tem- 
 perature of the air. The air is warmed by the presence of men 
 and horses; it is cooled by the ventilation carefully kept up. 
 Hence the surface of the working is not at the true temperature 
 of the rock. The result of careful experiments made by Sir G. 
 Elliot showed that when thermometers were inserted in the 
 coal in a long-wall working, at distances of 3, 6, and 12 feet 
 from the face, no alteration could be detected in the indications 
 given beyond 3 feet from the face of the coal ; and his observa- 
 tions were accordingly taken at 4 feet. It is evident, as will be 
 seen by what will be said hereafter, that the necessary distance 
 must be governed by the difference between the temperature of 
 the ventilating air and of the seam, and that the greater this 
 difference the farther it would be necessary to bore into the 
 coal to obtain an estimate of its true temperature. If it be 
 attempted to ascertain the law of increase by means of an 
 Artesian bore-hole, there are here also disturbing causes present. 
 The action of the tool warms the rock by mechanical means, the 
 friction or pounding action developing considerable heat. Hence 
 while the work is in progress no reliable observations can be 
 taken, except during intervals of suspension, and then it ap- 
 pears as will be seen further on that the interval needs to 
 consist of weeks rather than of days. When the work is com- 
 pleted, and the bore stands nearly full of water, it is the tern- 
 
CH, i.] ON UNDERGROUND TEMPERATURE. 5 
 
 perature of the water which is obtained on lowering a thermo- 
 meter into it, and we cannot be sure that that coincides with 
 the temperature of the rock. In fact many reasons may be 
 assigned why it should not do so. Springs may enter on one 
 side and flow out at the other ; or they may rise from lower 
 levels and flow away at higher. The very act of lowering the 
 thermometer tends to mix up the differently heated layers of 
 water, and to confuse the result. 
 
 A single instance will suffice to illustrate the irregularity of 
 increase referred to. At Rose Bridge Colliery the temperatures 
 were taken by drilling a hole a yard deep at the bottom of the 
 shaft during the process of sinking. If the mean temperature 
 of the surface there be taken at 50 F., the mean rate of increase 
 for the whole depth was 1 degree for 55 feet. But at the suc- 
 cessive depths of 605, 630, 663, 671, 679, 734, 745, 761, 775, 783, 
 800, 806, 815 yards respectively the rate appears to have been 
 1 degree for 70, 25, 49, 24, 24, 110, 66, 32, 42, 48, 51, 36, 54 feet. 
 
 Within the last few years a very deep boring has been 
 carried down at Sperenberg, near Berlin. This has reached 
 the extraordinary depth of 4052 Rhenish feet, or 4172 British 
 feet. A most surprising geological fact about this boring is that, 
 with the exception of the first 283 feet, which were carried 
 through gypsum with some anhydrite, the remainder passed 
 entirely through rock salt. This seemed to offer an exception- 
 ally good opportunity for observing temperatures in a homo- 
 geneous rock, which might be expected to be comparatively free 
 from the sources of error arising from variable heat-conducting 
 power in the layers successively penetrated 1 . The observations 
 
 1 If F be the flow of heat from below, K the conductivity of the rock, v 
 the temperature, and x the depth, then 
 
 ti&. 
 
 dx 
 Now the flow of heat at depths beyond the reach of the influence of the 
 
 seasons will be the same for moderate depths, or F is constant, and -^ gives the 
 increase per foot of descent. 
 
 Hence = shows that the increase of temperature per foot is inversely 
 
 proportional to the conductivity of the rock, so that where the rock conducts 
 heat badly the increase will be more rapid, and vice versa. 
 
6 ON UNDERGROUND TEMPERATURE. [CH. i. 
 
 in the bore were taken with much precaution, under the direc- 
 tion of Herr Eduard Dunker, Inspector of Mines. A resume of 
 his paper upon them will be found in "Nature," Vol. xv. p. 240, 
 1877, as contained in the "Ninth Report of the British Asso- 
 ciation Committee on Underground Temperature." In Vol. xil. 
 p. 545 of the same publication (1875) there had previously ap- 
 peared a notice of a contribution by Prof. Mohr, of Bonn, to 
 the "Neues Jahrbuch fur Mineralogie" (1875), in which that 
 gentleman had commented upon the law of increase which he 
 supposed to be deducible from the observations made in this 
 bore-hole. The result at which he arrived was remarkable 
 enough, and, if it could not have been explained away, would 
 have justified the conclusion which he drew from it, which 
 was that the source of heat within the crust of the earth 
 was situated within the crust itself, for that after a certain 
 depth was reached which he put at 5170 feet the increase 
 would be nil. However, in the Report of the British Associa- 
 tion just published, it is explained how this result had been 
 arrived at, and it is distinctly shown that Prof. Mohr's con- 
 clusion was in reality not based upon the original observations 
 themselves, but that it arose from the form of an empirical 
 mathematical formula, representing a parabola, which Dunker 
 had assumed to express the law. In fact it had been implicitly 
 assumed that the increase would come to an end, and all that 
 Mohr did was to find out at what depth it would do so, sup- 
 posing that assumption true. 
 
 This bore-hole, from the favourable circumstances already 
 referred to, and the care with which the observations were 
 made, deserves full consideration. The temperatures were 
 taken in two manners. In one set of observations the tem- 
 perature of the water in the bore-hole was observed with a 
 suitable thermometer ; in the other an apparatus called a geo- 
 thermometer was lowered, which cut off a portion of water from 
 that above and below it by two disks or bags. A thermometer 
 was enclosed in the space between the disks, and, after the 
 thermometer had been down not less than ten hours, the tem- 
 perature shown by it was assumed to be that of the rock at the 
 corresponding depth. This was found to differ sometimes by 
 
CH. i.] ON UNDERGROUND TEMPERATURE. 7 
 
 more than a degree Re'aumur from the temperature of the water 
 at the same depth, as shown by the first-named thermometer, 
 when the water above and below was not cut off. Now, it can 
 hardly be supposed that so great a difference as this really ex- 
 isted simultaneously between the surface of the rock exposed to 
 the water in the bore-hole and the water itself. On the con- 
 trary, it seems evident that the surface of the rock, being ex- 
 posed to the action of the water, must have assumed the tem- 
 perature of the water, whatever that might be, at any given 
 depth. But the water was undoubtedly affected by convection 
 currents, and consequently its temperature was not the same as 
 that of the rock in mass at a distance from the bore-hole. 
 Hence, when the circulation of these currents was stopped by 
 the disks, the surface of the bore-hole would begin to tend 
 towards the true rock temperature. If the water at any depth 
 was warmer than the rock in mass, its temperature would begin 
 to fall when the currents were cut off, and if the water was 
 cooler than the rock it would begin to rise. 
 
 Let us, then, shortly consider the general effect of con- 
 vection currents as they would affect the water. 
 
 These currents arise from the circumstance that when water 
 is warmed it expands, and consequently becomes lighter. This 
 expansion is exceedingly small ; yet in a substance of such ex- 
 treme mobility as water it is sufficient to cause the expanded 
 portions to rise, while the denser portions above sink to supply 
 their place. The expanded portions in rising carry their heat up 
 with them, and the cooler portions in sinking reduce the tem- 
 perature of the lower part of the column. If therefore we had a 
 column of water originally warmed towards its lower portion, 
 but not supplied there with fresh accessions of heat, the whole 
 would, if open to the atmosphere, shortly assume an equable 
 temperature throughout. 
 
 Let us now invoke the aid of a diagram to render our ideas 
 more clear; and suppose the depths in the bore-hole to be 
 measured along the vertical line OX, and let lines drawn at 
 right angles to this represent, in proportion to their lengths, 
 the temperatures at the corresponding depths. Let OA repre- 
 sent the mean temperature of the surface of the ground. Then 
 
8 
 
 ON UNDERGROUND TEMPERATURE. 
 
 [CH, I. 
 
 on the supposition that the temperature of the rock in mass 
 increases proportionally to the increase of depth, the tem- 
 perature of the rock will be represented by a straight line, as 
 AC. If, then, the temperature of the water in the bore-hole 
 correctly gave the temperature of the rock, its temperature 
 would be likewise represented by the same straight line A C. 
 But since it is affected by convection currents this cannot be the 
 case ; for they tend to warm the upper portions of the column 
 of water, and to cool the lower. Hence, so far as we have gone, 
 the water in the upper part of the bore-hole will be warmer 
 than the body of the rock, and in the lower part it will be 
 cooler ; and in our diagram we must draw a line to represent its 
 temperature, more distant from OX in the upper part, and 
 nearer to it in the lower. It need not, however, be a straight 
 line, the law of increase of temperature being possibly altered. 
 Suppose, then, DE to be this line, or the curve of temperature 
 of the water on the supposition now made. It will be seen that 
 it must intersect the line A C. 
 
 There is a further consideration to be taken into account. 
 If the bore-hole is nearly full of water, and of considerable 
 dimensions, it will present a considerable surface to the atmo- 
 sphere. At Sperenberg the water stood seven feet from the 
 stage of the bore-pit, and the bore-hole was a foot in diameter. 
 
CH. i.] ON UNDERGROUND TEMPERATURE. 9 
 
 The consequence would be that the open surface of the water 
 would be cooled, sensibly to the temperature of the air. This 
 would bring the curve of temperature of the water at the surface 
 nearly to the same point as the temperature line of the rock 
 there, and it would also have the effect of reducing the tem- 
 perature of the water throughout the column, below what it 
 would be if it had not this extrinsic cause of cooling. The 
 ultimate result would be that the temperature curve of the water 
 would assume some such form and position as AF. It will be ob- 
 served that this line also intersects AC', and the signification 
 of this is, that the water in the bore-hole is warmer than the 
 rock mass in its upper portion, and cooler than the rock mass in 
 its lower portion; or, in other words, the water tends to warm 
 the rock in the upper portion, and to cool it in its lower portion. 
 Consequently, if the circulation of the currents be interrupted, 
 the water imprisoned between the disks of the geo-thermometer 
 would in the upper portion of the hole gradually become cooler, 
 as heat was conducted away from it into the body of the rock ; 
 and it would gradually become warmer in the lower portion, as 
 heat was conducted into it from the body of the rock. But at 
 the particular depth at which the two lines AC and AF intersect 
 no alteration would take place. 
 
 That such an effect was actually produced is shown by the 
 following table, the first two columns of which are taken from 
 Dunker's Table II., in his paper entitled " Ueber die Benutzung 
 tiefer Bohrlocner zur Ermittelung der Temperatur des Erdkor- 
 pers, und die desshalb in dem Borloche I zu Sperenberg auf 
 Steinsalz angestellten Beobachtungen." The two temperatures 
 marked with asterisks differ from those quoted in the British 
 Association Report from Dunker's quarto paper of 1872 in the 
 "Zeitschrift fur Berg-Hutten und Salinen-Wisen." But they 
 are printed as here given in the octavo paper from which they 
 have been copied, and are stated there to be the mean results of 
 several observations. Dunker considered the deepest observation 
 with the geo-thermometer unsatisfactory. 
 
 The difference between a Prussian and an English foot is 
 so small that, for the purpose in hand, they may be considered 
 equal. 
 
ro 
 
 ON UNDERGROUND TEMPERATURE. 
 
 [CH. I. 
 
 Water Surface Temp. Being at 
 
 Depth Temp. E. Temp. R. shut off, 7*18. Abso- the rate 
 
 in Water Water not consequent lute Increase of 1 R. 
 
 feetr shut off. shut off. alteration at each depth per No. 
 
 of Temp. in CoL -2. of feet 
 
 2-98 33 
 
 4-44 45 
 
 0-20 500 
 
 0-36 277 
 
 1-90 105 
 
 0-44 455 
 
 1-40 143 
 
 1-20 166 
 
 1-70 118 
 
 1-30 154 
 
 1-80 111 
 
 1-80 111 
 
 0-80 250 
 
 1-20 166 
 
 0-80 250 
 
 Being at the 
 Absolute rate of 
 
 Increase <- * ., 
 
 at depths. FR. 10 F. 
 
 per ft. per ft. 
 
 15 
 
 9-40 
 
 10-35 
 
 -0-95 
 
 30 
 
 9-56 
 
 10-20 
 
 -0-64 
 
 50 
 
 9-86 
 
 10-40 
 
 -0-54 
 
 100 
 
 10-16 
 
 12-30 
 
 -2-14 
 
 300 
 
 14-60 
 
 13-52 
 
 + 1-08 
 
 400 
 
 14-80 
 
 14-30 
 
 + 0-50 
 
 500 
 
 15-16 
 
 14-68 
 
 + 0-48 
 
 700 
 
 17-06 
 
 16-08 
 
 + 0-98 
 
 900 
 
 18-50 
 
 17-18 
 
 + 1-32 
 
 1100 
 
 * 19:90 
 
 19-08 
 
 + 0-82 
 
 1300 
 
 21-10 
 
 20-38 
 
 + 0-72 
 
 1500 
 
 22-80 
 
 22-08 
 
 + 0-72 
 
 1700 
 
 24-10 
 
 22-90 
 
 + 1-20 
 
 1900 
 
 25-90 
 
 24-80 
 
 + 1-10 
 
 2100 
 
 *27'70 
 
 26-80 
 
 + 0-90 
 
 2300 
 
 28-50 
 
 28-10 
 
 + 0-40 
 
 2500 
 
 29-70 
 
 29-50 
 
 + 0-20 
 
 2700 
 
 30-50 
 
 30-30 
 
 + 0-20 
 
 2900 
 
 
 
 31-60 
 
 
 
 3100 
 
 _ 
 
 32-70 
 
 
 
 3300 
 
 
 
 33-60 
 
 
 
 3390 
 
 36-15 
 
 34-10 
 
 + 2-05 
 
 3500 
 
 
 
 34-70 
 
 
 
 3700 
 
 
 
 35-80 
 
 ___ 
 
 3900 
 
 
 
 36-60 
 
 
 
 4042 
 
 38-25 
 
 38-10 
 
 + 0-15 
 
 11-72 
 
 94 42 
 
 7-80 128 
 
 2\SO 214 
 
 57 
 
 95 
 
 5-65 
 
 2-10 310 
 
 7'75 212 
 
 95 
 
 In the above table the first column gives the depths in 
 Prussian feet, at which the observations of temperature were 
 made. 
 
 The second column gives the temperatures observed at the 
 respective depths when the convection currents were stopped 
 by the use of the geo-thermometer. 
 
 The third column gives the temperature of the water in 
 the bore-hole when the convection currents were allowed to 
 circulate. 
 
 The fourth column gives the alteration of temperature at 
 each depth which arose from stopping the convection currents 
 mm^s-when the temperature Ml, plus when it rose. 
 
 The fifth column gives the increase of temperature at 
 each depth over that- at the previous one, as taken from the 
 second column. 
 
 The sixth column gives the rate of increase at each 
 depth, measured by the number of feet which it would be 
 required to descend to gain an increase of 1 degree Keaumur, 
 
CH. i.] ON UNDERGROUND TEMPERATURE. II 
 
 on the supposition that the increase per foot remained con- 
 stant for that number of feet ; consequently large numbers show 
 a proportionately slow increase. 
 
 The seventh column, like the fifth, shows the increase of 
 temperature at the depth against which the number stands, 
 over that at the depth at which the previous number stands; 
 the object of this column being to obtain averages at longer 
 distances apart. 
 
 The^eighth column, like the sixth, shows the rate of increase 
 of temperature with longer averages, measured by the number 
 of feet of descent for 1 Reaumur. 
 
 The ninth gives the same increase when measured in feet of 
 descent for 1 F. 
 
 In discussing this table the first point to be noticed is that 
 the rate of increase is by no means so equable as, from the 
 homogeneity of the rock, it might have been expected to have 
 been. In order to obtain anything like a general law of increase, 
 it is necessary to take the average of the increase at considerable 
 distances apart. 
 
 The second point has been already adverted to, viz., that 
 the shutting-off of the convection currents caused a diminution 
 of temperature in the upper part of the bore-hole, and an in- 
 crease of it in the lower. This shows clearly that the tempera- 
 ture of the rock was altered temporarily, by the action of the 
 convection currents, to some distance away laterally from the 
 bore-hole. The hole was lined with three tubings, one behind 
 another, for the upper 440 feet, and, on account of the pre- 
 sumed convection currents still existing behind the tubing, 
 the observations in the upper part of the column were not 
 considered trustworthy. But this circumstance does not mili- 
 tate against the conclusion at which we have arrived, because 
 whatever effect convection currents might have upon the tem- 
 perature would be pro tanto produced by these concealed 
 currents, so that all they could do would be to lessen the 
 effect of shutting off the currents in the main channel. And 
 we may reasonably suppose that the change of temperature 
 arising from that proceeding would have been still greater than 
 recorded, if the tubing had been in close contact with the rock. 
 
12 ON UNDERGROUND TEMPERATURE. [CH. i. 
 
 In the discussions of these observations 1 the observations 
 made with the geo-therrnometer have been in general looked 
 upon as giving a near approximation to the temperature 
 of the earth's crust at this locality; and, consequently, it 
 is these which we propose to consider further. Although 
 the sixth column ghows that the rate of increase of tempera- 
 ture was far from equable when comparatively short inter- 
 vals are taken into account, yet, when we pass to the eighth 
 and ninth columns, we observe that on the whole there is a 
 decided diminution of the rate of increase in the lower depths. 
 It was probably this circumstance which induced M. Dunker 
 to assume that empirical formula for the law of increase which 
 led Prof. Mohr to believe that, at the depth of 5170 feet, the 
 increase would be nil, and thence to conclude that the source 
 of the heat of the crust must be situated within the crust itself, 
 instead of as is usually supposed coming up from the pro- 
 found depths below. The question which presents itself 
 therefore (and it is a most important question) is Can this 
 diminution of the rate of increase in the indications of the geo- 
 thermometer be consistent with an equable rate of increase in 
 descending as deep as the observations went into the earth's 
 crust ? The answer, that it can, seems to follow from the considera- 
 tions already made on the effect of convection currents upon the 
 temperature, not of the water only, but of the' rock itself. It is 
 obvious that the continued contact of water at a different tempe- 
 rature from that of the rock must alter the temperature of the 
 rock itself where it is in contact with the water. And it has 
 been remarked that, almost beyond dispute, it had actually 
 that effect ; consequently the rock in contact with the water 
 must have been cooled in the lower part of the bore-hole. 
 Moreover, the principal cooling effect of the currents would occur 
 towards the bottom of the hole, where the cold water coming 
 down from above would tend to accumulate, because there would 
 be no warm currents coming up from below to disturb it. 
 
 When, therefore, we enquire how far the observations 
 
 1 The writer has met with a course of lectures entitled " Vcrtrage iiber 
 Geologie, von F. Henrich, Wiesbaden, 1877," in which the Sperenberg obser- 
 vations are discussed with much acumen. 
 
CH. i.] ON UNDERGROUND TEMPERATURE. 13 
 
 made with the geo-thermometer can be depended upon as 
 having given the true temperature of the rock in mass, two 
 questions present themselves. First, could the water enclosed 
 between the disks assume eventually the temperature of the 
 rock mass, if the instrument were left down long enough ? And, 
 secondly, if it could do so, was it in fact left down long enough ? 
 
 It appears that this result could be only partially at- 
 tained, however long it were left in the bore-hole. The 
 convection currents in the water would affect the tempera- 
 ture of the column at the upper and under surfaces of the 
 enclosing disks of the instrument. And even if the disks 
 were purposely made of such badly-conducting material as to 
 prevent any temperature effect from the currents being carried 
 through the disks, still such effect would be conducted round 
 the edges of the disks, through the substance of the rock itself; 
 consequently, however long the instrument might have been 
 allowed to remain down, the temperature of the water enclosed 
 between its disks would have been to some extent affected by 
 the convection currents ; and their tendency in the lower parts 
 of the column would be to reduce the temperature, and diminish 
 the rate of increase. 
 
 A method of obviating this source of error is mentioned 
 in the British Association Report, already referred to, as having 
 been lately suggested by Sir Wm. Thomson. It consists in 
 using a series of india-rubber disks placed at considerable dis- 
 tances apart. 
 
 Putting the above-discussed source of error aside, we come 
 to our second enquiry, whether the geo-thermometer was left 
 down long enough for the water between its disks to assume 
 the temperature of the rock mass 1 ? Let us, then, consider 
 the conditions of the system before the geo-thermometer is 
 introduced. We have a very long vertical column of water 
 
 1 It appears that at the depth of 1100 feet an observation of ten hours 
 duration gave the same result as one of nineteen hours; whence it was con- 
 cluded that ten was long enough. But considering the great thermal capacity 
 of water, and the small changes which, except just at first, might be expected 
 in the rock, as well as the difficulty of the operation, this trial can hardly be 
 held conclusive against the probability of a further increase of temperature, if 
 the geo-thermometer had remained down longer. 
 
1 4 ON UNDERGROUND TEMPERATURE. [CH. i. 
 
 enclosed in a cylindrical hole within a mass of rock, the rock 
 extending to an infinite distance both sideways and downwards. 
 The water in the bore-hole at any given depth has, in con- 
 sequence of the currents, a temperature which differs from that 
 of the rock on the same horizon at a distance from the hole. 
 This temperature of the water may be higher or lower than that 
 of the rock ; but we will suppose it lower, as it will be in the 
 deeper parts of the hole. The rock surface of the bore -hole, 
 being constantly laved by the water, has been brought to the 
 same temperature as the water. It necessarily follows from 
 this that if we could examine the temperatures of the rock 
 at greater and greater distances laterally from the bore-hole, 
 we should find them become higher and higher, and we should 
 have to penetrate to some considerable distance before the 
 increase came to an end, and when it did so we should feel 
 assured that at last we had reached rock of the true temperature 
 for the depth. The greater might be the difference between 
 the temperatures of the water and the rock in mass, the further 
 we should have to penetrate for that purpose, and this would 
 be furthest in the lower portions. Now suppose the currents 
 interrupted by lowering the geo-thermometer, so that the heat 
 ceases to be conveyed away from the rock surface of the bore- 
 hole : and we will now dismiss the consideration of the effect 
 of the water above and below the disks of the instrument. The 
 heat which flows out of the sides of the bore-hole into the 
 imprisoned water is now no longer conveyed away by the 
 currents, and begins to accumulate there. The rock in the 
 neighbourhood of this water begins to get warmer. The region 
 of the true rock temperature approaches nearer and nearer to 
 the bore-hole, until at last it reaches it, and then, and not until 
 then, the imprisoned water assumes the true temperature of 
 the rock. This process will require time, and that a long time. 
 In the first place, on account of the great capacity of water 
 for heat, it requires, much more heat to warm up a volume 
 of water through a given range of temperature than it would 
 require to warm up an equal volume of rock. In the second 
 place, it requires a -long time for the heat to travel through 
 the rock to reach the water. And although the conductivity 
 of rock salt is said to be considerably higher than that of 
 
CH. i.] ON UNDERGROUND TEMPERATURE. 15 
 
 ordinary rock, so that the heat wovild pass more quickly through 
 it 1 , yet there will be a compensating effect in the present 
 instance, because, on account of the greater conductivity, the 
 true rock temperature would not be reached within so small a 
 distance from the bore-hole, so that the heat would have a 
 longer distance to travel before the true temperature could 
 be restored. That the geo-thermometer was not left in place 
 sufficiently long for this purpose seems to be proved by the 
 following instance of the extreme slowness with which the 
 passage of heat under such circumstances takes place. From 
 comparing the British Association Reports for 1872 and 1873 
 we gather that, in the course of the observations made at the 
 Artesian well of La Chapelle, at St Denis, it was noticed that 
 the temperature at the bottom of the hole was much affected by 
 the action of the "trepan " or boring tool. It appears to have 
 been expected that this effect would have passed off in a few 
 days. Accordingly, a week after the tool was stopped, observa- 
 tions were taken, and there was found what was thought to be 
 an unaccountably sudden increase of nearly 8 F., in 60 feet 
 of descent, near the bottom of the hole. But in the following 
 year a second set of observations were made "some months" 
 after the boring had been suspended, and the abnormal increase 
 was found to have entirely disappeared. We learn, then, that a 
 week was not sufficient for the rock wall of the bore-hole to 
 regain its balance of temperature after having been disturbed 
 through about 7 F. How much longer was required we have 
 not the means of knowing. It seems a necessary inference that 
 a few hours would be quite insufficient for a correct observation, 
 and the time allowed at Sperenberg did not exceed such an 
 interval. The conclusion must therefore follow that, on both 
 the accounts referred to, the geo-thermometer must have shown, 
 in the lower depths a temperature less than the true tempe- 
 rature of the rock of the earth's crust existing at that depth. 
 
 The reasons given above seem quite sufficient to account for 
 the diminished rate of increase of temperature shown in the 
 table; and they would lead to the conclusion that in all ob- 
 servations made in bore-holes of a sufficient width to allow 
 
 1 This however is doubtful, for if it were so, the rate of increase ought to 
 have been less than the normal rate. Such was not the case. See note, p. 5. 
 
1 6 ON UNDERGROUND TEMPERATURE. [CH. i. 
 
 convection currents full play, the temperatures taken at the 
 lower parts will even with the geo-thermometer be less than 
 the true rock temperature. The conclusion appears a legitimate 
 one that the diminution in the rate of increase in a bore-hole, 
 even when the convection currents are temporarily shut off, 
 does not necessarily imply that there is any such diminution of 
 the rate in the body of the rock ; or, in other words, that the 
 temperature curve within the rock may be a straight line, 
 although that given by the geo-thermometer be concave to the 
 axis of depths. It will also follow that the mean rate of increase 
 for the whole depth within the rock will exceed that shown by 
 the geo-thermometer. The mean increase, for instance, in the 
 above table, between the temperature of the surface and that at 
 4042 feet, is 1 E. for 129 feet, or 1 F. for 57 feet; and it is 
 stated in the Association Eeport that, when the observations are 
 corrected for pressure, the mean rate to 3390 feet is 1 F. for 
 51*5 English feet. This is about the usual average. We may 
 therefore conclude that at Sperenberg the actual rate of increase 
 in the body of the rock is greater than this. 
 
 The most important conclusion from the above is that, in 
 spite of the decreasing rate shown at Sperenberg (and also at 
 St Louis, and perhaps other places), the old assumption is pro- 
 bably correct, that for such depths as have been reached, the 
 rate if it could be truly observed, and setting aside local causes 
 of disturbance is probably a uniform rate, amounting to, or, as 
 the above reasoning would lead us to infer, rather exceeding, 
 1 F. for 51 feet of descent. And this is all that we know ex- 
 perimentally respecting the rate of increase of temperature 
 within the earth. We have reason, however, to believe that 
 at still greater depths the temperature continues to increase, 
 .because many thermal springs deliver water at the surface at 
 a much higher temperature than has been reached by any 
 artificial perforations. And yet the waters yielded by Artesian 
 wells are in their degree thermal springs, so that the hotter 
 natural springs, such at least as are not obviously situated in 
 volcanic regions, are probably exactly in the same category as 
 the deeper Artesian wells. For instance, it appears extremely 
 probable that the Bath waters are simply springs supplied by 
 the rainfall on the Mendip hills. The water following the sub- 
 
CH. i.] ON UNDERGROUND TEMPERATURE, \J 
 
 terranean course of the limestone is kept down by the imper- 
 vious beds of the basin-shaped coal-measures, and reascending 
 to the surface along the fault from which the springs are 
 known to rise, brings with it the temperature of the rocks 
 through which it has percolated. The temperature is 120F., 
 which is 70 above what may be taken as the mean surface tem- 
 perature, and would require, at the rate of one degree for fifty 
 feet, a depth of 3500 feet to give the required increase. This is 
 by no means an unlikely depth to be attained by the synclinal 
 trough of the carboniferous limestone in Somerset. 
 
 But the phenomena of volcanos, which are situated in all 
 regions of the globe, and of which relics remain almost every- 
 where among ancient rocks, point to an intensely high tem- 
 perature at still greater depths. They afford however no clue 
 as to what the depth may be from which their liquid ejecta- 
 menta are derived without first assuming a law of temperature. 
 
 Thus, it is a most important point to be borne in mind, that 
 we know nothing by observation respecting the law of increase of 
 temperature within the earth, beyond the facts that near the 
 surface the average rate of increase is 1 F. for between every 
 50 and 60 feet of descent, and that the temperature at greater, 
 but unknown, depths is very high, and sufficient to fuse what, 
 from that very cause, we term igneous rocks. This temperature 
 cannot be lower than between 2000 and 3000 F., and may be , 
 much higher. 
 
 But if an average rate of increase of 1 F. for every 60 feet 
 were to continue to all depths, the temperature in the interior 
 would become enormous. In fact, at the depth of from 200 to 
 400 miles it would amount to from 18000 to. 36000 F., which 
 is what Prof. Rosetti has estimated from his experiments with 
 the thermopile to be the probable temperature of the sun 1 . 
 
 1 His words are these: "I think then that I may fairly conclude that the 
 true temperature of the Sun is not very different from its effective temperature ; 
 and that it is not much less than ten thousand degrees [cent.] if we only consider 
 the absorption of the terrestrial atmosphere; nor much more than twenty 
 thousand degrees if we also take into consideration the absorption by the solar 
 
 * go 
 
 atmosphere, estimating the latter at of the total radiation of the^Sun." 
 " Phil. Mag." Vol. vm. Fifth series, p. 550. 
 
 F. 2 
 
CHAPTEE II. 
 
 CONDITION OF INTERIOR 
 
 Little known about the condition of the interior of the earth Results of the 
 mathematical " Theory of the Earth" point to a former condition of fluidity 
 Determination of the mean and surface densities The question proposed 
 whether the fluid condition still partially exists more or less Connection 
 between this question and that of the law of internal temperature Two 
 modes of attacking the question, (1) Precession, (2) the tides Opinions of Sir 
 Wm. Thomson, Hopkins, Delaunay, and others Possibility of a cooled 
 crust resting on an internal fluid layer. 
 
 VARIOUS suppositions may be made respecting the condition 
 of the interior of the earth. What we actually know about it is 
 very little. Whether any portion of it, or how much of it, is at 
 the present time liquid can only be determined by secondary 
 considerations. But we may feel almost certain on account of 
 its present form and the law of variation of gravity upon its sur- 
 face that it was once wholly melted, and that it consists at 
 present of concentric spheroidal shells, each of equal density 
 throughout, and of definite form ; such form having been deter- 
 mined by the velocity of rotation and law of density, coupled 
 with the law of mutual attraction of all the mass. The ellip- 
 ticity of these shells decreases from the surface towards the 
 centre. The mean density of the surface has been estimated at 
 from 2*56 to 275. The mean density of the whole is nearly 
 twice as great. The summary of the experiments from which 
 these constants may be determined is as follows : 
 
CH. ii.] CONDITION OF INTERIOR. 19 
 
 1. Maskelyne, 1775, by means of the deflection of the 
 plumb-line by the mountain Schehallion determined the mean 
 density of the earth at 5'0. 
 
 2. Cavendish, 1798, by the torsion rod and two leaden balls 
 as attracting masses, weighing together 700 pounds, in 23 ex- 
 periments determined the mean density at 5'448. 
 
 3. Reich, 1837, using one large leaden ball of 99 pounds for 
 the attracting mass, in 57 experiments determined the mean 
 density at 5 '44. 
 
 4. Baily, 1842, using two large leaden balls, each weighing 
 380J pounds, in 2004 experiments determined the mean density 
 at 5-67. 
 
 5. Airy, 1856, by experiments with the pendulum in 
 Harton Colliery, at a depth of 1260 feet, determined the mean 
 density of the earth at 6 '566. The mean density of the ordi- 
 nary beds of rock above was determined by W. H. Miller at 
 2 '5 6, and of the coaly beds at 1*43. Airy considered that his 
 determination may " compete with the others on at least equal 
 terms." 
 
 6. Col. James, 1856, by observations on the deflection of 
 the plumb-line at Arthur's Seat determined the mean density of 
 the earth at 5*316. The mean density of the rocks at Arthur's 
 Seat was determined at 2*75. 
 
 7. Mallet estimates the weight of a cubic foot of granite 
 at 178'34 pounds, which makes its density 2'69. 
 
 8. Waltershausen finds the specific gravity (or density) of 
 
 Albite 2-52 
 
 Quartz 2-62 
 
 Limestone 2'63 
 
 Mica . .2-92 
 
 Mean 2-66 
 
 which he takes as the mean density of surface rock. Such a 
 mean, however, would require these minerals to occur in equal 
 proportions in the rock. 
 
 We have then for the mean densities according to the ex- 
 periments respectively of 
 
 22 
 
20 CONDITION OF INTERIOR. [CH. n. 
 
 Whole earth. Surface rock. 
 
 Maskelyne 5'0 
 
 Cavendish 5-448 
 
 Reich 5-44 
 
 Baily 5-67 
 
 Airy and Miller .... 6 -566 2 -56 
 
 James 5-316 2'75 
 
 Mallet 2-69 
 
 Waltershausen 2'66 
 
 If we select Col. James' determination for the density of 
 surface rock, viz. 2"75, and double it, we get 5'50, which is a fair 
 representation of the mean value of the density of the whole 
 earth ; being somewhat greater than the mean 5*375 if Airy's 
 determination is omitted, and somewhat less than the mean 
 5-573 if it be included. 
 
 These are the values used by Archdeacon Pratt in his 
 " Figure of the Earth." 
 
 The increase of density in approaching the centre will 
 depend partly upon the pressure, and partly upon the nature of 
 the materials. We do not know enough about the ultimate 
 constitution of matter to reason satisfactorily about the effect of 
 pressure. It has been thought that by that means the density 
 of a substance can be increased up to a certain limit, but no 
 further. If this be so, it renders it probable that the high 
 density of the central parts of the globe is due to the intrinsic 
 nature of the materials there, and that a large proportion of the 
 heavy metals occupy that position. 
 
 The assumption of a law of density for the purpose of deter- 
 mining the forms of the strata of equal pressure and density 
 within the earth will also give a corresponding form for the 
 outer surface. And it is found that a law (due to Laplace and 
 suggested by analytical necessity) which, using the mean values 
 for the surface and mean densities indicated above, leads to an 
 ellipticity of -^3 for the outer surface, is consistent with the sup- 
 position that the density, if it depended on pressure alone (without 
 asserting -that it does so, which has been shown above to be 
 highly improbable), would be such, that i>he increase of the square 
 
CH. ii.] CONDITION OF INTERIOR. 21 
 
 of the density would vary as the increase of the pressure 1 . 
 Now the actual ellipticity being known by measurement to be 
 ^g- it is highly probable that the law of density above in- 
 dicated expresses a close approximation to the truth. 
 
 The conclusions here enumerated are the results of re- 
 markably refined mathematical investigations which have 
 exercised the ingenuity of the greatest masters in the science, 
 and the methods and results of which will be found collected in 
 the work by Archdeacon Pratt just referred to. 
 
 To guide us in our reasoning concerning the condition of the 
 interior we have then the following data : 
 
 The observed rate of increase of temperature near the sur- 
 face is perfectly compatible with the existence of such a tem- 
 perature within the earth as would fuse all known substances, 
 and fused substances continue to flow up from below, and, what 
 is more, there is almost positive evidence that the earth was at 
 qne time wholly fluid. The question arises, does this fluidity 
 still normally exist within it, wholly or partially ? 
 
 The true law of increase of temperature is inextricably 
 mixed up with this other question of the condition as to solidity 
 or fluidity of the interior; because any law of increase of 
 temperature is compatible with the law that the increase is 
 proportional to the depth near the surface. For if we represent 
 the law of temperature by a curve starting from the surface 
 whose axis of abscissae is vertical, this merely amounts to saying 
 that any number of different curves may be drawn which have 
 the same tangent at the origin. But the law of increase of tem- 
 perature below that outer part or crust of the earth, which we 
 know to be solid, will be governed by the laws of convection if 
 the interior be fluid, modified by change in the value of gravity, 
 and by those of conduction if it be solid. Hence if there be a 
 change of state from fluid to solid, there will necessarily be a 
 break in the law at the depth where that occurs; and it will 
 then be further complicated by the thermal changes which 
 accompany the change of state. 
 
 Now the question as to whether the interior of the earth is 
 at the present time solid or fluid, or partly solid and partly fluid, 
 1 Pratt's "Figure of the Earth," 4th eil. Arts. 115118. 
 
22 CONDITION OF INTERIOR. [CH. n. 
 
 may be attacked in two ways. The first of these is by consider- 
 ing what is the difference of effect that bodies exterior to it, 
 namely the sun and moon, would have upon the motions of 
 the earth in either case, and secondly by considering the sequence 
 of events according to which a molten globe, such as the earth 
 once was, may have passed into its present state. 
 
 For the first, Mr Hopkins, in the Phil. Trans, for 1839-40- 
 42, investigated the consequences which, according to certain 
 assumptions, would have resulted from the effect of internal 
 fluidity upon the phenomenon of precession of the equinoxes, 
 and he came to the conclusion that the solid crust of the earth 
 could not be less than from 800 to 1000 miles thick. 
 
 His argument was assailed by Delaunay 1 , but strongly sup- 
 ported by Sir Wm. Thomson and Archdeacon Pratt: while General 
 Barnard a believed that Hopkins' result was vitiated by an over- 
 sight. It is however scarcely worth while to consider this argu- 
 ment further, because Sir Wm. Thomson has himself given up this 
 particular reason against the doctrine of a fluid interior. "In- 
 teresting in a dynamical point of view as Hopkins' problem is, 
 it cannot afford a decisive argument against the earth's interior 
 liquidity 3 ." To this change of opinion he was led by a conver- 
 sation with Prof. Newcomb in America. 
 
 But there is another manner in which the sun and moon 
 affect terrestrial motion ; namely by raising the ocean tides. If 
 the earth were not exceedingly rigid the globe itself would be 
 raised in tides as well as the water which covers it, and since the 
 measurable tide is the distance between the floor of the ocean 
 and the surface of the sea, it is plain that if the floor of the 
 ocean was drawn up along with the surface of the sea, the tide 
 would be thereby diminished. Sir Wm. Thomson says: "The 
 solid crust would yield so freely to the deforming influence of 
 the sun and moon, that it would simply carry the waters of the 
 ocean up and down with it, and there would be no sensible tidal 
 rise and fall of water relatively to land 4 ." Mr George Darwin has 
 
 1 "Geol. Mag." Vol. v. p. 507. 
 
 2 "Problems of Eotary Motion." "Smithsonian Contributions," No. 240, 
 New Addendum, p. 42. Vol. xix. 1871. 
 
 3 Sectional Address to British Association, 1876. 4 Ibid. 
 
CH. ii.] CONDITION OF INTERIOR. 23 
 
 confirmed this conclusion. It does not however appear necessary 
 that the earth should be absolutely solid from the surface to the 
 centre in order to satisfy these requirements. May not the 
 argument for rigidity drawn from the tides, after it has received 
 that definite weight which proper observations (yet to be made) 
 are expected to give it, be satisfied with a rigid nucleus of radius 
 nearly approaching to that of the entire globe ? Such tides as 
 would be formed within the liquid substratum of the crust 
 would not be of the nature of the tides, contemplated by Sir Wm. 
 Thomson as affecting the entire spheroid, but more nearly ana- 
 logous to the ocean tides ; since they would involve a horizontal 
 transference of fluid backwards -and forwards, and might be 
 expected to be of small amplitude, owing to the viscosity of the 
 substance and its confinement beneath the crust. However, 
 even the modest requirement of a fluid substratum is refused. 
 "But now thrice to slay the slain. Suppose the earth this 
 moment to be a thin crust of rock or metal resting on liquid 
 matter. Its equilibrium would be unstable ! And what of the 
 upheavals and subsidences? They would be strikingly analogous 
 to those of a ship that had been rammed ; one portion of crust 
 up and another down, and then all down. I may say with 
 almost perfect certainty that whatever may be the relative 
 densities of rock, solid and melted, at or about the temperature 
 of liquefaction, it is, I think, quite certain that cold solid 
 rock is denser than hot melted rock; and no possible degree of 
 rigidity in the crust could prevent it from breaking in pieces 
 and sinking wholly below the liquid lava 1 ." 
 
 However, in a note to an address before the Geological 
 Society of Glasgow, 14 Feb. 1878, Sir W. Thomson wrote, 
 " Since this address was delivered, some important experiments 
 have been carried out, at the request of Dr Henry Muirhead, 
 by Mr Joseph Whitley of Leeds. His experiments were made 
 on iron, copper, and brass, and on whinstone and granite ; and 
 the general result hitherto arrived at seems to be, that these 
 substances are less dense in the solid than in the liquid state at 
 the melting temperature 2 ." And D. Forbes stated that glass 
 
 1 Sectional Address to the British Association, 1876. 
 
 3 ' Trans. Geol. Society of Glasgow," Vol. vi. Pt. 1, p. 40. 
 
24 CONDITION OF INTERIOR. [CH. n. 
 
 floats on melted glass, and similarly Bessemer steel on melted 
 steel, and says that Messrs Chance found the castings made from 
 fused Rowley Rag were of the same size precisely as the wooden 
 pattern. It is right to state however that the sand moulds were 
 made red-hot to allow of slow cooling and devitrification 1 . 
 
 If we now turn to Mr Hopkins' " Researches in Physical 
 Geology 2 /' we find that he had gone into this question some- 
 what fully, and held an exactly opposite opinion to the 
 above. He considered that, so long as the matter of the earth 
 retained a sufficiently high state of fluidity to admit of the 
 circulation of convection currents, no crust could form : but that 
 when, by those means, the temperature had been so far reduced 
 that the currents became arrested, immediately a crust would be 
 formed. " Since the heat increases with the distance from the 
 surface, while the mass is cooling by circulation, the tendency 
 to solidification, so far as it depends on this cause, will be 
 greatest at the surface, and least at the centre. But on the 
 other hand, the pressure is least at the surface, and greatest 
 at the centre ; and consequently the tendency to solidify, as 
 depending on this cause, will be greatest at the centre, and least 
 at the surface 3 ." For want of experimental evidence, " the only 
 conclusion at which we can arrive is this, that if the augmenta- 
 tion of the temperature with that of the depth be so rapid that 
 its effect in resisting the tendency to solidify be greater than 
 that of the increase of pressure to promote it, there will be the 
 greatest tendency to become imperfectly fluid, and afterwards 
 to solidify, in the superficial portions of the mass : whereas, if 
 the effect of the augmentation of pressure predominate over 
 that of the temperature, this transition from perfect to im- 
 perfect fluidity, and subsequent solidity, will commence at the 
 centre 4 ." 
 
 Assuming the latter to be the case, when the mass should 
 have arrived at that stage of cooling that " a solid nucleus had 
 been formed, surrounded by an external portion of which the 
 
 1 " Chemical News," Vol. xvm. p. 191. 
 
 2 "Phil. Trans. Eoy. Soc." Part n. 1839, quoted in his "Report to the 
 British Association," 1847, p. 33. 
 
 s Ibid. 4 Ibid. 
 
CH. ii.] CONDITION OF INTERIOR. 25 
 
 fluidity would vary continuously from the solidity of the nucleus 
 to the fluidity of the surface, where, at the instant we are 
 speaking of, it would be just such as not to admit of circula- 
 tion ;... a change would take place in the process of solidification 
 which it is important to remark. The superficial parts of the 
 mass must in all cases cool the most rapidly, and now (in con- 
 sequence of the imperfect fluidity) being no longer able to 
 descend, a crust will be formed on the surface, from which the 
 process of solidification will proceed far more rapidly down- 
 wards, than upwards on the solid nucleus." And in a note to 
 the Report 1 , he 'writes thus decidedly: "Supposing the earth 
 once to have been fluid, it must be now, or have been at some 
 antecedent epoch, in that state in which a solid exterior rests 
 on an imperfectly fluid and incandescent mass beneath. It is 
 important to know that this state of the earth, assuming its 
 original fluidity, is one through which it must necessarily have 
 passed in the course of its refrigeration, whatever might be the 
 process of its solidification." 
 
 These remarks of Mr Hopkins deserve serious consideration, 
 and are not lightly to be set aside. They are entirely indepen- 
 dent of his subsequent calculations by which he considered he 
 had proved (and was until very lately considered by the greatest 
 mathematicians to have proved) 2 that this crust is not at the 
 present time a thin one, but has grown to the thickness of at 
 least not far short of a thousand miles ; even if its downward 
 growth has not already met the upward growth of the solid 
 central nucleus. 
 
 The reasoning by which Mr Hopkins concluded that a crust 
 would be formed (and he clearly supposed it would be supported 
 also), seems to be assailable only on the supposition that upon 
 solidification a sudden considerable contraction, and consequent 
 increase of density, would occur, which would enable the frag- 
 ments to sink in a fluid, too viscous to admit of the sinking of 
 portions cooled to the verge of solidification. But there is no 
 reason whatever to suspect such a sudden considerable contrac- 
 tion. Indeed the experiments above referred to, .point in a 
 contrary direction. 
 
 1 Page 48. 2 Vide supra, p. 22. 
 
26 CONDITION OF INTERIOR. [CH. n. 
 
 It is practically seen that a crust can be formed and sup- 
 ported upon liquid lava by what is known to happen in the 
 crater of Kilauea. This is of an elliptical form, three miles in 
 its longer diameter : consequently the attachment to the cliff- 
 like sides can have little effect in supporting the crust over so 
 large an area. Moreover, this has been observed to rise and 
 sink with variations in the level of the lava, showing that it 
 really rests upon the fluid support. " The floor of the pit is 
 described as usually presenting a crust over a vast pool of lava, 
 which is from time to time broken through by a fresh upboiling 
 of the incandescent mass beneath. It cools 'and hardens so 
 rapidly on exposure, that it may be walked upon within a few 
 hours after its coagulating. Sometimes upwards of fifty small 
 cones and craters, more or less in activity, have been counted 
 on the floor of this great pit. They were from fifty to a hun- 
 dred feet high V " It is nine miles in circumference, and its 
 lower area, which not long ago fell about 300 feet, just as ice 
 on a pond falls when the water below it is withdrawn, covers 
 six square miles 2 ." 
 
 The conclusion which we may draw from these premises is 
 that the earth is on the whole extremely rigid, but that from 
 anything which we have as yet referred to, we cannot decide 
 whether it is solid from the surface to the centre, or whether 
 there may be a liquid substratum of fused rock, of no great 
 depth perhaps, intervening between the crust solid from cold, 
 and the nucleus, solid in spite of its high temperature from 
 pressure. That such solidity is the case with the nucleus, 
 appears necessarily to be the result of pressure, without refer- 
 ence to experiments regarding the contraction or expansion 
 of rocks upon solidifying, for otherwise the proved rigidity 
 of the earth would not be compatible with a high tempera- 
 ture unless indeed, as suggested by Sir Wm. Thomson, the 
 nucleus be a cool sphere, around which a stratum of meteoric 
 matter has accumulated, heated to the temperature of fusion 
 by its collision with the pre-existing nucleus. This latter 
 
 1 Scrope's " Volcanos," p. 477, ed. 1872. 
 
 2 Miss Bird's "Hawaiian Archipelago." See "Nature," Vol. xi. p. 324. 
 
CH. ii.] CONDITION OF INTERIOR. 27 
 
 supposition however may be passed over as not affecting the 
 aspect of the subject at present under review. 
 
 It is possible that a future generation of geologists may be able 
 to gather some information regarding the interior of the earth 
 from the mysterious phenomena of magnetic variation. .But at 
 present we cannot hope for much help from that quarter. The 
 temptation, however, is too great to forbear quoting from Captain 
 Evans a very striking passage 1 . " These are a few facts relating 
 to secular changes going on in two magnetic elements within 
 our own time ; and what are the inferences to be drawn there- 
 from ? They appear to me to lead to the conclusion that move- 
 ments, certainly beyond our present conception, are going on in 
 the interior of the earth ; and that so far as the evidence pre- 
 sents itself, secular changes are due to these movements, and 
 not to external causes. We are thus led back to Halley's con- 
 ception of an internal nucleus or inner globe, itself a magnet, 
 rotating within the outer magnetised shell of the earth." This 
 is, to say the least, in very remarkable accordance with the 
 conclusion that a liquid stratum underlies the cooled crust of 
 the earth. 
 
 1 Lecture at the Eoyal Geographical Society, March 11, by Capt. F. J. Evans, 
 C.B., F.K.S., Hydrographer to the Admiralty, "Nature," May 16, 1878. 
 
CHAPTER III. 
 
 INTERNAL DENSITIES AND PRESSURES. 
 
 Speculations concerning the materials in successive couches Waltershausen' s 
 theory His law of density open to correction His tables of densities and 
 pressures Fluid pressures within the earth calculated from Laplace's law of 
 density Fluid pressure at the centre. 
 
 THE law of density in the interior of the earth has naturally 
 led to speculations concerning the composition of the successive 
 couches, or shells, of which it is composed. Waltershausen, in his 
 " Rocks of Sicily and Iceland," has formed a theory of the earth 
 on this basis. It is thus epitomised by Mr Clarence King in the 
 "Geological exploration of the fortieth parallel," Vol. I. p. 710 *: 
 " To sum up the theory of Waltershausen ; the earth is a hot 
 globe, of which a considerable portion is fluid, an unknown 
 fraction of the centre having been rendered solid by the raising of 
 its fusion-temperature by pressure. The downward increment of 
 density is expressed by the chemical increment of the heavy 
 bases, and the fluid region directly under the crust consists, 
 first, of a feldspathic and acidic magma which passes downwards 
 by successive replacements of bases into an augitic, and finally 
 into a magnetitic magma." 
 
 The formula used by Waltershausen 2 for the calculation of 
 the density p at a distance r from the centre is of the form 
 p' = P-(P- P )r*: 
 
 1 Washington, Government printing office, 1878. 
 
 2 " Bocks of Sicily and Iceland," p. 315. 
 
CH. in.] INTERNAL DENSITIES AND PRESSURES. 29 
 
 where p is the surface density, and P the density at the centre. 
 The radius of the earth is here taken as unity. In order to 
 render the equation homogeneous we may write it, a being the 
 earth's radius, 
 
 P-p r 
 
 or -^ *- = 2 . 
 
 P~/> a 2 
 
 Now Laplace's equation, which leads to the law of density 
 already referred to 1 , is 
 
 , n sin qr 
 P ^C^T-' 
 
 where Q and q are constants to be determined. Consequently 
 the central density will be given when 
 
 or P = Q - ? q when r 0. 
 
 qr 
 
 Also the surface density will be given by putting 
 
 sn qa 
 
 sin qr qr sin qr 
 
 i /v M* /y$ 
 
 P p sin qa a 2 qa sin qa 
 
 q ~aT a* 
 
 _ 
 
 
 
 This is the correct expression for the ratio -= . And 
 
 P-/> 
 
 / r 2s 
 
 consequently Waltershauseri's value of that ratio (viz. -J is 
 strictly true only when the relation is satisfied, 
 
 qr sin qr _ qa sin qa 
 ~~ ~~ 
 
 When the constants Q and q are determined in accordance 
 with the mean values above given of the density of the whole 
 
 1 p. 20. 
 
30 INTERNAL DENSITIES AND PRESSURES. [CH. m. 
 earth and of the surface density, it is found that 
 
 qa = 2-4605 = 140 58' 35" ; 
 and Qq, or P = 10'74/ 
 
 which is therefore the density at the centre of the earth. 
 
 In order to see to what extent Waltershausen's formula is 
 incorrect let us apply it to the instance where 
 
 a 
 
 T) _ / 
 
 -p - 
 
 We find that the value of 
 
 ing to Laplace's formula, is 
 
 i x 1-2566 : 
 whereas "Waltershausen's formula gives 
 
 for this value of r, accord- 
 
 P-p 4* 
 
 Consequently it gives too small a value for this ratio. 
 
 DENSITIES ACCORDING TO WALTERSHAUSEN. 
 
 KADIUS. 
 
 DENSITY. 
 
 1-00 
 
 2-66 
 
 0-99 
 
 2-79 
 
 0-98 
 
 2-93 
 
 0-97 
 
 3-07 
 
 0-96 
 
 3-20 
 
 0-95 
 
 3-34 
 
 0-94 
 
 3-47 
 
 0-93 
 
 3-60 
 
 0-92 
 
 3-72 
 
 0-91 
 
 3-85 
 
 0-90 
 
 3-99 
 
 0-80 
 
 5-15 
 
 0-70 
 
 6-29 
 
 0-60 
 
 7-09 
 
 0-50 
 
 7-85 
 
 0-40 
 
 8-47 
 
 0-30- 
 
 8-96 
 
 0-20 
 
 9-31 
 
 0-10 
 
 9-51 
 
 0-00 
 
 9-59 
 
 Lime. 
 Magnesia. 
 
 Alumina. 
 
 Iodine, Iron oxide. 
 
 Tellurium, Chromium. 
 
 Zinc, Iron, Tin. 
 
 Cobalt, Steel. 
 
 Uranium, Nickel. 
 
 Copper. 
 
 Bismuth, Silver. 
 
 1 Pratt's "Figure of the Earth," 4th ed. Art. 115. 
 
CH. m.] INTERNAL DENSITIES AND PRESSURES. 3 1 
 PRESSURES ACCORDING TO WALTERSHAUSEN. 
 
 RADIUS. 
 
 ATMOSPHERES. 
 
 1-00 
 
 
 
 0-99 
 
 17138 
 
 0-98 
 
 34591 
 
 0-97 
 
 53070 
 
 0-96 
 
 72195 
 
 0-95 
 
 92432 
 
 0-94 
 
 113180 
 
 0-93 
 
 134600 
 
 0-92 
 
 156840 
 
 0-91 
 
 179680 
 
 0-9 
 
 203320 
 
 0-8 
 
 471680 
 
 0-7 
 
 786080 
 
 0-6 
 
 1125690 
 
 0-5 
 
 1468000 
 
 0-4 
 
 1701500 
 
 0-3 
 
 2297500 
 
 0-1 
 
 2441900 
 
 o-o 
 
 2492600 
 
 It is an interesting enquiry what the fluid pressure would 
 be according to Laplace's law of density now assumed. For the 
 actual pressure is probably not very different from the fluid 
 pressure ; because, if the rigidity of the interior be due to 
 pressure, it will have been fluid at any given level until the 
 temperature had fallen sufficiently for the pressure to overcome 
 the fluidity, so that the pressure there will be the fluid pressure. 
 But even if that be not a true account of the process of solidi- 
 fication, still it is not probable that the couches can be 
 appreciably supported in the manner of an arch ; in which case 
 we may consider the pressure at any point in a prism from the 
 surface to the centre to be due to the weight of the portion of 
 the prism above the level under consideration 1 . 
 
 Let p be the pressure at the distance r from the centre of 
 the sphere, p the density and g the gravity at that level. 
 
 Then as r is increased p is diminished, and we shall have 
 
 dp 
 dr 
 
 -gp 
 
 (1). 
 
 1 At Dukinfield colliery at 2500 ft. circular arches of brick, probably five 
 to six feet in diameter, and four feet thick, were crushed. Hull's ' ' Coal Fields 
 of Great Britain," p. 447, quoted in "Jour, of Science," No. xxxrx. 
 
32 INTERNAL DENSITIES AND PRESSURES. [CH. in. 
 
 Since the attraction of the portion of the sphere exterior to 
 the shell, whose radius is r, upon a particle within it is nothing, 
 the value of g' , due to the remaining portion, will be, 
 
 Substituting for p its value -^ ^- and integrating, we have 
 
 , 47rQ , . 
 g = y-f (sm qr qr cos gr), 
 
 and therefore, 
 
 , / 477-Q 2 , . , 
 
 <7p = j-j (sinqr qrsmqrcosqr). 
 
 Hence, g and p being the values of g and // at the surface, 
 
 gp _ a 3 sin 2 gr qr sin qr cos qr 
 gp r 3 sin 2 <?a qa sin ga cos qa ' 
 
 . sin 2 $r qr sin gr cos qr 
 
 = j3. 5 = . 
 
 r 3 
 
 Substituting for gp from (1), and integrating by parts, 
 p _ A sin 2 qr ~ 
 
 when r = a, p = 0'; 
 
 _ gpA /sin 2 gr sin 2 qa\ 
 
 A ^""^^"T^ ~^" y* 
 
 Tf we write %a for r, and restore the value of A, this may 
 be put in the form, 
 
 gpa 
 
 sin 2qa (tan ga - qa) 
 
 This gives the pressure at any depth, the only variable quantity 
 in the expression being 
 
 sin 2 qna 
 
CH. in.] INTERNAL DENSITIES AND PRESSURES. 33 
 
 which at the centre, where n = 0, becomes unity. Hence the 
 pressure at the centre is 
 
 ~ rr~ s (<I a + sm Q a ) (<l a sm <7&)' 
 
 sm 2qa (tan qa - qa} " 
 
 To calculate the pressure in pounds on the square foot, we 
 observe that gp is the weight of a cubic foot of rock at the 
 surface, or 
 
 gp = 275 x weight of a cubic foot of water ; 
 = 171 875 pounds. 
 
 Archdeacon Pratt has found for the mean values of the 
 axes of the spheroid corrected for local attraction 1 , 
 
 a = 20926184 feet, 
 = 20855304 feet. 
 
 If we define the mean sphere as one of equal volume with 
 the spheroid, then 
 
 a 3 =a 2 /?, 
 
 and .-. a = 20,902,520 feet ; 
 
 which we will take to be the value of the mean radius. 
 
 Then, with the values of qa already given 2 , we obtain for the 
 pressure upon a square foot at the earth's centre 
 
 6,351,810,000 pounds. 
 
 Reducing this to atmospheres at 147 pounds per square inch, 
 the fluid pressure at the centre of the earth will be found 
 to be 
 
 3,000,660 atmospheres. 
 
 This, as will be observed, considerably exceeds Walters- 
 hausen's estimate 3 . 
 
 1 Pratt's "Figure of Earth," 4th ed. Art. 173, 
 
 u p. 30. 
 
 8 See Table, p. 31. 
 
 F. 
 
CHAPTER IV. 
 
 LATERAL PRESSURE, ITS AMOUNT. 
 
 Generally received views regarding the contortion of rocks by lateral pressure 
 Calculation of the possible amount of such pressure at the surface Attempt to 
 estimate the same within the earth Mountain chains elevated by lateral 
 pressure The Himalayas. 
 
 THE well-known fact that great lateral compression has 
 affected the stratified rocks of the earth's crust, not once, but 
 again and again from the earliest to the latest of the extended 
 periods of Geological time, is now generally explained by the 
 supposition that the globe has contracted through secular cool- 
 ing 1 . Without enquiring whether the whole globe did or did not 
 become solid at the same time, we may admit that when the 
 outer crust became solid it must have assumed very nearly the 
 temperature of the atmosphere, owing to its heat being radiated 
 away into space. It is thought that as the cooling proceeded, 
 the interior shrunk away from the crust, and the latter became 
 wrinkled ; and that it was by this means that the crumpling 
 and contortions of the rocks were produced. The simile some- 
 times made use of in Geological text-books is that of the skin 
 of a shrivelled apple. Where these wrinkles have not yet been 
 
 1 The earliest publication of this theory appears to have been in a foot-note 
 to a memoir on the mountains of L'Oisans ("Memoires de la Societe d'Histoire 
 Naturelle," t. v. 1829) by M. Elie de Beaumont. The passage is quoted by Prof. 
 A. de Lapparent, in a paper entitled " L'origine des inequalities de la surface 
 du globe," in the " Kevue des Questions Scientific," Juillet, 1880. 
 
 Prof. Sedgwick proposed the same theory two years later, in his paper on 
 the structure of the Cumbrian mountains, "Trans. Geol. Soc.," Jan. 5, 1831. It 
 occurred also to the Author, as he believes independently, about 1841, and was 
 suggested to him by the wrinkles formed on old ice, when the surface of the 
 water had sunk away from it. He has however been led to change his opinion 
 concerning the cause of contraction, as will appear further on. 
 
CH. iv.] LATERAL PRESSURE, ITS AMOUNT. 
 
 35 
 
 denuded and levelled down, they now form mountain chains, in 
 which the crumpling of the rocks is usually conspicuous. In 
 other cases the tracts so elevated have been planed down by 
 meteoric and marine action, afterwards covered by horizontal 
 deposits, and re-elevated with greater or less secondary crump- 
 ling, into the positions where we now see them. That enormous 
 force has been concerned in this crumpling of the hardest rock 
 is obvious. Let us estimate its amount; premising that we 
 make no assumption whatever regarding the condition of the 
 interior of the globe nor the cause of contraction, but merely 
 assume that it has shrunk away from a rigid upper crust. Tha 
 problem is mathematically analogous to that of finding the 
 tension of a flexible surface exposed to the pressure of a fluid. 
 
 The form of the earth approaches very nearly to that of an 
 oblate spheroid of revolution whose equatorial semiaxis (a) is 
 20926184 feet and whose polar semiaxis (b) is 20855304 feet 1 . 
 Its ellipticity as already stated is very nearly -^s- 
 
 Suppose PTQS to be a rectangular element of the crust, 
 the four sides being equal and the thickness being T, and let 
 
 p. 33. 
 
 32 
 
36 LATERAL PRESSURE, ITS AMOUNT. [CH. iv. 
 
 PQ and ST be the curves of greatest and least curvature on its 
 surface. These are by a theorem in geometry necessarily ortho- 
 gonal. Let RO, RO', the corresponding radii of curvature, be 
 called r, r. 
 
 Let T be the pressure on unit of area of the section of the 
 crust in the directions of the tangents at P and Q which is 
 produced by the lateral thrust. Similarly let T' be the pres- 
 sure in the direction of the tangents at S and T. The weight 
 of the element is gp PQ x ST x r, and acts in the normal R 0'. 
 
 Let the angles POQ = 6, 
 
 SO'T=<I>. 
 
 If then we suppose this element supported by a pressure R 
 on unit of area from beneath, resolving the forces vertically 
 we have for the equation of equilibrium 
 
 2iy$r sin + 2TV0T sin | = gprdr'Qr - RrOr'^. 
 In the limit, dividing by r6r<f> this gives 
 
 ,/TT rpi\ 
 
 If we regard the surface as spherical and of radius a, T and T' 
 become equal, and we have 
 
 2 = gpr-R. 
 a y ^ 
 
 If the support beneath is withdrawn altogether R becomes 
 nothing and then 
 
 which gives the maximum thrust which would be produced by 
 the shrinking away of the underlying mass. 
 
 The meaning of this result is that the horizontal force of 
 compression thrown into a stratum at the earth's surface by the 
 shrinking away of the underlying parts would be equal to 
 the weight of a piece of the same stratum of the same section 
 as the stratum and two thousand miles long enough to crumple 
 up and distort any rocks. It would be about 830200 tons upon 
 the square foot 1 . 
 
 1 Calculated from a cube of granite weighing 178-339 Ibs. 
 
CH. iv.] LATERAL PRESSURE, ITS AMOUNT. 37 
 
 The pressures T and T r being orthogonal cannot affect one 
 another. Suppose then T and r given. It follows that if r is 
 increased or diminished T' must be increased or diminished in 
 the same proportion. Hence, if the curvature be diminished 
 the pressure will be proportionately increased and vice versd. 
 Hence there will be no greater tendency to compression where 
 the curvature is greater, as about the equator, than where it is 
 less, as about the poles, but the reverse. This answers an objec- 
 tion which has been sometimes brought against the theory; 
 although apart from the above reasoning it is scarcely likely 
 that so small a difference of curvature as that referred to can 
 have any appreciable consequence. 
 
 It is inconceivable that such rock as we find at the surface 
 of the earth could support so great a pressure as this without 
 bending and breaking. Hence, if it be supposed possible that 
 for a moment a shell of moderate thickness, say a few miles, 
 should be self-supporting, and therefore exert no pressure upon 
 that immediately beneath it, this state of things could not 
 continue, and the outer shell would give way, and settle down 
 upon the next stratum below it. 
 
 We are not able however to estimate the downward pressure 
 which will be exerted by it at any point upon the next lower 
 stratum, because the lateral pressure T might not be wholly 
 relieved, but only partially so, and so to some extent help to 
 support the shell. 
 
 It is evident that in such a case the downward pressure 
 would not be the same everywhere, the tilted rocks in some 
 places supporting each other, and pressing with diminished 
 weight upon the subjacent matter. 
 
 If the rock were perfectly rigid T would have its full value, 
 the shell would be self-supporting, and the vertical pressure on 
 the next stratum would be nothing. If on the other hand the 
 rock were fluid, such pressure would be that due to the depth r 
 of the upper layer. Its actual value will be something inter- 
 mediate. 
 
 We will next make an attempt to estimate the lateral pres- 
 sure at points within the earth, upon the supposition that the 
 interior is solid, in order to see whether any stratum would be 
 
3 LATERAL PRESSURE, ITS AMOUNT. [CH. iv. 
 
 likely to be crushed under the circumstance of a contraction of 
 the mass beneath. 
 
 Suppose that, on a unit of area, P is the pressure towards 
 the centre at a distance r from the centre, caused by so much 
 of the weight of the superincumbent rock as is sustained by 
 the next inferior stratum (which is supposed not to be yet 
 crushed). Then, if we consider the effects of the crushing of 
 the rock above it to be uniformly distributed, P cannot be so 
 great as the pressure which would arise from the same rock 
 were it fluid, because part of the weight of the crushed rock 
 will be sustained by lateral pressure. 
 
 Hence if we consider the conditions of equilibrium of an 
 element of the stratum in question lying next beneath the rock 
 which produces the pressure P, and suppose this shell and the 
 superincumbent mass to be in equilibrium without resting upon 
 the interior mass, we shall be able to calculate the horizontal 
 pressure which tends to crush the shell. 
 
 Let T' be the horizontal pressure upon a unit of area of 
 any vertical section of this shell, r the thickness of the shell, 
 and g', p, the values of g, p, at that depth. 
 
 Then we shall have, by the same reasoning as in the pre- 
 vious proposition, 
 
 Let us compare this horizontal pressure T' with the cor- 
 responding pressure T at the surface, which has been shown to 
 
 a 
 be equal to gp , 
 
 As 
 
 T & A 
 
 As Pr > = < (gpa - g'rr) T. 
 
 As P> 
 
 gp 
 
 Let y be the depth of a column of rock of a unit of section 
 and density p, whose weight at the surface would equal the 
 
CH. iv.] LATERAL PRESSURE, ITS AMOUNT. 39 
 
 pressure gp f- T ' - TJ upon a unit of surface, with which 
 
 we have now to compare P. 
 Then 
 
 In order to express the right-hand side in terms of r, we 
 
 must assume a law of density and calculate the value of . 
 
 9P 
 This has been already done (p. 32), and it has been found that 
 
 g'p _ a 9 sin 2 qr qr sin qr cos qr 
 gp r 3 sin 2 qa qa sin qa cos qa ' 
 
 Now 
 
 sin 2 qr qr sin qr cos qr = sin 2 gr f 1 - J . 
 
 Let us next divide the earth as Archdeacon Pratt has done 1 
 into four shells and a central nucleus, the radius of the nucleus 
 and the thickness of each shell being equal to one-fifth of the 
 earth's radius. 
 
 The corresponding values of qr and of - are there given, 
 
 viz. commencing at the surface, 
 
 in arc 
 qa = 2-4605 = 140 58' 35", 
 
 &n 
 
 q^ = 1-9684 = 112 46' 52", 
 
 q~ = 1-4763= 84 35' 9", 
 z 5 
 
 q~= 0-9842= 56 23' 26", 
 o 
 
 ^ = 0-4921 = 28 11' 43", 
 
 -3-035906. 
 
 1 Art. 119, 4th ed. 
 
40 LATERAL PRESSURE, ITS AMOUNT. [CH. iv. 
 
 And the other values of - are for the several shells, 
 tangr 
 
 - 0-826756, 
 + 0139920, 
 + 0-654135, 
 
 -f 0-91794*4. 
 Hence calculating the value of 
 
 sin 2 qa qa sin qa cos qa, 
 equation (1) becomes 
 
 y = -r'- 0-62499 -* sin 2 or (l - -^-} T'. 
 r r \ tan^r/ 
 
 It is easily seen that sin 2 or ( 1 ) is of four dimensions 
 
 * V tan^r/ 
 
 in r, so that the second term vanishes when r = 0. 
 
 Moreover, between the values of qr = qa and qr=~> r~* 
 
 2 tan qr 
 
 increases from S'035906 to 0, and continues to increase from 
 
 to 1 when qr = : so that between those limits 1 - 
 
 tan^r 
 
 decreases from 4-035906 to 0. It appears then that de- 
 
 9P 
 creases from 1 at the surface to at the centre. 
 
 And if we give to r the values 
 
 r a, then y = 0. 
 
 r = |a, 2/ = - 0-6455 /. 
 
 r = {o, 2/ = - 07997 r'. 
 
 r = fa, 2/= 0-1573/. 
 
 r = a, y= 3'5689r'. 
 
 r = 0, y = oo . 
 
 So that the curve representing the values of y from r = to 
 r= a will be of the subjoined form, having the axis of y for an 
 asymptote. 
 
CH. iv.] LATERAL PRESSURE, ITS AMOUNT. 41 
 
 The reason why the ordinate of this curve contains T, is 
 because it is obtained from the conditions of equilibrium of an 
 element of an internal shell supporting, besides its own weight, 
 part of that of the rock above it, so that, the thicker the shell, 
 the less will be the lateral pressure on a unit of vertical 
 section ; because the vertical pressure is not proportional to the 
 thickness of the shell, as it is in the case first considered of a 
 shell at the surface of the earth. 
 
 It must be borne in mind that, in the two cases which have 
 been discussed, T and r must be taken so small, that gravity 
 and density may be considered constant through those thick- 
 nesses. 
 
 Kesuming ; 
 
 It has been shown that the horizontal pressure T on a unit 
 of surface of a vertical section of a shell of thickness r at a 
 distance r from the centre will be > = < than the corresponding 
 pressure at the surface, 
 
 as the downward pressure P at that depth 
 
42 LATERAL PRESSURE, ITS AMOUNT. [OH. iv. 
 
 a , g'p 
 
 ~ ~ T 
 gp 
 
 > <gp x the height of a column of rock represented 
 by the ordinate of the curve. 
 
 Represent P by the weight of a column of rock at the sur- 
 face of height equal to z. 
 
 Then P = gpz ; where g, p are the values, at the surface, and 
 are constant. 
 
 And z f(r) will be some curve whose ordinate will bear 
 the same ratio to P which that of the above curve (1) does to 
 the pressure with which we have to compare P. 
 
 Now all we know about this curve z=f(f) is from the 
 nature of the case, which shows that its ordinate is always 
 positive, that it is zero when r = a, and does not become infinite 
 between r = and r a. 
 
 Hence, comparing the two curves, they will have a point in 
 common when r = a, y ; and the ordinate of the latter 
 (which represents P) will be greater than that of the former (it 
 being negative) until they intersect, which they must do some- 
 where between r = and r = fa. 
 
 Hence, the inequality shows that the lateral pressure within 
 the earth becomes equal to that at the surface when r = a (as it 
 ought to do) : while for values of r less than a it is always 
 greater than that at the surface, until some point is reached, 
 which cannot be further from the centre than f of the radius, 
 and is probably much nearer to it. There the curves will inter- 
 sect and the lateral pressure within the earth will be equal to 
 that at the surface. Afterwards it becomes smaller and even- 
 tually infinitely smaller. 
 
 The inference from this is that no shell is likely to have suffi- 
 cient strength to resist the crushing effects of lateral pressure 
 unless it be at a very small distance from the centre. And hence 
 the supposition made by some geologists that the internal strata 
 will be able to sustain the superincumbent weight on account of 
 their dome-shaped form seems on the whole untenable. The 
 result of this will be that, even if the earth be solid, foldings 
 and dislocations of the strata commencing at the surface, will be 
 
CH. iv.] LATERAL PRESSURE, ITS AMOUNT. 43 
 
 propagated downwards as far as the causes which tend to 
 duce them are felt. 
 
 Let us now return to the consideration of, 
 layers of rock, supposed to consist to the depth 
 acquainted with them chiefly of sedimentary strai 
 
 It has been shown that if an external layer wei 
 for a moment to be unsupported from beneath, it would 
 upon horizontally in any two directions at right angles to each 
 other, by pressures which, upon a given area of section, would be 
 equal to the weight of a column of rock of the same sectional 
 area, and of the length of half the earth's radius. 
 
 We may admit then that the crumpling by lateral pressure, 
 which is such a common phenomenon among rocks of all ages, 
 and especially among the older rocks, is due to the force, whose 
 amount has here been approximately calculated. Wherever 
 from any local weakness the superficial strata have been dis- 
 posed to yield, they will have formed a ridge, or a series of 
 ridges ; and the pressures at any point being resolvable hori- 
 zontally into two at right angles to one another, which can in 
 no way neutralize each other, the chains of mountains which 
 traverse a country, if of equable elevation, may a priori be 
 expected to form a network, or if there be one great master 
 chain, like the Andes, it may be expected to be supplemented 
 by a number of smaller chains at right angles to it, the amount 
 of relief which has been afforded by the great chain in one or 
 two great folds, being equal to the sum of what has been 
 afforded in the perpendicular direction by the lesser chains in 
 many lesser folds. A semi-lunar arrangement of a chain would 
 give relief in both directions at once. But whether the for- 
 mation of a chain of mountains in this manner is compatible 
 with a solid globe is doubtful. 
 
 To take an instance of the mode of action of lateral pressure 
 we may refer to a very instructive comparison between the Alps 
 and Himalayas which has been made by Mr Medlicott, and pub- 
 lished in the Journal of the Geological Society 1 . He there 
 shows that the reversed apparent faulting by which the older 
 rocks of the central chain of the Himalayas appear to overlap 
 1 "Jour. Geol. Soc.," Vol. xxiv. p. 34. 
 
44 
 
 LATERAL PRESSURE, ITS AMOUNT. [CH. iv. 
 
 the younger of the Nahun range, and these again the still 
 younger rocks of the Sivalik range, is due to lateral pressure, 
 which must have compress- 
 ed the rocks horizontally, at 
 least at two distinct epochs 
 since the central chain was 
 first elevated. 
 
 An inspection of MrMed- 
 licott's diagram will show 
 that the lateral pressure, 
 which caused the overhang- 
 
 ing surfaces of junction at i limm Sivalik 
 
 A and B, acted with greater 
 force in the lower than in 
 the upper part of the sec- 
 tion. This could not have 
 been the case unless the 
 chain had been already rais- 
 ed when compression last 
 took place. 
 
 Nahun 
 
 Lower 
 Himalaya 
 
CHAPTER V. 
 
 ELEVATIONS AND DEPRESSIONS. 
 
 Distinction betiveen compression and contraction Definition of datum levels 
 General geometrical relation betiveen the compression of a portion of the earth's 
 crust and the elevations and depressions referred to the upper datum level 
 resulting therefrom The same extended to the whole surface of the globe 
 Modification of this relation if the globe is supposed to be wholly solid 
 Average lieight of all the elevations above the datum level upon the supposi- 
 tion of solidity, expressed in terms of depth of sea and height of land, and 
 of areas of the same This average height of actual elevations estimated in 
 feet. 
 
 IT was proved in the last chapter that the horizontal thrust, 
 or force of compression, thrown into a stratum at the earth's 
 surface, or into any stratum to a very considerable depth below 
 the surface, by the shrinking away of the underlying parts 
 would be abundantly sufficient to crush the strata so left un- 
 supported ; and it was explained how this crushing is supposed 
 to have given rise to mountain chains. / 
 
 The object of the present chapter is to find a relation 
 between the quantity of the matter elevated and the amount 
 of compression to which its elevation has been due. It is 
 necessary to distinguish between the terms " compression " and 
 "contraction." Contraction of the underlying rocks causes 
 compression in the rocks above them. Of course contraction 
 and compression may go on simultaneously in the same stratum. 
 It may be compressed by the contraction of the rocks beneath it 
 and it may contract by itself cooling, or by losing some portion 
 of its constituent substance. But for the present we shall con- 
 sider, that the stratum which is compressed does not at the 
 
4 6 
 
 ELEVATIONS AND DEPRESSIONS. 
 
 [CH. V. 
 
 same time contract, nor lose anything in volume by the com- 
 pression to which it is subjected. 
 
 Let A BCD be a layer of rock of unit of width, length I, 
 and depth k. And suppose the abutments at AC and BD to 
 approach each other through the space le, where e is a small 
 
 fraction, which we may call the coefficient of compression. Then 
 the layer of rock in question would assume some new form, 
 suppose one of those given in the figure, or any other whatso- 
 ever conceivable 1 . 
 
 Let us now seek for some simple laws which must govern 
 the disturbed strata in spite of the confusion which appears to 
 reign among them. Let a } a, &c., be the areas formed by the 
 upper curved line above AB, and b, b, &c., the areas formed by 
 the same line below AB. It is not necessary that the a's should 
 be equal to one another, nor yet the b's. They are used simply 
 to designate the areas in respect of their positions. We will 
 call AB " The datum level." 
 
 In like manner let <x, j3, be similar areas for the lower datum 
 level CD. Then the space included between the curved lines 
 must be equal to A Cdb kl(\ + e). 
 
 It is also evidently equal to 
 
 A CDB + a + a -f- &c. + /3 + /5 + &c. 
 bb &c. a a &c., 
 
 1 Some interesting experiments have been made by Prof. A. Favre of Geneva 
 upon the effect of compression in raising elevations of a plastic substance. He 
 placed a layer of clay upon a stretched band of Caoutchouc, and then allowed it 
 to contract. A description of the experiments, and figures illustrating some of 
 the results, which closely resemble the contortions sometimes seen in the earth's 
 strata, will be found in " Nature," Vol. xix. p. 103. See also Ch. x. seq. 
 
CH. v.] ELEVATIONS AND DEPRESSIONS. 47 
 
 or, denoting the sums of the quantities in like positions by the 
 symbol, 2, we get 
 
 kl(l+e) = M + 2 (a) -2 (6) + 2 () - 2 (a). 
 
 .*. Me = % (a) 2 (6) +2 (/3) 2 (a) (1), 
 
 which we shall call a " datum-level equation." 
 
 Since the pressure is supposed to take place in a horizontal 
 direction, it will not have any direct effect to raise the centre 
 of gravity of the portion of the crust under consideration ; so 
 that, if the layer in question rest upon a liquid substratum, 
 we may expect some portions of the disturbed crust to dip 
 into the superheated rocks. But in that case, if the datum- 
 level be unaffected in position, a corresponding volume of such 
 subjacent rock must rise into the anticlinals. 
 
 Hence, 2 (a) = 2 (/3). 
 
 And the equation becomes 
 
 In order to render this reasoning applicable to the section 
 of a surface of any form it is only necessary that the pressure, 
 which causes the compression, should be everywhere tangential 
 to the surface, and that gravity should be perpendicular to it. 
 Hence it is applicable to the earth's surface, although that 
 surface is not strictly regular, and may contain local elevations 
 and depressions affecting the mean figure (that is the figure as 
 unaffected by corrugation), which, though of small amount as 
 compared to the dimensions of the earth, may be large as com- 
 pared with the quantities of which we have to take cognizance 
 in this investigation. 
 
 But the above suppositions cannot represent accurately what 
 has occurred in nature. For they assume the upper and under 
 parts of the crust of the earth to have been, compressed hori- 
 zontally by the same amount. In reality compression must 
 have gone on gradually ever since a solid crust was first formed, 
 and must be greatest at the upper datum level. We must 
 therefore consider e to be the mean coefficient of compression. 
 In the next place it will be necessary to extend our considera- 
 
48 ELEVATIONS AND DEPRESSIONS. [CH. v. 
 
 tions from a section of unit of horizontal width to any pro- 
 posed area of the earth's surface, and eventually to that of the 
 whole globe. 
 
 A clear conception of what will then be the upper " datum 
 level" is important. It will be an imaginary surface which 
 occupies the position that the surface of the crust would occupy 
 at the present time, had it been perfectly compressible in a 
 horizontal direction ; so that no corrugations would have been 
 formed in it. At present we regard it as affected in position 
 by the contraction of the interior, but not by the compression of 
 the crust. 
 
 As soon as elevated tracts had once been formed by the cor- 
 rugation of the cooled crust, all the material above the datum 
 level, however distributed, must have been derived from matter 
 originally beneath it, and subsequently raised above it. As 
 often as further compression of the crust has taken place, every 
 fresh addition to the sum total of the quantity of matter above 
 the datum level must have accrued by the elevation of matter 
 from below it. For the matter which was already above it, 
 however freshly corrugated, or re-arranged by water action, or 
 otherwise, cannot have been thereby altered in quantity. More- 
 over each additional contraction will have acted upon a crust 
 thicker than it was before, on account of its having become in 
 the meanwhile solid, or if solid contracted, to a greater depth. 
 
 A 
 
 We have hitherto confined our symbols to a vertical section 
 of unit of width. We will now extend them as in the diagram 
 to a portion of the crust whose length is I and width w, and 
 the depth &; e and e' being the mean coefficients of com- 
 pression in the directions of length and width. Then, if we 
 
CH. v.] ELEVATIONS AND DEPRESSIONS. 49 
 
 neglect the product ee, our equation will become 
 
 where A and B are now the volumes of the elevations above and 
 depressions below the datum level. 
 
 If in this equation we put w = 1 and e 0, it reduces to 
 our former equation. 
 
 If we put e = e we get 
 
 2&fa*=5(^)-2(5) (2), 
 
 which we may take as the general expression corresponding to 
 any area of the surface. 
 
 The relation just found manifestly assumes that before any 
 compression took place, that is at the epoch when the crust 
 first solidified, there were neither elevations nor depressions 
 upon its surface ; or in other words it assumes that the surface 
 was one of equilibrium, like that of the ocean. And if the 
 crust passed from a liquid, through a viscous, to a solid condi- 
 tion, this seems to be the natural supposition. And this suppo- 
 sition is strengthened by the fact tihat all the rocks we see at 
 the surface have either been water-deposited, or else have been 
 protruded through water-deposited rocks. So that no evidence 
 of any pristine inequalities can be adduced which is opposed to 
 this natural supposition. 
 
 The tendency of the corrugations over a given area will be 
 to form two systems at right angles to one another, thus re- 
 lieving the whole compression. Where one corrugation inter- 
 sects another, we shall have a part of the volume common to 
 both. But physically the same space cannot be occupied by 
 two distinct volumes of rock. Hence at every such intersection 
 there must be an increase of altitude in the ridges sufficient to 
 contain within the contour an additional volume equal to the 
 common portion. This appears to occur in nature where a 
 peak often occupies the place of intersection of two ranges, as 
 if the denudation which has shaped out the -mountains has had 
 a greater amount of matter to remove in such a situation. 
 
 The result expressed by the equation (2) may be extended to 
 F. 4 
 
5P ELEVATIONS AND DEPRESSIONS. [CH. v. 
 
 the whole globe by considering its surface composed of elemen- 
 tary rectangular areas, and summing them ; whence 
 
 = 2 (,4)- 2 (B) .................. (3). 
 
 In which expression 
 
 r is the radius of the earth measured to the present 
 position of the datum level. 
 
 k is the present thickness of the cooled crust. 
 
 e is the mean total linear compression of the crust. 
 
 2 (A) is the volume of the total elevations above the 
 datum level. 
 
 S (B) is the volume of the total depressions below it. 
 And ?r = 314159. 
 
 It is worthy of remark, that the relation between lateral 
 compression and elevation expressed by the above equation, (3), 
 in no way depends upon the arrangement of the disturbed 
 rocks, nor upon the time at which the successive movements 
 have taken place, nor upon the elevations occupying their 
 original positions on the globe, nor upon whether or not subse- 
 quent denudation, or any other mode of action, has redistributed 
 the elevated matter. Nay, even if- by human agency excava- 
 tions have been made, their results will be included in our 
 equation, which is perfectly general and true, so long as it is 
 strictly interpreted. It requires also in particular to be noticed 
 that it is not assumed that mountain-ranges need be anticlinals. 
 All that is assumed is that they are carved out of tracts ele- 
 vated as a whole by lateral pressure. 
 
 An opinion seems to have lately gained ground among geolo- 
 gists, that the continents and oceans have at all periods occupied 
 nearly the same positions upon the globe that they do now. It 
 may be as well to remark that, whether this opinion be true or 
 not, it has no effect whatsoever upon the correctness of the 
 result at which we have arrived. Our equation does not 
 depend in the least degree upon the intermediate history of the 
 earth's surface ; but requires only that in the primeval state it 
 
CH. v.] ELEVATIONS AND DEPRESSIONS. 51 
 
 should have been a level surface, and that it is at present what 
 we see it to be. 
 
 Another point to which the reader's attention is requested 
 is that no assumption whatever has been hitherto made either 
 as to the amount of contraction or of compression, except that 
 the latter is small compared to the dimensions of the area com- 
 pressed. The rude diagrams, which have been used in proving 
 our equation, are not supposed to represent any thing in nature. 
 
 This appears to be the proper place for considering the 
 manner in which the results of the deposition of sediment over 
 a limited area would enter our equation. Geologists believe 
 thick deposits to have been accumulated upon sinking areas, and 
 attribute the subsidence of the area to the weight of the deposit 
 itself. If rocks, liquid or plastic from heat or any other cause, 
 come within a moderate distance of the surface this is possible, 
 and many instances both among ancient strata and modern river 
 deposits seem to be explicable on no other hypothesis. But 
 the displacement of such plastic matter from beneath- the new 
 deposit must cause the rise of an equal volume somewhere else, 
 so that if the terms of our equation were in any way affected 
 (which would depend upon whether the effect extended below 
 the datum level) it would be by an addition to the term 2 (/3), 
 and a consequent equal addition to "2 (a), and their sura would 
 be zero. So that, as already intimated, our equation will in- 
 clude any such effect of denudation and the resulting deposition. 
 
 Such an action as has been just referred to would produce 
 a slight amount of crumpling in the strata^ but only a very 
 slight one, unless the new deposit sunk through some subjacent 
 strata, and pressed them sideways out of its way ; as the Author 
 has shown to have happened in the contorted drift of Norfolk 1 . 
 But it is only possible for this to have happened where the de- 
 posit produced a very much greater pressure upon the area which 
 it occupies, than the rocks displaced by it did; that is when it is 
 very much thicker than they were. And it is clearly impossible 
 that it should elevate any displaced strata to a greater altitude 
 
 1 "Geol. Mag.," Vol. v. p. 550. 
 
 42 
 
52 ELEVATIONS AND DEPRESSIONS. [CH. v. 
 
 than its own, which is necessarily limited to that of the sea- 
 level where the deposit is going on. The test of such a mode of 
 action would be to ascertain whether any portion of the strata, 
 which ought to lie beneath the thick deposit, can be discovered 
 in a contorted condition abutting upon it. 
 
 Thus far, for the sake of perfect generality, it has been as- 
 sumed that the disturbed upper strata rest upon a liquid, or at 
 least a plastic, substratum. In what follows, the enquiry will be 
 made whether this condition of the subjacent rocks is probable. 
 And the method taken will be to consider whether the contrary 
 supposition, that the subjacent rocks are solid, will account for 
 the amount of inequalities which the earth actually exhibits. 
 
 If the earth had cooled as a solid body, the outer layers at 
 any epoch having attained their complete amount of contraction 
 sooner than the interior, would have been too large to fit the 
 interior after the cooling had proceeded further. They would 
 therefore become corrugated. But in this case the corrugation 
 would have necessarily taken place wholly in an upward direc- 
 tion, the solidity resisting the intrusion of corrugations into the 
 lower regions ; and there could be no places where any portion 
 of the surface could have become depressed below the datum 
 level. Hence upon this hypothesis we may introduce into our 
 datum-level equation the supposition that 2 (B) = 0. And it 
 becomes 
 
 Since 4?rr 2 is the area of the globe, it follows from this rela- 
 tion that 2ke is the average height of all the elevations above 
 the datum level, which make up the volume X (A}. In other 
 words, if all the elevations were levelled down, they would 
 form a coating above the datum level whose thickness would 
 be 2ke. 
 
 The actual amount at which we may estimate this quantity 
 is of great importance to the argument we are about to. adduce 
 regarding the physics of the earth's crust. We will now en- 
 deavour to obtain a fairly reliable measure of it from the data 
 obtainable. 
 
CH. v.] ELEVATIONS AND DEPRESSIONS. 53 
 
 A little consideration will give the following geometrical 
 relation : 
 
 The volume of the Sea above the datum level = the area of the 
 whole surface of the globe x the depth of the datum level below 
 the sea-level the volume of rock displacing water between those 
 levels. 
 
 Let S = area of the Sea. 
 
 D = its mean depth. 
 
 L = area of the Land. 
 
 W = volume of the Land above the sea-level. 
 
 c = the depth of the datum level below the surface of the 
 Sea, considering these as parallel. 
 
 Now the volume of rock displacing water between the datum 
 level and the sea-level will be 2 (A) W, and since in the 
 case supposed 2 (A) = Sjrr^ke, we shall obtain the following 
 relation : 
 
 SD =-(S+L)d- (Strike -W). 
 
 But it is to be observed that this relation assumes the sur- 
 face of the ocean to be everywhere parallel to the datum level, 
 which is itself supposed to be parallel to the original surface of 
 the globe when it was first covered with a solid crust. But the 
 distribution of the great continents and oceans, as well as 
 observations on the plumb-line, render it probable that there 
 is some cause which increases the density beneath the great 
 oceans, and tends to accumulate the water upon them, so that 
 their depth is greater than it would be, were that solely due 
 to a relative depression or locally diminished curvature of the 
 sea-bed. 
 
 Let us then call X the accumulated volume of water in 
 excess of that which the oceans would contain, were their sur- 
 face parallel everywhere to the datum level ; retaining D as 
 the observed mean depth of the sea, but using d as measured 
 from the supposed surface as just defined. 
 
 In order to allow for the accumulated water, we must correct 
 
54 
 
 ELEVATIONS AND DEPRESSIONS. [CH. v. 
 
 our equation by subtracting X from the actual volume of the 
 ocean, so that 
 
 Observing that $'+ L is tbe whole area of the globe, and there- 
 fore equals 47r^ 2 , and that -~ -^ would be the depth of a layer 
 
 of water of the volume of X if it were equably spread over the 
 whole globe, which depth we will call 8, the above equation 
 gives, 
 
 vol. of sea vol. of land 
 area of the globe 
 
 The area of the ocean is estimated to be 146 millions of 
 square miles, and that of the land 51 millions 1 '. 
 
 Mr 3>. Carrick Moore 2 has shown that Sir John Herschel was 
 misled by an inaccurate expression in "The Cosmos" in his 
 estimate of the mean height of the land being 1800 feet 3 , and 
 that it uglt to be put at half that, or 900- feet. The average 
 depth of the ocean is reckoned at three miles, and its volume 
 at 438 millions' of cubic miles. By substituting these numbers 
 we obtain, 
 
 &- 
 
 A- 
 
 -y 
 
 AB the datum level. 
 
 SS the sea level supposed parallel to it. 
 
 O the actual surface of the ocean. 
 
 S'S' the surface of the accumulated water levelled down. 
 
 1 Herschel's " Physical Geography," second edition, p. 19. 
 
 a "Nature," Vol. v. p. 479. 
 
 * "Physical Geography," p. 118. 
 
CH. v.] ELEVATIONS AND DEPRESSIONS, 55 
 
 Our next step must be to fix upon a value for d + 8. This 
 is the depth of the datum level below the surface of an imagi- 
 nary ocean, which is rather less deep than the actual one. 
 
 Now it is not probable that there is any place where the 
 bottom of the ocean would coincide with the datum level. Never- 
 theless there seems reason to think that this would approximately f 
 be the case in the deeper parts. If this be so, d + 8 will not differ^/ 
 greatly from the measure of the deepest parts of the ocean, and 
 it is not likely to exceed it by much, because, as already men- 
 tioned, the surface from which it is reckoned is somewhat lower 
 than the actual surface of the ocean. 
 
 If the deepest parts of the ocean do not coincide with the 
 datum level they must be one of two things. They must be 
 either depressions below it, belonging to the series ^ (B), or else 
 they must be the places where the ocean bottom is least raised 
 above the datum level. That they should be depressions be- 
 neath that level is scarcely possible under our present assump- 
 tion that the earth has cooled as a solid ; whence we have 
 concluded that S (B) = O 1 . But if we take the other alternative, 
 and suppose the ocean-bottom to be raised above the datum 
 level, even where the depths are very great, then we are taking 
 d + 8 too small, and our estimate for %ke will be too small. And 
 this appears by far the more probable case. 
 
 On the whole, then, we may feel pretty well assured that 
 we are within the mark if we put for d + 8 the measure of the 
 more profound parts of the ocean. The mean depth being taken 
 at three miles we shall not be much in excess if we put d + 8 
 as equal to four miles. Our value for 2ke then becomes 
 
 ZJce = 4 - 2-2 miles, 
 = T8 miles, 
 = 9504 (feet about), 
 a value which is more likely to be too small than too large*. 
 
 1 p. 52. 
 
 2 Prof. Haughton ("Proc. Koy. Soc.," Vol. 26, p. 53, 1877) puts the area of the 
 sea at 145 millions of square miles, and that of the land at 52 millions, and the 
 
56 ELEVATIONS AND DEPRESSIONS. [CH. v. 
 
 mean height of the land at 1000 feet. Sir Wyville Thomson, in his Eede lecture at 
 Cambridge in 1877, stated that the mean depth of the Atlantic was about 2500 
 fathoms. In places its depth was 3000 fms. or a little more, and in one place 
 4000 fms. The greatest depth in any ocean was perhaps in the Pacific, where 
 in one place it was 5000 fms. 
 
 If we adopt Prof. Haughton's estimate of the areas of sea and land, and of 
 the mean height of the land ; and Sir Wyville Thomson's estimate of the mean 
 depth of the sea, viz. 2500 fms., and if we take 4000 fms. as the depth of the 
 more profound parts (though we might apparently be entitled to take it greater), 
 we obtain 
 
 2fc = 13224 feet. 
 
 This value is very much larger than that which the former estimates give. 
 But since the Author has used the lesser value in his previous publications, he 
 thinks it better to allow it to remain, seeing that precision is not attainable, and 
 that the larger value merely strengthens the argument drawn from the smaller. 
 
CHAPTER VI. 
 
 ELEVATIONS ON THE HYPOTHESIS OF SOLIDITY. 
 
 Any physical hypothesis regarding the condition of the interior of the earth may 
 be tested by comparing the average height of the elevations it would produce 
 with that which exists in nature Sir Wm. Thomson regards the earth as a 
 solid cooling by conduction Some of the results of his paper "On the Secular 
 Cooling of the Earth"- His mathematical formula for expressing the law of 
 temperature in descending Calculation in general symbols of the average 
 height of the elevations which would be produced upon the supposition of the 
 earth cooling as a solid Numerical result obtained with a value of the 
 coefficient of contraction deduced from Mallet's experiments and Sir Wm. 
 Thomson's estimates of the melting temperature and conductivity The same 
 with Mallet's estimate of the melting temperature of slag The corresponding 
 age of the earth Amount of radial contraction. 
 
 IN the preceding chapter an estimate has been made of the 
 average height above the datum level of all the elevations upon 
 the earth's surface, which exist at the present time, it being 
 supposed that the most profound depths .of the sea coincide ( 4- 
 nearly with the datum level. And it has been found that a 
 very moderate computation gives 9504 J feet for this average 
 height : but there are good reasons for supposing that 13224 2 
 feet are nearer the mark. It has also been proved that upon 
 the supposition that these elevations are the result of lateral 
 compression, their average height above the datum level is ex- 
 pressed by the product 2ke, where k is the thickness of the 
 corrugated crust, and e the mean coefficient of compression. 
 If then we are able to calculate the value of 2ke upon any 
 physical supposition we choose to make regarding the condition 
 
 1 p. 55. 3 P. 56. 
 
5 8 ELEVATIONS ON THE [en. vi. 
 
 of the interior of the earth we have a means, by comparing our 
 result with that already approximately obtained in the case of 
 nature, of judging whether our supposition bears the test of the 
 comparison ; it being always premised that lateral compression 
 is the cause of the existence of these elevations ; because it is 
 upon this premise that our definition of a datum level, and 
 calculation of 2ke, have been based. 
 
 Nevertheless our estimate of the average height of the 
 r elevations above the profound depths of the sea would hold good 
 as the expression of a fact apart from all theory. 
 
 In the second chapter it was shown that there is very little 
 question but that the earth was at one time fluid, yet that at 
 the present time we are compelled to admit that it is on the 
 whole rigid : but that it is still open to question whether it is 
 rigid throughout, or whether there is a certain level couche 
 beneath the cooled crust where the pressure is not sufficiently 
 great to induce solidity in rocks which, on account of the 
 increase of temperature in descending, will otherwise be liquid. 
 We have also pointed out how the true law of increase of 
 temperature is inextricably mixed up with the question of the 
 solidity or otherwise of the interior. And if the law of increase 
 of temperature be so, it is evident that the law of cooling, upon 
 which it depends, is also mixed up with the question of the 
 condition of the interior ; and the contraction depends on the 
 law of cooling, and the compression on the contraction ; so that 
 all these questions are interdependent. Now the laws of cooling 
 of a solid by conduction have been long brought under the 
 dominion of mathematical calculation. Not so those of the 
 cooling of a liquid by convection. 
 
 Sir Wm. Thomson having satisfied himself that the earth 
 is as a whole extremely rigid, has assumed that it is wholly rigid 
 from centre to surface, and has applied to it the laws of cooling 
 of a solid by conduction. Consequently he has paved the way 
 for an investigation of the amount of compression, which might 
 accrue upon the supposition that the earth has cooled as a solid 
 sphere. To calculate the average height of the elevations, 
 which would have been formed up. to the present time under 
 these conditions,- is the object of the present chapter. 
 
CH. vi.] HYPOTHESIS OF SOLIDITY. 59 
 
 The paper by Sir Wm. Thomson "On the Secular Cooling 
 of the Earth 1 " is of great interest and well known. From his 
 mode of viewing the manner of its solidification, he believes that 
 it passed from the state of a liquid to that of a solid globe in 
 a comparatively short space of time ; since which period all 
 geological events have happened. His formula expresses the 
 rate of increase of temperature at any given depth in terms of 
 the length of time since complete consolidation took place. 
 The resulting curve of temperature is of such a form that, for 
 reasonably large values of the time in question or of the age of 
 the habitable world and for all such depths as the puny efforts 
 of man can reach, it would be impossible to perceive at the 
 present day any deviation from a uniform rate of increase. But 
 if it were possible to reach very great depths, the rate would be 
 found to be sensibly diminishing ; and even at the centre of the 
 earth a greater temperature need not exist than what the uniform 
 rate of one degree F. for 60 feet, which obtains at the surface, 
 would bring us to at about sixty miles. The greater the value 
 we assign to the presumed age of the world, the deeper we should 
 have to dig before we should find the rate sensibly diminishing. 
 Some interesting particulars concerning the relation between 
 different assumed values for the world's age, and the depths at 
 which it might be practicable to detect a diminution in the rate 
 of increase of temperature, will be found in Sir Wm. Thomson's 
 sectional address to the British Association, 1876. But the con- 
 clusion at which we must arrive is, that no mine nor bore-hole 
 is ever likely to be put down deep enough to solve the question 
 whether the earth is solid from centre to surface or not. If ever 
 it could be conclusively proved by observation, due allowance 
 being made for disturbing causes, that the rate began to diminish, 
 that would be an argument that the earth is a solid cooling 
 by conduction from its entire mass, and not from an internal 
 liquid reservoir. But the shortest age that can be assigned 
 to the world's history is too long to allow us to expect that the 
 depth requisite to test this question can ever be reached. 
 
 1 "Trans. Boy. Soc. Edinburgh," Vol. xxm. Pt. i. p. 157; also "Phil. 
 Mag.," 4th Series, Vol. xxv. p. 1, 1863, and Thomson and Tait's "Treatise on 
 Nat. Phil.," p. 711, 1867. 
 
6o ELEVATIONS ON THE [CH. vi. 
 
 Sir Wm. Thomson writes 1 , "The earth, although once all 
 melted, or melted all round its surface 2 , did, in all probability, 
 really become a solid at its melting temperature all through, or 
 all through the outer layer, which had been melted ; and not until 
 the solidification was thus complete, or nearly so, did the surface 
 begin to cool." The conclusion at which he arrives on these 
 grounds, respecting the present distribution of temperature, is 
 that the rate of increase from the surface downwards would be 
 sensibly ^ of a degree F. per foot for the first 100,000 feet (19 
 miles) or so. Below that depth the rate of increase per foot would 
 begin to diminish sensibly. At 400,000 feet (76 miles) it would 
 have diminished to about y^- of a degree per foot, and so on 
 rapidly diminishing as shown in the curve. "Such is on the 
 whole the most probable representation of the earth's present 
 temperature, at depths of from 100 feet, where the annual 
 variations cease to be sensible, to 100 miles; below which the 
 whole mass is, whether liquid or solid, probably at or very nearly 
 at the proper melting temperature for the pressure at each 
 depth" that is to say, the cooling process not having at present 
 reached so far, the state of the matter there cannot in any way 
 influence the law of temperature in the strata above. 
 
 Having given this summary of Sir Wm. Thomson's theory 
 concerning the condition of the interior of the earth, we will 
 now proceed to form an estimate of the average height of the 
 elevations above the datum level (or of 2ke) which might be 
 formed by the contraction of a globe so constituted. 
 
 In order to do this, we must first of all estimate the com- 
 pression, Me, corresponding to the present thickness k of the 
 crust and to a length I upon the present surface. 
 
 1 "Nat..Phil.,"p. 722. 
 
 2 Dr Sterry Hunt supports the latter view. " American Journal of Science," 
 Vol. v. p. 2G4, 3rd series, 1873. 
 
CH. VI.] 
 
 HYPOTHESIS OF SOLIDITY. 
 
 Let ABDC be a section of a portion of 'the crust of length I 
 and depth k. Then e is the mean coefficient of compression 
 for the whole, which will depend upon the depth to which the 
 cooling down to the melting temperature under pressure has 
 advanced. The area which by its having become compressed 
 will have gone to form the corrugations AFB will be BDE, in 
 which BE is the quantity by which AE has been compressed, 
 while CD has not been compressed at all. 
 
 Then if BMx, and c = the compression at the depth x, 
 
 And 
 
 /: 
 
 = I cdx. 
 
 o 
 
 We now require to express c in terms of x. 
 
 For this purpose we avail ourselves of Sir Wm. Thomson's 
 paper "On the Secular Cooling of the Earth," using the 
 symbols and formulae, and the diagram there given slightly 
 altered, but not necessarily adhering to his values of the con- 
 stants. In the event we think it will appear that we must 
 
 Diagram altered from Sir W. Thomson's paper "On the Secular Cooling of the 
 Earth." ON the depth below the surface = x. NP the excess of tempera- 
 ture at that depth above the temperature of the surf ace = v. Oq the excess 
 of the melting temperature above that of the surface = V. 
 
62 ELEVATIONS ON THE [en. vi. 
 
 adopt some modification of his views as to the condition of the 
 globe at the time at which a rigid crust commenced to form, 
 because we shall find that they lead us to a value of 2ke which 
 is not in accordance with natural appearances. 
 
 The point which is material in the application of his inves- 
 tigation is, that cooling is to take place by conduction and not 
 by convection. 
 
 F is the melting temperature of rock ; which Sir William 
 Thomson places provisionally at 7000 F., a very high esti- 
 mate. Mr Mallet has shown that the temperature of slag run 
 from an iron furnace is less than 4000 F. 1 6 is a temperature 
 such that, 
 
 F 7000 _ 7qoo F 
 ~i,/~ 0*8622- 
 
 The quantity a is thus defined : a 2jfct, where K is the 
 conductivity of rock, found by Sir Wm. Thomson to be " 400 for 
 unit of length a British foot and unit of time a year." And t 
 is the number of years since the earth became solid, which 
 must have elapsed in order that the rate of increase of tem- 
 perature in descending into the earth should be what it is 
 observed to be. Consequently t is 100,000,000 years, and a = 80 
 miles. We learn ( p. of Sir Wm. Thomson's paper), that 
 
 'When then the rigid crust was commencing to form, the 
 whole globe, or at any rate its outer portion to a considerable 
 depth, was at the melting temperature F F. represented on 
 the diagram by Oq or Nn. At a subsequent time the tempera- 
 ture at the depth ON or x was v, represented by the ordinate 
 NP. Hence at that depth cooling had taken place through 
 (V v), represented by Pn. Now the compression which each 
 layer of the crust undergoes is caused by the contraction of all 
 the matter beneath it. 
 
 let r be the present mean radius of the earth; E the 
 cubic contraction for 1 F. Hence the layer of the sphere at 
 i "Phil. Trans. Koyal Soc." 1873, Vol. 163, p. 199. 
 
CH. vi.] HYPOTHESIS OF SOLIDITY. 63 
 
 the depth #, whose area is 4<7r(r xf y will have contracted by 
 
 b t x -- 
 
 E^TT (r xfdx x Pn ; where Pn = V -- e 2 dx. Consequently 
 
 &./ o 
 
 the whole contraction from that depth downwards will be 
 
 where the integral ought to be taken from x to the value x 
 has at the depth at which contraction ceases to be felt. It is 
 evident from the diagram that this is almost the case at the depth 
 2a, where the temperature differs but little (by Fx 0*00468 ') 
 from the melting temperature V. 
 
 1 Generally 
 
 -v 
 
 la 3 i I B _ 
 
 "* + 
 
 The general term of the series is 
 
 Suppose the superior limit of the integral to be 2a. Then this becomes 
 
 1 02W+1 
 
 And the next term to this will be 
 
 I 2 2 < n+1 H-i 
 
 And the sum of the two terms 
 
 n+l(2m-l)(2n + 3) 
 
64 ELEVATIONS ON THE [en. vi. 
 
 There will remain the effect of the contraction of the re- 
 mainder of the sphere from the depth 2a to the centre. This 
 we will assume to be as great as at the depth 2a, and then we 
 shall be sure that the whole cubic contraction at and below the 
 depth a is a quantity less than 
 
 - xfPndx + E y x Q-00468. 
 
 & 
 
 Suppose E' to be the mean coefficient of contraction for all 
 the matter below the depth x. Then the whole contraction 
 from x to the centre of the sphere will have been 
 
 0-00468. 
 
 And the coefficient of linear compression at the depth x will be 
 the same as the coefficient of linear contraction of the spherical 
 
 W 
 
 surface at that depth. That is to say, c = -~- ; 
 
 ., C< Z f* (r _ ayPn te + Xr,r--2a\' 
 
 (r-x) 3 ] x ^ 3 \r-xj 
 
 If we then take 2a as the limit of depth to which compres- 
 sion has reached, which we may do because the cooling below 
 
 In this expression n=0 "will give the first and second terms of the series, 
 n=2 the third and fourth, w=4 the fifth and sixth, &c., &c. 
 
 Making n successively 0, 2, 4,... 18 (for which last value the first significant 
 digit will not occur before the 7 th place of decimals), we get for the sum of the 
 first 20 terms 
 
 =0-882083, 
 
 / V \ 
 
 whence at the depth 2a, Pn= V- b x 0-882083, ( where 6 = ^ ) , 
 
 V WTT/ 
 
 7x0-00468. 
 
CH. vi.] HYPOTHESIS OF SOLIDITY. 65 
 
 that has been inconsiderable, the entire compression of .the 
 
 /k 
 cdx, will be less than the inte- 
 3 
 
 gral of the above expression taken from the surface to the depth 
 2a, that is 
 
 rE ( C 2a ) 
 
 -r-^] (r-x?Pndx\dx 
 , (r x) (J x ) 
 
 + -g- x 0-00468 
 
 or very approximately, 
 
 E [' 
 * e< ~f]< 
 
 o 
 
 + x 0-00468 
 
 rr2a 
 P/i^a; = Q, and I ocPndx = It. 
 J X 
 
 Then 
 
 E f 
 - 
 r Jo 
 
 Performing the integrations 1 , we obtain for the larger re 
 sulting terms, 
 
 a*--a*b x 1-55280 + -=~ a x 0'00468; 
 
 r r 6 
 
 1 It has been already proved that 
 
 , b ( la; 3 1 z 5 
 
 Pn=V-- 5- 0-5 + 1 Sl- 
 at 3 a 2 1 . 2 a 4 
 
 6 { 8 1 la; 4 1 1 la; 6 
 ^ Vx-- I ^ - g . 5 - a + j-2 .g g- 4 
 
 1 1 1 a; 2n+a | 
 L) a 2 " + j ' 
 
 F. 5 
 
66 ELEVATIONS ON THE [CH. vi. 
 
 and for the smaller, 
 
 - j-^V + -a*bx 11393 - ZEVa x 
 r { 3r r 
 
 The general term of the series is 
 
 ( _ l)n 5 1 1 a 2 /* 
 
 1 1 
 
 Taking 2a as the superior limit of the integral, the general term becomes 
 (-l) n a& 
 
 And putting n + 1 for w the next term to this will be 
 
 And the sum of the two terms 
 
 22n+l r i 2 2 1 
 
 )j 
 
 Giving to n the series of values 0, 2, 4, 6, ..., 14, we obtain for the sum of 
 the terms to the 16 th inclusive, 
 
 abx 1-273320. 
 
 Hence we have for the value of J Tndx, when x= 2a (or at the superior limit), 
 V2a-abx 1-273320; 
 
 l pndx= V (2a - x) - ab x 1-273320 
 
 5 |a; 3 _ 1 1# 4 1 1 Iic 6 _ 
 + a|2"~3'4o 2 + "^'5'6a*~ 
 
 . -.! 1 1 a 2n+2 
 
 \ 
 
 273320a&a 
 
 = ( ( [^Pndx^ dx=V (tax - ~\ - l- 
 
 
 '1 1 1 1 x~ n+ * 
 ' 
 
CH. vi.] HYPOTHESIS OF SOLIDITY. 67 
 
 As yet no definite values have been assigned to any of the 
 constants. 
 
 Taking the observed rate of cooling at -g^th of a degree F. 
 per foot in descending, the time since the supposed solidification 
 
 The integral has to be taken from #=0 at the surface to that value of x 
 which expresses the thickness of the rigid crust beyond which corrugations will 
 not have been formed. 
 
 Now the melting temperature V is reached within an extremely small error 
 at the depth 2a. We may therefore take 2a as the superior limit, and the above 
 quantity becomes 
 
 ( 2<t ( F a 
 
 dx=V (4a 2 - 2a 2 ) - 1-273320 x 2a 2 6 
 
 . 
 
 3.4.5 a 2 
 
 of which series the general term after simplification becomes 
 
 02n+2 1 
 
 / 1\n fl 2l,Jl_ __ * __ . 
 
 n + l 
 and the next to it 
 
 and their sum, after reduction, 
 
 This is the sum of the two corresponding terms in the former series (A) 
 multiplied by the factor 
 
 2 f 2(n + 2) 1 
 "2n 2 -(-2)j ' 
 
 Giving to n the values 0, 2, 4, 6,... 14, we obtain for the sum of the terms of 
 the series to the 16 th inclusive, 
 
 a 2 6 x 0-993840. 
 Hence 
 
 " Pn dx\ dx = F2a 2 - a 2 6 x 2-546640 + a 2 6 x 0-993840. 
 
 jRand 
 
 Or I Qdx = F2a s - a ? 6 x 1-552800. 
 
 jo 
 The calculations for obtaining 
 
 . \(%Qx-\ 
 
 are of a similar character. 
 
 The numerical results of these series have in every instance been verified 
 independently from the general terms by friends. 
 
 5-2 
 
68 ELEVATIONS ON THE [CH. vi. 
 
 at 7000 took place will have been 100,000,000 years, whence as 
 already stated, a = 2*J/ct = 400,000 feet, or about 80 miles. And 
 
 l = ^= = 7900. 
 
 iyw 
 
 In order to fix upon a value of E, the coefficient of contrac- 
 tion for 1 F., reference is made to some experiments on a large 
 scale conducted by Mr Mallet 1 . And upon reducing his results 
 
 we find for slag from an iron furnace E '0000215 2 , whence 
 -pi 
 
 -s- the linear contraction = '000007; which does not differ more 
 
 3 
 
 than might be expected from the estimates made at much 
 lower temperatures for rock by Mr Adie 3 . 
 
 If we take the earth's mean radius at 20,902,520 feet, we 
 obtain as the final result for the two first terms, 286 feet. 
 
 The third term gives the effect of the contraction of the 
 entire volume of the sphere, from the depth 2a to the centre, 
 in corrugating the crust to the depth 2a, on the supposition 
 that the contraction continues to the centre as great as it is at 
 
 1 "Phil. Trans. Eoyal Soc.," Vol. 163, p. 201. See also " Nature," Vol. zxn. 
 p. 266. 
 
 2 To obtain the coefficient of contraction for 1F. from Mr Mallet's ex- 
 periments. 
 
 The cones of slag began to solidify when the containing iron cones were at 
 450 F. At that time the mean contents -of the cones was 8231-9229 cubic 
 inches, and the volume of the slag when measured at 53 F. was 7700-2303 cubic 
 inches. 
 
 The slag entered the cones at a temperature of 3680. 
 
 By Mr Mallet's estimate, founded on the time in which solidification com- 
 menced, the solidification commenced at about "3062, or say 3000 F." 
 Hence the number of degrees through which the temperature fell was 
 
 3062 -53 -3009. 
 
 We have therefore to determine E, the coefficient of cubical contraction 
 between incipient consolidation and 53 F. 
 
 7700= 8232 (1-E3009); 
 .-. = -0000215, 
 
 and f = -0000071. 
 
 u 
 
 3 The mean of Mr Adie's six results for the coefficient of expansion is '0000057. 
 "Trans. Boy. Soc. Edin.," Vol. xm. p. 370. See also "Geol. Mag.," Vol. x. 
 p. 260. 
 
CH. vi.] HYPOTHESIS OF SOLIDITY. 69 
 
 the depth 2a. But no account has been taken of the corruga- 
 tions which would arise from the compression of this portion 
 itself. However Sir W. Thomson concludes that below the 
 depth of 100 miles the earth will be at the proper melting 
 temperature for the pressure, whilst 2a = 160 miles. Conse- 
 quently our assumption on the first account makes the effect 
 of the cooling of this portion of the sphere enormously too great, 
 whilst on the second account it is made somewhat too small. 
 If we take half the calculated effect we may feel certain that 
 we have taken it large enough. We will therefore put this 
 term at 94 feet. 
 
 The first two terms of the bracket multiplied by - "give 58 
 
 feet. 
 
 And half the third gives 5 feet, and is negative. 
 On the whole, therefore, we may conclude that 
 ke = 286 + 94 + 53 feet, 
 
 = 433 feet. 
 
 And 27ce = 866 feet ; 
 
 a result which is probably considerably too large, 
 
 In other words, if all the elevations which would be pro- 
 duced by compression, through the contraction of the earth 
 cooling as a solid upon the above suppositions, were levelled 
 down, they would form a coating over the whole globe of about 
 800 feet in thickness. This is an exceedingly small result. 
 
 We will now enquire how the result of our calculation will 
 be affected by assuming a different value for the melting tem- 
 perature, about which we have no very certain knowledge. 
 
 b C x _- 
 The function - I e & dx, by which Sir William Thomson has 
 
 a Jo 
 
 expressed the temperature within the earth at the depth #, 
 requires that the law of its increase shall not be affected by 
 the sphericity of the surface; which he has shown under the 
 circumstances to be an admissible supposition. This assump- 
 tion is therefore involved in our value for Pn ; and it evidently 
 
70 ELEVATIONS ON THE [CH. vi. 
 
 tends to diminish the rate of increase of temperature in descend- 
 ing, and to make the value of ZJce too large, by giving too 
 great a thickness to the cooled crust. 
 
 It is easily seen that, if we had taken our integrals from 
 the surface to such a depth that the cooling represented by Pn 
 becomes any given inappreciable fraction of the melting tem- 
 perature, we need not have introduced the supplementary term 
 which is multiplied by 0*00468. If we suppose pa to be the 
 depth in question, the corresponding value of Pn would be 
 
 r{i-, 
 
 = Vf(p). 
 
 This shows that the value of p> y which corresponds to any 
 assumed fraction of F, does not involve any of the constants of 
 the problem. But Pn will not altogether vanish until the 
 integral becomes equal to -Javrr, which, from a known definite 
 integral, will not be until p is infinite. We have assumed^? = 2 
 for convenience of calculation, since even so small a value 
 makes Pn small. But the relation 
 
 ke 
 
 rpa / ft rpa 
 
 e= (T-%-3 (r- 
 Jo \(r-x)*J x 
 
 can be made as exact as we please by taking p large enough. 
 Had that been done we can see that the larger terms of the 
 
 V 
 result would have been proportional to EVa?, since 6 
 
 and the small terms of the bracket multiplied by - would have 
 
 been proportional to'EVa 3 , a being equal to Z*jKt. We can 
 therefore, by means of a proportion, deduce from the value of 
 2ke already found, its value corresponding to any other values of 
 E } V, or K. For instance, if we introduce for V the temperature 
 which Mr Mallet has determined for melting slag, viz. 4000 F., 
 
CH. vi.] HYPOTHESIS OF SOLIDITY. 7 1 
 
 instead of 7000, and the corresponding value for t, viz. 
 33,000,000 years 1 , the result becomes surprisingly small in- 
 deed. For then 2ke would be about 149 feet. 
 
 In this case 2a would be about 100 miles. 
 
 It is however important to remark that as far as our determi- 
 nation of the average height of the inequalities is concerned the 
 conductivity of the rock is not required to be known, nor yet 
 the time since solidification took place, but only the value of 
 the constant a, which is known at once from the rate of increase 
 of temperature near the surface and the temperature of solidi- 
 fication. Because (see Sir William Thomson's paper) 
 
 dv V _* 2F Jt 
 
 -j- = . - _ 4" t - 7= a* , 
 
 fc Jirict ajir 
 
 hence near the surface, putting a = 0, 
 
 1 _ 2V 
 
 51 ajir ' 
 and therefore, when F= 7000, 
 
 a = 102J= 402832. 
 
 VTT 
 
 But although the actual value of the conductivity is not 
 involved, nevertheless the equations assume that its average 
 value continues constant, as indeed it is found to do by obser- 
 vation near the surface 2 . 
 
 1 To find the time since the earth was all melted, on the supposition that it 
 has cooled as a solid, and that the temperature was then 4000 F. as deter- 
 mined for slag in Mr Mallet's experiments. 
 
 v i . 
 
 Taking -^ of 1 as the rate of increase of temperature at the surface where 
 oi 
 
 # = 0, we get from the above 
 
 = 33 millions of years. 
 
 2 Principal Forbes found that the conductivity of iron diminishes as the 
 temperature increases. Tait's "Becent Advances in Ph. Science," 2ud ed., 
 
7 2 ELEVATIONS ON THE HYPOTHESIS OF SOLIDITY. 
 
 It is desirable to know what the radial contraction of the 
 globe would have been, that is, how much nearer to the centre 
 any point on the surface would be at present, than it was when 
 solidification took place. In this case we must find the con- 
 traction along a radius. But we must also remember that any 
 point on the surface must be considered raised by the average 
 height due to the compression which results from the sphericity 
 of the surface, i. e. by 2ke. 
 
 Now the contraction along any radius will evidently be 
 
 E r 2 " 
 
 if as before we take 2a as the depth to which the cooling, and 
 therefore the contraction, is sensible. Hence the actual con- 
 traction will be 
 
 f l**Pndx -2ke = f (VZa-ab x 1-273320) - 2ke. 
 o Jo & 
 
 p 
 If we give to F the value 7000 F., and ^ = '000007, with the 
 
 value just found for a this gives 
 
 radial contraction =11112-866 feet, 
 = 10246 feet, 
 = 1*9 miles. 
 
 If however we assume 4000 for the temperature of solidifi- 
 cation, since the result is proportional to Va, and therefore to 
 F s , we get in this case, in which 2ke = 149 feet, 
 
 radial contraction = 3479 feet, 
 
 = 0'65 of a mile. 
 
 p. 264. If such be the case with the earth's crust, then the temperature would 
 increase more rapidly, and the depth at which we might suppose the tempera- 
 ture of solidification to be "reached would be nearer the surface. This would 
 make the average height of the elevations less. 
 
CHAPTER VII. 
 
 HYPOTHESIS OF SOLIDITY FAILS. 
 
 Summary of results of Chap. VI. ^ Grounds on which Physicists have restricted 
 geological time within certain limits-^-Discrepancy between height of the 
 actual average elevations and of those which would be produced upon a cooling 
 solid globe Necessary alternative suppositions Captain Dutton's argument 
 Ocean basins Opinions about them of Pratt, Mallet, Hopkins, LeConte 
 Eadial contraction cannot explain them Still less oscillations of surface 
 Examples of oscillation N. Wales, Appalachians, New Zealand, India, 
 Colorado Plateau 'Givyn Jeffreys on changes of level -Babbage The dis- 
 tribution of elevations in ranges requires a fluid substratum This suppo- 
 sition explains other surface movements The pressures under which any 
 part of the crust is in equilibrium The so-called " contractional hypothesis " 
 not to be abandoned Captain Dutton's objections to it considered. 
 
 THE results at which we have arrived in the preceding 
 chapter are that, if the elevations on the earth's surface are due 
 to the contraction of a hot solid globe, cooling by conduction to 
 and radiation from its outer surface, then the average height of 
 the elevations above the datum level can be expressed within 
 the limits of error of a few feet, by a formula which we have 
 there obtained. And if into this formula we introduce the 
 following suppositions 
 
 (1) That the average rate of increase of temperature near 
 the surface is 1 F. for 51 feet of descent ; 
 
 (2) That the temperature at which the rocks solidified was 
 7,000 F. ; 
 
 we then arrive at the result, that the average height of the 
 elevations produced from the era of solidification to the present 
 time would be between 800 and 900 feet. But if, instead of 
 
74 HYPOTHESIS OF SOLIDITY FAILS. [OH. vn. 
 
 7,000 F., we suppose that the rocks solidified at 4,000 F., which 
 is about the temperature of melting slag, then the average 
 height of the elevations would be less than 200 feet. 
 
 These results do not require a knowledge of the conductivity. 
 But if the conductivity be known, then the time elapsed since 
 solidification took place is also known, and if we accept the 
 value for this constant found for certain rocks in situ at Edin- 
 burgh by Sir Wm. Thomson, viz. 400 *, it appears that it would 
 have been about 98,000,000 years ago, if the temperature of 
 solidification was 7,000 F. ; and about 33,000,000 years if 
 it was 4,000 F. 2 These are the grounds, and these are the 
 data, upon the strength of which physicists have restricted 
 geologists to a term of years for the evolution of the present 
 state of the earth 3 . If the earth be not solid their argument 
 fails. We have also found that with the temperature 7,000 F. 
 the cooling would have sensibly penetrated to a depth of about 
 160 miles, and with a temperature of 4,000 to about 100 miles. 
 This is irrespective of the conductivity 4 . The condition of the 
 sphere below the depth to which cooling has extended, that is 
 whether it be liquid or solid, would not influence the conclusions 
 regarding the amount of the elevations arrived at in the last 
 chapter. Its temperature there, however, must be supposed 
 that of solidification of the surface. 
 
 1 " Trans. Koyal Soc. Edin.," Vol. XXIL, 1861; 400 is nearly the mean of the 
 2nd column in the table at p. 426. See also "Nat. Phil.," p. 718. 
 
 2 See p. 71, note. 
 
 8 "If we suppose the temperature of melting rock to be about 10,000 F. 
 (an extremely high estimate) the consolidation may have taken place 200,000,000 
 years ago." Sir Wm. Thomson, "Trans. Eoyal Soc. Edin.," Vol. xxm. p. 157, 
 1862, and Thomson and Tait, "Nat. Phil.," p. 716, ed. 1867. "Geology, in 
 framing its conclusions, is compelled to take into account the teachings of other 
 sciences. If we felt disposed to give an indefinite amount of time to the evolution 
 of cosmos out of chaos, as has sometimes been thought possible, the student of 
 heat, and mechanics comes in, and asserts upon the authority of his branch of 
 science, that a limit must be put to the time available for bringing about the 
 present condition of things': he will grant 100,000,000 to 300,000,000 of years 
 as the extreme allowance of time ; if geologists cannot be content with this allow- 
 ance, a distinguished professor has said, ' so much the worse for the geologists, 
 for more they cannot have' (Prof. Tait on 'Some recent advances in Physical 
 Science')." Bp. of Carlisle on "Origin of the World, &c.," S. P. C. K. 1880. 
 
 4 p. 71. 
 
en. vii.] HYPOTHESIS OF SOLIDITY FAILS. 75 
 
 We have previously, in the fifth chapter, estimated the 
 average height of the elevations which actually exist upon the 
 earth's surface above the datum level, which we have assumed 
 to coincide approximately with the profound depths of the 
 ocean, and we have found it to be at the lowest estimate about 
 9,500 feet. This is more than ten times as great as the theo- 
 retical estimate belonging to the temperature 7,000 F., and 
 about fifty times as great as the estimate corresponding to the 
 temperature 4,000 F., upon the hypothesis of a cooling solid 
 globe. It does not seem probable that an error in the assumed 
 values of the temperature of solidification on the one hand, nor 
 in estimating the average height of the actually existing in- 
 equalities on the other, can explain the discrepancy. We 
 appear then to be compelled to accept one of the two alterna- 
 tives. (1) Either the inequalities of the earth's surface are not 
 altogether, or even chiefly, due to lateral compression, or (2) 
 there has been some other cause involved in producing the 
 needful amount of compression of the crust, besides the contrac- 
 tion of a solid interior through mere cooling. 
 
 Captain C. E. Dutton, of the United States army, has like- 
 wise noticed this inability of the contraction of a solid globe 
 through cooling to account for the geological facts 1 . His argu- 
 ment is of a similar character to that of the author here re- 
 published. 
 
 The question now for consideration is whether we are right 
 in attributing the inequalities to lateral compression, or whether 
 there may not be some other hypothesis which better explains 
 the phenomena. 
 
 The principal difficulties appear to be with regard to the 
 basins of the great oceans. Were the earth a perfectly smooth 
 spheroid, without any inequalities on its surface, even in that 
 case an excess of density in particular regions would determine 
 a flow of water towards them, and it is conceivable that dry 
 
 1 " American Journal of Science and Art," Jan. 1874, Vol. vm., 3rd series, 
 p. 113. This article was posterior to the author's first publication on the subject, 
 but entirely independent of it. A subsequent brochure by Capt. Dutton upon the 
 same topic appeared in the " Penn Monthly," Philadelphia, May, 1876, which 
 was reviewed in the " Geol. Mag." Decade n. Vol. iv. p. 322. 
 
76 HYPOTHESIS OF SOLIDITY FAILS. [CH. vn. 
 
 land and oceans might exist, even although the radial distances 
 of the land-surfaces and of the sea-bottoms from the centre of 
 figure might be perfectly equal. That the distribution of the 
 oceans is to some extent actually due to such a cause appears 
 certain ; for otherwise a whole hemisphere could not be almost 
 entirely covered with water. On this point Archdeacon Pratt 
 remarked, " There is no doubt that the solid parts of the earth's 
 crust beneath the Pacific Ocean, must be denser than in the 
 corresponding parts on the opposite side, otherwise the ocean 
 would flow away to the other parts of the earth." And after 
 explaining the reason for this statement he adds, " There must 
 therefore be some excess of matter in the solid parts of the earth 
 between the Pacific Ocean and the earth's centre, which retains 
 the water in its place. This effect may be produced in an 
 infinite variety of ways ; and therefore, without data, it is use- 
 less to speculate regarding the arrangement of matter which 
 actually exists in the solid parts below 1 ." And Herschel con- 
 sidered that the prevalence of land and water in two opposite 
 hemispheres "proves the force by which the continents are 
 sustained to be one of tumefaction, inasmuch as it indicates 
 a situation of the centre of gravity of the total mass of 
 the earth somewhat eccentric relatively to that of the general 
 figure of the external surface the eccentricity lying in the 
 direction of our antipodes: and is therefore a proof of the 
 comparative lightness of the materials of the terrestrial hemis- 
 phere 2 ." 
 
 A like conclusion as to the greater comparative density of 
 the bed of the ocean, was arrived at by Archdeacon Pratt from 
 the fact that at seven Coast Stations out of thirteen, six being 
 in the Anglo-gallic, and one in the Russian arc, it has been 
 found that a deflection of the plumb-line exists towards the sea 8 . 
 "In fact," he remarks, "the density of the crust beneath the 
 mountains must be less than that below the plains, and still less 
 than that below the ocean-bed. If solidification from a fluid 
 
 1 "Figure of the Earth," 4th ed., p. 236, 1871. A great ice-cap would also 
 have its effect. See Croll's " Climate and Time," Chaps, xxm. xxiv. 
 
 2 " Physical Geography," 13, 1862. 
 
 3 Figure of the Earth," pp. 200 and 206. 4th ed. 1871. 
 
CH. vii.] HYPOTHESIS OF SOLIDITY FAILS. 77 
 
 state commenced at the surface, the amount of radial contrac- 
 tion in the solid parts beneath the surface of the mountain- 
 region has been less than in the parts beneath the sea-bed. In 
 fact it is this unequal contraction which appears to have caused 
 the hollows in the external surface, which have become the 
 basins into which the waters have flowed to form the ocean." 
 Latterly, however, he attributed the formation of mountainous 
 regions to horizontal compression 1 . 
 
 Mr Mallet, in his paper on Volcanic Energy, takes a similar 
 view. He thinks that the land- and sea-boundaries were shaped 
 out by radial contraction during the first great stage of the 
 operation of refrigeration, while the crust was thin and flexible, 
 owing to the rapid contraction of its viscous portion, which 
 must then have been much thicker than the solid sheet above 
 it 2 . 
 
 Mr Hopkins appears to have been opposed to these views 
 which suppose a difference of radial contraction ; and to have 
 held that lateral compression was the cause of the formation of 
 the greater inequalities as well as of the lesser ones, for we find 
 him in discussing M. Elie de Beaumont's theories to have 
 used these words: "The physical cause to which our author 
 refers the phenomena of elevation the shrinking of the earth's 
 crust is that which appears to me most unlikely to produce 
 that paroxysmal action which his theory so essentially requires ; 
 and most likely to produce those slow and gradual movements 
 which it scarcely recognizes. The actual depressions of the 
 great oceanic basins, and generally the more widely extended 
 geological depressions of the present or former periods, may, I 
 think, be referred with great probability to this cause 3 ." 
 
 The theories respecting the formation of the larger features 
 of the earth's surface have been discussed by Professor LeConte 
 
 1 In the third edition of the " Figure of the Earth " no mention was made 
 of horizontal compression, but mountains were attributed to vertical expansion. 
 In the fourth, p. 203, note, the author's estimate of the horizontal force of 
 compression is referred to. 
 
 2 " Trans. Koyal Soc." 1873, 52 and 60. 
 
 3 Presidential Address to the Geol. Soc. 1853, " Geol. Journ.," Vol. ix. 
 p. Ixxxix. 
 
78 HYPOTHESIS OF SOLIDITY FAILS. [CH. vn. 
 
 in so lucid and unprejudiced a style, that his papers are well 
 worthy of study. The following passage conveys his conclu- 
 sions. " Mountain chains and mountain ranges are therefore, I 
 think, beyond question produced by horizontal thrust crushing 
 together the whole rock mass, and swelling it up vertically; 
 the horizontal thrust being the necessary result of secular con- 
 traction of the interior of the earth. The smaller inequalities, 
 such as ridges, peaks, gorges, and, in fact, nearly all that con- 
 stitutes scenery, .are produced by subsequent erosion. I feel 
 considerable confidence in the substantial truth of the foregoing 
 statement of the formation of mountain-chains. As to the mode 
 of formation of continents and sea-bottoms, I feel less confidence. 
 It is possible that even these may be formed by a similar un- 
 equal yielding to horizontal thrust, and a similar crushing 
 together and up-swelling. If so, it would be necessary to suppose 
 the amount of horizontal yielding in this case much less, but 
 the depth effected much greater than in the case of mountain- 
 chains. But, as we find no unmistakable structural evidence of 
 such crushing, except in the case of mountain-chains, I have 
 preferred to attribute the formation of continents and sea- 
 bottoms to unequal radial contraction 1 ." 
 
 The last sentence of this passage appears to invite the 
 remark that we cannot expect in general to have evidence of 
 crushing except in those areas which are open to investigation, 
 viz. on dry land. But there it is not confined to mountain- 
 chains. Contorted strata are to be also found in what would be 
 termed level countries, often covered with horizontal deposits of 
 later date 8 : and this fact in itself proves that these contorted 
 strata have been once covered by an ocean, offering a strong 
 presumption that there are contorted strata now at the bottoms 
 of the oceans. 
 
 In fact it is clear that, on account of the sedimentary 
 character of the rocks that compose continents proving that 
 they cannot be prinrseval protuberances, the only hypothesis 
 which can compete with that of lateral compression is that of 
 
 * "American Journal of Science," 3rd series, Vol. iv. p. 462, 1872. 
 
 3 For example the highly contorted carboniferous strata of parts of Belgium. 
 
CH. vii.] HYPOTHESIS OF SOLIDITY FAILS. 79 
 
 unequal radial contraction. But we have shown in the pre- 
 ceding chapter that 10,246 feet, or about 1/9 miles, would be the 
 radial contraction of the whole thickness of the cooled crust on 
 the supposition of the higher, and 3,479 feet, or about O65 
 of a mile, upon the supposition of the lower temperature that 
 we have assumed. 
 
 Now we must remember that, if the oceans be due to radial 
 contraction, it is only the difference of radial contraction beneath 
 them and the land that can be appealed to, to account for their 
 relative depression. But we see by the above that the entire 
 radial contraction is not sufficient for the purpose. This seems 
 conclusive against this cause being capable of explaining the 
 existing difference of level between the land-surface and the 
 ocean-bottom. 
 
 Of course it will be seen that the reasoning of the above 
 paragraph applies only upon the hypothesis of the inequalities 
 of the earth's surface being due to the cooling of a solid globe, 
 or at least of one solid to the depth to which cooling has ex- 
 tended. There may be other causes producing radial contraction, 
 .and perhaps also expansion, of which no account has been taken. 
 
 After what has been said, it seems hardly necessary to 
 adduce any further arguments against the production of ocean 
 basins by radial contraction from cooling. Yet it will be well 
 to observe that there are additional difficulties in explaining by 
 this means the oscillations of the surface up and down, which 
 are known to have occurred in the same areas again and again. 
 For that land and sea might interchange places by radial con- 
 traction, the land must sink far below the bottom of the sea, so 
 that the sea should flow into the depression thus caused, leaving 
 its former bed forsaken and dry. This is an event which, 
 according to our numerical results, would be quite impossible. 
 
 The more one considers the instability of the earth's crust 
 and the magnitude according to our standards of the move- 
 ments, the more one is lost in amazement : and it is im- 
 possible to avoid using the kind of exaggerated language which 
 is the opprobrium of popular geology. Bocks of a single 
 geological period, thicker than the heights of the highest moun- 
 tains, have been deposited over certain areas, sunk, been re- 
 
8o HYPOTHESIS OF SOLIDITY FAILS. (CH. vn. 
 
 elevated, crumpled, and denuded, and still stand as lofty moun- 
 tains. In North Wales, Cambrian rocks were measured by 
 Mr Aveline of the thickness of 23,000 feet 1 . The deposits of 
 the Appalachian chain, we are told, attain a thickness of 
 eight miles 2 . In such cases as these, not only must the rocks 
 now exposed at the localities, where the lower beds of the 
 series are at the surface, have been at one time as far below 
 the sea ; but the areas now occupied by sea must have presented 
 land surfaces, in the latter instance believed to have been to 
 the north-east, in order to furnish the detritus out of which 
 these great piles of strata were formed. Again the islands of 
 New Zealand occupy a central position in the aqueous hemi- 
 sphere ; and yet they contain a series of deposits chronologically 
 analogous to those of the northern hemisphere 3 ; whence it 
 follows that they must have been often submerged during 
 periods, when there existed, in what is now an extended ocean, 
 land surfaces, from which the materials of their rocks must have 
 been derived. 
 
 The Himalayan area presents some peculiarly interesting 
 features in this connection. The sub-Himalayan range consists 
 of tertiary strata which are now highly disturbed. All, with the 
 exception of the lower portion, which is nummulitic and conse- 
 quently marine, are composed of sub-aerial deposits, formed by 
 detritus brought down by torrents from the Himalayas. These 
 deposits are together between 12,000 and 15,000 feet thick. 
 The sandstones, which form the chief portion of these beds, and 
 the red clays which are intercalated with them, are exactly like 
 the alluvial deposits of the plains. " Thus it was suggestive, and 
 not altogether misleading, to say that the Siwaliks were formed 
 of an upraised portion of the plains of India 4 ." The surface 
 movements indicated by this history suggest a level area at the 
 foot of the Himalayan range, sinking continuously during the 
 former part of the tertiary period. Then a great movement of 
 
 1 Jukes' " Student's Manual of Geology," 3rd ed., p. 526, 1872. 
 
 2 Hall's "Natural History of New York," Part vi. Palaeontology, Vol. in. p. 67. 
 
 3 Capt. F. W. Button, " Geol. Mag.," Decade n. Vol. i. p. 27, note. See 
 also Hochstetter's " Geology of New Zealand," Auckland, 1864. 
 
 4 " Manual of the Geology of India," Medlicott and Blandford, p. 525. 
 
CH. vii.] HYPOTHESIS OF SOLIDITY FAILS. 8 1 
 
 lateral compression and elevation took place. Again it sunk, 
 and unconformable beds were deposited. These were again 
 elevated and compressed. Such at least appears to be the 
 interpretation of the description given by the surveyors 1 . But 
 the point which is material to our present subject is the sinking 
 of the land surface to the depth of nearly three miles, while 
 river deposits to that thickness were being laid down ; the whole 
 being denuded off mountains whose spoils have in more recent 
 times provided materials for the great plains of India ; and still 
 those mountains stand the highest in the world. That a sink- 
 ing of the area of the plains of a similar character is yet in pro- 
 gress, is shown by the boring at Fort William, near Calcutta, 
 in which to the depth of 400 feet fresh-water deposits occurred. 
 The conclusion seems irresistible that corresponding to the long, 
 though occasionally interrupted, depression of these plains, a 
 correlative elevation of the great range which has supplied 
 the deposits has been going on. 
 
 This sinking of river plains and estuaries is an apparently 
 universal occurrence : the great thickness of fluviatile deposits 
 in them cannot otherwise be accounted for. Thus the fluviatile 
 accumulations have been proved in the case of the Po to the 
 depth of 400 feet, of the Ganges to 481, and of the Mississippi to 
 630 feet 2 . 
 
 The recent explorations of the region of the Rocky Mountains 
 by the Government Survey of the United States, has greatly 
 added to our knowledge about the movements of the earth's 
 crust both in kind and in degree. The rocks affected are of 
 many periods, down to the newer tertiary, and even the quater- 
 nary 3 . They are cut up by enormous faults into blocks, the 
 throw of the faults being sometimes as much as 40,000 feet. 
 Yet the movements have been so gradual that the rivers have 
 had time to deepen their channels as the plateaux rose, so that 
 they now flow in the profound " Canons of the Colorado" some- 
 times more than a mile deep. 
 
 1 See Diagram, p. 44. 
 
 2 Dr Eicketts, " Valleys, Deltas, Bays, and Estuaries," p. 22. Liverpool, 1872. 
 
 3 "High Plateaus of Utah." Capt. Dutton, Prefatory note by Major Powell, 
 p. viii. See a review of this work by Prof. A. Geikie in " Nature," Vol. xxn. p. 324. 
 
 F. 6 
 
82 HYPOTHESIS OF SOLIDITY FAILS. [en. vn. 
 
 Reference has already been made to the opinion that the 
 continents have occupied nearly their present positions from the 
 earliest times. It is doubtful whether there are sufficient 
 grounds to render this doctrine quite certain. In spite of the 
 advance which has been made within the last few years in our 
 knowledge of the nature of the ocean floor by dredging and 
 sounding, we must probably always lack experimental know- 
 ledge as to whether it covers submerged land or not. Dr Gwyn 
 Jeffreys has described some facts regarding the occurrence of 
 marine shells of existing species at different heights above the 
 present level of the sea, showing how recently much of the 
 present land has been raised. And he has asked, " Can we 
 rightly assign to the present oceans that geologically remote 
 antiquity which is claimed for them 1 ?" 
 
 Enough 'has been said to show that difference of radial con- 
 traction from mere cooling is utterly inadequate to account for 
 the existing inequalities of the surface, and still more so for the 
 oscillations which have affected those surfaces during all geo- 
 logical periods. The theory of Babbage 2 that the heat, con- 
 ducted upwards into the thick deposits laid down at the bottom 
 of the ocean, expands and elevates their surface, is possibly a vera 
 causa, but quite incapable by itself of explaining great changes 
 of level. Moreover the heat conducted into the new deposits 
 must be abstracted from the couches beneath, so that there can 
 be no absolute increase in the amount of heat beneath the area 
 in question except such as is supplied to it laterally, so that the 
 process must be excessively slow. 
 
 We have previously been reasoning upon the hypothesis that 
 a solid globe, in the process of cooling, might, owing to the 
 compression of the crust, protrude a certain quantity of the 
 matter of the crust above what would have been its surface had 
 the crust been perfectly compressible i e. above our " datum 
 level." But are we justified in supposing that that matter 
 
 1 " Quart. Journ. Geol. Soc." Vol. xxxvi. p. 351. See also a paper by 
 Mr T. Mellard Eeade, " Geol. Mag." Decade n. Vol. vn. p. 385. 
 
 2 On the Temple of Serapis, " Geol. Journal," Vol. in. p. 186 ; a paper 
 containing the germ of much true reasoning about the physics of the earth's 
 crust. 
 
CH. VIL] HYPOTHESIS OF SOLIDITY FAILS. 83 
 
 would have been so distributed as to have formed continents 
 and their back -bone mountain ranges ? Unless the material of 
 which the crust was composed was extremely unhomogeneous, 
 and unhomogeneous in strips corresponding to the axes of 
 elevation, and unless these strips changed their positions and 
 directions at different periods, it is impossible that such com- 
 pression can have produced the present distribution of the 
 elevated ranges; much less different distributions at different 
 epochs. What is required to explain the phenomena is a liquid, 
 or at least a plastic substratum for the crust to rest on, which will 
 allow it to undergo a certain amount of lateral shift towards the 
 ranges. 
 
 Neither is it easy to explain the sinking of areas in pro- 
 portion to their becoming overloaded with sediment, whether 
 beneath the ocean or sub-aerially, upon any other supposition. 
 But if such a liquid substratum be granted, many of the facts 
 are more easily explained. In that case the semi-rigid crust 
 would assume a position of rest upon this substratum, which, 
 within certain limits depending upon its rigidity, would be one 
 of hydrostatic equilibrium. That is to say, the distribution of 
 load might be made somewhat different from what it is without 
 disturbing the equilibrium, but it could not be made very 
 different. For instance, if the present configuration of the 
 Himalayan region be one of approximate equilibrium, which it 
 clearly is, if much sediment is brought off the mountains and 
 spread over the plains, the mountains become after a while 
 too light and the plains too heavy, and accordingly the moun- 
 tains rise and the plains sink to restore the contour. This 
 appears to be what has happened. 
 
 The pressures under which any portion of the crust would 
 be in equilibrium will be (1) the tangential stress, (2) its 
 own weight, and (3) the upward pressure of the substratum. If 
 any one of these is changed beyond a certain amount the equi- 
 librium will be destroyed and a movement of the crust will 
 ensue. 
 
 Here are three forces involved, each of which is due to a 
 different proximate cause : the tangential pressure producing 
 compression of the crust (from whatever arising); the distribution 
 
 62 
 
84 HYPOTHESIS OF SOLIDITY FAILS. [CH. VH. 
 
 of the weight of the crust, which will depend upon the transfer 
 of sediment, and is therefore caused partly by solar energy ; aod 
 pressure from beneath, which may be attributed to elastic 
 matter confined by the superincumbent crust. 
 
 No true theory of crust movements can be propounded, 
 which does not involve all these simultaneously. But it is 
 hardly unfair to say that in general this consideration has been 
 overlooked, and one or other, or perhaps two together of these 
 causes, have been invoked, and the theory has been incomplete 
 accordingly. 
 
 We henceforward assume the existence of a substratum 
 which is either continuously and continually fluid, or at least 
 plastic. It might be supposed that a stratum whose solidity is 
 due to pressure, and which becomes plastic when the pressure is 
 lessened, would satisfy the requirements of the problem. But 
 if it be true that the overloading of an area with sediment 
 causes it to sink, this cannot be the case ; because by that 
 means the pressure, and therefore the solidity, ought to be in- 
 creased instead of diminished ; and the crust would not yield to 
 the pressure. 
 
 The possibility of the existence of such a liquid substratum 
 as is postulated, has been explained in the second chapter. We 
 now perceive that its existence is necessary for the explanation 
 of the phenomena of geology. We no longer regard the globe 
 as solid from surface to centre. But we do not on that account 
 give up what has been called the contractional hypothesis, but 
 rather seek other causes adequate to produce the compressing 
 stress, which we believe has been one of the forces to which the 
 production of the inequalities of the surface is due. 
 
 It will be as well at this point to refer to some ob- 
 jections raised by Captain Button against this hypothesis, and 
 if possible to reply to them. "The displacements which the 
 strata have suffered are frequently extreme. Not only are they 
 buckled up into great wave-like ridges ; but are frequently 
 inclined past the vertical, and are sometimes turned almost 
 completely upside down. In New England and the Middle 
 States the palaeozoic strata are so extremely flexed and the 
 folds so closely pressed together that they present in many 
 
CH. vii.] HYPOTHESIS OF SOLIDITY FAILS. 85 
 
 localities nothing but a series of beds all dipping to the south- 
 east at a high angle. Yet in spite of the extreme displacement 
 there is no chaos. The different beds are not crushed into 
 fragments nor disorganised, but preserve their relative positions 
 as perfectly as when they were deposited. However vast the 
 disturbing force must have been, we may well wonder at the 
 gentleness and ease with which they have been lifted up or let 
 down. As if to remind us how destructive the force might have 
 been, we find here and there a few acres which have unmis- 
 takably been subject to lateral thrusts in consequence of the 
 sliding of a large mass down a steep incline, or some other local 
 cause, and the strata have 'gone into pi.' This preservation 
 of continuity would suggest to the investigator who might 
 endeavor to apply mechanical principles to the problem, 
 that the force which produced the movements was a minimum 
 force that is, a force having the smallest intensity which is 
 capable of producing the movement. But this is demonstrably 
 a system of forces acting upwards at the anticlinals and 
 downwards at the synclinals. It is equally capable of de- 
 monstration that of all possible modes in which a force could 
 be applied to produce a fold, the horizontal or tangential ap- 
 plication would require the greatest intensity. It is the latter 
 force which the contractional hypothesis supplies. It is diffi- 
 cult to admit that it could produce plications at all : the most 
 probable result of it would be the annihilation of all traces of 
 structure and stratification. This inference will be strengthened 
 by recalling a well-known law of mechanics that tendencies to 
 rupture (' moments of rupture') increase with the cubes of 
 dimensions, while resistances to rupture ('moments of resist- 
 ance ') increase only with the squares. The masses under con- 
 sideration are, collectively, of the extent of states and empires ; 
 the individuals are mountain ranges and valley bottoms, and 
 their coherence in the presence of the forces which are adequate 
 to move them becomes by virtue of the foregoing law a vanish- 
 ing quantity. Such masses, under the action of the supposed 
 force, would be the merest rubble, and quite incapable of pre- 
 serving their integrity. The action has been frequently illus- 
 trated by subjecting a pile of paper to compression edgewise. 
 
86 HYPOTHESIS OF SOLIDITY FAILS. [CH. vn. 
 
 A closer analogy would be presented if the paper were reduced 
 to ashes or charcoal before applying the pressure. A better, 
 though far from an adequate one, may be found in the chaos 
 produced in the Arctic regions when a great ice-floe is driven 
 upon a rocky coast 1 ." 
 
 The former part of this quotation gives a very graphic 
 description of the phenomena which we have to explain. But 
 the objection is not perhaps of great force. In the first place, it 
 is difficult to understand how the extreme flexure, with folds 
 so closely pressed together as to present a mere series of beds 
 dipping all in one direction, can be produced by any conceivable 
 " system of forces acting upwards at the anticlinals and down- 
 wards at the synclinals." Nor yet does it seem necessary that a 
 horizontal compressing force should reduce the strata to the 
 "merest rubble." Such a force would accumulate until the 
 beds yielded along some line. But when that had happened the 
 movement would not become any the more rapid. The com- 
 pression would be capable of attaining great intensity, but need 
 not be impulsive, and would quickly cease when satisfied. 
 
 Some very interesting experiments upon the effect of com- 
 pression upon layers of clay have been made by Professor A. 
 Favre, of Geneva, the results of which closely imitate the con- 
 tortions seen in real mountains. Some of them are figured in 
 " Nature 2 ." The original quasi stratification of the clay experi- 
 mented on is nowhere obliterated. It has not "gone into 'pi.'" 
 
 1 Theories of the Earth's Physical Evolution, " Penn Monthly," 1876, p. 376. 
 See also " Geol. Mag." Dec. n. Vol. in. p. 327. 
 3 " Nature," Vol. xix. p. 105. See also chap. x. 
 
CHAPTER VIII. 
 
 FLUID SUBSTRATUM. 
 
 The extravasation of water substance from beneath the crust suggested as a 
 cause of contraction -of volume Igneo-aqueous fusion Dissolving power of 
 water when above the critical temperature Scrope LeConte Escape of 
 steam from volcanic vents Opinion that sea water gains access to volcanic 
 foci Objections to this hypothesis Experiment of Daubree not in point 
 Views on cosmogony Dr Sterry Hunt's theory Objections to it Fails to 
 account for the facts A suggestion to explain the presence of water substance 
 below the cooled crust. 
 
 WE have now to seek for causes of compression by con- 
 traction of the volume of the globe beneath the cooled crust, or 
 otherwise ; and we have arrived at the conclusion that we are 
 at liberty, or rather are obliged, to seek them compatibly with 
 the existence of a liquid or plastic substratum. Accordingly, 
 when the Author's paper on " the Inequalities of the Earth's 
 Surface viewed in connection with the secular Cooling" was 
 read, it contained the following suggestion: 
 
 "There may have been a considerably larger nucleus in- 
 closed within the crust in early times than we have at present, 
 and a great portion of such nucleus may have consisted in 
 superheated water, the rocks being in a state of igneo-aqueous 
 solution: and much of this water may have been blown off in 
 steam during volcanic eruptions, by that means materially con- 
 tributing to the diminution of the volume. I have suggested 
 in my former paper read before this Society, that Mr Sorby's 
 observations on the water enclosed in granitic crystals, along 
 
88 FLUID SUBSTRATUM. [CH. vm. 
 
 with crystals of chlorides, renders it probable that the steam 
 emitted in eruptions may be a constituent part of the deep- 
 seated rocks, for it is probable that but a small part of the 
 water contained in any magma would become confined in the 
 interior of the crystals 1 . 
 
 "Here, however, the question arises whether it would be 
 possible for a crust to form over a layer of molten rock in a 
 condition of igneo-aqueous fusion. Would not the escape of 
 the water cause a state of constant ebullition which would pre- 
 vent the formation of any crust until it had ceased through the 
 escape of all the water ? 
 
 ********* 
 
 " We can conceive that at depths where the heat and pressure 
 were sufficient there might be no tendency to evaporation and 
 consequent ebullition, so that after the water had escaped to a 
 certain depth ebullition would cease, and a crust be formed; but 
 that more water would be ready to separate to a greater depth 
 when its affinity for the rock became lessened through the 
 abstraction of heat, or diminution of pressure owing to the 
 crust being partially supported by corrugation. 
 
 " If such was the condition of the interior in the early stages 
 of the cosmogony, a large portion of the oceans now above the 
 crust may once have been beneath it, and thus we gain a novel 
 conception of a sense in which the fountains of the abyss may 
 once have been broken up 2 ." 
 
 Upon this passage the Referee made the following anno- 
 tation. 
 
 " The Author suggests other causes of shrinking besides loss 
 of heat, namely the escape of water. 
 
 " It is probable, or rather certain, that water substance, if 
 it exists at great depths under great pressure and at high 
 temperature, is neither a gas nor a liquid, being above its 
 critical point. 
 
 "In this state substances are easily dissolved in it, not how- 
 ever so much on account of a greater tendency to combine with 
 water, as on account of a greater tendency of their own to 
 
 1 "Trans. Camb. Phil. Soc." Vol. xn. Pt. 1, p. 505. 
 
 2 Trans. Camb. Phil. Soc." Vol. xn. Pt. 2, p. 431. 
 
CH. VIIL] FLUID SUBSTRATUM. 89 
 
 dissipation. At still higher temperature the water substance 
 becomes itself dissociated into oxygen and hydrogen. But it 
 does not follow that the dissolved substances will be precipi- 
 tated. The magma may be all the more complete the higher 
 the temperature, because, though the bonds of affinity have 
 fallen away, the prison-walls prevent the elements from escap- 
 ing. But of all the known regions of the Universe the most 
 unsafe to reason about is that which is under our feet." 
 ********* 
 
 "There is a suggestion as to shrinkage by escape of water, 
 the objections to which so far as they are stated in the paper" 
 viz. those in the second paragraph on the last page " I do not 
 think of great moment, considering the slowness of diffusion 
 through a thickness equal to that of the earth's crust 1 ." 
 
 This suggestion of the escape of water was subsequently 
 repeated in a paper upon " Mr Mallet's Theory of volcanic 
 energy," in the Phil. Mag. for October, 1875: and upon receiving 
 a copy of it, Mr Scrope wrote : " There is one of the points 
 you put forward which never struck me before, but which now 
 appears to me most valuable; namely, that the enormous 
 amount of steam that has escaped from the interior in early 
 times, as well as down to the present, has been, and is, the 
 cause of those subsidences of the crust, to which the basins of 
 seas and oceans, and the crumplings of the terrestrial rocks are 
 owing, far more than to any general contraction of the nucleus 
 
 1 " The general result obtained from these experiments was, that the solvent 
 power of water was found to be determined by two conditions : 1. Temperature, or 
 molecular vis viva ; and 2. Closeness of the molecules on pressure, which seems to 
 give penetrative power. From these observations it will be seen that, if a body has 
 any solvent action on another and does not act upon it chemically, such solvent 
 action may be indefinitely increased by indefinitely increasing the temperature 
 and pressure of the solvent. In nature the temperature has been at one time 
 higher than we can obtain artificially, and the pressure obtained by a depth of 
 200 miles from the surface is greater than can be supported by any of the mate- 
 rials from which we can form vessels. It will thus be seen that, whereas in 
 nature almost unlimited solvent power could be obtained, we are not as yet able 
 to reproduce these conditions artificially. Could pressure alone increase solvent 
 power, then much might be done, but pressure only acts by keeping the molecules 
 close together when they have great vis viva ; and this latter is only obtained 
 by high temperature." Hannay on the Artificial Formation of the Diamond. 
 Paper read at the Koyal Society. See " Nature," July 15, 1880. 
 
90 FLUID SUBSTRATUM. [CH. vm. 
 
 by cooling." The hypothesis has also been favourably men- 
 tioned by Prof. Joseph LeConte 1 . Under these circumstances 
 it appears worth while to follow it out somewhat further, and 
 to examine its validity. 
 
 There can be no question regarding the fact, that enormous 
 quantities of steam are emitted from volcanos when in erup- 
 tion ; and some amount almost continually from many. To be 
 assured of this, it is sufficient to look at the frontispiece of 
 Scrope's " Volcanos/' or at the view, copied from a photograph, 
 of Vesuvius on the 26th April, 1872, in Palmieri's " Vesuvius," 
 translated by Mr Mallet 2 . That intrepid observer relates, on 
 that day " two large craters opened at the summit, discharging 
 with a dreadful noise, audible at a great distance, an immense 
 cloud of smoke and ashes, with bombs and flakes, rising to the 
 height of 1300 metres above the brim of lava." The Author 
 remembers that in the narrative of a correspondent of a news- 
 paper at the time, the sound, as heard at Naples, was compared 
 to four lions roaring in the four corners of the room in which 
 he sat. These and similar descriptions give a notion of the 
 enormous quantities of steam, and of the force with which it is 
 emitted on these occasions. The question is ; not regarding the 
 fact that water is present in the volcanic emanations, but how 
 it comes to be there. 
 
 This of course opens up the whole subject. The circum- 
 stance that many of the best-known volcanos are near the sea, 
 that many actually form islands in the wide ocean, and that 
 great trains of volcanos skirt the shores notably of the Pacific, 
 has led to the opinion that the waters of the sea by some 
 means find access to what have been called the volcanic foci, 
 and are there heated, and find exit through their vents. This 
 explanation has been thought to receive support from the " sea 
 salts," which are deposited by the emanations 3 . 
 
 There are but two ways in which the waters of the sea 
 
 1 American Journal of Science and Arts, Vol. xvi. p. 107, 3rd Ser. 1878. 
 
 2 Asher and Co., London, 1873. See Plate iv. A., and p. 91. 
 
 3 " Even chloride of iron, which was so abundant in the lavas, was scarcely 
 perceptible in the smoke, which almost exclusively deposited sea-salt on the 
 surrounding rocks; I say sea-salt advisedly, and not chloride of sodium, to 
 show that I include all that sea-salt contains." Palmieri, Op. cit. p. 121. 
 
CH. VIIL] FLUID SUBSTRATUM. 9 1 
 
 could possibly find access to the hot interior; and these are, by 
 open fissures, and by capillary absorption. If a fissure were to 
 open at the bottom of the sea, so that water were to gain access 
 to heated rocks, it seems incredible that the steam, if such were 
 formed, should not be formed at once, and the water be forced 
 back again through the same fissure by which it entered. Or if 
 we suppose, as is probable, that the pressure of the water would 
 prevent the formation of steam, still there would be a highly 
 expansive fluid, which would rush upwards at the same place, 
 rather than traverse a long underground journey to find exit 
 at a neighbouring volcanic vent. 
 
 The more plausible opinion is, that the water gains access 
 by capillary absorption, and slowly accumulates in the supposed 
 "volcanic foci," until at last it bursts forth in an eruption. 
 Capillary attraction can be made to do great things, as for 
 instance to split blocks of granite, by driving in dry plugs of 
 wood and wetting them. But it cannot cause a liquid to flow con- 
 tinuously through a tube, however short ; for, if it could, it would 
 give us perpetual motion. And after all it is a finite force and 
 requires special conditions for its development. The chief of 
 these is that surfaces of three media should meet two and two in 
 contact. Thus when water rises in a capillary tube of glass, we 
 have the three media of glass and water and air. The tension of 
 the surface separating water and air is greater than that of the 
 surface separating water and glass 1 . In the present case, there 
 is no third medium present, vapour of water, which might act as 
 such, being prevented from forming by the pressure, so that it 
 does not appear how the action can be set up. If there were a 
 cavity filled with vapour, it is possible that the density of that 
 vapour, and therefore its pressure, might be increased to a 
 certain extent, by the evaporation of the water from the ex- 
 tremity of the capillary tubes, and that was what occurred in 
 the experiment of M. DaubreV. But under the conditions 
 
 1 See Maxwell's " Heat," 2nd ed. p. 286. 
 
 2 M. Daubree (vide " Rapport sur les progres de la Geologie experimentale," 
 Paris, 1867) deduced a theory of volcanos from the following experiment. He 
 separated two chambers by a circular plate of rock two centimetres in thickness. 
 The upper chamber communicated freely with the atmosphere, the plate of rock 
 forming its lower face. The second chamber was empty, and communicated 
 
92 FLUID SUBSTRATUM. [CH. vm. 
 
 present the pressure is too great for the formation of vapour, 
 and the temperature too high for capillary attraction to be 
 developed 1 . 
 
 Still further the existence of capillary communication of 
 water from the surface may be doubted. For if there were sup- 
 posed a capillary tube extending from the bottom of the ocean, 
 the pressure at the lower end of this tube would be that of the 
 water contained in it plus that, if any, arising from capillarity, 
 while the pressure of the crust around its mouth would be that 
 due to the weight of the crust. This latter would be the 
 greater of the two, consequently the liquid upon which the 
 crust rested, having a tension equal to the weight of the crust, 
 would force back the water in the tube, and if it were not too 
 viscous would itself occupy the tube. Thus it appears that the 
 waters of the ocean cannot supply the steam emitted from 
 volcanic vents. The conclusion seems inevitable that water 
 substance holding sea salts in solution, is an original constituent 
 of the magma from which these vaporous emanations are de- 
 rived. What is this magma ? 
 
 with a manometer. The entire apparatus having been raised to 160, water was 
 poured into the upper chamber ; and soon afterwards the manometer was found 
 to indicate two atmospheres of pressure. When a portion of the vapour accu- 
 mulated in the lower chamber had been allowed to escape, the pressure soon 
 recovered its former value. There was then a true feeding across the partition 
 of rock, the cause of which was the desiccation of the lower face of the partition 
 by vaporization of the water in its interstices, and the subsequent replacement 
 of that water by capillary attraction. (Capillary attraction acted the part of the 
 force-pump which feeds a high-pressure boiler.) 
 
 M. Daubree conceives that if the layer of rock were of great thickness, and a 
 very high temperature maintained in the cavity, a correspondingly high steam- 
 pressure would result, which would be sufficient to raise lava in the vent of a 
 volcano, and to produce earthquakes; while the force so obtained might after 
 expenditure be again and again renewed. 
 
 This theory requires the occurrence of cavities at great depths (" supposons 
 une cavite separe'e des eaux de la surface") communicating with the volcanic 
 vents. But the only argument in favour of cavities existing seems to be that the 
 requisite mechanical force is supposed obtainable by means of them; but it 
 seems a priori impossible that there should be such cavities. 
 
 1 "In all liquids on which experiments have been made the superficial 
 tension diminishes as the temperature rises, being greatest at the freezing point 
 of the substance, and vanishing altogether at the critical point where the liquid 
 and gaseous states become continuous.". Maxwell's "Heat," 2nd ed., p. 290. 
 
CH. viii.] FLUID SUBSTRATUM. 93 
 
 There is a natural unwillingness among Geologists to involve 
 themselves in speculations concerning the cosmogony. This is 
 due partly to the inherent uncertainty of the subject, and partly 
 to the deeply implanted doctrines of the uniformitarian school, 
 which in effect teaches that there are no grounds for sound 
 reasoning upon any state of things different from what we now 
 see. However, we are obliged to form some theory on this 
 question if we would speculate on the constitution of the depths 
 beneath the cooled surface of the globe. 
 
 Among those who have written upon the question, Dr Sterry 
 Hunt, of Montreal, has perhaps offered the most plausible ex- 
 planation. Impressed with the necessity of accounting for the 
 presence of water in the volcanic laboratory, and assuming that 
 all the water belonging to this planet must have existed origi- 
 nally as a gaseous envelope surrounding a still incandescent 
 solid ball, he appears to have seen no means of accounting for 
 this subterraneous water, except by supposing it to have been 
 subsequently derived from the atmosphere by precipitation. 
 
 " While admitting with Hopkins and Scrope the existence of 
 a solid nucleus and a solid crust, with an interposed stratum of 
 semi-liquid matter, I consider this last to be, not a portion of 
 the yet unsolidified igneous matter, but a layer of material 
 which was once solid, but is now rendered liquid by the inter- 
 vention of water under the influence of heat and pressure. 
 When, in process of refrigeration the globe had reached the 
 point imagined by Hopkins, when a solid crust was formed over 
 the shallow molten layer which covered the solid nucleus, the 
 farther cooling and contraction of this crust would result in irre- 
 gular movements, breaking it up, and causing the extravasation 
 of the yet liquid portions confined beneath. When at length 
 the reduction of temperature permitted the precipitation of 
 water from the dense primaeval atmosphere, the whole cooling 
 and disintegrating mass of broken up crust and poured out 
 igneous rock would become exposed to the action of air and 
 water. In this way the solid nucleus of igneous rock became 
 surrounded with a deep layer of disintegrated and water- 
 impregnated material, the ruins of its former envelope, and 
 the chaotic mass from which, under the influence of heat from 
 
94 FLUID SUBSTRATUM. [CH. vm 
 
 below and air and water from above, the world of geologic 
 and of human history was to be evolved 1 ." 
 
 And further on he explains the relation, which this supposed 
 reconstituted outer layer holds to his volcanic theory. 
 
 "Considering the conditions of its formation, water would 
 seem to be necessarily absent from the originally fused globe, 
 in which the older school of Geologists conceive volcanic rocks 
 to have their source. Scheerer supplemented Scrope's view by 
 showing that the presence of a few hundredths of water, main- 
 tained under pressure at a temperature approaching ignition, 
 would probably suffice to produce a quasi-solution, or an igneo- 
 aqueous fusion of most crystalline rocks ; and subsequent obser- 
 vations of Sorby have demonstrated that the softening and 
 crystallization of many granites and trachytes must have taken 
 place in the presence of water, and at temperatures not above 
 a low red heat. Keeping in view these facts, we can readily 
 understand how the sheet of water-impregnated de'bris, which 
 as we have endeavoured to show must have formed the envelope 
 to the solid nucleus, assumed in its lower portion a semi-fluid 
 condition, and constituted a plastic bed on which the stratified 
 sediments repose. These sediments which are in part modified 
 portions of the disintegrated primitive crust, and in part of 
 chemical origin, by their irregular distribution over different 
 portions of the earth determine after a lapse of time, in the 
 regions of their greatest accumulations, volcanic and plutonic 
 phenomena. It now remains to show the observed relations of 
 these phenomena both in earlier and later times to great accu- 
 mulations of sediment 2 ." 
 
 On these passages the following remarks suggest themselves. 
 The first process towards obtaining " a deep layer of disinte- 
 grated and water-impregnated material, the ruins of the former 
 envelope " of the solid nucleus, is supposed to arise from " the 
 further cooling and contracting of a solid crust formed over a 
 shallow molten layer." 
 
 Let us consider this point. The solid crust supposed may 
 
 1 Sterry Hunt's "Lecture on Volcanoes and Earthquakes," p. 6. This short 
 lecture, without date or name of publisher, contains a clear resume" of the 
 writer's views. 2 Ibid. p. 8. 
 
CH. viii.] FLUID SUBSTRATUM. 95 
 
 be compared to the surface of a lava stream. When once this 
 surface had attained the temperature of the atmosphere, it 
 would contract no further, and the hotter subjacent parts would 
 cool by conduction through the exterior. It does not appear 
 therefore that gaping cracks would be formed in it, but on the 
 other hand corrugations, the lateral pressure rather hindering 
 extravasation than promoting it. But this does not appear to 
 be the condition that Dr Hunt contemplates for the formation 
 of a water-impregnated layer. 
 
 The proximate cause of mountain elevation he considers to 
 be the depression of this supposed water- impregnated layer 
 through the covering of it by thick deposits of detritus, in 
 consequence of which the isogeotherms have risen, the water- 
 impregnated layer has entered on a state of igneo-aqueous 
 fusion, and the globe contracting by general loss of heat has 
 caused the crust to be wrinkled along the elongated areas in 
 this manner weakened. 
 
 It is obvious however, that the theory thus developed, 
 admirable in some respects, offers no special facility towards 
 affording sufficient compression. The contraction of the matter 
 of the globe through mere cooling is alone appealed to. All 
 the objections therefore to the adequacy of this cause, which 
 have been brought forward in the previous chapters, apply with 
 equal force to Dr Hunt's explanation. It may also be ques- 
 tioned whether a layer of material simply deposited from water, 
 in a manner similar to that of the ooze or sand of the ocean 
 bed, would after consolidation into rock supply sufficient water 
 to account for the immense quantities of steam given off during 
 volcanic eruptions. It appears that there ought to be, under 
 this view of its derivation, the same equivalence between the 
 amount of the lava and of the gaseous emanations from a vent, 
 as between the earthy sediment and the water incorporated with 
 it when it became consolidated after precipitation. Although no 
 exact measures are known, still it seems that the water given off 
 in steam bears too large a proportion to the solid matter to be 
 thus accounted for ; especially when we remember that, besides 
 the emanations from the crater, a large quantity of steam is 
 emitted by the lava stream after eruption, before it becomes cool. 
 
96 FLUID SUBSTRATUM. [CH. vm. 
 
 The presence of so large a quantity of water substance in 
 the deep-seated and molten rocks is still to seek. 
 
 The following supposition is offered with considerable diffi- 
 dence. It has been suggested by a paper lately read by Mr 
 Mallet before the Geological Society 1 , although it will be apparent 
 that it is not the same theory as Mr Mallet's. That gentleman 
 has pointed out the undoubted fact, that, if all the water upon 
 the face of the globe were to be at the present moment con- 
 verted into vapour, the pressure which it would exert at the 
 earth's surface would be the same as would be exerted by the 
 present oceans, were they spread in an equable layer over the 
 surface. He then enters into speculations regarding the tem- 
 perature to which water might be raised under such pressure, 
 and its effect upon rocky matter. 
 
 Let us then revert to the far distant time when the tem- 
 perature of the earth had fallen to that point, when the oxygen 
 and hydrogen were first able to combine. The pressure, caused 
 by the gravitation of the water substance formed from them, 
 would have been that due to a layer of liquid water its exact 
 equivalent. This would have been the same as the pressure of a 
 column of an ocean somewhere about two and a half miles deep. 
 The water substance would at that time have been at far above 
 its critical temperature, and possessed of great solvent power 
 upon silicates and some other minerals. It may then be asked, 
 Is it necessary to suppose that the rocky materials had already 
 formed a solid globe, upon which this water substance was 
 supernatant ? Might not rather such substances as were soluble 
 have been in solution with it, even to that depth at which the 
 magma was succeeded by denser materials insoluble in super- 
 heated water? If that were so, then as cooling proceeded a 
 crust of rock would have been formed by crystallization at a 
 certain level, and would have gradually extended downwards. 
 But there may be even still remaining an intensely hot layer 
 of original water-dissolved silicates, underlying the solid crust, 
 ever in readiness to furnish the steam, gases, and ejectamenta 
 of the volcano; and by the extravasation especially of the 
 former of these to contribute to the contraction of volume of 
 the globe. 
 
 1 " Quart. Journ. Geol. Soc." Vol. xxxvi. p. 112. 
 
OH. vni.] FLUID SUBSTRATUM. 97 
 
 In our ignorance of the properties of water at the high 
 temperatures and under the pressures we are now considering, 
 it is not possible to arrive at any but the most general con- 
 clusions. 
 
 If we take the mean depth of the ocean to be 2500 fathoms, we 
 find that the pressure due to a layer of water of this depth would 
 be 442 atmospheres, or 236424 mm. of mercury. But we must 
 reduce this in the proportion of 146 : 197 1 , because the depth 
 will be inversely proportional to the area, and we are now sup- 
 posing the ocean spread over the whole globe. This will make 
 the pressure about 327 atmospheres or 249329 mm. of mercury. 
 We do not know what temperature corresponds to this pressure. 
 It was found by M. Cagniard de la Tour that the critical tem- 
 perature of water is about 773 F., but the pressure was not 
 determined. At that temperature the water began to dissolve 
 the glass tube which contained it. At the temperature 230 C., 
 or 446^ F. the pressure of steam is 20926 mm. of mercury 2 . This 
 appears to have been the highest determined by Regnault. 
 
 It is at once apparent that the temperature corresponding 
 to 249329 mm. of mercury must be greatly above the critical 
 temperature. 
 
 The lower portion only of the aqueous envelope would have 
 been sufficiently compressed to hold silicates in solution. These 
 would have begun to be deposited in a solid and probably 
 
 1 Ch. v. p. 54. 
 
 2 Balfour Stewart's "Heat," 2nd ed. p. 402. Locomotive engines are con- 
 structed to work up to a pressure of about 10 atmospheres. 
 
 Extract from a letter by Mr J. Aitken in " Nature," vol. xxm. p. 34, 1880 : 
 " A. free surface is any surface of the body under examination at which it IB free 
 to change its state.". . . . "As to what the freezing, melting, and boiling points 
 are when these free surfaces are absent, we have at present no knowledge what- 
 ever. All we know is, that the freezing point is lower, and the "melting" and 
 "boiling points" are higher, than when free surfaces are present. The first of 
 these points is too well known to be referred to here. The last point was illus- 
 trated in the paper referred to " (Royal Scottish Society of Arts, 1874-5) "by an 
 experiment in which water was heated in a metal vessel under atmospheric 
 pressure to a temperature far above ' the boiling point,' when the water exploded 
 and violently ejected itself from the vessel. The superheating of the water was 
 accomplished by carefully excluding all free surfaces, by bringing the water into 
 as perfect contact with the metal of the vessel as possible." 
 
 F. 7 
 
9 FLUID SUBSTRATUM. [CH. vm. 
 
 crystalline state before any rain could fall from the atmosphere, 
 because precipitation of water could not take place until the 
 temperature had decreased to about 773 F., and before that 
 the water substance must have lost the greater part of its 
 solvent power on the earthy salts. The sea salts would have 
 remained in solution in the primitive ocean after the silicates 
 had crystallized out, and they would still continue to form a 
 constituent part also of the hot magma supposed to exist beneath 
 the solid crust in a state of igneo-aqueous solution. 
 
 This magma is probably of the nature of an elastic liquid, 
 for, "above the critical temperature for the substance no amount 
 of pressure will produce the phenomenon which we call con- 
 densation 1 ." 
 
 i Maxwell's "Heat," 2nd ed. p. 119. 
 
CHAPTER IX. 
 CRUST NOT FLEXIBLE. 
 
 The "datum level" equation has sewed an important purpose Supposition of a 
 flexible crust Mode of determining the general character of the undulations 
 which a thin flexible crust icould assume when resting upon a liquid 
 Mathematical investigation of the problem Certain negative conclusions 
 therefrom regarding the earth's crust Alternative assumption to which we 
 are led. 
 
 WE have thus arrived at the conception of an elastic highly 
 heated layer of rocky matter 1 combined with water substance, 
 kept in a state of compression by the superincumbent pressure 
 of the crust, but ready to burst forth with the evolution of 
 steam and gas wherever and whenever a vent is opened for its 
 escape. 
 
 We are now freed from the trammels imposed by the hypo- 
 thesis of a solid globe, contracting from the effect of cooling 
 only. In reverting to our original relation between the hori- 
 zontal compression and the volumes of the inequalities which 
 we have called our datum level equation viz. 
 
 we are no longer obliged to consider (J5) as non-existent : 
 for it is now conceivable that the solid crust may dip downwards 
 into the fluid substratum, which in its turn may rise into the 
 anticlinals. 
 
 It is true that under our new hypothesis this equation is in- 
 determinate, because we do not know where to place the 
 
 1 This layer will be usually termed "fluid" rather than "liquid," because 
 the term "liquid" does not convey the idea of elasticity which, when the pres- 
 sure is sufficiently diminished, will be an attribute of the substratum. 
 
 72 
 
100 CRUST NOT FLEXIBLE. [en. ix. 
 
 datum level. But it has already served a most important pur- 
 pose by enabling us to prove that the inequalities, as we now 
 see them, are far greater than can be accounted for upon the 
 supposition of a solid globe contracting from cooling only. 
 
 Assuming then that a solid crust rests in corrugations upon 
 a fluid layer, which is capable of yielding to such forces as the 
 gravitation of the crust exerts, we have to consider the condi- 
 tions of its equilibrium. Now the disturbances which we see 
 that it has experienced, to the greatest depths which denudation 
 exposes to observation, would lead us to suppose that, when 
 once disturbed in lengths of any extent, it might perhaps be 
 considered flexible. Moreover, if it rests in corrugations upon 
 the subjacent fluid, it must be in unstable equilibrium ; that 
 is, the corrugations can have no particular relation to the places 
 where they occur, but might exist equally well at some other. 
 Here we should at once encounter a condition which would render 
 oscillations of the surface possible, provided we could account 
 for the disturbance of the position of equilibrium. 
 
 It will however be seen that the results of the following 
 investigation are so remotely akin to natural appearances, that 
 it must follow that the assumption of the flexibility of the 
 crust is not true to fact. So that rigidity appears to play an 
 important part in determining the position and form of the in- 
 equalities. This negative result is of itself of sufficient import- 
 ance to make it worth while to give the investigation, irrespec- 
 tive of the intrinsic interest of the problem from a mathematical 
 point of view. 
 
 In order to obtain some insight into the general character 
 of the corrugations, we will begin by enquiring what form would 
 be assumed by a heavy flexible crust, resting upon a liquid 
 within a rectangular trough shorter than the crust, for this 
 would give an approximate idea of the contour of the surface 
 upon the course of a section of the sphere perpendicular to its 
 surface and cutting a set of corrugations at right angles. 
 
 It maybe assumed that the trough and crust were originally 
 of the same length, and that the corrugations have been pro- 
 duced by the ends of the trough having been made to. approach 
 each other. 
 
CH. IX.] 
 
 CRUST NOT FLEXIBLE. 
 
 101 
 
 Suppose 
 
 COX to be a vertical section of the trough, 
 CPA the section of the crust whose thickness is k, 
 OX, horizontal, the axis of #, 
 Y } vertical, that of y, 
 OM=x t MP = y, PTM=0, 
 r the radius of curvature at P, 
 p the density of the crust, 
 cr that of the liquid, 
 p the pressure of the liquid at P, 
 
 t the force of compression in the crust in the direction of 
 the tangent at P. 
 
 We may suppose for the present that the flexibility of the 
 crust is not impaired by its thickness. 
 
 Then applying the conditions of equilibrium we obtain the 
 following equations : 
 
 (1) t = gpk (G y), where C is an arbitrary constant. 
 (2) p=gpk<x>*0 r . 
 
 Let h be the value of the ordinate at the highest point A, 
 andy the depth of a layer of fluid of the density of the crust, 
 which upon a unit of area would produce a pressure equal to 
 the compression at A. Let 8 be the depth of a layer of fluid 
 of the density of the crust, which would produce a pressure equal 
 to the fluid-pressure at A. 
 
102 CRUST NOT FLEXIBLE. [ CH . ix. 
 
 Then from (1) we have 
 
 compression at A = gpkf=gpk (C h] ; 
 .-.f=C-h. 
 
 Also p = the pressure due to the depth below A + the pressure 
 at A ; 
 
 Therefore, substituting in (2), 
 
 / y~C\ 
 aa~ (h y J + Qpv Qpk ( cos 6 + 1 . 
 
 t7 \ *J / ' t/ I c/ " 
 
 \ r ) 
 
 Change the origin to 0' by putting y = y C ; 
 
 Hence when y = h, y' = -f, so that/ is the depth of A 
 below the new origin, and 
 
 whence, by substituting for y, 
 
 
 /-(-/- />) = ** + 
 
 Integrated this gives, 
 
 try'* . , s . , 7 ,dx 
 
 - - - (-f- p$ y 
 
 / U6 ., ~ . <T 
 
 or / 3 ^ ~i H (<v pfyy -{- y D (A). 
 
 If this equation be solved with regard to y' it will give two 
 
 (i / Y* 
 
 values of y for one value of --,- or cos 6. 
 
 ds 
 
 And if it be solved with regard to -=- , or cos 0, it will give 
 the same value for cos 6 whenever y is the same. 
 
 The curve is therefore of an undulating form as in the 
 figure. 
 
CH. ix.] CRUST NOT FLEXIBLE. 103 
 
 If the two values of y be made equal, they will give the 
 points of contrary flexure. 
 
 dec 
 If we put -j- = 1, this will give the maximum and minimum 
 
 ordinates. 
 
 Now we know that one of these is f. Hence we may 
 findZ) 
 
 . 
 Substituting this value we get for the said ordinates, 
 
 and their difference, 
 
 O" 
 
 We have from equation (2), by making r infinite, since t is 
 not infinite, at a point of contrary flexure, 
 
 p = gpk cos 0, 
 or - ga (/ +/) + gpS = gpk cos 0. 
 
 Substituting the corresponding value of cos in the general 
 equation, we get 
 
 (7 
 
 for the depth of the point of contrary flexure. The negative 
 sign must be taken. 
 
 The radii of curvature are, at an anticlinal, 
 
 -N . ' -" r -, ^ V 
 
 and at a synclinal, 
 
 r , * + 2 k. 
 k o a- 
 
 To determine the constant f we must discuss the conditions 
 at an anticlinal. Consider any element ds of the curve, and let 
 the horizontal and vertical components which act upon it from 
 beyond at one extremity of it be 
 
104 CRUST NOT FLEXIBLE. [CH. ix. 
 
 R and Q, and, as before, 
 p the fluid pressure, 
 t the compression, 
 
 6 the inclination of the tangent to the 
 horizon. 
 
 Resolving vertically, we have for equilibrium, 
 p cos dds + t sin - gpkds + Q = 0, 
 
 and horizontally, 
 
 p sin 6ds t cos 6 + R = 0. 
 Eliminating , 
 
 pdsgpkcos0ds + Qcos + .Rsin0 = (1). 
 
 Now this being true when ds is indefinitely diminished, since 
 Q and R are not thereby altered, we have generally, 
 
 Q cos 6 + R sin 6 = 0. 
 
 But at an anticlinal Q and R must be the vertical and 
 horizontal components of the compression at one side of the 
 anticlinal. From the nature of the case the vertical components 
 of the compression on either side of the anticlinal must act in 
 the same direction ; and therefore they cannot be in equilibrium 
 unless they are separately zero. And Q is one of them ; 
 
 .*. also R sin 6 = 0, 
 whence either sin = 0, or R = 0. 
 
 Let us consider these two cases in order. When the element 
 is under the action of the forces Q and R at one extremity of it, 
 and ds is indefinitely diminished, observing that 
 
 /""I . . /3 i 73 * ZJ i\ 
 
 (J cos t/ + M sin v = U, 
 we have from (1) in the limit 
 
 pds gpk cos 6ds = 0, 
 pds 
 
 grk cos Bds 
 
 = 1. 
 
CH. ix.] CRUST NOT FLEXIBLE. 10.5 
 
 Now at an anticlinal we know that p=gpB, and (in the case 
 we are now considering) cos = 1, and these are the values 
 which these quantities assume there when ds is indefinitely 
 diminished. 
 
 Hence at an anticlinal the above becomes in the limit 
 
 gpk 
 that is, when the curve is horizontal at an anticlinal, 
 
 This condition evidently belongs to the case of a crust lying 
 horizontally upon the liquid, which is a particular case of the 
 general problem. In this instance the difference of the maxi- 
 
 mum and minimum ordinates (k S) as found p. 103 vanishes, 
 as it ought to do. 
 
 Next consider the second case, viz. when R = 0. In this case 
 f= since / measures R. 
 
 The relation f= shows that there is no compression at the 
 anticlinal. 
 
 In this case tan 6 = - takes the form of ^ . 
 H U 
 
 The origin of co-ordinates is by the same relation for/ 
 brought to the level of the anticlinals. 
 
 Our equation (A) now becomes, suppressing the dash over 
 the y, 
 
 dx y n 
 
 ""- ' 
 
 ds pky 
 
 dx 
 
 This expression shows that D = 0, otherwise -y- (or cos 6) 
 
 would be infinite at an anticlinal where, reckoning from the 
 newly -determined origin, y = /= 0. 
 
106 CRUST NOT FLEXIBLE. [en. ix. 
 
 Dividing the numerator and denominator by y, 
 
 , '- * <*-*l 
 
 Integrating this equation, and taking the origin at an anti- 
 clinal, we obtain 
 
 a? + y _ x tfv _ By = . 
 o- er * 
 
 % This represents a circular arc. 
 
 If X be the distance from one anticlinal to the next, we 
 obtain for B the value 
 
 and for the final equation 
 
 which gives the co-ordinates of the centre 
 
 2 ' 2 
 
 and the radius A;, 
 cr 
 
 These conditions are possible so long as X is less than 
 &; when it has that value the festoon between the anti- 
 
 <T 
 
 clinals becomes a semicircle. 
 
 It appears therefore that, when no extraneous force acts 
 upon the crust, a section of it will assume the form of a series of 
 equal circular arcs, the radii of which depend solely upon the 
 mass (pk) of a unit of length of the crust, and upon the den- 
 sity a- of the liquid on which it is supported. The degradation 
 of the undulating curve into a series of circular arcs takes place 
 through the compression at the anticlinal / becoming zero. 
 The curvature (p. 103) at an anticlinal in this case becomes 
 infinitely great. 
 
CH. ix.] CRUST NOT FLEXIBLE. 107 
 
 The next step is to conceive a long trough, bent lengthwise 
 into a circular form of large radius, and that the crust and 
 liquid are acted upon by a force gravitating towards the centre, 
 and so we approximate to what would be, in the case we have 
 supposed, a section of the earth's surface, taken along a great 
 circle. In this case we must suppose the curve reentering. 
 No extraneous force acting, the circular festooned form will 
 approximately represent the curve of equilibrium. 
 
 But for simplicity of conception it will be better to return 
 to the idea of the rectangular trough, and to suppose that the 
 curve is in the phase of an anticlinal where it meets the trough 
 at either end ; which condition is necessary for equilibrium 
 if there is no friction there : and that there are m festoons. 
 
 Having found the form of equilibrium we have now to 
 enquire what relation it holds to the length of the trough. 
 
 We will consider that the trough was originally of the 
 length L, and that it is compressed until its length becomes 
 
 L(\ e). Then since k is the radius of every circular arc 
 
 which can admit of equilibrium, and that the chords of the 
 m festoons, or arcs, must equal the reduced length of the 
 trough, putting </> for the angle subtended by each festoon, we 
 must have 
 
 and because the whole length of the crust is that of the trough 
 before compression, 
 
 m k<j> = L j 
 
 Sin 2 
 whence = 1 e ....... . .................. (1), 
 
 9 
 
 2 
 
 and m = -=- j-, ........................... (2). 
 
 2/> k(f> 
 
 Any value of e less than unity substituted in (1) will give a 
 corresponding value of <[>, and thence from (2) a value of m. 
 
108 CRUST NOT FLEXIBLE. [CH. ix. 
 
 But none but integral values of m will be compatible with 
 equilibrium, because the curve must meet either end of the 
 trough at an anticlinal. 
 
 cf> diminishes as m increases, and when m is infinitely great 
 and <j) infinitely small, 
 
 sin | 
 
 - 1 - 
 
 2 
 
 becomes unity, and therefore e = 0, or there is no compression. 
 
 m also increases as Jc diminishes. Hence, cceteris paribus, 
 the festoons are more numerous with a thin crust than with a 
 thick one. The geometrical relations show that the lengths 
 of the festoons must increase, and their number diminish, as 
 the compression is increased. 
 
 Consider now the crust to be in equilibrium with a certain 
 pair of values of m and e, m being integral, and let the trough 
 then be shortened, but not sufficiently so for the next integral 
 value of m to be reached. What will happen ? The festoons 
 cannot alter their curvature so as to adapt themselves to their 
 lessened chords. It seems then that the compression at the 
 anticlinals must become finite, instead of being zero, and that 
 the ends of the festoons will be pushed up against each other, 
 by which means material will be accumulated there, and Q 
 and R will become finite at the anticlinals. This will accord 
 with the undulating form of the curve, but it seems that the 
 equilibrium must become unstable, on account of the weight 
 resting on the anticlinal in the highest possible position. It 
 will therefore be liable to slide down upon the surface of the 
 liquid on one side or other of the anticlinal. 
 
 Let us suppose then that a portion of the 
 crust PQ, whose weight is Q, has become 
 thickened by the accumulation of material, 
 and let P be the mean fluid-pressure upon 
 this portion of crust. And let it be supposed 
 that the curve is cut off above Q. 
 
en. ix.] CRUST NOT FLEXIBLE. 109 
 
 Then we have for the equilibrium of PQ, 
 
 QsmB = t 
 and Q cos 6 = P x PQ. 
 
 The first of these equations combined with (1) p. 101, and 
 with the equation to the circle, will give the position of the 
 point P to which PQ will descend, balancing the curve below it 
 in the same manner as it would be balanced if the curve were 
 continuous above instead. 
 
 The fluid-pressure need not be altered by the above sup- 
 position, because the general pressure will keep the anticlinal 
 filled, although some of it should tend to escape above PQ. 
 But if the crust which was upon the other side of the anticlinal, 
 surmounts it, and follows PQ down the incline, it will produce 
 compression above Q, and it seems that Q must, in that case, 
 descend to the synclinal, where if p be less than cr it will float 
 and not disturb the general form of the curve beyond it. PQ, 
 while thus descending, will force up the crust on the other side 
 of the festoon, which in its turn surmounting the anticlinal, 
 will descend the next incline. These changes, however, will 
 take place rather by a relative movement of the liquid, than by 
 an absolute movement of the crust, and will cause alternate 
 elevation and depression of any given point in the crust. 
 
 If the conditions of perfect fluidity in the liquid and perfect 
 flexibility in the crust were fulfilled, and the crust were of 
 insensible thickness, then our result would be true, and the 
 festoons be all equal circular arcs. But under such circum- 
 stances as may be supposed to exist in nature, these conditions 
 would be so imperfectly fulfilled, that all we can assert is 
 that the above considerations will serve as a rough guide to 
 what we might expect to occur. The conditions of equilibrium 
 would be satisfied from point to point not very widely distant 
 from each other, and we might expect the compression to be 
 distributed unequally. Hence the festoons would be larger, 
 and the anticlinals higher, in some regions than in others. 
 The local thickenings of the crust would also render the forms 
 of the curve locally to differ from the normal form. The effect 
 
HO CRUST NOT FLEXIBLE. [en. ix. 
 
 of the hydrostatic pressure of the oceans must also be taken 
 account of. 
 
 For suppose that any portion of the curve be covered by a 
 heavy fluid (the ocean) of density //,. Let c be the height of 
 this ocean above the level, upon which the origin was taken in 
 the first instance (on p. 101). Then, in forming the equations of 
 equilibrium, we shall have as before 
 
 t = gpk(C-y). 
 But for p we shall have, 
 
 p pressure at A + pressure due to the depth below A 
 
 pressure due to the ocean, 
 = go- (h - y) + gpS - gp (c -y\ 
 
 This is an equation of the same form as before. We cannot 
 find the values of the constants exactly as we did before, but 
 we can see that the curve must consist of two portions, one 
 above the ocean and one below it. 
 
 At the point where these two portions meet one another, 
 the direction of the curve must be continuous. The portion 
 above this point will evidently follow the law already investi- 
 gated in all respects. For the part below we have 'expressions 
 for p and t of the same form as before. This part will, there- 
 fore, follow the law of a curve, which may be supposed to rest 
 upon a liquid of the density a ^ instead of cr. The law of 
 form will, therefore, be the same as before, the constants being 
 determined according to this supposititious case. 
 
 The compression () of the part of the curve beneath the 
 ocean will, however, be greater than in the supposititious case, 
 the crest being higher. But that will not alter its form, be- 
 cause (t) in any case varies according to the height of the anti- 
 clinal. The radius of the portion beneath the ocean will be 
 
 The diagram illustrates the effect of increased general com- 
 pression in elevating and depressing points in the crust. The 
 
CH. IX.] 
 
 CRUST NOT FLEXIBLE. 
 
 1 1 I 
 
 point A is supposed for simplicity to remain 
 fixed. Then the points B, C, D, E, F, #, upon 
 further compression assume the positions 
 b, c, d, e,f,g. 
 
 If we now pass to the case of any rectangu- 
 lar vessel, and suppose it to be compressed in 
 two orthogonal directions, then the form of 
 the corrugations in these two directions would 
 be approximately governed by the laws we 
 have investigated, provided the plane crust be 
 supposed capable of adapting itself to a form 
 not developable into a plane. And even in the 
 case of a contracting sphere, the character 
 of the corrugations may be assumed to be 
 on the whole similar to that investigated, 
 and they would be arranged about polygonal 
 areas. 
 
 The consequence of the crust not being 
 absolutely flexible would be, that it would rest 
 within certain limits in forms either more or 
 less curved than the proper surface of equi- 
 librium, and it is obvious that the considerable 
 ratio, which the thickness of the crust may 
 bear to the radius of the festoon, renders the 
 result of the investigation much more difficult 
 of application to the case of nature than it 
 would otherwise be. But we may use it for 
 what it is worth. 
 
 Still further, the general compression along 
 a great circle will very inadequately represent 
 what would occur when the compression over 
 the whole surface has to be taken into account. In short, 
 the case of nature is so extremely complicated, that it is very 
 difficult to reason satisfactorily upon it. Nevertheless the conclu- 
 sions we have arrived at concerning the case of a thin heavy 
 flexible crust resting on a perfect liquid, have a certain value as 
 far as the results may be summed up in the following proposi- 
 tions : 
 
112 CRUST NOT FLEXIBLE. [OH. ix. 
 
 (1) A vertical section of the lower surface of the crust, 
 where it meets the liquid, when carried across a series of the 
 corrugations, would present a series of festoon-like arcs approxi- 
 mating more or less to a circular form, concave upwards. 
 
 (2) The anticlinals would be of cusp-like form, resulting from 
 the intersection of contiguous festoons. There would not be 
 found anything of the character of rolling undulations with 
 flat-crested anticlinals. 
 
 (3) The degree of curvature of the festoons would not 
 depend upon the amount of the general compression, though 
 their amplitude, or the distance from crest to crest, would be 
 increased, under circumstances of equilibrium (i.e. where ra, p. 
 107, is integral), upon the compression being increased. The 
 curvature would diminish upon the thickness being increased 
 
 because r = 2-k. 
 a 
 
 (4) But the curve of equilibrium, even if it were once 
 exactly established, could not be strictly maintained during 
 successive contractions of the sphere, because we have seen 
 that, in the case of a trough of given length, a flexible crust 
 and a perfect liquid, equilibrium can only subsist for certain 
 special amounts of contraction having relation to the length of 
 the trough. No doubt the limits within which this would be 
 possible would be enlarged by defects in flexibility and liquidity, 
 and they would also be enlarged by a great increase in the 
 length of the trough as compared to the thickness of the crust : 
 for then m would always be nearly an integer. 
 
 It can scarcely admit of a doubt that the results we have 
 just obtained do not represent the case of nature. There is no 
 reason to believe that the crust of the earth is flexed on the 
 whole in such a manner, that a section carried across a series 
 of anticlinals would give a series of circular arcs of the dimen- 
 sions required by ou'r results ; and accordingly our assumptions 
 
 cannot be in accordance with the facts. The radius k, cr being 
 
 necessarily greater than p, is too small to suit the arrangement 
 of the chains. 
 
en. ix.] CRUST NOT FLEXIBLE. 113 
 
 Now a negative conclusion of this kind is far from being 
 without importance ; for it is by a method of exhaustion that 
 we are best able to attack our problem. What then are the 
 assumptions upon which we have arrived at this unsatisfactory 
 result ? They are, that the crust is (1) thin, and (2) flexible, 
 and (3) that it rests on a liquid substratum. Of these assump- 
 tions the first cannot be wrong. The crust is no doubt thin 
 as compared with the other dimensions with which we have 
 to deal; as, for instance, the width of a continent. That it 
 rests on a fluid substratum has been already shown to be almost 
 certain. It remains then that the error in our assumptions lies 
 in supposing the crust flexible. 
 
 It follows that, when a horizontal pressure acts upon a tract 
 of crust, we must not suppose that the yielding will take place 
 by the bending of the crust, while its uniform thickness is 
 maintained; for, if that were the case, an arrangement of 
 anticlinals, bearing a close resemblance to the result of our 
 investigation, would be produced. But we must rather suppose 
 that the yielding takes place through a crushing together and 
 thickening of the crust. 
 
 The consequence will be that elevations above the datum 
 level will be accompanied by depressions beneath. The anti- 
 clinals will not be filled with fluid from below, but will be the 
 upper portions of double bulges, which will dip into the fluid 
 below as well as rise into the air above. And this is the condition 
 of things with which we shall attempt to deal in the following 
 chapter. 
 
 F. 
 
CHAPTER X. 
 
 DISTURBED TRACT. 
 
 i 
 
 Conditions of equilibrium of a disturbed portion of the earth's crust Probable 
 result of compression Part of the crust sheared upwards andpart downwards 
 These separated by a "neutral zone" Calculation of its position Confused 
 contortions in highly metamorphosed rocks explained Depth of neutral zone 
 Probable thickness of crust Prof. A. Favre's experiments on contortions 
 Inverted flexures Formation of a mountain chain and its elevation above the 
 ocean Subsequent effects of denudation and accumulation of additional 
 sediment Consequent tilting of tract Also general elevation from the same 
 cause Why areas of deposition are sinking areas Degree of tilting depends 
 upon width of tract and the existence of a mountain chain. 
 
 IN this chapter we shall consider the process of elevation of 
 a mountain chain by horizontal compression under the condition 
 of a certain degree of rigidity in the crust, without making any 
 particular assumption regarding the cause of compression, as- 
 suming only that it acts in a horizontal direction, and that the 
 crust rests on a fluid substratum of greater density than its 
 own. "Under these circumstances, if a hole were made anywhere 
 in the crust, the fluid would rise in it to a certain level, which 
 we may call the effective level of the fluid. 
 
 Let us as before call the density of the crust p, and that of 
 the fluid 0-, cr being greater than p. And let our sections be in 
 'all cases supposed to be of unit of width. 
 
 In the figure let A'B'V be the effective surface of the fluid, 
 the crust beyond A C and BD being undisturbed by compression. 
 Then by the principles of hydrostatics 
 
CH. x.] 
 And 
 
 DISTURBED TRACT. 
 
 But if we suppose an ocean 00, of depth B and density p, to 
 
 A' 
 
 
 
 [B 
 
 B' 
 
 IT- 
 
 D d 
 
 cover the crust, we must add the pressure of the ocean to that 
 of the crust and then 
 
 And 
 
 BE' 
 
 To avoid circumlocution, we shall in future call the portion of 
 the crust AB, which has been either partially or generally 
 compressed, and disturbed from its original position between AC 
 and BD, " the tract." 
 
 We shall also make a fresh supposition about the levels, 
 above and below which 2 (a) &c. are measured ; no longer re- 
 garding them as what would have been the upper and under 
 surface of the crust if it had been perfectly compressible in a 
 horizontal direction; but now, as "mean levels," above and 
 below which the tract is disturbed as compared with undis- 
 turbed regions. The consequence of this alteration will be, 
 that when a volume /3 is depressed into the fluid, it will not 
 follow that an equal volume a will rise into the anticlinals, 
 because the positions of the mean levels themselves will be 
 affected. Hence 2 (a) will not be equal to 2(/0), and we cannot 
 say that 2 (a) S (6) is equal to Jde. 
 
 Supposing no attachment at AC and BD, if there be equili- 
 brium of the whole as a rigid mass, we must have two conditions 
 fulfilled, (1) that the weight of the fluid displaced equals the 
 weight of the whole mass, and (2) that the centre of gravity of 
 the whole mass is vertically above that of the fluid displaced. 
 
 82 
 
Il6 DISTURBED TRACT. [CH. x. 
 
 Let us consider the former condition first. Then, using the 
 same letters, but dashed, to refer to the effective surface of the 
 fluid, as we have used for the upper surface of the crust, p. 46, 
 and supposing that a volume 2) (d) of water covers the hollows 
 of the disturbed region, since the weight of the fluid displaced is 
 
 gcrA'EB'DFC, or ga [M (1 + e) - 2 (a') + 2 (V)}, 
 and the weight of the mass supported is 
 
 we have for the first condition of equilibrium, 
 
 <r [M (1+ e) - 2 (a 7 ) + 2 (V)} = pkl (1 + e) + /*2 (d). 
 
 But we also have the geometrical relation, 
 
 2 (a) - 2 (a) + 2 (6) - 2 (&') = rectangle AA'B'B, 
 
 = BB'xl, 
 
 = ^LP k l-?tl, 
 a a 
 
 therefore subtracting, 
 
 2 (a) - 2 (ft) = ^^ Jcle + (8J-2(d)). 
 
 <7 CT 
 
 Since SI is the volume of water which would have covered the 
 tract if there had been no elevations, and 2(c) is the volume 
 of the water which rests upon it after elevation, we may in 
 general take S 2 (d) to be the volume of rock elevated so as 
 to replace water below the water level. If there be no com- 
 pression, or e= 0, then %(d) is 8; so also if <r = p, for in that 
 case the crust would float in the fluid without any part emerged, 
 so that %(d) would be &l. Thus either of the conditions 6 = 0, 
 or <r = /o, should reduce each side of our equation to zero, as it 
 will evidently do. 
 
CH. x.] DISTURBED TRACT. ll'J 
 
 Since 
 
 .. 208) - 2 (a) = kk- Jcle + 
 
 Hence 
 
 Now S 2(<), is evidently the volume of the water which 
 has been displaced from the elevated part of the crust by its 
 being elevated. And if we compare the densities of water 
 
 and rock, it is evident that - is less than 2, and therefore 
 
 or 
 
 2 - (81 2 (d)) less than the volume of water which has been 
 
 (7 
 
 displaced. But the latter is obviously less than the entire vol- 
 ume which has been added to the part of the crust between A 
 and B by compression, that is less than kle. This shows that 
 2(/8) 2(a) is always greater than 2 (a) 2(), but that this 
 excess is diminished by an ocean, so that it will increase the 
 amount of elevation of the surface above the upper mean level. 
 
 If we neglect the effect of the ocean, because - is small and 
 8 much less than Jc, then 
 
 a-p J7 <r-p 
 
 Hi My 
 
 a 
 
 And consequently, if a- were infinite we should have 
 2 08) -2 (a) = 0, 
 
 as would be the case, for under such circumstances the crust 
 could not dip down into the fluid, nor the fluid rise into anti- 
 clinals. If we suppose the crust to be of the density of granite, 
 
Il8 DISTURBED TRACT. [CH. x. 
 
 viz. 2*68, and the subjacent fluid of the density of basalt, viz. 2 - 96/ 
 we have, 
 
 -- 
 
 SOS) -*() 
 
 or about $. The diminution of density by elevation of tempe- 
 rature need not be regarded 2 . 
 
 "We have thus far had under consideration the relations of 
 the elevations and depressions above and below the mean levels, 
 as they would depend upon the conditions of equilibrium of a 
 mass of any form, floating without external constraint upon a 
 fluid, so far as the vertical forces are concerned. We must 
 however also consider how much importance belongs to the 
 attachments of the tract at its extremities AC and BD\ and on 
 this account, and from our general ignorance of the amount of 
 rigidity which must be attributed to the mass, it is obvious 
 that we can only arrive at the most general conclusions. 
 
 Let us then suppose as before, that the portion of crust AbdC 
 is compressed into the position ABDC. The lateral pressure 
 will act in some straight line drawn from a point in A C to a 
 corresponding point in BD. Consequently it will have no ten- 
 dency to open any fissures in the crust. We may therefore 
 dismiss from consideration such a condition of things as is 
 represented in our second figure of the diagram, p. 46. 
 
 If the crust were flexible and elastic, such a form as that 
 represented in the first figure might be possible. But the con- 
 dition more in accordance with natural appearances is that it 
 is partially plastic and partially brittle. It is capable of with- 
 standing considerable pressure until it gives way, but when it 
 does so, the harder portions will break up, and the plastic 
 accommodate themselves among the interstices of the harder. 
 
 1 Calculating from Laplace's law of density, 
 
 ^.at the surface =0-00000053, 
 AT 
 
 r being expressed in feet. Consequently the increase to p in 20 miles would be 
 0-056 and the density of Basalt would be met with at 100 miles. But Laplace's 
 law is empirical, and does not give information as to the actual arrangement of 
 the successive couches. 
 
 2 Note, p. 68. 
 
CH. x.] DISTURBED TRACT. 119 
 
 Under these circumstances we may suppose that, upon the 
 pressure increasing at any place, the crust will give way first 
 at some place where it is weakest. It cannot give way at two 
 places at once. Once having given way, the weak condition 
 will be propagated from that place, but more in one direction 
 than the opposite. In which direction this will be, will depend 
 upon the nature of the first rupture ; for it is not likely that it 
 should be perfectly symmetrical : and if not so, this will render 
 the neighbouring crust weaker on one side than on the other, 
 and in that direction we may expect the disintegrating process 
 to extend. The pressure approximately horizontal will produce 
 a shear more or less vertical. It will become a question there- 
 fore whether the compression is to be compensated by great 
 elevation above, and great depression below the mean levels 
 for a short horizontal space, or by lesser elevation and de- 
 pression for a longer. But the resistance to be overcome in 
 shearing will increase as the thickening increases, for not only 
 will a higher column of rock then have to be pushed up against 
 gravity above the upper mean level, but also the resistance to 
 depression below the lower mean will be increased on account 
 of the increased upward pressure of the fluid down into which 
 the lighter rock is forced. The friction will be increased also. 
 There will therefore arise some relation between the amount of 
 vertical shear, and the strength of the crust. In other words, 
 2 (a) -2 (6) +208) -2 () being equal to Me, the length I of 
 crust, broken up to give the necessary relief by the formation 
 of the inequalities represented by these symbols, will depend 
 upon the strength of the crust; such length being greater or 
 less according as the crust is weaker or stronger, because, if 
 strong, it will resist further fracture, and the part already dis- 
 turbed will be utilised to satisfy any subsequent additional com- 
 pression. 
 
 The horizontal force causing a compression which as already 
 remarked will be relieved rather by crushing or corrugating 
 the rocks than by flexing the crust as a whole, will not as a 
 primary consequence produce the hollows belonging to 2(&) 
 and 2 (a). It will rather result in a swelling of the crust up- 
 wards and downwards. 
 
120 DISTURBED TRACT. [CH. x. 
 
 The experiments which M. Tresca made upon the flowing of 
 plastic, and even very hard, substances have a bearing upon 
 this subject. His paper has the appropriately paradoxical title, 
 "De Te'coulement des corps solides 1 ." In it he showed that 
 solid, ductile, soft, or pulverulent, bodies can, without changing 
 their state, flow in a manner analogous to that of liquids, when 
 sufficiently great pressure is exerted on their surface. The 
 substances were subjected to pressure confined in a rigid cylin- 
 drical envelope, pierced at the bottom with a concentric orifice 
 of varied dimensions. These experiments would lead us to 
 expect, that the materials of the earth's crust, when laterally 
 compressed by a sufficient force, would "flow," or be strained, 
 vertically. What would be analogous to the stream lines in 
 a liquid would represent the distortions of the rocks; thus 
 might be produced cleavage, foliation, or contortion, according to 
 the conditions of the rocks themselves, or of the neighbouring 
 masses which adjoined them 8 . 
 
 But although we cannot predict the exact manner in which 
 the material will be arranged which constitutes the protu- 
 berances that will be produced above and below the mean 
 levels of the crust, yet we may arrive at some conclusion 
 as to whether the material at any given level within the crust 
 will on the average be sheared upwards or downwards by 
 the compression. For this compression acting horizontally, 
 will have no tendency in itself to determine whether the 
 motion which it causes in an elementary portion of the crust 
 subjected to its action shall be upwards or downwards. That 
 
 1 Comptes rendus, 1865, Vol. LX. p. 1228. 
 
 2 M. Tresca's experiments appear to have led to the misconception, that 
 great pressure causes solid substances to become liquid. A writer under the 
 initials E. L. C. has said that, if the earth were of steel, at the depth of one or 
 two leagues it would be of flowing steel, and that we should have to decide 
 whether flowing steel was solid or fluid (Eng. Mechanic, Vol. xn. p. 254). But 
 in M. Tresca's experiments, one surface of the substance was subjected to 
 enormous pressure, while the orifice from which it flowed was subject to none at 
 all. This is quite a different case from that of the interior of the earth, where 
 the pressure is alike in all directions. So far from great pressure rendering the 
 interior fluid, it appears from the proved great rigidity of the earth as a whole, 
 that it has an opposite effect. 
 
en. x.] DISTURBED TRACT. 121 
 
 circumstance will therefore be determined by the resistances 
 which operate to resist the motion of the element in question. 
 These will be the weight of the element acting downwards, 
 the friction tending to resist the motion, and opposite to it 
 in direction, and the pressure of the crust upon the fluid 
 beneath. It is evident that the friction, among the particles of 
 the crust will depend upon its physical state. If it were rigid 
 it would be infinite ; if liquid it would be zero. As it is, we 
 may conclude that its plasticity is increased in the lower parts 
 by the influence of the high temperature there. We will 
 therefore assume the friction to be some function of the depth. 
 It will be sufficient for our purpose to consider the density 
 constant throughout the thickness of the crust. 
 
 Let then ABk be the thickness of the crust before motion 
 commences. When the lateral pressure has become so great 
 
 that compression begins to take place, suppose that the portion 
 AZ of the column AB is sheared upwards, and the portion ZB 
 downwards, and let us call the locus of the point Z the "neutral 
 zone." 
 
 Let p be the force at P which resists the upward motion of 
 the element PQ ; 
 
 f the frictional force, which we assume to be a function 
 of x. 
 
 Then dpg pdx +fdx ; 
 
 * P 
 
122 DISTURBED TRACT. [OH. x. 
 
 At A, x = ; and / has some constant value ; and there is 
 no extrinsic pressure at A ; 
 
 ~ ft* a). 
 
 Again, if p be the force at P' which resists the downward 
 motion of ZP ', 
 
 dp gp dx +fdx ; 
 
 (2). 
 
 Now, at the neutral zone, the forces which resist the upward 
 motion must be equal to those which resist the downward 
 motion. If then h be the depth of the zone, the integral (1), 
 taken from to h, must be equal to (2) taken from h to Jc, 
 when to the second we have added the extrinsic force gpk, 
 arising from the pressure of the fluid ; 
 
 rh fk 
 
 fdx = -gp(lc-li) + \ fdx+gpk] 
 
 JO J h 
 
 rh rk 
 
 /. fdx = fdx. 
 
 JO J h 
 
 This result shows that the position of the 'neutral zone 
 depends solely upon the condition, that the friction upon the 
 column above it shall be equal to that upon the column 
 below it. 
 
 Let us first of all make the assumption that the friction is 
 constant at all depths, and equal to X. 
 
 Then XA 
 
 or the neutral zone is situated in the middle region of the 
 crust. 
 
 But if we consider the plasticity of the material to be 
 increased by heat in the lower parts of the crust, we must 
 
CH. x.] DISTURBED TRACT. 123 
 
 assume some function to express the value of f which has a 
 constant value X at the surface, and decreases, at first slowly, 
 and afterwards more rapidly, as the depth x is increased. 
 
 For the purpose in hand we may admit that it becomes zero 
 at the bottom of the crust, although this is of course not 
 strictly true. An appropriate function for our purpose appears 
 to be, 
 
 TTX 
 
 The corresponding force upon an element at P will there- 
 
 rrrnp 
 
 fore be X cos -^j- dx ; and the whole factional force upon AZ 
 
 will be 
 
 f* TTX , 
 XCOSTTT doc, 
 
 X ^ SlU 2k' 
 
 If we make h = k, we find the friction across the whole crust 
 
 2k 
 to be X . And it is evident that the friction along AZ t 
 
 IT 
 
 plus the friction along ZB t make up the whole friction across 
 AB. 
 
 Hence the friction along ZB = X f 1 sin ^ J . 
 
 Our condition for the position of the neutral zone then 
 gives us, 
 
 2Jc . Trh 2k A. 7rh 
 
 2Jc . Trh , 2k A. 7rh\ 
 
 X - Sin ^ry- = X - [ 1 -* 8SII 57 I j 
 
 TT 2k TT \ 2kJ 
 
 Trh 1 
 
 r Sin 2^ = 2' 
 Trh 1 TT 
 
124 DISTURBED TRACT. [CH. 
 
 In this case then the neutral zone would be at one-third or 
 the depth. 
 
 In finding the position of the neutral zone no assumption 
 has been made respecting the value of k. So long as the crust 
 at the place under consideration was not under constraint, but 
 in equilibrium as a floating body, the neutral zone would hold 
 the same relative position within it. So that if this condition 
 of flotation remained fulfilled it would be always horizontal. 
 For the purpose we have in view it will be sufficiently accurate 
 to assume, that it occupies a position whose distances from the 
 upper and lower surfaces of the crust, whether before or after 
 compression, are always in the same ratio. 
 
 It is also observable that the position of this zone does not 
 depend upon the absolute value of the frictional force, so long 
 as it can be expressed as a function of the depth multiplied by 
 the value which the friction has at the surface. If however the 
 friction were to vanish, which it would do if the material were 
 to become liquid, we should have h indeterminate. The signi- 
 fication of this appears to be, that the tendency of the liquid at 
 every depth would then be indifferently to move upwards or 
 downwards, and therefore it would be affected with confused 
 internal currents, somewhat similar to convection currents. 
 
 Now it will be observed that, since the shear, whether up- 
 wards or downwards, increases continually as we get further from 
 the neutral zone, it follows that if there were to be a relative 
 motion, in the opposite direction to that which they actually 
 have, impressed upon the particles at any given level, that 
 level would become a neutral zone relatively to the particles 
 above or below it. If then the material above or below any 
 zone were to become liquid, it would behave under this relation 
 as the whole crust would behave if it were liquid, and would 
 be affected with confused currents. This consideration goes 
 far to explain the confused contortions constantly observable in 
 highly metamorphosed rocks ; which are supposed to have been 
 softened by heat, and consequently to have approached the 
 condition of a liquid. 
 
.x.] DISTURBED TRACT. 125 
 
 ' The function X y , which we have provisionally adopted 
 ZK 
 
 to express the friction at the depth x, would actually vanish at the 
 bottom of the crust. This of course represents what could not 
 really happen. It is however evident, that any softening of the 
 lower parts would tend to raise the neutral zone to a higher posi- 
 tion, and that the more complete the softening the higher it would 
 be. We have here assumed an amount of softening which is 
 too great, and find that the corresponding position of the neutral 
 zone would be at the depth of J of the crust. On the other 
 hand we have found that, if the crust were equally rigid through- 
 out, it would be situated at the depth of J of the thickness. 
 Comparing the two cases, we may fairly conclude that it will be 
 in fact in a position intermediate between these two, and shall 
 be probably justified in placing it at about f of the thickness. 
 
 On different, and geological, grounds we have likewise the 
 following considerations to help to guide us in affixing a limit 
 below which we must place the neutral zone. It is well 
 known that granite frequently occupies the central axis of 
 mountain chains. Now Mr Sorby has taught us in his sec- 
 tional address at the British Association, 1880, 1 that granite has 
 been usually formed in the presence of liquid water; although 
 he speaks of a single instance in which the temperature 
 at the commencement of crystallization may have been higher 
 than that at which water can exist in the state of a liquid. 
 The critical temperature for water is about 773 F. At the 
 rate of increase of one degree F. for 51 feet, this temperature 
 would be reached at the depth of about seven miles and at the 
 rate of one degree for 60 feet at the depth of about eight and 
 a half miles. We may therefore conclude, that rock, which was 
 once at seven or eight miles' depth, has been forced upwards, 
 and consequently, that the neutral zone is lower than that. 
 
 But we know of no rocks at the surface except the truly 
 
 eruptive, which have come from a greater depth than has 
 
 granite. Had it come from the neutral zone, this would have 
 
 made f k equal from 7 to 8 J miles, and therefore k would have 
 
 1 Nature, Vol. xxn. p. 392. 
 
126 DISTURBED TRACT. [CH. x. 
 
 been from 17 to 21 miles. But since it is very improbable that 
 any portion of the neutral zone should be brought so near the 
 surface as to be exposed, we may conclude that the crust is 
 thicker than when thus estimated. 
 
 Again, Mr Mallet has determined the temperature of melting 
 slag to be about 3000 F. 1 , and we can hardly suppose that the 
 materials of the crust could be solid at such a temperature, as 
 can melt silicates without the presence of water. This tempe- 
 rature would, at the same rates of increase, be found at the 
 depths of about 28 or 30 miles, consequently we may conclude 
 from this argument that the crust is certainly less than 30 miles 
 thick. One of these reasons then leads us to think that it is 
 more than 17 or 21, and the other that it is less than 28 or 30 
 miles in thickness, according as we assume the higher or lower 
 rate: and we have given reasons for preferring the higher 2 . Per- 
 haps we shall not be very wrong in assuming 25 miles as its 
 average thickness between the upper and lower mean levels. 
 
 In equation (1) p is the whole force which resists motion 
 upwards, and at the neutral zone it is equal to 
 
 rh 
 
 Jo 
 
 o 
 
 which consists of two parts, namely the weight of the column of 
 rock above that zone and the frictional force above it. 
 
 Similarly p in equation (2), taken between the neutral zone 
 and the bottom of the crust, gives the whole force which resists 
 
 motion downwards, and this is found to be 
 
 rk 
 ffph + | fdcc. 
 
 j h 
 
 The first term of this expression is the same as in the previous 
 one, and the second term is the frictional force below the neutral 
 zone. By the property of the neutral zone these second terms 
 are equal, and will evidently increase with the thickness of the 
 crust. So also will' the first term. And, since the' depth h of 
 the neutral zone has been shown to be proportional to the 
 thickness of the crust, it follows that the first term is propor- 
 tional to that thickness, and the second possibly may be so. 
 1 p. 68. 2 p. 16. 
 
CH. x.] DISTURBED TRACT. 12 7 
 
 This however depends upon the constitution of the crust. It 
 
 /ft 
 fdx may be greater for a 
 ) 
 
 small value of h when / is great, than for a considerably larger 
 value of h when f is small, that is the strength of the crust 
 may present a greater obstacle to shearing than its thickness. 
 This confirms what has already been said at p. 119 respecting 
 a relation between the amount of vertical shear and the 
 strength of the crust. 
 
 By the favour of Messrs Macmillan and of the proprietors of 
 La Nature, one of the woodcuts is exhibited overleaf represent- 
 ing the results of some interesting experiments made by Prof. 
 A. Favre of Geneva. The following description is from the trans- 
 lation given of Prof. Favre's article in Nature, Vol. xix. p. 103. 
 " I placed the layer of clay employed in these experiments on a 
 sheet of caoutchouc, tightly stretched, to which I made it adhere 
 as much as possible ; then I allowed the caoutchouc to resume 
 its original dimensions. By its contraction the caoutchouc would 
 act equally on all points of the lower part of the clay, and more 
 or less on all the mass in the direction of the lateral thrust " 
 
 " The arrangement of the apparatus is very simple. A sheet 
 of India rubber 16mm. in thickness, 12 cm. broad, and 40 cm. 
 long, was stretched, in most of the experiments, to a length of 
 60cm. This was covered with a layer of potter's clay in a 
 pasty condition, the thickness of which varied, according to the 
 experiments from 25 to 60 mm. It will be seen from the di- 
 mensions indicated that pressure would diminish the length of 
 the band of clay by one-third. This pressure has been exerted 
 on certain mountains of Savoy " 
 
 " The strata, which appear to divide the masses of clay, and 
 which are represented in the figures, are not really strata, but 
 simply horizontal lines at the surface of the clay" probably he 
 means ruled along the side of the mass before the compression 
 was allowed to act. After describing the varied appearances, 
 he observes, "The strata are less strongly contorted in the lower 
 parts than in the neighbourhood of the upper surface. They are 
 disjoined in certain parts by fissures or caverns. They are tra- 
 versed by clefts or faults inclined or vertical. All these deforma- 
 
128 
 
 DISTURBED TRACT. 
 
 [CH. X. 
 
 fi 
 
 r? 
 
 1 
 
 f 
 
en. x.] DISTURBED TRACT. 129 
 
 tions are the more varied, in that they are not similar on the 
 opposite sides of the same band of clay." 
 
 It appears then that instead of producing contortion at the 
 layer which adhered to the caoutchouc band, the compression 
 was there relieved by mere thickening, and that contortion 
 became more and more pronounced at greater distances from 
 this layer. To this uncontorted layer our neutral zone would 
 correspond. As the upper surface of the crust was approached, 
 the contortion would become more marked, simple compression 
 accompanied by upswelling characterising the disturbance of 
 the strata nearer to the neutral zone. On the character of the 
 disturbance below this we cannot safely speculate. But pro- 
 bably, on account of the continually increasing pressure, and 
 the softening of the material by heat, the contortions would, 
 as already explained 1 , be of a more confused character than 
 above it. 
 
 It must not however be concluded that, because Prof. Favre's 
 experiments so happily illustrate the point in hand, it follows 
 that the theory which he proposed to illustrate by them is the 
 same as the one which is now advanced ; for the object he had 
 in view was to test the effect of secular cooling alone, in pro- 
 ducing inequalities upon the earth's surface, without the hypo- 
 thesis of a fluid substratum. We can however easily see, that 
 such a theory would require the entire globe to be covered, like 
 the caoutchouc band, by these corrugations; instead of their 
 being arranged, as they are, in mountain chains, to say nothing 
 of the other objections which have been already stated in oppo- 
 sition to that theory. 
 
 Prof. Favre's experiments may also be fairly adduced to 
 show how hopeless it would be to predicate the exact form which 
 contortions would assume. Scarcely any conditions can be con- 
 ceived more favorable to uniformity of result than those which 
 he devised ; and yet it is evident at a glance how varied was 
 the result obtained at various points of the longitudinal section. 
 In no respect do the experiments illustrate the case of nature 
 more strikingly than in this apparent complexity of the disturb- 
 
 1 p. 124. 
 F. 9 
 
130 DISTURBED TRACT. [CH. x. 
 
 ances. Yet it is certain that these must have been governed by 
 unerring laws resulting from a slight want of homogeneity in 
 the material : and perhaps even, as the figures seem to suggest, 
 from the local weakness caused by the horizontal lines, which 
 had been traced upon the face of the clay before compression. 
 
 In the case of Prof. Favre's experiments the compression 
 was uniform along the tract. In that which we are considering 
 it would be otherwise. The pressure would increase until the 
 crust gave way at one place. There it would be crushed up- 
 wards and downwards, above and below the neutral zone, until 
 the thickening had attained a certain limit, which would depend 
 upon the rigidity of the material, its weight, and perhaps oni 
 the angle of repose. When this limit had been attained, a 
 fresh region would be involved in the process ; and this would 
 probably adjoin the former. But as the lateral force expended 
 itself, the thickness disturbed would become less and less, and 
 the disturbance would gradually die out towards that side from 
 which the movement came. 
 
 Since the portion of the crust which lay within the limits 
 of the original thickness would suffer greater compression than 
 the raised and depressed portions above and below it, being 
 more in the direct line of the pressure, we might expect that 
 the flexures would hang over towards the side from which the 
 movement came, thus causing inversions of bedding. This 
 phenomenon is common on the flanks of mountain chains, and 
 especially marked in the Appalachians. In the explanation 
 usually given, the pressure has been supposed to have come 
 from the side, away from which the flexures incline : so that if 
 the flexures incline towards the west, the movement is supposed 
 to have come from the east 1 . According to the explanation 
 now proposed the case would be the exact opposite, and if 
 the flexures hang over towards the west, the movement came 
 from the west. Where we find inverted bedding on both sides 
 of an anticlinal, or a fan-shaped structure, we infer that a 
 
 ": 
 
 1 Prof. Green's Geology for Students, p. 377, with a reference to SUUmarfs 
 Journal, 1st Series, XLIX. 284. 
 
en. x.] DISTURBED TRACT. 131 
 
 relative movement towards that region has occurred from the 
 opposite sides. 
 
 We will now attempt to trace the formation of an elevated 
 region by the compression of a tract of crust. We suppose that 
 the compression has thickened the tract by crushing and 
 corrugating the rocks of which it is composed, and that this 
 thickening is greater about that part of the tract which was first 
 compressed, and gradually subsides towards the region or 
 regions from which the movement came. We also conclude 
 that there will be what we have called a neutral zone, or level 
 within the crust, above which the material will on the average 
 be sheared upwards, and below it downwards. It will corre- 
 spond with the caoutchouc band in Professor Favre's experi- 
 ments. The position of the neutral zone will depend upon the 
 law, according to which the plasticity of the material changes at 
 different depths. 
 
 We have however seen that its position below the surface 
 lies probably at between J- and \ of the total thickness of the 
 crust, and that this result, combined with our knowledge of 
 the temperature at which granite has been formed, shows that 
 the total thickness must exceed twenty-one miles, and that this 
 conclusion agrees well with the fact that the melting tempera- 
 ture of rock in the dry way may be expected to occur at a 
 depth of less than about thirty miles. 
 
 We will take therefore as the bases of our working hypo- 
 thesis, that the undisturbed crust is about twenty-five miles 
 thick, and that the neutral zone is at the depth of about ten 
 miles from the upper and fifteen from the lower mean level. 
 Consequently, where the tract is compressed, it is easily seen 
 that the thicknesses of the elevated and depressed portions 
 above and below the mean levels will be in the same ratio, 
 viz. of 2 : 3. Since the compression along the tract acts in a 
 line which falls within the crust it will not have any tendency 
 to open fissures, but on the contrary to prevent their being 
 formed or to close them if they exist, so that the subjacent fluid 
 will not as a rule gain access to, and overflow, the depressed 
 parts (b) of the upper surface. 
 
 92 
 
132 
 
 DISTURBED TRACT. 
 
 [CH. X. 
 
 In the diagram suppose compression to have taken place by 
 a movement of RS towards PQ. A portion of the crust will 
 
 Scale T V of an inch to 5 miles. 
 
 The upper line 00 is the sea level. 
 
 The upper broken line is the upper mean level. 
 
 The middle broken line is the neutral zone. 
 
 The lower broken line is the lower mean level. 
 
 A the volume above the sea level. 
 
 the volume below the lower mean level. 
 
 G is the centre of gravity of the tract. 
 
 The thickness of the crust is about 25 miles. 
 
 The length PR is 400 miles. 
 
 The height of A above the sea level is 5 miles. 
 
 The length of the compressed portion is here represented as about 100 miles. 
 
 have become thickened, accompanied with internal corrugation 
 and disturbance : and the thickening will die out gradually 
 towards R8. This corrugated portion is represented in the 
 diagram as about 100 miles across, but it would have been 
 better had space permitted to have drawn it wider. 
 
 If the neutral zone between PQ and US were now to main- 
 tain its horizontality, we should have the volume elevated above 
 the mean line PR : that depressed below the mean line 
 QS :: 2 : 3. 1 Such a condition of horizontality would require 
 that S (fr) = and 2 (a) = 0. It would also give for the condition 
 of floating equilibrium, 
 
 2 (o) - 2 ft) _ . 
 
 which would require that -- - = f , or 0'666, and the subjacent 
 
 fluid would need to be f times as dense as the crust. This is alto- 
 gether unlikely. We have on the other hand hitherto assumed, 
 
 1 p. 135. 
 
CH. x.] DISTURBED TRACT. 133 
 
 on grounds likely to make cr too large, that - = 0'104. The 
 
 crust must then be so rigid that it cannot bend or break (and 
 the points Q and S are not fixed points, but may retreat from 
 one another so as to give any requisite smallness to the curva- 
 ture of the bent tract between them) or else it must either bend 
 or break, and hollows corresponding to 2 (b) be formed in which 
 the ocean would exceed the average depth. It is not likely, 
 from the nature of the case, that any will be formed below, 
 belonging to the series 2 (a). It will consequently take such 
 a position as indicated in the diagram, in which the condition 
 is intended to be approximately satisfied that 
 
 The volume A above the ocean level is supposed in the 
 diagram to be about five miles high. 
 
 Here then we have exhibited the primary idea of the forma- 
 tion of a mountain ridge according to our theory. 
 
 Let us next proceed to enquire what effects would be pro- 
 duced upon our tract by denudation, and the transference of 
 sediment. 
 
 It has been shown that 
 
 2 (a) - 2 (b) = ^^Me -f ^ (SZ - 2 (d)}. 
 
 (7 <J 
 
 Hence 2 (a) is always greater than 2 (b) ; so that even if 
 sufficient material was denuded off 2 (a) and carried into 2 (b) 
 to completely fill it up, 2 (a) would not have been all carried 
 away. This shows that, when once an elevated tract has been 
 formed, it must be permanent. The presence of an ocean 
 also, since the term in p is necessarily positive, will render the 
 excess of 2 (a) over 2 (b) greater than if there were no ocean. 
 
 It does not however follow that, after 2 (b) is filled up, 
 2 (a) may not be denuded down below the ocean level, which it 
 must be carefully remembered is distinct from, and above, 
 the upper mean level. All that we assert is that an elevation 
 
134 DISTURBED TRACT. [CH. x. 
 
 once formed must be permanent above the mean level, so far as 
 denudation can affect it. 
 
 In the position which the tract has now assumed, there will 
 be at first a certain amount of residual horizontal pressure 
 at PR and QS, because the rigidity of the crust opposes a 
 resistance to the horizontal thrust, which is only able to distort 
 it to a certain degree. Since however, with sufficient time 
 allowed, any substance not absolutely rigid will gradually yield 
 to distortion under the action of pressure, we may assume that 
 eventually the pressures at PR and QS will disappear, and the 
 mass of the tract be under the action of the vertical forces only; 
 and that these will be in equilibrium. 
 
 As we have drawn our diagram the centre of gravity of 
 the mass bounded by PQ and RS will be at G. And since the 
 resultant of the vertical forces acts through G t it follows that 
 if the cross stresses atPQ and RS are just such as the crust will 
 bear, and equal, G will be equidistant from PQ and RS. 
 
 We have now arrived at the conception of a ridge, of which 
 our diagram represents a section, steeper upon one side, say the 
 west, than upon the other, the east. It is bordered by an 
 ocean upon either side. The ocean extends beyond the limits 
 of the tract disturbed, which is defined by P and R, and is 
 there of its average depth. But there are channels, corre- 
 sponding to 2 (6), running parallel to the ridge, where the 
 
 In this diagram the vertical scale is double the horizontal. The latter is 
 somewhat reduced from the scale of the previous diagram. 
 
 The shaded part is the sediment. 
 
 The ocean level is omitted ; and no attempt has been made to represent the 
 changes of level, which, although of the greatest importance, would have been 
 scarcely visible upon the figure. 
 
CH. x.] DISTURBED TRACT. 135 
 
 ocean is abnormally deep ; and of these the deeper is upon the 
 side where the ridge is steeper. That this will be the case 
 is obvious, on account of the position of the centre of gravity of 
 the tract being half way between PQ and US. 
 
 When atmospheric influences begin to act on the ridge, and 
 denudation comes into play, we may expect that the principal 
 and longer streams will be formed on the east side, which is 
 less steep. The crest of the ridge will then be lowered, the 
 basset edges of the contorted strata exposed, and the material 
 removed will be deposited on the low grounds, and along the 
 shore line, more on the east side than on the west. 
 
 We must remember however that our diagram represents 
 only a section across an isolated ridge. But it will be proper 
 to contemplate the existence of other elevated tracts, which, 
 either by rivers flowing from them, or by ocean currents, or by 
 shore drifts, or by iceberg deposits, may contribute to the 
 deposition of sediment to the east of the ridge. For instance, 
 in the case of a section taken from Valparaiso to Buenos Ayres, 
 we should need to consider the sediment brought down by 
 the Eio de la Plata, which would not be derived from any 
 area crossed by the line of section. 
 
 In endeavouring to trace the mechanical results of such 
 denudation and deposition, let us call x the material denuded 
 off the ridge A, and z that brought from some distant region 
 and deposited along with x. If we assume the centre of gravity 
 of the tract to be originally at Gf, then the denudation of the 
 material x off A, and its transference towards the east, will shift 
 this centre towards the east. The deposition of the additional 
 sediment z, brought from a distance and deposited along with 
 or near x, will have a like additional effect. Let G' be the 
 position to which this centre is shifted. 
 
 If the crust were flexible, this would produce deformation, 
 and an alteration of curvature on either side of G'\ but it 
 would not tend to cause rotation. Since however it is only 
 partially flexible, the deformation will proceed as far as the 
 forces acting will carry it, and when they can bend it no further, 
 
136 DISTURBED TRACT. [CH. x. 
 
 it will afterwards behave as if it were rigid. Suppose at this 
 stage that the centre of gravity of the displaced fluid is brought 
 to H. This point will evidently be to the east of G. The 
 upward pressure of the fluid at .//will tend to produce rotation 
 round G', raising the tract to the west, and depressing it towards 
 the east. One of two effects may be expected to result. Either 
 the crust will break off at US and perhaps also at PQ, where 
 before the change of pressure it was only just able to bear 
 the downward stress, or else, as in the diagram, the limits of the 
 depressed tract will be shifted eastward to P'Q' and R'S'. In 
 either case, an additional volume of the crust will be depressed 
 into the fluid towards the east, and the effect will be, that 
 the centre of gravity of the displaced fluid will be also shifted 
 towards the east ; in which direction it will move, until equili- 
 brium is restored by its arriving beneath G'. 
 
 The centre of gravity of the tract will thus continually 
 travel eastwards, as more and more sediment is deposited in 
 that direction. And since the centre of gravity is the point, 
 about which the tract will tend to rotate under the action of 
 the shifted and of the additional weight above, and of the fluid 
 pressure beneath, it follows that, if the ends of the tract at P Q 
 and RS are not tilted upwards and downwards, as would happen 
 if the tract were rigid, there will be a kind of wave of eleva- 
 tion travelling from west to east, whose crest will carry with it 
 the centre of gravity of the tract. We see then a priori that 
 the region which receives the sediment from A will sink, 
 but at the same time A from which it came will rise, and 
 if there be additional sediment brought from distant regions, 
 these effects, not only the sinking of the sedimented parts, but 
 the rise of A, will be intensified. We might even expect, that 
 some of the sediment earliest deposited nearest the west, might 
 be raised above the ocean by this rotational action alone. 
 
 We will now endeavour to obtain a somewhat closer insight 
 into the character of the movements, in doing which we shall 
 for simplicity neglect the weight of the ocean. 
 
 If a mass floats in a fluid, as we have supposed our tract 
 virtually to do, the densities being respectively p and <r, we 
 
en. x.] DISTURBED TRACT. 137 
 
 know that, whether the mass be rigid or not, 
 
 p x whole volume <rx volume immersed. 
 
 And, since the centres of gravity of these volumes must be in 
 the same vertical, if we multiply each side of the above by 
 the distance of its corresponding centre from any assumed 
 vertical we have, considering the moments about that vertical, 
 
 p x moment of whole volume = cr x moment of volume immersed. 
 
 Let A be the volume which before denudation stood above 
 the ocean level, and, as already supposed, let a mass no be 
 denuded off it, and carried down towards the east, and let 
 another mass z be also brought from a distance and deposited 
 along with x. This, as has been explained, will tend to depress 
 the tract on the eastern side, and to raise it on the western, 
 and our object is to determine as far as possible the situations 
 and amounts of the depression and elevation. 
 
 Let y 2 be the additional volume of crust depressed beneath 
 the lower mean level on the eastern side, and y l the volume by 
 which the portion previously depressed is now diminished on 
 the western side. The whole volume beneath the lower mean 
 level will now be /3 y^ + y^ . 
 
 Let us call the horizontal distances, from the assumed 
 vertical, of the centres of gravity of the volumes A, x + z, y l} 
 2/ 2 , respectively A, x, y lt y z . 
 
 Let B be the volume of the tract which is exclusive of A, 
 and /3 the volume at first below the lower mean level ; B and ' 
 j3 the distances of their centres of gravity from the assumed 
 vertical line. Then the relation just proved gives us, before 
 the transference of sediment, 
 
 p(A.A+B. B) = <rp. /3. 
 
 After the transference of x and deposition of z, A becomes 
 A x, and we may suppose the distance of the centre of 
 gravity of the diminished A to be unaltered by this change. 
 B and B remain as before. /9 is diminished by y^ and increased 
 by 7/ 2 . Hence the relation of the moments will now be 
 
138 DISTURBED TRACT. [CH. x. 
 
 whence, subtracting, 
 
 p {(as + z) x - xA] = a- Q/ 2 # 2 - 7/^J. 
 
 If then we assume the vertical to pass through the centre 
 of gravity of the volumes y^ and 7/ 2 , the second side will vanish, 
 and we have 
 
 (x + z) x = xA. 
 
 This shows that the centre of gravity of the mass x before 
 its removal, and of x + z after their deposition in their new 
 position, is in the same vertical with the centre of gravity of y^ 
 and 2/ 2 . Hence we can find the position of the centre of gravity 
 of these latter volumes but not the position of the volumes 
 themselves. It shows that the centre of gravity of y^ and y 2 
 travels eastward at exactly the same rate as that of x before 
 denudation and x + z after deposition. 
 
 We may next compare the rate at which the centre of 
 gravity of the whole tract travels, relatively to the vertical 
 through the centre of gravity of y lt y 2 . For if M be the mass 
 of the whole tract before the transference and deposition of 
 sediment, and consequently M + z afterwards, M, M' the dis- 
 tances of their centres of gravity from an assumed vertical, 
 then we have at first 
 
 M.M = xA + B.B', 
 and afterwards 
 
 But if we measure from the vertical which passes through 
 the centre of gravity of y L , y z , we know that 
 
 x A (x-\-z)Xy 
 
 If * = 0, then M' = M. 
 
 So that by the transference of oc alone, the centre of gravity 
 of the whole mass remains at a constant distance from the 
 vertical through that of y^y^ not depending upon the amount 
 of x. 
 
CH. x.] DISTURBED TRACT. 139 
 
 If z is considerable compared to M, we see that M! is less 
 than M, and the centre of gravity after transference is nearer to 
 the vertical through that of y t , / 2 than it was before. But since 
 M must be always much larger than z, it will not approach very 
 near to it. For instance, even if z = \M, M' would be f If. 
 
 This result shows that the rotation round 6r', which will 
 depress the centre of gravity of sc + z, would not be likely to 
 bring up any of this sediment above the sea level, unless x + z 
 was spread out very thin, so that its western boundary con- 
 siderably overlapped the point Gr'. 
 
 But although an elevatory effect upon the newly deposited 
 sediment can hardly be expected to result from the rotation 
 of the tract round 6r', nevertheless there is a further considera- 
 tion which leads us to expect that this consequence will follow 
 upon the transference of sediment from a distance, for the 
 following reason. 
 
 It is evident that we must regard the tract under considera- 
 tion, whose volume was kl (1 + e) before it received the new 
 accession z y as now become Id (1 + e) 4- z. Hence, if S (a) and 
 S (6) become now 2 (of) and S (ft) we have, neglecting the 
 effect of the ocean 1 
 
 We see then that the absolute volume above the upper 
 mean level, and therefore probably also above the ocean, is in 
 
 consequence of the accession of z increased by - - z t or by 
 about -Jth of the new accession of material to the tract. 
 
 In a similar way it appears that the volume below the 
 lower mean, or y z y^ must be increased by - z, or by T 9 oths of 
 
 the hew accession. Although therefore there will be an ad- 
 dition to the absolute volume above the upper mean level, and 
 
 1 See the last equation on p. 116. 
 
DISTURBED TRACT. [CH. 
 
 possibly above the ocean, there will be at the same time an 
 addition of about nine times as much to the volume below the 
 lower mean. Or nine-tenths of the sediment brought down 
 will disappear from view. This explains how it is, that much of 
 the enormous quantity of sediment brought down by a great 
 river appears to be. as it were swallowed up in a bottomless 
 abyss. It will be recollected, that this was one of the facts 
 primarily adduced to show a priori the improbability of an 
 entirely solid earth 1 . 
 
 We appear to have now learnt all we are able about the! 
 character of the movements produced by the transference of 
 the sediment. We cannot find the actual positions of the 
 volumes y^ and y^ because these will depend upon the degree 
 of rigidity of the crust. And even if we knew what this is, 
 the determination would probably be impracticable. However, 
 we can see that the less readily the crust replies by bending or 
 breaking to the altered strain upon it, the less the curvature 
 will be altered, and therefore the further will be the centres of 
 2/ x and y z from the axis of rotation of the tract. 
 
 A consequence of the rotation round Q-' will be to give the 
 tract a certain degree of inclination, or "hang" towards the east, 
 so that the resultant pressure of the fluid will have a certain 
 amount of eastward direction ; and in assuming the new 
 position of equilibrium there will be a general shifting of the 
 whole tract eastwards. The result (and it is a very important 
 one) will be to subject the crust in the region of y^ to tension, 
 which will possibly open fissures downwards on the western side 
 of the ridge. 
 
 The smaller the distance apart of y v y 2 , the greater this 
 "hang" will be for given values of them. 
 
 It is evident that the existence of y lt the uptilted volume, 
 depends entirely -upon the crust possessing a certain degree 
 of rigidity. If there were no rigidity there would be no tilting. 
 A certain additional rigidity will be imparted to the tract as 
 a whole, by the existence of a considerable ridge, which, with 
 
 1 p. 81. 
 
CH. X.] 
 
 DISTURBED TRACT. 
 
 141 
 
 its accompanying depression, will act as a brace to prevent 
 bending, strengthening the tract in the neighbourhood of the 
 quasi fulcrum at the centre of gravity. 
 
 The removal of material off A by denudation, independently 
 of its subsequent deposition towards the east, will have the 
 effect of shifting G to the east, and causing the ridge to be lifted 
 by the pressure of the fluid beneath. The mere degradation of a 
 mountain chain, without taking into account the tilting caused 
 by the weight of sediment in the bordering hollows, would 
 consequently be accompanied by a corresponding rising of that 
 part of the mass. 
 
CHAPTEE XL 
 
 THE REVELATIONS OF THE PLUMB-LINE. 
 
 Mountains the " backbones " of continents They have "roots " These are revealed 
 by the plumb-line Pratt' ' calculation of the attraction of the Himalayas 
 The actual attraction less than that calculated His attempted explanation of 
 the discrepancy Sir G. B. Airy's explanation more satisfactory Prates 
 reply shown to be inconclusive The result confirms the reasoning of the 
 preceding chapter The plumb-line reveals a greater density beneath oceans. 
 
 WE have now arrived at a point at which we may begin to 
 test our theories by comparing the results of them with ob- 
 served phenomena. 
 
 In noticing the section on p. 132, which is roughly drawn to 
 scale, we are at once struck with the importance assumed by a 
 mountain range with reference to a continent, when the de- 
 pression below the lower mean level is taken account of, as well 
 as the elevation which appears above the level of the sea. The 
 latter has been usually regarded as the sufficient expression of 
 the magnitude of the range, and the importance of the highest 
 mountains has accordingly been minimized, and they have been 
 called mere wrinkles upon the surface of the globe. Wrinkles 
 no doubt they are , but they must be regarded as thicker, than 
 they appear above ground to be, in the ratio of perhaps 5 to 2, 
 and they may be fairly called the backbones of continents. 
 
 According to the consequences which we have traced, as 
 resulting from their denudation, we are also led to look upon a 
 mountain range as truly the parent of a continent, and to 
 
CH. xi.] THE REVELATIONS OF THE PLUMB-LINE. 143 
 
 consider the latter as gradually evolved out of the former: so 
 that, even if there is no present range of sufficient altitude to 
 be dignified as a mountain chain, such must have at some 
 former time existed. 
 
 We also see why a range of mountains as a rule skirts an 
 ocean shore, or at least did so when it was first formed. And 
 we also see why it usually presents its steeper face towards the 
 ocean. 
 
 It is not a little remarkable that popular expressions, even 
 when grounded on no scientific basis, have often a foundation 
 in truth which justifies them. Such an expression is that 
 which speaks of the " roots of the mountain." This is amply 
 justified by our theory; for every mountain must possess a 
 corresponding protuberance projecting downwards into the 
 fluid substratum. 
 
 These roots of the mountains, though they cannot be seen, 
 can in a most remarkable manner be felt by the plumb-line; 
 and this certainly affords a strong support to the truth of our 
 theory. "The attraction of the Himalaya Mountains, and of the 
 elevated regions lying beyond them, has a sensible influence 
 upon the plumb-line in North India. This circumstance has 
 been brought to light during the progress of the great trigono- 
 matrical survey of that country. It has been found by triangu- 
 lation that the difference of latitude between the two extreme 
 stations of the northern division of the arc," that is, between 
 Kalianpur and Kaliana, "is 5 23' 42"*294, whereas astronomical 
 observations shew a difference of 5 23' 37"'058, which is 5"'236 1 
 less than tbe'former 2 ." The latitude of Kalianpur is 24 7' 11" 
 and that of Kaliana 29 30' 48". 3 
 
 It having thus appeared that the plumb-line was attracted 
 at the station near the mountains in a direction towards the 
 
 1 "This is the difference as stated hy Colonel Everest in his work on the 
 measurement of the meridianal arc of India published in 1847, See p. clxxviii." 
 
 2 "On the Attraction of the Himalaya Mountains, and of the elevated regions 
 beyond them upon the Plumb-line in India." By the Venerable John Henry 
 Pratt, M.A., Archdeacon of Calcutta. Phil Trans, of Royal Soc. Vol. 145, 
 p. 53. 
 
 3 Ibid. p. 56. 
 
144 THE REVELATIONS OF THE PLUMB-LINE. [CH. xi. 
 
 mountains, thereupon Archdeacon Pratt set himself what ap- 
 peared the Herculean task of actually calculating what the 
 effect of the attraction of that great mountainous region ought 
 to be, and in a second paper upon the same subject he says, 
 " My calculation has been before the public three years ; and, 
 though some small numerical errors have been detected, they 
 are not of sufficient importance to affect the result; and the 
 data I have every reason for believing to be correctly taken, as 
 the Surveyor-General who first called my attention to the 
 subject in 1852, as an unsolved difficulty in the operations of 
 the great Trigonometrical Survey of India has been requested 
 to forward to me any corrections which may appear to him to be 
 advisable, and none have been sent 1 ." The result at which he 
 arrived was, that the attraction of the mountainous region 
 ought to have made, between the true and astronomically ob- 
 served differences of latitude of the extreme stations, a dis- 
 crepancy of 15"*885 instead of 5"'236 as it did. That is to 
 say, the effect of the attraction of the mountains was in fact 
 considerably less than it ought to have been, according to what 
 their mass above the sea should produce, taking 275 from 
 Maskelyne's determination for Schehallion for the density of 
 the attracting mass. Thus the mountains' attraction not only 
 accounted for the discrepancy discovered by the Survey, but 
 accounted for too much. They ought to have attracted the 
 plumb-line more than they did. 
 
 The Archdeacon then applied himself to explain this un- 
 expected anomaly, and the conclusion he came to in his first 
 
 paper was, that the assumed ellipticity was too large for 
 
 oUU'o 
 
 the Indian arc, the curvature there having been, as he thought, 
 probably increased by the upheaving of the mountains. This 
 would have the effect of making the difference calculated upon 
 the triangulation larger, so as to compensate for the effect of 
 the mountains 2 . 
 
 1 Second Paper by Archd. Pratt, Phil. Trans, of Royal Soc., Vol. 149, p. 746. 
 
 2 If X be the amplitude of the arc (i. e. the difference between the latitudes 
 of its extreme stations), I its length, p the latitude of its middle point, and e the 
 
CH. XL] THE REVELATIONS OF THE PLUMB-LINE. 145 
 
 However the very next paper in the Phil. Transactions 1 
 disposes of the difficulty in a very satisfactory manner. It 
 was communicated by the late Astronomer Royal about a year 
 after Archdeacon Pratt's great paper appeared. This paper is 
 short and simple, and with the author's permission the following 
 passages are extracted from it. 
 
 ''Although the surface of the earth consists everywhere of a 
 hard crust, with only enough of water lying upon it to give us 
 everywhere a couche de niveau, and to enable us to estimate the 
 heights of the mountains in some places, and the depths of the 
 basins in others; yet the smallness of those elevations and 
 depths, the correctness with which the hard part of the earth 
 
 ellipticity, the usual formula is 
 
 length of arc (Z) 
 
 sm X cos 2,.). 
 
 equatorial radius (a) 
 X is also affected by the mountain attraction, wilich w may call H. 
 Consequently 
 
 X=/(a, I, ju, H, e). 
 
 Consequently if the observed value of X be not such as accords with the 
 usually assumed value of when H is determined, some different value of e may 
 be found which will bring X into accordance with its observed value. And this 
 is the mode in which Archd. Pratt proposed to explain the difficulty. 
 
 Eliminating a from the above equation by means of another measured arc, 
 the latitude of whose middle point is M, he obtains the following approximate 
 formula : 
 
 de _<fo 2 
 
 ~^ 3 (cos 2/ji - cos 2J/) * 
 
 In order to give this as small a value as practicable he takes the Eussian arc 
 for the other, for which M=70, and after applying the formula to the case 
 in hand, finds 
 
 = 39585 = 132 ' 
 if we put ^^5- for e. 
 
 "Hence for an error of 5" '236 in defect in the amplitude, the effect on 
 
 K.OQA - 
 
 the ellipticity will be to dimmish it by e = nearly, or by nearly y \ part 
 
 Loi &O 
 
 of its whole value under the most favourable circumstances." 
 
 1 "On the computation of the Effect of the Attraction of Mountain -masses 
 as disturbing the Apparent Astronomical Latitude of Stations in Geodetic 
 Surveys." By G. B. Airy, Esq., Astronomer Eoyal. Feb. 15, 1855. Phil. 
 Trans. Royal Soc., Vol. 145, p. 101. 
 
 F. 10 
 
146 THE REVELATIONS OF THE PLUMB-LINE. [CH. xi. 
 
 has assumed the spheroidal form, and the absence of any parti- 
 cular preponderance either of land or of water at the equator as 
 compared with the poles, have induced most physicists to sup- 
 pose, either that the interior of the earth is now fluid, or that it 
 was fluid when the mountains took their present forms. This 
 fluidity may be very imperfect, it may be mere viscidity; it may 
 even be little more than that degree of yielding which (as is 
 well known to miners) shows itself by changes in the floors of 
 subterraneous chambers at a great depth where their width 
 exceeds 20 or 30 feet, and this yielding may be sufficient for 
 my present explanation." 
 
 He then proves that a table-land, say of 100 miles broad 
 and two miles high, could not rest upon the surface of a crust 
 ten miles thick. 
 
 "Now I say that this state of things is impossible, the 
 weight of the table-land would break the crust through its 
 whole depth from the top of the table-land to the surface of the 
 lava" (which is merely used as a generic term for a heavier 
 subjacent non -solid material), " and either the whole or only the 
 middle part would sink into the lava." To prevent this happen- 
 ing, with the assumed dimensions, it would be necessary that 
 the cohesion of the rock should be sufficient to support a 
 suspended column of the same twenty miles long. " I need not 
 say that there is no such thing in nature. If instead of sup- 
 posing the crust ten miles thick we had supposed it 100 miles 
 thick, the necessary value of the cohesion would have been 
 reduced to th of a mile nearly. This value would have been 
 as fatal to the supposition as the other 1 ." 
 
 " Yet the table-land does exist in its elevation, and therefore 
 it is supported from below. What can the nature of its support 
 be ? I conceive there can be no other support than that 
 arising from the downward projection of a portion of the earth's 
 light crust into the dense lava; the horizontal extent of that 
 projection corresponding rudely with the horizontal extent of 
 the table-land, and the depth thus gained is roughly equal to 
 the increase of weight above from the prominence of the table- 
 land 2 ." 
 
 1 Ibid. p. 102. a Ibid. p. 103. 
 
CH. XL] THE REVELATIONS OF THE PLUMB-LINE. 147 
 
 It will be at once seen that this reasoning produces an 
 arrangement of the crust upon the subjacent fluid exactly 
 analogous to that which has been arrived at in the preceding 
 chapter. Of course we from our point of view cannot contem- 
 plate the independent formation of a table-land apart from 
 the downward projection, so that it should afterwards break and 
 form one. But it does not seem that it concerned Sir G. B. 
 Airy to show that the one cannot be formed without the other. 
 The object he had in view was to explain how this arrange- 
 ment of matter would produce a smaller deviation of the plumb- 
 line. He says, "It will be remarked that the disturbance 
 depends on two actions ; the positive attraction produced by the 
 elevated table-land, and the diminution of attraction produced 
 by the substitution of a certain volume of light crust (in the 
 lower projection) for heavy lava. The diminution of attractive 
 matter below, produced by the substitution of light crust for 
 heavy lava, will be sensibly equal to the increase of attractive 
 matter above. The difference of the negative attraction of one 
 and the positive attraction of the other, as estimated in the 
 direction of a line perpendicular to that joining the centres of 
 attraction of the two masses (or as estimated in a horizontal 
 line), will be proportional to the difference of the inverse cubes 
 of the distances of the attracted point from the two masses." 
 
 " Suppose then that the point C is at a great distance, where 
 nevertheless the positive attraction of the mass A, considered 
 alone, would have produced a very sensible effect on the astro- 
 nomical latitude, as ten seconds. The effect of the negative 
 
 CA S 
 attraction of B will be 10" x - and the whole effect will be 
 
 CB 5 CA 3 
 x - Trm -- > which probably will be quite insensible. 
 
 G-D 
 
 " But suppose that the point D is at a much smaller 
 
 10 2 
 
148 THE REVELATIONS OF THE PLUMB-LINE. [OH. xi. 
 
 distance, where the positive attraction of the mass A would 
 have produced the effect n". The whole eifect, by the same 
 
 , . , DB Z - DA* i DA 3 \ 
 
 formula, will be n x -- j^m - > or n x 1 1 -FT ) > an( l as m 
 
 DA 
 
 this case the fraction --r is not very nearly equal to 1, there 
 
 may be a considerable residual disturbing attraction. But even 
 here, and however near to the mountains the station D may be, 
 the real disturbing attraction will be less than that found by 
 computing the attraction of the table-land alone." 
 
 The extreme felicity of the above explanation of a remark- 
 able phenomenon and the lucidity with which it is stated must 
 be sufficient apology for the length of the extract. One remark 
 more must be added because it is very pertinent to the subject 
 and reasoning of the preceding chapter. "It is supposed that 
 the crust is floating in a state of equilibrium. But in our entire 
 ignorance of the modus operandi of the forces which have raised 
 submarine strata to the tops of high mountains, we cannot 
 insist on this as absolutely true. We know (from the reasoning 
 above) that it will be so to the limit of breakage of the table- 
 lands, but within those limits there may be some range of con- 
 ditions either way 1 ." We believe however that since this 
 passage was written geology has made some advance towards 
 explaining the modus operandi of the elevatory forces ; but the 
 proviso respecting the limits of breakage of the rocks is of great 
 importance and must not be forgotten. 
 
 Archdeacon Pratt replied to the Astronomer Royal's paper 
 three years later 2 . He brought against the explanation proposed 
 three objections, not one of which appears in the present state of 
 our knowledge to be of weight 3 . (I) It supposes the thickness 
 of the earth's solid crust to be considerably smaller than Mr 
 Hopkins concluded it to be. This objection has been disposed 
 of 4 . (2) It assumes that the crust is lighter than the fluid on 
 which it rests, whereas in becoming solid we should expect it to 
 
 1 Loc. cit. p. 104. 
 
 2 "On the Deflection of the Plumb-line in India, &c." Phil. Trans, Royal 
 Soc., Vol. 149, p. 745. 
 
 * Ibid. p. 747. 4 p. 22. 
 
CH. xi.] THE REVELATIONS OF THE PLUMB-LINE. H9 
 
 contract and become more dense. This argument is answered 
 by Mr Whitley's experiments 1 , and is contrary to Walters- 
 hausen's most reasonable theory 2 that the successive couches 
 increase in density according to their chemical composition. 
 (3) If every protuberance outside a thin crust must be accom- 
 panied by a protuberance inside down into the fluid mass, then 
 wherever there is a hollow as in deep seas in the outward 
 surface, there must be one also in the inner surface of the crust 
 corresponding to it ; thus leading to a law of varying thickness 
 which no process of cooling could have produced. But we 
 appeal to a mode of action, namely compression, which is quite 
 capable, in the case of a crust not perfectly soft and compres- 
 sible, of producing such surface hollows 3 and corresponding 
 downward protuberances, as we have explained in the preceding 
 chapter. In spite however of these three objections, which the 
 Archdeacon believed to be fatal to the form in which the 
 Astronomer Royal offered his explanation of a deficiency of 
 matter below the mountains, the Archdeacon adopts in the 
 remainder of this paper another form of the same theory, appa- 
 rently preferring it altogether to his former hypothesis of an 
 increased ellipticity for the Indian arc. 
 
 We have thus established our assertion that the roots of the 
 mountains can be felt by means of the plumb-line. 
 
 The converse proposition ought to be true, that where the 
 land is not elevated above the sea, there the heavier substratum 
 ought to be within a less distance of the surface, and the conse- 
 quence ought to be that attraction at the surface should be 
 greater. This also is known experimentally to be the case. 
 The subject is discussed by Archdeacon Pratt in the fourth 
 edition of his Figure of the Earth. He establishes the fact, but 
 raises upon it theoretical conclusions not warranted by geology. 
 There can however be no doubt that he has demonstrated the 
 existence of increased density beneath the oceans. He says 
 " in fact the density of the crust beneath the mountains must be 
 less than that below the plains and still less than that below the 
 
 1 p. 23. 2 p. 28. 3 p. 133. 
 
150 THE REVELATIONS OF THE PLUMB-LINE. [CH. xi. 
 
 ocean bed 1 . " That part of the theory" (of unequal radial con- 
 traction, which he proposes but we disbelieve 2 ) "which shows 
 that the wide ocean has teen collected on parts of the earth's 
 surface where hollows have been made by the contraction and 
 therefore increased density of the crust below, is well illustrated 
 by the existence of a whole hemisphere of water, of which New 
 Zealand is the pole, in stable equilibrium. Were the crust 
 beneath only of the same density as that beneath the surround- 
 ing continents, the water would be drawn off by attraction and 
 not allowed to stand in the undisturbed position it now occu- 
 pies." The greater density must then clearly exist ; but it will 
 appear in the following chapter 3 , that the phenomena are not 
 sufficiently explained by supposing the lighter crust thinner, and 
 the heavier substratum nearer the surface in those regions. 
 
 1 "Figure of the Earth." 4th Ed. Art. 192, pp. 201, 202. 
 
 2 p. 79. 3 p. 164, 
 
CHAPTEE XII 
 
 THE REVELATIONS OF THE THERMOMETER 
 
 Recapitulation of results of previous chapter Roots of mountains should be 
 revealed by phenomena of underground temperature Conditions upon which 
 the mean rate of increase of temperature will depend Rate greater in plains 
 and less in mountains Dr Stapff His observations on temperature of rocks 
 in St Gothard tunnel His explanation of the smallness of the rate Why 
 not satisfactory Effect of convexity of mountain upon the rate The rate 
 may be considered uniform above The conclusion from the premises is that the 
 mountain has roots The rate may be regarded as nearly uniform throughout 
 General method of determining the thickness of the crust at the sea-level, 
 and the melting temperature, from the rates beneath the mountain and the 
 usual rate Application to St Gothard Thickness of crust at sea-level and 
 melting temperature deduced numerically from the data The like for Mont 
 Cenis Results confirmatory of previous conclusions Considerations about 
 the oceanic areas How the water u retained there The thickness of the 
 sub-oceanic crust and its density, 
 
 WE have seen in the preceding chapter that certain results 
 of geodesy agree well with the conclusion arrived at in the 
 tenth chapter, that mountains have " roots," that is that there 
 is, for all regions elevated above the mean level of the crust, a 
 corresponding downward protrusion of the lighter material of 
 the crust into the heavier substratum. This is in substance the 
 same thing which Herschel expressed by saying that, "the 
 force by which continents are sustained is one of tumefaction 1 ." 
 According to our theory these roots will consist of the lighter 
 material of the crust, in an unmelted state, projecting into a 
 heavier molten fluid. The amount of this projection may be 
 roughly determined by the relative densities of the crust and 
 fluid, in the same way as if the crust floated without constraint 
 in equilibrium. For although, as we have argued in the tenth 
 
 1 See p. 76. 
 
152 THE REVELATIONS OF [CH. xn. 
 
 chapter, the partial rigidity of the crust will render this 
 assumption in strictness incorrect, yet the deviations from 
 accuracy consequent upon it cannot amount to anything con- 
 siderable when compared to the whole thickness; and this 
 will be especially true in the neighbourhood of the chains, near 
 which the centre of gravity of a disturbed tract will lie ; and 
 which will therefore be least depressed or elevated by any slight 
 tilting action. 
 
 If this be a true statement of the case, then the existence 
 of these roots ought to be revealed in another and entirely 
 distinct manner, namely by the phenomena of underground 
 temperature. Where the roots of the mountains are in contact 
 with the molten fluid, they must be slowly and gradually 
 becoming fused. At other localities, where there is no such 
 protuberance, the bottom of the mean crust must either remain 
 sensibly at a permanent temperature, which will be that of 
 solidification (the same as of fusion), or else it will be slowly 
 and gradually freezing, and growing thicker. At all localities 
 we shall therefore have, maintained at the bottom of the solid 
 crust, sensibly the melting temperature of the materials of 
 which the crust is there composed, modified perhaps by the 
 difference of pressure at their different depths, which we need 
 not for the present purpose consider. 
 
 Now it is evident that, if the two surfaces of a plate of any 
 substance are maintained at two different constant tempera- 
 tures, the mean rate of increase of temperature within the 
 plate will depend solely upon its thickness irrespectively of its 
 conductivity. The mean rate therefore of increase of tempera- 
 ture within the crust, at any locality where we may suppose 
 these conditions approximately fulfilled, will depend upon the 
 difference of the temperatures of its upper and under sur- 
 faces at that locality, and on its thickness, and not upon the 
 conductivity of the -material, nor upon the absolute tempera- 
 tures. For although contortions in the bedding, or difference 
 of composition, may affect the rate as between one level and 
 another at that locality, still they will not affect the mean rate. 
 Nor yet need such geological accidents be considered in com- 
 paring the mean rate at one place with that at another. The 
 
CH. xii.] THE THERMOMETER. 153 
 
 result is that the mean underground rates at all places at. the 
 same height above the sea, and where the mean annual surface 
 temperature is the same, ought to be equal, irrespectively of 
 the nature of the rocks, provided only that the temperature at 
 the bottom of the crust is the same. 
 
 But if on the other hand the heights of two localities be 
 different, the mean rates there ought to differ, not in inverse 
 proportion to the heights above the sea, but approximately in 
 inverse proportion to the total thicknesses of the crust, in- 
 cluding the roots down to the molten substratum. Is there 
 any reason to believe that this is the case ? If we find it to be 
 so, we shall have a presumption, in favour of our theory, not 
 only that there is a downward protuberance of lighter material, 
 as already shown to be corroborated by geodesy, but that this 
 protuberance consists of unmelted crust projecting into molten 
 fluid. 
 
 Of course the above reasoning requires the state of tempe- 
 rature to be sensibly permanent, and that a sufficient time 
 should have elapsed, since the mountains were elevated, for the 
 heat brought up from below along with the uplifted matter to 
 have become so far dissipated, that the flow of heat through 
 the crust has become steady. 
 
 Mr Mallet, in his paper on Volcanic energy 1 , refers to a 
 dissertation, which he considers " the most complete and valua- 
 ble collection and discussion of all the observations on record 
 up to June, 1836," by A. Yrolik, who, he states, " believes it 
 proved, that in general the rate of increment is greater in 
 plains and valleys than in mountains." 
 
 The great engineering achievements of the present time 
 have afforded exceptional facilities for testing this question ; 
 and the above statement has been found to be strictly true. An 
 extensive series of observations was carried out more especially 
 in connection with the construction of the tunnel through the 
 Alps at Mont St Gothard, by Dr F. M. Stapff, geological engineer 
 
 1 Phil. Trans. Eoyal Soc., Vol. 163, p. 158. 
 
 The title of the dissertation is "Disputatio physica Inauguralis de Galore 
 telluris infra superficiem augescente." 4to., 101 pages. Miiller, Amsterdam, 
 1836. 
 
154 THE REVELATIONS OF [CH. xn. 
 
 to the company; and very interesting results were obtained, 
 which are recorded in his published papers 1 . 
 
 Dr Stapff points out that the rate of increase of temperature 
 beneath the mountain differs from that beneath the plane surface, 
 and gives it as his opinion that the influence which the mass of 
 the mountain superimposed, and free on each side, exercises on 
 the temperature of the rocks, is very different from that which 
 an envelope would exercise, formed of the crust of the earth of 
 a thickness equal to the height of this same mass 2 . This con- 
 clusion is ostensibly corroborated by the fact, that the augmen- 
 tation of temperature is observed to be more rapid beneath the 
 hollows and flat spaces of the open surface above the tunnel 
 than beneath the summits. 
 
 It may however be shown that the contour of the mountain 
 cannot account for a general rate of increase of temperature 
 beneath it so much slower than the usual one. The mean 
 rate at Mt St Gothard for the whole tunnel is found by Dr 
 Stapff to be 0'0206 C. per metre of descent, which is about 
 ^g degree F. per foot 3 . This is little more than half the 
 usual rate of increase. The rate was found to exceed this 
 mean on the north more often than on the south side of the 
 mountain. 
 
 To estimate roughly the effect which the contour of the 
 mountain would produce in lowering the rate of increase, we 
 may argue thus. As we ascend in the atmosphere the tempe- 
 rature decreases. The temperature of the summit of the moun- 
 tain is found to be zero centigrade, or the freezing-point. 
 Calculate then the altitudes at which the observed rate at 
 
 1 " Studien iiber die Warmevertheilung im Gotthard." Bern, 1 877. " ]tude 
 de 1'Influence de la Chaleur de 1'Interieur de la Terre sur la possibility de con- 
 struction des Tunnels dans les hautes Montagnes. Premiere partie, 1879. Do. 
 deuxieme partie, 1880. Eevue universelle des Mines, etc. Annuaire de 1' Asso- 
 ciation des Ingenieurs." Paris, 9, Hue des Saints-Peres. Londres, 5, Bouverie 
 Street. Liege, 24, Hue d'Archis. "Bepartition de la temperature dans le grand 
 tunnel du St Gothard. Annexe xiv au volume vm des rapports trimestriels du 
 Conseil federal sur la marche des travaux du chemin de fer du St Gothard 
 (rapport N. 30)." 1880. 
 
 2 "Iiltude de 1'Influence de la Chaleur de I'lnt^rieur de la Terre," &c., p. 2. 
 
 3 The factor which reduces the former to the latter system of units is 
 0-548. 
 
CH. XIL] THE THERMOMETER. 155 
 
 equal horizontal distances along the tunnel would bring us to 
 the freezing-point within the rock supposing it extended to a 
 sufficient height, and draw a curve through these points, which 
 will touch the summit of the mountain. This curve will define 
 what may be called the effective profile of the mountain, that 
 is to say, the form of outer surface, which would give the same 
 temperatures within the mountain as actually exist, were the 
 temperature of the surface uniform. It will be seen that the 
 contour so obtained is very considerably less convex than the 
 actual contour. This shows that the real effect of the convexity 
 of the surface upon the internal temperatures cannot be so 
 great as at first sight it might appear likely to be. 
 
 The isogeotherms within the mountain will evidently con- 
 sist of a family of surfaces corresponding to the external effective 
 profile, but decreasing in convexity with increasing depth. 
 Eventually a plane horizontal isogeotherm will be reached. But 
 it does not follow that the isogeotherms will continue to be 
 planes beneath it. 
 
 Let 8 be the area of one of these surfaces, through which 
 the same heat passes in a given interval of time as that which 
 crosses the area A of the plane isogeotherm in the same interval. 
 Let n be measured along the normal drawn to a point in the 
 surface $, v being the temperature at that point, and K the con- 
 ductivity. Then the flow of heat across the elementary area dS 
 will be 
 
 dv , 
 
 K-j-dS. 
 
 an 
 
 Properly speaking -=- will vary from point to point of the iso- 
 an 
 
 geotherm. But if we consider it to be the average rate along 
 the normal at every point of a given isogeotherm, then the flow 
 across the whole of that surface will be 
 
 dv 
 K-J- S. 
 an 
 
 But the same flow of heat crosses the plane area A, where 
 let us call r the average rate of increase of temperature in 
 descending ; wherefore the whole flow there will be tcr'A. 
 
156 THE REVELATIONS OF [CH. xn. 
 
 Hence we must have 
 
 Z.S-SA. 
 
 dn 
 
 , dv A , 
 and /. -j- = -~ r . 
 dn S 
 
 This gives the proportion according to which the average rate 
 along any normal to an isogeotherm is diminished in con- 
 sequence of the convexity of its surface. This rate will clearly 
 become more and more nearly equal to that through the plane 
 isogeotherm, as that is approached. 
 
 Now the whole length of the St Gothard tunnel is 14920 
 metres, and the greatest height of the mountain above it is 
 
 A 
 
 1127 metres. It is therefore obvious that the ratio -~ must be 
 
 & 
 
 nearly one of equality. Indeed, if we suppose the contour of the 
 
 surface of the mountain to be a segment of a circular cylinder, 
 
 ^ 
 
 we shall find that the value of -~ for the outer surface, where 
 
 o 
 
 that ratio will differ most from equality, will be 0*996. And 
 consequently, if we suppose that the temperature of this sur- 
 face is everywhere C. (an unfavourable supposition), then 
 
 This shows that the convexity of the mountain can only slightly 
 affect the rate along the vertical anywhere, and in the central 
 
 part, where -^- becomes -*- , scarcely at all. We are therefore 
 
 at liberty to regard the rate in the central part of the mountain 
 as very nearly constant and equal to r. 
 
 Now the temperature at the upper surface being C., if h 
 be the height of the mountain above the tunnel, and t the 
 temperature of the rock in the centre of the tunnel, the rate 
 
 t 
 
 n* - _ 
 
 h' 
 
 But at the depth where the plane isogeotherm is encountered 
 the temperature beneath the mountain must equal that of the 
 
CH. xii.] THE THERMOMETER. 157 
 
 neighbouring crust, because the isogeotherm is plane. It is 
 obvious therefore from geometry, the rates beneath the moun- 
 tain and at any place in the neighbourhood being both of them 
 uniform yet not the same, that this plane isogeotherm cannot 
 be elsewhere than at the bottom of the crust, unless the isogeo- 
 therms beneath the mountain become concave upwards after 
 the plane isogeotherm is passed. Suppose then the former to 
 be the case, and that k is the mean average thickness of the 
 crust, and k' its thickness beneath the mountain ; at which re- 
 spective depths (if the isogeotherm s beneath the mountain do 
 not become concave) the temperatures become equal. Then we 
 must have, 
 
 But observation shows that r is about Jr, 
 
 .-. &' = 2&; 
 
 or the height of the mountain above the mean level of the 
 crust would in such case be equal to the thickness of the crust. 
 This would make the crust far thinner than it can be admitted 
 to be ; and therefore shows that the isogeotherms below the 
 plane one must have a convexity downwards, answering to their 
 convexity upwards in the upper portion. There must therefore 
 be a protuberance of solid crust below corresponding to the 
 elevation of the mass above. We see then that we have here 
 an additional proof of the existence of roots to the mountains 
 derived from thermal phenomena. 
 
 The downward protuberance will be much greater than the 
 upward elevation, and therefore we perhaps ought not to assume* 
 that the extreme value of the ratio of A : S will be so nearly one 
 of equality below the plane isogeotherm as above it. But it is 
 probable that the downward protuberance, although it may be 
 ten times as deep as the other is high, will be very much wider, 
 because the St Gothard mountain is only a remnant, carved by 
 subaerial denudation out of a much more extended elevated 
 tract, with which the root was originally conterminous : and 
 whatever denudation, or what may be analogous to it, the roots 
 of the mountain range may have undergone, it is not likely 
 
158 THE REVELATIONS OF [CH. xn. 
 
 that their contour should be reduced to the semblance of in- 
 verted mountains and alternating valleys, like those which 
 characterise the upper surface of an Alpine region. The ratio 
 of A : S may therefore be still regarded as nearly one of equality 
 even in the lower portions. 
 
 If we are at liberty to regard the rate beneath the moun- 
 tain as approximately uniform, it is possible to estimate from 
 the data the thickness of the crust at a place on the sea-level, 
 and likewise the melting temperature at the bottom of it, if we 
 assume a ratio for the densities of the crust and fluid sub- 
 stratum. For generally let 
 
 c be the depth of a point in the crust from the surface, 
 a the temperature at that depth, 
 b the temperature at the surface, 
 r the rate of increase of temperature in descending. 
 Then we have the general relation, 
 
 a -I f 
 
 = r 
 
 If v be the rock-temperature in the tunnel, b' that at the top 
 of the mountain, ra the height of the mountain above the 
 tunnel, / the rate, we have in like manner 
 
 '-4-* . 
 
 whence r' may be obtained from the observed data. 
 
 Now suppose equation (1) to refer to some place A, any- 
 where near the sea-level, where the total thickness of the crust 
 is c, and the rate the usual one r. 
 
 Then . a = cr + b. 
 
 Similarly, if c' be the thickness of the crust at the mountain, 
 the temperatures at the bottom of the crust being the same 
 at both places because it is the melting temperature, 
 
 a = c'r' + b f . 
 
CH. XIL] THE THERMOMETER. 
 
 Consequently 
 
 159 
 
 (3). 
 
 In this equation r, r', 6, I' are known, and therefore, if 
 we can obtain another relation between c and c', we shall be 
 able to find the thicknesses of the crust at the place on the 
 sea-level and at the mountain. If we are at liberty to apply the 
 conditions of hydrostatic equilibrium, such a relation is easily 
 obtained, as shown on the left-hand side of the figure, from 
 which it appears that. 
 
 But from (3) we have 
 
160 THE REVELATIONS OF [CH. xn. 
 
 whence 
 
 r <r T b b' ,,>. 
 
 c=- - -h- , (4). 
 
 r r a p r r 
 
 If we assume a value for the ratio - , this expression gives 
 
 <7 
 
 the thickness of the crust at a place at the sea-level, where 
 the surface temperature is b, and the rate r. The place ought 
 not to be in the mountainous region, in order that the rate 
 may not be affected by the additional thickness of crust beneath 
 such a region. 
 
 Let us now apply equation (4) to find the thickness of 
 the earth's crust at a place at the sea-level, from the data 
 obtained from the St Gothard tunnel. In Table vili. of 
 Dr StapfFs paper 1 , the rate at the exact middle of the tunnel 
 is not given, but from the plate which illustrates his "Re- 
 partition de la Temperature" it can be found. The height 
 of the mountain above the sea over the middle point is there 
 seen to be 2839 metres, and the altitude of the tunnel itself 
 1127 metres. The temperature of the rock in the tunnel 
 is 30'8 C., and of the ground, at the summit of the mountain 
 above, C. Hence the rate is -fffi degree C. per metre, 
 which is nearly yj^ degree F. per foot. We will first assume 
 the rate at the place A at the sea-level to be -fa degree F. per 
 foot, and the mean surface temperature there to be 50 F. 
 Also if we take, as we have previously done, the ratio of p : a- 
 as that of granite to basalt, viz., 2'68 : 2'96, we find that 
 
 = 10'57. Then, expressing the altitudes in feet, we have 
 
 <r- p 
 
 for the values of our symbols, 
 
 51' T 102' 
 
 1 " liltude de 1'Influence de la Chaleur de 1'Interieur de la Terre, &c." p. 7. 
 See note, p. 154. 
 
CH. xii.] THE THERMOMETER. 161 
 
 -^-, = 1, -?-= 10-57, h = 9315, 
 r r cr p 
 
 r r 
 
 The thickness of the crust at the place A then comes out, 
 
 c = 96623 feet = 18'3 miles. 
 And for the melting temperature, 
 a cr + b 
 
 = 1944 F. 
 We also find for the thickness of the crust at the mountain, 
 
 c = ,- = 1913 x 102 feet 
 
 = 36'9 miles, 
 
 If however we assume ^ degree F. per foot as the rate 
 of increment of temperature at the place on the sea-level, 
 instead of ^ we then obtain for the thickness of the crust 
 there, 
 
 c^ 138032 feet 
 
 = 26-1 miles. 
 
 And for the melting temperature 
 a = 2350 F. 
 
 And for the thickness of the crust at the mountain 
 c = 235734 feet 
 = 44'6 miles. 
 
 The observations which were made upon the temperature 
 of the rocks in the Mont Cenis 1 tunnel, appear to have been 
 less systematic than in the tunnel through Mont S. Gothard. 
 The highest temperature recorded was 85 F. at a distance of 
 21000 feet from the southern opening, while the whole length 
 of the tunnel was 40094 feet ; so that that temperature oc- 
 curred at about the middle of the tunnel. At that point the 
 elevation of the tunnel above the sea was about 4391 feet, and 
 
 1 "Nature," Vol. iv. p. 36, p. 415, and p. 434. 
 F. 11 
 
1 62 THE REVELATIONS OF [CH. XH. 
 
 the greatest height of the pa ass of the Alps over the tunnel 
 was 5307 feet. If we assume the temperature of the rock 
 at the surface to be the freezing temperature, as in the case 
 of S. Gothard, the above data give / = j^-. And if we take 
 the rate at a place on the sea-level to be J T , and the tem- 
 perature there 50 F., these data, when introduced into" our 
 equation, give 
 
 c = 20'2 miles, 
 
 and a the melting temperature = 2141 F. 
 But if we take ^ as the rate at a place on the sea-level, then 
 
 c = 291 miles, 
 and a = 2612F. 
 
 The rates of increase of temperature have been found to 
 vary so much in different localities, that the rates at these 
 two tunnels, though so nearly the same (and yet they are 
 distant more than 130 miles), may differ somewhat from what 
 might prove to be the average, were a greater number of moun- 
 tains to be pierced. We may however feel assured that the 
 rates determined represent pretty accurately the true rates 
 at those places, because the amount of cover is so great, that 
 the average is obtained for a great depth ; a depth greater than 
 has been reached in almost any other artificial excavation 1 . 
 
 The results obtained in the present Chapter are decidedly 
 corroborative of the views put forward in the tenth Chapter 
 respecting the configuration of a section across a disturbed tract. 
 For it is not easy to see on what hypothesis the conclusion 
 regarding the downward convexity of the isogeotherms beneath 
 a mountain can be explained, except on that of a protuberance 
 of un melted into melted matter. Indeed the existence of such 
 roots to the mountain appears to be proved even more fully 
 by the argument from temperature, than by that from geodesy. 
 
 Again, the melting temperature at which we have arrived, 
 without making any assumption about the temperature at which 
 the rocks would melt, agrees very nearly with that of cast iron, 
 which is about that which has been assumed by the older 
 
 1 An Artesian well is said to have been carried down to the depth of 5500 
 feet at Potsdam, Missouri. "Investor's Guide," Feb. 1881, 
 
CH. XIL] THE THERMOMETER. 163 
 
 geologists as the probable temperature below the solid crust, 
 whence the usual estimate for the thickness of the crust has 
 been derived of about 20 miles. 
 
 But there is reason to think that the crust may be some- 
 what thicker, and consequently the temperature somewhat 
 higher than we have just estimated them, even on the showing 
 of our own formulae, and that for the following reason. The 
 value of c in equation (4) is increased if the ratio of a : p is 
 made more nearly one of equality. We have taken this ratio 
 to be that of basalt to granite, viz. 2'96 : 2*68 ; and the reason 
 why we have done so is because the denser eruptive rocks 
 are of the basaltic type, so that we may reasonably infer that 
 the heavier fluid substratum is, as regards mineral character, 
 a basic magma. But it by no means follows that, while not yet 
 erupted, it should be as dense as basalt. Indeed the probability 
 is in the other direction ; because if, as we believe, it is in a 
 condition of igneo-aqueous solution, its high temperature may 
 diminish its density. Whether the water-substance combined 
 with it will have such an effect will be hereafter discussed 1 . 
 
 There is yet another reason, though perhaps a less cogent 
 one, to lead us to suppose that we are taking the density of 
 the substratum too great, if we assume it equal to that of 
 basalt; for it has been already pointed out 2 that, according 
 to Laplace's law, the density of basalt would be found at the 
 depth of 100 miles, which is much more than that, at which we 
 should expect the temperature of fusion to commence. It 
 seems therefore almost certain that the value of a- is nearer 
 to that of p than it has been assumed to be, and the resulting 
 value for the thickness of the crust greater, and the tempera- 
 ture higher than those found; while the downward protu- 
 berance below the mountains will be also greater than estimated. 
 
 It is probable that the water, which is believed to be pre- 
 sent, will render the rocks fusible at a lower temperature, and 
 increase the liquidity of the magma. 
 
 Again we see, from the difference in the results for the 
 thickness and melting temperature according as we take -^ or 
 
 1 p. 190. 2 See note, p. 118. 
 
 112 
 
1 64 THE REVELATIONS OF [CH. xn. 
 
 $ for the average rate, that the question we are dealing with 
 is a delicate one, at the same time depending upon data about 
 which we have no very precise knowledge. The thickness may 
 therefore differ from the above results by a few miles, and the 
 temperature by a few degrees either way. But if we are led 
 to seek relief from the somewhat unexpectedly small values, 
 which we have obtained by using the rate ^-, for the thickness 
 of the crust, (because it will be recollected we have previously 
 assumed it at 25 miles 1 ) and of the melting temperature, it 
 seems on the whole that it is to be found rather in assuming a 
 lesser density for the substratum, than in assuming the lower 
 value g^ for the temperature rate 2 . But with every allowance 
 made for some uncertainty, it must be admitted that the 
 results at which we have arrived are singularly near what on 
 other grounds we may expect to be the truth, while no gra- 
 tuitous assumption has to be made in obtaining them. 
 
 It is also not unimportant that the two lines of argument 
 in the preceding and present chapters, so diverse in their cha- 
 racters and yet pointing in a like direction, are drawn from 
 observations made in regions as far apart as the Himalayas and 
 the Alps ; the conclusion from both being the same, namely 
 that there is a protrusion of the lighter material of the crust 
 into the denser subjacent fluid beneath the mountains in both 
 these regions. 
 
 If we assume that the relative densities of the crust and 
 subjacent fluid continue the same beneath the ocean as else- 
 where, a reference to the right-hand side of the figure gives for k, 
 the least thickness of the crust, which in this case will be 
 beneath the ocean, because it is everywhere thickened beneath 
 the continents, 
 
 p <r~ P 
 
 o--p 
 
 1 Chap. X. p. 126. 
 
 2 For reasons for supposing ^ T to be rather below than above the average 
 rate, see p. 16. 
 
CH. XIL] THE THERMOMETER. 165 
 
 With the values hitherto used for cr and p, 
 
 k = c-7S. 
 
 If we now give to S any value approaching to that of the 
 mean depth of the ocean, this will make the mean thickness 
 of the crust very much less than it can be in fact. Indeed if c 
 be less than about 25 miles, with the usual value 3'5 for 8, 
 k would be negative. 
 
 It is evident therefore that this assumption cannot be cor- 
 rect, and that the relative densities of the crust and fluid 
 beneath the oceanic areas cannot be the same as beneath the 
 continents. We must therefore examine this point. 
 
 Now it is certain that, whatever be the form or law of 
 density of the nucleus of the earth which is believed to be 
 solid, in any fluid strata which may occur above it, surfaces of 
 equal density will be also surfaces of equal pressure ; for this is 
 always true of a fluid in equilibrium under the action of such 
 forces as exist in nature. This therefore must be the case within 
 the fluid substratum. Let us then suppose that the depth 
 measured from the bottom of the crust to such a couche de 
 niveau, not far below the place A at the sea-level, is #, and 
 that the depth of the same couche below the bottom of the 
 crust under the ocean, where the crust has the mean thickness, 
 is x. And because the surface is one of equal pressure it will 
 be also one of equal density, and a- will be the same at both 
 these places. But the crust, being solid, may differ in density 
 at the two places. Let its density then be p' below the ocean, 
 where its thickness has the mean value k. 
 
 The surface of the ocean is likewise a couche de niveau. In 
 order therefore that the hydrostatic pressure may be the same 
 at the two places, taking the density of the ocean as unity, we 
 must have, considering gravity constant for a depth so small 
 compared to the radius, 
 
 8 + p'k + <rx' = pc + <TX. 
 But these couches de niveau may be considered parallel, 
 
 whence (a- - 1)8 + (cr -p')A?= (a- - p)c ....... .....(1). 
 
1 66 THE REVELATIONS OF [CH. xn. 
 
 This is the general relation upon our view of the constitution 
 of the outer parts of the globe, and suffices to explain the col- 
 lection of water in the oceanic areas, and it shews that the 
 crust beneath the ocean must be more dense than beneath 
 the continents, for if we make p r = p we get for k the value on 
 p. 164 which makes it much less than it can possibly be. This 
 greater density is in accordance with observations made with 
 the pendulum, by which it has been found that gravity has a 
 larger value at oceanic stations. 
 
 In order that the crust may not sink into the fluid we must 
 have p less than er. If then we put p a in (1), this gives a 
 limiting value for c and it is 
 
 <T-p 
 
 With the values previously assumed this gives 
 
 -028- 
 
 In this case k is of course indeterminate, for if the crust is 
 of the same density as the fluid its position of equilibrium will 
 be independent of its thickness. 
 
 With the same values for p and cr we may write 
 
 (2-96 -V)fc = 0'28c- 6-80. 
 
 This is the equation to a rectangular hyperbola, in which the 
 abscissa is the difference of the densities of the fluid substratum 
 and the sub-oceanic crust, and the ordinate the thickness of that 
 crust. 
 
 Since p cannot be greater than a or than, as assumed, 
 2 '96, (cr p)c must be greater than (<r 1) 8 ; or, as assumed, 
 
 0'28c > 6-86, 
 
 Or the thickness of the crust at the sea-level is not less than 
 about 25 miles. It will be noticed that this is the first time, 
 as far as the author is aware, that any estimate whatever 
 regarding the thickness of the crust has been arrived at entirely 
 independent of considerations of temperature. It is remarkable 
 
CH. XIL] THE THERMOMETER. 167 
 
 how well it agrees with the others previously made, in which 
 those considerations are involved. 
 
 Neither can p be less than p (or as assumed than 2'68). It 
 must therefore have some value between* this and a (or as assumed 
 2'96). Now if we suppose the sub-oceanic crust to consist of basic 
 crystalline rocks, their density approaches very nearly to that 
 of the basic eruptive rocks, and the probability is that cr p is 
 very small, and consequently k need not be small. But we 
 have reason to believe it to be smaller than c, because at the 
 locality A, which is continental, the crust has been probably 
 thickened by compression. Let us then assume c = 25 miles 
 and k = 20 miles. 
 
 We then obtain p' = 2*953, a value which would admit of 
 the sub-oceanic crust floating. This result is not unsatisfactory 
 considering that we are dealing with densities about which we 
 have no certain knowledge. It is probable that the absolute 
 values of all the densities have been taken somewhat too high. 
 
 It is impossible to attain accuracy in such estimates as we 
 have been engaged in making, but we may conclude as the 
 result of our inquiries, that the crust of the earth at a place 
 near the sea-level is about 25 miles thick; that beneath the 
 central parts of the ocean it is about 20 miles thick, or perhaps 
 less, and that it is more dense in those regions ; and that it is 
 by such increased density of the crust itself that the collection 
 of water is to be explained, and not by increased density in the 
 more deeply seated matter. 
 
CHAPTER XIII. 
 
 AMOUNT OF COMPRESSION. 
 
 Our ideas respecting the sub-oceanic crust necessarily speculative. Compression 
 possibly confined to continental areas. Compression might arise from extrava- 
 sation of matter from beneath the crust, or from expansion of the crust. 
 Amount of compression needs to be estimated afresh. Datum-level equation 
 transformed to mean level. Formula to egress compression in terms of 
 inequalities. Estimate of inequalities from Atlas (1) on supposition tliat 
 Oceans are due to compression, (2) that they are due to denser crust. 
 
 THE great problem of the Physics of the Earth's Crust is, 
 how to account for the compression which geology shows to 
 have affected, at one time or another, almost every portion of 
 the area of the surface with which we are acquainted. And 
 this latter expression itself suggests a large and difficult ques- 
 tion. To what extent are we acquainted with more than the 
 land surfaces of the globe ? It is hardly too much to affirm 
 that our ideas respecting the nature of the earth's crust 
 beneath the oceans are entirely derived by speculation from 
 geology. We cannot explore it directly ; but we know that 
 most of the strata of the exposed portions of the surface have 
 been deposited beneath seas, and from them we reason perhaps 
 wrongly by analogy concerning the rocks at present composiug 
 the entire ocean floor. For it is the conviction of a large 
 number of geologists 1 , whose judgment is of weight on such a 
 point, that the continents have always occupied the positions 
 which they now occupy : by which it must be understood, that 
 
 1 See a resume of the history of this theory in a short letter by Dana, 
 " Nature," vol. xxin., p. 410. 
 
CH. xiii.] AMOUNT OF COMPRESSION. 169 
 
 they have oscillated about their present positions, sometimes 
 more extended on one side and sometimes on another ; but that 
 the great oceanic areas and the great continental areas have 
 never, within times to which geological records go back, inter- 
 changed places. If this be a true statement of the case, then 
 it may be asserted that we know nothing about the geological 
 constitution of the earth's crust beneath the great oceans. We 
 can affirm from observation that all land surfaces have been 
 more or less subjected to compression, but we cannot affirm 
 with any certainty that the same has been the case with the 
 ocean bottoms. We appear in the present state of our know- 
 ledge to be free to speculate upon this point. It is possible that 
 the compression, which is so striking a feature in all true 
 mountain ranges, and is by no means confined to them, may be 
 a continental phenomenon only; that is, may belong only to 
 continents, and to islands which are geologically remnants of 
 continents. The results at which we have arrived at the end 
 of the last chapter tend to confirm this view, and to throw 
 more than a doubt upon the doctrine that the abnormal eleva- 
 tion, or radial excess, of the surface of dry land above the 
 ocean floor is due altogether to compression. We need not how- 
 ever decide at once upon this question, but, using general symbols 
 in our reasoning, leave it for the present open. 
 
 There are two ways in which compression may have acted 
 to elevate the crust, supposed to rest on a fluid substratum. In 
 the one the anticlinals would form ridges, whose sections would 
 be cusp-like and the subjacent fluid would rise into them. 
 This hypothesis has been discussed in the ninth chapter, and 
 has been shown not to accord with natural appearances. It is 
 one however which has been more or less assumed in many 
 geological writings 1 . The other is that developed in the tenth 
 chapter, and shown in the eleventh and twelfth to be capable of 
 explaining two classes of phenomena perfectly independent of 
 each other, but which, it may be observed, would be absolutely 
 reversed were the doctrine true, that the heavier and hot molten 
 liquid rises into the anticlinals. 
 
 1 See Prof. A. de Lapparent, "L'Origine des inegalites de la Surface du 
 Globe." Ilevue des Questions Scientijics. Juillet, 1880. 
 
1 7 AMOUNT OF COMPRESSION. [OH. xm. 
 
 We have then to seek for the cause of this compression, 
 which has effected the continental areas. 
 
 If we have given a sphere of a certain radius, whose outer 
 crust is solid and rests upon a fluid substratum, compression of 
 the crust may arise from contraction of the volume of the sphere, 
 either through cooling, or by the extravasation of some portion 
 of the matter which was originally beneath the crust. In these 
 cases the compression of the upper surface of the crust would 
 be equal to the contraction of the sphere; that is to say, if the 
 radius of the sphere before contraction was r + er, and after 
 contraction became r, e being the coefficient of contraction, then 
 the mean coefficient of compression along any line drawn upon 
 the sphere would also be e. If the length of the line after com- 
 pression was I, then before compression it must have been I + el. 
 
 But there may be another cause for the compression which 
 has elevated continental areas. The solid crust may have 
 expanded horizontally. It is quite possible that these two 
 causes of compression may have coexisted. The sphere may 
 have contracted, and the crust expanded simultaneously; in 
 which case the contraction of the volume of the sphere will be 
 no measure of the compression of the crust. 
 
 We have already made it apparent, that the cooling of the 
 earth considered as a solid sphere cannot account for the inequali- 
 ties, and therefore neither sufficiently for the compression of the 
 crust. And if we regard the crust as resting on a liquid sub- 
 stratum, it does not appear how its contraction through mere 
 cooling can have been so much greater than in the case of a 
 solid globe, as to account for what the latter will not explain. 
 We have therefore to examine whether other hypotheses will 
 more satisfactorily explain the phenomena. Bat it is obvious 
 that our first step, before we can reason at all about the com- 
 pression under the "condition of a fluid substratum, must be to 
 estimate its amount afresh : for the grounds upon which that 
 must be done are very different from those upon which we 
 formerly estimated the compression in the case of a solid 
 globe 1 . 
 
 1 See chap, v., p. 55. 
 
CH. XIIL] AMOUNT OF COMPRESSION. I/I 
 
 If we revert to the datum level equation (1) in the fifth 
 chapter 1 , which is perfectly general for a vertical section of 
 the crust under compression, and adapt it to volumes, as has 
 been done in equation (3) 2 , but retaining terms answering for 
 volumes to % (a) and S (/3) in equation (1), which terms we will 
 call 2 (X) and 2 (F), we then have, 
 
 87rr 2 ke = 2 (A) - 2 (B) + 2 (F) - 2 (X), 
 
 for our general datum-level equation of volumes for a solid 
 crust resting on a fluid substratum. And we know that in this 
 expression 2.(F) 2 (X) = 0. In this equation it will be recol- 
 lected that e is the mean linear compression of the crust, and 
 that the surface above which the volumes 2 (A), and below 
 which the volumes 2 (B), are reckoned, is the imaginary surface 
 which occupies the position that the upper surface of the crust 
 would occupy at the present time, had it been perfectly com- 
 pressible in a horizontal direction ; and that 2(-3T) and 2(F) are 
 the volumes similarly situated with respect to the lower surface 
 of such a crust 3 . Let .us now transform this equation to the 
 upper and lower "mean levels" of the crust, which by the defi- 
 nition will be at the same distance apart as the datum levels 4 . 
 
 In the same manner that A, B, X, Y are referred to the 
 datum levels, let A', B', X', Y be referred to the mean levels ; 
 and, in the figure, let in the first place the outer circle be the 
 lower mean level, and the inner one the lower datum level ; 
 
 1 p. 17. 2 p. 50. 
 
 3 p. m 4 p. 115. 
 
1 72 AMOUNT OF COMPRESSION. [CH. xnr. 
 
 and let the distance between the two circles, that is the 
 distance between the lower mean and the lower datum level, 
 be er, where r is the radius of the sphere to the upper datum 
 level. Then if k be the mean thickness of the crust, 
 
 4?rer (r &) 2 
 
 is very nearly the volume of the shell between these two levels. 
 And so it is easily seen from the figure, that 
 
 47rer (r - k)* = 2 (X) - 2 (JT) + 2 (F) - 2 (F). 
 But we know that, by the datum level equation, 
 
 and 
 
 ^ 
 
 4?rr (r k) 2 
 
 Secondly, suppose the outer circle to be the upper mean 
 level, and 'the inner one the upper datum level. Then the 
 volume of the shell between these two levels is nearly 4?rr 2 er. 
 
 And from the figure, 
 
 2 (A) - 2 (A*) + 2 (B) - 2 (B) = 47rr 2 er ; 
 .'. 2 (A) -2 (B) = 47r/er+ 2 (A'} - 2 (B) ....... (A). 
 
 But, by the datum level equation, 
 
 2 (A) - 2 (B) = STrr^ke. 
 And the value of e has just now been found. 
 
 Hence, substituting for 2 (A) 2 (B) and e in (A), 
 
 We suppose for the present that the crust beneath the 
 oceans is of the same density as elsewhere, and attribute their 
 presence to depressions of the surface, owing to the crust being 
 thinner beneath them. This is the particular case in the 
 last chapter 2 when p is put equal to p. 
 
 1 This follows from the relation S (a) = 2 (/3) ; p. 47. z p. 164. 
 
CH. xin.] AMOUNT OF COMPRESSION. 173 
 
 Again, for a section across a disturbed tract of unit of width 
 we have the two relations 1 , 
 
 2 (a) - 2 (b) = ^ He +^ {Si- 2 (d)}... ....... (1), 
 
 and 
 
 . ..... (2). 
 
 If instead of a section of unit of width we substitute a 
 rectangular area of length I, and width w, these equations 
 become 8 
 
 2 04') -2(B')=^2klwe + ^ [Uw - 
 and 
 
 2 (F) - 
 
 As has been shown for Z 2(cZ) in the case of unit of area 3 , 
 so it is evident here that 81 w 2(D) is the water displaced by 
 rock owing to the elevation ; I and w being the length and 
 width of the disturbed tract, and 2 (D) the volume of any 
 water which may happen to lie over it. 
 
 We have then the proportion 
 
 ........ (3). 
 
 Now it is evident that the same proportion will hold for the 
 area of the whole globe. In this case the " tract " becomes the 
 entire area (for there is nothing in our reasoning to confine the 
 relations (1), (2), to any particular portions of it whether dis- 
 turbed or not). 2 (D) then becomes the whole ocean ; Blw 2(D) 
 becomes the water displaced by all the elevated regions, and we 
 will assume this to be equal to L8, where L is the area of the 
 land ; the reasons for which assumption will appear by and bye. 
 
 1 Pp. 116, 117. 
 
 2 See chap, v., p. 49. 
 
 3 See chap, x., p. 116. 
 
174 AMOUNT OF COMPRESSION. [CH. xm. 
 
 Making this substitution we obtain from (3), 
 
 2 (F') - 2 (X 1 ) = {S W - 2 (BOJ - 8. 
 
 And substituting this value in 
 
 whence 
 
 & = i ZI /Iv-J ~f~ * 
 
 If we can estimate S (A') 5 (5') and iS we shall now be 
 able to find e for any assumed value of k. 
 
 Let us pause to consider what the symbols involved import. 
 If we regard the compression to arise solely from diminution 
 of volume beneath the cooled crust, and not from the ex- 
 tension of the crust itself, then e is the mean coefficient for the 
 compression of the whole crust, which has arisen from this cause 
 since the existing inequalities began to be formed. If however 
 we neglect the contraction of the matter of the crust itself, 
 which for a thickness of 20 miles or so the results of Chapter VI 
 show that we may do, then the coefficient of compression for 
 the crust will be the same as that of contraction for the sphere. 
 We do not know exactly the laws which govern, either the 
 contraction of the matter of the crust, nor yet those which 
 determine the rate at which it thickens through solidification. 
 But it is evident that the compression of the surface must 
 be greater than the mean compression. 
 
 For the remaining symbols r is the present radius, k is the 
 mean thickness of the crust, considered of equable density, that 
 is to say, it is the thickness which the crust would have, if it had 
 been perfectly compressible, so that the contraction of the globe 
 should not have caused it to be wrinkled or thickened anywhere. 
 
en. xiii.] AMOUNT OF COMPRESSION. 175 
 
 Consequently, any thickening from sedimentation is not included 
 in k ; for that will be derived from matter elevated by compres- 
 sion. 2 (A 1 ) and 2 (B f ) are the volumes of the elevations and 
 depressions above and below the upper mean level of this crust; 
 the position of the crust as a whole being affected by the lateral 
 flow of the subjacent fluid, through the intrusion into it of the 
 downward protuberance of the mountain roots. This is allowed 
 for in the equation as if the fluid were a perfect fluid. 
 
 If we assign to cr the value infinity in this expression it 
 ought to reduce to the datum-level equation, for in that case 
 there would be no downward protuberances, and therefore the 
 mean level of the crust would not be altered from the datum- 
 level, because there would be no flow of fluid beneath it. Now 
 this it does, for when a oo the equation becomes 
 
 which is the datum-level equation. 
 
 It is self-evident that it will be quite impracticable to arrive at 
 anything approaching to an accurate estimate for 2 (A') 2 (-?')> 
 because, in the first place, we can only guess at the position of 
 the mean level; and secondly, we can only roughly estimate the 
 amounts of 2 (-4') and S(-B') respectively. Nevertheless it will 
 appear that we may draw important conclusions even from such 
 guesses as we can form. 
 
 Referring to Atlases 1 which have been published since the 
 voyage of the Challenger, we find the oceanic area divided into 
 five portions, whose mean depths are taken to be, 
 
 (1) from 1 to 2 miles, 
 
 (2) from 2 to 3 miles, 
 
 (3) from 3 to 4 miles, (=8), 
 
 (4) from 4 to 5 miles," 
 
 (5) above 5 miles. 
 
 The first may be taken as extensions of the elevations which 
 have produced the continents. The second, where not connected 
 
 1 For example, "Letts's popular Atlas" maps 3 and 4. See also "Thalassa" 
 by J. J. Wild, Ch. i. Marcus Ward, 1877. 
 
176 AMOUNT OF COMPRESSION. [CH. xm. 
 
 with and prolongations of the first, may be considered as sub- 
 marine elevations, and it is possible that they may be the re- 
 mains of ancient lands levelled down. The third which occupy 
 the larger portion of the oceanic area we will regard as indi- 
 cating the mean upper level of the crust. The fourth and 
 fifth will then be depressions below it, corresponding to the 
 series % ($'). If then we set the fourth and fifth against the 
 first and second, we shall have remaining for the excess of 2 (-4') 
 over 2 (B r ) only the volume of the continents above the mean 
 level. If we then adopt Prof. Haugh ton's estimates 1 for L the 
 area of the land, and for its mean height h above the sea, 8 being 
 the depth of the sea over the area which we take as defining 
 the mean level, we shall have, 
 
 L = 52 x 10 6 square miles, 
 
 h = 1000 feet = 019 mile nearly, 
 
 S = 3*5 miles. 
 
 Then 2 (A') - 2 (') = 52 x 10 6 (3'5 + 019) cubic miles, 
 
 = 52 x 3-69 x 10 6 cubic miles. 
 If we put T = 4000 miles, 
 
 k = 20 miles, 
 
 r 2 
 ' = D1 ' 
 
 and -=9.57 
 
 tr-p 
 
 and introduce these values into the expression for e, we find 
 for the first term, 0'254 
 
 As regards the second term, it depends upon the water 
 displaced by rock owing to the elevation. Now we have, in 
 the above classification of the ocean depths, Nos. (1) and (2) 
 which are less than the mean, and therefore cover upraised 
 crust. We have also Nos. (4) and (5) which are greater than 
 the mean, and therefore cover depressed crust. All these be- 
 long to the disturbed regions, and consequently we may roughly 
 set them off against one another. 
 
 1 p. 55. 
 
CH. XIIL] AMOUNT OF COMPRESSION. 177 
 
 We then shall have Blw 2 (D), or the water displaced, 
 equal to a layer of the area of the land, and of the mean depth 
 of the ocean, or equal to LS, as already assumed. 
 
 To calculate the second term, we may assume 
 
 L 52 , 
 
 and 4^ = 197* 
 
 = z o 
 
 and we obtain 0*083; 
 whence e = 0*254 - 0*083, 
 
 = 0171. 
 
 The contraction indicated by this result is greater than 
 can be admitted ; remembering that e is the mean compression 
 for the whole thickness of the crust, and that the contraction 
 of the outer surface of the globe, and therefore of its radius, is 
 probably nearly the same, it would require that the radius 
 of the earth should have been shortened by nearly 700 miles 
 since a crust began to be formed. If we suppose the substratum 
 of lesser density as compared with the crust than the density 
 of basalt as compared with that of granite, then, owing to the 
 smaller value of a- p, this contraction would have to be put 
 higher. Nevertheless on our conclusions regarding a fluid sub- 
 stratum, we cannot put the ratio at a less estimate than 
 
 ar-p 
 
 we have done ; for even that is probably too small, since it is 
 not likely that the density of the substratum should not be 
 lessened both by its exalted temperature, and possibly by the 
 combined water; so that a- will be more nearly equal to p than 
 the density of basalt is to that of granite. Our hypothesis 
 must therefore be in fault. 
 
 Now in obtaining the above estimate, we have taken the 
 crust to be of the same density beneath the oceans as beneath 
 the continents. But we have shown 2 that that cannot be the 
 case, for that it must be there more dense, and that the equili- 
 brium of the ocean is due to that circumstance. We must 
 
 1 See ch. v., p. 55, note. 2 ch. xn., p. 165. 
 
 F. 12 
 
I? 8 AMOUNT OF COMPRESSION. [CH. xm. 
 
 therefore admit that, if the continental areas have been gradually 
 elevated by compression out of sub-oceanic crust, a diminution 
 of density must have been a consequence of their elevation. 
 For this we shall attempt to account hereafter. 
 
 If we suppose that, instead of the existing denser crust 
 beneath the ocean, we substitute a crust of the same thick- 
 ness as at the sea-board, and of the density p, and omit the 
 consideration of the ocean, then the compression of such a crust 
 parallel to the direction of its surface (which would be the same 
 as the existing sea-level) would, on a section of unit of width, 
 produce elevations of the mass pkle for the compression e. And 
 on the supposition that these occurred in the same areas that 
 the existing elevations do occur, their mass would be the same 
 as that of the existing elevations. The radius to the surface of 
 such a crust would be the same as to the surface of the existing 
 ocean. We are therefore at liberty to make use of this suppo- 
 sititious case for the purpose of obtaining an approximate value 
 for the compression, in order to avoid the difficulties which would 
 occur in reasoning about a crust of density differing in different 
 regions. 
 
 Keverting therefore to our expression for the value of e, it is 
 evident that the second term must be omitted, for that depends 
 upon the amount of water lying upon the surface of the dis- 
 turbed area. It reduces therefore to 
 
 - 
 
 Next in estimating 2 (-4') ~ ^ (-#') we must om ^ tne conside- 
 ration of the elevation of the sea-level above the mean level of 
 the crust beneath the ocean, using the surface of the ocean as 
 if it were the mean level. Consequently the part involving 
 or 3 '5, will disappear, and we have 
 
 2 (A') 2 (B'} = 52 x 10 6 x 019 cubic miles. 
 We must also use for k the value of the thickness at the sea- 
 level, which we put at 25 miles. If we now substitute the 
 values which we have been using for p and <r, we get for the 
 mean coefficient of compression 
 
 6 = 0-0105. 
 
CH. xm.] AMOUNT OF COMPRESSION. 1 79 
 
 This would make the radial contraction of the sphere, supposing 
 the compression to be caused by the contraction of the matter 
 beneath the crust, about 42 miles. 
 
 Lastly, if we regard compression as a continental pheno- 
 menon only, since the area of the land is -ffaths of the whole 
 area of the globe, the compression of this would be 
 
 x 0-0105 or 0-0204, 
 or about 2 per cent. 
 
 The estimates we have now been making, inexact as they 
 must be allowed to be, nevertheless go far to confirm our 
 previous conclusion that the ocean basins are not caused by 
 depressions in the upper surface of a crust of the same density 
 as that beneath the continents, but that they are due to a 
 greater density and general depression of the sub-oceanic crust. 
 
 122 
 
CHAPTER XIV. 
 
 EXTRAVASATION OF WATER WILL NOT ACCOUNT 
 FOR COMPRESSION. 
 
 Hypothesis that oceans consist of water that has been extravasated. Density 
 of the water before extravasation volume of interior which would need to 
 have contributed it. Hypothesis shown to be inadequate to produce the entire 
 compression. Disturbance of crust by change of ellipticity of spheroid. 
 Inequalities do not appear connected with such ft cause. 
 
 IN a former part of this book 1 we have suggested the 
 extravasation of water substance from beneath the crust as a 
 possible cause of contraction, and of the consequent compres- 
 sion, of which we are in quest 2 ; and have proposed to examine 
 its validity 3 . This we will now proceed to do, availing ourselves 
 of the approximate values for the compression obtaining in the 
 preceding chapter. 
 
 We have already pointed out how large a portion of water 
 is emitted in volcanic eruptions, and submitted a hypothesis to 
 account for its presence beneath the crust 1 . It is certain that it 
 immediately falls in rain and goes to increase the volume of 
 the ocean. If then we put the ocean out of the question, and 
 consider the configuration of the solid surface of the earth, we 
 have before us, on the present hypothesis, the surface of a globe, 
 which has been compressed solely by the contraction of the globe, 
 caused by the extravasation of a certain portion of its original 
 internal substance. This then falls under the case, where the 
 coefficient of contraction will be the same as that of compression. 
 
 1 p. 88. See also Judd's "Volcanoes," fig. 5. London : Kegan Paul and Co., 
 1881. 
 
 * See chap. vm. 3 See p. 90. 
 
CH. xiv.] EXTRAVASATION OF WATER, ETC. 181 
 
 In order to estimate the contraction of the globe as a 
 whole, which would arise from the extravasation of a certain 
 quantity of water-substance from beneath the crust, we may 
 proceed as follows. 
 
 Suppose s to be the volume of the water-substance in ques- 
 tion mingled with the rocky matter in the magma, and we will 
 assume that when s is extravasated the volume of the magma is 
 diminished by s. This assumption is most favourable to the 
 diminution of volume, but excessive ; because, if the rocky matter 
 of the magma be in solution under pressure along with the 
 superheated water, the volume of the combined substances 
 is probably less than what the sum of the two volumes would 
 be separately. 
 
 Let fju be the density of the water substance. Then ps is its 
 mass. Now if this goes to form a layer of water of depth & 
 and density 1 over the whole globe, the mass of such a layer 
 will be 4?rr 2 S / very nearly, because 8' is very small compared 
 with r. 
 
 Hence ps = 477T 2 S'. 
 
 Now the radius of the sphere before the extravasation of this 
 water substance having been r + er, the diminution of volume 
 caused thereby will be f 7r{(r + erf r 3 }, and this must be equal 
 to s ; that is to 
 
 ff 
 
 
 ,2 
 
 Putting the area of the ocean at 145 millions of miles, the area 
 of the globe being 197 millions, it is obvious that 
 
 ' 145 
 
 being the mean depth of the ocean, and =3*5 miles., 
 
1 8 2 EXTRA VASATION OF WA TER [CH. xiv. 
 
 Consequently, with the value 0*0105 just found for e, 
 fji = 0'061. 
 
 If we know how much the volume of a given existing volume 
 of the interior has been diminished by the abstraction of the 
 water it contained, we can find the depth to which the loss of 
 water has extended. 
 
 For instance, if V be the volume of a mass of the interior 
 at present, after the extravasation of the volume V of water 
 substance at the density /JL which was previously mingled 
 with it, and if we consider the abstraction of the mass /juV to 
 diminish the volume of the magma by V, which is probably 
 too much, but we may assume for our purpose as true, then the 
 
 mass was originally a-V+ftV and its density -^== TFT. Now 
 
 let us assume that this density was at that time, before any 
 water was extravasated and the crust had but just begun to be 
 formed, equal to the density of the crust as it now exists be- 
 neath the ocean; for if it had been but little less the crust 
 would have sunk ; 
 
 o-F + 
 
 p being the density beneath the ocean ; 
 
 whence F=^F'. 
 
 <r-p 
 
 But V is supposed to be equal to s, or to the volume which 
 the ocean would have if all the water were reduced to the 
 density p ; 
 
 This is the present reduced volume of the portion of the in- 
 terior, which must have formerly had all the water of the ocean 
 mingled with it at the density JJL, so as to have then reduced it 
 from the present density /u to the then density //. 
 
 We now wish to find what portion of the sphere is comprised 
 within this volume. Suppose it to be a shell of thickness z 
 situated immediately beneath the crust. 
 
CH. xiv.] WILL NOT ACCOUNT FOR COMPRESSION. 183 
 The volume of this shell will be 
 
 And this must be equal to V, or to 
 
 C7-p p 
 
 whence, giving to p the value 2'953 X , 
 
 = 9183 + 3980 = 13163 miles. 
 
 The two other roots of the equation are impossible. Hence the 
 entire remaining portion of the sphere beneath the crust could 
 not have contributed sufficient contraction to have caused the 
 requisite compression, even under circumstances more favourable 
 than are likely to be true regarding the increase of volume due 
 to the presence of the water. 
 
 From this result we feel obliged to abandon the hypo- 
 thesis that the existing inequalities can be accounted for by the 
 extravasation of the water, now composing the oceans, from 
 beneath the crust. 
 
 There is one other cause which must necessarily have dis- 
 turbed the equilibrium of the crust during the lapse of ages, 
 and that is the diminution of the oblateness of the spheroid. 
 The friction of the tides, whether oceanic or bodily, must neces- 
 sarily have diminished the rotational velocity, and lessened the 
 oblateness. The parts of the crust about the poles will con- 
 sequently have been subjected to stretching, and those about the 
 equator to compression. There is however no apparent reason 
 immediately to connect the inequalities with this cause, for the 
 continents do not occupy an equatorial belt, as they would do 
 under this hypothesis, nor have the polar regions been free from 
 the compression which all continental areas have experienced. 
 
 1 See p. 1G7. 
 
1 84 EXTRAVASATION OF WATER, ETC. [CH. xiv. 
 
 If however a radial contraction of 42 miles would have been 
 sufficient to have produced the whole of the existing inequali- 
 ties, it is difficult to understand how the cause now alluded 
 to can have been without appreciable effect. We are there- 
 fore tempted to suggest, that the apparent want of relation 
 between the areas of compression and the axis of rotation 
 favours the idea, so strongly supported by phenomena of cli- 
 matal changes, that the latitudes of places on the earth's surface 
 are liable to change, a change which would be impossible were 
 the earth solid, but which with a fluid substratum is brought 
 within the range of possibilities. 
 
CHAPTER XV. 
 
 COMPRESSION AND VOLCANIC ACTION. 
 
 Compression not being sufficiently accounted for by contraction of the globe, 
 alternative hypothesis that the cause of it is situated within the crust 
 Attraction of thickened crust not operative Intrusive dykes may afford a key 
 to the problem may be widened by fluid pressure Excess of horizontal over 
 vertical pressure so caused Their connection with volcanic vents Hypothesis 
 concerning the constitution of the magma mode of its elevation in a fissure 
 Pressure on the sides of the fissure Comparison of the work of compression 
 with that done against gravity Mineral veins Prof. Judd and Baron 
 Eichthofen on the relation of volcanic energy to continental movements 
 Possible additional compression upon solidification of dykes Analogies of 
 Earth's crust and ice Prof. Nordenskib'ld's theory of compression Analogy 
 of ice disturbed by skaters and Earth's crust by sedimentation Corrugation 
 attributed to cracks opening from below, and a continental phenomenon 
 Vieivs of American Geologists as set forth by Dr Sterry Hunt Their observed 
 facts agree with the present theory Effect of increased thickness of crust on 
 compressing force Whence the energy invoked Circulation of rock Sug- 
 gestion to explain diminished density of continental areas "Red clay" of 
 profound ocean. 
 
 THUS far the compression, which is known to have affected 
 many regions of the earth's surface, has been considered on three 
 hypotheses, as arising (1) from a diminution of the volume of the 
 sphere through cooling as a solid by conduction ; (2) from the 
 collapse of a thin flexible crust covering a contracting interior 
 and resting upon a subsiding liquid substratum ; and (3) from 
 a general diminution of the interior beneath a solidified and 
 
 o 
 
 partially rigid crust through the extravasation of water-substance 
 from beneath it. But we have found that none of these hypo- 
 theses account sufficiently for the phenomena. We will now 
 proceed to examine the alternative hypothesis, that the causes of 
 compression of the crust are situated within the crust itself. 
 
 At first sight it might seem that, when the crust had been 
 thickened in any region, the increase in the mass of the crust 
 there through thickening might add to the attractive force of 
 
1 86 COMPRESSION AND VOLCANIC ACTION. [CH. xv. 
 
 that region, and cause compression, by drawing the neighbouring 
 parts towards itself. But the discussion of the attraction of 
 mountain masses by Sir G. B. Airy, quoted in the eleventh 
 chapter, suffices to show that such a supposition would be erro- 
 neous. Indeed it is easy to see that, when a column floats 
 vertically in a heavier fluid, the horizontal attraction upon a 
 particle, at or near the surface of the fluid, will be somewhat 
 less for a longer than for a shorter column. It is not possible 
 therefore that the cause of compression can be explained by the 
 attraction of the thickened crust upon the neighbouring parts. 
 
 To guide us in this new branch of enquiry, let us enquire 
 whether any geological appearances in the crust itself can give 
 a key to the cause of compression. 
 
 When we examine any district where considerable sections 
 of metamorphosed strata are exposed, we are struck with 
 the abundance of dykes of intrusive rocks, which permeate 
 them 1 . These are commonly, though not always, more or 
 less vertical in position. Likewise in any section, carried 
 across an extensive range of country, large and wide dykes are 
 'laid down, sometimes as actually determined by the surveyors, 
 and sometimes as the supposed channels, through which over- 
 lying sheets of igneous rock have been raised to the surface. 
 What have been the conditions under which these intrusive 
 more or less vertical sheets of matter have found their way into 
 the positions in which we see them ? That they have come up 
 from below no one doubts ; but what has been the force that has 
 injected them ? How have the chasms originated which they 
 occupy ? If the separation of their walls has been effected by 
 any pressure acting within the chasms themselves, then we have 
 an indication of the existence of some force tending to compress 
 the crust. 
 
 Upon the hypothesis that a crust of about 25 miles thickness 
 rests upon a fluid substratum of highly heated rocky matter in 
 a state of igneo-aqueous fusion, let us suppose that a crack is 
 
 1 Prof. Liveing, from an estimate by the eye alone, made at my request in 
 the Channel Islands, thinks that the horizontal area occupied in the cliffs of 
 Guernsey and Serk by intrusive dykes cannot be less than from 2 to 3 per cent, 
 of the whole area. Jersey consists largely of volcanic products. 
 
CH. xv.] COMPRESSION AND VOLCANIC ACTION. 187 
 
 produced by any cause in the under surface of the crust. The 
 pressure of the fluid at the bottom of the crust is that due to 
 the weight of the superincumbent crust, and consequently the 
 tension of the water-substance in the magma there must be the 
 same. If therefore, upon the opening of a fissure which did not 
 reach the upper surface, the magma beneath were able to fill it 
 with water-substance, which we may provisionally call vapour 1 , 
 at a tension equal to the pressure which it sustains from the 
 weight of the crust (about 10066 tons upon the square foot), the 
 fused rock could not rise into the fissure at all, but the sides of 
 the fissure would be subjected to a vapour pressure, only less 
 than the pressure of the entire crust by the diminution upwards 
 due to the decreasing weight of the superincumbent vapour, 
 which, compared with its tension at the bottom of the chasm, 
 would be inconsiderable. Thus we should under the circum- 
 stances supposed (which could never be fully realised) have a 
 horizontal pressure upon every elementary area of the sides of 
 the chasm equal to the weight of a column of rock of the same 
 sectional area and about 25 miles high. 
 
 Generally, let t be the tension of the water-substance which 
 occupies the chasm, h the height to which the magma rises in 
 the chasm, then, if we neglect the weight of the water-substance 
 
 compared with that of the magma, which owing to its high 
 temperature we are probably justified in doing, 
 
 This will be the horizontal pressure upon the side of the fissure 
 everywhere above the surface of the fluid magma in the fissure, 
 
 1 Perhaps it Bought rather to be called gas. See Hannay "On the states of 
 matter," Proc. Royal Soc., Vol. xxxii. p. 412. 1881. 
 
1 88 COMPRESSION AND VOLCANIC ACTION. [CH. xv. 
 
 while the horizontal pressure at a depth z below the same surface 
 will be 
 
 t' = gpk gah + gvz. 
 
 At the same time the vertical pressure upon an element of 
 the rock in the crust near the chasm at a height y above the 
 bottom of it will be 
 
 p=gp(k-y\ 
 
 Hence the difference between the horizontal and vertical 
 pressures on such an element situated above the level to which 
 the magma rises in the chasm, will be 
 
 And the like difference below that level will be 
 
 The excess of the horizontal over the vertical pressure, which is 
 the force that will cause lateral compression, increases as y in- 
 creases, and also increases as h diminishes. This force will 
 therefore be greater towards the upper part of the chasm, and it 
 will also be greater the greater the tension of the vapour, which 
 will tend to decrease h by preventing the magma rising. If the 
 rock should allow the vapour only slowly to escape, and if the 
 magma below the chasm can supply fresh vapour sufficiently 
 rapidly to keep up the temperature, it is conceivable that the 
 tension of the vapour in the chasm may be nearly equal to gpk, 
 in which case h will be nearly evanescent, and the horizontal 
 pressure . much greater than the vertical especially in the upper 
 part of the chasm where y is nearly equal to k. We can there- 
 fore understand how a chasm, commencing below, may be rent 
 open upwards, and at last reach the surface of the ground. 
 When that occurs, vapour at a high tension will escape at what- 
 ever point is first broken through, and after issuing at a diminish- 
 ing pressure for a certain time, it will be followed by the magma 
 itself, which will overflow at the surface because the water-sub- 
 stance in the upper part of the column, expanding owing to the 
 diminished pressure there, will render the whole column of less 
 weight than an equal column of crust. This appears to be the 
 mechanism required to explain the formation of a volcano, and 
 of the earthquakes which precede its appearance. 
 
CH. xv.] COMPRESSION AND VOLCANIC ACTION. 189 
 
 It is probably to this kind of action that we may attribute 
 the opening of fissures radiating from volcanic vents, along 
 which subsidiary craters are established. Thus for instance an 
 earthquake, caused by a volcanic explosion in Iceland on the 
 4th January, 1875, "opened rifts forty miles in length in the 
 plains north of Dyngjufjoll, and it was from fissures in a tract 
 twenty miles in length and about three in breadth, which sank 
 to some depth between two of these rifts, that the lava welled 
 forth 1 ." 
 
 If however the water-substance should not be able to escape 
 from the magma sufficiently rapidly for the vapour pressure to 
 accumulate so as to prevent the magma from almost entirely 
 occupying the fissure, or if the fissure should open to the surface 
 so that the vapour above the fluid should escape, then the magma 
 would rise into the fissure pressed upwards by the weight of the 
 crust around the base of the ascending column. In this case it 
 would not behave within the fissure like an inert liquid, for it 
 would carry with it the water-substance which is one of its con- 
 stituents, and that, when raised within the fissure, would have^' 
 an expansive force of its own. For this expansive force, although 
 equalised at the bottom of the crust to the pressure of the 
 crust, arises from the store of energy due to the temperature of 
 the water-substance, and to whatever place it may be transferred 
 it will carry that energy with it. 
 
 In order to come to any conclusion about the amount of this 
 force we must make some supposition concerning the constitu- 
 tion of the rnagma, which for convenience we will call "lava" 
 after it has risen into the fissure, retaining the name of magma 
 for the fluid substratum. 
 
 The supposition which we will make shall be that the 
 magma consists of hot rocky matter in combination with super- 
 heated water. In a given mass of the magma there is a certain 
 proportion of rocky matter which is inelastic, and the remainder 
 consists of water-substance at the same exalted temperature, 
 the presence of which renders the magma elastic, and if the 
 pressure were infinitely increased the whole would be reduced 
 
 1 "Volcanio History of Iceland," by Mr W. G. Lock, Geol Mag. Dec. n., 
 Vol. vin. p. 214. 
 
COMPRESSION AND VOLCANIC ACTION. [CH. xv. 
 
 to the volume of the rocky matter. We conceive this associa- 
 tion between the two at an exalted temperature and under 
 great pressure, which has been called igneo-aqueous solution, to 
 be not an ordinary solution of the rock in the water, but rather 
 of the water in the rock, for we cannot suppose that the small 
 relative quantity of water which is present can hold the rock 
 in solution as salt is held in solution in water. And the water 
 perhaps acts in the manner of a flux rendering the rock fluid 
 at a lower temperature than that at which it would be fusible 
 without it. Prof. Judd compares the process with the power, 
 known to be possessed by " various solids and liquids, of absorb- 
 ing many times their volume of certain gases 1 ." We know 
 from the behaviour of lava in a volcanic vent that when the 
 pressure is diminished the water separates from the rocky matter 
 into vesicles which are at first of microscopic minuteness, but 
 eventually these join one another, expand, and ascend to the 
 surface, producing ebullition. Since then there is apparent 
 this tendency for the water to separate when the pressure is 
 diminished, and since when it does separate it rises through the 
 lava, it seems a necessary conclusion that under the pressure 
 of the crust the density of the magma is uniform, for if it were 
 not so, the water would rise to the surface of it and form a 
 layer upon it. 
 
 That there should be a layer of water-substance interca- 
 lated between the crust and the substratum is on many accounts 
 in the highest degree improbable. We must therefore arrive at 
 the conclusion, startling though it may appear, that the water- 
 substance in the magma is reduced by solution under pressure 
 to the same density as the rocky matter with which it is 
 combined. 
 
 The fact that the water-substance separates from the lava 
 when the pressure -is diminished, leads us to conclude that the 
 quantity of it which the magma is able to hold in solution at a 
 given temperature must be dependent on the pressure. If then 
 
 1 "Volcanoes," p. 345. See also a notice by Mr Hannay "On the absorp- 
 tion of gases by solids," Proc. Royal Soc., Vol. xxxu, p. 407. 1881. His 
 experiments appear to be in accordance with the assumptions here made. 
 
CH. xv.] COMPRESSION AND VOLCANIC ACTION. 191 
 
 a fissure should commence to be formed at any place in the 
 bottom of the crust, some portion of the water-substance would 
 escape from the magma into it, its place in the magma being 
 partially supplied from the magma in the vicinity. By the 
 continuation of this process the fissure would become filled by 
 what we have called vapour, at the elastic pressure due to 
 the temperature l . The case would be analogous to that of a 
 liquid confined in the presence of its own vapour. The upper 
 portion of the lava in the fissure would retain only so much 
 water as the pressure of the vapour upon its surface would 
 enable it to keep in solution. But at lower levels, where the 
 pressure would be increased by the weight of the superincum- 
 bent lava, it would retain more water. 
 
 Suppose then that at the depth x below the surface of 
 the crust the volume of a certain mass of lava is V + v, where 
 F is the volume of the rocky matter which we suppose in- 
 compressible and v is the volume by which it is increased 
 owing to the water-substance which is combined with it. We 
 have no means of knowing what law connects v with the 
 pressure p\ but we feel assured that it diminishes as the 
 
 pressure is increased. If we assume v = - , a is probably some 
 
 function of p ; but for want of a better hypothesis we will sup- 
 pose a. constant, and then v becomes subject to Boyle's law. 
 The rocky matter may itself contain water as one of its 
 chemical constituents, which we leave out of the question. 
 Let fj, be the mean density of the mixture and ft the mass 
 under consideration. Then our hypothesis gives the relation 
 
 P 
 
 The temperature is taken as constant. 
 
 i Richthofen (p. 56, note) refers, though not without hesitation, to a calcu- 
 lation by G. Bishof that " the elastic force of steam is at its maximum when it 
 has the same density as water." This appears to imply that at temperatures 
 above the critical it becomes more compressible. "Natural System of Volcanic 
 Rocks," California Academy of Sciences, Vol. i., Part n. San Francisco, 1868. 
 
I9 2 COMPRESSION AND VOLCANIC ACTION. [CH. xv. 
 
 To express the increment of pressure due to the increment 
 dx in the depth we must have 
 
 dp 
 
 _ 
 
 Integrating 
 
 Vp + a log p = g$x + C. 
 
 At the bottom of the crust the depth is k and the pres- 
 sure gpk ; 
 
 which is the equation connecting the pressure with the 
 depth. 
 
 To determine the relation among the constants we have 
 already seen that 
 
 p 
 
 At the bottom of the crust the density is cr, which we have 
 hitherto assumed to be that of basalt, and the pressure is there 
 , whence 
 
 gpk 
 
 If then the mass of lava under consideration be taken 
 as that which occupies unit of volume when it is in the state of 
 magma, we have 
 
 And .'. a = . 
 
 That is to say that the mass of unit of volume of the 
 magma is equal the mass of unit of volume of basalt. Conse- 
 quently if the rock constituent be of the density of basalt 
 the water constituent must be so likewise, which agrees with 
 our previous conclusion. 
 
en. xv.] COMPRESSION AND VOLCANIC ACTION. 1 93 
 
 Substituting for a and /3, our equation may now be 
 written 
 
 1 V, gpk p 1 a k x , 
 
 , r log 2C - -^ - 1. 
 
 V ' p gpk V p k 
 
 We are so little acquainted with the behaviour of matter 
 under the circumstances which environ it beneath the earth's 
 crust that it is dangerous to speculate upon the laws which 
 govern it, but it is thought that the consequences of the hypo- 
 theses above made will be sufficiently near the truth to justify 
 our arguing upon them. 
 
 At the surface x = 0, and then 
 
 1-F 
 
 gpk p a- 
 
 ^T --VF; = Tr - 1 ; 
 
 V > p gpk-V P 
 whence 
 
 P 
 
 P 
 The condition that F< 1 is satisfied if 
 
 1--P- <? 
 
 gpk p ' 
 
 Now -~j is necessarily <1, and - > 1. Consequently this 
 
 condition is always satisfied, and therefore if there be any 
 water-substance at all in the magma it will raise the lava 
 to the surface under the supposition that the same identical 
 water remains always in the same portion of lava. 
 
 If F= 1 we obtain p = - (<r p) k. This value is without 
 meaning, but being the same that we obtain from the equation 
 
 p = go- 1 dx + C, 
 
 after determining the constant by the condition that p = gpk 
 at the bottom of the crust and then giving to x the value zero, 
 that being the value we should arrive at when there is no 
 water in the lava, it verifies our result. 
 
 F. 13 
 
194 COMPRESSION AND VOLCANIC ACTION, [en. xv. 
 
 In the equation which connects the pressure p of the lava at 
 the surface of the crust with V the proportion of rock substance 
 in the magma, if we assume one of the quantities we can find 
 the other, but we have no sure guide to lead us to the choice of 
 either of them. We will assume V= 0'9, and it will hereafter 
 appear when we are treating more particularly of volcanic 
 action that this assumption is not unreasonable. If we put 
 
 - = n in the equation for the pressure at the surface and 
 
 assume the usual values for p and a, then with the above value 
 for V it may be put into the form 
 
 n (log n - 2-044) = 9. 
 
 Using a table of hyperbolic logarithms we find by trial that 
 the value 14*4 substituted for n gives 8*97 and the value 14'5 
 gives 9'13. Hence 14'4 is a near approximation, and the pressure 
 of the lava at the level of the surface of the crust would be that 
 
 25 
 
 due to a column of the crust =-^ r or 1*7 miles high. The 
 
 14*4 
 
 weight of a column of vesicular lava would not be so great as 
 that of a column of solid crust of equal height. We see then 
 that if T ^th of the volume of the magma consisted of water- 
 substance it would be sufficient to produce an overflow of lava 
 from a lofty crater, or to raise a range of mountains consisting 
 of eruptive rocks above an elongated fissure. 
 
 The relation 
 
 enables us to find the whole horizontal pressure upon the sides 
 of a fissure which is filled with lava under the conditions 
 implied by it. 
 
 For -^(Vp + a) dp = pdx \ 
 
 But I pdx taken from the surface to the bottom of the crust 
 is the whole pressure upon a vertical section of the side of 
 
CH. xv.] COMPRESSION AND VOLCANIC ACTION. 195 
 
 the fissure. If we substitute the values already found for 
 ft and a. in this equation, it becomes 
 
 Now at the bottom of the crust p = gpJc, and putting 
 V 0'9 we have found that the value of p at the surface 
 
 will be . And = 
 14'4 a 
 
 Using these values at the limits we obtain 
 
 rk 
 
 gpk* x O489 = pdx. 
 
 Jo 
 
 And if we give to k the value 25 miles 
 
 1 [ k 
 
 gp x 12*2 miles =y I pdx. 
 J o 
 
 That is to say the mean horizontal pressure of the lava 
 throughout the vertical section is equal to what would be 
 produced by the weight of a column of the crust rather more 
 than 12 miles high. 
 
 The work done by the compressing force in raising a moun- 
 tain chain (which we use as a generic term for any elevated 
 tract) will consist of two parts, (1) the work producing deforma- 
 tion of the crust, which will include the work of distortion and 
 cleavage, and is done against the molecular forces, and (2) the 
 work done against gravity. This last will in itself consist of 
 two parts, viz. the elevation of the mass of the mountain above 
 the upper mean level of the crust, and the depression of its 
 root into the fluid, below the lower mean level. 
 
 If we take yf(l) to define the contour of the elevated 
 mass along a section across the tract, the work against gravity 
 on a section of unit of width will be 
 
 And similarly, if y' be the ordinate corresponding to y 
 for the root of the mountain below the lower mean level, the 
 
 132 
 
196 COMPRESSION AND VOLCANIC ACTION. [CH. xv. 
 work against gravity in depressing the root will be 
 
 But 
 
 Hence the whole work against gravity, which is the sum of 
 these, will be 
 
 Now if M be the volume of the mountain, and m the height of 
 its centre of gravity above the upper mean level, 
 
 and the work done against gravity will therefore be 
 
 Again, if A be the area of the fissure which is exposed to the 
 pressure t, and le the space through which it is opened by the 
 action of t, then the work done by t is tAle. 
 
 But since the opening of the fissure gives rise to the eleva- 
 tion above and depression below the mean crust, it follows by 
 equality of volumes that 
 
 Hence the work of compression is equal to 
 
 Consequently, 
 
 work done against gravity _ gpm 
 work of compression t 
 
 If the fissure be closed above, this = - r / 
 
 p/c all 
 
 1 p. 187. 
 
CH. xv.] COMPRESSION AND VOLCANIC ACTION. 197 
 
 where h is the height to which the pressure t allows the 
 magma to rise in the fissure. In the most favourable case 
 h = 0, and then, 
 
 m 
 
 work done against gravity = -j- work of compression. 
 
 It is of course to be understood that what we have spoken 
 of as the fissure of area A and width le is in reality the aggre- 
 gate of all the fissures which occur within the length I of the 
 tract, each of which is under an equal, or nearly equal, tension t, 
 so that the compressing action takes effect throughout that 
 length. 
 
 The height m of the centre of gravity of the elevated tract 
 is evidently very small compared with the thickness of the crust 
 k, for the entire mean altitude of the continents is put at only 
 
 1000 feet, so that -j- is probably considerably less than -^ in an 
 
 extreme case. We see then that but a very small part of the 
 available force, arising under the conditions suggested, will 
 be expended in raising the mountains, and by far the larger 
 part of it will be available for overcoming the molecular forces 
 which resist distortion of the rocks. 
 
 But if a fissure be open to the surface so that a massive 
 eruption takes place through it, then the pressure t, statically 
 considered, upon the side of the fissure is what we have found 
 in that case to be about gp x 12*2 miles, which is less than the 
 pressure that would arise, if it were filled with a liquid of the 
 density of the crust. This latter obviously could not produce 
 compression. Hence, after the lava has gained access to the 
 surface, the lateral force may cease to be effective, which agrees 
 with the common observation, that earthquakes cease when a 
 volcano breaks into action. In this limited sense the saying is 
 justified, that volcanoes are the safety valves of the globe. 
 
 Now it is not probable that any considerable volume of the 
 crust could support continuously a horizontal pressure much ex- \ 
 ceeding the vertical pressure without becoming distorted. If 
 these orthogonal pressures were equal, they would tend only to 
 
198 COMPRESSION AND VOLCANIC ACTION. [CH. xv. 
 
 compact the rock, and render it more dense. But if the hori- 
 ' zontal were considerably to exceed the vertical, the rock would 
 be sheared upwards and downwards. Whether the force at our 
 disposal under the hypothesis now offered would be sufficient 
 for this purpose is of course open to argument, but considering 
 that, with time given, all known substances yield more or less 
 to deforming forces, it seems quite possible that it may be so. 
 And the facts which we shall bring forward presently make it 
 almost certain that the work has been effected in this manner 1 . 
 Moreover the rocks fissuring from contraction, will detract from 
 their rigidity, and render shearing more easy, when large- 
 volumes of them are under consideration. 
 
 If our chasm did not extend upwards to the surface, when 
 
 the tension of the vapour in it diminished through cooling the 
 
 lava would ascend further, until it became too viscous to rise 
 
 higher. At such a juncture we might have vapours still at a 
 
 very considerable pressure occupying the upper portion of the 
 
 fissure, while the lower part would be filled with the magma, 
 
 solidified at its upper surface and more and more fluid below. 
 
 In this manner we may conceive gaping chasms to have been 
 
 . formed, which might be for a long time occupied by heated 
 
 A Lvapours, and gradually converted into mineral veins. 
 
 When the molten rock injected by hydrostatic pressure into 
 the fissures came to solidify into the dykes which so abundantly 
 intersect metamorphic strata, it is probable that another efficient 
 cause of compression would come into play, for, as already 
 mentioned, the result of recent experiments appears to show 
 that such substances as whinstone and granite are less dense in 
 the solid than in the liquid state at the melting temperature 2 . 
 In this respect then they behave like water. 
 
 1 pp. 203, 204. 
 
 2 p. 23. If this fact be established, then it appears that pressure lowers the 
 melting temperature of such rock masses. But it has been considered proved 
 that the greater portion of the globe is extremely rigid, and it has been 
 considered to owe its rigidity to pressure. We must conclude then, either that 
 the central part consists of materials of a different kind from those which have 
 yielded these experimental results, or else that it is cool. The former sup- 
 position is the more likely to be true. 
 
CH. xv.] COMPRESSION AND VOLCANIC ACTION. 1 99 
 
 Indeed there are points of analogy so close between the cir- 
 cumstances of ice resting upon water, and such a crust as we 
 have supposed resting upon a fluid substratum, that we may 
 expect to receive suggestions for explaining the phenomena of 
 crust movements from the behaviour of ice. In both cases the 
 floating substance is but slightly less dense than that upon 
 which it floats. In both cases the one is incorporated with the 
 other by congelation. In both cases the floating substance has 
 a considerable amount of rigidity, but yields somewhat freely to 
 differences of pressure when sufficient time is allowed. These 
 analogies have been noticed by many. Thus, in travelling 
 across the frozen sea to the north of Spitzbergen, Prof. 
 Nordenskiold gives this description of the condition of the ice 
 and deduces conclusions from it regarding movements in the 
 crust of the earth : 
 
 "The ice we passed is formed not of colossal blocks or ice- 
 bergs, but of angular blocks of ice, not waterworn, piled loosely 
 over each other, so as to form pyramids, or walls of ice, up to 
 thirty feet high, which were so close to each other that the 
 space between them was frequently not large enough for our 
 tent. 
 
 "The cause of the formation of these ice-walls, which were 
 also observed by Wrangel on the north coast of Siberia, is pro- 
 bably to be sought for in the changes of volume which ice 
 undergoes when its temperature is changed. According to 
 Pliicker and Geissler the linear expansion-coefficient of ice 
 is = 0-0000528. If, therefore, ice at C. be cooled to - 15 C., 
 cracks must arise which, for 1,000 metres, have a breadth of 
 thirty-two inches. The cracks naturally freeze together im- 
 mediately afterwards," [which must mean that they become 
 filled with water and the water in them freezes], "and when 
 the ice is again warmed, for instance to 5C M a piling-up must 
 take place of twenty-one inches per kilometre. During the 
 course of the winter this phenomenon is repeated innumerable 
 times, one layer of ice being piled upon another, till the whole 
 ice-field forms a confused mass of blocks heaped up against each 
 other. Similar forces are also in operation in the crust of the 
 earth, with less intensity, indeed, in consequence of the smaller 
 
200 COMPRESSION AND VOLCANIC ACTION. [CH. xv. 
 
 expansion-coefficient of the rocks which compose it, and the 
 inconsiderableness of the changes of temperature which occur 
 in them, and the cracks thus formed may here come together 
 again, provided no chemical or mechanical sediment has been 
 deposited in them, as is, perhaps, often the case. On the other 
 hand, the forces operate in the earth's crust during millions of 
 years, and I doubt not that in the circumstances here noticed 
 the cause of the strata being contorted, dislocated and thrown 
 over each other, is to be sought for. This last, perhaps, to judge 
 by the observations I had the opportunity of making on the polar 
 ice, happens far oftener than we commonly suppose, and when 
 it takes place there often occurs no considerable disturbance in 
 the original horizontal position of the stratum. Certainly in 
 most cases the veins filled with foreign minerals, by which the 
 upper strata of the earth in particular are intersected in all 
 directions, derive their origin from similar causes ; that is to say, 
 from cracks which have, in consequence of changes of tempera- 
 ture, many times over opened and come together again, pro- 
 vided they were not prevented by the falling in of debris. This 
 has however often taken place, considerable masses of sediments, 
 formed chemically or mechanically, have frequently collected in 
 the cracks, and during the immense duration of geological ages 
 they have hardened and been metamorphosed to solid crystal- 
 line rocks, limestone, quartz, felsite, pegmatite, &C." 1 
 
 We find in this extract a theory of the compression of the 
 strata of the earth, proposed by a philosopher of high repute, and 
 no doubt suggested to him by the analogy between ice arid rock. 
 It is remarkable however that he does not attribute any part of 
 the compression of ice to the expansion of the water when it 
 freezes in the cracks, and he has missed that part of the analogy 
 on which we insist, which arises from the flotation both of the 
 ice and of the earth's crust. It is rather to a cause analogous 
 to the expansion of the freezing water, than to variations of 
 temperature in the ice, that we should be disposed to attri- 
 bute such part of the compression as may possibly be connected 
 with the solidification of fluid rock in chasms. It will be noticed 
 
 1 " The Arctic Voyages of Adolf Erik Nordenskiold," 13581879. London, 
 Macmillan, 1879, p. 239. 
 
CH. xv.] COMPRESSION AND VOLCANIC ACTION. 2OI 
 
 that Prof. Nordenskiold does not make any reference to such 
 injection of fluid rock into the earth's crust. 
 
 The ice upon a sheet of water that has been much skated 
 on, after a few days' frost assumes an appearance very much 
 akin to that of a moderately disturbed area of the earth's crust. 
 This no doubt arises from the cracks which are formed, and by 
 day are filled with water, which during the night freezes and 
 expands, ridging up the ice on both sides of them. The trans- 
 fere ace of sediment from one locality to another has an effect 
 analogous to the irregular distribution of load by the skaters' 
 movements, and produces cracks opening upwards from below, 
 carrying out the analogy. 
 
 But besides the unequal pressure caused by local deposits of 
 sediment, which must tend to crack the crust from below 
 upwards, the mere contraction of sedimentary rocks, when they 
 sink by becoming overloaded into hotter depths, and there 
 become metamorphosed and assume a denser character, must 
 cause them to crack during the process. It is to the opening of 
 cracks from below that we now venture to attribute the sequence 
 of operations which result in the corrugation of tracts of the 
 earth's surface. It necessarily follows that this action is the con- 
 sequence of changing conditions, and is to be looked for where 
 sediment is being deposited, and sedimentary rocks are becoming 
 metamorphosed as along the shores of continents, rather than 
 beneath the quiescent depths of the profound oceans, where the 
 conditions are more fixed and changeless. Thus we are again 
 led to regard compression as a continental phenomenon. 
 
 Prof. James Hall, Dr Sterry Hunt, Prof. Joseph LeConte and 
 other American geologists connect the exhibition of compression 
 of the crust with those regions of the earth's surface where thick 
 sedimentary deposits have been previously laid down. Thus 
 they conceive the corrugation of the Appalachian chain to have 
 been a consequence of the extremely thick series of deposits of 
 nearly the same age, of which that range consists. In the 
 lecture already quoted 1 , Dr Sterry Hunt thus makes reference 
 to a former publication by himself 2 : "The effects of heat and 
 
 1 p. 94. 
 
 2 " American Journal of Science and Art," May, 1861 (II., xxxi. 411). 
 
202 COMPRESSION AND VOLCANIC ACTION. [CH. xv. 
 
 water upon the buried sediments would be condensation, from 
 the diminution of porosity and still more from the conversion 
 of the earthy materials into crystalline species of higher 
 specific gravity, thus causing contraction of the mass. A 
 further and very important result of this accumulation there 
 pointed out was by the softening of the underlying floor, or the 
 ' bottom strata to establish lines of weakness or of least resistance 
 in the earths crust, and thus determine the contraction which 
 results from the cooling of the globe to exhibit itself in those 
 regions, and along those lines where the oceans led is subsiding 
 beneath the accumulated sediments' Hence, I added, ' we con- 
 ceive the subsidence invoked by Mr Hall, though not the sole 
 nor even the principal cause of the corrugations of the earth's 
 strata, is the one which determines their position and direction 
 by making the effects produced by the contraction, not only of 
 sediments but of the earth's nucleus itself, to be exerted along 
 the lines of greatest accumulation"' \ 
 
 The theory so epitomised appears to have gained very 
 general acceptance among physical geologists. But if the reason- 
 ing of the earlier chapters of the present volume is correct, 
 the cooling of the globe cannot be appealed to to furnish the 
 requisite compression (in the above extract called "contraction"), 
 much less would it furnish a sufficient balance of compression 
 along a belt of crust, itself contracting through metamorphic 
 action. But upon the view now suggested, the circumstances 
 fit in very well. The thick deposit depressing the crust, in- 
 duces metamorphism in its lower portion. This cracks in con- 
 sequence. The magma fills those cracks with highly expansive 
 vapour, and compression is the result. 
 
 It is also important to remark, that the vapour pressure in a 
 chasm would be increased when the crust was thickened, because 
 the tension at the bottom of the crust is proportional to its 
 thickness. On this account, although it would require a greater 
 horizontal force to compress the crust where it is thicker, yet 
 the requisite increase would be furnished to the force by the 
 very fact of the increased thickness. If our theory of the 
 
 1 ." American Journal of Science and Art," 1873, Art. xxvm. p. 265. 
 
CH. xv.] COMPRESSION AND VOLCANIC ACTION. 203 
 
 formation of volcanic vents be accepted, it will be also apparent 
 that the force which opens them will for the above reason be 
 proportionally greater where the crust is thicker, so that their 
 occasional occurrence on lofty plateaux is no argument against 
 the theory. 
 
 T? he conclusions to which we have been led as to the cause 
 of compression, and of the elevation of mountain ranges, have 
 been arrived at independently, and entirely upon the grounds 
 already mentioned. They appear however to be decidedly in 
 accordance with geological observations, and agree well with 
 the history given by Prof. Judd, in his recent work on Volcanoes, 
 of the connection between volcanic activity and the elevation of 
 mountain ranges 1 . He there shows that the Alpine chains 
 have been raised contemporaneously with the manifestation of 
 strong volcanic outbursts along lines parallel to them. He 
 appears to adopt in general what we may call the American 
 theory of the formation of mountains, but he supplements it 
 by specially connecting volcanic outbursts with the actual 
 throes of their elevation. He does not appear however to 
 trace the connection of cause and effect between the two as we 
 have done. " The movements which resulted in the crushing 
 and crumpling of the thickened mass of sediments along the 
 Alpine line of weakness, also gave rise to the formation of a 
 series of fissures from which volcanic action took place 2 ." We 
 should however expect that, had the crushing and crumpling 
 arisen from any external cause, it would rather have kept 
 fissures closed than opened them. It is the synchronism to 
 which we desire to draw attention. Thus again: "We have 
 abundant evidence that just at the period when these great 
 movements were commencing which resulted in the formation 
 of the great Alpine and Himalayan geanticlinal, earth-fissures 
 were being opened upon either side of the latter 3 from which 
 volcanic outbursts took place. At the period when the most 
 
 1 "Volcanoes," Chap. x. 
 
 2 Ibid. p. 297. 
 
 3 The word "latter" strictly should confine this assertion to the Himalayan 
 range. But from the enumeration of the localities, most of which are European, 
 this cannot be intended. Ibid. p. 298. 
 
204 COMPRESSION AND VOLCANIC ACTION. [CH. xv. 
 
 violent mountain-forming movements occurred, these fissures 
 were in their most active condition, and at this time two great 
 volcanic belts stretched east and west, on either side of, and 
 parallel to, the great Alpine chain." 
 
 Of the same purport are the remarks of Baron Richthofen 
 on the connection between the distribution of volcanic rocks 
 and elevated regions of the surface. He asks, " Was the par- 
 ticular structure of certain portions of the crust of the globe, 
 which is indicated by the situation of elevated regions on its 
 surface, among the causes of the eruption of volcanic rocks? or 
 were the inequalities of level on the surface, in the volcanic 
 regions, due to the processes attending and the agencies causing 
 the eruptions? The answer to both these questions must be in 
 the affirmative 1 ." 
 
 The same author writing of the mode of geological oc- 
 currence of the rocks which have formed massive or fissure 
 eruptions, says of andesite that " preeminently the greater part 
 of it has to all appearance been ejected through extensive 
 fissures; that is, it has been produced by what are styled mas- 
 sive eruptions Andesitic mountains are characterised by 
 
 monotony in scenery. They form continuous ranges which are 
 often of considerable elevation and extent 2 ." Again of this 
 rock he tells us that in Hungary, "andesite composes entirely 
 the Hargitta-range, which extends over one hundred miles in 
 length and twenty-five in width ; the Vihorlat-Gutin-range, 
 which is of still larger dimensions, and the Eperies-Kaschau- 
 range; all of which are densely wooded, and of a gloomy 
 monotonous aspect 3 ." Similarly he mentions belts and ranges 
 of basalt 4 . 
 
 If the eruption of these extensive ranges, through fissures 
 which must have been of great width, was indeed synchronous 
 with the compression that raised the mountains which they 
 skirt, there appears to be no escape from the conclusion that the 
 rending of the fissures was the cause of the compression, because 
 no pressure from beyond, greater than their own, could have 
 
 1 " Natural System of Volcanic Kocks," p. 82. 
 
 2 Ibid. p. 75. 3 Ibid. p. 30. 
 4 Ibid. p. 27. 
 
CH. xv.] COMPRESSION AND VOLCANIC ACTION. 205 
 
 been transmitted across such fissures filled with fluid, nor could 
 they have supported a pressure propagated from the further 
 side of the elevated tract, so that the intervening region could 
 have been compressed. 
 
 According to the suggestions offered in the present chapter 
 to explain the compression of the crust, the store of energy 
 from which the mechanical force is derived resides (1) in the 
 heat of the interior, and (2), if we refer any part of it to 
 expansion of the rocks on solidifying, in the molecular force 
 attending a change of state ; while in the theories discussed in 
 the former chapters the force is derived from the gravitation of 
 the crust towards the centre of attraction of the globe. This 
 latter force is practically infinite compared with the work it 
 would have to perform in shearing the crust, but it has been 
 shown that the limit to the space through which it can have 
 acted, owing to the small amount of the globe's contraction, is 
 so quickly reached, that it cannot fully explain the pheno- 
 mena. The case is entirely different with regard to the theory 
 now suggested. Here the force (1) is limited, since it never can 
 exceed, or indeed practically reach, the pressure of a column of 
 the earth's crust, viz. about 23,547,900 pounds, or 10,066 tons, 
 upon the square foot, but there is no limit to the space through 
 which it might act, so long as the fissures did not reach the 
 surface. The limit imposed is the resistance which the crust 
 offers to shearing. And it is probable that this may have 
 been reached, where a tract has been thickened to such an 
 extent, that its surface has been elevated to the normal height 
 of the highlands of the globe. 
 
 The direction orthogonal to a fissure in which motion 
 would take place when the crust yielded, would depend upon its 
 rigidity; and it is conceivable that, although thicker beneath 
 continental areas, it may be weaker there, because less homo- 
 geneous and less dense ; and we know that surfaces of rupture, 
 once formed and faced with slickenslide, are ready prepared for 
 repeated movements. If such be the case, the tendency would 
 be for compression to take place in the direction from the shore 
 margin towards the mountain ranges. The latter being continu- 
 
206 COMPRESSION AND VOLCANIC ACTION. [CH. xv. 
 
 ally denuded down, and the material carried to the shore margin 
 again, and there accumulating, sinking, and being again pressed 
 towards the ranges, would cause a kind of circulation of rock 
 from the coast-line inland, and back again by way of the surface. 
 Since by this means every part would in its turn be subjected 
 to atmospheric action, the more soluble basic constituents would 
 be carried out to sea, and it is possible that it may be to this 
 cause that the lesser density of the continental crust may be 
 owing, even although the continental rocks have these con- 
 stituents to some extent continually restored by the intrusions 
 of the magma from below 1 . It has been ascertained that in the 
 deeper parts of the ocean, from 2700 fathoms and more, the 
 dredge invariably brings up a fine red clay, consisting of silica, 
 alumina, and oxide of iron ; and everywhere containing nodules 
 of the peroxide of manganese 2 . It matters not what the mode 
 of transference and deposit of this clay may be, whether directly 
 as sediment, or indirectly, as believed to be the case, from the 
 kM insoluble remains of animal exuviae, for what is material to our 
 present argument is, that these heavy minerals, iron and 
 manganese, are accumulating over the floor of all the deeper 
 parts of the ocean, thus rendering the mean density of the 
 crust increasingly greater there, and necessarily abstracting 
 these substances from elsewhere, which can be nowhere except 
 from the continental areas, and diminishing their density by 
 that means. 
 
 The relation between the amount of compression, and 
 the quantity of lava injected into and solidified in the 
 fissures, is easily found. Referring to the figures on page 46, 
 suppose the tract, which before compression gave the rect- 
 angular section ABCD, to be distorted by the opening of fis- 
 sures. These will become partially or wholly filled with lava. 
 The parts of them which do not become so filled, become filled 
 / with debris, forming veinstone, and this will be derived from 
 
 1 See an interesting paper on the stratified rocks considered with respect to 
 the contributions which the internal parts of the globe have made towards them 
 by M. Daubrde, "Bulletin de la Socie'te' de France," 2ce Sdrie t. xxvin. p. 363. 
 Seance du 7 Sep. 1871. 
 
 a "Nature," Vol. xi. p. 116. Dec. 10, 1874. 
 
CH. xv.] COMPRESSION AND VOLCANIC ACTION. 2O7 
 
 the pre-existing crust. But the solidified lava is a new ac- 
 cession to it. 
 
 If (/) be the volume of the lava injected into the fissures, 
 we shall have by the figure, 
 
 or 2(/) = 2(a)-2(6)+2(/3)-2( a ). 
 
 If e were the compression which would produce a similar 
 tract out of the length I and thickness k of crust we perceive 
 from this expression that 
 
 2 (/) = Me. 
 
 We have estimated the value of e to be in the case of 
 nature 1 about 0*02 ; taking the thickness of the crust as 25 
 miles. With these values we get 
 
 that is to say the vertical sectional area of the dykes, occurring 
 in each horizontal mile of crust 25 miles thick, would be half a 
 square mile, or one-fiftieth of the whole sectional area. This 
 does not appear unreasonable, especially when we remember 
 that the dykes will be most numerous and widest in the lower 
 parts of the crust, which are probably never brought under our 
 observation. 
 
 1 p. 179. 
 
CHAPTER XVI. 
 
 ON FAULTING. 
 
 Faulting due to contraction " Hade to the downthrow" Faults may die out 
 in the deptlis The fissure which gives rise to the fault Fissure will have 
 the same hade as the fault Course of fault in a straight line Fissures 
 which cause faults commence at the surface Faults of Utah described by 
 Captain Dutton Faulting superimposed on corrugation Extent of throio 
 of great faults Faults will not usually admit the fluid magma If they 
 do so may give rise to fissure eruptions of igneous rock Application 
 of datum-level equation to faulting Faulting must depress the tract 
 affected General theoretical conclusion respecting the connection of fault- 
 ing and corrugation. 
 
 BESIDES corrugation the strata of the earth's surface have 
 been extensively affected by faulting. This has been usually, 
 and probably correctly, attributed to the contraction and con- 
 sequent shortening of the crust over those areas where it 
 occurs; for by faulting a portion of the crust is enabled to 
 occupy the same horizontal area after contracting, that it did 
 before, without gaping fissures being formed in it. 
 
 The well-known fact that faults commonly " hade to the 
 downthrow," which in untechnical language means that the 
 divisional plane, which constitutes the fault, inclines downwards 
 towards the side upon which the corresponding beds are found at 
 a lower level, appears to be explicable in the following manner. 
 If we had a series of superimposed beds perfectly homogeneous 
 each in itself, and each having its upper and under side strictly 
 parallel and horizontal, and if contraction were to commence 
 in these at the upper surface, it is conceivable that vertical 
 cracks might be formed in them, dividing the whole area into 
 
CH. xvi.] ON FAULTING, 209 
 
 blocks, as we see in the drying mud of a pond that has been 
 drained. Afterwards, or rather concomitantly, the vertical 
 pressure arising from the weight of the material in the blocks 
 might cause the cracks to be again filled up, at any rate to- 
 wards the bottom of them, by pressing out the material of the 
 blocks laterally so as to fill up the cracks. In such a case 
 there would be neither throw nor hade, and in fact no fault 
 at all, but merely a divisional plane or joint. 
 
 But if after a Y-shaped fissure had been formed, running 
 say North and South, the strata on one side, say the East, were 
 to settle downwards more than those on the West, the material 
 upon the East side would then be pressed out laterally, by 
 this settling, against the West side of the fissure. This side of 
 the fissure would accordingly form the divisional plane of the 
 fault, and would necessarily slope downwards to the East, 
 towards the sunken strata, or " hade to the downthrow." For 
 the sake of simplicity the two movements of the opening of 
 the fissure, and the settling down of the strata, have been 
 supposed to have occurred separately. But in nature the two 
 movements would go on together, and the pressure of the 
 subsiding beds would support those on the opposite side, 
 assisting to prevent their settling down to the same extent 
 as if they were not so supported. 
 
 If this explanation be admitted, it appears that an ordinary 
 fault of small throw might be formed through a very slight 
 defect from homogeneity of the beds on either side of it, for 
 the open space afforded by the fissure itself would give a 
 certain amount of room for the downcast beds to expand into 
 when they subsided. But if there was a considerable change 
 in passing from West to East in the condition of the beds, 
 the less dense layers becoming thicker and the harder ones 
 thinner within a moderate distance of the fault on the down- 
 cast side, then a larger displacement would result. 
 
 It is obvious that this explanation of the phenomena would 
 require the throw of the fault as a rule to become less and 
 less at greater depths, as is believed to be the case. In- 
 deed the Author has a note of having seen, in stratified brick- 
 F. 14 
 
210 ON FAULTING. [en. xvi. 
 
 earth in a pit at Copford in Essex, the complete phenomena 
 of an ordinary fault exemplified in miniature within the thick- 
 ness of about a foot, the dislocation being greatest at the upper 
 part, where the layers had been denuded to a level and again 
 covered up unconformably, and dying out entirely at the 
 bottom of the fault. In ordinary strata sections cannot be 
 seen of sufficient depth to exemplify this fact ; but Mr Curry 
 informs us l that " it is found, especially in the Alston Moor 
 district, that the throws and shifts are greatest at and near the 
 surface, and that they diminish in descending into the earth." 
 He also mentions the fact that "hades are greatest in shales, 
 or argillaceous strata," a fact agreeing well with the explanation 
 above offered of their origin. 
 
 "When a V-shaped fissure is propagated downwards the 
 angle of the V will follow some definite course or path in its 
 descent through the strata. We may call this the axial surface, 
 or, with sufficient accuracy, the axial plane of the fault. It 
 is obvious that, according to the above theory, it will not 
 coincide with the plane of the fault itself, which may be coin- 
 cident or nearly so with one of the branches of the V. Even 
 should the axial plane be vertical, the fault need not be so ; 
 as has been explained above. 
 
 But it seems more probable that the axial plane will have 
 an inclination corresponding to the hade of the fault, though 
 not so great. Of this the following quasi proof is offered. 
 
 * H,if r - 
 
 S. b,|~|Fa |b 2 B_ 2 
 
 C, c,| | F Jc a C 2 
 
 D, 
 
 a 
 
 |d.a D 2 
 
 E, 
 
 E 2 
 
 Suppose the strata A^A Z , BJB 9 , C^, &c., to be super- 
 imposed ; and suppose that a fissure is commenced by A t A 2 
 cracking at F^ Conceive the strata to contract more towards 
 
 1 "Proc. Literary and Phil. Soc. of Manchester," Vol. ix. p. 44. 1869. 
 
CH. xvi.] ON FAULTING. 21 1 
 
 A 2 , so that when contraction has proceeded to a small extent, 
 the end a 2 of the ruptured stratum has moved further from 
 its original -position F t than a l has moved from the same place. 
 Now let the stratum B^B^ crack. It is probable that it will 
 crack at F^ half way between a t and a 2 . At any rate, the 
 probability that it will crack to the right being the same as 
 that it will crack to the left, for a large number of layers the 
 average position of the crack will be central. Now, if the 
 thickness of the strata be indefinitely diminished and their 
 number indefinitely increased, we get the actual circumstances 
 of the formation of the fissure, and the locus of the points 
 F lt F^ &c. is the axial surface; and it is obvious that if our 
 demonstration be admitted it will hade to the downthrow, 
 because the beds which contract most in the horizontal direction 
 will also contract most in the vertical and form the downcast 
 side of the fault. 
 
 The fault itself would also have its throw and its hade in 
 the same direction as the fissure, and would run on slantingly 
 downwards until it reached some stratum or massive rock 
 which did not contract at that place, or where unconformity 
 occurred and contraction had previously been satisfied in the 
 underlying beds. 
 
 It would seem that vertical rather than horizontal con- 
 traction (though the two would go on together) determines the 
 course of faults. For horizontal contraction would tend to 
 divide a country into polygonal areas like a bed of basaltic 
 columns, but faults run in approximately straight lines. Now 
 this is the direction followed by a crack which is formed by 
 the depression of a lamina as may be observed in the case of 
 ice. When one first steps on a sheet of ice that has never 
 been disturbed it is usual to notice a crack run with a ringing 
 sound, quite, or nearly, across the surface in a straight line from 
 beneath one's feet. This is of the nature of a fault and is 
 another instance of the analogy between the behaviour of ice 
 and the strata of the earth's crust. 
 
 We propose therefore to explain the phenomena of faulting 
 
 142 
 
212 ON FAULTING. [en. xvi. 
 
 by the occurrence of fissures, commencing at the surface and 
 running downwards ; and among the causes which may have 
 given the first impetus to their formation may possibly have 
 been the drying of a surface from which either the sea or inland 
 lakes had been drained off, or even where the climate had 
 changed and become arid. That some faults have originated on 
 land surfaces appears from the observations of the United States 
 Survey, who tell us that in the High Plateaux of Utah " The 
 great displacements began in early tertiary time, and are 
 probably yet in progress. The evidences of the recency of 
 some of these movements appear in the escarpments frequently 
 seen along the line of faults where Quaternary beds have been 
 broken at a time so recent that the escarpments have not 
 been destroyed by atmospheric agencies, and further evidence 
 is exhibited in the small amount of talus frequently found at 
 the foot of a recently formed fault-scarp 1 ." 
 
 The connection of faults with surface changes is indicated 
 by the following passage from Captain Button's work : "It 
 yet remains to speak of another interesting relation of the 
 later system of faults. They have throughout preserved a 
 remarkable and persistent parallelism to the old shore line 
 of the Eocene lake following the broader features of its trend 
 in a striking manner. The cause of this relation is to me quite 
 inexplicable, so much so, that I am utterly at a loss to think of 
 any subsidiary facts which may be mentioned in connection 
 with it and which can throw light upon it V It .appears that 
 the area of the Eocene lake has been raised by the faulting 3 . 
 May nut the removal of the superincumbent weight of water 
 have been the proximate cause of the disturbance, and of the 
 uprising of the lightened area ? 
 
 Indeed we might expect that all such readjustments of 
 the equilibrium of the crust as do not arise immediately from 
 
 1 "Beport on the Geology of the High Plateaus of Utah, by C. E. Button, 
 Captain of Ordnance, U. S. A. Prefatory note by Major Powell," p. viii. Washing- 
 ton, 1880. A description of perhaps the most magnificent system of faults in 
 the world is to be found in Chap. n. of this work. 
 
 2 Ibid. p. 45. 3 Ibid. p. 38. 
 
CH. xvi.] ON FAULTING. 213 
 
 horizontal compression would be effected by faulting. The 
 features produced by this kind of movement would therefore be 
 superimposed upon the features previously or subsequently 
 determined by compression and consequent corrugation. 
 
 The blocks into which the strata were cut up would on the 
 whole follow the "lie" of the country as previously or con- 
 comitantly determined by the forces of compression, a general 
 law thus lucidly enounced by Prof. Green : "We find that we 
 can account for the observed facts only on one supposition, and 
 that is, that the rocks have been folded into a series of troughs 
 and arches, or thrown into domes and basins. This is the great 
 general law which governs everywhere the arrangement of the 
 disturbed portions of the earth's crust. Faulting, or violent 
 contortion and inversion, often complicate and obscure this 
 structure and interfere with its symmetry, but never to such 
 an extent as to prevent its being recognised as the great leading 
 feature in the arrangement of the rocks 1 ." 
 
 Faults occur of very different extent of throw, varying from 
 a few inches to many fathoms, or even miles. In Captain 
 Button's "Geology of the High Plateaus of Utah" we read of 
 displacements by faulting of 5,500, 1,800, 12,000, 4,000, and 
 7,000 feet 2 . Prof. Bonney tells us that the perhaps largest 
 known fault in the world is in the Appalachian Chain, where, 
 on opposite sides of a crack over which a man can stride, beds 
 are brought together that were once 20,000 feet apart 3 . 
 
 It is of course possible that a fault may cut quite through 
 the earth's crust, and indeed where the throw is so great as 
 to be measured by several thousand feet, as in some of the 
 larger faults referred to, it is scarcely conceivable that it should 
 not do so, if our estimate of about 25 miles for the thickness of 
 the crust is correct. If however the fault originate in a fissure 
 formed by the contraction of the strata near the surface, and 
 they settle together as the fissure extends downwards, thus 
 forming wedge-shaped blocks, broader at the top than the 
 
 1 "Geology for Students and General Readers," 1876, p.. 374. 
 
 2 Chap. n. 
 
 3 " Manuals of Elementary Science. Geology." S. P. O.K. 1874, p. 43. 
 
214 ON FA ULTING. [CH. xvi. 
 
 bottom, on account of the direction of the hade, it seems that 
 the fissure will be kept closed, and not admit the magma from 
 below. If however the contraction were very nearly equal on 
 both sides of the fissure, so that there was no greater settlement 
 on one side than on the other, a fissure might be actually opened 
 downwards through the whole thickness of the crust ; and being 
 open above so as not to form a chamber for the accumulation 
 of -high-pressure vapour to prevent it, the magma would rise 
 into it, and one of those great fissure eruptions would ensue, 
 which have, at one or another geological epoch, covered 
 large portions of the globe with beds of igneous rock. The 
 notion of a vast crevasse extending downwards to the fluid 
 magma may seem a wild dream, and certainly has no parallel in 
 anything known to occur at the present day. But neither has 
 any event of the nature of a fissure eruption come under the 
 cognizance of man; and yet their former occurrence seems 
 incontestible. And consequently the existence of such fissures 
 becomes a necessity \ 
 
 The datum-level equation, (1) p. 47, is at once made ap- 
 plicable to the case of faulting, when that arises from con- 
 traction of the rocks, by making e negative. But since the 
 rocks are supposed to contract in the vertical as well as in 
 the horizontal direction, e will represent the quadratic contraction 
 of the vertical section ; that is to say, upon the contraction 
 taking place, the sectional area Jcl will become the area kl(l e). 
 
 We shall then have, 
 
 JMe = 2 (b) - 2 (a) + 2 (a) - 2 () 
 
 It is easily seen that this is correct, because the area of 
 vertical section, which was before contraction occupied by kl, is 
 after contraction occupied by 
 
 M(l - e) + 2 (&) - 2 (a) + 2 (a) -2() \ 
 
 1 "The Lava Fields of North Western Europe," Prof. A. Geikie. Nature, 
 Vol. xxm. p. 3. 1880. Also Eichthofen's "Natural System of Volcanic rocks," 
 p. 17. Menu, of California Academy of Sciences, Vol. i. Ft. ii. San Francisco, 
 1868. 
 
en. xvi.] ON FAULTING. 215 
 
 whence, equating these quantities, 
 
 Me = S (5) -2 (a) + 2 (a) -2 (), 
 
 which is the datum-level equation with the sign of e changed. 
 It follows as before 1 that 
 
 28 (a) -2(0) p 
 
 = 0104, 
 
 if we suppose a- and p to be the densities of basalt and granite. 
 Combining this with the expression for He we get, 
 
 S (6) -S (a) =0'09&fe. 
 Whence 2 (6) S (a) is a positive quantity. 
 Indeed generally, 
 
 and is positive because cr is greater than />. 
 
 But S (6) S (a) is the mean depression of the tract below 
 the mean level. Hence we see that such faulting as arises 
 from subsidence owing to contraction, must on the whole 
 depress the surface of the tract disturbed by it. But the 
 
 depression will be small because - is small on account of 
 
 cr 
 
 the difference of the densities being small compared with the 
 greater. 
 
 The general conclusion now offered for the consideration of 
 geologists therefore is, that both corrugation and faulting are 
 ultimately dependent upon the contraction, and consequent 
 fissuring, of the crust, when it undergoes those changes, varying 
 in degree from mere solidification to intense plutonic action, 
 which convert aqueous sediments into denser rocks, and are all 
 included under the generic term, metamorphism. The fissuring 
 consequent on the contraction, which accompanies these changes, 
 
 1 p. 118. 
 
2 1 6 ON FA ULTING. [CH. xvi. 
 
 when it commences below and is propagated upwards, gives 
 rise to the phenomena of compression, owing to the intrusion 
 of highly elastic matter from below, and corrugation is the 
 consequence. Volcanic phenomena are believed to be another 
 manifestation of the same mode of action. On the other hand, 
 when the fissures commence above and are propagated down- 
 wards, they give rise to ordinary faulting, and if formed on 
 so large a scale that they reach through the crust, it is suggested 
 that great fissure eruptions of igneous rocks may take place 
 through these* 
 
CHAPTER XVII. 
 
 GEOLOGICAL MOVEMENTS EXPLAINED. 
 
 Eecapitulation of the four suggested causes of compression Three of them 
 negatived The fourth possibly the true one The fact of compression certain, 
 and the duplex character of the corrugations most probable The conse- 
 quences of denudation followed out Elevation its correlative Fresh-water 
 strata covered by marine Movements most energetic near, but not confined to, 
 continents Degradation of mountains a law of nature Enormous thickness 
 of certain strata accounted for Raised sea beaches Two classes of elevatory 
 movements Drainage across dip Theories of compression compared. 
 
 IN our endeavour to discover the cause of the compression, by 
 which it is generally believed that the elevations existing upon 
 the earth's surface have been produced, it must be admitted that 
 we have not arrived at any degree of positive certainty. The 
 results obtained have been mostly negative. But even negative 
 results have great value, because the disproof of a theory, which 
 for want of close examination may long hold its ground, removes 
 a chief obstacle to further advance in knowledge. It is submitted, 
 then, that the theory has been disproved (1), That the earth is a 
 solid body cooling by conduction, and that the inequalities which 
 appear on its surface have been caused by the contraction of the 
 interior through cooling. 
 
 It has further been shown that the geological phenomena re- 
 quire us to suppose that the crust of the earth rests upon a fluid 
 substratum, and this belief has led to the examination, and rejec- 
 tion, of a second theory, (2) That the crust is thin, and is so far 
 flexible that the fluid may rise into the anticlinals formed by the 
 corrugations of the crust; a view held by some who have written 
 on the subject 1 , and at one time entertained by the Author him- 
 
 1 See note, p. 169. 
 
2 1 8 GEOLOGIC A L MO VEMENTS [en. xvn. 
 
 self. The rejection of this hypothesis has led to the supposition 
 that the crust is flexible only to a small degree, and that, under 
 compression, the corrugations which are raised upon the surface 
 must be accompanied by corresponding downward protuberances 
 of larger dimensions projecting into the fluid below, thus causing 
 them to be duplex : and it has been pointed out that certain 
 facts, brought to light by experiments made with the plumb- 
 line upon the attraction of mountainous regions, have been 
 better explained by Sir G. B. Airy upon the supposition of 
 such protuberances, than in any other way that has been 
 suggested. We have also shown that certain other facts of 
 an entirely different class, connected with the observed slow 
 rate of increase of temperature beneath mountains, are also 
 better accounted for in this manner, than in the way originally 
 proposed by the observer, who has studied and described the 
 phenomena most carefully. 
 
 These two circumstances appear to lend a very con- 
 siderable amount of support to this view of the subject, so 
 that the diagrammatic sections of Chapter X., which represent 
 the outcome of it, are thus far corroborated. 
 
 But in seeking for a cause of compression, which may have 
 produced corrugations of the duplex character and amount 
 required, our first attempt has failed. Here has therefore been 
 a third hypothesis examined and found insufficient. It was 
 (3) That the compression which has caused these corrugations 
 has arisen from a diminution of the earth's volume through 
 extravasation of water-substance from beneath the crust. The 
 Author himself had some years ago suggested this idea, and 
 it had been not unfavourably received by some leading geo- 
 logists. But when he came to write the chapter in which 
 the hypothesis is discussed, he found it, as he now believes, 
 insufficient alone to produce the compression requisite. 
 
 All these explanations having failed, and the fact of com- 
 pression still remaining patent, a fresh suggestion has been 
 put forward, which is not intended to be more than tentative 
 and may possibly share the fate of the rest. But it has this 
 
en. XVIL] EXPLAINED. 2 1 9 
 
 advantage, that it brings the phenomena of faulting, that 
 other form in which the disturbances of the earth's crust are 
 manifested, into harmony with those of compression, attributing 
 both to the same ultimate cause. The reader is however re- 
 quested not to consider the suggestions last offered, regarding 
 the cause of compression, to rest on so firm a foundation as 
 the results arrived at concerning the existence of a fluid sub- 
 stratum, and of the characteristic duplex shape of the corrugations 
 formed in the crust by compression, let the causes of it be what 
 they may. 
 
 We will now trace somewhat further than was done in the 
 tenth chapter, the results of denudation and of additional com- 
 pression upon an elevated tract constituted thus, and compare 
 them with natural appearances. It is evident that, as the 
 upper and exposed part of the chain is degraded, the equili- 
 brium will be roughly speaking restored by the whole mass 
 being lifted up, so that the part above the effective level of 
 the fluid should hold approximately the same ratio as before, 
 that of a p : /?, to the part below it. Consequently, before 
 a mountain chain can be completely levelled down, not only 
 must the originally elevated portion be degraded, but the crust 
 beneath must also be lifted up and brought under the influence 
 of the denuding agents, possibly down to the neutral zone, and 
 the whole of the material so removed converted into sediment, 
 and transferred to some lower level 1 . 
 
 1 To determine to how great a depth denudation might be ex- 
 pected to expose the crust, suppose that A is the crust of a corru- 
 gation, and B the bottom of the corresponding protuberance, Z the 
 place of the neutral zone; and let Xbe the point that is ultimately 
 
 brought to the surface by denudation. We have concluded that, 
 
 AZ=%AB, and ZB=%AB. 
 
 Now if X is ultimately brought to the surface, B will at the same 
 time be brought to the lower mean level. Hence 
 
 XB=c. 
 And therefore 
 
 .'. AX-AZ=(AB-5c). 
 
220 GEOLOGICAL MOVEMENTS [CH. xvn. 
 
 It is not however necessary to suppose that the roots of 
 the elevated tract ever at any one time bore this proportion 
 of p : a- p to the whole volume which has ultimately been 
 denuded away ; for this would not be the case unless the 
 compression and accompanying elevation were due to a single 
 effort. For if, after a part had been denuded off, and the 
 roots of the mountain had been concurrently lifted up, a second 
 period of compression had ensued, the neutral zone would then 
 have had its position along a lower line of "particles, and the 
 depression produced might not have been so great at the 
 second as at the first effort. The same may be said of a 
 third, or of any subsequent effort. In fact, according to the 
 ordinary reasoning of the method of limits, we may, by 
 diminishing the intervals and increasing their number, pass 
 to the case of a continuous movement of elevation, growing less 
 and less until it ceased altogether; denudation going on all 
 the while at a greater rate than, except at first, material was 
 brought up for it to act upon. 
 
 If the tract were now to become free from farther com- 
 pression, the sequence of events we have sketched out would 
 be terminated by its being reduced in thickness approximately 
 to the normal thickness of the crust in its neighbourhood. 
 But its internal structure, as exhibited in sections, would betray 
 the results of the treatment to which it had of old been sub- 
 jected. It would form a nearly level tract, consisting of the 
 lower parts of the folds of highly contorted rocks, which had 
 been subjected to the action of a temperature probably above 
 the critical temperature of water, and to great pressure. 
 
 The sediment, which had been transferred from the tract 
 thus denuded down, would some of it have probably been 
 spread over low lying land, and some of it have gone out to 
 sea, and formed marine deposits not very far from the shore. 
 
 Hence if AB<5c AX<AZ 
 
 that is the neutral zone will not be brought to the surface unless AB > 5c. 
 
 But AB is about 11 times the height of the mountain. 
 
 Therefore the height of the mountain must have been T 5 T c, or say 10 miles, 
 before denudation commenced, in order that the neutral zone should come to the 
 surface. 
 
CH. xvii.} EXPLAINED. 221 
 
 Both these would have sunk nearly as fast as they accumulated, 
 and by this means unmetamorphosed strata would have been 
 depressed into regions where their temperature would have been 
 gradually raised, and metamorphism set in. This would render 
 them more dense. They must necessarily contract in con- 
 sequence, and those results follow to which in the preceding 
 chapter we have attributed compression. This compression 
 might act directly upon the mass itself, or it might be com- 
 municated to a neighbouring tract ; but on the whole it seems 
 probable that the mass itself would be the first affected, and 
 this agrees with the theory that compression and elevation 
 are the consequences of the accumulation of thick deposits. 
 The difference between the theory now offered and that pro- 
 posed by American geologists consists in the cause from which 
 the compressing force originates. 
 
 The suggestions now put forward appear to give a fairly 
 satisfactory explanation of the causes of the deposition of series 
 of marine strata of great thickness, of unconformity, of meta- 
 morphism, of contortion and elevation. The phenomenon which 
 seems omitted from the explanation is that of the depression 
 of fresh-wa.ter strata beneath the ocean, as for instance of the 
 coal measures of various ages. This however might arise from 
 such deposits being depressed below the level of the sea, though 
 not under the sea, through being loaded with fresh-water sedi- 
 ment, as is known from borings to be going on at present 
 in great deltas and river valleys ; and then, the process being 
 checked, the sea might cut away the upper part of the sub- 
 aerial deposit, and a marine stratum might take its place. It 
 is possible that the fresh-water deposits becoming scanty, and 
 the district arid, faulting might be induced through contraction 
 of the beds before the sea had time to advance, and thus we 
 should find the fresh-water beds much broken up before the 
 marine were laid down over theni. 
 
 The exciting cause of the movements of the crust, as we 
 have attempted to explain them, is the transference of sedi- 
 ment. Wherever that goes on, movements of the crust may 
 be expected to take place. And although not altogether con- 
 
222 GEOLOGICAL MOVEMENTS [OH. xvii. 
 
 fined to these regions, it is obvious that it is in continental 
 areas, and along their shores that these processes are the more 
 energetic. It is therefore conceivable that the medial regions 
 of the great oceans may have been comparatively free from 
 disturbance at all times. Nevertheless the growth of coral, 
 the deposits from icebergs, and the sinking of the exuviae of 
 marine organisms, are causes which may contribute to the 
 unequal deposition of sediment, over such areas as these, 
 and we would not therefore relegate even them to perpetual 
 repose. 
 
 It is certain that most of the existing greater mountain 
 chains are comparatively modern ; for it is possible to assign 
 dates, geologically not remote, to the movements to which they 
 owe their exceptional altitude. At the same time their struc- 
 ture usually betrays that the original effort which raised them 
 was not the final one, for they have been subjected to repeated 
 compression. This comparatively modern character of the 
 greater chains leads us to believe that the gradual degradation 
 and obliteration of a mountain range is a law of nature, in 
 accordance with which the older chains have been levelled down 
 and disappeared. The corrugated rocks which may have formed 
 parts of them are still to be discovered as fundamental gneiss 
 for instance, showing by their chemical and mechanical condi- 
 tion that they have been subjected at some former time to 
 a high temperature and to great compression. They are now 
 frequently covered up by later deposits. 
 
 The rising upwards of an elevated region by floatation con- 
 currently with its degradation, explains some well known facts, 
 among which are the following. 
 
 When the original contours of the strata are restored, which 
 must have gone to form a disturbed tract, the enormous amount 
 of subsequent denudation appears at first sight incredible. 
 This is extremely well shown in Prof. Ramsay's restored con- 
 tours along some sections in South Wales 1 , where the heights 
 vand distances are laid down upon the same scale, a method 
 
 1 "Memoirs of the Geological Survey of Great Britain," Vol. i. 1846, 
 pi. iv. 
 
CH. xvii.] EXPLAINED. 223 
 
 which enables us at once to appreciate the immense amount of 
 material that has been removed. This is not a singular case. 
 It is a universal phenomenon. Now there is much less diffi- 
 culty in conceiving strata to have been slowly lifted up from 
 below concurrently with their degradation, than in supposing 
 that the dry lands of old time were thousands of feet high 
 where now we measure them by hundreds. 
 
 We have also the correlative fact of the excessive amount of 
 sediment which an elevated tract has been found capable of 
 yielding, and yet it remains an elevated tract still. Series of 
 strata, five, six, or seven miles thick, and of great superficial 
 extent, can be more easily thus accounted for, than by supposing 
 the area from which they have been derived to have been five, 
 six, or seven miles higher than it stands at present, even if it 
 be now reduced below the sea-level. 
 
 The doctrine that areas must sink when loaded, and rise 
 when relieved of a load, may perhaps explain other known 
 phenomena. It is not impossible that the raised shell beds of 
 Scandinavia may be partly accounted for by the country having 
 been depressed owing to its being formerly loaded with heavy 
 ice-fields, and that its gradual subsequent rise may have been 
 caused by the ice having been melted off. These beaches are 
 found up to an altitude of about 700 feet 1 . Putting three feet 
 of ice as equivalent to one of rock, a liberal estimate, 2310 
 feet additional of ice would, upon the suppositions we have 
 made respecting the relative densities of the crust and sub- 
 stratum, effect this amount of depression 2 . This would be 
 
 1 LyeU's "Elements of Geology," Vol. i. p. 133, 10th edn. 1872. It may, 
 however, be objected to this idea that several of the species in the shells' beds are 
 of a Mediterranean type. Croll's "Climate and Time," p. 253. 
 
 2 Let x be the height of the surface above the mean upper level when there is 
 no ice, y the depth of the root under the same circumstances. x', ?/', the like 
 quantities when there is a thickness of z ice. 
 
 Then we have the four equations, 
 y=Wx, 
 
 /=w, 
 
 x'=x- 700 + z, (see text) 
 x' + y'=x + y + \z. 
 Whence z = 2310 feet. 
 
224 GEOLOGICAL MOVEMENTS [CH. xvn. 
 
 less than the average thickness of the icebergs seen from the 
 Challenger in the Antarctic ocean 1 . 
 
 Similar movements have occurred, and are now going on in 
 Greenland. Raised beaches are found up to 326 feet above 
 the sea. But the land is now slowly subsiding at the rate of 
 about from 6 to 8 feet per century. This may possibly be 
 accounted for by the snowfall being at present greater than 
 is carried off by the glaciers and by evaporation 2 . 
 
 It is clear that vertical movements of the earth's crust will, 
 according to our theory, be of two kinds ; one resulting from 
 the laws of hydrostatic equilibrium simply, and the other 
 connected with compression. The former, although it may for 
 a long time continue to lift up the rocks of a given area from 
 below, can yet never by itself restore them to their pristine 
 height. Degradation must always make more rapid progress 
 than elevation. But the two are necessarily correlatives of each 
 other. The degradation of the tract causes more rock to rise 
 up, to be in its turn degraded. Such slow and continuous 
 upward movement explains how rivers can cut across the dip of 
 hills. It explains the drainage of such areas as the Weald, and 
 of valleys of elevation on even a grander scale. It explains 
 perhaps even the drainage of the great plateau of the Colorado 
 region. It also explains the fact that we find what once were 
 perhaps river gravels perched on the highest hills of a district. 
 But the vertical movements arising from compression are of a 
 different character. The effect is to elevate a tract to a higher 
 average level than before. There may be troughs and depres- 
 sions formed by it, but their amount will be more than counter- 
 balanced by the elevations. The internal heat of the earth is 
 the ultimate cause of this class of movements. The contrac- 
 tion of the interior from cooling may possibly contribute to 
 
 1 Sir Wyville Thomson, "On the Conditions of the Antarctic," Nature, Vol. 
 xv. p. 105, states that these stand about 200 feet high above water. Calculating 
 from a specific gravity of 0-92 this gives 2,500 feet for the entire thickness. 
 
 2 M. Johnstrup, " On the Interior of Greenland," reviewed in Nature, Vol. 
 xxi. p. 344, 1880. The above passages were written before the appearance of 
 Mr J. S. Gardner's article in the " Geol. Mag." Dec. 2, Vol. viu. p. 241, where 
 somewhat similar views are propounded. 
 
CH. xvii.] EXPLAINED. 225 
 
 produce compression, and the extravasation of water-substance 
 from beneath the crust may also play its part, but it appears 
 that neither of these, nor yet both together, can account for an 
 appreciable portion of the grand result. Whether the mode of 
 action suggested in Chapter XV., more immediately derived from 
 the same source, is capable of doing so is not easily decided. It 
 must be remembered that the amount of compression calculated 
 in Chapter XIII., as requisite to account for the existing eleva- 
 tions, refers to the whole time elapsed since they began to be 
 formed. But the act of compression connected with the forma- 
 tion of the dykes beneath any given region would be confined 
 to a comparatively limited geological period. We should there- 
 fore expect to find in them evidence of compression belonging, 
 as regards time, only to a part of the whole amount required. 
 On this account, ocular evidence of a smaller amount of expan- 
 sion might be deemed sufficient. On the other hand, our theory 
 localises the compressing force, and on this account we should 
 look, as regards space, for evidence of a larger amount than if 
 the expansion producing it were evenly distributed. Another 
 difficulty arises, namely, that the width of the dykes will be too 
 large a measure of the expansion arising from them, because the" 
 fissures will have been partly opened by the contraction of the 
 rocks themselves, and only partly forced asunder by the pres- 
 sure to which we are now attributing compression. It cannot / 
 be denied that, as the former three hypotheses have proved in- < 
 adequate when brought to numerical tests, so, if it could be done,} 
 might also this last. Still the estimate at the end of Chapter 
 XV. may be considered favourable. The theory possesses the 
 advantage over the others that, if the lateral pressure be deemed 
 sufficient, the range through which it is capable of acting is 
 practically sufficient. These conditions are the exact reverse 
 of the former ; for in them there could be no question regard- 
 ing the sufficiency of the lateral force, but the range was found 
 to be insufficient. In the present case, the difficulty consists in 
 applying any test to see whether the phenomena indicate that 
 the force now appealed to can in fact have acted through a 
 sufficient range to have produced the requisite compression. 
 
 F. 15 
 
CHAPTER XVIII. 
 
 ME MALLET'S THEORY OF VOLCANIC ENERGY. 
 
 Early opinions regarding the seat of volcanic energy Hopkins' lava lakes 
 Mallei's theory Opposed to the results of the present work His mode of 
 estimating the temperature derivable from crushing rock His results pub- 
 lished in the "Phil. Trans.'" differ from those given in an earlier publica- 
 tion Latent heat of fusion Localization of heat from crushing not possible 
 More favourable hypothesis suggested and considered A pressure, the 
 greatest obtainable on the hypothesis, incapable of causing volcanic phe- 
 
 IT has been taken for granted more than once in the preceding 
 pages, that the seat of volcanic energy is situated in the fluid 
 substratum, which we have endeavoured to prove must underlie 
 the cooled crust of the earth. This is the natural supposition, 
 and was formerly generally assumed by geologists. But when 
 Hopkins published his supposed proof of the great thickness of 
 the earth's crust, he was constrained to offer a fresh explanation 
 of this class of phenomena. Hence his theory of subterraneous 
 lakes of lava. When Sir Wm. Thomson corroborated Hopkins' 
 view, and carried it further to the extent of asserting the entire 
 solidity of the globe as a whole, the old assumption concerning 
 the universal distribution of fluid matter beneath the crust 
 received a further blow. The theory of Hopkins' lakes was 
 permitted to stand, but it was felt to be so improbable, that 
 physical geologists in general could not rest satisfied with that 
 explanation. 
 
 At this juncture Mr Mallet published his theory of volcanic 
 energy 1 , which at the time of its publication was received with 
 
 1 "Phil. Trans. Eoyal Soc." Vol. 163, p. 147. 1873. 
 
CH. xviii.] THEORY OF VOLCANIC ENERGY. 227 
 
 considerable favour by many. Impressed with the necessity of 
 admitting the doctrine of a solid earth upon the authority of the 
 highest masters of physical science, they saw in Mr Mallet's 
 hypothesis a way of escape from the difficulty in which they 
 were placed. If the earth be a solid body cooling by conduction, 
 and if the corrugations upon its surface are caused by the con- 
 traction of the mass and consequent compression of the super- 
 ficial layers, what, it has been thought, can be more in accord- 
 ance with probability, than that the work of compression should 
 be converted into heat, and that volcanic energy should be its 
 manifestation, and have its seat no deeper than the compressed 
 crust. Like many simple explanations, the only wonder was 
 that no one had suggested it before. Yet how often had been 
 long delayed the discovery of some theory, which when once 
 proposed seems simplicity itself. 
 
 If Mr Mallet's theory be true, it is obvious that that now 
 propounded must be untenable. It will therefore be necessary 
 to examine it. 
 
 The theory is enunciated in the following terms 1 : 
 "The heat from which terrestrial volcanic energy is at present 
 derived is produced locally within the solid shell of our globe by 
 transformation of the mechanical work of compression or of 
 crushing of portions of that shell, which compressions and crush- 
 ings are themselves produced by the more rapid contraction, by 
 cooling, of the hotter material of the nucleus beneath that shell, 
 and the consequent more or less free descent of the shell by gravi- 
 tation, the vertical work of which is resolved into tangential pres- 
 sures and motion within the thickness of the shell" 
 
 As regards the lateral pressure to which Mr Mallet appeals 
 as the cause of compression, and of crushing portions of the 
 shell, there can be no doubt that, if there were a continual 
 contraction of the interior and subsidence of the shell going on, 
 the pressure arising from the descent of the shell would be per- 
 fectly adequate to produce the crushing attributed to it. 
 
 We have however, as we believe, seen grave reason to doubt 
 
 1 Op. cit. 67, p. 167. 
 
 152 
 
228 MR MALLETS [OH. xvm. 
 
 whether this contraction exists, at least to such an extent as to 
 produce any appreciable movements of the crust during such 
 periods of time as history embraces. Yet volcanic phenomena 
 are of daily occurrence. This appears to dispose of the theory 
 in limine. Nevertheless it is possible that this argument 
 against it may not meet with general acceptance, and it is 
 therefore desirable to examine Mr Mallet's theory upon his own 
 assumptions. 
 
 No one can study the paper, in which the theory is pro- 
 pounded, without admiring the amount of knowledge displayed 
 in it, and the numerous and laborious experimental investiga- 
 tions which he undertook to form the basis of his theory. The 
 records of these alone will render his work of lasting value. 
 Nevertheless we cannot avoid the conviction, that they do not 
 warrant the conclusions which he has drawn from them. 
 
 The experiments which form the foundation of the theory 
 may be shortly thus described : 
 
 Cubes of rock of sixteen different kinds, varying in respect 
 of hardness from soft oolite to hard porphyry, were carefully 
 cut into cubes of 1^- inches on the edge. These were then 
 crushed by means of a powerful lever, under a cylindrical piston 
 or plunger of 3J inches diameter. The cubes of rock appear 
 not to have been confined at all laterally, so that, when they 
 gave way, they were compressed into a cake of powder beneath 
 the plunger. 
 
 The pressure upon each square inch of the face of the cube 
 was calculated from the accurately known pressure laid upon 
 the plunger, and the vertical descent of the plunger, while the 
 crushing was going on, was also carefully measured. These 
 multiplied together gave the "work" of crushing, and by divid- 
 ing the work so obtained by Joule's equivalent the correspond- 
 ing quantity of heat was calculated, it being assumed that all 
 the work was transformed into heat. 
 
 If we consider the summary of the series of experiments in 
 crushing cubes of rock *, it is evident that the vertical descent 
 
 1 Op. cit. Tab. i. column 19, p. 187. 
 
CH. xviii.] THEORY OF VOLCANIC ENERGY. 229 
 
 of the plunger must have been rendered much greater by the 
 cube of rock having been free to fall asunder on all sides. If it 
 had been confined in a box of its exact size it might still have 
 been crushed; but the amount of descent would have been in 
 that case dependent solely upon the increase of density which 
 could be given to it after disintegration by the pressure. If the 
 box had been somewhat larger, the plunger would have de- 
 scended further, and if the rock was altogether unsupported, 
 as seems to have been the case, further still. The value of H 
 (the heat) found in accordance with the experiment is correct; 
 but the form of the experiment cannot represent at all closely 
 what would happen deep in the earth's crust. It seems that the 
 cubes should have been confined, that the experiment might 
 more closely represent the case of nature. 
 
 But accepting the results as given, the equation connecting 
 the quantities involved may be thus arrived at. Let 
 
 W= the pressure laid upon the plunger. 
 h = the height through which the plunger descended. 
 J Joule's equivalent, or the number 772. 
 
 H=fhe number of units of heat into which the work of 
 crushing was transformed. 
 
 rru TT 
 
 Then #=. 
 
 J 
 
 Also, t = the temperature through which the rock was raised 
 by the crushing. 
 
 s = the specific heat of the rock, i.e. the number of units 
 of heat requisite to raise 1 Ib. of rock through 1 F. 
 
 _ quantity of heat requisite to raise w of rock 1 
 
 w 
 
 quantity of heat requisite to raise w of rock t 
 .*. ts ^ - . 
 
 w 
 
 w 
 
 Hence t = . 
 
 sw 
 
230 MR MALLETS [CH. xvm. 
 
 f 
 
 This is Mr Mallet's equation (6), 102, where he takes w to 
 be the mass of one cubic foot of rock, and of which we have for 
 clearness given a demonstration. His experiments gave for the 
 mean value of 5 the number 0*199; and for the mean weight w of 
 a cubic foot of rock 177 lb. The mean number of British units 
 of heat developed by crushing one cubic foot of the harder rocks 
 is estimated by him at 5G50 ; and it appears upon calculating 
 the value of t, that the mean temperature by which a cubic foot 
 of such rock would be so raised is 172 F. Or if we take the 
 particular kinds of rock selected by Mr Mallet ( 133), these 
 means are found by him to be 6472 and 183*74 F. And if the 
 rock was previously at 300 F., taking 2000 as the fusing tem- 
 perature, he finds 0*108, or rather above one-tenth, as the frac- 
 tion of a cubic foot of rock which the heat developed by crushing 
 one cubic foot of rock could fuse. Or, to put it otherwise, it would 
 require the heat developed by crushing ten volumes of rock to 
 fuse about one. 
 
 Here we meet with a remarkable discrepancy between the 
 results given in the paper in the Philosophical Transactions 
 and those previously given in the introductory sketch to the 
 same author's translation of Palmieri's "Vesuvius 1 ," for it is there 
 stated that using the mean of 6472 units of heat as derived 
 from crushing one cubic foot of rock "each cubic mile of the 
 mean material of such a crust, when crushed to powder, deve- 
 lopes sufficient heat to melt 0*876 cubic miles of ice into water 
 at 32, or to raise 7*600 cubic miles of water from 32 to 212 F., 
 or to boil off 1'124 cubic miles of water at 32 into steam of 
 one atmosphere, or, taking the average melting point of rocky 
 mixtures at 2000 F., to melt nearly three and a half cubic 
 miles of such rock, if of the same specific heat." It is obvious 
 that it makes no difference in the ratio, whether the unit be a 
 cubic mile, or a cubic foot, or a cubic inch. So that the state- 
 ment here amounts to saying, that the crushing of one cubic 
 foot would melt 3 J cubic feet, instead of 0*108 of a cubic foot ; 
 or more than 32 times as much as subsequently stated in the 
 
 1 p. 69. 'There is a foot-note to the paper in the Transactions which speaks 
 of a modification of 102. This may be connected with the discrepancy re- 
 ferred to. 
 
CH. xviii.] THEORY OF VOLCANIC ENERGY. 231 
 
 Transactions. Indeed the experimenter must have felt sur- 
 prised that the cubes were not melted, seeing that the heat 
 developed ought to have been three and a half times as great 
 as necessary for the purpose. 
 
 It will also occur to the reader, that Mr Mallet has not 
 made any allowance on account of the latent heat of fusion, but 
 has assumed that, when sufficient heat had been supplied to a 
 mass of rock to raise it to the temperature of fusion, it would 
 become wholly fused. This of course is not the case, because 
 much of the heat would be employed in producing the change 
 of state from solid to liquid, without producing any effect on the 
 temperature. 
 
 But accepting the conclusion that the heat resulting from 
 crushing one cubic foot could fuse 0*108 of a cubic foot, since 
 this is not capable of fusing the whole of the cubic foot crushed, 
 Mr Mallet considers that this heat may be localized, and that 
 the heat developed by crushing ten cubic miles of rock, may 
 fuse one mile. But it may be conclusively shown that this is 
 not possible; for let us consider a horizontal prism of rock of 
 any length. This is itself a part of the earth's crust, and by 
 its rigidity has, up to the moment of its giving way, resisted, 
 and so permitted, the necessary accumulation of the pressure 
 which eventually causes it to yield. Conceive that in this prism 
 there are portions situated here and there which are weaker 
 than the average, and that these weak portions when crushed 
 allow of the prism being shortened at the places where they 
 are situated by the quantities eq, 2 , 3 , &c. respectively. It is 
 clear that the weaker places will yield first and under a less 
 pressure, and by the relief so afforded delay the crushing of the 
 others, because the pressure must accumulate afresh. But, for 
 argument's sake, we will suppose all to yield together, and the 
 pressure throughout the action to be equal to the value it had 
 at the first yielding. 
 
 Now suppose that when the prism has yielded the whole of 
 it becomes shortened by the length a. If, then, P be the 
 pressure which caused it to yield, Pa will be the whole work 
 done upon the prism. The length a is made up of the portions 
 
MR MALLETS [CH. xvm. 
 
 a i> a 2 > a s > & c -> by which the weak portions have been shortened; 
 while Pa lt Pa 2 , Pa 3 , &c. are the portions of work done at these 
 places. And these taken together make up Pa, since 
 
 or, + a 2 -f- 3 + &c. = a. 
 
 We see, then, that the work must be confined to these places ; 
 for if there were work done elsewhere we should have more 
 work than Pa, which is impossible. Hence the work convertible 
 partially into heat takes place at all these places, and at each 
 in proportion only to the yielding, and nowhere else; so that it 
 cannot be localized at any one place. We may then conclude 
 that, unless the heat got out of crushing any portion of rock is 
 sufficient to fuse that particular portion, none will be fused. 
 Indeed we may go so far as to assert that, if Mr Mallet's experi- 
 ments give the amount of heat which can be obtained by 
 crushing rock, and the heat so obtained can fuse it, then the 
 cubes experimented upon ought to have been fused. 
 
 But it is scarcely satisfactory to leave the question at this 
 point. It is conceivable that the pressures, which were experi- 
 mentally applied to the cubes of rock, might be far exceeded 
 within the earth's crust, if compression were caused there by the 
 contraction assumed in the theory under discussion; which it 
 must be recollected is quite opposed to the results obtained in 
 the preceding Chapters. Let us then survey the supposed con- 
 ditions of the problem. A contracting globe induces in its en- 
 veloping crust a state of compression, which owes its existence 
 to the gravitation of the whole towards the centre of the figure. 
 The interior goes on contracting until the compressing force 
 accumulates sufficiently to cause a movement of some kind 
 among the particles of the crust, be it crushing, or faulting, or 
 corrugation, or what not; and the motion being arrested, the 
 work becomes transformed into heat. This heat, as already 
 proved, can be developed only at those places where the move- 
 ment occurs. The question is whether it would be sufficient to 
 give rise to a volcano. If some places are weaker than others, 
 the movement would necessarily occur at them. Let there be 
 several such, which for simplicity we will suppose to be situated 
 at points upon a great circle. The force of compression will go 
 
CH. xviii.] THEORY OF VOLCANIC ENERGY. 233 
 
 on increasing until one of these places gives way. Let P x be a 
 general symbol for this increasing horizontal force, measured 
 by the pressure, in terms of the weight of a cubic mile of 
 mean rock at the surface, upon a square mile of vertical 
 section of the crust. 
 
 Now it is evident that no greater lateral shortening, or ap- 
 proach of the particles of the crust among themselves, can take 
 place at one place than at another, except through a lateral 
 movement of the layers of the crust over the nucleus towards 
 the place in question. Hence any localization of work at a 
 given place must require this to occur more or less. Conse- 
 quently if the pressure goes on accumulating until it becomes 
 equal to P x all round, and under that pressure the crust begins 
 to yield at A, the yielding there cannot relieve the pressure 
 anywhere else, unless the crust is shifted over the nucleus 
 towards A. 
 
 Having premised thus much, we will endeavour to find 
 the utmost amount of heat which could be developed along a 
 vertical section at any one place in the crust. 
 
 Conceive a strip of the crust, one mile in width, situated 
 along a great circle; and suppose the pressure to have gone on 
 increasing to some value P x , which has caused the crust to yield 
 
 at A ; and that by such yielding the pressure has been reduced 
 to P A at A, and partially relieved over AB and AB on either side 
 of A, but not just beyond B and B. Hence at B, B the pres- 
 sure will still be P x . Somewhere beyond B and B it will have 
 been relieved by yielding at other places; and it is supposed 
 that it does so yield all round, so as to fit the reduced nucleus. 
 Hence the amounts to which the pressure will accumulate at 
 different places will depend upon the strength of the crust; 
 but the amount of shortening of the whole crust will not depend 
 upon the amount of the pressure, but solely upon the amount 
 of contraction of the nucleus. Consequently if e be the coef- 
 ficient of linear or radial contraction, seeing that the points 
 
234 MR MALLET'S [CH. xvni. 
 
 B, B r are not shifted upon the nucleus, it follows that the com- 
 pression of BB' is eBB'. 
 
 Let //, be the pressure which a unit in length of the crust 
 would just resist, so as under its action not to move over the 
 nucleus. Then, before motion commenced, yu, would depend on 
 the adhesion, but after motion had commenced, on friction ; 
 and pAB is the force which the length AB would just resist. 
 Let k be the thickness of the crust. In general //, will not be 
 the same for B A and B'A ; but we will suppose it so, in which 
 case BA and B'A will be equal. Hence, after compression has 
 taken place, we shall have for equilibrium, at sections passing 
 through B and B', 
 
 and 
 
 Adding 
 
 whence 
 
 P P 
 
 x A Jc. 
 
 Therefore the compression between B and B 1 ', which is supposed 
 to be localized at A, being eBB f y we have, 
 
 P P 
 
 compression at A 2 ^. - ek. 
 
 P 
 
 Respecting the force which has acted at A to give rise to 
 this compression, w r e observe that it was P x Jc when the com- 
 pression began, and P A k when it ceased. We may therefore put 
 
 P + P 
 it at their mean, or ^ -k. Hence the work at A, which is 
 
 the product of these two quantities, = k 2 e. 
 
 We will now find a limit which must exceed the greatest 
 value that the above can reach. It is evident that this will be 
 given by assigning to P s the utmost value of the compressing 
 
CH. xviii.] THEORY OF VOLCANIC ENERGY. 235 
 
 force 1 , viz. the weight of a column of rock 200.0 miles high and 
 1 mile in sectional area and of the density of the crust, which 
 we will term P, and by giving to P A the value zero. 
 
 A superior limit to the whole work on a vertical section of 
 the strip of crust will therefore be 
 
 P 2 
 
 72,, . 
 
 K e : 
 
 P 
 
 and upon a square mile of this section, 
 
 P\ 
 
 ke. 
 P 
 
 Mr Mallet, at p. 8 of his paper in the "Philosophical Maga- 
 zine" for July 1875, states that the friction may be as great as f 
 of the pressure. Let us, then, suppose first that the nucleus is 
 solid, and that the force requisite to move a column of the crust 
 horizontally over the nucleus is f of the weight of the column; 
 and P is the weight of a column 2000 miles long. Hence 
 
 2000' 
 
 whence, if k = 400 miles 2 , which is the thickness suggested by 
 Mr Mallet, 
 
 Hence the work upon a square mile of section cannot be so 
 great as 
 
 which 
 
 = Pex (2000 miles). 
 
 To assign a value for P, we use the weight of a cubic foot of 
 granite, given by Mr Mallet as 178*3392 pounds (say 200 pounds). 
 And for the supposed va]ue of e, which we may obtain from the 
 radial contraction during one year as given by the same Physi- 
 cist in his Addition, &c., Tab. n. 3 for 400 miles thickness of crust, 
 
 1 
 
 '= 9 
 
 10 1 
 
 6 4 1A12 
 
 1 p. 36. 
 
 2 We must recollect that the crust is assumed to be thick. 
 
 3 "Addition to the paper on Volcanic Energy." "Phil. Trans. Hoy. Soc." 
 Vol. 165, Part i. 
 
236 MR MALLET'S [en. xvm. 
 
 Hence we find for the work for one year, 
 
 work = 76908 foot pounds ; 
 and dividing by Joule's equivalent, 772 ; 
 
 heat per square foot = 99 units. 
 
 The corresponding value for BB' will be 5333 miles. 
 
 Now, according to Mr Mallet's results in his principal memoir, 
 133 (1) and (6), we are informed that 6472 units of heat 
 would fuse 0*108 cubic foot of mean rock previously at 300 F., 
 taking 2000 as -the fusing temperature. Hence with a solid 
 earth, according to our calculation, a limit greater than the 
 greatest possible gives 0'0015 cubic foot of mean rock that could 
 be fused annually for each square foot of the plane of vertical 
 section. With this value it would take a thousand years to fuse 
 one vertical slice of a foot and a half thickness within the 
 range of crust defined by the distance BB\ or 5333 miles, on a 
 great circle of the sphere. But the place of weakness cannot 
 but have a considerable width throughout which the heat 
 would be distributed. If, then, it were, say, a mile wide, the 
 number of units of heat to each cubic foot would be ^f f ^ , or 
 about 0'02 unit. 
 
 The force of compression, besides the work of crushing at A 
 where the yielding takes place, also does work over the plane of 
 shearing in overcoming adhesion and friction. Let the whole 
 force expended in overcoming adhesion and friction along BB' 
 be fj!J3B ' . The space moved over increases from nothing at B 
 
 7} TV 
 
 and B' to eAB and eAB' at A. The mean is e^- . Hence 
 the work along this plane is 
 
 P P P P 
 
 =- 2// * A k xe -*=-* k. 
 P P 
 
 And making the same suppositions as before for a superior limit, 
 this becomes on the whole plane 
 
 P 2 
 
 2f*'~ek*. 
 
CH. xvin.] THEORY OF VOLCANIC ENERGY. 237 
 
 We took fj, at the value f of the weight for friction. We will 
 take it as equal to the weight for the adhesion, since that is 
 probably greater than the friction, although its ratio to the 
 friction probably diminishes as the pressure increases. Hence 
 
 A*' = iA*> 
 
 P 2 
 
 /. the work = f eJ<?. 
 
 But the whole work on a vertical section was found to be 
 
 P 2 
 
 ek* ; hence the whole work along the plane of shearing is 2 J 
 
 of the work along the vertical section. This work will not be 
 evenly distributed, but will be greatest upon the unit of the 
 length nearest A, where the space moved over will be eAB, and 
 the force upon it is ///. Hence work upon the last unit 
 
 fi'e 
 
 upon the suppositions made, this becomes 
 
 And the work upon a square mile of section on the same suppo- 
 sitions was found to be 
 
 Hence the work, and therefore the heat, upon the last unit of 
 the plane of shearing, where it will be greatest, is only one- 
 fifth of the work and heat respectively on a unit of the vertical 
 section. 
 
 This result seems unfavourable to the view that the heat 
 arising from friction of the rocks along horizontal planes can 
 account for the heat concerned in producing even metamorphism, 
 
 It must be fully understood that the results just arrived at 
 with respect to the heat developed at a vertical section, as well 
 as along the plane of shearing, have reference not to any pro- 
 bable values, which under the assumed conditions could arise, 
 but to a superior limit which must be greater than the greatest 
 possible. In fact they involve several impossible assumptions, 
 all of which make it too large. These are: 
 
238 MR MALLETS [CH. xvm. 
 
 (1) That the contraction from cooling would take place in 
 the matter of the nucleus and not in the crust, for this suppo- 
 sition is involved in Mr Mallet's value for the contraction. 
 
 (2) That the above circumstance would allow the coeffi- 
 cient of contraction to be nearly four times as large as on the 
 more probable supposition. 
 
 (3) That the pressure increases to the utmost attainable 
 value, viz. that of a column of rock 2000 miles long, before 
 yielding takes place. 
 
 (4) That when yielding does take place, the pressure at 
 the place of yielding is entirely satisfied. 
 
 The above assumptions, besides making the amount of heat 
 impossibly great, also localize it to an impossible degree, as may 
 be seen by observing that BB r would be lessened by diminishing 
 Py, and also by increasing P A ; that is, by lessening the pressure 
 which causes the yielding, and by increasing the pressure at the 
 place of yielding after the compression has taken place. 
 
 The calculations indicated above will be found given at 
 greater length in the Author's paper on this subject in the 
 " Philosophical Magazine 1 ," together with an extension of the 
 investigation to some further hypotheses as to the crust sliding 
 over a fluid nucleus. But it is thought unnecessary to repro- 
 duce more here to show that the theory does not account satis- 
 factorily for volcanic phenomena. 
 
 We see then that Mr Mallet's own experimental mode of esti- 
 mating the pressure requisite for crushing the strata cannot give 
 rise to sufficient heat for the purpose; and that if we go far 
 beyond this, and use in forming our estimate the utmost pressure 
 under the circumstances conceivable, we still fall far short of 
 obtaining the requisite amount of heat. Accordingly, we are 
 
 1 Fourth series, Vol. 50, p. 302, 1875 (in which occurs the following erratum. 
 At p. 316, line 6, insert fe, for "1| mile" read "533 miles," and dele the follow- 
 ing line). See also Mr Mallet's reply, fifth series, Vol. i. p. 19, and the Author's 
 rejoinder, Ibid, p. 138. 
 
CH. XVIIL] THEORY OF VOLCANIC ENERGY. 239 
 
 thrown back upon the old explanation of volcanic phenomena 
 assumed in the preceding pages to be true, that they are a 
 manifestation of the intense temperature existing at great 
 depths, and that the fused rocks are conveyed to the surface 
 through channels of communication. 
 
CHAPTEE XIX. 
 
 THE VOLCANO IN ERUPTION. 
 
 Theories of volcanic eruption Scrape, Dutton, Mallet Local and temporary in- 
 crease of temperature not probable Richthofen's theory unsatisfactory Ex- 
 planation of phenomena on hypothesis of fluid substratum in igneo-aqueous 
 fusion Amount of water-substance beneath vent probably variable Mechanics 
 of an eruption Estimate of amount of water-substance in magma Eruption, 
 how brought to an end Evisceration of cone State of intermediate activity 
 Stromboli Unsympathetic craters Richthofen's difficulties met Renewal 
 of activity Comparison with Geyser. 
 
 THE theory of the existence of an intensely hot substratum 
 of rock in a state of igneo-aqueous fusion, underlying a crust 
 of 'about 25 miles thickness, seems on the whole to offer the 
 conditions calculated most readily to explain volcanic pheno- 
 mena. The alternative view may fairly be stated to consist in 
 the hypothesis that periodical local increments of temperature 
 occur beneath volcanic areas, temporarily fusing the rocks, and 
 causing their eruption. This was Scrope's opinion 1 ; Captain 
 Button holds the same view, viz. "that the proximate cause 
 of eruptions is a local increment of subterranean temperature, 
 whereby segregated masses of rocks, formerly solid, are liquified" 2 . 
 Neither of these writers attempts to explain the cause of the 
 supposed increment of temperature. Mr Mallet's theory, 
 discussed in the preceding chapter, is of the same kind, except 
 that he proposes to account for the local and periodical ele- 
 vation of temperature by mechanical means. In whatever way 
 
 1 " Volcanoes," p. 263. 
 
 2 " Geology of the High Plateaus of Utah," p. 120. Washington, 1880. 
 
CH. xix.] THE VOLCANO IN ERUPTION. 241 
 
 we regard it, the hypothesis of a local and periodical heating of 
 the rocks appears to be surrounded by great difficulties. Such 
 a rise of temperature can be produced only in one of three ways ; 
 (1) by mechanical work being locally converted into heat, or (2) 
 by local chemical reaction, or (3) by heat being transferred from 
 some hotter neighbouring region. The first is Mallet's hypo- 
 thesis, and is believed to be insufficient. The second was 
 Davy's, and has been long abandoned. There remains only 
 the third. Now there are but two ways in which heat can 
 be in such a case conveyed from hotter to cooler regions, and 
 these are by convection and by conduction. If the former be 
 the mode appealed to, then we have necessarily a fluid con- 
 dition of the underlying rocks, which is our hypothesis. But 
 if conduction be the process involved, then we must have an 
 unfused mass, beneath, and adjoining, the area affected, at a 
 temperature higher than is requisite to fuse other rocks ; which 
 is in itself improbable. But that such a condition of excessive 
 temperature should be local and temporary, is still more so, 
 because the tendency of conduction would be to equalize the 
 temperature along isogeotherms approximately parallel to the 
 outer surface. 
 
 There is however, the theory of Richthofen to be considered. 
 Instead of invoking a rise of temperature, he supposes a tem- 
 porary increase of fusibility. He appears to think that there 
 are heated couches of rock, in a condition which he calls 
 "glowing lava 1 ," but which are not in a state of fusion. 
 Fissures being formed in the crystalline crust above this, water 
 gains access to it, and it enters into a state of " aqueous fusion," 
 and thereby becomes increased in volume, and "this expansion 
 would immediately cause a motion of the masses rendered 
 liquid, in the direction of least resistance, that is, upwards 
 in the fissure, and would, if continued for a sufficient time, 
 make the same overflow on the surface of the crust, even if 
 unassisted by other ejecting agents, such as the vapour of 
 water 2 ." 
 
 The difficulties attending the accession of superficial water 
 
 1 " Natural system of Volcanic Rocks," p. C6. 2 Ibid. p. 36. 
 
 F. 16 
 
242 THE VOLCANO IN ERUPTION. [CH. xix. 
 
 to the volcanic foci have already been pointed out 1 , and it 
 seems hard to believe that the mode of action here described 
 can have a real existence. Moreover Eichthofen appeals to 
 the cooling of the globe as the ultimate cause, of which cause 
 we claim to have proved the inadequacy. He says, " elevations 
 and eruptive activity, even when locally not quite coincident, 
 are co-ordinate effects of the cooling of the globe ; but while the 
 one is its immediate effect, the other results from it only by 
 the concurrence of other agencies, which by themselves alone 
 would have been incapable of producing results of such mag- 
 nitude." The memoir from which these passages are taken 
 is of great interest, and contains many very suggestive obser- 
 vations, and sage generalisations well worthy of study. On 
 the whole his theory of volcanic action approaches more nearly 
 than any other to that which we now advocate. 
 
 We have already indicated in a general way the manner 
 in which we would explain the phenomena with such a crust as 
 we have supposed, subject to disturbances from transference 
 of sediment, and consequent local depression. The contraction 
 of the lower parts of the crust, where it becomes depressed into 
 regions of higher temperature, will induce metamorphism, and 
 shrinking, and shrinking will cause fissuring. Changes in the 
 distribution of load by transference of sediment will also have a 
 tendency to produce fissures, and it has been pointed out how 
 these, commencing below, may be propagated until they reach 
 the surface, and become filled with lava, in which the expansion 
 of the water-substance, at a temperature far above the critical 
 point, will render the column of molten rock on the whole 
 specifically lighter than the mean crust, so that it will escape at 
 the surface. 
 
 In a general way this seems probable, but we have already 
 shown that, under certain admissible suppositions, what we have 
 just stated will necessarily occur. It is true that we have con- 
 sidered the problem only as a statical one, for the ascent of 
 vesicles of water through the lava, causing ebullition at the 
 surface, has not been taken account of, but merely the decrease 
 in density of the lava upwards, caused by the expansion of 
 1 p. 90 et seq. 
 
CH. xix.] THE VOLCANO IN ERVPTION. 243 
 
 the water-substance in it through decrease of pressure, the same 
 identical water being supposed to remain always engaged in the 
 same portion of lava \ But ebullition would help to raise and 
 eject the lava. 
 
 In the equation which we have arrived at, connecting the 
 pressure p of the lava at the level of the surface of the crust 
 with the proportion 1 V of water-substance, which the magma 
 contains as it exists below when subject to the pressure of the 
 crust, if we assume a value for one of these quantities, we can 
 find the other. The equation in question is a , 
 
 . 
 
 F * p gpk V P 
 
 Probably in different localities, and at the same locality at 
 different times, these quantities, p at the surface, and 1 F, are 
 different ; and "it is to the connection between the quantity of 
 water and this pressure that the well-known fact is due, that a 
 long continued state of repose in a volcano is followed by an 
 exceptionally violent eruption, and vice versd. In order that 
 the pressure at its base may bring the lava to the surface of the 
 crust, it is requisite that the mean density of the column should 
 be lowered by a certain amount of water being vesicularly 
 mingled with it. But the vesicles rise through it, and even- 
 tually leave the column of lava deficient in enough -water-sub- 
 stance to enable it to be raised to the surface. At the same 
 time the magma around the base of the funnel has been to a 
 certain extent exhausted of its superabundant water, and thus 
 an eruption will have the effect of diminishing the proportion 
 of water in the magma, or 1 F. Exceptionally powerful erup- 
 tions might be expected to occur when a volcano had been 
 quiescent for a long while, and the water had become again 
 equably diffused, and regained its average proportion, beneath 
 the vent ; or when a volcano has newly burst through the crust 
 at a place where the water-substance had never, or at least 
 had not for a long period, been drained away. We have of 
 course no means of knowing with any degree of certainty the 
 values of either of these quantities, p at the surface, or 1 F. 
 
 1 p. 189. 2 P. 191. 
 
 162 
 
244 THE VOLCANO IN ERUPTION. [CH. xix. 
 
 There is however to guide us the consideration, that the 
 quantity of water, which is given off along with the lava, will 
 bear a ratio to the quantity of the lava depending upon the 
 value of F. If it be true, as we have seen reason to think to be 
 the case, that the water- substance in the lava must be of the 
 same density as the rocky matter with which it is combined, 
 then the proportion of water-substance to rocky matter being 
 1 V : F, the proportion of ordinary water to the lava in the 
 erupted matters will be nearly cr (1 F) : F. Thus if F were 
 0'9, or the compressed water-substance occupied one-tenth of the 
 volume of the magma, and if cr were 2*96, the water given off 
 would bear to the lava given off the ratio of 2*96 x 0*1 : 0'9, or 
 about 0'3 : 1 ; that is the volume of the lava stream would be 
 about three times the volume of the water; which does not 
 appear improbable. 
 
 When we take into account the passage of the vesicles of 
 water-substance through the lava in their ascent towards the 
 surface, we cannot doubt that this takes place with greater 
 rapidity than the ascent of the lava itself, and the exhaustion of 
 water in the column goes on much more rapidly than diffusion 
 can repair it. Consequently the lava in the upper part of the 
 column at last becomes so deficient in vesicles of water-sub- 
 stance, that its weight balances the expansive force beneath 
 it. The vesicles beneath it will then cease to expand, and 
 their upward motion will be checked, and the evolution of steam 
 gradually almost cease. But the column of lava has been for 
 some while rising in the vent, and at this juncture the forces 
 which press it upwards are just in equilibrium with those that 
 keep it down. The vis viva which it already possesses will be 
 only gradually destroyed, and it will continue to well forth 
 steadily and without much evolution of vapour for a little while 
 and then sink back into the vent. In this manner the eruption 
 will be brought to a -close 1 . 
 
 1 Instances are recorded in which an eruption of lava has been followed by a 
 great evolution of steam and ashes. It is conceivable that vapour may accumu- 
 late in parts of the chasm which are closed above, and when the level of the lava 
 which confined it there has sunk sufficiently, steam may find an exit by the open 
 vent, rushing with violence through the lava, now no longer deep enough to 
 restrain its escape, and blowing it into dust ; the mode of action being some- 
 
CH. xix.] THE VOLCANO IN ERUPTION. 245 
 
 The ultimate cause of its cessation has been the exhaustion 
 of water-substance in the column of lava. It is not by any 
 means requisite however, that the whole of the water-substance 
 shall have been exhausted, or that none shall be passing through 
 the column which still remains in the funnel. This is seen to 
 be the case, because much vapour is continually given off by 
 volcanoes when they are not in eruption, though the quantity is 
 incomparably less than what is given off when they are so. 
 
 According to the formula we have made use of to express 
 the density of the lava, we find that if it rose in the vent, con- 
 taining in its composition the same amount of water with which 
 it started from below the crust, its density at the level of the 
 surface of the crust would be little above that of ordinary 
 water ; for 
 
 /* = 
 
 P 
 
 and giving to F the value 0*9 and to the corresponding 
 
 value at the surface, which, with er = 2 '9 6, we have found to be 
 14*4, we obtain for //, the value 1*26. And when a volcano is in 
 full eruption, and immense volumes of superheated water are 
 passing upwards, it does not seem at all improbable that the 
 mean density of the lava at that level, which will be at the 
 base of the mountain, may be as low as this. Such a low 
 density would agree well with the evisceration of a cone during 
 a great eruption, so well described by Scrope 1 . We may 
 conclude that a large supply of water is requisite for such 
 manifestations of activity. 
 
 If so much water must be present in the column to produce 
 an active condition, we can understand how moderate quantities 
 of superheated water passing upwards, although insufficient to 
 cause eruption, may nevertheless be enough to keep the column 
 of lava, or at least its axis, in a state of fusion. But if the 
 
 what similar to that which was proposed to explain the phenomenon of a geyser, 
 before Bunsen suggested a better. 
 1 "Volcanoes," p. 186. 
 
246 THE VOLCANO IN ERUPTION. [CH. xix! 
 
 means of supply of water-substance be more liberal, and be just 
 balanced by the means of escape, a gentle and perpetual state 
 of eruption like that of Stromboli, may result. That the main- 
 tenance of the temperature of fusion in a habitual vent is due 
 to the cause suggested, appears probable from the following 
 consideration. Molten lava sometimes fills the bottom of a 
 crater for a long period, its surface being maintained in a con- 
 stant state of ebullition by the vapour and gases which pass 
 through it. In such a case it must be the high temperature of 
 these vapours which keeps it melted: for if the fusion were 
 due to a continual supply of fresh lava from below, there would 
 need to be a continual escape of it above. But this does not 
 appear to be requisite. If such be a correct view of the case, it 
 shows that the hot vapours are capable of fusing rocky matter, 
 and accordingly, when once they have obtained a passage of 
 escape, they may convert the sides of the channel into lava and 
 fuse their own way through, carrying the fused matter with 
 them 1 . 
 
 It has been often urged that volcanic vents cannot com- 
 municate with a common reservoir below, because, even in the 
 same mountain, contiguous craters are not sympathetic. But 
 this sympathy does not seem really necessary, for as soon as a 
 column of ascending vapour has established itself in one crater, 
 the tendency will be for it to continue to hold the same position, 
 since its presence renders that the vertical of least pressure, and 
 consequently the channel of easiest escape. We see the same 
 sort of thing take place when water begins to boil in a vessel 
 heated below. Before it passes into general ebullition, a column 
 of bubbles will appear here and there, and rise from the same 
 points of the bottom of the vessel for a considerable time. So, 
 when the escape of vapour has commenced through one of the 
 craters, it may carry ,off the vapour as fast as it is supplied, and 
 determine the eruption to that channel, the neighbouring crater 
 remaining quiescent, although they may both of them be in free 
 
 1 See the author's paper "On the Inequalities of the Earth's Surface upon the 
 hypothesis of a liquid substratum." " Camb. Phil. Trans.," Feb. 1875. 
 
CH. xix.] THE VOLCANO IN ERUPTION. 247 
 
 communication with the same subterraneous reservoir 1 . The 
 level of the lava in the crater which is in eruption will be raised 
 above that in the other, because the column beneath it is 
 rendered lighter by the expansion of the increased quantity of 
 superheated water which is passing through it at the time. 
 The case will be somewhat like that of an inverted syphon, the 
 liquid in one leg of which is lighter than that in the other. 
 
 The explanation now offered for the elevation of the lava to 
 the surface, differs from previous theories of the same kind, on 
 account of the supply of water-substance being drawn from the 
 entire liquid substratum, and not from the access of it to the 
 lava at some point higher up. The importance of this dis- 
 tinction appears from an objection made by Rich th of en 2 . " It 
 must here be remarked that some of the most eminent writers 
 on the subject of volcanoes, chiefly Poulett Scrope, Prof. Dana 
 and others, have suggested long ago, that the ascent of lava in 
 a volcanic channel must be due to both the fluidity and ex- 
 pansion imparted to it by the globular state of the water which 
 finds ingress to the channels of the lava and enters into its 
 composition. They have anticipated, by this suggestion, in some 
 measure, the results of experiment established by Daubre'e. 
 But the supposition was only made for the case of lava, and not 
 for that of rocks which were ejected without volcanic action 
 proper " (that is by massive, or fissure eruption). " Yet even in 
 regard to volcanoes it did only explain the extension of lava to 
 the surface from a place at a limited distance below it, and 
 failed to give a clue to the manner in which the constant 
 supply of matter to those places was kept up" 3 . Both of these 
 objections appear to be met if the entire liquid substratum is 
 laid under contribution for the supply of the water-substance 
 which acts as the intermittent agent in raising the column to 
 the surface. 
 
 1 Another explanation suggested has been that the craters, though contiguous, 
 may be connected with different fissures. 
 
 1 /" Natural system of Volcanic Kocks," "Memoirs of the California Academy 
 of Sciences." Vol. I. Part 11. 1868. 
 
 3 Ibid. p. 54, note. 
 
248 THE VOLCANO IN ERUPTION. [CH. xix. 
 
 The mode of action suggested appears competent to account 
 easily for the eruption of steam and lava in a case where a chan- 
 nel of communication has been freshly opened between the liquid 
 substratum and the surface. There is more difficulty in under- 
 standing how, when an eruption has taken place, and the water- 
 substance has been exhausted to that degree at which the lava 
 becomes too dense to rise any longer, the action can be after a 
 period renewed. And as there is a difficulty in understanding 
 the process, so also is there evidently a difficulty in the process 
 itself, otherwise the periods of repose would not be so long and 
 so irregular as they are, and sometimes perpetual. 
 
 The comparison between the geyser and the volcano is no 
 new one. Bunsen's explanation of the former turns upon the 
 temperature at each depth in the column of water becoming 
 raised above the boiling point for the pressure there. Our 
 account of a volcanic eruption is somewhat similar, except that 
 the boiling point of the lava depends, not so much on the tem- 
 perature, which we have regarded as constant (although that 
 cannot be strictly so), but upon the presence of a sufficient 
 quantity of water mingled with the lava, to cause the requisite 
 expansion of volume under the pressure at each depth. What 
 will be required therefore to repeat the eruption, will be the 
 diffusion afresh of sufficient water into the column for this 
 purpose, and it seems that the escape of vapour from the surface 
 becoming reduced below the supply gained by diffusion from 
 below, must be the requisite condition. This may be perhaps 
 caused by the cooling of a plug of lava at the top of the column, 
 except a narrow passage through which what escape there is 
 takes place, and which serves as the leading channel for the 
 next eruption. Or else, when the period of repose has been 
 protracted until this channel has become blocked with cooled 
 lava, some fresh movement of the crust may open the necessary 
 communication between the surface and the fluid substratum. 
 
CHAPTER XX. 
 
 SEQUENCE OF VOLCANIC BOCKS. 
 
 Flow of matter melted off roots of mountains Force causing it considerable 
 Formation of lavas These will differ in different areas and at different 
 times Law of Bunsen Eichthofen's " Natural System of Volcanic Rocks" 
 Hoiv explained by him Difficulty arising Captain Dutton's explanation 
 Prof. Judd on Eichthofen's System Melting of roots of the mountains 
 affords an explanation of the sequence And of the variation of volcanic 
 products in adjacent regions. 
 
 IT has been already remarked that, where the roots of the 
 mountains project downwards into the hot fluid substratum, 
 they must be slowly and gradually becoming fused 1 . The 
 material that becomes fused is derived from the crust, which is 
 of less specific gravity than the substratum, and it must be like- 
 wise remembered that the roots of the mountain extend down- 
 wards to a considerable depth, perhaps 10 times the height of 
 the upper mountain, into the substratum, which will be more 
 dense in its lower layers. The consequence of this must be, 
 that the fused rock which is melted off the roots will have a 
 tendency to flow upwards, and to accumulate along the under 
 side of the crust much in the same way that lava, coming from 
 a vent, runs down a mountain's side, and spreads itself out upon 
 the surface. We must in the present case, as it were, invert 
 our ideas of the usual movement of a liquid mass. The fused 
 rock which runs up these roots will not be cooled as subaerial 
 lava is, but will retain its liquidity. On the other hand, moving 
 in a medium about as dense as itself, its motion will be very 
 
 1 p. 152. 
 
250 SEQUENCE OF VOLCANIC ROCKS. [CH. xx. 
 
 slow, and there will be a tendency for the two fluids to become 
 mhigled in varying proportions according to circumstances. If 
 the fused rock creeps along the top, itself in contact with the 
 under side of the crust from which it has been derived, its com- 
 position on the upper side of the flow will be little altered, but 
 on the lower side it will be more or less mingled with the sub- 
 stratum, owing to the friction between the two. 
 
 There can be no doubt that there will be sufficient heat in 
 the substratum for the above purpose, because the magma, even 
 after the water which it contains has been blown off in vapour, 
 and so carried away a vast amount of heat, retains sufficient 
 heat to afford liquid lava. There must therefore be heat to 
 spare in the substratum to melt matter off the roots without it- 
 self becoming congealed. 
 
 It will be desirable to compare the force which urges the 
 fused rock up the inclined root, with that which would urge a 
 liquid down the incline at the point vertically above it on the 
 surface of the mountain. 
 
 Let 6- be the angle of inclination to the horizon at a point 
 on the side of the mountain at a height h above the mean level, 
 and let & be the angle of inclination to the horizon at the point 
 vertically beneath it upon the side of the root at the depth h f 
 below the lower mean level. And suppose, as usual, that 
 
 Neglecting the thickness of the crust, which is immaterial to 
 the demonstration, the tangents at these two points will meet 
 at the same point in the crust. This follows because ti bears a 
 constant ratio to h. Let I be the distance from the common 
 ordinate h + h', where the tangents meet. Then, resolving the 
 forces along the two tangents, we have, 
 
 Force below _ (a- p) g sin & 
 
 Force above ~~ g sin 6 
 
 JF+T? 
 
CH. xx.] SEQUENCE OF VOLCANIC ROCKS. 251 
 
 Consequently the 
 
 force below > = < force above, 
 
 OC _ >. - 
 
 do ^ 
 
 or, with the usually assumed values of p and <r, 
 
 as - > = < 37. 
 
 /t 
 
 But |=cot0; 
 
 fir 
 
 and 37 = cot 15 nearly; 
 and cot 6 > cot 15 if < 15. 
 
 Hence, when the angle of inclination of the mountain is less 
 than 15, the force beneath, which urges the melted rocks along 
 the surface of the root, will be greater than that which would 
 urge a liquid along the surface of the mountain vertically above 
 it. Hence, by comparing it with the behaviour of _subaerial 
 lava, we can see that the tendency for the rock fused off the 
 root to spread itself beneath the crust will be considerable. 
 We shall therefore have beneath the bottom of the crust areas 
 where the matter fused off the roots of the mountains, and 
 more or less mingled with the denser substratum, is spread out. 
 It is probable that these areas will be local, and not extend 
 beyond a certain distance from the roots of the ranges. They 
 will be analogous to the alluvial deposits, which cover the 
 plains of the upper world. When an eruption occurs above 
 any of these areas, this fused matter will be the first to be 
 ejected, mingled with water-substance already imparted to it 
 by diffusion from the magma beneath it; and, if this fused 
 matter is supplied sufficiently rapidly, it will be the only kind 
 of rock ejected, except such as may be derived from the sides of 
 the funnel. Having been derived from the material of the 
 roots, and in its flow mixed with the denser magma in various 
 proportions, the resulting lava will conform to the law of Bun- 
 sen, which asserts that all eruptive rocks are compounded of 
 
2 5 2 SEQUENCE OF VOLCANIC ROCKS. [en. xx. 
 
 two normal magmas, an acid and a basic, mingled in definite 
 proportions. Such will be the case with our lava, if the roots 
 of the mountains have been formed out of a crust consisting in 
 its lower parts of granitic rock beyond reach of the region 
 penetrated by sedimentary deposits. But when we remember 
 that all sedimentary deposits have been ultimately derived 
 from these two normal magmas, it seems that, if samples of 
 every sedimentary deposit proportional in mass to the whole 
 deposit, were mingled together, we should obtain a mixture 
 chemically equivalent to a mixture of the magmas. Accordingly, 
 if many varieties of sedimentary rocks were to contribute their 
 share to the fused matter, it might be difficult to say that the 
 resulting rock had not been directly derived from the two 
 magmas. It does not appear requisite therefore that, because 
 a volcanic product conforms to the law of Bunsen, it should be 
 necessary to exclude the presence of such small contributions 
 as might be expected to be made by sedimentary rocks, de- 
 pressed here and there into the region of fusion, as would 
 happen if the views of Prof. James Hall and other American 
 geologists are correct 1 . 
 
 It is now possible to account for the changes in the character 
 of the lava which is emitted from the same volcano at different 
 times. For the fused matter will be distributed in layers, that 
 which is nearest to the bottom of the crust being the most 
 similar to it in composition. It might happen that all this 
 fused matter within reach of the vent might be erupted, and 
 before it accumulated afresh, the lava of the next eruption 
 might be supplied by a denser couche beneath. But before a 
 third took place, the fused matter might have collected again, 
 and possibly this time mingled with the substratum in a 
 different proportion. Thus successive eruptions would produce 
 different lavas. The volcanoes more distant from mountain 
 ranges might be expected, on the whole, to erupt the more 
 basic lavas. It would be worth while to inquire whether there 
 is any reason to suppose this generally to be the case; for we 
 gather from Richthofen, that certain basaltic fissure eruptions 
 
 1 p. 201. 
 
CH. xx.] SEQUENCE OF VOLCANIC ROCKS. 253 
 
 have taken place at a greater distance from the mountain 
 range, than those of a more acid character 1 . 
 
 The "Natural System of Volcanic Rocks," established by 
 Richthofen and confirmed by Captain Dutton 2 and other 
 geologists, appears to be explicable upon the principles we have 
 been now advocating. Richthofen defines the volcanic era, 
 as that which came in towards the close of the Eocene period, 
 and extends to the present day. This period includes the 
 epoch of the chief elevatory efforts, which have affected the 
 greater mountain chains of both hemispheres. He classes the 
 eruptive rocks of this era under five orders, which are 
 
 (1) Rhyolite iv, 
 
 (2) Trachyte iii, 
 
 (3) Propylite i, 
 
 (4) Andesite ii, 
 
 (5) Basalt v. 
 
 These are arranged in order of the proportion of silica which 
 they contain. But their order of successive eruption in regard 
 to time is different, and is 
 
 (i) Propylite 3, 
 
 (ii) Andesite 4, 
 
 (iii) Trachyte 2, 
 
 (iv) Rhyolite 1, 
 
 (v) Basalt 5. 
 
 Thus the first erupted were the rocks intermediate in respect 
 of their acidity and specific gravity, (i) and (ii). These were 
 followed, according to Richthofen, by those of greater acidity 
 and less specific gravity (iii) and (iv) ; and later by those of 
 least acidity and greatest specific gravity (v). This order of 
 succession appears inexplicable on the simple theory of fluid 
 
 1 Bichthofen says that Andesite occurs on the southern slope of the Carpa- 
 thians, p. 25 ; and that Basalt occurs in the neighbourhood of the more ancient 
 volcanic rocks (among which he classes Andesite), accompanying their ranges at 
 some distance, itself forming extensive ranges : p. 27. Putting these state- 
 ments together, it appears that the basaltic range is distant from the moun- 
 tains. 
 
 2 " Geology of the High Plateaus of Utah," Chaps, iv., v. 
 
254 SEQUENCE OF VOLCANIC ROCKS. [CH. xx. 
 
 couches, superimposed in reverse order of their specific 
 gravities. 
 
 The manner in which Eichthofen explains this succession 
 is satisfactory as regards the first and last, but not equally so 
 as regards the intermediate rocks. Premising that the eruptive 
 rocks of palaeozoic times were chiefly of an acid character, 
 and that little eruptive activity was manifested during the 
 mesozoic, he proceeds 1 , " Those siliceous compounds especially, 
 of low specific gravity, which had formerly yielded the material 
 of the vast accumulations of quartziferous eruptive rocks, 
 would have been consolidated, and the limit as it were between 
 the solid and the viscous state of aggregation receded into 
 regions where the matter would be of a less siliceous com- 
 position and of greater specific gravity." * * * When the eruptive 
 activity was renewed, " The first rocks ejected would neces- 
 sarily be of a more basic composition than the predominant 
 rocks of the granitic era, while the repetition, at a later epoch, 
 of the process of fracturing would give rise to the ejection of 
 rocks in which silica would be contained in still lower proportion. 
 The greater portion indeed of the ejected rocks consisted of 
 propylite and andesite, in the first, and of basalt in the second 
 half of the volcanic era." Thus far all is plain. But when 
 he offers an explanation of the intermediate ejection of a 
 more acid and lighter rock than any of these his reasoning is 
 less convincing. "A notable but only apparent anomaly in 
 the regular order of succession has been the emission of trachyte 
 and rhyolite, between the andesitic and basaltic epochs. But if 
 it is considered that these rocks were ejected partly from the 
 same fractures through which andesite had ascended, and partly 
 from others in their immediate vicinity, while the distribution 
 of basalt has been independent, to a certain extent, of all fore- 
 going eruptions, it is evident that the occurrence of trachyte 
 and rhyolite is closely dependent on that of andesite and bears 
 only a very remote relation to basalt. It appears that after 
 the ejection of the chief bulk of andesite, when other processes 
 ending in the opening of fractures into the basaltic region 
 were being slowly prepared in depth, the seat of eruptive 
 1 " Natural system of Volcanic Bocks," p. 58. 
 
CH. xx.] SEQUENCE OF VOLCANIC ROCKS. 255 
 
 activity ascended gradually to regions at less distance from the 
 surface. There is within the limits of conjecture based on 
 physical laws, no lack of processes which could co-operate 
 to that effect. The consolidation of the ejected masses within 
 the fissures would probably proceed simultaneously, by loss 
 of heat, from the surface downwards and, by pressure, from 
 below upwards. The opening of new branches from the main 
 fractures, the remelting (by the aid of the heat of the molten 
 mass within the latter, and of water finding access to it) of 
 solidified matter adjoining the fracture, the emission of that 
 remelted matter through those branches : all these are secondary 
 processes depending on the first almost necessarily. The sup- 
 position that to those is due the order of time in which trachyte 
 and rhyolite have been ejected to the surface, is corroborated 
 by the fact that these rocks occupy generally a subordinate 
 position in regard to quantity and have had to a great extent 
 their origin in volcanic action " that is, as distinguished from 
 massive or fissure eruption. It is clear that, in order to obtain 
 the acid magma required for the production of the eruptions of 
 trachytic rocks subsequently to the andesitic, some method 
 must be devised to explain the refusion of the granitic crust, 
 lying, already consolidated, above the andesitic magma. Kicht- 
 hofen proposes to do this by "the aid of the heat of the 
 molten mass" within the main fracture, "and of water gaming 
 access to it." This appeals to the very doubtful hypothesis 
 already referred to, which supposes " glowing lava," not already 
 liquid, to absorb water admitted to it from without, and thereby 
 to become liquid and light. Moreover it requires the " molten 
 mass within" the fissure to contain an excess of heat sufficient 
 to melt an additional mass of a more refractory rock than itself. 
 But it is evident that it could not transfer more than so much 
 of its own heat to another mass, as would raise the two to a 
 common temperature, less than its former temperature. 
 
 Captain Button's discussion of the same sequence is interest- 
 ing and instructive, and well worthy of study, but still not satis- 
 factory. The general principles employed by him are indicated 
 in the following sentence : " In order that any eruption of lava 
 may take place two preliminary conditions are requisite. First, 
 
256 SEQUENCE OF VOLCANIC ROCKS. [CH. xx. 
 
 The rocks must be fused. Second, The density of the lavas 
 must be less than that of the overlying rocks. Having shown 
 from independent considerations that the proximate cause of 
 volcanic activity may be a local rise of temperature in deeply 
 seated rocks, it only remains to follow the obvious phases of 
 the process." He then founds, upon a previous discussion of 
 the respective temperatures at which the different rocks would 
 become at once fusible and sufficiently light to reach the 
 surface, an argument to show that Richthofen's order of succes- 
 sion agrees with the order so arrived at. " It is just possible 
 that the acid rocks may be light enough to erupt at an early 
 stage of the process " of a local rise of temperature " but are 
 not yet melted, and that the basic rocks may be melted, but must 
 await a further expansion in order to reach the surface. The 
 first selection would then fall upon some intermediate rock. 1 " 
 Several objections to this explanation are mentioned in a short 
 critique upon this, in general admirable, Work by Prof. A. Geikie 2 . 
 But the fundamental objection already brought against it, of the 
 impossibility of explaining the " local rise of temperature " pos- 
 tulated, seems to us fatal 3 . 
 
 It appears however to Prof. Judd that the exceptions to Richt- 
 hofen's law as precisely stated, " are so numerous as to entirely 
 destroy its value. The generalisation that in most volcanic dis- 
 tricts the first ejected lavas belong to the intermediate group of 
 the andesites and trachytes, and that subsequently the acid 
 rhyolites and the basic basalts made their appearance, ' is one 
 that appears to admit of no doubt, and is found to hold good 
 in nearly all volcanic regions of the globe which have been 
 attentively studied" 4 . But even this generalisation is sufficient 
 to necessitate some explanation. Prof. Judd says also that "it 
 lends not a little support to the view that under each volcanic 
 district a reservoir of more or less completely molten rock exists, 
 and that in these reservoirs various changes take place during 
 the long periods of igneous activity. During the earlier period 
 
 1 " Geology of the High Plateaus of Utah," p. 131. 
 
 2 "Nature," xxn. p. 324. 1880. 
 
 3 p. 241. 
 
 4 " Volcanoes," p. 200. 
 
CH. xx.] SEQUENCE OF VOLCANIC ROCKS. 257 
 
 of eruption the heavier and lighter elements of the contents of 
 these subterraneous reservoirs appear mingled together ; but in 
 the later stages of the volcanic history of the district, the 
 lighter or acid elements rise to the top and the heavier or basic 
 sink to the bottom, and we have separate eruptions of rhyolite 
 and basalt." But he gives no reason for this original mixture 
 of the magmas and for their subsequent separation. 
 
 According to our view, however, the succession of Eichthofen 
 seems to be the necessary one. Before the rending of the 
 fissures occurred, which we suppose to have elevated the moun- 
 tain chain, the different magmas occupied the positions and 
 sequence determined by their densities, and consequently the 
 acid magma being already solidified in the crust, the first 
 erupted of the rocks would be intermediate in respect of their 
 specific gravity, and acidity. But this very injective action 
 itself would depress the acid crust in a protuberant ridge, 
 presenting to the denser substratum an under surface, which 
 would be but just below the temperature of its fusion. This 
 surface now becoming fused, would underflow the crust, and the 
 next time that an eruption took place in that region, a more 
 acid and lighter lava would make its appearance. But at other 
 places, out of the reach of the flow of this acid remelted matter, 
 or at the same place after the layer of it thus formed had been 
 ejected, the subjacent basic magma would furnish the lava next 
 in sequence. 
 
 The same hypothesis appears capable of accounting for such 
 a circumstance, as that mentioned by Prof. Judd regarding the 
 adjacent volcanic districts of Hungary and Bohemia 1 . The pro- 
 ducts of the contemporaneous later tertiary outbursts in these 
 adjacent areas were "as different in character as can well be 
 imagined," so that "it is scarcely possible to imagine that such 
 very different classes of lavas could have been poured out from 
 vents which were in communication with the same reservoirs of 
 igneous rock, and we are driven to conclude that the Hungarian 
 and Bohemian volcanoes were supplied from different sources." 
 According to our view they were so ; because the areas which 
 
 1 Ibid. p. 202. 
 F. 17 
 
258 SEQUENCE OF VOLCANIC ROCKS. [CH. xx. 
 
 supplied these lavas were separated by the roots of the Car- 
 pathian mountains, and we should no more expect exactly 
 similar flows of rock on opposite sides of the inverted moun- 
 tains below, than we should expect similar alluvial deposits 
 over the two subaerial areas separated by their watershed. 
 Indeed the difference might be even greater, because a mere 
 difference in the steepness of the root on the two flanks, by its 
 effect on the friction between the two, would cause the melted 
 matter and the substratum to be mingled in different pro- 
 portions. Moreover the substratum itself, owing to the dis- 
 turbance caused by eruptions, may have some amount of cir- 
 culation set up in it, and since it goes to make up a consider- 
 able portion of the erupted matter, this, if it occur, would 
 cause the lavas to be different. 
 
 It must be borne in mind that we have not been engaged 
 in inventing a theory, to account for the natural sequence of 
 volcanic rocks ; for we have, as we believe, already established 
 the existence of our mountain roots, and have been doing no 
 more than to show how they serve to explain the succession 
 in the order of eruption. 
 
CHAPTER XXI. 
 
 GEOGRAPHICAL DISTRIBUTION OF VOLCANOS. 
 
 The Linear arrangement of Volcanos accords icith the doctrine of a thin crust 
 and fluid sub stratum Volcanic bands related to the boundaries of continents 
 Distinction between coastline and oceanic volcanos Darwin on coral islands 
 Platforms on which oceanic islands stand their possible origin Great vol- 
 canic band of the Pacific coast Sinking and rising areas adjoining it 
 It follows nearly a great circle of the sphere and divides the land from the 
 water-hemisphere Is not equally active at every part Suggested cause of 
 local activity Other possible causes of the same Unknown cosmical causes 
 have operated Conclusion. 
 
 THE Geographical distribution of volcanos presents perhaps 
 fewer difficulties upon the supposition of a thin crust and a fluid 
 substratum, than upon any other that can be made, regarding 
 the constitution of the outer parts of the globe. The linear 
 arrangement of the greater number of the vents, points to their 
 situation along systems of fissures, and represents on a grand 
 scale the same phenomenon, which occurs, when subsidiary cones 
 of eruption are established upon fissures radiating from a central 
 volcano. To explain why these fissures, extending for thou- 
 sands of miles, should range in certain directions rather than in 
 others, is probably a hopeless task. The causes which contribute 
 to determine the direction of any fissure are very complicated, 
 and in the case before us generally unknown ; and the positions 
 of those which underlie the at present active vents, are not the 
 same as of those which did so in more ancient times. The post- 
 17 2 
 
260 DISTRIBUTION OF 70LCAN08. [OH. xxi. 
 
 eocene volcanic bands are no doubt nearly related to the recent 
 ones, but those of previous periods have probably little connec- 
 tion with any now existing. 
 
 The great volcanic bands of the present day have an obvious 
 relation to the boundaries, which separate the oceans from the 
 continents. They skirt the coast-lines, either upon the edge of 
 a continent, as along Western America, or else they occupy 
 chains of islands parallel to the continental shore, as is the case 
 along the Eastern coast of Asia. 
 
 Besides these coast-line vents, others are found in the open 
 ocean. These also appear to hold still a certain relation, though 
 an altogether different one, to the coast-lines. Their position is 
 medial. Thus in the Atlantic they occupy a medial line, rudely 
 parallel to the opposite coasts ; and in the Pacific, the boundary 
 of which is somewhat circular, they are found in a central patch 
 in the Hawaian group. 
 
 It also appears that an important distinction may be drawn 
 between the modes of occurrence of coast-line and of oceanic 
 volcanos. The cones raised by the former in some instances, no 
 doubt, emulate in height, if they do not overtop, the crests of 
 the ranges upon which they are parasitic. But they can by no 
 means be considered as constituting a largely integral part of 
 any mountain chain. If then such a chain were to be sub- 
 merged, until only the tops of the highest mountains were left 
 uncovered, the resulting islands would not as a rule consist of 
 volcanic products, but, on the other hand, they would chiefly 
 present crystalline or schistose rocks. Now the case is exactly 
 the opposite with oceanic islands. They are all volcanic. Dar- 
 win, in his work on " Coral Reefs," tells us that " the geological 
 nature of the islands which are encircled by barrier reefs varies; 
 in most cases it is of ancient volcanic origin ; owing apparently 
 to the fact that islands of this nature are the most frequent 
 within all great seas ; some however, are of madreporitic lime- 
 stone, and others of primary formations, of which latter kind 
 New Caledonia offers the best example 1 ." So also are some of 
 
 1 "On the Structure and Distribution of Coral reefs." Second Ed. 1S74, 
 p. G2. 
 
CH. xxi.] DISTRIBUTION OF VOLCANOS. 261 
 
 the Comoro Islands, and the Seychelles 1 . Now madreporitic 
 rock, having probably grown upon a volcanic basis, need form 
 no exception to the general law. And a glance at the map will 
 show that neither New Caledonia, nor the Comoro and Sey- 
 chelles Islands, are properly speaking Oceanic; the former belong- 
 ing to the submerged ridge, which connects New Zealand with 
 Australia and South-Eastern Asia, and the latter being a con- 
 tinuation of the axis of the great Island of Madagascar. The 
 oceanic islands of the Atlantic are likewise volcanic. There is 
 then it seems the important distinction to be drawn between 
 coast-line and oceanic volcanos, that the former are connected 
 with axes of elevation, and the latter not so. 
 
 At the same time it is known that the volcanic oceanic 
 islands rise from platforms elevated above the general level of 
 the ocean floor. Still, if these were formed by compression, we 
 ought to find some of the islands presenting exposures of the 
 inclined strata of their higher ridges, which is not the case. Of 
 what then do these platforms consist ? Is it not possible that 
 they may be accumulations of the ejectamenta of the volcanos 
 themselves ? With the fact before us that 665 feet of volcanic 
 ash and tufa were pierced in sinking an Artesian well at Naples 2 , 
 we may well believe that the enormous volcanos, whose ruins 
 now remain in the shape of Oceanic islands, may have laid down 
 an immense thickness of deposits around their bases. 
 
 If this be a true account of the condition of these areas, the 
 agency required for their production is one of fissuring without 
 resulting elevation. To account for this we can but speculate. 
 It may be that the suboceanic crust is too rigid to yield to the 
 compressing force, which, as will be remembered, is not exces- 
 sive; for the doubt which we have felt is whether it is sufficient 
 for the elevation of continental ranges. Or it may be that the 
 fissures beneath the ocean do not stop short until they reach the 
 surface, and so the compressing force has not time to act ; for, 
 as we have seen, when a fissure is completed to the surface 
 compression ceases. Another suggestion to be offered is that, 
 
 1 ibid. p. 69. 
 
 3 "Comptes Eendus," tome XLVIII. p. 994. 1859. 
 
262 DISTRIBUTION OF VOLCANO S. [CH. xxi. 
 
 if as believed the suboceanic crust is not much less dense than 
 the substratum, even if there were compression, the resulting 
 elevation would be comparatively small, because much more of 
 the compressed matter would go to form the roots, than would 
 be the case, with a lighter crust. 
 
 There is a distinction to be observed between an erupted 
 cone and a mountain produced by compression. The process of 
 formation of the latter causes a downward protuberance, which 
 assists by floatation to support the weight. But no such pro- 
 tuberance accompanies the piling up of a volcanic cone. Con- 
 sequently, where that is formed distant from any mountain 
 chain, the tendency to rupture, and sink through the crust, will 
 be uncompensated. In the oceanic areas the downward pressure 
 of the cone will of course be lessened by the weight of the 
 water displaced by it ; but on the other hand the difference of 
 specific gravity of the crust and the substratum being, as we 
 believe, less than in continental areas 1 , the support furnished 
 from below will be less. The result will be that an oceanic 
 volcanic area will have a tendency to perpetuate its own exist- 
 ence by fissuring the crust around its margin, and along the 
 fissures so formed fresh eruptions might be expected to break 
 forth. The elliptical form of many coralline archipelagos may 
 perhaps lend countenance to such a supposition, for a train of 
 volcanos, established originally upon a single line of fissure, 
 would develop a figure of that form during the process we have 
 suggested. 
 
 Reverting to the trains of volcanos which range parallel to 
 the coasts of the great continents, we observe that, along the 
 boundary of the Pacific Ocean, where near the American shore 
 deep water is found not far from land, there the volcanos stand 
 on the edge of the continent. But where, as in the Aleutian 
 Islands, Japan, and the more southern parts of the western 
 area of the Pacific, no great coast-range of mountains exists, 
 and deep water is not found near the continent, there is found 
 a great fall in the bed of the ocean on the outer, or Eastern, 
 side of the Islands which carry the volcanos. Here then, if the 
 
 1 p. 165. 
 
en. xxi.] DISTRIBUTION OF VO LOAN OS. 263 
 
 water were removed, the same fact would be apparent, that the 
 volcanos occupy an elevated tract, which borders the great con- 
 tinent. Such an arrangement of the vents, regarded as the 
 indication of systems of fissures below, of which probably a few 
 only reach the surface, is in accordance with our theory, that 
 the same ultimate cause underlies the phenomena both of com- 
 pression and of volcanic activity. 
 
 Kichthofen has made the remark that "active volcanoes 
 have been found to be particularly numerous in those regions 
 where the narrow terminations of two continents verge towards 
 connection, as in the case of Central America, between Alasca 
 and Kamtschatka, and between Australia and Farther India 1 ." 
 The crust movements of the last-named region, and of the sur- 
 rounding oceans, have been made more familiar to us than those 
 of most other parts of the world, through the researches of Dr 
 Darwin on Coral Reefs. He has shown that the areas occupied 
 by Atolls and Barrier reefs are sinking areas ; while those in 
 which active volcanos prevail are rising; as testified by the 
 occurrence of beds of recent shells at considerable heights above 
 the sea level, and corroborated by the fringing reefs without 
 lagoon-channels, that encircle the islands. The chart prefixed 
 to his work gives at a glance the relative positions of the sink- 
 ing and rising areas within the coralline seas ; and we perceive 
 that the trains of volcanos, which are the most active in the 
 world, are of the coast-line type, and that they follow the axial 
 trend of the land masses. The rising areas are confined to 
 comparatively narrow bands, bordered by the broad areas that 
 are sinking. This arrangement of the masses agrees well 
 enough with our section of a disturbed tract 2 , in which we see 
 that, if compression were to affect the elevated ridge A, A would 
 become part of a rising area, whilst wide regions at b, b, on 
 either side of it would sink. 
 
 We may, perhaps, conclude that the continent of Australia 
 is at present in process of becoming united to Asia, as .we are 
 led by geological reasons to believe that North and South 
 America have been comparatively recently joined. 
 
 1 "Natural System of volcanic rocks," p. 79. 
 
 2 p. 132. 
 
264 DISTRIBUTION OF VOLCANOS. [en. xxi. 
 
 We are not obliged to suppose that those oceanic areas, now 
 shown by Atolls and Barrier reefs, attached respectively to 
 sunken or existing islands, to be undergoing depression, were 
 ever continental areas, because, as already mentioned, these 
 islands are not composed of elevated strata, but, where visible, 
 consist of volcanic rock of a former age, a type of island belong- 
 ing then, as now, to the open ocean. 
 
 The great Pacific train of volcanos divides the world very 
 nearly into two halves, as may be seen by placing an ordinary 
 globe so that the wooden horizon passes over the Isthmus of 
 Panama, the southern extremity of Kamtschatka, and the 
 straits of Sunda. Near the latter place, however, the train 
 becomes more complicated ; for it takes a turn to the east at 
 the Philippines, and is joined by that other train which passes 
 through Java, New Guinea being at the place of junction, and 
 the great Island of Borneo occupying the angle. Afterwards 
 the combined train turns round towards the south, till it reaches 
 Ne*w Zealand, following a course nearly parallel to the eastern 
 coast of Australia. 
 
 If we look at the globe thus placed, we observe that we 
 have nearly all the land on one side of this great train, and that 
 the other hemisphere, except Australia, is occupied by water. 
 It appears then that, with this exception, the said volcanic 
 band defines the elevated part of the surface. But the excep- 
 tion proves the rule. For, when it nears Australia, the direc- 
 tion of the main band is diverted by its junction with the 
 second, and within the great curve which their united course 
 follows, this insular continent is embraced. 
 
 Regarding the great Pacific volcanic band under this aspect, 
 it is seen to follow nearly a great circle of the sphere for more 
 than half its circumference, when it is disturbed by encounter- 
 ing a second, which diverts it from its direct course. It can 
 hardly be that any cause, less than one of a very general cha- 
 racter, affecting the spheroid as a whole, can have produced 
 this unique, so to speak, nearly straight fissure. We are dis- 
 posed to attribute its origination to some unknown cosmical 
 cause. 
 
en. XXL] DISTRIBUTION OF VOLGANOS. 265 
 
 But this great band is not now equally active at every part. 
 In seeking the conditions which produce those disturbances of 
 the crust that determine the regions of present activity, by 
 admitting at intervals of time the elastic fluids from below, we 
 may look to changes in the distributions of load upon the 
 surface, as has been more particularly discussed in the tenth 
 Chapter. It has been there shown, that the less steeply in- 
 clined side of the elevated range will be that on which the 
 principal sedimentation will go on, and, acting as it were on the 
 longer arm of a lever, w T hose fulcrum is at the centre of gravity 
 of the tract, it will tend to rupture the crust on the margin of 
 the steeper side of the ridge, at the same time causing a certain 
 hang of the tract towards the region of deposit, which will open 
 rather than nip the crust at the place of fracture. We may 
 possibly trace this connection between the situation of the 
 active regions of the Western American volcanos, and the 
 great rivers of that continent, which deposit their sediment on 
 the eastern side. For instance, in Central America, we find a 
 comparatively narrow tract, the western side of which is moun- 
 tainous, while on the Eastern the Mississippi deposits vast 
 quantities of sediment. The region of its deposit is known to 
 be a sinking area, and must tend to give a tilting movement to 
 the tract so disturbed, raising and fissuring it along its western 
 border, near which its centre of gravity lies. The very same 
 sedimentation may also be the cause of disturbance, where the 
 West Indian volcanos occur. 
 
 The wide plain of the Amazon is also an area of great 
 sedimentation, and may have an effect, similar to that just 
 described, upon the coast line adjoining the Andes of Quito. 
 In like manner the deposits from the Bio de la Plata may have 
 a connection with the volcanic series of Chili. 
 
 Accumulations of snow and ice would have a like effect, 
 and the subsidence of Greenland and the volcanos of Iceland 
 may be possibly due to the accumulation of snow upon the 
 former. These are however speculations which are merely put 
 forward as suggestions. 
 
 There are other causes which, if the crust be no thicker 
 
266 DISTRIBUTION OF VOLCANOS. [CH. xxi. 
 
 than we have concluded it to be, may not be without effect 
 upon its equilibrium, such are the action of ocean currents and 
 winds. Slight as is the momentum of a mass of water, moving 
 with the velocity of an ocean current, as compared with the 
 mass of crust upon which it may act, nevertheless its effect 
 cannot be nil. And the same may be said of winds, which, on 
 the average of the year, have definite directions over a given 
 tract of continent, and their friction upon the surface cannot be 
 quite inappreciable. These two causes cooperating, may have 
 had some share in producing the peculiar form of the land 
 masses of the globe. These are however questions which do 
 not come within the scope of the present work. 
 
 In bringing this volume to a conclusion, the reader is 
 reminded that it deals with a great number of questions, each 
 in a very superficial manner, and that indeed entire treatises 
 might be written upon the subjects of some short chapters. 
 The whole, with the exception of the attempt to account for 
 the presence of water substance in the fluid magma, has been 
 treated in a manner that can hardly offend the most strict 
 disciple of the uniformitarian school. 
 
 But there are phenomena which appear to require for their 
 production causes hitherto unexplained, which must be looked 
 for possibly outside the globe itself. Such are climatal changes. 
 Such is also the remarkable fact that the grand efforts of 
 elevatory action appear to have been paroxysmal, and after 
 slumbering for long ages, to have been more intense at certain 
 periods; the last of which was subsequent to the Eocene. 
 These questions are left for a rising generation of physicists and 
 astronomers, who it is hoped may think the ascertained facts of 
 Geology a worthy field for the application of exact scientific 
 methods. 
 
CHAPTER XXII. 
 
 SUMMAKY. 
 
 [The Roman numerals refer to the Chapters.] 
 
 I. On underground temperature II. Condition of interior III. Internal den- 
 sities and pressures IV. Lateral pressure, its amount V. Elevations and 
 depressions VI. Elevations on the hypothesis of solidity VII. Hypothesis 
 of solidity fails VIII. Fluid substratum IX. Crust not flexible X. Dis- 
 turbed tract XI. The revelations of the plumbline XII. The revelations 
 of the thermometer XIII. Amount of compression XIV. Extravasation of 
 water will not account for compression XV. Compression and volcanic 
 action XVI. On Faulting XVII. Geological movements explained 
 XVIII. Mr Mallei's theory of volcanic energy XIX. The volcano in 
 eruption XX. Sequence of volcanic rocks XXI. Geographical distribution 
 of volcanos, 
 
 I. WE have commenced our discussion of the wide subject 
 of the Physics of the Earth's Crust with underground tempera- 
 ture, because the distribution of heat in the interior of the 
 earth is one of the cardinal conditions upon which all physical 
 questions connected with it depend. We have pointed out that, 
 having regard to such depths as artificial excavations reach, the 
 law of increase is on the whole an equable one, amounting on 
 an average to about one degree Fahrenheit for every 51 degrees 
 of descent. It has been asserted that the rate has been found 
 to decrease towards the bottom of some deep boreholes, and it 
 has been even maintained that at a depth of about 5000 feet the 
 increase of temperature would come to an end. But we have 
 shown reasons for believing, that the observations, in which a 
 diminution in the rate has been said to have been noticed, have 
 really been vitiated by the disturbance of the column of water 
 in the borehole by convection currents, and that the supposed 
 cessation of the increase at about 5000 feet has arisen from 
 a delusive method of computing the general result. Neverthe- 
 less it is unquestionable that this equable law of increase of 
 temperature, though probably true near the surface of the 
 earth, cannot extend to all depths; for, if it did, we should 
 
268 SUMMARY. [en. xxn. 
 
 have, at the depth of from 200 to 400 miles, temperatures which 
 would equal those, which have been on good authority attribu- 
 ted to the sun himself. The equable law of increase, however, 
 may be so far depended on, as to lead us to expect a tempera- 
 ture at which the rocks would melt at a depth of not more than 
 30 miles. 
 
 II. We are next led to speculate about the condition of the 
 earth's interior. And first we enquire what is the law of 
 density ? The density of the surface rocks can be fairly esti- 
 mated by actual observation in more ways than one, and is 
 found to lie between 2'56 and 275 times that of water. The 
 mean density of the whole earth has been determined by ex- 
 periments with the plumbline, and torsion balance, and may be 
 taken to be about 5'5. There is little doubt that the interior 
 of the earth is in a sense stratified, and consists of layers, or 
 couches de niveau, each of equable density, and that the density 
 is greater towards the centre, and diminishes towards the sur- 
 face. But it is not known for certain what the actual law of 
 density is ; that is to say, we do not know how great the density 
 is at any given depth, nor how thick any stratum is, which may 
 be supposed to have a particular density. All that we really 
 know is that the heavier layers are deeper down than the 
 lighter, and that the forms of them are spheroidal, becoming 
 more and more flattened about their poles as they approach the 
 outer surface. 
 
 Now these are the arrangements and forms which the strata 
 of a liquid spheroid would assume under the action of rotation 
 and gravitation. It has been consequently concluded that the 
 earth was once wholly melted. 
 
 Here, then, two lines of argument meet. The present 
 law of temperature is such that we may expect to find heat 
 enough at the present day to melt the materials of the earth at 
 the depth of about 30 miles, and mathematical investigations, 
 concerning the figure of the earth and its law of density, lead to 
 the conclusion that it has been melted. The question arises, 
 whether it is at this day molten within, either wholly or par- 
 tially, or has the molten condition passed away, so that it 
 is now solid ? There is however a tertium quid. Some have 
 
CH. xxii.] SUMMARY. 269 
 
 thought that it is what has been called 'potentially fluid/ that is, 
 wholly solid in consequence of the pressure to which the internal 
 strata are subjected, but ready to become fluid, on account of 
 its high temperature, whenever the pressure is relieved. This 
 is the great subject of controversy, towards the determination of 
 which the present volume is intended as a contribution. 
 
 The increase of temperature below the outer crust, which 
 we know to be solid, will be governed by the laws of convection 
 of heat if the interior is fluid, but by the laws of conduction if 
 it likewise be solid. 
 
 The question whether the interior of the earth is at present 
 solid or fluid, or partly solid and partly fluid, may, apart from 
 geological considerations, be attacked in two ways. The first 
 of these is by enquiring, what is the difference of effect that 
 the moon and sun would have upon the motions of the earth 
 in these cases ; and the other way is by considering the se- 
 quence of events, according to which a molten globe may have 
 passed into its present state. For the first, there are two kinds 
 of effect produced by the attraction of the rnoon and sun upon 
 the earth ; and these are precession and the tides. Mr Hop- 
 kins, between 1839 and 1842, investigated the difference be- 
 tween the precessional effects in the cases of a solid and of 
 a fluid interior, and came to the conclusion that the crust of 
 the earth could not be less than from 800 to 1000 miles thick. 
 But the arguments of Mr Hopkins were, in 1876, abandoned by 
 Sir William Thomson. 
 
 With respect to the tides the case is different. The last- 
 named eminent physicist says that unless the earth as a whole 
 were extremely rigid, "the solid crust would yield so freely to 
 the deforming influence of the sun and moon, that it would 
 simply carry the water of the ocean up and down with it, and 
 there would be no sensible tidal rise and fall of the water 
 relatively to land." It does not however appear necessary that 
 the earth should be absolutely solid from the centre to the 
 surface to satisfy the requirements of great rigidity as a whole. 
 May this not be satisfied by the hypothesis of a rigid nucleus, 
 nearly approaching the size of the whole globe, covered by a 
 
270 SUMMARY. [CH. xxn. 
 
 fluid substratum of no great thickness compared to the radius, 
 upon which a crust of lesser density floats in a state of equili- 
 brium ? This is the supposition as to the condition of the earth 
 which appears on the whole to satisfy best the requirements 
 both of geology and of physics, as we have attempted to show 
 in the preceding chapters. 
 
 That the above arrangement of the materials of the earth 
 is compatible with the laws of cooling of such a body, has been 
 proved by Mr Hopkins to be the case. The nucleus owes its 
 solidity to the enormous pressure of the superincumbent matter 
 while the crust owes its solidity to having become cool. The 
 fluid substratum beneath it is not under sufficient pressure to 
 be rendered solid, and is sufficiently hot to be fluid. As to the 
 degree of its fluidity, we have no certain knowledge. It is pro- 
 bably more viscous in its lower portions through pressure, and 
 likewise passes into a viscous state in its upper parts through 
 cooling, until it joins the crust. But how fluid the most fluid 
 intermediate parts may be we cannot determine. 
 
 III. It has been stated that the mean density of the whole 
 earth is known, and also the density of surface rock. But the 
 actual densities of the successive layers, and their corresponding 
 forms and thicknesses, are not known. There must be certain 
 relations among these attributes in order to satisfy the ascer- 
 tained facts regarding the earth's shape, and its mean and 
 surface densities. But these requirements may be satisfied in 
 more ways than one. Laplace suggested a law of density, suit- 
 able for purposes of calculation, which satisfies these require- 
 ments very closely ; and that law has been generally assumed, 
 as representing the true state of the case, in investigations on 
 the figure of the earth. It makes no assumption as to the 
 actual cause of the variation of density with the depth, al- 
 though it is assumed to be such as might be caused by a certain 
 relation between density and pressure. But it is much more 
 likely that the increase in density towards the centre of the 
 earth arises from the heavier materials gravitating thither. 
 Waltershausen has formed a theory on the ground that the 
 earth is a hot globe, of which a considerable portion is fluid, 
 
CH. xxii.] SUMMARY. 271 
 
 an unknown amount of the central parts being rendered solid 
 by pressure. The downward increment of density is expressed 
 by the chemical increment of the heavy bases : and the fluid 
 region directly under the crust consists, first of a felspathic and 
 acid magma, which passes downwards by successive replacement 
 of bases into an augitic and finally, into a magnetitic magma. 
 This theory appears to have a great deal to recommend it. 
 Waltershausen has given the probable densities and pressures 
 at different depths, but the formula by which he has calcu- 
 lated them appears to be arbitrarily assumed. He makes the 
 density at the centre of the earth 9*59, or about that of sil- 
 ver, and the pressure there that of about 2,500,000 atmo- 
 spheres. If, however, we use Laplace's law of density, the 
 pressure at the centre comes out considerably greater, reaching 
 that of 3,000,000 atmospheres. 
 
 There will be found given in the appendix a new theory 
 of the constitution of the interior of the earth by M. Roche, 
 which will satisfy the requirements of geology, provided the 
 difficulty, connected with the change of rotational velocity, 
 which we have suggested, can be satisfactorily met. 
 
 IV. Having devoted the first three chapters to the con- 
 sideration of the more general questions regarding the consti- 
 tution of the earth as a whole, we now approach the geological 
 aspect of the subject. The outer crust of the earth is the pecu- 
 liar domain of geological enquiry. And enquiry leads to the 
 conclusion that this crust has been subjected to great violence, 
 being compressed, ruptured, raised, and depressed, and also 
 subjected to heating. A special phenomenon of a most start- 
 ling kind, did not frequency of description render us familiar 
 with it, is that in certain districts, outbursts of fiery vapours 
 and molten rock, accompanied by violent earthquakes, mark 
 the volcanic regions of the surface. To account for both 
 these classes of phenomena a source of energy is required, and to 
 the earth's interior we must look to supply it. Here we find 
 gravitation, and heat stored up ready for our purpose. How 
 have these agents produced the results we witness ? This is 
 our problem. 
 
272 SUMMARY. [en. xxn. 
 
 The well-known fact, that great lateral compression has 
 affected the stratified rocks of the earth's crust, is now generally 
 explained by the supposition that the globe has contracted 
 through secular cooling. It is thought that, as the cooling 
 proceeded, the interior shrank away from the crust, and the 
 latter became wrinkled ; and that by this means the crump- 
 ling and contortions of the rocks were produced. We have 
 accordingly calculated what' the lateral pressure would be, 
 which would be available for crushing the strata of the earth's 
 surface, supposing that the interior were to shrink away 
 from the crust, and to leave it unsupported. We find that 
 it amounts to the enormous pressure of the weight of a 
 column of rock of the surface density, of the same section as 
 the stratum, and two thousand miles long, or about 830,200 tons 
 upon the square foot. We need not doubt that this pressure 
 would be competent to perform the work expected of it. 
 
 Nor would any solid stratum in the interior of the earth be 
 capable of sustaining the lateral pressure upon it: for these 
 lateral pressures would be still greater within the earth than at 
 the surface, except very near the centre. 
 
 V. That the pressure thus produced would ber abundantly 
 sufficient for the purpose, is however no proof that the work has 
 been accomplished in that way. It has been an assumption 
 often repeated, but never proved. The first task which we have 
 proposed to ourselves is therefore to examine this point. We 
 admit that the inequalities of the earth's surface have been 
 caused by lateral compression, but we are not sure that this 
 has arisen from the secular cooling. We therefore commence 
 our enquiry by seeking for some measure of the inequalities of 
 the surface, as a preliminary step towards determining how 
 they have been produced : and in the first instance we include 
 the greater inequalities, which constitute the oceanic and con- 
 tinental areas. But although we have ocular proof that moun- 
 tain chains have been formed by compression, it is mere matter 
 of inference that the elevation of continents above the ocean 
 floor, is likewise due to the same cause. 
 
 Suppose then the earth to have contracted through cooling, 
 
en. XXIL] SUMMARY. 273 
 
 and suppose (winch is of course impossible) that the crust had 
 shrunk down upon it without becoming either thickened or 
 wrinkled by the process. The position which the surface would 
 have occupied under this impossible supposition, gives us a 
 definite level, at a definite distance from the centre of the 
 earth, and this level we call the 'upper datum level.' Simi- 
 larly, the position which the under side of the crust would 
 occupy, we call the 'lower datum level.' To these levels we 
 refer the elevations and depressions (if any) of the surface, 
 caused by the crumpling action; and we can express their 
 amount by saying how deep a layer of material the elevations 
 would form, if they were levelled down, and spread out upon 
 our upper datum level. 
 
 Now if we assume that the earth is solid, i.e. that there 
 is no fluid substratum beneath the crust, it is clear that all the 
 inequalities which compression could produce would be of the 
 nature of elevations above the upper datum level. There could 
 be no depressions. Moreover the bottom of the ocean basins 
 would either coincide with this datum level, or else they would 
 be the parts of the disturbed surface least raised above it. 
 
 Assuming the former to be the case, we find, upon an 
 estimate as near as we see our way to form, that the whole 
 of the existing inequalities of the surface, if levelled down and 
 spread out, would form a layer of from 9500 to 13000 feet 
 thick over the whole earth. This estimate is not likely to 
 be too large, but rather the other way. 
 
 VI. Our next step is to enquire, what the amount of the 
 inequalities would be, if they had been formed by lateral com- 
 pression through cooling. If we can make an estimate of these, 
 and compare it with that which we have already made of the 
 existing inequalities, we shall be able to form an opinion as to 
 whether the cause assigned is, or is not, adequate for the 
 purpose. 
 
 Now it is fortunate that Sir William Thomson has already 
 
 paved the way for such an investigation, by establishing the 
 
 law which the temperature within the earth must follow, if it 
 
 be a solid cooling by conduction. We are consequently able to 
 
 F. 18 
 
274 SUMMARY. [CH. xxii. 
 
 say how much it would have cooled at any specified depth from 
 the surface, since the whole became solid. If then we know the 
 amount of contraction on cooling for such rocks as exist near 
 the earth's surface, we shall have the means of calculating how 
 great the contraction would have been ; and consequently what 
 amount of inequalities this cause could have produced. Again, 
 Mr Mallet has made a series of careful experiments on a large 
 scale, on the contraction through cooling of silicious slags from 
 a state of fusion, and his results are sufficiently applicable to 
 our problem. These we have used, and calculated the amount 
 of inequalities of the earth's surface, which would have been 
 formed had they been due to a hot solid globe cooling by con- 
 duction, and we have found the amount to be very far smaller 
 than that which actually exists. For whereas, as we have seen, 
 the actual inequalities, if levelled down, would form a layer of 
 about 10,000 feet thickness, those which would be formed on 
 the present hypothesis would form a layer not exceeding 900 
 feet in thickness on the most extravagant supposition. But if 
 we adopt a more moderate basis of computation, 200 feet would 
 be nearer the mark. 
 
 VII. The large discrepancy between these quantities shows 
 that the hypothesis, that the inequalities of the surface have 
 been caused by the cooling, and consequent contraction of the 
 earth regarded as a solid globe, is untenable. We appear 
 then to be compelled to accept one or both of the alterna- 
 tives, (1) either the inequalities of the surface are not altogether, 
 or even chiefly, due to lateral compression, or (2) there has been 
 some other cause involved in producing the inequalities of the 
 crust, other than the contraction of a solid globe through mere 
 cooling. 
 
 In the estimate we have .made of the inequalities of the 
 surface, which might arise through compression from the cool- 
 ing of a solid globe, we have included the basins of the oceans. 
 If these be due at all to the contraction of the materials of the 
 globe, there does not appear to be any other way of accounting 
 for them except by compression : because, if they had been 
 caused by direct radial contraction, they would require a differ- 
 
CH. xxii.] SUMMARY. 275 
 
 ence of linear contraction equal to their depth in the matter 
 beneath themselves and beneath the land. But in the course 
 of our calculations it has appeared that the entire radial con- 
 traction would not be equal to the depression of the ocean bed 
 beneath the land surface. We have then sufficiently proved, 
 that the contraction of a solid earth through mere cooling is 
 not adequate to account for the inequalities of the surface ; and 
 it also appears probable that the other alternative must be 
 accepted likewise, because the ocean basins being regarded as 
 inequalities, or depressions, of the surface, they cannot be 
 directly accounted for by compression ; either as depressing 
 them, or relatively raising the continents. Still further, the 
 distribution of land and water upon the globe, as Herschel has 
 observed, proves the force by which the continents are sustained 
 to be one of tumefaction, and is therefore a proof of the com- 
 parative lightness of the materials of the terrestrial hemisphere ; 
 so that an excess of density appears to be requisite to retain the 
 water over such extensive areas as are occupied by the greater 
 oceans. 
 
 Well-known geological phenomena, which prove the insta- 
 bility of the earth's surface, also negative the hypothesis of 
 solidity. Alternate elevation and depression have frequently 
 affected the same areas. But especially the shifting of the crust 
 towards a mountain-range, which is testified by the corrugation 
 of the rocks of which it is formed, requires a more or less fluid 
 substratum to admit of it. The sinking of areas such as deltas, 
 and other regions of deposition, demands a like arrangement ; 
 and in short, it appears that the crust, in the form in which it 
 exists, must be in a condition of approximate hydrostatical 
 equilibrium, such that any considerable addition of load will 
 cause any region to sink, or any considerable amount denuded 
 off an area will cause it to rise. 
 
 VIII. If we admit that the cooled crust of the earth rests 
 upon a fluid substratum, we cannot doubt that the fluidity is a 
 consequence of its high temperature ; and it probably follows 
 that volcanic eruptions arise from emanations from the sub- 
 stratum gaining access to the surface. All volcanic eruptions are 
 
 182 
 
276 SUMMARY. [CH. xxn. 
 
 accompanied by a great emission of steam : but it is not agreed 
 whether this water-substance forms an integral part of the 
 substratum, or whether it becomes in some way subsequently 
 mingled with the lava during, or just before, its eruption. 
 The position of volcanos near the sea, and the sea salts given 
 off by the lava, have been held to favour the latter supposition. 
 Water can be conceived to gain access to masses of heated 
 rock only in two ways ; by open fissures, or by capillary ab- 
 sorption. We have, we think, shown that neither mode of 
 access is possible. It remains that this water, and the ele- 
 ments of sea salts, must be original constituents of the magma. 
 The question then is, how this water-substance comes to be 
 there. To answer this it is necessary to go back to the 
 cosmogony, and we suppose that, under the pressure due to 
 the water-substance which would have, in a state of vapour 
 or gas, formed the outer layers of the still incandescent earth, 
 this vapour or gas would not have been necessarily superin- 
 cumbent on an anhydrous globe, but that such rocky matters 
 as were soluble with it would have been in solution with it. 
 As cooling proceeded, an upper crust of rock would have been 
 formed by crystallization at a certain level, and would have 
 gradually extended downwards. But we conceive that there 
 still exists an intensely hot layer of water dissolved silicates, 
 in a state of what has been called igneo-aqueous fusion, under- 
 lying the solid crust, ever in readiness to furnish the steam, 
 gases, and ejectamenta, of the volcano. 
 
 This igneo-aqueous fusion has usually been spoken of as 
 a state of solution of the rock in water. It is a condition of 
 which we know little. Perhaps it may be more correctly 
 described as a state of solution of water in rock. And some 
 recent experiments by Mr Hannay throw an interesting light 
 upon the subject. He doubts the conclusions of Andrews 
 as to the continuity of the states of matter, and it would appear 
 from his reasoning 1 , that, when a substance is confined at a 
 temperature above the critical, it is really in the gaseous state ; 
 and that in this state it is capable of holding solids in solution, 
 
 1 Proc. Roy. Soc., Vol. xxxn, p. 410, June 1C, 1881. See also ibid. p. 407. 
 
en. xxii.] SUMMAR Y. 277 
 
 which in the vaporous state it cannot do 1 . We may therefore 
 look upon the state of igneo-aqueous solution as one, in which the 
 water-substance is in a gaseous state, and that the combination 
 between the water-substance and the rock is probably of that 
 kind, which has been termed "occlusion " of gas by a liquid. 
 
 IX. In considering the form and arrangement of the 
 inequalities which a thin crust might assume, if it rested upon 
 a liquid substratum which had from any cause fallen away 
 from it, so that it became subjected to lateral compression, 
 the supposition may be made that the crust is flexible that is 
 to say, that it accommodates itself to its new position by bending 
 without breaking, or becoming thickened anywhere. Under 
 these circumstances the fluid would rise into the anticlinals. 
 The form which such a crust would assume has been approxi- 
 mately determined in the ninth chapter, and it has been shown, 
 that there is no reason to think that it accords with the arrange- 
 ment of the inequalities on the earth's surface. We therefore 
 dismiss this hypothesis. 
 
 If the crust does not maintain a uniform thickness, it must 
 accommodate itself to compression by being crushed together, 
 and thickened in places. The very important consequence 
 follows, that elevations above the datum level will be accom- 
 panied by depressions beneath. The anticlinals will not be 
 filled with fluid from below, but will be the upper portions 
 of double bulges, which will dip into the fluid below, as well as 
 rise into the air above. From whatever cause compression 
 might arise this result would be the same. 
 
 1 " The definition of the gaseous state as a state of matter not alterable by 
 pressure alone leads us to a clear division of aeriform matter into two states, 
 the vaporous and gaseous, the first alterable, the second unalterable by pressure 
 alone. Another distinction between vapour and gas is this : gases are solvents 
 of solids ; vapours are not. Let' a liquid be coloured by having some non- 
 volatile coloured solid dissolved in it, and let it be heated under pressure the 
 liquid will remain coloured while the vapour will be quite colourless, and wii so 
 remain up to the critical point. Now let the fluid be raised above its critical 
 point, all the internal space will be coloured, showing that (the contents being 
 gaseous) the gas dissolves the solid while the vapour does not." Proc. Royal 
 Soc. Vol. xxxn. p. 412. This has a bearing upon what has been said about the 
 formation of mineral veins, p. 198. 
 
278 SUMMARY. [CH.XXII. 
 
 X. We next attempt to deal with the condition of the 
 earth's crust just described. It will be observed that it is 
 analogous to the case of a broken-up area of ice, refrozen and 
 floating upon water. The thickened parts which stand higher 
 above the general surface also project deeper into the liquid 
 below. We have supposed the crust to have the specific 
 gravity of granite, and the fluid substratum to have that of 
 basalt. Hence their ratio is about 0'905, whilst the specific 
 gravity of ice is 0*9176. These numbers are so nearly the 
 same that the cases are exceedingly analogous, and the down- 
 ward protuberance of the crust, as compared with the elevations 
 above the surface, will agree closely with the immersed part 
 of an iceberg as compared with the part exposed. 
 
 When the crust is crushed together along a mountain-range, 
 part of the mass will be sheared upwards and part downwards. 
 If it be equally rigid from top to bottom, half of it will go up 
 and half of it down, and the neutral zone, as we have termed it, 
 will be at half the depth. But, if the lower parts be softened 
 by heat, a greater thickness will be sheared downwards than up- 
 wards. If the softening were to follow a certain assumed law, 
 which would make it increase slowly at first but more rapidly at 
 last, until it mingled with the fluid substratum, the neutral 
 zone would be at the depth of one-third of the crust. This 
 would be probably an excessive estimate. We accordingly have 
 assumed a value between the two and place the neutral zone 
 at the depth of two-fifths of the whole thickness. 
 
 And here we arrive at a stage at which we make our first 
 attempt at estimating the actual thickness of the crust. Granite 
 has been formed in the presence of liquid water. Water cannot 
 remain a liquid at a higher temperature than 773 F., what- 
 ever pressure may be placed upon it. This temperature, at the 
 rate of increase of l a F. for from 51 to 60 feet, would be found 
 at the depth of from 7 to 8 J miles. Hence rock, which was 
 once at the depth of .from 7 to 8J miles, has been forced up- 
 wards ; and therefore the neutral zone is not so deep as that. 
 But if | of the thickness were 7 to 8| miles, the whole thickness 
 would be from 17 to 21 miles. Hence we conclude the whole 
 
en. xxii.] SUMMARY. 279 
 
 thickness is greater than this. Again, taking the temperature 
 of melting slag at 3000 F., such a temperature would be met 
 with at the depth of from 28 to 30 miles, and we can hardly 
 suppose the temperature of the substratum to be so high as 
 that of melting slag. Hence we place, roughl^JJie-thickness 
 of the undisturbed crust as a first attempt between tl 
 estimates, at about 25 miles. 
 
 Now supposing a tract of the crust crush( 
 compression ; and that about two-fifths of 
 up, and three-fifths goes down. If it were to 
 position, we should have the ratio of the part above the 
 effective level of the fluid to the part below it as 2 to 3. 
 This would be impossible if it floated; just as it would be 
 impossible that an iceberg should stand 200 feet above the 
 water while only 300 feet were immersed. But the tract 
 of crust does not exactly float ; for it is held up to some extent 
 by its attachment to the neighbouring crust. Nevertheless 
 it cannot be held up long in what would be so constrained a 
 position. It must then sag downwards ; and the most thickened 
 part would sink the most. Hence depressions would arise 
 on both sides of the ridge, and the ocean, which covers the 
 general surface, would be deeper than elsewhere along two 
 channels parallel to, and at some little distance from, the ridge. 
 But should the ridge be steeper on one side than on the other, 
 as seems inevitable, the ocean would be deeper on the steeper 
 side. This relative position of the depths of the ocean to 
 mountain-chains is in accordance with nature. 
 
 Next suppose the ridge thus elevated to be denuded. The 
 chief streams will be formed on the less steep side, and the 
 sediment will go partly into the sea and be deposited along 
 the shore line, and partly on to the lower lands. This will 
 depress that portion, and it will sink ; and the whole tract will 
 be more or less tilted down on that side, and up on the other, 
 because it will turn about an axis through its centre of gravity, 
 which will be situated somewhere beneath the ridge. The 
 ridge also, owing to the great downward protuberance, will 
 stiffen the tract, and give it rigidity to bear this tilt. The 
 
280 SUMMARY. [CH. xxn. 
 
 tendency will be for fissures to form, chiefly along the shore 
 line on the steeper side of the ridge. The depressions, in which 
 the deep water lies, will also by the same action be moved 
 further away from the ridge on both sides. 
 
 XI. We apply to the downward protuberance of the crust 
 into the substratum, under any elevated tract, the popular 
 expression of "roots of the mountains." The existence of these 
 roots of the mountains are not a mere matter of speculation. 
 They have been felt by aid of the plumb-line in the following 
 manner. The great mass of the Himalaya mountains was, 
 during the Indian Trigonometrical Survey, found to attract 
 the plumb-line. But upon its being calculated how much 
 attraction ought to be attributed to this mountainous mass, 
 it was found that, though they attracted the plumbline, yet 
 they ought to have attracted it still more than they did. 
 Sir G. B. Airy explained this anomaly by the existence of 
 downward protuberances of a lighter crust into a heavier sub- 
 stratum ; which is exactly the same supposition to which our 
 reasoning has just led us. This then is a strong confirmation 
 of our theory of the constitution and arrangement of the 
 crust. 
 
 Another point to be observed is, that the floatation of a 
 crust, thus dipping downwards into a heavier fluid at the places 
 where it rises upwards into the air, precludes the transmission 
 of any unequal stresses to the parts below, and renders unneces- 
 sary the supposition of extreme rigidity, either in the crust 
 itself or in the subjacent matter, in order to support such 
 stresses. 
 
 XII. Again, the existence of the roots of the mountains 
 ought to be revealed by phenomena of underground tempera- 
 ture ; and we find such to be the case. Whether the crust be 
 thick or thin at any given locality, the temperature of its under 
 surface ought to be the melting temperature. This tempera- 
 ture may practically be considered the same everywhere. 
 Accordingly any difference in the rates of increment of tem- 
 perature in descending at two localities ought to depend only 
 upon the thicknesses of the crust, and upon the mean surface 
 
CH. xxii. ] SUMMARY. 281 
 
 temperatures ; and the rate ought, as a rule, to be greater in 
 lowly ing than in elevated regions. This is known to be the 
 case. Careful observations of temperature were made during 
 the construction of the tunnel through Mont S. Gothard, and 
 sufficiently reliable ones also at Mont Cenis. In both these 
 tunnels the rate was found to be about 1 F. for 100 feet, which 
 is only about half the usual rate. 
 
 The rate being known, and the height of the mountain, and 
 also the rate at a place elsewhere near the sea level, if we 
 assume the relative densities of the crust and substratum to be 
 those of granite and basalt, we can calculate the thickness of 
 the crust and the melting temperature from these data, without 
 making any assumption about the melting temperature. In 
 this way we have obtained for the thickness of the crust about 
 25 miles at the sea level ; and for the melting temperature 
 about 2500 F. The first of these values agrees with that 
 already estimated in X., and the latter is by no means im- 
 probable from what we know about the melting temperatures of 
 silicates. The calculations which we have made respecting the 
 thickness of the earth's crust at the sea level, necessitate a 
 corresponding thickness beneath the ocean. The result at 
 which we have arrived is that, if the crust were of the same 
 density there as beneath the continents, it would have to be 
 thinner than is possible beneath the oceans. We therefore con- 
 clude that it is not of the same density beneath the oceans, and 
 thus we are led, by another line of argument, to the same con- 
 clusion as that mentioned in VII., viz., that the crust beneath 
 the oceans is denser, and that it is to this cause that the ac- 
 cumulation of water over one-half the sphere is to be attributed. 
 
 If we put the mean depth of the ocean at three and a half 
 miles, with our assumed values of the densities of the crust and 
 substratum, we have found that on these data the thickness of 
 the crust at the sea level cannot be less than about 25 miles ; 
 which so far agrees with the estimates before made. And in 
 this last calculation no considerations of temperature whatever 
 are involved, as they were in the former, and have always been 
 in previous estimates. 
 
 We conclude on the whole that the density of the sub- 
 
282 SUMMARY. [CH. xxn. 
 
 oceanic crust may be about 2'955 ; that its thickness is there 
 about 20 miles; while, in the continental areas, its density 
 is about 2'68, and its thickness at the sea level about 25 miles. 
 
 XIII. We cannot explore the sub-oceanic crust, and do not 
 know from direct evidence whether it has been compressed, 
 as we know has happened to the continental areas. Many 
 geologists feel assured that the oceanic areas have always been 
 oceanic, and that they have never interchanged places with the 
 continents. If that be the case they have never been com- 
 pressed and elevated. 
 
 Referring to the two modes in which compression may have 
 caused elevation, namely, by either raising the crust into anti- 
 clinals, into which the subjacent denser fluid would rise, or by 
 producing ridges on the surface, which would be accompanied 
 by corresponding depressions of the lighter crust, into the fluid 
 beneath, we remark that, if the former were the arrangement, 
 the two phenomena we have lately discussed would be abso- 
 lutely reversed. For the attraction of mountain masses would 
 be greater than if they consisted of matter of the mean density 
 of the crust, instead of being less ; and the increase of tempera- 
 ture would be also greater in mountainous regions, instead of 
 being less. 
 
 Compression may have arisen from contraction of the in- 
 terior, or from expansion of the crust, or from these two pro- 
 cesses going on together. We have shown that the contraction 
 of a solid earth through cooling cannot explain the existing 
 inequalities. Neither does it appear that the contraction of a 
 liquid substratum from mere cooling can have been much 
 greater than that of a solid globe, for, before the time when a 
 crust began to form, the liquid must have become reduced by 
 convection to nearly the -temperature of solidification ; and sub- 
 sequent cooling, accompanied by solidification and thickening of 
 the crust, would have proceeded downwards, almost as if it 
 rested on a solid nucleus, the loss of heat taking place from the 
 crust alone. 
 
 In order to estimate the amount of contraction, which w r ould 
 have produced the existing inequalities on the hypothesis of a 
 fluid substratum, we must proceed somewhat differently from 
 
en. xxii.] SUMMARY. 283 
 
 what we did under the hypothesis of a solid globe. This then 
 we have accordingly done upon two suppositions, first that the 
 crust beneath the oceans is 20 miles thick, and of the same 
 density as beneath the continents, the oceans being supposed to 
 lie in veritable depressions caused by the greater thinness of the 
 crust beneath them. In that case we find that the radius of 
 the globe, since the inequalities began to be formed, must have 
 been shortened by about 700 miles. 
 
 This is a much greater shortening than can be supposed 
 possible, and is an additional reason against the hypothesis of 
 the sub-oceanic crust being of the same density as that beneath 
 the continents. In the next place, we suppose compression to 
 have been confined to the continental areas, which is equivalent 
 to attributing the oceans to a denser crust beneath them. We 
 have taken the thickness of the continental crust at the sea 
 level at 25 miles ; and in this case we find the shortening of the 
 radius, which would produce the existing inequalities, to be 
 about 42 miles ; and then the horizontal compression of the 
 continental areas would average about two per cent. 
 
 These results confirm the conclusion, that the ocean basins 
 are not caused by depressions, in the upper surface only, of a 
 crust of density everywhere uniform, but that they are due to a 
 greater density, and general depression, of the sub-oceanic 
 crust. 
 
 XIV. It being certain that a vast amount of water is given 
 off in volcanic eruptions, we next examine the question whether, 
 supposing all the water of the oceans to have been once beneath 
 the crust, it would be possible to obtain a sufficient contraction 
 of the globe to have produced the inequalities, by the trans- 
 ference of this water from beneath to above the crust. But we 
 find that, upon the supposition, the most favourable that we can 
 make, respecting the decrease of volume which the abstraction 
 of this water would impart to the substratum, the hypothesis 
 fails. For the entire remaining portion of the globe beneath 
 the crust would not suffice to afford a sufficient amount of con- 
 traction to have caused the existing continental compression, 
 under circumstances, more favourable than are likely, with 
 
284 SUMMARY. [en. xxn. 
 
 regard to the original addition of volume, which the presence of 
 the water could contribute. 
 
 Changes in the earth's rotational velocity may have altered 
 the oblateness, and compressed some parts of the surface and 
 stretched others ; but there does not appear to be any indi- 
 cation, in the arrangement of mountain chains, of their having 
 been connected with such a mode of action. 
 
 XV. We have thus examined two probable causes of com- 
 pression of the earth's surface, originating in contraction of 
 the interior, namely, cooling, and extravasation of water-sub- 
 stance from beneath the crust. Neither of these appears to be 
 adequate to produce the amount of compression which exists. 
 No other cause of contraction of the globe suggests itself. 
 
 We next look about us for a possible cause of extension of 
 the surface, which, it is obvious, would, equally with contraction 
 of the interior, produce compression. The numerous more or less 
 vertical dykes of igneous rock lead us to enquire, whether the 
 rending of the fissures which they occupy, may not be indica- 
 tive of the extension of which we are in search. The pressure 
 of the crust upon the fluid substratum is about 100G6 tons upon 
 the square foot. If the water-substance from the magma were 
 to escape into a crack in the under side of the crust, it would 
 exert this pressure towards rending it wider ; and so long as the 
 vapour or gas was supplied with sufficient rapidity, it would 
 prevent the magma from rising into the chasm so formed. 
 When the rent reached the surface, the vapour would rush forth 
 and be followed by the magma itself, now appearing as lava ; 
 and thus a volcano would be established. But this would be an 
 exceptional occurrence. It would be only here and there that 
 the vapour would escape at the surface, because its doing so at 
 one point would relieve the internal pressure for a long distance. 
 
 The above-described process appears to be the mechanism 
 requisite to establish a volcanic vent, and agrees well with the 
 series of earthquakes which usually for a long while precede an 
 eruption, and very often occur without any eruption at all. 
 Nevertheless permanent elevation of the tract is said to be a 
 common result of their action. 
 
en. XXIL] SUMMARY. 285 
 
 In order to arrive at some conclusion regarding the amount 
 of force, with which the lava would be elevated in an open 
 chasm, we have made a supposition respecting the constitution 
 of the magma from which it is derived. Some late experiments 
 by Mr Hannay, since published 1 , appear to warrant our as- 
 sumptions. We suppose the state of igneo-aqueous solution to 
 be such as has been already described in VIII., and that dimi- 
 nution of pressure allows the water-substance to separate from 
 the lava. This will rise through the column of lava and pro- 
 duce ebullition. But in our calculations we have omitted the 
 consideration of this ebullition, and supposed the water-sub- 
 stance to remain in the identical mass of lava, simply expand- 
 ing when separated from it by diminution of pressure. If the 
 magma contains one-tenth of water in a given volume, it would 
 be capable of thus rising to the summit of a lofty cone. And 
 if a fissure was to be opened to the surface, the mean pressure 
 of the lava upon the sides of it would be that of the weight of 
 a column of rock about twelve miles high. This however 
 would not be sufficient to produce compression, for which we 
 must look to the pressure of the gas or vapour, confined in 
 closed fissures, which at its maximum would be twice as great. 
 The work of compression would be chiefly expended in de- 
 forming the materials of the crust, producing cleavage and so 
 forth, the work of raising the mountains, and depressing their 
 roots into the fluid substratum, being comparatively small. 
 The ease with which masses of rock would move over surfaces 
 of dislocation, once established and lined with slickenside, 
 would appear to render regions, once disturbed, more liable 
 than others to further disturbance. The quantity of jgneous 
 rock subsequently injected into the fissures would go to in- 
 crease the solid crust in the disturbed regions, and, with the 
 estimate we have already made, that the compression amounts 
 to about two per cent., one-fiftieth of a vertical section through 
 'the crust ought to be occupied by dykes. But it must be 
 remembered that these would be most numerous and widest 
 in the lower side, so that much of them would never come under 
 observation. 
 
 1 See p. 276, and p. 277, note. 
 
SUMMARY. [CH. xxn. 
 
 XVI, Compression is not the only kind of disturbance 
 which has affected the rocks. Faulting is quite as common a 
 phenomenon ; and the amount of dislocation produced by it 
 varies from a few inches to miles. We attribute faults to the 
 formation of fissures, originating at the surface through con- 
 traction of the rocks, and propagated downwards. We attribute 
 their usual hade to the downthrow, to the greater compressi- 
 bility of the rocks on the downthrow side of the fault. Faults 
 on the whole must tend to depress the surface of any tract 
 dislocated by them. 
 
 Thus it will be seen that the two classes of disturbance 
 which have affected the crust, are ultimately traced to the 
 same exciting cause, namely the formation of fissures through 
 metamorphic changes. When these fissures originate below and 
 are propagated upwards, they become filled with elastic vapour 
 and compression results, and when they originate above and 
 are propagated downwards, faulting is the consequence. 
 
 XVII. The peculiar arrangement which is requisite for 
 the equilibrium of a disturbed crust resting upon a heavier 
 fluid substratum is, that, for every subaerial elevation above 
 the mean surface, there must be a corresponding protuberance, 
 dipping downwards into the fluid below ; and according to 
 the relative densities which we have assumed, the depth of 
 these protuberances must be about ten times the height of 
 the elevations. We have already seen that this circumstance 
 explains two remarkable phenomena, connected respectively 
 with mountain attraction and with underground temperature. 
 We now proceed to show that it also agrees extremely well 
 with many of the well-known geological movements of the 
 surface. As the surface is denuded down, it will be concurrently 
 raised up from below by floatation, and the immense quantity 
 of material denuded - off a tract will not require the tract at 
 any one period to have had the altitude, which the amount 
 of denudation at first sight appears to necessitate : nor yet 
 will any additional exciting cause of elevation be required, 
 beyond the mere fact of the denudation. The course of drainage 
 across the dip is also explicable on this hypothesis. 
 
en. XXIL] SUMMARY. 287 
 
 XVIII. Volcanic energy is the motive power on our view 
 of compression. It will be easily seen that we reverse the 
 sequence of cause and effect, as the subject has been sometimes 
 regarded. The well-known theory propounded by Mr Mallet, 
 to account for volcanic energy, makes it the result of com- 
 pression instead of the cause. It also removes the seat of it 
 from where we believe it to reside. We therefore feel it neces- 
 sary to reply to his arguments. Mr Mallet based his theory 
 upon the results of experiments in crushing cubes of rock, from 
 which he calculated the amount of heat obtainable in that 
 way, and concluded that the whole of the heat, that would arise 
 from crushing one cubic foot of rock, would fuse about one- 
 tenth of a cubic foot of the same. Supposing the heat so 
 obtained should be localized, he considered that the crushing of 
 rock within the crust of the earth would originate volcanic 
 action. He assumes with Hopkins, that the crust is thick, 
 and postulates 400 miles for the thickness. We however show 
 that the heat obtained could not be localized, but must be 
 distributed through the crushed portion, appearing only where 
 crushing took place, and appearing everywhere in proportion to 
 the work done there ; so that if say ten miles of the crust was 
 crushed, it could not fuse one mile selected out of those ten. 
 
 We however do not leave the question here, but go on 
 to calculate the utmost conceivable amount of heat obtainable 
 under Mr Mallet's hypotheses, and find it quite inadequate for 
 the purpose. 
 
 XIX. Having cleared the ground of the fascinating, but 
 as we believe misleading, theory of Mr Mallet, we review 
 theories that have been propounded to account for volcanic 
 action, on the supposition that it is a manifestation at the 
 surface of the intense temperature existing below ; and that the 
 lava and vapours, which are erupted, are brought up from an 
 intensely hot substratum. Some of these theories require local 
 increments of temperature, of which no explanation has been 
 attempted; while others require the absorption of water by 
 hot rock when applied 'to it externally. We believe that our 
 theory of the constitution of the magma removes the difficulties 
 
288 SUMMARY. [en. xxii. 
 
 which are involved in the above suppositions, and we have 
 made an attempt to explain the mechanics of an eruption, and 
 the sequence of events connected with it. For the details of 
 this part of the subject the reader is referred to the body of 
 the book, since they cannot be very easily epitomized. 
 
 XX. The downward protuberances of the crust into the 
 fluid substratum, which we have termed the roots of the moun- 
 tains, will be gradually melted ; and the material melted off, 
 being lighter than the substratum, will flow upwards, and 
 spread itself beneath the crust. This fact appears capable of 
 explaining some hitherto not sufficiently explained phenomena, 
 respecting the order of succession, in which different kinds of 
 lava have been erupted. The Natural System of Volcanic 
 Rocks of Richthofen, as generalized by Prof. Judd, asserts that, 
 since the Eocene period, the earliest erupted rocks have been of 
 an intermediate type, as regards the proportion of silica which 
 they contain and their specific gravity. These were succeeded 
 by more silicious lavas of less specific gravity ; and finally 
 followed by basaltic lavas, with the lowest proportion of silica 
 and highest specific gravity. It is obvious that, if the couches 
 of molten rock had been erupted in the order of their super- 
 position, in which they must necessarily lie, those of inter- 
 mediate specific gravity ought to have followed, instead of 
 preceding, those of less. Our theory accounts for this circum- 
 stance. The more highly silicious rocks being solidified in 
 the crust, were underlain by a magma of intermediate character, 
 and, during the movements which raised the mountains and 
 depressed the roots, this made its appearance at the surface 
 as lava of intermediate type. Subsequently the depressed 
 silicious crust was melted off, and underflowing the crust, 
 the next eruptions were more silicious. When this layer, a 
 thin one, had been erupted, or at distances from the ranges 
 to which it had not extended, the denser substratum followed 
 next in order, producing basaltic lavas. 
 
 The theory of mountain roots also accounts for the fact 
 mentioned by Prof. Judd, that the ejections in regions, lying 
 upon opposite sides of a mountain chain, appear to have come 
 
CH. xxii.] SUMMARY. 289 
 
 from different reservoirs of molten rock : for according to our 
 view this would be actually the case. 
 
 Thus we find five classes of phenomena explicable on the 
 theory of mountain roots : 
 
 (1) The support of the mountains themselves, 
 
 (2) The apparently insufficient attraction of the Himalayas, 
 
 (3) The slower increment of temperature beneath moun- 
 tains, 
 
 (4) The gradual elevation of a tract concurrently with its 
 denudation, 
 
 (5) The natural sequence of volcanic rocks. 
 
 XXI. The geographical distribution of volcanos presents 
 fewer difficulties upon the supposition of a thin crust and fluid 
 substratum, than upon any other. Their linear arrangement 
 points to their being situated along great systems of fissures ; 
 and such systems of fissures are indicative of a thin crust. 
 Fissures, which run for long distances in nearly straight courses, 
 point, either, as already mentioned when discussing faults, to a 
 movement perpendicular to the fissured surface, or else to a 
 rending pressure within the fissure itself; while on the other 
 hand fissures, which are caused by contraction in a direction 
 parallel to the surface, would divide up an area into polygonal 
 figures. The former arrangement of the fissures accords best 
 with the distribution of volcanic ranges, and suggests a thin 
 crust. 
 
 We recognise two principal types of volcanic regions, coast- 
 line, and oceanic. We believe the former to be connected with 
 the agencies which have raised the continents which they skirt. 
 Trains of vents are attached laterally to the great compressed 
 and elevated ranges, and usually stand near the edge of a steep 
 shore. The oceanic volcanos on the other hand appear un- 
 connected with true elevatory action, for the oceanic islands 
 consist almost all of them of volcanic rocks : whereas, if they 
 were connected with areas of elevation, the peaks of schistose 
 or other hard inclined strata could not well be absent. 
 
 F. 19 
 
290 SUMMARY. [CH. xxn. 
 
 Volcanic cones, having no roots projecting downwards into 
 the substratum to support them, would sink, and rupturing the 
 crust around them, tend to perpetuate volcanic activity in the 
 same region. The fissures would be formed around the cones, 
 and thus a train of volcanos, originally linear, would give 
 occasion to an elliptical ring of vents, to which the peculiar 
 shape of some of the coral archipelagoes may possibly be 
 due. 
 
 The existence of some kind of connection, between volcanic 
 action and the elevation of continents, is- indicated by the re- 
 markable course of the great volcanic band which borders the 
 Pacific ocean : for it approximately divides the world into two 
 hemispheres, one of which contains nearly all the land, and 
 the other, except Australia, is covered with water. Eut the 
 course of this great band being turned aside by its junction with 
 another, which comes from the N. W. through Sumatra and 
 Java, the exceptional continental area of Australia has been 
 elevated within the oceanic hemisphere, in connection with the 
 thus abnormally deflected continuation of the great band. 
 
 Our theory of volcanic action needs only the opening of 
 fissures which shall reach the fluid substratum, without refer- 
 ence to how those fissures may be caused. We think therefore 
 that the present localization of volcanic activity, at interrupted 
 regions along the flank of an elevated range, may be traced to 
 the deposition of sediment, eve a ai: a considerable distance, 
 upon the side of the range opposite to thai on which the 
 volcanos lie. An inspection of our diagram on page 132 will 
 explain how this would be : and there appears some reason 
 to suppose that this suggestion is supported by geographical 
 facts. 
 
APPENDIX. 
 
 Mr G. H. Darwin " On the stresses caused by continents and mountains " his 
 argument for solidity met by Sir G. B Airy's explanation If. Roche "0 
 the constitution of the interior of the earth " his theory, though in accord- 
 ance with Geology, requires fuller statement than is yet published. 
 
 NOTICES of two yet unpublished memoirs have lately ap- 
 peaied bearing on the Physics of the Earth's Crust. Mr G. H. 
 Darwin read a paper in June, 1881, before the Royal Society, 
 " On the stresses caused in the interior of the earth by the 
 weight of Continents and Mountains 1 .'* It is based upon the 
 hypothesis that "the existence of dry land proves that the 
 earth's surface is not a figure of equilibrium appropriate for the 
 diurnal rotation. Hence the interior of the earth must be in a 
 state of stress, and as the land does not sink in, nor the sea-bed 
 rise up, the materials of which the earth is made must be 
 strorg enough to bear this stress." After describing the nature 
 of the investigation, he concludes that it " must be regarded as 
 confirmatory of Sir William Thomson's view, that the earth is 
 solid nearly throughout its whole mass. According to this view, 
 the lava which issues from volcanoes arises from the melting 
 of solid rock, existing at a very high temperature at points 
 where there is a diminution of pressure 2 , or else from com- 
 paratively small vesicles of rock in a molten condition." 
 
 1 "Proc. Royal Soc." Vol. xxxn. p. 432. 1881. 
 
 2 See the Author's paper on "The Elevation of Mountains by Lateral 
 Pressure." Trans. Cambridge Phil. Soc., Vol. xi. Pt. in. p. 504. 1871. 
 
292 APPENDIX. 
 
 It will be seen that the facts, upon which Mr G. H. Darwin 
 bases his investigation, are the same as were perceived by Sir 
 G. B. Airy to require explanation. Admitting that the ma- 
 terials of the earth cannot be strong enough to bear the 
 stress, the difficulty was explained by him in the manner 
 given in his own words in our eleventh chapter. If that ex- 
 planation be accepted, the stresses arising from the inequalities 
 of the surface can exist only within the elevated tracts them- 
 selves, which possess no doubt sufficient rigidity to keep them 
 from flowing down into flatness. If the crust is of appropri- 
 ately varying thickness in different parts of the land surfaces, 
 and denser beneath the oceans, and floats in equilibrium on a 
 fluid substratum, it cannot transmit any unequal stresses to the 
 subjacent parts. 
 
 The other notice referred to appears in the Comptes Rendiis 
 de VAcademie des Sciences 1 , and is by M. Ed. Roche. He 
 points out that " the conditions which every hypothesis ought 
 to satisfy respecting the distribution of the interior mass of 
 the earth are, that it should agree with the value of the 
 superficial ellipticity and also with a certain constant depending 
 upon the phenomenon of precession. These conditions are 
 very nearly satisfied upon the hypothesis of fluidity if we 
 admit that the ellipticity of the earth is about -3^; but if 
 the ellipticity is higher than -^, as appears to result from 
 more recent determinations, the agreement no longer exists." 
 
 " There is then room to undertake these investigations 
 again upon a different hypothesis ; for example, by considering 
 the globe as formed of a nucleus or solid block nearly homo- 
 geneous, covered by a lighter layer, whose density from geo- 
 logical considerations may be estimated at three times that of 
 water. This constitution of the globe being premised I find 
 that it is possible to reconcile the actually admitted values of 
 the precession and ellipticity if we take account of the fact that 
 the interior nucleus of the globe is solidified and has received 
 its definite form under the influence of a rotation less rapid than 
 that with which the earth is actually animated." 
 
 1 Tome xciii. No. 8 p. 364 (22 Aodt, 1881). Paris. 
 
APPENDIX. 293 
 
 " In any case, the contraction due to the cooling of the globe 
 ought to introduce a progressive acceleiation of its angular 
 velocity. But, if this globe is fluid, the form of the different 
 layers adapt themselves continually to the rotation such as it is 
 at every instant, so that, finally, there remains no more trace of 
 the successive changes which their ellipticity has undergone 
 since the beginning. If on the contrary at a certain epoch of 
 the cooling, the interior layers have passed into the solid state, 
 these layers have taken and retain an ellipticity very different 
 from that which the general hydrostatical equation would at- 
 tribute to them, applied to a mass entirely fluid possessing a 
 rotation common to all its parts. The formula calculated on 
 the hypothesis of the solid nucleus contain at once the constant 
 q, the actual ratio of the centrifugal force to gravity at the 
 equator, and the value q of the same ratio at the epoch of the 
 solidification of the central block. This last element not being 
 determined, we may give it a value such that the superficial 
 ellipticity agrees with the coefficient of the precession. It is 
 necessary, for this, to suppose q less than q, whence it results 
 that the rotation of the earth has undergone an acceleration 
 since the consolidation of the interior nucleus." 
 
 " The physical and astronomical conditions of the problem 
 allow us moreover to determine with sufficient precision the 
 dimensions and the specific weight of this block. If we neglect 
 the purely superficial shell, as well as a slight condensation 
 towards the centre, where the heaviest materials must be col- 
 lected, observe what will be the constitution of the globe : a 
 nucleus of which the density is about 7, covered with a layer of 
 density 3, of which the thickness will not attain ^th of the 
 entire radius." 
 
 " The terrestrial block is then as regards the specific weight, 
 analogous to meteoric irons, whilst the layer which envelopes 
 it is comparable to the aerolites of a stony nature, into which 
 iron enters only in small proportion." 
 
 It need hardly be said, that the results obtained by M. 
 Roche are such as most Geologists would be ready to accept. 
 Until the memoir appears in full, it is not possible to form a 
 
2Q4 APPENDIX. 
 
 decided judgment upon the argument. But it will be ob- 
 served that the notice makes no mention of the amount of 
 contraction of the spheroid, which would be required to give 
 the additional velocity of rotation. This is a very important 
 point ; for it must be remembered that, while contraction is 
 accelerating, tidal friction is in the meanwhile retarding the 
 rotational speed 1 . It is hardly conceivable that the supposed 
 central block could have solidified very long before a crust 
 could form, and the results of our pre?ent investigations tend 
 to show, that the contraction since that epoch has not been 
 great. 
 
 1 The remarkable and profound investigations of Mr G. H. Darwin, upon 
 The remote history of the Earth, and on The Tides of a viscous Spheroid, will 
 be found described in a popular manner by Prof, Ball, in " Nature," Vol. 25, 
 p. 79, 1881. 
 
INDEX. 
 
 Adie, contraction of rocks on cooling, 
 68 
 
 Age of the world on hypothesis of so- 
 lidity, 59, 62, 71, 74 
 
 Airy, on mean density, 19 ; on at- 
 traction of mountain masses, 145 
 
 Amount of compression, chap. xm. 
 168, 282 
 
 Appalachians, thickness of sediment 
 in, 80 
 
 Av.line, thickness of Cambrian rocks, 
 80 
 
 Axes, mean of earth, 33 
 
 Babbage, on temple of Serapis, 82 
 Baily, mean density, 19 
 Barnard, on thickness of crust, 22 
 Bath waters, 16 
 Bedding, inversions of, 130 
 Bird, Miss, on Kilauea, 26 
 Bunsen, law of, 251 
 
 Cambrian rocks, thickness of, 80 
 
 Capillary absorption, 91 
 
 Carlisle, Bp of, on geological time, 74, 
 
 note 
 
 Cavendish, mean density, 19 
 Channel Islands, 186, note 
 Colorado Plateau, 81 
 
 Compression; and contraction, 45; 
 effect of, on disturbed tract, 118; pos- 
 sible causes of, 170 ; amount of, 
 chap. xui. 168, 282; on hypothesis 
 of fluid substratum, 171, 177; conti- 
 nental, 179; and volcanic action, 
 chap. xv. 185, 284 ; work of, 195 ; 
 may be caused by vapour pressure, 
 197; from solidification of dykes, 
 198 ; American geologists on, 201 ; 
 energy producing, 205 ; amount of, 
 if due to volcanic action, 206 ; causes 
 of, examined, 218 
 
 Conclusion, 266 
 
 Condition of interior, chap. n. 18, 21, 
 268 
 
 Conductivity of rock ; effect on increase 
 of temperature, 5, note, 62 ; not in- 
 volved in estimating amount of 
 elevations, 71 
 
 Continents, antiquity of, 82, 169 
 
 Contraction in cooling, 23 ; theory of, 
 34 ; Capt. Button on, 84 
 
 Convection currents in a bore hole, 7 
 
 Coral reefs, Darwin on, 260 
 
 Corrugations of a thin crust, mathe- 
 matical problem of, 100 ; do not 
 represent the case of nature, 112 
 
 Cosmogony, 93 
 
296 
 
 INDEX. 
 
 Couches, successive, 28 
 
 Cracks formed in bottom of crust, 201 
 
 Craters, unsympathetic, 246 
 
 Creep, 3 
 
 Crushing rock, Mallet's experiments on, 
 228 
 
 Crust, equilibrium of, 83 ; primitive, 
 97 ; not flexible, chap. ix. 99, 113, 
 277 ; vertical shearing of, 120 ; thick- 
 ness of, see " Thickness" ; equilibrium 
 of, disturbed by denudation, 219; 
 how restored, 220 
 
 Currents in bore-hole, 13 
 
 Darwin, Dr, on coral reefs, 260 
 
 Darwin, G. H., on stresses caused by 
 mountains and continents, 291 ; 294, 
 note 
 
 Datum level, 46, 171 
 
 Daubree, experiment on capillary ab- 
 sorption, 91, note 
 
 Davy, Sir H. , theory of volcanos, 3 
 
 Delaunay, on thickness of crust, 22 
 
 Density, internal, law of, 20, 28 ; dif- 
 ference of, would produce oceans, 76 ; 
 of granite and of basalt, 118 ; of 
 crust beneath oceans, 166 ; of conti- 
 nents, why less, 206 
 
 Denudation, effect on disturbed tract, 
 135 
 
 Deposition causes sinking of surface, 
 140 
 
 Depressions of crust, 113 
 
 Depths of ocean, 175 
 
 Diamonds, artificial, 89, note 
 
 Disturbed tract, chap. x. 114, 278; 
 equilibrium of, 115; effect of com- 
 pression on, 118 ; tilting of, 136 
 
 Dunker, Herr E., on Sperenberg bore- 
 hole, 6 ; table of temperatures there, 10 
 
 Dutton, Capt., on contraction from 
 cooling, 75, 84 ; on sequence of vol- 
 canic rocks, 253 
 
 Dykes, 186 
 
 Elevated region, formation of, 131; 
 
 diagram of, 132 
 Elevations, average height of, 52, 55 ; 
 
 and depressions, chap. v. 45, 272 ; 
 
 on hypothesis of solidity, chap. vi. 
 
 57, 273 
 
 Elie de Beaumont, 34, note 
 Elliot, Sir G., observations on tem- 
 perature in coal-mines, 4 
 Ellipticity, 20 
 Energy, whence derived under different 
 
 views of compression, 205 
 Equilibrium of disturbed tract, 115 
 Equinoxes, precession of, 22 
 Eruption of volcano, theories of, 240 ; 
 
 Eichthofen on, 241 ; causes of, 242 ; 
 
 quantity of water emitted during, 
 
 244 ; cessation of, 244 
 Evans, Capt., on magnetic variation, 27 
 
 Faulting, on, chap. xvi. 208, 286; 
 datum level equation applied to, 214 
 
 Faults, hade of, 208 ; throw of, 211, 
 213 ; straight course of, 211 ; Mr 
 Curry on throw, 210 ; of Utah, 212 ; 
 connected with surface changes, 212 ; 
 may cut through crust, 213 
 
 Favre, Prof. A., experiments on com- 
 pression, 86, 127 
 
 Fissures, opened by vapour pressure, 
 187; pressure of lava on sides of, 
 194 
 
 Fluid substratum, 83, chap. vin. 87, 
 275 
 
 Freshwater strata, 221 
 
 Ganges, deposits of, 81 
 
 Geikie, Prof. A., on geology of Utah, 
 
 256 
 Geological movements, chap. xvn. 217, 
 
 286 
 
 Geothermometer, 6 
 Greenland, changes of level in, 224 
 
 Haughtoii, Prof, estimates of areas of 
 land and sea, 55, note 
 
 Hannay, on artificial diamonds, 89, 
 note 
 
 Herschel, continents due to " tume- 
 faction," 76, 275 
 
 Himalayas, 43 ; structure of lower 
 
INDEX. 
 
 297 
 
 ranges of, 80; attraction of, calcu- 
 lated by Pratt, 143 ; Airy on, 145 
 Hopkins, on thickness of crust, 22 ; on 
 
 Elie de Beaumont's views, 77 
 Hungary and Bohemia, Judd on, 257 
 Hypothesis of solidity fails, chap. vn. 
 73, 274 
 
 Ice, analogies with earth's crust, 199, 
 
 278 
 Igneo-aqueous solution, 87, 94, 190, 
 
 276, 285 
 Internal densities and pressures, chap. 
 
 in. 28, 270 
 Inversion of bedding, 130 
 
 James, Col., on mean density, 19 
 Judd, Prof., absorption of water by 
 lava, 190 ; connection of compression 
 and volcanic action, 203 ; on Bicht- 
 hofen's law of sequence, 256 
 
 Kilauea, crater of, 26 
 
 La Chapelle, well at, 15 
 
 Laplace, law of density, 29 ; corre- 
 sponding internal pressures, 31, 270 
 
 Lateral pressure, its amount, chap. iv. 
 34, 271 ; compression, theory of, not 
 to be abandoned, 84 
 
 Lava, pressure in column of, 192 ; 
 habitually liquid in some craters, 
 246 ; partly derived from crust, 251 ; 
 conforms to Bunsen's law, 251 
 
 LeConte, on formation of mountains, 
 77 
 
 Level, mean, equation referred to, 171 
 
 Liquid substratum, 83, 84, 275 
 
 Lock, W. G. "Volcanic History of 
 Iceland," 189 
 
 Magma, 98; supposition as to consti- 
 tution of, 189 
 
 Mallet, theory of volcanos, 3 ; on den- 
 sity of granite, 19; on contraction 
 of slag, 68; on temperature of primi- 
 tive ocean, 96; on volcanic energy, 
 chap, xviii. 226, 287; experiments 
 F. 
 
 on crushing rocks, 228 ; temperature 
 calculated from, 229 ; locah'zation of 
 heat impossible, 230 ; utmost tem- 
 perature obtainable, 233 ; theory 
 untenable, 238 
 
 Maskelyne, mean density, 19 
 
 Mean density, 18 
 
 Medlicott, on Himalayas, 43 
 
 Metamorphosed rocks, contortions in, 
 124 
 
 Mines, temperature in, 1 
 
 Mississippi, deposits of, 81, 265 
 
 Mohr, on bore-hole at Sperenberg, 6 
 
 Mont Cenis, temperature in, 161 
 
 Mont S. Gothard, temperature in, 
 153 
 
 Moore, J. C., estimate of mean height 
 of land, 54 
 
 Mountain chains, 43 ; formation of, 131 ; 
 backbones of continents, 142 ; roots 
 of, 143 ; geologically modern, 222 
 
 Movements, connected with shorelines, 
 222 ; causes of ,224 ; geological, chap, 
 xvii. 217, 286 
 
 Muirhead and Whitley, on contraction 
 of rocks in cooling, 23 
 
 New Zealand, 80, 264 
 
 Neutral' Zone, defined, 121; position 
 
 of, 125 
 Nordenskiold, on Arctic ice, 199 ; his 
 
 theory of compression, 200 
 
 Oceans, due to difference of density in 
 crust, 76 ; density greater beneath, 
 76 ; not due to radial contraction, 
 79 ; pressure of, 97 ; density beneath 
 150, 165 ; crust beneath, 164 ; anti- 
 quity of, 169 ; zones of depth, 175 
 
 Palmieri's Vesuvius (Mallet), 90, 230 
 
 Plumb-line, revelations of, chap. xi. 142, 
 280 
 
 Po, deposits of, 81 
 
 Pratt, Archdeacon, on " Figure of the 
 Earth," 20 ; on thickness of crust, 
 22 ; on Pacific Ocean, 76 ; on at- 
 traction of Himalayas, 143 
 
 20 
 
298 
 
 INDEX. 
 
 Precession, 22 
 
 Pressure, alone cannot develope heat, 
 3; relation to density, 20; internal, 
 calculated according to Laplace's law 
 of density, 31 ; at earth's centre, 33 ; 
 lateral, chap. iv. 34 ; lateral internal, 
 37; of vapour on sides of fissure, 
 187 ; in column of lava, 192 
 
 Eadial contraction, on hypothesis of 
 solidity, 72; cannot have produced 
 ocean beds, 79 
 
 Eaised beaches, 223 
 
 Bamsay, Professor, sections in South 
 Wales, 222 
 
 Beich, mean density, 19 
 
 Bevelations of the thermometer, chap, 
 xii. 151, 280 
 
 Bichthofen, connection of elevation 
 with volcanic action, 204 ; theory of 
 eruption, 241, 247 ; sequence of vol- 
 canic rocks, 253, 257 
 
 Bigidity of earth, 28 
 
 Boche, M., on constitution of earth, 
 292 
 
 Bock, conductivity of, 62 ; circulation 
 of, 206 
 
 Boots of mountains, 143 ; melted off, 
 249, 288 
 
 Bose Bridge Colliery, temperatures in, 5 
 
 Bosetti, temperature of Sun, 17, note 
 
 Bowley rag, experiments on, 24 
 
 S. Gothard, temperatures in, 153 
 Scandinavia, raised beaches of, 223 
 Scrope, extract from letter of, 89 
 Sea salts, emitted from volcanos, 90 
 Sequence of volcanic rocks, chap. xx. 
 249, 253, 288 ; Button on, 255 ; Judd 
 on, 256 
 
 Shearing, vertical, of crust, 120 
 Siberia, temperature in, 1 
 Sinking areas, 83, 139 
 Siwaliks, 80 
 
 Slag, contraction of, in cooling, 68 
 Solid or fluid interior ? 21 
 Solidity, amount of elevations upon hy- 
 pothesis of, calculated, chap. vi. 57, 
 
 273 ; hypothesis of, fails, chap. vn. 
 73, 274 
 
 Sorby, cavities in crystals, 87, 125 
 Sperenberg, bore-hole at, 5 ; convection 
 
 currents in do., 11 
 Spheroid, oblateness of, 183, 292 
 Stapff, Dr, on Mont S. Gothard, 153 
 Steam from volcanos, 90 
 Sterry Hunt, Dr, on early condition of 
 the globe, 93 ; on igneo-aqueous fu- 
 sion, 94 ; on compression, 201 
 Summary, chap. xxn. 267 
 Sun, temperature of, 17, note 
 
 Temperature, law of increase in, on 
 hypothesis of solidity, 60 ; rates may 
 vary locally, 152; Vrolik on, 153 ; at 
 Mont S. Gothard, 154 ; melting, from 
 observations at do., 161 ; and at Mont 
 Cenis, 162 
 
 Thermometer, roots of mountains re- 
 vealed by, 152 
 
 Thickness of strata, 80 
 
 Thickness of crust, 126 ; at sea level, 
 158; from observations at S. Gothard, 
 161 ; from do. at Mont Cenis, 162 ; 
 beneath ocean, 164 
 
 Thomson, Sir Wm. , device for checking 
 convection, 13 ; on thickness of crust, 
 22 ; on solidity of earth, 22, 23 ; on 
 tidal distortion, 22 ; on secular cool- 
 ing, 59 ; on connection between tem- 
 perature rate and world's age, 59 ; 
 re'sume' of his views, 60 
 
 Thomson, Sir Wyville, estimate of 
 ocean depths, 56 
 
 Time, geological, on what grounds re- 
 stricted to a term of years, 74 
 
 Tresca, "De 1'ecoulement des corps 
 solides," 120 
 
 Underground temperature, chap. i. 1, 
 267 ; average rate of, 2 ; observations 
 on, 4; how affected by changes in 
 conductivity, 5, note ; British Assoc. 
 Beports on, 6, 15, 16 ; in S. Gothard 
 tunnel, 153 ; in Mont Cenis, 161 
 
INDEX. 299 
 
 Volcanic emanations, 90 ; action, 185 ; 28 ; table of do., 30 ; table of pres- 
 
 dykes, 186 sures, 31 
 
 Volcano, in eruption, chap. xix. 240, Water, superheated, 87 ; extravasation 
 
 287 of, 88, chap. xrv. 180 ; subterranean, 
 
 Volcanos, how far "safety valves," 197; 96; critical temperature of, 88, 97, 
 
 geographical distribution of, chap. 125 
 
 xxi. 259 ; oceanic, 260 ; deposits Weald, drainage of, 224 
 
 from, 261 ; Pacific train of, 262 ; re- World, age of, on hypothesis of solidity, 
 
 gions of activity, 265 59, 62, 71, 74 
 
 Waltershausen, densities of rocks, 19 ; Yakoutzk, frozen soil at, 1 
 formula for densities within earth, 
 
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