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Quid pariat nubes, veniant cur fulmina ccelo, Quo micet igne Iris, superos quis conciat orbes Tam vario motu.” _

J.B. Pinelli ad Mazonium.




Mr. Robert Mallet on the Temperature attainable by Rock- Grasnine and, is Consequerices. so... re cee ae Prof. W. G. Adams on a new Polariscope ..........+..;5.. eee Malls of Nintited Poldol ec gg be a

- Mr. J. C. Glashan on the Motion of a Particle from Rest towards an Attracting Centre; Force « (Distance)—2 .... Mr. H. Bauerman on an Experiment for showing the Electric

Conductivity of various forms of Carbon................ |

- Prof. R. Clausius on the Theorem of the Mean Ergal, and its Application to the Molecular Motions of Gases ....... - Captain Abney on Photographic Irradiation .............. Mr. C. J. Woodward on an Apparatus to illustrate the Peyenraeon-o1 Voleania Cones oe ie ee es see ns MM. A. Kundt and E. Warburg on Friction and Heat-con- uememioth dtl Pareto (ases £6. ok Se ee le eee wees Proceedings of the Royal Society :—

Prof. O. Reynolds on the Refraction of Sound by the At-

ER LOM ae ee Re ete al wae tg 8 ae tea ne ale oo

On the Action of Magnets on rarefied Gases in Capillary Tubes rendered luminous by an Induced Current, by J. Chautard. On the Velocity of Magnetization and Demagnetization of Iron, Paduiton, and’ Steel, by Mo "Depreg, . . ) ney. cep Gf. «'-


~- Dr. W. M. Watts on a New Form of Micrometer for use

SIE PICELEUREO TI TANNED 6 Screed. gis kee e shee viay

Mr. ©. Tomlinson on some Phenomena connected with the

EA 26 907701 neem Pe ea a

~ Prof. R. Clausius on the Theorem of the Mean Ergal, and its

Application to the Molecular Motions of Gases..........

~ Mr. W. H. Walenn on Unitation—IV. The Unitates of

Powers and Roots : developments of these, with applications.

Mr. Robert Mallet on the Origin and Mechanism of produc- tion of the Prismatic (or columnar) Structure of Basalt.

Prof. J. P. Cooke on two new Varieties of Vermiculites, with

a revision of the other members of this Group ..........




Proceedings of the Royal Society :— Mr. J. Norman Lockyer on a New Map of the Solar SPCCHUN ~ eGieic ps py pre cereeehe CLO yaya eae 144 Prof. J. Tyndall on Acoustic Reversibility ............ 146 Proceedings of the Geological Society :— Prof. H. A. Nicholson on species of Chetetes from the Lower Silurian Rocks of North America .......... 152 Mr. L. C. Miall on the composition and structure of the Bony Palate of -Crenodus os ..-6'saio%, > oie opp eae eee 152

The Rev. P. B. Brodie on a Railway Section of the Lower Tias and Rhetics between Stratford-on-Avon and Benny Compton . .. 2. p.e igs oe ee Gee ne nen 153

Mr. H. G. Seeley on the Resemblances of Ichthyosaurian Bones to the Bones of other Animals; on the Resem- blances of Plesiosaurian Bones to the Bones of other Animals; on the Tibia of Megalornis ; on Cervical and Dorsal Vertebree of Crocodilus cantabrigiensis........ 153

_ Mr. H. G. Seeley on the base of a large Lacertian Skull from the Potton Sands ; on a Section through the Devo- nian Strata of West Somerset; and on the Pectoral Arch and Fore Limb of Ophthalmosaurus .......... 154

On the Temperature of the Sun, by J.-B. Soret............ 155

On Fused Boracic Acid and its Tempering, by V. de Luynes. 158

On the discovery of a method of obtaining Thermographs of the Isothermal Lines of the Solar Disk, by A. M. Mayer .... 159



Mr. H. A. Rowland on Kohlrausch’s Determination of the Absolute Value of the Siemens Mercury Unit of Electrical

TGSISURIUGS Fc5, es ee ak wie s, cs as Ghia gs aa oes pny se 161

/ Mr. Rk. H. M. Bosanquet on Temperament, or the Division ERO MOCHAVE.——INO. 60 tv ieieie ne staph ueve s helen See ee 164 Mr. M. Merriman on the Flexure of Continuous Girders .. 179

Prof. R. Clausius on the Theorem of the Mean Ergal, and its Application to the Molecular Motions of Gases.......... 191

Mr. R. Mallet on the Origin and Mechanism of production of the Prismatic (or columnar) Structure of Basalt ........ 201

/ Sir W. Thomson on an Alleged Error in Laplace’s Theory of TO MINGES, cava c ek vs spear tC twain Cath 227

Mr. J. Croll on the Challenger’s’ Crucial Test of the Wind and Gravitation Theories of Oceanic Circulation. ........ 242 Prof. P. E. Chase on the Cosmical Activity of Light ...... 250

On a Property of an Electrized Water-surface, by G. Lipmann. 254 On the Influence of the Texture of Iron upon its Magnetism, by

Leg El (os ANE ADS URN Tia io oc. inc dar vaio Bare 0 see Sei ie 255 Ou Magnets formed from Compressed Powders, by J. Jamin. 255



Mr. H. A. Rowland’s Studies on Magnetic Distribution ... Sir G. B. Airy on a controyverted Point in Laplace’s Theory of RE ERS RSS CAAT INN Leos hate a AR wr ee RE Ce ea es Sir W. Thomson on the Oscillations of the First Species” in Laplace’s Theory of the Tides Prof. J. H. Gladstone and Mr. A. Tribe on the Augmentation of the Chemical Activity of Aluminium by Contact with a more peer MOEN 25 a or ated Side as tog oh od RU > Professor Gladstone and Mr. A. Tribe on the Action of the BNR PATG ONE MO rycyeis a) Laie niscaed aimsiels teh operates x Sl doce ays Mr. J. Croll onthe Wind Theory of Oceanic Circulation.—Ob- ea RATT OG LO boa. 6 hike laine deine. We Pods aCeiets + Log ¥ Frederick Guthrie on Stationary Liquid Waves............ The Rey. O. Fisher on Mr. Mallet’s Theory of Volcanic Energy Notices respecting New Books :— Dr. H. L. F. Helmholtz on the Sensations of Tones as a Physiological Basis for the Theory of Music ...... Mr. J. Croll on Climate and Time in their Geological Re- lations: a Theory of Secular Changes of the Earth’s Rte A, ca owt Spamalot} cit le. ee RR Proceedings of the Geological Society: Mr. J. G. Goodchild on the Glacial Phenomena of the Eden Valley and the Western Part of the Yorkshire- Me DSH Ct iA sys) ynibin tod hardy Karten ds +s ERR Dr. F. Stoliczka’s Geological Observations made on a visit to the Chaderkul, Thian-Shan range .......... Mr. C. Gould on a recent Discovery of Tin-ore in Tas- DMRS Sek bl Rete herd cis So he Sabet S3heishisth eg ts 4. Boda Mr. L..C. Miall on the occurrence of a Labyrinthodont in the Yoredale Rocks of Wensleydale ............ Dr. F. Stoliczka’s Geological Notes on the Route traversed by ime VarleundMmpassy <9 ic 2. isa ds decniga) <> Mr. J. D. Kendall on the Hematite Deposits of White- mayen and Mornesay 's 44 h5 ateissiieh Os adivad aan Mr. J. Milne on the Physical Characters and Mineralogy of Newfoundland; and on the Sinaitic Peninsula and North-western, Aralian ss) 2 discs «Usha» erie aioe MM. W. C. Brogger and H. H. Reusch on Giant’s Kettles PgRe MEMURATEET 0 Selec als oa sease eiehele winks eo 8 dia, be sce eye Mr. J. C. Ward on the Comparative Microscopic Rock- structure of some Ancient and Modern Volcanic Rocks Prof. Owen on fossil Evidences of a Sirenian Mammal.. The Rey. J. E. Cross on the Geology of North-west Lin- OMIT. CROSS 2 GERI OD TAY dal a pies « Nece On the Cold Bands of Dark Spectra, by MM. P. Desains and Aymonet

Soe ae ee ow, oe ee) 1, we, ee) eae |e 16 Oe sw 8 a 8 OF 8. & 8 O58, BS CT ee

Page -257

277 279

284 285 286

290 302

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325 325 326 326 326 327

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Experiments on the Plasticity of Ice, by Prof. Dr. Fr. Pfaff. 338 On Musical Consonance, by Professor ‘Pyndall, FES. see 336

NUMBER CCCXXXII.—NOVEMBER. Dr. J. Kerr on a new Relation between Electricity and Light :

Dielectrified Media Birefringent ....................-- 337 Mr. H. A. Rowland on Magnetic Distribution ............ 348 Mr. O. J. Lodge on Nodes and Loops in connexion with Che-

mical Wormule}: cece de pee et ates). 367 Frederick Guthrie on Stationary Liquid Waves....... are Sir Wiliam Thomson on the General Integration of Laplace's 8

Differential Equation of the Tides .................... 388

Dr. W. B. Carpenter on Mr. Croll’s Crucial-Test Argument. 402 Professor A. Stoletow on Kohlrausch’s Determination of the Absolute Value of the Siemens Mercury Unit of Electrical ARESISUANES o5 ici. tee esis) wg OR ee oe er 404 Notices respecting New Books :— Mr. W. Whitaker’s Geological Survey of England and Wales. Guide to the Geology of London and the Neh beurhoode 0-0 TRIO. oO ae er 406 Proceedings of the Geological Society :— Prof. H. G. Seeley on the Femur of Cryptosaurus ewmerus 409 Mr. H. Hicks on the Succession of the Ancient Rocks in the vicinity of St. David’s, Pembrokeshire .......... 409 Messrs. J. Hopkinson and C. Lapworth on the Graptolites of the Arenig and Llandeilo Rocks of St. David’s .... 410 Mr. H. F. Blanford on the Age and Correlations of the Plant-bearing series of India i. 8. 2. 008. 5 ee 411 The Rev. J. F. Blake on the Kimmeridge Clay of England. 412 Prof. H. G. Seeley on Pelobatochelys Blakei and other

Vertebrate Fossils from the Kimmeridge Clay ...... 412 Mr. A. J. Jukes-Browne on the Cambridge Gault and Greensand 4s. 66s. ee ee ee ee 412

Artificially Crystallized Oxide of Zine from a Blast-furnace, by Richard Cowper, Associate of the Royal School of Mines. 414 On the Chemical and Spectroscopic Characters of a New Metal

(Gallium), by Lecog de Boisbaudran ...30.0.....0.. 040. 414 On the Influence of Light upon the Conductivity of abba) Selenium, by Worier siemens: 2). 02. e200 ae 416

NUMBER CCCXXXTIT.— DECEMBER. Prof. R. Bunsen’s Spectral-Analytical Researches. (With a BLLO,) 8s 2% cosine GE WG os we sa dp ay ave er 417. Mr. G, Darwin on Maps of the World. (With a Plate.).... 431 Dr. G. F. Barker on a new Vertical-Lantern Galvanometer.. 434


Page Sir J. Cockle on a Differential Criticoid ..... dR Soe ee 440 Dr. J. Kerr on anew Relation between Electricity and Light : Preleeprimed Media Birefrmpent. ..... 066600 oe ee 446 Mr. L. Schwendler on the General Theory of Duplex Tele- RMR we a A Stars Gow ek does cae. 458 Messrs. G. C. Foster and O. J. Lodge on the Flow of Electri- city in a uniform plane conducting-Surface.—Part IT... .. 475 Mr. J. Croll’s further Remarks on the Crucial-Test Argu- (PU. cote Schade cg pouch EG balla einai blag nate Ome aie ie sid ae 489 ~On the Rotatory Polarization of Quartz, by J. L. Soret and SEE. POEL ae ke. OR PPE ed 8 492 On Thermic Equilibrium and Heat-conduction in Gases; and on the Integration of Partial Differential Equations of the First Order, by Prof. Ludwig Boltzmann .............. 495 On Soundng Flames, by M.Decharme ...............4.5: 496 NUMBER CCCXXXIV.—SUPPLEMENT. Mr. R. H. M. Bosanquet on the Polarization of the Light of Re Sh a rere. 4 iors vi, gic taeans eald 497 Mr. W. H. Walenn on Unitation.— V. Some of the Applica- tions and Developments of the General Formula ........ 521 Prof. R. Bunsen’s Spectral-Analytical Researches. (With BEET Vk 6 oe ck oop ih, Sl semen oa vu hs eRe 527 Mr. J. W. L, Glaisher on some Identities derived from Elliptic- na PORN...) ge Se eee ae ae eae RED 539 Mr. W. Weston on the Application of Phosphorus to the Setsuuee Ol COPpCi gs oS iss. toe 4. Bree ee ue ae ae 542 Prof. Challis on the Mathematical Principles of Laplace’s MEE yO OE TIES Peete oles. 8 NPRM Cit Se ee 544 Proceedings of the Royal Society :— Prof. W. G. Adams on the Forms of Equipotential Curves and Surfaces and Lines of Electric Force .......... 548 Mr. W. C. Roberts on the Liquation, Fusibility, and Den- sity of certain Alloys of Silver and Copper.......... 553

Mr. T. E. Thorpe on the Specific Volumes of Liquids .. 554 Proceedings of the Geological Society :— Mr. J. W. Judd on the Structure and Age of Arthur’s

Rede. Vaniron sen he net ee eee Pe 556

Mr. J.C. Ward on the Glaciation of the Southern part of then ake test.) WS Weep hs a Rr eh SORE. 0 0 557

Mr. R. Pennington on the Bone-caves in the neighbour- hood of Castleton, Derbyshire if: Yee. ee 557

On the Density of pure Platinum and Iridium and their Alloys, by H. Sainte-Claire Deville and H. Debray..:........... 558

Examples of Contemporary Formation of Iron-Pyrites in Ther- mal Springs and in Sea-water, by M. Daubrée .......... 562

Fridges (ore pee tt 565

Wika wag Ss ei ale ws le, oo) e MS eC as Be CO RES we ae


I. Illustrative of Mr. G. Darwin’s Paper on Maps of the World. I1.—V. Illustrative of Prof. R. Bunsen’s Paper on Spectral-Analytical Researches.


VoLUME 49.

Page 457, line 9 from bottom, for 0 read O. line 7 from bottom, for CQ read OQ. 466, lines 5 and 6, for intersection read intersections, and dele and to the origin. line 13, for flow-line read straight line. 471, first line of § 42, for § 39 read § 38. Plate IX. fig. 3.—The middle point of the straight lme AB should be marked O. Plate X. fig. 6.—The circle should not extend into the left-hand half of the figure, or should be shown there only by a dotted line.

VouumME 50.

Page 281, line 12 should read :— =B,y'+B,p4+ ...+&ce. Page 316, lines 6, 7 should stand :—

= 533 miles. And dele line 8.






I. On the Temperature attainable by Rock-crushing and tts Con- sequences. By Rosert Matcet, F.R.S.*

N developing the theory of volcanic heat and energy embraced in his s paper “Qn the Nature and Origin of Volcanic Heat and Energy (Phil. Trans. Part I., 1873), the main object of the author was to prove that the annual work of secular contraction in our globe, when transformed into heat, was more than ade- quate for the supply of voleanie activity existing upon our planet. While indicating generally the circumstances which must attend as results of the descent of the exterior shell upon the more rapidly contracting nucleus, it was not necessary to his argument to follow into detail the mechanism of local dislocation and crush- ing dueto such descent. Nor would the limits of his paper admit of his entering into much detail as to the circumstances attending subterranean dislocation and crushing of rocky matter, or point- ing out how some of these must greatly tend to exalt the tempera- tures due to the transformation of the mechanical work locally done. It was necessary to a truthful examination of the question whether or not the annual supply of heat transformed from the work of secular contraction were sufficient to meet the demands of existing volcanic action, that he should not overrate the work so transformed; and accordingly, in determining by experiment a measure for the amount of that work, the author viewed the work of crushing of unconfined or unsupported masses alone as the source of heat, this method being that only which could afford perfectly trustworthy experimental results. He paid no regard to the additional work that must attend the collision and friction

* Communicated by the Author. Phil. Mag. 8. 4. Vol. 50. No. 328. July 1875. B

2 Mr. R. Mallet on the Temperature attainable

of already crushed masses in the further progress of their defor- mation and forced transport to points more or less distant from those at which the crushing had taken place. The work of crushing in free air was capable of rigid determination; the work of subsequent deformation and transportation can only admit of estimation upon assumed data, and these necessarily of a somewhat arbitrary character, seeing how little we know accu- rately of the nature and disposition of the rocky materials of our earth’s crust, except at the most inconsiderable depth from its surface. Nor were any of the circumstances pointed out by which high temperatures are capable of being attained locally in rocky masses crushed beneath our surface and which we must assume as those actually occurring in nature. The writer’s object here is to point out, Ist, that, taking the annual supply of heat from transformed work of contraction, by expe- riment in the way he has done, the result, though more than sufficient to sustain his theory, affords alone no complete mea- sure of the highest temperature that may through its means be locally developed; 2ndly, to answer some doubts which have been raised as to whether the temperature to which subter- ranean rocky masses can become raised by the heat evolved in their crushing and transportation of particles can be sufficient to bring more or less of these at such foci of crushing and disloca- tion to the fusing-point of such materials, which the author in his original paper assumes to be 2000° Fahr.

Professor Hilgard, occupying the chair of geology in the Uni- versity of Michigan, U. S., im an able paper published in the American Journal of Science, vol. vii. June 1874°*, has, in terms as clear as they are courteous, pointed out these lacune in the author’s original paper in the following passage :—

“One point, however, must strike every reader of the original memoir, viz. the preeminence given by Mallet to the crushing of solid rock as the means of producing heat and fusion. One would naturally look to the results of his experiments on this subject for the proof of the efficiency of this agency. But we find that the maximum ¢emperature resulting from the crushing to powder of the hardest rock is something over 217° Fahr. This, then, represents the maximum increment of temperature that can be rendered efficient toward the fusing of rocks by the crushing process under the most favourable circumstances, viz. upon the supposition that it takes place instantaneously, or under such circumstances that the heat cannot be conducted away, and, further, that the resistance of the rock has not been materially diminished by the downward increase of hypogeal temperature. At the most moderate depths at which volcanic phe-

* Phil, Mag. July, 1874, p. 41.

by Rock-crushing and its Consequences. 3)

nomena can be supposed to originate the last-mentioned factor must exert a very considerable influence, reducing materially the available heat-increment. Hence the numerical results of Mal- let’s laborious experiments on rock-crushing, however interesting and useful as affording a definite measure of the thermal effects producible by this means, yet fail to carry conviction as to the efficacy of this particular modus operandiin reducing large masses of solid rock to fusion, unless essentially supplemented by friction, not so much of rock walls against each other, but more probably by the heat produced within more or less comminuted detrital or wgneoplastic masses by violent pressure and deformation.

“Tt may be doubtful what would be the physical and thermal effect of enormously great pressures upon rock powder such as was produced in Mallet’s experiments; but it would seem that if made to yield, the frictional effect must produce very high temperatures. A fortiori, solid detrital masses of variously sized fragments in- termimgled (such as, rather than powder, would be likely to result from steady pressure), yielding rapidly under great pres- sures, might, under the combined influence of friction and rock- crushing, well be supposed to reach the temperature of fusion, which a simple crushing of a solid mass by pressure would have failed to produce. Mallet mentions the probable influence of friction and of the squeezing of igneoplastic masses, but does not attach to these agencies such importance as they seem to me to deserve.

““ Of the complex thermal effects of the movements of detrital masses under great pressure Mallet’s figures of course offer no measure whatsoever; nor is this, or even the thermal coefficients resulting from his rock-crushing experiments, at all necessary to the establishment. of the postulates of his theory.”

Subsequently the Rev. O. Fisher, in a paper read before the Geological Society of London, May ]2, 1875, entitled “‘ Remarks upon Mr. Mallet’s Theory of Volcanic Energy,” has repeated the observations of Professor Hilgard, and extended his objections to the author’s theory in general im a way which appears not warranted. It will be sufficient here to quote the following from My. Fisher’s paper :—“ Indeed the form in which the objection to Mr. Mallet’s reasoning suggested itself to my mind on first reading his paper was simply this. If crushing the rocks can induce fusion, then the cubes experimented upon ought to have been fused in the crushing; and I still adhere to this simple mode of expressing my objection.” Again :—“ He considers that the heat so developed may be localized, and that the heat developed by crushing, say 10 cubic miles of rock, may fuse 1 cubic mile, But I ask why so? The work is equally distributed throughout ; why should not the heat be so also? or if not, what determines

: B2

4 Mr. R. Mallet on the Temperature attainable

the localization ? For example, suppose a horizontal column 10 miles in length and 1 in sectional area to be crushed by pres- sure applied at its ends, which of the 10 cubic miles is to be the one fused? But if no cause can assign one more than another, it is clear that they will all be heated by 170° and none of them fused.”

Ifa cube of rock, which in free air is found to crush under a certain pressure, be imagined situated deep within a mass of similar rock and there crushed, it does not admit of dispute that the work necessary to effect crushing must be largely increased ; the particles of the cube and of the entire mass of surrounding rock are under the insistent pressure of the supermcumbent rock in a state of elastic equilibrium. It follows, therefore, that the pressures of the surrounding rock produce the same effect upon the cube as regards resistance to crushing as if they were cohesive forces acting within the cube; and the work necessary to crush the cube by its finally giving way, im whatever direction this encastrement by pressure may be least, will be increased over that which would crush it in free air nearly in the ratio in which the imaginary cube is exposed to external pressure greater than that in air. Thus, if the cube of Guernsey granite (No. 12, Table I. Phil. Trans. part 1, 1873, p. 186) which required 4,336,712 lbs. per square foot to crush it in air, equivalent to a superincumbent column of the same rock of the mean specific gravity 2°858, or weighing 178°3392 lbs. per cubic foot, be supposed situated at a depth of ten totwenty statute miles, it will require rather more than 2°14, or, at twenty miles, 4°28 times as much pressure upon two opposite faces to crush it that it did when in air; and if we assume the displacement of the crushed particles after crushing to be the same as in the case of the cube crushed in air, then the work and the heat due to its transformation will be also 2°14, or 4-28 times as great. And as in the case of the cube crushed in air the heat developed was sufficient to fuse (at 2000° Fahr.) 0:108 of its own volume, or, in other words, the crushing of 10 cubic feet of the rock would be required to raise to that point one cubic foot, then in the case of the imaginary cube situated at the depth of ten miles enough heat would be evolved by the work of crushing each cubic foot to fuse 0:231 cubic foot, or, at twenty miles, to fuse 0'462 cubic foot of the same rock, or nearly half the volume crushed,—and this assuming that the initial temperature of the rock at 10 or 20 miles depth was only 57° Fahr. as in the author’s experiments, instead of from 500° to 1000° Fahr. or more as it may be at 10 to 20 miles depth. Therefore, under the pressure due to a depth of 20 miles and an initial temperature of 1000° Fahr., the heat developed by the work of crushing each cubic foot of rock will be sufficient to

by Rock-crushing and its Consequences. 5

fuse its own volume. Thus also if we assume the fusing-point of the rocks not to be 2000° Fahr., as indicated by the author’s experiments on the cooling of slags, but considerably higher, say 2500° or more, we have still a sufficient supply of heat due to crushing alone to bring 0°8 of the entire volume to the fusing- point.

These considerations, apart from all others yet to be adverted to, appear fully sufficient to refute the Rev. O. Fisher’s first ob- jection above quoted; indeed the statement that if under any circumstances and in the rock-masses of nature “crushing can induce fusion, then the cubes experimented upon ought to have been fused in the crushing,” seems as unsupportable as it would be to affirm that no heat is developed by the slow oxidation (ere- macausis) into water and carbonic acid of a pound of wood, which when burned develops a well-known amount of heat.

The depths above assumed do not widely differ from those at which the foci of earthquakes have been found by the author (Report on Neapolitan Earthquake) in 1857, and by others smece that time, and which may be presumed to indicate some degree the possible depth of volcanic activity.

The writer now proceeds to reply to the second objection of the Rev. O. Fisher as above quoted, which appears to him based entirely on a misconception of the physical conditions involved. Let us consider what will happen in the case of a prism or column of rock crushed against the face of an unyielding mass. If the prismatic mass be not homogeneous throughout, crushing will commence’ at the weakest place; if it be perfectly homoge- neous, crushing will commence and continue where the prism is in contact with a fixed mass, and that whether the prism be crushed at one or both ends—because it is at such surface of contact that the compression of the particles of the prism is greatest, and where therefore the elastic limit of their cohesion is first and successively overpassed. This may be seen illustrated in the stonework of buildings the material of which is overloaded, where crushing or spalling off of the ashlar stones only occurs at and near the joimts*. In either case, whether the prism be homogeneous or not, the crushing must be localized either to the end or ends of the prism, or to the plane of weakness where it first yields, and which then becomes the crushing surfaces of two opposed prisms. It is these physical conditions which “determine the localization” of crushing in the prism, and which conditions have been disregarded in the Rev. O. Fisher’s objection. Let us now consider the subsequent effects of the

* See also E. Hodgkinson’s experiments on the directions of fracture

of crushed materials, Brit. Assoc. Report, vol. vi.; and Tredgold on Cast Iron, by Hodgkinson, part 2, p. 319, and vlate L.

6 Mr. R. Mallet on the Temperature attainable.

successive crushing of a column or prismatic mass of rock, one extremity of which is continually urged against the face of a fixed mass of rock which does not yield, a case which approxi- mates to that which most frequently occurs innature, and which, to fix our ideas, we may suppose presents a face for crushing of one square foot; and being continually urged forward, and the pres- sure being greatest where the pressing column comes into contact with the fixed mass of rock, the extremity of the column sup- posed homogeneous, or the parts adjacent thereto, are continu- ally crushed by a succession of per saltum movements. The first cubic foot of the column that is crushed has its temperature raised, let us suppose, by the minimum of 217°. The crushed fragments at this temperature are pushed aside by the advan- cing column, whose extremity is thus surrounded by crushed material at.a temperature of 217°, and the second foot in length of the column becomes crushed. But the material of this second cubic foot is at a higher temperature before it is crushed than was the first cubic foot; so that the heat due to the trans- formed work of crushing of each successive cubic foot of rock raises its temperature to a higher point, than that of the prece- ding one, because each successive cubic foot at the instant before crushing is at a temperature already higher than the preceding ones, resulting from the heat taken up by the uncrushed column from the hotter portions of material surrounding it that have already been heated by crushing; so that, if T be the tempera-

ture produced in the first cubic foot crushed, and ¢ be the tem- _ perature of the crushed material which communicates a portion of its heat to the next cubic foot crushed, the temperatures of successive cubie feet crushed may be illustrated by some such series as the following :—

Cubic feet crushed.

ae a

ar No. I. No. I. No. LI. Zz t t T Te oa T+ ae aa, bl a8 &e. 7 n m

We have here supposed the column crushed at atmospheric pressure ; but if crushed under an insistent column of 20 miles, then the temperature T would be 4°28 times 217°=928°, and the subsequent temperatures correspondingly increased.

No limit arises to this continual augmentation of temperature while the rock retains its rigidity; after that has been seriously impaired or lost, any further exaltation of temperature apart from the detrusion or transport of fragmentary matter, as hereafter re- ferred to, becomes dependent upon the deformation and detrusion of a more or less plastic mass. It is well ascertained, however, by observation on a great scale, that granite remains rigid at a

by Rock-crushing and its Consequences. 7

temperature nearly approaching the softening point of cast iron* ; so that a large range of rigidity must exist for the exaltation ot its temperature in the way above suggested; and in the state of aggregation which we are warranted in supposing rocky masses to exist at considerable depths, it is probable that this range of rigidity would be even further extended than in the ease of granites found at or near the present surface of our globe.

There is a close analogy between the conditions of gradual exaltation of temperature above sketched, and those by which aérolites, flying at an immense velocity through our atmosphere, are heated from the temperature of the stellar spaces to that of incandescence or even fusion of those bodies. The aérolite, which, according to Schiaparelli, may in some instances be forced through our atmosphere with a relative velocity exceeding 3500 feet per second (one enormously exceeding that at which air can rush into a vacuum), compresses the stratum of air immediately in advance in almost the same manner as if at the first instant of contact the air were a rigid body. The temperature developed is greater as the velocity of compression is so, and as the volume compressed is less; the most highly heated air is therefore the | stratum directly in contact at any instant with the stone; and the latter licks up more or less of the heat asit passes through a succession of such compressed strata, and so receives continual accessions of heat until the temperature of the meteoric stone itself reaches the limit given by that of the stratum of compressed air in immediate contact with it at any instant. Ifa body as mobile and compressible as air can thus by sufficiently rapid compression be raised above the temperature of incandescence, we may readily conceive how great an exaltation of temperature may be produced in the rigid materials of our earth’s crust when exposed to a pressure which may be viewed as limitless in refer- ence to the resistance opposed to it, and which, in consequence of the conditions of elastic resilience hereafter referred to, may give rise to motion and crushing with velocities even exceeding those with which aérolites traverse our atmosphere.

The well-known experiment of cutting a hard steel file in two by the rapid rotation of a thin disk of soft sheet iron pressed against it is another example. The heat developed at the work- ing-point, so far as it is communicated to the disk, is rapidly

* The observations upon which these statements are founded have been made after various great conflagrations of stores or warehouses at London, Liverpool, and Dublin, into the construction of which granite blocks and cast iron in columns, girders, &c. largely entered. The cast iron was either melted or softened to the consistence of soap; the granite heated to like temperature, except being split in various directions, was found un- altered, except more or less ‘in colour, after having been again cooled,

8 Mr, R. Mallet on the Temperature attainable

carried off and dissipated by its rotation, and it thus remains cool enough to be touched by the hand, although the heat de- veloped by it and accumulated at and near the working-poit in the file is sufficient to raise that to the temperature at which cast steel becomes softened and approaches fusion.

The cutting of steel railway bars across when at a very low red heat by a rapidly revolving circular saw, which revolves par- tially immersed in cold water, and from whose action a torrent of ineandescent fragments of steel is discharged, is a hike case.

Besides the heat transformed from the work of compression and crushing, a large amount of heat must also be generally produced by transformation of the work expended in friction and detrusion. No experiments have as yet, to the author’s knowledge, been made upon the amount of heat developable in fragmentary pulverulent masses, such as sand, by the forcible transposition of more or less of the particles; nor do we know with certainty the conditions under which external mechanical pressure is transmitted through sand or like discontinuous matter. As in rigid solids exposed to unequal mechanical pres- sures there exist planes or surfaces within the mass such as have been denominated by Moseley planes of easiest shearing,” or sliding, so in masses of pulverulent matter, whatever be the shape or size of the particles, provided these be small in relation to the whole mass, and their mutual adhesion (if any) small also, such planes must by unequal mechanical pressure be brought into existence. Along any such plane we may imagine the sand or other pulverulent matter forced to move over itself in opposite directions at opposite sides of the plane; that is to say, we may suppose the sand forced along such a plane much in the same way that a mass of sandstone or of granite would be forced along such a shearing plane as had been produced in it previously by mechanical pressure. If this reasoning be admitted, we must suppose that heat would be developed along such a plane and at short distances from it in a way more or less analogous to that produced by forcing one rough surface of stone over another. What the coefficient of friction in this case would be can only be determined by experiment ; but we may justifiably conclude that the amount of friction per unit of surface would increase propor- tionately to the pressure applied externally to the entire mass— exposed to more or less of which, motion at any such sur- face of friction must take place. Coulomb, Morin, and others have found the friction of some sorts of rough stone upon other rough stone to reach as much as three fourths the pressure; and should this coefficient increase proportionately under the enor- mous pressures to which a discontinuous mass at several miles depth may be subjected, we can readily see that the trans-

by Rock-crushing and its Consequences. 9

formed heat of friction produced by internal movements taking place in such materials after crushing has occurred, must be the source of a large amount of heat over and above that originally due to the crushing itself. Thus, for example, if we assume a surface of such disintegrated material sliding over a similar sur- face, or over a rough surface of coherent rock, and under the pressure of ten miles of rock of the specific gravity of granite, at the rate of one foot per second, and if we take the coefficient of friction as low as 0°5, we have 4,326,600 foot-pounds of fric- tional work per second, which, divided by J (=772), gives 5604 units of heat evolved per second from each square foot of sur- face ; and to this development there is no limit while the cireum- stances continue the same, except that of the distance that one surface is forced over the other. And great as is this evolu- tion of heat under such enormous pressures, it would be further increased in the event of the fragmentary particles being heated so as to present incipient viscosity of surface and more or less of mutual agglutination.

Temperature with respect to any given solid TEES 4 is depen- dent upon the units of heat present in a unit of mass or of