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Las diagrammes suivants iiiustrent la m^thode. 1 2 3 1 2 3 4 5 6 T MADE IN CANADA Singh e Copy Pamphlet Covers Photic Mv ant Lcathcrbtuird Cover Maximum Maximum Maximum Maximum Size Capacity Capacity Capacity Capacity V2" 1 Va" 1 7 X 5 No. 4340 No. 4360 No. 4380 No 4400 8" X 6 4341 4361 4381 4401 9 X 6 4342 4362 4382 4402 9V2'x 61/2 '■ 4343 4363 43113 4403 10" X 7" 4344 4364 4384 4404 10 X 8" 4345 4365 4385 4405 11" X 8I/2" 4346 4366 4386 4406 12" X 8" 4347 4367 4387 4407 12" xlO" 4348 4368 4388 4408 13" X 8V4" 4349 4369 4389 4409 lavjxio 4350 4370 4390 4410 14" X 8V2" 4351 4371 4391 4411 14" xlO" 4352 4372 4392 4412 15" xll" 4353 4373 4393 4413 16" xl2" 4354 4374 4394 4414 17" xll" 4355 4375 4395 4415 18" xl2' 4356 4376 4396 4416 Abo made in other cover sizes, capacities and bindings MacMILLAN OFFICE APPLIANCES COMPANY Westboro, Ont., Canada Manufacturers of Office and Library Filing .Supplies Loose Leaf Devices and Specialties - ,ti25\ai^ An Investigation into the Elastic Constants ot" Rocks, More Especially with Reference to Cubic Compressibility HY TRANK I) ADAMS ani. ERNEST G. COKER \VASHIN(.T<)N, D, L PuHishctl liv the Cairugie In^litution ut Wj^hmijtjii jui.c. tyuo. An Investij^ation into the Elastic Constants of Rocks, More Especially with Reference to Cubic Compressibility BY KRANK I). ADAMS ani. hRNfcST G. COKER 'Z7 WASHINCTON, I). C. . I'ublishcil !•> the ( arncgie Inslitutiun of Washington June, 1000. CARMlA," INSrUUTKJN Ol- WASHINGTON I'llll ICATillN N.p. fO I'KKSS OF CIRSON BROS. WASHINGTON, D. C. i CONTKNTS. lan one Miiitrul: Iiitrcjdiictjiiri Metl„„l, «l„d, may I* um-.I in ilu- IK-H„,u,uii.m .,( i:i.,.,ii.- i„„s, „„, A,.,.luMl...n , f the M,, f sin.pU- Cn„„.,cvsi.,n ,„ ,1,.. lH-,>r,„i„.,„„„ f)rcssilii|ity i.f Mil. lis Applicati..!! „f .Ik- .\k-.l,.Hl „f Simple 0.n,pa>.i„i. i„ ilu- IVlvrt, pri-ssiliiliiv of Kinks The MetlHid ,,f Measiirenunt The iilastie Omstant. „f k,„ks C..mp..se.l „f ,, Siir.-K^ Mi.ierul- Maililes and I.iniest.iiie> ~ I. Dlack IteUian MarMe i" N.iir l-iti'i 3. Whit.- Carrara Mirlilt .1. While \eriiii.nt Marlile 4. Ttnnesvte .Marble (■• I'ink i'enneswe ") •r. ... . ^' '''"'■-''''''■'""•'■'■""'"" 'ini'-'^l'ne, M.mlreal. Canada The hlastic C.mstants m K„eks C..ni|K.Hvl „f in„re th Acid Plnlimic Rucks — C.ranile 6. Cranile — Havenii, Italy 7. C.ranite— Peterhead, Si'iilland «. Granite I.ily r.ake, .Neiv Hrinisvvick, Canada . 9 Granile-Westerlv. Uh.ide Isl.in.l, T S. .\ 10. Granite -Onincy, Mas.i.ichiisetts, ('. S .\ 11. Granite Stansle.i.l. I'r.ivinii ,,f (Jiiel,ec. C.ina.la .\epheline Svenite: i.v N'eplii'hne Svenile, Mmiireil, Can.i':.i li.l^ie I'liitcnic U.K-ks t.\. Aii„rth..siie, New Glas-.nv, IVninee ,,f ( Hu'Ikt C.ini.l. 14. Fvsse.xile, .\I...mt .Johnson, Province of oaelH-c, Canada IS Green G.dihn., New Glasgow, Province of ' )„elK'C, Canada K '"'^""■' »'■'•«•*. S»'lln.rv, Province of M,„.,rio, Canada Seduneniary Nocks (Cl.istic) • 17. Sandstone, Clevel.ind. ' i|,io The Elastic Constants of Glass Summary of Kesnits ■I' "laerials • f the Com- iii.ilioii ,if the Coni- I.S JO it) 38 JI 40 4-' i i SJ .5 5 57 60 60 'L'51-6 liip LIST OF PLATE^- Plate I. II III IV. V. VI. VII. VIII. IX. X XI XII. XIII. XIV. XV. XVi Hl,uk H( l«ian Marble '^ C;irr.ira Marble ,,, \irninni Marlile ^„ Marble- Tinness«i- I'iiik rinnes^it" ) ,„ Treiilim Liiiiesiim Momrial, Canada \j Oranile — Huvrnii, Italy OraiiilP I.ily l.akt. Canaila . ',j( OraTiili- Weslerlv. Rliuile Uland ,„ C.ranilf Quim-y, Massailni iits ,, Ctranilc St:instrane Cleve ( ihiu ^ 3 AN INVKSTIGATION INTO THH Hl.ASTIC CONSTANTS OF ROCKS, MORli HSriXlALLY WITH RHl-T'RHNCi; TO CUBIC COMl'KHSSllMLlTY. INTRODUCTION. The question as to the amount of cubic compression which rocks may undergo under the stresses to which they are subjected in the earth's crust is one which lias a direct bearing on inanv very important problems in geophysics. It is. liowever, a subject whieli has been l)Ul httle in\isii gate, there will be a str.iinin the direction of this stre^-, i amount />, /•,', where /•,' is Vonnj^'s modulus, and lateral strain of mai;ullu(le p, nili. where m is the ratioof the lontjitudiual ciiiupression to the lalerd ixtension per tmit of length If we suppose f\irther that a bod \ is subjected to cubical stress of in- teusilv /!,, we easily see that for small and therefore superposable strains the cubical strain i , is \ r = ? In an important paper by Nagaoka* this latter method has been used to determine the elastic constants of a series of rocks The value of /•'was deter- mined bvsupixirlini; a bar at the ends and measurins the angular change at the sup])ort due to a j;iveu load applied at the center; the value of /•,' is then obtained bv ll'.e formula /■. - .;a7' 4/11/ H. wlure / is the length of the bar between the s\ip|)orts, /> is the breadth of the bar. 1! the depth, and II the anj;ular chani;e at the euils for a load, 11' In order to determine the value of m, a s|Hcimeii of rectausular section was twisted by a given tortpie, T, and the amount of the strain measured It has been shown by St V'enant that for such a case the value of (" is given b\ the I'ormiila ■' tan h [2)1 + 1 1 r =. ciih" "■] l\ wlure /' is the angular change, and from this formula values < if C" were calculated from the observations This meth;es is nevertheless I'ulv approximate, and it is well known that values of /•," obtained by llexure exixriments in this manner often differ from the values of /■. obtained bv direct compression experiments by not inconsiderable amoimts F;:rther. in exi)erimeuts upiin the (klliclion of beams cut from rock", it is dilVieult to obtain eonsistenl readings, because of the timeelTeel of tlie load- ing, and this dilVieuIty is noticed in the jiaper cited As an example of the results obtained in this way. we niav (ptotc the results of certain experiments made bv us with a pure white marble from Vermont. Lath-shaped pieces of the marble were carefully prepared and were sus- pended on two wedge shajjcd supports and then loaded in the middle The weights were placed in a light brass pan. hanging from a thick wire which passed over the middle of the lath and lav llat upon it. Each experiment occupied about half an hour, and the deflection was measured by attaching a scale to the 1 larbic and reading it with reference to a thin wire stretched in front of the specimen, a properly moimted tele- scope being employed for this purpose The marble was in all cases placed so that its broader surface rested on the terminal supports. ♦lilastic Ciinstants of Kocks and the Veloeity of Seismic \V:!vts. H. Nagaoka. Mag., Vol. L, i<)"' 5'j tnuicc-.; .."»'\^ r.ooiinfrs ■^"'^ (.11 oiim-is (:il'lu J niiiiuu-.! ^^^' (1) iriiiu-c>-.. -^'^ (il iiniici"; iMliir il iiiiium 1 .^''' (<<• nlliu-o-i ■^'' (,■^ ..lino- ••''■■'* 1.^ iiiim-i... (alu 1 1 5 liiiiiut^-^i ■■'-" 70 '.itn.;i- ■"'-* -2 ..iiiut"- "*" ;_' .imKi- latlir 1 )iumiu 1 ■.^-- 7 } (iiinccs ..^ - • 7.. ..inu-.-.; ■-'^-'■'" ■i> ..iHH'i"- I HUT I |. iiiimitc-.l . ■^'-' 7'- "Hint—. ..^.V^ ^....mu•.- . ■^'4 ,^. I ..iin.T I J I'll r J iiiiinm-. ni'.viii'^' I.!--! St" v: ..iin.a- .^41 ,^.' ..inui- l.iltir 1 ;. iiiimili-. ' -^4.1 --' .ilinc'cs i\ui.;lit rc.liux'il, l.ir.'C pcrm.inciu -i 1 1 -S^^ ■ S4 iniiiccs ■■^4/ -■(1 iiiiiu-fs ■S4'l M. .mncis iLiltir i iiiiiniu-; l.i..kui ,S.S4 T.>! il fknrrti..n I f.irc lirnkinc; "''4 'f KLASTIC CONSTANTS OF ROCKS. In the second cxpcim Jilt the marble lathwa; longer and at the same time somewhat thicker. Its dimensions were as follows: Length, 16 inches; length between supi)cirts, .'.s iiulies; breadth, i 23<)to i ^84 inches; thickness, 347 to .,^56 inch. Inch. I.uacl with pan only 343 with pan plus s uum-cs. . 349 16 onnct'S .i^S J4 ounces 3*9 24 ounces (after i J niiuules) 39' 25 ounces 4^1 32 ounces 4**' 32 ounces (alter 1 J niimues) 4^3 36 ounces 43^ 40 ounces 4*^ I.nirl witli i)an unly (\vei;4ln rem.. veil, lari."- pewi' .iiciit set) 412 with pan plus 40 ounces (after 2 nr'.uites) 47< 44 ounces 492 44 tiunces {afle. a fc.v ..^ee.ilKis) ..SOO 4 ( ounces (after i niimite; limke) 520 Total from the values vjiven in N'ai,'aoka's list and obtained by his method, it is found that a nei;alive valueis actually obtained in about one third of the rocks which he has examined Mis liijures, however, were intended chielly for the purpose of calculatim; the velocityof the propagation of earthquake shocks mmm ^ J n x^zm Vh\. I. — IiistrnuuMit fur ili icrniiniiiu' tlic iiumIiiIu^ <'1" a vimplo striiiii. In consequence of tlie somewhat unsatisfactory results obtained in our pre- liminarv experimeuis with this method, as well as the facts with regard to N'aijaoka's fiijures just mentioned, it was decided to adopt a somewhat (lilTerent method and one wliich avoided both torsion and flexure and depended sinqth ou str.iin produced bv simple comi)ressive stress. This will be termed th<- ■method of simple compression .\moU;i the possil)le indirect methods, this seems to be the most satisfae- tor\. as the assuuiplious necessary in the calculation ol compressibility are redui-ed to a minimum, and the ranifc of stress for which the ratio of stresr to str.iin is practically constant is <;reat We were able to measure the strains obtained very accurately, bv means of an ajjparatus forminjjpart of the equipment of the testini; laboratory of Mi-Gill University, for the use of which we are indebted to Dean Bovey. This is an instrument designed by Professor Ivwing, and of which a diagram- matic representation is given in figure i, in which A is a specimen of the rock ELASTIC CONST.'* VTS OF ROCKS II gripped by .,cre\vs passir.),' through a pair of collars, fl, which are i 2,s inch apart, to which latter trctal rods, C, are attached. The upper rod carries a glass plate. I), with a fine '.ine scrat-hed upon it, the position of which can be adjusted hv a screw. /;, while t le lower rod carries a micrometer microscope, F. The upiHT and lower collars, H. are connected by a stud, G, the upper on • engaging with tl • conical hole of the swivel pi^ce // in the lower, and contact is maintained by a spring, /, while the weights of the microscope and projecting arms are balanced by lead cylinders, J A buzzer was attached to the upper lead cylinder which, when operated, caused a slight vibration in the instrument, producing a perfect adjustment as the pressure was applied. I'IG. 2. — I'ersl>cctive view of lateral extensomcter. The proportions of this instrument were so adjusted that one division on the micrometer scale corresponded to ,-'„„ of an inch, and before using it the instrument was calibrated li\ aid of a Whitworth measuring machine and was found to be in correct adjustment This instrument enabled us to determine the modulus of simple compressicm with great accuracy. The linear strain perpendicular to the length of the specimen vas measured bv an instrument which had bet ii designed by EG. Coker some time previously for experiments on the lateral strains developed in metals * Figure 2 is ♦."mjc Proceedings Royal Soc., Uiiinburgh. Session 1904-5. Vol. xxv, pt. VI. 12 AN INVKSTIGATION INTO THE a ili ii;r;iintii:itic view of tin- appunitiis. which consists iif u pair of lirass lubes. li. /(', proviilcd with set screws, .1, 1', for atlachmiiit to tlic spccinuii, ami coiiiicctcil to.i,'ctlicr l)V a llcxiblc steel plate. /', lormiiiL; the fulcrum The ends of the tubes near the fulcrum plate arc pressed apart by an adjustable sprini; S", to insure a uniform pre-,snre on the screw points -ripping the specimen On the opposite eml of the tubes is a spriu',' finger, /', of tb(]ny, pressing aijainst a double knife cdi,'i-, /v.se.ited in a shallow V notch cut in the end of the other arui The knife ed;,'c c.irries an adjustal)le mirror, M. so til at if anv chalice in tlie diameter of the specimen occurs the two tubes move relatively to one another in a horizontal |)lane and tlureby cause the knife edL;e mirror to rotate; the rotation of this latter is obbcrved and measured be a telescope and scale placed at a suitable distance. I'or convenience in adjustment there is a screw, /., for tiltins the apparatus .i1)oul the axis of the ^'ripi)inL; screws, and the tubes U. /<' are trussed to prevent vibration This instrument w. is calibrated bv aid of a Wliilworth measurim; machine and the scale adjnste pounds, after'vards reluming to the origin;il load The readings obtained for the longitudinal and lateral strains will show- in such ;i case that >ipial increments or deerements of loail produce strains which are \ery exactlv i)roportional tliereto. This is clearly shown in a plot of these readings, where the ordinates represent the total load and the alisciss.e represent strains In both cases the relation of stress to strain is represented bv a straight line returning upon itself Traces which varv bnl little from the i to the strain e, we have p=Ee ELASTIC CONSTANTS OP ROCKS 13 If we cull .4 the cross sectional area of tlie spednieii when stressed by a loud, /'.ami r the decrease of leUKtli over a nieasiired leiiKlh, L, gripped between the screw points of the measuring apparatus, we obtain PL t = x.\ which, in case of a specimen of wrought iron examined for a rangeof S,(XX) pounils, ),'ave a value of jS. mo.ooo, the units beiii); ixiuiuls and inches. The ratio m of the loni;itudiual strain to the lateral strain in llie same case was }i 65. and usinu Ihe formula 1)^ E ,1 '" - we obtain for the modulus of cubical compression (or bulk modulus) I), the value .11, v>o,ixK), a constant for the material, the reciprocal of wliicli f,'ives the decrease in volume of 1 cubic inch for 1 pound of pressure While certain rocks, ^.uch as many of the inarblcs, have a structure identical with that of wrought inm, most of the rocks constitutini; the earth's crust are composed of several minerals, and thus resemble cast iron in character, the grav variety of this substance bein^ .m a>;i;r.j,'atc of crvslals or individ- uals of tlie metal iron (wrouiflit iron;, (graphite, etc It will therefore be of interest to ascertain how a specimen of cast iron be '.aves under compression stress, and how far its elasticit v fills short of that which would be exhibited bv a perfectly elastic boily !*i,r this purpose a tine ,i,'rained siiecimcn of somewhat hard cast iron was faced and tested The results of this test are tjiven in the following' table, and the stress-strain curves are plotted in lij;ure ;, I represents Icjuijitudinal compression and II lateral extension The behavior of cast iron, .is exhibited hv these experimental res dts, shows .1 falliiif,' awav from the theoretical standard of perfect elasticity, but even in the most i)erfecllv elastic bodies there is i)robablv ,1 sliijht hysteresis effect, so that w\ are justilied in usiiii; the results obtained to calculate the mod- ulus of compressibility, il the error intnidticecl thereby is iie,i;li,s'ible or very small It may be ijoinled out (hat tills method .and others of the indirect type have been freelvused to obtain values of the liulk modulus for east iron and metals of like character, and it will be shown that the composite crystalline rocks are very similar to cast iron in their behavior under stress, although generally more perfectly elastic. 8 % \\\ •4 AN iNvi;>ii(i.\Tin\ iNTii Tin; I u-i /,, Sl/.- Aril.. I 1141 1 •■ (HMHHH I "nKilii.lin il (■■minis. i, ,„ „,u|||,,iy ri.Kliniis t»V 4 f'T iiiilliKntliM. I.ua(J lin [Hiundb). 1 ,,(XK). :.tx»o <,CK10. ».(XK>. \1)1K) ■.(KKl. I, (NX). ;,INX). I.IXXI. Side P. <9 4" fHJ So lex) I ..'O I ID llil) lis !-'« 104 Sidi- V. 37 58 7,s K)0 'H ['■11 '43 1 -■ i I 10 Liiti-rul extt'tisiim— imillitmttiK). Side i'. JO 21 4> >S») 3 J ><3 III) iir. imi lo.-i 1)1) 7" 'id lin -II (11 Ml -•1 Kidc 5 TRAIN l-tG. 3. — Cast irim Strcss-slniiii mm-. Kr.AsTIC Cii.NVrANTN (IK KUCKS APPLICATION OK THE MKTHOD OK SIMPLE COMPRKSSION TO THE DKIKKMINAIION OF TllK COMPRESSIBILITY OK KOCKS It li I- l..'.n n.,t(.l ni ilir .MM- ..r iii.irl.U wli> ■ Mihjivlr.l to tHtidiin,' >lri>.s tli;.l Ih, -lr.Mii.,s,Aliil..i.-.|l,vtli,Mk.||>fli.m.,i ..Mil..lllu.lMrinma.rs-.v, >! the time iii.l iIk' sin ii,.tli iiii I, r .lir.r pn. Im<-,i| hv ,i t.,n|iK. w:i^als.) I.mim.I t.. hc-i., Muall tint ,1 .l.lrniiiii ,li,,„ ,,1 ilu- slriiTi «a> vrvliiMi»;,rv .■xiKTiin.nt.cti ^r„iii<- .li,,» tl,,,i ri.,.,k,.\ |,,„ .|..,.srM.| Imlil .-vvn for vt-rv small lU-xi,r,. ,,n,l i.-hm,.,,, .,n,| ||,.,I ,1,.- ,,IIit i llVrt K wrv .■,.„si,|,.r,,l,k. fr.,m ||„. pressure «-lK-„tl,.. ,,r,„n iss„liUu„.lvl.,,„l,..|„r , » j.u.l. ,1,.. ,|,u,„i,„, ir,.,„ ,!„. .lir.ct i.r.'|.or.i.,„-' ..li.v l,.i«..i.„ s,r.,iM ami s,,..., „.,s „k-o,„,, ,ral,lv ,„ „ a. oMnparv,! v.i.l, that oLs^rvi.,! "1 Mutal I his nnis, l„. . |,i..||v ,I,k. t.. t'u- l..« 1,„mi nf ..laMi. itv. „, ,!,:„ „ i, n.ves^arv f. ex|K.riMU.„t „nlv w,il,i„ very narr,,w linui, ,,| l„a,l,„K a,„l uvis,,,,,.. iU,.,- lj,„its are «iclclyHini.r s„.-h s,».s,es as will a|,,.r..xin,atelv ,.ro,l,H-c strains proporiioi.ai ,o ,Ik.,„ ||,e ,leviatin„ fro,,, ||o„k.', law was pro,,,,',,.,,, i„ ,,.,,,,i„ spiT„„e,is of samlMoiK-. ami it was ,nor.- ,„arkc-.| i„ t.asio,, tliari i„ ,l,.x„ri. cxiHTiincnts Ml ivriain roots I. is i,„k.iMl ,lo„l„f„lir anv,l,i„,. lik.- a pr ., li..„alit v hHw.en stress an, Mrain can Ik- fnnn.l, . vt-,. for cxir.andv s,„a!I rlian^,. of s|,a,,v. i mi la-U-asin.- tl,i.,e r,H-ks fro,,, s,r.-ss ,|,, return toward tl,.. fortner slate i. ext,..„,e!v s,„all, .l,owi„,. .n „ , |„. elasttcir. "f ihe rock is of a very inl.rior or.l.r. These ..l.s^TVutions of \a:,M,)k.. lor lumlin- and twistiii- have Incn con- liriiuil by our own .Ullci-liou .xiHriiiu nis. as ahovt- iii.iili..in-,| If, howcvr. tlR- rock lu sul.itTt.d to uinrt i-o,„,,r.ssioti. strains in wliid, t K' tune elTcc-l ts stnall and the la-of thfstrai.nsalsosn.allareahip.st invari- al)lvol.ta,ned fhisis csiKciallv tlie ease if before the aelnal experiment is earned ont the niaterial be several times stilijeeted to a ranLre of stresses at preliminary IS also eonimonlv least as -real as those emplovcd in the experiment itself This prel stressiiii; brin.;s the material to 'a state of ease,' adopted when the elastic coiislants of metals are d It is evident, therefore, that this direct eomi fulence beapplied to lh<- mi. i.;tiroo,,. .t ..i- .i.. letermined )ression method m: vith although as mentioned bel with dilTereiit classes of rocks e I'leisiireine It of the cubic low the accuracv of the result so obt cotiipression of rocks lined \vi lldifTei If the rock be be safely the rock employ massive, eompact. ami cr\ slilline (orghissv) tli ed and j;ood results will b; obtained I rs seliiitosc, porous, le method ciin f. on the (ither h.ind. nature of the case be very miicl less satisfaclorv )sely coherent, the method ,vill f roni the The plutonic igneous rock in structure, beins holocrvstalline and s .IS a class most iiearlx resemble the metals lassive, and therefore i)resent tli Mag., ♦Klastic Constants of Kock vol. L, 1 yoo, p. 5t( ocks and tlie Wlocily of .Seismic Wavt H. .\;, I'hil. m^^&yiM' ift .W IWICSTIC ATION INTO TIIK lUMPsI .i|)|)rM u'h jniMll,; nuk-. In pi rl'ifl il.isliiiU ; llirv lire ltirrtfvvli''"'l"xik il pmlilciiis, nmsl'tiil - l.ii; .IS Iticv 111 tin- i;i. iliT p:!t! iif llu- c^irlll's crilsl. A sioiiimI class iif riifks vvliii h arc lunip aralilc willi lluiii in lliiir appn Ii In pirfci-l ilastii'itv t iinprisis llic in irl)Us ami iirlaiii liiiu slums A sirii'S 'if sj^inii t\pual rmks ripnsciilativf i>f tlii-si' two classts were ai-,'irilin.;lv silicli'l lor imasiiriiiuTit I'mlir llic first class a iiuimIht nf ijriiiilcs were cliosiii IS nprcsi iiiiiij; ilic aciil pliilmiic mcks ami a iiiiinlicr of Ivpcs nf tlic Kahbrn cssixitc scries were sclecled as reprcsciilini; the basic philntiic rucks III all these cases L;reat care was taken tn clinose the nmst hnTnnL:enenMs ami ma sive nicks of eacli st ries and tn secure test pieces free frnin all llaws ami c; icks As n presiiitiiii; the sicnnil class a miinlHi nf typical inarliles ami lini'^lnms. also pirfu'lh massive in i li aracter, were srlecled I'or pinpnsis nf cnniparisnii, or cnnlrast, a sanilstoiic was added tn the list as luini; a mck which, mi accniinl of its imire or less porous iiatiiri' caild hardlv he e\[iectcd to vield salisfaclorv results hy this niilluid An c\aniinalion of the stress strain curves of t'ase ifi rocks, oiniltin^; the sindstoiie, shows that on the averai^e Ihev possess a rather more perfect elislicitv and exhibit less hxstensis than cast iron Some of them, as for instance the lia\ eiM ,'r mile. I he n']ilieliMe svi uite, the diabase, and the black Iieli,'ian m.irble. show much lietler curves, approximaliu!,' in fact to the straiijht lines i,'i\ en b\ \m .U'.;hl iron, which may be considered for our present purpose as exprissiii^' perfiil elaslicil\ The close approximation to perfeit elastieitx is shown b\ the relnrn of the curve to its initial or siariiii:; point, and the amount of the lusteresis is shown bv the widlli of ihe loop The width of this Insteresis (or kit;* curve or loop, imlicitis theaniouut of the divir^'eui-e from Hook's l.i . wliiih the material exhibits this law beini,' that the stressand strain are •liially proportional. When the curve is narrow, as it is in aP cases except the Statistead ^wilc and thes,indstone, the diver.:iiue from Hook's law is not ^'re.it enoui;h to seriously alTcct the resnll 'llie rocks, ihirefore, with thest' exceptions, fulfil thecnnditioas of elastic- ilv luccs- ir\ to the siucessful application of the method In these twn cases the risulls arc less certain, owinij In the ijreater hvsteresis of the rock It mii^ht at first si'j;ht ap[)i>ar tint while the luethod emplir, ed is tiieorelic- allv prrl'eci I applied to the imasuremenl of the conipressibilit v of vilreo-.is rocks and of verv fine '.^'raiu'-d crvstalliue rocks, a considerable error iri.ijht be inlroihiceil wluu the rocks are co.irser in ;;raiu In the case of all the com- mon crystalline rocks, the individual grains of which the rock is composed KI.Asm .INSTANTS < 4. V*^O.OIHt Srio,cxx> 1 t. I7o.nlIO,IMK1 'M io.'Hio .S, 7;il,IKH> ,U">,o Hnvetiii Kranitc (cnafM'i ii> tritis Siiil'iurv (lialiiise (very liiu-l m iri.ils f' . .' Klass, I.! trials ' Tennessee inarlile (ralhir OKirsei 7 trials It will thus he seen that there is no correspondence between the coarse- ness of Rrain and the maKuitmlc oi' the variations in the readin-s obtained The differences in ,'1 iss. which isau isotropic material in which the elasticity is ei|nal in all directions, are greater than in the Tennessee aiarhle, whi-'i is rr.ther coarse in i;rain. and in Baveno granite, which is the corT—'- ..■■ '-- i8 \N IN\ liSTIC.ATKlN INTi) THi; tin- --rt riir :;rc;ilc^l dilTcniux'- nlitaiiicd ;irc lliosf fotiiul in tlie finest nr.iiiKil riK-k in the si-rn -. \ i/. tin- Siidhnrv dialM^cv It is'vickiit. Ilunlnn. iliat tin- (lillVniit nKJihili of clasliiily (.f tlu' tonstit niiit L;rains(ii ,i nuk (1m mi'I iiilmihu^' an\' ]iiT(.-cplil)U- iTmr in nii-aMiri'inents iiiaili li\ tlii> nitlliinl. win n a inlunni an iTii-li in dianuur is tnipliiycd. and ulna llii- locks arc n.il i-narsir in ,^'rain llian tlic liavcmi ,i;raiiitf In fact, uliilc surrmnidid mi all sides In iUhcr ,i,Tains. no iiu'iNidnal ),'rain can cxjjand fnch .a-, it \Maild if snUjiclcd to i-oniprcssion nidia iip'.rcd by any snrnunidinR incdinni. and tlms llf anisoiro|)iccliaracUr of ihc indi' idual ;^'rains prodnccs but liltlc cITccl o.i l!ic clasiuitx- of the rock as a uliolc Tlicsc cNiicrinicnts also skiw that in llu- case of rocks composed of several minerals it makes no |nrcepli!ile dilTerince wlietlicr tlic points of attach- ment of the instrumeiii are eiiihedded in llu' ^'raiiis of one mineral or of another The cliiif sonrcc of error and the one to which tlic variations observed arc for Ihi- most part to bi' ;■' iilmted seems to be a mcclianical one, viz, the diHicuU\ of ■^(■1 till i; an id.al contact belwi I'li these points of altachineni and the spieinuii to ire nu astired. especi,dl\ in \ie\v of the extremely small dinnnsioiis of the movement to be ineasnred ■rhei|uesliouof iluinlhienceof temperature on the elasticity and compressi liilit\ of roi-ks is of conrse one which has an important bcarini; o!i certain problems of ■jeophvsics TheoidN' invesli,;ationof this snbicct, so I'ar as can he asecrliined, consists of a few preliniiuar\ exiHiimcnls In N'aj^aoka and Kas,ikal)e * In Ihesi' the torsion melhoi] w;i> employed, and the experi- ineiiis wi re eirrieil out on a sim;!e rock, viz, s.mdstone This rock, as has alreadv bicii mentioned, bein^; porons and stnitil'ied in character, is a material whose elastic properties are far from ideal The results are summed upbv the authors in the following words: l'reliniiii,ir\' i\jh riiiuiil s wiili s;m,Isii.Mf s]if cKisticitv is luucll a!Tei.t( <1 i'v- 1 lie \ it i il imi i>i t rinptT't n; <■. ; i , ;!..iul o :^ per ecTlt periU".:ree It il'tes fli-t, lidWfM r, ut i-e •- nil\- ili'iiMu^lMv if li i lie inerei'*- "1 tt'iii]nT;il are where tlie leuipcT.Uure is lew, J , . ii is 111 txinmni iL.iiit >) ^" .\s h,is lueii shown liowi'Vir. the values for the elastic constants obtainicl bv this I ision and luiidin;,' iiiethtid have vielded results whicli can not in all easi'S ln' correct and uhich dilTer \ er\ cotisiderabU fmm tln'se obtained bv the miife dirit'l and simpU' nuthod which has been emplo\((l in tin present p.ijier These results bearing; on tl'.e vari,ition of ilasticit \ induced b\ diailKcs of temi>eralnri', especialh in \ iew of tln' fact that tlii\ are stated bv the *M uluhis of I';i.ist icily of Keeks Line 1 Wloeities i>f Siisniic Waves, ruhlicalions ef the l.aillii|iKike Invesligalicii Coniniillie. No. 17. Tokyo, 1904, p. 43. KLASTIC CDNST.WTS OF ROCKS. IP investigators to hf "proliininary, " can as yet hardly be taken asof general application toallnnks, even if correct lor tlie specimen of sandstone exaiiiin'd In our own in\csliL,Mtions the laboratory wis maintained at a ttinpiratiire of from ()f to (),s' 1'' (i; j- to 20° C ), and a tlioroii.i,di iiivc^tii;ali(iM into the effect of tempt lal lire nas not iindrrlaken. as this would be \ ereent l"or each dei;ree ceiltii,'rade. wliieli a:is \a;.iok.rs result, would mean .1 dilTerence of about :!.s per cent in rait;;e of temperature eniploved bv .Mr .McKeri^ow While, therefore, this experinunt cannot beconsidered as siip])l vim; accurate information coiicernini,' the effect produced b\- a risi- in temperature on the elasticcouslantsof rocks, for theinstruments tluniselvesare in some measure affected bv the same chaiises of temperature. tlie\- serve to show th.it in the CISC ol the m.issive ervstalline rocks tlu' inlluenceof temperalure is piobablv not very i;i-eat I'he subject is one which reipiires further iu\ esii^MtiiJU .<^;''.,:rf' , -30' ViWE».« 1.. ' W«»P.i Pmii AN INVi:sTI(;.\TI(IN INTO TIIIC THE METHOD OK MEASUREMENT. Ill iMrr\iii^ iJiil tluTiicasurriiuiils. iirisins nf the rmk apprdNiiiuilcIy i iiu-li S(|iiarr and ;, iiR-la-s Imit; ucrt- iisiiallx' ciiiplcyid (sii- li;; 4). 'riu-sc were iMit and ,i;t"!iii(1 w-lli siiinotli faas, but uiro 11., t piilislu-d In Uusi- two Miiall nnnid Imlis \vcn> drilkd in tiii' imdial liiii- <>i ladi vertical I'licv for tlic purpose ,,i' attaehiii^' the iii>lriiineiit. when \'oi:ni,'s uioilidiis was to he measured Tluse holes uere made l)\ means of a small diamond drill and Wire ]Hrfeetl\ r.iniid and sm.ioth The> were eaeh 00s tocli column, In drill- in:,' ei:;ii I ))iirs i.f holes, as abive de,erilieil, \i ii.we planes intersected at anodes of 45 iusie.id of 01 " as in the si|ii:ir, prisms It was 111 enurse uecessar\ in e\ ei\ i ase. w hi tliir prisms or Columns were er) ELASTIC CONSTANTS OF ROCKS. o carefully faced and absolutely parallel to one another Refore the actual measurements were made, the rock in evervease was hrnujjht toa "stale of ease" iti the niamur already deserihed The pressiiri' uns apiilicd in most cases hv a luo ton Wiekstead tcstini,' machine, which was so carefully adjusted that it was sensitive to a load (pf 4 pounds Thespecimen, ha\ inijbcen placed in the i)ress and reduced toa stateof ease, was then after careful adjustment submitted to loads incre.isiuj; in successive sta^'es of r.ooo iiounds until the liniil of su\'t\- liad been reached, when (he load was reduced successively bv the same aiuounls. accurate readings beins; taken at each increment and decrement of load The maximiun load emploved in the case of most rocks w.is ij.ooo pounds, e(|uivalent to from <),()()(> pounds to about 11,500 pounds per scpiare inch, accordinj; to whether a sfjuare or round prism was cTUploxed In the case, however, of some of the stronger rocks a load of as much as 15.000 pounds pir s(|uare inch was enqjloved In the determination of the lateral strain, which was Tuade upon the same set of eohunns as those useek. Ilie points of the inslru meiit biini; fixed in some casesin ,t;rainsof one inineraland in oilier cases in ),'rains of another It was found, however, as has alread\- been mentioned, that themeasuremeiitsi.il two sets of prism faces made in Ihe maimer ab..\e described, or on the four planes interseelim; thexerlieal columns, where these had been provided with eit;ht pairs of holes, showed tlKit in Ihe case of the rocks examined the differences between the several nuasuremi tits oil the same prisiu ;,eein to be imaiTected by the eiicumst.iiiee al/.m- nferied W INVI.'.-TK.ATIiiN INT'i Tllh to Till' ilifftioiu'is hi'twciii llic iiR;isiiriiiiiiits thus iiiiulc on rocks composed of scvira! iiiim rnls were no >;n iiter tliaii lliose round in tlie ea>e ol' the linic- >lones, uliieli were e'iMjiioseil cif ilie -^iii'^li- mineral e.ileile. or on i,'lass In tile ea^e of llie ina joril \ i if I lie re.eks iii\eslii;aleil, a niirnlur of prisms or eMhiuiii^ eiil fi. an I he same lil. lek of n.( k U( ri' measnri'il in onler lo aseertain vvlulhi r (lilTerelil tesi pieei s \\oiilil ,i;i\e iili-nliial reailim;'^ ll was foiuid as a ri^iill of ihesi- i!i\a'sti:;alions thai the ilil'fueuees In twenine\ i^ranite, list jjiei'is from two dilTirent hloeksof the roek u in- ])iepan d, and it was I'oinid that while the several miMsnremeiits made on eaeh test ))ieee aL^ieid anioie^ t heiiiMl'. cs. there was a di^tiliet ilieer^'enee in the elaslii' (on^lanls of tin two ■-peeiiin lis of the rio from \i w ( '.las.jow . the re-^iill-. olitaiiu d In mr i^nienu ii's made upon dil'fereiit pirKof ilusame pri^m wire diseordaiit. for Ka^iiis which will I" poiiiOil out and which were di aleiil upon the ^truelure ■ if the roek I'iflv ll\a' si)ecinH'iisiif rock, iiiiu Inn of -las^, and two of iron wereeiu]i|ii\ ed in this Investigation and e\cr\ conceivalile pieiMulioii uas taken toiiisnri' the attaimiKail of leenrale re -lilts I'lu roek- in all case ■. wen airdr\ . liavint; been allowed to remain in the Ialioi,iior\ for -.e\eral vMcks aftir the\ had heen cut. In fore the me i-nreau nt ■ w< n m iih- In tile ac.-onipaii\in,' tallies the followiii'^ elastic constants arc ijivcn: /■• ^'■lllll';■■s niodnhis, I, , llie ipioiient of the longitudinal stress l>y the liiii,;ilndiiial compression - I'oi'-son's Ratio; this i^ the reci]iroeal eif m. IJ .Modulus of Culiie Compression / ) /■." The reciprocal of ihi- ,;i\. s the deeri i-e in \olmiU' of a cubic inch of the HI III rid for a ] ire-- -.me of i pound ]Hr sipuire inch apjilied on I ver\ -ide C r= Modiiln-. of Shear ( )/■.'. which is the (piotient of tor- 2 Ul . i ' -ioual stre-.s to torsional str.iin m The ratio of loiinilniliiial conipres-iou to lateral rxtcusion per unit of length. il and ni an- measnred directlc; the other cahics arc calculated from till m ■# •• KI.ASTIC CONSTANTS OK RoCKS. 23 Those valircs in the case of each rock are (jiven in the respective tables, expressed in inch and pound units, and tlie results are summarized in a ijeneral table on jiaj^e 6<) The nieasurenienls wire made in llie-c units on account nf the fact (jf the teslini; machine iniploved was jjrailuatid in read pounds I'lir purpn^is i'). In the case of mel il. 1' lisvui's ratio is generally arrived at bv strelchiut; the l)ar and iletermiuiui; llu- value of tlu lone;itudinal extension dividid bv tlu'l.iliTalconiracliou Incase, f rocks the teu^ileslren^'th beini; low and the materials bein;; brittle, it is more couvenient and more accurate to make the determination bv coinpre-.sin,i; a short bar or cohimn, anmooth and also was sli^dillv oiled It was fouml that, these precautions bciui; observed, Ihr expansion at the euils of the column was practicalh- as j;reat as at the center, where the nie.isnre menl was taken, tin- dilTireuees beiuL; so small that no serious discrepancv was iutro<|uci'd In the tallies the first traus'.arsi' line desiijnalis the speci iieil emploxad as li, h, c, or (/ The second line ijives the diameter of the specimen, which is often sliijhth- ditTertiit in the two directions The lenjjth of the column in all cases was about finches, but this is not staled in the table, as the compression is not mei the c:.>e of eacl. siH-eiuun. f.rst for coiupress.on wlun ll,e r,'-M,res n.ullil.lic.l hv four «ive nnllionU.s of an inch, an.lllun for lateral .■M. iMsion uiven .lireetlv in tnillinntl.s of an inch These affonl the .lata lor eak-nlatin-'the constants an,l for ..lotting the curves which accompany iveiv ' In' the hRures for the constants of iron an.l of one or two of the rocks, which arc. the result of n.easureinents which w.r- made at the iK-.nnms ol the inv.sti.^ation. a sliijht correction has been „, ..le,owin« to the tnaccurate cah l.ration of the ,v;tensonuler. which will explain a certain l. ami is used verv extensively in interior decoration U has a splmlerv Irac ture, breakini; almo-t like ;i I,(Kh> ),(X)0 ■,(KK> >,fKX> . \(NK> •,(JfX> , .CKM) . Wi X ,9(i .96 ■<22 1 I.OVIMHM) .278 8..KI.I.IIIXI 4,.V1().(MH» I.ri-^--iini uniiltiplv ri-inliiii;> liv -1 for tinlli'>ntl)>l. I .■l.T.ll t Nt« n^iiiii Miiilli.iiith-j. o O ^4 ,SI -(> 1 1(1 KM 147 ..'., .-40 i\ I I no 14.S lis .S,S hi .1° .'DC J l>i I.S7 ■ ,u 104 7,s ,S1 4 Tlic elastic consttiiits were fmind to be ;is follows: £■ = ii).o7u,(xM); 1 ' o 2-i>\ I) S,.v 1,1.000 : C-4,?^o,o<)o 9000 dSOOO Xy V^ .^ f ^ y V^ X /^ 4 C 8 li '(? 16 21 10 I'll S TRA IN ('}.- lilack Hi-l^ia:! MarliU', Stri-ss-slriiin curvi'S. A plot of till' reiulinss is jjivi-ii in fiijuri' 6, from which it is clcarlv seen that the rock is practically free from hysteresis, and that within the range of pres- sures emplove'l its elasticity is almost perfei! ! represetil'; longitjj.-Una! compression and II lateral extension. 26 AN INVI'STK; \TTc>\ INTil THK wiini: \i\Kiii.i:, i'\wi<\u\, it\i,v A \v!iik>, v.rv liii.- ■;imii!.i1 suvliin.iil.il mirlili' lliiiU-r llir iiiirmsi'Dpi' il isMtn toi()iHi>i"i';i tiio-,:iU-,,tc:iUitii;r;iiii^ In this iii(.s;iic wmif uruiiis :.ri> liirucr lli;iii .itluTs. ImiI llur.- i- no in.il .lilT. nil. .• in tluir r.l;itivf si/is iitid llu- ivir.ii;!' ;i:iin n|- ili. ro.k is iiiiilorin tlir..ii.;li"nl Tlif ;iv«r;ii;f di^nnctir nf i-.,Uiu".rvslaK clnMls i]ii)r>\imal.s,, _■ iiiiii •nuM;niins.>>iiir a^iiinsl mic .iiintli. r aloii- sliarp and nsuallv s(iai.;lil lin. -, Tin re is no tracf of I'olialion in 111.- rock, nor i- tlur.' anv traiv ..f llallmini; urr S lUK- of lln-iii >li nv a fi-u- Iwili laiiulla- A oilor |)ro.-.-s-, |)li.ilo-|-.i|)li ..I a polisli.d siiriai-i- of llic rock (1111)1.01.1 is ^liowii in I'litr II \ and a plw .i.nnioro-rapli of a lliiii vrtimi ,,f llu- roi-k, lakni in ..rdnnr\ li^lil and iiia;nilird -■: dianuUrs. is sli,.uii in Hale- II :> Tlir.-i- ^iHTini.-ns ,,f lIu- rork wm ii->d in uiiasurinii llu- (-laslir toilslaiils, lv>n s,;n.ir'- iirisMi, i.i and !■) and a roiiiKl odiiuin U ) Tw.. s.ls ..f iiuasiin- iiuiils'vvnv mad. on h^ih /. A\h] r. ili.- iiislnnn.nt lu-iii- as usual alllx.-.l to 111, spc-,iin.-iiinU\o p i-ilioii^ al rl-lil aiij.-s l.,,,ii,- aiiot lu-r iil.-a.li ■p.-.-iin.n !n lliis wav liv.- .-oiirilrt,- s.is ..f ni. asur.inn:!-, w.-r.- inadt- Tlu- r.-.nlls an- s.t fnrlh in 111. 1 ilili- on pa-;;i .•;. Ttu- imaii- of 111.- n Mills ..l.l lin.-.l for tin- r.-spr,-tivi- ilastic i-oiislaiits an- as f. ilI.lWs. /•: - S,.,((. o.io; T -u -744; /' 5,.l4'i.: ' -i.lsf.ooo ■ni.-.lilTircii.->-l).-tiv,-.n llu-liii;lu-st andl.iu.-sl d.U-rinin ilioi|s..f /Ms 4.'.).. .00 pounds ^ .^ la... I, ;irr,ii 1 111.11 1'U", 5 FRAlIM ti'iiij.ii'J S;u>^ ^iTiiiii i-ur\t-s I'i-^iiri- 7 shows till- n-snlls .,l)laiiu-.l fr.iin >pi-..iiiu-ii .( in -^'raphic form. I upn-sonts lonnitu.linal onnprc-ssion ami II Uit.nil .-xU-iisi..n Tin- Ins- U-rcsis is-r.al.r than in lli.- cas.- of lUl--;i-ni Ma. k ..r I', nm-ssi-v iiiarbU-, Init is abont llu- sanu- m ani.iuiii as liiai sl„.un i;> l'... Wrmont murbk- and tin- Tri'iUon linicslom- fniin Montrt-al >*f*:^^ *. PMOIOOWAPM Of^ P(.ii ISMFO "i. «F*CF, (NATLHAI. S'ZE' i • d %,itf,ii*. RI.ASTIC CONSTANTS i>F ROtKS '7 No. Arc.i I- n I (iij I "> I f)7 s I >n 1 b b I IIU ■H M A IMIO H J 1 1 1 Ml H I H, IIS.IHK) »7 * .•■•^ ^.,'1 s •'.' ) 114 in *.. IIHI (HHI >. '•iit,lHHl \.\ .11 IK HI * .JIltl'tHI V 1 ;n iHKi f..M.mi'iN\i L<'*ii'ki >jii-.N MrLiillv kKAl'iN'i'^ nv 4 iok MiiM'iNini. fo.i.l III Si lit' ,..UII,I~ r. I.OtKI o ?.»"H> 15 (.!""' :s 1.1 I"' I rn K . 1 IS (l.lXXl 1 ^o 7,(MM( -■Ml ?(,(MK> li.Otxl S,( M M I 7.( N M 1 .M'l 6.()S 5,1 N H 1 I S-' 4.1 1 » 1 1 l> (,<«H1 .^.' .'.(KH) 44 I ,(XX> (1 Slilf irri> -'I'l 1 7' 4,s .'(Kl -MS irui II IS S( II Kl 1 SS .'f>S .'S^ I.AII.k VI. l^XII.SMCN Mri LlltSlHS N... II 6 fc c Si/i . - . 1 lUi 1 016 1 IIU 98S 1 Sulf Siilf ! LuLid in ix.tituNt. /'. U. 1,1 X Ml () 1) 1" IS 17 4S ),(MMI (>2 T.S ;.« •aS . 4.1" X' I'.S 1 10 1(1^ 1 i<> S.lHHl I, ill 14s 14' '7S O.ixxi T'lS I".! 177 217 7,(XH) . .'IH> S/KHt II 1 II M > .... 170 .... .... ^ 177 i ,K ( N H 1 fl.lXXI J'7 5,(XK). . '54 i IS" Iho iNc 4.(K«l ms l.'O 1 1.' i.V (.(««! 70 ,s ^ 75 11:0 2.""" IS 40 IS ,S ) j i,acx>. ■ ,V * 1 ' i 4 i 28 AN INVI'STlGATKiN INTl) Tlli; wiiiTi: m\i;i;m:. \i:;jMii\r, r\iTi:ii stati:> riiis is .1 pmv uliilc iiMihU' iiiili-,liii^iii-!i,il)li I'r.im tin- CiriMra iii:irl)I( ill :i li.iiiil >|HciiiU'ii I'lulir tile iiiicri>>i'n|H' iKo \i n-.r'iil)Ks lliis ruck \rc ivnisidi nil sal'tr to rilv iiiion tlu' Carrara niaiiil.' in nuasuiiiii,' tin- I'lastii- i-oiislanls of this class of rocks. In the |ii:sni of WrnioiU niarlilc cniplox cil. the I'oliation lav ill llic ilircclion of tin lon-cr axis of tlic ])risni It is prol.aldc that this folia tion uonlil not be lonml in all Wrinoiit niarlilcs. but happcniil to be [ircscnt in the specimen procured I'or exaniinalion .\ph.s S Ul.oi 1 1 KiiKitiKliii.il fniiiiirt^'-iMn, ' iiitiltiph icuinii.!- I.\ 4 for inilliiiiithsi I.itfr.il \Il llsHUl lltUoUttls () o 4" I JO KK) ■57 l,vS J i^M .EhMCN' V',HBLt. PHOTCV CROii'ilfM wt Iii'i SH.T o->. '■> 31 D'iV-M'. 'J S r^-.^stC'^ I I I I rf-»\>^»^ Ti'-'^ir mS ni.ASTIC CONSTANTS OF ROCKS. 29 I { A s(|ii:iri' prism iif tlir in;irhU' was i-mpli.vvil in iiuasiiniii;llipil;i .tic i-on- slaiils, aii'l i!h- (k'Uiilc I ri'^ulls ari' ') j.oou : 7000 ZlSOOO 1000 I) 2h\: II 3, y-\ I .txyn C I'M. S. \\.iinitiil liiiilik'. Si rfss-sir;iiii I M \niii.i:. ti;\m;ssi:i;, r\iii;i> static. This i-. a niarhlc kn'iun in tradi- as "I'ink Ti'nni.sMc, " and is Iarj;.h- nst-d I'lir (k-oiiralivi- unrk II lias a hmwnisli pini< coicr and wlii-n polislu-d shows a sDnu'whal niollk-d siirfaco. I'ndtr llu- microscope it is seen to consist of rather lari,'e irrcjjniar shaped and often disliiiell\' roimTi('..\TiiiN INTO Tin; I. nil U.'»W., St., . , - , II M,.,. i I II i; ■'■I \ri.i I "" /, •),lli.,n,i, 1 .«.! Ml /. S.TTn.ODI l,slo,u(ii> ,i.S7i.i"«l l,.l lO.IB" ,.s,;ini.iNM i..MrKi-i"N Mil mil Kiamm.- "\ 4 fn Mii.i-l.'Nriii.. r 1 1 i.M.i 111 1 ,n. M 1 1 J,i«»> o 2ii 1 ^,< M H 1 '>S i ).(.<"' 1(KI i ^,.hh. T V» 1 (.,(M !■ • I'lS ^•l.k■ r. 7 S t ii> I ^i> I in Si.k I 1 1^ I M I --I I ,(1 1 1" 1 lO !0 IMIKAI, ^;\ll.^^l■r^ - Mllll^MII- „ /, I, 'I'll, 'Ml I "" Si.l.- SicU- l.,,.„l ,.1 p. 1111.1- I Mill /■ t.l»"l |,0(K'- -15 1 |1 > I ) 1 ,\ .1 tll.U'Kl .S40,I)IK) h. Sidt P. 170 Jit) 2')0 I' «i «M'. PL4TE IV . I 1 B, ^f,,jloM^r:«oaH«FM OF thin SECriON. (X 27 Di«M,- OBDINiR-T liOHIi MABBIF, Tfr.riES'.Et, ("pink TENNHSSfc'E"!. J I. ■-r. ..,'j*r .*.'^'''^'iiitu'|" pure caUite, siirt lundiiifj; it. I'rtii'.i'i I.tmt^ti'Hf, Montual, Canada. N.. Size. .\rc:i '184 I, 9K4 u c 'J.JM(l.fHK) .nt»0 I y,I»0,tMM) 8,9JU.(HM) (I, ISO. (KM) h 4.Sll.(MHt .(.7II»,(HM1 l,77,S,uim 2,«5 j .2482 I (..I'>n.(MH» I .S.820.(HM) ' ,t,f>4'i.n (inilhiinthH). I.iiuil I in piiutul I.OOO. ^,ooo. J.ooo 4,cx». 5,ooo 6,ooo 7,ooo 8,ooo. Q.OOO. S.ooo. 7,ixx). f>,aoo. 5,ooo. 4,ooo. 3,ooo. 2,000 I.OOO Side V. ,SO f(0 I to ISO SiJe o i|0 '7.S J JO Side t'. ISO Suit i)o ' .\" 170 -,io ,U <).S MK* I.VS 140 ■T.'i ISO :,;: I So -^ f "-o I 111' i^.S i.pi 147 I'l 1 1,5 I 1" l)o IOf> 106 'I.S '1,5 18) j ys '■5 7.5 .'SS 54 54 ! 55 3-' 35 4 5 J .1 BO 120 16(1 ZOO 140 S TRAIN Kiu. 10, — Tri'iitoii linicstoiie. Stress-slrain curves. TOMiCROGRAPH OF Th'N SfCfrON, U ^ .' UAM- OH JINAM TRENTON LIME'^TONE. VONThtAl, CANADA. ^tm I'l \TK- CciNsT.WT Tile .li.li.- r..,i-.t.,nls ,,r i|„- „„k u.Ti- iii.isi,r..l ..ti Iwc rnmiil (■(.Itiiiiiis, fniir iiUNisMH 111, ni , Ml V, tti.- ilo.riipr. -,si,,„ ,,,i,| ,«,. n| l,,|,ril , At.iisi,,n 1„ i,i^^ IIIIHIC 'lllC n-Mllls ;in ,;l\( 11 Ml tllr l.lhlr im [);i;;,. ;j Tlw MSiri-.-, .if ihr h ,iill , oIiIiJihmI ,in ,i^ loll.uvs: >l. _'i >>.i » M ) ; /' *i.i»>-,>( !.fHf),{)(>n, ^ Thi^ cliiririm-.' IhIu.cii iIic lii-lusi mi.l luw.st ri;i is Wk,,,hk The .vsiiits n|- il„. Mi.iMiniii.iil ,,i s,Hriim'ii ,i :irf >li.iuii In -nipliic form liKtirc lo I iipri^iiii-, l..ii-iui,liii,,l o.mprisN|,,ii ;,ii.l II lali r;il ixl.nsi.ni Ml't in THE KLASTIC COWSTANTS OK KOCKS COMPOdliD OF MOKE THAN ONh; MINERAL. AC.D PLUTONIC KOCKS i.K Win;, iiA\i:\M. n\i,v riii.u.ll kiMuii -ruiil.- i^ pile pink III color, aii.I iilHioii-li oiarsrr in )>niin 111 111 tlu' rocks iiisi iliMTilM'!. is M -r.iiiilc .,f nuiiiiiin -r.iiii ;iii.| is v.rv iiiiilonn in cli:ir,u-i,r It rcscinhU s ih.- I.ilv l.ukr -r.niilc closclv in appcanincc, :illlioii',;li it is a little (iiur in i;raiii It is coiiipos.-.! cssciitiallv of ipiarlz an. I ..rtliod.is,-. uitli vcrv siaall pro- portion of liioiiic: ilH. hiotii,. i, in places sonuuli.it allcrcl todiloritc, and llu- orthoclascis in places soiir.wIi.u turbid from tlu- presence of kaolin, Inil the rock may nevecllieless hi' cliaracteri/e,IM«) , 6,H40.(M>O j 6,62(>,l>00 € .978 .75 ^47 2hS 2SltS 2V»,S 4..SJ0.1MM) 4,HH0,tKMt 4.M.S,(MM) 4, M.S. 000 4.470,(HHi 4.H.SO.0(H) 2,6H2,(100 2.9Ht).tHHi 2,780,(MM) 2,7«O.IMM» J,7iO,000 2,700,IKW 4th holes 6.730,000 I 6,620.000 261 2495 4.540.000 i 4.680,000 4,420,000 2,63l,OIK) 2,670,000 | 2,645,000 257 Load (in I pounds). I I.OOO i I 2,0(X) ! i 3,0(xj i 4,ooo ! i 5,ooo ; I 6,(KX> , 7,f>fK) H,CXM} (),0 I 7,(KH.( f»,(KK.) 4,0(K> I ^,rKyc^ j :;,ooo I I.OOO ! No . . , Size . . Areii,. . Side. . . I.OOO -\ooo 3,ooo 4,(X)(). 5,0(X> O.tHlO 7,ootj. S.ooo . 0,000 8,Nt;iri!lilNAL LOMI'KLSSia.S -MlM.TIl'LY Kli.\l>IN ,i « () f><) 7" ll.>- i.V> '7.i I So -\V> J.ll) J NO VKI .iVi .!4-' (.Sil 400 4ln tv> (■"-.S 410 Vli ,((|u -■'*.^ U-' -V!i -'.i4 I 7(1 J114 I JO 1 1.^; ,?"5 ,!",i I.A1I:KAL lixri:NSH)N — MlLLIliMHS, .f7X 2,15 80 ■45 .60 .¥>=. .■il.S ,<'o l(i,S 4i') 4''5 420 ,?o.i .!"5 ^45 245 2.*5 2,!5 978 25.? 225 ityo rlnnt;ilii(IinaU-oiiii)r(>si(in. and, aswlll Ik- seen, al'ur the Im^i cvile nl o.iui.ri-.-i..n the roek .lid not return .inite to its original position, hut thi- iniperleetiou in ela-^tieitv beeonies proijressively smaller ill the sul)sei|iienl loadin-^ till ill tlie fourth eomi)re-.si.in evele the return is ahnii-.t perUet and the !i\>leresis ver\ Mnall l'i,Mire I 1 shows tlie eiirve- obtained l)v i.lotlin- the values seeured from the measiirenunl of the .lasli.- eonslanis of sp.vinun h aflet llie slate of ease ha.l been indiieed, and if the curve for lon-iln.linal eompresMon in Ihis he eoin- with lint sliouii in li.,Miie i ? ihe -real iiiiprovemeill ill the elaslieil> ncsenls loiiijitvidinal com pare; of the roek will al oiiee be -., i n In li'^iire i i. 1 I pres^ioii and II lateral e\leiisi.,n gooo ■ •O 700C - til i ^ 1 Q S0(^0 \ ' / \ 3000 ^ ^ 'K)0 500 600 7O0 800 STRAIN 900 lOOO l-l., \: Sir.- -ir.iiii .■Mi\.-..hl,nTU(l in llie lit^l f.»u evele- "f oMlipri-^iuii frnnl .1 eohuiiii ..I ll,i\en.i -iiiiiu-, ~liowiiiK tlie |in.i;res^ t,.u.iril a st i'e A e.ise. CK \Nlli:, I'ini-KlllCAIl, se. .Tl.ANIl. A pink uraiiite which is ahii..sl in.listiii:iiipnssi..u iiniiltiply nadiuKs l.y 4 for niillifiitlisV I.iitiTul fxttnsion iniilHimths). Lnail (in SUli-. pouuils). ! u. I.CWMI, , 1 o J, . 4" ^,(HKi. . ■s.s 4,(I-',S S.IKK). K'.S (i.mx). . .KM) 7,fMH>. . -■!'> S.tKnt. . J 70 . ,^>" h,IXK) . 2~0 7,()0,?5 J,«X>. . <).') 7,O(30. . 50 I.ooo. . s Sidf. V ,0 .so I JO .'6(1 Si«K'. 4" s.s ■ -'.s 1(10 l')S J-VS jdi. SicU'. So I JO l(.o J(K) J.V) J 70 Side. -4 /eo 160 100 S TRAIN 140 o *a so Imu. i.v — Peterhead granite. Slress-slrain curves. !"f I 38 AN INVESTIOATKIN INTO TUB given by ft are shown in lifiiire i;, <>1" tlu'sc mines, I represents lungitudinal cdinpressidii and II lateral extension Tile averages of the resnlts obtained are as follows: /•-'= 8,2<)5,(KK); 1 = 02112; /' = 4,7<)2,(H)<): (' = ,^,^<)9.ooo The differenee beween the highest and lowest values obtained for/' aniouiits to ,^S().(MM), or if one abnorniallv low deteriiiinatioii be oniillid the differ- ence is I lO.CKK) CRANITIC, I.II.V I.AKi:, rKDVINCi: Ol" NICW IIKINSWICK, CANADA A tvpieal rather coarse grained pink granite I'ndir the microscope it is seen to present the usual liv])idioniorpliic structure of this rock, anil to be composed of biotite. microi)erlliile. and ipiartz as essential const it iieiits A small amount of plagioclase occurs asanaccessorvconstiluent There are also afew minute crystals of a highly ars, in neither of which can twinning be detected One is. ill all ])robabilit\ . orthoclase and the otiuralbite The former is more or less turbid from the presence of alteration products, such as are coinmonly foi'.nd in this mineral species, while thi' latter is clear and fnsh The fjuartz shows 'narked undulatorv extinction as in the case of the \\esterl\ granite. The biotite is fresh and deep brown in color This rock is, as st.iled .d)ove.a typical gr.inite. rather coarse in grain, and which has undergone but verv little alteration A color process photogra])h of a polished surfai-e of lh<' rock is seen in Plate VII A and a ])lioloinicrograph of a thin section magiiilied ,V) dianu'ters and taken bet ween crossed nicols in polarized light, is shown in PlateVIIli Two s()uare jirisnis of the rock were prepared and their elastic constants deteriniiied The results are given in the tiitie on page ,V) The stress straiiicurves given bys])eciiiien i areshown in figure 14 Inthis figure I rep ients longitudinal co..iprission and II lateral extension The means of the results obtained are as follows: £ = 8,i65, = 4,,si7,.SO<); C = ,^,,v'^o,ocx5. The difference between the two determinations of U is only 105,000. 'I N mam ^ •%■.» .^. w. . lil.ASTlC CONSTANTS liF ROCKS 39 fliii'iilf, l.ih Ijike, f'nr.inc- »/ Xru' Hkidku ick, I'liiitiila. Nil (J Size .'•'''i ■f'is Arci 'J2.' /■; I S.JJO.IKKI .._ __ i"' 2 ,| 4,'i7ll,IKIO .' t„l7n,(M)0 C 1W5 I 05 1 ()45 I 8,I(I0,IKM) I .I96S > 4.46.S,(IOO I a — c — - .... 1 .... Lnnwituilitial coiiipri-ssiini iiiiultipK rt>a(lin;:s li% 4 fur milliiinth-^t. I.(i.hI 'in'ixiiiniUi. I I ,Of)») 2,000. ,5,(x» . 4,OCK>. 5, 7,ooo. .H,(JOO . o,ocx> f.ooo. 7.cx)o. A.ooo. ,S,ooo 4,c)oo. ,5,ooo. 2,000. I.OOO. -'7 t Vi> .so o I" ,S() I 2n 'SS Hid - -S .■(.!> -•'IS -M4 170 '):r .so -4 L.itiTj! extt-nsioii iinillioiitlis). .V) .Si| .Si no I I'l I (■ 150 140 20 o 1.5 41 fl2 >i4 K/i 1,^1' i.s:; i.s.s '.S.S i.VS 1 10 7'* 10 lb -J q" SOOO o 3000 L^i ..^ k' K ^ ^ ^ f^ u ^ ._. 4iJ «o ..?£; /6tT joa i-io ^80 STRA IN I'll; 14 — I.ily I. iiki' Granite. Stress-strain curves 4<' AN INVKSTKlATKiN- INTO TIIi: rt CKAMTi:, \VI:sTI:K1.V, KIliiDI- ISI.ANU, INIT i> -TATliS llii> n K-k i- ;i Irt-sh, vnv Inir ^'niiin .1, in:issivf, pale pink i,'raiiiu-. IkIiij; niiirli limr in ^r^ii" "'^i" •'"• "''"'' '-;'-"i''*'^ n hrrid to in iIiIn p.ipiT I'ndir till' mirrosonpr it i^ ., < n to l)f loinpoMtl i-^SfiHially of biotitc, micro iliiw.ortlioi-laNi, .itkI (iiiart/ In aiMilioii to llusfoonstiluiiits a small piT- i-inlaL,'c oi' pla«iodasian.la I'rw ,i;rains of nia'^'ncliti- a'l- priM'iil as aivi-ssorv lon^tilnints. loj,u.tlK.r with a litlU ililoritc and mnscovitc as altiration ]>ro(hnts Tlu tildspar- I'onu tlir ynatir part oi llu- nuk. miiToi-lini' lu'ins l>y fartlu' most ahnndant of iIrm- li allows in a slrikini; nianiur the cliaractcristii- cnKs liatclud twinning of llii-, -.piiits, and is nsnallv (piilr frisli The ortho dasc- in untuimuil individuals is fri(|ni!illv distin.'tlv turbid from the dtvilopmiiit of kaolin, and in a frw l)lai'tsninso)\ itc in larf,'ir individuals lan Ijo si'iu inclosed in it, api)arinllv divilopin« as a secondary i)rodnit at its expense The n lUv nIiows marked undnlitory extinction, and some ,s,'ranis have been so strained that thev fall into areas with dislinetlv different optical orientations The (piartz, instead of occupviuK corners between the feldspar individuals, nsualh occurs as subanjjuUir or more or less ronndeed as a distinctly fresh rock luuch fresher than ijranites usn.dly are A color process photoijraph of the rock isseen in Plate VIII A and a photo- niicroi;raph of a thin section taken between crossed nicols in jxilarized lii,dil and masnilied ;,() dianuters is shown in Plate \'!II n. I'onr test jiiices were used in measuring the elastic constants, viz, two stpiare prisms. II and/), and two round columns, r and ./ Two sets of determinations .veremadcoueachofllK first three specimens, the instrnnieiits being attached I.I different pairs of sides in each e;isi', and four sets of delerminations were made on specimen Jin planes making angles at 45° witti one another Ten determinations of vertical compression and three of lateral extension were thus made the results of which are given in the following table: B ^MOiOMiCROCiMAPH Of- liN SECTION, Ix 30 0t*M.-NCOL3 CROSSED^ GH4Nl'"R, WLStLRl/, ^-iHJlliE ISLAND. \ Kl.ASTIC (.mNsT ANTS oF kocKS 41 Cr.iiilU-. \\,~l,rly.l2 IJMI 'I!') '»M T, s Aril 1 III Ill 7^ 1 TS >mU' ( r r /* ' h..U . M \u l.-s tst llnl /., 7.1M1.IIIHI yi 1011,11 Kt .' 2h III HI " 7)S HHI 7 »,;.( iHiii ■ t ; ^ HMl ,,S7'4,"" 1 « ■ .'1 I'lHt Jll -M 1 1 - -* ^ : II 4.nii,i"«i 1 ij^ii •> Ml 1 ■ ..,l«,„ t >|-' ...n 4/,iin.>i ' .>'.;ii.iB..i ,' 'Kill Ih Ml i.l • TO.IUH) ( IKS , tll'KMH ! •il hi.lis 111 lic.li , Ith li.iU-^ 7 ^^ IMiii 7 1 7m IK"' 7,iSll,(MMt I diIKH) 4.l2lMMHt;4..140.(KMIi 1 > ilSd IIIMI .11)111 l>INl!.Vl>'>l,INKI I I IMS VI V .'VIIWI Ml Mill'. t J,(MM> 1 V> ,;.(KHt t*^ i.iXN-. 1 )■• >.'««> i>. . (t,IMM> - - s 7.(H Ml -■'•S >.I»(MI ,1'tS «>,I«M» .ui S,tKM> .^n» 7,(KKI ' J7<» fi,(MMI . -' 1 S 5,(MH1 Jt M » .(,.Hk. r(ii. ;,iMH» 1 ii> 1 IMHt 2 (MHI } ntH> 4 (HM> S 5 iXM) 4 (KH) .\ o t 1' llMt 1 Jt 1 S -■ r* -' ;s :>K -'7 S .^^!! I'lS I MIKAI |-:xrKN*HlN - MllLlllNUM l.(i:ul ill |>5 ,l'>i 1 15 I 4'> ' V> ! lo i IS a I h i.mn i 929 A" 5" KHl 1-5 1,(1) 1 77 Il)<) -•-•O li)S ■ '..s . 14" ! 177 I IS I ;5 1)1) KX) ■44 4()0 .W).S 140 12 .97.1 .V> .So I.>(> I7S 20f) 1(1.1 I.V) 6o 70 <)<» M> i .^o i 4.5 vr»* 42 AN INVICSTH.ATIOV r.TO THK 1 w The slrrss-Ktrain .•urvi> ..btaima l"r..m spiv imeu .. i.^,. ^ivon in ix- i s Inthis r.«urf.I r.|>r.sints l..nKitli-. of Ha v.iUi.- ■>!il niu'l are as fallows; i: .;,.,, .5.-: . '■■)5. /'-4.V.70-.; ^■"■"■. -■ I'lu- iHlTcRiK. , 1. uvi.M iJic liii,'!i'-t am! !,>wc>l val.KS ..1 'iir <1. " • . ,MU,,ns..| /'„n.,».nm.>, ,/w,..o„lv.s,,,K., Mf ,1,. .tin-. -nns ..iv ,„i 111 ;ivcni-r sniiu-wli.it lowri, mil '• iiuuli.i iijli nsiill- I.RS\ 11; •>rlM-Y. \I.\SSAClirs';TT-, UNITi;.- lATK^ TiK :'.rk is ;. ■ .tiuT o irsc ;;r.;i.icli ' ic n..H.arstol,fav. !U. am.Miul.).. v.r -Uu . -.Innd ,> r,.-- ne 1 lies. ....ustitiu'iils h.-l..,„ I.. i!u alkali ri. !i v.iruti. -. ilu-ir r. ,,hcI r- <■ tainilu- ■,„• s.. opaiiuc ih.il it is .liltkul' In .Ut.rnii auirpr. ise clian.cttr ..,,,K ,.,'irr.«uUrin.lu.p.',n.H' .,0. - >..-^. -n th. ' Isparsram .,,,1, .,1, ,",utralc■ - anmaranc. .vere secured and exar d llm-c -o. ire pnsms, a, c ^4- pr.- -.1 from .•■•nr -specimen a -. srpian- pnsra, b. from the iher %- •^ , «e& ii.lv of ■Sflltl ■' lati. mile IS ••<1 in lUllT ■i ELASTIC CONSTANTS OF ROCKS 43 Granili, Quincy, Maaiichu^ilh, I'liil,'! Slatr I'ir'-t s iH'cinu-n. SditiHl -pi-cinipn. Ka (1 (( r r ,/ 1 ./ /. b Si/e .ystj 1.(171 l,(lf..( OSS 1 1111 '(S4 '14 s »>I2 Area , . 1 (>(> 1 m. 1 111 1 01 ')(,.S lM.(MM) (..(.((l.IMM) (i.Hid.iKMl 7,(MNI,IMm S.l ts (HIM H..t(>ll,(H)0 *..... 18,S IV.'.'i .'1 21 244 ^■i I"*1S 2I>4 n J,47(1.0()(l 2,7ft5.(HK> .»,7l(l,(HH) 2.H(..S.()(«l .t.Kll).(XM) T,7(,<1 IHMI .t.KHl.lWlO 2,7(i(l,(MI(l 4.44I1.I1(H1 2, 74(1, (MM) 2,H(«),(HMf 4. 1'^D.IMMI .(.4l(i.(l(KI 4,72(l,iHK) f .l,4«il.lH)0 ; Ia>ngiti:i>inai C<>.Mi'l(l:-ssl(i.N Side -MuLTii'LV Re Side APINGS HV 4 PI Side R MiLLtoNTllS. Side ,; Side Side Load (in Side Side pounds). 1,000 U. U. P. V. P. u. P. 2,000 60 5" S'' 4.S 50 3,000 1 10 >).'> 1(«) I(X) I(X> 4,fxx> 160 '45 ■III '5" 142 ■i,OlX) 2(X) ■ 85 206 ,5 355 H,ooo ,?^> MS .v.s 340 314 7,000 282 280 2(K> 298 1 .... 274 6,000 HS 2.VS 2'l( ) 2.150 .... .... 235 5,000 -'o.i ■ '(.S 210 210 I()0 1 4,000 162 140 .'.,s If'.S 145 ^,000 112 ()0 1 in ■■5 .... 1 .... 100 2,000 6., 1" 60 .... to .... 50 1,000 4 ,s 5 ° .S 5 3 5 Lateral HXTESSION - J lIlLLIONTlIS. rst specimtn. K-t.-iiiicn. a .9(0 d 1 nil 1 Scinini s 1 No.. . ■■-'1 b 892 b .94S -■■ ■ -- — 1 1,000 2S 3^ 24 20 ' .^.o*x» 4,(HM» S,5 70 SI 45 210 CJO H5 I4S 17.S 200 24" 20.S 180 I.S.S 1 10 l.so IiK> 2.iO 270 -•75 240 i<»5 "55 7 ' >75 153 i 127 i"3 KM) I-VS 155 I Ml 219 192 164 .*^ (KM) .S.fXM) '34 j .^.(NM* i 4,0(X) 'Oi 95 12U 77 88 1 ,1,000 2,000 1,000 60 75 50 50 j 30 40 35 25 ,5 5 10 2 3 44 AN IN\ i:sriC.\T|il\ INlcl Tin: i spi'ciiiun. uliii'li was ratlitr ihirkiT in i-olur '{'\\n sirii's of cntnprcssiim (liti riiiiiialinus urn- ninli' nii t;uli nf llusi- [iiiMiis. I{ij;lit siricsof nuasiin iiKiits ui II' t!iii> iiiadi- 111' MTtical oniipris^inii ami li\ i' of laUral t'NU'ii>iiiii III llic sii-(iii(l spciiauii iif '111' rin'k, /' u.is fdiiiid In luivc a ratliir liii;lu'r valm- lliaii in lli'.' casi nf llu lir-l "-pi-ciiiuii, alllioiiHli prism ■/, fill fioni tin- first iipt'ciini'ii, ap])niaclu's this valiu' dosdv Tlii' iliiplicati' ik'tiriiiinatiiiiis iiuuk- iiiu-ai'li 'i\ tln' prisms a'^ri'f vcrv cliisi.'l\ uilli oiu' anntlirr Tho rt'Siilts nf till- im'asiin.'iiu Ills arr ,i;i\rii in llu- talili'uii paj;i' 44 riif avi'raijf of IIk' valius nblaiiR-d in tlii' case (if llie first spccinuii are as f(ill.iu>: /'. '1.7 |.7.'i'> >; ■' -I) -MS-'; /' - ;.')>!4.i)i)<): C -- -;,7Mi.6ducts In addition to orlhoclase, the rock a' \ KI.ASTIC CONSTANTS OF ROCKS 45 tains a coiisidcralilc pcroontaKc of tiiicrnclim- and of a plaRioclaso of tlic soda linu' sirics Tlii' mica is nla lively more al)'.indaiit lliaii in llir oilier granites dcscrilHcl in the prcsiiil ])ai)er 'I'lie (jiiart/ allows marked undii- latorv extinction and in some cases even an incipient jjranulation Tlie si/e of the jjrain of this rock is intermediate between that of the \\'csterl\- and tlie other granites, which latter are themselves ahont ecpiallv coarse The elastic constants were measured on three stpiare prisms, four sets of measurements of verlicai eoni])ression and three of lateral extension being made The results are given in the following table: (iriinili, Shinsli-ail, /'ruMiic i>/ Oiiihn, Ciiiiilila. No a Sue. , Area .9S4 .M . 9(W» Side U 6.000.000 » .253 I) 4.040.1)00 c 2..i95,IH«. b \ h \ 1 ,(HS 1 .(«X)9 I .Ol.-i I .(MM)*>H 1 (110 (• S.d.tO.OOO .251 .?..i60,000 2.015.000 I lllr, ;'. 5.540.000 .282 4.250,0mpresston (multiply readinfs by 4 for millionths). I-oad (in pounds). i,0()n 2,ooo 70 ,l,rx)(> i,vs .4 ,(XX1 2(X» sj.rKMI -,sn f).(XX> .V'> 7,(KK> y.o S,(XX1 41s , »),(KM1 460 S.OOO 7,f»(i(i 6,rKx> 4,f)no 2-M> ,!,<»< K) 160 .\(XK) ()<> I.fXX) in mo J so .|')o tt" .w ISO '.S.S 2(K1 2»0 iq.s 2.tfi 280 2,15 ^OS ,1,VS 27.'i .vs.s 400 120 .t-'o .M" -''l.l 27.S .'■)<) 2<1,S 2.(0 25(1 2.<0 LSI) 100 201) M" i,;o if^iO <»" 70 1 10 4.S .;n .SO ~5 -., ■5 The averages of tlie results obtained are as follows : /; = 5,6,Ss,oo(); " =0 2,sH5; /. =^ .;,i;4i>. <'<><>; ( = 2,258,700. This rock, as will lie seen, has a low modnltisof elasticity, and likeother rocks of which this is true, the lateral extension varies considerably in different specimens and the rock does not come readily to a state of ease. This is seen dB 46 AN INVI'STir.ATION INTO THK fr..„, f.Kure .7, ^^l.u•l. slunvs the results ol.udncl in tlie first tl,r.. ovc-U-s --f , ,n^si„„ „K..U. upon a clunn, ot .h. rock llu hvM.ros.s sl,n.„ ,s \Ju ,n,,u. .]K,n in .1,. ..s. of :nn of ,„.■ o,l,.r cr.^ s,:.Ihnc. rocU .xan,in.d.n,d.v.„ after repeated strc-ssn,,. his l,vs,.vs,s.l..,on..r..ln^^^^^ does not disappear, as is seen fro.n the curve o, the results ohta ..ed f n cohuun „ .dveu in ll.nre ,8. In this f,«ure 1 represents lon^.trnhnal co .^^ press.ou and II lateral esteusiou The variation iu the results ol.tan.ed for /; aeeordinuK i> hi;;h. auiountin- to S.,o,...k) 9000 1000 200 300 400 500 600 STRAIN 70O 800 ,.■„ , - Stress-s,n,i.. cnrves .,l,t;,me| 111 .It Mjx. ,ouU iiiili.il 1111(1. tl Iliad iMT sq fiiiluri t.iilurt-. I inclt. ' 1 J S'l liy .'.^i liv .','•(. 'I =;-•- ( /.' -• t; li\ .' )(i li> .■ 5-' '' ' Ksscxitr. < 1 -■ (7 t'v j (i> liv .■ ,j (. f Mt. JiihiiMiii.fJtiilm- I /; .'..(N liv .• ^1. Iiy _• s<' '' ;■ ■^ [It.cxKi I7.;i(i I ?_(,.t i.^.ii.'ii ■.-i.',>i J,?..V)0 1 I ;.'^.m»i .'<• ■ HI 1 t^,7iK) 2J.)'>5. 1.^1, (xKi -'j.rii i'i7,7(^» 26.,;a4 Granite, ( 1 .• fn liv _• mi li> -•, ^.' '• ,S-'> i SI15 i|.'.7i« Stanstiad, IJiii-ln-i- . \ /; .'.5(1 l.v .'.55 liv .>.47 d. ,s.'> i sii NN..iix «)J,7(K> 14.206 Si;. 300 13,526 ■; latter is taken in oniinary liijlit and inaKniliid -•; ilianutiTs Tlic fact that this photoinicrot^raph is takin in (irdinary lij,'ht, uhilt- tliosi' of ntliiT granites just discriljfd arc taki-n bitwecii im^si-d nicols, ^'iyi-s this rock an appear ance of being coarsirin grain than il really is, owing to the honndaries of the colorless constituents being ill delined The >ize of the grain may be seen, however, by comparing the diniensitmsof theiron magnesia constituents (M the rocks or still better by com])arit!g the gi ain of the several rocks as shown in the ])hotographs of the polished surfaces ao I20 ISO zoo no zao 3zo ^to .1 TRAIN I'"|(i. iS. — Staiistead (iraiiite. Stress-straiti curves NEPHELINF. SYENITE NHPIIEI.INR SVKMTl!, COKroKATION ol'ARRV. M( iNTKK Al,, CANADA This is a typical nephelinc syenite which forms a portion of Mount Royal, one of the .VIontcregian Hills ami which cuts an e;irlier intrusion of esse.xite like that to he described later from Mount Johnson It is a hard and tough rock used as road metal on the streets of the city of Montreal. It is rather light gray in color and often shows locally a more I \N INVKSTir.ATIDN INTO THK is also ,,ns.n, in „o. -K-ou.wUral.l. '""'"' ;".^.„„,„ ,,- UKMUon-r Uss Q av ■"' STRAIN Z80 fl.,,a. s,n,cu.re a,.,.v. nK.n.i,.,,... r.-suhs As«^t.c, with J^^ ;;^;«;;.-,;; ncplHlinc in r.alur s.nall a.noun,, an.l also "-■'"' ;;'f^,„,,,,, ,„ :£, Uav. „v..naU.„ ..,..., ... .,ui.. i^ ^f i;;;;' -[^^.t XI .. an.. v., .lor process ,.hoto>,ra,,l. of a r-''^- ^^'^^''\ '^ ^"" '" , I.,, ,, , i,,„. a photon 'icrograph taken bctwc.-n crov. • mcols and ntagn.tu.l ,, . .hant tiers IS shown in Plate XI u. TOMCROURAPh Ot ■-■<:U SECnON, (x 30 D^AV.- NXOl.^ CROSSED^ NfcPHELiNt SYFNirr, V ;NTftfAL, CANADA, i KI.ASTIC CONSTANTS OP RDCKS 40 Tw.i S.IS of Ml. iMir.uuiits lor Ihf ,l,isli.-innstimts wire tna.I.' ..n a >iiiKle s<|iiaro |.ii>M.o|- tlir VK-k. Msiii- lir-toiu' mI n| liioi-s ;in.l tli.n iIicoHkt The rt'sulls art M-t loiili in ilu h.ll.nMii.; l.iMc; \,l-li.!iti' '^l.«'^ \l„iilr,.ll. I ilml.lil. II il \r..i ft . I 1 .Ml 1 r..ii 1 'I. Ml 1. lis mill i o ■('» i>, isii itoo ( \ ; s I III! 1 I l.liIluilUllilLlli !■ -11.11 IMlllllliK fl "l"l>.'- I.\ 1 ft.r iiiilli..iitlt> . I 1^1. Ill .III IMUlIll].- 4.I' S.I 'i.i Mill' -.fHKl ,OtMl .fMXl. ,ooo ,(XXJ ,0 .l)*K1 I'lS -',vt Id 14" loo 7n 'IS I7*> -'"5 :!4.S -7S -MO ^lo 17" 140 11 I.ittrr.il i-xtcnsiiin iniilli..iilli... I l"S I.i" Ifio i.>^=; -•Id HI" i''5 t^s 1 10 «S S.S ,1" - .) Si 1 10 1 IS ITS .'(to - (" J"0 ISO 1S5 1-5 '»S ''S .ss 5 The stress St n in curves ohliiiu .1 in the first si'l of itiea^urements are seen i„ Il , ,, ,, 4S). in whieh ! represents lonsitudinal coiupresMon and II -hows laural extension An exaniiiuition of these will show that the rock . Uiihits very little hvsteresis, the v.ilius for l(m«ilii.litial compression fiivijig a straight line, a> in the case of wroni;1it iron and other metals The averages of the results obtained are as follows : /•;-<). I, w. .SIX'; "-oj.s*). /'=- f>,-\^7..s™>; ("- ,v6(,s.'KX) Til. (iilTerencesliet ween the iwoiUl.nninalions for the value of /^ amounted to only 2.\^.i«K. piuin.ls As will he ol. rved, the value of D for this rock is much higher than that for any of the granites. so AN IWESTir.ATION INTO THK ! I' BASIC PLUTONIC KOCKS WMKTII'isl II., \i:\v l,l.\sr.i,u, I'KiiMMi; ill; >ili;iPi:c, CANADA I 111-. rmV, In III. Ill till i;n.il Miiiiii :iinirtlii.sii( iiilrii>iiiii wliiili (iciiipiis ail .ircii ipf i,iH> si|ii;irc luilis mi ilii- luiriUr ul the I.MitrinliHii iinil^ixis, M.iM. (,) niilis iii.nli III till' ,itv nf .Mmilnul* Tlic ~|«iiimii i-, fmm llif iiiaryiii nf llic iiilrii-.il III. «lur<- llic miss Ii.is iiiiiUijjnm i Alciisixt- iiiiivciiiciit 111 ilu iwliiri' III rorklliiu whiili iiium nuin li.is tutu linnitilit about liy |)i -lire.' ixcrti'il iipiiii liic i-.irlli's iriisl in tliis distriii Tin. fluw has lak. II [ilicc tliriMii;li a j,'r niiilaliuii ul' tin. Luiicr iiidix iduals risf in a riidi' liandini; in t\w rmk This Kraiiiilaliiiii has iinl. ImwcviT. hi'i'ii a(.'oiiii[)aiiii'd liv aii\' Inss uf slriiij;th, for thtrmk is a hard and i \.tiMliiii;l\ Iniiijli oiic. hiiiij; used as paving sets in siiim- of the strit ts in the city of Mcmtrral, wliiff thiTt- is an fsi«ciallv heavy trallic Most of the Morin intrusion consists almost exchisivel\ nt plagioclase felilspar. whieli lias the eoiiiposition of lahradorite. with onlv a \er\ snuill [Hirlionof iron iiiai,'iiesi;i eonstituiiits, and lieiue the roek is projierly termed "aiiorlhosile " The speeinun used for the detirmination ui die elaslie constants of tlie rock wa- t iit frmii a paviiii,' set wliich was richer tlian usual in the iron inaj^nisi;! i imslitmiils .md whirli luiiseipienlly mi>;ht he more properly referred to as j,'al)hro, althoinjli il is iiii reha part of the Miorlhosile locally 1: 'ler in I hese darker constituents It li is u riideU streaked structure, as Men III the accoiiipaiiviiv;; color process photo^'raph of a polished specimen Plate. \n \ This si riicture crossed the vertical face of the test piece diag- onally, SI, that if llurc he a \ariation in the \.iliies of ihe elastic constants dependent on the direction of the streaking, the readings attained will rejiresent a mean, or at aiiv rate an intermediate value ruder the microscope the rock is seen tobe con.jxised chieliv of pla,i;iocl., o, associated with which is a pale jjreen aiifjite, a deep E;reen hornbluMle, with a feu grains of ihiienite, and an occasional individual nf hyper-t iiene, now altered to serpentine, and of pvrite The plaijioclase forms a mosaic of well twinned grains. Ihrough which are distributnl the other coiistitiieiils in little irregular shaped grains of rounded or siibnnmded oulliiie Of these the augite in the most abundant With the exception of the alteration whieli haso\ crtaken the few hypersthene grains *.-\il:iins, F, [), Kuj.iirt mi Ihe Ociiliii,'viif ;i ruriinnuf ilie l.anrcnliaii .\r':i Ivingtothc Norlli iif the island of Montreal. Annual Report of the Geological Survey of Canada, Part J, vol. VIII, lSi/j, p in. ED S■.■^^FACf . (NAT . »4 . ^. .' ^ ■ ■ 4 / WBT K 1, J "^ 1 1ll i- 'lUrnV.rrROf'.SAPH QC ■ -, N section. (K 3Q DiAV.-NtCOLS CRuSSt:;! ' I ELASTIC CONSTANTS OF ROCKS. 5« the'rock is absolutely fresh. The stnicture is allotriomorphic, and there is a teiulenev to a panilUl arrangeinetit among the grains of the darker con- stituents .■\ phi>t(iTuier(i.jrai)li of a thin secliim of the roek taken between erossed nieols in polarized light and niagnilied .v)diaineters is shown in Plate XII n The elastie constants were determined on a scpiare prism of the roek. and as the rock is very strong, the loading was carried up to i.s.'xxj pounds instead of <),o ,000 ,000 ,ocm ,000 ,000 ,000 SI 101 I S7 264 31** 373 3J-H ^7^ J -'7 '73 llf> 5» 3 .99 ■ .99 981 1 1 ,9M).(MK) .262 8,368,000 4,750,000 I.4ttitntudinal coinprfssinn Lateral Iniulliplv exlinsiiin readiiiKs by 4 . (millionlhs). , fori.ullitmths). 81 ^14 .'60 j56 ■7') '3.'i 00 44 o The averages of the values found are as follows ; £=11,960,000; -7 = 0.262; D= 8,368,cxx); t"= 4,750,000. The stress-strain car\cs of the rock arc shown in figure 20, in which I represents longitudinal compression and II lateral extension 5i AM iNvi;sTi(;.\ri<>N' into tiii; icssicxiTi:, 'MINT J'il!N> i\. I'KilVIXCi; i|.- i)ri:ilICC. CANADA •U : This is a ratluTOKirsi' -raimd rssoxit.' frmn a qiiarrvcii the sln,K. ,,f Mnmt John..,,, vvhich i> a tvpu-al InilU' arisin,- In,,,, the I'aU-ozoic ,.la,n In ihc- s.mth of the citv of Montreal an.i f..r,iii,ii; one of the Monlere-,an H.lls The rook is massive an.l nniforn, in eharaeter and .la,k ^rav „■ eolor, and is extensively used as a building' stone and also for nionnnients The iron ,n iK-nesia eonMilnenls are represent.d l.va violet an-ite.a deep brown hornblende, and a biotite also verv (U ep bmvvn in eolor.the hrst n>en tioned beinu the n„.st abundant an.l all three bein.; fre.iuentlv ,ut„nately inter-rown The liulU eolored e.mstitnenls are pIa',doelas,' and nephehne. the former btinu n.ore abundant than the latl.r. uhieh often oe.urs as.neh, sions in the feldspar Mllmni^'h p..|>-MillKlie twinuin- is Ire.p.enth seen in ,he feldspar, a eonsi.lerable pioporlion of i, i> uutwinne.l A separat,..,, bv Thonlefssoh,f:on, h.wever. .hou>lliat the fel.lspar is all plas.oelase there lei,,),' "" orthoelase in the roek Magnetite in the forn, ol s.uall er.iusan.lapatit. in rather larue.well delin. ,1 ervstalsare present '"n"'s.d- erable u,nount asaeees-orv enuslituents Tne roek is perfeetlv Iresh I he eonstituentsof tin. rork, and >n,,re e-peeiallv the fel.lspar, have a tendeney .A.l;a,i^, I- II 11- M-i't,i,i.u, Ihll.. .1 l.-:n,:,.l,an IVI .oi;,.,,l,icMl Province. JounMl.!(l..irv, Apill Miv. 1 CM ni.ASTIC CONSTANTS OF ROCKS 53 ' No. . Size I Afea E... Eisexik, Mount John.um. Province oj Quebec, Canada a a 975 V)l .in .9'»2 975 «92 .9025 ■ .9H25 971 1 007 .966 .966 9.580.000 6.(40.000 3,781.000 9.SIIO,000 .266} 6,840.000 3,781,000 .966 •ifim.ooo 2663 6,840,000 3 781,000 886 9,56.5,000 2363 6,060,000 3.860.000 978 10.430.000 2563 7.170.000 4,160.000 LONGITUDINAI. COMPRESSION— Ml'LTlILV REAHlNCiS BY 4 FO» M1I.I.IONTBS Load (in pounds). 000 , OOCI. . ,000. 000, . CXIO. . ,(X)0. . ,000. . ,000 . OCX}. ,000 000 OCX) ,OCXl. .000 (.XX> ,CXXJ ,cxx>. - I 2'; OT ()0 M i)."; ICX) 1,11 '.Vi ifj.S \<,n 20Ci 200 2,?K 240 270 270 2ib 2.1.S 100 2<«) l6 IllO 68 '>.s ,10 .(O — 1 -4 -4 (>.\ 100 1 '•>•> U)(> 2.t'> 2flfi -V(3 JIJO I'l.S 1.12 ux> 6f) 31 -.S I.ATKRAI. ICXTKNSION— MlLLlONTHS. O ,1o 6(> ICK) 140 l.SO 21.S 2fl() 2'l.5 2f)0 220 140 no 70 2S -5 No... Size a .975 h .9825 Loud tin pounds). ,IHK» .IK 10 . ,tMKi. ,000. r,(MK> . (KXI. ,tKX». (MM). 000. [.000. l.oou 27 25 .vs 4.S !(2 70 no 95 i.tfc 1.10 i()i I. so :HH 1X0 22s 220 IQ.S l.So ■72 I.S.'i 146 i,?5 118 100 c)0 75 4') 45 y> 20 5 o 28 50 <*o 115 1,50 l8o 210 245 210 ISO I. so 115 <)0 50 e .971 195 54 AN INVESTIGATION INTO THE toassunu- a more lath-shapcd devi-lopnicnt than in the case of the granites. Tlie laths nniniiigas they (In in all ilireeticms thrcush the roek, iimbahly have a tendency to l)in.ix>; '7=^ () j.sS.^; /' (.,7,s<'.oa Tliis rook Idriiis ;i hxTfiv dyke* iiittiiii; the aiiorlliusitc from the locality (li'Scribi'd ahovo It is a rock wliu h isdarkcr iiioolnr iliaii llic aiiortlio>itc. owiii); toa miicli liij,'lirr content of iron-maijiusia coiistitiuiits, out which, like that rock, is {|iiarried and nsed for pavinjj sets I'nder the ndcroscope this rock is seen to differ entlrelv in structure from 'he other igneous rocks eXiiiiiiiicd It is composed of a cirv pale green auj.;- ile, a rh ) nbic pvrixeiie of the same color, and pl,ii;iocl;-.se, the two former minerals beinj^ present in ahont eipial amount, and the plajjioclase tint forni- ini; more than al)onl one (piarter of the rock: ther- is also present a small amount of u pale Kreeii spinel. The rock is seen to liave been crushed in a most extraordinary niai:ner anil to present a most striking cataclastic structure The plagioelasc occurs in .groups of indis-iduals which are well twinned, and are freqnentlv verv unicli bent and twisted Hine individual being bent through an angle of ds^ Tlie mineral is also filled with very minute roimded inclusions, which give to it a green color These ])lagioelase grains, (piile irregular in form, lie embedded in a mass of little irregular shaped grains of aiigite and rhombic pvroxene These vary somewhat in size The two pyroxenes are sometimes intitnatelv intermixed and at other times sei)aratL(l into groups of grains of their respective species, which are distinguished from one another bv the ditTerent values of their dout)le refraction and by the fact that one has parallel and the other inclined extinction The spinel is associated with this mimitelv granulated pyroxene The original structure of the rock has been entireiv broken down, and it now presents an assemblage of grains of the minerals varving in size and differing in arrangement from place loplace in theslide. The pyroxenes arc granulated, the plagioelase twisted, and the whole presents a perfect cataclas. tic appearance, differing entirely in this respect from that of the anorthosite just described. This cataclastic structure is combined in some specimens of the rock with a more or less distinct parallel arrangement of the constit- uent minerals, although this is not very distinct in the specimen shown in the color-process photograph of a polished surface (Plate XIV a) To this irregularity in structure may be attributed the irregularities in the elastic deportment of the rock A photomicrograph of a lli.- section of the rock taken between crossed nicols in polarized light and magnified 30 diameters is given in Plate XIV b It is found that satisfactory measurements of t he elastic onnsiants could not be made in the case of this rock, the same specimen giving a great variation *Adams K D. Op. cit., p. 121. L ,N INVKSTir.ATION INTO THE ,,r variation i-tl.o„t,l,..nc.,lvNUh.ht" ,„,,ui,.,u.l, .1 .s -v-t Uie follovviiiK l;>W'^' li L I,,i..il in i."UmU I,1«KI 4."' 5,(x«> (»,(i*»' > ( M K I 5" I vS I do l.|0 >4i> I lo O I t -'*! 47 S't 7'> 'U I :>) L.tirul .-xK-n^i"" 1 imilUitnlli-ii ! s.t ,s.s ,!.S hi 4S ,\.S -\S I.S ! »' r*s' ,,,:,.,,.„.. •on rin.l it. tl..'..tlH'- '- V«M«"' '" As will IH. ..en. /Mnnn.-.as. '• ■ ;; „„ ,..,„u,,„- ,1k nu.i- „n.nu.n. of l>r,-,m /■ ar. ..vc,.. |u„! ^^ ^ ^^ ^^^^,_^^^ ,on,iu,.linal o,nn..a:>.n.lv 1ml. Lv^u-n^.s "'";_;;;.,.„,.,,„ ,„„aUv ,o.,.U-urve. „ ,'.,„iu. probable llKU both arc .orrcU KI.ASTIC CONSTANTS oK koCKS S7 In tin- table RivitiR a siiimiiary i>f results (scf page 60), tin- values (;iveii fcir this r(K-k repres<-iil the tman of llusi- IukIiIv diverijeiit readings ami sllimld be useil <>i)ly in the liRht of the explaiiatinii 1,'ivcii above. 1000 40 i'CX} no so im ISO S TKJIIN Ku; -'-' ("ptirii ('i.ililirii, New CiliisKow. Stress train iiirvrs. UUIVINIC l>IAllSSi;. NKAK Slimt k\. I'RUVIN-Ci; UK ONTARIO, CANADA This is a verv tvpiial frish olivine diabase, which occurs in the form of a larKecHke, ciittinj;roeksof HuronianaKe jiist northwest of the Murray Mine near Sndbiirv It is one of a number of similar diabase dyk»s, which occur in this district of yre^it nickel bearing; ),',d)bro iiitriisions It is rather coarse in jjiain for a diabase, but nevertheless much liner in jjrain than any of the granites described in this paper, except that from Westerly. Rhode Island, these two rocks beiuR approximately e(|iial in coarseness of Krain, iilthonsh dilTerini; entirelv in structure The rock is composetl of violet brown au);ite, pale j,'rteu olivini', colorless i)laj,'ioclase, and opa . 2,000 ,^,000. 4, (XX) ,S,oo" 6,(XX)- 7,000 H.ooo. «),(XX>. 7, I, coo Side U. Side Side Side 25 50 7.S 102 i-'7 ■ .S,i 220 19(3 ',S7 1 V> o 25 51 7'> 10 ( 130 155 i«7 2>7 I')0 '.s7 1 U ins .So .14 2- i 25 52 .So i"5 i.Vi >5J IMJ ii5 i«5 ■ 55 1 U li'.i So .V> -'5 o 26 5» »5 no 140 169 SOS ^iS 200 1 7,s > ts I 10 so SI Side ' Side , Side 1 V. 25 .50 75 100 50 75 100 25 49 74 98 124 148 17.? ■25 1,-0 i-,o 124 146 16K 200 I9H 1'I4 l(iK 147 1 12.S ! 99 7.S 5" o ! 3^ jV.CHOO-t-^H Of TMirj SECT ON, U 2! DAV.-O'-OiNiU- iGhTI .■i UINF IrARASE, SIID3URV, CANADA- 5: '. \ I I! ELASTIC CONSTANTS OF ROCKS. Olivine Diabase, Sudbury, Province of Ontario, CoBoda -Continued. 59 : No a 1 " h 6 ' c c 1 Siic .981 .981 983 983 .>83 .983 Area ... .756 736 1 .738 i .738 758 .758 E 13,2,'iO.OOO 1.1.780. OOU ' 14,020,000 , 14,320,000 14,020,000 14,320,000 V 286.5 281 291 .277 .291 283 D c ..... . 1 I0.J40,()0() 5,160,{XX) 10,460,000 5,.18O,00O 11. 170,000 10,720,000 1 3.620.000 11,170,000 5,430,000 11,000.000 3,430,000 5,380,000 LuNOITUUINA L CoMPKEsaioN —Multiply Readings by 4 FUR MiLLIONTHS. Load (in Side Side Side Side Side Side oounds). I.OOO. . U. ''• U. P. U. P. ! 2,ooo. .10 .10 ,?o ! 2.S 30 ,1" 3,ooo . 60 60 60 ! s-"* 60 6n 4,o'5 1 10 120 'I.S 6,000 I5.S i.SO >4.'> 140 '.SO '4.S 7,000. . 185 180 >7.S 170 180 '75 8,000. . 22,S 215 210 200 210 ^05 9,000 . 2. SO 240 2.1 .S 2. 30 23.S 230 8,000 . 220 210 2 m 2(X) 210 205 7,000. . 190 i«.S 170 ■7S I. So '75 6,000 16.S i.S.S 14.S 140 IS.. '45 5.000. 1,10 12.S IIS ",S 120 "5 4,000 105 100 8.S o.s 90 85 3,0(X> -^ 60 .s.s .s.s do 60 2,(K)<» . 4.") ^.s 3" ^5 30 3" 1,000 . i,S " Lateral Extension — MaLIONTHS. No ! a a ft 983 b c 983 c Siie .981 .981 983 .983 Load (in ! Side Side Side Side Side Side pounds), j U. P V. P. I.'. P. 1,000. .1 2,000. .1 78 28 28 25 21 27 3,000. . .'54 .SI .S4 40 49 53 4,o . 1 1 I 1 0.1 1 10 100 K'S 107 6,000 .1 140 l.^o 1 I. IS I 22 131 '.V ! 7,o(X).. 169 i.sA : l(,4 149 1()<> 'S4 1 S, . 1 98 1 8,? lifi I 72 185 '83 9,fXjo 2^,S 1 210 1 -'I.S 21 K1 2IS 205 H,ooo 200 I.'*'; 1 1 1 S'l 170 166 6.(K^( 1 U 1 i=i 1 1(1 I 25 1 IS '.V> 3. ^f^^ „;,„ those vuMe-l hv anv other rock of the senes exanune.l It. the s.x ;;.Wn, nu.asurc:.nents earrie.l out on the first three M^---; ^ ,i,Te eneebeuveenthe highest an.l lowest vah.es for P a.nounte, t S. V.ooo ' ,„.ls, while o„ the four uu.asure,neu,s nuule on speeunen ./ tlur. .s a r iiher L'reiter .liffereuee amounting to I'^.iioo pounds Th^ a^nisllf the .leternnnations uK.le on each of these colun.ns are as follows: _. /. I ■ ■ d Average E M, 5 15.000 io,4,ooo 14.170,000 ' 10,1)45.000 I 1 \-cifyoo '. ii,oS.s,ooo • 017,750 io,07(",ooo 13,763,1X7 j 10,626,500 o.2!5.oo<> 1 0.2H12 I 5.1S5.0OO 0.2840 i 5,36,1.750 The stress-Strain curves siven bv a specinien this rock are shown in fignre . , As^n,: ;;;« from these curves, in its approach to perfect elasticity the rock isconipural)le to plate sjlass. 80 120 '*" .I-ir,. -SiuUmiy Diab;ise. Stress strain curves. SANUSTONI!, ei.i:Vi:i.ANl>. OIll«l. t'NITKD STATES. This is a fine an 1 even ,raine,l vellowish san-lstone used verv extensivel v for hui ,.' purp .ses l-he hed.lin, is marked by a sh.ht varution in colo b 1 T^e It .eds The prism of the rock used in determining its ekst.c on US was cut from a siuK-e bed of uniform character and color, and was taken in the plane of the beddin, A color-process photograph of a smooth surface of the rock is shown in I'late X\'I a . ... . . Uuer the microscope it is seen to be a typical highlv feldspathic sandstone. The constituent minerals arc present in grains which arc. approximately V' ^' WAPM OF TMtN SFCTiON, ', X ;; ,' D' AM - C'i 0' N AK > I i -.iV/ V-*k'i^'«?^- .-.■«•- ".tarvMi^ttwaiaQrrh? '..^jJf^Latr ELASTIC CONSTAN'S OF ROCKS 61 uniform in size and of rmlfly rounded or suhaiiRular outline The <|uarlz >;rains are clear and fresh; the feldspar indiviiliials. which are abtnulant, on the other hand, are for the most part in an advanced sta^eof alteration, hi inij alvvavs turbid and in most easeS(|uileopa(pie. from the presence of alleraliiui products .Some few jjrains of comparali\ elv tmaltericl planioclase are. how ever, present, and scaltered IhrouKh the rock there is a consideral)le amount of hydrated oxide of iron, which often lies between the Rraiiis, furmiiiK a cement The rock, however, also contains a not inconsiderable .imount of calcite. which causes it to effervesce slishtlv when treated with dilute hvdro- chloricaeid. and which is also seen ' ■ lie between the clastic grains also form- ing a cement, often in the form ol individuals of a size comparal)le to those of the other minerals The rock, however, is not a ervstalline rock, but a typical clastic one There is not a continuous crystalline web or mosaic. Init a mass of roundedorsub ansular strains which are in part cemented together as above described, but in part are separated by minute open spaces. It is to be expected, therefore, that the rock will show serious defects in elasticity, as proves to be the case when attempt is made to determine its elastic constants A pholomicroj;raph of the rock taken in ordinary light and multiplied 27 diameters is shown in Plate XVI n A square prism of the rock was employed, and it was f(mnd to be dangerous to submit it to a load of over 4.(kx) pounds, the crushing weight of the rock being much lower than that of the other rocks, which are crystalline in texture The figures obtained are given in the following table: Sandstone, Clenlanii. Ohio, Umtfil Slitles. I Size D . C . ill ponnilsi. I,CXX>. 4,fKN). _1.00(J. i.OOO. 1 000. i.ooox 1.02s 1.023 2,290,000 .29 1,816.000 gSD.OOO I,i>li^ituclin;it ctiiiipris^inn (iiiitllipK rf;i(llii^:'- \>\ 4 for iiiiiliiiinhsi. I. Si 2S,S 4 it. 1.000 — I.aUT.il iiilliotith^i. '73 63 AN INVESTIGATION INTO TH'i The stress-strain curves are sMdwh in figure .'4 As will be seen, the rock displavs a marked hysteresis and is nut there fore an ideal material fur the ajiphcation of tliis method of deterinininKConi- pressibihty The rcsidts obtained are as follows : E 2,2()ti,i>* Hi; " = Jij; n ,8l().'Kx;; 8S.S,<)iXJ. § 2000 •J 1000 ao no mo too 2*o lao 320 5 TRAIN Fio, 24. — Sandstone. Stress-strain curves. 400 440 % THE ELASTIC CONSTANTS OP GLASS. As in geophysical speculations, the earth in aspect to its rigiditv and com- pressibilitv is often compared to a globe of glass, it seemed advisai.le to deter- mine as accurately as possible the elasticconstantsof glass, for the purp'ise of comparing them with the results obtained in the case of the various rocks considered in this paper, employing the >-,ime methods and carrying out the work underexactly the same conditions. This material lends itself excellently to this method of measuring these consta'its, provided the glass is free from all irregularities in its substance and is isotropic in character he first diffi- culty experienced was that of obtaining such a glass. At the outset it was thought that thick glass rods such as arc used for various purposes in the chemical and physical lab iratorv might be employed, but although several lots of the purest variety of this material were procured, the gK.ss constituting it was found in all cases to contain minute air bubbles, and when examined between crossed nicols in polarized light, -allowed brilliant colors — red, yellow, and blue. This indicated a state of marked tension in the glass, evi- dently due to the rod having been drawn when the giass was in a viscous state, which was also shown by the circular arrangement of the little bubbles in the rod, following the direction of its surface .Short lengths of this rod, moreover, when tested in compression, so soon as the maximur.i load had been exceeded, instead of splitting from top to bottom, broke as if composed of a series of rudely concentric shells All attempts on the part of the various glass makers to whom this glass wa submitted for a thorough annealing, failed to remove or in fact to redu' to any considerable extent this anisotropic condition. ik ELASTIC CONSTANTS oK KoCKS 63 The fiKurisobtaiiU'd fmiii one of llusc glass ro«ls approximately an inch in diameter are giveii in the foUowins Uble: Gttiis Koti. Arc*.. E ... D C I.oiid (in p^mnds). 000 OCX) ,000 , ,ocx> . .CXJO . ,rK)0 . ,IKH» ,0 . 000 000 . ,(XX> . 000 . ,CXX) . OC» . 000 . ,000 . ,000 . 774 H.075,000 2 .t,j6l,oaa l.nni[itmlitl.il inmpriMsioii (muUit)ly nMilinu** liy 4 for mjllionths). o .S.S 2 VI .'S<> .ISO .V'.-i -'".1 l^Hl I IS ,S l.atrrni rxlrnsiim (inillionths). W hi <)5 I.!.( I. S.S I Si US 1(X) .vs That the tension in this glass senonsly affected the results obtained— as might t.e e.xpected -i.s clearly seen in the value for U being much too low, as will be shown latei'. 9000 160 zoo STRAIN '•;g. 25. Glass RihI. Stress-strain curves. The stress-strain curves plotted from these values are shown in figure 25. As will be seen, the material »xhibits a distinct hysteresis. 64 AN INVKSTIOATION INTil TIIK Aftir a pn limited search for ivitropic j;lass in niassfs of Miflicicnt size to ini' isiirt' the tiastic cnnstants, it was fiiuml that platv i;lass answert'd the ref|iiiriiiifiils A piece iif mu- inch plate glass made in (Ireat llrilain was accurditiijlv seciirwl and was cut into strips an inch wide, and these' again into tline inili lengths The sipiare prisms thus produced were then pro|K rl\ faced and polisluil Till' u'^'ss was found to he al)solutelv free from all Haws aiul iuipuriliesand when examiiud l)elween crossed nicols tin- prisms, although an inch thick, showed in one direclion at right angles to vertical axis ahsolute hiackiu'ss lhron;;liout a coiupleii' revolution, while in the other direction at right angles to this there was during a revohilion an alternation of blackness with a pale grayish illumination This change w.is so -.light that, considering the thickness of the glass mil the sensitiveness of the lest, the material may = 6,448,000; C=4, 290,000 The stress-strain curves given by one of the prisms is shown in figure 26. In this figure I represents longitudinal compression and II lateral extension. Kl.ASTIC CONSTANTS Of RDCKS «S h'UtU- (ilao. Si/i- . *ms\ . I u ' Ana 1 IHIS7 K til \Mt . fiMo.onit 1, tm.ww C 1 jiD.mio 4,110,111111 'I'!} fi.SNit.iHMI 'tNl > I Ml tS I ■♦•SO. 4.1'*il,tHM) III, mtiiuMi »(. »Sl>,»W -l.iltl 'KM) 4..Ml),t«NI 1121 >' •»'>SS I (I. I 11 ; Ii(.4Mi.(M>n III 'MO iHtti I IMIJS I n.MV ,'1'*4 (i.M I nl<. ' in iso.MMi 10, 2*11. 'xm 22't .2i^ ti,4tll.(MM) 4,22l).IMH» I, tin, (MM) f.,I40,iMKI 4. tMMNNl I^^NOl^^'rl^^JAt. v ovmBssiDN^MuLriftv Khaihnus mv ♦ rtm MiLLioNrHH. IahuI un s,,u. SUIv S1.I. ^I4le Si-lr Si-If Siilr Siiir Siile Stit» Siilr SmIc Sidr Sul« IMlUtKliI (.' (■ /• /> «' f. I'. ;• ('. /• C. /'. U. )*, I.OfJO (1 c» 1. ,v> 3'> -'5 30 V> 30 3" 3" V> 3" JS 2S V* U' v'HMI fK) 55 55 (m (Kl (K. (m Im (xi 55 ss SS (m (HI 4,(¥K1 IJ 1)11 •(O 110 ss ■s S5 Ss 1)11 5.<«K. 1 io 1 15 "5 120 1 20 1 20 1 JO 1 1 5 1 15 1 10 s no 1 IIS 12s (l,(»0*> 14,^ '45 '45 145 1-,.. 1 SO 150 '45 145 135 : ■ 15 14" i 145 ' 15 7,ooo '7S '75 '75 '75 ISll fSo l>-.l 175 '75 170 ' '75 170 i ISO '75 «,OtX3 JIO -'"5 -'"5 21C1 210 J 10 21>5 20 s Jo s l')5 JIKI i'J5 i 211s 210 9,oon -'4" -'35 -'.V 2(1) 24" 243 2 15 2 vs J IS 22s 235 2 VI 2,1.5 -']■•> 8.00C1 JU» -•"5 -'" = 2ni 210 211) 2115 20 i ■■' 15 "(5 2115 liic> I.S« 1(5 '45 15" 15I' ' v5 1 Vi 1 IS 1 15 1 IS I |i I 111 'IS ISO 5.w)i> l,!<> "5 "5 I .»o I 20 1 20 1 JO 1 ■ s 1 15 ,10 1 15 115 IIS I 20 4,ooo ')<> !<5 1*5 i)0 .(11 1|0 1(1 > <(0 ss SS ' ^5 ss S,s i|o 3.000 (Kl 55 55 60 (.0 f«l (HI is 5S (Ml "• (>0 (H) (.0 2,ilOO 30 3" 25 3'> 3" 3" 3i> 3" 3" (O 3" 3" 3" 3" I.OOO II " 1) 1) 11 1 tArUK AL iCxi BNSl. S -Mill 1 l> ISTIM. I.OOO 2,nno 2 J 2 2 21 22 ") 22 211 Hi •11 1') 20 II) 1 21 2(1 3.(K1«> 44 45 42 45 3S 4I' i'l 11) 4" 4' 3if i 42 42 5 ^*** OS ()S ()6 6S (Ml 1..) ><>, MO 5'( '15 (.0 ; (10 (•2 S.) «() 8S S.) Si ')2 -1 So Si( 7'l ' S<) ! **3 (l.(KX> 1 1 1 III IO<> 1 1 1 im "5 ' ' Ills 10 ■ UK) UK) 100 1 100 1 '"3 7,ooo >ii 133 '2') '33 '-•1 13s »^ 12(1 I J I I 22 I.V> 122 \ 122 i '-'- 8,ooo '53 15<> '5' '5" '4- K.o '57 Its I 15 I 1 1 '55 145 ; 144 ! '■♦4 9,ooo '73 '75 '72 '79 170 ISO 17H l(,.( 1(.|( Ili.S 17!) Ids "'7 '<>5 8.000 '55 '55 '52 '57 ■4'» I'M 159 l»'l 1 |'> -45 155 '47 •4') ■47 7,ooo '35 133 '30 '35 12s 140 '35 121) I 2f) I2S IV> 125 '25 125 6,oon 1 15 1 1 J 110 "5 '03 I >5 100 llMi "'5 105 112 '"5 '"3 ! 1116 <>3 <|o '(«> C)0 So i)l> S,( SS ss H8 QO !<5 82 Sq 4.H.H) 7'* 71 75 04 62 6j 62 '"1 65 1 f)2 (,Q *'> 45 45 51) 41 > (2 4'> 42 4' 4' 45 43 42 49 2.(KX1 23 22 25 _'l 20 20 2 1 ji 21 22 22 22 2S I.OOO ° " 66 AN INVKSTK-.ATION INTO TIIIC jl .' nitmnin.itions of the cul)ic coniimssihilitx of ylass, />,liave hern iiiaiK' hy otliiT ohscrx ITS usitiK various nulliods Tlu- risults u" tosliow that dilTcrcnt vaiitti.s (if k'la^s vary coiisidirablv in thi'ir omprissibihty 'I'hcsc di-tirttii- nations tiiav hv tahulatid as fiillo\v>;* l-lviriit 5,o;.t,(.iH.ln(.,,(7'M"<' il-' <■ ^ "=- '^ '" t t '""'■ AniMKal C.iinmcmKlass. . (,,; i,s.ih«i i .i"-'»>"-i M per ;i I inn-,], lure). Aiii:iK:il Crysl;il Klass . (,,, u, (.«> i (xhkk.j ,i>s per ;itTin.s|,1,m-i. •|-.,j, ^,li;i;,7i«) (.(KXKKl.'d JHT alinn'-plllTll. As will bt seen, the tlRures obtained for plate Rlass in the present iiiveslis;a- tion lie a little above the average of the various values here given, and e nearlv those of the highest value obtained bv Iiveretl SUMMARY OK RESULTS. The table on page 6<) gives a sunnnarv of tin- average values obtained for /•:, ■'. (■ and /' in f'e ease of all roeks examined in this investigation With these are placed, for purjwises of eoniparisou, the results obtained for these eonstanls in the e.ise of wrought iron, east iron and glass In the second table .^n page 69 these \ alues are again presented, recalculated into C (» S units The rocks fall naturallv into three groups, dilTering from ime another in eonipressi')ilitv, but the several members of each group agreeing fairly closely among themselves These thrie groups show a correspouiling dilTeretiee in composition The first group consists 1 >i the marl)les and limestones These have an aver- age value for /> of 6, u.s.ooo Oneof these, however, the Ulack Belgian marble which is verv much finer in grain than the 1 it hers and breaks alm t" 'H- The figures there expressed in various units have been here recalculated int(i Inch -pound values. ^^VlVrfri u. KI.ASTIC CONSTANTS OF ROCKS. °7 If the nc-pl.cliiu. syonitf be incUuled with the basic n.cks, an averafie vaU.e of /) is obtained (pf .S,;,()H,iKX) This omits In.m o.nsideration the sandstone, it Ixing a rock of an entire! .lilTerent elass fnm. the ,.thers, an.l fnrther.nore one whieh shr.ws so nineh I,vstere,is th,.l the appheation ..f this method to it is less sat.slactorv than in the case of the other rocks of the series 'I'liese results inav he presented as follows ; . , „ (i,^4S.ooo Marhlc. .M.,1 lM„est..nc 4,,.,r,,oo., ^■■•■'""" : . H,;v>H,o ll.isic intnisivi-s The cause ..f the much greater compressibility of Rranite as cr.mpare.l w,th the marbles and basic i.Urnsives is not clear, but would seem to be connected with the presence of ,,nar.. The only detennination of the cub,c co.npress- ibilitv of .p.art.. s. far as can be ascertained, is one bv \o,«t,* the value obtaine.1 beint; 5,504. .')o poun.ls (.,S7 < ">" Rrams per sq cu. ) Tins com_ nr.ssibilitv as will be seen, is m.ich greater than thai found m the case ol either the liM.estones or the basic intrusives, a.ul while not m itsell suf- fu-ientlvK-reat toaccount for the hifih compressibility of the «ra.utes j^oes to show that m the .p.nrtz we have a mhural which is n.ore con.press.ble than theonlinarv rock makinj; minerals which f.,rm the chief constituents m the rocks of the series examined .-,,•. , ■Ihe marbles and the limest.mes of the earths crust are confined to Us most superhcial portion, resultiu-,; as thev do from the process of sednnentatu.n. There is everv reason to believe, however, that what we may term the sub- structure of the earth's crust is imposed of acid an.l basic plutomc isneous rocks These make up the lowest part of the crust to which we have access and are found comin;; up from the still K'reater depths The cubic cotnpressibihtv P of the earth's crust must he between the values LMven above for the granites and the basic intrusives, appn-achniR one or .,ther of these values according to the relative pn.portion m it oi one or other of these classes of rocks If we t ike .he average of the values obtained from these two classes of rocks as r .resented bv the seven granites and the five basic intrusives {includnig the nei.helincsvenite) the values obtained for Oof 6,.15,V,5'X>. , . ,, This, as will be seen, :) to 37,s47,(«k) (iH to i>) x lo", C G. S ).* The c 'Uipression to which tlie rocks were subjected in this investigation ranged from 6,000 to 17,^4(1 pounds to the square inch Most of the rocks, however, were subjecled to a load of from (),(>oo to iS.oim) jjounds per square inch.aiil ihiir Iv.ilk compression was determined for thesf loarls as maxima Hiiiher pressures could n.it be emijloyed without running the risk of breaking the specimen and at the same time of destroying the measuring apparatus One apparatus was in fact so destroyed The questi, >ii aris.s as to whether under still higher pressures, if rupture could be avoided, the ratio of load to compression would be maintained Judging from the deportment of much stronger substances such as steel, when similarlv ttsled, it is iuferiiil tliat this ratio of bulk compression will remain coiistiiut fur very uujch liiglur pressures, or until deformation sets in and the rock begins to llow With regar.l to the aceur.icv of the r..sults obt;iined by this method as com- pared with those obtainable bvany method in which cubic compression is actually produced and measured, it mav be observed that by fir the best methodof this kind hithertosuggested seems to be that proposed b>, Kichards and Stull t We have endeavored lo make use of this method in order to obtain results for purposes of comparison with those given in the present paper but have not hitherto succeeded in overcoming certain experimental dilliculties. The exi)erimeutal errors in this method, though appareutiv small, still exist, and in applying it to rocks, which are much Kss compressible than the sub- stances examined bv Richards and Stull, these errors become proportionately more serious Moreover, higher pressures than those used in the method emploved in tlu> pese-it p,q)er could scircelv be emploVefl in this direct method, while dil1icidli/s de[)fU!leul on the possible lack of absolute contin uitv in the substance- of the rock and the danger of minute air lilleUNn ITnits. Specimen. Wrfiimht iron.. Cast ir 2HfX. 1 1, 2.500 fi,00-*, jfno 3,o^x>.0(X> i),(K>6,3 3.f)07,ooo (J.JO'i.tXKl 2522 3,636,tx)o 6.8,^,1,0(X) 2528 2,724,8<.X) S.JQS,™*' 2112 3,399,000 8,|65,0 8,303.000 5,946,(K)0 5,34i,fXKi 5.967, 6,167,500 4,fj04,cxx) 4,792,000 4,517,500 4..W7.,SOO 3,984,000 4,555,000 3,940,000 6,237,500 8,368,000 6,750,000 9..'i.S5,ooo 10,626,500 1,816,000 6,448,000 Summary op Rbsolts (Avbraoe) Bxprbssbd in C. O. S. Units. Wrought iron iq 37 X 10" Cast iron 10.34 X '"" RIack Belgian marble. . 7 24 X m'' Carrara marble 5 54 X ii>" Vermont marble 5 24 X 10" Tennessee marble 6 21 X 10" Montreal limestone '■ 35 X in" Haveno granite 4.71 ,X ni" Peterhead granite 5 71 X 10" Lily Lake granite 5 63 X 10" Westerly granite 5 09 X i"" Quincy granite (1) ... 4 64 >: 10" Quincy granite I 2) 5 6.s x 10" Slanstead granite 3 o.' X m" Nepheline syenite fi. jo < id" New Glasgow anortlKisitc 8 25 X 10" Mount Johns32 X 1 t 6 . 897 X 10" 2780 2.9S2 X 1 >" .S.7.1f> X 10" 2744 2 171 X 1 )" 4 0(X1 X 1.1" 26 v> 2 (tftt) X 1 3 , 680 X 10" 2513 2 482 X I >" 4 "S X to" 2522 2 ,504 X 1 4 250 X 10" 2528 ■875 X 1 .1. '7') X In" 21 12 2 .U" X I ■V.V" X 1.." 1982 2 .3.10 X 1 3 '03 X m" 2195 2 080 X 1 3 "29 X 1,." 2I.S2 1.916 X 1 ) 2 . 7.'iO X m" 1977 2 . 37."- X 1 l" 3 >4" X in" 25f',S " .S.56 X 1 2.71^ X in" 2560 2 50.S X 1 > 4. 2I)0 X 10" 2620 .1 275 X 1 1" S 760 X in" 2583 2 670 X 1 4 f'.SO X 10" 2192 4.3KO X 1 )" 6.589 X 10" 2840 3.700 X 1 7 329 X in" 29fX) 612 X I )" 1 . 250 X 10" 2273 2.960 X I >" 4 439 X 10" MMk