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 1 2 3 
 
*«aOCOfY IBOlOTtON TBT CHART 
 
 (ANSI and ISO TEST CHART No 2) 
 
MKPAKTMKNT OF TIIK INTKKIOK 
 
 Ul>N. CLirroNU tlli'TI>N. MlNINTBH, 
 
 On thk Liocatiox ani> Examination 
 
 iir 
 
 Maunktk Okk Dei*ohith 
 
 HT 
 
 Maonf.tometric Mbamuhkmenth 
 
 KUUKXK IIAAXBL. PH. D. (llHBttLAUi 
 
 NUPMBIirTHEiDIIWT or MlWRM. 
 
 «>TTAWA, CANADA. 
 
 I nut. 
 
Sir — 
 
 I have the honour to nuhmit herewith a iei>ort on tl>c 
 Location and Examination of Macjnetic Ore Deposits by Mag- 
 netoinetric Measurements, which was read at tiie Annual 
 Meeting of the Canadian Minin<r Institute on March 5tl», 1908. 
 
 I have the honour to lie, 
 Sir, 
 Your obedient sei'vant, 
 
 EUGENE HAANEL, 
 
 Sitpi'riiiti'iKlciit of Miiu'n. 
 
 HoNoiJRAiu.E Clifford Sutox 
 
 Minititcr of the Interior, 
 
 Oltiiu'H. 
 
 00u;d5055 
 
TABLE OF CONTKXTS. 
 
 Introrlnction 
 
 I".m;ks 
 1 2 
 
 CHAPTER I. 
 
 MAtiNETS AXf) THErif IMIOl'EHTIKS. 
 
 IX'Hnition of inajjni't. Poles. I^aw of iittnictioii and 
 
 repulsion. Theory of the constitution of nuii;nets 'A 4 
 
 CHAPTRK II. 
 
 THE .MA(iXET|c KIELD. 
 
 Lines of force. .Streno;tli of a niajrnetic tielrl at a point. 
 Cott.servation of flow of U>n-t: Construction of 
 (liairranis of niajfiiftic fields. I)iaj;rains of uni- 
 jxjlar niajfnetic fields. Diajiranis of bipolar niaj;- 
 iietic flelds. 1st : Two unlike poles of e()Ual 
 strenjjth : 2nd : Two (inlike poles of different 
 strenifths. Kipiation of a line of force. Inductive 
 effect of tin- niai;netic Held upoi: niai;netic IkmIIcs . . 4 i;{ 
 
 CHAPTKH III. 
 
 The earth's normal MiajTiietic Held 14 1(j 
 
 CHAPTEH IV. 
 
 THE DISTIRHED TERRE.STKIAI. FIELD OK K(>U< E. 
 
 Relation of dip to intensity of inajjnetization Iti-LS 
 
 CHAPTER V. 
 
 Effect of a magnet on a compass needle in a normal 
 
 terrestrial field \Hi'A 
 
CHAPTER VI. 
 
 THE THAhto-TIBEBO MAOSETOMETEK. 
 
 ;,...,.;,.....• The ccnpass. The support of the co.n- 
 
 pasH with it8 detlocting magnet. 
 T..Hn, and .uijv^tinr, the nuu,nH..n.t.r^ 
 ,1. Exa.nination of error due to eccentne suspens.o, 
 „f compass needle. 
 
 i, perpendicnkr to plan.- "' 1™"'"'' 
 base plate l\- 
 
 pass V«x rende,. c.ou.pa.ss box horizontal. 
 
 , Kxannnation whether the ^^^^^^^^'^^ 
 bar Q when in contact wnth plate P^ of con. 
 pass box indicates its vertical pomtion. 
 ,, Neutralization of the vertical con.ponent ot the 
 
 earth's normal Held. 
 Precautions to be observed in takin, observations with 
 the magnetometer 
 
 P.MIBS 
 
 24-32 
 
 CHAPTER VII. 
 
 r ,. (With the Thalen-Tibergnmjj- 
 
 netometer). . ^ m lV^-'^Q 
 
 HorizonUl Intensity of a magnetic held 
 
 CHAPTER VIII. 
 
 ,.H.HU>MS MOn,K,CAT.O. OK THE S.NE MKTHOa 
 
 r^aUhrfttion of millimeter 
 Method of observat-i. Cal br^on ^ 
 
 scale and construction ol scale lo ^ ^^^^ 
 
 direct ■•■ 
 
VII 
 
 CHAPTER IX. 
 
 The value of tlie horizontal inti'iisity in a terreHtrial 
 Held of force, disturl)ed by the presence of a mag- 
 netic ore iKxly 
 
 i-.i-iH 
 
 CHAPTER X. 
 
 THK VEKTICAL INTENSITY OK THE UISTLKBEI) KIELI). 
 
 Theory of the Inclinator. Determination of the value 
 of K. Method of observation 
 
 CHAPTER XI. 
 
 THE THOM.SON-THAbKN M.\(JNET(>METEK. 
 Dewription. Theory. C'alibration 
 
 CHAPTER XII. 
 
 Dti.scription of the Swedi.sh nunint; conipas.s 
 
 CHAPTER XIII. 
 
 INVfcSTICiATION OK MAGNETIC OKE DEFtJSlTS ISV 
 MAONETOMETRIC MEA.Sl'REMENTN. 
 
 C'hart of the Horizontal Intensity. Charts of Vertical 
 Intensity 
 
 CHAPTER XIV. 
 
 Information conveyed by tin; charts of nia^nietic in- 
 tensity 
 
 CHAPTER XV. 
 
 Determination of the distance of the upper [lole of a 
 magnetic ore Ixxly beneath the .surface. Four 
 methods 
 
 CHAPTER XVI. 
 
 Deterniinatioli of the extension in depth of a ii>agnetic 
 ore Ixxly. 1st: Method by Dahlblom. 2nd: 
 Method by Rolx-rt Thalen 
 
 4!)-5(i 
 
 .)(j-6.5 
 
 ()o-(j6 
 
 (»7-74 
 
 74X0 
 
 81-8fi 
 
 «7-94 
 
Vlll 
 
 I'HAITKK XVII. 
 
 Lilx.ratoiy I'nittii"' 
 
 H.UIKS 
 
 APl'KXDIX. 
 
 rilK I(.UI1-III,<>M MAliXKToMKTKK. 
 
 l)..«-iii.ti..ii <>|- tl..- Maj;iHl...ii.-UT. A.ljustiiK-nt ..I' tl.r 
 Ma«iR-t<.iiHt.i-. >u-usu.viMi-i.l of H..ri/.ontttl lu- 
 tfiisity. Mi-asuiviiunt i>i N'.-rtiial liitt-iisity 
 
 LIST OK TABLKS. 
 
 Ml II '/(I 
 
 !)!» M).") 
 
 mil a 
 
 10()- 
 111 
 
 „ „ = 0.01 U) 
 
 I'ahlv I. 'rahlr <.!' valu.H of 
 
 in ml «o 
 Tabii- II. 'riH.il- of valius of ^^j^^ • - 
 
 Table III. Tahit- of vaiu.s of ^- J Iroi 
 
 to.»=o.»>0 
 
 Table IV. Trtblf of iiatmal taiijjentH 
 
 Table V. Table for tlie leduetion of tlie aiijrles -■ 
 observed with the Tibei;; Ineliimtor : 
 
 r,.fro.n 1 to 41: /,„ from 0.50 // to O.ltO // 
 r" from 4-2 to !»0 ; /.,, from 0..50 H to O.itO H 
 \\ from 1 to 4!> : /■„ from O.ito // to 1.40 H 
 r" from .50 to !»0: /.„ from 0.!».5 // to 1.40// 
 l{ from 1 to .■)! ; /•„ from 1.4.5 // to l.HO // 
 l{ from 52 to !tO : /.„ from 1.45 H to l.HO // 
 
 Table VI. Table of '"'.'■ aixl •'•'^^ '" 
 
 110 
 115 
 
 116 
 117 
 
 IIH 
 11!> 
 120 
 121 
 122 
 128 
 
 125 
 
 Inde.K 
 
 127-1 82 
 
 I » 
 
IX 
 
 
 LIST OF I'LATKS. 
 
 I'l.ATE A. 
 
 The Dul»ll)loiu l'(xkL't Ma<;iiftuiui-Ur. 0'''ici'). 
 
 Plate B. 
 
 The Dalilliloi I'ot-kct Mii;,'mt..iii.tir. (IJiiek). 
 
 I'r.ATE C. 
 
 ThaU'ii-Tihcr;; .Majjii.'toiitL'U-r. (Set up as luclinatoi). 
 
 PhATE 1). 
 
 Tlialt'u-Tiherji Jhi>;iii-t'imi'tt.'r witli Dahlbloiii's arm. 
 
 Plate K. 
 
 Tliuinson-Tlialen .Ma<,nii'l()im'tL'r. ((ilass cap reinovwl). 
 
 Plate I. 
 
 Vei'tical section of the tiuld <>t' t'orco thi(juf;]i the statimi 
 lino /;( of Plates II and III. 
 
 Plate II. 
 
 Isodyuaniic lines of horizontal intensity R. 
 
 Plaie III. 
 
 Isodyuaniic lines of vertical intensity G. 
 
 Plaie IV. 
 
 Isojjonic lines <•". 
 
 Plate V. 
 
 Isodynainic lines of the iiori/.oiital intensity of a deposit of 
 magnetite. 
 
 Plate VI. 
 
 ls(xlynaniic lines of the vertical intensity of a deposit of 
 magnetite. 
 
 Plate VII. 
 
 Chart of isodyuaniic lines of an a<* ' d ore bo<ly. 
 
 Pl.\te VIII. 
 
 Field of force of au ideal magnet. 
 
Introdiiftion. 
 
 IX 1M4.'J. Frfilii'M' von Wrcdf. iiiipri'ssril witli tlic work ilfnic 
 l»y I^uiiont ill (Ictfriiiininj; tlic clianiftiTiHtit cIcinciitH cif 
 till' curtirs iiiaitiictic tii-Id witli liin iicwlv iiivciitfd tlH'ofloliti'. 
 WHS tin- first to realizf tliat l)y iiicasiirin;; tlic ciian^irs in tlic 
 cartli's normal tii-ld. canscd l>y tiu' jircsfncf of nia;;ni'tif ore 
 d('j>osits, tlif liK-ation and fxti-nt of tlicw oi'c di'iiosits iiiij;lit lii' 
 dftfrniint-d. 
 
 Xotliini; was dom- l)y him. however, to carry this thoii;;lit 
 into t'xwntion. nor was Ids method |)uhlishe(l initil he iM-canie 
 ac(|uainte<l witli Professor RolM-rt Thalen's puhlieation in IHlU: 
 "On the Kxandnation of Iron Ore l)e|M)sitH l>y AFa<,'netie Measnre- 
 nient.s." Tins inil)lieation laid the foundation for the practice 
 of the niii<;netoinetric nieth(Kl in the Held. 
 
 As experience accumulated, new methods were invented. 
 ;;ivin<; Ix'tter results, or solviiijf new i)rol)lems. The old niaj;- 
 netometer also became transformed Ity reconstruction, which 
 permitted the use of the compass as a Tilier;; indinator, into the 
 convenient tielil instrument — the Thalen-Tiheri; mcjjnetometer 
 — as now furnished hy tlie Swedish mechanicians.* To these 
 instrumental a])pliances for ma<;netic sin'veys of ore deposits 
 has recently* heen adde<l the Thomson-Thalen ma<;netometei', 
 wliich, based upon a zero niethixl. especially facilitates the 
 determination of the distribution of the vertical intensity over 
 nuii;netic ore fields. 
 
 In the liaiids of r.rjti'iis, fiu'Mished with such instruments, 
 the Swedish methods yield data from which maj;netic ore bodies 
 may Im; located, and in tnan,\ cases their .strike, direction of di]), 
 and dei)th l)elow the surface determined. 
 
 * Instrumontm.'tkar, J. Fr. Bt-rj;, Slockliolin, 
 + .899. 
 
;()Uiitrii 
 
 li ii 
 
 mhlf A iiuthncl Mhonia fail )f rt«oj;niti<)ii in 
 xl »»• conHiu'd in its iipplictition ninioMt alto- 
 ftMu'v t.. SwimLm.. 1.«I tlH' Iftt.- FroffHsor N..nK-nHtro»i, of Stock- 
 holm* to fxpn'SH liimm-lt us follows: "It is astoniKhinK that 
 lR..)i.l.« in thorn, ountries " (ivf.rrin^ to EuroiM-a.. countries 
 „th..r than Swt-d.^n) " haw not alivady l.'arni.(l to appn^iate 
 the «r''«t a.lvantaj:i's whirl, ar.- oHVml tlu- {.ractical miner l.y 
 the use of majjnetic instruments." 
 
 As late as March, 1H09, F. Uhlich states + that nothing had 
 ftpp.are.1 on this suhjeet in (Jerman literature except an article 
 in 1H7H hy A. Felix, on Thalen's nietluxl. This also is the ca8e 
 as rejpmls the English literat.ire on the subject, no (letaile<l 
 account of the Swedish meth.id having yet av.iH-ared in the 
 English lanjjuase. What has lK..en puhlishtHl contains so meap-c 
 an account, and is ho fragmentary, that it is useless for puriK.ses 
 
 of instruction. 
 
 In view of this, it occurred to tne that a service nnght In; 
 renderiHl the mining profession hy furnishinj; so full an .vcco.uit 
 of the Swedish metluKl and practice as would enable any minu.K 
 engineer, with proper training ajid in posseH.sion of the proi)er 
 instruments, to employ the metluxl in the field. 
 
 The tables which accompany this pain-r are intended to 
 facilitate the calculation of results, and ha- l)een calculated for 
 ,„e through the courtesy of Mr. King, chief astronomer of the 
 Department of the Interior, or have !>■.■. taken from P. Uhlichs 
 " Markscheidekunde,": unless otherwise stated. Tin drawings 
 and plates have l)eeu prepared for the engraver by Mr. Erik 
 Nystrtim, M.E. 
 
 ~^The most Prominent and CharaL-leristic Features of Swedish Iron Ore 
 Mining," by Professor G. Nordenstrom, London, iSgq, page "• 
 
 t " Ueber Magnetische Erzlagerstatten und deren UntersiichunK durch 
 Maenetische Messungen," von Th. D^hlblom. 
 
 .. Ubersetzt aus dem S. hwedischen,"by P. Ul.lich, Freiberg. .899. Vorwort 
 
 des Ueberselzers. 
 
 J "Lehrbuch der Markscheidekunde. ' von P. Uhlich, Freiberg in S., 1901. 
 
CIlAPTKIl I. 
 
 MAONBT8 AND THBIR PROPERTIBS. 
 
 Definition of Magnet. — By tht- term nmxuft we 
 tiMUiilly <leHii;imt»' a pit-ri; of Hti'i-I whieli Iihn titu jirojaTty of 
 attracting; certain Nulwtancfs tcrnitMl inu^ni-tic bodieM, mucIi oh 
 iron, nickt'l, coImiH, t'tc. 
 
 Poles. — Tiiis attraetivf |H)wt'r is c)iKvntnitt'«l at ctTtain 
 jwints in tlu; nmjjnftH tornicd |M)lfM. In lonjj anil very tliin 
 niagnetH thew; iM)it's an* Hituated at tin- t-iids. In niaHNivo nmg- 
 netH the poleN are Hitiuitt;)] at |>ointN atxmt i'; '*f ^^e len^^th uf 
 the niagnetH from eacli ei: 1. The line joining the ixjles is 
 termed the mii<inefu' <i.ri». A magnet susj)ende<l so that it may 
 swing in a horizontal plane comes to rest in a definite jH)Mition, 
 with its axis in general in a north-stnith direc .on. If the end 
 pointing north l)e marked, it will Ir' found that this end at every 
 successive trial jwints north. Hence this jiole is termed the 
 north-seeking p<jle, or sliortly, the north pole, the other the 
 south [Kile. 
 
 Law of Attraction and Repulsion.— If a north iH)le 
 of one magnet is made to approach the north pole of another, 
 suspended front its center of gravity, tlie latter will Ir- repelled; 
 if made to approach its south jK)le, it will Ih" attracteti. Simi- 
 larly, two south poles will repel. Hence like poles repel, un- 
 like attract. The force with which this attraction and repulsion 
 acts has been found to !>»> jiroportioiuil directly to the pnxluct 
 of tlie strengths of the poles and inversely as the .sijuare of the 
 distance betweei! the acting poles. If a and /i are the strengths 
 of the re.spective poles and d the di.stance between them, the 
 
 force /, acting between them == .^-. 
 
 Theory of the Constitution of Magnets. — If a 
 
 glass htti-dened steel spring be magnetized it is found that 
 when broken each piece constitutes an independent magnet, with 
 
,„.„,,. .....1 ..Mtl. ,H.l... Tins will l..l.i.,u,.|.r.l.-nml-t 
 
 ,,i..... wl.irl. .■-... »H. ..l.lai y tl... ,..•..— ul fnM-tu.v ll..s 
 
 i.,„.|H 1., tl... n.n.v,,ti..n tlml .■>..■> .........1 is .... ..-;:.vKat.. <-» 
 
 ,,.,,„.,„„1 ,..„jj„..t« will, tl..i.- ..x.s so ,,r.a..-..l tl.at tl..y a.v 
 
 ,«mll..| .m.l lik.. ,H.l..s ,H,i... in tl- ■.„ UnHi..,,. Tl..^ inst,.v 
 
 ;,,. „,., ,„„...,,,ti.,n tl.at tl... ..mK...tis.n uf a nm^'.-t .l.p.n.U ui..... 
 
 ,1 ,,»../ ..r tl... -l.n.rntal ...a«....ts -f wl.i.l. .t .•onsist., 
 
 ,..,.,iv..H ,.un-..lH.mti.m fn.n. tl... int.n.al st.-.i.tn.v an.l l.f..lM.,t...H 
 
 , ir...t...l l.y a «1- t„lH. .ill...l will. HI-..1 r.liM«H in tl... ....... 
 
 ,..a,n...ti.. a...l in tl- n.a,M...ti.- .t..t... \.li.n ti.st hM.-l w. 1. 
 „,,„n.l Ht...l tilin;r>*. tl.- tnl.. us a >vl...l.. hI.-.wh ,...,... ..I tl... 
 ,„ .,„.Hi..H ..r a n,..«...t. ( h. n.a«n..ti/.iti..n, tl..- tiling, at ..».•.• 
 Uun... n..v. ,...Hiti....s a...l anan«.. tl...n.H..lv,.H i,. tl.,- ..nn "I 
 
 ,i,,u,...„ts, >vl.i..l. t.av..,s.. tl... tuU IV n.l t- -n. . 1 1-- .•"..- 
 
 t..„tH ..»• tl... tuU- now ..xl.il.it Hl.r..ns stnu-tin.-, «...! tl... tnlH- «m 
 ,1 WI...1.. will n..w iH.l.av.. lik.. an .-i.Una.y n.a>;n..t. l<..ml.l.. 
 ,l..stnu.ti..n of thin amu.«.n...nt l.y shaking is a.-.-.n.,........! Ly 
 
 a..s(nu-ti.... ..»■ n.anir..Htation ..f n.a;:n.tiH,„. t- 1.. v.voy.v>.\ only 
 
 |,y i...,.r.Hl u-i..^' tl- til.u....nt....s «..ninp.n...nt l.y 1.v.k...hh oI 
 
 n.. ' t'tization. 
 
 ■ I „,av ..all att..nti.a. at ..nn. !....v t.. tl... in.i....ta..t la.t tl.at 
 ,..a«n..ts.;i.n.u;;l. .iani..j: -r otl... n.n.,'l. tn...tn,..nt wl.,.-l. pn- 
 ,hu...H int..,nai n.-.L-ulav n.ov..n...nt, lus.. str..n«tl., an.l 1....... tl... 
 
 „..,,sMtv of car.fu.ly «'""•'«*"« '^>i"i'"'' ^"••'' ''"^ "'"'" ""-"*''; 
 in n.nkin« a s..t ..f n.a;.n.'ton..tri.. ....as.nv..,. -ts, f.-r .hn-...« tl..- 
 
 tin... .K.,.,.,.i...l l.v •!...«.. n,..asnr..n,....ts tl... M.nj,n...ts ..n.,.lny...l a.v 
 
 ass..i....d to ivn.ai.i '.V tl.f san..' str....«tl.. 
 
 CirAl'TKU II. 
 
 THE MAGNETIC FIELD. 
 
 Tl... s,.ao.. alK.ut u ...a-,...t, in wl.icl. it ..x-.tn l-.r... is l-n.-.l 
 its ,nii<lii<'i'fi<l'l- . , 
 
 Lines of Force.— A.-co.<lii.i,' to tl..- .■onc.i't. I »'"'•"- 
 
 .lav, this ti.-l.i is favors...! l.y lines ..f ...aj,n..-tic foi-c.', wl.iil. ar.- 
 
l.Kiiffl iiM tlif I'ulliH »mir<l Dill l.y 11 IK'.' ii.iith j«.lf |.lii<.'.l m 
 
 il' tlicw liitiH \h tlif liirH-tioh <>)' till' 
 
 I 
 till' fiiltl. Tlif iliicctiiiii 
 
 iiHiM'lnrlit • 
 
 ,f III.' Il iioltli |M.I.' II' il -.w.-.-!.-* out II lilM- "t 
 
 Imicv In 111.- niH.- ..r 11 lliiti. i'-ii;j may;ii.l, with \»>\>-* at tli.- 
 
 // xtiiit ti"iti till' til I'lilf ami ill 
 
 rlliU, tlir lilli'H til' I'liri'f •' 
 
 tlirim;.'li tin- inlfrvi'iiiii;.' h|«H'' to tli.- wmtli jNilr ami 
 
 .ilistaiH-i' of till- iim^nit Uiik to llii- lli JhiI.-. 
 
 TIli'Hi' lili'S 111' loicr im-. tliiivloiv, closiil clllv.'H, witll till- v\r>\>- 
 tioll of til.' iilK- IMlsHJli;: out of tlir Mm-,'llit ill tin- l.rololi;:atiou 
 
 curvi'H jiawH 
 tlil'oU;'ll till' H 
 
 iif its axiM. 
 
 Tl 
 
 II' niiii'iii 
 
 I jiiMt i|i'H«'iil»'il in an iiliai uia;,'iu't. 
 
 lii'lil iii'mIuci'iI liy a inussisi 
 
 not at till' I'litls. am 
 
 ;iift i" not NO siniplf. 'I'Im' jhiIi'"' 
 I lini'H of foici' Htait out, not Iri'iii u jiolt 
 
 HiiiToum 
 
 .•onsi.l.'ii'.l as a |.oiiit, Imt lioin tin- m.itli |m.I.- aiva. ami aUi 
 fioni till' sul.-N of till' nia;,'n.'t. to timl tlitir way tliroiiyli tin- 
 li'ij; nu'iliinii into coin'spomlin;,' jmints on tin- moiiIIi intl 
 of till' nmjinit. 'I'lii' liiu's of foiri- play an iiiii>oi'tant part in 
 l|,i-«li'tiiiiiinatioii of tli.Mliptli of nia;,'n.'ti<' on- il.'l«.HitH. Tin' 
 
 .'onc-ption of a I'll' i.' nli poli-, .•niployil in ili'linin^ a lii f 
 
 llii'ii- ' -111 tiftion ami cannot !»' nali/i'il 
 
 forri'. is a foiivrnii'iit ninlhi'i 
 in pi'aitii'f, sim-f nori' polun 
 
 itv caniiol Ih- scparalril fiom soutli 
 
 1" 
 
 iiilv in a iiia;;m'ti/..'«l sulistann-, so that om- pii'<-'' mi: 
 
 rhl 
 
 xliihit oniv south 
 
 siniplv Ix' north polar ami aiiothi-r pirci' t 
 polar niay;m'tisiii. 
 
 A i-oimiion way of showing' tlu-si' liiu's of forci' consists in 
 sprinklin;,' iron tilin;;s ui«m stiti' hut siinH.th jMipcr, pimcil ovi-r 
 a nia;;nct. 'I'hi' lilin^cs arian;,'.' tlii'insi'lvcs aloii<,' lim-s of force, 
 and may Im- photoyraphiil for further rcfiivnci' ; or since a line 
 of force iii'licates at every point of it the (lirictioii of the nia;;- 
 netic force, these lines may he tniceil out hy 11 <lclicati' small 
 compass, ahout ; inch in iliaineter. Tiie ncilie of the compass 
 will pliiff itself with its axis tan;,'ent to a line of force. To 
 employ this methoil the conii>ass is placeil in the tiel ! of force 
 upon a sheet of paper of sutticient size to contaiu the tielil of 
 force to i)c' mappcil ami the position of its poles inarkeil hy a 
 pencil iMiint. The compass is now iulvanccd a (listiince ei|iial to 
 its liiameler, ami placcl with its north pole uVcr the iH>iiit 
 
r" 
 
 6 
 
 pi-oviously occupied by the south pole aiul the new point indi- 
 euted by a pencil mark. The line resultinj; by .joiniiifj these 
 points is a line of force. In this tnanner the whole Held of force 
 may be mapped out. 
 
 The representations of lines of force thus obtained are lines 
 of force in a plane, and to form a conception of their distribu- 
 tion in space it is necessary to revolve the representation of tiie 
 tiehl alx)ut the axis of the ina>;net. The lines of force will then 
 sweep out surfaces upon which the lines of force lie. 
 
 Strength of a Magnetic Field at a Point.— The 
 
 strength of a ma<,'netic Held at a point is a nund)er expressing the 
 force exerted by the majjnet on a unit north pole at this point 
 in terms of unit f(irce-the dyne*— and this nund)er is by 
 convention taken as eipial to the number of lines of force pass- 
 injr perpendicularly throujjh unit area ( I cm.-) placed with its 
 fTL^metric center at the },'iven point. From this it follows that 
 in the stronjjer parts of the Held the lines of force are crowded 
 more closely tojjetlu-r than in the waker parts of the Held. 
 This is shown by representations of Helds of force by iron Hlinjjs. 
 The lines of force are seen to be crowded more closely tojrether 
 in the region of the poles than in the space midway between 
 the poles. 15ut it must not be imagined that in this crude 
 representation of a magnetic Held of force the spaces between 
 the trains of iron Hlings are regions wliich are not traversed by 
 lines of f.jrce. No space in the Held of a single magnet is free 
 from lines of force. The d.'Hnition of the strength of a Held of 
 force by the numlicr of lines of force passing through unit area 
 is merely a convenient convention : attention being drawn to 
 just that lunnber of lines of >ill the lines passing thnmgh the 
 unit area whi.h coi'respond to the number of dynes exerted by 
 the Held upon a unit north pole at the given point. 
 
 A ^(6,'(.//.>c«v' isachainiel Inmnded laterally bylines of 
 
 force. 
 
 * The dyne is a lorii- whiili iulinn lor om- si'coiul upon unit of niiis^ i-qiial 
 to one Kramme inipails to il an aiivl.-r.ilion oqual to om- c.Miiimeter. 
 
Til'- ffinr offoi-rf F is the piodHct of tlic cross-Hwlioii « of 
 a tube of force into the vtihu- of the magnetic foiee // ut the 
 place of tlie croxs-sectioii n, lieiice : 
 
 F -- //«. 
 
 Conservation of Plow of Force.- Considerinj; the 
 
 tield of force of a single ideal magnet, it is evident that tlu' 
 numlKT of lines of foree of its tield are constant, *'.'•., no new lines 
 are originated, nor do those existing vanish. Through every cross- 
 section, therefore, of the same tuhe of force the same inimher ol 
 lines of force must pass. If .x and s' are the cro.ss-secti<ins ol 
 the .same tuhe of force at ditlennt places in the tiehl, the How 
 of force for ImiIIi cross-sections nuist remain the same. We 
 have, therefore : 
 
 /' Us n's'. 
 Construction of Diagrams of Magnetic Fields.— 
 
 If we imagine a sphere descrihed with radius unity (1 cm.) 
 alM)ut a magnetic pole of unit .strength, the magnetic force due 
 to this pole will at every point on the spherical surface t^cpial 
 vuiity. Since there are 4" stpiare ct-ntimeteis in the .sinface of 
 this sphere, it is evident that if we desire to represent the ni- 
 tensity of the tield hy the nuiriher of lines of force pa.-sing 
 through unit iuva, we must conceive 4r lines passing out of the 
 pole into the surrounding space. The whole How of forct- in this 
 case is 4- If the strength of the jjole o, -iza will he the 
 numher of lines pas,sing out from such a pole and the whole How 
 of force will equal 4-(J \niits. 
 
 Diagrams of Unipolar Magnetic Fields.- A pole 
 
 of strentfth <i ' will send out :{() lines of force and the entire 
 
 " 4- 
 
 How of force is equal to 4-rt or :{() miits. To repri'sent this 
 
 distrihution of magnetic force diagramatically, we rei|inre to 
 sulnlivide the space siUToiniding the magnetic pole into :{() single 
 spaces, through each of which unit How of force pusses. This 
 is accomnli.shed as follows : — 
 
 About the pole /' (see Fig. 1). ol strength —, describe a 
 
circlf with any ooiivcnicnt nulins uiul draw a iliaiiictir tliroujili 
 I'. Tliis (liameter is (livi<ii<l into :U) f(|ual parts iiml liiu-s an- 
 drawn iMip.-ndiLular to tlic diaiiu-tor tlnoujili the ]M)iiits of 
 division, until tlu'V inti-rs.rt with the cirfuniliTcnci-. Tln-on<;li 
 thcsi' intersirtions iini-s an- (hawn Iroiii the Cfiitrc of the t-iiclc. 
 Thfso lines i»'i)i«'Sfnt sonii' of the lines of foree whieh pass from 
 the 1M»1.- into space. If now we inia>;ine the 1i.u;nie to revolve 
 
 aliout the diameter, these lines of force will descrilie cones which 
 cut out of the surface of the sphere zones of eipial area. Since 
 the »1ow of force proceeds imifoniily in all directions from the 
 pole, each unit area of the sphere will he trav.-rsed hy the same 
 ipiantity of How of force, hence each /one is traversed hy >uut 
 How of force. In the tijjure those lines of force only appear 
 which pass at the limit of the zones of ecjual area. 
 
Diagrams of Bipolar Magnetic Fields :— 
 
 Ist - Two unlike poles of einuil ,stn'ii;,'tli. 
 
 Let tile j)()les. as in the iirevious ease, lie of streiif^li 
 
 4r" 
 
 Tlie north \»>\f will send out :{(» lines of foree and 
 
 tile south pole receive an e(|ii!il nuniher. To represent dia;;ra- 
 niatieally tlie How of force in this case, join the poles hy a line 
 to serve as axis and con.struct upon this axis the luiipolar Held 
 for each pole. (See Fij;. 2). If now we iniajjine tiie Hj;ure to 
 revolve about the axis, tiie lines of force descrihe 2 x :U) inter- 
 penetratinj; cones. Thron<;h :U) of these the north pole sends 
 out for each a unit flow of foice, which enters the :{() corresixMid- 
 iu" cones of the south pole. This system of cones iiiu.st eoah-sce, 
 dividin-; the space into channels of th • of force, wliich pass 
 continuously from the north pole to the south pole. The coiii- 
 hination of the two Held' ' \to one is eHected hy drawiii;; the 
 diaj;onals of tin- four-sidi .ijjures, which result from the cuttinj; 
 of the lines of force. We thus obtain lines of force pa.ssiiijj from 
 the nortii poK' to the soutli iwli-, which appear as broken lines : 
 which, however, approach continuous curves with increase of the 
 Hulxlivision of the cliannels of force. 
 
 2ud -Bipolar Helds of majjnetic force of two unlike ptiles 
 of ditterent strengths. (Fij;. .S). 
 
 The construction is the same in priiicipK- as in the previous 
 case. The leiijrth of the radii of tlie circles is taken in the ratio 
 of the total flow of force sent out or ab.sorbed by tlie pole, and 
 the number of subdivisions of the diameters of each circle cor- 
 responds to tlie total How of force emitted by, or vanishing; into, 
 
 aiitl tlu! 
 
 the pole. Thus, if the north pole is of streiijjth 
 
 4- 
 
 10 
 
 south pole of -." , the radii of the circles are maih- respectively 
 
 80 and 10 and the subdi-' lions also of their diameters are :{0 
 and 10 respectively. 
 
 + Norlll >ookinK pohirity is iiidicati-d I)) - , M>iith s.vkin^f polarity by - . 
 
10 
 
 ^'i8V- 
 
 /X /I/ ^ 
 
 ik :li 
 
11 
 
12 
 
 Equation of a Line of Foroe. 
 
 Till- Mm jHisMiiii; tliii)U;;li tlio poiiitH .V '• ,</ : (Fij;. 4) is 
 |iait III' a liiii' III' U)Vi-i: Let ^V>', tile li-nytli (if the iiiii;,'lift, 
 
 Fia*. 4 
 
 / I 
 
 11, /• tlu' radius of tlu' ivuxiliiuy circles, the iuii;le Ji X A « 
 
 aiiil tlie aiiiile (,',S\1 (i ; then for the point .'• of the line of 
 
 foice we have : 
 
 A iV — (■ cos a 
 
 A S =-- 1' (■<>» ,i 
 
 A t< — A X - <t ~- r (roK ,} — ros u) 
 
 and - (cox, if — r(w «)= C, a constant. (1) 
 
 r 
 
 This relation is termed the eiiuation of the line of force anil 
 (■ its paianuter. To each line of force helonj^s a separate value 
 of ,•. 
 
 Inductive Effect of the Magnetic Field Upon 
 Magnetic Bodies. — If a ma^fnetic Ixxly, such as a piece of 
 soft iron, be placed in a niajjnetic Held, the orij^inal field is 
 <,'reatly altered. The lines of force of the tield in the vicinity 
 of the iron concentrate in the space occupied by the iron. A 
 south pole will be developed in the iron where the Hues of force 
 enter, a north pole where they pass ont of the iron into the 
 s]iace of the tield. The .soft iron, while in the tield, is thus a 
 
l.S 
 
 iiin;;iirt with its <i\vn tii-l<l iii'luccd liy tin- (tii^ci""! ♦''"''' "'"' ''"' 
 iiiii;;ii(tii' tichl as IV wltolc is u (•(miimsitc titld of two iiia<,Muts 
 Tlie soft iron, wlu-ii takt-ii out of tin- tii-ld loses its polmity. If 
 the jiitrc of soft iron !)•■ iilac-cd tiaiisversfly ucioss tlic poli- of a 
 •t, without toucliin<; it, it will \>r sen that the lines of 
 
 niairnt 
 
 loifc t-nti'V the n-on, < 
 
 th 
 
 divide, and j>ass out at iMitii enils, so that a 
 .south pole will 1h' developed in tlie center of the pieee of iron 
 and two north poles, one at eaeh end. The spaee heyond the 
 iron in the direction A will he free from lines of force. (S.'e 
 
 Fi-. 5). 
 
 Th.- li 
 
 >f force are thus 
 
 shfjwn to pass more readdy 
 tln-ou;;h iron and in <;eneral 
 throiii;h ma<;netic IkkUcs tlian 
 ImkIIcs which are non-ma;;netic. 
 Tliis is usually exjiressed hy say- 
 inij that the /Hriticiihilitif of 
 maj;netic ImmUcs is <;reater tlian 
 that of non-nia<;netic IxMlies, and 
 is <,;reatest for soft iron. The 
 intensity of tlie disturhanci' of a 
 niaj;netic field of force pnKluced 
 hy a nia<;netic hody is in <;eneral 
 pi-oportional to the penneahility. 
 The penneahility of hardened steel is much less than that of 
 soft iron, hut the polarity developed in it hy a stron;,' field is 
 retained hy it after removal from the field. Mai,'netite, jakoh- 
 site and pynhotite hehave in this respect like steel, and wh 
 
 onc( matcnetized, aiv capr 
 
 iihle with their own field of acting' in- 
 
 ductively upon other ma;rnetic hodies. These have heen desij;- 
 1 hy the Swedish authorities as " attractorily " majjnetie 
 als: menaccanite, olivin, auirite. hornhlende 
 
 Tl 
 
 lie nuneni 
 
 nat!;( 
 
 hodi 
 
 and p\-rite are termed " refractorily " ma;;netic iiodies. Th 
 
 thouijh attracted hy a stroiij,' majjnet and of permeahility ;,n'''!>ter 
 
 than that of noii-ma<;netic hodies (/./•., hodies indifferent to 
 
 I'se 
 
 nia^ni 
 
 ■tic force, as glass, (piartz, etc.), lose the polarity developed 
 
 in a inaj^nctic field, when removed from it. 
 
h r 
 
 U 
 
 CHAPTER HI. 
 
 THE BARTH'S NORMAL MAONBTIO PIBLD. 
 
 A iiiaj;nutic needlt', free to swinjj in any piano, placed in a 
 nmynitic field will place itself tanj;eiit to a line of force. If this 
 experiment W' made on the surface of the earth in different 
 localities, it will Ix' f<jnnd that the needle will in {jenenil place 
 itself with its axis in a plane noiih and south, stand horizontal 
 in the vicinity of the e(|uator, but dip more and more, with its 
 north end toward the perjH'ndicidar, with increase of latitude 
 north, and stand vertical at 70.5° north latitude and 08.5° W. 
 lon;citude On-enwich. Passing south from the equator, the dip 
 is reversed, the south jx)le of the needle dippinjj more and more 
 toward the peii)endicular with increase of southern latitude, until 
 at 74° .south latitude and about 148° east lonjjitude Greenwich, 
 the needle again stands vertical. In each place of observation 
 the position of the axis of the needle indicates the direction of 
 the lines of force of the earth's magnetic field. If the places, 
 for which the angles of dip are ecpial, l)e joined, curves result, 
 wliich are similar to the parallels of latitude, but do not coincide 
 with them, nor are they even parallel to each other. The.se 
 lines are termed ixiH^linulK The line of no dip is termed the 
 
 A compa.s.s needle does not in general point to the astro- 
 nomic north on the surface of the earth, but the vertical plane 
 passing through its axis, when at rest, includes an angle with 
 the astronomic meri<lian. This angle of deviation from the 
 astronomic meridian is termed the HDtjlf ofiifctiinitioii. If these 
 angles be observed for different localities on the surface of the 
 earth and the localities, having eipial declination, Ix^ Joined, lines 
 result, which are termed tw«/(>/ur lines, and which have in general 
 similar directions as the a.stronomic meridians, but do not coincide 
 with them, nor will their contours l)e .similar. A.iother set of 
 lines, termed intMlynamic lines, may be drawn on the surface of 
 
15 
 
 the ,ar;h, which connect placfs of e(|ual intensity of nmynotic 
 
 Thew! are the usual elenients, whicli enter into the mapping; 
 out of the earth's nia^ietic field of force. 
 
 Althoujjh tlu! total intensity of the earth s majfnetisni may 
 for eaeii locality Ih' readily measured, it is foun<l to Ik- more 
 convenient to represent the total foi-ce l>y its horizontal and 
 vertical comi)onents and to measure these. 
 
 If the circle (see Fij;. 
 I'iv- «i G) NASH he in the 
 
 plane of the majjnetic 
 meridian and the majj- 
 netic needle at the place 
 of observation come to 
 rest, making an angle v 
 with the horizon X S, 
 the needle will Ik; tan- 
 
 - sjent to the line of force 
 
 of the terrestrial field 
 passing through the 
 jKjint of suspension 0. 
 
 The force of the field 
 acts with equal intensity 
 on the north pole at D 
 and the south pole at K, 
 but in opposite diree 
 The resultant is zero and the needle at rest. 
 Let D K ^ K M represent by tlieir length the intensities 
 of the acting forces and the arrow points indicate the directions 
 in which they act. We may then regard D K and E M the total 
 intensities as the resultants of the components H and V, of which 
 the former represents the horizontal intensity, the latter the 
 vertical intensity of the earth's field. 
 From the figure we have : — 
 
 V= H kiiKj V (2) 
 
Ill 
 
 10 
 
 DK KM r , ipr rw,„r 
 
 rim »• 
 
 (••n 
 
 Ih'iici' 7' mill r Im'ciiiiii- known, wlu-n //ami /• iirt- kni>wii. Tlif 
 vahii'M // an<l <■ afc ;;ivcn for <liHii-fiit jilaffs in tlir piililiHJii'il 
 niujjnctic cliarts of tli'' tfiTi'stial field. 
 
 It ri>i|iiii'('M to Ih' |Hiint<'i| out tliat tii<- rlfini'iitN of tin' 
 nia;;n('tit' Held of tin- cartli, rciircwntt'd liy tlic iwiyonii', iniN-linal 
 luid isixlynainic linrs. arr not constant, lait arc Hiilijirt : 
 
 Isi- To Nnddcn variations, due to ••osniic inayni'tic ilisturW- 
 aiKM's. 
 
 2n«l— To annua! variations, wliicli jiroj;rcss at a dcllnitc 
 rate and in a dctinitf direction, wliicli, when known, render the 
 true value for any year calculalile. 
 
 .'{nl — To daily variations, wliicli in {general are small. 
 
 1 
 
 ('iiai»ti:r IV. 
 
 THB DISTURBED TERRESTRIAL FIELD OF 
 FORCE. 
 
 We have already seen that if part of a majjiietic field of 
 force includes a medium of j^'reatei- pei-nieahility than the rest, 
 th<' lines of foire hy preference pass throujjh the more perniealile 
 me<lium, thus miMlifyin;r the di.strihution of the lines of force of 
 the ori<rinal Held of force, so that moie lines of force pass 
 throujjh the more permealile meilium than throui;h the less per- 
 niealile me<lium immediately surroundiiii; the former. From 
 this it results that de]iosits of " attractorily " nia<;netic IkkHus, 
 such US maffuetite or pyrrhotite. attract the lines of foi'ce of 
 terrestrial magnetism and hecome themselves niai;netic. The 
 extent to which these ImmUcs mcKlify the distrihution of the 
 normal* terrestrial fielil de|ien<'., u]ion their volume, shape, posi- 
 tion with reference to the lines of force of the normal terrestrial 
 
 field, and their de|ith lii'low the surface of tl arth. In the 
 
 case of the " retractorily " maf^netic sulistances, the permealiility 
 
 * Tin- UTivMri.il field uiulistiirbed by niiijjuetic Kdies or deposits. 
 
17 
 
 in not iiMwIi HU|M'ri(ii- to tliiit of iioii-iim;C""'t''' Htil»*tiiiu-fH, hidI 
 lifiic-i' tlu'ir trttft in inoililVin;; tin- <JiHtiiliution of tlif lines of 
 fortv of tlif tciTfutiiiil Hi'itI in concNiMinilin^fly Nnmll. 
 
 ('list's (K'cur wlicrc non-Hiiijjnctic ons iinti rot-ks U'eonic 
 niiijjnftii" tliioU'^li the picscnci- of nm;;nftitc as an ttcet'sMory 
 inj,'iv<lifnt iuhI tiins iKcuni.- ciiusfs of (listuilnincc of the terifs- 
 tiiui tii'ld. The li.'nmtit.-s of Sw.<l.n, unil cfituin roj)|MT, liwl, 
 iinil zine ores iirc illustrations of oifs whiuli aiv ot'tcii \uiin- 
 nctitif, ami diahasi', ilioiitc ami hyi» ritf often contain so larj^o a 
 jKTCi'nta;{c of nia;;m'titi', ami of sncli uniform ilistriluition 
 tlu<)U*,'li tlifir mass, that tiii- nia;;nitoniftrif nu-thod may Im; 
 cmiiioytMl "in ttacin;,' tlu-ni front l«Kalitifs wlu-n- tlu-y outcroj), 
 
 through areas in wliieh they are huried and in duter- 
 
 minin>t whether the rcK-ks are t!at lyin;j '.;• hi;;lily tilted, the 
 direction of tlieir strike and dij», and, in some cases, the deptli to 
 wliii-h they are lairied."* 
 
 If the niajrnetite is arran>;ed tlnou;;h the igneous r(K;k 
 alon^ lines corresjMindin;; to the lines of force of tlie normal 
 terrestrial Held, the majcnetic effect prinluced may iM'come very 
 <freat.+ Majjnetic disturlmnces of tlie earth's tield, however 
 ;,Teat, do not therefore justify the conclusion that they are 
 caused hy witrhihlr niaifuetic ore (h-posits. 
 
 Relation of Din to Intensity of Magnetization.— 
 
 If a soft iron Uiv 'le jiiaced *ith its axis parallel to the lir i of 
 force of terrestrial !na<;netisiii, it will Ik' fouml, if the experiment 
 U'. made in the northern hemisphere, that the upper end of the 
 Iwir has accpiired ntath-pcjie attraction, the lower end .south-pole 
 attraction, and tliat th.- bar in this position exhibits all the 
 characteristics of a inujjnet, with the poles near the ends of the 
 Imr. If the stren;,'th of the maj;neti/.ation of the bar be tested, 
 it will be found tliat it is a maximum in this position : a mini- 
 mum when tlie len;^h of the Imr occupies a position perpendicular 
 
 * Homy Lloyd Smyth : " MaKnelic Observation-, in Geolotfical ,Mappin>r," 
 Triiiisiii lions .American Inslilule of Minini; Enjfineers, Vol. XXVI, pp. 641 
 and 642. 
 
 + See page 3. Theory of the Consiilulion of Magnets. 
 
 
t(i tin- liii«'N of fon-f of thf ttirrt'Htrial Ht'l«l ; iiml <»f iiiU-riiiu<liiiU« 
 intt'iiMity ill int<Tiiif<liiitv jHwitioiiM. 
 
 It the iiiihictivf action of tlif fiirth'H nM U' rt-jpinU-il as 
 the cause i.i till- iiiatjiH'ti/iitioii of a iiia)fii«'tit' orf-lnxly, it in 
 tviil>nt that Wf may cxjH'ct that the ilij> of the orc-<U'|Mmit will 
 ill a Hiiiiilar iiiann<>r U- (■oiiiiiK-tcd with the Mtrcnj^th of \U 
 iiiaj{iifti»itioii, an in tiii' ciih.' of tlif iron Uir, »'.'., it will U- at a 
 niaxiiiiuni wlicn tin- ilip in iMii-alit-l to thf Hih-m of force of the 
 tciTcHtrial Hi'lfi, a inininiuin in a jioHition at ri;{ht an^U's to tlicw 
 linen, ami of intcrniwliati- intcnsit- wiicn the flip correniKMidM to 
 intermediate jxiHitions. 
 
 In ju(l){in^, therefore, of the inasMiveiienM of an ore depwit 
 from the intensity of itn magnetic effect, the direction of the lUp 
 of tlie depoHit in relation to the lines of force of the terrentrial 
 tield iiiUMt evidently U' taken into consideration. 
 
 C II A FT EH V. 
 
 ■rPBCT OF A MAGNET ON A OOMPA88 NBBDLE 
 IN A NORMAL TBRRB8TRIAL FIELD. 
 
 Tliroujjhout a space of small dimensions, comparwl with 
 that of the earth's radius, the normal mai^ietic terrestrial tield 
 is sensibly uniform, the lines of force of the horizontal maj^netic 
 tield will in this space be parallel. 
 
 If a compass be set up horizontally in such a tield, the 
 lu-wlle will come to rest and In- in e(|uilibrium when it occupies 
 a iK)sition such that its nia;,ni«tic axis is in the magnetic meridian 
 JV ,Si of fij^re 7. In this position the forces of the horizontal 
 tield acting on the needle are of eijual intensity and in opjKisite 
 directions and the resultant is eiiual to zero. If, under these 
 conditions, a magnet .S" N' \h> placed with its axis in a pt>sition 
 at right angles to the magnetic meridian and in the same hori- 
 zontal plane with the compass needle and with the center of its 
 axis at distance d from the point of suspension o, the neetUe will 
 be deviated and come to rest in a new position with its axis 
 
10 
 
 [Mmlli-I to thf liiii-M of foitf of till" rfMiiltiuit Hflfl, ••oiii|h>iiih1i'«I 
 of that of tin- I'lirtliH Hfltl iitul tliiit of the tl.-tlfctiii),' iim},'iift. 
 If llif Month IK)U' of tlu" (It'rtt'Hiii;; iim;{in'l (m-vh the i'om|MiHM (.ih 
 
 hIiowii ill the Hyuiv) tlif iioitli jiolc of tht- ii Ilo will 1h' ili-- 
 
 rtectfd toward the ejixt of tin- tiiiipa-tif iiicriilitiii. 
 
 i iv i 
 .V K I 
 
 i / 
 
 JH V 
 
 \ Mil. 
 
 K* it'* ■/» 
 
 Kit{'. 7 
 
 S' .'• .V 
 
 
 I'o ) Uiii ivii v.\j)ifHKioii fof the iHi-ct of the ik-flectin;; 
 iim^nut, let : 
 
 ft — the stii'iij^th of a |>nlt' of till- c-oiiipasM neeilif, 
 a — the stienj^li of a pole of the (lefleetin-; iiia;;net, 
 2 i — the lenjjth of the coiiipasM needle, 
 2 L ■— the len>;th of the defleetiii}; ina^^iet, 
 2 // I -"- m • the moment of the compasH needle. 
 2 La = M the moment of the deflecting; magnet. 
 H — the intensity of the earth's horizontal Held. 
 d — the distance of center of deflecting; mai;net from o, 
 the point of suspension of compass needle. 
 
 * The moment of a magnet is defined us the product of the streiiKth of one 
 pole into the length of the magnet. 
 
20 
 
 '4 1 
 
 Fn till- forcf witli whicli »'" .anli- hoii/.oiital Hi'ld 
 
 acts ujjon tlic ))()k ■ "i li" cfini ss m-eclK'. 
 f'p the I'orcf exert. '.l l.y t. I'l" ■■ ,' iiia<,'iiet upon 
 
 the poles of the coiiipiiss needle. 
 .!/„ the iiioliient of the eouple due to the eiutli's Held. 
 ,l/i, = the moment of tin- eouple due to the field of the 
 deflectinj; majfiiet. 
 It is assumed that tlie field produced hy the deHectinj; ma<;net 
 is of v(\\m\ intensity at the points ;( and •>< and that the lines of 
 action of tlie force pr.K-eedinj; from the poles of the dcHectinj; 
 majciift are paiallel to <> .'■, which is not .strictly true. 
 
 For the position of e(|uilil)rium the momi-nts of tlie two 
 oppositely directed couples .!/„ and Mj, must he eipial, hence: 
 
 t\ 2 / x'nt a = Fo 2 / rox « 
 
 F„ r-. H ft (-I'l) 
 
 : nd Fp is tlie residtant of the action of tlie jwles f)f the deHect- 
 in;r nia<,'iiet upon the poles //, .s of the compass needle. Denoting; 
 attraction hy the minus si<;n and repulsion hy the plus si;,ni, 
 we have for tlie attraction of the south pole of the deHectinj,' 
 iiia<,niet upon the north [wle of the needle : 
 
 - " f' 
 
 id-L)- 
 
 and for the repulsion of the north pole of the deflecting' ma<;net 
 upon tlu' north polo of the compass needle : 
 
 The action line of these two forces is assumed to coincide, 
 hence : 
 
 f 1 • 1 _ ■* " f^ ^' '^ 
 
 ^'•' = '''"\(T-rZo'^~^^7^^>J 
 
 li 
 
 ■'t-^'-,^;) 
 
21 
 
 Nt'i'lt'ctiiif' -.7 iiH tix) snmll scnsililv tu aHrct tln' icsiilt. w<- liavc : 
 
 1 
 
 n = 
 
 2 J// / 
 
 1 - 
 
 2/;-'l 
 
 (5) 
 
 I'llL'tll 
 
 If (/ is iiiiulf liii';;t' ill L-oinimrisoii witli 2 L, tli 
 
 (IcHwtin;; iiiii<;iict, till' expression II ^j i lues not ;;r« .lly 
 
 (••'.ler from unity jinil we iiiiiy write : 
 
 2 ,1/ n 
 
 K = 
 
 ,P' 
 
 («) 
 
 Suhstitutiui; values for F^ and f',, in ei|uati<)n (4) we liave: 
 
 2 .1/ ft 
 
 // It tdiii) a 
 
 2 .1/ 
 
 // til /*(/ « — ; — rp - 7 - I' n. 
 
 and 7 '/■' 
 
 2 JA - a constant V. 
 
 
 1 
 
 Retaininjj tlie factor _ 2 IJ- of .Mjuation (o) we have from 
 
 eiiuation (7): 
 
 .1/ 
 
 / 2 L-\ 
 
 liiiiil a H (/I II j^j 
 
 (10) 
 
 an e(|Uation useful for determiniii«f tiie moment lii a majjnet in 
 terms of //, or in absolute units, when the value of H in ahsu- 
 lute uin'ts for the place of observation is known. 
 
 In the fore>;(jin;; demonstration it was assumi'd that the 
 strenj,'th of the field of the deHectiii",' ma<cnet was the same at 
 the points ii and a, but it is evident that the strenj^th of the 
 Held, due to the deHectinj; ma;;net iii'itr the compass needle, will 
 be the same only for points at e(|ual distances from the center 
 (jf the detlectini; iiia^'uet, and that, therefore, the force of the 
 deflecting magnet exerted upon the compass needle will, with 
 this methotl of prixlucinj; the anijle of deflection, vary with tiie 
 anjfle «. This taiit^ent metluxl will, therefore, yield only ajjproxi- 
 iiiately coi'rect results. 
 
 I 
 
22 
 
 The value of 7 can, lunvever, W- reiulered independent of 
 tlie nnj;le of deHection by revolvinj; the compaHs with its ami, 
 whieh carries the deHectin}r niuffnet, alwut a vertical axis, pass- 
 ing,' throuijh the point of suspension of the compass needle, until 
 the needle stands at rijiht anj;les to the deHectin;; arm, as shown 
 in tivure H. 
 
 .V 
 
 // 
 
 f 
 
 1-is'. '» 
 
 .Ay \ V 
 
 ■/,•■ 
 
 "4^ 
 
 I 
 
 
 
 In this position both north and south poles of the compass 
 needle are at e(|ual distances from the center of the deflecting; 
 matriK-'t, and therefore occupy positions in its field of equal 
 strenj;tli. 
 
 The number of defnees through which the needle pa.sses 
 back to a position in the plane of the majcnetic meridian, when 
 the deflectinjr magnet is removed, measures the angle of deflec- 
 tion in this case. 
 
 k 
 
 bJ I' j. -y g^ r; 
 
23 
 
 Lt't tliis anjrie he denoted by «„' we hIuiU then have (see 
 
 Fisj. «) : 
 
 q'^Hi*iva„' (11) 
 
 Since 7' for this method (the sine laethcxl), is constant, and 7 
 for the tanjjent nietliod very nearly so, we liave for ditferent 
 points in a niajnit-'tic fitUl, in which tlie value of // differs : 
 q = H tang a = H' tanij «' 
 tiimi a 
 
 or H'^H, , 
 
 and q'= H sin «o'= H' •*'i« «" 
 
 or H — H —. « 
 
 (12) 
 
 (13) 
 
 From these ecjuations it follows that the value of //' differ- 
 infj from H may be found by either of these two methods, in 
 terms of H, the value of the horizontal component of the mag- 
 netic field at one station taken as a unit. 
 
24 
 CIIAPTKU VI. 
 
 THE THALi^N-TlBBRG MAGNETOMETER. 
 
 Desoription. — This nppaiutus is II combination of Tliak'n's 
 nia<'nftunictfr and 'I'ihiTjj's inclinator, Jind us now const nifti-tl 
 l)y mechanician Bel};, of Stocl<hohii, constitutes a very conven- 
 ient instii'ment lor tieltl worii. It permits l>y its construction 
 tlic determination not alone of the ditierent vahies of tlie hori- 
 zontal comi)onenls of a disturl)ed ma;;netic tield, Init also the 
 more important determination of the different vahies ot the 
 vertical components. Its principal parts are the compas,s and 
 its support. 
 
 The Compass (See Ki<{s. !), 10, 11 and 12.) Tlie com- 
 
 pa.s.s K, consists (jf a low, hollow cylinder, of .ihout « cm. diameter, 
 closed top anil I ottom by (piadratic plates 1\ and l\ witli sides 
 of alxmt !t cm. The top i)late is hroken thro'ii;li by a circular 
 openinj;, concentric with the cylinder and 7..') cm. in diameter. 
 This opeiiin;; renders tlu' interior accessible and is closed by a 
 reniovat>le ^^lass cap. The center of the bottom of the '-ylinder 
 carries a jewel for the reception of (Jiie end of the a\..^ of rota- 
 tion of the ma;;netic needle, the other end of the axis is s.ipported 
 by a jewel ciuried by an arm, screwed to the inner side of the 
 cylinder. .\ Hat rin;;, of diameter (i em., <;raduated into dejjrees, 
 is fa.stened to the inside of the cylinder, parallel to the ipiadratie 
 plates, at such distance from the base tiiat its edj,'e bisects the 
 knife-edj;e poles of the majjnetic needle. The north and south 
 directions, parallel to one parallel pair of side.- of the (|Uadratic 
 plates, are marked !)(> . The ends of the east and west diameter 
 are at divisions marked . The directions marked west and 
 ea.st correspond, when the needle marks !M) N., to the astronomic 
 directions. 
 
 Screwed to the compass 1m)X, in the proloiifjation of the 
 east and west directions, are two cylinders Z\ and Z-i, of W mm. 
 diameter, whicii permit the compass to W- placed into beaiing.s 
 
25 
 
 at 
 
 ,Lh 
 
 
 
 M 
 
 1 
 i 
 
 1 
 
 1 
 1 
 
 1 
 1 
 
 
 1 
 ■ 
 
 ^ : 
 
 ! k| 
 1 1 
 
 c 
 
 1 
 1 
 
 1 
 
 k ' 
 
 k> 
 
 1 
 
 jj^ 
 
 
 
 y 
 
 It-K 
 
If ll 
 
 26 
 
 ! i 
 
 (A tht' Hupjiort aixl tlnTc sccur- 
 
 I'ti. HutWv'fll tlu' two plutl'S 
 
 and visible tliroujili />, tin- 
 eoiiiiMiM.s 1m)X IM jii-Dvidi'd witli 
 a lx)X level of a weii.sihilit^' of 
 (i' tor 1 mm. deviation of Iml)- 
 hlc. This lx)X level permits 
 the levelliiii; of the compass 
 when in use without its usual 
 support. On the diaj;(jnally 
 opposite corner, on the top 
 plate, is situated the sciew 
 head .S'l, which operates the 
 arrest of the needle. 
 
 The needle, for the i;reater 
 part of its lentjth. is har 
 
 Vi'i.M 
 
 O 
 
 ^^^^ri^i^— ^" 
 
 Do I 
 
 
 
 shaped, with cross sections of 
 al)out 2.9 mm-'. The ptjles are 
 {nound into knife edjfes, par- 
 
 
 ^aa 
 
 ifHHI 
 
27 
 
 iillol to till- iiNis of rotation. 'I'hi- axis of lotiitioii is icprtHenttd 
 hy a sttcl cyliiHlir, wliicli jiuhhcs jRTjHMicUcuhuly tlii<m;;li tlic 
 niidflK- of the iiia;,'nttic axis of tla- iRrdic In the vicinity of 
 this axis till- sluipi' of tiic iictdlc is sucli tluit the ffiiti-r of 
 •gravity, when tin nirdli- swing's in a vt rtiiai i)lani', is situated, 
 
 r fi^ 
 
 I, 
 
 A 
 
 |-i^i;i 
 
 as in the case of the In-ani of a hainnee, l)elow the axis of sus- 
 pension. A slidinj; wei;;lit permits of the counteiaftion of the 
 vertical intensity of tlie normal terrestrial field, so that when 
 free to swinj; in a vertical plane perpendicular to tlie niaj^ietic 
 meridian the needle K'vt>* 'i midin;; in such a Held. 
 
 A bra.sM arm, endin<,' in a rin<; Ji, is pivoted on tlie compass lx)x 
 midway Itetvveeu the ,s(|uare plates. This arm serves as a sus- 
 pension when the compass is to be used hy an observer as an 
 inclinator, without the sui)poit. 
 
 The Support of the Compass with 
 its Deflecting Magnet.— (See Fi<;s. », 10, 
 11, LS and 14.) Two uprights Ai, Lj. screwed 
 perpendicv.larly upon the ba.se plate i'n, sup- 
 port in their bearinijs the cylinders Zi, Zi of 
 the compass. Zi, Z-, are retained in their bear- 
 inijs by tlie slides C'l, ('% The hei<;ht of the 
 bearinjj above the Imvsc plate is such that the 
 compass may be revolved into a vertical posi- 
 tion. Two set-screws, passinj;, the one vertically, the other hori- 
 zontally, throu;ch the hmI Q, connectinj; L\ with I^, limit the 
 rotation of the comi)ass box to one-cpiarter revolution. These 
 set-screws, when once refjulated, enable the observer, by orinjfinji 
 the stjuare plate P^ into cont^ict with either one of them, to 
 
28 
 
 phu'c the coinimss 1h)x witliont ili-liiy into jioMition citlitT |)iir- 
 alli'l or iHTiHiuliculiir to thi- Uxsr plat.' /':,. A 1m)x hv.l. of 
 siMiMiliility :{' to I mm. <K'vi.ition ol" ».ul)l.l.', s.-fuifil to l)iis.' plutt- 
 /':i at />i Nerves to iiidieate its lioii/ontal jHysition. Tlie iiinler- 
 side of tlie base pliiU' is sfiewed upon a eoiie F ( Ki;.'s. l.'i and 
 Iti), wliieli tits into a Uill and soeket joint, firmly secured ni>on 
 a tiii«Hl Hy means of two sciews Xj, S-.i. and spriny;, operating; 
 (as sliown in Fi;,'s. 1.') and Hi), upon the extension of the hall 
 and socket joint, the i)ase plate /';, may he hovelled. Rotation 
 alM)Ut a vertical axis of the support is accomplished l.y the 
 movemi-nt of the cone in its liearin;,', and may he secured in any 
 position hy the clanip-serew .s'4 sliown in the ti;i;ure. 
 
 Fasti-ned to the ui)rii;ht A], and ]>arallel to the axes Zi. Z«, 
 ■A cylindrical arm K of 22 cm. in lenjith is situated (see Fi>;s. !• 
 and 10). To render this arm lijjht and yet sufticieiitly rijjid, it 
 is made of two concentric cylinders )f hrass soldered to;;ether. 
 This arm carries a frame (i for the reception of the deHectinj; 
 majjnet. Thi.' frame is movealile aloni; the rod and may !)»■ 
 clampe<l in any position by screw .S'.-„ and is of such hei«,dit that 
 when the dettectinif ma<;net is placed upon it the axis of the 
 dertectinif magnet will be in tho htnizontal plane in which the 
 compass needle swinjjs. A millimeter scale on one side of the 
 arm, with its Zero point in the cuntef ot the axis of rotatior. 
 uf the compass needle, serves to indicate the position of the 
 
29 
 
 dcllcftin;; inii;;iift Irom tin- ci'iitcr of tin- cohhmish ix-cdlr. At 
 tlif I'li'l i)l" the arm mid vntically dnwiiwaril, a fi>rfNi;;lit A' 
 of special and very coiivi'iiifiit coiiMti'iU'tioii is attaclicd. ■iiist 
 lifliiiid till' l«is li'Vfl />! is till' liacksii^dit //. cniisistiii^ of a lirass 
 platf witli its vertical slit. 'I'll iii>ri;;lits A, and /-■.. are hrokeii 
 tlirou;;li, and when tlie coiii|iass is in tlie liori/.untal jioHition the 
 si^jlits may Im- eni]ili>yed to luinj; the arm K into any desired 
 direction. 'I'lie detlectinj; maj;net is I, I cm. wide. 10 cm. Ion;;, 
 and 0.2 cm. thick. Its north iiid is marked, as in the case of 
 thee()m|iass needle, hy an inserted liriiss |iin. A hntton attad-ed 
 to the middle of the ma^^net [lei'mits its removal from and insei-- 
 tion into the fi'anie. without tonchin;,; the steel, of which it is 
 composed. A sprin;; It retains the ma;;net in its frame. 
 
 Testing and Adjusting the Magnetometer. Al- 
 
 thon;;h the instrument is tested and adjusted hy the maker 
 iM'lore it leaves iiis shop, it is advisjilile for the ohserver not to 
 rely uihhi tlie shop adjilstinelit, Init to test the majinetometev 
 for liimself liefore nse, and make any i-etjuired corre<-tioii. 
 
 1. Examination of error due to eccentric suspension of compass 
 
 needle. 
 
 Till- compass is reniove<l from its support and placed upon 
 a level plane. The needle is now read at hoth eliils and the 
 compass turned throu;;h an anjjle and a second readiu}; taken as 
 l)cfore. This pi. cess is conti'iued until a complete revolution 
 lias Ih'cu made. .\ constant ditf'erence in the reiidin^js of the 
 north and south ends indicates that tin' ma^jiietic axis of the 
 needle does not pass thioue;h the sUs]iellsion of the needle. A 
 periodic variation of a ditterence in the readin;;s indicates that 
 the axis of rotation of the lu-edle does not pass throu;;h the 
 center of the ;;raduated circle. Hy readin<; hoth ends of the 
 needle ami taking; the mean the eccentricity error is eliminated. 
 
 2. Examination whether axis of rotation of support is perpendi- 
 
 cular to plane of box level D, on base plate F:,. 
 
 The majiiietometer is screwed oii the liead of the trip(Ml, 
 rotateti so that the arm K is over one of the screws of the ball 
 
 I 
 

 .«■ 
 
 a 
 
 ii 
 
 80 
 
 ,11.-1 H,K-kK Joint, luul l.y i.i.uMH of tlu- two l,.v.-llin« scivwh tlir 
 l.ul.hl." of tlu- Ik.x U'V.'l is l.ioujtht to til.- ••.'iit.r 'I'Im- iimpi.-to- 
 m.-tiT is now ivvolvv.1 tlnou;;li un .in;;!.- of IHO , wliid. is .'UHily 
 ,.»WU-i\ l.y tiikiii;,' tl..- iviuliny; uf tlu- i-oiiiihimh. If t!i.' l.ul.l.ie 
 ill this n.-w iioHitiun is .lisj.im-.Ml, iiHliciitini,' tlmt tli.- axis of n.tii- 
 tioii is not iH-n«-n.lii-ular to tlio plan.- of tli.? 1h)X l.-v.-l, corivction 
 isnmd.l.y d.rivasin;; tlw .lisi.lac.-in.'iit (.f tli.> l.nl.l.l.- to A.whifli 
 is awoniplislu'.! liy ni. ans of tli.- tliiv- s<t.'Ws passinj; throuyli 
 th.' iK.ttoni of platf /':, provi.ltMl for tliis pniixts.'. 
 
 3. Bxamination whether axis of oompasii box is perpendicular 
 
 to vertical axis of rotation of support. 
 I'lttci" IV rid.-r K-vt-l upon ax.s ^, Z. ami rotat.' sujiixiit 
 .ilK)Ut vfitiwil axis until Zi. Z, is in line with on.- l.-vtllin^' s«t.>w. 
 By nieauH of tlu- lovellini; scii'ws lainy th.- I.ul.hl.- of ri<K-r It-v.l 
 to the center. Now i-v..lv, ..jwit ilK.ut v.-itii-al axis thr<.u<;h 
 1«0 , as indx-atcl hy compass ii-a.lin^'. If, in this lu-w position, 
 the bubble is .lisplaceil, the vertical ami hori/.)iital ax.s are n.)t 
 perpendicular to each other. Correct throujjh .1 the displace- 
 ment of the Imbbl.- by screws pntvi.led f.>r that pu- 'st,, „i._ if 
 these Ixj wantiii",', by el.-vatinj,' the prop.-r upri-;h I i . L, by 
 placinj; jmper In-tw.-en it ami the Uise plate /'i. 
 
 4. Examination whether the vertical screw of bar Q, when in 
 
 contact with the lower plate of compass box. renders 
 
 compass box horizontal. 
 The inaj;n.-toniet(-r upon its tripo.l is l.-v.-lled, the low.-r 
 plate of compass box brouj;ht into contact with the vertical 
 screw .>n Ixir Q. \ sij;ht is n..w taken alonj; th.- t..p .)f the 
 compass Ijox an.l at rij;ht auj^les to the arm H. ..n a scale sus- 
 iwnded vertically b.-yond tlu- niai,ni.-tomet.-r, an.l tlu- rea.lin;; 
 r.-corde.l. The support is now revolv.-.l alwrnt tlu- vertical axis 
 throu<;h 1«0 , imlicated by the compass rea.lin^', ami a second 
 readinj; taken on the scale as before. If the r.-adin},'s .litter, the 
 screw must be turiu-d in the pr.)p.-r .lirecti.)n until this ditier- 
 .-nce is ma.le om--half. The bubble of the 1h)X level /), lietween 
 plates I'l. P., niu-st now t)e in tlu- c.-nt'-r. Any deviation of the 
 bubble must be corrected by the screws provided for that purpose. 
 
:n 
 
 ft. Sxamination whether the horliontal lorew of the bar Q when 
 in oontaot with plate P, of oompaaa box, indloatea its ver- 
 tical position. 
 
 The lllti;;ilftiili|t'ti'l' i^ srt up llllll IcVclli-ll us Im-I'iiI'i-, illlil I'i 
 
 \ni>i\jrht into coiitiwt viUi lioiizKiitiil wicw. Viiticalitv i»f platf 
 /'•.> may imw U' tcsti'd liy a pliiinliliiic oi- si^lit tiikfii aloii;; |ilatf 
 /'•J, 111! a Mcalf jdacftl lioi'i/niitally In-iicatli tin- iiia;;nt't()iii«'tt'r, an 
 ill 4. C'oiTf«'ti()ii iv(|uii't'<l is inadt- witli lioi-ixiiiitiil wivw. Biimc 
 phitf I':, is hiokcii tlirou;;li to iH-niiit this ailJiiNtiiifiit to Im- 
 iiukIc. 
 
 6. Neutralisation of the vertical component of the earth'a nor- 
 mal field. 
 
 Tin- itia;;iiL'toiiiftfr in tin- nonnal fit'M. pi-operly li'vcili-d, 
 
 is rotated until the nfcdic reads !K) . tin coiiiihiss is tlien phvced 
 
 vertical, tlie small slotteil ahiiiiiniiim plate. [H'ovided for ])ro- 
 
 diiein;; tliis correction in modern instrumuiitM, iiioved towanl 
 
 the south arm ot" the sompass needle until the newlle reads 
 
 zero. The plate is then fixed in position hy means of screws 
 
 pi-ovided for that puri)ose. A thread, tied on the south ai'iii 
 
 and cautiously pushed into the re<|i;ired position hy a sharjicned 
 
 liintch, limy, in case of necesMity, replace the small \vei<;ht. The 
 
 thread iH'inj;, however, moi'e or less hyjjroscopic, its weijjht will 
 
 not Im' constant, hut depend upon the state of the weather. 
 
 Precautions to be Observed in Taking Observations 
 with the Magnf eter. 
 
 1. The observer should assure himself that his person is 
 free from iiiaj;ni'ti" InHlies, such as pocket knives, keys, etc., 
 which wouhl influence the readin;; of his instrument. 
 
 2. -MajiiU'tic Ixxlies which <K'CUr in the field and which can- 
 not Ik.' removed, such a.s iroji r<x)fs of huildinjrs, majjnctic ore 
 dumps, etc., must have their hxratiun accui-ately determined and 
 their position marked in a sketch, to lie transferrefl to the accur- 
 ately drawn plans of the inaifitetic field, when their disturbiiij; 
 effect may Ik- estimated. 
 
 ',i. Wiping the glasn cap of the magnetometer tends to 
 
\l 
 
 '.\2 
 
 .lirtiil'v til.' yliiHx, wlii<-li ivmlfiH tli.- ih.li.utioiiH ..f tlir iif.illf 
 mitiiwtwuitl.y. lU- LivatJiiiiK «iH.n tl..- .•I....Mitir.l «Ihn^ iI.- 
 fifftiifity ix <liHrlmr;;<«l I'lom its Murfiu-f. 
 
 4. Amuiiuliition .if .lu^t in tli.- jfw.ll.'d l«ariiiKH ..I' tlir 
 
 SUsp-IIHioll ..r tl..- IU'.mII." .I..|.IVSS..H til.' S,.|l«itiv.MI.-HH . .f tlf f.llll- 
 
 l„is^.. It i« mMsiihl.-, tli.-ivr.)!-.', to .)|M-ii tlu" ii\i\^'* ',i\> as m..1.|.,mi 
 as jmismH)!.'. 
 
 .-). K.iurm^rH ill til.' ti.'ld aiv Ix-st tak.-ii on cliai.ly ilays. In 
 t.ii;;lit sUMsliin.' tlu- iiia;iii.-t.. ..t.T niiist Im- prot.'.-t.-.! ri-..iii tli.- 
 ilim-t mys of tlif nnii l.y a wiv.-ii not contaiiiinjr iron ..r stf.'l in 
 its stnu-tuiv. Kl.-vation of t.-miH'iatniv of tli.' iim^n.ts to any 
 ;;ifat .'Xtt'iit is always to In' avoi.l.'.l, sine., tli.- ni.aii.Mit of a 
 nia^'iit't .l.-crt-rtscs with incrt'asc of t.iin>fiatnif, nt-ovcrin;,' its 
 noniial vahu' only wli.-ii tli.- iiiaj;n.t ivtunis t.. n..niial t.-ni- 
 
 pi'iatuii'. 
 
 A inoiv st-rious patisi- atftrtinj; llif value of tin- nionifiit .it 
 a majini't is roiimMMl,,,,. sine.- tliis .liniinishcs tli.- str.'iijjtli ..f a 
 nuijcn.'t iM'iiuaiifntly wli.'n sulij.-ct.'.! to it. Tl..' .'xt.nt of tlu- 
 .IfrtiTtion of a oniiHiss n.'f<ll.' hy th.- .l.-fl.'ctinj; nia;,ni.a .i.-j).'n«ls 
 uiion th.' iii.Mii.-nt of til.- latt.-r; tli.- valii.- of A', tli.- constaiit 
 of tilt- iiu-linator, ui'oii tli.- nioim-iit of th.- i-oiiiimiss n.-.-<llt-. It 
 is, therefor.-, .-vi.l.-nt that in th.- inv.-stipition of a nia;;n.-tie 
 ti.'l.l. <'..iicortlant n-snlts of r.-adinjrs can only Ik- ohtain.-.l, wh.n 
 .hniiij; this iiiv.-sti;,'ati.iii th.- iiioin.-nls .)f th.- iiia;cii.-ts hav.- 
 I'.'main.'.l unchanj,'.'.!. II.'iic'. .'Very im-caiition shoul.l !»' tak.-n 
 to k.'.'P th.-s.' nioiii-'iits ('..iistaiit l>y avoi.jin'; all caus.'s whieh 
 tcnil to tlet-r.-ase thi-iii. 
 
 (). Afi-uniulatioii ol iiioistuit' on th.- ii.-.-.H.' of th.- niaj;iit'to- 
 ni.-ter .luiini; daini) w.-athcr may impair its lialaiu-i-. and thus 
 ;;ive i-is.- to error wh.-ii usinj; the iiia;;ii.'tomet.-r as an iiu-linator. 
 M.iisture from Inith the <;lass over and the ne.-.lh- is U-st rt- 
 mov.-d hy allowing; th.- ina},'ii.-toni.'t.-r to stan.l ol.en in a warm 
 r.)Oiii until dry. Wiiiinj; tlu- ;i.;edle <a- iiit<;rior of the comiiass 
 with a cloth sh.mid Im- avoided. 
 
.«! 
 
 ( IIAl'TKIf VII. 
 METHOD OP OBSERVATION. 
 
 Horisontal Intensity uf a Magnetic Field. I'li' 
 
 li(»ri/.<iiitiil iiitiii«it\ 1)1 a iiia>;iiitic liihl iiiiiv U' cLtt-niiiin'tl witli 
 till* iiiMtniiiM-iit iiH ilcM I'ilitMl l)\ iiii'iixiiriii^' till' iiii<;lc 1)1' i|crii'<'ti>>n 
 of the i'<)iii|Miss ixMilli- |)|im|ii<i'"| I)\ till' ilftli'itiii).' iiiiijiiift. whfh 
 it iH'ctipics II (Icfiiiiti- position dii thf arm H i>\' the iiia;;iifti)- 
 iiii'ttT. Kitli till- tHiijji'iit and sini' iiirtli<)<l may !»• i'mj)l")>'i''l 
 in priHlufiny; tlir an^l<' ol' ili'tlfi'tiim 
 
 In till' applii'ation dI' tln'Hf iiii'tl)i"|H tin' mai^jnt'tomt'tiT, witti 
 (•oiii|mHN in liDii/.Dntal position, i> placiMl with its tiijMxl over ttif 
 plticf of oUcivatioii ami tin- l)ul)l>l<' of tin' Ik)X ii-vt-l />i hioU'tlit 
 to tlif fcnti r liy tln' i-mploymi'nt of tin- Icm-IIIii;; hi-ivwm. 
 
 In tlif <a«<f of tli>' tan^jfiit untluxl. tin- niaijiu'toiiii-tt'i' in 
 ifvoivi'il aliout a Mitical axis nntil tlic i-om|>iiss ncfdic n-ails 
 !tO . Tliiw ivadinj: is niaili' n rluin \>y tappinj; tin- «;laHM cover 
 liijhtly with tin- nihlx-r cml of a p>ii(il. to i )Vfi-comt' tlu- friction 
 of the pivots on which th.' nci'dic moves. 'I'll.' magnetic axis of 
 till- compass nciMlic is now paralli'l to the ma;;ne(ic meridian o, 
 the jtlace of ohs.rvation. and ih"' arm H is perpendicular to the 
 plane of th.' ma;,'netic meridian. The detleetin}: ma;;net is now 
 l)lace<l in its frame on aim A' and secured in its position hy the 
 spring l{ and hindnii; screw >'-,. It is neecssjiry, in placin;; the 
 ma<,'net upon tlie frame, to avoid settin;.' the needle into violent 
 oscillations, as otherwise too much tinn' is lost in waitinj; for it 
 to come to rest ill its new ])osition its jH)sitioii is made more 
 d.-tiiiiti- hy ta])piiiji the ;.;lass case as iM'fore. The rtn;,de a„ is 
 now read and 00 a„ «,, will correspond to the aii;;le of de- 
 Hection pnKluced. Assume that the ma^iietoineter is set up in 
 a tjornial terre.strial field, we then have: 
 
 ///(//!(/ «„ </ H I'll n„. (I4) 
 
 If liie.vevef. the ma^'iietouieter lie svt up ill a tield distiirU'd 
 l)y a majiiH'tii" ore IhkIv. the needle with deHectiuK may:net re- 
 
 f'ij 
 
M 
 
 iiinved, when readinj; !»0 , will Ik; paiallel ti« the direction of the 
 horizoutiil coiuiMHieiit of ii compound field of force. This hori- 
 zontiil coniptnient K will evidently l>e the resultivnt of H, the 
 ho. .ontwl component of the norimvl terreHtrial field, and F the 
 horizontal component of the individual field of force of the maj,'- 
 iH'tic ore body. These two components will in {{eneral include 
 an anjjle n in their directions at the place of observation, and 
 we shall obtain for the value It in terms of H and /' and the 
 angle included iK^ween them from the triangle of forces (Fij;. 
 17": 
 
 Fis. I" 
 
 (15) 
 
 If « is the angle of deflection, produced by the deflecting 
 magnet in this compound Held, we shall have : 
 
 K ta 11 (J a ~q — R coin ny a (16) 
 
 hence from equations (14) and (Hi) we have : 
 
 R 
 
 taiuj «o „ cota iiy ap 
 
 H = — : W 
 
 (17) 
 
 fdngu " cotanij a 
 
 In this ecjuation, R is obtained in terms of the horizontal 
 component of the normal terrestrial field, for which the angle 
 of deflection was found to be «o- 
 
 As stated before, this method yields only approximate 
 values. For more accurate work the sine metho<l is employed. 
 In this method, after the magnetometer has been placed over 
 the point of observation in a normal terrestrial field and levelled, 
 the deflecting magnet is first secured in its frame and the mag- 
 netometer is then revolved until the needle reads (after tapping) 
 ))0 . In this position the axis of the needle is perpendicular to 
 
35 
 
 the direction of tlie axis of tlie deHecting inajjiiet. On removal 
 of the deflectiiifj nia;;iiet, the needle moves thi-oujjh an anjjle into 
 a position of panvllelism of its axis with tlie mai;netic meridian 
 of the place of observation. The angle ao' is now read, and 
 00 — a,)' «()' will correspond to the angle of deflection prodviced 
 by the magnet. We then have : 
 
 H xiii tin' = H COM Hi,' = </' (\^) 
 
 If «" is the angle of deflection in a conijiound fleld, we 
 
 have : 
 
 Hsi,, «"=«,-.« a" = 7' (ISa) 
 
 hence : 
 
 I{ = 
 
 mil do 
 
 H 
 
 roH ao 
 
 H 
 
 (l!» 
 
 Ml ti a vim a 
 
 From equation (14) it follows that since H varies with the 
 locality, if 7, the deflecting force of the deflecting magnet, re- 
 mains constant, the angle Oo must also var\- with the locality. 
 This angle «o for the locality in which a disturbed Held is to be 
 examined, is best taken as the mean of a number of observations 
 made in ditterent parts of the normal terrestrial Held, surround- 
 ing the disturbed Held. It is only when angles are obtained by 
 this method, which do not ditter to any extent, that the observer 
 can at all t)e sure that his oKservations have lieen made in a 
 normal terrestrial Held. 
 
 The tangent method is very convenient when only approxi- 
 mate results are required. It absorbs little time, and the instru- 
 ment set up for it is, by the removal of the deflecting magnet 
 and the .setting of the compass vertical, converted into an inclin- 
 ator, ready for observations of the vertical intensity of the Held. 
 Moreover, from e(|uation (1(j) we have: 
 
 q 
 tillU) «= u 
 
 that is, a deHnite angle will always corresjwjnd tft the ratio „ 
 whatever the separate vahies of q and R may Ik-, since the tan- 
 gents of all angles are comprised between 1- x and — x. 
 
 The sine methofl, on the other hand, gives ;uTUrate results, 
 
r 
 
 i 
 
 II 
 
 liut is less c-onvfiiifiit, in tluit more time is ab«.)ilH.'(l in makii';; 
 „„.• observation, an.l that it rwjuires that the instrument must 
 l„. revolved into proper position In-lore the compass can Ik- 
 phice<l vertical to convert tlie instrument into an inclinator. 
 Further, from the et|uation : 
 
 ■ '/' 
 
 SI II a = 
 
 It 
 
 it is .■vi.lent that since the limits witJiin whicli tlie sines of all 
 an^'les are comprise.1 are 1 and - 1. no anjfle corresponds to 
 a value of ^' > 1 . or when 7' > H. At a station where this takes 
 place the compass ne.'dle cannot Ik- made to .Krni.y a position 
 perpendicular to the axis of the deflectinj; maj-net. This serious 
 def.-ct of the sine method can to some extent he overc(jme by 
 increasinj; the distance -/ of the center of the .lellectinj; maj;net 
 from tlie center of suspension of the conqjass needle. Since 7 
 varies hiversely as ,r\ 7 rapidly diminishes with increase of '/, 
 and witli smaller 7 the methyl can \w employed to measmc 
 smaller values of R. As 7 diminishes, «„ also In-comes smaller. 
 In order, therefore, to measure small values of It small values 
 .)f «„ must l)e chosen by the observer: j;reater values ..f H re- 
 ,|uire, on the other hand. >ri"cater values of «,^ 
 
 To facilitate the calculation of results by the metlunls just 
 
 HI II «0 , '"",'/ 'Ai 
 
 described, tables are appended of the rati., of ^^r^^ a«"l ,— -; 
 (see tables 1 and II). The anjjies «„, corn'spondinj: to the detlec- 
 tion of the normal terrestrial field, are jriven from 10 to 'M) 
 inclusive, projjreHsini; by single de>;rees. 
 
37 
 
 CHAPTER VIII. 
 
 DAHLBLOM'S MODIFICATION OF THE 
 SINE METHOD. 
 
 In the methods described, tlie (leflcctinj; inajjin-t i-ftiiincil ii 
 definite position (jn the arm A\ind (/ was, tiierefore, Icept coiistuiit 
 while the anjjie of deHection constituted the variab' 'm l)iild- 
 bloni's ineth(xl the iinjjle of deflection is liept coi ' ■ !' 
 
 made the variable. This method jfives ;;(H)d results u ., r- 
 
 comes the defects of the sine method, as commonly employed. 
 
 To apply this method an extra arm A'l (see Fij; I^S) is 
 screwed to the compa.ss Im)x of the Thalen-Tilwr^ ma>;iiet()- 
 
 Kio- i» 
 
 =^.S, 
 
 T-fJVM^. 
 
 - — £ — i-ii-TS ^' 
 
 « ®— • ' J — 
 
 meter. This arm £i points to the centei- of the suspension 
 of the compass needle and makes an aujfle of :{()° with tlii' ai'iii 
 E. It carries a frame for the reception of the deflectinj; majiiu't, 
 till maijnetic axis of which, when placi'd in position, is in the 
 Huiiie horizontal plane with the majj^ietic axis of the compa.ss 
 needle. The fninie can lie moved Ijack and forth alon;; tie arm 
 by means of wires attached to the franu'. These wires pa.ss ovi'r 
 pulleys and are operated by the screw >S'o. Alon;; one side of the 
 arm is a millimeter scale, the zero of wtiicti i^ at tlf crnt'-r of 
 
 HI 
 
w 
 
 \ I'; 
 
 HI 
 
 i * 
 
 the axis of rotation of the coinpasH needle. The frame is pro- 
 vidtKl with an index, ho that the position of the center of the 
 deflecting magnet can be read to some tenths of a millimeter. 
 The other side of the arm can Vw provided with a scale, which 
 gives R direct for the different distances of the center of the 
 deflecting magnet from the zero. 
 
 Method of Observation.— Tiie instrument is set up 
 
 exactly as in the case of the tangent method. The deflecting 
 magnet is placed on the frame and screw .S, manipulated until 
 the^deflecting magnet occupies its proper distance on the arm 
 El, ie.. when the compass needle stands at right angles to Ei 
 and reads 60° in the north-east quadrant. The position of the 
 deflecting magnet is now read on the millimeter scale and R 
 corresponding to this reading taken from a table calculated for 
 the instrument, or R is read off" direct, if the arm is provided 
 with such a scale. The deflecting magnet is now removed, the 
 compass needle returns t« the read!r,g 90° and the instrument, 
 by placing the compass vertical, is indy for observation of the 
 vertical intensity. 
 
 OaUbration of MiUimeter Scale and Construction 
 of Scale for reading R direct.— We have seen, equation (})), 
 that the product of the eflect of the deflecting magnet <j into the 
 cube of the distance of its center from the zero of the scale is a 
 c()n.stant quantity, hence : 
 
 go ''o^- = <]i <h^ = 72 ''2' = 7« ''n^' = <^' "^ constant. 
 
 If H is the horizontal intensity of the normal terrestrial 
 held and 70 the eff-ect of the deaecting magnet when the compass- 
 needle .stands perpendicular to the Dahlblom-arm in this field 
 and R and 7 corresponding values for a compound tteld, we have 
 for the Dahlblom method : 
 
 Hsiv 80° =70 
 /J«,;w30°=7, 
 from this, H=2 70 and ft=2 q=}> H (20) 
 
 but7rf='=C'. («) 
 
SuhHtitutinj; in tliis b(|uatiun for 7 its value from e(|uuti<>ii 
 (20) R=2q, we have: 
 
 4*=f, 
 
 or R 
 
 2t' 
 
 2C'\i /2C'vi 
 
 (21) 
 (22) 
 
 From e(|uati(>n (21) H can be calculated for any value of <l 
 and from ecjuution (22) d can lie calculated for any value of //, 
 when C is accurately known. The value of (' may l)e experi- 
 mentally obtained as follows : 
 
 The mafjnetometer is set up in a norn<al terrestrial field 
 with compass horizontal and properly levelled. The magneto- 
 meter is then revolved about the vertical axis until the Dahlblom 
 arm coincides in direction with the magnetic a\..> of the compasH 
 needle. The north end of the needle will then read 80°. The 
 deflecting magnet is now carefully placed upon its frame on the 
 Dahlblom arm, with its north pole facing the north pole of the 
 compass needle and cautiously moved, by manipulation of screw 
 .STg, toward the compass needle, until the needle is at right angles 
 to the arm. The deflection produced is !)0° and the distance '^i 
 of the center of the deflecting magnet from the zero is now 
 accurately measured. For this position di we have : 
 
 and C'i=l di' 
 
 The deflecting magnet is removed, the frame pushed back 
 and the magnetometer revolved until the axis of the compass 
 needle makes an angle of 5° with the Dahlblom arm. The north 
 end of the needle now reads :{5°. The deflecting magnet is now 
 placed in its frame, cautiously moved forwai-d until the compass 
 needle is again at right angles to the Dahlblom arm. The dis- 
 tance di of the center of the deflecting magnet is again accurately 
 measured. The deflection produced is Ho° and : 
 
 g2=ff ain 85° and C'a=73 di^= 1 {sin «5° (/2'')=0.<»9 d-J' 
 
 f 
 
 * // taken equal to unity. 
 
40 
 
 Similarly tiit- .iittV'reiit vuIh.-h for '/ art' iiieamiiwl with tin- 
 following dertfftiiiK aii>;li« : 
 
 
 
 
 " 
 
 Corrcspt'ndinjc 
 di'floction when 
 
 
 
 
 Compjiss nfi. 
 
 dU- hi 
 
 (ore 
 
 needle stands 
 
 
 \' .lines of ('. 
 
 
 ilefloftion 
 
 reads 
 
 
 verlieal to 
 
 
 
 
 
 
 
 
 Dahlblom-aim. 
 
 
 
 
 40° 
 46° 
 50° 
 56° 
 60° 
 66° 
 70° 
 75° 
 80° 
 
 
 80° 
 
 f:, = 
 
 sin 80° </;)■' 
 
 ().«8 f/s-' 
 
 
 
 
 7.-)° 
 
 (-U 
 
 «;<» 75° ./v' 
 
 ().!»() (/4'' 
 
 
 
 
 70'' 
 
 t\ 
 
 «u< 70° »/.v' 
 
 0.04 (/.,•' 
 
 
 
 
 (io° 
 
 (\ 
 
 . . » o i '1 
 
 O.IIO (/«■' 
 
 
 
 (iO° 
 
 C't 
 
 «;« (>o°(/r' 
 
 0.8() »/;■' 
 
 
 
 .-,5° 
 
 cv 
 
 «;„ 55°r/8-' - 
 
 0.82 '/h'' 
 
 
 
 .-,0° 
 
 f„- 
 
 «n* 50° '/»•' 
 
 0.7t) '/»•• 
 
 
 
 
 4o" 
 
 t'lO 
 
 N/'yi 45° </io'' 
 
 0.70 (/i„' 
 
 
 
 
 40° 
 
 C'n= 
 
 Mi,, M)° <lii'= 
 
 0.()4 »/„■' 
 
 85° 
 
 
 
 
 .•(o° 
 
 fl2- 
 
 h;„ :15° «/,2^- 
 
 0.57 </i2' 
 
 no° 
 
 85° 
 
 
 
 
 :l()' 
 
 (•l3^ 
 
 d: •{0°f/i3-''= 
 
 0.50 </i»' 
 
 X.K. 
 
 Qna< 
 
 hunt 
 
 25° 
 
 e,« 
 
 x/i( 25° 'lu^~ 
 
 0.42 '/w' 
 
 80° 
 75° 
 70° 
 
 
 .. 
 
 
 20° 
 
 C'l5 
 
 .-;„ 20°</i5''- 
 
 0.:U '/i.%' 
 
 
 
 
 15° 
 
 C'l6 
 
 .x//( 15° '/uj-' 
 
 0.2(i '/iH^ 
 
 
 ■• 
 
 
 10° 
 
 Cn 
 
 -;/- 10° «/ir' 
 
 0.17 <hr' 
 
 
 
 
 
 
 -, 
 
 
 _ 
 
 
 'I'he 17 values of C, thus deterniiiied. which ditfer amonfj them- 
 selves, are combined into a mean value f„and with this n.eaii 
 value the distai.ces .1,. </,, etc.. ...ay l.e c.rrected by substituting 
 
 in the equation 
 
 (' 
 
 - » = ft' 
 
 'I 
 the separate values of i/i, 72, etc. 
 
 We may now pnx^eed either to calibrate the millimeter 
 scale of the Uahlblom arm by tindinj; the values of R, corres- 
 ponding to the separate millimeter divisions on the scale, or we 
 may construct a scale on which the different values of It for the 
 different distances are n.arked, which n.ay then l)e transferred 
 to the I>.hlblom arm on the side opposite to that on which the 
 millimeter scale is placed. 
 
41 
 
 Calibration of the Millimeter Scale. -By stil>Htitii- 
 ting ill tlit> ei|uuti<>ii 
 
 li 
 
 til- 
 
 the ceiitiiiieter diviHioiiH of tlu' scale, we ohtiiiii tlu- vulues of H 
 correHj)on(Jin>; to these divisions. A curve nmy now Im- plotted 
 with the millimeter scale us tihscissivs iind the correspond injj 
 values of li as ordinates. For the plotting' of li, a scale shoulil 
 lie chosen, which will not make the ordinates inconvenientlv 
 long and yet show the differences for the ditierent ndllimeter 
 divi.sions .sufficiently distinct. From this curve the value of li 
 may Ik- taken out for any division of the millimeter scale. 
 
 Construotion of Soale for reading R direct.— By 
 
 su>)stituting in the e(piation 
 
 H „ H 
 
 ./■' 
 
 •'-'^•'■■-'M^)' 
 
 (2.S) 
 
 values for ii. we obtain the corresponding values of d. To 
 facilitate this calculation, a table giving tlie ditterent values (jf 
 
 I- 1' and their logarithms for values of n from 0.01 tct .").00 is 
 appended (.see table III). 
 
 A curve may now \w jjlotted, as before describwl, with values 
 of H as absci.s.siis and corresponding values of d in centimeters 
 as ordinates. These ordinates appear as al)sci8sas on the scale. 
 The scale is first marke<l on paper and tested. If x is found on 
 test to Jx- the value of R fm a deviation of .•J0°, for which the 
 sine is .i, 2 ./• must Ik* inflicated l)y the index of tlie frame for a 
 deviation of !(0°, for wiiich the sine = I. 
 
 I^rge values of //are l)est determined with Dahlblom's 
 metliod by the employment of a special deflecting magnet of 
 great iwle strength. For this magnet the value of ('„ will differ 
 from that calculated for the usual magnet, and nuist, of course, 
 be separately determined and curves constructed for it, as pre- 
 viously descrilx'd. The value of ('„ depends on tlie permanency 
 
 I!' 
 
42 
 
 V 
 
 ! k 
 
 111 
 
 of the st.viii{th of the .leflecting magnet and on the value of H 
 at the place of observation. Change of either of these values 
 ..ecessitates a new .leterniination of C'». Tin- iK^iiuaneney of 
 the Htren>,4h of both compass needle and deHectinjj nia},niet can- 
 not Ik.. j;uarantee(l. Magnets jji-adtially weaken, which may in 
 a gre^t" measure k' obviat.-d by using molylnlenum steel for 
 their construction and aging them artificially by lM)iling in oil. 
 It need scarcely Ik- mention.-d that accidental dropping of the 
 dertecting magnet renders a new determination of ('„ imp.-rative. 
 
 From the equation ; 
 
 2t' 
 
 K = 
 
 <r< 
 
 we obtain for the same '/. but for a new value rj. the expression : 
 
 •2CJ 
 
 It' 
 
 and hence, 
 
 K' = 
 
 VJR 
 
 (24) 
 
 from which it follows that in the ca.se of a new determination 
 of C'„ the ordinates of the calibration curve of the millimeter 
 scalt"of the Uahlblom arm are converted into the new ordinates <)f 
 the new curve, corresponding to the new value (',„', by multi- 
 plying the old ordinates with the ratio -^r . In the case of the 
 reconstruction of the scale, giving H .Hrect. due t<. a new value 
 VJ, the table giving the values of (^)^^ is always applicable. 
 
 The applicability of Dahlblom's m.-th-Rl is base<l on e.pia- 
 tion (9) : q '/=•== C. 
 
 This equation is, as has been shown, not strictly correct, an<l 
 
 Uhlich* has found that an ^luation of the form : 
 q<l?+cq(P-^ V. 
 
 in which the factor -■ is smaller than unity, gives k-tter results. 
 
 Experience, however, has shown that for all practical purp..ses 
 
 the equation : (/ (/•= C 
 
 is sufficiently accurate. 
 
 Tpage 36^, .. Lenrbuch der Markscheidekunde, I'. Uhlich, 1901. 
 
48 
 
 CIIAPTKH IX. 
 
 THE VALUE OF THE HORIZONTAL INTENSITY IN 
 A TERRESTRIAL FIELD OF FORCE, DIS- 
 TURBED BY THE PRESENCE OF A 
 MAGNETIC ORB BODY. 
 
 In II disturlxnl tii-ld. tlio horizontal iiitt-iiMity A', us luis lM«n 
 previoUMly mIiowh * is tin- ivsultunt of tiif horizontal intt iisity 
 of the eartliM normal tiehl and tht- horizontal conipont-nt of thu 
 niaifnetic 'orci- of the niaj^netic ore-lKK]y. If the former is 
 Hymlxjlized by H, the latter by F, 
 
 R = l m+Fi-2HFcmv. 
 In the €iiHturl)e<l Held, H remains constant in direction and 
 intensity, F variable in direction and intensity, the latter 
 dejHjndinjj on the horizontal distance of the point of olwervation 
 from the point over the jrole of the ore-lMxly. 
 
 Assume the normal terre.strial field to be disturU-d by a 
 majjuetic ore-l)ody, with its pole, exhibitinif nortli [M)le attrac- 
 tion, in a vertical direction Ix'low the point U, and (see P'ijj. 1!)) 
 the ore-l)ody to extend vertically downward to .such depth that 
 the effect of the lower pole upon the field of inv.sti<,'ation may 
 l)e nej;lected. It will then l)e evident that for the point of 
 observation A, if //and /' in intensity and direction repre.sent 
 at this point the horizontal components of the field, the diagonal 
 R of the parallelogram con.structed on these coniponentH will in 
 direction and intensity represent the resultant horizontal in- 
 tensity of the field at .^4. For every point at etjual <listance A 
 from 0, lx)th H and /' remain constant in intensity, // remains 
 constant also in direction, but F, being directed to the center 0, 
 varies in direction for every point of the ciicuniference. There 
 are four points in this circumt'erenc< of special interest : 
 
 At E the angle ;; is 180° and the equation for the resultant 
 Iwcomes : 
 
 (; 
 
 I 
 
 f w 
 
 tf'K- 17> '■q- '.S. paKC34. 
 
44 
 
 ff^f 7/2 :|. iri! _ -2 7/ Fn^ I n<)°= // + >' < -■> > 
 
 Tl..- n'sult4iiit for thw |K)iiit i'.iu.iIh tlu' muiii of tin- cotniK.iuntH. 
 At A' thf aii){li' " = " '"»• 
 //^l //a 4 A's 2//A'..wO"= - (//-A') <-J<i> 
 
 Ki"". 1!» 
 
 .V. 
 
 I 
 
 
 Sr --t — V-'-^ 
 
 \ 
 
 / 
 
 . 1 \ X 
 
 1 
 
 \ 
 
 \ 
 
 / 
 
 T 1* III 
 
 - ^n 
 f 
 
 >i / 
 
 \ 
 
 -t 
 
 .V 
 
 or the resultant for this point is .'.|iwl to the (iiHei-ente hetween 
 tlie components. The litn-izontal intensity is, therefore it a 
 n.axinmni at E au.l at a n.ininin.n at A'. For the«e two points 
 the angle of deHiftion is respectively a niinin.uni and n.aximuin. 
 
4A 
 
 Tlif liiif .liiiwii tliiou^'li thf tliiv.- |Niiiit!s n A'uikI A', con- 
 MtitiiU'M till- iiiiijriK-tif meridian nf tin- Ht-lil. 
 
 l(.-tw....|. tl.fs.- t\v.>|Miii,ts for //„.,mi.l //„„„tli.' viihu- of /,' 
 for iiif.nii.'.liat.- puintH on X\u- <irfiiinlVrciici- hhmiiiucn all iiitfr- 
 
 IIDMlJatc VHlllfN. 
 
 If ill tin- >M|imtiuii f,,r tlu- r.-siilttt it. w.- put 1{=^U, Wf 
 
 liavi' : 
 
 /•' ■2Hr,,Hi,=0 
 
 F 
 
 UIkI IIIM II ^ 
 
 2H 
 
 Hv i-oiiMtructin;; tliis aiiyh- tli.- two |M)iiitN I) and //on tlu' c-ir- 
 cnniffniic.. wli.iv /{~fl nu- found. Tlif conHtnittion may In- 
 furrifd out iim follows ( Fiy. I!»): 
 
 Kroiii toward A' on line O A' lay oHtlu- U-nytli /'to obtain 
 |Knnt N. At tliiH jMjint crt'ct a juTja-ndicniur and from O, witli 
 li'n<,'tli 2 //, cut pt-rpfiidieular in 7'. The Iim- T cuts tin- cir- 
 einiilVrcncf at />. At this and tin- eorrcNiK)ndinj{ |)oint D' the 
 anj,dc of deflection is «„, the uiiyjc of deflwtion of tiie normal 
 terrestrial field 
 
 At the point O the force of the j)ole of the ore-lxxly is 
 directed \eitically downward and A'=:0, eonse(|ui'ntly the an<;le 
 of deflection at this inant is due only to //and is, therefore, also 
 e<|ual to M)h 
 
 So h>n<' /'does not I'econie ^eater than 2^, there will 
 exist two p s .)ii every ciiMiiuierence drawn within tlie field, 
 afKiut O a> liter, at which the anj;lc of deflection is «„. 
 
 If the iK)ints in the disturliwl field, for which the aiijjle of 
 deflection ecpials «„, are found, tlie curved line resulting (termed 
 hy the Swedish authorities the " neutral line ") will pass throu<;h 
 th.. point (). which is also the [Miint throu«;h which the line 
 Joiiiin;; /C« and /;„,„ |)a.s,se.s. 
 
 This fact may Ih- employed for the Icxiation of the pole of 
 the ole-lKKly, when /' is siimll compared with H. which will U- 
 the case with a weak magnetic ore-lvvly. or when t!ie i.K-ati..., 
 i)f the pole is at considerable distance from the surfiw*. 
 
 . I 
 
 h : f-l 
 
r 
 
 46 
 
 (Tl..- aii"l.- «„ iimv U- mlfiiliit.il from Hi.- kncwii \,t\wn of 
 
 -i, uikI 'h. wl.Tcl iivHjxm.! ifH|HH^^tiv..ly to tJu- iimxiinu... an ! 
 
 iiiiiiiiiiuiii viilii."* of fi Kor wf hiivi-: 
 
 «/ =^ ( // t >') "' " "I = < // '"> "'" "•■''^ " "'" ""- 
 Kniiii tliin wi' ulttiiiii : 
 
 // _Mill «,. _ »>•• 'Ai 
 
 , J L_J ,.7 
 
 ■n... .alriihilion of «„ is fiK-iliUUtl by UHinj; th.- foiniula : 
 
 Ml It III Ml II ll-i 
 
 "' " "" ^ Mill \ {Ui^ai)'<<m A («.i «i) 
 It is .vidint that if«„.in(l either «, or «.j aiv kii..wii th. " 
 known «i or «a mav !).■ eak-ulatwl from fiuation (27). I. ; 
 UHefulnt-sN of suc)i 'calculation U-a-Wnn to the .letorin.nation -l 
 the location of thi- i^ole of tlu- <hv dep<.sit wil apj^ur by c .- 
 si,l,.rin.r that, if o.i a n.cri.Han, north of th.- lH.lf ol the deposit, 
 the an;Th. of deviation «, has l)een oWrv.Kl tor any p«iint / ,, 
 chis value n.ust c..rreHp<«u> to the n.ininunn value ot K ur a 
 certain cireu.nference, of which the p.le .- the center, but the 
 radius of which is unknown. If th.n, we deternnm- Iron. e.,«u- 
 tion(27)the antile «.. c..rres,,on.lii>i; to the n.ax.mun. value ot 
 «and find anu.nt; the ,.bserv..i values upon the nundian he 
 point P,, conesiKuidinj; tr. this value ol li, /'•/'•^;;'>' "• ^'V; 
 re.,uire<l dian.eter of the circund-rence and the pile ol the .leiK.s,t 
 will 1r' midway l)etween /'i, I'i) 
 
 This neutral line divides the ti.-ld of investi^ition into an 
 area of minimum horizontal intensity, lyinjj north of the neutral 
 line .lud an area of maxinuim horizontal intensity, lying s<mth 
 
 of it. 
 
 At <> the value of F is zero : fn.m this value, pnx-eedm^' 
 outward in the H.ld. the value of F increases to a maximum. 
 U'vond this /'ajiaiii diminishes practically to zero at the limit 
 of the Held. Then- is then one circumference, for which F is a 
 maximum, Ix^yoiul this are the concentric circles with decreasing 
 values of F and within the area bounded by the circumference 
 for tlu- niaxiinuu) are the concentric circles with valu.-s of /', 
 correspondiu); to those of the circun.i.rences lieyon<l that, fu. 
 which F is a" naximum. In croing outward, therefore, from 0. 
 
47 
 
 i-'* 
 
 ^'„,, i«.ia'..uiil.ir.l l.ui .,int liiit iiit.iiii,-.|iatf vhIii.-n of /'twic- 
 
 " '■•■ //. tl"- •><•<• c-oiiiiMiHs iiowllf will itlwuyH |M)iiii 
 
 north hImiij; the Uirfctiun ..f ttir iim;fiu'lic iiii'iuhaii. If F„ = 
 
 // ti iHiiiit will Ix- IouikI 1)11 Hi,. nifniJiaii, whi-ri- i''„„.,-y/iMr.(iiiil 
 
 tu /.to. At tlHM |«,uit, iUr ,H,il.t of ill.lirt-,.iviir,., wllifl. li.-M to 
 
 the north of O tht- fr.i- .•on.|.HM« n,'...|l.- will in.lirt'.-ifntly .K;fUj)y 
 any |M>Mtion. If 2 // ./'„„ //. th.-r.- will W- two jmintM of in"- 
 .lirt'.ivnc.v onr Iviny; vmH,!,, tli.. fii-cunif.i-.n«-.. for th.- nmxinitnii 
 ,111(1 .moth. I k.\uu(l it. Pn^^mn U-yon.l the Hr-t |H,int of in- 
 .liH'erenc.', the newlle revei>«s un<l (Miints Month, until the w-contl 
 poiutol indirterenee i« reache.!, where it rev. !m..m ajftiin. to |Kjint 
 north one., more. 
 
 In thi.s i-uMe ttjso ,,iie neutral line will divide the Held into 
 the twoareiiHof nui.^iniuin and luininiuni horizontal inteiwitv. 
 
 When, however, A'„ ,. ,>2//^,two neutral line.H will In- found 
 U-tween the two iiidiH; ,vnt i«)int.s. « )ne a ,;I<,..<«<1 eurve, jMMwinjf 
 through the pole point O. "the frtlHi- neutral line,' unit a swond 
 open curve, lyiMM^ ih.yond the former, to the north, the true 
 neutral line. ' In th.' ea.se of such stroncr fields. a.s may ocenr 
 Ml th.- case of nia;;n.-tie or.- iKxlie.s riNinj; uliove the Nurfiice, the 
 rul.- for finding' th.- pole |)oint 0. hy means of the neutral lin.- 
 is, .>f eo.iis.-. no lon^ri.,- applicul.l,-, since the true neutml line 
 does not pass through the jjole jmint. 
 
 The resultant horizontal JTit.-nsity aloiijr the uieridian in 
 
 H.-lds where /•„,,. //. ■> II > F„„ 
 K.'ntt(l liy tiffures 20. 21, 22. 
 
 ■ H and b' 
 
 H, is reju-e- 
 
 l''i<>". IM) 
 
 Tf |!';' 
 
 
 hlAlhll .ildLi_ JxiiiL 
 
 7*.\' 
 
 i 
 
48 
 
 1 . 1 ' M 
 
 l-i«|-.-'l 
 
 
 ■*\' 
 
 I'iR- 
 
 
 '^1 
 
 ^\ 
 
 \, 
 
 In tl 
 
 iMlliI 
 
 ti;;uivH tlu- eurve 
 
 »»■ *• 
 
 ■TIUIIIIIO. 
 
 alKjv.' the line .S .V represents the 
 
 W' 
 
 vat 
 
 iation ..!• ^■ ulon^^ the nieri.Han. with .4 as the poh. point. 
 The line. /.parallel t.> .S .V, is .Irawn at a distance = W. In 
 H.„,v 20 H is constantly positive an<l the free co.npass needle 
 points continuously north alon,' the n.eridian. In hgures 21 
 Ind 22 , and A are points of indirterence. K-tween these pom s 
 the resultant is negative, the free con.pass needle pomts south. 
 At ,• and ... (tijxnre 22) the resultant is e-iual to-H, through r 
 passes the ■' false." thnrngh .. the • true " neutral hue. 
 
4!t 
 
 ClIAI'TKli X. 
 
 THE VERTICAL INTENSITY OF THE 
 DISTURBED FIELD. 
 
 Theory of the Inoliuator. It Ims 1),.,.|, shown that 
 <•.• tn swiiijr in any plane, will tend to pljifi' 
 
 11 niai'nutic ncfd 
 
 li' 
 
 its.ll' in till' tciTcsti-ial Held with its i 
 
 na;,nntic axis tani^fnt to 
 
 lini' of nia^'nctif foicf and that in the noitli.Tii hcniisphcrc thr 
 axis of the ncMJlf with north pole pointing downward will in 
 ;;fnfral make an anjjl.' /• with th.- horizon. In tliis position ol' 
 rest the total nia<;n<"tic I'orcc oj' the field, aetin;,' alonj; tl 
 
 le axis 
 
 .r th. 
 
 tile, nia\- he r 
 
 e.solved n 
 
 n two dneetions per])en(lifiilar 
 
 to each otiier: //.the liori/ontal eoniponent. and I', tlie verti 
 component. For the vertical component we have ohtained th. 
 expression, eipiation (2). paj,'e I."). 
 
 r- // ^ 
 
 "",'/ 
 
 With the needle a 
 
 s constiucted tor the inclii 
 
 depends ii: addition to the action of th 
 the action of ;;ravity. 
 ai)plied at the center of 
 <;ravity of the needle. 
 
 lator, the an;;le /■ 
 ma;;netic forces upon 
 
 •I •4. S.i 
 
 I'hich 
 
 ituated In-low 
 
 the point of suspension. 
 •I'o ohtain an expression 
 
 tl 
 
 le value o 
 
 f r 
 
 ni 
 
 terms of the anj^le /• and 
 the constant of the in- 
 clinator, when the needle 
 is in iMpiilihriuni nniler 
 the action of these 
 
 // 
 
 forces, let till 
 
 plat 
 
 th 
 
 e p{ij)er represent tilt 
 
 plane of the nmirnetic nieriiliim .•ind :issuin>' the neetile to U' 
 the j)<),sition shtmii in the fijrure. its axis 
 
 ni CI 
 
 uilil 
 
 )riuni in 
 
50 
 
 
 iiiiikiiu 
 
 tin' aii''lf 'o w 
 
 itli till' liuri/.im 
 
 XS. Let " !«■ til 
 
 .•liter (if ^riiv 
 
 itv (>r the iii'i 
 
 (11." 1111(1 '/ its (listiuiee fiDiii the |K)int 
 
 (iT SUNl>t'll'*l<>ll "• 
 
 Let ir, tlif wfij; 
 
 lit of the lU'wUf. Iw if},'iuik-<l 
 
 i tho lcii<,'th ol" tlie iif«><llc. 
 
 ■Iv the licni/.ont.il and vertical coiupouents of 
 
 tlie licl<l. iiiui /' the stieiifjth of the \m\v f 
 
 Then it is evident that V tends to inc-ivase the 
 
 oiieentrated in «'. l-et / "/ 
 // and rresi>ective 
 the inaj,'iieti<- foire ol 
 of the needle 
 
 an>;le 'o, 
 
 teiul .1 
 
 •1' 
 
 (lodlice l( 
 
 ■ft handed rotation, w 
 
 hereas // luid ;;ravit y 
 
 I iointlv to decrease the allude '„. JinKlucinj: ri<; 
 
 irht handed 
 
 •otatioii. 
 
 In the nosition of e(inilihriuiii the nieiits of couples 
 
 |)roduciii>; oj»j 
 
 e(|Ua 
 
 The nioliieiit o 
 
 ositely directed rotation alwnt the point <> arc 
 f couple due to // = .!/„-// ,« :2 " /' = // /' ^ / "' " 
 
 Tl 
 
 le nioilK 
 
 The nioiiient 
 
 ■nt of coui>le due to 1'= 
 i)f irravitv referred 
 
 M,=.\'ff2. 
 
 V If! I CDS 
 
 to axis of rotation 
 
 .1/. 
 
 =.!/,=-- ir». 
 
 =^ir./: 
 
 ,„. {Ufi-21 ir./)N''/' '0 =-'',« -''■"••* '" 
 
 he : r=^(// ^*;;;). ""./'•"=(/' ^'':V""'''" '^^> 
 
 if the vertical plane in which the needle swinj;s makes an anj;le j- 
 with the i.iH>;netic meridian, we have for the component of W. 
 actin- alon- that plane, its projection // ...s r and the esi.res.s.on 
 hecomes: 
 
 With the inclinator the ol.servations are made in a i-lane per- 
 pendicular to the ma-iietic meridian, ;.<-., r = !tO°. 'Uid we have 
 foi the value of the vertical intensity ; 
 
 In this e.,uatioi, " '' is a constant. Let this constant he repre- 
 
 ' III 
 
 seiited l>y A' and the e(|Uatioll hecomes: 
 
 V'-=K tiiii;l •■■; '■*'> 
 
 I„ a Held disturhed hy the presence of a majrnetic ore deposit, 
 
till' viTtiVal loici' is tlif ivsiiltmit of tlir vcrtiral i'((iiii«)iu'iit of 
 tlie iioriiial tcncstriiil Hi-ld ruiid tlii' vcrtit-iil comiMMiciit of tlu' 
 Held of tlif ma^^ni'tic m-i' liody - <i. Tin' |)lu.s Mi;;ii siirnifyin;; 
 nortli poll- attrjutioii, the iiiiiiiis siKn noutli polt- attraction on 
 tlic ini'linator ncfdlc. Tlif horizontal forct' H acting on tiic 
 nt'fdU' is tln' n'Muittint of tin- liori/ontal i-oinnoncnt of tli 
 
 rnial 
 
 ti'i-rvstrial Held // and tlic tiori/ontal component of the ore 
 tifld F. 
 
 If the- plane of the inclinutor is in the plane of the nia;;- 
 netic meridian, we hav.- (si'c e(|. 2H) f<ir (r. if it acted alone: 
 
 '(,■(/{ K)l<n,<i >■„' (:J2) 
 
 If ;- is the anj;le made hy the plane of the inclinator witli 
 the plane of the maj,nietic meridian, we have (see vi\. 2i»): 
 
 (/.' 
 
 A-)/. 
 
 '".'/ '1 
 
 (:{2a) 
 
 • = !tO 
 
 »'.'., when the plane of the inclinator is at ri^^lit 
 
 angles to the maj;netic meridian, we have (see ei|. ol ) : 
 
 h'/ 
 
 I III/ /■•_> 
 
 (:{21)) 
 
 The expression foi' the resultant vertical intensity is. there 
 
 fore 
 
 r ' a 
 
 K{f 
 
 '"II '': 
 
 1,1, 
 
 II '■■: ) 
 
 (••«) 
 
 In the Tiher;; inclinator the vertical f.K f the norn 
 
 Fi' 
 
 o 
 
 \ 
 
 lal 
 
 terrestrial tield 1' is coun- 
 terhalancod hy a small 
 wei<;ht on the south arm 
 of the needle and 
 
 0. 
 
 With this adjustment made 
 tlie workinjjf e(|Uation for 
 determining; the vertical 
 
 nitensity 
 hecomes : 
 
 if the 
 
 Held 
 
 (r ~ K tiiiiij I.,' (.SMa) 
 
 If th 
 
 djilst 
 V 
 
 meat lor 
 
 iii'Utralizni*; I is not per- 
 fect, hut leaves an index 
 
 eri'or of u small 
 
 iinirle '■ . aiHive the zero 
 
 (due t 
 
 o over correction). 
 
 ? 
 
52 
 
 Im-Iow it ('l\ii' In nii'ltT con 
 
 ction). Wf Iiiivc ill tin- iioriiial 
 
 t=,tl(l for till' I' 
 
 Diulitioii uf fnuilil>iiuiii, i 
 
 f («• is till' small wei{{ht 
 
 tin- soiitli anil <it' tlif iicfdlt 
 
 V -2 It I niM >• 
 
 II' witli ail iiiili'X error > 
 
 \V<h 
 
 W,l 
 
 ni 
 
 III iiij 
 
 K III IKJ 
 
 Im-Iow tlif /I'lo. Wf iciu 
 
 1' 
 
 ,1.. ill tlie <listuri).'(l H.'lil '•,. tlif ivailiiij; 
 
 IS CVK 
 
 I for tlif luiith 
 iK'iitlv «lue to: 
 
 ('• ^n 
 
 ^' 
 
 K III 
 
 A' linii/ i\^ ' u -- i\ l<ii"J '', 
 „n,l '-■ A' ('"",'/': '"".'/'•.» 
 
 ir til.' iiult'X I'lior is alK)Vf the /ero, we have. 
 
 (:i5) 
 
 A\' ^j - c, i\ iifi'n I-, 
 
 ,„. (1^ K(f"i>iir : I'l'iiJ'J ^^^•'^ 
 
 IJv the use of epilations (:<-,) aii.l (Mi) the .•orreetion of tlie er.o,-, 
 intro.liK-e.l hy defective ailjustiiieiit is easily made. 
 
 If th.' aii;;le r^^ is very small, we may put: 
 
 a - Kl"i,.,{>\ , I- J '=^'> 
 
 Determination of the Value of K. -In the exi.ns- 
 
 sioi. A' " '' . »»■ 'Hxi '" '""> '"^' '>'-t^'"''"^"' ^^■■'*'' '^'='='"*«y' ^""^ 
 
 ,„ ,.l,a,.-es"with time, .lecreasinj; in value, and <l cannot Ix- 
 a.rurat.^y as<-ertained : the value of K is, therefore, Ix-st obtanied 
 experimeiitallv hv the following: metluxls:* 
 
 1 'I'he ma-'iietoiiieter, set up in a stron>;ly ma>;n''tic held, 
 with compass Ik.x horizontal, is revolved until the axis of the 
 ,„,,,lle is parallel to th.' axis ^, ^^ of the compass Ik.x. 
 
 •riu' compass hox is now set vrtical and the needle is Iree 
 ,„ swin.' in a plan.' parall.'l to the nia-netie meridian. If R is 
 ,1... h,.i^/,oiital intensity ..f th. field and -'„ the reading of the 
 „„rtli end <.f th.- n.'.-dle, .'.|uation (:i2) heconies : 
 
 ^•=(«+A')^"^</'•..' <'^^^ 
 
 ' H.'lori- priuerdin.1,' lo I'l'"'"" '■" ^■""' ■ , ,,. „ „„„, 
 
 rc.>,.nsil.' u. .omp.-..-..,.- ll.o needle for V, the vertic.-.! con,,«nent of the normal 
 
 field. (See pi'i-'e ,v). 
 
.->:? 
 
 Tht* tompasM Ihix is a^jaiii placfil hori/.oiital. tln' iiia^im'timictcf 
 revolved throu<;h a ri;;ht anj{le, the coiiipaMs Ixix placed vertical 
 and a second reading; of tln' needle taken ; let it lie e._,'. In this 
 position R. liein<4 at ri;;ht an;;li's to tlie plane of motion oi' tlie 
 
 needle, its ett'ect on the position cil' the eunipass i die i-. /.ein 
 
 and We have for this position : 
 
 (i = K 1,1111/ '■./ (:J!») 
 
 From eiptations {W) and (■'!!)): 
 
 U liiiin '(,'- ; A' (liiiiij '-j' '"(''/ 'ii') 
 
 -r- II 
 
 (4(1) 
 
 H may then Im- determined liy the sine method and siilistitnted 
 in the e(piation. 
 
 2. In the normal field we may employ eithi'r of the two 
 following metiiods : 
 
 (ff) Beneath the nia;;netometer snspend centrally and ver- 
 tically, south polo upward, a strong magnet. A reading is taken 
 with the plane of the inclinator at right angles to the magnetic 
 meridian, angle y --!)()" and hence from et|. (:{21)); 
 
 (i^= K til III/ /;. 
 
 A second rea<ling is taken, with tht mni A' turned south, /.'., 
 with inclinator tin'ued IJSO"" -om the magnetic mei-idian ;- of 
 e(|Uatiou t:{2a*) \W" and we have: 
 
 ({ {K-H)liiii;l r;i 
 hence: /{{tunii r., — Ihikj r-,)~-H In iuj 'ii 
 
 III ml I't 
 
 and A'--, V f^ <-^'> 
 
 ti'iiij i'3 — liiiii/ r-i 
 
 A mean value A'^, ohtained from iliti'ereiit values of A' for dif- 
 ferent distances of the south ])ole heiieath the magnetometer, is 
 made tlie working value. 
 
 (I)) The magnetometer is set up in the normal field, as for 
 the tangent metiiod, the com|las^; box is placed vertical and the 
 deflecting magnet in its frame on arm A', with its north pole 
 facing the north pole of tl'.-. compass needle, ivK'^trHi.i/i/ nioveil 
 
 * Since the horizontal intt-iisity (>t"lhi' ni;ii,fiu'l arlinj; on the tu-etilc is /rro 
 
 m 
 
o4 
 
 forwani until tlic i'i)|ii|miss lu'cdlo stiuulH lumly vfitical. I'lic 
 icso1v>m1 iMirt of // al.inu {\u- \>\ium' <>I' rotiitimi In-iiij: zi-ro. "<• 
 liavi'. 
 
 y 
 
 KiR. !•.'> 
 
 '1 
 
 Wi 
 
 if f'n ivpivHcnt til.' fore- .-x.Tt.-d l>y tin- .IfH.-ftiii.i; iimjjii.-t on 
 poll' of stivn^jtli ,'( of til.' iiicliiuitor ii.'.'<ll.', .Uj.tli.' coiiiii.' .in.- to 
 til.- .l.-rifctinj; iiiat;M.'t. .l/^tli.' niom.'iit <lu.' to loir.' of ^;ravily 
 a|i|ili.'<i at 'I : 
 
 
 Koi- iiositioii of .■c|iiililnimii. 
 
 and 
 and 
 
 llfllC 
 
 F„ 2 / -= M' '/' 
 
 - •'/ ," 
 
 ^'" ' ,!■■' 
 
 M n I i M Hi ... ,, 
 2.1/ 
 
 '/■- ,7, 
 
 — = A 
 
 (ti) 
 
 (■S) 
 
 'I'lie viiluf of (/ is tiifii ilfl.-rinin.'<l witli n ,irh<i ii;i<'<l i>i>^,li,ni of 
 dt'Hcftiii" iiiaijii.'t l.y tli.- sin.- iiu^tiiotl. ami \vc liuv.- liiiaily : 
 
 ,y = /v = //«;„ «„ (H) 
 
55 
 
 Prom this (.•i|uati<>ii it in I'urtlici- evident that A' can only tie 
 (ieterniiued in tile normal tiuid it' A' - //. If A' //, it must lie 
 determined in a distiirlied field moiuIi of tlie neutral line. 
 
 The NensitivenesM of the inelinator increases with di-crease 
 of A'. A' itself varies directly as II' and </' and inveisely as 2 ii I. 
 Sensitiveness is tiest uttuinetl tiy makin;^ </' small and t;<itli n and 
 / f^reat. In the Swedish instruments the value of A' varies from 
 0.5 H to I.') //. 
 
 The value of /^obtained by ttie methods described is in 
 terms of // and, therefore, fr, as determined tiy the inelinator. is 
 also expressed in terms of //. 
 
 Kor till' purpose of determinini; the value of the ma;;netic 
 moment of the compass nee<lle and the dellectiny; maj;net, the 
 followinj; simple metho<l may 1h' emi)loye<l : 
 
 l)raw upon a plane table a line in the directi<in of the maj;- 
 netic meridian, as indicated by a compass and a line perpendi- 
 cular to it, intersectinj; the meridian line. (Jn this intersection 
 place a small compa.ss, with the axis of rotation of the needle 
 coincidin;; with the intersection. Place the ma^fuet (com|iass 
 needle, or detlectinji mai;net», the moment of which is to be 
 determined, with its axis coinciding; with the line drawn perpen- 
 dicular to the maifuetic meridian and with its center at a certain 
 distance (/ from the intersection of the lines. Head the deviation 
 of the compass needle if, reverse the ma;;net, maintainin<; the 
 same distance of its center from the intersection, and read the 
 deviatit)n (f', which will now be in tlie ojiposite direction. Take 
 the mean y„, of the two readings, then, if 2 / is taken as ,'; of the 
 actual lenj^th of the ma;;iiet, measuied in centimeters, anil '/, the 
 distance of the center of tlu' ma;;net from the intersection of the 
 lines, Ije accurately measured in centimeters, wi? have fioin 
 equation (10) pa<;e 21 : 
 
 i=A«/^//(l -ijhonnif^ 
 
 i 
 
 In this equation m i.s jjiven in terms of the value of the Imri- 
 /.ontal component of the earth's normal Held. If this is known 
 
m 
 
 in iil)M<)lu.' units mill intiiMJuci-d in llif .cumtiun. »/ is <tl)tiiin«'il 
 in liliHolutc iinitN. 
 
 Method of Observation. Tl"' nui;,'n.>t<)ni.-t.'r i^ s..t up 
 
 at the place of oltsfivution, us .l.-sciilHtl for tli.- tiiny;i-nt inttliiHl. 
 the eoniiNiMN nt-cdlc iciidin;.' !»0". Tlir conipiiss 1m)X is i>liu-e«l 
 vfitical anil tlif au>;li' of ineliniition < of tin- nei'iilc ivail tVoiii 
 its nortli I'm! (after taiipinj;, by allowing brasM i-in;; of suspen- 
 sion arm to fall trently upun tiie Ih)x). For preliiiiinai y obser- 
 vation the eoinpasM Ijox is lifteil from its lH-arin>,'s. lelil horizon- 
 tallv over place of observation, rotatid about a vertical axis 
 until the needle ivads JM)", and tuined into tlie vertical iMisition 
 al)out the axis passing; throu;,'h d' -0' and the an;.de -• read as 
 before from its north end. 
 
 >; 
 
 ! 
 
 it 6" 
 
 .t 
 
 t 
 
 lit 
 
 CNAPTKIi XI. 
 
 THE THOMSON-THAL^N MAONETOMETBR. 
 
 Desoription. The latest form* of this instrument con- 
 Mists of two parallel ma;rnetic needles .li, A-j (see VU^s. 2(i and 
 27), of cylindrical form. 2] inches Ion-; and alHmt i'„ inch in 
 diameter. These ma;,'uets are mounted upon a brass rin;; /, witn 
 like poles in tlie same direction. The rin>j is provided with 
 pointed hai-dened steel screws /<,, Hi. which rest U])on a<;ate sup- 
 ports (.'i, t'a, carried by the pillai> Ih- /'•->• and permit the muj;- 
 netic needles to swiny; in vertical planes aUmt the diameter of 
 the rin;; which passes throu^di the niai.nietic equator of the 
 needles. 
 
 To prevent the motion of the majjurtic .system and lift the 
 points of suspension from the a<;ate su]iports, when the instru- 
 ment is not in use for oliservatiou, an arrest is provided, which 
 consists of a second brass rin;; A' A', situated U-low the ma<;netic 
 sy.stem. Upon this rin<; are mounted four forks, Ai, Li. A:i. /.|. 
 which receive and support the riu;; of the ma>rnetic system. 
 
 * February, 1WJ3. 
 
57 
 
iM 
 
 Ki«. J? 
 
 Hi 
 
 Hflciiw iiikI lurtHt ail' iicioinjilisli- 
 I'll liy liMI- .1/, lUlUiltfW li.v .s«ltw 
 
 O. aiitl wlifh riii;; A' A' i« iiiiN<<l 
 liy IcviT .1/ to its limit tlif mount - 
 illy; / i?* |irfssi'(l firmly a;;aiiiHt tln' 
 slupM I'x /'•... iHildiiiu' till ma^rmtic 
 HV>*tfiii iiimi(>val)li' in imsitioii. 'I'lif 
 (TiitiT t>t i^iavity of tli«- majriiftif 
 .svstcm is Ih'Iuw till' [Miiiit of •-iis- 
 |ii'iisioii. as ill till' <'iiM' nfTiU'ijis 
 incliiiator. Imt in tli"' 'riiomsmi- 
 Tlialt'ii ma;;iii'tnmi'l« r may Im' ad- 
 iiisti-*! to (Iffi'fasi' or inci'iasi' tin- 
 si'iisitivini'ss of till' -ysti'iii, liy 
 raisin;; or lowrriiiy; tin' pivot 
 
 SCI'l'WS /<l, H-i. 
 
 Tilt" iiu-liiiatitiii of tlu' mayiu-tii' 
 svstrin |iro<liU'i'il l>\ till' MTtical 
 comiioniiits of till' iiia^'iu'tii- fon-cs 
 ill-tin^ upon till' iii'i'illi's may 1k' 
 .•om|n'iisati'il liy a cyliinlrical ma;;- 
 iii'l A', iiortli poll' upwanl. iiiouiitf<l 
 in a brass (•ylinilrical rasing, as 
 slu'wii in Kiy:s. -it; anil 27, ami 
 attaclii'il to a liiass scri'W /'. liy tin- 
 cli'vatioii or lU'prcssioii of wliicli 
 till- distanci' of tlic uppi-r poll- of 
 ma^'iii't A' from tin- plant' of tin' 
 ma^riH'tic nri'dlfs may In- vaiii-il. 
 Tliis siTt'w is opi'iatt'd liy tlu- screw 
 liiail N. situati'il on lop of tlu' ciui- 
 tainiiij; case. Tlic jiositiiiii of tlif 
 north poll- of till' fuinpciisatiiijr 
 ma^'iu't with nfi rt'iici' to tin- cciitiT 
 of tin- liujf carrying; the nHi<;m'tt<- 
 iR'i'ilk's is indieati'd on a siali' I'li- 
 
5» 
 
 
 yrilVitl 1)11 till" fncc»l-(iH |Nll( III' thr •»crf«. Til |iillilit ll^ Irinlin;; 
 
 (»!' tlir ><ciilf. tlir liniHN cyliiDlrical I'lisi' ut' ilic iiiiij,'iiil !>* Tor .1 slmri 
 <liHtaiii-i' i-iil ii\Miy ill I'i'iiiil. Ill \'"\'^ -Ji) till' <liv iNiniiN :{ anil i 
 an- M-rii. TIh' ili><taiii-i' iH'twi'i'ii tin' tlirrailsul' tin' scirw i»(Mi:l 
 
 of an inch ami iIh' liraii n( tli< 
 
 <liviil.<l intu liM) 
 
 jMirts Tliin |H'i'niits tiic ili-tiTiiiiiiatioii <'t' llic iii--tMiirc <>\ lli 
 (icrtiK'tinjr niai'iict iVuni tin' axis nl rc\ uliitidn nf il 
 
 iu-fdIt'N til within the ll.OOO:! nl' an im-li 
 
 Th. 
 
 orkiii^ jtartH tii'scrilM-il arr iiioiintiil 
 
 iiinL.'iictic 
 
 i'\ liiiiii'ii-al 
 
 linnHHfiisf, fhiMiil rnint ami ri'ar l>v irnici\aii|i' ;;lass |ilal>s r|i(iii 
 
 I'licli 1)1' tlit'Hi' ;;las.s jiiatfN a li<iri/iintal 
 
 liiif is iii;^iaM'<l til imlicali 
 
 when thf nrcillcM ,tri- in linri/iintai |iiisiti<iii ami tin- MTtical nmi- 
 |MiliclitH of the iiia^lii'tii- lurccs artiii;; ihmui liir in'i-dli's Iium' iiccn 
 (■<)iii|H'iiMat«'<l l)y thf nia;{iii't /■,'. A smi 
 
 ill Ikix-Ii-viI /.', sitnaiiil 
 within tlir i-UHf. indii-ati-s when the .i\is n\ intatinii nl' tin' mau- 
 tictic systi-ni In hiiri/Dntiil. 
 
 A Hiniill coiiipaHs r. niiiiniti'il mi a Inass Htnii '/'. li\i' inclns 
 loni;, iilaci'il. as nIiowii. un tun ol tin' cast' and ri'iimval 
 
 lilc, "TIM'S 
 
 thf dirfctioii iil the niajjiiftic nifridiaii and sfrvcs thf |iui'|Misf 
 111' lirin;;iiin' thf hnri/untal axis ul' riitatinii ul' thf iiia^iiftic 
 !»y>*tfni into thf niajciiftic nifridian. 
 
 'I'lif iiiaiir<i«'t<iiii<'tcr is nioiintfd mi a tiipcHi with lirad I'm 
 IcVfllin;;. as |)i'f\ iniisly dfsciilifd for thf 'riial(''n-'rilifii,' inaunitn- 
 I net IT. 
 
 As at 1 
 
 irfsfiit consiriictfd. thf iiistrunifnl lia> 
 
 tl 
 
 If scl'llllls 
 
 (lefcet 
 
 ol i-fiiiifniiif 
 
 tli< 
 
 diliit of thf scale of the dftlfcti 
 
 inii^nft ditticiilt. Thf lu'as.s pillar, which limits thf motion of 
 
 th 
 
 lU'iest. is |iaiallfl lo 
 
 and in front of the scale, ohstrnctiiif 
 s and scalf nnnilifrs aif iii- 
 
 tlie field of view, and the division 
 di.stinct. H^' replacinj; the pillar with a lirass piece, U'nt as 
 sliowii in the tijoire (the ori;;inal pillar is indicated liy the dotted 
 lines) and ceincntinj; upon the front flass plate, with Canada 
 lialsaiii, a plano-conve.x leiise of proper focus, the readini; of iIh- 
 
 sciile would \h- irreatlv ini 
 
 pr. 
 
 (I, 
 
«)(» 
 
 Theory of Thomson-Th&len Mftgnetometer. 
 
 Ki.j-'n 
 
 V 
 
 J-^-^ 
 
 f . 
 
 I 
 
 In Ki>fim-(2H) let 
 
 .V N Ih- tin- (•i>iniM'ii>*jitini; miijriift, 
 A I, llif iliMliiiH-f tVi)iii ci-ntfi- ofiixiM nf iivulutioii <>l' 
 tin- iim;,'iii"tic Mystfiii tu tlif |mi1«- « i>l' <>iif "I 
 tilt; lit'tKlU's. 
 ./ .1 V.tlir ilistiinc- of tlic iiuitli JM)!.' i.f thf coni- 
 
 IM'iiMjitin;: iiiiii;iut fioiii .1. 
 ./, = .4 ,s'. tlif <listiiiie«' of tlif soiitli iH)K' of tlif <(iiii- 
 
 jM'iisiitiiiji iiia;;ii<-'t from .1, 
 o Til." stivii;jth of on. of tli.- ih.I.-s of tli.' coniin'n- 
 siitinj; nrnjiut't, 
 
 n Tilt' Stll'll^rtll of OIK- of till' IKll.H of till' i.uijjiiftif 
 
 iR'ttlk'N, 
 H Thf ilisUinL't' of north pol-' of coniiM'nwtinj; 
 
 niai;nt't frmi u, tin- noiili polf of o"*' »>!" tlu' 
 
 iiiiifiu. tic ncetUL-.s, 
 «, Tlif (listauft; of south ixii.' from thf sjime point //. 
 
<\\ 
 
 .<■ Allele .1 N .' 
 \V«' Imvi- ior tin* I'oiii' / ••xiH<-<l l>.v .V up. ti 
 
 for the Ncrtiral riiiM|i<.Miii 
 
 t 111' lliis Cnrcf I ' 
 
 (1 II ItM I' It II < IW .1' 
 
 ' tr- ' </■■ 
 
 Siniilarl\ lor tlif \.itival cniiijiKiifiit iil ili<- inn / cm n.il lis 
 
 N ii|M)ii II : 
 
 ti It 
 
 Kr 
 
 (ini 
 
 I lor its viTtii'iil (■iiiii|Hiiii'iit 
 
 <t II tl>M ./' It It (•!»«•', I 
 
 (I Hiiii'i' tlu'Ht' lu-t in up|M>sitf ilii-cc-tii>iiH, wt- lin\r lur llir Vf 
 
 Militant vertical fi>rcc 
 
 jciW.r riur' ,r \ 
 
 If 2 / is tin- lcii;,'tli i>f till' iiiu;;iiftir m-cdlfM, Wf liav< l'..r the 
 etinplf iltit! to tlif i'i)iiij)fii!H4itiiiy inae;iift u)m>ii diie ik'ciIIi' : 
 
 21 = It It -2 1 
 
 Irrw' X rns"* .i' 
 
 /'=^'l ,1-^ i/,^ I 
 
 if I 
 
 , 
 
 It III 
 
 l~7/-- ./,-■ I 
 
 (42» 
 
 Kor till' HfCDiiil iHTille with strength <<( \»i\rs n' we ulitiiiii 
 similar cxprcsNiuii : 
 
 21 = 11 , 
 
 I ,/■-• </,-•' I 
 
 (4L'a» 
 
 The resultant couple ilue to the eoiMpelisntin;; lim;;iiel upon ImiII 
 needles will eipial the sum of the separate couples, hence: 
 
 ('• 
 
 •)2/ !»( 
 
 nt lit ) 
 
 \'1T^ ilr 
 
 (421.) 
 
 The rotHtion of the uia^^netic system pnHluced hy this couple 
 wilt !«■ n";lit or left haixled, us {>'" - •i") is |M,.sitive ui- iieiju- 
 
 tivc. 
 
 ■lit 
 
(i2 
 
 ir( r ti) is till' viM'ticnl iiitriisit\' ol' tin- (lisliirliril trrrrs- 
 
 Iri.il lii'lil. niiii|M'iisjtliipii is cH'ccti'il wIumi : 
 
 (T 't') = (' 
 
 '■i I 
 
 11 
 
 H- Mtllll' ( I 
 
 '1 " ) lll'|lcril!s U|lllll tllf llislllllCC ul' till' |Mlll'S X 
 
 i| >' ul' till' ili'llri'tiiiu; iiiii>;int t'l'inii O. as will lii' si'fii iVmii tlir 
 
 rllI'M' funs: 
 
 tnictrii I'lir till' in.stniiiiriit ili'scrilM'il. 
 
 Ill ti^^iiri' cJit) .li .li is mil' of 
 
 ll 
 
 II' iii'i'iiii 
 
 II. 
 
 ll the iiiai^iictic 
 
 systi'iii. willi II its iKiiili jiuli'. V 
 its siiiitli ]ii(lf, /'i. !'■• till' iiiirtli 
 
 ml siiiitli 
 
 |if<'ti 
 
 I liull' I-|'S|M'<'tlV('l\ II 
 
 till' ilt'Hrctinu iii,ii;ii('t. 'I'lu'ilis 
 liiiiri' /', /'•_>=;; III' till' nctuiil 
 
 li'iiirtli III' till' ili'tlfctini: iii.-iiriH'i. 
 
 F is till' 1) 
 
 I'li'W. til wliirl 
 
 llu'tlctli'ctiii!; iiiiij^'iii't is iittai-liril 
 liy iiii'iiiis III' wliicli till' ilistaiii'i' 
 111' l'\ iynui <> may lif alti'i'i-il. 
 Tile ;rrailiiati(in is sluiwii un tlir 
 raci'il-iiH'|iart ut'tlii' scri'W. 'I'Ih' 
 
 al'sci;sjls (if till' <Mir\r, ll . ll. r. il . 
 
 i',/,i/.nvv till' ilistaiici's (/„ lit' /'i 
 
 1.^ 
 
 K5 
 
 
 Fiv. '.1) 
 
 4??:- 
 
 ^ 
 
 -^-:E^^ 
 
 iiiim ". till' ciiiii'sjiciiiiliii;; mdi 
 iiati's till' I'ali'iilaliil \alili's nl' : 
 
 (I-1IS-- ,/■ ins-' .1- \ 
 
 tfi 
 
 Ni'Liati 
 
 ijinalis iiiilirali' li'I'l 
 
 liami. jHisitiM' (ii'iiiiiati's ii;r|ii 
 liaiiil lotatinii ul' ill!' ma;;iirtii' 
 s\stiiii. ijiii' |u tin- ruiii]ii'iisaliii;; 
 
 -// 
 
 'Tl 
 
 m 
 
ii:{ 
 
 iiiiii;iii't. When iinrtli imiIc /'i is situati'<l 'pist alM>\c <ir<liiiati' <• 
 till- otf'cct III' till' (Irricctiii;: iiia>;iu't iiiiKii n of the needle Ai At i> 
 
 zero. Wlli-n /'i uectljiies position /'», tile etfect oV the conipeli- 
 satiii^f n>ii;;net to |ii-o<hice ri<;tit liamleil rotation ol' the nia>;netic 
 system is a niaxinniin. corresjiouflin;; to oitlinate </. 
 
 It will lie si'en IVoni ti;;iire (2!>) that the ijreater the force 
 reijuired to comiieiisate north ]>ole attraction of the iJistiirlH'il 
 tield, the ^neater will Im' tile valtle of the scale readin;; /„. Iiut 
 that the ^'reater the force rei|nired to coni|iensate south i)olc 
 
 attraction, tin 
 
 he th 
 
 .f tl 
 
 le value ol the scale readni"', 
 
 lil 
 
 If 
 
 /.„ IS the real 
 
 li..^' 
 
 th 
 
 scale when 
 
 tl 
 
 le neeilles o 
 
 n. 
 
 >f th 
 
 <rnetonietcr stand liori/oiital ill the normal Held and /|. /.'_>. A;, 
 
 •tc., the readin;:;s f( 
 d 
 
 ditr. 
 
 rent ]i 
 
 leadings cories|ion(hn;; to the \alue 
 
 in a distiirlM-d field, the 
 if the verti<-al coni|K)neiits 
 •videntK- he /., /.„. 
 
 of the ore deposit for these places wi 
 
 /,._> /„, /:i /.ii. etc. 'I'liese readilii;s will, therefore, tie |Hisiti\e or 
 
 iic;;ati\e as /„ or /„. In the first case north pole attraction. 
 
 in the second case south pole attraction is liein;; conipensjtted 
 
 anil the iiuiiierical value /„ /.„ iiidica'es the compensated inten- 
 
 sitv of the \erlical coiiiponent of the oil' hody on an arhitrarv 
 
 scale. 
 
 Till' readiny;s /.I. /.._.,/;,. etc.. depend, in addition to the inten- 
 sity of the ma;;netic fol'ces to lie measured, U|Hin the moments 
 of the may;netic needles of the instrument and that of the com- 
 pensatin;; niaenet. It is, therefore. I'vident that since these 
 
 uantities \ar\ for i 
 
 lirt; 
 
 itfe 
 
 ■eiit instruments are not comparali 
 
 rent nistrunieii 
 
 ts. tli< 
 
 e readinifs of two 
 
 For that r 
 
 eason anil 
 
 for the purjiose of e; Iculalions of the depth of ore liodies. etc., it 
 
 is necessary to express the readin;;s /.„ for U in terms of //. This 
 niav Ih' accomplislied liy the following methixl of calihration: 
 
 Calibration of the Thomson - Thalen Magneto- 
 meter. The iiisiruiiient. set up ill the normal field, is properly 
 lexelled and the axis of rotation, hy means of the small compass. 
 I nought into thi' magnetic nii'ridian and the compensatin<.r nia;;net 
 ele\ated or dipiessed li_\ screw, until the ma;;nelic axes of the 
 
(i4 
 
 iici'dlc^ arc ill tlic siiiiu' plane w 
 
 itii till' linri/.oiital liiii' on tli 
 
 "•lass cover. 
 
 Tlic ivailin;; '/.» is olitaiiieil rruiii tlic scale ami 
 
 I'raduated screw-licad. 
 
 stroll: 
 
 out 
 
 airiict is now jilaced verticaiiy and centrally, 
 li jMtle upwards. Iieiieatli tlie iiia;;netoiiiei. r at distance il\. 
 
 •v\ 
 
 ic neei 
 
 lies .ue now rendered iioiizontal liy coinpensatini; iiia<c 
 
 net 
 
 iiid readme; /.\ o 
 
 ilitaii 
 
 11 
 
 lis is repeatci 
 
 1 I'or dittereiit distance' 
 
 of the iiia;;net Ironi a.xis of revolution ol' the needli's and the 
 ieadin<;s/2, /.:). /|. etc.. lor the diti'eieiit accmat 
 
 el\ liieaslirei 
 
 I di 
 
 tances 
 
 reliiov e( 
 
 '/■J. '/;). ''4 <'l<--. olisei-M'd and recorded. The ina^niet is now 
 1 and the Thoiiisoii-'riialeii Mai:iietonieter replaced liy an 
 
 inclinatoriiiin (see Ki;,'. ti). with axis of revolution ot the needle 
 
 dh 
 
 [•uiately perpendicular to the iiia;;netic nieridiai 
 
 south pole ilownwaids. is suspended cent 
 
 rall\- '"■' /• the inclina- 
 
 A iiiairnet, 
 li 
 
 loriuin. at a < 
 
 listance which will exactly conii>ensjite 1'. tli 
 
 vertic 
 
 al coin|>oiient of the earth s tield 
 
 Th 
 
 if the iii- 
 
 clinatoriuiii i^ 
 iM«tic Mieridian 
 
 now horizontal and its majiJietic axis in the iiia;n'- 
 
 Tlu' former iiia;;ni't is now 
 
 -.ilcci'ssively ]ilaced at distances 
 
 '/i. '/j. ''.1. >'<•■■ I''"' ''"' P"'"' "I Mispelisioll "\ ll 
 aiK'les /i. I>. /;. •te. coires|pondinu to the di- 
 ascertained and recurdi'il. 
 
 i. needle aiHl 
 
 tances il\ 
 
 /,.</..'/;;. etc., 
 
 Since V. the vertical coiniioiieni of the earth's mafrneti.siii 
 
 has l«'ell <-uln].ellslted. the olilv forces actill.L.' to pr<«ln« 
 
 th. 
 
 ani'le ol < 
 
 letli'Ct 
 
 loll l\ 
 
 /, /'.. 
 
 the earths inaLrnet ism , 
 llia-fliet helow the illst lllllielit 
 
 are H the horizontal Hiteiisffy of 
 ^r'. the \ertil'al eoinpolMip! •'' the 
 
 w, 
 
 ihelelole 
 
 ^' 
 
 /// 
 
 .',-;/ 
 
 / 
 
 //. 
 
 A curve iiiav now 
 
 lie const iiicled with taiiei 
 
 Its /„ 
 
 a-- aliseis>as and 
 
 leadiniTs /„ 
 
 lor .inv reai 
 
 etc. 
 
 V 
 
 rom tills eiir\ e (s. 
 
 li";; ''■■, 
 
 I it a 111 
 
 di 
 
 taiiu /„ 
 
 
 lia\e then 
 
 /,/ 
 
 ".'/ 
 
 '„ '•■^1>" 
 
 sed in term-- 
 
 if //. 
 
 II 
 
 *// t.ikin eqiial 
 
(!.') 
 
 Thus for ii (•(•rtuiii iti'trmm-nt (sim- Fij;. -SO). /,„ was luiiinl ti 
 
 3 f 
 
 1h? ('(jiial lor a (•crtaiii 
 locality to Itl.TO si-n\<' 
 • livLsioiis, I'or /., IX 
 the eorrcspoiKliii;; 
 value of tanj; /j 
 0.52. lor /.-.- lit. I') 
 tun;; I2- I . iiinl so 
 on. By the i)lottiiiii 
 
 of ♦licsc values, the 
 curve of V\ii. •'{<> was 
 ohtuiiied. 
 
 Ki«; Mi 
 
 
 
 
 
 
 •■ 1 
 
 ■ 
 
 
 ^ 
 
 
 
 
 
 
 ^ 
 
 ^ 
 
 ^^ 
 
 
 
 
 
 ^ 
 
 ^ 
 
 
 
 
 
 '-nfl" 
 
 j^ 
 
 
 ^ 
 
 ^^ 
 
 
 
 
 
 
 ^ 
 
 
 
 
 
 
 
 ^ I»*i4 1 
 
 ^ 
 
 
 
 '1 
 
 
 
 f n flfl 1 
 
 1 : »•. ■ 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 ■ 
 
 
 (Ml Vl'TKIJ XII. 
 
 DESCRIPTION OF THE SWEDISH MINING 
 COMPASS. 
 
 This valuahle iiistiiiiiient for prelir«iiiHi'y examination of u 
 nia^netie ore Held, as now eonstiMK-ted '.>\ .Swedish ineelumicians, 
 is suhstantially the same as the one mviiited Ky l)aniel Tilas in 
 the eighteenth century. 
 
 It consists of a li;;ht cylindrical hrass case /i/o (see Fii: :{| ) 
 emunelefi white on its inner surface. The case is i-losfd at 
 lK)ttom hy a I'eniovahle hrass plate (/»/, on which, facing' the 
 interior, the points of the compass are marked out in hlack on 
 white ^rotuid. PVom tiie center of this plate rises a li;;'ht lirass 
 pillar *, which ends in a tine, pointed, steel m-edle. Th - m-edli- 
 acts as the vertical axis of rotation of the suspension /),.i. <.,. 
 The suspension is provided at // with a jewel. The horizontal 
 axis of the mae;netic needle is supported hy tlu' suspen-i mi at 
 '1.1.,. To peiinit the needle 1(1 move in a veitical plane the 
 needle is hroken thron;rh in the rejjiou of its eipi.-itor, as shown 
 in tij^ure :\2. This method of siispi^nsioii permits the movement 
 of the needle hi .oiy plane. 
 
 i > 
 
66 
 
 i 
 
 Kiv. :ii // 
 
 To prevent the uiiHhip- 
 ping of the suspeiiMioii. imi 
 ivory stop « Ih cemented to 
 the curved gla«» cover. A 
 line h h, in black on the 
 inner face of the cast', in- 
 dicates when tile needle is 
 horizontal. Through the 
 eyes ili, 'l-i- 'h, the three 
 cords f/i', ili', 1I3, are knot- 
 ted, 1)_\ whi«4i the instru- 
 ment is held susjjended. 
 whef iili>*.'rvations are 
 made. 
 
 To compensate the vertical coHifxment of the earth's normal 
 fi.M. the huse plate '/.</, •iinyiii'; th.' iiiagiietM needle and its 
 support, is removed and the nee<lle tendered horizontal by means 
 of a small piece of wav attached fc.» IV south end of the ne.slle. 
 
tr 
 
 CHAPTER XIII. 
 
 INVBSTIOATSON OT MAONSTIC (MIE DBPOMTS 
 BY MAOMBTOMCTRIC MBASURBMBNTa. 
 
 If a preliminary' investigation of a Held, mad*- with tlic 
 Tibwjj Incliitator. or preferable' with a mining compass, reveals 
 by tb*- varyiag inclination of the needle in passiujj over the 
 field tb«t we have to do with a disturbed terrewtrial field, places 
 of jji'eaUwt inclination* are firwl Uicatwl and marked. A line 
 
 * It is to be noted that in the case of the mimnjf compass, the needle of 
 which always swin);s in the vertical plane pasistnj; IhrouKh the resultant of the 
 actinf; horizontal forces, the tnaximunn inclimition will not be found directly 
 t»ver the pole of the majfnetic i-e-body, but north ot it, as is evident from the 
 -Mlowing (see Fi^f. 33) : 
 
 fit 
 
 II /•• 
 
 , V*li 
 
 The resultant /■ alon^; the meridian .V'.S'inthe ore field to the north of the 
 upper pole of the ore-bixiy is equal to// — i'' and the vertical resultant =- 
 F + G. We have, 1 herefore : 
 
 F+ G 
 
 or, if /"is compensated: 
 
 7f^ '""<'' 
 
 This value will bo jjreatest for // — F — O, which can only lake place north of 
 the pole olthe ore bodv. 
 
HH 
 
 I 
 
 I 
 
 M 
 
 jdiniii;,' tlit'Mi' ijivfs tin- yt'iii-ral cliri-ctii)!) of tin- stiikt' oi' tin- ore 
 lii-ld. The iiiai,'iiftoiiiett!r is then set up in the tield over one of 
 the places of jjreatust inclination and a line run in the direction 
 of the strike by means of the si;;lits of the nuijjnetonieter and 
 this line is extended throujjjh the field to places where (i O. 
 
 ( )ii this line, the principal line, are then laifl otl" distances con- 
 veniently of ;{0 feet, coniiuencini; at the stake for niaxiinuni value 
 of ff, and stakes driven to mark these distances. From these 
 stakes and at ri^jht an<jles to the principil line, suhsidiary lines 
 are run to the limit of the disturlx-d Held and on the lines dis- 
 tances of .{() fet't laid otf, cominencinj; at the stake on the 
 principal line. In this manner, the whole field to U- investiijated 
 is laid out in sipiares. 
 
 For the i)urpose of identifyin;; individual sipiares in the 
 field, the rows of stakes, i)arallel to the principal line, are 
 marki'd with letters, those at ri;jht an;;les with numerals, I.e., 
 on each stake is marked the letter and number of the respective 
 rows to which it l)el(jni;s. For the purpose of re-measurement 
 of certain valiKs of U or (i. or for the extension of the field, 
 should this |)ri>ve advisable, it is neces.sary to mark more per- 
 manently some of the stjitions, l)oth in the principal line and in 
 the lines perpendicular to it. 
 
 The stations are then transferred upon .s<|uare<l paper, c»)n- 
 v.niently on a scale of I inch ~ tiO feet. On this preliminary 
 sketch are also marke<l in their proper location import^mt objects 
 iK-currin;j in the Held, such as hou.ses, roads, shafts, ditches, 
 streams, etc. F<»r the correct inlerpretati(Hi "I liie results of tlu' 
 ma;inetoiiietric nieasuiements made, it is very desirable vluit on 
 the sketch the terrane be representiKl i|uantitatively l)y approxi- 
 mately corn-et eoiitonr lines. 
 
 .Uter tlies.' |ire]iatiitions of the tieltl and the |irelimiiiary 
 sketch till' iiia;;nelometer is ixaiiiined in the normal Held and 
 tesicij u> to it- adjustment and ne<'es.sary corrections maiie. The 
 inciinator neeille is bn>u;;ht to the zero by adjustinj,' the little 
 weight, or the index error- read and noted, .<o that it may bi' 
 taken account of in the final calculation of the vertical intensity. 
 
 J 
 
en 
 
 'I'lif work of iiitikii)<; tlic iiiiiifiiftoiiietric inciiMtirciiii'iitN iimy 
 now Im' Ih'^111. The majpu'toiiiftfr is first set up in Mevcrul 
 phiet's in tlic normal Hi'id un<l tin- flmnictvi'istic anfjli' »/« dfttT- 
 iniiied for tlifst- plaws.* Tlic ina;;nt'tonii'tfr is tlu-n set U|) 
 siicci'ssively at fael) stakt'iiml tin- respfotivc xaliu-s of an;;li's a 
 (or A' I and r detcrniincil foi' tlicsc stations. Tlicsf, ns s«H)n us 
 niwiMurfd, art; transferred to tiie preliminary sketch at tlie eor- 
 ri'spondini; jxtints. Soutli pole attraction is indicateil hy placiii;; 
 the lainuH «ij;n in front of the recorcU'd an;;le. In fasi- of rapid 
 chan;;e of the niajjnetif intensities measured, it l)eeomes necessary 
 to take ohservations at stations intermediate hetween the stakes, 
 on tht! sides of the scpiares and also within the si|uares. The 
 additional vahies of the anjfles « (or A') and '■. thus ohtained. 
 are recorded in their proper place on the sketch. 
 
 It is in many cases valuahle. anil for a complete investiga- 
 tion of the Held, necessary, to observe the anj,de which the re- 
 sultant R makes witli the lines either at ri>;ht anj;les to or parallel 
 to the principal line. For this purpose the magnetometer, set 
 up over a stake, is hrou^^ht with its arm K. l>y means of tin' 
 si<{hts. into line with the .stake line and the angle « included 
 l)etween the stake line and the magnetic axis of the nee<lle read 
 and recorded on the sketch for that point c)f the sipiare. The 
 observation does not take tint much time ami should !»• made 
 at every station. The mean of the angles <»„ observed at the 
 limit of the field where ^; = and // = //. indicates the mean 
 diri'ction of the magnetic meridian of the field of investigation. 
 
 If observations are to be made with the Thomson-Thali'h 
 magnetometer, which permits only the determination of the 
 different values of the vertical intensity of the ore field, the 
 method to be purstied is as follows: 
 
 The instrument is set up in the noiiiial field and levelled. 
 I!v means of the small eompiiss. moinited <im to|i nf the case, the 
 horizontal axis of revolution of the needles is i-endered parallel 
 to the magnt'tic meriilian. the magnetic needles released, and. Ii\- 
 
 ■I 
 
 Sei' p.'ii^e 't.'*. 
 
 II- ■■■' 
 
70 
 
 If. I 
 
 I i 
 
 11 ■? 
 
 meaiiH of the coiniK'nsatiiijj iimjjiiet, hnmjjlit into horizontal 
 jKwitio!!, K) w then read. Thin operation niUHt Iks repeated for 
 different places and only nuch values* joineil to a mean value ^, 
 which do not differ much fnHu each other. The instrument is 
 then set up over the different Htokes of the Held and tlie position 
 of the compensating majjnet /j, /«, /a, etc., which brinj;H the needle^ 
 to the liorizontal position, read for every station and recorded. 
 
 The values obtained hy these measurements are then utilized 
 for the construction of charts, which show the distribution of 
 the horizontal and vertical intejisities and the varying direction 
 of R in the field of investigation. It is usual to construr, a 
 separate chart for each of these (piantities. By joining the 
 ]K)ints of eipial horizontal intensity in the one chart lind the 
 ix)ints of eipial value of for the other chart, we ol)tain for 
 each a system of isodynamic lines. By joinhig the points of 
 •<|ual declination for the third chart, we obtain a system of 
 ...ogonic lines. 
 
 Plates II. Ill and I\' are illustrations of such charts, con- 
 structed for an ideal magnet 100 nieterc in length and including 
 an angle of 5.S° with the horizon, with its upper pole 80 meters 
 below the plane of observation and of pole strength 5,400,000 
 C. (J. S. units. 
 
 Plate I is a vertical section of the field of force through the 
 
 station line m of Plates II and III. giving the curves of the 
 
 verticjil and horizontal intensities of the upper and lower pole 
 
 respectively of the magnet. The arrows indicate the direction 
 
 in which the forces act, the onlinates the intensities on a scale 
 
 of (),()0 = .'j inches, and the abscissjis the different stati<ms along 
 
 the line iii, on a .scale of 20 meters to the inch. The calculation 
 
 of the intensities is shown by diagram for st<ition 4 to the right 
 
 ff 5,400,000 ,.,. , „ 
 
 of zero, in which the line /',- ,., =^ -,,,^xr. -:, =0214 ni length 
 
 <l' \ny)i\l I'll! )' 
 
 i<tu\ ilirection rcprtscnts tiie total intensity of the pole S at 
 
 t> 5,400,000 ... ., , 
 
 station 4. The line y'„= . „= vT ioon ..... >■■ =(>.04:<.sniiilarly re- 
 
 presents in length and direction the total inti iisity of the pole 
 
71 
 
 .Viit tlu- Name statioii. F,. t\ ami fi,. (i„ iiif tlif liuii/«iital uii.l 
 vertical coiiiponeiitH of /'.and /'„rfsjMctiv»'ly. 
 
 From the curveM, Plate I, tlie liori/.oiital ami vertieal in- 
 teiwitieM ami tlie an>;le rJ which tin- lesuitaiit of tin- lioii/oiital 
 inteimity iiialteH with tlie maj;iietic meriiiiaii iir.- iiiMily l<minl 
 for any station in the plane of oltMcrvation, as will mipeur fiom 
 the following illustrations: Fij{. 4'), Plate I, for tlie station./ :{. 
 
 /', and /'„ correH|)on(l to the points m and m t! n-speetivfly. 
 The point/=j 'i lies to the rij{ht of /'., therefore, from to the 
 right lay off 7',/^ O;/ on line m and /'„/to the left of m (i 
 (since / lies to the left of /',.) ti A, (i,= ;i ", <r'„^ <• h and (f 
 for station 7 8 =,'/<'<•/'. Similarly /',= ,'/''. acting along /',/, 
 as vihown in Fig. 45. and /'„ = '/ /'. acting along /'„/'. By con- 
 structing the i>arallelogram and drawing the diagonal, we find 
 A' in intensity and direction for the st^vtion j :<. rix)n/''/and 
 / W (the horizontal intensity of the normal Held) construct the 
 jjarallelogram and draw the diagonal, which will !»• It for the 
 station /■ 3 and and angle lif H » the angle which the re- 
 sultant horizontal intensity makes with the magnetic meriilian. 
 
 Chart of the Horizontal Intensity. -In these charts 
 
 the isodynamic lines are curves, which result from joining jKiints 
 for which either the angles of deflection a or R have the siime 
 values. In the tir.st case the curves are constructed f(jr maxinnnn 
 values of «, corresponding to It < //. from 10° to 10° and foi 
 minimum vahies of «, corresponding to H> H. from 5° to .') . 
 In the second cashpoints may Im- Joined, for which A' 1.00, 
 1.20, \:.iO, 1.70, 2.50.« 
 
 It i.s cu.stom!P V ill Swedish practice to employ coloins in 
 representing the distribution of H. The ' neutral lin*- " {R = H 
 or «- «o) niay he drawn out in hrown (burnt sienna), curves of 
 
 » It i-i not importjiiit lo adhere to the vaUu■sju^t <ivfn lorthi- lonstruction 
 of isodynatnii- lines, which are reiommended by the Swedish authorities. They 
 are stated to serxe only as a Riiide. The point lo be kept in miiul in the eon- 
 sirnction of ma^ieti. i harts is to ehoose such values lor the lines as will most 
 fully represent the distribution of tlie maKnelu- lorce in the field, without over- 
 loading' the chart with loo many lines, which would obscure, rather than 
 umphaxize the salient features of the deposit. 
 
 ■| 
 
 ■4 
 
 I 
 
 II 
 
 ■J. ^ 
 
 ■i 
 
72 
 
 iiiitxiiiiiiiii viiliir III' «. (•i)iri'> xtiuliii;; tuiiiin 
 
 iiiiiiiii value of H iimv 
 
 h 
 
 »' IVIIl't'MI'll 
 
 t...l 
 
 III jjrt'ci 
 
 (H<><)k 
 
 IT M •'fl'fll 
 
 !), iiiii 
 
 I (III 
 
 •r 
 
 (.1" H. 
 
 iiiiiiiiiiMui miImi- >>t' 'i(, r(HiVN|ii<'ii<liii^ to iiiaxiiiiiiiii valiir < 
 r.(l (ciiiiisoii lakr.> Tin- anaM within tlic lKHiinliii;.' Iiiif« air 
 laid ill with th«ir pinpfi- cdliiur ari<l ol' a tint the iiioic int, imr 
 the ;,'i»'atii tiic vaiialiim of thv U-iiiKlin;; ciiivch Iioiii tli> valiif 
 H= II. OlijcclN, Mich ri-. lidUNtH, itc.ai"' riiin'H.iitf<l l>y liiu -^ in 
 Iiiilia ink. 
 
 It is iniiMirtaiit for luturi' nt.rcncc anil lor (diii|i;iiisnn 
 with charts of other ile|)<)sils to iii'lieate u|m)1i tin |ilaii lieside 
 tile name of the oljserser, the exai-t JiH-ation of the ilepo- it and 
 time when oKservatioiis were made, also tlie method einiiloved. 
 the instrument usi-d and the normal aii;;le «„ if It lias not Uen 
 olitained direct with tlii |)alill>lom arm. 
 
 Charts of Vertical Intensity. If the ..li-.rvationH 
 have Ix'eii made with tlie TilM-rj; Inclinitoi. the eui es in these 
 eharlH may join either points for which the aii;;le '■ ,,r the value 
 of (/ = h' III III/ r is the HJiiiie. For tlie ealenlatioii of <> from the 
 aii<;les of oliservatioii r, a talile of iiaturiil Ian;." 'i|^( is a|)peiidc(i. 
 (See Tal.le IV). 
 
 The curves may Ih- coii^triHied for dc;;rees varyine from 
 10° to 10' or from 5° to 5°, or for (i in terms of H fur values 
 0.0, 0,1. 2 ni.. ox. l,»i, :i.± 
 
 III ;lie ca-ie of r.hser vat ions havinij lieeii made with the 
 'i noitisoiiThrtlcn mn^jnetometei , lines are dnivvii throu;;h jilaces 
 tor which /„ or (/„ — A.), or the corresjxmdiu;; values of tan;; /„, 
 ;;ivili;; (I ill terms of //, are the same. 
 
 The colourn in these charts to hrin;; out the distrihiitioii of 
 the vertical intensity adopted an . Idue ( 1'rus.si.ni hlue) for north 
 pole atliMction, and y^ llow (;;aiii!io;r.') for .smitli pole attraction. 
 Till- areas Ix-tweeii the lMniti<liii;,' curves are laid in with ajipro- 
 pii-ite tints, as i|iseiilii-cl for the jilans of the hori/.ontal intensit;- , 
 
 Kim the |iiir|M)se of comparing; diti'ereiit maps, plotted fro'e 
 ohservatioiis with instruments, for which /v' iliHeis, in addition 
 to the name of the oliserver, etc, the \alue of K must he statt-^l. 
 
7S 
 
 To t'iicifitiit)- tliin (■(iiii|Mii'i>uiii. hy I'l'iliiciii^ A'„ of any ihstniiin'iit 
 to A' 1,(1 //• a !,il)lf is ii|ijH'rnli'<l (Ncf tnlih V.>, in which : 
 
 l'^ - til <iliHt'rVf<| tXHjilf lit" thr iliclirfittul' liii'<ili' willi 
 
 coiftiint A'„. 
 unil r the un;;li' whicli iM(i-rcs|„,ii>ls tu thf iiii;,'li' i', I'mi- 
 an iiiclinatov with conHtant l.o //. 
 
 'I'hr viihn- III <! ill a liilil uiHtiirU-d hy thi- |ii-i'.scni I uiily 
 
 diH' iiia;;n*'ti(' tu. (|f|iiisit varicM from a niaxiniiin.. ilirt'ctly over 
 til'' |«ilf lit' tin' till' tHKJy, with iliHtanci' fmni thi' inaviiiiiiin in 
 ^t'lK-ral at first rajiidiy, tiu'ii imoit MJuwly, to /.ito. Ix't-oun's 
 wfalcly iM'uativj- aiiii at ^^rcatfr tlistanc'cs U'conii-s a^iMin /t-ro 
 (si'i K'ij. :{4). Khitt»'niii'_' of the i-rcst of tin- cin-vi-, ('ori'i's|H)ni|- 
 
 li'^.:'. I 
 
 in;^ to slow ih>crt'a.s»' from inaxiiiuini iiuHeatrn citlicr y^'t-at ilepth 
 Ik'Iow the surface, or a small ,.ii;,'lr (> dip of the ore deposit. 
 
 In the case of very complex rielils, due to t!ie presence of a 
 num)H-r of niajjuetic on' Ixxlie'. it hecoiiies necessary, for the 
 
 *ll In t'vitifiit ih.'it ill llircjise ot this fi-iliK-lion thi- vjihu' ol" A' imisl be r*'- 
 I'errod lo the Kiinie livalily, sime // itiffers lor dilKn'iil placis. For Ottawa, 
 Ont., " - l».l.-). (C. C. S.) 
 
 if 
 
MKiocorY mounioN tbt chart 
 
 (ANSI and ISO TEST CHART No. 2) 
 
 |£ |2^ 
 
 |M 
 
 U£ _ 
 
 
 Li iii 
 
 ■ 2.2 
 
 lll^ 
 
 ■■■ 
 
 ■e ■!£ 
 
 12.0 
 
 I 
 
 1.8 
 
 I^Ui^ 
 
 ^ /APPLIED IIVMGE Inc 
 
 BP: 1653 Cast Main Street 
 
 B^ Rochester, New York U609 USA 
 
 •JB (716) *82 - 0300 - Phone 
 
 as (716) 288 - 5989 - Fox 
 
74 
 
 {)urjK)st' of dettTinininj; tin- extent of the individual ore depasit, 
 to construct profile curves (see Fi}{. 35). These curves are 
 obtained by takini; the values of G across the deposits for ordi- 
 nates and the distance between the stakes of the field (niarkinj; 
 
 1 
 
 ii 
 
 l:t 
 
 It Si 
 
 Kii;.:»ri / 
 
 /' 
 
 /i ; 
 
 / 
 
 i : I 
 
 : ! ; 
 
 ^ 
 
 L .. :..J : _v- 
 
 the points of observation) for abscissas. A number of such 
 profile curves constructed for different parts of the field may be 
 recjuired for the determination of the extent of the different ore 
 bodies. 
 
 CHAPTER XIV. 
 
 INFORMATION CONVEYED BY THE CHARTS OF 
 MAGNETIC INTENSITY. 
 
 Plate II. shows the distribution of the isodynamic lines of 
 the horizontal intensity of an ideal magnet. The neutral line 
 is seen to intersect with the magnetic meridian over the pole 
 y^g. A and R are points of indifference. Between these points 
 the compass needle points south. Plate V* shows the distribu- 
 tion of the horizontal intensity of a deposit of magnetite. The ore 
 body being buried about 10 feet, the terraae nearly level and 
 the ore body of a regular lense shape, consetjuently the ciirves, 
 
 * Redrawn and coloured for this report by E. N'ystrom from illustration in 
 "Teknijsk Tidskrift," January i$X\\, 190J. by H. SuiidhiMm. 
 
75 
 
 Hhowinj; tlie iiia<jiit'tic inteiiHity, iiiv fdiiipiimtivi'ly r«'j;uliir. Tin' 
 intersectii)!! <it' tlie neutral liiu- vviti: tlic liiii' comicctiii^' tin- 
 inaxiniuin and uiiniinun) i;ivfs in tliin case tin- IcK-ation of tin' 
 pole. 
 
 Plate VII. sliow.s the distribution of the liori/onta! intensity 
 of another niajjnetic ore deposit. Here the neiUniJ line ,1/ X 
 divides the field into two ijeneral areas of niaxinittiii and mini- 
 mum value of «. The niaxiinuni value of « is at (r. the mini- 
 mum value at F. The letters ^/ in front of the ninnerals indi- 
 cate that for these stations the sine method eould not 1m' 
 employed, and « was obtained by the tani;ent nietluKl. The 
 neutral line M X is deflected by the small minimum area K. 
 which is suJTOunded by another neutral line. The intersection 
 of the neutral line M X with the majjiietie meridian at (^ does 
 not in this case deteimine the location of the pole of the main 
 ore body at this point, the pole l)einjj situated much further 
 north. 
 
 Within the minimum area (X.'curs at // a small maxinuim 
 area surrounded by a neutral line. The pole <;ivin<j rise to this 
 maximum area is located at /•*, thi^ intersection of the neutral 
 line with the magnetic meridian, which is drawn out in black. 
 
 From a mere inspection of the map it wouM ai)pear that 
 the areas ff and / correspond to an independent small ore-lKxly 
 and it is only by a study of the distribution of the vertical in- 
 tensity of the ore field (which is triven in the same plate) that it 
 is found not to be an independent ore-body, but a strinj^er in 
 connection with the main ore-lnxly. 
 
 From these illustrations it will b seen that charts for the 
 horizontal intensity are useful for sini^le and simply shapeil ore- 
 bodi" but that they become complex in the case of a iiumlier of 
 ore-bodies, or an ore-body with several branches. For the 
 solution of the problems presented by the more complex maj;- 
 netic fields, produced by the joint distributinjf action on the 
 normal terrestrial field of a numlx-r of mai;netic ore-twdies, the 
 charts of the vertical intensity, in conjui''*ion with profile 
 
 I ,- 
 
 m 
 
t- I 
 
 76 
 
 iMUV<!s, funiisli most inloniiutioii. Tlii' iscMlyniiinic muvcn of 
 tlifsc clmrts umy lie lookcil ujkhi us foiitour lines ami the chart 
 as a t<)()();;ra])hical eliart of tlie ofeiureuee of the ore-b(Mly. 
 (.'uives, lonjr, narrow and of somewhat re^'ular elliptical f(jrni, 
 ]>oint to an on' (lo|)osit of re;;nlar form. Tlie strike of the ore- 
 l)oily i-i alonj; the dii-ection of the loni;est axis of the curve of 
 maximum intensity. Irrej;ularities in these curves ai«' occasioned 
 either by nei<^hl)ourini,' ma;,nietic ore-hiwlies, or l>y tlie topo- 
 ^rraphical features of the terrane, which necessitated measure- 
 ments at eijual distances from the pole to he math' at diH'erent 
 altitudes. Hence tlie necessity, as pointed out previously, to 
 incorporate the toi)oj;raphical features of the terrane in the 
 chai't. 
 
 Very irrejjular curves indicate irrej^ular distribution of ore 
 masses. Sucli deposits often show nearly circular areas of 
 maximum intensity which chanjjes very little within the area. 
 Calculations of depth below the surface ;jive, in mo^t cases, very 
 <lisc(jrdant results. It is not ])ossible to decide from niajjuetic 
 measurements alone whether such deposits are workalile or not. 
 
 If the di.stance between the curves on the on" side of the 
 maxima is farther apart ('.''., the vertical iuten.sity decreases 
 more .slowly in tliis direction) than on tlie other side, either the 
 ore deposit dips in this direction,* or the altitude of the terrane 
 diminishes rapidly in this direction. 
 
 The action of the lower pole of ttu' oiv-ImmIv comes into 
 evidence in the production of an area of south pole attraction, 
 which t)ccurs witli every ma<;netic ore deposit and wliich sur- 
 rounds the area of north pole attraction. If the ore-botly extends 
 vertically to a <;reat dej)th, tin- south pole attraction is corres- 
 pondini;ly feeble, but increases in intensity as tlie dij) of the 
 ore-body decreases and tht> lower pole apprwiches the surface. 
 (See Kigs. ."{(i and 37). 
 
 * Va.^e 45, " Om Ma);ni'li>ka KyndiKlii'liT oih iliTiis UndiTsokninj; 
 modelst Magnetometer,' al Tli. Oahlhlom. FaUiti, i8(}8. 
 
77 
 
I f 
 i I 
 
 South pole attraction will in <;i'neral \>e ohserved in the 
 level ternini', free from ore, contijfiKjUH to a clift' in which the 
 ore cropN out. The extent of the area of this south pcjle attrac- 
 tion increases with tlii' depth of the ore-lxMly, and this may 
 serve as a valuuitle indication of the extension of the ore-ljody 
 in depth. 
 
 Plate III shows the distribution of the vertical intensity 
 in a liorizonhil plane of an ideal majjnet. The upper pole is 
 vertically Iwueath 1',. the lower pcjle In-neath /'„. the inclination 
 of the !na;;netic axis is toward the area of muxiuuim south pole 
 attraction. 
 
 Plate VI shows the di itrilmtion of the vertical intensity of 
 a deposit of ma;, I'tite (see paj;e 74). The curves jvre here re^jular 
 and of elliptical shape, indicatinj; a concentrated nia.sM of ore of 
 reffular shape, the .strike Ixiinjj in the direction of the lonjfest 
 axis of the curves of maximum intensity and the dip to the 
 north (alxjut (i")°). The influence of the rock dump (containing; 
 Ht)nie ore) in j^vinjj rise to new curves at the portion of the field 
 covered l)y the dump is especially instructive*. The width of 
 the deposit was about 15 feet and the lenj^th about 1(J5 feet. 
 
 In the case of the ore field, Plate VII, A, li and C aw 
 areas of maximum north pole attraction. A and B are eleva- 
 tions of the pole area of the main ore body, .wtween these areas 
 the pole area is concave. V is a stringer >n connection with the 
 main ore bcjdy. The magnetic axis of the deposit dips toward 
 the south-east. The strike of the upper pole area is north-east 
 and dips in that direction. The area of south pole attraction to 
 the west of .4 is due to the fact that the terrane slopes rapidly 
 from A t(jward f), which locates the jtations of observation of 
 area D Ix'low the pole of the main ore lx)d\\ 
 
 In the case of an ore deposit with extension in length 
 several times greater than i!i depth, south pole attraction is in 
 general developed at the north end of the deposit, particularly 
 when the strike of the deposit is in the N. S. direction and the 
 
 * Si>e aUo iii.'ip of liorizom.il inti?nsity, Pl.ito \'. 
 
79 
 
 yf'> 
 
 intenHJty of such attraction is especially manift'st in casfs wlu-if 
 the north end of the de{)osit pinches out wed^^i- sliape. Tlif 
 lines of force of tiie eai'Ts nia<;netisiii filter the north -nd of 
 tlie deposit and there develop south pole attraction. They then 
 travel, on account of the {greater permeability of the ore ileposit, 
 throujfh the <;reater lenjjth of the deposit, leavinj; it at the south 
 end, where north pole attraction is conseciueiitly developed (see 
 
 Two nia;;nets of equal strenj^h, with extende<l pole areas, 
 placed with their axes parallel, a slu)rt distance apart and with 
 like poles in the same direction, produce a field of force, in 
 which the lines of force are shown crowded tojjether in tin- 
 space adjacent to the space separating; the ma;;nets. The lines 
 of force proceeding from the north pole areas, which would 
 return through the space between the magnets to the south 
 pole, art -Hected outward in a direction parallel to the axes of 
 the magnets. The conseijuence of this is that the Held of force, 
 in plane perpendicular to the axes of the magnets and a short 
 (Ustance from the poles, shows only one maximum of vertical 
 intensity directly over the point midway between the magnets 
 From this maximum the intensity decrea.ses, at first slowly, then 
 more rapidly, .so that a profile curve will exhibit flattening of 
 the crest. Two maxima will appear, when the distance Ijetween 
 the poles is greater than the distance of the p<jles from the plane 
 of observation. The maxima will, however, not l)e directly over 
 the centers of the pole areas, but their position will be found 
 shifted in the direction of the space .separating the magnets. 
 
 These observations will evidently also be made in the case 
 of two parallel magnetic ore bodies. If the distance separating 
 them be not great, only one area of maximum vertical intensitj- 
 
 • If the magnetic north pole of the earth be regarded as the north pole ol 
 a magnet, a magnetic needle will point with its north seeking pole in a direc- 
 tion north, and since opposite poles attract, this pole will be the true south 
 pole (Lord Kelvin's designation of north seeking pole). We shall, therefore, 
 ha-e at the north end ot the deposit the south seeking, or true i th [ ole, at 
 the south end the north seeking, or true south pole of the neei ' attracted 
 down»ard>. 
 
 f it 
 
 ■ H 
 
80 
 
 will U- olwi'ivfd, iiM ill tlif ciiMf of a siiijilc oif IkkIj-. If the 
 Hjuiet- tH-twfc'ii the i»n- iMHiics is ;,ni'utt'r tlmii thf (iistaiicf of tJic 
 ]M)li-H from tlif |)liiiic 111' ol)si'rviitioii, tin- diHt-rt'iitiatiim into two 
 
 (lie l)o<lieM will Ik- mIiowii l)y the otTUirciK f two iiiaxiiiia of 
 
 virtifal iiiteiiNity. 
 
 Wlit'iitjvt'r till' proKIc iiiivi'm show coinplicatLMl or iiiiusual 
 foiiiis, it lii'coiiii'H nccfssaiy to analyse tlic complex curvf into 
 its compoiu-nt cuivcs. tiy eonstructiii^ trial curves witliin the 
 complex curve, until tlie aljjehraic sum of tlie oriliiiates of tlie 
 overlappinj; trial curves eorrespijiids to tlie actual oriliiiates ol 
 tlie complex curve. 
 
 ,«-,,, 
 
 f 
 
 •■***^***^P^-«-'V^«^*!-55i 
 
 Figure (38)* is an illustration of a complex profile curve, 
 representinjj the actual (K;curreiice of an ore deposit, consistiiifi; 
 of four separate layers. The dotted curves show the final trial 
 curves, 'i'lu! al<;ehraic sum of their ordiimtes corresponds to the 
 ordiiiates of the curve obtained hy tlie iiia>;netometrie measuie- 
 inents. 
 
 » From Uhlicli, Markscheidekunde, pa^e 3S3. 
 
HI 
 
 ClIAI'TKiJ XV. 
 
 DBTBRMINATION OP THE DISTANCE OP THE 
 
 UPPER POLE OP A MAGNETIC ORE BODY 
 
 BENEATH THE 8URPACE. 
 
 let Method. — By tri'atiiij; a iiiii;;ii<-ti(- nvv IhmIv un an 
 iilt-al magnet, in (letcTiiiiiiin;; tlic <ltNtaiii-r ol' its |h>Ii' I'i-dih tin' 
 plane ot" (jlwiTvation, i-esults ai'f olituint-d. wliidi <-x|)i-rii'iic>- lias 
 sliown afford fairly- Wfll with t'aft. 
 
 fift the line ^1 //in Fij;. Mi !«• a line drawn tlnuu;i;h thf 
 plafc of niaxiniuni 
 veitifal iniunsity Ki««'..'l!i 
 
 (f„. L.'t G Ih- th." 'V'L ^. J:: U _ 
 
 Vttlui' of the vcrti- ' \ <_ 
 
 cal intensity at H. j O 
 and further, let ii = 
 the distance of the 
 plane of observa- 
 tion alH)ve /', tile 
 
 pole of the maifnet. | ^ 
 
 Let '•„ le the anjjle ! / 
 
 asfertaiiied with I ,. / 
 
 the I... . -t.!, _ *" 
 
 'A H . . the */' 
 
 inc <y le at ' 
 
 stati. , . = streiijjth of pole l*,li\ the nia^netit force at A, due 
 to the pole /^,/'b the nia^^lietic force at li. ihle to the pole I', .r the 
 aiijrle lietween .1 /'and // /', then : 
 
 >- 
 
 / 
 
 / 
 
 ./a 
 
 '(■^ 
 
 Kl'ii'H 'm—^'u 
 
 {B P)- 
 
 V /.' , 
 
 \fos .rf 
 
 ;, , *7W- ,/' 
 
 (.' /.' 
 
 U 
 
 <P 
 
 K till/;/ 
 
 (4:i) 
 (44) 
 
 (45) 
 
 i H 
 

 
 
 
 11 
 
 H-i 
 
 I'luiii (4.{) .Mill <4.">» wi- liiivi-: 
 
 ./•^ A' 
 ami 
 
 '"/"/ '■„ 
 
 III III) •■ 
 
 ill ml I 
 
 ciw' .1' '• 
 
 I.I,,.; .• 
 
 \Vf liiiv.'. Illllln r. si'i' Ki;;iliv (.{!•): 
 
 ,1 ,1 li,;,t.r 
 
 {Mi) 
 (47) 
 
 /(»ii;/ '■ 
 
 Till' viilui'H .(■ mill '•"' '•. ciirn'siininliii;; U> tli<' viilm-n ' - iiiay 
 
 '''".'/ in 
 
 Im- tiikfii at mill' Iroi" tin- taltli-n aicniiiiiuiiyin;: thiw \\a\m: (Sw 
 
 Tal.l.' VI). 
 
 Kor tin- apiilicatiDii kV tliis imtluHl two vali •> ot ^' ai-f 
 ifiiuin-d to •>»• awuiatiiv ilitiTiiiiiicii, (r„ lur .1 and (1. wliit-li 
 sliDulil not Ik- Ii-sn than ', 'r'„. for li. 'V\\i- ilistHiiei- A H \s atriii- 
 atrlv niwiHiiii-il. Tilt' Ix'st ii'Hults ait- iilitaiiu-il wlicu A /< is laid 
 uH'IriHii till' jKiint of nnxiiiiuni iiiti-iisity ai-ross tin- strike and 
 on till' sidi' of most rapid variatinii .if U. 
 If y' and .»/" an- the distaiuis from tin- jioiiit wlii'ii- d is a maximum 
 
 to iM.ints wlii'iv ^' 4f'»>'' ["ivsiMctivi'ly. \vi' liavi'. si-.- i'i|ua- 
 tioiis 4:{, 4') and 4<i : 
 
 W hi ,nt t' ( i 
 
 (4H) 
 
 KhiiKfi- li 
 
 and lu'iict' for (i ^-= ., 
 • I 
 
 l-nx / f \ 
 
 and for I! = \y '"■"' ' f* i 
 'I'lii' I'otaiiji.'nts of .''aiid-'Cciual nt-arly 1 and I', ri'spcctivi'ly. 
 
 ,1 ,/■ ^>i <■*"> 
 
 lirni'i' : 
 
 or the iK'ptli of till' upper pole of tlit' ore d('))osit Ih'Iow point A. 
 for wliicli a is a maximum, is fiiual to tlic liori/ontal distance 
 from .1 to the jxiint for which (i \ ^'„. or eipial to 1 \ times the 
 distance from .4 to the point for which (I f. '/„. 
 
 Kipiation (45) ,.,-,<.«•' r = r,' represents the eipiation of the 
 vertical intensity curve. 
 
M.H 
 
 Kroni t'i|uuti<>ii (44) : 
 
 we liavf for till' liiiri/.oiitiil iiitfiinity F. tlif cxpri-Hsiiiii ; 
 
 If, XI II .<■ 
 
 fllM' ./* Ml II ,1' 
 
 (.■.(>) 
 
 wliicli n-pivHt'iitH till' i'<|Uutii)ii loi liit- hurixmitul inti-iiMity I'lirv*'. 
 'I'liix iiiL'tliixl in ii|)|ilic-itl)lc only to ore ImhIIi-h wliicli uri' 
 
 I'rticiil 
 
 or viTv nt'iirlv so. 
 
 2nd Method. -Till- linfs of t'orcc |)iisNin;.rout of till' iiorlli 
 P<j1*' of II iim;;nt't. whic-li iiiiiki' a miiiuH iiii;^Ii' witii tlu- |)i'oloii<^ii- 
 tioii of it>* axis, an- vorv iimriv stiai;;!!! iim-N. TliiH fat-t itia\ 
 Ih' einpioywl for tlm foilowiiij; iiiftliiMl of dctt riiiiiiiii;; fiiipirirally 
 till' (listaiicf of till' |M)li' U'lifatli tlio Nurfiu-c : 
 
 A liiu' in laid ott tii!'oii;;li tlir |M>iiit of iiiaxiiiiiiiii valui'of (i 
 iukI jH,'rj)eiiiii(,'ular to tlic strikt- of tlu' ort'-lxHly. Oii this Hmi', 
 coiniiii'iicin^ from the |Kjint of iiiaxiiiuiiii intousity d^, diMtaiici'H 
 of from 2 to /> yards are stakrd out and for tlu'st- |>oiiits (r. A' 
 and ii ail' at'curati'ly di'terminwl. If tiic nia^jiietic muridiiin has 
 
 |)ri'vioUsly Ik'cii 
 
 •14) 
 
 d.'t 
 
 friiiiiii'i 
 
 I, th 
 
 i)ni|M 
 
 lit F of n 
 
 is found t)V the foi- 
 lowiiij; I'oiistnii'- 
 tion : 
 
 Li't 
 
 III' till 
 
 iiiijilc inoludt'd Iw- 
 twi't'ii till' luajriiftic 
 
 V« 
 
 iiit-rK 
 
 iiaii 
 
 d till' 
 station lini' and ><) 
 the anjjle includid 
 y; ,S iK^wei'ii this line 
 
 and Ii at station .SV 
 (See ¥Uj,. 40.) 
 Throucrh .S'l, reprev'^ntinj; a station, lay otf a line iiiakint; 
 anifii' «o with the station line, nd on it, from .S, eut otf any 
 
 I 
 
 * l|! 
 
I 
 
 N4 
 
 loiiMiiifiit iliisiiuifi' tiikfii iiM unity. Kr ihf Niniif l»<»int Ni 
 
 sit ..rt" i. liiM- i>|' l.ii;;tli ,' // /i'. making an an;;!.' »i with iln- 
 station liiM' ami coniiil. !.• llii- iiarallcioyiani with li an thf 
 
 i|ia«ji>nal. >'i H will ih.n Ik- F. tl .iui|K)nfiit of // i«M|iiir<'<l, 
 
 anil it- int<nsily will U- i<|.nstiil.il liy its li'n>.th mi thr sa 
 
 stall' .•ni|.l.>y..l ji.r // ami H. T\u- vahiis i.f F aiv thiin dI taiiiiil 
 '■. ciinHtnirtiun fur cscry station ami the anyh- y which tin- 
 iliiiTtion of thr total nm;;nctii- IoiitiIui- to thf mapu'tic (lf|(oHit. 
 niaki' with the hoii/on, can now !••• caliiilatril from tin- i-x- 
 iirfssioii : 
 
 a 
 
 III III/ (,' A 
 
 or niav 1m' constrmliil for tin' ilitlinnt stations from tlu- known 
 \ali!is of <i ami A'. 
 
 A line is now drawn to sijtl.-, on which tin- ilitiV-n-nt stiitiuiis 
 
 an- sft oti', ami at cafh station S^ S-,. S,, I'tf., thf cuU-u- 
 
 latiil an;;li's (fi,<f->.<f:i I'tf., laiil ott'. 'riii-si- lim-s tin' pro- 
 
 loni;i'il until tiny intirscct, ami tin- nuan ilistancf of the inttT- 
 sii'tions from tlir linv, ri|ins.iitiny; thf iilanf of oltsirvation, is 
 
 takfii in tiinis of thf scalf i-niiiloyfil. as thf distam f the 
 
 jiolf of thf ilf])osit from tin- snrfacf. 
 
 3rd Method. - A third im-thiMl is hasfd iqion thf faft 
 that thf finvfs of /-</.»/ iiilrnxlhi drawn alnait thf jtolfs ot iilful 
 iiiaiciK'ts arf in thf vicinity of thf jiolfs very nfarly circular. 
 Thf nifthoil consists in timlini; thrci- jioints for which the total 
 intensity is tin- siinf. Tlifsc thn-f j)oin ■< will lif on thf cir- 
 
 cumffrfiice of i if the isixlynainic curves of total intensity 
 
 alnait thf jiolc (.Sff Ki>;. 41). 
 
 To apply this incthml stakf ot! a linf throiijih thf point .1, 
 at wh'ch (1 is a inaximui-i, at riy:ht an;;lfs to tin- strike of the 
 ore iKHly and olisfrve at "es of three yards alon;; the line 
 
 very accurately the valius oi II. It and it. Krect a scatioldinir 
 or a step-ladder over the point .1. for the purpose of deter- 
 i;inin<; the value of (i at different heij;hts alKjve .1, for which 
 station the values of /' alonj; the vertical line of ohservation 
 
till) iIki'i-ImH'. till' ililliii'iil iili><i rvi')| \iiliii' 
 
 i-i".n 
 
 art- ri|Uill In /I'I'ii I 
 
 III' It i'i|iiiil to till' tiitiil iiili'ii>-ilii»< '/'. ( 'aliMiliili' t> |)n-viou>tly 
 
 iiiilicnt)')!. till' viiliii' /'' 
 
 for fttfli lit' till Htrt- 
 
 liiitiN (III till- liiH' siiik- 
 
 • *l iitf thriiti};li .1 anil 
 
 timl twn itiitiiih-' nil 
 
 tliiH liiii' I'lir wliicli till' 
 
 total iiilriiMitv '/' 
 
 I K- H- lia- thr 
 Hiiiiir viiliii' as mil' III 
 i\w oltNi'i-vtHJ vahii's of 
 
 
 H ,r 
 
 ( f 
 
 \ \ 
 
 I alMivr 
 
 ti a I 
 
 tl 
 
 .1. If A 
 
 IS 
 
 If iM'ciiratiMV iin-as- 
 
 Uri'd llfi;ilit alnivr .1 , 
 for wliirli till' vahir 
 'f is i'i|iial to till' 
 valucj* I A'-' (i-. fur 
 tin* otiit'i' two Htatioiis 
 \vi' have, if tl is llic 
 iliHtaiiff from .1 to 
 one of tlii'sc stations. 
 It tlir ilistaiicf of till' 
 
 piilf of till' iH't' IkkIv 
 I flow .1 Hllli (• till' 
 
 raiiitis of till' furvf of 
 total iiitfiisity (sff 
 Ki-. -H). 
 
 '/- /-■-■ 
 
 '■ - -nr 
 
 \ \ 
 
 ^; 
 
 / 
 
 / / 
 
 / ■ / 
 
 \ \ \ 
 
 / / 
 
 
 / / 
 
 / 
 
 /// 
 
 / / / 
 
 \ \ 
 
 \ 
 
 ^ \ > 
 
 
 /.•'■/// 
 
 ^ 
 
 l)=r- h 
 
 .1- /,•-• 
 2 h 
 
 h 
 
 •IlT 
 
 ( .-. I ) 
 
 As ail illustration of tliis iiiftluKl wr timl for tlir iileal may;!! 
 
 (Fliitf 1), for A 
 
 10 
 
 L'ters iilxiVf tlif [loiiit (), //(. 'r -• +.")..') a I 111. 
 

 
 
 h 
 
 
 if 
 
 
 n 
 
 
 
 ! 
 
 I 
 
 m 
 
 1)V tl 
 
 If list- 1) 
 
 I' tl 
 
 ic curvt's 
 
 (Plati- !»,'/= l+-"> ii»'t<'i>*. '"'"■ ^^' 
 
 hicli 
 
 I yi _^ (p l„is the siuiu- value, licliee : 
 
 100 
 
 /> = 
 
 14..V- 
 •20 
 
 a 
 
 !l 
 
 •2!t.H7 meters, 
 
 wliifl. (lirters only by 0.18 inetei-H from the true value. 
 
 4th Method The following; meth(Kl» requires only the 
 
 ,l,.termination of fr„„ and a value of (; at a short <listane.- ver- 
 tically ahove the point for which d = (im,^. It is, moreover, 
 indepentlent of the nature of the terrane. 
 
 U-t ff equal the pole strenj,'th of the maf,'netic ore deposit, 
 I) the distance of the pole from the plane of ohservation at the 
 point where G = r;„„, an.l '/ the distance between this point 
 and the one vertically alM)ve it, for which G umy have the 
 value ^1. 
 
 We then have 
 
 
 f.' 
 
 . = 'm 
 
 id 
 
 
 •D- 
 
 (.V2) 
 
 I fin,.. ' '^'l 
 
 To illustrate the applicability of this method. G^^^ o7.0 ior 
 point 0, m, Plate III, ^'i for a point at a distance of :i meters, 
 vertically aixive it, was found to be 4(>.7. Hence : 
 
 :i . I 4(5.7 
 Z>- — ==- 
 I 57.0 
 
 
 ■M).\:i 
 
 I 40.7 
 
 which result differs oidy by 0.l:{ meters from the actual depth 
 ,,f tlie pole beneath tlu' plane of ob.servation, which was taken 
 as .SO meters. 
 
 * Diililblom loir, cil., pp. .S3 and 54. 
 
87 
 
 r, 
 
 CIIAPTKK XVI. 
 
 DETERMINATION OF THE EXTENSION IN DEPTH 
 OF A MAGNETIC ORE BODY. 
 
 Tliis ilctcniiiiiatioii i-oiisists in rimlin^' tlic Ifiij^tli of tlir 
 iiiilijlii'tic iixis of thf iiiv deposit, '.'., till' (listiiiicc Ix-twcfii the 
 upper uiul lowiT pole of the ore iMxly. wliieli. in the ease of 
 massive niajinets, is ;] of the actual length.* 
 
 1st Method. -Tlie followin;; method is due to Dahllilom 
 and is Iwsed uixai the fact tiiat tli.- contouis of the lines of foice 
 of a ma<,'net are independent of the leii>;tli of tin- majinel. as is 
 evident from the fact that in tlie e.pmtion of tiie lines of foree, 
 
 (K(i. 1 ) - is constant. The ma^iiietic ore deposit is treated as an 
 
 ideal ma<,'net and the inclination of its lines of force to the plan.- 
 of ohservation determined alone; a section perpeiitlicular to the 
 strike of the ore (lep<jsit. For tliis purpose a line is staked out 
 across the point of maximum vertical intensity and extended 
 over a distance on lK)th sides of ^',„„ double tlie length of the 
 north pole attraction. Distances of :W feet an- laid ott" on this 
 line and for each station the values o. R and <1 are accurately 
 determined. {It hy the .sine method). 
 
 The direction of the meridian is determined from the avera;fe 
 value of o at places wiiere <i is nearly etjual to z.-roand A' nearly 
 e.|ual to H. or from the known declination of the locality and 
 the astronomic meridian. Prom the vahies <",. R and // the values 
 Fare ohtained for the diH'erent stations .s',„ as previously ex- 
 |)lained,+ and f , the an<;le of the lines of forc«' with th.' plam- of 
 ol).servation for these stations, calculated from the eipiation : 
 
 a 
 
 F 
 
 III ml C 
 
 ' .XiioiiliiiK '" llalillilem. I'l, ini responds in pnuliie l»-ltec- in tin- ims>- nt 
 ore deposits. 
 
 V See p.t,v;e >*,?. 
 
 
 ii 
 
 
I ' 
 
 8K 
 
 A line .1 h\s now clmwii tliiouj,'li tlic (liajiram of tin- linrs 
 ol" lorcf ol' iiii i«lt!»l imiKiiit (sff Fii;. 42), iit an inclination to 
 
 /'. /'„ com'siiondinjr to tlic (iil> ol' tli.' on- Uody. At tlu- points 
 of iiiLTNirtion ln't\v<'cn tlif lini- .1 /< ,uul tlic liii.'s of force, tlii' 
 
H9 
 
 iiiijjles y, whicli tlic liiit-s of force iiuiki- with tin- line . I H.tivr 
 iiieiistiiid witli II protractor. Tin- line is now Hepuriitfly druwii, 
 (see Fij,'. 4.S), tlie points of intersection of the lines of force with 
 it laid off and the convs|)onrlin<; aiiijles if written l)eside them.* 
 
 It becomes now a (|Uestion to ascertain on what scale the 
 diap-ani of the lines of force of the ore-deposit ret|uire.s to he 
 drawn, in order that the observed values of if may coincide with 
 those points on the line A H, at which the lines of force of the 
 exi)erimental diajjiam (see Fij;. 42) include the same anjjle with 
 the line .1 li. If the scale of the two diaj,nams were as 1 : 200(1. 
 the ma^nietic a.xis of the ore deposit would he 2000 times the 
 lenj^tli of the niajjnet of the exi)erimental diu;;iam. 
 
 The followinj; example, taken from the plotting' of the 
 isodynamic lines (sec Plates II and III) of an ideal majjnet 100 
 meters in lenjjth. with its «])per pole 'M) meters Ixlow the plane 
 of observation and ilip of ."):{° to the liorizon, will show the pro- 
 cedure of determininjr this scale. 
 
 i-i..-.4:t 
 
 Throufjli the point ('. (see Fiij. 4:J) correspond inj^ to the 
 value y =!K)°, another line 1) K. makin}^ any convenient anjjie 
 
 * Instead ol measuriii); tlu' an^jlos of the intersection with ^ />' ol'rt// the 
 lin.'s offori-e of the iliajfram ( Ki>;. 4^), il is, in most cases, sufficient to choose 
 alonff the line .1 B points at equal distances apart, correspondinjf to the stations 
 in the ore field, and to determine the anjfles of intersection of the lines of 
 force with .^ Aat these points only. If lines of force in the diagram (Fi>;. 4JI 
 do not pass throui;h these points, such lines are easily intercalated and the 
 angle of intersection with .//>' ascertained. 
 
 i ' 
 
 \i 
 
ill 
 
 ii t 
 
 I '"■ 
 
 !t() 
 
 witli .1 /<. in (Iriiwii. and ui».n it, stmtiii;; Iroin tlif l><>iiil ''• 
 a.nvHi...n(lii.K to (i„.,^. tli- stations N,, .s'-., etc.aiv niaiki-.l on .■aeli 
 side of r. on any convenient st-ale. as 1 : 2()(t(». 'I'lu- scale eni- 
 ploywl in this particular case is 1 : 2:{ti2. Tlie points for wliicl. 
 ,f Um the same value on A li and /> K are now joined l.y lines, 
 which would »H' parallel, if the construction were free from eriov. 
 If 2 /, = the len<;th of the niaicnetic axis repres. iitin^i that 
 of the ore deposit. 
 2 I = -t.Ofi-l cm., the len^.'th of the nm<;netic axis of the 
 ideal nm};net. (Fi},'. ■1-2). 
 ll.fSt cm., the distance on a scale of 1 ; 2:{()2 
 on the line in the ore field throufrh ^'„„». he- 
 tween the points for which if has the value ol 
 H°and H+°. 
 ll.:{5 cm., the distance on scale 1 ; I on the line 
 .4 B, Iwtween points for which the an;,des if 
 have the same values. 
 We ha\ e the proportion : 
 
 ■2 1. -11 =^'li ■ 'A. 
 
 and 
 
 II. X4 
 
 'li 
 
 ./., : 
 
 ■2L = 
 
 1 1.:{5 
 
 2:J02. 4.()ii4= I()(ll2. cni.=-- KM). I 2 meters. 
 
 Such nearly perfect parallelism of the lines joininj; e(pial 
 anjiles on .1 H and D E cannot he expected in the case of an 
 actual ore body, because it is not an ideal ma<,niet nor are the 
 observati(.ns free from error. Moreover, the distance of the 
 plane of observation from the upper pol.- and the inclination of 
 the magnetic axis to this plane are not accurately known. It 
 ma>, here.ore, become necessary to try other lines at different 
 inclinations to l\ /'„ (Fig- +-^). "'"l '^^ different distances from /', 
 and select that one for the final calculation, which furni.shes th.> 
 most sati.sfactory i)aralleli.sm. F. Thlich states that more pei-- 
 fect agreement, between the fields of force of a magnet and 
 magnetic ore deposits, is often obtained by employing the diagram 
 of the field of force of two unlike i)oles of une.pial pole strength. 
 (See Fig. -S). 
 
ni 
 
 T<» fm.-ilitatt' till' aiipli- 
 cation of tliJH iiii'tliii<l II 
 traciiit; iiiiulc ol' I'lati 
 VIII, wliicli rciircsi'iits n 
 
 .|.|. 
 
 field 
 
 I" 
 roi'ci' i)t' an 
 
 net. nia\' \>f 
 
 i.i.al 
 
 ploytMl. 
 2nd Method. I'll. 
 
 rollowin^ iiu-tliDil. il«'- 
 lit'iidinj; im tht- ili'tiTini- 
 iiation lit' till' an;;li' 
 which the iin)li)ni;ation 
 of tl 
 
 u' niairni'tic axis o 
 
 the ore deposit includes 
 
 ith the lit 
 
 ne drawn 
 
 IVoni the center ol" th 
 
 iiatrnetic axis ti 
 
 th 
 
 ic (Pie ilelioslt , 
 
 jioint of observation, is 
 due to Professor Knliert 
 Thalen.* 
 
 Let : .1 /) he the jilane of oliser\ali<iii. 
 
 Dtlie point of ohservation for which 'r and fliavi 
 
 heen deterinined. 
 N .V the niaj;netic axis of tl 
 2 / the lenjjth of this axis. 
 : the Vertical distance from plane of ohservation to 
 
 center of the iiiimiic'tic axis. 
 '■ the distance ..1 I), i.r.. from point for which 'r is a 
 maxininm to jioiiit where vertical intensit\ has 
 the oliserved value (i. 
 le allele made hy proloiiy;atioii of magnetic axis 
 with line drawn from center of mai;netic axis 
 
 th: 
 
 to />, 
 
 int of ohser\ati( 
 
 lentrth of this lin 
 
 J 
 
 ern-KontoriMs AniiaK'i, Kt'iniioiuifl Ji'rtlt' Arifanyvii, 'K()i>, Sji'lto Haltt't. 
 
 !i 
 
 I • 
 
 ii 
 
 1j 
 
 n 
 
92 
 
 ;• tlif aii;;li' iiu-ludi-il at uiiiicr lM)lt iHtwccii tin- liiifs 
 
 N .1 ancJ S I). 
 M tlif anj;le infludt-d at lower iKilt', lictwei'ii linun .V .1 
 
 and .V /), 
 rt = till- stivn;,'tli of tlu' (lolf Nor .V, 
 
 /', tlif ton xcrted l).v Nat />, 
 
 /'.J tlu- t'orcf exerted by A' at D, 
 /.■,;,,ld^'I=tlle liori/,oiitrtl and vertical eoniponiMits respect i v. ly 
 
 of y'l, 
 
 /i'3andr,'j=the horizontal and vertical coini)onentM respectively 
 
 of /V 
 
 We tlien have : 
 
 (J 
 
 '■ ..■-•-! (:- \f 
 
 It 
 
 /.',= /', N/K j-, f\,- I'isitI lit 
 
 ./■ •'■ 
 
 . Ml II ll> = 
 
 A'. 
 A',. 
 
 I r2 + (---f/)- 
 
 
 If .1/ is the nionien( c)f the inaj^net, we have: 
 
 M 
 
 ■21 
 
 M. 
 
 I 
 
 f ;, = l\..u<y, Cfi = I'-, cox o) : 
 
 :-/ -.4/ 
 
 ^. (5S) 
 
 II IS Y 
 
 
 I .'■•--[ (:+/)'•' 
 
 
98 
 
 ii = (i\ — (ti 
 
 = ''J 
 
 : + / 
 
 
 ('>4) 
 
 If we can ne^lcet .^ whieli is a very snuill (|iiaiitity •;i-iior- 
 
 *lly : 
 
 
 /' = 
 
 1 i»/.. 
 
 [• 
 
 :{/ 
 
 :{/ 
 
 •] 
 
 :{.)/. 
 
 = (■ ('(« If: .1= <• «#// 
 
 /' = 
 
 liM 
 
 ■lUt* ( 
 
 (".) 
 
 Further 
 
 Air. -I . a/ 
 
 2/ r" 
 
 — _ r-__ 
 
 (I 
 
 ■y) 
 
 : + ' . :»/ 
 
 (I 
 
 :</« 
 
 r/>.v L'" ) 
 
 ■M 
 
 ] 
 
 a/« 
 
 
 ==27r'L7^'"^^ - ■^']-7'b^'"'"^' '] 
 
 =;ij[...v- i] 
 
 r; = -^ ro.>r* y 8 (■(«* ^1 ( 
 
 )0) 
 
 
 (■osfc . st:l 
 
 f u:::::. 
 
 il/c(w*f (.S <7w*y 1 ) 
 
 and 
 
 '•i cim If Hin If .'< fun;/ if 
 
 li ('(ufl If. — 1 2 — fati<i^if 
 
 finii/^if + '.] jp /"/((/ If = 2 
 
 (T)?) 
 
 From whieli formula if is ulitained. 
 
!»4 
 
 \Vf havi- fiirtlifr: 
 
 '"".'/ V 
 
 ,(• fiilii III/ If 
 
 TliiN lonnulii is iipplimlilo only in tin- i'Uh.' of <.iv IxHli.-s 
 an- vfftieiil. or very iiuaily so. 
 
 Tlu- point /'. for wliith <f iiii.l /•' ivquiif to »h. di-ter 
 should Iw fhosfii ill til.' liiH' passing tlirou;.'!" '',„.. "t "'Jil'' 
 to tilt' stvii «'. 
 
 (5M) 
 
 wliifli 
 niiiiecl 
 
 I 
 
 (MIAPTKU XVII. 
 LABORATOKY PRACTICE. 
 
 For purposes of lal)orat.ay piactic- in tlif vari.ms methods 
 d.!scribed iu the torecroiiij; report, the followin;: experimental 
 t»iV)le will lie found convenient. 
 
 The frame consists of 4 ui)riKl>ts of hard, well seasonwl 
 Wixxl, 4 X 4 X 40 inches, with side pieces of same material. 
 2 X (i inches, dowelled into them. (See Fi^js. 4(i and 47). Two 
 parallel side pieces cany the brass rails N, (Fij;H. 4ti and 47) 
 which are fastened with brass screws to th.' side pieces, as shown 
 
 in Figs. 4S and 4!t. 
 
 On these rails move the castings .V X. which are each pro- 
 vided with three rollers, /',, l\ i's, to obviate friction. The 
 screws Q tit in slots of the rails to prevent upward displacement 
 of the castinjfs iV and .serve to tis the latter in any desired 
 position on the rails. The rails are jrraduated into 5 centimeter 
 divisions and the position of .V is rea<l from the knife edjje K, 
 which is in the plane pas.sinf; throujrh the center of the maj;neto- 
 
 meter. 
 
 The tube A which carries tlie majjnetometer and its support 
 is fastened rijfidly to the castin<;s .V by the screws 0. (See Fijj. 
 49). The tube .4 is jrraduated tlirou>;liout its leiij^th into centi- 
 meters and the position of the center of the tube D, which 
 
!■ 
 
 ciirrioH tin- iiiiit;iifti)iiift«-r, is rciul from tlif iiuli-x on tin- U-vfllcd 
 Miilf of the lipikt'ii tlii'oii;;li |)iirt A' of tlir siijiiMirt ('. 'I'ri jin-- 
 
 ;iJi-t=E»tj-. 
 
 W^ 
 
 
 Scale l:20 
 
 
 H 
 
 'tit till' rotation of the support ^ ' on the tulu" ^1, the tul)*' is 
 rovitli'il witli ii ki'\- tliroii<rliout its K-iii'tli. wliieli fits into its 
 
DU 
 
 Scale Vl 
 
 
 
 hi 
 
 I'i 
 
 If; 
 
 
 ' 11 
 
 ^.-'■■r--^- -, 
 
 
07 
 
 MfMt.iiM hIiowii lit H. (KijjK 4h mill 4!>l. Smw fi In-hii- llf 
 Nii)>|Hii-t r ill iiiiy iltMirtHl |MiMitii>ii <>ii tiiln- .1 
 
 Till' tiilH- /*. wliicli, tiy iiH'rtiis (if ".cifw |iliiy .1/ ranifs tlii' 
 iim;;iii'tonii'tiT. is ;;r'uliiiitf(l tlii<iu;;luiiit its K-ii^li iiil'i i im 
 tlivisimis mill is wftirc*! Uy wn-w H. Ki'tafimi nf tin' iiiIm' 
 in itH MU|iiMiit is |)ivvi'iiti'il liy h k«y K. Httiiij: into its wut. a«. 
 hIiiiwii ill Kij;. V). 'riic lfnj,'Hi of IiiIm- /> ' •oiivtiiit-ntly takni 
 iiM 4.'i cm. Ill tlif fiiw iif fxamiiiin;; ri'|iit'Mfiitativi' on- iKxIiis 
 fluHc I 1 tlif |»iain' of (ittHiTMition. a IuIm- mIioiiIiI Ih- pmvidtil 7 
 ci'iitiiiutfi-N ill lfii;;tli. If i>tlit r iii>*tnnin'iits an- to U- attacliril 
 tu IuIm' h. ajiproiniatf hcicw \A»gH. tittinj; tin- iiiNtiuiiifiit. ir- 
 i|iiirf III Im' pidviilfil. Tin- iKotitiiiii of I) \h nail at A. ( V\}i- 4H( 
 It svill 1h' sfi'ii timt l>y iiii-aiiM of tin- ;{iailuatioiiN on tli>' 
 rail N ami tiilH- .1, tin- wliolf tit'UI of olwiTvatioii n-pivMcntcil liy 
 till' iiiti rior iliiiK-iisioiisof tin- fX|H.'rinii'iitul talilf may U- dividi-il 
 into .si|iian-s of i (liriiiHtiT on tin- siilf. anil tlic ma;;nrto!iittfr 
 may Ik- liroiij^lit into jMiMitions witli its centt-r vi-rticall;. alKivf 
 tin- coriKT of till' •it|uari's. Kor intfiniofliatf jiositions tin- siili- 
 ilivisioiis uii IiiIk- .1 may U- usfil and tliosf on rail N I'stimattd. 
 
 'I'lic fxiii'iimt'iital talilf should lie sci up in a Uisc nt iikhii 
 
 as fri'f from iron us poHsililf, at least fit-f from movcalilc piins 
 of iioii. and tlif upii;;lits should have a solid foundation fiic 
 from contact with the Hckii-. Brass angles may Ih' cniploycd 
 to stcuic the iipri;jhtH tirnily to the fliKir. as shown in Ki;;. 47. 
 The ore body or IkmHcs may U-st lie lepreseiited l>y lai>;e 
 pieces of hard cast iron or hardened steel. These should he ..f 
 diH'ereiit shapes and dimensions, some lenticular, others thick 
 plates with rectani;ular cross sections and some of irre;;ular 
 sliape. These may Ix- mai;neti/.ed in any desirahle direction by 
 canyinf; a ma<;netiziii}; ciirieiit around them. The a.xis of the 
 area enclosed by the current will constitute the niajjiietic axis 
 and since Initli hard cast iron and steel retain niajfiietism after 
 the current is withdrawn these txKlies will now constitute per- 
 manent inajniets. which, placed mider the plane of observation 
 of the tabic in any desirable position, may lie examined siuirly 
 
 
 t 
 
 n 
 
!»H 
 
 .ii Ih- jiMiiii.il ill iiiiy iiiiii'iiir /iiiil tliiir inin^iutir tii'liU <lftiT- 
 
 • 1 .1 .iimI i-lhiii-^ ..I till' li.iii/Miitiil mill \crtinil iiiti'iiHity coii- 
 
 -iiih iiil. 'I'lir ili-iiiiii I till' ii|ii'.-i|itiitivf iiff IbmIv I'riiin t\u 
 
 ,.t III. <i\ iilisiiMitidii iiiav I'l' i-.-;;iiliiicil liy ».ii|i|Hirtx nt' |iru|H>r 
 li. i:,'lil pLii'il iMliiiitli till' iiiii:;ii.li/.r<l InxlicM. 'I'll rimlilf iIh' 
 
 oil crMI- |i. \,ll\ till' ti'llillH' 111 till' tii'lll. till' sll)l|l"lll of till' 
 
 in.ii_'iii'liiiMi'li r is sii niriiii;;i'il tlmi it iiiiiv Im' ritisftl nr lnwiTi'ii ii 
 |.ri'i|iii'iiiiiiii'i| iiiiiMiiiil liir iiiiv piist 111' iiliHi'i'Mitiiiii. tliii« ('(tityiii;; 
 
 ;ili ;i ,'r' ''il iri.ill lii|i'i;;l'il|iliy. 
 
 I,\l> rliii. iii.iiiiiii wiili siii'li a liilili- anil tin- riiii>*triii'tiiiii of 
 i-li irli III' till' lin'a-'liri'mrlllM iiiiiili' 111' till' tirlil |ll'mllli'i'il l>\ thi' 
 i'\|ii'i-iiiii'iii,il 'III' liiiilii'«. ill ^r.iii]is mill siii;.'ly, with tlif pliuif <il' 
 i.li-i TMitiiiii li'MJ .iinl at (iilliri'iil ili-taiii-i'^ ri'mii tlif mi' lt<Mlif><. 
 :iiii| wJH'ii II III' -.,'iiliii- a ilillii'iilt li'i'iaii'-. will ruiil.T U]ii ii tln' 
 i'\|i.'iiiiii iiiir an iii-i^lil iiit.i ilii- riiiii|il.'\ ciii'M's ii'sulliiiu:- wliicli 
 ■uiiiiii 111' ailiiiiii il liy aii> .11111111111 nl tln'mi'lii'iil stiiily. Cuiii- 
 ]■ iiiii:; his 1','siilts with thi' kimwii si/r. .Iis|iii>tiiiiiii and ilfjith 
 liiii ath th.' |ilaiii' nl uliscrvatiiiii nl' his i'\|ii'i'iiiii'iital ui'i' hiHlii-s. 
 Il' will siiiiii lii'i'iiiiii' piissi'ssi'il 111' a siiiinil kiiiiwli'ij;,'!' ul' tln' v»r- 
 i.iiiiiii ul' th.' lii'M |irii(liii'i'il liy tlu' varyiiij; fiiiiijitions iif liis 
 .'\|.i'i'iiiii'iits. wliii'li w'll I'lialiii' him In intirprrt with moiih' 
 il .;iii' 111' I'liiitiili'iii'i' till' i-liarts ciiiistnicti'il I'lniii iiii'asiiii'iiii'iits 
 111 a-tihil ..1'!' liiMJii's niMilr ill iIh- tiilil. Withmit siu-h an .'Xjii-ri- 
 iii. iiial Uii'iwli -l^i' ;;aiiii'il in ihr lahciatiiry. anil I'flyin;; simply 
 ;i|i III his ih. Ill 'lira! kiiuwliil'^i' ul' tlif siiliji'ct, thi' (ihsiTVir will 
 
 il'lcii. ai'tiT liaviii'_' pliittril his ulisri'vation anil ilrawii his cufvi's. 
 liml liinisi'ir iinahli' tu airi\i' .it --iiiinil ciiiu-liisiiins ri'i^afiliii;; tin' 
 hiiiil aiii| ilisVi iliiitiiiii 111' till' nil' limlii'H in any cuiiipliix cast'. It 
 is i.ir ilii'-i' ii'Msiiiis striin:,'ly I'l'i-nmnii'iiilcil that iniiiin;; schniils 
 wliii'li ili'sii'i' 111 taki' ii|i this siiliji'ct as part of tlu'ir riiirifulmii 
 ]ii'ii\iili' I'Miy I'arility tn tliiir stmli'iits to fcniliT thriiisi'lvi's 
 «• >iii|iri.'nt. i.\ I'Xtinih'il laliiiratory woi'k. In niiili'i'taki' iiia;;iii'f ic 
 
 111 \. y^, ami niahii' ihi'iii rniri'ctly tn iiitiTpii'l tlif ifsults iil 
 ihi'ir iiii'M-iU'cnii'iits. 
 
 I!-.' .•ll.'lU.rili^- till' _;!'n!l|fill^'s .,(' ill,. i',.';i: 'si'lltUti* .' nl'i- limlifS 
 
 ami thi' a^siiiiii'il tnpn;^'rapliy I'ni- each siicci'i'iliii;; flilHs, a siitli- 
 
!M» 
 
 ••ii-iit iiiiiiiIht kI' rluii't>> will -iiii Ih ai'iiiiiiiilai.il «!ii.ii \mII 
 i-iiiistitiiti' lulilitioriiil miIimIiI' )iiiittii;il t'<ii ni<l< l.\ iiiini' 
 
 I'lltssi'X. 
 
 A im'i:mm \. 
 
 THE OAHLBLOM MAGNETOMETER. 
 
 Vi'fv rrci'iilly 'I'll. l>Mli|liiiiiii li,i» iiiv.iiliil .1 \'i. 1 . ,ii> . ui' iil 
 I'lM-ki't Maiiiii'tiiiiK'tiT* ii' V lii.-ii 111- lia-kiiii|!\ - '■■ III. i -<ii|. 
 li'iii ami |ilii tu;;rii|i|i>' ■*■ 
 
 Description of the Magnetometer. IIm iii:i;^ii' I' 
 
 .1 (M'i' I'Lll.' A .III I ll -ll'l« ill'; 
 
 I ) wliirh i> iiirMili.'il t.p ill 
 
 iiii'ti r rimsists III' a fniiiiia'- 
 
 liter aiH 
 
 I lurk III' ll 
 
 11' iiisiniMii'iii I 
 liiti 
 
 I //. IMiiiiitI ill'' 1 ' viiliit inn III ill. iiiiiipa 
 
 .\ alw'ii .11 
 
 111^ CM 
 
 iU|>|>iil'l /(. I 
 
 axis ]ms-.iii;; tliiiiil;;li tln' piMitx nl' llir nnnjia-.^ 11 •■■lli 
 
 •4ii|i|iiirt ll is )irii\ iili'il witli a IniX I<mI I''> an .iim with 1 
 
 I'lir vi'ilical sii>|M'iisiiiii, twii r\ liii'liii-al ii\>'» ' 1 • .■ .iii'l i'l''.' 
 
 inilici's, '/j, </.j. '/;,. Ill' wliicli '/i ami '/:i ail' ailarli.''! i' ili' i\'- 
 
 1 1. i''i, iiml '/;; I" I 111' I'lai r till' l"X Ji'M'l {ll) 
 
 'i'lii- hi'i'iili' (') is sii|i|iurti'il ill jiwi'ljiil Inaii 1^- T" liii- 
 liiwiT piMit III' till' in-iilli' mil' I'liil III' a sjiiral -.|iiiii'_' ( / 1', i- 
 I'asti'iifd, till- iitliiT ••ill! is I'Miiiiil In till' atlai-liiiiiiil (;/iuli!i-ii 
 pi'l'liilts li\- iisi. lit' a sci'i'W till' ri'iiiilaliiiii ul' ll'i- liii--inii ..I 1' . 
 
 spriri;;. Tin' ai'l'i'st ami I'l'lt-asi' "I lln' n ll'' ^H'' > tli I'lnl I., 
 
 turniii;!; axis (A) wliicli uiii'iutr- iiimii a sjiiin^. 
 
 Adjustment of the Magnetometer. I'll. Tn.ii.ii 
 
 'rilii'i'ij iiislruiiii'iit is si't iiji ami li'Vi'lli'il ami arm /•,' ma'' I" 
 I'diiiciil." U"i'iiriti'l\- with till' iiia^iii'tic axis III' iln' m'lilh'. 'rhi 
 finu)'ass is ri'iiinvi'il ami thi'iixi's 'i.'-j. nl'thr I lalijlilnii! .M.i^nt'i 
 iiicU-r iuscrtril in tin' Mii'iimis. 'I'hi' ;,'lass caii lia\ in^- i. '.n i. 
 iiiovi'd tltf iiiii;;!!. tic axis nf tin' miilli' i- inailr In rnimi'l. 
 with the axis ni' tlii' unii A' li.\ liiiiiim^ tin' si-i-.'w nf atta'lini. nl 
 ('/) ill tin- ai>lirii|)riati' iliri'i'linii. 'I'ln- mi'.lli' will n 'W I" ni ili- 
 
 * Mwilf by J. I.. Kosc. I'psahi, .Svveiieii. 
 
 t Letter ilati'il I'liluii, Swoili'ii, -Mi'l .N-'<.iiili'i , ni" ;. 
 
 t S,)ir.il ■^piiiii.' is not ^l-.mvii in illnsii-.iii.vi. 
 
S f- 
 
 M 
 
 a r. : 
 
 ■ Si'S; 
 
 I- 
 III 
 
 KM) 
 
 iim;;n»tic iiifrirliaii iiiiil i><)iiit to 0° on tlu' siiile <>l' tlir ooiiijmiss 
 1m)X. .4»< thus iiiljiixli'il. Ilif <ii'iii'i-iil finiilfiiiit iif ll'i' fori-is iirtiiiii 
 iijHiii tlif iiii'illi' M z<'ri>. 
 
 It limy l)f wnivciiiciit, tluiu>;li not iifccssiirv. to coiiiiti'iiict 
 till' vcrtiwil iiitfiisitv of tin- iioniml ti<-l<l l>y the iii)|)liciitioii of a 
 Miiall |)ioef of wax on tin- soiitli iiriii of tin- needle. 
 
 Measurement of the Horizontal Intensity. 'I'Ih' 
 
 coiiijiass liox is turned in its su|H)ort until one of the indices, 
 sav ill, points to 0^, Tlie llia<;netollieter. ks h irhiilr, is now 
 turned until the needle aecurately reads 0". This operation 
 hrinirs the iiiafjiietio axis of the needle into a position parallel to 
 the nia^'iietic ineridiaii of the place of ohservation. Tlie support 
 // of the iiia;;netoiiieter is now held tiindy. while the compass 
 liox is turned in the support in one or the other direetion. until 
 
 tlie needle is forced hy the sjain^' 
 
 l-icj. Til 
 
 // 
 
 to occupy a position at riy;ht 
 aiij;les to the position when in 
 the niai;uetic meridian. Toetfect 
 this the compass liox will re<|uiri' 
 to he turneil throu;;li an aii<de 
 
 i\ ii'ieater than !H)° and the aii<;ulai 
 '■;■ ' ditf'ereiice <t hetween the rota- 
 tion of the compass 1m)x and !•()" 
 will measure the tension of tlie 
 spring; which is couuterlwilanced 
 hy the horizontal intensity act- 
 iiij;' at rii;ht anj;les to tlie inaj;- 
 iieticaxisof the ueedli'. (Fi<f..")l). 
 If M„ is the moment of rotation due to the horizontal 
 inteiisitv of the tield. .!/« the moment of rotation in the opjiosite 
 <lirection due to the spriiijr. we have: 
 
 ,n -IH fil = h'a* ((iO) 
 
 ■A' i> a laclor wliii-li, when multiplioil liv tlu- .imkU' oI li>r>.ioii, roprfsciils 
 111,' in.Mm-iit ot rotation fxerU'd by Iho i(<rin>; ni>on '>'•• .■.inip.i-.s lu-i'illi-. 
 Within hiiiils this laitur may lu- ii'Kardoil as a i-onslanl. 
 
101 
 
 It', for iiiMtuiice, the ohservatioii is nmch- in a iKiniial tifid 
 and an;;lc «|,^ 2.")° wliilc in tlic ilistuilH-d ti.'ld «,= 4I°, \vc 
 liavi- : 
 
 2///W-yv'2.V 
 and 1 llfil ^ A' 4 1 
 or //:/; = 2.V:4r 
 
 and /.' //i^o = Hi4// 
 
 In till' I'asc ol' a Held of i^rcat inttMiNity, to avoid citlu-r too 
 i;rt'at a tension or laxity of the spriii";. for wliicli extremes A' 
 would have diti'ei-ent values, it is iHtter to force tiie nei'dle l)y 
 revolution of the C(anpa.s.s over an an;;le of ."{O" only. 
 
 To eHeet the measurement of 1{ in terms of //, inider this 
 
 condition, the index is set at :{(»" and tin 
 turned until the neeflle reatls 
 
 lie whole instrument 
 
 0" 
 
 Tl 
 
 le com]iass hox IS then 
 
 rotated in its support until th 
 needle ))oilits to the index. (Se 
 Fiji. •"'-■) \Vt' xliall then ha v. 
 if «i for example e(pials :U" : 
 
 H 
 
 •■W 2: 
 
 id A' --2 
 
 A' 
 
 ^'^^S^ 
 
 r-'i. 
 
 IW 
 
 H 
 
 •M)° : II 
 
 II 
 
 '^ 
 
 
 Dahlhlom states that he has 
 made comparative measurements \ ' 
 with the Pocket Maixnetoineter y 
 
 .^;\. 
 
 /J. 
 
 and the'rhah'n-'rilii 
 
 .M 
 
 \.'(i. 
 
 iltrneto- 
 
 N"<* 
 
 meter, and finds tluit the result 
 
 shows a clo.se aj;reement of the I 
 
 measurements made with tlie 
 
 two instruments, even when the I'cK-ket Ma;.'net(inieter was used 
 
 entirt^ly without support and simply carried hy hand. 
 
 To show the conijiarativoly slijrht ettect of the uncertainty 
 of the manipulation when usini; the I'm-ket Maicnetouieter with- 
 out a support, the follow in>; illustration isijisen In- the inventor 
 of tiie instrinnent : 
 
 I 
 
 ' 
 
 \ 
 
 
ill 
 
 
 102 
 
 .\ssuiM.-(Fi<;. .'>:{) tli.it tlif uia^iiirtic nxis ul' the iir-^dlf is 
 nut iiariillfl with tin' nm;;- 
 rii'tic iiu'ridiilii of tlii' ])iuc-f 
 <,l'(.liscrv!iti(m, Imt iiielu(l<'s 
 witli it ail aii<;li' of 4° ami 
 that when the olisoivcr 
 rotati's tin- coiii|iass hox 
 in its supjiort to l(iin<; tiif 
 nci'dif into a position piT- 
 l)cii(lieulai- to the iiiaj;nctic 
 nn-ii(lian. he rotati-s tlic 
 instrntiicnt and support in 
 tilt' opjio-^ite ilirt'ctioii oviT 
 an iinj:it' i'<iual to •">°. Thf 
 lU'wlle will tlu'ii evidently 
 hav,. ii.uv,'(l not ov.T Wf hut only over Kl", aii.l th.- ivadiiiii- will 
 
 mIvc a small. ■!• value for //. for we hav.'; 
 
 /,'j O.'.IW It 
 
 U the .iiors are not, as in the example -iven, in the same 
 .lireetion the resultant error has little inriueiice. 
 
 When employing a deviation of 'Mf iu the n.easureinent ol 
 
 stron- fields, DahU > expresses the opinion that l.y takinj; tlu' 
 
 aveni- of three ohservation for one locality the re.sults olitan.ed 
 with the Pocket Ma>;net<.metcr are more accurate than those 
 uhtaiiied from measurements made with instruments re.iuin.iK a 
 dell.'Ctinj,' majinet. 
 
 Vertical Intensity. If the indices ,/i. -/:, i)oint to zero 
 
 and the n.a-netometer he turned vertical, the ma-netic needle 
 will include some an-le with the horizon represents hy the 
 i,„lices </,,./,. By rotating the compass Ik.x in its support m 
 the appropriate direction the magnetic axis of the needle may he 
 l.vou.'ht to coincid.. with the indices </,, -/,. In this position the 
 vertkal component of the magnetic force of the h-I.! is perpen- 
 dicular to the majruetic axis of the needle and the tension ol 
 
103 
 
 till' .s|iriiii; ciniriti'ilMiliuici's this fuicc. Tlii' ifiisiuii uT iln' s|)iiiiu 
 WHS ildjUsttMi MO that, wlii-ii the needle pointed to (), thr cticcl 
 of tlie sprini; to ]>ro(hice rotation was zero also ; then-rori-, when 
 tile needle is hroili^lit hy rotation ol' the eonipass hox in its sup- 
 port into the hori/ontal position the amount of rotation IVoni d, 
 to the zero ])oint measures the an;;le <■ which produces the tension 
 of the sprin;^ just sutfii-ient to counteihalance the \ei-iical force 
 of the Held. This an;,de is read at the north end of tin- needle, 
 positive intensity from 0° downward.s and iiei;ative intensity 
 from 0° ni>wards. 
 
 If <i is the vertical component due to the maijnetic ore 
 deposit and rthi' vertical component due to the noiinal Held. ' 
 and '•„ the aiedes due to <i + I'and !' respectivelv, w.> have : 
 
 ■2i<l I'),"' l< 
 ■1 H n I A'« 
 
 (••h 
 
 a V 
 
 II 
 
 II 
 
 II 
 
 ('■- '■„» 
 
 // 
 
 (112) 
 
 If, therefore, an ohserv.'r reads in the normal Held 
 I.")' and ill a disturbed Held lespectiv cly ."> and 
 
 Ulell 
 
 !-i: 
 
 // 
 
 // 
 
 10 
 
 ,.-// <>.4(»// 
 
 // 
 
 2.2.S // 
 
 If the coni]ia.ss needle has heen compensfiled for I he vertical 
 
 component ol the normal 
 
 Held, 
 
 0° and the ailirle ohseivecl 
 
 <i= 'II 
 
 (f>:!) 
 
 n measuriii;; the \ertical eonijioiienl of a \ ei-\- stnuii;- Held 
 
 it isadvisaliie to eiiipio\ a de\iation of onl\- oO from tii 
 
1 ■' 
 
 f 
 
 i 
 
 li 
 
 104 
 
 tinil. In this cas.', I.owvlt, it is iv.|uisit.-. t.) .•liniinalf tli 
 cHw-t of tlu- homontai coniiMHii'iit, that th.- iilaiif (.1' the iimniiet. 
 iiictfr he placed at ri;,'lit 
 
 I'i'J. .'i-l- 
 
 A 
 
 r 
 
 ;^- 
 
 ''/ 
 
 A 
 
 A 
 
 
 ■^•f' 
 ^-^x 
 
 ' -*,■•, 
 
 \'fi 
 
 
 ^W.- 
 
 ani'li's to tlic iiiajiiiftif 
 i.HTidiaii. To facihtatc the 
 iiicasuriiiu'iit an extra in- 
 dex, </4, should he provided 
 and fixed at :i(»° from <l->. 
 as shown in Fi<;. ")4. 
 
 Assume the Miai;neto- 
 
 meter with its face at rijcht 
 
 aii<;les to the nmj;netic 
 
 meridian and the needle 
 
 stainlint; us shown hy the 
 
 dotted outline. (Fi;;. .")4.). 
 
 The eompass is now ro- 
 tated in its supi)ort until 
 
 the needle points to index 
 
 ,U. The readinj; from the zero point of the graduation to th. 
 
 „„rth end of the needle jri' es th anjjle r. and w.- shall have. 
 
 // 
 
 {(i-i V)m,i •M)° 2 ft I l\ r 
 If 2 n I K '/„ 
 
 <«4) 
 
 <; V 
 
 V 
 
 a 
 
 2 II 
 
 2 '■„' 
 //* 
 
 2 ( '■ 'hj 
 "(I 
 
 // 
 
 (<).")) 
 
 Til 
 
 • an^ 
 
 <„ lor the normal field r.M|uires u) he det.'rmined with 
 
 
 and luMice / 
 
 On 
 
 -// 
 
I'l.MI A 
 
 i 
 
 llll PmIIKIaMI I'lHKI.I ,M M.M U'MI ] I U 
 
 M 
 
?! J 
 
 i i 
 
 P 
 
 I ! 
 
I'l.MI I'. 
 
 i 
 
 I 
 
 ■l!UK'- 
 
 
 i 
 
 I I 
 
I 
 
 ' 1 
 
 [i 
 
 s i 
 
 I 
 
 X •- 
 
 w 
 
105 
 
 fxiietitmlf. Tims, if f,,' = H" in tl.i- mniiml tifidand '• in tin- 
 ilisturlxMl tit'M is fiHUKJ to !«• .'t^^, we luivf: 
 
 a 
 
 H 
 
 Tlic follnwinj; iin- sdnic nl' tlic iMl\antn;,'i's nf tin' Diililhluin 
 l'(K'kft .Ma;;nftniiu'ti'r : 
 
 1st.— For not tcMi stron;; tii'lds tin- nii'tisin'fini'nts of tin- 
 
 vertical intensity iim' indt-pendrnt of tlif nmj^iii'tif 
 
 iiicridiaii. 
 2nd. — Till' iiia;;nrtii' t'oin-s U-inu iMtlanccd a<;ainst tlif 
 
 trnsion of a sprini; render tlie Ion;; an A' and a 
 
 detlectin;; ina;;net unneeessarv. 
 •'{rd. — }!y rotating; tlie eoinpa.ss 1k)x, wlien held vertical, 
 
 initil tlie needle stands liori/oiital in the noniial 
 
 field, the nia;;net()ineter may Ik- used for prospectin;;, 
 
 iiidicatin;; hy the dellection of the iiet'dle approxi- 
 mately the vertical force of the ore Held. 
 
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 •2I> 
 
 .•2H 
 .21) 
 .31 
 .33 
 ..34 
 
 :w. 
 
 .3S 
 .3! I 
 
 41 
 .43 
 
 44 
 .Ui 
 .47 
 .4(1 
 ..'ill 
 
 S4° 
 
 17 
 .111 
 
 |i 
 
 .•2ti ' 
 
 •2s ; 
 
 .•2!t 
 
 .31 
 
 .33 
 
 .34 
 
 .3I> 
 
 ..3S 
 3il 
 
 .41 
 4-2 
 
 .44 
 .4ti 
 .47 
 .4it 
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 17 
 
 lit 
 •21 
 
 ■23 
 .24 
 .M 
 .•2S 
 .•2!t 
 .31 
 
 33 
 
 34 
 
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 3S 
 3!» 
 .41 
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 .47 
 .411 
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 17 
 IH 
 ■21 
 
 •24 
 
 .•2ti 
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 31 
 .33 
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 3S 
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 .41 
 .42 
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 S7' 
 
 17 
 III 
 •21 
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 •24 
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 .31 
 .33 
 .34 
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 .37 
 .3! I 
 .41 
 .*-2 
 .44 
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 .47 
 .4i» 
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 17 
 lil 
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 ■2li 
 
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 17 
 ■ 111 
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 .211 
 
 .31 
 
 .31 
 
 .33 
 
 .3-2 
 
 .34 
 
 .34 
 
 3i> 
 
 :«> 
 
 .37 
 
 .37 
 
 311 
 
 .311 
 
 .41 
 
 .41 
 
 .4-2 
 
 .42 
 
 .44 
 
 .44 
 
 .4.-) 
 
 .4.-> 
 
 .47 
 
 .47 
 
 .4S 
 
 I .4H 
 
 .."■" 
 
 i ..-HI 
 
 17 
 
 lit 
 
 •21 
 
 ^.>> 
 
 !24 
 .■2ti 
 •27 
 .•211 
 .31 
 .32 
 .34 
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 .41 
 
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 .4,-. 
 
 .47 
 
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 17 
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 21 
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 34 
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 311 
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 l!t 
 
 ■_'ir 
 
 «(> 
 
 I-' 
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 14 
 
 IH 
 l!l 
 
 •M 
 
 .'.II 
 
 .s 
 
 I.IHI 
 
 .!! 
 
 I.IK) 
 
 I.m 
 
 l.l!l 
 
 l.ii 
 
 l.-js 
 
 I.I 
 
 i.;is 
 
 1.--' 
 
 1.(7 
 
 l.:i. 
 
 l.liT 
 
 I..-1 
 
 1.77 
 
 1 ti 
 
 
 I.H7 
 
 1.(17 
 
 •2. OH 
 •_'.IH 
 •2. 2! I 
 ■J. 41 1 
 2 ,-.l 
 •i.tVI 
 •'.T.i 
 
 •is.-. 
 ■J.i»7 
 
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 •-'.40 
 
 .lUi 
 
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 :i l.iHi 
 
 7 , I .lis 
 
 11 I I. Hi 
 
 r. I 1. 24 
 4 I.;f2 
 :i 1.41 
 
 > l.4!l 
 1.71 1..-.H 
 LSI l.liO 
 l.iHl l.7.-> 
 2.IKI I S4 I I.7II 
 2.ll'.l l.iKJ j 1. 711 
 
 I. mi 
 
 1. 117 
 
 l.l.-i 1.07 I .tHI 
 
 i.2:i I I.I t I 1. 117 
 
 I. INI 
 
 I.. ill 
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 l.4li 
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 I .(i2 
 
 I.S7 
 
 .111 2.(11 2. 
 
 2. '12 
 
 I .INI 
 
 1.21 I l.i:i l.iH'i 
 
 I.2S : 1.2" I l;i 
 
 l.:ui : I. 
 
 I. .-.I 1.41 
 
 I .l»i I . 
 
 2.11 ! I.flli I.S2 I 
 2.21 2 111 I.IHI I. 
 
 2.:«i 2.i:i i.(ts I. 
 
 I.l'l 
 
 l.t:{ i.:!t 1.211 
 
 I.. -12 
 
 I..-.S 1,4s l.rt'.i 
 
 I. Ill 
 
 1.74 I (,;! I..1 
 
 I 117 
 1.74 
 l.'.i.! I. SI 
 2. Ill l.sii 
 
 .1111 
 .11.1 
 
 ."ill 
 112 
 
 .S2 
 
 7s 
 
 SS 
 
 s;j 
 
 .'.14 
 
 ,S'.I 
 
 INI 
 
 ill 
 
 .INI 1 
 
 INI 
 
 .12 1 
 
 IHl 1 
 
 .Is 1 
 
 II 1 
 
 24 1 
 
 17 1 
 
 :il 1 
 
 2.'! 1 . 
 
 :f7 1 
 
 •'|| 1 
 
 l.-i ' 1 
 
 :!.-. 1 
 
 •111 1 
 
 12 1 
 
 •">7 ' 1 
 
 4S 1. 
 
 114 1 
 
 .■>4 1 . 
 
 7s 1 
 
 IW 1 
 
 4S 
 
 SI 
 
 HI 
 
h; 
 
 ! i ' 
 
 I 
 
 10° 
 
 II 
 \i 
 i;i 
 
 14 
 
 \:< 
 It) 
 17 
 
 IS 
 1!) 
 
 •J I 
 •Jl 
 
 •is 
 
 •J4 
 
 a" 
 
 '2» 
 29 
 30 
 
 112 
 
 Table II. 
 
 ^f )l «o 
 Tlll)U' of \ IllUfS ot ; 
 
 •-'1° 
 
 .4(5 
 ..■>1 
 . •"» 
 .<)0 
 
 .»>.*! 
 
 .70 
 ."> 
 
 .80 I 
 .S.'i 1 
 .!MI 
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 I .(Nl 
 
 1 .0.-. 
 
 1.11 
 l.lli 
 l.-il 
 1 27 
 1.33 
 1.3S 
 1.44 
 
 i.r>o 
 
 .44 
 .4S 
 ..■.3 
 
 .Oli 
 
 .71 
 
 7l> 
 
 .HO 
 
 .S.'i 
 
 .!HI 
 
 .!!.■) 
 
 1 .INI 
 
 I ll.-> 
 
 1.10 
 
 1.1.-. 
 
 1 il 
 
 l.-_'(i 
 
 I .:« 
 1.37 
 1.43 
 
 •23° 
 
 24° 
 
 .41 
 
 .41) 
 
 ..■>0 
 
 ..•■4 
 
 ..'>!• 
 
 .Ii3 
 
 .ti7 
 
 .72 i 
 
 .7H 1 
 
 M 
 
 .H() 
 
 .iM( : 
 
 .!••'> 
 1 .IKI 
 
 1 .0.-. 
 
 1.10 
 1.1.-. 
 
 I. -20 I 
 I. -2.-. ; 
 1.31 { 
 
 i.:i*i I 
 
 .40 
 .44 
 
 .48 
 ..->2 
 . .-.•> 
 .liO 
 .114 
 .(ill 
 .73 
 
 !h2 
 .8'. 
 .!tl 
 .!».-. 
 I. Oil 
 
 1 .o.-> 
 
 I.IHI 
 1.14 
 l.lll 
 1.^24 
 
 i.:<o 
 
 2.-.° 
 
 •26° 
 
 .38 
 
 .36 
 
 .42 
 
 .40 
 
 .4ti 
 
 .44 
 
 .411 
 
 .47 
 
 ..-.7 
 
 ■% 
 
 ..il 1 
 
 .70 ! 
 
 .74 
 
 .78 
 
 .82 
 
 .87 
 
 .ill 
 
 .!l.-. 
 i .IKI 
 1.0.-. 
 1 .IK) 
 1.14 
 l.llI 
 1 .24 
 
 In 
 
 
 111° 
 
 .•2i> 
 
 U 
 
 .32 
 
 12 
 
 .;}.-. 
 
 13 
 
 .38 
 
 14 
 
 1 .41 
 
 In 
 
 \ Ait 
 
 16 
 
 .48 
 
 17 
 
 .51 
 
 IH 
 
 ..■>4 
 
 1» 
 
 .57 
 
 20 
 
 .61 
 
 21 
 
 ' .64 
 
 22 
 
 .67 
 
 23 
 
 .71 
 
 24 
 
 .74 
 
 'i> 
 
 .78 
 
 26 
 
 .81 
 
 '27 
 
 .85 
 
 '28 
 
 .88 
 
 •2« 
 
 .i»2 
 
 :«i 
 
 
 32° 
 
 33° 
 
 .•28 
 
 .31 
 
 .34 
 
 .37 
 
 .40 j 
 
 .43 I 
 
 .46 i 
 
 .4!» ! 
 
 ..-.2 
 
 ,55 
 ..-.8 
 .61 
 .65 
 .68 
 .71 
 .75 
 .78 
 .81 
 .85 
 .81) 
 .112 
 
 34° 
 
 ..•JO 
 .33 
 .36 
 .38 
 .41 
 .44 
 .47 
 ..-)ll 
 ..-.3 
 ..56 
 ..-.9 
 .62 
 .65 
 .69 
 .72 
 .75 
 
 .26 
 
 .•29 
 
 .31 
 
 .34 
 
 .37 
 
 .40 
 
 .42 
 
 .45 
 
 .48 
 
 .51 
 
 ..->4 
 
 ..->7 
 
 .60 
 
 .63 
 
 .66 
 
 .69 
 
 .7S 
 
 .75 
 
 .82 
 
 .79 
 
 .85 
 
 .82 
 
 .89 
 
 .86 
 
 ..-.!) 
 
 .63 
 
 .67 
 
 .71 
 
 .75 
 
 .79 
 
 .83 
 
 .87 
 
 .91 
 
 .96 
 
 1 .Oil 
 
 1.04 
 
 I .09 
 
 1.14 
 
 I.IH 
 
 .•28 
 
 .:«i 
 
 .33 
 
 .36 
 
 .38 
 
 .41 
 
 .44 
 
 .46 
 
 .49 
 
 .52 
 
 .55 
 
 ..-)8 
 
 .61 
 
 .64 
 
 .67 
 
 .70 
 
 .73 
 
 .76 
 
 .79 
 
 .82 
 
 28° 
 
 - 
 
 .35 
 
 .38 
 
 .4 
 
 .4 
 
 .49 
 
 ..-.3 
 
 ..-.6 
 
 .60 
 
 .64 
 
 .68 
 
 .71 
 
 .79 
 
 .S3 
 
 .87 
 
 .91 
 
 .111. 
 
 I. INI 
 
 1.04 
 
 1 .09 
 
 1.13 
 
 .33 
 ..•<7 
 .40 
 .43 
 .47 
 ..-)ll 
 .54 
 .57 
 .61 
 .1)5 
 .68 
 -.J 
 
 .76 
 
 .SO 
 
 .84 
 
 .88 
 
 .92 
 
 .96 
 
 I .INI 
 
 1.04 
 
 1.09 
 
 •29° 
 
 .."12 
 .35 
 
 .38 
 .42 
 .45 
 .48 
 ..-)2 
 . .-).-) 
 ..-.9 
 .62 
 .66 
 .69 
 .73 
 . i~ 
 .80 
 .84 
 .88 
 .92 
 .96 
 I.IKI 
 1.04 
 
 311° 
 
 .30 
 .34 
 .37 
 .40 
 .43 
 .46 
 ..-)0 
 .,-.3 
 
 .:*\ 
 
 .60 
 .63 
 .66 
 .70 
 .7.3 
 .77 
 .81 
 .84 
 .88 
 .1)2 
 .96 
 I.INI 
 
 37° 
 
 •24 
 
 .•23 
 
 -' i 
 
 .•26 
 
 •29 
 
 .•28 
 
 .•12 
 
 .31 
 
 34 
 
 .33 
 
 37 
 
 .36 
 
 39 ; 
 
 .38 
 
 42 
 
 .41 
 
 45 
 
 .43 
 
 47 
 
 .46 
 
 .•>o 
 
 .48 
 
 ,->6 
 
 ..54 
 
 ..58 
 
 .56 
 
 .61 
 
 ..59 
 
 .64 
 
 .62 
 
 .67 
 
 .65 
 
 .70 
 
 .68 
 
 .73 
 
 .71 
 
 .76 
 
 .74 
 
 .79 
 
 . 1 / 
 
 38° 
 
 .39° 
 
 .23 
 
 .'25 
 
 .27 
 
 .30 
 
 .32 
 
 ..34 
 
 .37 
 
 .39 
 
 .42 
 
 .44 
 
 .47 
 
 .49 
 
 ..52 
 
 .-)4 
 
 ..-)7 
 
 .611 
 
 .62 
 
 .65 
 
 .68 
 
 .71 
 
 .74 
 
 .'22 
 
 .'24 
 
 .•26 
 
 .•28 
 
 .31 
 
 .33 
 
 .35 
 
 .38 
 
 .40 
 
 .42 j 
 
 .45 
 .47 
 .,-H) 
 ..52 
 .5.5 
 ..58 
 .60 
 .63 
 .66 
 .68 
 .71 
 
 40° 
 
 .21 
 .•23 
 .25 
 .■27 
 .:<ii 
 
 .32 
 .34 
 .36 
 .39 
 .41 
 .43 
 .46 
 .48 
 .51 
 ..53 
 ..56 
 ..58 
 .61 
 .63 
 .66 
 .69 
 
113 
 
 Tall 
 
 10° 
 
 IS 
 
 It 
 
 IS 
 19 
 ■Jl) 
 21 
 ■22 
 23 
 24 
 25 
 26 
 27 
 28 
 29 
 
 an 
 
 42° 
 
 43° 
 
 .2(1 
 
 .111 
 
 'ht 
 
 .21 i 
 
 .24 
 
 .23 ! 
 
 .•2ti 
 
 .-jr, 
 
 .2.S 
 
 .27 . 
 
 ..Mil 
 
 .2!! ' 
 
 .:t2 
 
 .31 
 
 .■(4 
 
 .33 
 
 .-.w 
 
 ..T. 
 
 .:tH 
 
 .37 
 
 .411 
 
 .:«i 
 
 .4S 
 
 .41 
 
 .4.-. 
 
 .43 
 
 .47 
 
 .4.". 
 
 .4!t 
 
 .4S 
 
 ..VJ 
 
 .."ill 
 
 ..")4 
 
 ..".2 
 
 .•)< 
 
 . ."»."► 
 
 .(>2 
 
 .■'lil 
 
 .04 
 
 .(>2 
 
 . .32 
 
 .3,S I 
 .411 1 
 .42 I 
 .44 
 
 .41) 
 
 AX 
 
 .32 
 
 .3H 
 .411 
 42 
 
 • >~ 
 
 •Jtl 
 
 •JS 
 
 .»- 
 
 i ..-III 
 
 •J*» 
 
 ..34 
 
 
 ..311 
 
 3.-. 
 
 .:is 
 
 .31 i 
 
 .44 
 
 .47 
 
 .4>.l 
 
 . ."..S 
 
 .41 
 .43 
 
 .41 
 .43 
 
 ..')<! 
 
 .14 
 .It) 
 
 .19 
 
 .2« 
 .2S 
 .29 
 .31 
 .33 
 
 .:« 
 
 .30 
 .38 
 .39 
 .41 
 .43 
 .45 
 
 14 
 
 28 
 
 :<2 
 
 .33 
 3.-. 
 3ti 
 38 
 4(1 
 41 
 43 
 45 
 
 .19 
 .2(1 
 
 .23 
 .24 
 
 .29 
 ..3(1 
 ..32 
 .34 
 
 .43 
 
 
 
 5.->° 
 
 -f 
 
 ... 
 
 7 
 
 r. 
 
 . I(i ' 
 
 s 
 
 .17 
 
 9 
 
 .19 
 
 il 
 
 .211 
 
 h> 
 
 .21 
 
 il 
 
 .23 
 
 .'.") 
 
 .24 
 
 >H 
 
 .27 
 
 .Il 
 
 .28 
 
 
 .*( 
 
 ,_ 
 
 .31 
 
 14 
 
 .33 
 
 15 
 
 .34 1 
 
 i7 
 
 .3ti 
 
 »> 
 
 .,39 
 
 12 
 
 .4(1 
 
 i 
 
 28 
 
 .311 
 
 .44 
 
 .4s 
 
 .IS 
 
 .-^l 
 
 .29 ! 
 ..3(1 
 
 ,3(i 
 
 ,.39 
 
 is 
 .19 
 
 .21 
 
 .41 
 .43 
 
 .48 
 
 13 
 14 
 
 12 
 
 13 
 
 .12 
 
 .13 
 
 
 \'t 
 
 14 
 
 .:> 
 
 
 .Hi 
 
 li'i 
 
 \r, 
 
 
 .17 
 
 17 
 
 .Hi 
 
 
 .19 
 
 IS 
 
 .17 
 
 
 .111 
 
 19 
 
 .18 
 
 
 21 
 
 2tl 
 
 .19 
 
 
 .*.* 
 
 •'1 
 
 .21 
 
 
 .24 
 
 23 
 
 '>'> 
 
 
 .25 
 
 24 
 
 .23 
 
 
 .2(i 
 
 25 
 
 .24 
 
 
 .28 
 
 2(i 
 
 .25 
 
 
 .2<» 1 
 
 28 
 
 .27 
 
 
 .3(1 1 
 
 *'9 
 
 .28 
 
 
 •■'- 1 
 
 .'Ml 
 
 .29 
 
 
 33 
 
 .32 
 
 .31 
 
 
 34 
 
 33 
 
 .32 
 
 
 3(i 
 
 35 
 
 .33 
 
 
 37 
 
 31) 
 
 .35 
 
 
 .1(1 
 
 14 
 
 23 
 
 28 
 
 :5 
 
 
 i 
 
 i 
 
 i 
 
 p 
 
 :i 
 
 : . . 
 
 • ^ 
 
 ■ 
 
fi: 
 
 'I 
 
 114 
 
 iji:; 
 
 i ' 
 
 I 
 
 Taiii.i: II. 
 Tul>l>' lit' X'aMics uf 
 
 liiii a 
 
 Vu" 
 
 tiH" 
 
 tm° 
 
 .('7 ! 
 
 .'•7 
 
 ."7 
 
 .(PS 
 
 .OH 
 
 .07 
 
 .<KI 
 
 .!«» 
 
 .OS 
 
 .1" 
 
 .Ill) 
 
 .IKt 
 
 1 1 
 
 .1" 
 
 .10 
 
 II 
 
 .11 
 
 .lo 
 
 . IJ 
 
 .IJ 
 
 .11 
 
 l.t 
 
 .1-2 
 
 .12 
 
 .14 
 
 .i:{ 
 
 .l-.» 
 
 .i:> 
 
 .14 
 
 .i:t 
 
 I.-. 
 Ill 
 
 .17 
 
 .IS 
 
 .lii 
 .•21 > 
 .•-'1 
 
 >M 
 .J.) 
 
 .-.'4 
 
 .!.■> 
 .!.■■ 
 
 .Hi 
 
 .17 
 .Is 
 .1!' 
 
 . ■-'! . 
 
 .-.'I 
 .J I 
 
 .J.J 
 
 .14 
 
 .1.-. 
 .1.-. 
 
 .Hi 
 .17 
 
 IS 
 .1!! 
 .•io 
 
 .'JO 
 
 ■ J I 
 
 
 -,o 1 
 
 ~'° 
 
 a 
 
 
 
 a„ 
 
 
 
 10° 
 
 .IKi 
 
 Oli 
 
 II 
 
 .07 
 
 IMi 
 
 !.•{ 
 
 .MS 
 
 .07 
 
 14 
 
 .O'l 
 
 OS 
 
 1.-. 
 
 .o;i 
 
 .IKt 
 
 ir> 
 
 .lo 
 
 .011 
 
 17 
 
 .lo 
 
 10 
 
 IS 
 
 • 1 
 
 .11 
 
 Ml 
 
 .li 
 
 II 
 
 ■ill 
 
 . li 
 
 • '■- 
 
 \i\ 
 
 . I.'! 
 
 . li 
 
 •>•> 
 
 U 
 
 l.i 
 
 ■2:i 
 
 .1.". 
 
 .It 
 
 ■J* 
 
 .!•■. 
 
 .11 
 
 •j."> 
 
 ir, 
 
 .1.". 
 
 •_>ii 
 
 .17 
 
 Ill 
 
 
 
 
 
 
 
 •js 
 
 .IS 
 
 17 
 
 •ill 
 
 lit 
 
 IS 
 
 .Ml 
 
 : ■■-'' 
 
 .I'.l 
 
 7H° 
 
 7!l° 
 
 .IMi 
 
 .07 
 
 .OS 
 .OS 
 .IKI 
 .10 
 .10 
 
 .11 
 
 .14 
 .1.-. 
 .l'> 
 
 . 'o 
 .17 
 
 .IH 
 
 .IS 
 
 lit 
 
 ill 
 il 
 
 o.-> 
 
 .0.") 
 
 .0.") 
 
 .04 
 
 .04 
 
 .04 
 
 .0:! 
 
 .o:{ 
 
 mi 
 
 IKi 
 
 . 1 i.'i 
 
 .0.-. 
 
 111 
 
 .114 
 
 .04 
 
 .ii:i 
 
 INi 
 
 Oli 
 
 Oli 
 
 . 1 i."i 
 
 .0."l 
 
 .04 
 
 .04 
 
 .04 
 
 07 
 
 07 
 
 .Oli 
 
 .IKi 
 
 . 1 '■"> 
 
 .11.") 
 
 .04 
 
 .11+ 
 
 IIS 
 
 .07 
 
 .07 
 
 Oli 
 
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 .ii."> 
 
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 OS : 
 
 .OS 
 
 07 
 
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 IN) 
 
 INI 
 
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 IKI 
 
 .OS 
 
 OS 
 
 .07 
 
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 nil 
 
 .IKI 
 
 .OS 
 
 .OS 
 
 07 
 
 IKi 
 
 .IKi 
 
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 HI 
 
 .IKI 
 
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 OS 
 
 .07 
 
 .07 
 
 .INi 
 
 .INi 
 
 lo 1 
 
 HI 
 
 .IKI 
 
 .O'l 
 
 OS 
 
 .07 
 
 .07 
 
 .•Hi 
 
 II ' 
 
 HI 
 
 III 
 
 .IKI 
 
 .OS 
 
 .OS 
 
 .07 
 
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 HI 
 
 .10 
 
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 1-^ 
 
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 i:( 
 
 li 
 
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 It 
 
 l:{ 
 
 li 
 
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 III 
 
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 .OS 
 
 1.". 
 
 II 
 
 .l:< 
 
 li 
 
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 .1" 
 
 .IKI 
 
 ' .IKI 
 
 Hi 
 
 1.-. 
 
 .14 
 
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 .10 
 
 IKI 
 
 Hi 
 
 1.-. 
 
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 .l.t 
 
 li 
 
 .11 
 
 HI 
 
 .0!) 
 
 17 
 
 Hi 
 
 .1.-. 
 
 II 
 
 .1:1 
 
 .li 
 
 11 
 
 .10 
 
 i'^ ; 
 
 .17 
 
 .1". 
 
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 .i:i 
 
 .li 
 
 11 
 
 .10 
 
I-.' 
 
 I.S 
 14 
 
 IS 
 
 
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 .ii:i 
 
 iir. 
 
 Tai;i.i: 11. 
 
 8'*° 
 
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 h;<° 
 
 .r Vah 
 
 il 
 
 
 M° 
 
 .ii:t 1 
 
 ii;t 
 
 i>2 
 
 .ii:t 
 
 ii;t 
 
 ii:i 
 
 .114 
 
 ii;i 
 
 ii;t 
 
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 ii:t 
 
 ii:< 
 
 .lit 
 
 114 
 
 II.) 
 
 .114 
 
 114 
 
 ii:t 
 
 ip.'i 
 
 114 
 
 III 
 
 (p."> 
 
 ii.-> 
 
 114 
 
 .<i."i 
 
 ii.'i 
 
 114 
 
 INI 
 
 ii."> 
 
 114 
 
 IHi 
 
 ii.'> 
 
 1 i."i 
 
 IN! 
 
 • Wi 
 
 ll."i , 
 
 .117 
 
 IN> 
 
 tl."> ' . 
 
 "7 
 
 *Ni 
 
 II.-. i . 
 
 • 17 
 
 ii7 
 
 IMi 1 . 
 
 lis 
 
 117 
 
 IHi 1 . 
 
 IIS 
 
 ii7 
 
 IHi 1 . 
 
 IIS 
 
 117 
 
 IKl i . 
 
 ll<l 
 
 IIS 
 
 117 1 
 
 111! 
 
 IIS 
 
 ii7 I . 
 
 I in 
 
 III 
 
 .III 
 
 . I i:t 
 .ii:i 
 
 ii.-f 
 
 .114 
 .114 
 
 .III 
 .III 
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 .ii-J 
 
 .ii:t 
 
 .114 i .ii:i 
 
 .nr> ; .114 
 
 .114 
 
 III 
 .111 
 
 .III 
 III 
 
 .til 
 
 .i:i 
 
 .III 
 
 III 
 
 .III 
 
 .III 
 
 III 
 
 111 
 
 .ll-J 
 
 111 
 
 ll-J 
 
 ."1 
 
 ll-J 
 
 .III 
 
 ll-J 
 
 .III 
 
 IIJ 
 
 111 
 
 ll-J 
 
 .111 
 
 IIJ 
 
 .111 
 
 IIJ 
 
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 IIJ 
 
 . 1 1 J 
 
 ii:t 
 
 II-' 
 
 ii:i 
 
 .IIJ 
 
 ii.i 
 
 .11"-' 
 
 
 
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 Tahlk III. 
 
 ? 
 
 Tal>l.' of vuliK'M of i j ' f!-' 
 
 oiii n 0.()l to (( 5.00 
 
 '■O' {'S 
 
 (I.IMI 
 
 ii.irj 
 
 Il,tl4 
 ll,o.'i 
 II.IKi 
 11,(17 
 l>,ll!4 
 O.lltl 
 0,111 
 
 o,ll 
 
 0,1-J 
 0,!l 
 
 (I, It) 
 
 II.!; 
 
 o,is 
 ll,l<) 
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 111 
 
 111 
 
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 114 
 
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 lilt ii 
 
124 
 
 T.Mtl.E VI. 
 
 Table of ret. •'' a"'! ''" 
 
 til II '• 
 til II '■„. 
 
 |,(NIIIII 
 
 O.iHMI'.t 
 
 (l,!HI!l."i 
 
 0,<.l!l!NI 
 
 0,!tl»s-J 
 
 (l,!l".17l 
 
 ( I, < I! ).*><) 
 
 O.'KMI 
 
 (l.!M»-.'7 
 
 ll,!HNIH 
 
 (l.'.tSHIi 
 
 ll,<)H(i:i 
 
 o.its.'iT 
 
 O.IISOS 
 
 0,!(7T'< 
 
 (1,',17-lli 
 
 CI,!I711 
 
 0,>.»(i74 
 
 O.lHi.-i.') 
 
 ll,il.V.I4 
 
 (l.it.V.l 
 
 0,<l.'>IKi 
 
 II,'.I4.V,» 
 
 II.!I4|II 
 
 11,'I.T.!! 
 
 <I,<.):<IH> 
 
 0,!h>.">l 
 
 l»,!M!t4 
 
 tt,!tl:i."> 
 
 0,!HI7r) 
 
 (t,!Kll-_' 
 
 ll,S<t4H 
 
 (l,SSS-.> 
 
 (l,SSI."> 
 
 ll,H74(> 
 
 ii,S(>7."i 
 
 II.S.ViH 
 
 o,s4.">:t 
 
 0,SH7(> 
 
 o,s-iii.s 
 
 (l,S-ilS 
 
 (i..si:t7 
 
 tl,HII.">4 
 
 <',7!17l 
 
 (l.7SSIi 
 (l,7,HIHI 
 
 o,771J 
 
 u.Tli'.'t 
 0,7,-.:{r> 
 
 ii4.r>s!i 
 
 ."i7,-.'!HI 
 
 :w,iss 
 •iH,(i:t(> 
 
 l!t,MM| 
 
 Hi,:i.'iii 
 I4,:«ii 
 l--',7i«i 
 
 iii,;ts.-i 
 !i,r.l4 
 s,777 
 .S,I44 
 7..'>!Mi 
 7,11". 
 li.li'.tl 
 
 (i,:ti4 
 
 ."i,!l7(i 
 .-..(i7l 
 
 .-.,14.-> 
 4,!ll.-. 
 4,7'l."> 
 4,.'>1 1 
 
 4.:i:« 
 4,nM 
 
 4,011 
 
 .•t,sii7 
 :i,7:i-' 
 :!,i>iNi 
 :i.4s7 
 :t,:!7(i 
 :t,-.>7i 
 :!,I7-' 
 .•i,ti7s 
 
 •.',!»H!I 
 2, '.till 
 •.',H-.'4 
 •J,74S 
 •i,i>7."> 
 •2, 1 )•»."> 
 ■J,-"i:!'.t 
 •-•.47."> 
 ■.>,414 
 
 ■.',:i.'.(i 
 2,:tiKi 
 
 2,-'4t> 
 ■> liM 
 
 (),0 
 0,."i 
 
 1," 
 I,.'. 
 
 •2.11 
 
 til II r 
 
 - i 
 
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 4,(1 
 
 4,"> 
 
 .".,0 
 
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 I),U 
 
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 H,0 
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 10,11 
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 11,0 
 
 1 1 ,.■> 
 12,0 
 12,.-> 
 i:t,o 
 1 :<,.-. 
 
 14,0 
 14,.-. 
 l.\o 
 1. ■.,.-. 
 l(i,0 
 
 Hi,.-. 
 
 17,0 
 17,.-. 
 
 IS,(I 
 
 l,s,.-. 
 l!l,o 
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 20,0 
 20,.-. 
 21, o 
 21,,-| 
 22,0 
 22,.-. 
 2:1,0 
 
 2:t,.-. 
 
 24,o 
 24,.-. 
 
 till! i\ 
 
 0,li4<.).-. 
 
 o,(i:v.i7 
 
 o,l)2'.is 
 o,til!(>t 
 o,iiiiU'.l 
 0,.-.!l!»!» 
 0,.-.S!t'.l 
 o,.-i7".'s 
 
 0,.-.(i!IS 
 o, .-..-.! 17 
 o,.->407 
 
 o,.-.;f!Mi 
 o,.-.2'.l.-. 
 0,,-.l!(l 
 0,,-.0!t4 
 0,4!Hi;t 
 
 ct,4s'.»:{ 
 
 0,47!Kt 
 0,4I1<.)4 
 0,4.".!I4 
 0,44'.l.-. 
 0,4:i>»7 
 o,42!l!l 
 (),420| 
 0,4104 
 0,41 K IS 
 0,:HII2 
 
 o,:t.si7 
 
 0,;t722 
 0,:l(i2H 
 
 o, ••{.-.:«> 
 o,:t44:t 
 o,:!:i.-.2 
 o,:t2ti2 
 o,;ti7'.' 
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 lt,2il'.Mi 
 0.2'.»KI 
 0,2S24 
 n,27;H» 
 0,2li.->li 
 o,2.-.74 
 o,24!l2 
 (1,2412 
 o,2:!:i4 
 o,22.-.(i 
 o,2IH(l 
 (t,21o."> 
 
 o,2ii:u 
 
 I (»,1!».-.H 
 
 I 
 
 fiit..r 
 
 !,7;i2 
 l,(i!IS 
 I,('.('i4 
 
 I ,(>;t2 
 
 |,(UHI 
 
 I. .-.7" 
 l,.->40 
 l,.-.ll 
 
 i,4s:t 
 
 1,4.-..-. 
 I.42S 
 l,4(f2 
 l,:{7(i 
 
 i,:t.-.i 
 I ,;i27 
 i,:!ii:i 
 
 l,2S0 
 
 l,2.-.7 
 
 1 ,2:1.-. 
 i,2i:i 
 
 l,li>2 
 1,171 
 l,l.'.o 
 
 i,i:fo 
 1,111 
 
 l,o!)l 
 l,o7i 
 l,o.-i4 
 l,(l.'<(i 
 l,olS 
 1,000 
 
 o,!ih:i 
 
 0,! !('.(> 
 0,!I4<.I 
 o,!t:t2 
 0,tll(i 
 0,!HIO 
 (l,HH.-. 
 0,S(i>> 
 0,H.-.4 
 
 ((,s:«t 
 
 0,M24 
 o,.slo 
 o,7'.i.-( 
 o,7SI 
 < 1,7(17 
 o,7.-.4 
 0,740 
 (»,72() 
 o,7i:» 
 
 tun r 
 t'lii '•„.. 
 
 - rot. .!• 
 
 :<o,o 
 :to,.-. 
 :n,(i 
 :u,.-. 
 :i2,ii 
 :t2,.-. 
 .•i:i,o 
 :t;i,.-. 
 :t4,o 
 :t4,.-. 
 .•i.-.,o 
 :».-...-. 
 
 3(i,0 
 
 :!(i,.-. 
 .•t7,o 
 ;i7,.-> 
 :!s,o 
 .•w,.-. 
 ;tit,o 
 ;«),.-. 
 40,0 
 
 40,.-. 
 41.0 
 41,.-. 
 42,(1 
 42,.-. 
 4:t,0 
 
 4;t,.-. 
 
 44,0 
 44,.-. 
 4.->,0 
 4.->,.-. 
 4('.,o 
 4(i..-. 
 47,0 
 47,.-. 
 4S,0 
 4S,.-. 
 4!l,0 
 4!»..-. 
 .-^1,0 
 .-Kl..-. 
 .-.1,0 
 .-.1,.-| 
 .-.2,0 
 •■.2,.-. 
 .■.:t,o 
 ,-..1,.-. 
 ' ;v».o 
 
 ; .■.4,.-. 
 
 0,I2.'.0 
 0,11!I4 
 
 (•,ii:i!i 
 
 O.IOHd 
 O.IO.X". 
 0,(KIS.-> 
 
 o,(Ki:s(i 
 
 0,OHSS 
 
 o,o,s4:< 
 o,o7'.ts 
 0,07.-..-. 
 tt,(>71.{ 
 o,(M>7:t 
 o,<H):<4 
 
 0,0.->!t(i 
 o,o.->(io 
 O,0.-.2C. 
 
 o,(mi2 
 
 O,04(i(l 
 
 o,o4:!o 
 0,0400 
 o,o:i7-' 
 o.o:m.-> 
 o,o:)i!i 
 
 (l,02!t.-. 
 0,027-2 
 o,o2.-.o 
 o,o221t 
 (i,(r20il 
 o.ol'll 
 0,01 7."! 
 0,01. -.7 
 O.0142 
 o,ol27 
 
 0.0114 
 
 0,0101 
 
 II.IHKKI 
 0,0(i7!l 
 O.IKN'.'.I 
 (l,(KN»l 
 (i.(Kl.->2 
 0,(NVt.-| 
 tl.(Ni:tS 
 0,00:12 
 o,0(h27 
 0,o»i22 
 O.OOjS 
 0,(KII.-> 
 0,001 I 
 0,(NIO<) 
 
 o,.">77 
 
 0,,'lt'.t> 
 
 o,.-,.-.4 ' 
 
 o,,-.4:t 
 
 o,.->:t2 
 
 o,.->2l 
 
 o,,->io 
 
 (),4!)n 
 
 0,4(<S 
 0,477 
 
 0,4(i(> 
 0,4.".ti ' 
 0,44.-. 
 
 <t,4:r. 
 
 0,424 
 0.414 
 0,404 
 0,:til4 
 
 o,:ts4 
 o,:»74 
 
 Il,:i(i4 
 
 o,:i.-.4 
 o,:t44 
 o,:t:r. 
 o,:<2.-. 
 o,:ti,-. 
 o,:<o(i 
 
 o,2H(i 
 o,2s7 
 o,-J77 
 0,2tiS 
 0,2.Vt 
 o.24!t 
 0,240 
 0,2.(1 
 0,222 
 
 0.2 i:t 
 o,2o:! 
 
 0,1 ".t4 
 0,18.-. 
 0,1 7(i 
 
 0,1(17 
 0,l.-.H 
 O.U'.I 
 0,141 
 
 o,i:t2 
 
 ; 0,12:1 
 
 I 0,114 
 
 I 0,IO.'i 
 
 i O,0!Mi 
 
 Ko.o 
 tM),.-) 
 1)1,0 
 (-.!,-> 
 «2,o 
 ti2,.-. 
 
 )i:i,<t 
 ti:<,,-> 
 
 (14,0 
 (i4,.-> 
 (m,0 
 
 «.■>,.-> 
 
 ())i,0 
 
 ()«,.■> 
 
 (i7,<l 
 
 (17,.". 
 
 (iH,(t 
 
 (iS,.-> 
 
 ('.!),0 
 
 (!!»,.". 
 
 70,(1 
 
 7o,."> 
 
 71,0 
 
 71,.". 
 
 72,0 
 
 72,.-. 
 
 7:t,o 
 
 7:t,.". 
 
 74,(» 
 
 74,,-. 
 
 7.">,(» 
 
 7.".,."> 
 
 7(i,o 
 
 7(i,'. 
 
 77,0 
 
 77.."> 
 
 7s,o 
 
 7s,.-. 
 
 7'.i,o 
 
 7i»,."> 
 
 so,(( 
 
 so,.-. 
 
 si,o 
 
 SI,.-. 
 
 s2,o 
 
 S2,.-. 
 
 s:?,(» 
 s:t,.-. 
 
 S4,(» 
 S4,.-> 
 
12", 
 
 TABI.K VI.— I'oiilimii'il 
 
 tiiv r 
 
 rot. .;• 
 
 ./•° 
 
 fflli r 
 
 l-llt. .!■ 
 
 1 
 
 /((/( *• 
 
 rnf ,r 
 
 .r° 
 
 *<"> ''■»„ 
 
 
 '"" 'mux 
 
 '"" ''m» 
 
 (t,7444 
 
 •-'.UK 
 
 ■-'.-.,0 
 
 11,1 SS7 
 
 0.7(KI 
 
 .-,.-,,0 I 
 
 0,IKHI7 
 
 ii,os7 
 
 S.-i,(l 
 
 0,73.">3 
 
 •.•,.Ht7 
 
 ■-'.-> 
 
 5 
 
 IMS17 
 
 l»,(>H7 
 
 .V...-, i 
 
 l),IIIMI.~> 
 
 <l,ll7!l 
 
 ,S."l,."> 
 
 l),7J<il 
 
 •i,lt.->t) 
 
 ■iti 
 
 
 11,1 74!t 
 
 i>,t>74 
 
 .vi,i. ; 
 
 it,i)«Mi;j 
 
 ti,ii7ii 
 
 Nli,ll 
 
 O.THiS 
 
 ■J.INNi 
 
 ■Ji 
 
 
 iMtWI 
 
 ii,r.()i 
 
 rM.rt 
 
 ll,INN)-i 
 
 ii,ii<il 
 
 .Sli,.'> 
 
 <l,7<t74 
 
 1 ,!Hi;< 
 
 L'7 
 
 
 ll.lOIti 
 
 11,1)4!) 
 
 r,- i 
 
 lt,tNNt| 
 
 ll.ll.Vi 
 
 H7,ll 
 
 0,ti!»7!t 
 
 l.if.'l 
 
 •-'7 
 
 
 11,1. V.I 
 
 ti,(i;t7 
 
 .-.7..-. ! 
 
 It.tNNtI 
 
 • 1,1144 
 
 «7,."> 
 
 (»,<ws:t 
 
 I.HXI 
 
 ■2H 
 
 
 1), USH 
 
 (i,(U."> 
 
 .">S,(I 
 
 (l,lllllllt 
 
 ii,ii:u 
 
 ,SS,II 
 
 0.(>7.S7 
 
 l,H42 
 
 •JM 
 
 
 lM4-.t( 
 
 ti,)ii:t 
 
 .-.s,.-i 
 
 0,1 NN III 
 
 l>,ll-_ti 
 
 SM,."i 
 
 O.lili'H 
 
 I.S(I4 
 
 Lit 
 
 
 0,1 :{))(! 
 
 ii,)iiii 
 
 .">!»,H 
 
 ll,IIIIINI 
 
 11,1117 
 
 S!l,ll 
 
 o,(i.v.):< 
 
 I,7(i7 
 
 •.".I 
 
 
 11,1. {(17 
 
 It, .■>)<! 1 
 
 .">it,.-. 
 
 ll,IIIMNI 
 
 II.IHItl 
 
 S'l,.-. 
 
 D.IUil.'i 
 
 l,7« 
 
 ;iii 
 
 
 o,li'.<i 
 
 "•,."■77 
 
 <>l),0 
 
 ll,IIIKIII 
 
 lt,IKHI 
 
 INl.tl 
 
, (. 
 
 Hi 
 
INDKX 
 
 Allele of dfcliiialion 
 
 Aniuial variation ol Icrroslrial tiold 
 Attrai'tion and ri'|nilsion, law ot . . 
 Altrai'lorily maifnclii- 
 
 BorK, J. Kr .... 
 Bipolar niaijnflic .1 
 
 14 
 
 III 
 
 :t 
 i:t. Hi 
 
 I 
 
 II 
 
 Calibration ol tin- Tliomson-Tliakn .M; 
 
 i^ni'tonit'ti' 
 
 Charts of m. 
 
 iKiiotii- inli'iisity, information ronvovfd bv lluv 
 
 tin- horizontal intonsii 
 tho vi-rtical intensitv. 
 
 Compass needle in a normal terrestrial held, eHei-t of 
 
 I inajfnet on. 
 
 components ol the total intensity of the earth's ma).tnetisni. 
 L.'onservation of tliuv of force 
 
 Constitution of maj;nets, theory ol 
 
 Constriietion of dia^-rams of matjnetir fields. . . . 
 Coneetion of error due to defeilive neutrali/atii 
 
 i>f '' in the normal 
 
 field . 
 
 ii:i li.'i 
 
 74 SI I 
 71 7-.' 
 :■> 74 
 lH--j:{ 
 I.-. 
 I 
 
 ■il .-■; 
 
 J I 
 
 Oahlbloni, Th 
 
 Dahlblom's niodilii.'atioii of llu' sine niellioil. 
 
 /!>, .SH.S7 
 
 .Method ol observation. 
 
 :t7-4J 
 .is 
 
 Calibration of 
 
 niilltnu'ter 
 
 Si-ale and eonslruetii 
 
 if seale for 
 
 failing 
 
 llahlblom s .Majfnetoniet.'r, tin 
 He 
 
 seription ol 
 
 .\djust 
 
 niem ol 
 
 .•t.S-4J 
 
 <)•) III.-) 
 
 il'l 
 
 !l>t-lll«l 
 
 ■asnremenl ol the hori 
 with 
 
 !ital 
 
 lit of I he \ert 
 
 leal inteiisiti' 
 
 ith 
 
 Ad 
 
 vantajfes of 
 
 Oaily variations ol the terrestrial field 
 iVelin.itioii 
 
 anjfle of 
 
 liHI lil-i 
 
 lil-i HI.". 
 
 HI.-. 
 
 Hi 
 
 14 
 
 14 
 
 |i 
 
i I 
 
 12K 
 
 iVfiiiition ol iiia^iu't . . 
 
 IVflrrtinjr ma>;iu'l 
 
 IX'ptli ot a niaj;'ii"li>-' <"i" IhhI\, ilflfrniiiialion olthf ext»'ii>ii>n in. 
 
 Dt'scripliiMi of tin- Swodish mining compass 
 
 " " Thali'n-TibiT}; .Matfiu-lonuMiT 
 
 " " Thoinson-Thalin Ma^riu'lonu'lor. . 
 
 IVslruilion ol inatfu-tisni 
 
 IVlfiniination ot Ihi" valuf ot A' 
 
 nia!^i*aiiis ^y\' liipolar nia^iu*tiL' tit'lds 
 
 ** unipolar ina>;n(>tii' tiolvis 
 
 '* ina>;netii' ti^'ltis, oonslnu'lit»n i^t . . ■ ■ 
 
 Dirt'(.'tit»n ot lint's ol' Km ^ »■ 
 
 Oistanci' of the iippir poll- ot a nia«neiii' oro hod)- bi-ncatli tlio siir- 
 
 t'ai-f, detfiniinalion of the 
 
 Dislurbanrcs ot' the earth's tnai^notii' lit»ld 
 
 Disturbed torrestrial field iff foree 
 
 n\ tie, detiniliiin i>t" 
 
 Karth s tield, niaxiniuin ot niannelizalioti produied by the. 
 
 " '* minimum ** '* 
 
 " nia^netie field, variations ot the 
 
 magnetism, eomporients ot' the total iiitensitj ot the 
 
 Kflict ol a niajfiiet on a compass needle in a normal terrestrial tield 
 Kquation lor determination ot the moment ot a ma>{nel 
 
 " of a line vif force 
 
 Krrordue to defective neutralization >.■•< l'\n the normal tield, correc- 
 tion K'^i the 
 
 Faraday 
 
 Felix, A 
 
 Field, ma^Mietic, variation of the earth s 
 
 ol lorce of an ideal and of a massive niaynet 
 
 " the disturbed, the vertical intensity ol 
 Fields, niaffnetic. construction of dia>;ranis ol . 
 l-'low i»f Forci' 
 
 '• '* conservation o\ . . . 
 
 Force, direction of the lines \>( 
 
 ** tlow i»f 
 
 lirt 
 
 vich 
 
 .•t 
 
 lit, :»:t 
 
 ST-iU 
 (i.".-IMi 
 
 ,-.« .".(• 
 4 
 
 » 
 
 SI-,SK 
 
 Hi 
 
 II)- is 
 
 li 
 
 IT 
 IT 
 III 
 I.-, 
 in -.'.t 
 •21 
 li 
 
 .-.I .-.•-' 
 4 
 
 Hi 
 
 4!l-.>li 
 
 H 
 
 hematite 
 
 Horizontal component of the earth's field for Ottawa, Ontario, value t.'^i 
 
 14 
 IT 
 
 t:< 
 
I2!t 
 
 Horizontal inlensiiy, iliarl ol Iho 
 
 " •' in a liTroslrial fii-UI of lum', disliirbfd by tlio pif- 
 
 si'iHH' ot" a ina^itt'lii' ori'-boily, tlu* \ahu' of. 
 
 7I-7-' 
 
 4:1 4s 
 
 Inclination of ncetlle of mining rompass 
 
 Inclinator 
 
 " theory of the 
 
 " sensitiveness of the 
 
 Inductive effect of the magnetic field uixjn magnetic bodies 
 
 Influence of magnetite as an accessory ingredient in ores or roiks 
 
 Information conveyed by the charts of magnetic intensity 
 
 Intensity, charts of the horizontal 
 
 charts of the vertical 
 
 " horizontal, the value of, in a terrestrial field of force, dis- 
 
 turbed by the presence of a ni.'ignelic oi\' bodv. 
 
 of m.ignetization, relation of dip to 
 
 ol ! ■• earth's niagnelism, components M the tot.il 
 
 " the vertical, of the disturbed field 
 
 Introduction 
 
 Investigation t>f magnetic ore deposits by niagnctoinetric ineasuri'- 
 
 ments . 
 
 Isoclinals 
 
 Isody naniic lines 
 
 Isogv>nic lines 
 
 1, 
 
 1.7 
 •17 
 
 4f» 
 
 .■r.> 
 
 7-t 
 
 17 
 
 Sll 
 
 71 
 
 y.j 
 
 ••> 
 
 74 
 
 4:t 
 
 4S 
 17 
 
 t!t 
 
 -.'ill 
 
 1 
 
 _ ■> 
 
 •17- 
 
 -74 
 
 
 14 
 
 
 14 
 
 
 14 
 
 H 
 
 111 II 
 
 Jakobsili* 
 
 Kiiij;, William F . 
 
 K 
 
 Laboratory Practice 
 
 Lamont 
 
 Law of attraction ,-ind repulsi,>M 
 
 Line of Force, equation ot a 
 
 Lines of Force 
 
 " " direction of 
 
 ** " method iif showing the . 
 
 18 
 
 <I4 !l!l 
 I 
 
 ;( 
 
 lL> 
 
 4 
 
 Magnet, definition of. 
 
 " deflecting 
 
 " effect oi\ on a compass needle in a Uiirmal terrestrial field. 
 
 '* equation for determination of the moment of a . 
 
 Magnetic attraclorily 
 
 :! 
 
 Ill, .Ti 
 
 IS lM 
 
 •J I 
 
 l:t. 111 
 
\w 
 
 
 4-13 
 
 <1 
 HI 
 
 MaifiiflK' .ixis 
 
 h.nlii-s, imliulivc ••ff.-rt I'l till' niinfiu-lic lii-UI ii|)i'ii. I- 
 
 iK>|)i>sils, iiiM-^liir.iiion of, by iiiairiu'toim-lrii- miMsiiriMin-nl. liT 74 
 
 I'miiiliT ' ' 
 
 liolil. 111.- 
 
 t'u'Ul, iiidiiclivi' i-ITivl upon m;i>{iiftii- boilifs ol llif. 
 
 •• til-Ill, stri-nxlh of, nl .i poiiil 
 
 lii-Ul, vaii;ilions of thi- i-arlh's 
 
 til-Ills, i-oiiNliiK-lion of ili.ifframs ol 
 
 " iliaj{r.u)is of hipol.u 
 
 " ■• iliaKritin-, of unipolar 
 
 ■' till- i-arlli's nonnal. . 
 
 intinsily, information lOiiM-M-d by tin- ihart- ot 
 
 on- body, doti-rtniiialioii of the extension in depth c\ a. . 
 
 ore deposits, workable 
 
 ri-traetorily 
 
 Magnetism, eoinponents of the total intensity of the e.irth's 
 
 •• deslruetion of 
 
 Magnetite - 
 
 as an aeeessory in>;redient in ores or rocks, influence ol.. 
 
 Maifneli/.ation, maxinui:ii ol, produced by the earth' , field 
 
 -' ininiiuuni '* " *' '* • 
 
 relation of ilip to intensity ol 
 
 .\Ia<lH-lonieler. nalllblom s • ■ ■ 
 
 Pi'scription oi 
 
 14 Hi 
 74-H(> 
 
 s; 94 
 17 
 
 i;i, ii> 
 I.-. 
 
 4 
 
 lit. Hi, 17 
 17 
 17 
 17 
 17 
 '.III |ii.'> 
 m 
 
 Adiustnient of '■''■' '•"• 
 
 Measurement of the liorizoiit.il intensity 
 
 with IlKl-liI--' 
 
 Measmenient of the verticil intensity witli |ii-J-|ll."> 
 
 .\dvanlai;i's ot.. I"-* 
 
 llL-iUn-TilH-ri;- '• -+-*• 
 
 nescription of --^--JH 
 
 Teslin^; and adjustiiiK -J!*-:)! 
 
 '• I'lecautioiis to be observed in t.ikini; 
 
 observ.ilions with llie .'il-H-i 
 
 Method of observ.ilion 'M 'Mi, M 
 
 Thoinsoii-Th.ilin I , .Vi ti."* 
 
 Oesi riptlon ol" 
 
 Thenry of 
 
 (.'.ilibratioTi of. 
 
 Mayiiels .md their properties. . 
 
 '■ theory of the constitution ot 
 
 Maxiuuiin of ni;ii;neli/.ation produced by the earths field 
 
 Mi-tl;tcii'.tiilt- 
 
 Method of slunviui; the lines of force 
 
 .Mi-iV* 
 lill-<i:t 
 Il3-ti.'. 
 
 a 4 
 
 ••( 
 17 
 l.-t 
 
l.-il 
 
 .Minimum ot mii^nu'li/atioii proJvu^'d l»y tin* I'arih s f'u'M, . , 
 
 Mining" I'lMiip.iss, Jt'si'ri|M ion ot tlu* SwrJish 
 
 >;ri'att'st iru'iination ol'noi'dK' 
 
 MoiiitMit ot a maifiu't 
 
 " *' " t'(,nialioii I'ov ili'li'rinitiaiii>ii ot" the . ... 
 
 N 
 
 Ni'ulraliz.ilioii ol llu" vt'ilk'al lOiiipiiiuMil of llu- oarlli ■. iioniKil ("u'lil 
 
 ■' " /'111 tin- normal flflil, lorn-rlioii ol I'lmr ilm' i» 
 
 ilol'ectivi- 
 
 Nordenstroin, G 
 
 Normal terroMrial fii-Ul 
 
 North si'i'kinj; polarity 
 
 " " pv>k', or north poll* 
 
 Nvstrom, K 
 
 I'arametor 
 
 IVrmoahiiilN 
 
 Polarity, north seeking' 
 
 ** south set'kinj; 
 
 Poles 
 
 " of a magnet, situation of the. 
 
 Pyrite 
 
 I'vrrlioliif 
 
 t- ti.l-s 
 
 i: 
 
 (i.'i-IUi 
 
 liT 
 
 l!t,-'l,.V. 
 
 -.'I 
 
 Relation of ilip to in;ensit\- ^A' magnetization 
 
 Repulsion and altrailion, law of 
 
 Refractorily magnet i,- 
 
 Rose, j. 1 
 
 Sensitiveness of till* iiulinali'f 
 
 Sine melhoil . , . 
 
 " Pahlblom's modification of the. 
 
 .Metlu>d ot observatitiii . . 
 
 t'alibrat i tit millimeter 
 sca'-j and consli'uetion 
 of scale tor reattinir /»' 
 tlirecl 
 
 Smyth, Henry l.lo>d 
 
 Sleuth pole 
 
 " seekinjr polarity 
 
 Strenfflh of a magnetic field at a point . 
 
 Sundholm. H 
 
 Swedish mining t-ompass, description of the 
 
 .J 
 lU 
 !l 
 3 
 
 1-J 
 
 i:<. iti 
 » 
 
 :< 
 :i 
 
 i:t. l)i 
 
 i.'i. Hi 
 
 .•;t-4J 
 .Is 
 
 .■tS-4J 
 
 17 
 
 :) 
 
 !l 
 
 (i 
 
 74 
 (i.1-f>fl 
 
 ll 
 
 i 
 
 ■1 " 
 
f I 
 
 »!: f 
 
 182 
 
 T 
 
 TanKL-nl method ; 
 
 Terrestrial field, the disturbed 
 
 " " the normal 
 
 Testinjf and adjusting the maKnetomeler (Thalen-Tibenr). . 
 
 Thai n, Rolx>rt 
 
 Theory of the constitution of ma>fncts 
 
 '• " inclinator 
 
 " " Thomson-Thalcn maRnetometer 
 
 Thomson, Sir Wm. (Lord Kelvin) 
 
 Tibcr>f, E 
 
 Tilas, Daniel 
 
 Total intensity of the earth's magnetism, comptinents of the . 
 Tube of force 
 
 , 33, 3.% 
 
 Uhlich, r 
 
 Unipolar magnetic fields, diaKrams of 
 
 Upper pole of a magnetic ore body beneath the surface, determina- 
 tion of the distance of the 
 
 Itt'lS 
 lt> 
 
 •J1»-3I 
 I 
 3 
 
 4H-.Vi 
 
 «l>-«3 
 
 1 
 
 I 
 
 <!.'> 
 
 
 
 HI-M6 
 
 \'alue of K, determination of the 
 
 " the horiiontal component of the earth's field for Ottawa, 
 
 Ontario 
 
 " the horizontal intensity in a terrestrial field of force, dis- 
 turbed by the presence of a magnetic ore-body 
 
 Variations of the terrestrial field, annual 
 
 " daily 
 
 11 11 •• " Juu to cosmic maffnetic disturbance 
 
 •• " earth's man;netic field 
 
 V'ertical intensity, charts ol the 
 
 '1 " of the disturbed field, the 
 
 w 
 
 Workable majfnetic ore deixisils 
 Wrede, Freiherr von 
 
 iVi-.'U 
 
 73 
 
 4.'J-48 
 IB 
 lU 
 lU 
 10 
 72-74 
 49.10 
 
I'l.ATK C. 
 
 H 
 
 
 X 
 
 I ii 
 
 ll 
 
 
 f^ 
 
 
 !■ i 
 
 
 
 
 J 
 
 
1 
 
 1 
 
 I; : 
 
 III 
 
 Iff 
 
 if : f 
 
 V I 
 
 1 i 
 
 !: ( 
 
I'l.UK I). 
 
 ■A 
 
mkr 
 
I'l.MK K 
 
 
 TlllVMMlN-TllM.] N .\lA(iNKIilMKl KK ( (.".I.ASS (.' M'S RKMH\H>I. 
 
I' 
 
 i 
 
K S'l: 
 
 
 
 
 
 
 
 
 
 
 1 
 
 .-.. 
 
 _! 
 
 — 
 
 . 
 
Vl'lirnCAL SIKTION OK Till': KIKM) OF KOHCJ': 1111 
 
 ftm 
 
: riiuoiciHTiiK station linm moi- lMAri:s iiandiii. 
 
 PLATF. I 
 
 The Wo'ti Tier Co . -■•-• 0"flwd 
 
i !! 
 
 1.^ 
 
 ill Ji 
 
 n 
 
ivriixs 
 
 ,_ 
 
 
 
 
 
 
 
 ffiiL__ 
 
 PZ 
 
 
 - 
 
 W.1 
 
 /7' 
 
 
 166 
 
 no 
 
 
 1 
 J«.g 
 
 no 
 
 
 
 1 
 i«7 
 
 n..i 
 
 — ' 
 
 
 ^ __J 
 
 7.i 
 
 
 5 t ¥ W 
 
 I' I 
 
ISODYNAMIC LINKS OK 
 
 iiiiiiiiniitii H 
 
 iMMbi 
 
soK iionr/oNTAL i.\Ti:\srrv \i 
 
 FLATi- II 
 
 JH^— . /■ '•■■' ,«** .JJii_ W7 
 
 7 
 
 yo // Z2 i» 
 
 iJ y. i7 
 
 P? Vo^t rif?^ ".O . - V : 
 
 riiiixiiiiiirii H 
 
 Sciilf- 1 iiuh-L'O III . 
 
 iiiMii liil liii." I; , II lc"i 
 
 1- 
 
U- - 
 
 L 
 
L ''I'l ' 
 
 niN sr 
 
 u 
 
 u 
 
 -t. 
 
 'J 
 
 14 -li 
 
 f», 
 
 ^' 
 
 1 
 
 ^ 
 
 M -U 
 
 t 
 
 If 
 
 -1 
 
 
 
 
 ,1 
 
 1 
 
 
ISODYNAMIC LINKS OF 
 
 positivv iiiteuai'y ^nortli jxili- niirai non 
 
 Sral»* 1 iiic 
 
 1^* 
 
S OK VKHTICAMNTKNSny (; 
 
 i'LATE III 
 
 .^^.. -i«w -*• -im "Xi 
 
 » JO 
 
 J:.' It li IS IS 
 
 lit 
 
 The Mort'ner Co L:m we o-t»v« 
 
 ne«(Btrv'p intenniry !i<«uih p-.U- uttmction ' 
 
 til*' 1 iiirh=l'() III. 
 

 |;j ^ 
 
 
 J 
 
 
 
 
 
 
 
 i 
 
 
 i 
 
 ■ ; ' ' 
 
 t 
 
 ' ' 1^ 
 
 r 
 1 
 ! 
 
 ; 
 
 a 
 
 
 1 
 
 1 
 
 & 
 
X 
 
 -^«!te__ 
 
 - i 
 
 --iti>l- , 
 
 'i 
 
 ^' 
 
 m 
 
ISOCfONIC 
 
 Sr.ilf 1 illi 
 
 ■Miii 
 
NIC LINKS 6*. 
 
 PLATE IV 
 
 H 9 W n 12 13 I^ /> * n J^ 
 
 ^leMc^ "^ftf '^ ~ T-^-c Q-tjvhs 
 
 ilf I inrl»-=l'<) in 
 
\\ 
 
'OSIT Ol- .MA(,.\KTnj. 
 
 l~ 
 
 arj 
 
 ai 
 
 'T^ 
 
 /ft 
 
 •ATE V 
 
 us 
 
 1« 
 
 ■1 — 
 
 k 
 
 -^^- 
 
 ,ct:i 
 
 --M 1» 
 
 :3,t 
 
 33 
 
 — A 
 
 I 
 
ISODYNAMIC LINKS OK Till-; noiii/o.vi 
 
 M 
 
 i» 
 
 !» 
 
 ! ! 
 
 4?- 
 
 kX 
 
 !l 
 
 
 juiiTXjm'in. « 
 
 HMl:intllUt « 
 
 S.-.il.- I .'.(• 
 
oxTAi, ix'n:Nsi'['v ov a i)i:pnsn oi ma(;ni;'iit1': 
 
 PLATE V 
 
 .■*4 
 
 -r ' 
 
 3S 
 
 ) 
 
 XI 
 
 
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