gelit values were slio\vii usiiall!. to be caiisetl 11). the great iiinltiplication of errors of observation i i i the calcnlatioii. ( l~suall!-throuK11 t h e iise of Riot’s formula for the calciilatioii of the
a I-’
a factor aT’ n-liicli as necessarj- for tlie calciilatioii of the lieat of \-apoi-izatioii tlieriiiod~.iiaiiiically.j Occasioiinll!. tlie iiatiire of the ~111)stance rendered the ohsen-atioiis at tlie teiiipernture considered les:; accurate than iisual. -1s a coiicliision fi-oiii tlie ivoi-k of tliese papers, we believe that there can lie iio further douljt tliat et1iJ.l oxide, di-isopropj-1, isopentaiie, iioi-iiial peiitaiie. iioriiial hexane, benzene, liesametliylene, fliio-lienzeiie, clilor-benzene. 1)rombenzene, iodo-benzene, and carlioii teti-achloride q r e e Ivitli the theory as closel!- as the expel-iiileiital data ]\.ill perillit o\-er tlie entire raiige of temperature esmiilied, aiitl eTwi at tlie critical temperature itself.’ Sonnal heptane, 1101-iiial octaile, aiid diisobutj.1 shon- an uiiesplaiiied di\-ei-gence i i i tlie iiiiiiietliate neighborhood of the critical teiiiperature. These siihstaiices having each giI-eii agreement lvitli the tlieor!. o\.er a \.er!. \\-ide range of temperature it wo~ilclseeiii tliat their dii.erg-eiice at the critical temperature (aiiimiitiiig- iii iio c x w to teii perceiit fro111 the iiieaii coiistaiit aiid tlie entire \m-iation froiii coiistanc!- e s tending in 110 case iiiore tliaii teii degrees), is iiioi-e probabl\- due to ail increased iiiaccur:ic>- iii soiiie oiie of the iiieasiireiiieiits entering into the calculation, or to soiiie iiicipieiit cliaiiae or decoinpositioii takiiig place in the sulistaiice nt this liig-li teiiiperatnre than to any iiiliereiit dep:ii-tiire froiii the geiieral lan-. Stannic chloride was slio\vn i i i the second paper to give a coiisiderahle unexplained cli\-erg-eiice froiii tlie theor!.. I3ut i i i that paper, Dr. ’ITouiig,\vho iiiade tlie iiieasiireiiieiits, is ciiioted (p. 402)as sa)-iiig, “Staiiiiic chloride spoils tlie siirface of iiiercury even at low temperatiires aiid special iiietliocls liad to lie used throughout. T h e accui-ac!. is ccrtaiiil!. not so great as TTith most of t h e other sulxtaiices, b u t this \\.ill not, I tliiiik) explain the regular fall in the \-alue of the constant.” I n the fourth paper, liowei-er, w e again qtioted (p. 10;)Dr. Yoiiiig as sa)-ing, T h e ohserved i.alues of the ~ ~ i p pressure or abol-e 2S0° (r
I
J o u r . I’li!s, C l i e m , , 9, 413 I, 1 9 0 j
,
( T h e agreeiiieiit bet\\-een Griffitlis aiid Kegiiaiilt becomes closer with rise in temperature, at 100' C., liotli \ d u e s beiiig iii accord to 0.04 of a calorie.) T h e cleiisit!. of the vapor used \vas dependent 011 Regiiault's heat of vaporization, liaviiig been calciilated from his iiieasiii-eiiieiits li!. Iiaiiisa!- aiitl Yoiiiig.' ITsiiig Griffiths' value for the heat of T-aporizatioii and recalculating the deiisitj- of the vapor tlierefroiii and siibseciiieiitl!- El! aiid siilistitutiiig as before in Equation I abo\.e, lye obtain : I I y R . .~ ~ ~ ~
Temperature
oo
Latelit lieat
~
El
I,- E:,
c.
IO 20
30
2 40 250 2 60
270
T h e 1.alue of the mechaiiical eciiii\-aleiit of lieat used alio\.e iti recalculating the densit!, of tlie \.apoi- \vas tlie J-alue previously used bj- KaiiisaJ- aiitl Youii:i. for tlieir calculation. It is one-half of oiie percent loiver tliaii the 1-alue of ~ o n l a i i t as l corrected by Day \vliicli we 1iaI-e used in these papers. l y e iiiade !.et aiiotlier error in tixstiiig to the IIiot foriiiula gil-eii by Iiegnatilt for calciilatiiig the heat of \.apoi-izatioii at 240' to 2 j o o C. T h e vFLpor-pressiires calcu1:iteci froiii this foriiiula were u p to 23oC C.in spleiitlitl ageeiiieiit n-it11 the values of the vapor-pressure esperiiiieiitallj- determined I)!. Ramsay aiid Young. But if tlie Iiegiinult-I:iot foriiiiila is forced beyond this poiiit the divergence iiicreases aiid beconies ver>marked. A new Biot formula could be calculated iisiiis- the vapor pressures as given by Iiaiiisa!- ant1 X-oiiiig tliroug-liout, but ~~~
~
Phil, Trails., 183A, 115 (1S92't.
the calculation is laliorious. T*alucs ciiiite sufficieiitl!- accurate for
om- p i i i p s e caii lie oljtained I]?. getting the
aT for a coiisiderable
range of teiiiperatiirc directlj. froin the obseryecl yapor-pressures of Raiiisa!- aiitl X-oiiiig and dran-iiig a siiioothed curve through tliese values plottetl agaiii,Gt tlie teiiiperature aiid then reading ap from 230' from tlie curl-e. In t1ii.c iiiaiiiier the 1-alues of the
aT
to 270' C.gil-en alio\-e, irere olitniiied. ['sing these values the lnteiit lieat ~ T X S calculated and tlie Txlues of the coiistaiit, p', corrected as slion-ii abo\-e. Cliaiigiiig the iiieaii i d u e foriiierlj. atlopted froiii 556 to 5 j S . 4 .n.e see that all valses of the coiistaiit are \vitliiii t n o percent of this mean l-alue except at oo C., which s l i o i ~a divergence of three aiid tu-o-tenths percent, aiid a t 10' C.,which slions a dii-el-gence of a little 01-er two percent. I t seeiiis to 11s citiite p x s i b l e that the explanation foriiierlj- given1 \vi11 suffice to explain tliis dii-ergeiice, especiall!. when it is reiiieiiiliered that the iiieaii i - d u e gi\.eii is itself subject to soiiie u ii cer t ai 11t j.. nut n-e \vis11 to make it clear here that we have recorded these cliaiiges aiid correctioiis aiid pointed out the reinaiiiiiig soiirce of error which it is iiiipos.siiile to correct only as a matter of fact. I'ersoiiall?. xve iielie1.e that the dil-ergeiice of three aiid tn-o-teiiths percent abol-e iioted is !-et greater than can he accounted for li!. tlie reiiiaiiiiiix soiirces of error. TT'ith associnted substances n-e never expected the equation to j-ield a coiistniit. Bnt when the results ol-er wide ranges of temperature prox-ed i/ccrr(ig musiirirf ivc thought it a n iiidicatioii that the associatioii must lie caiised lij. tlie iiiolecular attraction which we were coiisideriiig. If this is true-if the molecular associatioii is caiised 1 3 ~ . this iiioleciilar attraction-we do iiot belie!-e that the equation iii its modified foriii n-ould then yield a n c.unct constaiit for tliese substances for the reasoii pointed outYwhen this siiggestioii \\-as first iiiade, zmi;., the iiiolecules could not be
coiisidered iiiiiforiiil!. tlibtr-ihutetl tlii-oiixlioiit tlic space occupied b!. them-a supposition eiiilirncetl i i i tlie foriii111a. l y e desire to iiialcc it cleni- esactl!- ivli!. \\-e t l i o i i ~ l i tthis n/J/Ji-onr.hto a coiistniit \ - a l i ~ exi\.c.ii 11) tlie eqiiatioii iiitlicated that the associatioii is c:~~i,\etl l)!, tlic :ittractioii iiiitler coiihirlerntioii. If the iiietliorls for iiicnsitriiix tliis iiioleci~lnrassociatioil are of an!- \-aliie. the!- iiit1ic:ite tlint tlie (leg-ret: o f associatioil cliaiiges rather rnpitll!- \\.it11 ;i c l i a i i ~ ei i i tciiil)er:itiirc. So\\. if this associatioil is cniised 1)). ,soiiie force otlier tlinii tlic iiioleculnr force nnder coiisideixtioii ive \voiil(l l i : t \ ~ a s tlie teiiiperatiii-e altered a coiitiiiual a i i d rnpitl cliaiig-c : i i i tlie iintiirc of tlie su1)stance under consideratioii ; i i i tlie ioi-ces, a t least t\vo i n iiiiiiiber, actiiix liet\veen tlie tliffcreiit .\iil)~t:iiice~ : i i i tlie uiiiiilier of iiiolec~ilesacting- : 2Liitl i i i tlic pobitioii of tli iii ( 11ec I I 1ai- g-roil11s with respect to eacli otliei-. 1khitle.s :ill of tliese cli:iiige.\. it iiiiist be renienil~eredtlint, if :~ii:il(~x>. i h \\-oi-tli :iii>-tliiiig-\a i i t l i i i this case we l)elie\.e tlint i t i q ? tlie lciiietic t r ~ ~ i i s l n t i i ~eiiei-').~. ~ i a l . of tlie inolecules as \vel1 ;is tlieii- iiiteriial tAiiei-x>-iiiiist cliaiig-e \\.it11 every cliaiige i i i the coiiiplesit>- of tlie iiioleciile. For nil!. considerable chanxe iii the coiiiplcxit>. of tlic iiicileci~lest h e eiierx?. changes abo\-e iiotetl \voiiltl 1)c \.vi.! lnrge aintl it ,s;eeiiietl iiiipossihle to 11s that these \xriclIib eiierg-!. cliaiixe,\ slioultl 50 cancel ah to leave the iiet restilt of tlie c.qii;itioii c \ w i iie:irl!. ;I coiistniit. On the other liantl, if tlie iiiolcciilar a*.wci:itioii i \ c;iii~edlj!. the iiiolecnlai- atti-actioii iiiitlcr coiibitlei-:itioii, :i cliaiixe i i i tlie coiiiplesit>- of tlie iiiolec~ilc,~ c l i a i i x v ~ iiotliiiig- l i i i t tlieir distaiice apart. Biit tlie clistniice apart o f tlic iiiolec~ile. is not rexular as in the case of iioii-:Lsboci:itetl .*iil)*t:iiice,-$1)iit ii-i-exiIlar$as n - e ha\-e to consicier 1)otli tlie clihtaiicc l)et\\-ec.ii x r u i i p o f iiiolec~iles and 1ietn.een tlie iiiolecIiles of :i groiip. \\-e \\-ere i i o t able to follon-- lial-e not, i i i fact, atteiiilitctl to foll(i\\ -tlie c l i a i i ~ ethis n-ould necessitate i n tlie eqiiatioii givcaii. j T1.e tliiiik, lio\ve\-er, that the effect ~ ~ o i i lie l d to c:iii.w tlie coiistaiit xi\-eii 11!- tlie ecliiati oii to i 11crease \Yi t 11 i i i c rea b i i ig 11i o 1ec I I 1:ir c o 11111ICs i t !. , for t 11e reason, briefly, tliat iiiolecu1:~r aw)ci:ition tciit1.s to c l r a \ ~the molecules, indepeiideiitl!- considered, oii the a\.erag-e. closer together. T1ii.s iieariiess \~-onltlrebult i i i :iii appai-eiitl!- illcreased
attraction, 1’. c., n o u l d cause the coiistaiit of attraction, p’, to show an increase iii ~ - a l u e) . E3nt cjnite coiiceiyably the change required in the equation nonld not lie great. IYheii, tlierefore, we foiuid tlie valiie gi\.eii 11~.the equation for the associated snlxtances sni-prisiiigl!- coiistaiit, aiid since these same associated sulxtaiices showed a iiiucli larger absolute attraction, p, than tlie non-associated sitbstaiices, tlie conclusion that the association n a s caused li>. the attraction was suggested as a probable causal explaiiatioii of the tn-o facts. ;Inother point has seJ-eral times beeti brought to our attention. Decause n-e 1ial.e used iii these papers the terms ‘(moleciile and iiiolecular attractioii ’’ aiicl “ distance between tlie niolecules,” ive do not possess the idea that a iiiolecule is necessarilJ- a little, hard sphere, or some other particular shape of a pi.ece of matter. For oiir part, in the present part of this discussion we do not care to consider the nature of a molecule. 11-e do iiot care n-liether it consists \vlioll>. of matter, or wlioll~. of energ!.\ or is a ,judicious mixture of tlie two. T h e law of gravitatioii has ljeeii sho~\-iito hold between large masses of matter. If later it liappeiis to lie proved that matter is iiot reality and that onl!- energ!- exists, we do iiot suppose that the proof will greatl!. affect tlie calcnlations of tlie astroiioiiiers, or the position of tlie l i e a ~ - e i i Ibodies ~or tlieir iiictveiiieiit in accordance with tlie lan- of gi-avitatioii. T h e object of tliis series of papers is to sliow that tliis same I n n of attraction exists between siiialler masses of the saiiie material of wliicll these larger bodies are more conspicuoiis represeiitati~.es. Folloning considerable precedent we lia\.e called these siiialler iiiasses,” iiiolecllles,” a teriii which con\-e!.s to e1-ei-J.scientist, ho\\-e\-erbroad-iiiiiided, a group of properties siifficientl!. clearl!. clefiiied for tlie purpose in 1-ien-. Ily the expression distalice betn-een the iiioleciiles,” n-e iiieaii tlie distalice lietuxmi tlieir celiters of iliass-ai1 espressioii esactl!- a i i a l o ~ o u sto the distalice betnee11 tu-o heavenl!. lioclies. T h e expression * ‘ ceiiter ol: mass ’’ is ilsed 0111~-to designate a realit!. and those \vlio ha\-e grasped the realit>-call 11se all!- iioiiieiiclature for its representation that is iiiore pleasing to theln. ”
& +
‘ k
“
TYliatevei- opiiiioii \\.e 0 1 1 l\.e-; lioltl ;ii t o tlie iiltiiiiatt nature of tlie groiil) of prol)ertic.; rcl)rc\ciite(l 11). tlie teriii iiiolecule rests 011 grouiitls that :ire too iiis'eciii-e to iiialce tlisciissioii of these Tien-s at this staxt: profitable. / / - e oiil!. \\.is11 to ciiipliasize tliat one iiiny liold i r i c l ' : , I ' , T to tlie ultiiiiate coiistitutioii of matter and !-et piirsiie ai1 iii\-estixatioii of this clinracter. In this paper lye coii,\itlcr tlie teii .siili,staiicc\%iiictli!.l forinate, et hy1 f orii in t e, i lie t 11!-I ace t a t c. c 11loi-oio ri i i ;ice t 01 i e , ea rlio I i tl i s 1. 1ph ide, aiiiiiioil ia c:irb oii t 1i t i s i d c i i i t roI I i( 11 i ti ta :I I i d si1I p li t i I- d i oxide. Some of tliesc sii1)staiicc.s \yere cli;ciissetl, hut iiiadequatel!., in tlie first paper. Tlic tletaili of tlie iiieahtirciiiciits used are gi\-eii 11elon-. I\-e i i i a > . .si!. liei-e tliat \vlieii clioict. lietween the iiieas1ireiiieiit.s of difiereiit ol)scr\.crb \\-:ispo,Gsilile. it was iiot possilile tliat tlic choice of tlie xtitlior coiiltl lia\-e liccii influenced tiiicoiiscioiisl!. 1)). iiii!. 1)i-c,iii(lic-e i i i fa\-or of tlie tlieor?., for in e\-ery case tlie iiiea;ureiiieiit\ \\-erec l i o w ~ ilwfore an!. inkliiig of their possilile lmiriiig- oii tlic tlieoi-!. \\-;isobtniiietl. ~
~
Constants f o r Biot's Formula Hefore the heats of \.nporiz:ltioii of iiietli!.l I-'oriii:itc, etli!-l forinate, nietli!.l acetate rriitl 1111- tliositle coiild 1)c calculated theriiiod~-iiaiiiicnll!,~ it \\-:i> 11 .:11->. to 11n\.e .;0111e illcalls for ohap taiiiiiig the and, as ii.~ii:il, 1;iot'h ioriiiiiln for \~~ii)oi.-i)i-cssiii-e aT was used. The coiistaiits for tliib loriiiiiln foi- etli!.l foi-inate aiid methyl acetate n.ere kiiicll!. ,seiit iiie 1 ) ~ .I )r. Y t j ~ i i i x . "lie!. liai-e never been piiblislied aiitl so ai-e xi\.cii l ) c l o \ ~ . I)r. Youiig- also sent the details of the iiictliotl tisetl i i i iiialciiig tlie calci~lations and with this aid tlic coii,\taiits for iiictli!-l loi-iiiate and for snlp h ~ rdioxide \yere cnlcu1:itetl a i i t l a r e like\\-i>c g - i ~ w ilxlon.. For sulphur dioxide tlie \.a])oi--1)rebs~ii-c.;iisetl as ;i 1 those giyeii 11~. I'ictet, -
