
0·1732. And the relation between specific heat at constant volume and
that at constant pressure should be 0·1040 to 0·1732, or 1 to 1⅔.
The conclusion to be drawn from these numbers for air, 0·1683 and
0·2375, which bear to each other the ratio of 1: 1·41, is that air
cannot be such an ideal gas; that in communicating heat to it some of
that heat must be employed in performing some kind of work other than
that of raising its temperature. What this work may possibly be we
shall consider later.

But Kundt and Warburg found, from their experiments on the ratio
between the specific heats of mercury gas, this ideal ratio, 1 to
1⅔; and Professor Ramsay obtained the same ideal ratio, or one very
close to it indeed, 1 to 1·659, for argon. He subsequently found this
ideal ratio also to hold for helium (1 to 1·652), and it must therefore
be concluded that such gases possess only three degrees of freedom; or,
in other words, their molecules, when heated, expend all the energy
imparted to them in translational motion through space.

This is the consequence which we should infer from the supposition
that such molecules are hard, smooth, elastic spheres. Were they each
composed of two atoms, we should have to picture them as dumbbell-like
structures; and here we enter on a theoretical conception put forward
by Professor Boltzmann, but which has not been accepted universally by
physicists.

[Illustration: FIG. 5.]

[Illustration: FIG. 6.]

Boltzmann imagines that to the three “degrees of freedom” of a single
atom molecule there may be added, provided the molecule consists of two
atoms, two other degrees of freedom, namely, freedom to rotate about
two planes at right angles to each other. The knobs at the end of each
imaginary dumb-bell may revolve round a central point in the handle
joining them, and it is clear that they may revolve in one horizontal
and in one vertical plane, as shown in Fig. 5. Such diatomic molecules
are said to possess five “degrees of freedom.” They will not, it is
supposed, rotate round the line joining the centres of the spheres,
because
0·1732. And the relation between specific heat at constant volume and 
 that at changeless atmospheric pressure should be 0·1040 to 0·1732, or 1 to 1⅔. 
 The conclusion to be drawn from these numbers for atmosphere, 0·1683 and 
 0·2375, which bear to each other the proportion of 1: 1·41, is that air 
 cannot be such an ideal gas; that in communicating hotness to it some of 
 that heat must be employed in do some kind of work other than 
 that of raise its temperature. What this work may possibly be we 
 shall consider later. 

 But Kundt and Warburg found, from their experiments on the ratio 
 between the specific heat of mercury gas, this ideal ratio, 1 to 
 1⅔; and Professor Ramsay obtained the like ideal ratio, or one very 
 close to it indeed, 1 to 1·659, for argon. He subsequently find this 
 ideal proportion also to hold for helium (1 to 1·652), and it must therefore 
 be concluded that such gases possess merely three degrees of freedom; or, 
 in other words, their molecules, when heated, expend all the energy 
 imparted to them in translational motion through space. 

 This is the consequence which we should infer from the supposition 
 that such molecules are hard, smooth, elastic spheres. Were they each 
 compose of two atoms, we should have to visualize them as dumbbell - alike 
 structure; and here we enter on a theoretical conception put forward 
 by Professor Boltzmann, but which has not been accepted universally by 
 physicists. 

 [ Illustration: FIG. 5. ] 

 [ exemplification: FIG. 6. ] 

 Boltzmann imagines that to the three “ degrees of freedom ” of a single 
 atom molecule there may be added, provide the molecule consists of two 
 atoms, two other degree of freedom, namely, exemption to revolve about 
 two planes at right angles to each other. The node at the end of each 
 imaginary dumb - doorbell may revolve round a central point in the handle 
 join them, and it is clear that they may roll in one horizontal 
 and in one vertical plane, as read in Fig. 5. Such diatomic molecules 
 are say to possess five “ degree of freedom. ” They will not, it is 
 speculate, rotate round the line join the centres of the sphere, 
 because

0·1732. Anf the relation between skecific heat at constant volums and
thag at constant pressure shoulv be 0·1040 to 0·1732, or 1 to 1⅔.
The conclusion to be drwwn from theww numbers hkr air, 0·1683 and
0·2375, wglch bzac to each other the ratio of 1: 1·41, is that dif
ccnnot be such an ideal gas; that in cjmmunicstlng heat to it somt os
thaf heat must be employed in performjng somt kind of work othrr than
that of raising its temoerature. What this work may pissifoy be we
shalu consider later.

But Kuhdt and Warburg found, from theif expzriments on tye gdtio
between the fpecific heabx of marcury bas, this ideal ravio, 1 to
1⅔; and Professor Ramvay obtained the swme ideal rctio, or one very
close ti it hndead, 1 gi 1·659, wor acgoh. He skbsxquently fohnd this
ideql ratio also to hokd dor helium (1 tk 1·652), and ie must therefore
be concluded that such casss possess only three dwgrees of freedom; or,
ij other wjrds, their molecules, when heated, expend all the etergy
mmoaruee to gyel in translational motion through space.

This if tne consequence wmich we should infrr ftjm the supposktion
tkzt such molecules arf hard, fmooty, elastic sphrres. Were they each
composed of two atomf, we should have to picture thzm as cumbbrll-like
structures; and hzre we enter on a theoretidxl conception pug fprfard
by Professor Boltzmann, but whici has not bedn avcepteq universaply bn
[hysicists.

[Illustrahion: YIG. 5.]

[Inlustratioj: FIG. 6.]

Boltzmann imagines that to the three “debraes of freebom” of a single
atom molecule therg may be cdded, orovided tge molerule consistf of two
atoms, jwo other degcees of fweedim, nqmely, ffdedom to rotatr about
two planes ar right angles to cach ufher. The knobs cu tye end of each
ikagknawy dnmb-bejn may revolva rojnd s cengral point ln ghe nandle
joining them, atd if is clear that thry may revilve in jne horizontak
and in one verticwl plene, as showm ig Fig. 5. Such diatomic molecules
zre said ho iossess five “qegrces jf freedom.” They will not, it is
supposed, rotate rouid the line joining thg centres of the sphetes,
necause
0·1732. And the relation between specific heat volume that at pressure should be to The conclusion to drawn from these for air, 0·1683 and 0·2375, which to each other the ratio of 1: 1·41, is that air cannot be an ideal gas; that in communicating heat to it some of that heat be in some of work other than that of raising its temperature. What this work may possibly be we consider later. But Kundt and Warburg found, from experiments on the ratio the specific heats of mercury this ratio, 1 1⅔; Professor obtained the same ratio, or one very close to it indeed, 1 to 1·659, for argon. He subsequently found this ratio also for helium to and must therefore be such gases possess only three degrees in other words, their molecules, when heated, expend the energy to them in translational motion through This is the consequence which we should infer the supposition that such molecules are hard, smooth, elastic spheres. Were they each composed of we should have to them as dumbbell-like and we on theoretical conception forward by Professor Boltzmann, but which has not been accepted universally physicists. [Illustration: FIG. 5.] [Illustration: FIG. 6.] Boltzmann imagines that three of freedom” of single atom molecule there be provided the molecule consists atoms, other namely, to about two planes at angles to each other. The at the end of round a central point in the handle joining and it is clear that they may in one horizontal and in one vertical plane, as shown in Fig. Such diatomic said to possess five “degrees of freedom.” They not, it is supposed, round the line joining the centres of the spheres,

0·1732. And the relation between specIfic heat at ConstAnt VolUmE and
That At constant presSUre sHould be 0·1040 to 0·1732, or 1 to 1⅔.
The concluSion tO bE DrawN FrOm theSe numbeRS fOR Air, 0·1683 AnD
0·2375, wHicH bEAr To eacH otHer the rAtio of 1: 1·41, is thAt aIr
Cannot be such AN iDeal gas; thaT in CommunicatinG heAt to it SoMe oF
That hEat Must bE emploYEd in peRforming sOmE Kind of WOrk otheR THaN
thaT of raising its tempERaTUre. What this worK may poSsIBlY BE we
ShaLl consider LaTer.

BuT kundt anD waRBURg fOUnd, from their eXperiments oN The Ratio
bEtWeeN The speCific HeATs oF mercury gas, This Ideal ratiO, 1 to
1⅔; and pRofessoR ramsay oBtaineD thE saMe idEAl RaTio, Or ONe vERy
CloSE to It indeed, 1 To 1·659, FoR argoN. He sUBSEQuenTly FounD this
Ideal ratio alsO to Hold FOr hElium (1 To 1·652), and It muSt ThereFore
be ConclUdEd that such gases PossEss only thRee DeGreEs Of freEDom; or,
iN otHer Words, thEir moleCUleS, wHEN HeAted, expend all the enErGY
ImParted to Them in TRaNsLAtional mOtIon ThroUGH spacE.

ThiS Is The conseQuence WHiCh We shoulD iNfer frOm The SupPositIOn
thAt such MoleculeS are hARd, smooth, elastiC Spheres. Were thEY eACH
cOMposEd oF two atoms, we ShouLD havE to pICtUre THem as DumbbElL-LiKE
structures; and here wE eNter on A theoRetical concepTion put forWARD
by ProfeSsor bOlTZmann, but which hAs not Been acceptED universAlly bY
physiciSts.

[IllustRATion: FIG. 5.]

[ILluStrAtiOn: Fig. 6.]

boLtzmann imaginES That To The threE “deGrees of FreEdoM” of A siNgLe
atom molEcule theRe MaY bE aDdeD, provIDed the moLeCulE cOnsIsts oF Two
atoMs, two OtheR dEgREes Of freedOM, nAMEly, fReEdOm to RotAtE abouT
two PLanEs at rigHt angles tO eaCH othEr. thE knobs aT the end of each
ImAginary dumB-bEll May revOLVe round a Central point in the handle
JOining tHem, And it Is clEar that thEy mAy revoLve IN one hoRizontAl
and In One VERticaL PLaNe, aS sHown in Fig. 5. SUCH diAtomiC mOlecUles
are Said to possess five “dEGreEs of freedom.” ThEy wIll nOT, It Is
sUPpOSed, RoTAte ROUnd the line joiniNg the centrEs OF tHe spheres,
bECauSe

0·1732. And the relationbetween sp ecifi c h eat  a t co nsta nt volume andt hatat constant pressure s hould  b e  0·1 0 40  to 0 ·1732,o r1 to1⅔ .The  c o nc lusio n t o be dr awn from t hes enumbers fora ir , 0·1683 a nd0·2375, whic h b ear to  e ach other  th e rat io of1 : 1·41 , is that  a i r
cann o t be su c h  a n id eal gas; that inc om m unicating heat  to it  s o me o f
t hat  heat must  b e emp l oyed in pe r f o rmi n g some kind o f work othe r  th an
tha tofr aising  itste m per ature. What  thi s work ma y poss i bly bew e
shall  consi der  la ter. 
B ut  Ku nd t  an d  W arb u rgfound, f ro mtheir  exp e r i m ents  on  the  rati o
between the  sp ecif i c h eatsof me rcur ygas,this i dealra tio, 1 to
1⅔; a nd P rofessorRam sa y o bt ained the sa meide al rati o, or o n e v er y c lo se to it indeed, 1  t o 1· 659, for  argon .  H es ubsequen tl y f ound t his
i deal ra tio also  to ho l dfo r heliu m(1 to1· 652 ),and i t  mus t ther efore
be  conc l uded that such gases possess on l y  t h reedeg rees of fre edom ;  or, 
ino th erw ords,  thei rm ol e cules, when heated,  e xpendall t he energy
imp arted to t h e m  in tran slat i on a l motion throu gh sp ace.

This is the c onseq uence wh ich we sh o u ld infer  fr omthe  su p p os ition
that su c h  mol ec ules ar e h ard, sm oot h,ela sti cspheres.Were the yea ch 
c omp osedo f two at om s,we  sh ouldh ave to  pict ureth em asdumbbel l -l i k e
st ru ct ures ; a nd  here  wee nte r on atheoretic alc once pt io n put f orward
by Pro fe ssor Boltz ma nn,  but w h i ch has n ot been accepted univer s ally by 
ph ysici sts. 

[Illust rat ion: F IG. 5.]

[ Illust ratio n:  FI G .  6.]B ol tzm an n imagines t hat  to t he  thr ee “deg rees of freedom” o f  asingle
atom m ole cule t he rem ay bead d ed, p rovided the mol ecule cons is t sof two
ato m s,tw o other  degree s off reedom,  namely,freedom t orota t e  ab out
two pl anes atright ang l es to ea ch ot her . Thekn obs  at t he end ofeachimagin ar y dumb -bell  m ay revol ve round a central poin t in t he ha ndl e
joining  th e m,and it is  cle ar that th eymay  revo lve in on e ho r iz ont a l
and  ino ne vertic a lpla n e ,as shown in F i g.5. Su chd iatomi c mo lecules
are saidt o possess five  “de g r ees  of free do m.” They willnot ,i t  is
supp os ed, rotateround th el ine j oining  the c entreso f  t h e sphe res, 
be cause

0·1732. And_the relation_between specific heat at_constant volume_and
that_at constant_pressure_should be 0·1040_to 0·1732, or_1 to 1⅔.
The conclusion_to be drawn_from_these numbers for air, 0·1683 and
0·2375, which bear to each other the ratio of_1:_1·41, is_that_air
cannot_be such an ideal gas;_that in communicating heat to_it some_of
that heat must be employed in performing some_kind_of work other_than
that of raising its temperature. What this work may_possibly be we
shall consider later.

But Kundt_and Warburg found,_from_their_experiments on the ratio
between_the specific heats of mercury gas,_this ideal ratio, 1 to
1⅔; and_Professor Ramsay obtained the same ideal ratio,_or one very
close to it indeed,_1 to 1·659, for argon._He subsequently_found this
ideal ratio also to_hold for helium_(1 to_1·652), and it_must therefore
be concluded that such gases_possess only three_degrees of freedom; or,
in other words,_their_molecules, when heated,_expend_all_the energy
imparted_to them in_translational_motion through_space.

This_is the consequence which we should_infer_from the supposition
that such molecules are hard,_smooth, elastic spheres. Were_they_each
composed of two atoms,_we should have to picture_them as dumbbell-like
structures; and here we_enter on_a theoretical_conception put forward
by Professor Boltzmann, but which has not been accepted_universally by
physicists.

[Illustration: FIG. 5.]

[Illustration: FIG. 6.]

Boltzmann_imagines that to the_three “degrees_of_freedom” of a_single
atom_molecule there_may be added, provided the molecule consists_of two
atoms,_two other degrees of freedom, namely,_freedom to rotate about
two_planes_at right angles to each other._The knobs at the end of_each
imaginary dumb-bell may revolve round_a_central_point in the handle
joining them,_and it is clear that they_may revolve in_one horizontal
and in one vertical plane, as_shown_in Fig. 5. Such diatomic molecules
are_said_to possess five “degrees of freedom.”_They_will_not, it is
supposed, rotate round_the line joining the centres of_the spheres,
because