136 
MR. MACQUORN RANKINE ON THERMO-DYNAMICS. 
When the relations between pressure, volume, and heat, for a given substance, are 
known, the equation (21.) may be transformed into one giving the volume V B corre- 
sponding to the point at which the required curve of no transmission cuts the iso- 
thermal curve of Q 2 . 
Suppose, for instance, that for a perfect gas 
PV=NQ sensibly ; and -^=1 sensibly ; . . . (22.) 
N being a constant (whose value for simple gases and for atmospheric air and car- 
bonic oxide is about 0'41) ; then the thermo-dynamic function for a perfect gas is 
sensibly 
F=hyp. log Q+N hyp. log V ; (22 a.) 
and equation (21.) gives, for the equation of a curve of no transmission, 
whence 
(23.) 
(24.) 
Equations (23.) and (24.) are forms of the equation of a curve of no transmission for 
a perfect gas, according to the supposition of Mayer ; and are approximately true for 
a perfect or nearly perfect gas on any supposition. 
According to the hypothesis of molecular vortices, the relations between pressure, 
volume, and actual heat for a perfect gas are expressed by these equations : — 
PV=NQ+A; x V ='+PCT’ < 25 -> 
where h is a very small constant, which is inversely proportional to the specific gra- 
vity of the gas, and whose value, in the notation of papers on the hypothesis in ques- 
tion, is 
//—Nit*, (25 a.) 
* being the height, on the scale of a perfect gas thermometer, of the point of abso- 
lute cold above the absolute zero of gaseous tension. Hence we find, for the thermo- 
dynamic function of a perfect gas, 
N h 
F=hyp. log Q— nq^t^+N hyp. log V, (26.) 
and for the equation of a curve of no transmission, 
V3 
V A 
h h \ 
NQ 2 + A~NQ l + A-* 
( 27 .) 
For all practical purposes yet known, these equations may be treated as sensibly 
agreeing with equation (23.), owing to the smallness of h as compared with NQ. 
