the Primary Laws of Elastic Fluids. 287 
retical cooling effect for 100 lbs. pressure.” Oncomparing this with 
the adjacent column of experimental results, we find such complete 
accordance that apparently Prof. Thomson’s calculus has enabled 
him to predict in a satisfactory manner the results of observation. 
This is the test of a successful theory. On inquiring further what 
this theory is, we come to what Prof. Thomson calls an “ empirical 
formula” (that is, a formula derived from experiment), communi- 
cated by Mr. Rankine, who states that its constant coefficient a “has 
been determined solely from Regnault’s experiments on the increase 
of pressure at constant volume between 0° and 100° C.” Mr. Ran- 
kine further states, that ‘‘it gives most satisfactory results for expan- 
sion at constant pressure, compression at constant temperature, and 
also (I think) for cooling by free expansion [i.e. the cooling effect 
in our (Messrs. Thomson and Joule’s experiments) ]. 
The formula is PV T+C ahi Veg 
No explanation is given as to the method of determining a, nor is 
there any proof of it giving satisfactory results for compression at 
constant temperature, or how any results of this kind are possibly 
derived from M. Regnault’s experiments. 
P'V'—PV aap he t 
LNG tacit 
given by Prof. Thomson at p. 340. No explanation is given of how 
J has been determined “ from the results derived by Regnault from 
his experiments on the compressibility of air, of carbonic acid, and of 
hydrogen.” Prof. Thomson must be sensible that upon these the 
proof of the soundness of his “theoretical deductions” mainly 
depends. 
The value of f for air is 00082 (p. 340), and the formula ex- 
presses that the deviation from the law of Mariotte (or of Boyle) 
for a difference of pressure equal to one atmosphere is ‘00082 or 
1 
1220° 
How this has been deduced from M. Regnault’s observations is 
not explained; but both formule cannot be right, inasmuch as they 
contradict each other. 'The deviation may be computed from either, 
and they give different results. 
If, in Mr. Rankine’s formula, we put T=0, V=2Vo, we have 
pee anal eg Ri =e) 
Po. om ae o( ~ 288)" 
Hence the deviation for carbonic acid is _ By the value of f 
The same remark applies to the formula 
given by Prof. Thomson at p. 340, it is ‘0064 or 5G 
If we test the formula of Mr. Rankine by taking T=0, we have 
19 V 
PV=P pee Vat. 
Vo 274 V } 
