588 
DE. J. P. JOULE AND PEOEESSOE W. THOMSON ON 
We have not experiments enough to establish the law of variation with temperature 
of the thermal effect for the pure gases oxygen and nitrogen, or for any stated mixture 
of them other than common air ; but there can be no doubt, from the general character 
of the results, that the same law will be about as approximately followed by them as 
it is by air. 
Hence we may presume that in all these cases the cooling effect is very well repre- 
sented by the formula 
-dd ^ /27S'7y 
dp t ) • 
Comparing this with the general formula given above, we find 
4-*=ajk 
The general integral of this differential equation, for v in terms of is 
^;=P^_iAJK 
2 
9 
P denoting an arbitrary constant with reference to t, which, so far as this integration is 
concerned, may be an arbitrary function of p. To determine its form, we remark in the 
C 
first place, in consequence of Boyle’s law, that it must be approximately -, C being 
independent of both pressure and temperature ; and thus, if we omit the second term, 
we have two gaseous laws expressed by the approximate equation 
Now it is generally believed that at higher and higher temperatures the gases approxi- 
mate more and more nearly to the rigorous fulfilment of Boyle’s law. If this is true. 
the complete expression for P must be of the form — , since any other would simply 
show deviation from Boyle’s law at very high temperatures, when the second term of 
our general integral disappears. Assuming then that no such deviation exists, we have, 
as the complete solution. 
This is an expression of exactly the same form as that which Professor Baj^kine foimd 
applicable to carbonic acid, in the first place to express its deviations from the laws of 
Boyle and Gay-Lussac, as shown by Eegnault’s experiments, and which he afterwards 
proved to give correctly the law and the absolute amount of the cooling effect demon- 
strated by our first experiments on that gas*. 
That more complicated formulae were found for the law of elasticity for common 
ah' both by Mr. Bankine and by ourselves, now seems to be owing to an irreconche- 
ability among the data we had from observation. The whole amounts of the devia- 
* Philosophical Transactions, 1854, Part II. p. 336. 
