588 MR W. J. M. RANKINE ON THE 
( D 
af ("a -P)av=-4 p (77,72) ¢D=-P, Vv af? ae aD aye pap} 
a? ava — f py: t2ap=-P,V, 4 8 (= byp. log D+ Bear ) 2 Oise 
For carbonic acid, the first of these formule becomes simply 
\ 
+P,Vo'G Gtos) =5(2- -p,) } | 
and the second, 
1 D, a (D, _D, | 
+P, V, (= hyp. log Da De (Fs =) } 
Guascow, 27th December 1852 
(113 A.) 

APPENDIX. 
Nore A (to Article 58). Since this section was read, the theoretical views 
relative to the relation between heat and temperature contained in it and the 
previous sections of this paper, have received a strong confirmation by the publi- 
cation by M. Recnavt of the fact, that he has found the specific heat of air to 
be sensibly constant at all temperatures from —30° centigrade to +225", and at 
all pressures from one to ten atmospheres (Comptes Rendus, 18th April 1853) ; 
so that equal lengths on the scale of the air thermometer represent equal quanti- 
ties of heat. 
Norte B (to Article 62). Until very recently, there existed no exact experi- 
mental determination of the specific heat of any gas. The specific heat of air at 
constant pressure, as compared with that of water, was calculated theoretically 
in the previous part of this paper, from JouLE’s equivalent and the velocity of 
sound, and found to be 0°24. This value has since been confirmed very closely 
by Mr Jouur’s experiments, whese mean result was 0°23, and still more exactly 
by M. Reenauut’s experiments, already referred to, which give the value 0°2379. 
The following table shews the results of the application of the formule of this 
paper to the specilic heats of five different gases at constant pressure, selected 
from M. Recnauut’s table (Comptes Rendus, 18th April), as being those in which 
the velocity of sound can be computed, and has been determined experimentally. 
The table shews also a comparison of the calculated and observed velocities of 
sound. This table appeared originally, in French measures, in the Philosophical 
Magazine for June 1853: the metres are here reduced to feet. Kr, Ky, and Keys 
are expressed in feet of fall per centigrade degree. Kw (JouLE’s equivalent) 
=1359°6. 

