520 Intelligence and Miscellaneous Articles. 
4 
is therefore > = °405285, and we have 
K 3 is: 405230 8. 
In 1877, Preston (Phil. Mag. ii. p. 453; iv. p. 209) showed 
‘“‘ that a physical relation exists between the velocity of the particles 
of a medium constituted according to the kinetic theory, and the 
velocity of propagation of a wave in the medium.” Maxwell 
calculated the numerical value of this relation at »/3, which repre- 
sents Chase’s ratio of relative vis viva; but he did not give the 
method by which he reached that result, and no record of it was 
found among his papers. The followimg thermodynamic demon- 
stration may therefore be satisfactory to those who have found 
any difficulty in accepting the more simple and more general 
photodynamic proof which is furnished by reference to oscillatory 
centres. 
If we represent the density of a gas, ue by p, the fundamental 
equation of pressure becomes , A 
Alexander Naumann (Ann. Pharm. 1867, pp. 142, 267; J. B. 
1867, p. 62) showed that oni baaae 
Sis 
u==5 (yy hcylis ae ae Relic nice (2) 
pu being the heat of molecular motion, or mean vis viva of a periect 
gas; y', the specific heat under constant pressure ; y, the specific 
heat under constant volume; y'—y, the heat of expansion, or vis 
viva of mean velocity. The total specific heat is therefore’ 
6=pt+y at Aa (3) 
Hence yippee ira Series Percent Sc amererr tracts 5 <0 = (4) 
PR erate gory come Sommers oS. (5) 
Prof. d’Auria, in a special investigation relating to the dynamics 
of direct-acting pumping-engines, not yet published, has found, 
by analogy, that 
Vimaewes pelt coraalny sis. 2 Ee (6) 
Substituting this value in eq. (2) we get Chase’s result :— 
y¥-y= "A05285y ©. o Weve ip de welusl tame tte ke) Vol letunite (7) 
y= 1:-405285y, « Solhedorxe Mele gel me lepes lage (8) 
The exactness of agreement between this @ priort value and the 
one which was found by Rontgen (1°4053 ; Pogg. Ann. 1873, pp. 148, 
603) is very remarkable.— Communicated by the Author, having 
been read before the American Philosophical Society, April 17, 1885. 
