526 Mr. Rankine on the Centrifugal Theory of Elasticity, 



-A^ = ^£ Ci-.„»; . . . (20) 



Ci+m^eingthe coefficient of 0?^+"* in the development of the 

 reciprocal of the series 



1 - {co')x + (co")x^ - (o)" V + &c., 

 when (ft)') &c. have the values given in equation (9). 

 Equation (19) is thus transformed into 



^=^,Cc-^-^'-^-ym. . (21) 



The series in tenns of the negative powers of the absolute 



temperature converges so rapidly, that I have found it sufficient, 



in all the calculations I have hitherto made respecting the elas- 



A 

 ticity of gaseous bodies, to use the first term only, . 



(22.) Instead of making any assumption respecting the laws 

 of the attractions and repulsions which determine the functions 

 A and /(D), I have endeavoured to represent those functions by 

 empirical formulae, deduced respectively from the experiments of 

 M. Regnault on what he terms the coefficient of dilatation of 

 pases at constant volume, which ought rather to be called the co- 

 efficient of increase of elasticity with temperature, and from his 

 experiments on the compressibility of elastic fluids at constant 

 temperature. 



From the data thus obtained I have calculated, by means of 

 the theory, the coefficients of dilatation of pases under constant 

 pressure, which, as a test of the accuracy of the theory, I have 

 compared with those deduced by M. Regnault from experiment. 



(23.) The mean coefficient of increase of elasticity with tem- 

 perature at constant volume between 0° and 100° of the Cen- 

 tigrade thermometer is found by dividing the difference of the 

 elasticities at those two temperatures by the elasticity at 0°, and 

 by 100°, the difierence of temperature. It is therefore repre- 

 sented by V —V 



==I^' (22) 



where E represents the coefficient in question, and Pq and P, 

 the elasticities at 0° and 100° Centigrade respectively. 



Now by equation (21), neglecting powers of - higher than the 



'^^*'^^'^^V^o=„4(l-^)+/(B) 



p _ D /'100°+C A \ „^. 



^'- m\ — 100*+ c J ■'■•^"'' 



whence -^(L + ^ „) (zv^ 



