178 Mr. T. R. Edmonds on the Elastic Force of 



deviates from the true formula at the third term exactly twice 

 as much as approximate formula No. 1 does. 



The Roche formula, as given above, differs considerably from 

 the Roche formula used by M. Regnault. In the correct for- 



mula, A= ku and M= —are constant for all temperatures, begin- 

 ning with £ = 0. In the modified formula used by M. Regnault 

 and others, A and M are made to vary (in a small degree) accord- 

 ing as t varies. For example, in the pure Roche formula, where 

 P is taken equal to unity at —20° C, the value of A or ka. is 



•037679, and the value of M or - is -0044973. In the mixed 



a 



Roche formula, constituted by changing A and M, in order to 

 force the formula to give true values of P at 100° C. and at 

 220° C. (as M. Regnault has done for the Roche Table, con- 

 tained in column 5 of Table II. hereunto annexed), A is changed 

 to -038232, and M to -004774. The consequence of these alte- 

 rations of the constants belonging to the real curve at its origin 

 is to produce a fictitious curve of great irregularity, more espe- 

 cially at points near those of forced coincidence with a real curve 

 belonging to an equation whose constants are really constants. 

 As an instance of the defect of the Roche formula constituted 

 as above, I may mention that the true elastic forces (yielded by 

 the new formula) at temperatures —20° C. and 0° G. are -92 

 and 4*52 millims. respectively, whilst the elastic -forces at the 

 same temperatures given by the Roche formula constituted as 

 above are '92 and 4'59. The error thus found to exist in the 

 Roche formula is 4'59— 4*52, or -07 millim. at the temperature 

 Q°C, when —20° C. is taken as the point of departure. This error 

 is a near representation of the whole of the discrepancy, at 

 temperature 0° C, between the forces given by the new formula 

 and by M. Regnault in his adjusted Table. 



A comparison may be usefully instituted between the laws of 

 variation with temperature of the elastic force (P) of steam of 

 maximum density and of the elastic force (p) of a perfectly elas- 

 tic gas or vapour of constant density. It is generally acknow- 

 ledged that the equation p = 1 + - represents the elastic force of 



a perfectly elastic gas of constant volume and density when 

 raised to the temperature /, compared with a unit of elastic 

 force possessed at temperature 0°. We have consequently, on dif- 

 ferentiating, 



, , dp a 



P 1+- 

 a 



