368 Mr. Meikle on the Law of Temperature. [Nov 



which are obtained from Equation (A) by making p and ^ alter- 

 nately to vary with ^, whilst the other is constant. 



Let the point A represent — 448° F. or — 266*7° cent, and 

 let the temperature be reckoned on the straight line A B as on 

 the common scale of an air thermometer. Also let C I be a 

 line of such a nature, that any ordinate as B C, E F, H I, &c. 

 may be respectively proportional to the specific heat of a mass 

 of air under a constant volume at the temperatures B, E, H, &c. 

 so that the intercepted areas will denote the corresponding 

 variations in the quantity of heat, under a constant volume. But 

 MM. Gay-Lussac and Welter have ascertained by experiment, 

 that the specific heat of air under a constant pressure, exceeds 

 that under a constant volume, in a constant ratio, which call 

 that oi k '. 1 ; wherefore, if these ordinates be every where 

 increased in tiiat ratio, another line G D passing through their 

 extremities must be of the same nature with C I, whatever that 

 may be, and the intercepted areas, of course, to the former as 

 kio 1. 



Let B D X 1° be the specific heat of a mass of air under a 

 constant pressure, and let its temperature be raised from B to 

 E, under the same pressure : then area BDGE will denote the 

 increase in the quantity of heat, and E G x 1°, the specific heat 

 under a constant pressure at the temperature E. Now E G : 

 EF :: A; : i, wherefore E F x 1° will be the specific heat of the 

 dilated mass at the temperature E, under a constant volume. 

 But E F X 1° would still have been the specific heat had the 

 air under its original volume been raised to the temperature E ; 

 and because EF : EG :: 1 : A:, E G x 1° would have been 

 the other as before. Hence the const aut ratio of the specific 

 heats renders them independent of the actual density or pres* 



sure ; and, therefore, j- and j- are constant quantities. From 



which it appears, that the algebraic expressions for the specific 

 heats vary inversely as 1 + a ^ ; or that any ordinate B C, or 

 B D, is inversely as A B, which is the well-known property of 

 a hyperbola ; and, therefore, C I and D G are both hyperbolas 

 having A for their centre, and A H for an asymptote.* 



Hence, as before, the variations of volume, under a constant 

 pressiire, or the variations of temperature on the common scale, 



♦ The quantities — and -p are only linear expressions, such as B D and B C. 



To be complete, they must be multiplied by the particular linear degree of the scale to 

 which they belong. 



The result which I have obtained is the only one which can make the algebraic and 

 geometrical values of the specific heats agree together. The hypothesis of M. Laplace 

 gives two inconsistent values to both quantities, even algebraically, and a third different 

 from these, but the same with mine geometrically. (See Annales de Chimie et de Phy- 

 sique, xxiii 339, and Mecanique Celeste, livre xii. 98.) 



