106 Prof. T. Carnelley on an Algebraic Expression of 



In Table II. is given not only the atomic weights as 

 accepted by the best authorities and as calculated by the 

 formula A = 6*6(m + \/v), but also the specific gravities*, 

 together with the specific volumes as calculated both from 

 the experimental and from the calculated atomic weights, by 

 dividing each of these respectively by the corresponding 

 specific gravities. From the Table it will be seen that the 

 specific volumes as found by each of these two processes agree 

 closely. Further, if two curves be constructed in the manner 

 first suggested by Lothar Meyer, by taking in the one case 

 the experimental atomic weights as abscissae, and the corre- 

 sponding specific volumes as ordinates, and in the other case 

 the atomic weights calculated from A = 6*6(m + -yV) a s 

 abscissae and the corresponding specific volumes as ordinates, 

 then the result represented in Diagram I. will be obtained, in 

 which the dotted curve, being constructed from the experi- 

 mental atomic weights f , may be called the experimental curve; 

 while the continuous one, being constructed by using the cal- 

 culated atomic weights, may be called the calculated curve. 



It will be seen from both Table II. and from Diagram I. 

 that the greatest differences between the calculated and ex- 

 perimental atomic weights occur chiefly at the end of series 

 IV., v., and VII., and at the beginning of series xi. 



It has been shown that in the equation A = c(m 4- \/v) the 

 constant c has a mean value of Q'Q. Supposing that there is 

 any truth in the equation, what is the meaning of the constant 

 6* 6 ? This number at once suggests the constant 6*4, obtained 

 according to Dulong and Petit's law, by multiplying the 

 atomic weight by the specific heat. If in the equation 

 A=c(m-f- s/v) we assume that the constant c represents the 

 atomic heat, then, 

 Atomic weight = atomic heat x (in + \/v) 



= atomic weight x specific heatx (m+ */v) ; 

 1 = specific heat x (in + V v), 



or specific heat = -r=- 



m+ V v 



If the specific heats of the several elements be calculated 

 by this equation, we find that in almost all cases the calcu- 

 lated numbers agree very closely with the experimental specific 

 heats. This will be seen from the following Table : — 



* Taken from Lothar Meyer's Mod. Theories, p. 123 ; translated by 

 Bedson and Williams. 



t It is identical with Lothar Meyer's curve. 



