26 CLAUSIUS ON THE MECHANICAL EQUIVALENT 



Further, we have quite generally the equation 



j + g'=-(aV + ^V'), (31) 



wherein a and j3 are two positive constant quantities, which, like 

 k, depend upon the nature of the jar, and hence in the case be- 

 fore us, where we have simply to do with equal surfaces, 

 possess throughout the same value. For a battery of n jars, 

 and with the quantities Q and Gl' of electricity, both equations 

 pass into 



V-V'=-l®^' ...... (32) 



ns 2 ^ 



Q + Q'=-w(aV + ^V') (33) 



By means of these equations, in connexion with equation 

 (29), if any two of the quantities (28) be given, all the others 

 may be found. 



The experiments conducted by Dove and Riess consist in both 

 cases of two different series. In the first, the number of jars in 

 all the connected batteries was the same, but the number of 

 batteries was varied ; in the second, on the contrary, the number 

 of the batteries made use of remained constant, namely, always 

 two, but in each of these batteries the number of jars was varied. 

 Both series of experiments present many difficulties to a com- 

 parison with the theory. In the second series, however, these 

 are less considerable than in the first, and we will therefore com- 

 mence with the consideration of the second. 



The experiments were arranged as follows: — the batteries were 

 both insulated, and the inner coating of the first w^as connected 

 with the conductor of the electric machine, the outer of the 

 second with a Lane^s unit jar. The number of sparks from the 

 unit jar gave the quantity of electricity communicated to the 

 second outer coating, and we can set the potential function upon 

 this coating after the passage of each spark equal to zero, the 

 potential function of the quantity remaining in the unit jar being 

 neglected. 



There are therefore, as above required, two of the quantities 

 (18) known, and to deduce the others from these we can proceed 

 from the second outer coating to the second inner one, to the 

 first outer, and finally to the first inner coating. If the quantity 

 of electricity as measured by the unit jar be — Q, and thenum- 



