OHM ON THE GALVANIC CIRCUIT. 449 



X {Mi—u) dt 

 d X 

 is the quantity of electricity passing over from M^ to M when 

 the expression is positive, and from M to M, when it is nega- 

 tive. The total change of the quantity of electricity which the 

 disk M undergoes from the motion of the electricity in the in- 

 terior of the body in the particle of time d t, is consequently 

 k{u' + Ui — 2u) d t 

 dx ' 



and an increase in the quantity of electricity is denoted when 

 this value is positive, and when negative a diminution of the 

 same. 



But according to Taylor's theorem 



, du , d^u dx^ 

 -^ = '^ -"r -r- ' dx + ^—^ . —- -\- , 



-ci^d X dt. 



dx' d x"^ ' 2 



and in the same way 



_ du ^ d'^u dx^ 



' dx dx^ 2 ' 



consequently 



u' + u, = 2 u + —. — 3 dx^. 

 ' d X- 



According to this the expression just found for the total change 



of the quantity of electricity present in the disk M is converted 



during the time d t into 



d'^u 



where x represents the power of conduction which prevails from 

 one disk to the adjacent one, which we suppose to be invariable 

 throughout the length of the homogeneous body. It must here 

 be observed, that this value x is, on account of the infinitely 

 small distance of action, proportional to the section of the cylin- 

 dric or prismatic body ; if therefore we denote the magnitude of 

 this section by w, and separate this factor from the value x, 

 always calling the remaining portion x, the former expression 

 changes into the following : 



X CO——, dx dt, 

 dx^ 



in which x now represents the conductibility of the body inde- 

 pendent of the magnitude of the section, which we will term 

 the absolute conductibiUty of the body in opposition to the for- 

 mer, which may be called the relative. Henccforw^ard wherever 



