460 OHM ON THE GALVANIC CIRCUIT. 



places of contact, by the springing over of which, in the direc- 

 tion of the abscissae, we arrive from the greater to the smaller 

 electroscopic force, are to be regarded as positive, in the con- 

 trary case as negative, where, however, it must not be over- 

 looked that every positive force has to be taken as greater than 

 every negative, and the negative as greater than the actually 

 smaller), we obtain ^ 



a=f {l+l) + d -c, 

 and 



a! =fl-fl + c-d, 



whence directly results 



« + «'=//+/'/'. 

 But now at each of the places of contact when x and w repre- 

 sent the power of conduction and the section of the part P, and 

 x' and oJ the same for P', in accordance Avith the considerations 

 developed in § 13, there arises the conditional equation 



(du\ _ , I /du'\ 



\dx) ~ ' \dx)' 



where ( -7— | and ( -7— ) represent the values of ~j- and -r— 

 \ax/ \dxj ^ dx ax 



at the place of contact. From the equations at the commence- 

 ment of this paragraph for the determination of the electroscopic 

 force in each single part of the circuit, we, however, obtain the 

 value of X to be allowed to each, 



4^=/and^=/', 

 dx '' dx •' ^ 



which converts the conditional equation in question into 



■>(.mf=. y.' uci' f. 



From this, and the equation a -i- a' =fl + f'V just deduced 



from the tensions, we now find the values of /and y' thus ; 



(a+a') x' eo' 



/ = 



x' O)' / + X w Z" 



^ _ {a + g') X to 



•^ "~ x' Co' / + X CO Z" 



and with the help of these values we find 



K Cli' L -\- X. w U 



Hence the electroscopic force of the circuit in the part P is ex- 

 pressed by the equation 



