206 M. E. Edlund on the Nature of Galvanic Resistance. 



effected also for the case in which the cross section and the con- 

 stitution are different at different parts of the circuit. 



4. Ohm's law can be deduced, in accordance with the general 

 principles of mechanics, in the following manner : — Electromo- 

 tive force is measured, just like other motive forces, by the acce- 

 leration which it can impart to the unit of mass in the unit of 

 time. If no galvanic resistance existed to obstruct the motion, 

 the velocity would increase perpetually. But there is a resist- 

 ance in the conduction, which sets a limit to this increase. If 

 the velocity has become constant, the acceleration by the electro- 

 motive force is annihilated by the resistance. The two must 

 therefore be equal. If ds is the increment of the current-inten- 

 sity in the time dt, E the electromotive (accelerating) force, ms 

 the total resistance with the current-intensity s, and L the length 

 of the entire conduction, we have 



L-T-=E~-ms*. 

 dt 



If, now, the current has become constant (that is, ds=0), then 



E 



m 



The deduction we have given of Ohm's law shows that it does 

 not hold before the current has become constant. When the 

 preceding equation is integrated and the time from the first 

 commencement of the current calculated, we obtain the follow- 

 ing formula for the increment of the current — 



s=— (1— e <*). 



Herein no account is taken of extra currents; so that the 

 formula holds only on the hypothesis that the path of the cur- 

 rent is so constituted that no currents of that sort arise on its 

 being closed. The formula shows that the less the length of the 

 current-path, and the greater the resistance for the intensity 1, 

 the more quickly does the current become constant, but that the 

 electromotive force has no influence on the time required for this. 



5. We will now adduce some applications of the formula 



* Because the total length of the conduction L is equal to the sum of all 

 its parts (£ x -f l 2 -\- l 3 + ...), its total volume is a-J,^ a 2 l 2 -\- a 3 l 3 -\- ... , if those 

 parts have respectively the cross sections a lt a 2 , a 3 , &c; and multiplying 

 this sum by 8, we obtain the total mass of aether which is in motion. If 

 now the increments of the velocity in the time dt are expressed by dh 1} dh 2 , 

 dh 3 , &c. respectively, the total mass of aether receives in the time dt an in- 

 crement of its quantity of motion which is expressed by ^(ajidh^ a 2 l 2 dh 2 

 ■\- a 3 l 3 dh 3 -\- ... ). But 8a 1 dh l =da 2 dh 2 =iba 3 dh 3 r=ds, by which, therefore, 

 the increment of the total quantity of motion becomes equal to hds. 



