162 Mr. H. A. Rowland on the Determination of the Absolute 



divided into two principal parts — first, that due to the resistance 

 of air and viscosity of suspending- fibre, and, second, that due to 

 the induced current in the coils. The first resistance is usually 

 taken as proportional to the velocity, and thus assumes the vis- 

 cosity of the air to be the most important element. This is pro- 

 bably true in most cases where the motion is slow. This factor 

 is quite small compared with the second when the magnet is large 

 and heavy and the coils wound close to it, as in Kohlrausch's 

 instrument. Kohlrausch's principal error lies in the omission 

 of the coefficient of self-induction from his equations. 



For the sake of clearness, and because the subject is quite 

 often misapprehended, I shall commence at the beginning and 

 deduce nearly all equations. 



Let us proceed at first in the method of Helmholtz, using the 

 notation of Maxwell's e Electricity/ 



Let a current of strength I be passing in a circuit whose re- 

 sistance is R, and coefficient of self-induction L. Also let a 

 magnet be near the circuit whose potential energy with respect 

 to the circuit is IV. Let A be the electromotive force of the 

 battery in the circuit. 



The work done by the battery in the time dt is equal to the 

 sum of the work done in heating the wire, in moving the mag- 

 net, and in increasing the mutual potential of the circuit on itself*. 

 Hence we have 



Aldt=I*Rdt + I^*+b ^tr-dti 

 dt 2 at 



and if A is equal to zero, we find 



T 1 /dV _ dl\ 



r =~lW +L *> 



If we apply this to the case of a magnet swinging within a coil, 



the angle of the magnet from a fixed position being x, we have 



dV . 

 since -j- is the moment of the force acting on the magnet with 



unit current and maybe denoted by q, 



^-Wi^y « 



where my R is Kohlrausch's w. 



This expression differs from that used by Kohlrausch in the 

 addition of the last term, which is the correction due to self- 

 induction. The last term vanishes whenever the magnet moves 

 with such velocity as to keep the induced current constant ; but 

 in the swinging of a galvanometer-needle it has a value. 



* See remarks in Maxwell's ' Electricity,' art. 544, near bottom of page. 



