Resistance according to an absolute Standard. 239 



is directly proportional to the magnetism M, to the cosine of the 

 angle <£, and to the intensity, and is inversely proportional to 

 the diameter r ; and if i is expressed in absolute measure, is de- 

 termined by 



~d6 2ttM . 



D-£ = . i cos 6. 



dt r r 



For small oscillations in which <f> differs little from 0, we have 



_2ttM d<j> 



e ~~r~"dt' 



^dcb 2ttM . 



dt r 



If K is the inertia of the oscillating magnet, upon which the 

 directive force MT, arising from the horizontal part of the 

 terrestrial magnetism, acts, the equation of its motion becomes 



' ddd> MT J D dd> 



and hence by integration, 



-— //MT 1DD\ 



■^7 is the logarithmic decrement on the natural system of the 



diminution of the amplitude of oscillation reduced to the unit of 

 time : hence if t is the time of oscillation under the influence of 

 deadening, 



Dt_ttM dt_ . 

 A_ 2K~ rK'd<f>' n; 

 and the intensity of the current is 



._ rK\ # 

 % ~ ttMt' dt' 



From this we obtain for calculating the resistance, 



, e 27T7rMM 

 i rrKK 



From the above equation for (/> we get for the determination of 

 the time of oscillation under the influence of the deadening, 



//MT 1DD\ //MT \\\ 



T V U ~i kiJ = 7r=T V \ic-^h 



from which 



