154 HENRY A. KOWLAND 



from the earth-inductor is uniform through a time t'", and the com- 

 plete solution then depends on the elimination of nine quantities from 

 ten complicated equations, and which can only be accomplished approx- 

 imately. If f is the true value of the angular velocity, as given to the 

 needle by the earth-inductor, and f is the velocity as deduced from the 

 ordinary equation for the method of recoil, I find 



where A is the logarithmic decrement, the base of the natural system 

 of logarithms, T the time of vibration of the needle, and t the time 

 during which the uniform current from the earth-inductor flows. In 

 the actual case, the current from the earth-inductor is nearly propor- 

 tional to sin t, and hence it will be more exact to substitute 



/ / \2 /iir / / 



4 (--) I taiiitdt = l( 

 V * / / v * 



in the place of t 2 . The formula then becomes 



This modification is more exact when ), is small than when it is large, 

 but it is sufficiently exact in all cases to give some idea of the magni- 

 tude of the error to be feared from this source. Kohlrausch does not 

 state how long it took him to turn his earth-inductor, but as T = 34 



seconds, we shall assume -^ J^ and as / = \ nearly, we have 



-?- = 1-0008, 



r 



which would diminish the value of the resistance by -16 per cent. 



As the time we have allowed for turning the earth-inductor is prob- 

 ably greater than it actually was, the actual correction will be less than 

 this. 



The correction for the extra current induced in the inductor and 

 galvanometer, as given by Maxwell's equation, 9 has been shown by 

 Stoletow to be too small to affect the result appreciably. 



We may sum up our criticism of this experiment in a few words. 

 The method is defective because, although absolute resistance has the 



dimensions of - , yet in this method the fourth power of space and 

 9 ' Electricity and Magnetism,' art. 762. 



