336 Lord Rayleigh's Comparison of Methods for the 



would arise in respect of errors in the measurement of the coil ; 

 but an almost fatal uncertainty would be introduced from the 

 influence of self-induction. 



The important advantage of III., obtained, as I believe, 

 without any really important sacrifice, arises only when the 

 inductor is set into uniform rotation. In II., if the connexions 

 were maintained without a commutator, the current in the 

 galvanometer-coil would be alternating, and therefore unsuit- 

 able for measurement with a magnetic needle ; but in III., 

 although the current in the coil itself alternates, the reversal 

 of the coil relatively to the needle causes all the impulses to 

 operate finally in the same direction. When, therefore, the 

 coil is caused to revolve in a periodic time small relatively to 

 that of the free vibration of the needle, a steady deflection is 

 obtained which varies inversely with the absolute resistance 

 of the coil. 



If we omit for the moment all secondary considerations, 

 although some of them may not be without importance, the 

 formula by which the resistance (R) of the revolving circuit 

 is given in terms of the mean radius (a), the number of turns 

 (n), the angular velocity of rotation (o>), and the angle of 

 deflection (</>), runs 



R = 7r 2 w 2 c/&)Cot </>; 



from which it appears that, in respect of errors arising from 

 the measurements of the coil, this method is much superior to 

 those hitherto discussed. There is only one linear quantity 

 concerned; and the error committed in its determination enters 

 but singly into the final result. Indeed we may say that in 

 this respect no improvement is possible, unless it be in the 

 direction of substituting for the mean radius of a coil of 

 several layers some other kind of linear quantity more easy to 

 deal with. 



In requiring the absolute measurement of angle, II. and 

 III. stand precisely upon a level. 



The time of vibration in the experiments of MM. Weber 

 and Zollner was 17 seconds or 30 seconds — none too long 

 relatively to the time (2 seconds) occupied in turning the 

 inductor. If we suppose the coil to be uniformly rotated at 

 the rate of, say, 2 revolutions per second, there would be 68 

 or 120 impulses upon the needle in the time of 1 vibration. 

 It would no doubt be a great exaggeration to represent the 

 increase of sensitiveness as being in any thing like this pro- 

 portion, since by the method of recoil it is possible to make 

 several observations of impulses during the time required for 

 one observation of steady deflection. Nevertheless it cannot 



