84 Messrs. Ayrton, Mather, and Sumpner 



An important and difficult question to decide is whether the 

 factor of merit of a galvanometer should be stated for a con- 

 stant periodic time of oscillation of the suspended system, or 

 for a constant controlling-moment for unit angle-deflexion, or 

 for a constant controlling-field irrespective of the magnetic 

 moment of the suspended system. The first condition is the 

 most simple to realize experimentally with different instru- 

 ments, and the results so obtained are the most convenient for 

 use in subsequent calculations ; this condition is, further, the one 

 most easily understood. We therefore give, in columns 3 and 



4, the values of D and S, which respectively denote the deflex- 

 ion per micro-ampere and the swing per micro-coulomb, each 

 in scale-divisions, when the period is 10 seconds and the scale- 

 distance is 2000 scale-divisions. The corresponding values at 

 any other period T are of course DT 2 /100 and ST/10. It 

 would, however, be unfair to rest satisfied with the results 

 given in these tables for the purpose of comparing different 

 galvanometers. For a galvanometer having a large mirror, 

 and intended to be used at a considerable distance from the 

 scale, would appear to be an inferior instrument, because on 

 the one hand the large moment of inertia of the mirror would 

 necessitate the controlling-moment being large to reduce the 

 period to 10 seconds, while, on the other hand, the magnifica- 

 tion arising from the much greater distance that separated, 

 in practice, the scale from this particular galvanometer would 

 have no weight in the values given in the columns for D and 



5. We have therefore given in column 2 the values of M, 

 which are the millimetres deflexion per micro-ampere when 

 the period is 10 seconds and the scale placed as in the ordinary 

 use of the instrument. We have further, in the following way, 

 reduced the numbers to their corresponding values under the 

 condition of constant controlling-moment, the condition of 

 constant controlling-field being rejected, because it is inappli- 

 cable to instruments of the d'Arsonval type. 



The periodic time T equals 



Moment of inertia x sin 



v- 



Controlling-moment for a deflexion ' 

 therefore, in order to obtain the comparative deflexions that 

 would be obtained with the same controlling-moment per 

 unit angle, we must find the deflexions that would be pro- 

 duced with periodic times proportional to VI, where I is the 

 moment of inertia of the suspended system, the values of 

 which for the various galvanometers are given approxi- 

 mately in C.G.S. units in column 6. Hence, to obtain the 

 values in columns 7 and 8, which give numbers respec- 



