Damping of Galvanometer Needles. 561 



so that the logarithm of the decrement to the base e, known 

 as the logarithmic decrement, is 





V p 2 — n 2 



The true periodic time, T, of the swinging system, that is to 

 say the periodic time it would have if the damping forces 

 were absent, is given by 



T = t " , 

 yV + A 2 



From the expressions above found for the observed periodic 

 time t and the logarithmic decrement \, we get 



t_ _ 2 41 



X ~ n ~~ JN ' 



so that the ratio £/X is independent of the strength H of 

 the controlling field, and will remain constant when t is 

 varied by altering this strength, provided I and N remain 

 constant. 



The time t for the reduction of the deflexion to — of its 

 original value is given by 



T = ilog e m-, 



and is therefore constant so long as t/X is constant, or, conse- 

 quently, so long as I and N remain constant. 



With a view to testing the conclusion arrived at by the 

 above reasoning, experiments have been made at the Central 

 Technical College, beginning in 1891 and continued at inter- 

 vals since that time, the results of which have shown a decided 

 discrepancy between theory and experiment. The method 

 adopted was to observe the periodic time and the corre- 

 sponding decrement with different strengths of controlling 

 field. Calculating out from these observations the values of 

 the ratio t)k, i.e. the ratio of the periodic time to the loo-a- 

 rithmic decrement, showed that in most of the instruments 

 tested the value of this ratio was not constant as indicated 

 by theory. As examples of the results obtained, three sets of 

 experiments on galvanometers of different types may be 

 quoted. 



The first set of experiments was made by Mr. Seaman in 

 1891, on a Mudford's Thomson galvanometer similar to that 

 illustrated in fig. 6 of Messrs. Ayrton, Mather, and Sumpner's 

 paper on ""Galvanometers" (Phil. Mag. July 1890, p. 70). 

 The suspended system consists of an aluminium wire haying 

 small magnets affixed to the upper and lower ends, and the 



