374 Prof. Ayrton and Mr. Mather on Galvanometers. 



It is to be noted, however, that the weakly controlled 

 system will take longer to return to zero, so that a longer 

 wait is necessary before another test can be made. On the 

 other hand, should the sensitiveness of the strongly controlled 

 instrument be only just sufficient to get the desired accuracy, 

 then half a period must elapse before the want of balance can 

 be detected, whereas the weakly controlled instrument would 

 have moved over a greater distance iu that time. Taking 

 the controls in the ratio of 4 to 1, and therefore periods as 

 1 to 2, the movement of the weakly controlled instrument 

 will be double that of the other in the case here considered. 

 In this instance therefore the long periodic time is advan- 

 tageous because it will show a very small want of balance 

 more quickly, but the advantage is somewhat discounted by 

 the longer time occupied in the return to zero. 



Undamped Motion. 



To consider the matter in further detail let us first take 

 the case of undamped simple harmonic motion. Assuming 

 the ratio of the controls to be as m 2 to 1, the periods will be 

 in the ratio of 1 to m. 



Fig. 2. _ 



Draw two circles touching at A, centres at B and C, and of 

 radii in the ratio of 1 to m 2 . Draw lines BP and CQ making- 

 angles ft and 7 with AC and such that /3= my. The distances 

 from A of N and M, the projections on AC of P and Q 

 respectively, will then represent the displacements from zero 

 after a given time of the short and long period galvanometers 

 respectively. From the figure (to scale) it will be seen that 

 these are nearly equal when the time is, say, one-sixth of a 

 period of the quick-moving system. And even when the 

 time is one-fourth of the period of the strongly controlled 

 instrument, the difference in the displacements is not very 



