Galvanometer Deflection. 405 



for different relative positions. These points of intersection 

 correspond to the positions of equilibrium of the needle ; and 

 the stability or instability of the equilibrium is seen at a glance. 

 For example, take the case a = 0. The points corresponding 

 to = in (1) and (2) must be superposed ; thus, for a large 

 value of B we have fig. 1. Here 0, P, P', Q, and Q' give 



Fig. 1. 



positions of equilibrium ; but is obviously unstable, because 

 on going to the right (increasing 6) the curve (2) lies above 

 the curve (1), i. e. the force tending to increase 6 preponde- 

 rates ; and similarly, if we go to left (decrease 6), the force 

 tending to decrease 6 preponderates. Similarly, Q and Q' are 

 unstable positions ; but P and P' are stable positions symme- 

 trically situated with respect to 0. The positions of P and P' 



IT 



lie nearer a point distant ^ from 0, the greater B. This case 



is best illustrated experimentally with a tangent-galvano- 

 meter of the usual construction, where the motions of the 

 needle can be traced all the way round. We have thus ex- 

 plained Poggendorft's case, which is the limit to the state of 

 the phenomenon*. 



Next, suppose B to be small, we have fig. 2. The positions 



Fte. 2. 



-7T 



* There are some points in PoggendorfPs observations which did not 

 appear in mine : but the difference might arise from the inductive influence 

 of the earth being sensible in his experiments, which was not the case in 

 mine. 



