132 Prof. C. V. Raman and Mr. Ashutosh Dey on the 



electromagnet alone is excited, the wire remains practically 

 at rest. But this state of rest is unstable, and, gradually, a 

 vibration develops and attains a large amplitude, its frequency 

 being a submultiple of the frequency of the field. Investigation 

 by the method of vibration- curves shows that, in the motion 

 thus excited, the components having the same frequency as 

 the field or any multiple thereof are practically or entirely 

 absent. Records (not reproduced) have been obtained of the 

 motion at various selected points of the wire for these and 

 other cases. 



Theory of the Experiments. 



The attractive force of the electromagnet in the experi- 

 ments described is exercised over a very small region of the 

 wire which may practically be treated as a mathematical 

 point. The essential feature of the case which enters into 

 the explanation of the phenomena noticed above is that this 

 attractive force is not a simple function of the time, but 

 depends also on the position, at the particular epoch, of the 

 point on the wire with reference to the pole of the electro- 

 magnet. In other words, the expression for the maintaining 

 force is not independent of the form of the maintained 

 motion. For our present purpose, w T e may write it as the 

 product of two functions, one of which involves only the 

 time and the other is determined by the position of the 

 wire in the field. Thus, 



Force = F(y )f(t) 



"=°° rlirrnt \ 



= h(y ) Z a„cosl -^— — e n U 



where T/r is the periodic time of the field and y is the 

 displacement of the wire at the point x (opposite the pole of 

 the electromagnet) from its position of equilibrium. y being- 

 positive when measured towards the pole, F(?/ ) increases 

 with y , and may be taken to be unity when y = 0. We 

 may expand F( t y ) by Taylor's theorem and write it in the 

 form (l-t-by + cy 2 + &c). If the force varies inversely as 

 some power of the distance between the pole and the wire *, 

 it may readily be shown that the constants b, c, &c, are all 



* From the measurements made by Klinkert over a limited range, 

 it would appear ihat the attractive force on the wire varies inversely as 

 the square root of the distance. 



