701 



cos lo t ^ 1 and for the second cos m t ^ — 1 so that we find, 

 using (8) 



B,= — /, (ii; 



Instead of (6) we now get the equation 



B, ros ivt = Qit 4- 0« + P«, . . ... . . (12) 



the periodic solution of which is 



B, 



«^ CO.S (cot I'), (13) 



u 

 if the constants u and v are determined by 



H COS V =z Ut)„^ — U)^) Q I 



' ^ (14) 



U sill V = 2 X M (^ ) 



Here the qnantitj ii, to which we sliall give the positive sign, 

 determines tlie amplitude whereas the phase of the oscillations is 

 given by the angle v. For the amplitude, which we shall denote 

 by |«|, we find 



B, U Is 



\a\=^ = y, , , .... (15) 



For <u = («0 it becomes a maximum |«|,„, viz. 



Ills 

 |«|,„ = --^ (16) 



As to the phase, we first remark that according to (14) v ^ - 

 for to = (o^. If the frequency of the alternating current is higher 

 than that of the cylinder, we have v^- and in the opposite case 



v<C^- When lo is made to differ more and more from «o., the 



phase V approaches the value .-r in the first case and in the second. 

 If the constant of damping x is small we may say that these 

 limiting values will be reached at rather small distances from co^ 

 already. In our experiments this was really the case and we ma}- 

 therefore say, exce[)ting only values of to in the immediate neigh- 

 bourhood of «>„ that V ^= ST for to ^ co„ and y =r for to <^ (t>„. 

 Taking into account what has been said about the positive direction 

 one will easily see that, if the current ^ and the deviation a had 

 the same phase, the cylinder would at every moment be deviated 

 in the direction the current in the coil has just then. In reality the 



