401 Mr. G. Ghrystal on Bi- and Unilateral 



that first attracted my attention ; and the reason which seemed 

 to me to explain this suggested the existence of the first set 

 (I was not then aware of Poggendorff's description). Fact 

 III. shows that the phenomena have nothing to do with any 

 departure from Ohm's law in the case of induction-currents ; 

 and it seemed clear that the cause must be sought for in 

 alterations of the magnetism of the needle. 



Bilateral deflection w T as observed and minutely experi- 

 mented on by Poggendorff. Unilateral deflection does not 

 seem to have come under his notice, and has not, so far as I 

 am aware, been described elsewhere*. Poggendorff gave a 

 general explanation of the phenomenon he observed, attribu- 

 ting it to the effect of the alternating currents on the mag- 

 netism of the needle. His description has led others to sup- 

 pose that the effect never appears otherwise than in rendering 

 the needle unstable f. It will be seen, however, from the above 

 facts that this is not so. It is easy, moreover, to show that a 

 general theory of the phenomenon would predict this. 



Let a be the inclination of the needle to the plane of the 

 galvanometer-coil windings w T hen no currents pass, 6 its incli- 

 nation at any time ; then the magnetic couple tending to 

 bring the needle back to its position of rest may be represented 

 by sin (# — «), supposing there were an alteration of the mag- 

 netism in any position proportional to the magnetic force due 

 to the current resolved parallel to the needle (a more accurate 

 statement will be given below) ; then the couple due to this 

 tending to drive the needle from its position of rest would be 

 proportional to B sin 20, B depending on relative strengths of 

 electrical oscillations and magnetic field ; thus the force tend- 

 ing to bring the magnet back to position of rest would be pro- 

 portional to 



sin(0-a)-Bsin20. 



(We neglect the inductive action due to the permanent mag- 

 netic field.) 



Suppose we draw on two pieces of thin paper the curves 



y=sin0, (1) 



and 



?/ = Bsm20 (2) 



Then, by superposing the pieces of paper and looking through 

 them towards a light, we can see where the curves intersect 



* Since writing this paper I have learned from Lord Rayleigh that 

 similar phenomena have come under his notice. Beyond Poggendorff's, 

 I know of no published account of the matter. 



t Schuster, Phil. Mag. [IV] vol. xlviii. p. 257. Also Wiedemann, Gal- 

 vanismus, Bd. ii. 2, p. 284. 



