98 Mr. K. H. M. Bosanquet on the Mathematical 



tion a diminution of the magnetic moment of the needle. I 

 think that this strange effect must be explained thus : — The 

 direct extra current of the coil, without magnetic effect in its 

 interior, momentarily increases the polarization of the pile, 

 whence a current of very perceptible depolarization in consequence 

 of the interruption; this current partially demagnetizes the 

 needle. We have here, therefore, to do with a reflex effect, 

 analogous to that of the condenser of the Ruhmkorff coil, 

 although incomparably more feeble. 



If the circuit contains two coils, P and Q, one very powerful, 

 the other very feeble, the direct extra current of P and the reflex 

 action of the pile succeed each other in Q, and produce a very 

 singular effect. Interruption of the circuit augments greatly 

 the magnetic moment of a needle magnetized in Q by a great 

 number of passages ; but the same operation diminishes the 

 magnetic moment of a strongly magnetized needle placed in Q 

 with its south pole to the left of the principal current. This 

 effect is much more pronounced when P contains a core of soft 

 iron. Example : — 



Moment. 

 Needle magnetized in Q by passages . . 1*16 



Interruptions 11*10 



Needle strongly magnetized .... 36*28 

 Interruptions 35*40 



Thus one and the same complex instantaneous current mag- 

 netizes needles which were not magnetized, and partially de- 

 magnetizes needles which were strongly magnetized. The same 

 thing can be easily reproduced by the alternation of a conti- 

 nuous direct current and a weaker inverse current. 



We thus see that, in certain cases, magnetized and non- 

 magnetized steel needles permit us to analyze a complex in- 

 stantaneous current, and recognize in it a change of sign. 

 [To be continued.] 



XII. On the Mathematical Theory of Mr. Baillie Hamilton's 

 String- Organ. By R. H. M. Bosanquet, Fellow of St John's 

 College, Oxford*, 



THE investigation which follows was completed more than a 

 year ago (1873). The endeavour was then made to test 

 the theory by experiment; but difficulties were encountered 

 which, notwithstanding the assistance kindly afforded by Mr. 

 Hamilton, were not got over. The subject has now been brought 

 repeatedly before the public by Mr. Hamilton, who has read 

 * Communicated by the Author. 



