432 The Hon. J. W. Strutt on an Electromagnetic Experiment. 



rather complicated*. However, we are concerned principally 

 with the first part of the electrical motion, the manner in which 

 the currents wear down under the action of resistance being of 

 subordinate importance. Now it appears that, if the motion be 

 decidedly of the oscillatory type, the first few oscillations will 

 take place almost uninfluenced by resistance ; and on this suppo- 

 sition the calculation becomes remarkably simple. 



L, M, N being the induction-coefficients, as before, let the 

 total flow of electricity in the two circuits from the moment of 



fi it tin 

 the break be x, y, so that the currents at any moment are — , -4 . 

 >in - rlt at 



Then the equations to the currents are 



^&+f=°> w 



M £ +N S =°> w 



where S is the capacity of the condenser. 

 Eliminating y, we get 



/ T M 2 W 2 ^ x 



The oscillation in the primary wire is accordingly the same as if 



the secondary were open and the self-induction changed from L 



M 2 

 to L ~-. (2) gives immediately the connexion between <2?and?/, 



, , dx XT dy 

 M -j- + N ■£ = const,, 

 dt dt 



which shows that the currents in the two circuits oscillate syn- 

 chronously, the maximum of one coinciding in time with the 



dy 

 minimum of the other. Since -~ =0 at the moment of break, 



dt 



dx dv 

 the constant of integration must be equal toM-r-; -j- denoting 



Clin atr\ 



the value of the primary current at or before the break. Ac- 

 cordingly 



dy _ M (doc dx\ _ 



di ~N\dF ~di)' 



fi i fi IT 



so that when after half an oscillation -r- = j-j 



at dt Q 



dy _ M dx 



~di~ N a% 



* It would depend upon a cubic equation. 



