THE 

 LONDON, EDINBURGH, and DUBLIN 



PHILOSOPHICAL MAGAZINE 



AND 



JOURNAL OF SCIENCE. 



[FIFTH* SERIES.] 



MA Y 1886, 



LI. The Reaction upon the Driving-Point of a System 

 executing Forced Harmonic Oscillations of various Periods, 

 with Applications to Electricity. By Lord Rayleigh, 

 D.C.L., F.R.S.* 



THE object of the present communication is to prove 

 some general mechanical theorems, which may be re- 

 garded as in some sort extensions of that of Thomson relating 

 to the energy of initial motions. The question involved in 

 the latter may be thus stated f: — 



" Given any material system at rest. Let any parts of it 

 be set in motion suddenly with any specified velocities possible, 

 according to the connections of the system ; and let its other 

 parts be influenced only by its connections with these. It is 

 required to find the motion." And the solution is "that the 

 motion actually taken by the system is that which has less 

 kinetic energy than any other motion fulfilling the prescribed 

 velocity conditions." On the other hand, if the impulses are 

 given,, a theorem of Bertrand tells us that the kinetic energy 

 is the greatest possible. 



For our present purpose we suppose the system to be set 

 in motion by an impulse of one particular type, which we 

 may call the first. The impulse itself may be denoted by 

 fj^idt, and the corresponding velocity generated by ^ 

 Under any given circumstances as to constraint, the velocity 

 and the impulse are in proportion to one another ; and the 



* Communicated by the Author. 



t Thomson and Tait's 'Natural Philosophy/ §§ 316, 317. 



Phil. Mag. S. 5. Vol. 21. No. 132. May 1886. 2 D 



