( 345 ) 



We may write for the displaceiiicut in tlie most general case We sliall 

 liave to consider 



3 n, , a no , 3 y,,, , 



where each term represents a vector ahing the surface in the manner 



indicated in § 4, so that Hias different meanings in the different terms. 



The potential and the kinetic energy will now be found to be 



U= k flu pi~ + i 022^2^ 4- i 033^32 + etc. . . + 



+ ^hiPiPi + «i3Pi?>5 + etc., 

 ^' = Ï hi h' + h hih' + 4 hs i':^ + etc. . . + 



+ ^12 i'l h + ^13 P\ P-i + etc., 

 where 



Cfi,.= -'h, I y~L^dfo, a^, = A,, i y,,^ Y,,, do), 

 bi,^ = Bi, I Y~^^ (ho, h^, = /?/, I Yi,^ Y,,, d(o . 



As long as we limit the investigation to tlie vibrations of order /i, 

 we may ignore tlie other degrees of freedom ; we may then consider 

 the 2 /* + 1 coefficients pi, p-x, p-.i ... as the general coordinates. 

 The equation of motion for the coordinate /^ will be 



-1 flL\ - _ 1£ . 



dt \ 3/v / 3/v 



it w'ill take the form 



d /a7'\ dU 



dt \ d/'iM / 3,0^ 



Q., (0) 



if, besides the forces which we have considered thus far, there are 

 other forces whose general components are Q^- 



§ G. If an electrified system be vibrating in a magnetic field, its 

 parts will be acted on by electromagnetic forces proportional to the 



