INDEXED. 



THE 

 LONDON, EDINBURGH, and DUBLIN 



PHILOSOPHICAL MAGAZINE 



AND 



JOURNAL OF SCLE^QE. 



[SIXTH SERIES^ 



m %a 



MARCH 1903. N§JA ^ 

 . ^%*Jwjc-, 



XXVII. On the Free Vibrations of Systems affected iviffi"i&M$P 

 Rotator?/ Terms. By Lord Kayleigh, 6.M., F.R.S.* 



BY a suitable choice of coordinates the expressions for the 

 kinetic and potential energies of the system may be 

 reduced to the forms 



Trrl^ + l^H-..., . '. . ' . (1) 



V=ic 1 ^ 1 2 + i^ 3 3 + (2) 



If there be no dissipative forces, the equations of free 

 vibration are 



«1$1 + £l$l + #L2$2 + j3 u <j> s + . . . = 0, "J 



«2<j>2 + ^2</> 2 + Ai*i + Pnfo +....= 0. L . • (3) 



where /i rs = — ft r ; and under the restriction contemplated all 

 the quantities /3 are small. 



If in equations (3) we suppose that the whole motion is 

 proportional to e i(T \ 



(c 1 — o-^^-f i<r0 12 <l)2 + i<r@i3<l>s + ' • - = 0' 

 (c 2 ~(7 2 ^)(/) 2 + io-^ 21 (/) l +i -/5 2 3^ + . • . = I ; . (4 N i 



and it is known that whatever may be the magnitudes of the 

 /3's, the values of the a's are real. The frequencies are equal 



to 0-/27T. 



* Communicated by the Author. 



Phil. May. S. 6. Vol. 5. No. 27. J/arcA 1903. X 



