722 Sir J. J. Thomson on some Optical Effects 



Similarly, a term in -~ represented by sin-— {vt — a? ) 

 dt A 



would give rise to vibrations represented by 



. 2ir, , 2tt 2tt , 



sin -(vt — x ) + x„-^- cos — —(vt— o? ). 

 A- A A, 



Treating the collection of electrical charges as a rigid 



body, we proceed to calculate the value of 2<? ~ due to the 



rotation of the molecule produced by the couples arising 

 from the electrical forces in the light wave. 



Let .the principal axes of inertia of the molecule be taken 

 as the axes of ,i y , y', z' ; let (l u m u ni), (Z 2 , w? 2 , ^2)5 (hi m $-> ^3) 

 be the direction cosines of those axes with respect to the 

 fixed axes x, y, z. 



Then the moment of the forces about the axis of x' is 



Xel Z + -, . xj(n 3 y'~n 2 z') 



Now X = lyC* + l 2 y' + l 3 z\ 



hence the moment of the forces about x 



= Z O 3 2«/-« 2 S<..t') + ^(«,M-n 8 N). 

 i L = %e(l 1 .v'.v' + h.' / >/ + l i y~'), 



Similarly the moment of the forces about the axes of 

 ?/ and 2' are respectively 



ZoO iSez' - w t 2«*') + ^ t N -* S L), 



2-7T 



Let Z = cos ^O't — ®o)- 



If A, B, C are the moments of inertia of the molecule 

 about the axes x\ ?/, z', and o) 1? ft> 2 , ®3 the angular velocities 

 about these axes, we have, if we retain only the first powers 

 of &>!, ft> 2 , ft> 3 , and suppose that the only forces acting on the 



