276 



Dr. Gr. J. Stoney on the Resolution of Light 



of the loops occurring upon the planes where (<£ 2 ~~ 4>i)* v 

 (which is of cipher dimensions) is one of the series 0, 1, 2, 3, 

 &c, and with nodes lying upon the planes that are midway 

 between these positions. This may be represented diagram- 

 matically by fig. 10, in which the axis of Y is supposed to 



Fia-. 10. 







a 



+ e, 



a. 



a 



■x 



mr 



% 





Zero 

 of<P 



be perpendicular to the plane of the paper; and in which the 

 lower figure represents a spectrum of wave-frequencies. 

 Draw the planes « 1? « 2 , fce. parallel to the plane YZ and at 

 the distances furnished by the equations 



1 2 3 . 



a?= -k, x— s-, ./•= ~. (fee.,. ... (7) 



8' 



where 8 is an abbreviation for <j> 2 — <l>i- Then the middles of 

 the loops of the rigid undulation represented by eqn. (6) are 

 on these planes, and the nodes of that undulation lie on the 

 dotted planes midway between them. These latter planes. 

 <?i, e-2, H-i & c -j are accordingly the situations where the tran 

 versal of the waves 

 The nearest of the 

 e x and — e l3 viz. : 



1 



the situations where the 

 that form the undulation becomes cipher, 

 dotted planes to plane YZ are the planes 



28* 



una #= — - r 



28' 



(8) 



which, therefore, mark the limits of the central loop. 



Let us now indicate upon the spectrum the positions that 



