of Light and Heat in uncrystallized Media, 341 



from which it appears that of the three disturbances either 

 one gives rise to a vibration, and two do not, or vice versd. 



Let us then examine the circumstances which will deter- 

 mine each of these results respectively. 



We have conceived that the action of a particle in advance 

 of the given particle is to draw it forwards, which is in fact 

 supposing the force attractive. 



Now, V =i X, -^ — IT sm^ -- — , 



where r', Sjt', sy, are partictdar values of the unaccented 

 quantities. 



Now, for every value of 8 y' there is a corresponding value 

 of Ix' equal in magnitude, and the term in the series will 

 therefore be ^ 



S pj sm -^, 



8y being now a particular value of ix', and so on. 

 Hence v^ consists of the sum of a series of the form 



:, { ?i^!=i^sin« 4^ + ^^:!=ii^%in' '4^} 



= 2Vr»^^(sin^^-sin^^). 



And, restricting ourselves to the same limits as before, if lyf 



be greater than 8 x' sin^ — -^ is greater than sin® ^ and 



the above expression is clearly negative. Also it is perfectly 

 evident, from what we have before observed, that the sign of 

 the whole will be the same as that from the particles within 

 the range of the first half-wave. 



Hence v^ is negative, or a vibration in the direction of 

 transmission impossible : and since t^^ = v"^ = — ^v\ the 

 vibrations which result from disturbances perpendicular to 

 the direction of transmission are transmitted with the same 

 velocity whatever be the direction of disturbance. 



Hence the vibrations in a medium exerting attractive forces, 

 varying according to the inverse square of the distance, are 

 , necessarily transversal. 



In the same manner it may easily be shown that were the 

 force repulsive, the particles must vibrate in the direction of 

 transmission. Of the last conclusion, that repulsive forces give 

 rise to direct, and attractive forces to transverse vibrations, I 

 have offered a popular explanation as follows : 



" A series of repulsive particles constituting any vertical 



