and the Dynamical Theory of Diffraction. 421 



Hence we have, by replacing n— 1 by «, and changing the 

 sign of all the terms, 



M 1 =-C„sin 2 ^Q'„€ c tp- v «. 



From which we find, writing P for the radial component, 



©i=0, 



Pi=0, 



N 1= . 



9= sin 00/ e^" v «, 

 P 



© 2 = (2w + 1) {(n + l)0»- 1 +nO« +1 }. sin0Q'„e' 

 n(n + l) 



■c(p-Vt) 



P 2 =- 



N 2 =0, 



C„Q n e< 



fi(fi-Vt) 



We can also go backward and write 



Hence, as I have remarked before, each of the vectors indi- 

 cated by these components can be made equal to some one of 

 the vectors used in the theory of light. Thus 



Elastic-Solid Theory. 



Linear displacement of par- 

 ticle. 



Rotation of particle. 



Linear velocity of particle. 



Angular velocity of particle, 

 &c. 



Electromagnetic Theory. 



Vector potential. 



Electric current or electro- 

 motive force. 



Magnetic force, or induction, 

 or magnetomotive force*. 



Rate of change of current &c. 



Rate of change of magnetic 

 force, &c. 



Should we add another term with — % in the place of + i, 



* As Mr. Bosanquet lias shown a disposition to claim this term, I may 

 say that the idea expressed by it is of common occurrence in the works of 

 Faraday, and I myself have" used the term and given it mathematical 

 expression in the i American Journal of Mathematics.' Mr. Bosanquet's 

 article appeared in the Philosophical Magazine for March 1883. 



