Mechanical Phosphorescence. 355 
The solution of this equation is of form * 
= 2 a 2r _iCos«| (p — 2r — 1 n)t + e I + a_<2r-i->-C0S \ (p + 2r — ln)t+e M, 
where € is arbitrary. .... (iv.) 
On substitution in (iii.) we find 
+ |4n 2 -(p -27+1 . n) 2 |a 2r+1 ] =0 . . . (2r- 1) 
aA fi?— [p-3ny \ — j \ 4;n 2 — (p — n) 2 Va i 
+ (±n 2 -(p-5n) 2 \ a 5 1=0 . . . (3) 
+ |472 2 -(p-3>2) 2 | a s ~l=0 ... (1) 
iL 1 {M f -(p+») , }-x[{^ f -(P"») i }«i 
+ Arc 2 - (p + 3??) 2 j a_ 3 ] = . . ( - 1) 
a_ 3 |/* 2 - O + 3w ) 2 } - £ [ |^ 2 - (p + ™) 2 } ol_, 
+ |4« 2 -(p + 5n) 2 ~ja_ 5 ] =0 . . (-3) 
a_ (2r _ 1) | / ^ 2 -(p + 2^I . rc) 2 | - j^4:n 2 -(p + 2^3n) 2 Ta_ (2 ,_3) 
+ |4n 2 -(p + 2^+ln) 2 |a_ (2r+1) ] =0 . . . (-2r + l). 
* The method is similar to that employed in the paper already 
quoted ; a change of notation is introduced which makes the solution 
easier to handle for our present purpose, although the simple idea 
underlying the method is thereby rendered less readily apparent. For 
the general principle reference may be made to the previous work. The 
solution is here carried to a higher approximation. 
