484 Lord Kelvin on the Production of 



where ¥ 1 and F 2 are put for brevity to denote arbitrary 



functions of (t J and it I respectively. Hence the 



most general solution fulfilling the conditions of § 5 is 





rf.# <iy r 



rf<z? fte r 



(16) : 



where for brevity <£ denotes a function of r and £, specified 

 as follows : — 



^.,0 = F I ((-3 + F 2 («-'-) . . . (17). 



Denoting now by accents differential coefficients with respect 

 to r, and retaining the Newtonian notation of dots to signify 

 differential coefficients with reference to t, Ave have 



Working out now the differentiations in (16), we find 





J- • (!»)• 



§ 8. For the determination of the force-components by 

 (7), we shall want values of 8, e,f, and c. Using therefore 

 (2) and going back to (16) we see that 



dx u 2 dy r 



(20;. 



Hence, and by (19), we find 



^1 L V»' 4 r 5 + r 6 r' rr* r 1 + ^J 



+^4+^} • • • (21). 

 r' 2 vr r 6 ir ) v ' 



By (16), (14)', and (15)' we find 



B ^£*..._Jj£. + i*.\ . . (22) . 



