508 MR. A. E. H. LOVE ON THE SMALL FREE VIBRATIONS 



These are the l lt m lt n t . . . , referred to axes at each point determined by three 

 certain line-elements at the point, if 8 denote the change in the value of these as we 

 go from any point P to a near point on the middle-surface, then referred to the fixed 

 axes at P, we have 



\I \7 



8/j = r- 1 da. -j- -^ dfl m, 80,j -f- n, 80.,, and so on ; 



vet op 



so that 



f-\ \h ^ _ ^ ft M .fL /* \l_i_ A/^ 9 Jf_ u \\ 



, ra r, a , . a /i\i , a mi 



8m, = rfa [ |^ a - - ^ V a^ (,j} - A 2 ^ ^ j J 



, ra / dio i i 



g^ = da. U~ 1 % a -- - \ T~ 

 |_3a 1 3a pj l,ft 



J0 ra r, a tti i r, a a /i 



+ c?y8 UT; Mi a --- \ T l ^i 5 -- *i8 ^ 



M La/9 1 s* h/ SAI aa ' s^v 



in the same way 



j f a fi ^ i j. 9 / 

 8L a = aa r- \ ho ^- /i^oW - 



aa 2 a3 l sA 



SM = - da 



K IT 



- hJt. 2 v 5- ( 







We may form the K' Z , \\, K\ from these, for m^a, n^ are small quantities of the 

 second order, and l s * > Z 3 -* - are also of the second order; hence, to the first 

 order, using equations (5) we obtain 



