62 K. HONDA, T. TEKADA, Y. YOSHIDA, AND D. LSITANI. 



If we assume for X an expression of the same form as 

 would be obtained, if *S were constant, the length being straight 

 or curved, that is 



or 



then l'^^'«^"^^- 



and 3^-2^-— •^.; 



hence K.E. = l-p f—l^] »iu — .(j>Xdx 



V^ >r^ f 1 r 1 . IcTtx . mnx 7 1 r ,* 

 and P.E. ---. 1 i/p|l {2-^ cos i:^ ^\lx 



-^1 2 p J b I r' 



yr\ -^l 1 kmn'-qo C 1 hnx imtx 7)1, 



k III ^ -J t J U i i 



where the summation imder the sign ^ 2j must be taken such 

 that k:^m. 



Since <^'s are approximately normal co-ordinates, the quan- 

 tities under the sign ^^ are small, so that for simplicity's 

 sake, we may write 



K.E. = 2^(J, + oX)^r + Z E''^'^"^^'^'" ' 

 P.E. = 2(6; + oa) <^,^ + 2?2'^^^^-4'.4>"< , 



