by the Red Corpuscles of the Blood. 667 



so that on account of the arbitrary nature of the variations 

 we have as part of the conditions 



"bx ~ ds~dx 

 JNow 



usiDg (1) and (6) 



•'• V ~*V : -y^r- =constant^=a. , . (7) 

 (5) now reduces to 



[«.A^ + [|J. A ., + ^. y ]^0. . (8) 



Now £V 



^ =cxy + 2<f>{s)x, 



.'. from (7) V=a+cxy . d 4-2^(0 (# 2 + # 2 ), 



?'. ?. 



« .T + o«y . * + <£(*) ( t r 2 + 7/ 2 -l) =*a + ca?y. « + 2</>(s)(tf 2 +2/ 2 ), 

 i-e. ffT=a+20(s), 



This determines <£(s) as i(a?T — a). 



Further we can determine a as follows ; — 

 The condition (8) requires that 



[a A. *]*=<), 



and since the length of the curve is not given 



.'. a = 0, 

 and so by (9) 0) = %x . T, 



and integral (4) now becomes 



{ c xy . + \xT . (,/■ » + f + 1) } <fe . , . (9) 

 2X2 



J, 



