839 



jt 1 0,609 



,,, =- ^, Vk=V^ + ^^^ (2 1/2-1, = 1,414 + ^^ I 



/ (6) 

 l 0,039i 



u^l//:-%(^/2-l)4V24-^y^|3%(|/2-l) + l/2 + M=0,532--^] 



2 

 <^fi=^ ^^1/^ = 2 + —— UB[/lc = . . . (7) 



3jr 1 1,276 



«X)»/* = fcp(l/2 + l)-l/2 + -i-!3%(l/2 + l)- (1/2-1)1) (8) 



* 1 0,372' 



= -|Ml/2-l)+l/2}-^^|3%(p/2-l) + (v/2-l! = -0,532+^^-^, 



We shall not try to cany on the approximation any fnrther. 



^ 4. We now come to the central part of tiie meridional curve. 

 Since in that part rp is infinitely small, we may put sin (p = (f =z 

 z=t(mff^^z', and may thus write equation (J) to a first approxi- 

 mation in the form • 



--'^{.vz') = kz or z"^^-—kz=zO . . . . (9) 

 By the snbstitiition ix\/k^^'è> - = >/, the equation reduces to 



V' + ^' + ^i = '^ (9') 



S 



which is Bksski/s equation of order zero. Therefore, considering that 

 at ./; = z is finite, we have 



z=hJ,{ixV^k), (10) 



./„ being Bessel's fnnction of the 1^^ kind and order 0; the inte- 

 gration-constant h is equal to the value of z for x = '). 



1) Since Jp© " ^ '^oi' - = Ö- Consequently for a very large meniscus (very large 



1 



i?„l in the neigbourhood of the axis of rotation, replacing h by its value 



(cf. Leiden Comm. Suppl. N". 4^c; these Proc. XXI (1) p. 357)), we have 

 1 I 1 kx^ 1 //fex'Y j 



' "^ Wn, i ^ ^ (Fir T ^ (2 !)« (^tJ + • • i ' 



as is also found directly by solving the differential equation of the meridional 

 section by development in a series (cf. Schalkwijk, Leiden Comm. N". 67, (1900 — 

 1901) these Proc. Hi, p. 421, 481) and putting Ey = oc. 



