36J 

 and correspondingly 



//.4(/>.4') = ^ -i|^.4 = ^-i^'/?,M2%2 f 1)') . . (iO') 



and 



yA {y.i) = R,-R, ^A=Ro — i kR,' (2 % 2 + 1) . . (10") 



« § 6. From the equations (6) and (8') il follows that in tlie neigii- 

 bourhpod of i)^ = jt, putting vf = .t — s, 



r,= -ikR,^(^logj A and r\=lkR,^l; . . (11) 



in order therefore that ihese equations may still be valid in that 

 region, seeing that r\ has to be small, it is necessar\ , (hat f must 

 remain large with respect to kR^^ This is still the case in B, where 

 y has its maximum, for (comp. 4, 6 and 11) 



y = 2R-iR^e'^\kR,'flog'^^l\. . . . (U') 



dy 

 SO that it follows from -^ z= that 



de 



8B = y^^kR,\ rjB = 2R, [1 f i kR, log (| kR,*) - | kR,^] . (12) 

 and, also to a third approximation, 



xB=R,^B = R,y^Wö^ • (1^') 



These coordinates are only real, when h is positive. 



If k is negative, cp has a maximum in B' (fig. 1) corresponding 



d(f dxi^ 



to a value of e wiiich is determined by 0= — =^-\ (see eq. 



du di'J 



8) ; this gives : 



S£' = l/:=4^7V ') ; henae yBz^2R,[\ ^\kR,Hog{—\kR,')] . (13) 

 xB- = Ro^^^kR^' and (pB = ^ — 2V~JkR^' . . (13') 



^ 7. It is possible to go a step further in the analysis of the 

 meridian section of the capillary surface. Close to i> = n the curve 

 has a sharp bend (fig. 3): BCD with a double point E foi- /(■ > 0, 



dx 

 ^) Obviously this expression is also found by putting -— = 0. 



^) £b' may also be found by putting = —^,= ^ir-r -r-7. (see eq. 11'). 



dx R*de 



