ana 



This gives for .r = .c/j 



,ifj = -^kR,Uog{ikR,^)-}kR,' (18) 



whence 



yr = yn - nn = 2 R, + | kR,' log {\ kR,') - ^ kR^ '), . (1 6') 

 and similarly, if xp, jfo and Ihe coordinates of />, 

 .vjj = XB = R, ^/p/?„'' .Vi) = ye -i]B^2,R, V- kR.; log (| kR,') (19) 



§ 8. In the case of (he ondiiloid, where sin (f^ goes ihrongii a 

 minimum in B' , we liave 



?•„ X sin ff =r .?•' -|- ,7;/j '....... (20) 



The maximum- and minimum-valnes of ,y(.s7n(/=l) are now 

 approximately 



x,=B., x,=xr='^^=~^kR^ . . . (21) 



u 



Moreover in that case 



± >i = .V, log '^ ^ + .rrr .tV.^-'--^*. . . (22) 



whence 



.in- 3^-1 ytS/ /or/ ( - I kR,') + I /■/?/ .... (23) 



yr- =: ///.— 7]£. r:. 2R, 4- | ^72/ % (- i ^-^o') - i fcR,' ■ (21') 



.<^Z)' = R, V^^fkRj , 3/z;= 2/2„ + A-/?/ log (- ^ ^7?/) - | ^K/ (24) 



§.9. It follows from (7') that the volnme of a drop from the top 

 to the horizontal plane passing through B or H' {{)■ = :^ — e), in 

 second approximation is given by 



V = i jtR,' (l-kR,') (25) 



With the same degree of approximation this is also the volume of 

 a hanging drop up to the level of the neck; indeed the volume 



^) If .r is large with respect to x.^ we have 



2.V .v' 



±n = xJog , (17) 



X, 2R, 



so that the equation to the branch CBE (fig. 3) is 



y = y, 1- .Ï+ = 2R, -ikR,^ -f j kR,^ log ^ - ^ 



in agreement with (IT) [ since £ = -—1. 



From this the abscissa of the node E{gE = yc) is found to be 

 xf^^.-^kR,*logkR,\ 



