849 



Properly speaking, with the lueaiiiiig given above to "weight- 

 method", Gay-Lussac's nietliod does not belong to this class, but is 

 rather to be ranged under the 3"' group ^). Proper weight-methods 

 are those in wliicli the capillary force is measured acting on a plate 

 suspended vertically in a liquid ') or the force which is retpiired to 

 detach a thin horizontal ring from a liquid. The laltei- force, inde- 

 pendently of the weight of the ring, is given by 



F = 2:tO (r, sin fp^ — ;■, sin 7 ,) + rr (r,' — r,') fi <jz, . . (40) 



)\ and ;•, being the internal and external radii of the ring; the 



angles 7, and 7^, for given values of z are determined by equations 



(4') and (22). The ring detaches itself, when z has become a little 



bigger than the ordinates of .4 (fig. 1) and D (fig. 3); putting 



rt 3jr 

 r/), =r - -j- 6,, r/), =- 6„ ^ (r, + /•,) = /" and r, — r, = rf, 



P is found to be a maximum, when Si := f, = \(fy2k, whence 



^^'^ =1 + i(fl/2l + ^M»4-|'~(2v/2- 1)*^ . (41). 



4jr<Jr ' - ^ 'lb 1 b ^. 



According to (39) the force applied serves mainly (when = tt, exclusively) 

 to balance the hydrostatic pressure; the determination of the weight is therefore 

 principally an indirect way of measuring the height z. 



') Wilhelmy's method. See Winkklmann. p. 1156. 



^) This equation was found previously by others (cf. Winkelmann, loc. cit., p. 

 1157), all but the last term which, however, is of the same importance as the one 

 preceding it. 



The equation also holds in the case of a ring, which is forced down into a 

 liquid like mercury. 



