374 



contractb a little more, tlie volume thereby increasing slighdj, until 

 it reaches a maximum. For according to eq. (17) of the previous 

 communication, when .i- == r differs very little from /■, = 7-', the 

 volume contained between the circles of radii r and ;•' is equal to 

 .-ir" y 2r^Jr^-^y), so that the volume of the drop up to the plane 

 of suspension is equal to , 



y'^^l!^!^ + . . . . ^ jrr" l/2r'"(7^r'), 



and this is a maximum, when 



r'=:r(l-iFO (15) 



The maximum-volume will still be represented with sufficient 

 accuracy by e(j. (14), if /•' is replaced by r. 



Wlien the maximum is reached, the smallest further supply of 

 liquid must necessarily make the drop break off. If G is the weight 

 of the drop'), it follows from eq. (14) with r instead of r' that 



2.ni\ ^ rJ 2jrr 27Tr\ V ^ v J 



This is therefore the formula which in the case of a very small 

 drop has to re|)Iace the simpler expression used by Quincke. '). 



1) 6r = (^j— ^i) (/y; G is therefore the apparent weight, not reduced to a 

 vacuum. 



^) It is perliaps not superfluous to point out, that the expression (16) may be 

 deduced iu the following simple manner. The molecular forces (surface tension) 

 along the circular neck of the drop make equilibrium with its weight and the 

 hydrostatic pressure on the plane of the neck; hence according to (3') of the 

 previous communication 



2o 



2nrr> — (?-[--. nr\ 



where the term — xr^ {u<i— ,Ux) gij has been neglected. This equation agrees with 

 the relation which is found in calculating the capillary rise by the so-called weight- 

 method (see previous comm); in a certain sense, however, it must be considered 

 as its opposite: in both cases the surface tension balances a hydrostatic pressure 

 and a weight, but whereas in the case of the capillary rise the weiglit is introduced 

 as a correction, here on the other hand the same is true for the hydrostatic pressure. 

 Seeing that lor mercury k = 30 about and for water /c = 1 3, r must not be 



r 

 greater than U,07 to 0,11 mm. in order that the correction-term -- be 0,1. in 



order that this term may be still further reduced, as is necessary for the accuracy 

 of the method, in view of the further unknown terms which have been neglected, 

 much narrower capillaries would have to be used and this would diminish the 

 accuracy of the measurement of r. This shows that the method of the weighing 

 of falling drops is nol a very suitable one for the determination of surface tensions. 

 *) Pogg. Ann., 134, (1868) p. 365. See also Winkelmann, loc. cit., p. 1147 

 and 1161, and Th Lohnstbin, Ann. d. Phys., 20. (190Q) p. 288. 



