373 



nients on drops without pressure-rneasiii'emeuts. ') With small drops 



the surface tension is then derived from the deviation from the 



spherical shape; in tiiat case pi'inci|)ally equations (10) and (10") of 



the previous communication (or (2) of the present paper) are to be 



applied, whicli lead to the relations: 



IL—r 

 1 - 2- (3% 2 -2) 

 r 



r 

 «„ — r 



(12) 



,8 



^'=i(f',-f',).9-'^- %2, (13) 



r — V 



r being the largest radius of the drop (its half breadth) and // the 



distance from the top to the plane of the section with radius r. 



Seeing that here the determination of u depends on the exact 



liiiowledge of the numerical value of terms which only served 



as correction-terms in the method of the pressure-measurement, 



this method cannot but give much less accurate results than the 



previous one. But its use seems indicated fot' liquids which can oid}- 



be obtained in very small quantities. 



§ 11. A third manner of determining surface-tensions by mean of 

 small drops consists in measuring the weight of small falling drops. 



It follows from the equations (25) and (19') of the previous com- 

 munication, that the volume of a small constricted hanging drop is. 



2nr'G f r'\ 

 v= 1 . (U) 



0*2 -Ml).'/ V ^'O/ 



r' being the radius of the circular neck. When the drop is made 

 to fall from a very thin rod — this would be the method, if the 

 liquid moistens the wall — or from a very narrow tube — in the 

 opposite case — ^) r' is not equal to the radius r of the rod or 

 tube, but the difference is very small. Indeed the drop does not 

 fall at the moment, when r = r' ; before it falls away the drop 



1) See WiNKELMANN, loc cil., p. 1160. See also J. E. Verschaffelt and Gh. NicAisE, 

 Bull. Acad, de Belg., 1912 p. 192. 



3) Properly speaking equation (14) only holds for a drop Jianging in equilibrium 

 and not for a drop forming from a tube while flowing (cf. Winkelmann loc. cit. 

 p. 1162). It appears from § 7. that a constricted drop cannot hang in equilibrium 

 from the opening of a tube, if the drop is in free connection with liquid in a 

 wide tube. A strongly constricted drop is only possible, if the connection with the 

 free surface in the wide tube is broken, for instance by the interposition of a tap; 

 by opening the tap very little the drop may be made to form very slowly, until 

 it falls : at any moment it can then be looked upon as in equilibrium and its 

 further deformation may be prevented by closing the lap. Similarly a strongly 

 constricted drop may form at the end of a long capillary, through whicli the 

 liquid flows very slowly (cf. also § 3). 



