Physics. — -'(yn thp ineasurement of surface tensions by means of 

 small drops or bubhles." By J. E. Verschaffelt. Supplement 

 N°. 42c/ to tlie Commiiiiications from the Physical Laboratory 

 al loeiden. (Coniinnnicated by Fiof. H. Kamkrlingh Onnes.) 



(Gommunicaled in the meeting of June 29, 1918). 



§ 1. The usual methods for the determination of surface tensions 

 by means of small drops or gas-bubbles, to which properly speaking 

 the method of the capillary rise also belongs, are based on the 

 measurement of the difference of hydrostatic pressure between the 

 two media inside and outside the drop or bubble; indeed the sur- 

 face-tension is given by the formula 



<5 = i(/*i-/^,)5'^i^o' (1) 



where f<, — yi, is the difference of the densities of the two contiguous 

 njedia, g the acceleration of gravity, R^ the radius of curvature at 

 the top of the meniscus and h the pressui-e-difference on the two 

 sides of the surface, measured as a column of the liquid in the 

 surrounding medium. If the drop (or the bubble) is so small, that 

 it may be considered as spherical, we may take for /i\ lialf of the 

 diameter of the drop (or bubble), or the radius of the capillary 

 tube, in which the liquid ascends, at least if there is no angle of 

 contact; in order, however, that the approximation obtained in that 

 way may be sufficiently close ^), the radius must be taken so small, 

 that as a rule the relative accuracy; of the measurement of the radius 

 remains far behind that which can i)e reached in the measurement 

 of h, whei-eas naturally it is desirable to linow R^ and h with the 

 same relative accuracy. In order that this may be possible, it is necessary 

 to make the measurements on drops oi- bubbles which are not too 

 small, in which case at the same time the necessity ai-ises of a 

 correction on account of the deviation from sphericity. *) 



1) The relative error is of the order kR,;^, where A; = ^ —-^ [d. eq (2)). 



O 



') E() can also tje measured directly by an optical method icf. H. Siedentopf, 

 Diss. Göltingen, 1897); il may also be determined by uieasuiements on photographs 

 (cf for instance A. Ferguson, Phil. Mag., (6), 23, (1912) p. 417. A high accuracy 

 is, however, not obtained in that way. 



