from the Dimensions of Flat Drops and Bubbles. 65 



approaches 2 centims. the term - is generally insignificant, 



1 



though, the corrective factor C, which now reduces to , c ^ , , 

 6 3*282 L ? 



is still important. In fact a drop or bubble may be con- 

 sidered flat before the radius can be regarded as indefinitely 

 great. 



In those cases where the corrected value still exceeds the 

 mean value obtained by the method of capillary tubes, the dif- 

 ference w T hich w T as previously considerable is now for the most 

 part insignificant ; witness water, olive-oil, turpentine, and 

 alcohol. It must also be remarked that the measures of flat 

 drops or bubbles agree among themselves far less satisfactorily 

 than the measures of capillary elevations. Thus the numbers 

 quoted as obtained with capillary tubes are themselves the 

 mean of several observations, not differing from each other 

 as a rule by more than 2 per cent., though made with tubes 

 of various diameters; while the observations of flat drops or 

 bubbles differ often by as much as 15 per cent., or even 

 more. 



This very variation is indeed a matter of interest, and not 

 easily accounted for*. For though M. van der Mensbriigghe 

 has well pointed out | that the bubble when first blown must 

 exhibit a higher surface-tension, owing to the absorption of 

 heat from, and consequent lowering of temperature of, the 

 surface-layers, yet it is not easy to believe that this deviation 

 from the normal value would be of long persistence ; nor 

 indeed do Prof. Quincke's measures always show a diminution 

 of tension with the time. 



I think, however, that we may draw the conclusion that 

 the method of capillary tubes, when care is taken thoroughly 

 to wet the walls above the meniscus, leads to values which 

 are not discredited, as we had been led to think, by the results 

 of the method of flat drops or bubbles. This is a satisfactory 

 conclusion to come to, since the method of elevation in capil- 

 lary tubes is that which has been most frequently employed 

 for measuring the surface-tension. Prof. Quincke's value 

 (*0825 gr. = 81 C.G.S. units) of the surface-tension of water 



* Mr. Bashforth (see ' An Attempt to test the Theories of Capillary 

 Action/ p. 10) remarks on the difficulty of making any accurate direct 

 measurement of the height K — k, and Prof. Guthrie has somewhere 

 noticed the same difficulty. But Prof. Quincke's measures of K — k do 

 not show a percentage-variation much greater than that of the quantity 

 K\^, in determining which the same difficulties do not occur. 



t u Etudes sur les variations d'energie potentielle des surfaces liquides/' 

 Mem. de VAcad. de Belgique, t. xliii. 1878. 



Phil. Mag. S. 5. Vol. 20. No. 122. July 1885, F 



