844 Shape of Capillary Surface in Contact with a Cylinder. 



slope of the tangent at any point enables a 2 — and therefore 

 the surface-tension — to be calculated by means of the simple 

 equation (xvi.), with much greater ease than would be the 

 case were equation (x. a) to be used. 



A knowledge of a 2 is, of course, necessary before i can be 

 computed. This can be obtained from a photograph of the 

 capillary curve by means of equation (xvi.) above, or directly 

 by measuring, at the same time that the photograph is taken, 

 the weight (mg) necessary to balance the pull due to 

 surface-tension on a vertical plate of known perimeter p, 

 just touching the surface of the liquid. We then have 



pT cos i = mg, 



or 2 . m , ... N 



<rcos2 = — — k, .... (xvm.) 

 pp 



where k is a known quantity. We can now eliminate a 2 

 between (xviii.) and (xi.), or (xviii.) and (xvii.). The first 

 elimination gives a cubic for i ; the second gives a much 

 simpler form, thus : — 



Substituting for a 2 in (xvii.), we have 



= sin (*+~)> 



. . h 



= sin i 4- — cos z, 

 r 



whence sin i + A cos i — 1 = 0, 



where 



cos i 



2/c 



This gives finally 



r 2k 



2A 



COS 1 = 



A 2 -t-l' 



giving i in terms of known quantities. 



Having determined cos i, equation (xviii.) gives a 2 , or T. 



In a future communication the writer hopes to give the 

 results of experiments based on the formulae detailed above. 



University College of North Wales, Bangor, 

 June 1912. 



