838 Mr. A. Ferguson on Shape of Capillary Surface 



been recently devoted to the photography of the capillary 

 surface formed by pendent drops *, and it seemed possible 

 that photographs of the meridional curve of the capillary 

 surface in external contact with a cylinder might give useful 

 information as to the angle of contact of a liquid and solid. 

 A few preliminary experiments have been made which indi- 

 cate the feasibility of the formulae developed below. The 

 present paper will, however, be devoted to the discussion of 

 these formulae, leaving the experimental results for future 

 presentation. 



In the paper referred to above, several approximations to 

 the outline of the capillary curve have been discussed. To 

 these may be added the equations 



^+^-£(^2-1), 



and 



V2cos^ fiV 2 cos^ 3/V^cos 2 ^ 



z z z 



(l-.Bb'f), 



originally due to Poissonf, and modified by MagieJ. All 

 of them have reference to the capillary surfaces formed by 

 drops, pendent or sessile ; the writer has not found any dis- 

 cussion of the particular capillary curve which forms the 

 subject of the present paper. 



In the discussion which follows it is important to bear in 

 mind that the angle of contact of the liquid and solid is 

 assumed to be acute : that the radius (r) of the cylinder is 

 assumed to be large in comparison with the other quantities 

 to be measured ; and in the discussion of the signs of the 

 various quantities involved — a point which has an important 

 bearing on the shape of the resulting formulae — the signs 

 will always be chosen in accordance with the diagram given 

 in fig. 1 below. 



Let Y' 0' 0" Y" be the trace of the cylindrical surface, 

 of which OY is the axis, immersed in the fluid. Let OY be 

 vertical and OX any horizontal line drawn in the " level " 

 surface of the fluid. 



The capillary surface will be a surface of revolution about 



* Phil. Mag. March 1912. 

 t Nouvelle Theorie, p. 217. 

 T Phil. Mag. vol. xxvi. (1888). 



