496 Sir William Thomson [Jan. 29, 



of the liquid and the shape and dimensions of the solid are given. 

 When I say determine, I do not mean unambiguously. There 

 may of course be a multiplicity of solutions of the problem ; as, 

 for instance, when the solid presents several hollows in which, 

 or projections hanging from which, portions of the liquid, or in 

 or hanging from any one of which the whole liquid, may rest. 



When the solid is symmetrical round a vertical axis, the figure 

 assumed by the liquid is that of a figure of revolution, and its form is 

 determined by the equation given above in words. A general 

 solution of this problem by the methods of the differential and 

 integral calculus transcends the powers of mathematical analysis, 

 but the following simple graphical method of working out what 

 constitutes mathematically a complete solution, occurred to me a great 

 many years ago. 



Draw a line to represent the axis of the surface of revolution. 

 This line is vertical in the realisation now to be given, and it or any 

 line parallel to it will be called vertical in the drawing, and any line 

 perpendicular to it will be called horizontal. The distance between 

 any two horizontal lines in the drawing will be called difference 

 of levels. 



Through any point, N, of the axis draw a line, N P, cutting it at 

 any angle. With any point, 0, as centre on the line N P, describe a 

 very small circular arc through P P', and let N' be the point in which 

 the line of P' cuts the axis. Measure N P, N' P', and the difference 

 of levels between P and P'. Denoting this last by 8, and taking a as 

 a linear parameter, calculate the value of 



Va^^OP NP N'PV 



Take this length on the compasses, and putting the pencil point 

 at P', place the other point at 0' on the line P'N', and with 

 0' as centre, describe a small arc, P'P". Continue the process 

 according to the same rule, and the successive very small arcs 

 so drawn will constitute a curved line, which is the generating 

 line of the surface of revolution inclosing the liquid, according 

 to the conditions of the special case treated. 



This method of solving the capillary equation for surfaces of revo- 

 lution remained unused for fifteen or twenty years, until in 

 1874 I placed it in the hands of Mr. John Perry (now Professor 

 of Mechanics at the City and Guilds Institute), who was tiien 

 attending the Natural Philosophy Laboratory of Glasgow University. 

 He worked out the problem with great perseverance and ability, 

 and the result of his labours was a scries of skilfully executed 

 drawings representing a large variety of cases of the capillary 

 surfaces of revolution. These drawings, which are most instructive 

 and valuable, I have not yet been able to prej^arc for publication, but 

 the most characteristic of them have been reproduced on an enlarged 



