C A PILLAR Y A TTRA CTION. 3 1 



course be a multiplicity of solutions of the pro- 

 blem ; 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 follow- 

 ing 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 realisa- 

 tion 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, 



