76 Mr. C. Y. Boys on the Drawing 



that it may be used for the purpose of approximate numerical 

 calculation when, as is often the case, the equation cannot be 

 solved. The accuracy is certainly considerably in excess of 

 that which can be attained by the same degree of care, using 

 rule and compasses according to his instructions. I hope 

 therefore that though there is no principle involved which is 

 not perfectly well understood, the practical character of the 

 modification and its utility more especially to teachers are 

 such as to render it w r orthy of the attention of the Physical 

 Society. 



Lord Kelvin's rule for drawing the generating curve of any 

 capillary surface of revolution is as follows : — " Through any 

 point, N, fig. 1 (PI. I.) of the axis draw a line, NP, cutting 

 it at any angle. With any point, 0, as centre on the line 

 NP, describe a very small circular arc through PP', and let 

 N' be the point in which the line of 0P ; cuts the axis. 

 Measure NP, WP', and the difference of levels between P and 

 P'. Denoting this last by S, and taking a as a linear para- 

 meter, calculate the value of 



W ^ OP NP WP'J ' 



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 can be explained to those not already familiar with the 

 principle in a few w r ords. At any depth below the plane 

 surface level of a liquid there is a hydrostatic pressure which 

 is proportional to the depth. At every point of the surface of a 

 drop this is balanced by the surface-tension which is constant 

 over the surface multiplied by the total curvature. The total 

 curvature at any point P in a surface of revolution is defined 



as being equal to ^p + ^rp' where OP is the radius of 



curvature of the generating curve at the point P, and NP 

 is the distance normal to the curve from P to the axis of 

 revolution. 



Since at any depth the curvature of the tense surface with- 

 stands the hydrostatic pressure and since the hydrostatic 

 pressure is proportional to the depth, it is clear that the 

 total curvature measured as defined above must be propor- 

 tional to the depth, being concave to the liquid below and 



