of Curves by their Curvature. 81 



they can be drawn each in a few minutes only, it is possible 

 to set them out correctly to the thickness of a fairly fine 

 pencil-line ; and so they do more than give a general idea of 

 the shape, they serve to make a true scale-drawing. 



In the case of capillary surfaces of revolution, in which the 

 fluids on the opposite sides of the surface are of different den- 

 sity, e. g. water and air as already explained, the curvature of 

 the surface must be zero at the plane surface level, and must 

 be proportional to the distance above or below this level, being 

 — or convex to the denser liquid above, and + or concave 

 below. The readiest way to determine the curvature when 

 drawing one of these generating curves is to work on a sheet on 

 which a series of equidistant lines have been ruled parallel 

 to the plane surface level, and at such a distance apart that 

 the hydrostatic pressure due to this distance is balanced by a 

 curvature of '01 or some small and simple number. These lines, 

 then, give by inspection, especially if each fifth and tenth line 

 is a little darker, a scale of curvature, and exactly the same 

 process that was followed when describing the curves of constant 

 curvature may be as readily applied when the curvature is 

 constantly varying. In the case of water this distance is, 



ct 

 using the formula already given, d= -r- , = '0128 for cur- 

 vature c=l, or '000128 for c = *01. If, therefore, the drop 

 or other capillary surface is drawn to ten times the true scale, 

 to effect which the vertical scale of curvature must be mul- 

 tiplied 100-fold, the dimensions are such as to allow of 

 considerable accuracy. I am able to show a very beautifully 

 executed series of capillary curves for alcohol and water 

 drawn to a scale of 10, which Miss Stevenson has been good 

 enough to prepare ; but as Prof. Perry has constructed a 

 large number which are printed in the Royal Institution 

 Proceedings, to which reference has been made, there is no 

 occasion to publish them. He, however, would have been 

 able to draw his in as many hours as he required weeks had 

 he made use of the method described in this paper. 



In order to originate the reciprocal rule I used a screw- 

 cutting lathe as a dividing-engine, and scratched the wax off 

 a strip of plate glass with a fine point at the places where 

 divisions were required. Of course as the distance from oo 

 increases and the readings become smaller, the distance 

 between marks corresponding to a regular series of figures 

 becomes greater, and new subdivisions are with advantage 

 added, as is usual where a scale is not one of equal parts. 

 The glass scale was etched, and the divisions transferred to a 

 strip of celluloid by means of the well-known method with a 



Phil. Mag. S. 5. Vol. 36. No. 218. July 18^3. Q 



