78 Mr. C. V. Boys on the Drawing 



but in less degree; the second and third are as nearly perfectly 

 eliminated as is possible. These, though they may be indi- 

 vidually too minute to be observed, yet tend to be cumulative, 

 so that as the number of steps employed is increased with 

 the view to obtain accuracy, so do these accumulated errors 

 tend to increase when the ordinary method is followed. It is 

 on the elimination of these that the accuracy of the method 

 of curve-drawing, which forms the subject of this paper, 

 mainly depends. The increase in facility is also of im- 

 portance, as the operator is not tempted to make his steps 

 unduly long ; it is brought about as follows. I make the 

 rule of a thin strip of transparent celluloid with a small 

 hole at the centre of the scale marked go . A small brass 

 tripod with three needle-feet (fig. 2) is placed so that two 

 feet just penetrate into the paper and the third rests on the 

 longitudinal straight line of the strip (which of course passes 

 through the small hole), and just pricking into it forms a 

 temporary but rigid and stable centre of rotation for the 

 strip. A pencil-point or a capillary glass pen made short 

 and fastened with wax or a spring clip into its place at oo 

 will then draw an arc of a circle of which the curvature is 

 equal to the reading on ihe strip at the place where the 

 needle-point presses. Now it will be clear that at every 

 stage the two numbers which represent the two parts of the 

 curvature are always visible to the eye, there is no necessity 

 to rule any of the normals to the curve, and no necessity to 

 set compasses. Supposing for simplicity that a curve of 

 constant total curvature (unduloid, nodoid, or catenoid), that 

 is where hydrostatic pressure need not be considered, is to be 

 drawn through any point and normal to any definite direction. 

 Then all that has to be done is to set the strip with its longi- 

 tudinal line in this direction and with its central hole at the 

 point. E. g. } let the point be 6 inches from the axis, let the 

 line through the point to which the curve is to be normal be 

 perpendicular to the axis, and let the total curvature be 

 arbitrarily chosen as '5. Then when the strip is placed in 

 position the reading on the scale where it crosses the axis 

 will be '16. The difference between '5 and *16 is *3. The 

 needle-point must therefore be set on the scale at *3, and on 

 the side of oo towards the axis. A very short arc must then 

 be drawn with the pencil or pen piercing the hole at oo . The 

 reading on the axis will now be found very slightly less (the 

 distance being greater), say *16, the needle-point must now 

 be transferred to the '34, care being taken to hold the strip 

 firmly upon the paper to prevent its moving. A new short 

 arc may now be drawn and the process continued. As soon 



