Revolving Liquid under Capillary Force. 



165 





in succession at the points for which o: = 4*8, 4*6, 4*4, &c. 

 For these portions we employ the mean curvatures corre- 

 sponding to ^ = 4*9, 4*7, &c. calculated from (19). It is 

 convenient to use squared paper and fair results may be 

 obtained with the ordinary ruler and compasses. There is 

 no need actually to draw the normals. But for such work 

 the procedure recommended by Boys * offers great advan- 

 tages. The ruler and compasses are replaced by a straight 

 scale divided upon a strip of semi-transparent celluloid. At 

 one point on the scale a fine pencil point protrudes through 

 a small hole and describes the diminutive circular arc. 

 Another point of the scale at the required distance occupies 

 the centre of the circle and is held temporarily at rest with 

 the aid of a small brass tripod standing on sharp needle 

 points. After each step the celluloid is held firmly to the 

 paper and the tripod is moved to the point of the scale re- 

 quired to give the next value of the curvature. The ordinates 

 of the curve so drawn are given in the second and fifth 

 columns of the annexed table. It will be seen that from 

 x—0 to x — 2 the curve is very flat. 



±x. 



±y- 



±y'> 



±x. 



±y. 



±y'- 



00 



216 



o-oo 



2-6 



206 



075 



02 



2-16 



o-oi 



2-8 



203 



0-83 



04 



2-16 



003 



30 



1-99 



090 



06 



216 



006 



3-2 



1-95 



0-95 



0-8 



210 



010 



34 



1-89 



099 



10 



215 



0;14 



3-6 



1-81 



101 



1-2 



215 



020 



38 



1-72 



102 



1-4 



215 



0-27 



40 



1-61 



1-00 



1-6 



215 



034 



42 



1-49 



098 



T8 



214 



042 



44 



1-32 



089 



20 



212 



050 



4-6 



111 



0-78 



2-2 



2-11 



0-58 



4-8 



080 



0-67 



2-4 



2 09 



065 



4-9 



059 



041 









50 



000 



000 



Another case of special interest is the last figure reaching 

 the axis of symmetry at all, which occurs at the point x = 0. 

 We do not know beforehand to what value of fl this corre- 

 sponds, and curves must be drawn tentatively. It appears 

 that H = 2*4 approximately, and the values of y obtained from 

 this curve are given in columns 3 and 6 of the table. There 

 is a little difficulty in drawing the curve through the point 

 of zero curvature. I found it best to begin at both ends 

 (.r = 0, y = 0) and (#=5, y = 0) with an assumed value of O 

 and examine whether the two parts could be made to fit. 



* Phil. Mag. vol. xxxvi. p. 75 (1893). I am much indebted to Mr. Boys 

 for the loan of suitable instruments. The use is easy after a little practice. 



