The Dissolution of an Isotropic Solid. 163-. 



sented in the figure. The branch CD cuts a portion of the 



normals to AB ; at D is a cusp and the remaining normals 

 in the first quadrant are cut by HD ; the normals to the 

 lower quadrant are cut by the branch FCEH, there being 

 a second cusp at E, and C being a double point ; to the left 

 of the axis of j there is another portion of the curve sym- 

 metrical with that to the right. Of the curve thus found 

 the portions ECD, LMK, have no physical existence, the 

 undissolved area at any time will be represented by CGKF. 

 The position of the cusps is given by the equations, 





and 



^-±^jJTi^-l^^^^^ 



the final positions of the cusps corresponding with total dis- 

 solution of the cylinder will be obtained by writing b for c, 

 they will be 



b 





The position of the double points is given by the equations 



In order to trace the progress of the dissolution of the 

 cylinder it will be necessary to express the area as a func* 



