TJie Dissolution of an Isotropic Solid. 159 



if in (13) y = ^ the corresponding values of x are ±t: 



and a-\ — > this latter quantity will be the distance 



OE of the double point from the origin. In order to 

 assign some definite volume to the cylinder, we may 

 suppose it to be bounded by two planes, of which the 

 sections by a plane normal to the length of the cylinder 

 are the lines GL, LH ; furthermore let these lines be normals 

 to the parabola at G and H, let also the planes just men- 

 tioned, and the extremities of the cylinder be covered with 

 some insoluble compound so that dissolution is confined to 

 the curved surface. The first stage of dissolution will be to 

 remove a thin shell in the element of time dt, this shell 

 having everywhere the same normal thickness dc ; to the 

 new surface the same lines will be normal, and in another 

 element of time dt a second shell will be removed, having 

 everywhere thesameinfinitesimal thickness, and sotheprocess 

 will continue until the solid be exhausted. Of the curve 

 in Fig. 2 the portion EAD has no physical existence ; the 

 portion bounding the undissolved area will be BEF ; as 

 dissolution proceeds there will be a progression of the point 

 E on the axis of x, at the same time the area BEF 

 diminishes, and the length of c increases, hence the object 

 of the enquiry will be to represent this area as a function of ^, 

 and if c be some ascertainable function of the time, we 

 may determine, either exactly or with any required degree 

 of approximation, the area of BEF, and consequently 

 the dimensions of the undissolved cylinder at any time. 

 At this point then we may see that the doctrine of solution 

 consists of two enquiries, the determination of the volume of 

 the undissolved solid as a function of c, and the determina- 

 tion of ^ as a function of the time, the first is a geometrical 

 question, the second a chemical one, to be decided by ex- 



