TJie Dissolution of an Isotropic Solid. 167 





^-'t 



A&hm<^y 



if in these equations we substitute for the differential coeffi- 

 cients their values in terms of the co-ordinates, we may write 



x=MX,Y,Z,c) (2 1) 



y=MX,Y,Z,c) 



z=MX,Y,Z,c) 



from these equations we may deduce 



X = F,{x,y,z,c) (22) 



Y = F,{x,y,z,c) 

 Z = F3(^-,j',5,c) 

 These values of X, Y, Z substituted in the equation 

 (/)(X,Y,Z) = 0, or in (18) will give the instantaneous surface 

 generated by the solution of the given surface. By the 

 variation of c, we shall obtain the successive surfaces from 

 the commencement until the completion of dissolution ; the 

 equation will also include the primitive surface if we write 

 for c. 



In order to test the accuracy of the above reasoning, 

 suppose the primitive surface to be the sphere 



X" + Y' + Z' = r- 

 then, since 



dz _ X ^_^_ _Y 

 dx~ ~ V dY" Z 

 we shall have the additional equations 



