TJic Dissolution of an Isotropic Solid. 



Next suppose the solid to have the form of a right cylinder 

 with a circular section, and first suppose that the ends of 

 cylinder are covered with sealing wax or some other 

 material not acted upon by the acid, so that dissolution is 

 confined to the curved surface ; the three differential 

 equations assume the form 



n-KX- + ?• 

 dx 



-Idt 

 -Idt 

 -Idt 



mtx- — 



7117,1 



n denoting the length of the cylinder, and x the radius of 

 the base at any time. The complete integral of the first 

 expressions will be 



The time required for complete dissolution of the c}-linder 

 will be 



(tan-fi5Y.,)_J_,. 

 V \r ) Jl{mrrf 



The complete integral of the second expression is 



2 t^'o \/ niT + r'^ x^ iiTT - r^j 

 If the quantity of acid be just sufficient to dissolve the 

 cylinder, the complete integral is 



- - = flirlt. 



As a variation of the problem, suppose the whole surface 

 of the cylinder to be exposed to the action of the solvent. 



