174 Dl<- J- BOTTOMLEY on 



given by the formula 



If the quantity of acid be just sufficient to dissolve the 

 cube, the equation of dissolution becomes 



the complete integral will be 



\/ I + 2ltx^ 

 If the solid to be dissolved have the form of a sphere, x 

 being its radius at time /, the differential equations are 



^^= -Idt 



3 



dx 

 = -Idt 



3 

 the integral of the first expression is 



the constant to be determined by the condition x^x^ when 

 /=() ; the time required to dissolve the sphere may then be 

 found by making ,r=0. If the quantity of acid be insuffi- 

 cient to dissolve the sphere, from the second equation we 

 obtain the following relation between the radius of the 

 sphere at any time, and the time which has elapsed. 



\3A 6'°^\47r.--3r V(4-)*^-(3'-)Vf 



/ 2(47r)^a?+ (3r)4 _ A^-^f^o-^^V'f \ ^ 



If the quantity of acid be just sufficient to dissolve the 



