XODULKS. (39 



The surface of the sphere is, say, S = 4 tt r' and 



3/" 



S/^' = 3r-3r+l- 



The surface of the material exposed to the action of the fluid per unit 

 of volume of the shell acted upon, orS/V, may readily be seen from this 

 equation to diminish rapidly as the radius of the sphere increases.' For' 

 example, if the radius is unity, or just equal to the depth to which the 

 solid is permeable, S/V = 3; if r i^l', 8/ Vzzl.7 ; if r =r4, 8/Vz=1.3, and 

 if the radius is infinite or if the attacked surface is flat, S/Vzzl. 



Suppose a unit of volume of a thoroughly porous, solid substance in 

 any given shape and exposed to the action of a solvent liquid: the liquid 

 will become partially saturated near the surfiice of the solid and will act 

 less vigorously upon the underlying portions. It is clear, therefore, that, if 

 the body is given the shape of a slender rod and is acted upon by the fluid 

 from one end onh', it will dissolve less rapidly than it would if the same 

 mass were formed into a thin sheet and were attacked over the whole of 

 one surface of this sheet. It is easy to see that the rate at which solution 

 will take place in this case is nearly proportional to the surface exposed to 

 the action of the fluid. 



Hence it is sufficiently accurate for the present purpose to assume that 

 the rate at which a spherical mass will be attacked by a corrosive fluid will 

 be proportional to the surface exposed per unit of volume of the permeable 

 shell, or to S/V. This function (and therefore, also, the rate at which so- 

 lution will take place), as has been shown above, varies in a certain inverse 

 ratio to tlie radius of the sphere." 



If, therefore, any comparatively dense, irregular body is acted upon 

 by solvent or decomposing solutions, the portions the radii of curvature 



' 'rile portion of tbe sphere which is not reached by the tluid is essentially a positive quantity, and 

 4 

 ■when )• becomes less than unity, , ^ (''— 1)^ disappears froui tbe value of S/V, which thus becomes 



equa'. to Wr. This is a hyperbola, asymptotic to both axes, aa(i S/V is iufiuite forc = 0. At the point 

 at which r = \ this hyperbola passes over into the curve of tbe third degree given in the text. The 

 hyperbola would be asymptotic to S/V = 0, while the higher curve is asymptotic to S/V = l. 



'^ This conclusion is not affected by the uncertainty which exisis as to the exact lunction represent- 

 ing the rate of solution in terms of S/V ; for it is clear that in any case this function and S/V must 

 vary directly, and that both of tliem, therefore, vary iuver.srlv as the radius of curvature. 



