32 Mr Wilson, On Velocity of Solidification. [Oct. 31, 



dr ± 

 ~dt 



But _*i = 0(0o-0), 



^ ^ K(0-0 1 ) 

 so that r 1 CsF = -- 



Therefore 



i r 2 

 log - 



K(0 O -0 1 ) 



r.CsFlog^ + K 



cms 

 If ^-^rzlO ^ K = 00015, F=80, (7=1-2 and 



° J ' sec 



?- 2 = 2 cms, the following table gives the values of (0 O — 0) for 

 several values of r, according to this formula : 



Since r x log — is a maximum when r 1 =— , the supercooling of 

 the water in the cylinder is a minimum for this value of r a . 



Since -^=C(0 o -0), 



dr, K(0 O -0 1 ) 

 dt „ . r 2 K' 



I shall now consider the case of an infinite quantity of the 

 supercooled liquid beginning to solidify all over an infinite plane. 

 Since everything is symmetrical about the plane, the solid will 

 form a plane slab half on each side of the original plane. Let X 

 be half the thickness of the slab at a time t reckoned from the 

 instant when X = 0. Since when the supercooling is small the 

 latent heat of fusion is very large compared with the supercooling, 

 practically all the heat produced goes into the liquid. Hence 



F dX = R d0 

 dt dx' 



d0 

 where -=- is the slope of temperature in the liquid at the surface 



CLOG 



of the solid. 



