CASE OF THE CONTACT ZONE 393 



by u, of initial temperature by ?<,„, of thickness of effective contact zone 

 by 2/, and of total thickness affected by c) in this first period by g^ 

 (k, X, u, Uo, y, c) we have 



(5) g' (^k, X, n, ./„, y, c) = g' ( k, x\ u - ^ . ^ , 0, 2iv^ . 



Suppose, as Queneau* does, we let m = =z^ and w^ = = and 



2a]/ 1 2a]/ 1 



suppose the grain p' to be = ^ — , then we may find the general 



\/l>^U 



formula 



Cfi) 



«]/?'., 



1 





kc X 





1 _ 





9/iol/ 2'ni^ J\^^ 



U 1 Uo C 



m\ 



■'^2m. D^^uluo 





kc 



aVuo 



3re h represents the ratio 



X 



1 



For 







" h{n 



•Juo)' 1/2 





wh( 





quite a range of 



vail 



aes of ulUo h is practically 



constant, 



and it is not a 



function of x near 



the 



margin when 



U/Uo = P^^ = 





Uo 



If 



we let m and h' 



stand in the same 



relation to x' 



u 

 ' and to - 



u^ 



m and h do to x and to 



It 



then we have 







2 







(7) 





ayuo 



x' 



1 







' h 



r \(2U 



f 





With the little table for h in case ulvo== Pm, which we give, it is easy 

 to find approximate values for the ratios of temperature of injection 

 and consolidation, finding which we may insert in equation 7 a closer 

 value for h, and so proceed. It is obvious that unless the consolidation 

 temperature is very near that of injection the value of h of .8 or a little 

 more will be a fairly close approximation. 



The next stage, when simple formulae for the grain can be obtained, 



*Loc. cit. 

 LV— Bull. Geol. Soc. Am., Vol. U. 1902 



