392 A. C. LANE — PORPHYRITIC APPEARANCE OF KOCKS 



the beginning of cooling and conditions otherwise the same in a sheet 

 whose thickness was equal to c at a distance of w + ^ from the margin 

 and Wp_ , is the temperature at a point at a distance of iv — z from the 



margin in the same sheet, or if ic — z becomes negative — that is, the point 

 lies in the contact zone — we must assume 



(3) u = — u 



IV — z z — IC 



Now if we let x' be the distance of the point in the sheet with a contact 

 zone from the margin of the sheet — that is, x = l~ — z — iu\ 



(4) V = — I u , , ^ -\- u \. 



So if we take y to be ^V o^ c? '•^^^ei'^ ^oi' various values of re' from to 11 

 the center we shall have as corresponding values of v respectively one- 

 half the values of curve 2 of plate 54, values half way between curves 1 

 and 3. 2 and 4, 3 and 5, 4 and 6, 5 and 7, 6 and 8, 7 and 9, 8 and 10, and 

 at the center the values of curve 11 for the same time. 



Similarly if y be 6, the margin will have half the values of curve 12 

 and the center will have the values of curve 6 for the same times. Thus 

 we can obtain plates 55 and 56 either graphically (very rapidly) or by tak- 

 ing means of appropriate rows of a table of solutions of the case where 

 the margin is kept at a fixed temperature, a table which is given in the 

 Isle Royal report for an initial temperature of .7854, and here for the 

 initial temperature of 1. 



We see from these plates that the temperature of the margin begins 

 half way between the temperatures of the magma Uo, and that of the 

 contact zone, which is taken as 0° initially. There will be a certain space 

 of time, the longer the broader the contact zone, before it drops appre- 

 ciably from this initial temperature of i(o/2. 



Now, until the margin has thus cooled it is not hard to see that the 

 cooling will be as though the temperature of the margin were perma- 

 nently fixed. The fact that it is going to cool by and b}" will not make 

 any antecedent difference. 



It will be the same as the cooling of a sheet with the constant marginal 

 temperature Uo:'2 to be taken as 0°. The temperature of consolidation 

 will have to be reckoned from this — that is, will be w — Uol2 — and the 

 position of the point will have to be reckoned from the margin of the 

 sheet — that is, will be :c' = x — y. Thus representing the grain formed 

 (under conditions of diffusivity and other constant factors represented 

 by A", of distance from the margin by x, of temperature of crj^stallization 



