CASE OF THE CONTACT ZONE 395 



We may make the following comments : 



(1) The shape of the curves depends almost wholly on the ratio of 

 the initial temperature to that of consolidation. 



(2) Unless these temperatures are very close together the grain at the 

 center does not vary with their ratio, but is proportional to (kc I a]/u ), 

 being greater the greater the size of the sheet and the less the conductivity 

 and temperature of consolidation. 



This last condition may be more significantly worded by sajdng that 

 the grain is coarser the nearer the country rock temperature is to the 

 temperature of consolidation. 



(3) The grain at the margin should be if the initial temperature is 

 more than twice the temperature of consolidation. 



(4) The grain will be greater at the margin than at the center if the 

 initial temperature is more than twice the temperature of consolidation ; 

 but if it is much more the grain will practically even throughout, as with 

 some aplites. (Curve .40 of plate 58.) 



(5) If there is a broad contact zone and the initial temperature is not 

 far below twice the temperature of consolidation, there will be a belt of 

 coarse grain not at but parallel to the margin. (Curve .52 of plate 58.) 



(6) When the contact zone is quite small and the initial temperature 

 below the twice the temperature of consolidation the increase of grain 

 will at first be linear and very rapid, then linear and less rapid. This 

 leads to a practically somewhat puzzling uncertainty. Take a straight 

 line, such as is deduced by Queneau from his observations to be the line 

 of grain for the Palisades augite and feldspar. Can we safely assume 

 this to be of the type g" or may it not be of the form g\ the slight grain 

 at the margin which it would give being due to inaccuracies of observa- 

 tion or little irregularities of the temperature. In my Isle Royal report 

 I have not made allowance for this ambiguity. The conclusions drawn 

 on page 243 are probably wrong accordingly, the ratio of the tempera- 

 ture of consolidation to that initially is probably too low, and the initial 

 temperature calculated is too high. 



Approximate Formula 



Now, if we suppose that we can make certain simplifications, which 

 can often be done, we can obtain approximate formulae which are very 

 easy to handle. We will assume that y is equal to y' and that the frac- 



tion ^^^o: — '-^ = 1. This we may do when the contact zone is 



relatively small. We will also introduce h and call a/ao=f'\ Also we 

 call the expression (k c/a i/uo) iTand we have the following formulae : 



