GRAIN op ROCKS. 



405 



If we remove the condition that the surfaces of a sheet be kept at a fixed tem- 

 perature and assume the appreciable alteration of temperature due to the intrusion 

 of the hot sheet B C, figure 2, to be confined to a zone A D, the center of which is 

 also the center of the cooling sheet 1? C — suppose the conductivity uniform and 

 constant throughout — then the temperature of an}' point P of this zone, within or 

 without B C, is very easily derived from those of two points in a hypothetical hot 

 sheet of width equal to that of J. D, whose initial temperature, conductivity, et- 

 cetera, are those of the intruded hot sheet B C, the temperatures of the margin of 

 the hypothetical sheet E F being kept the same as that which A i>'and C D initially 



D 



C 



B 



A 



P, 



Figure 2. — Temperature Diagram. 



Pi 



E 



Illustrating relation between sheets, which have margins kept at a fixed temperature and those 



which have not. 



had. For the temperature of P, any point between B and C is an average of that 

 of the temperatures of two points, P l and P. i} as far distant from the surfaces E and 

 F as is P from B and C respectively— that is, P B is P 1 E; P Cis P 2 F; but if P 

 lie outside B C, then the difference of the temperatures of P x and P 2 at the same 

 time must be taken. Thus the solution of this case may be made to depend upon 

 the other. The temperature at B will be half way between the temperatures of 

 A B and B C, to start with, and will fall more slowly from that temperature than 

 will the center when it has cooled down to that temperature. Hence, if tlie tem- 

 perature of solidification of a given mineral is about half way between that of the molten 

 dike and its contact zone, the grain might be coarser at tlie margin than at the center. This 

 is suggested as a possible explanation for the so-called marginal porphyritic facies 

 of granites in some, not all, cases. In the case of a contact zone, therefore, there 

 may be no marginal zone of finer grain. 



Verifications 



In experimental verification I have made use of the principle that if A B C D, 

 figure 3, represent the cross-section of a cooling mass, A B, B C, and C D being 



Figure 3. — Temperature Diagram. 

 Illustrating cooling from one surface only. 



