RECORDS 163 



ticularly emphasized the contact between the Bullhead Rock 

 and the overlying Blue Limestone, and noted the occurrence of 

 a sandstone dike extending to the top of the Bullhead series. 

 The paper was discussed by Dr. Julien. 



Mr. Queneau in his paper said that a general observation 

 might be made in regard to intrusive dikes. Near the margin 

 the rock is dense, often glassy, without any appreciable grain, 

 whereas the grain begins to grow coarse according to some defi- 

 nite law, progressively as the distance from the wall increases. 

 The present paper is based on the study of the laws governing 

 such increase. It appears that the loss of heat is of paramount 

 importance.^ The problem taken up is very analogous to the 

 one presented by the cooling of a slab of finite thickness and of 

 great length and depth with respect to the first dimension, viz., 

 the thickness. The method followed rests on the TJicoric dc la 

 CJialciu\ of Fourrer, and on the general theory of cooling by 

 Professor R. S. Woodward. ^ The following laws have been 

 deducted : (i) The zone of varying grain will vary indirectly as 

 the initial temperature. From this follows that : [a) Plutonic 

 rocks very deeply seated will not present a zone of varying grain 

 to any extent. {U) Rocks which come to rest at a temperature 

 nearing their consolidation point will present a wide zone of 

 varying grain. (2) The time of cooling, other conditions being 

 the same, varies as the square of the thickness of the dike.^ 



From this last law it is assumed that the size of the crystals 

 vary as the square of their distances from the nearest margin ; 

 then the square root of their area which can be measured varies 

 directly as the distances from the margin. Thus we have a sim- 

 ple law of easy application. 



The paper was discussed by Professors Kemp and Dodge, 

 and Dr. Julien. 



Adjourned. 



Richard E. Dodge, 



Secretary pro te))i. 



^ Alfred C. Lane, Geol. Surv. of Michigan, Vol. VI. 



2 Annals of Mathematics, Vol. III. 



^Riemann, " Partielle Differentiel Gleichungen." 



