390 A. C. LANE — PORPHYRITIC APPEARAXCE OP ROCKS 



of example 1 is equation 11 of the Isle Royal report. Recently Wood- 

 ward and Queneau have made an addition to the theory of practical 

 importance. It will be simpler first to consider that the sides of the dike 

 are kept at a constant temperature, which we shall take at 0°, and 

 then proceed to a more general case, leaving the mathematical treat- 

 ment to a separate place. 



Marginal Temperature kept Constant 



From a mathematical solution of this case, which is illustrated in 

 plate 54 and the Isle Royal report, we find that close to the margin the 

 grain is dependent on the distance therefrom by a comparatively simide 

 formula (the same as Eq. (8) below, letting y and y' == 0). Near the 

 center the grain does not vary with the distance from the margin, 

 but is given by formula (9), and only depends on the ratio of the 

 temperature of consolidation to that of the initial magma. These two 

 approximate formulae may, if we represent the grain by a curve whose 

 ordinates are proportionate to the coarseness of the grain and whose 

 abscissae are proportional to the distance from the margin, be considered 

 as tangents to the true curve of the grain, which it will follow very 

 closely except for small easement curves near their intersection. 



An interesting question is where these two tangents meet — that is, 

 where would the grain be equal to that of the center if the rate of in- 

 crease at the margin kept up ? We have for this a very simple formula : 



(1) ^ = ^J^ . '' =A5h, '\ 



c - u^ u^ 



where x' is the distance of the point sought from the side of the dike c, 

 its breadth, and — , the ratio of the crystallization temperature to that 



at the beginning, the fixed temperature at the margin being taken as 0°. 

 In this formula A, which is given in table I, will run from .866 down, so 

 that we have almost directly a connection between the ratio of the 

 breadth of the zone of increase to the relative temperature of consolida- 

 tion, and the greater the latter the greater the former. This is the basis 

 for the existence of the early formed and centrally occurring phenocrysts 

 or eocrystals. 



