372 A. C. LAXE — STUDIES OF GRAIN OF IGNEOUS INTRUSIVES 



From this table it appears that the increase of grain is irregular at the 

 margin, but that from 1500 to 17400 it is fairly uniform and thereafter 

 it rapidly diminishes. 



The ratio of increase of grain or slope is : 

 (.8560 - .0692) / (17400 — 1500) = (.7868) / (15900) = .0000494 = s. 



If we suppose s to be A, as seems natural, since the value of the grain 

 at 390 millimeters is greater than at 1,500 millimeters, indicating a curve 

 like .49 of plate 57, we get very small or negative values for B. We are 

 led, therefore, to believe that either there is practically no contact zone 

 or s is C. 



As to the grain at the center, we have unfortunately no definite obser- 

 vations, and we don't know with any great exactness the thickness of the 

 Palisade sheet at the point of observation. But if we start with the 

 coarsest grain observed and suppose the increase to continue to the 

 center at the last observed rate, and also suppose the center to be about 

 100 meters farther in, and all these suppositions are probably not far 

 from the truth, we shall find E to be somewhat less than 1.8. This value 

 we will take in our calculations. We will also assume that c is about 

 300 meters, then for the ratio of uju^, if we suppose there is no contact 

 zone and B is 0, Ej .45 hsc will be .327. But it is difficult to imagine 

 that the magma was injected three times as hot as the temperature of 

 consolidation of augite with no effective contact zone (which Andreae 

 and Osann have shown exists as a matter of fact) and without melting 

 down the country rock very markedly. Moreover, such initial tempera- 

 ture would lead us to find practically the same belt of increase of grain 

 for the feldspar. This is not true, for the feldspar continues to increase 

 at a rapid rate farther in than the augite. We are again led to try the 

 other alternative that the slope .0000494 represents C. From this sup- 

 position we shall find the following equation : 



• 2u|u^=i + i.^27f(2uilO^ 



Whence we can find the ratio u I u^ .774, but for this value of i4/m„ we 

 shall find that h' is .85 instead of .88, and this will give us a revised 

 value of u / Uq of .78. 



Moreover, noticing that the values of Cx' hold closely for the grain up 

 as far as 17,400 millimeters, we may infer from equation 21 of the previ- 

 ous paper that 2y is not less than 17,400 /.55 or 31,600 millimeters, so 

 that the thickness of the dike would be for the assumed value of c 

 (300,000 millimeters) about 269,400 millimeters, which agrees well 

 enough with Kiimmell's estimate. The width of the contact zone would 

 then be about 15,800 millimeters, and Andrea? and Osann have shown 

 that there is a well marked contact zone of new crystallization of notice- 



