CONCEIVABLE CLASSES OF PHEXOCRYSTS 389 



minerals. The olivine is attacked at the center of the diabase dikes by 

 the concentration of a salic (waterglass) residue. 



I wish, however, to call especial attention to the early formed and 

 border phenocrysts, the third and fourth classes, whose ver}^ existence 

 has been almost overlooked except by Pirrson* and a few others. 



I will consider as briefly as may be the theoretical basis on which the 

 assumption that such crystals may occur rests. Those who are willing 

 to take this for granted and the resultant plates, table, and formulae may 

 skip the next section, which depends on the calculus, although this does 

 not appear in the approximate formulae derived. 



For the conclusions that we shall draw to be generally applicable, it 

 is by no means necessary that the case in nature should be extremely 

 close to the mathematically assumed conditions. B. 0. Peirce has shown 

 that in the case of cylinder whose radius is twice its thickness it makes 

 but little difference with regard to the final axial temperatures, if the top 

 and bottom are kept at certain fixed temperatures, what intermediate 

 temperatures the cylindrical surface has. Similarly, it is by no means 

 necessary that the igneous sheet should be infinite or very regular for 

 our results to apply in a general way. 



Differences in diffusitivity and convective currents, absorption of 

 heat by evaporation, and similar factors may be in part allowed for by 

 supposing that the contact zone, whose temperature is assumed to var}^ 

 is of suitable width. The mathematically effective contact zone will then 

 not necessarily be of the same width as the actual. At the same time, 

 near the margin there may be a cooling effect carried in by currents 

 from the friction of the side which will disturb the temperatures ; but 

 initial irregularity of the temperature, which may occur, and which will 

 naturally follow flow lines, will tend to smooth themselves out and be 

 most apparent only in crystallization at the higher temperatures and 

 earlier time. Around inclosures there may be spots thus cooled, which 

 will, according to circumstances, have either an extra fine grain or an 

 extra coarse grain. 



Application of the Theory of cooling to Questions of Grain 



In my Isle Royal report f I treated oi the theory of a cooling slab and 

 its application to the grain of a dike or sheet. A recent treatment is 

 given in Byerly's text-book on Fourier's series. J I had called my old 

 teacher's attention to the geological interest of this case, and the solution 



*Loc. cit. 



fGeol. Survey of Michigan, vol. vi, part i. 



I Page 105. 



