394 A. C. LAXE — PORPHYRITIC APPEAR AXCE OF ROCKS 



is when the cooling has proceeded so far that the cooling and the tem- 

 perature at the margin are practicall}^ the same as that of a certain 

 plane in a sheet whose walls are kept at a fixed temperature. Thence- 

 forward the temperature at the margin is the same as a point at a cer- 

 tain fixed distance y from a margin of a sheet whose walls are kept 

 fixed at the initial temperature of the country rock and whose breadth 

 is the whole breadth of the whole zone affected. The same thing is true 

 of the cooling at the center of the sheet in the contact zone compared 

 with the cooling at a certain distance from the margin of the same ideal 

 cold walled sheet. From this we may derive formulae (8) : 



r g" {l, X, u, ,u, 2/, c^= 9 (^-^ '~^^^y''^ ^' + 2/', u, i/., 0, c,) = A,' -^ B = g" 

 (8) \ where 



At the center these formulae or formula (9) will hold : 



(9) g'" (h, X, u, V,, 2/, c) = -^ . —L= = — ^ = E. 



ay Uo ~|/ y /I'o rt-|/ u 



It will be observed in studying the curves of cooling (plates 55 and 56) 

 that that of the margin very soon becomes practicall}^ coincident with 

 one of the cooling curves of the sheet whose walls are kept at a fixed 

 temperature (plate 54), so that thenceforward the temperature at the 

 margin is the same as it would be at a point at a certain fixed distance 

 y' from the margin of the cold walled sheet. The same thing is true of 

 the cooling at the center of the sheet. This is the same as the cooling 

 at a certain distance from the margin of the cold walled sheet whose 

 breadth would cover the whole zone affected. 



From the formulae above given not onl}^ can the grain be roughly con- 

 structed from the data Jc, w, ^(o, y, and c, but if from observation we can 

 construct the curve of grain for a given mineral with such accuracy that 

 we can locate the tangents in question we can then conversely draw 

 inferences regarding some or all of these data. But we shall usuall}^ 

 have to use approximate formulae, and a glance at a few typical curves 

 of grain will show us what inferences may be drawn without any special 

 calculation. Plate 57 shows a number of curves of grain for different 

 values of u/Uo and a small contact zone. Plate 58 gives curves of grain 

 when the contact zone is large. As the contact zone becomes smaller 

 and smaller the curves approach those appropriate to the case when the 

 contact belt is kept at a constant temperature. 



