404 



PROCEEDINGS OF WASHINGTON MEETING. 



curves show by ordinates parallel to B the temperature corresponding to the 

 times after the, beginning of cooling represented by their abscissae parallel to T. 

 As above described, the sheet is assumed to cool from a uniform initial tempera- 

 ture, u, toward the constant unvarying temperature of the margin (0). The same 

 plate is applicable to other conductivities, sizes of sheet, and initial temperatures, 

 by changing the scales appropriately. 



So long as the center has not cooled perceptibly, which, in the case of figure 1, is 

 .2 of a year, the time required for any point to cool down to a certain amount, or by 

 a certain amount, may be shown to vary as the square of the distance of the point 

 from the margin, independently of the size of the flow. Experiments later men- 

 tioned show that when consolidation takes place in this period the grain of the 

 constituent granules of the substances used is such that — the linear dimensions are 

 as the distance from the margin; hence, the grain, measured by areas of cross-sections of 

 constituent granules* is as the slowness of cooling. 



Initia.1 Temperature 



Figure i. — Curves of Cooling in igneous Schist 



After the cooling has so far proceeded that the center has cooled about one-fourth 

 of the interval between the initial temperature and the margin — that is, in the case 

 of figure 1, a year — the rate of cooling when a point reaches a particular tempera- 

 ture is practically the same, regardless of the position of the point. This is when 



all terms but the first of the sesries in the mathematical equation given at the end 

 may be neglected. 



So far as the solidification falls in this period the grain will be uniform and not 

 vary with the distance from the margin. 



If the formation of a mineral is controlled wholly by the rate of cooling and no 

 latent heat evolved by chemical reactions or other disturbing factor need be 

 considered, then according as its range of formation is near to the marginal tem- 

 perature or to the initial temperature will we have a more or less broad central 

 zone of uniform grain. The hotter the temperature at which the margin is kept, 

 or the hotter the initial temperature of the sheet, or the lower the temperature of 

 consolidation, the broader the central zone of uniform grain. 



*In measuring the grain in rock-se*ctions, as such a section may merely cut a small marginal 

 section from a grain, I took the largest section in each of several areas of observation. — A. C. Iy. 



