406 PROCEEDINGS OP WASHINGTON MEETING. 



covered by nonconductors and cooling allowed only through A D, the. heat flow 

 and attendant phenomena will practically be the same as in a sheet of twice the 

 thickness A B. Hence I have used a baking-powder can set on ice and swathed 

 in flannel. The curves of cooling agreed with theory. 



Sulphur melts at 1 15 degrees Centigrade and solidifies at 111 J degrees Centigrade. 

 If melted near 115 degrees and poured off to cool, we find (1) that the grain is 

 coarser from margin {A D) to the center (C B) ; (2) that the grain is equally coarse 

 /it the same distance from the bottom in pourings, differing in thickness, but other- 

 wise alike, and (3) that a linear magnifying power of 2 will make the grain appar- 

 ently twice as coarse as at twice the distance from the margin. 



The melilite slags, already described,* show similar laws. 



The augite of the Keweenaw luster, mottled melaphyres — that is, ophites — fol- 

 lows the same laws. It increases in size to the center, the size being nearly inde- 

 pendent of the size of the flow. In the great flow known as the Greenstone the 

 average diameter of the augite patches at 400 feet from the margin is about one 

 inch and in direct proportion for greater and less distances. 



We find, however, this law modified by chemical considerations, so that where 

 the augite is more abundant it is coarser, and where less abundant finer. Some of 

 the Keweenawan flows show considerable variation of this sort, the augite being 

 more abundant in the bottom part of the flow. Large dikes in the Huronian, 

 probably of the same period of eruptive activity, show a central zone, where the 

 augite has a uniform grain. 



Sugar and water illustrate aqueo -igneous fusion. Sugar fuses at 164 degrees Cen- 

 tigrade, and a solution of sugar and water can be raised to that temperature with 

 continual loss of water without crystallization. Solidification as a clear glass takes 

 place at a comparatively low temperature — about 60 degrees Centigrade. Hence 

 there is always a central zone of uniform grain. The more water there is, the 

 more is the tendency to be crystalline rather than glassy, and aqueous glasses 

 readily devitrify. Spherulites may be obtained, and by stirring during cooling, or 

 partial cooling during heating, porphyritic texture. The analogy in behavior to 

 Si0 2 and silicious glasses is very strong. 



Mathematical Equations 



Let u be the temperature at a time t after the beginning of the cooling of a point 

 at a distance of x from the margin of the zone of affected temperatures. Let u be 

 the initial temperature. Let e be the exponential base, tt the ratio of circumference 

 to diameter in the circle and a a constant depending on the conductivity. Let 



— (vr ale) 2 t 



Suppose the whole zone whose temperature is affected to have breadth c, and a 

 sheet of breadth 2w to be inserted at a point at a distance from the same margin 

 from which x is measured such that its center is at m. 



Then by Riemann,f 



n = co 



tt/ 4 . u/u = J sin^nxm/c) . sin(nrrw/c) . sin (mrx J c) . q n2 /n. 



n = I 



* Bull. Geol. Soc. Am., vol. 6, p. 469. 

 f Differential-gleichungen. 1882, §57. 



