590 



SCIENCE 



[N. S. Vol. XXVII. No. 693 



800° C. A fundamental crust of the earth 

 without any original quartz would be a geolog- 

 ically novel conception. The atmosphere above, 

 being vastly heavier perhaps than at present, 

 should certainly be at over 0° 0. I should 

 guess very much over 100° C, and it would 

 seem that Becker's 1,300° might well be cut 

 in two, if, indeed, there were any sudden jump 

 between the atmospheric temperature and the 

 rock surface temperature. 



Now, when we come to the denominator, he 

 fixes the original gradient, which will still 

 persist below the relatively thin rim of the 

 earth that has cooled appreciably, so that the 

 earth may remain rigid. That seems reason- 

 able, and is practically the hypothesis of 

 Chamberlin and Lunn. But with regard to 

 the present geothermal gradient, Becker's work 

 seems defective in that he has made no at- 

 tempt to get his geothermal gradient and 

 diffusivity for the same rocks, though they 

 depend on each other. The diffusivity in dry 

 sand and peat is very low and the gradient 

 proportionally high. Moreover, most deter- 

 mined values of the geothermal gradient are 

 in that " ragged pellicle " of detrital matter 

 which he would leave out of consideration. 

 On this account alone, as well as the fact that 

 they may occupy several thousand meters, out 

 of some 114,000 meters discussed, the omis- 

 sion is a serious one. Thus to " abnormally 

 high diffusivity " as a possible cause of de- 

 ceptively low gradient we may add depression 

 under a load of sediment, downward water 

 circulation, endothermic reactions. 



It so happens that in our Michigan copper 

 mines we have an unusually good chance to 

 coordipate gradient and diffusivity, for: 



1. There has been but little net erosion or 

 deposition since a very early date. 



2. The rocks are very uniform in character. 

 The average of thousands of feet of diamond 

 drilling shows only about 7 per cent, of sedi- 

 ments in the main range. The traps are quite 

 uniform in character, mainly ophitic auverg- 

 noses. 



3. Sulphides are rare and reactions that 

 generate much heat are not present. 



4. The gradient is known for an unusual 

 depth. 



5. The conductivity of the three main types 

 of rock has been determined by Professor B. 

 O. Peirce, of Harvard.' The mean conduct- 

 ivity of the formation is about .0035, the dif- 

 fusivity .0064 in c.g.s. units, or in Becker's 

 units the meter and year about 20. 



The rate of increase of temperature throw- 

 ing out the first 100' of drift* is 1° F. in not 

 over 110'; 107' seems better, i. e., 1° C. in 59 

 to 60 meters. 



Varying diffusivity, if the same depends 

 merely on the depth, will be no great hin- 

 drance. We need merely to peel the earth 

 up into layers like an onion, each of which 

 shall offer the same resistance to the trans- 

 mission of heat. They will be of unequal 

 thickness really, but we shall have to call it 

 for each of them an equal increment of z, 

 z being a new variable in terms of which to 

 express the flow of heat. Then we shall have 

 to express x also in terms of z, x being the 

 real distance from the surface or some other 

 place of reference. We can then use all the 

 old diagrams of Kelvin, King and Becker, but 

 have to change the divisions on the scale 

 corresponding to the earth's radius and make 

 them unequal. 



Becker is also quite safe in neglecting the 

 curvature of the earth. The cooling of a 

 sphere has been treated by Woodward," and, as 

 I have elsewhere remarked," if we represent 

 hy Vm and Um the temperatures, respectively, 

 in an infinite slab with plane sides at a dis- 

 tance (c) apart and in a sphere (radius c) 

 cooling under certain similar conditions, at 

 points, in the one case at a distance x from 

 the plane face such that x/c = m, and in the 

 other case at a distance from the center such 

 that u/c = m, then 



Now, for points near the surface m = u/c is 



'Proo. Am. Acad. Sci., May, 1903, XXXVIII., 

 No. 23, p. G5S. 



* See discussions in my reports. Board of Geol. 

 Surv. of Mi.h., 1901, pp. 244 ff., 1903, pp. 195 flf. 



" R. S. Woodward, Annals of Mathematics, Vol. 

 III., 1S87, Eq. 10. 



° Geological Survey of Michigan, Vol. VI., Part 

 I., p. 121. 



