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Tim American Geologist February, 1896 
equal stresses ;il righl angles with one another, the cavity will be closed 
up when the stresses equal two thirds the ultimate strength of the rock. 
With ;i single stress the full crushing pressure is needed. Assumingthe 
strongest rock for these conditions, in order to determine a maximum 
depth below which cavities must be an impossibility, and taking the 
(specific gravity of the crust at 2.7, from which 1 is subtracted for the 
water that penetrates all fissures, the calculation gives for the first 
noted relation of forces 6,670 meters, and for the second 10,000 meters, 
as the depths where cavities become impossible. 
In the discussion. Prof. A. ( '. Lank compared this investigation with 
his former paper on the escape of the earth's internal gases ; Prof. 
Kemp referred to its bearing on the origin and possible depth of forma 
tion of mineral veins ; and Prof. IS. K. Emerson cited the Cambrian 
gneisses of Massachusetts, in which quartz crystals are flattened ou1 
as thin as paper, yet with their optical properties unimpaired. 
Mr. J. P. [ddings mentioned the interesting experiments of Dr. O. 
Mugge on ice crystals, as recently reported in the Neues Jahrbuch, 
showing that the) shear along gliding planes across the optic axis with 
out altering its direction. 
Possible Depth of Mining and Boring. Alfred ('. Lank, Hough 
ton. Mich. From a curve representing the minimum cost of mining at 
\ arious depths, with figures of the value' of various deposits, an idea as 
to the probable depth of mining is obtained. The two chief factors of 
cost are the the increased length of time in hoist and the increasing 
temperature. The escape of compressed air helps to overcome the kit 
ter difficulty. Figures were given from the Tamarack and the Calumet 
and Hecla mines, showing that nearly down to 5,000 feet the increase 
has been a little less than l t! Fahrenheit for each hundred feet, so that 
a depth <>f 10.000 feet can probably be reached there with no greal 
difficulty. One Calumet shaft is now down 4,800 feet vertically, and 
one Tamarack shaft is started which will not reach the lode until it is 
down 5,000 feet. [This paper will be published in " The Mining In- 
dustry," for 1896.] 
In discussion. Prof. Shalek suggested that the very low temperature 
gradient thus found in the Lake Superior copper mining district may 
be largely the effect of compressed air. The temperature gradient for 
the Calumet and Hecla mine recently published by Alexander Agassi/ 
appears to give only 1° F. of increase for each 223.7 feet down to 4,580 
feet. To supply this gradient a mean rock temperature at 105 feet of 
59° F. is used, whereas the mean annual temperature of that district is 
about 40°, and approximately this temperature of 40° has been deter 
mined at slight depths in other neighboring mines. A mean annual 
temperature of 59° F. is not met north of Kentucky, and this fact 
makes corroboration desirable before important inferences are based on 
these exceptionally low gradients. 
Prof. Lank suggested that, as the Wheeling record indicates, the low 
gradient may he due partly to a rise in the surface temperature since 
the Glacial period, or may also in part be due to the cooling effect of 
