BtTE TO THE WEIGHT OF CONTINENTS. 
207 
The directions of the stress-axes are given by 
cot 2f9-=~~~~= cot ^ 
so that 
. ( 40 ) 
Equation (39) gives the stress-difference at a depth £ below the mean surface, and 
is very remarkable as showing that the stress-difference depends on depth below the 
mean horizontal surface and not at all on the position of the point considered with 
reference to the ridges and furrows. 
Equation (40) shows that if we travel along uniformly horizontally through the 
solid perpendicular to the ridges, the stress-axes revolve with a uniform angular 
velocity. 
They are vertical and horizontal when we are under a ridge, and they have turned 
through a right angle and are again vertical and horizontal by the time we have 
arrived under a furrow. 
Since the function xe~ x is a maximum when x—1, the stress-difference A is a 
maximum when £=b } —that is to say, at a depth equal to 1 / 27 r of the wave-length— 
and is then equal to 2 gwhe~ l or in gravitation units of force to *736 wh. It is inte¬ 
resting to notice that the value of this maximum depends only on the height and 
density of the mountains, and does not involve the distance from crest to crest. The 
depth at which this maximum is reached depends of course on the wave-length. 
Plate 19, fig. 2, shows the distribution of stress-difference, the vertical ordinates 
represent stress-difference, and the horizontal ones depth below the surface. The 
numbers written on the horizontal axis are multiples of b; the distance OL on this 
scale is equal to 6' 28, and is therefore equal to the wave-length from crest to crest, 
and the distance OH is the semi-wave-length from crest to furrow. 
In the case of terrestrial mountains w is about 2*8, and if we suppose h to be 2000 
meters, or a little over 6000 feet, we have the case of a series of lofty mountain chains 
*—for it must be remembered that the valleys run down to 2000 meters below the 
mean surface, so that the mountains are some 13,000 feet above the valley-bottoms. 
Then h—2 X 10 5 , iv—2'8, and the maximum stress-difference is 
'736 X 2'8 X 2 X 10 5 =’412 X 10 6 grammes per square centimeter. 
This stress-difference is, in British measure, 2 ‘6 tons per square inch. 
If we suppose (as is not unreasonable) that it is 314 miles from crest to crest of the 
mountains, then the maximum stress will be reached at 50 miles below the surface. 
From Table VII., § 9, it will be seen that if the materials of the earth at this depth 
of 50 miles had only as much tenacity as sheet lead, the mountain chains would sink 
down, but they would just be supported if the tenacity were equal to that of cast tin. 
