350 Archdeacon Pi-att on the Thickness of 



distance 6 from 0, h . (j>-^d is the depth at a distance <l>, and the 

 moment a . k 



— iy —n^as\n(pad<p = ~ha-'l-^ cosaj. 



The equation of moments becomes 



t'i -t^ + 2{a vers e-h)t= bha^ (-^ - cos e\ . 



Suppose the sea is two miles deep at S, a point between Aus- 

 traha and Madagascar in south latitude 22°; then ^ = 30°, since 

 Cape Comorin is in north latitude 8°. The equation becomes 



/'2_ ^2 + 2(4000 X 0-134-2)^=160,000,OOo(- -0-866 Y 



/'2-/2+ 1068^=14,240,000. 



11. As in the former case, /' cannot be very small, otherwise 

 t^ is negative. The least value of t' is given by the equation 

 -2^ + 1068 = 0, or ^ = 534; 

 .-. ^'2= 14,240,000-5342= 13,954,844, 

 f'=3735 miles. 



This of course I do not consider to be a correct result. Before 

 reaching such a depth as this, the cohesive force will have so 

 altered that it will be improper to consider that the resultant of 

 the cohesion will pass through the mid-])omt% of the joints. 

 Moi'eover, if the thickness is so great as this, the point x would 

 fall below P, and the joint sv would not open; but the crust 

 would crack at some place further on, if it crack at all, where x 

 does not fall below P. In any case the crust, under these circum- 

 stances, must be very thick Other points there are in which the 

 calculation above given will not apply if the crust be exceedingly 

 thick ; but in that case, as before, what I am contending for is 

 conceded. And the conclusion, I think, may be fairly drawn 

 from this case, that the thickness must be very great to resist the 

 tendency of the ocean-bed to rise up in consequence of the upward 

 pressure of the lava below not being counterbalanced by the 

 weight of the ocean itself. 



12. These two cases strengthen each other. For the excess 

 of pressure on the lava under the mountains is communicated to 

 the lava under the ocean-bed, and increases the upward pressure 

 there, and vice vo'sd. 



Finally, then, since all things are in equilibrium, the mountains 

 maintaining their elevation and the ocean-bed continuing unal- 

 tered, the fair inference is that the crust must be very thick, 



