348 Archdeacon Pratt on the Thickness of 



I will apply this numerically to the case in hand : 



A= 15,000-2000 feet =2'46 miles; mB=115 miles, 

 B 1=140 miles. 



I might consider AB6 to be a triangle ; but I will take a more 

 unfavourable case, and suppose it part of a parabola with its 

 vertex at A ; 



.*. a = area cB + area bA = am . mB + ^bB . BA 

 =2-46 (115 + ^x 140) = 397-7 square miles, 

 A; = yAm, almost exactly, =170 miles. 

 Hence, putting C = j mile, then 



^^^ =10 X 397-7 X 170=676,090. 



Also a vers 6 = 4000 vers 3° 40' = 8-32 miles. 



7. Hence the equation of moments becomes 



t!^ + 2U'-t^ + lO'7S /=676,090. 

 This shows that t' cannot be very small, because then t^ becomes 

 negative. The minimum value of i' is found by differentiating 

 the above, considering i' constant ; 



.-. 2i'-2^ + 10-78 = 0, 



.-, ^' = ^-5-39. 



Putting this in the original equation, 



(2^-5-39)2-2^2 _,. 10-78 ^ = 676,090, 



2^2= 676,090 -27 = 676,063, t^ = 338,032 ; 



.-. ^=581, ^' = 576 miles. 



These make the crust very thick both at A and also at a. 



As far as the equation in t and t' teaches us, t may be as small 

 as we please, even zero ; but /' will be correspondingly great. 

 And such great variations in the thickness of the crust cannot 

 have been produced by any law of cooling that we can conceive. 



8. The above reasoning seems clearly to show that the crust 

 must be of great thickness to enable it to resist fracture arising 

 from the weight of the superincumbent mountain mass. 



9. I will now pass to the other case, the effect of deficiency of 

 matter in the ocean south of Hindostan, and the consequent 

 effect of the lava beneath to burst the crust upwards. 



Let (fig. 2) be Cape Comorin ; Q S the ocean stretching 

 south ; qs the gradually deepening bottom ; On, sv two imagi- 

 nary joints, and w and x their mid-points. The forces which we 

 have to consider in calculating the conditions of equilibrium of the 

 portion of the crust qsvuO, are the upward buoyancy equal 



