,907.] AND CONTRACTION OF THE EARTH. 201 



— sin^^ I 



x^dx \ ; and when x = I 



^ Qio'aZY^ \(7 — sin q cos a sin' ^ 



^ = l^^y 1 ^ 2^— - V) = 748.843 atmospheres. (7) 



And the average rigidity of all the earth's matter is : 



47^/^ Jo ^ ^ 2(o-^<ry^i 1 Jo ^^ 

 ' 2 "1 

 2"^ [sin (^,r) — ^,r cos (^;r)] [ = 1,028,702 atmospheres. (8) 



The rigidity of steel is generally taken to be 808,000 atmospheres, 

 but that of nickel steel is at least 1,000,000. The true rigidity of 

 the earth probably lies between the limits set above, and it seems 

 certain that it exceeds that of common Bessemer steel. 



In these calculations no account is taken of the increase of rigidity 

 due to the earth's solid crust, the effect of which is known to be 

 considerable; for even the viscous layers just beneath the crust 

 remain quiescent except when set in motion by the dreadful parox- 

 ysms of an earthquake. So difficult is this motion to effect that the 

 throes thereby arising may perceptibly disturb a whole continent, 

 and become sensible to observation throughout the world. 



Accordingly if the matter of the interior, in confinement under 

 great pressure, behaves as an seolotropic elastic solid, with a rigidity 

 depending on the pressure and therefore increasing with the depth, 

 it naturally follows that no currents can circulate at great depths ; and 

 we see that it obviously is not true, as some geologists have imag- 

 ined, that liquid lava is extruded from deep down in our globe. 

 Neither is it permissible to suppose, as Professor Chamberlin has 

 done (cf. " Geolog>%" Vol. I., p. 630, and Vol. II., p. 120), that our 

 present volcanoes had their start at a depth of some 1200 to 1500 

 miles. 



It follows from the theory developed in the paper on the cause 

 of earthquakes that the original roots of volcanoes were but little 

 deeper than the explosive forces which give rise to world-shaking 



