190 SEE— FURTHER RESEARCHES ON [April 24, 



3 I /> • 4'7rr^x' ■ rdx ■ a- 

 Jo 



P' 



R' = 



Siraj'^ ^TTO-^r^ (lO) 



3' 



= ^{cr^gW^ (i ~^v ^^- t-n {g.)-gxcos (,.)] ) . 



On putting- qx=^ 144° 53' 55". 2, the value of the integral is found 

 by quadrature to be 0.9592502, and when the rest of the formula is 

 reduced to numbers we have {A. N., 4104) : 



R' = 1028702 atmospheres. 



The rigidity of nickel steel is taken to be 1,000,000 atmospheres. It 

 thus appears from this calculation that the average rigidity of all 

 the earth's matter somewhat exceeds that of nickel steel. The 

 actual rigidity of the earth almost certainly lies between the limits 

 thus established, namely i? = 748,843, based on the rigidity of the 

 layers deduced from the pressure to which they are subjected, and 

 i?'= 1,028, 702, derived from the product of the mass of each layer 

 by the pressure acting upon it. 



In the paper, " Researches on the Rigidity of the Heavenly 

 Bodies," A. N., 4104, the rigidity of the earth is discussed as 

 follows : 



" When one considers the effects of the enclosing crust and the viscosity 

 of the whole earth, which must be assumed to increase towards the centre, 

 owing to the increasing density and rising temperature of the imprisoned 

 matter, it seems not improbable that the actual effective rigidity of our 

 globe may be nearer the upper limit than the lower, and probably we shall 

 not be far wrong in concluding that it is approximately equal to that of 

 nickel steel. 



" Leaving aside the consideration of the eft'ects of the solidified crust, 

 it is evident from the nature of the forces at work that most of the yielding 

 of our globe, due to the periodic action of small forces, is in the outer layers ; 

 and in general the yielding in any concentric layer may be taken to be in- 

 versely as the pressure to which the imprisoned matter is subjected. It is 

 remarkable that the curve of pressure as we descend in the earth becomes 

 therefore also the curve of effective rigidity for the matter of which the 

 earth is composed. Thus the rigidity of the matter at the earth's center 

 probably is at least three times that of nickel steel used in armor plate; as 

 we approach the surface the effective rigidity constantly exceeds that of 

 nickel steel until we come within less than 0.4 of the radius from the sur- 

 face, where the pressure is less than 1,000,000 atmospheres. 



