328 Mr. Ivory oji the Variation of Density and Pressure 



Again, excluding from the value of x quantities that become 

 infinite when a = 0, we get from the second of the equations 



— ./pa- da: 



a' <l a a3 



and at the surface when a = 1, 



(^■) = -Tijim- (:p))y 



(rf . T a5 \ „ m 



If these last values be substituted in the formula (2), C will be 

 found, and ?i will be the only quantity left indeterminate. The 

 calculation being made, I have found these definitive formulae 

 which agree with the determinations of Legendre and La- 

 place, viz. 



n- tan n 



A — 



tan n — n 



m 3 



, \ , s 5 (3 - x) 



Now, if we take ?i equal to an arc of 138°, then, 

 X = 1-578 

 -^ = 0-526 



m, 



The ellipticity agrees with the experiments of Captain Sabine. 

 If we suppose the mean specific gravity of ihe eartli to be 5*48, 

 that of the outer crust will be 2-88, which is about the specific 

 gravity of the rocks that compose the mountain Schehallien, 

 and therefore not far from the truth. 



With regard to the pressure, we have, from the last of the 

 equations (3), 



rf P 4 "■ 4 '^ sin a n 



-T— = — r X P = — r X • 



a J n- M- an 



It thus ajopears that — — increases from the surface to the 



centre; that is, the increment of pressure requisite to produce 

 a given increment of density is a quantity continually increas- 

 ing in descending to the centre. Now this is a property that 

 may be fairly, if not necessarily, ascribed to the law of pres- 

 sure that actually prevails in nature with regard to fluid and 

 solid bodies. The greater the compression, the greater a re- 

 sistance 



