of the Figure of the Earth, 411 



in the arrangement of the materials is in reality very small. It 

 simply supposes the density in the thin curved layers A A' and 



CC'j as well as bbf and dd' } to be doubled, and the excess of 

 matter for this purpose to be drawn from the whole of the shell 

 by a very trifling attenuation. 



5. I shall take four examples of depth below the surface; viz. 

 four, three, two, and one fifths of the radius. The following will 

 be the values of the several quantities to be used, and the results 

 which the formula of paragraph 2 leads to : — 



Surface. 

 qa = 140° 45' 



Second 

 ellipse. 



112° 36' 



Third 

 ellipse. 



84° 27' 



Fourth 

 ellipse. 



56° 18' 



Fifth 

 ellipse. 



28° 9' 



or 2-458 



1-966 



1-475 



0-983 



0-492 



Z 1 = 4-008 



1-818 



0-857 



0-344 



0-081 



6 



0-915 



0-859 



0-814 



0-540 



E 



0-663 



0-337 



0-113 



0-015 



E and E' are the masses of the whole earth and of that part of 

 it which lies within the outer surface of the shell which is under 

 consideration. The above values of E' are the approximate 

 values, neglecting the ellipticity of the strata, because E' will be 

 used only in small terms : it is calculated from the formula 



E'= f W. A ^ da= ±£ sin (j _ <E_ \ . 



; a q l * \ tan qa/ 



2E2 



