24:8 Wisconsin Aademy of Sciences, Arts and Lettirs. 



Coimutatioa now gives for attraction jj^g^^, g^xxV^ + a^T^ =3Fa_T^' 

 Average g for the layer equals a trifle less tha i ^ (33^^ g ^ + 33L -^ or -^-^. 

 Equitorial radius of sixth layer less that of fifih equals 127 4194 X ||f"|^ 

 127 8038, or equitorial radius of sixth layer is 766.8303 miles. The polar 

 and equitorial radii now found for sixth layer tests the assumptioQ for 

 ellipticity. Thus the process is continued from layer to layer in order. 



For the surface of the earth, Table 4 gives attracti n g|^. gravity -jl^ 3, 

 and ellipticity afais- It is accepted that attraction is ^^y^, gravity j|^g and 

 el ipticity -^^^. It is accepted also that the m an density of the earth is 

 5.65 times that of water, and that the surface crust density is not far from 

 one-half of th -> mean. Further, it is accrpted that a flu'd of uniform em- 

 perature is compressed directly as applied pressure. Table 4 is made up 

 in accordance vs^ith these known facts, making a due allowance for an in- 

 crease in crust temperatui-e. It seems reasonable, then, to accept there- 

 suits of the Tables. 



The expression already developed for the sine of the angle made by 

 radial direction with the direc ion of attract on is, f h n- m sin O cos O. 

 Columns 8, of Tables 1, 2 and 3, gives the values for |- h n- m. From these 

 results the direction of attraction at any point on the surface of the earth 

 is, 005137xf sin O cos O. When angle O becomes 45°, 



.005137X1 sin O cos O =.001712. 

 At 45° the centrifugal force changes the direction of attraction! 



4xaT)-=54^ = -001730. 

 The direction of gravity or of normal thus computed is: 



.001712 + .001730 = .003442. 

 The direction of the normal for 45" is: 



^1^ = . 003401. 



The error is -^-^, while the limit of error in the results attained by exper- 

 iments for the mean density of the earth, or the ratio of surface density 

 to mean is a fraction greater than this The tables can be adjused to 

 meet the discrepancy -^-^r, but it would add nothing to Hccuracy as long as 

 the accepted results of observation are equally uncertain. 



To one now doubting the theory of the geologist, I have to say in due 

 time, I shall give him a result for the precession of the equiooxe?, com- 

 puted from the data of Table 4. agreeing with observation. 



Tiie one effect of the attraction of the sun and moon on the earth wholly 

 liquid, is changeable figure; the other effect on the earth wholly solid, is 

 precession of equinoxes. The effect of the attraction on the particles of 

 a liquid or solid just fillit g the solid unyielding crust container is the 

 same. To be otherwise the container must instantaneously yield to certain 

 changes of figure due certain effects of the attraction on the particles of 

 the enclosed liquid. In such event the container has the liquid property 

 and from the logic of the astronomer there should be no precession. 



