The Variation in Attraction Due to the Attracting Bodies. 347 



130 m'les thickness must be kept intact, while the interioi* layers are 

 made infinite in n'miber. This shows that the law of compressibility is 

 inapplicable to the crust on account of increase in temperature, while it is 

 applicable t > the interior from uniformity of tenperature. 



The numbers in column 2, table 4, divided by 56745 are the proportional 

 masses c unposingtha earhh taken in thirty-one layers, the outside liyer 

 having an assume i average density of unity, or 2.96. times that of water, 

 the mean density of the t arth being 5.65 times th it also of water. The 

 other layers have masses the same as if earth were taken in laye-'S infinit- 

 esimally thin. The numbers in column 3, divide 1 by 56745 are the pro- 

 portional masses of thirty-one ellipsoids composing the earth under condi- 

 tions explained for second column. The first number in column 4 is the 

 average deusity of layer 31, and the other numbers of the column taken 

 in order are the densities at division surfaces between the layers The 

 fractions in column 6 represent the quotients of centrifugal force divided 

 by attraction at the surface of each layer. These results are easily at- 

 tained, the one at the surface of the earth and the masses of layers beiag 

 known. 



Column 9 gives the polar radii of the thirty-one laj ers, the polar radius 

 of the earth being a^out 3,950 miles. 



The formulee already developed for the attraction at the pole of any 

 layer less, that at the equator is: 



Mr 6c T 2h 9 



Dif. Att. = T-rl Jh + g7(H— h) I +-j-j(m + m,+etc.)— ^,(mh+m, n-h +etc.) 



The values for c are given in column 5. These numbers are easily com- 

 puted when the densities and the ellipticities of the layers are knosvn. 

 Before making Tab'e 4, I had so unraveled its net- work by a system of 

 assumptions and corrections that I knew to a close approximation each 

 result. The values for 1 are givtn in column 4. M of the formulae for the 

 surface of any layer is found by adding numbers in column 2 from layer 

 1 to tht^ layer required inclusive. M equals M less the sum of numbers in 

 column 8 not inclusive of the required layer, m, m,, m^, etc., ai"e given in 

 column 3. For the sirface of any lay^r H equals ^Jj, and for any layer 

 from 1 to 5 Jf equals M, 1 equals 3.05; c, 1.57; and m, m,, etc., are each 

 zero. For the fifth layer the fi-actionfor ellipticity equals that for gravity; 

 and the frdcti>n for gravity equals the sum for attraction and centrifugal 

 force. For fifth layer, then, 



1.57x6 



g = h = lh + 3-^j5^GJj-h) + 4j?.« = 3k,rtf- 



Equatorial radius = 637.0956 X §gf § = 639.0165. 



For layer sixth: 



^, = ^U ffft , c = 1.57. 1 = 3.04. Assume ;,.',. ,tt, for h. 



