182 GEOPHYSICAL THEORY UNDER THE PLANETESIMAL HYPOTHESIS. 



= 



4n^k p^ 



M 



l+2cos2/9i' 



o sin i^i 

 Pi 



'■! 



(35) 



The constants p^, q, may be determined, for example, so as to give 

 accordance with any assumed values for mean density p^ and surface den- 

 sity pi, or the latter may give place to the condition resulting from obser- 

 vations of precession and polar flattening,^ which, according to somewhat 

 uncertain theory, indicate for the angle /?i a value in the neighborhood of 

 140°. The following computations are based on the assumed value 141.8°, 

 together with the numerical constants as listed in the introduction, giving 

 the following table under the assumed law: 



/?!= 2.475 = 141.8° 5=3.885X10-" 



pjp,= 0.25 H, = 4.096X10" 



p,= 2.717 £; =3.620 X10=^« 



^„ = 10.87 <? =2.456X10^^ 



h= 5.549X1010 <?>, = 1.768X10^* 



The resulting value of the surface density p^, though perhaps rather 

 small, accords fairly well with estimates of the mean density of superficial 

 strata, and an additional check on the applicability of the density-law in 

 question is found, as pointed out by Fisher, in the fact that the surface 

 value Hi of the elastic bulk-modulus ranges close to values found by direct 

 measurement.^ 



The accompanying tables, then, show the distribution of the principal 

 magnitudes at the close of the epoch of aggregation. The columns referring 

 to p, p, g are of course not novel, but are inserted for the sake of having all 

 computations based on an uniform set of numerical constants. 



Table 1. 



' Tisserand, M^c. Cel., ii, p. 235. 



' Fisher, loc. cit., p. 417; also Kelvin and Tait, Natural Philosophy, n, p. 415. 



