Chase.] ^08 [Nov. 4, 



inversely as radius-vector, (d -r- P). Equating these two expressions for 

 centrifugal energy, at the centre of condensation, we get 



i^oc- . (16) 



SCCpioc^ (17) 



f <x p^ oc (Jis (18) 



The limit of circular-orbital time, 2^ A/— , for Earth, is U = 5073.6 



g 



seconds, Earth's orbital time being ^i = 1 year = 31558149 seconds. If 

 these times were fixed by the above relations of "subsidence" we should 

 have 



31558149^ : 5073.62 : : d^^^ : oV (19) 



o\ = 3.8341 d, (20) 



- p. •■ po-- oV •• C : •■ 316.0944 : 1 (21) 



Earth's present density, as deduced from the combined influences of sub- 

 sidence, linear oscillation, conical oscillation and orbital Aelocity, (Notes 

 5, 23), is 3.9231 S^, as is shown by the following calculations : 



w„ =: (2 X 3 X 4)* m^ = 331776 m^ (22) 



p^ — (m„ -^ mg)^ X (^1 -^ tji X r.^ = 92,785,700 miles. (23) 



^^ = ^3 H- 214.4472* — 432673.8 miles. (24) 



(% : ^0 : : mj -V- r./ : m„ ~ p^^ : : 3.9231 : 1 -^ 



or, from (20), (21) and (22), 8^ : d^ : : 216.0944=» : 214.44723 I 

 : : 3.9231 : 3.8341 ' j 



ds:8,: 3.9231 : 1 J 



In (21) the radius of early lunar-telluric subsidence, p^, includes : — 

 a. Moon's orbital radius of incipient subsidence, or locus of apogee, .5824 p^; 

 /5. Earth's semi-axis major, 214.4473 P„, (24) ; and /. The semi-axis 

 major of the centre of gravity of Sun and Jupiter, 1.0647 p^. 



a. According to Von Littrow, Moon's locus of apogee = 1,054908 X 

 60.2776 X 3962.8 == 251,985 miles = .5834 p„, (34). 



y. According to Stockwell, (Smithsonian Contrib., 333, p. 38), Jupiter's 

 maximum eccentricity is .0608374. This gives, for the semi-axis major of 

 the chief centre of gravity of the solar system, (Note 113), p„ -4- .9391836 



= 1.064767 p„. 



The influence of nascent vis viva, at the centre of the belt of greatest 

 condensation, is further shown by the relations which are maintained, with 

 close approximation, between Earth and its adjacent planets. 



Nascent velocity at Laplace's limit, and consequent orbital vis viva, is 



* See Note 113. 



