9.] 



9 



[Chase. 



8, The ratio of variation between Laplace s limit, r^, and the nucleal 



4 



radius, ?■„ ; r^ oc 7-g^. 



From Struve's constant of aberration, equation A, and other well-known 



measurements, we find : V = 214.5365ro ^ 497.827 = .43094.58/^ 



214.5365^ 



= 4.9075 



X 2 'To -^ 31558150 = .00063564ro ; »o = ( 

 v,=^2- X 3962.82 ^ 86164 = .288974; 



962.83 X 32.088\^ 



5280 / 



V^ Vo = 688.815 ; 



0, «o) «r. pQ and 



.B. 



«o -H -y^.^ 16.98337. The combined nodal action of V., V, 



2?' are represented by the equation : 



V 



688.815 X 16.98337 = p^ -^ 7935.64. 



^0 = 93,711,850 miles. 



V = />o ^ 497.837 — 186,333 miles = 399,705 kilometers. 



rg — po-^ 314.5365 = 433,495 miles. 

 p^-^r = 33,395.4. 

 Sun's mass 

 Earth's mass -g^Q'9^^^- J 



If we adopt Newcomb's estimates of Sun's diameter, mass and distance 

 [Popular Astronomy, p. 528), the nodal value of V. would be 185,334 



miles ; the value as determined by Struve's constant of aberration, 185,475 

 miles ; the discrepancy being only ^^ of one per cent. Michelson's esti- 

 mate (299,820 km.) is about -^-^ of one per cent, greater than mine, and 

 about A of one per cent, greater than Newcomb's. 



Newton's law of the ratio of elastic densities to distances (8), the laAV of 

 projection under uniform resistance (9), and the ratio of variation between 

 Laplace's limit and the nucleal radius, all are illustrated by the lunar 

 equations : 



32 „„ „„_ 1 



~ X -g r-/>i 



60.3815r. 



it) 



Pq very nearly = 23, 622?*. 



.C. 



J. J. von Littrow's estimate for Moon's semi-axis major, cited by Searle 

 (p. 406), is 60.3778, or about yVo of one per cent, less than the above result. 

 The velocity of light, as deduced from the lunar value of p^^, is 188,040 

 miles, or nearly one per cent, greater than the value found in equations B. 



I think no one will be likely to attach much weight to the larger value, 

 but it is interesting on account of its indication of elliptical nebular influ- 

 ence, with a nucleal radius about one per cent, larger than Sun's pres- 

 ent radius, and a major axis about one per cent, larger than Earth's pres- 

 ent mean vector-radius. The nebular influence may be inferred from the 



fact that — 

 9 



X 



(4): 



PROC. AMER. PHTLOS. SOC. XIX. 107. B. PRINTED MAY 5, 1880. 



