1882.] ^^^ [Chase. 



partly among the asteroids, partly in satisfying special requirements of 

 the dense belt, and partly in the variations of pethereal vis viva. The mass 

 of Mercury is so imperfectly known that it is unsafe to put much trust in 

 the accuracy of any merely harmonic indications of its value, but its 

 virtual area is unquestionably of the same order of magnitude as (|)' of 

 that of Mars, or /^Vg of that of Earth. This would give, for an approxi- 

 mate estimate of the quotient of Sun's mass by that of Mercury, 4054440. 

 The two intermediate steps may, perhaps, be partly absorbed by the intra- 

 Mercurial harmonic nodes and the meteoroids of the zodiacal light. 



165. Belative Masses of Neptune and Mars. 



An intermediate step between the virtual areas (Note 159) and the nodal 

 masses (Note 156), is indicated by the ratio between the masses at the 

 outer limits of the supra-asteroidal and the intra-asteroidal belts. The 

 quotient of the square of Neptune's harmonic virtual area, 22.644^ by its 

 harmonic radius, 30.036*, is 17.071 ; the quotient of the squared area of 

 Mars, (|)«, by its harmonic radius, 1.669, is .10664 ; the ratio of the masses 

 and the mass-ratio of Sun to Mars are approximately shown in the follow- 

 ing proportions : 



m,g ■.m^■.■. 17.071 : .10664 : : 160.09 : 1 

 m„ : m^ : : (160.09 X 19380 = 3102544) : 1 



166. Various Harmonic Indications and Tests. 



If K represents Earth's limiting nucleal radius (Note 159), the corres- 

 ponding atmospheric radius would be a:3 ^= 43.653. Herschel's locus of 

 incipient subsidence, in the controlling two-planet belt, or Saturn's secular 

 aphelion, is 1.0843289 times the outer limiting locus of the belt (Stockwell, 

 Smithson. Contrib., 232, p. 38); a.-! -.- 1.0843289 = 40.258, wliich is, with 

 close approximation, the ratio of the instantaneous virtual area at the inner 

 locus of the controlling belt, to the corresponding area at the chief centre 

 of condensation. The tendency of exponents, in elastic media, to become 

 coefficients of elastic vis viva, is shown in Note 159. If we use the sym- 

 metrical harmonic areas for Mars and Mercury, the percentages of differ- 

 ence between the harmonic and virtual areas are, respectively, f of 

 .01, f of .01, f of .01, f of .01, } of .01, .045, .099. In testing the com- 

 bined harmonic influences of a vera causa which is subject to internal per- 

 turbations, there is room for a possible deviation of 50 per cent, and a 

 probable deviation of 25 per cent. The combined probability that the 

 approximations in Note 159 are owing to sethereal influence is, therefore, 

 30 X H^ X 175 X ^1^ X 175 X -%"- X W = 15664091727 : 1. 



The following points of symmetry and alternation may be noted in the 

 nodal mass-factors of the two outer placets. Note 156 : 



1. The tendency to equality of mean ofbital vis viva in Earth, Uranus 

 and Neptune, as indicated by the factors y^, y., and ^'g. 



<?Proe. Am. Ph. Soc, xiii, 239. 



