CERTAIN HARMONIES OF THE SOLAR SYSTEM. 25 



in the former state ; we shall, by the application of the equation here adopted, in 

 eifect obtain QN or Q'N, and hence also SN, the distance of the neutral point N 

 from the sun's centre. With the same data from Tables (A) and (B) in (3) and in 

 (14), as before, we shall then have 



with the sun's horizontal parallax 8".8448, *S'iV= 0.85383, ) 

 and with " " " 8.78 , SN 0.85459. j 



While, (14), limit (© 9 ) due to a whole planet dis- 

 tance in Table (B), is . . . . 0.85101,. 

 exhibiting all but a perfect coincidence ; while, as 

 before, the distance of the centre of 



. ^ , , . o^ f 0.88665, or ) 



gyration irom the sun s centre . . ^^ ~ ] a qqi^^q | 



(40) Summing up then the specialities of the two half-planets. Earth and Venus, 

 which are consistent with the theoretical considerations now exhibited, we have 



1. In accordance with the conclusion in (39), the greater density of the exterior 

 half-planet, the Earth. 



2. The tilti7ig up (if the expression be allowable) of the equator of Venus and 

 its parallels — as if by the attraction outward, due to that same greater density — in 

 the antecedent arrangement of the half-planet masses. 



3 and 4. The decided approximation to agreement in position of — 

 {<i) The whole planet limit (©9) in Table (B). 

 (h) The neutral point, or point of equal attraction between the two half-planet 



masses, and 

 (c) The distance from the sun's centre of the centre of gyration of the same 



two half-planet masses, thus — 



(©?) = 0.851 + 



Neutral position is at 0.8541: 



Centre of gyration is at 0.886 i. 



Determination of the Mass due to a Half-Planet gi {now missing), interior to 



Uranus. 



(41) The distance due to such a half-planet has already been determined in 

 accordance with Law M, (10), and the salne is recorded in Table (B), in (14). 



The mass of this half-planet may be determined by means of the equation for 

 the centre of gyration of it and Uranus ; the case being similar to that of the 

 Earth and Venus,^ and the whole planet limit here being limit (u), in Table (B). 



Now let d represent the mean distance of Uranus from the sun, and m! the mass 

 of that planet ; while a and m, respectively, represent like quantities in the instance 

 of §i. Then, as limit (u) represents the position due to the centre of gyration, 

 Eq. (c) of (17), will read 



' But here the agreement of the position of the centre of gyration with the whole planet limit, 

 will have this favoring condition ; that under the less stringent circumstances, in this region of the 

 planetary system, it is not probable that any considerable portion of the more dense material was 

 carried to the outside, in the half-planet formation (or the tendency to it), as, (39), seemed to have 

 been true in the instance of the Earth. 

 4 December, 1874. 



