34 STATEMENTANDEXPOSITIONOF 



1867) has given us the following equation, dependent on the necessity of an 

 admitted increase in the motion of the perihelion of Mars. 



He states that, in so far as we now Ivnow — 



Ten times the correction of the mass of the Earth, plus three times the mass of 

 the small planets, in a mean distance reference of the group, would make a sum 

 equal to 1.38 j the mass of the Earth deduced from the parallax of Encke, 8".58, 

 being taken for unity.'^ This mass is 3^54^93 e- 



The mass of Mars which M. Le Verrier employed in his investigations, would 

 seem to be the same with that which he has, provisionally, attributed to that planet 

 in the Gomptes Rendus for July 22, 1872; viz, 0.000000333 of the sun. 



With these values of the data, the equation of M. Le Verrier will give us, for 



THE ASTEROID MASS, THE SAME FRACTION OF THE MASS OF MarS WITH THAT WHICH JUS- 

 TIFIES THE TERM [^(A)] IN DUE TaBLE (F); if we make THE SOLAR PARALLAX 8".896;^ 



which is a value included within the present limits of uncertainty, and 7iear to the 

 mean of all the more recent determinations. 



(48) If, then, fortified by these several coincidences, we allow any weight to 

 the determination of the value of the Asteroid mass derived from the justification 

 of the term \_i (A)] of the series here in question ; it may be noted that this value, 

 (41), depends on the ratio of the diff'erence of the squares of the terms [?j(A)] and 

 Mars to the diff'erence of the squares of (A) and [% (A)]; and the tabular values of 

 the quantities represented in the terms thus involved, may all be considered as 

 being approximately well-determined. 



[It will, moreover, be observed that the several independent elements which have 

 entered into the computation of this result are: — 



1. The leading ratio r, in Table (B), in (14). 



2. The leading ratio i?i, in Table (F), in (45). 



3. The application of the formula for the centre of gyration; and 



'...." on doit dire qne dix fois la correction de la masse de la Terre, plus trois fois la masse de 



I'ensemble des petites planetes distribuees en moyenne, d'apres ce qu'on en salt aujourd'hui, doit faire 



une somme egale a 1.38 ; I'unitc ctant la masse admisc pour la Terre quand on la dcduit de la paral 



laxe d'Encke, 8". 58." 



, ^ /8".896\' increMsed mass of Earth, M ,, 1^11 o'/ co 1 • i 



2 Eor, I I = ^ '- — ; tno mass due to parallax 8 .58, beinff=l 



Is". 58/ 1 ' 1 . e 



M being thus determined — 



Then M — 1 = increment of Earth's mass = i. 



Then m' being asteroid mass, M. Le Terrier's equation gives — 



lOi + 3m' = 1.38 ; whence 



3m' ==1.38— lOi, and 



asteroid mass, m' = ^ ; the mass of the Earth due to parallax 



8". 5 8 being 1. 



Then «i'= asteroid mass m" in terms of the Sun's mass 1. 



354936 



And this last value is otir fraction (0.58929) of 31. Le Verrier's mass of Mars, i.e. the same fraction 



of the mass of Mars (taken = ]), wWch justifies the value of our ['S(A)] term in our Table (F). 



