272 



RECENT RESEARCHES OX THE 



a fiDitc iiicreraeut to eacli of the planetary masses. Then, taking the 

 diiierence between the two sets of constants, and dividing by the incre- 

 ment which produced it, we get the coefficient of the variation of the 

 constants for any other finite increment of mass to the same planet ; but, 

 on account of the importance of the earth's mass, and the probable in- 

 accuracy of its assumed value, we have prepared separate solutions cor- 

 responding to the several increments of gV? -ioi ''^^^ yo ^f its assumed 

 mass ; and a comparison of the values which the different solutions give 

 for the superior limit of the eccentricity of, the earth's orbit has sug- 

 gested the inquiry whether there may not be some unknown physical 

 relation between the masses and mean distances of the different planets. 

 The same peculiarity in the elements of the orbit of Venus is also found 

 to depend upon particular values of the mass of that planet. But with- 

 out entering into details in regard to the peculiarity referred to, we 

 here give the several values of the masses of these two planets which 

 we have employed in our computations, and the corresponding values 

 of the superior limit of the eccentricity of their orbits : 



These numbers show that if the mass of Venus were to be increased, 

 the superior limit of the eccentricity of her orbit would also increase 

 until it had attained a maxunum value, after which a further increase 

 of her mass Avould diminish that limit ; and the same remark is also 

 applicable to the eccentricity of the earth's orbit. 



The above numbers indicate that the superior limit of the eccen- 

 tricity of the orbit of Venus is a maximum if the mass of that planet 

 is equal to w'o(l+-^'^'-), or, if J»'=3^Viro of the sun's mass; and the 

 superior limit of the eccentricity of the earth's orbit is a maximum if 

 the earth's mass is equal to m"o{l+^W), or, if m"=^^^j^^ of the sun's 

 mass. But this value of the earth's mass corresponds to a solar paral- 

 lax of 8".730, a value closely approximating to the recent determina- 

 tions of that element. 



If, then, the mass of Venus is equal to a^^^gd) ^^^ ^^^ ^^^^ ^^ ^^® 

 earth is equal to -.,-,^V(hjj i^ follows that the orbits of these two planets 

 will ultimately become more eccentric from the mutual attraction of the 

 other planets than they would for any other values of their respective 

 masses; and we may now inquire whether such coincidence between 



