INTRODUCTION. xvii 



difference between the two sets of constants, and dividing by the increment, 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 inaccuracy of its assumed value, we have pre- 

 pared separate solutions corresponding to the several increments of ,,\ 1 , .,-,,, and -,\ 

 of its assumed mass ; and a comparison of the values which tbc different solutions 

 give for the superior limit of the eccentricity of the earth's orbit has suggested 

 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 without entering into details in regard to the pecu- 

 liarity 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. 



For Venus. For the Earth. 



Mass ml Maximum e' MaSS in" Maximum el'. 



m' 0.0T0G33 m" 0.0G7135 



"*'o(l+3V) 0.074S72 mVl + s'o) 0.069389 



»»'o(l+3&) 0.07G075 m" (l+^r) 0.0G9G49 



•»'o(l+&) 0.075029 m" u (l+ 5 \) 0.0G8089 



»*'(,( l + s 4 o) • 0.072098 



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

 rior limit of the eccentricity of her orbit would also increase until it had attained 

 a maximum value, after which a further increase of her mass would 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 eccentricity of the 



orbit- of Venus is a maximum if the mass of that plant is equal to wi' M -j- -^ — ); 

 or, if rri ===____— 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 in" N -j — -\ 



or, if m" ^= ^ . of the sun's mass. But this value of the earth's mass corre- 



o4U70u 



sponds to a solar parallax of 8". 7 30, a value closely approximating to the recent 



determinations of that element. 



If, then, the mass of Venus is equal to , and the mass of the earth is equal 



3o4J:90 



to , it 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 the superior limits of the eccentricities and the masses of these 

 two planets has any physical significance, or is merely accidental. 



C July. 1872. 



