METEORS OF AUGUST AND NOVEMBER. 127 



The capital letters denoting the same quantities for the earth. Now, as Pro- 

 fessor Olmsted supposes the velocities common, and the radii vectores are known 

 to be common to terms of the order of the earth's radius divided by its radius 

 vector, the semiaxes majores, a and A, must be common, as well as the periods 

 to the terms of the same order. Again, since u and U are supposed to be com- 

 mon in quantity and position, the parameters and consequent eccentricities, 

 and also the planes of orbit must be common, that is to say, the two bodies 

 must belong to the same system, and must have the ordinary secondary rela- 

 tion of primary and satellite, or they would immediately fall together. It ap- 

 pears, then, that such a coincidence as that which these authors refer to, is not 

 possible in any part of the orbits of two bodies having respectively a half yearly 

 and yearly period. 



The mean angular second's motion w of a satellite round the earth, in se- 

 conds of space, at the distance of its own radius, c = sin «y, abstracting per- 

 turbations and resistance of medium, is 



(2) n = 



^^ V(?y^ + m') ^ 257".08 



86400 sin 1" ' sin^ xs 



n 



V ■= — = 4.285 geoff. miles, 



60 ^ ° 



y/2 X V = 6.06 geog. miles. 

 Where 



!{, = Gauss' constant given above, 

 m — the earth's mass in parts of the sun's, 



m! = the satellites 



m = 0.0000028192, 

 m' = 

 cj = 8".5776 = sun's horizontal parallax, 



V = mean second's velocity in geographical miles. 



Whence we have, as already stated, about six geographical miles as the great- 

 est seconds motion which, a periodical satellite can have round the earth. 

 Hence the necessity of the cosmical theory; for we cannot refer them, with 

 Professor Olmsted, to a radiant body with a yearly period, keeping itself con- 

 stantly near the earth.; nor can we suppose them satellites of the earth — nor 

 projectiles from the moon — nor from the earth's volcanoes— nor atmospheric 

 scintillations; and there remains no other plausible source of motion but the 

 sun's attraction. 



