18C9.] ^^«^ [Lowiie. 



this product of the central force may not be entirely merged in the pro- 

 duct of some disturbing force. 



Dr. Whewell regards the discovery of the precession of the equinoxes, 

 resulting from the attraction of the sun and moon on the earth's equa- 

 torial protuberance, as a remarkable example of the consilience of induc- 

 tions ; but surely this consilience is more impressive when Ave notice 

 that that form of attraction is enterely singular, not being known to exist 

 in any other, even analogous, case ; whereas, the form here suggested ap- 

 plies to every case where there are revolving nodes ; that it presents the 

 motion as a perfectly normal consequence of the central force of each 

 system or sub-system, operating diiectly upon its dependent body according 

 to the relation of its orbit ; and that it recognizes a jihysical, along with 

 a formal, unity in the plan of the whole system, and satisfies the second 

 of Newton's "Eules of philosophizing," that "Natural effects of the 

 same kind are to be referred to the same cause, so far as can be done." 

 The other theory has this difficulty to contend with : that we suppose all 

 planets to have equatorial protuberances, as an effect of rotation ; and, so 

 far as we know, all have inclined axes ; and yet we do not attribute to 

 them precession of equinoxes and recession of nodes as two different 

 motions. Both exist, but only as different aspects of the same motion. 



But the views here presented are not without serious difficulty in their 

 ulterior application. If the cause here suggested is true, then it seems 

 natural to seek some proiDortion in time between the revolutions of the 

 nodes and those of the central bodies on which they depend ; a proportion 

 modified by the differences of relation in space and time in which the 

 several secondaries stand to their primaries. I do not discover the law of 

 such a proportion, or even that it surely exists. If it were discovered it 

 would probably be of use in seeking the period and orbit of the sun's revo- 

 lution. 



So far as our knowledge goes at present, we find that it always requires 

 many revolutions of a planet or satellite for one revolution of its nodes, 

 and they differ very greatly. In one revolution of its nodes Mercury re- 

 volves in its orbit over 500,000 times ; Yenus, 100,000 ; the earth, 35,000 ; 

 Mars, 27,000 ; Jupiter, near 7,000; Saturn, 2,200 ; and Uranus, 428. No 

 others revolve in so short a time as those of the earth. Among the satel- 

 lites, the moon revolves 230 times for one revolution of its nodes ; Jupi- 

 ter's 2d satellite, 3,000; its 3d, 7,000; its 4th, 11,000 times. 



And in all known cases the central body revolves more frequently than 

 the nodes of its dependent. Thus the earth revolves in its orbit near 19 

 times for one revolution of the moon's nodes; Jupiter 3| times for once 

 of the nodes of its 3d satellite, 12 times for its 3d, and 45 times for 

 its 4th satellite. All this would seem to indicate a period for the sun's 

 revolution round its unknown centre, which would be a very small frac- 

 tion of any estimate of it that I have seen, founded on observations of 

 stellar parallaxes. I find no clue to the solution of this apparent anomaly; 

 I hope some other inquirer may. 



