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PROCEEDINGS OF THE AMERICAN ACADEMY 



contraction of the radius of its orbit from 36 to 35, and that this disa- 

 greement would have still farther increased by a still farther contrac- 

 tion, there was a distance at which the disagreement ceased to in- 

 crease, and would, on the contrary, begin to diminish, until at the 

 distance 30 it would have vanished, and the disturbed motions of Ura- 

 nus would have been wholly explained. But this singular change in the 

 character of the disturbing force, if it really occurs, — and the only 

 doubt in regard to it is derived from a supposed but unproved inaccu- 

 racy in Leverrier's investigations, — was excluded from the range of 

 this geometer's investigations, and now that observation has led to its 

 discovery, geometry cannot claim it as one of its predictions. The 

 defect of the theory must be as frankly admitted as the more serious 

 charge of error is boldly repelled. 



" From some indistinct remarks which have been thrown out in re- 

 gard to the mass of Neptune, which is not too small to be excluded from 

 the limits of the theory, there seems to be an indisposition to confess 

 this defect. But on turning to the original formulae, it will be found 

 that, although this small mass is not positively excluded, its adoption 

 does not contribute to advance the claim of geometry upon the planet. 

 It shows, on the contrary, most decisively, that the orbits of theory are 

 all of them fundamentally different from those of Neptune. For the 

 mean distance which corresponds to this mass in the theory is about 

 35^, and the eccentricity very much greater than in the best hypothet- 

 ical orbit, while the discrepancy between the theoretical and observed 

 action on Uranus is increased beyond the admitted limits. 



" The case might safely rest there, but I desire to dwell upon the 

 essential and radical difference between Neptune's action upon Uranus 

 and that of the planets of theory. For this purpose, I will read an 

 extract from a report made by me last September to the honorable 

 committee of the Overseers of Harvard University who visited the Ob- 

 servatory. 



" ' The differences are not accidental, but inherent in the very nature 

 of the case, while the points of resemblance are purely accidental. 

 The solutions of Adams and Leverrier are perfectly correct for the as- 

 sumption to which they are limited, and must be classed with the bold- 

 est and most brilliant attempts at analytical investigation, richly enti- 

 tling their authors to all the eclat which has been lavished upon them, 

 on account of the singular success with which they are thought to have 

 been crowned. But their investigations are nevertheless wholly inap- 



