534 Prof. G. B. Airy on the History of the Discovery of 



though the observations will not be so well represented as 

 before, yet the errors of observation will be tolerable. At last, 

 on continuing the variation of elements, one error of observa- 

 tion will be intolerably great. Then by varying the elements 

 in another way, we may at length make another error of ob- 

 servation intolerably great; and so on. If we compute, for 

 all these different varieties of elements, the place of the planet 

 for 1847, its locus will evidently be a discontinuous curve or 

 curvilinear polygon. If we do the same thing with different 

 periodic times, we shall get different polygons: and the ex- 

 treme periodic times that can be allowed will be indicated by 

 the polygons becoming points. These extreme periodic times 

 are 207 and 233 years. If now we draw one grand curve, 

 circumscribing all the polygons, it is certain that the planet 

 must be within that curve. In one direction, M. Le Verrier 

 found no difficulty in assigning a limit; in the other he was 

 obliged to restrict it, by assuming a limit to the excentricity. 

 Thus he found that the longitude of the planet was certainly 

 not less than 321°, and not greater than 335° or 345°, accord- 

 ing as we limit the excentricity to - 125 or 0*2. And if we 

 adopt 0*125 as the limit, then the mass will be included between 

 the limits 000007 and 0'00021 ; either of which exceeds that 

 of Uranus. From this circumstance, combined with a proba- 

 ble hypothesis as to the density, M. Le Verrier concluded that 

 the planet would have a visible disc, and sufficient light to 

 make it conspicuous in ordinary telescopes. 



M. Le Verrier then remarks, as one of the strong proofs of 

 the correctness of the general theory, that the error of radius 

 vector is explained as accurately as the error of longitude. 

 And finally, he gives his opinion that the latitude of the dis- 

 turbing planet must be small. 



My analysis of this paper has necessarily been exceedingly 

 imperfect, as regards the astronomical and mathematical parts 

 of it: but I am sensible that, in regard to another part, it fails 

 totally. I cannot attempt to convey to you the impression 

 which was made on me by the author's undoubting confidence 

 in the general truth of his theory, by the calmness and clear- 

 ness with which he limited the field of observation, and by the 

 firmness with which he proclaimed to observing astronomers, 

 "Look in the place which I have indicated, and you will see 

 the planetwell." Since Copernicus* declared that, when means 

 should be discovered for improving the vision, it would be 



* I borrow this history from Smith's Optics, sect. 1050. Since reading 

 this Memoir, I have, however, been informed by Professor De Morgan, 

 that the printed works of Copernicus do not at all support this history, and 

 that Copernicus appears to have believed that the planets are self-luminous. 

 — G. B. A. 



