







Astronomy. 443 



it is easy to see, would amount to from 5" to 7". Combining the pos- 

 sible effects of these three causes, there results, as I have already ex- 

 plained, in 1846, the uncertainty of the data. It may fully amount to 

 10" or 12", although the uncertainty of modern observations is not 

 greater than 2" or 3". 



And after having added, in the same memoir, that the magnitude of 

 the discrepancies which might be allowed between observation and cal- 



culation, is thus indeterminate, I fixed it arbitrarily at 5" for all the po- 

 sitions of Uranus observed from 1781 to 1845. It is on this arbitrary 

 hypothesis that I have made my calculations of limits. But it will be 

 seen, and should not be forgotten, that instead of 5", I could have ta- 

 I ken 10" and even 12". 



J All this being granted, if any one will completely develope the nu- 



merical calculations of my theory of limits, a brief synopsis of which 

 I have given in the memoir of 1846, it will be found, even reducing the 

 uncertainty of the modern data to 5", that during 120 years which I have 

 j compared as above, the differences of the longitudes of Neptune in 



my predicted orbit and in the orbit of Walker, are always within the 

 uncertainty of the data. It is the same whether before or after these 

 120 years. But I confine myself to the consideration of this period 

 •sufficiently long however — because I can, in regard to it, support 

 myself upon the Compte Rendu of the 31st of August, 1846, and upon 

 my complete memoir published ia the Connaissance des Temps. 



I showed, the 31st of August, 1846, before the discovery of Nep- 

 I tune, that it might be necessary to push the search 18°*5 beyond the 



position which I had assigned as the most probable. I printed it anew 

 after the discovery of the body. 



Thus, since 1846, I have acknowledged that the uncertainty of the 



data might cause an uncertainty of more than 18 degrees in the place 



of the planet, at one of the epochs when we could best answer for its 



1 position. It is evident that the discordance in the longitude calculated 



j by my theory, has never been, during 120 years, equal to that which 



J I considered in 1846 as possible. Upon which I ought to remark : 



1st. It is proved that, whether before the discovery of Neptune, or 

 after that discovery in 1846, or at the present day, I have always held 

 the same language relative to the uncertainties in the results, produced 

 by the uncertainty of the data. 



2d. The orbit calculated by Mr. Walker upon the position taken in 

 1795, and upon the whole of the small arc observed since the discove- 

 ry, may very possibly be in error many degrees, either in 1887 or 

 1757; and that, if I have admitted as exact, the positions which it fur- 

 nishes at these epochs, it was only through courtesy, and because it 

 was no embarrassment to me. 



3d. Although the discordance of my theory might be 18°-5, in 1846, 

 without furnishing occasion for complaint, yet the real discordance is 

 found to be much less, and has never exceeded 3° "7 during the period 

 in which the perturbations were sensible. This is a point upon which I 

 insist in a very particular manner, and I pray that it may receive some 



attention. 



II. I shall be brief upon the distance from the sun, because it is vir- 

 tually comprised in the elements of the ellipse, which I shall consider 



