444 Scientific Intelligence. 



in detail. My orbit gives 33-0 for the distance of Neptune from the 

 sun at the time of discovery. 



The orbit of Walker gives 30*1 for the distance from the sun at the 

 same period. 



Now in reducing to numbers my theory of limits, I find, without sup- 



>f 



, that the 



theory of Uranus would be satisfied, if a planet were situated at any dis- 

 tance from the sun comprised between the limits 29 6 and 35*2. The 

 two numbers above mentioned are really contained between these 

 limits* 



I pass to the elements of the ellipse themselves, elements which I 

 did not directly consider in my first discussion, but in which they are 

 found to be virtually contained. The elements, I have said to the 

 Academy, are only mathematical auxiliaries, suited to lead to the 

 knowledge of the direction and distance; these auxiliaries might vary 

 considerably, without failing to give the position of the disturbing body 

 at the epochs of the perturbations. 



I did not then know that foreign astronomers would be so ready to 

 send me declarations conforming to those of my illustrious brethren, 

 Messrs. Biot, Cauchy and Faye ; and that among these testimonies 

 would be found a thorough discussion of the question, signed Herschel; 

 a discussion superior to any that could emanate from my pen, and 

 whose publication would have been my only defense, had I then pos- 

 sessed it, and if even at the present time I am not in haste to reveal it 

 to the friends of science, they will not reproach me when I inform 

 them that this illustrious English Astronomer is engaged in putting in a 

 clear light all the scientific points of this discussion with the intention 

 of soon publishing the result of his researches. 



I give meanwhile the following extract from the letter of Herschel. 



"The elements are intellectual objects, suited to represent to the 

 mind the general relations of the planet with time and space, while the 

 direct object of your efforts was to say where the disturbing body was 

 placed at the epoch of the research, and where it was during the forty 

 or fifty years preceding. Now it is this which you have made known 

 with perfect accuracy. 11 



These remarks being made let us consider the elements. 



III. Longitude of the perihelion.— I assigned 284°'8 for the longitude 

 of the perihelion of Neptune. 



Mr. Walker gives 360° -2 for the longitude at the same epoch. The 

 difference, 75° -4, it is said, is enormous, and without doubt it is. But the 

 question is, to know if the uncertainty of the data authorizes this dif- 

 ference. 



In reducing to numbers my theory of limits, without carrying the 

 uncertainty of the modern data beyond 5", I find that the perihelion 

 may be placed at any distance between 229^9 and 366° -4. 



The numbers 284*8 and 360*2 are both within these limits. 



IV, Mean Longitude. — This element is variable with the time. What- 

 ever may be the epoch to which it is referred, the same results wilt 

 necessarily follow. Let us take the epoch of January 1st, 1847. 



I have given in my memoir 318° # 8 for the mean longitude. 



Mr. Walker finds 328°' J. 



