4 THEOBBITOFURANUS. 



tioii of the perturbations of the elements into perturbations of the co-ordinates, to 

 carry this transformation to terms of tlie second order also. This Le Verrier avoids 

 by showing that the terms of tlie lowest order with respect to the eccentricities 

 thus introduced are destroyed by certain terms in the perturbations of the elements, 

 so that it is only necessary to omit both classes' of terms. These terms are of that 

 fictitious class which disappear of themselves by a simple change of elements. 

 When, instead of the eccentricity and longitude of the perihelion, we take h and Ic, 

 which represent the products of the eccentricity into the sine and cosine of this 

 longitude respectively, these terms disappear of themselves both from the perturba- 

 tions of the elements and of the co-ordinates. It is not likely that any of the 

 neglected terms of this class exceed 0".l. 



As soon as the elements of Neptune were known, the nature of its general action 

 on Uranus became of interest. This subject was taken up by Prof. Peirce, whose 

 results are found in the Proceedings of the American Academy of Arts and Sciences, 

 Vol. I, pp. 33-i-337. Tliis paper is accompanied with a comparison of his theory 

 of Uranus with observations, to which similar comparisons of the theories of Adams 

 and Le Verrier are added. This comparative exhibit is of sufficient interest to be 

 given here. The numbers given are probably excesses of computed over observed 

 longitudes. 



In this paper Professor Peirce presents the results of a complete computation of 

 the general perturbations of Uranus by Neptune in longitude and radius vector, 



