582 The Smithsonian Institution 



" The first chapter of the work gives an exposition of the 

 method employed in calculating the action of the disturb- 

 ing planets Jupiter, Saturn, and Neptune on the motion of 

 Uranus. In the second chapter this method is illustrated by 

 quite a detailed calculation of the perturbations of Uranus 

 produced by Saturn, including, however, only those which 

 are of the first order with respect to the disturbing force. In 

 the third, the perturbations produced by Jupiter and Neptune 

 are given, but the computations are not presented with the 

 same detail. The fourth chapter opens with a preliminary 

 investigation of the orbit of Saturn, using Hansen's per- 

 turbations and the Greenwich observations, the object being 

 the accurate determination of the terms of the second order. 

 This is followed by the computation of the terms of the second 

 order produced by Saturn, which includes those containing as 

 a factor either the square of the mass of that planet or the 

 product of its mass by that of Jupiter or by that of Uranus. 

 The most remarkable of these terms is one of very long pe- 

 riod, in which the results differ materially from those of other 

 authorities, including Leverrier, Delaunay, Adams, and Han- 

 sen, who all agree among themselves. I cannot find any 

 error in my work, and so must, of course, retain my own re- 

 sult, leaving it to future investigators to find the cause of the 

 discrepancy. The difference is of such a nature that it cannot 

 affect the computed position of the planet until after the lapse 

 of more than a century. 



" The sixth chapter gives a discussion of all the observations 

 of Uranus which have been published and reduced in such 

 manner as to be made use of. The entire number is 3763. 

 The correction to a provisional theory given by each series 

 of observations is deduced. The object of the seventh chap- 

 ter is to apply such corrections to the elements of Uranus and 

 the mass of Neptune that the observations shall be repre- 

 sented with the smallest possible outstanding errors. The 

 mass of Neptune comes out 19 7 00> almost exactly the same as 

 that found by Professor Peirce more than twenty years ago. 1 



1 The mass of Neptune determined by Professor Newcomb's observations with the great 

 telescope in Washington in 1874 and subsequently is T?i?5- E. S. H. 



