REPORT OF THE SECRETARY. 13 



in 1871, was erroneously predicted by the Nautical Almanac to the 

 extent of some six minutes, and in consequence a number of observers 

 who were on the alert to see so rare a phenomenon missed it entirely. 

 An outcry was raised against the almanac in consequence, but it was 

 met by the remark that that work could use only such tables as were 

 at its disposal, and that the construction of new ones corresponding 

 to the present state of astronomy was now almost beyond the power 

 of any individual, and could -only be undertaken under the auspices of 

 some sufficiently liberal government. 



" The disinclination of astronomers to undertake such a work as this 

 may be illustrated by the fact that the tables of Jupiter and Saturn, as 

 well as those of Uranus, are more than fifty years old, and are, of 

 course, considerably in error. The Astronomical Society of Germany 

 has been engaged in preparing the data for new tables of Jupiter during 

 the past five years, but I am not aware of any recent report of progress. 



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

 employed in calculating the action of the disturbing planets Jnpiter, 

 Saturn, and Neptune on the motion of Uranus. In the second chapter 

 this method is illustrated by quite a detailed calculation of the pertur- 

 bations 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 perturbations 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 include 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 period, in which the results differ materi- 

 ally from those of other authorities, including Le Verrier, Delaunay, 

 Adams, and Hansen, who all agree among themselves. I cannot find 

 any error in my work, and so must, of course, retain my own result, 

 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 a manner as to be 

 made use of. The entire number is 3,763. The correction to a provis- 

 ional theory given by each series of observations is deduced. 



" The object of the seventh chapter is to apply such corrections to the 

 elements of Uranus and the mass of Neptune that the observations 

 shall be represented with the smallest possible outstanding errors. The 

 mass of Neptune comes out y^-i^, almost exactly the same as that found 

 by Professor Peirce more than twenty years ago. 



