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handed and unassisted, without coadjutor, rival, or competitor.” He gives 
reasons for questioning whether Sir W. Herschel really saw the inner satel- 
lites. It can surely make little difference, so far as Mr. Lassell is concerned, 
whether Sir W. Herschel saw them or not. Lemonnier and Flamsteed 
saw Uranus long before Herschel did, hut Sir W. Ilerschel’s credit is in no 
sort affected by the circumstance. 
Present State of M. Delaunay's Investigations on the Lunar Theory . — 
Professor Simon Newcomb states that u Delaunay’s two published volumes 
form a substantially complete work, so far as the problem of three bodies is 
concerned. It remains or.ly to add the terms due to the motion of the 
earth round the common centre of gravity of the earth and moon, which is 
a simple matter. In the preface to the second volume Delaunay promised 
a third volume, to contain the investigation of the other actions to which 
the moon was subjected, in the spring of 1871. I learned from him that he 
had done substantially nothing towards preparing this volume, except to 
compute the secular acceleration. The result of this was published in the 
* Comptes Rendus.’ He was so much occupied with observatory manage- 
ment during the remainder of his life, that I feel confident he did little or 
nothing in addition. Last summer all his theoretical investigations were at 
the Observatory of Paris in charge of M. Loewy, who was desirous of con- 
tinuing them. So far as the perturbations due to the action of the sun 
were concerned his tables were completed in 1871. It remains not only 
to finish the supplementary researches and tabulate the results, but to 
investigate the lunar elements, and to form the arguments of the tables. 
This work had not then been taken into consideration, and so far as I know 
was not commenced at all before his lamented death.” 
Relations between the Motions of some of the Minor Planets . — Professor 
Kirkwood, of Bloomington, Indiana, in a letter to Mr. Proctor, says : If 
your theory of planetary accretion be true, the zone of asteroids must pro- 
bably furnish instances of special relations between the mean motions of its 
different members. I refer to such relations as those found by Laplace 
between Jupiter’s first three satellites. Soon after your brief visit to 
Bloomington in March, I commenced comparing the mean motions of certain 
members of the group with those of Jupiter and Saturn. The research has 
already been crowned with success. My results, in part, are as follow : — 
Let n y , w Ti , represent the mean motions of Jupiter and Saturn ; 
n( 50 >, n( 78 ), &c. those of Pales, Diana, &c. ; the numerals in 
parentheses denoting the minor planets in their order of dis- 
covery ; 
Let also L(50) ? L( 78 ), &c. represent the mean longitudes at a given 
epoch ; then 
rc(50)_3rc(78) + 2w ( n > = 0 ... (1) 
L(50) _ 3L( 78 ) + 2L (H) = 180° . . . (2) 
The exact similarity of these equations to those of Laplace, referred to 
above, is at once apparent. The origin of the relation, whether we accept 
the nebular hypothesis or your own theory recently announced, may be 
accounted for as in Note 7, vol. ii. of Laplace’s “System of the World.” 
But were the relations expressed by (1) and (2) rendered rigorously exact 
