Royal Astronomical Society. 527 



lunar perturbations, which presents difficulties of a peculiar kind, is 

 not so far advanced, and much is still wanting to render it complete 

 even as a symbolical theory. But in a recent number of the Nach- 

 richten* he has announced that the calculations, on which he has 

 been for some time engaged, are now proceeding towards a conclu- 

 sion ; and he has given some results which show that the new me- 

 thods apply with as much advantage to the moon as to the planets. 



Thus, gentlemen, I have endeavoured to place before you a sketch 

 of M. Hansen's researches, which, brief and imperfect as it is, will 

 enable you to understand their object, and appreciate their import- 

 ance. Should it be thought that these investigations refer only to 

 matters of detail, and that the results at which he has arrived in- 

 clude none of those grand discoveries which enlarge the boundaries 

 of science, and give us, as it were, a new insight into the constitu- 

 tion of the universe, let it be remembered that the progress already 

 made in physical astronomy has narrowed the field to the present 

 inquirer, and that, in proportion as science advances, its processes 

 become more and more intricate. The problem of the universe, dif- 

 ficult as it is, is still a limited problem ; and the successive steps in 

 its solution may be assimilated to the terms of one of those con- 

 verging series expressing the perturbations we have been speaking 

 of, in which each succeeding term is not only smaller in value than 

 the preceding, but also more difficult of calculation. It is with the 

 smaller terms only that the theoretical astronomer has now to con- 

 cern himself ; but his labours, though necessarily attended with less 

 brilliant results, are not on that account the less necessary or useful. 

 On the contrary, no more valuable service remains to be rendered 

 to astronomy, in the present state of the science, than the improve- 

 ment of the existing methods of computing the lunar and planetary 

 perturbations. The labours of M. Hansen have been steadily, and 

 perseveringly, and successfully directed to this end. Whether the 

 new methods which he has so ingeniously developed will be found 

 in all cases preferable to those with which we are already familiar, 

 or whether they will ultimately be adopted by astronomers as afford- 

 ing the most convenient forms under which the conditions of the 

 solar system can be expressed, is a question which your Council do 

 not venture to decide, and on which, perhaps, it would at present 

 be premature to form an opinion. But with respect to the pro- 

 found ingenuity and consummate analytical skill which he has 

 brought to bear on the intricate subjects of his investigation, there 

 can be but one voice. His researches, which have been of the most 

 laborious and abstruse kind, have been directed to the highest and 

 most important questions of astronomy ; and the means by which 

 he has sought to conquer the still remaining difficulties, present 

 more of novelty and originality, and afford stronger hopes of re- 

 moving the differences which still exist between the tables and ob- 

 servation, than any which have been employed since the variation 

 of arbitrary constants was propounded by Lagrange. On the whole, 

 having respect to the importance of the subject, the results which 



* No. 403. 



