Anniversary Address of the President, 1840. 153 



mark and ne plus ultra of our progress, thus at once rooted up and 

 cast aside, as it were, by a tour de force, ought surely to have com- 

 manded all suffrages. It is understood, however, that we have not 

 yet all M. Bessel's observations before us. There is a second 

 series, equally unequivocal (as we are given to understand) in the 

 tenour, and leading to almost exactly the same numerical value of 

 the parallax, and not yet communicated to the public. Under these 

 circumstances, it became the duty of your Council to suspend their 

 decision. But, should the evidence finally placed before them at a 

 future opportunitjr justify their coming to such a conclusion, it 

 must not be doubted that they will seize with gladness the occasion 

 to crown, with such laurels as they have it in their power to extend, 

 the greatest triumph of modern practical astronomy. 



J\I., Plana is well known to the astronomical world as the director 

 of the Observatory at Turin, from which have emanated some valua- 

 ble series of observations. In conjunction with M. Carlini, he also 

 carried on that extensive and important triangulation of the Savoy 

 Alps, which have made his name celebrated as a geodesist. His 

 works, too, on many other subjects, both astronomical and purely 

 analytical, are of great importance ; particularly his investigations 

 on the subject of refraction prefixed to the ' Turin Observations,' 

 from 1822 to 1825, published in 1828 ; those on the motion of a 

 pendulum in a resisting medium, &c. But it is of his researches on 

 the lunar theory for which our medal has been actually awarded ; 

 and of these it behoves me now to speak ; and I cannot do so in 

 more clear, concise, and discriminating terms, than those used by 

 Mr. Airy in his Report already alluded to : — 



" The method pursued by Plana, in his ' Theorie de la Lune,' is 

 slightly, but not importantly, different (I mean in the fundamental 

 equations) from those of his predecessors, Clairaut, Laplace, and 

 Damoiseau. He first starts with the method of variation of ele- 

 ments, and pursues it to such an extent as to ascertain generally 

 the form of the expressions connecting the longitude, the latitude, 

 and the time. He then reverts to Clairaut's equations ; and, as 

 these equations require for the successive substitutions an approxi- 

 mate expression for time in terms of longitude, he adopts a peculiar 

 form (suggested by the variation of elements) for the principal part 

 of it, and attaches to that principal part a subordinate part marked 

 with the prefix c. The same thing is done for the latitude. The 

 process then is tolerably direct, and is almost similar to that of an- 

 tecedent writers. In the fundamental algebra, therefore, there is no 

 very great originality in the plan ; but the mode followed in the 

 detail of the work is beyond all praise. In the whole of the analy- 

 tical combinations of this immense work, every part arising from the 

 combination of any one term (however small) with any other term, 

 is given separately, in such a form as to leave no difficulty in the 

 detection of error to any careful examiner. The terms of peculiar 

 difficulty (as, for instance, that depending on twice the distance 

 between the node and the perigee) are made the subject of special 

 diecussion ; and, in some instances, the origin of discordance be- 



