Royal Astronomical Society. 561 



guage with Hipparchus and Ptolemy, unless we have reason to 

 know that these elements continue sensibly unaltered. In addition 

 to the imperfect presumptions derived from observation (imperfect on 

 account of the large liability to error of the older astronomers) 

 Lagrange had shown that the mean motions have no secular in- 

 equalities depending on the first power of the disturbing forces ; or, 

 so far as this first power was concerned, on any powers of the ec- 

 centricities or inclinations. Laplace had shown that a certain se- 

 cular equation, which should in theory be applied to the sidereal 

 day, would always be too small to be of any importance. Poisson 

 extended the conclusions of Lagrange to the second power of the 

 disturbing forces, and, relatively, to any powers of the eccentricities 

 and inclinations ; or rather, we may say, that he showed any se- 

 cular equation of the mean motions to depend only on the fourth 

 power of disturbing forces ; for, in the course of the investigation, 

 it appears that no such equation of any odd order can exist. As far 

 as the fourth powers of eccentricities and inclinations, he actually 

 shows the mutual destruction of an infinite number of non-periodic 

 disturbing terms ; the rest of the powers are completed by a general 

 and different investigation. In the problem of the rotation of the 

 earth, he generalises the investigation of Laplace, by taking into consi- 

 deration the actual change of the axis on the earth; the former investi- 

 gation considering only the change of the axis, supposed to be fixed 

 in the earth, relatively to the stars. The result agrees with that of 

 Laplace as to the non-existence of any sensible secular inequality. 



" Poisson belongs to a class of investigators of whom many are 

 always wanted, but one is permanently indispensable. 



" The applications of the newest powers of mathematical language 

 should always be made as near as may be to the time when they are 

 first exhibited. But such peculiar combination of address and power, 

 with a perfect knowledge of existing materials, is not of every-day 

 occurrence; nor is it permitted to say, uno avulso non deficit alter*. 



" His Majesty the King of Denmark, who was elected an honorary 

 member of this Society at the last anniversary, has been pleased to 

 continue the offer of the gold medal founded by his royal prede- 

 cessor, for the first discovery of a telescopic comet ; subject to the 

 conditions and regulations already inserted in the Monthly Notices 

 of this Society for November 1835 f. One of these conditions 

 (which is indispensable as far as it affects persons resident in Great 

 Britain) is, that notice of such discovery must be sent by the first 

 post to Mr. Baily. 



" The Council cannot conclude this Report without expressing a 

 hope that the future efforts of the Society for the promotion and 

 encouragement of astronomy, will be marked with the same success 

 as has hitherto attended their career : and that they may continue 

 to show to the world the happy effects of unanimity and zeal in the 

 pursuit of a favourite science." 



[* Another obituary notice of M. Poisson will be found at p. 74 of the 

 preceding volume. — Edit.] 



[f See Phil. Mag., Third Series, vol. ix. p. 294.— Ed.]. 



