26 



MATHEMATICAL AND PHYSICAL SCIENCE. 



[Diss. VI. 



the curious mathematical difficulties which it pre- 

 sents, renders it very interesting to analysts. La- 

 place had applied to it his method of Generating 

 Functions; Kramp had introduced into his (now 

 scarce) treatise the almost new Calculus of Factorials ; 

 and others, like Bessel and Atkinson, had skilfully 

 combined theory and observation for the construc- 

 tion of useful tables. One of the most curious re- 

 sults of recent enquiries into this subject is, that Sir 

 Isaac Newton's table of refractions (Phil. Trans., 

 1721) must have been founded on a profound con- 

 sideration of the problem, such as no one else thought 

 of till a much later period, and is so numerically ex- 

 act as to agree closely with the later tables, Kramp's 

 for example. 1 



(108.) Mr Ivory attained the age of seventy- seven, dying 

 His death. 



on the 21st September 1842. Probably his unceasing 

 devotion to a confined and abstruse topic of enquiry, 

 reacting on a sensitive frame, rendered him in some 

 degree irritable and unsocial. He was not altogether 

 responsible for this ; but students of science should 

 recollect that diversity of occupations and interests is 

 subservient not only to bodily health, but also to men- 

 tal equanimity and vigour. 



The historian of science dwells with a special in- O 09 ;) 

 i i . /. T 111 i His emi- 



terest on the results of Ivory s labours, when we re- nent pogi _ 



cal the singular destitution of higher mathematical tion as a 

 talent which had reigned in this country for so long a British M 

 period, and which left us not only no position in the*.* 

 great struggle going on abroad for the advancement 

 of physical astronomy, but scarcely even the rank of 

 intelligent spectators. 



4. Progress of Physical Astronomy since the publication of the Mecanique Celeste. POISSON. 

 Theory of Rotation (Poinsot). Mr AIRY The Solar Theory. MM. PL ANA and HANSEN 

 The Lunar Theory. Physical Astronomy in America. 



(110.) The more that any theory of a mathematical kind, 

 Increasing Uke that rf Grav i tat i on advances to perfection, 

 difficulty ot , , x , . ., . 



physical as- the less reason have we to expect great and striking 



tronomy. results in the prosecution of it, and the more intense 

 and continuous is the labour in matters of detail ne- 

 cessary to make any advance at all. 



(ill.) AS regards the general and popular view of the 

 In^the 688 subject, we might pass at once from the epoch of La- 

 publication grange and Laplace to that of Leverrier and Adams, 

 of the Notwithstanding, however, the necessity of extreme 

 Mecamque com p ress i OI1) I must devote one short section to men- 

 tioning the chief labours in connection with physical 

 astronomy of four eminent men mentioned in our title, 

 who may fitly be considered as the immediate succes- 

 sors of Laplace. Two of them will be again referred 

 to in this discourse. 



C 112 -) SIMEON DENIS POISSON, born in 1781, may be 

 said truly to have been brought up at the feet of La- 

 grange and Laplace. He was their pupil in the first 

 and brightest years of the Polytechnic School, where 

 he was especially noticed by the former. He had 

 the distinguished privilege of being literally their 

 fellow-worker, his early memoirs having reference to 

 their labours, and stimulating the still vigorous mind 

 of Lagrange to the production, in his latest years, of 

 several memoirs, which have been considered worthy 

 of his best days. I refer more particularly to Pois- 

 son's proof that the stability of the planetary system 

 the system ; holds when perturbations of the second order are 

 taken into account, as has been stated in the first 

 section of this chapter, Art. (55.) This was in 1808. 

 Soon after, following out another of Lagrange's ad- 

 mirable generalizations of his theory of Arbitrary 



Poisson 



on the 



Constants, he embraced in a common series of for- 

 mulse the result of those mechanical laws which 

 regulate the rotation of bodies, together with those 

 concerned in their translation in space. This im- 

 portant subject (rotation) continued at intervals to 

 engage the attention of Poisson, not only as re- 

 gards the motions of the heavenly bodies on their 

 axes, but also as a branch of common mechanics. 

 The basis of this intricate doctrine was laid by Huy- 

 gens ; Euler, in a celebrated and original work, 

 gave it a general and analytical form ; D'Alembert 

 solved by it the problems of precession and nutation ; 

 Laplace demonstrated the constancy of the time of 

 the earth's rotation round its axis. This last pro- 

 blem was more fully discussed by Poisson, who showed 

 by theory that neither can the earth ever rotate round 

 an axis different from its present one, nor can the 

 time of its rotation vary in consequence of any ex- 

 ternal attractions to which it is subject. These two 

 matters are of the utmost moment ; the first prevents 

 the latitude of places from varying, and also renders 

 impossible the extensive flooding of dry land by the 

 waters of the ocean, which would be the evident con- 

 sequence of such a change ; the second assures us 

 that the grand unit of reckoning in all ages, 

 basis of astronomical chronology and of physical golj 

 astronomy generally, the length of the mean solar day, day. 

 has not varied, and never will perceptibly vary under 

 the action of known forces. Laplace had long be- 

 fore proved, by a comparison of ancient eclipses with 

 modern observations, that, practically, the length of 

 the day had not varied in 2000 years. It appears, 

 indeed, that since the earliest recorded Chaldean 



1 See Biot in Connaissance des Temps } \839 ; and Baily's Life of Flamsteed. 



