824 
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 t 
of till a much later period, and is so numerically ex- 
act as to agree closely with the later tables, Kramp’s 
for example.* 
(108.) Mr Ivory attained the age of seventy-seven, dying 
His death. 
MATHEMATICAL AND PHYSICAL SCIENCE. 
[Diss, VI. 
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- Ape 
terest on the results of Ivory’s labours, when we re-,,, : pe 
eal the singular destitution of higher mathematical tion asa 
talent which had reigned in this country for so long a British Mine 
period, and which left us not only no position in the themati- 
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 Mécanique Céleste.—PoIsson.— 
Theory of Rotation (Poinsot)—Mr A1try—The Solar Theory—MM. Puana and HANSEN— 
The Lunar Theory.—Physical Astronomy in America. 
: (110.) ‘The more that any theory of a mathematical kind, 
difficulty of ike that of Gravitation, advances to perfection, 
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, 
han As regards the general and popular view of the 
sine the Subject, we might pass at once from the epoch of La- 
publication grange and Laplace to that of Leverrier and Adams. 
ofthe = Notwithstanding, however, the necessity of extreme 
—— compression, 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. 
Stmzon Denis Porsson, 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 
-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 
(112.) 
Poisson 
on the 
stability of 
the system ; 
on Rota- 
Constants, he embraced in a common series of for-?" 
> 
mule 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, the hg 
basis of astronomical chronology and of physical |*¥ fe 
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,1839 ; and Baily’s Life of Flamsteed. 
