822 
the marvellous power of analysis, in unravelling intri- 
cate consequences of admitted or assumed Jaws, could 
supply deficiencies of primary conceptions of the laws 
of nature, or could teach men fundamental truths in 
natural science. 
MATHEMATICAL AND PHYSICAL SCIENCE. 
[Diss, VI. 
exposition of astronomy in thevry and practice en- 
tirely original in its plan and execution, and though 
frequently imitated, it is still perhaps the first of its 
class. 
Laplace was born in Normandy 23d March 1749, 94.) 
and died the 5th May 1827, leaving in the Academy tae of 
he had so long honoured no one within many degrees ae 
of his ability in the same peculiar walk of science. 
_ (93.) To add to the remarkable list of Laplace’s endow- 
ay eae ments one more; he was a perspicuous and elegant 
“mone Sriter. His Systéme du Monde contains a popular 
§ 3. LEGENDRE—IvorY.—Theory of Integration; Elliptic Transcendants (Abel, Jacobi). 
The Attraction of Spheroids, and Theory of the Earth’s Figure. Atmospherical Refractions. 
(95.) Aprien Mariz LeGenpre was born in France in 
Legendre. 1752, and died in 1833 (10th January); he was 
consequently three years younger than Laplace, and 
survived him by nearly six years. He formed, there- 
fore, an integral part of that constellation of mathe- 
matical talent of which Paris was for more than 
two generations the main centre. Like his illustrious 
compeers Lagrange and Laplace, he laboured with 
enthusiasm all the days of his life, and like them was 
engaged in editing and improving his works down 
almost to the day of his death, at the ripe age of four- 
score, 
mS The mathematical career of Legendre was less 
= tished ag SPlendid than that of the other two whom we have 
anable just mentioned. He did not possess the wonderful 
mathe- powers of generalization of Lagrange, and he wanted 
matician. the flexibility of mind, and the general physical 
knowledge, of Laplace. Legendre was very strictly a 
mathematician ; and he has been exceeded by none 
in the unquenchable zeal with which he pursued sub- 
jects of a dry and even repulsive character, often 
till he had hunted them down by sheer force of ap- 
plication, or, to adopt the metaphor applied to him by 
Lagrange, until he carried, sword in hand, the strong- 
hold which he besieged. 
_ (97) No more striking proof can be given of these state- 
eee on ments than the unflinching pertinacity with which, 
Elliptic during nearly fifty years (1786-1833), he studied and 
Functions, improved the theory of Integration, applicable to those 
cases frequently occurring, which involve the higher 
powers of the independent variable, and which do not 
usually admit of finite expression, Two large works, 
the Ewercises du Caleul Integral (1811), and the 
Traité des Fonctions Elliptiques (1827-32),—the lat- 
ter in good measure a republication of the materials of 
the former,—bear testimony to his diligence; and these 
works were almost entirely original, and contained 
tables of most laboured construction, calculated by 
himself. Hardly any mathematician entered into 
competition or co-operation with him until his 
labours were drawing to a close, when, with a libe- 
rality worthy of all commendation, he welcomed the 
analytical discoveries of Abel and Jacobi, which 
were to give an unlooked-for extension to his own. 
These methods of integration, and their reference to 
certain properties of the Lemniscate and the Ellipse, 
originated in the early part of the last century 
with Fagnano and Euler. Legendre took up the 
subject exactly where Euler left it, and finally re- 
duced the large class of expressions to which his 
methods are applicable to three standard forms or in- 
tegrals in which the independent variable is always 
expressed by a circular function, and to which a 
numerical approximation may always be made by 
means of the tables calculated by himself. 
Azgt, who succeeded in generalizing Legendre’s 98.) 
methods to a far greater extent, was a native of Abel’s dis- 
Norway, born in 1802 (25th August),’ and died teeters, 
at the premature age of twenty-six (1829, 26th subjects his 
April). His principal memoir was presented to the personal. 
Institute when he was only twenty-four years old ; Mistry. 
and, to use the language of Mr Leslie Ellis, “ when 
the resources of the integral calculus were appar- 
ently exhausted, Abel was enabled to pass into 
new fields of research by bringing it into intimate 
connection with a new branch of analysis, namely 
the Theory of Equations. The manner in which 
this was done shows that he was not unworthy to 
follow in the path of Euler and of Lagrange.’’?? 
Legendre’s eulogy of Abel was concise :—* Quelle 
téte celle du jeune Norvegien!” It is less agreeable 
to add that the life of Abel was perhaps shortened by 
poverty and care. Though ultimately befriended by 
Legendre, Poisson, and others, his first visit to Paris (in 
1826) occasioned nothing but disappointment, and his 
great memoir (no unusual lot, for the same happened 
to Fresnel) lay hopelessly lost amidst the papers of the 
Institute for fifteen years. Much, however, to their 
credit, the geometers above mentioned at length ad- 
dressed the King of Sweden on behalf of the rare genius 
his dominions contained ; but in vain. Abel died ne- 
glected, unable even to print his researches, which were 
tardily given to the world in a collected form, at the 
expense of the government which refused to support 
1 There is some discrepancy, as to the year of his birth, but I believe this to be correct, 
? Report on the recent progress of Analysis. 
British Association Report for 1846. 
