GRANGE, 
_ Granada, or Santa ¥’é as it is sometimes called, gives 
name to an extensive viceroyalty, which is sometimes 
_, confounded with the rit scat yp so denomina- 
ted. This kingdom of New “da was originally 
established in 1547, and was governed by a royal au- 
dience eee ccna regu In 1718, 
_ it was formed into a vi , which was sup) 
in 1724, and finally restored in 1740. It comprises the 
vinces of Panama, Santa Martha, Mara- 
Soho, Porto Bello, Antiognia, Choca, Granada Proper, 
Vi a, Mariquita, Rio de la Hacha, Giron, Neyva, 
ante Llanos, which form the northern division, un- 
der the jurisdiction of the royal audience at Santa Fé ; 
and the southern districts, Jaen de Bracamoros, Loja, 
Cuenza, Macas, Riobamba, Popayan, Quito, Guaynquil, 
&e. which are under the jurisdiction of a governor and 
royal audience at Quito, who ‘are ‘subordinate to. the 
viceroy of New Granada. This ‘extensive territory, 
_. when first subjected to Spain in 1536, was more popu- 
lous, and its inhabitants more civilized, than ary thes 
portion of America ; but the amount of its whole 
pulation is now calculated by M. Humboldt only at 
1,800,000. Nothing is wanting for its prosperity, but 
the revival of industry and commerce ; and nothing 
ts it from enjoying these benefits, but the impo- 
restrictions ant oppressive system of its European 
rulers. See Robertson’s Histo 4 America, vol. iii. ; 
Playfair’s Geography, vol. vi. ; Piss <erton’s Geography, 
vol. iii.; and Humboldt’s Account of New Spain. y 
GRANGE, Josrru-Louis va,* a celebrated Th 
matician and natural philosopher, was born at Turin, on 
the 25th of November, 1736. He was the son of Jo- 
> Saat la Grange, treasurer of war, and of Marie- 
erese Gros, only daughter of a rich physician of 
Cambiano. 
_. His father was rich, and had made an advantageous 
matriage ; but was ruined by hazardous undertakings. 
Let us not, however, lament the situation of M. la 
Grange. He himself viewed it as the first cause of all 
the good fortune that afterwards befel him. “ Had I 
been in possession of a fortune,” said he, “ I should 
not have studied mathematics.” In what 
other situation would he have found advantages that 
could enter into comparison with those of a tranquil 
and st s life, with that splendid series of discove- 
ries in a branch of science considered as the most diffi- 
cult, and with that personal respectability which was 
gape increasing to the very last period of his 
‘fe? 
His taste for mathematics did not appear at first. 
He was passionately devoted to Cicero and Virgil, be- 
fore he could read Archimedes and Newton. He then 
became an erithusiastic admirer of the geometry of the 
ancients, which he preferred to the modern analysis. 
A memoir which the celebrated Halley had composed 
before, to demonstrate the superiority of the ana- 
method, had the glory of converting him, and of 
teaching him his true ny. He devoted himself to 
this new study with the same success that he had in 
the synthesis, and which was so decided, that at the 
of 16 he was of mathematics in the Royal 
Military School. The extreme youth of a professor is 
a great advantage to him when he has shown extraordi- 
nary abilities, and when ‘his > pated no longer chil- 
dren, All the pupils of M. Ia range were older than 
447 
himself, and were not the less attentive to his lectures La Grange, 
on that account. He distinguished some of them, 
whom he made his friends. 
From this association ng the academy of Turin, 
which in 1759 published ‘a: first volume entitled Acts 
of a private Society. We see there the young La 
Grange directing philosophical researches of the 
yA ag Cigna, and the labours of the Chevalier de 
uces, e furnished to Foncenex the analytical 
part of his memoirs, leaving to him the task of deve- 
‘oping the reasoning upon which the formule depend- 
. In these memoirs, which do not bear his name, 
we observe that vay d analytical method, which after- 
wards characterised his tt productions. He had 
discovered a new theory ofthe lever. It constitutes the 
third part of a memoir, which was very successful, 
Foncenex, in recompense, was placed at the head of 
the Marine, which the king of Sardinia formed at that 
time. The two first parts have the same style, and 
seem written by the same person. Do they likewise 
belong to La Grange? He never expressly laid claim 
to them; but what may throw some light on the 
real author is, that Foncenex soon ceased to enrich the 
volumes of the new academy, and that Montucla, ig- 
norant of what La Grange revealed to us during the lat- 
ter part of his life, is astonished that Foncenex inter- 
rupted those researches which might have given him a 
great reputation. 
M. la Grange, ;while he abandoned to his friend in- 
sulated theorems, published at the same time, under 
his‘own name, theories which he promised to devel 
further. Thus after having given new formule of the 
maximum and minimum in all cases, after having shown 
the insufficiency of the known methods, he announces 
that he will treat this subject, which he considered as 
important, in a work which he was preparing, in which, 
would be deduced from the same principles all the me- 
chanical properties of bodies, whether solid or fluid. 
Thus at the age of 23 he had laid the foundation of the 
great works, which have commanded the admiration 
of philosophers, 
In the same volume he reduces under the differential 
calculus the theory of recurrent series and the doctrine 
of chances; which before that time had only been 
treated by indirect methods. He established them 
upon more natural and general principles. 
Newton had undertaken to submit the motions of 
fluids to calculation. He had made researches on the 
gation of sound; but his principles were in- 
sufficient, and his suppositions inconsistent with each. 
other. La Grange demonstrates this. He founds his 
new researches on the known laws of dynamics, and, 
by considering only in the air the particles which 
are in a straight line, he reduces the problem to 
that of vibrating cords, respecting which the greatest 
mathematicians differed in opinion. He shows that 
their calculations are insufficient to decide the question. 
He undertakes a general solution by an analysis ly 
new and interesting, which enables him to resolve at 
once an indefinite number of equations, and which em~ 
braces even discontinued functions. He establishes on 
more solid grounds the theory of the mixture of simple 
and regular vibrations of Daniel Bernoulli. He shows 
the limits within which this theory is exact, and be- 
yond which it becomes faulty. Then he comes to the 
* This excellent life of La Grange is taken, with a few slight abridgments, from the eloge of the Chevalier Delambre, with whose kind 
Permission it is here published. AS we have not been able to 
ttanslation in Dr Thomson’s Annels of Philosophy, vol. iii. 
get n copy of the original eloge, we have been obliged to make use of the 
Ep. 
Joseph 
Louis. 
_— 
