(99.) 
9 Legendre’s 
4 researches 
1 on the at- 
4 traction of 
Ellipsoids, 
Cuar. IL, § 3.] 
him when alive. The French Academy, which had 
buried his memoir in their most inaccessible ‘‘archives,”’ 
decreed too late the unprecedented honour of a post- 
humous medal to his mother. Jacobi, the friendly 
rival of Abel in his discoveries, died recently, at a 
mature though not advanced age, at Kénigsberg, 
where he was professor. 
But to return to the labours of Legendre. The 
theory of the figure and attraction of the earth 
and of other planets naturally divides itself into two 
parts—(1.) the law of attraction of an ellipsoid on 
a material point without or within it ; (2.) the figure 
_of equilibrium of a fluid subjected to no forces but 
the mutual attractions of its particles, and the cen- 
trifugal force due to its rotation. The latter of 
these problems is still imperfectly solved, the former 
completely so, and that mainly in consequence of the 
PHYSICAL ASTRONOMY—LEGENDRE—IVORY. 
823 
cians, and, at a period when but few Englishmen 
were able to understand those difficult works, he 
showed his capacity of adding to their value by ori- 
ginal contributions, not unworthy of the first ana- 
lysts. We pass over his earlier contributions con- 
nected with mathematics and astronomy, several of 
which are contained in the Transactions of the 
Royal Society of Edinburgh, and proceed to his 
most celebrated paper, published in the Philoso- 
phical Transactions for 1809, in which he com- 
pletely and definitely resolves the problem of attrac- 
tions for every class of ellipsoidal bodies. After 
what has been stated above as to the position of the 
problem as treated by Legendre, a few words will 
explain the precise import of Ivory’s Theorem, one of 
the most celebrated mathematical results of that time. 
We have seen that the attraction of an ellipsoid 
(104.) 
labours of Legendre and Ivory,' 
Though the services of Legendre are well known 
and admitted, the superior address of Laplace in the 
applications of mathematics has occasioned his re- 
on a point within or at its surface had been assigned His import 
by Maclaurin. The theorem in question enables pesos 
us at once to reduce the case of an exterior attracted attraction 
point to that of a point on the surface of the ellipsoid. of Ellip- 
h sometimes 
in part at- 
tributed to soids 
Laplace. 
(101.) 
History of 
the subject. 
ee ee ee ee 
ceiving the credit of what in some instances belonged 
to the former. 
Maclaurin, by an exercise of synthetic skill not 
exceeded since the death of Newton, had demon- 
strated the attraction of an ellipsoid of revolution 
upon a material point anywhere within it or on its 
surface, as well as for an exterior point in the 
prolongation of its axis or in the plane of its 
equator. The same problem was afterwards ana- 
lytically solved by D’Alembert and Lagrange. In 
1782, Legendre, by a profound and complicated 
analysis, obtained an expression, by means of series, 
for the attraction of an exterior particle generally, 
and he was the first to imagine and employ those 
artifices of calculation known usually by the name 
of “ Laplace’s functions.” Laplace made a step 
towards the simplification of the expression of ex- 
terior attractions, but the complete solution was 
reserved for Mr Ivory, as I shall mention below. 
The other labours of Legendre need not be spe- 
cified here. He co-operated in the trigonometrical 
survey of France, and gave the formula, known by 
his name, for approximately reducing a spherical to 
a plane triangle. He also wrote on the orbits of 
comets, and on the method of least squares, 
James Ivory, the most considerable British mathe- 
matician of his time, or that had appeared since Mac- 
laurin, was born at Dundee in 1765, and studied at St 
Andrews along with Sir John Leslie. The most ac- 
tive period of his life was passed as mathematical pro- 
_ fessor at the Military College of Marlow (afterwards 
removed to Sandhurst). He was essentially a self- 
taught mathematician, and spent much of his time in 
retirement. He fathomed in private the profoundest 
writings of the most learned continental mathemati- 
Suppose an ellipsoid having the same excentricity, 
and with the principal sections parallel to the first, 
but whose surface passes through the given exterior 
point. Let points on the surface whose co-ordinates 
parallel to the three axes of the respective solids are 
proportional to those axes be called corresponding 
points; then the attraction parallel to each axis 
which one of these bodies exerts on a point situated 
on the surface of the other is to the attraction of the 
latter on the “ corresponding point” of the sur- 
face of the former, as the product of the two other 
axes of the first ellipsoid is to the product of the two 
other axes of the second. By this means the attrac- 
tion on an exterior point is accurately expressed in 
terms of the attraction on an interior point, which 
is known. It is fair to add that both Legendre and 
Laplace had some glimpses of the principle, though 
they failed to apply it to the direct solution of the 
problem, and between the publication of their Me- 
moirs and that of Mr Ivory there elapsed nearly a 
quarter of a century. 
Besides this paper, Ivory contributed many others 
(105.) 
on the subject of the attraction of spheroids and the His other 
theory of the figure of the earth, during a period of P*P°* 
nearly thirty years; several of these were controversial, 
and did not add materially to the progress of the sub- 
ject; others are considered as masterpieces of analyti- 
cal skill. One of the last subjects which occupied his 
attention was the possible equilibrium of a spheroid 
with three unequal axes, which Jacobi had discovered. 
Between the labours of Ivory and those of Legen- 
dre a great analogy subsists; for the doctrine of ellip- 
tic integrals also occupied the attention of the former. 
But next to the theory of attractions, that of At- 
mospherie Refraction most seriously engaged Ivory’s 
attention. 
1 See the articles ATTRACTION and Figure or THE Haru (the former by Ivory) in this Encyclopwdia. 
(106,) 
(107.) 
Atmo- 
. : heric R 
Its great importance in astronomy, and faction. 
