JAMES JOSEPH SYLVESTER. 
45 
[900 
900] 
Mathematics at the 
n in 1877. Finally, 
metry at Oxford, in 
s on Fresnel’s optical 
was accompanied by 
s (January 23, 1874) 
Conversion of Motion.” 
which opens out such 
>n, descending to the 
the revolutionising of 
other domestic con- 
in the other, soaring- 
idem analysis, lending 
on the researches of 
Its head towers above 
believe, are: (1) “A 
n Committee and the 
nber 4, 1854,” a slight 
notice; (2) “Laws of 
, which have appeared 
he honours that have 
f the Royal Society on 
Copley Medal (1880), 
On this last occasion, 
is, “ His extensive and 
itions to the theory of 
>dern geometry, may be 
ird.” He is a Fellow 
ites National Academy 
nces, Gottingen, of the 
M Sciences of Boston; 
rial Academy of Science 
rlin, of the Lyncei of 
athique. He has been 
l of Mathematics (under 
December 12, 1885, with the 
c cable containing the single 
pointed Savilian Professor of 
f filling the post and drawing 
one or another of its titles), and was the first editor of, and is a considerable 
contributor to, the American Journal of Mathematics', and he was at one time Examiner 
in Mathematics and Natural Philosophy in the University of London. He was not 
an original member of the London Mathematical Society (founded January 16, 1865), 
but was elected a member on June 19, 1865, Vice-President on January 15, 1866, 
and succeeded Prof. De Morgan as the second President on November 8, 1866. The 
Society showed its recognition of his great services to them and to mathematical 
science generally by awarding him its De Morgan Gold Medal in November 1887. 
Wherever Dr Sylvester goes, there is sure to be mathematical activity; and the 
latest proof of this is the formation, during the last term at Oxford, of a Mathematical 
Society, which promises, we hear without surprise, to do much for the advancement 
of mathematical science there. 
The writings of Sylvester date from the year 1837; the number of them in 
the Royal Society Index up to the year 1863 is 112, in the next ten years 38, and 
in the volume for the next ten years 81, making 231 for the years 1837 to 1883: the 
number of more recent papers is also considerable. They relate chiefly to finite analysis, 
and cover by their subjects a large part of it: algebra, determinants, elimination, the 
theory of equations, partitions, tactic, the theory of forms, matrices, reciprocants, the 
Hamiltonian numbers, &c.; analytical and pure geometry occupy a less prominent 
position; and mechanics, optics, and astronomy are not absent. A leading feature is 
the power which is shown of originating a theory or of developing it from a small 
beginning; there is a breadth of treatment and determination to make the most of 
a subject, an appreciation of its capabilities, and real enjoyment of it. There is not 
unfrequently an adornment or enthusiasm of language which one admires, or is 
amused with: we have a motto from Milton, or Shakespeare; a memoir is a trilogy 
divided into three parts, each of which has its action complete within itself, but the 
same general cycle of ideas pervades all three, and weaves them into a sort of 
complex unity; the apology for an unsymmetrical solution is—symmetry, like the 
grace of an eastern robe, has not unfrequently to be purchased at the expense of 
some sacrifice of freedom and rapidity of action; and, he remarks, may not music 
be described as the mathematic of sense, mathematic as the music of the reason ? 
the soul of each the same! &c. It is to be mentioned that there is always a 
generous and cordial recognition of the merit of others, his fellow-workers in the 
science. 
It would be in the case of any first-rate mathematician—and certainly as much 
so in this as in any other case—extremely interesting to go carefully through the 
whole of a long list of memoirs, tracing out as well their connexion with each other, 
and the several leading ideas on which they depend, as also their influence on the 
development of the theories to which they relate; but for doing this properly, or at 
all, space and time, and a great amount of labour, are required. Short of doing so, 
one can only notice particular theorems—and there are, in the case of Sylvester,