598 
NATURE 
| April 26, 1883 
Jones as Honorary Secretary to the Royal Institution. 
President of Section A, 1865 ; of the British Association, 
1878 ; of the London Mathematical Society, 1870 to 1872; of 
the Royal Society, 1879, which office he still holds. 
Correspondent of the Institut (Académie des Sciences), 
March 27, 1876. He is also LL.D. of the Universities of 
Cambridge, Dublin, and Edinburgh, D.C.L. of Oxford, 
and F.R.A.S., F.R.G.S., F.RS.E. In addition to these 
honours he bas many other literary and scientific dis- 
tinctions. 
Of Mr. Spottiswoode’s willingness to communicate 
from his stores of knowledge many have had frequent 
proof. We are breaking no faith, we believe, when we 
mention that it was his wish to purchase the late Prof. 
De Morgan’s valuable library to present it to the Mathe- 
matical Society, of which that distinguished mathematician 
had been the first President. 
Few students of the present day are acquainted with 
Mr. Spottiswoode’s earliest work which appeared in the 
shape of five quarto pamphlets (136 pp. in all) with the 
title, “ Meditationes Analytica” (London, 1847). The 
author's dedication runs thus: ‘To those who love to 
wander on the shore till the day when their eyes shall be 
opened and they shall see clearly the works of God in the 
unfathomed ocean of truth, these papers are inscribed; ” 
and in his preface he says, “The following papers have 
been written at various periods, as the subjects presented 
themselves to notice from time to time. If leisure had 
been afforded, an attempt would have been made to draw 
some of them up into a distinct treatise ; but it was 
thought that even in their present form they might in- 
terest some of those who take pleasure in the pursuit of 
mathematical science. Some of the papers are entirely 
original.” The papers are entitled, “Symmetrical Inves- 
tigations of Formule relative to Plane Triangles,” “ On 
some Theorems relative to Sections of Surfaces of the 
Second Order,’’ ‘‘On the Reduction of the General 
Equation of the Second Order,” “On the Partial Dif- 
ferential Equations of certain Classes of Surfaces,” 
“On some Theorems relating to the Curvature of Sur- 
faces,” “On certain Formule for the Transformation of 
Coordinates,” “On the Principle of Virtual Velocities,” 
“On Infinitesimal Analysis,” “Examples of the Appli- 
cation of the Infinitesimal Calculus,’ “On certain For- 
mule made use of in Physical Astronomy,” “On the 
Calculus of Variations,” ‘‘Problems in the Calculus of 
Variations,” and “Note on Lagrange’s Condition for 
Maxima and Minima of Two Variables ”—a fair epitome 
of his subsequent mathematical labours, The treatment 
calls for no special comment, except that we may note 
that “in the form of the equations symmetry has been 
preserved wherever the circumstances of the case would 
permit.” 
Ata slightly later date (1851) appeared, of a uniform 
appearance with the “ Meditationes,” a much more 
notable pamphlet (63 and viii. pp.), “Elementary Theo- 
rems relating to Determinants,’’ of which a writer re- 
marks, “ full of interest for the mathematician, but terrible 
to the unmathematical vision.” A second edition of this, 
rewritten and much enlarged, was published in Cred/e’s 
Fournal (vol. li. 1856, occupying pp. 209-271, 328-381).! 
_' “On the request of the editor of this ¥ournad to reproduce it he (Mr. 
Spottiswoode) requested permission to revise the work. The subject had, 
This was the earliest elementary treatise on a subject 
which has since risen to such importance, and contains a 
— 
good sketch of what had previously been done in the 
same direction. The friend, some of whose words we 
have already cited, remarks, ‘that Spottiswoode should 
have devoted himself at an early period to its cultivation 
is to me perfectly natural, for the prevailing character of 
all his mathematical work is symmetry (one might gene- 
ralise still further indeed and say that it, combined 
with graceful elegance, is the salient feature of all his 
activity, mathematical, physical, and literary). Bertrand 
once said of Serret that he was ‘wn artiste en formules, 
and in a far more general sense one might say that 
Spottiswoode is the ‘incarnation of symmetry.’” To 
go back to the criticism just now quoted, Mr. Spottis- 
woode is indeed a leviathan in symbols, and he takes his 
pastime amongst them: the “gay determinant” is a 
familiar form nowadays, and ‘‘ Hamilton’s weird delta 
turned ” (the Vaé/a of Clerk Maxwell) is conspicuous on 
many a page devoted to physics, but in some of the 
papers we are about to describe there are not only in- 
verted deltas, but Nablas turned to the right and to the 
left run riot on the pages. 
It is since 1870 that Mr. Spottiswoode has more 
especially divided his attention between physics and 
mathematics. ‘‘ His nearest friends,’ we are informed, 
“induced him to take up the less abstract one of these 
two branches of science in order that the general public 
might have better opportunities of appreciating his abili- 
ties. His work in the new field has been of the same 
character as in the former one. It aims less perhaps at 
exhaustive treatment than at a study of subtle and 
beautiful phenomena.” 
An early consequence of his new study was the publica- 
tion in 1874, in the NATURE Series, of his ‘‘ Polarisation 
of Light.’’ This contains a popular exposition of the 
subject, and its pages “ constitute a talk” with his work- 
people “rather than a treatise’’ on “‘this beautiful branch 
of optics.” ? 
Before we give a list of the several papers which, of 
course, do not admit of quotation and passing over, as 
still within the recollection of most of our readers, the 
most admirable address delivered before the British 
Association at Dublin in 18782—though one finds it hard 
to pass over the many brilliant passages, of more special 
interest however to the mathematician, who alone can be 
supposed to care for any other than the ordinary space of 
three dimensions—we must trespass to the extent of 
taking the following passage from the earlier address to 
Section A in 1865. This address, in the words of Prof. 
Sylvester, is a combined history of the progress of mathe- 
matics and physics, and of it Clerk Maxwell said he had 
endeavoured to follow Mr. Spottiswoode, “as with far- 
reaching vision he distinguishes the systems of science 
into which phenomena, our knowledge of which is still in 
the nebulous stage, are growing.” 
“A detailed summary of recent progress in pure 
mathematics would probably prove either interesting to 
the mathematician or unintelligible to the general hearer; 
proved neces- 
however, been so extensively developed in the interim, that it S 
i The result is 
sary not merely to revise but entirely to rewrite the work. 
given in the following pages.” : 
* He has also contributed a lecture on the same subject to the ‘‘ Science 
Lectures at South Kensington ”” Series. 
2 See NATURE, vol. xvill. pp. 404-415. 
