‘724 REPORT—1890. 
theories and to bring remote ones near; and I think it is safe to predict that the 
increased knowledge of principles and the resulting improvements in the symbolic 
language of mathematics will always enable us to grapple satisfactorily with the 
difficulties arising from the mere extent of the subject. 
Quite distinct from the theoretical question of the manner in which mathe- 
matics will rescue itself from the perils to which it is exposed by its own prolific 
nature is the practical problem of finding means of rendering available for the 
.student the results which have been already accumulated, and making it possible 
for a learner to obtain some idea of the present state of the various departments of 
mathematics. This is a problem which is common to all rapidly moving branches 
of science, although the difficulties are increased in the case of mathematics by its 
wide extent and the comparative smallness of the audience addressed. The great 
mass of mathematical literature will be always contained in journals and transactions, 
but there is no reason why it should not be rendered far more useful and accessible 
than at present by means of treatises or higher text-books. The whole science 
suffers from want of avenues of approach, and many beautiful branches of mathe- 
matics are regarded as difficult and technical merely because they are not easily 
accessible. ‘Ten years ago I should have said that even a bad treatise was better 
than none at all. Ido not say that now, but I feel very strongly that any intro- 
duction to a new subject written by a competent person confers a real benefit on 
the whole science. The number of excellent text-books of an elementary kind 
that are published in this country makes it all the more to be regretted that 
we have so few that are intended for the more advanced student. As an example 
of the higher kind of text-book, the want of which is so badly felt in many 
subjects, 1 may mention the second part of Professor Chrystal’s Algebra, published 
last year, which in a small compass gives a great mass of valuable and fundamental 
knowledge that has hitherto been beyond the reach of an ordinary student, though 
in reality lying so close at hand. I may add that in any treatise or higher 
text-book it is always desirable that references to the original memoirs should 
be given, and, if possible, short historical notices also. JI am sure that no 
subject loses more than mathematics by any attempt to dissociate it from its 
history. 
There is no more striking feature in the mathematical literature of our day than 
the numerous republications in a collected form of the writings of the greatest 
mathematicians, These collected editions not only set before us as a whole the 
-complete works of the masters of our science, but they make it possible for others 
besides those who reside in the vicinity of large libraries to become acquainted 
with the principal contributions with which it has been enriched in our century ; 
and, besides being of immense advantage to the science at large, they even go some 
way towards supplying the want of systematic introductions to the advanced 
subjects. Among these republications the collected edition of Cayley’s works, now 
in course of publication by the University of Cambridge, is deserving of especial 
notice. By undertaking this great work, not only in the lifetime of its author, but 
while in the full vigour of his powers, the University has secured the inestimable 
advantage of his own editorship, and thus, under the very best auspices, the world 
is now being placed in full possession of this grand series of memoirs, which 
already cover a period of nearly fifty years. 
Although it may not be possible to contemplate the actual position of pure 
mathematics in this country with any great amount of enthusiasm, we may yet 
feel some satisfaction in reflecting that there is more cause for congratulation at 
present than there has been at any time in the last hundred and fifty years, and 
that we are far removed from the state of affairs which existed before the days 
of Cayley and Sylvester. Unfortunately, we cannot point with pride to any 
distinct school of the pure sciences corresponding to the Cambridge school of 
mathematical physics, and I am afraid that the old saying that we have generals 
without armies is as true as ever. For this there is no immediate remedy; 
a school must grow up gradually of itself, as the study of mathematical physics 
has grown up at Cambridge. I certainly should not wish, even if it were possible, 
to obtain more recruits for the pure sciences at the expense of the applied, nor do I 
a 
