il hat subject had lost its charm, 
NATURE 
383 
holds a position intermediate betweer a public depart- 
ment and an independent institution. While on the one 
aand this intermediate position presents some advantages, 
it all events in the present stage of the subject asa 
science, it undoubtedly, on the other, requires no incon- 
siderable tact and judgment in its management. For 
the yearly administration of a large sum of public 
noney, for the management of a considerable staff at 
yome, and of a variety of observers at out-stations in all 
varts of the country, and for communication with similar de- 
yartments of State in foreign countries, science alone 
would not have sufficed. But at the same time few 
pranches of natural knowledge stand more in need of a 
strong scientific guide to keep it from the crotchets of 
jJabblers in the subject, or from relapsing into an indis- 
priminate accumulation of loose observations from which 
ao valuable result can ever be derived. For this post the 
President and Council of the Royal Society unanimously 
nominated him, nor had they ever reason to regret the 
ep which they then took. 
_ The case of the Meteorological Council was, however, 
Jt one instance out of many in which his name came 
jpermost in the minds of men when they were looking 
for a leader, or a chairman, or a president. 
sident of the Mathematical Society (1874-6), or of the 
Mathematical and Physical Section of the British Asso- 
ation (1873), or as Chairman of Committees too many 
{0 enumerate, he always succeeded in commanding the 
respect of those with whom he was associated, and in 
ing through the business to a satisfactory issue. 
In one matter only did he fail of success; but in that 
e the failure was not really his, but that of those who 
should have given him support. The case was that of 
ge. aces of the candidature of leading Uni- 
ersity men, both in Oxford and in Cambridge, have not 
been unknown, from the time of the late Sir John Lefevre 
o that of Prof. Stuart; but all have terminated in the 
ame result, namely, the total defeat of every man of 
Niversity distinction, whatever other qualifications he 
y have for the office. With these instances we may 
compare, not without interest and instruction, the choice 
: Oxford, when, in 1878, Lord Cranbrook received his 
‘Joccurred. 
It was sometimes thought that his mind became 
iverted from mathematics by his many other distracting 
\@vocations; there are, however, reasons for doubting this. 
\fle is true pre he did not pour out the amount of ane 
|matical papers of which he was certainly capable ; but 
\|hose which he did publish showed that he cared little to 
at he reserved himself for questions of real importance. 
e remember his alluding to the subject of one of his 
ter papers contributed to the Mathematical Society, on 
fodular Equations, as relating to “a point on which people 
| ke fringe-work to the borders of our knowledge, and 
Q 
at 
aad puzzled themselves for a long time,” and the follow- 
passages from his address to the London Mathematical 
ociety were certainly not penned bya president for whom 
“ Of all branches of 
athematical inquiry, this is the most remote from prac- 
ical applications ; and yet, more perhaps than any other, 
< Pern 
hich has been made by the University of London on | 
€ only two occasions on which a vacancy has yet | 
it has kindled an extraordinary enthusiasm in the minds 
of some of the greatest mathematicians.’ Then he 
quotes Gauss as having held Mathematics to be the 
Queen of the Sciences, and Arithmetic to be the 
Queen of Mathematics. I do not know that the great 
achievements of such men as Tchébychef and Riemann 
can fairly be cited to encourage less highly gifted in- 
vestigators ; but at least they may serve to show two 
things—first, that nature has placed no insuperable 
barrier against the further advance of mathematical 
science in this direction; and secondly, that the boun- 
daries of our present knowledge lie so close at hand that 
the inquirer has no very long journey to take before he 
finds himself in the unknown land. It is this peculiarity, 
perhaps, which gives such perpetual freshness to the 
higher arithmetic. It is one of the oldest branches 
perhaps the very oldest branch, of human knowledge ; 
and yet Some of its most abstruse secrets lie close to its 
tritest truths. I do not know that a more striking 
example of this could be found than that which is fur- 
nished by the theorem of M. Tchébychef. To under- 
derstand his demonstration requires only such algebra 
| and mathematics as are at the command of many a 
Whether as | 
schoolboy; and the method itself might have been 
| invented by a schoolboy, if there were again a schoolboy 
with such an early maturity of genius as characterised 
Pascal, Gauss, or Evariste Galois.” 
The following is another instance of the interest which 
| he retained in mathematics to the very last. In the 
address above quoted he alluded to a problem, at that 
time still unsolved, in the following terms :—“ It was first 
shown by M. Liouville that irrational quantities exist 
| which cannot be roots of any equation whatever, having 
his candidature for the representation of the University 
integral coefficients. We may perhaps be allowed to 
designate by the terms arithmetical and transcendental 
the two classes of irrational quantities which M. Liouville 
has taught us to distinguish ; and it becomes a problem 
of great interest to decide to which of these two classes 
we are to assign the irrational numbers, such as e and z, 
which have acquired a fundamental importance in analysis. 
To Lambert, the eminent Berlin mathematician of last 
century, the first great step in this direction is due. He 
showed that neither 7 nor x” is rational; with regard 
to « he was even more successful, for he was able 
to prove that no power of e, of which the exponent 
is rational, can itself be rational. There (with one 
slight exception) the question remained for more than 
a century; and it was reserved for M. Hermite, in the 
year 1873, to complete, by a singularly profound and 
beautiful analysis, the exponential theorem of Lambert, 
and to prove that the base of the Napierian logarithms is 
a transcendental irrational. But, in a letter to M. Bor- 
chardt, M. Hermite declines to enter on a similar research 
with regard to the number 7. ‘Je ne me hasarderai 
point,’ he says, ‘a la recherche d’une démonstration de 
la transcendence du nombre 7. Que d'autres tentent 
Yentreprise ; nul ne sera plus heureux que moi de leur 
succés ; mais croyez m’en, mon cher ami, il ne laissera 
pas que de leur en cotiter quelques efforts.’ It is a little 
mortifying to the pride which mathematicians naturally 
feel in the advance of their science to find that no pro- 
gress should have been made for a hundred years and 
more toward answering the last question, which still 
