Fan. 6, 1870] 
NATURE 
263 
than I originally intended on the subject, which, as 
standing first on the muster roll of the Association, and 
as having been so recently and repeatedly arraigned 
before the bar of public opinion, is entitled to be heard in 
its defence (if anywhere) in this place,—having endea- 
youred to show what it is not, what it is, and what it 
is probably destined to become, I feel that I must enough 
and more than enough have trespassed on your forbear- 
ance, J. J. SYLVESTER 
The remarks on the use of experimental methods in 
mathematical investigation led to Dr. Jacobi, the eminent 
physicist of St. Petersburg, who was present at the delivery 
of the foregoing address, favouring me with the annexed 
anecdote relative to his illustrious brother,C. G. J. Jacobi*— 
“En causant un jour avec mon frére défunt sur la nécessité 
de contréler par des expériences réitérées toute observation, méme 
si elle confirme Vhypothése, il me raconta avoir découvert un 
jour une loi trés-remarquable de la théorie des nombres, dont il 
ne douta guére qu'elle fit générale. Cependant par un excés de 
précaution ou plutét pour faire le superflu, il voulut substituer un 
chiffre quelconque réel aux termes généraux, chiffre qu'il choisit 
authasard, ou, peut-étre, par une espéce de divination, car en effet 
ce chiffre mit sa formule en défaut ; tout autre chiffre qu'il essaya 
en confirma la généralité. Plus tard il réussit & prouver que le 
chiffre choisi par lui par hasard, appartenait 4 un systtme de 
chiffres qui faisait la seule exception a la régle. 
“Ce fait curieux m’est resté dans la mémoire, mais comme il 
s’est passé il ya plus d’une trentaine d’années, je ne rappelle plus 
les détails. “M. H. JAcoBI 
“Exeter, 24 Aotit, 1869.” 
THE NEW PELESCOPE AT ETON 
N furtherance of natural science work at Eton, an ex- 
cellent telescope has been recently given to the school 
by the energy and liberality of some of the masters. 
The instrument is a refractor, with object glass of 5'9 
inches clear aperture, and 88 inches focus, and was made 
by Messrs. Cooke and Sons, of York, who also supplied 
the observatory and superintended the erection of the 
telescope. It is, as will be seen from the engraving, 
mounted equatorially on the German system, with decli- 
nation circle reading to 10” of arc, and hour circle reading 
to 2” of time. The mechanical details do not, with one 
exception, deviate materially from; the pattern usually 
adopted by Messrs. Cooke, whose name is a guarantee 
for skill of design and excellence of workmanship. The 
exception alluded to is in the construction of the driving 
clock, the speed of which is not regulated, as usual, by a 
centrifugal governor, or fly, alone, but by a fly supple- 
mented by an ordinary clock escapement. This arrange- 
ment is quite new, and is the invention of the late Mr. T. 
Cooke, the senior partner in the firm. It was described 
by him in a paper read before the Royal Astronomical 
Society a short time ago. The details would hardly be 
intelligible without drawings, but the general mode of 
action is as follows :— ; 
The barrel is connected with two trains of wheel-work : 
one (the lowest wheel of which gives motion in the ordinary 
* It is said of Jacobi, that he attracted the particular attention and friend- 
ship of Béckh, the director of the philological seminary at Berlin, by the 
zeal and talent he displayed for philology, and only at the end of two years’ 
study at the University, and after a severe mental struggle, was able to 
make his final choice in favour of mathematics. The relation between these 
two sciences is not perhaps so remote as may at first sight appear; and 
indeed it has often struck me that metamorphosis runs like a golden thread 
through the most diverse branches of modern intellectual culture, and forms 
a natural link of connection between subjects in their aims so remote as 
grammar, philology, ethnology, rational mythology, chemistry, botany, com- 
parative anatomy, physiology, physics, algebra, versification, music, all of 
which, under the modern point of view, may be regarded as having mor- 
phology for their common centre. Even singing, I have been told, the 
advanced German theorists regard as being strictly a development of 
recitative, and infer therefrom that no essentially new melodic themes can 
be invented until a social cataclysm, or the civilisation of some at present 
barbaric races, shall have created fresh necessities of expression, and called 
into activity new forms of impassioned declamation, 
way to the telescope) is terminated by a fly of insufficient 
power fer se to reduce the speed within proper limits ; the 
other train is terminated by a half-dead escapement of the 
usual kind. One of the wheels of the fly-train has a broad 
rim, on which presses a brake actuated by a wheel in the es- 
capement train. When the escapement is stopped, this brake 
presses on the wheel with sufficient force to stop the motion of 
the clock entirely. When the escapement is set to work the 
brake is released, and the fly-train moves, communicating 
motion to the telescope. If the speed becomes too great, 
so as to outrun the escapement, the latter immediately 
applies increased brake-power, and checks the motion of 
THE ETON EQUATORIAL 
the fly ; and wéce versd, if from increased friction or other 
cause the motion is too slow, so that the fly lags behind 
the escapement, the brake-spring is relaxed by the latter 
until the due speed is regained. Thus the two trains are 
balanced against each other, and since one of the wheels 
of the escapement-train is, as in some forms of train 
rentontoires, supported in a swinging-frame (which frame, 
in fact, controls the brake-spring), the intermittent motion 
of the escapement does not reach the telescope. This 
clock seems to work very smoothly; and not the least 
advantage of the arrangement is the facility with which 
