(259.) 
demon- 
strating the 
Earth's ro- 
tation. 
(262.) 
Professor 
Encke. 
Periodic 
Comets, 
(263.) 
Halley’s 
Comet— 
period 76 
years, 
Cuap. IIT., § 5.] 
Suppose a considerable weight suspended by a wire 
of regular elasticity from a fixed point or stand con- 
nected firmly with the ground; and let us first ima- 
gine the place of the experiment to be exactly over 
the North Pole. Let the wire pendulum be swung 
so as to coincide with the plane of the meridian of 
London. As the earth rotates, the wire and the ball 
must evidently rotate too. But the motion of the 
mass originally impressed parallel to a given plane 
will continue in that plane, and consequently the 
plane of motion will coincide in the course of 12 hours 
with every meridian in succession, and the apparent 
rotation will be entirely completed in a uniform man- 
ner in 24 hours. In any other latitude than 90°, 
but greater than 0°, a continuous and regular appa- 
rent change of motion must also occur, since a me- 
ridian of the globe does not preserve its parallelism 
during diurnal motion, excepting only at the equator; 
consequently, at all points of the earth’s surface, ex- 
cept at the equator, the plane of motion of the pendu- 
lum will vary uniformly in azimuth—quicker, how- 
ever, in high than in low latitudes. To find this 
velocity, it is only necessary to decompose the rota- 
tion of the earth round its axis into two, one of which 
(which is alone effective) is round the vertical of the 
place of observation. The apparent angular motion 
is thus proportional to the sine of the angle of lati- 
tude. Thus, in an hour, it is 15° x sine lat. 
ASTRONOMY.—M. FOUCAULT——M. ENCKE. 
855 
M. Foucault’s experiment was made, in the first in- 
stance, with a pendulum of steel wire from ‘03 to 05 
inch in diameter, bearing a ball of 12 pounds weight. 
Itis desirable to make the pendulum vibrate in small 
ares, in consequence of the tendency to ellipticity in 
the vibrations, which is necessarily accompanied by a 
rotation of the major axis of the ellipse, which might 
easily be mistaken for the influence of the earth’s 
motion. To take account of this disturbing force, 
we have only to measure accurately the greater and 
less axes of the ellipse described. Then a revolution 
of the apsides (from this cause only) will be per- 
formed in a time which will be found by multiply- 
ing the time of a double vibration of the pendulum 
by 8 times the square of the length of the pendulum, 
divided by 3 times the product of the two axes of the 
ellipse. This formula is due to Mr Airy. The theory 
of M. Foucault’s beautiful experiment has been 
verified by numerous experiments in different la- 
titudes, 
Very recently the theory of the motion of a pen- 
dulum suspended by a thread or wire has been con- 
sidered in the most general manner by M. Hansen, 
the physical astronomer, with reference to the earth’s 
motion. It is an intricate problem of analytical 
mechanics, But the results show, as might have been 
anticipated, that all the sensible results are those which 
the geometrical treatment of the question indicate. 
§ 5. M. Encxn. Cometary Astronomy—Periodic Comets of Halley and Encke. GAMBART’S and 
Biela’s Comet—Comets of 1811 and 1843. Mr Hinp—WNew Planets or Asteroids, 
Mr Las- 
SELL—Newly discovered Satellites. Mr Bond. 
Proressor JOHANN Franz Encxe, Director of the 
Observatory of Berlin, is one of the most eminent 
physical and practical astronomers of the present day. 
The author of many valuable observations and im- 
portant memoirs, he is best known by those which 
are connected with the motions and theory of Comets. 
I shall therefore devote this section to an abstract of 
the progress of this interesting subject, and more 
particularly of M, Encke’s discoveries and specula- 
tions. I must premise, however, that, easy and 
agreeable as it would be to introduce here a detailed 
essay on Cometary Astronomy, the design and extent 
of this discourse alike forbid it, and at the cost of 
some self-denial, I will endeavour to confine myself 
entirely to what is most new and characteristic in the 
Cometary history of later years. 
Halley’s Comet.—Before proceeding to describe 
the remarkable comet especially connected with the 
name of Encxg, it will be proper to resume the his- 
tory of Halley’s Comet where it has been left off by 
Sir John Leslie in his Dissertation. That Comet— 
the comet of 1682—must ever remain memorable, 
perhaps the most so of its class, as being the first 
‘whose return was confidently predicted, in firm reli- 
ance on the Newtonian Theory of Gravity. Halley’s 
announcement—grounded not on vague analogies, 
but on laborious computations—that it would reap- 
pear early in 1759, was realized almost to the letter ; 
and Clairaut, whose surprising analytical ability often 
left but little to his successors to accomplish, caleu- 
lated the perturbations with an accuracy which even 
the present state of physical astronomy has hardly 
exceeded. Indeed no general method for calculating 
perturbations in highly elliptic orbits is as yet in use, 
and though the methods of Clairaut have been. super- 
seded by those of Lagrange and Bessel and Lever- 
rier, the summation of the effects by the method of 
“ quadratures” is always used,—the periodic time of 
the comet being divided into short intervals through- 
out which the elements are considered invariable, and 
during which the configurations and perturbing effects 
of the principal planets are computed with much 
labour. 
The chief improvement in the calculation of per- 
turbations is the introduction by Lagrange of the cele- 
brated method of the Variation of the elements (44.) 
1 Theorie der Pendelbewegung. Dantzig, 1853. 
(260.) 
Corrections 
to be at- 
tended to. 
(261.) 
Its theory 
investi- 
gated by M. 
Hansen. 
Its return 
in 1759, 
(264.) 
