— 
Cuar. III., § 4.] 
Connection Jatitude with the compression of the terrestrial ellip- 
of gravity oid.’ The pendulum is the readiest and most accu- 
and the *s re A 5 
figure of Yate means of determining variations in the force of 
the earth— gravity ; the repetition of its oscillations enabling 
a 8 the observer to ascertain their average duration with 
* extreme nicety. ‘The more rapid the oscillation the 
greater is the force of gravity, because the heavy 
body is more quickly drawn into its lowest posi- 
tion. Two sets of observations, made in different lati- 
tudes, would, rigorously speaking, suffice to deter- 
mine the polar compression, supposing the earth to 
be a geometrical ellipsoid, and composed of homoge- 
neous and concentric layers ; a larger number would 
serve to test the accuracy of these assumptions, and 
would, at all events, be imperatively required to 
eliminate the errors of observation. 
(236.) It might be supposed that to swing a pendulum, 
Farly pen- count its vibrations, and measure its length, is a 
dulum ob- very easy thing. Experience shows that a more 
servations. |, : 
difficult practical problem can hardly be proposed. 
Those persons, therefore, who have in a good mea- 
sure overcome the difficulties, are to be regarded as 
promoting materially an enquiry which has always 
ranked amongst the most interesting connected with 
astronomy. Some of the observations of the eight- 
eenth century, especially those of Lacaille at the 
Cape of Good Hope and of Phipps in the Arctic 
Regions, appear to have been made with much care ; 
but the French ‘astronomer Borda seems to have 
given the initiative to observations of a higher degree 
of accuracy, and his methods were ably carried out 
in connection with the great French meridian are, 
by M. Biot, who even extended his stations to the 
Island of Unst in Shetland. 
(237.) Jean Cuartes Borpa, who was born in 1733 and 
Borda im- died in 1799, was devoted to the promotion of the 
ASTRONOMY.—BORDA—KATER—BAILY. 
851 
has had a very great reputation in France. He was 
one of the principal designers of the measurement 
of the French are, and was employed in its superin- 
tendence, especially as regards the measurement of 
the base. His experiments on the pendulum were 
originally undertaken (I believe) in 1790, with a view 
to making it the basis of the national measures, but 
were afterwards subordinated to the greater scheme 
of terrestrial measurement. Baily records a fact 
connected with Borda, not unworthy of mention, as a 
caution to observers :—the year in which many of 
his experiments were made is not discoverable from 
the account of them, though the day, hour, minute, 
and second, are recorded with praiseworthy fidelity. 
From this time pendulum experiments assumed an 
astronomical and geodetical importance. The appa- 
ratus of Borda consisted of a slender metallic wire, 
attached at one end to a knife-edge suspension, and at 
the other to a small brass cap, nicely fitted by grind- 
ing to a sphere of platinum which formed the bob or 
weight of the pendulum. The oscillations were counted 
by the method of “ coincidences,’’ that is, by placing 
the experimental pendulum in front of a good clock 
with a known rate, and observing after how long a 
time the two pendulums (having started in the same 
direction) again coincided in their motions by one of 
them having gained or lost exactly two vibrations ; 
a method which has been used at least since the 
time of Bouguer. The time of vibration being thus 
known, the distance from the knife edges to the bot- 
tom of the ball was measured by means of a scale; 
and due corrections for the position of the centre of 
oscillation were then applied. 
By English observers, an invariable pendulum of : 
the form of a flat bar, provided with a bob or weight, an, 
has usually been preferred, and on the whole it ap- 
(238.) 
Relative 
sures, 
oles exact sciences, and contributed in an eminent degree pears to be more satisfactory. Such a pendulum, 
making to the precision attained in physics and astronomy after being compared with an astronomical clock at 
them. towards the close of the last century. The name of Greenwich, or any other place of reference, is taken 
Borda deserves a record in the history of science, to different stations and its rate of vibration deter- 
since it has been said of him, by no Jess an authority mined, and it is then brought back and compared once 
than Dr Young, that “he seems to have possessed a more at the point of starting. Important series of 
considerable share of that natural tact and sagacity observations of this kind have been made by Colonel 
which was so remarkable in Newton.” His earlier Sabine and Captain Foster, and also by Admiral Du- 
researches were connected with hydrodynamics, and __perrey. 
the resisted motion of projectiles; in later years he But the two individuals who have most studied ,, 29%) 
was chiefly devoted to practical astronomy and geo- the practical determination of the length of the se- and abso- 
desy. The portable repeating circle invented by him conds pendulum as a mechanical problem, are Kater lute mea- 
Laplace 1 Clairaut (besides giving a theorem which, in the case of an ellipsoid, connects the polar compression with the increase of 
and Mr _— gravity there) showed that the increase of the force of gravity from the equator will vary as the square of the sine of the lati- 
Stokes on tude. This he proved to be true when the spheroid is homogeneous, or when it is composed of similar concentric layers of 
the earth’s varying density. Iaplace confirmed the result by a different analysis, and farther showed, that if the earth be composed of con- 
attraction. centric strata which are severally homogeneous, and nearly spherical, but otherwise arbitrary in form, and if the surface be that 
of a fluid in equilibrium (as it practically is when we refer the earth’s figure to the sea-level), there exists a necessary connection 
between gravity and the superficial figure, which, in the case of an ellipsoid of revolution, leads to the same relation of the square 
of the sine of the latitude. 
In this case, also, the strata are presumed to be concentric. 
But in a recent and remarkable paper 
by Professor Stokes, it is shown that the law connecting the force of gravity and the figure of equilibrium still holds when no hypo- 
thesis whatever is made as to the distribution of the matter within the earth, provided always that it be consistent with the observed 
fact of the ellipsoidal figure of the earth’s fluid covering. Thus the confirmation, by means of pendulum experiments, of Clairaut’s 
Theorems cannot be regarded as a proof of the concentric arrangement of the strata, nor (so far) of the primitive fluidity of 
the earth. See Cambridge Transacti: 
s, Vol. viii. ; and for a simpler proof, Cambridge and Dublin Math. Journal, vol. iv. p. i94. 
