CHAP. III., 4.] 



ASTRONOMY. BORDA KATER BAILY. 



Connection latitude with the compression of the terrestrial ellip- 

 of | r t a J lty soid. 1 The pendulum is the readiest and most accu- 

 figure of ra te means of determining variations in the force of 

 the earth gravity ; the repetition of its oscillations enabling 

 > ut ' 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, 

 Early pen- count its vibrations, and measure its length, is a 



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 arc, 

 by M. Biot, who even extended his stations to the 

 Island of Unst in Shetland. 



JEAN CHARLES BORDA, who was born in 1733 and 

 ^j e( j j n 1799^ was devoted to the promotion of the 

 lethod of exac ^ sciences, and contributed in an eminent degree 

 to the precision attained in physics and astronomy 

 towards the close of the last century. The name of 

 Borda deserves a record in the history of science, 

 since it has been said of him, by no less an authority 

 than Dr Young, that " he seems to have possessed a 

 considerable share of that natural tact and sagacity 

 which was so remarkable in Newton." His earlier 

 researches were connected with hydrodynamics, and 

 the resisted motion of projectiles ; in later years he 

 was chiefly devoted to practical astronomy and geo- 

 desy. The portable repeating circle invented by him 



(237.) 

 3orda im- 

 jroves the 



hem. 



has had a very great reputation in France. He was 

 one of the principal designers of the measurement 

 of the French arc, 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, ; 

 has usually been preferred, and on the whole it ap- 

 pears to be more satisfactory. Such a pendulum, 

 after being compared with an astronomical clock at 

 Greenwich, or any other place of reference, is taken 

 to different stations and its rate of vibration deter- 

 mined, and it is then brought back and compared once 

 more at the point of starting. Important series of 

 observations of this kind have been made by Colonel 

 Sabine and Captain Foster, and also by Admiral Du- 

 perrey. 



But the two individuals who have most studied \ . ? ' ' 

 i -11 nii i Kelative 



the practical determination of the length or the se- an( j a b so . 



conds pendulum as a mechanical problem, are Kater lute mea- 

 sures. 



( 23 8-) 



japlace J Clairaut (besides giving a theorem which, in the case of an ellipsoid, connects the polar compression with the increase of 



.nd 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- 

 >tokes on tude. This he proved to be true when the spheroid is homogeneous, or when it is composed of similar concentric layers of 

 he earth's varying density. Laplace confirmed the result by a different analysis, and farther showed, that if the earth be composed of con- 

 ittraction. 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 Transactions, vol. viii. ; and for a simpler proof, Cambridge and Dublin Math. Journal, vol. iv. p. 194. 



