CHAP. III., 5.] 



ASTRONOMY. M. FOUCAULT M. ENCKE. 



57 



(259.) Suppose a considerable -weight suspended by a wire 

 demon- o f regular elasticity from a fixed point or stand con- 

 Btratingthe nected fi rm i y ^fa tne g roun d ; and let us first ima- 

 Earth s ro- . . , ^ ,, -, 



tation. gme 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. 



M. Foucault's experiment was made, in the first in- (260.) 

 stance, with a pendulum of steel wire from '03 to -05 Corrections 



inch in diameter, bearing a ball of 12 pounds weight. * 

 It is desirable to make the pendulum vibrate in small 

 arcs, 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- (261.) 

 dulum suspended by a thread or wire has been con- f ts tne . OI 7 

 sidered in the most general manner by M. Hansen, gate( j by M. 

 the physical astronomer, with reference to the earth's Hansen. 

 motion. 1 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. ENCKE. Cometary Astronomy Periodic Comets of Halley and Encke. GAMBART'S and 

 Biela's Comet Comets of 1811 and 1843. Mr HIND New Planets or Asteroids. Mr LAS- 

 SELL Newly discovered Satellites. Mr Bond. 



PROFESSOR JOHANN FRANZ ENCKE, 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 ENCK.E, 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; Its return 

 and Clairaut, whose surprising analytical ability often in 1759 - 

 left but little to his successors to accomplish, calcu- 

 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- (264.) 

 turbations is the introduction by Lagrange of the cele- 

 brated method of the Variation of the elements (44.) 



Theorie der Pendelbewegung. Dantzig, 1853. 



