M. FOUCAULT'S PENDULUM DIAL.
_London, 24th April.1851.
Ma. Seneraron—The description. of the elegant experiment devised by M. Foucault to show the motion of the world does not appear to me to place its principle in so clear a light as it might. I think that principle may be made more easy of comprehension by the supposition of two very extreme cases of the experiment ; one where it shall give a maximum of result, and one where the. result shall be zero. Allow me to try the illustration. Imagine that-just over the spot of the Arctic regions where geographers fix the imaginary pivot of the world, there is a mountain with a lofty cavern in it, from which you can hang a bullet by a skein of unspun silk. Then, mentally, on the surface of the rock underneath the bullet, prepare a level circular space like the table in the experiment of M. Foucault; and round the-margin.of this table mark in two circular. bands, one within the other, the twenty-four hours- of the day and their minutes and seconds, anti the three hundred and sixty degrees of a "great circle" with their minutes and seconds. You will thus have made an earth-dial, the registering " sha- dow" on the face of which might be the fleeting wake of the bullet as it should- swing to and fro. Such a table would correspond with a small circle of latitude visibly marked on the earth ;. it would show the longitude of every place on it compared with some fixed point;. and if you drew through. it meridians from the North Pole to the South Pole, it would show the ton- gitude of all places on the earth. It would alio show the time of day,. if you coed cause the bullet to pass over the hour-figures, or the hour-figures to pass under the bullet as it vibrated. Now, by the motion of the earth,. the figures on this table will actually be carried round the pole once in twenty- four. hours ; and if the bullet can be kept vibrating in. its original plane, and- prevented from following the figures, the latter, iu running round with the table and the world, will come successively under the bullet in the way we want. But the suspending skein of silk is so loose that it cannot do the least towards twisting the bullet round with the world and the roof- of the cavern to which it is fixed ; therefore the bullet is stationary in the way we want; and-as much unconnected with the earth as if it. hung from the pole-- star, which is not part of the solar system,. but for the purposes of this ex- periment may be taken as a fixed point in infinite space. Ibis would be the- experiment of M. Foucault in its simplest form, with positive results mani- fested in the greatest and purest degree. We can never actually perfbrm it till we pass over the eleven degrees which have hitherto separated navi- gators from the. Pole at the nearest approach they ever yet have made to it. If now you imagine the experiment- to be repeated at the Equator,. your meet a wholly different and a negative result. At the Equator, the suspend,- ing point for the bullet would go round with the earth, and no vibration of any bullet underneath that suspending point could mark the rate at which any point of the earth revolved in space ; for the two points and the bullet would all be running in the same direction at the same late.- If the ballet swung East and West, it would at each oscillation in space merely passlie yond, or fall short of, the termini of its swing in the preceding oscillation; and if it swung North and South, it would describe in space a zigzag com- posed of conoidal angles, the bases of which would be the distance the earth' had passed between each half oscillation, and the points of which would be the returning point of each oscillation. Such a course in space could not be marked on any table or other apparatus on the earth;, but could be-re- gistered only by means of some belt. like Saturn's- ring, which should be sta- tionary in space, and have the degrees and minutes marked on it as they are marked on the ecliptic of out globes. This would be the experiment in its-purely negative form, with the indications at zero.
But as you recede from the Equator you would be getting out of exact parallelism with the plane of the earth's revolution; and would, by a geo- metrical law not comprehensible to the popular mind, be obtaining a. more complex indication. The general reader will gain some feeling of the changed result from the image presented to the eye by a diagram- showing. the very complicated track that would be-given- to the bullet by the combi- nation of its independent swing to and fro with its. circular advance on the world. At the pole, to use the poetical but strictly exact illustration-of Me.. Sylvester in the. Times, " its track would be a series of loops or festoons re- gularly and symmetrically arranged around a common centre, much like a very composite corolla of a flower with a large number of extremely elongated and crowded petals grouped around its seed-vessel." As the composite flower became larger by the movement of the pendulum away from the Pole, I suppose the petals would become shorter and more obtuse;. the centre of, the flower would open, and become a free space ; further towards the Equa- tor, the petals would be resolved into a succession of small eccentric circles;. and on the line of the Equator itself, there would be only a thin line of a different sort of efflorescence, not very unlike the slanting edges of a wheel with- acute teeth set more in one direction than the other:- Mr. Sylvester, who is known to Cambridgemen as one of the. profoundest. though not yet one of the most distinguished mathematicians of the day, has corrected the loose explanations of the experiment which appeared in the Times; and has stated the time which the bullet will take to make a revo- lution round the table at the latitudes of Paris andlondon. He asserts that the revolution will occupy thirty-two hours and eight minutes at Faris; and thirty hours forty minutes at more Northerly London. So much for the principle of the experiment : a Word of doubtf on its me- ehanical details. The descriptions I have read convey the. idea that the metal ball continues to swing to and fro for twenty-four hours, and from day to day. This cannot be the case without the help of machinery; for the ball will be brought to a stand-still by friction (or the torsive power of the suspending wire,) and the opposition of the air to its passage. You could not apply external machinery except in the way that- you apply it to the pendulum of a clock. But in a clock the pendulum is imprisoned in a- guide which twists it with the world ; and you could not in fact strike the pen- dulum by unconnected machinery of any but the most elaborate character; in such a manner as not to change the plane in which the pendulum vibrates.. The impulse to the pendulum would, unless its aim were most delicately cab. culated and directed, have a tangental direction similar to that which tine
torsion of aatiffipendulum rod would give.- A.- Vt.-
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