Imatges de pàgina
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be distinguished by this character. The supposed test is no test, because the character, in place of being peculiar to the particles of organic matter, or, even as some have thought, to the particles from a peculiar organ, belongs to all solid matter; and here Mr. Faraday took occasion to state, in correction of public misapprehension, that Mr. Brown by no means intended to say, or ever had said, that the motion was an indication of vitality, and that, consequently, all matter had life, or that the particles he had made his observations upon were the ultimate particles of matter.

Friday, February 20.

Specimens of ancient armour from Mr. Balmanno were exhibited in the library.

Among the presents were specimens of chalcedony in basalt from the Giants' Causeway, by the Rev. Mr. Caton.

The apparatus for certain phonic experiments were also placed on the table..

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In the lecture-room Mr. Ainger explained some of the properties of simple pendulums, and the principle of those contrivances which have been invented for compensating the effect of temperature on the pendulums and balances of time-keepers. With respect to what is called the isochronism of the vibrations of the same or similar pendulums, and which is frequently supposed to be a peculiar property of such bodies, especially fitting them for the purpose of time-keepers, it was shewn that this property is not at all peculiar to the pendulum, for that the isochronism of the pendulum was merely one instance of a very general principle, namely, that perfectly equal and similar actions must of necessity be performed in equal times; which is as true of any other repeated action, as of the vibrations of the pendulum. Any other alternating or repeated action or motion would therefore equally well serve the purpose of measuring time if we could ensure the perfect similarity of such repetitions. The peculiar advantage of the pendulum, therefore, is not in its principle, but in the ease with which it can be freed from those disturbing causes which would prevent the perfect similarity of the successive actions of a more complex body or motion. The simplicity of the pendulum's form, the small quantity of its friction, and the necessary identity of its successive oscillations in every thing but the extent of their arcs, render it peculiarly fitted formeasuring time; the means by which the length of those arcs are made constant by means of the escapement, were explained in a former lecure, the substance of which is given at p. 418, vol. iii. of this Journal. APRIL-JUNE, 1829.

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Mr. Ainger then described the means by which Huygens had proposed to render the vibrations of the pendulum isochronous, whatever were the length of its vibratory arc, a mode which, without entering into those mathematical investigations which led Huygens to the discovery, may be thus rendered intelligible by considerations merely mechanical. In the first place, it is known that a short pendulum vibrates more quickly than a long one. In the second, it is also known that the same pendulum occupies more time to vibrate in a large arc than in a small one. Shortness of pendulum and shortness of arc both conduce to rapidity of vibration; length of either produces the reverse effect, or slowness of vibration. It follows, then, that a long pendulum vibrating in a short are might be found to be isochronous with a shorter pendulum vibrating in a longer arc. It follows, indeed, that within certain limits a diminution of the pendulum's length may compensate for the increase of its vibratory arc, and vice versa. It is not probable that this was the sort of reasoning which led Huygens to his beautiful and scientific invention; but it will serve probably to make that invention more intelligible to most readers than it is generally found. What are com monly called the cycloidal cheeks of Huygens act upon the principle above described; if by any means the arc of vibration be increased, the pendulum becomes shortened during such excessive vibration, exactly so much as will accelerate its motion by a quantity equal to the retardation produced by the increase of its arc. The figure in the margin may serve to explain this; suppose a b

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to represent the upper end of a pendulum, consisting of a thin, perfectly flexible line, closely embraced at the point a by two metal cheeks c and d. When the pendulum first departs from the perpendicular situation a b, it moves from the extreme point a; but as it inclines. to the right or left, it comes in contact with the metal cheek d or c, and its motion takes place only from the point where it ceases to be in contact with those cheeks;

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thus, when the position is a e, it touches the curved edge of the cheek c from a to f, and thus in this position its virtual length is only fe; if the pendulum swing to h, it will be in contact with the cheek as far as g, and therefore its virtual length will now be diminished to g h; for it is clear that the part a g is absolutely passive, and might in this position be considered as part of the solid block or cheek c. It would be evident, therefore, that a pendulum placed under these circumstances will become a shorter pendulum, as it extends the arc of its vibration; the rate at which it will shorten as compared with the increase of its arc, will of course depend on the nature of the curve given to the cheeks c and d; for if the curve of c were altered to that shewn by the dotted line a k, it is clear that the pendulum's length would diminish less rapidly as compared with the increased arc; if the curve of d were altered, as shewn by the dotted line a l, it is equally clear that the pendulum's length would diminish more rapidly as it increased its arc. Since, then, it is evident that the length of the pendulum may be made to diminish at any rate we please by altering the curve of the cheeks, it is equally evident that some curve may be found which shall make that diminution of length an exact compensation for the increase of the vibration arc. The particular curve which effects this purpose is that called the cycloid; and it is a curious fact that a pendulum, whose vibrations are thus modified, itself describes a cycloid exactly similar to those cheeks which modify it. Such are the general principles of the most elegant and refined contrivance ever introduced into horology, a contrivance whose merit is not in the least affected by the circumstance that it is too refined for practice. The difficulty of making and applying the cycloidal cheeks with perfect accuracy has prevented their actual use; and therefore the attention of clockmakers has been directed rather to making the pendulum describe equal arcs, than to causing unequal arcs to be performed in equal times. This has been effected by means of the escapement described in the lecture before alluded to. One of the chief and most obvious difficulties in the application of the cycloidal cheeks may be worth explaining. In the diagram, the part a b of the pendulum is said to be perfectly flexible, and this condition is essential; but perfect flexibility is not attainable even with a riband, nor with any animal or vegetable fibre; there is always a certain portion of elasticity, however small; it is clear, however, that animal or vegetable fibres could not possibly be used as suspenders to a pendulum; metal only can be admitted, and in this material the elasticity of a b

would be considerable; and the state of tension in which the part abdwould be placed as it bent against the cycloidal cheeks, would operate like an addition to the force of gravity, and would totally destroy the compensatory qualities of the curve. If indeed a b could consist of a metal chain perfectly flexible at every point (which is, of course, impossible) the application might possibly succeed better than it has hitherto done.

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M. Ainger next described the nature of the point in a pendulum which is called its centre of oscillation, and which is that point in which, if all the matter of the pendulum were collected, it would vibrate in the same time as before. This will be best explained by an example: suppose a b to represent a uniform rod or bar of any b919bi uniform substance, suspended from the upper end a; suppose it be divided into three equal parts, by the points c and d. Such a bar vibrating round the point a, will perform of those vibrations in precisely the same time as if all the madodterial of the bar were concentrated in the point c, when, of Jag course, the suspending portion a c would be without any dweight, and the part cb annihilated; so if the bar were 18 roused and made to vibrate round b, it would vibrate as quickly 19tecas if all its substance were collected in d. For these reasons 260 ic is called the centre of oscillation of such a bar when vibratmbing round a, and d would be its centre of oscillation when 1806 vibrating round b. Every pendulum has its centre of oscilla dotion, but with such complicated forms and various materials dodas are found in actual pendulums it would be impossible to 5 define its exact place, as is here done for a simple homogenebarous pendulum. The most curious and useful fact, in regard 9 9to the centre of oscillation, is, however, this: that if the -bár a by which was vibrating round a, be raised and suspended from its centre of oscillation c, it will vibrate with exactly the same rapidity as before. It follows of course, that the bar will vibrate round d in the same time as b. If then a pendulum vibratring round any point, as a, be reversed, and if, while in the reverse position, it is found to vibrate in exactly the same time as before round two other points b and c ; one of those points c, will be the previous centre of oscillation, and the other point b will be merely the duplicate point to a, at the opposite extremity of the bar. The two points b and c may therefore be easily distinguished from each other, whatever be the form of the pendulum, so as not to mistake b for the centre of oscillation to a. This property of the pendulum, the reciprocity, or convertibility of the centres of suspension and

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oscillation, had never been applied to any useful practical purpose, till Captain Kater began his investigations into the actual length of the pendulum vibrating seconds, which has of late years become an important problem, in consequence of the use of the pendulum to de termine the figure of the earth, and of its being made the basis of the British system of weights and measures. The length of the pendulum vibrating seconds had long been an object of research in France, but the French philosophers had attempted to find it by making a pendulum so simple, that its centre of oscillation could be calculated, and thus measured from the point of suspension; for it should have been premised, that what is called the length of the pendulum, is the distance between the centres of oscillation and suspension; thus, in reference to our bar a b, the length of that bar considered as a pendulum is a c. But the most simple pendulum may be of different densities at different parts, and even a bar such as is described in the figure may vary sufficiently in its size to affect so delicate an operation as ascertaining the pendulum's length, though no difference should be sensible to the best means of measurement in our possession. It being impossible, therefore, accurately to calculate the centre of oscillation in the most simple pendulum that can be constructed, Captain Kater abandoned the plan altogether, and availed himself of that convertibility of the centres which has been described, and which allowed him to make use of a pendulum as complex as he pleased. This pendulum consisted of a bar having two sliding points of support and other adjustments, which were regulated experimentally till he found two points, from both of which the pendulum vibrated seconds, taking care, of course, that the two points were related to each other as a and c, and not as a and b. Captain Kater had then only to measure the distance between the two points, and the distance was the pendulum's length.

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Mr. Ainger next described some of the contrivances which had been employed for correcting the effect of temperature upon the pendulums of time-keepers. The elongation of the pendulum in warm weather of course diminishes the rate of the time-keeper, while the shortening in cold weather increases it. The general principle of these contrivances by the use of unequally expansive → metals is very well understood; but there is one important distinction between the two most familiar compensation pendulums, which is not so universally understood; and which may be thus explained. What is called the gridiron pendulum, consisting of alternate bars of brass and iron, acts upon the following principle:

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