Page:The American Cyclopædia (1879) Volume IV.djvu/709

 CLOCKS AND WATCHES 697 sally admitted to have been the first not only to apply the pendulum to clocks, but to demon- strate the mathematical principles involved. A pendulum which oscillates in an arc of less than 10 may have that arc diminished without sensibly affecting the time ; but when it moves through larger arcs the time will be sensibly increased, although not in proportion to the increase of the arc. It was demonstrated by Huygens that if the oscillations were made in the curve of a cycloid, they would occupy the same time whether the arcs were small or large. A simple pendulum may be defined to be a particle of matter suspended by a right line devoid of weight, and oscillating by the force of gravity about a fixed point, called the point of suspension. It follows, therefore, that a truly simple pendulum can only exist in the imagination. The nearest approach to it is a lens-shaped bob, made of the densest matter, as platinum, suspended by a fine steel wire. But it is evident that the particles of matter in the bob which are nearest the point of suspen- sion will tend to oscillate oftener than those at & greater distance, and therefore to accelerate the motion, while those which are furthest will tend to retard it. There will therefore be a certain distance from the point of suspension which will divide those particles which are moving slower than natural from those which Are moving faster, which may be designated the centre of oscillation of the system. If all the matter in the pendulum could be collected in this point, the time of vibration would not be changed. The length of a pendulum is imderstood to be the distance between the point of suspension and the centre of oscilla- tion. The centre of oscillation is generally be- low the centre of gravity, and within the pen- dulum ; but it may be entirely beyond it, as in the metronome. The length" of a pendulum which oscillates in a given time may be ascer- tained from the laws of falling bodies. If it moves in a small circular arc, the time of one oscillation is to the time a body occupies in falling freely half the length of a pendulum as the circumference of a circle is to its diameter. It having been demonstrated that the spaces through which a body falls by the force of gravity are in proportion to the square of the time occupied in falling, therefore the time will be equal to the ratio of the circumference of a circle to its diameter (which is 3-14159) mul- tiplied into the square root of the quotient arising from dividing the length of the pendu- lum by twice the distance through which a body will fall in one second, which in the lati- tude of Washington is about 16 "08 ft. Thus : Time = 3-14159 x 4/ length -H 32-16 ft. ; from which all calculations as to the number of wheels in the train, the distance through which the weight should descend, &c., may be made. From the above equation, by a very simple algebraic process, the following is derived : Length = square of time x 32-16 -f- 3-14159"; therefore the length of a pendulum is in propor- tion to the square of its time of oscillation. The length of a pendulum which oscillates in one second in the latitude of Washington will be found by the following equation : L=l a x 32-16 ft.-=-3-14159 a =39-l in. If the pendulum is re- quired to oscillate once in two seconds, it must be four times the length of a seconds pendu- lum, because the square of twice the time=4. As it is necessary in a good clock to have the pendulum always of the same length, a diffi- culty was encountered on account of expansion and contraction from heat and cold. This was obviated by using in its construction two dif- ferent materials having different degrees of ex- pansion. Such pendulums are called compen- sation pendulums, and are principally of two kinds, called mercurial and gridiron. The bob of the mercurial pendulum is made of a hollow FIG. 2. Huygens's Clock. cylinder of glass or iron containing mercury, whose expansion tends to shorten the distance of the centre of oscillation, while the expansion of the rod tends to lengthen it. The gridiron pendulum is usually constructed of iron and brass, whose unequal contractions cause the bob to remain during varying degrees of tem- perature at the same distance from the point of suspension. The clock constructed by Huygens is represented in fig. 2. The train of wheels resembles that in Vick's clock, with the exception of having two crown wheels, with different-shaped teeth, and a train of wheels behind the dial and in front of the plate for the purpose of turning both hour and minute hands around a common centre. This train of wheels for moving the hands has precisely the same disposition as that now in use for