Many very curious and useful theo rems have been discovered relative to the pendulum, most of which originated with Huygens, among these one of the most noted is, that " the times wherein pendulums of different lengths perform their vibrations, are to one another in the same proportion with the square roots of the lengths of the pendulums." And from these data, and the above theorem, the lengths of pendulums to vi brate any other required time may be determined.
The next improvement of consequence on clocks, after the pendulum, was the es capement performed with anchor pallets, which Berthoud states to have been the invention of Clement, a London clock maker, in the year 1680. The escape ment used by Huygens, and still continu ed in many chamber clorks and all the wooden clocks, is that made by two flat pallets attached to an horizontal arbor, acting at opposite sides of the upper part of a horizontal crown wheel ; the anchor pallets, on the contrary, act on a vertical swing wheel, and move in the plane of the wheel. The chief advantage of the anchor pallets is, that they will permit the escape to take place with a small angle of vibration, so as to prevent the maintaining power from acting on the pallets a long time by a direct push, as was the case with the crown wheel es capement.
Dr. Hooke also claimed the invention of the anchor escapement, which he as serted that he exhibited to the Royal So ciety in a clock of his construction in 1666.
At the same time with the anchor es capement, the mode of suspending the pendulum from a clock by apiece of watch spring was introduced.
The anchor escapement causes a re coil in the swing wheel, from the same face of the pallet striking the tooth, of the wheel in its descent, which is after wards impelled by the same tooth in its ascent ; this occasions the clock, in which it is used, to go faster, when the maintaining power is increased, or when the weight of the pendulum ball is dimi nished.
The advantage gained by the anchor escapement shewn above may be consi dered in reality an approximation to a de tached escapement ; a farther step was made towards this improvement about the year 1715, by the celebrated George Graham, in the contrivance of the dead beat escapement, which is principally distinguished tfrom the anchor escape ment by having no recoil. This is ef fected by increasing the depth of the pallets in the line towards the centre of the swing wheel, and so forming the teeth of that wheel, that the pallet in ac tion, in its descent, does not touch the teeth at all, but lies between them, and the tooth that impels it only comes in contact with its inclined plane at the in stant previous to its ascent, when the op posite pallet becomes free. To avoid the
wearing out of the parts most in action, and the influence of friction, the best clocks of this construction have swing wheels of hardened steel, with pallets of ruby or agate.
The detached escapement completed the improvement of this part of clock work. Its object is, to make the pendu lum perform the greatest part of each vi bration entirely free from contact, or con nection, with any part of the train. To effect this, a catch, or locking piece, re strains all the motion of the swing wheel, till the instant when the pallet is to be impelled by it, when it raises the catch, sets the wheel free, and is driven for ward by its impulse ; immediately after which, the catch again falls into its place. A great variety of escapements have been contrived on this principle by vari ous ingenious men : those in which springs are used in the locking pieces instead of pivots, invented by Arnold, seem now most preferred.
The detached escapement was applied first to chronometers, or time-pieces, but is now used for astronomical clocks. From the best accounts, Julien Le Roy invented the first about 1748 ; since that time, Grignon, Mudge, Cummins, Nichol son, and Arnold, have contrived various escapements of this kind in England; and Peter Le Roy, Sully, Du Tertre, De Be thune, Le Paute, Arnaut, Robin, Ber thoud, &c. on the continent. See CURO NO.METEU.
In the year 1715, Mr. George Graham, before mentioned, made a most material improvement in pendulums, by affixing an apparatus which tended to raise the centre of gravity of the whole, as much as the lengthening of the rod by heat tended to depress it : this he performed by sub stituting a glass cylinder, containing mer cury, for the pendulum ball. He after wards suggested the idea of using the opposite expansions of different metals, as a compensation for the effects of vari ation of temperature of the air in pendu lumS, which was directly afterwards adopted by Harrison, at that time an ob scure carpenter in the village of Barton, Lincolnshire, who surprised the world with the invention of the gridiron pendu lum on this principle.