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In addition to the work which caused him so great misfortunes he published Discorso e Demonstr. interna alle due nuove Scienze, Delia Scienza Meccanica , Tractato della Sfera ; and the telescope, the isochronism of the vibrations of the pendulum, the hydrostatic balance, the thermometer, were all invented by this great leader of astronomical and scientific discoverers.

It was thus in sundry of the cases we have quoted as at variance with M. Comte's doctrine. It was thus with the application of Huyghens's optical discovery to astronomical observation by Galileo. It was thus with the application of the isochronism of the pendulum to the making of instruments for measuring intervals, astronomical and other.

The angular velocity is regulated by a Watt's governor, which secures an isochronism of the motion independently of the charge.

The latest improvements in the balance to secure perfect isochronism under varying conditions of temperature would delight the soul of Harrison, who worked from 1728 to 1761 on the problem of a compensator for the changes of rate due to the expansion and contraction of the metal, and received the reward of twenty thousand pounds sterling offered by the Board of Longitude.

The purity of the note emitted by a sound has been often invoked as a proof of the perfect isochronism of the oscillation, and, consequently, as a demonstration a posteriori of the correctness of the early law of Hoocke governing elastic deformations. This law has, however, during some years been frequently disputed.

Akin to this was Galileo's discovery, when, standing in Pisa Cathedral, he watched the oscillations of a hanging lamp. He observed that the oscillations were all completed in the same space of time, and the isochronism of the pendulum was the beginning of the measurement of time for all men, and of the measurement of worlds for the astronomer.

At an early age he discovered the principle of isochronism of the pendulum, which, in the hands of Huyghens in the middle of the seventeenth century, led to the invention of the pendulum clock, perhaps the most valuable astronomical instrument ever produced.

One of these last is nearly identical with the armillae of Tycho; and the other with his "armillae aequatoriae maximae," with which he observed the comet of 1585, besides fixed stars and planets. The discovery by Galileo of the isochronism of the pendulum, followed by Huyghens's adaptation of that principle to clocks, has been one of the greatest aids to accurate observation.

He also discovered the isochronism of the pendulum. He saw that the pendulum at certain seasons of the year looked yellow under the eyes, and that it drooped and did not enter into its work with the old zest. He began to study the case with the aid of his new bamboo telescope and a wicker-covered microscope. As a result, in ten days he had the pendulum on its feet again.

Besides, I have left such repairs as the chain and fusee, uprighting wheels, repairing cases, adjustment to position, heat and cold, isochronism, enlarging jewels, or changing angles of pallet stones, etc., etc., all of which I do as necessity demands, as well as the care of striking watches, fly backs, etc., which, too, I make a specialty of, and of chronometer escapement watches, which would take more space than I feel disposed to ask you to give me.