1651, on the quadrature of the hyperbola, ellipse, and circle, following it with a criticism of Père Gregory de Saint Vincent's treatise on the same subject, and, three years afterward, with his discoveries on the magnitude of the circle (de circuli magnitudine inventa nova).
In 1655 he went to France, and received a degree in law from the Protestant Academy at Angers. Returning to Holland, he engaged with his brother in the manufacture of large lenses. With one of these, an objective of twelve feet focal distance, he discovered the first satellite of Saturn (the sixth in the order of distance), and announced the fact, after the manner of his time, in an anagram. It is said that, in the excitement attending his achievement, he engraved his anagram upon the glass itself by the aid of which the discovery was made. He afterward made glasses with one hundred, one hundred and seventy, and two hundred and ten feet of focal distance, which could not be inclosed in a telescopic tube on account of the swagging, to which so long an instrument would be subject, but for which he contrived a kind of framework support, while the observer stood at the focal point, eye-glass in hand. The necessity of using such cumbrous contrivances has happily been dispensed with by the introduction of reflecting telescopes.
In 1656, Huygens published, in Dutch, a memoir on the calculation of probabilities, for which Pascal and Feitnat had prepared the way, and which was translated into Latin by his preceptor, Schooten, to be inserted as an appendix to his "Mathematical Exercises," in illustration of the usefulness of algebra. In the same year he invented the escapement of watches and clocks. Galileo had already recognized the synchronism of the motion of pendulums, and experimenters had begun to avail themselves of it in timing their observations; but they knew of no better way of using the pendulums than to employ a man to keep them in motion and count their vibrations. Huygens connected them with clock-work, very much as we now have them, and made the whole operation automatic.
In 1659, having constructed an objective of twenty-two feet focal distance, Huygens turned his attention to Saturn's ring, which Galileo had perceived but dimly, discovered its true character, calculated its elements, and predicted its temporary disappearancee in 1671; a prediction which his fellow-astronomers saw fulfilled twelve years after it was made, with great admiration for his genius. In his work, giving an account of these observations, "Systema Saturninum," he also described the nebula in Orion, and the bands of Jupiter and Mars, announced that the fixed stars had no perceptible diameter, and made known his device for measuring the apparent diameters of the planets, an incipient micrometer. He discovered but one of the satellites of Saturn, and did not seem to care to look for any other; for his enterprise in this direction was bound by the opinion he entertained that there was a relation between the number of planets and of satellites;
