416 HUYGENS received the rudiments of his education, which was con tinued at Leyden under Vinnius and Schooten, and com pleted in the juridical school of Breda. His mathematical bent, however, soon diverted him from his legal studies, and the perusal of some of his earliest theorems enabled Descartes to predict his future greatness. In 1649 he accompanied the mission of Henry, count of Nassau, to Denmark, and in 1651 entered the lists of science as an assailant of the unsound system of quadratures adopted by Gregory of St Vincent. This first essay (Exetasis quadra- turce circuit, Lsyden, 1651) was quickly succeeded by his T/teoremata de quadratura hyperboles, ellipsis, et circuli ; while, in a treatise entitled De circuli maynitudine inventa, he made, three years later, the closest approximation hitherto obtained to the ratio of the circumference to the diameter of a circle. But another class of subjects was about to engage his attention. The improvement of the telescope was then justly regarded as a sine qua non for the advancement of astronomical knowledge. Owing, however, to the difficul ties interposed by spherical and chromatic aberration, little progress had been made in that direction when, in 1655, Huygens, working with his brother Constantin, hit upon a new method of grinding and polishing lenses. The im mediate results of the clearer definition obtained were the detection of a satellite to Saturn (the sixth in order of dis tance from its primary), and the resolution into their true form of the abnormal appendages to that planet. Each discovery in turn was, according to the prevailing custom, announced to the learned world under the veil of an anagram removed, in the case of the first, by the publica tion, early in 1656, of the little tract De Saturni luna ohservatio nova ; but retained, as regards the second, until 1859, when in the Systema Saturnium the varying -appear ances of the so-called " triple planet " were clearly explained as the phases of a ring inclined at an angle of 20 to the ecliptic. His application of the pendulum to regulate the movement of clocks was another fruit of his astronomical labours, springing, as it did, from his experience of the need for an exact measure of time in observing the heavens. The invention dates from 1656; the Ilorologium, contain ing a description of the requisite mechanism, was published in the following year, and on the 16th of June 1657 Huygens presented his first u pendulum-clock " to the states-general. His reputation now became cosmopolitan. As early as 1 655 the university of Angers had distinguished him with an honorary degree of doctor of laws. In 1663, on the occasion of his second visit to England, he was elected a fellow of the Royal Society, and imparted to that body in January 1669 a clear and concise statement of the laws governing the collision of elastic bodies. Although these conclusions were arrived at independently, and, as it would seem, several years previous to their publication, they were in great measure anticipated by the communications on the same subject of Wallis and Wren, made respectively in November and December 1668. Huygens had before this time fixed his abode in France. In 1665 Colbert made to him on behalf of Louis XIV. an offer too tempting to be refused, and between the following year and 1681 his residence in the philosophic seclusion of the Bibliotheque du Roi was only interrupted by two short visits to his native country. His magnum opus dates from this period. The Horologium Oscillatorium, published with a dedication to his royal patron in 1673, contained origiml discoveries sufficient to have furnished materials for half a dozen striking disquisitions. His solution of the celebrated problem of the " centre of oscillation " formed in itself an important event in the history of mechanics. Assuming as an axiom that the centre of gravity of any num ber of interdependent bodies cannot rise higher than the point from which it fell, he arrived, by anticipating in the particular case the general principle of the conservation of vis viva, at correct although not strictly demonstrated con clusions. His treatment of the subject is especially note worthy as being the first successful attempt to deal with the dynamics of a system. The determination of the true relation between the length of a pendulum and the time of its oscillation ; the invention of the theory of evolutes ; the discovery, hence ensuing, that the cycloid is its own evolute, and is strictly isochronous ; the ingenious although practi cally inoperative idea of correcting the " circular error " of the pendulum by applying cycloidal cheeks to clocks were all contained in this remarkable treatise. The theorems on the composition of forces in circular motion with which it concluded formed the true prelude to the Princijria, and would alone suffice to establish the claim of Huygens to the highest rank among mechanical inventors. In 1681 he finally severed his French connexions, and returned to Holland. The harsher measures which about that time began to be adopted towards his co-religionists in France are usually assigned as the motive of this step. He now devoted himself during six years to the production of lenses of enormous focal distance, which, mounted on high poles, and connected with the eye-piece by means of a cord, formed what were called " aerial telescopes." Three of his object-glasses, of respectively 123, 180, and 210 feet focal length, are still in the possession of the Royal Society. He also succeeded in constructing an almost perfectly achromatic eye-piece, still known by his name. But his researches in physical optics constitute his chief title-deed to immortality. Although Hooke first proposed the wave theory of light, Huygens gave reality to the conception, establishing it on a foundation so sure that it has never since been shaken. His powerful scientific imagination enabled him to perceive that an undulation may be broken up into an indefinite number of parts, each of which is the origin of a partial wave, and that the aggregate effect of all these partial waves will reconstitute the primary wave at any subsequent stage of its progress. This resolution of the main undulation is the well-known "Principle of Huygens," and by its means he was enabled to prove the fundamental laws of optics, and to assign the correct construction for the direction of the extraordinary ray in uniaxial crystals. These investigations, together with his discovery of the " wonderful phenomenon " of polarization, are recorded in his Traite de la Lumiere, published at Leyden in 1690, but composed in 1678. In the appended treatise S-ur la Cause de la Pesanteur, he rejected gravitation as a universal quality of matter, although admitting the .Newtonian theory of the planetary revolutions. From his views on centrifugal force he deduced the oblate figure of the earth, estimating its compression, however, at little more than one-half its actual amount. Huygens was never married. He died at the Hague, June 8, 1695, bequeathing his manuscripts to the university of Leyden, and his considerable property to the sons of his younger brother. In character he was as estimable as he was brilliant in intellect. Although, like most men of strong originative power, he assimilated with difficulty the ideas of others, his tardiness sprang rather from inability to depart from the track of his own methods than from reluctance to acknowledge the merits of his competitors. In addition to the works already mentioned, his Cosmothcoros a speculation concerning the inhabitants of the planets was printed posthumously at the Hague in 1698, and appeared almost .simultane ously in an English translation. A volume entitled Opera PostJiuma, Leyden, 1703, contained his Dioptrica," in which the ratio between the respective focal lengths of object-glass and eye-glass is given as the measure of magnifying power, together with the shorter essays
De vitris fiyurcmdis, DC corona etparheliis, &c. An early tract De
