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 98 HUYGENS tablished. In 1665, at the invitation of Col- bert, he went to France and became a mem- ber of the academy of sciences, then recently formed. Apartments were assigned to him in the royal library, and he resided in Paris for the greater part of the next 15 years, during which time he presented many papers to the acade- my, some of which still remain unpublished in its archives. In 1670 he visited Holland to restore his health, which had become impaired by his great labors ; and on his return to Paris in the following year he completed his great work Horologium Oscillatorium (fol., Paris, 1673). To this book are appended 13 theorems on centrifugal force, which will be noted fur- ther on. About this time he invented the spiral spring which is applied to the balance wheel of watches, a description of which was published in the journal of the academy of sci- ences in 1675. The invention was claimed by Hooke of England and Hautefeuille of France, but the evidence that it is the invention of Huy- gens is too strong to be any longer questioned. It is said that the first watch provided with a hair spring was made by Thuret under Huy- gens's direction, and was sent to England. In 1675 he again went to Holland for the benefit of his health, and in 1676 he read before the academy of sciences his famous treatise on light, and also a treatise on the cause of grav- ity, in which he attempts to account for the force by supposing that ethereal matter revolves about the earth with a velocity greater than that of the planet, and compares it to the force which causes bodies a little heavier than wa- ter, and lying lightly upon the smooth bottom of a cylindrical vessel containing water, to move toward the centre when the circular mo- tion of the vessel by which its fluid contents have been caused to revolve is arrested. In 1681 he returned to his native country, and immediately began the construction of an au- tomatic planitarium to represent the true mo- tion of the bodies of the solar system. This invention led to the important discovery of continued fractions, which he found it neces- sary to employ in order to establish the rela- tion between the number of teeth contained in two wheels which play into one another. After this he resumed for several years, in conjunction with his brother Constantine, the construction of telescopes. He made two ob- jectives, one of 170 and another of 210 ft. focal length, which he presented to the royal society of London. As a telescope of such di- mensions would be difficult to manage, Huy- gens proposed to dispense with the tube and place the object glass in an elevated position so that it could be adjusted to any angle, and then to place the eye piece at the focus. This arrangement continued to be used until the introduction of reflecting telescopes. While Huygens was absorbed in these occupations a great revolution was going on in the mathemat- ical world. Leibnitz had invented the differ- ential calculus, which he published in 1684, and had proposed as a test to the followers of the old methods the problem of finding the curve of equable approach, or that which a sus- pended body must follow in order to approach or recede from equal heights in equal times. Huygens accomplished the solution by the old methods, but he was the only one who suc- ceeded. Soon after this Newton published his Principia, and Huygens, with a desire of becoming acquainted with the author, visited England for the third time, and on his return published his treatise on light under the title Traite de la lumiere, oil sont expliquees les causes de ce qui lui arrive dans la reflexion, dans la refraction et particulierement dans Vetrange refraction du cristal d'Islande (Ley- den, 1G90). Soon after this he investigated the properties of the catenary curve, a problem which had just been proposed by James Ber- noulli, who had become proficient in the meth- ods of the differential calculus ; but Huygens solved the question by the old methods, which was considered a wonderful achievement. He nevertheless found the task so difficult that his opposition to the differential calculus was shaken, and he entered at once into corre- spondence with Leibnitz. He had previously, whenever meeting with difficulties, attributed them to himself and not to defects in the methods. After examining the differential calculus he admitted its superiority, imme- diately commenced its use, and soon gave a wider development to the invention than it had yet attained. At his death he left his manuscripts to the library of Leyden, intrust- ing their publication to two of his pupils, Voi- der and Fullen. Huygens was never married, and aside from his scientific pursuits his life was not eventful. He had a fine personal ap- pearance, and his character was eminently noble. Newton spoke of him as the summits ffugenius, and considered his style as an au- thor more classic than that of any other mathe- matician of that time. He was affable and kind, and was easily accessible to young stu- dents, whom he was always delighted to assist in their investigations. His labors were im- mense, and the practical value of their results is inestimable. -His discovery of the laws of the double refraction of light in Iceland spar, and of polarization, perhaps as much as any other cause, led to the reexamination of the undulatory theory, and, with the necessary adaptations, to its employment to account for all the phenomena of radiation of both heat and light. In accordance with this theory the most important researches in modern physics have been made, as those upon the diather- manons properties of bodies, and upon the ab- sorption of radiant heat by gases and vapors, by which great light has been thrown on the science of meteorology. Besides his invention of the pendulum clock and of the balance wheel to the watch, the first chronometers taken aboard ships were made under his direc- tion, and he was far in advance of all others