KLINGENSTIERNA, SAMUEL, a Swedish mathematician and philosopher, was born in 16S9 at Tolefors, near Linkoeping, and received his educatiou at Upsal. It was intended by his parents that he should follow the law as a profession; but, after having made some progress in the study of jurisprudence, he abandoned that pursuit, his taste inclining him to the cultivation of the mathematical sciences.
His first production was a dissertation on the height of the atmos phere; and this was followed by one on the means of improving the thermometer: both dissertations were, in 1723, inserted in the ' Memoirs' of the Royal Society of Upsal. In 1727 he set out from Sweden for the purpose of improving himself by travelling; and, after passing through parts of Germany and France, he made a visit to England, whence he returned in 1730. At Marburg he became known to the celebrated professor Wolf, and applied himself diligently to the study of his philosophy with a view of introducing it into Sweden on his return. At Paris he was introduced to Clairaut, Fontanelle, and Mairon; and he is said to have communicated to those eminent mathematicians some useful remarks concerning the integral calculus and the figure of the earth.
Shortly after his return to Sweden he was appointed professor of mathematics; and being thwarted in his project of teaching the philo sophy of Wolf, which was supposed to be in some respects at variance with the doctrines of Christianity, he devoted hinieelf the more ardently to the immediate duties of his professorship. He numbered among his pupils Stroemer, Wargentln, Melanderbeiltn, and Mallet; and at the same time he contributed greatly by his writings to the improve ment of mathematical science.
On the retirement of Dalin, the tutor of the Prince Royal of Sweden, afterward. Gustavus III., Klingenstierna was chosen to fill his post : he acquitted himself in the performance of this important duty with great success ; and, na a recompence of his zeal, be received the title of Councillor of State, and was made a Knight of the Polar Star. On the termination of this public duty, Klingenstierna, feeling his health decline, quitted the court and passed several years in strict retirement. The Academy of Sciences at St. Petersburg having however offered a prize for the best essay on the means of correcting or diminishing the chromatio and spherical aberrations of light in refracting telescopes, he once more exerted himself; and, having collected his various papers on optics, he composed from them a general theory with relation to the proposed subject, which he sent to the Academy, when the mem bers of that body unanimously awarded him the sum of cue hundred ducats. This work, which was entitled ' Tentemen de defluiendis at
corrigendis aberrationibus rwliorum luminis spluericis refracti, et de perficiendo telescopio dioptrico,' was published at St. Petersburg in 4to in 1762.
While the improvement of refracting telescopes engaged the attention of mathematicians it happened that Dollond, in England, proposed objections to an assumption of Euler, that when light passes from air to glass and from air to water, the logarithms of the refractinas of the mean refrangible rays are proportional to the logarithms of the refrac tions of the least refrangible rays; and assumed as a principle deduced from the experiments of Newton, that with a prism of glass contained in a prism of water, a constant ratio subsisted between the differences of the sines of the refractions of the red and violet rays in passing from air into the first medium, and from that medium into the second.
This principle, and the accuracy of Newton's experiment on which it was founded, were impugned by Kliogenstierna, who, from his own experiments, found that the light emergent after the refractions was affected with colour, under the circumstances in which Newton sup posed that it would be wholly free from it. In 1754 he transmitted to Dollond an account of his experiments, together with some investi gations relating to the dispersions of heterogeneous light in lenses; and these papers induced that distinguished artist to have again recourse to experiments with a view of discovering more precisely the phenomena of refraction. It was in the prosecution of those experiments that Dollond discovered that combination of lenses of flint and crown•glass by which the dispersions of light have been so nearly corrected in optical instruments.
Klingenstierna published in Latin an edition of Euclid's 'Elements; a translation in Swedish of Musachenbreek's Physics; and two discourses in Swedish, which were delivered before the Academy of Stockholm one of these is an 6loge on the mechanician Polhen, and the other relates to some electrical experiments which had been made at that time. Ho was early made a member of the Royal Society of Upsal, and be was afterwards received in the Academy of Sciences at Stockholm. He was elected a Fellow of the Royal Society of London in 1780, and in the ' Philosophical Transactious' for 1731 there is a paper by him on the quadrature of hyperbolic curves. Klingenstierna died October 28th, 1785.