About this time our author invented the spiral spring for regulating the balances of watches, without knowing what had been done by Dr Hooke ; and he applied to the French government for the exclusive privilege of employing it. The Abbe Hautefeuille had, however, conceived the first idea of this invention, and communicated to the Academy of Sciences, in 1674, the secret of regulating the balances of watches " by a small straight spring made of steel." He therefore disputed Huygens' right to the exclusive privilege, and the affair was accommodated in consequence of Huygens renouncing his claim. The observations of Montucla on this subject are certainly unjust towards the Abbe Hautefeuille, when he characterises his invention as rude and clumsey, and claims all the merit for Huygens. The idea of regulating the balance by a spring was certain ly the, principal part of the invention, which is unquestion ably due to the Abbe Hautefeuille ; while `Huygens is enti; tied to the credit of having perfected the invention, by givj ing a spiral form to the spring.
Huygens would probably have continued in France dur ing the remainder of his life, had it not been for the revo cation of the edict of Nantz. He resolved to remain no longer in a country where his religion vhs proscribed, and its professors persecuted ; and, anticipating the fatal- edict, he returned to his native comi•y in 1681.
After his return to Holland, he continued to prosecute his favourite studies with his usual zeal. In 1684, he publish ed his ilstroscopia Compendiaria tubi Optic! molimineliberata, in which he gives an account of a method of using tele scopes of great focal length, without the incumbrance of a tube. He published also in 1690, at Leyden, his Troia. de la Lumiere, and his Tractatus (Sc Gravitate. The first of these works contains his Theory of Light, which he sup poses to be propagated like sound, by the undulation of an elastic medium,* and the beautiful law by which he repre sented all the phenomena of double refraction, as exhibited in Iceland spar. The remainder of our author's life was oc cupied in composing a work on the plurality of worlds, en titled Koci.c09mgios. she de tcrris celestibus, eorunupte ornatu conjecture. While this work was in the printer's hands, Huygens was seized with an illness, which proved fatal on the 5th of June 1695.
All his papers were bequeathed by his will to the Libra ry of Leyden, with a request that Bucher dc Voider and Fullenius, two excellent mathematicians, should print such of them as seemed of most importance. In the year 1700, this posthumous volume was published. The Cosmothco rios had appeared in 1698, and was speedily translated into French, English, German, and Dutch. In 1703, there ap peared another posthumous volume, entitled CHRISTIANI Huc t Dioptrica,Descriptio Automat! planetarii ; de par heliis, Opuscula Posthuma. This work contains Huygens' interesting dissertation on corona, and mock suns, of which we have given a short account in our article HALO. And which was reprinted by Dr Smith in his Com plete System of Optics. A complete edition of the works
of Huygens was published, in four volumes, by M. S'Gra vesencle. The two first appeared at Leyden in 1724, in 4to. entitled Opera Varia, and the two last at Amsterdam in 1728, entitled Opera Reliqua. He published also several papers in the early volumes of the Philosophical Transac tions...111d in the Memoirs of the .dcadenzy of Sciences. In the Machines 4pprourees par l'ilcademie, tom. i. p. 71 and 72, he has published two papers, one of which is entitled Machine pour Mcsurer la force mouvante dr l'air ; and the other, Maniere d'empechcr lea vaisscauz' de se briser echouent. Ile also published a letter on a new microscope, in the Collections ?cademiques, tom. i p. 281; and another on the Toricellian experiment, in the second volume of thc same work.
Christian Huygens was unquestionably one of the most eminent mathematicians and natural philosophers of the age in which he lived. His application of the pendulum to regulate the motion of clocks; his beautiful investiga• Lion of the isochronism produced by making pendulums swing between cycloidal cheeks; his discovery of the :in and satellites of Saturn; his application of the spiral spring to regulate the balances of watches, (in which, however, he was anticipated by Dr Hooke ;) his discovery of the law of collision, which he shares with Dr Wallis and Sir Christo pher Wren ; his theory of the centre of oscillation; his in vestigations respecting central forces; and the beautiful law, by which he has represented the phenomena of double refraction, exhibit the depth and variety of his attainments, and entitle him to a very high rank among those illustrious men who have done honour to their species. In our arti cles ASTRONOM Y, HALO, HOROLOGY, Mieciinsies, and ()riles, the reader will find an ample account of his vari ous labours.
HUYGEN's TEMPERAMENT of the musical scale. In 1682, M. Christian Huygens published his Cyclus Har monicus, or commensurate system, of thirty-one equal divi sions in the octave ; of which his mean tone is five, and major limma 3, of these divisions. The temperaments calculated by Mr Farey's 12th scholium, in the Philosophi cal Magazine, vol. xxxvi. p. 5f,', are as follows, viz. V.- 2.651765z, 111+0.400802E, and 05256E. In p. 224. of the second edition of Dr Smith's Harmonics, he gives the monochord lengths of strings for each of the notes of this system ; and at p. 207. he mentions a method by which the beats of its concords may nearly be obtained : but this being neither sufficiently easy of application, or exact enough, we have calculated them anew, as follows, viz.
In column 2. the values of the notes are given as they arise in calculating by the series of tempered fifths, as above, its wolf fifth G b E being V+17.161553Z. Col. :3. is as usual, adapted to the octave above the tenor cliff C. All the beatings in columes 5. to 9. are sharp or flat, as marked at the bottom of each column, except the 4th and Vth wolves, which are contrary to all the others of these concords.