We shall give the list of Huyghen's works in the order of subjects, with a short description of what is now memorable in each.
I. Geometrical Works.
Theoremata de Quadratura Hyperboles, Ellipsis, et Circuli, ex dato portion= Gravitatis Centro; quibtis snbjuncta est 7.0-rauts Cyclometrias CL Viri Gregorii it S. Vincentio,' Lugd. Bat., 1651. The theorems have more merit than use: it is to be remembered that they followed the work of Guldinus. [Gottitsfus.] The answer to the quadrature of the circle by Gregory of St. Vincent will be further noted in the article on that subject.
'De Circuli Magnitudine invent,- Accedunt ejusdem Problematum quorundam illuatrium Constrnctiones,' Lugd. Bat, 1651. In this work Hnygliens gives some new and very close approximations to the quadrature of the circle; he was also engaged in a controversy with James Gregory on this subject, for the details of which see 'Journal des Scavans, July and November 1663, and 'Phil. Trans.,' Nos. 37 and 44. There are some minor geometrical writings of Huyghens in the ' Divers ()images de Math6matique et de Physique,' Paris, 1693.
II. Mechanical Works.
Horologium; Hag. Com., 1658, and Horologium Oscillatorium, sive de Motu Peedulorum a Horologia nptato Demoustrationee Geomatricas,' Pariaiis, 1673. In the first of these tracts Huyglieus simply describes the application of the pendulum to the clock, of which improvement he is the inventor. The idea came to him in 1656, and the pendulum employed was the common circular one. In the second he describes the well-known but now disused apparatus by which the geometrically iaochronous or cycloidal pendulum was obtained. But this is the least part of the celebrated work before us, which contains four distinct and new discoveries of first-rate importance. The first is that of the cycloid being the curve ; all whose arcs measured from the lowest point are synchronous. The second is the invention of the involution and evolution of curves, in which the proposition is established that the cycloid is its own evolote. The third is the method of finding the centre of oscillation, being the first successful solution of a dynamical problem, in which connected material points are supposed to act on oue another. The fourth is the announcement (without demonstration) of those relations between the centrifugal force and velocity of a body revolving in a circle, which were afterwards proved in the 'Principle.' It thus appears that Huyghens was in complete possession of the solution of the problem of circular motion : had his mind not been pre-occupied by the Cartesian system, it is most probable that he would have gone at least to the extent of deducing Kepler's laws from the assumption of gravitation. Demonstrations of the theorems on centrifugal force were found among his papers, and published in the Opera Reliqua.' It is possible that these might have been written after he had seen the Principle.' of Newton.
The publication of this treatise above mentioned drew on a con troversy with the Abb6 Catalan, in which John Bernoulli, De L'IlOpital, and others took part.
In the 'Journal des Scavans,' February 1675, Huyghens described the spring pendulum, such as is now used in watches. Though there can be no doubt that this was an independent invention, yet its priority has been questioned.
Huyghens wee one of the first who gave the laws of impact ; the Royal Society of London had invited attention to the question, and Huyghens, Wren, and Wallis sent eolutious to the Royal Society about the same time (1669). There is an extract from his paper in the 'Phil. Trans.' for that year ; but the whole paper (perhaps enlarged) appears among the posthumous works.
The treatise 'Sur la Cause de la Pdsanteur' was first printed in French (Leyden, 1690), at the end of the 'Traitd de la Lumiere: Both are Latinithd in the Opera Reliqua.' There are several minor pieces on different problems of mechanics.
III. Astronomical Works.
`De Saturni Luis, Observatio Nova,' ling. Com., 1656. This is a tract of two pages printed at the end of Borelli, 'De vero Telescopii Iuventore: It announces the discovery of a satellite to Saturn, beiug that which we now call the fourth. This took place on the 25th day. of March 1665, and Huyghans immediately (as was then common) communicated the following cipher :—"Admovere oculis distantia sidera nostril vvvvvvvcccri•hmbqx ;" which being transposed will make the following :—" Saturno luna sus eircum ducitur diebus sexdacim horis quatuor." In the present tract he explains this enigma, and adds that he is about to publish on the Saturnian system. In the meanwhile he adds another logogryph to substantiate his right to another discovery ; it is as follows:—"aaa a aaacceeedeeeeeghiiiiiiiIIIInsinannnstnnaneoeopp ger stitttuuuuu." The explanation of this dark saying was given in the 'Systeme Saturnium; printed at the Hague in 1759. It should be remembered that Galileo's telescopes showed him nothing more as to Saturn than that it appeared to have some lateral appen dages which looked like handles. In 1655, Huyghens had applied himself, in conjunction with his elder brother Constantine, to the manufacture of large telescopes. The meaning of the enigma was, Annulo cingitur tenni, piano, nusquam eohmrente, ad eclipticam inclinato ; that is, he had discovered Saturn's ring. The 'Systems Saturnium' gives an account of the discovery, fixes the position of the ring, and explains the phenomena of its appearance and disap pearance, &c. This work also occasioned some controversy, now forgotten. It is worth while to take notice that Huyghene was pre vented from looking for any more satellites by the notion, then not uncommon, that the whole number of satellites in the solar system could not exceed that of the planets.