One of his first endeavors in science was to attempt an improvement of the telescope. Reflecting upon the process of making lenses then in vogue, young Huygens and his brother Constantine attempted a new method of grinding and polishing, whereby they overcame a great deal of the spherical and chromatic aberration. With this new telescope a much clearer field of vision was obtained, so much so that Huygens was able to detect, among other things, a hitherto unknown satellite of Saturn. It was these astronomical researches that led him to apply the pendulum to regulate the movements of clocks. The need for some more exact method of measuring time in his observations of the stars was keenly felt by the young astronomer, and after several experiments along different lines, Huygens hit upon the use of a swinging weight; and in 1656 made his invention of the pendulum clock. The year following, his clock was presented to the states-general. Accuracy as to time is absolutely essential in astronomy, but until the invention of Huygens's clock there was no precise, nor even approximately precise, means of measuring short intervals.

Huygens was one of the first to adapt the micrometer to the telescope - a mechanical device on which all the nice determination of minute distances depends. He also took up the controversy against Hooke as to the superiority of telescopic over plain sights to quadrants, Hooke contending in favor of the plain. In this controversy, the subject of which attracted wide attention, Huygens was completely victorious; and Hooke, being unable to refute Huygens's arguments, exhibited such irritability that he increased his already general unpopularity. All of the arguments for and against the telescope sight are too numerous to be given here. In contending in its favor Huygens pointed out that the unaided eye is unable to appreciate an angular space in the sky less than about thirty seconds. Even in the best quadrant with a plain sight, therefore, the altitude must be uncertain by that quantity. If in place of the plain sight a telescope is substituted, even if it magnify only thirty times, it will enable the observer to fix the position to one second, with progressively increased accuracy as the magnifying power of the telescope is increased. This was only one of the many telling arguments advanced by Huygens.

In the field of optics, also, Huygens has added considerably to science, and his work, Dioptrics, is said to have been a favorite book with Newton. During the later part of his life, however, Huygens again devoted himself to inventing and constructing telescopes, grinding the lenses, and devising, if not actually making, the frame for holding them. These telescopes were of enormous lengths, three of his object-glasses, now in possession of the Royal Society, being of 123, 180, and 210 feet focal length respectively. Such instruments, if constructed in the ordinary form of the long tube, were very unmanageable, and to obviate this Huygens adopted the plan of dispensing with the tube altogether, mounting his lenses on long poles manipulated by machinery. Even these were unwieldy enough, but the difficulties of manipulation were fully compensated by the results obtained.

It had been discovered, among other things, that in oblique refraction light is separated into colors. Therefore, any small portion of the convex lens of the telescope, being a prism, the rays proceed to the focus, separated into prismatic colors, which make the image thus formed edged with a fringe of color and indistinct. But, fortunately for the early telescope makers, the degree of this aberration is independent of the focal length of the lens; so that, by increasing this focal length and using the appropriate eye-piece, the image can be greatly magnified, while the fringe of colors remains about the same as when a less powerful lens is used. Hence the advantage of Huygens's long telescope. He did not confine his efforts to simply lengthening the focal length of his telescopes, however, but also added to their efficiency by inventing an almost perfect achromatic eye-piece.

In 1663 he was elected a fellow of the Royal Society of London, and in 1669 he gave to that body a concise statement of the laws governing the collision of elastic bodies. Although the same views had been given by Wallis and Wren a few weeks earlier, there is no doubt that Huygens's views were reached independently; and it is probable that he had arrived at his conclusions several years before. In the Philosophical Transactions for 1669 it is recorded that the society, being interested in the laws of the principles of motion, a request was made that M. Huygens, Dr. Wallis, and Sir Christopher Wren submit their views on the subject. Wallis submitted his paper first, November 15, 1668. A month later, December 17th, Wren imparted to the society his laws as to the nature of the collision of bodies. And a few days later, January 5, 1669, Huygens sent in his "Rules Concerning the Motion of Bodies after Mutual Impulse." Although Huygens's report was received last, he was anticipated by such a brief space of time, and his views are so clearly stated - on the whole rather more so than those of the other two - that we give them in part here:

 "1. If a hard body should strike against a body equally hard at rest, after contact the former will rest and the latter acquire a velocity equal to that of the moving body.

"2. But if that other equal body be likewise in motion, and moving in the same direction, after contact they will move with reciprocal velocities.

"3. A body, however great, is moved by a body however small impelled with any velocity whatsoever.

"5. The quantity of motion of two bodies may be either increased or diminished by their shock; but the same quantity towards the same part remains, after subtracting the quantity of the contrary motion.

"6. The sum of the products arising from multiplying the mass of any hard body into the squares of its velocity is the same both before and after the stroke.

"7. A hard body at rest will receive a greater quantity of motion from another hard body, either greater or less than itself, by the interposition of any third body of a mean quantity, than if it was immediately struck by the body itself; and if the interposing body be a mean proportional between the other two, its action upon the quiescent body will be the greatest of all."[10]

 This was only one of several interesting and important communications sent to the Royal Society during his lifetime. One of these was a report on what he calls "Pneumatical Experiments." "Upon including in a vacuum an insect resembling a beetle, but somewhat larger," he says, "when it seemed to be dead, the air was readmitted, and soon after it revived; putting it again in the vacuum, and leaving it for an hour, after which the air was readmitted, it was observed that the insect required a longer time to recover; including it the third time for two days, after which the air was admitted, it was ten hours before it began to stir; but, putting it in a fourth time, for eight days, it never afterwards recovered.... Several birds, rats, mice, rabbits, and cats were killed in a vacuum, but if the air was admitted before the engine was quite exhausted some of them would recover; yet none revived that had been in a perfect vacuum.... Upon putting the weight of eighteen grains of powder with a gauge into a receiver that held several pounds of water, and firing the powder, it raised the mercury an inch and a half; from which it appears that there is one-fifth of air in gunpowder, upon the supposition that air is about one thousand times lighter than water; for in this experiment the mercury rose to the eighteenth part of the height at which the air commonly sustains it, and consequently the weight of eighteen grains of powder yielded air enough to fill the eighteenth part of a receiver that contained seven pounds of water; now this eighteenth part contains forty-nine drachms of water; wherefore the air, that takes up an equal space, being a thousand times lighter, weighs one-thousandth part of forty-nine drachms, which is more than three grains and a half; it follows, therefore, that the weight of eighteen grains of powder contains more than three and a half of air, which is about one-fifth of eighteen grains...."

From 1665 to 1681, accepting the tempting offer made him through Colbert, by Louis XIV., Huygens pursued his studies at the Bibliotheque du Roi as a resident of France. Here he published his Horologium Oscillatorium, dedicated to the king, containing, among other things, his solution of the problem of the "centre of oscillation." This in itself was an important step in the history of mechanics. Assuming as true that the centre of gravity of any number of interdependent bodies cannot rise higher than the point from which it falls, he reached correct conclusions as to the general principle of the conservation of vis viva, although he did not actually prove his conclusions. This was the first attempt to deal with the dynamics of a system. In this work, also, was the true determination of the relation between the length of a pendulum and the time of its oscillation.

In 1681 he returned to Holland, influenced, it is believed, by the attitude that was being taken in France against his religion. Here he continued his investigations, built his immense telescopes, and, among other things, discovered "polarization," which is recorded in Traite de la Lumiere, published at Leyden in 1690. Five years later he died, bequeathing his manuscripts to the University of Leyden. It is interesting to note that he never accepted Newton's theory of gravitation as a universal property of matter.