Christiaan Huygens was a Dutch mathematician, astronomer, and physicist, who founded the wave theory of light, discovered the true shape of the rings of Saturn, and contributed to the science of dynamics - the study of the action of forces on bodies. Using a lens he ground for himself, on March 25th, 1655, he discovered the first moon of Saturn, later named Titan. In 1656, he patented the first pendulum clock, which he developed to enable exact time measurement while observing the heavens. Huygens studied the relation of the length of a pendulum to its period of oscillation  and stated theories on centrifugal force in circular motion which influenced Sir Isaac Newton in formulating his Law of Gravity. Huygens also studied and drew the first maps of Mars. On January 14th, 2005, a NASA space probe, named after Huygens, landed on Titan.
"Saturn's Ring in Systema Saturnium"
When Galileo made use of the telescope, noblest invention of nation of Belgium, for observation of the heavenly bodies, and, before all other men, disclosed to mortals those very celebrated phenomena of the planets, the most wonderful of his discoveries, it would seem, were those relating to the star of Saturn. For all the other phenomena, though justly calling for our wonder and admiration, were still not of a kind to make it necessary to question strongly the causes of their existence. But Saturn's changing forms showed a new and strange device of nature, the principle of which neither Galileo himself nor, in all the time since, any of the astronomers (with their permission be it said) has succeeded in divining. Galileo had first seen this star shining, not as a single disk, but in what seemed to be a triple form, as two smaller stars in close proximity to, and on opposite sides of, a larger star, in line with its centre. And seeing this form continue for nearly three years with no change, he had become firmly convinced that, just as Jupiter was provided with four satellites, so Saturn was provided with two, which, however, had no motion, and so would always cling to the sides of Saturn in the same position. But when Saturn came forth alone, quite destitute of his former retinue of satellites, Galileo was obliged to change his opinion. Astonished by what he saw, he tried to reach by conjecture the cause of the appearance, and made a few predictions as to the time when the former phase was due to recur. But, it was shown by the event, these predictions were not then fulfilled according to his expectation, nor, it appeared, was Saturn satisfied with having only two aspects. For a succession of other strange and marvellous forms was revealed, which I find first described by Josephus Blancanus and Franciscus Fontana - forms of such unusual appearance that they were considered by many as a mockery of the eyes, shapes adhering to the lenses rather than existing in the heavens; but after the same forms had been seen by more, it became clear that it was no false evidence that revealed them.
And so I was also drawn by an urgent longing to behold these wonders of the heaven. But I had only the ordinary form of telescope, which measured five or six feet in length. I, therefore, set myself to work with all the earnestness and seriousness I could command to learn the art by which glasses are fashioned for these uses, and I did not regret having put my own hand to the task. After overcoming great difficulties (for this art has in reserve more difficulties than it seems to bear on its face), I at last succeeded in making the lenses which have provided me with the material for writing this account. For upon immediately directing my telescope at Saturn, I found that things there had quite a different appearance from that which they had previously been thought by most men to have. For it appeared that the two neighbouring appendages clinging to Saturn were by no means two planets, but rather something different, while, distinct from these, there was a single planet, at a greater distance from Saturn and revolving around him in sixteen days; and the existence of this planet had been unknown through all the centuries up to that time. Following the wise advice of a distinguished man, one equally conspicuous for his ability and his character, Johannes Capellanus, I three years ago informed astronomers of my new observation. For while I was sojourning at Paris, I told Capellanus, as well as Gassendi and others, of the satellite of Saturn which I had seen, and Capellanus gave me many reasons for believing that I ought not to withhold an announcement that would be so pleasing to all men until I should finish the work on the complete System of Saturn, which I was then engaged upon. And so, on the 5th day of March [later in the article Huygens says it was the twenty-fifth of March, so one of these is a misprint], I in the year 1656, I put forth the result of my observation on the Moon of Saturn (for so I have quite properly named the, new star), and, together with it, an hypothesis containing an explanation of the other phenomena of Saturn; in the case of the latter, however, I confused the order of the letters in which it was written, that it might witness to the fact simply that I was not unacquainted with it at that time, and also that others might be induced in this way to publish the results of their speculations and might not complain that the glory of the discovery had been snatched from them. Afterwards, however, in response to the request of the same distinguished man, I also solved this literary riddle, and set before him in outline the entire hypothesis; whence perhaps my theory about the phases of Saturn has already found its way to the ears of others. But, in any case, the wonderful and unusual creation of nature shown in connection with this planet demands a fuller treatment, and I ought not to expect that either my account of the phenomena or the assumptions I make for explaining them will gain general support unless it is seen that the latter, rest on the principles of reasoning, and the former is backed by the evidence of observation. Therefore, I now propose to fulfil both of these requirements. And, in the first place, I will determine as accurately as possible from my observations the facts which have to do with the motion and the period of revolution of the planet's satellite, and I will construct tables of its motion. Then I will assign the various phases of Saturn himself to their separate causes, that thus we may have a ready means of determining beforehand what the future phases will be ...
That neither you [Hodierna] nor those distinguished men whose opinions I have previously reviewed have reached the truth of the matter, is not at all to be wondered at or to be imputed to you as a fault, since for the most part false phenomena were reported to you as true, and other phenomena which were observed in connection with Saturn, free from the deception of sight, did not come to your notice at all. If you had been so fortunate as to observe these phenomena with me, it is reasonable to suppose that you would have drawn from them the same conclusions with regard to the real form of the planet that I have. Now I was greatly helped in this matter not only by those more genuine phases, but also by the motion of Saturn's Moon, which I observed from the beginning; indeed it was the revolution of this Moon around Saturn that first caused to dawn upon me the hope of constructing the hypothesis. The nature of this hypothesis I will proceed to explain in what follows.
When, then, I had discovered that the new planet revolved around Saturn in a period of sixteen days, I thought that without any doubt Saturn rotated on his own axis in even less time. For even before this I had always believed that the other primary planets were like our Earth in this respect that each rotated on its own axis, and so the entire surface rejoiced in the light of the Sun, a part at a time; and, more than this, I believe that in general the arrangement with the large bodies of the world was such that those around which smaller bodies revolved, having themselves a central position, had also a shorter period of rotation. Thus the Sun, its spots declare, rotates on its own axis in about twenty-six days; but around the Sun the various planets, among which the Earth is also to be reckoned, complete their courses in times varying as their distances. Again, this Earth rotates in daily course, and around the Earth the Moon circles with monthly motion. Around the planet Jupiter four smaller planets, that is to say Moons, revolve, subject to this same law, under which the velocities increase as the distances diminish. Whence, indeed, we must conclude perhaps that Jupiter rotates in a shorter time than 24 hours, since his nearest Moon requires less than two days. Now having long since learned all these facts, I concluded even then that Saturn must have a similar motion. But it was my observation in regard to his satellite that gave me the information about the velocity of his motion of rotarion. The fact that the satellite completes its orbit in sixteen days leads to the conclusion that Saturn, being in the centre of the satellite's orbit, rotates in much less time. Furthermore, the following conclusion seemed reasonable: that all the celestial matter that lies between Saturn and his satellite is subject to the same motion, in this way that the nearer it is to Saturn, the nearer it approaches Saturn's velocity. Whence, finally, the following resulted: the appendages also, or arms, of Saturn are either joined and attached to the globular body at its middle and go around with it, or, if they are separated by a certain distance, still revolve at a rate not much inferior to that of Saturn.
Furthermore, while I was considering these facts in connection with the motion of the arms, these arms appeared under the aspect which was exhibited at the time of my previous observations of the year 1655. The body of Saturn at its middle was quite round, while the arms extended on either side along the same straight line, as though the planet were pierced through the middle by a kind of axis; although, as indicated in the first figure of all, these arms, as seen through the twelve-foot telescope that I was then using, appeared a little thicker and brighter toward the ends on either side of the planet than they did where they joined the middle of the sphere. When, therefore, the planet continued day after day to present this same aspect, I came to understand that, inasmuch as the circuit of Saturn and the adhering bodies was so short, this could happen under no other condition than that the globe of Saturn were assumed to be surrounded equally on all sides by another body, and that thus a kind of ring encircled it about the middle; for so, with whatever velocity it revolved, it would always present the same aspect to us, if, of course, its axis were perpendicular to the plane of the ring.
And so was established the reason for the phase which continued through that period. Therefore, after that, I began to consider whether the other phases that Saturn was said to have could be accounted for by the same ring. I was not long in coming to a conclusion on this point through noting in frequent observations the obliquity of Saturn's arms to the ecliptic. For when I had discovered that the straight line along which on. either side these arms projected did not follow the line of the ecliptic, but cut it at an angle of more than 20 degrees, I concluded that in the same way the plane of the ring which I had imagined was inclined at about the same angle to the plane of the ecliptic - with a permanent and unchanging inclination, be it understood, as is known to be the case on this Earth of ours with the plane of the equator. From this inclination it necessarily followed that in its different aspects the same ring showed to us at one time a rather broad ellipse, at another time a narrower ellipse, and sometimes even a straight line. As regards the handle-like formations, I understand that this phenomenon was due to the fact that the ring was not attached to the globe of Saturn, but was separated from it the same distance all around. These facts, accordingly, being thus brought into line, and the above-mentioned inclination of the ring being also assumed, all the wonderful appearance of Saturn, I found, could be referred to this source, as will presently be shown. And this is that very hypothesis which, in the year 1656, on the 25th day of March [earlier Huygens says the fifth of March, so one is a misprint], I put forth in confused letters, together with my observation on the Saturnian Moon.
Now the letters were: a a a a a a a c c c c c d e e e e e g h i i i i i i i I I l l m m n n n n n n n n n o o o o p p q r r s t t t t t u u u u u, which, being restored to their proper places, signify the following: Annulo cingitur, tenui, plano, nusquam cobaerente, ad eclipticam inclinato. ["It is encircled by a ring, thin, plane, nowhere attached, inclined to the ecliptic."] That the width of the space intervening between the ring and the globe of Saturn is equal to the width of the ring itself or even exceeds it, is shown by the figure of Saturn as observed by others. and then more definitely by its figure as seen by myself; that, likewise, the ratio of the greatest diameter of the ring to the diameter of Saturn is about 9 to 4. Thus the true appearance is such as I have indicated in the appended scheme.
I believe that I should digress here to meet the objection of those who will find it exceedingly strange and possibly unreasonable that I should assign to one of the celestial bodies a figure the like of which has up to this time not been found in any one of them, although, on the other hand, it has been believed as certain, and considered as established by natural law, that the spherical form is the only one adapted to them; and that I should place this solid and permanent ring (for such I consider it) about Saturn, without attaching it by any joints or ties, although imagining that it preserves a uniform distance on every side and revolves in company with Saturn at a very high rate of speed. These men should consider that I do not construct this hypothesis from pure invention and out of my own fancy, as the astronomers do their epicycles, which nowhere appear in the heavens, but that I perceive this ring very plainly with the eyes; with which, obviously, we discern the figures of all other things. And there is, after all, no reason why it should not be possible for some heavenly body to exist having this form, which, if not spherical, is at least round, and is quite as well adapted to the possession of circumcentral motion as the spherical form itself. For it certainly is less surprising that such a body should have assigned to it a shape of this kind than that it should have some absurd and quite unbeautiful shape. Furthermore, since, owing to the great similarity and relationship that exists between Saturn and our Earth, it seems possible to conclude quite conclusively that the former, like the latter, is situated in the middle of its own vortex, and that its centre has a natural tendency to reach toward all that is considered to have weight there, it must also result that the ring in question, pressing with all its parts and with equal force toward the centre, comes by this very fact to a permanent position in such a way that it is equally distant on all sides from that centre. Exactly so some people have imagined that, if it were possible to construct a continuous arch all the way around the Earth, it would sustain itself without any support. Therefore, let them not consider it absurd if a similar thing has happened of itself in the case of Saturn; let them rather regard with awe the power and majesty of Nature, which, by repeatedly bringing to light new specimens of its works, admonishes us that yet more remain.
Christiaan Huygens [Wikipedia]
Unrolling Time: Christiaan Huygens and the Mathematization of Nature
Joella G. Yoder
Joella G. Yoder