# Huygens Sentence Examples

**Huygens**, in his Systema saturnium (1659), describes a micrometer with which he determined the apparent diameters of the principal planets.Gascoigne was killed at the battle of Marston Moor on the 2nd of July 1644, in the twenty-fourth year of his age, and his untimely death was doubtless the cause that delayed the publication of a discovery which anticipated, by twenty years, the combined work of

**Huygens**, Malvaison, Auzout and Picard in the same direction.Two Dutch friends, Constantijn

**Huygens**(von Zuylichem), father of the more celebrated**Huygens**, and Hoogheland, figure amongst the correspondents, not to mention various savants, professors and churchmen (particularly Jesuits).Attempts have been made, principally founded on some remarks of

**Huygens**, to show that Descartes had learned the principles of refraction from the manuscript of a treatise by Willebrord Snell, but the facts are uncertain; and, so far as Descartes founds his optics on any one, it is probably on the researches of Kepler.At the beginning of 1680 he presented a paper to the Royal Society, De nova temporis dimetiendi ratione et accurata horologiorum .constructione, in which he attempted to deprive

**Huygens**of the honour of applying the pendulum to the measurement of time.He was the second son of Sir Constantijn

**Huygens**.The invention dates from 1656; on the 16th of June 1657

**Huygens**presented his first "pendulumclock" to the states-general; and the Horologium, containing a description of the requisite mechanism, was published in 1658.**Huygens**had before this time fixed his abode in France.Although Robert Hooke in 1668 and Ignace Pardies in 1672 had adopted a vibratory hypothesis of light, the conception was a mere floating possibility until

**Huygens**provided it with a sure foundation.This resolution of the original wave is the well-known "Principle of

**Huygens**," and by its means he was enabled to prove the fundamental laws of optics, and to assign the correct construction for the direction of the extraordinary ray in uniaxial crystals.Advertisement**Huygens**never married.The publication of a monumental edition of the letters and works of

**Huygens**was undertaken at the Hague by the Societe Hollandaise des Sciences, with the heading ¦uvres de Christian**Huygens**(1888), &c. Ten quarto volumes, comprising the whole of his correspondence, had already been issued in 1905.The principle employed in these investigations is due to C.

**Huygens**, and may be thus formulated.Any obscurity that may hang over

**Huygens**'s principle is due mainly to the indefiniteness of thought and expression which we must be content to put up with if we wish to avoid pledging ourselves as to the character of the vibrations.We imagine a wave-front divided o x Q into elementary rings or zones - often named after

**Huygens**, but better after Fresnelby spheres described round P (the point at which the aggregate effect is to be estimated), the first sphere, touching the plane at 0, with a radius equal to PO, and the succeeding spheres with radii increasing at each step by IX.AdvertisementAlthough the matter can be fully treated only upon the basis of a dynamical theory, it is proper to point out at once that there is an element of assumption in the application of

**Huygens**'s principle to the calculation of the effects produced by opaque screens of limited extent.When, in order to apply

**Huygens**'s principle, the wave is supposed to be broken up, the phase is the same at every element of the surface of resolution which lies upon a line perpendicular to the plane of reference, and thus the effect of the whole line, or rather infinitesimal strip, is related in a constant manner to that of the element which lies O in the plane of reference, and may be considered to be represented thereby.These curves attracted much attention and were discussed by John Bernoulli, Leibnitz,

**Huygens**, David Gregory and others.A collection of formulae relating to the circle, for instance, would comprise not only geometrical and trigonometrical formulae, but also approximate formulae, such as

**Huygens**'s rule (§ 91), which are the result of advanced analysis.The length of the arc of a circle, for instance, is known if the length of the chord and its distance from the middle point of the arc are known; but it may be more convenient in such a case to use a formula such as

**Huygens**'s rule than to obtain a more accurate result by means of trigonometrical tables.AdvertisementFor this reason, formulae which will only give approximate results are usually classed together as rules, whether the inaccuracy lies (as in the case of

**Huygens**'s rule) in the formula itself, or (as in the case of Simpson's rule) in its application to the data.If we use c 1 to represent the chord of the whole arc, c 2 the chord of half the arc, and c 4 the chord of one quarter of the arc, then corresponding to (i) and (iii) of § 70 or § 79 we have a (8c 2 - c i) and4 5 (256c 4 - 40c2+ci) as approximations to the length of the arc. The first of these is

**Huygens**'s rule.The only aether which has survived is that which was invented by

**Huygens**to explain the propagation of light.Now the direction and phase of the light are those of the ray which reaches the eye; and by Fermat's principle, established by

**Huygens**for undulatory motion, the path of a ray is that track along which the disturbance travels in least time, in the restricted sense that any alteration of any short reach of the path will increase the time.Descartes helped to generalize and establish the notion of the fundamental character of uniform motion in a straight line, but otherwise his speculations did not point in the direc tion of sound progress in dynamics; and the next substantial advance that was made in the principles of the subject was due to

**Huygens**(1629-1695).AdvertisementBut

**Huygens**'s most important contribution to the subject was his investigation, published in 1673, of the motion of a rigid pendulum of any form.Newton tells us that this agreement led him to adopt the law of the inverse square of the distance about 1665-1666, before

**Huygens**'s results as to circular motion had been published.The use of the pendulum clock in its present form appears to date from the construction of such a clock by

**Huygens**in 16J7.He was a great mathematician in an age which produced Descartes, Fermat,

**Huygens**, Wallis and Roberval.Solutions were furnished by Wallis,

**Huygens**, Wren and others; and Pascal published his own in the form of letters from Amos Dettonville (his assumed name as challenger) to Pierre de Carcavy.Formerly classified by the ancient Greeks with halos, rainbows, &c., under the general group of "meteors," they came to receive considerable attention at the hands of Descartes, Christiaan

**Huygens**, and Sir Isaac Newton; but the correct explanation of coronae was reserved until the beginning of the 19th century, when Thomas Young applied the theories of the diffraction and interference of light to this phenomenon.The first powerful telescopes of this construction were made by

**Huygens**, after much labour, in which he was assisted by his brother.**Huygens**states that he and his brother made object-glasses of 170 and 210 ft.**Huygens**contrived some ingenious arrangements for directing such telescopes towards any object visible in the heavens - the focal adjustment and centring of the eyepiece being preserved by a braced rod connecting the objectglass and eye-piece.Among other writers, Leibnitz and

**Huygens**give testimony which is the more valuable as being critical.Leibnitz speaks of Bacon as " divini ingenii vir," and, like several other German authors, classes him with Campanella;

**Huygens**refers to his " bonnes methodes."It was as an optician that he was first brought into connexion with

**Huygens**and Leibnitz; and an optical Treatise on the .Rainbow, written by him and long supposed to be lost, was discovered and reprinted by Dr Van Vloten in 1862.It was probably at the suggestion of

**Huygens**that he bent his steps towards Spinoza's lodging.**Huygens**(Descriptio automati planetarii, 1703) uses the simple continued fraction for the purpose of approximation when designing the toothed wheels of his Planetarium.There he entertained the poet Vondel, the scholar Barlaeus, 1 Constantin

**Huygens**, Vossius, Laurens Reael and others.He also received the De Morgan medal from the London Mathematical Society, and the

**Huygens**medal from Leiden.The mechanical properties of the cycloid were investigated by Christiaan

**Huygens**, who proved the curve to be tautochronous.He was, however, intimate with Constantin

**Huygens**, whose political opinions were more nearly in agreement with his own.**Huygens**, in a letter dated the 8th of June 1694, wrote to Leibnitz, " I do not know if you are acquainted with the accident which has happened to the good Mr Newton, namely, that he has had an attack of phrenitis, which lasted eighteen months, and of which they say his friends have cured him by means of remedies, and keeping him shut up."The improvement of telescopes was prosecuted by Christiaan

**Huygens**from 1655, and promptly led to his discoveries of the sixth Saturnian moon, of the true shape of the Saturnian appendages, and of the multiple character of**Huygens**.It was further investigated by John Wallis, Christiaan

**Huygens**(who determined the length of any arc in 1657), and Pierre de Fermat (who evaluated the area between the curve and its asymptote in 1661).That this is not a necessary characteristic of light was discovered by Christian

**Huygens**, who found that, whereas a stream of sunlight in traversing a rhomb of spar in any but one direction always gives rise to two streams of equal brightness, each of these emergent streams is divided by a second rhomb into two portions having a relative intensity dependent upon the position with respect to one another of the principal planes of the faces of entry into the rhombs - the planes through the axes of the crystals perpendicular to the refracting surfaces.The phenomenon of polarization observed by

**Huygens**remained an isolated fact for over a century, until Malus in 1808 discovered that polarization can be produced independently of double refraction, and must consequently be something closely connected with the nature of light itself.This result is not, however, conclusive; for an application of

**Huygens**'s principle shows that it is a consequence of the rotation of the plane of polarization by an amount proportional to the distance traversed, independently of the state of affairs within the active medium.Before the close of 1610 the memorable cycle of discoveries begun in the previous year was completed by the observation of the ansated or, as it appeared to Galileo, triple form of Saturn (the ring-formation was first recognized by Christiaan

**Huygens**in 1655), of the phases of Venus, and of the spots upon the sun.In their numerous allusions to the subtle mercury, which the one makes when treating of a means of measuring time by the efflux of the metal, and the other in a treatise on the transit of the planet, we see traces of the school in which they served their first apprenticeship.

**Huygens**, moreover, in his great posthumous work, Cosmotheoros, seu de terris coelestibus, shows himself a more exact observer of astrological symbols than Kircher himself in his Iter exstaticum.**Huygens**contends that between the inhabitants of different planets there need not be any greater difference than exists between men of different types on the earth.In the same volume are treatises on "Geometric Loci, or Spherical Tangencies," and on the "Rectification of Curves," besides a restoration of "Apollonius's Plane Loci," together with the author's correspondence addressed to Descartes, Pascal, Roberval,

**Huygens**and others.The actual calculation follows a similar course to that by which

**Huygens**'s conception of the resolution of a wave into components corresponding to the various parts of the wave-front is usually verified (see Diffraction Of Light).It is beyond doubt that

**Huygens**independently discovered that an object placed in the common focus of the two lenses of a Kepler telescope appears as distinct and well-defined as the 3 Delambre, Hist.But the difficulties interposed by spherical and chromatic aberration had arrested progress in that direction until, in 1655,

**Huygens**, working with his brother Constantijn, hit upon a new method of grinding and polishing lenses.The theorems on the composition of forces in circular motion with which it concluded formed the true prelude to Newton's Principia, and would alone suffice to establish the claim of

**Huygens**to the highest rank among mechanical inventors.He continued his scientific correspondence with unbroken interest and undiminished logical acumen; he thought out the application of the pendulum to the regulation of clockwork, which

**Huygens**successfully realized fifteen years later; and he was engaged in dictating to his disciples, Viviani and Torricelli, his latest ideas on the theory of impact when he was seized with the slow fever which in two months brought him to the grave.According to

**Huygens**'s principle (see Diffraction) each aether particle, set vibrating by an incident wave, can itself act as a new centre of excitement, emitting a spherical wave; and similarly each particle on this wave itself produces wave systems. All systems which are emitted from a single source can by a suitable optical device be directed that they simultaneously influence one and the same aether particle.