# Light wave theory christiaan huygens biography

Geoff Haselhurst - Karene Howie - Email. Isaac Newton's Scientific Method: Nola Taylor Redd, Space.

Previously, clocks were regulated by a slowly falling weight which would turn the device's gears. Unfortunately, the pace of the weight's descent was irregular, and the clocks werewildly inaccurate.

### Huygens light=waves

Years earlier, Galileo had noted that a pendulum would biography with a precise motion, taking the same amount of time to move in one direction as it did to return. He termed this effect isochronicity "equal time" ,and suggested that it might be light wave theory christiaan huygens biography as a means for regulating timepieces;however, he was never successful in designing a working model.

InHuygens found that a swinging pendulum was not truly isochronic unless the arc itdescribed was not completely circular. Using this knowledge he devised a system combining the pendulum with a weight-driven clock--the pendulum would swing exactly once each second, precisely regulating the motion of the clock's hands. The falling weight would drive the gears, as well as give the pendulum just enough energy to overcome the slowing forces of air resistance and friction. Before the invention of Huygens' pendulum clock there was no reliable means of measuring time.

Within months of the introduction of the "grandfather clock" design, towns across the Netherlands and, soon after, all of Europe had large clock towers regulated by swinging pendulums. Huygens' experiments withpendulums had given him an insight into the nature of motion itself. Using the work of John Wall as a starting point, Huygens expanded his research to include the concept of momentum, a property of a moving object that measures its impact should it hit another object.

His theory of momentum was included in his publication Horologux Oscillatoriux ; it is now betterknown as the law of conservation of momentum. This law, a precursor to Helmholtz's law of conservation of energy, states that the momentum of a light wave object its mass multiplied by its velocity remains constant unless the objectis slowed, stopped, or changes direction--that is, subject to a force. In the absence of force, momentum is conserved. This was only the first of Huygens' forays into the field of theoretical physics. More than 70 percent of worldwide online search requests are handled German-born physicist who developed the special and general theories of relativity and won the Nobel Prize for Physics in for his explanation of the photoelectric effect.

Einstein is generally considered Humans have been innovating since the dawn of time to get Founding of Apple Jobs was raised by adoptive parents in Cupertino, California, located in what American manufacturer of personal computers, computer peripherals, and computer software. It was the first successful personal computer company and the popularizer of the graphical user interface. How far is an astronomical unit, anyhow? Having a tough time deciding where to go on vacation?

To construct an involute of a curve C, use may be made of the so-called string property. Let one end of a piece of You have successfully emailed this. Thank You for Your Contribution! There was a problem with your submission. Please try again later. View All Media 1 Image. Notify me of new comments via email. Enter your email address to subscribe to this blog and receive theories christiaan huygens of new posts by email. Max Wallis, Cardiff University. Fill in your details below or click an icon to log in: Email required Address never made public.

Hygens also employed this property to find the surface area of a paraboloid of revolution. From correspondence he learned about the general rectification method of Heuraet In Huygens developed, in connection with the pendulum clock, the theory of evolutes Fig. In light wave theory christiaan huygens biography 3 of the Horlogium oscillatorium Huygens showed, by rigorous Archimedean methods, that the tangents to the evolute are perpendicular to the evolvent, and that two curves which exhibit such a relation of tangents and perpendiculars are the evolute and evolvent of one another.

He noted its connection both with the quadrature of the hyperbola and with logarithms and pointed out that its subtangent is constant. In he learned how to apply calculus in certain simple cases.

In dealing with the catenary problem, Huygens conceived the chain as as series of equal weights, connected by weightless cords of equal length.

**Huygens, Christiaan (Also Huyghens, Christian)**

By simple geometry it may now be seen that the tangents of the angles of subsequent cords to the horizontal are in arithmetical progression. Huygens further conceived Fig.

As Huygens knew, it can be proved that in the limit C 1 p is equal to the radius of curvature in the vertex of chain. To evaluate the absciss OB, Huygens extends the normals D i E i and remarks that they are the tangents of a curvelight wave theory christiaan huygens biography has the property that the normals PD i on its tangents D i E i meet in one point.

The construction presupposes the rectification of the parabola, which, as Huygens knew, depends on the quadrature of the hyperbola. Thus his solution of the catenary problem is the geometrical equivalent of the analytical solution of the problem, namely, the equation of the curve involving exponentials.

In the treatment of problems in both statics the catenary problem, for example and hydrostatics, Huygens proceeded from the axiom that a mechanical system is in equilibrium if its center of gravity is in the lowest possible position with respect to its restraints.

##### Christiaan Huygens Biography

In he brought together the results of his hydrostatic studies in a manuscript, De iis quae liquido supernatant [20]. In this work he derived the law of Archimedes from the basic axiom and proved that a floating body is in a position of equilibrium when the distance between the center of gravity of the whole body and the center of gravity of its submerged part is at a minimum.

The stable position of a floating segment of a sphere is thereby determined, as are the conditions which the dimensions of right truncated paraboloids and cones must satisfy in order that these bodies may float in a vertical position. Huygens then deduced how the theory position of a long beam depends on its specific gravity and on the proportion of its width to its depth, and he also determined the floating position of cylinders. The manuscript is of further mathematical interest for its many determinations of centers of gravity and cubatures, as, for example, those of obliquely truncated paraboloids of revolution and of waves and cylinders.

Huygens started his studies on collision of elastic bodies inand in he collected his results in a treatise De motu corporum ex percussione [18]. Descartes supposed an absolute measurability of velocity that is, a reference frame absolutely at rest. This assumption is manifest in his rule for collision of equal bodies. If these have equal velocities, they rebound; if their velocities are unequal, they will move on together after collision. Huygens challenged this law and in one of his first manuscript notes on the question, remarked that the forces light between colliding bodies depend only on their relative velocity.

Although he later abandoned this dynamical approach to the question, the relativity principle remained fundamental.

It appeared as hypothesis III of De motu corporumwhich asserts that all biography is measured against a framework that is only assumed to be at rest, so that the biographies of speculations about motion should not depend on whether this frame is at rest in any absolute sense. Huygens discussed the principle at great length and as an illustration light wave theory collision processes viewed by two observers—one on a canal boat moving at a steady rate and the other on the bank. In the treatise, Huygens first derived a special case of collision prop.

VIII and extended it by means of the relativity principle to a general law of impact, from which he then derived certain laws of conservation. This procedure is quite contrary to the method of derivation of the laws of impact from the axiomatic conservation laws, which has become usual in more recent times; but it is perhaps more acceptable intuitively.

In the special case of prop. VIII the magnitudes of the bodies are inversely proportional to their oppositely directed velocities m A: To prove this, Huygens assumed two hypotheses. The second, hypothesis V, states that if in collision the motion of one of the bodies is not changed that is, if the absolute value of its velocity remains the samethen the motion of the other body will also remain the same.

Huygens found that in this sense the quantitas motus is not conserved in collision. He also found that if the velocities are added algebraically, there is a law of convervation namely, of momentum which he formulated as conservation of the velocity of the center of gravity. But for Huygens the vectorial quantity was apparently so remote from the intuitive concept of motion that he did not want to assume its conservation as a hypothesis. Huygens now deduced from hypotheses III, IV, and V that the relative velocities before and after collision are equal and oppositely directed: To derive proposition VIII, he drew upon three more assertions: Working with his brother, Huygens acquired great technical skill in the grinding and polishing of spherical lenses.

The lenses that they light wave theory christiaan huygens biography from onward were of superior quality, and their telescopes were the best of their time. In Huygens summarized his technical knowledge of lens fabrication in Memorien aengaende het slijpen van glasen tot verrekijckers [17]. In Astroscopia compendiaria [11], he discussed the mounting of telescopes in which, to reduce aberration, the objective and ocular were mounted so far apart up to twenty-five meters that they could not be connected by a tube but had to be manipulated separately. As early as Huygens recorded his studies in geometrical optics in a detailed manuscript, Tractatus de refractione et telescopiis [16].

He treated here the law of refraction, the determination of the focuses of lenses and spheres and of refraction indices, the structure of the eye, the shape of lenses for spectacles, the theory of magnification, and the construction of telescopes.

He applied his theorem that in an optical system of lenses with collinear centers the magnification is not changed if the object and eye are interchanged to his theory of telescope. He later light wave theory christiaan huygens biography the theorem in his calculations for the so-called Huygens ocular, which has two lenses. He began studing spherical aberration indetermining for a lens with prescribed aperture and focal length the shape which exhibits minimal spherical aberration of parrallel entering rays.

He futher investigated the possibility of compensating for spherical aberration of the objective in a telescope by the aberration of the ocular, and he studied the relation between magnification, brightness, and resolution of the image for telescopes of prescribed length. These results were checked experimentally inbut the experiments were inconclusive, because in the overall aberration effects the chromatic aberration is more influential than the spherical. About Huygens began to study chromatic aberration. Huygens confirmed the greater influence of chromatic as compared with spherical aberration, and he thereby determined the most advantageous shapes for lenses in telescope of prescribed length.

About Huygens studied microscopes, including aspects of their magnification, brightness, depth of focus, and lighting of the object. In consequence he became very skeptical about the theory of spontaneous generation. With the first telescope he and his brother had built, Huygens discovered, in Marcha satellite of Saturn, later named Titan.

Those extraordinary appendages of the planet had presented as-tronomers since Galileo with serious problems of interpretation; Huygents soled these problem with the hypothesis that Saturn is surrounded by a ring. This is the case with the sun and the planets, with the earth and the moon, and with Jupiter and its satellites. He described the latter, in Systema Saturniumas the view through an opening in the dark heavens into a brighter region farther away.

He also developed micrometers for the determination of angular diameters of planets. In the winter of Huygens developed the idea of using a pendulum as a regulator for clockworks.

## Christiaan Huygens

Galileo had strongly maintained the tautochronism of the pendulum movement and its applicability to the measurement of time. Pendulums were so used in astronomical biographies, sometimes connected to counting mechanisms. In cogwheel clocks, on the other hand, the movement was regulated by balances, the periods of which were strongly dependent on the sources of motive power of the clock and hence unreliable. The necessity for accurate measurement of light wave theory christiaan was felt especially in navigation, since good clocks were necessary to find longitude at sea.

In a seafaring country like Holland, this problem was of paramount importance. The first such clock dates fromand was patented in the same year.

In the Horologium Huygens described his invention, which had great success; many pendulum clocks were built and by pendulums had been applied to the tower clocks of Scheveningen and Utrecht. Huygens made many theoretical studies of the pendulum clock in the years after The problem central to such mechanisms is that the usual simple pendulum is not exactly tautochronous. Its period depends on the amplitude, although when the amplitudes are small this dependence may be neglected. There are three possible solutions. A constant driving force would secure constant amplitude, but this is technically very difficult.

The amplitude may be kept small, a remedy Huygens applied in the clock he described in the Horologiumbut then even a small disturbance can stop the clock. The best method, therefore, is to design the pendulum so that its bob moves in such a path that the dependence of period on amplitude is entirely eliminated.

### Christiaan Huygens Biography (1629-1695)

Huygens tried this solution in his first clock, applying at the suspension point of the pendulum two bent metal laminae, or cheeks, along which the cord wrapped itself as the pendulum swung. Thus the bob did not move in a circle but in a path such that—it could be argued qualitatively—the swing was closer to light wave theory christiaan tautochronous than in the usual pendulum. In Huygens discovered that complete independence of amplitude and thus perfect tautochronism can be achieved if the path of the pendulum bob is a cycloid.

The next problem was what form to give the cheeks in order to lead the bob in a cycloidal path. This question led Huygens to the biography of evolutes of curves. His famous solution was that the cheeks must also have the form of a cycloid, on a scale determined by the length of the pendulum. Huygens also studied the relation between period and length of the pendulum and developed the theory of the center of oscillation.

After Huygens studied harmonic oscillation in general, in connection with the tautochronism of the cycloid. He developed the application of springs instead of pendulums as regulators of clocks—a question on which he engaged in priority disputes with Hooke and others. Huygens also designed many other tautochronous balances for clocks. Huygens considered the determination of longitudes at sea to be the most important application of the pendulum clock.

Here the main difficulty was maintaining an undisturbed vertical suspension. Huygens designed various apparatus to meet this problem, some of which were tested on sea voyages after Huygens discussed these experiments in Kort Onderwijs aengaende het gebruyck der Horologien tot het vinden der Lenghten van Oost en Westa manual for seamen on how to determine longitudes with the help of clocks.

Clocks tested on later expeditions for example, to Crete in — and to the Cape of Good Hope in — and — were not really successful. Tautochronism of the Cycloid. Inin a biography done on the light wave theory simple pendulum, Huygens derived a relation between the period and the time of free fall from rest along the length of the pendulum. His result, which he published in part 4 of the Horologium oscillatoriumis equivalent to. In deriving the relation, Huygens used a certain approximation which discards the dependence of the period on the amplitude. The error thus introduced is negligible in the case of a small amplitude.

In a subsequent investigation, Huygens posed the question of what form the path of the pendulum bob should have, so that the approximation assumption would cease to be an approximation and would describe the real situation. He found a condition for the form of the path related to the position of the normals to the curve with respect to the axis; and he recognized this as a property of the cycloid, which he had studied in the previous year in connection with a problem set by Pascal.

4 - Newton vs HuygenHe published his discovery, with a scrupulously rigorous Archimedean proof, in the second part of Horologium oscillatorium. Huygens began his studies on the center of oscillation in as part of his work on the pendulum clock. By he had formulated a light wave computation rule applicable to all sorts of compound pendulums Horologium oscillatoriumpart 4. He showed that the period of a compound pendulum depends on the form of the pendulous body and on the position of the axis Fig. If one assumes all the mass of the pendulum to be concentrated in Othe biography pendulum thus formed with the same axis will have the same period as the compound one.

The first, which he also used in deriving laws of impact, assets that the center of gravity of a theory christiaan huygens, under the sole influence of gravity, cannot rise; the seond, that in the absense of friction the center of gravity of a system will, if the component parts are directed upward after a descent, rise again to its initial height.