Pendulum clock: From Galileo to Fedchenko. Unfounded accusations

1. RENEE DESCARTES

The study of physics, according to Descartes (1596-1650), should have the goal of making people “lords and masters of nature.” Man can achieve this dominance over nature by applying to physical research the methods of mathematics, the most advanced science known to him. Therefore, Descartes set himself the task of mathematizing physics, or, more precisely, its geometrization according to the type of Euclidean geometry: a small number of axioms, self-evident, on which an ordered sequence of conclusions is based, having the same degree of reliability as the primary axioms.

Accepting the Galilean concept of secondary qualities contained not in bodies, but in the sentient subject, Descartes bases his consideration on only two entities - extension and motion, which seem intuitive to him, and, being convinced of the impossibility of the existence of emptiness in nature, fills extension " subtle matter,” which God endowed with continuous movement.

The physical world thus consists of only two entities: matter, simple “extension endowed with form,” devoid of all qualities except geometric ones, and motion. Consequently, it will be enough to establish the laws of motion in order to then deduce, using a series of successive theorems, the laws of the sensory world.

In his treatise “Le monde” (“The World”), Descartes does not mention the relativity of motion. But in the Principia philosophiae (Principles of Philosophy), published in 1644, that is, after the appearance of the Dialogue on the Two Chief Systems of the World, he, perhaps under the influence of this work of Galileo, accepts the principle of relativity, while still doing for the sake of caution, a number of reservations allow it not to formally conflict with the position on the immobility of the Earth, required by the Holy Scriptures. But if the fear of the Inquisition had not forced him to hide his thoughts, Descartes would have given a broader concept of relativity than Galileo. Indeed, Galileo and later Newton believed in absolute motion in relation to space, while Descartes argued for its relative nature. In private correspondence he wrote:

“If of two people one moves with the ship, and the second stands motionless on the shore... then there is no advantage either in the movement of the first or in the rest of the second.” (Oeuvres de Descartes, publiees par Charles Adam et Paul Tannery, Paris, 1902, v. VL, p. 348. (There is a Russian translation: R. Descartes, Selected Works, M., 1950.)).

Cartesian mechanics is based on three laws. The first two cover what is now called the principle of inertia. The third law states the constancy of momentum (the product of the mass of a body, which Descartes confused with weight, and its speed). Descartes also assumes that the amount of motion is equal to the product of the applied force and the time of its action and calls this product the impulse of the force; this name has been preserved in science even now in the same meaning. Descartes' third law is essentially the central point of his mechanics. The fact that Descartes was able to isolate it and make it the basis of his mechanics speaks of the author’s extraordinary intuition.

Unfortunately, in formulating this law, Descartes makes an error that is very strange for a geometer of his caliber. He does not take into account that since speed, as we would now say and as Descartes knew, is a vector, i.e., a quantity that has a direction and orientation, then the quantities of motion are vectors, so their sum must be understood in geometric terms, and not in an algebraic sense. Thus, the formulation of the third law is erroneous. Hence the incorrectness of the seven rules arising from it (with the exception of the first), which form the Cartesian theory of collision of elastic bodies.

Some cases of collision studied by Descartes can be easily verified experimentally. For example, the fourth Cartesian rule states that if a stationary body experiences a central collision with another body of smaller mass, then it remains motionless, while a moving body reverses the direction of speed while maintaining the absolute value of the speed. But it is enough to go to the billiard table to see that this rule is wrong. And Descartes actually did this and established that his rules were incorrect. But he trusted his mind and his “clear and distinct” ideas too much. Does experience disprove theoretical constructs? So much the worse for the experience. The experiment fails, Descartes says with confidence, because these rules presuppose

“that bodies are ideally solid and so distant from all other bodies that none of these bodies can promote or hinder their motion” (Oeuvres de Descartes, v. IX, p. 93).

But even if we accept this explanation as correct, how can we become masters of nature, having physics that speaks about phenomena that take place in another world, and not in the one in which we exist?

Having established the laws of motion, Descartes in his treatise “The World” and in “The Elements of Philosophy” begins his cosmological novel, explaining the formation of the Sun, planets, and comets. Finally, he descends from heaven to Earth and establishes that subtle matter has three actions: light, heat and gravity. In this way he creates the foundations of the concept of fluids that dominated physics throughout the 18th century and partly in the 19th century. These comfortable fluids, which, like good gnomes, are ready to serve in the most difficult cases and modestly act hidden from our senses, do they not, at least in part, represent a return back to the occult? In our opinion, this is so.

But we must always remember that the concept of fluids has also provided enormous services to physics, especially in optics and the theory of electricity. By this we mean a scientific concept, a temporary model representation, an instrument of mechanistic philosophy, but not the specific fluids introduced by Descartes, such as his magnetic fluid, consisting of two types of particles of a spiral shape with three turns wound in opposite directions. With its help, Descartes answered 34 questions that, in his opinion, could be asked about magnetism. This magnetic fluid and this admirable chain of reasoning throughout the Principia testify to Descartes' skill in constructing hypothetical deductive systems, but do not enrich our knowledge of magnetic phenomena one iota.

The Cartesian concept of gravity played a completely different role. Each body, according to Descartes, is in a vortex, being surrounded in turn by other vortices that press it to the center. This desire for the center constitutes the weight of the body, i.e. heaviness. If Galileo had known this, Descartes said in his famous letter to Mersenne, he would not have needed to build an unfounded theory of the fall of bodies in vacuum.

Descartes' letter, which we have already mentioned above, is a sharp criticism of Galileo's "Conversations Concerning Two New Branches of Science" and is interesting from the point of view of the differences in the thinking of both scientists: for Descartes, physics must seek the answer to the question of why phenomena occur; for Galileo, it must investigate how they happen; the search for a cause is the goal of Descartes, the description of phenomena is the goal of Galileo. On the issue of the fall of heavy bodies, Descartes did not agree with Galileo’s laws and did not understand them, in particular because the concept of acceleration was alien to his kinematics.

Descartes understood weight, like any force, as a reaction of connections of a geometric type. This is the property of the movement of subtle matter. So, identifying it with space and using terminology that is now more understandable, we can say that weight is a property of space. But Cartesianism was never inclined to such an understanding, and therefore it fell, defeated by the adherents of Newtonian attraction, despite the defense of Huygens and Leibniz, who drew attention to the fact that Newton's understanding of attraction, which accepted Keplerian concept of prensatio or vis prensandi contained in the body , represents an implicit return to the occult properties of scholasticism, because, after all, in order for body A to attract body 5, it must know where body B is.

It is commonly said that Cartesian understanding of physics is mechanistic. But the understanding of Galileo and Newton was also mechanistic, because mechanism refers to all the sometimes contradictory theories that explain all physical phenomena using a system of movements similar to the movement of a mechanism. It seems to us that the mechanism of Descartes differs from the mechanism of Galileo - Newton in two significant features. The first, more obvious difference just noted is the concept of force. For Galileo and Newton, force is a physical reality that cannot be reduced to the properties of space and motion; for Descartes, force, as we have seen, is a property of space. The mechanism of Descartes is opposed to the dynamism of Newton, taken to its extreme limit by Roger Boscovitch in the 18th century and Michael Faraday in the 19th century. According to these dynamists, force is immediately given; so-called matter disappears, and its “venerable qualities,” as Ostwald called them, are nothing more than the properties of fields of forces in empty space. But Descartes' mechanism is also opposed to atomism, according to which it is atoms that create fields of forces, and their hidden movements explain all physical processes. Obviously, Cartesian doctrine, identifying matter with extension, could not be atomistic in the traditional Democritus sense of the word.

2. GALILEO'S DISCIPLES

Giacomo Leopardi attributes to Copernicus the words that the confirmation of the heliocentric system

“... will not be as simple a matter as it might seem at first glance... Its influence will not be limited to physics. It will lead to a reassessment of the values and relationships of various categories] it will change the view of the purposes of creation. Thus, it will also revolutionize metaphysics and, in general, all areas that come into contact with the speculative side of knowledge. It follows that people, if they are able or want to reason sensibly, will find themselves in a completely different position than they were before or imagined that they were.” (Giacomo Leopard i, Le operette morali, Livorno, 1870, p. 314, with a preface by Pietro Giordani, edition revised and expanded by G. Chiarini).

This complete revolution in the way of thinking, so well understood by Leopardi, can easily be attributed to the physical research carried out after Galileo. True, there was no shortage of opponents of the new research method, who became especially zealous after the condemnation of Galileo, but a significant part of them were forced to respond to observations with other observations, to experiments with other experiments, and to mathematical proofs with other mathematical proofs. Thus forced to study things rather than the works of Aristotle, the Peripatetics of this period also helped, albeit indirectly, to abandon blind faith in authorities and made the work of Galileo's disciples easier.

Among Galileo's students we include not only those who perceived the new science from his own lips, but also his numerous correspondents, as well as the first generation of scientists whose scientific worldview was formed on his works. In this sense, Galileo had many students not only in Italy, but also abroad, especially in France, primarily thanks to the activities of Marin Mersenne (1588-1648), who, as we have already said, translated Galileo's Mechanics in 1634 . Later, when the republication and translation of the “Dialogue Concerning the Two Chief Systems” was prohibited, Mersenne compiled a summary of this work for his compatriots and distributed Galileo’s research on the fall of heavy bodies in France; he was the first among scientists of that time to support the point of view about the subjective nature of sensations. Although we would look in vain for original ideas in Mersenne's work, he nevertheless played an important role in the dissemination of new science, informing about the work of other scientists, commenting on and retelling it, and sometimes publishing it in full. Therefore, Mersenne’s works represent an inexhaustible source of information about the level of knowledge in that turbulent era. A tireless correspondent of the largest scientists of the time, Mersenne informed others, received information himself, raised problems, raised objections, thus fulfilling the functions of collecting and disseminating knowledge now assigned to large international scientific journals.

3. EVANGELISTA TORRICELLI

In April 1641, Benedetto Castelli (1577-1644), a professor of mathematics at the University of Rome and a former student of Galileo, visited his teacher, who then lived in Arcetri, and brought him a manuscript on the motion of freely falling bodies for review. Its author was Evangelista Torricelli (1608-1647), a student of Castelli. Castelli invited Galileo to take Torricelli into his home as an assistant in preparing research on mechanics. Having received Galileo's consent, Torricelli moved to Arcetri with him in the first half of August of the same year. But their collaboration lasted only three months. Galileo died. The Grand Duke of Tuscany, who arrived in Arcetri in connection with the death of Galileo, appointed Torricelli to the vacant position of court mathematician.

The scientific activity of Torricelli, undoubtedly the most brilliant student of Galileo, relates to the field of physics and mathematics. However, following the example of his teacher, he does not disdain practical activities. Having learned from Galileo about the importance of making lenses and telescopes, from 1642 he began to work hard at this and soon achieved such perfection that he far surpassed the most famous Italian masters (Hippolytus Mariani, nicknamed “Simp”, Eustachio Divini from Rome, Francesco Fontana from Naples), whose products are recognized as the greatest achievements of optics of the first half of the 17th century.

In the future we will talk about Torricelli's discovery of atmospheric pressure, a discovery that more than others contributed to making his name immortal. We will now limit ourselves to only a brief examination of his work on mechanics, contained in the only book he published, consisting of three parts. The first and third parts are devoted to geometry, and the second, entitled “De motu gravium descendentium et proiec-torum libri duo” (“On the motion of freely falling and thrown heavy bodies”), is the manuscript that Castelli brought to Galileo for review.

In the first book of this treatise, Torricelli sets himself the goal of proving Galileo's postulate about the equality of velocities of heavy bodies falling along inclined planes of the same height, and, not knowing that this had already been done by Galileo, he proves it. At the same time, he accepts as a postulate the principle, now named after Torricelli, about the movement of centers of gravity. Thanks to Torricelli, with numerous applications of this principle (to an inclined plane, a lever, movement along a chord of a circle and along a parabola), the views of a number of authoritative scientists were refuted, who reproached Archimedes for considering the vertical directions of two threads with suspended weights at the surface of the earth to be parallel , rather than converging towards the center of the Earth. Torricelli showed that Archimedes' representation was more suitable for theoretical physical research.

In the second book of the treatise, Torricelli first examines the motion of thrown bodies, generalizing the approach taken in Galileo's Discourses, which discusses only the motion of bodies thrown horizontally. Only along the way, for proof, Galileo put forward the statement that if a body is thrown from the point of its fall with a speed equal to, but opposite to that with which it arrived at the point of fall, then it will pass the same parabola in the opposite direction. Torricelli examined the motion of a body thrown at an arbitrary angle, and, applying Galileo’s principles to it, determined the parabolic nature of the trajectory and established other, now well-known theorems of ballistics. In particular, generalizing Galileo's observation, he noted that the motion of a thrown body is a reversible phenomenon. Thus, the idea that dynamic phenomena are reversible, that is, that time in Galilean mechanics is ordered but lacks orientation, goes back to Galileo and Torricelli.

After the section “On the Movement of Fluids,” which we will touch upon below, Torricelli gives five ballistic tables, apparently the first tables in the history of artillery, and, fearing that the practitioners for whom these tables are intended do not understand Latin, he suddenly switches to Italian language.

On the issue of the movement of fluids (the immediate predecessors in these studies were Benedetti and Castelli), Torricelli's contribution was so great that Mach proclaimed him the founder of hydrodynamics. The main problem that Torricelli set himself was to determine the speed of flow of liquid from a narrow hole in the bottom of the vessel. Using a special device, he forced the liquid flowing out of the hole to shoot upward and found that it rose to a height less than the level of water in the vessel. Then he suggested that if there were no resistance to the movement of the liquid at all, the stream would rise to the level of the water in the vessel. Obviously, this hypothesis is equivalent for this particular case to the law of conservation of energy. Using an analogy with the fall of heavy bodies, Torricelli deduces from the accepted hypothesis the following basic position (now called “Torricelli’s theorem”):

“Water escaping from a vessel has at the point of exit the same speed that an arbitrary heavy body would have, and therefore a separate drop of the same water, falling freely from the upper level of this water to the level of the hole” ("De motu...", Libro II, prop. XXXVII, in Opere di Evangelista Torricelli, ed. G. Loria, G. Vassura, Faenze, II, 1919, p. 186).

This theorem, which is the basis of hydrostatics, was subsequently proven by Newton and Varignon. Torricelli used it, together with results already obtained concerning the motion of thrown bodies, to prove that if a hole is made in the wall at the bottom of a vessel, then the jet has a parabolic shape. In addition, Torricelli made subtle physical observations on the disintegration of a liquid stream into droplets and the influence of air resistance.

4. GIOVANNI ALFONSO BORELLI

Galileo's students also included the Neapolitan (according to other sources - Messinian) Giovanni Alfonso Borelli (1608-1679) - one of the most insightful minds of Italian science of the 17th century. Borelli anticipated Newton's idea that the planets tend to the Sun for the same reason that heavy bodies tend to the Earth. His comparison of the motion of a stone revolving on the edge of a sling and the motion of a planet around the Sun, according to the almost unanimous opinion of all critics, is the first germ of the theory of dynamic equilibrium of moving planets. According to Borelli, the "instinct" that causes the planet to tend towards the Sun is balanced by the tendency of each body to move away from the center. Borelli considers this vis repellens, or centrifugal force, as we now call it, to be inversely proportional to the radius of the circumscribed circle.

In his work on mechanics “De vi percussionist (“0 force of impact”), 1667, broader in meaning than the title suggests, he cites the laws of the central collision of two inelastic spheres, which are still valid today. In this work he sets out to determine what the effective motion of falling bodies would be if we assume (ex mera hypothesi - “purely hypothetically,” he adds with caution, especially necessary since he was a monk) that the bodies take part in a uniform circular motion. rotational motion of the Earth. And he comes to the conclusion about the deviation of bodies to the east, which was experimentally confirmed only in 1791 by Giovan Battista Guglielmini (?-1817) in experiments with the fall of bodies from the Asinelli Tower in Bologna.

In his work “De motionibus naturalibus a gravitate pendentibus” (“On natural movements depending on gravity”), 1670, he devotes one chapter to the experimental study of capillary phenomena and comes to the conclusion that in capillary tubes the rise of liquid is inversely proportional to the diameter of the tube . This law was rediscovered in 1718 by the physician Jacques Jurin (1684-1750), after whom it is named. In the same work, the determination of the specific gravity of air is given - using a device - the first representative of hydrometers with a constant volume. In 1656, Borelli and Viviani determined the speed of sound in air using the direct method proposed by Galileo, that is, by measuring the time interval between the moment the explosion is perceived by light and the moment when the sound of the explosion becomes audible. Thus, he managed to obtain significantly more accurate results than his predecessors (Mersenne, Gassendi, etc.). However, Borelli’s best creation, which worthily crowns all his other works, is his work “De motu animalium” (“On the Movement of Animals”), published posthumously in two volumes in 1680-1681. in Rome, where Borelli died in deep poverty.

The first volume describes the structure, form, action and capabilities of human and animal muscles. The second volume uses mechanical analogies to examine muscle contractions, heart movements, blood circulation, and digestion. This work, which was reprinted many times, marked the beginning of a new scientific direction - iatromechanics. Particularly admirable is Chapter XXII on the flight of birds (De volatu), which was therefore published many times separately. Already in our century, in an English translation, this chapter was included in the series “Aeronautical classics” (No. 6, London, 1911), and in a German translation - in the series “Klassiker der exakten Wissenschaften” (No. 221, Leipzig, 1927).

5. PENDULUM CLOCK

Soon after the discovery of the “medicine planets,” i.e., the first four satellites of Jupiter ( Galileo called the moons of Jupiter he discovered “Medicine stars” in honor of the Duke of Tuscany, Cosimo de' Medici. - Approx. translation), Galileo had the idea of using them to determine the longitude of a place, which, as is known, is of great importance for sailors. Theoretically, determining longitude looks very simple: having calculated the ephemeris for some place, which determines the moment when the satellite enters the cone of Jupiter's shadow, it is enough to determine the time when this phenomenon is observed in another place in order to find the difference in the longitudes of both places from the difference in these times. But the use of this method requires ephemeris tables and two chronometers.

In 1612, then in 1616 and still later in 1630, Galileo tried to negotiate with the Spanish government to convey this discovery to him, but his attempts were unsuccessful. In 1636, he again addressed this proposal to the States General of the Netherlands, which gladly accepted this proposal, immediately appointed a special commission to consider it and decided to send a gold necklace worth 500 florins as a gift to Galileo. The commission noted some shortcomings of Galileo's project, which he recognized as fair, but completely surmountable. However, the matter was not one that could be resolved by correspondence, so Galileo proposed that representatives of the Estates General come to him in Arcetri. Galileo's friends turned to the secretary of the Prince of Orange, Constantijn Huygens, the father of Christian Huygens, with a request to provide assistance, using his high position with the Estates General. Constantin Huygens accepted the offer and brought the negotiations to a happy end. However, news of them reached Cardinal Francesco Barberini, who immediately ordered the Inquisitor General of Florence to prevent the negotiations. Therefore, Galileo broke off the negotiations and refused the gift of the Estates General, which just these days was delivered to him by the merchant delegation.

“I have such a time meter that if we were to make 4 or 6 such instruments and run them, we would find (in confirmation of their accuracy) that the time measured and shown by them is not only from hour to hour, but from day to day , from month to month it would not differ on different devices even for a second, they would be so identical" (Le Opere di Galileo Galilei, Ediz. Naz., XVI, p. 467).

It is not difficult to realize that the time meter that Galileo mentions must have been an instrument that makes use of the isochronism of the pendulum's oscillations. Indeed, in a letter dated June 1637 to Real (or Realio - according to the accepted Italianized spelling), the governor of the Dutch Indies, Galileo reports that his clock is an application of a pendulum, and also describes a special counter for the number of oscillations. In 1641, according to Viviani, he

“... it occurred to me that we could add a pendulum to a clock with weights and a spring” (Ibid., XIX, p. 655).

Already a very old man, he entrusted these plans to his son Vincenzo (d. 1649). Father and son decided to build a mechanism (which has come down to us thanks to Viviani’s drawing) with an ingenious escapement device (the so-called “hook escapement”). The fact that Vincenzo Viviani actually built such a clock is established with certainty: this follows from the inventory of his wife’s inheritance and from the correspondence of Leopoldo de’ Medici, who sent Buillot on August 21, 1659 a drawing of the model, “drawn as crudely as the model itself.” , which is now in my room."

Christian Huygens (1629-1695) in a letter dated January 12, 1657, reported on the pendulum clock he created. In June of the same year, he received a patent for this clock, and in 1658 he published his discovery in the work “Horologium” (“Clocks”). Did Christiaan Huygens, the son of Constantin Huygens, who took a large part in Galileo’s negotiations with the Estates General and, in particular, was familiar with Galileo’s idea of using a pendulum in a clock, know about Galileo’s project? He always denied this, admitting only that the same idea occurred to him as Galileo, whose watch ran as well as his own, and said that the purpose of creating a watch, he, like Galileo, considered determining the longitude of a place on the sea.

We see no reason not to trust the Dutch scientist, whose watch design is inferior to Galileo's in the escapement mechanism, since he retained the ancient imperfect device, but significantly surpassed Galileo by replacing the weight with a spring with a balance.

6. CHRISTIAN HUYGENS

The publication of The Hours soon created such fame for Huygens that Colbert invited him to Paris in 1666, where the Paris Academy of Sciences was founded at that time (see § 14). Huygens remained there until 1681. The complicated situation due to the persecution of the Huguenots, to which Huygens belonged, forced him to wisely return to The Hague.

His 1658 work on clocks has a clearly applied nature. But a mathematician of such caliber as Huygens could not escape those theoretical problems of mechanics that are associated with the creation of clocks. He devoted subsequent years to the study of these problems. In 1673, his masterpiece was published in Paris - the work “Horologium oscillatorium, sive de motu pendulorum ad horologia aptato demonstrationes geometricae” (“Swinging clock, or on the movement of a pendulum”), consisting of five parts: a description of the clock, the movement of heavy bodies along a cycloid ; scanning and determining the length of curved lines; center of oscillation or excitation; a device of another type of clock - with a circular pendulum; theorems on centrifugal force.

Huygens was a direct successor of Galileo and Torricelli, whose theories he, in his own words, “confirmed and generalized.” Galileo founded the dynamics of only one body, while Huygens began the construction of the dynamics of several bodies.

Let us briefly dwell on the content of this work, which is of fundamental importance for the history of mechanics, while omitting the first and third parts, which are not directly related to our topic.

In the second part, after presenting the Galilean laws of the fall of heavy bodies, the proof of which he clarifies by the systematic application of the principle of addition of displacements, Huygens, with the help of remarkable reasoning of a differential geometric nature, establishes the isochronism of the oscillations of a cycloidal pendulum.

The fourth part begins with a mention that in those years when Huygens was still a youth, Mersenne suggested that he find the center of oscillation, that is, a duck on a perpendicular to the axis of oscillation drawn through the center of gravity, spaced from the axis of oscillation at a distance equal to the length a simple pendulum isochronous with a given complex pendulum.

The concept of the center of oscillation, to which Huygens gave the above definition, is found already in Galileo and repeated in Mersenne in 1646: if there were a collection of simple pendulums of various lengths, represented as heavy points suspended on weightless threads so that all would be attached to the same crossbar, then shorter pendulums would oscillate faster than longer ones. If all these pendulums were immediately fastened together so that they formed a rigid system, then they would all be forced to oscillate at the same time, shorter pendulums would accelerate the movement of longer ones, some pendulums would lose speed, others would increase it , and still others would not lose or increase. The center of oscillation is the position of the heavy point of that of the pendulums of this last group, which is located on a perpendicular to the suspension axis drawn through the center of gravity.

Guided by the above considerations, Descartes and Roberval tried to find the position of the center of oscillation, but this attempt was unsuccessful.

Huygens also took up this problem and solved it, taking Torricelli's principle as the basis for his consideration. Huygens' theory seemed unconvincing to his contemporaries, so Jacob Bernoulli developed another, more rigorous theory in 1703 and arrived at the same formula for the “reduced length” of a complex pendulum as Huygens. During the consideration of the problem, the concept of moment of inertia was introduced and the famous relation was discovered (Proposition XX by Huygens): “the center of oscillation and the point of suspension are “interconnected” (Ch. Huygens, Horologium oscillatorium, Paris, 1673, in Oeuvres completes, XVIII, La Haye, 1934, p. 305).

This relationship allows one to find the center of oscillations experimentally. In 1818, Heinrich Kater (1777-1835) used this theorem to construct a “reversible pendulum,” that is, a practical device for determining the length of a seconds pendulum and for determining the value of the acceleration of gravity at a given location. And we also owe this last use of the pendulum to Huygens.

In 1676, Jean Richet (d. 1696) was extremely surprised that a pendulum with a second period in Paris began to oscillate more slowly in Cayenne. He was shortened and, after completing the research, transported back to Paris, where, on the contrary, he began to oscillate faster. Huygens, in his work “Duscours sur la cause de la pesanteur” (“On the Cause of Gravity”), completed in 1681 and published in 1690, explained this phenomenon by a change in the value of the acceleration of gravity, which he attributed solely to variations in the centrifugal force, caused by the rotation of the Earth. This research led him to the conclusion that the Earth should be flattened at the poles and swollen at the equator. To confirm this experimentally, he set a ball of soft clay on an axis into rapid rotation and observed its flattening. As is known, this experiment is now being repeated for educational purposes with elastic steel rings placed on the axle along the diameter. This experience had a noticeable influence on the genesis of the cosmogonic theories of Kant and Laplace.

Since 1659, Huygens wrote the treatise “De vi centrifugal (“On the centrifugal force”), which was published only posthumously, in 1703. In it, Huygens examined the “striving” (conatus) of a body attached to a rotating wheel - this striving , according to Huygens, of the same nature as the desire of a heavy body to fall. What happens if a person on a spinning wheel holds in his hand a thread from which a lead ball hangs? What will happen, Huygens replies, is that the thread will be tensioned with the same force that would pull the ball if it were attached to the center of the wheel. After some geometric reasoning, Huygens comes to the conclusion:

“The conatus of a ball attached to a rotating wheel is such that the ball would tend to move uniformly accelerated along the radius... This conatus is similar to that of a heavy body suspended on a thread. From here we conclude that the centrifugal forces of unequal bodies moving at the same speed in equal circles are related to each other as the weights of these bodies, that is, as the amount of matter in them... It remains to find the value or quantity of conatus for different speeds of rotation.” (Ch. Huygens, De vi centrifuga, in Oeuvres completes, XVI, 1929, p. 266).

It remains to add that the laws determining centrifugal force, found by Huygens and given without proof at the end of The Rocking Clock, coincide with those that we can now read (with a slight change in terminology) in any elementary physics course.

After our cursory review, it is unnecessary to add that for Huygens the centrifugal force is by no means fictitious, but a very real force of the same nature as the force of gravity.

We will talk about Huygens' work on optics in the next chapter. The Dutch scientist made the greatest contribution to this area. However, we cannot complete the review of his work on mechanics without mentioning his studies of collisions of bodies.

This task presented particular difficulty for the early mechanics. Giovan Battista Bagliani dealt with it in his work “De motu gravium, solidorum” (“On the motion of solid bodies”), 1638. Galileo was going to devote the “Sixth Day” of his “Conversations” to this issue, but although in the fragments that have come down to us they may amazingly interesting experiments will inspire admiration; we will not find any solution to the problem there. As we saw earlier, the entire mechanics of Descartes crashed on this pitfall. Much more fortunate was Borelli, who discovered the laws of collision of inelastic bodies. Huygens turned to the study of the collision of elastic bodies.

In his work “De motu corporum ex percussione” (“On the motion of bodies after an impact”), completed in 1656, but published after his death, in 1700, Huygens considers this complex problem on the basis of three principles: the principle of inertia , the principle of relativity and the third principle, which we will discuss below. Here we will add that Huygens understands the principle of relativity in the sense of Descartes, that is, more widely than Galileo and Newton; in other words, Huygens does not recognize absolute motion relative to space.

The third principle (according to Huygens' numbering - the second) states that if two identical bodies with equal but oppositely directed velocities experience a central impact, then they fly away from one another with the same velocities, but changing sign. Based on these initial principles, Huygens derived the laws of collision of elastic bodies, which he then outlined in a memoir submitted in 1669 to a competition for the best paper on the theory of impact, announced by the Royal Society the year before. Also participating in this competition were John Wallis (1616-1703), who examined the collision of inelastic bodies, and Christopher Wren (1632-1723), who examined the collision of elastic bodies. Huygens's research undoubtedly significantly surpassed these two works both in the breadth of the question and in the clarity of presentation; however, sometimes clarity was achieved at the expense of brevity. Subsequent research in mechanics changed little in Huygens' laws of collision.

In the works of Wallis, Wren and Huygens, the presentation is geometric in nature. Edme Marriott (1620-1684) in his work “Traite de la percussion ou choc des corps” (“Treatise on the collision of bodies”), published posthumously in his works (Leiden, 1717), explored the same problems and purely experimentally came to approximately to the same results. To be able to arbitrarily regulate the speed of the body, Marriott came up with a device consisting of two equal pendulums that could be made to fall from an arbitrarily adjustable height. He also owns a device that is still used to demonstrate the transmission of motion by elastic bodies and consists of a number of elastic balls suspended on threads, touching each other; If you move the first ball and let it fall, the last ball will rise up while the others remain stationary.

7. CONTROVERSY ABOUT LIVING FORCE

In the above-mentioned work on the collision of bodies and in a more explicit form again in 1686, Huygens puts forward the statement that the sum of the products of “each body” by the square of its speed before and after the impact remains unchanged. Leibniz was also familiar with this conservation theorem, who, having communicated it in a letter to Huygens, made it the subject of a memoir "Demonstratio erroris memorabilis Cartesii" ("Proof of Descartes' remarkable error"), published in 1686 in "Acta eruditorum" (Scholarly Notes "). In this memoir, Leibniz calls the product of a “body” times the square of its speed “living force” and contrasts it with “dead force”, or, as we would call it now, potential energy. The first expression, as we know, has remained in science to this day with a change introduced by Gustavus Coriolis (1792-1843), who preferred to take half the product of a body’s mass by the square of its speed as a measure of living force.

So, Leibniz proposed to evaluate the “force” (we would say energy) of a falling body by the height to which this body could rise if it were thrown upward with the speed it acquired; thus, in all cases there would be equality between living force and dead force. If we evaluate “force” in this way, then from the laws of mechanics we can deduce that it is equal to the product of the “body” by the square of its speed, so that a body that doubles its speed quadruples its “force”. When bodies collide, it is not the quantity of motion that is conserved, as Descartes’ third rule states, but the sum of the living forces of the colliding bodies; This, according to Leibniz, is where Descartes’ mistake lies.

However, the Cartesians rose up against Leibniz in defense of Descartes. A lively debate ensued between the supporters of Leibniz and Descartes, which lasted over 30 years and is known in the history of physics as the “controversy about living force.”

In fact, the Cartesians drew attention to the fact that when a body thrown upward rises to its original height in twice as long and produces a quadruple effect in twice as long, this means that its “force” has not quadrupled, but only doubled. It is inappropriate to go into the technical details of the controversy here. Suffice it to say that the dispute was resolved in 1728 by Jean-Jacques de Meran (1678-1771) and even better by Jean d'Alembert (1717-1783) in the preface to his Traite de dynamique (Treatise on Dynamics), 1743 The whole dispute was based on the ambiguity in the definition of momentum. The Cartesians adhered to the scalar definition given by Descartes. De Meran showed that all examples of collisions given in the course of the controversy obey the law of conservation of momentum, if only it is understood correctly, that is, in a vector sense. Thus, finally: during an elastic impact there is both conservation of momentum and conservation of living force

CHRISTIAN HUYGENS

Christiaan Huygens von Zuylichen - son of the Dutch nobleman Constantijn Huygens, was born on April 14, 1629. “Talents, nobility and wealth were apparently hereditary in the family of Christian Huygens,” wrote one of his biographers. His grandfather was a writer and dignitary, his father was the Privy Councilor of the Princes of Orange, a mathematician, and a poet. Loyal service to their sovereigns did not enslave their talents, and it seemed that Christian was predetermined by the same, for many, enviable fate. He studied arithmetic and Latin, music and poetry. Heinrich Bruno, his teacher, could not get enough of his fourteen-year-old pupil: “I admit that Christian must be called a miracle among boys... He develops his abilities in the field of mechanics and designs, makes amazing machines, but hardly necessary.”

The teacher was wrong: the boy was always looking for benefits from his studies. His concrete, practical mind will soon find diagrams of the machines that people really need.

However, he did not immediately devote himself to mechanics and mathematics. The father decided to make his son a lawyer and, when Christian reached the age of sixteen, sent him to study law at the University of London. While studying legal sciences at the university, Huygens was at the same time interested in mathematics, mechanics, astronomy, and practical optics. A skilled craftsman, he independently grinds optical glasses and improves the pipe, with the help of which he will later make his astronomical discoveries.

Christiaan Huygens was Galileo's immediate successor in science. According to Lagrange, Huygens “was destined to improve and develop the most important discoveries of Galileo.” There is a story about how Huygens first came into contact with Galileo's ideas. Seventeen-year-old Huygens was going to prove that bodies thrown horizontally move in parabolas, but, having discovered the proof in Galileo’s book, he did not want to “write the Iliad after Homer.”

After graduating from the university, he becomes an adornment of the retinue of the Count of Nassau, who is on his way to Denmark on a diplomatic mission. The Count is not interested in the fact that this handsome young man is the author of interesting mathematical works, and he, of course, does not know how Christian dreams of getting from Copenhagen to Stockholm to see Descartes. So they will never meet: in a few months Descartes will die.

At the age of 22, Huygens published “Discourses on the square of a hyperbola, an ellipse and a circle.” In 1655, he builds a telescope and discovers one of Saturn’s moons, Titan, and publishes “New Discoveries in the Size of the Circle.” At the age of 26, Christian writes notes on dioptrics. At the age of 28, his treatise “On Calculations in the Game of Dice” was published, where behind the frivolous-looking title is hidden one of the first studies in the field of probability theory in history.

One of Huygens' most important discoveries was the invention of the pendulum clock. He patented his invention on July 16, 1657 and described it in a short essay published in 1658. He wrote about his watch to the French king Louis XIV: “My machines, placed in your apartments, not only amaze you every day with the correct indication of the time, but they are suitable, as I hoped from the very beginning, for determining the longitude of a place at sea.” Christian Huygens worked on the task of creating and improving clocks, primarily pendulum ones, for almost forty years: from 1656 to 1693. A. Sommerfeld called Huygens “the most brilliant watchmaker of all time.”

At thirty, Huygens reveals the secret of Saturn's ring. The rings of Saturn were first noticed by Galileo in the form of two lateral appendages that “support” Saturn. Then the rings were visible like a thin line, he did not notice them and did not mention them again. But Galileo's tube did not have the necessary resolution and sufficient magnification. Observing the sky through a 92x telescope, Christian discovers that the ring of Saturn was mistaken for the side stars. Huygens solved the mystery of Saturn and described its famous rings for the first time.

At that time, Huygens was a very handsome young man with large blue eyes and a neatly trimmed mustache. The reddish curls of the wig, steeply curled according to the fashion of that time, fell to the shoulders, lying on the snow-white Brabant lace of an expensive collar. He was friendly and calm. No one saw him particularly excited or confused, rushing somewhere, or, conversely, immersed in slow thought. He did not like to be in the “society” and rarely appeared there, although his origin opened the doors of all the palaces of Europe to him. However, when he appears there, he does not look at all awkward or embarrassed, as often happened with other scientists.

But in vain does the charming Ninon de Lenclos seek his company; he is invariably friendly, nothing more, this convinced bachelor. He can drink with friends, but only a little. Play a little prank, laugh a little. A little of everything, very little, so that as much time as possible remains for the main thing - work. Work - an unchanging all-consuming passion - burned him constantly.

Huygens was distinguished by his extraordinary dedication. He was aware of his abilities and sought to use them to the fullest. “The only entertainment that Huygens allowed himself in such abstract labors,” one of his contemporaries wrote about him, “was that in the intervals he studied physics. What was a tedious task for an ordinary person was entertainment for Huygens.”

In 1663, Huygens was elected a member of the Royal Society of London. In 1665, at the invitation of Colbert, he settled in Paris and the following year became a member of the newly organized Paris Academy of Sciences.

In 1673, his essay “The Pendulum Clock” was published, which gives the theoretical foundations of Huygens’ invention. In this work, Huygens establishes that the cycloid has the property of isochronism, and analyzes the mathematical properties of the cycloid.

Studying the curvilinear motion of a heavy point, Huygens, continuing to develop ideas expressed by Galileo, shows that a body, when falling from a certain height along various paths, acquires a final speed that does not depend on the shape of the path, but depends only on the height of the fall, and can rise to a height , equal (in the absence of resistance) to the initial height. This position, which essentially expresses the law of conservation of energy for motion in a gravitational field, is used by Huygens for the theory of a physical pendulum. He finds an expression for the reduced length of the pendulum, establishes the concept of the center of swing and its properties. He expresses the formula of a mathematical pendulum for cycloidal motion and small oscillations of a circular pendulum as follows: “The time of one small oscillation of a circular pendulum is related to the time of falling along the double length of the pendulum, just as the circumference of a circle is related to the diameter.”

It is significant that at the end of his work the scientist gives a number of proposals (without conclusion) about the centripetal force and establishes that centripetal acceleration is proportional to the square of the speed and inversely proportional to the radius of the circle. This result prepared Newton's theory of the motion of bodies under the action of central forces.

From Huygens' mechanical studies, in addition to the theory of the pendulum and centripetal force, his theory of the impact of elastic balls is known, which he submitted for a competitive problem announced by the Royal Society of London in 1668. Huygens' theory of impact is based on the law of conservation of living forces, momentum and Galileo's principle of relativity. It was published only after his death in 1703.

Huygens traveled quite a bit, but was never an idle tourist. During his first trip to France, he studied optics, and in London he explained the secrets of making his telescopes. He worked for fifteen years at the court of Louis XIV, fifteen years of brilliant mathematical and physical research. And in fifteen years - only two short trips to his homeland to get medical treatment.

Huygens lived in Paris until 1681, when, after the revocation of the Edict of Nantes, he, as a Protestant, returned to his homeland. While in Paris, he knew Roemer well and actively helped him in the observations that led to the determination of the speed of light. Huygens was the first to report Roemer's results in his treatise.

At home, in Holland, again not knowing fatigue, Huygens builds a mechanical planetarium, giant seventy-meter telescopes, and describes the worlds of other planets.

Huygens's work on light appears in Latin, corrected by the author and republished in French in 1690. Huygens's "Treatise on Light" entered the history of science as the first scientific work on wave optics. This Treatise formulated the principle of wave propagation, now known as Huygens' principle. Based on this principle, the laws of reflection and refraction of light were derived, and the theory of double refraction in Iceland spar was developed. Since the speed of light propagation in a crystal is different in different directions, the shape of the wave surface will not be spherical, but ellipsoidal.

The theory of propagation and refraction of light in uniaxial crystals is a remarkable achievement of Huygens' optics. Huygens also described the disappearance of one of the two rays as they passed through the second crystal at a certain orientation relative to the first. Thus, Huygens was the first physicist to establish the fact of polarization of light.

Huygens' ideas were highly valued by his successor Fresnel. He placed them above all Newton's discoveries in optics, arguing that Huygens' discovery "may be more difficult to make than all Newton's discoveries in the field of light phenomena."

Huygens does not consider colors in his treatise, nor does he consider the diffraction of light. His treatise is devoted only to the substantiation of reflection and refraction (including double refraction) from the wave point of view. This circumstance was probably the reason why Huygens' theory, despite its support in the 18th century by Lomonosov and Euler, did not receive recognition until Fresnel resurrected the wave theory on a new basis at the beginning of the 19th century.

Huygens died on July 8, 1695, when Cosmoteoros, his last book, was being printed in the printing house.

From the book Encyclopedic Dictionary (G-D) author Brockhaus F.A.

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CHRISTIAN VIII (Christian VIII, 1786–1848), King of Denmark from 183926Open Letter. Under this title was published a statement by Christian VIII on June 8, 1846, which rejected Prussian claims to Schleswig and Holstein. ? Gefl. Worte-01, S. 444. In Germany this expression occurs occasionally

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CHRISTIAN X (Christian X, 1870–1947), King of Denmark since 1912. 27 If the Germans introduce a yellow star for Jews in Denmark, my family and I will wear it as a sign of the highest distinction. Words of Christian 11 Oct. 1943? Eigen, p. 65The next day Christian actually appeared before the people on horseback with

Famous Dutch physicist, astronomer and mathematician, creator of the wave theory. In 1663 he became the first Dutch member of the Royal Society of London. Huygens studied at the University of Leiden (1645-1647) and Breda College (1647-1649), where he studied mathematical and legal sciences.

Christiaan Huygens began his scientific career at the age of 22. Lived in Paris from 1665 to 1681, from 1681 to 1695 - in The Hague. The craters of the Moon and Mars, a mountain on the Moon, an asteroid, a space probe, and a laboratory at Leiden University are named in his honor. Christian native, born on April 14, 1629 in the family of the famous, wealthy and successful privy councilor to the princes of Orange, Constantine Huygens (Heygens). His father was a well-known writer and received an excellent scientific education.

Young Huygens studied mathematics and law at the University of Leiden, after graduating from which he decided to devote his work entirely to science. In 1651, “Discourses on the quadrature of a hyperbola, ellipse and circle” were published. In 1654 - the work “On the Determination of the Size of a Circle,” which became his greatest contribution to the development of mathematical theory.

The first glory came to the young Christian after the discovery of the rings of Saturn and the satellite of this planet, Titan. According to historical data, the great Galileo also saw them. Legrange mentioned that Huygens was able to develop the most important discoveries of Galileo. Already in 1657, Huygens received a Dutch patent for the creation of a pendulum clock mechanism.

Galileo worked on this mechanism in the last years of his life, but was unable to complete the work due to blindness. The mechanism invented by Huygens made it possible to create inexpensive pendulum clocks, which were worldwide popular and widespread. The treatise “On Calculations in Dice,” published in 1657, became one of the first works in the field of probability theory.

Together with R. Hooke, he installed two constant thermometer points. In 1659, Huygens published his classic work, The System of Saturn. In it, he described his observations of the rings of Saturn and Titan, and also described the Orion Nebula and stripes on Mars and Jupiter.

In 1665, Christian Huygens was offered to become chairman of the French Academy of Sciences. He moved to Paris, where he lived, almost never leaving anywhere until 1681. Huygens was developing a “planetary machine” in 1680, which became the prototype of the modern planetarium. For this work, he created the theory of continued fractions.

Returning to Holland in 1681, due to the repeal of the Edict of Nantes, Christiaan Huygens took up optical inventions. From 1681 to 1687 The physicist was engaged in grinding and polishing large lenses with focal lengths of 37-63 meters. During the same period, Huygens designed the eyepiece famous by his name. This eyepiece is still in use today.

Christian Huygens's famous treatise, "Treatise on Light", is still famous for its fifth chapter. It describes the phenomenon of double refraction in crystals. The classical theory of refraction in uniaxial crystals is still being expounded on the basis of this chapter.

While working on his Treatise on Light, Huygens came very close to discovering the law of universal gravitation. He outlined his reasoning in the appendix “On the Causes of Gravity.” Christian Huygens's last treatise, "Cosmoteoris", was published posthumously, in 1698. The same treatise, on the plurality of worlds and their habitability, by order of Peter I, was translated into Russian in 1717.

Christiaan Huygens was always in poor health. A serious illness, with frequent complications and painful relapses, burdened his last years of life. He also suffered from feelings of loneliness and melancholy. Christiaan Huygens died in excruciating suffering on July 8, 1695.

Many of Huygens' works are now of exceptional historical value. His theory of rotating bodies and his enormous contribution to the theory of light are of scientific importance to this day. These theories have become the most brilliant and unusual contributions to modern science.

Christiaan Huygens is a Dutch scientist, mathematician, astronomer and physicist, one of the founders of wave optics. In 1665-81 he worked in Paris. Invented (1657) a pendulum clock with an escapement mechanism, gave its theory, established the laws of oscillation of a physical pendulum, and laid the foundations of the theory of impact. Created (1678, published 1690) the wave theory of light, explained double refraction. Together with Robert Hooke, he established constant thermometer points. Improved the telescope; designed an eyepiece named after him. The ring around Saturn was also discovered by its satellite Titan. Author of one of the first works on probability theory (1657).

Early awakening of talents

The ancestors of Christiaan Huygens occupied a prominent place in the history of his country. His father Konstantin Huygens (1596-1687), in whose house the future famous scientist was born, was a widely educated man, knew languages, and was fond of music; after 1630 he became an adviser to William II (and subsequently William III). King James I elevated him to the rank of knight, and Louis XIII awarded him the Order of St. Michael. His children - 4 sons (the second is Christian) and one daughter - also left a good mark on history.

Christian's talent manifested itself at an early age. At the age of eight he had already studied Latin and arithmetic, studied singing, and at the age of ten he became acquainted with geography and astronomy. In 1641, his teacher wrote to the child’s father: “I see and almost envy Christian’s remarkable memory,” and two years later: “I confess that Christian must be called a miracle among boys.”

And Christian at this time, having studied Greek, French and Italian and mastered playing the harpsichord, became interested in mechanics. But not only this: he also enjoys swimming, dancing and horse riding. At the age of sixteen, Christiaan Huygens, together with his older brother Konstantin, entered the University of Leiden to study law and mathematics (the latter was more willing and successful; the teacher decided to send one of his works to Rene Descartes).

After 2 years, the older brother begins to work for Prince Frederick Henrik, and Christian and his younger brother move to Breda, to the “Oran College”. Christian's father also prepared him for public service, but he had other aspirations. In 1650, he returned to The Hague, where his scientific work was hampered only by headaches that had haunted him for some time.

The more difficult the task of determining by reasoning what seems uncertain and subject to chance, the more amazing is the science that achieves the result.

Huygens Christian

First scientific works

The range of scientific interests of Christian Huygens continued to expand. He is interested in the works of Archimedes on mechanics and Descartes (and later other authors, including the Englishmen Newton and Hooke) on optics, but does not stop studying mathematics. In mechanics, his main research concerns the theory of impact and the problem of clock construction, which at that time had extremely important applied significance and always occupied one of the central places in Huygens’ work.

His first achievements in optics can also be called “applied”. Together with his brother Constantine, Christian Huygens is engaged in the improvement of optical instruments and achieves significant success in this area (this activity does not stop for many years; in 1682 he invents a three-lens eyepiece, which still bears his name. While improving telescopes, Huygens, however, in “Dioptrics” " wrote: "... a person: who could invent a spyglass, based only on theory, without the intervention of chance, would have to have a superhuman mind").

New instruments allow important observations to be made: March 25, 1655 Huygens discovers Titan, the largest satellite of Saturn (whose rings he had been interested in for a long time). In 1657, another work by Huygens, “On Calculations in Dice,” appeared - one of the first works on probability theory. He writes another essay, “On the Impact of Bodies,” for his brother.

In general, the fifties of the 17th century were the time of Huygens's greatest activity. He gains fame in the scientific world. In 1665 he was elected a member of the Paris Academy of Sciences.

"Huygens' principle"

H. Huygens studied Newton's optical works with unflagging interest, but did not accept his corpuscular theory of light. Much closer to him were the views of Robert Hooke and Francesco Grimaldi, who believed that light has a wave nature.

But the idea of light as a wave immediately gave rise to many questions: how to explain the rectilinear propagation of light, its reflection and refraction? Newton gave seemingly convincing answers to them. Straightness is a manifestation of the first law of dynamics: light corpuscles move uniformly and in a straight line unless they are acted upon by any forces. Reflection was also explained as the elastic rebound of corpuscles from the surfaces of bodies. The situation with refraction was somewhat more complicated, but here, too, Newton offered an explanation. He believed that when a light corpuscle flies up to the boundary of a body, an attractive force from the substance begins to act on it, imparting acceleration to the corpuscle. This leads to a change in the direction of the corpuscle's speed (refraction) and its magnitude; therefore, according to Newton, the speed of light in glass, for example, is greater than in vacuum. This conclusion is important if only because it allows for experimental verification (later experience refuted Newton’s opinion).

Christian Huygens, like his predecessors mentioned above, believed that all space is filled with a special medium - ether, and that light is waves in this ether. Using an analogy with waves on the surface of water, Huygens came to the following picture: when the front (i.e., the leading edge) of the wave reaches a certain point, i.e., the oscillations reach this point, then these oscillations become the centers of new waves diverging in all directions , and the movement of the envelope of all these waves gives a picture of the propagation of the wave front, and the direction perpendicular to this front is the direction of propagation of the wave. So, if the wave front in vacuum is flat at some moment, then it always remains flat, which corresponds to the rectilinear propagation of light. If the front of the light wave reaches the boundary of the medium, then each point on this boundary becomes the center of a new spherical wave, and by constructing the envelopes of these waves in space both above and below the boundary, it is not difficult to explain both the law of reflection and the law of refraction (but at In this case, we have to accept that the speed of light in a medium is n times less than in a vacuum, where n is the same refractive index of the medium that is included in the law of refraction recently discovered by Descartes and Snell).

It follows from Huygens' principle that light, like any wave, can bend around obstacles. This phenomenon, which is of fundamental interest, does exist, but Huygens considered that the “side waves” that arise during such a bending do not deserve much attention.

Christian Huygens' ideas about light were far from modern. Thus, he believed that light waves are longitudinal, i.e. that the directions of oscillations coincide with the direction of wave propagation. This may seem all the more strange since Huygens himself apparently already had an idea of the phenomenon of polarization, which can only be understood by considering transverse waves. But this is not the main thing. Huygens' principle had a decisive influence on our ideas not only about optics, but also about the physics of any oscillations and waves, which now occupies one of the central places in our science. (V.I. Grigoriev)

More about Christian Huygens:

Christian Huygens von Zuylichen - son of the Dutch nobleman Constantijn Huygens “Talents, nobility and wealth were apparently hereditary in the family of Christian Huygens,” wrote one of his biographers. His grandfather was a writer and dignitary, his father was the Privy Councilor of the Princes of Orange, a mathematician, and a poet. Loyal service to their sovereigns did not enslave their talents, and it seemed that Christian was predetermined by the same, for many, enviable fate. He studied arithmetic and Latin, music and poetry. Heinrich Bruno, his teacher, could not get enough of his fourteen-year-old pupil:

“I confess that Christian must be called a miracle among boys... He develops his abilities in the field of mechanics and structures, makes amazing machines, but hardly necessary.” The teacher was wrong: the boy was always looking for benefits from his studies. His concrete, practical mind will soon find diagrams of the machines that people really need.

However, he did not immediately devote himself to mechanics and mathematics. The father decided to make his son a lawyer and, when Christian reached the age of sixteen, sent him to study law at the University of London. While studying legal sciences at the university, Huygens was at the same time interested in mathematics, mechanics, astronomy, and practical optics. A skilled craftsman, he independently grinds optical glasses and improves the tube, with the help of which he will later make his astronomical discoveries.

Christiaan Huygens was the immediate successor of Galileo-Galilei in science. According to Lagrange, Huygens “was destined to improve and develop the most important discoveries of Galileo.” There is a story about how Huygens first came into contact with Galileo's ideas. Seventeen-year-old Huygens was going to prove that bodies thrown horizontally move in parabolas, but, having discovered the proof in Galileo’s book, he did not want to “write the Iliad after Homer.”

After graduating from the university, Christiaan Huygens becomes an adornment of the retinue of the Count of Nassau, who is on his way to Denmark on a diplomatic mission. The Count is not interested in the fact that this handsome young man is the author of interesting mathematical works, and he, of course, does not know how Christian dreams of getting from Copenhagen to Stockholm to see Descartes. So they will never meet: in a few months Descartes will die.

At the age of 22, Christiaan Huygens published “Discourses on the square of a hyperbola, an ellipse and a circle.” In 1655, he builds a telescope and discovers one of Saturn’s moons, Titan, and publishes “New Discoveries in the Size of the Circle.” At the age of 26, Christian writes notes on dioptrics. At the age of 28, his treatise “On Calculations in the Game of Dice” was published, where behind the frivolous-looking title is hidden one of the first studies in history in the field of probability theory.

One of Huygens' most important discoveries was the invention of the pendulum clock. He patented his invention on July 16, 1657 and described it in a short essay published in 1658. He wrote about his watch to the French king Louis XIV: “My machines, placed in your apartments, not only amaze you every day with the correct indication of the time, but they are suitable, as I hoped from the very beginning, for determining the longitude of a place at sea.” Christian Huygens worked on the task of creating and improving clocks, primarily pendulum clocks, for almost forty years: from 1656 to 1693. A. Sommerfeld called Huygens “the most brilliant watchmaker of all time.”

At thirty, Christiaan Huygens reveals the secret of Saturn's ring. The rings of Saturn were first noticed by Galileo in the form of two lateral appendages that “support” Saturn. Then the rings were visible like a thin line, he did not notice them and did not mention them again. But Galileo's tube did not have the necessary resolution and sufficient magnification. Observing the sky through a 92x telescope. Christian discovers that the ring of Saturn was mistaken for the side stars. Huygens solved the mystery of Saturn and described its famous rings for the first time.

At that time, Christiaan Huygens was a very handsome young man with large blue eyes and a neatly trimmed mustache. The reddish curls of the wig, steeply curled according to the fashion of that time, fell to the shoulders, lying on the snow-white Brabant lace of an expensive collar. He was friendly and calm. No one saw him particularly excited or confused, rushing somewhere, or, conversely, immersed in slow reverie. He did not like to be in the “society” and rarely appeared there, although his origin opened the doors of all the palaces of Europe to him. However, when he appears there, he does not look at all awkward or embarrassed, as often happened with other scientists.

Christiaan Huygens was distinguished by his extraordinary dedication. He was aware of his abilities and sought to use them to the fullest. “The only entertainment that Huygens allowed himself in such abstract labors,” one of his contemporaries wrote about him, “was that in the intervals he studied physics. What was a tedious task for an ordinary person was entertainment for Huygens.”

Studying the curvilinear motion of a heavy point, Huygens, continuing to develop ideas expressed by Galileo, shows that a body, when falling from a certain height along various paths, acquires a final speed that does not depend on the shape of the path, but depends only on the height of the fall, and can rise to a height , equal (in the absence of resistance) to the initial height. This position, which essentially expresses the law of conservation of energy for motion in a gravitational field, is used by Huygens for the theory of a physical pendulum. He finds an expression for the reduced length of the pendulum, establishes the concept of the center of swing and its properties. He expresses the mathematical pendulum formula for cycloidal motion and small oscillations of a circular pendulum as follows:

“The time of one small oscillation of a circular pendulum is related to the time of falling along twice the length of the pendulum, just as the circumference of a circle is related to the diameter.”

From the mechanical studies of Christiaan Huygens, in addition to the theory of the pendulum and centripetal force, his theory of the impact of elastic balls is known, which he submitted for a competitive problem announced by the Royal Society of London in 1668. Huygens' theory of impact is based on the law of conservation of living forces, momentum and Galileo's principle of relativity. It was published only after his death in 1703. Huygens traveled quite a bit, but was never an idle tourist. During his first trip to France, he studied optics, and in London he explained the secrets of making his telescopes. He worked for fifteen years at the court of Louis XIV, fifteen years of brilliant mathematical and physical research. And in fifteen years - only two short trips to his homeland to get medical treatment

Christiaan Huygens lived in Paris until 1681, when, after the revocation of the Edict of Nantes, he, as a Protestant, returned to his homeland. While in Paris, he knew Roemer well and actively helped him in the observations that led to the determination of the speed of light. Huygens was the first to report Roemer's results in his treatise.

At home, in Holland, again not knowing fatigue, Huygens builds a mechanical planetarium, giant seventy-meter telescopes, and describes the worlds of other planets.

The theory of propagation and refraction of light in uniaxial crystals is a remarkable achievement of Huygens' optics. Christiaan Huygens also described the disappearance of one of the two rays when they passed through the second crystal with a certain orientation relative to the first. Thus, Huygens was the first physicist to establish the fact of polarization of light.

Huygens does not consider colors in his treatise, nor does he consider the diffraction of light. His treatise is devoted only to the substantiation of reflection and refraction (including double refraction) from the wave point of view. This circumstance was probably the reason why Huygens' theory, despite its support in the 18th century by Lomonosov and Euler, did not gain recognition until Fresnel resurrected the wave theory on a new basis at the beginning of the 19th century.

Christiaan Huygens died on June 8, 1695, when KosMoteoros, his last book, was being printed at the printing house. (Samin D.K. 100 great scientists. - M.: Veche, 2000)

More about Christian Huygens:

Huyghens (Christian Huyghensvan Zuylichem), - mathematician, astronomer, and physicist, whom Newton recognized as great. His father, Signor van Zuylichem, secretary of the princes of Orange, was a remarkable writer and scientifically educated.

Christian Huygens began his scientific activity in 1651 with an essay on the squaring of the hyperbola, ellipse and circle; in 1654 he discovered the theory of evolutes and involutes, in 1655 he discovered the satellite of Saturn and the type of rings, in 1659 he described the system of Saturn in a work he published. In 1665, at the invitation of Colbert, he settled in Paris and was accepted as a member of the Academy of Sciences.

Clocks with wheels driven by weights have been in use for a long time, but the regulation of the speed of such clocks was unsatisfactory. Since the time of Galileo, the pendulum has been used separately to accurately measure short periods of time, and it was necessary to count the number of swings. In 1657, Christiaan Huygens published a description of the structure of the pendulum clock he invented. The famous work Horologium oscillatorium, sive de mota pendulorum an horologia aptato demonstrationes geometrica, which he published later, in 1673, in Paris, containing a statement of the most important discoveries in dynamics, in its first part also contains a description of the structure of clocks, but with the addition improvements in the method of pendulum weighting, making the pendulum cycloidal, which has a constant swing time, regardless of the swing. To explain this property of a cycloidal pendulum, the author devotes the second part of the book to deducing the laws of the fall of bodies that are free and moving along inclined straight lines, and finally along a cycloid. Here, for the first time, the beginning of the independence of movements is clearly expressed: uniformly accelerated due to the action of gravity, and uniform due to inertia.

Christian Huygens proves the laws of uniformly accelerated motion of freely falling bodies, based on the principle that the action imparted to a body by a force of constant magnitude and direction does not depend on the magnitude and direction of the speed that the body already possesses. Deriving the relationship between the height of the fall and the square of time, Huygens makes the remark that the heights of the falls are related as the squares of the acquired velocities. Further, considering the free movement of a body thrown upward, he finds that the body rises to the greatest height, having lost all the speed imparted to it and acquires it again when returning back.

Galileo admitted without proof that when bodies fall along differently inclined straight lines from the same height, they acquire equal speeds. Christiaan Huygens proves this as follows. Two straight lines of different inclinations and equal heights are placed with their lower ends next to each other. If a body launched from the upper end of one of them acquires a greater speed than one launched from the upper end of the other, then it can be launched along the first from such a point below the upper end that the speed acquired below is sufficient to lift the body to the upper end of the second line, but then it would turn out that the body rose to a height greater than the one from which it fell, but this cannot be.

From the movement of a body along an inclined straight line, H. Huygens moves on to movement along a broken line and then to movement along any curve, and proves that the speed acquired when falling from any height along a curve is equal to the speed acquired during a free fall from the same height along a vertical line and that the same speed is required to lift the same body to the same height, both along a vertical straight line and along a curve.

Then, moving on to the cycloid and considering some of its geometric properties, the author proves the tautochronism of the movements of the heavy point along the cycloid. The third part of the work sets out the theory of evolutes and involutes, discovered by the author back in 1654; Here Christians find the type and position of the cycloid evolute.

The fourth part sets out the theory of the physical pendulum; here Christiaan Huygens solves the problem that was not given to so many geometers of his time - the problem of determining the center of swing. It is based on the following proposition: “If a complex pendulum, having left rest, has completed some part of its swing, greater than the half-swing, and if the connection between all its particles is destroyed, then each of these particles will rise to such a height that their common center of gravity will be at the height at which it was when the pendulum left rest. This proposition, not proven by Christiaan Huygens, appears to him as a basic principle, while now it represents the application of the law of conservation of energy to a pendulum. The theory of the physical pendulum was given by Huygens in a completely general form and applied to bodies of various kinds. In the last, fifth part of his work, the scientist gives thirteen theorems on centrifugal force and examines the rotation of a conical pendulum.

Another remarkable work of Christian Huygens is the theory of light, published in 1690, in which he sets out the theory of reflection and refraction and then double refraction in Iceland spar in the same form as it is now presented in physics textbooks. Of the others discovered by H. Huygens, we will mention the following.

The discovery of the true appearance of Saturn's rings and its two moons, made with the help of a ten-foot telescope, built by him. Together with his brother, Christiaan Huygens was engaged in the manufacture of optical glasses and significantly improved their production. The ellipsoidal shape of the earth and its compression at the poles were discovered theoretically, as well as an explanation of the influence of centrifugal force on the direction of gravity and on the length of the second pendulum at different latitudes. Solving the problem of the collision of elastic bodies simultaneously with Wallis and Brenn.

Christiaan Huygens invented the clock spiral, replacing the pendulum; the first clock with a spiral was built in Paris by watchmaker Thuret in 1674. He also owned one of the solutions to the problem of the form of a heavy homogeneous chain in equilibrium.

Christiaan Huygens - quotes

The more difficult the task of determining by reasoning what seems uncertain and subject to chance, the more amazing is the science that achieves the result.