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Mr Leibnitz was is first to suggest that the force of a moving body is not proportional to the velocity according to general understanding but to the square; so if one doubles the velocity then the force is quadrupled

Willem ’s Gravesande He dropped brass balls with varying velocity onto a soft clay surface and showed experimentally that: a ball with twice the velocity of another left an indentation four times as deep, one three times the velocity yielded one nine times the depth etc

4 D - s’Gravesande dropped a brass ball into soft clay to check 3 D - - v 2 D - - √ 2 v 1 D - - √ 3 v E = ½ mv 2 1 D - E = ½ mv 2 1 d - - v - 2 v 1 d 2 d 3 d 4 d - E = ½ m 4 v 2 4 x the depth

v = k√d 0 - Distance dropped in arbitrary units 1. 0 √ 1 = 1. 0 2. 0 √ 2 = 1. 414 3. 0 √ 3 = 1. 732 4. 0 √ 4 = 2. 0 Relative Velocity

So s’Gravesande should be a hero of Classical Physics as he checked to see if Newton’s theory is correct experimentally s’Gravesande experiment ≡ Higgs experiment

Willem ’s Gravesande His chief contribution to Physics involved an experiment in which brass balls were dropped with varying velocity onto a soft clay surface. His results were that a ball with twice the velocity of another would leave an indentation four times as deep, that three times the velocity yielded nine times the depth, and so on.

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Newton in the Netherlands The Dutch have on occasion prided themselves on the Low Countries being the pivot of intellectual and cultural Europe. The extent of the Dutch cultural area may indeed be small in comparison with that of neighbouring countries such as Germany, France and England, but by the very fact of its central situation the Netherlands was thought to occupy a special position. Ideas from the surrounding cultural areas are absorbed, digested and passed on again to others, the Dutch détour thus making possible an intensive cultural and intellectual exchange. This view was especially popular in the first half of this century and was based more on a self-centred neutralist mentality - the Netherlands, with its own partieular mission, stood outside the power politics of the great nations, or so people thought - than on an impartial evaluation of its own cultural history. The fact was that, in most cases, cultural exchange between European nations took place in an entirely natural manner without the Netherlands as intermediary; the notion of the Netherlands as the pivot for ideas from other countries was largely an illusion. But this was not always the case. Instances can be found in history where the Low Countries did indeed fulfil such a function. One such example is the reception and diffusion of the ideas of

But this was not always the case. Instances can be found in history where the Low Countries did indeed fulfil such a function. One such example is the reception and diffusion of the ideas of the English mathematician and physicist Isaac Newton (16421727). His ideas, which were the crowning achievement of the Scientific Revolution of the seventeenth century, were diametrically opposed to those which people were accustomed to at that time. Initially, therefore, a great deal of reserve could be perceived amongst leading scientists throughout Europe. It is partly or even mainly thanks to intellectual circles in the Dutch Republic that Newton's ideas were after all accepted in the rest of Europe; Dutch scientists and Dutch manuals were responsible for the spread of Newtonianism through Europe. For once, the Netherlands was indeed the pivot of intellectual Europe. Yet in the Republic, too, there were grave doubts about the value of Newton's natural philosophy. Just as in other countries, the history of Newtonianism was preceded by the history of antinewtonianism. The only difference was that here the latter was of comparatively short duration. [p. 187] The reservations were principally based on the fact that in his great work, the Philosophiae naturalis principia mathematica

[p. 187] The reservations were principally based on the fact that in his great work, the Philosophiae naturalis principia mathematica (Mathematical Principles of Natural Philosophy) of 1687, Newton had introduced a notion which appeared irreconcilable with current ideas and views in physics. Newton had advanced theory that two physical bodies (for example the earth and the moon) mutually attract each other (he called this force attraction or gravitation), but without giving any mechanical explanation for this phenomenon. However, in the seventeenth century such an explanation was a sine qua non for any proper account of physical phenomena. People were no longer satisfied with what they considered to be all sorts of purely verbal elucidations derived from Aristotelian natural philosophy; they had determined that natural phenomena could be explained only in terms of the pressure, push or collision of physical bodies. For one body to act on the other, direct contact was always necessary; influence through a void, or ‘actio in distans’, was inconceivable and therefore scientifically unacceptable. Various systems of natural philosophy had been formulated on the

illustratie Isaac Newton (1642 -1727) by L. Delvaux. Museum voor Kunst en Geschiedenis, Brussels (Photo acl, Brussels). [p. 188] illustratie Willem Jacob 's Gravesande (1688 -1742) (Photo Atlas Van Stolk, Rotterdam). basis of this premise. The best known was that of the French philosopher René Descartes, laid down in his Principia philosophiae (1644), which was regarded as the model for the mechanistic natural philosophy of the seventeenth century. Descartes proceeded on the assumption of a completely filled space, but there were others who preferred to assume that there were small particles of matter (we should say atoms) in an otherwise empty space. But the only explanations which everybody accepted were those based on the effects of contact between these small particles. And it was precisely on this point that Newton diverged from the orthodox mechanistic views of the seventeenth century: his gravity was indeed effective through the void, here it was indeed a question of ‘actio in distans’.

It is therefore quite understandable that Newton's Principia could at best count on a mixed reception among leading scientists in Europe. The assessment of Christiaan Huygens (1629 -1695), around 1690 still the uncrowned monarch of European natural philosophy, was typical. In principle, an anti-Cartesian work such as Newton's could be assured of a positive reception from Huygens. In his earlier years he had been a staunch supporter of the Cartesian doctrine, but as he grew older his doubts increased; he became less and less convinced that Descartes' theories were always correct. Moreover, Huygens was well acquainted with English natural philosophy. He had been in England, and maintained close contacts with the Royal Society and a number of English physicists. However, Huygens was sharply opposed to Newton's conception of gravitation. He wrote to the German philosopher [p. 189]

NLeibniz: ‘I am not at all happy with the explanation which Mr Newton gives us for the tides, nor with all the other theories which he bases on his principle of gravitation, which seems to me absurd. ’ Other people in the Republic were of the same opinion. The Leiden professor Burchardus de Volder (1643 -1709), who like Huygens had excellent contacts in English scientific circles and was himself in correspondence with Newton, could not be won over to Newton's new ideas, despite his admiration for Newton's mathematical genius and his increasing reservations regarding the Cartesian system. The best Newton could count on was an obligatory reference to his contribution to experimental science, such as the mention made of him by the well known Leiden medical professor Herman Boerhaave (1668 -1738) in his academic orations in the period round 1700; but in these cases Newton was always referred to in the same breath as numerous others, of whom Bacon and Boyle could expect much more sympathy from Boerhaave. In this initial period, positive interest in Newton's unorthodox ideas was only to be found amongst those on the fringes of the scientific world. It was only around 1710 that any change began to take place in the mainly hostile attitude of Dutch scientists. A particularly acrimonious dispute between Newton and Leibniz about priority in the discovery of differential and integral calculus led incidentally to increasing discussion of Newton's theory of gravitation. Newton's opponents tried to destroy the credibility of his claims in the mathematical field by demonstrating the absurdity of his ideas in the realm of natural philosophy. However, these tactics only resulted in Newton's ideas receiving more attention, being seriously discussed and also, for the first time, beginning to gain supporters. An important role in this change of attitude was played by the Journal littéraire, which was published in The Hague. In 1712 and 1713 one of the editors, Willem Jacob 's Gravesande (1688 -1742), originally a lawyer, but keenly interested in mathematics and natural science, published some articles in which he attempted to find a way out of the senseless wrangling between the supporters of Newton and of Leibniz. In this context 's Gravesande also included a discussion of Newton's natural philosophy. One reason why the Journal littéraire, in particular, sought to play such a mediatory role, was the fact that the paper was in part run by French Huguenots who had fled to the Republic after Louis xiv's revocation of the Edict of Nantes in 1685. It was greatly in the interests of the Huguenots to help maintain and strengthen the Anglo-Dutch coalition against France, which had been formed when William iii crossed to England in 1688. In this connection it was also to their advantage to encourage intellectual contacts between the Republic and England. Thus the particular political constellation of the time was a crucial element in the Dutch role as go-betweens in disseminating Newton's ideas in the rest of Europe. But all this would still not have been enough if Newton himself had not produced a second edition of his Principia, adding a new general discussion (Scholium Generale) in which he attempted to remove the objections to his principle of gravitation. More emphatically than in his earlier writings he stated that his new principle was purely a mathematical notion, that is to say a notion which described the phenomena without at the same time giving a [p. 190] deeper explanation, whether in the mechanistic or the non-mechanistic sense. He did not intend to venture such a speculative explanation: ‘I do not feign hypotheses’, he wrote. In fact he believed that the physicist, too, should be satisfied with the mathematical description of the phenomena observed; it was not given to man, but reserved exclusively for God, to penetrate deeper into reality. Newton thus not only removed some of the misunderstandings, but also made his modest, almost positivist point of view into a programme with a broader, even religious purport. To fathom the ultimate structure of the world was no longer the objective of physics; such a desire was on the contrary a sign of hubris, an attempt to penetrate a realm which God had reserved for himself. The emphasis was all on the phenomena to be observed and their interrelationships, not on the hidden structures behind them. With this explanation of his natural philosophical standpoint Newton associated himself with an anti-rationalist trend in the Republic's intellectual life which was becoming apparent in the same period. Instead of the rational scrutiny of nature, people began to lay ever increasing emphasis on the pure observation of, and sometimes even humble reflections on, the wonders of nature. This change was manifest in, amongst other things, the rise of so-called physico-theology, a movement within popular physics in which natural phenomena were interpreted as proof of the omnipotence and providence of God. The existence of an all-wise Creator was deduced from the visible method and order in nature; nature, so people thought, could be interpreted as a second revelation of God. This way of thinking had made considerable headway in England at the end of the seventeenth century; from there it had been propagated in the Netherlands, though here it also had original Dutch representatives. There was such a degree of correspondence between this movement on the one hand Newton's natural philosophy on the other hand, that the popularity of the one was conducive to the popularity of the other.

With this explanation of his natural philosophical standpoint Newton associated himself with an anti-rationalist trend in the Republic's intellectual life which was becoming apparent in the same period. Instead of the rational scrutiny of nature, people began to lay ever increasing emphasis on the pure observation of, and sometimes even humble reflections on, the wonders of nature. This change was manifest in, amongst other things, the rise of so-called physico-theology, a movement within popular physics in which natural phenomena were interpreted as proof of the omnipotence and providence of God. The existence of an all-wise Creator was deduced from the visible method and order in nature; nature, so people thought, could be interpreted as a second revelation of God. This way of thinking had made considerable headway in England at the end of the seventeenth century; from there it had been propagated in the Netherlands, though here it also had original Dutch representatives. There was such a degree of correspondence between this movement on the one hand Newton's natural philosophy on the other hand, that the popularity of the one was conducive to the popularity of the other. After the publication of the second edition of the Principia the spread of Newtonianism in the Republic gained momentum. A pirate version of the second edition had already been published in Amsterdam in 1714. In leading journals there was suddenly a great deal of interest in the work of Newton and his followers and one by one the universities were converted to Newton's point of view. Boerhaave began to praise Newton to the skies and in 1717 the long vacant chair of De Volder was filled by the appointment of 's Gravesande. As secretary to the Dutch diplomatic mission in London he had made Newton's acquaintance in 1715, and since then had been completely won over to the Newtonian philosophy. In 1720 he was already publishing his Leiden lectures under the self-explanatory title Mathematical Principles of Physics, Confirmed by Experiments. Or an Introduction to Newtonian Natural Philosophy. At that time he had the reputation of being the person best able to explain to a public not fully versed in the mathematical niceties of the Principia what the significance of the work was and what results Newton had achieved. Not only did students from the Netherlands and abroad come to listen to his explanation, but such a well-known intellectual as Voltaire also came to Leiden especially to follow 's Gravesande's lectures. Those who could not come to Leiden could [p. 191] acquaint themselves with 's Gravesande's views in other ways, for his books had been translated into many languages. And not only his books, but also those of other Newtonians, such as his pupil and fellowprofessor Petrus van Musschenbroek (1692 -1761), whose works achieved if possible even greater popularity. Did scholars such as 's Gravesande and Van Musschenbroek merely pass on what they had discovered in Newton, or did they set their own stamp on it? The latter is certainly the case. As can be deduced from the title of 's Gravesande's book, the Dutch Newtonians tried above all to steer clear of the knotty problems of higher mathematics and convince their listeners and readers of the truth of Newton's views through experimental demonstration. In the writings of a man such as Van Musschenbroek we may even detect a definite Baconian tint to a natural philosophy which was in essence strictly mathematical. This not only made a concession to the powers of comprehension of students and others with enquiring minds, but also forged a link with the prevailing physico-theological trend. And thus Newton, divested of the difficult mathematical figures and formulae, began his triumphal progress through Europe. This is how Voltaire, after his return from Leiden, presented Newton to his French readers; and this is how the Italian abbot Algarotti presented Newton to his female readers in his highly popular Il Newtonianismo per le dame (1737). k. van berkel Translated by Rachel van der Wilden. http: //www. dbnl. org/tekst/_low 001199301_01_0027. php

Still No Equation!

2 D - Experiment to prove E = ½ mv 2 1 D - 1 d - 1 D - 1 d 2 d 3 d 4 d - s’Gravesande dropped brass balls into soft clay

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2 (mathématiques) faire la quadrature de, construire un carré de même surface qu'une figure délimitée par une courbe fermée

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Gabrielle Émilie Le Tonnelier de Breteuil, marquise du Châtelet (17 December 1706, Paris – 10 September 1749, Lunéville) was a French mathematician, physicist, and author during the Age of Enlightenment. Her crowning achievement is considered to be her translation and commentary on Isaac Newton's work Principia Mathematica. The translation, published ten years after her death in 1759, is still considered the standard French translation. Voltaire, one of her lovers, declared in a letter to his friend King Frederick II of Prussia that du Châtelet was "a great man whose only fault was being a woman". [1][2] http: //en. wikipedia. org/wiki/%C 3%89 milie_du_Ch%C 3%A 2 telet

1675: Newton begins his fundamental work on the topic and eventually lays the foundation of classical interpolation theory. His contributions can be found in: A letter to Smith, dated May 8, 1675, and also a letter to Oldenburg, dated October 24, 1676, in the latter of which he wrote: (. . . ) I have another method not yet published by which the problem is easily dealt with. It is based upon a convenient, ready and general solution of this problem. To describe a geometrical curve which shall pass through any given points. (. . . ) Although it may seem to be intractable at first sight, it is nevertheless quite the contrary. Perhaps indeed it is one of the prettiest problems that I can ever hope to solve. A manuscript entitled Methodus Differentialis, published in 1711, but probably written in the mid-1670 s.

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