Gresham GI Special Edition Stainless Steel Tonnaeu Case White and Blue Colourway Watch G1-0001-WHT

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This lecture is part of the seriesThe Victorians: Culture and Experience in Britain, Europe and the World 1815-1914

Spiral-like shapes crop up regularly in nature. There’s a particular kind of spiral, called a logarithmic spiral that was familiar to Wren. Logarithmic spirals were first mentioned by the German artist and engraver Albrecht Durer, and studied in great detail by the mathematician Jacob Bernoulli – he gave them the name “spira mirabilis”, or “miraculous spiral”. In a logarithmic spiral, the distance r from the centre is a power of the angle we’ve moved through (or conversely the angle is a logarithm of the distance, hence the name). This means that the gap between consecutive rings of the spiral is increasing each time. One example of a logarithmic spiral, shown below, is r= 2 θ/360(where we are measuring our angles in degrees). With every complete revolution, the distance of the spiral from the origin doubles. It crosses the x -axis at 1, 2, 4, 8, 16 and so on.When buying a luxury watch, the brand is a key factor. Whether you're a loyal collector or looking for fashion-forward, we have a wide range of designer watches from leading brands such as Rolex, Tag Heuer, Omega and Breitling. All of our watches are individually assessed and valued by our expert buyers to ensure pristine quality. Shop by Watch Movement Wren’s solution of Kepler’s problem manages to relate the areas into which the semicircle must be divided to lengths of specific circle arcs. These are then equated to carefully positioned “stretched” or “prolate” cycloids – which of course Wren already knew how to find the length of, from his own earlier work. And so he was able to solve Kepler’s problem. His solution was published by John Wallis in a 1659 treatise on the cycloid (which also included Wren’s rectification of the cycloid). If your Latin is tip-top, you can give it a read: John Wallis: Tractatus duo, prior de cycloide et corporibus inde genetis: posterior, epistolaris in qua agitur de cissoide. In a 1668 letter, the English mathematician John Wallis said that although the challenge of Kepler’s problem had been issued to the French mathematicians almost a decade previously, “there is none of them have yet (that I hear of) returned any solution”. Take that, Jean de Montfort! Christopher Wren, who died 300 years ago this year, is famed as the architect of St Paul’s Cathedral. But he was also Gresham Professor of Astronomy, and one of the founders of a society “for the promotion of Physico-Mathematicall Experimental Learning” which became the Royal Society.

The three conics, by Pbroks13, CC BY 3.0, via Wikimedia Commons https://commons.wikimedia.org/wiki/File:Conic_sections_with_plane.svg Within major cities, tram systems, and suburban and underground railways began to speed up traffic, just as the main roads were becoming clogged with horse-drawn cabs and carriages, automobiles and omnibuses. In 1863 the world's first underground railway, the Metropolitan, opened in London, and was soon extended, but steam locomotives posed many problems, and the cut-and-cover method of construction soon ran out of roads that could be dug up, and London turned to boring deeper lines for 'tube' trains powered by electricity, the first of which was opened in 1890. Above ground, the electric tramway system devised by Werner von Siemens began running in Berlin in 1879, and soon spread to many other countries. We remember Christopher Wren as a great architect. But he was so much more. Today I’m going to tell you about Christopher Wren the mathematician. We’ll look at his work on curves including spirals and ellipses, and we’ll see some of the mathematics behind his most impressive architectural achievement – the dome of St Paul’s Cathedral.This course of lectures looks at the Victorians not just in Britain but in Europe and the wider world. 'Victorian' has come to stand for a particular set of values, perceptions and experiences, many of which were shared by people in a variety of different countries, from Russia to America, Spain to Scandinavia and reflected in the literature and culture of the nineteenth century, up to the outbreak of the First World War. The focus of the lectures will be on identifying and analysing six key areas of the Victorian experience, looking at them in international perspective. The lectures will be illustrated and the visual material will form a key element in the presentations. Throughout the series, we will be asking how far, in an age of growing nationalism and class conflict, the experiences of the Victorian era were common to different classes and countries across Europe and how far the political dominance of Britain, the world superpower of the day, was reflected in the spread of British culture and values to other parts of the world.

Keen to recapture the initiative from the British, the French government organized an International Conference on Time in 1912, which established a generally accepted system of establishing the time and signaling it round the globe. The Eiffel Tower was already transmitting Paris time by radio signals, receiving calculations of astronomical time from the Paris Observatory. At 10 a.m. on 1 July 1913, it sent the first global time-signal, directed at eight different receiving stations dotted around the world. Thus, as one French commentator boasted, Paris, 'supplanted by Greenwich as the origin of the meridians, was proclaimed the initial time centre, the watch of the universe'. The coming of wireless telegraphy had indeed signaled the death-knell for the remaining local times. You’ll find everything from classic models to modern styles, featuring materials such as gold, silver and diamond, so you’re sure to find the perfect men’s or ladies' designer watch. Don’t worry about finding the perfect watch for your budget, because our collection of luxury watches also boasts new and pre-owned watchitems with a price-match promise, meaning if you find it cheaper elsewhere, we could match it (T&Cs apply). The scale of the British Empire and the dominance of British industry ensured that in 1890 nearly two-thirds of the telegraph lines in the world were owned by British companies, which controlled 156,000 kilometers of cables. But the influence of the system extended far beyond the British Empire. The growth of the new global communication networks meant, as the writer Max Nordau noted in 1892, that the simplest villager now had a wider geographical horizon than a head of government a century before. If he read a paper he 'interests himself simultaneously in the issue of a revolution in Chile, a bush-war in East Africa, a massacre in North China, a famine in Russia'.The Genesis GI Features a hybrid Steel and Aluminium Exo frame chassis which embodies the exposed skeleton custom automatic movement with self-winding mechanism. The case is seamlessly integrated on a custom designed high density rubber strap. This, in essence, is what I propose to do in this series of six lectures, beginning today and stretching over the next few months. I'm not going to attempt a comprehensive survey of the Victorians, or offer any kind of chronological narrative, though change over time will indeed be one of my themes. But what about the support for the outer dome and lantern? What Wren did there was to build a third, middle dome – and for this he wanted the strongest possible dome shape. While the catenary is optimal for an arch, that doesn’t guarantee it’s optimal for a dome. Wren and Hooke believed that the perfect shape would in fact be the positive half of the curve y= x 3 . Why did they think this? Well, we can do a bit of investigation here. It’s similar in flavour to the fact that a parabola ( y=a x 2 ) is a good approximation to a catenary. If we think about trying to find the equation of a catenary, we see that in equilibrium, the forces at every position along a hanging chain must balance. If we think about a point (x,y)on the chain, the weight Wof the section of the chain between 0 and xwill be pulling vertically downwards, the force Fexerted by the tension from the entire left-hand half of the chain will be acting horizontally to the left, and the tension Tfrom the remaining upper right-hand part of the rest of the chain will be acting upwards along the chain, at an angle of θto the horizontal. The vertical forces balance, so we get W = Tsin θ , and F=Tcos θ . That means tan θ = W F . We can make an approximation that y x =tan θas well (this would be true if we had a straight line from the origin to (x,y) , but we actually have a curve). The final step is to make another approximation, that W is proportional to x ; this would again be true if we had a straight line from the origin to (x,y) . So we get the approximation that y x =axfor some constant a , and hence that y=a x 2 , a parabola. This is a reasonable approximation and gets better the smaller the curvature. The actual general equation of a catenary curve passing through the origin is y= 1 2b ( e bx + e -bx -2 ), where bis a chosen fixed constant. There’s an infinite series we can use to calculate this expression: y= b x 2 2 + b 3 x 4 24 + b 5 x 6 720 +… (higher powers of x ). If xis small, then successive powers of xare even smaller, so the term doing all the hard work here is b x 2 2 .If we choose a= 1 2 b , we can see that the parabola matches this very closely. Right, that was the warm-up. Now think about a dome. If we try to resolve the forces this time, the weight pulling downwards at a given point will be (approximately) proportional, not to a length, but to a surface area, and so our equivalent of y xthis time is going to be proportional, approximately, to x 2 , not x . (This is all extremely rough and ready!) So we can understand why Hooke and Wren arrived at the approximation of a cubic curve, y= ax 3 , for (a cross-section of) the ideal dome. Again, the true equation has been found since then. It’s extremely complicated! There’s a series expansion of it that begins y=a( x 3 + x 7 14 + x 11 440 +…)so for small xthe cubic equation is a good approximation. Yet as I argued in my Gresham lectures last winter, what one might call the 'long Victorian era', bounded by the end of the Napoleonic War and the beginning of the First World War, does possess a certain unity and coherence, despite its various and rapidly changing nature. This was the era when Europe, and above all Britain, achieved a leadership in and dominance of the world never matched before or since. This fact alone and the spreading consciousness of it amongst the British and European populations, helped frame attitudes and beliefs in a way scarcely possible in other epochs. One of my aims in this series is to explore how this consciousness worked itself out in practice, and how and why it grew and developed.