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

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Loft of Casa Batlló, designed by Antoni Gaudí, image by Francois Lagunas, CC BY-SA 3.0, via Wikimedia Commons https://en.wikipedia.org/wiki/Casa_Batll%C3%B3

So the focus of these lectures will be on identifying and analyzing six key areas of the Victorian experience, looking at them in international and global perspective: time and space, art and culture, life and death, gender and sexuality, religion and science, and empire and race. I'll try to tease out some common factors amongst all the contradictions and paradoxes, and trace their change over time. And in no area was change more startling to contemporaries than in the topic I want to deal with this evening, namely the experience of time and space. As the century progressed, people felt increasingly that they were living, as the English essayist William Rathbone Greg put it in 1875, 'without leisure and without pause - a life ofhaste'. Comparing life in the 1880s with the days of his youth half a century before, the English lawyer and historian Frederic Harrison remembered that while people seldom hurried when he was young, now 'we are whirled about, and hooted around' without cessation. 'The most salient characteristic of life in this latter portion of the 19thcentury', Greg concluded, 'is its SPEED.' Time was becoming ever more pressing. How a watch keeps time is vital to how accurate its timekeeping is. Quartz movement watches are often prized for their accuracy, while a well-crafted automatic watch is a true investment piece. Prefer something vintage? Browse our collection of stunning manual watches. Ramsdens Watch Services

Professor Sir Richard Evans

Have a designer watch you want to sell? Or, have your eyes on a particular brand and want to part exchange? Ramsdens is happy to help. Learn More About Watches 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. John Wallis had shown in the 1650s how to “rectify” a logarithmic spiral, in other words how to find its length (or more properly the length of any part of it), by transforming, or “convoluting”, it into a straight line without changing the length. Wren managed to show that a version of this idea could work a dimension higher, and could be used in reverse to convolute or twist a cone into a kind of three-dimensional or solid logarithmic spiral. He suggested these spirals could be behind the growth of snail shells and seashells. And it’s since been found that this is absolutely right. The story of the y = x 3approximation to the perfect masonry dome, and a derivation of the correct equation, is given in Hooke's Cubico-Parabolical Conoid, by Jacques Heyman, in Notes and Records of the Royal Society of London, Vol. 52, No. 1 (Jan., 1998), pp. 39-50 https://www.jstor.org/stable/532075. 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.

All logarithmic spirals are self-similar, in that they retain precisely the same shape as they grow. In nature, if we think of how plants and animals grow, if they are growing out from a central point at a fixed rate, as happens with something like a Nautilus shell, then the outer parts continue to grow while they expand out from the centre. Logarithmic spirals allow for this to happen while keeping the same shape. The spiraling makes room for new growth. The three-dimensional version of a logarithmic spiral that Wren studied is just the right solution for shells, and is achieved in nature by one side of the structure growing at a faster rate than another. By varying the parameters in the general equation for a solid logarithmic spiral, many different shell-like shapes can be created. Wren’s ideas continue to inspire. In 2021, a team at Monash University came up with a “power cone” construction generalizing the cone-to-spiral idea (and Wren is referenced extensively in their article) that gives a mathematical basis for the formation of animal teeth, horns, claws, beaks and other sharp structures. Wren was educated at Oxford and later held the Savilian chair in astronomy there, as well as his Gresham professorship in London. These roles and others place him right at the heart of an exceptionally active and exciting community of scientific thinkers. The group around Gresham College included not just Wren as Gresham Professor of Astronomy but also Robert Hooke, who was Gresham Professor of Geometry at a similar time. Wren was not just a founder member of the Royal Society (which arose out of weekly meetings at Gresham beginning in November 1660) but served as its president. And he was an active contributor in meetings – if perhaps not in subscription fees, which he had to be chased to pay up. In short, he was a key contributor to the scientific and mathematical thought of the time. We can see this, not just from his own work, but by the amount he is mentioned in the writing of others, giving credit to him for certain ideas. For example, when Isaac Newton introduces the idea of a force governed by an inverse square law in his Principia Mathematica, he says that one example is the force governing the motion of the planets “as Sir Christopher Wren, Dr. Hooke, and Dr. Halley have severally observed”. Wren’s name appears seven times in the Principia. In fact, the leading architectural historian John Summerson (1904-1992) wrote that if Wren had died at thirty, he would still have been a “figure of some importance in English scientific thought, but without the word “architecture” occurring once in his biographies”. Wren’s contributions to astronomy are the subject of a lecture by the current Gresham Professor of Astronomy, Katherine Blundell, which you can watch online: today I want to explore his mathematical contributions. 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. If you’d like to read more about Wren’s life, two very good places to start are Lisa Jardine’s 2002 biography On a Grander Scale, and Adrian Tinniswood’s 2001 biography His Invention so Fertile.You can play with the effects of different shaped lenses – spherical, parabolic, and hyperbolic – using Lenore Horner’s Geogebra simulation at https://www.geogebra.org/m/Ddbpxd5X Gresham College, Wellcome Collection, https://www.lookandlearn.com/history-images/YW011977M Attribution (CC BY 4.0) 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!