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.

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. 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'.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. 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’ve got a huge range of 100% genuine luxury watches from leading brands such as Rolex, Tag Heuer, Omega and Breitling, all individually assessed and valued by our expert buyers. There were two key questions people always had about curves, known as “quadrature” and “rectification”. Quadrature is finding the area under a curve. Galileo approximated the quadrature by making a cycloid out of metal and weighing it, but he didn’t know the exact formula. We don’t know for sure when he did this, but he wrote in 1640 that he’d been studying cycloids for 50 years. At any rate, it took until the 1630s for the correct solution to be found (probably first by Gilles de Roberval): if the rolling circle has area π r 2 , then the area under each cycloid arch is 3π r 2 . Very nice. But the cycloid had still not been “rectified”: this means finding its length. The first person to do this, of all the illustrious mathematicians who had studied it, was Christopher Wren. He showed that the length is another beautifully simple formula. If the rolling circle has diameter d , its circumference is πd , and each cycloid arch has length precisely 4d . (Actually, Roberval claimed to have done this first too, but he did that a lot. He only started making this claim after Wren told Pascal the result, and Wren’s proof was the first to be published, as far as I know. The general consensus at the time and since seems to be that Wren was indeed the first to rectify the cycloid.)

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 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. At the beginning of the nineteenth century, communication was slow, even relatively short journeys were uncertain and time-consuming, and people were dependant on the forces of nature for energy; this lecture charts the development of new modes of communication, from the railway to the radio, the telegraph to the telephone, the steamship to the motor-car and examines their efforts on perceptions of time and space.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. 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. 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. The portrait of Christopher Wren is from the National Portrait Gallery https://www.npg.org.uk/collections/search/portrait/mw06939/Sir-Christopher-Wren

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 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. The following paper is a helpful summary of Wren’s mathematical work which gives detail of the original sources, for example the places in Wallis’s Tractatus de Cycloide where he explain’s Wren’s rectification of the cycloid and solution to Kepler’s problem. Wren the Mathematician, D.T. Whiteside, Notes & Records of the Royal Society, 15, pp107-111 (1960).In February 1658, mathematicians in England received a challenge from France. It read “Jean de Montfort [possibly a pseudonym for Pascal] greatly desires that those distinguished gentlemen, the Professors of Mathematics, and others in England renowned for mathematical skill, may condescend to resolve this problem”. The problem was, given an ellipse of known dimensions, and a chord of the ellipse crossing the major axis at a known point and angle, to find the lengths of the segments of that chord. Wren solved the problem, and then in return challenged the mathematicians of France to solve another problem about ellipses, which I’ll tell you about now.