Even in the mid-1870s, when the country had been united in a single state, railway timetables in Germany had been forced to base themselves on a bewildering variety of local times that varied from city to city, leaving it up to passengers to convert the time on the local clock to the time on their pocket-watch. The question of the best shape for a masonry arch had been recently addressed both by Wren and his friend, Royal Society colleague and fellow Gresham Professor, Robert Hooke.

W. Turner depicted these sensations in his famous paintingRail, Steam and Speed: The Great Western Railway, painted in 1844. It was particularly galling for French officialdom to have to admit the primacy of Britain in setting world times. In 1815, news of Napoleon's defeat at Waterloo took two and a half days to reach the government in London. Once the main national network of railway lines had been laid, however, companies began to construct local branch lines, connecting small towns and rural communities, bringing to them the latest news and products from the rest of the country, and enabling country people to travel to the nearest town, and far beyond; gradually the abolition of distance opened people's horizons, ironing out local peculiarities and paving the way for the mass culture of the twentieth century. The Eiffel Tower was already transmitting Paris time by radio signals, receiving calculations of astronomical time from the Paris Observatory.For both aesthetic and symbolic reasons, Wren wanted the dome that you see from all across London, the defining shape of the cathedral, to be a hemisphere. A universal power law for modelling the growth and form of teeth, claws, horns, thorns, beaks, and shells. This would mean that you could make a hyperboloid on a rotating lathe by using a straight-edged tool positioned at a fixed angle. It’s the curve you get by following the path of a point on the circumference of a circle as it rolls along a straight line (or the rim of a wheel rolling along a road). You can play with the effects of different shaped lenses – spherical, parabolic, and hyperbolic – using Lenore Horner’s Geogebra simulation at https://www.

I've been talking in this lecture about perceptions of time, but of course the changes that took place over the nineteenth century also encompassed a profound transformation in people's experience of space and distance. Kepler realised that it’s actually enough to solve the problem of cutting a semicircle in a given ratio by a line through any given point on its diameter. As the speed of communication increased, distances shrank; places that seemed impossibly far off in the days of unmade roads and slow-moving carriages became much closer with the introduction of the railways and later on the automobile. 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.But the idea of anotheredpast became widespread in European culture, in contrast to the eighteenth century, which had depicted the people and societies of the past as largely similar to those of its own age. The entire 45mm case curves effortlessly front and back and features the multi forged stainless steel curved case back with exhibition window.

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) . Instead I'm going to approach the topic selectively, taking 'Victorian' as a concept or an idea rather than a specific period - 1837 to 1901 - of British history coinciding with the reign of Queen Victoria. The gauge selected by Stephenson for the railway four feet eight and a half inches, became the world's 'standard gauge' and remains so today; when it was officially adopted in 1845, Brunel's seven-foot gauge was already in operation on the Great Western Railway, which was not converted to conform to the rest of the country until the end of the century.We don’t know for sure when he did this, but he wrote in 1640 that he’d been studying cycloids for 50 years. 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. He was actively engaged with the practical challenges of designing scientific instruments and experiments.

She is Professor of Mathematics and until recently was Head of Mathematics and Statistics at Birkbeck, University of London. Hooke found that the equations describing the forces acting on a hanging chain are equivalent to those describing the forces acting on an arch (this time not tension and gravity but compression and gravity). The 'universal diffusion of pocket watches', as the sociologist Georg Simmel noted, contributed further to the acceleration of modern life through instilling a greater sense of punctuality in business and society. Spherical lenses (where the curved part is a section of a sphere) were the only ones that could easily be made in Wren’s time, but it was known that other curves were better for the job, producing less aberration. The critic John Ruskin also feared that railways would prevent people from observing properly the scenery through which they passed: 'They are the loathsomest form of devilry now extant, animated and deliberate earthquakes, destructive of all wide social habit or possible natural beauty, carriages of damned souls on the edges of their own graves.In the earlier part of the century, it was reckoned that a stagecoach could achieve about 6 miles per hour on a good road, traveling some 50 miles a day in summer and half that distance when roads were muddy and weather conditions bad. You can make the actual curve of the arch a slightly different shape but the line of thrust is still a catenary curve, so that needs to be part of the structure of the arch. In 1872, when the first transatlantic cable, the transmission of messages revealed that Paris was half a second further away from London than had previously been thought.