Mathematics, science, technology and engineering of the Victorian era refers to the development of mathematics, science, technology and engineering during the reign of Queen Victoria.
Professionalisation of science
Founded in 1799 with the stated purpose of "diffusing the Knowledge, and facilitating the general Introduction, of Useful Mechanical Inventions and Improvements; and for teaching, by Courses of Philosophical Lectures and Experiments, the application of Science to the common Purposes of Life," the Royal Institution was a proper scientific institution with laboratories, a lecture hall, libraries, and offices. In its first years, the Institution was dedicated to the improvement of agriculture using chemistry, prompted by trade restrictions with Europe. Such practical concerns continued through the next two centuries. However, it soon became apparent that additional funding was required in order for the Institution to continue. Some well-known experts were hired as lecturers and researchers. The most successful of them all was Sir Humphry Davy, whose lectures concerned a myriad of topics and were so popular that the original practical purpose of the Institution faded away. It became increasingly dominated by research in basic science.
The professionalisation of science began in the aftermath of the French Revolution and soon spread to other parts of the Continent, including the German lands. It was slow to reach Britain, however. Master of Trinity College William Whewell coined the term scientist in 1833 to describe the new professional breed of specialists and experts studying what was still commonly known as natural philosophy. In 1840, Whewell wrote, "We need very much a name to describe a cultivator of science in general. I should incline to call him a Scientist." The new term signalled the recognition of the importance of empiricism and inductive reasoning. But this term was slow to catch on. As biologist Thomas Huxley indicated in 1852, the prospect of earning a decent living as a scientist remained remote despite the prestige of the occupation. It was possible for a scientist to "earn praise but not pudding," he wrote. Since its birth, the Royal Society of London had been a club of gentlemanly amateurs, though some of whom were the very best in their fields, people like Charles Darwin and James Prescott Joule. But the Society reformed itself in the 1830s and 1840s. By 1847, it only admitted the new breed of professionals.
The Victorians were impressed by science and progress and felt that they could improve society in the same way as they were improving technology. Britain was the leading world centre for advanced engineering and technology. Its engineering firms were in worldwide demand for designing and constructing railways.Lionel Thomas Caswell Rolt, Victorian engineering (Penguin, 1974).Herbert L. Sussman, Victorian technology: invention, innovation, and the rise of the machine (ABC-CLIO, 2009)
Ease of discovery and rate of progress A necessary part of understanding scientific progress is the ease of scientific discovery. In many cases, from planetary science to mammalian biology, the ease of discovery since the 1700s and 1800s can be fitted to an exponentially decaying curve. But the rate of progress is also dependent on other factors, such as the number of researchers, the level of funding, and advances in technology. Thus the number of new species of mammals discovered between the late 1700s and late 1800s followed grew exponentially before leveling off in the 1900s; the general shape is known as the logistic curve. In other cases, a branch of study reached the point of saturation. For instance, the last major internal human organ, the parathyroid gland, was discovered in 1880 by Ivar Viktor Sandström.
This does not mean that basic science was coming an end. Despite the despondency of many Victorian-era scientists, who thought that all that remained was measuring quantities to the next decimal place and that new discoveries would not change the contemporary scientific paradigm, as the nineteenth century became the twentieth, science witnessed truly revolutionary discoveries, such as radioactivity, and basic science continued its advance, though a number of twentieth-century scientists shared the same pessimism as their late-Victorian counterparts.
Mathematics and statistics
In the field of statistics, the nineteenth century saw significant innovations in data visualisation. William Playfair, who created charts of all sorts, justified it thus, "a man who has carefully investigated a printed table, finds, when done, that he has only a very faint and partial idea of what he has read; and that like a figure imprinted on sand, is soon totally erased and defaced." For example, in a chart showing the relationship between population and government revenue of some European nations, he used the areas of circles to represent the geographical sizes of those nations. In the same graph he used the slopes of lines to indicate the tax burden of a given population. While serving as nurse during the Crimean War, Florence Nightingale drew the first pie charts representing the monthly fatality rates of the conflict, distinguishing deaths due to battle wounds (innermost section), those due to infectious disease (outer section), and to other causes (middle section). (See figure.) Her charts clearly showed that most deaths resulted from disease, which led the general public to demand improved sanitation at field hospitals. Although bar charts representing frequencies were first used by the Frenchman A. M. Guerry in 1833, it was the statistician Karl Pearson who gave them the name histograms. Pearson used them in an 1895 article mathematically analyzing biological evolution. One such histogram showed that buttercups with large numbers of petals were rarer.
Normal distributions, expressible in the form , arose in various works on probability and the theory of errors. Belgian sociologist and statistician Adolphe Quetelet discovered that its extremely wide applicability in his analysis of vast amounts of statistics of human physical characteristics such as height and other traits such as criminality and alcoholism. Quetelet derived the concept of the "average man" from his studies. Sir Francis Galton employed Quetelet's ideas in his research on mathematical biology. In his experiments with sweet peas in the 1870s, Galton discovered that the spread of the distributions of a particular trait did not change over the generations. He invented what he called the "quincunx" to demonstrate why mixtures of normal distributions were normal. Galton noticed that the means of a particular trait in the offspring generation differed from those of the parent generation, a phenomenon now known as regression to the mean. He found that the slopes of the regression lines of two given variables were the same if the two data sets were scaled by units of probable error and introduced the notion of the correlation coefficient, but noted that correlation does not imply causation.
During the late nineteenth century, British statisticians introduced a number of methods to relate and draw conclusions from statistical quantities. Francis Edgeworth developed a test for statistical significance that estimated the "fluctuations"—twice the variance in modern language—from two given means. By modern standards, however, he was extremely conservative when it comes to drawing conclusions about the significance of an observation. For Edgeworth, an observation was significant if it was at the level of 0.005, which is much stricter than the requirement of 0.05 to 0.01 commonly used today. Pearson defined the standard deviation and introduced the -statistic (chi-squared). Pearson's student, George Udney Yule, demonstrated that one could compute the regression equation of a given data set using the method of least squares.
In 1828, miller and autodidactic mathematician George Green published An Essay on the Application of Mathematical Analysis to the Theories of Electricity and Magnetism, making use of the mathematics of potential theory developed by Continental mathematicians. But this paper fell on deaf ears until William Thomson read it, realised its significance, and had it re-printed in 1850. Green's work became a source of inspiration for the Cambridge school of mathematical physicists, which included Thomson himself, George Gabriel Stokes, and James Clerk Maxwell. Green's Essay contained what became known as Green's theorem, a basic result in vector calculus, Green's identities, and the notion of Green's functions, which appears in the study of differential equations. Thomson went on to prove Stokes' theorem, which earned that name after Stokes asked students to prove it in the Smith's Prize exam in 1854. Stokes learned it from Thomson in a letter in 1850. Stokes' theorem generalises Green's theorem, which itself is a higher-dimensional version of the Fundamental Theorem of Calculus. Research in physics—in particular elasticity, heat conduction, hydrodynamics, and electromagnetism—motivated the development of vector calculus in the nineteenth century.
Arthur Cayley is credited with the creation of the theory of matrices—rectangular arrays of numbers—as distinct objects from determinants, studied since the mid-eighteenth century. The term matrix was coined by James Joseph Sylvester, a major contributor to the theory of determinants. It is difficult to overestimate the value of matrix theory to modern theoretical physics. Peter Tait wrote, prophetically, that Cayley was "forging the weapons for future generations of physicists."
Theoretical mechanics and optics
Early contributions study of elasticity—how objects behave under stresses, pressures, and loads— employed ad hoc hypotheses to solve specific problems. It was during the nineteenth century that scientists began to work out a thorough theory. In 1821, using an analogy with elastic bodies, French professor of mechanics Claude-Louis Navier arrived at the basic equations of motion for viscous fluids. George Gabriel Stokes re-derived them in 1845 using continuum mechanics in a paper titled "On the Theories of Internal Friction of Fluids in Motion." In it, Stokes sought to develop a mathematical description for all known fluids that take into account viscosity, or internal friction. These are now referred to as the Navier–Stokes equations.
In 1852, Stokes showed that light polarisation can be described in terms of what are now known as the Stokes parameters. The Stokes parameters for a given wave may be viewed as a vector.
Founded in the eighteenth century, the calculus of variations grew into a much favored mathematical tool among physicists. Scientific problems thus became the impetus for the development of the subject. William Rowan Hamilton advanced it in his course to construct a deductive framework for optics; he then applied the same ideas to mechanics. With an appropriate variational principle, one could deduce the equations of motion for a given mechanical or optical system. Soon, scientists worked out the variational principles for the theory of elasticity, electromagnetism, and fluid mechanics (and, in the future, relativity and quantum theory). Whilst variational principles did not necessarily provide a simpler way to solve problems, they were of interest for philosophical or aesthetic reasons, though scientists at this time were not as motivated by religion in their work as their predecessors. Hamilton's work in physics was great achievement; he was able to provide a unifying mathematical framework for wave propagation and particle motion. In light of this description, it becomes clear why the wave and corpuscle theories of light were equally able to account for the phenomena of reflection and refraction. Hamilton's equations also proved useful in calculating planetary orbits.