Mathematical and Physical Papers, Volume 1
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Tait and James Clerk Maxwell. Such a strong performance meant that a fellowship at Pembroke inevitably followed. Stokes went on, in October , to be elected the 13th Lucasian Professor of Mathematics. Tait, a student at Cambridge at the time, declared that he and his fellow undergraduates had not even heard of Stokes before his appointment.
Stokes, Senior Fellow of Caius, who had been appointed. Stokes was amused rather than piqued by the error. Today the Lucasian Chair is seen as a stellar appointment, associating the incumbent with previous holders such as Newton, Dirac, Hawking and Stokes himself.
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However, it was not quite seen that way in his day. A Lucasian Professor from 20 years before Stokes, George Biddell Airy, complained that he had to take a one-third cut in pay to take the role, and matching his action to his complaint stayed in the job for scarcely more than a year.
While in post, Airy cunningly used his position to arrange an increase in the salary of the Plumian Professor of Astronomy and Experimental Philosophy at Cambridge, before switching chairs. Early in his time as Lucasian Professor, Stokes augmented his inadequate salary by lecturing at the Royal School of Mines in London, but unlike Airy, he remained in the chair until his death.
I thought I would try my hand at original research; and following a suggestion made to me by Mr Hopkins while reading for my degree, I took up the subject of Hydrodynamics, then at a rather low ebb in the general reading of the place [i. From that suggestion flowed over 20 papers, clustered at the beginning and end of his life —50 and —98 , covering the nature of fluid flow and the theory of water waves. Certainly an accurate understanding of pendula for timekeeping and geodesy was important in the 19th century, but it is not the paper where he writes down what we now call the Navier—Stokes equation.
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Stokes was not the first to write the equation down. Stokes notes that on finishing the paper [4, p. I afterwards found that Poisson had written a memoir on the same subject, and on referring to it I found that he had arrived at the same equations.
The method which he employed was however so different from mine that I feel justified in laying the latter before [the Cambridge Philosophical Society]. Navier had built his model on ideas of molecular forces, whereas Stokes preferred to avoid any molecular speculations. The work by Stokes and his predecessors was little enough known to be rediscovered again by Helmholtz in , and you can read textbooks up to the midth century which, while giving due credit to Navier and Stokes, do not name the equation after them.
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Here are three of the best known. For a vector field and surface bounded by a simple curve :. Actually, Stokes did not come up with this theorem! It was his long-term correspondent William Thomson. The drag on a small sphere of radius , moving with speed through a fluid with viscosity is given by. Stokes points out that the result explains why very small particles, including those that make up clouds, are suspended in air. At the beginning of the 20th century, the result was key to enabling Robert Millikan to indirectly measure the size of oil drops in his famous experiment to determine the charge on the electron.
For an incompressible fluid, the velocity field of a fluid, where is the fluid density, is the pressure, is the dynamic viscosity and are external forces, is given by. The ubiquity of fluids makes the Navier—Stokes equation a cornerstone of modern physical science and engineering.
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While in contemporary science the name of Stokes is best known for fluid dynamics, in his lifetime he also had a high reputation in optics. In this his contributions ranged across the whole subject, encompassing theory, experiment and instrument design. Stokes was an excellent and elegant experimentalist. Those aspects of his work which were entangled with that most Victorian snare, the ether, have not aged well, but other studies have stood the test of time. Thus, in his work on aspects of interference and diffraction, he was able to bring new depths of mathematical and physical insight.
However, one of his most significant contributions contained no mathematics whatsoever. In , John Herschel noted the blue glow produced within a thin layer near the surface of a quinine solution.
Under the then current understanding that monochromatic light was immutable, this phenomenon was difficult to explain. Stokes realised that if he took the dramatic step of assuming monochromatic light was mutable then the phenomenon was easily explained. He performed a series of experiments to test the hypothesis, and tracked the matter down to the absorption of ultraviolet.
In a paper published in he considered the nature of the convergence of a Fourier series near a finite discontinuity, and in the same paper introduced the idea of uniform convergence. I hope it will be satisfactory to all my Baltimore coefficients still alive in our world of science, when this volume reaches their hands; to find in it dynamical explanations of every one of the difficulties with which we were concerned from the first to the last of our twenty lectures of Nixon in attendance at Johns Hopkins at this period, we do find several mentions of a Nixon in the finding aids to Lord Kelvin's correspondence at the University of Glasgow, including reference to a testimonial for Nixon in a letter to his older brother James Thomson in Two octavo volumes only, of an eventual six.
Original olive green cloth, lettered in gilt on spines; pp. Volume 1 with mounted presentation on Glasgow University stationery: "To [in separate hand]: A. Publisher's catalog present at rear of each volume, both dated December making volume 1 presumably a later printing, though not otherwise indicated.