In scope, Stokes' work covered a wide range of physical inquiry but, as
Marie Alfred Cornu remarked in his
Rede Lecture of 1899, the greater part of it was concerned with waves and the transformations imposed on them during their passage through various media.
Fluid dynamics Stokes's first published papers, which appeared in 1842 and 1843, were on the steady motion of incompressible
fluids and some cases of fluid motion. These were followed in 1845 by one on the friction of fluids in motion and the equilibrium and motion of elastic solids, and in 1850 by another on the effects of the internal friction of fluids on the motion of
pendulums. To the theory of sound he made several contributions, including a discussion of the effect of wind on the intensity of sound and an explanation of how the intensity is influenced by the nature of the gas in which the sound is produced. These inquiries together put the science of
fluid dynamics on a new footing, and provided a key not only to the explanation of many natural phenomena, such as the suspension of clouds in the air, and the subsidence of ripples and waves in water, but also to the solution of practical problems, such as the flow of water in rivers and channels, and the skin resistance of ships.
Creeping flow s and forces. Stokes' work on fluid motion and
viscosity led to his calculating the terminal velocity for a sphere falling in a viscous medium. This became known as
Stokes' law. He derived an expression for the frictional force (also called
drag force) exerted on spherical objects with very small
Reynolds numbers. Stokes' work is the basis of the falling sphere
viscometer, in which the fluid is stationary in a vertical glass tube. A sphere of known size and density is allowed to descend through the liquid. If correctly selected, it reaches
terminal velocity, which can be measured by the time it takes to pass two marks on the tube. Electronic sensing can be used for opaque fluids. Knowing the terminal velocity, the size and density of the sphere, and the density of the liquid, Stokes' law can be used to calculate the viscosity of the fluid. A series of steel
ball bearings of different diameters is normally used in the classic experiment to improve the accuracy of the calculation. The school experiment uses
glycerine as the fluid, and the technique is used industrially to check the viscosity of fluids used in processes. The same theory explains why small water droplets (or ice crystals) can remain suspended in air (as clouds) until they grow to a critical size and start falling as rain (or snow and
hail). Similar use of the equation can be made in the settlement of fine particles in water or other fluids. The
stokes, the
CGS unit of
kinematic viscosity, was named in recognition of his work.
Optics Perhaps Stokes' best-known researches are those which deal with the wave theory of light. His
optical work began at an early period in his scientific career. His first papers on the
aberration of light appeared in 1845 and 1846, and were followed in 1848 by one on the theory of certain bands seen in the
spectrum. In 1849, Stokes published a long paper on the dynamical theory of
diffraction, in which he showed that the plane of
polarisation must be perpendicular to the direction of propagation. Two years later, he discussed the colours of thick plates. Stokes also investigated
George Airy's mathematical description of
rainbows. Airy's findings involved an integral that was awkward to evaluate. Stokes expressed the integral as a
divergent series, which were little understood. However, by cleverly truncating the series (i.e., ignoring all except the first few terms of the series), He obtained an accurate approximation to the integral that was far easier to evaluate than the integral itself. Stokes' research on asymptotic series led to fundamental insights about such series.
Fluorescence In 1852, in his famous paper on the change of
wavelength of light, he described the phenomenon of
fluorescence, as exhibited by
fluorspar and
uranium glass, materials which he viewed as having the power to convert invisible
ultra-violet radiation into radiation of longer wavelengths that are visible. The
Stokes shift, which describes this conversion, is named in Stokes's honour. A mechanical model, illustrating the dynamical principle of Stokes's explanation was shown. The offshoot of this,
Stokes line, is the basis of
Raman scattering. In 1883, during a lecture at the
Royal Institution, Lord Kelvin said he had heard an account of it from Stokes many years before, and had repeatedly but vainly begged him to publish it.
Polarisation In the same year, 1852, there appeared the paper on the composition and resolution of streams of polarised light from different sources, and in 1853 an investigation of the metallic
reflection exhibited by certain non-metallic substances. The research was to highlight the phenomenon of
light polarisation. About 1860 he was engaged in an inquiry on the intensity of light reflected from, or transmitted through, a pile of plates; and in 1862 he prepared for the
British Association a valuable report on
double refraction, a phenomenon where certain crystals show different refractive indices along different axes. Perhaps the best known crystal is
Iceland spar, transparent
calcite crystals. A paper on the long spectrum of the electric light bears the same date, and was followed by an inquiry into the
absorption spectrum of blood.
Chemical analysis The chemical identification of
organic bodies by their optical properties was treated in 1864; and later, in conjunction with the Rev.
William Vernon Harcourt, he investigated the relation between the chemical composition and the optical properties of various glasses, with reference to the conditions of
transparency and the improvement of
achromatic telescopes. A still later paper connected with the construction of optical instruments discussed the theoretical limits to the aperture of microscope objectives.
Ophthalmology In 1849, Stokes invented the
Stokes lens to detect
astigmatism. It is a lens combination consisting of equal but opposite power
cylindrical lenses attached together in such a way so that the lenses can be rotated relative to one another.
Other work In other areas of physics may be mentioned his paper on the
conduction of heat in
crystals (1851) and his inquiries in connection with
Crookes radiometer; his explanation of the light border frequently noticed in photographs just outside the outline of a dark body seen against the sky (1882); and, still later, his theory of the
x-rays, which he suggested might be transverse waves travelling as innumerable solitary waves, not in regular trains. Two long papers published in 1849 – one on attractions and
Clairaut's theorem, and the other on the variation of
gravity at the surface of the Earth (1849) –
Stokes's gravity formula—also demand notice, as do his mathematical memoirs on the critical values of sums of periodic series (1847) and on the numerical calculation of a class of definite
integrals and
infinite series (1850) and his discussion of a
differential equation relating to the breaking of railway bridges (1849), research related to his evidence given to the
Royal Commission on the Use of Iron in Railway structures after the
Dee Bridge disaster of 1847.
Unpublished research Many of Stokes's discoveries were not published, or were only touched upon in the course of his oral lectures. One such example is his work in the theory of
spectroscopy. In his presidential address to the
British Association in 1871,
Lord Kelvin stated his belief that the application of the prismatic analysis of light to solar and stellar chemistry had never been suggested directly or indirectly by anyone else when Stokes taught it to him at Cambridge University some time prior to the summer of 1852, and he set forth the conclusions, theoretical and practical, which he learnt from Stokes at that time, and which he afterwards gave regularly in his public lectures at
Glasgow. These statements, containing as they do the physical basis on which spectroscopy rests, and the way in which it is applicable to the identification of substances existing in the sun and stars, make it appear that Stokes anticipated
Gustav Kirchhoff by at least seven or eight years. Stokes, however, in a letter published some years after the delivery of this address, stated that he had failed to take one essential step in the argument—not perceiving that emission of light of definite wavelength not merely permitted, but necessitated, absorption of light of the same wavelength. He modestly disclaimed "any part of Kirchhoff's admirable discovery," adding that he felt some of his friends had been over-zealous in his cause. It must be said, however, that English scientists have not accepted this disclaimer in all its fullness, and still attribute to Stokes the credit of having first enunciated the fundamental principles of
spectroscopy. In another way, too, Stokes did much for the progress of mathematical physics. Soon after he was elected to the Lucasian chair he announced that he regarded it as part of his professional duties to help any member of the university with difficulties he might encounter in his mathematical studies, and the assistance rendered was so real that pupils were glad to consult him, even after they had become colleagues, on mathematical and physical problems in which they found themselves at a loss. Then during the thirty years he acted as secretary of the Royal Society, he exercised an enormous if inconspicuous influence on the advancement of mathematical and physical science, not only directly by his own investigations, but indirectly by suggesting problems for inquiry and inciting men to attack them, and by his readiness to give encouragement and help.
Contributions to engineering Stokes was involved in several investigations into railway accidents, especially the
Dee Bridge disaster in
Chester in May 1847, and he served as a member of the subsequent Royal Commission into the use of cast iron in railway structures. He contributed to the calculation of the forces exerted by moving engines on bridges. The bridge failed because a cast iron beam was used to support the loads of passing trains.
Cast iron is
brittle in
tension or
bending, and many other similar bridges had to be demolished or reinforced. from the north He appeared as an expert witness at the
Tay Bridge disaster, where he gave evidence about the effects of wind loads on the bridge. The centre section of the bridge (known as the High Girders) was completely destroyed during a storm on 28 December 1879, while an express train was in the section, and everyone aboard died (more than 75 victims). The Board of Inquiry listened to many
expert witnesses, and concluded that the bridge was "badly designed, badly built and badly maintained". As a result of his evidence, he was appointed a member of the subsequent
Royal Commission into the effect of wind pressure on structures. The effects of high winds on large structures had been neglected at that time, and the commission conducted a series of measurements across Britain to gain an appreciation of wind speeds during storms, and the pressures they exerted on exposed surfaces.
Work on religion ,
Church of Ireland in
County Sligo Stokes generally held conservative religious values and beliefs. In 1886, he became president of the
Victoria Institute, which had been founded to defend evangelical Christian principles against challenges from the new sciences, especially the
Darwinian theory of biological
evolution. He gave the 1891
Gifford lecture on
natural theology. He was also the vice-president of the
British and Foreign Bible Society and was actively involved in doctrinal debates concerning missionary work. However, although his religious views were mostly orthodox, he was unusual among Victorian evangelicals in rejecting eternal punishment in hell, and instead was a proponent of
Christian conditionalism. As President of the Victoria Institute, Stokes wrote:
"We all admit that the book of Nature and the book of Revelation come alike from God, and that consequently there can be no real discrepancy between the two if rightly interpreted. The provisions of Science and Revelation are, for the most part, so distinct that there is little chance of collision. But if an apparent discrepancy should arise, we have no right on principle, to exclude either in favour of the other. For however firmly convinced we may be of the truth of revelation, we must admit our liability to err as to the extent or interpretation of what is revealed; and however strong the scientific evidence in favour of a theory may be, we must remember that we are dealing with evidence which, in its nature, is probable only, and it is conceivable that wider scientific knowledge might lead us to alter our opinion". == Family ==