of the plane of its vibration to that of its polarisation. Such a determination, though fundamental for a purely dynamical view, is not essential to the construction of an adequate formal account of the phenomena of radiation, and the workers in the modern electric theory have been content in the main to stop short of it.
The calculations relating to corrections for pendulums had led him into pure analysis connected with Bessel functions and other harmonic expansions; in various subsequent memoirs he established and justified the semi-convergent series necessary to their arithmetical use over the whole range of the argument, thus making practical advances that were assimilated only in later years into general analysis. Likewise the discrepancies which he encountered in practical applications of Fourier's theory led him as early as 1847 to a reasoned exposition of doctrines, now fundamental, relating to complete and limited convergence in infinite series. Here and elsewhere, however, his work developed rather along the path of advance of physical science than on the lines of formal pure analysis; and the recognition of its mathematical completeness was in consequence delayed.
In 1859 great interest was excited by the announcement of the discovery and development of spectrum analysis by Kirchhoff and Bunsen, and its promised revelations regarding the sun and stars by means of the Fraunhofer lines, an advance which was introduced to English readers by Stokes's translation of their earlier papers. It was soon claimed by William Thomson (Lord Kelvin) that he had been familiar with the scientific possibilities in this direction since before 1852, having been taught by Stokes the dynamical connection between the opacity of a substance to special radiation and its own power of emitting radiation of the same type. The theoretical insight thus displayed, on the basis of the interpretation of isolated observations, was, of course, no detraction from the merit of the practical establishment of the great modern science of spectrum analysis by the former workers: yet the feeling in some circles, that such a claim for Stokes was not quite warranted, was only set at rest by the posthumous discovery, among his papers, of a detailed correspondence with Lord Kelvin on this subject, mainly of date 1854, which is now printed in vol. iv. of his 'Collected Papers' (cf. pp. 126–36 and 367–76).
But in fact it was hardly necessary to wait for this evidence: for the same general considerations had already entered essentially into Stokes's discussion of one of his most refined and significant experimental discoveries. Shortly after he entered on the study of optics as a subject for his activity in the Lucasian chair at Cambridge, his attention was attracted to the blue shimmer exhibited by quinine in strong illumination, which had been investigated by Sir John Herschel [q. v.] in 1845. He soon found (1852) that the phenomenon was at variance with the Newtonian principle of the definite prismatic analysis of light, as the blue colour appeared when it was not a constituent of the exciting radiation. He discovered that this emission of light, called by him fluorescence from its occurrence in fluor-spar, was provoked mainly by rays beyond the violet end of the visible spectrum; and as a bye-product he thus discovered and explored the great range of the invisible ultra-violet spectrum, having found that quartz prisms could be used for its examination, though glass was opaque. Discussion of the exceptional nature of this illumination, created by immersion of the substance in radiation of a different kind, necessarily led him into close scrutiny of the dynamics of ordinary absorption and radiation; and the idea of a medium absorbing specially the same vibrations which it could itself spontaneously emit was thus fully before him (cf. § 237 of the memoir).
Another mathematical memoir (1878), suggested by the feeble communication of sound from a bell to hydrogen gas, elucidated the circumstances which regulate the closeness of the grip that a vibrating body gets with the atmosphere; and its ideas have also wider application, to the facility for emission and absorption of radiations of all kinds from and into the vibrating bodies which are their sources. In two memoirs of date 1849 (Papers, ii. 104–121), on the variation of gravity over the earth's surface, he became virtually the founder of the modern and more precise science of geodesy. The fundamental proposition was there established, as the foundation of the subject, that the form of the ocean level determines by itself the distribution of the earth's attraction everywhere outside it, without requiring any reference to the internal constitution of the earth, which in this regard must remain entirely unknown.
His earlier scientific work, with that of Helmholtz and Lord Kelvin, may be said to mark the breaking away of physical science
