* Cf. the cognate indicatrix of the French geometers.

* This belongs to the period of Thomson's perplexity about thermodynamics. See Excursus, pp. 748–50.

* The latter part of this letter is included because it reveals Maxwell's early concern (in 1855) with Stokes' hydrodynamic investigations of 1842–7, reprinted in Math. and Phys. Papers, vol. i, pp. 1–235. In this very extensive work, including his classical Report on Recent Progress in Hydrodynamics, Stokes had curiously missed, as has been remarked often, the fertile physical principle which lay exposed in the velocity potential theory of Lagrange with which he was closely concerned, namely that what he named rotational motion remained always confined to the same parts of the fluid, as is indeed stated explicitly in his Report on Hydrodynamics (1846), cf. Reprint, p. 160. That train of thought was soon originated and fully developed in the momentous classical memoir of Helmholtz on vortex motion which appeared two years later, in 1857: this memoir was translated by Tait ten years later, with experiments in air which immediately gave rise to the Kelvin outburst of generalized hydrodynamic theory, with its dynamical field of vortex atoms. Maxwell soon tried to translate these ideas into a dynamical theory of magnetism as described infra (cf. p. 730). The source of his knowledge at this early period was doubtless Lagrange's Mécanique Analytique and Stokes' early papers.

* Including his perplexities about Thermodynamics? Cf. Excursus, pp. 748–50.

* When Faraday re-discovered a specific static induction across dielectrics, to the detriment of current ideas regarding action across a distance, he was delighted to find how promptly W. Thomson subsumed it under the general theory of polarized media, as later systematized in his development of the Poisson theory of magnetization; this initiative became refined and expanded in time into Clerk Maxwell's scheme of gradual electric transmission (pp. 729–33 infra). Cf. Thomson's earlier papers, now strangely neglected, in the reprint of Papers on Electrostatics and Magnetism (1872): in its preparation the author recorded assistance from Clerk Maxwell and P. G. Tait.

† Maxwell does not here refer to the Young-Helmholtz trichromatic theory of vision. But according to Helmholtz (1868) the exact numerical laws of composition, on which it and all other theories must repose, were the discovery of Maxwell Cf. an illuminating account in his Popular Scientific Lectures, vol. i, pp. 214, 219.

* The Sadleirian Professorship at Cambridge was created for Cayley in 1863.

* Identical in principle with the modern short astronomical spectroscope.

* These developments were published by Maxwell in Phil. Mag. 1861–2. Weber's ratio was half the speed of light on account of his special units. Soon after the law of attraction between moving Weberian electrons appeared, G. Kirchhoff (Pogg. Ann. 1847) developed the theory of their oscillations, and the resulting wave forms in a cylindrical conductor, finding as he remarked that provided the waves are short enough they travel along the surface of the cylinder with the speed of light.

As to Maxwell's prediction connecting index of refraction with square root of dielectric capacity, there is a most striking record in a letter from Boltzmann that is published in Königsberger's Life of Helmholtz. It appears that Boltzmann's earliest investigation long after (in 1872), in the laboratory of Helmholtz, was to test such a relation for the gases. But he thought that Maxwell required the index of refraction to be proportional to the dielectric capacity, and finding no such relation between his measures, dropped the subject. However, after he left Berlin, he happened to take up his records again, and noticed that they showed good agreement between the index and the square root of the capacity. On looking up Maxwell's Memoir he found that this was just what his theory required, and so reported, to his great delight, to his master Helmholtz. This confirmation was not in time for Maxwell's Treatise (1873).

* This subject of the mechanical reaction of magnetization is now much developed, resting on experiments of Einstein and de Haas, Bennett, Sucksmith, and many others.

* In generalization of Thomson's theorem of maximal energy, in Thomson & Tait's Natural Philosophy (1867).

* Of course you (oh [Lewis] Campbell [his biographer]) know this is Maxwell's favourite signature! [W.T.]