I did that even when such were not ostensibly present, they were present in a trace (thus alcohol burnt on a watch-glass and a candle snuffed close, so that the wick does not project into the incandescent envelope, do not show bright D), I concluded in my own mind that dark D was due to absorption by sodium in some shape. In what shape? I knew that such narrow absorption-bands were only observed in vapours; I knew that as a rule vapours agree in a general way with their liquids or solutions as to absorption, save that in lieu of the capricious absorption of the vapour, we have a general absorption attacking those regions of the spectrum in which the vapour-bands are chiefly found. Hence as the sodium compounds, chloride, oxide, etc., are transparent, I concluded that the absorbing vapour was that of sodium itself. Knowing the powerful affinities of sodium, I did not dream of its being present in a free state in the flame of a spirit-lamp; and so I supposed that the emitting body in the case of a spirit-lamp with salted wick was volatilised chloride of sodium, capable of vibrating in a specific time, or rather two specific and nearly equal periods, by virtue of its sodium constituent; but that to produce absorption the sodium must be free. I never thought of the extension of Prevost's law of exchanges from radiation as a whole to radiation of each particular refrangibility by itself, afterwards made by B. Stewart; and so I failed to perceive that a soda flame which emits bright D must on that very account absorb light of the same refrangibility.

"When Foucault, whom I met at dinner at Dr Neil Arnott's when he came to receive the Copley Medal in 1855, told me of his discovery of the absorption and emission of D by a voltaic arc, I was greatly struck with it. But though I had pictured to my mind the possibility of emitting and absorbing light of the same refrangibility by the mechanism of a system of piano strings tuned to the same pitch, which would, if struck, give out a particular note, or would take it up from the air at the expense of the aërial vibrations, I did not think of the extension of Prevost's theory, afterwards discovered by Stewart*, nor perceive that the emission of light of definite refrangibility necessitated (and not merely permitted) absorption of light of the same refrangibility.

[* Trans. R. S. Edin., xxII, March 1858; cf. Lord Rayleigh, Phil. Mag. 1, 1901, pp. 98-100, or Scientific Papers, Vol. iv, p. 494.]

"Reviewing my then thoughts by the light of our present knowledge, I see that my error lay in the erroneous chemical assumption that sodium could not be free in the flame of a spiritlamp; I failed to perceive the extension of Prevost's theory, which would have come in conflict with that error*.-Yours sincerely, (Signed) "G. G. STOKES.

"To CHAS. WHITMELL, Esq."

"P.S., Dec. 31.—As Sir Wm. Thomson has referred in print to a conversation I had long ago with him on the subject, I take the opportunity of describing my recollection of the matter.

"I mentioned to him the perfect coincidence of bright and dark D, and a part at least of the reasons I had for attributing the latter to the vapour of sodium, using I think the dynamical illustration of the piano strings. I mentioned also, on the authority of Sir David Brewster, another case of coincidence (as was then supposed, though it has since been shown to be only a casual near agreement) of a series of bright lines in an artificial source of light with dark lines in the solar spectrum, from which it appeared to follow that potassium was present in the sun's atmosphere. On hearing this Thomson said something to this effect: 'Oh then, the way to find what substances are present in the sun and stars is to find what substances give bright lines coincident with the dark lines of those bodies.' I thought he was generalising too fast; for though some dark lines might thus be accounted for, I was disposed to think that the greater part of the non-terrestrial lines of the solar spectrum were due to the vapours of compound bodies existing in the higher and comparatively cool regions of the sun's atmosphere, and having (as we know is the case with peroxide of nitrogen and other coloured gases) the power of selective absorption changing rapidly and apparently capriciously with the refrangibility of the light.

If (as I take for granted) Sir William Thomson is right as to the date [1852] when he began to introduce the subject into his lectures at Glasgow (Address at the Edinburgh Meeting of the British Association [1871], page xcv.†), he must be mistaken as to

[* For another statement, see the author's Burnett Lectures on Light, second series, 1885, pp. 42-50.]

[ This Presidential Address is reprinted in Lord Kelvin's Popular Lectures and Addresses, Vol. 11, see pp. 169-175.]

the time when I talked with him about Foucault's discovery, for I feel sure I did not know it till 1855. Besides, when I heard it from Foucault's mouth, it fell in completely with my previous thoughts*.

"I have never attempted to claim for myself any part of Kirchhoff's admirable discovery, and cannot help thinking that some of my friends have been over zealous in my cause. As, however, my name has frequently appeared in print in connexion with it, I have been induced to put on paper a statement of the views I entertained and talked about, though without publishing.

"In ascribing to Stewart the discovery of the extension of Prevost's law of exchanges†, I do not forget that it was re-discovered by Kirchhoff, who, indeed, was the first to publish it in relation to light, though the transition from radiant heat to light is so obvious that it could hardly fail to have been made, as in fact it was made, by Stewart himself (see Proceedings of the Royal Society, Vol. X, p. 385). Nor do I forget that it is to Kirchhoff that we owe the admirable application of this extended law to the lines of the solar spectrum."

[* This is borne out by four existing letters, Feb. 24-Mar. 28, 1854, of Stokes to Thomson, with replies: also letters of Nov. 26 and Dec. 6, 1855, relating to the Foucault experiment. (Printed in Appendix to this volume.)]

[† See Kirchhoff's criticism on this and other matters in Pogg. Ann. CXVIII, 1862; Ges. Abhandl. pp. 625, 641; translated in Phil. Mag. xxv, 1863, pp. 250–262, as "Contributions towards the History of Spectrum Analysis and of the Analysis of the Solar Atmosphere"; and Stewart's rejoinder, ibid. pp. 354–360. Also Rayleigh, loc. cit. supra, and a rejoinder by Kayser, Handbuch der Spectroscopie, Vol. II, 1902, p. 10.]

[+ "On the Light radiated by Heated Bodies," Feb. 7, 1860. It is convenient to record here that in a supplementary paper, received by the Royal Society on May 22, 1860, "On the Nature of the Light emitted from Heated Tourmaline," Balfour Stewart expresses his obligations to Prof. Stokes for suggesting "an apparatus" by which an investigation of the polarization of the light was successfully made; namely a thick spherical cast-iron bomb, about 5 inches in external and 3 inches in internal diameter-the thickness of the shell being therefore 1 inch. It has a cover removable at pleasure. There is a small stand in the inside, upon which the substance under examination is placed, and when so placed it is precisely at the centre of the bomb. Two small round holes, opposite to one another, viz. at the two extremities of a diameter, are bored in the substance of the shell....Let the bomb with the substance on the stand be heated to a good red heat, and then withdrawn from the fire and allowed to cool...." See Proc. Roy. Soc. x, 1860, p. 503; Phil. Mag. xx1, 1861, p. 391. Kirchhoff had already made similar observations on a tourmaline heated in a Bunsen flame: cf. Phil. Mag. xx, 1860, p. 18.]

NOTE ON INTERNAL RADIATION.

[From the Proceedings of the Royal Society, XI, 1861, pp. 537-45.
Received Dec. 28, 1861.]

IN the eleventh volume of the Proceedings of the Royal Society, p. 193, is the abstract of a paper by Mr Balfour Stewart, in which he deduces an expression for the internal radiation in any direction within a uniaxal crystal from an equation between the radiations incident upon and emerging from a unit of area of a plane surface, having an arbitrary direction, by which the crystal is supposed to be bounded. With reference to this determination. he remarks (p. 196), “But the internal radiation, if the law of exchanges be true, is clearly independent of the position of this surface, which is indeed merely employed as an expedient. This is equivalent to saying that the constants which define the position of the bounding surface must ultimately disappear from the expression for the internal radiation." This anticipation he shows is verified in the case of the expression deduced, according to his principles, for the internal radiation within a uniaxal crystal, on the assumption that the wave-surface* is the sphere and spheroid of Huygens.

In the case of an uncrystallized medium, the following is the equation obtained by Mr Stewart in the first instance.

* To prevent possible misapprehension, it may be well to state that I use this term to denote the surface, whatever it may be, which is the locus of the points reached in a given time by a disturbance propagated in all directions from a given point; I do not use it as a name for the surface defined analytically by the equation (x2+y2+z2) (a2x2 + b2y2+ c2x2) — a2 (b2 + c2) x2 -- b2 (c2 + a2) y2 — c2 (a2+b2) z2 + a2b2c2=0. As the term wave-surface in its physical signification is much wanted in optics, the surface defined by the above equation should, I think, be called Fresnel's surface, or the wave-surface of Fresnel.

Let R, R' be the external and internal radiations in directions OP, OP', which are connected as being those of an incident and refracted ray, the medium being supposed to be bounded by a plane surface passing through O. Let OP describe an elementary conical circuit enclosing the solid angle 84, and let do' be the elementary solid angle enclosed by the circuit described by OP'. Let i, i' be the angles of incidence and refraction. Of a radiation proceeding along PO, let the fraction A be reflected and the rest. transmitted; and of a radiation proceeding internally along P'O let the fraction A' be reflected and the rest transmitted. Then by equating the radiation incident externally on a unit of surface, in the directions of lines lying within the conical circuit described by OP, with the radiation proceeding in a contrary direction, and made up partly of a refracted and partly of an externally reflected radiation, we obtain

or

R cos i 84 = (1 − A′) R′ cos i' do' + AR cos i dø,

(1 -- A) R cos i dμ = (1 — A′) R′ cos i' dø′ ...............
R'

2

In the case of a crystal there are two internal directions of refraction, OP, OP2, corresponding to a given direction PO of incidence, the rays along OP1, OP, being each polarized in a particular manner. Conversely, there are two directions, P10, P20, in which a ray may be incident internally so as to furnish a ray refracted along OP, and in each case no second refracted ray will be produced, provided the incident ray be polarized in the same manner as the refracted ray OP1 or OP2. In the case of a crystal, then, equation (1) must be replaced by

(1 − A) R cos i dμ = (1 — A1) R1 cos & d‡1 + (1 − A2) R2 cos i1⁄2§‡2 .......(2).

2

In the most general case it does not appear in what manner, if at all, equation (2) would split into two equations, involving respectively R1 and R. For if an incident ray PO were so polarized as to furnish only one refracted ray, say OP1, a ray incident along PO and polarized in the same manner as OP, would furnish indeed only one refracted ray, in the direction OP, but that would be polarized differently from PO; so that the two systems are mixed up together.

But if the plane of incidence be a principal plane, and if we may assume that such a plane is a plane of symmetry as regards