Denote these by ni, na, na, etc. Hence the general value of v is given by : In this particular case we have at x=0, v=0, hence At x=b, vconstant temperature V. .. V=α11 cos n1y cos n12+α12(cos n1y cos nz + cos ny cos n ̧2) .... + A22 COS nay cos n2z + .... +App COS np. Y cos np. z + αpq(COS ny cos nqz + cos nq y cos np2) + αqqcos nqy cos nqï+ To determine the coefficients a11, a12, a21, . . . etc. .... To find the general coefficient apq multiply both sides of equation by cos np.y.dy, and integrate from a to +a. On left-hand side we have: On right-hand side we have a series of terms involving an integral of the form 1 +a -α cos2 ny. dy cos nąz. cos (n-v)y.dy+ cos (n+v)y.dy = n + v a 0 1 Į (n + v) sin (n−v)a+(n−v) sin (n+v)a } . 21 value of n satisfies .. n sin na cos va-v sin va cos na =0. Thus the foregoing integral, which reduces to Multiply both sides by cos ng .z.dz, and integrate as •f*(1+ cos 2np.y)dy f* (1+ cos 2n,c)d2, 0 sin na sin na (a+ sin 2npa npa) 2np 3) (a+ sin 2n,a 2ng The solution of this equation is most simply performed by obtaining an approximate solution by means of a graph and then solving more accurately by "trial and error." E. g. Suppose specimen is of granite: XXIX. Anti-Stokes Radiation of Fluorescent Liquids. By R. W. Wood*. [Plate V.] XCEPTIONS to Stokes's law in the case of the fluorescing vapours of sodium, iodine, and other elements are the rule, as has been shown in numerous previous papers. In the case of solutions of organic dyes it is less easy to show the phenomenon; in fact its existence was a matter of dispute for nearly a quarter of a century. The very careful photometric work of Nichols and Merritt established its existence, but the observations appear to have been extremely difficult, and so far as I know no photographs have ever been published showing the presence of anti-Stokes radiations in the case of solutions. In preparing an article on fluorescence for the new edition of the Encyclopædia Britannica it appeared to be of interest to secure photographs establishing the reality of the phenomenon, and I was surprised at the ease with which results were secured. A very dilute solution of fluorescein (alkali-salt), rendered slightly turbid with a precipitate of silver chloride, was illuminated in a square bottle with the beam of light issuing from the slit of a two-prism monochromator. The function of the silver chloride was to scatter a small portion of the monochromatic light so that the narrow spectrum band of the illuminating beam would appear superposed on the fluorescent spectrum. The slit of the prism spectrograph faced the fluorescent track from the side. With blue light excitation the fluorescence was very bright and an exposure of half a minute was sufficient. A sodium flame was then placed behind the bottle for a few seconds for the purpose of securing a reference mark on the spectrogram. The result of this exposure is reproduced on Pl. V. fig. a, the exciting monochromatic band scattered by the silver chloride is at the left, while the D lines are at the right, the green fluorescent spectrum lying between the two. In figs. b and c the exciting band has moved up into the region of fluorescence, and the spectrum is seen well developed on the short wave-length side. The intensity of the fluorescence was much less in this case, exposures of four and five minutes being necessary. In fig. d the wave-length *Communicated by the Author. of the exciting band has increased to such a degree that fluorescence no longer manifests itself. Keeping in mind the principles of the quantum theory, the question presents itself as to where the energy comes from that makes the anti-Stokes radiation possible. In the case of sodium and iodine vapours there is no difficulty. The absorbing molecule may be in states of vibration and rotation higher than the zero states, and after excitation may revert to the zero state. In this case the excess energy necessary for the anti-Stokes term or terms was stored in the molecule before it absorbed the monochromatic exciting radiation. Or when in the excited state, say the 27th vibrational level, it may, by collision with another molecule, either of the same or a different gas, be carried to a higher vibrational and rotational level, and thus, on its reversion to the lower initial state, release more energy than it absorbed. Both of the above processes will be facilitated by high temperature, for in the case of the first process there is a greater chance of a molecule being initially in a state higher than zero, and in the second case the energy which can be delivered by the colliding molecule will be greater. High temperatures favour the development of anti-Stokes lines in the case of iodine vapour excited to fluorescence by the mercury line, as was shown by Pringsheim. green We might therefore expect that heating a fluorescent solution would favour the production of anti-Stokes radiation. To test this point the monochromator was set to deliver radiation as in the case of fig. b (Pl. V.), i. e., to excite with a wave-length inside of the fluorescence band. A test-tube was filled with fluorescein solution at 0°, and the upper part heated to boiling with a bunsen flame. On holding the test-tube in front of the slit of the monochromator, and moving it up and down, the upper portion (at 100°) was seen to fluoresce with much greater intensity than the lower (at 0°). This was not the case with excitation by blue light. In general the effect of high temperature is to decrease the fluorescence of organic dyes. Some samples of rhodamine are non-fluorescent at 100° while shining brightly at room temperature. There is another factor, however, which must be considered in this connexion. The absorption band advances towards the region of longer wave-lengths as the temperature is increased. This is a very general effect, and very obvious in the case of some coloured glasses. In the case of fluorescein upper part of the solution (at 100°) is, by transmitted the |