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but B is supposed, in fact, to consist of an infinite number of terms, the type of which is the above, hence, omitting all terms which do not come under this type, for 3' we shall write # bog.
Similarly for 3-y", we shall write g 3 and we obtain by substitution,
putting also b = c,
which shews that the introduction of this term will affect the third term of the expansion for v", but not the second.
In fact to now takes the form
2A being the coefficient of bo sino above.
48. Of course, I do not mean to offer this as a solution of the equation, but merely as a proof of the possibility of its taking the above form: the quantity A may, in fact, be very different indeed from that above exhibited.
49. Now we found in the case of the ten substances examined by Fraunhofer, that eight of them gave the coefficient * negative,
whilst the other two gave it positive; the value of Ab must then be considerable (supposing the explanation of the fact to be contained here), and greater in the cases of glass than of water.
Now b', in the view above given, will determine the quantity of heat transmitted with the spectrum under any given circumstances, it follows therefore that substances which transmit heat most freely give ! small, and hence referring to the list in my former paper, I obtain the following order for transmission of Heat, beginning at that in which the freedom of transmission is the greatest.
50. I am not aware that the transmissibility of these substances has been accurately ascertained: it appears, as far as I have had opportunity of judging, that they exactly coincide with the above table.
But further, the velocity of transmission of the heat depends on the quantity b% according to the view of the subject which I have given above. We ought then to find the refractive index for heat, or rather that for the point of greatest heat in the spectrum, diminishing as bo increases, that is, as l in my former paper diminishes: the above table then must represent the order in which the points of greatest heat deviate from direct transmission, beginning with that of least deviation.
This subject has not been examined so extensively as to enable me to compare the results of theory with those of observation, numerically.
M. Seebeck’s results for Water, Crown Glass and Flint Glass, coincide with the above, and they are the only ones which he has given for Fraunhofer's substances.
51. It would be leading me too far into loose speculation, were I to proceed to consider the effect produced in the refractive index by the increase of temperature. In fact, we have so few experiments, by which such speculations could be guided, that it would be almost impossible to enter upon this subject. If we had a variety of substances, whose specific heat was well determined, and refractive indices known very accurately, it might be possible to trace the analogy that exists between light and heat with considerable accuracy. Admitting that the two fluids (which we have, for the sake of distinction, designated ether and caloric) are what we usually mean by those terms, it appears from the investigation that a transfer of caloric corresponds to an expulsion of ether. Hence, if the temperature (i. e. the density of the surrounding ether), and also the density of the body remain the same, whilst the latent heat is increased, we should expect the
ether proportionably diminished, and anticipate a corresponding increase of the refractive index.
Of course I am guided, in saying increase of the refractive index, by the hypothesis that the refraction increases as the density of the ether diminishes, which I have, elsewhere, shewn reasons for supposing true (Trans. Camb. Phil. Soc. Vol. vi. Part 1. p. 165.); on this ground
we may explain the high refractive power of water compared with that of ice.
52. Following this reasoning a little further, it is evident that the refractive indices for bodies should increase, catteris paribus, with the specific heat corresponding to equal volumes. We will assume the ordinary expression for the refractive energies of the different gases,
, s being the specific gravity, and compare the results with
their specific heat.
In the following Table I have placed, on the left-hand side, the order of the refractive energies of eight different gases, calculated from the above formula, and, on the right, the order of their specific heat; in each beginning with the one lowest in the scale.
The Table of Refractive Energies has been derived principally from M. Biot's Précis Elémentaire; that of Specific Heat entirely from MM. de La Roche and Berard.
Refractive Energy. Specific Heat.
The only want of coincidence in these two Tables occurs in the case of carbonic acid. It arises from the specific gravity being very great compared with those of the gases below it. Had we taken some root, as the cube root of the density instead of the simple power for our denominator in the formula for the refractive energy, which seems more correct, it is not improbable that all our results would have agreed.
Vol. VI. PART II. () o
The above, however, is sufficiently accurate for my present purpose, which is merely to give a colour to my investigations, and to shew that, at least, they tend towards the truth.
53. I do not suppose the same results would be applicable to solids, even if they are to fluids. For in solids the effect is modified or altogether destroyed by the action of the material particles. Indeed, the quantity of either kind of particles, and the arrangement of them within the body must depend so much on the constitution of the body, that, in many cases, I could imagine no ether, and, in others, no caloric, according as either from the disposition of the material particles or their peculiar nature, the forces which the one or the other exerts would keep up an equilibrium with the external forces of the mixed ether and caloric.
And even fluids from their greater or less fluidity would in like manner essentially modify the effects of transmission of vibrations through them; instances of the above we have seen in the case of light, to which I have before alluded. At the same time that I make these remarks, I have not attempted either to verify or disprove the above analogy.
54. The connexion which we thus establish between light and heat is of the most intimate description. I shall briefly mention one or two circumstances in the latter, which can be readily explained.
Reflexion of light must arise from the vibrations at the reflecting surface being stopped: it is evident then that the transmission, put in play by such vibrations, will also be stopped; hence if heat be in the act of emerging from a polished metal, when the pulsations reach the surface they will diminish greatly in magnitude, and thus the corresponding impulse of radiation will be small, whilst from an unpolished surface, the converse will be the case. The same is true of the acquisition of heat. This is abundantly confirmed by experiment. The same reasoning applies to total internal reflexion for heat as for light, with the exception that in the former the word total would refer only to such motion as is due to the action of the vibratory forces.