^{page 134 note *} This fluctuation appears to have been wholly, or almost wholly, owing to the imperfect communications established between the pile and the galvanometer, which, when I received the instrument from Paris, were in a very rude state, and the want of continuity gave rise to some curious phenomena. Since I had the more important junctions soldered, these anomalies disappeared.

^{page 135 note *} This remarkable effect, which may be described as an increase of tension by confinement, seems generally to exist where the conductors of imponderable agents oppose considerable resistance to their passage. It is familiar in Voltaic electricity, and I have often observed it in magnetic electricity. It is similar to the action which I have attempted to demonstrate in the passage of heat from good to bad conductors (see the 12th Volume of these Transactions), where we have the full advantage of the dynamical effect; whilst the existence of statical tension in heat seems likewise to be proved (as we might have anticipated) by the beautiful experiment described by Professor Powell in the Philosophical Transactions for 1834.

^{page 136 note *} Annales de Chimie et de Physique. December 1831.

^{page 138 note *} This might best be done by adapting a differential thermometer of extreme delicacy, so that the balls might be in contact with the two extremities of the pile, and the spaces round them filled up with copper filings, or some such material. But the experiment could hardly be quite decisive.

^{page 139 note *} The moon's image contained 0.114 square inches, whilst the area of the pile is about 0.40. Hence little more than a fourth of the pile was brought fully into action; but any dispersed light (for which we have made allowance), would act on the neighbouring parts.

^{page 142 note *} In operating with tourmaline, and also with other substances which transmitted directly but little heat, and which, therefore, required to be placed near the source of heat, in order to get distinct results, I have always found that the small differences of effect of which I was in search, became gradually less as the process of conduction advanced. The first result was generally the best marked. This effect may be compared to the destruction of the phenomena of diffraction in light, by the interference of other undulations than those producing the phenomenon sought. Such interfering waves would, in this case, proceed from the secondary radiation of the interposed bodies. But there seems also some inaptitude in the pile to accommodate itself to reiterated and very slightly different alternations of temperature.

^{page 142 note †} The oil lamp used when not expressly called “argand,” was Locatelli's lamp with a solid square wick, which is what M. Melloni employed.

^{page 144 note *} It appears that the axes of E and F were not precisely crossed in these experiments.

^{page 146 note *} Memoires d'Arceuil, tom. iii.

^{page 147 note *} See Professor Powell's papers in the Edinburgh Journal of Science Second Series, vols. vi. and x.

^{page 147 note †} The importance of analogies in science has not perhaps been sufficiently insisted on by writers on the methods of philosophizing. A clear perception of connexion has been by far the most fertile source of discovery. That of gravitation itself was only an extended analogy. The undulatory theory of light has been preeminently indebted to the co-ordinate science of acoustics, which afforded to Dr Young the most plausible basis of his curious and original investigations; and unless that science had existed, it may be doubted whether such a speculation would ever have been invented, or, if invented, would have been listened to. The penetrating sagacity of M. Fresnel, in his prosecution of the subject, has led him to draw from mechanical and mathematical analogies, accurate representations of laws which no strict reasoning could have enabled him to arrive at. Of this his marvellous prediction of the circular polarization of light by two total reflections in glass, is the most prominent example, a conclusion which no general acuteness could have foreseen, and which was founded on the mere analogy of certain interpretations of imaginary expressions. The mere reasoner about phenomena could never have arrived at the result,—the mere mathematician would have repudiated a deduction founded upon analogy alone. The cause of the long postponement of the discovery of electro-magnetism was the complete apparent breach of analogy between the modes of action of the electric and magnetic forces, and any others previously known.

^{page 148 note *} I did not see M. Melloni's second paper till the 10th of December, after I had obtained the chief fundamental results contained in this paper. It does not appear, however, that M. Melloni had thought of applying his instrument to any question of polarization except that of tourmaline, and in a note he alludes to the objections, which had been urged against Berard's conclusions, objections which he does not consider to have been overcome.—Ann. de Chimie, lv. 374.

^{page 150 note *} Plate B was used to polarize in this experiment.

^{page 151 note *} It should be remarked, that these experiments contain all the measures I have made with a view to this determination, except two, which were made the very first day I discovered the fact, and which were not accurate enough to be employed. I mention this, because, in such experiments, it is important to be assured of the constancy and marked nature of a result, which can only be appreciated by keeping back no fairly made observation.

^{page 151 note †} Though I am not aware of any source of error, I cannot help thinking, that, in this case, and in that of the tourmaline, Art. (21.), the defalcation of light is estimated too high.

^{page 156 note *} Observed by Dr Traill.

^{page 159 note *} I made one attempt to obtain polarizing effects by means of Mr Nicol's very elegant single-image calc-spar prisms, but without success, as I had anticipated, from the great proportion which the thickness of the spar necessarily bears to its aperture.

^{page 160 note *} That is, not reflected when the light is analyzed by reflection, or not transmitted when it is analyzed by refraction. In these experiments the latter method was always used.

^{page 162 note *} This corresponds to the formula of Airy's Tract on the Undulatory Theory, Art. 172. Both are only restricted expressions of more general theorems.

^{page 163 note *} Of course this is only true on the supposition that rays of heat and light are equally retarded. This is not demonstrated, but it is probable that they are nearly so, since that part of the heat which accompanies th,e spectrum is so, and the dispersion in the case of double refraction is inconsiderable.

^{page 167 note *} These conclusions were stated nearly in their present form (excepting the 6th), to the Royal Society at their meeting of the 5th January. The whole of the experiments detailed in this paper (excepting only the repetition of M. Melloni's experiment on the refraction of heat (16)), were made between the 22d November and the 16th January, but all the general consequences had been clearly made out before the close of 1834.