tensely heated in the oxyhydrogen jet only a continuous spectrum was seen*. "2. Experiments with Lime.-A platinum wire of the same thickness as the last was moistened with the phosphoric acid, some calcium nitrate was then taken up in the loop, and heated in the hydrogen flame until a residue of lime was obtained. At the outset the calcium-spectrum was observed, but the light speedily gave only a continuous spectrum. The lime and loop of wire were kept well enveloped in the hydrogen flame for nearly half an hour in order to ensure the complete decomposition of the nitrate. During this time no lines could be detected on the background of the continuous spectrum, or in the spectrum of the flame surrounding the lime. More hydrogen was now turned on and oxygen slowly admitted, the light being examined with the spectroscope during the time. When the proportion of oxygen had reached a certain point, faint traces of the two brightest Ca lines appeared on the bright background, and the intensity of these lines increased with the amount of oxygen admitted up to a definite extent. When a certain proportion of oxygen was exceeded, the lines became less distinct. The best results were obtained when the hydrogen was decidedly in excess of the oxygen in the flame, that is to say, more than in the proportion of 2: 1. "When the slit of the spectroscope was pointed in such a way that only the light from the flame surrounding the incandescent lime entered the instrument, all the Ca lines and bands were observed with great ease without a continuous spectrum. On looking at the mantle of flame with the naked eye it was easy to perceive a reddish tinge. I next maintained the small fragment of lime at the highest temperature its supporting wire was capable of resisting for three hours; at the end of this time the Ca lines were as strongly marked as before, and the lime on the wire had very appreciably diminished in amount. The same results were obtained when no phosphoric acid was employed to attach the calcium nitrate to the wire in the first instance. "Again, a piece of well-burned quicklime, of very small size, was heated alone on a platinum wire for more than an hour, and the bright Ca lines were seen during the whole time. "From the results of these experiments, we must draw the conclusions (1) that when lime is sufficiently heated the light which it emits is derived in part from the incandescent solid, and partly from ignited vapour; (2) that lime is either volatile as such, or that in the first instance it suffers reduction by the excess of hydrogen in the flame, the luminous vapour of calcium then giving its own peculiar spectrum. "3. Experiments with Erbia.-The specimen of erbium nitrate which * "Since writing the above, I have succeeded in observing the bright lines described by Mr. Huggins as occurring in the spectrum of the flame surrounding the incandescent magnesia. In the earlier experiments I probably admitted too much oxygen to the mixed gas-flame in the first instance." you kindly gave me was attached to a platinum loop with syrupy phosphoric acid as usual, and decomposition of the salt effected in the plain hydrogen flame. After heating for a short time in this way, the chief green line of erbia became visible, but seen upon the continuous spectrum. Oxygen was now turned slowly into the flame. As the temperature rose, two of the other bright lines of the earth were seen. The best observations were made when the oxyhydrogen flame had hydrogen in excess, and the erbia was kept in such a position that it was very strongly ignited. The erbia lines were most distinctly seen when the slit of the spectroscope took in the light from the extreme edge of the incandescent solid. When the bright lines were best observed, the continuous spectrum was relatively faint. Again, when the slit was made to cut the edge of the ignited bead of the earth, the strong green line of erbia was seen to extend to a very small but appreciable distance above or below (as the case might be) the continuous spectrum. I could only observe this for the strong line. I failed to get any trace of lines in the spectrum of the flame beyond the incandescent erbia. "The erbia was next heated in the oxyhydrogen flame to the maximum temperature that the wire would bear for three and a half hours, but the green line was seen to be just as strongly marked at the end as at the beginning of the experiment. The bulk of the erbia was so much reduced by this treatment, that I have now scarcely a trace left. "From the results of these experiments, I think we must conclude (1) that the light emitted by incandescent erbia is derived chiefly from the ignited solid, but that the bright lines observed in its spectrum have as their source a luminous vapour of extremely low tension at even the highest temperature of the oxyhydrogen flame; (2) that this interrupted spectrum belongs either to erbium or to its oxide. "If these conclusions are true, it follows that erbia is not an exception to the ordinary law. "It would appear that in these experiments three substances have been employed, varying in their degree of volatility. At the temperature of the oxyhydrogen flame magnesia appears to be less volatile than lime; but I am in doubt what relative volatility to assign to erbia, since its spectrum of bright lines can be seen when the earth is heated in the plain hydrogen flame, and yet at the much higher temperature of the oxyhydrogen jet the volume of luminous vapour does not appear to materially increase. "Finally, we have yet to learn whether or not in all these cases reduction of the oxide precedes volatilization; if reduction takes place, the luminous vapour must be that of the metal. The settlement of this question would no doubt be very difficult. But I rather incline to the view that the vapour whose spectrum is obtained on igniting these earths is that of the metal; for I find that the bright lines are most easily observed when hydrogen is present in excess in the oxyhydrogen flame. Moreover, the actual amount of matter volatilized on very prolonged heating is really very small, and this circumstance appears to favour the view that a slow surfacereduction is in progress." XII. “On the Values of the Integrals ("'Qn, Qu', dp, Qu, Qu' being Laplace's Coefficients of the Orders n, n', with an application (Abstract.) These integrals present themselves in calculations dealing with arbitrary functions on the surface of a sphere which vary discontinuously in passing from one hemisphere to the other. When n, n' are both even or both odd, the values of the integrals may be immediately inferred from known theorems in which the integration extends from −1 to +1, or over the whole sphere; otherwise a special method is necessary. In the present paper a function of two variables is investigated, which, when expanded, has for coefficients the quantities in question. As an example of the method, the problem is taken of a uniform conducting sphere exposed to the heat proceeding from a radiant point. It will appear at once that the heat received by any element of the surface is expressed by different analytical functions on the two hemispheres-a source of discontinuity which renders necessary a special treatment of the problem. The solution is afterwards generalized to meet the case of a sphere exposed to any kind of radiation from a distance. One remarkable result not confined to the sphere is, that the effect of a radiation which is expressed by one or more harmonic terms of odd order is altogether nil, with the single exception of the term of the first order. XIII. "Note on the Construction of Thermopiles." By the EARL OF ROSSE, F.R.S. Received June 14, 1870. Although in the measurement of small quantities of radiant heat by means of the thermopile much may be done towards increasing the sensibility of the apparatus by carefully adjusting the galvanometer and rendering the needle as nearly astatic as possible, there must necessarily be some limit to this, and it therefore appears desirable that the principles on which thermopiles of great sensibility can be constructed should also be carefully attended to. With the view of obtaining a pair of thermopiles of greater sensibility and of more equal power than I had been able to procure ready made, I made a few experiments with various forms of that instrument, and I was led to the conclusion (one which might have been foreseen) that the C you kindly gave me was attache "The erbia was next heated in the oxyhydr temperature that the wire would bear for three green line was seen to be just as strongly ma beginning of the experiment. The bulk of the by this treatment, that I have now scarcely a t "From the results of these experiments, I that the light emitted by incandescent erbia ignited solid, but that the bright lines observe their source a luminous vapour of extremely highest temperature of the oxyhydrogen flame; spectrum belongs either to erbium or to its oxide "If these conclusions are true, it follows that to the ordinary law. "It would appear that in these experiments thr employed, varying in their degree of volatility. At oxyhydrogen flame magnesia appears to be less volat in doubt what relative volatility to assign to erbin bright lines can be seen when the earth is heated flame, and yet at the much higher temperature of the volume of luminous vapour does not appear to mater "Finally, we have yet to learn whether or not in ai of the oxide precedes volatilization; if reduction tak vapour must be that of the metal. The settlem would no doubt be very difficult. But I rather incli vapour whose spectrum is obtained on igniting the metal; for I find that the bright lines are most hydrogen is present in excess in the oxyhydrogen actual amount of matter volatilized on very prolonged 20 size to catch all the radiant heat required to be measured, with it of a pile of (n) pairs, each of equal dimensions with those of the pair, the area of face being the same in the two cases. increasing the number of elements from one to n, we increase the r of solderings in that proportion; consequently the average 1 · of heat reaching any soldering is as great as that reaching the n of the single pair; therefore, if the same percentage of the be lost by conduction, the total electromotive force is the same "O cases. But inasmuch as the total cross-section of metal to The heat away from the anterior face is n times as great in the the pair, and the resistance of the pile is n times as great as epair, the pile will be inferior in power to the pair, unless causes of inferiority are counterbalanced by the loss due to the rage distance to the soldering from the points where the heat face, in the case of the pair, than that of the pile of n pairs. iments already referred to were made with three different ic pairs. These consisted each of a pair of bars of bismuth of twelve parts of bismuth and one part of tin of different f about equal lengths in each case, and soldered about inch on disks of sheet copper of inch diameter. A slip of wood 'ween the two bars, to protect them from injury, and to which 1 with thread. The three piles were compared with a pile of made by Messrs. Elliott, and the deviation due to the latter qual to unity, the following deviations were obtained for the pairs: light pile were also compared, taking the interval bedepressing the screen, first minute, and then =2 was found that, in the first case, |