Scientific Memoirs/1/Memoir on the Free Transmission of Radiant Heat through different Solid and Liquid Bodies

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SCIENTIFIC MEMOIRS.





VOL. I.— PART I.




Article I.

Memoir on the Free Transmission of Radiant Heat through different Solid and Liquid Bodies; presented to the Royal Academy of Sciences of Paris, on the 4th of February, 1833, by M. Melloni.

From the Annales de Chimie et de Physique, t. liii. p. 1.

Mariotte was the first, so far as I am aware, who attempted to appretiate the action of diaphanous substances in transmitting or intercepting the calorific rays which emanate from terrestrial sources. After having observed that solar heat concentrated at the focus of a metallic mirror, suffered no sensible diminution of intensity by being made to pass through a glass plate, he took and placed his apparatus before the fire of a stove, and found, that at the distance of five or six feet the temperature of the reflected image at the focus, when the rays were allowed to meet there without impediment, was such as the hand could not bear; but that when the plate of glass was interposed there was no longer any sensible heat, although the image had lost none of its brilliancy. Whence he concluded that none[1], or certainly but a very small portion, of the heat of terrestrial fire passes through glass.

About a century after Mariotte's time, the same experiment was repeated by Scheele, who, instead of imitating the cautious reserve of his predecessor, asserted that from the moment when the glass was interposed there was no longer any heat whatever at the focus of the mirror[2]. Pictet, however, corrected the mistake by means of the apparatus known by the name of conjugate mirrors. A very transparent square of glass was placed between a thermometer and the heat of a lighted candle concentrated by the apparatus; the mercury in some moments rose several degrees; there was a perceptible elevation of temperature also when the candle was removed and a small jar filled with boiling water put in its place[3].

Some years later Herschel undertook a very extensive series of experiments on the same subject. They are described in the volume of the Philosophical Transactions for 1800. The author employs no artifice to increase the action of the rays of heat, and contents himself with the direct measurement of their effect by placing the thermometer at a very short distance from the diaphanous body.

But doubts were started as to the conclusions drawn from these different results. It was objected that part of the radiant heat was first stopped at the nearer surface of the glass, that it was gradually accumulated there and afterwards propagated from layer to layer, until it reached the further surface whence it began again to radiate on the thermometer. It was maintained even that nearly the whole of the effect was produced by this propagation. In short, some went so far as to deny altogether that the heat emitted by terrestrial bodies can be freely transmitted through any other diaphanous substance than atmospheric air.

M. Prevost, by means of a very ingenious contrivance, demonstrated the erroneousness of this opinion. Having attached to the pipe of a fountain a spout consisting of two parallel plates, he obtained a strip of water about a quarter of a line in thickness. On one side of this he placed an air thermometer and on the other a lighted candle or a hot iron. The thermometer rose, almost always, some fraction of a degree[4]. Now it is quite evident that, in this case, a successive propagation through the several layers of the screen, which was in a state of perpetual change, could not take place. It was admitted, therefore, that other diaphanous media besides atmospheric air sometimes transmit the rays of heat as instantaneously as they always transmit those of light.

M. Prevost's process could not however be applied to solid bodies. It was therefore impossible to determine, by means of it, whether caloric was immediately transmitted through screens of glass. Delaroche completely solved this problem by employing a method invented by Maycock[5]. The method consists in observing the thermometer as in the preceding cases; that is, when the caloric rays fall upon it after having passed through the plate of glass. We thus obtain a complex measure of the effects produced by immediate transmission and by that conducting power of the layers to which we have given the name of successive propagation. If we know the value of either of these, we have that of the other. Now it is easy to determine the influence of the conducting power by repeating the experiment after having blackened with Indian ink that surface of the plate which is turned towards the calorific source. In this case, the immediate radiation being intercepted, it is clear that the elevation of the temperature at the other side must be attributed only to the conducting power of the layers. Should the elevation be now found less than it was at first, it will be a decisive proof of immediate transmission. And such was the fact in almost all the experiments of Delaroche; I say almost all, because it was found that the quantity of heat freely transmitted varied with the temperatures of the source. For temperatures lower than that of boiling water it was nothing, and when an Argand lamp[6] was employed, it was found to be more than half of the whole quantity.

No doubt can be raised as to the truth of this beautiful discovery of Delaroche; and yet the method which he has employed to measure the quantities of heat freely transmitted is by no means exact, especially in respect to high temperatures. In order to understand this seeming paradox two things are to be observed; 1st, the difference produced by change of surface between the two quantities of heat which penetrate the glass by reason of its conducting power; 2nd, the difference produced between those two quantities by the total or partial interception of the calorific rays.

It is fully proved by the experiments of Leslie and others, that glass, when blackened with Indian ink, absorbs all the rays of heat, though, in its natural state, it reflects a certain number of them. The quantity of heat which penetrates the screen will therefore be greater in the former than in the latter case. However, as polished glass reflects but a very small portion of caloric rays, the error arising from a difference in the state of the surface will be reduced to a very inconsiderable quantity and may be safely disregarded. But the case is different when we examine the error produced by the total or partial interception of the caloric radiation. In some of the experiments of Delaroche one half, at least, of the incident rays immediately passed through the screen. Thus it was evident that it was the other only which was stopped at the first surface of the glass. The effect of conduction must therefore be limited to this latter half. But as the screen, when blackened, stops the whole radiation, it is then exposed to a heat twice as strong, and therefore exhibits a far greater effect of conduction. Hence it follows that when we deduct from the observation furnished by the transparent glass the observation furnished by the glass blackened, the result obtained will be lower than the true temperature of the rays transmitted freely. But the error will not be the same in all cases. Being of no account when boiling water is employed, it will increase in proportion as the temperature of the source is raised. The measures of the free radiations which suffer the greatest diminution will be those furnished by the highest temperatures. Hence it is evident that this latter cause of error in the measure of the immediate irradiation, instead of invalidating the law of Delaroche, serves only to give it greater certainty. We are therefore justified in saying, as we have said, that the want of exactness in the method has no influence whatsoever on the truth of the law which it has served to establish.

To Delaroche we are also indebted for a discovery, no less important than the foregoing, relative to the amount of loss sustained by the same rays of heat in passing successively through two squares of glass. But I abstain, for the present, from entering into any detail on this subject, as I shall have occasion to speak of it hereafter[7].

None of those whose labours we have been thus briefly noticing has thought of making an exact comparison between the transmissions of caloric rays through screens of different kinds; and, if we except the experiments of M. Prevost and those of Herschel, from which no consequence can be deduced, all the others were confined to the single purpose of ascertaining the law of transmission through glass only. Neither has sufficient attention been given to the influence of the state of the surface, or that of the thickness of the layers and their internal structure on the quantities of heat which freely pass through them. I have endeavoured to supply these different omissions, but the undertaking has proved too vast for me, and several parts of it are therefore incomplete. I hope however that I shall be able hereafter to return to these, and to treat them in a manner more satisfactory.

In the mean time I present to the Academy the results of my first researches disposed in two memoirs. That which I offer at present contains an account of the method pursued in the measurement of calorific transmission and the application of the method in the case of an unvarying source acting on bodies of different kinds. In the second I shall explain the facts connected with the succession of the screens and the variation of the sources.

General Considerations on the Free Transmission of Caloric through Bodies, and the Manner of Measuring it by means of the Thermomultiplier.

We have already observed that a diaphanous screen placed at a certain distance from a calorific source stops a portion of the rays which strike its first surface, while the rest pass freely through. We have remarked besides that after a certain time the heat stopped at the anterior surface, and accumulated there by successive radiations, passes on from layer to layer till it reaches the other surface, whence it begins to radiate anew; and that this radiation mingling with the heat which passes through the screen by immediate transmission, prevents its being measured exactly.

When the screens are liquid, the influence of the conducting power of the layers may always be destroyed if we incessantly renew the matter of the screen by means analogous to the strip of water employed by M. Prevost. But it would be always very difficult, and often impossible, to apply this artifice to solid bodies and even to such liquids as can be obtained only in small quantities. In order therefore to attain the same end in a general manner, and to render the experiments in some degree independent of conduction, other means must be employed.

If we consider with due attention the manner in which the second surface of the interposed plate is heated, and the radiation which results from it, we shall see that the latter possesses properties very different from those that belong to the caloric which is freely transmitted. In order to be satisfied of this, we have only to observe that its action changes with the change of distance between the screen and the source; a thing which does not happen, even in the slightest degree, to those rays that are transmitted freely. In fact, it is with the caloric transmitted immediately, as it is with light.

If between the flame of a candle and the eye we interpose a plate of glass or any other substance more or less transparent, we find the diminution of the intensity of the light always the same, however the distance between the plate and the candle may vary. The effect produced by distance on the freely transmitted caloric is exactly similar; and if at a certain distance from the active source there be a thermoscopic apparatus sensible to this portion of heat, the apparatus will always give the same indication, whether the screen be laid close to the source or to the thermoscope.

But it is clear that it must happen quite otherwise to the conductible caloric; for this portion of the heat, when it has reached the further surface of the screen, leaves it in the form of diverging rays which become weaker in proportion to the distance. In other words, the further surface of the screen being heated becomes a new calorific source whose intensity of radiation must decrease as the distance increases.

We possess, therefore, a very simple contrivance for destroying the influence of conduction, if we keep the action of the free radiation intact. This contrivance consists in removing the screen so far from the thermoscope that the radiation of its own heat may, on account of its extreme feebleness, be totally disregarded.

There are, however, some precautions to be taken; for in proportion as the distance between the screen and the thermoscope is increased, the distance between the source and the screen is diminished. The latter is therefore more heated, and radiates with greater force upon the instrument. It is easy to show by calculation that we always gain; that is, that we always weaken the conductible caloric more and more by removing the screen from the thermoscope, until we have placed it midway between the thermoscope and the source[8]. Let us, therefore, put the screen in this position (which is the most favourable of all), and we shall see that its heat has then no appretiable influence on the results obtained by means of the thermomultiplier[9], and a source whose radiation is much weakened by distance.

The apparatus is disposed in the following manner. A thermoelectric pile of thirty pairs is closed at one end and enveloped, at the other, in a small tube blackened inside to prevent reflection. At a certain distance there is placed a large metallic diaphragm, with an aperture at the centre equal to the section of the pile. On the other side, in the same line, there is a lighted lamp, which is brought more or less close, until the needle which serves as the index of the galvanometer, marks an elevation of 30°. The radiation is afterwards intercepted by a screen of polished metal placed between the lamp and the diaphragm, and the needle returns to zero. Then there is placed on the other side of the diaphragm a stand, with a plate of glass fixed on it, and the whole apparatus is moved gently until it is brought midway between the pile and the calorific source.

This being done, the opake screen is removed; the rays passing through the glass fall on the pile, and immediately cause the galvanometer to move. In 5s or 6s it is driven through an arc of nearly 21°·5, but it afterwards returns nearly to zero, oscillates in an arc of greater or less extent, and at last settles definitively at 21°. This last deviation decidedly marks the whole effect; for it is useless to continue the experiment for 15s or 20s. There is no longer any perceptible movement.

The time which the needle takes to attain its position of steady equilibrium is a minute and a half[10]. When the experiment is repeated with other plates of glass, or of any transparent substance whatsoever, possessing different degrees of thickness, from the hundredth part of a line to five or six inches, the galvanometer exhibits deviations greater or less than 21°; but the time requisite to attain the equilibrium is in all cases the same. In short, if we mark the time which the needle takes to arrive at 30°, we shall find it to be one minute and a half.

The invariability of this time, in such a variety of circumstances, affords the most decisive evidence that the deviations of the galvanometer are exclusively due to that portion of heat which reaches the pile by immediate transmission. Whence it follows, that in the arrangement we have adopted, the heat of the transparent body has no appretiable influence on the instrument.

But a direct proof of this proposition may be obtained by operating on opake screens.

I take a plate of glass a millimetre in thickness. I blacken it on one side, and put it in the place of the transparent plate, taking care to turn its blackened surface to the lamp. The needle remains stationary, although the caloric rays continually fall on the anterior surface. It will be found immoveable also, if we employ a plate of copper coated on both sides with black colouring matter, or a thin flake of wood, or even a sheet of paper. Thus, though we should suppose the screen to be diaphanous, exceedingly thin, an excellent conductor of caloric, and possessing great powers of absorption and emission, the utmost elevation of temperature that can be acquired during the experiment would not furnish rays sufficiently strong to move the index of the galvanometer.

One is surprised at first to see caloric rays capable of giving a deviation of 30° fail to produce any effect when they are absorbed by the screen, which must necessarily send its acquired heat upon the apparatus. But our surprise ceases when we reflect that this heat is sent equally in all directions by every point of the heated screen, and therefore that the portion of total radiation which reaches the apparatus is but a very small fraction.

We shall see hereafter, that the anterior surface of the pile does not measure six square centimetres. With these data, if we suppose even that the thirty degrees of heat are completely absorbed by the screen, and afterwards dispersed through space, we find that the quantity of the rays which reach the thermoscopic body does not amount to the six-hundredth part of the whole. But the galvanometer that I use is capable, at the most, of marking only the 150th part of the force which moves the needle to 30°. Thus, even though the instrument were capable of discovering the presence of a heat four times as feeble, there would be no perceptible action.

The experiments which I have been describing seem to me to leave no doubt whatsoever as to the truth of the proposition just now enunciated; namely, that in my mode of operating the deviation of the galvanometer proceeds entirely from the heat instantaneously transmitted through the screen. These proofs, though so conclusive to my mind, seem however not to have been equally convincing to others; for I have heard some persons say, "We grant that the deviation of 21° obtained through the screen does not arise from the caloric propagated by conduction from the anterior to the other surface, but it may be maintained that it is caused by a heat instantaneously diffused, in the same manner as light, over all the points of the glass." Before we admit such a mode of transmission, it seems to me that we ought to demonstrate its existence by some decisive experiment. But supposing it true, then we must also suppose one of these two things,—either that the molecules of the glass acquire from the action of the source such modifications that they themselves become so many calorific centres, and return to their natural state when the radiation is stopped; or that the heat, which is supposed to be diffused through the material points of the screen, is but common caloric obeying the known laws of equilibrium. In the first case we should be only attempting to explain the very cause of the transmission, and the hypothesis, true or false, does not at all invalidate the fact which we are desirous to establish. In the second case, this heat, when it has reached the interior of the body, must take some time to issue from it; besides, this time must vary with the thickness of the screen, and its powers of conduction and emission. But let us intercept the calorific communication in our apparatus; let us remove the diaphanous screen from its stand, and expose it for some moments to the free radiation of the lamp on the other side of the diaphragm: if the supposition be true, the internal molecules of the glass will instantaneously acquire some heat. In order to see whether this heat really exists, let us replace the screen on its stand before the pile, still leaving the calorific communication with the lamp intercepted. The further surface of the plate of glass will, according to the hypothesis, immediately begin to emit towards the pile that caloric which reaches it successively from within, and the index of the galvanometer must lose its equilibrium. But whatever be the nature or the thickness of the screen with which this experiment is performed, we never obtain the slightest indication of a movement in the magnetic needle. It is therefore completely demonstrated that the deviations of the galvanometer exhibited in the experiments made with the diaphanous screens are not to be attributed, in the least degree, either to the external or the internal heat of the screen itself, but solely and exclusively to free transmission. Thus, whenever, in consequence of the radiant heat of the source being made to fall on a screen, a deviation of the galvanometer is perceptible, we may rest assured that the whole of the effect produced is to be ascribed to the rays of heat immediately transmitted through it, in the same manner as luminous rays.

Before I conclude these preliminary considerations, it is necessary to remark, 1st, that galvanometers of very great sensibility, such as must be used for the thermomultiplier, do not directly indicate quantities less than half-degrees; 2ndly, that the ratios of the degrees of the galvanometer and the forces of deviation are unknown. But it is often useful to have the fractions below the half-degree, and in certain circumstances it is absolutely indispensable to know the ratios of the several degrees of calorific action which move the magnetic needles to different distances from their primitive position.

To find the fractions sought, we have only to take the means of a certain number of observations. As to the ratio of the deviations and the forces, it is difficult and, in the present state of the science, perhaps impossible to determine it generally. But electric piles, such as those employed in the construction of the thermomultiplier, furnish sufficiently simple means of solving the question in each particular case. Indeed there is nothing easier than to keep the index of the galvanometer at any degree of deviation. All that is required for this purpose is to place a lighted lamp at proper distance from either side of the thermoelectrical pile. To prevent the possibility of mistake on this point, let us suppose the axis of the pile to be perpendicular to the magnetic meridian, and the communications so fully established that, when the left or the right side of the pile is heated, a corresponding deviation will be exhibited by the galvanometer. Let there be now produced a sufficiently marked deviation by placing a lamp near enough at the same side. Let this deviation be 44°. After having brought the needle back to 0° by interposing a metallic screen, let us make it move to the 42nd degree of deviation on the left, by means of a second lamp placed on the other side. To bring the needle back again to the zero point of the scale, we have only to stop the radiation by means of a metallic screen, as before.

It is natural to ask what will be the effect now produced by the heat of both lamps being brought to bear simultaneously upon the opposite sides of the pile. The calorific effects will be partially destroyed, and the instrument will mark but their difference. If the same force were always required to make the needles describe arcs containing the same number of degrees, the index would stop at the second degree of deviation to the right; but we know that these effects continually increase to the right and to the left of zero. The difference of two degrees just now observed between the partial deviations of 44° and 42° was owing to the application of a force greater than what is required to make the index traverse the first two degrees of the scale. The position marked 2° will therefore be exceeded, and the more so in proportion as the first force is greater than the second, and the arc described will, when compared with the difference of the two deviations, immediately give the measure of the corresponding force. If, for instance, the needle stops at 8°, it will be inferred that the force required to make the needle pass from 42° to 44° is four times greater than that required to make it pass from zero to 2°. This effect would be five times greater if the needle stopped at 10°, and so of the rest.

I shall not attempt to conceal the fact, that in this process the proportionality of the forces to the degrees in the arc employed as a comparative measure is tacitly assumed. But the assumption is fully justified by experience; for we find that in galvanometers whose astatic system has been brought to a high degree of perfection, the magnetic needles, through the whole extent of the arc comprised between zero and the twentieth degree nearly, describe arcs proportional to the action of the electric current to which they arc subjected. To be convinced of this, it is by no means necessary to review in succession all the degrees that contribute to the formation of this arc. The application of our method to the angles of 20° and 10° will be quite sufficient. This being done, we shall find an equal quantity between their difference and the effect produced by the simultaneous action of the moving forces. In other words, let us produce a deviation of 20° to the right and one of 10° to the left: let us then simultaneously expose the two opposite faces of the pile to the two radiations which produce these galvanometric indications: the index will move to the right, and stop precisely at 10°. Hence we infer that the force necessary to make the needle describe the arc comprised between 10° and 20° is equal to the force required to make it pass over the first ten degrees of the scale. Thus the proportion of the degrees to the forces is perceptible as far as the 20th degree on each side of zero.

This fact seems opposed to the inference which might have been made in examining the nature of the galvanometric action; for, in the successive rotation of the astatic system, the poles of the magnetic needles depart from the mean line of the electric currents. The intensity of the repulsive forces, therefore, decreases in proportion as the angle of deviation increases. Whence we should conclude that the effort necessary to make the needles exceed a given arc should change as soon as the first degrees of the scale are passed. This would undoubtedly take place if all the electric currents lay in a vertical plane passing through the line marked 0°; but the circumvolutions of the metallic wire which is wound on the frame placed under the graduated circle are distributed to a certain extent on each side of this plain. In the galvanometer which I have employed in my experiments, they cover the two opposite arcs of 76°, the chords of which are perpendicular to the line marked 0°. Thus so long as the oscillations take place within certain limits there will always be electric currents situated on each side of the needles. Now when the intensity of these currents is extremely feeble, their sensible effect on the needles must cease at a very short distance. Let us suppose this distance to be 18° of the division of the galvanometer intended to show the degrees of electric action which cause the deviations to the right and left for the first 20° of the scale. These degrees of action must be extremely feeble in a very delicate galvanometer. If, during these oscillations, the system of the needles is confined within the two initial arcs of 20°, it is clear that it will always be subject to the same action, whatever may be the position in which it is placed; for there will always be near its plane a series of currents extending to 18° on each side, even when the system will occupy the extreme limits. The influence of the currents that are further distant will, according to our hypothesis, be nothing. As the moving force will therefore have a constant value, we shall have to consider only the modifications which the active part of this force is made to undergo by the different inclination of the needles to the direction of the currents; and these modifications are quite analogous to those which take place in the portion of gravity that acts on the pendulum in different arcs of oscillation.

Now the force necessary to make the pendulum vibrate from one inclination to the other, is proportional to the difference of the cosines of the angles which the two directions form with the vertical. Whence it is clear that it remains sensibly constant in the arcs that are not far removed from the line of rest. The same effect must therefore be produced in the galvanometer also; or, in other words, the force required in this apparatus to increase the deviation of the index by a degree will be constant near the line of zero, as is shown by experiment.

From what we have just said it will be easy to see that the relation between the degrees of the galvanometer and the forces which cause the deviations of the needles, must depend on the sensibility of the astatic system and the distribution of the wire on the frame[11]. It will vary, therefore, according to the construction of the instrument, but may be always determined by the method we have mentioned.

Experiment having shown that in my galvanometer the proportion of the degrees to the forces was perceptible as far as the twentieth degree of the scale, I have attentively observed the passage of the index through every 4°, by commencing with this position and continuing my observations as far as the forty-fourth degree. There I stopped; for my experiments on calorific transmission were to be confined to radiations considerably weakened by distance.

The arcs passed once in virtue of the forces acting on the system of the needles at different points of their course are in the following ratios to one another:

The arc comprised between

20° and 24° is equivalent to ·12, commencing at zero.
24 28 ———— 6 ·44
28 32 ———— 8 ·00
32 36 ———— 9 ·92
36 40 ———— 12 ·44
40 44 ———— 19 ·04

Each number in the third column represents the mean of eight observations, which agreed with one another as exactly as could be expected from the nature of the instrument. Often equal, sometimes differing by 0°·5, their greatest disagreement never exceeded 1°. A better proof cannot be given of the exactness of the method.

The linear construction of these results, which gives a very regular curve convex towards the axis of the xes, has enabled me to obtain the values of the intermediate forces, degree by degree, from 20° to 45°. By connecting them with the fundamental observations, I have formed the following: table of the intensities:

Degrees. Forces. Degrees. Forces. Degrees. Forces.
 20° 20·0  29° 33·4  38° 55·4
21 21·1 30 35·3 39 58·5
22 22·3 31 37·4 40 61·9
23 23·7 32 39·6 41 65·5
24 25·1 33 41·8 42 69·3
25 26·6 34 44·1 43 73·4
26 28·2 35 46·7 44 78·0
27 29·9 36 49·5 45 83·2
28 31·6 37 52·4
The use of a table requires no explanations. All the forces are referred to that which makes the index describe the first degree of the scale. The values corresponding with the first twenty degrees are not exhibited in it; for through the whole extent of this arc the number representing the force is equal to the number of degrees contained in the arc passed over by the index. Thus, for instance, when we look for the forces which produce the deviations 35° and 16°, the first (46·7) will be found in the table, but the second, being under 20°, will have the same value as the arc; that is to say, 16. When we want to find the forces which correspond to fractions of a degree, we have only to ascertain the proportional part of the degree in question; for, in the interval between one degree and another, the curve visibly coincides with the tangent. If, for example, we wish to know the force that corresponds to the deviation 31°·7, it will be sufficient to take at first the difference between 37·4 and 39·6 (the intensities of the forces belonging to 31° and 32°); this difference being 2·2, we shall find the value (x) of the force corresponding to seven tenths of the degree contained between 30° and 32° by this proportion,

1° : 0°·7 :: 2·2 : x 1·5.

Adding this to the number 37°·4, which represents the force corresponding to 31°, we shall have 38·9 as the value sought.

Of the Polish, the Thickness, and the Nature of the Screens.

The suggestions which we have offered as to the manner of measuring the quantity of caloric instantaneously transmitted by diaphanous bodies, and as to the precautions to be taken during the experiments, leave us scarcely anything more to say on this subject. Nevertheless it may not be amiss to mention some particulars relative to the construction of the apparatus before we proceed to the exposition of the results.

The pile employed in these researches is of the form of a quadrangular prism; its two ends are plane surfaces, each measuring 4·24 centimetres; it consists of 27 pairs and a half, or 5 elements of bismuth and antimony, 32 millimetres long, 2·5 broad, and 1 in thickness. It was not without considerable difficulty that we succeeded in combining and soldering together these minute bars. The facility with which liquid antimony oxidizes, the difference between its fusibility and that of the bismuth, and the extreme fragility of the two metals, presented so many obstacles, that it cost many an effort to overcome them. But a pile of very small dimensions was indispensable in the investigation of the laws of immediate transmission through rare liquids and crystallized solids. This was, therefore, to be obtained, or the experiments to be abandoned. By this conviction we have been induced to persevere in spite of repeated disappointments, and by redoubling our patience have at last succeeded.

The electric pile is passed into a ring formed of a thin square flake of copper internally lined with pasteboard and having a screw which serves to fix it on the stand, so that the axis naturally takes that horizontal position which it is to keep during the greatest part of the experiments. To each side of the ring there is fitted a tube of six centimetres in length, blackened on the inside; and at a certain distance from the mouths of these tubes are placed the stands destined to receive the screens. In strictness, a single tube and a single stand would be sufficient, and one of the sides of the pile might be closed by means of a small metallic cover; but, when we have to operate on bodies differing in quality and thickness, it often happens that they differ in temperature not only from one another but from the pile also. Then if we place but one screen before the apparatus, the calorific actions at the two sides are unequal, the index of the galvanometer moves away from zero, and we must wait for some time until the equilibrium of the temperature is established and the index returns to its original position.

Now this inconvenience cannot occur when the pile is furnished with two tubes and two stands; for, by placing before each side of it a plate of the same quality and thickness, it is clear that, if care be previously taken to place the two in the same circumstances, they will have the same temperature, and will consequently emit the same quantity of heat on the two sides of the pile. The index of the galvanometer will remain stationary, whatever may be the difference of temperature between the plates and the thermoscopic body, and we may therefore immediately proceed with the experiments. Hence, if we would save time, we should always have a pair of screens of each sort; and, as we have just observed, put both sides of the pile in the same state.

In order to ascertain the influence exercised on free transmission, by the different circumstances relating to the surface, the volume, and the composition of the screens, we must procure a constant source of heat. For this purpose, there is nothing better than a good lamp with a double current of air and a constant level. When this apparatus is well prepared and filled with oil freed from mucilage, by means of sulphuric acid, we obtain a flame which maintains an invariable temperature for more than two hours. Of this I have been able to satisfy myself by means of the thermomultiplier. But in order to have things in this preparatory state, we must wait some moments until the pipe, the oil, and the glass funnel of the lamp shall have attained a maximum of temperature. This time, which varies a little with the construction of the lamp, is about ten or fifteen minutes.

There may be some objections raised against the employment of an Argand lamp as a calorific source. It will be said, perhaps, that in this lamp the heat acts only through the glass funnel; that the funnel itself becomes heated, and mixes its rays of nonluminous heat with the luminous caloric of the flame; and lastly, that such a source of heat is neither uniform nor separated from the agent which usually accompanies it in high temperatures.

But I wish it to be particularly observed, that the only thing about which we are interested at present is, to know whether the state of the surface, the colour, and the internal structure of a body, as well as its chemical composition, have any influence whatever in the quantity of heat which it transmits immediately; and that, in this point of view, the origin and the qualities of the caloric rays become objects of perfect indifference; for it is enough for our purpose that the rays be invariable and identical in all the circumstances in which they are employed. Now this actually is the case with the rays issuing from the well supported flame of a Quinquet lamp placed at a fixed distance.

When we shall have found the ratios of the quantities of heat transmitted by screens of different kinds under the influence of a constant source, then, agreeably to what we have stated in the introduction, we shall examine the changes which those ratios undergo in consequence of the variation of the sources.

All our experiments of comparison have been made with the same calorific radiation. Previously to the commencement of each series the rays were allowed to fall directly on the pile, and the distance of the lamp was modified until the needle of the galvanometer fixed itself at 30° of the scale.

We have remarked in the preliminary considerations, that all the external parts of the thermoscope are sheltered from the caloric rays by means of a large screen of polished metal, having in its central part a hole to correspond with the opening of the pile turned towards the lamp.

In order to establish or to intercept the communication between this aperture and the source of heat securely and commodiously, we make use of a moveable copper screen, consisting of two or three parallel plates fixed on the same support. The side of the pile opposite to the lamp may also be closed and opened by means of a screen altogether similar, and for the following purpose:

When, after having observed the effect of any radiation whatsoever, we intercept the action of the source, we must wait until that face of the pile on which the rays of heat are darted has been restored to it natural state before we make a second observation. Now it appears that the heat emitted by the flame penetrates the apparatus with greater ease than it issues from it, because of its natural tendency to an equilibrium. At least the experiment shows that the time requisite to produce the deviation is to that in which the needle recovers its original position nearly as one to five; for the latter is from 7s to 8s and we have seen that the whole deviation is produced in a minute and a half. Whatever be the cause of this difference between the time required for heating and that required for cooling, we must always allow 8s to elapse after one experiment before we proceed to another, if we confine ourselves to the placing of the first moveable screen before the radiating source. But let the opposite side of the pile be opened and a lighted candle brought close to the corresponding face: it is evident that if the candle be held for some minutes at a suitable distance, and the communication then intercepted, the needle will be forced back to zero in an interval of time less than 8s. These operations would be impossible if the side of the pile opposite to the lamp were hermetically closed. The second moveable screen serves then to abridge the duration of the experiments. It is particularly useful when the calorific action has been very powerful or considerably prolonged, which sometimes happens in the first attempts at adjustment. During these, the portions of heat penetrate the pile to a great depth, and cannot return until a considerable time has elapsed. Before these simple means of correction had occurred to me, the difficulty of restoring the equilibrium of the two extremes of the pile, as well as that which I experienced in respect to he different temperatures of the screens and the apparatus, often obliged me to stand still for fifteen or twenty minutes between two consecutive experiments.

When any object of research requires numerous experiments, we should endeavour from the very outset to avail ourselves of all that contributes to make them more expeditious; for the least delay arising from imperfectness of method will, by gradually accumulating, ultimately render the labour of whole days utterly fruitless. Yet, the attention being absorbed by the main object, these little defects are at first unnoticed. At length, however, we become sensible of them, and endeavour to apply a remedy when it is almost too late. But the result of the experiment is not without its use, since it may be more or less serviceable in analogous circumstances. This consideration must be my apology for the minuteness of detail into which I have entered.

The first problem that presents itself, in the series of questions relative to the passage of radiant heat through solid bodies, is to determine the influence which the degree of their polish has, and the quantity of rays transmitted. In order to solve this, we have but to apply our thermometrical method to several screens perfectly similar in all respects, except as to the state of the surface.

Out of the glass of a mirror which was very pure, and nine millimetres in thickness, I cut eight pieces sufficiently large to cover the central aperture of the screen when they were placed on the stand; and, after having removed the quicksilver, I wore them down with sand, emery, and other such substances, so as to form by their succession a complete series of plane surfaces more or less finely wrought, from the first and coarsest to the highest and most perfect polish. These different pieces reduced to one common thickness of 8mm·371[12] and expose to a radiation of 30° of the thermomultiplier, have furnished the following results:

Order of the screens. Deviations of the
galvanometer.
1. Translucid 5°·38      
2. ————— 6·50
3. ————— 8·66
4. Dull 12·58
5. —— 14·79
6. Slightly dull 17·42
7. Transparent 18·79
8. —————— 19·15

These transmissions present nothing extraordinary: the quantity of heat which passes through the medium is greater in proportion as the surface is more finely polished, as it happens in respect to light. The only thing to be remarked is, that in the high degrees of polish a slight difference produces a very slight effect. This is evident from the observations made on Nos. 7 and 8.

Similar processes enable us to determine the influence of thickness, which is one of the elements most necessary to be known in the theory of transmission.

Four pieces cut out of a fine mirror were reduced with great nicety to different degrees of thickness in the ratio of 1, 2, 3, 4: particular care was taken to give to their principal surfaces a perfect parallelism, and the highest polish possible. The following are the deviations which they successively produced in the index of the galvanometer under the action of the same radiation, namely 30°:

Thickness of the screens
in millimetres.
Deviations of the
galvanometer.
Corresponding
forces.
2·068 21°·625 21·850
4·136 20·312 20·343
6·202 19·687 19·687
8·272 19·375 19·375

Each number in the second column is deduced from fifteen observations: the quantities registered under the denomination of forces, representing in this particular case the respective temperatures or quantities of rays transmitted, have been calculated according to the principles with the exposition of which we concluded our general observations. The force or temperature answering to 30°, as given by the table of intensities, is 35·3; now, by dividing each number of the third column by 35·3, we shall obtain the ratios of the transmitted rays to the incident rays. The difference between each of these quotients and unity will give the corresponding loss; that is, the proportional part of the rays that are stopped. By performing these operations, and representing the whole radiation by 1000, we obtain

Table A.
Order of the
screens.
Transmitted
rays.
Rays stopped.
1. 619 381
2. 576 424
3. 558 442
4. 549 451
Let us imagine the thickest of the screens split into four equal layers; the quantities of heat falling upon each will be

1000,619,576,558,

and the quantities lost in successively traversing the four intervals

381, 424—381, 442—424, 451—442;

that is to say,

381, 43, 18, 9.

We shall then have for the ratios of the respective losses to the incident quantities,

3811000, 43619, 18576, 9558,

or

0·381, 0·071, 0·031, 0·016.

Thus the losses continue to decrease with great rapidity as the thickness increases by a constant quantity.

We have seen that the action of the radiation on the thermomultiplier commences at the instant when the communications are established, produces the greatest part of its effect in the first five or six seconds, and ceases entirely after a minute and a half. These facts, which are equally true of the direct rays and of those which reach the pile after having passed through screens of any thickness whatsoever, constitute the best proof that caloric is transmitted by radiation through the interior of the diaphanous bodies. If, nevertheless, a new confirmation of this truth were desired, it would be found in the successive diminution of the losses which the rays undergo in crossing the different layers of a transparent medium. Were the heat, which is the subject of our immediate inquiries, the effect of a species of conducting power, the losses would continually increase from layer to layer, or would remain constant, from the moment when the rays penetrated the medium, and could never follow the opposite law of decrease.

The progressive diminution of the losses is, moreover, entirely peculiar to the calorific radiation, whose properties in this and in many other respects are altogether different from those of the luminous rays. In fact, everything leads us to believe that the equal layers which succeed one another in a diaphanous medium, act in the same manner on the rays of light which come in succession to pass through them, and that they consequently absorb or reflect a quantity of light proportional to the intensity of the incident rays; that is to say, that the loss sustained by the luminous radiation at every layer of equal thickness is constant. In the case under consideration, the invariable decrement of the light at each of the layers into which we suppose the screen divided is found to be none at all, or extremely feeble, because of the perfect transparency of the glass; and yet the caloric rays undergo in their successive passages an absorption, the sum of which is equal to about the half of their whole value; and the losses at each layer, instead of being constant, as happens to those sustained by the luminous rays, are found to differ enormously from one another, being in the proportion of the numbers 381, 71, 31 and 16.

The resistance of diaphanous media to the immediate transmission of the rays of heat is therefore of a nature altogether different from that which is presented by the same media to the propagation of light.

Whatever be the cause of this singular difference, it is highly important to determine with certainty whether it takes place at great distances from the surface at which the rays enter; and this may be done by repeating the experiments on layers of glass much thicker than those which we have been using.

With this view I took several pieces of the glass of Saint-Gobain, and caused them to be recast. This operation was not completely successful. The matter either formed itself into layers that were too thin, or was slightly striated. From among the thick pieces I selected that which was the purest. It was six inches in length. I divided it into three parts, of one, two, and three inches in thickness. The defects being uniformly distributed over all the points of the mass might probably enough alter the quantity of the caloric rays that would have passed through a perfectly pure mass of the same matter and thickness; but it is clear that they could have no influence on the nature of the progression of the losses which these rays might undergo in passing from one layer to another.

The following are the results obtained by exposing these screens to the ordinary radiation of 30°:

Thickness of the screens
in millimetres.
Galvanometric deviations.
27 17°·105
54 13·458
81 10·702

By a calculation exactly similar to that already made we find that, of every thousand rays emanating from the source, each screen transmits or stops the following quantities:

Order. Rays transmitted. Rays stopped.
1. 484 516
2. 380 620
3. 303 697
By means of these data we obtain as the values of the calorific losses, considered with reference to the quantities of rays which present themselves successively to pass through the three equal layers into which we may suppose the last screen divided,

0·516 0·215 0·203.

These losses are still greater than those preceding, because of the badness of the material and the greater thickness of the layers, but they are still in a decreasing progression. Thus the diminution continues beyond 54 millimetres.

To compare this diminution with that which took place in the last screen in the preceding experiments we must multiply 0·012 (the difference between 0·215 and 0·203) by 2·068, and divide the product by 27. In this way we obtain the mean diminution for a thickness of 2mm·068 in passing from 54 to 81 millimetres, which is nearly 0·001; in the preceding experiment it was fifteen times as much while the rays passed through the same layer of 2mm·068 placed at a distance of 6 millimetres. The difference would be still greater if we had used very transparent layers of glass, such as flakes of the glass of a mirror attenuated.

Nevertheless I had some doubts as to the homogeneity of the glass: I was afraid that the striæ might not be equally distributed over all the points of the mass. But not being able to procure large pieces of this material entirely free from defects, I thought that analogous experiments performed with liquids might answer quite as well. In employing these instead of glass there was, in case of success, the additional advantage of extending the law of calorific transmission by making it independent of the physical constitution of the medium.

I procured therefore several copper troughs, of the same breadth but of different lengths, bounded at each end by a glass plate. These I placed successively between the perforated screen and the pile in such a manner that the anterior glass plate was quite near the screen, the distance of which remained constantly the same. The common section of the troughs was much larger than the central aperture of the screen; the reflexions on the lateral faces could not take place, and the only rays that entered a little out of the perpendicular direction reached the anterior surface of the pile. The lamp was moved up so near that the needle of the galvanometer exhibited a deviation of 30° through the two glass plates of each trough. The radiation was then intercepted, the trough filled with oil of colza[13], and after having waited until the needle recovered its original position we reestablished the calorific communication.

The deviations obtained through the different thicknesses of the liquid are exhibited in the following table.

Degrees of thickness of
the liquid layer.
Deviations of the galvanometer.
mm °
6 ·767 15 ·642
13 ·535 12 ·831
27 ·069 10 ·389
54 ·139 9 ·540
81 ·209 8 ·988
108 ·279 8 ·512

The free radiation being always represented by 1000, the respective quantities of the rays transmitted and those stopped are found to be:

Table B.
Degrees of thickness of
the liquid layer,
Rays transmitted. Rays stopped.
mm
6 ·767 443 557
13 ·535 363 637
27 ·069 294 706
54 ·139 270 730
71 ·209 255 745
108 ·279 244 756

If we suppose the last layer (of 108mm·274) subdivided into six parallel slices of the following degrees of thickness: 6mm·767, 6·767, 13·535, 27·069, 27·069, and 27·069, we shall be able to determine, by means of the numbers contained in the two last columns, the quantity of heat incident to the first surface of each of these slices and the quantity lost in the passage. Dividing the second by the first we shall ascertain the loss. It is unnecessary to exhibit the operations in detail, as they are in all respects similar to those which have been performed in reference to the screens of glass. Here are the final results:

Degrees of thickness of the six
successive slices into which
we suppose the layer of
108mm·274 to be divided.
Losses in the respective transmissions
referred to the quantities of
rays which arrive at the
surface of each slice.
mm
6 ·767 0 .557
6 ·767 0 ·180
13 ·535 0 ·190
27 ·069 0 ·082
27 ·069 0 ·056
27 ·069 0 ·040
Whence it is concluded that the losses still decrease at a distance of about 100 millimetres.

To comprehend at a single glance the law of the propagation of caloric radiating through diaphanous media we have only to reduce the results contained in the first two columns of the Tables A. and B. to a linear construction.

The mere inspection of the curves thus constructed shows that the rays lose very considerably when they are entering the first layers of the medium. But in proportion to their distance from the surface we see that the loss decreases and that at a certain distance it is almost imperceptible, and the rays seem to continue their progress, retaining all their intensity; so that in glass and in oil of colza, and probably in all other diaphanous media, the portion of heat which has forced its passage through the first layers must penetrate to very great depths.

Delaroche had found that the heat which has passed through one plate of glass becomes less subject to absorption when it is passing through a second. The identity of this fact with the law of resistance in continuous media shows that the solution of the continuity and the interposition of the atmosphere between the two screens do not alter the nature of the modifications which the rays undergo in the first plate of glass. It is therefore exceedingly probable that the proposition of Delaroche is true with respect to a very numerous series of thin screens; for we have just seen that in the same medium the losses still diminish to the depth of 80 or 100 millimetres. In reference to this point, the following is the result of the experiments I have made with four plates of the same glass that had been employed in the first attempts to investigate the law of propagation through continuous media The common thickness of these plates was 2mm·068.

Numbers of
the screens.
Deviations of the galvanometer.
°
1. 21·62
2. 18·75
3. 17·10
4. 15·90

It is scarcely necessary to observe that the common radiation to which the screens had been exposed was always 30 degrees, answering to a force or temperature of 35·3. If we represent this radiation by 1000, as we have done in all the foregoing cases, we have:

Numbers of the screens. Rays transmitted. Rays stopped.
1. 619 381
2. 531 469
3. 484 515
4. 450 540
Whence we have

0·381, 0·134, 0·087, 0·058,

as the losses suffered by the rays in successively passing through the four plates of glass; it being carefully kept in mind that these values are not referred to the initial quantity, but to the number of rays which arrive at the surface of each screen.

Thus the proposition of Delaroche is true as far as the third and the fourth screens; for in the transition from one loss to another a diminution of each loss is observable.

It will have been observed that the losses were not so great in respect to the four equal layers of the screen of a fourfold thickness; and that this should happen will be easily conceived if we consider that in the latter case there is a solution of continuity which causes a greater dispersion of the heat by reflexion. But we see that in both cases the difference between two successive losses becomes less in proportion as the distance from the surface, at which the rays entered, is greater.

Let us now proceed to consider the influence exercised on calorific transmission by the composition of the substance of the screen.

M. Prevost had concluded from the experiments described in a memoir already quoted, that water and glass ought to transmit rays of heat in different quantities; for by causing the sheet of water to fall between the lighted candle and a very delicate air-thermometer, he obtained no indication of heat being transmitted unless when he had blackened the ball of the thermometer, and even then the increase of temperature was extremely small; whilst a plate of glass substituted for the sheet of water produced effects sufficiently manifest[14]. But it was objected to him that the difference between the action of the water and that of the glass was owing to the conductible caloric which was perceptible in the latter case only. Delaroche subsequently observed that a square of greenish glass transmitted more heat than a plate of another species of glass perfectly pure. However, as the first flake was much thinner than the second, it was insisted that the difference in the effects was owing to the difference of thickness. At length, some time after the invention of the thermomultiplier, M. Nobili and myself made some experiments on olive oil, alcohol, water, and nitric acid; whence we inferred that water opposed a greater resistance than any of the three other liquids did to the passage of rays of heat emanating from a hot iron[15]. But these experiments are to be regarded only as mere trials, tending to show the facility with which the thermomultiplier may be employed in all sorts of inquiries relative to calorific radiation; for we did not take sufficient precautions to prevent the heat from passing by means of conduction, and to be sure that the temperature was the same throughout. Thus it was still believed that the portion of heat transmitted through solid or liquid substances was governed by the same laws as the transmission of light, and that, cæteris paribus, the most diaphanous bodies transmitted the greatest quantity of caloric rays.

The results which I am about to state seem to me to establish beyond the possibility of doubt a fundamental proposition in the theory of radiant heat, namely, that the power of transmitting caloric rays is by no means proportioned to the transparency of the media; it is subject to a different law, which, in bodies without regular crystallization, appears to have many affinities to refrangibility. In crystals the phænomena are still more interesting, since in them we find that bodies possessing a high degree of transparency intercept nearly the whole of the caloric rays, while some others act in a manner directly contrary. These properties are invariably manifested whatever be the temperature of the source, and become yet more singular at low temperatures; for in the latter case we find that the ordinary heat of the hand passes immediately through a solid body of several inches in thickness. Let us not, however, anticipate as to the facts, but first of all examine the methods pursued in this third series of experiments.

In the first place it is unnecessary to dwell on the manner in which the solid screens have been exposed to the radiation and the indications of the thermomultiplier, for in this respect everything was the same as in the previous experiments. As to the liquids, these bodies are less permeable to radiant heat than solid bodies are. They must therefore be brought nearer to the thermoscope in order to obtain a well-marked transmission; but then the proper heat of the molecules themselves might be able to act on the instrument, and this the more certainly as the motions always developed in liquids unequally heated easily transfer the particles of the anterior to the further surface of the layers exposed to the source of heat. This effect of conductibility cannot be neutralized in a general manner by continually renewing the interposed layer, as in the experiments of M. Prevost; for some of the liquids can be procured only in small quantities; others, as soon as they are exposed to atmospheric air, undergo considerable alterations and evaporations which produce corresponding elevations or depressions of temperature that prove very annoying in experiments of this kind. The contrivance which I have employed for the purpose of avoiding these inconveniences is very simple. It consists in putting the liquids into very flat glass recipients, whose two large lateral surfaces are perfectly parallel, and the height four or five times that of the surface of the thermoelectrical pile. The lower part Of these vessels is applied to the mouth of the tube that envelops the face of the apparatus turned towards the source. The heat stopped by the anterior face of the vessel penetrates the first infinitely thin layer of the liquid; but this layer, while it is becoming hot, undergoes a certain dilatation, becomes lighter than the rest of the fluid mass, and ascends immediately to the upper part of the vessel, whence it can have no longer any influence on the pile. It is replaced by a second layer, which undergoes a similar process, and this again by others; so that by these partial renovations of the liquid screen, the hinder part of the glass applied to the aperture of the tube is not in contact with heated molecules, and retains the same temperature for a long time.

It was extremely difficult to make flat glass vessels with very regular surfaces of the same thickness throughout, and with the opposite sides exactly parallel. Metallic frames and glasses joined with gum could not be employed because of the corrosive action of the several liquids. After many a fruitless effort to surmount this difficulty, I thought at last that the process by which the index of refraction of liquids is measured in optics might be available in this case also. With this view I had quadrangular pieces of two centimetres in breadth and nine centimetres in length cut out of several pieces of the same mirror unsilvered and sufficiently thick. I laid close to the two faces of each of the pieces from which the excision had been made two flakes made out of another and a much thinner glass. It is known that the mere adhesion of two plates of polished glass is sufficient to prevent the passage of liquids. However, in order to be more secure, I introduced each recipient between two metallic frames, which held the thin glasses in their places by means of four screws placed at the angles. The liquid was poured into these vessels at a small aperture made at the top, and furnished with a glass stopper. In such a system there could be no doubt of the parallelism of the faces and the equal thickness of the layers.

The results furnished by the several bodies, both solid and liquid, I have disposed in several tables, each of them exhibiting at the top the common thickness of the screens employed and, beside the substance, the indications of the thermomultiplier and the quantity of rays transmitted as compared with the whole radiation. This distribution, while it allows the use of plates of different thicknesses, has the additional advantage of presenting distinct groups of each class of bodies. The free radiation in each case was 30°. In order to link the results of these tables together, I have commenced the second and the third with the numbers given by a flake of glass placed in the same circumstances as the plates which constitute each group: thus the glass set down in the table of liquids was contained between the two thin plates of the recipients, and made of the thick looking-glass employed in their construction. It was therefore exactly of the same thickness as the liquid layers, and, like them, came into contact with the thin plates which formed the faces of the recipients. But as those faces themselves intercepted a portion of the heat, the lamp was brought nearer and nearer until we obtained, through the combination of the three plates, the same indication of 19° that was furnished by the thick glass when exposed singly to the radiation of 30°.

Table I.—Glass (uncoloured). Common thickness 1ᵐᵐ·88.
Deviations of
the galvanometer.
Rays
transmitted.
°
No screen 30·00 100
Flint-glass (of Guinand) 22·90  67
Flint-glass (English) 22·43  65
Flint-glass (French) 22·36  64
Another kind 22·19  64
Mirror-glass 21·89  62
Another kind 21·10  60
Another kind 20·78  59
Crown-glass (French) 20·58  58
Window-glass (common) 19·25  54
Another kind 18·56  52
Another kind 17·83  50
Crown-glass (English) 17·22  49


Table II.Liquids. Common thickness 9ᵐᵐ·21.
Deviations of
the galvanometer,
Rays
transmitted.
°
Mirror-glass 19·10 53
Carburet of sulphur (colourless) 21·96 63
Chloride of sulphur (of a strong brownish red colour) 21·83 63
Protochloride of phosphorus (colourless) 21·80 62
Hydrocarburet of chlorine (colourless) 13·27 37
Nut-oil (yellow) 11·10 31
Essence of turpentine (colourless) 10·83 31
Essence of rosemary (colourless) 10·46 30
Oil of colza (yellow) 10·38 30
Oil of olives (greenish yellow) 10·35 30
Naphtha (natural—a light brown yellow)  9·77 28
Balsam of copaiba (a sufficiently decided brown yellow)  9·39 26
Essence of lavender (colourless)  9·28 26
Oil of pink [huile d'œillet] (very slightly yellowish)  9·26 26
Naphtha (rectified, colourless)  9·10 26
Sulphuric æther (colourless)  7·59 21
Pure sulphuric acid (colourless)  6·15 17
Sulphuric acid (of Nordhausen, of a sufficiently decided brown)  6·09 17
Hydrate of ammonia (colourless)  5·47 15
Alcohol (absolute and colourless)  5·30 15
Hydrate of potassium (colourless)  4·63 13
Acetic acid (rectified, colourless)  4·25 12
Pyroligneous acid (of a slightly brownish colour)  4·28 12
Sugared water [eau sucrée] (colourless)  4·20 12
Alum water (colourless)  4·16 12
Salt water (colourless)[16]  4·15 12
White of eggs (slightly yellowish)  4·00 11
Distilled water  3·80 11


Table III.Crystallized bodies. Common thickness 2ᵐᵐ·62.
Deviations of
the galvanometer,
Rays
transmitted.
°
Mirror-glass 21·60 62
Rock salt (diaphanous) 28·46 92
Iceland spar (diaphanous) 21·80 62
Another species (diaphanous) 21·30 61
Rock crystal, colourless (diaphanous) 21·64 62
Rock crystal, smoky (diaphanous and very decidedly brown) 20·25 57
Brazil topaz, colourless (diaphanous) 19·18 54
Carbonate of lead (diaphanous) 18·35 52
White agate (translucid) 12·48 35
Sulphate of barytes (veined, dully diaphanous) 11·72 33
Emerald (diaphanous, of a light blue) 10·16 29
Yellow agate (translucid, yellow) 10·10 29
Borate of soda (translucid)  9·87 28
Green tourmaline (diaphanous, green)  9·54 27
Adularia (diaphanous, dull, veined)  8·30 24
Sulphate of lime (diaphanous)  7·15 20
Fluate of lime (diaphanous, dull, veined)  5·40 15
Citric acid (diaphanous)  5·15 15
Sardoine (translucid)  4·98 14
Carbonate of ammonia (diaphanous, dull, striated)  4·50 13
Tartrate of potash and soda (diaphanous)  4·40 12
Alum, crystal (diaphanous)  4·36 12
Sulphate of copper (strongly diaphanous, blue)  0·00  0

Table IV.Glass (coloured). Common thickness 1mm·85.
Deviations of
the galvanometer,
Rays
transmitted.
°
Deep violet 18·62 53
Yellowish red (flaked) 18·58 53
Purple red (flaked) 18·10 51
Vivid red 16·54 47
Pale violet 16·08 45
Orange red 15·49 44
Clear blue 15·00 42
Deep yellow 14·12 40
Bright yellow 12·08 34
Golden yellow 11·75 33
Deep blue 11·60 33
Apple green  9·15 26
Mineral green  8·20 23
Very deep blue  6·88 19

It is sufficient to cast the eye rapidly over the second and third tables to be fully sensible of the truth of the proposition, that "the capacity which bodies possess of transmitting radiant heat is totally independent of their degree of transparency."

In fact, the liquid chloride of sulphur of a tolerably deep red brown transmits a considerably greater number of caloric rays than the fat oils of nut, the olive, and colza having a clearer tint; while these oils, although of a very decided yellow colour, are more permeable to radiant heat than several other liquids which are perfectly limpid, such as concentrated sulphuric and nitric acid, æther, alcohol, and water. The case is the same with solid bodies, among which we see sulphate of lime, citric acid, and other very diaphanous substances allow a much smaller quantity of heat to pass than some other bodies coloured or translucid, such as emerald, agate, tourmaline, borax, adularia, and sulphate of barytes.

But nothing is better calculated to demonstrate that transparency has little or no effect in the transmission of heat than a comparison of the effects obtained by the crystal of alum with those obtained by means of the smoky rock crystal. The table shows that, in respect to these substances as well as the others which we have just mentioned, the capacity to transmit radiant heat is inversely as the capacity of transmitting the rays of light. I was anxious to try how far this inverse ratio of the calorific to the luminous transmissions might extend, by varying the degrees of thickness so as to give to the light all the advantage and the whole of the loss to the caloric. We submitted to the test a plate of well-polished and perfectly transparent alum only one millimetre and a half in thickness, and a smoky rock crystal the thickness of which in the direction of its polished faces was 86 millimetres. The brown colour of the crystal was so decided that when it was laid on a printed page in which the letters were very large, and placed in the fullest light, even the traces of the letters could not be distinguished. The paper and the printed characters became confounded together and presented the same dark hue. This crystal, however, transmitted 19°, while the thin plate of alum transmitted only 6°.

A body may then be very opake and afford a very easy passage to the rays of heat; or very transparent and intercept the greatest part of them. It is therefore necessary to distinguish those bodies which possess a capacity for calorific transmission from those which possess a capacity for luminous transmission, by giving them different denominations. The terms transcaloric and diathermanous[17] (transcaloriques ou diathermanes) seem to me to be best suited to this purpose, as being most analogous in form to the epithets transparent and diaphanous, applied to bodies endowed with the property of transmitting light.

After the statement made in respect to the smoky rock crystal, one might be tempted to ask whether there are any transcaloric substances totally opake. To that question no answer can be given until the effect of calorific radiation upon all known bodies has been tried, and this I am far from having done. I can only go so far as to say that pyroligneous acid in the rough state, and Peruvian balsam, though almost completely opake, afford perceptible transmissions of radiant heat. But all the diathermanous substances that I have subjected to experiment are comprised within that class of bodies which possess some degree of transparency. Those kinds of metal, wood, and marble which totally obstruct the passage of light obstruct that of heat also. Some other bodies, such as carburet of sulphur, rock salt, and Iceland spar, allow both kinds of rays to pass at the same time. It is therefore probable that calorific transmission cannot take place without a certain degree of transparency[18]; but it cannot take place abundantly without the cooperation of another quality, which varies as the bodies happen to be crystallized or without crystallization. We find, in fact, that in the different sorts of glass and liquids it follows the order of the different degrees of refrangibility; for flint-glass possessing a greater refracting power than crown-glass affords an easier passage to the caloric radiation. Carburet of sulphur is at the same time more refracting and more diathermanous than the essence of turpentine; the same may be said of turpentine as compared with olive oil, and so on until we come to pure water; a liquid which, as it possesses the least power of refraction, possesses also the least power of transmitting heat. It is very true that, in the tables, glass appears almost as diathermanous as carburet of sulphur, although its refracting power is considerably less; but this equality is but in appearance; and to be convinced that it is so, we have only to recollect the manner in which the liquids have been subjected to the experiments. Before they can reach the liquid layer, the rays must have passed through the anterior face of the vessel containing it, and the glass gives but a transmission of from 21 to 22 for 35·3. Thus the radiation that will penetrate to the interior of the vessel will be of no greater force than this; so that even if the liquid transmitted all the rays that reached it, the quantity issuing from the recipient cannot exceed 22. This explanation is confirmed in a very striking manner by the transmissions of the chloride of sulphur and the protochloride of phosphorus. The indices of refraction of these two liquids, though not well known, are certainly higher than that of glass, and have different values; a fact from which it may be inferred with great probability that the quantities of transmitted heat are also different, though in the tables both these quantities appear equal to the transmission assigned to the carburet of sulphur.

There are, it is true, some real anomalies in the transmissions through balsam of copaiba and sulphuric æther. But the differences are very small, and may probably be referred to some slight error in the measure of the transmission or the refraction. The proportionality of these two elements is obvious, and so fully established in such a variety of cases, that it may hold as a general law for liquids, for the several kinds of glass, and probably for all those bodies which are without regular crystallization.

But this law totally fails with respect to crystallized bodies. We see, in fact, that carbonate of lead, a highly refractive and colourless substance, transmits less heat than Iceland spar and rock crystal, which are much inferior to it in refracting power; while rock salt, possessing the same transparency and the same index of refraction as citric acid and alum, gives six times their amount of calorific transmission.

The transparent and colourless bodies contained in the third table are nine in number, namely, rock salt, Iceland spar, rock crystal, topaz, carbonate of lead, sulphate of lime, citric acid, tartrate of potash and soda, and alum. These crystals transmit the following quantities of heat respectively:

92, 62, 54, 52, 20, 15, 12.[19]

Differences so striking in bodies of the same aspect seem to arise rather from the particular structure of each crystal than from the chemical composition of the molecules; for a block of common sea salt being divided into flakes instantly arrests calorific radiation; and we perceive besides, by means of the second and third tables, that the transmissive power of pure water is increased nearly in the same degree whether we dissolve in it alum or rock salt, two substances which, in their solid state, transmit very different quantities of heat. But we perceive no relation between the power of transmitting heat and the primitive or the secondary form of crystallization.

M. Mitscherlich has found that the dilatation of crystals, when they are submitted to the action of heat, is not equal on all sides. Although such an effect may not proceed from the radiant heat, yet it might be thought that a difference in the direction in which the plates are cut out of the crystal would produce a difference of transmission. I have had plates of equal thickness cut out of rock crystal in all the principal directions relatively to its axes. The transmission varied in no case. I obtained the same results from Iceland spar.

Radiant heat is capable of passing through crystallized bodies of very considerable thickness. It may be affirmed, also, that the rays do not lose so much in the interior of these bodies as they do in the masses of glasses and of liquids. For we have seen that the deviation changed only from 21°·6 to 19°, though the smoky rock crystal first employed was replaced by one of fifty-seven or fifty-eight times its thickness.

I have exposed to the action of radiant heat a piece of Iceland spar 92 millimetres[20] in length. The deviation, which was 21°·8 through a flake of the same substance 2ᵐᵐ·6 in length, fell no lower than 18°·5; a circumstance which shows that the diminution of effect was only about one seventh for an increase of thickness equal to thirty-five times that of the first piece. The experiment was still more interesting when I employed rock salt, in which I was unable to discover that thickness had any influence whatever on the amount of the transmission: for pieces of 2ᵐᵐ gave the same galvanometric deviation as pieces of 30ᵐᵐ and 40ᵐᵐ.

From these observations it follows that the numbers in the second column of the table of crystals, though they express the ratios of the calorific transmissions of those bodies reduced to the common thickness of 2ᵐᵐ·6, may be employed also to represent approximately the ratios of the transmissions, even when the common thickness is greater. I say approximately, because, in order to determine the true specific transmissions, it would be necessary to know the exact law of the loss at the several points of the media. If the losses, as compared with the quantities of heat which arrive at each of the thin laminæ into which we may imagine the medium to be divided, were constant, the intensity of the rays would decrease in a geometrical, while the layers increased in an arithmetical ratio; and in order to know how much one substance is more diathermanous than another, we should vary the relative degrees of thickness of the plates until we obtained the same transmission in the two cases. The ratio sought would be inversely as the degrees of thickness which produced an equality of action[21]. Now we have seen that this constancy in the loss does not exist. But in the particular case of crystallized bodies, the differences are so very small when the thickness is increased beyond 3ᵐᵐ, that the ratios obtained by operating on thicker screens would not differ materially from those which we have found.

But even if we had succeeded in ascertaining the specific transmissive powers of the different substances, the question would not yet be solved in a general manner; for we shall see in the second Memoir, that if, while we vary the temperature of the calorific source, we do not change the order of the transmissions also, the relations of these quantities are no longer the same. To perceive this we have only to recollect what has been already stated as to the action of rays emitted from a source of low temperature on certain substances; that is, that the heat of the human body instantly passes through a certain crystal, and that crystal is rock salt.

It is known that the caloric rays of the hand are completely stopped by glass. Hence, although the ratio of transmission between glass and rock salt, when the source is an Argand lamp, be 62 : 92, it becomes 1 to infinity when we consider the effects produced by sources of a low temperature.

Hitherto we have made no account of the colours [of the diathermanous bodies], or, rather, have considered them only in relation to the diminution of transparency, or to the greater or less opacity which they always cause in diaphanous substances[22].

We must now examine them more particularly, and determine their influence on transmission. Such is the object of the fourth table. The tints of those kinds of glass marked with an asterisk are the purest, and approach nearest to those prismatic colours that bear the same names. Of this I have satisfied myself by the following experiments. Having by means of a heliostat introduced a horizontal sheaf of solar rays into a dark chamber, I divided it into two by causing it to pass through two apertures made in an opake screen. I contrived to make one of the sheaves fall on a vertical prism, and the other on a coloured glass which I wished to try. Thus the solar spectrum was seen cast on one side, and a coloured spot in the line of the direct rays. To bring this spot into contiguity with the corresponding colour of the spectrum, I placed behind the glass a second vertical prism which turned about until the desired effect was obtained. The two analogous tints are always easily compared when they are near each other, and at the same time we are able to judge whether the colour of the glass be more or less pure by the new tints which are always developed in the passage of the coloured rays of the glass through the prism. Of fourteen colours selected from several species of glass, I have found but five making any near approach to the prismatic colours and producing very feeble secondary tints. These tints were absolutely imperceptible only in the case of red glass.

There is another mode (and it has not been overlooked) of appretiating the influence of colour in diaphanous media. It consists in causing corresponding rays of the spectrum to pass through the glasses. The passage is attended only with a very inconsiderable loss when the tints are very pure. Now by fixing one side of my five plates of glass at proper distances on the margin of a sheet of pasteboard exposed to the coloured sheaf of the prism, I found that each prismatic ray traversed glass of the same colour without suffering any loss of intensity. At least, the alteration produced by these glasses on the corresponding solar rays was nearly the same in all cases. This fact is inferred from a comparison of the prismatic rays which fall on the wall directly and those which reach it after having passed through the coloured pieces of glass. The shadows brought by the latter rays are so very light as to be almost imperceptible. In every other case they are very strongly marked. If for instance we substitute the violet for the red, the spot on the wall is almost dark; if the violet be not perfectly pure, it will not at least transmit a quantity of red rays less than that which passes through the red glass.

It is known that in the solar spectrum produced by a prism of common glass, the greatest heat is found in the red, and that the intermediate temperatures continually decrease until we come to the violet. Does this calorific distribution in the coloured rays, separated by the refracting power of the prism, exist also when they are separated by the absorptive power of the colouring matter?

In order to ascertain this we have only to compare, at the different temperatures of the spectrum, the numbers which represent the calorific transmissions of our five coloured glasses; they are as follows:

violet red yellow blue green
53, 47, 34, 33, 26.

The order of the colours considered relatively to their degrees of heat and the numerical relations of those degrees are so altered that the violet light, which in the spectrum possesses a temperature twenty-five or thirty times lower than that of the red light, appears here of a higher temperature. Such a difference is not to be explained by supposing that, in the transmission of the violet glass, there passes a great quantity of red rays; for it should, on this hypothesis, be found to transmit them in a greater proportion than they are transmitted by the red glass; which, according to the preceding experiments, is impossible.

These facts seem to be opposed to the opinion of those philosophers who hold that in luminous heat the same rays simultaneously excite the two sensations of light and heat, but would be easily comprehended if we supposed caloric and light to be two distinct agents. In the latter case we should say that in the prism the refractive force acts unequally on the different caloric rays, as it does, in a greater or less degree, on the different luminous rays, and thus throws certain quantities of heat on the very spaces occupied by the different colours of the spectrum; but that in the coloured glasses and, generally, in bodies more or less diathermanous, the absorbent force does not act in the same manner as the force of refraction, which sometimes extinguishes more heat than light and at others more light than heat.

But those who maintain the identity of the two agents will reply, that the differences observed in the calorific and luminous transmissions of the diaphanous or coloured media are produced by rays of obscure heat which mix in great quantities with the rays of light emitted by the flame.

In order to decide how far it is allowable to maintain the one or the other hypothesis, we should have data which, at present, are not within our reach. We shall resume this subject at the end of the next Memoir, and conclude the present one with an account of a very remarkable application of the numerical results contained in the foregoing tables.

It had been established by the beautiful experiments of Seebeck that the place of the maximum of temperature in the solar spectrum varies with the chemical composition of the substance of which the prism is made. This eminent philosopher observed that the highest degree of heat which, in the spectrum furnished by a prism of crown glass, was in the red, passed to the orange when the prism employed was a hollow glass one filled with sulphuric acid, and was found in the yellow when the same prism was filled with pure water[23].

I discovered some months since that the caloric rays scattered on the colours given by a common prism do not undergo the same alteration in passing through a layer of water; the loss varies inversely as the refrangibility, so that the most refrangible rays pass undiminished and the least refrangible are entirely stopped by the liquid[24].

This experiment led to a very simple explanation of the results obtained by Seebeck.

The solar heat which presents itself to the anterior face of the prism of water contains rays of every degree of refrangibility. Now the ray which has the same index of refraction as the red light, suffers in passing through the prism a loss porportionally greater than the ray which possesses the refrangibility of orange light, and less is lost by the latter in the passage than by the heat of the yellow ray. These increasing ratios in the losses of heat sustained by the less refrangible rays have an evident tendency to transfer the maximum to the violet. It may therefore be stopt at the yellow.

If we suppose the action of sulphuric acid analogous to that of water, but not so energetic, we shall see the reason why, with the prism of acid, the maximum takes place in the orange. In short, the very glass of which the common prisms are made must operate in a similar manner, and cause in each ray a loss inversely proportioned to its refrangibility. Therefore, if we employed in the construction of the common prism a substance less active than common glass, the losses sustained by the less refrangible rays would be diminished in a greater ratio; so that they would gain on the more refrangible rays, and the maximum would pass in a direction opposite to the preceding, that is, fr»m the violet to the red.

This is exactly the result obtained by Herschel, Englefield, and Seebeck by operating on prisms of flint glass; for the maximum was transferred to the obscure space quite close to the last red stripe of the spectrum.

Let us compare these effects with the numbers which represent the calorific transmissions. We shall find that the maximum of heat, in passing from the yellow, where it is found when we use a prism of water, departs from it always in the same direction in proportion as the substances of the prisms substituted for the water are more diathermanous. It passes a little out of the spectrum when, instead of crown, we employ flint glass. Admitting then the correctness of such a theory, the line of greatest heat must pass quite beyond the colours into a space far distant from the red limit if we employ rock salt, a substance possessing a far greater diathermancy as compared with flint glass than flint glass does as compared with crown. I tried the experiment; it was completely successful. I found that the maximum of temperature in the spectrum derived from the prism of salt was thrown into the dark space as far at least from the last band as the blue is (in an opposite direction) from the red. At the moment I cannot assign more exact measures; for in the first place I operated with very small prisms, and when I subsequently obtained larger pieces the season did not allow me to reconsider and study the result more nicely. But the effect has been so marked in the experiment which I made, and so invariable in several successive repetitions, that I look upon it as decisive, and have not the least doubt as to the removal of the maximum of temperature to the last band of the red rays in the spectrum produced with rock salt[25].

The distribution of the degrees of temperature in the solar spectrum is therefore a phænomenon entirely depending on the order which we have found to exist in respect to the calorific transmissions of diaphanous bodies.

This phænomenon now constitutes a striking relation between the properties of the caloric rays of the sun and those of the radiant heat of terrestrial bodies; but we shall see relations yet more intimate appear between these two species of rays when we examine the alterations produced in calorific transmissions by changing the temperature of the radiating source.




  1. Mariotte, Traité de la Nature des Couleurs; Paris, 1686, part 2, at the end of the Introduction.
  2. Scheele, Traité de l'Air et du Feu; Paris, 1781, §56.—The original work of Scheele was published in 1777. Mariotte died in 1684.
  3. Pictet, Essai sur le Feu, § 52 et seq.
  4. Journal de Phiysque, de Chimie, d'Histoire Naturelle et des Arts, par M. Delametherie, 1811.—P. Prevost, Mémoire sur la Transmission du Calorique à travers l'Eau et d'autres Substances, § 42 et 43.
  5. Nicholson, A Journal of Natural Philosophy, Chemistry and the Arts, vol. xxvi. May and June 1810.—J. D. Maycock, Remarks on Professor Leslie's Doctrine of Radiant Heat.
  6. Journal de Physique, &c., par Delametherie, 1812.—Delaroche, Observations sur le Calorique rayonnant.
  7. I must not omit to mention that, notwithstanding the results obtained by Delaroche, some most eminent philosophers (and of these it will be sufficient to name Laplace and Brewster) continued to deny the immediate transmission of heat through transparent solid bodies. Their principal objection was founded on an experiment of that author, from which it was inferred that a thick glass intercepted a greater quantity of radiant heat than a thin glass, though the former was much more transparent. It was insisted that this circumstance proved the presence and action of heat successively propagated from one surface to the other, and every elevation of temperature observed on the other side of the screen was assigned to the conductible caloric. This opinion can no longer be maintained in defiance of the results furnished by the application of the thermomultiplier to this species of phænomena. It will be seen, further, that the calorific action through a transparent layer is instantaneous, and that the time necessary for the instrument to mark its total effect is the same, whatever be the quality or thickness of the screens. Let the direct rays from an unvarying source of heat be received on the thermoelectric pile; let them be first made to pass through any diaphanous screen of one hundred millimetres in thickness: the index of the galvanometer sets itself in motion from the instant when the communications are established, and stops after having described an arc of greater or less extent in an unvarying interval, which, with my apparatus, I find to be ninety seconds.
  8. Let be the distance from the source to the thermoscope, the distance from the thermoscope to the screen, the calorific intensity of the source, we shall have as the expression for the radiation which strikes the anterior surface of the screen. This quantity will become at the further surface, being a constant quantity depending on the conducting power of the matter of the screen. In fine, the radiation of the further surface on the thermoscope will be expressed by ; its minimum is to be determined. Now, by differentiating we obtain ; the equation which gives the quantity will then be , whence .
  9. For the description of this instrument see the number of the Annales de Chimie for October 1831.
  10. Although the velocity with which radiant heat is propagated is unknown, we are nevertheless pretty certain, since the experiments of Saussure and Pictet, that this agent traverses spaces of from fifty to sixty feet in a time altogether inappretiable. It might be asked, therefore, why does not our apparatus instantaneously indicate the presence and the intensity of the rays emitted by the source? To this I answer, 1st, that the index of the galvanometer deviates at the very instant when the calorific communications are established, and we have just seen that in five or six seconds it describes almost the whole arc of deviation. If a few seconds more are required to mark the entire action steadily, it is because the great conducting power of the bismuth and the antimony, and the great powers of absorption and emission belonging to their blackened surfaces, render the lapse of a certain interval necessary, in order that a balance may take place between the rays which enter the pile and those which leave it or are extinguished within its interior. But the time required for the definitive equilibrium is much greater when common thermometers are used. If, for instance, one of Rumford's most delicate thermoscopes, having the ball blackened, and a metallic cover perforated on the side towards the source of heat, be submitted to the action of calorific radiation, it will be found that the time requisite to mark the whole effect is four or five times more than that required by the thermomultiplicr. This delay is the consequence of the obstructions encountered by the conductible heat in its passage through the glass, and in its uniform distribution over all the points of the mass of air within,—a distribution which will necessarily take place, because of the fluidity of the thermoscopic body.

    Another inconvenience produced by the interposition of the glass, and from which the thermomultiplier is free, is the lapse of a perceptible interval between the commencement of the action and its manifestation on the instrument; for there is always some time required, in order that the heat may pass from one surface to the other. I speak not here of the caloric which might pass to the air by free transmission through the diaphanous sides of the cover; for when we have to estimate the intensities of caloric rays by means of thermoscopes, we cannot dispense with the blackening of the glass. So necessary indeed is this, that in order to make sure of the opacity of the glass, it must be overlaid with several coats of colouring matter. Otherwise, a portion of the rays would freely pass through the mass of air contained in the ball without dilating it.

    Now, in the common thermoscopes, we always measure the radiation through an opake plate of glass. This plate, however thin, must offer a considerable resistance to the propagation of heat, because of the feebleness of its conducting power, and will therefore, as we have already observed, render the apparatus insensible during the first moments of action. Let it be observed, moreover, that the more we endeavour to increase the sensibility of the thermoscope by enlarging the dimensions of the balls, the more we diminish the promptitude of its indications; for the increase of volume is proportionally greater than that of the part of the surface turned towards the source, and the mass of air within is increased in a proportionally greater degree than those points of the glass which can communicate to it the heat they have acquired. Hence arises a greater difficulty in attaining the moment of equal temperature in all the points of the fluid mass, and, of course, the necessity of a longer time to mark the entire effect.

    In fine, the thermoscopes are utterly useless when it is required to measure caloric rays that are very feeble, and distributed according to given lines, or forming sheaves of small dimension. In fact, it would be necessary in this case to preserve the whole sensibility of the instrument by considerably reducing the size of the balls. But this is impossible.

    Whoever takes the trouble to weigh these considerations duly, will not, I think, hesitate for a moment to prefer the thermomultiplier to every other thermoscopic apparatus in studying the subject of caloric radiation.

  11. In order to understand this clearly, it is sufficient to suppose a galvanometer in which the circumvolutions of the wire are move numerous towards the extremities than towards the central part. It is evident that under the action of such a system the forces which produce the deviations, instead of increasing or being merely proportional in the arcs near zero, must decrease as we approach the extremities of the frame, in order to increase afterwards when the index haspassed these positions.

    As to the influence of the sensibility of the astatic system, we shall be able to form a tolerably exact idea of it, if we imagine a galvanometer with the two needles possessing very different degrees of magnetism. Then the terrestrial globe will very powerfully affect both combined; and, in order to produce the least deviations, electric currents must be employed possessing much greater force than those required to produce small deviations in a more perfect astatic system. In the positions near zero, the electro-magnetic action produced by the most distant currents, that is, the action of the currents situated at the extremities of the frame, will possess an energy sufficient at least to overcome the resistance arising from the twisting of the suspension thread and the inertia of the astatic system. It will therefore always contribute to move the oscillating mass. Hence it is evident that if the needles are displaced in the slightest degree, the consequence will be a loss in the moving force; for if the system approaches a certain arc at a certain extremity, it recedes at the same time double the distance from the opposite extremity. Now we have already seen that, in delicate galvanometers, the moving force is constant when the angles are small; and we have assigned the cause of this fact upon the incontestible principle that, in small deviations of the instrument, the action of the currents situated towards the extremities of the frame must be disregarded, not indeed because they have no value, but because it becomes, in consequence of its distance, extremely feeble, and incapable of surmounting the obstacles opposed to it by the torsion of the silk thread and the inertia of the needles.

  12. All the measures of small degrees of thickness contained in this Memoir have been taken with a pair of calipers with pivots, a species of double compasses, with a spring and with legs of unequal lengths, much used in the manufacture of clockwork. This instrument measures directly, and with great nicety, even the fortieth part of a line.
  13. [It may be proper to inform the English reader that "oil of colza" is an oil expressed from the seeds of the Chou Colza of the French, Brassica arvensis, Linn. It must not be confounded with the rape oil of England, obtained from the Rape, Brassica Napus.Edit.]
  14. His own words are: "It appears, therefore, that water does not allow so much caloric to pass immediately as glass does. At least it affords a passage of that kind only to a quantity of caloric more minute than that which passes through the glass." (Mem. already quoted, § 48.)
  15. See the note in page 4.
  16. In this solution we used very diaphanous pieces of rock salt; the same may be said of the solution immediately preceding—the water was completely saturated with the alum.
  17. The first of these terms requires no explanation. The second is derived from διά, through, and ξερμαίνω, to heat, as the word diaphanous is derived from διά, through, and φαίνω, to show.
  18. I have since found that the perfectly opake glass employed in the construction of mirrors designed to show the polarization of light transmits a considerable quantity of caloric rays. These obscure rays emerging from the dark glass may be employed in some curious experiments which we shall mention in the second Memoir.
  19. Such as have not a thermoscopic apparatus similar to that which we have employed may easily satisfy themselves that rock salt transmits almost all the radiant heat that falls on its surface, by fixing vertically, on the same stand, a plate of this substance and a plate of glass or alum of the same dimensions, and by bringing the stand quite close to the fire of a stove. If it is allowed to remain in this state for five or six minutes, the glass becomes burning hot, while the rock salt, if applied to the most tender part of the hand, will produce no sensation of heat. These differences of temperature exist not merely in appearance, but are as palpable as those that are felt when we touch wood and marble that have been exposed to the sun. To prove this, we need only lay some pieces of wax or suet on the two bodies. Those laid on the glass will melt rapidly, but those laid on the rock salt will continue in their solid state. We may also demonstrate in a direct manner, and without the aid of a thermomultiplier, the great transmissiveness of rock salt as compared with other diaphanous substances. Let the two plates be brought close together in the same plane, and behind them let two metallic tubes be placed, with the blackened balls of two common thermometers of equal sensibility fixed at their further extremities. If we now place a red-hot bullet at a certain distance from the plates, the thermometer that is to indicate the transmissive power of the alum will ascend but 1°, while the other will ascend 8° or 10°.
  20. [A millimetre, it will be remembered, is equal to ·03937 of an English inch.—Edit.]
  21. For the demonstration of this proposition, see Bouguer, Traité d'Optique sur la Gradation de la Lumière, Paris, 1760, liv. iii. sect. 1ʳᵉ, art. 1, 2, 3, 4.
  22. I was lately told by an eminent philosopher, that to think of comparing the intensities of different colours would be as absurd as it would be to institute a comparison between heterogeneous elements. Waiving all inquiry as to the correctness of such an assertion, I beg leave to remark that in certain cases it is unanimously agreed that a tint is more or less clear than another tint of a different kind, without giving rise to any metaphysical ideas opposed to the general opinion. Let us take, for instance, the solar spectrum. Has it not been always held that the maximum of brightness is to be found in the yellow, and that on each side of it luminous intensity decreases? The principle put forward by me seems equally plain. When I assert that colours always introduce some opacity into diaphanous bodies, no one is at a loss for my meaning. Put some pure water between two parallel plates of colourless glass: let an observer be placed at one side, and at the other a piece of writing, which is to be moved just so far from its first position as to become illegible. Now, for the water substitute wine or oil or any other diaphanous liquid more or less coloured; the distance at which the writing may be read will become less in proportion to the greater depth of the colour independently of its kind. Thus when the writing will be legible at the same distance through a yellow and a red liquid, these two media will, in respect to us, be equally transparent.
  23. Schweigger's Jahrbuch der Chemie und Physik, vol. x. [A translation of the memoir of Seebeck here referred to will be found in the Philosophical Magazine, first series, vol. lxvi. p. 330, et seq.Edit.]
  24. Annales de Chimie et de Physique, Décembre 1831.
  25. I have since obtained the same results with five prisms of rock salt whose angles of refraction vary between 30° and 70°. These prisms have been made out of several pieces taken from the mines of Cordona, Wieliecza, and Vicq: they have been cut in different directions relatively to the axis of crystallization. I shall give the numerical data in a work in which it is intended to treat specially of the analysis of the caloric solar rays.