;

the distance of one foot from the thermometer, and the wall of the room be at the distance of eight feet from the same, the screen intercepts from the thermometer an area of 2304 square inches but the intensity of the radiation from the wall, which is at eight times the distance of the screen, is to the intensity of the radiation from the screen only as one to 64, or as 36 to 2304; and thus the difference in quantity of radiating surface is compensated by the difference in intensity.

Now by mere reflection the actual number of rays, or the intensity of any given number, cannot be either increased or diminished. The intensity (whether of light or heat) is increased in the focus solely by the direction to one point of a number of rays subtracted by a change of direction from other points on which they would have fallen in their natural course; for it is self-evident that whatever radiation is superadded by mere reflection on one spot, must be subtracted from some other; and if the sensible heat is increased in the focus, it must be diminished somewhere else.

Some kinds of surfaces receive and emit heat by radiation with great facility; others reflect more and radiate less; as Mr. Leslie has shown. Mr. Leslie has also shown that the powers of receiving and giving out heat are in the same surface equal; and also that its powers of radiation and reflection are in inverse ratios. This seem also demonstrable from all usual appearances; for if any body could radiate either more or less than it receives, or reflecting a part only of what falls on it, did not give out by radiation a sum equal to that which enters, not only would adjacent bodies be affected by it, but the sensible heat of the body itself must continue to increase or diminish, without apparent limits: but it is not found that the temperatures of adjacent or remote bodies differ from each other by mere position, where there is no source of heat or active cause of increase or diminution of the actual quantity of free caloric; and since different surfaces of the same body radiate or reflect one more than another, if the emission and intromission by radiation were not equal in the same surface, or if the reflecting surface did not radiate all which it does not reflect, bodies exposed near one surface must be affected differently from those on the other. Thus if a flat plate of metal were polished on one side, and blackened on the other, two bodies of equal temperature with the plate must receive different temperatures from it; still more would a body in the principal focus of a reflecting mirror be affected; for there is an actual accumulation of reflected rays upon it. Yet a body placed in or out of the focus, or even before the concave or behind the convex side of the mirror, suffers neither increase nor decrease of temperature, neither is it affected by the proximity or removal of either the plane reflector or the mirror. Where is the compensation? In the case of the plane reflecting plate, the radiation of nearly one half of the surrounding sphere is intercepted, viz. all behind the plate; but the same quantity of radiation from the hemisphere in front of the plate which would have (which has, indeed,) passed

the object, is reflected on it; and so much as the imperfection of the reflecting power of the plate suffers it to absorb, is radiated by it in the same direction. Here, then, is the compensation; and here I think Mr. Murray's objection fails. A blackened surface

radiates much, it is true; but it intercepts an equal volume of radiation or reflection from behind. A polished surface radiates less, but it reflects as much as it fails to radiate. So when the writer in the Encyclopædia says "a hot body ought to cool more slowly when near a large body of inferior temperature than when near a small one," he forgets that this large body intercepts an equal volume from beyond it, and therefore the hot body so placed ought not "to cool more rapidly." He says the reverse is the case; but I apprehend it would be found, by careful experiment, that if the adjacent body be of the same temperature as those whose rays it intercepts (the screen, for instance, of the same temperature as the wall), the reverse will not be the case, but the time of cooling will be the same. (N. B. Dr. Wells's lately detailed interesting experiments on the formation of dew, in consequence of the loss of heat by uncompensated radiation, will be found to be in perfect conformity to this view of the subject.)

Then in the case of the concave reflector it is true that one hemisphere of converging rays is intercepted from behind, and only a cylinder of parallel rays in front, brought to the focus by reflection; yet this is a compensation: for the intensity of the rays so brought to the focus is equal to that of the converging rays which would have passed in the same direction through the space occupied by the disc, as might be easily shown by the general laws of radiation and reflection. When a second mirror faces the first, all this cylinder of rays is intercepted; but then all the rays which pass through its focus to its face are reflected in the direction of the intercepted cylinder, and a cylinder is formed of reflected rays, similar to, and in lieu of, the intercepted one. The whole cylindric space comprised between the two mirrors now consists of two sets of rays proceeding in exactly opposite directions from and to both the foci.

Let us now place a hot body in the focus of the second reflector. This last cylinder now consists of extraordinary calorific rays; and of course a body (as a thermometer) in the focus of the first mirror receives superabundant heat. Substitute an extraordinary cold body; then, as all the rays which would have passed through this focus, and would have constituted the second cylinder, are now absorbed by a body which has very little to radiate, the radiation of the thermometer towards the first mirror is uncompensated; and it indicates decrease of temperature.

In Mr. Pictet's detail of the experiment it was observed that when the temperature of the ice was lowered by the addition of nitrous acid, the thermometer sunk several degrees lower than before. The theory proceeds here with perfect regularity. Ice at +32 radiates something towards the compensation: at 20, still

something, though much less; and therefore the small compensation was again reduced by the refrigorating mixture.

.

The comparing of the reflection of heat to that of light (though they are in many respects analogous) is apt to lead into some error, because in the latter case the reflector is presented in a particular direction towards a particular source (as to the sun, or to an aperture admitting the rays); but the rays of heat are received equally from every point of the surrounding sphere: but if we bear this difference in mind, the analogy between them will afford an evident illustration of the theory. Vision is merely the sensation of rays of light on the retina of the eye. We see a white or coloured object by means only of light reflected by it. Black, we say, reflects no light; yet we see a black object. If the blackness of the surface were really perfect, and reflected no light, we could not (strictly speaking) see it at all; we perceive or distinguish it by its interception of other forms and objects; but we can also magnify it by dioptric lenses or mirrors. To put the comparison in a still stronger view, suppose a white object (as a paper box blackened within), and a small hole cut in one of its surfaces, we say we see that hole. Do we see darkness? Through a convex lens, or by a concave mirror, or by the intervention of two mirrors (placed exactly as in Pictet's experiment, the eye being in the place of the thermometer), we may magnify that dark hole. Do we say darkness radiates? And where is the difference between the two cases; the one, where the ice in the focus of the second mirror lowers a thermometer in that of the first; the other, where a dark spot in a similar situation gives the sensation of a magnified dark spot on the retina of the eye? A perfect analogy holds here, and applies to all the cases, and removes at once (as it appears to me) all the objections made to Mr. Prevost's theory. It is true that in the quotations I have met with of Mr. Prevost's explanation he has not expressly described the interception by means of the ice, of radiation aliunde; but I think it follows by necessary inference that he had it in his mind as a part of his theory, and meant to be so understood. I have said before that his own words I have not met with.

I have now to answer the supposed objection arising from the experiment with the metallic tube; but if the explanations above given of the several phenomena are satisfactory, I have only to trace the analogy between them and this new one.

I think we are in possession of facts that warrant the following conclusions :

1. That all bodies receiving and admitting heat by their surfaces emit by radiation an equal quantity; and that as much of what falls on them as they cannot so admit, they reflect.

2. That when the radiation of any body is not compensated by counter radiation, its temperature must decrease.

3. That the proximity or the form either of radiating or reflecting surfaces produces no difference in the quantity or intensity of the rays received by any given point, provided there is no active cause

of increase or decrease of the actual quantity of free caloric in the surrounding sphere; but that where there is such cause, such given point will be affected by the form and nature of the reflecting surfaces which change the direction of rays that fall on, or proceed from, the point where such active cause exists.

4. That where heat is increased by more reflection on one spot, it must be diminished somewhere else, and vice versâ.

5. That when any body whose temperature (arising from extraneous causes) varies from that of others in its neighbourhood, if hotter, it affects a body placed in any given point, by throwing on it a more intense radiation than that which it gives out; if colder, by intercepting and absorbing rays of free caloric from some part of the sphere by which it is surrounded, and thereby depriving it of its due and usual compensation.

If, then, by means of the conical tube, or by any other means, a thermometer indicates decrease of temperature from its relative position with that of a cold body, we have only to see where and how are radiations that would have fallen on the thermometer intercepted by that cold body.

The mechanical form of the polished interior of this tube will effect this according to the known laws of optics. The effect of this reflection differs from that of the mirrors; for instead of a single focus at one point, there is an indefinite number of foci all along the axis. The incident rays which are parallel to the axis are reflected in the form of cones, and cross in the axis: however, the largest hollow cylinder of incident rays will form the focus of greatest intensity, and a multitude of other rays will be brought by complex reflections from the polished interior to the same spot. The tube is of course a truncated cone; for the smaller end has a diameter. The principal focus is not at the apex of the cone, but short of it; and we suppose the thermometer to be placed at this spot near the aperture. I need not trespass more on you by specifying all the circumstances of the situation; but it is easy to see that a large portion of the rays of the surrounding sphere is intercepted from this point by the tube, and reflected from its exterior surface in foreign directions. The loss of these rays is compensated by the concentration of the cylinder of rays brought to this point by reflection from within the tube, else the thermometer in this place must indicate decrease of temperature without the presence of the cold body, contrary to the rule No. 3. But when the bottle of ice is brought to the wide aperture, all this cylinder of radiation is intercepted and absorbed, and the radiation from the thermometer is uncompensated. A hot body in the place of the ice would have its radiation condensed on the thermometer. A visible object would be magnified in an eye placed in the room of the thermometer, and a dark hole in a white surface would have its diameter apparently increased; and thus a perfect analogy subsists between this experiment and those of Mr. Pictet.

Mr. Pictet's theory appears also capable of accounting for the

phenomena of his experiment, but appears to have been misunderstood. Still it involves some strong inprobabilities; while that of Prevost, if we only admit certain analogies (some of which we know exist) between the radiation of heat and that of light, is even demonstrable. I was about to add a comparison between these two theories; but I have already made my letter much longer than I intended.

ARTICLE VI.

On the Cerebellum. By W. Elford Leach, M.D.

In the last number of your Annals of Philosophy Mr. A. Walker claims the merit of being the discoverer of what Dr. Cross has stated respecting the structure of the spinal marrow and the use of the cerebellum. He has at the same time answered my letter to Dr. Cross, and has stated that the work of Gall and Spurzheim actually contains no such statements as those to which I alluded.

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Permit me, Sir, to assure you that the letter from Hufeland to Portal contains precisely the same opinion respecting the use of the cerebellum as that given by Mr. Alexander Walker and by Dr. Cross.*

When I perceived Dr. Cross's observations on the anatomical structure of the spinal mass of nerves, 1 recollected that in the work of Gall and Spurzheim the same statements were given, not as existing in nature, but as erroneous suppositions. In the folio edition of their Anatomie et Physiologie du Systême Nerveux en général, vol. i. p. 35 and 40, the following statements may be found:-"Bartolin says that the spinal marrow is composed of four fibrous cords; "-" Soemmerring maintains the opinion that the spinal marrow is composed of four cords."†

My object in answering Dr. Cross was merely to show that although his opinion might have been original, yet that the same opinion had been entertained by preceding writers. Since writing that answer, I have carefully examined the structure of the spinal mass of nerves; and I most certainly agree with Drs. Gall and Spurzheim in maintaining that the spinal mass of nerves does not consist of "four columns," and that Mr. A. Walker merely participates in an error common to older writers in maintaining this opinion.

Willis likewise considered the cerebellum as the source of voluntary power. + Highmore even goes farther: he pretends that the spinal marrow is formed of gight little cords.