periments on which it is grounded, though somewhat varied in their plan, never give the true expansions of water, but only the differences between those expansions and the corresponding expansions of glass. Having filled a thin glass ball, terminating in a fine tubular stem, with distilled water, and cooled the whole down to the point of congelation, I plunged it into a large bath, whose temperature was four or five degrees above zero. The water in the stem sunk at first consider. ably, owing evidently to the dilatation of the glass, and, by conse quence, the enlarged capacity of the ball; but it then rose a sensible space, which must be ascribed to the expansion of the water itself. In like manner, when the procedure is reversed, and the ball, heated up a few degrees, is plunged into a bath at the point of congelation, the water rises in the stem as the ball contracts, and then, by its own contraction, partially subsides. The dilatation of glass by heat is indeed so very small, that in most cases it may be safely disregarded. But the rate with which water contracts is perpetually diminishing as the heat declines, and therefore, at some particular point, this effect is exactly counteracted by the opposite contraction of the glass, and beyond it the latter must predominate. Nor is it difficult to determine, at least theoretically, the position of the minimum, or limit of apparent condensation. Water expands about the 24th part of its bulk between freezing and boiling; and glass, in the same interval, expands longitudinally the 1200dth part, and consequently its dilatation, in all the three dimensions, must amount to the 40cdth part of its whole volume. The expansion of water that corresponds to any temperature x is therefore denoted by () and that of glass by- Equating these two expressions, we obtain

x2

24

x

40,000

I

x and therefore x = 6°. This remarkable coincidence seems

4

to dispel every shadow of doubt, and we may embrace it as an established fact, that the successive dilatations of water, counting from zero, are as the natural progression of numbers.'

This objection, against the principle of the minimum of the expansion of water being at a point above congelation, seems to us very weighty and formidable; and we hope that it will give rise to new experiments, in order that the fact may finally be

determined.

If, then, the refrigerating cause, which arises from the recession of the heated particles, vary as the square of the température, let its effect at 100 be denoted by f; then at any other temperature (b) it =ƒ(). Let the conducting power of water; and since it appears by experiment that the rate of cooling is five times greater at the boiling than at the freezing point,

100

с

..c+f. = } c+f. (10)2 and f=4c.

ICO

ཀ

Suppose e. ƒ= 4, and the sum of the two refrigerating =

b 2 100

causes at any temperature h, 1 +4. ) or = 1 +

12

2500

when the water-bath is at the point of congelation: but, let the temperature of the water-bath be b', then the two refrige

rating causes are 1 and

އ

b2-biz
2500

Let 2500 a2, then -dh

≈m (h—b1) (1+

.dt, m a constant co-efficient ;

b'db

bab (a" — b'" =b') .. m t = b. l. q "'q. + { b. l (b2 +b2) +

b2+b2

b

X Arc (tang b and rad b) + corr".

2 Arcs, rad' = b, and tangents being H, h.

When b'o, or the water-bath is at the point of congelation,

b

62

+ b.l.√b2+b2

+
b2+H2 b2

x difference of X

b2+H2

Mr. L. puts for ,, but we do not perceive his method of determining that co-efficient; which he ought to have explained.

It appears to us that the foregoing solution depends on the supposition of b', the temperature of the water-bath, remaining constant; which will not be the case, except the bath, comparatively with the immerged ball, be very small :-the solution in that case will demand modification, and become more difficult.

Mr. Leslie has not verified these theoretical deductions by actual experiment; and we are surprized at his neglect, in this instance. We suspect that a very near coincidence of theoretical and experimental results will not be manifested, when the times of cooling bodies in water are observed: for it seems to us that the agency of refrigeration, produced by the continual ascent of the heated particles, is greater than the author seems willing to allow. He indeed admits this agency, and, in discus sing it, notices several curious phænomena which can only be explained by the very imperfect conducting power of fluids; and here is the difference between Count Rumford and Mr.

Leslie: the former asserting that fluids are totally destitute of a conducting power, while the latter maintains that their conducting power is very small. The difference is material, then, since it involves a question not merely about degree.

We have mentioned the name of Count Rumford; and it was our intention to have noticed and commented on the remarkable coincidence between the inquiries, with respect to their object, conduct, and result, of that gentleman and of the present author: but we find ourselves obliged to refrain. We only observe that, among other points of resemblance, the similarity of the two instruments, (the thermoscope and the differential thermometer,)-and the identity of the curious result that, although repeated folds of linen or flannel retard the cooling of a metal body, yet one fold may accelerate it,-suffice to convince any person, not determined to call in the aid of a miracle, of a connection between one of these writers with the experiments and discoveries of the other; and it is a duty incumbent on him, to whom the right of originality belongs, to step forwards and assert it.

In the 18th chapter, the author applies his theory to discover the diminution in the rate of cooling, produced by surrounding the heated body with concentric septa. Suppose a series of hollow cylindrical vessels, made of very thin brass, to be so constructed as to fit the one into the other like a nest of boxes, and to be kept separate from each other by resting on the protuberant parts of a chequered ring: let a, b, c, &c. be the diameters of the cylinders, h, b', b", &c. the temperatures of their sides, H, H, H", &c. the temperatures of the included portions of air; then, rejecting the pulsatory communication of heat, (which, in the case of a series of cylindrical vessels, would be exceedingly attenuated,) we have these sin.ilar equations:

and hence, by elimination, "" may be determined in terms of a, b, c, &c. and of h.

Suppose, for instance, that there are two cases, a.being the diameter of the vessel that contains the heated fluid: then

ď2 b b "=

b2c2+2a2c2+2a2 b2

and

1

b2 + za2 + 2a2.

expresses the diminished rate of cooling.

Suppose a, b, c, nearly equal; and experiment shews that the diminution in the rate of cooling, (which beyond a certain limit, is a very inconsiderable quantity) is not affected by the thickness of the confined portions of air: then the diminished rate is expressed by ; and if an additional case be added, by , &c.

The author next considers the case in which the concentric cylinders are vitreous:-but it is time for us to check our progress. We must not, however, pass over in silence the photometer, or an instrument for measuring the intensity of light; which, in the principle of its construction, resembles the dif ferential thermometer and hygrometer constructed by Mr. Leslie Two tubes, into which sulphuric acid tinged with carmine is introduced, are joined together by means of a blow-pipe, and made to stand parallel to each other, the interval between them being occupied by a graduated scale: the ends of the tubes are closed by two hollow glass balls, one transparent, the other blackened when the instrument is exposed to the action of light, the blackened ball absorbs light, and, according to the author, a proportional quantity of heat; or, by varying the expression of the fact, a proportional quantity of heat is excited, which produces a dilatation in the air contained in the blackened ball, and causes the coloured liquor to rise in the tube terminated by the transparent ball, which, absorbing no light, receives no accession of heat. The instrument, no doubt, is uncommonly ingenious; and subsequent experiments and researches may prove the exactness of its principle: but, at present, it appears to us to rest on this supposition, that Jight and heat are the same fluid, or, in the words of the author, only different states of the same identical substance. What is it, of which the ascent of the coloured liquor is a token and indication? Increased elasticity of the air contained in the black ball. The cause of that increased elasticity, from analogy, we infer to be heat; and of that heat, no doubt, light is the cause, since the two balls differ only in this, that the one absorbs light and the other does not: but, although, in a certain sense, light may be said to be the cause, yet, how do we know that the accession of heat is in exact proportion to the absorption of light? The instrument exposed to the action of light shews, by the rise of its coloured liquor, an accession of beat (b): now let the heat indicated be 2h; is it a strict inference that the light is doubled?

03

doubled? No, except we admit the principle that light excites heat exactly in proportion to its own quantity: or that heat is only light under a latent form, in consequence of detention and absorption.

These are objections which, in the present state of facts and theory, are proper and reasonable; but we wish that they may be removed: for if we are permitted to have belief in these cases, we believe that trial and research will establish the accuracy of the instrument.

Mr. L. surrounds the photometer with a glass case, in order to prevent the dissipation of heat; and he argues, with his cus tomary acuteness, that the instrument, thus cased, will indicate truly the absorption of light, since the expenditure of heat, caused by the process of refrigeration, varies as the excess of temperature between the heated body and the surrounding air.

The application of the photometer is very various and curious it announces some results which are contrary to common belief, and others which are contrary to received opinion, The author dislikes the distribution of the prismatic light into seven colours, and throws considerable doubts on the reality of the distinction of calorific and colorific rays.-As his investiga tions are so much implicated with those of Count Rumford and Dr. Herschell, we anticipate a controversy, in which we think Philosophy will be a gainer.

As our limits are already transgressed, we must refer the inquisitive and philosophic reader to the volume itself for farther gratification; and he will find it a work which is not produced every day, nor by an intellect of an ordinary size. Some of its discussions are rather intricate, and the author's mathematical mode of arguing throws over it an air of abstruseness*: but the general scope of the reasoning, the experiments, and the results of the inquiries, are not above the capacity of common understandings. Of these experiments and results, the most curious and original undoubtedly are those which relate to the difference of power, possessed by various substances, in emitting heat that can be reflected and again concentrated; that is, according to Mr. L.'s hypothesis of emitting heat by pulsation. Hence his theory chiefly derives its eminence and character; and, among the causes on which the process of refri geration depends, the pulsatory is most clearly ascertained.

*Mr. Leslie uses the differential notation, and gives his reasons for adopting it. Our opinion on this head is already known. See account of La Croix on the Differential Calculus, Rev. Vols. xxxi. and xxxii.

Con