containing its usual quantity of mica; whereas what composes the veins has always a slaty fracture, contains little or no mica, and has a white chalky appearance.

"A protruding mass of granite from the base of the eastern side of this recess to the height of 25 or 30 feet (f). It is of a very singular outline, yet does not appear to have shown the slaty laminæ reposing on it out of their usual direction." This I should also denominate a granitic vein, which soon becomes hid and lost on the beach from the ruins of the cliff above. It has in every respect the same characters as the granite of the other veins by careful examination the slate may be observed beneath the vein, making it about 18 feet thick. Its other end soon becomes lost behind the mound of rubbish in the recess, and from its inclination, I should think the vein (g) on the western side its continuation. "The mound of rubbish in the recess enabled us to ascend more than half way up the cliff, and trace the two large veins before mentioned into an enormous bunch of granite, which here reposes on the top of the cliff, and is supported by undisturbed beds of slate; the line of demarcation being nearly horizontal, and at an elevation of 60 or 70 feet above the level of the beach. The denuded face of this bunch of granite is 30 or 40 feet thick. Two or three veins appear to take their origin from this anomalous overlying mass. One spreads out in minute ramifications towards the part of the cliffs which abuts towards Trewavas Point, at the termination of the killas in that direction. Two others descend obliquely, and are lost behind the large mound of rubbish before mentioned."

The whole of the slate has an evident inclination to the east at an angle of about 15°; and in no part of it traversed by the granitic veins, are its laminæ, &c. interrupted. There are evident symptoms of these veins being formed subsequently to the slate; for in one part of the vein (c), there is a slight fissure running perpendicular through the slate until it meets the vein, which fissure may be again seen on the opposite side of the vein holding its direct course. Several small quartz veins traverse the slate in all directions, but observe the same law as regards the granitic vein; and in no part whatever could I find either fissure or quartz vein of the slate to penetrate the granite (except the one before mentioned, where the granitic vein is heaved by it); but in every instance to present themselves as in fig. 5. The slate does not make its appearance more than 200 feet west of this recess.

I am, dear Sir, your humble servant,

M. P. MOYLE.

ARTICLE III.

An Abridged Translation of M. Ramond's Instructions for the Application of the Barometer to the Measurement of Heights, with a Selection from his Tables for facilitating those Operations, reduced (where necessary) to English Measures. By Baden Bowell, MA. of Oriel College, Oxford,

SIR,

(To the Editor of the Annals of Philosophy.) ̈

THE dissertations and tables of M. Ramond are of such acknowledged excellence for the purposes of the barometrical observer, that I trust the following abstract of them brought into a form more convenient to the English student will not be unac ceptable. On a careful perusal of his publication, it appeared to me that the valuable information contained in it was very susceptible of being reduced into a smaller compass; and that among the various tables he has given, those of more essential use might be selected, and, as far as requisite, reduced to English measures. In this way I conceive the most valuable materials of the author may be very usefully collected; and within the compass of three, or at most four papers of such length as is proportionate to the size of a number of the Annals, I trust I shall be able to present the scientific inquirer with a compen dium of much information highly requisite to be attended to in the measurement of heights by the barometer, and with a set of tables which seem to unite facility of operation with correctness of result, in a greater degree than any extant. B. P.

General Principles of Barometrical Measurement.

It is well known that in the barometer the mercury sinks as we are elevated above the level of the sea; this indeed must be the case, for the barometer may be considered as a balance in which the column of mercury keeps in equilibrio with the corresponding column of air. At the level of the sea, it balances the whole weight of the atmosphere at a greater elevation, only a part of it. The quantity by which it has sunk expresses the weight of the stratum of air intercepted between the levels of the two stations. Considered in relation to the measure of height, it expresses the difference of level in a ratio depending on that of the densities of mercury and air. What then is the thickness of the stratum of air whose weight is equal to that of an inch of mercury? To such a question may the problem of the mensuration of heights by the barometer be ultimately reduced. This question, however, apparently so simple, has nevertheless occasioned much difficulty to philosophers.

If the air were, like mercury, an incompressible fluid and of uniform density, the solution of the problem would not have presented any difficulty. It would then have sufficed to establish once for all the ratio of the densities in order to infer that of the volumes, and to determine the thickness of the stratum of air whose weight was in equilibrio with a given column of mercury of the same diameter.

But air is elastic; it dilates or condenses in proportion to the pressure it undergoes; and in proportion as we rise in the atmo❤ sphere, we perceive its density diminish along with the weight by which it is compressed. If then we suppose a column of air divided into strata of equal thickness, these strata beginning from below will diminish gradually in weight, and will correspond respectively to portions of the mercurial column gradually smaller in such a manner that equal differences of elevation will be marked in the barometer by successive depressions of the mercury so much the smaller as we rise higher.

:

We perceive then that in a column of air supposed at a uniform temperature, the density of the strata decreases in proportion as the compressing weight diminishes, which is represented by the height of the column of mercury. Setting out from this first datum, and imagining the column of air divided into strata bounded by planes indefinitely near each other, we are led to perceive that the differential variation of the density is propor tional to the product of this density multiplied into the variation in vertical height. And if we make this height vary by quantities constantly equal, the ratio of the differential of the density to the density itself will be constant, which is the characteristic property of a decreasing geometrical progression whose terms approach indefinitely near to each other.* Hence it follows, that if the heights of the strata increase in arithmetical progression, their density, and consequently their weight, and consequently also the heights of the barometer will decrease in geometrical progression. This law is the fundamental principle of the application of the barometer to the measurement of heights.

Long before philosophers were aware of it, there existed a book which seemed made expressly for facilitating the application of this principle. The logarithmic tables, the admirable artifice of which had already so much abridged the long calculations of astronomy, offered a double series of corresponding numbers, one of which proceeded in arithmetical, the other in geometrical progression; numbers, which even the most courageous patience would doubtless never have had resolution enough to calculate solely for the sake of the measurement of heights, even if, in other respects, this art, as yet in its infancy, had been .capable of suggesting the idea. It required some genius even to

# Exposit. du Syst. du Monde. Third Edit. tom. i. p. 155,

conceive this new application of tables hitherto signalized by so many services of a totally different kind. The name of Mariotte remains coupled with a happy approximation, which seemed as if it ought to have been made at once by every one, but which he himself did not turn to any advantage. We know, however, that the heights of the barometer at the two stations being expressed whether in inches or any other measure, the difference of level is represented by the difference of the logarithms of these heights.

But this representation is only an abstract one; it indicates a ratio, and not absolute measures, because the system of the tables is not framed in the particular system belonging to the measures of heights.

In order that the difference of the logarithms may be trans→ formed into feet, we must apply to it in a particular manner the value corresponding to these measures,* combined with the ratio of the densities of mercury and air. These conditions are more easy to fulfil than it might appear. The whole operation consists in finding once for all the number of feet, fathoms, &c. which, multiplied by the difference of the logarithms, will reduce the abstract expression to one, giving absolute measures regulated by the ratio of the densities. Nothing is more simple provided we know this latter ratio. Let us suppose that at the pressure of 29.921 inches of mercury, and at the temperature of melting ice, the weights of air and mercury were as unity to 10477-9. The heights of the two columns being inversely as their densities, it is clear that we must ascend 1-100th of 10477-9, or 104-779, in order that the barometer may sink 1-100th of the same denomination as that in which our ascent is expressed, or nearly 8.7 feet, that it may sink 1-100th inch. Now the pressure being supposed equal to 29.921 inches, we shall find the number sought by dividing 104-779 by the difference of the tabular loga rithms of the barometrical heights, 29-921 and 29.911.

The exact ratio of the densities being on the contrary supposed unknown, the operation will not be at all more difficult if we have measured geometrically and with great exactness a difference of elevation: for then, taking the barometer to the two extremities of the measured height, and dividing the difference of the logarithms by the difference of elevation, we shall equally obtain the number we seek; it will, however, correspond only to the particular temperature and pressure under the influence of which we have been operating. If, from hence, we wished to deduce the absolute ratio of the densities of mercury and air, we may arrive at it very easily by means of a formula, which is extremely simple, given in the "Astronomie Physique," of M. Biot. My first memoir contains the application of the methods of proceeding which I have here alluded to.

"Le Type de ces Mesures."

New Series, VOL. VI,

H

† Tom. i. p.

142,

This number, in fact, once determined either by observation or experiment, serves for all subsequent operations; by making the modifications which the difference of circumstances in each case requires: this is what we call the constant coefficient of the formula.

Thus, in order to measure the height of a mountain, the fundamental operation consists in observing the barometer both at the foot and the summit: taking out of the ordinary tables the logarithms corresponding to the barometric heights expressed in units of the same denomination and decimal parts of those units; subtracting the smaller from the greater logarithm, and multiplying the difference by the constant coefficient. The product will give the height required in measures of the same denomination as those which entered into the determination of the coeffi cient: and this height will be correct if we operate under the same circumstances which were supposed in determining the coefficient.

These circumstances are, as has been observed, a certain atmospheric pressure and a certain temperature, from whence results a certain ratio between the densities of air and mercury. The coefficient supposes them constant: they are in reality very variable; it must, therefore, undergo certain modifications analogous to the changes with which these circumstances may be affected.

In the formula of M. de Laplace, for example, the coefficient is determined for the level of the sea, the temperature of melting ice, and the latitude 45°. It is then only accurate for this single case, and the formula would be incomplete and inapplicable to other cases, if it did not comprise corrections suited to the variations of these first data.

The most important of these corrections relates to the variations of temperature; it is easy to conceive the principle of this, and to feel its necessity. Heat dilates air: it augments its volume, and diminishes its density. With equal weight, it occupies more space; with equal volume, it has less weight. If we suppose a stratum of air of 1000 feet in thickness intercepted between the levels of the base and summit of a mountain, this stratum will weigh less at a temperature of 10° centigrade than at zero. The difference of the heights of the barometer observed at the two stations will be less in the former than in the latter case; and if we apply the same coefficient to the two logarithmic differences, we shall have two very different measures of one and the same height; the mountain will seem to diminish in height in proportion as the temperature increases. Now the coefficient being calculated for the temperature of melting ice, we must, in consequence, increase or diminish its value, according as the temperature rises above, or sinks below, that point.

Experiment has taught us that the variation of air in volume is nearly 1-167th for a variation of 10 centigrade: supposing the