number of yards in the height of Etna; which appears to be 3776, or 2 miles 98 fathoms.

76-23

2

By the new method, the difference between the two last logarithms is to be taken as before; and when that difference is divided by 1000, (which is done by changing the three last figures into decimals,) the quotient expresses the number of English fathoms; which is 1797. The correction being made for the contraction of the mercurial column, by 408 degrees of Fahrenheit's thermometer, according to Mr. De Luc's rule, applied to Mr. Brydone's observation, the number is diminished by about 33 fathoms. And the same being farther corrected according to Mr. De Luc's equation for the temperature of the air, we have nearly 33 fathoms, as before, to be added to the last corrected number; so that the number of fathoms is 1797, as at first; and differs but 21 fathoms, in more than 2 miles, from the number according to the old method: and it is probable, that, in so great an elevation, the error from the uncertainty of the air will generally exceed this difference. As there is reason to suppose, upon other considerations, that Etna is much above 2 miles in

2

height,

height, Mr. Brydone suspects that the barometer does not agree with the theory in very great elevations; particularly, that, in the superior elevations, when we get above the region of vapours, the spaces corresponding to given differences in the mercurial column are greater than according to the rule. And I must own it appears probable, that, in the lower elevations, while you are within the region of gross vapours, the column ought to diminish much faster than in the superior elevations; and that the same law cannot truly be applied to both*. I cannot venture to pronounce how this may be, without farther and more accurate observations. I must therefore content myself with adding some notes relating to the system of the atmosphere, for which I am chiefly indebted to the learned observations of Dr. Horseley, who has gone deeper into this subject than any writer before him.

1. It is probable that the elasticity of the air may be affected by other causes beside heat, such as humidity and electricity.

2. If Mr. De Luc's formulæ, expressing GG 4

the

* Omnis aer, quo proprior est terris, hoc crassior; quemadmodum in aqua et in omni humore fæx ima est; ita in aere, spississima quæque desidunt. Senecæ Nat. Quæst. 4. 10.

the effect of temperature on the air's elasticity, are universally true, it will follow, that there is a certain temperature at which the air would totally lose its elasticity, and that elasticity owes its origin to heat. I thought I saw this consequence twenty years ago; and placed the supposed temperature, at which this would happen, at about 300 degrees below the freezing point*. Dr. Horseley, from the formula of Mr. De Luc, places it at 409; but denies the inference, and seems rather to suppose (if I do not misunderstaud him) that such a consequence does not obtain in nature; which is the more probable opinion. When I thought formerly upon this matter, we had no expectation that nature or art would ever exhibit a degree of cold any thing like to what experiment hath since discovered.

3. The diminution of the air's density, as we ascend from the earth's surface, is subject to a limit, and the atmosphere may be of an infinite height; though at that height Dr. Horseley reduces its comparative volume to the 100th power of 3069. This is the case. when the subject is considered mathematically. When it is considered physically,

* See the Essay, p. $19.

he

he is so candid as to allow, that we have no data from experiments to limit the height of the atmosphere. I apprehend there is a certain height at which the matter of the heavens has no immediate reference to our earth as a part of its atmosphere, but is independent of the earth and all its appendages as it passes through the heavens in its orbit; somewhat after the manner as those waters of the sea are independent of the ship, which lie without the limits of her wake. When the air has no longer any reference to the earth as an atmosphere, and has no sensible gravitation towards the earth, it is questionable whether it would have any effect on a barometer, whatever its density might be. If some air were brought down from the top of Etna, according to the second method of making the Torricellian experiment above described, and its absolute density were properly compared with the air below, it might give us some farther light into this interesting part of the subject.

4. It is possible that the density of the air may increase above, while it is diminished below; and that the condensation of the superior part will follow from the rarefaction of the inferior by heat. It may sound like a

paradox

paradox that heat should condense; but it is true by necessary consequence. When the heat increases near the earth, the air is there expanded into a larger volume; and having no liberty below, where the earth is opposed to it, the redundant quantity must go up wards, and bring the whole nearer to an uniform density.

5. If at any height above the surface of the earth, an increasing heat diminishes the density of the air in the same proportion as it increases its elasticity, a barometer will there be stationary*. At lower heights it will sink, and at greater heights it will rise, This case Mr. De Luc actually met with, and was much surprised at it. When the heat of the day has been increasing, a barometer has sunk at the foot of a hill, while another at the top has risen. Scheuchzer was perplexed formerly on the same occa sion he found his barometer rise at the higher station, while it sunk at the lower, contrary to the rule; and he endeavoured to account for it from the greater elasticity of the

This is the very case I have mentioned under another form in a foregoing section, on the Elasticity of the Air. See law 5.