space of air answering to an inch of mercury, grows continually greater as we ascend higher from the earth. Learned geometers have considered in what proportion the air will be rarefied at different elevations above the earth; and they find, that if the elevations are taken in an arithmetical progression, the density will decrease in a geometrical progression, and consequently, that the logarithms of the densities will be reciprocally as the elevations. But the weight of the air being as its density, and the height of the barometer being proportional to the weight of the air, it follows that the logarithms of the heights of the mercury are reciprocally as the elevations*. Hence we have a rule for measuring elevations by the barometer; for if there is a known ratio between the elevation and the density, the barometer, so far as it measures the density, will measure the elevation; and thus we have a compendious method of finding the altitude of mountains, with little more trouble than that of ascending them. The order of the calculation is this. First, to find accurately what elevation is required to make the barometer fall one tenth of an inch, VOL. IX. G G * See Phil. Trans. Abr. vol. vi, part ii. P. 45, inch, (or any other quantity,) which let us suppose to be 86 feet: and let us also suppose that this is done when the barometer, at the lower station, is at 29.5 inches at the level of the horizon, that is, when the atmosphere is at a middle state. Then say, as the difference between the logarithms of 29.5 and 29.4 is to 86 feet, so is the difference between the logarithms of 29.5 and 27.5 (or any other height of the barometer in inches and tenths of an inch) to the number of feet required. On this principle tables were composed many years ago by two learned mathematicians of our own country, Dr. Halley and Dr. Nettleton, and by others in France. And, thus far the calculation is very easy. But all observers were sensible of some irregularity in the theory on account of the uncertainty of the air, which it was very difficult to provide against. In conclusions which depend on mathematical reasoning and actual observation, it is generally easy to approximate; but, to attain to accuracy and precision, is difficult. Every common navigator can find his time by the sun to a minute or two: but to find it to seconds requires the best instruments, and a more laborious borious calculation: so that while the former may be executed at the expence of a few shillings, the latter will require an expence of many pounds. Two difficulties arise to disturb the theory; one from the imperfection of the instrument, the other from the uncertainty of the atmosphere. At different elevations the temperature of the air alters; and the greater elevation being generally attended with a colder temperature, this occasions a contraction of the mercurial column, so that the barometer falls lower than it ought to do, and observation gives an elevation greater than the true. And as the elasticity of the air alters with heat and cold, the density of the air cannot be truly inferred from its absolute pressure: and thus we are liable to a second error. More heat, at the same elevation, will increase the elasticity of the air, and the pressure being greater than it ought to be by the theory, the elevation will be found too little. More cold will diminish the elasticity, and then the elevation (which commonly happens) will be found too great. The barometer is liable to another error: for in the common upright tube the mercury never rises so high as it ought to do, from a repulsive GG 2 repulsive effect of the glass upon the mercury. But this is corrected by a siphon-tube instead of the straight one; for thus there are two repulsions which correct one another. Some other niceties might be mentioned, concerning the different degrees of expansion in glass and mercury under the same degrees of heat and cold. These are the difficulties in measuring altitudes by the barometer, which of late have exercised the ingenuity of Mr. De Luc, a learned and philosophical native of Geneva, to whom the public is much indebted for some valuable improvements in this part of philosophy, which are the fruit of great labour and attention. His work is too large and complex for me to attempt a particular account of it: and his improvements have already been represented to great advantage by two very learned members of the Royal Society, Mr. Maskelyne the AstronomerRoyal, and the Rev. Dr. Horseley, who have given two excellent papers in the Transactions upon the new Theory and Practice of Barometrical Mensuration*; to which I must refer the learned reader. From the ingenious Mr. Brydone's obser * See vol. lxiv. part. i. N° 20, and 30. vations vations of the barometer, in his Travels into Sicily, which I suppose are very near the truth, I have calculated the height of Mount Etna, according to the old and new method: and by every rule I can apply, I can make the height of that mountain but a trifle more than 2 miles; whereas by geometrical observation it is more probably 3 miles high, or nearly so, if accounts are true. I take Dr. Halley's observed difference of the barometer at the top and bottom of Snowdon Hill, with its height as found by geometrical mensuration: with this I compare Mr. Brydone's difference at the top and bottom of Etna; and the result is as follows: In. Tenths. Barometer at the level of the sea, 29. 9 log. 14756712 Barometer at the top of Snowdon, 26. 1 log. 14166405 Difference... 590307 Height of Snowdon, taken geometrically, 1240 yards. As the first difference 5903 (rejecting the two last figures as superfluous) is to 1240 yards; so is the second difference 17978 (rejecting the two last figures as before) to the number GG 3 |