There are other forms of the barometer, but their comparative unimportance renders it unnecessary to describe them here. We shall, therefore, proceed to consider the most important purposes to which this instrument is applied.
The most immediate use of the barometer, for scientific purposes, is the ascer tainment of the amount and variation of atmospheric pressure. The fluctuations in the pressure being observed in connexion with changes in the state of the weather, a general correspondence is supposed to prevail between these effects. The instrument has, from this circumstance, been called a weather Rules have been attempted to be established, by which the approaching state of the weather may be predicted from the height of the mercury, and the words rain, fair, changeable, &c. are engraved on the scales of common barometers. These marks are, however, entitled to no attention, since it is the changes that occur in the height, and not the absolute height, that indicates approaching changes in the weather. The variation in the altitude of the barometer in a given place, together with the corresponding changes of the weather, have been regularly recorded for a considerable time; and it is by an exact comparison of these results that general rules are to be found. At present, the best rules are liable to some uncertainty at times. Those which have been considered least liable to error are the following : 1. Generally, the rising of the mercury indicates fair weather ; its fall shows the approach of foul weather. 2. In sultry weather the fall of the mercury indicates coining thunder. In winter, a rise indicates frost. In frost, its fall indicates thaw, and its rise indicates snow. 3. Whatever change of weather suddenly follows a change in the barometer, may be expected to last but a short time. Thus, if fair weather follow immediately the rise of the mer cury, there will be very little of it; and in the same way, if foul weather follow the fall of the mercury, it will last but a short time. 4. If fair weather con tinue for several days, during which the mercury continually falls, a long suc cession of foul weather will probably ensue; and again, if foul weather continue for several days, while the mercury continually rises, a long succession of fair weather will probably succeed. 5. A fluctuating and unsettled state in the mer curial column indicates changeable weather. fhe other important purpose to which the barometer is applied, is the measurement of altitudes. If the atmo sphere were a liquid of nearly equal density, like water, the measurement of heights by the barometer would be the simplest process imaginable : for we should have then only to make one experiment to ascertain how much the mer cury would fall, in rising to the height of 100 feet for example, and then the fall for 200 or 300 feet would, of course, be double or triple the former one. But the density of air is well known to decrease as we ascend from the earth, so that at the height of 31 miles, it is only one half its density on the surface of the earth. From this it must be evident that if the mercury fall one-tenth of an inch in rising through the height of 100 feet, we must rise through a greater height to cause a fall of another tenth. The height of the surface of the atmo sphere above that of the earth is considered to be about 50 miles ; and we have already observed, that at the height of 31 miles the density is reduced to one half. Hence we should find, by ascending to the height of 31 miles in the
atmosphere, the mercury would stand at one-half the height of another barometer at the surface of the earth. If, however, the decrease of density were affected by the height alone, the determination of altitudes would be com paratively easy, as a simple formula may be given, which would immediately show the relation between the height and density. The circumstance that interferes with barometric observations, is temperature, which affects them in two ways. 1. Increase of temperature expands the mercury in the barometer, and thereby causes the column to be longer than at lower temperatures. 2. The air itself becomes expanded by heat ; and hence the column becomes lengthened without any increase in its absolute weight. It might be thought that these effects were too trivial to influence sensibly the results of our obser vations ; but it must be remembered, that as we ascend from the earth, the temperature of the air rapidly decreases, so that at a certain height, dependent on the latitude of the place, a freezing temperature constantly prevails. Putting aside the effect of change of temperature, the simplest rule for deter mining heights is as follows :—Observe the height of the mercury at the bottom and top of the altitude to be ascertained; take the logarithms of these heights, and multiply their difference by 10,000, the product is the answer in fathoms. Then suppose the mercury at the foot of a mountain to stand at 29.5 inches, and at its summit 26.4 inches, the calculation would be as follows :— Lower barometer. . . 29.5 log. .469822 Upper ditto 26 4 log. .421604 Difference .048218 10000 482,180,000 Fathoms, or, 2893 feet, which is the altitude, supposing the temperature to be at Fehr. If the temperature differ from this, it must be observed at the upper and lower station, and a mean of the two taken, by adding them together, and dividing the sum by 2. If the mean thus obtained exceed 31', the altitude before obtained must be increased for every degree of difference between them, and vice versa. If we wish to cofiect the other error arising from the expansion or contraction of the mercury in the barometer, we must observe the temperature of the mercury at the upper and lower station ; then the altitude of the lower one must be increased, or the higher one diminished, part for each degree of difference between their temperatures. To those who are unaccustomed to the use of logarithms, the fol lowing rule may be preferred :—Take the sum and difference of the upper and lower barometric heights, and divide one by the other ; multiply the quotient by 55000, and it will then answer in feet for a temperature of Suppose, as before, the height at the lower station to be 29.5, and at the upper, 26.4 then 29.5-26.4 = 0554 29.5 + 26.4 And .0554 X 5500 = 3047 feet.
This result, it will be seen, exceeds the other by 154 feet ; it is not so exact, but, in many cases, it may serve to furnish a tolerable approximation, when logarithmic tables are not at hand. The corrections for temperature may be applied as in the other formula.