where M is the column of mercury which is equal to the pressure or weight of the atmosphere at the bottom, and m that at the top of the altitude a; and where M and m may be taken in any measure, either feet or inches, &c.

However, a comparison of the observed heights of the column of mercury at different stations, is not in itself sufficient to give their difference of altitude; because mercury expanding or contracting with every change in its temperature, the same weight of the atmosphere will not counterbalance, with altered temperatures of the mercury, the same height of the mercurial column. The expansion in mercury due to an increase of 1° of Fahrenheit is th* of its bulk. When comparing, therefore, distinct observations of the barometer, the heights of the column must be reduced to a common standard, by deducting th of the height, for every degree of temperature above the standard. To obtain this necessary element in the calculation, a thermometer is fastened to the tube of the instrument.

00

A correction is also required for the temperature of the atmosphere, for a similar reason. The density of the atmosphere is greatest near the surface of the earth, and diminishes as the distance from it increases. But by an increase of temperature, air expands th* of its bulk for every degree of Fahrenheit. A consequent rarefaction of the column that supports the mercury takes place, and the denser parts of that column are raised higher than they were at the previous lower temperature. Under this circumstance, when the barometer is placed at some elevation above the sea, the mercury has to sustain an additional weight, namely, a weight as great as it would have had to sustain, if brought down in the atmosphere to the place formerly occupied by the denser air now raised [above it,

*HUTTON'S Mathematical Dictionary.

supposing that the upper strata do not roll back upon the colder parts and restore the equilibrium. Upon this supposition of the vertical column not disposing laterally of part of the atmosphere forming the increased height, the same difference of height of the mercurial column at two stations, indicates a difference of altitude, increasing as the density of the air diminishes by an increase in its temperature. It is only at the level of the sea, that the pressure would remain constant.

M

m

The formula above given, a 10558 x log. fathoms, is adapted to the mean temperature of the air at 55°. It may be rendered much more convenient for use, by reducing the factor 10558 to 10000, by changing the temperature proportionally from 55°. This reduction is made as

follows:

Inasmuch as for each degree of diminution in the temperature of the atmosphere, the contraction of th part takes place (see page 243) in the entire height of the column, so in the height of 10558 fathoms

1° will produce a diminution of

10558

fathoms, and

435

435

At a temperature therefore of

(55° -23°) or 32°, the formula becomes

M

a = 10000 × log. fathoms,

m

and for every degree above that, the result is to be increased by so many times its 435th part."

As considerable differences of altitude are found to cause only small changes in the height of the mercurial column, it becomes necessary, in order to obtain accurate results, to measure with great precision very minute changes in the height of the mercury. Great mechanical improvements have, with that view, been made from time

R

to time in barometers of different constructions. Among these we select for description, the following construction of mountain barometer, as one of the most exact and convenient hitherto constructed *.

The glass tube, containing the mercurial column, is connected with a glass cistern open to the influence of the atmosphere. A brass casing or tube, to protect the mercurial tube and cistern, is suspended from a tripod stand, by rings or gimbals in the same manner as the mariner's compass, so as to assume by its own weight a truly vertical position. In the upper half of the brass tube, two opposite vertical slits are made, so that the surface of the mercury can be seen against the light. The brass tube is divided into inches and twentieths, to measure the height of the mercury, the zero point being in a plane passing through the upper edges of two rectangular slits made

horizontally on opposite sides of the tube, near the bottom. These slits enable the observer to see the inferior surface of the mercury, which should at each observation be made

* BIOT's Traité de Physique, and SIMMS on Mathematical Instruments.

to coincide with the zero of the scale. The adjustment of the zero point is made by means of the moveable base of the cistern, which is raised or depressed as required by an attached screw, until the upper edges of the slits exclude the light, by forming a tangent to the slightly convex surface of the mercury. The height of the upper surface of the mercurial column is obtained by means of a sliding vernier, the zero point of which is, by a similar contrivance of the exclusion of light, made to coincide to the greatest exactness with the central part of the convex surface of the mercury. The reading of the vernier then indicates the height of the column of mercury, counterbalancing the pressure of the atmosphere at the time of observation. The vernier is usually made to indicate the minute quantity of th of an inch;—the primary scale being divided into inches and twentieths, a space equal to ths of an inch is divided on the vernier into 10 parts; consequently a division on the vernier is smaller than a division on the primary scale by 16th, and the vernier reads therefore to th of an inch.

For the purpose of indicating the changes in the temperature of the mercury, and the consequent changes in its bulk, a thermometer is attached to the instrument. As this thermometer forms a constituent part of the barometer, it is not capable of indicating, with sufficient exactness, changes of temperature that affect the atmosphere much more rapidly than they can influence a solid mass like the barometer. To estimate, therefore, the changes of temperature in the atmosphere, an extremely delicate and sensible thermometer is required. When in use, it should be sheltered from the sun, and suspended some feet above the ground in such a position as to allow a free circulation of air around it.

The observed differences of temperature of the attached and detached thermometers constitute, with the difference

of height in the mercurial column, the principal elements required to obtain the relative altitude of two or more stations, and the results are obtained as follows.

The formula forming the basis of the operation is, as before deduced,

Observe, therefore, the height of "M" of the mercury, and the temperature of the attached and detached thermometers at the lower station.

Observe, in the same manner, the height "m" of the mercury, and the temperature of the attached and detached thermometers at the upper station.

Reduce the mercury to a common temperature, by increasing the colder, or diminishing the warmer, by

th part of the height, for every degree of difference between the two*.

*It must be borne in mind that the formula from which these precepts are deduced aims only at approximate results. Were it otherwise, it would be inconsistent thus to leave it as a matter of choice to increase the colder or diminish the warmer column of mercury, by th part of its height, for when the warmer column is reduced, the difference of altitude obtained is less than when the colder column is increased. The difference noticed is, however, less than the limits of error otherwise inseparable from the operations.

Working out the example given in the text, by increasing the colder instead of diminishing the warmer, a difference of altitude of about 4 feet is the result, as is shown,