CHAPTER VIII.

MOUNTAIN BAROMETER.

THE Mountain Barometer presents another method of determining comparative altitudes, which is not susceptible of so much accuracy as those already described, but is of course a far quicker mode of operation. It is also capable of being used extensively by one individual, and the observations if performed with care will in most cases give results very near the truth. The instrument, as made at present, is very portable, and not liable to injury in travelling, if the proper precautions are taken; the most essential of which is, always to carry the cistern inverted, and in this position to turn the screws at the bottom of the cistern, till the mercury almost touches the top of the tube, and thereby prevent the oscillations from breaking it. In barometers considered of the best construction, and which are the most expensive, the surface of the mercury in the cistern is brought by a screw to the zero of the instrument, which marks the height at which it stood there when the scale was first graduated.* In others not furnished with the means of effecting this adjustment, and in which the cistern is entirely enclosed from view, an allowance must be made to reduce the reading on the scale to what it would have been if the mercury in the cistern had been adjusted to zero. It is evident that this correction of the height of the column of mercury must be proportioned to the relative capacities of the cistern, and the bore of the tube.

Thus supposing the interior diameter of the tube to be 1., its exterior 3; and the diameter of the cistern 9 inches: the ratio of the areas of

* It is doubtful if this is any advantage: a barometer of this kind takes a long time to adjust and read; and as a tangent to the surface of the mercury is required, both in the tube and the cistern, there is more chance of error in the observation.

the surfaces will be (81-9) or 72 to 1.* The difference then between the observed reading of the barometer, and that of the "neutral point," which is the height at which the mercury stood in the tube above the zero mark of the cistern, when the instrument was first made (and is always marked NP), is to be diminished in this proportion, and the quotient applied to the observed reading, additive when it is above this standard, and subtractive when below. The small correction for the capillary attraction of the glass tube is constant and additive; and is generally allowed for by the maker in laying off the neutral point, in which case no further notice need be taken of it.

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The principle upon which the density of the atmosphere, measured by the height of the column of mercury, is applied to the determination of comparative altitudes, is too generally known to need explanation; but the mere comparison of the observed heights of mercury, at the places of observation, will not suffice for the purpose; as every change of one degree of temperature by Fahrenheit's thermometer, causes an expansion or contraction of the fluid of of its bulk; and all observations must be corrected on this account, if made under different degrees of temperature. The method of using the mountain barometer is shortly as follows: it is carried, as before observed, inverted, until required for use, the cistern being always above the horizontal, at an angle of at least 45°, when the screw at the bottom of the cistern being first turned, until it no longer acts against the leather bag, or the end of the tube (according to the construction of the barometer), the instrument is reversed, and the guage-point (if there is one) is set to zero. The index is then moved till its lower edge is a tangent to the globular surface of the mercury, the height of which in the tube is read off to of an inch, by means of the index vernier; the thermometer attached to the instrument, showing the temperature of the fluid, and the detached thermometer, that of the atmosphere at the time of observation, are also noted together with the heights of the mercury. The following form is convenient, as containing the observations, and leaving a space for the results :

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1000

*This correction, termed the "capacity," is generally ascertained by trial. A certain quantity of mercury is first poured into the tube, which it fills to the height, say of 14.4 inches: this same quantity is then transferred to the cistern, and found to rise to 2 inches. The capacity is therefore as 14.4 to 2, or 72 to 1; and this ratio is always marked by the maker on the instrument.

It is of course preferable to have two barometers, and to make simultaneous observations, as, during changeable weather, dependence cannot be placed upon results obtained with only one; particularly if any considerable interval of time has elapsed between the comparison of the heights of mercury at the different stations. Even the method that has been suggested by Mr. Howlett of noting the time of each observation, ending the day's work at the spot where it was commenced, and then correcting the readings of the barometer and thermometer at each station for the proportion of the total change between the first and last reading due to the respective intervals of time, cannot of course render observations taken with one barometer equal in accuracy to those observed simultaneously with two instruments, unless the rise or fall of the barometer, and particularly of the thermometer, was ascertained to have been uniformly progressive during the whole day. Observing, however, the barometer again at the first station at the close of the day has this advantage, that any great change during the period will be immediately detected, and the degree of dependence to be placed upon the observation made evident. The difference of readings, owing to these changes, will also be generally subdivided among a number of observations, though instances may occur, where this caution, as regards the thermometer, will be productive of error in the result. There are several methods of calculating altitudes from data thus obtained. That according to a formula given by Mr. Bailey, in page 183 of his invaluable "Astronomical Tables and Formulæ," is perhaps the most simple: it is deduced from the rule given by La Place, reducing the French measures to English feet, and expressing

the temperature by Fahrenheit's Thermometer, whence the difference of altitude will be found equal to 60345.51 x {1 + ·001111 (t + t'— }× (1+002695 cos. 24)

B

64°)} × log. of 18

X β'

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1+0001 (r-r')

t being the temperature of the air at the lower, and t'at the upper station ―r and r—that of the mercury, ẞ the barometer at the lower, and B' at the upper-station, and the latitude of the place of observation. In the table framed to facilitate this computation,* A denotes the

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log. of the two first, C of the last term, and B that of 1+ ·0001 (r—r')' the formula then is rendered simply A+ C + log. D;-D being =log. 6-(log. ß' + B).

The following example, showing the calculation of the two first observations tabulated above, will explain more clearly this method of computation :

2.0666306= log. 116.58, the altitude in feet. By a section taken with a spirit-level, the height of the parade above high water mark was ascertained to be 115 feet. Altitudes are also very easily (but not always so correctly) obtained by the tables in a pamphlet, entitled "A Companion to the Mountain Barometer," published by Mr. Jones, and sold with the instruments made by him. The barometrical observations are first brought to the same temperature, by applying to the coldest a correction found in the first table for the

* In Mr. Baily's table, the column B is calculated on the supposition that the thermometer is always the highest at the lowest station, which in great altitudes will be the case; but as the barometer may be used with advantage in a comparatively flat country, this omission has been remedied in a table published by Mr. Howlett, in the "Professional Papers" of the Royal Engineers, from which the column B has been taken. The more accurate method is to correct the barometer for temperature, independently of the tables.

difference* of the attached thermometers. The approximate height is then obtained by inspection, taking the difference between the numbers corresponding to the corrected readings of the barometer, from the second table.

Lastly, the correction in the third table, opposite to this result, multiplied by the mean of the detached thermometers, and added to the approximate height, gives the true difference of altitude. Below, the same example as before is worked out by means of these tables; the temperatures being converted from Fahrenheit to the centigrade scale to correspond with the tables.

* In Mr. Jones's Pamphlet the Centigrade Thermometer is supposed to be used (the comparison of which with Fahrenheit's is given in p. 176). The Centigrade, or Centesimal Thermometer, derives its name from the interval between freezing and boiling water being divided into one hundred parts. It is adapted to the decimal system of measurement, and since the Revolution has been very generally used in France. Its zero, like that of Reaumur's, commences at the freezing-point.