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by contours, can be traced so as not to exceed in any part a given inclination.
The application of contours to the object of defilading a work to secure its interior from fire (almost the first use to which they were applied) can hardly be entered upon here. The subject is fully treated by many French authors on fortification; and extracts from Captain Noizet's paper, in the "Mémorial du Génie," will be found in the sixth volume of the Royal Engineers' Professional Papers*.
The method of measuring altitudes by the barometer and the temperature of boiling water is reserved for the next chapter.
* See also the chapter upon Defilade in Captain Macaulay's "Field Fortification,"
MOUNTAIN BAROMETER, &c.
THE Mountain Barometer presents a method of determining comparative altitudes not susceptible of so much accuracy as those already described, but far more expeditious when applied to isolated stations separated from each other by considerable distances. 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, though liable to injury in travelling if the proper precautions are not invariably taken, the most essential of which is that of always carrying the cistern inverted, and in this position tightening the screw✶ at the bottom of the cistern to prevent the oscillations of the mercury breaking the tube. 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
* Mr. Howlett remarks that, in barometers where the bottom of the cistern is formed by a leather bag, the mercury should be forced up nearly to the top of the tube by the bottom screw, whilst the instrument is held upright. It should then be carefully inverted, in which position it must always be carried. When required for use, it should again be placed upright before the pressure of the screw against the bag is relaxed; otherwise the bag is liable to be burst.
+ 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.
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 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 N P), 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. Should air by any means have found its way into the tube, it can, if this is of large bore, be nearly got rid of by holding the barometer upright, with the cistern downwards, and turning the screw at the bottom as far as it will go without forcing. The instrument must then be sloped to an angle of about 45°, when more air will rush into the tube. If the screw is now unloosed, and the instrument held with the cistern upwards, at an angle of 45°, and gently tapped, the air will nearly all escape; the test of which is the mercury striking the top with a clear, and not a muffled sound, showing that the vacuum is nearly perfect.
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 of Fahrenheit's thermometer causes an expansion or contraction of the fluid of
* 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 2 inch. 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.
oo of its bulk; and all observation 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 end of the tube, the instrument is reversed, and the gauge-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 too 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:—
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, and becomes by the use of the Table* in the next page A+C+log D. D being log (log + B) where
t represents the temperature of the air at the lower station.
t' that at the upper.
r the temperature of the mercury at the lower station.
r that at the upper.
A the correction for temperature dependent upon t+t'.
B that for the temperature of the mercury dependent upon r-r', and
C the correction for the latitude of the place.
* In Mr. Bailey'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.