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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 (8129) 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.
gobo 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 to robo 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 B - (log B + 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. go ou that at the upper. A the correction for temperature dependent upon t + t.
. B that for the temperature of the mercury dependent upon r-m', 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 thermo meter 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.
40 4•76891 110 42 4.76989 112 44 4•77089 114 46 4.77187 116 48 4.77286 118 50 4.77383 | 120 52 4:77482 122 54 4.77579 124 56 4.77677 126 58 4:77774 128 60 4•77871 130 62 | 4•77968
132 64 | 4•78065 134 66 4•78161 136 68 4.78257 138 70 4.78353 140 72 4.78449 142 74 4:78544 144 76 4:78640 146 78 4•78735 148 80 4:78830 150 82 4:78925 152 84 4:79019 154 86 4•79113 156 88 4•79207 158 90 4•79301 92 4.79395 162 94 4.79488 164 96 4•79582 166 98 4•79675 100 4:79768 102 4.79860 172 104, 4.79953 174 106 4.80045 176 108
0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90
10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31
0.00117 0.00115 0.00111 0.00100 0.00090 0.00075 0.00058 0.00040 0.00020 0.00000 9.99980 9.99960 9.99942 9.99925 9.99910 9.99900 9.99890 9.99885 9.99883
Make D=log. B–(log. B'+B)
then the log. of the differ-
The following example taken from page 102 will explain the method of computation :
t = 58°-t' = 57°-r=61° -1' = 60°
By a section taken with a spirit level, this altitude was found to be exactly 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 difference + of the attached thermometers. The approximate height is then obtained by inspection, taking the difference between the numbers corre
* As a proof, however, that the results given by the barometer are not always to be depended upon when extended to very great distances, the observations consequent upon which occupy a considerable time; it may be mentioned that Professor Parrott who was em. ployed in determining by barometrical measurement the level of the Black Sea above that of the Caspian, made this quantity by a series of the most careful simultaneous observations in 1811 exactly 300 feet; the same operation repeated by him in 1830 gave a result of only 3 or 4 feet. In 1837 this altitude was determined geodesically by the Russian Government to be 83.6, and was afterwards made by a French observer between 60 and 70 feet.
+ In Mr. Jones's Pamphlet the centigrade thermometer is supposed to be used (the comparison of which with Fahrenheit's is given in Table 19). 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.