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4.82986 29 104 4.79953 174 4.83072 30 0.00130 ⚫99869 106 4.80045 176 4.83158 31 0.00134 108 4.80137 178 4.83234
then the log. of the differ-
Make D=log. 6-(log. B'+B)
The following example taken from page 102 will explain the method of computation :—
t=58°-t' = 57° — r = 61° — r′ = 60°
B30-409-B'30-278; latitude 51° 24'.
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 employed 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.
sponding 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.
Dr. Hutton's rule for the calculation of altitudes by the barometer is as follows:-First, correct the heights of the mercury, reduce them to the same temperature, increasing the colder, or diminishing the warmer, by part, for every degree of difference between them, as shown by the attached thermometer.
2nd. Take the difference of the common logarithms of the heights of the barometer thus corrected, setting off four figures
from the left hand for integers, which will be an approximate height in fathoms.
3rd. Correct the number last found for the atmospheric temperature, shown by the detached thermometers, as follows:-For every degree that the mean of the two differs from 31°, take so many 35 parts of the fathoms above found, and add them if the temperature be above 31°, but subtract them if below, for the true difference of altitude, in fathoms *. The same example as before is thus solved by this rule :
Where no table of logarithms is at hand, the following rule is given in Mr. Howlett's paper for the altitude :—
a diff. bar. x
4882058.4 x sum detached thermometers
sum of barometers.
Approximate altitude aa (00006 x lat. in degrees).
This is nearly correct up to 2500 ft.; for a greater altitude apply the following correction :
True alt. approx. alt. + 1⁄2 approx. alt. ×
* In this rule of Dr. Hutton's, as in Jones's tables, there is no correction for latitude. One of the latter, I have also been informed, is erroneous; but they will, at all events, give good approximate results, which is all that is generally required of the mountain baro
A new description of barometer, termed an Arenoid, has lately been invented, which, if more accuracy and minuteness can be introduced into the mode of reading off the graduation of the dial by the indication of the hand, will be found a most valuable substitute for the mercurial barometer in the determination of moderate* altitudes; being much more portable, and not subject to the same derangement and risk of fracture by carriage as the other more delicate instrument. The pressure of the atmosphere is also the motive power in this invention; but its application is totally different from that of the barometer, as it is made to act not on the surface of a fluid, but upon the sides of a shallow cylindrical metal box, from which the air has been exhausted and a small quantity of gas introduced into what otherwise would have been a vacuum, for the purpose of compensating (by its expansion with the increase of temperature) for the tendency to collapse consequent upon the loss of elasticity thereby caused in the metal. The top and bottom of the box are forcibly separated and kept in this state of tension by a plate acting as a lever, the end farthest from the central point, by which the box is supported, resting upon a spiral spring. The increase or diminution of the atmospheric pressure upon the surface of the box depresses or elevates this end of the lever, with which two other levers are connected; the last acting by means of a piece of watch spring on the roller upon the axis of which is fixed the hand that indicates upon the dial the degree of pressure; a flat spiral spring also acts slightly upon this roller, always against the levers; and thus keeps the hand, which would otherwise remain stationary after being propelled to its full distance, in constant unison with the varying fluctuations of the atmosphere.
In measuring altitudes by the arenoid the same rules for calculating the heights hold good as with the barometer; but in the present imperfect state of the instrument the precaution appears necessary to be attended to of ascertaining by trial the actual value in feet of the graduations on the dial; and also the effect produced upon these results by any change of temperature; as different instruments will be found to vary in these particulars.
* The very limited range of the instrument, as at present constructed-only 2.5 inches below 30°-confines its power of measuring altitudes to about 2000 feet above the sea.