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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, or reduce them to the same temperature, increasing the colder, or diminishing the warmer, by pobo 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 :
48820 + 58.4 x sum detached thermometers a = diff. bar. x
sum of barometers. Approximate altitude = a - a (.00006 < lat. in degrees). This is nearly correct up to 2500 ft.; for a greater altitude apply the following correction :
diff. bar. True alt. = approx. alt. + š approx. alt. X
* 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 barometer.
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 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.
The sketch below of the interior of the aneroid, the dial plate being supposed to have been removed, is taken from an extract from Mr. Dent's treatise on the instrument in the "Aide Mémoire.'
D D is the cylindrical vacuum box; CC the lever, to the end of which is attached the vertical rod i, connecting it with the other levers acting by means of a piece of watch spring upon the roller carrying the index hand. An alteration in the
distance of leverage to regulate the movement of this hand, so as to correspond with the scale of a mercurial barometer, is managed by means of the screws e and b.
The position of the hand is made to coincide with the indication of a barometer by means of the screw A (to be touched for no other purpose), which effects the object by raising or depressing the lever C.
At present there is no probability of much improvement in this instrument, as it can only be made by the patentee; but on the expiration of the period for which this patent is granted, it is to be hoped that it will be taken in hand by our best mathematical instrument makers, and rendered capable of supplying the place of the mercurial mountain barometer; at all events under circumstances where the latter would be liable to injury or even destruction.
A substitute for the mountain barometer was proposed by Sir John Robinson, Secretary to the Royal Society of Edinburgh, at one of the meetings of the British Association at Newcastle*. The instrument consisted of a glass tube, about one and a quarter inch in diameter, and fourteen inches long, with a small bulb at the end, the capacity of which was three or four times that of the inside of the tube; and the graduations on the stem of the tube were formed experimentally by the maker, in the following manThe instrument was suspended within the receiver of an airpump, over a cup containing water at the temperature of 620, the mercurial barometer standing at 30 inches. The air in the receiver being exhausted to a degree of rarefaction corresponding to twenty-nine inches of the barometer, the lower end of the instrument was immersed in the cup of water; and air being admitted into the receiver, the exhaustion was repeated until the barometer gauge indicated a pressure equal to twenty-eight inches, when a corresponding mark was made on the tube, the air being in like manner admitted after its re-immersion. By the repetition of this process, the graduation of the stem was carried on as far as was necessary
* A description of this instrument is given in the “Mechanics' Magazine,” for October, 1839.
With several tubes thus graduated, an observer in a hilly country may ascertain the density of the atmosphere on the summits of different elevations, by sending an assistant to each, with one of these tubes, and a tin case containing water. They are taken up with the stems open; and the air within each partaking of the density of that at the station, the mouth of the tube is put into the water, and left in it as the assistant descends. The water will rise in the stem as the density of the atmosphere increases, and will indicate by its height the degree of rarefaction of the air at the upper station—a correction being made for the variation of the barometer from the standard height, and also for that of the temperature of the atmosphere.
This substitute for the expensive and delicate mercurial mountain barometer would, from its portability and simplicity, be particularly useful in determining comparative altitudes in a mountainous country, but of course the same accuracy cannot be expected from it.Another method of obtaining approximate differences of altitude is by a comparison of the temperatures of boiling water (which vary with the pressure of the atmosphere), upon which a paper was some years since published by Colonel Sykes, who practised it extensively in India *.
As the necessary apparatus is exceedingly simple, and the in
* I ascertained lately the approximate altitudes above the sea of a number of places in Australia by this method; many of these were afterwards tested by the triangulation, and the results proved even more satisfactory than I had anticipated.