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 part, for every degree of difference between them, as shown by the attached thermometer.

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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.

3rdly. 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 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:

A substitute for the mountain barometer was proposed by Sir John Robinson, Secretary to the Royal Society of Edinburgh, at the last meeting of the British Association at Newcastle.† The instrument consisted of a glass tube, about one and a quarter inches in diameter, and fourteen inches long, with a small bulb at the end, the capacity of

* In this rule of Dr. Hutton's, and 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 can be required of the Mountain Barometer.

† A description of this instrument is given in the "Mechanics' Magazine," for October last.

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 manner:

The instrument was suspended within the receiver of an air-pump, over a cup containing water at the temperature of 62°, 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 guage 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 reimmersion. By the repetition of this process, the graduation of the stem was carried on as far as was necessary.

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, 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. The mountain barometer is not so quickly affected by any change in the pressure of the atmosphere as those of different construction. The Royal Society have three descriptions of these instruments near together-a water barometer, forty feet long; a mountain, and a standard mercurial barometer. The first of these instruments is affected by minute fluctuations in the

density of the air, which have no influence whatever upon the mercury; and it always precedes the standard mercurial barometer in its rise and fall by about an hour; which instrument again is about the same period of time in advance of the mountain barometer.

That the table may be applicable when the temperature is lowest at the lowest station, the column B is divided to meet both cases, as in the table given by Mr. Howlett.

A paper has lately been published by Lieutenant-Colonel Sykes on the method already alluded to, of determining heights by the different temperatures of boiling water, ascertained by the common thermometer, which he has practised extensively in India.

As the necessary apparatus is exceedingly simple, and the instrument not so liable to injury as the barometer, and so much more pcrtable and easily replaced, I have taken from this paper, which will also be found in the 8th number of the "Geographical Journal," the tables computed by Mr. Prinsep, to facilitate the computation of altitudes, and also the examples given by Colonel Sykes, which render their application evident without further explanation.

The results deduced from the use of these tables appear always rather less than those obtained from careful barometrical observations, and also than those calculated from the different formulæ, which have been arranged for the determination of altitudes by this method, but which do not all agree. The results of a number of careful observations made with the thermometer, compared with those obtained at the same time with the barometer, or which have been ascertained by levelling, or trigonometrically, will afford the means of making any necessary corrections in those tables; which, however, giving so close an approximation, deserve to be more generally known and made use of.

The accompanying sketch and explanation, taken from Col. Sykes's pamphlet, show the whole apparatus required:

A. A common tin pot, 9 inches high by 2 in diameter.

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B. A sliding tube of tin, moving up and down in the pot the head of the tube is closed, but has a slit in it, C, to admit of the thermometer passing through a collar of cork, which shuts up the slit where the thermometer is placed.

D. Thermometer, with so much of the scale left out as may be desirable.

E. Holes for the escape of steam.

The pot is filled four or five inches with pure water; the thermometer fitted into the aperture in the lid of the sliding tube, by means

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D

of a collar of cork; and the tin sliding tube pushed up or down to ad

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mit of the bulb of the thermometer being about two inches from the

bottom of the pot.

Before using a thermometer for this purpose, it is necessary to ascertain if the boiling point is correctly marked for the level of the sea by a number of careful observations, and the difference, if any, must be noted as an index error. It is always desirable to have two or more thermometers which have been thus tested, and in all observations the temperature of the air at the time should be noted.

A few minutes will suffice for the whole operation; and where very great accuracy is not required, this method is certainly preferable to the barometer for determining altitudes, on account of the portability and cheapness of the apparatus,* and its not being, like the other more costly and accurate instrument, constantly liable to injury.

TABLE I.

TO FIND THE BAROMETRIC PRESSURE AND ELEVATION CORRESPONDING TO ANY OBSERVED TEMPERATURE OF BOILING WATER BETWEEN 214° AND 180°.

*This can be procured, ready for use, at Newman's, optician, Regent-street.