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Volume 2, 1869
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Art. LVI.—On a series of Tables for facilitating the Calculations of Altitudes from Barometrical Observations in Mountainous Countries; with explanations.*

[Abstract, by the Assistant Secretary, of Paper read before the Wellington Philosophical Society, November 13, 1869.]

The author commenced by explaining, that in the year 1865, when engaged in exploring the Canterbury Alps, for the purpose of finding a route available for the construction of a coach road, between the eastern portion of that province, and the then newly-discovered goldfields on its western coast, the necessity for such tables as he proposed to describe had been manifest to him.

“The broken character of the country, and the denseness of the forests, which stretch everywhere from the banks of the rivers up to the line of

[Footnote] * The valuable tables appended to this paper, not being suitable for insertion in this volume, have been returned to the author for separate publication in a convenient form for the use of engineers.—ED.

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perpetual snow, would have rendered futile any attempt to obtain a connected series of levels by the use of the spirit level, and therefore not only the trial levels, but those required for the location of the selected route were calculated from barometric observations.

“As this, however, involved a great mass of calculations, the author was led to consider whether the reductions of the barometer observations could not be effected by simpler means than those commonly used. It then occurred to him that if the altitude corresponding to any reduced barometer reading were divided by the difference in the height of the mercurial column at the sea level, and at the given altitude, the resulting quotient would be a factor, which might be used for calculating approximately the altitudes corresponding to other barometric readings within a certain limited range.

“Thus, assuming the height in inches of the mercurial column at the sea level=30,

And taking a series of reduced barometric readings as 29 28 27 26 etc.
The differences between these readings and that at the sea level are 1 2 3 4 etc.
And the corresponding altitudes at a mean temperature of 32° Fah. ft. 886·9 ft. 1804·8 ft. 2756022 ft. 3743·5
Which altitudes divided by the differences of pressures would give the factors 886·9 902·4 918·8 935·9

which could be used for calculating approximately the altitudes corresponding respectively to the barometer readings between 30 and 29, 29 and 28, 28 and 27, 27 and 26, etc.

“Following up this idea, it further became apparent, that as the differences of mercurial pressure are expressed in inches and decimals, the decimal division of the differences between these factors would supply the means of calculating factors for all intermediate barometric readings, not, it is true, with perfect accuracy, but within limits of error which may be practically disregarded; the maximum error, from the employment of the factors in the calculations, in the resulting altitudes, for elevations under 3250 feet, not exceeding four inches.

“It will be seen at once, that in this system of calculating altitudes, the correction for the difference between the actual and the tabular mean temperature will be most readily made, not by reducing the barometer readings, but by correcting the tabular altitudes; and also that if each of the factors be divided by 480, the resulting quotients will give the constants by which they must be respectively altered, for each degree of difference between the actual and the tabular mean temperature. the result of the above considerations was the construction of the following table (calculated for a mean temperature of 32° Fah., and a mercurial pressure at the sea level of 30 ins.) by which the calculation of altitudes from barometric observations may be effected rapidly, and with the use of very few figures, without the necessity of referring to a table of logarithms, and with a corresponding diminution in the liability to numerical errors.

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Reduced Barometer readings. Difference in the height of the mercurial column, at the sea level, and at given altitudes. Height, in feet, per inch of difference in the height of the mercurial column. Corrections per 1° Fah. difference in temperature. Altitudes, in feet, above the sea level.
inches. inches. feet. feet. feet.
26 4 935·9 1·9 3743·5
Diff. 17·1
27 3 918·8 1·9 2756·2
Diff. 16·4
28 2 902·4 1·9 1804·8
Diff. 15·5
29 1 886·9 1·8 886·9
Diff. 14·9
30 0 872·0 1·8 Sea level.

“The table in the above form having proved of great service in the author's professional practice, it has been extended for publication, by calculating the altitudes for every hundredth of an inch difference in the height of the mercurial column, from 30 inches to 26 inches; and a column of temperatures has been added, which will be found of considerable assistance in calculating the difference between the actual and the tabular temperature at any given altitude.”

Mr. Dobson then proceeds to give the principles upon which the tables are framed, at greater length; with full explanations of the tables themselves, directions for registering the observations, and for using the tables in the calculations of altitudes.

A chapter is devoted to “General Observations,” in which he states that, “in tolerably level country, and in clear, calm weather, the observations may be extended to a distance of from fifteen to twenty miles from a well-ascertained bench-mark without risk of serious error. If, however, there is much wind, not only must these limits be greatly reduced, but it will be advisable that the observations at each of the upper stations should be twice repeated at ten minutes intervals, in order that it may be ascertained whether the barometer is rising or falling, and that the index error may be adjusted according to the directions whence the changes come.

“It must, however, be remembered that the fluctuations of the barometer due to variations in the quantity of aqueous vapour in the atmosphere, as well as to other causes, are so great as to render all barometric observations valueless, as engineering data, which cannot be corrected for the deviations from mean atmospheric pressure, by comparison with a register kept at some neighbouring station, of which the altitude has been ascertained.”

The author suggests that “although the mercurial barometer should always be used, when practicable for the observations at permanent meteorological stations, it is at once too cumbrous and too fragile for the rough work of a reconnaissance survey. For this purpose a properly compensated aneroid barometer may be substituted, with advantage, for the more perfect instrument. Up to the present time, the use of the aneroid barometer has, with trifling

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exceptions, been confined to forecasting the weather, the somewhat intricate nature of barometric calculations, having prevented its general adoption as an instrument for taking levels. It is hoped that these tables, by removing the difficulties referred to, will pave the way to a more extended use of this valuable instrument which is especially adapted for taking trial sections in wooded and mountainous districts, and with which, under proper management, very close results may be obtained, without that expenditure of time and money, involved in the use of the spirit level under such circumstances.”