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When the thermometer has been boiled at the foot and at the summit of a mountain, nothing more is necessary than to deduct the number in the column of feet opposite the boiling point below from the same of the boiling point above: this gives an approximate height, to be multiplied by the number opposite the mean temperature of the air in Table II., for the correct altitude. Boiling point at summit of Hill Fort of Púrun
When the boiling point at the upper station alone is observed, and for the lower the level of the sea, or the register of a distinct barometer is taken, then the barometric reading had better be converted into feet, by the usual method of subtracting its logarithm from 1.47712 (log. of 30 inches) and multiplying by .0006, as the differences in the column of "barometer" vary more rapidly than those in the "feet" column.
Example.- Boiling point at upper station
Barometer at Calcutta (at 32°) 29in. 75
185° = 14548
Temperature, upper station, 76°
Ditto lower, 84°
Assuming 30.00 inches as the average height of the barometer at the level of the sea (which is however too much), the altitude of the upper station is at once obtained by inspection of Table I., correcting for temperature of the stratum of air traversed by Table II.
GEODESICAL OPERATIONS CONNECTED WITH A TRIGONOMETRICAL
In the words of Sir J. Herschel, "Astronomical Geography has for its objects the exact knowledge of the form and dimensions of the earth, the parts of its surface occupied by sea and land, and the configuration of the surface of the latter regarded as protuberant above the ocean, and broken into the various forms of mountain, table land and valley." The form of the earth is popularly considered as a sphere, but extensive geodesical operations prove its true figure to be that of an oblate spheroid, flattened at the poles, or protuberant at the equator; the polar axis being about part shorter than the equatorial diameter.* This result is arrived at by the measurement of arcs of the meridian in different latitudes, by which it is ascertained, beyond the possibility of doubt, that the length of a degree at the equator is the least that can be measured, and that this length increases as we advance towards the pole, whence the greater degree of curvature at the former, and the flattening at the latter, is directly inferred.
* The exact determination of arcs of the meridian measured in France, and also the comparison of the three portions into which the arc of the meridian between Clifton and Dunnose was divided, presenting the same anomaly of the degrees appearing to diminish as they approach the pole, are opposed to the figure of the earth being exactly a homogeneous or oblate ellipsoid; but its approximation to that figure is so close, that calculations based upon it are not affected by the supposed slight difference. The proximity of the extreme stations to mountainous districts has been partly the cause of this discrepancy, as the attraction of high land, by affecting the plummet of the Zenith sector, may vitiate the observations, for the difference of latitude between any two stations. A survey was undertaken by Dr. Maskeylene, solely to establish the truth of this supposition, the account of which is published in the “Philosophical Transactions" for 1775. A distance of upwards of 4000 feet was accurately measured between two stations, one on the north and the other on the south side of a mountain in Perthshire. The difference of latitude between these extremities of the measured distance was, from a number of most careful observations, determined to be 54".6. Geodesically this arc ought to have been only 42". 9, showing an error of 11".7, due to the deflection of the plummet.
Our "diminutive measures can only be applied to comparatively small portions of the surface of the earth in succession; but from thence we are enabled, by geometrical reasoning, to conclude the form and dimensions of the whole mass.
There are two difficulties attending the measurement of any definite portion of the earth's circumference, such as one degree, for instance,* in the direction of the meridian, independent of those caused by the distance along which it is to be carried: the first is the necessity of an undeviating measurement in the true direction of a great circle, and the second the determination of the exact spot, where the degree ends.
The earth having on its surface no landmarks to guide us in such an undertaking, we must have recourse to the heavens; and though by the aid of the stars † we can easily ascertain when we have accomplished exactly a degree, it is far more convenient to fix upon two stations, as the termini of the arc to be measured having, as nearly as possible, the same longitude; and to calculate the length of the arc of the meridian, contained between their parallels, from a series of triangles connected with a measured base, and extending along the direction of the arc. From the value thus obtained, compared with the difference between the latitudes of the two termini, determined by a number of accurate astronomical observations, can be ascertained of course the length of one degree in the required latitude.
The measurement of an arc of the meridian, or of a parallel, is perhaps the most difficult and the most important of geodesical operations, and nothing beyond a brief popular description of the mode of proceeding adopted in this country, and on the continent, can here be attempted. For the details of the absolute measurement of the bases from which the elements of the triangles were deduced, as well as the
*More than an entire degree (about 100 miles) was actually measured on the ground in Pennsylvania, by Messrs. Mason and Dixon, with wooden rectangular frames, twenty feet long each, laid perfectly level, without any triangulation. Page 10, "Discours Preliminaire, Base du Systeme Métrique," and "Philosophical Transactions," for 1768.
The stars whose meridional altitudes are observed for the determination of the latitude, should be selected among those passing through, or near, the zenith of the place of observation, that the results may be as free as possible from any uncertainty as to the amount of refraction. With proper care and a good instrument, the latitude for so important a purpose ought to be determined within one second of space, unless local causes interfere to affect the result.
various minute but necessary preliminary corrections, and the laborious analysis of the calculations by which the length of the arcs were determined from these data, reference must be made to the standard works descriptive of these operations.
At the end of the second volume of the "Account of the Operations on the Trigonometrical Survey of England and Wales," will be found all the details connected with the measurement of an arc of the meridian, extending from Dunnose, in the Isle of Wight, to Clifton, in Yorkshire. The calculations are resumed at page 354 of the third volume; the length of one degree of the arc resulting from which, in latitude 52° 30', (about the centre of England,) being equal to 364,938 feet.
An arc of parallel was also measured in the course of the trigonometrical survey between Beachy Head and Dunnose, in 1794, but fault has been since found with the triangulation, and corrections have since been applied to the longitudes deduced therefrom, which are alluded to in "The Chronometer Observations for the difference of the longitudes of Dover and Falmouth," by Dr. Tiarks, published in "The Phil. Trans. for 1824," and in Mr. Airy's paper "On the Figure of the Earth."
The arc measured by Messrs. Mechain and Delambre between the parallels of Dunkirk and Barcelona, and the operations of which are described in detail in the "Base du Système Métrique Decimal,” had for its object, as the title of the work implies, not only the determination of the figure of the earth, but also that of some certain standard, which being an aliquot part of a degree of the meridian, in the mean latitude of 45°, might be for ever recognised by all nations as the unit of measurement. To have any idea of the labour and science devoted to this purpose, it is necessary to refer to the work itself, in which will be found the reasons for preferring a portion of the measurement of the surface of the globe, involving only the consideration of space, to the length of a pendulum, vibrating seconds having reference both to time and space. In addition to the determination of this standard of linear measurement, which was denominated the " metre," and defined to be the ten-millionth part of the quarter of a great circle passing through the poles*, the committee, consisting of all the most
*The French Commissioners, however, having in their calculations employed as their value of the earth's compression, now known to be incorrect, the metre, strictly speaking, can no longer be so defined.