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explorer in a wild unknown tract of country. He would not probably find it convenient always to obtain his latitude at noon; but he can generally do so, and more correctly, at night*, by the meridian altitude of one or more of the stars of the first or second magnitude, whose right ascension and declination are given in the Nautical Almanac. His local time can, immediately before or after, be ascertained by a single altitude of any other star out of the meridian (the nearer to the prime vertical the better); and if he carries a pocket chronometer upon which any dependance can be placed, he has thus the means, by comparison with his local time, of obtaining his approximate longitude, and of laying down his position upon paper.
In travelling, the rate of the chronometer will probably be found to vary; but as frequent halts of two or three days are likely to occur, these opportunities should never be lost of ascertaining the change of rate. The longitude should also be obtained occasionally by lunar observations on both sides of the meridian; or by some of the other methods given in the last chapter.
The results deduced from such observations must not be relied upon within ten or twelve miles, but a careful observer should rarely exceed these limits; and his latitude ought always to be within half a mile, or under the most unfavourable circumstances, one mile, of the truth.
With these all-important data, enabling him to fix with approximate accuracy point after point† in his onward course, the explorer can have no difficulty in interpolating by angles, taken with a sextant or with an azimuth compass, all strongly-marked prominent features, or in laying down his route upon paper correctly enough for the purposes of identifying particular spots, and giving a faithful general representation of the features of the ground he has travelled over. The value of this sketch will be much enhanced by its having recorded on it, as nearly as they can be ascertained by the mountain barometer or aneroid‡, or by the temperature at * See chapter xi. on Practical Astronomy.
The distances between positions, the latitudes and longitudes of which have been determined, can be easily calculated in the manner described in the next chapter; by which means they can be laid down with more accuracy, if the extent of ground travelled over is not very great.
See chapter xi.
which water is found to boil*, the altitudes of the most important positions, as the summits of hills, the levels of plains, and sources of springs and rivers.
Daily meteorological observations, even of the most simple character; such as merely recording the readings of the thermometer and barometer at stated times, will also prove of essential service as illustrative of the climate; and these will be of additional value if accompanied by a record of the quantity of rain fallen on different days, should any portion of the party be stationary for sufficient length of time at any one spot, to make these observations. If not provided with a rain garge of a better description, a tin pipe with a large funnel, the area of the top of which bears a certain proportion to that of the tube, will answer perfectly to measure the quantity of water fallen. A light graduated wooden rod is fixed in a cork float, and indicates, above the level of the top of the funnel, the number of inches ;—the graduations of the rod of course being proportioned to the ratio between the areas of the surface of the funnel and that of the tube. Thus, if the proportion is 10 to 1, the measuring rod will be lifted 10 inches for every inch of rain.
* See page 111.
GEODESICAL OPERATIONS CONNECTED WITH A TRIGONOMETRICAL SURVEY.
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
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 was supposed to have been partly the cause of this discrepancy, as the attraction of high land, by affecting the plummet of the Zenith Sector, might have vitiated the observations for the difference of latitude between 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 429, showing an error of 11′′-7, due to the deflection of the plummet.
greater degree of curvature at the former, and the flattening at the latter, is directly inferred.
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 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
* 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, 20 feet long each, laid perfectly level, without any triangulation. Page 10, "Discours Préliminaire, Base du Système 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.
modes of proceeding which have been adopted in this country, and elsewhere, 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 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 a 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 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, described in detail in the "Base du Système Métrique Décimal," 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