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measurements, for which we are not yet able to account: it is, therefore, impossible to say from analogy what number of English miles, yards, feet, &c. exactly correspond to a degree of latitude at any given spot.
As the meridians all terminate in the poles, it is evident that whatever distance may be between any two at the equator, that distance must continually diminish to the poles, where it entirely disappears. If the earth were a perfect sphere, the length of a degree of Jongitude on any given parallel of latitude would be found by stating this proportion; as radius to the sine-complement of the latitude of the given place, so are the number of English miles in a degree of longitude on the equator, to the number in a degree of longitude at the given latitude : as, for example, if it be required to know how many English miles correspond to a degree of longitude at London, situated in north latitude 51', 30', 49", by adding together the sine-complement of the latitude, and the logarithm of 69,2, the number of English miles in a degree of longitude on the equator, and subtracting radius from the sum, we have the logarithm of 43,06 miles, for the space on the surface of the earth at London, or in its parallel, corresponding to a degree of longitude : and on this principle has been calculated the following table, containing the length in English miles of a degree of longitude at every degree of latitude, from the equator to the poles. Viz.
0 69,2000 23 63,6936 46 49,0705 69 24,7992
From this table it appears, that a degree of longitude on
In the account laid before the Royal Society of London, in 1787, by the late Major General Roy, of the mode proposed to be followed in the trigonometrical operations for determining the relative situations of the Royal Observatories of Paris and Greenwich, are contained some very important observations on the magnitude and figure of the earth, together with tables of the degrees of latitude and longitude on its surface, calculated agreeably to various hypotheses, in particular to those of the celebrated French mathematician Bouguer. From these tables the following is extracted, exhibiting the lengths of degrees of latitude and longitude in English fathoms (of 6 feet each) calculated for every 5 degrees, from the equator to latitude 70°; from 41° to 60', both included, for every single degree ; and from 60° to the pole for every 5 degrees.
This table is founded on the hypothesis, that the earth, instead of being an ellipsoid of any proportionate axes, is a spheroid of such a description, that the lengths of the degrees of the meridian increase as they approach ihe pole, above that of a degree at the equator, in the proportion of the biquadratic, or fourth power, or squared squares of the sines of the latitudes. By this hypothesis the polar axis of the earth will be to the equatorial as 178,4 to 179,4 ; and, consequently, their difference will be 38,1 geographical miles, or 43,9 English miles ; allowing 69,2 to be equal to a degree at the equator.
This difference between the axes is greater than that before mentioned, namely, 34 English niles; but, at the same time, the degrees of latitude, calculated upon this hypothesis, come much nearer to those actually measured on the earth, than such as result from calculations founded on any other supposed figure of the globe.
TAB L E
of the Lengths of Degrees of Latitude and Longitude in English
Fathoms of 6 Feet each, of which 880 are equal to 1 Statute Mile, calculated on the Hypothesis that the Increase of the Degree of the Meridian, above that at the Equator, follows the Ratio of the 4th Power, or squared Square, of the Sine of the Latitude.
50 50 50 50 50 50
5 10 15 20 25 30
51 51 51 51 51 51 51 51 51 51 51
60864,37 25 - 60866,14
40 60667,44 30
38490,90 38422.00 38353,03 38283,97 38214,82 38161.69 38145,57 38076,24 38006,83 37937,34 37867,77 37798,12 37728,40
53 54 55 56 57 58
36885,35 36030,83 35165,08 34288,36 33400,91 32503,54
Equal to Deg. of Longitude on Equator.
3159 1,90 30676,86
25947,37 21012,06 15908 82 10677,85 5360 40
60867 92 35
60900,30 60922,35 60944,70 60967.33 60990,16 61013,16
61174,10 61281,46 61374,25 61445,89 61491,13 61506,60
80 85 90