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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.

1

TABLE.

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0 69,2000 23 63,6936 46 49,0705 69 24,7992
i 69.1896 24 63.2177 47 47,19 14 70 23,6678
269, 1578 25 62,7167 48 46,3038 71 22,5294
369,1052 26 62,1963 49 45,3994 72 21,3842
409,0312 27 61,6579 50 44,4811 73 20,2320
5 68.9363 | 28 61,1001 5143,5489 74 19,0743
6 08,8208 29 60,5237 52 42,503775 17,9103
7 | 68,634.5 30 59,9293 53 | 41,6453 76 16,7409
8 68,5267 31 59,3162 54 40,6751 177 15,5665
9 68,3481 | 32 58,6851 55 39,0917 78 14,3874
10 68,1489 33 58,0360 56 | 38,6959 79 13,2041
11 | 67,9259 34 57,3696 | 57 37,6891 80 12,0166
12 67,6990 35 56,6852 58 36,6705 81 10,8250
13 67,4264 36 55,9842 59 35,6408 82
14 67 1448 | 37 55,2659 60 34.6000 83 8,4334
15 66,9424 38 54,5303 61 33,548984 7,2335
16 66,5192 39 53,7788 62 32,4873 85 6,0315
17 66,1760 40 53,0100 63 31,4161 86 4,8274
18 65,8134 41 52,2259 64 30,3352 87 3,6219
19 65,4300 42 51,4253 65 29,2453 88 2,4151
20 65,0265 43 50,6094 66 28,1464 89 1,2075
21 64,6037 44 49,7783 | 67 | 27,0385 90 0,0000
22 | 64,1609 45 | 49,9313 68 25,9230

9,6306

From this table it appears, that a degree of longitude on
the equator may be considered as equal to the first degree of
latitude on each side, or equal to 69,2 English statute miles,
or 69: instead of 69', or even 69, both of which quantities
give results greater than the truth. It will also be observed,
that at the latitude of 60°, the degree of longitude is reduced
to 34,6 English miles, or to one half of a degree on the
equator ; and that at the poles, or in latitude 90°, longitude
disappears, because there the meridians uniting in one point,
the intervals between them entirely vanish.

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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.

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TABLE

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.

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50 50 50 50 50 50

5 10 15 20 25 30

60838,19
60839 92
60841,64
60843,37
60845,11
60846,84

39311,29
34243,39
39175,37
39107,32
39039,18
38970,94

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Greenwich

51 51 51 51 51 51 51 51 51 51 51

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5

60859,08 10

60860,84 15

60362,61 20

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

51

52

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.

58

31856,42

59 60

3159 1,90 30676,86

65 70

75

25947,37 21012,06 15908 82 10677,85 5360 40

COO

60867 92 35

60869,69 40

60871,47 45

60873,25 30

60875,04 55

60876,82 60878,61

60900,30 60922,35 60944,70 60967.33 60990,16 61013,16

III

42 47,4

61029,62

11

61036,27 61059,43

61174,10 61281,46 61374,25 61445,89 61491,13 61506,60

80 85 90

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