obſervation of the ſtar Canopus[1], made by himſelf. He remarked,
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° ′ Height of the North Pole at Rhodes 36 27 Diſtance from the Pole to the Equator 90 Declination of Canopus South 52 31 Subtract this ſum 178 58 From 180 Remainder 1 2 Add for refraction 24 Apparent altitude of Canopus at Rhodes 1 26 Height of North Pole at Alexandria 31 11 Diſtance from the Pole to the Equator 90 Declination of Canopus South 52 31 Subtract this ſum 173 42 From 180 Remainder 6 18 Add for refraction 8 Apparent altitude of Canopus at Alexandria 6 26 subtract for its apparent height at Rhodes 1 26 Remainder 5 which is the difference between its apparent height at the two places. Five degrees of latitude, at 69.2 5 Engliſh miles each, = 346 Engliſh miles, == 302.3 Olympic ſtadia; which ſhould he, according to this calculation, the diſtance between Alexandria and Rhodes, ſuppoſing them to lie under the ſame meridian. But Alexandria is 1° 51′ to the eaſt of Rhodes, a ſpace in the latitude of Alexandria equal to 110 Engliſh miles.
Square of 346 119716 Square of 110 12100 Sum 131816 Square root 363.6 5 E. miles. for the diſtance from Alexandria to Rhodes, = 3177 Olympic ſtadia. But this diſtance is too ſmall, owing to the proportionally greater refraction at the altitude of 1° 2′, than at 6° 18′, which amounts to 16′ in altitude, and to about 17′ in diſtance.
° ′ The altitude of Canopus at Rhodes 1 2 The altitude of Canopus at at Alexandria 6 18 Difference 5 16 Equal to 364.71 Engliſh miles. Square of 364.71 133013.37 Square of 110 12100 Sum 145113.37 Square root 380.97 E.miles. Equal to 3 32.8 Olympic ſtadia, for the diſtance from Alexandria to Rhodes.
Let us now ſee how the calculation of Poſidonius, reſpecting the circumference of the earth, would ſtand, had his obſervations of the reſpective altitudes of Canopus at Alexandria and Rhodes been correct, though without allowing for refraction. The apparent difference of altitude at the two places was, as I before obſerved, 5°. Say then 5°: 360::5000 ſtadia to 360,000 = 41207.4 Engliſh miles, juſt double to his later calculations, being 1000 ſtadia to a degree. By his other computations, derived from the gnomonic meaſurements of Eratolihenes, and which eliminate the diſtance only at 3750 ſtadia, it would ſtand thus—5:360::3750:270,000, or 750 ſtadia to a degree.Poſidonius, it is evident, made two miſtakes, betides that of ſuppoſing Rhodes and Alexandria to lie, under the ſame meridian; the firſt in ſuppoſing Canopus to have no altitude at Rhodes, whereas it has a real one of
