518 PHILOSOPHICAL TKANSACTIONS. [aNNO 1721. 



it will appear that the distances of all the stars are seen less than they really are, 

 in whatever position they are taken, and that not less than a second per degree 

 of the distance ; that is, a distance of 30*^, for example, is contracted at least 

 so many seconds, and one of 6o° no less than a minute, if the distances be taken 

 by an instrument truly divided. So that when Mr. Hevelius, to show the 

 exactness of his observations, brings 8 distances, as taken by his sextant, which 

 exactly complete the circle, both in longitude and right ascension ; the con- 

 sequence is really quite opposite to his design : for if those distances were the 

 true ones, they being all contracted by appearing through a refracting medium, 

 the sum of the 8 differences of both longitude and right ascension, ought to 

 fall short of a whole circle or 36o°, by at least 6' ; so that I am inclined to be- 

 lieve that the 60° of Mr. Hevelius's sextant wanted about a minute of its true 

 quantity. 



Such an allowance as this may perhaps be a proper expedient, to avoid ac- 

 counting for refraction in celestial observations, provided the objects be nearly 

 parallel to the horizon, or at a good height above it. For all distances of stars 

 are contracted by refraction, when they are parallel to the horizon, by the same 

 constant quantity, be they high or low, that is by about one second per degree ; 

 the chords of the arches of the real and visible distances being always in the 

 same ratio as is the sine of the angle of incidence to that of the refracted 

 angle. 



And this is the case where the refraction of the air affects the distances of 

 the stars the least, which distances are still more and more contracted, as they 

 are nearer to a perpendicular situation : so that a distance, for example, of 30° 

 loses but half a minute in a horizontal site ; but if the one star be 20" high, and 

 the other 50, it will be lessened by above 3 times as much, or by l' 41". If 

 the one be 30 and the other 6o^ high, the same distance will appear less than 

 30° by about one minute ; the difference still decreasing as the objects are more 

 elevated above the horizon. But in all cases to account for the effect of the 

 refraction on the distances of the stars requires, besides some trigonometrical 

 work, the help of the beforementioned table, which I here subjoin for the use 

 of the curious, such as 1 long since received it from its great author; it having 

 never yet, that I know of, been made public. 



