422 



NOTES. 



person at A to be in s. So that refraction, which always acts in a verti- 

 cal direction, raises objects above their true place. For that reason, a 

 body at S', below the horizon H AO, would be raised, and would be seen 

 in s'. The sun is frequently visible by refraction after he is set, or before 

 he is risen. There is no refraction in the zenith at Z. It increases all 

 the way to the horizon, where it is greatest, the variation being propor- 

 tional to the tangent of the angles ZAS, ZAS', the distances of the 

 bodies S S' from the zenith. The more obliquely the rays fall the greater 

 the refraction. 



NOTE 186, p. 149. Bradley' s method of ascertaining the amount of re- 

 fraction. Let Z, fig. 50, be the zenith or point immediately above an 

 Fiff. 50. 



observer at A ; let H O be his horizon, and P the pole of the equinoctial 

 A a. Hence P A a is a right angle. A star as near to the pole as * 

 would appear to revolve about it, in consequence of the rotation of the 

 earth. At noon, for example, it would be at s above the pole, and at 

 midnight it would be in s' below it. The sum of the true zenith 

 distances Z A s, Z A s', is equal to twice the angle ZAP. Again, S and 

 S' being the sun at his greatest distances from the equinoctial A Q, when 

 in the solstices, the sum of his true zenith distances, Z A S, Z A S', is 

 equal to twice the angle Z A Q. Consequently, the four true zenith 

 distances, when added together, are equal to twice the right angle Q, A P; 

 that is, they are equal to 180. But the observed or apparent zenith 

 distances are less than the true, on account of refraction ; therefore the 

 sum of the four apparent zenith distances is less than 180 by the whole 

 amount of the four refractions. 



NOTE 187, p. 150. Terrestrial refraction. Let C, fig. 51, be the 

 center of the earth, A an observer at its surface, A H his horizon, and 

 B some distant point, as the top of a hill. Let the arc B A be the path 

 of a ray coining from B to A ; E B, E A, tangents to its extremities; 

 and A G, B F, perpendicular to C B. However high the hill B may be, 

 it is nothing when compared with C A, the radius of the earth ; conse- 

 quently, A B differs so little from A D that the angles A E B and 

 ACB are supplementary to one another; that is, the two taken together 

 are equal to 180. A C B is called the horizontal angle. Now BAH 

 is the real height of B, and E A H its apparent height'; hence refraction 

 raises the object B, by the angle E A B, above its real place. Again, 

 the real depression of A, when viewed from B. is F B A, whereas 

 its apparent depression is F B E, so E B A is due to refraction. The 

 angle F B A is equal to the sum of the angles BAH and ACB; that 

 is, the true elevation is equal to the true depression nnd the hori/ontM 



