NOTES. 



493 



NOTE 186, p. 173. Bradlcy's method qf ascertaining the amount nf refraction. 

 Let Z, fig. 50, be the zenith or point immediately above an observer at A; let 



Fig. 50. 

 Z 



H O be his horizon, and P the pole of the equinoctial A Q. Hence P A Q is a 

 right angle. A star as near to the pole as s would appear to revolve about it, 

 in consequence of the rotation of the earth. At noon, for example, it would 

 be at * 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. 



Fig. 51. 



NOTE 187, p. 193. Twrestrial 

 refraction. Let C, fig. 51, be the 

 centre 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 coming 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; 

 consequently, A B differs so little 

 from A D that the angles A E B 

 and A C B are supplementary to 

 one another; that is, the two taken 

 together are equal to 180. ACS 

 is called the horizontal angle. Now 

 B A H is the real height of B, and 

 E A H its apparent height ; hence 

 refraction raises the object B, by 



