446 Mr. Carrington on the Evidence of the 



Let/3 = ySE; p' = SE9 = m. (R) . sin (p + p') 

 = 1 6' X sin p, nearly 



sin Srq = ^ . sin 8qr =- — ^ . sin {p + p') 



sin Srp=— . sin Srq =^ — j • sin ip + p') 



sin Spr= (1 + h) . sin Srp = sin 8qr 

 .'. p8q=prq; and ASp = p + Sr^r — S?p. 



Let ASp — p be denoted by {p), 



(p)=sin-'j^^.sin(p-}-p')-sin-'^-^.sin(p + p')- • (1) 



If m be but little greater than unity, this expression may be 

 written with advantage in a different form. 



= b + {m-l).b. 



Since sin~' e — sin"' Z» = sin~' {a V'l—b^ — b -/!—«-), we find, 

 after some reductions, neglecting powers of (m — 1) above the 

 second, 



(p) = sin-». ({m-1) . L^+l.(,„_l)2. ^1. 



Accordingly, if sin t=.j — r • sin {p + p') 



+ / 



sin (p) = (m — 1) . tan t + ^ (m— 1)^ .tan^ t, very nearly. . (2) 



The atmosphere speculated on will bear a bold assumption, 

 and we will accordingly assume its height h = ^ . sun's radius, 

 and compute the values of (p) for the three following values of 

 TO... 1-005, 1-010, and 1-020; corresponding roughly to the 

 refractive index of common air, of which the density has been 

 increased respectively 17, 34, and 69 times. Either of the for- 

 mulae above given may be used for the purpose. The first is 

 the more readily worked, and has been used in forming the 

 following Table. 



