ox REFIIACTION, ^CC. ;20 1 



IX. 



Method ofjinding the Quantity of Refraction from the Dis^ 

 tauce and Altittule of tico hioicn Stars ; and of solving by 

 Construction a Problem in Spherical Trigonometry. In a 

 Letter fr^^tn a Correspondent. 



To Mr. NICHOLSON. 

 SIR, 



JL HE following method of finding the quantity of the re- New method 



fraction bv observinjj the distance and altitudes of two known °^"""'"S the 



J r> ^ quantity of re« 



stars is, as far as I know, new: and as it seems to possess fraction. 



some adA'antages over the common methods, I will venture 



to request its insertion in the Philosophical Journal. 



Let Z, PI. VI, fig. 8, be the zenith, S and X the appa- 

 rent, ^ and j; the true places of the stars. 



Let d be the difference between their true and appa- 

 rent distance ; then S s the refraction of the star S ~ 

 d X tang. Z S X cos. M S X cos. M X 

 S. S X X rad. * ~~' 



Demonstration. 



cos. Z X X X X + Demonstration. 



It is evident that rf(=zXm+Sn) = 



rad. 



cos. ZSXS.9 , Tlxovxi. 



[xm and sn being perpendicular to S X); but 



S^:Xx::tang. ZS:tang.ZX.-.X.r=: ^^^^^"S-^^ ; 



tang. Z S 



hence by substitution we get c? = S ■$ X — ^-^ —^ 



■' tang. Z b 



Z X -J- cos. Z S X tang. Z S , ^^ cotang. Z X 



; but cos. X ~ 



X rad. 



X tang. MX, ^ cot. Z S X tang. M S . 



— i — and cos. S r= t — ; hence 



rad. rad. 



, . . , ^ tang. M X + tang. M S , ^ 



by substitution, d — ^ s X — 1 rrs. J hut 



*' tang. Z S 



sura of tang. : S. of sum : : rad.* : D of cos. i. e. tang. M X 



+ tang. M S : S. S X : : R*: cos. M X X cos. M S ; hence 



