168 ON THE SQUARE BAR MICROMETER. 



8. Correction for refraction tvhen the square is adjusted to the apparent diurnal mo- 

 fion. — In this case the above formula} for the right ascension, (18), or the first 

 of (21), will require modification, on account of the efiect of the difference in 

 position angle between the true and the apparent motion. Call Ap the angle 

 which the apparent path of a star, traversing the square, makes with its true 

 path. This angle will be the ratio which the change in refraction in declination 

 bears to the length of the chord, or 



_ 1 A;g — A^8 



^P ~~ 15 sin 1" ■ cos8[(<2— <i) — (iijo — Aja)]' 



By the preceding article we find 



Ao S — Ai S = 15 K (4 — t^) j-^ ; 

 consequently we have, neglecting terms of the second order, 



Ap = ^Y' [3 ^^^^ ^ sin 2 g' + tan ^ sin 5' tan 8]. (22) 



Substituting this value for p in (25) we obtain 



15^ [2{d'- d) - (± f T f)] (1 tan^^ sin2^ + tan C smg tan 8), (22*) 



as the correction to the difference of right ascension obtained by assuming the 

 square to have been adjusted to the true diurnal motion. Adding (18) and (22*) 



^{a'-a)^ j5^^ id' - d) tan^ ^ sin 2 q, (23) 



which is the correction for refraction in right ascension when the square is 

 oriented to the apparent diurnal motion, by the methods of article 10. 



The declination correction is unaffected by the mode of adjustment. 



It should be borne in mind that (23) has been deduced by assuming that 

 the values of k, C, and q are identical in (18) and (22); in other words, that 

 the adjustment has been made with the telescope pointed in the same direction 

 as for the comparisons of the comet and star. Ordinarily this assumption is 

 nearly enough true; but near the horizon, for considerable hour angles, it may 

 sometimes be requisite for accuracy to correct for refraction in right ascension 

 by applying (18) and (22) separately, with the particular values of i and q 

 pertaining to the comet comparisons and to the adjustment observations, respec- 

 tively. With care, however, the necessity for this may almost always be avoided. 



