168 



OX THE SQUARE BAR MICROMETER 



8. Correction for refraction ivhen the sqitm 



2 is adjusted to the apparent diurnal mo- 

 the above formulae for the right ascension, (18), or the first 

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



tion. 



In this 



posit 



betw 



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 



Ap 



1 



A 2 S 



A 1 8 



15 sin 1" ' cosS[(£ 



h) 



(A 2 a 



*!«)]' 



By the preceding article we find 



A,S 



2 



AjS 



15 k (4 



dv 



~dt 



consequently we have, neglecting terms of the second order, 



Ap 



sfayi H tan 2 £ sin 2 q -\- tan £ sin q tan §]. 



(22) 



Substituting this value for p in (25) we obtain 



15 



*b0(* 



± 



sf 



(I 



2 =F 2/. 



£ sin 2 q + tan £ sin q tan 8) 



(22 



# 



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

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



the 



# 



we have 



A (a 7 



K 



a 



15 cos 8 







(d' 



d) tan 2 £ sin 2 q, 



(23) 



which is the correction for refraction in 



g 



ascension when the square is 



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

 The declination correction is unaffected by the mode of adjustment. 



ien deduced by assumin 



It should be borne in mind that (23) has b 



r> 



that 



k, £, and 



the values of 



the adjustment has be 



q are identical in (18) and (22); in other 



ds, that 



made 



th the 



ope pointed 



the same direction 



is 



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

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



requisite for accuracy to correct for refraction in right ascension 



sometimes be 



b y applying (18) and (22) separately, with the particular values of 



nd q 



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



ely 



With 



however, the necessity for this ma}' almost always be avoided 



