170 ON THE SQUARE BAB MICROMETER. 



and zenith distance at which the comparisons of the comet and star are to be 

 made immediately subsequent, and set the position circle so that a star will 

 skirt along one side of the square, parallel to it. With several trials the posi- 

 tion of parallelism can be approximated to quite closely. Then turn the posi- 

 tion circle 45° and proceed with the comet comparisons. This, while not a refined 

 method of observation, will answer well enough when the comet and its com- 

 parison star are nearly on a parallel ; as the effect of an error in setting is 

 then small. 



Case II. For greater accuracy than the preceding method affords, when the 

 difference of declination of the objects is considerable, or in the case there is no 

 position circle, we can determine the error of setting as follows. Point the tele- 

 scope as before, as nearly as possible in the direction in which the comet com- 

 parisons are to be made. Set the square by trial approximately so that a star 

 will ti'averse the diagonal, or parallel to it. Observe the transit of a star as 

 described in article 12, and deduce p by equation (32). Then proceed with 

 the comet observations, and in their reduction apply the correction computed by 

 (25) or (26), putting p for j^- 



Case III. A better way of proceeding is to arrange the observations so that 

 p' can be determined simultaneously with a — a, and h' — S. This method can 

 be adopted, also, when the telescope is not mounted equatorially. If S'— 8 is 

 not much greater than the half diagonal, the comparisons of the comet and. 

 star may be so arranged that the latter passes near the centre and its transits 

 observed as described in article 12. This will determine y by (32), whence 

 we get the correction for position zero by (25). If 8'— 8 is too great to allow 

 this mode of observation, any star which traverses the central portion of the 

 square during the comparisons, may be observed in conjunction with the comet 

 and its comparison star, and p' thus determined. 



The refraction corrections to be used in reducing observations made with the 

 square adjusted by the methods of this article, are (23) for the difference of right 

 ascensions, and (20), or the second of (21), for the difference of declinations. 



11. Gorreciion for position zero. — Let p expressed in arc be the small angle 

 which the diagonal makes with the hour circle passing through the centre of 

 the square, or the position angle of the north angle of the square. It is evi- 

 dent that the time when the star is on the diagonal is 



^2 + ^1 P sin 1" 

 2 15 cos 8 



H-"), 



