196 STELLAR PHOTOGRAPHY. 



upon a star near the meridian, if the axis points west of the true pole, the star 

 ■will appear to be moving to the north, or will move below the horizontal cross- 

 wire. It must then be brought back by one half the amount of the deviation, 

 by moving the axis. The opposite effect will be produced if the axis is directed to 

 the east. 



The following discussion of the path described by stars at various declina- 

 tions, Avhen the axis is not properly adjusted, has been prepared by Professor 

 Searle. 



The effects resulting from an imperfect adjustment of the polar axis of any 

 equatorially mounted telescope are partly indicated in treatises upon practical 

 astronomy. Equations relating to the subject here to be considered may be found, 

 for example, in Chauvenet's Spherical and Practical Astronomy, Vol. II., pages 375 

 and 378 ; but, for the present purpose, they may be somewhat simplified. 



It will be convenient to give the names of instrumental poles and instrumental 

 hour circles to the points of the celestial sphere towards which the ends of the 

 polar axis of the telescope are directed, and the great circles passing through these 

 points. One of the instrumental poles will be situated in the same celestial hemi- 

 sphere with the star to be photographed. Let y denote the distance of this pole 

 from the nearer of the two celestial poles, and 8 the declination, regarded as posi- 

 tive, of the star. Let p denote the corresponding distance of the star from the 

 instrumental pole, always regarded as positive. Let t denote the angle between 

 the planes of two hour circles, one, which may be called the fixed circle, passing 

 through the instrumental pole, and the other through the star. Let v denote the 

 corresponding angle between the fixed circle and the instrumental hour circle of 

 the star, and consider t and v as equal to when the celestial pole lies between 

 the instrumental pole and the star, so that the star is crossing the fixed circle and 

 p =: i TT — 8 + 7- Suppose t and r, at this time, to be increasing with the diurnal 

 revolution of the star. Then 



cos/? = sin S cos y — cos 8 sin y cos t. (1.) 



sin V sin p = cos 8 sin t. (2.) 



cos V sin JO =^ sin y sin 8 + cos y cos 8 cos t. (3.) 



It will be assumed, in order to simplify the inquiry, that the photographic plate 

 is placed so that its plane is perpendicular to that of the fixed circle when t — 0. 

 If y is small, this will be nearly true in practice ; in other cases, this will be the 

 most convenient position for the plate if it is to depict the whole of the apparent 



