194 STELLAR PHOTOGRAPHY. 



such a fixed point, and would accordingly describe a circle with a radius equal to 

 the distance between the pole of the earth and that of the instrument. Since the 

 photographic surface sensibly coincides with a sphere whose radius is the focal dis- 

 tance of the lens, the deviation in seconds, s, of the axis may readily be determined 

 from the radius r of this photographic cu-cle. The relation between them will be 

 expressed by the formula /• = .i^^r^, or s = "^^ — . No star is visible exactly at 

 the pole, nor would it remain there, owing to precession. Adjacent stars will, how- 

 ever, describe nearly the same j^ath, as will be shown below. 



Since an exposure of twenty-four hours is impracticable, a portion only of the 

 circle is obtained, the length of which is generally given with sufficient precision by 



Til T 



the formula / = 777771, in which / is the length of the trail and m the exposure in 

 minutes. Combining this with the previous formula, we deduce s = " , - — . 



The curvature of the trail is here neglected, but is readily allowed for if the expos- 

 ure much exceeds an hour. If the exposure is much less than half an hour, it 

 becomes difficult to detect the curvature, and to know on which side of the trail 

 the centre of the circle lies ; in other words, to decide whether the polar axis is 

 too high or too low, to the east or the west. This difficulty may be remedied by 

 stopping the clock and allowing each star to make a second trail for a minute or so 

 by the diurnal motion. When the plate is developed, the trails formed when the 

 clock was on will be parallel and of equal length; the others will be at right angles 

 to a line drawn through the pole, and will have a length proportional to the polar 

 distance. The second trail will also be fainter than the first, if the instrument is 

 nearly in adjustment, except for stars very near the pole. The direction in which 

 the first trail is described may be known from the fact that its following end is 

 alwaj'S attached to the preceding end of the second trail. Moreover, the direction 

 in the northern hemisphere as seen from the object-glass is always opposite to that 

 of the hands of a watch. Accordingh'^, if the observer holds the plate so that the 

 first trail is horizontal with the second trail attached to its right-hand end, and the 

 side of the plate to which the film is attached towards him, the centre of the trail 

 will always be above. The simplest rule, however, is to make a second exposure 

 after moving the axis, and to notice the efiect on the trail. From this establish an 

 empirical rule, and always hold the plates in the same position. "When the trails 

 are very short, it is sometimes better to detach them by covering the plate for a 

 minute or so to prevent their interferins. Care must then be taken in makinsr the 

 exposures that the telescope is not disturbed. 



