STELLAR PHOTOGRAPHY. 193 



the time of exposure, or in the angular aperture of the telescope, is not to be 

 desired. As shown above, with a given linear aperture the light of the sky or 

 other luminous surface will diminish rapidly as the focus is increased. The light 

 of a star will be diminished only so far as the diameter of its image is increased 

 hy the increase in focus. A great saving in time and expense might, however, be 

 effected by more sensitive plates, since smaller lenses and shorter exposures could 

 be employed. 



In order that the stars shall leave trails, it is not necessary that the telescope 

 shall be at rest. If its motion deviates in any way from that of the star, a trail will 

 evidently be produced having a length proportional to the rate of deviation and to 

 the length of exposure. If the speed of the driving-clock is greater or less than it 

 should be, trails will evidently be formed having a length proportional to the hourly 

 rate of the clock as compared with a sidereal clock, to the time of exposure, and to 

 the cosine of the declination of the star. The light required to produce a trail of 

 given intensity will bear the same relation to that required to produce the same trail 

 when the telescope is at rest, as the hourly rate bears to an hour. Accordingly, if 

 the clock gains or loses one minute an hour, trails will be formed by stars having 

 one sixtieth part of the brightness of those which form similar trails when the 

 telescope is at rest. This corresponds to a difference of about four magnitudes 

 and a half.' A rate of a second an hour should give the ratio of one to thirty-six 

 hundred, or nearly nine magnitudes. The limit is soon reached, however, in conse- 

 quence of the size of the images of the stars, and the impossibility of giving long 

 enough exposures to enable them to traverse distances great enough to form an 

 appreciable trail. The method of electrical control above described enables the 

 rate of the driving-clock to be varied at will. The deviation from this cause can 

 be rendered entirely insensible if desired. 



Trails will also be formed if the axis of the instrument is not parallel to that of 

 the earth. If we wish to make the images of the stars perfectly circular, instead of 

 elongated into trails, this is a much more troublesome source of error. The simplest 

 case to be considered is that in which we should give an exposure of twenty-four 

 hours to the region in the vicinity of the north pole. The plate may here be 

 regarded as revolving around a line passing through the optical centre of the object- 

 glass and parallel to the polar axis of the instrument. The intersection of this line 

 with the plate will form a centre around which the plate will appear to revolve. If 

 a photograph should be taken of any fixed point in the sky, it would describe a circle 

 around this point. If a star were situated exactly at the north pole, it would form 



