PHOTOGRAPHIC RESEARCHES NEAR THE POLE OF THE HEAVENS. 55 



truth by the same constant, and a system of polar distances which all differ 

 from the truth by a constant factor. This result is of course subject to the 

 condition that the telescope did not move during the night. In this respect 

 it suffers from precisely the same liability to systematic error as do the 

 conclusions obtained from double transits with the meridian circle. But it 



meridian 



substitutes observations of 



about 20 different stars for the extremely small number that are actually 

 bright enough to be observed frequently above and below pole on the same 

 day with existing meridian instruments. And instead of giving but two 

 points in the diurnal circle of each star, the fixed photographic telescope 

 gives any desired number. Lastly, it substitutes the precision of micro- 

 metric measures for observations of times of transit and circle readings. 

 That the observed stars are all within a degree of the pole does not in the 

 least impair the precision of the method as far as concerns the determin- 

 ation of the constants of stellar astronomy. 



We come now to the discussion of our observations on the assumption 

 that the telescope moved, and that the position of the pole on the plate 

 described a small curve. Let us imagine that this motion of the pole was 

 compounded of two distinct motions, viz.: 



1. Motion in a circle at the uniform rate of 15° per hour in the di- 

 rection of diurnal motion. 



2. Motion of the centre of this circle on some assumed curve, the 

 constants of which are to be determined. 



Then it may be shown without difficulty that just as in the case al- 

 ready discussed, that part of the total motion mentioned under 1. will 

 remain indeterminate, while the part arising under 2. can be subjected to 

 approximate computation. But as we have already stated, every precaution 

 having been taken to make the telescope stand still, and the observations 

 admitting of a simple and probable explanation without assuming the 

 motion 1 , it would perhaps be unreasonable to suppose that it has a phy- 

 sical existence. We shall therefore for the present assume that there is no 

 motion 1 , so that the results we shall obtain are subject to such systematic 

 error as may arise from this cause. In any case we shall thus carry the 

 approximation of our knowledge as to the true position of the pole among 

 the stars a step further than can be done by assuming that the telescope 

 remained unmoved, or by the method of observing above and below pole 

 with a meridian instrument. For the meridian instrument, or the fixed tele- 

 scope, must be in exactly the same position all the time, whereas in the 

 present method the instrument may have any assumed motion except that 

 described under 1. And we have already pointed out that an azimuthal 



*K3.-MaT. cTp. 55. 15 



