PHOTOGRAPHIC RESEARCHES NEAR THE POLE OF THE HEAVENS. 7 





results, if based on more complete measures of several plates, would enjoy a 

 freedom from systematic errors hitherto unprecedented in fundamental astro- 

 nomy. Most especially would this be the case if we could dispose of plates 

 taken with a suitably constructed fixed telescope, instead of an ordinary 

 equatorial. 





4. A Method of Determining the Constants of Aberration, Nutation and 



Precession. 



As we have now deduced the formulas for extracting all the information 

 possible from a single polar trail plate, let us consider the results derivable 

 from a comparison of plates taken on different nights. In doing so, a slight 

 change will be made in our notation, this being possible because we shall 

 now consider each star by itself. "We shall therefore drop the subscript s 

 from u and v because there can be no ambiguity as to the meaning of u 



and v when we are considering for the moment one star only. On the other 

 hand, as we shall compare the values of w and v obtained on different nights 

 from different plates, we shall denote by the subscript t quantities belonging 

 to the plate taken on the night designated by the number t. 



When we come to compare the values of u and v obtained on different 

 nights for any given star by the methods already set forth, we must expect 

 them to differ from various causes. Of these we shall consider the following; 



1. Precession, 



2. Nutation, 



3. Aberration, 



4. Any variation in the scale value constant d w ? 



5. Any variation in the orientation constant d A. 



From a study of the variations of u and v, therefore, we ought to be 

 able to arrive at a knowledge of the constants which occur in the mathema- 

 tical laws governing the effects on star-places of the phenomena numbered 

 1 to 3 above. 



The first step in attacking the problem, is to adopt some fundamental 



designated (a) and 



equinox and equator. To these should be referred the 

 ascension and polar distance of the star, which we have 

 (tc). Values of (a) and (tc) must be had for each star, and they can be ob- 

 tained readily enough by a preliminary reduction of one plate. The next step 

 is to calculate the effects of precession, nutation, and aberration upon (a) 

 and (u), between the moment of observation t, and the fundamental epoch, 

 which we will call t Q . 



*H3,-MaT. dp. 77. 37 



