of the Butherfurd Photographs. 241 



III. Precession and Nutation. 



These merely change the position of the axes to which the 

 group is referred ; it follows therefore that their differential ef- 

 fect upon X and Fis simply to rotate the coordinate axes through 

 a small angle. When we determine the constants of a plate by 

 comparing the measures of some of the stars with their true posi- 

 tions, it is evident that we need appty no corrections for preces- 

 sion and nutation to the measures of the comparison stars. Thus 

 if we employ the places of the latter as referred to the equinox of 

 1875.0. then the value for the orientation which we shall get will 

 include the necessary correction for precession and nutation. 

 On the other hand, if we correct the places of the comparison 

 stars for precession and nutation, then it would not only be 

 necessary to apply the resulting orientation correction to the 

 other stars, but we should also have to apply to them additional 

 corrections for precession and nutation. 



IV. Aberration. 



It was shown by Bessel* that aberration changes the position 

 angles around a point equally, and changes the distances by a 

 constant factor, no matter in what direction the distance is meas- 

 ured. Consequent^, as in the case of precession and nutation, 

 we need apply no correction for aberration to the measures of the 

 comparison stars, since the resulting orientation and scale-value 

 corrections will be appropriate^ modified to include its whole 

 effect. 



Thus we see that the coordinates of our five comparison stars 

 need be corrected onty for transformation and refraction. We 

 must bear in mind, however, that the orientation and the scale- 

 value which we shall then obtain are not the true values of these 

 constants : the former must be corrected for precession, nutation 

 and aberration, and the latter simply for aberration. 



We are now ready to find the constants of the plates. Let 



p=.-the correction to the scale-value, so that the true scale- 

 value is 52". 87 (1 -fp). 



r=the orientation correction, or the small angle through which 

 the axes are to be rotated in the direction of decreasing posi- 

 tion angles. 



* " Astronomische Untersuchungen," Vol. I, page 207. 



