STELLAR PHOTOGRAPHY. 



189 



equal to its diameter, and T ^ -. ^Ye therefore shall have / = — ^j— , and as long 

 as the instrument remains unchanged I is proportional to v. If the telescope is at 

 rest and the motion of the star is due to the rotation of the earth, v = " , , cos S, 

 and I = 86400 «- 1 — ' ^'^"oting the declination of the star by 8. AVhen stars of 

 different declinations are photographed with the same instrument, S is the only 

 variable in the right-hand member of this equation ; hence we may write / = C cos 8, 

 and I is proportional to the cosine of the declination of the star. "We then have 

 VI = —2.5 log/= — 2.5 log C — 2.0 log cos 8. When we wish to compare the rela- 

 tive brightness of different stars from the intensities of the trails they leave, this 

 correction must first be applied. The trails must first be reduced to a scale of stellar 

 magnitudes, as will be described later (page 211), and then the correction 2.5 log cos 8 

 added to each. This correction is facilitated by the aid of Table I., which gives for 

 every degree of declination the correction in hundredths of a magnitude. 



TABLE I. 



It is generally sufficiently precise to carry the computations to tenths of a 

 magnitude. In this case. Table II. is more convenient, especially for polar stars 

 where the correction changes rapidly. The limits of declination within which the 

 corrections of each tenth of a magnitude should be applied are given in this table. 

 The correction for any declination given in the table is found by adding the whole 

 number of magnitudes taken from the top of the column to the tenth of a magnitude 

 at the beginning of the line. The correction for intermediate declinations is the 

 same as that of the next smaller declination given in the table. Thus, the correction 



