186 KEPOET ON 



But as P is liable to undergo a slow change, we introduce a term depending upon 



the time, and the equation becomes 



c PI, AP t ,, n , 



O = -i? 1 +.AC 1 + ^tan0+ T X_:+__X- i? (17) 



where APis the change of the value of P in one day, and t is the elapsed time in 

 days, counted from November 1st, 1865. 

 We have further 



e = Ci + AA 

 and also 



« = £ tm • + -?** 



Hence 



= - C x - A& + {tan + -| X ^ 



But as. § is liable to undergo a slow change* we introduce a term depending upon 

 the time, in the same manner as above, and the equation becomes 



O^-C.-A^ + ^tane+lx^ + ^X^ (18) 



Each observed value of B x and G x gives two equations of condition ; one of the 

 same form as (17), the other of the same form as (18); and from all the equations of 



condition thus obtained for any compass, the values of A u -, — , — — , J ■, —-, and — -, 



A A AAA A 



for that compass, have been computed by the method of least squares. 



The value of J. t thus found we will designate as the "true A" in order to dis- 

 tinguish it from the "apparent A" obtained directly from the corrected observed 

 values of the deviations. The value of the true A x depends only upon the value 

 of the constants a, b, d, and e, in equations (1) and (2); but the apparent A y is 

 made up of the true A x , together with any errors that may exist in the placing of 

 the lubber line of the compass, or in the determination of the true magnetic bearing 

 of the distant object used as an azimuth mark in swinging the ship. 



The equations of condition, formed in the manner just explained; the normal 

 equations derived from them by the method of least squares; and the resulting 



values of the constants, A u _, — , , Zj — , and — — , for each compass are as fol- 



A A A A A A 



lows: the values of B x and G x being expressed in parts of radius. 



