212 



REPORT OX 



la the same way, the first equation of condition for the After Binnacle Compass is 

 = — 220 + A x + 0. 195 B x + 0.981 C x + 0.383 D x + 0.924 E x . 



Equations of Condition at Ceara. 



Absolute Terms. 



Coefficients of the Unknown Quantitie 



















Z?~° 

























« .s 



j3 



3 



13 73 



1 1 

 pn 



13 <U 













^55 



A, 



*i 



c, 



A 



*l 



I70' 



— 220' 



— 820' 



— 1 So' 



— no' 



— 430' 



+ 1. 000 



+ 0.195 



+ 0.981 



+ 0.383 



+ 0.924 



2IO 



— 310 



— 820 



— 270 



IIO 



— 520 



-j- 1. 000 



+ 0.383 



+ 0.924 



+ 0.707 



+ 0.707 



260 



— 39° 



— 820 



— 280 



IIO 



— 600 



+ 1. 000 



+ 0-556 



+ 0.831 



+ 0.924 



+ 0.3S3 



— 35° 



— 470 



— 97° 



— 280 



— 180 



— 480 



-j- 1. 000 



+ 0.707 



4- 0.707 



+ 1. 000 



0.000 



— 34° 



— 420 



— 99° 



— 211 



— 130 



— 380 



+ 1. 000 



+ 0.S31 



+ 0.556 



+ 0.924 



— 0.383 



— 33° 



— 410 



— 1 140 



— 200 



IIO 



— 300 



+ 1. 000 



4- 0.924 



+ 0.383 



+ 0.707 



— 0.707 



— 310 



— 410 



— 1020 



— 130 



— 40 



— 420 



-j- 1. 000 



+ 0.9S1 



+ 0.195 



+ 0.383 



— 0.924 



— 230 



— 260 



— 850 



— IIO 



+ 40 



— 170 



-j- 1. 000 



-j- 1. 000 



o.oco 



0.000 



— 1. 000 



— 210 



— 240 



— 690 



IIO 



+ 130 



— 40 



-j- 1. 000 



+ 0.981 



— 0.195 



- 0.383 



— 0.924 



— 170 



— 170 



— 660 



— 40 



+ 140 



— 30 



-j- 1. 000 



+ 0.924 



— 0.383 



— 0.707 



— 0.707 



From these equations of condition five normal equations Avere obtained for each 

 compass by the method of least squares; but on attempting to solve them the 

 numerical coefficients of D x and E x came out so small that no confidence could be 

 placed in the resulting values of these quantities ; and moreover, the uncertainty of 

 them vitiated the values of A x , B x , and G x . It was therefore considered best to 

 reject the normal equations in B x and 2? l5 and to employ in their stead the equations 



= -S) + Di-f : .J(^-C 1 2 ) 

 Q.= -@ +V X + B X C X + A X D 1 



using for £5 and (£ the numerical values already found. The following are the 

 normal equations thus formed, and the resulting values of A x , B x , O x D x , and E x , for 

 each compass. For convenience of computation, the unit of the absolute terms of 

 the normal equations has been changed from minutes of arc to radius. 



Admiralty Standard Compass. 



o = — 0.7505 + 10.000 A i + 7.482 B t + 3.999 C x + 3.938 D x — 2.631 E x 

 o = — 0.5789 + 7.482 A x + 6.317 B x + 1.969 C x + 2.334 D x — 3.774 E x 

 ■ 03183 + 3-999 A x + 1.969 B x + 3.685 C x + 3.708 D x + 1.665 E x 



Hence 



- — 0.0169 + A + i (A 2 — Q) 

 = + 0.0009 + Ex + B x C x 



A x = — 0.0102 = — o° 35'. 1 

 B x = + 0.0833 = + 4 46-3 

 Cj = + 0.0405 = + 2 19.2 

 D x = + 0.0142 = + o 48.8 

 E x = — 0.0043 = — o I 4-8 



