Marine Collimating-Compass 185 



For the determination of the constants of marine collimating-compass 1 (CI), the theodo- 

 Ute is mounted on an arm which may be turned about the vertical axis of the compass (see 

 PI. 11, Fig. 7). The distance, d = 28.1 cm., is therefore constant for this particular 

 arrangement. If this value be introduced in equation (7), and if D be expressed in kilo- 

 meters, the above equation becomes 



, 0.97 sin ST,M 



' = D 



It is readily seen that the formula is general, and applies to any scale with the mark in any 

 quadrant, and in general the correction is numerically the same with opposite signs for 

 opposite scales. 



A specmien of observation and calculation of the constants, Ac and ?n, determined at 

 Suva Vou, Fiji, June 15, 1912, for scale south and for scale west, is given on page 186. (For 

 a view of shore observations, see PI. 11, Fig. 7.) The observations were made at station 

 A simultaneously with the magnetometer observations at station B. The resulting values 

 are 



m = —1°A1 &nd Aa = + 0?35, for scale south; 



m = +0?59 and A^ = +90?78, for scale west. 



Adjustment of A^. — Where the horizontal angles between adjacent scales have been 

 determined independently of the magnetic decUnation or of the magnetic direction of 

 each scale, by simultaneous readings of the two scales with two theodolites which have 

 been collimated one upon the other, then the individual determinations of A^ for each 

 scale serve to detennine the A^ for all the other scales. The values of A^ for each scale 

 can then be made to depend upon all the observations of A^ for the four scales. 



Before proceeding to this adjustment, which, by the method of least squares, finally 

 leads to very simple expressions, let us first consider the adjustment of the horizontal 

 angles between adjacent scales when measured with two theodolites, as above explained. 



Let R', R", R"^, R'^, be the most probable values of the angles between the scales 

 E, N, W, and S, so that the measurements give : 



Ri +i/ = Ac. -Acn + i/ = R^ with weight p' 

 R'J + v" = Acn -Ac^ + i/'^ R" with weight v" 

 Ri" + i/" = Ac.-Ac + t/" = R'" with weight p'" 

 RV + v''' = Ac - Ac. + v"'' = R'"" with weight p"' 



We have the condition equation / 



360° - {Ri + R'J + R"J + R'"") = v' + v" + /" + r^^ f^f L I B R '. 



The one correlate, Ci, is given by \^\ "^^^ 



^ 360° - {Ri + Ri' + Ri" + R7) ^■rlr'.>..- 



Ci= 



V 



and 



which are the most probable corrections to Ri, R", Ri", Ri^, respectively. 

 If p' = y" = pi'J = yiy^ then 



/ = v" = v"' = i/^- = ^ [360° - {Ri + Ri' + Ri" + R'/)] 



The angles R', R", R'", R'^ remain constant if no structural changes take place in 

 the optical systems, but the constants Aa, Acu,, A„, and Ac. are subject, each equally, to 

 changes that may occur in the direction of the magnetic axis of the system of parallel 

 magnets. 



