188 Ocean Magnetic Observations, 1905-16 



r. — The value v of one scale division is obtained from the theodolite pointings on the 

 various divisions. In a well-constructed instrument it should be so nearly 1 degreee that 

 for a fraction of a degree it may be taken as unity. This ofTers the opportunity of saving 

 one step in the sea calculations. It is, however, most important that v remain constant 

 throughout any one scale. 



?«.— The inchnation of each scale is determined independently, but for opposite scales 

 the values are connected by the relations 



(90° - m,) + (90° - m,d = Ri (90° - m„) + (90° - m,) = Ri' 



or 



Ws + r«„ = 180° - Ri m, + m„ = 180° - RV 



where Rj and R'J are constant, so long as there are no structural changes in the optical 

 systems. They also may be determined by simultaneous observations with two theodoUtes. 

 From simultaneous measurements made with two theodohtes at Antipolo, March 

 1912, the following relations were estabhshed: 



?«, + m„= + 0?18 wi, + ?n„= + 0?40 



The values of m^ and m„ are constant. The values of m, and v\n change with varying 

 vahies of the vertical component Z of the Earth's magnetic field. The relation to Z is 

 deduced from observations, and appears to be expressed by the linear equation 



m = a-\- cZ 

 Then, for each station there is an observation equation of the form 



a + cZ = m, 

 and, on account of the relation 



w, + m„=+0?18 



another, thus: 



a + cZ =+0?18-m„ 



Writing TOs„ for |(»i» +0?18 - m„), the above two observation equations may be written 

 as a single equation as follows : 



a + cZ = nisn 



The adjustment may then be made with a single equation for each station. 

 The adjustment for the first and second cruises of the Carnegie gives 



m^ = m, = - 0?75 + 1?27 Z 



and from the relation m, + m„ = +0?18, there results 



m„ = + 0?93 - 1?27 Z 



The observed values of ?w™, and the values computed from the above are given, together 

 with their differences, in Table 50. The values of m, and vi^, after having been adjusted 

 to the condition of m, + r?!„ = +0?40, are likewise found in the table; their mean values 

 are also given, since m„ and rrii do not vary with Z. 



A word of caution may not be out of place regarding determinations of all constants 

 of this compass, but particularly for R', R", R'", R''\ R\, R". The instrument should 

 be shielded from the dkect rays of the Sun, which, by heating certain parts unequally, may 

 cause small displacements that may be magnified many times through the optical system. 

 The bowl should be drummed just before making each pointing on the scale, to overcome 

 friction at the pivot. 



