122 HANDBOOK OF MAGNETIC COMPASS 



In figure Gl, 2a is easily calculated from: 



E E E 



tan 2Q:=y^or 2Q!=tan ^y^or Q;=y2tan ^y^ 



This angle, 2a, is the phase position angle of the resultant quadrantal 

 error with respect to the D error, in terms of the quadrantal fre- 

 quency. It is apparent that this angle indicates the amount of slew 

 necessary for the spheres to correct both the D and E errors; but, 

 since the quadrantal curves experience two cycles of deviation for one 

 cycle of swinging ship, the actual angle to slew the spheres from the 

 D position will be only half this phase position angle. Therefore, 

 a IS the angle to slew the spheres from the D axis. If the D and E 

 coefficients are positive, the spheres should be slewed clockwise from 

 the athwartship position, whereas if the D coefficient is positive and 

 the E coefficient is negative, the spheres should be slewed counter- 

 clockwise from the athwartship position. 



The resultant amount of quadrantal correction necessary to handle 

 the D and E coefficients directly with the spheres in the slewed posi- 

 tion is found by the formula : 



Resultant quadrantal =\/^^+^^ 

 This resultant correction is then corrected by moving the spheres in 

 or out on the axis, indicated by a. 



140. Figure 33 is a graphical arrangement which can be used to 

 quickly solve any vector problem similar to the one described above. 

 It not only solves the angle of slew and the resultant quadrantal 

 error, but indicates the proper direction of slew for any given values 

 of I) and E. The solution of a sample problem, using this chart, is 

 presented in article 94. 



The need for slewing spheres may be observed on any single lati- 

 tude adjustment by merely determining the coefficients D and E. The 

 same principles of needle induction and latitude effects on quadrantal 

 errors hold true for E error as for D error, as discussed in article 92. 



Although the average binnacle does not have movable sphere 

 bracket arms, special E links may be made to allow slewing the 

 spheres to any desired position using the existing bracket arms. 



