COEFFICIENTS OF DEVIATION 31 



A check on the coiiiponeuts in (igure 21 will reveal that their sum- 

 mation equals the original curve. 



This method of analysis is accurate only when the deviations are 

 less than 20°. The mathematical expression for the deviation on 

 any heading, using the approximate coefficients, is : 



Deviation =.i+^ sin c/) + 6^ cos </> + /> sin 2 (/> + i^' cos 2 </> (where (f> rep- 

 resents compass heading) 



39. Reasons for analysis. — This method of estimating approximate 

 coefficients is convenient for : 



(1) Analyzing an original deviation curve in order to anticipate 

 necessary corrections. 



(2) Analyzing a final deviation curve for the determination of 

 additional refinements. 



(3) Simplifying the actual adjustment procedure by anticipating 

 effects of certain corrector changes on the deviations at all other 

 headings. 



40. Approximate and exact coefficients. — It is emphasized that the 

 above estimations are for the so-called approximate coefftcients and not 

 for the exact coefficients. Approximate coefficients are in terms of 

 angular deviations which are caused by certain magnetic forces ; and 

 as stated before, some of these deviations are subject to change with 

 changes in the directive force, H. The exact coefficients are expres- 

 sions of magnetic forces, dealing with; (a) arrangements of soft iron, 

 (&) components of permanent magnetic fields, (c) components of the 

 earth's magnetic field, and {d) the shielding factor A. Thus, the 

 exact coefficients are expressions of magnetic force which produce the 

 deviations expressed by the approximate coefficients. The exact coef- 

 ficients are for mathematical considerations, while the approximate 

 coefficients are more practical for adjustment purposes. For this rea- 

 son, the exact coefficients and the associated mathematics are not ex- 

 panded further in this text. The German capital letters are used to 

 designate the exact coefficients, whereas the English capital letters are 

 used to designate the approximate coefficients. 



41. Compass heading and magnetic heading. — ^When deviations 

 are large, there is an applicable difference in the deviation curve if 

 it is plotted on cross-section paper against compass headings or against 

 magnetic headings of the ship. Not only is there a difference in the 

 shape of the curves, but if only one curve is available navigators will 

 find it difficult in applying deviations when converting from magnetic 

 heading to compass heading, and vice versa. When deviations are 

 small no conversion is necessary. Figure 22 illustrates the differences 



