472 



Mr. S. G. Starling on the Equilibrium of 



shown in dotted line alongside of it. From the parallelism of 

 the two, it is apparent that a fair approximation to a proper 

 correction might be obtained, if the movement of the 

 magnets could be arranged to be proportional to the tilt of 

 the machine. 



.Effect of earth's horizontal component alone. — If the earth's 

 vertical component of magnetic field could be entirely elim- 

 inated, the errors of the compass due to tilt would be 

 reduced, but not entirely eliminated. On putting V = in 

 the equation from which equations (1) and (2) are derived, 

 we have 



cos (j) r sin ((f>—x) = sin <£' cos 6 cos ((£ — #), 

 or tan (</>— x) — cos#tan<£' (3) 



It is now possible to find % in a manner somewhat similar 

 to the former, for the values of $ and of cos 6 tan cf>' are 

 already known, so that ((£>—■ x) and x can be tabulated. 

 These are now done for the values of tilt 20°, 40°, 60°, 80°, 

 and 85°. 



e. 



20°. 



40°. 



60°. 



80°. 



85°. 



*'• 



(<j>-x). 



<p. 



X. 



(<p-x). 



f 



X. 



{<p — x). 







X. 







(0-tf). <p. 



X. 



(<p-x). 



0. 



X. 



























































10 



9 



11 



2 



8 



13 



5 



5 



19* 



14£ 



2 



45 



43 



1 



64 



63 



20 



19 



21 



2 



16 



25 



9 



10 



36 



26 



4 



64 



60 



2 



77 



75 



30 



28 



31 



3 



24 



37 



13 



16 



49 



33 



6 



73 



67 



3 



81 



78 



40 



38 



42 



4 



33 



47 



14 



23 



59 



36 



8 



78 



70 



4 



84 



80 



50 



48 



52 



4 



42 



58 



16 



31 



67 



36 



11 



82 



71 



6 



86 



80 



60 



58 



61 



3 



53 



66 



13 



41 



74 



33 



17 



84 



67 



9 



87 



79 



70 



69 



71 



2 



65 



74 



9 



54 



80 



26 



i 25 



86 



61 



13 



88 



75 



80 



79 



81 



2 



77 



82 



5 



71 



85 



14 



| 45 



1 



88 



43 



27 



89 



62 



These curves (fig. 10) are now plotted to the same scale 

 as the previous set. They then make it clear that whereas 

 the total disturbance is semicircular, being of the same sign 

 (positive) from 270° to 90° and negative from 90° to 270°, the 

 disturbance due to the tilt for horizontal component of the 

 earth's field acting alone is quadrantal. It is the combination 

 of the semicircular disturbance due to the earth's vertical 

 component and the quadrantal disturbance due to the 

 horizontal component that gives the want of symmetry 

 about the 0° and 180° ordinates in the first set of curves. 

 It is also seen why the curves at B become negative, for 

 here the quadrantal effect predominates, at the large tilts 

 the disturbing effects of the earth's vertical field being 

 small, since the card approaches to parallelism with the 

 resultant field. 



