464 



Mr. S. Gr. Starling on tlie Equilibrium of 



components (fig. 2), E'a = H??icosc/>' in the plane of the 

 compass-card, and parallel to OQ and E7> = Hmsin <£', not 

 in the plane of the card. The latter is resolved into E'c 

 normal to the card, and E'd=Hmsin</>'cos0 in the plane of 

 the card and perpendicular to OQ. 



Equilibrium of the needle. — There are now three forces 

 acting on each pole of the needle, namely, Ym sin 0, Hw cos <£', 

 and Hm sin <f>' cos 0. 



In fig. 2, x' is the angle between the magnetic meridian 



Fig. 2- 



and the vertical plane through the axis of the magnet, 

 while x is the corresponding angle in the plane of the card, 

 that is, $ / RE / (fig. 1) . x is therefore the deviation of the 

 compass from magnetic North, as seen by an observer in the 

 aeroplane. 



If 21 be the length of the magnetic needle, the magnetic 

 moment is 21 . m, and the couples due to the three components 

 of field acting on the needle are 



21 . m . V sin cos (<£ — #), 21 . m . H cos <j>' sin (cjy — x), 

 and 21 .m . H sin (//cos cos($ — a?), 



and the needle will be in equilibrium if 



H sin <£>' cos cos (<£— x) = V sin cos (</>— x) 



+ H cos <£' sin (</>— x). 

 V 



or 



But ^f = tan d. 



cos cj> tan (<f>— x) = sin <£' cos — tan d . sin 0, 



x ,, tan d sin 

 tan (6 — x) — cos # tan $' 77 — . . 



vr y r cos <p 



(i) 



