ACTION OF A MAGNET ON A COMPASS NEEDLE. 125 



Fig. 42. 



The effective attraction in the horizontal plane is the 

 excess of the former over the latter. 



If the magnet be at a considerable distance, or if a 

 be much smaller than c, so that it will suffice to include 

 the first power of a, an approximate value will be 



- 5 (c sin <f> a) (c 2 + 3ca sin <f>) -j (c sin + a) (c 2 3ca sin 0) ; 

 or, nearly, 



-5 (c 3 sin (j> + 3c 2 a sin 2 <f) c 2 a) - s (c 3 sin < 3c 2 a sin 2 ^ + c 2 a) ; 

 c c 



Consequently, when sin = * /- , or ^> = 35 16', there 



is no horizontal action : when < is less than this angle, 

 the action is of the opposite character. 



