CORRECTIONS FOR THE EFFECT OF INDUCTION. 167 



efficient magnet-power of A at the second station 

 when its distance from the needle is 1. At any other 

 distance c, let the angle of deviation be <f>'. Then 

 the induced magnet-power will be 



E'.&ind) tan J (0-0,) 



-p xAx cotan. original local dip x - ^~ --' . 



But (see Article 27), putting 2 for ra, E' for E, and <fi 

 for 0, 



, ., 2A , E' sin $ 1 2A 1 

 E . sin 6 =5- , and -- p--*- = - 3 . -= = -3 sin : and 

 c j& c Jii c 



the total effective magnet-power of A will be 



l 3 sin x cotan. original local dip x 7^ 7ff ^ 2 \ ' 



Second, for the force producing the vibrations of A. 

 The red pole of A will be turned to the north, and 

 therefore the inducing force will be -f E r ; the induced 



Tf" 



magnet power will be -f- -^ . A x cotan original local dip 



x i rr^ *\ ' an ^ the real power of the magnet 

 tan (, + 6/J 



will be 



A ! 1 + -4 x cotan. orisrinal local dip x - f-7/r ^ 

 1 E tanH^ + ^ 2 



Here the factor of A does vary from station to station. 



The reader will have little difficulty in investigating 

 the corrections which these considerations shew to be 

 necessary in the formulae terminating in Article 32. 



