DIP IN EXTRAMERIDIONAL PLANE. 89 



The investigations above apply to the case of the 

 needle vibrating in the magnetic meridian : and they 

 then give for result the true magnetic dip. It is only 

 necessary that the direction of the magnetic meridian 

 be nearly known : a small error is unimportant, and the 

 determination of the meridian by a common compass is 

 abundantly accurate for this purpose. 



But the investigations also apply when the needle 

 vibrates in any other vertical plane. They do not then, 

 however, give the true dip ; they give only an apparent 

 dip, corresponding to the proportion of the vertical 

 magnetic force to the resolved part of the horizontal 

 magnetic force in that plane. (For it is obvious that 

 the part of the horizontal magnetic force which is per- 

 pendicular to that plane, being parallel to the needle's 

 axis of rotation, can have no effect on its rotation or 

 vibration.) If ^ and < 2 be the azimuths from the mag- 

 netic meridian, measured in the same direction, of two 

 vertical planes in which the dip is observed ; d t and d 2 

 the apparent dips observed in those planes : then the 

 resolved horizontal forces in these planes will be 

 -Hcos</>, and ZTcos </> 2 , and the equations between the 

 apparent dips and the azimuths will be, 



, H . cos <f>. , H . cos <> 

 cotan. d l = ^- ; cotan. d a = ^ 2 . 



i 



TT 



But -y cotan. True Dip ; therefore 



cotan. d t = cotan. True Dip x cos <, ; 

 cotan. c? 2 = cotan. True Dip x cos < 2 . 



