MAGNETIC OBSERVATIONS. 347 



As P moves towM-d the magnetic belt the horizontal component at first 

 increases, and with it the westward deflection of the needle. Finally, the 

 maximum westward deflection is reached, beyond which the needle beg-ins to 

 return; it is evident, therefore, that at this point the horizontal component 

 has reached a maximum value. 



3. DEFLECTIONS OF THE DIP NEEDLE. 



The balanced dip needle (i. e., without index error), in an area of 

 no local disturbance, is in equilibrium under the action of two couples, 

 namely, the vertical component of the 

 earth's magnetism and the added weight. 

 When displaced from the position of _ "" 

 equilibrium, the horizontal couple re- 

 stores it. 



In Ilg. 17 let rr be a balanced Fig. l?.— The forces acting on tlie dip neetUe. 



dip needle which has been displaced 



through the angle a. At the two ]3oles the attraction and repulsion of the 

 earth's magnetism may be resolved into horizontal and vertical components, 

 H and V. 



Taking moments about C, we have, if o^rzO, the needle in equilibrium 

 under the couples, 



V. 26 — ««^. rt = 0, 



where 2&r=PP, «i^rrthe added weight, and a its distance from the center. 



If this needle, so balanced, is carried to a station within the influence 

 of a magnetic rock, its dip will be determined by the composition of the 

 new forces with the old. The vertical plane will be that in which the hori- 

 zontal needle points at the same station. The equations above give us a 

 ready means of determining the ang'le of dip in terms of all the forces. 



Suppose the needle finally comes to rest at the angle a. with the hori- 

 zontal (the north pole being' depressed). Then 



V^ . 26 . cos a. — mga cos a — H^ . 26 . sin a^O, . . . (2) 



where H^ and V^ signify the resultants of the horizontal and vertical com- 

 ponents of the earth's and the local force. 



