OBSERVATION OF DEFLECTIONS. 263 



It is useless to carry the table further; for if the damping is 

 more rapid, the oscillations of the needle extinguish themselves so 

 rapidly that we need not trouble about them. 



881. Changes in intensity of the external field are corrected 

 by often repeating the control of the galvanometer ; but we are 

 more particularly concerned to eliminate the changes of direction, 

 which, for the terrestrial field, correspond to changes of declination. 

 Instead of determining zero at each observation, it is better to 

 reverse the current and observe the elongations on either side, 

 which gets rid of the position of zero. This inversion is par- 

 ticularly necessary in continuous observation : the current is then 

 reversed at regular intervals every three oscillations, for instance. 

 In order that they may be very small, the current is broken for 

 the time of a single oscillation before making it in the opposite 



direction. If x lt x 2 , x 3 , x, etc., are the deflections observed 



on each side, starting from an arbitrary zero, we shall have for the 

 permanent deflection, a series of values such that 



') 



882. MEASUREMENT BY FIRST SWING : METHOD OF MULTI- 

 PLICATION. We may also calculate the permanent deflection a 

 from the position of equilibrium. The needle being first of all 

 at rest, this deflection is 2# when the damping is zero. If the 

 damping is considerable, the angle of throw is an oscillation the 

 first part of which is a Q and the second tf ~ A , so that the total 

 swing #! is 



0j=0 (i+*- x ), from which a Q = [ L 



When the deflection is very small, we may obtain vibrations 

 which are more easily measurable by appropriate reversals of the 

 current. When the needle stops at its extreme position, and is 

 just about to move back, it is sufficient to change the direction 

 of the current, keeping it constant during the whole of the next 

 vibration. 



The angular deflection of the first swing is 



