Dip-Needle Errors 



367 



where w is weight of needle in grams, g is acceleration of gravity, r is radius of axle at 

 point of support, and m is magnetic moment of the dip needle. Of these quantities, 

 w, g, r, and m are constant for any needle, though m will vary slightly according to the 

 treatment the needle receives. If freshly magnetized with bar magnets of sufficient 

 strength before each set of observations, the moment will be fairly well maintained. 



Now, if we write =A, equation (8) becomes 



A sin (/3+0 =F sin e (9) 



whence, since /3 and are small angles, 



\F-A) 







(10) 



Equation (10), however, holds only while the needle is turning from the position shown 

 in Figure 8a through the angle 0, when it will rest upon the tangent TG. At that point 

 the maximum e occurs, and we have 



= 8-0 



-ft) 



(11) 



G G 



Fig. 8a. Fig. 86. 



Theory of Minute Pivot-Defects on Dip-Needle Axles. 



As still further increases, the direction, CM, of the magnetic axis of the needle (Fig. 

 80) remains fixed and is gradually approached by the direction of the field CI. Hence, 

 over this portion of the curve the relation between and e is simply 



0+t = O 



(Ho) 



Now the angle e has been taken so as to represent the error which would be introduced 

 into the observed value in a single position of the needle if the weight of the needle were 

 all upon the irregular end of the pivot. Since a complete determination of inclination 

 with a needle requires readings to be made in four positions, the other three being pre- 

 sumably unaffected, and since the weight rests equally upon the two ends of the pivot, the 

 maximum correction produced by a particle of rust as assumed would be 



8\F/ 



(12) 



The constant A was determined for each of 10 needles taken at random from those 

 in stock; 8 were of the usual land type as made by Dover, and 2, also made by Dover, 



