VARIATION APPARATUS. 615 



The number N of oscillations of the bar oscillating about a vertical 

 axis will give, in like manner, 



\ 

 N 2 HM 



ri* Q cos /3 ' 

 from this follows, as verification, 



1187. The best method consists in determining the coefficients 

 of the three instruments of variation by a direct comparison. Apart 

 from the effects of temperature, the variations of the two components 

 are given by expressions such as 



~M6, or - 

 H Z 



An auxiliary bar M' is placed successively at the same distance 

 from the three apparatus of variation, in such a manner that its 

 action F is perpendicular to the component H for the declinometer, 

 parallel to H for the bifilar, and vertical for the balance. If the 

 deflector is, for instance, in Gauss' second position in each experi- 

 ment, the corresponding deflections 8, 8', and 8" of the three 

 apparatus, supposed to be very small, give 



the values of the coefficients are 



us 



1188. Variations of inclination may be directly observed on a 

 dip-needle, supported by a knife-edge, and carefully adjusted ; but 

 it is generally preferable to calculate the variations of the two prin- 

 cipal components. 



From the equation 



Z = HtanI 



