221 



in which Vi - v-i is the angle contained between the two posi- 

 tions of the arm of the torsion circle, and is therefore known ; 

 and Ml - M2 is the difference of the observed scale-readings con- 

 verted into angular value. 



The value of u\ - u%, in this expression, must be corrected 

 for the actual changes of declination which take place in the 

 interval of the two readings; or else the observations must be 

 instituted in such a manner as to eliminate, of themselves, 

 these changes. The former course is that recommended by 

 Gauss, and usually followed, the actual changes of declina- 

 tion being determined by simultaneous observations with an 

 auxiliary apparatus. But in this, and in all similar cases in 

 which the interval of the observations is small, the effect of 

 such changes may be eliminated with more certainty by re- 

 peating the readings alternately in an opposite order for a few 

 successions. Thus the errors arising from a want of exact 

 correspondence either in the movements, or in the times of 

 observing the two instruments, are avoided. 



In order to determine the deviation of the plane of detor- 

 sion, V, the coeflScient p must be altered, so as to change the 

 value of u, while that of v is unchanged. The usual course 

 adopted for this purpose is to diminish the magnetic moment, 

 m, by substituting a weaker magnet. The value of the altered 

 coefficient is to be determined experimentally in the manner 

 already described : let it be denoted by p', and let u be the 

 new angle which the magnetic axis forms with the magnetic 

 meridian. Then S denoting the angle which the magnetic 

 axis of the second bar forms with the lower diameter of the 

 suspension thread, the angle of torsion is ?; - m' + S ; and the 

 equation of equilibrium is w + S = pu. Eliminating v between 

 this and the original equation, 



•pu = pu + d. 



Now S is a small angle, of the same order of magnitude as u 



T 2 



