Determination of the Earth's Horizontal Magnetic Force. 387 



} 



Table IX. — Mean Values of Constants in Sub-groups. 



Group. 



Sub-group 

 in order 

 of fl. 



ii 

 r- 



in. 



Mean m. 

 Mean 



TT 2 K. 



10 6 5- 



10 V- 



10 5 x Ffr 2 . 



B { 



First 6 . . . 

 Second 6 . 



D 4o 



5-58 



r>/4 

 660 



l\J-± 



120 



9QOO 



2606 



257 



1 /LI 

 141 



96 



-385 



E { 



First 5 . . . 

 Second 5 . 



7-70 

 7-42 



860 

 815 



112 

 110 



2575 

 2465 



345 

 353 



141 

 17 L 



+ 909 

 + 401 



Values of P were wanting for three of the twelve magnets of 

 group B. 



In one respect Tables VIII and IX unquestionably agree with the 

 results established for group C ; they show a distinct tendency in m/ft 

 to be large when m is large. There is, however, in Table IX no asso- 

 ciation of large values of ^ and q. In the case of group B there is an 

 apparent association of large values of both m and /x with large values 

 of K, suggesting that the size of the magnets has exerted a slight but 

 sensible influence. In the case of group E the differences between the 

 various magnets are so extremely small that we could hardly hope to 

 detect any relationship that was not very intimate and potent. 



The previous part of the paper has been mainly historical and 

 descriptive; it remains to consider the subject from a more critical 

 standpoint. 



Probable Errors in Determination of Horizontal Force due to Errors in 

 Values of " Constants" 



§ 19. Let us first assume that the methods of determining the 

 • constants " and the formulas employed in calculating the horizontal 

 force are alike above suspicion, and investigate on this hypothesis the 

 uncertainties introduced by the probable errors in the values found for 

 the several " constants." To do this, we mnst consider the formulae. 

 The notation not already explained is as follows : — 



X = horizontal component of magnetic force ; 



Ti = semi-period of vibration, corrections having been applied, if 

 necessary, for rate of chronometer and for finite arc of 

 vibration ; 



® = torsion couple, during vibration experiment, when torsion 

 angle unity ; 



u = deflection angle, during deflection experiment, when r distance 



apart of magnets' centres ; 

 t = temperature during vibration experiment ; 

 f = „ „ deflection „ 



