Determination of the Earth's Horizontal Magnetic Force. 411 



Equating to one another the two values of Pr 2 at 30 em., the one as 

 given above, the other as given in Table I, we have 



0-57X2 x 30~ 2 = 655 x 10~ 5 . 



Thus A. = 3*21, approx., 



and so n EE 2\/l 



= 6-24^9-17 = 0-67, approx. 



The practically exact agreement with Coulomb's relation 



2\ = 21/3 



seems to warrant the conclusion that if we employ this relation in 

 calculating Q the result is likely to be of at least the right order of 

 magnitude. 



On this hypothesis, taking the values 9*35 and 9 '17 for ?, as fairly 

 representative of the two groups, we have with r = 30 cm., 



Probable value of Qr~ 4 in unifilar of group B = - 5 x 10~ 4 , approx. 



E = -3xl0" 4 „ 



Assuming the value of P to be correctly determined, the error in X 

 due to the omission of the Q term is given by 



SX/X = -4Q/30 4 . 



Taking the numerical values found above for Q, we should have 

 when X = 0*18— 



For mean unifilar of group B, SX = +5 x 10~ 5 , approx. 



E, SX = +3x10-5, „ 



There is admittedly much uncertainty in these numerical estimates, 

 but they undoubtedly indicate that the neglect of Q requires justifi- 

 cation. 



If the Q term is not negligible then the ordinary method, which 

 assumes that the P term is the sole cause of the difference between the 

 two values of m/X, given by the first approximation formula with 

 r = 30 and r = 40, must lead to a wrong value for P. 



Now the P correction does not strike a mean between the results at 

 30 and 40 cm., but adds to or subtracts from both values of m/X. 

 Thus the indirect consequences of neglecting Q may be as important as 

 the direct. 



[Lamont, in his 'Handbuch des Erdmagnetismus ' (Berlin 1849), dis- 

 cusses the general case of the action of one magnet on another, the 

 distribution of " free " magnetism being arbitrary. The results (16) for 



