Horizontal Component of the Earth's Magnetic Field. 49 J 



where 2a is the length, d the diameter, and w the weight of 

 the deflector-bar. From (4) and (8) we obtain, 



7r 2 (a 2 +-^:d 2 )rw 



3PV-^) 2 tan0 o - * ' ' * W 

 From (5) and (8), 



4^ 



K***™^^^* ( 10 > 



When two deflectors are used, as described above, equations 

 (9) and (10) take the form, 



3 

 7r*r 



*~(a 2 +|^)(PK+I>i) 



H2 ~3 (r 2 -a*) 2 P 2 P;;tan0 o ' ' ' 



and 



4"" 



3 (a 2 +^d 2 )(P^c 2 + PIw 1 ) 



3 (r» + a;)iPJP|tan^ '' * * V - ' 



where P x and P 2 are the periods of oscillation of the two de- 

 flectors respectively, 2a x the mean of their effective lengths 

 (supposed nearly equal), and w ] and iv 2 their masses in grammes. 

 Equations (9) to (12) give, of course, the same value for H 



M . 



if a x has been properly calculated. The value of — is always 



calculated, as it gives an idea of the quality of steel used for 

 the deflector. The results are given along with the values of 

 H in tabular form below. 



The values of H derived from equations (9) to (12) require 

 correction, in the oscillation experiment, for arc of vibration, 

 for virtual increase of inertia due to air moved, and for change 

 of inertia, due to change of dimensions of the deflector, if the 

 temperatures when the bar is measured and when it is vibrated 

 are different. Neither of these produced a sensible error in 

 the experiments, and hence they were neglected. There are 

 besides a correction for the effect of variation of temperature 

 during the experiment in altering the magnetic moment of 

 the deflector, and a correction for the change of magnetic 

 moment between the oscillation and deflection experiment, due 

 to the deflector having its length in the direction of the mag- 

 netic meridian in the former, and at right angles to it in the 

 latter experiment. 



