Horizontal Component of the Earth's Magnetism at Oxford. 439 



difference of two quantities which are nearly equal ; so that 

 the effect of experimental errors is very large. This is 

 illustrated by the following set of four double observations 

 (the constants are uncorrected, so that nothing depends on 

 the absolute values) : — 



Distances 100 centim. and 75 centim. 



M. H. A 9 . 



20 Feb. (1) . . . . 12098 '18014 74*7 



(2) . . . . 12008 -18055 98*7 



21 Feb. (1) . . . . 12047 -18011 144 



(2) .... 12065 -18079 117 



It is extremely improbable that A 2 varies thus. Physically 

 it is 2L 2 , where 2L is the distance between the poles of the 

 magnet. 



As a guide to the certainty of single observations, the four 



observations of the above set at 100 were reduced with 



2M 

 A 2 = 0, i. e. by the approximate formula -^-=r 3 tan 0. 



H. 



20 Feb. (1) -17953 



(2) -17972 



21 Feb. (1) -17969 



(2) ..... -17980 



The consistency of the single observations is therefore good. 



To determine A 2 independently, we have to find 2L, the 

 effective distance between the poles. Now the conception of 

 poles is not perfectly true. I have therefore taken the mean 

 between two measures. 



The first is the distance between the points where the lines 

 of force are at right angles to the magnet. My magnets are 

 nearly 20 centim. long, and this distance was 18*6 centim. 

 The other measure is obtained by combining the expression 

 for the moment ( = 2Lyu,) with 



number of lines of force 



/*= -& , 



which would be true if the lines of force were radii of a 

 sphere. 



(For a unit pole would have 4-7T lines of force, and pole fju 

 would have 47r^ lines of force.) 



The lines of force in the magnets were measured by com- 

 parison of their inductive effect on a coil of 4 turns with that 

 of H on a large coil of 21 turns, turning through half a 

 revolution so as to cut H twice. The method is in substance 

 that of Rowland. Mean radius of coil =25*65 centim. The 



