Deter ra inatioii of the Eartlis Horizontal Magnetic Force. .">97 



not apply very exactly to the'particular samples of brass and steel em- 

 ployed in any individual case ; and there is the further criticism that the 

 coefficient 12 x 10~ 6 is applied to a composite moment of inertia K, 

 of which 25 to 30 per cent, is contributed by the magnet's appendages, 

 which are mainly brass. The expansion coefficients are employed first 

 in deducing the value of K at 0° C. from the value found at some 

 higher temperature, and then in calculating from the value at 0° C, 

 thus found, a table giving K at all temperatures likely to occur in 

 actual use. Any error that may^arise in this way will be larger the 

 more remote the temperature from that existing during the special 

 inertia experiments. Its probable magnitude cannot, however, be 

 directly arrived at in the absence of measurements' of the expansion of 

 specimen magnets, their appendages and auxiliary bars. 



A second source of uncertainty is the fact that one is obliged to 

 assume uniform density in the auxiliary bar. 



§ 33. Torsion of suspending thread. — This is required (1) in reducing 

 the declination experiment, (2) in the vibration experiment determining 

 the horizontal force. 



For a considerable time prior to a declination experiment at Kew, the 

 suspending silk fibre is stretched by hanging from it a non-magnetic 

 plummet similar in weight to the magnet and its appendages. As the 

 magnetic meridian is very approximately known, it is easy to arrange 

 that when the plummet is replaced by the declination magnet there 

 shall be very little twisting of the silk ; we may thus, with at least 

 reasonable probability, regard the thread at the beginning of the experi- 

 ment as practically free from torsion. After the experiment is con- 

 cluded, the magnet is again replaced by the plummet, and after some 

 hours its position is noted. In this way we can tell approximately the 

 angle 0' through which the lower end of the thread has turned since the 

 last declination reading was taken. It is assumed that 6' represents the 

 amount of torsion in the silk when the experiment ended, and that 

 this torsion was introduced gradually in the course of the experiment. 

 As the magnet has to be variously manipulated, there is no antecedent 

 mprobability in the hypothesis ; but it will, I think, be recognised that 

 the taking 6' 2 as the mean torsion angle during the experiment is an 

 emendation whose success is likely to be variable. 



To allow for 6' 2 of torsion, one introduces a given twist into the 

 thread and notes the consequent change of azimuth in the suspended 

 magnet. The procedure adopted at Kew, is to turn the suspension 

 head carrying the thread through 180° first in one direction then in 

 another, noting the corresponding equilibrium positions of the magnet. 



£ 34. The occasion for a torsional correction in the vibration experi- 

 ment is the existence of the couple &0 in (6), and consequently of the 

 term ®/mX in (7). The value of //'X is deduced from the observed 

 changes in the azimuth of the collimator magnet when the suspension 



