Determination of the Earth! s Horizontal Magnetic Force. 403 



5X/X = - 8fir~ s cosec u - 8/aV~ 3 , 



connecting the error SX in X with the departures 8jx and 8// of /x from 

 its assumed value during the vibration and deflection experiments. 



As cosec u exceeds 1, we see that if Sfx and S/x be equal, the first 

 term on the right of the equation is the larger of the two ; thus an 

 error of given amount in /x has most effect in the vibration experiment. 



We have approximately 



?-~ 3 cosec u = X/2m, 



and putting r = 30, we should find for an average collimator magnet 

 at Kew 



8X = - 10- 6 (208/x + 78/*), approx. 



The average value of /* in Table I is 5*85 ; thus if S/x and 8// ex- 

 ceeded 3 per cent, of the value of /x the consequent error in X would 

 become sensible. 



A change of 30° C. in temperature seldom alters m by more than 

 2 per cent., so in temperate regions the neglect of temperature varia- 

 tion in (a seems hardly likely to lead to error, unless of course tern 

 porary magnetism is more susceptible to temperature changes than 

 permanent magnetism. 



In tropical countries the neglect is likely to be more serious. 



[Since this paper was written, Professor Mascart, in ' Terrestrial 

 Magnetism,' has called attention to a source of uncertainty which I had 

 supposed negligible. He points out that in the vibration experiment 

 the proper induction coefficient is really /x - v, where /x has the meaning 

 attached to it here, while v is the coefficient of induction for a magnetic 

 field perpendicular to the magnet's length. Professor Mascart describes 

 a method of determining experimentally fx, v, and // — the coefficient 

 when temporary and permanent longitudinal magnetisations are opposed. 

 The method is, he says, easily applied and the results consistent ; but 

 the apparatus required seems a little complicated. Professor Mascart 

 quotes no numerical results. 



In the Kew pattern collimator magnet I should anticipate v//x to be 

 small, but it may not be negligible. Experimental investigation of the 

 point is certainly desirable.] 



Asymmetry in Magnets. 



§ 39. In the deflection experiment it is customary to describe the 

 collimator magnet as being on the east or west side of the mirror magnet, 

 and as having its north pole east or west The directions are not strictly 

 east and west, but perpendicular to the mirror magnet, as deflected out 

 of the magnetic meridian. As the sense intended, however, is quite 

 clear, I shall employ the usual terminology. 



