216 On the Intensity of the Earth's Magnetic Force. 



771 



thod, we may neglect the errors in the values of wX and v , 



common to both processes, as they are small in the high lati- 

 tudes in comparison with those which arise from the friction 

 of the needle on its supports. Now in the ordinary method, 

 R is deduced from the equation R cosfl = X; and differentia- 

 ting this with respect to R and 0, and denoting by e, as before, 

 the limit of the error of position due to friction, 



AR 



-n- = • tan 0. 



But, in the proposed method, the corresponding error is 

 AR_ g 

 R sin u ' 



which is to the former as tan (90°— 0): sin u. This method 

 is therefore to be preferred to the old in the high magnetic 

 latitudes, provided that the angle of deflection be sufficiently 

 great ; and the relative accuracy increases indefinitely as the 

 observer approaches the magnetic pole. 



It should be observed that the two observations for the 

 determination of m may be made in a room, where the mag- 

 nets are under the action of local disturbing forces ; it is only 

 necessary that these forces should not be so great as to alter 

 the magnetic distribution in the deflecting bar, and that they 

 should remain unchanged during the observation. This cir- 

 cumstance of course will contribute to the facility of the ob- 

 servation, and to the exactitude of the result. It will pro- 

 bably not be necessary to repeat these observations on every 

 occasion on which the value of R is sought by deflection ; the 

 repetition being, in fact, unnecessary so long as the moment 

 of the deflecting bar continues unchanged. 



For the observation of deflection it is only required that the 

 inclinometer should be provided with a revolving arm, move- 

 able round the centre of the divided circle, for the support of 

 the deflecting magnet; while a second arm, connected with 

 the former, and at right angles to it, carries the microscopes 

 by which the position of the needle is observed. The general 

 plan of the instruments, now in course of preparation for 

 the Arctic expeditions, is similar to that of one made for me 

 by Mr. Barrow in 1846 (see Proceedings of the Royal Irish 

 Academy, vol. iii. No. 56). The plane of the divided circle is 

 separate from that in which the needle moves, but parallel to 

 it; and there is an adjustment, by which the axle of the needle 

 is brought to coincide in direction with the axis of the divided 

 circle. The circle is six inches in diameter; it is divided to 



