268 ON THE DETERMINATION OF THE TOTAL 



in azimuth until the deflected needle is vertical. Then, if a,, 

 denote the corresponding azimuth, we have 



- X cos a y = m U ; 

 whence there is 



U = F cosa . 

 cos a 



Thus the uncertainty of the result, arising from the smallness of 

 the angle of deflection at the usual distances, is removed from the 

 regular series of observations, and is thrown upon the determina- 

 tion of the constant, which may be made at leisure, whenever 

 convenient, and may be repeated as often as is required for 

 accuracy. 



In speaking of U as constant, and independent of the changes 

 of the magnetic moments of the needles, I have expressly limited 

 the statement to those small and regular losses of magnetism 

 which occur in time. It would not be safe to extend the assump- 

 tion to the case of the larger changes brought about abruptly by 

 concussion, or by any other accidental cause; and still less to 

 those in which the magnetic distribution of the needles is altered 

 by contact with, or proximity to, magnetic bodies. In such cases 

 (the occurrence of which is easily detected), the value of the 

 constant U should be re-determined. 



It may be useful to add a few words respecting the order of 

 the observations. 



The apparatus should be furnished with three needles, all of 

 the same size, viz., 3^ inches in length. One of these (which we 

 shall denote by the letter A) is to be employed in observations 

 of inclination : the other two, B and 0, are to be used in the 

 observations of intensity, B being the loaded needle, which is 

 also used as a deflector, and C the deflected needle. The two 

 latter needles should not have their poles reversed, nor be touched 

 with a magnet. 



The observations may be conveniently taken in the following 

 order : 



1. Needle A is to be placed on the agate planes, the other two 

 needles being removed, and a complete observation of inclination 

 taken in the four usual positions of the needle and limb, and with 

 the poles of the needle direct and inverted. 



