the Intensity of the Earth's Magnetic Force. 543 



Di^D^, &c. ; and a,, a^, 03, &c., the corresponding azimuths observed ; then it is 

 obvious that 



F2 cos a, — Fi cos oa = 0, V3 cos a, — F, cos 03 = 0, &c., 



from which equations the values of the coefficients p, q, &c., are obtained by 

 elimination in the usual manner. Hence F is completely determined. 



Now let the deflecting magnet be removed from the horizontal bar, and 

 placed in its ordinary position between the microscopes; and let the observa- 

 tion be repeated, the instrument being turned in azimuth until the deflected 

 needle is vertical. Then, if a^ denote the corresponding azimuth, we have 



- X cos oo = 3IU ; 

 whence there is 



cos oi) 

 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 observa- 

 tions, and is thrown upon the determination of the constant, which may be 

 made at leisure, whenever convenient, and may be repeated as often as is re- 

 quired for accuracy. 



In speaking of ?7as constant, and independent of the changes of the mag- 

 netic 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 assumption to the case of the larger changes brought about 

 abruptly by concussion, or 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 observa- 

 tions. 



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 C, are to 

 be used in the observations of intensity, — B being the loaded needle, which is 



4b2 



