46 REPORT ON 



u = angle of deflection, corrected for torsion force of the suspending thread. 

 P = a constant depending upon the distribution of magnetism in the deflecting 



and suspended magnets. 

 m = magnetic moment of the deflecting or vibrating magnet. 

 X— horizontal component of the earth's magnetic force. 



— , = value of ^ before the application of the correction ( 1 —\ 



i , ,H\ _ 5400 + v 

 \ + Ft ~ 5400 



where v = the angle, expressed in minutes of arc, through which the suspended 

 magnet is deflected by a twist' of 90° h. the suspension thread. 



*=*(i-bbb)(*-£) 



T>=r'{i+.§\ {x-ci'-0*} {i + f§} 





i = du (l -J- yj 



■== = If 1 tan u 

 X 2 



m in ' l 

 X = X'\ 



1-3 



mX x 

 x=^ 



m 



In order to facilitate the finding of log. tan u, in the reduction of observations 

 of deflection, the following table has been prepared. With the argument log. u 

 (u being expressed in minutes of arc) it gives the quantity (log. tan u — log. u), 

 or, in other words, the quantity which it is necessary to add to log. u in order to 

 obtain log. tan u. The arrangement of the table is such that the quantity (log. 

 tan u — log. u) is to be added to the log. u on the same line with it, or to any 

 other log. u less than the one on the line next below. For example, if it were 

 required to find log. tan u corresponding to any log. u from 8.0000 to 1.4340, it 

 would only be necessary to add 6.46373 to the given log. u. 



