215 



Ay_ 2Au 2tan?/ Ax 



Y cos^u{tanu -{-tdnu') tanu -\-tanu'' x 



But from the relation y = x tan 9, we have 



Ay _ Ax Ad 



— ~~ r 



Y X sin COS 0' 



and suhstituting, 



A9 _ cos u'Au J sin (ti — u') Ax 



sin 20 ~ cosM sin(M + w') ^sin(M + M') x" 



The second term of the right-hand member of this equation 

 contains a correction required for the simultaneous changes 

 of the horizontal intensity; but this correction will be gene- 

 rally small, and, when the bar has no permanent magnetism, 

 will vanish altogether. In this latter case, in fact, it appears 

 from (1) and (2) that u' =■ ti; so that the preceding equation 



is reduced to 



^„ sin 20 



AQ = ^^-Au. 7 



We must remember that the angle u in the preceding 

 formulae, being the deviation of the suspended magnet from 

 the position which it would assume under the action of the 

 earth alone, its changes are the differences between the ob- 

 served changes of position of the suspended magnet, and the 

 corresponding changes of declination. Let a denote the de- 

 viation of the suspended magnet, measured from some fixed 

 line, and a the corresponding angle when the iron bar is 

 removed ; then 



u— a — a', Ati = Aa — Aa'. 



But Aa = hi, Aa' zz k'n' ; in which n denotes the number of 

 divisions of the scale of the instrument corresponding to the 

 angle Aa, n' the number corresponding to the angle Aa', as 

 shown by the dechnometer, and h and Tt the arc-values of a 

 single division in each instrument. Hence 



Am = hi - k'n'. (8) 



