BILATERAL DEFLECTION. 287 



is right or left of the plane of symmetry, the passage of the current 

 always increases the deflection by an amount which is at first pro- 

 portional to the original deflection. This deflection, which Professor 

 Chrystal calls unilateral^ is independent of the rapidity with which 

 the alternating currents succeed each other. 



Let a and /3 be the angles which the direction of the needle 

 makes with the mean plane of the windings in its position of rest 

 and at the time t, and let I be the intensity of the current at the 

 same instant. If the magnetism of the current were invariable, the 

 moment of the couple which acts upon it would be 



C = HM sin(/3-a)-GMI cos/3 = M[H sin(/3-a)-GI cos/5]; 



r\to 



but assuming that the magnetic moment varies proportionally to the 



component of the forces which act parallel to the axis of the needle, 

 we may put 



with 



sin/? + H cos (/3- 



The moment of the couple is then, at the time in question, 

 C= i+[GIsin/3 + Hcos(/3-a)] H sin (ft - a) - GI cos ft M . 



To obtain the mean value C m , this expression must be multi- 

 plied by dt, integrated from to #, and the result divided by 0. 

 The terms which do not contain the intensity do not vary; those 

 which contain the first power of I disappear; those which contain 

 the second should be multiplied by the mean square 1^ of the 

 intensity. We have thus 



,-t 



G 2 ! 2 



As the coefficient k is very small, the third' term in the bracket 

 may be neglected in comparison with the two others, and putting 



