Sine Galvanometer 391 



zero, is turned in azimuth until the center of the scale is on the cross-hairs of the 

 telescope. Then the central plane of the coil, normal to its axis, will make with the 

 magnetic meridian an angle a+p y , as in Figure 17, which would be zero if all adjust- 

 ments were perfect. The angle 70 is due to incorrect adjustment of telescope and scale, 

 and would be zero if the vertical plane containing the axis of collimation and the center 

 of the scale contained also the axis of the coil. p is the angle between the axis of the 

 magnet and the face of the mirror, and a is an angle due to the imperfect elimination of 

 torsion in the suspension. In the actual instrument no one of these angles need exceed 

 a few minutes at most, as will be seen below. 



Suppose now that a current I is passed through the coil in such a direction as to 

 deflect the magnet in the clockwise direction, which will be assumed positive, and that 

 the coil is then turned (in the same direction) through such an angle 6 that the angle 

 by which the mirror is ahead of the coil in azimuth is reduced to a small value 7. Then, 

 if M denotes the moment of the magnet, <p the angle by which the torsion head and top of 

 the suspension are advanced in azimuth beyond the bottom of the suspension, and K 

 the torsional constant, we get from the lower half of the figure the relation 



GI COS (p-y)=H Sinle+a+iy-y,) j - ~ (<p + y-y a ) (12) 



If now a current I' is passed through the coil in the opposite direction, and the coil 

 moved counterclockwise through such an angle 6' as to give to the angle by which the 

 mirror is ahead (clockwise) of the coil in azimuth a small value 7', we get from the upper 

 half of the figure the relation 



<?/'cos(/3-7')=tf'sin (0'--( 7 -7o)} + |^+y'-Yo) (13) 



If the horizontal intensity is nearly the same for the two settings, we shall have 

 H', I', and d' but slightly different from H, I, and 6; and we get, by combining (12) and 

 (13), remembering that a, p, 7, and 7' are small quantities, and rejecting small quantities 

 of the second and higher orders, the relation 



If in a separate experiment, in the usual way, the axis of the magnet is turned from 

 approximate parallelism with the horizontal intensity through a small angle fi by turning 

 the torsion head through a much larger angle X, we have, with sufficiently close approx- 

 imation, 



m-l < 15 > 



Making this substitution in (14), writing H now for the mean of the two values of 

 the horizontal intensity, 9 for the total angle (6 + 9') through which the coil is moved, 

 and J for the mean of the two values of the current, we get, with a negligible error of 

 the second order in H and 7, the equation 



H 



GJ _ . e 



- sm - - vr -. tJ ^. 2 xgin e;( 



2 



which gives, after a simple transformation, and on solution for //, the final equation 



TT- GJ 



