new Absolute Galvanometer. 275 



are the values of the current proportional to the tangent of 

 the deflection. With a single coil this is not the case. By 

 increasing the number of coils and suitably placing thein, the 

 magnetic field may be rendered more uniform. 



In reading the deflection, either a divided circle or a tele- 

 scope and scale are used. With the divided circle the deflec- 

 tion may be as great as 45 7 , but not more, or else the instru- 

 ment would not be sensitive to changes in the current. The 

 use of telescope and scale necessitates much smaller deflec- 

 tions. To regulate the strength of the current, shunts of small 

 resistance often have to be used, and render the proportion of 

 the current through the instrument doubtful. 



If, instead of placing the plane of the coils parallel with the 

 magnetic meridian,? they are placed perpendicular to it, the 

 sum of the force of the current and of the directive force of 

 the earth would influence the magnet. 



The formula 



^ = MT(l + <9) W 



expresses the relation between the time of oscillation of a 



magnet, its magnetic moment M, its moment of inertia K, 



and the horizontal component of the earth's magnetic force T. 



If the current is passing, the following formula will hold: 



t 2 K 



^ = M(T + F)(l + 0)' • • • • ( 2 ) 



F being the force due to the current. From (1) and (2), 



^-? « 



The moment of the force F on the magnet is 



C(G 1 ^ 1 sin + G 2 #2 sin 6Q f 2 (6) + &c.) : 



is the angle between the axis of the coil and of the magnet ; 

 and C is the strength of current. From this 



C(G 1 ? 1 + G^ 2 Q' 2 (0) + &c.)=F. 



For the small angles through which the magnet need vi- 

 brate, the second factor of the first term may be considered 

 constant, and equals the constant of the instrument used as a 

 tangent-galvanometer when the deflection is supposed equal 

 to 90°. Let 



Oiyi + a 2 ^Q / 2 (0 o ) + &c. = K 90 o, 

 and 



fr+ChfoaQ' i (tf) + 4o.:*K f> 

 Y2 



