92 Mr. C. Y. Boys on Apparatus for the 



where they cut the solenoid, are nearly horizontal ; so that 

 practically the whole of the force developed tends to drag the 

 solenoid downwards, instead of being partly spent, as before, 

 in producing a stretching strain. The consequence is that the 

 movable solenoid may be made very much shorter than would 

 be necessary if no rings were present. The tubes, having a 

 higher coefficient of induction than air, merely serve to increase 

 the number of lines of force, rather than affect their distri- 

 bution. 



If a movable solenoid, arranged as described, is hung by a 

 band passing over the arc of the beam B, then the turning 

 moment due to a down-pulling force is, within certain limits, 

 constant, while the force restraining motion varies as the sine 

 of the inclination of the beam; but had it been hung from the 

 point p, the turning moment would have been proportional to 

 the cosine of the inclination, and the tangent of the incli- 

 nation would have measured the force. What is wanted 

 is to make the tangent of the inclination proportional to the 

 product of the two currents; and, as explained, this could 

 be attained by using a long solenoid hung from the point p. 

 But such an arrangement causes a double inconvenience; 

 for not only is a long solenoid itself inconvenient, but the 

 fact that it is hung from an arm and not from an arc causes a 

 lateral shifting of the solenoid when the beam B is inclined, 

 thus necessitating a wider annular space for it to pass through. 

 Now the use of a comparatively short solenoid hanging from 

 an arc introduces two errors which are almost absolutely 

 equal and opposite. The error due to the arc is an increase 

 of moment in the ratio of the cosine of the inclination of the 

 beam to 1 ; that is, the error is equal to the versed sine of the 

 inclination ; and, like a thing that increases as the square of a 

 quantity, it is at first quite inappreciable, and it increases in 

 amount with increasing speed as the quantity grows. Now 

 the error due to a short solenoid, such as shown in the figure, 

 is at first nothing; for a given movement will cause the sole- 

 noid to enter as many lines of force at one end as it leaves at 

 the other, but as it gets displaced it enters rather fewer than 

 it leaves ; and this difference in the number of lines of force 

 increases in amount with increasing speed. Now, if the pro- 

 portions are so taken that when the inclination of the beam 

 is a little less than the greatest amount permitted to it the 

 actual magnetic error is equal and opposite to the versed-sine 

 error, then, since each is a quantity which grows according to 

 the same kind of law, those errors will be always approximately 

 equal, and their differences very small compared with the 

 errors, and absolutely inappreciable in comparison with the 



