68 Messrs. Ayrton, Mather, and Sumpner 



through the zero more than twice*. With galvanome- 

 ters in which less damping is desired, a portion of the strip of 

 mica is cut away, so as to make it narrower, and in extreme 

 cases, when for example no damping is required, as in the 

 case of a ballistic galvanometer, the mica strip is replaced by 

 a vertical piece of wire. 



With a ballistic galvanometer, especially when intended 

 for teaching-purposes, it is desirable to have some easy means 

 of adjusting the amount of damping. In the case of the 

 galvanometer used by our students for experimenting on the 

 variation produced in the swing of the needle of a ballistic 

 galvanometer by variations in the amount of damping, this 

 variable damping is effected by enclosing the mirror in a cell 

 whose glass ends can be simultaneously made to approach or 

 recede. This motion of the ends of the cell is effected by 

 turning a milled head outside the instrument which works a 

 right-and-left-handed screw inside. 



In order to correct the throw of a ballistic galvanometer for 

 the damping of the oscillations of the needle, it is well-known 

 that it is necessary to multiply the sine of half the angle of 

 throw by the expression 



where X is the logarithmic decrement of the oscillations. 

 The value of this quantity when X is so small that its square 

 may be neglected is 



It seemed, however, desirable to work out the value of V 

 more fully and also to express it in terms of the numerical 

 ratio of each amplitude to its successor, since in this way the 

 need of finding the Napierian logarithm is avoided. This we 

 did at first by direct calculation, but while forming a table of 

 values connecting V and the decrement we observed that the 

 matter could be treated much more simply as follows : — 



By taking logarithms of the complete expression for V we 

 have 



* Quickness in the needle coming to rest, which is produced by using 

 a powerful controlling field, must not, of course, be confounded with 

 considerable damping, since, other things being the same, the decrement 

 is the greater the weaker the controlling field and the slower the motion 

 of the needle. 



