240 Prof. E. Taylor Jones on a 



lens and is reflected by the small mirror on to a rotating 

 concave mirror, driven by a motor. It is finally focussed so 

 that an image of the aperture is formed on a plate of ground 

 glass or on a photographic plate. 



A tuning-fork carrying a small mirror is mounted vertically 

 in front of and close to the' window of the oil vessel. A part 

 of the beam of light falls upon this mirror, whence it is 

 reflected to the rotating mirror and focussed on the plate. 

 When the concave mirror rotates, two horizontal lines are 

 thus traced by the spots on the ground-glass plate. By 

 adjusting the small platform one of these traces can be 

 brought to a short distance from the other. At a certain 

 point of the rotation of the mirror the tuning-fork is struck 

 by a hammer worked by a lever, after the manner of a 

 pianoforte-key action. 



The arc-lamp is enclosed in a light-tight case and the 

 whole apparatus is set up in a dark room . 



The electrometer is very easily constructed, and a single 

 suspension will last a long time if the platform N is removed 

 from the mirror after use. 



The sensitiveness of the arrangement may be considerably 

 increased by removing the ebonite sheath K, thus allowing 

 the attracting plate to be brought nearer the strip. 



(2) Theory of the Arrangement* 



If a decaying simple harmonic electromotive force pro- 

 portional to e"^ sin nit is applied to the electrometer, the 

 equation of angular motion of the mirror may be written : 



d t (i r 



-rV -f k ~ + n?sc = Ar 2 ^ sin 2 nit 



at 2 at 



= iAe- 2 ^— ^Ae-W cos 2mt, 



where n, which is 2tt times the frequency of the natural 

 (undamped) oscillations of the mirror, depends, among other 

 things, on the tension of the strip, and k on the viscosity of 

 the oil. 



The force applied to the strip thus consists of an exponential 

 part and a decaying simple harmonic part of double the 

 frequency of the applied E.M.F. Taking the two parts 

 separately the solution is 



_1 Ae'W 1 Ag- 2 ^cos(2m£ + a) 



~ 2 V-2^ + n 2 ~ 2 V{ (V - 4m 2 - 2k/* + n 2 ) 2 + (8/^- 2^) 2 p 



where Q 7 



, bum— A km 



tan a = 



4yu 2 -4m 2 -2/^-f-r^ 



