132 CEETAIN INDICATING AND RECOEDING APPARATUS. 
made to turn at a speed always corresponding to that of the 
body or machine whose velocity is to be measured, e., cor- 
responding to the frequency of the making and breaking of 
electric contact. The other roller, C, is fixed to its axis, D, 
which, for convenience, is hollow, working freely upon the 
continuation of E, and is turned at a uniform speed by a clock. 
Suppose, now, both axes to be in motion ; the clock, by means 
of the roller, drives the disk, and thus the other roller, B. If 
now the speed of the moving body gives a less angular velocity 
to the screw than the roller, B, derives through the disk from 
the clock, then B will be screw^ed by the disk inwards, until it 
rolls upon a smaller circle, and the two angular velocities are 
equal. If the body gives a greater angular velocity to the 
screwy then the screw itself will draw the roller outivards, until 
the angular velocity of screw and roller are equal. Thus it is 
clear that the position of the roller on the disk is a direct 
measure of the velocity of the moving body. This is easily and 
conveniently expressed in symbols. 
Let w = angular vel, of screw. 
t(; = angular vel. of axis. 
Zi = radius of disk. 
?/ = distance of roller, B, from centre of disk. 
Then since the radii of both rollers are equal 
veloc. of B _ 
^ y 
I veloc. of (7 w B’ 
tv 
or w=y^ = yK) 
where 
a Constant. 
Therefore ?/ is a direct measure of tv, that is of the velocity of 
the moving body, and is independent of the time over which the 
observation extends. Moreover, it does not matter if the 
motions derived from both the clock and body in motion are 
