CERTAIN INDICATING AND RECORDING ‘APPARATUS. 135 
now draws along both rollers with the evident result of a much 
more rapid adjustment. Now the formula becomes : — ■ 
IV y 
— Z=Z 5 
VO z 
z = R-y, 
V ' 
lf)~ -1 tv, 
H-y 
y =3 0, IV = 0, 
y = z = R—y, iv^^iv, 
y = R, fo-=oo. 
So that now the range of velocity is from 0 to oo. The 
graduation of the scale is not so simple as in the first case, but 
inasmuch as the arrangement has still the‘ radical defects of the 
disk and roller, it is not suitable for practical application. The 
author then endeavoured to ascertain whether there was not 
some simpler relation between these two forms than appears at 
first, and with the following result. 
Let 0 [Fig. 3) be the centre of a sphere which works on two 
fixed centres, M and N, that is about the axis, MN. Let Q 
be the point of contact of the roller (7, which works against the 
great circle of revolution {i. e., the equator) and P, the point of 
contact of a movable roller, P, working in the figure against a 
small circle whose radius is PR. 
Let angle of plane of B with MN — a ; 
where 
when 
Then 
/ vel. of B _iv _ 
F' vel. of C~ tv~' 
but 
OQ 
OP 
= sin a 
OQ' 
IV 
-i=sin a; 
IV 
or tv "tv sin a. 
In Fig. 4 the roller C is now movable as well as the roller 
