CONTINUOUS CALCULATING MACHINES. 
375 
In the limit when 
o) = 0 y=o 
2ndly. If the rate of change of the other quantity, that is, the one connected 
with the disk, becomes very small, then the roller B moves outwards and reaches the 
edge of the disk, at which point 
2 /=It and 6)=&q 
that is, with the equal rollers (A and B) it is impossible to indicate a ratio less than 
unity. It should be noted that any increase, however great, of the quantity now 
being considered can be (in theory) measured, for if oq becomes very great, y becomes 
very small, and may approach as nearly as desired the limiting case when 
y— 0 oq= co . 
Any advantage arising from this latter consideration does not counterbalance the 
disadvantage that when cu=aq any further decrease in the speed of the roller A causes 
B to leave the disk and necessitates special arrangements, not so simple as it might at 
first be supposed, to bring B on the disk again. 
In the cases in which this kind of mechanism would most probably be applied in 
practice, a clock would be used, so as to make one of the two speeds constant, and 
only introduce one variable quantity. It is evident from what has been said that the 
clock would always be employed to drive the disk by means of the roller A, for then 
the maximum rate change of the variable, which variable might for instance be velocity, 
would be previously ascertained. The dimensions could then be arranged so that the 
indicating roller B would never leave the disk, while the lowest velocities, down to 
the stopping of the body in motion, would be recorded. The author found that in 
designing the speed indicator previously alluded to, a suitable velocity of the disk 
was not easy to attain without unduly increasing its size and introducing consequent 
mechanical disadvantages. 
In order to obtain unlimited range within a small compass, the author therefore 
designed the arrangement shown in fig. 5. The driving roller A' is directly connected 
with the other roller B', so that their radial positions on the disk change together and 
to an equal extent, their distance apart being equal to the radius of the disk (R). At 
the same time their angular motions are independent of each other. 
Let %—distance of A' from centre of disk, then 
but 
®__y 
(O l z 
z=U-y 
oi — 
y 
B-y 1 
3 c 2 
therefore 
