385 
CONTINUOUS CALCULATING MACHINES. 
delicate forces may be dealt with by the mechanism, and accuracy of numerical results 
ensured. 
(2.) With regard to range of action it is clear that theoretically this is now infinitely 
great in both positive and negative direction, as may be seen by examining the travel 
of the movable frame (fig. 21 ).* 
Figs. 20 and 21. 
Applications for discontin uous calculation. 
It has been already shown how, with the sphere and roller, areas may readily be 
integrated and the operation of differentiation (by employing a screw) be performed. 
Various other results may however be obtained in a third way which has already been 
alluded to (p. 371). Before discussing this it may be well to point out that a very 
simple numerical computator is at once formed by the sphere and roller integrator in 
the special case where the position of the movable frame is constant during any given 
motion of the driving roller. A product or quotient of two given numbers may be 
* See note at end of the paper. 
