CONTINUOUS CALCULATING MACHINES. 
389 
calculator. The effects to be obtained by using two or more sets of spheres ancl 
rollers in one or both the primary ways, that is for purposes of integration and 
differentiation, must now be considered. 
First let two sets of integrating mechanism be employed. In fig. 24 let 
then 
MN = a. 
QN = b. 
Ax = width of element NQ. 
M = moment of area of MN about Ox where O.x is the trace of 
the roller A on the cylinder. 
Fig. 24. 
Fig. 25. 
Suppose, now, that as the pointer of the integrator travels along the upper portion 
of the curve, the wheel B, which in the simple integrator records the area, now drives 
another sphere which has its frame kept so that the value corresponding to y of the 
original proof is always for that frame equal to |. This result is easily effected by 
keeping the frames perpendicular to each other, as in fig. 25, the axes being h l Jc L and 
/% respectively, and using suitable proportions of wheels or rollers. 
Then when the roller A travels a small distance Ax at M (fig. 24), the pointer 
MDCCCLXXXV. 3 E 
