PALMER: THE DESIGNING OF CONE PULLEYS. 53 
THE FINAL DIAGRAM. 
A glance at Fig. 3 shows that there is no reason why the curve 
FVXH may not be replotted with the R’s as abscissas, the r’s as 
ordinates, or the reverse. 
Fig. 4 shows the result of replotting Fig. 3 in this way from A, 
as the origin; the curves BFE being the resulting curve, replacing 
PME of Fig. 3. 
Simply construct the rectangular as before, with AB=d, and 
AD=rd, and draw the diagonal ‘‘7-line,”” BD. 
Then taking A for origin, and AB and AD for co-ordinate axes, 
lay off from A horizontally any value of R, from Fig. 3, as QU, 
to U, letting the reference line be AD, that for1 maximum. Then 
from U, upward, lay off the corresponding r from Fig. 3, QV, 
when the result will be a point P of the desired curve. Plotting a 
large number of pairs of radii obtained from drawing a series of 
verticals through curve FXH, at small intervals, there will result a 
series of points which will determine the curve BFPE. 
This curve BF PE now gives all the possible pairs of radu from 
the maximum ], just as curve FXH did in Fig. 3, but here R is an 
abscissa and r an ordinate. 
It is at once seen that the curve must be symmetrical with respect 
to a 45°-line through A, from the fact of R and r, exchanging 
values as they do, as can be seen in Fig. 3. QU was taken as k, 
and OV asr. Now in passing through the entire range of values 
for R and r, eventually, R will become QV, and r, QU. This 
means that while we are plotting R andr, Fig. 4, r may also be 
laid off on AD as an abscissa, and R upward from it as the corres- 
ponding ordinate, thus at the same time securing another point P’ 
of the curve BP’FPE, plainly making it symmetrical. 
CURVE BFE A CIRCLE ARC. 
Having actually plotted the points to determine curve BFE, and 
being ready to join them by a smooth curve, the general character 
of the curve is seen to possess every appearance of a circle arc, 
the center of which would of course be somewhere on AF, since 
the curve is symmetrical to the 45°-line, though not at A. 
A careful trial proved that the very best curve with which these 
plottings could be fitted was an arc of a circle the center of which 
was at point O on AF, below A, located as shown on the figure at 
a distance AO equal the diagonal of a square the sides of which 
are one-tenth of AB, or a. 
