PALMER: THE DESIGNING OF CONE PULLEYS. 69g 
lar pair of cones. Through A! draw a horizontal and produce 
it to its intersection with BD, when we have at once 1, the half 
length of belt required for these cones, as shown. 
Now having fixed A', the portion of the curve between N and M 
gives all the possible pairs of radii for steps which this length of 
belt will fit, horizontal measurements being the R’s, and verticals 
the r’s; and it only remains to pick out from all these possible 
pairs of radii those having the proper ratio to give the desired 
speeds. 
This is quickly done thus: Take the next speed n!! and N the 
revolutions of the driving shaft. Lay off n'! from A! to W, and 
N up from W to R, using any convenient scale. Draw A‘'R, and 
we have at once A'Q for R11 and QS for r!! in the same scale as 
d and |, and the other radii. And so for each speed a pair of radii 
with which to draw the required pair of steps can be had at once 
from the curve BE. 
If a case of crossed belts proceed in just the same way, using the 
straight line BE of Fig. g in place of the curve BE of Fig. 8 for 
the radii of the steps. The only difference is in finding the length 
of belt. Draw the horizontal through A! as before, and now the 
half length of belt, 1, is the portion of this horizontal included be- 
tween the intersection with the circle arc at point 6, and the point 
U on the ‘‘belt line” WD. 
(b) SPEEDS TO BE IN GEOMETRICAL PROGRESSION. 
Usually the speeds will have to be arranged to form a geomet- 
rical progression. Generally the end speeds will be given or de- 
termined upon independently, and the intermediate ones have to 
be adjusted to form this series. In this event if we are to have, 
say five, steps on the cones, we have known 
N, n 
Fecustolaairg 
And we know that the five speeds will be: 
2 3 4 — } 
lig peg is desk .a ll a~ (==), 
if the series is to be a geometrical progression, ‘a’ being some mul- 
5 
ae 5 n ; 
tiplier. Then a*=—*, and by use of a table of roots, ‘a’ can be 
n 
1 
found, and then each of the five speeds to the nearest convenient 
fraction of a revolution. 
Now these values can be used as before, under (a), and the radu 
quickly found. 
