68 KANSAS UNIVERSITY QUARTERLY. 
as for the case of open belts, making AB—d the distance between 
centers to any convenient scale, and BC=7d, that is 3,1416 times 
this distance between centers to the same scale. Draw a 45°-line, 
BE, from B, and a 45°-line, AX, from A, cutting BE at X. Draw 
a horizontal line through X and vertical from E, intersecting at W, 
and join W and D, thus obtaining the ‘‘belt line” WD. 
Now from point 2, where WX produced cuts AB, draw the 
45°-line 21. Through point 1 draw a horizontal line. Bisect 41 at 
3, and with 43 mark off O from 4, making O4=—43. Then with O 
as center and O2 as radius, draw the arc 26A, and the diagram is 
ready for use. 
CASE [—Cones Unlike. 
(a) SPEEDS ALL GIVEN. ; 
When the speed of the driving shaft is given, and the speeds to. 
be produced on the driven shaft are already determined by condi- 
tions of the design, and circumstances are such that cone pulleys 
of unequal size must be used, proceed as follows: 
For illustration take the case of open belts. Construct the dia- 
gram as explained under the heading of ‘‘Open Belts,” p. 65. (See 
Fig. 8.). From the nature of the design of the machine on which 
the cones are to be used determine what values are best to choose 
for the first pair of radii. If there are obstructions which the belt 
must pass, or the room for the cones is limited, this may require 
several trials. To do this draw a line from A, as AK, inclined so 
; : : : : n 
that any vertical to it as GJ, will be to its horizontal AJ, as = 
N 
That is, make AJ=N, and GJ=-n, to.any convenient scale) Then 
choose a size for R (or r may be chosen first) and lay it off from A 
to H with the scale used for AB. Then HK is the proper value 
for the other radius r, for this R, chosen. See if this meets the re- 
quirements of the machine. If not lay off another value for R and 
draw the vertical to the straight line for r. Aftera few trials a pair 
of radii will be found which will be of a suitable size for the re- 
quirements of the machine, and which will allow the belt to pass 
the obstructions, unless the design has in some way made this 1m- 
possible. 
This pair once found the other radii all depend on them. Sup- 
pose AH and HK to represent the pair R and r, found as just ex- 
plained. Through K draw a 45°-line parallel to KA, and SA 
parallel to AK, finding At. Now A! remains fixed for this particu- 
