PALMER: THE DESIGNING OF CONE PULLEYS. 51 
this curve FUXVZH give all the possible pairs of radii which will 
run correctly to this length of belt. For this particular length of 
. belt only the portion of the curve between verticals through X and 
Z is useful, evidently. This portion gives all possible pairs of 
radii for this 1, while for any other value of | more or less of the 
curve would be brought into service. 
The entire curve would, plainly, come into use only for the 
theoretical limiting case of one step, R—d, and the other, ro, 
when l=7zd, or the length of the rectangle of Fig. 3. 7d is the 
theoretical maximum half length of belt for any distance between 
centers. . 
Having | assumed, as shown, and the reference line JS, fixed, 
R and r can vary from the limit 
( Reo f R ] 
i er 1 at Z to X, where R=r, back to Z again where~ “— > 
ae. r==—O 
including all possible values for this |. 
Or if we have a given first pair of radii the reference line JS can 
be determined from them for their length of belt, and all other 
pairs of radii suitable for this length of belt will be at once shown. 
It is only necessary to take the difference of these radii and find the 
position of a vertical through the curve, such that the intercept 
VU equals this difference, Then measuring R downward from U, 
or r from V, the reference line JS is determined, and the length of 
belt can be shown at once by projecting the intersection S, up to L. 
PRACTICAL DIFFICULTIES. 
Now, while this diagram is remarkably complete in showing all 
of the intricate relations existing between the quantities of the 
problem, very clearly and perfectly, there are numerous objections 
to it, at once apparent from the standpoint of the draftsman who 
must deal with the problem. 
Recalling the five requirements to which the desired solution 
must conform, which were determined upon in the beginning, 
page 42, we see that this diagram does not meet them fully. In- 
vestigating it closely in view of these requirements we have the 
following particulars in which each of them is, or is not, fully met 
by this diagram as now determined. 
I. Any distance between centers may be assumed, but this 
would require plotting the irregular curve FXH, each time the 
inethod is used. Or else the scale each time would have to be 
