46 KANSAS UNIVERSITY QUARTERLY. 
Rose’s ‘‘Complete Practical Machinist,” gives a rule for the radius 
of a circle arc upon which the middle of the steps of the cone will 
lie, in terms of the length of belt. This necessitates calculating 
the length of belt for the first, or assumed radu, which is difficult 
except for cones just alike, with an odd number of steps each. 
Then when this is done there is no means of obtaining another 
pair of radii for the same belt, which shall be in predetermined 
ratio, except tentatively. 
Rankine’s ‘‘Applied Mechanics,’ page 457, uses approximate 
equations. Wholly unsatisfactory. 
Weisbach, Vol. III, page 262; approximate equations. 
Kent’s ‘‘Mechanical Engineer’s Pocket Book,” page 874, gives 
an approximate graphical diagram. Not satisfactory in view of 
the five requirements discussed. Also gives approximate analytical 
treatment. 
Robinson’s ‘‘Principles of Mechanism,” page 247, an approxi- 
mate graphical method. Diagram inconvenient in use. 
Reuleaux’s ‘‘Constructor,” H. H. Suplee translator, page 189. 
A non-approximate graphical treatment of great interest. The 
final figure, offered as a permanent working diagram for all cases of 
cone pulleys, approaches very nearly to an entirely satisfactory 
form. It, however, embodies two objections: rst. A permanent 
diagram, with an irregular curve, does not appear to be as desira- 
ble as a simple construction which can be performed at any time 
from memory for any particular case; 2d. Unless the cones are to 
be alike, and have an odd number of steps, so that the radii of the 
middle pair of steps may be the assumed radii, with ratio 1:1, it is 
impossible to find the position of the reference line from which the 
other radii are to be determined for this length of belt, except 
tentatively. : 
? 
Of all the methods examined, however, the graphical treatment 
of Reuleaux presents by far the greatest possibilities. Follow- 
ing this very closely, with all the desirable features of a complete 
treatment constantly in mind, it developes that by a slight yet 
very essential modification at the close of the discussion the desired 
method may be had in full. 
It will be necessary, therefore, to follow the Reuleaux analysis, 
with no deviation whatever, up to the final step, where, by a spe- 
cial modification of the last figure, the clue to the new method is 
found. 
