44 KANSAS UNIVERSITY QUARTERLY. 
\ 
i 
9 i, We cs | 
R—r : ; an Oh ey aoe 2 ene 
SIN 0 SS 8 | 
(2 
d \ hs 2) 
This is the equation for the relation between the two radu, length 
of belt, and distance between the centers of the shafts. It is trans- 
cendental, and plainly of such a form as to be of no value for 
direct use in working to the desired result. It serves merely to 
show the relation existing between these quantities, and the difh- 
culty of attaining the desired form of solution. 
CASE II—-CROSSED BELTS. 
Fig. 2 shows the other general case, that of crossed belts. 
Bien 2) 
Treating this in the same way as the other case, we have for the 
half length of belt: 
l= _RyaRtd cos a+ : rtar, 
the sign of the last term being positive instead of negative as before. 
And, here, 
: Rr 
sin o==——_——_ 
d 
and 
Tf Mier = eR = 
cos a—- Omran ile 2 
a d (R-r)?. 
From which we have 
rs 
l==dcosna He a a)(RY ry: (3) 
