AND VIBRATION OF SHAFTS. 
353 
57. Values of 9 in the equation o) = 9 ^(^EI/Wc®); c being the distance of the 
pulley from the nearer heo,ring. 
FaZMes of b = cjl. 
Very 
small 
1 
1 0 
1 
6 
1 i 
Jl 
3 
*> 
Values of a = c/h. 
Superior 
limit 
1^732 
1-907 
2-013 
2-157 
2-356 
3-.303 
•25 
1-677 
1-862 
1-975 
2-129 
2-.340 
3-303 
•50 
1-500 
1-729 
1-867 
2-055 
2-.300 
3-303 
•75 
1-146 
1-523 
1-714 
1-957 
2-250 
3-303 ‘ 
1-00 
0 
1-304 
1 -563 
1-864 
2-203 
3..303 
1-25 
do. 
1-145 
1-451 
1-792 
2-166 
3-303 
1-50 
do. 
1-052 
1-372 
1-741 
2-138 
3-303 
1-75 
do. 
•997 
1-323 
1-705 
2-117 
3-303 
2-00 
do. 
-963 
1-291 
1-680 
2-102 
3-303 
Inferior 
limit 
do. 
-863 
1-185 
1-587 
2-040 
3-.303 
The superior limit thus varies from 2 •21 times the inferior limit (when the pulley Is 
near the bearing) to equality with it (at the centre of the span). 
Moreover, when the span is very long, and the pulley near the bearing, so that cjl 
may be taken to be very small, no whirling can take place provided the radius of 
gyration is less that the distance of the pulley from the bearing. (See also §§ 27, 32, 
37, 41, 42, 52, 53.) 
58. Comparing these results with those obtained in Case X., § 27 (that is, with the 
case of a single span), we see that in the case of three equal spans, the middle one of 
which is loaded, the calculated speed for the pulley alone exceeds that in the case of a 
single span in a certain ratio—that ratio depending on the position and size of the 
MDCCCXCIV.—A. 2 Z 
