316 
MR. S. DUNKERLEiT ON THE WHIRLING 
Values of 0 in the Equation w = 6^{(jVAjWe^), c being the length of the overhanging 
'portion. 
1 
( 
Values of h — cjl. 
V ery 
small. 
1 
1 O' 
1 
8* 
6 • 
5 * 
■i* 
Very 
large. 
II 
05 
Superior 
limit 
1-732 
1-905 
1-942 
2-000 
2-043 
2-103 
3-464 
•2.5 
1-677 
1-857 
1-897 
1-956 
2-000 
2-062 
3-422 
•50 
1-.500 
1-712 
1-756 
1-822 
1-871 
1-938 
3-356 
•75 
1-145 
1-456 
1-512 
1-595 
1-653 
1-7.32 
3-225 
i-oo 
0 
1-111 
1-188 
1-297 
1-370 
1-464 
3-048 
T25 
do. 
•837 
•920 
1-037 
1-116 
T217 
2-841 
T50 
do. 
•706 
•782 
•889 
•963 
1-058 
2-628 
1-75 
do. 
•644 
•713 
•812 
•880 
•968 
2-437 
2-00 
do. 
•809 
•674 
•769 
•832 
•923 
2-282 
Inferior 
limit 
do. 
•522 
•577 
1 
•665 
•707 
•774 
1-732 
Conipaiing these results with those in Case X., § 27, it will he noticed that ndien 
the span is very long and the pulley near the bearing, so that cjl is very small, the 
whirling speeds in the two cases are the same for the same values of c/Z;, whether the 
2 )ulley be placed between the bearings, or overhang an equal distance on one side. 
For any other value of cjl, the superior limit in the present case is greater, and the 
inferior limit less, than the corresponding limit in Case X., the values of c and I being 
the same in both cases. 
In the present case the superior limit varies from 3’65 times the inferior limit to 
twice that limit (when cjl = co, i.e., the shaft works in a shoulder at one end). 
33. E3cp)eriniental Results .—The same remarks apply here as in ^ 28, page 310. 
