AND VIBRATION OF SHAFTS. 
339 
48. Values of 0 in the equation of oj = 6 ^f(qVl|^vc^), c being the distance of the 
‘pulley from the nearer shoidder. 
Values of h — c/l. 
Very 
small. 
1 
1 0 
6 
1 
4 
1 
3 
r 
2 
o 
II 
e 
Cc 
Superior 
limit. 
3-464 
3-466 
3-478 
3-5-28 
3-674 
4-899 
•25 
3-437 
3-440 
3-453 
3-508 
3-651 
4-899 
•50 
3-356 
3-363 
3-382 
3-451 
3-627 
4-899 
75 
3-225 
3-240 
3-272 
3-366 
3-577 
4-899 ' 
1-00 
3-048 
3-082 
3-135 
3-266 
3-521 
4-899 
1-25 
2-841 
2-901 
2-981 
3-197 
3-467 
4-899 
1-.50 
2-628 
2-824 
2-856 
3-076 
.3-419 
4-899 
1-75 
2-437 
2-594 
2-743 
3-001 
3-379 
4-899 
2-10 
2-282 
2-479 
2-653 
2-941 
3-.346 
4-899 
Inferior 
limit. 
1-732 
2-028 
2-277 
2-667 
3-182 
4-899 
It will be noticed that when the span is very long and the pulley near the shoulder, 
so that cjl may be considered very small, the whirling speeds, for the same sized 
pulleys, are the same as those obtained in Cases IX. and X., §§25 and 36—the value 
of c being the same in all three cases. 
The superior limit varies from twice the inferior (when the s])an is long and the 
pulley near the shoulder) to equality with it (when the pulley is at the centre of the 
span). 
49. Comparing the results contained in the previous article with those under 
Case XII., §§ 36, 37 (that is with the case of a shaft working in a shoulder at one end 
and resting freely on a bearing at the other), we see that in the case where both ends 
2x2 
