AND VIBRATION OF SHAFTS. 
293 
Conditions. 
- 
Percentage error being 
, nr\ observed-calculated 
-K- A -■ 
observed 
Number of 
Experiment. 
Date. 
Ratio = ~ . 
Span in 
inches (Z). 
Overhanging 
portion in 
inches (c). 
Observed 
speed. 
Calculated 
speed. 
24 
1892 
Oct. 19 
1 
To 
29-10 
2-91 
1309 
1301 
+ -6 
25 
„ 19 
1 
9 
28-80 
3-20 
1355 
1324 
-P 2-3 
'21 
„ 20 
1 
S 
28-44 
3-56 
1372 
1356 
+ 1-2 
26 
„ 19 
1 
7 
28-00 
4-00 
1435 
1397 
+ 2-6 
28 
„ 20 
1 
G 
27-42 
4-57 
1456 
1448 
+ -5 
29 
„ 20 
5 
•26-66 
5-33 
1472 
1516 
- .3-0 
30 
„ 20 
1 
‘k 
25-60 
6-40 
1545 
1603 
- 2-9 
31 
„ 20 
1 
3 
•24-00 
8-00 
1606 
1704 
- 6-1 
32 
„ 20 
1 
2 
21-33 
10-66 
1558 
1606 
- 3-1 
33 
„ 20 
3 
4 
18-30 
13-70 
1201 
1256 
- 4-6 
34 
„ 20 
1 
16-00 
16-00 
1002 
1031 
- 2-9 
These results show that the calculated speeds are less tlmn the observed speeds 
provided a (that is cjl) be less than one-fifth (which is always the case in practice), 
and in excess for greater values of cjl. In only two cases is the percentage error 
greater than 3 per cent., thus ang^ly verifying the theory. The maximum observed 
speed is when cjl — 1/3, a result which has been shown to follow immediately from 
the equations. 
Case IV. 
14. Shaft, length I resting freely on a support at one end and fixed 
IN direction at the other. 
Thus— 
Fisr. G. 
We have (§ 8, p. 287, equation 7) 
y = A cosh mx -fi B sinh mx + C cos mx -f D sin mx. 
Taking the origin at A, we have, when a; = 0, 
dyidx = 0 ; 
2 /= 0 , 
