AND VIBRATION OF SHAFTS. 
297 
(w/i®) (38a8 _|_ 23a7 - 488a0 - 562a5 + 76a^ - 562a3 _ 488a3 + 23a + 30} 
- 31680 {mlY {Sa^ + - 4a3 + 4a + 3} + 19958400 = 0. 
The following are the results obtained from this equation, the value of ml having 
been calculated for different values of a. 
Value of « = loll]. 
Value of mlj. 
Very small 
3-9003 
—— — or — 
1 9 ’ 8 
3-7620 
1. X or i 
7 J 6 ’ 5 
3-6480 
1 
4 
3-6056 
1 
3-5101 
^ in ^ 
2 CO 4 
3-3282 
f to 1 
3-1416 
The formula is not sufficiently approximate if a > 
When a is very small (< tlie result closely approximates to the result obtained 
for a shaft working in a sleeve at one end, viz. : 
ml = 3-9266. (§ 14, p. 294.) 
16. Experimental Results. 
The following are the mean results, the calculated speeds being obtained according 
to the formulae in the preceding article when the particular value of IJl^ is taken. 
Number of 
Experiment. 
Date. 
Conditions. 
Observed 
speed. 
Calculated 
speed. 
Percentage error being 
observed — calculated 
Ratio iPi 
Shorter 
span (Z 2 ) 
in inches. 
Longer 
span (Z,) 
in inches. 
observed speed. 
1892. 
36 
Oct. 21 
1 
\ 0 
2-91 
29-10 
1942 
1943 
•0 
37 
„ 21 
1 
7 
4-00 
28-00 
2051 
1974 
+ 3-7 
42 
„ 22 
1 
6 
4-57 
27-42 
2035 
2058 
- 1-1 
38 
„ 21 
4 
6-40 
25-60 
2-251 
2307 
- 2-4 
41 
„ 22 
1 
3 
8-00 
24-00 
2500 
2487 
+ -5 
39 
22 
5? 
X 
10-66 
21-33 
3020 
2830 
+ 6-2 
40 
„ 22 
3 
4 
13-70 
18-20 
3873 
3889 
- -4 
3 
May 9 
1 
15-00 
15-00 
5137 
5100 
+ -7 
56 
Nov. 5 
1 
16-00 
16-00 
4390 
4484 
-- 2-1 
2 Q 
MDCCCXCIV.—A. 
