AND VIBRATION OF SHAFTS. 
317 
The following are the results of experiments made (1) with Pulley I. (p. 285), and 
(2) with Pulley II. at the end of the overhanging portion, the ratio of the overhanging 
portion of the span being made to vary. The shaft without the pulley lias been 
investigated in §§ 12, 13 ; whilst the calculated speeds for the pulleys alone have 
been calculated from equation A, § 31, page 313. The calculated speed obtained from 
the formula N^N 2 /-v/(N^^ + Ng®) where N^, Ng are the separate speeds of whirl for the 
shaft and pulley, gives results, in every case, much lower than the observed results. 
To bring the calculated results more in accordance with the observed residts, the 
resulting calculated speed is taken to he N;^N 2 /v^(Ni^ + Ng^a), the vcdue of a deter¬ 
mined from Experiment 64— chosen because the observed and calculated values of the 
lohirling speed for the shaft alone are practically the same (see § 13, page 294, Experi¬ 
ment 24)— being ‘885. In this expression, a is the multiplier of the greatest term in 
the denominator. 
Pulley I. 
Number of 
experiment. 
6 
rt 
P 
Conditions. 
Observed sjH'ed. 
Calculated speed 
for sliaft only (N,). 
Calculated speed 
j for pulley only (No). 
.A 
'C "c, 
S'" + 
^ + 
^ s%. 
£ Slz 
A =« 87 
3 
A 
Corresponding- 
percentage erroi-. 
1 
I 
^ ' ' 
^ ^ + 
g £ ’ 
l-AS ! 
1 
C ' 
P 1 
' 
1 
in 
inches. 
C 
in 
inches. 
1892. 
63 
Nov. 11 
30-70 
1-00 
1223 
1175 
16390 
1170 
+ 4-3 
1246 
- 1-9 ‘ 
1 64 
5> 
29-10 
2-61 
1329 
1.301 
4808 
1256 
+ 5-5 
1329 
0-0 
65 
;? 
28-00 
3-69 
1384 
1397 
3318 
1288 
+ 6-9 
1410 
- 1-9 
' 66 
?? 
26-66 
5-02 
1407 
1516 
2428 
1286 
+ 8-6 
1343 
+ 4-5 
1 67 
24-00 
7-69 
1224 
1704 
1572 
1156 
+ 5-5 
1199 
+ 2-0 
! 68 
1 
55 
21-33 
10-35 
968 
1606 
1162 
941 
+ 2-8 
: 979 
- 1-1 
Pulley II. 
c;_f 
o c 
. 
o B 
0 ) 
Conditions. 
Calculated speed 
for shaft only (N,). 
%'z 
^ "N— 
'S § 
'’ci 
0 ) ^ 
CL. ^ 
(/i ^ 'T 
"CJ S 
^ u 
tf) 0 
a ^ 
C OP 
0 to 
S a « 
'I 0 
'S Cl 
5s* 
Cb 
5s 
5s 
2 ® 
3 
£ 
C3 
P 
1 
in 
inches. 
G 
in 
inches. 
5«. 
30 
0 - 
- 1 ^ c 
d cw ^ 
a A 
P d 
^ a 
d ^ 
0 2 
0 05 
•3 -s, N 
J.--. 
s S . 
2 S-Zi 
s? 
62 
1892. 
Nov. 9 
30-63 
1-00 
1227 
1175 
13816 
1173 
+ 4-6 
1224 
+ 1-4 
57 
n 7 
29-10 
2-54 
1276 
1301 
3353 
1213 
+ 5-0 
1278 
0-0 
58 
„ 7 
28-00 
3-63 
; 1281 
1397 
2277 
1191 
+ 7-0 
1256 
+ 1-9 
59 
• „ 7 
26-66 
4-96 
' 1215 
1516 
1643 
1114 
+ 8-3 
11.50 
+ 5-3 
60 
„ 9 
24-00 
7-63 
i 928 
1704 
1056 
898 
+ 3-2 
937 
- 1-0 
61 
„ 9 
21-.33 
10-29 
712 
1606 
782 
703 
+ 1-1 
738 
— 0 b 1 
These experiments show that the same value of «(-= ‘885) in the formula for the 
