522 Dr. C. Chree on the Whirling and 
with those obtained from (3). The large difference between 
the observed values answering to the values 1/3 and 1/2 of 
c/l and those calculated from (14) is to be ascribed to the fact 
that the type ot displacement assumed in (7) answers more 
nearly to a higher harmonic than to the fundamental vibration. 
This serves to illustrate a contingency which must never be 
lost sight of when applying Rayleigh’s method. We know 
from his general theory that the value so calculated for k can 
never be too low—excluding of course errors of caleulation— 
so that when results have been obtained from more than one. 
assumed type of vibration we need never be at loss which 
to prefer. | 
§ 25. Table V. compares the results observed by Dunkerley 
in a shaft carrying a pulley with those variously calculated. 
Taste V.—Loaded overhanging Shaft, critical speeds. 
ar 
| Calculated speeds from 
U e¢ Observed 







— *\inches. inches. speed. | _. = . a 
| / |} ()&(5)by |} © | (fF) | @ | @ 
| | | Dunkerley. | (12). | (14). | (20). | (25). 
30:70 | 1:00 | 1223 1970. 4 | 1215 
1342 | 


(29-10 | 261 1329 | 1256 
| 

, [28:00] 369) 1384 (1288) [1678] | 1385 
- | 9666 | 5:02) 1407 (1286) |(1578) | 1454 [1839] | 1394 
(24:00) 769 1224 1156 1267 4 1229 
/21:33 /10°35 968. | 941 971 | (1073 
}30-63 | 1-00} 1227 | - 18 | 1220 | | 
99:10 | 254 1276 | 1213 | (1416) 
! 
ry |2800| 363 1281 (1191) [1473] | 1811 [1927] | 
- 19666 | 496 1215 |- (1114) | 1280 |(1326) / 1200 
(2400 763 928 s9s | «(947 | (944 
/21-:33 |1029 | 712 705° 1 EET | | 
| 
i | | 


Calculated results differing widely from the observed are 
put in [ ] brackets ; those whose divergence is less but still 
conspicuous are put in ( ) brackets. When c/l is small all 
the formule necessarily supply results which approach closely 
to those for an unloaded shaft. 
When there is a conspicuous difference between observed 
and calculated values, the latter, in accordance with Rayleigh’s 
principle, are invariably the larger, except in the case of 
Dunkerley’s own calculations. 

