930 Dr. C. Chree on the Whirling and 
where. | 
R=M|(a—c)*—4a*(a—c) ) 
— C4 (a—c)*?—3a?(a—c)}— D(a—c) |? 
Be ns 6. tee ane bs a GAG 
+ op[ (a + 6°) + 35 (C?a? + C07) + 3D (a? + Lb?) | 
ES 7 Pein: ser § (26) 
— SG (Cat + C8) + 5 D(a? +b) — SD(Ca? + cy |, | 
Q= [4fa?—(a—c)?} —3{a?—(a—c)*!C+ D]?, | 
S= a {31° — 10ablt— 5a°b7?? + 200503}, | 
the notation being the same as in (¢). 
Omitting & in (25) we obtain the critical angular velocity. 
If, for instance, the spans are equal, and I’ is negligible, we 
obtain 
or 215 ay Ate =) sata 2 
97°55 HI ne [i+ 315 M 2 a) i+ = at }e7) 
opa* air apa a 
Numerical calculations are here simplified by noticing 
that the coefficient of M involves ¢ and a—c symmetrically ; 
this implies that the critical velocity is unaltered when the 
distances of the load from the central and terminal piers are 
interchanged. 
As (27) is based on a displacement which omits the effect 
of the load, we may expect it to prove less exact the larger 
the load. 
§ 31. Table VI. compares the results calculated by Dun- 
kerley from (18), with & omitted, for the critical number of 
revolutions per minute in his shaft, supposed massless but 
carrying one of his pulleys, with corresponding results from 
the simpler formulz (19) and (23). The spans are supposed 
equal. 
w= 

TABLE VI. | 



ClO tees 1/16. 1/4. 1/2. 3/4. 15/16. 



Palley...:) 4 4h II. TW ee Be | ae lee it II. 
Dunkerley 
from (18)...| 31664 | 24173 | 8114 | 4842 | 4987 | 3325 | 6318 | 4288 | 24550 | 18816 


», (19)...| 24760 | 16510 | 7175 | 4784 | 4987 | 3325 | 6284 | 4190 | 19464 | 12978 

5, (28)...| 32676.) DIZVO ne eee? ee teen 
