[ 279 J 
VIIL On the Wh irling and Vibration of Shafts. 
By Stanley Dunkerley, M.Sc., Berheley Fellow of the Owens College, Manchester. 
Communicated by Professor Osborne Reynolds, F.R.S. 
Received July 13,—Read November 23, 1893. 
Revised June, 1894. 
Table of Contents. 
Chapter I. 
Art. Page. 
I Introduction. Object of investigation.280 
2-6 Experimental apparatus. Method of making experiments. Experimental shafts 
and pulleys.281 
Chapter IT. 
7-8 General theory (as given by Professor Reynolds) .285 
Chapter III. 
Special cases.—Unloaded Shafts. 
9 Case I.—Overhanging shaft fixed in direction at one end.288 
10-11 Case IT.—Shaft resting on a .support at each end. Experimental results . . . 289 
12-13 Case III.—Shaft resting on two bearings and overhanging on one side. Experi¬ 
mental results. 290 
14 Case IV.—Shaft fixed in direction at one end and resting freely on a bearing at 
the other.293 
15-16 Case V.—Shaft resting on three bearings. Experimental results.295 
17 Case VI.—Shaft fixed in direction at each end.298 
Chapter IV. 
Special cases—Loaded Shafts. 
18 Two methods of solution. First method.299 
19 Case VII.—Overhanging shaft fixed in direction at one end and loaded with a 
pulley at the free end, the effects of both shaft and pulley being taken into 
account.299 
20 Case VIII.—Shaft resting on a bearing’ at each end and loaded with a pulley, the 
effects of both shaft and pulley being taken into account.301 
14.8.94 
