284 
MR. S. DUNKERLEY ON THE WHIRLING 
was attainable. The motion was naturally unstead}^, and available only for short 
periods, whilst an additional observer was required. By driving the shaft from the 
turbine a practically constant steady speed was obtained, and the increased duration 
of the trial considerably reduced the personal errors with the counter. Moreover, by 
an arrangement for regulating the turbine valve at the bench, the action of the shaft 
could be carefully observed whilst the speed was increased, and so personal errors in 
determining the precise moment of whirl reduced to a minimum. 
5. The EXPERIMENTAL SHAFT was of cast steel. It was 32’18 inches long, and 
•2488 inch diameter. The greatest variation in the diameter was lo.oo M^s of an 
inch. It was turned by Mr. Thos. Forst^R of the Whitworth Engineering Laboratory, 
Owens College, Manchester, to whom the author is indebted for the preparation of 
the greater part of the experimental apparatus. 
The shaft v/eighed 200'2 grins., or ’4414 lb. The weight per foot run was ’1646 lb. 
The determination of E (Young’s Modulus), or rather El (I being the geometrical 
moment of inertia of the cross-section about a diameter), w^as accomplished as 
follows :—The experimental shaft was placed in bearings, 2 feet 8 inches apart, and 
loaded at the centre. The deflection was measured by means of a micrometer, the 
distance measured being taken between the top of the shaft and the bottom of a pin 
fixed in one of tlie guard castings. 
The mean of the results so obtained Mves for the 
o 
Value of El = 36‘554 
„ E = 4,028,200,000, 
the gravitational system of units being employed. 
[Note. —The value of E expressed in pounds per square inch 
is 27,974,000]. 
6. The EXPERIMENTAL PULLEYS Were of brass and of the 
section (fig. 2). 
The moment of inertia taken (for a reason wdiich will appear 
later) is 
A - B, 
where A, B are the mass-moments of inertia about the axis of 
the shaft, and about a diameter passing through the centre of 
gravity of the pulley perpendicular to the axis—both moments 
being expressed in gravitation units which, it may be remarked, 
are the ones adopted throughout the investigation. 
