AND VIBRATION OP SHAFTS. 
283 
and 
h — height of liquid, from level of still water, measured in inches. 
The scale was graduated for every 100 revolutions per minute. 
The hearings in which the experimental shaft ran consisted of brass castings of 
L section with their bottom faces planed. They wmre bored at exactly t-he same 
height as the headstock, and the length of the bearings was about an eighth of an 
inch. The deflection of the shaft, when whirling, was limited by tlie use of guard 
rings, which consisted merely of ordinary bearing castings bored to a slightly larger 
diameter than the diameter of the shaft. 
The motion wars transmitted from the shoulder end of the headstock spindle to the 
experimental shaft by means of a piece of steel wore (about 1|- inch long and 
21 B.W.G. diameter), one end of wdrich was soldered into the end of the shaft, the 
other end being soldered into a piece of brass coned to fit into the headstock spindle. 
By this means the shaft was subjected to very little constraint. * 
The headstock spindle was driven from a turbine which was 20 yards away 
from the experimentalist’s bench. The motion wms transmitted through 140 feet 
of quarter-inch cotton rojre, the rope ascending vertically from the turbine and 
descending vertically to the headstock spindle. The admission of wmter to the 
turbine was controlled by a hand-wdreel close to the apparatus, by wdrich an almost 
indefinitely fine adjustment of the speed of the turbine could be made from 200 to 
2000 revolutions per minute. By having speed-pulleys on the turbine shaft and 
headstock spindle, a range of speed of from 100 to 10,000 revolutions per minute of 
the headstock spindle was obtained. 
3. In taking the number of revolutions corresponding to any period of whirl, an 
ordinary counter pushed into the end of the headstock spindle was used. The 
whirling speed was taken to be at the commencement of wdrirl, that is to say, at the 
lowest speed at which the shaft definitely whirled. Headings were taken, in each 
trial, over a period of from 3 to 5 minutes, the speed (if it varied from some cause) 
being kept constant by means of the valve regulating wheel. The constancy of speed 
was shown by the steadiness of the liquid column of the indicator. In making any 
experiment three trials were made, and the mean of the results taken. 
In all ckses the theoretical speed was unknown when the actual whirling speed was 
obtained. 
4. The headstock spindle was originally driven by hand. This was accomplished 
by means of two cast-iron speed pulleys turning on pins bolted to the twm ends of a 
cast-iron bracket, the bracket being bolted to the headstock. By running from a 
large pulley on the hand-wdieel to a small one on the second wheel, and from a large 
pulley on the second wheel to a small one on the headstock spindle, a very high speed 
2 o 2 
