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• PROFESSOR OSBORNE REYNOLDS AND MR. J. H. SMITH ON A 
means of a telescope and mirror, so arranged as to bring the images of the two 
columns next to each other. The fluctuations of velocity of the engine and the 
machine could thus he easily compared, and any slipping at once detected. 
It was found that, using this method of regulation, the fluctuations of velocity of 
the machine and engine corresponded with one another, and that the fluctuation 
could be kept within very small limits, namely, about Tth per cent. A certain 
amount of experience was necessary to ensure this steady motion for a long period, 
as in varying the water passing out of the brake, a little too much either one way or 
the other, oscillations of speed were set up which took some time to die away. It 
was also found that the reading of the two speed indicators did not correspond at 
once when the machine was started after a period of rest, but that after a few 
minutes’ run they settled down to corresponding positions. 
The telescope and mirror were discarded after some time, but the speed indicators 
were occasionally checked in each experiment. Mr. Joseph Hall, the engine 
attendant in the Whitworth Engineering Laboratory, soon became quite expert in 
keeping the variations of speed within surprisingly narrow limits, even when an 
experiment extended over seven or eight hours without a stop. 
The author often found it impossible to be in attendance the whole time occupied 
by long tests, and in such cases the machinery was left in charge of Mr. Hall. The 
author found that he could leave the apparatus in his charge with the utmost 
confidence. 
The maximum error in the determination of the stress, due to errors in the 
measurement of co, is finally estimated at '3 per cent. 
Modes of Vibration of a Specimen. 
The specimen may vibrate during a test in three ways, longitudinally, transversely, 
and torsionally, and it is important that, either the periods of the free vibration of 
the specimen do not coincide with the period of any unbalanced force in the machine, 
or that the vibrations are prevented from taking effect by the use of suitable guides. 
The central cylindrical part of most of the specimens was half an inch long and 
'25 inch diameter. The greatest load suspended from it was 43 77 lbs., and the 
smallest 1 2'42. Taking 30 X 10 6 as Young’s modulus for mild steel, the number of 
longitudinal vibrations per minute was calculated and found to be between the 
limits 130,000 and 50,000 approximately. 
The highest speeds at which the machine was driven with the greatest and least 
loads were 1,800 and 2,500 revolutions per minute respectively. It is thus evident 
that the free period of the longitudinal vibration of the specimen can never coincide 
with, or be any simple multiple of, the speed of the machine, and hence can never 
coincide with any periodic force arising from the imperfect balancing of the moving 
