274 
PROFESSOR OSBORNE REYNOLDS AND MR. J. H. SMITH ON A 
area of the specimen, then the compressive stress in the specimen at the upper end 
of the stroke is ecpial to 
W or R / _ R\ _ W 
(j A \ L ) A 5 
and the tensile stress at the lower end of the stroke to 
AY or R 
S' A 
i+!)+?• 
The range of stress is equal to the sum of these, or is equal to 
2 W or R -4- gA. 
The values of W, the weights of the vertical loads used below the specimen, were 
determined to one hundredth of a pound, and were as- follows :— 
Spindle and lock-nut 
. . 6T5 
one weight 
. . 12-42 
two weights . 
. . 18-69 
three ,, . 
. . 24-96 
four ,, . 
. . 31-23 
five ,, 
37"50 
six ,, . . 
. . 43-77 
The error in the determination of the stress due to the maximum error in the 
estimation of these weights would not in any case exceed '3 per cent. 
The throw of the crank was measured to a ten-thousandth of an inch, the value 
obtained being ’5067 inch. The maximum error in this measurement would not 
affect the stress by more than *1 per cent. 
The areas of the specimens were determined by finding their diameters by means 
of an ordinary micrometer gauge which was graduated to ten-thousandths of an inch. 
Assuming that the greatest error in actual measurement would not be more than 
three ten-thousandths of an inch, then the error from this cause for a specimen 
\ inch diameter would not exceed ’25 per cent. 
It is thus seen that the errors incurred in the estimation of AAfi R and A are 
negligible. 
There are three sources of errors in the estimation of the angular velocity. They 
O J J 
are— 
(1) The variation due to fluctuation in the energy of the parts; 
(2) The variation due to fluctuation of the velocity of the engine in a cycle ; and 
(3) The variation due to the fluctuation of velocity over a long interval arising 
from the difficulty of regulating the motive power. 
