ON THE MECHANICAL EQUIVALENT OF HEAT. 
313 
The equation of velocity is thus approximately expressed by 
0)~0)c\ 
1 + 1 Y cos 2nt + cos 2 {nt - ^-tt) + cos nt 
In the low-pressure engine used in these experiments, the values of the several 
quantities are, the units being linear feet, lbs, seconds. 
I ='126, i = 2-47, r = 0^625, W = 200 , rW = 125, U = 1650, 
Ty = 0-0049, 
U 
81^ 
148 
W ’ 
rW _ 90^ 
whence, substituting 
OJ 
148 
= coq (1 -f- 0-0049 cos 2 wq^ -f- cos 2 ^ 
TT \ 90 
3 / ^ ’ 
from this the approximate joint error can be found. But it is sufficient here to 
show that the individual errors are negligible. 
The first o’ives an error in the mean moment 
O 
± M (rV < 0-000024). 
The second and third are inversely proportional to N-*-, if N is 300, which is the 
lowmst value. 
The second error is between 
The third 
± M < 0-0000025). 
± M(«32 < 0-0000001). 
These are all negligible quantities, and, as the corresponding effects in the high- 
pressure and intermediate engines, owing to the cranks being set at angles of 60 , 
would only be to compensate those of the low-pressure engine, the greatest error 
would not exceed 4 000 'oth part. 
9 . Besides the errors resulting from the terminal differences in the moment of 
momentum of the water and the fluctuations of speed in the engine, error in the 
measurement of the work may arise from imperfect balance of the brake, from the 
frictional resistance of the automatic gear, from unequal resistance in rising and 
falling of the piston of the dash-pot, and from the end oscillation of the brake. 
2 s 
VOL, CXC.—A. 
