ON THE MECHANICAL EQUIVALENT OF HEAT. 
315 
The Work done in the Brake hy End Play in the Shaft. 
The clearance in the brake-case would allow of nearly g^-inch end play along the 
shaft; and when the brake is running, owing to the slight end play of the engine- 
shaft, there is at times a slight backwards-and-forwards movement, in the period of 
the engine, of the brake-case on the shaft, but not more than the 64th of an inch at 
the greatest. This end play, when it existed at 300 revolutions and 1200 ft.-lbs. load, 
could alwa^'s be prevented by an end pressure on the case of < 50 lbs. Hence the 
limit of work done on the brake is <2 X 50/12 X 64 — 0T3 ft.-lb., which, 
compared with the work in one revolution with a load of 1200 ft,-lbs., is 
0-13/1200 X 27t — 0-000017. This would be the limit if the error is proportional 
to the load, while, if constant, the error on the difference of two trials would be 
zero: so that the greatest relative error is less than 
-f 0-0000L7. 
The Error from the Dash-Pot. 
Since the piston is suspended freely in the oil-cylinder, and the resistance of the 
oil is viscous and expressed by yvs j a, where /x is the coefficient of viscosity, v the 
velocity of the piston, s the area of surface, and a the distance between the surfaces, 
the total resistance is thus ys/a multiplied by the total displacement (which 
never exceeds O'l ft.) divided by the time (3600 seconds). This is infinitesimal. 
Besides which, with 1200 or 600 ft.-lbs. load at 300 revolutions, the lever remains per¬ 
ceptibly steady, there being no vertical vibration perceptible to the finger on the 
lever. Hence, as long as there are no oscillations, the limit of error from the dash-pot, 
if any, is imperceptibly small. 
The only circumstances under which the lever oscillates is when the water flowing- 
through is less than about 4 lbs. a minute ; then a slow oscillation appears, the lever 
moving some half-inch, which causes the automatic gear to lean on the fixed support, 
and may cause a small error. 
The Development of the Thermal Measurements. 
The appliances were originally designed, in 1887, solely for the purpose of the 
study of the action of steam in the engines, and certain problems in hydraulics and 
dynamometry, without any intention of their being used for the purpose of measuring 
the heat equivalent of the work absorbed, but rather the other way. 
It was, of course, obvious that, as the primary purpose of the brakes was to aflord 
accurate measurement of the work spent in heating water, it was only necessary to 
measure the change of temperature of the water between entering and leaving the 
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