ON THE MECHANICAL EQUIVALENT OF HEAT. 
339 
The dead load on the scales, including the empty tank, came to 340 lbs., about, 
and between this and 2200 lbs. the scales would weigh any quantity with the lever 
swinging to O’Ol lb. 
The weights to which the scales had been adjusted were then exclusively used on 
the brake. Thus the brake was balanced by the same w'eights as were used as the 
standard in weighing the water, with a sensitiveness which gave the error less than 
ojie forty-thousandth part of the weight of water in the smallest trials, while the 
casual error, which would not exceed this in a single weighing, would be eliminated 
in the mean of a large number of w^eighings. Thus the relative limits of error in 
weighing would not exceed ’000025. 
llie Correction for the Weight of the Atmosphere. 
41. The balances being made in air it is necessary to add the weight of air 
displaced in each case. 
As the relative weights only are concerned, if is the weight of a unit volume of 
air, that of water, and that of cast-iron, the weights in air of unit masses 
are :— 
1 - D„/D,, .... for water, 
1 — Da/D^ .... for cast iron. 
The load on the brake is therefore subject to the correction expressed by the factor 
(i _ D„/l-)i), wdiile that of the water balanced against cast-iron weights, has the cor¬ 
rection factor 
1 - W/W 
1 - D„/D„ ’ 
and the relative correction for the actual weight of water, as against the load on the 
brake in air, is 
I / ! — or approximately 1 -j- p—, 
/ \ Hk)/ ^10 
for the temperature 67° Fahr., D« = 0*0752, = 624. 
Hence, the relative correction factor for the equivalent 
(1 - 0*001205). 
