ON THE MECHANICAL EQUIVALENT OF HBAT. 
341 
negligible, and it would seem to be an open question whether the standard condition 
of water, as regards capacity for heat, does not involve the inclusion of this air. But 
the indirect effect of such air on the heat necessary to raise water from normal 
temperatures to near the boiling-point, is by no means negligible. 
It does not appear that any definite study has hitherto been made of this effect; 
but it is a matter of common observation that as water reaches a temperature some 
40° Fahr. below the boiling-point, bubbles appear on the sides and bottom of the 
vessel, which gradually increase in size and rise to the surface, increasing rapidly in 
size as they rise. The bubbles are usually referred to as bubbles of gas or air. But, 
a moment’s consideration will show that, although the air or gas is the immediate 
cause of the premature formation and subsequent expansion of the bubble, it is none 
the less certain that the space occupied by the bubble is filled with saturated steam 
at the temperature of the water, the function of the air being merely that of 
balancing the excess of pressure of the surrounding water over the pressure of the 
saturated steam. 
It thus appears that every bubble so formed represents a quantity of heat wliich 
is the latent heat of the volume of the saturated steam in the bubble over and above 
the heat of the weight of water in this steam. 
Thus, if bubbles of air exist in water at a temperature of 212° Fahr., the weight 
of air per lb. of water being a, 0’0000323, and p the pressure, in inches of mercury, 
of the water, then, since the pressure of the air is p — 30, and the volume of 
1 lb. of air at 212° Fahr. under 30 inches of mercury is 16'9 cubic feet, the volume 
of air per lb. of water is 
or, p = 40, 
16-9 X 30 
p - 30 
X a, 
V = 507 X a. 
This is the volume, in culnc feet, of saturated steam at 212°; whence, since the 
latent heat per cubic foot is 36’6 at 212°, the excess of heat will be per lb. of water 
V X 36-6 = 1855 X «, 
and this, divided by 180°, gives a relative error 
10‘31 X a. 
If «, = 0‘0000323, the error is 
0’00033, or 0‘033 per cent. 
The water, after being exposed to the atmosphere in the service reseiwoir, where it 
discharges any excess of air, enters the brake cold with this normal air, there it is 
