After the bomb is placed in the calorimeter, and before the coal is
ignited, readings of the temperature of the water should be taken at one
minute intervals for a period long enough to insure a constant rate of
change, and in this way determine the initial radiation. The coal is
then ignited by completing the circuit, the temperature at the instant
the circuit is closed being considered the temperature at the beginning
of the combustion. After ignition the readings should be taken at
one-half minute intervals, though because of the rapidity of the
mercury's rise approximate readings only may be possible for at least a
minute after the firing, such readings, however, being sufficiently
accurate for this period. The one-half minute readings should be taken
after ignition for five minutes, and for, say, five minutes longer at
minute intervals to determine accurately the final rate of radiation.
Fig. 25 shows the results of such readings, plotted in accordance with
the method suggested. It now remains to compute the results from this
plotted data.
The radiation correction is first applied. Probably the most accurate
manner of making such correction is by the use of Pfaundler's method,
which is a modification of that of Regnault. This assumes that in
starting with an initial rate of radiation, as represented by the
inclination of the line AB, Fig. 25, and ending with a final radiation
represented by the inclination of the line CD, Fig. 25, that the rate of
radiation for the intermediate temperatures between the points B and C
are proportional to the initial and final rates. That is, the rate of
radiation at a point midway between B and C will be the mean between the
initial and final rates; the rate of radiation at a point three-quarters
of the distance between B and C would be the rate at B plus
three-quarters of the difference in rates at B and C, etc. This method
differs from Regnault's in that the radiation was assumed by Regnault to
be in each case proportional to the difference in temperatures between
the water of the calorimeter and the surrounding air plus a constant
found for each experiment. Pfaundler's method is more simple than that
of Regnault, and the results by the two methods are in practical
agreement.
Expressed as a formula, Pfaundler's method is, though not in form given
by him:
_ _
| R' - R |
C = N|R + ------ (T" - T)| (19)
|_ T' - T _|
Where C = correction in degree centigrade,
N = number of intervals over which correction is made,
R = initial radiation in degrees per interval,
R' = final radiation in degrees per interval,
T = average temperature for period through which initial radiation
is computed,
T" = average temperature over period of combustion[39],
T' = average temperature over period through which final radiation
is computed.[39]
The application of this formula to Fig. 25 is as follows:
As already stated, the temperature at the beginning of combustion is the
reading just before the current is turned on, or B in Fig. 25. The point
C or the temperature at which combustion is presumably completed, should
be taken at a point which falls well within the established final rate
of radiation, and not at the maximum temperature that the thermometer
indicates in the test, unless it lies on the straight line determining
the final radiation. This is due to the fact that in certain instances
local conditions will cause the thermometer to read higher than it
should during the time that the bomb is transmitting heat to the water
rapidly, and at other times the maximum temperature might be lower than
that which would be indicated were readings to be taken at intervals of
less than one-half minute, _i. e._, the point of maximum temperature
will fall below the line determined by the final rate of radiation. With
this understanding AB, Fig. 25, represents the time of initial
radiation, BC the time of combustion, and CD the time of final
radiation. Therefore to apply Pfaundler's correction, formula (19), to
the data as represented by Fig. 25.