hat the
maximum temperature was reached by the thermometer slightly over one
minute after the time of firing. If this period between the time of
firing and the maximum temperature reported was exactly one minute, the
radiation through this period would equal the radiation per one-half
minute _before firing_ plus the radiation per one-half minute _after the
maximum temperature is reached_; or, the radiation through the one
minute interval would be the average of the radiation per minute before
firing and the radiation per minute after the maximum. A plotted chart
of temperatures would take the form of a curve of three straight lines
(B, C', D) in Fig. 25. Under such conditions, using the notation as in
formula (19) the correction would become,

2R + 2R'
C = ------- + (N - 2)R', or R + (N - 1)R' (20)
2

This formula may be generalized for conditions where the maximum
temperature is reached after a period of more than one minute as
follows:

Let M = the number of intervals between the time of firing and the
maximum temperature. Then the radiation through this period will be an
average of the radiation for M intervals before firing and for M
intervals after the maximum is recorded, or

MR + MR' M M
C = ------- + (N - M)R' = - R + (N - -)R' (21)
2 2 2

In the case of Mr. Peabody's deductions M was found to be approximately
2 and formula (21) becomes directly, C = R + (N - 1)R' or formula (20).

The corrections to be made, as secured by the use of this formula, are
very close to those secured by Pfaundler's method, where the point of
maximum temperature is not more than five intervals later than the point
of firing. Where a longer period than this is indicated in the chart of
plotted temperatures, the approximate formula should not be used. As the
period between firing and the maximum temperature is increased, the
plotted results are further and further away from the theoretical
straight line curve. Where this period is not over five intervals, or
two and a half minutes, an approximation of the straight line curve may
be plotted by eye, and ordinarily the radiation correction to be applied
may be determined very closely from such an approximated curve.

Peabody's approximate formula has been found from a number of tests to
give results within .003 degrees Fahrenheit for the limits within which
its application holds good as described. The