Determination of the "Null Point" and an alternative Method of calculating the Results.
As stated in the introduction we append a full analysis of the "null point" i.e., the point at which the radiation is self-eliminated.
Using a similar notation to that on p. 478, we have as the equation of condition
where the temperatures are measured from that of the surrounding envelope.
For the sake of simplicity we can assume that the values of and remain constant.
Integrating and putting , and determining the constant from the fact that when , we obtain the equation
If there had been no radiation, , and the equation of condition would have been .
Integrating, and using the same constant as before
If we find the points of intersection of (2) and (3) one point is that at
which the experiment commenced, the other is the point on (2) at which the
radiation is eliminated.
It is more convenient, for experimental work, to obtain an expression involving
rather than ; substituting therefore the value of given by (3) in (2), we obtain
This equation can be solved for when the values of are known.
In order to obtain , we can take the following observations: Commence an experiment at , note the time when , and again note the time , when .