1909-10.] Illuminating Power of Groups of Pin-hole Burners. 51 
therefore agree with the formulae quoted within the error limit, while the 
other series do not agree, though the only excessive divergence in D is *02, 
for x= L96. It will be observed, however, that the observed and calculated 
values agree in each case except C for the higher values of P, which are 
the more important values. 
A more closely approximate formula for the C, D, and E series of 
observations was found as follows : — Let the ratio of the observed value to 
the calculated value of (P — 1) be w. Graphs were drawn of w against x, 
which suggested an exponential law of the form 
w = ae ~ P( x ~ y) 2 . 
P L3 
3 
Log w was plotted against x, giving parabolic curves ; the maximum point 
was observed from the graph, giving an approximate value of y. (x — y) 2 
was then plotted against log w, and that value of y was selected which 
gave the best straight line. From this straight line, a and 3 were 
determined. P was then calculated from the formula 
P = 1 + (ae~ bx )( ae-P( x -y¥). 
The curves in fig. 3 are the graphs of these latter formulae. 
The following table shows the correspondence between the observed 
values of the illuminating power and those calculated according to the 
above formulae. It will be seen that all the observations are now in 
agreement with the empirical formula. 
