1909-10.] Illuminating Power of Groups of Pin-hole Burners. 49 
For a group of 2 burners : h= +x 2 /Sr 
l 3 „ k=+-2887x-^ 
or 
where x is the distance of the adjacent burners and r the distance B 0. 
To correct for small variations in pressure, preliminary experiments 
were made, from which a curve was obtained giving the variation of the 
illuminating power throughout a small range of pressure. Again, some 
observations were spread over several days. Here the additional precaution 
was taken of repeating the last observation of each day on the next one. 
When the burners in the group were moved apart from each other more 
and more, the illuminating power was found to decrease and to approach a 
constant value asymptotically. Practically, it was constant for values of x 
greater than, say, 6 cm., and therefore this constant value was taken as unity 
in any one group of observations. Of course the constant value will vary 
from group to group of observations, depending on the pressure selected, the 
number of burners, atmospheric conditions, etc. 
Group of two Burners. 
In the experiments with this group, the burners were placed on the rod 
of the frame parallel to the screen, in positions 1 and 2 in fig. 1. The results 
of five series of observations are given in the following table, and are plotted 
in the diagram fig. 3 on page 51. The relative positions of the plotted points 
suggested an exponential law of the form 
P = 1 + ae~* x 
where P is the illuminating power expressed in terms of the constant 
illuminating power for large distances, x the distance of adjacent burners, 
and a and b constants. The values of a and b were found by plotting log 
(P — 1) against x, and drawing straight lines among the points obtained. 
The values of these constants, and the values of the illuminating power 
calculated by aid of them, are included in Table I. 
The possible error in <ps (fig. 1) was roughly found, by a small number 
of repetitions of the observations, to be about T4 cm. when x = 'S cm., and 
about TO cm. when x = 8*9 cm. Hence, by interpolation, the possible error 
in > which will also be the possible error in ^ ^ > is found to vary 
from -6 per cent, to *9 per cent., corresponding in each case to a possible 
divergence of '01 in P. When the pressure is not so constant as usual, the 
error will, of course, be slightly greater. Series A and B of the observations 
VOL. xxx. 4 
