1909-10.] Illuminating Power of Groups of Pin-hole Burners. 47 
observations made. The manometers were read before and after, and 
generally also in the middle of each set of twenty observations, the average 
pressure of each set being taken, for correction purposes, as the pressure at 
which each of the twenty observations was made. This involves no appreci- 
able error, since the variations in pressure from minute to minute were 
gradual, and never more than 1 or 2 mm. of water. In cases where this 
average pressure was not constant from set to set of twenty observations, a 
correction was applied, as indicated later. 
A plan of the arrangement is shown below in figs. 1* and 2 for the case 
of four burners and three burners respectively. B is the centre of the frame- 
work carrying the group of burners, </> is the photometer, and s the standard 
burner. The distance (ps was observed by means of an indicator fixed to 
the photometer block vertically below the centre of the screen. B0 is 
therefore known, and the illuminating power of the group would be given 
by (B (p/<ps) 2 if B^> were infinite compared to the distance of adjacent burners, 
since in that case B could be regarded as the position of the group. The 
above condition is not satisfied in the present case, therefore some point 
must be selected as the position of the group. This point was chosen such 
that, if its distance from the screen be R, (R/(ps) 2 would give an illuminating 
power equal to the sum of the illuminating powers of the individual burners 
on the assumption that the screen was perpendicular to the incident light. 
This assumption is approximately true, since all the angles of incidence are 
less than 3°. Thus if r v r 2 , .... r n be the distances of the individual 
burners from the screen, 
1 VI 2+ ,i\ 
j >2 n \ r ^ + r 2 . ’ r n 2 / ’ 
* In the ease of four burners, the frame was of course placed slightly squint, so as to 
allow 3 and 4 to be visible separately at <f>. 
