54 
Proceedings of the Koyal Society of Edinburgh. [Sess. 
The greatest observed increase in illuminating power was in all cases 
30 per cent, roughly, 1*31 being the average of the various values obtained. 
Groups of three and four Burners. 
The procedure was on the same lines as in the case of the two burners, 
the arrangement being as in figs 1 and 2. The possible error of observation 
was assumed to be 1 per cent, as before, and no pressure corrections were 
necessary. The results are given in Tables III. and IV., and are plotted in 
figs. 4 and 5, pages 54, 55, for the three and four burners respectively. 
Fig 4 
The graphs in each case suggested a law of the same form as the law 
connecting w and x given above, namely, 
P x = 1 + ae~ b[x ~ c)2 , 
the constants a, b, c being obtained in the same manner as a, 3, y were ob- 
tained above. Tables III. and IV. contain the values of P calculated accord- 
ing to the above formulae, also the values of the constants. In every case 
except series C of the four-burner observations, it will be noted that the 
observed and calculated values agree for the larger values of P, but do not 
agree for the smaller values. 
A more closely approximate formula for P was obtained as follows : — 
Let the ratio of the observed to the calculated values of (P —1) be w, as 
