58 
Proceedings of the Royal Society of Edinburgh. [Sess. 
due to slight inclinations of the burners themselves, were reduced as far as 
possible by wedges inserted under the burners. Again, when the mutual 
distance of the burners was less than l - 5 cm., the flames became smoky 
at the top, and the light emitted assumed a ruddy hue. This ruddiness, of 
course, made it difficult to use the photometer accurately, since the standard 
burner emitted white light. When the burners were very close together — 
say less than 1 cm. apart — the smokiness increased so much as to make the 
atmosphere quite stifling before the observations were completed. Thus 
the atmospheric conditions gradually changed during the course of an 
experiment. The only series of observations in which the small distances 
were worked with last was series A of the four-burner observations. Here, it 
will be observed, there is the smallest maximum value of P, and it occurs at 
a smaller value of x than in the other sets. 
Writing the general formula 
l'=l 1 + Al 1, 
I hi 10” i 
the values of a, b, c, l , m, n are collected in the following table : — 
Table V. 
a. 
b. 
c. 
l. 
TO. 
n 
Series A, 3 burners . 
•38 
4*9 
IT 
13 
8 
10 
,, B, 55 
•36 
6-7 
IT 
9 
2*5 
6 
Average .... 
•37 
5-8 
IT 
11 
5 
8 
Series A, 4 burners . 
•30 
5-8 
1-06 
17*3 
1 
9 
13 
„ B, „ . . . 
•32 
5T5 
1T9 
11 
1-5 
9 
n 
99 99 
*45 
53 
1T0 
8*4 
2 
6 
3) ^3 33 
•34 
5*6 
1T3 
9 
1*2 
7 
Averages for 4 burners 
•35 
5-45 
1T2 
11 
3-7 
9 
Averages for B, C, D 
•37 
5*35 
1T4 
9-5 
T 6 
7 
So far as turning values and inflexion points are concerned, the simpler 
formula P = 1 + ae ~ i(x ~ c] 2 will suffice, for the remaining factor in the full 
formula is unity until x is greater than 2 cm. Hence column a in Table Y. 
gives the maximum increase in illuminating power, while column c gives 
the corresponding distance of adjacent burners in centimetres. 
