60 
Proceedings of the Koyal Society of Edinburgh. [Sess. 
numerical data there is a regular gradation as we pass from the two to 
the four burners. 
Starting with a group of several burners a large distance apart from 
each other, the illuminating power in all cases slowly increases, then begins 
for x = about 2 cm. to increase more rapidly, passes through an inflexion 
point, comes to a maximum, and then decreases. This suggests that there 
are two main factors acting, one tending to increase the illuminating 
power, the other tending to decrease it. Suppose there are burners 1, 2, 3, 
4 present, and consider 1. 2, 3, 4 will increase the heat and the draught, 
and therefore cause 1 to burn better, by increasing the supply of oxygen 
and the temperature. But 2, 3, 4 will also diminish the supply of oxygen 
available for 1, since they also need oxygen to burn. The first factor seems 
to be the important one for the larger values of x, and always preponderates 
(since there is never a decrease in illuminating power), but begins to lose 
its relative importance when the distance becomes very small. Taking 
such factors into account, the curves show that when the flames are very 
close together the second factor is rapidly approaching the first one in 
importance, but whether it ever overtakes the first one is not evident from 
the graph. For instance, the completed curves (see figs. 4 and 5) might 
very well cut the P axis below P = 100 rather than above. 
The data for turning values are consistent with the two causes suggested. 
Starting with the burners far apart from each other, we should expect the 
needs of the other flames to come into relative importance sooner with the 
three and four burners than with the two burners, and hence the turning points 
to come sooner ( i.e . further from the origin). And since the draught and the 
heating effect of the other flames, the predominating factors, decrease with 
the distance from the origin, the maximum increase should be less for the 
three and four than for the two burners. Again, the two do not outline a 
space, while the three and four do; therefore, for small distances, the three and 
four burners should suffer more from the second cause than the two burners 
would be expected to do. For those parts of the streams of gas that are 
being supplied with oxygen from inside the volume outlined will burn less 
readily than those parts outside the volume. For the three and four burners 
(see figs. 1 and 2) the fractions of the streams are ^g° 0 and respectively, 
or J and This fraction approaches a limiting value J when the number 
of burners is increased indefinitely ; therefore, on this reasoning, we should 
expect the second cause to increase asymptotically to its limit. If parts of 
the gas are not being properly supplied with oxygen, we should expect the 
flames to be smoky. The two-burner flames were not very smoky, though 
for small values of x the light showed a tendency in this direction, being 
