52 
Proceedings of the Royal Society of Edinburgh. [Sess. 
Table II. 
Distance between 
Adjacent Burners 
(x). 
Illuminating Power. 
Observed. 
Calculated (P). 
Series C. 
10= lT2e~ 6 ’ 2(x ~' 94)2 
P = 1 + *0048e 
— 6‘2a: 2 +10‘3a; 
*77 cm. 
•98 „ 
1-14 „ 
8-53 „ 
1-33 
1-30 
1T9 
1-00 
1-33 
1*30 
1T9 
1-00 
Series D 
/ w= PO60 
' lP = l- 
+ ’51e 
-•68(a:-l-13)2 
68a: 2 — ‘26a: 
•78 cm. 
•80 „ 
1-00 
1*46 
1-96 
3-05 
6T3 
1-27 
1-27 
1-20 
1-08 
1-01 
1-00 
1-00 
1-275 
1*27 
1-20 
1-08 
1-02 
POO 
1-00 
Series E. 
/ 10 = 1 - 
\P = 1- 
= l-05 e - 2 ‘ 7(a: - 94)2 . 
+ *12e 
-2 7a; 2 +3-28a; 
•78 cm. 
1-28 
1-28 
•90 „ 
1-23 
1-24 
1-06 „ 
1T8 
1T7 
P26 „ 
1-09 
1-09 
1-50 „ 
1-04 
1-035 
2-03 „ 
1-01 
1-00 
3-00 „ 
1-00 
1-00 
8-00 „ 
POO 
1-00 
The values of the constant ft in the expression for w do not agree with 
each other at all, and this makes a wide difference in all the constants in 
the expression for P. This can be accounted for by small errors in P near 
the point x = 10. For, assuming x and all the constants except /3 to be so 
well determined as to make da, da, etc., negligible compared to d/3, we have 
dP = (l -F)(x-y) 2 d/3. 
If 05 = 1*0, (x — y) 2 is small, say about TOO’ while P is 1*2 approximately, so 
that a small error in observing P would alter the position of the point on 
the w-x graph in such a way as to give 500 times as large an error in 8- 
Each series of observations includes two readings near x = 1*0 cm., and 
