244 
DR. T. R. MERTON AND PROF. J. W. NICHOLSON ON 
degrees. Thus, for the wave-length 6678, or 6‘678 x 10 -5 cms., a/Xr is equal to 
(l'445)l0 5 /(6'678 x 3750) and is of order about 6*0. With wave-lengths in centimetres, 
the following results are obtained. The ratios exhibited are those for the given 
wave-length, with I for X = 3888 taken arbitrarily as unity. 
Carbon Arc with Wien’s Law. 
X. 
I/L888- 
T = 3750. 
I/I 388 S- 
T = 3650. 
. 
Percentage 
differences. 
7065 
4-347 
4-910 
12-9 
6678 
4-200 
4-703 
12-0 
5876 
3-623 
3-970 
9-6 
5047 
2-639 
2-808 
6-4 
5015 
2-595 
2-758 
6-1 
4922 
2-464 
2-609 
5-8 
4713 
2-148 
2-253 
4-9 
4472 
1-810 
1•8755 
3-6 
4438 
1-761 
1-821 
3-4 
4388 
1-688 
1-741 
3-1 
4144 
1-339 
1-362 
1-7 
4121 
1-308 
1 • 328 
1-5 
4026 
1-178 
1-189 
0-9 
3965 
1-098 
1-104 
0-6 
3889 
1-000 
1-000 
o-o 
These percentage differences correspond to 100° C. As there is no reason to believe 
that the possible error in the temperature is of this magnitude, we may in any case 
adopt the values for 3750° C. with sufficient accuracy for the present purpose. 
These are the absolute relative intensities in the carbon arc according to a certain 
scale. 
Dispersion .—Uniformity of dispersion has been assumed in the calculation of 
these numbers. But the actual law of dispersion of the prism on the plates, is 
approximately of the form 
X — X 0 + 
B 
x + x 0 
5 
where x is the distance measured along the plate from a certain standard position, 
X, B and x 0 being constants. Thus 
Sx = —J5 8x/(x + x 0 ) 2 
and on the plate before enlargement an energy distribution of amount f(x) dX 
between wave-lengths X and XxdX is represented by the distribution of an amount 
