80 KANSAS UNIVERSITY QUARTERLY. ‘ 
D being the difference of path of the interfering pencils in mms. 
(read from the screw M). ‘The limits of integration are chosen so 
as to include the entire source. The visibility, V, is defined as the 
difference of intensities of a bright and a dark band divided by the 
[Lbright—I dark 
sum of these intensities, or algebraically V—- see ‘ 
I bright-+-I dark 
And it has also been shown by Michelson’s investigations that 
eye estimates of visibility agree fairly with the true values. 
The distribution of light in the source resulting from Maxwell’s 
Dy 
law of molecular velocities is given by $(x)==e ° and it has 
been further shown experimentally that the actual distribution of 
light in a single spectral line in most cases approximates closely to 
that given by the formula. ‘The visibility curve resulting from a 
fash li 
single line with this distribution is V=e Band for a source 
consisting of two such lines, the distribution in each being given by 
the above formula, the visibility 1s given by 
ey 
an? 
p { 1+r®+-arcosarDa | 
\% 
Ve 
{ t-Har--r* \ 
Under the conditions of temperature and pressure existing in a 
bunsen flame this formula represents very well the visibility curve 
given by the yellow sodium lines. 
For convenience of calculation this formula may be put in the 
form 
2 ( 1+r?--arcosarDa |} 
| tort r? } 
and d(x)j==2 
In these expressions A is a constant not greater than unity, r is 
the ratio of intensities of the two lines constituting the source, a 1s 
a quantity proportional to the distance between the centres of the 
lines in wave numbers, and D is the difference of path in mms. of 
the two interfering pencils as determined by the screw M. 
/\ is a quantity which varies inversely as the half breadth of one 
of the lines in the source. 
The formula shows that the visibility is a periodic function of 
the difference of path D, and hence that as the difference of path is 
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