DISTRIBUTION OF INTENSITY IN BROADENED SPECTRUM LINES. 
47B 
there is only a discontinuity in the slope of the form shown in the figure (fig. 5), the 
dotted lines being parallel to x and y. 
If q x = q 2 , the lower branch is straight. 
We may pass at once to the general case of a central component and n doublets 
Y 
symmetrically arranged round it. Between the centre and x = o-j, an axis of the first 
doublet, the intensity curve I c becomes 
l c e py tan “ = I (J e~ z3 "+ 2 2l r cosh xq r . e~ q,<Jr . 
1 
Between this axis and one of the second doublet at x = <r 2 , 
n 
j^pytana _ +2I : cosh q l <r l . e _z?1 + 2 2l r cosh xq r . e -?r0V . 
2 
Between x = cr 2 and x = <r 3 , relating to the third doublet, 
oo 
I c e pytana = I 0 e _a:?o + 2l 1 cosh q 1 a 1 . e~ I?1 + 2l 2 cosh q 2 a- 2 . e~ x92 + 2 2l r cosh xq r . e -?r<rr , 
3 
and so on. In any special case, the branches of the curve may be studied from these 
equations. The whole curve has discontinuities in dy/dx at x = o- 1} <r 2 , ..., cr n , and 
these may be of the form shown above, or actual peaks, such as can be seen in the 
photographs of which have been taken by this method. Much depends on the 
relative values of the quantities q for the various components. When a peak occurs, 
say at x = a r , it is easy to calculate the lowest depth of the curve between x = cr r _ 1 
and x = <r r before it rises to the peak, and also the rates of slope from the peak, by 
differentiating the preceding equations. 
When there is no previous knowledge of the values of the q s or of the intensities, 
a complete mathematical analysis of the curve is extremely difficult when there are 
