DISTRIBUTION OF INTENSITY IN BROADENED SPECTRUM LINES. 
467 
in a broadened line is represented on the photographic plate, after passage through 
the wedge, by an equal number of “kinks” in the bounding curve of the darkened 
patch, provided, of course, that the separations exceed certain limits. A smooth 
curve, containing no abrupt change of curvature—shown, for example, very definitely 
in the upper part of the plates for the line H a (Plate 2)—indicates either a regular 
law of intensity in the corresponding portion of the original spectral line, or a number 
of components of very small separation. If in passing across the line, on the wave¬ 
length scale, a place was reached where, through the presence of a new and sufficiently 
separated component, a definitely new law of intensity appeared, a kink would be 
found on the final plate in the corresponding position. No such kink occurs in the 
upper portion of the H a curve, which therefore presents us with one of these 
alternatives. A first inspection indicates that, for some value of n, y n = Ax should 
be a good approximation to the shape of this curve, where A is positive, the axis of x 
being that of the curve and the origin being at the vertex. 
The curvature is away from the axis of x, so that dyldx increases with x, and 
d 2 yldx 2 is positive. Thus n is less than unity. The curve is, in fact, not unlike the 
two branches of a semi-cubical parabola, in which n = f. This property of curvature 
away from the axis is general throughout the plates, as a casual inspection shows, in 
all regions where the curvature appears fairly continuous, and therefore determined 
by only one or by several very close components in the primary broadened line. A 
single component must therefore ultimately produce, after passage through the 
wedge, a curve whose equation is at least approximately of the form 
y n cc x, 
where n is less than unity. 
Consider now the curve to be expected for a component satisfying the probability 
law of intensity. 
T = T e -* 2 * 2 
where I 0 is the intensity of its centre, and x is the distance of the intensity I from 
the centre. The wedge diminishes intensity in an exponential manner, and can be 
defined by a constant p such that, if an intensity Ii falls on the wedge, traverses a 
thickness and emerges as an intensity I 2 , Ig/C = e~ p \ The intensity I is diminished 
to I c , the critical intensity already defined, by a thickness of wedge given by 
I c = Lr" = 
In the figure (fig. 2) ABCD represents the lower surface of the wedge, AB being 
the intersection of the upper and lower faces, where the thickness diminishes to zero. 
The shaded area on the lower face of the wedge denotes the final record of the 
broadened line, whose plane was originally parallel to the lower face and above the 
upper. Around the boundary of this shaded area the intensity is everywhere I c , 
VOL. CCXVI.-A. 3 S 
