476 
PROF. J. W. NICHOLSON AND DR. T. R. MERTON ON THE 
and some other cases, but in H a a closer scrutiny is required to reveal them. In order 
to cover such cases the theoretical discussion has been made somewhat complete. 
(VIII.) General Theory of a Symmetrically Compound Line. 
If H a has close components, the law of attenuation of each component from its 
maximum is now certainly that of the simple exponential, 
I = I 0 e~ gx , 
for the whole of the curve for H a is very close to a straight line, and for nearly half 
its length is almost entirety straight. Afterwards it broadens convex to its axis, but 
not rapidly, and although so irregularly as to invalidate attempts to interpret it by a 
single exponential of any possible argument, the curvature is nevertheless at every 
y 
point away from the axis. Several close components with somewhat different rates of 
attenuation, but with axes nearly coincident, are at once suggested, and will be shown 
to provide a complete explanation of these peculiarities. No other exponential 
arrangement appears capable of doing so. 
As the components of H a are symmetrically arranged, we consider first the effect of' 
a pair of equal components separated by an interval 2<x. 
Let I 0 (fig. 4) be the axial intensity of either. A dotted line in the figure is mid¬ 
way between their axes, and is taken as the axis of y. Then at a point P of 
co-ordinate x outside both axes the intensity is I = I 0 + I 0 e _?(z+<r) = 2l 0 cosh qae^ qx 
and this would be produced by a single line of axial intensity 2l 0 cosh q<r midway 
between. But at a point Q (x') between the axes the intensity is 
I = = 2l u e~ ?<r cosh qx\ 
