OPTICS. 133 
Now, as the particle of ether at 5 is equidistant from p and p’ ( fgb = fhb), 
it will receive an impulse from both systems of waves, at the same instant 
and in the same direction. The intensity of oscillation will thus be doubled, 
and with it the amount of light. On the other hand, the particle, s, will be 
impelled at the same instant with the same intensity, but in a diametrically 
opposite direction. The oscillation of the particle of ether being thus 
neutralized, darkness at s must be the result. And, in general, in a system 
such as we have represented, increased illumination will be found to occur 
whenever the homogeneous circles intersect, while darkness will result 
from the intersection of a dotted circle or are, and one that is 
continuous. 
Fig. 90 illustrates still more fully the principle of interference. Let the 
lines AB and CD here represent two rays of light, which, proceeding from 
the same source, intersect each other in a very acute angle in a, reaching 
this point by different paths. If the distance traversed by the one ray, alter 
leaving the original starting point, be as long as, or longer by one, two, 
Bees, Lie. n, entire wave lengths, than the path of the other ray, the 
two will act in concert on the particle of ether at a, and the intensity of 
light will thereby be increased. If, on the other hand, the path of the ray be 
n 
eae 3 that of the other, darkness will ensue at their meeting. 
When the difference of the interfering rays falls between the limits of a 
raultiple of whole wave lengths, and an odd multiple of half wave lengths, 
the effect produced will be intermediate between a double intensity of light 
and total darkness. 
To explain the reflection of light by the undulatory theory, let am 
(fig. 91) be a ray impinging at m upon mk, the surface of union of two 
media. Let a’m’' be a second, and a’’k a third ray from the same source : 
if this be at a very great distance, all these rays may be assumed to be 
parallel to each other, and the wave surface passing through m and n to 
be plane. This plane wave meets the surface of union (or separation) first 
at m, later at m’, and still later at &. While the wave is proceeding from 
n to k,a spherical wave is propagated from m, the first point of impact, with 
a radius mo =nk. Moreover, if m’n' be parallel to mn, the spherical wave 
propagated from m’ will have acquired a radius, m’o' = n’k, in the time 
required for the upper wave to pass from n'to &. In a similar manner 
spherical waves will be. propagated from all points lying between m and k. 
and a surface, tangent to all of these at the same time, will be the reflected 
wave. Now, as mo:m'o'::nk:n'k::mk:m’'k, the tangent surface will be 
plane. The rays which the reflected wave produces, namely, m/, m’s, kr, 
&c., are all perpendicular to ok, and answer to each other, the corresponding 
particles of ether, J, s, r, &c., being always in similar phases of oscillation 
or vibration. Finally, as the triangles nkm and omk are equal, the 
homologous angles nkm and omk are equal, according to the well-known 
law of reflection. 
The law of refraction is explicable in a similar manner. In pl. 21, fig. 92, 
let mk be the surface of a transparent medium, met-at m, m’, and k, by 
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