Mathematical tracts on the lunar and planetary theories, the figure of the earth, precession and nutation, the calculus of variations, and the undulatory theory of optics.

314 UNDULATORY THEORY 0F OPTClS,
mn is a large whole number. This has a great number of
maxima corresponding nearly to the values of 0 which make
mO an odd multiple of -t; but the greatest maximum is
that found by making sin 0 = o. Its value is then m2, which
is much greater than any of the others. For, the next,rr. T1 4m2
maximum, when marly, is nearly, is
4 m2m n
the next is nearly = - &c.: and when sin 0 is nearly= 1
97r2
the maximum is nearly 1. As we approach to the value
0 = 7r, one or two values are sensible, and then we reach the
large maximum, of the same value as before. Suppose now
we have placed on the object glass of a telescope a grating
consisting of 100 parallel wires. There will be a bright
image of the luminous point formed at the center of the
field, and one or two less bright on each side, so close that
they cannot be distinguished: after this there will be others,
but their intensity will diminish so rapidly (being at one
of the maxima only of that of the brightest) that they
10000
will be invisible; and at a distance there will be another
point as bright as the first: and at an equal distance beyond
it, another: and so on. Thus there will be a succession
of luminous points at equal distances from each other, with
no perceptible light between them. The distance of these
points is found by making
bX 2bX
0 =0, or, or 27r &c.; or p = 0, or -- or —, &c.
e+g' e+g
This applies to any one kind of homogeneous light. When
there is a mixture of differently coloured lights (as in white
light), there will be a union of bright points of all the
colours where p = 0, but at no other place. For, to arrive
at the second bright point, we must go to a distance from
the first proportional to À. Consequently the next blue point
will be nearer to the center than the next red point, &c.
Thus in the center there will be a bright white point, but