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.

ON THE
UNDULATORY TTHEORY 0F OPTICS.
ON UNDULATIONS GENERALLY.
PROP. 1. To explain the nature of an Undulation.
1. The characteristic of an undulation is, the continued
transmission in one direction of a relative state of particles
amongst each other, while the motion of each particle separately considered is a reciprocating motion. The disturbance
of the particles from their state of rest, and their motion,
may be in any direction whatever.
2. For example: in fig. 1, let the line (a) represent a
number of particles in their position of rest: and suppose
that in consequence of a disturbance they are at a given
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time T in the position (f3): at the tiine T + i, in the
position (y): at the time T +-, in the position (s): at
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the time T + -, in the position (e): and at the time T + -,
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in the position (r): and in intermediate positions at times
intermediate to these. At the time T the particles are in
the state of greatest condensation about a, a', and a". Suppose we fix our attention on one of these condensed groups,
as for instance that of which a' is the center. At the time
T + the center of the condensed group has glided from a'
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to d', not by the motion of all the particles in that direction,
but by such a difference of motions that the particles about
a' are not so close together as they were, and the particles