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.

326 UNDULATORY TIIEORY OF OPTICS.
101. The reader will perceive that it is absolutely
necessary to suppose, either that there are no vibrations in
the direction of the wave's motion, or that they make no
impression on the eye. For if there were such, there ought
in the experiment of (98) to be visible fringes of interferences: of such however there is not the smallest trace.
102. As we now suppose light generally to consist of
two sets of vibrations which cannot interfere with each
other, it becomes important to establish some measure of
the intensity of the compound light. It seems that this
cannot be any other than the sum of the intensities corresponding to the two sets of vibrations. So that if
the displacement from one vibration be represented by
a sin (vt-x+A), and that from the other by b. sin (vt-x+B),
the intensity of the mixed light will be a2+b2. This then
is the expression which we ought in strictness to have used
in our former investigations. But as in all these (except
those relating to reflection from plane glasses and lenses)
the quantities a and b have in every part of the operation
the same proportion, it is evident that the results, considered as giving the proportion of intensities of light, are
in every instance correct.
Ptor. 21. To explain on mechanical principles the
transmission of a wave in which the vibrations are transverse to the direction of its motion.
103. In fig. 25 let the faint dots represent the original
situations of the particles of a medium, arranged regularly
in square order, each line being at the distance h from the
next. Suppose all the particles in each vertical line disturbed vertically by the same quantity; the disturbances of
different vertical lines being different. Let x be the horizontal abscissa of the second row; - h that of the first,
and x+ h that of the third: let u, ut, and u' be the corresponding disturbances. The motions will depend upon the
extent to which we suppose the forces are sensible. Suppose
the only particles whose forces on A are sensible, to be
B, C, D, E, F, G,