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.

278 UNDULATORY. THEORY OP OPTICS.
47. Join GH, bisect it in L, and produce LC to meet
the screen in O: let M be any point at a small distance from
O; AC =a: CO= b. Since the angle between the mirrors
is a, it is easily seen that GCH = 2a. And since GC = AC
= HC, CL is perpendicular to GH and bisects the angle
GCH. Consequently
GL = LH= a. sina: andLO = acosa + b.
Then for the disturbance produced at M by the wave coming
from G {taking the same expression as in (8) and (24) we
have
sin (v t- GM + MA).
The variation in the value of GM is so small that without
sensible error we may in the coefficient put GO or LO instead of GM; and thus the disturbance produced at M by
the wave coming from G is
sin - (vt- GM + A).
LO À
Similarly the disturbance produced by the wave coming
from IH is
C 2 7
sin - (vt - HM + B).
EL À
B however must be equal to A, because the waves on
leaving G and H respectively are in the same phase at
the same time (which is represented by putting o for GM
and -IM, and requires B to be the same as A). Hence
the whole disturbance of the ether at M is
c 22r 7r
sin { i (vt - GM+ A) + sin - (vt - HM + A)
LO X -
2e f7r(GM HM 2. GM + HM
or L'cosi (GA -)(vt - + A),
LO cos X ÀGH IIMX 2