rack themselves through the dust
of the room. The mere inspection of the two angles enclosed between
the index and the two beams suffices to show their equality; while if
the graduated arc be consulted, the arc from 5 to _m_ is found
accurately equal to the arc from 5 to _n_. The complete expression of
the law of reflection is, not only that the angles of incidence and
reflection are equal, but that the incident and reflected rays always
lie in a plane perpendicular to the reflecting surface.

[Illustration: Fig. 3.]

This simple apparatus enables us to illustrate another law of great
practical importance, namely, that when a mirror rotates, the angular
velocity of a beam reflected from it is twice that of the reflecting
mirror. A simple experiment will make this plain. The arc (_m n_, fig.
3) before you is divided into ten equal parts, and when the incident
beam and the index cross the zero of the graduation, both the incident
and reflected beams are horizontal. Moving the index of the mirror to
1, the reflected beam cuts the arc at 2; moving the index to 2, the
arc is cut at 4; moving the index to 3, the arc is cut at 6; moving
the index at 4, the arc is cut at 8; finally, moving the index to 5,
the arc is cut at 10 (as in the figure). In every case the reflected
beam moves through twice the angle passed over by the mirror.

One of the principal problems of science is to help the senses of man,
by carrying them into regions which could never be attained without
that help. Thus we arm the eye with the telescope when we want to
sound the depths of space, and with the microscope when we want to
explore motion and structure in their infinitesimal dimensions. Now,
this law of angular reflection, coupled with the fact that a beam of
light possesses no weight, gives us the means of magnifying small
motions to an extraordinary degree. Thus, by attaching mirrors to his
suspended magnets, and by watching the images of divided scales
reflected from the mirrors, the celebrated Gauss was able to detect
the slightest thrill of variation on the part of the earth's magnetic
force. By a similar arrangement the feeble attractions and repulsions
of the diamagnetic force have been made manifest. The minute
elongation of a bar of metal, by the mere warmth of the hand, may be
so magnified by this method, as to cause the index-beam to move
through 20 or 30 feet. The lengthening of a bar of iron when it is
magnetized may be also thus demo