his sketch the four posts and other objects are represented standing
on a plane level or almost level with the water, in order to show the
working of our problem more clearly. It will be seen that the post _A_
is on the brink of the reflecting plane, and therefore is entirely
reflected; _B_ and _C_ being farther back are only partially seen,
whereas the reflection of _D_ is not seen at all. I have made all the
posts the same height, but with regard to the houses, where the length
of the vertical lines varies, we obtain their reflections by measuring
from the points _oo_ upwards and downwards as in the previous figure.

[Illustration: Fig. 292.]

Of course these reflections vary according to the position they are
viewed from; the lower we are down, the more do we see of the
reflections of distant objects, and vice versa. When the figures are on
a higher plane than the water, that is, above the plane of reflection,
we have to find their perspective position, and drop a perpendicular
_AO_ (Fig. 293) till it comes in contact with the plane of reflection,
which we suppose to run under the ground, then measure the same length
downwards, as in this figure of a girl on the top of the steps. Point
_o_ marks the point of contact with the plane, and by measuring
downwards to _a'_ we get the length of her reflection, or as much as is
seen of it. Note the reflection of the steps and the sloping bank, and
the application of the inclined plane ascending and descending.

[Illustration: Fig. 293.]

CLXVII

REFLECTION IN A LOOKING-GLASS

I had noticed that some of the figures in Titian's pictures were only
half life-size, and yet they looked natural; and one day, thinking I
would trace myself in an upright mirror, I stood at arm's length from it
and with a brush and Chinese white, I made a rough outline of my face
and figure, and when I measured it I found that my drawing was exactly
half as long and half as wide as nature. I went closer to the glass, but
the same outline fitted me. Then I retreated several paces, and still
the same outline surrounded me. Although a little surprising at first,
the reason is obvious. The image in the glass retreats or advances
exactly in the same measure as the spectator.

[Illustration: Fig. 294.]

Suppose him to represent one end of a parallelogram _e's'_, and his
image _a'b'_ to represent the other. The mirror _AB_ is a perpendicular
half-way between them, the diagonal _e'b'_ is