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FIRST CLASS OF OBJECTS FOE THE SUBJECT. 77
the sense, in which it is to be understood, can only be
gathered from its connection with the rest. An object
subtending the same visual angle may in fact be small
and it is only when we have
and near, or large and far off ;
previously ascertained its size, that the visual angle enables
us to recognise its distance : and conversely, its size, when
its distance is known to us. Linear perspective is based
upon the fact that the visual angle diminishes as the dis
tance increases, and its principles may here be easily de
duced. As our sight ranges equally in all directions, we
see everything in reality as from the interior of a hollow
sphere, of which our eye occupies the centre. Now in the
first place, an infinite number of intersecting circles pass
through the centre of this sphere in all directions, and
the angles measured by the divisions of these circles are
the possible angles of vision. In the second place, the
sphere itself modifies its size according to the length of
radius we give to it ; therefore we may also imagine it as
consisting of an infinity of concentric, transparent spheres.
As all radii diverge, these concentric spheres augment in
size in proportion to their distance from us, and the de
grees of their sectional circles increase correspondingly:
therefore the true size of the objects which occupy them
likewise increases. Thus objects are larger or smaller ac
cording to the size of the spheres of which they occupy
similar portions say 10 while their visual angle re
mains unchanged in both cases, leaving it therefore un
decided, whether the 10 occupied by a given object belong
to a sphere of 2 miles, or of 10 feet diameter. Conversely,
if the size of the object has been ascertained, the number
of degrees occupied by it will diminish in proportion to
the distance and the size of the sphere to which we refer
it, and all its outlines will contract in similar proportion.
From this ensues the fundamental law of all perspective ;
for, as objects and the intervals between them must ne-