508 Prof. Forbes on an apparent Inversion of Perspective^ 
served, the spectator has previously determined by his eye the 
real position of the plane of the object towards which he di- 
rects his telecope: and when he views that object with a mag- 
nifying power of two, he believes himself to be looking at an 
object twice as large in the same plane as before; or else 
(what comes to the same thing) the same object as before 
brought twice as near to him, but moved parallel to itself. 
In either of these cases, the vanishing point ought to remain 
exactly the same for the enlarged as for the original object. 
ah c dhQ?L board 4? feet long and 1 foot high,* the eye expects 
to see through the telescope magnifying twice, a figure similar 
to that which a board 8 feet long and 2 high would present 
in the same situation, that is, a figure a' 5' d d of which the 
upper and lower lines converge to the same point V as before; 
ut the eye really sees through the instrument a merely mag- 
nified image of ah c d^ namely d (5 c d, in which a! (3 is 
t 
V 
parallel to a 5, and consequently the vanishing point V is 
thrown twice as far off. What must the mind, reasoning 
through the information lent by the eye, infer respecting this 
enlarged object? One of two things. Either that the sign- 
board so seen is really not a parallelogram, but has its further 
extremity h- d higher than the nearer one ; or else^ that the 
board is a true parallelogram, but that the plane in which it 
lies is more nearly perpendicular to the line joining the eye 
and the object, a plane in short which will give to horizontal 
lines a vanishing point as far beyond V as that is from d. 
The former is the case when we look at an object to which 
we direct a telescope after having mentally formed an estimate 
of its position ; the latter, or an erroneous estimate of a plane 
of the object, occurs when a person looks suddenly through 
a telescope previously pointed in an unknown direction. 
I am not sufficiently conversant with works on perspective 
to be aware whether such a circumstance has before been no- 
ticed, but it was new to those whom I have had occasion to 
consult. 
At all events it is very singular that it should have remained 
so long generally unknown that all objects (generally speak- 
ing) are seen through a telescope in false perspective, 
Iffie general principle may be thus stated in a single sen- 
tence. By common perspective, all parallel lines in a single 
