Bopxin—The Automatic Image-Finder. 283 
principal axis. The position of this line presents no difficulty 
whatsoever ; in fact it is absolutely fired and constant, no matter 
what the position of the object may be. This of course is at 
once quite clear when stated, for a ray parallel to the principal 
axis must of necessity pass through the principal focus, and so we 
have two points fixed in this straight line (viz. the point where it 
cuts the lens and the principal focus), and therefore the position of 
the line is determined. In fact, to indicate its position, we have 
only to draw a straight line from the point where the parallel 
ray cuts the lens to the principal focus, and produce this line 
indefinitely. In a word, one of the lines (viz. the parallel line) 
is constant in position, and the other moves up and down along it. 
It therefore only remains to determine the position of one of the 
lines at any moment, and that is easily done, since one of the 
points is fixed, and acts as the centre of a circle, and the other is 
immediately determined by the position of the extremity of the 
object as it moves along in its course. 
In order to apply these principles with greater ease, attention 
is here directed to figure l. 
Let AB represent the object; then the rays drawn from the 
extremities of the object and passing through the centre of the 
lens, will proceed as straight lines, as seen in the figure (lines 
AA and BB). 
Now another straight line drawn parallel to the principal axis, 
and meeting the lens at H, must pass through /, and so we have 
its position determined. 
From a consideration of these principles we arrive at a very 
simple rule for drawing the images of any object placed anywhere 
before a lens (or mirror). It is this :— 
1. From the extremities of the object, draw secondary axes 
(or straight lines ‘passing through the centre of the 
lens). 
ww 
. From the extremity of the object, draw a straight line 
parallel to the principal axis and cutting the lens. 
3. From the point where this line cuts the lens, draw a 
straight line through the principal focus, and produce 
it indefinitely. 
4. Where this line cuts the secondary axis there is the image 
Y 2 
