Bopx1n— The Automatic Image- Finder. 285 
the centre of the lens; these represent the secondary axes, and by 
their motion round the pivot (caused by the mere approach and 
recession of the object) they indicate the various positions that 
must be assumed by the secondary axes, corresponding with the 
various positions of the object. Now according to the principles 
above laid down, where the lines (in their motion) intersect the 
refracted parallel ray, there is the image. 
2°.—How to work the Image-Finder. 
In order to work the Image-Finder, and see how it enables 
us to know the position of the image at any moment, and to 
discover the laws of lenses, we have only to slide the arrow or 
object backwards and forwards, and then note where the rays 
intersect : there then isthe image. The mere motion of the arrow 
causes the secondary axes to travel in and out, and to assume 
their proper positions according to circumstances, thus intersecting 
the refracted parallel ray (which is constant in position) at various 
points, showing thereby where the image is, whether it is real 
or virtual, larger or smaller than the object, erect or inverted. 
To discover the laws of lenses by means of the Image-Finder 
we have only to observe that— 
1. If the object or arrow is at infinity (or as far away as 
possible), the rays meet at f, and so the image is there: 
it is real and smaller than the object. 
2. If the object is at 27, we find that the rays meet at 2f, and 
so the image is there. Further we see that as the rays 
really meet, the image is real, of the same size as the 
object, and inverted. 
3. If the object is at f the rays go out parallel, and so never 
meet. In this case the image is said to be at infinity. 
4. If we place the object anywhere between infinity and 2/f, 
we observe that the rays really meet somewhere between 
f and 2f. Consequently the image is there ; it is real, 
smaller than the object, and inverted. 
5. If we place the object anywhere between 2f and f, we 
note that the rays really meet only between 2/ and 
infinity. Therefore the image is there ; it is real, larger 
than the object, and inverted. 
