540 
SUMMARY OF CURRENT RESEARCHES RELATING TO 
I 1', i. o. the retinal image, diminishes. Thus in order to obtain images 
as large as possible, the eye must be placed as close as possible to the 
lens. 
Now let the distance of the lens from the object be varied. The 
more the lens is separated from the object, the nearer is the latter to the 
Fig. 78. 
f ocus and the greater is the image. But the retinal image diminishes 
as 1 1' recedes, and in fact 1 1' recedes more rapidly than it increases, 
Ip'. p' 
for the formula — = - put in the form 1 = 0— shows that, 0 being 
Op p 
constant, in order that I may vary uniformly with p\ p must be constant. 
This is not the case, however ; p varies much less rapidly than p\ but 
in the same direction as it. In order to obtain the largest retinal image, 
then, the lens must be approached to the object. But in this direction 
there is a limit, for as p diminishes, so docs p r , until it becomes equal to 
A, the minimum distance of distinct vision. 
To put this in a more mathematical form, let A be the distance C Q 
of the lens to the nodal point of the eye, and consider only the half of 
the figure situated above or below the optic axis M m. The retinal 
image is measured by the tangent of the angle a of the extreme rays. 
But tan a = — — - . The retinal image will therefore be so much 
p + A 
greater as A is smaller ; which shows that the eye must be placed as near 
as possible to the lens. 
On the other hand, from the similar triangles F' Q H, in which 
HQ = 0 and Q F' = /, and F'MI: we have 
.*. tan a = 
0 
/ 
i p'+f 
O f 
X = constant x £&£ 
p + A p ' + A 
Now by varying p\ the fraction 
£±f 
p’ 4- A 
will vary in the same direction 
or in the opposite, according as it is less or greater than unity. Thus 
tan a will be a maximum when p' is a minimum, so long as A is less than 
