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SUMMARY OF CURRENT RESEARCHES RELATING TO 
axes of a convex lens, and are under the same laws as the primary 
foci. 
Each point in an object has its conjugate point in the image of it 
formed by a lens, and this image, if on the opposite side of the lens, is 
real and inverted ; if on the same side, is virtual and erect. The linear 
dimensions of the object and image are directly as their distances from 
the optical centre of the lens ; so that, if the object be nearer than the 
image, then the image is magnified, and vice versa. 
Formulae. — The formulas for the determination of the conjugate foci 
when 
/ = principal focus (or focal length) ; 
p = one conjugate focus ; 
p' = the other conjugate focus. 
When the conjugate foci are on opposite sides of the lens (real image) : 
1 i _ 1 
p + p' ~ f ' 
This formula suffices for the determination of either of the conjugate 
foci, the other conjugate focus and the focal length being given ; or of 
the focal length, the two conjugate foci being given ; and as it applies 
equally well to points in the secondary axes, it suffices equally to deter- 
mine the distances of the object and image (and thence their relative 
linear dimensions), if one of these distances and the focal length of the 
lens be given. 
When the conjugate foci are on the same side of the lens (virtual 
image) the formula becomes 
1 l l 
p~p'~ 7 ' 
The plus sign here becomes minus, or, to express it in other terms, 
as the two conjugate foci are now on the same side of the lens, it is the 
difference instead of the sum of their reciprocals that equals the reciprocal 
of the focal length. This formula is as applicable as that for real con- 
jugate foci to the determination of the places, and therefore of the 
relative linear dimensions, of image and object ; but, of course, the 
change of sign produces marked differences in the results when the given 
quantities are the same ; that is to say, with a given focal length and 
image distance, the distance of the object, and therefore the ratio between 
its linear dimensions and those of the image, will vary according as the 
image is real or virtual. 
In the compound Microscope we have to deal with both real and 
virtual images ; the real produced by the objective, and the virtual by 
the ocular. 
The real and inverted image produced by the objective becomes in 
its turn the object of which the ocular produces a virtual image ; erect 
so far as it is concerned, but, of course, still inverted as regards the 
original object. 
The degree of amplification of the real image produced by the objec- 
tive depends upon two factors : 1st, the focal length of the objective, 
and, 2nd, the distance from its optical centre at which the image is 
