COMPOUND OBJECT-PIECES. 
The power of the object-pieces is usually indicated by the 
makers, by assigning their focal lengths; but as these object- 
pieces are composed of several lenses, having different focal 
lengths, it is necessary to explain what is meant by the focal 
length of the combination. 
Let L be a single convex lens, and o the compound object-piece; 
suppose then, the same object placed successively at the same 
distance from l and o, and let L have such a convexity that it 
will produce an image, I, of the object equal to the image i', which 
the object-piece, o, produces, and that the distance of this image, 
i, from the single lens l, is equal to the distance of the image i' 
from the object-piece o. In that case, the single convex lens l, 
being, in fact, the optical equivalent of the compound object-piece 
o, its focal length is taken to be that of the object-piece o. Thus, 
for example, if the lens L, having a focal length of one inch, 
produce the same image of the same object similarly placed before 
it, as would the object-piece o, then the focal length of the object- 
piece o is said to be one inch. 
In short, the single lens l, and its equivalent compound object- 
piece o, differ only in this, that the images produced by L are 
defaced more or less by aberration, from which the images pro¬ 
duced by o are altogether exempt. 
These object-pieces are sold by some makers so fixed that their 
component lenses are inseparable, the observer being unable to use 
any one of them as an object-glass without the others; other 
makers, however, mount them in such a manner that the first and 
second lenses, L l and 1/ i/, may be unscrewed or drawn off, and 
the lens l" l" alone used as the object-glass; or l' l' may be 
screwed on, the two lenses i/ i/ and l" l" then making an object- 
piece of greater power ; by this arrangement the observer obtains, 
without increased expense, three object-pieces of different powers. 
After what has been said, however, of the exact manner in 
which the aberrations of the field and eye glasses are corrected 
and balanced by the contrary aberration of the object-piece, it will 
be easily understood, that the economy by which three powers are 
thus obtained, is gained at the expense of the efficiency of the 
instrument; for if the aberrations of the triple object-piece are so 
adjusted as exactly to balance those of the other lenses, that balance 
will no longer be maintained when the lens L l, and still less 
when the lens jJ i/, is removed. It is on this account that some 
makers, who are the most scrupulous as to the character of their 
instruments, refuse to supply separable object-pieces. 
The imperfection, however, produced in this case by disturbing 
the balance of the aberrations is of less importance, inasmuch as 
by removing the lens l l, and still more by removing i/ i/, the 
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