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, haying 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 I/ I/, may be unscrewed or drawn off, and 

 the lens L" L" alone used as the object-glass ; or i/ L' may be 

 screwed on, the two lenses L' L' 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 L' L', 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 L' L', the 



