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dered achromatic, if the aberrations' from their sphesical^ 

 figure remain, after those from refrangibility are removed: 

 which aberrations, taken laterally, as they always ought to- 

 be, are as the cubes of the aperture*. So tha<t, if the li- 

 neal aperture be doubled, and the light admitted, whieb 

 is as the square of the aperture, quadrupled, in order to^ 

 increase the magnifying power four times, (or to double." 

 the lineal amplification,.) preserving an equal brightness i» 

 the image; the telescope must be made four times longer, 

 that it may remain equally distinct;* an inconvenience, 

 from Avhich it must be very desirable to exempt this te- 

 lescope, by correcting the figure, and,^ with it, the aber- 

 rations of its object glasses. 



It is not the object of this essay, to investigate any 

 particulars, in the construction of the telescope; (which 



would 



* A conception of this n}ay be, perhaps, most familiarly acquired, by con- 

 sidering, that if, of two object lenses, the aperture, and also the focus of one, 

 be twice as great as those of the other, the angles of incidence, and refrac- 

 tion, of the extreme rays, which come fi-om a very remote object, and forin 

 the cones or pencils made by both, will be equals •^n'l 'he pehcils themselves, 

 and their aberrations, will be similar figures; all tli« lineal measures of that 

 of the larger lens, being double those of the other. In order, therefore, to 

 reduce the lateral error or diameter of the circle of abenations of the former, 

 to an equality with that of the latter, while the aperture, which is the base 

 of the pencil, remains double; this pencil must be made twice more narrow 

 or acute than before. And, to effect this, its length or focus (which, at first, 

 was twice as great as that of the other pencil) must be doubled ; so that now 

 it ihuSt Be' four times as long as the smaller pencil : i. e. the lengths should 

 be as the squares of the apertuiees, 



