THE FUNCTION OF LARGE TELESCOPES. 129 



focus. The large lens, then, has a diameter four times that of the small 

 one, which means that its area is sixteen times as great. It will thus 

 receive upon its surface from a given star sixteen times as much light, 

 and all of this will be concentrated in the point-like image of the star, 

 except that portion which is lost in transmission through the lens. On 

 account of its greater thickness the large lens transmits only about 65 

 per cent of the visual rays that fall on it, while the small lens trans- 

 mits about 77 per cent. But after allowance has been made for the loss 

 due to both absorption and reflection it is found that the image of a 

 given star produced by the large telescope will be nearly fourteen times 

 as bright as that given by the small one. In this instance all of the 

 light is concentrated in a point, but in the case of a planet or other 

 extended object, on account of the fact that the focal length of the tele- 

 scope increases as its aperture increases, the brightness of the image is 

 no greater with the large glass than with the small one. The image is, 

 however, four times as large, and this has a most important bearing 

 upon certain classes of observations, particularly in photographic and 

 spectroscopic work. 



There remains still another peculiarity of the large lens as distin- 

 guished from the small one. On account of the nature of light, the 

 power that a lens possesses of separating two luminous points which 

 are so close together as to be seen as a single object by the unaided eye 

 depends directly upon its aperture. Thus, if we consider a double star 

 the two components of which are separated by a distance of 0.5" of arc, 

 it will be barely possible with a 10 inch telescope to resolve the star 

 into two points of light just touching one another. If the members of 

 the pair are closer than this, they can not be separated with a 10-inch 

 glass, no matter what magnifying power is used. With a 40-inch tele- 

 scope, on the other hand, it is not only a simple matter to separate 

 stars 0.5" apart, but it is even possible to distinguish as two points of 

 light the components of a double star of only 0.12" separation. 



To sum up, then, we see that the principal advantages of a 40-inch 

 object glass as compared with one of 10 inches aperture are, first, its 

 power of giving much brighter star images, and thus of rendering 

 visible faint stars which can not be seen with the smaller telescopes; 

 second, the fact that it gives at its focus an image of any object, other 

 than a star, four times as large as the image given by a lens of one- 

 fourth its aperture and focal length; and, third, its capacity of render- 

 ing visible as separate objects the components of very close double 

 stars or minute markings upon the surface of a planet or satellite. 

 Mention should be made here of the fact that the large glass assuredly 

 has some disadvantages as compared with the smaller one, particularly 

 in that it requires better atmospheric conditions to bring out its full 

 qualities. But I think it will be seen from what follows that these dis- 

 advantages are by no means sufficient to offset the great advantages 

 possessed by the larger instrument. Let us now consider what practi- 

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