resolve two points which, from the center of the objective, appear 

 under an angle of 5". An objective of two inches aperture will 

 resolve iy z " . 



The importance of resolving power cannot be too much 

 emphasized. To make the matter more concrete, an angle of 

 5" will include about 15.3 in. at a distance of one mile. Two points 

 separated by 15.3 in. will just be resolved by an objective of 1 in. 

 aperture. They will be visible as two points if the illumination of 

 the object and the magnification of the telescope are sufficient. If 

 the aperture of the objective is less than 1 in. no amount of magni- 

 fication nor of light will suffice to dispel the appearance of the image 

 as a single point. 



As has been intimated, resolving power alone is not sufficient 

 to make the two points visible as such through the telescope. Be- 

 fore two points can be seen as separate they must be made to appear 

 under an angle of at least 1'. This makes necessary a certain 

 degree of 



Magnification in the telescope. The degree of magnification 

 necessary is determined by the resolving power of the objective. 

 The power to resolve 5" requires a magnification of at least 12. 

 Without this magnification, two points separated by 5" will be 

 imaged separately in the focal plane of the objective but they will 

 not be separately visible because the angle under which they would 

 appear to the eye through the eyepiece would be less than the 

 necessary minimum of 1'. Magnification exceeding this amount, 

 while it would increase the angle under which the two points would 

 appear, could not render visible a third point lying between the 

 two. The explanation lies in the fact that the objective cannot 

 image a point as a point, but only as a disc of finite size surrounded 

 by alternate concentric bright and dark rings. The larger the 

 objective the smaller the diameter of the disc, hence the greater the 

 resolving power. Magnification exceeding the necessary minimum, 

 while increasing the angle subtended by the centers of the disc 

 images, increases the apparent size of the discs at the same time 

 thereby preventing detection of any intermediate detail. 



-sive magnification in addition to being useless is positively 

 detrimental under any but the best of light conditions. 



The Brightness of the Image of a telescope is inversely 

 proportional to the second power of the magnification and directly 

 proportional to the second power of the aperture. The expression 



for the absolute illumination of the image is, I A ,where A is a 



I 



constant when comparing two instruments side by side on the same 

 object, d is the aperture of the ob|tn tivc. and m the magnification. 

 A lOTc increase of aperture will give over 20V increase in bright- 

 vhile \to% increase in magnification will result in about \1% 

 loss in illumination. 



