VOL. XC.] PHILOSOPHICAL TRANSACTIONS. 58Q 



close to the line connecting the two objects as possible, in order to render the re- 

 flected rays nearly perpendicular. The result was, that out of 100 thousand inci- 

 dent rays, 67262 were returned; and therefore, if a double reflection takes place, 

 only 45242 will be returned. Before this light can reach the eye, it will suffer 

 some loss in passing through the eye-glass; and the amount of this I ascertained, 

 by taking a highly polished plain glass, of nearly the usual thickness of optical 

 glasses of small focal lengths. Then, by the method of the same author, page 

 21, fig. 5, I found, that out of 100 thousand incident rays, Q4825 were trans- 

 mitted through the glass. Hence, if 2 lenses be used, 89918; and with 3 lenses, 

 85265 rays will be transmitted to the eye. Then by compounding we shall have, 

 in a telescope of my construction with one reflection, 63796 rays, out of 100 

 thousand, come to the eye. In the Newtonian form, with a single eye lens, 42901 ; 

 and with a double eye-glass 40681 will remain for vision. There must always re- 

 main a considerable uncertainty in the quantities here assigned ; as a newly-polished 

 mirror, or one in high preservation, will give more light than another that has not 

 those advantages. The quality of metal also will make some difference; but if it 

 should appear by experiments, that the metals or glasses in use will yield more or 

 less light than here assigned, it is to be understood that the corrections must be 

 made accordingly. 



We proceed now to find a proper expression for the power of penetrating into 

 space, that we may be enabled to compare its effects, in different telescopes, with 

 that of the natural eye. Since then the brightness of luminous objects is inversely 

 as the squares of the distances, it follows, that the penetrating power must be as 

 the square roots of the light received by the eye. In natural vision therefore, this 

 power is truly expressed by Va 2 !; and, since we have now also obtained a proper 

 correction x, we must apply it to the incident light with telescopes. In the New- 

 tonian and other constructions, where 2 specula are used, there will also be some 

 loss of light on account of the interposition of the small speculum; therefore, 

 putting b for its diameter, we have a 2 — U 2 for the real incident light. This being 

 corrected as above, will give the general expression */ {xl X (a* — U 1 )) for the same 

 power in telescopes. But here we are to take notice, that in refractors, and in 

 telescopes with 1 reflection, b will be = 0, and therefore is to be left out. Then, 

 if we put natural light / = 1 , and divide by a> we have the general form ^' ^ A """ il 

 for the penetrating power of all sorts of telescopes, compared to that of the 

 natural eye as a standard, according to any supposed aperture of the iris, and pro- 

 portion of light returned by reflexion, or transmitted by refraction. 



In the following investigation we shall suppose a = 2 tenths of an inch, as 

 being perhaps nearly the general opening of the iris, in star-light nights, when 

 the eye has been some moderate time in the dark. The value of the corrections 

 for loss of light will, stand as has been given before. 



We may now proceed to determine the powers of the instruments that have 



