566 BIBLIOGRAPHY OF HERSCHEL's WRITINGS. 



Herscliel, W.: Synopsis of the Writings of— Coutiuued. 

 A.D. Vol. P. 



of tlie sixth maguitutlo to that of one of the seventh, is hut httle 



more than 1^ to 1. 

 1800 90 62 The faiutness of the stars of the 7th magnitude gives us little room 



to helieve that we can penetrate much farther into space with oh- 



jects of no greater brightness than stars. 

 63 I think, from the faiutness of the stars of the 7th magnitude, and 



from the foregoing considerations, we are authorized to conclude that 



no star, eight, nine, or at most ten times as far from us as Sirius, 



can possibly be perceived by the natural eye. 



63 Where the light of single stars falls short, however, the united lustre 



of sidereal systems will still be j)erceived. We easily see the united 

 lustre of the stars in the sword-handle of Ferseus, though the light 

 of no one of the single stars could have aflected the unassisted eye. 



64 Perhaps, among the farthest objects that can make an impression on 



the eye, when not assisted by telescopes, may be reckoned the 

 nebula in the girdle of Andromeda discovered by Simon Marius in 

 1612. 



64 It has been shown that brightness or light is to the naked eye truly 



represented by — _; in a telescope, therefore, the light admitted will 



A- 1 

 be expressed by --. Hence it would follow that the artificial 



power of penetrating into space should be to the natural one as A 

 to a. But this proi)ortion must be corrected 1)y the practical defi- 

 ciency in light reflected and transmitted. 



65 As the result of many experiments with plane mirrors, polished like 



my large ones, and of the same composition of metal, I find we shall 

 have, in a telescope of my construction, with one reflection, 63,796 

 rays, out of 100,000 come to the eye. In the Newtonian form, 

 with a single eye-lens, 42,901 ; and, with a double eye-glass, 40,681 

 will remain for vision. 



65 Since 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. 



66 In natural vision, therefore, this power is truly expressed by V^T 



and since we have now also obtained a x^roper correction x, we must 

 apply it to the incident light with telescopes. 

 66 In the Newtonian and other constructions where two specula are 

 used there will also be some loss of light on account of the inter- 

 position of the small speculum ; therefore, putting 1) for its diameter, 

 we have a- &- for the real incident light. This being corrected as 



above, will give the general ex])ression ■\/xl x A- &- for the same 



power in telescopes. 

 66 Then, if we put natural light I =^ 1, and divide by a, we have the 



general form ^-^ " for the iienetrating power of all sorts of 

 a 



telescopes, compared to that of the natural eye as a standard. 



66 In the following investigation we shall siippose a = two-tenths of an 



inch. 



67 *' In the year 1776, when I had erected a telescope of 20 foot focal 



length, of the Newtonian construction, one of its effects by trial 

 was, that when towards evening, on account of darkness, the nat- 

 ural eye could not penetrate far into space, the telescope possessed 



