5Q0 PHILOSOPHICAL TRANSACTIONS. [ANNO 1800. 



been used in my astronomical observations; but, as this subject will be best ex- 

 plained by a report of the observations themselves, I shall select a series of them 

 for that purpose, and relate them in the order which will be most illustrating. 

 First, with regard to the eye, it is certain that its power, like all our other facul- 

 ties, is limited by nature, and is regulated by the permanent brightness of objects, 

 as has been shown already, when its extent with reflected light was compared to its 

 exertion on self-luminous objects. It is further limited on borrowed light, by the 

 occafional state of illumination ; for when that becomes defective at any time, the 

 power of the eye will then be contracted into a narrower compass; an instance of 

 which is the following. In the year 177^, when I had erected a telescope of 20 

 feet focal length, of the Newtonian construction, one of its effects by trial was, 

 that when towards evening, on account of darkness, the natural eye could not 

 penetrate far into space, the telescope possessed that power sufficiently to show, by 

 the dial of a distant church steeple, what o'clock it was, notwithstanding the naked 

 eye could no longer see the steeple itself. Here I only speak of the penetrating 

 power; for though it might require magnifying power to see the figures on the 

 dial, it could require none to see the steeple. Now the aperture of the telescope 

 being 12 inches, and the construction of the Newtonian form, its penetrating power, 

 when calculated according to the given formula, will be 4V (.429 X (120 Q — 15 2 )) 

 = 38. 99, a, b, and a, being all expressed in tenths of an inch.* From the 

 result of this computation it appears, that the circumstance of seeing so well, in 

 the dusk of the evening, may be easily accounted for, by a power of this telescope 

 to penetrate 39 times farther into space than the natural eye could reach, with 

 objects so faintly illuminated. 



This observation completely refutes an objection to telescopic vision, that may 

 be drawn from what has also been demonstrated by optical writers; namely, that 

 no telescope can show an object brighter than it is to the naked eye. For, in 

 order to reconcile this optical theory with experience, I have only to say, that the 

 objection is entirely founded on the same ambiguity of the word brightness that 

 has before been detected. It is perfectly true, that the intrinsic illumination of 

 the picture on the retina, which is made by a telescope, cannot exceed that of 

 natural vision; but the absolute brightness of the magnified picture by which 

 telescopic vision is performed, must exceed that of the picture in natural vision, 

 in the same ratio in which the area of the magnified picture exceeds that of the 

 natural one; supposing the intrinsic brightness of both pictures to be the same. 

 In our present instance, the steeple and clock-dial were rendered vfsible by this 

 increased absolute brightness of the object, which in natural vision was 15 hun- 

 dred times inferior to what it was in the telescope. And this establishes beyond a 

 doubt, that telescopic vision is performed by the absolute brightness of objects; 



* 1 have given the figures, in all the following equations of the calculated penetrating powers, in 

 order to show the constructions of my instruments to those who may wish to be acquainted with them.— 

 Orig. 



