586 PHILOSOPHICAL TRANSACTIONS. [ANNO 1800. 



coming from the sun to the planet, has to pass through an equal space, before it 

 can be reflected, by which it must be so enfeebled as to be above 368 times less 

 intense on that planet than it is with us, and when probably not more than one- 

 third part of that light can be thrown back from its disc* 



The range of natural vision with self-luminous objects, is incomparably more 

 extended, but less accurately to be ascertained. From our brightest luminary, the 

 sun, we pass immediately to very distant objects; for, Sirius, Arcturus, and the 

 rest of the stars of the first magnitude, are probably those that come next; and 

 what their distance may be, it is well known, can only be calculated imperfectly 

 from the doctrine of parallaxes, which places the nearest of them at least 412530 

 times farther from us than the sun. In order to take a 2d step forwards, we must 

 enter into some preliminary considerations, which cannot but be attended with con- 

 siderable uncertainty. The general supposition, that stars, at least those which 

 seem to be promiscuously scattered, are probably one with another of a certain 

 magnitude, being admitted, it has already been shown in a former paper,'}- that 

 after a certain number of stars of the first magnitude have been arranged about the 

 sun, a farther distant set will come in for the 2d place. The situation of these 

 may be taken to be, one with another, at about double the distance of the former 

 from us. 



By directing our view to them, and thus penetrating one step farther into space, 

 these stars of the 2d magnitude furnish us with an experiment that shows what 

 phenomena will take place, when we receive the illumination of 2 very remote ob- 

 jects, equally bright in themselves, of which one is at double the distance of the 

 other. The expression for the brightness of such objects, at all distances, and 

 with any aperture of the iris, according to our foregoing notation, will be — ; and a 

 method of reducing this to an experimental investigation will be as follows. Let 

 us admit that a Cygni, p Tauri, and others, are stars of the 2d magnitude, such 

 as are here to be considered. We know, that in looking at them and the former, 

 the aperture of the iris will probably undergo no change; since the difference in 

 brightness, between Sirius, Arcturus, a Cygni, and (3 Tauri, does not seem to 

 affect the eye so as to require any alteration in the dimensions of the iris; a there- 

 fore becomes a given quantity, and may be left out. Admitting also, that the latter 

 of these stars are probably at double the distance of the former, we have d 2 in one 

 case 4 times that of the other; and the 2 expressions for the brightness of the stars, 

 will be / for those of the 1st magnitude, and ±1 for those of the 2d. 



The quantities being thus prepared, what I mean to suggest by an experiment is, 

 that since sensations, by their nature, will not admit of being halved or quartered, 

 we come thus to know by inspection what phenomenon will be produced by the 4th 

 part of the light of a star of the 1st magnitude. In this sense, I think we must 



* According to Mr. Bouguer, the surface of the moon absorbs about \ of the light it receives from 

 be sun. SeeTraitc d'Optique, p. 122. f p *"l. Trans, for the year 1796, P- 1&>, 1^7, 168.— Orig. 



