5°* Penetration into Space by Tele/copes. 



In order to take a fecond ftep forwards, we muft enter into feme preliminary confidera- 

 tions, which cannot but be attended with confiderable uncertainty. The general fuppofi- 

 tion, that ftars, at leaft thofe which feem to be promifcuoufly fcattered, arc probably one 

 with another of a certain magnitude, being admitted, it has already been fliewn in a former 

 paper *, that after a certain number of ftars of the firft magnitude have been arranged about 

 the fun, a farther diftant fet will come in for the fecond place. The fituation of thefc may 

 be taken to be, one with another, at about double the diftance of the former from us. 



By diredling our view to them, and thus penetrating one ftep farther into fpace, thefe 

 ftars of the fecond magnitude furnifti us with an experiment that fhews what phsenomena 

 will take place, when we receive the illumination of two very remote objefts, equally bright 

 in themfelves, whereof one is at double the diftance of the other. The expreffion for the 

 brightnefs of fuch objects, at all diftances> and with any aperture of the iris, according to 



our foregoing notation, will be -^; and a method of reducing this to an experimental 



inveftigation will be as follows : 



Let us admit that « Cygni, (3 Tauri, and others, are ftars of the fecond magnitude, fuch 

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

 ture of the iris will probably undergo no change ; fince the difference in brightnefs, between 

 Sirius, Arfturus, « Cygni, and 3 Tauri, does not feem to afFe£l the eye fo as to require any 

 alteration in the dimenfions of the iris ; a, therefore becomes a given quantity, and may be 

 left out. Admitting alfo, that the latter of thefe ftars are probably at double the diftance 

 of the former, we have Z)i in one cafe four times that of the other ; and the two expref- 

 fions for the brightnefs of the ftars, will be / for thofe of the firft magnitude, and \ I for 

 thofe of the fecond. 



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

 fince fenfations, by their nature, will not admit of being halved or quartered, we come thus 

 to know by infpe£tion what phaenomenon will be produced by the fourth part of the light of 

 a ftar of the firft magnitude. In this fenfe, I think we muft take it for granted, that a cer- 

 tain idea of brightnefs, attached to the ftars which are generally denominated to be of the 

 fecond magnitude, may be added to our experimental knowledge j for by this means, we 



are informed what we are to underftand by the cxpreflions , ■=====r:, - „ ^" 



' ^ O* Sirius^* /5Tauri> 



We cannot wonder at the immenfe difFerence between tlie brightnefs of the fun and that of 



Sirius ; fince the two firft cxpreflions, when properly refolved, give us a ratio of brightnefs 



of more than 170 thoufand millions to one; whereas the two latter, as has been fliewn, 



give only a ratio of four to one. 



• Phil. Tranf. for the year 1796, page 166, 167, 16S, 

 ■f- The names of the objects Q , Sirius, /3 Tauri, are here ufed to exprefs their diftance from us. 



What 



