Penet fatten Into Space hy Tele/copes, 505 



fig. 3,; but r brought the mirror, during the trial, as clofe to the line connc£tIng the tw» 

 objects as pollble, in order to render the refle£ted rays nearly perpendicular. 



The refult was, that out of 100 thoufand incident rays, 67262 were returned; and 

 therefore, if a double refleiflion takes place, only 45242 will be returned. 



Before this light can reach the eye, it will fuiFer fome lofs in pafling through the eye 

 glafs ; and the amount of this I afcertained, by taking a highly poliftied plain glafs, of nearly 

 the ufual thicknefs of optical glafles of fmall focal lengths. Then, by. the method of the 

 fame author, page 21, fig. 5. I found, that out of 100 thoufand incident rays, 94825 were 

 tranfmitted through the glafs. Hence, if two lenfes be ufed, 89918; and, with three" 

 lenfes, 85265 rays will be tranfmitted to the eye. 



Then, by compounding, we (hall have, in a telefcope of my conftru£tion with one reflec- 

 tion, 63796 rays, out of 100 thoufand, come to the eye. In the Newtonian form, with a 

 fuigle eye lens, 42901 ; and, with a double eye glafs 40681 will remain for vifion. 



There muft always remain a confiderable uncertainty in the quantities here affigned ; as 

 ancwly.poliflied mirror, or one in high prefervation, will give more light than another that 

 has not thofe advantages. The quality of metal alfo will make fome difference ; but, if it 

 fbould appear by experiments, that the metals or glaffes in ufe will yield more or lefs light 

 than here affigned, it is to be underftood that the corre£lions muft be made accordingly. 



We proceed- now to find a proper expreffion for the power of penetrating into fpace, 

 that we may be enabled to compare its effefts, in different telefcopes, witli that of the na- 

 tural eye. 



Since then the brightnefs of luminous objefts is inverfcly as the fquares of the diftances, 

 it follows, that the. penetrating power muft be. as the fquare roots of the light received by 

 the eye. 



In natural vifion, therefore, this power is truly expreffed by .^Z <*' ^ > ''u<l> fince we have 

 now alfo obtained a proper corre£lion a;, we rauftapply.it to the incident light with te- 

 lefcopes. 



In the Newtonian and other conftru£lions where two fpecula are ufed, there will alfo be 

 fome lofs of light on account of the interpofition of the fmall fpeculum ; therefore, putting 

 b for its diameter, we have A^' — b-'- for the real incident light; This being correcled as 



above, will give the general expreffion V x I x Ai — b^ for the fame power in telefcopes. 

 But here we are to take notice.- that in refra£lors, . and in telefcopes with one refleilipn, 

 ^ will be IT 0, and therefore is to be left out. 

 Then,, if we put natural light /iz i,, and divide by a, we have the general form 



v^ X-. A* — b* . , 



-—— for the penctratmg power of all forts of telefcopes, compared to that of the 



nattiral eye as a ftandardj according to any fuppofed aperture of the iris» and proportion* of 

 light returned by refleftion, or tranfmitted by rcfradlioir. 

 Vol. IV.— February i8or; 3-T In 



