VOL. LXXXVI.] PHILOSOPHICAL TRANSACTIONS. 7^9 



and the expression of its lustre will be had by ri-/.y. And as Flamsteed marks the 

 magnitudes of these stars 3 m 4 m 3 m, my arrangement does not agree with 

 his. If we should now suspect x to have changed its lustre, recourse may be 

 had to another star on both sides, which gives ^myi. The magnitudes of Flam- 

 steed are 3m 3 m 4m 3m 3.4 m, where x. again seems to be placed in a situa- 

 tion to which it is not intitled. 



A defect of this arrangement, which was not immediately perceived, is that 

 in taking the stars of a constellation we have not always a proper connection of 

 the steps of the series that may be formed of them: there being too much dif- 

 ference in the lustre of some of the stars, and too little in others. Other in- 

 conveniences will also arise from the multiplicity of the members of a general 

 series, and the trouble of arranging them when they are nearly equal. To get 

 over these difBculties, I marked the stars that differed much in lustre by mag- 

 nitudes or degrees of difference; in which I assumed 3 different sorts of each: 

 namely, 1' 1" l" 2' 2" 2'", &c. For instance, " May 12, 1783. Order of 

 the stars in Bootes; al' si" y,2"' yfiSS' ^3" ^3'" 7r4." That this is not recurring 

 to the old method of magnitudes, will appear when we consider that the stars 

 are strictly compared. The series xiny^S^l^Tr remains established, but the differ- 

 ence in the gradation of brightness between the members of the series is added 

 to it. At first this seemed to answer the intended purpose; for ain not being 

 sufficiently distinguished, the addition 1' to a, and 2" to i, showed that a was 

 very much brighter than i, while 2'" added to » denoted only a very small dif- 

 ference between this and £. The difficulty which immediately after arose in the 

 choice of the magnitudes however, soon convinced me that the fallacy of them 

 would still have some influence on the arrangements. 



The same evening I marked the stars in Leo thus: " Order of the stars in 

 Leo; xl'" y2' (32' Ss ^Gn fxo ^kt." Here I parcelled them together in the order of 

 brightness, but could not find a convenient way to denote the different degrees 

 by using any derivation from magnitudes; therefore I contented myself with 

 placing those close together that agreed nearly with each other, and kept a little 

 distance between those that differed rather more. This might perhaps have an- 

 swered the required end, if the confusion which would arise from the distance of 

 letters had not proved a great objection. And that it would unavoidably bring 

 on mistakes we may see by the other constellations which were arranged that 

 evening. " Draco yn(i J^i GAax g Cygnus a yi (iSC, 6 Hercules (3(^a Syitt yijj. r* 

 changed." 



* I called it r changed, because this star, which in my edition of 1725 is marked 3 m, is only of 

 the 5th magnitude. At that time I ascribed the difference to a change in the star; but I have since 

 found tliat there is an error in the edition of 1725 which is not in that of 1712, where the star is 

 marked as it ought to be, of the 5th magnitude. — Orig. 



