VOL. LXXXVl.] PHILOSOPHICAL TRANSACTIONS. 7"^^ 



the series has been strictly ascertained. The reason of this is obvious. For by 

 the order in which they are placed, it appears that 30 has been deemed equal to 

 24, and 24 equal to 77 i but it is not affirmed that 30 has been compared to 77- 

 There will be a great probability that these last two stars do not differ sensibly or 

 materially; but since actual comparison is what we are to goby, the order in 

 which the stars are given must remain. 



When two stars are so nearly alike in their lustre that they may be almost 

 called equal, and even now and then leave us doubtful to which to give the pre- 

 ference; but when on a longer inspection of them we always return to decide it 

 in favour of the same, I separate the numbers that denote these stars by a 

 comma. For instance, 41 , 94 Leonis. This expression can certainly not be 

 changed to 94 , 4 1 Leonis ; much less can the order of three such stars, as 20 , 40 

 , 39 Librae, admit of a different arrangement. If ever the state of the heavens 

 should be such as to require a different order in these numbers, we need not 

 hesitate a moment to declare a change in the brightness, of one or more of the 

 stars that are contained in the series, to have taken place. 



When two stars differ but very little in brightness, but so that even a doubt 

 cannot arise to which the preference ought to be given, I separate the numbers 

 by which they are to be found in the catalogue by a short line. For instance, 

 17—70 Leonis; or 68 — 17 — 70 Leonis. If, in the former instance, a 

 breaking in on the order is to be considered as a proof that at least one of the 

 stars has undergone a change in its lustre, much more must that change be evi- 

 dent in this case, where the stars are separated by lines instead of commas. 



When two stars differ so much In brightness that one or two other stars might 

 be put between them, and still leave sufficient room for distinction, they become 

 partly unfit for standards by which the lustre of other stars can be ascertained. 

 But as proper intermediate stars sometimes cannot conveniently be had, we are 

 often obliged to retain them ; and in that case I distinguish them by a line and 



comma — , or by two lines, as 32 41 Leonis. A difference which exceeds 



those that are expressed by the above marks, I denote by a broken line thus 



, for instance 10 29 Bootis. It would be very easy to give a more 



extensive signification to lines by adding cross marks to them, such as, -(- 44. 

 -!_LJ- -fJ-fr &c. ; but in estimations that are to ascertain the brightness of stars, 

 such expressions would rather throw us back again to look for imaginary differ- 

 ences, resembling those which have been rejected in the old system of magni- 

 tudes. On the contrary, the marks I have introduced admit of so precise a defi- 

 nition, that they cannot possibly be mistaken: a point denoting equality of lustre: 

 a comma indicating the least perceptible difference: a short line to mark a decided 

 but small superiority: a line and comma, or double line, to express a consider- 

 able and striking excess of brightness: and a broken line to mark any other 



VOL. XVII. 4 Z 



