714 PHILOSOPHICAL TRANSACTIONS. . [aNNO I796. 



a clear one, our author, who marked (3 1 .2 m, and y 2 m, ought to be under- 

 stood to mean that (3 is larger than y ; but we now find that actually y is larger 

 than p. Every one of the 1 1 stars here pointed out may be reduced to the 

 same contradiction ; and as the subject is of some consequence, we shall give a 

 few other instances of them, a- by Flamsteed is 4.5 m ; npuAxTrg are all marked 

 4 m, and therefore ought to be larger ; but o- is larger than any of them. 



TT is marked 4m; d 6.5 m, ^ and e 4.5 m, c and 72 5 m; therefore tt should be 

 larger than all the former ; but it is less. 



g is marked 4 m ; but there are 1 1 stars, namely, a-O 54 Acl^ec 72 27 48 6g, 

 all marked in various manners less than that star, yet they all exceed it in 

 magnitude. 



Not to proceed any farther with particulars, we ought to account for this by 

 allowing that Flamsteed did not compare the stars to each other, but referred 

 each of them separately to its own imaginary standard of magnitude. This is the 

 real source of all such contradictions, which therefore cannot be charged to our 

 author. As we should however take it for granted, that the magnitudes were 

 affixed to the stars with as much care as the nature of an unsettled standard 

 would allow, a short inquiry into the extent of the confidence we may place on 

 the method of magnitudes will be of considerable use. 



We have observed that in this method the brightness of stars is referred to 

 unsettled standards ; but admitting that a pretty general, though coarse idea, 

 may be formed of these magnitudes, it may be granted that a mistake of a 

 whole order in the first class cannot be supposed. The difference between a star 

 of the ] st and 2d magnitude is so palpable, that it excludes all suspicion of 

 taking one for the other. When sub-divisions are introduced, the case becomes 

 doubtful. 1.2 m may easily pass for 2.1m. But though these 2 notations 

 should not be sufficiently clear to be distinguished from each other, yet I am 

 inclined to believe that the former may be precise enough to point out a differ- 

 ence from 2 m, and the latter from 2.3 m. 



With the next order of stars the difference is much less striking ; but yet 2 m 

 will convey an idea which may be pretty well distinguished from 3 m ; however 

 2.3 m cannot be sufficiently kept apart from 3.2 m, or either of these expres- 

 sions from 3 m, or from 2 m. Perhaps the former may be distinguished from 

 3.4, and the latter from 4 m. The following step from 3 m to 4 m, or indeed 

 from 3.4 m to 4.5m, is less decisive than from 2 to 3 m. Again, if a star had 

 changed from 4 m to 5 m, or from 4.5 m to 5.6 m since Flamsteed's time, we 

 could hardly entertain more than a very slight suspicion of the alteration. 

 From 4 to 5.6 m, or from 4.5 to 6 m, would be a pretty considerable step, and 

 might serve as a foundation for an argument. A change from 5 m to 6 m is 

 such as no stress could be laid on ; and such are the changes from 5.6 to 6.7 m, 



