VOL. LXXXIX.] PHILOSOPHICAL TRANSACTIONS. 475 



greater altitude ; then will the error in the result be to the whole correction of the 



i L /• \ fk — tk . tk th tz lyS'—dx. r . 

 lat. ( l ) : : - : tz : : —- : — - : : -— : rrr x X l : : 7-5 X tz : s L . 



\ ' 2 2 15TA 2 15Ay^ y 



This error will consequently be equal to — ' ; and hence it appears that, if we 



had pursued this method in the last example, and there had been an error of a mi- 

 nute in the time given by the clock, there would not have been an error of a single 

 second in the conclusion. 



4. If the time were determined by equal altitudes, and one of them were to be 

 employed in computing the area gb, it is manifest that we should entirely exclude 

 the error which has just been considered. It would be necessary however, in order 

 to correct by the 2d observation, any inaccuracy that may have occurred in reading 

 off at the first, to move the index, and then bring it apparently to the same posi- 

 tion again, before we proceeded to take the 2d altitude. A 5th example is then 

 calculated according to these remarks ; after which is given a short specimen of the 

 tables before mentioned. 



The process observed in this table will require very little explanation. The first 

 column contains the observed double altitudes, as they were read off from the sex- 

 tant ; the 2d contains the corresponding times given by the clock ; the third con- 

 tains the times from noon determined, with sufficient exactness, by taking half the 

 interval between the first and last observations, (in which the altitudes are equal,) 

 and supposing this to be the time elapsed between the first observation and the sun's 

 reaching the meridian. The fourth column is formed of the log. cosines of the hour- 

 angles taken immediately from the argument of the first table ; and the last column 

 exhibits the latitudes deduced from every two corresponding altitudes, and is in- 

 tended to show the agreement between these results. 



It is not necessary that we should employ the tables in this operation : for we 

 may take the log. cosines of the hour-angles from Taylor's Logarithms, after the 

 time is reduced into degrees, minutes, and seconds ; and, by dividing the area gb = 

 7537, by the area gc = 203, (the natural number belonging to the log. 3.3081,) we 

 shall obtain the correction required. 



VIII. A Fourth Catalogue of the Comparative Brightness of the Stars. By Wm» 

 Herschel, LL.D., F.R.S. p. 121. 



After the usual list of the stars, are added the following notes. 



Notes to Auriga. — y Is (3 Tauri. 



f Is 32 Camelopardali. 



h " Oct. 5, 1798. The time of this star, in the observation of Flamsteed, 

 vol. 2, p. 18Q, is marked :: ; but it cannot be much out, as the star seems to be in 

 the place assigned to it by the British catalogue." 



6l. The ra in the Atlas Ccelestis requires a correction of — 42'. 



Notes to Draco.-*-i Is 87 Ursae. 



3P2 



