Oi tht; Chancres in the Declination of the Stars. 175 



Ex. 5. Transform the lunction x^ — yx^-^-i-jx—ir, into 

 another which shall have .r— 2-333 instead of .r. 



Operation. 

 417 —15(2-333 



+7 



+1 -1 



+0-79 



+0-67 —0-763 



-fO-6679 



+0-6667 -0-742963 

 -0-007 



— 0-001- +0-666679 

 1 —0-001 +0-666667-0-740962963 

 Here I =2-333 &c. and the coefficients of the transformed 

 function are continually approaching respectively to 1 S 

 and |iJ. . 5 5 T 



Comparing this example and the next precedhig ; it appears 

 that the length of the operation is greatly increased by re- 

 ducing the vulgar fraction to a decimal. 



Exanij)les in the extraction of roots will not be necessary 

 at this time, as these have already been given in the Philoso- 

 phical Magazine for September 1822, before alluded to. 



XXXVI. On the Changes 'which have taken phtce in the De- 

 clination of some of the ■principal Fixed Stars. Bu Jojjn 

 Pond, Esq. Astronomer Roijal, F.R.S.* 

 nPHE mural circle Iiaving in September last been put into 

 complete repair, and declared by Mr. Troughton to be in 

 as perfect a state as when first erected, I resumed my exami- 

 nation of the principal fixed stars which form the Greenwich 

 catalogue. In the course of a very short time, I found that 

 several anomalies, which had previously given me much per- 

 plexity, still subsisted: some of these were of such a nature as 

 to lead to a suspicion that a change might possibly have taken 

 l)lace in the figure of the instrumeiit; on the other hand, there 

 were circumstances that strongly militated against such a sup- 

 position. 



Several of the stars in which the supposed discordance ap- 



* I'Vom the I'liilosohliical Transactions of the Hoval Socirtv of London 

 \H2:\. I 'art 1. ... 



peared 



