158 Miscellanies. 



assume x,p — x,m—p,r, s, i, Stc. for the roots of the cubes, then by- 

 proceeding as in the question, we shall have (3p^ — 6pa;)^=9p^ 

 {jp~2mY + \'2ap — \2p{in'^ -\-r^ -\-s^ ■}- , &;c.= sq. ~[Zp{p — '2m)-\- 

 2c]^=9p^(;o -2m)2 + 12;?c(p — 2m)+4c^, then asinthequ.p = 



c2 ( c^\ 



o~' c(2m— p)=cl 2m — o") =?ra^+^^+5^ + } &^c. put c=mn, r= 



6an 

 mr' , s=ms', &;c. .'. we shall have m=5 — ; — —-. — 77—; — j-—. — i — » 



12an* 

 hence, » = 7^ — ; — z— — tt— — tt-. — -g- — t^j and m — » = 



18a'' n-6an'^ -]- 6an{r' ^ -{-s"^ -\- , &c.) 



(3a+n3+r'3+/3 + , he.)'- 



-3 r=mr — 



6anr' 6ans' 



) s=ms'=n — ; — T', — 7r~, — r^r; — 5 — ' and 



3a+w=' + r'='+5'3 + , fee. da+n^-{r'^-\-s'^ + ,Uc. 



c a a 6an 



so on ; we also have a;=m-3- = m--=?n-- - =7^ — ; — ^1 — jr—. — q — 

 ' Sp c mn 3a+n^+r^-|-, occ. 



{3a + n^+r'^-^, he.) S6an^ - {3a+n^+r'^ + , hc.)^ 



~ 6w^ ~ 6n'{3a-{-n^-{-r'^-{-, &£C. 



_72awM-[(3a+n3+r'3+, he.)- -36an^]X(3a'{-n^+r'^+, hc.) 



p-x- ■ 6w2(3a4-M^+r'3 + , hc.)^ ' 



which with the values found above, are the roots of the required 



cubes. 



New Brunswick, Aug. 3, 1836. 



MISCELtANIES. 



FOREIGN AND DOMESTIC. 

 ASTRONOMY. 



Supposed new Planet. — On the 15th of February, M. Arago 

 read to the Academy of Sciences an extract of a letter from M. 

 Cacciatore, Astronomer at Palermo, to Capt. Smyth. The Sicil- 

 ian Astronomer announces in this letter, that he saw in the month 

 of May, 1835, near the 17th star of the 12th hour of the Catalogue 

 ofPiazzi, (right ascension 181° 30', and southern declination 4° 

 45',) another star of the 7th or 8th magnitude. Having taken the 

 distance of the two stars, he found that in three days the distance 

 had increased. The motion of the star was about ten seconds of 



