158 RMisdellantes: 
assume v, p—a,m—p,r, 8, t, &c. for the roots of the cubes, then by 
proceeding as in the question, we shall have (3p? — 6px)? =9p? 
(p—2m)? +12ap — 12p(m? +r3+s°+, &c.= sq. =[8p( p —2m)+ 
— 9p? ( p — 2m)? +12pe( p —2m)+4c?, then as in the qu. p= 
3a ¢ (2m — p)=e(2m—<-) =m*+ré+s?+,&c, put c=mn, r= 
mr’, sme’, &c.-2'5 
we shall have m= snr ited, wee. 
12an* 
a ome (8a4+n?+r/3+4 s3+4, &e.)? > and m— PS 
18a*n—6an‘ + Gan(r’? +8/3 +, &e.) 4H 
(Ba+n*+-r'3+5/3+, &e.)? Rar Ye 
F 6ans’ 
s=ms Bain? trots, ec.” and 
c a a 6an 
soon; we also have o=m— 3 =m— = m=" San? r+, ar 
A casted Ge.) _ scieam (3a+n?+r/3+, &c.)? 
n*(3a+n>-+-r/5+, &c. f and 
egies Pil )? -36an* |X (Batn?+r/3+,&c. ) 
ese 6n?(8a+n*+r/2+, &c.)? 
which with the values found above, are the roots of the required 
cubes. 
New Brunswick, Aug. 3, 1836. 
hence 
, 
6a 
Satnitr3+s'3+, &e. 
- 
MISCELLANIES. 
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- 
jan Astronomer announces in this letter, that he saw in the mouth 
of May, 1835, near the 17th star of the 12th hour of the Catalogue 
of Piazzi, (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 
