278 New Algebraic Series. 
Culm about 20 inches high, leafy ; leaves sheathing, short- 
er below, reddish brown at the root, linear-lanceolate, 
slightly scabrous on the margin, higher ones longer than 
the culm ; sheaths white or yellowish white opposite the 
leaf. and like the leaves, pubescent: bracts scarcely 
sheathing the peduncles except the lowest, leafy and lon- 
ger than the culm, less. pubescent than the leaves; an- 
drogynous spike from the same bract as the upper pistillate 
spike: spikes filiform with a flexuous rachis, alternate, 
at pendulous and rather loose flowered, peduncles 
longer than the sheaths ; staminate scale lanceolate, long, 
acute, hyaline with a green keel ; pistillate scale oblong- 
lanceolate, extending more than half the length of the fruit 
and terminating in an awn beyond the fruit, hyaline witha 
green keel. According to Muh. the upper spike is some- 
times wholly staminate and the scale shorter than the cap- 
sule. The latter variation I have rarely seen, and the for- 
mer has not occurred to me. ) 
MATHEMATICS AND MECHANICS. 
pile 
_ Art. X.—New Algebraic Series y Prof. J. Wallace, Co- 
lumbia, S. C. 
z 2? 23 
Let 1+ap+a(a+h)> 5 +a(a+k)(a+2k) 39 1 
23 
2 2? 
and 1+bp +3(6+4)7y+b(b+k)(b+2k) Fog tH 
be the given series, the latter differing from the former 00° 
ly, in the substitution of 6 for a. If these two series 
multiplied into each other, the resulting series will be ° 
the same form; a+é6 being taken for a or 6 in the above; 
or the form will be ; 
z 2 
I+(a+8)5 + (a-+b)a+b+h)—> +(atb)(a+b-+h)(at 
23 
pte ue 
or the series being actually multioli d the term: 
placed in order, A en es 
