Notice of the Report on the Fishes of New York. 275 
lar value is assigned to x, provided that none of the quanti- 
: dpx d’ gx 
Hes 92, Go Gaz &c. becomes infinite when the particular 
value of x is substituted in them, and if any one of the aforesaid 
quantities is infinite, the true development will be given by (A) 
no further than to the term that first becomes infinite; and in 
order to obtain the development of the rest of the series, recourse 
must be had to particular processes of algebra. If we substitute 
: : a a 
the particular value z=0 in (A), and denote what gx, 4—, ke. 
, 
; A px 
become when we substitute z=0 in them, by ¢’a, a? é&c., then 
© 
if we write x for h, (which we may evidently do,) (A) will be 
dy’ d? y'x 
changed to ¢(v)=9'x+ —— 2+4 a x? + &c., (A’), which is 
Maclaurin’s theorem; and which is applicable always when the 
om Px 4 : 
quantities 9x, 7, &c. are none of them infinite; should any 
of these quantities be infinite, then we are to apply particular 
processes to obtain the development (when it is possible). If h 
is negative, the odd powers of h in (A) are negative, and must 
have the sign — ; and similar remarks are applicable to (A’). 
New Brunswick, April 21, 1843. 
Arr. VII.—WNotice of a portion of Dr. Dekay’s Report on the 
Fishes of New York; by D. Humpureys Storer, M.D. 
[Read before the Boston Society of Natural History, June 21, 1843.] 
Wuen I read to this Society a few weeks since a notice of Dr. 
Dekay’s Report on the Reptiles of New York, I promised to re- 
view his report on the fishes also of that state. Unavoidable 
circumstances have prevented me thus far from redeeming my 
pledge; but fearing I may still longer be detained from giving 
that careful attention to the volume referred to, which, from the 
munificent patronage under which it has been produced, will 
undoubtedly be looked upon as authority in the department upon 
which it treats, by scientific men abroad, if not in this country, 
I would at the present time offer you a few general remarks upon 
the descriptions of those species which are also found in the wa- 
