Notice of the Report on the Fishes of New York. 275 
lar value is assigned to a, provided that none of the quanti- 
dyx d? ox ; 
ties 92; Ge? de®? 
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 eee of algebra.’ If we substitute 
&e. becomes ‘infinite when the ‘particular 
dpr 
the particular value x2=0 in (A), oad denote what 92, age ke. 
dy’'x 6 
become wien we substitute x=0 in them, by 92, Gp» &c., then 
if we write x for h, oe we may evidently do,) (A) will be 
d® 
changed to 9(x)= caet r+h se at + bite (A’), which is 
Maclaurin’s theorem; and which is applicable always when the 
dy’x 
quantities vx, ‘ae &e. are. hone 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). ae h 
is negative, the odd powers of / in (A) are negative, and must 
have the sign — ; and similar goer are tas seer to oar 
~ New Brunswick, Api 1843. oy 
; pal ; 
Ane. VIL—Notice se vinden of Dr Dekjs Report ‘ai the 
1 tate CT York ; ch r, M.D. 
[Read before the Boston Society of Natural History, June 21, 1843.] 
he aaa I read to ae ociety 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 ‘put fearing I may still longer be detained from giving 
that careful attention to the volume referred to, which, from the 
popes patronage under which it has been produced, will 
ubtedly be looked upon as authority in the department upon 
whale 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- 
