392 '  Miscellanies. 
We shall notice —_ more than the most important alterations 
from the edition of 18 
1. Ten pages are Kreee to the progress of Geology in America. 
In this the author professes to confine himself, chiefly, ‘to that field 
where he has been a continual laborer.” 
2. Twenty two pages ate occupied» with descriptions of organ- 
ized remains, and sixty eight lithographic figures are inserted, to 
represent the most common species, which he has personally exam- 
ined in situ. 
3. The author confesses, that Dr..Morton has’ demonstrated that 
the Marl beds of New Jersey are the genuine chloritic chalk of 
Brongniart ; but treats them as alternations with Tertiary clays. 
4. The red sandstone group of De La Beche, he says, appears 
to be equivalent to his saliferous, ferriferous, liasoid, and geodife- 
rous rocks; which he treats as subordinates. 
5. Near the end of the book, he gives an alphabetical list of local- 
ities; and he solicits materials for extending it, in another edition. 
His references to localities are much extended. Whether we 
agree or disagree with Mr. Eaton in his speculative views, his col- 
lection of facts, and very particular local references, are important 
contributions to the general stock of geological knowledge. - 
2. Rational expressions for sines, tangents and secants; by Davip 
Govtpy.—The following expressions have some peculiar properties, 
which, it is presumed, will entitle them to a place in the Journal of, 
Science, if they have not been before published. 
Let r be the radius of a circle, e, an arc of the same, n and Ps 
other quantities either known or unknown, and let 
"sine (Of o)== 2 F 7 ot te 
then, (rad.? —sin. 2)3 = 
(r¢—(2rmp)* + (0"-+*y ah cos. =r(n? —pt)- (ap) 
rad. ?-~s 
prin. (2arpe(a™-+p? )) =cosec.=7(n? +p? )-=2np, 
rad.?——cos.= 
72-1 (r(n? —p*)-+(n* +p*))—=secant=r(n? + p?)-=(n? =p) 
rad. X sin.+cos. 
(*X2rnp-+(n* +p +S 
(r(n2 —p serie +p?))= tan. = 2 rn p—~+(n?—p?), 
rad.?-+tan, = 
r?-(2rnp~ (n? — p?))=cotan. =r(n? —p?)+2np. 
