220 Miscellanies. 
logarithmic formula, is that of Euler, but so modified and improved as 
scarcely to be recognized. The method of finding “ the number cor- 
responding to a given logarithm,” is different from any we have before 
seen. The method usually employed is by “ the reversion of series,” 
as it is called, a method which ‘is tedious and liable to the great objec- 
tion, that it does not reveal the law of the resulting series, by which 
any succeeding term may be inferred or deduced from the preceding 
terms, however numerous. ‘That law has been invented and applied by 
the author. ; 
In short, we consider the work to be a valuable one, and one from 
which almost any mathematician may derive advantage. 
6. Transactions of the Association of American Geologists and 
Naturalists, 1840-1842. Boston: Gould, Kendall & Lincoln. Royal 
8vo, pp. 544, with 21 plates.—This volume embraces the reports of 
the doings of the three first years of the Association of American Ge- 
ologists and Naturalists, at their meetings held at Philadelphia in 1840 
and ’41, and in Boston in 1842. Several of the papers it contains, and 
all the proceedings of the sessions, have already been before our read- 
ers in the pages of this Journal ; but the great bulk of the volume ap- 
pears now for the first time, and embraces all the papers read before 
the Association at its.three first meetings. .We shall not attempt any 
notice of its contents, but can assure our readers that the volume is 
every way creditable to American science, and must be considered as 
an essential companion to all who would keep up with the rapid pro- 
gress of American geology and the cognate sciences; while it gives 
& 
to the body from whichsit emanates a character which at once places 
it among the permanent ints of scientific progress. 
—= 
MISCELLANIES, 
DOMESTIC AND FOREIGN. 
_ 1, Notice of certain siliceous tubes (Fulgurites) formed in the earth; 
in a letter from Cuartes E. West, to the Editors, dated Rutgers Fe- 
male Institute, New York, March 21, 1843.—A remarkable natural 
phenomenon was observed a few years since in the town of Rome, state 
of New York. I was particular at the time, to gather what information 
I could respecting it, which is now submitted to the readers of your 
valuable Journal. 
A lambent flame was seen playing at night upon the surface _ of a 
sand bank, some seventy or eighty feet high, which forms the east bank 
