On the Curves of Trisection. 343 
trary, if the earth becomes positively electrified, and there 
happens a storm, it will escape or be conducted in to the up- 
per regions. In this case if it escapes in a large quantity at 
one point, the brilliant flame and noise mentioned by the 
Marquis de M. would be produced; but if it escapes in not 
very large quantity and at many points, it would produce 
those curious appearances recorded in history, and the lights 
seen in Vermont. 
The opinion that the earth at times becomes positively 
electrified appears to have, in amount, been entertained by 
the ancients. ‘The Tuscans divided thunder into two kinds, 
celestial and terrestrial; or that which falls from the clouds, 
and that which rises from the earth. The identity of light- 
ning or thunder and electricity, since the investigations of 
Franklin and Buffon is probably unquestionable. 
Bratriesorouen, Oct. Sth, 1821. 
P. >. That species of Epidote called Zoisite 1 have 
found in beautiful large crystals at Wardsborough Vt. : 
Some of which I shall put into the box which I am prepar- 
ing for the American Geological Society. 
N. B. This box has been received —Hditor. 
MATHEMATICS. 
—j- — 
Arr. XX.—On the Curves of Trisection ; by the Rev. 
Wiuuram Auten, D. D. President of Bowdoin College, 
Maine.—Communicated for this Journal. 
Two new curves may be called Curves of Trisection, 
since by means of either of them any angle may be trisected, 
and thus the problem be solved, which has engaged the at- 
tention of mathematicians for above two thousand years. 
These curves, if I mistake not, may justly claim to be con- 
sidered as geometrical curves, for they are distinctly defined, 
and also accurately described by points, and by a continued 
motion, instruments for which description I have invented. 
In this respect they are very different from the Quadratrix 
of Dinostratus, and that of Tschirnhausen, the Spiral of 
