Description of a Burning Mirror. 133 
whieh happened on February 17th. The observed: place, 
which he has done me the honour to communicate, agrees 
with surprising exactness to the computed one deduced 
from the last and most improved elements. Mr. Groom- 
bridge, I believe, is the only astronomer in this country 
who has observed this opposition. 
XXVI. Description of a Burning Mirrer, by means of 
which we may reflect and fix on any Object, whether at 
Rest or in Motion, the solar Rays in as great a Quantity 
as we please. By F.PEYRARD, Professor of Mathematics 
in the Bonaparte Lyceum. Translated from the French, 
Report made to the Class of Physical and Mathematical 
Sciences of the French Institute on the above Subject. 
M. Pryrarp, who has recently published an elegant trans- 
jJation of the works of Archimedes, naturally turned his 
attention to the way in which that great geometrician is 
said to have set fire to the fleet of Marcellus before Sy- 
racuse. The ancients aud the authors of the middle aye 
assert that he employed a burning mirror; but none of 
them enter into details ample enough to give us an exact 
knowledge of his process. Anthemius, who in the sixth 
century built the church of St. Sophia at Constantinople, 
and who seems to have been an excellent architect, sug- 
gested an assemblage of plain mirrors which might produce 
the same effect with the mirror,of Archimedes. Since that 
period, Kircher, who perhaps was not acquainted with the 
works of Anthemius, preposed something similar. Fi- 
nally, within these few years, M. de Buffon contrived a 
burning mirror composed of 168 plain glasses, and every 
person 1s acquainted with his experiments on the subject. 
The above three processes, which are all closely alike, are 
attended with serious inconveniences. 
In order that a mirror may reflect upon one point the rays 
of the sun, regarded as parailc} to each other, we know that 
its reflecting surface ought to form part of that of a parabo- 
Joid of revolution, the axis of which is parallel to the rays 
of light, and the focus of which ts a point of union. If the 
mirror should be composed of a great number of plain 
Mirrors of a middling size, the planes of these last ought to 
be parallel, each to the tangent plane at the surtace of the 
paraboloid, at the point where it is cut by the corresponding 
vector ray. Now, in virtue of the sun’s motion, the posi- 
tion of the axis of the paraboloid changes in a very rapid 
; 3 manner 
