184 Description of a Burning Mirror. 
the straight line AB and by the point D, the middle of the 
band CDE. It is evident that the mirror DK willbe 
placed perpendicularly to the plane of the equator. 
This being done, let 2 person by turning the screw KL 
be instructed to keep the mirror in a position perpendicular 
on the vertical plane which passes by AB, and by the centre 
of the sun, and let another person adjust the mirror so as 
that the images reflected may be borne on a point Lof the 
axis. The mirror being adjusted, it is evident that the 
images reflected at the point D will there remain fixed 
during the whole of the time that the sun is upon the 
horizon. 
. By means of a quadrant GG and a needle fixed with the 
axis AB, it ‘will be easy, the hour of the day being known, 
to keep the mirror in its proper position. 
I have demonstrated that, the burning mirror of Archi- 
medes remaining perpendicular on the piane of the equator, 
it would be possible to fix on an object the solar images 
during the whole of the time that the sun was upon the 
horizon, and J have shown that this might be done in two 
ways. But itis evident that with the constructions which 
-I have given, the thing is not physically possible, except 
when the distance between the object to be inflamed and the 
mirror does not exceed certain limits. It remains to show, 
that by modifying the second construction we may set fire 
to an object placed at a great distance. 
While the straight line DK turns round the axis AB, 
the perpendicular drawn from the point K on AB engenders 
a circle parallel to the equator, and the straight line drawn 
from the point K parallel to AB engenders an ellipsis in 
the horizontal plane. Hence it follows that if we move 
the mirror DK in such a manner that this straight line 
prolonged moves according to the horizontal ellipsis, and 
that the pomt D is moved “according to the circumference 
of the circle parallel to the equator, the plane of the mir- 
ror remaining always parallel] to the axis of the earth and 
perpendicular upon the vertical plane which passes ‘by the 
centre of the sun and by the centre of the mirror, it is evident 
that the images reflected by the mirrors would remain fixed 
at the point L, as before. 
This being dune: let us see how we should srbcehd to 
burn an object placed at a great distance. 
The height of the pole and the distance of the object to 
be set fire to being known, the ellipsis which it is requisite 
ta 
