In this manner M. Peyrard proposes to construct eve ry individual mirror, so that if each of them is managed by one person, and directed to the same point, the heat of the solar beams may be multiplied to any extent. As the motion of the sun, and consequently the change of position in the image, is very slow, one person may di rect ten or more of the mirrors, without any injurious enlargement of the focus.
If the object required to be burnt is in motion, each mirror must be managed by two persons, one of whom is constantly employed in directing the intersection of thc wires upon the moving object, while the other takes care that the shadows of IK and N shall fall upon their pro per places.
The attention of AI. Pcyrard was next directed to the effects which might be expected from any given combi nation of mirrors ; and the following arc the data upon which lie proceeds. They arc dented, from the expe 1 imcnts of Buffon.
1. The light of the sun reflected by a plane glass mir ror, does not lose more than one half by reflection at short distances.
2. At great distances it loses almost none of its force, from the thickness of the air through which it passes ; and, 3. Its force is diminished solely by the int crse ratio of the augmentation of the spaces which the image occu pies upon a plane perpendicular to the reflected rays.
From these principles, and from the consideration that the rays reflected from a circular piece of mirror on a line perpendicular to its surface, form a cone whose an gle is 32' the diameter of the sun, AI. Pcyrard has com puted the distances at which the reflected image of a mirror five decimetres' in diameter, is doubled, tripled, quadrupled, thus : 3. On the I 1th of April, a beech plank, partly burned, was set on fire by 54 times the sun's heat.
4. On the same day, sonic small combustible substan ces were burnt by three times the sun's heat.
5. On the same day, a large pewter flask, weighing 6 pounds, was melted by I li times the sun's heat.
6. Some thin pieces of silver were melted, and a piece of sheet iron was made red hot, by 29! times the sun's hcat.t 7. Silver plates melted with 374 times the sun's heal.
By supposing thatfive times the heat of the sun is suf ficient to set lire to tarred planks, Pcyrard imagines that eight times the sun's boat will be sufficient to set on lire all kinds of wood, and upon this principle Ito has computed the following table, suited to his own mirrors of live decimetres in diameter.
If these distances were double, triple, quadruple, the tiiameters of the mirrors, instead of being five would be ten, fifteen, twenty, Scc. decimetres.
It follows from the preceding table, that if any given combination of mirrors produced a certain degree of heat ..t a small distance, in order to produce the same degree of heat at the distance of 22,25 metres, double the num ber of mirrors would be required ; at the distance of 39,33 metres, triple the number would be required, and so on.
From an examination of Bunn's experiments, Al. Peyrard has obtained the following results, respecting the multiplication of the direct heat of the sun, lvhich is necessary to burn different substances.
I. On the 23d of Alarch, at noon, a plank of tarred beech-wood was set on lire by 41 times the direct heat of the sun.
2. On the loth of April, in the afternoon, a tarred plank was set on fire by the sun's heat.
In order to find the number of mirrors x necessary for burning wood at any distance d, we have the following analogy : 53.72: 53.72 + d = 1 : and
+ = By making the height and breadth of the mirrors dou ble, triple, quadruple, Stc. it is obvious that they would inflame wood at double, triple, and quadruple distances.
Peyrard is of opinion, that with 590 glasses five deci metres in diameter, he could reduce a fleet to ashes at the distance of a quarter of a league ; that if they were a metre in diameter, he could produce the same effect at the distance of half a league ; and that if they were two metres in diameter, the same result would be obtained at the distance of a league. In this calculation, however, M. Pcyrard has completely omitted to take into account the great diminution of effect which must neces sarily arise from any deviation in the surfaces of the mir rors, from a perfectly plain figure, and from a want of parallelism in the surfaces. Even if all the mirrors trete parallel glasses ground with the same care as those which are used for reflecting instruments, the diminution of effect would be enormous at the distance of a league, as the angular deviation increases exactly with the dis tance. An experimental proof of this operation may be obtained, by looking into a mirror at different distances At a short distance the worst mirror will give a tolerable representation of the observer, but as the distance in creases, the distortion becomes very great. Even in the finest mirrors that are now made as articles of furniture, we are confident that the image will be very perceptibly distorted at the distance of 50 feet. This cause is, we fear, the most insurmountable obstruction to the process of burning objects at a great distance. By a numerous combination of large mirrors, it may be possible to in flame wood, at the distance of a quarter of a mile ; but we think that this is the greatest distapee at which ef fects of this kind will ever be produced.
Having thus given a full account of the various catop tric burning instruments which have been constructed, we shall conclude this part of the article with sonic gene ral remarks.
In the present state of military science, it is very ob vious that burning instruments can never be employed as an engine of war ; and therefore any attempt to con struct mirrors for burning at a distance must be con sidered more as a matter of curiosity than of use. The formation of instruments, however, for burning at short distances, is a subject of the first importance to science ; and we have no doubt that they will, some time or other, be employed as the most powerful agents in chemistry and the arts. Though catoptric burning instruments of great power have been constructed, yet their effects have never been so great as those of lenses, and they are be sides liable to numerous disadvantages. The burning point must evidently lie between the centre of the mir ror and the sun ; and therefore the operator cannot so easily perform his experiments as when the focus lies on the other side of the instrument. All his operations, in deed, have a tendency to obstruct the light before it falls upon the reflecting surface. This evil will not admit of a remedy, and consequently we must have recourse to instruments of a dioptric or catadioptric nature, which are alone capable of uniting great power with great faci lity of management.