I had, therefore, once more, recourse to experiments. I took metal mirrors of different focuses and different degrees of polish, and by comparing the different actions on the same fusible or combustible matters, I found, that at an equal intensity of light, large focuses constantly have more effect than small, and I discovered the same to be the case with refracting mirrors.
It is easy to assign the reason of this difference, if we consider that heat communicates nearer and nearer, and disperses, if I may so speak, when it is even applied on the same point: for example, if we let the focus of a burning glass fall on the centre of a crown piece, and that this focus was only a line in diameter, the heat produced on the centre disperses and extends over and throughout the whole piece: thus all the heat, although used at first to the centre of the crown, does not stop there, and consequently cannot produce so great an effect as if it did. But if, instead of a focus of a line which falls upon the centre of the crown, we let fall a focus of equal intensity on the whole crown, every part being alike heated, then instead of experiencing the less heat, it acquires an augmentation; for the middle profiting of the heat with the other points which surround it, the crown piece will be melted in this latter case, while in the first, it will only be slightly heated.
After these experiments and reflections, I began to entertain sanguine hopes of making mirrors to burn at a great distance; for I no longer dreaded as before, the great extent of the focus; I was persuaded, on the contrary, that a focus of a considerable breadth, as two feet, and which in the intensity of the light would not be near so great as in a small focus of four lines, might, nevertheless, produce inflammation, and with more power; and that, consequently, this mirror, which, by mathematical theory, ought to have at least thirty feet diameter, would be reduced to one of eight or ten feet at most, which was not only a possible, but even a very practicable thing.
I then thought seriously of executing my project: I had at first a design of trying to burn at 200 or 300 feet distance with circular or hexagonal glasses of a square foot in surface, and I was desirous of having four iron carriages for them, with screws to each to move them, and a spring to adjust them; but the considerable expense that this required made me quit that idea, and I took two common glasses of six inches by eight, and a wooden adjustment, which, in fact, was less solid and precise, but the expence was more consistent with a mere experiment: the mechanism of which was executed by M. Passement.
It is sufficient to say, that it was at first composed of 168 glasses of six inches by eight each, about four lines distant from each other; these glasses moved in all directions, and the four lines of space between them not only served for the freedom of this motion, but also to let the operator see the place where he was to conduct his images. By means of this construction, 168 images could be thrown on one point, and, consequently, burn at several distances, as at 20, 30, and to 150 feet. By increasing the size of the mirror, or by making other mirrors like the first, we are certain of throwing fire to still greater distances, or to increase as much as we please the force or activity of those first distances.
It is only to be observed, that the motion here spoken of is not very easy to be executed, and that also there is a very great choice to be made in the glasses; for they are not all equally good, though they appear so at the first inspection. I was obliged to pick out of more than 500 the 168 I made use of. The method of trying them is to receive at 150 feet distance the reflected image of the sun, as a vertical plane; we must select those which give a round and terminated image, and reject those, whose thicknesses being unequal in different parts, or the surface a little concave or convex, have images badly terminated, double, treble, oblong, &c. according to the different defects found in the glasses.
By the first experiment which I made the 23d of March, 1747, at noon, I set fire to a plank of fir at 66 feet distance, with 40 glasses only, about a quarter of the mirror. It must be observed that not being yet mounted, it was very disadvantageously placed, forming an angle with the sun of twenty degrees declination, and another of more than ten degrees inclination.
The same day I set fire to a pitchy and sulphureous plank at 126 feet distance, with eighty-eight glasses, the mirror being still placed disadvantageously. It is well known, that to burn with the greatest advantage the mirror should be directly opposed to the sun, as well as the matters to be inflamed; so that, by supposing a perpendicular plane on the plane of the mirror, it must pass by the sun, and, at the same time, through the midst of combustible matters.
The 3d of April, at four o’clock in the afternoon, the mirror being mounted, produced a slight inflammation on a plank covered with pitch at 138 feet distance, although the sun was weak and the light pale. Great care must be taken, when we approach the spot where the combustible matters are, not to look on the mirror; for if, unfortunately, the eyes should meet the focus, inevitable blindness will ensue.
The 4th of April, at eleven in the morning, although the sun appeared watery, and the sky cloudy, yet it produced, with 154 glasses, so considerable a heat at 158 feet, that in less than two minutes it made a deal plank smoke, and which would certainly have flamed, if the sun had not suddenly disappeared.