SOMETHING ABOUT ILLUMINATION.

From time to time we hear of plans to illuminate whole cities by a great light from a single point. The credulity of the newspaper public about affairs belonging to Physics is so great, that we are not surprised if such plans are spoken of as practicable; though, indeed, one needs but cast a glance of reflection on them, to be at once convinced of their impracticability.

The impracticability does not consist so much in this, that no such intense light can be made artificially, as in the circumstance that the illuminating power of light decreases enormously as we recede from it.

In order to explain this to our readers, let us suppose that on some high point in New York city, say Trinity-church steeple, an intensely brilliant light be placed, as bright as can be produced by gases or electricity. We shall see, presently, how the remoter streets in New York would be illuminated.

For the sake of clearness, let us imagine for a moment, that at a square's distance from Trinity church there is a street, intersecting Broadway at right angles. We will call it "A" street. At a square's distance from "A" street let us imagine another street running parallel to it, which we will call "B" street; and again, at a square's distance, a street parallel to "B" street, called "C" street; thus let us imagine seven streets in all—from "A" to "G"—running parallel, each at a square's distance from the other, and intersecting Broadway at right angles. Besides this, let us suppose there is a street called "X" street, running parallel with Broadway and at a square's distance from it; then we shall have seven squares, which are to be illuminated by one great light.

It is well known that light decreases in intensity the further we recede from it; but this intensity decreases in a peculiar proportion. In order to understand this proportion we must pause a moment, for it is something not easily comprehended. We hope, however, to present it in such a shape, that the attentive reader will find no difficulty in grasping a great law of nature, which, moreover, is of the greatest moment for a multitude of cases.

Physics teach us, by calculation and experiments, the following:

If a light illuminates a certain space, its intensity at twice the distance is not twice as feeble, but two times two, equal four times, as feeble. At three times the distance it does not shine three times as feeble, but three times three, that is nine times. In scientific language this is expressed thus: "The intensity of light decreases in the ratio of the square of the distance from its source."

Let us now try to apply this to our example.

We will take it for granted that the great light on Trinity steeple shines so bright, that one is just able to read these pages at a square's distance, viz., on "A" street.

On "B" street it will be much darker than on "A" street; it will be precisely four times darker, because "B" street is twice the distance from Trinity church, and 2 × 2 = 4. Hence, if we wish to read this on "B" street, our letters must cover four times the space they do now.

"C" street is three times as far from the light as "A" street; hence it will be nine times darker there, for 3 × 3 = 9. This page in order to be readable there, would then have to cover nine times the space it occupies now.

The next street, being four times as remote from the light as "A" street, our letters, according to the rule given above, would have to cover sixteen times the present space, for it is sixteen times darker there than on "A" street.

"E" street, which lies at five times the distance from the light, will be twenty-five times darker, for 5 × 5 = 25. "F" street, which is six times the distance, we shall find thirty-six times darker; and, lastly, "G" street, seven times the distance from the light, will be forty-nine times darker than "A" street, because 7 × 7 = 49. The letters of a piece of writing, in order to be legible there, must cover forty-nine times the surface that our letters cover now.

But the reader will exclaim: "This evil can be remedied. We need but place forty-nine lights on Trinity steeple; there will then be sufficient light on "G" street for any newspaper to be read." Our friend will easily perceive, however, that it is more judicious to distribute forty-nine lights in different places on Broadway, than to put them all on one spot.

This is sufficient to convince any one that we may be able to illuminate large public places with one light, but not the streets of a city, and still less whole cities.