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To persons not familiar with optical researches it may appear incomprehensible that a star presenting, even with the telescope, no disk of sensible magnitude, could, nevertheless, appear so splendid. There is, however, a law of light, clearly established in optics, which will probably remove this difficulty. It is demonstrated that the apparent brightness of an object is not diminished by its removal from the eye, although the quantity of light which it gives is decreased in a high proportion. This statement may appear at first paradoxical; let us, however explain it.
If the sun, for example, were removed to twice its present distance it would appear to the eye with half its present diameter; yet, in its diminished size, the apparent brightness of its surface would be the same as that with which we behold it at the lesser distance. To illustrate this, let us suppose that a small circular opening is made in a card, and that the card is presented to the sun, so that a portion of the sun's disk only shall be seen through it, but that that portion shall be circular; the opening will present to the eye the appearance of a sun of less magnitude than the real one, but of equal brightness. Let the card then be held at such a distance from the eye that the circular portion of the sun's disk visible through it shall have a diameter equal to half of the entire disk. A sun will thus be seen of equal brightness with the true sun, but of only half the linear diameter, and one fourth the superficial magnitude. From this illustration it will be easily perceived that one object may smaller than another in apparent magnitude, and that it may give less light, but, nevertheless, be equally bright.
This being clearly understood, it remains to be shown, that if the sun were removed to double its present distance it would exhibit a surface to the eye as bright, though only half of the diameter. To comprehend this, let it be remembered that the light which proceeds from the smaller sun seen from double the distance, issues from the entire surface of the sun, while the light which would proceed from an equal portion of the sun's disk seen at its present distance, would only proceed from one fourth of the entire area of the disk. The actual quantity of light, therefore, which issues from the small sun, seen from the larger distance, is greater, in the proportion of 4 to 1, than that which proceeds from the small portion of the larger sun, seen at the lesser distance. It follows, then, that the actual quantity of light by which the object is rendered visible at the greater distance, is four times more than that by which the equivalent part of the nearer object is rendered visible at the lesser distance; but in consequence of the distance being less in the latter case, the intensity of the lesser quantity of light is four times greater. In short, it follows that as the object recedes from the eye the quantity of light which proceeds from a given portion of the visual area is increased in the same proportion as the square of the distance, while the intensity of the light is diminished in exactly the same proportion. What is, therefore, lost in intensity by increased distance, is gained in quantity; and the effect is, that the splendor of the object is not changed by distance, but only its apparent magnitude.
The apparent diameter of the sun is very nearly 2,000 seconds of a degree. If it were removed to 2,000 times its present distance it would present a diameter of one second; but it would appear as bright as a small portion of the present disk would appear having an apparent diameter 2,000 times less than its present apparent diameter; or if a pin-hole be made in a card, and a portion of the sun seen through it, which would subtend to the eye at an angle of one second, the appearance of such portion would be, as to brightness as well as to magnitude, that which the sun would have at 2,000 times its present distance.
Since, then, the brightness of the stars, in the proper sense of the term brightness, is not diminished by increased distance, we shall be the less sur
WATER-SPOUTS AND WHIRLWINDS.
Character and Effects of Water-Spouts.-Difference between Water and Land Spouts.-Land-Spout at Montpellier.-Land-Spout at Esclades.-Columns of Sand on the Steppes of South America.-Meteor at Carcassonne.-Meteor at Dreux and Mantes.-Land-Spout at Ossonval.-Meteor witnessed and described by M. Peltier.-Conversion of a Storm into a Land-Spout.-M. Peltier's Tables of Water-Spouts and Land-Spouts.-Analysis of the above Tables.-Water-Spouts seen by Captain Beechy.-Experimental Illustration of the Phenomena.-Illustration of the gyratory Motion of Water-Spouts.-M. Peltier's Deductions concerning Water-Spouts.-Action of charged Clouds on light Bodies.-Noise attending Water and Land Spouts.-Transition from direct to gyratory Motion.-Effect of Induction on watery Surfaces.-Disappearance of Pools, &c.