we are often deprived at the same time of the light of both sun and moon. To have accomplished this end, it would have been sufficient to have placed the moon at first in opposition to the sun and in the plane of the ecliptic, at a distance from the earth equal to the one hundredth part of the distance of the earth from the sun, and to have impressed on the earth and moon parallel velocities proportional to their distances from the sun. In this case, the moon, being constantly in opposition to the sun, would have described round it an ellipse similar to that of the earth. These two bodies would then constantly succeed each other, and as at this distance the moon could not be eclipsed, its light would always replace that of the sun." *

The plan here proposed was one of startling boldness; but without assuming to defend the doctrine of final causes, it must be said in fairness that to afford light by night had never been claimed as the only design for which the moon was given. Other purposes no less important may be readily imagined. Moreover, the moon's light at the distance named by Laplace would have been little more than one twentieth part of that afforded by the full moon at its actual distance, or less than that of our new moon two days after the change. Such moonlight, though perpetual, would have had little comparative value. Again, the tidal effect upon the earth would have been scarcely perceptible. But without further insisting on these points, however important, let us compare the proposed arrangement with that of Nature. Would it have involved nothing inconsistent with the system's stability? or would its adoption have resulted in depriving our world of the moonlight enjoyed in the existing system?

The annexed figure illustrates Laplace's proposed arrangement. The distance at which he would have placed the moon from the earth is about 1,000,000 miles, or a little more than four times the actual distance. An eclipse of the moon is caused by its falling into the earth's shadow. This can extend into space only about 860,000 miles, and, as this is less than the distance of Laplace's proposed moon, the latter, as he remarks, could never be eclipsed.

Let us suppose the distance of the moon from the earth to be increased, what changes would be effected in the observed phenomena? At 478,000 miles, twice the present distance, the length of the lunar month would be seventy-seven days; the quantity of moonlight would be one fourth of what we now enjoy; and the height of tides in the open seas would be but a few inches. At 717,000 miles, three times the present distance, the length of the month would be one hundred and forty-two days, and the appar

* Système du Monde, Hart's translation, vol. ii, p. 79.

Figure omitted.

ent size of the moon would be reduced to one ninth of its present value. With increasing distance the phenomena would still further change, till at the orbit named by Laplace the month would be equal to the year, and the moon's enlightened hemisphere would be turned constantly to the earth. But the great astronomer's dream of perpetual moonlight-how long would it be realized?

Another question of vital importance is here involved in the theory under consideration-the variation of the earth's attraction on the moon supposed to be removed to a greater distance. This variation is more rapid than that of the sun's attractive force on the same body, as the distance between the sun and moon is four hundred times that between the moon and the earth. At what point, then, would our satellite escape from the earth's controlling influence and commence to revolve as an independent planet about the sun? This question, strangely enough, seems never to have received Laplace's consideration; at least his statement was continued without change in a later edition of his Système du Monde. This problem touching the moon's limit of stability was not solved until sixteen years after Laplace's death.*

The relative distances as well as the direction and force of the impulses necessary to produce the required motions in the scheme of Laplace were given by himself in the paragraph quoted. The state of things at double the moon's distance has also been estimated. At four times the distance, or somewhat more, we find Laplace's position of perpetual moonlight; but just here we find the region where the earth loses its control over the moon's motion. The moon escapes from the earth's influence, and henceforth owns allegiance only to the sun. She becomes a primary planet, with a year somewhat greater than ours and a day of doubtful length. As regards the earth, lunar tides can no longer exist. Moonlight and the moon would forsake us together; and the new condition of things, could it be realized, would be worse than the first.

From the case here considered we may learn (1) that dogmatism in regard to the divine plan in the structure and constitution of the universe is not always wise. Final causes may engage the attention of thoughtful minds, but who shall set limits to their extent or application? "Touching the Almighty," said Elihu, we can not find him out." (2) The wisdom manifested in the adaptations of material things around us transcends that of man's highest efforts. Attempts to disparage the skill of Nature's handiwork must end in failure and disappointment.

66

*The solution was first given by M. Liouville in 1842.

The failure of the theory proposed in the case of the earth and moon is no less striking when applied to Mars, Jupiter, or any other planet. In every instance the position of the satellite assumed to afford permanent moonlight would be one of instability. This striking fact renders the oversight of Laplace the more remarkable. It may be stated, however, that by the arrangement of several moons about the same planet almost, if not entirely, perpetual moonlight might be possible. The system of Jupiter and his moons furnishes a clear illustration.

In conclusion, we have seen, then, that where one of the greatest mathematicians of all time suggested a change-a so-called improvement in the system of the world-the modification would have left us without tides, or, worse still, the earth in the system proposed would have lost control of her satellite, and we would not only have been deprived of moonlight, but also of the moon. itself.

THE

ELECTRICITY AT THE WORLD'S FAIR.

BY CHARLES M. LUNGREN.

II.

HE facility with which a high temperature may be obtained with electricity, and the heat controlled and located just where it is wanted, makes this agent peculiarly well adapted to the heating of metals for welding and forging purposes. This was early recognized by Prof. Elihu Thomson, to whom the development of the art is chiefly due, and who has devised a great variety of apparatus capable of performing all classes of work, from the simple welding of two wires to the making of large and complicated joints.

The principle involved is very simple. If a current be passed through a rod or wire, heat will be developed in it if the current be of sufficient volume. If this circuit, instead of being formed of a continuous conductor, be a broken one, such as would be furnished by two rods whose ends abut, the heat will be developed first at the surface of con' act, as this is the point of greatest resistance, and then spread along the rods. And if, while the rods are in a heated condition, they be pressed together, they will become strongly united and form a perfect joint. On account of the radiation of heat from the surface and the cooling effect of the air, the rods become hotter at the center than at the surface, which is the reverse of what happens with a forge-heated bar, where the heating begins at the outside and gradually extends to the interior. This feature of the electric welding process has an important advantage in producing a firmer and more perfect joint, and

in diminishing the formation of surface scale. Tests show that the electric weld is much stronger than that made in the ordinary way in a forge, and, indeed, is in some cases stronger than other parts of the bar.

The machines designed by Prof. Thomson for carrying out this method of welding are extremely simple, the mechanical part consisting essentially of one or more pairs of clamps to hold the pieces to be united, and means for pressing them together while in a heated condition. In operating the machines the current is turned on by the workman by means of a switch; but Prof. Thomson has taken advantage of the movement of the pieces toward each other while the weld is being made to break the circuit, thus rendering the operation automatic and insuring the equal heating of the welded pieces. In machines for wire and small rod the welded wires and rods are pressed together by means of springs, but in those for larger work the necessary pressure is applied by hydraulic apparatus. The necessity for this will be appreciated when it is stated that the pressure requisite for steel is 1,800 pounds to the square inch, that for iron 1,200 pounds, and for copper 600 pounds.

Electrically the apparatus is as simple as it is mechanically. The alternating current, which has shown itself so flexible in the hands of the engineer in other departments of electrical work, is here called into requisition. Through the medium of converters the high potential machine current is transformed into others of great volume and low voltage suitable for this class of work. Currents of this character are rendered necessary by reason of the fact that all metals are very good conductors of electricity, and can therefore be heated only by currents of great amount. These currents range, in fact, from a few hundred ampères to eight and ten thousand. The voltage, however, is very low, rarely being more than four or five volts, and in large and heavy work sometimes not more than a single volt. On account of this very low electrical pressure all danger from the current is eliminated and the apparatus may be handled with the same freedom as any ordinary metal-working machine. In the distribution of the electrical appliances the current is usually generated by a machine conveniently located with reference to the source of power, and the current carried by wires to the welders, where the transformation takes place, each welder being provided with its own converter, proportioned so as to supply the character of current best suited to the special work of the machine. The current is under perfect control by means of regulating devices operated by the workman, the usual device employed being a reactive coil. The range of work possible with this method of welding is very great. It not only may be used in forming all ordinary welds with iron and steel, but

silver, platinum, gold, aluminum, and even cast iron may not only be welded together, but may also be welded to one another in many different combinations. In addition to welding, all sorts of brazing may be done by this method, as the same heat which

VOL. XLIV.-4

has been found capable of welding metals which have heretofore resisted all attempts to unite them direct, and which have therefore had to be brazed or soldered. Wrought iron, copper, brass,