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graduated wooden pillar, which is placed in a vertical position by leveling screws. Two stages, A and B, slide along the pillar, and can be fixed at any part of it by means of clamps. One of these stages, A, has a circular hole cut in it, so as to allow the cylinder, p, to pass freely through it; the other is un- broken, and intercepts the passage of the weight. A pendulum, chronograph, or other device is used with the machine to measure time. The weight of the cylinders, p and g, being equal, they have no tendency to rise or fall, but are reduced, as it were, to masses without weight. When a bar is placed on p, the motion that ensues is due only to the action of gravity upon it, so that the motion of the whole must be considerably slower than that of the bar falling freely. Suppose, for in- stance, that p and g are each 7½ ounces in weight, and that the bar is 1 ounce, the force acting on the system — leaving the friction and inertia of the pulley out of account — would be 1-16 of gravity, or the whole would move only 1 foot in the first second, instead of 16. If the bar be left free to fall, its weight or moving force would bring its own mass through 16 feet the first second; but when placed on p, this force is exerted not only on the mass of the bar, but on that of p and g, which is 15 times greater, so that it has altogether 16 times more matter in the second case to move than in the first, and must, in consequence, move it 16 times more slowly. By a proper adjust- ment of weights, the rate of motion may be made as small as we please, or we can reduce the ac- celerating force to any fraction of gravity. Sup- pose the weights to be so adjusted that under the moving force of the bar or circular weight the whole moves through 1 inch in the first second, we may make the following simple experiments: Experiment I. — Place the bar on p, and put the weight in such a position that the lower sur- face of the bar shall be horizontally in the same plane as the 0 point of the scale, and fix the stage A at 1 inch. When allowed to descend, "the bar will accompany the weight, p, during 1 second and for 1 inch, when it will be arrested by the stage A, after which p and g will con- tinue to move from the momentum they have ac- quired in passing through the first inch. Their velocity will now be found to be quite uniform, being 2 inches per second, illustrating the prin- ciple that a falling body acquires, at the end of the first second, a velocity per second equal to twice the space it has fallen through. Experi- ment II. — Take, instead of the bar, the circular weight, place the bottom of p in a line with the point, and put the stage B at 64 inches. Since the weight accompanies p throughout its fall, we have in this experiment the same conditions as in the ordinary fall of a body. When released, the bottom of the cylinder, p, reaches 1 inch in 1 second, 4 inches in 2 seconds, 9 inches in 3

seconds, 16 inches in 4 seconds, 25 inches in 5 seconds, 49 inches in 7 seconds, and 64 inches and the stage in 8 seconds — showing that the spaces described are as the squares of the times. Experiment III. — If the bar be placed as in Ex- periment I., and the stage A be fixed at 4 inches, the bar will accompany the weight, p, during 2 seconds, and the velocity acquired in that time by p and g will be 4 inches per second, or twice what it was before. In the same manner, if the stage A be placed at 9, 16, 25, etc. inches, the velocities acquired in falling through these spaces would be respectively 6, 8, 10, etc. inches — 2 inches of velocity being acquired in each second of the fall. From this it is manifest that the force under which bodies fall is a uniformly accelerating force — that is, adds equal incre- ments of velocity in equal times. By means of the bar and the stage A, we are thus enabled to remove the accelerating force from the falling body at any point of its fall, and then determine the velocity it has acquired.

Atwood's machine will be found described and explained in almost any treatise on physics, and complete directions for performing the experiments are given in Glazebrook and Shaw's Practical Physics (New York, 1893).

A'TYS. See Attis.

AUBANEL, 6'ba'nel', Théodore (1829-86). A French author. He was the son of a printer of Avignon, and while following his father's profession, sought, throughout a period of thirty years, to bring about a regeneration of the language and literature of the troubadours of Provence, to which end he long collaborated with Mistral, Roumanille, and other félibres. He was called by some of his more enthusiastic admirers, 'the Petrarch of France.' He is best known by his poems La Miòugrano entreduberto (Paris, 1860). A drama of his in five acts, entitled Lou pan dóu pecat, was performed with great success at Montpellier in 1878.

AUBE, 6b. A central department of France, occupying the southern part of the old Province of Champagne, and a small portion of Burgundy (Map: France, L 3). The eastern part belongs to the basin of the Aube; the western to the basin of the Seine. Area. 2317 square miles. Population, in 1896, 250,907; in 1001, 245,596. The climate is mild, moist, and changeable, but on the whole healthful. A great portion of the area is arable land, producing grain, hemp, hay, and wine. There are some deposits of limestone, marl, and potters' clay. Capital, Troyes.

AUBE. A tributary of the Upper Seine (Map: France, L 3). In rises on the plateau of Langres, in the Department of Haute-Marne, and falls into the Seine at Pont-sur-Seine, after a course of 150 miles, for a small part of which it is navigable. It is used for the transportation of coal, lumber, and grain.

AUBE, Hyacinthe Laurent Théophile (1826-90). A French admiral. He was born at Toulon; entered the navy in 1840; served with distinction in the colonies, and was in charge of some coast defenses during the Franco-German war. In 1879 he was appointed governor of Martinque, and on his return to France in 1881 was made a rear-admiral. His appointment to the ministry of the navy and to the rank of vice-admiral followed in 1886. Aube was a strong