one of them was in a vertical position, or at the middle of its immersion, the next one should be just entering the water. A great many reasons were assigned for this mode of construction, which however are contradicted by calculation, as well as by experience.

It is now demonstrated, that the more float-boards such a wheel has, the greater and more uniform will be its effect. This result is proved by the researches of the abbé de Valernod, of the academy of Lyons, and those of M. du Petit-Vandin, to be found in the first volume of the Mémoires des Sçavans Etrangers.

The abbé Bossut, who examined, by the help of experiments, the greater part of the hydraulic theories, has demonstrated also the same thing. According to the experiments which he made, a wheel furnished with 48 float-boards, produced a much greater effect, than one furnished with 24; and the latter a greater effect than one with 12; their immersion in the water being equal. M. du PetitVandin therefore observes, that in Flanders, where running water is so exceedingly scarce, as to render it necessary to turn it to the greatest possible advantage, the wheels of water-mills are furnished with 32 float-boards, at least, and even with 48, when the wheel is from 16 to 19 feet in dia

meter.

PROBLEM XL.

If there be two cylinders, containing exactly the same quantity of matter, the one solid and the other hol low, and both of the same length; which of them will sustain, without breaking, the greatest weight

suspended from one of its extremities, the other being fixed?

SOME, and perhaps several of our readers, may be inclined to think that, the base of rupture being the same, every thing else ought to be equal. On the first view, one might even be induced to consider the solid cylinder as capable of presenting greater resistance to being broken: this however would be a mistake.

Galileo, who first examined mathematically the resistance of solids to being broke by a weight, has shewn that the hollow cylinder will present the most resistance; and that this resistance will be greater in the transverse direction, according as the hollow part is greater. He even shews, from a theory which approaches very near the truth, that the resistance of the hollow cylinder will be to that of the solid one, as the whole radius of the hollow is to that of the solid. Thus the resistance of a hollow cylinder, having as much vacuity as solid, will be to the resistance of a solid one, as ✓2 to I, or as 1141 to 1000; for the radius of the former will be 2, while that of the latter is unity. The resistance of a hollow cylinder, having twice as much vacuity as solid, will be to a solid one, as 3 to 1, or as 173 to 100; for their radii will be in the ratio of 3 to 1. The resistance of a hollow cylinder, the solidity of which forms only a twentieth part of the whole volume, will be to that of a solid cylinder of the same mass, as 21 to 1, or as 4'31 to roo; and so forth.

REMARK.

It may be readily observed, and Galileo does not fail to take notice of it, that this mechanism is that which nature, or its Supreme Author, has employed on various occasions to combine strength with lightness. Thus the bones of the greater part of animals are hollow: by being solid, with the same quantity of matter, they would have lost much of their strength; or to give them the same power of resistance, it would have been necessary to render them more massy; which would have lessened the facility of motion.

The stems of many plants are hollow also, for the very same reason, In the last place, the feathers of birds, in the formation of which it was necessary that great strength should be united with great lightness, are also hollow and the cavity even occupies the greater part of their whole diameter; so that the sides are exceedingly thin.

PROBLEM XLI.

To construct a lantern, which shall give light at the bottom of the water.

THIS lantern must be made of leather, which will resist the waves better than any other substance; and must be furnished with two tubes, having a communication with the air above. One of these tubes is destined to admit fresh air for maintaining the combustion of the candle or taper; and the other to serve as a chimney, by affording a passage to the smoke: both must rise to a sufficient height above

the surface of the water, so as not to be covered by the waves when the sea is tempestuous. It may be readily conceived, that the tube which serves to admit fresh air, ought to communicate with the lantern at the bottom; and that the one which serves as a chimney, must be connected with it at the top. Any number of holes at pleasure, into which glasses are fitted, may be made in the leather of which the lantern is constructed; and by these means the light will be diffused on all sides. In the last place, the lantern must be suspended from a piece of cork, that it may rise and fall with the waves.

A lantern of this kind, says Ozanam, might be employed for catching fish by means of light; but this method of fishing has, in some countries, been wisely forbidden under severe penalties.

PROBLEM XLII.

To construct a lamp, which shall preserve its oil in every situation, however moved or inclined.

To construct a lamp of this kind, the body of it, or the vase that contains the oil and the wick, must have the form of a spherical segment, with two pivots at the edge, diametrically opposite to each other, and made to turn in two holes at the extremities of the diameter of a brass or iron circle. This circle must, in like manner, be furnished with two pivots exactly opposite to each other, and at the distance of 90° from the holes in which the former are inserted. These second pivots must be made to turn in two holes diametrically opposite in a second circle; and this second circle must likeivise be furnished with two pivots, inserted in some

concave body, proper to serve as a covering to the whole lamp.

It may be readily seen that, by this method of suspension, whatever motion be given to the lamp, unless too abruptly, it will always maintain itself in a horizontal position.

This method of suspension is that employed for the mariners compass, so useful to navigators; and which must always be preserved in a horizontal situation. We have read in some author, that Charles V, caused a carriage to be suspended in this manner, to guard against the danger of being overturned.

PROBLEM XLIII.

Method of constructing an ancmoscope and an ane

mometer.

THESE two machines, which in general are confounded, are not however the same. The anemoscope serves for pointing out the direction of the wind, and therefore, properly speaking, is a weather-cock; but in common this term is used to denote a more complex machine, which indicates the direction of the wind by means of a kind of dial plate, placed either on the outside of a house, or in an apartment. In regard to the anemometer, it is a machine which serves to indicate, not only the direction, but the duration and force of the wind.

The mechanism of the anemoscope is very simple. (Fig. 41 pl. 9.). It consists, in the first place, of a weather-cock, raised above the building, and supported by an axis, one end of which, passing through the roof, is made to turn in a socket fitted