To reduce any of the weights in the preceding table to English averdupois pounds, nothing will be necessary but to divide the grains Troy, in the first column, by 7000.

FRENCH WEIGHTS.

THE Paris pound, poids de mark of Charlemagne, contains 9216 Paris grains: it is divided into 16 ounces, each ounce into 8 gros, and each gros into 72 grains. It is equal to 7561 English Troy grains. The English Troy pound, of 12 ounces, con

* Sometimes the gros is divided into 3 deniers, and cach denier into 24 grains.

tains 5760 English grains, and is equal to 7021 Paris grains.

The English averdupois pound, of 16 ounces, contains 7000 English Troy grains; and is equal to 8538 Paris grains.

Myriagramme

Eng. Troy grains.

15445'79386

A decagramme is 6 dwts.

154457*93860 10:45 grs. Troy, or 2 drs. I scr. 14'45 grs. apath. weight, or 5648 drams, averdupois.

A hectogramme is 3 oz. 8.48 drs. averdup.

A chiliogramme is 2 lbs. 3 oz. 4·87 drs. aver. A myriagramme is 22 lbs. 1 oz. 073 drs. aver.

MATHEMATICAL

AND

PHILOSOPHICAL

RECREATIONS.

PART FOURTH.

Containing many curious Problems in Optics.

THE properties of light, and the phenomena of

vision, form the object of that part of the mixed mathematics, called optics; which is commonly divided into four branches, viz, direct optics, or vision, catoptrics, dioptrics, and perspective.

Light indeed may reach the eye three ways: either directly; or after having been reflected, or after having been refracted. Considered under the first point of view, it gives rise to the first branch of optics, called direct optics, or vision; in which is explained every thing that relates to the direct propagation of light, or by a straight line from the ob ject to the eye, with the manner in which objects are perceived, &c.

Catoptrics treat of the effects of reflected light, and the phenomena produced by the reflection of light from surfaces of different forms; plane, concave, convex, &c.

When light, by passing through transparent bodies, is turned aside from its direct course, which is called refraction, it becomes the object of dioptrics. It is this branch of optics that explains the effects of refracting telescopes, and of microscopes.

Perspective ought to form a part of direct optics, as it is merely a solution of the different cases of the following problem: On a given surface to trace out the image of an object in such a manner, that it shall make on the eye, when placed in a proper station, the same impression as the object itself a problem purely geometrical, and in which nothing is required but to determine, on a plane given in position, the points where it is intersected by straight lines drawn to the eye from every point of the object. Consequently, the only thing here borrowed from optics, is the principle of the rectitude of the rays of light, as long as they pass through the same medium: the rest is pure geometry.

Without confining ourselves to any other order than that of method, we shall now take a view of the most curious problems and phenomena in this interesting part of the mathematics.

On the nature of light.

BEFORE we enter into any details respecting optics, we cannot help saying a few words on the nature and properties of light in general.