cities, where sundials serve only to regulate clocks and watches.

Solar, lunar, and aftral dials were formerly constructed: but of these the first were without comparison most in use. A dial is commonly a simple plane, on which the hours, and parts of hours, are marked by the projection of a shadow, or by a luminous point passing through a perforated plate. Sometimes however dials are drawn on curved surfaces, as on those of a cone, a cylinder, a sphere, &c. The principles of the construction are the same in every case: the only difference is in the length and multiplicity of the operations requisite. I shall confine myself, therefore, to giving a general idea of sundials, traced on planes, and denoting the hour by the projection of shadows. The solution of this problem is easily reducible to a simple question in geometry, as will clearly appear.

Let us suppose, that the Sun moves daily round the concavity of an immense sphere, the centre of which is that of the terrestrial globe considered as immovable; and let us conceive an axis passing through this centre perpendicularly to the equator, as well as to all the parallels which the Sun successively describes: it is evident, that, if we attribute a certain magnitude to this axis, the Sun will continue to project it's shadow on the dial, that is in this instance on a plane in a given position, and passing through the centre of the celestial sphere. Hence it follows, that, to mark the hours of the day on the dial, we have only to determine the intersections of the plane of the dial by the series of planes, which pass through

the

the Sun at each instant of it's motion and through the axis of the globe; a problem, which to the geometrician has no difficulty.

The principle of this construction supposes, as we see, that the radius of the terrestrial globe is infinitely small in proportion to the radius of the circle described by the Sun's diurnal motion; and this may be considered as true in practice.

On the dial no more lines are traced, than are indispensably necessary. The style fixed in the dial, and making part of the axis of the World, may be Jonger or shorter, at pleasure.

Sometimes the artist is content with marking the hours by the arrival of the shadow of the point of the style on the lines drawn to denote them. There are dials, however, on which not only the hours and parts of hours are marked, but in addition some remarkable points of the path traced by the shadow of the point of the style, and the entrance of the Sun into the different signs of the zodiac. For instance, let us suppose a horizontal sundial made for the city of Paris: the solar ray, which passes by the point of the style, being indefinitely prolonged, and considered as a physical and inflexible line, we see, that, during the revolution of the Sun, this line will describe the surfaces of two cones joined together at their summit, which is the point of the style; and that the shadow, projected by this point, will form on the dial a portion of an hyperbola, for each day, or each parallel, since by prolonging the plane of the dial it will cut the two opposite cones. Another parallel gives another portion of an hyperbola,

Now

as all these portions of an hyperbola, being different magnitude and position, would produce confusion on the dial, if they were traced out completely, the diallist contents himself with marking the points of the shadow for the entrance of the Sun into each sign of the zodiac; and these points being joined together, a series of arcs is formed, which are called the arcs of the signs.

menes.

The inventions of dials is very ancient. Diogenes Laertius ascribes the first idea of them to Anaxi-. In the ninth book of Vitruvius we find a concise description of several ancient dials, the names given to them, and those of the persons by whom they were invented. To this work therefore I refer my reader, and likewise to the excellent notes, with which Claude Perrault has accompanied his translation of this author.

CHAP.

CHAP. VI.

Origin and Progress of Optics.

Ir would be waste of time to enter into the physical explanations, which the ancients, and Aristotle in particular, have given of the phenomena of vision. In these the abuse of occult qualities is carried to excess but sometimes they were satisfied with exploring nature by the torch of experiment, from which they failed not to reap advantage. Thus the school of Plato, for example, was clearly acquainted with the first principles of optics, namely the propagation of light in a straight line, and the property it has of being reflected at an angle equal to that of it's incidence.

Long before this mirrors were constructed of metal; and the use of glass was likewise known, for which, according to Pliny, mankind were indebted to accident. Some merchants, who traded in mineral alkali [nitrum], having occasion to dress their victuals on the borders of the river Belus, in Phenicia, where they had landed, and not finding any stones at hand to support their kettles, fetched some pieces of the alkali from their ship for the purpose. These the fire melted' with the sand of the shore, and caused to flow in valuable translucent streams, whence originated the making of glass. Nat. Hist. lib. xxxvi, chap. 26.

In the time of Socrates [A. c. 433] the manufacture of glass had made considerable progress, and the use of burning glasses was already become very common. This the following passage from the second act of the Clouds of Aristophanes shows.

debts, proposes the folStrepsiades, You have fine transparent stone,

The author introduces Socrates giving lessons in philosophy to Strepsiades, a citizen of Athens, and a man of low cunning. The subjects of these lesson's are silly trifles, intended to make Socrates appear ridiculous. Strepsiades, after having asked him how he should avoid paying his lowing expedient himself. seen at the druggists that with which they kindle fires. Socrates. You mean glass, do not you? Strepsiades. The very thing. Socrates. Well, what will you do with that? Strepsiades. When a summons is sent to me, I will take this stone, and, placing myself in the sun, I will melt all the writing of the summons at a distance.' The writing, as we know, was traced on wax spread upon a more solid substance.

Such a proof of the antiquity of burning glasses is irrefragable. However, the effect mentioned by Strepsiades may casily be explained in three ways: either a concave mirror, reflecting the rays of the Sun, might be employed for the purpose; or a convex glass, transmitting the rays; or an assemblage of several plane mirrors, operating by reflection. But in the first case the summons must have been held up high between the mirror and the Sun, at the spot where the solar rays, after having struck on the con