An article on the subject, recently published by us, has gained for us the communication of two very interesting sun dials, which we shall describe. The first, which we owe to the kindness of General Jancigny, is of the type of the circular instrument, of which we explained the method of using in our preceding article. The hour here is likewise deduced from the height of the sun converted into a horary angle by the instrument itself; but the method by which such conversion operates is a little different. Fig. 1 shows the instrument open for observation. We find here the meridian circle, M, and the equator E, of the diagram shown in Fig. 3 (No. 4); but the circle with alidade is here replaced by a small aperture movable in a slide that is placed in a position parallel with the axis of the world. Upon this slide are marked, on one side, the initials of the names of the months and on the other side the corresponding signs of the zodiac. The sun apparently describing a circle around the axis, PP¹, the rays passing through a point of the axis (small aperture of the slide) will travel over a circular cone around such axis.

If, then, the apparatus be so suspended that the circle, M, shall be in the meridian, the slide parallel with the earth's axis, and the circle, E, at right angles with the slide, the pencil of solar light passing through the aperture will describe, in one day, a cone having the slide for an axis; that is to say, concentric with the equator circle. If, moreover, the aperture is properly placed, the luminous pencil will pass through the equator circle itself; to this effect, the aperture should be in a position such that the angle, a (Fig. 3, No. 4), may be equal to the declination of the sun on the day of observation. It is precisely to this end that the names of the months are inscribed upon the slide....

FIG. 1. - TRAVELER'S SUN DIAL.

The accessories of the instrument are as follows: A ring with a pivot for suspending the meridian circle, and the position of which, given by a division in degrees marked upon this circle, must correspond with the latitude of the place; two stops serving to fix the position of the equator circle; finally the latitude of various cities. The instrument was constructed at Paris, by Butterfield, probably in the last quarter of the eighteenth century.

The second instrument, which is of the same nature as the cubical sun dial - that is to say, with horary angle - is, unlike the latter, a true trinket, as interesting as a work of art as it is as an astronomical instrument. It is a little mandolin of gilded brass, and is shown of actual size in Fig. 2. The cover, which is held by a hook, may be placed in a vertical position, in which it is held by a second hook. It bears in the interior the date 1612. This is the only explicit historic datum that this little masterpiece reveals to us. Its maker, who was certainly an artist, and, as we shall see, also a man of science, had the modesty not to inscribe his name in it.

FIG. 2. - SUN DIAL IN THE FORM OF A MANDOLIN, CONSTRUCTED IN 1612.

No. 2 of Fig. 3 represents the instrument open. It rests upon the tail piece and neck of the mandolin. The cover is exactly vertical. The bottom of the mandolin is closed by a horizontal silver plate, beneath which is soldered the box of a compass designed to put the instrument in the meridian, and carrying upon its face an arrow and the indications S. OR. M. OC., that is to say, "Septentrion" (north), "Orient" (east), "Midi" (south), "Occident" (west). One of the ends of the needle of the compass is straight, while the other is forked. It is placed in a position in which it completes the arrow, thus permitting of making a very accurate observation (Fig. 2, No. 3). Around the compass, the silver plate carries the lines of hours. It is perfectly adjusted, and held in place by a screw that traverses the bottom of the instrument. In front of the compass it contains a small aperture designed to permit of the passage of the indicating thread, which, at the other end, is fastened to the cover. The silver plate is not soldered, in order that the thread may be replaced when it chances to break. On the inner part of the cover are marked in the first place the horary lines, traversed by curves that are symmetrical with respect to the vertical and having the aspect of arcs of hyperbolas.

At the extremity of these lines are marked the signs of the zodiac. At the top, a pretty banderole, which appears at first sight to form a part of the ensemble of the curves, completes the design. Such is this wonderful little instrument, in which everything is arranged in harmonious lines that delight the eye and easily detract one's attention from a scientific examination of it. Let us enter upon this drier part of our subject; we shall still have room to wonder, and let us take up first the higher question.

FIG. 3. - DIAGRAM EXPLANATORY OF THE MANDOLIN SUN DIAL.

Let us consider a horizontal plane (Fig. 3, No. 2) - a plane perpendicular to the meridian, and a right line parallel with the axis of the world. Let P be a point upon this line. As we have seen, such point is the summit of a very wide cone described in one day by the solar rays. At the equinox this cone is converted into a plane, which, in a vertical plane, intersects the straight line A B. Between the vernal and autumnal equinoxes the sun is situated above this plane, and, consequently, the shadow of P describes the lower curves at A B. During winter, on the contrary, it is the upper curves that are described. It is easily seen that the curves traced by the shadow of the point P are hyperbolas whose convexity is turned toward A B. It therefore appears evident to us that the thread of our sun dial carried a knot or bead whose shadow was followed upon the curves. This shadow showed at every hour of the day the approximate date of the day of observation. The sun dial therefore served as a calendar. But how was the position of the bead found? Here we are obliged to enter into new details. Let us project the figure upon a vertical plane (Fig. 3, No. 1) and designate by H E the summits of the hyperbolas corresponding to the winter and summer solstices.

If P be the position of the bead, the angles, P H H¹, P E E¹, will give the height of the sun above the horizon at noon, at the two solstices. Between these angles there should exist an angle of 47°, double the obliquity of the ecliptic, that is to say, the excursion of the sun in declination: now P E E¹-P H H¹ = E P H = 47°.

Let us carry, at H and E, the angles, O H E = H E O = 43° = 90°-47°; the angle at 0° will be equal to 180-86 = 94°. If we trace the circumference having O for a center, and passing through E and H, each point, Q, of such circumference will possess the same property as the angle, H Q E = 47°. The intersection, P, of the circumference with the straight line, N, therefore gives the position of the bead.

Let us return to our instrument. We have traced upon a diagram the distance of the points of attachment of the thread, at the intersection of the planes of projection. We have thus obtained the position of the line, N S. Then, operating as has just been said, we have marked the point, P. Now, accurately measuring all the angles, we have found: N S R = 50°; P H H¹ = 18°; P E E¹ = 65°. The first shows that the instrument has been constructed for a place on the parallel of 50°, and the others show that, at the solstices, the height of the sun was respectively 18° and 65°, decompounded as follows:

The polar height of the place where the object was to be observed would therefore be 41½°, that is to say, its latitude would be 48½°.

Minor views of construction and measurement and the deformations that the instrument has undergone sufficiently explain the divergence of 1½° between the two results, which comprise between them the latitude of Paris.

After doing all the reasoning that we have just given at length, we have finally found the means by which the hypothetic bead was to be put in place. A little beyond the curves, a very small but perfectly conspicuous dot is engraved - the intersection of two lines of construction that it was doubtless desired to efface, but the scarcely visible trace of which subsists. Upon measuring with the compasses the distance between the insertion of the thread and this dot, we find exactly the distance, N P, of our diagram. Therefore there is no doubt that this dot served as a datum point. The existence of the bead upon the thread and the use of it as a rude calendar therefore appears to be certain.

The compass is to furnish us new indications. After dismounting it - an operation that the quite primitive enchasing of the face plate renders very easy - we took a copy of it, which we measured with care. The arrow forms with the line O C-O R an angle of 90° + 8°. The compass was therefore constructed in view of an eastern declination of 8°.

Now, here is what we know with most certainty as to the magnetic declination of Paris at the epoch in question:

On causing the curve (Fig. 3, No. 3) to pass through the four points thus determined, we find, for 1612, the declination 8½°. This is, with an approximation closer than that of the measurements that can be made upon the small compass, the value that we found. From these data as a whole we draw the two following conclusions: (1) The instrument was constructed at Paris; and (2) the inventor was accurately posted in the science of his time.

Certain easily perceived retouchings, moreover, show that this sun dial is not a copy, but rather an original. We are therefore in an attitude to claim, as we did at the outset, that the constructor of this pleasing object was not only an artist, but a man of science as well.

Let us compare a few dates: In 1612, Galileo and Kepler were still living. Thirty years were yet to lapse before the birth of Newton. Modern astronomy was in its tenderest infancy, and remained the privilege of a few initiated persons. - C.E. Guillaume, in La Nature.

[MIND.]