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....
[Illustration: 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.
[Illustration: 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.
[Illustration: 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:
18° = polar height of the place -23½°.
65° = " " " " +23½°.
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:
Years. Declinations.
1550. 8° east.
1580. 11.30
1622. 6.30
1634. 4.16
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._
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[MIND.]