Regiomontanus, Apian and Capuchin Sundials

by
Fer J. de Vries
Mac Oglesby
William S. Maddux
Warren Thom


Article from Compendium, volume 6, number 1, 1999 :

A "Universal" Capuchin Sundial ( or The Sailing Wooden Shoe )

"Long ago, as a boy living in a small village in the countryside [of The Netherlands], I used to wear wooden shoes as all the children and many of the adults at that time and place. A wooden shoe also was a boat for us to play with at the waterside and I spent a lot of hours there. But even now my wife and I sometimes wear wooden shoes at work in the garden. They are safe, warm, easy to put on and off and you never need to polish them.

Many more of the members of our [Dutch] society have had this experience and we were very surprised at the moment in 1992 that Jan Kragten introduced his 'sailing wooden shoe' sundial which is described here. In our language we would say 'zeilende klomp'."
Fer de Vries.


In The Compendium Vol. 5, Nos.1, 3 and 4, we described and discussed divers card dial designs, but we did not cover the well-known Capuchin card dial. We here particularly address this important type, including a "universal" variation, designed for multi-latitude use.

The Capuchin card dial:

A conventional Capuchin dial is much easier to lay out than card dials we described previously, but it can only be used for one latitude. An example is shown in Figure 1.

figure 1

Figure 1

There is one scale of dates, in this example drawn as a zodiacal calendar, and parallel hour lines lie between two intersecting arcs. Typically, a slot is made along the line of dates.

To use the dial, the adjustable suspension point of a weighted string, or plummet, with a friction-fit sliding bead, is positioned along the slot at the proper date. Next, stretch the string to the hourpoint 12 at the right side, and move the bead to this point. This sets the length of the string for date and latitude. To read the local apparent time (L.A.T.), hold the dial vertical with its upper-left corner toward the sun. When the shadow-sights (not shown here) along the top edge of the dial aim at the sun, the position of the bead on the vertically hanging string indicates L.A.T.

If the string is held parallel to the card's hour lines, a set date's times of sunrise and sunset may be read.

Construction:

The construction for a typical Capuchin sundial can be seen in Figure 2.

figure 2

Figure 2

Draw a semicircle ALB with center M, and diameter AB. Draw the line KML perpendicular to AB. Divide the semicircle into equal parts of 15 degrees, and draw from these points the hour lines for local apparent solar time, parallel to KL.

From B draw line BK, with angle MBK equal to the latitude. Draw CD perpendicular to BK.

To locate the zodiacal calendar's divisions on line CD, draw lines at each side of BK with angles equal to the sun's declination. Useful values are 23.5, 20, and 11.5 degrees.

Finally, draw line CE parallel to KL.

(Of course, line CD may also be marked off to show calendar months and days.)

A construction method called "menaeus" is another way to graduate the scale of dates. (Construction with the help of the menaeus makes it easier to draw lines for the sun's declinations other than 23.5 degrees.)

Construct CD as given before.

Draw the isosceles triangle BCD with angle CBD equal to 2 x 23.5, or 47 degrees. Draw arc CD with center at B. Draw semicircle CD with center at K, and divide this arc into 6 equal parts of 30 degrees for the zodiacal signs or "houses".

Draw lines from these division points perpendicular to line CD as shown for PQ.

Draw lines from B to the points where these PQ-lines intersect arc CD.

Keep in mind not to draw the lines from B to the intersection points of the PQ- lines with the straight line CD. If you do so, you commit the infamous "Error Orontii", of which Clavius remarked, "hallucinates est Orontius". (Orontius Finaeus or Oronce Finé, 1532, in Protomathesis). It should be noted that Orontius also drew, in the same book, a Regiomontanus card dial with a correct menaeus construction.

The area which can be reached by the bead is bounded by the line CE and the arcs, with centers C and D, and radius BC, drawn between B and line CE. It is this area that gives this kind of dial its special appearance. The parts of the hour lines lying outside this area may be removed, as in Figure 1.

However, even more of the hour lines may be deleted. To get the minimum area needed, we have to draw more arcs starting at B, with centers at the intersection points of declination lines with the scale of date, and with radii from those points to B, as is shown in Figure 3. The length of each of these arcs must terminate at a point vertically beneath the center of the arc.

figure 3

Figure 3

By drawing a curved line through the endpoints of these arcs, we define the minimum area necessary. If these arcs are drawn on a real card dial, as is done in Figure 3, and labeled with their respective zodiacal signs, the bead on the string is no longer needed.

If such a Capuchin card dial is calculated for a latitude between the tropics, parts of the declination curves outside the noon hour line also may be removed. In the accompanying Qbasic program this isn't done, because in that case the characteristic appearance of the Capuchin delineation would be lost.

"The Sailing Wooden Shoe:"

From our article about the universal dials of Regiomontanus and Apian, (Compendium Vol. 4, No. 4, Dec. 1998,) we redrew, for Figure 4, a part of an historical example by Apian. We then added the construction of a Capuchin dial for a latitude of 50 degrees, shown with the thick lines. Now it becomes apparent that the universal dial of Apian is equivalent to a series of Capuchin dials for different latitudes, combined into one schema. The center point of the date scale of each component Capuchin dial is their common joining point for Apian's universal dial.

figure 4

Figure 4

In 1992 Jan Kragten, a member of De Zonnewijzerkring (The Dutch Sundial Society), used the same principle to develop another combined Capuchin universal dial by choosing the points on the latitude scale at the left side as common joining points. (See X and Y in Figure 4.) Kragten's dial is represented in Figure 5. In this schema, because all of the 12 o'clock points of the separate Capuchin dials coincide as a single point, no scale of latitudes is needed at the side of the dial, unlike the Apian solution.

figure 5

Figure 5

However, we now need a means to place the string at its proper suspension point in the combined scales for latitude and date. A brachiolus has, therefore, been added in the drawing.

By drawing arcs, the area that can be reached by the bead may be delimited. Jan Kragten added, at the left side of his dial, his own delineation of this area, with a result that looks like a wooden shoe, and the scale for latitude and date resembles a sail. Hence the subtitle of this article, "The Sailing Wooden Shoe."

Fanciful imagery aside, the principles underlying this, offer insights into the relationships among these several kinds of card dials. The principles described here may be similarly used to analyze the Regiomontanus card dial, although we are not aware of historical examples of such cards restricted to only one latitude. We leave it for the reader to seek further connections.

The Capuchin Card Dial by Eise Esinga: [1]

As an historical example of a Capuchin dial, one made by Eise Eisinga, is shown in Figure 6. He drew this dial in 1762, when only 18 years old, on the last page of his large book with more than 160 drawings of sundials. His actual dial, on a copper plate with oak backing, was long in private possession, but in 1992 the dial was donated to the famous Planetarium at Franeker, Nederland.

Click for picture, 32 kB

Figure 6

In the drawing, Eisinga also made the "error Orontii," although he was aware of the correct construction, as can be seen on another page in his book.

(Had not Orontius notoriously done the same? Did Eisinga perhaps repeat this consciously, to demonstrate and underscore the possible pitfall?)


A Qbasic program, CAPUCHIN.BAS, which can be downloaded from the start page, calculates these dials and prints out their delineations. This program draws directly onto the screen, but also saves calculated points in a text file, xxxx.txt. With the conversion program, CNVXXXX.EXE, the text file can be converted into xxxx.rlt and also into xxxx.dxf files. These converted files may be used as input for Zonwvlak or a CAD program such as Deltacad.


Sources:

Much of the material presented here was found in the writings of various authors, including Hagen, Kragten, Meyer, De Rijk, Schepman, De Vries and Van der Wijck, as previously published in several articles in the "Bulletins" of "De Zonnewijzerkring", by the Dutch Sundial Society. Bulletin No. 47, July 1992, was a special issue about Eise Eisinga and his card dial, replete with other interesting information about Capuchin dials, including many related demonstrations, proofs and constructions - among them, that of the menaeus.


Notes:

[1] Eise Eisinga (1744 - 1828), Netherland. Eise Eisinga was an autodidact, who, by 18 years of age, had already written his book with many drawings of plane sundials, titled: "Gnomonica of Sonnewijsers, alle door passer en lijnjaal afgepast op de Noorderbreedte van Dronrijp, 53° - 13', 1762." ("Gnomonics or Sundials, all constructed by compasses and ruler for the Northern latitude of Dronrijp, 53° - 13', 1762.")

The book comprises 170 large pages, nearly all filled with drawings of plane sundials, all for the same latitude, but for several declinations and inclinations of the planes, and almost all provided with lines for the sun's declination. On page 170 he drew the Capuchin card dial discussed here.

His most famous accomplishment was building the planetarium at Franeker, Netherland. He wanted to show the real things that were happening in the sky. He constructed this planetarium on the ceiling of the living room of his house. Around the sun, the planets Mercury, Venus, Earth with Moon, Mars, Jupiter and Saturn run in real time, all driven by a mechanical clock.
Several other instruments are placed upon the walls of the room. They show the time of sunrise and sunset, the phases of the moon, the time the moon rises and sets, and include many other interesting astronomical phenomena.

It took Eisinga 7 years, from 1774 to 1781, to complete his task, all done in his spare time after his day's work. World-renowned, this unique planetarium is still in running order, and its moving display is the focal attraction of the museum.


Supplementary Notes:

The oldest picture of a Capuchin dial we are aware of was published by Sebastian Münster in his book "Horologiographia", 1533. He named it "Parallelogramum," for its parallel hour lines.

According to a note by the late M.J. Hagen, founder of "De Zonnewijzerkring," this book is a reprint of "Compositio Horologiorum", 1531, so the Capuchin dial was at least known by 1531. And the universal Capuchin dial was known by Apian at least by 1533.

The universal Regiomontanus dial was, however, already known in 1474, although no example for only one latitude is known to us. So perhaps we may suspect that the Regiomontanus dial is older then the Capuchin dial, but we cannot be certain. We should be pleased if anyone could give us other references bearing upon this question.

In the book "Sundials" by Frank W. Cousins, on page 168, a Capuchin dial is called a "Saint Rigaud Card Dial," but this seems inaccurate. A drawing by St. Rigaud (1606 - 1673), which appears to be the basis for such an identification, is called "Analemme de St. Rigaud," but it shows a different delineation, and certainly is not a Capuchin dial.


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