Regiomontanus, Apian and Capuchin Sundials

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


Article from Compendium, volume 5, number 4, 1998 :

Universal Card Dials with Nomograms for Babylonian, Italian, and Antique Hours

In Compendium volume 5, number 3, September 1998, we described card dials that directly indicate Italian and/or Babylonian time. In the present article, we will examine two examples of sixteenth century card dials which can also find Italian and Babylonian hours, and Antique hours as well, but read these hours by an indirect method. One of the dials is based on the universal card dial of Regiomontanus [1] and the second is an approach as by Apian. [2]

We will first present their two respective variations of design, either of which can read local apparent time (L.A.T.) over a wide range of latitudes. We next describe, for each historical example, an additional set of lines, a "nomogram" [3], which is included on that dial. In each case, the nomogram may be used to convert the dial's direct indications of L.A.T. into Italian, Babylonian, or Antique hours.

The Universal Portions of the Dials:

These card dials can read L.A.T. at any longitude, and at any latitude from 0 to 66.5 degrees. (See Figure 1, where the type of "Regiomontanus" is showed.)

figure 1

Figure 1

In this kind of dial, the point of suspension for the plummet must be adjustable in two dimensions. This is often provided for by a device called a "brachiolus" (Latin for "little arm") consisting of 2 or 3 links joined by pivot-pins, whose friction is such that the plummet's suspension-point on the end link can be set to any position on the scales near the top of the card, and will remain fixed during use of the dial.

For simplification, a brachiolus is not depicted in subsequent figures, but it, or its functional equivalent, must be provided for an actual dial. [4]

The scales nearest the top of the dial are an arrangement of lines for latitude and date. The scale of dates is drawn as the older gnomonists did, with a zodiacal calendar, where the year is divided into 12 "houses," or "signs," of 30 degrees each. This arrangement, as shown in Figure 1, is a simplified representation of that used on our first historical example, a dial made by Johann Stab in 1512. [5]

A weighted string, with a friction-fit sliding bead, is attached at the movable end of the brachiolus. To prepare the dial for use, the brachiolus is adjusted to set the string's suspension-point at the appropriate latitude and date. Next the string is swung over to the proper date in the second scale of dates on the right side of the dial, and the bead is moved along the string to the date point. Keep in mind that the bead must be set on the 12 hour line, not on the line between the zodiacal signs. By this means we set the length of the string between the brachiolus' end and the bead for the date and latitude. The dial is now ready to be used.

Hold the dial vertical with the upper-left corner toward to the sun. When the top edge, parallel to the sight-line, points to the sun, the position of the bead on the vertically hanging string indicates L.A.T., which is read along the scale at the bottom of the card.

(It is necessary to know if the reading is made before, or after, noon. If this is in doubt, compare successive observations to see whether the sun's altitude is increasing or decreasing.)

When holding the dial with its top edge horizontal, as if the height of the sun were zero degrees, the string is parallel to the hour lines and the L.A.T. for sunrise or sunset for the specific latitude and date can be read. Again, the hour scale along the bottom edge is used.

As seen on historical dials, the scales at the top used to set the latitude and date may be arranged in more than one way. (We have confined ourselves here to just two of the possible variations.) One alternative arrangement is shown in Figure 2, modeled after a dial made in 1533 by Peter Apian. [2] At the top of Apian's dial there is a vertical scale for the date, and a horizontal scale for the latitude. The date scale at the side of the dial now is replaced by a scale of latitude, and in this example it is at the left side. As drawn, it is the right top corner of Apian's card that must be directed toward the sun. The manner of use is otherwise essentially the same as described above.

figure 2

Figure 2

The Two Dials, with Their Added Nomograms:

Figures 3 and 4 are simplified drawings, representing the two illustrated historical examples with nomograms that we found and chose to describe in this article. The principle design elements discussed above are readily recognizable.

In these figures we show only the nomograms' lines for Babylonian and Italian time. The lines for Antique time have been left off, for the sake of clarity.

figure 3 figure 4
Figure 3
Figure 4

Figure 3 shows the nomogram on Stab's dial. At the far left edge are paired, opposed vertical scales of 1 to 12, labeled AM and PM. Adjacent are vertical scales, labeled "Bab." for Babylonian hours and "It." for Italian hours, and numbered from 1 to 24, but in opposed order. Similar Bab. and It. horizontal scales are below the nomogram, but above the L.A.T. hour scales.

To convert a L.A.T. that has been read on a certain day into one of the other time systems, proceed as follows:

With the brachiolus still set to the date and latitude, stretch the string parallel to the straight vertical hour lines for L.A.T.

To use the conversion nomogram, it is necessary to know which lines to use for Babylonian time, and which lines for Italian time. This depends on whether it is before or after noon. The following legend summarizes how to read the lines.

AM
PM
// lines: Italian time\\ lines: Italian time
\\ lines: Babylonian time// lines: Babylonian time

Suppose that the L.A.T. is read before noon. Find this time on the AM scale at the left side of the card and from this point move horizontally to the right to find the reading point at the intersection with the string. To find the Babylonian time, the legend tells us to use the \\ lines, and to find the Italian time, the legend tells us to use the // lines. The desired time then is read on the scales labeled Bab. or It.

(For morning Italian hours, the scale of numbers along the upper curved line of the nomogram may also be used.) If the L.A.T. is after noon, find the L.A.T. on the vertical hour scale labeled PM, follow the legend, and use the same lines in reversed fashion to convert L.A.T. into corresponding Babylonian or Italian times.

For example, suppose for a certain date and latitude we have sunrise at 5 AM, sunset at 7 PM, and a local apparent time of 4 PM. Then the Italian hour is 21 and the Babylonian hour is 11.

Apian used a different arrangement for the numerals in the conversion graph. (Figure 4.) Along the upper curved line of the nomogram are two scales, each counting from 0 to 24, but in opposed order. In the nomogram itself there is a second scale counting from 0 to 24, however some numerals aren't present. Apian provided Latin text to tell which scale is used for the conversion, as well as other information. In our figure, these legends are given English abbreviations.

"LD" means length of the day,
"LN" means length of the night,
"AM-BAB" means use as Babylonian time if hour is AM and so on.

Their use follows the same legend described previously for Stab's dial. There is, however, an oddity in the arrangement of Apian's design, which leads to a problem for using his conversion graph. If the dial is set according to the date and latitude, and the string is held along the vertical hour lines, the L.A.T. of sunrise and of sunset may be read from the scale at the bottom, as was described previously. However, for use in the conversion graph the string is now not correctly placed. If the lengths of the day and night are directly read on the scales concerned, their values are reversed. This means that in order to use this conversion nomogram, the string has to be relocated to the same- numbered hour at the other side of the 6 o'clock line. It appears that it would have been better to change the arrangement of the date scale at the top of the card dial by reversing the zodiacal signs and by reversing the hour scale at the bottom of the dial. Did Apian have some special rationale for his arrangement? We have been unable to think of any, but perhaps a reader can offer a plausible one.

In both of the historical examples we are discussing, there are also lines drawn for converting L.A.T. into Antique time.

As mentioned earlier, these lines make the nomogram even more complicated, and for that reason we show them only separately, as in Figure 5.

figure5

Figure5

In the Stab dial the length of each variable day is divided into 12 equal parts, according to the usual practice for Antique hours. Once again, we find a strange thing in the dial of Apian, for his 12-part division is not linear. So we have another question left open for speculation.

It isn't easy to make good copies of the pictures of the historical examples we have found, but in Figure 6, an image of the Peter Apian dial is reproduced.

figure 6Click for picture,103 kB

Figure 6


Basic Construction for Regiomomtanus and Apian Dials: (See Figure 7.)

figure7

Figure7

For both dials:

Draw a semicircle AOB with center M, diameter AB, and draw the line KMO perpendicular to AB. Divide the semicircle in equal parts of 15 degrees and draw from these points the hour lines for local apparent time parallel to KO.

For the Regiomontanus dial:

Draw OP perpendicular to KO. This line intersects the outer hourline at P.

Draw lines from P (as PQ) onto KO with angle OPQ equal to the latitude. In Figure 7 this has only been done for latitude 50 degrees.

Draw horizontal lines for the latitude scale. Draw lines at both sides of OP an OK with angles equal to the sun's declination for the zodiacal calendar's divisions. Useful values are 23.5, 20, and 11.5 degrees.

For Apian dial:

Draw lines from M (as MQ) onto the outer hourline with angle BMQ equal to the latitude. In Figure 7 this has only been done for latitude 50 degrees.

Draw through M lines N'N, perpendicular to each latitude line MQ for the scale of latitude.

Draw from A, at both sides of MA, lines with angles equal to the sun's declination. Only one half has been drawn in Figure 7.

Draw horizontal lines for the zodiacal calendar.

For the nomograms:

The hour lines for L.A.T. are used as a part of the nomogram.

Draw a second set of horizontal hour lines, divided along a vertical linear scale as can be seen in Figures 3 or 4.

Connect the intersecting points of these two hour scales with curves in / and \ directions for the Babylonian and Italian time.

For the Antique time divide the vertical space between the outer curved line and the bottom line into 6 equal parts and draw the lines.


A Qbasic program, REGIOM.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.


Notes:

[1] Johann Regiomontan, or Regiomontanus: (Johann Mller von K”nigsberg, 1436 - 1476) In 1474, Regiomontanus disclosed his universal card dial, which is described in a Latin publication, "Quadratum horarium generale"and in a German publication, "Algemeinen Uhrt„felchen".

[2] Peter Apian or Apianus: (Peter Bennewitz, 1495 - 1552) "Bennewitz" means "bee-keeper." "(Apis" is Latin for "bee.") Apian discussed quadrants in his, "Instrument Buch," 1533.

[3] Nomograms (also called nomographs) are graphical devices by which corresponding values of functionally related quantities can be found. They are close kin to slide rules.

[4] For a modern realization of a universal card dial where the brachiolus is replaced by a nomogram, refer to "A Universal Nomographic Sundial" by Frederick W. Sawyer, in his "Sciatheric Notes - I" NASS 1998. The article appeared previously in the Bulletin of the British Sundial Society 94.3, October 1994:14-17.

[5] Johann Stab ( ? - 1522 ) Published in 1512 his "Horoscopion," the source relied upon here. Supplementary Notes: Recently we saw in a Cristies' catalog a third example offered for sale. The dial, about 22.6 cm by 14.8 cm in size, was made by Erasmus Habermel around 1590. (Its listed price is about 300,000 British pounds.) The delineations on this dial are of the same form as those on the example by Johann Stab. Erasmus Habermel ( ? - 1606 ) is a well-known instrument maker, as a number of his instruments have survived.


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