**Simón García**

**"EAAE Summerschools" Working Group**

**I.E.S. Aljada. Murcia (Spain)**

#### Abstract

The Pyrenean Shepherd's dial is one of the simplest and most widely used portable dials. It is also called the pillar's dial and the cylinder. Although the shepherd's dial is not very accurate, it is easy to make and inexpensive. It indicates the time of day from the Sun's altitude, which depends not only on the time of day, but also on the latitude and time of year. It is designed for a particular latitude and is adjustable for the date.

This class of dial consist of a cylinder capped by a movable top to which a gnomon is attached. The cylinder is usually hollow to contain the gnomon when it is not in use.

The hour lines are either drawn on a paper which is glued to the cylinder or inscribed directly on the surface of the cylinder. The hour lines appear as curves on the rounded face of the cylinder.

The months of the year are traced around the base of the cylinder.

This workshop tries to provide a didactic material that allows to make a structured observation of our star and a rigorous study of its movement.

Every participant will receive complete material to draw and to do:

The Shepherd's or Pyrenean dial

The Herculaneum "ham dial"

The ring dial.

#### Introduction

Although everyone knows that sundials are often to be seen on the walls of churches or on stone pedestals in gardens, and though we all understand that such dials were the immediate ancestors of our public clocks, still there are comparatively few who know any members of the younger branch of the family, namely, the pocket dials, the rude forefathers of the modern watch. And it will probably be a surprise to most people to learn how many the varieties have been and how protean the forms of the portable dials that were used in various ages and countries, and what a vast amount of time and thought was expended on their design and construction.

Among the simplest and most widely used of the portable dials was one which was variously called the shepherd's dial, the pillar dial, the traveler's dial, the chilindre and the cylinder. It was not very accurate, but was easily made and inexpensive. It has a long history.

#### History

There is no doubt that fixed dials preceded portable ones by many ages, and that the length of his own shadow long continued to be the only visible timekeeper that a man carried about with him, and one that was in recognized use in classical times, to which period the earliest known specimen of a portable dials must also be ascribed. This dial, which is made in the shape of a ham, was found in excavations at Herculaneum in 1754, and is now in the Naples museum, where Miss Lloyd made the drawing.

Its material is bronze, and on its flat side are vertical lines enclosing six spaces, below which are engraved the shortened names of the months, with the winter month under the shortest space and the summer under the longest; while across the upright lines are curved ones dividing the spaces each into six sections to represent six hours from sunrise to noon, and from noon to sunset, in accordance with the plan adopted in other Roman dials, which gave to the day twelve long hours in summer and twelve short ones in winter. The age of this dial is fixed within narrow limits by the fact that it must have been made after B.C. 28, when the month Sextilis was changed to Augustus in honour of the emperor and before A.D. 79 when the great eruption of Vesuvius buried Herculaneum, while it seems probable that it was made after A.D. 63 when the town was greatly injured by an earthquake.

As an altitude Sundial an instrument of this kind could only be used in one latitude, and that the later Romans knew and felt the disadvantage of this fact is shown by another dial on the same principle found at Aquilea. This is a circular disc of bronze 1 ¼ inch diameter by 5/16 inch thick, with dials on each side of it, one being lettered RO for Rome and the other RA for Ravenna; the lines dividing off the month spaces in this instrument are not parallel but radiate from an apex opposite which the gnomon once projected. The lettering for the month is practically the same as in the "ham" dial, and the division of the day is the same, but it was probably not made until about the fifth century. The hour lines were originally inlaid with silver, but much of this is now wanting, as well as the gnomon and the attachment for suspending the dial.

This class of dial, in which the hour lines are drawn on a vertical surface and the gnomon stands out horizontally above them, has continued in use ever since it was first invented; but the form of it that was most common, because it was the easiest to make, was a cylinder, the "Kalendar" or "Chilindre", on which treatises are extant written as early as the thirteenth century. We recall that the "gentil monk" of the Canterbury Tales by Geoffrey Chaucer (1340 to 1406) , inviting the Good Wife of Bath to dinner, says to her:

"Goth now your way quoth he, all stille and let us dine as soon as that ye may, for by my chilindre it is prime of day"

This dials were small cylinders of wood or ivory , having at the top a kind of stopper with a hinged gnomon in it. When in use, this stopper had to be taken out and replaced with the gnomon turned out and projected over the proper month space, or line.

When the dial was allowed to hang vertically with the pointer towards the sun, a shadow fell on the curved hour lines and gave the time. The illustrations (Fig.2) shows dials of this kind used in the sixteenth and seventeenth centuries in all parts of Europe, and in the nineteenth in the Pyrenees.

A dial of this type adapted to a walking-stick is to be seen in the Ashmolean Museum, Oxford, and another made by Edmund Culpepper (1666 to 1706), which forms also a telescope. The same type, but in an exaggerated form, was used by the Indian pilgrims, who carry staves 4 feet 6 inches to 5 feet 6 inches long with dials on them when making a pilgrimage to Benares.

Other modifications of this class of dial are given in the illustrations (Fig. 3) one which, showing the back of a German nocturnal dial of brass, dated about 1650, closely imitates the Herculaneum "ham", except that the gnomon is hinged to a sliding piece of metal which allows it to stand over any desired month, whereas in the Roman dial this adjustment was got by bending the wire gnomon. The seventeenth century dial, engraved on the gilt brass tablet-covers, is also German, and serve as its "style". The side illustrated is made for use in the Summer, the winter dial being engraved on the other cover.

The earliest form of the dial was only another modification of the same type, a hole being pierced in the side of a very wide ring and the hour lines marked by sloping or curved lines drawn across the breadth of the ring inside so as to suit the various seasons. When in use these dials were turned towards the sun so that a ray of light might shine though the small hole and show the time on the hour lines inside the ring. From this developed the ordinary form of ring dial, which was in such general use in this country during the seventeenth and eighteenth centuries, in which the hole was drilled in a separate band of metal that moved in a groove round the ring so that it might be adjusted to its proper place for the time of the year, as shown by the initials of the months engraved on the outside of the ring; by this means the hour lines could be drawn much straighter and with greater accuracy (Fig.4).

Another improvement was the introduction of a second hole and a second set of markings, one half of the ring being used in the summer and the other in the winter.

Ring-dials were more used in England than elsewhere. The dial Shakespeare had in his mind in As You Like It, act II, scene 7:

*And then he drew a dial from his poke,*

*And, looking on it with lack-lustre eye,*

*Says very wisely, "It is ten o'clock;*

*Thus may we see," quoth he, "how the world wags".*

may have been a ring dial, a shepherd's dial, or even a compass dial, all of this were in use in his time, and all probably equally common.

#### The Shepherd's Dial

Shepherd's dial is an altitude Sundial.

Altitude dials are dials that use the altitude of the Sun to tell time. The best known altitude Sundial is the Shepherd's dial. It is also a portable dial which was a cylinder of wood (Fig.6). The style is a horizontal projection across the top of the cylinder, the shadow of which show the time.

#### How it works

The length of the shadow of an object depends on the altitude of the Sun in the sky (Fig. 7). Since the altitude of the Sun is dependent on the time of the year, the gnomon has to be swung to the correct position of the year. Letters around the base of the years indicate the months (Fig. 8).

In use, the dial is hung by a string fixed to the tip of the cap, with the gnomon extended toward the Sun. The shadow of the gnomon then falls straight down and ends somewhere between the hour lines. The shadow give us hour in local time.

#### How to construct it

The hour lines are either drawn on paper glued to the cylinder or inscribed directly on the surface of the cylinder. As a preliminary to construction, we make up a table showing the sun's altitude at each hour of the day in the latitude where the dial is to be used for selected days of the year. One can look them up in published tables or using computational methods. The finished chart of hour lines will look like figure, and our first step must be to determine the length and height of this chart for our own case. Since the chart is to be wound around a cylinder, its length must be equal to or slightly less than the circumference of the cylinder. The height of the chart is related to the length of the gnomon. If either one is fixed, the other is thereby determined. The relationships depends on the latitude, φ; and if we let G represent the length of the gnomon and H the height of the chart we have the relationships:

G = H cot ( 113 ½º - φ )

If, for example we design a dial for a cylinder 77.5 mm. high for use at latitude 47º, the length of the gnomon should be 33.8 mm.

Having the length and height of the chart of Fig. 9, we divide the length into 12 vertical bands representing the 12 months. Intermediate lines may be added if desired to represent the 10th and 20th days of the month. We then find the place where each hour line intersects each of these vertical lines, working either graphically or mathematically.

#### Graphically Approach

Lay out lines AD and CE of Figure 10 at right angles, with CD equal to the length of the gnomon. With D as the centre and with any convenient radius draw the circular arc BF and divide into 10º arcs. From D draw straight lines to the divisions on BF, and the places where these lines intersect CE will form a scale for drawing the hour lines. For any given day of the year , say August 22, we look up in our table the sun's altitude at each our of that day, and lay our scale (CE) along the vertical line corresponding to that date with C at the top. We mark the point on the vertical line corresponding to the scale division showing the sun's altitude at each hour of the day, continuing this for the other days, and finally connecting the points for each hour to give the hour lines themselves as shown in Figure 9.

#### Arithmetic Approach

If we prefer, we can draw the hour lines by computation. Given the sun's altitude, A, at given hour on a selected day, we compute the distance, D, of the hour line from the top of the chart as follows:

D = (tan A)(G)

Where G is the length of the gnomon. For example, in latitude 47º N at 10 a.m. on August 22nd the sun's altitude is 52.7º .Our formula tells us that the 10th o'clock hour line should intersect the August 22 line 44.3 mm. Down from the top of the chart if the gnomon is 33.8 mm. long. We repeat the operation to find where each of the hour lines crosses each of the date lines, and connect all the points for any hour line itself. Since the sun's altitude will be the same at 2 p.m. and 10a.m., we draw a single line for these two hours - and for any other two hours - and from any two other hours which are equidistant from noon.

The hour lines on a shepherd's dial lie close together in winter, and also near noontime, so that the instrument is least accurate at those dates and times.

#### Our inexpensive shepherd's dial

My pupils and I have thought about using cans and tins and some other standard containers in order to fix on then a sheet of papers showing a picture of a Shepherd's dial.

We have chosen one of the most common cans of beverages (Fig.11). These cans have one problem, that is, the vertical surface doesn't reach the upper part. For that reason we had to incline the gnomon so as to get the point remained at the same level that the first line of the hours. The distance or length of the gnomon for all the calculations will be the one that exists between the point of the gnomon and the surface of the can.

These cans have the additional charm that the same ring that serves to open them will also serve if it is curved adequately as a hanger for the dials (Fig. 12).

To make one of this historic dials, the style should project radially a distance d from the edge of the can (Fig. 13).

The maximum length of the shadow is 77.5 mm when the Sun is at maximum altitude of 66.44º at noon midsummer, at Latitude 47º, so that

77.5/d = tan 66.44º and d = 33.8 mm

To plot the shadow hour lines from the dial to sow how they vary the Hour Angle of the Sun (HA), the altitude of the Sun (alt), the declination d and the latitude f of the observer, we use the spherical trigonometrical relation,

Sin (alt) = Sin φ sin δ + cos φ cos δ cos HA

Non-mathematticiams should not be put off by this, but use it as a program for a calculator or computer to produce the Table 1 which all the data for plotting the set of graphs that is wrapped round the drinks can which are contained in Fig 9.

As an example, considerer the altitude of the Sun on May 21st when its declination is 20.5º, in latitude 47º N and hour angle 75º, that is Sun Time = 7 am or 17 pm, 5 hours before or after midday.

Sin (alt) = sin 47º sin 20.5 + cos 47º cos 20.5 cos 75

The calculator gives: (alt) = 24.92º as in Table 1

**References**

SOLER GAYÁ, Rafael.:Diseño y construcción de relojes de sol y de luna. Colegio de ingenieros de caminos, canales y puertos. Baleares. 1997.

PALAU , Miquel.; Historia y trazado de los relojes de sol al alcance de todos. Millá. Barcelona. 1982

WAUGH, Albert E.: Sundials. Their theory and construction. Dover Publications, Inc. New York. 1973.

MILLS, H Robert : Practical Astronomy. Albion Publishing. Chichester. 1994.

GATTY, Alfred.: The book of sun-dials. George Bell and Sons. London. 1872.

SAVOIE, Denis.: La gnomonique. Les Belles Lettres. Paris. 2001.

FAVERO, E; and GARETTI, C.: Meridiani dei Comuni d'Italia. A cura di Favero...Unione Astrofili Italiani (UAI).

**Internet**