Sundials: Their Construction and Use

Overview


To many people, the construction of a sundial implies laborious mathematical calculations and a knowledge of astronomy. Nothing could be farther from the truth. This fascinating handbook, used in conjunction with ordinary tools and materials found around the home, makes it easy to design and construct a sundial on almost any surface and in virtually any position.
Introductory chapters offer a wealth of information on the sundial's development from ancient times to the present, ...
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Overview


To many people, the construction of a sundial implies laborious mathematical calculations and a knowledge of astronomy. Nothing could be farther from the truth. This fascinating handbook, used in conjunction with ordinary tools and materials found around the home, makes it easy to design and construct a sundial on almost any surface and in virtually any position.
Introductory chapters offer a wealth of information on the sundial's development from ancient times to the present, why the sundial tells time, how to design and make a dial, and more. These chapters are followed by full instructions on how to construct the hour lines for many kinds of sundials, by the graphic or geometric method. The use of this method doesn't require a knowledge of mathematics or astronomy. It simplicity and accuracy, together with the ease and quickness of delineation, make it very practical. Readers will also find fascinating chapters on dial furniture, portable sundials, constructing a heliochronometer (a highly precise solar timekeeper), sundial classification, and other topics.
Accompanying the text are 150 well-chosen illustrations, many published for the first time. They depict scale models, as well as a moon dial, a cathedral dial, and other actual dials from around the world, including the world's largest, in Jaipur, India. If you've ever wanted to build your own sundial, or if you simply want to know more about these ancient timepieces that can show the time of day as accurately as many clocks, this clearly written, easy-to-follow guide is "the best book available." — Commonweal.
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Editorial Reviews

From The Critics
Two fine guides to timekeeping and sundials are recommended picks. James Jespersen and Jane Fitz-Randolph's From Sundials To Atomic Clocks appears in its second revised edition to provide a history of human understanding of the nature of time and its calculation. From natural clocks to the relation of time, frequency and navigation issues, this provides a treatise on man-made timekeeping systems. R. Newton and Margaret Mayall's Sundials (41146-X, $9.95) considers the construction and use of sundials, and appears as a republication of the 1994 third edition. Chapters provide fine details on how sundials tell time and how to construct all types of sundials, from portable instruments to furniture.
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Product Details

  • ISBN-13: 9780486411460
  • Publisher: Dover Publications
  • Publication date: 6/20/2000
  • Edition description: Unabridged
  • Edition number: 3
  • Pages: 320
  • Sales rank: 975,746
  • Product dimensions: 5.38 (w) x 8.46 (h) x 0.70 (d)

Read an Excerpt

SUNDIALS

Their Construction and Use


By R. Newton Mayall, Margaret W. Mayall

Dover Publications, Inc.

Copyright © 1994 R. Newton Mayall
All rights reserved.
ISBN: 978-0-486-15707-8



CHAPTER 1

THE DEVELOPMENT OF THE SUNDIAL


IT is not at all surprising that the present generation knows little about the sundial, which in our present complex existence has become the forgotten timekeeper. It is reminiscent of a more leisurely existence when "time waited for no man", whereas today no man waits for time.

When the Pilgrims landed on our shores and up to the time of the American Revolution sundials were the most common timekeepers on the Continent, even though many cities and towns had erected towers containing primitive mechanical clocks similar to the one in Milan, Italy; and despite the fact that at the beginning of the 20th century mechanical timekeepers had been perfected, sundials were still used by one of the leading railroads in France to regulate the watches of their trainmen. Furthermore, how many, except perhaps the most adventurous travelers, know that in many places throughout the world the sundial is, even today, the principal or only timekeeper; that in parts of Japan and China, a simple noon mark dial is used by government post offices. A recent letter from a postmaster in a small Japanese country town states that he uses a noon mark dial "to regulate the time and it is quite punctual than to depend on cheap watches."

Man has always regulated his life and work by time in one form or another. Primitive man may have been content with a day of two periods—starlight and sunlight. As it became necessary for him to travel farther afield he soon would have observed that a constant watch must be kept on the apparent motion of the sun in the sky. He could travel outward as long as the sun rose, but as it began its descent toward the opposite horizon he must hasten to retrace his steps in order to return before nightfall. This division of the day into two parts must soon have become insufficient. It is not improbable that primitive woman may have caused man to devise a means of apportioning the day into smaller parts which could be relied upon, for reasons easily imagined. His solution to the problem is readily conjectured. Surely our caveman ancestor noticed the phenomena of shadows cast by upright objects—how the shadows lengthened and shortened in relation to the position of the sun. By placing a stick firmly in the ground he could watch and study the shadow it cast. Probably stones or sticks were placed at the extremity of the shadow at various times during the day, giving him definite periods of short duration, and the length of these periods could be arranged to suit his comfort and needs.

But, another problem arose. How could the traveler return at a prearranged time? Here again the solution is obvious to us. He could carry with him a stick equal in length to the height of the one which had been securely placed in the ground near his cave. Thus, the first stationary and portable sundials may have been born. No doubt Mrs. Caveman frequently remarked, "Don't forget your shadow pole and return when the shadow's length is one pole."

If the perpendicular stick or gnomon type was the first dial, there is nothing to indicate what was produced between the time of its invention and the appearance of those early dials of which we have information. In order to preserve clarity and continuity in tracing the development of the dial, no detailed definitions of terms explained elsewhere will be given here.

Therefore we leave conjecture behind and let the sundial tell its own story, beginning about 1500 B.C. At the beginning of the 20th century the earliest dial known was devised about 370 B.C., whereas today we have examples of dials used in Egypt about 1500 B.C., which were brought to light through archeological exploration. As the archeologist has made us more familiar with the life and work of early peoples, so has our knowledge of early timekeeping instruments penetrated the dark recesses of history.

We know the Egyptians were well versed in astronomy and mathematics; that they understood at a very early date the motions of the earth and planets; and that they had fixed the year at about 365 days; but, very few Egyptian sundials have been found. However, the oldest dial, Figure 1, is among them. This dial was made of stone in the form of a flat bar about 12 inches long with a perpendicular T-shaped piece fixed at one end. The time of day was deduced by the position of the shadow cast, by the upper edge of the cross piece, between the marks cut at irregular intervals on the top surface of the bar. When in use, the cross piece must be turned toward the east in the morning and toward the west in the afternoon. The plumb line is used for placing the instrument in a level position.

Figure 2 shows another Egyptian dial of similar character constructed during the period of about 660-330 B.C. (Later Period), which tells time throughout the day without being turned for the afternoon hours. In addition to the flat dial surface, ramps and steps have been cut into the sides. The position of the shadow on them will also give the hour. This arrangement enabled the dial to be set without the aid of a standard line or meridian, for it was only necessary to place it in a level position, then move it until the time shown by the shadow on the ramps or steps agreed with the time shown on its upper level surface. Such a dial if made small and light enough, could easily be carried about.

One more Egyptian dial, Figure 3, is of particular interest. It is of the period about 330-30 B.C. (Hellenistic Period), and shows a decided advance over the previous dials in that in-stead of a horizontal surface to record the position of the shadow cast by the upper edge of a perpendicular block or gnomon, the surface was inclined at an angle equal to the latitude of the place. Its width was divided to show the months and across these divisions diagonal lines were drawn representing the hours of the day. When in use the instrument was first placed in a level position by means of the plumb line, then turned so that the perpendicular block was pointed directly toward the sun. The position of the shadow upon the hour lines corresponding to the proper month would show the time for any day. This was an ingenious device, because the Egyptians did not make use of hours of equal length, as we do today—they used temporary or unequal hours.

Temporary hours resulted from the division of the period between sunrise and sunset into twelve equal parts. Because the length of this period varies throughout the year, it was not possible to obtain equal divisions of time by such a method except on any one specified day. Therefore it was necessary to observe the position of the shadow at each hour on several days during the year, preferably at the time of the equinoxes and the summer and winter solstices. If lines drawn through these points were crossed by others designating the months the true temporary time could thus be obtained any day in the year.

Timekeeping was not the only incentive for making these dials, for they were often used as votive offerings and placed in temples. The period of production is our only clue to the age of Egyptian dials—their makers are unknown. A contemporary device—the clepsydra or water clock—made it possible to tell time at night or when the sun did not shine, by measuring or indicating the height of water in some receptacle from which the flow could be regulated.

We must now retrace our steps a few centuries to pick up the threads of a lost sequence. Those who are familiar with their bibles will remember Ahaz was the King of Judah about 742—727 B.C. Perhaps you will even recall the "Dial of Ahaz", attributed to one of his Babylonian astronomers, which is mentioned twice in the scriptures:—In II Kings XX:9—11

"And Isaiah the prophet cried unto the Lord; and he brought the shadow ten degrees backward, by which it had gone down in the dial of Ahaz."


and in Isaiah XXXVIII:8


"Behold, I will bring again the shadow of the degrees, which is gone down in the sundial of Ahaz, ten degrees backward. So the sun returned ten degrees, by which it had gone down."


This phenomenal movement of the shadow on the Dial of Ahaz has given rise to as much discussion as the squaring of the circle and the trisecting of any angle. For years, it has puzzled layman and scientist alike. The form of the dial remains a matter of conjecture.

More than a century after the reign of Ahaz we learn of a dial erected, about 560 B.C., by Anaximander of Miletus (611—547 B.C.), a Grecian astronomer. This was probably a vertical rod or gnomon erected in the public square, similar to, but more carefully constructed than the upright stick of the caveman, because more information about the movement of celestial bodies was at hand as evidenced by the work of the Egyptians.

The Chaldeans had made substantial progress in mathematics and astronomy. By constant observation of the heavens they became familiar with the constellations and saw in them the likenesses of human beings and animals; they divided that band in the sky called the "Zodiac", in which the sun and planets move, into twelve parts or signs each containing a configuration, named and referred to as the Zodiacal constellations. They also divided the year into twelve parts, devised the week of seven days, and foretold eclipses.

One of the simplest forms of the sundial—the hemispherium, Figure 4—is attributed to the Chaldean priest and astronomer, Berosus, who lived at the time of Alexander the Great (356—323 B.C.). This dial was carved out of a block of stone, its concave hemisphere resembling the inverted vault of the heavens. A perpendicular pin or style was placed in the center, pointing to the zenith; then as the sun traversed the sky, the shadow of the top of the pin would trace out the apparent motion of the sun in a reverse direction. That portion of the inner surface upon which the sun shone was divided into twelve parts representing the temporary hours. The hour lines were crossed by three or seven other lines corresponding to the seasons or months, which were determined by the same method used in Egypt.

Although inaccurate, the hemispherium was far superior to the waterclocks in common use at the same time, because they were bulky, needed attention and could not be carried about easily; whereas the hemispherium could be made small enough to be carried in the pocket and set up anywhere.

The hemicyclium, Figure 5, is also attributed to Berosus and it is often referred to as the "dial of Berosus." There is a difference of opinion concerning the inventor of these two dials which may be due to a loose use of the two words in modern literature as meaning the same kind of dial. Although there is no difference in the construction of the lines, the hemicyclium has the front or south portion cut away at an angle, and a horizontal gnomon is used instead of a perpendicular one. The portion cut away is useless for timekeeping purposes because the shadow would never enter that part. Some early writers considered the hemicyclium a great improvement over the hemispherium, which was probably due to the greater ease in reading, and its lighter weight. Both dials were made in forms and sizes too numerous to mention.

Although the introduction of Euclid's "Elements" (ca. 300 B.C.), with which all of us have struggled at one time or another, gave great impetus to the progress of mathematics, no great improvement was made over the hemicyclium for many years. The writings of Albategni show that these concave dials were commonly used in Arabia as late as 900 A.D., and the same construction was followed.

About 100 years after the appearance of Euclid's work, Apollonius of Perga (250—220 B.C.) made public his treatise on the theory of conic sections, which laid the foundation for the geometry of position. The advent of this new study soon brought about a change in sundials, resulting in the conical dial, Figure 6.

The conical dial was an improvement over previous dials in that its essential factor was greater accuracy. Its appearance was not unlike that of the hemicyclium, although the concave segment of a circular cone was used instead of the hollow section of a sphere. The surface was delineated in much the same manner, with the twelve unequal hour divisions crossed by three or seven arcs corresponding to the seasons or months. Very few dials of this type have been found in the ruins of Egypt, Greece, and Italy; but they were probably not introduced before 200 B.C. Either the lower surface or axis of the dial was inclined at such an angle that it pointed to the north star. At this time a wider knowledge of conic sections was necessary to further improve the sundial.

After the fall of Alexander the Great we find such names as Aristarchus (ca. 280—264 B.C.), Hipparchus (160—125 B.C.), and Strabo (29 B.C.—14 A.D.). Hipparchus was the founder of scientific astronomy and it was he who laid the foundation for our present trigonometry. Contemporary scientists quickly grasped this new method of computing, but it was left to others, later, to apply the theory to the improvement of the sundial.

We now find ourselves at the beginning of the Christian Era, with a picture cf the type of dials evolved by the Egyptians and Greeks. Through the centuries little advance had been made in timekeeping quality.

Other countries employed the sun as a timekeeper—the Arabians attached great importance to the science of sundial construction, which they learned from the Greeks. They had dials of similar construction, as did the Romans who also adopted them from the Greeks. They did not add any new types or evolve new methods of figuring and laying out the hour lines. That dials were prevalent in Rome and throughout the Empire is evident by this choice morsel from the pen of Maccius Plautus (ca. 250—184 B.C.), a comic poet and writer of that city:

"The gods confound the man who first found out
How to distinguish hours! Confound him, too,
Who in this place set up a sun-dial,
To cut and hack my days so wretchedly
Into small portions. When I was a boy,
My belly was my sun-dial; one more sure,
Truer, and more exact than any of them.
This Dial told me when 'twas proper time
To go to dinner, when I had aught to eat.
But now-a-days, why, even when I have,
I can't fall-to, unless the sun give leave.
The town's so full of these confounded dials,
The greatest part of its inhabitants,
Shrunk up with hunger, creep along the streets."


Be that as it may, we are indebted to the Romans for a valuable contribution, which is found in the "Treatise on Architecture", written by their renowned architect Vitruvius, who died during the reign of Augustus (30—14 B.C.). This is the only accessible literary work of Roman origin mentioning sundials. We cannot lightly skip over this ancient record, for Vitruvius says that he will "state by whom the different classes and designs of dials have been invented. For I cannot invent new kinds myself at this late day, nor do I think that I ought to display the inventions of others as my own." He lists thirteen dials, in the following order:

"The HEMICYCLIUM of Berosus
The HEMISPHERIUM of Aristarchus
The DISCUS ON A PLANE of Aristarchus
The ARACHNE of Eudoxus
The PLINTHIUM of Scopas
The UNIVERSAL DIAL of Parmenio
The UNIVERSAL DIAL of Theodosius and Andrias
The PELICONON of Patrocles
The CONE of Dionysidorus
The QUIVER of Apollonius


"The men whose names are written above, as well as many others, have invented and left us other kinds: as for instance, the CONARACHNE, the CONICAL PLINTHIUM, and the ANTIBOREAN."

The appearance of a few of the dials listed is known, but there is no definite knowledge about the rest. Vitruvius credits Aristarchus with the invention of the hemispherium. Presumably he has arranged the list of dials in order of their age (as is the sequence of diagrams included in this chapter), but it would have been more logical to place the hemispherium first because of its simplicity. Furthermore Berosus preceded Aristarchus by 100 years.

Vitruvius also mentions the fact that other writers have left directions for the construction of dials for travelers, "which can be hung up." He then states that anyone can construct such dials from the directions in books on the subject, "provided only he understands the figure of the analemma." (The analemma was an instrument and method of projection which demonstrated and solved some of the common astronomical problems,—not the figure eight we see on modern globes and atlases. It is not of sufficient importance here to warrant detailed explanation, which can be obtained from any modern reference work.) This leads to the supposition that, up to the time of Vitruvius, no geometrical method had been evolved to construct the hour lines for a dial.

At the end of the pre-Christian period the use of sundials extended over the greater part of the Western World, but up to that time few improvements had been made on the known types other than simplifying their form and the addition of certain embellishments.


(Continues...)

Excerpted from SUNDIALS by R. Newton Mayall, Margaret W. Mayall. Copyright © 1994 R. Newton Mayall. Excerpted by permission of Dover Publications, Inc..
All rights reserved. No part of this excerpt may be reproduced or reprinted without permission in writing from the publisher.
Excerpts are provided by Dial-A-Book Inc. solely for the personal use of visitors to this web site.

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Table of Contents

I THE DEVELOPMENT OF THE SUNDIAL
    A brief outline from ancient times to the present.
II WHY THE SUNDIAL TELLS TIME
    What you ought to know.
    Invention of the armillary and its use.
    Mean Time and Standard Time.
III HOW TO DESIGN AND MAKE A DIAL
    Simple instructions how to go about making a sundial.
IV SELECTING THE DIAL TO MAKE OR BUY: GUIDELINES AND MATERIALS
    What to look for when buying a dial.
    Notes concerning individual dials and suggested locations or settings to aid in selecting the type of dial best suited to your needs.
    Various materials commonly used in making dials.
    Classification of dials.
V PARTS OF A DIAL YOU SHOULD KNOW
    Descriptions of terms and parts commonly associated with sundials.
    How to determine a true north line or meridian.
    How to find the declination of a plane or dial.
    How to find the reclination of a plane or dial.
    How to set your dial.
    How to make and use a vernier.
VI TIME AND STANDARD TIME DIALS
    How time is obtained.
    The equation of time explained and its use.
    How Standard Time may be obtained from the reading of a sundial.
    How to make Standard Time Dials.
    The heliochronometer.
VII HOW TO LAY OUT THE HOUR LINES
    The graphic method of laying out hour lines on many types of dials.
    Hour limitations of the various dials.
    Setting the dials.
VIII DIAL FURNITURE
    "Description and use of various lines, figures and symbols which may be added to the dial that it may be of more interest and use."
    Educational value of the sundial and its furniture.
    The signs of the Zodiac defined.
IX HOW TO LAY OUT THE LINES OF DECLINATION
    The graphic method of laying out the lines of declination on many types of dials.
X PORTABLE SUNDIALS
    "Types of Azimuth and Altitude Dials: Ring, Cylinder, Quadrant, Capuchin, O-G, Horizontal Altitude, Horizontal Azimuth, Magnetic Azimuth. "
XI VARIABLE CENTER DIALS
    Analemmatic and Lambert Dials.
XII THE HELIOCHRONOMETER
    Details and construction.
    The Analemma.
    How to use the Heliochronometer.
    Formulae for the Analemma.
XIII SUNDIAL CLASSIFICATION
    Oridinary and Special Types.
    Definitions and criteria for distinguishing various kinds.
    Classification scheme and register card.
XIV INTERESTING DIALS OF THE WORLD
    The Great Dial at Jaipur
    A Desirable Instrument
    A Noon Mark Goes to Sea
    An Armillary
    The Whitehall Dial
    Flower Time
    A Moon Dial
    Cathedral Dials
    Singing Tower Dial
    Exploration
    And Fired the Shot Heard at Noon.
XV HUNTING SUNDIALS
    Where to look for dials and how to photograph them.
  APPENDIX
  I FORMULAS
      "Formulas for computing the position of the hour lines on many types of dials, by trigonometry."
      The tangent method of laying out the hour lines.
      How to compute the azimuth and altitude of the sun.
      Computing the azimuth and time of sunrise and sunset.
  II TABLE FOR CONVERTING DEGREES OF ARC INTO MINUTES OF TIME OR VICE VERSA
      A convenient table to relieve you of a laborious calculation.
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