Astronomy

How does the geometry for constructing a declining vertical sundial work?

How does the geometry for constructing a declining vertical sundial work?


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I understand how to construct South-facing vertical an horizontal sundials and the geometry behind their construction by projecting an equatorial sundial into a plane, but I can't quite get how to do that for a declined plane.


You might find the following useful; scroll down to "Vertical Declining Sundial".

http://www.walkingshadow.info/Publications/Scratch.pdf


Question : Give details regarding use of the simulated, Celestial Globe or Sphere (Lab 3 done for TWO weeks and connected a little with the angles from Lab 4's Sundials) and how one describes the exact position of objects in Astronomy, utilizing Celestial Longitude (R.A.) and Celestial Latitude (Declination or Dec.) Describe in great detail, all the objects and

Give details regarding use of the simulated, Celestial Globe or Sphere (Lab 3 done for TWO weeks and connected a little with the angles from Lab 4's Sundials) and how one describes the exact position of objects in Astronomy, utilizing Celestial Longitude (R.A.) and Celestial Latitude (Declination or Dec.)

Describe in great detail, all the objects and reference lines, that are shown on the Celestial Globe, and how to we set-up this object, for our Latitude on Earth that we are observing from. How would you go about locating a particular Star or Constellation on the Globe? How would you find its RA and Dec, and then describe its exact position using them? Are you able to give a star and its RA and Dec, that is popular, by looking it up, and listing it here?

How specifically would you explain the position of a sky/night object, that you located on the Globe, and then up in the actual sky?

Please compare and contrast using this web Stellarium, to give us a representation of our nighttime sky as seen from various places on Earth, to our use of the remote link for the Star & Planet Locater in Lab# 1? What reference lines/areas that show on the Lab#1 Star & Planet Locater, that also appear on this Lab#3 Cel. Sphere?

List the ranges for both RA and Dec, for objects being listed in the sky?

What is the RA and Dec for our Sun, on our first day of Spring, and on our first day of Fall?

What (2 things each) were represented by the horizontal and vertical metal bars (4 total) on the Cel. Globe?

extra credit: Describe, in Lab #4, how we used the (7) hour angles that come from the Celestial Globe, to construct a working Sundial?

Once we had the PM angles, why did we not have to find the AM angles, but only strike them on the Sundial base, and draw them?

Does the Sundial we constructed, work at any latitude on Earth, or only for ours? How do we thus construct the Nomon, and its angles?

In the next Lab (Lab 4) we constructed what special object, using the hour angles obtained from a Celestial Globe? Describe how one draws the base hour angle lines for a Sundial, and one goes about constructing it? Attach a picture to your response, with Drawn and labeled details of the parts of the Globe, and what they show!

What are all the many things that we can determine from our study of the Celestial Globe, and how did it help in ancient times, before electricity and computers?


Babylonians and Egyptians built obelisks which moving shadows formed a kind of sundial, enabling citizens to divide the day in two parts by indicating noon.

The oldest known sundial was found in Egypt and dates from the time of Thutmose III, about 1,500 years BC. There were two strips of stone, one that did the needle and another where the hours were marked.

After this first known sundial, we must advance to the 750 BC to have references from another sundial, and is found in several Old Testament passages that describe a sundial, that of Ahaz. A biblical reference tells how Yahweh did the shadow go back ten degrees on the dial. However, we are sure that there were other much earlier among almost all peoples of antiquity, although there is no evidence so clear as in this case.

Moreover, the earliest description and design of a concave sundial is attributed to the Babylonian Berossus in the IV century BC.

Picture 1: Greek sundial III-II century BC.

Picture 2.

With the Greeks, sundials are studied thoroughly and for the first time, the gnomon stops of being installed vertically and passes the correct position, parallel to the Earth's axis. They developed and constructed complex sundials using their knowledge of geometry.

The watch Greek is called "scaphoid" (bowl) and consisted of a block in which a cavity was emptied hemispheres, at whose end is fixed the needle bar serving.

Put the gnomon parallel to the direction Earth's axis allowed the clock signal throughout the year the hours of a constant duration, making measuring instruments, really. In the previous vertical needle had clocks where summer hours were different from those of winter (as we have already commented above). It should also be mentioned that the scaphoid were also the first sundial that measured time by the direction of the shadow and not, as heretofore, by its length.

In fact, almost all posterior cultures, at least, those who had direct or indirect contact with the Greeks used for their design sundials Greeks: the Romans, Arabs, Indians, Afghans and so on. The Greeks sundials used refinements like the orientation of the object that casts the shadow or gnomon, which did not have to be perpendicular to the ground, and the geometric shape of the surface on which the shadow cast, which did not have to be flat, and they got excellent precision for the time, precision of a few minutes that would not be surpassed for centuries.

In picture 2 we can see a splendid Greek sundial called Horologion or Tower of the Winds. It consists of an octagonal marble building oriented according to the cardinal points and topped with a conical dome. This building was entrusted to Andronicus Cirrus that he did in 50 BC. With the Roman domination the ancient Agora of Athens was too small for their duties and it was decided to build a new one to move their business activities of the city. This new place was endowed with this advanced sundial: the Horologion.

The Romans copied the Greek scaphoid, which he called hemispherium. The ancient Romans, from the scientific point of view, did not add anything new with regard to measuring time, continued to use sundials developed by the Greeks.

Pliny the Elder in his Natural History relates the history of the sundial that Emperor Augustus ordered to build in the Campus Martius, using an Egyptian obelisk of Pharaoh Psamtik II, called the Solar Clock Augustus or Augustus Meridian.

Picture 3: Drawing of the Augustus meridian can be seen in the Champ de Mars, close where the sundial was.

Picture 4: The Agrippa Pantheon in Rome. The hole in the roof acts as a sundial (I century BC).

On the astronomical content found in the architecture of the Pantheon in Rome, built by Agrippa in the first century BC, there is no doubt. But now some researchers argue that the Roman building acts as a huge sundial (Picture 4).

According to Roman architect and engineer Vitruvius, were used at least thirteen different types of sundials. Vitruvius wrote a book about gnomonics in which he describes a geometric method for designing sundials called analemma.

The Roman Empire's decline and fall because of the barbarian invasions, led in Occident a long period of intellectual darkness.

In the early centuries of the Christian era, the gnomonic, dimly lighted by studies of Hellenistic astronomy is entering a decline that characterizes the entire science of European medieval cultural and economic. There are few items (mostly archaeological) we can find there are just written to show further progress. Although in this period to the general public cared little time measurement, there are no precise scientific descriptions. However, as oddities at the time, there were two surveyors: the Venerable Bede and Higinio Gromat (II century).

You need to wait until feudalism assist the dissemination of sundials on the European continent. It was the religious order Benedictine (529 AD) and his dedication to comply with the schedule dictated by its founder, what encouraged these monks to study the construction of sundials.

Since its origin, the Catholic Church wanted to sanctify certain times of the day with a common prayer. The gnomonic of these centuries led to the construction of Mass clocks or watches of canonical hours and in them the hours of prayer were indicated. These watches are generally located in the southern facades of churches or monasteries.

Picture 5: Sundial on the south facade of stone in the church of Revilla (Huesca, Spain).

First sundials carved on the stone facades of churches and cathedrals are starting to appear early VIII century. In the year 1000 horizontal sundials were constructed for which holes were used in the vaults of cathedrals.

In the IX century Arabic astronomy comes in. The caliphate of Al Mamun marks the beginning of an intense cultural activity would continue in later centuries with writers such as Averroes, Ibn Thabit Qurraa (826-901) and Al-Biruni (973-1048) as example. While Christian Europe at the time followed the works of the Venerable Bede, the Arabs had a hectic continued intellectual activity from the destruction of the Alexandria Library. It is only from the X century when Europe begins to look timidly vast compilation of ancient knowledge work done by the Arabs.

The majority of Arabs watches were flat at that medieval times, constructed of marble or copper plates. They all have an indication of the direction of the Kaaba in Mecca because of the religious precept of praying with the face turned to that place regardless of where they are located.

Picture 6: Sundial at the Sidi Okba Mosque in Kairouan (Tunisia).

Picture 7: Sundial at the garden of Topkapi Palace in Istanbul (Turkey).

The XI century, a German mathematician who knows the Arabic language, wrote a treatise on the astrolabe retaining some Arabic terminology. In this treaty are some indications for the shepherd's sundial. The translation of two Arabic manuscripts gnomonic was most important cultural advance of the time in this field.

Picture 8: Cathedral of Teruel. Two sundials, one south facing and one west. Teruel Cathedral began to be built in the Romanesque style in 1171 and concluded with the establishment of the Moorish tower in 1257. It is one of the most characteristic Moorish buildings in Spain.

Picture 9: Sundials of the Terual Cathedral in the south facing right and the left of the west face.

In the XIII century in Spain, King of Castile Alfonso X the Wise put together in the city of Toledo a large group of Christians, Greek, Hebrew and Arabic astronomers to translate into Latin many of the works written in Arabic. Thus the Arabic knowledge spread throughout Europe to leave behind all the cultural obscurantism in which it was immersed. Also the gnomonic was developed, like all sciences.

In the XIV century, the first mechanical clock is made. It is a large iron-framed structure, driven by weights. The function of the first European clocks was not to indicate the time on a dial, but to drive dials that give astronomical indications, and to sound the hour. They are located in monasteries and public bell towers. The earliest surviving example, constructed in 1386, is in Salisbury Cathedral, England. Mechanical clocks utilize equal hours.

In Spain during the reign of Enrique III, in 1400, the first mechanical watch with bells was installed in the tower of the church of Santa Maria de Sevilla.

The following centuries were the great age of the European sundial. In the XV century a great effort was made in Europe by the divulgation of the Gnomonic. Sundials with equal hours gradually come into use.

In the American colonies were built many sundials, some of which are still preserved. In the tropics you have to build a double disc with time. The south-facing disk is used for part of the year, from August to April, and the disk on the other side facing north would use the rest of the year. Two days a year, when the Sun passes directly above the site hours can be seen on both sides.

By the mid-XVI century the first mechanical clocks appear. It is in the XVII when these devices are refined and slowly getting more accurate operation.

The onset of the Renaissance saw an explosion of new designs. Giovanni Padovani published a treatise on the sundial in 1570, in which he included instructions for the manufacture and laying out of mural (vertical) and horizontal sundials. Also, Giuseppe Biancani published (1620) other treatise where discusses how to make a perfect sundial with accompanying illustrations.

In the XVIII century clocks and watches begin to replace sundials. They have advantage of not requiring sunny skies. There are, however, often unreliable and depend upon sundials to set the true time.

In the early 1800’s mechanical clocks become accurate enough and inexpensive to displace sundials as timepiece of choice.

At present, although the accuracy of mechanical clocks outweighed sundials, they continue be built, primarily as a decoration on buildings, monuments and public places. They are constructed of many types with precision and beautiful designs. The support of the computer to calculation and design of the sundial has been fundamental. As a result of this technological support, are living the revival of this ancient instrument for measuring time in recent years, but as mentioned above, its function is currently not precisely what sundial was born but only as a decoration.

In any case, I welcome the resurgence of the sundial!!

Picture 10: Modern equatorial sundial in Tarragona (Spain).

Picture 11: Vertical sundial faced to the west a private house in Grañen, Huesca (Spain).


The Age of the Earth and the Formation of the UniverseHonors Seminar (UHON 390), Fall 2005

The sun can make an effective natural clock for measuring time between sunrise and sunset. It meets the criteria of a natural clock. The initial condition (sunrise) and final condition (sunset) are known. The progress of the sun in the sky is irreversible in that it always rises in the east and sets in the west. Its progress occurs at a relatively uniform rate from day to day, and adjustments can be made for the variations.

People have used the sun to tell time since time immemorial. It is possible to approximate the time of day just by glancing at the position of the sun in the sky. Without using tools, it is probably impossible to perfectly guess the time by looking at the sun for two reasons: (1) the period of daylight is longer during the summer than during the winter, and (2) the sun rises and sets at different times throughout the year. But for our purposes, it would be reasonable to say that on average there are twelve hours of daylight each day starting around 7:00 AM and ending at approximately7:00 PM. That would mean the sun is at its highest in the sky, a point called solar noon, around 1:00 PM. Technically, it is safer to say that you can estimate what fraction of sunlight is left before the sun goes down (i.e. a relative measurement) instead of saying you can guess the actual time (i.e. an absolute measurement), but that might not be as easy to understand or quite as useful.

Unfortunately estimating the position of the sun in the sky is inexact. For example, it is very difficult to tell the difference between 2:00 PM and 2:30 PM just by looking at the sky. In order to solve this problem people need to use tools. Because the angle of the sun in the sky affects the shadows cast by objects, it is possible to use those shadows cast to tell time instead of using the sun itself. A sundial, a tool with an elevated point, called a gnomon, to cast a shadow and a series of markings to judge the movement of the shadow, makes possible much more accurate measurements. Scientists have discovered 3,500-year-old sundials from Egypt. These tools allowed the ancients to better measure the passage of time each day.

In the modern world, time has become a trickier proposition. Daily work schedules need to be consistent throughout the year. Businesses, governments, and the military need individuals separated by thousands of miles to act simultaneously. We use time zones, milliseconds, and atomic clocks. It is, however, possible to construct sundials that largely meet the demands of modern society. There are three main sources of difficulty: (1) the Earth&rsquos orbit around the sun, (2) the modern time zone system, and (3) changing seasons.

The first problem, called the Equation of Time, is the combination of two factors. First, Earth&rsquos orbit around the sun is elliptical, not truly circular. Second, Earth&rsquos axis is inclined at an odd angle compared to the plane of its orbit. These problems cause the sun&rsquos motion across the sky to be slightly variable, causing apparent sun time as measured by sundials to be up to sixteen minutes off compared to clock time. The Equation of Time is the process of adjusting apparent sun time in order to ensure its accuracy against normal clocks. The graph shows how obliquity (axis tilt) and eccentricity (elliptical orbit) combine to cause the total distortion between our clocks and the actual position of the sun.

Another adjustment must be made for the modern system of time zones because sundials measure local solar time. This modification depends on the longitude where the sundial is located. The one hour difference between time zones is an average based on the geographic center of each zone. So any sundials that are not exactly in the middle of a time zone need to be adjusted based on their distance from the center. The Earth rotates a full 360° around its axis every twenty-four hours, i.e. 15°/hour. Dividing the sixty minutes in an hour by fifteen degrees shows that each degree of longitudinal separation between two places will cause four minutes of difference in time readings. For example, Vermillion, SD and Chicago, IL are both in the Central Time Zone, but because they are separated by 9° of longitude, the apparent sun time in Chicago will be thirty-six minutes later than in Vermillion.

Finally, an adjustment needs to be made for different seasons of the year. Because the Earth&rsquos axis is tilted, the sun&rsquos path through the sky changes slightly every day. Moreover, sundials that cast shadows onto the ground face another problem. Earth&rsquos surface is curved, so the surface onto which the gnomon is casting shadows is not parallel to the equator. That will cause the shadow to move at an uneven rate throughout the day. If the demarcations are evenly spaced, then the sundial will only be accurate at noon. Alternatively, one would need to figure out the proper but irregular spacing of hour markings this can be somewhat difficult without doing a good bit of trigonometry. Even with appropriate spacing (as in the graph to the right), the irregularity of the scale would make it less easily readable by humans. One solution to that problem is to create a sundial where the base plate is angled to match the latitude where the sundial is located. The gnomon is set perpendicular to the base plate. Hour marks can then be evenly spaced. Such sundials are called equatorial sundials. More detailed information about equatorial sundials can be found on the NASA website listed as link number one below. Suffice it to say that the math is comparatively simple.

It is also worth noting that, in addition to measuring the passage of a day, the sun can also be used to measure the passage of a year. This is another effect of the tilt of Earth&rsquos axis. The way this process works is much more easily explained by graphs than by text. The tilted axis results in the sun moving through the sky during the course of a year. If you were to record the position of the sun at noon every day for a year, the result would be a figure eight-shaped graph called an anelemma. The anelemma can be rotated along the sun&rsquos arc for every hour of the day. The end result is that during the winter, when the days or shorter, the sun cuts a significantly smaller arc across the sky than it does during the summer.

Using these methods, the sun can make an effective natural clock for telling both the time of day and the time of year.

More Information on Sundials:
  1. Schlecht, Clifford. August 24, 1999. Sundials. NASA Liftoff. Retrieved from http://liftoff.msfc.nasa.gov/Academy/Earth/Sundial/Sundial.html Last accessed 9-18-2005.
  1. History of the sundial. No date. National Maritime Museum. Retrieved from http://www.nmm.ac.uk/site/request/setTemplate:singlecontent/contentTypeA/conWebDoc/contentId/353 Last accessed 9-18-2005.
  1. Aubert, Jack. March 17, 1996. Sundials. Retrieved from http://cpcug.org/user/jaubert/jsundial.html Last accessed 9-18-2005.
More Information on the Equation of Time:
  1. The equation of time. No date. National Maritime Museum. Retrieved from http://www.nmm.ac.uk/server/show/conWebDoc.351 Last accessed 9-18-2005.
  1. Holtz, John. December 21, 2003. Eccentricity, Obliquity, and the Analemma's Width. Retrieved from http://members.aol.com/jwholtz/analemma/eq-of-time.htm Last accessed 9-18-2005.
  1. Mukai, Koji Palmer, Koji Kallman, Tim. January 16, 1998. The equation of time. NASA's Ask the Universe! Retrieved from http://imagine.gsfc.nasa.gov/docs/ask_astro/answers/980116c.html Last accessed 9-18-2005.
  1. The equation of time. January 28, 2004. Sundials on the Internet. Retrieved from http://www.sundials.co.uk/equation.htm Last accessed 9-18-2005.
  1. The equation of time. October 14, 2005. Wikipedia. Retrieved from http://en.wikipedia.org/wiki/Equation_of_time Last accessed 12-2-2005.
  1. Science and Engineering Research Council at the Royal Greenwich Observatory. November 25, 1993. The equation of time. Information Leaflet No. 13. Retrieved from http://www.oarval.org/equation.htm Last accessed 9-18-2005.
  1. National Weather Service Forcast Office Austin/San Antonio, TX. December 12, 2004. Equation of Time. Retrieved from http://www.srh.noaa.gov/ewx/html/wxevent/2004/eoftw.htm Last accessed 9-18-2005.
  1. Barnes, Howard. July 29, 2005. Equation of time. Ask a Scientist by Argonne National Laboratory. Retrieved from http://www.newton.dep.anl.gov/askasci/ast99/ast99588.htm Last accessed 9-18-2005.
  1. Steiger, Walter R. Bunton, George W. No date. Equation of time. Night and Day by Caltech Submillimeter Observatory. Retrieved from http://www.cso.caltech.edu/outreach/log/NIGHT_DAY/equation.htm Last accessed 9-18-2005.
  1. Tang, Donny. No date. The Equation of Time. Retrieved from http://www.ithaca.edu/students/dtang1/Pages/SophSem.html Last accessed 9-18-2005.
  1. Müller, M. 1993. Equation of Time - Problem in Astronomy. Retrieved from http://info.ifpan.edu.pl/firststep/aw-works/fsII/mul/mueller.html Last accessed 9-18-2005. (technical)
More Information on Anelemma:
  1. Holtz, John. December 21, 2003. Why the Earliest Sunset, Latest Sunrise, and Shortest Day of the Year Occur on Different Dates. Retrieved from http://members.aol.com/jwholtz/analemma/analemma.htm Last accessed 9-18-2005.
Cool Stuff:
  1. Giesen, Juergen. 2005. Sun & Earth applet. Retrieved from http://www.jgiesen.de/sunearth/index.htm Last accessed 9-18-2005. (Java applet to plot the sun&rsquos position in the sky for any location at any time)

Timothy H. Heaton: E-mail, Homepage, Phone (605) 677-6122, Fax (605) 677-6121


What direction should a sundial point?

Sundials need to point in the direction of True North, and the style (either a sharp straight edge or thin rod, often located at the edge or tip of the gnomon) must be aligned with the Earth's rotational axis. You can also position your sundial so that there is no shadow shown at high noon.

Secondly, how do you use a sundial compass? Flip the gnomon up and lock it into place. The gnomon is used to cast the shadow from the sun so you can determine the time of day. Adjust the gnomon until the tip points in the same direction as north based on your compass. The sundial will not tell the correct time unless the gnomon is facing north.

In this way, how do you position a vertical sundial?

  1. A wall facing the south (north) will be adequate for a vertical direct south (north) dial.
  2. A wall facing east (exactly or declining between 80° and 100°) or facing west, is an excellent place for a nice direct east, a direct west or a vertical declining sundial.

How accurate is a sundial?

A sundial is designed to read time by the sun. This places a broad limit of two minutes on accurate time because the shadow of the gnomon cast by the sun is not sharp. Looking from earth the sun is ½° across making shadows fuzzy at the edge. The actual construction of a sundial can be very accurate.


Update: The 2016-2020 Award Scheme – summary of entries

Update Mar 7, 2021. We regret that, due to an oversight, four submissions from Tim Chalk were not published previously or included in the following summary. This has now been remedied and we apologise for the delay.

This, the sixth scheme, has had a record number of entries, boosted in part by time available due to the COVID-19 lockdown. Visitors to the website are encouraged to submit comments on any or all of the sundials, using the reply box at the bottom of each page, on aspects such as design, craftsmanship and overall function of the dial. These comments will help the Trustees to choose the entries for particular Awards.

In summary, we have a large ‘monumental’ dial in Malaysia a restoration of very old polyhedral dial a ‘first venture’ to commemorate a ruby wedding the restoration of a stained glass window dial a number of dials (conventional and unconventional) by experts in Cambridge an obelisk for a garden in Cornwall a novel altitude dial linked to human activities rather than just the hours, and a number of precision dials of different types cut in slate.


Sundial

Our editors will review what you’ve submitted and determine whether to revise the article.

Sundial, the earliest type of timekeeping device, which indicates the time of day by the position of the shadow of some object exposed to the sun’s rays. As the day progresses, the sun moves across the sky, causing the shadow of the object to move and indicating the passage of time.

The first device for indicating the time of day was probably the gnomon, dating from about 3500 bce . It consisted of a vertical stick or pillar, and the length of the shadow it cast gave an indication of the time of day. By the 8th century bce more-precise devices were in use. The earliest known sundial still preserved is an Egyptian shadow clock of green schist dating at least from this period. The shadow clock consists of a straight base with a raised crosspiece at one end. The base, on which is inscribed a scale of six time divisions, is placed in an east-west direction with the crosspiece at the east end in the morning and at the west end in the afternoon. The shadow of the crosspiece on this base indicates the time. Clocks of this kind were still in use in modern times in parts of Egypt.

Another early device was the hemispherical sundial, or hemicycle, attributed to the Greek astronomer Aristarchus of Samos about 280 bce . Made of stone or wood, the instrument consisted of a cubical block into which a hemispherical opening was cut. To this block a pointer or style was fixed with one end at the centre of the hemispherical space. The path traveled by the tip of the pointer’s shadow during the day was, approximately, a circular arc. The length and position of the arc varied according to the seasons, so an appropriate number of arcs was inscribed on the internal surface of the hemisphere. Each arc was divided into 12 equal divisions, and each day, reckoned from sunrise to sunset, therefore had 12 equal intervals, or “hours.” Because the length of the day varied according to the season, these hours likewise varied in length from season to season and even from day to day and were consequently known as seasonal hours. Aristarchus’s sundial was widely used for many centuries and, according to the Arab astronomer al-Battānī (c. 858–929 ce ), was still in use in Muslim countries during the 10th century. The Babylonian astronomer Berosus (flourished c. 290 bce ) invented a variant of this sundial by cutting away the part of the spherical surface south of the circular arc traced by the shadow tip on the longest day of the year.

The Greeks, with their geometrical prowess, developed and constructed sundials of considerable complexity. For instance, the Tower of the Winds in Athens, octagonal in shape and dating from about 100 bce , contains eight planar sundials facing various cardinal points of the compass. Moreover, numerous ancient Greek sundials feature conical surfaces cut into stone blocks in which the axis of the cone (which contains the tip of the gnomon) is parallel to the polar axis of Earth. In general, it appears that the Greeks constructed instruments with either vertical, horizontal, or inclined dials, indicating time in seasonal hours.

As with the Greeks, the Romans’ sundials employed seasonal hours. In 290 bce the first sundial, which had been captured from the Samnites, was set up in Rome the first sundial actually designed for the city was not built until almost 164 bce . In his great work De architectura, the Roman architect and engineer Vitruvius (flourished 1st century bce ) named many types of sundials, some of which were portable.

The medieval Muslims were especially interested in sundials, for these provided means for determining the proper times for prayer. Indeed, most Muslim sundials contain lines indicating these times, and on a few they are the only lines at all. Although the Muslims learned the basic principles of designing sundials from the Greeks, they increased the variety of designs available through the use of trigonometry. For example, they invented the now-ubiquitous sundial with the gnomon parallel to the polar axis of Earth. At the beginning of the 13th century ce , Abū al-Ḥasan al-Marrakushi wrote on the construction of hour lines on cylindrical, conical, and other types of sundials and is credited with introducing equal hours, at least for astronomical purposes.

With the advent of mechanical clocks in the early 14th century, sundials with equal hours gradually came into general use in Europe, and until the 19th century sundials were still used to reset mechanical clocks.

The Editors of Encyclopaedia Britannica This article was most recently revised and updated by Adam Augustyn, Managing Editor, Reference Content.


Spectrum Scientifics' Store Blog

On August 21st, 2017 a large portion of the Continental US will experience a total solar eclipse. Much of the rest of the continental US will experience at at least a partial eclipse: Philadelphia will have about 78% totality, NYC 75%, Washington DC 84%, Chicacgo 88%, Los Angeles 70%, Seattle 93%, etc.

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Solar Power – Active vs. Passive

Solar power is one of the great potential sources of energy we hope will replace polluting fossil fuels over the coming years. Specturm Scientifics has sold many teaching toys that use solar energy to demonstrate different effects, But did you know there were technically two types of Solar Energy generation? They are called active and passive solar energy and how they work is very different, despite coming from the same energy source (of course, pretty much everything has the sun as an energy source when you dig deep enough). Let’s discuss passive solar energy and the items we have that demonstrate it first:

PASSIVE SOLAR POWER:

If you’ve ever walked barefoot on a black asphalt street on a very hot, sunny day you are experiencing Passive Solar power in action. You might be fine on the brighter colored concrete sidewalk, but the black asphalt absorbs heat much better and can get uncomfortable to walk on barefoot. This is a very rudimentary demonstration of the sun’s power.

Another example is when you use a magnifying glass to concentrate light to start a campfire. Here the surface area of the magnifying glass is all concentrated into a single point that can get quite hot.

So how do we use this kind of solar power to make power that we can use? Well the present technique is Conctrated Solar Power. With this a large fields of parabolic or other curved mirrors are set up to track the sun and conctrate as much of the light as possible. The light is concntrated at some central point where a thermochemical reaction or heat engine is placed to convert the solar energy into electrcity.

While we lack the ability to ‘scale this down’ to a toy level, there are more than a few solar demonstration items that can be used to show the power of passive solar energy. The first being called (surprise) Solar Science

With this kit students will heat water using a passive solar heating system as well as as construct a miniature solar oven where they can cook and egg!

OK, so what if you want to step this up a bit? Well there is the Sun Spot Solar Oven

The Sun Spot is a much larger version of the solar oven you build in the Solar Science kit. Large reflective panels concentrate light at a wired point. Objects can be placed there (such as a hot dog). Temperatures at that point can easilt reach 350 degrees F.

Active Solar Energy

Active solar energy generation is probably more familiar to most of us, especially as solar panels become more ubiquitous. We use them to charge our smartphones, they power garbage compactors right outside our store.

Active solar power uses photvoltaic cells to convert sunlight into electricity. While this does have the advantage of direct electricity generation (no thermochenical or heat engines are needed at a focal point) they do have a problem with efficiency. The solar cells you can see on this trash compactor will each generate about 0.5V and 2W in direct sunlight, with 18 cells in total, you have about 9V and 36W. Presumably the power generated goes to a battery that can operate the compactor motor when it has sufficient power.

As for active solar items we have, where do we begin?

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So your Radiometer stopped working…

Radiometers, or as people who come into our store describe it: “That thing that spins in a bulb in sunlight” are a great little demonstration of solar energy.

There’s no assembly required, just remove the Radiometer from the box and put it under light. The vanes should start spinning right away.

But every now and then the Radiometer may stop working. You can put it in the brightest lights and yet nothing happens. What to do?

Well repairs to a stopped Radiometer are almost painfully simple, and yet sometimes they need to be explained carefully. This is especially true since Radiometers are made with thin glass and can be easily damaged.

First Repair: Two finger tap

Most of the time the reason a Radiometer stops working is because the vanes have come dislodged from the needle-like post. The vanes are supported from the post by an upturned cup of glass with a pointed bottom. To operate the needle point must fit in that bottom perfectly. This is not always as easy as it sounds as the vane’s momentum can cause the cup to slip off the needle. To get it working again you will need to reset the cup onto the needle with a tiny bit of external force.

Give your Radiometer a gently but firm tap with two fingers directly on the very top of the bulb. Do not tap too hard as the bulb is made of thin glass. If the cup has simply dislodged itself from the needle this gentle impact may cause it to reset itself. It is also possible that the vanes have gotten a little stuck from one reason or another and this impact can loosen them.

Second Repair: Upside Down time.

If tapping does not fix the problem it is time for the ‘full resetting’ of the cup on the pin.

Take the Radiometer and turn it directly upside-down. Then quickly flip it so it is right-side up again. When you invert the Radiometer the cup will come completely off the needle and when you revert it the cup should reset exactly on top of the needle. Place it back into the sun and see if this reseting worked. If it did not, try it again.

Still not Working? Troubleshooting tips:

So after trying these your Radiometer is still not working? Try these helpful hints to see if there is another issue:

1) Not enough light. Some Radiometers may operate by a glimpse of moonlight but most aren’t that sensitive. Try putting the Radiometer in direct sunlight or very close to a lamp and see if it works. Sometimes Radiometers just can’t get enough energy from a cloudy day! Keep in mind that the sensitivity is unmeasurable and there can be great variations of sensitivity even within a brand of Radiometer.

2) Unlevel surface. If there is anything under the base of the Radiometer, remove it and see if that helps. A Radiometer won’t work if it is tilted for any reason so check the shelf or windowsill you place it on is reasonably level. If not, try another sunny location.

3) It’s cold outside. If your windowsill is very drafty the Radiometer may have problems. See if you can find a warmer location.

4) It just won’t work! While not all Radiometers are created equal, it is very, very rare that one simply won’t operate. But it does happen. To make certain either place the Radiometer in direct bright sunlight or mere inches from a lamp bulb. If it won’t work even under those conditions (after you follow the tap and flip repairs above) it is likely a non-operating radiometer. Time to replace it.


How does the geometry for constructing a declining vertical sundial work? - Astronomy

"On the Construction of Sun-Dials." By J. Wigham Richardson.
From: The Book of Sun-dials . By Mrs. Alfred Gatty [aka Margaret Scott Gatty] (1809-1873). Enlarged and re-edited by H. K. F. Eden (1846-) and Eleanor Lloyd (fl.1900). London: George Bell & Sons, 1900. Fourth edition. pp. 487-499.

APPENDIX
ON THE
CONSTRUCTION OF SUN-DIALS

PAGE
Sir Norman Lockyer's description 489
Works on Dialling 489
Different kinds of dials 490
Astronomical principles 490
Geometrical terms 490
Horizontal dials 492
Wall dials facing south 493
Wall dials declining west 493
Wall dials declining east 494
Trigonometrical methods 495
Equation of Time 495
True mean time dials 496
Dial at Monaco 497
Size and materials 498
To orient a Sun-dial 498
Conclusion 498

Apparent Declination of the Sun and the Equation of Time at noon for each day in the year 1899 500-503

SUN-DIAL. AB axis of cylinder MN, PQ, two sun-dials, constructed at different angles to the plane of the horizon, showing how the imaginary cylinder determines the hour lines.

ON THE CONSTRUCTION OF SUN-DIALS

IN this short chapter I shall confine myself, as far as may be, to the mechanical construction of sun-dials. Those who wish to study the theory may refer to any encyclopædia, and almost all works on astronomy have something to say on the subject. The student who will take the trouble to master thus the whole subject will not fail to find it at once interesting and highly instructive. But by the courteous permission of Sir Norman Lockyer and Messrs. Macmillan I am permitted to reproduce the woodcut from the "Elementary Lessons in Astronomy," which shows at a glance the theory of a sun-dial, and Sir Norman's description is both clear and concise, viz.: "To understand the construction of a sun-dial, let us imagine a transparent cylinder, having an opaque axis, both axis and cylinder being placed parallel to the axis of the earth. If the cylinder be exposed to the sun, the shadow of the axis will be thrown on the side of the cylinder away form the sun and as the sun appears to travel round the earth's axis in 24 hours, it will equally appear to travel round the axis of the cylinder in 24 hours, and it will cast the shadow of the cylinder's axis on the side of the cylinder as long as it remains above the horizon. All we have to do, therefore, is to trace on the side of the cylinder 24 lines, 15 degrees apart (15 × 24 = 360), taking care to have one line on the north side. When the sun is south at noon, the shadow of the axis will be thrown on this line, which we may mark XII when the sun has advanced one hour to the west, the shadow will be thrown on the next line to the east, which we may mark I o'clock, and so on."

I can also recommend the following works, viz.:

"Clocks, Watches, and Bells," by Edmund Beckett Denison, published by John Weale, 1860. This work contains an account of the Dipleidoscope, invented by J. M. Bloxam, by which form of sun-dial Mr. Dent, the maker of the Westminster clock, used to rate his chronometer.

"Dialling," by William Leybourn, published by A. and J. Churchill, 1700. This is the most exhaustive work which I know on sun-dials of every form and shape.

"Treatise on Dialling," by Peter Nicholson, published in Newcastle-on-Tyne, 1833. This last is perhaps the clearest work of all on the construction of sun-dials, but it requires some patience to master the author's method of projection.

Sun-dials may be either fixed or portable. For the latter I would refer the student to the new edition of the "Encyclopædia Brittanica."

Fixed sun-dials may be in any plane. That is to say, the dial itself may be horizontal or sloping (usually called inclining), or vertical, as on the wall of a house, in which case they may face in any direction, and if not facing due south they are usually called declining, or the dial may be spherical or cylindrical and either convex or concave.

Again a dial may either be opaque, as is usually the case, or the shadow may be cast upon a window of ground glass. This latter type is called refractive, and it a singularly elegant form, having the advantage, very suited to our climate, of being observable from indoors, and the shadow of the gnomon will appear to go round the same way as the hands of a clock, instead of the reverse way, as must be the case in a wall sun-dial.

A further variety of sun-dials are those called reflective. In the numbers of "Aunt Judy's Magazine" for March and April, 1878, there is a charming account of how Sir Isaac Newton placed a mirror on the floor of his room which reflected the sun's rays on to the ceiling, upon which the hour lines were traced.

I propose to explain the way to construct two kinds of sun-dials only, viz., horizontal dials and wall dials, the latter facing either due south or facing towards the east or towards the west.

The gnomon, or stile of the sun-dial, must always be parallel to the polar axis of the earth. Otherwise expressed, the gnomon must always point to the pole star, or to speak more precisely, to the centre round which the pole star appears to revolve.

The simplest form of a sun-dial is a watch face marked to 24 hours, i.e., 12 and 12 hours, with a wire passed through the centre hole. Stretch the wire so as to point to the pole star and place the mark for XII or noon at the bottom, and you have a complete but inconvenient form of sun-dial inconvenient because the shadow would sometimes fall on the upper and sometimes on the lower face.

Another simple form is a concave half cylinder or half sphere, with a wire stretched down the middle, and on the surface where the cylinder (or sphere) has been cut in two, the hour lines will be at equal distances of 15 degrees apart. This form of dial will, however, evidently only show the time between 6 a.m. and 6 p.m.

In a horizontal dial, the angle of the gnomon will always be equal to the latitude of the place. In a vertical sun-dial facing due south, it will equal the complement of the latitude, or in other words it will equal 90 degrees minus the latitude, i.e. what is left of a right angle after deducting the angle of the latitude. The woodcut, Fig. I, will make this clear to anyone having the least knowledge of geometry.

Let E Ebe the equator of the earth.
C Pthe polar axis.
L the position of the sun-dial on the earth's surface.

The angle, E C L, will be the latitude of the place.

The level of the earth's surface, and of the horizontal dial at L will be the line, T P, which is a tangent to C L, the radius.

The line A L G will be the gnomon, parallel to C P, the polar axis.

It is evident that the angle G L P, the angle of the gnomon, is equal to the angle E C L, which is the latitude. Q.E.D.

Also, the line V L will represent a wall dial, and since the angle V L P is a right angle, the angle V L G will be the complement of the angle G L P.

But the angle G L P is equal to the latitude, therefore the angle of the gnomon in a wall dial is the complement of the latitude. Q.E.D.

How to set off a given angle. – The best way to set off an angle is to use a scale of chords, which is usually marked on the ivory ruler of a box of compasses. It is preferable, however, in each case, to make for yourself a scale of chords on a large scale at the side of the drawing paper and, inasmuch as only two or three angles for each dial are required, this involves no trouble worth mentioning.

Draw an arc of a circle with the radius 60, and then open the compasses to the required angle, as shown on the scale, and so mark off the angle required. This will be seen by referring to Fig. 2, which will also make clear other terms used in treatises on sun-dials.

From the centre, C, describe a circle with the radius of 60 on the scale of chords.

From the end of the diameter at D, measure off with the same radius, D X, and draw C X S.

Draw N X and D S perpendicular to the diameter d D.

Then X D is called the Chord of the Arc of 60 degrees, and the chord of 60 degrees is always equal to the radius.
D S is called the Tangent of 60 degrees.
C S is called the Secant of 60 degrees, and
N X is called the Sine of 60 degrees.

All these scales are marked on the ivory ruler in a box of instruments, and the seller of them will explain how to use them.

There is also another Scale, called the Scale of Half Tangents, but it would be more correct to call it the Scale of Tangents of half the angle.

On the left side of the centre in Fig. 2 the small italic letters indicate the chord, etc., for 30 degrees, thus:
xd is called the Chord of the Arc of 30 degrees.
ds is called the Tangent of 30 degrees.
nx is called the Sine of 30 degrees.
Cs is called the Secant of 30 degrees.

It is evident that the angle may be set off by either of the three Scales of Chords, of Tangents, or of Sines, but the Scale of Chords is the most convenient. All are more accurate than the brass semicircle sometimes called a protractor.

To construct a Horizontal Sun-dial for the latitude of 54 degrees. Fig. 3 – Draw a square or rectangle, as shown in Fig. 3, and near the centre draw a perpendicular line P S. On the left of this draw a parallel line, and make its distance from P S equal to the thickness of the gnomon. This double line is called the substile (or substyle). In all horizontal dials, and in all wall dials which face due south, the substile will be perpendicular, and the VI o'clock hour line will be horizontal or at right angles with the substile.

At any convenient point draw the horizontal line VI O VI, cutting the substile in O.

Draw O F, making the angle XII O F equal to the latitude of 54 degrees.

Draw XII F perpendicular to O F.

Extend the top line on each side as shown.

The angle of an hour is 15 degrees. Draw lines P 1, P 2, P 3, P 4, and P 5, so that the angles at P are each 15 degrees.

Then the true hour lines of the dial will be drawn from O to the points 1, 2, 3, 4, and 5. The VI o'clock line will be horizontal as already drawn, and the hours before VI a.m. and after VI p.m. will be continuations of the hour lines above the VI o'clock lines, taking care to allow for the thickness of the gnomon.

If the dial be divided into half and quarter hours, or into minutes, the angles must be correctly set off at P.

The gnomon will be a right-angled triangle, having one angle of 54 degrees at O, and placed on the substile O XII.

Fig. 4 – Another method is as follows, and for the sake of clearness in this and in the subsequent examples I assume the gnomon to have no thickness.

Describe a circle N E S W, and draw the lines N S perpendicular, and E W horizontal.

From S, set off by the Scale of Chords, the arc S a equal to the latitude or 54 degrees, and from W set off the arc W b also 54 degrees.

Join E a and E b, cutting N S in P and in Æ.

Describe the arc of a circle W Æ E. This may be done by trial or from the centre, C, making Æ C equal to the Secant of 36 degrees, for 36 is the complement of 54. That is to say, 36 + 54 = 90 degrees.

Divide the semicircle W N E into arcs of 15 degrees each at the points 7, 8, 9, 10, 11 and 1, 2, 3, 4, 5.

From O draw O 8, cutting the arc W Æ E in 81.

From P draw P 81 x, cutting the circle N E S W in x.

Draw VIII X O VIII, which will be the VIII o'clock hour-line.

The other hour-lines will be drawn by the same method.

The gnomon will be a right-angled triangle, having one angle of 54 degrees, and placed on the substile N O, with the 54 degree angle at O.

It is advisable to use both methods so as to correct any error.

To construct a Wall Sun-dial, facing due South, for the latitude of 54 degrees, the above methods may be followed, the only difference being that the complement of the latitude must be taken in every case in lieu of the latitude, that is (in our example) 36 in lieu of 54 degrees. (Figs. 3 and 4.)

Similarly the Secant of 54 degrees must be taken instead of the Secant of 36 degrees. (Fig. 4.)

If a horizontal and a wall diall be drawn, the one on the bottom and the other on the side of the inside of a box, the gnomon will be common to both, and the hour-lines of the respective dials will join where the bottom and the side of the box meet.

To construct a Wall Sun-dial for the latitude of 54 degrees, declining from the South towards the West 30 degrees. Fig 5. – Draw a horizontal line H T.

From any point A in this line draw a line A S, making the angle T A S equal to 30 degrees.

If the dial had been declining towards the East this line A S would be drawn to the left instead of to the right.

Draw A Z perpendicular to H T, and A C perpendicular to A S.

Make A C the XII o'clock or meridian line of a horizontal dial, and draw its hour-lines, C I, C II, C III, etc., and C XI, C X, C IX, etc., as explained ante.

Draw C P, cutting A S in P, and H T in B, and make the angle A C P equal to the latitude of 54 degrees.

Make A Z equal to A P. Then is Z the centre of the declining dial, and lines drawn from Z to I, II, III, etc., will be the true hour-lines of the declining dial.

To find the position of the substile, draw B G perpendicular to H T, and cutting A S in G.

Make A R equal to B G, and join Z R. Then will Z R be the position of the substile.

From R draw R Q perpendicular to Z R, and make R Q equal to A B.

The angle R Z Q will be the angle of the gnomon.

Fig. 6 – Another method is as follows, and let us in this case take a wall sun-dial declining 30 degrees from the south towards the East.

Upon C as a centre, with the radius C A, describe the quadrant A X Q, and with the same radius from A (which shall be the centre of the dial) describe the arc C L, and with the Scale of Chords make the arc C L equal to 36 degrees, the complement of the latitude, and draw the horizontal line R C Q.

Draw A L D, cutting R Q in D.

Cut off from Q to A the arc Q X equal to 30 degrees, the declination of the dial.

Join X C, prolonging the line down to S.

From the centre C with the radius C D describe the arc D S.

Draw S R perpendicular to R D.

Make C Y equal to S R, and join A Y.

Then will A Y be the position of the substile.

Through Y draw the long line G Y P M perpendicular to A Y.

Make Y G equal to C R, and join A G.

Then will the angle Y A G be the angle of the gnomon.

From Y draw Y g perpendicular to A G, and make Y O equal to Y g.

Then will O be the centre of the equinoctial circle. Draw one half of this circle with any radius from F to F, making F F parallel to G Y P M.

Draw O P 12, cutting the equinoctial circle in 12.

Then the true hour lines will be drawn from A to I., II., etc., and to XI., X., IX., etc.

Dialling Scales. – The simplest of all methods of dialling is by the use of dialling scales as explained in Ferguson's astronomy, by means of which the hours and minutes may be measured off as simply as inches from a foot rule. Such scales have not hitherto been obtainable, at least not of a size to be of any use but they are now made and sold, along with directions for using them, by Mr. E. C. Middleton of Stanmore Road, Birmingham, a practical diallist who also undertakes the setting out of dials in any plane.

Trigonometrical Calculations. – There are various other methods of delineating sun-dials, but I think that those which I have given are the simplest. It can never be amiss, however, to check the geometrical or projective methods by trigonometrical calculations which are fully explained and illustrated in Leybourn's work.

Equation of Time. – A sun-dial will only agree with the clock on four days in the year.

There are two reasons for the two not agreeing. One is that we divide the year into 365 days, whereas there are really about 365 ¼ days in the twelvemonth, the other is due to the revolution of the earth round the sun.

In the appended tables the number of minutes and seconds which must be added to or deducted from the sun-dial time (called apparent time), are given for every day in the year 1899.

The equation and declination are not quite the same every year. They move on annually about a quarter of a day until leap year comes and puts them back again.

It is always well to engrave such a table (more or less in extenso) on the sun-dial itself, unless it be graphically shown by a curve, as I shall now proceed to describe.

To construct a sun-dial which at noon on each day of the year shall show true mean time. Figs. 7, 8, and 9. – Let G W (Fig. 7) be the face in section of a wall sun-dial, and G P the gnomon thereof.

When the sun at noon (Fig. 7) on the 21st of June is high in the heavens, as at S1, it will cast the shadow of P on the dial at s1.

In the Spring or Autumn, when the sun is at S2, it will cast P's shadow at s2.

When the sun is on the horizon, as at S3, it will cast the shadow of P horizontally to s3.

In the tables will be found the sun's apparent declinations, which means the distance of the sun at noon for each day of the year north or south of the heaven's equator in 1899 (Fig. 9).

Let E be the earth, and Æ Æ the line of the equator extended to the heavens.

Through L draw a tangent H H, which will represent the horizon at the latitude L, say 54 degrees north.

Inasmuch as, on account of its great distance from the earth, a line drawn from the sun to L will be practically parallel to the line drawn from the sun to the centre of the earth, the sun when on the celestial equator will at L appear to be 36 degrees above the horizon. But 36 degrees is the co-latitude.

Wherefore the altitude of the sun at noon above the horizon can be ascertained for any day in the year by adding the co-latitude of the place the
497
[Full Image]

Fig. 8. north declination or subtracting the south declination respectively, as the case may be.

Fig. 7 – Construct a table of altitudes as above, and set off from s3 to w, by the scale of sines, or of tangents, the distances s1, s2, – s3, s1, – etc.

Or, set the angles off along the arc by the scale of chords.

Fig. 8. – Having now ascertained the vertical height of the shadow of P for every day of the year, transfer them to the face of the dial, and write the dates opposite each line.

From the table of the equation of time set off the number of minutes and seconds on the right or the left of the meridian according as they have to be added or subtracted, and you will have a series of points forming a curve like a figure of eight.

If the above is done with accuracy when the shadow of P falls on the curve, you will not only have the true mean time (subject only to the slight error for Leap year, which will average only about ¼ minute), but you will have the day of the month as well.

By the true mean time I mean the mean or clock time for the longitude of the place. If it is desired to show Greenwich clock time you must move the figure of eight to the right or to the left, as the case may be, or otherwise state on the sun-dial how many minutes the place is before or after Greenwich time. This latter will probably be considered the better plan.

Such a sun-dial as the above is of real value in country places. There is a fine example on the Guard House at the Palace of the Prince of Monaco, and there the end of the gnomon is flattened out to a disc with a hole in the centre having knife edges, and when I saw it the bright sun of Italy cast a clear spot of
498
[Full Image] light about the size of shilling on the lines of the curve, which, as well as the hour lines, were about ¾ inch broad. The sun-dial itself must have been 12 or 14 feet high.

On the size, the material, and the fabrication of sun-dials. – I sometimes think that when our architects are fain to put in a blank window to relieve part of the wall of a house, they might give us a sun-dial of large dimensions in place thereof. A sun-dial can hardly be too large, and it might very well cover the whole end of a barn, or even of a house.

If made of small size as is usual in England, the best material for horizontal dials is brass, and for wall dials slate, or marble, or granite.

In all cases the dial itself, or a full-size model, should be made first in the workshop.

To orient a sun-dial. – It will be useless to make a dial accurately, unless it be truly placed as regards the points of compass.

I recommend the following procedure in fixing a horizontal dial.

First consult a large Ordnance map (scale of an acre to a square inch), and place your dial approximately due north and south. Then level it by means of a spirit level.

Correct the line of the gnomon both by a compass and by the sun at noon, as rectified for the equation of time.

Then at the distance of some four or five yards north of the dial drive two long poles into the ground with a cross-piece at the top, like a tall Greek letter &Pi. The like, but not so tall, to the south of the dial.

Hang both north and south plummet lines, and during the day make the two lines and the gnomon in one line.

Ask any astronomical friend, or any ship's captain, at what hour the pole star crosses the meridian, at that hour get the two plummet lines in a line with the pole star 1 . Be careful in doing this to move the one as much to the right as the other to the left, for otherwise the gnomon will not be in the same line.

Having got the plummet lines true to the pole star, it will not be difficult in the morning to adjust the gnomon.

For a wall declining dial the plan will be similar, but it will be necessary for one pair of the poles to project above the eaves.

I shall be much gratified if this appendix to the Book of Sun-dials adds to its value. If any youthful reader will take the trouble to construct a sun-dial he will find that it will teach him more astronomy than a course of popular lectures could afford him, and he will almost surely be led to study further the mysteries of the great firmament on high, and in so doing he will every year of his life more and more marvel at the extent of the Divine power and wisdom, and be prepared hereafter, when we shall no longer see only as through a glass darkly, to truly enjoy that fuller knowledge which will be one of the joys which an infinite Love destines for us above.

On a tomb in Westminster Abbey you may read:

1 The pole star is on or very near the meridian when the star &epsilon Ursæ Majoris appears to be either directly above or directly below it. The star &epsilon Ursæ Majoris is the third star (counting from the tip) of the tail of the Great Bear.
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[Full Image] which suggested the following lines in a lady's album:

Our neighbors of a southern clime,
forgetting the true gauge of Time,
in their bright tongue have coined the phrase
(suggestive of luxurious ways)
of "dolce far niente."

But "carpe diem" is the rule,
which we, dear friend, were taught at school
each day more swiftly fleets away,
the gnomon's shadow will not stay,
"old Time is still a-flying!"

But oh! we need not fear his flight,
each day is long if spent aright,
that year is long where much is wrought,
'tis sloth alone we count as nought,
the cypher of existence.

The keen steel blade may wear away,
but rust more surely brings decay
ah! then of cankering sloth beware,
bright be thy steel with work and wear,
its temper true and trusty.

Then should our mortal foe appear
and from thy life cut half its years,
say not that shortened is that life,
say rather ended is the strife –
beyond the grave thy resting.

This chapter has been put on-line as part of the BUILD-A-BOOK Initiative at the
Celebration of Women Writers.
Initial text entry and proof-reading of this chapter were the work of volunteer
Elizabeth Pysar .


Using Ancient Chinese and Greek Astronomical Data: A Training Sequence in Elementary Astronomy for Pre-Service Primary School Teachers

A great amount of research has been carried out world-wide to promote history of science as a powerful science teaching tool. Because the ways of choosing and using historical elements depend on teachers’ or researchers’ educational purpose, any attempt to support a single model-to-use seems difficult and probably irrelevant. However, specific purposes may reflect specific and prescriptive terms for using historical materials. Our work aims to show up this aspect. It is an attempt to make elements of the history of astronomy involved in the elaboration of a training session for future primary school teachers. Here, ancients’ Greek and Chinese historical elements are chosen and organized according to specific educational and conceptual constraints that include the construction of the quasi-parallelism of solar rays reaching Earths’ surface, and the spontaneous modeling of the propagation of Sunlight leaning on divergent rays. This leads to an original teaching sequence were historical elements are mixed with non historical ones. This organization forms the support of a pre-service training session developed for future primary school teachers. This session aims to provide future teachers with elementary cosmological knowledge (parallelism of Sunrays, shape and size of the Earth, Sun-Earth distance…), to provide some reference marks of history of ancient cosmologies (spherical and flat Earth) resulting from two distinct contexts, and to approach some aspects associated with Nature of Science (NOS).

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Watch the video: Ηλιακά ρολόγια στο Αστεροσκοπείο Αθηνών (January 2023).