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Idea Seeds #18 – Time, the Sundial and the Pendulum (Part one)
“Your time is your most valuable asset; invest it where you get the best returns” (Apoorve Dubey)
Replicating Experimental Work
One of my father’s mentors told him that, after doing a bachelors degree, he decided to travel to the USA to start his post-graduate studies there at one of the swanky ivy-league universities. On arrival he and his fellow post-graduate students were very surprised, even disappointed, by the first introductory projects their supervisor set them. They had to replicate the experimental work done by three already dead but very famous scientists and establish for themselves the results reported by these scientists, All of them thought it was going to be a big waste of time but after doing the work they all agreed it was an excellent learning experience and a great return on the time they had invested in actually doing the work.
Building your own Evolutionary Understanding of Time
It is to be expected that the present generation know little about sundials so my father always tries to persuade them to invest some of their time to study and experiment with them. He believes it will produce the same sort of response reported by his mentor and give a big boost to their spatial ability. But, you ask, with all the information available today on the internet why not just look it up or view the many excellent You-Tube video clips on offer? Sure, you can and must do this but don’t miss out on building your own evolutionary understanding of time and getting it properly stored in your memory and don’t forget to make the necessary slips for your filing system. It is a fantastic topic to hone your skills on using the approaches introduced to you in previous articles, in particular the systems thinking approach. To really fully understand the workings of the three most common sundials (horizontal, vertical, and equatorial) you also need to know a lot more about the rotation of the earth on its axis and its path and speed while orbiting the sun. When and where, for example, are measurements started from when everything is moving and nothing is fixed?
Time Over Time
You won’t find ‘time’ lurking around anywhere in the real world. It is a man made construct that allows us to sequence and compare when events took or take place. Clearly the day was an obvious first choice for a reliable time period for the ancients to adopt. The year followed and was defined as the number of days taken for the earth to complete one orbit round the sun. The year was divided into months and, with their allotted days, marked on a calendar. The day was divided into hours, minutes and seconds and kept track of by using sundials, then clocks and watches. Sounds simple enough but there are a number of problems; the speed of rotation of the earth on its own axis, as well as its speed while orbiting round the sun, are not perfectly uniform rendering them unsatisfactory for highly accurate time measurements. It is also important that a calendar accurately reflect seasons recurring on the same dates for successive years but this is complicated by the fact that the earth with us on it takes three hundred a sixty five and about a quarter day to travel round the sun on its elliptical path. To correct for this, every fourth year is made a ‘leap year’ when an extra day is added in February. Other corrections are made by highly specialised astronomers who make sure that the ‘Co-ordinated Universal Time’ that now keeps us all in step is kept correct by skipping certain ‘leap years’ or adding a ‘leap second’ if and when required. But to get to this stage it has taken more than two thousand years to develop the system we now use for keeping track of time.
The 12/12 and 24 Hour Day
The Egyptians are credited as being the first to break the day down into two smaller parts, day and night, each having 12 hours. They used a sundial to measure time during the day and water clocks to measure time at night. The Greek astronomer Hipparchus round 150 BC proposed that it was more sensible to treat day and night as a whole and divide it up into 24 hours of equal length.
And So Came 60
The Sumerians and then the Babylonians made calculations using 60 as a base. They chose this number, it is thought, because it can be broken down into a wide range of fractions. There were no calculators then so everything had to be based on whole numbers and fractions that are also based on whole numbers. Map making was being refined and the concept of latitude and longitude had been proposed. Expanding on Hipparchus’s work, the famous astronomer, Claudius Ptolemy, (139 – 161) divided each degree of latitude and longitude into 60 equal parts. These parts were further subdivided into 60 smaller parts. He called the first division “partes minutae primae”, or first ‘tiny’ where ‘tiny’ means ‘minute’. Oh that English language using the same spelling again to mean two completely different things. The subdivided smaller parts he called “partes minutae secundae”, or ‘second tiny’, which has simply been shortened to ‘second’. In map making one minute of arc means one sixtieth of a one degree angle and one second of arc means one sixtieth of one minute of arc.
Do not Confuse Time with Angles
The division of time into 60 minutes and 60 seconds followed the same route but do not confuse time with angles, they are not the same. The ‘second of time’ has been chosen to be one of the six ‘fundamental units of the SI measurement system’. All other measurements in the SI system are derived from these six fundamental units which is why it is so important to understand them. The six are: ‘Length (metre - m); Mass (kilogram - kg); Time (second – s); Electric Current (ampere – A); Thermodynamic Temperature (Kelvin – K); Luminous Intensity (candela – cd)’. To date only Mass has been dealt with in these articles, now it’s time for the ‘second’.
Measuring a Second
The first accurately measurable means of producing a second came with the advent of the pendulum. A ‘second’s pendulum’ 0.994 metres long at sea-level takes one-second to swing from one side to the other. This gave birth to the grandfather clock that provided accurate timekeeping for more than 250 years, until the introduction of the quartz clock in 1927 and then the atomic clock in 1967. (Please note, ‘the period of a pendulum’ is defined as the time it takes for the pendulum to go through a full cycle; the time to swing from one side to the other and back. This means the period for the pendulum in a Grandfather clock is 2 seconds. Be careful when reading about pendulums or doing calculations to remember this.)
Making a Pendulum
Find a reel of cotton, unwind a length of about 1,5 metres off the reel and jamb the cotton in the slit on the edge of the reel to stop it from unrolling any further. Put a drawing pin into the middle of the top of a door frame and fasten the end of the cotton to it. You now have a pendulum to play with. Find the period with that length of cotton and then shorten it and check the period again. Keep doing this until you get a period of 2 seconds. Measure the distance from the pin to the centre of the cotton reel. If you have done the experiment properly it it will be very close to a metre. Mission accomplished! Much more about the pendulum in future articles, but think on this in the meantime; a stationary pendulum acts in the same way as a plumb-bob used for erecting vertical lines. These vertical lines are actually ‘radial lines that point directly at the centre of the earth and therefore not parallel to each other!‘
The Equation of Time
But in olden times, how did they reset stopped clocks and watches to the correct time? They used a sundial. Sundials can still be seen in parks, gardens and on old buildings all over the world. A standard sundial tells the time for the longitude of the place where it is set up. When the sun is overhead at midday (noon) a properly aligned sundial will show 12h00. The ‘solar day of 24 hours’ can be taken as the time it takes the earth to rotate from one noon to the next noon but, as explained earlier, the rotations of the earth on its own axis and its orbital speed round the sun are not constant so small corrections, (the adding or subtracting of up to sixteen minutes) have to be made if very accurate time keeping is needed. Some of the better sundials have the corrections for various times of the year engraved on them. These corrections are usually referred to as ‘The equation of time’. This then gives rise to two types of solar time, ‘apparent solar time’ (sundial time) which, after applying the corrections, gives ‘mean solar time’ (clock time).
The Greenwich Meridian
But there is another problem. With 360 degrees in a circle and 24 hours in the day it means the sun moves through 15 degrees in every hour. When it is noon and the sun is directly above you on your line of longitude, 15 degrees to the East the time will be 13h00 and 15 degrees to the West it will be 11h00. This resulted in towns and cities across a country each using their own time based on the sun. This became a real problem, after railway lines were built that linked these towns together. How were train operators to schedule the arrival and departure times in particular in North America where when it is noon, 12h00, in New York it is 09h00 in San Francisco? After a number of train crashes resulting from errors due to time differences, a conference was held in Washington in 1884 where it was agreed that the Longitude at Greenwich in London be the Prime Meridian from which the world’s time would be calculated. Time Zones of 15 degrees were to be established where the time would be the same from 7,5 degrees to the East and 7,5 degrees to the West starting from the Prime Meridian that passes through Greenwich in London. Countries do however modify these zones to suit their own needs often using their borders to keep the time across the country the same. Make sure you understand what this means and how it works in practice. In particular make sure you know where the meridian is situated where a new day starts and finishes.
Measurement When Nothing is Fixed
Next, as explained earlier, you also need to know a lot more about the rotation of the earth on its axis and its path and speed while orbiting the sun and where measurements are started from when everything is moving and nothing is fixed? To get a clear picture of this in your brain the use of a globe of the earth on its inclined axis is essential. (If you haven’t got a globe make a simple model of one by using an old tennis ball and fashioning a wire coat-hanger into a stand and frame to mount it in.)
Some things need to be kept the same so that explanations remain coherent. The first is the orientation of the globe shown in the adjacent picture. The inclination of the axis must be kept exactly as it is in the picture.
Spins and Orbits
You can now model the earth orbiting the sun by, for example, placing the globe on a table and moving it round an imagined sun in the centre of the table as shown in the adjacent picture of the seasons for the northern hemisphere. You will see in this picture that the axis of the earth points in the same direction at all times while it travels in a counter clockwise direction round the sun in a plane called the plane-of-the-ecliptic. The earth also spins on its own axis in a counter clockwise direction when viewed looking down on the North Pole. The reason why most explanations are still referenced to the Northern Hemisphere is because the early astronomers all lived there. I am going to continue for now to do the same.
The Vernal Equinox
There are a number of very important things you need to understand from the four positions of the earth shown in the picture. ‘The starting point for measurements is the Vernal Equinox’ (Eqi = equal; Nox = night) when the night has the same length of time as the day. For now accept that this occurs during March at some time between the 19th and 21st. Also accept for now that the Summer Solstice occurs in June, the Autumnal Equinox in September and the Winter Solstice in December.
The Planes Intersect
The next important thing to understand requires a bit of geometry. You have to imagine where a line drawn from the centre-of-the-sun to the centre-of-the-earth enters the earth’s surface. Imagine where the dot created by the beam of a laser pointer set up in the middle of the table at the same height as the centre of the earth and pointing at it would shine. At the Vernal Equinox that would be exactly where the plane-of-the-ecliptic intersects with the plane-of-the-equator. If you now rotate the earth on its axis the laser dot will stay fixed at this point of intersection and shining on the equator. The same will happen for the Autumnal Equinox.
June and December Solstices
Now consider the June and December Solstices as referenced to the Northern-Hemisphere. The line from the centre-of-the-sun to the centre-of-the-earth hits the line of latitude 23,5 degrees North, the Tropic of Cancer, in June and 23,5 degrees South, the Tropic of Capricorn in December. If you again point your laser at the centre of the earth and turn the earth on its axis the dot will stay fixed on the Tropic of Cancer as the earth turns in summer and the Tropic of Cancer in winter. If you used a plumb-bob and dug a vertical well anywhere on the Tropic of Cancer then the sun at the June Solstice at noon at that position would be seen reflecting from the water at the bottom of the well. This occurrence was used by the Egyptians to calculate the diameter of the earth by measuring the height of the lighthouse in Alexandria, the length of the shadow cast by it at noon and the distance from the well to the lighthouse that was some distance due North of it. (The same would occur in a well on the Tropic of Capricorn in the South during the December Solstice.) Make a quick sketch to see if you can work out how the Egyptians used this information to work out the diameter of the earth.
Start Making Sketches
That is more than enough information to digest for the moment. Start making sketches, in particular sketches like the picture of the Seasons and make sure to label them properly. These are the basic building blocks you need to fully understand if you want to better your understanding of the workings of our universe. More on actual sundials in Part Two.