PRECISION VIEWING / RECORDING SYSTEMS
A simple shadow system with daily markings on a flat surface is quite adequate for the more widely spaced markings that will occur up until a week or so before the solstice.
However, since the sun's movement on the days immediately surrounding the solstice is very small it is desirable to devise a method to be able to mark the position of only the leading or trailing edge of the sun, with an accuracy of only 1/60th of it's angular diameter, during those final days. Thus, a dual marking system would include a simple system for the approach to the solstice period and a precision marking system for the last few days when the marks would overlap.
As previously stated, this article does not include the use of expensive modern equipment such as a sextant and has observed that an accurate astrolabe would have to be sufficiently large that it would be unwieldy.
FOCUSING AN IMAGE OF THE SUN
While it is possible to devise a system for focusing an image of the sun, which would move with the movement of the sun, the use of a simple magnifying lens has several problems, including the need for a rigid fixed mounting point during the observations and the fact that it needs very exact perpendicular positioning at its focal length distance from the surface in order to give a good focus. This approach is also not recommended.
REFLECTION OF THE SUN
These are the easiest methods, but require considerable care and/or the use of light filters due to the brightness of the mid-day sun.
Click here to view an article about the hazards of viewing the sun, either directly or by a reflection from a mirror.
While you can purchase light filters there are several ways to make your own. You can also reduce the amount of light reaching the eye by use of screens or limiting the size of the mirror to a narrow slit or a pin point. However, although these methods may make the sun's image appear dim, they do not reduce the ultra-violet component and should not be used alone without an adequate filter.
1. Use a uniform thick dark glass, such as welders glass, to cover your viewing eye. (Placing the glass just in front of the mirror does not work since the dark glass will also act as a mirror.)
2. Use the thin dark plastic recording surface from the inside of an old 3 1/2 inch computer floppy disk. Carefully open the disk (destroying it in the process). Remove the circular liner and affix it to sunglasses so that it covers your viewing eye. (Do not let it extend beyond your head so that it reflects sunlight back into your eye.)
3. Close or cover your other eye.
Use a thin flat very narrow sliver of a mirror, placed parallel to the shadow line on the marking surface so that a reflection of the leading edge of the sun is visible.
DO NOT LOOK AT THE REFLECTION OF THE FULL SUN!
Note the emphasis on THIN, FLAT and VERY NARROW SLIVER. A thick mirror will introduce a parallax error and a mirror that is not flat against the marking surface will distort the apparent position of the sun on the marking surface. (A common steel kitchen spatula will do if it is flexible enough to be pushed completely flat on the surface at the end being used for the reflection. Covering all but a very narrow portion of the end of the spatula with dull black tape will create the very narrow sliver of a mirror which will prevent an accidental viewing of the full image of the sun. )
Further, note that the mirror is not likely to be perpendicular to the rays of the sun, and that the angle of reflection from the mirror to your eye will be equal to the angle of incidence of the rays of the sun - both taken with respect to the surface of the mirror. Thus, as you move your eye the image of the sun will move. To protect your eye from a view of the full sun you should start with your eye only viewing the shadow. Then slowly move your eye down until you can just barely see the lower edge of the sun and mark that position.
(DO NOT USE THIS METHOD UNLESS YOU ARE USING A PROTECTIVE LIGHT FILTER!)
HINT: In order to be able to more easily make your mark on the marking surface without having to imagine a horizontal line to the edge of the mirror, it will be helpful to gradually move the mirror back so that it's edge is just at the place where you are observing the sun's image.
TECHNIQUE (Done at the same time every day.)
1. Place the filter material so that it covers one eye.
2. Place the narrow reflecting surface so that it is parallel to and just barely crosses the dark edge of the shadow.
(If you have the mirrored surface vertical you will view a vertical slice of the sun and will not be able to know whether or not you are viewing the exact middle to obtain the full diameter - and the true leading edge.)
3. Move your head so that your eye is behind the shadow.
4. Then, by carefully moving your eye from above the shadow line downwards the sun's image will start to come into view.
5. Then slowly move your eye up so that the leading or following edge is just aligned with the reflected shadow. You may also need to move slightly to the left or right so that the center of the image of the sun is centered on your vertical sliver of a mirror.
6. Then slowly back the mirror surface towards the shadow so the image of the sun is close to its edge so that you can make a dot with a fine point marker on your marker surface.
7. Then withdraw the mirror, remove the filter from your eye, and draw a fine horizontal line at the level of the dot that you made.
8. Enter the date to keep a record of when the mark was made.
HINT: On days close to the solstice these marks, and dates, will overlap. If so, do not "overwrite" the mark but make a new mark and date alongside so that there will be no confusion.
This method both diminishes the light from the sun even further by using a poor reflector, making the viewing less risky, and provides a method of recording observations that are so close that daily marks would overlap.
There are probably many ingenious ways to do this. Here is the author's favorite.
Tape or otherwise attach a 4 inch strip of ordinary office staples on a flat board. These are standardly available with about 50 staples per inch. The surface of each of the staples should be somewhat shiny so that each staple acts as a miniature mirror, but the total effect is far from being a good reflector.
This is an overall picture of the staples mounted to a board with the board firmly fixed to a drain pipe on a south facing wall. (Ignore the odd stripes at the top of the staple column. They are an artifact of taking a picture of straight lines with a digital camera at a small angle. The view of the staples at the bottom is more of a true picture.)
About a week before the predicted day of the solstice firmly mount this board at the dark edge of the shadow, with the lower end just barely extending into the lighted area. (It must not be moved during the period of observations.) It should also be located along the mid-day sun dial vertical line if you are using that method to make your observations at the exact same time each day.
The picture on the left is a close-up on a bright but cloudy day, showing good detail of the individual staples acting as separate tiny horizontal mirrors.
The one on the right was taken much closer up and at an upward angle to take advantage of the mirror effect of each individual staple. Note that there is still a small width to this shadow area due to the diffraction of the sun light around the shadow object. It is immaterial whether you take your observation at the apparently full light or full dark position, just be consistent so as to provide accurate information on the daily movement. (The light on the lower portion shows up much brighter than it looks to the naked eye due to the adjustment of the camera to be able to view the darker shadowed area. You can minimize this light by adjusting the position of the staples so that only a very few extend below the shadow area at the start of the week before the solstice.)
Then, instead of marking the board, place the point of a pin at the leading edge of the sun and by moving the tip downwards across each staple count the ticks until you get to the bottom of the strip.
Then record on a separate paper the number of ticks counted to the bottom. This will change every day, giving you the needed relative position of the sun to an accuracy of 1/50th of an inch. Remember, you do not need the actual position of the shadow. You only need the relative position to determine whether it is going up, standing still, or going down again on subsequent days.
If the length from your shadow object to your staple board is 10 feet the shadow width, which is a projection of the angular width of the sun, will be about one inch. Thus, an accuracy of 1/50th inch is all that is needed. If the length of your shadow object to the staple board is less you can tilt the staple board away from being perpendicular to the sun, thereby stretching out the shadow width by the amount of tilt. A backwards tilt of 45 degrees would increase your shadow width by a factor of 1.4, allowing a shorter shadow object distance. However, reading the shadow line will be more difficult and irregularities in the surface height of individual staples would cause errors.
The winter solstice will occur on the day when the tick count is the largest, i.e. when the edge of the shadow is the highest.