In my previous work I was trying to observe the east-west direction using the well known equal length shadow method described also on many pages in the internet. I then found that an accuracy of ±3' was easily achieved or even better, if a spherical gnomon had been used. In the present work the use of a spherical gnomon and it's accuracy in the shadow readings was studied in a more detailed way.
Equipment
The gnomon consisted of a 3447 mm high plumb line and a 40 mm diameter sphere at the top of it. The dimensions were so chosen that the angular diameter of the sphere, as seen from the center of the shadow, corresponded that of the sun. The arrangement used is shown in the Figures 1. and 8.
Figure 1.Observations
The shadow of the sphere was cast onto a millimeter paper from which it's place was photographed for a later analysis. On some observations the shadow's place was also marked with a template which was then photographed as well (fig. 2). Note that the shadow on the template in fig 2 doesn't coincide with the template's midpoint because the picture was taken only 4 to 7 seconds later than the template was set.
Figure 2.The observations were carried out at Turku (lat 60.°369 N) at noon on 26 july 2008. Alltogether 207 observations were made from which 72 were template observations. As an extra precaution the time of the observation was also recorded. The result of the templates xy-coordinate analysis is shown in the figure 3. In it the mean error of one observation is ±1.023 mm and the accuracy of the best fit curve through the points is about ±0.5 mm.
Templates x-coordinate was compared also against time at wich the mean error of one observation was ±0.933 mm (Fig. 4). Correspondingly, when the same analysis was made to the shadow observations, the mean errors were ±0.709 mm and ±0.735 mm (Fig. 5 and 6).
Figure 7.
