At this point, you have plotted the positions of Mercury and the Sun on a sky map, then measured the latitudes and longitudes of Mercury, and calculated the elongation of Mercury. If you have made no errors, you COULD go on to the final parts of the project without any further work. But of course there may be many errors, either large or small, in the data that you have tabulated, because of plotting errors, measurement errors, or arithmetic errors. To make sure that any such errors are negligible, we need to graph the latitudes and elongations, so that we can see any non-negligible errors and remove them.
Part 2b: Plotting the Latitudes
To plot the latitudes, construct a graph of latitude against date. You can use any scale you want, but I would recommend using two 10th-inch squares per degree of latitude, so that any errors in latitude measurements will look as large as on the original sky map, and at least two 10th-inch squares per 4-day interval, so that the date measurements in parts 4b and 5b (shown below) can be done as accurately as possible.
Plot the latitude for each date. If all of the values are accurately measured (and accurately re-plotted!) then you should be able to draw a very smooth curve exactly through all of the plotted values. Thus you can see erroneous data by looking for dots which do NOT fit exactly on a smooth curve. In the figures you can see that the latitudes should increase smoothly to the North, then to the South. At the top and bottom of the curve, bad data will show up by falling above or below a smooth curve; in the rising and falling portions of the curve, extremely bad data may appear to fall above or below a smooth curve, but some bad data may be made to fall on the curve by bending it very slightly. In these cases, you need to make sure that the separation of the dots increases or decreases smoothly.
(Left: Good Data; a smooth curve fits dots with gradually varying separations)
(Middle: Poor Data; no smooth curve can be fit through the dots)
(Right: Poor Data; a smooth curve can be forced, but only with erratic separations)
Above, an example of how to plot the latitudes, at 5 degrees/inch vertically and 20 days/inch horizontally
Part 2c: Plotting the Elongations
The elongations should be plotted in the same way as the latitudes. The only difference is that latitudes will only vary by about 5 degrees North or South, since Mercury is always close to the Ecliptic; while elongations may vary by over 25 degrees East or West, so that you can't use quite as large a scale for the degrees of elongation; you'll probably be limited to two 10th-inch squares per degree, whereas you COULD use a larger scale for latitudes.
After plotting each of the two graphs, examine it carefully to make sure that all the plotted positions look reasonably good. Errors of only a tenth of a degree or so may be ignored, but any larger errors should be rooted out by checking all of the work that you did to get the value that you plotted: make sure that the positions of Mercury AND the Sun that are near the questionable values are correctly plotted on the original sky map, check that you have measured the latitudes and/or longitudes correctly, and check the arithmetic of finding the elongation.
When you are done, your graphs of latitude and elongation against time should look nice and smooth; and when they do, you can be confident that you now have good values for the last step of the project.
Next: Part 3a