Hi Luke,
Here is one idea
Although not a measurement of the sun itself, you could use the sun as a light source to measure the absorption spectrum of the Earth's atmosphere. Use the lowest resolution grating to give maximum wavelength range (most of the interesting atmospheric absorption lines are in the far red/IR) and record the sun at different heights above the horizon. By dividing one by the other you get the absorption due to the extra atmosphere at the lower elevation. Simple geometry will give you this as a ratio to the vertical thickness of the atmosphere.
What causes the absorption lines ? Is the intensity of the lines constant or do some vary in intensity from day to day eg with humidity. What causes the general shape of the absorption spectrum ? Does this change with time?
Here are some potentially useful references
http://www.astrosurf.com/buil/extinction/calcul.htm
http://www.astrosurf.com/buil/atmosp...ansmission.htm
(In French but google translates well enough)
Cheers
Robin