Conclusions
There is probably a structural difference between the inner and outer portions of the Eskimo Nebula, and certainly an ionization difference, probably caused by temperature difference.
There is approximately the same relative prevalence of SII and OIII in the inner vs. outer parts of the nebula. Both are more prevalent in the outer part, SII being about 70% as prevalent in the inner as the outer and OIII 63% as prevalent in the inner as the outer. HeII is also less prevalent in the inner part of the nebula, being about 80% as prevalent. This prevalence, though, may not necessarily indicate a prevalence of the elements but instead indicates prevalence of certain ionization energies.
The distribution of these elements may be consistent with stellar evolution theory, which posits that planetary nebulae are formed from dying low-mass stars as they pulsate. They expand and eject an outer layer of material, then collapse, and expand again, ejecting more material. This process continues, but each time the star expands, it spews heavier elements formed as the star's fusion process achieves more advanced stages. In the first layer of gas expelled, most of it will be unfused hydrogen, and there will also be a lot of helium, which is the first product of stellar fusion. As the star gets older and fusion proceeds further, oxygen, nitrogen, carbon, sulfur, and sodium will be produced. More of the heavier elements will be produced and sprayed from the star in later pulses. However, it is possible that we see more oxygen in the outer band because the temperature is too great to allow OIII emission in the inner part of the nebula. Helium is expected to be more prevalent in the outer parts, since it is the first (outermost) product of stellar fusion.
It may also make sense to conclude that the Eskimo Nebula is a fairly old planetary nebula. Planetary nebulae will spray elements up to 1.5 light years away before they cease to be visible. Since the outermost visible layer of the nebula contains substantial amounts of oxygen and sulfur, the star is probably in the later stages of its evolution. Elements are produced in order of increasing mass up until Iron, which has the most stable nucleus, but Iron is not produced in low-mass stars that produce planetary nebulae.
Sources of Error:
The sky was brighter later in the night, as some slight cloud cover moved in. This may have caused problems with some of the measurements, particularly of the elements providing smaller counts.