what capacitor would i use for a 26 watt sox-e lamp,ballast,etc.it has an SX26 ignitor, aBSX26L32 ballast, and 26 watt sox-e lamp.     

What I have seen up to now:
1) Either the capacitor is essential for the ballast operation (form the ballasting impedance, component in a resonant circuit, starting voltage booster,...), then the specification is listed on the ballast label (capacitance, it's tolerance, required voltage rating and eventually safety class).
In this case the capacitor specification is tied to the exact ballast design (so model), so with different ballast model even for exactly the same lamp the capacitor may differ.

2) Or it is  not necessary for the ballast functionality and it's purpose is only to correct the power factor. Then the ballast should work even without this capacitor.

For SOX-E 26W , you will need an across-the-mains capacitor of about 6 ... 8uF/250VAC. It is not needed to light up a SOX-26W lamp.

Ballast example: BSX26L81 or BSX26L82 with SX26 igniter.

would a 7 UF capacitor work?

would a 7 UF capacitor work?

If it is just parallel to the mains input, you do not need any capacitor for the ballast to work...
Only if you really need high power factor (I do not exactly see why, unless we are talking about 10's of fixtures on a single branch) and taking the range from LampWizard, it mean the 7uF will work well.

Sorry for bumping an old thread, this thread probably has all the information I needed when it comes to using a capacitor.

I have a few questions though, does the no-capacitor-is-needed rule in this thread applicable to other types of non-SOX lighting? like running a single or two 150w mercury, HPS, or metal halide lamps I don't actually need to use a capacitor?

If the capacitor is purely for power factor correction, then no it isn't electrically necessary for the operation of the circuit. But I'm a perfectionist (probably due to my ASD) so I always fit one.

Ballasts such as the North American CWA types do need one though, in series with the lamp. Other types may well do as well; it's always best to follow the manufacturer's instructions I think, after all they designed the ballasts so know what is required.

Sorry for bumping an old thread, this thread probably has all the information I needed when it comes to using a capacitor.

I have a few questions though, does the no-capacitor-is-needed rule in this thread applicable to other types of non-SOX lighting? like running a single or two 150w mercury, HPS, or metal halide lamps I don't actually need to use a capacitor?

It does, but there is one caveat: The semiparallel ignitors (like SN57; for HPS/MH) have the input in the high current path for the high frequency high current primary of the ignitor. These do need this capacitor and it needs to be wired with very short loop (capacitor-ballast-ignitor-capacitor), otherwise the ignitor looses its ability to deliver sufficient ignition pulses. But the capacitor does not have to be exactly the one specified, anything above about 1uF will do the job of high frequency bypass for the ignitor to work correctly (to solve the problem with specified capacitor being too big to fit,...)
Of course, all above valid for European series choke style circuits.

In the US, the ignitors have the primary circuit loop just between the ballast and ignitor, so do not need that high frequency bypass on the input.
So if the capacitor is really directly across the mains input, you don't need it.
But if it is elsewhere, (even on an input voltage tap that is not used) the specified value capacitor is needed.

So if the capacitor is really directly across the mains input, you don't need it.

You don't need it for the circuit to function, I agree, but my innate sense of correctness says if the designer/manufacturer specifies it, then it goes in.