Lol. What capacitor should be use with a 400w mercury vapor? can I use the 10uf or can I run it without the capacitor?
In which circuit/ballast (you didn't let us know where are you from, so I do not know if you are a 120V or 230V guy...)?
If it is just a power factor correction (so plain parallel to mains input), you do not need any for the lamp to work. For high power factor and 230V/50Hz and a typical series reactor ballast it is around 39uF (exact calculation gave 41uF, but usually a bit less is used to make sure the circuit is never capacitive).
For 120V/60Hz HX ballast:
The capacitance depends on the voltage tap, where it is connected and the exact ballast OCV:
C = sqrt((Ilamp*OCV)^2 - (Plamp+Plosses)^2)/(Vtap^2 * 2 * Pi() * Freq)
Or you may base your calculation on measurement of the ballast input current:
C = sqrt((Iuncompensated * 120)^2 - (Plamp+Plosses)^2)/(Vtap^2 * 2 * Pi() * Freq)
So for an example of OCV=220V, Vtap=240V (the voltage tap, where the capacitor is connected), 10% losses, 3.5A lamp current it will be about 29uF.
The most uncertain are the CWA ballasts, where the capacitor is the main ballasting component (in series with the lamp): There you have no other option then find out, what capacitance the ballast was designed for, so find the makers instructions. There are way too many free choice parameters the CWA ballast designer has, so it may really differ a lot among different ballast models, all for the same lamp.