We calculate filling factors ( \varepsilon ) and ionized masses ( M _ { i } ) for a total of 84 galactic and extragalactic planetary nebulae ( PNe ) at known distances .
To do these calculations , from the equation of energy propagation within a gaseous nebula , we have chosen forbidden line electron densities , observed angular diameters , and H { \beta } fluxes , from the most recent measurements available in the literature .
Statistical analysis on the distributions of { \varepsilon } and { M _ { i } } show that ( 1 ) the ranges of values of these parameters is wider than what was previously found ; ( 2 ) the mean value of the filling factor is between 0.3 and 0.4 , for the different sets ; ( 3 ) the mean value of the ionized mass is between 0.1 and 0.25 M _ { \odot } , 0.2 M _ { \odot } representing an upper limit to the ionized mass for galactic disk PNe , and a typical value for galactic bulge and extragalactic PNe ; ( 4 ) a clear correlation between \varepsilon and the dimensions of the PNe was not found when distance-independent sets of PNe were used ; ( 5 ) for extragalactic PNe , where distance errors are not a factor , the filling factors and the ionized masses anticorrelate tightly with the electron densities .
The results indicate that the modified Shklowsky distance method is correct .