  Electron density diagnostics based on the triplets of Helium-like CV, NVI,
and OVII are applied to the X-ray spectra of Capella and Procyon measured with
the Low Energy Transmission Grating Spectrometer (LETGS) on board the Chandra
X-ray Observatory. New theoretical models for the calculation of the line
ratios between the forbidden (f), intercombination (i), and the resonance (r)
lines of the helium-like triplets are used. The derived densities are quite
typical of densities found in the solar active regions, and also pressures and
temperatures in Procyon's and Capella's corona at a level of T=10^6K are quite
similar. We find no evidence for densities as high as measured in solar flares.
Comparison of our Capella and Procyon measurements with the Sun shows little
difference in the physical properties of the layers producing the CV, NVI, and
OVII emission. Assuming the X-ray emitting plasma to be confined in magnetic
loops, we obtain typical loop length scales of L_Capella > 8 L_Procyon from the
loop scaling laws, implying that the magnetic structures in Procyon and Capella
are quite different. The total mean surface fluxes emitted in the helium- and
hydrogen-like ions are quite similar for Capella and Procyon, but exceed
typical solar values by one order of magnitude. We thus conclude that Procyon's
and Capella's coronal filling factors are larger than corresponding solar
values.
