Context : The sharp temperature and density gradients in the coronal transition region are a challenge for models and observations .

Aims : We set out to get the average electron density \langle n _ { \textrm { e } } \rangle in the region emitting the S vi lines .
We use two different techniques which allow to derive linearly-weighted ( opacity method ) and quadratically-weighted ( Emission Measure method ) electron density along the line-of-sight , in order to estimate a filling factor or to derive a thickness of the layer at the formation temperature of the lines .

Methods : We analyze SoHO/SUMER spectroscopic observations of the S vi lines , using the center-to-limb variations of radiance , the center-to-limb ratios of radiance and line width , and the radiance ratio of the 93.3 – 94.4 \ > \mathrm { nm } doublet to derive the opacity .
We also use the Emission Measure derived from radiance at disk center .

Results : We get an opacity \tau _ { 0 } at S vi 93.3 nm line center of the order of 0.05 .
The resulting average electron density \langle n _ { \textrm { e } } \rangle , under simple assumptions concerning the emitting layer , is 2.4 \cdot 10 ^ { 16 } \ > \mathrm { m ^ { -3 } } at T = 2 \cdot 10 ^ { 5 } \ > \mathrm { K } .
This value is higher than ( and incompatible with ) the values obtained from radiance measurements ( 2 \cdot 10 ^ { 15 } \ > \mathrm { m ^ { -3 } } ) .
The last value leads to an electron pressure of 10 ^ { -2 } \ > \mathrm { Pa } .
Conversely , taking a classical value for the density leads to a too high value of the thickness of the emitting layer .

Conclusions : The pressure derived from the Emission Measure method compares well with previous determinations .
It implies a low opacity of 5 10 ^ { -3 } to 10 ^ { -2 } .
The fact that a direct derivation leads to a much higher opacity remains unexplained , despite tentative modeling of observational biases .
Further measurements , in S vi and other lines emitted at a similar temperature , need to be done , and more realistic models of the transition region need to be used .