The continuum in the spectrum is the light with wavelengths between the lines.  Polarization in the continuum is due to Rayleigh scattering by neutral hydrogen atoms (H I) and Thomson scattering by free electrons.   Most of the opacity in the sun is due to the hydride ion, H which however does not alter polarization. In 1950 Subrahmanyan Chandrasekhar came up with a solution for the degree of polarization due to scattering, and predicted 11.7% polarization at the limb of the Sun.  But nowhere near this level is observed. What happens at the limb is that there is a forest of spicules poking out from the edge, so it is not possible to get parallel to such a rough surface.
For most of the solar disk the degree of linear polarization of the continuum is under 0.1%, but it rises to 1% at the limb. The polarization also depends strongly on the wavelength, and for near ultraviolet 3000 Å the light near the limb is 100 times more polarized than red light at 7000 Å. At the limit of the Balmer series a change happens where at shorter wavelengths more bound-bound Balmer series transitions cause more opacity.  This extra opacity drops the polarization degree by a factor of two near 3746 Å.