https://www.comsol.de/blogs/heat-transfer-in-participating-media-and-the-discrete-ordinates-method/
In the discrete ordinates method (see above) there are three (0th, 1st, 2nd) moments equations to determine the quadrature sets. $s_i$ are the directions vectors and $w_i$ the corresponding weight.
$\sum_{i=1}^n w_i = 4\pi$
$\sum_{i=1}^n w_i s_i = 0$
$\sum_{i=1}^n w_i s_i s_i^T = \frac{4\pi}{3} I_3$
The zeroth equation makes sure the total weights equal the total solid sphere angle. The first equation is about the symmetry preference.
But I can not figure out what is the function of the last (2nd) equation? What does it do?