"Gauss's theorem can be established as follows. consider an attracting particle of mass m at the point P, and let a cone of small solid angle ω be generated by radii through P. This cone cuts the surface at the points Q1, Q2, ... taken in order from P; the parts of the surface cut off by the cone at these points are S1, S2, ... and the outward-drawn normals are denoted n1, n2, ... Now if P lies outside Σ (region of masses, each at points Q1, Q2, ...), the cone will cut S an even number of times, and the signs will be plus and minus alternately, so that the total normal force across S1, S2, ... will be zero. On the other hand, if P lies inside Σ, the cone will cut S an odd number of times, the sign being minus and plus alternately, so that the total normal forces across S1, S2, ... will be -mω." Source: Spherical harmonic T.M.Macrobert Help with this text! I don't understand the second paragraph as to why the cone will cut S an odd number of times, the sign being minus and plus alternately when P lies inside Σ vs when P lies outside Σ. I know the cone is just a mathematical object but I can't follow the author thought process here. How did he use the cone to cut the surface at Q1, Q2, ... ? Why will the normal force across S due to particle at P be zero when P is outside the mass but not inside the mass?