The solid angles subtended by all normal sections of a cone at the vertex are therefore equal, and since the attractions of these sections on a particle at the vertex are proportional to their distances from the vertex, they are numerically equal to one another and to the solid angle of the cone.
A solid angle is definable as the space contained by three or more planes intersecting in a common point; it is familiarly represented by a corner.
The earth would intercept an amount of it proportional to the solid angle it subtends at the sun; that is to say, it would receive a deposit of meteoric matter about one-tenth of a millimetre, of density say 2, over its whole surface in the course of the year.
The electric density on the sphere being uniform, the quantities of electricity on these areas are proportional to the areas, and if the electric force varies inversely as the square of the distance, the forces exerted by these two surface charges at the point in question are proportional to the solid angle of the little cone.
Accordingly, since the total solid angle round a point is 47r, it follows that the total flux through the closed surface due to the single point charge q is 41rq, and what is true for one point charge is true for any collection forming a total charge Q of any form.