Well you see that in flatland--we're just doing this in two dimensions,

在平面中我们先讨论两维情况
we'll get to three in just a second--in flatland,

之后再讨论三维在平面中
in two dimensions,

两维体系中
the circumference through which all these lines of force pass,

场力线通过的圆周长度
the length of the circumference is proportional to the radius. Right?

与半径成正比对吧
So if you go out twice as far there's twice the circumference.

当距离变为原来的两倍周长也变两倍
So the density of lines passing through it is half as big.

若蓝线的长度不变那通过的场力线会减半
Everybody got that?

都明白吗
Okay, so that means the force,

因为力
which is proportional to the line density,

与场力线密度成正比
must be proportional to 1/r. Okay?

所以力与距离的倒数成正比
So then as you move out twice, there'll be half as many lines;

因此距离变为两倍场力线就会减半