Annus MirabilisEinstein in 1905
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special relativity

The equation explained

ϱ=∂X∂x+∂Y∂y+∂Z∂z\varrho = \frac{\partial X}{\partial x} + \frac{\partial Y}{\partial y} + \frac{\partial Z}{\partial z}
In wordsThe density of electricity, four pi times over, is how much the electric force spreads out from a point, its slopes along the three coordinates added together.OverviewWhat the paper means by ϱ\varrho: the divergence of the electric force, which is 4π4 \pi times the density of electricity.Full explanationThe sum of the three slopes, each component of the electric force changing along its own axis, measures how much the electric force spreads out from a point. Where there is no electricity it is zero, as in the empty space of § 6; where there is electricity it is 4π4 \pi times its density, in the units the paper uses. So ϱ\varrho in the current uxϱu_x \varrho of the previous display is this same quantity. The paper says so in words: ϱ\varrho denotes 4π4 \pi times the density of electricity.Every step∂X∂x,∂Y∂y,∂Z∂z\frac{\partial X}{\partial x}, \quad \frac{\partial Y}{\partial y}, \quad \frac{\partial Z}{\partial z}How fast each component of the electric force changes along its own axis.ϱ=∂X∂x+∂Y∂y+∂Z∂z\varrho = \frac{\partial X}{\partial x} + \frac{\partial Y}{\partial y} + \frac{\partial Z}{\partial z}Their sum, the divergence of the electric force: 4π4 \pi times the density of electricity, as the paper says.Also

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