spring_layout does not use the correct Fruchterman-Reingold aglorithm

The documentation for spring_layoutsays, that the algorithm uses the the forces

Attractive force:  f_a(d) =  d^2 / k
Repulsive force:  f_r(d) = -k^2 / d

but what it actually does, is using

Attractive force:  f_a(d) =  d / k
Repulsive force:  f_r(d) = -k^2 / d^2

where d is the distance between two vertices and k is some constant. That also works, so I'm wondering, if we want to keep using this modified version or use the original version by Fruchterman and Reingold.
Networkx uses the same modified version, so either this is done on purpose or the error was copied when implementing it in Julia.

Start with the spring_layout implementation and its documentation, then compare the documented Fruchterman-Reingold formulas with the formulas actually used. Determine whether the modified forces are intentional or should match the original algorithm; done means the implementation and documentation agree, with behavior checked against the chosen formulas.