  Magnetism in the orthorhombic metal CaFe$_4$As$_3$ was examined through
neutron diffraction for powder and single crystalline samples. Incommensurate
(${\bm q}_{\rm m}\approx (0.37-0.39)\times{\bm b}^{\ast}$) and predominantly
longitudinally ($\parallel b$) modulated order develops through a 2nd order
phase transition at $T_{\rm N}=89.63(6)$ K with a 3D Heisenberg-like critical
exponent $\beta=0.365(6)$. A 1st order transition at $T_2=25.6(9)$ K is
associated with the development of a transverse component, locking ${\bm
q}_{\rm m}$ to $0.375(2){\bm b}^{\ast}$, and increasing the moments from 2.1(1)
to 2.2(3) $\mu_{\rm B}$ for Fe$^{2+}$ and from 1.3(3) to 2.4(4) $\mu_{\rm B}$
for Fe$^+$. The {\it ab-initio} Fermi surface is consistent with a nesting
instability in cross-linked FeAs strips.
