We add 20, 6, and 3.6 cm VLA observations of two wide-angle tails (WATs), 1
231 + 674 and 1433 + 553, to existing VLA data at 6 and 20 cm in order to s
tudy the variations of spectral index as a function of position. We apply t
he spectral tomography process that we introduced in our analysis of 3C 67,
3C 190, and 3C 449 (Katz-Stone; Katz-Stone & Rudnick). Both spectral tomog
raphy and polarization maps indicate that there are two distinct extended c
omponents in each source. As in the case of 3C 449, we find that each sourc
e has a flat spectrum jet surrounded by a steeper spectrum sheath. The stee
p components tend to be more highly polarized than the flat components. We
discuss a number of possibilities for the dynamics of the jet/sheath system
s and the evolution of their relativistic electron populations. Although th
e exact nature of these two coaxial components is still uncertain, their ex
istence requires new models of jets in FR I sources and may also have impli
cations for the dichotomy between FR I and FR II galaxies.