  In this paper we investigate the properties of a sample of six BL Lacs by
fitting their spectra using our inhomogeneous jet model with an accelerating,
magnetically dominated, parabolic base, which transitions to a slowly
decelerating conical jet with a geometry based on observations of M87. Our
model is able to fit very well to the simultaneous multiwavelength spectra of
all the BL Lacs including radio observations. We find that the BL Lacs have
lower jet powers and bulk Lorentz factors than the sample of Compton-dominant
blazars investigated in Paper III, consistent with the blazar sequence.
Excitingly, we find a correlation between the radius at which the jet first
comes into equipartition and the jet power, in agreement with our prediction
from Paper II. We interpret this result as one of two physical scenarios: a
universal jet geometry which scales linearly with black hole mass or a
dichotomy in Eddington accretion rates between flat spectrum radio quasars
(FSRQs) and BL Lacs. If we assume that the jet geometry of all blazars scales
linearly with black hole mass then we find a plausible range of masses
(10^7-10^10 solar masses). We find that the quiescent gamma-ray spectrum of
Markarian 421 is best fitted by scattering of external CMB photons. We are
unable to fit the spectrum using synchrotron self-Compton emission due to
strong gamma-ray absorption via pair production even using a compact, rapidly
decelerating, jet with a very large bulk Lorentz factor (50), as has been
suggested recently. Finally, we fit to the SEDs of the four high power HSP BL
Lacs recently found by Padovani et al. 2012. We find that their high peak
frequency emission is caused by high maximum electron energies whilst the rest
of their jet properties are typical of relatively high power BL Lacs and
consistent with our predictions.
