  Two sets of measurements utilizing hot-wire anemometry and oil film
interferometry for flat-plate turbulent boundary layers, exposed to various
controlled adverse and favorable pressure gradients, are used to evaluate
history effects of the imposed and varying freestream gradients. The results
are from the NDF wind tunnel at ILLINOIS TECH (IIT) and the MTL wind tunnel at
KTH, over the range $800 < Re_\tau < 22,000$ (where $Re_{\tau}$ is the friction
Reynolds number). The streamwise pressure-gradient parameter $\beta \equiv
(-\ell/\tau_{w}) \cdot (\partial P_{e}/\partial x)$ varied between $-2 < \beta
< 7$, where $\ell$ is an outer length scale for boundary layers equivalent to
the half height of channel flow and the radius of pipe flow, and is estimated
for each boundary-layer profile. Extracting from each profile the three
parameters of the overlap region, following the recent work of \cite{mon23}
that led to an overlap region of combined logarithmic and linear parts, we find
minimum history effects in the overlap region. Thus, the overlap region in this
range of pressure-gradient boundary layers appears to be in ``quasi
equilibrium".
