  We present results of measurements of the radial extent of the accretion disc
corona in low mass X-ray binaries. These results prove conclusively the
extended nature of the ADC, with radial extent varying from 20,000 km in the
faintest sources to 700,000 km in the brightest, a substantial fraction of the
accretion disc radius, typically 15%. This result rules out the Eastern model
for LMXB which is extensively used, in which the Comptonizing region is a small
central region. The ADC size depends strongly on the 1 - 30 keV source
luminosity via a simple relationship r_ADC = L^{0.88 +/- 0.16} (99% confidence)
close to a simple proportionality. We also present limited evidence that the
ADC size agrees with the Compton radius r_C, or maximum radius for hydrostatic
equilibrium. The results are consistent with models in which an extended ADC is
formed by illumination of the disc by the central source. The dependence on
luminosity may reflect the known decrease of coronal temperature as the source
luminosity increases leading to an increase of r_C. The extended nature of the
ADC means that the seed photons for Comptonization must consist of emission
from the disc to the same radial extent as the corona, providing copious
supplies of soft seed photons. We demonstrate the importance of the size of the
ADC to the correct description of Comptonization, and derive the Comptonized
spectrum of a LMXB based on thermal Comptonization of these seed photons and
show that this differs fundamentally from that of the Eastern model which
assumes a cut-off below 1 keV. Finally, we argue that our results are
inconsistent with the assumption often made that the X-ray emission of
accreting Black Holes and Neutron Stars has a common mechanism depending on the
properties of the accretion flow only.
