  4U 1822-37 is a Low Mass X-ray Binary (LMXB) system with an Accretion Disk
Corona. We have obtained 16 new mid-eclipse time measurements of this source
during the last 13 years using X- ray observations made with the RXTE-PCA,
RXTE-ASM, Swift-XRT, XMM-Newton and Chandra observatories. These, along with
the earlier known mid-eclipse times have been used to accurately determine the
timescale for a change in the orbital period of 4U 1822-37. We have derived an
orbital period Porb = 0.23210887(15) d, which is changing at the rate of \cdot
Porb = 1.3(3) x 10-10 d d-1 (at T0 = MJD 45614). The timescale for a change in
the orbital period is Porb/ \cdot Porb of 4.9(1.1) x 106 yr. We also report the
detection of 0.59290132(11) s (at T0 = MJD 51975) X-ray pulsations from the
source with a long term average \cdot Pspin of -2.481(4) x 10-12 s s-1, i.e., a
spin-up time scale (Pspin/ \cdot Pspin) of 7578(13) yr. In view of these
results, we have discussed various mechanisms that could be responsible for the
orbital evolution in this system. Assuming the extreme case of conservative
mass transfer, we have found that the measured \cdot Porb requires a large mass
transfer rate of (4.2 - 5.2) x 10-8 M\odot yr-1 which together with the spin up
rate implies a magnetic field strength in the range of (1-3) x 108 G. Using the
long term RXTE-ASM light curve, we have found that the X-ray intensity of the
source has decreased over the last 13 years by ? 40% and there are long term
fluctuations at time scales of about a year. In addition to the long term
intensity variation, we have also observed significant variation in the
intensity during the eclipse.
