************************************************************************* 51039 We attempt to solve one of the hardest questions on the theory of pulsar magnetosphere; why millisecond pulsars operate just as ordinary pulsars in spite of the fact that their polar magnetic field is four orders of magnitude weaker? A key parameter of the magnetospheric particle acceleration is the magnetic field strength at the light cylinder. We propose to observe a millisecond pulsar B1937+21, whose light cylinder field is the strongest in the millisecond pulsar population and is as same as that of the Crab pulsar, being expected to exhibit X-ray pulsation from the accelerated particles. This observation clearly differentiates several theories for the relativistic particle acceleration in the pulsar magnetosphere. *************************************************************************