Murphys {em Positive definite kernels and Hilbert C${}^*$--modules} reorganized

The paper the title refers to is that in {em Proceedings of the Edinburgh Mathematical Society}, {bf 40} (1997), 367-374. Taking it as an excuse we intend to realize a twofold purpose: to atomize that important result showing by the way connections which are out of favour and to rectify a tiny piece of history.