'The way (michi) according to the kami (kannagara)' is an alternative rendering of 'Shinto' used in the prewar period with the meaning of orthodoxy. Like kodo it is sometimes used to make a distinction between Shinto as variegated popular beliefs (minkan shinko) and 'orthodox' Shinto; i.e. that directed principally towards the emperor.
A Popular Dictionary of Shinto. Brian Bocking.