The paper attempts to elucidate and evaluate William Whewell's notion of a "consilience of inductions." In section I Whewellian consilience is defined and shown to differ considerably from what latter-day writers talk about when they use the term. In section II a primary analysis of consilience is shown to yield two types of consilient processes, one in which one of the lower-level laws undergoes a conceptual change (the case aptly discussed in Butts [1977]), and one in which the explanatory theory (...) undergoes conceptual "stretching." In section III both consilient cases are compared to the non-consilient case in reference to L. J. Cohen's method of relevant variables. In section IV we examine the test procedures of the theory in all three cases, and it is shown that in the event of genuine consilience (consilience of the second type) a theory acquires extraordinarily high support. In the final section something is said of the short-comings of standard Bayesian confirmation theories that are highlighted by Whewellian consilience. (shrink)