Janet Godolphin’s paper “On the connectivity problem for m-way designs” has been accepted for publication in the Journal of Statistical Theory and Practice.   The problem of ascertaining conditions which ensure that an m-way design is connected has occupied the attention of research workers for very many years.  One of the significant advances, as well as one of the earliest contributions, was provided by the classic work of J.N. Srivastava and D. A. Anderson in 1970 which gives a necessary and sufficient rank condition for an m-way design to be completely connected.  In this paper it is shown that the class of estimable parametric functions for an individual factor is derived directly from a simple extension of the Srivastava-Anderson result. This takes the form of a necessary and sufficient rank condition which is expressed in terms of the dimension of a segregated component of the kernel of the design matrix. The result has the interesting property that the connectivity status for all of the individual factors can be found simultaneously. Furthermore, it enables the formulation of several general results, which include the specification of conditions on designs exhibiting adjusted orthogonality. A number of examples are given to illustrate these results.