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A method of generating non-linear transformations for increasing the rate and expanding the domain of convergence of sequences is presented. These transformations represent in a certain sense a generalization of the well-known transformations due to Shanks, and in many cases are more efficient.The transformations would seem to have important application in computing results from formal solutions to problems in applied mathematics when these solutions are obtained in the form of series or sequences having poor convergence. An indication is also given of application to the"evaluation"of divergent formal solutions.

This paper purports a limited study of the concept of reason. It analyzes the claim of religious belief to be reasonable. The context for this analysis is an examination of some evidential (criteriological) connections between reasonable belief and '(good) reasons' for such belief. Consideration of the typical sort of evidential connection shows, not surprisingly, that religious belief cannot claim to be reasonable. But it is argued that there is (at least) one other sort of connection, and that it is philosophically plausible to regard this connection as definitive of a quite distinctive sense of 'reasonable', with its own kind and style of criteria, according to which religious belief can be thought reasonable.