How Does a Tautology Say Nothing?

In his wartime Notebooks Wittgenstein claims that a tautology ‘says nothing’. It is argued that this should be taken to mean that a tautology has a zero quantity of sense. Two distinct metaphors are operative in shaping this conception of a tautology. First, a proposition is treated on the model of a linear vector and a tautology is conceived as analogous to the null vector. Second, a tautology, being a limiting case of a truth condition, is conceived on the model of a degenerate conic section. The assumption that Wittgenstein is oscillating between these two guiding metaphors in the Tractatus and pre-Tractatus writings enables us to make sense of his otherwise obscure remarks about tautology, contradiction, negation, and sense.