Even at the level of the most elementary arithmetical operations, procedures and practices change. During the twelfth and thirteenth centuries an unusually well documented development took place: at the beginning of the period the authors of elementary manuals of computation taught the use of the abacus, whereas at the end they described the method of calculation which came to be known as the algorism. Their ideas about number, however, were still largely drawn from Boethius's rendering of Nicomachus of Gerasa's Introduction to arithmetic in the Arithmetica and there had been little progress in attempting to reconcile Boethius's teaching on the theory of number with the rather different assumptions that underlie the methods of practical calculation. Boethius and Nicomachus, for example, emphasize that one is not a number but the source of number, and they are aware of the special problems posed by ‘two’. Nicomachus questions whether ‘two’ is anything more than an embodiment of the principle of ‘otherness’; for him, it is open to dispute whether it can be rated a number in its own right. For the teacher of the skills of calculation, ‘one’ and ‘two’ are merely digits like any other. By the fourteenth century, collections of textbook material on elementary arithmetic provided the student with instruction in both theory and practice. The abacus manuals are missing from many such collections because by then the abacus has apparently been relegated to the status of a simple practical aid, but the other elements in medieval arithmetical studies are variously covered.

In The life of Richard Owen by his grandson there is an inference to the effect that Owen had objected to his name being used to authorize various statements that Whewell was drafting in opposition to the Vestiges. The inference is drawn from letters that Whewell wrote to Owen on 13 and 15 February 1845. Corroboration of this would corne from a letter of Owen to Whewell, dated 14 February 1845, if extant. Among the Whewell papers at Trinity College, Cambridge, there are several letters from Owen to Whewell, none of which bears that date. There is one, however, dated 14 February 1844 which, on doser inspection, turns out to be the missing link in their correspondance. The evidence for the misdating is not merely that the letter falls naturally into a later sequence. The conclusion is inescapable because Owen refers to an ‘opinion which I have always entertained, and still do strongly, on the subject of a refutation of “Vestiges”’. Since the first edition of Chambers's book did not appear until October 1844, the letter must belong to the following year. My object in this paper is to examine the implications of this letter for a reconstruction of Owen's attitude to that book which Adam Sedgwick could so detest for, among many things, its ‘gross (and I dare to say, filthy) views of physiology’.