Abstract
IF I had made a slip of the pen of the kind suspected by Mr. Cumming (p. 198), it would have been a serious error, because it constituted the essence of what I was writing about. I was sure that a number of teachers did not believe it, and I am obliged to Mr. Cumming for giving me another opportunity of emphasising what I believe to be a vital matter. He says “the multiplication of one length by another length [or, more generally, of one concrete quantity by another] is abhorrent to the mind of” certain mathematicians. Quite true, I know it. The idea was abhorrent to the mind of the late Mr. Todhunter, and I think that Prof. Greenhill has expressed himself in the same sense. But what then? That is exactly why the idea requires driving home; and until it is driven home there will be no real clearness or simplicity in dealing either with physical quantities themselves or with their numerical specification in terms of given “units.”
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