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Rh colleague interrupts the lesson to ask what evidence there is to show that this is the exact rate. Another asserts that the last rate quoted was 9/875d. per franc; and a third insists that the last quotation was 9/876d. They engage in a vehement discussion of the point; but all agree that such gross ignorance of facts as the teacher betrays, proves him to be incompetent; and that, as the statement on which his procedure rests is proved false, his whole chain of reasoning falls to the ground.

I will close these mathematical illustrations by narrating an incident which actually occurred. An intelligent girl, who had been badly taught arithmetic, joined my class. I set her a sum about some damaged articles worth, originally, £3 1 5s. each, but which were to be sold in a lump at an abatement of one pound and some shillings on the price of each. She was required to find what would be received for the whole. It so happened that the lump sum amounted to so many pounds and fifteen shillings. She came to me saying that she could not get her sum right; the shillings were right, but the pounds were wrong. I worked it for her; beginning, of course, by subtracting the shillings of the abatement from the original fifteen shillings. "But I had the shillings right," she cried; "now you are getting it all wrong!" There was something very touching in her dismay at seeing the poor little bit of rightness, which she had secured, put wrong, and I felt like a ruthless destroyer of the last refuge of an innocent soul; but Arithmetic tolerates no sentimental hesitations; and I had, of course, to persist. At last, by trusting in blind faith to accurate Logic, we got the whole right, to her great surprise. I asked her to explain her own method.