"Sir,--I have received your explanation of your proposition that the circumference of the circle is to its diameter as 25 to 8. I am afraid I shall disappoint you by saying that I see no force in your proof: and I should hope that you will see that there is no force in it if you consider this: In the whole course of the proof, though the word cycle occurs, there is no property of the circle employed. You may do this: you may put the word _hexagon_ or _dodecagon_, or any other word describing a polygon in the place of _Circle_ in your proof, and the proof would be just as good as before. Does not this satisfy you that you cannot have proved a property of that special figure--a circle? {248} "Or you may do this: calculate the side of a polygon of 24 sides inscribed in a circle. I think you are a Mathematician enough to do this. You will find that if the radius of the circle be one, the side of this polygon is .264 etc. Now, the arc which this side subtends is according to your proposition 3.125/12 = .2604, and therefore the chord is greater than its arc, which you will allow is impossible. "I shall be glad if these arguments satisfy you, and "I am, Sir, your obedient Servant, "W. WHEWELL." AN M.P.'S ARITHMETIC. In the debate of May, 1866, on Electoral Qualifications, a question arose about arithmetical capability. Mr. Gladstone asked how many members of the House could divide 1330l. 7s. 6d. by 2l. 13s. 8d. Six hundred and fifty-eight, answered one member; the thing cannot be done, answered another. There is an old paradox to which this relates: it arises out of the ignorance of the distinction between abstract and concrete arithmetic. _Magnitude_ may be divided by _magnitude_; and the answer is number: how often does 12d. contain 4d.; answer three times. _Magnitude_ may be divided by _number_, and the answer is _magnitude_: 12d. is divided in four equal parts, what is each part? Answer three _pence_. The honorable objector, whose name I suppress, trusting that he has mended his ways, gave the following utterance: "With regard to the division sum, it was quite possible to divide by a sum, but not by money. How could any one divide money by 2l. 16s. 8d.? (Laughter.) The question might be asked, 'How many times 2s. will go into 1l.?' but that was not dividing by money; it was simply dividing 20 by 2. He might be asked, 'How many times will 6s. 8d. go into a pound?' but it was only required to divide 240 by 80. If the right hon. gentleman were to ask the hon. {249} member for Brighton (Professor Fawcett),[397] or any other authority, he would receive the same answer--viz., that it was possible to divide by a sum, but not by money. (Hear.)"