"The present system, however, had not yet been changed into decimal system. That change might appear very easy to accomplished mathematicians and men of science, but it was one which it would be very difficult to carry out. (Hear, hear). What would have to be done? Every sum would have to be reduced into a vulgar fraction of a pound, and then divided by the decimal of a pound—a pleasant sum for an old applewoman to work out!" (Hear, hear, and laughter.) A pleasant sum even for an accomplished mathematician. What does divided by the decimal of a pound mean? Perhaps it means reduced to the decimal of a pound! Mr. Lowe supposes, as many others do, that, after the change, all calculations will be proposed in old money, and then converted into new. He cannot hit the idea that the new coins will take the place of the old. This lack of apprehension will presently appear further.
"It would not be an agreeable task, even for some members of that House, to reduce 4½d., or nine half-pence, to mils." (Hear, hear.) Let the members be assured that nine half-pence will be, for every practical purpose, 18 mils. But now to the fact asserted. Davies Gilbert[[301]] used to maintain that during the long period he sat in the House, he never knew more than three men in it, at one time, who had a tolerable notion of fractions. [I heard him give the names of three at the time when he spoke: they were Warburton,[[302]] Pollock,[[303]] and Hume.[[304]] He himself was then out of Parliament.] Joseph Hume affirmed that he had never met with more than ten members who were arithmeticians. But both these gentlemen had a high standard. Mr. Lowe has given a much more damaging opinion. He evidently means that the general run of members could not do his question. It is done as follows: Since farthings gain on mils, at the rate of a whole mil in 24 farthings (24 farthings being 25 mils), it is clear that 18 farthings being three-quarters of 24 farthings, will gain three-quarters of a mil; that is, 18 farthings are eighteen mils and three-quarters of a mil. Any number of farthings is as many mils and as many twenty-fourths of a mil. To a certain extent, we feel able to protest against the manner in which Kidderminster has treated the other constituencies. We do not hold it impossible to give the Members of the House in general a sufficient knowledge of the meaning and consequences of the decimal succession of units, tens, hundreds, thousands, etc.; and we believe that there are in the House itself competent men, in number enough to teach all the rest. All that is wanted is the power of starting from the known to arrive at the unknown. Now there is one kind of decimals with which every member is acquainted—the Chiltern Hundreds. If public opinion would enable the competent minority to start from this in their teaching, not as a basis, but as an alternative, in three weeks the fundamentals would be acquired, and members in general would be as fit to turn 4½d. into mils, as any boys on the lower forms of a commercial school. For a long period of years, allusion to the general ignorance of arithmetic, has been a standing mode of argument, and has always been well received: whenever one member describes others as knownothings, those others cry Hear to the country in a transport of delight. In the meanwhile the country is gradually arriving at the conclusion that a true joke is no joke.
"The main objection was, if they went below 6d., that the new scale of coins would not be commensurate in any finite ratio with anything in this new currency of mils." Fine words, wrongly used. The new coins are commensurable with, and in a finite ratio to, the old ones. The farthing is to the mil as 25 to 24. The speaker has something here in the bud, which we shall presently meet with in the flower; and fallacies are more easily nipped in flower than in bud.
"No less than five of our present coins must be called in, or else—which would be worse—new values must be given to them." This dreadful change of value consists in sixpence farthing going to the half-shilling instead of sixpence. Whether the new farthings be called mils or not is of no consequence.
"If a poor man put a penny in his pocket, it would come out a coin of different value, which he would not understand. Suppose he owed another man a penny, how was he to pay him ? Was he to pay him in mils? Four mils would be too little, and five mils would be too much. The hon. gentlemen said there would be only a mil between them. That was exactly it. He believed there would be a 'mill' between them." (Much laughter.) Mr. Lowe, who cannot pass a half-crown for more than a florin, or get in a florin at less than half-a-crown, has such a high faith in the sterner stuff of his fellow countrymen, that he believes any two of them would go to fisty cuffs for the 25th part of a farthing. He reasons thus: He has often heard in the streets, "I'd fight you for the fiftieth part of a farden:" and having (that is, for a Member) a notion both of fractions and logic, he infers that those who would fight for the 50th of a farthing would, a fortiori, fight for a 25th. His mistake arises from his not knowing that when a person offers to fight another for 1/200d., he really means to fight for love; and that the stake is merely a matter of form, a feigned issue, a pro forma report of progress. Do the Members of the House think they have all the forms to themselves?
"What would be the present expression for four-pence? Why, 0.166 (a laugh); for threepence? .0125; for a penny? .004166, and so on ad infinitum (a laugh); for a half-penny? .002083 ad infinitum. (A laugh). What would be the present expression for a farthing? Why, .0010416 ad infinitum. (A laugh). And this was the system which was to cause such a saving in figures, and these were the quantities into which the poor would have to reduce the current coin of the realm. (Cheers). With every respect for decimal fractions, of which he boasted no profound knowledge, he doubted whether the poor were equal to mental arithmetic of this kind, (hear, hear) and he hoped the adoption of the system would be deferred until there were some proof that they would be able to understand it; for, after all, this was the question of the poor, and the whole weight of the change would fall upon them. Let the rich by all means have permission to perplex themselves by any division of a pound they pleased; but do not let them, by any experiment like this, impose difficulties upon the poor and compel men to carry ready-reckoners in their pocket to give them all these fractional quantities." (Hear, hear.) We should hardly believe all this to be uttered in earnest, if we had not known that several persons who have not Mr. Lowe's humor, nevertheless have his impressions on this point. It must therefore be answered; but how is this to be done seriously? Dialogue between a member of Parliament and an orange-boy, three days after the introduction of the complete decimal system. The member, going down to the House, wants oranges to sustain his voice in a two hours' speech on moving that 100000l. be placed at the disposal of Her Majesty, to supply the poor with ready-reckoners. Boy. Fine oranges! two a penny! two a penny! Member. Here boy, two! Now, how am I to pay you? Boy. Give you change, your honor. Member. Ah! but how? Where's your ready-reckoner? Boy. I sells a better sort nor them. Mine's real Cheyny. Member. But you see a farthing is now .0014166666 ad infinitum, and if we multiply this by 4—— Boy. Hold hard, Guv'ner; I sees what you're arter. Now what'll you stand if I puts you up to it? which Bill Smith he put me up in two minutes, cause he goes to the Ragged School. Member. You don't mean that you do without a book! Boy. Book be blowed. Come now, old un, here's summut for both on us. I got a florin, you gives me a half-a-crown for it, and I larns you the new money, gives you your oranges, and calls you a brick into the bargain. Member (to himself). Never had such a chance of getting off half-a-crown for value since that —— fellow Bowring carried his crochet. (Aloud.) Well, boy, it's a bargain. Now! Boy. Why, look 'e here, my trump, its a farden more to the tizzy—that's what it is. Member. What's that? Boy. Why, you knows a sixpence when you sees it. (Aside). Blest if I think he does! Well, its six browns and a farden now. A lady buys two oranges, and forks out a sixpence; well in coorse, I hands over fippence farden astead of fippence. I always gives a farden more change, and takes according. Member (in utter surprise, lets his oranges tumble into the gutter). Never mind! They won't be wanted now. (Walks off one way. Boy makes a pass of naso-digital mesmerism, and walks off the other way).

To the poor, who keep no books, the whole secret is "Sixpence farthing to the half shilling, twelve pence halfpenny to the shilling." The new twopence halfpenny, or cent, will be at once five to the shilling.

In conclusion, we remark that three very common misconceptions run through the hon. Member's argument; and, combined in different proportions, give variety to his patterns.

First, he will have it that we design to bring the uneducated into contact with decimal fractions. If it be so, it will only be as M. Jourdain was brought into contact with prose. In fact, Quoi! quand je dis, Nicole, apportez-moi mes pantoufles, c'est de la prose?[[305]] may be rendered: "What! do you mean that ten to the florin is a cent a piece must be called decimal reckoning?" If we had to comfort a poor man, horror-struck by the threat of decimals, we should tell him what manner of fractions had been inflicted upon him hitherto; nothing less awful than quarto-duodecimo-vicesimals, we should assure him.

Secondly, he assumes that the penny, such as it now is, will remain, as a coin of estimation, after it has ceased to be a coin of exchange; and that the mass of the people will continue to think of prices in old pence, and to calculate them in new ones, or else in new mils. No answer is required to this, beyond the mere statement of the nature of the assumption and denial.

Thirdly, he attributes to the uneducated community a want of perception and of operative power which really does not belong to them. The evidence offered to the Committee of the House shows that no fear is entertained on this point by those who come most in contact with farthing purchasers. And this would seem to be a rule,—that is, fear of the intelligence of the lower orders in the minds of those who are not in daily communication with them, no fear at all in the minds of those who are.

A remarkable instance of this distinction happened five-and-twenty years ago. The Admiralty requested the Astronomical Society to report on the alterations which should be made in the Nautical Almanac, the seaman's guide-book over the ocean. The greatest alteration proposed was the description of celestial phenomena in mean (or clock time), instead of apparent (or sundial) time, till then always employed. This change would require that in a great many operations the seaman should let alone what he formerly altered by addition or subtraction, and alter by addition or subtraction what he formerly let alone; provided always that what he formerly altered by addition he should, when he altered at all, alter by subtraction, and vice versa. This was a tolerably difficult change for uneducated skippers, working by rules they had only learned by rote. The Astronomical Society appointed a Committee of forty, of whom nine were naval officers or merchant seamen [I was on this Committee]. Some men of science were much afraid of the change. They could not trust an ignorant skipper or mate to make those alterations in their routine, on the correctness of which the ship might depend. Had the Committee consisted of men of science only, the change might never have been ventured on. But the naval men laughed, and said there was nothing to fear; and on their authority the alteration was made. The upshot was, that, after the new almanacs appeared, not a word of complaint was ever heard on the matter. Had the House of Commons had to

decide this question, with Mr. Lowe to quote the description given by Basil Hall[[306]] (who, by the way, was one of the Committee) of an observation on which the safety of the ship depended, worked out by the light of a lantern in a gale of wind off a lee shore, this simple and useful change might at this moment have been in the hands of its tenth Government Commission.

[Aug. 14, 1866. The Committee was appointed in the spring of 1830: it consisted of forty members. Death, of course, has been busy; there are now left Lord Shaftesbury,[[307]] Mr. Babbage,[[308]] Sir John Herschel,[[309]] Sir Thomas Maclear[[310]] (Astronomer Royal at the Cape of Good Hope), Dr. Robinson[[311]] (of Armagh), Sir James South,[[312]] Lord Wrottesley,[[313]] and myself].