Among the paradoxers are the political paradoxers who care not how far they go in debate, their only object being to carry the House with them for the current evening. What I have said of editors I repeat of them. The preservation of a very marked instance, the association of political recklessness with cyclometrical and Apocalyptic absurdity, may have a tendency to warn, not indeed any hardened public-man and sinner, but some young minds which have yearnings towards politics, and are in formation of habits.
In the debate on decimal coinage of July 12, 1855, Mr. Lowe,[298] then member for Kidderminster, an effective speaker and a smart man, exhibited himself in a speech on which I wrote a comment for the Decimal Association. I have seldom seen a more wretched attempt to distort the points of a public question than the whole of this speech. Looking at the intelligence shown by the speaker on other occasions, {170} it is clear that if charity, instead of believing all things, believed only all things but one, he might tremble for his political character; for the honesty of his intention on this occasion might be the incredible exception. I give a few paragraphs with comments:
"In commenting on the humorous, but still argumentative speech of Mr. Lowe, the member for Kidderminster, we may observe, in general, that it consists of points which have been several times set forth, and several times answered. Mr. Lowe has seen these answers, but does not allude to them, far less attempt to meet them. There are, no doubt, individuals, who show in their public speaking the outward and visible signs of a greater degree of acuteness than they can summon to guide their private thinking. If Mr. Lowe be not one of these, if the power of his mind in the closet be at all comparable to the power of his tongue in the House, it may be suspected that his reserve with respect to what has been put forward by the very parties against whom he was contending, arises from one or both of two things--a high opinion of the arguments which he ignored--a low opinion of the generality of the persons whom he addressed. [Both, I doubt not].
"Did they calculate in florins In the name of common sense, ?" how can it be objected to a system that people do not use it before it is introduced? Let the decimal system be completed, and calculation shall be made in florins; that is, florins shall take their proper place. If florins were introduced _now_, there must be a column for the odd shilling. "He was glad that some hon. If the hon. gentleman make gentleman had derived benefit this assertion of himself, it from the issue of florins. His is not for us to gainsay it. only experience of their It only proves that he is one convenience was, that when he of that class of {171} men who ought to have received are described in the old song, half-a-crown, he had generally of which one couplet runs received a florin, and when he thus: ought to have paid a florin, he had generally paid I sold my cow to buy me a half-a-crown." (Hear, hear, calf; and laughter.) I never make a bargain but I lose half, With a etc. etc. etc.
But he cannot mean that Englishmen in general are so easily managed. And as to Jonathan, who is but John lengthened out a little, he would see creation whittled into chips before he would even split what may henceforth be called the Kidderminster difference. The House, not unmoved--for it laughed--with sly humor decided that the introduction of the florin had been "eminently successful and satisfactory."
The truth is that Mr. Lowe here attacks nothing except the coexistence of the florin and half-crown. We are endeavoring to abolish the half-crown. Let Mr. Lowe join us; and he will, if we succeed, be relieved from the pressure on his pocket which must arise from having the turn of the market always against him.
"From a florin they get to 2 Note the sophism of expressing 2-5ths of a penny, but who our coin in terms of the ever bought anything, who ever penny, which we abandon, reckoned or wished to reckon instead of the florin, which in such a coin as that?" we retain. Remember that this (Hear, hear.) 2 2-5ths is the hundredth part of the pound, which is called, as yet, a _cent_. Nobody buys anything at a cent, because the cent is not yet introduced. Nobody reckons in cents for the same reason. Everybody wishes to reckon in cents, who wishes to combine the advantage of decimal reckoning with the preservation of the pound as {172} the highest unit of account; amongst others, a majority of the House of Commons, the Bank of England, the majority of London bankers, the Chambers of Commerce in various places, etc. etc. etc. "Such a coin could never come Does 2-1/2d. never pass from into general circulation hand to hand? And is 2-1/2d. because it represents nothing so precisely the modulus of which corresponds with any of popular wants, that an the wants of the people." alteration of 4 per cent. would make it useless? Of all the values which 2-1/2d. measures, from three pounds of potatoes down to certain arguments used in the House of Commons, there is not one for which a cent would not do just as well. Mr. Lowe has fallen into the misconception of the person who admired the dispensation of Providence by which large rivers are made to run through cities so great and towns so many. If the cent were to be introduced to-morrow, straightway the buns and cakes, the soda-water bottles, the short omnibus fares, the bunches of radishes, etc. etc. etc., would adapt themselves to the coin. "If the proposed system were The confusion of ideas here adopted, they would all be exhibited is most instructive. compelled to live in decimals The speaker is under the for ever; if a man dined at a impression that _we_ are public house he would have to introducing fractions: the pay for his dinner in decimal truth is, that we only want to fractions. (Hear, hear.) He abandon the _more difficult_ objected to that, for he fractions which we _have got_, thought that a man ought to be and to introduce _easier able to pay for his dinner in fractions_. Does he deny this? integers." (Hear, hear, and a Let us trace his denial to its laugh.) legitimate consequences. A man ought to pay for his dinner in integers.
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Now, if Mr. Lowe insists on it that our integer is the pound, he is bound to admit that the present integer is the pound, of which a shilling, etc., are fractions. The next time he has a chop and a pint of stout in the city, the waiter should say--"A pound, sir, to you," and should add, "Please to remember the waiter in integers." Mr. Lowe fancies that when he pays one and sixpence, he pays in integers, and so he does, if his integer be a penny or a sixpence. Let him bring his mind to contemplate a mil as the integer, the lowest integer, and the seven cents five mils which he would pay under the new system would be payment in integers also. But, as it happens with some others, he looks _up_ the present system, with Cocker,[299] and Walkingame,[300] and always looks _down_ the proposed system. The word _decimal_ is obstinately associated with _fractions_, for which there is no need. Hence it becomes so much of a bugbear, that, to parody the lines of Pope, which probably suggested one of Mr. Lowe's phrases--
"Dinner he finds too painful an endeavor, Condemned to pay in decimals for ever."
"The present system, however, A pleasant sum even for an had not yet been changed into accomplished mathematician. decimal system. That change What does divided by the might appear very easy to decimal of a pound mean? accomplished mathematicians Perhaps it means _reduced_ to and men of science, but it was the decimal of a pound! Mr. one which it would be very Lowe supposes, as many others difficult to carry out. (Hear, do, that, after the change, hear). What would have to be all calculations will be done? Every sum would have to _proposed in old money_, and be reduced into a vulgar then _converted into new_. He fraction of a pound, and then cannot hit the {174} idea that divided by the decimal of a the new coins will take the pound--a pleasant sum for an place of the old. This lack of old applewoman to work out!" apprehension will presently (Hear, hear, and laughter.) appear further. "It would not be an agreeable Let the members be assured task, even for some members of that nine half-pence will be, that House, to reduce 4-1/2d., for every practical purpose, or nine half-pence, to mils." 18 mils. But now to the fact (Hear, hear.) 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 {175} 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 4-1/2d. 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 Fine words, wrongly used. The they went below 6d., that the new coins are commensurable new scale of coins would not with, and in a finite ratio be commensurate in any finite to, the old ones. The farthing ratio with anything in this is to the mil as 25 to 24. The new currency of mils." 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. {176} "No less than five of our This dreadful change of value present coins must be called consists in sixpence farthing in, or else--which would be going to the half-shilling worse--new values must be instead of sixpence. Whether given to them." the new farthings be called mils or not is of no consequence. "If a poor man put a penny in Mr. Lowe, who cannot pass a his pocket, it would come out half-crown for more than a a coin of different value, florin, or get in a florin at which he would not understand. less than half-a-crown, has Suppose he owed another man a such a high faith in the penny, how was he to pay him ? sterner stuff of his fellow Was he to pay him in mils? countrymen, that he believes Four mils would be too little, any two of them would go to and five mils would be too fisty cuffs for the 25th part much. The hon. gentlemen said of a farthing. He reasons there would be only a mil thus: He has often heard in between them. That was exactly the streets, "I'd fight you it. He believed there would be for the fiftieth part of a a 'mill' between them." (Much farden:" and having (that is, laughter.) 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 We should hardly believe all expression for four-pence? this to be uttered in earnest, Why, 0.166 (a laugh); for if we had not known {177} that threepence? .0125; for a several persons who have not penny? .004166, and so on _ad Mr. Lowe's humor, nevertheless infinitum_ (a laugh); for a have his impressions on this half-penny? .002083 _ad point. It must therefore be infinitum_. (A laugh). What answered; but how is this to would be the present be done seriously? expression for a farthing? Why, .0010416 _ad infinitum_. _Dialogue between a member of (A laugh). And this was the Parliament and an orange-boy, system which was to cause such three days after the a saving in figures, and these introduction of the complete were the quantities into which decimal system. The member, the poor would have to reduce going down to the House, wants the current coin of the realm. oranges to sustain his voice (Cheers). With every respect in a two hours' speech on for decimal fractions, of moving that 100000l. be placed which he boasted no profound at the disposal of Her knowledge, he doubted whether Majesty, to supply the poor the poor were equal to mental with ready-reckoners._ arithmetic of this kind, (hear, hear) and he hoped the _Boy._ Fine oranges! two a adoption of the system would penny! two a penny! {178} be deferred until there were some proof that they would be _Member._ Here boy, two! Now, able to understand it; for, how am I to pay you? after all, this was the question of the poor, and the _Boy._ Give you change, your whole weight of the change honor. would fall upon them. Let the rich by all means have _Member._ Ah! but how? Where's permission to perplex your ready-reckoner? themselves by any division of a pound they pleased; but do _Boy._ I sells a better sort not let them, by any nor them. Mine's real Cheyny. experiment like this, impose difficulties upon the poor and _Member._ But you see a compel men to carry farthing is now .0014166666 ready-reckoners in their _ad infinitum_, and if we pocket to give them all these multiply this by 4---- fractional quantities." (Hear, hear.) _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 {179} 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.
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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 {181} 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].
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