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.
{173}
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.
{180}
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].
{182}