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in the University of GLASGOW.IN TWO VOLUMES.VOL. I.LONDON:
PRINTED FOR W. STRAHAN; AND T. CADELL,
IN THE STRAND.
MDCCLXXVI.
Ten workers who split pin-making into eighteen operations make 48,000 pins a day.
Why Smith picked “a very trifling manufacture”
“One man draws out the wire; another straights it; a third cuts it; a fourth points it; a fifth grinds it at the top for receiving the head”
Making the head takes two or three operations; whitening the pins is another; putting them into the paper is a trade by itself.
In a small manufactory, ten men made about twelve pounds of pins a day, at upwards of 4,000 pins to the pound.
That is 4,800 pins per person per day.
An untrained workman “could scarce, perhaps, with his utmost industry, make one pin in a day, and certainly could not make twenty.”
Alone, each would make not the 240th, perhaps not the 4,800th part of what they make together.
Dividing labour raises output through dexterity, saved time, and machines.
First, the dexterity of every particular workman.
A smith who has never made nails makes “two or three hundred nails in a day, and those, too, very bad ones.”
A smith used to it makes 800 to 1,000; boys who make nothing else, upwards of 2,300.
Second, the time lost in passing from one sort of work to another.
A country weaver who also farms loses time going from his loom to the field, and back.
“A man commonly saunters a little in turning his hand from one sort of employment to another.”
Third, machines that facilitate and abridge labour.
When attention is on one simple object, people find easier and readier methods.
Many machines were invented by workmen with one simple task who wanted to save their own labour.
In the first fire engines, “a boy was constantly employed to open and shut alternately the communication between the boiler and the cylinder.”
One boy “who loved to play with his companions” tied a string from the valve handle to another part of the machine.
The valve then worked by itself: “the discovery of a boy who wanted to save his own labour.”
Other improvements came from machine makers, once making machines became a peculiar trade.
And some from philosophers, “whose trade it is not to do any thing, but to observe every thing.”
Philosophy subdivides too, and “the quantity of science is considerably increased by it.”
Even a day-labourer’s woollen coat is the joint labour of a great multitude of workmen.
“The shepherd, the sorter of the wool, the wool-comber or carder, the dyer, the scribbler, the spinner, the weaver, the fuller, the dresser”
Merchants and carriers move the materials; ship-builders, sailors, sail-makers, rope-makers bring the dyes from the remotest corners of the world.
Even the shepherd’s shears need the miner, the furnace builder, the feller of timber, the charcoal burner, the brickmaker and the smith.
Without the co-operation of many thousands, “the very meanest person in a civilized country could not be provided” for.
Dividing labour spreads universal opulence to the lowest ranks of the people.
Every workman has “a great quantity of his own work to dispose of beyond what he himself has occasion for.”
He trades it for theirs, and “a general plenty diffuses itself through all the different ranks of the society.”
Agriculture divides less: “the ploughman, the harrower, the sower of the seed, and the reaper of the corn, are often the same.”
So rich countries lead far more in manufactures than in corn: Polish corn is as cheap as French.
The division of labour is not the effect of any human wisdom but of a propensity to truck, barter, and exchange.
It is “the necessary, though very slow and gradual, consequence” of that propensity.
“Nobody ever saw a dog make a fair and deliberate exchange of one bone for another with another dog.”
Two greyhounds chasing one hare only seem to act in concert: “the accidental concurrence of their passions.”
Animals win help by fawning, as “a spaniel endeavours, by a thousand attractions, to engage the attention of its master.”
Man “has almost constant occasion for the help of his brethren,” and cannot get it from benevolence alone.
We get our dinner by appealing to their self-love, not their benevolence.
“Give me that which I want, and you shall have this which you want, is the meaning of every such offer.”
“It is not from the benevolence of the butcher, the brewer, or the baker that we expect our dinner, but from their regard to their own interest.”
“We address ourselves, not to their humanity, but to their self-love.”
“Nobody but a beggar chooses to depend chiefly upon the benevolence of his fellow-citizens.”
Even a beggar trades: old clothes for other clothes, for lodging, or for food.
In a tribe of hunters, the best bow-maker becomes an armourer because trading beats hunting.
He exchanges bows and arrows for cattle or venison, and gets more than if he himself went to the field.
Another becomes “a sort of house-carpenter”; a third a smith or a brazier; a fourth a tanner.
The certainty of exchanging his surplus “encourages every man to apply himself to a particular occupation.”
Differences in talent are more the effect than the cause of the division of labour.
A philosopher and a street porter, in their first six or eight years, “were, perhaps, very much alike.”
The gap comes “not so much from nature, as from habit, custom, and education.”
A mastiff, a greyhound, a spaniel and a shepherd’s dog differ far more, yet are “of scarce any use to one another.”
Among men, exchange brings every talent “into a common stock.”
The division of labour is limited by the extent of the market.
“When the market is very small, no person can have any encouragement to dedicate himself entirely to one employment.”
A porter “can find employment and subsistence in no other place” than a great town.
In the highlands of Scotland, “every farmer must be butcher, baker, and brewer, for his own family.”
A country carpenter is also a joiner, a cabinet-maker, a carver, a wheel-wright, a plough-wright and a waggon-maker.
A highland village buys one day’s work from a nailer who makes 300,000 nails a year.
“at the rate of a thousand nails a-day, and three hundred working days in the year”
“it would be impossible to dispose of one thousand, that is, of one day’s work in the year.”
So there can be no nailer “in the remote and inland parts of the highlands of Scotland.”
There you rarely find a smith, a carpenter, or a mason “within less than twenty miles of another of the same trade.”
One ship carries what fifty waggons and four hundred horses carry by land.
London to Edinburgh and back, about six weeks:
a broad-wheeled waggon, 2 men, 8 horses: near four ton
a ship with 6 or 8 men: two hundred ton
By land, 200 tons need “a hundred men”, “four hundred horses” and “fifty great waggons.”
“What goods could bear the expense of land-carriage between London and Calcutta?”
The first civilised nations grew up around the Mediterranean and along great navigable rivers.
The Mediterranean, smooth and full of islands, was “extremely favourable to the infant navigation of the world.”
Egypt: the Nile breaks into canals reaching “all the considerable villages, and even to many farm-houses.”
Bengal and eastern China, whose rivers form “a multitude of canals.”
Inland Africa and Tartary stayed poor: a frozen sea, and great rivers too far apart.
The Danube helps Bavaria, Austria and Hungary little, since none holds its whole course.
The first rich societies grew along coasts and rivers because water widened their markets.
A specialist needs enough buyers: a nailer’s year is 300,000 nails, a highland village buys one day’s worth.
One ship does the work of fifty waggons and four hundred horses, so goods reach far more buyers by water.
So industry “naturally begins to subdivide and improve itself” on the sea-coast and navigable rivers.
The Mediterranean, Egypt, Bengal, eastern China.
Inland Africa and Tartary stayed poor for ages.
Barter fails when the butcher already has his bread and beer.
“The butcher has more meat in his shop than he himself can consume, and the brewer and the baker would each of them be willing to purchase a part of it.”
But they have only bread and beer to offer, and he has all he needs.
“No exchange can, in this case, be made between them.”
So every prudent man keeps a commodity “few people would be likely to refuse.”
Before coins, people paid in cattle, salt, shells, cod, tobacco, and even nails.
In Homer, the armour of Diomede cost nine oxen; that of Glaucus a hundred.
Salt in Abyssinia, shells on the coast of India, dried cod at Newfoundland, tobacco in Virginia, sugar in the West Indies.
In a village in Scotland, a workman would “carry nails instead of money to the baker’s shop or the ale-house.”
Metals won because they keep, and can be divided and re-united without loss.
With only cattle to give, a man had to buy salt “to the value of a whole ox, or a whole sheep, at a time.”
Iron at Sparta, copper at Rome, gold and silver among all rich and commercial nations.
Weighing and assaying were troublesome, so states stamped the metal: “Hence the origin of coined money.”
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LONDON
Lightning strikes the rails at A and B. Were the strikes simultaneous?
“Lightning has struck the rails on our railway embankment at two places A and B far distant from each other.”
Einstein’s test: an observer at the mid-point M, with two mirrors.
“If the observer perceives the two flashes of lightning at the same time, then they are simultaneous.”
A definition, not a fact of nature: it says how to check.
A passenger at the train’s mid-point sees B’s flash first.
“he is hastening towards the beam of light coming from B, whilst he is riding on ahead of the beam of light coming from A.”
Light moves at the same speed for him as for the embankment, so he can’t blame his motion.
He must conclude “that the lightning flash B took place earlier than the lightning flash A.”
Simultaneous for the embankment, not simultaneous for the train.
“Every reference-body (co-ordinate system) has its own particular time; unless we are told the reference-body to which the statement of time refers, there is no meaning in a statement of the time of an event.”
Why nobody noticed before 1905
At everyday speeds the two answers differ by far less than any clock could show.
A light clock that moves ticks slower: its light runs a longer, slanted path.
Light bounces between two mirrors; each bounce is one tick.
Seen moving, the light zigzags. Same speed, longer path, fewer ticks.
Slower by a factor γ = 1/√(1 − v²/c²).
At 87% of the speed of light, γ = 2.
Moving clocks run slow, and c is a speed limit.
“As a consequence of its motion the clock goes more slowly than when at rest.”
Near c, γ grows without bound: c “plays the part of a limiting velocity, which can neither be reached nor exceeded by any real body.”
Moving rods are shorter along their motion.
“The rigid rod is thus shorter when in motion than when at rest, and the more quickly it is moving, the shorter is the rod.”
Only along the motion; widths stay the same.
Galileo’s rules give no such thing: “we should not have obtained a contraction of the rod as a consequence of its motion.”
Muons reach the ground only because their clocks run slow.
Cosmic rays make them about 15 km up.
They live 2.2 microseconds: about 660 m of travel, even near light speed.
At 99.5% of c their clocks run about 10× slow, so many cross all 15 km.
Minkowski: space and time are one four-dimensional world.
Einstein: the world “is naturally four-dimensional in the space-time sense.”
Minkowski, 1908: “space by itself, and time by itself, are doomed to fade away into mere shadows”.
An observer’s “now” is a slice through this world; moving observers slice it at an angle.
Light cones decide which events have a fixed order.
From any event, light spreads into a future cone; its past cone holds all that could have reached it.
Inside the cones, one event can affect the other. Every observer agrees on their order.
Outside both cones is “elsewhere”: no signal can link the two events.
Depending on your motion, the other event is earlier, simultaneous or later.
So what is “at the same time”?
A choice of slice through spacetime, not a fact about the two events.
E = mc²: one gram of mass is about 21 kilotons of energy.
c² is huge, so a little mass is a lot of energy: 9 × 10¹³ joules.
The sun turns about 4 million tonnes of mass into light every second.
Inside a pulled chest, acceleration feels exactly like gravity.
A rope pulls a closed chest “upwards” through empty space.
“He is then standing in the chest in exactly the same way as anyone stands in a room of a home on our earth.”
The equivalence principle: no experiment inside can tell the two apart.
So light bends near a mass.
In the accelerating chest a light ray curves; gravity must do the same.
“rays of light are propagated curvilinearly in gravitational fields.”
For starlight grazing the sun: “1.7 seconds of arc” (later 1.75″).
Clocks run slower deeper in gravity.
Einstein predicted light from the sun would arrive shifted to the red.
In 2010, NIST’s optical clocks caught the difference across 33 cm of height.
General relativity explains Mercury’s 43″ per century.
Mercury’s orbit slowly turns: “43 seconds of arc per century” more than Newton allows.
Newton could fit it only “on the assumption of hypotheses which have little probability”.
1919: the eclipse that made Einstein famous.
Expeditions to Sobral (Brazil) and Principe (West Africa) photographed the stars by the sun on 29 May 1919.
Measured: 1.98″ at Sobral, 1.61″ at Principe.
Newton’s gravity predicts only half the bend.
1959: light climbing a 22.5 m tower shifts red.
Pound and Rebka, Harvard’s Jefferson tower.
A shift of 2.5 parts in 10¹⁵, matching general relativity within 10%.
1971: atomic clocks flown around the world disagree.
Four caesium clocks on airliners, east then west.
Eastward −59 ns, westward +273 ns, against clocks left at home.
As both theories predict: speed slows them, height speeds them.
GPS would drift 10 km a day without relativity.
Satellite speed: clocks run 7 μs a day slow. Weaker gravity: 45 μs a day fast.
Net +38 μs a day, so the clocks are built to tick at 10.22999999543 MHz, not 10.23.
2015: LIGO hears two black holes merge.
14 September 2015, from 1.3 billion light-years away.
Its 4 km arms changed length by about a thousandth of a proton’s width.
Ripples in spacetime, predicted by Einstein in 1916.
Questions I still have
If the train and the embankment disagree, which one is right?
Why can’t anything go faster than light?
Does “now” mean anything far away?
Reading plan
Done: Part I, sections 1 to 17.
Next: Part II, from section 18; then Appendix III, the evidence.
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