Funding for this program
was provided by

when I was in college.
As you are now.

I took a course
in modern history.

One day during this course.
This professor said.

"That brings us to the end
of the 19th century."

I timidly raised
my little hand.

I said."Professor,sir."

We were very respectful
in those days.

I said,"Sir, you spent
two weeks teaching us

"About the theory
of 19th-century warfare.

"And you never
said one word

"About the theories
of james clerk maxwell.

"The theory
of 19th-century warfare

"Is a matter
of no lastingsingnificance.

"While what maxwell did

"Affects every day
of our lives.

"Don't you think

"That's a bizarre distortion

of what's important
about history?"

Maybe we weren't
so respectful after all.

To his credit.

He was embarrassed
by my question.

He did know
who maxwell was.

He briefly explained
what he had done.

The point is
that the history of science

is the step child
of the historical profession.

Most historians
just ignore it.

Because they don't
understand it.

They'er like the fellow
who searched for his keys

under the lamppost because
that's where the light is.

Even though he'd lost them
somewhere else.

I'm not going to say a word

about the history of theories
of 19th-century warefare.

I will tell you
all about

The beautiful theories
of james clerk maxwell.

Elegant mathematical thories

wern't the only things
of beauty

with which james clerk maxwell
surrounded himself.

There were his precious books.
Of course,

and outside
his well-appointed study

were the rolling wills
of glenlair.

The maxwell family estate.

Two days' journey
from edineurgh.

Every morning,
even nearer to his hert.

There was katherine. 

Good morning,
James.

you're a bonny lass.
You brought my tea?

They'd met in aberdeen,

at marischal college, where
he'd begun teachig in 1856.

Two years later,

James wrote his aunt cry,

"This comes to tell you
that I am going to have a wife."

He predicted a new bride

"Certainly won't
stop mathematics."

Characteristic of maxwell's
scientific predictions,

this one 
proved accurate indeed.

Of course,
maxwell was'nt the first

to make accurate predictions.

About the deep mysteries
of natural forces.

Two centuries earlier,

Isaac Newton had written
a book on the subject.

But he'd had to
express himself

in terms of
"Action at a distance."

That idea would come
to be applied

not only to gravity, 

but also to electricity
and to magnetism.

And then, in the 1830s,

on the heels of the frenchmen
couloumb and ampere 

and especially on the trail 
of hans christian oersted,

along came michael faraday.

He'd been increasingly drawn

toward electricity 
and nagnetism,

and by August of 1831,
his path was reasonably clear.

Pick up
where oersted left off,

faraday confirmed
that an electric current

can produce
a magnetic field,

and then,
going far beyond,

faraday demonstrated
that a changing magnetic flux

can create 
an electric current...

And that a chenging
electric current in one crcuit

can induce current
to flow in another.

Is this 
the right book,
james?

Right.
The faraday book.

Thereafter, especially
in light of similar discoverries

by America's joseph henry,

the principle of induction

in the nature
of electricity and magnetism

was there for
the scientific world to behold,

and certainly
within the maxwell house,

fraday's experimental
researches in electricity

was considered
the definitive text.

But by the time
he got hold of faraday's work,

maxwell was ready
to draw new conclusions,

an ability 
which he developed early on.

As a student at cambridge,

maxwell's mathematics
teacher observed,

"It appears impossible
for him to think incorrectly

on physical subjects."

Soon after that,

as a graduate student.

He wrote a paper

that gave the scientific
community reason to agree.

It was called
on faraday's lines of force,

and in preparation
for that work,

James clerk maxwell
had done his homework.

In the spring of 1846,

michael faraday 
had penned a paper

called
thoughts on ray vibrations.

In that prophetic
publication,

he speculated that light
is a type of vibration

in the lines of force.

"The lines of force,"
He wrote,

"Are known 
to connect particles

and also masses
of matter together."

In other words,
in faraday's imagination,

electric charges
were linked together

by lines of force
in empty space.

However,
even though his idea

was easy to see
in the mind's eye,

it introduced an intriguing
scientific question--

would a vibrating charge

set the lines of force
into vibration?

At this point,

faraday might have pictured
each line behaving

as if it were a linked row
of mechanical oscillators.

And in that case,

he would've seen a disturbance
propagate along the row,

either as a longitudinal wave

or as a transverse wave.

No matter how they might have
taken shape in his mind,

the singnificance
of those vibrations

was in the fact
that faraday had seen them.

And somewhere 
between the lines

of michael faraday's
thoughts on ray vibrations,

james clerk maxwell
would discover

his electromagnetic
theory of light.

However,
before he could read

faraday's handwriting
on the well,

to refine and polish it
with his elegant mathematics,

maxwell needed to decipher
a crucial clue.

Within the forces
of electricity and magnetism,

he found 
a very significant speed.

Any wave
has a definite speed,

depending on
what makes it go.

For example, in deep water,

the speed of waves depends
on the acceleration of gravity

and the length
of the wave.

In air,
the speed of sound

depends on the air pressure

as well as the density
of the medium.

And for linked oscillators,

the speed is given
by the spring constant,

the mass,

and the distance
between oscillators.

So it was time for maxwell
to get down to determining

the speed of waves
in faraday's lines of force.

From maxwell's
mathmatical perspective,

faraday's lines
ware an expression

of the 1/6-squared nature

of the forces of gravity,

of electricity,

and of magnetism.

At the same time,

each of those

has a specific constant.

In the right scientific hands,

those facts got around to this--

since the fundamental forces

of electricity and magnetism
aren't independent,

the electricconstant,
k sub p,

and the magnetic

constant, k sub m,

should be related,

but the quetion is how.

The ratio,
k sub p divided by k sub m,

has the units meters-squared
over seconds-squared.

In other words,
the square of a speed,

but what speed?

Its square is

9times
10 to the 16th meters-squared
per second-squared.

Divide the electric constant
by the magnetic constant.

And there it is,
the speed of light.

Itwas an amazing discovery.

After so years

of the closest scientific
scrutiny elsewhere,

james clerk maxwell
saw the light

and found its speed

in the forces
of electricity and magnetism.

But the fundamental forces

weren't all that occupied
maxwell's mind.

Around 1857,
an academic prize was offered

to anyone who could explain
the solid nature

of the rings of saturn

and their steady movement
around the planet.

Maxwell's answer
was right on the mark.

The only structure that could
account for such stability,

maxwell wrote,

was one made up of clusters
of disconnected particles.

Maxwell's essay not only 
won the cambridge prize,

it won the praise

of the scientific community
at large.

Sir george airy,
britain's royal astronomer,

called it a most remarkable
application of mathematics.

Perhaps because one good turn
deserves another,

maxwell immediately
set his sights

on moving particles other
than those of saturn's rings.

He developed



 





 a kinetic theory of gases
in which gas molecules
are smoll, elestic particles

that collide
witi one another

maxwell believe
all physics research

should advance on,
in his words,

"strict mechanical principles."

that belief led not only
to maxwell's theory of gases,

it led to his
great accomplishments

in electricity
and magnetism.

to pursue his research,

the maxwells moved
to kensington, lndon, in 1860.

for fibe years
at king's college,

he was productive

inkinetic theory
and electricity alike.

and here at london's
royal institution,

maxwell finally
met faraday.

faraday, remember,
had seen electricity


in mechanical terms,

not merely as an idea

in keeping with newton's
"action at a distance,"

but as a thing
of physical lines,

a solid structure of force
that radiated through space.

maxwell would state
with great admiration

that faraday
had seen a medium

where the strict newtonians
saw nothing but distance.

perceptively,
maxwell added,

"faraday sought the seat 
of the phenomena

in real actions
going on in the medium."

of course,
as it would later be seen,

the medium
is the electromagnetic field,

and that's where
the action really is,

but before maxwell could get 
the message from the medium,

he fad to determine
whether waves could travel,

through the electric
and megnetic fields


at the speed of light.

if so,
they would have to obey

the four laws 
of electricity and magnetism,


the electric flux
through any closed surface

is equal to 4 pi k sub e
times 

or \/epsilon-0,

where \ is the total charge
enclosed 8Y the surface.

and the magnetic flux
through anyclosed surface

is always equal to 0.

these are gauss' laws
for electricity and magnetism.

the circulation
of magnetic field

around any closed path

is equal to mu-0

times the electric current
passing through that path.

this is ampere's law.

the circulation 
of electric field

around any closed path

is equal to minus the rate
of change of magnetic flux


through that path.

this is faraday's law
of electromagnetic induction.

so suppose
that there can be a wave

in the intensity 
of the electric field.

this one's
a transverse plane wave,

and it travels, of course,
at the speed of light,

but consider the field
at any one instant.

since it's up
in one region

and down in the next,

it has a circulation 
about this path.

according to faraday's law,

that means that there 
must be magnetic flux

through that same path,

and furthermore,

that it must be 
changing in time.

and that can only
mean one thing--

amagnetic wavemust tag along
with the electric wave

everywhere it goes.


but--and here's
the crux of the problem--

that in turn means,
at any instant,

there's a circulation 
of the magnetic field

about this path.

and according
to ampere's law,

that can only be true

if there's current
flowing through it.

but in empty space,

there's no matter
and no electric currents,

so there's no way 
around the fact

that according to the laws 
of electricity and magnetism

in maxwell's time,

there could be absoolutely no
electromagnetic waves in space.

the point was this--

if the laws 
of physics stated

that waves couldn't exist
in empty space,

could it have been that
as fundamental as they were,

those laws
were somehow incomplete?

maxwell's task
was to examine

the fundamental laws
of his era,

and his triumph
was to find the missing piece,

and he did so,
by looking into 

a simple and altogether
conventional apparetus,

the capacitor.

the magnetic circulation
around any path

depends on the electric current
linked through the path.

the only way to be sure

that the current
goes through the path

is to imagine a membrane
bounded dy the path.

then the same current must
pass through the membrane

no matter what shape
the membrane takes.

but that's no longer true

if the current flows
into a capacitor.

then, even though 
current is flowing,

there may be none
through the membrene.

if so, what is the magnetic


circulation equal to?

seeking an answer
to that question,

maxwell took a page 
from faraday's book--

changing magnetic flux 
creates electric circulation--

and then, as usual,

he looked at things
the other way around.

coudo changing electric fulx,
he wondered,

create magnetic circulation?

the answer promised to solve
the capacitor problem.

as current flows
into the capacitor,

charge 3uilds up,

which creates 
an increasing elelctric field

between the plates.

the electric flux
through the membrane

can be deduced
from gauss' law

by imagining
a closed surface.

all the flux goes through 
the dome-shaped membrane,

and it's equal to the charge
on the capacitor plate


over epsilon-0.

the rate of change
of electric flux

can be found 
by differentiating

bogh sides
of the equation.

it's given simply

by the current
flowing in the wire.

in other words,

epsilon-0 times 
the rate of change

of electric flux through
the dome-shaped membrane

is the same
as the electric current

through the flat membrane.

this was maxwell's
crucial discovery--

the precise manner in which
changing electric flux

can generate
a magnetic field

as if it were
a kind of electric current.

in fact, maxwell himself
called this mathematical term

the displacement current.

in other words,
the magnetic circulation


around a closed path 
is given

not only by the electric current 
through it,

but also by the rate 
of change

of electric flux
through it.

this was how 
james clerk maxwell

completed the laws
of electricty and magnetism.

and with these laws,
maxwell could show

that electromagnetic waves of
every frequency and wavelength

would propagath
through empty space

at the speed og light.

maxwell's discovery,

which seemed purely theoretical
at the time,

would lead
to the sights and sounds

of the 20th century,

radiating through space
not only as visible light,

but also as radio waves,
microwaves,


and the entire
electromagenetic spectrum.

it was a discovery

that would lead 
far beyond the earth

into the deepest reaches
of space,

where a wave in the intensity
of the electric field

implies the existence
of a changing magnetic flux.

that means a wave 
in the magneticfield,

and that's made possible 
by changing electric flux,

and it's made clear
only because maxwell understood

that electric and magnetic
fields create each other

if they move in wave together 
at the speed of light.

and so it goes,
in lock step through eternity,

bogh fields propageting
throughout the universe.

and in that light,

always at the speed 
of light,

one can finally see

the power
and the glory


of maxwee's
equations.

just as newtion was born 
the year galileo died,

maxwell was born in 1831,

the year faraday discovered
electromagnetic in duction,

and he died in 1879,

the year
of albert einstein's birth.

what could be wore fitting?

for between newton
and einstein,

no men in scientific history
made a deeper mark.

maxwell went ahead 
to refine and redefine 

the fundamental laws
of nature,

and in the process,

tobuild a bridge
to modern physics.

the fact is
that maxwell was endowed

with one 
of the finest minds

that the human race produced
during the 19th century.

that, combined
with his cambeidge eucation,


enabled him
to do anything he wanted to.

i haven't told you 
about his sense of humor,

although once i read to you 
one of his comic verses.

the poem is in this book.

which is very old
and rare and valuable.

i don't want to handle it,

so i'll tear out some pages 

so that i can 
read it to you.

this is a homework poblem.

"an inextensible heavy chain 
lien on a horizontal plane.

"an impuleive force
is applied at a,

required,
the initial motion at k."

there's a chain 
lying on a table,

and somebody


jerks it at one end.

the question is, how does 
the other end of the chain 

begin to move?

that is typical 
of the kind of difficult

and utterly useless problem

that cambridge students have
traditionally been trained on.

having set out 
the problem,

he shows how to solve it 
in great detail.

i'd like you 
to go home tonight

and work out 
youe homework problems in verse

and bring them 
back with you

when you come here
next time.

captioning is mode possible by
the national captioning 
institute, inc.

captions copyright 1987
california institute
of technology,

the corporation for 
community college television,
the anninberg/cpb project

publicperformance of captions 
prohibited without permission of


national captioning institute 

fundeing for this progrem 
was provided by 

the mechanical universe
is a college course

with textbooks published
by cambridge university press.

for more informetion 
about the course,

video cassettes,
off^air videotaping,

and books based 
on the series, call...

end of file*****