DOC. 42 SPECIAL AND GENERAL RELATIVITY 285

TWELVE

The

Behaviour

of

Measuring-Rods

and

Clocks

in Motion

I

place a

metre-rod in the

x'-axis

of

K'

in

such

a manner

that

one

end

(the

beginning)

coincides with the

point

x'

=

0,

whilst

the

other

end (the

end of

the

rod)

coincides with

the

point

x'

=

1.

What

is

the

length

of the metre-rod

relatively

to

the

system K?

In order

to

learn

this,

we

need

only

ask where

the

beginning

of the

rod

and the end of the

rod

lie

with

respect to

K

at

a

particular

time

t

of the

system K.

By means

of the first

equation

of

the Lorentz transformation the values

of these

two points at

the time

t

=

0

can

be shown

to

be

[17]

x

=

0

(beginning

of

rod)

x(end of

rod)

1-v2/c2

the distance between

the

points

being

1-v2/c2.

But the

metre-

40