Hi,

I found a difficulty in reading the famous Einstein's paper "On the
electrodynamics...". He wants to study the effect of the Lorentz
transformations on the Maxwell's equations. Here are the transformations
(b=beta and V=speed of light)

t' = b(t-vx/V^2)
x' = b(x-vt)
y' = y
z' = z.

The first equation is (d means partial derivative, E = (X,Y,Z) and
B=(L,M,N))

1/V dX/dt = dN/dy - dM/dz.

and he finds

1/V dX/dt' = d/dy'(bN - bv/V Y) - d/dz'(bM + bv/V Z).


I've made the computation but I can't obtain such a result. Can someone
show me?

1/V dX/dt'
= 1/V dX/dt dt/dt' + 1/V dX/dx dx/dt'
+ 1/V dX/dy dy/dt' + 1/V dX/dz dz/dt'
= (dN/dy - dM/dz) dt/dt' + 1/V (-dY/dy - dZ/dz) dx/dt' + 0 + 0
= (dN/dy' - dM/dz') b + 1/V (-dY/dy' - dZ/dz') bv
= d/dy'( b( N - v/V Y) ) - d/dz'( b( M + v/V Z ) )

crucial steps:
dX/dx + dY/dy + dZ/dz = div(E) = 0 for empty space
and
t = b(t'+vx'/V^2)
x = b(x'+vt')
y = y'
z = z'.
so
dt/dt' = b
dx/dt' = bv
dy/dt' = 0
dz/dt' = 0
and
d/dy = d/dy'
d/dz = d/dz'

hth

Dirk Vdm