I found his book (on Sp. Rel.) on the internet at this page

Appendix 1. Simple Derivation of the Lorentz Transformation. Einstein, Albert. 1920. Relativity: The Special and General Theory

Over a period of days, weeks I have more or less come to terms with it but there is a little piece that is puzzling me still.

I should start by posting the two equations(5) he refers to a little earlier

So start quote

We should thus have the solution of our problem, if the constants a and b were known. These result from the following discussion. 5For the origin of k'we have permanentlyx'= 0, and hence according to the first of the equations (5)

If we callv the velocity with which the origin ofk' is moving relative toK, we then have

This is the point where I puzzle over -coming up

The same value vcan be obtained from equation (5), if we calculate the velocity of another point ofk'relative toK,or the velocity (directed towards the negativex-axis) of a point ofKwith respect toK'.In short, we can designate v as the relative velocity of the two systems.8Furthermore, the principle of relativity teaches us that, as judged from K,the length of a unit measuring-rod which is at rest with reference tok'must be exactly the same as the length, as judged fromK',of a unit measuring-rod which is at rest relative toK.In order to see how the points of thex'-axis appear as viewed fromK,we only require to take a “snapshot” ofk'fromK;this means that we have to insert a particular value oft(time ofK), e.g.t= 0. For this value oftwe then obtain from the first of the equations (5)

x'=ax.Two points of the

x'-axis which are separated by the distancex'=1 when measured in thek' system are thus separated in our instantaneous photograph by the distance

But if the snapshot be taken fromK'(t' = 0), and if we eliminatet from the equations (5), taking into account the expression (6), we obtain

From this we conclude that two points on thex-axis and separated by the distance 1 (relative toK) will be represented on our snapshot by the distance

But from what has been said, the two snapshots must be identical; hencex in (7) must be equal tox' in (7a), so that we obtain

OK I do follow his logic but I am not quite clear why we cant just usex'=ax. andto solve for "x".

I do see that this will not give the correct answer and "(a^-1)xprime=xprime*(a(1-v^2/c^2))^-1) just gives me a = a(1-v^2/c^2)

Am I just going down a wild goose chase path or is my mathematics also faulty?

As an aside , this relationship between x and xprime does it arise in other circumstances (in mathematics or physics)?

I mean can you find other pairs of functions where one functions "view" of the other is practically a mirror image of the other's although they are not inverse functions?

I hope I made some sense (it was difficult for me to copy out the equations in my browser)