The first synthetic rubber products where made as early as 1909. This episode is set after World War I.
The "secret" formula is written backwards and missing several components, but appears to be the dehydrogenation of butane into 1,3-butadiene. Butadiene is a rubber like substance produced shortly after WW2. It ended up being too soft to replace most rubber products.
Nathan Page and Tim Draxl also starred on stage in a production of A Midsummer Night's Dream at the Belvoir Theatre in Sydney, Australia