Bayliss, Thomas cross frame safety bicycle

This beautifully lined Bayliss, Thomas cross frame safety dates around 1888-1890 and is in the collection of the Velorama museum, alhough it is not exposed for public at the moment.

It is a very characteristic bike, which has a lot of details in common with the famous 'open head' Bayliss, Thomas ordinaries. Look here, and you will see that the twin frame tubes really look like the fornt fork of the older bicycles. No other firms made safety bicycles with this construction.

I do not know much about the history of this model, so if anyone can help me out on this?