I was glancing through a book that arrived for me today and the very
first illustration facing page 36 was an archaeopteryx.

TRUE!

Now here's a chance for some Researcher/Commenter to shine:

Which book is it?

Unfortunately amazon.com does not have a ?search inside? feature for
this book, so I cannot check it, but The Neck of the Giraffe by
Francis Hitching has one on page 36. Trouble is, you said "facing page
36".
answerfinder-ga

Good try, AF ...

But neither Amazon.com nor Amazon.co.uk even have the book which has
been out-of-print for ages!

Although they do have several other 'used' books by the same author.

CLUE: The author also wrote two tame 'thrillers' both of which are very rare.

I've got a copy of one but I have been unable to find tother except in
The British Library.

Does ABE have a copy?

Is the author English?

Hey, Mike, What sort of questions are those?

Are you trying to usurp the REAL Researchers?

Please see: 

http://answers.google.com/answers/threadview?id=432712

How about an edition of "The Lost World" by Sir Arthur Conan Doyle?

Archae0pteryx

Sorry Tryx but 'No' it wasn't in any of the Sherlock Holmes books
although the writer was a real life detective of sorts.

Oops ... I think I've said too much already!

Bryan, I'm surprised at you!  "The Lost World" is not a Sherlock
Holmes book.  It is a story of discovering a surviving land of
prehistoric creatures on an isolated plateau somewhere in, I think,
South America.  I read the book in my own ancient times and don't
remember that particular detail.  I thought you might have found an
illustrated edition.  "Page opposite" suggests a tipped-in plate of
the sort we rarely see anymore but that used to be found in fictional
works.

Tryx

Yeah, Tryx, but that's the OTHER Sir Arthur Conan Doyle known in the
trade variously as 'Conan the Barbarian' and 'Conan the Librarian'.
There are A LOT of them around.

The archaeopteryx in the book in question appears as a monochrome photograph.

I am not going to try to describe it because even I cannot do it justice.

However, it's climbing a tree looking for all the world like a winged
crocodile ... Would this be the same archaeopteryx that Conan the
Barbarian wrote about?

On second thoughts, it may be a fictional beastie concocted by
Pinkfreud using her Photoshop box of tricks.

You just can't believe anything these days, can you?

Is it a book by a paleontologist?