The hearth tax is no carbon tax.  It is not a levy on pollution.
Besides the tax existed in Byzantium as Kapnikon (from gr. kapnos=smoke).
It is mentioned in AM ANdreades History of the Bank of England where he
compares the Byzantine tax and the British hearth-money

http://books.google.com/books?id=cSy8chSFZ50C&pg=PA55&lpg=PA55&dq=kapnikon&source=bl&ots=q2ggyUhjE6&sig=gbmd-4n5qM6MCSkroGD0YgRwZ44&hl=en&ei=qNWKSuCnBoP0_Aa7tLSSCg&sa=X&oi=book_result&ct=result&resnum=1#v=onepage&q=kapnikon&f=false

For a more complete treatment of kapnikon see
Nicolas Oikonomides | The Role of the Byzantine State in the Economy in
Angeliki E. Laiou (Editor-in-Chief) THE ECONOMIC HISTORY OF BYZANTIUM:
 From the Seventh through the Fifteenth Century.

http://www.doaks.org/publications/doaks_online_publications/EconHist/EHB44.pdf


Nicholas Theocarakis