Thanks everyone...I think I may have a problem in the use of the term "double beat valve". From above I see that Hornblower and Woolf were involved in the steam valve development but West valve's were in the pitwork.
The sketch of the life of William West (pub 1880) states that he patended, in conjuction with Mr. Harvey, a double beat valve on the 12th June 1839. Way after the valve was developed by Woolf and Hornblower. West's valve was developed to solve a problem with the pump at the East London waterworks. Perhaps Mr West tansfered the concepts of the double beat steam valves into a pump. Or perhaps we have authors in the past misunderstanding the term.
Any ideas??