This website

Geoff's Great War Assessment

Under Worcestershire Regiment

http://www.hut-six.co.uk/GreatWar/index.html

lists both Francis B (Benjamin) LANSDOWN* - Private - 19950 and Arthur J LANSDOWN - Private 15941

with links the the National Archives (which you can download the records via the 'net')

Francis address: in 1914 - given as - Post Office, Lydbrook, Nr Ross