Hi again, still would like a yes/no the Arthur aged 6 in 1901 is yours or not, but this is a possible Arthur Betteridge serving in the Boer War ie 1899/1902:-
A Betteridge Soldier No: 4419 The Princess of Wales Own (Yorkshire Regiment) Unit 3
Casualties injured on 31st January 1902 at Nr Burgherdorp Unit 3 The Princess of Wales Own (Yorkshire Regiment.
Source South African Field Force J B Hayward & Sons
Notes Railway Accident
So the reason he is possibly not on the 1901 Census.
Keyboard86