first, welcome to the forum. I'm sure you will find lots of help rebuilding your Ariel.
BP frames seem to run over a couple of years - 46 to 48, and 350 through to 600's. I'm not sure where #2959 sits.
To get the machine dated you may need to join the AOMCC. This is a free service for members and you get all of the info that is in the original factory records. Engine / Frame no's. colour / extra's etc. There are heaps of other advantages in being a club member - including club spares (for the oil tank?) and pretty substantial web resources - parts books, brochures manuals and so on. Also a great magazine, insurance deals, rallies and branches. There is a section of the forum that you currently can't see. If you have been away from Ariels for a while, it might be a good investment. http://www.arielownersmcc.co.uk/joining.html
'51,'56 Squares, '48 VH, '27 Model C, R67/2, Mk IV Le Mans, '06 Super Duke and Ariel projects.