After reading the gearbox oil thread, I was wondering about the numbers used to indicate engine oil viscosity. What does 15W/40 or 20W/50 etc. actually mean?

WELL, WKIPEDIA SAYS:

" ...Grades

The Society of Automotive Engineers, usually abbreviated as SAE, has established a numerical code system for grading motor oils according to their kinematic viscosity. SAE viscosity gradings include the following: 0, 5, 10, 15, 20, 25, 30, 40, 50 or 60. Some of the numbers can be suffixed with the letter W, designating their "winter" or cold-start viscosity, at lower temperature.
Viscosity is graded by measuring the time it takes for a standard amount of oil to flow through a standard orifice, at standard temperature. The longer it takes, the higher the viscosity, and thus higher SAE code.

Note that the SAE operate a separate viscosity rating system for transmission oils which should not be confused with engine oil viscosity. The higher numbers of a transmission oil (eg 75W-140) do not mean that it is necessarily higher viscosity than an engine oil...."

so what do we put in our cars ,,,,
  i bought some asda semi synthetic 10w40 ?12.99 for 5lts as it last a while and doesn't brake down  but i've seen this gtx high millage 15w40 which says it conditions  hardenend seals
 http://cgi.ebay.co.uk/CASTROL-GTX-HIGH-MILEAGE-15W-40-4LITRE-ENGINE-OIL_W0QQitemZ270531853760QQcmdZViewItemQQptZUK_CarsParts_Vehicles_CarParts_SM?hash=item3efcf47dc0