The series is only part of the rolling diameter. it combined with the width determines the rolling diameter. series is how tall the sidewall is in percentage compaired to the width.
Tyres are labeled www/hh/rr lls
Where www is the overall width of the tyre in mm
hh is the height of the side wall from the rim to the outermost point and is expressed as a ratio of the width (see twilightproteges post)
rr the total diamater of the rim in inches (some BMW use mm but they are rare and obvious), multipy by 25.4 to convert to mm
ll is the load rating, the higher the number the higher the load rating
s is the speed rating, a letter, the closer to 'Z' the higher the speed rating
So the diamater of the standard BA 1.8 185/65/14 is 65% of 185 = 120.25mm top and bottom of the rim = 240.5mm plus the 14" rim (355.6mm).
Total 596.1mm
BA alloy option 195/55/15 is 55% of 195 = 107.25mm top and bottom of the rim = 214.5mm plus the 15" rim (381mm).
Total 595.5mm
Use this to calculate your original diamater then you can make variations to plan
http://www.miata.net/garage/tirecalc.html
and calculate the offset you need here
http://www.1010tires.com/WheelOffsetCalculator.asp
Or this one which does both:
http://www.rims-n-tires.com/rt_specs.jsp