622 and 559 Rims: What Size Tires?

I'm sorry, but after fifty years of riding and repairing bikes with wheel and tire sizes of 16", 20", 24", 26", and 27", I have never taken the time to understand the metric measurements of rims. I have a rim that's a 559 X 27mm and one that is 622 X 17mm. To this old dog, they appear to be 26"...