Confusing the hell out of the White Notation

The White Notation is a means of describing different types of engine but I've been exploring some more of A E Durrant's works on obscure steam railway engines and found a very curious pair that defy classification according to their wheel arrangement. Wheel arranging sounds suspiciously like flower arranging to me but is really a very serious business involving weight restrictions, chassis flexibility and maximising adhesion. Most engines can be classified very simply and the White system quickly allows an impression of the engine to be formed, whether it's a humble 0-4-0T or an express 4-6-2. The French, being the French, had to be different and used their own system that counted only the wheels you could see from one side, so a 4-6-2 became a 231 - perfectly logical but determinedly different. However, neither system copes perfectly with some engines. Look closely between the middle and trailing driving wheels and you'll see an extra pair of carrying wheels...