The difference between repeatable and non-repeatable substitutions can be indicated by the use of raised numbers. We can write 'N ¹ Nn = N ²' to indicate that 'N Nn' (which equals 'N ²' not 'N ¹') cannot be substituted for the 'N' of 'N Nn' itself, so that we cannot derive 'N Nn Nn = N': i.e. 'boyhood' is 'N ²' and therefore cannot be substituted for the 'N ¹' of 'N ¹ + -hood' to yield 'boyhood-hood'. In contrast, 'AN ¹ = N ¹' states that whenever we see 'N ¹' we can write 'AN ¹' in its place, and this permits us to replace even the 'N ¹' of 'AN ¹' itself by 'AN ¹', thus yielding 'A AN ¹ = N ¹'. The general method of assigning these raised numbers is as follows: We assign raised to each class symbol, say, 'N', when it first occurs in an equation. Next time the class 'N' occurs, in a new equation, we check to see if the equivalents of 'N' as stated in this new equation are substitutable for the previous 'N ¹'. If they are substitutable, we mark the new 'N' as 'N ¹'; if they are not we mark the new 'N' as 'N ²'. This checking is carried out for the 'N' of each new equation. Each time we test to see if the equivalent of the new 'N' is substitutable for all preceding 'N ¹', or for all preceding 'N ²'. If it is substitutable only for the 'N ²', we mark it as such. If in some equation (including the new equation itself, if it conyains more than one 'N'), the new 'N' is not substitutable for either 'N ¹' or 'N ²', we mark it as 'N ³'; and so on. In this way 'N ² –s = N ³': 'boys' or 'boyhoods' replace 'boy' in 'Such is the story of their —'. Note that we cannot write 'N ² –s = N ²' since that would permit boys to be equal to 'N ²' and so to replace 'N ²' before '–s', yielding 'boys + -s'.
- Harris (1951), a pag.265