The next vertical pair is W and T, or 22 and 19, which in normal arithmetic add up to 41, which has no letter equivalent; it’s too large. But it has been many years since Waterhouse did normal arithmetic. He has retrained his mind to work in modular arithmetic—specifically, modulo 25, which means that you divide everything by 25 and consider only the remainder. 41 divided by 25 is 1 with a remainder of 16. Throw away the 1 and the 16 translates into the letter Q, which is what Waterhouse writes in the second column. In the third column, O and H give 14 + 8 = 22 which is W. In the fourth, B and O give 2 + 14 = 16 which is Q. And in the fifth, Y and P give 24 + 15 which is 39. 39 divided by 25 is 1 with a remainder of 14. Or, as Waterhouse would phrase it, 39 modulo 25 equals 14. The letter for 14 is O. So the first code group looks like