When I was a kid I had an encoder bracelet made out of copper that was similar to this but much less powerful and versatile. The rotating outer ring of the bracelet had a row of very small alphabet characters and numbers 0 through 9 as well as several special characters. It also had four rows of numbers that were all rather randomly organized something like this (partial):

a b c d e f g h i j k l m n o p q r s t u v w x y z + * 1 2 3 4 5 6 7 8 9 0 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 3 4 5 6 8 9 0 1 2 7 15 14 13 12 20 19 18 17 16 28 27 26 25 24 23 22 21 10 9 8 7 6 5 4 3 2 1 0 28 27 26 25 24 23 22 21 20 19 18 17 16 15 14 13 12 11 6 5 4 3 2 1 0 9 7 8 10 21 22 23 24 25 26 27 28 16 17 18 19 20 12 13 14 15

You could write a message using the numbers that matched up to a sequence of letters by rotating the outer part of the ring with the letters to line them up with the predetermined starting point on one of the sets of numbers. Then even if someone else got the bracelet they would have a very difficult time deciphering the message because of the large number of different number sequences and the unknown starting point as well as the directionality of the encryption. As I recall my dad looked for that bracelet for a long time and when he found it I never got it back.

Quayle's encryptor looks like it could do the very same thing only much more powerfully. The person encoding would have a prearranged starting point and direction that the person decoding would know about. The message would be encrypted and sent to the person receiving who would arrange the characters of the message according to the table and they would be able to decipher the message. Without knowing the starting point or the direction it would be extremely difficult to read the message. Quayle's encryptor could even be used diagonally and a person could use a system of direction changes to further complicate the encryption scheme.

I used Quayle's system to write a simple message. Only I know the starting point and the direction. Can you decipher it?

17 30 36 18 45 60 13 4 34 17 30 15 4 46