The second item on the list was Australia 6%, and referring to the Daily Mail once more, French saw that Australia 6% was the first item on the second division. This was sufficiently interesting, but when he found that the next five items, Great Western, Associated News, Aerated Bread, Barclay’s Bank, and Alliance Assurance were each the first of their respective divisions, he felt he had stumbled upon something more than a coincidence.
He reexamined the list on this new basis, only to find his conclusions verified. Apparently the person writing it had simply copied down the stocks given in some paper—probably the Daily Mail. In order to obtain variety and to make an unsuspicious-looking list, he had not simply copied them consecutively; he had taken the first out of each division. Then he had gone over the divisions again, using the second name in each case, and so on until he had obtained the whole twenty-five names that he had required. It had not been done with absolute accuracy, but there was no doubt of the general method. From this it followed that any message which the list might convey was contained in the money columns, and French accordingly transferred his attention to the latter.
The amounts extended from 16s. 7d. up to £1,039, and varied surprisingly between these extremes. There were none in the £100’s or the £600’s, but all the other hundreds were represented. Speaking broadly, there were more of the £800’s and £900’s than of the lower numbers. But he could not see where any of these facts tended.
There being no obvious line of research, he began a laborious and detailed investigation into the possibilities of substitution, that is, one of those ciphers in which a number or other sign is used to denote a letter. It was clear that single numbers were insufficient for this purpose, as in that case only ten letters of the alphabet could be used. Some combination was therefore involved, and French tried various schemes of addition to meet the case. But though he got three men to assist him in the details of his various tests, he could not find anything which gave the least suggestion of an intelligible combination.
While engaged in this manner, he noticed that so far as the pounds were concerned there were no less than three similar pairs, numbers 2 and 22, 3 and 15, and 10 and 21. He examined these pairs for some time, and then he suddenly made a discovery which seemed to show that at last he was on the right track. He had put the figures down beside each other, so:
| £ | s. | d. | |
|---|---|---|---|
| No. 2 | 568 | 5 | 0 |
| No. 22 | 568 | 2 | 3 |
when suddenly he noticed that if the shilling and pence of each item were added the result would be the same: 5 + 0 = 5; 2 + 3 = 5. Eagerly he turned to the other pairs and wrote them out similarly,
| £ | s. | d. | |
|---|---|---|---|
| No. 3 | 1,039 | 1 | 3 |
| No. 15 | 1,039 | 0 | 4 |
and,
| £ | s. | d. | |
|---|---|---|---|
| No. 10 | 748 | 3 | 9 |
| No. 21 | 748 | 5 | 7 |
Here he saw at a glance that the same thing obtained, the pounds alone, and the pence and shillings added together, making two similar pairs, and therefore presumably standing for the same word.
This discovery restored all his eager interest. It seemed definitely to prove three things, each several one of which afforded him the liveliest satisfaction. First, these combinations of figures proved that there really was some underlying scheme, and that in its turn involved the hidden message; secondly, they showed that he, French, was on the direct road towards a solution; and thirdly, they indicated a code or cipher built up of pairs of numbers, a frequent combination, embracing many well-known varieties of cryptogram.
His next step was, therefore, to rewrite the list in dual column, the pounds in front, the pence and shillings added together behind. This gave him a new jumping-off place in the following:
| 328 | 6 |
| 568 | 5 |
| 1,039 | 4 |
| 936 | 9 |
| 713 | 11, and so on. |
On this he started his three men, making them try to work out keys on squares and parallelograms, as well as in other well-established ways. Then the pounds figure proving too large for this, he tried adding the various digits of these figures together. In this way, 328 became 3 + 2 + 8 or 13, and so he compiled a second list beginning:
| 13 | 6 |
| 19 | 5 |
| 13 | 4 |
But in spite of all his own and his men’s efforts he was unable to find any clue to the key. They worked until long after the usual quitting time, and at length he had to agree to an adjournment for the night.
Next day he again attacked the problem, but it was not until well on in the afternoon that he made an advance. Tired and dispirited, he had sent for a cup of coffee to clear his brain, and after it he had, contrary to his custom, lighted his pipe, while he leaned comfortably back in his chair still turning the matter over in his mind. He was beginning to think the puzzle insoluble, when suddenly an idea flashed into his mind, and he sat up sharply, wondering if he had hit on the solution.
He had been considering numerical ciphers of which the key is some book. These consist usually of sets of three numbers, the first representing the page, the second the line on that page, and
