French thought he had something that might help here. He rose, crossed the room, and after searching in his letter file, produced three or four papers. These were hotel bills he had incurred in France and Switzerland when he visited those countries in search of the murderer of Charles Gething of the firm of Duke & Peabody, and he had brought them home with him in the hope that some day he might return as a holiday-maker to these same hotels. Now perhaps they would be of use in another way.

He spread them out and examined their receipt stamps. From their analogy the . . . uit on his fragment obviously stood for the words “Pour acquit,” anglice: “paid.” The middle line ending in . . . lon was unquestionably the name of the hotel, and the third, ending in S, that of its town. And here again was a suggestion as to the size of the establishment. A street was not included in the address. It must therefore be well known in its town.

It seemed to him moreover that this fact also conveyed a suggestion as to the size of the town. If the latter were Paris or Brussels—as he had thought not unlikely as both these names ended in s—a street address would almost certainly have been given. The names of the hotel and town alone pointed to a town of the same standing as the hotel itself—a large town to have so important an hotel, but not a capital city. In other words, there was a certain probability the hotel was situated in a large town comparatively near the English Channel, Paris and Brussels being excepted.

As French sat pondering over the affair, he saw suddenly that further information was obtainable from the fact that the lettering on a rubber stamp is always done symmetrically. Once more rising, he found a small piece of tracing paper, and placing this over the mutilated receipt stamp, he began to print in the missing letters of the first line. His printing was not very good, but he did not mind that. All he wanted was to get the spacing of the letters correct, and to this end he took a lot of trouble. He searched through the advertisements in several papers until he found some type of the same kind as that of the . . . uit, and by carefully measuring the other letters he at last satisfied himself as to just where the P of Pour acquit would stand. This, he hoped, would give him the number of letters in the names of both the hotel and the town. Drawing a line down at right angles to the t of acquit, he found that the n of . . . lon projected slightly over a quarter inch farther along, while the S of the town was almost directly beneath. By drawing another line down from the P of Pour, and measuring these same distances from it, he found the lengths of the names of hotel and town, and by further careful examination and spacing of type, he reached definite conclusions. The name of the hotel, including the word hotel, contained from eighteen to twenty letters and that of the town six, more or less according to whether letters like I or W predominated.

He was pleased with his progress. Starting from nothing he had evolved the conception of an important hotel—the something-lon, in a large town situated in France or Belgium, and comparatively near the English Channel, the name of the town consisting of five, six, or seven letters of which the last one was S. Surely, he thought, such an hotel would not be hard to find.

If he was correct as to the size of the town, it was one which would be marked on a fairly small scale map, and taking his atlas, he began to make a list of all those which seemed to meet the case. He soon saw there were a number—Calais, Amiens, Beauvais, Étaples, Arras, Soissons, Troyes, Ypres, Bruges, Roulers, and Malines.

He had by this time become so excited over his quest that in spite of the hour—it was long past his bedtime—he telephoned to the Yard to send him Baedeker’s Guides to Northern France and Belgium, and when these came he began eagerly looking up the hotels in each of the towns on his list. For a considerable time he worked on without result, then suddenly he laughed from sheer delight.

He had reached Bruges, and there, third on the list, was “Grand Hôtel du Sablon!” Moreover, this name exactly filled the required space.

“Got it in one,” he chuckled, feeling immensely pleased with himself.

But French, if sometimes an enthusiastic optimist and again a down and out pessimist, was at all times thorough. He did not stop at Bruges. He worked all the way through the list, and it was not until he had satisfied himself that no other hotel fulfilling the conditions existed in any of the other towns, that he felt himself satisfied. It was true there was an Hotel du Carillon in Malines, but this name was obviously too short for the space.