"Is used to measure the number of perforations to the inch," Trenholm spoke slowly, to be sure that she understood his meaning. "By applying a perforation gauge to the edge of a stamp, if the position of one perforation is known, that of all the others will be indicated." Trenholm paused and opened one of the stamp albums. He turned the pages rapidly, and found the stamp he wanted, but no gauge. Taking up the other album he shook it over the table. A small shower of loose stamps, several odd envelopes and a piece of bristol board fell on the table. With a relieved exclamation, Trenholm clutched the perforation gauge, brushing the stamps aside. "Here is a Canadian stamp of the same issue," he said. "Paul wrote me when he was last in Canada, and I kept the stamp. Let's see--" Miriam waited with absorbed attention while he applied the gauge to the stamp. When he looked up his eyes were shining. "The stamp has exactly fifty-two perforations," he announced. "Can it be a coincidence or a--" "A what?" He looked at her without speaking for a moment. "The number is just twice that of the letters of the alphabet." Trenholm drew in his breath. "I have come to your way of thinking, Miss Ward. It must be a code, and it may be that two alphabets are registered on each stamp, the cuts corresponding to the letters according to the number of the particular perforation affected, counting from one corner of the stamp." Miriam, who had been following his explanation with close attention, nodded her head wisely. "I see," she broke in. "That would explain any irregularity in the cuts, because for coding it would be sufficient to indicate the perforation intended to be cut, without making a mark of a definite character, and with this gauge of yours the number of the perforation which has been cut would be recognized at once." "Exactly," he answered. "Without a gauge there would be great difficulty in determining the number of the perforation, because the cut might seem to create new indentations if carelessly made." Trenholm stopped and took up the envelope of the thirteenth letter and applied his gauge to the left-hand stamp, and Miriam, pencil in hand, assisted him. Trenholm counted clockwise. "Five perforations are damaged," he declared, "numbers 8, 20, 23, 27, 30. Now, if the code is based on a double alphabet, these would become 8, 20, 23, 1, 3, or the letters H, T, W, A, C. How are the letters to be arranged, Miss Ward?" She looked at her pad, where she had jotted down the letters as well as the figures. "There is only one vowel," she said. "It must be one word. Then why use two alphabets?" "Possibly because of the accidental chance that the stamp perforations count up to fifty-two," replied Trenholm. "It would be convenient, in case of a word with many letters, to prevent destroying the appearance of the stamp by cutting too many indentations close to one another. Have you solved the first word?" as she checked an exclamation. "Yes--'watch.'"