At the commencement, the first digit of any number, might be distinguished by a previous uniform continuance of the light during ten or twenty seconds, whilst the separation of each digit from the next in order might be denoted by a short pause of two or three or more seconds. Thus, if the number of a light-house were 253: after a cessation of any obscuration during ten seconds, two occultations should follow each other at intervals of about a second. A pause should then occur during three seconds, after which five occultations should occur, at intervals of one second, as before. Another pause of three seconds must then happen, and be succeeded by three other occultations occurring at intervals of one second each; after which ten seconds must elapse before the cycle thus described is repeated. These might be thus represented:— 2 hundreds. 5 tens. 3 units. 0000000000·0·000·0·0·0·0·000·0·0·0000000000 \-------------------------------/ Thus, at about every half minute the number of the lighthouse would be repeated. In this manner any number under 1,000 may be expressed in less than one minute; since the largest, 999, would require Seconds. For each digit 9, or in all 27 Two short pauses between the digits 6 One long long pause at end of the number 10 --- 43 Every light-house, therefore, would be continually repeating its own number. It would contribute still more to prevent mistakes, if the light-houses on a coast were not numbered in succession; for should any mistake be made in counting the obscurations, it would most probably be detected if the digits of the numbers of the light-houses on the same part of the coast were as different as possible. Lighthouse numbered in succession— 234 235 236 237 238 Ditto irregularly— 142 324 581 787 612 If a mistake of a single obscuration were made in the units of the number 237, and it had been counted 236, this observation might, until repeated, mislead the sailor, and induce him to suppose himself opposite the preceding light-house. On the contrary, if the irregular mode of numbering were adopted, the mistake of 786 for 787 could not mislead, because the seven in the hundreds place would point out the error. It would, however, be better to have the figure in the tens’ place also different in any two light-houses so near that a possibility of mistake is likely to occur. The general benefit which would result to all maritime nations, renders the practical application of these principles a peculiarly fit subject for a prize.