How would it be if this difficulty had been already overcome, and the intermediary language already created and proved to be serviceable? "But that would amount to adding a new language to be learnt to the ones we already have to learn; there would be no advantage in that!" If, however, this "new" language was really not "new," consisting mostly of words known to every educated person; if its grammar was so simple that its principles could be learned within an hour; and if, therefore, any educated person who knew a single Romance language could learn the whole language in an incredibly short time, would it not be an advantage to acquire it? To prove this is a simple problem of permutations and combinations, and the proof possesses all the certainty of mathematical reasoning. We shall demonstrate that by an example. Suppose a large town contains ten districts, each possessing a pneumatic post-office. In order to connect each district with all the others, one could lay from each of the ten post-offices nine tubes to the remaining nine post-offices. That would require (10 × 9)/2 = 45 tubes. The problem could, however, be solved much more easily and cheaply by connecting each of the post-offices by means of a single tube with a central post-office, which would receive and distribute all the letters, as is actually the case in practice. We should then require only ten tubes. Substitute now for the districts imagined above the languages, German, French, English, Italian, Russian, Spanish, etc., with the condition that every person speaking one language should be able to correspond with everybody speaking a different language. In the case of ten languages we should require for every correspondent nine dictionaries, or altogether ninety dictionaries. Every correspondent would have to know nine languages besides his own. If, however, we employed an intermediary language, each person would only require to know this language besides his own. The matter is so simple and the advantage so exceedingly obvious that one can only wonder why it has not been recognised and carried out long ago.