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The Barometer: Josephus

It is reported that Josephus, the author of the Jewish History, escaped the danger of death by means of this problem; for being governor of Joppa, at the time that it was taken by Vespasian, he was obliged to secrete himself with thirty or forty of his soldiers in a cave, where they made a firm resolution to perish by famine rather than fall into the hands of the conqueror; but being at length driven to great distress, they would have destroyed each other for sustenance, had not Josephus persuaded them to die by lot, which he so ordered, that all of them were killed except himself and another, when he might easily destroy, or persuade to yield to the Romans. Three Persons having each chosen, privately, one out of three Things, to tell them which they have chosen.

Let the three things, for instance, be a ring, a guinea, and a shilling, and let them be known privately to yourself by the vowels a, e, i, of which the first, a, signifies one, the second, e, two, and the third, i, three.

Then take 24 counters, and give the first person 1, which signifies a, the second 2, which represents e, and the third 3, which stands for i: then, leavingthe other counters upon the table, retire into another room, and bid him who has the ring take as many counters from the table as you gave him; he that has the guinea, twice as many, and he that has the shilling four times as many.

This being done, consider to whom you gave one counter, to whom two, and to whom three; and as there were only twenty-four counters at first, there must necessarily remain either 1, 2, 3, 5, 6, or 7, on the table, or otherwise they must have failed in observing the directions you gave them. But if either of these numbers remain, as they ought, the question may be resolved by retaining in your memory the six following words :- Salve certa 1 2 anima semita vita 3 5 6. quies. 7 As, for instance, suppose the number that remained was 5 then the word belonging to it is semita; and as the vowels in the first two syllables of this word are e and i, it shews, according to the former directions, that he to whom you gave two counters has the ring; he to whom you gave three coun ters, the gold; and the other person, of course, the silver, it being the second vowel which represents 2, and the third which represents 3.

How to part an Eight Gallon Bottle of Wine equally between two Persons, using only two other Bottles, one of Five Gallons. and the other of Three.

This question is usually proposed in the following manner: A certain person having an eight-gallon bottle filled with ex cellent wine, is desirous of making a present of half of it tu one of his friends; but as he has nothing to measure it out with, but two other bottles, one of which contains five gallons, and the other three, it is required to find how this may be accomplished?

In order to answer the question, let the eight-gallon bottle be called A, the five-gallon bottle B, and the three-gallon bottle C; then, if the liquor be poured out of one bottle into another, according to the manner denoted in either of the two following examples, the proposed conditions will be answered. 8 5 3 8 5 3 A B C A B C 8 0 0 8 0 0 3 5 0 5 0 3 3 2 3 5 3 0 6 2 0 2 3 3 6 0 2 2 5 ] 114 1 5 2 7 0 1 4 3 4 0 4 7 1 0 ] 3 3 A Quantity of Eggs being broken, to find how many there were without remembering the Number.

An old woman, carrying eggs to market in a basket, met an unruly fellow, who broke them. Being taken before a magistrate, he was ordered to pay for them, provided the woman could tell how many she had; but she could only remember, that in counting them into the basket by twos, by threes, by fours, by fives, and by sixes, there always remained one; but in counting them in by sevens, there were none remaining. Now, in this case, how was the number to be ascertained?

This is the same thing as to find a number, which being divided by 2, 3, 4, 5, and 6, there shall remain 1, but being divided by 7 there shall remain nothing; and the least number, which will answer the conditions of the question, is found to be 301, which was therefore the number of eggs the old woman had in her basket.