Page:Magic oracle, or, Conjuror's guide.pdf/20

 II. Let it be proposed to throw the same point 6 with two dice.

To analyze this case, we must first observe that two dice give 36 different combinations, for each of the faces of the die A, for example, may be combined with each of those of the die B, which will produce 36 combinations. But 6 may be thrown first 3, and 3; second by 2, with the die A, and 4 with the die B, which, as may be readily seen, forms two distinct cases; third, by 1 with the die A, and 5 with the die B, or 1 with B and 5 with A, which also gives two cases; and these are all which are possible. Hence there are five favourable chances in 36; consequently, the probability of throwing six with two dies, is 5-36, and that of not throwing it is 31-36. This therefore ought to be the ratio of the stakes or money deposited by the players. But analyzing the other cases, it will be found that of throwing two with two dice, there is one chance in 36; of throwing 3, there are two; of throwing 4, three; of throwing 5, four; of throwing 6, 5; of throwing 7, six; of throwing 8, five; of throwing 9, four; of throwing 12, three. If three dice were proposed, with which it is evident the lowest point would be three, and the highest eighteen, it will be found, by a similar analysis, that in 216, the whole number of the throws possible with three dice, there is one chance of throwing 3; three of throwing 4; six of throwing 5, &c.

Put thirty grains of phosphorus into a Florence flask, with three or four ounces of water. Place the vessel over a lamp, and give it a boiling heat. Balls of fire will soon be seen to issue from the water, after the manner of an artificial fire-work, attended with the most beautiful coruscations.

Pour a small quantity of clear water into a glass, and put a piece or two of phosphoret of lime into it. In a few seconds flashes of fire will dart from the surface of the water, and end in curls of smoke rising in regular succession.

Fix a small piece of solid phosphorus in a quill, and write with it upon paper; if the paper be then placed in a dark room, the writing will appear beautifully luminous.