Thus in the United States the gold Eagle, of $10, is required to weigh 258 grains, of it to be pure gold, and alloy. The silver Dollar is required to weigh 412 grains, of it to be pure silver, and alloy. The Eagle then contains 258.9=232.2 gr. of pure gold; The Dollar contains 412.5X.9-371.25 gr. of pure silver; 232.2 gr. of gold are equal in value to 3712.5 gr. of silver. 3712.5 — 232.2 = 15.988'. The value of gold in the United States is therefore 15.988' times that of the same weight of silver; in other words their relative values are as 15.988 to 1. The relative values of Gold and Silver are not the same in all countries. In the U. S. these values are as 15.988' to 1; in England, as 14.28 to 1; These differences in the relative values of Gold and Silver in different countries, will cause the one or the other of these metals to be employed in the payment of foreign debts-when the circumstances of trade require the transmission of money -according as the one or the other will be increased in value in the country to which it is sent. Thus in England, France, or China, silver is, relatively to gold, more valuable than in the United States. Silver, rather than gold, will therefore be sent from the U. S. to those countries. The relative valuation of these metals is sometimes changed in the same country. This occurred in the U. S., in the year 1834, as has been formerly shown (246). (249.) Foreign Coins and Moneys of Account. The Coin, or Specie, of a country consists of pieces of metal, chiefly of gold and silver, of fixed value, and stamped by public authority, to be used as money. Moneys of Account are those denominations of money in which accounts are kept-being those in which sales are ef fected; they are generally, but not always, represented by corresponding coins. always less than the £ sterling. 100 copecks make 1 rouble (silver); = $0.75. Prussia. 12 pfenings make 1 grosch (silver); 30 groschen 1 thaler or dollar (silver); = $0.69. Austria. 60 kreutzers make 1 florin (silver); = $0.484. Spain. 2 maravedis make 1 quinto; Sicily. 20 grani make 1 taro; $1.12. $2.484. 10 grani make 1 carlino; 10 carlini 1 ducat (silver); = $0.79. Turkey and Egypt. 3 aspers make 1 para; = in Turkey, $0.03 to $0.05. (250.) Foreign Coins made Greece. 100 lepta make 1 drachme (silver); $0.166. Mexico. 8 rials make 1 dollar (silver); $1.00. Brazil. 1000 rees make 1 milree; In the other S. American States, 8 rials make 1 dollar, sometimes more, sometimes less than, $1.00. current, and Moneys of Ac count determined, in the United States, by Acts of Congress. A Foreign Coin is made current when, by Law, it is made receivable, at a fixed value, in the payment of debts. This supposes the Coin to be of standard weight and purity. But other Foreign Coins will also circulate, at values corresponding to their weight and purity. CHAPTER XIV. MATHEMATICAL PROBABILITIES, AND THEIR APPLICATION TO LIFE ANNUITIES AND LIFE INSURANCE. (251.) The THEORY OF PROBABILITIES has respect to events which may be regarded as equally contingent; and, in the sense here intended, A contingent event is one of a number of events, some only of which will certainly occur, while no reason can be perceived why any one of them should occur rather than any other; as when one person is to be taken, by lot, from a company consisting of five persons Measure of Probability. (252.) The Probability of a contingent event is measured, and expressed, by the ratio of the number of chances favorable to that event to the whole number of chances favorable and unfavorable to the same event. Suppose that one person only is to be taken by lot from among five persons, represented by A, B, C, D, and E. The Probability that the lot will fall on any particular one of the five, as A, is expressed by, since he has one chance in five. In like manner the Probability that the lot will fall on any other one, as B, is, since each person has one chance in five. Opposite Probabilities. (253.) The Probability of the occurrence of a contingent event, and the probability of its non-occurrence, are opposite probabilities, the sum of the measures of which is unity. Suppose, as before, that one person is to be taken by lot from among five persons, A, B, C, D, and E. The Probability that the lot will fall on A is , because he has one chance in five; the probability that the lot will not fall on A is, because there are four chances in five against its falling on A; and the sum of and is unity. (254.) The Probability of the non-occurrence of a contingent event, is the same thing as the improbability of that event; and is measured by a unit minus the probability of the same event. Thus, in the preceding example, the Probability of the lot's falling on A is ; the improbability of its falling on A is ĝ; and = 1}. It follows from the preceding principles that, in the Theory of Probabilities, a unit is the measure of certainty. For it is certain that a contingent event will either happen or not happen, and the opposite probabilities thus, existing are together measured by unity (253). Compound Probabilities. (255.) The Probability of one, indifferently, of two or more designated contingent events, is measured by the sum of the separate probabilities of the same events. EXAMPLE. If one person is to be taken by lot from among five persons, A, B, C, D, and E; the Probability that the lot will fall on one of the three, A, B, and C, is because these three together have three chances in five. |