THE FOREIGN EXCHANGES 231
100 francs equivalent to 81 marks, and so on for other
pairs.
The United States gold coin, though of the same fineness
as the gold coin of the countries named above, has its
weight expressed in terms of Troy grains instead of in
metric weights. The eagle, or ten-dollar piece, is required
to weigh 258 grains by the law governing the operations of
the mint. Now a kilogramme is equivalent to 15432°35639...
grains. Hence, the sum, in dollars, equivalent to the amounts
of the various currencies expressed above would be $5081'534
nearly, and the par of exchange, between any of the countries
named and the United States, can at once be obtained.
Thus the French par of exchange with the United States
is 100 francs=19'2953 dollars nearly, or 1 dollar=51836
francs.
When we consider any par of exchange with England,
the fact that English gold coin has one-twelfth part of its
weight alloy, as compared with one-tenth in the cases above
cited, renders the equivalence of gold currency weight for
weight no longer an equivalence of pure gold contents. As
it is the latter we are seeking, we have to equate amounts of
coin which are of different gross weights! The English
sovereign is made so that 1869 of the coins weigh 40 Ibs.
Troy, or 230,400 grains, so that a sovereigns legal mint
weight is 12327447... grains of standard gold. The pure
gold it contains is, therefore, 113'0016... grains. The
details already given supply the data for calculating the pars
of exchange between England and the six countries to
which they refer. Thus the par of exchange with the United
States is obtained by dividing 1130016 by 23°22, the number
of grains of pure gold in the dollar, and the result is A=4'86656...
 dollars. Similarly, the par of exchange with
France is given by £1=252215... francs, with Germany
by £1=204335... marks, etc.
These pars are calculated from the weights of the coins
as defined bv law. In practice, coins in circulation have lost

+ It may be observed that 10 kilogrammes of coin, nine-tenths fine, contains
3 kilogrammes of pure gold, which would be contained in 9°81 kilogrammes of
English gold coin, or £1229°108276.....