316 Rivkw of the Cambridge Course of Malkematics. 



copper, not exceeding one half silver; in (he silver coins^ 

 the allay is entirely copper. The weight of fine gold in 

 the Eagle is 247,5 ; of standard gold, 270. The weight of 

 fine silver in the dollar, is, 371,25 grains; of standard sil- 

 ver, 416 grains. All coins, inferior to the Eagle, and dol- 

 lar, contain a quantity of pure metal and allay, proportion- 

 al to their denominations. The proportional value of 

 gold to silver is established by law to be in the ratio of 15 

 to I. 



Id page 78, the franc is valued at ^0.1 7963 which does 

 not agree with its value as obtained from the value of the 

 Napoleon, or piece of 40 francs given in the table on the 

 last page, and neither of these values agrees with that ob- 

 tained from the five franc piece, w^hich was declared by an 

 act of Congress of April 1816, founded, we understand, on 

 the report of the Assayer of the mint, and which is now in 

 force, to be 93 cents and 3 mills. 



The last 50 pages of the original, are omitted by the 

 translator, as they consist mostly of tables for converting 

 the old French measures into the new, arid the reverse; 

 and of oll)er subjects of local reference. Two articles in 

 thia! part, however, ought certainly to have been retained; 

 one on (he decomposition of a number into its factors, and 

 the other, on the nature and summation of a numerical con- 

 tinued fraction. The former is often of great practical 

 utihty, and the latter is indispensable to the completeness, 

 and even to the consistency of the course, because in Le- 

 gendre's geometry, which forms the fourth volume of it, in 

 investigating the approximated ratio of the diagonal to the 

 side of a square, the student is required to sum up a con- 

 tinued fraction, for which no means are furnislicd him. 



As the summation of a continued fraction is necessary to 

 the course, and not to be found in any of our arithmetical 

 books, we shall give a translation of JVL Lacroix's article 

 on the subject, for the benefit of those readers, who may 

 not have a copy of the origin^^l at hand. 



'' When we are conducted by a calculation to a fraction 

 whose numerator and denominator are pretty large, and 

 have no common factor, we seek approximate values of 

 this fraction, which are expressed by more simple num- 

 bers, with a view to form a more exact idea of it. 



If we have for example the fractional nmnber VVV? ^'^ 

 obtain, at first, the whole number, and there results 1 ai^« 



