Review of the Cambridge Course of Mathematics, 315 



tern is almost nothing in practice, as the approximations 

 may be carried to any required degree of exactness. 



In the translation, reduction and the rules for compound 

 numbers are written anew, and adapted to our system of 

 weights and measures. This was necessary, because the 

 original was prepared with reference to the new French 

 metrical system, the construction of which is strictly deci- 

 mals. Proportion is illustrated with admirable clearness, 

 and is freed from several distinctions made in the common 

 books, which serve only to embarrass the learner. The 

 rule for compound proportion, as generally given, is appli- 

 cable only to questions containing live terms, whereas La- 

 croix has investigated a rule which extends to questions 

 containing any number of terms. 



With all its merits, we think this treatise of arithmetic 

 is not without its defects. It would be more useful for 

 practical, and not less so, for theoretical purposes, if it con- 

 tained a few more applications to classes of questions aris- 

 ing from the social and commercial relations of man. The 

 translation is in this respect somewhat less valuable than 

 the original, as this contains a short article on the applica- 

 tion of arithmetic to banking and commerce. But even 

 the original is not sufficient. We know very well, that all 

 these questions belong to proportion or fractions, and 

 cause no possible difficulty to one theoretically acquainted 

 with the subject, but practical men are guided very mechan- 

 ically by rules, and are imnsediately alarmed and embar- 

 rassed if they are obliged to depart in the least from acquir- 

 ed habits. At page 65, on American money, the statute of 

 the Old Congress of Aug. 1786, is referred to, instead of 

 the Act of April 1792, by which the mint of the United 

 States was established on its present foundation. The note 

 upon the same page, is almost entirely wrong, as will ap- 

 pear from a comparison of it with what follows, which is 

 taken from the statute above referred to, and which furnish- 

 es a part of the materials, of which such a note ought to be 

 composed. By this act, Eagles, half-Eagles, and quarter- 

 Eagles in gold; dollars, half-dollars, quarter-dollars, dimes 

 and half-dimes in silver; and cents and half-cents in cop- 

 per; are the established coins. The standard for gold 

 coins only, is eleven parts fine, and one part allay. The 

 standard for silver coins, is, 1485 parts fine to 179 parts al- 

 lay. The allay in the gold coins is a mixture of silver and 



