1 



Review of the Cambridge Course of Mathematics. iil5 



tern is almost nothing in practice, as the approximations 

 ma}' 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 



th 



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

 cable only to questions contaiiiing five terms, whereas La- 

 croix has investigated a rule which extends to questions 

 <5ontainingany 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 purposcSj if it con- 

 tained a few more applications to classes of questions aris- 

 ^'ig 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- 

 ^on of arithmetic to banking and commerce. But even 

 the original is not suflicient. We know \evy well, that all 



Gse questions belong to proportion or fractions, and 

 cause no possible difficulty to one theoretically acquainted 

 y^\h the subject, but practical men are guided very mechan- 

 ically by rules, and are immediately 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 

 t|^e Old Congress of Aug. 1786, is referred to, instead of 

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

 States w\as established on its present foundation. The note 

 "ponthe sa ^ 



r*"^r from a comp.,.. _ , 



t^iken from the statute above referred to, and which furnish- 

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

 ^omposed. By this act, Eagles, half-Eagles, and^quarter- 

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

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



me page, is almost entirely wrong, as will ap- 

 \ comparison of it with what follows, which is 



per; are the established coins. The sti^ndard for gold 

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

 ^andard for silvercoins, is, 1485 parts fine to 179 parts al- 

 **y- The allav in the i^old coins is a mixture of silver and 



