June 16, 1905.] 



SCIENCE. 



923 



geometry and algebra, from which the special 

 study of weights and measures is excluded. 

 We can ignore these considerations because 

 the fallacy of Mr. Hedrick's claim is due 

 chieiiy to his assumption that the use and 

 study of fractions can be restricted to deci- 

 mals. That is impossible because the uni- 

 verse is not built that way. To save time by 

 abolishing the study of vulgar fractions is to 

 promote ignorance, not knowledge. Such a 

 policy of saving, carried to its legitimate con- 

 clusion, would do away with all study and 

 award diplomas for what the graduate from 

 the school of ignorance does not know. 



The earth, from which the French scientists 

 a century ago thought they had derived the 

 meter, persists in revolving on its axis 

 365 If f f xj times during one revolution around 

 the sun. Everything from the chemical com- 

 binations of the elements to the arrangement 

 of the planets and fixed stars proclaims the 

 eternal verity which John Quincy Adams thus 

 exj^ressed to Congress in 1821 : 



Decimal arithmetic is a contrivance of man for 

 computing numbers, and not a property of time, 

 space, or matter. Nature has no partialities for 

 the number ten, and the attempt to shackle her 

 freedom with them will foi-ever prove abortive. 



It seems like a waste of time to demonstrate 

 this self-evident proposition, but as many, in- 

 cluding the House of Lords and the chairman 

 of the Committee on Coinage, Weights and 

 Measures of the House of Representatives, 

 have reached the opposite conclusion, it may 

 be worth while to ask them to examine a 

 'French arithmetic. 'J'ake that excellent work 

 by Joseph Garnier, ' Traite complet d'arith- 

 metrique theorique et appliquee an commerce, 

 a la banque, aux finance et a I'industrie.' The 

 fifth edition (1900) contains not merely a few 

 incidental references, but many comprehensive 

 chapters dealing with vulgar fractions. Here 

 are a few chapter headings : ' Numeration et 

 proprietes des fractions ordinaires,' ' Reduction 

 des fractions au meme denominateur,' ' Simpli- 

 fication des f ractions ordinaires,' ' Conversion 

 d'un numbre entier, et d'une expression frac- 

 tionnaire,' ' Addition des fractions ordinaires,' 

 ' Soustraction des fractions ordinaires,' ' Mul- 

 tiplication des fractions ordinaires,' ' Division 



des fractions ordinaires,' ' Conversion des 

 fractions ordinaires en fractions decimales et 

 reciproquement,' ' Fractions decimales period- 

 iques,' ' Question sur les partages proportion- 

 nels, sur les melanges.' 



If these titles are not sufficient the metric 

 advocate in English-speaking countries can 

 be convinced by reading the French arithmetic 

 and studying its problems. It includes 43 

 pages on the metric system; 12 pages on old 

 pre-revolutionary weights and measures; 13 

 pages on the comparison of the old measures 

 with the new; 22 pages on compound num- 

 bers; and 36 pages on vulgar fractions. 



The chapter on the metric system, entitled: 

 ' Poids et Mesures — Nouvelles Mesures au 

 Systeme Metrique,' effectually dispels the 

 illusion that the metric system in its entirety 

 is simple. The system is explained there, not 

 to make converts to the metric cause, but for 

 practical application to every-day work. The 

 metric system in the French arithmetic with 

 its foreigTi nomenclature and combination of 

 decimal with binary divisions, such as hecto- 

 litre^ dem,i-hectolitre, double decalitre, deca- 

 litre, demi-decalitre, doiMe-litre, litre, demi- 

 litre, double decilitre, decilitre, demi-decilitre, 

 double centilitre and centilitre, is the very 

 uniformity of confusion. There are the same 

 complex vulgar fractions and weird problems 

 that one finds in all school arithmetics, only 

 in the French form perhaps a little more 

 weird. And all this in France more than a 

 hundred years after the following decree was 

 issued by Robespierre: 



Decree of August 1, 1793. 



Art. 1. The new system of weights and meas- 

 ures founded on the measurement of the earth's 

 meridian and the decimal division will be used 

 throughout the Republic. 



In the face of such evidence, what is left 

 of the claim that the metric system will save 

 two thirds of a year or two thirds of a minute 

 in the study of mathematics in school? 



That the teaching of the metric system in 

 American schools at the present time is but 

 a pretense can be proved by asking any grad- 

 uate a few simple questions. The fact is, that 

 the introduction of the metric system into 

 English-speaking countries, instead of making 



