I^BRUARY 18, 1921] 



SCIENCE 



157 



Mayas of Tuoatan are exceptions. However, 

 even in these systems, the ten (or five) forms a 

 subsidiary system, apparently developed first. 

 The further important fact should be noted 

 that vrith the development of these numerical 

 systems, both these civilizations included their 

 systems of weights and measures. We may 

 even say that it appears probable that the sys- 

 tem of weights and measures was first brought 

 to the sixty system among the Babylonians, 

 and weights and measures to the twenty sys- 

 tem among the Mayans, and from this carried 

 over to the number system. Note that this re- 

 duction took place in Babylon as much as 

 four thousand years ago. These ancient civ- 

 ilizations found it necessary, then, to make 

 their number systems conform to their systems 

 of weights and measures, including time. 



The first systematic treatise on decimal frac- 

 tions was printed iu 1585, first in Flemish and 

 then in French, by Simon Stevin, of Bruges. 

 This work is addressed to astronomers, survey- 

 ors, masters of money (of the mint), and to all 

 merchants. Stevin says, of this work, that it 

 treats of "something so simple, that it hardly 

 merits the name of invention." He adds: 

 . We wiU speak freely of the great utility of this 

 invention; I say great, much greater than I judge 

 any of you will suspect, and this without at all ex- 

 alting my own opinion. . . . For the astronomer 

 knows, . . . the difficult multiplications and divi- 

 sions which proceed from the progression with de- 

 grees, minutes, seconds and thirds . . . the surveyor, 

 he will recognize the great benefit which the world 

 would receive from this science, to avoid . . . the 

 tiresome multiplications in Verges, feet and often 

 inches, which are notably awkward, and often the 

 cause of error. The same of the masters of the 

 mint, merchants, and others. . . . But the more that 

 these things mentioned are worth while, and the 

 ways to achieve them more laborious, the greater 

 still is this discovery disme, which removes all these 

 difficulties. But how? It teaches (to tell much in 

 one word) to compute easily, without fractions, all 

 computations which are encountered in the affairs 

 of human beings, in such a way that the four prin- 

 ciples of arithmetic which are called addition, sub- 

 traction, multiplication and division, are able to 

 achieve this end, causing also similar facility to 

 those who use the casting-board (jetons). Now if 



by this means will be gained precious time;; 

 by this means labor, annoyance, errorj dafeage aiii 

 other accidents commonly joined with ^ttese Sflna.- 

 putations, be avoided, then I submit this plan'^w- 

 untarily to your judgment. , .l'_ 



■ What can one add to these words of the first 

 writer on the subject, and an independent dis- 

 coverer of decimal fractions? All that Stevin 

 says applies to-day, hardly with the change of 

 a letter. The genius of Stevin is evident in 

 the comprehensive grasp which he had of the 

 universal application of decimal fractions to 

 affairs. Much of the benefit of this invention 

 is lost to us in America, because we persist in 

 using non-decimal weights and measures. 



Louis 0. Karpinski 



TjNrVERSITT OF MICHIGAN 



SCIENTIFIC EVENTS 



THE ANNUAL MEETING OF THE BOARD OF 



TRUSTEES OF THE AMERICAN MUSEUM 



OF NATURAL HISTORY 



A REPORT of the nature and scope of the past 

 year's work of The American Museum of Nat- 

 ural History was made on the evening of 

 February Y by President Henry Fairfield Os- 

 born, at the annual meeting of the board of 

 trustees, which was held at the home of Dr. 

 Walter B. James. The president regards the 

 year 1920 as one of the greatest years in the 

 history of the museum, inasmuch as the in- 

 stitution's edticatioual value has for the first 

 time been fully recognized by the present city 

 administration, and gifts, collections and 

 funds for expeditions presented to the museum 

 represent a total of $500,000. 



Commenting on the financial condition of 

 the museum, it was announced that the year's 

 work had been concluded without the neces- 

 sity of requesting the trustees to make their 

 usual personal contributions to supplement 

 the budget. This was due to the enforcement 

 of the most rigid economy and to the fact 

 that the city authorities, after a searching in- 

 vestigation of its affairs^ recognizing the im- 

 portance of the institution as a vital and ever 

 developing adijunct to the city's educational 

 system, had increased the annual maintenance 

 allowance by $150,000 over the appropriation 



