Decembeb 3, 1920] 



SCIENCE 



525 



important feature in the work for whicli the 

 association exists. 



Those in attendance at the meeting may 

 obtain information of all sorts by applying at 

 the information desk in the registration room. 

 Before the meeting, information may be ob- 

 tained from the secretaries of the sections or 

 of the associated societies (regarding pro- 

 grams, etc.), from the chairman of the local 

 committee. Professor J. Paul Goode, of the 

 University of Chicago regarding local ar- 

 rangements, or from the permanent secretary's 

 office in Washington regarding general asso- 

 ciation affairs. 

 , Burton E. Livingston, 



Permanent Secretary 



Smithsonian Institution, 

 "Washington, D. C. 



A MORE NEARLY RATIONAL 

 SYSTEM OF UNITS 



Systems of units for physical magnitudes 

 are designed to permit arithmetical calcula- 

 tions on the basis of known physical laws, and 

 the test of the efficiency of any system is the 

 extent to which it facilitates such computa- 

 tions. There are two ways, in particular, in 

 which this can be accomplished: first, by re- 

 lating the units of any one magnitude in a 

 manner consistent with the system of arith- 

 metic in use; with a decimal arithmetic this 

 requires that the ratio of such units be a 

 power of 10, e. g., the erg and the joule; sec- 

 ond, by so relating the units of different " di- 

 mensions " as to prevent the appearance of 

 arbitrary and irrational factors in the equa- 

 tions expressing the fundamental laws of nat- 

 ural science, e. g., the " gas law " should take 

 the form " pressure = concentration X tem- 

 perature " (P =■ CT) rather than " pressure is 

 proportional to concentration X temperature " 

 (P = CBT). The failure of the "English" 

 system of weights and measures to meet these 

 requirements is a matter of common knowl- 

 edge, but it seems worth while to point out 



1 Forty-first Contribution from the Color Lab- 

 oratory of the Bureau of Chemistry, Washington, 

 D. C. 



how little superior in these respects is the 

 present " metric " system. 



The common basis of both these systems of 

 physical and chemical units comprises: (1) the 

 decimal arithmetic, (2) the mean solar second 

 and (3) the table of atomic weights based on 

 O = 16. It is not intended here to discuss 

 these fundamentals, beyond pointing out that 

 no one of them is entirely rational, and if they 

 are retained it will be only because the diffi- 

 culties in the way of superseding them out- 

 weigh the advantages of a change. The pur- 

 pose of this paper is an inquiry whether on 

 this common foundation there can be con- 

 strued a system of units superior to either of 

 the two now in common use. 



1. Two systems of arithmetic with a base other 

 than 10 are suggested by the methods of division 

 of units in the ease of "English" weights and 

 measures (a) the twelve-system, illustrated by the 

 dozen and gross and by the divisions of the foot 

 and the pound Troy; (6) the two-system, illus- 

 trated by the divisions of the inch, the gallon and 

 the pound avoirdupois. Both modes of division 

 are used in coinage, though not at all consistently, 

 (a) in the case of the shilling of twelve pence, (6) 

 in the penny of four farthings and the distinctly 

 non-decimal division of the dollar into quarters 

 (and even into "'bits" of IZi cents). In a recent 

 eulogy of the twelve-system (Science, N. S., 50, 

 239-242 (1919)), Dr. William Benjamin Smith 

 says: 



"This best of numerical systems is not the ten- 

 system (which is recommended only by the fact 

 that man has ten fingers and ten toes!) but the 

 twelve-system, whose vdrtues are imbedded in the 

 nature of number itself." 



2. The humor of basing a decimal system of 

 weights and measures on a unit of time obtained 

 by dividing the mean solar day successively into 

 24, 60 and 60 parts, hardly needs emphasis. The 

 mean solar day is the average interval between 

 the passage of the sun across the meridian for any 

 locality. The maximum difference between mean 

 solar time and true solar time is 16 minutes 

 (about November 1 of each year). 



3. The change from the H m l system of atomic 

 weights to the present O s 16 was made both be- 

 cause of the uncertainty of the H: O ratio and 

 because the oxygen standard made more of the 

 atomic weights approximate whole numbers. Ee- 



