THE METRIC SYSTEM. 193 



though these particular 12-divisions are undesirable, as being most of them 

 arbitrary and unrelated to one another, yet the facts make it clear that a 

 general system of twelfths is called for by trading needs and industrial 

 needs ; and such a system might claim something like universality, since 

 it would fall into harmony with those natural divisions of twelfths and 

 fourths which the metric system necessarily leaves outside as incongruities. 



But what about the immense facilities which the method of decimal cal- 

 culations gives us ? You seem ready to sacrifice all these ? 



Not in the least. It needs only a small alteration in our method of 

 numbering to make calculation by groups of 12 exactly similar to calcula- 

 tion by groups of 10 ; yielding just the same facilities as those now sup- 

 posed to belong only to decimals. This seems a surprising statement; but 

 I leave you to think about it, and if you can not make out how it may be I 

 will explain presently. 



m. 



The promised explanation may most conveniently te given by 

 reproducing, with various alterations and additions, a letter I 

 wrote about the matter last November twelvemonth to a dis- 

 tinguished man of science. Omitting the name, the letter ran 

 thus : — 



The inclosed memoranda concerning advantages to be derived from 

 the use of 13 as a fundamental number were written more than 50 years 

 ago, and have since been lying unused among my papers. 



I send them to you because you have lately been expressing a strong 

 opinion in favor of the metric system, and of course your opinion will 

 weigh heavily. From the days when the accompanying memoranda were 

 set down I have never ceased to regret the spreading adoption of a system 

 which has such great defects, and I hold that its universal adoption would 

 be an immense disaster. 



Of course I do not call in question the great advantages to be derived 

 from the ability to carry the method of decimal calculation into quantities 

 and values, and of course I do not call in question the desirableness of hav- 

 ing some rationally originated unit from which all measures of lengths, 

 weights, forces, etc., shall be deinved. That as promising to end the pres- 

 ent chaos the metric system has merits goes without saying. But I object 

 to it on the ground that it is inconvenient for various purposes of daily 

 life, and that the conveniences it achieves may be achieved without entail- 

 ing any inconveniences. 



One single fact should suffice to give us pause. This fact is that, not- 

 withstanding the existence of the decimal notation, men have in so many 

 cases fallen into systems of' division at variance with it, and especially 

 duodecimal division. Numeration by tens and multiples of ten has pre- 

 vailed among civilized races from early times. What then has made them 

 desert this mode of numeration in their tables of weights, measures, and 

 values ? They can not have done this without a strong reason. The 

 strong reason is conspicuous — the need for easy division into aliquot parts. 

 For a long period they were hindered in regularizing their weights and 

 measures by the circumstance that these had been derived from organic 

 bodies and organic lengths — the carat and grain, for instance, or the cubit, 

 foot, and digit. Organic weights and lengths thus derived were not defi- 



