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SCIENCE 



[N. S. Vol. L. No. 1289 



brous expression of many simple, important, 

 and frequent fractions, as 1/3, 1/4, 1/6, 1/8, 

 1/9, 1/12, etc. We protest most earnestly 

 against the adoption of the Latin-German 

 system, not because it is not better than our 

 present lack of all system, but because such 

 adoption would postpone perhaps forever the 

 introduction of a far superior system, which 

 is a capital desideratum of our modern civili- 

 zation and life. The meter-liter-gram is at 

 least in some ways comparatively good, but 

 the good is the enemy of the best, with which 

 only we can rest content, and it would be an 

 infinite blunder to establish and eternize such 

 a defective system as the M.L.G. when it is 

 almost as easy — at least, when it is entirely 

 possible — to introduce and establish once and 

 for all time the best system that the nature of 

 number and of the human mind permits. 



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 virtues 

 are imbedded in the nature of number itself. 

 Its notation requires at once the introduction 

 of two new symhols, one for ten, one for 

 eleven, which may be made as pretty and 

 simple as you will, but the initials i and e 

 will answer all present purposes. "We shall 

 have then the ciphers: 1, 2, 3, 4, 5, 6, 7, 8, 

 9, t, e. Twelve is then to be written 10, 

 and we shall have the next set; 11, 12, 13 — 

 19, It, le, 20 — to be read tel-one, tel-two, tel- 

 three, . . ., tel-nine, tel-ten, tel-len, twentel. 

 The reasons for such names are obvious, tel 

 and len are natural simplifications of twelve 

 and eleven. Our present forms, such as six- 

 teen, seventeen, which read the numbers 16, 

 17 hackivards, are a stumbling-block to begin- 

 ners, hindering and confusing them to no 

 purpose whatever. Twentel (20) equals of 

 course our present twenty-four. Similarly 

 thirtel-one, etc., fortel, fiftel, sixtel (sistel), 

 seutel (for seventel), eightel, ninetel, tentel, 

 lentel, teltel. This last, 100, equal to our 

 present 144, is of course the second power of 

 the base twelve (10), and should have some 

 appropriate name, as dipo, or two-po, or what- 

 ever may seem best, and similarly the higher 

 powers, as 1000(1728), 10,000(20,736, etc.). 



We see here at once the greater power of this 

 system; with four figures it expresses num- 

 bers up to 20,735 (e e ee in the twelve-system), 

 more than twice as many as are so expressible 

 at present — an advantage that steadily in- 

 creases with the numbers, and shows itself 

 clearly in logarithmic and other tables, where, 

 with the same number of figures, the accuracy 

 of expression would be sensibly higher. Thus, 

 a im.it in the sixth decimal place now signifies 

 a millionth, in the Tel-system it would mean 

 about a three-millionth. In the billions, the 

 Tel-notation economizes one place. 



Among the many advantages shared by this 

 system with no other, the chief is the high 

 faetorability of the base twelve, divisible ex- 

 actly by 2, 3, 4, 6, and simply related to 8 

 and 9. Thence result extremely simple ex- 

 pressions for the principal fractions : 



1/2 = .6 



1/3 = .4 



1/4 = .3 



1/6 = .2 



1/8 = .16 



1/9 = .14 



one twelfth = .1 



1/14 = .09 



1/16 = .08 



1/20 = .06, etc. 



The fractions 1/5, 1/7 one tenth, one 

 eleventh (111 . . . .) remain interminate series, 

 but for them we have little practical use. 

 With the forgoing compare the current dec- 

 imal expressions for the fundamental con- 

 stantly recurring fractions : 



1/2 = .5 



1/3 = .33333 --- 



1/4 = .25 



1/6 = .16666--- 



1/8 = .125 



1/9 = .111 



one tweLfth = .08333 . . . 

 and the great superiority of the tel-system 

 becomes evident. 



The multiplication table'^ becomes mark- 

 edly simplified. No one has any trouble now 

 in multiplying by 5, because of its simple 

 cycle, 5, (as in 5, 10, 15, 20, etc.) : 4 has the 

 much longer, more involved cycle, 4, 8, 2, 6, 0, 

 (as in 4, 8, 12, 16, 20, etc.) ; 6 has the cycle 6, 



