100 Transactions. — Miscellaneous. 



geometrical relations, which to the worker in any branch of 

 science or art are of essential importance, in a larger measure 

 than is possible under any other radix, are represented in their 

 real significance. 



This is in itself no slight advantage, for geometry is of all 

 sciences the most tangible and practical. How comes it to 

 pass that the dozen holds its ground so persistently in com- 

 merce, notwithstanding the convention of reckoning by tens? 

 Very much because there are so many ways of making a con- 

 venient and compact parcel of twelve equal units, while tens 

 and hundreds pack very badly indeed, making misshapen 

 parcels and wasting space. To those who have to pay freight 

 charges — as all must do, directly or indirectly — this is a con- 

 sideration of importance. 



The two ratios with which the practical work of life brings 

 us into constant contact are graphically represented respec- 

 tively on the clock-dial and the compass-card. With both 

 of these decimals are in constant discord. The old Baby- 

 lonian division of the circle into 360 degrees is comprehensive 

 enough to take in the decimal, but its place is subordinated 

 to the more important and significant geometrical angles, 

 which only duodecimal division can give. 



It may be regretted that a numerical system so nearly 

 perfect as the duodecimal — simplifying as t would all the 

 practical mathematical work of the world to an amazing 

 extent — can never, unless humanity develops an unforeseen 

 capacity for the acceptance of great reforms, be adopted. If 

 it were merely a matter of relative merit there could be no 

 doubt of the result, for mathematicians are unanimous as to 

 its superiority. But one of the great arguments against the 

 metric system applies witli equal force to duodecimalism. 

 The decimal radix is so strongly entrenched in tradition, in 

 notation, in thought, speech, and literature, that its dislo'dg- 

 ment may be reasonably assumed to be impossible. We find 

 a tacit recognition of the place that twelve should occupy of 

 right in the significant facts that our popular multiplication - 

 table extends to 12 x 12, and that children are taught simple 

 multiplication and division up to twelve, not ten. And ham- 

 pered though we are in all directions by our defective arith- 

 metical radix, we still are free to use, in weighing and mea- 

 suring, the divisions that the experience of many ages has 

 proved to be the best adapted to our needs. That freedom 

 it is the avowed object of the metrists to destroy. They would 

 widen still further the gulf that unfortunately divides arith- 

 metic from geometry, and make our bondage to the decimal 

 complete. 



In any notation two radices are required — a major as 

 well as a minor — and it is important that there should be 



