Scales of Computation. 
107 
the regular sale of produce adds to the surprise felt at the 
Grecian failure. The Arabs may even claim to have intro- 
duced a new disturbing element in their system of reckoning 
agricultural areas by ploughs. Even in the middle ages there 
were improvements in ploughs, and the number needed to 
the mile would also vary with the traction, by strong horses 
or oxen in some places, by women slaves in others. In India 
the system is now to reckon by a joint weight. An English 
pound is the basis, and eighty of these makes a maund which 
is an extremely convenient weight for the ryot, about as much 
as he cares to carry. We then get back to the English quarter, 
six maunds making a quarter. This system works well and is 
extending to the Native States. 
We have thus far no clue to any definite system at all 
and search must take what nowadays is an unwonted course. 
We must quit the inductive for the deductive. Here we at 
once find something interesting. Trouble appears to have 
begun in prehistoric days when primitive man commenced 
reckoning his thumbs as fingers. The earliest basis of civilised 
reckoning w^as clearly the digit, and if the human race had 
reckoned by eight fingers instead of ten — and eight is the 
number, not ten — a perfect system would have been evolved. 
Eight, as the older mathematicians pointed out, is the perfect 
number, not because it is the number of the Beatitudes as the 
schoolmen quaintly put it, but because it divides out : half of 
8 is 4, half of 4 is 2 and half of 2 is 1. There are no broken 
numbers, whereas, half of 10 is 5, an unbroken number ; but 
half of 5 is 21>, and half of 2^ is 1J, two broken numbers in 
the scale. Mr. H. G. Wells, in one of his clever novels, has 
forecast a scale of 8, and this reversion to a mediaeval truth 
has been called “ one of the wildest of his fantasies.” 
Of this scale of 8 we have an odd survival in the shipping 
trade, which in all countries divides a ship into a maximum of 
64 shares=8x8. We believe that The Times newspaper shares 
are similarly divided, the first Mr. Walter having started in the 
shipping trade. Other traces are to be found in the 8 pints to 
the gallon, in the 8 half crowns to the pound, in the 8 drachms 
to the ounce, and in the 8 furlongs to the mile. If we could 
establish a scale of 8, it would solve all our difficulties. We 
imagine, however, that no serious controversialist will suggest 
the enforcement of a scale of 8. 
The scale of 12 has its practical advocates. Its weakness, 
of course, is in the last stage of dividing out. Half of 3 is 1^, 
a broken number. The scale of 10 (the decimal system) has 
two weaknesses to this one. Where the 12 scale fails is in the 
higher figures : 12 x 12—144, the g?mss., is the highest that 
children usually reach, and few grown men could answer 
