90 KANSAS CITY REVIEW OF SCIENCE. 
lent and perplexing. The Mosaic and Babylonian cubits were in collision. The 
"cubit and a hand-breadth " of Ezekiel, by this time widely diffused and popu- 
larized, differed from the two-feet rule by about an inch. The Egyptian and 
Persian cubit was becoming confounded with the Indian^ cubit of eighteen inches. 
And the Greek measures were a new element of discord. Eratosthenes was 
charged by Ptolemy Philadelphus with the work of reform. To satisfy the pre- 
vailing preferences for the decimal method, and at the same time strike a reduci- 
ble mean among the cubits, an itinerary was invented which should be an even 
decimal of four terrestrial great circles. It is more than probable that the survey 
of Eratosthenes was simply to test the correctness of the ancient standards, and 
fix the adjustment of the royal cubit. The circumference was already known, 
according to the Egyptians, and if their account proved correct, the relation was 
apparent beforehand. The royal cubit would have to be |- of the Egyptian = |4 
of the Mosaic=i.75io4 English feet. 
(3.) This unwieldy division of the circle, unfit for geography or astronomy, 
along with the strong preferences of the Egyptians, Persians, Hebrews and kin- 
dred races for the ancient measures, and their wide-spread traditional sympathy 
as against Babylonian methods,- finally broke this system down. Accordingly, 
after the Roman supremacy was established, and in the reign of one of the later 
Ptolemies, Posidonias restored the Mosaic cubic, but in a 3-cubit fathom, so that 
his itinerary was decimally related to the hour angle. And so far from his sur- 
vey being the worst measurement of a degree ever made, it serves to verify in a 
very lucid way the work of his predecessors. The aptness of his system, as an 
itinerary, is attested by the survival of the Turkish mile, through all vicissitudes, 
and of its correlative fathom, by dozens of analogues, in the islands and along 
the Mediterranean and in Central Europe. And it may seem significant to many 
that in the Apocalypse, written 186 years later, the division of the circle by 24 is 
paramount. 
(4.) Finally, in the reign of Marcus Aurelius, a further attempt at unifica- 
tion seems to have been made, by re-instituting the Mosaic itinerary — the leuga 
of the ancient Gauls and the mile of Sardinia. This was the survey of Ptolemy. 
Possibly it involved some concession to the Egyptians, in that the schoenus became 
simply 20 fathoms, instead of 33^ as by their ancient method, or 26^ as by that 
of Posidonias. It lacked, however, the key-note of Ezekiel's reform — radius to 
be the base of direct and square measure, itinerary to be ruled by the division of 
the circle. 
There seems to be little, either in the accounts we have, the necessities of 
the case, or the character of the rulers under whom these operations were con- 
3. It is a peculiarity of the purely duodecimal method that, reckoning from the inch, it 
has no longer dimension than the 12-feet pole or " joktan." And, wherever it has taken root, 
this dimension, as well as its derivatives by bisection, the vulgar fathom, the yard, and the 
Indian cubit, as also the foot, when used as units, are, as a rule, but with occasional intermediar- 
ies of 3 and 6, reckoned upwards decimally. Its singular distribution — about the Meridian, among 
the islands, as Great Britain and Japan, and upon the salients of Africa and Asia — are strikingly 
suggestive of the maritime enterprise of busy Tyre. 
