A Note on the Roman Numerals. 
169 
1907-8.] 
origin, he suggests that this sign for 50 (\|/) may be merely a decussated 
V (5x10 = 50). Ten is, of course, the decussated I (X), and the half of 
that form is V ( = 5). The fact that the signs of the smaller values I, V, X 
had “ Doppelganger ” in the alphabet may, he thinks, have assisted the 
process by which, at a later date, the signs for 50, 100, 500 approximated 
to the letters L, C, D. Further, for numbers above 1000, in order to avoid 
unsymmetrical forms like CCXD or CXDD, which could readily be falsified, 
the sign for 500 was taken as the base : thus 
l> or D = 500 
03 = 5000; doubled as CCD3 = 10,000 
ODD = 50,000 ; doubled as CCCODD - 100,000 ; 
and, later, one finds the forms XV =XY millia, and jXl =1 million. 
As decussis, decussare, and the other forms are merely mentioned in a 
note, without reference or amplification, it may be inferred that Zange- 
meister had little expectation of deriving effective support for his hypothesis 
by means of quotation from the Roman authors. Decussis ( = decern asses) 
denoted ten aces, or units, whether in length, value, weight, or capacity ; 
then the number ten in general, as also the sign X which represented it. 
Decussare signified “to divide, or cross, like the letter X.” There is no 
suggestion that the word originally had, or ever acquired, a general 
mathematical meaning, as “ to multiply by ten,” or even “ to reckon by tens.” 
Thus the word had not the significance or value of, say, the Greek TreuTrd&iv- 
Nor is it evident why such importance should be attached to the forms 
h m mi etc., or how they are to be held as furnishing “ striking 
evidence ” for the existence of a decussating principle. Are they, it may 
be asked, not merely a device for representing a series of X’s ? If that be 
so, then we get = XX, which furnishes no stronger proof of the existence 
of a decussating principle than does a single X. 
Further, if we turn to the other forms, we find that OO, or CX3, alone 
is not problematic. For the doubtful and discarded sign X is regarded as 
standing for 100 only with “ great probability ” ; while any intermediate 
form in the supposed evolution of C, as e.g. is confessedly hypothetic 
(“Diese Form ist von mir nur erschlossen, sie findet aber ihre Bestatigung 
in dem . . . Zeichen fur 1000,” usw.). 
Thus, though the hypothesis in question is interesting, because it 
suggests not only a possible source of the several forms but also a principle 
connecting them, there is no direct evidence to prove the existence of such 
.a principle. The forms X and PO, indeed, lend themselves conveniently to 
explanation by means of the alleged decussating principle. But even the 
