164 Proceedings of the Royal Society of Edinburgh. [Sess. 
The various hypotheses that have been put forward in explanation of 
the form of the Roman numerals may conveniently be grouped according 
to their subject-matter, as follows : (1) the alphabetic form ; (2) the 
decussating principle ; (3) the pictographic method. 
I. First, then, of the hypothesis according to which the Roman numerals 
are explained by reference to independent alphabetic forms. According to 
the acrologic method, the Roman numerals should not only correspond to 
alphabetic forms, but also represent the initial letter of their several names. 
As an example of this method, at least for the purpose of illustration, the 
numerical signs employed by the Greeks in their Herodian system may 
be adduced, thus: II(eVTe) = 5, A(e/ca) = 10, H (the aspirate sign in H ckcitov} 
= 100, X(/Amt) = 1000, M.(vpioi) = 10,000. But, obviously, the acrologic 
method may be applied in two ways, according as we assume the priority 
of the name or of the sign. If the sign for a number be similar to the 
initial of that number’s name, we may still ask whether it be not more 
probable that the sign gave rise to the name, than that the name gave its 
initial as a sign for the number; for, although calculation by means of 
numbers is a late development, it does not follow that primitive man did 
not employ signs to represent numbers at a date antecedent to the use of 
alphabetic characters. This statement might be expanded and illustrated 
in various ways. But to do so is unnecessary; for it is clear that the 
acrologic method cannot afford a clue to the origin of the Roman numerals, 
as only two of the forms admit of comparison with the initials of their 
names, viz. C ( centum ) and M ( mille ). It remains to inquire whether the 
source of the Roman numerals can be found in alphabetic forms, apart from 
the acrologic method. 
According to Professor Zangemeister, the first scientific explanation was 
given by Professor Mommsen, the historian (see Die unteritalischen 
Dialekte, Leipzig, 1850, S. 19 & 33 ; and Romische Geschichte, Buch i. 
Kap. 14). But, in this connection, we shall quote the statement of Canon 
Isaac Taylor, who, in his great work The Alphabet (London, 1883, vol. i. 
p. 6, and vol. ii. p. 139), epitomises the alphabetic hypothesis which he 
had derived from Ritschl’s “ Zur Geschichte des lateinischen Alphabets” 
(. Reinisches Museum fur Philologie, 1869). Canon Taylor accepts Ritschl’s 
theory so far as concerns the numerals L, C, D, M, while he dissents from 
Ritschl with regard to the numerals Y, X, preferring to hold, with Mommsen 
and Grotefend, that these had an ideographic origin. 
Canon Taylor writes as follows : — “ The aspirated mutes, phi, chi, theta, 
were also retained in Etruscan, but not being required in Latin as phonetic 
symbols were utilised as numerals. For 50 the Romans used the Chalcidian 
