A Note on the Roman Numerals. 
167 
1907 - 8 .] 
with its pictographs for the lower values, with its limited use of place- 
value, and with its morphological termination at CD, points to another 
origin than the alphabetic, and would suggest rather a progressive evolution 
according to a definite principle or method. These considerations are non- 
technical and general, but they have this useful characteristic : they can be 
urged against any hypothesis that would account for the Roman numerals 
by means of mere alphabetic forms. “The system,” writes Sir E. M. 
Thompson ( Greek and Latin Palaeography , 1906, p. 105), “ was not an 
alphabetical one, for, although C (100) has been said to be the first letter of 
centum and M (1000) the first letter of mille, both these signs had a 
different derivation, and by a natural process only took the forms of the 
letters which they resembled most nearly.” 
II. The decussating principle, i.e. the hypothesis which explains the 
Roman numerals as formed by means of an additional decussation, or cross- 
line, for each tenth power. 
Professor John Leslie, in his Philosophy of Arithmetic (Edinburgh, 
1820, pp. 8-9), attempted to account for the symbols by means of this 
hypothesis, somewhat as follows : — Perpendicular lines, each denoting one , 
were repeated until ten was reached. A dash across the common unit, as 
X, then signified ten. The addition of a third stroke, or the mere drawing 
of three connected strokes, as E ( = C), would then denote 1x10x10 
( = 100); and four combined strokes formed M, “the utmost length to 
which the Romans first proceeded by direct notation.” “ But the division 
of these marks afterwards furnished characters for the intermediate 
numbers, and thence greatly shortened the repetition of the lower ones.” 
Thus the half of X is V ; E was divided as L ; and “ the four combined 
strokes M, which originally formed the character for a thousand , came 
afterwards, in the progress of the arts, to assume a round shape (~Q, 
frequently expressed thus CD,” of which the half, or D, was employed to 
represent 500. 
This ingenious, but curiously naive, presentation of the problem need 
not be seriously considered. It is here referred to, and briefly described, 
only in order to assert Professor Leslie’s title to be considered a forerunner 
of Professor Karl Zangemeister, the learned editor of the Pompeian tablets, 
whose explanation of the numerals by means of the same decussating 
principle is regarded by certain palaeographers as affording a plausible 
solution of the problem. Professor Zangemeister’s paper, entitled 
disadvantages are obvious and great. Its only rule is that the larger number precedes the 
smaller — with this exception, that fours and nines, of whatever rank, may be written in 
terms of fives and tens (as IY, XL, CD ; IX, XC, CM). 
