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Proceedings of the Royal Society of Edinburgh. [Sess. 
most ingenious explanation of one or two forms requires to be corroborated 
by independent evidence, or shown to be historically probable, before it can 
be accepted in regard to those other forms to which it does not directly 
apply. In fact, the method of comparison and analogy is the only safe 
guide where variation in form has obscured the source of the symbols. 
Also, it may be pointed out that, if the hypothesis of Zangemeister be 
accepted, the Roman numerals represent a denary system ; for the forms 
V, \y, D are regarded as mere arbitrary symbols, adopted from X, X, and 
[X| respectively, not independently evolved. Is it to be believed that the 
Roman system was not originally quinary like the Herodian system of the 
Greeks (of. 7rejULird£eiv), which so closely resembles it in method and in 
structure, though not in the form of the signs themselves ? If the de- 
cussating principle be the true explanation, then the Roman numerals 
were the creation of scholars, and not the natural product of a people ; and 
they were formed according to a principle which has left no clear record 
of itself in Roman literature, and not much trace even in the signs 
themselves. 
III. The pictographic method. In our examination of the two preced- 
ing hypotheses, attention has necessarily been centred on the forms of 
the numerical signs, while practically no’ corroborative evidence has been 
adduced in favour of either hypothesis from Roman literature or from a 
consideration of the numerical systems of other nations. In contrast with 
such procedure, an attempt will be made in treating of this third hypothesis 
to adduce corroborative evidence from a consideration of the acknowledged 
origin of all alphabetic forms, from the chance allusions of Roman authors, 
and from a few examples of numerical signs used by other nations. In L 
our question was : Can the Roman numerals be explained by reference to 
alphabetic characters ? In II. we inquired whether an examination of the 
several signs would enable us to recognise in each an exhibition of the 
principle of decussation. In III. we shall ask : Can the Roman numerals 
be plausibly accounted for by the pictographic method, on the supposition 
that their origin was analogous to that of all alphabetic characters ? 
“ If the history of any one of our alphabetic symbols be traced back- 
wards,” writes Canon Taylor (op. cit., vol. i. pp. 8-9), “it will be found to 
resolve itself ultimately into the conventionalised picture of some object.” 
Whatever problems remain in regard to the evolution of individual char- 
acters or the relative age and influence of particular alphabets, this view is 
regarded as axiomatic. On it is based the interpretation of Egyptian 
hieroglyphs, Hittite inscriptions, Cretan pictographs, the rude drawings 
of the North American Indians, and the rock-paintings of Australia. 
