176 
Proceedings of the Royal Society of Edinburgh. [Sess. 
the symbol of five, represented the open hand ; and that thereafter digits 
from the second hand were successively added until VIIII was reached, 
ten being denoted by a symbol representing the crossed arms, i.e. the 
summation of the two hands. We note that the fifth character is a new 
symbol, and that it is equivalent to the summation of five of the preceding 
symbols, for V = IIIII. Let us assume that the remaining symbols were 
likewise derived from ideographs of gesture-language, and that the principles 
governing their evolution were the following : — 
1. That no gesture shall be repeated more than five times in any 
one series. This natural limit may be regarded as due to the fact that 
the eye cannot easily count more than five similar gestures or signs ; 
or, more probably, it may be attributed to the influence of the hand 
(i.e. the five digits) in forming a habit of counting by fives. 
2. That the completion of a series of five similar gestures shall be 
signified by a position or gesture. This concluding position or gesture 
(analogous to a mark of punctuation in writing) would be required to 
facilitate the summation of the preceding gestures. But it would 
inevitably acquire the value of the preceding series of five similar 
gestures, and thus it would ultimately supersede that series. 
These two principles (which are involved in the pictographic formula, 
“ IIIII, the five digits = Y, the hand-gesture ”) provide the requisite clue for 
the construction of the later gestures, and thus of the numerical signs for 
the higher values. For, if these principles be granted, with the human 
body for instrument, and the smallest complement of instinct and faculty — 
a wish to count and the ability to draw — then signs corresponding to the 
Roman numerals will be the result, although their exact forms will be 
modified according as they are assimilated to this or that alphabet, and 
according to the other fluctuating conditions of time and place. 
The actual development of the gesture-notation, governed by the two 
principles just stated, is not to be regarded as having taken place on a pre- 
conceived plan. Rather must we view it as the slow and gradual evolution 
of an experimental method, new gestures being added to the system only 
as the general conception of numerical values extended, and as the gestures 
representing them became fixed. Each new gesture, when accepted and 
codified, would in turn become the basis of, and means to, a further 
development. And in order that it might become a means to such further 
development, it required to be, so far as was practicable, not a mere position 
but a definite movement — a real gesture — capable of being repeated 
without ambiguity and without uncertainty. This tendency — the tran- 
sition from mere stationary positions to actual gestures — is exemplified 
