172 Proceedings of the Royal Society of Edinburgh. [Sess. 
But, if man used his body as a standard of measurement, could he not 
employ it also in the process of counting ? Did not Nature provide him 
with a ready-made abacus — his fingers ? Were the objects before him, say, 
five or ten ; then one or both of his hands formed an unwritten record of 
the simple calculation. In this way the mnemonic stage was reached : he 
could at any time “ count ” the number of his few possessions by comparing 
them with his fingers. Did he wish to record the number for other persons, 
a rude sketch of the fingers was all that was necessary. And thus the 
pictographic stage was reached : he could now denote the number by 
means of a picture or drawing. When the picture became commonly used 
and understood, so that only a conventional symbol, and not an actual 
drawing, of the hand or fingers was required, then the final or ideographic 
stage was reached : man had invented idea-drawings or symbols to represent 
numbers, and could calculate. 
If we would see the old discovery or invention taking place to-day, we 
have only to glance at the practice of some uncivilised race. Thus, Mr 
Charles Partridge, Assistant District Commissioner in Southern Nigeria, 
describes ( Cross River Natives , London, 1905, pp. 244-5) the method of 
enumeration employed in his district : — “ The natives count in fives. One 
hand means jive ; two hands, ten. When yams are counted, they are 
arranged in little heaps, each containing five. Brass rods are counted in 
bundles of twenty each, and large quantities in heaps of five bundles each 
— a hundred rods in a heap. They have adopted our word “ thousand ” to 
express ten of these heaps. The Ik we [district of S. Nigeria] numbers are 
as follows : 1 olu, 2 abaw, 3 ataw, 4 anaw, 5 iso. 6 isi, 7 essa, 8 essataw, 
9 tulu, 10 ili.” 
The following four extracts are quoted from Lubbock’s Origin of 
Civilisation (2nd ed., London, 1870): — 
“ All over the world the fingers are used as counters, and although 
the numerals of most races are so worn down by use that we can no 
longer detect their original meaning, there are many savage tribes in 
which the words used are merely the verbal expressions of the signs 
used in counting with the fingers. ... In Labrador ‘ tallek,’ a hand, 
means also 'five,’ and the term for twenty means hands and feet 
together. So also [Crantz, Hist, of Greenland, i. 225] the Esquimaux 
of Greenland for twenty say ‘ a man, that is, as many fingers and toes 
as a man has ; . . . instead of 100 they say five men ’ ” (p. 336). 
“ ‘ The Aht Indians [Sproat, Scenes and Studies of Savage Life, 
pp. 121-2] count upon their lingers. They always count . . . by raising 
the hands with the palms upwards, and extending all the fingers, and 
