Any such mode of counting, whether involving the use of the fingers or not, is to be regarded simply as an extraneous aid in the expression or comprehension of an idea which the mind cannot grasp, or cannot retain, without assistance.

The German student scores his reckoning with chalk marks because he might otherwise forget; while the Andaman Islander counts on his fingers because he has no other method of counting,--or, in other words, of grasping the idea of number.

A single illustration may be given which typifies all practical methods of numeration.

More than a century ago travellers in Madagascar observed a curious but simple mode of ascertaining the number of soldiers in an army.[6] Each soldier was made to go through a passage in the presence of the principal chiefs; and as he went through, a pebble was dropped on the ground.

This continued until a heap of 10 was obtained, when one was set aside and a new heap begun.