in the manner we have described.' Mr. Mill's argument is taken from the mental conditions of people among whom there exists a highly advanced arithmetic. The subject is also one to be advantageously studied from the ethnographer's point of view. The examination of the methods of numeration in use among the lower races not only fully bears out Mr. Mill's view, that our knowledge of the relations of numbers is based on actual experiment, but it enables us to trace the art of counting to its source, and to ascertain by what steps it arose in the world among particular races, and probably among all mankind.
In our advanced system of numeration, no limit is known either to largeness or smallness. The philosopher cannot conceive the formation of any quantity so large or of any atom so small but the arithmetician can keep pace with him, and can define it in a simple combination of written signs. But as we go downwards in the scale of culture, we find that even where the current language has terms for hundreds and thousands, there is less and less power of forming a distinct notion of large numbers, the reckoner is sooner driven to his fingers, and there increases among the most intelligent that numerical indefiniteness that we notice among children — if there were not a thousand people in the street there were certainly a hundred, at any rate there were twenty. Strength in arithmetic does not, it is true, vary regularly with the level of general culture. Some savage or barbaric peoples are exceptionally skilled in numeration. The Tonga Islanders really have native numerals up to 100,000. Not content even with this, the French explorer Labillardière pressed them farther and obtained numerals up to 1000 billions, which were duly printed, but proved on later examination to be partly nonsense-words and partly indelicate expressions, so that the supposed series of high numerals forms at once a little vocabulary of Tongan indecency, and a warning as to the
- Mariner, 'Tonga Islands,' vol. ii. p. 390.