But we may once more turn aside from the physical to the intellectual aspect of available evidence, and find confirmation of a like kind in one of the earliest definite manifestations of cultured reason. Few tests of relative stages of civilisation are more trustworthy than that of the definite conception of high numbers. The prevalence of a decimal system of numerals among widely severed nations, alike in ancient and modern times, has been universally ascribed to the simple process of counting with the aid of the fingers. Mr. Francis Galton, in his _Narrative of an Exploration in Tropical Africa_, when describing the efforts of the Damaras at computation, states that the mental effort fails them beyond _three_. “When they wish to express _four_, they take to their fingers, which are to them as formidable instruments of calculation as a sliding rule is to an English schoolboy. They puzzle very much after _five_, because no spare hand remains to grasp and secure the fingers that are required for units.” Turning to the line of evidence which this primitive method of computation suggests, some striking analogies reveal a recognition of ideas common to the savage and to the cultivated Greek and Roman. Donaldson, in his _New Cratylus_, in seeking to trace the first ten numerals to their primitive roots in Sanskrit, Zend, Greek, and Latin, derives seven of them from the three primitive prenominal elements. But _five_, _nine_, and _ten_ are referred by him directly to the same infantile source of decimal notation, suggested by the ten fingers, as has been recognised in similar operation among the Hawaiians, and the Maoris of New Zealand. “One would fancy, indeed, without any particular investigation of the subject, that the number _five_ would have some connection with the word signifying ‘a hand,’ and the number _ten_ with a word denoting the ‘right hand’; for in counting with our fingers we begin with the little finger of the left hand.” Hence the familiar idea, as expressed in its simplest form, where Hesiod (_Op._ 740) calls the hand πέντοζον, the five-branch; and hence also πεμπάζω, primarily to count on five fingers. Bopp, adopting the same idea, considers the Sanskrit _pan’-cha_ as formed of the copulative conjunction added to the neuter form of _pa_, one, and so signifying “and one.” Benary explains it as an abbreviation of _pân’-i-cha_, “and the hand”--the conjunction being equally recognisable in _pan’-cha_, πέν-τε, and _quinque_. This, they assume, expressed the idea that the enumerator then began to count with the other hand; but Donaldson ingeniously suggests the simpler meaning, that after counting four the whole hand was opened and held up. To reckon by the hand was, accordingly, to make a rough computation, as in the _Wasps_ of Aristophanes, where Bdelycleon bids his father, the dicast, “first of all calculate roughly, not by pebbles, but ἀπὸ χειρός, with the hand.”