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is seen, for example, in repeated passages of the Old Testament, as in that of Jeremiah: "As the host of heaven cannot be numbered, neither the sand of the sea measured; so will I multiply the seed of David my servant, and the Levites that minister unto me."1 Assuming the Hebrew prophet to refer to the visible heavens as seen by the naked eye, the stars are very far short of innumerable; though to a pastoral people, dealing in no elaborate computations, the simile was as expressive of multitude as the numberless sand-grains on the sea-shore. The same idea is illustrated by the manner in which the term pupía is always used by Homer in its primary sense of an indefinite number.
Many of the languages of America are found to present the singular feature of a complete decimal vocabulary of numerals, with the power of combination in some of them sufficient to adapt them to elaborate computations. This is remarkable among rude hunter tribes standing as little in need of a system of arithmetical notation as the African Damaras; and it is deserving of consideration, whether there may not be in this some lingering trace of the civilisation which has left its memorials in the elaborate geometrical structures of the Ohio Valley. Practically, however, on entering into conversation with the Indian, it becomes speedily apparent that he is unable to comprehend the idea of abstract numbers. They exist in his mind only as associated ideas. He has a distinct conception of five dogs or five deer; but he is so unaccustomed to the idea of number as a thing apart from specific objects, that I have tried in vain to get an Indian to admit that the idea of the number five, as associated in his mind with five dogs, is identical, so far as number is concerned, with that of five fingers. Abstract terms and 1 Jer. xxxiv. 22; vide also Gen. xv. 5; xxii. 16-18.
ideas are equally absent from the language and thought of the Indian; and indeed, as we see in our own English speech, are of very late growth in any language. But the concrete form of thought controls the whole American vocabularies. The different directions in which they have expanded to embrace the novel ideas consequent on European intercourse, illustrate its influence on the multiplication of mutually unintelligible dialects among unlettered tribes; and this is specially noticeable in the singular contrast in the names of numerals in American languages, otherwise disclosing striking affinities, as compared with the uniformity of numerical nomenclature pervading the whole Indo-European tongues. But no corresponding variety of symbols meets the eye. In the most perfect of the native systems of notation the signs have advanced little beyond that primitive repetition of units which betrays itself as the natural form of numeration, even in the matured hieroglyphics of the Rosetta Stone.
Thus once more we appear to reach an infantile stage of human thought in this direction also, tracing back the associated ideas and signs of number so nearly to their beginning, that we seem to stand in need of no great lapse of centuries between that and the beginning of man himself. And so is it with his ARTS: his architecture, sculpture, weaving, pottery, metallurgy; and his SCIENCE his astrology, astronomy, and geometry; the beginnings of all of them lie within our reach. Egypt has her vague year, the evidence of the beginning of the recognition of solar time in a year of 365 days, but which could only remain in use unmodified for a few generations; and in the greater and lesser cycles of Egypt, Mexico, and Peru, we equally recognise divisions of time which could not have been perpetuated through many centuries without a manifest discordance with
actual astronomical phenomena, and the changing seasons, to which they always bore an intimate relation. Seed-time and harvest are inevitably bound up with all national and religious festivals. We can trace back man's progress in the history of his calendars: in the "New Style" of England, with her lost eleven days, still religiously preserved in the unreformed calendar of Russia; in the French calendar of the Great Year, anno 14, when the Republic, with far-seeing forethought, enacted that A.R. 3600, A.R. 7200, and A.R. 10,800 shall not be leap years; while the very first year of this comprehensive system did not live out half its days! Backward we trace our way amid the conflicting dates consequent on the independent adoption of the Gregorian Calendar at various successive periods, from its first enactment by the Council of Trent in 1582, to its tardy adoption by Protestant Sweden in 1753. As we retrace our steps, we find the Church divided from the second to the fourth century, until another Council, that of Nice, determined for her the true period of keeping Easter. Then behind this, and before the Christian era, we come to the determination of the Julian Year, and the correction of the accumulated errors of previous divisions of time, in the year B.C. 47. The names of Ptolemy, Hipparchus, Meton, and Euctemon, carry us back by further steps; until in the Nile Valley we seem to reach the beginnings of calendars, and recognise, in the sacred Vague Year of the Egyptians, the first definite determination of solar time, with its unmistakable relations to a beginning of time for man himself.
Astronomy has had its rise, alike in the Old World and the New, in elevated tropical table-lands, and fruitful valleys and plains, such as those through which the Euphrates and the Tigris roll their ample floods, or that strange river-valley which the Nile fertilizes with its
annual overflow. In those favoured regions agriculture involves little toil, and the harvest ripens almost spontaneously for the reaper's sickle. There, also, flocks and herds were tended and trained for the use of man; and, in the pastoral life of their earliest communities, the herdsmen watched their flocks under the mild beaming stars, and acquired an intelligent familiarity with the constellations, and the planets that wander through the spangled dome of night. In the infancy of our race, men studied the stars, bringing to the aid of their human sympathies the fancies of the astrologer, to fill the void which their imperfect science failed to satisfy. The Chaldean shepherds, who had never travelled beyond the central plain of Asia, where in fancy we recognise the cradle of the human race, began the work of solving the mystery of the heavens; and what the Scottish shepherdastronomer of the eighteenth century, James Ferguson, accomplished, proves what lay in their power.
"O honoured shepherd of our later days,
Thee from the flocks, while thy untutored soul,
Through all the splendid labyrinths of heaven,
It was impossible that intelligent man could look forth, night after night, on the constellations, as they varied their place with the change from twilight to the dawn, and from moon to moon, and on the planets that moved in timely courses amid the twinkling stars, without discovering some of their relations to the seasons of the revolving year. But amid the same scenes of mild pastoral life, empires and populous cities first arose; forms of worship, and periodical festivals and sacrifices, marked the annual return of the seasons, when the firstlings of the flock, and, the first-fruits of the harvest-home, were
1 Eudosia, a Poem on the Universe, by Capel Lofft.
offered by priests on national altars. The herdsman and the tiller of the soil traced to the warm beams of the bright god of day the sources of fertility in flock and field. They beheld the sun when it shined, and the moon walking in brightness, and their heart was secretly enticed, and their mouth kissed the hand.' Alike in the tropical seats of primitive Asiatic empire, in the African Nile-Valley, and on the plateaus of the Andes, the early astronomers became Sabians, and worshipped the hosts of heaven, while striving to solve their mysterious relations to the earth. But if we follow them in their first division of solar time; and conceive of an annual festival, with sacrifices of the firstlings of the flock, such as we recognise in the most ancient religious rites, with a calendar founded on a year of 365 days: only a very few generations, at most, could pass away, before altogether irreconcilable and ever-increasing discrepancies would occur between the appointed festival and the actual season with which it was originally designed to harmonize. The lambs would be wanting for the burntoffering; the festival of harvesting would return while the wheat was still green in the ear, or the bright tassel of the maize was unformed; and the incensed god would be assumed to look down on his worshippers with wrath, and tardily to withhold the increase of their flocks and the yield of their early seed-time, until the calendar was readjusted, and the sacred and solar years were restored to harmony. Here, also, as we retrace our way, and seek to follow up the stream of time, the way-marks are no less continuous and definite. Names memorable among the intellectual leaders of the human race, stand out as symbols of the progress of knowledge. Leverrier, Rosse, Herschel, Newton, Huygens, and Galileo; Kepler, Tycho Brahe, Al Batani, and Copernicus; Ptolemy, Hip
1 Job xxxi. 26, 27.