This is true of the other elements of ethnic culture. The localities where many such overlappings occurred became secondary centres from which in turn the circular activity of culture was propagated. A mart where many visitors from different nations congregated would receive some new learning from all and through its concentration would impart this higher potency in some measure to all. For example, the city of Nippur, on the Babylonian plain, attracted twenty-five hundred years ago to its markets not only Assyrians and Edomites, but Medes and Persians from the East, Syrians and Hittites from the West, and probably Greeks and Egyptians and Arabians from remoter lands. Human progress has been likened by some to a spiral figure where each advance is a repetition of a former stage but with improvements to it. This is a combination of the right line and the curve; but the notion that repetition or recapitulation exists in evolution in any other form than that of renewed effort finds little support in natural science. 3. _Variation in Waves, or Rhythmic Undulations._—Some of the most recent speculations on the ultimate forces of the universe lead to the belief that they are maintained in activity by an eternal rhythmic pulsation or undulation, generating its energy from its periods of repose. This doctrine has been applied by Professor Gerland to the progress of the human race. His teaching is that after a period of rapid advance there follows one of depression, which in turn is succeeded by another of advance, reaching a higher development than any which preceded it. Other writers have expressed this notion in the form that after a period of activity and invention follows one of repose and reflection, giving way in turn to another of activity. THE RATE OF PROGRESS.—Professor de Mortillet calculates from a wide range of data, geologic and archæologic, that man has lived on the earth about 240,000 years. The most conservative student of prehistoric records would not estimate the life of our species at less than fifty thousand years, and it is much more likely to be double that duration. The date of anything like civilisation is much more recent. Even in its oldest centres, as Egypt or Babylonia, to place its beginning ten thousand years ago is to exceed the demands of the boldest antiquary; while over most of the now civilised areas of the globe a condition of barbarism prevailed until less than two thousand years ago. These facts prove wide variations in the rate of progress, very slow movements in earlier times and lower conditions, singularly rapid advances in later high conditions. We are led to the conclusion, therefore, that the rate is not by one mode of progression but by several. 1. By arithmetical progression (addition). 2. By geometrical progression (multiplication). 3. By saltatory progression (permutation).