The considerations which have just been set forth have led to a third hypothesis, that of pulsatory climatic changes. According to this, the earth's climate is not stable, nor does it change uniformly in one direction. It appears to fluctuate back and forth not only in the little waves which we see from year to year or decade to decade, but in much larger waves, which take hundreds of years or even a thousand. These in turn seem to merge into and be imposed on the greater waves which form glacial stages, glacial epochs, and glacial periods. At the present time there seems to be no way of determining whether the general tendency is toward aridity or toward glaciation. The seventh century of our era was apparently the driest time during the historic period--distinctly drier than the present--but the thirteenth century was almost equally dry, and the twelfth or thirteenth before Christ may have been very dry. The best test of an hypothesis is actual measurements. In the case of the pulsatory hypothesis we are fortunately able to apply this test by means of trees. The growth of vegetation depends on many factors--soil, exposure, wind, sun, temperature, rain, and so forth. In a dry region the most critical factor in determining how a tree's growth shall vary from year to year is the supply of moisture during the few months of most rapid growth.[22] The work of Douglass[23] and others has shown that in Arizona and California the thickness of the annual rings affords a reliable indication of the amount of moisture available during the period of growth. This is especially true when the growth of several years is taken as the unit and is compared with the growth of a similar number of years before or after. Where a long series of years is used, it is necessary to make corrections to eliminate the effects of age, but this can be done by mathematical methods of considerable accuracy. It is difficult to determine whether the climate at the beginning and end of a tree's life was the same, but it is easily possible to determine whether there have been pulsations while the tree was making its growth. If a large number of trees from various parts of a given district all formed thick rings at a certain period and then formed thin ones for a hundred years, after which the rings again become thick, we seem to be safe in concluding that the trees have lived through a long, dry period. The full reasons for this belief and details as to the methods of estimating climate from tree growth are given in _The Climatic Factor_.