rhythm in the long Norwegian and shorter Austrian records, whose curves were given in figures 36 and 24 respectively, pages 105 and 77. Pattern *J* shows the 33-year cycle of the 400-year tree, N-2, from near the Arctic Circle in Norway. The Vermont hemlocks are shown in pattern *K*. Here is found a good rhythm with a change in phase about 100 years ago. The Swedish curve shows a good rhythm at 37 years. Several intervals of triple solar cycle appear in the 1,000 years of early sequoia growth in pattern *M*. All the 8 patterns *G* to *N* are taken from special curves prepared on a one-fifth scale, using 5-year sums in the plot.

The 100-year cycle. — Only two tree records are long enough to be tested for a cycle of this length. The sequoia gives a very excellent alinement at a period of 101 years, shown even better in the upper pattern of figure 40. The pattern of the present plate shows an increase to about 125 years in the last 600 years, which corresponds to the best analysis of the 500-year Arizona curve. This latter is at 120 years as shown in pattern *P*. Both of these are made from special curves plotted on one twenty-fifth of the usual scale.

Illustration by the periodograph. — The illustrations of periodograph analysis given above are practically the first made with this instrument and are therefore crude in many respects. Its advantage in the study of simple and obvious cycles such as the sunspot numbers is not at once apparent to the eye and its efficiency becomes evident only when one tries to select the exact period and state its accuracy. But one can foresee a useful application of this instrument in the study of mixed periods, such as appear in tree-growth here considered or in rainfall and other meteorological elements, a field as yet almost untouched on account of its complexity. However, in the brief presentation of its work given above, it is evident that the periodograph is found to corroborate and extend the results of the previous direct study of curves and to confirm the evidence there given of the great extent and importance of the solar cycles in the growth of trees.