The two columns (on the right of the table) showing the lag of Lake Erie behind the sun-spots at each period, furnish a remarkable confirmation of the general conclusions. (Comparing the two tables, it will be seen that the mean periodicity of the sun-spots is larger for the first half-century than for the last by 1·7 years. Yet the same relation to the lake periods is maintained throughout both cycles. The lag for the maxima and for the minima periods is the same in both tables, the means being 3·5 years and 4·5 years, respectively. This result is not merely remarkable; it would be incomprehensible on any other theory than that here contended for. Its truth or fallacy the reader has the means of determining if he will closely study the details given in the table and the diagram.
Another feature of too much importance to escape attention is the difference in all the curves between the scales of increase and of decrease. This is shown by the diagram, and is computable from the tables. Thus, the times of increase in the sun-spot curve, from minima to maxima, are almost uniformly four years; those of decrease, or from maxima to minima, six to eight years. The temperature curve attains its maxima at the same time or a year later than the sun-spots, but its minima are often reached a year earlier than those of the sun. The result is to nearly equalize the times of temperature increase and decrease, the rising scale being accomplished in 5, and the falling in 5·4 years.
The rainfall curves show a closer correspondence with the sun's times, but in reversed order, the rising scale being accomplished in about 6·5 years, the falling in about 4·5 years.
The lag of the lake curve behind the rainfall at its minima exceeds that of its maxima by nearly one and a half years (3·75 and 2·4). The tendency is to equalize the times of the lake increase and decrease, so that the "secular periods" exhibit nearly equal scales (5·4 and 5·25). During the cycle from 1779 to 1834 the scales differ more—rising 5·75 and falling 6·75 years. These are the closest correspondences I have been able to find to the traditional French period of 7 years.
Thus the cycle of change is "never ending, still beginning." On its restless sea, man is tossed at the caprice of billows, whose wavelengths are intervals of eleven years. The law of change runs through the scale from cold to warm, and from-warm to cold in nearly equal times, but demands half a year's less time in the descent from wet to dry; while the upward scale, or from dry to wet, is longer by two years than the downward scale of temperature, and with intervals or lag of one and a half years.
To sum up, it seems to me demonstrated, as regards this region:
1. That the so-called "secular" changes in the levels of the river and lakes are dependent upon the rainfall.
2. That these changes in their maxima and minima fall behind the rainfall extremes in time, varying from two to five years.