of coincidence is reduced to harmony. It will also appear that the rainfall extremes are not only followed invariably by corresponding fluctuations in the water-levels, but that these succeed each other in quite as marked and uniform periods.
The rainfall maxima of 1836, '44, '55, '68, and '80 have their corresponding extremes in the water maxima of 1838, '47, '58, '70, and '82—the intervals or lag varying from two to three years. The rainfall minima of 1839, '50, '60, '72, and '86 have corresponding lake minima in 1841, '53, '65, and '75—the intervals varying from two to five years. The mean lag is 2·9 years. The true relation—dependence—of the lake periodicities upon those of the rainfall is thus clearly shown.
It will be observed, that I have chosen to consider the Lake Erie levels rather than those of Detroit River. I do so for the reason that the relations of the former to the precipitation are more simple and direct, and are not influenced by causes already pointed out (page 375), which tend to create irregularities in the river. A marked illustration is shown between the years 1859 and 1870—where dotted lines represent the rainfall at Milwaukee, and the river-levels as compared with those of Lake Erie—of the effect of excess of precipitation on the lakes above, in keeping up the river to a disproportionate extent.
I do not consider it necessary to examine the various theories which have been broached from time to time, in explanation of the lake periodical fluctuations. Nor will I undertake to explain all the irregularities of the river and lake, which would demand many factors that are wanting to the present discussion. It will suffice if I have succeeded in making clear the relations which exist between the variations of the water-levels and the rainfall, and in defining their periodicities. Probably few at this day would dispute the fact that the rise and fall, or "secular" variations, in the waters are dependent upon the rainfall. This is the first attempt, to my knowledge, at demonstration of their true relations.
Thus far I have not alluded to the important element of Temperature in its relation to rainfall. That an intimate relation exists is an admitted fact; it shall be my endeavor to show what this relation is.
In the portion of the diagram devoted to the Detroit temperature curve, the horizontal lines represent the degrees of mean annual temperature, which varies from 42°, the lowest, to 52°, the highest extreme. Considering temperature as a controlling element, we should expect to find, a close correspondence between its curves and those of the rainfall. And we do so find, as is shown by the diagram. But, while the maxima and minima of the rainfall and the lake are directly as each other, we discover that those of the rainfall and the temperature are inverse to each other. For a full discussion of the relation between these two elements, no doubt we ought to take into account