shall see presently how far these statements tally with the data drawn from fuller sources, for the half-century succeeding.
Let us now turn to Diagram No, 2, which exhibits the sun-spot curves from 1834 to 1884, paralleled with those of the temperature, the rainfall, and the lake.
We see five "periods" of sun-spot maxima, culminating in the years 1838, '48, '60, '70, and '82, the number of spots at each varying from 95 to 150. And five of sun-spot minima—in the years 1834, '44, '56, '67, and '77, the spots in each varying from 5 to 10. The maximum periods recur at intervals of ten to twelve years—and the minimum periods at like intervals—the means being 10·8 years. With the aid of the accompanying Table No. 2, we may proceed to compare results.
Table No. 2 aims to give in a succinct form all the data which our discussion requires. These are grouped in columns, as follows;
The first group gives (in three columns) the sun-spot data, in the same manner as in Table No. 1, viz., the years of maxima and minima, the number of spots at each, and the lengths of the periods.
The second or temperature group gives (in two columns) for those years of maxima and minima which conform to the sun-spot maxima and minima, the degrees of temperature (the mean of the year at Detroit), and the lengths of the periods.
The rainfall has three groups. The first gives for Detroit (in three columns) the maximum and minimum periods, the precipitation in inches at each, and the lag or interval at which each follows, inversely, behind those of the temperature. Like data are given for the rainfall at Milwaukee and at Cleveland, so far as I possess data, omitting the column of lag.
For the water-levels there are two groups, each showing (in three separate columns) the periodicities, the measurements in feet and tenths below the plane of 1838, and the lag behind the rainfall at Detroit.
Lastly are given (as in Table No. 1) the lag of the lake behind the sun-spot periods—lake maxima behind sun-spot minima, and the reverse.
My aim is to exhibit those fluctuations in the elements under discussion which conform to the sun-spot periodicities, according to the law which seems to govern, viz., temperature directly as the sun-spots; rainfall inversely as the temperature; lake-levels directly as the rainfall, and the periodical changes in each, following uniformly those of the preceding or influencing element by a lag of short interval; and this increasing in length according to the remoteness from the original source of influence.
When we consider that the sun is itself the ultimate source of all