reduced to sea level, begin with March 12 in southern France and extend to April 21 in northern France. The dates of flowering begin with April 6 in southern France and extend to May 16 in northern France.

The sums of temperatures are counted from the last severe frost, and the most accordant results are obtained when the sums of daily maxima are taken, counting from 2° C. The sum total is 715° to date of leafing, and from leafing to flowering 1,070°.

The leafing of the birch is found by Angot to have the same rate of retardation—very little less than four days per 100 meters—and the reduced epochs of leafing begin the 9th of March at the southeast corner of France and extend to the 16th of April at the northern border. The sums of temperatures up to the time of leafing are best computed by taking the sums of daily maxima above 2° C., but are very uncertain.

The leafing of the common oak (Quercus pedunculata) has a retardation of four days per ascent of 100 meters, and the reduced epochs begin with the 6th of April in southern France and end with the 6th of May in northern France. We can provisionally admit that the leafing of the oak occurs when the sum of the maximum daily temperatures has attained 940 C., counting above 2° C. and from the date of the last heavy frost.

The flowering of the elder (Sambucus nigra) has an approximate retardation of four days per 100 meters. The reduced dates begin on the 6th of April in southern France and end on the 10th of June in northern France. The flowering of the elder occurs when the sum of the mean daily temperatures since the date of the last frost has attained 840° C. if we count from 2°, or 630° if we count from 4° C. The flowering of the common linden (Tilia europaa) or the Tilia silvestris is retarded three days per 100 meters' ascent for the mountainous countries, but four days is adopted for the whole of France, and the reduced dates of flowering begin with the 1st of May in southeastern France and extend to the 20th of June in northern France. The flowering of the linden occurs when the sum of the mean daily temperatures, counting from the last heavy frost and above 2o C., has attained 1,090° C.

It would seem to result from all this that the leafing of the trees and shrubs occurs when the sum total of the maximum daily temperatures, counting above a certain limiting value and from the date of the last heavy frost, has attained a certain value characteristic of each plant. But for a certain number of plants the flowering seems rather to depend on the sum of the mean daily temperatures.

In his second memoir Angot (1886) studied the additional data for the years 1882 and 1883. A new determination of the influence of altitude on the epoch of leafing again gave an average retardation of four days for each 100 meters of altitude for the lilac, the chestnut, the birch, and the oak. The average mean daily temperature of the air at the date of leafing varies between 5° and 12° C. for the lilac, with an average of 9.1°; from 4° to 14° C., with an average of 10.1°, for the chestnut; from 7° to 15° C., with an average of 10.7°, for the birch; from 5° to 16°, with an average of 11.3°, for the oak. These ranges are so large that it is impossible to indicate any simple relation between the leafing of these plants and the mean daily temperature at this epoch. The mean of the daily maxima were also computed for the epoch of leafing, and were 14.6° for the lilac, 15.7° for the chestnut, 16.1° for the birch, and 16.4° for the oak. But again the variations were too large to attach any phenological importance to these numbers.

As to the sum total of temperatures Angot adopts, not a constant date, as December 1 or January 1, but dates that are variable for each station and each year and approximately represent the close of the last period of freezing weather. They vary in this case between the 18th of January and the 13th of February. After laborious calculations by different methods and starting from different initial temperatures he concludes that the leafing of the four plants under consideration occurs when the sum of the mean daily temperatures, counted from 0° C., or the sums of the maximum daily temperatures, counting from 0° C. and beginning at the date of the commencement of vegetable growth as above defined, attains the values given in the following table:

In order to decide which of these two modes of calculation, daily mean or daily maxima, are most proper it will be necessary to operate upon a much longer series of observations.

The flowering of the narcissus, the lilac, the chestnut, the elder, and the linden was studied in a manner similar to that of the leafing. The retardation for altitude is, as before, four days to the 100 meters. The man daily temperature at the date of flowering is: For the narcissus, 6° to 14° C., average 9.4°; for the lilac, from 8° to 15° C.,

average 12.2°; for the chestnut, 8° to 16° C., average 12.0°; for the elder, 9° to 20° C., average 13.9°; for the linden, 12° to 21° C., average 16.4°. The mean daily maximum temperatures at the date of flowering for these same plants is as follows:

Evidently the maximum temperatures have no clearer connection with the date of flowering than have the mean daily temperatures. The sums of temperatures from the beginning of vegetation to the date of flowering have also been computed by different methods and from different initial temperatures. The following are the results when the initial temperature is 0° C.:

Here, again, as in previous cases, the relative value of the different methods of taking account of the temperature is determined numerically by taking the sums of the departures from the average for the individual stations and years. In the present case the mean departures as thus determined are exactly the same for both methods, so that four years of observations, 1880-1883, have not sufficed to decide as to which mode of calculation it is proper to adopt as the best. A similar calculation as to the amount of heat received by the lilac and the chestnut between the epochs of leafing and flowering leads to the same indecision as to the methods of calculation. The actual sums between the leafing and the flowering are as follows:

The flowering and ripening of winter wheat during 1882 and 1883 has been studied on the basis of data from about 500 stations, combined with the previous data for 1880 and 1881.

The mean daily temperature at the time of flowering is for rye 13.3°; but the individual numbers range from 9° to 18°; similarly for winter wheat the mean is 16.2° and the range from 10° to 21°. The commencement of vegetation for winter wheat is uniformly adopted as December 1. The sums of the mean daily temperatures have been calculated from several points of departure and seem to prove that the lower limit of useful temperatures is very nearly 5° C., so that we can take 6° C. as the point of departure, as has been done by many authors.

The sums of the mean daily temperatures, less 6° C., rejecting the negative remainders and counting from the 1st of December, are ast follows:

The harvest date for spring barley is shown to depend in 1882 and 1883 quite as little on the date of sowing as it did in 1881.

The retardation due to altitude is as before, four days per 100 meters. Adopting the 20th of March as an average date of sowing, the sums of the mean daily temperatures have been considered up to the date of harvest, with different assumptions as to the fundamental temperature. As before, the best result is given when the sums are taken of the excess of the mean daily temperatures above 6° C., and the resulting figure, 984, is seen to be between the two figures for rye and winter wheat.

In his third memoir Angot (1888) studies the phenomena of 1884 and 1885 in combination with the preceding. The same allowance is made for rates of retardation. The relation between the times of leafing, the mean daily temperature at that date, and the maximum

temperature at that date, is computed by the same process as before, with the following results for the years 1884 and 1885:

The mean values here given agree well with those of the previous years, but the individual numbers have such a wide range that we can not conclude any simple relation between the leafing and the mean temperatures.

The relation between the leafing and the sums of temperatures is found, as before, by assuming the end of the last period of frost as the commencement of vegetation; for these years this corresponds with the last few days of January. The useful temperatures are considered to be those above 0° C., and Angot has computed both the sums of the mean daily temperatures and also the sums of the maxima alone with the following results:

The reliability of these sums is, as before, determined by examining the departures, although not according to the strict rules of the law of probabilities of errors, but sufficiently so to show that the uncertainties of each of these figures is larger than the differences for successive years. The average of the two years, 1884 and 1885, are considerably higher than those for the previous four years.

The flowering of the lilac, chestnut, elder, and linden is again investigated by using the observations at some 1,200 stations or less. The reduction for altitude is as before. The mean daily temperatures