where the notation is as follows: C is the total heat from the date of sowing up to the date of sprouting; a is the thermal constant from one phase to the next, such as from sprouting to flowering; t is the number of days from sprouting to flowering; c is the mean daily temperature from sprouting to flowering; te is the total sum of mean daily temperatures from sprouting to flowering; as this temperature is principally active during the daytime, therefore one-twelfth of te represents the efficient heat during an hour; h is the duration in hours of an average growing day, viz, from sunrise to sunset; therefore one-twelfth of the product eht represents the total heat that has been utilized by the plant.

The method of reasoning by which Kabsch arrives at the above formula, which I have quoted from Fritsch, is not known, to me.

Sachs, by direct experiment, finds that for each plant there is a temperature most favorable to its growth and two other limits, minimum and maximum, beyond which it will not grow.

Deblanchis finds that the temperature on which vegetation depends is not the ordinary temperature of the air as given by a sheltered thermometer; he prefers to approximate to the temperature of the leaf of the plant by the use of his "vegetation-thermoscope," which is an ordinary minimum thermometer covered with green muslin and kept moist, as in the ordinary wet-bulb thermometer. He places his thermometer at one and a half meters above the soil and in full exposure to sun and sky. Evidently the sum total of his temperatures will be between the sums of the ordinary wet-bulb and the ordinary dry-bulb thermometers, but must differ greatly from the temperature of the roots on which the growth of the plant primarily depends.

Hoffmann prefers to take for the daily temperature the excess above freezing of the maximum thermometer exposed to full sunshine and free air. Hoffmann's temperatures approach more nearly the temperature of the roots within a few inches of the surface of the ground. Besides taking the sums of the average daily temperatures of the shaded air thermometer, omitting all negative values or all those below freezing point, Hoffmann also took the sum of the bright bulb in vacuo and of the black bulb in vacuo, both in full sunshine; these latter temperatures are generally higher than those of the roots and much higher than those of the leaves. Hoffmann prefers to use the readings of the bright bulb in vacuo.

Hervé Mangon (1879) modifies Gasparin's method slightly in that he takes account of the shade temperatures of the air from the date of sowing up to the date of harvest, rejecting all cases where the mean daily temperature in the shade is less than 6° C.; he had been led to think that the vegetation of cereals and other important crops ceases below this temperature. Thus he determines the sum total

needed for ripening the crops of the varieties of wheat ordinarily cultivated in Normandy, as shown in the following table:

By similar calculations Hervé Mangon obtains for other crops as cultivated in Normandy the following results:

Hervé Mangon concludes his essay with two important practical rules, deduced from his data relative to the climate and crops of the department of La Manche: (1) In a mild and uniform climate, like that of the northwest of France, there is always an advantage in sowing the seed early in the autumn; (2) by computing annually the sums of the degrees of temperature observed since the date of sowing and by consulting the numerical tables given in this memoir one can, with great accuracy, calculate four or six weeks in advance the date of the approaching harvests of the respective plants.

The tables given by Mangon for his locality can be reproduced for American stations wherever the meteorological observations and the dates of planting and harvesting are recorded; although it may be possible to consider more minute details of climate and soil than he has done, yet the success attained by him in his elementary collation of fundamental data must stimulate to similar work in this country.

From the data given by Mangon, Marié-Davy deduces some further phenological constants which will be useful, viz, for winter wheat in Normandy, the sum of the daily temperatures in the shade, rejecting all below 6° C., from sowing to germination is 85° C.; from germination to heading, 555° C.; from heading to maturity, 1,810° C. This gives from sowing to heading 640° C., whereas Gasparin, following his own rule, which takes the sum of all temperatures after the date at which the temperature of 5° C. is attained, finds 430° for this constant.

Wheat begins to grow visibly when the mean daily temperature is about 6° C. This mean daily temperature is attained on the average of many years on the dates given in the second column of the following table. (See Marié-Davy, 1881 and 1882, p. 184.) The average dates of harvest are given in the third column; the interval or growing period in the fourth column; the fifth column contains the sums of the mean daily temperatures of the air in the shade (after the date on which a mean temperature of 6° was attained), the sixth column gives the sums of the mean daily temperatures of the thermometer in the full sunshine, as determined by Gasparin. The close agreement of the two latter numbers is considered by MariéDavy an argument in favor of the idea that temperatures in the sunshine are better than those in the shade as a measure of the influence of heat and light on the growth of plants.

Balland (see Marié-Davy, 1881, p. 186) has made a perfectly similar computation with reference to the ripening of wheat cultivated on a large scale at Orleansville, in Algeria, with the following results:

1878

1879

2,498

2.433

Average

2,462

The results of Mangon, Balland, and Gasparin agree so closely that a strong argument seems to be afforded in favor of using the thermometer exposed to the full sunshine. The differences in their results. are quite comparable to the differences found by Vilmorin to exist between different varieties of the same seed.

The values of the thermometric constants, as computed by Herve Mangon's method, for other grains cultivated in Normandy are given

in the following table, where the figures represent the sums of sunshine temperatures necessary to complete the growth from germination to harvest.

Marié-Davy (1881), in his chapter on the influence of heat on the time required for vegetation, adopts the principle enunciated by Boussingault, of the equality of the sum total of the temperatures, but thinks that the temperature required to bring a plant to the flowering stage is the sum of the mean daily temperatures in the full sunshine, and not the temperature of the air in the shade. According to his view, the heat is needed in the soil in the early part of the growth of the plant; but after the flower is formed, or during the process of perfecting the fruit, sunlight is needed, and during this stage he uses the actinometric degrees of the Arago-Davy actinometer as an index of the progress of the plant. I have, therefore, in the following table collated the figures given by him for wheat. The third column gives the sum total of the mean daily shade temperatures, counted from February 1 of each year up to the date at which the total amounts to 1,264° C., or within half a day thereof, that being the adopted shade constant for the flowering of wheat that was sown on or about the 21st of March. The fourth and fifth columns give the dates and sum totals of temperatures observed with a naked-bulb. thermometer on the grass in the full sunshine, assuming 1,569° C. as the thermal constant for this thermometer. The sixth column. gives the observed dates of flowering. As these dates agree with those in the fourth column better than with those in the second column, Marié-Davy considers them as confirming him in the use of the unprotected solar thermometer. In order to bring out the total effect of sunlight and sun heat Marié-Davy has computed the sum total of actinometric degrees from February 1 up to the dates given in column 2 and in column 4, respectively. These results are given in columns 7 and 8, which show that 1878 was a very precocious year, as compared with the others, in that the date of flowering was very early, but the sum total of its actinometric degrees was very small and its crops were very poor. 1879 and 1877 show larger actinometric sums, but the largest sums are given by the years 1873, 1874, 1875, and 1876, which were also very excellent crop years,

Marié-Davy concludes that by keeping a daily summation of actinometric degrees it becomes possible, even at the epoch of flowering of wheat, to estimate in a very approximate manner what will be the final value of the resulting harvest. At this moment, even if we have already measured the sum of the products which should be applicable to the formation of grain, we can not be absolutely cert in that the harvest will correspond to our expectations. A certain time is necessary for the nutrient particles to traverse the various parts of the stem up to the seed, and a certain quantity of water is necessary for this transportation. An excessive dryness or heat will interfere with this movement and will give a poorly developed grain, notwithstanding the abundance of nutrition reserved for it within the plant. But although water and nutrition are as important as heat and light, still we find that predictions based on actinometric degrees alone are very reliable.

According to Georges Coutagne, the law that connects the rate of development of a plant with its temperature must be such that it has a maximum value for a special temperature and diminishes as we depart from this down to a zero rate at the freezing point and also to zero at some higher temperature at present unknown; all this is on the assumption that the sunlight, moisture, and winds are such as to enable the plant to do its very best at the given temperature. If this law were known we could then determine whether a plant would live and flourish in any given climate.

This law of growth has been expressed by Georges Coutagne, as quoted by Marié-Davy (1883, p. 227), by the following notation and formula. Let

be the rate of development of the plant, assuming that other conditions are so adjusted that it attains the maximum growth possible for the given temperature;

be the temperature of the plant;