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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 5o 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 MarieDavy 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:
2, 498 1879
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 fol. lowing 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 flowers ing 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
v 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;
x be the temperature of the plant;
a be a coefficient that defines the rate of development so that the reciprocal of a defines the longevity of the plant;
n be a coefficient that defines the sensitiveness of the plant to temperature, so that as n increases a given change in x has a less effect on the rate of growth and therefore the plant can flourish in a wider range of temperature; therefore its geographical distribution may be wider, hence Coutagne calls n a coefficient of ubiquity;
c be the temperature at which the most rapid development is possible under the most favorable conditions of growth or the temperature optimum; plants with a large value of c must live nearer the equator than those having small values of c; therefore c is called the index of tropicality.
According to Coutagne these quantities are bound together by the formula:
This formula represents the momentary rate of development, so that the total duration of the growth is to be found by integrating this expression, which result is written as follows:
Van Tieghem, like Coutagne and others, finds that for each special phase of vegetation, germination, heading, flowering, or ripening, and for each age of a perennial plant there exists a special relation between the temperature, the light, the moisture, and the chemical composition of the soil and water that is most favorable to growth. We have, therefore, to decide whether the same formula of development can represent the growth in each of these phases as well as throughout the whole career of the plant. As we have before said, the plant can only rearrange the inorganic products that it receives and develop its own structure by utilizing the molecular energy contained in the sunshine or some equivalent light. Its growth does not depend upon any force contained within the plant nor on the temperature, as such, but on the quality of the radiation; therefore any formula that considers temperature only must be a very imperfect presentation of the growth, especially in those stages subsequent to the full development of the leaf and flower.
Lippincott (1863, p. 506) gives a few items relative to the phenology of wheat in America and the origin of the varieties known as Lambert's Mediterranean China (or Black Tea), Hunter's, Fenton, Piper's, which were all due to judicious selection and careful culture.
The average wheat crop of England is stated to be 36 bushels per acre and that of the United States 15 or less, which large difference is, he thinks, the result of judicious cultivation and care in the choice
of seed rather than the influence of climate, since large crops have been and can be raised in this country. The injurious influence of hot, moist, and rainy weather has, he thinks, a general tendency to deteriorate the quality of American wheat, as the plant needs a hot and dry climate. Moisture defines the southern limit of wheat cultivation while the northern limit has not yet been found. In 1853 the growing season in England was too cold to ripen, the average being 57° F. for July and 59° F. for August, so that only one-half or one-third of the usual crop of wheat was harvested. In Bogota, Colombia, where the temperature of the high plains is quite low, wheat that is sown in February is harvested in the last week of July, or in 147 days, at a mean temperature of 58° or 59° F. At Quinchuqui wheat is sown in February and reaped in July at a mean temperature of 57° or 58° F. Hence Lippincott concludes that in general wheat requires a mean temperature of 60° during the last month of its maturity, or a mean temperature of 56° during the whole period of growth. • In England in 1860 wheat sown March 28 ripened August 20. Of these 145 days there were 133 that had temperatures above 42° F. In 1861 130 days were required of temperatures above 42° F. When the temperature of the soil during the last phase of growth (viz., from earing to maturity) falls below 58° to 60° F. no progress is made in the growth, and unless 60° is exceeded the crop never fairly ripens. These figures appear to accord closely with the requirements of the wheat plant in the United States, where it is found that those regions having a mean temperature for May between 58° and 60° F. can not mature the wheat in May, but those having a June temperature above 61° can ripen the wheat in that month. Those having a temperature of 61° in July can mature spring wheat which is sown the 10th of April or the 10th of May. Those having a mean temperature of 61° in May can mature the winter wheat in that month. Lippincott gives the following items: At Arnstadt, Germany, wheat requires from flowering to maturity 53 days at a mean temperature of 63° F., or a total of 3,339°F. : At Richmond, Va., Japan wheat headed April 30, 1860, and was reaped June 14, or 46 days, with a sum total of mean daily temperatures of 3,086° F.: At Haddonfield, N. J., Mediterranean wheat sown early, headed May 18, 1864, and matured June 30, or 44 days, with a sum total of 3,024°F. of mean daily shade temperatures: In Monroe County, N. Y., wheat headed May 10, 1859, and matured July 8, or 56 days, with a sum total of 3,562°F. The preceding meager data are all that Lippincott was able to find