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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 a 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:

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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:

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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

with regard to wheat in America after an extensive research, but within the past few years much more attention has been given to this subject.

The differences between-the quantities of heat required in England and America and the differences in the varieties of the wheat were apparent to Lippincott. Thus, he finds that in England the lengths of the periods and the sums of the temperatures were as follows: In 1860 a period of 59 days and a sum of 3,562° F.; in 1861 a period of 50 days and a sum of 3,225° F.; in 1862 a period of 56 days and a sum of 3,406° F. The reduction of the mean temperature during two months of 1853 by merely 2° F. cut off one-third of the crop and brought a famine that was already foreseen in July, 1853. On the other hand, it increased the exportation of wheat and flour from the United States from $14,000,000 in 1852 and $19,000,000 in 1853 to $49,000,000 in 1854.

A careful study of the sum totals of rainfall, temperature, and sunshine should enable one, in general, to foresee similar failures and corresponding successes in the crops of any region.

QUETELET.

The suggestive, but sketchy, studies of earlier writers on thermal constants were supplemented by more elaborate investigations and calculations of statistics by Quetelet (1849) in his Climate of Belgium, from his own summary (p. 62), etc., I take the following

notes:

The details hitherto given show sufficiently that the relative conditions of vegetation change at all times of the year in two countries situated at a distance from each other. Acceleration and retardation are quantities essentially variable, and it is erroneous to say that one locality has its budding period ten or twenty days sooner, for example, than another. This difference may be correct for one season of the year and entirely wrong for another; and, moreover, we can only pretend to state a fact which applies to the majority of plants.

Nevertheless the differences in the periods of budding are not so variable but that we can assign to them values very useful to consult in practice. On the other hand, science needs to establish some welldetermined facts in order to arrive later at the knowledge of the laws upon which these variations depend. I believe that in the actual state of things I shall be able to settle upon the following epochs, in order not to multiply too much the terms of comparison. Moreover, the numerical tables justify, to a certain extent, the distinctions which I lay down.

Let us first observe that the awakening of the plants is brought about by the cessation of the cold, and it suffices to consult the tables of temperatures for the different countries to determine the average epoch at which many plants will put out their leaves or their flowers. These first indications, which it is well to collect, still do not determine, however, the general movement of vegetation which may

manifest itself more or less slowly. They are given by the budding of the Galantus nivalis, of the Crocus vernus, by the appearance of the catkins of the Corylus avellana, of the leaves of the Ribes grossularia, of the Sambucus nigra, of the honeysuckle, and of some spireas. The falling of the leaves is also determined by the temperature, and in our climate generally takes place after the first frosts. This period and that previously mentioned come ordinarily at the two limits of winter, and they separate to make place for the different stages of vegetation in proportion as the cold of winter has a less duration. The winter sleep lasts in our climate from three to four months; in southern countries it is very much shorter. We can even imagine a line on the surface of the globe where it ceases altogether for the generality of plants."

The great movement of vegetation commences in Belgium in the middle of March and terminates at the end of April. I will call this the period of leafing (feuillaison), because during this interval the different plants are covered with their verdure and some of them show their first flowers.

The second period is that of flowering (floraison), which in our climate would include the months of May and June and the first half of July.

The third period would then come, which is that of ripening (fructification).

These three great periods should undoubtedly be in their turn subdivided, but the present state of the observations does not allow of such detail. It is understood, moreover, that the names I have given to them only serve to designate the principal phases of vegetation which take place. Thus, in making the general table [omitted-C. A.] I have classed the different plants according to the following seasons:

Awakening of the plants. This period is determined by the plants comprised in the [omitted] table.

Leafing. This period comprises the plants which, in Brussels, put out their leaves from the 15th of March to the 30th of April, and which bud during the same two months.

Flowering. I have made use of the plants which have flowered or brought forth their fruit from the 1st of May to the 15th of July.

a As I have already observed elsewhere, the awakening is an epoch that is not the same for all plants. I mean to speak here only of the epoch when the sap begins to circulate in the majority of the plants which grow in our climate. "All plants do not begin to vegetate at the same period," says M. Ch. Martins, in the Botanical Expedition along the Northern Coasts of Norway. "Thus in some the sap begins to mount when the thermometer is only a few degrees above zero (centigrade); others need 10 or 12 degrees of heat, while those in warm climates require a temperature of from 15° to 20° C. In a word, every plant has its own thermometric scale, whose zero corresponds with the minimum temperature at which vegetation is possible for it. Consequently, when we wish to determine the sum total of the temperature that has determined the date of flowering (fleuraison) of each of these plants it is logical to only consider for each plant the sum of the degrees of temperature above zero (centigrade), since these temperatures are the only ones that have been efficient in inducing or sustaining their growth." In tropical countries the great fluctuations in the vegetable kingCom are not regulated by the same meteorological elements as are effective with us; there the rainy season produces very nearly the same effects as the cold season does in our climates.

Ripening. This period comprises the stage of vegetation, which, for Brussels, extends from the 15th of July to the falling of the leaves, the last limit of the period with which we are occupied here.

This classification has allowed me to put into [the omitted] table the observations gathered from other sources, as well as from the system of comparative observations which the Royal Academy of Belgium has succeeded in establishing at Brussels.

The average influence of location on the annual progress of vegetation.

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