Thermal constants for the blossoming and ripening of 889 plants, etc.-Continued.

57. The fruit ripens during the following season. 168 and 175. Did not bloom during the ten years.

179 and 189. Tree too young to blossom.

203. The concealed blossoms can not be accurately observed.

270 and 271. The dates of blossoming are too variable to allow of determining a thermal constant. 304. These figures obtain for moist years, but for dry years we have September 9 and 2237, respectively.

308. Blossomed only once during these ten years.

518. The blossoming of the tree is not easy to observe.

577. The tree died in 1855.

580 and 581. Too young to blossom.

702 and 775. Did not blossom.

716. Blossomed only once and died in 1857.

756. Did not blossom and died in 1856.

800. Dates are too variable to allow determining a thermal constant.

834 and 880. The dates when the hull hardens and colors and when it springs open, allowing the fruit to fall, are both given.

LINSSER.

The most elaborate and, I believe, the most important investigation into the relation between plant life and climate is that published by Karl Linsser in a first memoir (St. Petersburg, 1867) and in a second memoir of 1869. My personal association with him during 1865 and 1866 greatly stimulated my own early interest in the subject. The conclusions arrived at by Linsser are based upon the study of all available European observations. His knowledge of physics and skill in numerical computations as the chief of the computing division of the Imperial Astronomical Observatory at Poulkova has given his results a precision based on the well-established principles of probabilities and a clearness of interpretation that specially commend them to the physiological botanist. Linsser states that the principal hypotheses that had up to his time been framed as to the form of the connection between the phenomena of temperature and of phenology are the following three:

(1) That for the same plant the same stage of vegetation occurs from year to year on the attainment of the same mean daily temper

ature.

(2) That the same stage of vegetation is attained when in the course of any year the sum total of the mean daily temperatures above freezing attains the same value.

(3) That the same stage of vegetation is attained when in the course of any year the sum of the squares of these positive temperatures attains a certain constant value.

The first of these hypotheses has, he states, long since been given up as of insufficient accuracy not only for any given station, but still more when we consider the temperatures belonging to a given stage of vegetation of the same plant in localities that differ much in latitude or longitude.

The third hypothesis is that which was favored by Quetelet, and the second is that which had for a hundred years been generally adopted by botanists. Both of these two latter hypotheses were most thoroughly investigated by Erman in his memoir, published in 1845 and 1849.a

Erman demonstrates that both these hypotheses are unsatisfactory, but Linsser proposes to reinvestigate the question on the basis of a much larger collection of material, both phenological and meteorological.

The first step in Linsser's investigation consists in finding a method of computing the sums of the temperatures or the sums of the squares of the temperatures above freezing when the average temperature of any day of the year is expressed by the so-called sine and cosine formula of Bessel. He computes the coefficients of Bessel's formula, and therefore knows the equations that express the mean daily temperature for any day in the year and for each of his. stations of observations."

The summation of the squares of the mean daily temperatures was computed by Linsser by the method known as mechanical quadratures. The following table illustrates his results for seven groups of

a I very much regret that I have not been able to examine these memoirs, which are published in the Archiv für Wissenschaftliche Kentnisse Russland, Vols. IV and VIII.-C. A.

A similar computation had been made by Erman, but for the benefit of those who may in the future have to go through similar labors I would suggest that it is not more laborious and is certainly more perspicuous to compute the actual daily temperature for every fourth day of the year, beginning with January 0, and in the adjoining column make up the continuous summations. The difference between the sums for any two dates is then the total mean daily temperature to which the plant has been subjected.—C. A.

plants that were observed at Brussels and at Poulkova, which is 12 miles south of St. Petersburg:

In taking these sums, which all relate to positive temperatures on the centigrade thermometer only, Linsser begins with April 8 at Poulkova, because on that date the gradually rising daily temperatures pass through the freezing point. It would have made no difference if he had begun with January 1, or December 1, or with the date of lowest mean temperature, which would be about the middle of January. On the other hand, for Brussels his sums begin with January 15, which is the date at which the lowest mean daily temperature occurs, which temperature is about +2.5° C., so that if he had begun with January 1 there would have been a constant slight addition to all the numbers in that column. The dates of blossoming are given in days counting consecutively from the 1st of January, and may be converted into the days of the month or vice. versa by the following table:

If we take the difference between the sums of the temperatures for the first and seventh groups of plants in the preceding table we obtain for Brussels 1,972° C., and for Poulkova 1,280° C., or a difference of about 700° C., which corresponds to about forty days at Poulkova, so that we must immediately conclude that the same stages of develop

ment are attained by means of very different sum totals of temperatures at Poulkova and Brussels.

But possibly we should have taken the initial point of vegetation at some other temperature than 0° C. In order to test this point Linsser performs the computations of the sums of temperatures above 1o, 2o, 3o, 4o, 5o, and 6° C., respectively. His result for 6° C. is as follows:

None of these successive hypotheses as to the initial temperature for vegetation gives a uniform constant any more than does the original hypothesis of 0° C.

A similar study of the sums of the squares demonstrates a similar result, so that in general at different places the same phase of development of vegetation requires different mean daily temperatures, different sums of temperatures, and different sums of the squares of temperatures, and there is no zero point that can be adopted that will make these sums equal.

Linsser then shows that, notwithstanding this result, there still is a thermal law concealed in the above figures. For evidently the sums for Brussels and Poulkova go on steadily increasing through the whole period of vegetation, and at any stage the numbers are very nearly in the same proportion, and that proportion is very nearly the same as the proportion between the sum total for the year at the two places. These annual sums total are for Brussels 3,687, and for St. Petersburg 2,253. If now the numbers in the fourth and sixth-columns of the table on page 213 be divided by these annual sums, respectively, we obtain the following:

Ratio of the individual sums to the total annual sums of temperature above 0° C.

The agreement of these numbers is quite close enough to justify the conclusion that in two different localities the sums of positive daily temperatures for the same phase of vegetation is proportional to the

annual sum total of all positive temperatures for the respective localities. The discrepancies between the above figures also show that a systematic influence is at work to slightly increase the ratio for the northern stations, since the ratios for Poulkova are appreciably larger than those for Brussels. This influence, as Linsser suggests, is probably to be found in the fact that a larger proportion of heat is consumed at the northern stations in melting the snow without changing the temperature, which heat is therefore lost to the growth of plants. The law thus discovered by Linsser is tested by him for each of the 15 phenological stations studied in his first memoir, and not only does the ratio appear the same for each phase, but the slight increase as the latitudes increase is also confirmed, or, in other words, the ratio increases slightly as the annual sum total of positive temperatures diminishes, the increase being nothing for the first group of plants that blossom early in the spring and about 0.1 for the seventh group of plants that blossom in midsummer per diminution of 2,000° C. in the annual sums.

Linsser also states this law in the following form, in which it has a more popular expression:

Every individual plant possesses the ability to regulate its vital activity as demanded by the total heat available in its dwelling place and according to the habit inherited from its ancestors, so that individuals of the same species living in different places arrive at the same phase of development by utilizing the same proportions of the total heat to which they are accustomed. The vegetable world, so far as we consider its vital phenomena, is indifferent to temperatures below the freezing point.

The preceding principle has been deduced primarily from the study of one phase, viz, the blossoming; but a study of the figures of the other phases gives a similar result, so that the method by which heat exercises its influence on plants is the same for all stages of develop

ment.

The phase recorded as "the falling of the leaves," which indicates the approach of the winter sleep of perennial plants, is the only one that to a high degree depends upon the actual temperature at that date.

Apparently the statement, frequently assumed as a general law, that the dates of leafing and of the falling of the leaf at the same place have the same temperatures is only approximately true for a single plant and a special locality, as, for instance, France and central Europe, and does not hold good for the same plant for northern or southern Europe.

Linsser's law has a most important application to the natural dissemination of seeds and the acclimatization of plants. When we, at a given place, from year to year, see the same cycle of vegetation recur without changing the behavior of the plant with reference to the annual sum total of heat, we must conclude that the ability to develop itself in proportion to the total heat is transmitted from each