trees and examining them very frequently Hoffmann seeks to determine how accurately the date of the beginning of vegetation or the flow of sap can be determined by the swelling of the buds and the visible cracking of the delicate pencil lines of paint. He finds that the date can be determined to within one day when spring comes on rapidly, but within eight days when it comes very slowly. The corresponding uncertainty or variability of the sums of the maximum sunshine thermometer from the swelling of the buds up to the date of the first blossom, for instance, for Castanea vulgaris, is 4 per cent while the uncertainty of similar sums, counting from January 1, is only 1 per cent. These and similar data are only deducible from observations made upon the same tree or bush from year to year; the variations are materially increased when different plants in different localities are observed; moreover, they are based upon observations for only four years, which period is not long enough to give a reliable value of the relative uncertainties. As in previous cases in making up these abstracts, I give Hoffmann's actual figures in the following summary, which I have compiled by collating the few observations published by him in the Zeitschrift during the years 1870-1890. I have selected only the few plants for which he has published the sums for several years or for two localities, so that comparisons may be made and a judgment arrived at as to the propriety of his method. It will be observed that Hoffmann has, when possible, observed the same tree or bush from year to year, so that the problem of the influence of heat is much more definite than when different plants or a general mass of plants is observed; but, on the other hand, single plants are more liable to irregularities produced by special disturbances which would exert no appreciable influence on the average of a large number of similar plants. Temperature sums at Giessen (Hoffmann's method) from the first swelling of the buds to the first blossom. [Z. O. G. M., Vol. XVII, 1882, p. 127. All in Réaumur degrees.] Temperature sums from January 1 to the date of first blossom (by Hoffmann's method) at Giessen and at Frankfort. [Z. O. G. M., Vol. X, 1875, p. 251, and Vol. XVI, p. 331. All in Réaumur degrees.] Temperature sums (by Hoffmann's method) at Giessen from January 1 to first blossom, for plants that blossom in midsummer and autumn. [Z. O. G. M., Vol. XVI, p. 331, and Vol. XVII, p. 130; M. Z., Vol. I, p. 407, and Vol. III, p. 546.] Aesculus macrostachya Aster amellus. Lilium candidum Linosyris vulgaris. 3,353 3,504 3,479 3, 191 3,254 3,929 3,846 3,639 3,546 3,556 5,386 5, 494 Plumbago europaea The contrast between the ordinary spring of 1881 and the very early spring of 1882 with its preceding warm winter, affords a test of the question as to how much the thermal constant is liable to change with the variations in the seasons. Hoffmann finds that although the first blossoms in the spring of 1882 occurred fifteen days earlier than usual, yet the sums of the maximum temperatures since January 1 were not much changed. The figures as given by him (Z. O. G. M., Vol. XVII, p. 460) are reproduced as follows: Many of the plants observed by Hoffmann show such discordant sums from year to year as to prove that his method has no meaning for them, but for others the agreement is such that he recommends them to be observed in connection with the observations of the sunshine thermometer, as follows: For the following plants observe the temperature sums from the first swelling of the buds to the first flower blossom: Castanea vesca, Bupleurum falcatum, Corydalis fabacea, Dianthus carthusianorum, Lonicera alpigena, Salix daphanoides, Syringa vulgaris, Amygdalus nana, Alnus incana, Alnus viridis, Atropa belladonna, Betula alba, Crataegus oxyacantha, Larix europaea (up to the date when the pollen first falls from the anthers), Ligustrum vulgare, Lonicera tatarica, Prenanthes purpurea, Prunus padus, Prunus spinosa, Rhamnus frangula, Ribes aureum, Rosa arvensis, Rosa alpina, Salix caprea, male (for the catkin, or the flowers of the willow, the beginning of pollination, as ascertained by a light stroke on the flower, is to be considered as the date of the first blossom). Hoffmann also applies his summation of sunshine maxima temperatures to the interval from January 1 to the ripening of the fruits and shows an excellent agreement between the numbers for 1880 and those for 1881 at Giessen. In the Zeitschrift for 1884 Hoffmann gives his results for 1882, 1883, and 1884 as collected in the preceding table and says that the vexed question of the thermal constant for vegetation is still far from being settled; either temperature and vegetation are independent of each other, which no one can easily believe, or they stand to each other in a relation for which the correct expression is still unknown. Pfeffer in his Pflanzen Physiologie (Vol. II, p. 114) has stated that the approximate uniformity of the sums of temperature, from year to year, can only mean that, in general, for each year the heat received from the sun amounts to about the same sum total for the same date annually; but this is not in strict accordance with facts, for if it were true a small change in the date should make a small change in the sums, which is not always the case. Thus, if for Linosyris vulgaris the dates of blossoming are August 15, 18, or 20, the sums from January 1 for different years will be as follows: From these figures we see that the sums vary from year to year quite independently of the change of date. The thermometer B1, similar to B2, having been sent to Upsala for observations at that place, it gave from January 1 to the first blossom 2667-05 M- -16 sums that agree so well with those found at Giessen that Hoffmann thinks no better can be expected. In the Zeitschrift for 1885 Hoffmann continues to give the comparative observations at Giessen and Upsala, and remarks that the question is not as to whether his method is correct and the others are wrong, but as to which of all methods is even a little better than the others. Of these others only one can, he thinks, be compared with his own, viz, that of Karl Fritsch, who takes the sum of all positive mean daily shade temperatures. Hoffmann applies Fritsch's method to the observations at Giessen and Upsala and finds the argument not in its favor. He also tries another form of thermometer, viz, the so-called black bulb in vacuo, but finds it too sensitive, which he thinks is because its bulb is too small. In the Zeitschrift for 1886 (p. 546) Hoffmann gives a summary of observations at Giessen and Upsala during 1886. In general the sums are smaller at Upsala and so also for high Alpine stations. He is thus led to the laws established by Karl Linsser, as published in St. Petersburg in 1867 and 1869, which laws he expresses as follows: Every wild plant has in the course of time so adapted itself to the surrounding local climate that it utilizes this climate to the best advantage. For any given phase of vegetation it uses a certain proportional part of the available annual sum total of heat. Thus, if the annual sum at Venice is 4,000 and if the corresponding sum at St. Petersburg is 2,000 and if the plant utilizes one-fourth in order to bring it to the flowering stage, then it will require 1,000 at Venice and 500 at St. Petersburg." From Linsser's law he concludes; (1) plants that have been raised in the north and are transplanted to the south reach their phenological epochs earlier than plants already living there, while southerly plants carried to the north are retarded as compared with those already acclimatized; (2) plants raised on colder highlands when transplanted to the warmer lowlands have their epochs accelerated as compared with those already domesticated; plants raised in the lowlands and transplanted to the colder highlands develop more slowly than the acclimatized plants. In the Zeitschrift for 1886 (p. 113) Hoffmann determines the relative retardation of vegetation as determined by the dates of the first blossom of several plants at different altitudes. The result is for the Pyrus communis (pear tree) and allied varieties a retardation of 3.7 days per 100 meters, and corresponding to this a retardation of 2.8 days per 1° of latitude. The analogous data for Pyrus malus (apples) are 2 days per 100 meters and 4.4 days per 1° of latitude. Charts are given showing by means of isophenological lines the gradual progress northward of the development of vegetation as spring advances, In Petermann's Geog. Mitth. for 1881 Hoffmann gives a general phenological chart for central Europe showing the acceleration or retardation of the phases of vegetation with respect to Giessen. In the Zeitschrift, 1882, Vol. XVII, page 457, Hoffmann gives the results of his study of observations collected by Karl Fritsch, showing the dates of blossoming and ripening of fruits in Europe, as reduced to the latitude and altitude of Giessen; and, second, the thermal constant by Hoffmann's method from observations at Giessen for the years 1881 and 1882, as collated in the preceding table. He also shows that the advance of vegetation in the early and very warm spring of 1882 did not materially diminish the sums total of maximum temperatures, the figures for which I have reproduced in the preceding table (p. 240). MARIE-DAVY. The extensive researches conducted at the observatory of Montsouris (Paris) are scattered through many annual volumes, from which I have culled sufficient to show the views held by Marié-Davy and his coworkers, who distinguish very clearly between thermometry and actinometry, and attempt to determine separately the constant amounts of air temperature and of sunshine which constitute the total molecular energy needed to develop the plant. In his Annuaire for 1877 Marié-Davy quotes from Tisserand (1875) and Schuebeler (1862) the results of a series of observations on the culture of grain in Europe. Special praise is given to the records from Norway and to the high state of education among the Norwegian farmers. The durations of the periods from sowing to ripening are as follows: For other plants-oats, peas, beans, vetches, etc.-the duration of the vegetating period diminishes in a similar manner as the latitude increases or as the temperature diminishes; therefore we can not assume at once that warmth hastens the ripening, for in this case cold appears to hasten it. I say "appears," because with the cold comes in another influence, viz, the amount of sunshine. Thus as we go |