quency is injurious, inasmuch as the cloudiness cuts off the influence of sunshine. The fact that years of low temperature are always years of poor crops is a fact that must be generally considered as a local phenomenon because of the simultaneous conpensation as to temperature that is continually going on in contiguous localities. HOFFMAN. Prof. Dr. H. Hoffmann published, first at Giessen and afterwards in the Memoirs of the Senckenberg Association at Frankfort (Vol. VIII, 1872), the details of a work which he began in Giessen in 1866 on the relation between the development of plants and the temperature recorded by a maximum thermometer in full sunshine. Some account of that work and its subsequent continuation at Giessen is given in successive papers published in the Journal of the Austrian Meteorological Association (Zeitschrift O. G. M.) during the years 1868 to 1891. The detailed references to these will be found in the list of papers appended to this present report. Hoffmann's first conclusion, as stated in 1868, was that he had found a precise, intelligible, and comparable expression for the quantity of heat that is needed for the attainment of any definite phase of vegetation. He would take the sum of the daily maxima of a thermometer fully exposed to the sunshine. His first work at Giessen was done with a naked glass bulb, self-registering, mercurial, maximum thermometer, graduated to Réaumur's scale, attached to a wooden frame and set out in full sunshine 4.5 French feet above the soil or green sod in an open portion of the botanic garden at Frankfort. The exposure was indeed not perfectly free, but was such that the sun shone upon the thermometer from sunrise to 2 p. m. in January and until 4.30 p. m. in June. Hoffmann's summations begin with midwinter, or January 1, and he gives the sums of the positive daily maxima (i. e., above 0° Réaum.) up to the dates of leafing and flowering for 10 plants. Apparently preliminary values are given in the Journal of the Austrian Meteorological Society for 1868 and 1869, but final values in the memoir published at Frankfort, 1872. In the Meteorologische Zeitschrift for 1875 Hoffmann says that after four years' work at Giessen (1866-1869) his thermometer was broken. A new one was constructed by Dr. J. Ziegler, of Frankfort, in accordance with their mutual understanding; this had a mercurial bulb, but was very many times larger than the former, and therefore very much more sluggish. Observations with such instruments, graduated to accord with the Réaumur scale, were begun in 1875 by Hoffmann at the botanic gardens at Giessen, and by Ziegler at the gardens at Frankfort. In order to compare these two series together and to unite them with the earlier Giessen series the ratios of the sums as given by the earlier and the later thermometers for the same plant were taken, and it was found that the ratios are very nearly the same for all plants; therefore the ratio given by the best series, viz, for Lonicera alpigena was taken as a standard and applied to the series for the other plants, so as to reduce all observations with the later thermometers back to agreement with what would have been given by the first thermometer had it not been broken. The ratios of the sums observed at Giessen with the new thermometer as compared with the sums observed at Frankfort, also with a similar new thermometer, agreed closely for all the plants, and as the two new thermometers agree closely with each other when placed side by side, it was assumed that the ratios thus obtained represent the reduction from the climate of Frankfort to that of Giessen. Adopting the same standard plant and the ratio of its sums for any place to its sums at Giessen as the standard ratio, all the sums for plants at that place can be reduced to what would have been given by the same plants at Giessen and to what would have been given by the first Giessen thermometer. Although these reductions are very arbitrary, yet the agreement of the sums thus computed for Giessen with those actually observed was quite close. But, as we shall see, subsequent years of observations have shown that such agreements do not always recur. In the Zeitschrift for 1881 Hoffmann shows that it is not the low temperatures but the subsequent too rapid thawing that injures most plants; thus the hill stations suffered less at the close of a period whose lowest temperature was -31° Réaum. than did the plants in the lowlands; the shady side of the tree suffered less than the sunny side. It is indifferent whether the sudden rise in temperature is caused by great solar rays or by a sudden warm wind; the sudden rise from -12° Réaum. to +13° Réaum. is as bad for plants as the sudden rise from -20° Réaum. to +5° Réaum.; the amount of injury is proportional to the extent and to the suddenness of the rise. In the same volume of the Zeitschrift (p. 330) Hoffmann give the results of observations at Giessen for 1880. He finds that the blossoming in springtime is so subject to disturbances by frost that the midsummer and autumnal phases of vegetation are more proper to show the accuracy of his methods. He finds that these later phases, as observed at Giessen (1866-1869), when reduced to the new standard thermometer at Giessen agree within 1 per cent with the actual observations of 1880 at that place. For plants that bloom in the spring he finds that if these are protected from injury by frost by placing them under glass covers there is then a better but still unsatisfactory agreement between the observations at Giessen and Frankfort. On computing the mean temperature of the air in the shade for the dates of blooming at Giessen he finds no apparent connection, so that from the date of blooming we can not infer the mean temperature of that day nor can we reason from the temperature to the date. The sum total of daily maximum sun temperatures at Giessen is much more nearly constant. In the Zeitschrift for 1882 Hoffmann gives the sums of the daily positive readings of his naked bright-bulb mercurial thermometer in the full sunshine; he also gives the sums of the temperature in the shade, and computes the average discrepancy or probable error of these numbers as deduced from their internal agreement year by year. He finds the probable uncertainty of the sums of maxima to be plus or minus 1 per cent and of the sums of shade temperatures to be plus or minus 10 per cent. These latter sums relate to low-lying stations, such as Vienna and Dorpat, and these discrepancies diminish very much when we consider high mountain stations, where the shade. temperatures of course give much smaller sum totals. He recognizes that the advantage of using the shade temperatures lies in the greater comparability of the observations made at different stations and with different instruments, but that the sunshine method is also greatly improved if the thermometers are perfectly similar and properly compared together, as in the instruments made by Doctor Ziegler at Frankfort. (See the report of the Senckenburg Association, 18791880, p. 337.) Hoffman's observations with a variety of instruments convinced him that this difficulty as to instruments and exposures is not insurmountable. He collects comparative readings at several places and shows that the difference between the average temperatures in the sun and in the shade is larger at higher altitudes; thus at Giessen the average difference in summer at midday is 5° Réaum., and the whole range of the differences between sunshine and shade is from 3° to 15° Réaum. The corresponding average in the Hochgebirge, 7,000 feet, is never less than 8° Réaum. At the Bernina hospice, 8,113 feet, it is 25° Réaum. The average temperature of these mountain stations is 16.4° Réaum., corresponding to an elevation of about 6,000 feet. Similarly, J. D. Hooker observing a black-bulb thermometer in the sunshine in the Himalayas, found a difference of -15° Réaum. at 7,400 feet elevation, as contrasted with 4.4° at sea level. R. S. Ball, also using a black bulb, finds a difference of 18° or 20° Réaum. in the Hochgebirge and of only 3° at Chiswick. These differences show the effect of the great dryness and mechanical purity of the air in the Hochgebirge. Hoffmann considers the smoke and clouds above us as affecting the difference between the sun and shade thermometers, but says nothing of the earth's surface which completes the "inclosure" of the thermometer. The date from which Hoffmann begins his summation for Giessen is January 1; but as it would seem more proper to begin with some definite phase of vegetation, therefore he investigates the accuracy with which we can determine the initial phase and the effect of errors therein upon the ultimate sums. By painting the buds of certain 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.] Thermometer B1. Ther- Plant (always same stock). eter A, 1866 1869. Thermometer B. Aesculus macrostachya 3,353 3,504 3,479 3, 191 3,254 3,929 3,846 3,639 3,546 5,386 5,494 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: |