hundred, a random sampling would give values diverging more widely from the theoretical than those actually found. Since the observed values agree so well with the theoretical values, it seems safe to assume that the growth rate is governed by constant internal forces rather than by external forces which would be expected to be more casual inoperation. The theoretical values for the consecutive increases in the mean height of the plants give a smoother curve than the observed values give, as shown in figure 2. The sag in the observed curve near the twenty-eighth day does not appear in the theoretical curve. The summit of the theoretical curve is near FIG. 3. COMPARISON OF OBSERVED AND CALCULATED VALUES FOR THE MEAN HEIGHT OF HELIANTHUS Observed the thirty-fifth day, thus agreeing with the computed value of t1 = 34.2 days, the time at which half the final height is attained and at which growth is most rapid. The assumption having been made that the growth was more largely governed by internal than external factors, and positive evidence in favor of the assumption having been obtained, it is next in order to investigate the relationship between growth and some of the more prominent factors of the external environment. Temperature is known to have a potent effect upon growth, especially if it departs widely from the optimum requirements of the organism. In a prob lem like the present, we are more concerned with the temperature summation than with the mean temperature unless the range is very large. It is clear that we shall not arrive at a correct value if we take an arithmetical average of the maximum and minimum daily temperatures, because we do not in that way take any account of the time during which either prevailed, or of the range of temperatures. For example, the minimum temperature on a given day may be 50° and the maximum temperature 90°, an average of 70° but if the maximum temperature prevails for only two hours out of the twentyfour, while the temperature varies between 50° and 65° for most of the daily period, it is obvious that the mere arithmetical mean, 70°, is a false expression of the temperature. The values must be weighted in order to give an average which correctly represents the temperature condition. A method of measuring temperature summations has been employed which is believed to be fairly satisfactory. It consisted in finding the product of hours multiplied by degree of temperature above 40°F. and is expressed in degree-hours. A degree-hour may be regarded as one degree of effective temperature acting for one hour. The point 40°F. was arbitrarily chosen as a basal point, at or near which plant growth will proceed. The method of obtaining the summation of effective temperature consisted in measuring with a planimeter the area between the pen tracing and the 40°F. line on thermograph records obtained from a self registering thermograph situated about 100 yards from the plantation of sunflowers. This method gives a direct index of temperatures above the 40° point, but does not take into account the efficiency of temperatures as assumed by the van't Hoff-Arrhenius principle. The coefficient of correlation between the degree-hours and the increase in height of the sunflower plants for each seven-day interval was calculated. Its value turned out to be r = 0.199 0.187. There are some indications here of a positive correlation, but, since the probable error nearly equals the coefficient in magnitude, no reliance can be placed upon the existence of a correlation. Reference to the graph showing temperature summations in figure 2, shows little correspondence with the curve representing growth increases, except in the first twenty-one days of the period. In a somewhat similar way we have investigated the possibility of a correlation between growth rate and the coefficient of the evaporating power of the air, the latter value being obtained from the readings of a spherical porousclay atmometer-bulb located about one hundred yards from the plants. The coefficient of correlation for these values was even less than that in the foregoing case, being 0.041 0.202. The coefficient in itself is so small as to lack significance, and when compared with its probable error it fails entirely to indicate any correlation between these two factors. These statements are not to be construed as arguments against the effect of temperature and transpiration upon the rate of growth of plants. Our argument is merely intended to emphasize the greater importance of the inter nal factors in determining the growth, reproduction and senescence of the plant, factors which are so potent that they overbalance external factors so long as the latter do not too closely approach minimum or maximum values. That the oncoming of reproductive processes induces changes in the growth rate of the organism is a fact too well known to require comment, but is well illustrated by the behavior of the sunflower. It appears that growth, its rate, its grand period, and, to some extent, its amount are so steadily controlled by factors inherent in the genetic constitution of the sunflower that these factors are prepotent unless the external conditions depart widely or repeatedly from the optimum. Plants in this respect are more sensitive to variations in their external environment than animals, yet these studies show that even plants are not entirely dependent upon environmental (external) conditions for determining their growth rate. It may be of interest to inquire whether the formula of autocatalysis applies, as well to the smaller plants as to the medium and large plants of this group and how the mean values of K for different groups agree. TABLE 3 HEIGHT AND GROWTH CONSTANTS OF PLANTS ENDING IN THEIR GROWTH IN DIFFERENT QUARTILES Final height of plants.... mean value of K....... 0.0052 0.0008 0.0079 0.0011 0.0079 0.0012 0.0111 0.0016 As a basis of classification we divided the plants into quartiles, based upon their heights at maturity. Quartile I, contained the smallest plants, quartile II, the next larger and so on. Since 58 is not exactly divisible by 4, the quartiles were not exactly of equal size: quartiles I and III contained 15 plants each and quartiles II and IV contained 14 each. An average of the heights of each group of plants at each time interval, t, gave a corresponding value of x, from which the several values of K were computed. (See table 3). The mean values. of K are remarkably constant for the different quartiles, in fact all are within the range of their probable errors. This may be regarded as evidence that the growth constant has the same value for all classes of plants in this population without regard to their relative heights, since the relation between the final height and the height at any given time obeys the same principle. ⚫ A brief consideration of a parallel case will make it evident that such a relation must exist in this sort of reaction. The inversion of cane sugar is a familiar case of autocatalysis in which one of the products catalyzes the reaction. It is plain that the amounts of invert sugar finally formed in four different flasks may vary, depending upon the amount of cane sugar originally present, yet the constant of autocatalysis remains the same and the time may be the same in each case. This relation exists because the quantity dx/dt is proportional to the quantity of cane sugar remaining, which may be represented by (ax) where a is the original quantity of cane sugar at the beginning, i.e., when t = 0. The senior author has discussed the distribution of these plants in the several quartiles in a paper soon to be published (Reed, 1919), showing that said distribution is due to some agency operating to cause variability in height other than purely casual agencies which might be expected upon the basis of pure chance. The data presented in table 3, indicate that no difference in the growth constants exists which can account for the larger or smaller size of a part of the population. Whether the differences in the amount of material produced, i.e., the size of the plants, is to be referred to differences in amount or activity of the catalyst, or of the substrate, cannot be discussed upon the basis of the data now in hand. An additional point may be discussed in this connection, viz., "Are the values of the growth constants more widely dispersed from their means in one quartile than in another?" We may take the standard deviations of the means as a measure of the dispersion of the individual values. Reference to table 3 shows that the standard deviations increase from the lower to the upper quartiles, which would seem to indicate that the growth rate of the larger plants fluctuates more from the mean than is the case in the smaller plants. Summary.-1. Measurements of sunflower plants at intervals of seven days showed that their growth rate approximated closely the course of an autocatalytic reaction. 2. The close correspondence of the actual mean height of plants to that required by the equation of autocatalysis is taken to indicate that the growth rate is governed by constant internal factors rather than by external factors which would be expected to be more casual in their influence. 3. The growth rate showed no strong correlation either with temperaturesummations, or with transpiration-summations. 4. The value of the growth constant was not perceptibly different for the larger or smaller plants in this population. *Paper 56 from the University of California, Graduate School of Tropical Agriculture and Citrus Experiment Station, Riverside, California. Church, A. H., quoted in Cockerell, T. D. A., Amer. Nat., Lancaster, 49, 1915, (609). Miyake, K., Soil Science, 2, 1916, (481-492). Pearl, R., and Surface, F. M., Zs. indukt. Abstam.- Vererbungslehre, 14, 1915, (97–203). Reed, H. S., (1919), Amer. J. Bot., (in press). Roberston, T. B., Arch. Entwicklungsmechanik, 26, 1908, (108-118); Ibid., 37, 1913, (497); Berkeley, Univ. Cal. Publ. in Physiology, 4, 1915, (211–288). Shull, G. H., Bot. Gaz., Chicago, 45, 1908, (103–116). ON SOME METALLIC DERIVATIVES OF ETHYL THIOGLYCOLLATE BY CHARLES A. ROUILLER PHARMACOLOGICAL LABORATORY, JOHNS HOPKINS UNIVERSITY Communicated by J. J. Abel, March 10, 1919 In 1910 Abel2 discovered that thioglycollic ester dissolves antimony trioxide with the greatest ease, forming an antimony derivative, Sb(SCH2CO2 C2H)3, according to the equation: 2Sb2O3+6HSCH2CO2C2H5=2Sb (SCH2CO2C2H5)3+3H2O. The antimony compound separates as a heavy oil which, when treated in absolute alcohol with ammonia, yields the corresponding amide, Sb(SCH2CONH2)3, obtained by precipitation from alcohol with ether as a colorless or slightly reddish, semiresinous mass soluble in water in all proportions with neutral reaction. The experiments of Rowntree, carried out in collaboration with Abel, showed that the new amide is a very powerful trypanosomicidal substance. Professor Abel found that the thioglycollic ester reacts energetically with mercuric oxide also, and in order to determine whether the reaction discovered by him is of general applicability, he suggested to the writer that he try the action of various other metallic oxides on the ester. It was hoped that the resulting products might be so slightly soluble as not to be toxic when applied on open wound surfaces, but yet soluble enough to be antiseptic and bactericidal. Abel's expectation that his reaction would prove to be general has been confirmed; whether the products formed are of pharmacological and therapeutic value we have not yet had an opportunity to determine. Following Abel's general method (for details see the forthcoming paper in the Journal of the American Chemical Society), the compounds listed below have been prepared and analyzed. Triethyl bismuthtrithioglycollate, Bi(SCH2CO2C2H5)3 Diethyl mercurydithioglycollate, Hg(SCH2CO2C2H5)2 Ethyl silverthioglycollate, AgSCH2CO2C2H5. A copper compound with 9.3 % of copper for which no simple formula can be derived; the normal compound, Cu(SCH2CO2C2H5)2, would contain 21.06% of copper. Zinc, arsenic, and tin compounds were also prepared but have not yet been analyzed. 1 A more detailed report of this investigation will appear in the May issue of the Journal of the American Chemical Society. Rowntree, L. G., and Abel, J. J., J. Pharmacology Exper. Therapeutics, 2, 1910, (108). |