K X 10-3 pressure by means of the equation, K= (pU)/760, where p is the pressure in mm. of mercury. The mobilities found in this manner were astonishingly high. At 600 mm. mobilities of the order of magnitude of 15,000 cm. /sec. were obtained, while the highest previous mobility determined3 in N2 was 500 cm./sec. Furthermore the value of K obtained was not a constant as one would expect. K was found to be a function of the field strength and pressure. For a given pressure the value of K plotted as a function of Vo/d the field strength was found to lie on a hyperbola of the form, K= a b + V/d For different pressures a family of such hyperbolae were obtained which were expressed by the equation, points plotted are the actual experimental values of K obtained under the conditions of p, Vo, and d given. When the inaccuracies of such measurements are considered it is seen that the above equation represents the behavior of K to a satisfactory degree of approximation. The success in measuring mobilities of such high values is probably due to the fact that especial care was taken to avoid contaminating gases, and to the fact that the frequencies employed were very high. The latter factor made it possible to measure the mobilities of purely electronic carriers only, for with the short intervals of time used only electrons which had made no attachments at all could succeed in crossing the plates. It seems likely that the low electronic mobilities observed by the previous workers were found for electrons which had been completely free for only a portion of their path between the plates because of the low frequencies of alternation used. The magnitude of the values obtained in these experiments is more nearly in accord with the values of electron mobilities predicted on the basis of the equations of Townsend and Lenard (i.e. of 6940 cm./sec. and 4260 cm./sec. respectively), than the earlier values. The fact that K is not a constant is most interesting. It indicates that the term mobility constant has no significance for electrons; since their velocity in the field is no longer directly proportional to the field strength and inversely proportional to the pressure. The way in which K varies with Vo/d and with p indicates that the velocity of drift of the electrons in the direction of the field is influenced by the energy gained by the electron in the electrical field between impacts. A variation of the energy of the electron in the field such as would cause the observed variation of K can only occur when the electrons make partially elastic impacts with the gas molecules. A more detailed account of these experiments will later appear elsewhere. The experiments are being extended to hydrogen and if possible to other gases. * National Research Fellow of the NATIONAL RESEARCH COUNCIL 'Loeb, L. B., these PROCEEDINGS, 6, 1920 (335). 2 Loeb, L. B., Physic. Rev. (N. S.), 17, 1921 (94). 'Haines, W. B., Phil. Mag., 30, 1915 (503). Townsend, J. S., Electricity in Gases, Oxford, 1914 (174 ff); also Phil. Mag., 40, 1920. 'Lenard, P., Ann. Physik, 40, 1913 (409). A METHOD FOR OBTAINING CONSTANTS FOR FORMULAS OF ORGANIC GROWTH* BY H. S. REED UNIVERSITY OF CALIFORNIA Communicated by R. Pearl, October 8, 1921 The growth of many organisms may be computed from the equation in which x represents the size of the organism at time t, A represents the size of the organism at maturity or at the end of a particular cycle of growth, t1 is the time at which x-A/2, and K is a constant. This is the equation for an autocatalytic reaction and we are indebted to Robertson (1908) for showing its applicability to growth processes. While the equation expresses the growth of plants with a high degree of accuracy, it often fails to fit the observed data in the early life of the organism. In other words, the computed values of x are too large when t is small. Recently this feature of the equation has been discussed by Mitscherlich (1919) and Rippel (1919). The present paper intends to show how a simple graphic method may be used to overcome the difficulty just stated. Let us assume that the true state of affairs is represented by the equation This is merely assuming that the exponent of (t-t1) may or may not be unity. We may write =log K+ c log (tt) (log) t This is the equation of a straight line if log log be used as ordinate and log (tt) as abscissa. The intercept on the y-axis will be log K and the slope of the line c. When t<t the values of (tt) are negative in sign, as t approaches the value of t1 the value of (t - t1) decreases to zero. Ast increases beyond to the values of (t-t1) are positive. However the sign of the quantity (t- t1) does not affect the logarithm. The result is that we actually get two lines on the chart, one for values of the equation when t<t1 and another for values when t > t1. These lines as determined from the observations, are seldom superimposed. With them as guides the "best" straight line is drawn from which the values of the slope and intercept are read off. If the lines make much of an angle with each other it usually means that the value of t1 has been poorly chosen. The choice of a value for tis facilitated if one ascertains all the values of log log them determines by inspection the values of (t-t1) which will bring approx distance from the ordinate. For this purpose, the highest and lowest values Graph of values for lemon shoots. Points represent values of log (t-9.5) when th; crosses represent same when t> h. The average length of 37 shoots on a group of lemon trees is given in the column headed x in table 1. The measurements were made each week for the first 21 weeks of their growth. From the observed length at intervals of a week the values of Table 1 contains in the column headed x1 the values computed from the equation GROWTH OF LEMON SHOOTS. COMPARISON OF OBSERVED And Calculated ValueS The root-mean-square deviation of calculated from observed values was 1.88 cm. In the column headed 2 will be found values computed from the equation x log The root-mean-square deviation of these values is 4.40 cm. |