j?*^ ff OF THE (( UNIVERSITY OF Statistical Laboratory Dept. of Mathematics University of California ! F _ CCUPLPTE I £ B £ of ; A R T K U R H A R R I Volume III 191? - 1921 Property of Statistical Laboratory University of California MATH-STAT. Volume III MATH.. 1 q STAT. — LIBRARY 1. Further Illustrations of the Applicability of a Coefficient Measuring the; Correlation Between a Variable and the Deviation of a Dependent Variable Frorr; Its Pro bable Value. Genetics 31 32° -3^2, July, 191?. 2. Practical Universality of Field Heterogeneity as a Factor Influencing Plot Yields. Journal of Agricultural Research. Vol. XIX, No. 7, July, 192C. 3. Permanence of Differences in the Plots of an Experi mental Field. (J. Arthur Harris and C. f. Scofield) . Journal of Agricultural Research. Vol. XX, No. 5, Dec.. 1020. 4. Tissue '"eight and Water Content in a Tetracotyle- donou? Llutant of Phaseolus vulgaris. Proceedings of the Society for Experimental Biology and Medicine. 1921, XVIII, pp. 2C-7-2C9. 5. Leaf-Tussue Production arid VJater Content in a ivlutant Rac<~ of F^ llif_Ji_ li.- Botanical Gazette. Vol.LXXII, No. 3, S€jt. , 1921. 6. Correlations Between Anatomical Characters in the Seedling of Phase plus vulgaris. (*J . Arthur Harris, Ecjmuncl W. Gii.r.ott, John Y. Pennyp. . and G. B. Durham) American Journal of Botany, °: 339-36:;, July, 1921. 7. The Vascular Anatomy of H^m.i trimerous Seedlings of Phase clus vi \ ^_s_. (J. Arthur Harris, Edmund VT. Sinnctt . Y. Pennypacki >•. anr1 G . 3. Durham). Journal of Botany, °: 375-3^1, ::t.. 1921. °. "nterrelati 1 Lp of " -.s of Vascular Bundles ' ' Trar: ' " n Zone of the '^ Phaseolus Vulgaris. (J. Arthur Harr ' ' ". lot, John Y. Pennypac'-er, an^ '" . B. Di c*ha ). Journal of Botany, °: - 2, fov. , 1921. M779976 Contents, Volume III . e 2. •9. The Vascular Anatomy of Dimerous and Trimerous Jllngs of Pha£_ _ luj ___ l__is.. (J. Arthur Harris, Edmui." ''. -'Lii'iott, John Y. Pennypacker, and G. 3. Durham) American Journal of Botany, P: 63-102, Feb., 1921. 10. The Vascular Anatomy of Normal and Variant Seed lings of Pliaseolus vulgaris. Edmund T"r. "innott) . Procer . ' of the National Acadeny el rciences, Vol. 7, No. 1, Jan., 19-"1 . 11. Correlation of Morphological Variations in the Seedling of ?„_. ___ 1 ___ __L___l£- (3 • Arthur Harris and B. T. A very" . Bulletin of the Torrey Botanical Club 4$: 109-119. 12. .-ther ftudies on the Interrelationship of Morphc- ical and Physiological Characters in Seedlings of Phase olus . Bro: lyn Botanic Garden Memoirs, 1: 167-174, June, b. 13. Note on the Relation of Blood Fat to ex, and on the Correlation Between Blood Fat and ^gg Production in the Domestic Fowl. (Oscar Biddle and J. Arthur Karris urnal of Biological Chemistry, Vol. XX7IV, I'o. 1, ril, 19GL&3 14. The Fgg Record of Limited Periods as Criteria for ^dieting the Egg-Production of the V/hite Leghorn Fowl. (J. Arthur Harris, ' kpatrick, A. F. lakeslee, . 6: 26:1-309, May, 1921. 15. The Prediction of Annual Egg Production From the cords of Limited Periods. (J. Arthur Harris, IV. F. "' -kpatr-' F. Blake s lee ). oceed"' J ' onal Academy of Scirnces, Vol. 7, T-i-iT-ii ] -.pi c - _ . j. , C- 4- . 16. A Bicmetric ,ctudy of Human Basal Metabolism. (J ' and Francis G. Benedict). Proceedings of the National Academy of rc-' &; Vol. 4, 17. Biometric Standards for Energy Requirement 5- triti: (J. Arthur Iferri. ' '0. cientific Monthly, May, Contents, Volume III Page 3. 18. Charles Buckman Goring. Science, N. f: . , Vol. LI., Ho. 1310, Feb., 1920. 19. The Variation and the Statistical Constants of Basal J.Ietabolism in Hen. (J. Arthur Harris and F. G. Benedict) . The Journal of Biological Chemistry, Vol. XLVI, No. 1, March, 1921. 20. On the Osmotic Concentration of the Tissue Fluids of Phanerogamic Epiphytes. American Journal of Botany, ';:, November, 19lB. 21. On the' Relationship Between Freezing Po^'nt Lowering, A . and Specific Electrical Conductivity, k, of Plant Tissue Fluids . (J.A.Harris , R.A. Gortner, J.V. Lawrence). Science, N. S., Vol. LII., No. 13;1, Nov., 1920. 22. The Specific Electrical Conductivity of the Tissue Fluids of Desert Loranthaceae . (J. Arthur Harris and A. T. Valentine). Proceedings of the "ociety for Experimental Biology and Medicine, "1920, xviii. 23. On the Differentiation of the Leaf Tissue Fluids of Ligneous and Herbaceous Plants V/ith Respect to Osmotic Concentration and Electrical Conductivity. Journal of General Physiology, Jan., 1921., Vol.iii, No. 3. (J. Arthur Harris, Ross Aiken Gortner, and John V. Lawrence) . 24. The Osmotic Concentration and Electrical Conducti vity of the Tissue Fluids of Ligneous and Herbaceous Plants. (J. Arthur Harris, Ross Aiken Gortner. and John V. Lawrence) . Journal of Physical Chemistry, Vol. 25, Feb., 1921. 25. Maximum values of Osmotic Concentration in Plant Tissue Fluids. (J. Arthur Harris, P. A. Gortner, W.F. Hofmann, and A. T. Valentine). Proceedings of the ^ociety for T xperimental Biology and Medicine, 1921, xviii. 26. The Transformation of the Plant Ovule into an Ovary. Proceedings of the Society for T xperimental Biology and Medicine, 1919, xvi . 27. rormulae for the Determination of the Correlations of cize and of Growth Increments in the Developing Organ ism. Proceedings of the Society for Experimental Biology and ... dicine, 1921, xviii. Contents, Volume III Page 4. 28. Inter -Periodic Correlation in the Analysis of Growth. (J. Arthur Harris and H. S. Reed). Biological Bulletin, Vol. XL., No. 5, Hay, 1921. 29. Notes on the Occurrence of Gammer us llrnnaeus Fmith in a Saline Habitat. (Ross Aiken Gortner, and J. Arthur Harris ) Science* N. S., Vol. LIII. , No. 1376, May, 1921. 30. Secondarv Parsitisra in Phoradendron. The Botanical Gazette, Vol. IXVI, No. 3, Sept., 1918. 31. The Interrelationship of the Number of Stamens and Pistils in the Flowers of Ficaria. Biological Bulletin, Vol. XXXIV, No. 1, Jan., 1918. 32. The Second -Year Record of Birds Y/hich did and. did not Lay During Individual Months of the Pullet Year. (J. Arthur Harris and Earry R. L^wis). Science, N. S., Vol. LIV. . No. 1393, Sept. 9, 1921. FURTHER ILLUSTRATIONS OF THE APPLICABILITY OF A COEFFICIENT MEASURING THE CORRELATION BE TWEEN A VARIABLE AND THE DEVIATION OF A DEPENDENT VARIABLE FROM ITS PROBABLE VALUE J. ARTHUR HARRIS Station for Experimental. Evolution, Cold Spring Harbor, New York Reprinted from GENETICS 3 : 328-352, July 1918 GENETICS A Periodical Record of Investigations Bearing on Heredity and Variation EDITORIAL BOARD GEORGE H. SHULL, Managing Editor Princeton University WILLIAM E. CASTLE EDWARD M. EAST Harvard University Harvard University EDWIN G. CONKLIN ROLLINS A. EMERSON Princeton University Cornell University CHARLES B. DAVENPORT HERBERT S. JENNINGS Carnegie Institution of Washington Johns Hopkins University BRADLEY M. DAVIS THOMAS H. MORGAN University of Pennsylvania Columbia University RAYMOND PEARL Johns Hopkins University GENETICS is a bi-monthly journal issued in annual volumes of about 600 pages each. It will be sent to subscribers in the United States, the Philippines, Porto Rico, etc., for $6 per annum for the current volume, and $7 per volume for completed volumes until the edition is exhausted. Canadian subscribers should add 25 cents for postage. To all other countries 50 cents should be added for postage. Single copies will be sent to any address postpaid for $1.25 each. All subscriptions, notices of change of address, and business corre spondence should be sent to the Princeton University Press, Princeton, New Jersey, and all remittances should be made payable to the Princeton University Press. Entered as second-class matter February 23, 1916, at the post office at Princeton, N. J., under the act of March 3, 1879. FURTHER ILLUSTRATIONS OF THE APPLICABILITY OF A COEFFICIENT MEASURING THE CORRELATION BE TWEEN A VARIABLE AND THE DEVIATION OF A DEPENDENT VARIABLE FROM ITS PROBABLE VALUE J. ARTHUR HARRIS Station for Experimental Evolution, Cold Spring Harbor, New York Reprinted from GENETICS 3 : 328-352, July 1918 FURTHER ILLUSTRATIONS OF THE APPLICABILITY OF A COEFFICIENT MEASURING THE CORRELATION BETWEEN A VARIABLE AND THE DEVIA TION OF A DEPENDENT VARIABLE FROM ITS PROBABLE VALUE J. ARTHUR HARRIS Station for Experimental Evolution, Cold Spring Harbor, New York [Received November 1, 1917] TABLE OF CONTENTS PACK INTRODUCTORY 328 Earlier applications 3 3 j Further illustrations 332 Illustration I. Proportionality of parts in Paramecium 332 Illustration 2. Absence of relationship between size of litter and sex in swine 336 Illustration 3. Proportion of pistillate and hermaphrodite flowers in the inflorescence of the composite Homogyne 336 Illustration 4. Fertility of capsules and viability of seed in carnation crosses 337 Illustration 5. Relationship between the total number of pedicels and the number of abnormal pedicels in Spiraea Vanhouttci 337 Illustration 6. Interrelationship of cotyledons and primordial leaves in a race of Phaseolus vulgaris highly variable in seedling characters 340 Illustration 7. Change in proportion of parts in developing trout 344 Illustration 8. Relationship between total solids and sucrose content in the j uice of sugar beets 346 Illustration 9. Relationship between total number of spikelets* and number of sterile spikelets in wheat 348 Illustration 10. Viability of dominants and recessives in F0 generation of Mendelian hybrids " 3^ RECAPITULATION -- LITERATURE CITED . 3o i INTRODUCTORY Eight years ago I pointed out (HARRIS 1909 a) that wheels some fraction of x the correlation between them, rxv, while of descriptive value, GENETICS 3: 328 Jl 1918 APPLICABILITY OF A COEFFICIENT OF CORRELATION 329 does not give all of the information which is required concerning the interrelationship of these two variables, and that a coefficient showing whether the value of y becomes relatively larger or smaller with increas ing values of x} would have considerable analytical value. I showed1 then that if s = px, where p = y/lc, the bars denoting pop ulation means, Vx— TI The purpose of this paper is to illustrate the range of usefulness of this coefficient by noting biological progress which has been made by its use, and by actually applying it to series of data which have not been heretofore fully analyzed by the higher statistical methods. Before passing to actual illustrations of applicability of the coefficient, some questions of method should be considered. In cases in which the coefficient rxz is desired the correlation table has usually been formed to determine rvu, where v -\- y = x. The mean and standard deviation for x made up of any number of components (HARRIS 1917 c) are well known (PEARL 1909, HARRIS 1918 a) ; when x = v + y •x = v + y, vx = V o-v2 + a-y + 2 rvy.r] is the first moment about zero as origin of z for any array, the product moment for the population is where S denotes summation of the values of the 3' arrays of x. Practically it is more convenient to determine the product moment from where S(xy) and S(S) are the product moments of x and y and the second moment of x for the population. APPLICABILITY OF A COEFFICIENT OF CORRELATION 331 EARLIER APPLICATIONS The method has been most extensively applied to problems of fertility and fecundity. Thus the relationship between the number of ovaries formed and the number of ovaries developing into fruits has been investi gated in the inflorescence of Staphylea (HARRIS 1909), Celastrus (HAR RIS 1909 b) and Crinum (HARRIS 1912). In Staphylea and Crinum inflorescences which produce larger numbers of flowers mature relatively fewer fruits. In Celastrus there is apparently no relationship between the number of flowers formed and the capacity of the inflorescence for maturing the ovaries into fruits. In the fruit, the relationship between the total number of ovules laid down and the deviation of the number of seeds matured from their probable number has been investigated in Sanguinaria (HARRIS 1910 a). For Phase ohts rulgaris a first study (HARRIS 1913) of 53 series comprising 166,130 pods and a supplemental investigation of 16 series comprising- 56,698 pods (HARRIS 1917 a) leave no doubt that the pods with the larger number of ovules mature relatively fewer of their ovules into seeds. The same relationship holds in the arborescent legume, Ccrcis canadcnsis, as is shown by studies based on massed data (HARRIS 1914 a) and on series from individual trees (HARRIS 1914 b). The relationship found in Cercis and Phaseolus is not universal for the Leguminosae. In a series of 1427 pods of Robinia (HARRIS 1909 a), the pods with larger numbers of ovules mature a relatively higher propor tion of their ovules into seeds. The correlation between the actual num ber of ovules formed and the actual number of seeds developing is rog •== .693 ± .009, while that between the number of ovules formed and the deviation of the number of seeds matured from their probable value is roz = .365 ± .015. That this result represents a real biological relationship is indicated by the correlations, hitherto unpublished, for the individual trees. Only three of the twelve constants in table i are negative in sign. No one of these can be regarded as statistically significant when the probable error is taken into consideration, while seven of the nine positive coefficients must be looked upon as statistically trustworthy. The formula has also been advantageously applied to the problem of the interrelationship of the number of male and female flowers in the inflorescence of the aroid Arisarum (HARRIS 1916 a) and that of the interdependence of numbers of stamens and pistils in the ranuncula- ceous genus, Ficaria (HARRIS 1918). In Arisarum the relative number GENETICS 3: Tl 1918 332 J. ARTHUR HARRIS TABLE i Relationship between seed and ovule number in Robinia. Number of Number of r r r IE OS oz OZ/ T tree pods OZ I 122 .524±x>44 — .O55±.o6i (— )o.oo 2 64 .802 ±.030 468±.o66 7.09 3 in .478 ±.049 .074 ±.064 1.16 4 102 .430 ±.054 . 105 ±. 066 1-59 5 122 .671 ±.034 .338±.054 6.26 6 I2O -533±.044 .2-2±.057 477 7 120 •259±-057 — .ii5±.o6i (-)i-89 8 159 .6i4±x>33 .2i6±.o5i 4.24 9 128 •5oo±.o40 •35o±.052 6-73 10 78 .507 ±.057 .225±.o73 3-o8 ii 105 .714^.032 — .044 ±. 066 (-)o.67 12 196 •797±.oi8 48o±.037 13-22 All trees 1427 .693±.oo9 .365 ±.015 24-33 of pistillate flowers increases as the total number of flowers per inflo rescence increases. In Ficaria the relative number of pistils increases as the total number of sporophylls becomes larger. Dr. BLAKESLEE and I (1918) have applied this coefficient to the deter mination of the relationship between the total annual egg production and the monthly egg production of White Leghorn fowl. We have there shown by means of this coefficient that the winter months, November, December, January and February, and the following autumn months! August, September and October, show an increase over their theoretical quota of eggs when the annual total egg production rises above the normal. That is, reg, the correlation between total annual egg produc tion and the deviation of the monthly production from its probable value, is on the whole significantly and substantially positive. The spring and summer months, April, May, June and July, show negative values of rn, that is, they make a lower relative contribution to the annual total than might be expected when the total varies in the direction of an in crease above the normal egg production of the flock as a whole. FURTHER ILLUSTRATIONS Illustration i. Proportionality of parts in Paramccinm JENNINGS (1911) in his masterly investigation of assortative mating in Paramecium, has given data for determining the relationships between APPLICABILITY OF A COEFFICIENT OF CORRELATION 333 (a) distance from the anterior end of the organism to the posterior mar gin of the mouth, (fe) distance from the posterior margin of the mouth to the posterior end of the organism, and (c) the total length in series of conjugant and non-conjugant Paramecia. He has calculated and discussed for a purpose which does not con cern us here the correlations between certain of these dimensions. All the correlations between the absolute measurements, calculated from his data, are given in table 2. TABLE 2 Relationship between total length, I, and anterior length, a, and between anterior length and posterior length, p, in Paramecium. Series* rap ria ri. ri,/Er MP Lot 7, table 40 .246 ±.O5O .735 ±.025 —.733 ±.025 3-0 Lot 7, table 41 .57o±.047 .893 ±.014 — .427±.o57 7-5 Lot 19, table 51 .382 ±.044 .832 ±.o 1 6 -434±.042 10.4 Lot 19, table 52 .67 1 ±.034 .939 ±.074 — .I96±.o6o 3-3 Lot 22, table 55 — .403 ±.026 .485^.049 — .282±.o6o 4-7 Lot 22, table 56 .62O±.O25 .906 ±.073 —.405 ±.034 I2.O Lot 24, table 64 .277 ±.040 .82o±.oi4 — .282 ±.040 7-1 Lot 24, table 65 .488±.03i .885 ±.089 — .288±.o38 7-6 * Lot /, table 40, conjugates of wild cultures. 2. Lot 7, table 41, non-conjugants of wild cultures. 3. Lot 19, table 51, conjugants of race g. 4. Lot 19, table 52, non-conjugants of race g. 5. Lot 22, table 55, wild culture conjugants not yet sep arated. 6. Lot 22, table 56, wild culture conjugants about twelve hours after separa tion. 7. Lot 24, table 64, unseparated conjugants of race k. 8. Lot 24, table 65, con jugants of race k about twelve hours after separation. In this table the constants for anterior and posterior length are ar ranged in pairs of conjugants and non-conjugants or ex-conjugants. In every instance the correlation between the anterior and posterior por tions of conjugants is lower than that between the same dimensions in non-conjugants or ex-conjugants.2 All of these values are low, as JENNINGS has noted. In the case of lot 22 the coefficient for the conjugants is actually negative in sign. The correlation between total length and the length of the section anterior to the mouth is high. In every case the value of ria is higher in non-conjugants or ex-conjugants than in conjugants. The additional relationship to be brought out by the formulae here under discussion is 2 See in this connection the discussion by JENNINGS (1911, pp. 65-66, 71-73)- GENETICS 3: Jl 1918 334 J. ARTHUR HARRIS that between the total length of the organism and the relative length of either anterior or posterior element. JENNINGS (1911, p. 63) has emphasized the high variability of the post-oral dimension. Table 3, in which all the coefficients of variation TABLE 3 Coefficients of variation for anterior and posterior fractions of length in Paramccium. Series Total length Anterior length Posterior length v»-va Lot 7, table 40 6.90 5-79 13-86 4-8.07 Lot 7, table 41 9.68 8.76 14-53 ~r 5-77 Lot 19, table 51 8.55 7v8 14-31 + 6.53 Lot 19, table 52 12.18 12.08 15.13 + 3-05 Lot 22, table 55 548 7.38 14.29 + 6.91 Lot 22, table 56 7.96 7.28 11.2O + 3-92 Lot 24, table 64 6-34 6.42 9.98 + 3o6 Lot 24, table 65 6.62 6-45 9-35 + 2.90 are laid side by side, fully confirms his conclusion in this regard. Utiliz ing these coefficients of variation we obtain the values for the correlation between total length and the deviation of the anterior length from its probable value, given in the fourth column of table 2. These constants are negative in sign throughout, and while variable in magnitude all may reasonably be considered statistically significant in comparison with their probable errors. Thus when Paramecium varies in length both anterior and posterior fractions of the body contribute to this variation, but as length in creases the anterior portion becomes relatively shorter. For one series, the unseparated conjugants of race k. I have deter mined the regression of the anterior length on total length and the re gression of the deviation of the anterior length from its probable value on the total length of the organism. The equations are a == 3-0359 + -4977 I ^==.7616, sa = 3.3743 --.1135 / The equations and empirical means are represented graphically in diagrams i and 2. In both cases the relationships are sensibly linear. APPLICABILITY OF A COEFFICIENT OF CORRELATION 335 -2J -20 •/s 2$ Tote/ 26 27 28 29 30 31 32 33 34- 3$ 36 DIAGRAM i. — Relationship of anterior length to total length in Paramecium, Com pare diagram 2. DIAGRAM 2. — Relationship of deviation of anterior length from its probable value to total length in Paramecium. Compare diagram i. GENETICS 3: Jl 1918 336 J. ARTHUR HARRIS Illustration 2. Absence of relationship between size of litter and sex in swine PARKER and BULLARD (1913) have discussed the possible relationship between the size of the litter and sex in the contents of 1000 uteri of swine. From a simple percentage table they state that the relative num bers of males and females are "even in the extreme cases so nearly uni form that we may conclude with reasonable assurance that there is no intimate relation between sex and the size of the litters." The correlations between the total numbers of pigs in the litter, /, and the number of males, m, and females, /, may be deduced from their data. They are rlm-= .6833 ± .0114 rtf = .6875 ± .0112 From these and the three coefficients of variation one may deduce For males rte = — -0177 ± -O2I3 For females rlz = + .0177 ± .0213 The correlation is sensibly zero, with regard to its probable error. This method of analysis therefore fully confirms the conclusion drawn by PARKER and BULLARD. Illustration 3. Proportion of pistillate and hermaphrodite flowers in the inflorescence of the composite Homogyne LUDWIG (1901) has given data for the correlation between the num ber of pistillate and the number of hermaphrodite flowers in the inflo rescence of Homogyne. From his data we deduce For hermaphrodite flowers, h, h = 31.8333- °» == 7-398i, Vh = 23.240 For pistillate flowers, p, P= I0-537o, °P = = 2.6460, Vp = 25.112 For total flowers, f, /"= = 42.3704, *f == 8.7749, V, = 20.7099 For hermaphrodite and pistillate flowers, r*P = -3899 ± -0449 For total flowers and hermaphrodite flowers, rfh = .9607 ± .0049, rfih = .2429 ± .0499 For total flowers and pistillate flowers, rfp == .6303 ± .0339, rfSf = — .2429 ± .0499 APPLICABILITY OF A COEFFICIENT OF CORRELATION 337 It follows, therefore, that in the larger heads the purely pistillate flow ers are relatively less, and the hermaphrodite flowers relatively more, numerous. Illustration 4. Fertility of capsules and viability of seed in carnation crosses STUART (1912) has recorded the number of seeds obtained and the number germinated, planted into the field, and producing flowers in various carnation crosses. Our problem is to determine whether the seeds which come from capsules producing a large number of seeds are relatively more (or less) viable than those from capsules producing small numbers. . Using his two larger tables of data, tables 3 and 6,3 and confining at tention to the relationship between number of seeds per capsule, and the number which germinated, I find For commercial X commercial, STUART'S table 3, N = 23, rsg = -775 ± -056, rsa = -.072 ± .141 For single flower X double flower, STUART'S table 6, N = 32, rg(J = .649 ± .069, rs~ = — .118 ± .118. The signs are both negative, indicating a relatively higher failure to germinate among the seeds which are produced many in a capsule. With regard to their probable errors, the constants are untrustworthy. Be cause so few observations are available, no biological significance is at tached to these two series, which serve merely as another illustration of the kind of problems to which the method may be applied. Illustration 5. Relationship between the total number of pedicels and the number of abnormal pedicels in Spiraea Vanhonttei In Spiraea Vanhouttei the pedicels of the umbel-like raceme normally produce but a single flower each. An abnormal condition in which one or more pedicels may bear a relatively large number of flowers is fre quently observed (HARRIS 1917 d). Let x be the total pedicels in an inflorescence and a the number which are abnormal. Then if abnormality be distributed purely at random among the pedicels one would expect material values of rxa. The cor relation rxs meets our requirements since it shows whether inflorescences with a large number of rays have relatively more or fewer of their rays abnormal than those with a small number. 3 In table 6 the cases in which the seeds are not normally developed are omitted. GENETICS 3: Jl 1918 33§ J. ARTHUR HARRIS During the last fifty years a great deal has been said about the in fluence of nutrition, vegetative vigor, etc., upon the development of anomalies. If a larger number of rays indicates greater vigor or better nutrition one might a priori expect larger inflorescences to have a pro portionately higher number of branched rays, providing of course, that the classic theories are true. The constants for a short series of data collected in 1906 were pub lished in 1909. Since then a large number of determinations have been made on a general sample of inflorescences from a number of shrubs in 1909 and from three large individual shrubs in 1913. In the latter series the data have been analyzed in two ways. First, the inflorescences which contain at least a single abnormal pedicel have been used as the basis of the correlations. These are designated as the ab normal inflorescences. Second, the normal inflorescences from the same plants have been included and counted as zero in the distribution of number of abnormal rays. The results are: For 1906* rm = • -f .121 ± .034 *W = — .071 ± .034 For 1909. Massed statistics. Inflorescences producing some abnor mal pedicels (N = 785), rM = + -1542 ± .0235 r** = — -0915 ± .0239 For 1909. Massed statistics. All 2040 inflorescences, rxa = + -1584 ± .0146 r« = + -0370 ± .0149. For 1913. Individual plants. Inflorescences producing some abnor mal pedicels, Plant i. N = 747 inflorescences. rXa = 4- .0880 ± .0244 TXZ = ~ .2846 ± .O227 Plant 2. N == 641 inflorescences. Tm = + .1148 ± .0263 « = - -3855 .± .022 * Since in the 1906 series only synanthies were observed, the total pedicels rinclud APPLICABILITY OF A COEFFICIENT OF CORRELATION 339 Plant 3. Ar = 548 inflorescences. rxa = + -0941 ± -0285 r*z = — -2849 ± .0265 For 1913. Individual plants. All inflorescences, Plant i. Ar = 1135 inflorescences. rxa = — .0067 ± .0200 rxz = — .2125 ± .0191 Plant 2. Ar = 975 inflorescences. rxa = — .0821 ± .0214 rxx = — .3681 ± .0187 Plant 3. Ar = 912 inflorescences. rxa = —.0360 ± .0223 rxg = - .2342 ± .0211 For all the samples of inflorescences in which there is at least one abnormal pedicel the correlations between the total number of pedicels and the number of normal pedicels is positive in sign and perhaps sta tistically significant, but low in actual magnitude. Thus the number of abnormal pedicels increases on the average as the total number of pedi cels per inflorescence becomes larger. The relationships are, however, very slight indeed. For these five series the correlation between the total number of pedi cels and the deviation of the abnormal pedicels from their probable value, is negative in sign. Thus the larger inflorescences have a rela tively smaller proportion of abnormal pedicels than do those with a smaller total number of pedicels. In the four series in which the wholly normal inflorescences are in cluded, the correlations between total number of pedicels and number of abnormal pedicels is positive in 1909 but negative throughout and insig nificant in magnitude in 1913. The three series from individual shrubs studied in 1913 show low but significantly negative correlations between the total number of pedicels per inflorescence and the deviation of the number of abnormal inflorescences from their probable value. The con stant for the heterogeneous data of 1909 is positive but insignificant. Taking the data altogether, there can be no reasonable doubt that the relative number of abnormal pedicels decreases as the total number of abnormal pedicels increases. This is shown in diagram 3, which represents the regression of the deviation of the number of abnormal rays from their probable value on GENETICS 3: Jl 1918 340 J. ARTHUR HARRIS the total number of rays in the series showing the lowest, and in one of these showing the highest, correlation. 23 25 27 29 31 33 35 36 DIAGRAM 3.— Regression of the deviation of the number of abnormal pedicels from their probable value on the total number of pedicels in Spiraea. The standard deviations are : For 1909, -i "-> rdered when the corrected galley-proofs are returned. Manuscripts and all editorial correspondence should be addressed to the Managing Editor, Dr. Georjje H. Shull, 60 Jefferson Road, Princeton, N. J. GENETICS, JULY 1918 TABLE OF CONTENTS PAGj SAX, KARL, The behavior of the chromosomes in fertilization. . . . 305 HARRIS, J. ARTHUR, Further illustrations of the applicability of a coefficient measuring the correlation between a variable and the deviation of a dependent variable from its prob able value 32! EAST, E. M., and PARK, J. B., Studies on self -sterility. II. Pollen- tube growth 35; WRIGHT, SEWALL, On the nature of size factors 36; ROBBINS, RAINARD B., Some applications of mathematics to breed ing problems. Ill 37; ROBBINS, RAINARD B., Random mating with the exception of sister by brother mating 39 G-196 PRACTICAL UNIVERSALITY OF FIELD HETEROGENEITY AS A FACTOR INFLUENCING PLOT YIELDS BY J. ARTHUR HARRIS Reprinted from JOURNAL OF AGRICULTURAL RESEARCH Vol. XIX, No. 7 : : : : Washington, D. C., July 1, 1920 PUBLISHED BY AUTHORITY OF THE SECRETARY OF AGRICULTURE. WITH THE COOPERATION OF THE ASSOCIATION OF LAND-GRANT COLLEGES WASHINGTON : GOVERNMENT PRINTING OFFICE : 1920 PRACTICAL UNIVERSALITY OF FIELD HETEROGENEITY AS A FACTOR INFLUENCING PLOT YIELDS By J. ARTHUR HARRIS Collaborator, Office of Western Irrigation Agriculture, Bureau of Plant Industry, United States Department of Agriculture INTRODUCTION With the development of a more intensive agriculture there must be a wider use and a progressive refinement of the method of plot tests in agronomic experimentation. Betterment of the method of plot tests must be sought along two lines, (i) the perfection of biological technic and (2) the more extensive use of the modern higher statistical methods in the analysis of the results. In 1918 Mr. C. S. Scofield, in charge of the Office of Western Irrigation Agriculture, and Prof. E. C. Chilcott, in charge of the Office of Dry-Land Agriculture, asked the writer to undertake an investigation of the statistical phases of the problem of the accuracy of plot tests. The present paper deals with one aspect only of the general problem, that of the lack of uniformity of the experimental field. This is both the most potent cause of variation in plot yields and the chief difficulty in their interpretation. Many of the careful writers on field experimentation have noted the existence of soil heterogeneity. Few have, however, sufficiently recog nized and none have adequately emphasized the importance of this factor. The problem of field heterogeneity is twofold. First, some measure of the amount of its influence upon crop yields must be obtained. Sec ond, some means of avoiding or of correcting for its influence must, if possible, be secured. An exact measure of the influence of field heterogeneity, and not merely a vague notion that it may influence experimental results, is the first and most fundamental step in the closer analysis of the factors determining the variability of plot yields. If the application of such a criterion to results obtained by practised agriculturalists from fields selected for their uniformity shows no evidence of heterogeneity, plot tests may be carried out along conventional lines with confidence that Journal of Agricultural Research, Vel. XIX, No. 7 Washington, D. C. July i, 1920 utn Key No. G-i$>6 (279) 280 Journal of Agricultural Research vol. XIX.NO. 7 with reasonable precautions reliable results will be obtained. If, on the other hand, the application of such a criterion shows a high degree of irregularity in fields selected for their uniformity by experienced agri culturalists, it is evident that very special precautions must be taken to obtain trustworthy results. Some quantitative measure, and some probable error of this measure, of the amount of irregularity of the soil of a field, as shown by actual capacity for crop production, and not merely a demonstration of its existence is, therefore, required. The purpose of this paper is to show by the analysis of the actual yields of test plots reported by agricultural experts that the securing of fields suitable for a direct comparison of yields is, practically speaking, an impossibility. The results show that unless special precautions are taken irregularities in the field may have greater influence upon the numerical results of an experiment than the factors in crop production which the investigator is seeking to compare. The results of this study may seem to be altogether negative — destruc tive rather than constructive. The unbiased student must, however, admit that a full evaluation of all the sources of error is an essential prerequisite to constructive work. Furthermore, large expenditures of public funds are being devoted to fertilizer tests, variety tests, and rota tion experiments. It is preeminently worth while to ascertain to what extent results derived from methods now in use may be considered reliable. Subsequent papers will treat other phases of the problem. FORMULAE A criterion of field homogeneity (or heterogeneity) to be of the greatest value should be universally applicable, be comparable from species to species, character to character, or experiment to experiment, and be easy to calculate. In 1915 the suggestion was made (5)* that we may proceed as follows: Suppose a field divided into N small plots, all sown to the same variety of plants. Let p be the yield of an individual plot. The variability of p may be due purely and simply to chance, since the individuals of any variety are variable and the size of the plots is small, or it. may be due in part to the diversity of conditions of the soil. If irregularities in the experimental field are so large as to influence the yield of areas larger than single plots,2 they will tend to bring about a similarity of adjoining plots, some groups tending to yield higher than the average, others lower. Now let the yields of these units be grouped into m larger plots, Cn, each of n continguous ultimate units, p. The correlation between the 1 Reference is made by number (italic) to " Literature cited, " p. 313-314. 2 Irregularities of soil influencing the plants of only a single small plot may in most work be left out of account, since they are of the kind to which differences between individuals are to a considerable extent due and are common to all the plots of a field. July i, i93o Universality of Field Heterogeneity 281 p's of the same combination plot, Cn, will furnish a measure (on the scale of o to ± i) of the heterogeneity of the field as expressed in capacity for crop production. If this correlation be sensibly o (under conditions such that spurious correlation is not introduced), the irregularities of the field are not so great as to influence in the same direction the yields of neighboring small plots. As heterogeneity becomes greater the cor relation will also increase. The value of the coefficient obtained will depend somewhat upon the nature of the characters measured, some what upon the species grown, somewhat upon the size of the ultimate and combination plots, and to some degree upon the form of the combina tion plots. Knowledge of the values of the correlations to be expected must be obtained empirically. Let 5 indicate summation for all the ultimate or combination plots of the field under consideration, as may be indicated by Cn or p. Let p be the average yield of the ultimate plots and • f\ f> O This formula assumes the combination plots to be of uniform size — that is, to contain each the same number, n, of ultimate plots. It may be desirable or necessary to have some of the combination plots smaller than the others. Such cases are frequently met in practical work. For example, the wheat field of Mercer and Hall is laid out in a 20 by 25 fold manner. This permits only 2 by 5, 4 by 5, or 5 by 5 combinations of the same size throughout. One of Montgomery's experiments with wheat covered an area of 16 by 14 plots which may be combined in only 2 by 2 or 4 by 2 fold groupings to obtain equal areas suitable for calculation. In each of these cases other groupings are desirable. The formulae are quite applicable to such cases; the arithmetical routine is merely a little longer. The formula is as above, but ~p and ffp are obtained by a (n-i)-fold weighting of the plots,1 where n is the variable number of ultimate plots in the combination plot to which any P may be assigned — that is, I /5[(n-i)/>]V \S[n(n-i)]J 1 That is, each ultimate plot is multiplied by the number less one of the plots in the combination plot to Which it is assigned. 282 Journal of Agricultural Research VOI.XIX.NO. 7 Ample illustration of the arithmetical routine has been given in the original paper. The formulae employed assume the symmetry of the correlation sur face. It has been shown elsewhere (4) that spurious values of the cor relation coefficient may arise in such cases. Since both p^2 and crp anc* the regression slope is identical with the correlation 1 2 coefficient. Thus, if one ultimate plot, pv of a combination plot be known, the most probable deviation of another plot will be p2 — J>= (p'i-p)r. Concretely, if the yield of a first plot of a combination plot be 10 pounds above the average of the field as a whole and if the interplot correlation be rp p = 0.60, the most probable yield of a second plot will be 6 pounds above the average. Similar reasoning applies throughout. Those who have difficulty in thinking in terms of correlation coefficients can most easily grasp the significance of the results by remembering that in this case the correla tion coefficients multiplied by 100 gives the most probable percentage of deviation of the yield of an associated plot when the deviation of one plot of the group from the general average is known. INFLUENCE OF SOIL HETEROGENEITY ON YIELD OF FIELD CROPS In the paper in which these formulae were suggested it was shown that yield of straw and grain and the nitrogen content of wheat, yield of roots and tops of mangolds, and yield of timothy hay are markedly influenced by irregularities in the carefully selected fields upon which plot cultures have been carried out by agriculturalists. We have now to ascertain whether this is a general phenomenon or whether it is merely a chance result of these particular cultures. The suggestion has been made that the latter is the case, that with the exer cise of a little care uniform fields may be secured, and that substratum July i, 1920 Universality of Field Heterogeneity heterogeneity was overemphasized as a factor influencing plot tests. This question can be answered only by actually determining the degree of heterogeneity existing in the fields which have passed the criticism of agricultural experts. It will be conducive to brevity to have a definite system by which the arrangement of the plots in a field may be described. We shall consider the plots arranged as soldiers in ranks and files. The worker inspects the plot records of a field as recorded on a map or table. By ranks we understand the horizontal rows of plots, by files the vertical rows. 1.80 1.83 2.00 1.91 1.90 1.89 1.79 i-75 2.03 1.83 2.18 i-93 1-77 1.86 i. 80 2.07 1-77 1.90 1.70 1-79 1.90 2.04 i-95 1.83 2.06 1.76 1.86 1.79 i-93 1.96 1.83! 1.92 1.69 I.9O i. 80 1.89 1.83 1.85 2.OO 2.13 1.82 1.83 1.89 1.96 1.92 1.86 1.79 1.86 1.79 1.94 1.92 i. 80 1.97 2.0O 1.87 i-73 2.OO 2.01 1.89 1.77 1.97 1.85 i-97 2.IO 1.99 1.83 2. CO 1.92 1.79 1.89 1.96 1.96 2.OO 1.82 J-93 1.82 1.87 1.87 1.92 i-99 1.87 1.83 1.92 1.96 1.89 2. II 1.99 1.87 1.86 1.84 2.06 1.90 1.90 1.82 1.81 1.97 i-79 1.89 2.03 1.86 1. 80 1.86 2.06 1.72 1.86 1.72 2.07 1.82 1.84 1-97 1.96 2.OI 1.83 1.82 1.82 i-75 1.77 1.72 1.90 1.83 1.90 1.83 1.90 1.85 1.76 2.07 1.87 2.14 1.96 I.8J 1.97 1.90 1.90 2.13 i. 80 1.83 1.90 2.O6 1.94 1.87 1.90 1.94 1.94 1.77 1.89 1.86 1.82 1.87 i. 80 1.84 1.87 2.04 1.94 1.89 1.94 1.76 1.96 1.99 1.87 2.04 i-93 i-77 1.74 1.89 i-93 1.96 2.04 1.97 1.83 1.99 1-97 2.08 1.99 1.96 2.15 1.82 1.78 1.83 1.98 1.89 1.85 1.87 1.85 1.87 1.85 1.82 1.92 1.89 2.13 1.82 i-73 1.83 1.96 2.04 1.86 2.08 2.IO 1.83 1.85 1.96 2.01 1.92 1.68 1.89 1.85 i.85 1.83 I-85 2.07 i-7S i-93 1.86 i-93 1.87 I.9O 1.86 1.99 1.89 1.83 1.82 1.96 1-99 1.99 2.06 FIG. i. — Montgomery's diagram of 5.5 by 5.5 foot plots of Turkey wheat, showing variations in the per centage of nitrogen in the grain. Thus figure i, showing the nitrogen content of wheat plots 5.5 by 5.5 feet given by Montgomery (17), may be considered made up of 16 ranks and 14 files. In considering rearrangements or combinations of plots we shall refer to the ranks and then to the files — an order easily carried in mind by remembering the trite expression "rank and file." Thus in referring to a 2 by 5 fold combination we mean that two adjacent ranks and five adjacent files of plots were combined. Individual plots may be easily designated. Thus, the plot belonging to the sixth rank * and the fifth file in the nitrogen contents of wheat yields contained 1.93 per cent nitrogen. J Ranks are numbered from the top of map, files from the left. 284 Journal of Agricultural Research vol. XIX.NO. 7 I . MANGOLDS The yields of 200 plots of mangolds studied by Mercer and Hall (15) may be grouped into combination plots in a 2 by 2 fold manner. When this is done, the correlation between the yields of associated plots has been shown * to be as follows: For weight of roots, r= 0.346 ±0.042^ r/Er= 8 24. For weight of leaves, r=* .466 ± .037, r/Er= 12.5. Thus, if one plot of a combination plot is higher or lower than the general average by a given amount, an associated plot may be expected to deviate from the general average by 35 to 40 per cent of this amount. 2. — POTATOES Lyon (14) gives the yield in pounds for each of six sections of a series of 34 rows of potatoes. This crop was harvested from " a piece of appar ently uniform land." Each section was 72 feet 7 inches in length. The distance between rows was 34 inches. Combining yields of rows and of sections of rows by twos, we reduce the field from a 34 by 6 fold to a 17 by 3 fold combination. The correla tions between the sections of the rows is then found to be rPlP2 = o.3n ±0-043. r/EP=7.30. Yield of potatoes in this field is, therefore, markedly influenced by irregularities of soil conditions. For data on a second test on the influence of field heterogeneity on the yield of potatoes we may avail ourselves of the valuable records of yields of individual hills reported by Stewart (19). Since these are recorded in quadruplets for the purpose of determining the influence of missing hills upon yield,3 it is not feasible to group them into plots. The influ ence of heterogeneity may be tested by determining the correlation between the yields of the plants of a quadruplet.4 1 For original data see Mercer and Hall (is. p. IOQ); also Harris (5, p. 434-436). * The probable errors have in all cases been computed on the basis of the actual, not of the weighted, number of ultimate plots as A'. * The planting scheme adopted was 0 ai a'i b'l bi 0 aj a'j b'j bj 0 aj a'j b'j bj . . . , •where a and a' are the two halves of the same tuber and b and b' are two halves of another tuber. Thus halves a and b were grown adjoining missing hills and were subject to competition on one side only, whereas halves a' and 6' were subject to competition from two adjacent plants. 4 Since a and a' are halves of the same tuber and b and 6' are halves of another, the correlations raa '. rt>b' might be due to a specific physiological influence of the characters of the tuber upon both plants developing from the corresponding half tubers rather than to an influence of differences in soil conditions. We have, therefore, determined the correlations between the plants occupying the same relative position in the quadruplet but derived from different parent tubers, that is Tab, Tab'. Hence Tab represents the correla tion between the two outside tubers and raV the correlation between the two inside tubers of the quad ruplet. As a control on the results the correlations between one outside and one inside plant have been determined. These are r<*' and r»a'. July i. i92o Universality of Field Heterogeneity 285 The data given by Stewart are number of tubers and total weight of tubers per plant. These two characters permit the determinations of the average weight per tuber. When all the pairs are omitted which have been omitted by Stewart1 or have been designated as affected by leaf roll, there remain 139 quad ruplets. Determining the correlations between the yield of the two plants derived from different tubers but exposed to the same conditions for growth, we have the following correlations: For number of tubers per hill — •fab = 0.31 8 ± 0.051, r/Er = 6.19. rab' = .i38± .056, r/Er= '2.46. ra'b = -23Q± .054, r/Er= 4.26. roy = .220± .054, r/Er= 4.04. For total weight of tubers per hill — rab =0.457 ±0.045, r/Er= 10.10. rab' = -3i2± .O52,r/Er= 6.00. ra'b = 427 ± .047, r/£; = 9.09. ra'b' = -290± .052, r/Er= 5.53. For average weight of tubers — »o6 = 0.237 ± 0.054, r/Er= 4-39- rab = -104 ± .057, r/Er= 1.82. ra'b = -°54± -°57. r/Er= .95. ra'b' = -H7± -056, r/Er= 2.07. The correlations are positive throughout and generally statistically significant with regard to their probable errors. They show, therefore, that this experimental plot was heterogeneous to an extent that influ. enced in a very measurable degree the number of tubers, the total weight of tubers, and the average weight of tubers of neighboring hills. For all four measures of interdependence the coefficients are lowest for average weight of tubers and highest for total weight of tubers, while the correlations for number of tubers produced are intermediate in value. The values of rab are consistently higher than those for ra'v, notwith standing the fact that a' and br are more closely associated than a and 6. The measures of interrelationship between the yields of pairs of plants, one of which occupies an inside and the other an outside position in the quadruplet, are sometimes intermediate between rab and ra'br and sometimes less than ra'v. On the assumption that the correlation is due solely to environmental influence one would expect the highest 1 Records have been abstracted from Stewart's Table I. Prof. Stewart has kindly furnished some additional information in regard to certain entries in this table. Journal of Agricultural Research vol. XIX.NO. 7 correlation between the most closely associated plants — that is ra>v > rob- Apparently the reverse condition, rarb' < rob, is due to some influence of the open space adjoining a and b, which allows the fuller development of those plants and in consequence renders them more representative of the extremely localized soil influences to which they are subjected.1 3. TIMOTHY HAY The records of plot yields of timothy hay published by Holtsmark and Larsen ( 255 225 295 340 265 255 310 295 235 225 320 3°5 250 280 310 315 240 265 3io 280 FIG. 2. — Diagram showing yield of al falfa in first cutting. 1913, on the Huntley experimental tract. The yield is expressed in pounds per half plot. cases been harvested in has been into halves, of 1 Possibly competition between closely associated a' and b' plants tends to make the yield of one lew when that of the other is high" July i, 1920 Universality of Field Heterogeneity 287 into thirds, and of 0.0425 acre when the division has been into quarters of plots. In the spring of 1912 the whole field was uniformly seeded to alfalfa; only one crop was harvested, and yields were recorded for the entire III II b a b a 70 95 "5 135 135 i55 135 i?5 no 75 85 160 145 «5 «5 165 80 90 "5 no 165 i55 150 160 100 65 130 130 145 180 145 180 "5 95 no «5 135 165 IOO 140 "5 "5 135 135 "5 185 130 155 no 95 120 "5 145 175 IOO 155 I2O 90 IOO "5 140 'So IOO 180 zoo 90 So 105 "5 150 45 15° 95 95 105 I2O "5 140 60 145 "5 80 95 IOO 120 140 65 IIO "5 90 90 K>5 "5 145 I2O 60 no 100 no 130 I2O 140 IIO "5 "5 85 I2O 165 130 150 IOO 130 i°5 i°5 IOO 145 130 15° 145 140 ;sp 95 IOO 95 IOO r5o IIO «S 135 "5 90 i°5 95 no IOO 130 155 "5 120 IOO 65 130 "5 "5 J45 130 145 95 I2O I2O IOO "5 170 i35 155 i°5 95 135 95 "5 135 «s 155 95 no I2O "5 IIO 140 "5 1 60 I2O 1 10 145 "5 130 150 IOO I2O 160 85 i5° i°5 85 I FIG. 3. — Diagram showing yield of alfalfa in second cutting, 1913. on the Huntley experimental tract The yield is expressed in pounds per quarter plot. plots only. In 1913 and 1914 three cuttings were made. The first cutting was harvested in half plots. The second cutting of 1913 and the first and second cuttings of 1914 were harvested in quarter plots. The 288 Journal of Agricultural Research Vol. XIX. No. 7 third cutting of 1913 was lost because of a heavy wind which mixed the plot yields at harvest time, so that it was implossible to secure III II b a b a i 85 85 13° 120 13° 150 140 165 i°5 IOO «>5 I2O i35 J5° 140 185 100 80 105 no I2O I5° 170 165 105 no 95 13° Vl65 155 15° 170 IOO IOO 105 13° I2O 140 i45 185 zoo 105 IOO i25 120 175 i95 i55 90 IOO IOO I2O 155 155 "5 200 90 IOO I05 I2O 85 155 i45 170 I2O 95 90 I2O "5 140 170 165 85 95 75 no i55 13° i°5 J55 75 95 85 i°5 85 13° i25 240 60 no 90 IOO I2O 140 1 60 i35 75 IOO 75 140 95 120 I2O 130 55 IOO 75 140 120 130 "5 165 75 95 85 "5 I2O 130 140 145 85 IOO 60 "5 I25 I2O . 140 1 60 85 105 IOO i°5 120 135 i35 150 "5 IOO 65 "5 "5 I4O i55 13° "5 I25 85 "5 150 "5 140 130 85 135 95 I2O 135 135 i35 i35 i°5 I2O I05 I°5 130 140 165 i45 IOO "5 125 J35 140 160 170 140 IOO "5 140 I2O 135 120 "5 I2O FIG. 4. — Diagram showing yield of alfalfa in first cutting, 1914, on the Huntley experimental tract. The yield is expressed in pounds per quarter plot. accurate weights on any of the plots. The third cutting for 1914 was harvested in subplots one-third the size of the original plots. The actual yield of these subdivisions is indicated in figure 2 1 for the first cutting and figure 3 for the second cutting in 1913 and in figure 4 1 Diagrams are set in type instead of being drawn to scale. July i, 1920 Universality of Field Heterogeneity 289 for the first cutting, figure 5 for the second cutting, and figure 6 for the third cutting in 1914. III II b a b a IOO no 135 125 I2C 145 MS 140 80 85 IIO I2O 130 US 175 155 70 IIO 140 "5 170 155 195 170 70 140 "5 125 1 60 190 MS I65 85 125 85 125 180 190 155 175 55 125 95 IOO 190 175 185 185 65 i°5 "5 "5 225 155 200 195 65 IIO 95 IIO 190 190 180 165 70 105 IOO 135 140 155 155 I65 no I2O 60 IOO IIO I2O TOO 175 IOO IIO 85 125 95 125 70 140 95 I2O 120 95 75 IOO 145 i°5 no 135 125 135 IOO 75 125 MS 130 I2O 95 15° 135 85 90 170 "5 "5 IOO 140 "5 125 105 170 130 130 80 "5 95 IIO 95 140 »3S 115 65 IIO no 85 90 15° no "5 80 120 I2O 130 95 180 145 1 60 75 135 I2O 125 i°5 140 140 135 80 125 105 145 155 IOO 135 135 90 I2O "5 155 140 125 120 155 IIO I30 130 J3° i35 13° QO 160 IIO "5 I2O 130 I2O 75 FIG. 5.— Diagram showing yield of alfalfa in second cutting, 1914, on the Huntley experimental tract. The yield is expressed in pounds per quarter plot. For the yield of alfalfa on quarter plots for the second cutting in 1913 and the first and second cuttings for 1914 and in third plots for the third cutting for 1914 the correlations are 1913, second cutting, r = 0.182 ±0.048, r/Er= 3.79. 290 Journal of Agricultural Research vol. xix. NO. ? 1914, first cutting, r = 0.432 ±0.040, r/Er= 10.7. 1914, second cutting, r= -449± .040, r/Er= 11.3. 1914, third cutting, r= .31 1± .052, r/Er= 5.99. Ill II X y z X y z 230 190 225 1 60 240 180 22O 170 13° 220 220 165 215 15° 130 200 205 190 175 150 "S 205 190 215 175 155 125 205 220 170 *55 155 105 J75 1 60 i7S 190 130 125 1 60 175 165 iSS 145 "5 170 165 165 170 i°s no 1 60 *ss 1 60 140 I2O 100 I5° 120 180 *55 90 140 95 1 60 ?45 i25 I2S I2O 125 I65 I5S 2IO TOO I25 »45 1 60 15° 175 I4O no 1 80 I6S 140 155 145 *5S 1 80 195 165 140 "5 i5S 165 185 I25 ISO 125 i55 170 170 120 "5 120 J5° 170 I5<=> J3S 1 60 J5° 165 15° ifS 150 140 165 140 !5° 165 1 60 i55 155 J55 165 i9S IS° 15° i?S 170 175 160 185 '85 15° 140 90 J55 J35 y experimental tract. Fto. 6.— Diagram showing yield of alfalfa in third cutting, 1914, on the Huntle The yield is expressed in pounds per third plot. It will be noted that the results are in very close agreement indeed for 1914. The second cutting for 1913 differs significantly from the others, but no explanation can be suggested. July i, i92o Universality of Field Heterogeneity 291 Grouping all yields in two comparable subplots, we find 1913, first cutting, y= 0.407 ± 0.059, r/Er= 6.93. 1913, second cutting, r= -343± .062, r/Er= 5.52. 1914, first cutting, r= .6o2± .045, r/Er= 13.4. 1914, second cutting, r= .657 ± .040, r/Er= 16.4. We note that all the correlations are higher for a 2-fold division than for a 4-fold division. The coefficients for the second cutting of 1913 are again lower than the otfier values. The foregoing results are based upon weightings of single cuttings only. It is now desirable to determine the correlations for yield of first and second cuttings combined. If the combined yield be considered in quarter plots as ultimate units in 1914 we find r= 0.517 ±0.036, r/Er = 14.2. Combining to obtain total yield in half plots in both 1913 and 1914, we have the following correlations between the yields of the two half plots : For 1913, r= 0.387 ±0.060, r/Er= 6.46. For 1914, r= -709± .035, r/Er= 20.2. 5. — STRAW AND GRAIN IN WHEAT The data of the Rothamsted wheat plots,1 analyzed in an earlier paper (5» P- 436-440 > 443~444)> show the following correlations when the 500 plots are grouped in 2 by 2 fold manner for the first 22 files and in a 2 by 3 fold manner for the twenty-third to the twenty-fifth file : For yield of grain, r = o.336±o.o27, r/Er= 12.5. For yield of straw, r= .483 ± .023, r/Er= 20.9. 6. — STRAW AND GRAIN IN RAGI, ELrEUSINK CORACANA Lehmann (12) has given a series of data derived from the yields of grain and straw of ragi cultivated on the dry-land tract of the Experi mental Farm at Hebbel, near Bangalore, Mysore State. The plots used were of i/io-acre area. The land was previously owned by several raiyats who have naturally treated it somewhat differently in regard to manuring and cultivation. The various pieces used as garden lands are of course in much better condition than those used for ordi nary dry crops. This causes considerable temporary differences to exist in some of the plots in addition to probably slight permanent differences. (12, 6th Rpt., p. 2.) From these conditions one would expect a high degree of heteroge neity in the series of plots. The data permit the testing of the possibility of a decrease in heterogeneity due to uniformity of crop and treatment for three years. 1 For data see Mercer and Hall (15, p. JIQ); also Map B of Harris (5). 292 Journal of Agricultural Research Vol. XIX, No. 7 These data are, furthermore, of particular interest since they consist of the records of yields for three successive years of the same crop on a series of unirrigated plots in a region where crop production is subject to many uncertainties because of inadequate rainfall. Fortunately for our present purposes the meteorological conditions during the three years covered by this experiment were very different from year to year. The values of the most significant factor, the July to October rainfall, are given in Table I. This shows that the rainfall in 1906 was practically twice as heavy as in either of the other two years.1 TABLE I.— Rainfall at Hebbel, near Bangalore, Mysore State, India Month. 1905 1906 1907 Average of 10 years. July Inches. I 77 Inches. Inches. Inches. August 6 75 o 08 • L7 • °4 September i. 50 e fifi 4- 33 a T. October c -6 • 5° 8 CT Ri o. 51 5- 97 Total 1C 7C ?i 08 2i. 47 Maps of the fields are given in the sixth annual report for 1904-1905. Further descriptive detail is given in the seventh, eighth, and ninth reports for 1905-1908. The yield of grain and straw in plots of i/io acre grown in 1905 is given in the seventh report. The eighth report gives detail of the crop of 1906 but does not contain the yields, which are summarized for the years 1905, 1906, and 1907 in Tables I and II of the ninth report. Unfortunately the yields of a considerable number of the plots have had to be omitted from maps I and II of Lehmann's report. In com bining in a 2 by 2 fold manner it is necessary either to disregard all com bination plots in which there are not four ultimate plots or to weight properly in using those containing 2 or 3 plots only. The course followed has been to group the plots by fours and to determine the correlation by the formulae for a variable number of plots when all of the ultimate plots were not planted. The following table shows the correlation between the yield of grain, of straw, and of grain and straw: 1905 1906 1907 Grain °-735±°-°3i . 424± .055 •4iS± -°SS o. 138 ±0. 065 . 164 ± . 065 . I45± -065 o. 7i6±o. 032 •S73± -°4S . 6j6± .040 Straw Total yield 1 A discussion of the growth of these crops in relation to the distribution of the rainfall appears in Leh mann's ninth report (12, p. 2-7). July i, 1920 Universality of Field Heterogeneity 293 The results are of unusual interest. In 1905 and 1907 the correlation between yields of grain are unusually high, falling only slightly below three-fourths of perfect correlation. The correlations for yields of straw and for both grain and straw are of medium value in those two years. In 1906, however, the correlations for all the characters are of a very low order; and any one of them taken alone might not be considered signifi cant in comparison with its probable error, which has been calculated on the basis of 103 plots, the number actually involved in the calcula tions. Apparently the unusual moisture conditions of 1906 tended to oblit erate the differences in the field to which the individuality of adjoining plots was due. . That the unusual weather had a profound influence on the yield of the plots is shown by Table II, in which the means, standard deviations, and coefficients of variation for the yield of the individual plots are set forth.1 TABLE II. — Means, standard deviations, and coefficients of variation for the yield of ragi at Hebbel, near Bangalore, Mysore State, India [Yield expressed in pounds per i/io -acre plot] Year. Grain. Straw. Total yield. Mean. Stand ard devi ation. Coeffi cient of vari ation. Mean. Stand ard devi ation. Coeffi cient of vari ation. Mean. Stand ard devi ation. Coeffi cient of vari ation. IQO<; . . IQ2.8 136.6 165.0 31-5 47.1 48.3 I6.3 34-5 29-3 360.8 191. 6 295-4 148.8 82.0 8o.2 41.2 42.8 27.1 553-5 328.1 460. 4 190.3 127.4 126. 9 34-4 ' 38.8 27. 6 1906 IOO7 The means show that yield of both grain and straw was much lower in the abnormally wet year than in either of the others. The standard deviations are of course largely influenced by the actual magnitudes of the yields and are, in consequence, difficult of interpretation. The rela tive variabilities, as measured by the coefficients of variation, are more orderly. They show that for grain, straw, and total yield the variability of the individual plot yields is greater in the wet year. Thus the influence of the wet season has not been to make the yield of all the plots alike. It has tended to decrease yield and to increase relative variability from plot to plot. But at the same time it has tended to screen certain factors which in drier years have a marked influence on the individuality of the plots. Further analysis is not desirable without more detailed information concerning the plots. From the information at hand it seems quite 1 These constants are obtained by weighting in an (n-i)-fold manner, since this was the method followed in obtaining the constants for the heterogeneity coefficient. 294 Journal of Agricultural Research Vol. xix, NO. 7 clear that the innate differences in different parts of the field do not in some seasons exert their full influence upon crop yield because of the weight of other factors. The practical conclusion to be drawn from this result is that an experimental field which might be demonstrated to be sensibly uniform for one crop plant or for one season might not prove to be so for another crop or in a different season. 7. — KHERSON OATS Kiesselbach (TO, n) has given records of yield for 207 i/3o-acre plots of Kherson oats. He says: These plats were planted . . . upon a seemingly uniform field for the purpose of studying variation in plat yield as a source of experimental error. The entire field had been cropped uniformly to silage corn for a period of eight years. It had been plowed each year and was also plowed in preparation for the oats in 1916. The oats were drilled during two successive days in plats 16 rods by 66 inches The plats were separated by a space of 16 inches between outside drill rows. A wide discard border of oats was grown around the outer edge of the field, so that all plats should have a similar exposure. Love (zj) has shown the existence of heterogeneity in this field. Grouping the entries of Kiesselbach 's Table 27 in a 3 by i fold manner the heterogeneity coefficient is found to be r= 0.495 ±0.035, r/Er=i4. For data on a second test of the influence of heterogeneity on the yields of experimental plantings of oats we turn to a small experiment by Montgomery (77), who has given the yields of thrashed grain in grams from 100 consecutive rows of Kherson oats (17, p. 35, Table XIII) each 12.5 feet in length. The plat chosen for this test was quite uniform and the appearance of the plat at harvest was very satisfactory. Combining by twos, we find for the correlation between adjacent rows r = 0.339 ±0.060, r/£r=5.65. 8. — GRAIN AND NITROGEN CONTEXT IN WHEAT Montgomery (17, p. 37, fig. I0) has given the yield of grain in grams on 224 blocks each 5.5 feet square. Combining in a 2 by 2 fold manner we deduce r= 0.391 ±0.038, r/Er=io.2. Again, Montgomery (17, p. 21-22, fig. 7) has given the values of nitrogen content from 224 Turkey wheat plots of the same size. These values are quoted in figure i of this paper. The correlation between the plots is found to be r— 0.020 ±0.045, r/£r = o.44. July i, 1920 Universality of Field Heterogeneity 295 finally, Montgomery (16) has given data for both yield of grain and nitrogen content on 224 plots of wheat grown at the University of Nebraska in 191 1. The plot (77 by 88 feet) had been sown continuously to Turkey winter wheat for three years. The plat was of about average uniformity and fertility. When grouped in a 2 by 2 fold manner these plots of wheat have been shown (5, p. 440-441, map C) to give the following correlations1. For yield of grain, r= 0.603 ±0.029, r/Er=2i. For percentage of nitrogen, r= .H5± .044, r/Er= 2.59. Yield of grain per plot is clearly influenced by irregularities of the experimental field, notwithstanding the fact that the plots are only 5-5 by 5.5 feet in area. The correlation for percentage of nitrogen is not certainly significant. 9. — HOPS Stockberger (20) has given a series of yields for 30 rows of hops which he believes to be quite typical of many thousands of acres in the Sacra mento Valley in California. The yields of these rows cover the period of 1909 to 1914. Combining the rows by twos and determining the correlation between the yield of the adjacent rows of the 15 pairs for each of the years, we obtain the following constants : Year. Correlation. rlEr. IQOO. . . O. 444 io. OQQ 4. so IQIO. .. . 60 ? i . 064. IO. QI IQII. . . 061 i • 123 8. co IOI2. ., • 326i . no 2. 07 IQI3. .. . 606 ± . 078 7. 7Q IQI4. ., • 386± . 105 7. 60 Average . 4IO e. 06 Without exception the coefficients are positive in sign. In general they are fairly large and indicate a substantial degree of heterogeneity in this limited area. Probably the heterogeneity would have been shown to be greater had it been possible to work with yields from the sections of the long rows instead of with the rows as a whole. 10. — UNHUSKED RICE Coombs and Grantham (2) give the yield in gantangs of a series of 54 square plots % by % chain in dimension. These plots are arranged in 18 ranks and 3 files. They were har vested from a field of standing rice on which — the crop was extremely regular, as judged before the cutting, and it had not been subjected to any attack of borer or any devastation of rats or birds. 296 Journal of Agricultural Research Vol. XIX, No. 7 The yields of the original plots are shown in figure 7. These may be combined in a 2 by i fold manner to give a correlation of r = 0.344 ±0.08 1, r/£r=4.25. These rice yields taken from a field described as "extremely regular" show that as a matter of fact the field is heterogeneous and that this irregularity influences in a measurable degree the yields of the plots. 13.6 12. O II.4 14. 6 14. o 12. 2 14.8 14-4 12. 0 13.0 12. 4 12.8 15.0 12. 0 12. O 13-4 I3.8 14. o 14. 2 12. 2 13.0 14. o 12. 0 12.8 14. o 12. 0 13-4 14. o 14. o 12-4 15.0 14. o 12. 6 14.8 14. o 12.4 14. o 14. o 12. O 14.4 13.6 12.4 12. 6 13.0 12. 0 12. 2 14. o 12.8 II. 6 12. O ii. 8 12.4 14. o 12.4 FIG. 7.— Diagram showing yield of unhusked rice on Coombs and Grantham's 54 plots Y* by Y* chain square. The yield is expressed in gantangs per plot. II. — EAR CORN Smith (18} has published a series of corn yields for three years on plots of Yio acre. The yields are given in his original paper. He has kindly supplied the map showing the relative positions of these plots, which are arranged thus : 101,201, . . .,601 IO2, 2O2, . . ., 6O2 I2O, 220, . . ., 62O July i, 1920 Universality of Field Heterogeneity 297 Combining yields in a 2 by i fold manner, we find for the correlation between the yields of adjacent Vuo-acre plots For 1895,7= + 0.830 ± 0.019, r/Er = 43.4. For 1896,1-=+ .8is± .021, f/Er= 39.6. For 1897, r=+ .6o6± .039 r/Er= 15.5. It is evident that the field was rather highly heterogeneous. II [ I [ b a b i i i33 i32 138 142 136 132 148 140 141 141 132 138 145 135 ' 162 156 i35 109 125 135 133 116 147 13° 132 iS3 J31 131 130 123 iS5 J5° 132 137 135 140 137 112 I31 129 i35 132 I3S 131 134 126 126 135 131 128 121 125 126 "5 122 136 i3S 125 128 I31 121 "5 129 137 i33 125 125 130 131 124 129 131 i37 124 117 I31 127 125 129 132 130 117 119 127 132 129 122 141 i34 122 "5 125 133 123 Iig 132 129 122 120 132 130 125 136 137 123 118 125 130 124 124 123 136 129 126 134 129 122 126 127 136 i34 124 I2O 121 126 130 132 136 128 125 "5 H5 122 123 140 135 128 121 no 110 116 "5 125 123 127 124 119 107 114 116 110 "5 i34 112 121 123 122 126 116 125 US 148 133 125 I32 127 126 i34 149 IS4 I65 1 6O l62 144 137 130 1 68 169 I6S JS2 158 169 143 1 08 KlO. 8. — Diagram showing yield of ear corn, 1915, expressed in pounds per quarter plot. on the Huntley experimental tract. The yield is Journal of Agricultiiral Research vol. xix, NO. 7 For a second test of the influence of field heterogeneity on the yield of ear corn we turn to the Huntley data. Ill II b a b a 78 94 104 128 IIO , 121 132 «JO 73 81 104 118 116 116 140 142 66 77 84 no "3 IO2 128 138 66 73 80 99 "5 "3 128 139 77 79 79 i°3 116 118 126 127 7i 73 86 82 IOO IIO 108 132 76 59 86 90 IIO 117 in IS1 94 65 86 IOO 1 02 105 118 116 98 75 80 IOO III IOI 104 118 88 76 74 99 108 92 IO2 "3 9* 82 69 80 IOO 97 IOI IOI 97 87 83 90 103 92 88 96 75 81 80 107 96 78 96 106 67 76 73 117 95 70 90 117 98 85 74 i°3 98 84 IOO 116 in 88 76 97 97 92 IIO no 108 88 73 84 84 86 104 "5 "5 97 66 89 IOO 87 98 123 104 I2O 86 IOO 94 94 97 119 no 106 92 99 96 IOO 83 104 118 no IOO 98 114 108 "3 120 108 TOO 105 no 93 99 117 IO4 108 98 95 IOO i°3 99 114 08 FIG. 9.— Diagram showing yield of ear corn, 1916, on the Huntley experimental tract. The yield is expressed in pounds per quarter plot. In 1915 and 1916 corn was grown on the Huntley experimental plots, described above, and was harvested in quarter plots. The yields for the two series are shown in figure 8 for 191 5 and in figure 9 for 1916. These records are of special interest in view of the fact that these are irrigated July i, 1920 Universality of Field Heterogeneity 299 fields, whereas the data provided by Smith are based on corn grown without irrigation. Retaining the original division into quarter plots, we deduce for the correlation between the subplots For 1915, r = 0.498 ±0.037, r/£r=i3-4- For 1916, r= -436± .040, r/Er= 10.8. The results for the two years can not, with due regard to their probable errors, be considered to differ significantly. They indicate a degree of heterogeneity in these Huntley plots quite comparable with that of fields planted to various crops by other observers. If the quarter plots be combined by adjacent twos and the correlation between the half plots be determined, we find For 1915, r = 0.494 ±0.053, For 1916, r = .043i± .057, The measure of heterogeneity has been only slightly lowered by divid ing the plots into halves instead of into quarters. INFLUENCE OF SUBSTRATUM HETEROGENEITY ON YIELD OF OR CHARD CROPS In the preceding illustrations the crops considered have been her baceous plants which are generally fairly superficial in their relation to the soil and most of which complete their development in one or two seasons. It seems of particular interest to extend the studies, as Batch- elor and Reed (i) have done, to the yield of large individual plants, such as orchard trees. For the purpose we employ the splendid series of data of Batchelor and Reed. They say of their various groves (i, p. 251} : The fruit plantations herein discussed, to judge by the surface soil, size, and con dition of the trees, as well as their apparent fruitfulness, appeal to the observer as uncommonly uniform. All the orchards studied are situated in semiarid regions and are artificially irrigated during the summer months. This fact is believed to be a distinct advantage for the purpose of reducing the variability of one year's yield compared with another, since it insures a fairly uniform water supply for the soil and reduces one of the variants inevitable in nonirrigated localities. In the case of the Arlington navel oranges grouped in 8-tree plots as the ultimate unit the authors (i, p. 264) report a correlation between plots of r = 0.533 ±0.085 when the plots are combined by fours. It has seemed desirable to test the homogeneity of the soil in each of the orchards studied by them. In determining the following coefficients the individual tree has in each case been the ultimate unit.1 Consider first the relationship between the yields of adjacent trees of two navel orange groves. 1 Yields are reported in pounds per tree of ungraded product 300 Journal of Agricultural Research VOI.XIX.NO. 7 Grouping the yield of the i ,000 trees at Arlington, shown in figure i of Batchelor and Reed, in a 2 by 2 fold manner we find r = o.5i7±o.oi6, r/£r=33.i. A navel orange grove of 495 trees at Antelope Heights, mapped as figure 2 by Batchelor and Reed, when combined in a 3 by 3 fold manner gives r = 0.375 ±0.026, r/Er= 14.4. Grouping the 240 Valencia orange trees of the grove shown in figure 3 of Batchelor and Reed in a 2 by 2 fold manner, we find for the correlation between yields r = 0.306 ±0.039, r/Er = 7-75- For the yield in pounds per tree of Eureka lemons as shown in figure 4 of the authors cited, we find for a 2 by 2 fold grouping r = 0.448 ±0.02 8, r/Er= 15.8. This last result is of particular interest, since Batchelor and Reed say of this plantation — This grove presents the most uniform appearance of any under consideration. The land is practically level, and the soil is apparently uniform in texture. The records show a grouping of several low-yielding trees; yet a field observation gives one the impression that the grove as a whole is remarkably uniform. Notwithstanding this apparent homogeneity there is a heterogeneity coefficient of over 0.4. Taking the yields of seedling walnuts in pounds per tree as given in figure 5 of Batchelor and Reed and grouping in a 2 by 2 fold manner, we find r = 0.232 ±0.038, r/Er = 6.og. Finally, if the yields in pounds per tree of the Jonathan apple trees mapped by Batchelor and Reed in their figure 6 be treated in a 2 by 2 fold grouping, the coefficient is r = 0.2 14 ±0.043, r/£r = 4-97- Without exception these groves show material values of the hetero geneity coefficients which are statistically significant in comparison with their probable errors throughout. PHYSICAL AND CHEMICAL BASIS OF THE HETEROGENEITY OF EXPERIMENTAL FIELDS In foregoing sections it has been shown that when tracts of land are judged by their capacity for crop production the yields are such as to indicate that heterogeneity is a practically universal characteristic of the July i, i92o Universality of Field Heterogeneity 301 fields which may be used for fertilizer tests, variety trials, or any other experimental purpose involving plot yields. In the vast majority of cases the heterogeneity is so great as to leave open to question conclu sions drawn from experiments not carried out with all biological precau tions and interpreted with due regard to probable errors. While the actual demonstration of differences in crop yields from one portion of the field to another is the result of final importance from the agronomic standpoint, and while it furnishes all but conclusive evidence that this heterogeneity in yield is due to irregularities in the soil itself, it seems desirable to show that such heterogeneity does actually obtain in the physical and chemical properties of the soil which are determining factors in plant growth. The desirability of determining the extent to which heterogeneity, in the sense to which the term is used here, obtains in the physical and chemical properties of the soil of experimental fields is emphasized by the following sentences from one of the pioneer papers (21) on the variability of soil samples. A number of papers have appeared dealing with the variation in the weight of the crop produced over different parts of an apparently uniform field. Such varia tions reflect the variability of the soil, serving simply as a substratum for the growth of plants, but it is evident that the variations between such measurements as those given do not depend upon the soil as the only variable factor. At the outset we must recognize that many factors may determine differences in yield. Even if one could secure a tract initially uniform in soil and exposure it is not always possible to be sure that it has all been in the same crop in preceding years. Previous cultures may influence tilth and soil composition by organic remains, by infection with disease-producing organisms, or by differences in the demand of various crops for certain of the plant foods.1 Such sources of hetero geneity are not readily detected by the eye or by physical or chemical analysis. Even if the experimenter secures a field of sensibly uniform texture, chemical composition, and previous cultural treatment, the uniformity may be readily destroyed in planting or tillage. Rain may interrupt the ploughing, thus exposing the soil of the different portions of the field to air and light for different lengths of time and affecting the physical condition very profoundly. Such sources of error are par ticularly great in the planting of large experiments. Thus the sources of field heterogeneity can never be fully determined in any case, although individual factors may be demonstrated. To determine whether an experimental field is heterogeneous with respect to physical or chemical factors, actual measurements of these factors should be made over the field and the heterogeneity coefficient applied. As a first illustration we take a series of soil-moisture 1 These are factors of particular importance in rotation experiments. 302 Journal of Agricultural Research Vol. XIX, No. 7 determinations uniformly distributed over a plot on a field at the San Antonio Experimental Farm of the Office of Western Irrigation Agriculture. Hastings (6) has given a condensed account of the soil conditions of the San Antonio region. A map of the experimental farm by Hastings (7, p. 2) shows the location of field C3 in which this plot of borings was located1 and gives meteorological conditions prevailing in 1915, the year in which the borings were made. Mr. C. S. Scofield kindly informs me that field €3 had been uniformly treated for some time previously and was in apparently uniform con dition. It is nearly level but with a gradual slope to the south and east. The soil has the superficial appearance of uniformity, but we know from experience that the subsoil, which is usually characterized by a high lime content, is in some I 2 3 4 5 6 7 8 9 10 II 12 13 14 IS 16 17 18 19 2O 21 22 23 24 25 26 27 28 29 30 3i 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 5° 5i 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 &o 81 82 83 84 85 86 87 88 89 90 9i 92 93 94 95 96 97 98 99 IOC FlG. 10. — Diagram showing location of sample areas examined for soil moisture in a field at the San Antonio Experimental Farm. places much closer to the surface than in others. However, from a general agronomic standpoint, this field would be regarded as extremely uniform, and observation of it during the growing season would tend to confirm this view. Borings were made 6 feet in depth and were sampled at every foot.2 Figure 10 shows the form of this field. In order to reduce the 100 sample areas to 2 by 2 fold combinations we have discarded the right file and a portion of one rank, retaining only those which can be grouped into fours as indicated by the cross lines. The percentages of moisture content of these 100 sample areas appear in Table III.3 1 The northern border of the sampled area is a line 60 feet south of the north line of the field and parallel to it. 2 The samples were all taken between March 31 and April 9. During this period there was no rain. Between March 15 and April 10 there were only two rains, one on March 17 of 0.2 inch, the other on March 29 of o.oi inch. Neither of these was sufficient to affect the soil moisture conditions, since in this region a precipitation of less than 0.25 inch scarcely penetrates the surface-soil mulch. Thus moisture changes during the course of the work can hardly influence the results. 3 The 13 sample areas which were omitted because of impossibility of combining by fours are starred (*). July i, 192° Universality of Field Heterogeneity 3<>3 TABLE III. — Moisture content of 100 sample areas of a field at the San Antonio Experi mental Farm [Expressed in percentages] Sample area No. First ', Second foot. foot. Third foot. Fourth foot. Fifth foot. Sixth foot. i 2O. 2 19. 1 I7-S I3-I 9-7 8.9 2 23-7 21. 6 19.8 16.8 15.0 15-9 3 20. 9 20.5 19.4 16. i 15.0 iS-i 4 21.5 20.3 I8.3 16. o 15-4 14.2 5 23-3 22. 4 20. 6 19-3 16. i 15.8 6 25.0 24. I 19.7 17.6 16.5 15-3 7 22.8 23. o 20.8 17.0 14.8 14.8 8 24. 6 24-3 20. 7 18.5 iS-8 14.8 9 25.6 25-3 25-3 25-5 23-7 18.7 10 22. 9 25-8 26. o 26. 2 23-5 18. 6 ii 28.0 30-4 30.6 29.8 26.8 21- 5 12 25.2 25.7 24.5 26.8 24. o 21. 2 13* 22. I 22. O 20. I 2O. I 16. o 14.9 14 2O. 2 19.7 17.0 14-5 11.4 9- i 15 22. I 21.3 18. i 14.6 13.8 12.7 16 2S.I 21. 2 20. o 16.3 I5-S 14- I 17 21.8 21. O 19. 2 16.6 iS-i 14-9 18 23-4 22. 4 2O. 0 16. i iS-7 IS-4 19 20-5 20.8 19. 6 15.6 13-5 12. 5 20 24. o 22. O 19-5 iS-i "•5 9-4 21 20. 4 20. 7 18.7 13.0 8.1 8.2 22 24-3 24. o 21. O 23-7 21.3 IS-2 23 21.3 22. 2 21.8 21.7 20.5 16. 7 24 24-3 25-7 24. o 22. 4 18.3 14.9 25 23. 6 | 23. 2 24.4 24-5 22. 2 18.4 304 Journal of Agricultural Research vol. xix. NO. TABLE III. — Moisture content of 100 sample areas of afield at the San Antonio Experi mental Farm — Continued | Expressed in percentages) Sample area No. First foot. Second loot. Third foot. Fourth foot. Fifth foot. Sixth foot. 26* 24. 2 23-7 23.0 20. 7 19.1 17.8 27 21. I 19.7 18.7 14-7 14-5 17.7 28 21. 2 19. 6 1 8. 4 I7.6 15-2 15-0 29 21. 2 20.5 19. 6 18.9 17-5 17.1 3° 22. 9 22. O 19.9 17-5 15-0 14.8 3i 21. 0 20.7 19. 6 16. 2 14. o 16. 4 32 23-4 21.6 19-3 18.6 16.8 15-9 33 22. 2 21.8 20. I 1 6. 6 14. o 14. I 34 23-9 22. 7 20. 4 17.0 14. 6 14.2 35 21. 6 20. 9 19.2 16.8 iS-3 16.3 36 21.4 21.6 20. 6 20. 0 18.4 16. 8 37 25-3 25.6 25.6 24.9 22. 2 17.9 38 26. 7 29. 2 27. o 25-9 23.0 19.1 39* 26. 2 29.8 30-4 28.6 26. I 21-5 40 21.8 2O. O 19-3 15-7 15-7 16.3 4i 19.9 19.4 19. o 15-3 14.8 14.9 42 21. 6 20. 0 1 8. 2 14- I 15-5 15.0 43 19. 6 21.7 19. o 14-7 14-2 13-9 44 21. 6 21.7 19.4 15-6 15-3 15-4 45 21. 6 20-5 19-3 16.3 7-5 14. 2 46 22. 6 21.3 12. 2 l6. 2 14.4 14-3 47 21. O 22. O 19-3 15-9 14-7 15.0 48 22. O 21-5 19.8 19.8 14-7 iS-2 49 22. 7 22. I 20. o 19-5 I 6. 2 16. 2 50 21. 9 23-3 21. O 19. I 16. 2 I6.S July i, 1920 Unvuersahty of Field Heterogeneity 305 TABLE III. — Moisture content of 100 sample areas of afield at the San Antonio Experi mental Farm — Continued [Expressed in percentages] Sample area No. First foot. Second foot. Third foot. Fourth foot. Fifth foot. Sixth foot. 51 20. o 20.3 19. o I7.6 15-7 17.2 p* 29. 6 28.4 27-3 22. O 13-2 16. 2 53 20. 6 19.8 18.5 IS-7 15-9 15- 6 54 21. 2 20. 7 18.8 I5-I 14-3 14-5 55 19-3 20. o 18.9 I6.3 14. I 14-9 56 21. 2 20.8 18.9 I6.3 14. I 14.9 57 22. I 21. O 19-5 15-7 I5-I iS-7 58 22. 7 21. 6 19.7 I8.3 14.7 15-8 59 21. 2 21. 0 19.7 17.4 15-2 1 6. 4 60 23.2 22.5 20. 7 I9.I I6.S 16.5 61 19.4 21.3 19.7 I7.8 16. 9 17.2 62 22. 6 21-3 18.6 18. 6 15.0 17. i 63 21-3 20. 6 19-3 17-5 17-3 17-9 64 21.7 20. i 18.9 15-8 iS-5 1 6. 6 65* 22.S 21. O 2O. 2 16.7 17.0 20.8 66 20. 6 21. 2 17.9 17.1 IS- 8 15.0 67 18.9 19. 2 18.2 15.0 14,4 15-0 68 23-4 14-5 19. o 17.7 15-5 IS- 5 69 21. 2 20. 4 18.8 17.0 14. o 13.9 70 21.4 2O. I 18.4 17.0 15-8 16. o 7i 21. O 21. I 18.9 15-6 14-5 15-3 72 22.8 21.4 20. O 16.5 i5-5 14.3 73 21. 9 21. 6 2O. 2 1 6. 2 14-4 17-9 74 22.8 21.8 20.3 18. o i5-5 17.9 75 21.3 22.8 22. I 21. 6 17.7 15-1 306 Journal of Agricultural Research Vol. XIX, No. 7 III. — Moisture content of loo sample areas of a field at the San Antonio Experi mental Farm — Continued [Expressed in percentages] Sample area No. First foot. Second foot. Third foot. Fourth foot. Fifth foot. Sixth foot. 76 21.5 22. O 19.7 17-3 17.2 16. 9 77 21.4 21. 0 19.7 15-8 15-6 18. o 78* 22. 4 21. O 19. 2 17.0 16. 2 15-6 79 l8-S 18. 8 l8.4 17.0 IS-* IS- i 80 20-3 19. 6 18.5 15.2 IS-0 IS- 8 81 20-3 2O. 2 18. 8 I6.5 14. 6 IS- 5 82 2I-S 21.7 18. 6 15-8 14. 8 14-1 83 20. o 20. 4 18.7 IS-7 16.3 IS- 4 84 20.3 20. o 18.9 17-5 14-7 14.7 85 22. 4 21.8 21.4 17. I IS- 9 14.8 86 23. 2 22. O 19. 6 16. o iS-7 15.0 KT* °l 21.8 21. 6 20.8 19. i 17.2 16.5 88* 23- 7 21.8 2O. 2 16. 4 16. 9 16. 4 89* 28.0 21. 6 2O. 2 18.3 17.0 18.5 90* 23. 2 21.7 19. I 16.3 16.3 16. 6 91* 22-3 22. 9 21.7 19-3 18.5 18. 6 92 20. 2 19.7 18. 2 17.4 14.7 15.0 93 19. o 19-3 I8.S 16. i iS-4 15-9 94 22. O 20. 4 l8.3 16. o 14.9 14. o 95 2I-5 19.7 1 8. 8 14.9 14.9 i4-S 96 20.8 20.3 18.7 16.3 14.4 i5-4 97 20. I ^9-5 19. i 17.9 15.0 16.3 98 22. 6 20.3 19. 4 i5-3 15.0 i5-3 99 20. 4 20.3 1 8. 6 16. 4 14. 6 i4-5 100* 22.6 21.6 19.4 i7-5 16.3 15.0 To determine whether the distribution of soil moisture in these plots is such that it might bring about a correlation between the yields of adjacent plots due to heterogeneity in regard to this physical factor in July i, 1920 Universality of Field Heterogeneity 307 the field we have merely to determine the correlations between the percentages of water content of associated plots. These are Depth. Correlation. rlEr. First foot O. 3I7±O. 065 A. O Second foot . ^2oi • O^2 IO. 2 Third foot . Cd.2± . OSI IO. 7 Fourth foot . 7O4± . Ol6 IO. 4 Fifth foot . 607 ± . 045 I?. 4 Sixth foot . 484 ± . o« 8.8 The correlations are of a very substantial order, ranging from 0.317 to 0.704. Notwithstanding the fact that there are only 88 stations upon which the probable errors are based, the constants may in every case be considered significant in comparison with their probable errors. Thus, notwithstanding the fact that we are dealing with a field only 150 by less than 264 feet,1 there is a marked and statistically significant heterogeneity in respect to so important a factor in plant growth as soil moisture at each level in the upper 6 feet of soil. This result seems of very real importance in its relation to the practical phases of plot-test work. It shows beyond all dispute that at least under soil conditions such as are found at the San Antonio Experi mental Farm, substratum heterogeneity may be very great at levels of the soil which are ordinarily left entirely out of account in the selec tion of fields which are to be used for plot tests but which are not below the extensions of the roots of the deeper-penetrating crops and not too deep to serve as reserves of soil moisture for the higher layers of the soil in the case of crops which draw their water from more superficial levels. It is of some interest to determine whether the correlations at one level in the field may be looked upon as sensibly higher than those at other levels. We have, therefore, determined the differences between the correlations at the different depths. These are given with their probable errors, and in relation to their probable errors, in Table IV. In the table the positive signs indicate higher correlations at lower levels. Of the 10 possible comparisons between the correlations of the first 5 feet, all but one show greater heterogeneity at the lower levels. The sixth foot seems to be somewhat more homogeneous than the second to the fifth foot. A number of the differences are apparently significant in comparison with their probable errors. Thus there is apparently a real difference in the amount of heterogeneity of this field at different levels. Heterogeneity is least at the surface and greatest at a depth of 4 feet. The significance of this result will perhaps be apparent at once. A field might be reasonably uniform for the surface foot of soil and hence 1 The total length is 264 feet, but this is reduced by discarding the right file. 308 Journal of Agricultural Research Vol. XIX. No. 7 fairly well suited to the testing of shallow-rooted crops. Below this it might show a higher degree of heterogeneity. Possibly this heterogeneity of lower-lying strata is the explanation of the large correlations obtained for the yields of neighboring trees in groves planted on apparently uniform soil. TABLE IV. — Differences and criteria of trustworthiness of differences in the correlation of adjacent plots in soil moisture determinations at various levels Depth. Second foot. Third foot. Fourth foot. Fifth foot. Sixth foot. r. r/Er. r. r/Er. r. r/Er. r. r/Er. T. r/Er. First foot +O. 212 ± .083 2.56 +0. 226 ± .082 + -013 ± -«73 2.74 .18 +0-387 ± .074 + -I7S ± .063 + .161 ± .062 S- 22 2.76 2.S8 +0. 291 ± .079 + .078 ± .069 + .065 ± .068 - .096 ± .058 3-63 I. 14 .96 1.66 +0. 167 ± .OSS — .045 ± .076 — .059 ± -074 — .aao ± .066 - .124 ± .071 1.97 .60 •79 3-34 1.74 Second foot Third foot Fourth foot Fifth foot We can pursue this question of the relationship between the water content of the plots somewhat further. If the factors which determine the similarity in the moisture contents of the combination plots affect more than a single layer, we should expect a correlation between the contents of the first and second foot, and so on, in the same boring. The possible correlations have been worked out for the first foot and the remaining layers and are as follows : Depth. Correlation r/Er. First and second feet 4-Q 7^8 -1- o First and third feet 4- . 660 4- °3-* J3- 59 16 &< First and fourth feet 4- 648 4- First and fifth feet. . . -1- t*rg _L J5- 53 First and sixth feet - fi~ • 353 3t • 063 5- °2 There is a statistically significant and even high correlation between the water content of succcessive levels in the same boring. When we turn to the problem of chemical heterogeneity, we find that while a number of soil chemists have noted the desirability of consider ing the variability of the soil in taking samples, the available data suit able for testing the degree of heterogeneity of experimental fields are not extensive. July 1. 1920 Universality of Field Heterogeneity 309 Kaserer's series of determinations (9) is not sufficiently large or prop erly distributed over the field to make desirable an attempt to measure heterogeneity. Fortunately Waynick and Sharp (22) have given four excellent series, two for nitrogen and two for carbon, derived from two California fields. Their samples were taken over a total area of a little more than i .3 acres on two fields of very different character — a silty clay loam at Davis and a blow sand at Oakley. The fields were both selected for their apparent uniformity, both being nearly level with no change in the soil mass from one part of the field to another great enough to be detected by the usual field methods. Both fields were practically free from vegetation when selected, and' before the samplings were made in March, 1918, all extraneous material had been carefully removed. Altogether they took 80 samples distributed at 30-foot intervals over the entire area. These samples were arranged in an 8 by 10 fold manner. The original data are given in their Tables 3 and 4. Arranging these in the order of the map of the borings given in their figure i and combining in a 2 by 2 fold manner, we derive the following heterogeneity coefficients : For the silty clay loam at Davis — For carbon, r = 0.417 ± 0.063, r/Er — 6.67. For nitrogen, r = .498 ± .057, r/Er = 8.75. For the blow sand at Oakley — For carbon, r = 0.317 ± 0.068, r/Er = 4.65. For nitrogen, r — .230 ± .072, r/Er = 3.20. All these values are statistically significant in comparison with their probable errors. Although the total number of samples is rather small, they indicate in each case a distinct heterogeneity for these important constituents of the soil. Apparently the two fields differ in their hetero geneity, the coefficients for both carbon and nitrogen being distinctly lower on the blow sand at Oakley than on the silty clay loam at Davis- The average carbon content at Oakley is only 0.444 as compared with 1.109 at Davis, while the nitrogen at Oakley is 0.033 as compared with o.ioi at Davis. Probably greater heterogeneity would be expected on general physical considerations on the silt loam than on the blow sand. The analysis may profitably be carried one step farther. If these fields are heterogeneous in respect to the soil constituents here under consideration, one might anticipate a correlation between the carbon and the nitrogen content of the samples distributed over these fields.. The results are For the Davis loam, rnc = 0.785 ±0.029, For the Oakley blow sand, rnc= .744 ± .034, r/£r = 310 Journal of Agricultural Research voi XDC.NO. 7 Both constants are large. They show that the field is not merely hetero geneous but that portions which are high in nitrogen are high also in carbon and vice versa. Waynick (21) has given a series of 81 determinations of nitrification in samples of soil drawn from a field on the University of California farm at Davis. The field had been planted to corn in 1914, to Sudan grass in 1915, and to grain sorghum in 1916. In 1917 it had lain fallow and was without vegetation when the samples were taken October 20. The particular area chosen was apparently as uniform as one could well find, being level, of uniform texture and color, and free from small local depression of any kind. These samples were taken on eight radii of a circle 100 feet in diameter. The samples were separated by a radial distance of 5 feet. Disregarding the one central sample, we may group the remainder by twos in order to determine whether there is a correlation between adjacent samples. The coefficients thus obtained will, of course, not be comparable with those deduced for cases in which the yields or soil samples were uniformly dis tributed over the field. They will, however, serve to indicate whether or not this field is heterogeneous in the sense that differences prevailed sufficiently large to influence the properties of adjacent samples in a manner to make them more similar than pairs of samples taken at random over the field. His samples were drawn in two series — the first from the superficial 6 inches, the second from the deeper-lying level, 6 to 24 inches. Waynick's Table i gives the residual nitrate in soil as sampled. From it we deduce For the upper 6 inches, r = 0.404 ± 0.063, */Er= 6.4. For the subsoil, r= .sg6± .049, r/Er= 12.2. Table 2 gives the nitrate produced from the soil's own nitrogen after 28 days' incubation. We deduce For the upper 6 inches, r = 0.065 ±0.075, r/Er = o.86. For the subsoil, r= .O59± .075, r/Er= .79. Table 3 shows the nitrate produced from 0.2 gm. of ammonium sul phate in 100 gm. of soil. The correlation coefficients are For the upper 6 inches, r = 0.298 ±0.069, r/£r = 4-34- For the subsoil, r= -35i± .066, r/Er = 5.31. Finally, Table 4 shows the nitrate produced from 0.2 gm. of blood in 100 gm. of soil. The results in this case are For the upper 6 inches, r = 0.120 ±0.074, r/£r= 1.62. For the subsoil, r= .297± .069, r/Er = 4.32. July 1. 1920 Universality of Field Heterogeneity 311 The coefficients show that for both the upper and lower soil layers there is a correlation of about medium value between adjacent samples for the residual nitrate in the soil. These coefficients are unquestion ably significant in comparison with their probable errors. While the coefficients for nitrogen produced from soil nitrogen after incubation are both positive in sign, neither can be considered statis tically trustworthy in comparison with its probable error. When nitrogen is added to the soil, in the form of either ammonium sulphate or of blood, the correlations between the nitrogen produced on incubation are larger. All are positive in sign, and three of the four may be reason ably considered statistically significant. Thus it is clear that this plot, only 100 feet in diameter, shows distinct heterogeneity in residual nitrate and in the amount of nitrification occurring on incubation after the addition of nitrogen. SUMMARY AND CONCLUSIONS The purpose of this paper, which is one of a series on the statistical phases of the problem of plot tests, is to show the extent to which the heterogeneity of experimental fields may influence plot yields. By heterogeneity we understand differences in capacity for crop production throughout the field of such a magnitude as to influence in like manner, but not necessarily to like degree, the yield of adjacent small plots. Thus, variability of plot yields does not necessarily indicate the heterogeneity of the fields upon which tests are made but may be due to other factors. Heterogeneity is measured by a coefficient which shows the degree of correlations between the yields of associated ultimate plots, grouped in combination plots. This coefficient has been determined for a relatively large series of experimental fields widely distributed throughout the world and planted to a considerable variety of crops, for which a number of different kinds of yields have been measured. The results show that in every field the irregularities of the substratum have been sufficient to influence, and often profoundly, the experimental results. It might be objected that by chance, or otherwise, the illustrations are not typical of what ordinarily occurs in plot cultures. But the series considered practically exhaust the available data for such pur poses. Furthermore the records are in large part drawn from the writings of those who are recognized authorities in agricultural experi mentation and who have given their assurance of the suitability of the fields upon which the tests were made. For example, Mercer and Hall (15) state the purpose of their research to be — to estimate the variations in the yield of various sized plots of ordinary field crops which had been subjected to no special treatment and appealed to the eye sensibly uniform. 312 Journal of Agricultural Research vol. XIX.NO. 7 Their mangolds — looked a uniform and fairly heavy crop for the season and soil, while in their wheat field — a very uniform area was selected. The data of Larsen were drawn from an experiment — auf einer dem Auge sehr gleichmassig erscheinenden, 3 Jahre alten Timotheegraswiese. Montgomery's data were secured from a plot of land only 77 by 88 feet in size, which had been sown continuously to Turkey wheat for three years — and was of about average uniformity and fertility. Coombs and Grantham selected a field on which — the crop was extremely regular as judged before the cutting and it had not been subjected to any attack of borer or any devastation of rats or birds. Lyon's potato field was selected from — a piece of apparently uniform land. Mr. C. S. Scofield kindly informs us that the Huntley tract was selected for apparent uniformity and that prior to the calculation of the constants presented in this paper there was no reason, from general observation, to suspect irregularities in the field. Batchelor and Reed have assured me that their orchards are to all appearances uncommonly uniform. Kiesselbach emphasizes the apparent uniformity of his oat field. Nothing could more emphasize the need of a scientific criterion for substratum homogeneity than the fact that correlations between the yields of adjacent plots ranging from r= +0.020 to r= +0.830 can be deduced from the data of fields which have passed the trained eyes of agricultural experimenters as satisfactorily uniform. A second phase of this investigation has been to ascertain whether the physical or chemical requisites for plant growth are so distributed over experimental fields that they may be reasonably looked upon as the source of the demonstrated heterogeneity in yield. The heterogeneity coefficients for percentage of water content for the upper 6 feet on the Experimental Farm of the Office of Western Irrigation Agriculture at San Antonio, Tex., range from +0.32 to +0.70 and are statistically significant for each of the 6 upper feet of soil. Hetero geneity is least at the surface and greatest at a depth of 4 feet. The surface layer of soil might, therefore, be apparently uniform in water content while underlying layers might differ greatly from one part of the field to another. This may be the explanation of the correlation between the yields of adjacent trees in groves planted in an apparently uniform locality. Analysis of the data of Waynick and Sharp shows that there is a correlation of from +0.23 to +0.50 between adjacent borings for so important soil constituents as nitrogen and carbon. The correlation July i, 192° Universality of Field Heterogeneity 313 between nitrogen content and carbon content of samples from two differ ent soils is of the order -f 0.75. It is interesting to note that these coefficients for water content and for chemical composition of the soil are of about the same order as those found for crop yields. While these results do not prove that the hetero geneity of experimental fields in their capacity for crop production is directly due to these and other physical and chemical factors, there can be little doubt that this is actually the case. The references here made to the existence of significant heterogeneity in fields passed by agricultural experts as satisfactorily uniform must not be interpreted as a criticism of the work of these investigators. There is, indeed, every evidence of care and thoroughness. The result merely illustrates the inadequacy of personal judgment concerning the uniformity in physical characters or in crop-producing capacity of fields under consideration for experimental work. The demonstration that the fields upon which plot tests have been carried out in the past are practically without exception so heteregeneous as to influence profoundly the yields of the plots emphasizes the necessity for greater care in agronomic technic and more extensive use of the statistical method in the analysis of the data of plot trials if they are to be of value in the solution of agricultural problems. To other phases of the problem we shall return in subsequent papers. LITERATURE CITED (1) BATCHELOR, L. D., and REED, H. S. 1918. RELATIONSHIP OP THE VARIABILITY OF YIELDS OP FRUIT TREES TO THE ACCURACY OP FIELD TRIALS. In Jour. Agr. Research, v. 12, no. 5, p. 245-283, ii fig. Literature cited, p. 282-283. (2) COOMBS, G. E., and GRANTHAM, J. 1916. FIELD EXPERIMENTS AND THE INTERPRETATION OP THEIR RESULTS. In Agr. Bui. Fed. Malay States, v. 4, no. 7, p. 206-216, i fig. (3) HARRIS, J. Arthur. 1913. ON THE CALCULATION OP INTRA-CLASS AND INTER-CLASS COEFFICIENTS OP CORRELATION FROM CLASS MOMENTS WHEN THE NUMBER OP POSSIBLE COMBINATIONS IS LARGE. In Biometrika, v. 9, pt. 3/4, p. 446-472. (4) 1914. ON SPURIOUS VALUES OF INTRA-CLASS CORRELATION COEFFICIENTS ARIS ING FROM DISORDERLY DIFFERENTIATION WITHIN THE CLASSES. In Biometrika, v. 10, pt. 2/3, p. 412-416. (5) 1915. ON A CRITERION OF SUBSTRATUM HOMOGENEITY (OR HETEROGENEITY) IN FIELD EXPERIMENTS. In Amer. Nat., v. 49, no. 583, p. 430-454. (6) HASTINGS, S. H. 1916. THE WORK OP THE SAN ANTONIO EXPERIMENT FARM IN 1915. U. S. Dept. Agr. Bur. Plant Indus. West. Irrig. Agr. 10 (Misc. Pub.), 17 p., i fig. (7) and BLAIR, R. E. 1915. HORTICULTURAL EXPERIMENTS AT THE SAN ANTONIO FIELD STATION, SOUTHERN TEXAS. U. S. Dept. Agr. Bui. 162, 26 p., 8 fig. 314 Journal of Agricultural Research VOI.XIX.NO. 7 (8) HOLTSMARK, G., and LARSEN, B. R. 1906. UBER DIE FEHLER, WELCHE BEI FELDVERSUCHEN DURCH DIE UNGLEI- CHARTiGKEiT DES BODENS BEoiNGT wERDEN. In Landw. Vers. Stat., Bd. 65, Heft 1/2, p. 1-22. (9) KASERER, Hermann. 1910. BEITRAG ZUR FRAGE DER FESTELLUNG DES NAHRSTOFFGEHALTES EINER ACKERPARZELLE. In Ztschr. Landw. Versuchsw. Oesterr., Jahrg. 13, Heft 8, p. 742-747. i fig- (10) KIESSELBACH, T. A. 1918. STUDIES CONCERNING THE ELIMINATION OF EXPERIMENTAL ERROR IN COMPARATIVE CROP TESTS. Ncbr. Agr. Exp. Sta. Research Bui. 13, 95 p., 20 fig. („) 1919. EXPERIMENTAL ERROR IN FIELD TRIALS. In Jour. Amer. Soc. Agron., v. ii, no. 6, p. 235-241. (12) LEHMANN, A. 1901-1909. SECOND TO NINTH ANNUAL REPORTS OF THE AGRICULTURAL CHEMIST. Department of agriculture, Mysore State [India]. 1900/01-1907/08. (13) LOVE, H. H. 1919. THE EXPERIMENTAL ERROR IN FIELD TRIALS. In Jour. Amer. Soc. Agron., v. 11, no. 5, p. 212-216. (14) LYON, T. L. 1912. SOME EXPERIMENTS TO ESTIMATE ERROR IN FIELD PLAT TESTS. In Proc. Amer. Soc. Agron., v. 3, p. 89-114, 5 fig. (15) MERCER, W. B., and HALL, A. D. 1911. THE EXPERIMENTAL ERROR OF FIELD TRIALS. In Jour. Agr. Sci., v. 4, pt. 2, p. 107-132, 10 fig. (16) MONTGOMERY, E. G. 1912. VARIATION IN YIELD AND METHOD OF ARRANGING PLOTS TO SECURE COM PARATIVE RESULTS. In Nebr. Agr. Sta. 25th Ann. Rpt., [i9ii]/i2, p. 164-180, 4 fig. d7) 1913. EXPERIMENTS IN WHEAT BREEDING: EXPERIMENTAL ERROR IN THE NURSERY AND VARIATION IN NITROGEN AND YIELD. U. S. Dept. Agr. Bur. Plant Indus. Bui. 269, 61 p., 22 fig., 4 pi. (18) SMITH, Louie H. 1910. PLOT ARRANGEMENT FOR VARIETY EXPERIMENTS WITH CORN. In PtOC. Amer. Soc. Agron., v. i, 1907/09, p. 84-89. (19) STEWART, F. C. 1919. MISSING HILLS IN POTATO FIELDS: THEIR EFFECT UPON THE YIELD. N. Y. Agr. Exp. Sta. Bui. 459, p. 45-69, 3 fig. (20) STOCKBERGER, W. W. 1916. RELATIVE PRECISION OF FORMULAE FOR CALCULATING NORMAL PLOT YIELDS. In Jour. Amer. Soc. Agron., v. 8, no. 3, p. 167-175. (21) WAYNICK, D. D. 1918. VARIABILITY IN SOILS AND ITS SIGNIFICANCE TO PAST AND FUTURE SOIL INVESTIGATIONS. I. A STATISTICAL STUDY OF NITRIFICATION IN SOILS. Univ. Cal. Pub. Agr. Sci., v. 3, no. 9, p. 243-270, 2 fig. (22) - — and SHARP, L. T. 1919. VARIABILITY IN SOILS AND ITS SIGNIFICANCE TO PAST AND FUTURE SOIL INVESTIGATIONS. II. VARIATIONS IN NITROGEN AND CARBON IN FIELD SOILS AND THEIR RELATION TO THE ACCURACY OF FIELD TRIALS. Univ. Cal. Pub. Agr. Sci., v. 4, no. 5, p. 121-139, i fig. G-212 BY J. ARTHUR HARRIS AND C. S. SCOFIELD Reprinted from JOURNAL OF AGRICULTURAL RESEARCH Vol. XX, No. 5 : : : : Washington, D. C., December 1, 1920 PUBLISHED BY AUTHORITY OF THE SECRETARY OF AGRICULTURE, WITH THE COOPERATION OF THE ASSOCIATION OF LAND-GRANT COLLEGES WASHINGTON : GOVERNMENT PRINTING OFFICE : 1920 PERMANENCE OF DIFFERENCES IN THE PLOTS OF AN EXPERIMENTAL FIELD By J. ARTHUR HARRIS, Investigator, Station for Experimental Evolution, Cold Spring Harbor, N. Y., and Collaborator, Office of Western Irrigation Agriculture, and C. S. SCOFIELD, Agriculturist in Charge, Office of Western Irrigation Agriculture, Bureau of Plant Industry, United States Department of Agriculture I.— INTRODUCTION Agronomists have long recognized the fact that the plots of an experi mental field may differ considerably among themselves. This varia bility is the source of the greatest difficulty in the interpretation of comparative cultures. A recent analysis (j)1 of the available data by adequate biometric formulae (/) has shown that heterogeneity is a practically universal characteristic of experimental fields and that it must be considered in the interpretation of the results of all plot tests. With the demonstration of this characteristic of experimental areas the questions naturally arise : Are the differences between plots tran sient or are they relatively permanent from year to year? Do these differences tend to increase or to decrease with cultivation ? Presumably the differences which obtain in the soil of an experi mental field are in part permanent and in part transient. Lyon (5) suggested that tillage and other factors will change the plots so that the results will not be comparable from year to year. Unfortunately he does not present data to show to what extent this may be true. He gives a series of yields for successive years on the same plots, which measured 33 by 66 feet or J/2o °f an acre m area, at the Nebraska Agri cultural Experiment Station and shows that the rank of the yield of these plots differs greatly from year to year. Thus he concludes that if they differ among themselves in their capacity for crop production this difference is very little constant from year to year. Smith (6) tcok advantage of the breaking up of a piece of land which had lain 16 years in pasture to investigate the effect of cultivation on the uniformity of a series of plots. Any influence of i or 2 years pre ceding cultures on the variation or correlation of yields should, he assumed, be apparent in the statistical constants deduced from these 1 Reference is made by number (italic) to " Literature cited," p. 356. Journal of Agricultural Research. Vol. XX, No. 5 Washington, D. C. Dec. i. 1920 ^ Key JTo. G-zit (335) 336 Journal of Agricultural Research VOI.XX.NO. s data. He gives a table which indicates that there is such a change. He says: It is noticeable that the variability as measured by the standard deviation becomes less in each succeeding year. This suggests the question as to whether continued cropping might not tend to induce uniformity. The records of a few of these plots which were continued in corn for three years longer do not support such a conclusion. It must be noted that in Smith's experiments seasonal conditions varied greatly from year to year. Thus 1895, which was exceedingly dry and also cool in the early part of the season, was highly unfavor able. The two following years were unusually favorable for corn. As a result the yields were, respectively, 31.6, 91.6, and 71.4 bushels per acre in the three years. Lehmann in his work at the experimental farm near Bangalore at tempted to use the experience of previous years in the standardization of experimental plots. His data will be considered in some detail below. II.— METHODS AND RESULTS The permanency of the differentiation of plots in their capacity for crop production may be measured in terms of correlation. If the plots of a field differ among themselves in a more or less permanent way there will, with reasonably uniform climatic conditions, be a correla tion between the yields of the plots of a series in two or more successive years — in short, an intera nnual correlation (2). The problem of the correlations between the yields of identical plots in different years is one of very great interest. If this correlation be high it should be possible to standardize a field of plots by one or more sowings to the same variety. A chief difficulty in the standardization of the field by the carrying out of a preliminary test in which the pro ductive capacities of the plots are determined once and for all lies in the fact that the factors which determine yield are in part edaphic — that is, pertaining to soil conditions — and in part meteorological. For example, in a very dry year sections of a field which are lower may pro duce the heaviest crops because adequate moisture is longer retained in these places. In a wet year the case may be just the reverse, for the crops in the lower-lying portions may be too wet for the best plant growth. Thus, it is quite possible that in cases in which there is a profound influence of environmental factors there may be a negative correlation between the yield of the same plots in different years. It is conceivable, therefore, that the interannual correlation for yield per plot may range from negative to positive values, zero correlation being found in cases in which edaphic and meteorological factors exactly counterbalance each other in their influence upon the yield of the plots of a heterogeneous field. Dec. i, 19,0 Permanence of Differences in Experimental Plots 337 A. — PUBLISHED DATA Unfortunately few data are available for analysis from the literature. Lehmann has given (4, p. 6) yields of paddy on the 17 plots of ranges B and C, respectively, of the wet tract of the Experimental Farm at Hebbel. Grouping the yields for the two ranges, we find for the corre lations between the yields of the same plots in the two years 1905 and 1906: Range B, r = 0.834 ±0.050, irIEr= 16.7. Range C, r = 0.799 ±0.059, r/Er= 13.5. Stockberger (7) gives data for the extremes of a series of hill yields for hops. The interannual correlations deduced from these data have been shown (2) to be as follows: Years. Lowest hills. Highest hills. - o. 29 ±o. 17 o. =;Q±O. 13 igio and IQII • 5S± • J3 . 52± . 14 IQOQ and. 101 1 . 43 ± .15 . 30± .18 Stockberger has also given (8) the yields for 30 rows, each 210 feet in length, from hop fields of several hundreds of acres in the Sacramento Valley of California : The plants in these rows averaged well in number and uniformity of growth with the plants on several hundreds of acres of hops in the midst of which the experimental area was located . Data are available for the years 1909 to 1914. Calculating the corre lation between the yields in the different years, we have the results set forth in Table I. It appears that with one single exception the con stants are positive throughout. In general they are significant in com parison with their probable errors, indicating a superiority in a subsequent year if a superiority is shown in a given year. The constants in the table are arranged in a way to show the change in the coefficient of correlation as the years become more widely separated in time. Thus, in the case of the correlation for the 1909 yields, the constant for "first and second" is that showing the relationship between the 1909 and 1910 yields, while "first and third" indicates the constant measuring the relationship between the yields of 1909 and 1911. Simi larly, in the series of coefficients for 1910 "first and second" designates the correlation between 1910 and 1911, etc. For the series beginning with 1909 we note a marked decrease in the magnitude of the constants as the yields correlated become more widely separated in time. The same is true for the series beginning with 1910. The other series are more irregular. 338 Journal of Agricultural Research Vol. XX. No. 5 TABLE I. — Interannual correlations for yield of hops Beginning of series. First and second years. First and third years. First and fourth years. First and fifth years. First and sixth years. 1909 +o. 768±o. 051 + O.622±O-O7S +o-38o±o. 105 + O- 2<;9±o- 115 + -45i± .098 + -3I3± -III — . I26± .121 The most reasonable explanation of the higher correlation of more closely associated years is that both field conditions and the productive ness of the individual vines change more or less as time goes on. The result of such changes would be a lower correlation between the yields of periods more widely separated in time. The data for the dry-land experiments in Mysore State have been discussed elsewhere (3) in relation to the problem of field hetero geneity. It was shown there that in two dry years the field showed marked hetereogeneity, but that in one unusually wet season there was marked abnormality of yield with little correlation between the yields of adjacent plots. It seems of unusual interest, therefore, to determine to what extent the differences between these plots are permanent from year to year. Correlating between the yields of ragi, we find the following correlation coefficients for the whole series of 105 plots for which data are available. Years. Grain. Straw. Total. 1905 and 1906 O. ?OI -f-O OA3 o 777 io 026 1905 and 1907 . 603 -+- OIA 855± 018 852 ± 018 1906 and 1907 . d.ZO-\- OC2 678 ± 036 The correlations are of very substantial order, and without exception they are clearly significant in comparison with their probable errors. They show that the differences in the plots are to a high degree per sistent during the three years of this experiment. For grain, straw, and total yield the correlations between the yield for 1905 and 1907 are higher than those for 1905 and 1906 or for 1906 and 1907. If there were a progressive change in the field one might have expected that the correlations would be higher between consecutive years. Apparently the influence of the abnormal conditions of 1906 has been to lower the correlations for this year. The results show that the capacity for production is to a high degree persistent from year to year, notwithstanding great diversity in meteorological conditions. A series of records of unusual interest is provided by Smith (6) for yields of com in three successive years, 1895, 1896, .1897. It has been Dec. i, 1920 Permanence of Differences in Experimental Plots 339 shown elsewhere (j) that this field, which had lain in grass for many years, is highly heterogeneous, showing correlations between adjacent plots of r = o.6i to r = o.83- The conditions for corn production differed very greatly in the three years. Thus the constants for yield were : Year. Mean. Standard deviation. Coefficient of varia tion. T 8oC 31. 7 7.91 25.0 1896 91. 6 10. 64 •ii. 6 1807 71. 4 6. 27 8.8 Yield is over twice as heavy in the second and third years as in the first. The variability in yield as measured by the coefficient of variation is far lower in the second and third years than in the first. Computing the correlations between the yields for the three years, we have the following results: For 1895 and 1896, r= -0.354 ±0.054, r/Er=6.6. For 1895 and 1897, r= —0.221 ±0.059, r/Er=3.8. For 1896 and 1897, r= +o.8i8±o.o2o, r/£r=4o.i. There is a negative correlation for 1895 and 1896 and for 1895 and 1897 but a high positive correlation for 1896 and 1897. Thus the plots which were better in the highly unfavorable year 1895 were poorer in the two favorable years 1896 and 1897. Plots which were better in the favorable year 1896 were also better in the favorable year 1897. B. — THE HUNTLEY UNIFORM CROPPING EXPERIMENT The most extensive series of records available is that for a uniform cropping experiment conducted for the past several years at the Field Station of the Office of Western Irrigation Agriculture, at Huntley, Mont. The Himtley field lies in the Yellowstone Valley on land having a very slight and uniform slope to the north. The detailed history of the field prior to 1910 is not known definitely. It was probably first broken from the native prairie sod in the spring of 1908. In 1909 it was planted to sugar beets, but the crop was destroyed in the late summer. It came under experimental control in 1910, when the major portion of it was sown to oats and yielded a crop of 66 bushels per acre. In that season a small tract in the northeast corner of the field was used as a machinery park or stack yard and was not put into crop. This tract occupied about two-thirds of the length of the first five plots in series II. It is possible that this difference of treatment in 1910 may have been reflected in the crop yields of 1911, but it seems hardly probable that any material effects could have persisted longer. 34° Journal of Agricultural Research vol. XX.NO. 5 In the spring of 1911 this field was laid out into 46 plots, each measur ing 23>£ by 317 feet and containing 0.17 acre, arranged in two parallel series of 23 plots each. The two series of plots were separated merely by a temporary irrigation ditch. In 1911 it was planted to sugar beets, and in the spring of 1912 it was seeded to alfalfa, and one cutting was harvested that year. This stand remained on the ground during 1913 and 1914, when the entire field was fall-plowed. In 1913 three cuttings were made, but the third cutting was lost in a heavy wind which scat tered and mixed the crop before weighings from the various plots could be made. The first cutting, designated as alfalfa I, was made on plots one-half the original size. The second cutting was harvested from plots one-quarter the original size. The first and second cuttings in 1914 were weighed for plots one-quarter the original size — that is, 0.0425- acre plots — while the third cutting was recorded for plots one-third the original size. These furnish the data for alfalfa I, II, and III for 1914. Total yields for the first and second cuttings in 1913 and 1914 and for the first, second, and third cuttings in 1914 are also considered. In 1915 and 1916 ear corn was grown. In 1917 * the fields were planted to oats, and records were made of grain, straw, and total yield. In 1918 silage corn was grown. In 1919 the land produced a crop of barley. It has been the practice each season to treat the whole field as a unit until harvest time, when the plot boundaries are established in order to measure the crop yields. In other words, all cultural operations, includ ing irrigation, are carried out on a field scale and uniformly throughout the field. No manuring has so far been attempted. An effort has been made to avoid any artificial causes of heterogeneity. The crop yields each year have been satisfactory — that is, they have not been abnormal — as is shown in Table II, where the mean yields per plot and per acre are set down. Fortunately, this experiment has also escaped injury from insect pests, plant diseases, and storms, which so often interfere with the success of long-term field experimentation. 1 Because of other activities the plots could not be harvested in halves and quarters in 1917-1919. Dec. i, 1920 Permanence of Differences in Experimental Plots 341 TABLE II. — Mean yields of the Huntley uniform cropping experiment Crop. Number of pounds per plot. Number of tons or bushels per acre. 1911, sugar beets 4, I7Q. OO 12. 29 1912, total alfalfa «6. CJ4 ' I. 04 1913, alfalfa I 541. 41 i. <;o 1913, alfalfa II . . . 483. 26 I. 42 1913 alfalfa I and II I, 024. 67 3. 01 1914, alfalfa I 48q. 13 T /j/| 1914, alfalfa II 4QQ. 34 i. 47 1914, alfalfa I and II 088. 47 2. QI 1914, alfalfa III . ... . 471. oc 1.38 1914, alfalfa I to III i, 460. 43 4. 29 1915, ear corn S22. <;8 52. 7 1916, ear corn 306. i1; 41. 6 1917, oat grain s1^- 80 IO2. I 1917 oat straw 521. u i. =13 1917, total yield i, 077. 34 3. 16 1918, silage corn 3, 17=;. 4"? Q- ^4 1919, barley grain 3^8. IQ 47.8 1919, barley straw 270. 5 /ific 1,52° 20 60 =; 1.500 21 c«0 1.5 o 22 16. 81 m, i 060 420 4 5 460 6 ,6c 7 ' 8 880 9 8.85 *6o sr> IO ii /iRe 1,115 12 13 14 >iRc 15 jgr 16 A6o 1,305 17 280 Afa 18 280 395 425 43° 19 480 395 425 38S 20 5i5 965 475 1,440 21 915 44S 915 465 23 475 515 990 495 1,485 475 475 95° 475 1,425 >er in pounds per plot with the exception of that for sugar beets, which is given in tons Dec. i, 1920 Permanence of Differences in Experimental Plots 343 TABLE III.— Yield of plots of field B at the Huntley (Mont.) Field Station «-— Con. Plot No. 1915. ear corn. 1916, ear corn. 1917, oat grain. 1917, oat straw. 1917, total yield. 1918, silage corn. 1919, barley grain. 1910, barley straw. 1919, total yield. II, i 556 580 574 1, 154 3,655 392 288 680 598 593 631 1,224 3,285 349 251 600 526 481 606 588 i, 194 3, 290 377 253 630 558 598 414 I,OI2 3,390 218 570 487 614 590 I, 2O4 3,570 414 660 6 596 584 1,180 3,240 264 690 7 489 458 1,030 3,005 262 725 8 574 524 1,098 3,010 276 700 9 1.048 3,060 425 265 690 10 513 614 606 i, 220 2,885 298 II 574 578 i, 152 2,955 386 610 12 548 510 1,058 3,055 365 605 13 528 537 i, 060 3, 125 350 14 507 1,062 368 15 511 398 518 616 i, 134 16 564 57° i, 134 2,870 389 481 980 18 408 538 518 1,056 241 19 455 637 605 20 489 383 21 567 i, 080 3, 180 316 22 206 23 578 288 Ill, I 563 3,685 2*8 2 1,082 •6* 218 cgc 3 260 6tK 4 318 18* 5 338 516 6 536 i, 088 7 538 1,082 2,8« 8 556 i, 108 260 660 9 260 660 10 i 066 ?K6 660 ii 2,7 o 665 12 ciSo 13 2 880 706 14 15 «8 160 16 r?ft 3. Tftr 17 483 1 88 18 <6? r&| cSn 19 e62 IK? 20 cfil 48l 400 21 486 cSo 22 628 7^9 218 23 c6i 0 All yields are given in pounds per plot with the exception of that for sugar beets, which is given in tons per acre. 344 Journal of Agricultural Research vol. xx, NO. = From the series of correlations as a whole it appears that of the 152 coefficients showing the relationship between crop yields in different years, 133 are positive while only 19 are negative in sign. If the differ ences in capacity for crop production demonstrated in different years were due to purely transient causes, one would expect to find an approxi mately equal number of positive and negative correlations with the gen eral average value sensibly zero. Instead we find the proportion of 133 to 19. This is a deviation from the ratio 76 to 76, which one might ex pect on the assumption that there is no correlation between the yields of plots in a series of years, of 5X0.5 = 57 + 4.16. The deviation from equality is 13.7 times as large as its probable error and is unquestionably significant. If we consider that coefficients, which are 2.5 times or more as large as their probable errors represent statistically significant interrelationships. we find that of the 82 relationships which may be regarded as falling in this class 78 are positive whereas only 4 are negative in sign. Averaging the values of the coefficients considered in Table IV, we note that the average for the 133 positive values is + 0.3346, whereas that for the 19 negative values is — 0.1475. Taking the constants altogether, the average value 15 + 0.2743. There is, therefore, an overwhelming body of evidence to show that plots, even of the small size and the apparent uniformity of those of the Huntley Station, which yield higher in one year will yield higher persistently throughout a series of years. It is now desirable to determine whether the same relationships hold when these plots are divided into smaller subplots. It is possible to subdivide a number of the plots into 2 subplots, each one-half the original size. Correlations may be determined for the 92 yields of these half plots in the same manner as for the total yields on the 46 original plots. The results appear in Table V. The constants are positive throughout. In general, they are statis tically significant in comparison with their probable errors. As a matter of fact, only 2 of the 22 constants are less than twice as large as their probable errors. Thus, they indicate a real biological relationship between the productions of the half plots in different years. Those which give a higher yield in one year give a higher yield in another year. For a smaller number of the crops it is possible to divide the original plots into quarter plots, thus securing 184 subplots to be used as a basis of calculation. The coefficients of correlation between the yields in the several years are shown in Table VI. • 9 1917, oat straw. 1917, total oats. 1918, 1919, silage orn. barley grain. 1919. barley straw. 1919, total barley. — 0.116+0.098 i —0.098+0.098 — i. 18 — i. oo +o. 348+0. 087 +4-00 —o. 539+0. 070 -7.66 —o. 262 + 0. 092 -2.82 — 0.449 + 0. 079 -5-66 - 5 +. i65±.097 +.229+. 094 + 1.71 +2.44 —.071 + .099 — o. 72 + 7-33 +.341 + - 087 +3-89 +. 483 + . 076 +6-34 • 7 + igo±. 096 + 1.98 +.317 + - 089 +3-56 ' + i. 56097 + . 78 — •03 +.043 + . 099 + •43 o + 2. 19 +.372 + . 086 +4-33 +.451 ±-079 + 5-7I +. 203 + .095 + 2. 13 +.025 + . 099 +.26 + . 131 + - 097 + 1-34 ;78 + 2.48 +4-87 +.350+. 087 +4. 02 + . 163 + . 096 + 1.68 + . OI2 + . 099 + • 13 +. zoi + .ogS + 1.03 So + . 28l±. O92 +3-05 +.429+. 081 +4.29 +. 209 + . 095 + 2. 2O +. 255 + . 092 + 2 75 + . I39 + -097 + 1-43 + . 22I + -094 +2-33 '74 +.80 +3-42 + 2. 52 +2- 90 + 1-47 + 2.44 73 +. I88+..096 +.39S±.o84 + 1. 96 +4. 70 + .242 + .094 +.283 + .09I + 2-57 +3-io + . I53 + - 097 + 1-57 +.244+. 093 + 2.61 :8o +.311 + . 098 +3-46 + 5. 60 + . 579 + . 066 + 8-77 +.086 + .098 +.87 + .066 + . 099 + .68 + .084+- 098 +.86 71 +.239+. 093 +.441 + . 080 + 2. 55 +5- 50 +.361 + .086 +4. 18 + 246+. 093 + 2.64 +. I39 + -097 + i 42 + 2. 27 99 +. Ii2±.og8 +.072±.099 + i. 14 +.73 +.459+. 078 + 5-88 +.42 + 1.91 +. Ii9±.og8 + 1.22 :;73 +. 220+.O95 +.407+. 083 + 2.32 +4.90 +•439 + -080 + 5-49 + .227 + . 094 + 2. 41 + 1.97 + 2. 72 — . 166+. 096 — i. 72 —.063 + . 099 -.64 -1.32 + 1.06 + .034+. 099 + •35 + .372 + . 085 +4-34 +• 294+. 090 +3- 24 — . 166 + . 096 — i. 72 + 1.48 —.020+ 099 — 20 +. 225+094 + 2 38 + i 6309 — 063 ± . 099 - 64 + i 39 + .009 + . 099 + .10 + .333 + - 088 +3-76 + 2. 71 — . I29 + - 097 — 1-32 + 2. 72 + . 294+ . 090 + 3- 24 + 1.63 +.253 ±.093 + 2.7I 994 399 =99 + 1.97 +4-34 '+2.38°94 +-333±-o88 +3-76 Dec. i, 1920 Permanence of Differences in Experimental Plots 345 o° o o o" 51 o o 1916, car corn -St4lc: 41^° 4IT4I'? 4)74)^ 'OOO OO ^t1 00 "O ^"(^5 OsfO O*O O\- OOH) MM sO« Tfr* fjw wro N*o ^+ ^+ 7+ 7+ 7+ »+ ?+ + + + + + + + "i o o o o o o o O O fO Oi « w N 4l°?4IT4l°4lT4l' • • o o 1914, alfalfa 11 ^r_i_ o i t^ t iD"r o 4" 10 ~r d • • M : : S+ J3- O r^ \fi '• • *^ w o" o1 o1 -'50 1914. alfalfa I 41^,417416 I4IT4I d M 10 00 Oi t- » 1913. alfalfa I and o i o i *o . t*t *o * r^ r « i r^ d § 2 J ^§ o2 _^H ?| 4l7+^4lc; 40" M H2'2V2V2'212 ^ 0 o J I 6 0 ° 0 ? 0 ° 0 .i ° 41 4 41 « 41 M 41 o 41? 9 ", + 3 + 1 N O\ + K. + S+ ^O 6 S + + + + + i 00 i 0 $ f „ * | 's o 41 °. 4i •° 4H ^ 41 ^ it ? •f" N ~h S O 6 + •— » + — ' • — i + -• «-v + •S | 1 o o S ^H o +1 " « ° 4i . 4i d O H c g 4§ 1 + M+ S.+ 1 OM-H 6 + + + >§•> »-» — ' S to Oi S HJ J •<)• 0 -22 "3 a 1 6 41 R » \** \l S a ^ -h . *O ~H * -H f-H > • ,4 m < H t >_ C i a j 1 0 0 7 J 0 0 ? •I ^ S S S > ! ' •< 10 10 c c c H \ c 346 Journal of Agricultural Research Vol. XX, No. s Unfortunately the number of crops which can be included in Table VI is rather small. The coefficients are positive in sign throughout, and in all cases they are statistically significant in comparison with their probable errors. The individual constants will receive attention in the following discussion. The fact that the yields are correlated in the different years for whole plots of 0.17 acre, for half plots of 0.085 acre, and for quarter plots of only 0.0425 acre emphasizes the permanence of the substratum differences. We now have to compare the correlations secured for these three divisions. The difference in the actual magitudes of the correlations appear in Table VII. The three entries, when all comparisons are possible, show: (1) the difference between the correlation for whole plots and half plots, (2) the difference between the correlation for whole plots and quarter plots, and (3) the difference between the correlation for half plots and quarter plots. The signs are positive when the correlations are larger for the larger areas. The comparisons show that in general the correlations decrease in magnitude as the areas upon which they are based are subdivided. Thus 1 6 of the 22 comparisons of the correlations deduced from whole plots and from half plots (first entry) show a lower correlation in the half plots as compared with 6 which show higher correlations in the half plots. TABLE VII. — Differences in interannual correlations for whole plots, half plots, and ' quarter plots 1913. alfalfa I. 1913. alfalfa II. IQI3. alfalfa I and II. 1914. alfalfa I. 1914, alfalfa II. 1914. alfalfa I and II. 1915. ear corn. 1916, ear corn. f... — o. 0863 1913, alfalfa I 1 f... 1913, alfalfa II {.... \ . 228O f... 1913, alfalfa I and II. . 1 {—0.0863 — o 1622 — o. 1442 + .0388 1914, alfalfa I — 2276 — • 1578 — 0653 — . 1018 [—0.0514 — 1335 — . 1044 1914, alfalfa II ~ 3615 I — 2280 {—0.0558 — 1462 — • 1152 1914, alfalfa I and II. — 2794 -+- . 0385 — n88 ...:::::: 1915. ear corn {+0.0910 — 0267 + -0403 + 0388 + 0705 + 0676 + O649 — .0492 ::::::::: 1916, ear corn 1+0.0387 — IO2I — 2081 - -0330 — 0560 - 1378 — 1018 — 0493 — 1599 — 0377 — n88 — .0492 + .0487 5 0004 Dec. i, 1920 Permanence of Differences in Experimental Plots 347 Of the 12 comparisons possible between the interannual correlations deduced from whole plots and from quarter plots (second entry), 9 show lower correlations for quarter plots as compared with 3 which show higher correlations for the quarter plots. Finally, all 12 of the correla tions deduced from quarter plots are lower than the correlations deduced from half plots. It appears, therefore, that 0.085 and 0.0425 acre are rather too small to give the highest values of the interannual correlations. On areas of this size other factors than the peculiarities of the plots themselves have too large an influence upon variation of yield to allow the indi viduality of the plots to express itself fully in its influence upon the yields of successive years. In support of the conclusion that the lower value of the correlations for half and quarter plots is due to the greater variability of the yields of these plots we note that the coefficients of variation for subplots are without exception larger than those for the plots of the original size. The coefficients of variation are as follows for the years in which the plots were subdivided. Crop. Whole plots. Half plots. Quarter plots. 1913, alfalfa I 12. C2 IA O3 1913, alfalfa II 13. 60 16 so 21 87 1913, alfalfa I and II II. II 13 3A 1914, alfalfa I 17. OA. 2O O4 23 68 1914, alfalfa II 19 81 21 77 OC 87 1914, alfalfa I and II 17 A7 1 8 oo 21 88 1915, ear corn 7 2O 8 A3 1916, ear corn 13 At is 88 17 68 It is now desirable to examine the results for the individual crops. In doing this it may be noted that there are two factors to be taken into account. First, there is the possibility of an inherent difference in the plots which is persistent from year to year and is quite independent of the crop grown. Second, it is conceivable that the crop itself may exert an influence upon the soil such that the yields of subsequent crops will be influenced by variations in its growth which are measured in terms of yield. The first of these factors would influence all correlations between plots — those between the yields of given years and the yields of both preceding and subsequent seasons. The second would influence only correlations with subsequent years. In a series of only 46 plots it will probably be impossible to distinguish between the influences of these two factors. We note that the higher yields of beets are followed by lower yields of alfalfa in 1912, but that there is practically no relationship between the yields of sugar beets in 1911 and the yield of other crops on the same Journal of Agricultural Research Vol. XX, No. 5 plots from 1913 to 1918. Possible exceptions are ear corn in 1915 and silage corn in 1918, for which the correlations are positive and perhaps statistically significant in comparison with their probable errors. The correlations for yields of sugar beets in 1911 and yields of barley in 1919 are negative in sign and apparently statistically significant in compari son with their probable errors. We have no explanation to offer con cerning this apparent relationship. The average value, with regard to sign, of the correlations between the yield of sugar beets and other crops is — 0.077. The correlations between the 9 different cuttings of alfalfa made during 1912 to 1914 and all other yields are generally positive and statistically significant in comparison with their probable errors. The only excep tions are the negative correlation with sugar beets in 1911 which have already been noted and the slight and statistically insignificant correla tion for the 1912 yield of alfalfa and the yield of silage corn in 1918. Since it is quite reasonable to assume that in a crop harvested more than once a year thickness of stand and variation in the size of the indi vidual plants will have a large influence on the yields of the different plots in the same year, the correlations between the different cuttings of the same year as well as those between single cuttings and totals of two or more cuttings in the same year have been omitted from the tables. The correlations between different cuttings in the same year are given in Table VIII. TABLE VIII. — Comparison of correlations bet-ween different cuttings of alfalfa in the same year Cuttings of alfalfa. Whole plots. Half plots. Quarter plots. 1913. first and second cuttings. . +o. 454 ±o. 079 +o. 442 ±o. 057 1914, first and second cuttings. . 1914, first and third cuttings. . . . + . 71 1 ± .049 + • 595 ± . 064 -1- .633± .042 +0.558 ±0.034 1914 (first plus second) and third cuttings 4- . 6 Permanence of Differences in Experimental Plots 349 TABLE IX. — Comparison of correlations between different yields of alfalfa with correla tions between yields of alfalfa and yields of other crops Cuttings of alfalfa. With other cuttings ot alfalfa. With yields of other crops. Difference. 1012 single cutting +O. 33 1 +O. 171 +o. 160 1013 first cutting + .611 + • 187 -j- . 424 1913, second cutting + • 604 + .282 + • 322 1913, first and second cuttings + • 72O + • 274 + . 446 1914, first cutting + .666 + • 20? + • 371 1914, second cutting + . 620 ~h • 244 + -385 1914 first and second cuttings + . 600 4- . 2QO + . 409 1914 third cutting . + . S24 + . 3O3 -f- . 221 1914 first, second, and third cuttings + . 706 + -316 T • 39O It is clear, therefore, that either stand or specific adaptation of the individual plots to alfalfa influences to an unusual degree the closeness of correlation between the yields of the plots of alfalfa in the different years. In the first crop of ear corn (1915) we find higher yields of ear corn in 1916, a negligible difference in the yield of oat grain and straw and total yield in 1917, higher yield of silage corn in 1918, and slightly but not significantly higher yield of barley grain, straw, and total yield in 1919 following higher yield of corn in 1915. Turning to the constants for ear corn in 1916, we note that higher yields of grain in this year are followed by higher yields of oat straw and grain in 1917 and of silage corn in 1918, and by slightly higher yields of barley grain and straw in 1919. -The average value of the correlation between the yield of ear corn in 1915 and the yield of other crops during the eight years is +0.167, whereas that for ear corn in 1916 and other crops is +0.486. These averages include the correlations .for alfalfa, which are, as shown by > Table VIII, high for the crop of 1916. Considering the correlations for oat straw, grain, and total crop on the several plots in 1917 and the yields of silage corn in 1918, we find that higher values of each of these measures of capacity for oat produc tion are on the average followed by slightly, but perhaps not signifi cantly, higher yields of silage corn in 1918 and generally by higher barley yields in 1919. For the oat yields the average correlations with other crops are : for straw, +0.202; for grain, +0.289; and for total yield, +0.293. The correlations of the yields of silage corn with the yields of the preceding crops are, with one exception, positive in sign. The average value for the eight years is +0.226. The averages of the correlations between barley yields and the yields of other crops on the same plots during the eight years of the experiment are +0.141 for grain, +0.086 for straw, and +0.126 for total yield. 35° Journal of Agricultural Research VOI.XX.NO. s Summarizing this discussion of the results for the individual crops, we have the following average values of the correlation coefficients : 1911, sugar beets —0.077 1912, total alfalfa + • 242 1913, alfalfa I + • 346 1913, alfalfa II + • 4°3 1913, alfalfa I and II + . 441 1914, alfalfa I + . 401 1914, alfalfa II + . 354 1914, alfalfa I and II -f • 4°7 1914, alfalfa III + . 366 1914, alfalfa I to III + .428 1915, ear corn -}-o. 167 1916, ear corn + . 486 1917, oat straw -|- . 202 1917, oat grain -f . 289 1917, total oats + . 293 1918, silage corn -f- . 226 1919, barley grain -f- . 141 1919, barley straw + . 086 1619, total barley -)- .126 General average + . 274 With the exception of the sugar beets the average correlation for every crop is positive in sign, and in many cases it is of a very material value. Returning to the averages for the individual crops, we note from Table IX that the lowest correlation for alfalfa, whether with other cuttings of alfalfa or with the yield of other crops, is that for the single cutting of 1912. It might be suggested that the 1912 yields of alfalfa are less likely to reflect the real producing capacity of the plots than the yields of the later cuttings of this crop, for the reason that the first cutting of alfalfa when sown without a nurse crop is subject to much variation because of slight differences in surface condition of the soil at seeding time and also because of differences in weediness of different plots. Both these conditions would become relatively less important in their effect on crop yield after the first cutting. Because of its nitrogen-fixing capacity and the resistance to decay of the roots and stubble of alfalfa the correlation between the various yields of this legume and the yields of subsequent crops is of especial interest. Fortunately two crops of ear corn were grown immediately after the alfalfa, which was broken up in the fall of 1914. A comparison of the correlations of these two series of corn yields with the preceding yields of alfalfa is made in Table X. These coefficients indicate a positive correlation between all the yields of alfalfa and the yields of ear corn in both 1915 and 1916^ Of the 19 correlations determined between the yields of alfalfa for 1912 to 1914 and the yields of ear corn in 1915 only 9 may be looked upon as probably significant in comparison with their probable errors. Of the 19 correlations between the yields of alfalfa in 1912 to 1914 and the yields of ear corn in 1916 only one coefficient — that for the 1912 yield of alfalfa and the 1916 yield of corn — can not be considered as represent ing a real agronomic relationship between yield of alfalfa and yield of corn. The constants for 1916 are without exception larger and with two exceptions significantly larger in comparison with their probable errors than those for 1915. Dec. i, 1920 Permanence of Differences in Experimental Plots 351 jj ft m *n ui 6 ooo ^S 4| *> 41° -Ho o» o SS OOs^M f a R «+ S 4! N 4| N m^. -^-toOvNooto »+ {:+ 2+ H + d ' ' S Difference. •S o to •* o dr- °0v °r- °0v °« °vc -S "?" -H* Hi* 41? 41" 41* Mt^« O''^ O1^ ^O^O l-^CO mOO \O_I_ CO_L ^J_ M-U w-4- 9«i> v>~r t^>~r »oT~ In T o T^ o T^ 600666 * f>. ? ? o o1 o o ^ 0, Ov -Hoo -H * -Ho 41 A -H w> 41^ fM COM 00 / r- M O o. Q 0 •f + + + + + + 4- + 1 r* 5 »/> .N ,O ,^O . N 'CO • O . 00 «j o § M1 r c5 i |l L" ll |l II |? | I 1 c H i c - ^— ! r |j S? 1| !; ?5 ! u i ^ 4 4 i \ 0 « z t-H H- 1 T3 -d „ g § M a a » a » ^ a rt rt cfi stages of development of the compound leaves in the tetracotyle donous plants, it did not seem feasible in the majority of determina tions to consider separately the weight of tissue formed by the* compound leaves. This, however, has been done indirectly in the case of certain samples based on the plants as a whole. Data The data fall in three groups: a series of weighings of primordial leaves of plants unclassified with respect to number of primordial leaves; a series of weighings of primordial leaves of plants classified HARRIS— PHASEOLUS 155 with respect to number of primordial leaves; and a series of weigh ings of total epicotyledonary tissue. TABLE I MEAN GREEN WEIGHT PER PLANT AND PER LEAF IN SEEDLINGS OF A TETRACOTYLE- DONOUS RACE AND IN NORMAL PLANTS OF THE ANCESTRAL RACE VALUES p ER PLANT VALUES PER LEAF SAMPLE Abnormal Control Difference Percentage difference Abnormal Control Difference Percentage difference ^Unclassified 226 0.6991 0.7516 — 0.0525 - 6.9 o. 1718 0-37S8 — o. 2040 — S4-2 227 0.6972 O. 7607 — 0.0635 - 8.3 0. 1680 0.3804 — o. 2124 - r- C — 55 -° 228 .... 0.6323 0.7568 — o. 1245 — 16.4 o. 1542 0.3784 — o. 2242 — 59-2 220 O. 7012 0.6862 +0.0150 + 2.1 o. 1793 0.3431 -0.1638 —47-7 , y 2 leaves 2<8 0.4520 o. 7263 — o. 2743 — 37-7 o. 2260 0.3632 — 0.1372 —37.7 M)(f O. 5958 o. 7994 — o. 2036 — 25.4 o. 2979 0.3997 — o. 1018 — 25.4 3 leaves 2*q. . 0.6313 o. 7760 —0.1447 -18.6 0.2104 0.3880 —0.1776 —45-7 273 0.5662 o. 7189 +o. 1527 — 21 . 2 0.1887 0.3595 — o. 1708 — 47 -S 283 0.5791 o. 7766 — o. 1975 — 25.4 o. 1930 0.3883 — o. 1953 —50.2 303 0.6577 0.8015 — o. 1438 — 17.9 o. 2192 o . 4008 -0.1816 —45.3 7IQ 0.6200 o. 7817 — o. 1617 — 20. 6 o. 2067 0.3909 — o. 1842 —47.1 ,-> y 4 leaves 2^3. . 0.6703 0.7786 — o. 1083 — 13-9 o. 1676 0.3893 — o. 2217 — 56.9 264 0.5994 0.6671 — 0.0677 — 10. i o. 1499 0.3336 —0.1837 — 55.0 286... . o. 7066 0.8103 — o. 1037 — 12.7 o. 1767 O . 405 2 — o. 2285 -S6.3 206 0.6556 0.8142 —0.1586 — IQ.4 o. 1639 0.4071 — o. 2432 —59.7 208 0.7368 0.9028 — o. 1660 -18.3 o. 1842 0.4514 — o. 2672 — 59.1 214 o. 7201 o. 7783 — 0.0582 — 7.4 o. 1800 0.3892 — o. 2092 — 53.7 320 o. 7375 o. 7529 —0.0154 — 2.O 0 IS/]/} 0.3765 —0.1921 — 51.0 5 leaves 254 o . 63 7 1 o . 7639 — 0.0998 — I?. < o. 1274 0.3685 — o. 2411 — 65.4 268... . o . 6409 0.6987 — 0.0578 — 8.2 o. 1282 o . 3494 — O. 2212 —63.3 287... o. 7334 0.7867 — o.o=;33 — 6.7 o. 1467 O. 3034 — o. 2467 —62.7 300. o . 803 2 0.8366 — 0.0334 — 30 o. 1606 0.4183 — o. 2577 -61.6 321 . o 712=; o. 7087 — o 0862 — IO 7 O. I42fscular) as well as in their external characters, (b) the demonstration jtlit the number of bundles at a given level in the seedling is a highly vari- kje rather than a constant character, and (c) that the various organs or rdions of the plant body (particularly, in the present case, those which: jaj separated by the vascular anastomoses at the cotyledonary node); dfer widely in the magnitude of their variability as to bundle number. I In this paper we propose to consider in quantitative terms the degree ofnterrelationship between the vascular structures in the different regions ojnormal and abnormal seedlings. The results of such an investigation ?wl evidently be of considerable morphological interest, since many of tfe problems of organic form are fundamentally problems of correlation. | Two morphological problems at once present themselves for considera- pK First, is there a high correlation between the vascular topography of to different levels of the same internode, i.e., is the number of vascular bridles constant throughout the length of an internode or is there more ojless extensive splitting or anastomosis within the length of such a con- vutional morphological unit? .Second, is there a definite correlation between the vascular topography blow a node and the vascular topography above it, or is the vascular sxtem so fully reorganized at the nodal anastomosis of bundles that, in bpdle number, successive internodes are practically independent of one anther? With the present material, these questions may be answered by de- temining the coefficients of correlation for bundle number between (i) * base and the mid-region of the hypocotyl, and (2) between the various teels of the hypocotyl and the mid-region of the epicotyl. It is these Harris, J. Arthur, Sinnott, E. W., Pennypacker, John Y., and Durham, G. B. « vascular anatomy of dimerous and trimerous seedlings of Phaseolus vulgaris Amer Jcr. Bot. 8: 63-102. 1921. 339 340 AMERICAN JOURNAL OF BOTANY problems which we propose first to consider. We shall also compare thf normal and abnormal seedlings as to the correlations which they exhibit and shall touch briefly on the problem of the correlation between bundle number in seedlings from the same parent plant. The frequency distributions of bundle number are in many cases ol very narrow range and very skew. There has, therefore, been consider able question as to the formulae to be employed. It has seemed best for various reasons which need not be detailed here, to employ the usua method of product-moment correlation. PRESENTATION AND ANALYSIS OF DATA The series of data considered here are in large part the same as thos< •discussed in our earlier paper, but have in some cases been supplements by the examination of additional sections. These have been included wher the dimerous and trimerous seedlings were not true siblings. In lines $ 93, and 98, the series compared were obtained from the same mothers. It so far as the data are the same as those used earlier, the variation constant for the different characters have already been presented and discussed an( require no further comment here. The data from which measures of in terrelationship may be computed are given in our fundamental tables A toL We have, therefore, merely to deduce and discuss the correlation coefficients Correlation between Bundle Number at Different Levels in the Same Internode We first turn to the problem of the relationship between the number o bundles — primary double bundles, intercalary bundles, and total bundles- at the base of the hypocotyl and the number in the central region of th hypocotyl. The reader who cares to do so may reconstruct the 24 correla tion tables necessary for a consideration of these relationships from ou fundamental tables A-L. TABLE i. Coefficients of correlation between number of primary double bundles, number > intercalary bundles, and total bundles at base of hypocotyl, and number of bundles in central region of hypocotyl Character of Seed lings and Line N Correlation for Primary Double Bundles rph Correlation for Intercalary Bundles n* Correlation for Total Bundles i'i,h Trimerous Line 75 I42 155 183 I O6 221 I42 155 183 305 420 + .378 ±.049 +.233±.05i +.321 ±.045 +.4i7±.054 +.556±.03i +.362^.049 +.641 ±.032 +.666 ±.028 +.344 ±-034 +.530±.023 7-79 4-55 7.17 7.71 17.8 7-35 2I.O 24.0 IO.I 22-5 +.329±.05i + .204±.052 +.253 ±.047 +.097 ±.065 +.305 ±.041 +.668 ±.03 1 +.390 ±.046 +-555±-035 + .898±.oo8 + .634±.020 6.51 3-92 542 1.50 7.40 21.3 8.50 16.1 119.7 32-2 + .649 ±.033 + .469 ±.042 +.586±.033 +.531 ±.047 + .753 ±.020 +.797±.o2i +.753±-023 + .786±.oi9 + .925±.oo6 + .802 ±. 01 1 19 ii i/ ii 38 38 32 4i 1 68 68 Line 93 Line 98 Line 139 Line 143 Dimerous Line 75 Line 93 Line 98 Line 139 Line 143 July, 1921] THE SEEDLING OF PHASEOLUS VULGARIS 341 rf c»> •^ rn CNJ 03 t-~ -t- -f- - ^ 5 2 >.i3 * £ O C •a si hi u O Q EC j 7A±ODOdi(H A// S37O~A//?& JO UJffW/lA/ A/V31S B ^ 2 "o C •«: 342 AMERICAN JOURNAL OF BOTANY [Vol. 8, /4 4 I; : 0 ; . /43 H=-0002 + 2-139 P £= 12-224 + 0-033 7> 4 $ • 139 SB £=/0 -941 + 0-301 P 7S £ = H=4-/30+/-3S2 P £ =/2 -928-0 -I7Q P //= 3-175+1-507 P = // -915+ 0-090 P JJOUBLE BUMZLES DIAGRAM 2. Regression of number of bundles in central region of hypocotyl and in central region of epicotyl on number of primary double bundles at base of hypocotyl in di merous seedlings. Empirical means represented by solid dots for hypocotyl and by circles for epicotyl. The correlation coefficients between the two classes of bundles which have been recognized at the base of the hypocotyl and the total number of basal bundles (i.e., the sum of the number of primary double bundles and the number of intercalary bundles in the base of the hypocotyl) and the number in the central region of the hypocotyl, appear in table i. July, 1921] THE SEEDLING OF PHASEOLUS VULGARIS 343 The correlations are without exception positive in sign and of a material Drder of magnitude. They have been expressed in terms of regression on iiagram I for trimerous seedlings and on diagram 2 for dimerous seedlings ;>f the five lines.2 Primary Double Bundles and Mid-region of Hypocotyl The constants showing the relationship between number of primary double bundles and number of bundles in the central region of the hypo- :otyl, rph, are shown in the first section of table I. They are positive and 'statistically significant in all cases in both dimerous and trimerous seedlings. The average value of the coefficient for the five lines investigated is +.3810 ifor trimerous seedlings and +.5086 for dimerous seedlings. Diagram 2 shows that in the case of the normal plants of lines 75, 93, and 143 a straight line represents very well indeed the changes in the mean number of bundles in the hypocotyl with variations in the number of pri mary double bundles at the base of the hypocotyl. In line 98 the agree ment is apparently not so good. This is, however, attributable to the fact that of the 183 plants only two have more than 5 primary bundles. Of these two, one plant is recorded as having 8, which is twice*the normal number. In line 139 only plants with two classes of seedlings, those with 4 or 5 primary bundles, are available, and since the regression line must connect the two means it is idle to discuss linearity of regression. Turning to the trimerous plants represented in diagram I , we note that because of the small number of plants with other than 5 or 6 primary double bundles the distribution of the empirical means is very irregular indeed. There is some suggestion of non-linearity, but the number of seedlings in the more extreme classes is so small for every line that little stress is to be laid upon them. In both normal and abnormal plants the slope of the regression line is rather steep, showing a material change in the number of bundles in the central region of the hypocotyl with variations in the number of primary double bundles at the base of the hypocotyl. Intercalary Bundles and Mid-region of Hypocotyl The correlation between the number of intercalary bundles and the total number of bundles in the hypocotyl, r^ are shown in the second 2 The equations on the diagrams show the regression of the number of bundles in the central region of the hypocotyl, H, and in the central region of the epicotyl, E, on the number of primary double bundles, P, at the base of the hypocotyl. The empirical means for the hypocotyl are represented by solid dots, while those of the epicotyl are represented by circles. In both cases the empirical mean number of bundles for the same organ are connected by solid lines when the number of sections averaged was five or more, but by broken lines when the number available was four or less. Fortunately for purposes of graphical representation, the mean number of bundles in both hypocotyl and epicotyl can be drawn on the same diagram. Only the lower lines in each of the five panels of the two diagrams require consideration for the moment. 344 AMERICAN JOURNAL OF BOTANY 7A±00/d3 F/VV JAJLOOOdAH A// SJ7ff/Vf)3 JO July, 1921] THE SEEDLING OF PHASEOLUS VULGARIS 345 o o "2 "rt § ~ e o ^ C O tn So 3 I., 13 S x £ ^ ^ §.S • ° — ^ c ^ <^> •" o ^ $ o ^ ^ I f "o R -M O rt R S « s o -a 346 AMERICAN JOURNAL OF BOTANY [Vol. 8, section of table I. The straight-line equations showing the regression of the number of bundles in the central region of the hypocotyl are recorded and represented graphically on diagram 3 for trimerous seedlings and on diagram 4 for dimerous seedlings. These diagrams, like the two preceding, also give the regression equations and their graphic representation for the epicotyl which will be discussed in a subsequent section. The correlation coefficients are positive in all cases, and with one ex ception may be considered statistically significant. They show, however, a considerable irregularity from line to line, presumably because of the varying range and distribution of number of intercalary bundles. The average value of the coefficient is +.2376 for trimerous seedlings and + .6290 for dimerous seedlings. Turning to the graphs, we may note that for the dimerous plants the agreements between the empirical and the theoretical means are very good indeed. The slope of the lines for the hypocotyl is very steep. The graphs for the trimerous plants show far greater irregularities be cause of the generally small number of the strands but the occasional oc currence of plants with a larger number. Reference to the tables will show that in line 75 there is one seedling with 6 intercalary bundles whereas the remaining 141 seedlings have only o, I, or 2 intercalary bundles. In line 93 there is only one seedling with more than 2 intercalary bundles and it has 4. In line 98 all the frequencies with two exceptions fall on o or I intercalary bundle. The correlations and equations have been recalculated, leaving these extreme cases out of account. The regression straight lines based on all the material are represented by solid lines. Those in which the extreme class were omitted are represented by broken lines.3 The removal of these aberrant cases has increased the agreement between the observed and the theoretical means but the fit is still far from satisfactory. The only con clusion which can be drawn from these diagrams is that there is a con siderable degree of positive correlation between the number of the inter calary bundles and the number of bundles in the hypocotyl. Total Basal Bundles and Mid-region of Hypocotyl The correlations between total bundles (primary double bundles -f in tercalary bundles) at the base of the hypocotyl and the number of bundles in the central region of the hypocotyl, rbh, are showrn in the third section of table i. The straight-line regression equations are given and represented graphically as the lower figures in each panel of diagram 5 for trimerous seedlings and diagram 6 for dimerous seedlings. As might be expected on a priori grounds, these coefficients agree with those for primary double bundles and for intercalary bundles in sign, and 3 For the curtailed series the regression equations are: Line 75, H = 12.194 + °- Line 93, H = 12.238 + 0.462 7; Line 98, H = 12.030 + 0.473 /. July, 1921] THE SEEDLING OF PHASEOLUS VULGARIS 347 w 19 IB II 16 IS 14 13 12 II 1C /43 H= 2-688 + /-S7S B E = 12-790 -/-0-S42 B SB! LINE /39 //= 4-790. + /-200 B E = 11-634- 0-400 B I5\ 13 12 II - (6 — -•12 L/A/E 93 H= 5-743 + /-078B E = 18-901 -0-523 B //= 6-331 + 0-949 B E = 12-807+0-342 £ a TOTAL BUA/3LES DIAGRAM 5. Regression of number of bundles in central region of hypocotyl and in central region of epicotyl on total number of bundles at base of hypocotyl in trimerous seedlings. Empirical means represented by solid dots for hypocotyl and by circles for epicotyl. AMERICAN JOURNAL OF BOTANY [Vol. 8, - c pq ft) - Nl July, 1921] THE SEEDLIXG OF PHASEOLUS VULGARIS 349 .are in general somewhat higher than those for either of these two classes. The average value of the 5 coefficients for trimerous seedlings is +.5976 while that for dimerous seedlings is +.8126. Turning to the diagrams, we note that the straight lines and the empirical means are in excellent agreement, considering the small number of seedlings, in the case of the normal plants, but show greater irregularities in the case of the abnormal plants. This is due to a considerable extent to the greater concentration of the frequencies into two classes in the case of the trimerous seedlings. We may now consider the relative magnitudes of the three correlations which we have been studying. Table 2 shows the differences existing be- TABLE 2. Comparison of correlations between the various types of bundles at the base of hypocotyl and the number of bundles in the central region of hypocotyl Character of Seedlings and Line Trimerous Line 75 +.271 ± Line 93 \ +.236db Line 98 +.26s± Line 139 i +.ii4± Line 143 j +.197 ± Dimerous Line 75 j +435± Line 93 i +.H2± Line 98 j -j-.i2O± Line 139 . 'Line 143. .581 ± •059 .066 .056 .071 •037 053 040 033 035 026 4-59 3-58 4-73 1.61 5-32 8.20 2.80 3-64 16.6 10.5 +.320±.o6i +.265 ±.067 +-333±-°57 +.434±-°8o + .448 ±.046 + .363 ±-051 +.231 ±.040 + .027±.OIO + .I68±.022 5-25 3-95 5-84 5-43 9-74 3-49 7.11 5-78 2.70 7.64 + .049 ±.07 1 +.029 ±.073 +.068 ±.065 + .251 ±.051 -.306 ±.058 +.251 ±.056 +-ii i ±.045 -•554±-°35 — .104^.030 0.69 0.40 1.05 3-81 4.92 5-28 4.48 2-47 15-8 3-47 tween the various correlations, i.e., the possible differences between the correlation for primary bundles and hypocotyledonary bundles, rvh, for intercalary bundles and hypocotyledonary bundles, r^, and for total bundles at the base of the hypocotyl and hypocotyledonary bundles, rbh. For both dimerous and trimerous seedlings, the correlations between the total bundles at the base of the hypocotyl and the number of bundles in the central region of the hypocotyl are higher throughout than those for either of the two separate types of bundles (primary bundles and inter calary bundles) individually considered. In general, the differences are sufficiently large in comparison with their probable errors to be considered statistically significant. The comparison of the magnitudes of the correlations between numbers of primary double bundles and of vascular elements at higher levels, and between numbers of intercalary bundles and of vascular elements at higher levels, shows that in 7 of the 10 comparisons the closer correlation of hypo cotyledonary bundles is with the primary double bundles. Lines 75, 139, and 143 present exceptions. In the normal plants of these lines the correlation between intercalary bundles and total bundles in the 35O AMERICAN JOURNAL OF BOTANY [Vol. 8, hypocotyl is apparently significantly higher than that between primary double bundles and total bundles in the hypocotyl.4 The fact that the number of bundles in the central region of the hypo cotyl is about equally correlated with the number of primary double bundles and with the number of intercalary bundles at the base of the hypocotyl shows that both types of bundles are of about equal significance in de termining the number of bundles in the central region of the hypocotyl. From the foregoing discussion it is clear that there is a rather close re lationship between number of bundles at the base and the number in the central region of the hypocotyl. This might, we believe, have been ex pected on a priori morphological grounds. The interesting feature of the results seems to be that the correlations are not larger. The results show that there is a very large amount of irregularity in the division of primary strands or in the formation of intercalary bundles, or in both, as one passes the short distance from the base of the hypocotyl to the central region. Correlation between Bundle Number in Different Internodes The data available for a consideration of the problem of the correlation between bundle number in adjacent internodes cover (A) the correlation between the three classes of bundles at the base of the hypocotyl [primary double bundles (£), intercalary bundles (i), and total bundles (&)] and the number of bundles in the central region of the epicotyl ; and (B) the correla tion between the number of bundles in the central region of the hypocotyl and in the central region of the epicotyl. (A) The coefficients showing the relationship between the numbers of primary double bundles, of intercalary bundles, and of total bundles at the base of the hypocotyl, and the number of bundles in the central region of the epicotyl, appear in table 3. The regression equations showing the actual change in number of epi- cotyledonary bundles associated with variation in the number of primary double bundles are given and are represented with the empirical means of arrays on diagram I for trimerous plants and on diagram 2 for dimerous plants. The graphs for the theoretical lines and the empirical means for the number of bundles in the epicotyl of both normal and abnormal plants show relatively little relationship between the number of bundles at the base of the hypocotyl and the number in the epicotyl. The differences in the slope of the lines for primary basal bundles and the number of bundles in central regions of hypocotyl and epicotyl show in a most striking manner the dif- 4 In line 75 the range of primary double bundles is only 3 while that of intercalary bundles is 6. In line 139 the primary double bundles fall in two classes only, with but 3 of the 305 frequencies on 5 as compared with 302 on 4 bundles. The correlation coefficient in such a case can have but little value. In line 143 practically all of the primary double bundles fall in two classes while the intercalary bundles are limited to three classes. Irregularity of results must be expected under such conditions. July, 1921] THE SEEDLING OF PHASEOLUS VULGARIS 351 ferences between correlations for groups of bundles lying on the same side and those lying on different sides of the nodal complex. (1) The correlation coefficients between primary double bundles and number of bundles in the epicotyl, rpe, as set forth in the first section of table 3, are in part positive and in part negative in sign. For the most part they can not be considered statistically significant. The average value of those for trimerous seedlings is —.0226 while that for dimerous seedlings is + .0768. (2) For the correlation between the number of intercalary bundles >and the number of bundles in the epicotyl, r;e, shown in the second section of table 3, the coefficients are not in general certainly significant in com- TABLE 3. Coefficients of correlation between number of primary double bundles, number of intercalary bundles and total number of bundles at base of hypocotyl, and number of bundles in central region of epicotyl Character of Seed lings and Line N Correlation for Primary Double Bundles rpe Correlation for Intercalary Bundles ''w Correlation for Total Bundles rle Trimerous Line 75. . I42 155 I83 I O6 221 142 155 183. 305 42O + .053 ±.056 -.087 ±.054 + .OO8 ±.050 — .IO5 ±.064 + .018 ±.045 -.ii5±.05o +.o84±.054 +.239±.047 +.i64±.038 + .oi2±.033 0-93 1.61 0.70 1.63 0.40 2.07 i-55 5.08 4-37 0.38 +.I26±.056 -.055 ±.054 +.070=^.050 +.oi6±.o65 +.233 ±.043 -.043 ±.057 + .I32±.053 + .109 ±.049 +.I45±.038 +.I34±.032 2.27 1. 01 1.42 0.25 544 0-75 2.48 2.21 3.84 4-15 +.i82±.055 -.I48±.053 +.099 ±.049 -.095 ±.065 +.I90±.044 -.054 ±.056 +.i67±.053 +.205 ±.048 +.I75±.037 + .121 ±.O32 3-33 2.79 2.OI 1.47 4-34 0.96 3-16 4.29 4.68 3-73 Line 93 Line 98 Line 139 Line 143 Dimerous Line 7"> . . Line 93 Line 98 . . Line 139 Line 143 parison with their probable errors. Two of the ten are indeed negative in sign. The coefficients for line 143 in both trimerous and dimerous seedlings and possibly that for line 139 in the dimerous seedlings may be significant. The fact that eight of the ten coefficients are positive suggests that there is a slight relationship between the number of intercalary bundles at the base of the hypocotyl and the number of vascular elements in the central region of the epicotyl. The general average is +.0780 for the trimerous and +.0954 for the dimerous. This suggestion is only slightly strengthened by inspection of the two sets of diagrams on which the regression equations are presented and drawn with the empirical means. Diagram 3 pictures the results for trimerous seedlings while the comparable representations for dimerous seedlings are shown on diagram 4. These show that while the slope showing the change in the number of bundles in the hypocotyl associated with variations in the number of intercalary bundles at the base of the epicotyl is very steep, it is practically nothing for the epicotyl, thus indicating a very close relationship in the former case but the practical absence of interdependence in the latter. 352 AMERICAN JOURNAL OF BOTANY [Vol. 8, As explained above (p. 346), the slopes for the trimerous seedlings are very greatly influenced by certain aberrant individuals. When these are removed we obtain the equations represented by the broken lines in the figures.5 The results for the relationship between the number of inter calary bundles and the number of bundles in the epicotyl indicate a positive correlation in all 3 cases when the one extreme plant is removed. (3) The coefficients of correlation between total bundles (double bundles plus intercalary bundles) at the base of the hypocotyl and the number of bundles in the central region of the epicotyl, r^e, are shown in the third section of table 3, and are represented graphically in terms of regression in the upper figures of each panel of diagram 5 for trimerous seedlings and of diagram 6 for normal seedlings. The very gentle slope and the differ ences in direction of the lines for the epicotyl of the trimerous plants, to gether with the irregularity of the empirical means, serve to emphasize the slightness of the relationship between total bundles at the base of the hypocotyl and the number of bundles in the central region of the epicotyl. In the normal plantlets the means are less irregularly distributed about the theoretical lines, but the slope of the lines is very slight, and in one case the regression slope has the negative sign. Turning to the correlation constants for more direct numerical com parison, we note that three of the ten constants are negative. The general average is +.0456 for the trimerous and +.1228 for the dimerous seedlings. Looking back over diagrams 1-6, one cannot but be impressed by the difference in the slope of the lines showing the changes in number of bundles in the hypocotyl and in the epicotyl respectively associated with variations in the number of bundles at the base of the hypocotyl. The lines for the hypocotyl, without exception, indicate an increase in the number of bundles in the central region of the hypocotyl with an increase in the number of bundles at the base of the hypocotyl. The lines for the epicotyl occasionally show a decrease. Furthermore, the slopes of the lines for the hypocotyl are in general conspicuously steeper — thus indicating closer dependence upon the number of basal bundles — than those for the epicotyl. Turning to table 4 for a numerical comparison of the correlations be tween the systems of bundles on the same side and on different sides of the cotyledonary node, we note that without exception the coefficients of corre lation measuring the interrelationship between the number of vascular elements at the base of the hypocotyl and in the central region of the epi cotyl are markedly lower than those measuring the correlation between the number of vascular elements in the base of the hypocotyl and in the central region of the hypocotyl. (B) We now have to consider the problem of the correlation between the numbers of bundles in the central regions of the hypocotyl and of the 5 When the extreme cases are omitted the equations are: Line 75, £ = 15.378 + o. 591 /; Line 93, E = 15.670 + 0.096 7; Line 98, E = 14.840 + 0.394 7. July, 1921] THE SEEDLING OF PHASEOLUS VULGARIS 353 TABLE 4. Differences between correlations for three classes of bundles at base of hypocoiyl and the number of bundles in the central regions of hypocotyl and epicotyl, respectively Character of Seedlings and Line rpe rph rit - Tih rbe - rbh Trimerous Line 75. . — .T.2S±.O74 4 3Q — 203=1=. O7S 2.71 — .467 ±.064 7.20 Line 93 — .-22O±.O74. 4 32 — 2^Q± O7 S -2 4.C — 6i7± 068 q 07 Line 98 — .^I^zb O67 A 67 — i83± 069 2 6s — 4.87 ± OSQ 8 25 Line 139 — 522 ± 084 6 21 — 08 1 =fc 092 o 88 — 626 ± 080 7 8-? Line 143 — .^8±.o=;s 9.78 — .O72=t=.OSQ 1.22 — .563 ±.048 1 1.7 Dimerous Line 75 — 4.774- O7O 681 — 7T T -h 06 S 10 9 — 8/11 -4- OSQ 14 3 Line QT, . . — •557 ±.O62 8 98 — 258=b 070 •3 6Q — s86± OS7 10 3 Line 98 — .427± OSS 7 76 — 446 zb O6O 7 AT. — S8l =fc OS2 112 Line 139 — . i8o± 051 •2 C7 — 7?7 -j- O3Q TO 7 — 7SO± O37 20 3 Line 143 — .5i8±.O4O 12.9 -.500 ±.037 13-5 -.681 ±.033 2O.6 epicotyl of the plant. The correlation surfaces are given in tables A-L. The results are set forth in table 5. TABLE 5. Coefficient of correlation between number of bundles in central region of hypocotyl and central region of epicotyl Line Trimerous Dimerous N r rlEr N r rlEr 75 . . 416 557 345 1 06 143 + .oi2±.033 + .075 ±.028 + .090 ±.036 — .061 ±.065 +.256±.042 0.36 2.68 2.50 0.94 6.10 416 557 345 305 420 -.017 ±.033 + .l62±.028 + .225=fc.o35 —.187 ±.037 +.107 ±.033 0.52 5-79 6-43 5-05 3-24 93 98 H9. . j? 143 The correlations are positive with the exception of that for dimerous plants of line 75 and of that for both dimerous and trimerous plants of line 139, which are negative in sign. Only one of the negative coefficients may be considered statistically significant in comparison with its probable error. Several of the positive coefficients are large enough in comparison with their probable errors to be considered possibly significant. The average correlation for the trimerous plants is +.074 while that for the dimerous plants is +.058. The correlations for the trimerous and dimerous plants can not be considered to differ significantly. The generally positive sign of the constants suggests that seedlings which have a larger number of bundles in the hypocotyl have on the average a larger number of bundles in the epicotyl. This is the condition actually found in the series studied, but the difficulties in the interpretation of the probable error in cases in which the correlation coefficient is so small should make one cautious in generalizing the results obtained. How slight the relationship between the numbers of bundles in the two organs is, may be shown by the regression lines giving the change in the mean number of bundles in the epicotyl associated with variations in the 354 AMERICAN JOURNAL OF BOTANY [Vol. 8, number of bundles in the hypocotyl and in the mean number of bundles in the hypocotyl associated with variations in the epicotyl. The straight line equations are as follows: Dimerous Trimerous Line 75, H = 10.325 - .o68£ H = 12.055 + .ooyE E = 12.347 - .ooSH E = 15.267 + .oi6H Line 93, H = 5.736 + 4OiE H = 11.501 + .Q5oE E = 11.494 + .065^ E = 14.273 + .ii2H Line 98, H= 1.374 + .6485 ff= 11.408 + .O42E E = 11.388 + .078H E = 12.538 + .i95# Line 139, H = 4.105 + -338£ H = 12.492 - .O33E E = 11.254 + .io3# E = 16.591 - .II3-H" Line 143, H = 6.677 + -i6iE H = 9-279 + E = 11.737 + .072^ E = 11.810 + All of these lines have been drawn, but it seems unnecessary to publish more than three sets. The comparison between the empirical and the theoretical mean number of bundles in the epicotyls of seedlings classified according to the number of bundles in the hypocotyl is made for three lines on diagram 7. Con versely, the comparison of the actual mean number of bundles in the hypo cotyl for plants with various numbers of bundles in the epicotyl is made on diagram 8. The slight slope of the lines and the irregularity of the empirical means show in a very convincing manner the laxness of the relationship between the numbers of bundles in the central regions of hypocotyl and epicotyl. These results are of decided morphological significance. The profound difference between the correlations for the hypocotyl and for the epicotyl emphasizes the completeness of the loss of individuality of the bundles at the cotyledonary node. Whereas the number of bundles in the central region of the hypocotyl is quite closely correlated with the number at the base of the hypocotyl, there cannot be asserted to be any significant correla tion in bundle number between either the base or the central region of the hypocotyl and the central region of the epicotyl, when we deal with seedlings of the same gross morphological structure. In other words, the reorganiza tion of the vascular system at the node is so complete that the portion of the system which is above the node shows practically no relation to the portion which is below the node. Comparison of Correlation in Trimerous and Dimerous Seedlings. In examining the results of the preceding tables the reader may have noted that the coefficients for the dimerous are preponderantly higher than those for the trimerous plants. This result is clearly brought out in table 6 uly, 1921] THE SEEDLING OF PHASEOLUS VULGARIS 355 16 15 /3 12 -c.. 8 3 i ' 10 II 1 « 12. i — • — 13 14 i 15 i 16 1 17 — i *i 18 i 19 20 HYPOCO TYL DIAGRAM 7. Regression of number of bundles in central region of epicotyl on number of bundles in central region of hypocotyl. Empirical means represented by solid dots for dimerous seedlings and by circles for trimerous seedlings. 356 AMERICAN JOURNAL OF BOTANY [Vol. 8, in which the differences between the coefficients for the two classes of plants are shown. The differences in this table are generally negative, thus indicating that the correlations are lower in the trimerous than in the dimerous seedlings. The exceptions are of some interest. L//Vf 98 i! 10 - 9 - *0 II 1 1 ^ 12 13 1 1 14 IS 1 i 16 11 b IS 19 20 21 22 DIAGRAM 8. Regression of number of bundles in central region of hypocotyl on number of bundles in central region of epicotyl. Empirical means represented by solid dots for dimerous seedlings and by circles for trimerous seedlings. There are only 4 exceptions among the 15 correlations between th_ numbers of vascular elements in the basal region of the hypocotyl and in the central region of the hypocotyl, as shown in the upper section of the table. These are without exception insignificant in comparison with thei probable errors. There are 9 exceptions among the 20 correlations ,e July, 1921] THE SEEDLING OF PHASEOLUS VULGARIS 357 FABLE 6. Comparison of correlations for trimerous and dimerous seedlings. Differences only (trimerous less dimerous) are given. See tables i and 3 for constants Correlation Coefficient Compared Line 75 Tph + .oi6±.o69 + .4o8±.o6o -.345 ±.053 +.073 ±.064 +.O26±.O39 rpe +.i68±.075 — .I7i±.076 — .231 ±.069 — .269 ±.074 +.006 ±. 056 rhe +.029 ±.047 — .087 ±.040 -.I35±.oso +.i26±.075 -M49±.053 0.23 6.80 6.50 1.14 0.67 2.24 2.25 3-35 3-64 O.II 0.62 2.18 2.70 1.68 2.81 r« -.339±.o6o — .i86±.o69 -.302 ±.058 — .8oi±.o66 -.329 ±.046 ?ie +.i69±.o8o -.i87±.o75 -.039 ±.070 — .I29±.075 + .099 ±.054 5.65 2.69 5-21 12. 1 7-15 2. II 2.49 5-57 1.72 1.83 fbh -.148 ±.039 -.284±.048 -.200 ±.039 -.394 ±.047 — .049 ±.022 Tbe +.236±.079 -.3i5±.075 — .io6±.o69 -.270±.075 +.069 ±.055 3-79 5-92 5-13 8.38 2.23 2.99 4.20 1-53 3.60 1-25 Line 93 Line 98 Line 139 Line 143 Line 75 Line en . . Line 98 Line 139 Line 143 Line 7^ . . Line Q^ . . Line 98 Line 139 Line 143 tween the numbers of vascular elements on different sides of the cotyledon- ary node as shown in the central and lower section. The exceptions occur, in short, among the relationships which in both types of seedlings are practically zero in intensity. We have no explanation to offer of this greater intensity of correlation in the sub-cotyledonary region of the normal seedling. The result is stated as one of the matters of fact demonstrated by the investigation. Correlation between Bundle Number in Siblings The question will naturally arise as to whether the variability in number of bundles in both hypocotyl and epicotyl and the correlation between bundle number in these two internodes may be due to a differentiation of the parent plants from which the seeds were obtained, either in their genetic composition or because of environmental influences. This problem pre sents many difficulties. Some light may be thrown upon it in the following manner. An abnormal and a normal seedling were taken from the same parent plant. Thus it is possible to determine in our series the correlation between the number of bundles in the hypocotyl of an abnormal plant and in the hypocotyl of a normal plant derived from the same parent. If a differentia tion of the parent plants due to either genetic or physiological factors is the underlying proximate cause of the variability and correlation in bundle number in seedlings which we have studied, there should be a correlation between the number of bundles in the seedlings derived from the same plant. The correlations between the numbers of bundles in the hypocotyls 358 AMERICAN JOURNAL OF BOTANY [Vol. 8, and epicotyls of the normal and abnormal seedling, i.e., of dimerous and trimerous seedlings, from the same parent plants are given in table y.6 TABLE 7. Correlations between bundle number in offspring of same parent plant Character of Plant and Organs Compared Line and Correlation Trimerous Dimerous Line 75 Line 93 Line 98 Hypocotyl .... Hypocotyl C. S. H. . . +.054O± 0406 -f- I7O"?± OT.27 — O^T2-I- O^O Storrs +.2151 ±.0540 + .OSS3± 0^4.0 -1- 08 ^rb O/1Q5 Epicotyl Epicotyl C. S. H — .0037 ±.0407 — 0027± O^T.6 -f~ I222it 0^22 Storrs +.0685 ±.0563 + .0432 ±.0541 + .0401 ±.0498 The coefficients are low throughout. Nine of the 12 are positive while 3 are negative in sign. Only 2 of the 12 can be reasonably regarded as significant. Both of these are positive. There is, therefore, a suggestion of a positive correlation between the anatomical characters of seedlings from the same parent. The values are too low, however, to justify the conclusion that there is a measurable differentiation in the genetic or physiological characteristics of the parent plants affecting bundle number in the offspring seedling. The absence of correlation here connotes an absence of (sororal or fra ternal) inheritance in bundle number. SUMMARY In an earlier paper we have shown that the number of vascular elements at different levels in the seedling of Phaseolus vulgaris is subject to consider able variation and that the amount of variation may itself differ from level to level. This is true both in normal seedlings with two cotyledons and two primordial leaves and in variant seedlings with three cotyledons and a whorl of three primordial leaves. These two types of seedlings are pro foundly differentiated in vascular anatomy as well as in superficial structure. The purpose of the present paper is to consider the correlations between the number of bundles in the various regions of the seedling. The characters considered are (i) number of primary double bundles, of intercalary bundles, and of total bundles at the base of the hypocotyl, (2) number of bundles in the central region of the hypocotyl, and (3) number of bundles in the central region of the epicotyl. i. There is a substantial correlation between each of the three classes of bundles at the base of the hypocotyl and the number of bundles in the central region of the hypocotyl. In the normal seedlings the coefficients 6 It has not seemed worth while to publish the tables upon which these very slight correlations are based. For purposes of comparison the series sectioned at Cold Spring Harbor and at Storrs are both given. ily, 1921] THE SEEDLING OF PHASEOLUS VULGARIS 359 :/erage +.509 for primary double bundles and hypocotyledonary bundles, -.629 for intercalary bundles and hypocotyledonary bundles, and +.813 !»r total bundles and hypocotyledonary bundles. In the trimerous plants lese correlations average +.381, +.238, and +.598, respectively. The correlations for normal plants are generally higher than those for onormal plants. 2. The correlation between each of the three classes of bundles at the ase of the hypocotyl and the number of bundles in the central region of ic epicotyl is low. The coefficients are sometimes positive and sometimes »egative in sign. On the basis of the data available it is impossible to ssert that there is any correlation at all between the numbers of bundles i these two regions. 3. The correlation between the numbers of bundles in the central region f the hypocotyl and in the central region of the epicotyl is likewise very pw. The coefficients are generally not significant in comparison with heir probable errors. If there be any correlation at all between the numbers f bundles in these two regions it is very slight indeed. These results for correlation fully substantiate the conclusions drawn n an earlier paper that there is a complete reorganization of the vascular ysteni at the cotyledonary node. 4. The correlation between the number of bundles (either hypocoty- edonary or epicotyledonary) in siblings is, if it exists at all, very low. The differentiation of the parent plants through either genetic or environmental actors cannot, therefore, be considered to be the source of the variation md correlation in bundle number demonstrated in this and in our preceding paper. CONCLUSIONS These results, and others for which the reader must turn back to the 3ody of the paper, justify the emphasis at this point of the following general inclusions: a. The vascular structures of the seedling are not constant but are decidedly variable within the species. They show different degrees of variability within the individual organism. b. Seedlings differing in external form are profoundly differentiated in their internal anatomy. This differentiation is evident both in mean number of bundles and in the degree of variability in bundle number. In short, the external form and the internal structure of the seedling are highly but not perfectly correlated. c. The different anatomical characters of the seedling are interrelated with varying degrees of intensity. Between some there is a very strong correlation, but between others practically none at all. The quantitative measurement and interpretation of such relationships, by means of the biometric methods hitherto little applied in the field of vascular morphology, will make possible material advance in the investiga tion of the fundamental problems of morphogenesis. 360 AMERICAN JOURNAL OF BOTANY [Vol. 8,. TABLE A. Data for correlation between bundle number at the base of the hypocotyl and in the central regions of hypocotyl and epicotyl in trimerous seedlings Base* Line Hypocotyl Epicotyl 3 2 I 3 i i i i 5 4 4 15 8 10 6 4 2 3 i 107 120 1 60 92 134 12 II 10 5 25 2 I 7 4 i 5 4 i i i I 8 9 ; u II 12 13 14 15 if, 17 18 10 2( 12 13 14 1.5 rf 17 18 19 20 21 31 (4)+6--- (5) +2... (6)4-1... 143 139 143 93 98 75 75 93 98 139 143 75 93 98 139 143 75 93 98 75 93 98 139 143 75 93 98 139 143 75 93 75 93 98 143 75 75 2 y y T I . . I T T i I T! T 1 . . T I y I I 3 i I 3 i I 2 I I I I I 2 2 2 2 6 3 l i i 3 3 2 I T 2 y r 2 3 2 3 3 i 3 i i 2 ( 3 •• I T I 1 y I 1 i 2 2 I i T f 2 1 1 13 2 1 4 _ 2 2 I 9 6 i 5 3 I 2 I I T 2 I j i I I 2 4 5 90 102 145 81 121 I 8 10 8 3 7 8 7 2 I I CO rt- CO w rt- (N COcOfN M 519 6 14 1336 421 7 H 43 47 67 35 34 6 6 3 y 22 25 2(, 21 31 3 2 2 2 u '5 8 8 22 I I 6 8 3 2 1 I 3 I 3 I I I I I I I 6 I I I I 3 I I _ 3 i I I I 1 I I 5 5 8 3 2 2 T y 7 4 2 y I 7 T 2 I I r 1 2 y 2 y I ' 1 i I y T y I (8) + i... 143 r .. I I . . " Numbers in parentheses are of primary double bundles; those following are of inter calary bundles. fuly, 1921] THE SEEDLING OF PHASEOLUS VULGARIS 7ABLE B. Data for correlation between bundle number at the base of the hypocotyl and in the central regions of hypocotyl and epicotyl in dimerous seedlings Base Line Hypocotyl Epicotyl 8 9 IO II 12 13 14 15 17 18 10 ii „ 13 14 i IS 16 2 Tot. 69 34 97 270 291 30 37 43 26 1 02 10 13 23 6 5 4 5 2 2 I 2 13 22 6 I 13 4 18 8 2 7 i 9 1C 3 i 2 I 4)+o... 4) + i -.- 4)+2 ... ;4)+3 ... 4)+4-.. §+5 ... 5)+o... :s)+i... (5) + 2 . . . (5)+3-.- (6)+o... (6) + i ... (4+2... (7)+o... (8 + 1) ... 75 93 98 139 143 75 93 98 139 143 75 93 98 139 143 75 93 98 75 93 75 75 93 98 139 143 75 93 98 139 143 75 93 98 75 93 98 75 93 98 75 93 143 93 H3 98 40 12 57 269 262 2 I 17 13 3; 21 .14 •14 26 .22 6l 7 6 9 4 3 T . I I 59 . 29 . 88 • 250 .229 22 • 31 • 37 . 21 • 72 • 9 . ii • 19 • 5 -z 4 4 8 18 43 3 3 5 4 17 i 2 3 i 2 I 2 13 2 3 I I II 6 13 • 17 13 3 27 . 2 • 9 13 . 2 • 3 2 3 3 i i 10 4 2 6 2 I . 2 . 3 2 4 2 I . 2 I I I I 2 T I I 3 2 I I I I 2 I ... . 3 I I T I T 4. -z T T 2 . I T 2 T I I T 2 . I . I 8 13 . 2 . I 2 4 3 I 3 i I I . 12 . 18 • 4 i i i i 2 I I . I II . i . 8 A 5 . 2 6 5 i • 4 2 7 i . I . I . I 3 i I . 12 • 7 i 3 i I 2 I 2 I i • 4 i i 2 • 5 . i 3 I . 6 I i 2 . I I I i T 1 T . i . i . i 3 8 T . I 4 • 9 i I i . i i . I 2 . 2 I i T a I I T I T T 362 AMERICAN JOURNAL OF BOTANY [Vol. 8, TABLE C. Correlation between numbers of bundles in hypocotyl and epicotyl of trimeroui plants of line 75 Epicoty 12 13 U IS 16 17 18 19 20 21 Totals 8 I I I I I •z 10 c 5 i 1 I 6 ll 12 * 2 36 12 2 1C 4.8 I2O 62 21 IQ •I 2 292 I-j s. IT. IO 7 4 I 40 Id. I IO 7 8 2 I 29 T c I 2 i I 5 16 I i 17 I I I I 4 Totals 3 16 63 164 93 4i 27 4 4 I 416 TABLE D. Correlation between numbers of bundles in hypocotyl and epicotyl of dimerous plants of line 75 Epicotyl Hypocotyl Totals 10 II 12 13 14 IS 16 8 116 17 6 4 143 Q. . I 2 78 13 5 2 2 103 IO 74 IO I I 86 II I 20 4 2 2 38 12 I 22 I I I 26 T9 6 I 8 I 9 1C 16 17 2 I 3 18 I i Totals I 4 336 46 16 IO 3 416 TABLE E. Correlation between numbers of bundles in hypocotyl and epicotyl of trimerous plants of line 93 Epicotyl Totals 12 13 14 IS 16 i? 18 19 20 21 22 IO I I 8 1 1 T. 14 7 •2 I 32 12 id •21 170 Q2 -18 26 • I 382 IV . I 4 5 "?O IS 6 16 7 I I 82 14. . I 17 q 2 •i I 38 1C . . J 2 c 2 2 12 16.. . I I 17 18 I I IQ 2O I I Totals 5 18 47 236 129 56 51 IO 4 I 557 uly, 1921] THE SEEDLING OF PHASEOLUS VULGARIS 363 "ABLE F. Correlation between numbers of bundles in hypocotyl and epicotyl of dimerous plants of line 93 Epicotyl Hypocotyl 10 n 12 13 14 15 16 Totals 8 i 1.1 2 '9 i i 8^ -2 9 34 o ! -z 14.7 \ 2 93 j i 88 Id. 2 2 78 i°5 3 71 90 4 16 39 *fi 5 i 8 : 2 2 Totals | i 6 479 42 18 10 I 557 TABLE G. Correlation between numbers of bundles in hypocotyl and epicotyl of trimerous plants of line 98 Hypocotyl Epicotyl 12 13 14 15 16 17 18 19 20 21 Totals 9 I I 2 58 6 i I 6 12 297 21 8 :o I I 2O 2 4 4 157 8 3 :i 3 4! 4 i 8 I 4 2 .2 8 I •-3 I I ;4 Totals . 8 24 69 176 49 9 7 I I I 345 TABLE H. Correlation between numbers of bundles in hypocotyl and epicotyl of dimerous plants of line 98 12 13 U IS Totals 16 8 j 107 6 9 103 6 * *3 10 7I II 26 c I I 77 12 7 2 32 13 2 I 17 I i i Totals 316 23 4 i i 345 364 AMERICAN JOURNAL OF BOTANY [Vol. 8, TABLE I. Correlation between numbers of bundles in hypocotyl and epicotyl of trimerous plants of line 139 Hypocotyl Epicotyl 13 14 IS 16 17 18 1 19 Totals 3 TO iU ; 4 I 5 I 4 8 84 6 3 I II I 19 I 32 2 2 I 20 2 I I 12 3 I? TA i TC I Totals 8 21 38 24 9 4 2 106 TABLE J. Correlation between numbers of bundles in hypocotyl and epicotyl of dimerous plants of line 139 Epicotyl Hypocotyl 12 13 14 Totals 8 24.Q 18 2 260 9. • 2O 7 77 IO ... I I II 2 I I 12 I I 13 I I Totals 278 23 4 305 TABLE K. Correlation between numbers of bundles in hypocotyl and epicotyl of trimerous plants of line 143 Epicotyl 12 13 14 15 16 17 18 19 20 21 Totals 8 I 2 9 I I 10 2 2 2 2 I 2 1 1 ii 2 2 c 2 I I I 1,1 12 7 q ^5 71 22 IQ 7 17.6 n I 6 ? • 2 I I 21 14. . 7 6 /i I 2 I •75 15 2 3* I 6 16 I I I 17 I I 18 I i Totals. . . . 5 9 19 54 49 37 31 9 6 2 221 July, 1921] THE SEEDLING OF PHASEOLUS VULGARIS 365 TABLE L. Correlation between numbers of bundles in hypocotyl and epicotyl of dimerous plants of line 143 Epicotyl Hypocotyl 12 13 14 IS 16 Totals 8 20=> 4'2 IO 9 6"> II 7 203 C2 10 -22 8 c °>3 II o -z 4. I 47 12 -z I I/ 13 I 2 14 I 15 2 Totals 318 66 27 5 4 ^:c f Reprinted from the AMERICAN JOURNAL OF BOTANY, 8: 375-381 October, 1921.] HE VASCULAR ANATOMY OF HEMITRIMEROUS SEEDLINGS OF PHASEOLUS VULGARIS ij. ARTHUR HARRIS, EDMUND W. SINNOTT, JOHN Y. PENNYPACKER, AND G. B. DURHAM (Received for publication January 17, 1921) INTRODUCTORY In an earlier paper1 we discussed the gross vascular anatomy of 'dimerous nd trimerous seedlings of the garden bean. By dimerous seedlings we nderstand those of the normal type, characterized by two cotyledons and NO primordial leaves, both sensibly opposite in insertion. By trimerous te mean those which have a whorl of three cotyledons and three primordial iaves. The cotyledons may be, and frequently are, more or less, irregular i insertion. The primordial leaves are, in the seedlings considered, inserted i a regular whorl. In addition to these two types of seedlings, those which are in a sense itermediate in superficial structure between the two types hitherto studied lay occur. These are seedlings with a whorl of three cotyledons but with normal pair of primordial leaves instead of three as in the case of trimerous 2edlings. These we have called hemitrimerous. They are extremely rare i occurrence, but during the four years during which these studies have een under way a number sufficiently large to justify a brief discussion of heir gross vascular anatomy has been secured. Our purpose in this paper is to compare the anatomy of these hemi- rimerous seedlings with the trimerous seedlings (in common with which hey have three cotyledons) on the one hand and with dimerous seedlings in common with which they have two primordial leaves) on the other. For convenience of reference the three types will in some cases be lesignated by the number of cotyledons and primordial leaves: 2-2 = dim- rous, 3-3 = trimerous, and 3-2 = hemitrimerous. MATERIALS The hemitrimerous plants and the trimerous and dimerous seedlings rith which they are compared were largely secured in the series of germina- 1 Harris, J. Arthur, Sinnott, E. W., Pennypacker, J. Y., and Durham, G. B. The 'ascular anatomy of dimerous and trimerous seedlings of Phaseolus vulgaris. Amer. our. Bot. 8: 63-102. 1921. [The Journal for July (8: 323-374) was issued August 31, 1921] 375 376 AMERICAN JOURNAL OF BOTANY tions which furnished the materials for our earlier discussion of dimerous and trimerous seedlings. The dimerous and hemitrimerous seedlings were derived from the same parent plants in lines 75, 93, and 98. In lines 29, 139, and 143 the germinations were made from mass seed instead of from the seed of individual parent plants. All of the seed, however, was grown in the same experimental field in 1917. Since it has been shown in an earlier paper2 that there is practically no correlation between the anatomical characters of the trimerous and dimero^i seedlings from the same parent plant, we are fully justified in using random samples of hemitrimerous, trimerous, and dimerous seedlings for a com parison of their vascular characters. A detailed account of the vascular topography of the dimerous and trimerous seedling is presented in a previous paper by the writers, but may be summarized very briefly here. Each primary polar bundle of the root bifurcates in the base of the hypocotyl to form a "primary double bundle," which gives rise to two distinct and well separated strands in the central region of the hypocotyl. In addition to these, there are usually present in the hypocotyl a number of "intercalary" bundles, arising either de n+i.. — — — — — 1 • ' 4 7) + 2. . i 8) +o.. — — — i — — • — ; i — 8) + i . . — — — ' — — i • — • i — — 56 43 99 142 57 199 Il83 43 226 I O6 42 305 221 114 420 Table 2 shows the average number of primary double bundles, inter- alary bundles, and total bundles in the three types of seedlings, and gives :he differences and probable errors of differences in the means upon which ve must depend for conclusions. The entries in the first section of this table show that the average lumber of primary double bundles is relatively lower in the hemitrimerous :han in the trimerous seedlings. It is also relatively higher than the lumber in the dimerous seedlings. The differences, while small, may reasonably be considered significant in comparison with their probable errors. The differences between the hemitrimerous and the dimerous class are much larger than those between the hemitrimerous and the trimerous. Turning to the statistical constants for intercalary bundles set forth in the second section of table 2, we note that in four of the five cases the hemitrimerous seedlings have a larger number of intercalary bundles than the trimerous seedlings. These differences are small, but may be significant. In the one case in which the hemitrimerous seedlings have a smaller number of intercalary bundles than the trimerous plantlets the difference is only - o.oi ± 0.04. In two of the cases the hemitrimerous show a larger number of intercalary bundles than the dimerous seedlings, but in three lines the reverse is true. The differences are in general not so large in comparison with their probable errors as in the case of the comparison for number of primary double bundles. 378 AMERICAN JOURNAL OF BOTANY TABLE 2. Mean number of bundles at base of hypocotyl [Vol. / Primary Double Bundles Intercalary Bundles Total Bundles - Line 29 1— T. . . 56 5.68 ± .05 5.21 ± .08 ! 4.04 ± .01 — 0.47 ± .09 + 1.17 ± .08 ; 5.98 ± .02 5-74 ± -05 j 4-24 ± .03 : - 0.24 ± .05 + T.50 zb .06 5.93 ± .01 5-67 ± -07 4-II =h .02 — O.26 ± .07 + 1.56 d= .07 5.91 ± .02 5-36 =fc .08 4.01 ± .00 - 0.55 ± .08 + 1.35 ± .08 5-8 1 ± .03 i 5-45 ± -04 4.06 ± .01 - 0.36 ± .05 + 1.39 ± .04 ' .27 ± .07 •53 ± .12 .16 ± .03 + .26 ± .14 + -37 ± -12 .25 ± .04 •44 it .07 .62 ± .05 + .19 ± .08 - .18 ± .09 .13 ± .02 .53 ± .09 .62 ± .03 + .40 ± .09 - .09 ± .09 .09 ± .02 •43 ± -05 .13 ± .02 + .34 ± .05 + .30 ± .05 .29 ± .02 .28 ± .03 .29 ifc .02 — .01 ± .04 — .01 ± .04 5-95 ± -04 5-74 ± -io 4.20 ± .03 — 0.21 ± .11 + 1.54 ± .10 6.23 ± .03 6.18 ± .07 4.85 ± .05 - 0.05 ± .08 + 1.33 ± .09 6.O6 ± .02 6.21 ± .08 4-73 ± -04 + 0.15 ± .08 + 1.48 ± .09 6.OO ± .02 5-79 ± -06 4.14 ± .02 — 0.21 ± .06 4- 1.65 ± .06 6.10 ± .03 5-73 ± -04 4.35 ± .02 - 0.37 ± .05 + 1.38 ± .04 3-2 ... 4. 3 2-2 99 (3-2)-(3-3) (3-2)-(2-2) Line 75 3—3 . . JA2 3-2 ... T4 103 .ine 93 3-3 .... 8 6l 18? A4 Q? •38 3 519 3-2 .... A 6 6°^ Q 38 i 557 2-2 . . . 1,6 Q3 T7O 17 ofi 7 Tb 43 .ine 98 3-3 .... y>) i 6 yo 4° Q 563 3-2 . . . •V7 345 2-2. . . I2S 126 8? -5 3 3 43 .ine 139 3-3 3-2. . . . I 4 6t 8 84 0 6 3 i — i 388 1 06 2-2 .... 26Q 21 7 X9 3 42 -ine 143 3-3. . . . 2 I | j lift 305 3-2. . . . I -> T7 *4 130 25 3 i I — 221 2-2 .... 263 |3 47 xy 17 54 4 • 4 3 i 5 2 4 — — — — 114 420 AMERICAN JOURNAL OF BOTANY since the sole superficial difference between the two types of seedlings is found at the primordial node. The frequency distributions in table 5 show that the nodal number of bundles is in general lower in the hemitrimer- ous than in the trimerous seedlings. It also indicates that they are higher in the hemitrimerous than in the dimerous seedlings. The averages and their probable errors in the second section of table 4 show that in each of TABLE 4. Mean number of bundles in central regions of internodes Line / Central Region of Hypocotyl Central Region of Epicotyl Line / Central Region of Hypocotyl Central Region of Epicotyl ' Line 29 56 43 99 416 103 519 557 43 563 I2.36±.i6 n.74±.i6 8.45 ±.05 — .62 ±.23 I2.32±.O8 9.52 ±.05 + 2. 80 ±.09 1 2. 29 ±.03 I2.26±.I3 IO.62 ±.04 I4.75±.i8 1 2. 05 ±. O2 - I.82±.25 + .88±.i7 I3.8.5±.io I2.26±.O2 - I.62±.II + i.59±.io 15.65 ±.04 I4.84±.i8 • I2.I9±.O2 - .8i±.i8 + 2.6s±.i8 Line 98 3-3 3-2 (3-2H3J3)' (3-2)-(2-2) Line 139 3-3 3-2 2-2 .... (3-2)-(3-3) (3-2)-(2-2) Line 143 3-3 3-2 (3-2M3-3)' (3-2)-(2-2) 345 43 388 1 06 42 305 221 114 42O I2.03±.O2 I2.O7±.I2 + .O4±.I2 + 2.83±.i3 1 1. 99 ±.05 ii.36±.i2 8. 19 ±.02 - .63 ±.13 + 3-i7±-i2 I2.29±.O6 n.89±.io 8. 66 ±.04 — 40±.I2 14. 89 ±.04 I3.72±.i$ I2.I2±.OI + i.6o±.i3 I3.93±.i8 I2.IO±.OI — 1. 31 ±.20 + i.83±.l8 i6.io±.o8 I3.68±.09 — 2.42±.I2 •z— 2. . 2—2 (3-2)- (3-3) • (3-2)-(2-2) . Line 75 -z— -z. . 7—2. . 2—2 (3~2)-(3-3) • (3-2)-(2-2) . Line 93 •z— -z. . •1-2 . 2—2 . . (3-2)-(3-3) - (3-2)-(2-2) . TABLE 5. Distribution of number of bundles in central region of epicotyl IO II 12 13 14 15 16 17 18 19 2O 21 22 Total Line 29 •z— -Z . . I 3 ii 13 15 4 2 4 i I I - 56 3-2 2—2 2 3 19 97 4 6 I 6 I 2 I — — 43 — 99 Line 75 3-3 3-2 2-2 Line 93 •z— -z . . I 3 4 3 16 422 5 1 6 28 58 18 63 27 21 47 164 H IO 236 93 9 3 129 41 4 S6 27 i 51 4 IO 4 i 4 I — 41 6 — 103 — 519 " i 557 3-2 2-2 I 6 5 483 4 42 9 20 13 IO 5 i 3 2 2 — 43 — 563 Line 98 -z— -z . . 8 24 69 176 49 9 7 I i I 345 "I— 2 . . I 6 12 13 8 2 i — — — 43 2—2 352 27 7 I i — — — 388 Line 139 •z— -z . . 8 21 38 24 9 4 2 1 06 •z—2 2 6 12 8 6 5 i 2 — — 42 2-2 Line 143 -z— -z . . — 278 5 23 9 4 19 54 49 37 31 9 6 2 — 305 — 221 3-2 2-2 3i 3i8 19 66 37 27 17 5 6 4 2 2 — — 114 — 420_ Oct., 1921] HARRIS AND OTHERS — • PHASEOLUS VULGARIS 381 \ the six lines the average number of bundles in the epicotyl is significantly Bower in the hemitrimerous than in the trimerous seedlings, and (probably) significantly higher in the hemitrimerous than in the dimerous seedlings. In epicotyledonary structure the hemitrimerous seedlings occupy as a matter of fact almost exactly an intermediate position between the dimerous iiul the trimerous types. •SUMMARY The purpose of this paper is a comparison of the gross vascular anatomy of hemitrimerous seedlings of Phaseolus vulgaris with those which are trimerous and those which are dimerous. By dimerous seedlings we under stand those with two cotyledons and two primordial leaves, by trimerous seedlings those with -three cotyledons and three primordial leaves, and by hemitrimerous seedlings those with three cotyledons and two primordial leaves. The hemitrimerous is, therefore, intermediate in external form between the dimerous and the trimerous seedling. In the internal structure of the axis at the transition zone, which here occurs at the base of the hypocotyl, the hemitrimerous seedling is clearly differentiated from the trimerous type by a slightly smaller average number of primary double bundles, and possibly by a slightly larger number of intercalary bundles. The total number of bundles in the basal region of the axis of hemitrimerous seedlings is not sensibly different in hemitrimerous and trimerous plantlets. The hemitrimerous are conspicuously differentiated from the dimerous seedlings by a larger number of primary double bundles and a larger total number of bundles. On the basis of the data available they cannot be asserted to differ significantly from the dimerous plants in the number of intercalary bundles. In the central region of the hypocotyl, the vascular anatomy of the hemitrimerous seedling conspicuously exceeds that of the dimerous in bundle number but agrees very closely indeed with that of the trimerous plantlet, although it may have a slightly lower average number of bundles. In the central region of the epicotyl the mean number of bundles in the hemitrimerous seedling is, roughly speaking, intermediate between that of the trimerous and that of the dimerous types. Recapitulating, it appears that in internal structure the hypocotyl of the hemitrimerous seedling is practically identical with that of the trimerous seedling with which it has in common a whorl of three cotyledons. The epicotyledonary internode in the hemitrimerous seedling, limited by a trimerous cotyledonary and a dimerous primordial node, is intermediate in anatomy between the trimerous type with three cotyledons and three primordial leaves and the dimerous type with two cotyledons and two primordial leaves. 2— [Reprinted from the AMERICAN JOURNAL OF BOTANY, 8: 425-44^. November, 1921.] THE INTERRELATIONSHIP OF THE NUMBER OF THE TWO TYPES OF VASCULAR BUNDLES IN THE TRANSITION ZONE OF THE AXIS OF PHASEOLUS VULGARIS [.ARTHUR HARRIS, EDMUND W. SINNOTT, JOHN Y. PENNYPACKER, AND G. B. DURHAM (Received for publication January 17, 1921) INTRODUCTORY In papers1 on the anatomy of dimerous2 and trimerous and of hemi- •imerous seedlings we have shown that Phaseolus vulgaris is characterized y a structure of the vascular system at the base of the hypocotyl which , rather infrequent in seedling anatomy in general. This is the presence f a variable number of accessory bundles which usually lack protoxylem tements. These are the "Zwischenstrange" of Dodel. We have elsewhere ailed them intercalary bundles. They may make their appearance in •ie upper part of the root or in the lower region of the hypocotyl, some :sing blindly below and others originating by division of a primary double undle. These intercalary strands may be distinguished from the other undies with perfect certainty because of their position and of the absence dthin them of any protoxylem elements. In another place3 we have dealt with the correlations between the umber of bundles at different levels in the seedling, that is, the relationship •etween the vascular system at the base of the hypocotyl and that in the entral region of the hypocotyl and epicotyl, and between the bundle ystem in the hypocotyl and that in the epicotyl. Our present problem is o consider the interrelationships between the two types of bundles present n the hypocotyl just above the region of transition from root to stem struc- ures, and between each of these types and the total number of bundles a this zone. 1 Harris, J. Arthur, Sinnott, E. W., Pennypacker, J. Y., and Durham, G. B. The •ascular anatomy of dimerous and trimerous seedlings of Phaseolus vulgaris. Amer. Jour. Jot. 8: 63-102. 1921. The vascular anatomy of hemitrimerous seedlings of Phaseolus ulgaris. Amer. Jour. Bot. 8: 375-381. 1921. 2 Dimerous seedlings have 2 cotyledons and 2 primordial leaves; trimerous seedlings lave 3 cotyledons and 3 primordial leaves; and hemitrimerous seedlings have 3 cotyledons .nd 2 primary leaves. 3 Harris, J. Arthur, Sinnott, E. W., Pennypacker, J. Y., and Durham, G. B. Correla- ions between anatomical characters in the seedling of Phaseolus vulgaris. Amer. Jour. 3ot.8: 339-365- 1921. [The Journal for Octobsr (8: 375-424) was issued Novembar 14, 1921]. 425 426 AMERICAN JOURNAL OF BOTANY Lack of space precludes the publication of the 30 individual correlation tables upon which the coefficients discussed in this section are based. These may, however, be easily formed from the schedules showing the formula for the basal bundles in other papers of this series.4 TABLE i. Correlation between Number of Primary Double Bundles and Number of Intercalary Bundles at Base of Hypocotyl Trimerous Dimerous rvff Line N r r E~r N r r Er Difference -Ediff. . 75 93 98 139 143 142 155 183 1 06 221 — .5004±.0424 -.6155 ±.0337 — .65I5±.0286 -.5053 ±.0488 — .3 184 ±.0408 n.8 18.3 22.8 IO-4 7.8 142 155 183 305 420 -.H77±.0558 -.1449 ±.0530 +.0643 ±.0496 +.I364±-0379 +.0338 ±.0329 2. II 2-73 1.30 3.60 1.03 — .3827 ±.0700 — .4706 ±.0624 -./i58±.0574 — .64i7±.o6i8 -.3522 ±.0530 5-46J 7-54 jl 12.4 , 6.0 5-4 ANALYSIS OF DATA i. Relationship between Number of Primary Double Bundles and NnmbeA of Intercalary Bundles. We shall first consider the relationship between the number of primary double bundles and the number of intercalary I bundles at the base of the hypocotyl in dimerous and trimerous plants! The correlation coefficients for the five lines appear in table i. Fo the trimerous plants of all five lines the correlations are negative in sign.] i.e., the number of intercalary bundles is greater in plants which have smaller number of primary double bundles, and vice versa. For dimerouij plants three of the five lines show a slightly negative coefficient, but tw« show a low positive correlation. The constants indicate that the corre' lations for the trimerous plants are much higher numerically than thos for the dimerous plants. Those for the trimerous are of the order — ., to —.6 while those for dimerous plants are sensibly zero, averaging + .00* The correlations for the trimerous plants are in all cases several times a large as their probable errors, while those for the dimerous plants cou hardly be regarded as statistically significant if only one of the lines we available. The differences, taken with regard to sign, between the corr lations for the dimerous and trimerous plants are in each case significan in comparison with their probable errors. Expressing these results in terms of regression we have the followin equations: 4 The entries to be selected from the published tables can be determined from the valu of N. In lines in which true siblings were available (75, 93, and 98) only siblings have bee used, even though additional sections of one or the other type were available. In the lines in which random samples of seed were used for the production of the dimerous an trimerous seedlings, the largest possible number of individuals available in the tables of t papers cited was employed for the constants here discussed. r., 1921] HARRIS AND OTHERS PHASEOLUS VULGARIS 427 Dimerous Trimerous Line 75: P = 4.255 - 0.058 / P = 6.059 - 0.318 / / = 1.641 - 0.239 P / = 4.968 — 0.789 P Line 93: P = 4.607 — o.uo / P = 5.992 — 0.448 / / = 1.398 — 0.127 P I = 5.200 — 0.846 P Line 98: P = 4.099 + 0.035 I p = 5-984 — °-392 I I = 0.114 + 0.117 P / = 6.559 — 1.084 P Line 139: P = 4.005 + 0.034 / P = 5-95§ - 0.558 / / = ._ 2.038 + 0.541 P / = 2.795 - 0.457 P Line 143: P = 4.060 + 0.019 / P = 5.924 — 0.408 / / = 0.047 + 0.059 P I = I-732 - 0.249 P The mean number of intercalary bundles associated with given numbers ^f primary double bundles and the theoretical means as given by the Degression straight lines are shown on diagram I. For the normal plants of lines 75, 93, and 139 the agreement between ihe observed means and the regression line is very satisfactory. In line 1)8 a single seedling with 8 primary double bundles and 4 intercalary bundles Hves a positive sign to the correlation and makes the agreement of theo retical and empirical means very poor indeed. In lines 139 and 143 the correlation is also positive. It must be noted that we are dealing here Ivith a very narrow range of both primary double bundles and intercalary )undles, and with very small frequencies in some of the classes. For the abnormal plants the agreement of empirical means and theo- •etical lines is apparently very poor indeed. This is perhaps largely attrib utable to two facts: (a) The frequencies of primary double bundles are, practically speaking, concentrated in two classes, 5 and 6 bundles. From 93 to 99 percent of the seedlings fall in these two classes. As a result of this condition, the ob- :aining of trustworthy averages for the extreme classes of primary double Bundles is, practically speaking, impossible. (b) The influence of the two principal classes (5 and 6) of primary double bundles is such as to throw the theoretical mean number of interca lary bundles for higher classes of primary double bundles on the negative side of o in four of the five cases. As a consequence, the actual mean number of intercalary bundles must lie above the line in all cases in which more than 6 primary double bundles are formed. Whether these irregularities represent a significant deviation from line arity can be determined only when far larger series of data are available. While the primary double bundles must probably be regarded as more fundamental structures than the intercalary bundles, it seems of interest to determine the mean number of primary double bundles associated with each number of intercalary bundles. 428 AMERICAN JOURNAL OF BOTANY The lines for the regression of number of primary double bundles on number of intercalary bundles are represented with the empirical means on diagram 2. These figures show that, with the exception of the normal plants of lines 98, 139, and 143, the number of primary double bundles decreases slightly as the number of intercalary bundles increases. The rate of decrease is somewhat greater in the abnormal than in the normal plants. T71/ME~ROUS SEEULJNGS 2/METtOUS 456184-56 7 4 5 B 1 PH/MARY UOUBLE BUNBLES DIAGRAM i. Regression of number of intercalary bundles on number of primary doublt bundles, at base of hypocotyl. Tov., 1921] HARRIS AND OTHERS — PHASEOLUS VULGARIS 429 It is suggestive to note that the negative correlation between number of >rimary double bundles and number of intercalary bundles demonstrated ere within seedlings of one class with regard to external structure is also Ivident when we pass from a type of seedling with a smaller to one with a igher number of primary double bundles. It has been shown in an earlier taper that (a) the number of trimerous seedlings having intercalary bundles generally smaller than the number of dimerous seedlings with these .ccessory structures, and that (b) the average number of intercalary bundles s generally smaller in trimerous than in 'dimerous seedlings. L/A/E 93 i/NE 14-3 0/2 LJ/VE 139 / DIAGRAM 2. 3U/VULES Regression of number of primary double bundles on number of intercalary bundles, at base of hypocotyl. 2. Relationship between the Total Number of Bundles and the Number of Bundles of the Two Types. We may now inquire to what extent the varia tion in the total number of bundles depends upon the primary double bundles and to what extent upon the number of intercalary bundles. As a first step we determine the correlation between the total number of bundles and the number of primary double bundles, and between the total number of bundles and the number of intercalary bundles. These results are set forth in table 2. We note that the correlations between the total number of bundles and the number of intercalary bundles are in all cases high, ranging from + .42 430 AMERICAN JOURNAL OF BOTANY to +.80 in the trimerous and from +.76 to +-97 in the dimerous plantJ The correlations for the dimerous plants are in all five cases slightly higher than those for the trimerous plants. TABLE 2. Comparison of Correlation between Total Bundles and Primary Double Bundles, rbp, and between Total Bundles and Intercalary Bundles, rbi, at Base of Hypocotyl Trimerous Dimerous Diff N r r E, N ' r r Er Difference Ediff. Line 75 r^i 14.2 +.7788±.0222 75 T 142 + 8872=1= 0120 •7-1 Q — .1084 ±.0245 4 42 14.2 + .I^2±. OS. ^2 *> 77 T/12 -1- 3.^7.6=1= O4QS 7 Id — 2004 =fc 0741 2 70 rbi— rbp. Line 93 r^ I'i'i +.6256^.0591 + .6934 ±.028 1 10.6 2/1 7 I S5 + .5336±.05io + 7628 ± 0226 10.5 T.T. 8 — 0694 ± 0361 I Q2 ?bp 155 +.1409=1=. 0531 2 6S ICC + S2Q2=b.O^QO IT, 6 — .388-?±.o6=.S C.Q2 rbi — rbp. Line 98 r^ T8l +.5525 ±.0600 + .8001 ±.0179 9.21 /i/i 6 181 + .2336=b.0447 -I- SS^^zt: OIOQ 5-23 81 o — 0832 ± 0200 4 16 Tbp T87 — .0664 ±.0496 I T.A. !l87 -1- =;2J.=>=b O^6l 14. S — .5909 dr. O6l6 Q SO Tbi— Tip- Line 139 r^ I O6 + .8665 ±.0529 + .42O^± O^Q 16.4 7 7O ins +.3588 ±.0374 + 9721 i OO2I 9-59 /l =7 ^ — S^lSztO^Q IO 2 I O6 + =,707=1= 042^ me + -lf\A(\ -\- (TZ7C 10 9 -U 20^8 -+- OSSS -? 71 rbi — rbp • Line 143 r^ 221 -.1504 ±.0697 + .4^82=t Ol67 2.16 T T Q 420 +.6072 ±.0336 + 877 c _J_ OO7Q 18.1 I IO 2 — 4^T*± O^7S T i ce 221 + 7126=1= 0223 + c rofS-l- 02 10 21 6 + TQ1O-4- O128 - OQ rbi— rip. -.2744 ±.0429 6.40 +.35i9±.0253 13-9 The correlation between the total number of bundles and the number of: primary double bundles is in general much lower. In line 98 the coefficient I actually has the negative sign in the trimerous series. The differences between the correlation coefficients for total bundles and intercalary bundles, and for total bundles and primary double bundles, range from —.27 to +.87 in the trimerous plants and from +.23 to +.61 in the dimerous plants/ It is clear that the two types of plants differ rather fundamentally in this' correlation. The correlation between the total bundles and the primary, double bundles is very low in the trimerous plants. It is a much more: substantial value in the dimerous plants. Pursuing this point one step farther, we may determine by a special formula the relationship between the total number of bundles and the deviation of the number of intercalary bundles from the number which would be expected if the number of primary double bundles and intercalary, bundles were in proportion to the total number of bundles formed. Determining the correlation between the total number of bundles, b, .. 1921] HARRIS AND OTHERS — PHASEOLUS VULGARIS 431 :nd the deviation of the number of intercalary bundles, i, from their prob- ble value by the formula5 where s = i — --b, b Ire have the values given in table 3. LIABLE 3. Correlation between Total Bundles at Base of Hypocotyl and Deviation of Number of Intercalary Bundles from Their Probable Number Trimerous Dimerous Diff N ' r Bf N r r R, Uirrerence -ftdiff. 75 93 98 139 H3 142 155 183 1 06 221 .7643 ±.0235 .6787 ±.0292 .7944±.oi84 .4066 ±.0546 .3841 ±.0386 32.5 23-2 43-2 7-45 9-95 142 155 183 305 420 .8si3±.oi56 .6693 ±.0299 .8433 ±.0144 .9701 ±.0023 .85io±.oo9O 54-6 22.4 58-6 421.8 94.6 — .0870 ±.0283 + .0094 ±.04 1 2 — .0489 ±.0224 -.5636 ±0.540 — .4669 ±03.96 3-07 O.22 2.18 10.3 11.8 The coefficients are positive and high, and very consistent for the two :ypes of seedlings. They show that within one morphological type of seedling6 an increase in the total number of bundles is primarily due to the formation of intercalary bundles, rather than to variation in the number of primary double bundles, although both types of bundles contribute to the end result. SUMMARY An investigation of the interrelationship of the numbers of primary double bundles, intercalary bundles, and total bundles (primary double bundles plus intercalary bundles) at the base of the hypocotyl in dimerous and trimerous seedlings of Phaseohis vulgaris leads to the following results: i. In the trimerous seedlings there is a negative correlation of about ;medium value (r = — .5 ±) between the number of primary double bundles and the number of intercalary bundles. Thus the number of intercalary 'bundles is smaller in seedlings with larger numbers of primary double bundles and vice versa. In dimerous seedlings the correlation is perhaps also negative in sign, but practically zero numerically. 6 Harris, ]. Arthur. The correlation between a variable and the deviation of a de pendent variable from its probable value. Biometrika 6: 438-443. 1909; also, Further illustrations of the applicability of a coefficient measuring the correlation between a variable and the deviation of a dependent variable from its probable value. Genetics 3: 328-352. 1918. 6 The differentiation of trimerous and dimerous seedlings has been shown to be due primarily to an increase in the number of primary double bundles. 432 AMERICAN JOURNAL OF BOTANY [Vol. 8. This result for seedlings of the same morphological type is suggestive in its relation to the results of a comparison of seedlings which are externally dimerous and trimerous, since in general trimerous seedlings show an increase in number of primary double bundles but a decrease in number of intercalary bundles as compared with dimerous seedlings. As a result of this numerical compensation, most conspicuously evident in the trimerous seedlings, the total number of bundles shows a lower variability than it would if the num bers of the two types of bundles were quite independent. 2. The correlation between the total number of bundles (primary double bundles plus intercalary bundles) and the number of intercalary bundles is high. The coefficients for the dimerous seedlings are somewhat higher than those for the trimerous seedlings. The correlation between the total number of bundles and the number of primary double bundles is generally much lower. The correlation between the total number of bundles and the deviation of the number of intercalary bundles from that which would be expected if they occurred in the same proportionate frequency throughout the entire range of total bundle number is positive in sign and substantial in magnitude. In both types of seedlings variation in the number of intercalary bundles is therefore an important factor in determining variation in the total number of bundles at the base of the hypocotyl. [Reprinted front the AMERICAN JOURNAL OF BOTANY, 2: 63-102. February, VASCULAR ANATOMY OF DIMEROUS AND TRIMEROUS SEEDLINGS OF PHASEOLUS VULGARIS ARTHUR HARRIS, EDMUND W. SINNOTT, JOHN Y. PENNYPACKER, AND G. B. DURHAM (Received for publication August 21, 1920) INTRODUCTORY The great majority of investigations dealing with the anatomy of lants have been purely descriptive in character. As a result of observation, he typical or average condition of plant structures has been recorded in erms which are general and often indefinite. Comparatively few morpho- ogical papers deal with the problem of the variation of the structures under -.onsideration, treat of their correlations with one another, or even present ;he detailed measurements which might serve for the solution of such funda mental morphological problems. The older comparative morphology is indispensable. It provides a general knowledge of plant structures and serves as a basis for the classi fication of the vegetable kingdom. The recognition that description must be supplemented by the results of experimentation has, however, led to the establishment of the newer special science of experimental morphology. The time has come to extend still further our study of plant form by calling to the service of vegetable morphology the methods of measurement and mathematical analysis. These methods are particularly useful in an attack upon the fundamental problems of morphogenesis. It is by measuring exactly the various plant structures during their successive stages of develop ment, in terms of size or number; by determining their relative variability in different organs or regions of the plant, or under varying external con ditions, and by discovering such correlations as exist, both among the structures themselves and between them and their progenitors and their environment, that we shall be able to build up a body of fact on which morphogenetic theory may rest. The present paper gives a portion of the results of a biometric analysis of a comparatively simple morphological problem, that of the gross vascular anatomy of certain normal and abnormal bean seedlings. Our purpose has been : 1. A study of the vascular anatomy of normal and of abnormal seedlings from the point of view of descriptive morphology — a preliminary which we believe to be essential to a sound interpretation of any statistical results. 2. A statistical study of the number and variation of the vascular elements in different regions of the seedling. 63 64 AMERICAN JOURNAL OF BOTANY [Vol. 8 3. An investigation of the correlations between these internal characters (such as those which exist between bundle number in different regions of the seedling) and between the internal characters and external features ol the plant. The results of the first and second phases of the investigation are set forth in the present paper; the third is reserved for a later publication. MATERIALS AND METHODS A priori considerations seemed to indicate that a promising line of attack upon the general field of quantitative plant morphology lay in the] investigation of vascular bundle number. Such an investigation should be on a scale sufficiently large to make possible the determination of trust worthy biometric constants, and should have as its subject a plant organ of relatively simple but variable structure. Because of the ease with which they can be grown in quantity, their sharply marked external characteristics; their convenient size for histological work, and their relatively simple j internal structure, seedlings of Phaseolus vulgaris furnish highly satisfactory] material for a study of variation and correlation in vascular structures. Among the many types of variant seedlings of the garden beans which i may be secured by extensive plantings, two were selected for investigation: (a) normal (dimerous] seedlings, with two cotyledons and two primordial leaves, and (b) trimerous seedlings, with three cotyledons and three pri mordial leaves. For brevity in table headings the dimerous plants will? sometimes be represented by "2-2" and the trimerous by "3-3," where the first figure gives the number of cotyledons and the second the number of primordial leaves. Since one of the purposes of this work is to carry out a comparison of bundle number in normal and teratological seedlings, the selection of a satisfactory control series of normal plants is a matter of primary impor tance. It is essential that the seedlings of the types to be compared be selected in a manner to reduce to a minimum any external influences tending to bring about differences between them. It is clear that if the abnormal and the normal seedlings were taken from different series of parent plants, either genetic differences or environmental influences acting upon the parent ~ plant might be effective in bringing about a differentiation in the characters of the seedling examined. A normal seedling from the same parent was, therefore, taken for comparison with each abnormal seedling1 in each series in which the seed was derived from individual parent plants. Closer, control of the influence of innate differences in the parents and of the possible influence of parental environment hardly seems practicable since the 1 In the vast majority of the cases one abnormal seedling only was sectioned from a parent plant. When more than one abnormal seedling was available a control was taken for each. Naturally it is immaterial whether control a or b be compared with abnormal seedling A or B, since all are siblings. eb., 1921] HARRIS AND OTHERS — SEEDLINGS OF PHASEOLUS 65 >airs of abnormal and normal seedlings were, in three of the lines investi- ated, derived from the same parent plant. Furthermore, care was taken that seedlings compared were grown inder essentially identical conditions, in order to reduce to a minimum the nvironmental influences which might possibly tend to bring about dif- rences between them. Seeds from individual plants were germinated n flats and harvested as soon as possible after they broke through the sand. Thus all seeds not only developed under the same parental environment but vere germinated under sensibly identical conditions, were collected simul- ;aneously, anjd were in consequence sectioned at essentially the same stage )f maturity. Because of the rapidity with which seedlings change and the great nfluence of temperature upon growth, it is difficult to standardize, or exactly :o describe, the stage of development at which the seedlings were taken. Most of them were placed in alcohol before or very soon after the primordial eaves had unfolded. Thus a fairly uniform and early stage of development was secured.2 Free-hand sections were cut and mounted temporarily. When neces sary, phloroglucin and hydrochloric acid were used to bring out the vascular bundles. The general vascular topography of the seedlings was studied, but the data for the statistical analysis of the seedling anatomy were derived from a careful count of the number of vascular bundles at various levels in the seedling. Because of a certain amount of variation in the number of bundles with position in the organ, counts were made in definite regions only — the basal region of the hypocotyl (just at the point of tran sition from "root structure" to "stem structure"); the median region of the hypocotyl; and the median region of the epicotyl. In three series counts were also made of the protoxylem poles in the upper portion of the primary root. The number of data available for the several regions differs because of a change in the plan of the work. Sectioning and counting were begun by two of us at Cold Spring Harbor in the summer of 1917 and continued with the assistance of Miss Eunice Kinnear in the summer of 1918. This work was confined to the mid-regions of the hypocotyl and epicotyl. From a statistical study of these data it seemed desirable to have a further series of countings made independently by a specialist in vascular anatomy. The work was, therefore, continued at Storrs during 1918, 1919, and 1920. We are greatly indebted to Miss Flora Miller for assistance in this phase of the work. At Storrs, sections were made at the base of the hypocotyl as well as in the mid-region of hypocotyl and epicotyl. In three series, sections were made of the root as well. The bundles vary considerably in size, the largest being well developed 2 Some of the seedlings of line 143 were allowed to become a little older, but there is no evidence of change in bundle number with age: 66 AMERICAN JOURNAL OF BOTANY and the smallest containing only one or two lignified xylem cells and a small patch of phloem. Some are even more reduced, consisting of a phloem patch alone. Any strand in which at least one well lignified xylem element could be made out was counted as a bundle. Some of the bundles are partially double in character, this condition being due either to partial fusion or to incipient division. Whenever such a strand was surrounded by one bundle sheath it was counted as one bundle; when the separation was so great that the bundle sheath itself showed signs of division, the strand was counted as two. The seedlings were harvested at a stage when the vascular tissues of the first epicotyledonary internode were not completely lignified, and the number of bundles counted was therefore possibly less than the number which would finally be developed there. None of these possible sources of error is believed to be great enough to affect the conclusions appreciably. THE STRUCTURE OF THE SEEDLING In order to provide a sound basis for the understanding and inter pretation of our later work, it is necessary to present a brief descriptive account of the structure of the seedlings. The Normal (Dimerous) Seedling The morphology of the seedling of Phaseolus has received the attention of several investigators, notably Dodel3 and Compton.4 Like most of the large seedlings of the Leguminosae it is normally tetrarch in fundamental plan; that is, there are four groups of protoxylem elements in the root. At a very early stage there is associated with each of these a group of metaxylem cells. It is these groups of metaxylem elements, throughout the whole seedling, which in the present paper are counted as "bundles," even though (as is sometimes the case) they are not associated with protoxylem clusters. At the stage when these seedlings were harvested, cambial activity had hardly begun to show itself, so that these primary bundles remained distinct and easy to identify. The condition in the upper part of the root of a normal seedling is shown in figure I. The four bundles, two in the cotyledonary plane and two in the intercotyledonary plane, are more or less V-shaped (with the protoxylem group in an exarch position at the apex of the V) and tend to extend laterally. They surround a large pith. In passing up into the base of the hypocotyl, each of these bundles divides into two (fig. 2), and typical stem structure, 3 Dodel. A. Der Ubergang des Dicotyledonen-stengels in die Pfahl-wurzel. Pringsh. Jahrb. 8: 149-193. 1872. 4 Compton, R. H. An investigation of the seedling structure in the Leguminosae. Jour. Linn. Soc. 41: 7-122. 1912. FJ., 1921] HARRIS AND OTHERS — SEEDLINGS OF PHASEOLUS 67 fo'th the protoxylem in an endarch position, begins to be assumed. Each pir is subsequently referred to as a "primary double bundle." Thus the li/el of transition from root structure to stem structure is low, being prac- FIG. I. Dimerous seedling. Transverse section through the root, showing its trarch condition (four protoxylem poles). FIG. 2. Dimerous seedling. Transverse s:tion through the base of the hypocotyl showing the four primary double bundles, each c which has been derived from one of the four root strands. FIG. 3. Dimerous seedling, "ansverse section through the mid-region of the hypocotyl showing the normal eight- tndled condition. No intercalary bundles are figured. FIG. 4. Dimerous seedling. 1'ansverse section just below the cotyledonary node. The four bundles or bundle groups tve originated by a more or less complete fusion of the adjacent members of each of the ciginal pairs. Each bundle, as shown by the two constrictions in it, is about to break up i;o the three strands shown in figure 5. FIG. 5. Dimerous seedling. Transverse section trough the cotyledonary node. Each group of three strands which have arisen by a leaking up of the large bundles in figure 4 is here enclosed by a dotted line. These three e'ands are a cotyledonary trace (solid black), an epicotyledonary bundle, and a small hndle which will fuse with its adjacent neighbor to form another epicotyledonary bundle. ?;G. 6. Dimerous seedling. Transverse section through the mid-region of the epicotyl sowing the twelve bundles which have arisen by the splitting of the six original epicoty- llonary bundles. The six strands which are to go off as traces to the two primordial lives are solid black. cally at the base of the hypocotyl. The members of each of these four ]iirs soon separate until the eight bundles are approximately equidistant ig. 3), a condition which persists throughout the hypocotyl until the coty- donary node is approached. In addition to these bundles, there are in a considerable percentage of le normal seedlings studied a variable number of accessory or intercalary undies, the "Zwischenstrange" of Dodel. These may make their appear- 68 AMERICAN JOURNAL OF BOTANY [Vol.' If ance in the upper part of the root or in the lower region of the hypocotyl, some ending blindly below and others arising by division of the primary bundles. These intercalary bundles, which are not a very common feature of seedling anatomy in general, perhaps serve to increase the conductive capacity of the hypocotyl and may be associated with the large size of the seedling. They usually lack protoxylem elements. At the cotyledonary node there is a rather complex anastomosis of the bundle system. The details of this vary somewhat, but its fundamental features are as follows: The two members of each of the two original pairs of bundles in the cotyledonary plane (that is, opposite the two points where the cotyledons will later arise) become widely separated, and each member fuses with the adjacent member of the intercotyledonary pair (fig. 4). Four large bundles or bundle aggregates are thus produced. Each breaks up immediately, usually into three parts. The lateral member of each group of three which is in the cotyledonary plane approaches the corresponding bundle of the next group of three, and these two strands become the coty ledonary traces and enter the base of the cotyledon. The lateral member of each group of three which is in the intercotyledonary plane approaches the corresponding bundle of the next group and fuses with it. The changes which are made and the resultant condition at this stage are shown in figure 5. Two strands (solid black) are here departing to each cotyledon, and six bundles are left as the basis for the vascular system of the epicotyl. The details of this nodal complex vary somewhat owing to the different levels at which fusion and separation of bundles take place, and to the presence of intercalary bundles. These intercalary bundles, as they ap proach the cotyledonary node, fuse with the others and are completely lost, exactly six epicotyledonary strands almost invariably emerging from the complex, quite regardless of the number of intercalary bundles which may have entered it from the hypocotyl. This fact we shall find to be of im portance when we consider the statistical relationships of bundle numbei in hypocotyl and epicotyl. Above the cotyledons, the six remaining bundles approach one another closing the cotyledonary gaps and forming a ring, the members of which almost immediately divide. The twelve bundles thus produced (fig. 6} persist throughout the first internode of the epicotyl. At the first node of the epicotyl are inserted the two primordial leav< Phaseolus, like other Leguminosae which have been investigated, possesse- a trilacunar node, the leaf being supplied by three traces, each of whicl causes a separate gap in the vascular ring.5 The two primary leaves there' fore remove six of the twelve bundles of the epicotyl (solid black in fig. 6) The six new bundles which appear just above the cotyledonary node are therefore, evidently downwardly extending leaf traces. These facts mak» 6 Sinnott, E. W. The anatomy of the node as an aid in the classification of Angio sperms. Amer. Jour. Bot. i: 303-322. 1914. feb., 1921] HARRIS AND OTHERS — SEEDLINGS OF PHASEOLUS 69 jnderstandable the almost invariably twelve-bundled condition of the lirst epicotyledonary internode. The structure of the normal seedling thus corresponds to the type found oy one of the writers6 to be characteristic of a large number of Angiosperm families, in which the vascular supply to each cotyledon, consisting of two strands, leaves but one gap in the vascular ring; and in which the foliage *eaf is trilacunar. The Trimerous Seedling • The seedling with three cotyledons and three primordial leaves is built on different plan from the normal one in that it is prevailingly hexarch, six FIG. 7. Trimerous seedling. Transverse section through the root, showing its ;hexarch condition. FIG. 8. Trimerous seedling. Transverse section through the base :of the hypocotyl, showing the six primary double bundles. FIG. 9. Trimerous seed ling. Transverse section through the mid-region of the hypocotyl, showing the nor mal twelve-bundled condition. FIG. 10. Trimerous seedling. Transverse section just below the cotyledonary node. The six bundles or bundle groups correspond in origin and character to the four bundles of the dimerous seedling at this level. FIG. II. Trimerous seedling. Transverse section through the cotyledonary node. Each group of three strands bounded by a dotted line corresponds in origin and character to a similar group at this level in the dimerous seedling. FIG. 12. Trimerous seedling. Transverse section through the mid-region of the epicotyl, showing the eighteen bundles which have arisen by the splitting of the nine original epicotyledonary bundles. The nine strands which are to go off as traces to the three primordial leaves are solid black. 6 Sinnott, E. W. Conservatism and variability in the seedling of dicotyledons. Amer. Jour. Bot. 5: 120-130. 1918. 70 AMERICAN JOURNAL OF BOTANY Vol. 8 bundles occurring in the upper part of the root (fig. 7). This number is soon reduced to five and eventually to four, in passing down the root. Passing upward into the hypocotyl, the six main strands (the primary double bundles) divide to produce twelve (figs. 8 and 9). Intercalary bundles are much less common than in the normal seedlings, appearing in only a small percentage of cases, and then being rarely more than one cm two in number. At the node the same general procedure is followed as im the normal seedling, except, of course, that there are more bundles concerned. Bundles of adjacent pairs approach and fuse (fig. 10). Each of these bundles or bundle aggregates then divides, generally into three. Three cotyledons are each supplied with two bundles (solid black), and three sets of three bundles each — each formed by the fusion of two lateral bundles in the intercotyledonary plane — remain behind. The bundle changes and the final condition at the departure of the cotyledonary traces are shown in figure 1 1 . The epicotyledonary ring which forms from the bundles which remain thus consists of nine strands instead of the normal six. Many of these divide at once, although the number is not usually doubled, as in normal seedlings, but varies from 12 to 1 8 or even more in the mid-region of the epicotyl (fig. 12). The bundles are much more crowded than in the normal seedlings, which may perhaps account for the failure of some of them to divide at once. A study of the first epicotyledonary node shows that three strands are given off to each primary leaf, leaving from 6 to 9 in the stem. It is therefore evident that within classes of seedlings which are uniform externally there are considerable anatomical variations and that the two classes investigated are profoundly differentiated in their anatomical organi zation. Our next task is to subject the mass of data upon which these general conclusions are based to a statistical analysis with the object of bringing out otherwise undeterminable relationships. BUNDLE NUMBER AND ITS VARIATION AT DIFFERENT LEVELS IN THE SEEDLINGS From the statistical side we have two problems to consider. The first is that of the relative numbers of bundles at different levels, i.e.t in the root, at the base of the hypocotyl, in the central region of the hypo cotyl, and in the epicotyl of the same plant in both normal and abnormal plants, together with the variability in bundle number in different regions. The second is that of the differences in bundle number, and in variation of bundle number, between normal and abnormal plants. Since it is impossible to consider type and variation of bundle number at different levels without noting differences in the trimerous and dimerous forms upon which the observations were based, we shall devote this section primarily to a parallel discussion of both problems. *.. IQ«] HARRIS AND OTHERS — SEEDLINGS OF PHASEOLUS JI \Ye shall consider in order the levels at which sections were made, begin- ing at the root. i. Root. Roots were sectioned in the cases of lines 93, 139, and 143. "he numbers of bundles7 in the roots of normal and trimerous seedlings of lines are shown in table I . TABLE i r " i" Lac - L« .39 Line 143 I-.: i £..-: -« - - - -- .- '_ - f _; . - ~ -.- : - • Dmeroos . • ~ - ~ _5 I ----: -5 ; _ 2 4 \. 31 '- 152 2O 15 - '- 149 37 i "3 219 2 6 34 36 — 66 — 7 — — i — The entries in this table show that most of the normal plants are tetrarch, Ithough a small percentage are pentarch. In the trimerous seedlings the ighest percentage are pentarch. but the remainder are distributed between etrarch and hexarch with a few in more extreme classes. Sections made at •ogressively lower levels in the root show that the hexarch and pentarch auditions, in the trimerous seedlings, soon give way to tetrarch. This act doubtless explains the relatively large number of non-hexarch cases CABLE 2. Vascular formula for base of kypocotyl of trimerous seedlings and their normal controls L-c^ L-rw L-e* L»e 139 Lnc 143 ri-, .-' -I -- . : :;. _--.-. ; - tr- - — --. : --:• : - ---- ; -.- j Trimer- Dwer- IT-.,: D»er- .- -• OUi ; _ - . ; - \ » 69 — 34 — 97 — :•- 2 150 _ — : 30 — 37 — 43 i 9 3 55 .i — : IO — 13 — 23 — — — 4 _ — - 4 — 5 — 2 — — — — _: — _ 2 i i — — — — - — . — - 2 — — i — — — — — I — — - — - — — — — I 13 5 22 4 6 4 i 15 5 = — : 8 4 10 18 6 - 4 2 31 5 K- 2 I 3 9 i i — — — — :- — i — I — I — — — — 107 : I2O IO 1 60 I 92 — *34 — I 12 i II 3 IO — 5 — • 25 i : 2 — I 2 — — — — — — ~ - — 4 — i — — — 5 i 7 — : — — • — — — — — — 4 — - I — — — — — — — — — -,8) I — — — — — — — i — • - : — — — — — i — — I — 142 142 J55 J55 183 183 106 : ; 221 221 7 Where the bundles were united in a ring, the number refers to number of protoxylem r.n-- = 72 AMERICAN JOURNAL OF BOTANY [Vol. 8 observed, for the zone within which the hexarch condition persists is narrow and its level is variable ; and there is necessarily more or less variation in the level at which the sections are cut. 2. Base of Hypocotyl. In the series of sections of the base of the hypo- cotyl made at Storrs, the number of double vascular strands (each of which is derived from a primary root bundle and corresponds to a pole of the root) and the number of intercalary strands were recorded separately. There is no difficulty in distinguishing between these two categories of bundles, since the latter are almost invariably without protoxylem elements and are irregularly placed. The original data for the five lines are condensed in table 2. The number of bundle pairs (the primary double bundles) is given in parenthesis, and the number of intercalary bundles, if such are present, follows the + sign outside the parenthesis. There are three outstanding features in this table. First, the wide range of variation in the number and in the combinations of primary double bundles and intercalary bundles in both normal and abnormal plants observed when reasonably large series of seedlings are sectioned. It is clear that an anatomist who deals with only a few seedlings may obtain an altogether inadequate picture of the conditions which actually prevail in the species under investigation. Second, notwithstanding the wide range of variation there are conspi cuous modal classes in both normal and abnormal seedlings. In the normal plants these fall in all cases on four primary double bundles, without intercalary bundles, or with but one intercalary bundle; and in the trimerous plants, on six primary double bundles without intercalary bundles. Third, the plants which are externally dimerous and trimerous are also clearly differentiated in internal morphology. The internal characters are, however, transgressive. It is impossible in some cases to distinguish from sections of the hypocotyl base alone between plants which superficially fall into the strictly alternative classes of dimery and trimery. For purposes of more detailed analysis these formulae must be split up into their component elements. A . Primary Double Bundles. The distribution of the number of primary double bundles in the five lines considered is shown in table 3 for dimerous and trimerous seedlings. These frequencies, reduced to a percentage basis, are represented graphically in figure 13. This shows that in all five lines the modal number of primary double bundles is two higher in the trimerous than in the dimerous plants. In the dimerous plants the modal class is in all cases 4; in the trimerous seedlings the modal class is 6. There is, there fore, a profound reorganization in the vascular anatomy of the seedling upon the assumption of a trimerous external organization. Limiting our attention to primary double bundles and judging from modal classes only, an increase of fifty percent in the number of vascular elements is Pel 1921] HARRIS AND OTHERS — SEEDLINGS OF PHA5EOLUS 73 ^E 3. dumber of primary double bundles at base of hypocotyl in trimerous and dimerous seedlings 4 3 6 7 - ~ '-- Lii 75 Trimerous . l-.i.J i II 121 I 142 Percent .... 0.70 7-75 -= :: 5.63 0.70 Dimerous 117 19 6 — — 142 Percent 82.39 I3-38 4-23 Lii 93 Trimerous . . . i 18 I32 4 rr Percent 0.65 11.61 85.16 : --- Dimerous .... 90 50 15 — — :- Percent .... 58.06 32.26 9.68 Lii 98 Trimerous i II 170 i 183 Percent 0.55 6.01 92.90 °-55 Dimerous I 165 16 I :r: Percent .... 90.16 8-74 0-55 0-55 U; 139 Trimerous i 8 97 — 106 Percent 0.94 7-55 9I-51 Dimerous . . i 147 3 — 150 Percent 98.00 2.OO Li-1 143 Trimerous 46 159 9 2 221 Percent 2.26 20.81 71.94 4.07 O.9O Dimerous i 209 10 i I — 221 Percent 94. S7 4.52 °-45 °-45 LINE 75 j. 11 \r. L/Af£ 93 LIME \ \ 98 * i _ '. - : -~ Z/l^t /*3 1 li 11 , 111 Inlll/M 1 1 v n mil *__L__1__I * 4 £ £ ~ 4 f c j . •* ^" e -t 5 * FIG. ivv Pea-em Jv^ faniuenoy distribution for number of prinvir\- double bundles at be of hypocotyl in dimoa>u# v.s».->li<.i dot^ and trimerous 74 AMERICAN JOURNAL OF BOTANY [Vol. associated with an increase of fifty percent in the number of cotyledons anc leaves. The distributions show, however, that this is only an incomplete and to some extent an erroneous, statement of the condition. In th< dimerous seedlings the modal number of primary double bundles is 4, and al departures from the modal number are higher. In the trimerous seedling! the modal number is 6, and the departures may be in either the positive 01 the negative direction. The frequency distribution for the dimerous plantf is therefore wholly skew, forming a typical J-curve; that for the trimerom plants more or less symmetrical,8 but with departures occurring chiefly a; smaller numbers of bundles. The variation of primary double bundle number in dimerous and trim erous plants is, therefore, transgressive. The number of externally dimerous seedlings which might be considered to be anatomically trimerous, and tin number of trimerous seedlings which might on anatomical grounds b( considered dimerous is, however, very small. Turning to the physical constants in table 4, we note that the meat TABLE 4. Statistical constants for number of primary double bundles at base of hypocotyl 0j trimerous plants and their normal controls Mean Standard Devi ation Coefficient of Vari ation Line 75 Trimerous (N = 142) 5.Q8±.O2 0.436-!-- 017 7.28=fc 2Q Dimerous (N = 142) 1 1 Q7 rfc 4Q _ .5 0 Actual difference -[-1.76-)- 04 — O 069 =b O26 — 4 6Q =t ^6 Relative difference 41.71 n.66 Line 93 Trimerous (N = 155) 5-9O=b 02 o 396± 015 6 72 =b 26 Dimerous (N = 155). 4.S2=fc 04 o 666 ± 026 14 74=t ^8 Actual difference . . . + 1 ^8=t 04 — O 2"O=fc O^O —8 02 ±.63 Relative difference . . ,o _- 4O S4 Line 98 Trimerous (N = 183) 5.93=1= 01 O 288 =b OIO 4 86 =b 17 Dimerous (N = 183) 4.I2=h.O2 O.427±.OI S O Jl Actual difference . . . +i.8i± 02 — o I39± 018 ~5 50^-41 Relative difference . . 4.7 Q7 -J2 SS Line 139 Trimerous (N = 106) . . 1 5 91 ± 02 o 323=t 015 c 17 4- 25 Dimerous (N = 150) 4 o"7 =fc 01 o 140=1= 005 1 j.8± 14 Actual difference . . . +1.89=1= 02 -f-o i83=t 016 + 1 Q9d=: 28 Relative difference . . 47 OI I -3Q 7 I Line 143 Trimerous (N = 22l) j 5.81 rb 03 O 581 zfc OI9 IO OI rb 32 Dimerous (N = 22l) . i 4 07 it OI o 315=1= oio 7 yc -4- 2$ Actual difference . . . + 1 74± 01 + O 266± O2I + 2 26± 41 Relative difference . . 42.75 84.44 8 Line 139 is probably only an apparent exception to this rule. In both dimerous an trimerous seedlings variations from the modal class are extremely rare, and variation above the modal class have not been found in the 106 trimerous seedlings of this lin sectioned. eb., 1921] HARRIS AND OTHERS — SEEDLINGS OF PHASEOLUS 75 umber of primary double bundles at the base of the hypocotyl of trimerous -lants is from 1.38 to 1.89 higher than in the dimerous controls. This epresents an excess of from 30.5 to 47.0 percent. The five lines are not, however, consistent in the relative variability of ; "he normal and abnormal seedlings. The standard deviation of the number of primary double bundles in the rimerous plants is lower than that in the dimerous plants in lines 75, 93, nd 98. The differences are from 13.7 to 40.5 percent of the control values. >ines 139 and 143 are in contrast to the foregoing. The trimerous plants ,1 line 139 have a standard deviation of 0.323 ± .015 bundles, whereas the limerous controls have a standard deviation of 0.140 ± .005, giving a lifference of +.183 ± .016, which is 11.4 times as large as its probable error, n line 143 the trimerous plants have a standard deviation of 0.581 ± .019 mndles as compared- with 0.315 ± .010 bundles in the normal controls, jiving a difference of +.266 ± .021, which is 12.7 times as large as its >robable error. These are relative differences of +130.7 percent for line 39 and + 84.4 percent for line 143. The same differences in variability between the lines is also conspic- lous in the relative variabilities as measured by the coefficients of varia- :ion. In the first three lines (75, 93, and 98) the coefficients of varia- ;ion in the trimerous plants range from 4.9 to 7.3 percent as compared with 10.4 to 14.7 percent in the dimerous controls, giving differences in relative FABLE 5. Number of intercalary bundles at base of hypocotyl in trimerous and dimerous seedlings 0 i 2 3 4 5 6 Total Line 75 Trimerous 116 20 5 I 142 Percent 81.69 14.08 ^.52 O.7O Dimerous . 87 ^5 n 5 2 2 14.2 Percent 61.27 2J..6S 7.75 7 C2 1. 41 1. 41 Line 93 Trimerous 129 21 4 I IS5 Percent 83 23 I? CC 2 58 o.6s Dimerous 66 58 24 6 I ISS Percent 42-58 ^7.42 15.48 •?.87 0.65 Line 98 Trimerous. . . . 165 16 T I 181 Percent 90.16 8.74 O SS O.55 Dimerous . 104 S.2 24. - 181 Percent 56 83 28 42 I'* 1 1 i 6j. Line 139 Trimerous 96 IO 1 06 Percent. . QO.57 q.j.7 Dimerous . . i^q 1 1 . . ISO Percent. . . 92.67 7.T.1, Line 143 Trimerous . . 157 64 221 Percent. . 7LO4 28.95 Dimerous .... 156 6l 4 221 Percent i 70.58 27.60 i. 80 AMERICAN JOURNAL OF BOTANY [Vol. 8 variability ranging from -4.7 to -8.0 percent. In line 139 the coefficient of variation for trimerous seedlings is 5.47, whereas that for dimerous seedlings is 3.48. In line 143, the coefficient of variation for trimerous seedlings is 10.01, whereas that for dimerous seedlings is 7.75. Thus the relative variability in these two lines is greater in the trimerous than in the dimerous seedlings. B. Intercalary Bundles. The distribution of the number of intercalary bundles (considered alone) in the base of the hypocotyl is shown in table 5. LM£ 15 L///E33 FIG. 14. Percentage frequency distribution of number of intercalary bundles at base of hypocotyl in dimerous (solid dots) and trimerous (circles) seedlings. The graphs in figure 14 show that for both dimerous and trimerous seedlings no intercalary bundles is the modal condition. In both cases the distribution is wholly skew. The normal and the abnormal seedlings of lines 75, 93, and 98 differ conspicuously, however, in that the percentage of seedlings with no intercalary bundles is much higher in the trimerous seedlings, while, conversely, the percentage of seedlings with from I to intercalary bundles is much higher in the dimerous plants. These ferences are not found in lines 139 and 143. As a matter of fact, the per centage of seedlings with no intercalary bundles is slightly, but perhaps nc significantly, higher in the dimerous seedlings of line 139. In both line 139 and 143 the number of seedlings with i or 2 intercalary bundles is very small indeed in both trimerous and dimerous series. The two lines are essentially alike in this regard and line 143 only is represented on the diagram. eb., 1921] HARRIS AND OTHERS — SEEDLINGS OF PHASEOLUS 77 The percentages of the seedlings with no intercalary bundles in the two ilasses of plants and the differences in the percentage are as follows : Tritnerous Dimerous Difference ine 7^ 81.69 61.27 + 2O.42 inp Q"? 83.23 42.58 +40-65 ine 98 9O.I6 56.83 +33-33 inp I ^Q 90.57 92.67 — 2.IO .ine 143 71.04 70.58 + 0.46 The physical constants in table 6 show that the mean number of inter- alary bundles in both normal and abnormal seedlings is small — less than a single bundle per plant in every case. TABLE 6. Statistical constants for number of intercalary bundles at base of hypocotyl of trimerous plants and their normal controls Mean Standard Deviation Coefficient of Variation Line 75 Trimerous (N = 142) . .25 ±.04 0.686±.027 270.69 ±42. 86 Dinierous (N — •*y 142) .63±.o6 I.024±.04I i6i.6o±i6.i3 Actual difference -.38 ±.07 — 0.338 ±.049 + 109.09 ±45.79 Relative difference 60.32 33-OO Line 93 ice) .21 ±.O3 .545 ±.02 1 255.8o±36.78 Dimerous (^ = I«) .83 ±.05 .874±.033 105.79 ± 7-29 Actual difference — .62±.o6 - .329 ±.039 + 150.01 ±37.50 Relative difference 74-69 37-64 Line 98 Trimerous (N — 181) .I3±.O2 •48o±.oi7 38i.67±73.88 Dimerous (N^ = 183) .60 ±.04 .776±.027 I30. 21 ± 9.62 , Actual difference — .47 ±.04 — .296 ±.032 +25i.46±74.50 Relative difference 78. w 38.14 Line 139 Trimerous (N — 106) .O9±.O2 .292 ±.014 30Q.84±64.50 Dimerous (N = mo). . .07±.oi .261 ±.oio 355.48 ±70.95 Actual difference + .O2±.O2 + .031 ±.017 - 45.64±95.89 Relative difference 28.57 u.88 Line 143 Trimerous (N — 221) . . . .29 ±.02 •454±.oi5 I56.62±I2.2I Dimerous (N = 221) • 3I±.O2 •5oi±.oi6 i6o.44±i2.76 Actual difference — .02 ±.O3 — .047 ±.02 1 - 3.82±i7.66 Relative difference . . 6-45 9-38 Again the lines fall into two classes, those in which the number of inter calary bundles is conspicuously higher in the dimerous plants (lines 75, 93, and 98) and those in which the numbers are essentially identical (lines 139 and 143). In the trimerous seedlings of the first group the average number ranges from 0.13 to 0.25, whereas in the dimerous it varies from 0.60 to 0.83 bundle. Thus the mean number of intercalary bundles is 78 AMERICAN JOURNAL OF BOTANY [Vol. | from 60 to 78 percent smaller in the trimerous than in the dimerous seedlings. In line 139 the mean number of intercalary bundles is actually larger in the trimerous seedlings, but the difference is only +-O2 ± .02. In line 143 the mean number of intercalary bundles in trimerous and dimerous seedlings is practically identical, the difference being only —.02 ± .03. In both of these lines the differences are insignificant in comparison with their probable errors. It is also interesting to note that in lines 75, 93, and 98 the differentia tion between abnormal and normal seedlings is greater with respect to the number of intercalary bundles than with respect to primary double bundles. Turning back to table 4, we note that the number of primary double bundles is from 31 to 44 percent higher in the trimerous plants, whereas the number of intercalary bundles is from 60 to 78 percent lower. In lines 139 and 143 the difference in the mean of the number of primary double bundles of trimerous and dimerous plants is practically the same as in the other lines, but in these lines the two types of seedlings are essentially identical in number of intercalary bundles. If we consider the comparative variability of dimerous and trimerous seedlings as to intercalary bundle number, we find that here, as in the case of number of primary double bundles, the lines differ among themselves. In all lines except 139 the standard deviations of number of intercalary bundles in the trimerous seedlings are smaller than in the dimerous. In lines 75, 93, and 98 the constants for the trimerous seedlings are from 33 to 38 percent smaller than those of the dimerous controls. In line 143 the difference has the same sign but is only —9.38 percent of the control value. In line 139 the difference is -}- n.88 percent. The coefficients of variation are very high in both normal and abnormal seedlings, and this great variation renders the probable errors of little value as criteria of statistical significance of differences between the two types • of seedlings. In lines 75, 93, and 98, the coefficients of variation for tri merous plants are conspicuously higher than those for the dimerous controls. In line 143 the coefficients of variation for the two types of seedlings are practically the same. In line 139, however, the coefficient of variation for the number of intercalary bundles is higher in dimerous than in trimerous plants. C. Total Bundles. Having considered the frequency distribution and ' statistical constants for the two types of vascular structures found in the base of the hypocotyl, it is now desirable to combine the two types of bundles in order to consider the total number of vascular elements at this level. This problem presents certain morphological difficulties. The primary double bundles are each derived from a single root pole, and do not become clearly divided into two bundles until the level of transition is reached from root structure to stem structure at the base of the hypocotyl. Many of the intercalary bundles appear at this level or a little lower. In determining j., 1921] HARRIS AND OTHERS — SEEDLINGS OF PHASEOLUS 79 "ABLE 7. Total number of bundles at base of hypocotyl in trimerous and dimerous seedlings. Primary double bundles are counted as one bundle only 4 5 6 7 8 9 10 Total :ne 75 Trimerous 115 21 3 I I 142 Percent O.7O 80.99 14.79 2. II 0.70 0.70 Dimerous . . . 69 43 19 6 3 2 142 Percent . . 48.59 "IO.28 13.38 4.23 2. II I.4I ne93 Trimerous 5 130 18 2 155 Percent 3.23 83.87 II. 61 1.29 Dimerous 34 59 41 17 4 155 Percent 21.94 38.06 26.45 10.97 2.58 ne 98 Trimerous 4 1 66 12 I 183 Percent 2.19 90.71 6.56 0.55 Dimerous 97 49 32 3 I I 183 Percent .... 53.OI 26.78 17-49 1.64 0.55 O.SS ine 139 Trimerous 5 96 5 I O6 Percent 4.72 90.57 4.72 Dimerous 138 10 2 , I5O Percent . .... 92.00 6.67 1.33 ine 143 Trimerous 2 18 165 30 5 I 221 Percent O.9O 8.14 74.66 13. 57 2.26 0.45 Dimerous ISO 60 9 2 221 Percent 67.87 27. IS 4O O.QI 75 LINE 93 FIG. 15. Percentage frequency distribution of total bundles at base of hypocotyl. Primary double bundles counted as single bundles. 8o AMERICAN JOURNAL OF BOTANY [Vol. 8 the total number of bundles at the base of the hypocotyl, it therefore becomes a question as to whether we should count each primary double bundle as a single strand or as a double strand; adding, of course, the number of intercalary bundles in each case. The distribution of total bundle number at this level according to the former method (primary double bundles counted as one, plus intercalaries) is shown in table 7, for both dimerous and trimerous seedlings. The results are shown clearly in figure 15. 9 The modal number is on 4 (lines 75> 98, 139, and 143) or 5 (line 93) bundles in the case of the dimerous seedlings, but invariably on 6 in the trimerous plantlets of the five lines. The distribution of number of bundles is almost wholly skew in the case of the normal seedlings, line 93 being slightly different from the others, but fairly symmetrical in the trimerous series. The constants given in table 8 show that on the average the trimerous plants have from 0.77 to 1.91 bundles more than the dimerous plants. This is an excess of from 14.4 to 46.7 percent instead of the 50 percent which one might expect if the increase in number of bundles were proportional to the number of cotyledons or primordial leaves. TABLE 8. Statistical constants for total number of bundles at base of hypocotyl of trimerous plants and their normal controls. Primary double bundles are counted as one bundle only Mean Standard Deviation Coefficient of Vari ation Line 75 Trimerous (N = 142) . . 6.23d=.O3 0.601 ±.024 Q 6Sdr 3Q Dimerous (N = *•+ y • 142) . 4. 85 ±. O6 i.o87± 044 22 4.1 -+- QJ. Actual difference . . . + I.38±.O7 — 0.486 ± 050 — 12 76d=I OI Relative difference. . 28. 4S 44 71 Line 93 Trimerous (N = 155) 6. 1 1 ±.O2 O.434d=.OI7 7 lodz 27 Dimerous (N = 155) S.34±.O6 I.OIQ±.O3Q IQ O7± 76 Actual difference . . . +o.77± 06 — O S8sd= O42 — II 97 d= 80 Relative difference. . 14. 4.1 S7.4I Line 98 Trimerous (N = 183) 6.o6=b.O2 o.36sd= on 6 02 ± 21 Dimerous (N = 183) . 4.72± OS O QOQzt O32 19 28± 70 Actual difference . . . + I.34db.OS — O.S44 db O3S — 11 26dr 1\ Relative difference. . 28.^9 en 8S Line 139 Trimerous (N = 106). . 6.ood= 02 O 3O7 -+- OT-i S 12 ± 24 Dimerous (N = 150) 4. 09 ±. 02 O.334dr Oil, 8 ISdz 32 Actual difference . . . + I.9I db 03 — o 027 ± 019 — -5 O3± 4O Relative difference. . 4.6 7O 8 08 Line 143 Trimerous (N = 22 1 ) 6.iod=.O3 o.6i3± 020 IQ O6dz -33 Dimerous (N = 22l) 4. 38 dr. 03 0.609 dr °2O 13 QI dz .4S Actual difference . . . + I-72d= 04 -)-O 004 d= O28 — 3 8Sd= S6 Relative difference. . 39.27 0.66 1 Lines 139 and 143 are in essential agreement with 75, 93, and 98, and are not drawn. b., 1921] HARRIS AND OTHERS — SEEDLINGS OF PHASEOLUS 8l The variability, both absolute and relative, of the number of bundles is gher in dimerous than in trimerous plants. It is conspicuously higher lines 75, 93, and 98. Thus the standard deviations for the trimerous ilants range from 0.37 to 0.60 in the three lines as compared with 0.91 to .09 in the dimerous controls. The relative differences show that the -ariability of the trimerous plants is from 45 to 60 percent less than that of he dimerous plants. In the case of line 143, however, the difference between the standard deviation of the two types of seedlings is very small- ess, indeed, than the probable error of the difference. Practically the ,ame condition is found in line 139. The coefficients of variation show that the trimerous plants have a /ariability in bundle number which is from 5.1 to 10.1 percent of the mean lumber of bundles, whereas the dimerous controls have a variability which s from 8.2 to 22.4 percent of the average number. In lines 75, 93, and 98 the difference between the two types is much more conspicuous than in lines '139 and 143. Since in practically all cases, however, the primary double bundles have already clearly become two strands at the point where the intercalaries appear, it probably gives us a better conception of total bundle number here to count each primary bundle as two, and to add thereto the number of intercalaries. The actual and the percentage distribution according to this method are shown in table 9. Lines 75, 93, and 139 are represented in TABLE 9. Total number of bundles at base of hypocotyl in trimerous and dimerous seedlings. Primary double bundles are counted as two 8 9 10 ii i 12 13 M 15 16 "7 Total Line 75 Trimerous . . — 2 8 109 12 10 I 142 Percent . . 1.41 5.63 76.76 8-45 7.04 0.70 Dimerous... 69 30 23 8 8 4 — — — 142 Percent..; 48.59 21.13 16.20 5.63 5.63 2.82 Line 93 Trimerous . . 5 10 124 n 5 — — — 155 Percent . . 3-23 6.45 80.00 7.10 3.23 Dimerous. . . 34 37 35 23 20 | 4 2 — — 155 Percent . . 21.93 23.87 22.58 14.84 12.90 2.58 1.29 Line 98 Trimerous . . i 4 6 161 10 I — — — 183 Percent . . 0-55 2.19 3.28 87.98 5.46 0-55 Dimerous. . . 97 ! 43 29 10 2 I _ I 183 Percent . . 53.01 23.50 15-85 546 1.09 0.55 0-55 Line 139 Trimerous . . — I 4 4 92 5 — — — — 106 Percent . . 0.94 3-77 3-77 86.79 4.72 Dimerous. . . | 138 9 I 2 — — — — 150 Percent . . 92.OO 6.00 0.67 1.33 Line 143 Trimerous . . 2 3 15 31 134 25 5 4 i I 221 Percent . . O.9O 1.36 6.79 14.03 60.63 11.31 2.26 1.81 0.45 0.45 Dimerous. . . 150 55 9 5 i i 221 Percent . . 67.87 24.89 4.07 2.26 0-45 0-45 82 AMERICAN JOURNAL OF BOTANY [Vol. 8 TABLE 10. Statistical constants for total number of bundles at base of hypocotyl of trimerotn plants and their normal controls. Primary double bundles are counted as two Mean Standard Deviation C^g^rf Line 75 Trimerous (N = 142) Dimerous (N = 142) . Actual difference Relative difference Line 93 Trimerous (N = 155) Dimerous (N = 155) . I2.I7±.04 9.07 ±. 08 0.750=13.030 1.351 ±.054 i4-90±.6i +3.io±.o8 34.18 I2.OIzb.O3 9.86±.o8 -0.601 ±.062 -8.73±.66 44-49 0.627 ±.024 5-22±.20 Actual difference +2.i5±.o8 -O.8s6±.o62 -9. Relative difference Line 98 Trimerous (N = 183) Dimerous (N = 183) . Actual difference Relative difference Line 139 Trimerous (N = 106) Dimerous (N = 150) . 21. 81 1 1. 97 ±.02 8.84±.o6 57-72 0.495 ±.018 9.82±.62 +3-i3±-o6 35-41 1 1.91 ±.04 8.II±.02 0.558 ±.026 Actual difference | +3.80^.04 Relative difference 46.85 Line 143 Trimerous (N = 221) ii-9O±.O5 Dimerous (N = 221) 8.45 ±.04 Actual difference. . Relative difference +3-45 ±-06 40.83 32.97 -0.695^3.046 -9. 58.40 4. 69 ±.22 5-43±-2i +o.ii8±.03i -o. 26.82 1. 105 ±.035 .831 ±.027 SO 80 70 60 r^ 40 30 20 '0 7S LIME 93 /O II 12 /3 14 /39 10 II /2 13 FIG. 16. Percentage frequency distribution of total bundles at base of hypocotyl in dimerous and trimerous seedlings. Primary double bundles counted as two. Ub., 1921] HARRIS AND OTHERS — SEEDLINGS OF PHASEOLUS Mjure 1 6. Comparison of these figures with those in figure 15 shows essen- rally the same type of distribution for the dimerous and trimerous plants, •'he grades of the classes are merely about double what they were in the ;rmer method of treatment. The statistical constants are compared in table 10. #ypocoTYi OF urn 7s = I/ME nous = TfflMEROUS 10 FIG. 17. Percentage frequency distribution of total bundles in central region of ypocotyl. For all five lines the constants show a higher mean number of bundles'in he trimerous than in the dimerous seedlings, the mean being approximately 2 in the former and 8 or 10 in the latter. Thus the trimerous seedlings from 21.8 to 46.9 percent more bundles than the dimerous seedlings. 84 AMERICAN JOURNAL OF BOTANY 1 0 vO O j->. t^. 1/51/5 MM IO IO "t" "I" Tf ^f io IO co co 00 MM O IO PI P4 MM P) PI o 1 1 -3 ' 1 1 ? I 1 i 1 00 rj- 00 O P) M CO 11 d M d PI d IO of M O * 0 PI . < r)- O co O i-1 C > IO 1 M C 13 •*• oo «. ^ MO - C ' "cO CO^? 1 P O IO OO p; 11 i-; ^rf- HJ IO cr\ i r^* ^^ 1-1 d 1 o P! n d * I-*. O Pt CO P) ON i OO P4 CO ONO ON P4 00 O' 00 co OO P4 P4 CO 11 CO Ml/5 oc co -f co pJ 10 M 11 d i? PI OO P) O ON t- O O t^ O O o< ^ o o o 5 O io CO J O 1/5 n ON CO n 2 MO IO P) O v£ P) CO P) < IO 't- O •i •* O* O n P« O 00 t^* COO H IO CO IO >O OO 01 O ft t^ OO **• C O 00 00 O> PI IO »OOC P* CO P) C co co co C " n co M } IO t^ CO PI 1 IO O CO IO r\ co f-^. M d 'd-o o ^i- O O tv. 'rf -+ rf ( i/5"'vod OOn'oNO Ou'l^C OO P< O co t^ C i r^. co oo n | M CS M Ox NO O ON 01 co d co TJ- coo 11 d o f O P4 ON i Mr ) Is-* io IO O ^1" */5 * o o' M d n od 0 11 "3-« 03 Tt- t-~ O * PI CO 11 t M O CO •*• rfO CO C Tf CO CO « t O CO O ^t- ^ CO ON '*• i r^ i PI o oo PI O co ON cOO o w s M o i- 2 i- o 1-1 2 i c Jy P v uuOQj u4>oc o;a^ fcCL, wD-ajCi S Q* u 0 .§6 .56 18 IO u *i CO u >i OO u -i o ft . ii .S .S .S 3 £yoi Sfeofe JJCL, ^Cn «MH ^CL, ^.S c **xS c o o .E .S 1 •« I ft •g •& s i i -= feb., 1921] HARRIS AND OTHERS — SEEDLINGS OF PHASEOLUS 85 In variability as measured by coefficient of variation, the dimerous slants exceed the trimerous throughout, conspicuously so in lines 75, •3, and 98. In their standard deviation, the dimerous also markedly xceed the trimerous in these three lines, but in lines 139 and 143 the rimerous plants slightly exceed the dimerous. FIG. 18. Percentage frequency distribution of total bundles in central region of hypocotyl. D. Summary for Base of Hypocotyl. For the base of the hypocotyl, therefore, it is evident that in total bundle number the trimerous seedlings decidedly exceed the dimerous ones. The intercalary bundles alone (which form but a small part of the total) tend to be more numerous in the dimerous seedlings. 86 AMERICAN JOURNAL OF BOTANY [Vol. 8 In variability in bundle number at this region, dimerous seedlings in general exceed trimerous ones; although two of the five lines studied furnish slight exceptions to this rule. FIG. 19. Percentage frequency distribution of total bundles in central region of hypocotyl. sb., 1921] HARRIS AND OTHERS — SEEDLINGS OF PHASEOLUS 87 3. Central Region of Hypocotyl. In the sections made in the central 5gions of the hypocotyl and of the epicotyl at both Cold Spring Harbor and 'torrs, the total number of bundles was counted, no distinction being made etween the bundles originating from the primary double bundles and those f intercalary origin. FIG. 20. Percentage frequency distribution of total bundles in central region of lypocotyl. The frequency distributions are shown in table n. The relative fre- juencies for line 75 are shown in figure 17. The form of the distributions in me 98 is in essential agreement with those in line 75 and is not represented. Hie distributions for line 93 are represented in figure 18. The distribution or line 139 is shown in figure 19. That for line 143 appears in figure 20. The conspicuous feature of these distributions is the wide variation in >undle number and the conspicuous skewness of the frequencies for the 88 AMERICAN JOURNAL OF BOTANY [Vol.8 normal plants of lines 75, 93, and 98. In these, bundle number ranges from 8 to 1 8 with a relatively large number of bundles in the lower classes. The modal number of bundles in the hypocotyl of normal seedlings of lines 75, 98, 139, and 143 is 8, while in line 93 it is 10. The normal plants of the five lines differ conspicuously in variability. The number of seedlings falling in the modal class is relatively small and the range of variation relatively wide in lines 75, 93, and 98 as compared with line 139. Line 143 occupies an intermediate position in this regard. In all the lines except 93 the distribution of number of bundles in the hypocotyl of normal seedlings is wholly skew, the frequency decreasing from the modal number (eight) towards the upper end of the range. In line 93 (figure 18) the distribution is also skew, but the frequency decreases from the modal number (ten) towards both ends of the range. In the trimerous plantlets of all five series the modal number of bundles in the mid-region of the hypocotyl is 12. The extent of concentration into the modal class and the range of variation differs greatly in the five lines. This is very narrow in lines 98 and 139 and relatively wide in line 143. The frequency distribution and figures bring out very clearly indeed the differentiation of the trimerous and dimerous seedlings in the number of vascular bundles. TABLE 12. Statistical constants for number of bundles in hypocotyl of trimerous and dimerous seedlings Mean Standard Devi ation Coefficient of Vari ation Line 75 Trimerous (N = 416) . . I2.I9±.O3 0.982 it. O23 8.o6±.i9 Dimerous (N = 416) Q.dOdb.OS 1. 645 ±.039 1 7. 34 ±.42 Actual difference. . + 2.7Orb.o6 — 0.663 ±.045 -9.28±46 Relative difference 28. 4S 4O.1.O Line 93 Trimerous (N = SS7) I2.2Q± O"? O.922±.OI9 7.5O±.i5 Dimerous (N — SS7) . . IO.62 dr. 04 i-525±-°3I I4-36±.30 Actual difference + I.67±.05 — 0.603 ±.036 — 6.86±.34 Relative difference IS. 71 39-54 Line 98 Trimerous (N = 345) • • 12. 03 ±. O2 o.532±.oi4 442±.n Dimerous (N = ^4S) 9- 22 ±.04 i.i97±.O3i I2.99±.34 Actual difference. . + 2.8I ±.04 — 0.665 ±.034 -8. 57 ±.36 Relative difference T.O.4.7 55.56 Line 139 Trimerous (N = 106) I I.OQzh.OS 0.694 ±.032 5.78±.27 Dimerous (N = i so) . . 8.II±.02 o.4O9±.oi6 5.04±.20 Actual difference. . +3.88±.05 +0.285 ±.036 -fo.74±.34 Relative difference 47.84 69.68 Line 143 Trimerous (N = 221) I2.29±.O6 i.283±.O4i io.44±-34 Dimerous ( N = 221) 8. 71 ±. OS i.i87±.038 13. 63 ±.45 Actual difference. . + i.58±.o8 +o.O96±.O56 -3.i9±.57 - Relative difference 41.10 1 8.09 ID., 1921] HARRIS AND OTHERS — SEEDLINGS OF PHASEOLUS 89 The differences between the lines can best be seen from the figures. ! For a more critical comparison we must have recourse to statistical lonstants and their probable errors. The results for the hypocotyl of trimerous seedlings and their normal jrntrols are set forth in table 12. Without exception the number of bundles fii abnormal plants is higher than that in the control plants. The differences I'nge from 1.7 to 3.9 bundles. These differences are many times as large i their probable errors and are unquestionably significant. The relative (inferences are about 16 percent in line 93, 30 percent in lines 75 and 98, 4 percent in line 143, and 48 percent in line 139. Both the standard deviation and the coefficient of variation of the num- !fer of bundles in the hypocotyl are lower in the abnormal than in the normal j.ants in lines 75, 93, and 98. In lines 139 and 143 the relationship of the sandard deviations of the trimerous and dimerous plants is exactly reversed, Hat of the trimerous plants being somewhat larger than that of the dimerous sries. The difference in line 143 is +.096 ± .056, which is nearly twice .5 large as its probable error and possibly statistically significant. In line i$9 the difference in standard deviation is +.285 ± .036. This difference is bout 8 times as large as its probable error and unquestionably significant, "he percentage differences in the standard deviations in lines 75, 93, and 98 inge from —40 to —56 percent. In line 143 the percentage difference + 8 percent, while in line 139 it is +70 percent. In line 143 the coefficient of variation is higher in dimerous plants (as is in lines 75, 93, and 98), but in line 139 the trimerous show a slightly ut perhaps not significantly higher relative variability. The results as a whole show that • the difference in the variability of undle number in the two types of seedlings in lines 139 and 143 is not the ame as that in lines 75, 93, and 98. In interpreting these results we must remember that each primary ouble bundle at the base of the hypocotyl almost invariably divides to Drm two bundles at higher levels in the hypocotyl. Occasionally one f these branches may further divide into two. It is impossible in sections aade in the central region of the hypocotyl to distinguish with certainty in very case between bundles originating through a division of the original irotoxylem strands and those of intercalary origin. The simplest working assumption is that the number of bundles in the entral region of the hypocotyl will be given by twice the number of primary louble bundles demonstrated at the base of the hypocotyl plus the number of ntercalary bundles found at the base of the hypocotyl; or the number of mndles, b, at the central region should be given by b = 2p + i vhere p = primary double bundles and i = intercalary bundles. AMERICAN JOURNAL OF BOTANY [Vol. 8 A comparison of the number of bundles calculated by this formula with the number actually observed in the central region of the hypocotyl may be best made in a table of double entry. Table 13 gives the results for dimerous and table 14 the results for trimerous plants of line 93. The TABLE 13. Comparison of actual ani theoretical number of bundles in hypocotyl of dimerous seedling Actual Number 8 9 10 ir 12 '3 M Totalf Theoretical, 2p -)- i 8 12 13 6 3 14 9 M 17 3 I I I 37 10 I 22 6 5 I — 35 ii — I 9 9 3 I 23 12 — — I 14 4 I 20 13 — — — i 3 4 H — — — — 2 2 Totals . . 12 28 46 22 29 10 ' 8 155 TABLE 14. Comparison of actual ani theoretical number of bundles in hypocotyl of trimerous seedling Actual Number JO ii 12 13 M -5 20 Totals Theoretical 2p -\- i . . 10 I I 3 _ 5 ii 6 ^ I 10 12 2 IO2 12 6 I I I24 13 8 3 II 14 — • — — 4 I 5 Totals . . I 9 1 08 20 «4 2 I 155 frequencies for the cases in which the number of bundles at the mid-region of the hypocotyl calculated from the formula agrees with the number actually observed are printed in blackface type. The other lines give roughly comparable results. It is clear that the number of hypocotyledonary bundles is not far from twice the number of primary root bundles plus the intercalary bundles. In rare cases the number of bundles in the hypocotyl is less than twice the root strands plus the number of intercalary bundles, since one of the root strands sometimes fails to divide. It may be, and not infrequently is, higher because of the appearance of extra intercalary bundles at a level higher than that sectioned at the base of the hypocotyl. In many cases the full complement of intercalary bundles has not appeared at this low level. In some cases it may be higher because of the secondary bifurcation above mentioned. It is worth while to give the percentage frequencies of cases in which the number of bundles of the central region of the hypocotyl is given by the formula, and for comparison the relative number of cases in which it is in defect and in excess. The percentages are calculated from double entry tables like 13 and 14. b., 1921] HARRIS AND OTHERS — SEEDLINGS OF PHASEOLUS Trimerous Seedlings N In Defect 2/ + Z In Excess ne 75 142 7-0 76.1 16.9 ne Q"? 155 1.3 78.1 2O.7 ne 98 183 3-3 86.3 IO-4 ne i^Q 1 06 7-6 80.2 12-3 ne 14.^ 221 0.9 74-7 24.4 Dimerous Seedlings N In Defect 2/ + Z In Excess ne 7S. . 142 2.1 5I-4 46.5 ne Q"} . 155 1.9 47-7 50-3 ne 98 183 3.8 59.0 37-2 ne i^o ISO 0.7 98.7 0.7 ne id"* 221 O.g 81.0 18.1 With the exception of the dimerous seedlings of line 139, the actually bserved number of bundles is in excess of the number given by the formula. In lines 75, 93, and 98 the excess is far greater in dimerous than in tri- terous seedlings. Thus in the dimerous class about 40 percent of the jedlings show a number of bundles in the central region of the hypocotyl hich is in excess of twice the number of primary double bundles plus the umber of intercalary bundles at the base of the hypocotyl. In the case f the trimerous seedlings the excess is much smaller, being roughly 20 ercent. Thus it is clear that, especially in the normal seedlings, a large umber of the intercalary bundles do not extend to the base but appear in le axis, ending blindly below, or that a considerable proportion of the rimary double bundles divide into more than two bundles. In line 143 the number of cases in which the observed number of bundles ; greater than the calculated number is much more nearly equal in the two ypes of seedlings. Thus in the trimerous seedlings 24.4 percent of the sedlings have a number of bundles in the central region of the hypocotyl reater than 2p + i, whereas in the dimerous seedlings there are 18.1 per- ent of seedlings of this class. In line 139 only 0.7 percent of the dimerous eedlings show a number of bundles in excess of 2p + i, whereas in the rimerous seedlings 12.3 percent are in excess. Thus lines 139 and 143 give results diametrically opposed to those of he first three discussed.10 Summary for Central Region of Hypocotyl. It is evident from the bove statements that the number of bundles in the hypocotyl of trimerous 5 decidedly higher than in that of dimerous seedlings; that in general the lundle number is more variable in dimerous than in trimerous seedlings; nd that the intercalary bundles generally extend to a lower level in the typocotyl of trimerous than in that of dimerous seedlings. 10 Note that the extremely small excess in line 139 may be due to the extraordinarily ormal character of the vascular system of the dimerous plants of this line. 92 AMERICAN JOURNAL OF BOTANY [Vol. 8 o H vovo r^ i^» ir> in voo HI HI HI 1C 1C ^" ^f" O 1C CM ^" ^t" 1C 1C co CO I-H HI M 1 I I 1 °° s Tj- ON O W N 0^ HI O HI 0 P) 0 to ? s ^ ?L| ^ ?L r)-6 «* O HI O VO PJ "3 6 V <0 "5 g 9 VO O ON ON t">» ON OO P« OO O 'i-O OHI Hid P4Hi ON-* HI £ » .vd •* IO HI f*} _ f trimero >2 VOP)VOOO OONTh t^. CO l^** I-H HI PI PI VO HH CO Pi CO O ON co HI O ON ^j~ HI O ^~ PJ ON Pi ( ON Pi PI P4 ^f >H PJ pj T^ M HI 0 s d -< vOninid O0>/) il-^i-i c pJ ^ e * T}~vO covO OO l^»vO O ON ^i" M ^M M ^T P)P) HIHI | 00 *IC •OHi 1 e **» to <>} 2 P) t^» O O OJ ON CO vO CO O vO O 1C O ONVO' OO pJ VO HI HI tv. 1C PI COOO t^OO HI ON COOO A >vd H 1 «fc-. H Ul (Ul i i i 0* J i ,» O Lf i Li i i i i i i 1 < ic w J CQ < H Mc.c OT c . c ^ c . c ^ c . c ^ c OUXU O l~ 5 L* OV-5l-i O H 5 M O >-< Si v PS Cudoj u.-^_i Q ON^_, Q ON£_, Q HI ^_, Q HI £_, ^ QJ QJ QJ O D .5 .S .5 c S »-5 J n2 H^ J Percent eb., 1921] HARRIS AND OTHERS — SEEDLINGS OF PHASEOLUS 93 4. Central Region of Epicotyl. The frequency distributions of the umber of bundles occurring in the mid-region of the epicotyl appear in able 15 for both the abnormal and the control plants. These distributions OF LJflf 7$ = 2 1 HERO US = TJt/ME'ROUS 20- 10- FIG. 21. Percentage frequency distribution of number of bundles in central region of epicotyl. reduced to a percentage basis are represented graphically in figure 21 for line 75, in figure 22 for line 98, and in figure 23 for line 143. The distributions 94 AMERICAN JOURNAL OF BOTANY [Vol. 8 90 - fP/COTVL OFL/M£ SQ = UJMEJfOUS = T7VMEROUS FIG. 22. Percentage frequency distribution of number of bundles in central region epicotyl. for line 93 are essentially the same as those for line 75. The graph for lint 139 is in essential agreement with that for line 98 and is not drawn. In the dimerous plants the difference between the form of the frequency distributions for number of epicotyledonary bundles in lines 75 and 93 01 :b., 1921] HARRIS AND OTHERS — SEEDLINGS OF PHASEOLUS 95 ic one hand and lines 98, 139, and 143 on the other is more apparent than sal. All five lines agree in showing the frequencies for the dimerous plants rgely concentrated in a single modal class with a slight but evident skew- EP/COTyt OF LIME /43 = Z/ME7?OUS = TTflMEROUS 17 18 19 20 21 /O FIG. 23. Percentage frequency distribution of number of bundles in central region of •picotyl. less toward higher numbers of bundles. In the case of lines 75 and 93 :here is a little over I percent of plants with fewer than the modal number )f bundles, whereas in lines 98, 139, and 143 these do not occur in series of Ae numbers sectioned. It is quite possible that the examination of a 96 AMERICAN JOURNAL OF BOTANY larger series of plantlets would result in the finding of such seedlings in lines 98, 139, and 143, thus bringing the five series into full agreement. In the trimerous seedlings the number of bundles shows rather wide, and fairly symmetrical, distribution about the modal class, which is ig bundles. The lines differ, however, to a considerable extent in the amount of variation from the modal class. In lines 75, 93, and 98 the frequencies are to a far greater extent concentrated into the modal class, which contauji from 39 to 51 percent of the frequencies, than in line 143, which contaifc only 24 percent of the cases. Line 139 is intermediate between these twi extremes. For a more precise comparison we utilize the constants set forth in table 1 6. TABLE 16. Statistical constants for number of bundles in epicotyl of trimerous and dimeroiu seedlings Mean Standard Deviation Coefficient of Variation Line 75 Trimerous (N = 4i6). . I 5.47:1=. O4 I.155±.O12 8.76± 21 Dimerous (N = 416) I2.27±.O2 0. 715=1- OI7 5 QQ± 11 Actual difference . + 1.2O±.O4 4-O.620 ±.036 + 2.77± 21 Relative difference 26.08 84.^5 Line 93 Trimerous (N = 5^7) I5.65±.O4 I 372 ± O28 8 77 ± 18 Dimerous (N = 557). • I2.I9±.O2 o.6i5±.oi2 5.o5±.io Actual difference . +3-46±.O4 4-o 757 ± O10 -r-1 72 ± 20 Relative difference 28 18 121 OQ Line 98 Trimerous (N = ^45) . . I4.8q±.O4 I.I52±.O3O 7 74 ± 20 Dimerous (N = ^45) . 12. 1 1 ±.02 o 4i6± on 1 44 =fc OQ Actual difference . +2.78±.O4 +0.736=1=. 032 -(-4. io±.22 Relative difference 22.06 176 02 Line 139 Trimerous (N = 106) i5-24± 08 I 285 ± 060 8 44 ± 10 Dimerous (N = 150) I2.I5±.O2 o.4o6±.oi6 1.15±.I1 Actual difference . +3-O9±.o8 +o 879 ± 062 -r- 5 OQ =t 41 Relative difference 25 41 216 50 Line 143 Trimerous (N = 221) 16 io± 08 I 7">O=fc O^6 TO 87 ± 15 Dimerous (N = 221) I2.36±.O3 O 757=t 024 6 11 ± 20 Actual difference . -l~-j.74.-4- OQ 4-O QQl-f- O6l 4-4 7/1 ± 4.0 Relative difference 30.26 131.18 These results show that without exception the average number of bundl' in the epicotyl is .higher in trimerous than in dimerous seedlings. Tl difference ranges from 2.8 to 3.7 bundles. The probable errors of the<< differences are so small that there can be no reasonable doubt of ther significance. In relative terms, the number of bundles in the abnorm plant is from 23.0 to 30.3 percent higher than that in the normal plant. fcb., 1921] HARRIS AND OTHERS — SEEDLINGS OF PHASEOLUS 97 The variability of bundle number, both absolute and relative, is far gher in the abnormal (trimerous) plants. The relative differences show dat the trimerous plants are from 84 to 217 percent more variable than ae dimerous in the number of bundles in the central region of the epicotyl. We now have to consider the relative number of bundles in the hypocotyl nd in the epicotyl of the same plant. The constants for the normal plants re shown in table 17 and for the trimerous seedlings in table 18. r\BLE 17. Comparison of statistical constants for number of bundles in hypocotyl and epicotyl of same plant. Seedlings with two cotyledons and two primordial leaves Mean Standard Deviation Coefficient of Variation iine 75 (N = 416) Hypocotvl . . Q 4.0 ± O=? I 64^ zt O7Q 77 -2 A _(_ ,12 Epicotyl 12 27± O2 O 77.^zt OI7 5OO-I- T/l Actual difference +2.78±.os — o 9io± 043 — II ^ ^ zt 4.4. Relative difference 2Q.2Q CC -21 ine 93 (N = 557) Hypocotyl io.62± 04 I ^2^zt O7.I T,J i(\-\- in Epicotyl I2.I9± O2 o 6i5± 012 5O? -4- TO Actual difference . -4- 1 cy -t- O4. — OQTO-I- Oil Relative difference 14.78 CO 67 ine 98 (N = 345) Hypocotyl 9-22± 04 I IQ7zt 071 T2 OO -4-7-1 Epicotyl 1 2.1 1 ± O2 O ,4 j6;t OT I Actual difference +2.89±.c>4 — o 781 ± OT,^ — n cc -)- -je Relative difference 71.7.4. 6q 24. ine 139 (N = 150) Hypocotyl 8.1 1 db O2 o 409 zt 016 SO/I -4- ?O Epicotyl 1 2 . 1 5 ± O2 o 406 zt 016 375 -4- T7 Actual difference ; . -I- A O4.zt O7. — O OO7-I- O27 Relative difference 4.Q.82 O 77. ine 143 (N = 221) Hvpocotyl 8.7i± 05 I i87± 038 T -} (.•} _(_ A C Epicotyl 12 7.6± O7. n 7C7-1- O24. Actual difference + •* 6^zt 06 — o A in -4- o/i 5 Relative difference 41.91 36.23 /.^uztz.4y Normal and abnormal plants have in common a larger number of bundles n the epicotyl. The differences between the means for the two organs are learly significant in comparison with their probable errors. The per- :entage differences show that the epicotyl has from 15 to 50 percent more mndles than the hypocotyl. In the dimerous seedlings the variabilities, both absolute and relative, is measured by the standard deviation and coefficient of variation, are -onsistent in indicating a higher variability of bundle number in the hypo cotyl. The difference is, however, very slight in line 139. The difference between the variability of the hypocotyl and that of the ipicotyl in the normal seedling as measured in terms of the standard devia- 98 AMERICAN JOURNAL OF BOTANY [Vol. 8 tion is from 0.8 to 0.9 bundle, or from 55 to 65 percent of the larger value in lines 75, 93, and 98. In line 143 the difference is only 0.4 bundle, or 36 percent. In line 139 there is practically no difference in the standard deviation of bundle number in the mid-region of the first two internodes of the seedling. TABLE 18. Comparison of statistical constants for number of bundles in hypocotyl and epicotyl of same plant. Seedlings with three cotyledons and three primordial leaves Mean Standard Devi ation Coefficient of f Variation , Line 75 (N = 416) Hypocotyl 0.982 zb 023 8 06 zb IQ Epicotvl i5-47± 04 I ^S^zb 07.2 8 76zb 21 Actual difference +3-28zb.os +O ^77. zb O4O -|-O 7Ozb 28 Relative difference 26.90 7.7 08 Line 93 (N = 557) Hypocotyl I2.29±.O3 0 922 zb OI9 Epicotyl I5.65± 04 I 372 zb O28 8 77zb 18 Actual difference . . Relative difference. Line 98 (N = 345) 27-33 48.81 [.27±.22 Epicotyl I4.8Qzb O4 I 152 rb 030 7 74 ± 2O Actual difference + 2.86zb.O4 -f-O.62Ozb 033 4-7. 72 ± 22 Relative difference 27.77 1 16 54 Line 139 (N = 106) Hypocotyl II.QQzb.OS O.6Q4zb O7.2 S 78 zb 27 Epicotyl 1 5- 24 zb. 08 I 285 zb 060 8/1A-4- 7Q Actual difference ~r"3 25 zb 09 -(-O 591 zb 068 +2 66 zb 48 Relative difference 27.11 85 16 Line 143 (N = 221) Hypocotyl 12 29 zb 06 I 283 zb 041 IO A \ -4- 7A Epicotyl 1 6 lOzb O8 jo 87 _(_ -jc •/5 • 5 Actual difference + 3 8l zb IO ~T"O 467 zb 069 -4-n 1 7 •+- IQ Relative difference 3I.OO 36.40 Basing the comparisons on the coefficient of variation, we note that the coefficients for the hypocotyl range from 13.0 to 17.3 percent, whereas those for the epicotyl range from 3.4 to 6.0 percent in lines 75, 93, and 98. Thus there is a difference of about 10 percent in the coefficient of variation of bundle number in the hypocotyl and epicotyl (of the normal seedlings) of these lines. In line 143 this difference is only —7.50 percent. In line 139 it is only —1.69 percent. The statistical relationship is in full accord with the anatomical findings recorded above (p. 68) where it was shown that the intercalary bundles of , the hypocotyl as they approach the cotyledonary node fuse with the (nor- , mally 8) bundles originating by the division of the (normally 4) protoxylem poles of the primary root and completely lose their individuality, exactly six bundles emerging from the complex irrespective of the number which ., 1921] HARRIS AND OTHERS — • SEEDLINGS OF PHASEOLUS 99 entered it from the hypocotyl.11 Immediately above the cotyledons : s.ix remaining bundles approach, closing the cotyledonary gaps and form- a ring, the six members of which almost immediately divide, giving rise b! the modal number, 12, which persists throughout the length of the ticotyl. It is apparently the disappearance of the intercalary bundles as a :aspicuous feature of the topography which results in the lowered variabil- \r of bundle number in the epicotyl as compared with the hypocotyl. If this conclusion be true, we should find the least difference in the mability of number of bundles in the central regions of the first two inter- ;des in the lines in which intercalary bundles are least conspicuous as a :'*ture of the vascular topography. As a matter of fact, this condition is i'ongly supported by the results for the five lines investigated. Turning :ck to table 6, showing the constants for number of intercalary bundles, K note that lines 75, ^93, and 98 have on the average from 0.60 to 0.83 :ercalary bundle per (normal) plant. These are the lines showing a vative difference of 55 to 65 percent in the standard deviations as com bed with 36 percent in line 143 with an average of 0.31 intercalary bundle, id of only 0.73 percent for line 139 which has an average of only 0.07 iercalary bundle per plant. The differences in the coefficients of variation V hypocotyl and epicotyl are from —9.3 to — 11.4 percent in the three lines ;th from 0.6 to 0.8 intercalary bundle per plant, —7.5 percent in line 143 ;th an average of 0.31 intercalary bundle, and only —1.7 percent in line 19 with an average of only 0.07 intercalary bundle. In the trimerous seedlings the relationship between the variation of the imber of bundles in the hypocotyl and in the epicotyl is just the reverse of :at found in the normal type. Variability as measured by the standard viation is significantly higher in the epicotyl of all lines studied. The me is true if the coefficient of variation be used as a measure of variability, though the differences for lines 75 and 143 are not large. The anatomical explanation of this fact seems to be found in the pecu- irities of behavior at the cotyledonary node. As pointed out above >. 70), the epicotyledonary ring is typically made up of nine strands stead of the six characteristic of the normal plant. There is, therefore, : the modal case an increase of fifty percent in the number of bundles in e epicotyledonary ring of the trimerous plant as compared with the merous plant. Many of these bundles, but not all, divide to form the indie system characteristic of the main course of the epicotyl. It is this inability in the extent of division of the bundles of the epicotyledonary ng which, in connection with the low variability of the hypocotyl due to ie formation of but few intercalary bundles (except in lines 139 and 143, here the number is about the same in normal and abnormal seedlings), "ings about the great variability in the bundle number of the mid-region 11 This statement is based on a more detailed anatomical study of a portion of the idlings. 100 AMERICAN JOURNAL OF BOTANY [Vol. 8 of the epicotyl as compared with the mid-region of the hypocotyl, in the trimerous plants. This condition furnishes an excellent example of the importance of a knowledge of descriptive morphology as an aid in interpreting biometric constants. COMPARISON OF BUNDLE NUMBER IN THE FIVE LINES STUDIED From the genetic standpoint it seems a matter of considerable interest to determine whether the three nominally pure lines12 are differentiated with respect to their vascular anatomy. A comparison of the percentage frequency distributions and the figures of the foregoing discussion will convince the reader that certain of the lines may be differentiated either in mean number of bundles, or in variability of number of bundles, or in both average number and variability of bundle number. Since we hope to return to this problem later with even more extensive data, it seems unnecessary to consider the differences in the distributions and constants in detail at this time. The results of this brief and superficial comparison seem to indicate that while different lines may not differ greatly in respect to certain of their vascular characters they may be differentiated with respect to others. SUMMARY This paper presents the results of a comparative and biometric study of the gross vascular anatomy of the seedling of Phaseolus vulgaris. Two morphological types are considered: the normal, or dimerous seedling with two cotyledons and two primordial leaves, and the trimerous seedling with three cotyledons and three primordial leaves. In normal seedlings, the vascular system of the root is typically tetrarcl (with four protoxylem poles), and gives rise in the base of the hypocoty to eight bundles which continue to the cotyledonary node. From the vascular complex at this point two strands are given off to each cotyledoi and six are left, each of which divides into two to produce the typical twelve bundled condition of the epicotyl. The trimerous seedlings typically possess six root poles instead of four twelve bundles in the hypocotyl instead of eight, and nine primary epicoty ledonary bundles instead of six. The nine primary epicotyledonary bundle may not all divide, however, so that the number of bundles in the centre region of the epicotyl is variable, ranging in general from fourteen t eighteen. 12 While the material employed in this study traces its origin from individual plant the possibility of hybridization in the field is not excluded. Thus any comparison whic may be made in this place must be regarded as preliminary merely. pi., 1921] HARRIS AND OTHERS — SEEDLINGS OF PHASEOLUS 101 In both types of seedlings, but more frequently in the normal ones, aditional or intercalary bundles appear in the hypocotyl, either de novo oils a result of division of the primary strands. The following constants13 (table 19) for bundle number (at the different leels studied) epitomize the differences which characterize the two types 01 seedlings. TABLE 19 Trimerous Seedlings Dimerous Seedlings Mean S. D C. V. Mean S. D. C. V. R\t poles •654 •739 .707 .288 .581 •405 .292 .686 .491 •532 1.283 .883 1.152 1-750 1-383 13.02 14.47 13.87 4.86 IO.OI 6.87 156.62 381.67 274.92 4.42 10.44 7.24 7-74 10.87 8.92 4.OI 4-13 4-05 4-02 4-52 4-19 .07 •83 •49 8.H 10.62 9-23 12. II 12.36 12.22 .081 •338 .171 .140 .666 .411 .261 1.024 .687 .409 1.645 I-I93 .406 •757 .586 2.03 8.18 4.19 3.48 14.7.4 9.66 105.79 355.48 182.70 5-04 17.34 12.67 3-35 6.13 4-79 . Minimum 5 02 Maximum 5 16 i Mean 5 09 Pmary double bundles Minimum • 581 Maximum . . c; 08 , , o-v° Mean 591 Inrcalary bundles Minimum 09 Maximum 29 Mean 19 Mi-region of hypocotyl Minimum. ... n 99 Maximum 12 29 Mean 12 16 Mi-region of epicotyl Minimum 14 89 Maximum 1610 Mean I S 47 The variability of root pole number is distinctly higher in trimerous than idimerous seedlings, because of the fact that in all seedlings a four-poled ccidition is characteristic of the main root system and prevails even in tf trimerous forms up to within a few millimeters of the base of the hypo- ccyl. Sections in the upper root region in such seedlings therefore show a ccisiderable number of four- and five-bundled individuals. The number of intercalary bundles is highly variable in both seedling tj>es. The standard deviation is distinctly larger in the dimerous forms, b : because of the generally lower average number of intercalary bundles in tmerpus seedlings, the relative variabilities as measured by the coefficient o:variation are higher in the trimerous type. In the central region of the hypocotyl the variability of bundle number, bdi absolute and relative, is far higher in the dimerous seedlings, due in Mge part to the generally higher standard deviation of the number of irercalary bundles in the dimerous type. In the central region of the epicotyl just the reverse is true, the varia- y of bundle number being higher in the trimerous than in the dimerous sedlmg. This is evidently due to the facts (a) that the intercalary bundles 1 Data for number of root poles are available for only three of the five lines. IO2 AMERICAN JOURNAL OF BOTANY of the hypocotyl are quite lost in the cotyledonary nodal vascular complex and thus do not affect the variability of the dimerous plants; and (/>) thai the doubling of the primary epicotyledonary bundles which almost invariablj occurs in the normal seedling may not always take place, at least not at ai low a level as the central region of the epicotyl, in the abnormal type. CONCLUSIONS The results of the foregoing morphological and biometric analyse justify the emphasis at this point of certain general considerations. 1. External differentiation such as that which characterizes dimerou and trimerous seedlings of Phaseolus vulgaris is accompanied by profouil differences in internal structure. 2. Anatomical characters are by no means constant. On the contrary they are very variable even in series of individuals which are genetical highly homogeneous. Morphological investigations based on limits! series of individuals may, therefore, result in inadequate conceptions. 3. Variation in anatomical structure is not constant for the plant as I whole, but may differ from region to region or from organ to organ. Thu in the regions of the seedling here under consideration, hypocotyl and epi cotyl differ widely in the variability of bundle number. Furthermol differences in variability from organ to organ or from region to region a* not constant, but may be conditioned by other morphological featured To illustrate from the case in hand, the variability of bundle number 0 normal seedlings is higher in the hypocotyl than in the epicotyl. In seed lings with three cotyledons and three primordial leaves, just the reverse i true. These differences in biometric constants are readily understandabl in the light of a knowledge of comparative morphology. 4. The results of this study emphasize the importance of the use of hot biometric and comparative methods to supplement each other in any attaa upon the problems of general morphology or of morphogenesis. THE VASCULAR ANATOMY OF NORMAL AND VARIANT SEEDLINGS OF PHASEOLUS VULGARIS BY J. ARTHUR HARRIS and EDMUND W. SINNOTT Station for Experimental Evolution, Carnegie Institution of Washington Reprinted from the Proceedings r.f the NATIONAL ACADEMY OK SCIENCES, Vol. 7, No. 1, pp. 35-41, January 1921. [Reprinted from the Proceedings of the NATIONAL ACADBMY OF SCIBNCBS, Vol. 7, No. 1, pp. 35-41, January, 1921.] THE VASCULAR ANATOMY OF NORMAL AND VARIANT SEEDLINGS OF PHASEOLUS VULGARIS BY J. ARTHUR HARRIS AND EDMUND W. SINNOTT STATION FOR EXPERIMENTAL EVOLUTION, CARNEGIE INSTITUTION OF WASHINGTON Communicated by C. B. Davenport, November 29, 1920 The investigations here summarized comprise a comparative and bio- metric study of the gross vascular anatomy of normal and variant seed lings of Phaseolus vulgaris. Three morphological types have been considered, (a) the normal or dimerous seedling with two cotyledons and two primordial leaves, (6) the trimerous seedling with three cotyledons and three primordial leaves, and (e] the hemitrimerous seedling in which there are three cotyledons and two primordial leaves. In normal seedlings, the vascular system of the root is typically tetrarch (with four protoxylem poles), and gives rise in the base of the hypocotyl to four pairs of double bundles which soon form a circle of eight bundles which continue to the cotyledonary node. At this point there is a com plex vascular anastomosis. From it two strands are given off to each cotyledon. The remainder of the vascular tissue is reorganized into six strands, each of which typically soon divides into two, the twelve bundles thus formed comprising the vascular system of the epicotyl. The trimerous seedlings typically possess six root poles instead of four, twelve bundles in the hypocotyl instead of eight, and nine primary epico- tyledonary bundles instead of six. The nine primary epicotyledonary bundles do not all divide, however, so that the number of bundles in the central region of the epicotyl is variable ranging in general from fourteen to eighteen. In both classes of seedlings, but more frequently in the normal type, additional or intercalary bundles appear in the hypocotyl, either de novo or as a result of division of the primary strands. Four main groups of problems as to the vascular topography of these seedling types have been considered biometrically : First, the number of bundles at different levels in the seedling ; second, the variability in bundle number; third, the differentiation in internal structure of seedlings which are externally dimerous, trimerous and hemitrimerous; and fourth, the interrelationship of bundle number in different regions of the seedling. The following table of constants1 summarizes the facts for number and variability of vascular bundles in various regions of the seedling and in the three types of seedlings.2 The constants in this table, and the frequency distributions from which the constants were computed, lead to the following conclusions. 36 BOTANY: HARRIS AND SINNOTT PROC. N. A. S. DIMEROUS SEEDLINGS TRIMEROUS SEEDLINGS HEMITRIMEROrS SEEDLINGS Me in S. D. C. V. Mean S. D. C. V. Mean S. D. C. V. Root poles Minimum 4.01 0.081 2.03 5.02 0.654 13.02 Maximum 4.13 0.338 8.18 5.16 0.729 14.12 Mean 4.05 0.171 4.19 5.09 0.707 13.87 Primary double bundles Minimum 4.02 0.140 3.48 5.81 0.288 4.86 5.21 0.608 10.59 Maximum 4.52 0.666 14.74 5.98 0.581 10.01 5.74 0.750 14.07 Mean 4.19 0.411 9.66 5.91 0.405 6.87 5.49 0.676 12.37 Intercalary bundles Minimum 0.07 0.261 105.79 0.09 0.292 156.62 0.28 0.449 ! 15.47 Maximum 0.83 1.024 355.48 0.29 0.686 381.67 0.53 1.148 214.68 Mean 0.49 0.687 182.70 0.19 0.491 274.92 0.44 0.737 163.82 Mid-region of hypo- cotyl Minimum 8.11 0.409 5.04 11.99 0.532 4.42 11.36 1.169 9.94 Maximum 10.62 1.645 17.34 12.29 1.283 10.44 12.32 1.524 12.87 Mean 9.23 1.193 12.67 12.16 0.883 7.24 11.94 1.307 10.96 Mid-region of epi- cotyl Minimum 12.11 0.406 3.35 14.89 1.152 7.74 12.93 1.245 9.07 Maximum 12.36 0.757 6.13 16.10 1.750 10.87 14.84 1.778 12.53 Mean 12.22 0.5«6 4.79 15.47 1.383 8.92 13.83 1 .560 11.29 The modal number of primary double bundles in the region of transition from root to stem structure at the base of the hypocotyl is four in the di-. merous and six in the trimerous and hemitrimerous seedling. In the normal seedlings more than four bundles may occur, but in no case have fewer than this number been observed. In the trimerous seedling varia tion both above and below the mode is found, the numbers ranging from four to eight. On the average the number is from 1.38 to 1.89 bundles higher (or from 30.5 to 47.0% higher) in the trimerous than in the dimerous seedlings. Intercalary bundles, which are rather uncommon in seedling anatomy in general, occur in from 11 to 46% of the normal seedlings, whereas they are found in only 9 to 29% of the trimerous and in 28 to 43% of hemi trimerous seedlings. The average number of intercalary bundles is alsc generally higher in the dimerous plantlets. Considering the total bundle number at the base of the hypocotyl. (primary bundles plus intercalary bundles) the trimerous and hemi trimerous seedlings have from 0.77 to 1.91 bundles, or from 14.4 to 46.7%' more than the dimerous seedlings. The differentiation of the dimerous VOL. 7, 1921 BOTANY: HARRIS AND SINNOTT 37 and trimerous seedlings is conspicuously shown by the frequency distri butions of two of the lines shown in diagram 1 . In passing upward from the base of the hypocotyl, each primary bundle pair normally divides into two so that in the central region of the hypocotyl the bundle number is normally twice the number of primary double bundles at the base, plus the intercalary bundles. In many cases the number is somewhat in excess of this, however, showing either that new (intercalary) bundles have appeared or that some of the bundles have become sub divided. The modal number of bundles in the mid-region of the hypocotyl is eight or ten in dimerous plantlets; in trimerous and hemitrimerous plantlets 10 II 12 13 14 IS IB 17 DIAGRAM 1 Percentage frequency distributions of total bundles (primary double bundles counted as two^l at the base of the hypocotyl in dimerous and trimerous seedlings of two lines. Abscissae represent bundle numbers, ordinates represent percentage frequencies. it is twelve. On the average the number is from 1.7 to 3.8 bundles higher (or from 15.7 to 47.9% higher) in the trimerous than in the dimerous seedlings. The differentiation of the two classes of seedlings in their vascular anatomy at the level is clearly shown in diagram 2. The bundles in the mid-region of the epicotyl show in dimerous plantlets a modal number of twelve, whereas in trimerous seedlings it is fifteen. On the average there are from 2.8 to 3.7, or from 23.0 to 30.2%, more bundles in the epicotyl of the trimerous than in the dimerous seedling. 38 BOTANY: HARRIS AND SINNOTT PROC. N. A. S. The form of the frequency distributions for two of the lines is shown in diagram 3. The epicotyl of the hemitrimerous is in essentials of anatomy identical with that of the dimerous seedling. Not only are there marked differences in the actual number of bundles, but the variability of bundle number changes from region to region of the seedling, and differs in the three seedling types. Whether judged by range, standard deviation or coefficient of variation, the variability of bundle number in the central region of hypocotyl tends to be distinctly higher in the dimerous than in the trimerous plantlets; but in the epicotyl just the reverse is true, the variability of the trimerous plantlets exceeding that of the dimerous. These differences are conspicuous in diagrams 2 DIAGRAM 2 Percentage frequency distribution of number of bundles in central region of hypocotyl in dimerous and trimerous seedlings. Abscissae represent bundle numbers, ordinates represent percentage frequencies. and 3. In the first case it is the dimerous plantlets, in the second case it is the trimerous ones which show the greater variability. Apparently thisi is due to differences in the number of intercalary bundles in the hypocotyl;; and to the extent of division of the bundles in the epicotyl, of the two type*' of seedlings. The coefficients of correlation between various bundle systems alsc differ widely. In both trimerous and dimerous seedlings there is a nega tive correlation between the number of primary double bundles and the' number of intercalary bundles at the base of the hypocotyl. Thus the number of intercalary bundles is smaller in seedlings with larger number; of primary double bundles and vice versa. This result for seedlings of the VOL. 7, 1921 BOTANY: HARRIS AND SINNOTT 39 same (external) morphological type is in agreement with those obtained by a comparison of seedlings which are externally dimerous and trimerous, since the latter frequently have a larger number of primary double bundles but a smaller number of intercalary bundles than the former. In both types of seedlings variation in the number of intercalary bundles is the primary factor in determining variation in the total number of bundles at the base of the hypocotyl. Turning to the problem of the interrelationship of bundle number at different levels in the seedling we find that there is a substantial correla- 12 13 /4 IS 16 11 IB 19 20 21 12 13 /4 /S 16 11 18 /9 20 21 DIAGRAM 3 Percentage frequency distributions of total bundle number in the central region of the epicotyl of dimerous and trimerous seedlings of two lines. Abscissae represent bundle numbers, ordinates represent percentage frequencies. tion between the numbers of the three classes of bundles — primary double ; bundles, intercalary bundles, and total bundles — at the base of the hypo cotyl and the number of bundles in the central region of the hypocotyl. In the normal seedlings the coefficients average +0.509 for number of primary double bundles and number of hypocotyledonary bundles, +0.629 for intercalary bundles and hypocotyledonary bundles, and +0.813 for total bundles and hypocotyledonary bundles. In the trimerous plants these correlations average +0.381, +0.238 and +0.598, respectively. The correlations for normal plantlets are practically without exception higher than those for abnormal seedlings. The correlations between the number of bundles in the hypocotyl (both basal region and central region) on the one hand and the number of , CORRELATION OF MORPHOLOGICAL VARIATIONS IN THE SEEDLING OF PHASEOLUS VULGARIS J. ARTHUR .HARRIS AND B. T. AVERY NEW YORK 1918 sprinted, without change of paging, from the BULLETIN OF THB TORREY BOTANICAL CLUB 45: 109-119. April 1, 19-18 [From the BCH.OTX or TH* TG«MT BoTAjncAi. CLC» 45: 109-119, aa Mk 191*.) Correlation of morphological variations in the seedling of Phaseolus vulgaris J. AKTHUK HARJUS AND B. T. AVERT INTRODUCTORY REMARKS During the past several years one of us has had under way e experiments on the differential death-rate of bean seed- fiiE. Individuals differing in structure also differ in their capa- cil for survival under field conditions.* and in such physiological chracteristics as capacity for the development of the tissues of the pmordialf and of the subsequent lea Some tens of thousands of seedlings of known morphological chracteristics have been exposed to risk, as the life insurance stasticians express it, in an attempt to determine the selective raie of the various morphological variations. These seedlings sne, for technical reasons, necessarily planted in the field at a tue when the cotyledonary node and the primordial node only ccld be studied. It is evident that the capacity of the plant for sivival may be in some degree dependent upon characters de- voped later in ontogenesis, but correlated with characters of the fit or second node of the seedling. However this may be, it is certainly true that a full knowledge ofche morphology and physiology of the variant bean seedling doands a thoroughgoing investigation of the correlation between tf structure of the first two leaf whorls and that of later whorls. \^ have, therefore, been forced to consider the problem of the rcrphological character of the leaf whorls produced at the third -•* Harris. J. Arthur. A simple demonstration of the action of natural Smoe II. 36: 713-715. 1912. t Hanis, J. Arthur. Studies on the correlation of morphological and physiologi- cacharacters: the development of the primordial leaves in teratologiral bean seed- lie. Genetics i: 185-196. 1916. * Harris, J. Arthur. Further studies on the interrelationship of morphological *i physiological characters in seedlings of Pkmseolms. Mem. Brooklyn Boc Card. I. In fress. 109 110 HARRIS AND AVERY: MORPHOLOGICAL VARIATIONS node in the case of plants showing various structural abnormalit \ at the first two nodes. Phaseolus is well suited for such investigations. The norrl seedling has two cotyledons, inserted at the same level, and ti opposite primordial leaves. A large number of structural vai- tions, four types of which will be considered in this paper, ii' occur. The chief disadvantage lies in the rarity of many of \ variations in the lines with which we have dealt. The securing adequate series is excessively laborious. The present paper; based upon a careful study of the variations in the first three no • of 16,348 plants, which were selected from about 450,000 seedli s examined for the characters of the first and second node. When in the following paragraphs we refer to normal <1 abnormal plants or seedlings, it must be understood that 1; applies to the characteristics of the individual as determined i the basis of the first two nodes, the cotyledonary and the ]- mordial only. In its later development the "abnormal" pit may remain "abnormal" or become "normal," and the "norm ' plant may either continue to be "normal" or become "abnorm; ' The nature and method of classification of the abnormal! s dealt with will be discussed in the presentation of the data belov MATERIALS AND METHODS The materials upon which this study is based are a series f lines of White Navy beans grown at the Station for Experimei .1 Evolution during the past several years. The seeds were !'• vested from field cultures in 1915 and germinated in sand in e autumn of 1916. Seedlings which were abnormal in the characters of the 1-t or second node, i. e., in the number or insertion of the cotyled s or of the primordial leaves, were sorted out for potting in soil d subsequent study of the third node, that normally giving ris< o the first compound leaf. For each abnormal individual, a normal control seedling fin the same parent plant was taken at random to serve as a basi >i comparison. Both were potted in soil and grown to a stage \v :i the characteristics of the third node could be accurately de'- mined. HARRIS AND AVERY: MORPHOLOGICAL VARIATIONS 111 or the onerous preliminary examination of nearly a half a mibn seedlings we are greatly indebted to Miss Edna K. Lock- wod, Miss Margaret Gavin and especially to Miss Lillie Gavin. • PRESENTATION AND ANALYSIS OF DATA he slightest abnormality which wre have been able to discover occrring in considerable numbers of bean seedlings is the vertical sep;'ation of the two normally opposite cotyledons. So imper- cepble is the line of transition between normal and abnormal that per^nal equation must play some part in classification. The ••cotjedons may be much more widely separated. The variation is amrely graduated one, with no sharp lines of demarcation be- twei the different degrees of separation. Generally we have recc;nized three grades, but because of the rarity of plants with moi widely separated cotyledons we have in this paper grouped ourlata into two classes only. The first comprises plants with cotjedons 2-3 mm. apart. The second includes all those in which themre more distant. 'he number as well as the position of the cotyledons may vary. Plars with three instead of two cotyledons fall into two groups ; the* with the normal pair of primordial leaves and those with a whd of three leaves. The latter are by far the more abundant, .bnormality developed subsequently to the selection of the seecngs in the preliminary sorting may affect either the inter- nod between the second and the third nodes, that is, between the orirordial leaf whorl and the point of insertion of the first com- ; ooud leaf or leaf whorl, or it may be confined to the number or ;truture (or number and structure) of the leaves inserted at the :hir node. i the original selection of individuals abnormal in the char- icte? of the first or second node, only those with sensibly normal ,:ixe<(hypocotyl and epicotyl) were chosen for the purposes of the )reait study. £ . Vo types of abnormality in the axis beyond the second (the )rirordial) node have been considered. iie first is a sensible broadening of the axis, identical with or ,'imiir to fasciation. This is a graduated character. The line of lemrcation between normal and abnormal is not clearly marked. 112 HARRIS AND AVERY: MORPHOLOGICAL VARIATIONS and personal equation may influence in some degree the classifi tion of the seedlings. The second is a division of the axis into two coordinate branc each with a terminal bud. The frequencies of the two types of axial variation are too sni to justify detailed discussion. The entries in TABLE I show t TABLE I FREQUENCIES OF ABNORMALITY OF SECOND INTERNODE IN NORMAL AND ABXOR.-, SEEDLINGS Class of abnormality Actual frequencies Percentage frequence* Normal inter- node Broad ened inter- node Di vided inter- node Normal internode Broadened internode Div intei Two cotyledons slightly separated; two primordial leaves 4,017 4-02Q — 12 878 881 -3 813 825 — 12 2,410 2,436 -26 5 o + 5 2 O + 2 12 O + 12 14 2 + 12 + 7 i 0 + i o o o 14 0 + 14 99.6774 99-9751 -.2977 99.6594 IOO.OOOO - .3406 98.5454 IOO.OOOO -1.4546 98.8515 99.9179 — 1.0664 .1240 + .1 Normal control Difference + .1240 .2270 Two cotyledons widely separated ; two primordial leaves Normal control Difference + .2270 1.4546 + 1.4546 •5742 .O820 + 4922 +.! .1 +.: Three cotyledons; two primordial leaves Normal control Difference Three cotyledons; three primordial leaves Normal control Difference in every instance in which any individuals at all are available hi seedlings which are abnormal in either the cotyledonary orb primordial node show a higher percentage of abnormality info structure of the internode beyond the second node than dot* normal controls. We now turn to a consideration of variation in the leave n serted at the third node. The leaves of plants with abnorm t] of the axis should not be combined with those having normal ;3 They are not sufficiently numerous for separate consideration Confining our attention to seedlings which have a normal1^ for at least the length of the second internode of the epicoty w HARRIS AND AVERY: MORPHOLOGICAL VARIATIONS 113 ia\ the frequencies shown in TABLES I I-V. * The character of the :orrol plants is also given. TABLE II SELLINGS WITH TWO COTYLEDONS SLIGHTLY SEPARATED AND TWO PRIMORDIAL LEAVES aber of per node Actual frequencies Percentage frequencies Difference Abnormal Control Abnormal Control I 2 3 3.791 225 I 3.853 I?6 O 94-37 5.60 .02 95-63 4-37 .00 — 1.26 + 1.23 + .02 f 4,017 4.02Q 99-99 IOO.OO TABLE III SE3LINGS WITH TWO COTYLEDONS WIDELY SEPARATED AND TWO PRIMORDIAL LEAVES Nnber of leav per node Actual frequencies Percentage frequencies Difference Abnormal Control Abnormal Control I 2 8zi 67 840 41 92.37 7-63 95-35 4.65 — 2.98 + 2.98 Tots.. 878 881 IOO.OO 100.00 >nbes of leav per node Actual frequencies Percentage frequencies Difference Abnormal Control Abnormal Control I 2 3 591 221 I ' 792 33 O 72.69 27.18 .12 96.00 4-OO .00 -23-31 + 23.18 +' .12 Tots. . 813 825 99-99 100.00 TABLE V SEEDLINGS WITH THREE COTYLEDONS AND THREE PRIMORDIAL LEAVES >mber of leav per node Actual frequencies Percentage frequencies Difference Abnormal Control Abnormal Control I 2 i 3 1,632 771 7 2,20O 236 O 67.72 31-99 .29 90.31 9.69 .00 -22.59 + 22.30 + .29 Tolls . . 2.410 2.<«6 IOO.OO IOO.OO In these tables the numbers of control plants are not exactly identical with the nuners of abnormal plants, since some of those selected as normal in the seedling sta; showed abnormality of the axis in subsequent development and are omitted her where we are discussing abnormalities of foliar characters only. 114 HARRIS AND AVERY: MORPHOLOGICAL VARIATIONS In each of the types of abnormality dealt with the abnoi a] series show a higher proportion of the individuals with two or t ee leaves at the third node than do their normal controls. Furthermore, seedlings showing different types of abnormity at the first nodes also differ among themselves in the exter of abnormality at the third node. Thus plants which are noi al except for slight separation of the cotyledons have two or t ee leaves at the second node instead of the single leaf normally fcid in 5.63 percent, of the individuals. Plants with the cotylems more widely separated have 7.63 per cent, of their numberwith w or three instead of a single leaf. When one turns to the groups of plants which have threi n- stead of two cotyledons, a conspicuous difference is at once appa: it. Plants which have three cotyledons and a normal pair of primo ial leaves produce two or three instead of a single leaf at the 1 rd node in 27.31 per cent, of the cases. Seedlings with three c y- ledons and a whorl of three primordial leaves instead of the no ial pair at the third node have 32.29 per cent, of the individuals th two or three leaves at the third node. Heretofore the number of leaves inserted at the third node as furnished the only measure of variation at this region of the is. We now propose to consider variation in the organization ol he leaves themselves. It will not be possible to do this in the d ail *n which we hope to treat the problem ultimately. The ran$ of variation in the division of the bean leaf is rather great, anc he laws governing it are doubtless very complicated. Some propss has already been made on the problem, but for the present we all limit our discussion to the number of leaflets, leaving the prol :m of their arrangement for treatment when even larger series of .ta are at our disposal. The actual frequencies of number of leaflets per leaf prod ed at the third node are shown in TABLE VI. The most conspicuous feature of this table is the biralal nature of the distribution. The modes are on three and six, is to be expected from the fact that the distribution of the \ule number of leaflets depends upon plants with from one to t 'ee leaves at the third node. Because of the wide range of variation in leaflet number i HARRIS AND AVERY: MORPHOLOGICAL VARIATIONS 115 lot feasible to reduce these frequencies for the individual classes o a percentage basis for comparisons. This has, however, been lone for larger groups secured by combining all the seedlings TABLE VI NUMBER OF LEAFLETS PRODUCED AT THE THIRD NODE BY SEEDLINGS OF VARIOUS TYPES Number Two cotyledons slightly separated and two primordial leaves Two cotyledons Three cotyledons widely separated and and two two primordial leaves primordial leaves Three cotyledons and three primordial leaves Abnormal Control Abnormal Control Abnormal Control Abnormal Control I S 2 I I 2 16 6 4 3 2 2 5 3 3.741 3,825 801 835 572 782 1, 6O2 2,185 4 27 21 5 4 14 5 28 8 5 10 2 i 2 6 3 9 2 6 215 173 65 40 203 33 751 236 7 g i i 12 I 12 9 i I 3 10 i 2 u I Totals 4,017 4,029 Q»Q 070 881 813 825 2,4IO 2,436 I howing merely separation of the cotyledons and all those showing hree cotyledons instead of the normal two. The results are shown n the accompanying TABLE VII, which is self explanatory. TABLE VII COMPARISON OF THE NUMBER OF LEAFLETS IN DICOTYLEDONOUS AND TRICOTYLEDO- NOUS SEEDLINGS WITH THAT IN THEIR NORMAL CONTROLS Number of Seedlings with cotyledons separated Seedlings with three cotyledons leaflets Abnormal Control Abnormal Control I .12 .04 •03 2 .41 .12 .16 .21 3 92.79 94.91 67.45 90.98 4 -65 •51 1.30 .40 5 .22 .08 •47 •IS 6 5-72 3-52 29.60 8.25 7 .04 .81 •74 8 • 03 9 .02 .12 10 .02 .06 ii -03 A comparison may be made without the combination of dif- erent grades of abnormality by grouping the number of leaflets 116 HARRIS AND AVERY: MORPHOLOGICAL VARIATIONS around the modal classes 3, 6 and 9. The results in TABLE VIII show essentially the same relationships as those given in TABLES VI-VII. First, the higher leaflet numbers are more extensivel} represented in the abnormal plants of each of the four types thar they are in the controls. Second, the tricotyledonous plants shov a far greater increase in the number of leaflets inserted at the thirc node than do those abnormal only in the position at which th< two cotyledons are inserted. TABLE VIII PERCENTAGE FREQUENCIES OF NUMBERS OF LEAFLETS IN SEEDLINGS OF VARIOUS TYPES Class of abnormality Number of leaflets J-4 5-7 8-11 Two cotyledons slightly separated and two primordial 94-32 95.66 - 1-34 92.37 95-23 - 2.86 72-57 95-64 -23-07 67.72 90.23 — 22.51 5.62 4-34 + 1.28 7.63 4-77 + 2.86 27.18 4.36 +22.82 32.03 9-77 +22.26 .05 +.05 24 +.2- ,2- +.2: Two cotyledons widely separated and two primordial Control Three cotyledo Control Three cotyledc Control Difference . . . In substantiation of these conclusions the reader will note th in the class with slightly separated cotyledons 5.68 per cent, of t, plants have from five to ten leaflets as compared with 4.34 \ cent, with five and six leaflets in the control series. In seedlir> with more widely separated cotyledons but no other abnormal there are 7.63 per cent, of the plants with five to seven leaflets > compared with 4.77 per cent, of the normal controls with five ' six leaflets. Seedlings with three cotyledons but the normal numlr of primordial leaves have 27.43 per cent, of the individuals wi from five to nine leaflets as compared with 4.36 per cent, with f 3 or six leaflets in the normal controls. Plants with a trimerous cotyledonary and primordial whl ' have 32.28 per cent, of the seedlings with from five to eleven leaf s HARRIS AND AVERY: MORPHOLOGICAL VARIATIONS 117 a compared with 9.77 per cent, with five and six leaflets in the nrmal controls. Taking the average number of leaflets per plant as a basis of cmparison between the abnormal plants and their controls we fid the results in TABLE IX. TABLE IX MEAN NUMBER OF LEAFLETS IN SEEDLINGS OF VARIOUS TYPES Class of abnormality Mean number of leaflets in abnormals Mean number of leaflets in controls Difference 7>o cotyledons slightly separated; two primordial 3.170 3-133 +0.037 To cotyledons widely separated; two primordial 3.228 3.191 + 0.037 Tree cotyledons' two primordial leaves 3.847 3.131 +0.716 Tree cotyledons; three primordial leaves 3-990 3-294 + 0.6O6 Note (a) that for each type of normality the average number o leaflets is greater in the abnormal individuals than in the nor- iil, and (&) that the difference between the abnormal class and its cntrol is far greater in the case of the plants with three cotyledons tan in those in which the abnormality in the cotyledonary whorl cnsists merely in the separation of the two cotyledons. Thus the results for number of leaflets substantiates the con cision based upon number of leaves. Evidently, however, the number of leaflets is to a great extent ctermirted by the number of leaves. The problem now arises: r'e there differences in the average number of leaflets per leaf in te abnormal and normal individuals? Means and their differences have been determined, but are s slight that conclusions must be deferred until further series of eta are available. Just one other method of dealing with the problem of the cor- rlation in structural variation may now be considered. : Number of leaflets is, in the materials dealt with, practically a integral variate. In examining a large series of plants those Uh partial division of a leaflet, representing transition stages Hween a leaf with n and one with n + I leaflets are sometimes fund. Such cases are, however, relatively rare. The lobing of 1e leaflet has therefore been disregarded in the foregoing treat- 118 HARRIS AND AVERY: MORPHOLOGICAL VARIATIONS ment. A leaf with three leaflets, one of which has a lobe, has bee recorded as 3 in the tables, not as an intermediate between thre and four. This has simplified the tabling of the data, and the ca culation of the simple constants necessary to the interpretatio the data, without any material loss in accuracy. One may, however, inquire whether there are differences in th degree of lobing of the leaflets produced at the third node in planl which are normal and in plants which are abnormal in the cha- acters of the first and second node. Because of the very low pe centages of lobing in the leaflet no stress whatever is to be lail upon the exact values found, even in samples containing seven hundreds or thousands of plants, because of the great difficult^ of determining the probable error of a small percentage. The results are given in TABLE X. TABLE X PERCENTAGE OF LOBING IN THE LEAVES OF SEEDLINGS OF VARIOUS TYPES Class of abnormality Abnormal plants Control plants Uifferer Two cotyledons slightly separated ; two primordial 0.349 0.273 +0.07 Two cotyledons widely separated; two primordial 0.456 O.II2 +0.3^ Three cotyledons' two primordial leaves I.59Q O.242 + i-3E Three cotvledons; three primordial leaves 0-954 0.328 +o.6s Here the percentage frequency of plants with one or two lob* on the leaflets* are given for each type of abnormality dealt wr and compared with that found in the control series. Two relationships seem clearly indicated by the constants this table. First, the tendency to the production of lobes is greater in £ leaflets produced by abnormal plants of all four types than their normal controls. Second, the tendency to the production of lobes is greater the leaflets of plants with a trimerous cotyledonary whorl, ai either a dimerous or trimerous primordial whorl, than it is plants in which the sole abnormality consists in the separation the two cotyledons in their insertion on the axis of the plant. * In the case of two lobes both may occur on the same leaflet or they may different leaflets. HARRIS AND AVERY: MORPHOLOGICAL VARIATIONS 119 RECAPITULATION This paper presents the results of a first attempt to determine scne of the correlations in the structural variations of the seedling OiPhaseolus vulgaris. The materials are drawn from a series of lines of Navy beans giwn for the past several years at the Station for Experimental Solution. The seeds used were harvested from plants of selected ai:estry. Neither of these factors will, we believe, invalidate the occlusions drawn in this paper. These conclusions will not neces- saly apply to certain entirely abnormal races. 'Fasciation-like broadening of the axis and longitudinal division of:he axis distal to the insertion of the primordial leaves are both rcre frequent in seedlings showing separation of the cotyledons ail in tricotyledonous seedlings than in those which are normal. Seedlings which are normal except for the separation of the ccyledons and those which have three cotyledons and a normal p;r of primordial leaves or three cotyledons and a whorl of three pmordial leaves produce a larger number of leaves, a larger num- b< of leaflets and a higher percentage of leaves with lobes at the thd node than do those which are normal in their cotyledonary ail primordial leaf characters. Seedlings which are tricotyledonous, with either a normal pair oia whorl of three primordial leaves, show higher percentages of/ariation in the axis, or the leaves produced by the axis, distal tothe primordial leaves than do those which are normal except fothe separation of the two cotyledons. These studies wrill be continued. STATION FOR EXPERIMENTAL EVOLUTION, COLD SPRING HARBOR, NEW YORK FURTHER STUDIES ON THE INTERRELATIONSHIP OF MORPHOLOGICAL AND PHYSIOLOGICAL CHARACTERS IN SEEDLINGS OF PHASEOLUS J. ARTHUR HARRIS [Reprinted from BROOKLYN BOTANIC GARDEN MEMOIRS, 1: 167-174. June 6, 1918.] [Reprinted from BROOKLYN BOTANIC GARDEN MEMOIRS, 1: 167-174. 1918.] FURTHER STUDIES ON THE INTERRELATIONSHIP OF MORPHOLOGICAL AND PHYSIOLOGICAL CHARACTERS IN SEEDLINGS OF PHASEOLUS1 J. ARTHUR HARRIS Station for Experimental Evolution, Cold Spring Harbor, N. Y. INTRODUCTORY REMARKS In a series of papers published during the past several years I have emphasized the importance of investigations of the relationship be tween the morphological and the physiological characteristics of the organ and of the organism. The structural variations of the organs of which the organism is made up are the resultant of intrinsic and extrinsic factors — of heredity and environment, or of nature and nurture. Morphogenetic processes must, therefore, be investigated by physiological methods, and be interpreted in physiological, and ultimately in physical and chemical, terms. The purpose of this paper is to supplement and extend the results of an earlier study2 in which it was shown that in bean seedlings char acterized by certain morphological variations from type, the develop ment of primordial leaf tissue is less than in normal controls grown under conditions as nearly as possible identical. The data then available indicated that a reduction of the volume of primordial leaf tissue is associated with abnormalities of all the types studied, but that the type of variation influences, in some degree, the amount of reduction. In these first experiments the conclusions were based on primordial leaves only. The use of such leaves has the obvious disadvantage that they are completely formed in the seed, and undergo merely an enormous expansion (and an undetermined amount of differentiation) in the Studies on the Correlation between Morphological and Physiological Char acters, V. Studies I-IV of the series are to be found in Genetics i: 185-196. 1916; 2: 186-212. 1917; 2: 282-290. 1917. 2 Harris, J. Arthur. Studies on the Correlation of Morphological and Physio logical Characters: The Development of the Primordial Leaves in Teratological Bean Seedlings. Genetics I: 185-196. 1916. 167 168 germination of the seed and the development of the plantlet to the stage at which measurements were made. Since the development of the primordial leaves during the germina tion and establishment of the seedling is relatively great, it seemed quite legitimate to use the weight of green tissue produced by these leaves as a measure of the physiological capacity of seedlings of various types. The fact that these leaves are differentiated in the seed, does, however, constitute a valid objection against their use as a measure of the physiological capacity of the seedling. For such purposes a constant based upon some organ developed later in the life of the individual is desirable. One of the purposes of this paper is to present the results of deter minations upon a later developed organ. The one chosen is the first trifoliate leaf. This leaf was used because groups of plants of a higher degree of uniformity can be selected at the time of maturity of this leaf thai? at any later stage in the development of the plant, and because the first compound leaf reaches a degree of maturity sufficient for the purposes of the present study before the primordial leaves are too old to be used for a series of determinations. It is, therefore, possible to repeat, at a slightly later stage of development of the plant, the determinations made on the primordial leaves in the first study as a basis of comparison with the work already done and with the series of constants to be obtained for the first compound leaves of the same plants. In the first investigation the green weight of the leaf tissue served .as the fundamental measurement. In addition to this character certain measurements on the sap properties were also made. In the study of the saps some difficulties were encountered, and it seemed most desirable to discontinue that phase of the study temporarily and to carry out determination of dry weight and water content instead. These new measurements have, therefore, been added to these for green weight. MATERIALS AND METHODS The materials upon which this study is based are the same as those previously employed — a mixture of slightly different strains of navy beans. The seeds which were germinated in the fall and winter months of 1916 were grown in field cultures in 1915. Seeds from individual plants were germinated in sand. In sorting, the morphologically aberrant seedlings were laid aside with a normal plant to serve as a check for each abnormal. An abnormal and a control seedling from the same seed plant and germinated in the same HARRIS: INTERRELATIONSHIP IN PHASEOLUS 169 seed flat were potted side by side in a three inch pot and allowed to grow to the proper stage of maturity under conditions as favorable as we were able to give them. Before the samples were taken, the plants were carefully inspected and all pairs, one member of which had died, had been injured or which showed in its subsequent development any abnormality in addi tion to these specified were discarded. Note that there was no direct selection for the characters of the abnormal plantlets in this process, since both abnormal and control were discarded if either was unsuited Jor the purposes of the experiment. There probably was a fairly stringent indirect selection, since the death rate and the mutilation rate of the variant individuals was probably greater' than that of the normals. Thus more pairs were probably discarded because of an injury to or the death of the ab normal member of the pair than because of the death or injury of a normal member. The probability that the materials were somewhat selected before the physiological measurements discussed in this paper were carried out renders the findings of greater significance than they would otherwise be. After the pairs of seedlings had grown until the first compound leaf had attained its full size, and the second compound leaf was developing, but before the primordial leaves had materially deteri orated, samples of leaves were taken by nipping off the laminae only, or the laminae and the single petiolule of the terminal leaflet in the case of the compound leaf. These samples of tissues, each from 100 plants, were enclosed in flasks, weighed, and dried to constant weight in a bath surrounded by boiling water. Thus the technique employed was exceedingly simple. Because of the size of the samples dealt with, the relative infrequency of the abnormalities, and the large number which had to be discarded, the routine has been excessively laborious. For example, the weighings of the 23 samples and checks discussed in the present paper involve 13,800 leaves gathered from 4,600 plants which were secured by germinating and classifying nearly half a million seedlings. The structural variation in the bean seedling which is probably the simplest, and the most frequent, is a slight vertical separation of the cotyledons which are normally sensibly opposite in insertion. The amount of the separation is difficult to express quantitatively, since it is in some degree dependent upon the length of the axis. In our studies of seedling variation in Phaseolus, three grades of separation of the cotyledons have been recognized. The line of demarcation between these grades is a quite arbitrary one. This is also true of 170 BROOKLYN BOTANIC GARDEN MEMOIRS the line between "normal," and "abnormal" as applied to the dis-: tinction between plants which have cotyledons inserted on the same; level and those which have one of the pair sensibly higher on the axis than the other. "Slightly but distinctly separated," has been the descriptive term used in our classification schedules. The cotyledons range in position from those which are just perceptibly not inserted ofl| the same level to those which are perhaps two or three or four milli meters apart. So imperceptible is the line of distinction between nor mal and abnormal plants that in the classification of the seedlings frequent discussions arose concerning the normality or abnormality of" individual plants. In the present paper I am considering only the simplest type of abnormality. This course has been followed for two reasons. First, the proof of the existence of a physiological differentiation associated with a very slight structural variation is of far greater in terest than the demonstration of measurable physiological differentia tion associated with great morphological variation. Second, other types of abnormality with which I have dealt are so difficult to secure in satisfactorily large series that the number of samples as yet avail able is not sufficient to justify detailed comparisons between the different types of abnormality. I hope ultimately to be able to meet these difficulties. For the present the one type of structural devia tion dealt with serves to illustrate the method and one phase of the results of the investigations. PRESENTATION OF DATA Consider first of all the green weight of the organs selected. The average green weight of the primordial and of the first com-: pound leaves for plants which are normal except for slight separation i of their cotyledons is shown in Table I. With one single exception, the average weight of the primordial leaves of the normal plants is higher than that of the abnormal plants. In the single exception to the rule, the difference is small in amount. The average weight of the first compound leaf produced by abnormal plants of this class is in every case but one lower than the weight produced by the sensibly normal individuals. The exception to the rule is the same sample as in the case of the primordial leaves. The average weight of primordial leaf tissue in the abnormal plants is -5873, the average weight for normal plants is .6680, and the average difference —.0807. The differences in mean weights range in the individual samples from +.0074 to —.1286. For the first compound leaf of the same plants the average weight of the tissues from abnorma individuals is .4797, from a normal plant it is .5610, while the average. HARRIS: INTERRELATIONSHIP IN PHASEOLUS 171 difference between the sample and the control is —.0813. ences in average weight vary from +.0368 to —.2492. The differ- TABLE I Mean Green Weight per Plant of Primordial Leaves and of First Compound Leaf Sample Primordial Leaves First Compound Leaf Abnormal Control : Difference Percentage Difference Abnormal Control Difference Percentage Difference 32 .6034 .7096 — .IO62 15.0 •5132 •5929 -.0797 13-4 35 .5648 .6767 — .1119 I6.5 •5444 .6l88 -.0744 12.0 36 •5951 .636! — .0410 6.4 •5931 .6254 -.0323 5-2 39 .5619 .6277 -.0658 10.5 .5160 •5549 -.0389 7.0 40 .6096 .7052 -.0956 I3.6 .5179 | .6138 -•0959 15.6 4i .6068 •7304 -.1236 16.9 •4877 .6140 -.1263 2O.6 42 .5879 .6141 — .0262 4-3 .4712 •7204 -.2492 34-6 43 .6222 .7508 -.1286 17.1 .5008 .6115 — .1107 18.1 46 •5956 .7160 — .I2O4 16.8 •4645 .6019 -•1374 22.8 47 .7058 .6984 + .0074 i.i .5841 •5473 + .0368 6-7 48 •6389 .7272 -.0883 12. 1 •5593 •6395 — .O802 12.5 49 .5902 .6674 -.0772 n.6 .4960 •5851 — .0891 15-2 53 .5402 .5990 -.0588 9.8 .4491 .4948 -•0457 9-2 54 .5720 .6530 — .O8l0. 12.4 .4091 •4547 -.0456 IO.O 56 .5380 .5921 -.0541 9-i •3994 .4646 -.0652 14.0 61 •5193 .5827 -.0634 10.9 •4443 .4811 -.0368 7-6 64 .5853 .7052 -.1199 17.0 •4530 .5848 -.1318 22.5 65 •5747 .6938 — .1191 17.2 .4402 •5717 -•1315 23.0 66 .5886 .6790 -.0904 13-3 .5246 .5960 -.0714 12.0 70 •6853 .7066 -.0213 3-0 •4794 .4998 ! —.0204 4.1 71 •5639 .6059 — .0420 6.9 .4132 •4534 -.0402 8.9 72 •5565 .6744 -.1179 17-5 •3799 .4882 -.1083 22.2 73 •5033 .6140 — .IIO7 18.0 •3933 .4887 -•0954 19-5 If these differences be reduced to percentages by using the weight of the normal plants as a base, as shown in the final columns of each section of the tables, it appears that the primordial leaves of the morphologically aberrant plants are from 3.0 to 18.0 percent lighter than the leaves of the normal plants in the 22 samples in which this relationship between the two types of plants holds for the primordial leaves. Thus the percentages are highly variable. The average for the 23 determinations is 11.95 percent. In the case of the first com pound leaves, the percentage reduction ranges from 4.1 to 34.6 with an average of 14.06 in the 23 samples. Note that the percentage shows that the difference between the abnormal and the control sample is far less in the case of the single exception, sample 47, than it is in the average series. Thus it is only i.i as compared with an average value of 11.95 f°r the primordial leaves and only 6.7 as compared with the average of 14.06 percent in the compound leaves. I now turn to a consideration of dry weight. 172 BROOKLYN BOTANIC GARDEN MEMOIRS The primordial leaves of the abnormal plants in which the two cotyledons are slightly separated are, as shown in Table II, lighter TABLE II Mean Dry Weight per Plant of Primordial Leaves and, of First Compound Leaf Sample Primordial Leaves First Compound Leaf Abnormal Control Difference Percentage Difference Abnormal Control Difference Percentage Difference 32 •0445 •0537 — .OO92 I7.I .0442 .0517 -.0075 14-5 35 .0366 .0483 — .0117 24.2 .0465 •0530 -.0065 12.3 36 .0422 •0457 -•0035 77 .0476 .0499 — .OO23 4.6 39 .0409 .0467 -.0058 12.4 .0430 .0470 — .OO40 8-5 40 .0438 .0511 -.0073 H-3 .0415 .0496 — .008l I6.3 4i .0431 .0526 -.0095 18.1 .0406 .0494 -.0088 I7.8 42 .0416 .0504 -.0088 17-5 .0383 •0519 -.0136 26.2 43 .0429 •0532 -.0103 19.4 .0391 •0493 — .OIO2 2O-7 46 .0408 .0501 -.0093 18.6 .0400 .0492 — .O092 I8.7 47 .0442 .0446 — .OO04 •9 .0442 •0433 + .OOO9 2.1 48 .0420 .0464 — .0044 9-5 .0444 .0525 — .OO8l 15-4 49 .0381 .0436 -•0055 12.6 •0397 .0472 -.0075 15-9 53 .0365 .0410 -.0045 II. 0 •0399 .0427 — .0028 6.6 54 .0384 •0445 — .OO6l 13-7 . -0339 .0412 --0073 17.7 56 •0349 .0491 — .0142 28.9 •0331 •0395 — .0064 16.2 61 .0356 .0402 — .0046 II-4 •0383 .0417 -.0034 8.2 64 •C354 .0438 — .0084 19.2 .0341 .0435 — .0094 21.6 65 •0357 .0410 -.0053 12.9 •0344 .0398 -.0054 13.6 66 •0354 •0395 — .OO4I IO-4 .0381 .0439 -.0058 13.2 70 .0426 .0465 -.0039 8.4 .0407 .0438 — .0031 7-i 71 .0279 .0303 — .OO24 7-9 .0274 .0299 -.0025 8.4 72 .0273 .0407 -.0134 32.9 .0265 .0392 — .OI27 3-2 73 .0298 .0378 — .0080 21.2 .0315 .0408 -.0093 22.8 than those of the normal controls in every instance. The average dry weight of the abnormal is .0382, that of the control .0452 and the average difference is —.0070 grams. If the differences be expressed as a percent of the control value as a base, they range from less than i to nearly 33 percent, with a general average of 15.21 percent. The results for the first compound leaf are very similar. In 22 of the 23 cases the primordial leaves of normal plants yield a greater weight of dry substance than those of the abnormal plants. The exception to the rule is again sample 47. The average dry weight of the first compound leaf of abnormal plants is .0385, that of normal plants is .0452 and the average difference is —.0067 grams. If the differences be expressed as percentages of the control constants they are seen to range from 3.2 to 26.2, for the 22 series in which the ab normal plants produce a smaller amount of dry substance. The differ ence in the single exceptional series is small, only 2.1 percent as com pared with a general average of 13.36 percent in the 23 samples. HARRIS: INTERRELATIONSHIP IN PHASEOLUS 173 Having shown that the abnormal plants produce both a smaller green weight and a smaller dry weight in both the primordial and in the first compound leaves, the problem of the relative quantities of water and dry materials in the leaves of the two types of plants naturally presents itself for consideration. The results have been expressed in terms of the percentage of dry substance in the leaves, i. e. (dry weight X 100) /green weight. The constants appear in Table III. TABLE III Percent of Dry Matter in Primordial Leates and in First Compound Leaf Sample Primordial Leaves First Compound Leaf Abnormal Control Difference Abnormal Control Difference 32 7-374 7.567 ~ -193 8.612 8.703 — .091 35 6.480 7.137 ~ -657 8.541 8-564 - -023 36 7-091 7.184 - -093 8.025 7-978 + -047 39 7.278 7-439 - .161 8-333 8.469 - .136 40 7-185 7.246 — .061 8.013 8.080 — .067 4i 7.103 7.201 - .098 8-324 8.045 + -279 42 7.076 8.207 -I.I3I 8.128 7.204 + -924 43 6.894 7.085 - .191 7.807 8.062 - -255 46 6.850 6-997 - -147 8.611 8.174 + -437 47 6.262 6.386 - .124 7.567 7.912 - -345 48 6-574 6.381 + -193 7-938 8.210 — .272 49 6-455 6-533 — .078 8.004 8.067 - .063 53 6-757 6.845 - .088 8.884 8.629 + -255 54 6.713 6.815 — .IO2 8.286 9.061 - -775 56 6.487 8.293 — 1. 806 8.287 8.502 - -2I5 61 6-855 6.899 - .044 8.620 8.668 - .048 64 6.048 6. 211 - -I63 7-528 7-438 + -090 65 6.212 5-9C9 + .303 7-815 6.962 + -853 66 6.014 5-817 + -197 7-263 7.366 - .103 70 6.216 6.581 - .365 8.490 8.764 - -274 71 4.948 5.001 - -053 6.631 6-595 + -036 72 4.906 6-035 — I.I29 6.976 8.029 -1-053 73 5-921 6.156 - -235 8.009 8-349 - -34° The results are not so consistent as those for the absolute values, green weight and dry weight. This condition is to be expected for two reasons. First, the abnormal plants show lower values of both green weight and dry weight than the normal controls. One cannot, therefore, expect such large differences in the indices calculated from these constants as if both measures did not differ in the same direction between abnormal and control series. Second, two sets of technical operations are involved in the indices, only one in each of the con stants used in calculating these ratios. While every effort to avoid error was made, the probabilities of error in an index are clearly twice as great as in either of the constants upon which it is based. 174 BROOKLYN BOTANIC GARDEN MEMOIRS Notwithstanding these two sources of difficulty in basing con clusions on relative amount of dry substance, there seem clear evi dences that the abnormal plants produce relatively as well as abso lutely less dry matter than the normals. In the case of the primordial leaves, there are 20 samples in which the relative dry weight is lower in the abnormal plants as against 3 in which it is higher. In the first compound leaf there are 15 samples in which the relative \veight in the abnormal plants is lower, as com pared with 8 in which it is higher than the normals. The average percentage content of dry substance in the primordial leaves of the abnormal- seedlings is 6.509 as compared with 6.779 'ln the normal controls, or a difference of —0.270. The average percent of dry matter in the first compound leaf is 8.030 in the abnormal as compared with 8.080 in the normal, or a difference of —.050 percent. CONCLUDING REMARKS The constants recorded in this paper are the results of one of the phases of an attempt to determine the nature of the relationship between morphological and physiological variations in plants. The results of the criteria applied are beautifully clear and con sistent. Seedlings of Phaseolus which show one of the smallest definite structural. variations, the slight vertical separation of the two coty ledons in their insertion on the axis, are differentiated from the struc turally apparently normal individuals in their physiological as well as in their morphological characteristics. This is shown by the facts that the morphologically abnormal plants produce a smaller weight of green leaf tissue, a smaller actual weight of dry substance in the leaf tissue, and a smaller relative weight of dry substance. This is true for both the primordial leaves and the first trifoliate leaf. OTE ON THE RELATION OF BLOOD FAT TO SEX, AND ON THE CORRELATION BETWEEN BLOOD FAT AND EGG PRODUCTION IN THE DOMESTIC FOWL BY OSCAR RIDDLE AND J. ARTHUR HARRIS FROM THE STATION FOR EXPERIMENTAL EVOLUTION, CARNEGIE INSTITU TION OF WASHINGTON, COLD SPRING HARBOR, NEW YORK) IEPRINTED FROM THE JOURNAL OF BIOLOGICAL CHEMISTRY VOL. XXXIV, No. 1, APRIL, 1918 Rented from THE JOURNAL OF BIOLOGICAL CHEMISTRY, Vol. XXXIV, No. 1, 1918 NdE ON THE RELATION OF BLOOD FAT TO SEX, AND ON THE CORRELATION BETWEEN BLOOD FAT AND EGG PRODUCTION IN THE DOMESTIC FOWL. BY OSCAR RIDDLE AND J. ARTHUR HARRIS. (Fm the Station for Experimental Evolution, Carnegie Institution of Washington, Cold Spring Harbor, New York.) (Received for publication, November 3, 1917.) i a recent number of this Journal Warner and Edmond1 hsje presented a considerable series of determinations of the blood fa1 of White Leghorn hens and cocks. Their interesting dis- ciiion of this subject requires a few words of comment on our pat. ti the treatment of their data these authors have not sufficiently poted out the bearing of their results upon earlier work, — indeed mst of the latter is ignored; the full value of their own work is mi clearly brought out; and some conclusions unwarranted by tlir data are drawn. The purpose of the paper is stated to be "1 show the relationship of blood fat of fowls to (1) egg produc- tiji, (2) presence of food in the alimentary tract, (3) color of .lep, etc., and (4) sex." "he clear and outstanding fact to be found in the 94 blood fat deerminations made by Warner and Edmond is that the blood ofihe actively laying hen contains a very disproportionately large anunt of fat; that of the non-laying hen a very disproportionately sull amount of fat. This fact, however, (and others soon to be mtitioned) for the blood serum of the fowl was published by L^vrence and Riddle2 2 months prior to the time that the samples fcthe above mentioned 94 blood analyses were drawn for examina- tii. This earlier work of Lawrence and Riddle on the blood of ; Warner, D. E., and Edmond, H. D., J. Biol. Chem., 1917, xxxi, 281. ' Lawrence, J. V., and Riddle, O., Am. J. PhysioL, 1916, xli, 430. 161 THE JOURNAL OF BIOLOGICAL CHEMISTRY, VOL. XXXIV, NO. 1 164 Blood Fat in Fowls Riddle utilized very much larger quantities of blood and probably the error involved in the individual determinations was thus reduced. The later and larger series of blood fat determinations therefore confirms the results obtained by Lawrence and Riddle. Most readers of Warner and Edmond's paper will certainly get the impression that the blood of 1 year old hens has an aver age fat value of 0.407 per cent, while that of 3 year old hens ha.' a value of only 0.171 per cent. The actual relation of thest two groups is as 0.199 to 0.171. The group of 3 year old hen: which gave an average of 0.171 were all non-layers and only non layers among the 1 year old hens may properly be compared wit! them. It may next be pointed out that the data "on the presence o food in the alimentary tract" do not justify the conclusion drawr nor indeed any conclusion whatsoever. The following state ment is made:7 "It has been reported by Mathews that in ma and animals the blood is much richer in fat after they have bee eating than it is after fasting. This is not true with hens, as show from Table VIII The [small] difference . . . would indicate that fasting for 16 hours has no effect upon tt amount of fat in the blood." In reality, 16 hours is not a fas ing period in the fowl. It more nearly represents the length > time between meals, at least on many of the very short days winter; and certainly there is some food still in the alimenta tract of a fowl for more than 16 hours after feeding. There are, however, two reasons why the data cannot answ the question of the relative amount of fat in the blood soon aft* as compared with 16 hours after a meal. These are, first, th the female fowl was used, and in these birds the individual variati is enormous, the really decisive factor associated with blood i values being the "laying" or "non-laying" condition of t hen. Other figures by these authors show that the blood fato laying hen (1.953) may be more than twenty times greater th that of a non-laying hen (0.083). Their figures (Table VI) a indicate that this value in laying hens may vary between 0.$ and 1.953. It is therefore obvious that one may not expect > find differences due to fasting for 16 hours in the averages obtaii 1 7 Warner and Edmond, ibid., 289. O. Riddle and J. A. Harris 165 f m twelve individuals of one group when compared with twelve ilividuals of the other group. An illustration of the unsuit- aility of the data for this purpose is the following: If the twelfth ( st) bird in each series be omitted from the averages, these latter a; changed from 0.405 and 0.396 to 0.268 and 0.263 respectively, dly in males, in which the fluctuations of the blood fat values a> much decreased, could one hope for success in a study of this cestion in the fowl. Still another reason for the inadmissibility c the data as submitted is that no basis for the selection of the prticular individuals chosen and compared is given. As the eta stand, and if one is permitted to select at will the "non- fiting" birds from the whole group of fat determinations, it is fusible to have those birds show more or show less blood fat than ! i "fasting" birds. These data, therefore, supply no evidence t it the fowl is an exception to the well known rule that the per < it of fat in the blood increases soon after the ingestion of food. I all of the fat determinations made by Lawrence and Riddle tis fact was recognized, and the blood samples were all drawn at cproximately the same time of day; namely, in the early after- ion. Our next point concerns the correlation between the fat content c the blood and egg production. Admitting that birds which are 1,-ing at the time the blood samples are taken differ from those Mich are not laying, a further problem arises concerning the i ationship of the percentage of fat found in the blood and the ttal egg record of the bird for the year. These authors say:8 "The fat content of the blood is corre- 1 od with egg laying activity, and there is also a slight correla- t n between the amount of fat in the blood and high yearly production." But in their summary, they conclude:9 "There is little or no (•relation between the amount of fat in the hen's blood and her yearly ffl yield. On the other hand the blood of a hen laying at the tne the sample is taken is much richer in fat than that of a hen \iich is not laying."10 Now both of these contradictory statements cannot be true. riere is, indeed, no reason why statements concerning correlation s Warner and Edmond, ibid., 288. 9 Warner and Edmond, ibid., 293. 10 The italics are ours in both quotations. 166 Blood Fat in Fowls should be of a general and vague nature. Correlation is a verj definite quantitative phenomenon, measurable on a universalh applicable scale of — 1 to + 1 . The numerical value of the cor relation coefficient, r, may be determined in any instance for twi measured variables, such for example, as fat content and annua egg record, by very simple and well known formulas. We now turn to the actual results which may be obtained b applying the correlation formulas11 to the data published by Wui ner and Edmond. Using a simple method of direct summatio of the actual values, their squares and their products,12 we find th following results for the whole series of 1 year old hens :13 rfe= +0.247 ±0.076 Thus, taking the whole series of 1 year old birds examined, tl hens which have a larger amount of fat in their blood in Octobi have, on the average, laid a larger number of eggs during the yea 11 Warner and Edmond must have been fully acquainted with the a vantages of applying the correlation formulas to such problems as the; for the data contained in the preliminary papers by Blakeslee and Warm cited and discussed by Warner and Edmond, together with far more extf sive data collected since these two preliminary papers were published, ha been carefully treated in great detail by the statistical methods in a paj by Harris, Blakeslee, and Warner (Genetics, 1917, ii, 36; Proc. Nat. An Sc., 1917, iii, 237). These papers, like that by Lawrence and Riddle, tl: have, quite inadvertently, failed to cite, although they contain much tl throws light upon the problems considered by them. A further investi: tion of the problem of the interrelationship between egg laying activ at various periods which also contains materials bearing very direc upon the problem of the physiology of egg production is now in pr (Genetics, 1918, iii, 27). 12 Harris, J. A., Am. Naturalist, 1910, xliv, 693. 13 Those unfamiliar with statistical formulas need only remember t ; the correlation coefficient measures the intensity of interrelations! ; between two variables on the scale of —1 to +1. Thus if annual egg f • duction is lower in birds with lower percentages of fat and higher in bi 3 with higher percentages of fat correlation between egg production and t content is positive in sign and lies somewhere between no correlation 1 perfect correlation. If high annual egg record is associated with low t content and low annual record with high fat content, correlation is nega a in sign and is measured by a coefficient lying between 0 and perfect n< • tive correlation. O. Riddle and J. A. Harris 167 Jit this group is highly heterogeneous. It comprises birds, wh'h were still laying at the time the blood samples were taken amthose which had ceased to lay.14 Dividing the birds into two. grcps on the basis of their laying activity at the time of sampling weind the following values for averages, variabilities, and cor- relions. ]tr 54 birds which had ceased laying, / = 0.199 e = 139.09 r 16 birds which were still laying at the time the samples we taken, / = 1.103 s = 163.37 eriod, for a bird of which the record of a limited period is known. Since the birds entered in the INTERNATIONAL EGG-LAYING CONTEST •t Storrs are drawn from a wide geographical area and are furnished by a arge number of breeders, and since the conditions in the different years re maintained as nearly constant as possible, it seemed desirable to utilize ecords from this contest subsequent to those upon which the equations re based in testing the value of the equations. The problem is: How Josely can the actual production of a bird entered in the contest in a given 'ear be predicted from equations based on the records of previous years /hen one or more months' performance of this bird is known from obser- ation? We have, therefore, as already noted, based the test of our series f equations first of all upon the records secured in Connecticut during the ontest year 1917 and 1918. The equations which we publish are based upon 1840 single-comb White -eghorn birds entered in the INTERNATIONAL EGG-LAYING CONTEST for EOTTICS6: My 1921 270 HARRIS, KIRKPATRICK, BLAKESLEE, WARNER AND CARD the years 1911 to 1917. The prediction equations have been tested upon 415 birds whose records were obtained during the year extending from November 1, 1917, to October 31, 1918. The justification for the course followed is found in the general principle that a theory should not be tested against the observations upon which it is based. For practical reasons this paper is limited to a test of the accuracy with which the egg record of a series of 415 birds trap-nested at Storrs during 1917-1918 can be predicted by a series of linear equations based on the experience of the six preceding years, 1911-1917, at the same place. It may be urged that conditions at Storrs are not representative of those prevailing in different parts of the country. Recognizing, for the sake ol argument at least, the validity of this objection we have been glad to avai ourselves of records taken elsewhere. These are now being used to tesi the accuracy with which the production of birds in any locality may b( predicted by means of equations based primarily upon experience in anothe: place or with another series of birds. The results of these studies wil eventually be published. NOTATION AND THEORY EMPLOYED We shall find it convenient to have a simple and rigid notation. Le e represent the recorded egg production of a bird in any month, 2 denot a summation of monthly egg records for a given bird, 1, 2, 3, ... 1. denote the twelve successive months of the pullet year, i.e., the Novembe of the year in which the bird was hatched until and including the followin, October. Then ei, e2, e3, . . ., e^ represent the November, Decembei January, . . ., October egg record of a bird with an annual record c 12 E = 2 (e) eggs. Further, En denotes the total number of eggs laid i i any month or group of months subsequent to any given month or grou of months used as a basis of prediction, i.e., 12 12 -En = E - ei = 2 (e), Eio =E - ei - e2 = 20), . . ., EI = en. 2 3 In the present paper we have used only the linear prediction equatior derived from the means, standard deviations and product-moment coeff cients of correlation between the periods, or groups of periods, of egg pr< duction, i.e., with equations of the type E = (E - r. \ VE p ) - re E — ep I P ••*• S» may be either positive or negative. Xa comparing taw to consider the question of over prediction or under prediction by two formulae which may be under consideration. If so our tables of criteria and not the difer- enots aa pnbnthed ahonU be consulted by the lender. characteristic equation given above is strictly valid only when to the population from which it is deduced. Its extension without modification to another population is justified only if the physical cons PREDICTING EGG PRODUCTION* IN WHITE LEGHORNS 273 - - 3 £ £ £ S3 £3 = '1 /i -!>" ~* s i -i c ; -; -? fi » «r- c — _ r - T - - . ~ ~ ~ ~ . OC^r^X — C C» --^ — -rac _ _ _ rs - _ tr. fc My 274 HARRIS, KIRKPATRICK, BLAKESLEE, WARNER AND CARD and the correlations of the variables in the two populations are essentially identical. Because of the uniformity of care and the wide origin of the birds exhib ited each year at the INTERNATIONAL EGG-LAYING CONTEST at Storrs the average productions do not differ widely in the different years. Thus the monthly and annual averages and standard deviations for the 1840 birds upon which the equations were based and the 415 birds upon which they were tested appear in table I.2 While certain of the differences are significant in comparison with their probable errors it is quite clear that the averages for the two periods are in fair agreement. Bird 997, Pen 100 i 2 3 4 5 6 7 8 N 143 1 -17 9 320 41 D 137.2 -23 8 566 44 161 143 1 — 17 9 320 41 T.. 3 148.1 -12 9 166 41 161 134 4 — 26 6 707 56 F 13 169 7 +8.7 75 69 158 135 6 — 22 4 501 76 M 24 189.1 +28.1 789 61 145 136 2 o o 77 44» A 21 169 2 +8 2 67 24 121 129 2 +8 2 67 24 M 29 199.6 +38.6 1489 96 100 99 4 -0 6 0 36 T 25 180.4 + 19.4 376 36 71 92 3 +21 3 453 69 T 27 193.2 +32.2 1036 84 46 61 8 + 15 8 249 64 A 13 142.0 -19.0 361 00 19 44 9 +25 9 670 81 s. 118 5 —42 5 1806 25 6 12 8 +6 8 46 24 O 6 162.0 + 1.0 1.00 6 -0 7 -6 7 44.89 Year . . 161 The method followed in the calculations may be illustrated by one o the calculation blanks for the individual bird — No. 997, pen 100. Th first column shows the production for the month indicated by the letter on the stub. This serves as the basis of prediction. The second colum shows the predicted number of eggs for the year, the third shows th deviation of this predicted number from the annual total of 161 egg; The fourth column gives the squares of these deviations of prediction froi observation. The fifth column shows the number of eggs in the remainin months of the year.3 The sixth column shows the number of eggs predicte 2 The percentage differences have been calculated by using the monthly averages for 19' to 1917 as a base. 3 The yields for the remaining months (columns 5 to 8) are dropped one space so as to coi cide with the first month of the period. For example, bird 997 laid 161 eggs in the period fro December to October; 161 in the period from January to October; 158 in the period from Fe ruary to October, and so on. PREDICTING EGG PRODUCTION IN WHITE LEGHORNS 275 for the remaining months. The seventh shows the deviations and the dghth the squares of the deviations of these predicted values from the ictual record for the remaining months. Calculation blanks for each individual bird were made on this principle ;or each of the equations used. The labor of testing the equation has, ;herefore, been very heavy, involving the calculation of 29,465 predicted /alues and the summations of the errors and squares of errors of the devi- itions of these predicted records from their true value. The excessive arithmetical routine has been ably handled by Miss EDNA VL PECKHAM, Miss IDA M. PECKHAM, Miss RUTH T. CRAWSON, and Miss KATHLEEN GAVIN of the Biometric Laboratory of the STATION FOR EXPERI MENTAL EVOLUTION. We are indebted to Miss EDNA K. LOCKWOOD for he diagrams, as well as for much assistance in the computations. TESTS OF EQUATIONS EMPLOYED Prediction of annual production from the record of one month Consider first of all the results of the attempts to predict the annual egg reduction of 415 White Leghorn birds observed at Storrs in 1917-1918 rom the records of a single month's production. The equations based >n the 1911 to 1917 experience are as follows: Month from which prediction is made Prediction equation November E = +143 . 186 + 2 .914 et December E = + 137 . 293 + 3 . 200 e2 January E = +138.271 + 3.308 e3 February E = + 1 18 . 689 + 3 . 926 e4 March £= +76.160 + 4.708 e-a April E = +62 . 688 + 5 . 074 e6 May £= +58.009 + 4.883 e7 June E= +59.977 + 4.818e8 July E= + 71. 137 + 4. 523 e9 August E = +90.391 + 3.974 fto September E = +118.509 + 3.381 en October E = + 141 . 470 + 3 . 429 ea These are in good general agreement with the equations for two of the ears, 1913-1914 and 1914-1915, published in a former paper (HARRIS, ILAKESLEE and KIRKPATRICK 1918, page 33, table 5). The graphical JSts for linearity of regression (loc. cit., diagrams 2-5, p. 34-39) for these tfo years, indicate a fairly close approximation to linearity throughout ie greater part of the range of variation of monthly egg production. A :itical test of linearity presents some difficulties because of the concen- : My 1921 276 HARRIS, KIRKPATRICK, BLAKESLEE, WARNER AND CARD tration of the bulk of the birds into a few of the classes, with the result that a rather large number of classes contain only a few birds each. A closer study of the fit of the regression line may, therefore, be deferrec until more data are in hand. The results of the tests of accuracy of prediction in the 415 White Leg horn birds of the 1917-1918 contest are given in tables 2 to 4. Since late TABLE 2 Average deviation with regard to sign of predicted annual egg record from actual record. Predictio of annual production from one- and from two-months performance. Equations based on Siort experience, 1911 to 1917. Test of equations on 415 White Leghorns, Starrs, 1917-1918. PERIOD FOR WHICH PREDICTION IS MADE PREDICTION FROM ONE MONTH PREDICTION FROM TWO MONTHS DIFFERENCE IN ACTUAL DEVIATION Drrna- EN'CE Df PERCEHT AGE DEVIATIC 1 Base of prediction Actual deviation Percent age deviation Base of prediction Actual deviation Percent age deviation ' November +2.39 1.52 Nov. + Dec. + 1.16 0.74 + 1.23 +0.7S December -0.49 0.31 Nov. + Dec. + 1.16 0.74 -0.67 -0.42 December -0.49 0.31 Dec. + Jan. + 1.15 0.73 -0.66 -0.42 January +2.58 1.64 Dec. + Jan. + 1.15 0.73 + 1.43 +0.91 January +2.58 1.64 Jan. + Feb. + 1.75 1.11 +0.83 +0.5.' February +0.06 0.04 Jan. + Feb. + 1.75 1.11 -1.69 -i.o; February +0.06 0.04 Feb. + Mar. -1.22 0.77 -1.16 -0.7: March -1.63 1.03 Feb. + Mar. -1.22 0.77 +0.41 +0.2( March -1.63 1.03 Mar. + Apr. -4.94 3.13 -3.31 -2.K April -6.23 3.95 Mar. + Apr. -4.94 3.13 + 1.29- +0.8: x1 or the wllnlp / April -6.23 3.95 Apr. + May +0.48 0.30 +5.75 +3.6.' W1HJ1C May + 7.02 4.45 Apr. + May +0.48 0.30 +6.54 +4.1.' year May + 7.02 4.45 May + June +0.82 0.52 +6.20 +3.9. June -5.21 3.31 May + June +0.82 0.52 +4.39 +2.7! June -5.21 3.31 June + July -6.60 4.19 -1.39 -0.8; July -5.27 3.34 June + July -6.60 4.19 -1.33 -0.8 July -5.27 3.34 July + Aug. -3.81 2.42 + 1.46 +0.9 August -0.82 0.52 July + Aug. -3.81 2.42 -2.99 -1.9' August -0.82 0.52 Aug. + Sept. +2.60 1.65 -1.78 -1.1 September +4.78 3.03 Aug. + Sept. +2.60 1.65 +2.18 + 1.3 September +4.78 3.03 Sept. + Oct. +5.34 3.39 -0.56 -0.3 ( October +3.95 2.51 Sept. + Oct. +5.34 3.39 -1.39 -0.8 we shall have to compare the results for prediction from one month performance with that from two- and from three-months record it has be< desirable to give the results side by side in the same table. The read need not, therefore, concern himself with the values for prediction fro two-months production until later. Since the errors of prediction of t1 annual record from each individual month must be compared with t. results for prediction from the combined production of two months, t. constants for the single months have been given in duplicate. PREDICTING EGG PRODUCTION IN WHITE LEGHORNS 277 The average errors with regard to sign are generally low, that for predic tion from November and from January production gives on the average 2.4 eggs too many for the year. For December, February, March and August the prediction is in error by less than 2 eggs. The values predicted irom April, May, June, July, September and October records are about 1 to 7 eggs in error. TABLE 3 Average deviation without regard to sign of predicted annual egg record from actual record. Pre diction of annual production from one- and from two-months performance. Equations based on Starrs experience, 1911 to 1917. Test of equations on 415 White Leghorns, Starrs, 1917-1918. , PERIOD FOR WHICH PREDICTION IS MADE PREDICTION FROM ONE MONTH PREDICTION FROM: TWO MONTHS DIFFERENCE IN ACTUAL DEVIATION DIFFER ENCE IN PERCENT AGE DEVIATION Base of prediction Actual deviation Percent- , IS6. deviation Base of prediction Actual deviation Percent- age_ deviation November 29.59 18.78 Nov. + Dec. 28.09 17.82 + 1.50 +0.96 December 29.26 18.57 Nov. + Dec. 28.09 17.82 + 1.17 +0.75 December 29.26 18.57 Dec. + Jan. 27.23 17.28 +2.03 + 1.29 January 30.09 19.09 Dec. + Jan. 27.23 17.28 +2.86 + 1.81 January 30.09 19.09 Jan. + Feb. 27.35 17.35 +2.74 + 1.74 February 27.28 17.31 Jan. + Feb. 27.35 17.35 -0.07 -0.04 February 27.28 17.31 Feb. + Mar. 1C r\t &*j . \JT 15.89 +2.24 + 1.42 March 27.95 17.73 Feb. + Mar. 25.04 15.89 +2.91 + 1.84 March 27.95 17.73 Mar. + Apr. 26.74 16.97 + 1.21 +0.76 April 28.72 18.22 Mar. + Apr. 26.74 16.97 + 1.98 + 1.25 r or trie April 28.72 18.22 Apr. + May 26.68 16.93 +2.04 + 1.29 whole * May 28.62 18.16 Apr. + May 26.68 16.93 + 1.94 + 1.23 year May 28.62 18.16 May + June 25.99 16.49 +2.63 + 1.67 June 29.03 18.42 May + June 25.99 16.49 +3.04 + 1.93 June 29.03 18.42 June + July 26.17 16.61 +2.86 + 1.81 July 28.35 17.99 June + July 26.17 16.61 +2.18 + 1.38 July 28.35 17.99 July + Aug. 24.88 15.79 +3.47 +2.20 August 26.87 17.05 July + Aug. 24.88 15.79 + 1.99 + 1.26 August 26.87 17.05 Aug. + Sept. 23.18 14.71 +3.69 +2.34 September 24.78 15.72 Aug. + Sept. 23.18 14.71 + 1.60 + 1.01 September 24.78 15.72 Sept. + Oct. 23.93 15.18 +0.85 +0.54 October 27.37 17.37 Sept. + Oct. 23.93 15.18 +3.44 +2.19 The average deviations without regard to sign are of course much larger since they constitute a measure of the error of prediction of the records of individual birds. They range from 24.8 to 30.1 eggs. The significance pf errors of this magnitude will be more clearly brought out later. The square root of mean square deviation also shows considerable regularity from month to month. These measures are naturally consider ably larger than the average deviation without regard to sign. They range from 32.9 to 38.8 eggs. JENETICS 6: My 1921 278 HARRIS, KIRKPATRICK, BLAKESLEE, WARNER AND CARD It is clear that the annual egg production of birds similar in origin to the series upon which the prediction equations were based and maintained under similar conditions may be predicted with a relatively high degree of accuracy providing their record for any month is definitely known. The accuracy with which prediction may be made will be clear if the errors of prediction are expressed in terms of the actual average annual production of the group of birds upon which the test is made. TABLE 4 Square root of mean square deviation of predicted annual egg record from actual record. Prediction of annual production from one- and from two-months performance. Equations based on Slorrs experience, 1911 to 1917. Test of equations on 415 While Leghorns, Storrs, 1917-1918. PERIOD FOR WHICH PREDICTION IS MADE PREDICTION FROM ONE MONTH PREDICTION FROM TWO MONTHS DIFFERENCE IN ACTUAL DEVIATION DIFFER ENCE IN PERCENT AGE DEVIATION Base of prediction Actual deviation Percent age deviation Base of prediction Actual deviation Percent age deviation November 38.65 24.52 Nov. + Dec. 36.46 23.13 +2.19 + 1.39 December 37.61 23.86 Nov. + Dec. 36.46 23.13 + 1.15 +0.73 December 37.61 23.86 Dec. + Jan. 35.50 22.53 +2.11 + 1.33 January 38.77 24.60 Dec. + Jan. 35.50 22.53 +3.27 +2.07 January 38.77 24.60 Jan. + Feb. 34.32 21.78 +4.45 +2.82 February 34.70 22.02 Jan. + Feb. 34.32 21.78 +0.38 +0.24 February 34.70 22.02 Feb. + Mar. 31.32 19.87 +3.38 +2.15 March 34.28 21.75 Feb. + Mar. 31.32 19.87 +2.96 + 1.88 March 34.28 21.75 Mar. + Apr. 32.89 20.87- + 1.39 +0.88 For the April 35.31 22.40 Mar. + Apr. 32.89 20.87 +2.42 + 1.53 whole * April 35.31 22.40 Apr. -f- May 32.76 20.79 +2.55 + 1.61 May 35.89 22. 77 Apr. + May 32.76 20.79 +3.13 + 1.98 year May 35.89 22.77 May + June 32.53 20.64 +3.36 +2.13 June 36.53 23.18 May + June 32.53 20.64 +4.00 +2.54 June 36.53 23.18 June +• July 33.00 20.94 +3.53 +2.24 July 35.89 22.77 June + July 33.00 20.94 +2.89 + 1.83 July 35.89 22.77 July + Aug. 31.83 20.20 +4.06 +2.57 August 34.34 21.79 July + Aug. 31.83 20.20 +2.51 + 1.59 August 34.34 21.79 Aug. + Sept. 30.39 19.28 +3.95 +2.51 September 32.94 20.90 Aug. + Sept. 30.39 19.28 +2.55 + 1.62 September 32.94 20.90 Sept. + Oct. 32.74 20.77 +0.20 +0.13 October 36.47 23.14 Sept. + Oct. 32.74 20.77 +3.73 +2.37 Remembering that the average annual production of the 415 test birds is 157.573 eggs, we use this as a base to determine the percentage errors for the equations for each month. These are given in columns with the caption "percentage deviation" in the tables. We note that in predicting from December, February and August record the average error with regard to sign is less than one percent of tkt average annual yield of the flock. In predicting from November, Januar> PREDICTING EGG PRODUCTION IN WHITE LEGHORNS 279 nd March the error lies between one and two percent. When April, lay, June, July, September and October records are used as a basis the verage errors of prediction are about 2.50 to 4.50 percent of the average nnual yield. The average deviations without regard to sign are less than 20 percent f the annual production. The values for the individual months range rom 15.7 for September to 19.1 for January. The square root of mean square deviations are less than 25 percent of he average annual production. The individual values range from 20.9 Dr September to 24.6 for January. These two latter tests may at first seem to indicate very unsatisfactory rediction. Such, however, is not the case. These give the average rrors either above or below the true record made in the prediction of the results jr an individual bird. The thing which is required in practice is generally ie prediction for a group of birds of a particular class. In a flock of 415 irds this has been shown above to be possible with an error of less than 5 ercent of the actual production for any month of the year and less than one er cent for a number of the months. The closeness of prediction may be made clear by a set of diagrams. In these the estimated production is shown by the straight line. The ctual average production for the year or for the group of remaining months )r which prediction is made is shown by solid dots for each group of birds s classified by monthly record. The shaded areas are determined as )llows. The birds were first grouped into classes of five-eggs range with aspect to number of eggs laid during the period of time used as a basis f prediction. The birds of these classes of five-eggs range were further ibdivided into those in which actual egg production was greater than the redicted and those in which the actual number was less than the predicted umber.4 The average error of prediction was determined for each of icse groups, and these averages represent the upper and the lower limits f the shaded areas. The upper limit represents, therefore, the average eviation (for the period for which prediction is made) of all birds which lake a higher record than that predicted for their class. The lower limit 4 A range of five eggs was used in order to obtain a number of birds sufficiently large to reduce 'inewhat the irregularities due to the errors of random sampling. The errors of prediction were each case determined for classes of unit range. Grouping is used for graphic representation erely. The average deviations represented by the limits of the shaded zone are to be thought as measured from a line perpendicular to the ordinates and intersecting the prediction line i the mid-ordinate of the 5-egg class. ;NEDCS 6: My 1921 280 HARRIS, KIRKPATRICK, BLAKESLEE, WARNER AND CARD of the shaded area marks the average deviation for all birds which show an egg record lower than that predicted. The graphs representing the prediction of annual production from the individual-months production appear in diagram 1 for the first six months of the year and in diagram 2 for the last half of the year. '"7V ^f \ / P\f V , f: ,/" * ,\ ' j**~ 02 4 G B 10 II 14 1C Id 20 21 24 26 DIAGRAM 1. — Tests of prediction of annual production from single-month records, of November to April. For explanation see text. Notwithstanding the irregularities which are inevitable in graphs base on such a highly variable character as annual egg production in a floe of only 415 birds, the most critical reader must admit that the predictio is excellent. PREDICTING EGG PRODUCTION IN WHITE LEGHORNS 281 of the production of a group of remaining months from the record of any month As noted above (pages 266-268) the worker may desire to predict either tie total egg production for the year or the egg production for a group f subsequent months of the year. 0 2 4 tf B 10 It 14 ie IS 10 I! 24 IS IS 30 DIAGRAM 2. — Tests of prediction of annual production from single-month records. Tests 3r May to October. In general the requirement will probably be the prediction of the total ;gg production of the remaining months of the year. Since, however, it s necessary to deal with other groups later, the errors of prediction of (a) he total egg production of the months of the year subsequent to the JENZTICS6: My 1921 282 HARRIS, KIRKPATRICK, BLAKESLEE, WARNER AND CARD month, where p is the base of prediction and of (b) the months of the year subsequent to the (p + l)th month will be considered in this place.5 The equations required are as follows: Month from uhich pre diction is made November November December December January January February February March March April April May May June June July July August August September Period for which prediction is made December to October January to October January to October February to October February to October March to October March to October April to October April to October May to October May to October June to October June to October July to October July to October August to October August to October September to October September to October October October Prediction equation £11 = + 143.186+ 1.914ei -Eio = + 139.262 + 1.403d £10 = + 134.491 + 1.835 e» £9 = + 131.461 + 1.373ft £9 = + 130.997+ 1.564ft Eg = + 123.011 + 1.215ft Eg = + 109. 824 + 2. 035 e4 £7 = +96.619 + 1.614ft E7 = +69.966 + 2.471 e-, E6 = +60.338+ 1.932 e, £e = +46.490 + 2.523e6 £5 = +39.849+ 1.786e, £5 = +27.639 + 2.233e7 £4 = +20.623+ 1.581*7 £4 = + 13.895 + 1.920*8 £.3 = +8.740+ 1.228 es £3 = +6.049+ 1.440e» £2 = +2. 323 + 0. 746 e, £2 = +0. 724 + 0. 935 do £1 = +0. 407 + 0. 264 ft0 £1 = -0. 726 + 0. 480 en The test of accuracy of prediction of these equations when applied to the 415 White Leghorns of 1917-1918 is given in comparison with the results for the prediction from two-months production (to be discussed later) in tables 5 to 7. Limiting our attention for the moment to the errors of predicting the production of the months of the year remaining after any given month used as a basis of prediction, we note that in general the average deviations 6 In the comparison between the egg production of a period of two months and the egg pro duction of a single month as a basis of prediction, it is necessary to base critical comparisons upon the results of predictions of the records of periods subsequent to the two months under consid eration. Concretely, if we are to compare November-plus-December record with November record and with December record as bases for the prediction of the annual production, the two- month period will contribute more to the annual record than either of the two months individually considered. Neither will contribute to the January-to-October production. We must, there fore, in testing prediction equations, base the test upon the results secured in predicting January- to-October egg record. For this purpose we must have equations which show the relation between the egg record of the individual months and the egg record of groups of remaining months. For example, we require for November the January-to-October production; for December, the February-to- October production; for January, the March-to-October production and so on. Fr>r conven ience merely the equations are given here in comparison with the other one-month equatior PREDICTING EGG PRODUCTION IN WHITE LEGHORNS 283 + 1 I++I++I+ + + + +I 1 1 l + z< H > §«§ Si" OOOOO'-iOO'-iO'-HCN'^-iCNOOOOOO +1 I++I++I+++++I 1 1 1+1 v> a ^ c> a ?' ++++++IIII++ III! i « ^ S) § £ I s> ^ t3 ^ s ^1 ++++++++ITI I++I 5§ w s iScn Is ss OOOOOOOOOOOOOOOOOOO OOOOOOOOOOOOOOOOOOO : My 1921 284 HARRIS, KIRKPATRICK, BLAKESLEE, WARNER AND CARD -* ^ 2w m o^.og^.co. ag^ssg^^sga 5 <=N "8s O S • If H lii $»* R ooooooooo OOO^HO 0 fc 0 2^ Ih 00^™-^- 8RSSSS2SSSS 1 ^ § fc ^ ^ a < ooooooooo ooooooooooo v c 3-° 0000^^ 00 =0^ S S S S S S S S S R $ i§ $.4 OvOvCCOOOvONOCNCv] c £$3g3go-SS£ orsgggoc-gg^^ •ft, S % - ONOCocOOu-j^r^tN-H -HOOOCI^'tfOOOstOTf 1"i § a *• 3 0 < || PREDICTI Base of prediction ^^QQ^J,^^^^ •^•^SS 3 3"3'3^-^ ° g « s ^ §1 I ^ "« ^ 0 + + + + + T + + ? i + ++++?+7^T 2< w > fcaJ65^g8H«ga cOOOgO^JOgJ. NS » u c < OOOOO'-^'-iOOOO + + + + + 1 + + + 1 + O^nOOOOOOO + + + + 1 + 1 + 1 u U) C 5.2 sssssssssss o^^oo^^oo g g Bl i IO ^O ^^ ^T *-O '-O IO ^O CO GO CO """""""§2 1 J a S i 'i S-S2SSSSSS* 9ac«99^^x« H -a 1 1 & % ^O 'O "^t* "^f f^l ^1 CO CO VO 'O '^ ^^^^^2^^ 0 & § a 1 £ '-3 I-, a wycc^^^S^^rt 1 +++++++++++ e<3 i— i i— i ^_i ^_ ^ ^ t_H ;_« +++++++++ C4 pq || o.,o.3ssis,sssso m^OO^oS^CN S.2 H SSSSSSSSSSS3 S3SS^SSSS i § g 1 o > g g 3 a 3 a g 6 5 g o g -aaiss-as.- S "^ S -3 IH _3 0 < sssssssassss ^^^^^^"^ PREDICT Base of prediction <3 S ^ "^ SS^^222H'"i^'^"73~< h 5 < 33 i w 2s §y oooooooooooo 0000000 jjjj |§ a, £ J • • ^ _£ IH' 1^ i; ^ >. >> « i-i-i^^iiil 6: My 1921 286 HARRIS, KIRKPATRICK, BLAKESLEE, WARNER AND CARD with regard to sign are small. No one of the errors is over 4 eggs. Tt percentage values, in which the actual average yields of the remainiD months in question are used as bases, range from 0.2 for the prediction < January-to-October production from December production to 13.6 percer in the case of the prediction of September-to-October production from th August record. The average deviations without regard to sign range froi 4.6 to 29.6 eggs. The percentage values range from 18.7 to 77.9 percec of the actual production for the given remaining period. IB IS 20 22 24 26 DIAGRAM 3. — Tests of prediction of production for a group of remaining months from singU month records. Tests for November to April. For explanation see text. The square root of mean square deviations vary from 5.7 to 38.7 eggs or from 23.9 to 97.3 percent of the actual yield. The values of the average deviation without regard to sign and o square root of mean square deviation decrease from the earlier to the late months. This is, of course, due to the fact that in predicting the eg record of the remaining months of the year the total record decreases a the number of remaining months becomes smaller. It is to be expecte . 1 n '\ )k--n fcl:.j..-j ii - _jr " ")[ - * v /?//CT / ' / N \ ( k M '' )f' /I 1 ' /I '(, _..'- l\ / \ >..••!•• 'S! ,)!' / ••!''' 1 1 / _.,.••' I ^ /V/1X ¥ 1 — 1 — 1 — 1 1 J II II I 1 _L 0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 DIAGRAM 4. — Tests of prediction of the production of a group of remaining months from single- ;onth production. Tests for May to September. ENETICS 6: 287 My 1921 288 HARRIS, KIRKPATRICK, BLAKESLEE, WARNER AND CARD therefore, that the absolute error of prediction will be smaller than when the prediction is made for a longer period. The relative errors of prediction are conspicuously larger than those found when the prediction is made for the year as a whole. Furthermore, these relative (percentage) errors increase as the period for which prediction is made becomes shorter. The test shows clearly that prediction of the results of short remaining periods cannot be made, — at least by means of the linear equations for prediction from one month's record tested in this paper, — with a satisfactory degree of accuracy. When prediction is made for the period subsequent to the (p + l)th month the average deviations with regard to sign vary from 0.56 to 3.32 or from 0.50 to 18.74 percent of the actual production for the period. The average deviations without regard to sign vary from 28.47 eggs for the prediction of January-to-October production from November production to 5.67 eggs for the prediction of October production from August record. The percentage values range from 19.38 to 96.59 percent. Similar results are found in the case of the square root of mean square deviation which ranges from 37.05 eggs for the prediction of January-to-October production from November record to 6.92 eggs for the prediction of October produc tion from August record. The percentage values range from 25.2 to 117.8 percent of the actual records. The graphic representation of the errors of the prediction of the remaining months of the year is made in diagrams 3 and 4. The slope of the lines and the moderate narrowness of the shaded areas as well as the fair agreement of the empirical and the predicted means for the remaining periods, evidence for fairly satisfactory prediction for the first six months of the year. As the end of the year is approached anc as the period of remaining months becomes shorter the slopes of the lines are more moderate. The narrowness of the shaded areas, representing the difference between the averages of the errors of over-prediction anc under-prediction, does not indicate great accuracy of prediction as com pared with that attainable in the earlier months, but merely that (because of the smaller egg record made by birds in the latter months of the year] great deviations from prediction are improbable. It is evident, therefore that for the prediction of the record of the later months of the year froir the record of immediately preceding months the equations have relativel} little value. It is quite clear that while the prediction of a group of remaining month: may be made with a relatively high degree of accuracy early in the year the predictions are relatively poor toward the end of the year. 289 Prediction of annual production from the sum of two monthly records Before considering the results of equations for the prediction of annual production from the combined record of two or more months, some general questions of theory must be considered. If the egg production of each individual month be correlated with that pf the whole year it would seem that a better prediction of the annual total may be made from the record of two or more individual monthly records than from one month's record only. This is a point emphasized by CARD (1917) who has correlated the total production of groups of nonths with the annual yield. ' There are several points to be taken into consideration here. First, it should be clear that the superiority of a group of months for predicting the annual yield of a bird is to a considerable extent due to the fact that the records of these months are included in the annual total. Thus in predicting annual total from November performance, the November record is included in the annual total. In predicting from November, December ind January production the records of these three months are included in the annual total. As far as their own contribution is concerned, predic tion can be made with absolute certainty. The importance of this factor vvould be especially great during the spring months when the number of 3ggs laid by practically all birds is high. If the principle of an increase n the number of months upon which prediction is to be based be extended :o its limit, it is clear that the annual total can be predicted with exactness :rom the record of twelve months. The importance of this factor was "ully recognized in our second publication (HARRIS, BLAKESLEE and KIRK- PATRICK 1918), in which we determined the correlation between the pro duction of each individual month and that of the remaining eleven months :>f the year, as well as that between the production of the individual months md the annual record. It is evident that it is impossible to compare directly and critically the errors made in predicting annual egg production from two-month periods md from single-month periods; in one case a single component only is included in the first and second variable of the pair whereas in the second :ase two components are involved. The problem of a direct comparison >vill be taken up in a subsequent section. Second, from the economic standpoint it is clear that trap-nesting for two months or three months is (disregarding initial investment) twice 3r three times as expensive as trap-nesting for one month. In general t is important to utilize the shortest practicable period on which predic tion may be based. GENETICS 6: My 1921 ir 290 HARRIS, KIRKPATRICK, BLAKESLEE, WARNER AND CARD Third, the mathematical theory of multiple correlation shows that L dealing with correlated characters the gain in accuracy of prediction rapidlj decreases with the number of characters employed. In our first detailed treatment of the problem of the correlation between the egg records ol the individual months we showed by the constants for a series of selected months that the egg records of the individual months are correlated among themselves. This has since been demonstrated for the entire series oi | n(n - 1) = 66 different combinations of the 12 months of the pullet year. It is evident, therefore, that very large gains in accuracy of pre diction cannot be expected to result from an increase in the number of periods, except in so far as the gain is due directly to the contribution of the months included. We now turn to the results of the test of equations for the prediction of annual record from two-consecutive-months production. The equa tions are as follows : Months from which prediction is made Prediction equation November and December E = + 132 .887 + 2 . 160 (ei + c2) December and January E = +130.822 + 2 . 176 (e2 + e3) January and February E = +146.040 + 2 .579 (e3 + et) February and March E = + 78 .008 + 2 .915 (et + eb) March and April E = +48.374 + 3.029 (e-3 + et) April and May E = +39 . 955 + 3 . 005 (et + e7) May and June E = +32 . 783 + 3 . 065 (e7 + e») June and July E = +44 . 650 + 2 . 864 (et + «,) July and August E = +62 . 861 + 2 . 625 (et + do) August and September E = +91 .865 + 2 .302 (e:0 + eu) September and October E =* + 122 . 597 + 2 . 140 (en + eK) Since a primary object of the present analyses is a comparison of equa tions based on two-months production with those based on a single month's record as a means of predicting the annual egg record of a bird, it is advan tageous to place the results for the two methods side by side in the same tables. The results are given in tables 2 to 4.6 Table 2 shows the average errors with regard to sign of the egg records of the 415 White Leghorns studied at Storrs in 1917-1918, when prediction is made from two-months production using equations based on the Storrs experience of the preceding six years. The average deviations with regard to sign are small. In 7 cases the equations have predicted values which are too large, whereas in 4 cases they have predicted values which are too small. The individual errors 6 It has seemed conducive to clearness to duplicate entries in order to secure the 22 differ ences which serve as a basis of comparison. PREDICTING EGG PRODUCTION IN WHITE LEGHORNS 291 e very small. Two are less than 1 egg, 4 are less than 2 eggs, while 5 e from 2 to 7 eggs. The percentage errors based on the mean annual eduction are less than 1 percent in 5 of the cases and less than 5 percent 160 140- 120 - 100 80 - • - * ^\ , , 1 1 1 0 2 4- 6 8 10 12 14 16 18 20 22 24 2S 28 30 32 34 3S 39 40 42 44 46 48 DIAGRAM 5. — Tests of prediction of annual production from combined record of two consecu- l e months. For explanation see text. Tests for November to February. i the other 6 cases. The average error in actual number of eggs, dis- igarding the sign of the error, is 2.72 eggs while the average of percentage : My 1921 294 HARRIS, KIRKPATRICK, BLAKESLEE, WARNER AND CARD The differences in the average deviations with regard to sign, as sho? in the first of the two final columns of table 2, range from less than a sinj egg (5 comparisons) to a maximum of less than 7 eggs. The avera difference is 2.21 eggs. If signs be considered the average difference only + 0.67 eggs. The differences in the percentage deviation when predi tion is made by single- and by two-month periods are shown in the fir column of the table. o 2 4 e 10 /2 14 IB IB 20 22 24 ^S 28 30 32 34 3ff 38 40 42 44 46 48 SO S2 54 St DIAGRAM 8. — Tests of prediction of annual production from the combined record of two cc secutive months. Tests of August to October. It is clear from these results that the results of prediction from tw months production are not materially better from the practical stan point than those for single-month's production although the labor entaili in recording the performance of a bird for two months must be appro? mately twice as great as that for a single month. The reader who cares to do so may verify these statements by a st of the results for average deviation without regard to sign and for sqi root of mean square deviation as shown in the two final columns of tat 3 and 4. PREDICTING EGG PRODUCTION IN WHITE LEGHORNS 295 ^rediction of the production of a group of remaining months from the sum of two monthly records We now have to consider the problem of the accuracy with which the gg production of a group of subsequent months may be predicted from tie sum of two consecutive monthly records. The equations are the following: Period jrom which prediction is made November and December December and January January and February Tebruary and March Vtarch and April Vpril and May VTay and June [une and July luly and August August and September Period for which prediction is made January to October February to October March to October April to October May to October June to October July to October August to October September to October October Prediction equation E= +132.887+ 1.160(e, + e2) E = +128.112 + 0.979 (e2 + «,) E = +124.959 + 0.336 («, + et) E = E = E = E = E = E = E= +76.542 + 1.320(>4 + e6) +44.586+ 1.363 («8 + <•„) +25.022 + 1.231 (c« + e7) +7.280+ 1.118 («T +e8) +0.994 + 0.827 («g + «,) -7.281 + 0.660 (e, + e10) -2.137 + 0.245 The results appear in the second section of tables 5 to 7. Here they are id beside the errors obtained for the prediction of the production of these ime periods from the record of the two months individually considered, 3 given by the equations shown on page 282. Table 5, giving the average deviation with regard to sign of the predicted 'om the observed values, shows that the actual deviations have a numerical inge of 0.05 to 3.73 eggs or from 0.04 to 17.6 percent. The largest relative percentage) deviations are, of course, in the final months of the year. The average deviations without regard to sign appear in the second }lumn of table 6. These vary from as low as 5.13 eggs in October to 28.09 ?gs for the period January to October. Since the average production ecreases as the number of remaining months becomes smaller we find le largest percentage errors in the later groups of months. These per- mtage values range from 18.9 for the period February to October to 87.4 >r the month of October. Similar results with somewhat different numeri- il values are found in table 7 which shows the square root of mean square aviation of the predicted from the observed values. These results show that when the number of remaining months is large, rediction of egg production can be made with relatively high accuracy om the combined record of two months. As the number of months icomes smaller the error of prediction is, as compared with the average reduction, relatively large. [trencs 6: My 1921 296 HARRIS, KIRKPATRICK, BLAKESLEE, WARNER AND CARD Turning now to the problem of the comparison of periods of one month and of two months as bases of prediction, and testing the efficiency of these two periods on the egg production of comparable remaining periods of time, we note that the differences in the two final columns of tables 5 to 7, expressed either in number of eggs or in percentages of the total production, are small. Thus the differences for the average deviation with regard to sign are all less than 3 eggs and all less than 6 percent. Most of the differences are far smaller than this. In some cases the predic tion from a single month gives the better result; in others prediction from two months gives the better result. The differences in the errors without regard to sign as obtained by the two methods are even smaller. No difference amounts to as much as a single egg per year. The large differ ences in the percentage errors by the two methods are found exclusively in the later months of the year where the total production is low. Com parable, but numerically somewhat different, results are found for the square root of mean square deviation. Thus it is clear that there is little practical difference between single- month and two-months production as bases of the prediction of the egg record of a subsequent period. Prediction of annual production from the sum of three monthly records The equations required for the prediction of annual production from the combined record of three consecutive months are the following: Months from which prediction is made Prediction equation November, December and January E = +126.742 + 1.770 (e\ + e2 + e3) December, January and February E = +113.940 + 1 .951 (e2 + e3 + e4) January, February and March E = +82 . 129 + 2 .266 (e3 + d + e6) February, March and April E = +50.502 + 2.323 (e4 + eb + e6) March, April and May E = +29.450 + 2 .267 (es + e6 + April, May and June E = + 19 . 349 + 2 . 324 (e6 + e7 + May, June and July E = +23 . 786 + 2 . 233 fa + es + June, July and August E = +41 .079 + 2.065 (e» + e9 + July, August and September E = +67.078 + 1 .895 (e9 + do + August, September and October E = +97 . 699 + 1 . 794 (ei0 + ea + The second section of table 8 shows the average deviation with regard to sign of the annual egg production predicted from the combined record of 3 consecutive months from the performance of the 415 White Leghorn birds studied at Storrs in 1917-1918. The results show that the trimonthly totals, like the monthly records and bimonthly totals considered in preceding sections, give excellent predic tions. December to February, January to March, March to May, and PREDICTING EGG PRODUCTION IN WHITE LEGHORNS 297 uly to September give average errors of prediction of less than 1 egg. November to January, April to June, and May to July give errors of predic- ion of between 2 and 3 eggs. August to October gives an error of predic- TABLE 8 •verage deviation with regard to sign of predicted annual egg record from actual record. Prediction , of annual production from one- and from three-months performance. Equations based on Starrs experience, 1.911 to 1917. Test of equations on 415 White Leghorns, Storrs, 1917-1918. 'ERIOD FOR WHICH •REDICTION IS MADE PREDICTION FROM ONE MONTH PREDICTION FROM THREE MONTHS DIFFERENCE IN ACTUAL DEVIATION DIFFER ENCE IN . PERCENT AGE DEVIATION Base of prediction Actual deviation Percent age deviation Base of prediction Actual deviation Percent age deviation November +2.39 1.52 Nov.-Jan. +2.09 1.33 +0.30 +0.19 December -0.49 0.31 Nov.-Jan. +2.09 1.33 -1.60 -1.02 January +2.58 1.64 Nov.-Jan. +2.09 1.33 +0.49 +0.31 December -0.49 0.31 Dec. -Feb. +0.78 0.49 -0.29 -0.18 January +2.58 1.64 Dec. -Feb. +0.78 0.49 + 1.80 + 1.15 February +0.06 0.04 Dec. -Feb. +0.78 0.49 -0.72 -0.45 January +2.58 1.64 Jan. -Mar. +0.49 0.31 +2.09 + 1.33 February +0.06 0.04 Jan. -Mar. +0.49 0.31 -0.43 -0.27 March -1.63 1.03 Jan. -Mar. +0.49 0.31 + 1.14 +0.72 February +0.06 0.04 Feb. -Apr. -4.07 2.58 -4.01 -2.54 March -1.63 1.03 Feb. -Apr. -4.07 2.58 -2.44 -1.55 April -6.23 3.95 Feb. -Apr. -4.07 2.58 +2.16 + 1.37 March -1.63 1.03 Mar.-May -0.73 0.46 +0.90 +0.57 ir flip April -6.23 3.95 Mar.-May -0.73 0.46 +5.50 +3.49 )I IflC May + 7.02 4.45 Mar.-May -0.73 0.46 +6.29 +3.99 WHO 1C ' April -6.23 3.95 Apr. -June -2.31 1.47 +3.92 +2.48 year May + 7.02 4.45 Apr. -June -2.31 1.47 +4.71 +2.98 June -5.21 3.31 Apr. -June -2.31 1.47 +2.90 + 1.84 May + 7.02 4.45 May-July -2.12 1.35 +4.90 +3.10 June -5.21 3.31 May-July -2.12 1.35 +3.09 + 1.96 July -5.27 3.34 May-July -2.12 1.35 +3.15 + 1.99 June -5.21 3.31 June-Aug. -5.35 3.39 -0.14 -0.08 July -5.27 3.34 June-Aug. -5.35 3.39 -0.08 -0.05 August -0.82 0.52 June-Aug. -5.35 3.39 -4.53 -2.87 July -5.27 3.34 July -Sept. -0.20 0.13 +5.07 +3.21 August -0.82 0.52 July -Sept. -0.20 0.13 +0.62 +0.39 September +4.78 3.03 July -Sept. -0.20 0.13 +4.58 +2.90 August -0.82 0.52 Aug.-Oct. +3.91 2.48 -3.09 -1.96 September +4.78 3.03 Aug.-Oct. +3.91 2.48 +0.87 +0.55 October +3.95 2.51 Aug.-Oct. +3.91 2.48 +0.04 +0.03 on of between 3 and 4 eggs. February to April gives an error of prediction 1 between 4 and 5 eggs. Finally June to August gives an error of predic- on of between 5 and 6 eggs. Considered in their relation to the average annual production these 'ilues range from 0.13 to 3.39 percent. These results certainly show :markable accuracy of prediction. 'NETICS 6: My 1921 298 HARRIS, KIRKPATRICK, BLAKESLEE, WARNER AND CARD The average errors without regard to sign, given in table 9 need not be considered in detail. They range from 21.4 to 25.9 eggs per year or from 13.6 to 16.5 percent of the annual total. TABLE 9 Average deviation without regard to sign of predicted annual egg record from aclual record. Pre diction of annual production from one- and from three-months performance. Equations based on Storrs experience, 1911 to 1917. Test of equations on 415 While Leghorns, Starrs, 1917-1918. PERIOD FOR WHICH PREDICTION IS MADE PREDICTION FROM ONE MONTH PREDICTION FROM THREE MONTHS DIFFERENCE IN ACTUAL DEVIATION DIFFER ENCE m PERCENT AGE DEVIATION Base of prediction Actual deviation Percent age deviation Base of prediction Actual deviation Percent- age_ deviation November 29.59 18.78 Nov.-Jan. 25.93 16.45 +3.66 +2.33 December 29.26 18.57 Nov.-Jan. 25.93 16.45 +3.33 +2.12 January 30.09 19.09 Nov.-Jan. 25.93 16.45 +4.16 +2.64 December 29.26 18.57 Dec. -Feb. 25.31 16.06 +3.95 +2.51 January 30.09 19.09 Dec. -Feb. 25.31 16.06 +4.78 +3.03 February 27.28 17.31 Dec. -Feb. 25.31 16.06 + 1.97 + 1.25 January 30.09 19.09 Jan. -Mar. 25.29 16.05 +4.80 +3.04 February 27.28 17.31 Jan. -Mar. 25.29 16.05 + 1.99 + 1.26 March 27.95 17.73 Jan. -Mar. 25.29 16.05 +2.66 + 1.68 February 27.28 17.31 Feb. -Apr. 24.16 15.33 +3.12 + 1.98 March 27.95 17.73 Feb. -Apr. 24.16 15.33 +3.79 +2.40 April 28.72 18.22 Feb. -Apr. 24.16 15.33 +4.56 +2.89 March 27.95 17.73 Mar.-May 25.42 16.13 +2.53 + 1.60 . For thp April 28.72 18.22 Mar.-May 25.42 16.13 +3.30 +2.09 . -L \Ji IL1L- whole ' May 28.62 18.16 Mar.-May 25.42 16.13 +3.20 +2.03 April 28.72 18.22 Apr. -June 24.33 15.44 +4.39 +2.78 year May 28.62 18.16 Apr. -June 24.33 15.44 +4.29 +2.72 June 29.03 18.42 Apr. -June 24.33 15.44 +4.70 +2.98 May 28.62 18.16 May-July 24.20 15.36 +4.42 +2.80 June 29.03 18.42 May-July 24.20 15.36 +4.83 +3.06 July 28.35 17.99 May-July 24.20 15.36 +4.15 +2.63 June 29.03 18.42 June-Aug. 23.49 14.90 +5.54 +3.52 July 28.35 17.99 June-Aug. 23.49 14.90 +4.86 +3.09 August 26.87 17.05 June-Aug. 23.49 14.90 +3.38 +2.15 July 28.35 17.99 July -Sept. 21.36 13.55 +6.99 +4.44 August 26.87 17.05 July -Sept. 21.36 13.55 +5.51 +3.50 September 24.78 15.72 July -Sept. 21.36 13.55 +3.42 +2.17 August 26.87 17.05 Aug.-Oct. 21.59 13.70 +5.28 +3.35 September 24.78 15.72 Aug.-Oct. 21.59 13.70 +3.19 +2.02 October 27.37 17.37 Aug.-Oct. 21.59 13.70 +5.78 +3.67 The square root of mean square deviation of errors of prediction giver in table 10 are, of course, larger than the average deviations without regarc to sign. They vary from 28.1 to 33.8 eggs or from 17.8 to 21.5 percent o: the annual production. 299 The range of variation in the egg production of three-month periods is ) wide that it is impossible because of the limitations of space to represent ie errors of prediction from three-month periods graphically for each of le equations. TABLE 10 juare root of mean square deviation of predicted annual egg record from actual record. Prediction of annual production from one- and from three-months performance. Equations based on Starrs experience, 1911 to 1917. Test of equations on 415 White Leghorns, Storrs, 1917-1918. ERIOD FOR WHICH REDICTION IS MADE PREDICTION FROM ONE MONTH PREDICTION FROM THREE MONTHS DIFFERENCE IN ACTUAL DEVIATION DIFFER ENCE IN PERCENT AGE DEVIATION Base of prediction Actual deviation Percent- age_ deviation Base of prediction Actual deviation Percent age deviation November 38.65 24.52 Nov.-Jan. 33.84 21.47 +4.81 +3.05 December 37.61 23.86 Nov.-Jan. 33.84 21.47 +3.77 +2.39 January 38.77 24.60 Nov.-Jan. 33.84 21.47 +4.93 +3.13 December 37:61 23.86 Dec. -Feb. 32.65 20.72 +4.96 +3.14 January 38.77 24.60 Dec. -Feb. 32.65 20.72 +6.12 +3.88 February 34.70 22.02 Dec. -Feb. 32.65 20.72 +2.05 + 1.30 January 38.77 24.60 Jan. -Mar. 31.58 20.04 + 7.19 +4.56 February 34.70 22.02 Jan. -Mar. 31.58 20.04 +3.12 + 1.98 March 34.28 21.75 Jan. -Mar. 31.58 20.04 +2.70 + 1.71 February 34.70 22.02 Feb. -Apr. 29.77 18.89 +4.93 +3.13 March 34.28 21.75 Feb -Apr. 29.77 18.89 +4.51 +2.86 April 35.31 22.40 Feb. -Apr. 29.77 18.89 +5.54 +3.51 March 34.28 21.75 Mar.-May 31.14 19.76 +3.14 + 1.99 jir the April 35.31 22.40 Mar.-May 31.14 19.76 +4.17 +2.64 whole < May 35.89 22.77 Mar.-May 31.14 19.76 +4.75 +3.01 April 35,31 22.40 Apr. -June 30.59 19.41 +4.72 +2.99 year May 35.89 22.77 Apr. -June 30.59 19.41 + 5.30 +3.36 June 36.53 23.18 Apr. -June 30.59 19.41 +5.94 +3.77 May 35.89 22.77 May-July 29.40 18.65 +6.49 +4.12 June 36.53 23.18 May-July 29.40 18.65 + 7.13 +4.53 July 35.89 22.77 May-July 29.40 18.65 +6.49 +4.12 Tune 36.53 23.18 June-Aug. 29.80 18.91 +6.73 +4.27 July 35.89 22.77 June-Aug. 29.80 18.91 +6.09 +3.86 August 34.34 21.79 June-Aug. 29.80 18.91 +4.54 +2.88 July 35.89 22.77 July -Sept. 28.10 17.83 + 7.79 +4.94 August 34.34 21.79 July -Sept. 28.10 17.83 +6.24 +3.96 September 32.94 20.90 July Sept. 28.10 17.83 +4.84 +3.07 August 34.34 21.79 Aug.-Oct. 29.23 18.55 +5.11 +3.24 September 32.94 20.90 Aug. -Oct. 29.23 18.55 +3.71 +2.35 October 36.47 23.14 Aug.-Oct. 29.23 18.55 + 7.24 +4.59 Two series, that for November to January and for March to May, have tan selected at random to represent the goodness of fit of prediction in " lese cases. The results for prediction from November to January record ;e shown in diagram 9. Those for prediction from March to May pro- 'Nines 6: My 1921 300 HARRIS, KIRKPATRICK, BLAKESLEE, WARNER AND CARD DIAGRAM 9. — Tests of the prediction of annual production (upper figure) and of the pro duction of a group of remaining months (lower figure) from the combined record of three con secutive months. Tests for the period November to January. C 2 « £ 8 10 I! 14 IS II SC SI 7S 7t >4 7t X it DIAGRAM 10. — Tests of the prediction of annual production (upper figure) and of the produc tion of a group of remaining months (lower figure) from the combined record of three consecu tive months. Tests for the period March to May. PREDICTING EGG PRODUCTION IN WHITE LEGHORNS 301 uction are shown in diagram 10. In both cases the upper figure represents he prediction of annual production. The lower figure shows the prediction f the groups of remaining months and will be discussed in a subsequent sction. After the discussion of the preceding diagrams these graphs are self- xplanatory. When these results are compared, as in the last two columns of the tables, ith those for prediction from a single one of the three months the differ- nces are surprisingly small. For example the most important test, — that f the average deviation with regard to sign, — shows that 11 of the 30 inferences are less than 1 egg per year; 3 are less than 2 eggs per year; rhile 16 are 2 eggs or more per year. In no case is the difference as much s 7 eggs per year. The difference in percentage deviation is in no case s large as 4 percent. Turning to the comparison of average deviation without regard to sign rhen prediction is made from trimonthly periods and from the records f individual months we note that the differences are without exception ositive in sign. Thus they show a greater error when prediction is made rom a single monthly record. The differences are, however, always less lan 7 eggs per year and are generally less than 5 eggs. The percentage ifferences vary from 1.3 to 4.4 percent when both percentages are based n the annual total. Similar results are obtained for the square root of mean square deviation, 'he deviations are larger throughout when prediction is made from single- ion ths records than when made from three-months records. The differ- nces are not, however, large. They range from 2.05 to 7.79 eggs, or from .30 to 4.94 percent of the annual average production. Thus while practically without exception a closer prediction of the nnual egg record of individual birds can be made from three-months reduction the difference between a three-month period and a single- lonth period is by no means so large as one unacquainted with statistical icory might have assumed. ENETTCS 6: My 1921 302 HARRIS, KIRKPATRICK, BLAKESLEE, WARNER AND CARD Prediction of the production of a subsequent period from the sum of thre( monthly records The equations required are the following: Months from which prediction Period for which predic- is made lion is made Prediction equation November, Dec. and Jan. February to October E9 = +126.742 + 0.770 (a + e« + «,) Dec., Jan. and Feb. March to October £8 = +112.051 + 0.806 (ez + e3 + et) Jan., Feb. and March April to October E7 = +81 .464 + 0.935 (e3 + e4 + «6) February, March and April May to October £6 = + 49.753 + 0.955 fa + e6 + «,) March, April and May June to October E& = +25 .210 + 0.850 (e& + e6 + «7) April, May and June July to October E^ = +7 .063 + 0. 770 (e6 + e7 + et) May, June and July August to October E3 = —1.975 + 0.594 (e7 + e8 + e,) June, July and August September to October EZ = —4.701 + 0.377 (e» + e9 + e10) July, August and September October EI = -3.343 + 0. 172 (e9 + do + «n) Table 11 contains the average deviations with regard to sign, of the predicted yield of remaining months, from the actual productions, when prediction is made from the total yield of three consecutive months. The deviations range from 0.20 to 3.30 eggs or from 0.27 to 18.22 per cent of the actually observed yield. As far as this criterion shows, predic tions are excellent for all periods from that including February to October to that for August to October. The September-to-October record and the October record, however, cannot be predicted with a high degree of accuracy, the errors being over 17 percent of the mean value for these months. The average deviations without regard to sign, shown in table 12, range from 5.24 to 25.93 eggs, the values decreasing as the length of the period for which prediction is made becomes smaller. The reverse is true of the percentage values which increase from 18.66 percent for the period February to October to 89.23 percent of the actual yield for the month of October. Similar results are obtained when the formulae are judged by the square root of mean square deviation of the predicted from the actually observed egg record as shown in table 13. These root mean square deviations range from 33.84 for February to October to 6.44 for the month of October alone, or from 24.30 percent for the group of 8 remaining months of the year to 109.67 percent for the last (single) month. The results for the prediction of two of the groups of remaining months from the combined records of three-months production are represented graphically for the three months November to January in diagram 9 and for the three months March to May in diagram 10. It is the lower figure which is to be consulted in each case. The gentle slope of the lines and the considerable irregularities of the means show that prediction of the record of a period of remaining mont PREDICTING EGG PRODUCTION IN WHITE LEGHORNS 303 £ w 8g2 Z £ H W fi. < r£ W « w ° > B H 8 F ;§ = 8 a < e S 1 1 1 + + + 1 1 1 1 1 1 1 1 1 1 1, 1+1+1111111 o z So 9B SSSSoooocDooooooooooooo : 32323333333333 & Cimcs 6: My 1921 304 HARRIS, KIRKPATRICK, BLAKESLEE, WARNER AND CARD " Ja 53 Ov o S »'i « 2 . o<§ 1 w < £«» s£Q B a< S° w a o y OOO^OO'-iOOOOOOOO'-iOO^OO^OOOOO +++++ 1 ++++++++++++++ 1 ++ 1 ++I CNCNCNCNCNCNCNCNCNCNCNCNCNCN CJ(JCJ(J(JUOU(JUOO(JOUUtJtJO(JOtJtJtJ • •• oooooooooooooooooooooooo : : . ooooooooooooooooooooooootil-i PREDICTING EGG PRODUCTION IN WHITE LEGHORNS 305 . • • § 333 fr # ff • i t 7 • r •. 3- /• • i n i- , • tion is made Period for which prediction ts made Prediction equation November February to October £9 = +134.546 + 1 . 143 d December March to October £8 = +122 .721 + 1 . 165 ej January April to October E7 = + 106 . 659 + 1 . 033 e, February May to October £6 = +80.512 + 1.342 e4 March June to October £5 = +47.994 + 1 .462 e5 April July to October £4 = +30. 111 + 1. 2 19* May August to October Ez = +13.094 + 1 .008 e? June September to October £•> = +3.462 + 0.649 e8 July October £, = +0.297 + 0.240 et When we compare the results for the prediction of the yield of a grouj of subsequent months from single monthly records and from trimonthh records of production we find that the differences in errors of predictioi are surprisingly small. Specifically we note that in the case of the averagi deviation with regard to sign, shown in the two last columns of table 11 [ the differences in actual errors range from 0.03 to 3.42 eggs while the differ ences in percentage values range from 0.05 to 10.55. In some cases th'i three-month period gives a numerically larger error of prediction whil< in other cases the one-month period gives the larger error. When the comparison is made on the basis of average deviation withou regard to sign (table 12) the single-month period gives a slightly large average deviation in most cases, 23 out of 27 cases. The differences however, very small, varying from 0.12 to 1.14 eggs. Similar results are obtained when the comparisons (between the singl component months and the three-months record as bases of prediction are based upon square root of mean square deviation (table 13). In 2. of the 27 cases prediction from a monthly record gives slightly more variabl PREDICTING EGG PRODUCTION IN WHITE LEGHORNS 307 rrors than prediction from the combined record of three months. The dfferences are, however, insignificant, varying from 0.02 to 1.68 eggs. It 5 clear, therefore, that if the linear equation be used for the purpose of predicting the yield of a group of remaining months, about as good results br practical purposes may be obtained from single month records as from he sum of three months records. It is quite possible that with equations other than the linear this will iot be the case. Such equations will be investigated in future work. Comparison of the two- and three-month periods as bases for the prediction of the egg record of the subsequent months In the foregoing discussion comparisons between the value of single- ionth periods and two-month periods and between single-month and three- lonth periods as base's for prediction have been made. It will be of some aterest to compare two- and three-month periods in the same way. Cer- ain of the data may be rearranged from preceding tables. Special calcu- itions would, however, be necessary to complete all of the possible com- •arisons. It is evident that for a critical comparison between the two roups it is necessary to deal with the egg record of a group of remaining months. Thus in comparing November-to-january production with sTovember-and-December or December-and- January production as bases f prediction it is necessary to determine the accuracy with which the egg 'reduction of February to October may be predicted since none of the lonths included in the base of prediction should also occur in the period pr which prediction is made. Limiting our attention to the comparisons which can be made from the .ata in the preceding tables7 we note that in some cases there is a larger verage deviation with regard to sign in predicting from two-months and i some cases a larger error in predicting from three-months production. The same may be shown to be true for the average deviation without egard to sign and for the square root of mean square deviation of the predicted from the actual values. Thus there is little practical advantage i dealing with three-months production as compared with two-months 'reduction as bases for the prediction of the record of a group of subsequent lonths. 7 The subsidiary tables upon which the following conclusions were based may be formed from ibles 5 to 7 and 11 to 13. It seems unnecessary to publish these tables here. ENETICS b: My 1921 308 HARRIS, KIRKPATR1CK, BLAKESLEE, WARNER AND CARD Comparison of the four periods as bases for the prediction of the egg record of the year In the introductory sections of this paper we called attention to the so- called periods or cycles of egg production which have been recognized by a number of students of fecundity in the domestic fowl. It might at first seem desirable to compare the results of predicting from these periods. Since these periods are consecutive and together make up the entire laying year it is impossible to obtain any common basis for testing their efficiency such as has been found in periods of subsequent months in pre ceding tests. In view of this fact it does not seem desirable in this place to go into the question of the comparison of these conventional periods as bases of pre diction. Practically all of the data required for such comparison as can be made appear in the foregoing tables 2 to 13. The reader who desires to do so may abstract the constants from these tables. SUMMARY AND CONCLUSIONS The specific purpose of the present paper, which is one of a series dealing with the general problem of variation and correlation of egg production in the domestic fowl, is to consider the possibility of predicting the future egg production or the total annual egg production of White Leghorn birds from the record of an individual month or a group of consecutive months. The investigation has been carried out because of two convictions: First, factors underlying the distribution, inheritance and interrelation ships' of fecundity in birds present a problem of first-rate biological impor tance. Second, that it is one of the functions of the biologist to provide the agricultural economist with the quantitative constants and formulae upon which the scientific agriculture of the future must largely rest. The method followed has been to determine a series of prediction equa tions based on the experience of six years (1911 to 1917) of the INTER NATIONAL EGG-LAYING CONTEST at Storrs and to test these equations upon an additional series of 415 birds studied at Storrs in 1917-1918. Thus the equations have been tested upon a different series of birds from that upon which they were based, but upon birds maintained under conditions com parable with those upon whose record the fundamental equations were based. The results show that the annual egg record of a series of birds may be predicted with a reasonably high degree of accuracy when their performance for a single month is known. Somewhat higher accuracy may be obtained PREDICTING EGG PRODUCTION IN WHITE LEGHORNS 309 ,hen the record of two or more months is taken into consideration, but the nprovement due to an increase in the number of months upon which rediction is based is not great. Prediction of the egg record which will be made by groups of birds sub- jquently to the month or group of months chosen as a basis of prediction !m also be made, but the accuracy of prediction decreases rapidly as the sriod for which prediction is made becomes shorter. ' The results show that in the case of a flock of White Leghorn fowl, which essentially identical in genetic composition and maintained under essen- ally uniform conditions from year to year, it is quite possible to estimate anual egg production from the record of either a single month or of two r three consecutive months with a high degree of accuracy. The same • presumably true of other breeds as well. This point is now under ivestigation. It is probably not feasible to use the equations given in this paper for Dcks differing greatly in genetic composition or in conditions of mainte- ance from that upon which these equations were based. The problem : the determination of corrective terms by which the equations may be pplied to flocks other than that upon which they are based is now under tvestigation. LITERATURE CITED .^DER, B., and EGBERT, A. D., 1918 A quick method of obtaining individual egg records without the trap nest. Bull. Utah Agric. Exp. Sta. 162. ^AKESLEE, A. F., HARRIS, J. ARTHUR, WARNER, D. E., and KIRKPATRICK, W. F., 1917 Pig mentation and other criteria for the selection of laying hens. Bull. Storrs Agric. Exp. Sta. 92, pp. 95-194. '\RD, L. E., 1917 A study of egg production in the White Leghorns. Bull. Storrs Agric. Exp. Sta. 91, pp. 41-90. ARRIS, J. ARTHUR, BLAKESLEE, A. F., and WARNER, D. E., 1917 Body pigmentation and egg production in the fowl. Proc. Nation. Acad. Sci. 3: 237-241. Fig. 1-3. ARRIS, J. ARTHUR, BLAKESLEE, A. F., and KIRKPATRICK, W. F., 1917 Interperiodic correla tion in the egg production of the domestic fowl. Proc. Nation. Acad. Sci. 3: 565-569. Fig. 1-2. ARRIS, J. ARTHUR. BLAKESLEE, A. F., and KIRKPATRICK, W. F., 1918 The correlation between egg production during various periods of the year in the domestic fowl. Genetics 3: 27-72. Fig. 1-11. ARRIS, J. ARTHUR, BLAKESLEE, A. F., WARNER, D. E., and KIRKPATRICK, W. F., 1917 The correlation between body pigmentation and egg production in the domestic fowl. Genetics 2: 36-77. Fig. 1-16. ENETICS 6: My 1921 THE PREDICTION OF ANNUAL EGG PRODUCTION FROM THE RECORDS OF LIMITED PERIODS BY J. ARTHUR HARRIS, W. F. KIRKPATRICK AND A. F. BLAKESLEE Station for Experimental Evolution, Carnegie Institution, and the Storrs Agricultural Experimental Station Reprinted from the Proceedings of the NATIONAL ACADEMY OF SCIENCES, Vol. 7, pp. 213-219. July, 1921. Reprinted from the Proceedings of the NATIONAL ACADBMV OF SCIENCES, Vol. 7, No. 7, pp. 213-219, July, 1921. THE PREDICTION OF ANNUAL EGG PRODUCTION FROM THE RECORDS OF LIMITED PERIODS BY J. ARTHUR HARRIS, W. F. KIRKPATRICK AND A. F. BL,AKESUSE STATION FOR EXPERIMENTAL EVOLUTION, CARNEGIE INSTITUTION, AND THE STORKS AGRICULTURAL EXPERIMENTAL STATION Communicated by C. B. Davenport, March 12, 1921 For the past several years the writers have been considering the possi bility of predicting the annual egg production of the domestic fowl from the records of short periods of time. Such records may be determined by trap- nesting, or by the use of other criteria when the maternity of the eggs is not required for breeding purposes. 1 The first definite step in the direction of the use of the egg record of a short period for the prediction of the production during a subsequent or a longer period was, as far as we are aware, taken in 1917 when it was shown2 that in a heterogeneous series of birds such as are submitted by practical breeders in egg laying contests, the October egg production is correlated with that of every other month of the year. The investigation was carried much further in a second memoir3 in which the correlations between the records of the individual months and the production of the whole year, between the records of the individual months and those of the remaining 11 months of the year, and between the production of 5 of the individual months and the production of all the other individual months, were pub lished for two series of birds. In this paper the equations for the prediction of total annual production from the record of the individual months were given. Our purpose here is to state briefly the results of a first test of the possi bility of utilizing the linear regression equation (which is strictly valid only for the population from which it is deduced) for the prediction of the records of the birds of a flock the performance of which is unknown as far as the determination of the constants of the equations is concerned. 214 GENETICS: J. A. HARRIS ET AL. PROC. N. A. S In a population the straight line relating the egg production of a period K/> with that of a period used as a basis of prediction, e, is where the bars denote means, the sigmas represent standard deviations, and r indicates the correlation of the two variables in the standard popu lation. The value of Ep given by the equation is the theoretical mean produc tion for the array of individuals of any class with respect to e. The as sumption to be tested is that we may write Ep' and e' instead of Ep and e, where E/ is the theoretical mean production for a period p of the array of birds of any grade of production e in the period used as a basis of pre diction in a series of birds which are not involved in the data upon which the equations were based, but to which the equations are to be applied for practical purposes. The essential practical requisites for such prediction equations are: (1) That the errors of prediction shall be distributed about the true numbers in such a manner that estimation will not in the long run be either too high or too low. (2) That the magnitude of the deviation of the predicted from the observed egg production shall be as small as possible. Let Ep" be the actual and EP' the predicted egg production of an in dividual bird for any period, p, in a flock to which the equation is being applied. The error of prediction is then EP' — EP." The average of these errors, with regard to sign N* furnishes a measure of the success with which the first requirement, (1) above, is met. The average of these errors without regard to sign fur nishes a measure of the average error above or below the true production of the individual birds of a flock. The square root of mean square devia tion furnishes a measure of this error which weights larger errors. The errors may be expressed in actual numbers of eggs, or, in relative terms, as percentages of the mean production of the period and flock for which prediction is made. Both methods have been used in testing the' equations. In testing the efficiency of such equations for purposes of predictic we have proceeded in a purely objective manner. Working on the sumption that the crucial test of any theory is its capacity for predict VOL. 7, 1921 GENETICS: J. A. HARRIS ET AL. 215 the unknown, we have calculated equations based upon the data of the International Egg Laying Contest at Storrs, Conn., during the six contest years, 1911-1917, inclusive. We have then used these equations to pre dict the annual production (and the production of groups of months) for the birds of the 1917-' 18 contest, using as a basis of prediction the individ ual months of the laying year separately, pairs of successive months and groups of three months. Our conclusions concerning the value of the equations depend, therefore, not upon a priori considerations but upon the results of actual tests of accuracy of prediction for series which were un known as far as the determination of the constants of the equations is Concerned. Consider first of all the results of the attempts to predict the annual egg production of 415 White Leghorn birds observed at Storrs from Nov. 1, 1917 to Oct. 31, 1918 from the records of a single month's production. The results of the three criteria of accuracy of prediction are summa rized in table 1. TABLE i ERRORS OF PREDICTION OF ANNUAL EGG PRODUCTION FROM THE RECORDS OF INDIVIDUAL MONTHS MONTH USED AS AVERAGE DEVIATION WITH REGARD TO SIGN AVERAGE DEVIATION SQUARE ROOT OP MBAN WITHOUT REGARD TO SIGN SQUARE DEVIATION BASK OF PREDICTION Actual deviation Percentage deviation Actual deviation Percentage deviation Actual deviation Percentage deviation November + 2.39 1.52 29.59 18.78 38.65 24.52 December - 0.49 0.31 29.26 18.57 37.61 23.86 January + 2.58 1.64 30.09 19.09 38.77 24.60 February + 0.06 0.04 27.28 17.31 34.70 22.02 March - 1.63 1.03 27.95 17.73 34.28 21.75 April - 6.23 3.95 28.72 18.22 35.31 22 .40 May + 7.02 4.45 28.62 18.16 35.89 22.77 June - 5.21 3.31 29.03 18.42 36.53 23.18 July — 5.27 • 3.34 28.35 17.99 35.89 22.77 August - 0.82 0.52 26.87 17.05 34.34 21.79 September + 4.78 3.03 24.78 15.72 32.94 20.90 October + 3.95 2.51 27.37 17.37 36.47 23.14 Considering first of all the absolute values we note that the average errors with regard to sign are generally low. Thus the prediction from No vember and from January production gives on the average 3 eggs too many ior the year. For December, February, March and August the predic tion is in error by less than 2 eggs. The values predicted from April, May, June, July, September and October records are from 4 to 7 eggs in error. The average deviations without regard to sign are of course much larger nnce they constitute a measure of the error of prediction of the records of ndividual birds. They range from 24.8 to 30.1 eggs. The significance }f errors of this magnitude will be more clearly brought out later. The square root of mean square deviation also shows considerable regu- 210 GENETICS: J. A. HARRIS ET AL. PROC. N. A S. larity from month to month. These measures are naturally considerably larger than the average deviation without regard to sign. They range from 32.9 to 38.8 eggs. It is clear that the annual egg production of birds similar in origin to the series upon which the prediction equations were based and maintained un der similar conditions may be predicted with a relatively high degree of accuracy providing their record for any month is definitely known. The order of the errors will be more readily understood by expressing them in relation to the average production of the flock, as shown by the percentage deviations. We note that in predicting from December, February and August records the average error with regard to sign is less than one per cent of the average annual yield of the flock. In predicting from November, January and March the error lies between one and two per cent. When April, May, June, July, September and October records are used as a basis of predic tion the average errors of prediction are from 2.50 to 4.50 per cent of the average annual yield. The average deviations without regard to sign are less than 20 per cent of the annual production. The values for the individual months range from 15.7 for September to 19.1 for January. The square root of mean square deviation is less than 25 per cent of the average annual production. The individual values range from 20.9 for September to 24.6 for January. These two latter tests may at first seem to indicate very unsatisfactory prediction. Such is not, however, the case. These give the average errors either above or below the true record made in the prediction of the results for an individual bird. The thing which is required in practise is generally the prediction for a group of birds of a particular grade of egg record for the month used as a base of prediction. In a flock of 415 birds this has been shown to be possibe with an error of less than 5 per cent of the annual produc tion when prediction is made from the record of any month of the year; and with an error of less than I per cent when prediction is based upon the re cords of a number of the individual months. Lack of space precludes a discussion of the results of the prediction of the annual record of the bird from the combined record of two consecutive months. We may, however, illustrate the accuracy of prediction from the combined record of two consecutive months by means of the figures in dia gram 1 which shows the accuracy of prediction from November plus Dec ember and from April plus May in comparison with the results of predic tion from November and April. In these the estimated production is slit >\vn by a straight line. The actual production for the year for which prediction is made is shown by solid dots for each group of birds as classified by monthly or bimonthly . 7, 1921 GENETICS: J. A. HARRIS ET AL. 217 „„' m A, , : 1 lllfflfil » 1 4 : 1 'in IIP ... , . NOV. +HE JJUllJ lu 68/0/2 14 IS 18 20 12 ? reduce somewhat the irregularities due to the errors of random sampling. The •rors of prediction were in each case determined for classes of unit range. Grouping used for graphic representation merely. The average deviations represented by the Tiit of the shaded zone are to be thought of as measured from a line perpendicular > the ordinates and intersecting the prediction line on the mid-ordinate of the 5-egg ass. A BIOMETRIC STUDY OF HUMAN BASAL METABOLISM BY J. ARTHUR HARRIS AND FRANCIS G. BENEDICT Nutrition Laboratory and Station for Experimental Evolution, Carnegie Institute of Washington Reprinted from the Proceedings of the NATIONAL ACADEMY Of SCIENCES Vol. 4, pp. 370-373, December, 1918 Reprinted from the Proceedings of the NATIONAL ACADEMY OF SCIENCES, Vol. 4, pp. 370-373, December, 1918 A BIOMETRIC STUDY OF HUMAN BASAL METABOLISM BY J. ARTHUR HARRIS AND FRANCIS G. BENEDICT NUTRITION LABORATORY AND STATION FOR EXPERIMENTAL EVOLUTION, CARNEGIE INSTITUTION OF WASHINGTON Communicated October 8, 1918 Investigators are now generally agreed that the metabolism, expressed in terms of calories per uriit of time, of the normal subject shall be taken as a basis of comparison in the investigation of all the special problems of human nutrition, for example, that of the requirements for muscular activity, that of the influence of specific diseases or of the level of nutrition upon metabolism, that of the change of metabolic activity with age, and so forth. Critical in vestigations in both European and American laboratories have shown that the gaseous metabolism is so affected by various factors that determinations which are to serve as a standard must be made under very exactly controlled condi tions. It is not merely necessary to devise apparatus in which the physical difficulties of direct calorimetry (or of the exact measurement of gaseous ex change from which heat production may be computed) are overcome. Cer tain biological factors must be ruled out. Those of greatest importance as sources of experimental error are muscular activity and the stimulatory ac tion of recently ingested food. The heat production of the individual in a state of complete muscular repose 12-14 hours after the last meal, i.e., i . the postabsorptive condition, has been called the basal metabolism. For a decade the Nutrition Laboratory has been engaged in carrying out a series of determinations of basal metabolism in normal human individuals of both sexes and of widely different ages. These have been made with all the modern refinements of method and manipulation. The subjects were in pre sumably good health. All those with febrile temperature were discarded. All were in the postabsorptive condition. Perfect muscular repose during the short periods required for indirect calorimetry was assured by an automatic record of all movements, even those imperceptible to a trained observer. 370 PHYSIOLOGY: HARRIS AND BENEDICT . 371 Measurements on 136 men, 103 women and 94 new-born infants have been analyzed biometrically with the purpose of determining the statistical con stants (means, standard deviations, coefficients of variation, coefficients of correlation, and regression equations) which may serve as standard constants in work on human metabolism until those based on more extensive series of data are available. In carrying out this analysis we have proceeded on the conviction that the widest possible usefulness of laboratory investigations of human metabolism will result from basing measurements upon individuals who are in presumably good health, but who are otherwise typical of the population at large. It is only when the subjects used for experimentation are representative of the general population in type, variability and correla tion that results of laboratory research upon limited series of individuals may be safely generalized for rationing or for other practical social applications. Statistical tests of the suitability of the series used in the present investigation have been applied. The relationship between certain of the physical and physiological measure ments of the individual and between the various physiological measurements has been determined. Our series of data show practically no relationship between basal or minimum pulse rate and stature or body weight in adults. There is a low but significant positive correlation between minimum or basal pulse rate and gaseous exchange and heat production. The Nutrition Labora tory has long emphasized the correlation between pulse rate and metabolism in the same individual, that is, the intra-individual correlation between the rate of the heart beat and the amount of the katabolism. Here, however, we are dealing with the problem of the relationship between the minimum or basal pulse rate of a series of individuals and their basal metabolism — that is, with inter-individual correlation. There is a substantial correlation between stature and heat production. The correlation between body weight and heat production is higher being of the order r = 0.75 to r = 0.80 in the new-born infants, of the order r = 0.80 in men and r = 0.60 in women. Analysis by means of partial correlation co efficients indicates that both stature and body weight have independent significance as bases for the prediction of the basal metabolism. The change in basal metabolism with age during the period of adult life has been shown to be well represented by the linear equations, For men (N = 136) h = 1823.80 - 7.15, a, hk = 28.703 - 0.112 a, hd = 1022.17 - 3.60 a. • For women (N = 103) h = 1420.47 - 2.29 a, hk = 28.308 - 0.124 a, hd = 942.25 - 2.96 A where h = total heat production in calories per 24 hours, hk = calories per kilogram of body weight, hd = calories per square meter of body surface as estimated by the Du Bois height-weight chart. Thus in men the daily heat 372 . PHYSIOLOGY: HARRIS AND BENEDICT production decreases about 7.15 while in women it decreases about 2.29 calories per year. Women are smaller than men and have a lower heat pro duction. When the decrease in metabolism with age is expressed in calories per kilogram of body weight or in calories per square meter of body surface, the results for the two sexes are much more nearly identical. The problem of the difference in the metabolism of men and women, dealt with in the past by a number of writers, has been reconsidered on the basis of the larger series of data now available. The average daily (24 hours) basal heat production of men is 1632 calories whereas that of women is 1349 calories. Thus women have an average daily heat production about 300 ca lories less than that of men. But women are smaller than men. If correc tion for body size be made by expressing heat production in calories per kilo gram of body weight, it is 25.7 calories in the 136 men as compared with 24.5 calories, or 1.2 calories per kilogram less, in the 103 women. On the basis of heat production per square meter of body surface as estimated by the Du Bois height-weight chart the men show an average daily heat production of 925 calories as compared with 850 calories, or 75 calories less, in the 103 women. The most critical test of the difference of men and women in the level of metabolism is that furnished by a modification and extension of the selected group method of Benedict and Emmes. In the new method the con trol values for the several groups of women are not the empirical constants for men of as nearly as possible like stature and body weight but are determined from equations taking into account stature, weight and age in all the available data for men. Analysis shows that, however expressed, the metabolism of American women is lower than that of the men. Our results show that the differentiation of the sexes is not evident in infancy. They do not confirm, the conclusion of Sonden and Tigerstedt that the difference between men and women tends to disappear with age. Instead we find the difference in the metabolism of men and women well-marked throughout the period of adult life. The validity of the so-called body surface law, according to which metab olism is proportional to the superficial area of the individual, i.e., h = aha where a = superficial area and ha = mean heat production per unit of time per square meter of body surface in a standard series, has been critically tested. It has been shown that the supposed proofs of its validity hitherto adduced are erroneous. Heat production is not 'proportional to body sur face but not to body weight' as has been asserted to be the case, but is highly and about equally correlated with both body weight and body surface. It has been shown that as a basis for predicting the heat production of a sub ject the above relationship is less satisfactory than multiple regression equa tions involving stature, weight and age. Thus the 'body surface law' deprived of its unique significance as a basis for the prediction of the me PHYSIOLOGY: HARRIS AND BENEDICT 373 ;abolism of an unknown subject. An analysis of the data of actual experi- nentation on subjects at changing levels of nutrition shows that the changes n metabolism are not proportional to those in body surface. Surface area nay not be looked upon as a determining factor in basal metabolism. The closest prediction of the daily heat production of a subject can be nade by the use of the multiple regression equations, For men, h = 66.4730 + 13.7516 w + 5.0033 s - 6.7550 a For women, h = 655.0955 + 9.5634 w + 1.8496 5 - 4.6756 a vhere h = total heat production per 24 hours, w = weight in kilograms, : = stature in centimeters, and a = age in years. These equations have )een tabulated for values of weight from 25.0 to 124.9 kgm., for stature from [51 to 200 cm., and for age from 21 to 70 years, so that the most probable oasal metabolism of an unknown subject may be easily determined. Such tables should render service in clinical and other fields of applied :alorimetry. Their usefulness has been demonstrated in testing the typical )r atypical nature of •series of metabolism measurements, in investigating ;he differentiation of the sexes with respect to metabolic activity, of the netabolism of athletes as compared with non-athletic individuals, and of ndividuals suffering from disease. The detailed measurements and statistical constants, with full discussions )f pertinent literature, are about to appear in Publication No. 279 of the arnegie Institution of Washington. By Dr. J. ARTHUR HARRIS and Dr. FRANCIS G. BENEDICT [Eeprinted from THE SCIENTIFIC MONTHLY, May, 1919.] COPYRIGHT 1918, BY THE SCIENCE PRESS, [Beprinted from THE SCIENTIFIC MONTHLY, May, 1919.] BIOMETRIC STANDARDS FOR ENERGY REQUIREMENTS IN HUMAN NUTRITION By Dr. J. ARTHUR HARRIS and Dr. FRANCIS G. BENEDICT CARNEGIE INSTITUTION OF WASHINGTON ONE of the primary requisites in all of the exact sciences is the establishment of standard bases of comparison. For aiecade the Nutrition Laboratory of the Carnegie Institution o Washington has been engaged in the precise investigations •wdch must underlie the establishment of such standards in hman nutrition. This is an undertaking of the greatest practical importance. I] times of peace, industrial efficiency and the physical well ing of the population demand exact knowledge of the amount ail proportion of the different kinds of food which should be tr.en by the individual. If communities or nations are to be siingently rationed during periods of emergency, it is also messary to know the minimum amounts of food required to mintain health and efficiency. The problem is also one of great complexity. Aside from al questions concerning the chemical composition, digestibility ail other physiological properties of the various foods, there ai a large number of problems concerning the characteristics ofhuman individuals which must be taken into account. For example, it is obvious that those who are engaged in seere muscular work must consume larger quantities of food suplying energy than those who are less active. It might sen reasonable to suppose that larger individuals would re- qire more food to carry on their normal activities than those wl) are physically smaller. It is a matter of common observa- ti(t that older men and women demand smaller rations than thse in the earlier stages of life. roL viii.— 25. i 386 THE SCIENTIFIC MONTHLY All these questions require precise investigation before one is justified in drawing conclusions concerning them. If such investigations are to be used as a basis of recommendation con cerning diet in peace or of regulation of diet in war, it is essen tial that the laws of energy transformation be expressed in a quantitative form. Nutritional physiologists agree that, as far as energy is concerned, the food requirements of the living organism shall be expressed in calories per unit of time. Thus a physical standard is taken over from the quantitative sciences of physics and chemistry. Theoretically, then, the metabolism must be determined by placing the subject in a calorimeter and directly measuring the number of calories produced. This has been done in a large number of cases. Since, however, the setting free of energy in the human body is merely a process of combustion, the measurement of the amount of oxygen consumed and the quantity of carbon dioxide excreted from the lungs should furnish a good index of heat production. Thus the nutritional physiologist may avail him self of the method of indirect calorimetry as well as of direct calorimetry. Heat production, in short, may be determined in a calorimeter or it may be computed from the gaseous exchange as measured in a respiration chamber. The development of apparatus by which the heat produc tion of the living organism may be directly measured in the calorimeter or by which the gaseous exchange may be precisely determined in the respiration chamber has occupied the atten tion of a large number of ingenious experimenters, among whom may be mentioned Lavoisier, Rubner, Zuntz, Atwater, Rosa, Lusk and Du Bois. The labors of these and others have brought the apparatus for the measurement of both heat pro duction and gaseous exchange to such a high degree of refine ment that the manipulative phases of nutritional physiology may be regarded as among the most exact techniques of biolog ical experimentation. Extensive comparative studies hav shown that, in the case of human subjects, it is much simple and essentially as accurate to calculate the heat production in directly from the gaseous exchange than to measure it in th calorimeter. The problem is not, however, solely one of physical am chemical measurement. A number of biological factors mus be taken into account. Muscular activity and the stimulator; action of recently ingested food are of chief importance. Th apparatus with which students of human nutrition now wor BIOMETRIC STANDARDS IN HUMAN NUTRITION 387 ias been brought to such a stage of perfection as to measure he energy transformation accompanying such slight muscular ictivity as that required in the raising of the hand from the ide to the mouth. The cost in calories of masticating food aay be directly measured. For example, recent studies at the Nutrition Laboratory by Carpenter and Benedict have shown hat the muscular work in chewing gum may increase heat (reduction approximately 17 per cent. The difference between he heat production of a new-born infant asleep in its basket ,nd crying can be precisely measured. Thus Talbot and Bene dict found that the metabolism of the new-born infant is in- reased on the average by 65 per cent, in crying with its attend- ,nt muscular activity. Students of animal nutrition have long ealized that the demands for energy of an animal standing ,re far higher than that of the same beast lying down. This act must be taken into account in computing the maintenance lequirements of cattle and other domestic animals. Heat production is greatly increased after eating, and the mount of the increase is closely dependent on the nature of he food consumed. For example, the metabolism of a subject lay be increased by 25 per cent, after a meal consisting chiefly f carbohydrates, but by as much as 45 per cent, after a heavy rotein meal. It is necessary, therefore, to eliminate all such factors in etermining the standards which shall serve as bases of com- arison in applied nutritional physiology. Since the outbreak of the war, and particularly since our wn participation in the conflict, the Nutrition Laboratory has, i addition to extensive investigations on the influence of sub- ormal rationing upon health and efficiency, pushed forward as apidly as possible its work on the establishment of nutritional tandards. One phase of this program has been the statistical ivestigation of the so-called basal metabolism of the human idividual.1 Physiologists have gradually come to a general agreement hat the heat production at complete muscular repose and in le post-absorptive state — i. e., about twelve hours after the last leal — shall be called the basal metabolism and shall be used as standard of comparison in the investigation of all the special roblems of human nutrition. 1 The detailed measurements and the statistical constants, with full iscussions of pertinent literature, are about to appear in Publication 279 : the Carnegie Institution of Washington. We shall not, therefore, arden this brief outline with references to literature or statistical detail, wo of the diagrams used here are redrawn from this publication. 388 THE SCIENTIFIC MONTHLY For several years the Nutrition Laboratory has been en gaged in the measurement of basal metabolism in normal human individuals of both sexes and of widely different ages. These have been made with all the modern refinements of method and manipulation. The subjects were in presumably good health. All those with febrile temperature were rejected. All were in the post-absorptive condition. Perfect muscular repose during the short periods required for indirect calor- imetry was assured by instruments providing an automatic record of all movements, even those imperceptible to trained observers. I — | -1 - n rrn M " ' h , , . . rn n~ /v' ; ' N ~| :> 1 | § I i lill^ii^ll ^ ? '0 1 | | :^ ^ 1 f 9 FIG. 1. FREQUENCIES OF MEN AND WOMEN PRODUCING VARIOUS NUMBERS OF CALOXIM PER TWENTY-FOUR HOURS. In carrying out a biometric analysis of the measurements which have been made on 136 men, 103 women, and 94 new born infants, we have proceeded on the conviction that the widest possible usefulness of laboratory investigations of nor mal human metabolism will result from basing measurements upon those in presumably good health but otherwise typical of human beings in general. It is only when the subjects used for experimentation are representative of the population at large in type, variability and correlation that the results of lab oratory research upon limited series may be safely generalized for rationing or for other practical social applications. An explanation of the statistical tests which have been applied to determine the suitability of the series used in the present inves tigation would lead us into too great detail for this discussion. The average basal metabolism per twenty-four hours is as follows : BIOMETR1C STANDARDS IN HUMAN NUTRITION 389 For 136 men 1631.74 calories. For 103 women 1349.19 calories. For 51 male infants 144.55 calories. For 43 female infants 140.37 calories. Thus it appears that the basal energy requirements of the American men are a little less than one half of the number of Hilories (3,300) established by the Inter-Allied Scientific Food this formula by a more rational one. The foregoing analysis has shown that weight, stature and age all have independent significance for predicting the metab olism of the individual. Availing ourselves of the constants showing the independent relationship between these easily ascertainable characters and metabolism, we deduce the follow ing multiple prediction equations : For men h = 66.473 + 13.752 w + 5.003 s — 6.755 a. For women h = 6^5.096 •+ 9.563 w + 1.850 s — 4.676 a. 6" where w=body weight in kilograms, s = stature in centi meters, and a = age in years. These equations make possible the closest prediction of the daily caloric output of an unknown subject. They are particu larly well adapted to practical work. To calculate the most probable metabolism of any subject it is only necessary to sub stitute the actual values of weight, stature and age in the equa tion ; for example, A. S. F. is a man 21 years old, weighing 69.3 kilograms, and 169 centimeters in height. His most probable daily heat production will therefore be given by h= 66.9173 + (13.752X69.3) + (5.003X169) — (6.755 X 21) = 1723 calories. f His actually measured heat production was 1,733 calories, or there was an error of only 10 calories per twenty-four hours or of 0.6 per cent, in predicting his metabolism from two physi cal characters and age. The result is unusually good. K. G. M. is 32 years old, weighs 68.8 kilograms and is 171 centimeters tall. His daily heat production should, therefore, be given by h = 66.473 + (13.752 X 68.8) + (5.003 X 171) — (6.755 X 32). The equation gives 1,652 calories as compared with 1,889 400 THE SCIENTIFIC MONTHLY together. In eleven cases the actual heat productions are higher, while in eleven cases they are lower than the values computed from the equations. The means of the actual and computed heat productions are practically identical. These results show clearly that there is no appreciable influence of vegetarian diet on the basal metabolism. Other illustrations might be given. Perhaps the most in teresting is the use of the equations in investigating the differ ence in the metabolism of men and women. This problem, which has attracted the interest of a number of investigators in the past, has been reconsidered from all sides on the larger series of data now available. The results show that the average daily (twenty-four hours) basal heat production of the 136 men investigated is 1,632 calories, whereas that of the 103 women studied is 1,349 calories. Thus the daily heat production of women is about 300 calories less than that of men. But women are smaller than men. If correction for body size be made by expressing heat production in calories per kilogram of body weight, it is 25.7 calories in the men as compared with 24.5 calories, or 1.2 calories per kilogram less, in the women. The men show an average daily heat production per square meter of body surface of 925 calories as compared with 850 calories, or 75 calories less, in the women. The most critical test of the existence of a difference in the metabolism of men and women is that furnished by comparing the actually measured metabolism of women with that calcu lated from biometric equations on the assumption that they are men of like stature, weight, body surface, age or combinations of these characters. The diagrams in Fig. 8 show the differ ences between the actual metabolism of women (circles and lower lines) and the heat production calculated on the assump tion that they were men of comparable physical characters and age (solid dots and upper lines). Diagrams A-C represent the results given by three different equations. The shaded zone shows a deficiency in the actual heat production of the women, who are classified according to body weight, throughout. These and further statistical tests which can not be dis cussed in detail show conclusively that the metabolism of Amer ican women is lower than that of men. Our results show that the differentiation of the sexes is not evident in infancy. They do not confirm the conclusion of Sonden and Tigerstedt that the difference between men and women tends to disappear with age. Instead we find the difference in the metabolism of men and women well marked throughout the period of adult life. B10METR1C STANDARDS IN HUMAN NUTRITION 401 FIG. 8. COMPARISON OP METABOLISM or MEN AND WOMEN. 402 THE SCIENTIFIC MONTHLY This brief outline may serve as an introduction to some of the problems which require consideration in the establishment of normal standards for work in human nutrition. It would be quite unfair to leave the reader with the im pression that the basal metabolism is a fixed and unchangeable physiological constant. While extremely valuable as a basis of comparison, the basal metabolism is subject, not only to great variation from individual to individual, but to modification in response to profound experimentally induced changes in the level of nutrition of the subject. Thus a man who underwent a 31-day fast at the Nutrition Laboratory, during which he took no food whatever and only about 900 cubic centimeters of distilled water per day showed a decrease of 28 per cent, in his basal metabolism. A more recent investigation of the influence of severely limited diet, undertaken by the Nutrition Laboratory on squads of men who volunteered for this purpose at the International Y. M. C. A. College at Springfield, Mass., in response to the need for more exact information concerning the influence of war-time diet on health and efficiency, has shown a striking influence of reduced diet accompanied by rapid alteration of body weight on the basal metabolism. One squad was kept for a period of four months on a restricted diet with an energy con tent of one half to two thirds of the requirements prior to the fast, when the normal demand of the men ranged from 3,200 to 3,600 net calories. After a reduction of only 12 per cent, in weight, 1,950 calories only were required to maintain this weight. Notwithstanding this fact, and the wide variability in basal metabolism in whatever units it may be expressed, the basal metabolism when measured on large numbers of individuals in good health and living under normal conditions, and described in terms of the proper biometric constants and equations, fur nishes a valuable, and as yet the only available, standard of comparison in the investigation of all the special problems of energy requirements in human nutrition. [Reprinted from SCIENCE, N. S.,Vol. LL, No. IS 10, Pages 1SS-1S4, February 6, 1920] CHARLES BUCKMAN GORING FEW of the readers of SCIENCE will be familiar with even the name of Charles Goring.1 His time was largely spent as a prison medical officer. His one monumental work, which may perhaps best be described as the biology of the convict, is still unfamiliar to all but a limited circle. Goring's work2 was based on thousands of data and is stringently biometric in form, but he was no mere measurer, card shuffler and constant computer. He knew his convicts as the trained student of animal behavior knows his organisms — and better, for he had not merely their physical measurements and an intimate personal knowledge and evaluation of their mental characteristics but knew much of their ancestry and family associations. To Goring, measurements were inviolate — not to be juggled with, modified or discarded because they did not substantiate a popular theory. 1 Goring was born in 1870 and died in 1919. He was a student and later a fellow of University College, London. He served on a hospital ship during the Boer War. At the tame of his death — met at his post combating the influenza epidemic — he was Medical Officer in Chief at Strangeways Prison, Manchester. Those who desire may find a portrait and a more adequate appreciation in Bio- metrika, Vol. XII., pp. 297-307, pi. 1, 1919. 2 Goring, C. B., "The English Convict; A Sta tistical Study." 444 pp. London, 1913. Abridged edition, Wyman and Co., 1915. The statistical work on this volume was carried out at the Bio- metric Laboratory with the cooperation of H. E. Soper and with the helpful suggestion and criti cism of Professor Pearson. Better proof of this could not be found than the fact that the raw data for his book were set up before the calculations were well under way. Goring as a thoroughgoing biometri- cian believed that in many fields of research valid conclusions must rest upon the mathe matical analysis of large masses of data. But in his research each constant was critically weighed against his own broad and intimate personal experience of the individual in stances which constitute the mass. I find it difficult to decide just what char acteristic of Goring impressed me most when we were working together at the Biometric Laboratory ten years ago. Sometimes it was the steadfast scientific purpose which had sup ported the years of painstaking detail upon which his great book rests — detail scrupulously executed notwithstanding the fact that there was at times little prospect of its ever serving as a basis for constants and generalizations. Sometimes it was the breadth of interests, knowledge and sympathies of one whose work lay in a field seemingly so circumscribed. Sometimes it was the entire freedom from both callousness and sentimentality of a man who had spent a decade, more or less, with the inmates of the British prisons. One sentence tells much of the man. One day I asked, " Why is this to be The English Convict instead of The English Criminal f" He replied instantly, " Perhaps some of them are not criminals, only convicts." J. ARTHUR HARRIS THE VARIATION AND THE STATISTICAL CONSTANTS OF BASAL METABOLISM IN MEN BY J. ARTHUR HARRIS AND F. G. BENEDICT (F)M THE NUTRITION LABORATORY AND THE STATION FOR EXPERIMENTAL EVOLUTION, THE CARNEGIE INSTITUTION OF WASHINGTON) Hi HINTED FROM THE JOURNAL OF BIOLOGICAL CHEMISTRY VOL. XLVI, No. 1, MARCH, 1921 i Reprinted from THE JOURNAL or BIOLOGICAL CHEMISTRY, Vol. XLVI, No. 1, March, 1921 THE VARIATION AND THE STATISTICAL CONSTANTS OF BASAL METABOLISM IN MEN. BY J. ARTHUR HARRIS AND F. G. BENEDICT. (From the Nutrition Laboratory and the Station for Experimental Evolution, the Carnegie Institution of Washington.) (Received for publication, January 6, 1921.) I. INTRODUCTION. i Physiologists now generally accept the so called basal metabolism pf the individual as a standard in all comparisons involving the ijonsideration of energy transformation. Furthermore, the tech nical conditions under which measurements of the basal metabol- sm shall be made are now generally agreed upon. The opinion lias even been widely maintained that heat production per square fieter of body surface area is a constant. A detailed review and discussion of the literature and the results 'f a biometric analysis of a series of basal metabolism data for ,36 men and 103 women have been given elsewhere.1 The results >f this analysis show the following coefficients of variation for ihe averages2 of the daily basal metabolism constants for the indi- idual subjects. Men. Women. Total calories per 24 hrs 12 . 54 11 . 50 Calories per kg. per 24 hrs 9.36 14.14 Calories per square meter per 24 hrs 8.05 9.17 1 Harris, J. A., and Benedict, F. G., Carnegie Inst. of Washington, Pub. V9, 1919, 129-200. These are averages of daily means in all cases in which measurements )uld be made on more than 1 day. For 35 subjects a single daily mean ily was available. In practise the catabolism of a subject is almost invariably measured in vo or more short periods on a given day in a respiration apparatus. Tech- Rally these are generally designated as minimum periods, since the lowest ilues are generally found in the absence of muscular activity. The term somewhat misleading when averages of two or more periods are taken, 257 THE JOURNAL OF BIOLOGICAL CHEMISTRY, VOL. XLVI, NO. 1 258 Basal Metabolism in Men These results indicate. a rather wide variability in basal metabc lism from individual to individual, even when heat production i corrected for body size by expressing it in calories per kilo c body weight or in calories per square meter of body surface area The problem now arises whether, under conditions such tha the age factor4 is practically eliminated, the basal metabolism c the individual is essentially constant from day to day or whether i shows sensible variations. In 1915 one of us5 discussed the ques tion of changes in the metabolism of the individual from day t day, and showed that, contrary to the early assumption that th basal metabolism of an individual remains essentially constan from day to day, it is really variable.6 since there can be only one term minimum. The calories produced or th volume of the gaseous exchange for any one of these periods which seems t those acquainted with the technical details of the experiment reasonabl free from experimental error, might serve as a measure of the metabolisn Since, however, the basal metabolism of the individual can probably b assumed to be sensibly constant for 1 day, it seems wisest to regard th individual periods which appear the most free from possible experiment; error as of the nature of duplicate, triplicate, etc. analyses, and to averag these values. This daily mean has served as the unit in work at the Nutr tion Laboratory. 3 The frequency distributions of total calories and calories per squai meter are shown in Figs. 1 and 2 of Harris and Benedict (Harris, J. A., an Benedict, F. G., Scient. Month., 1919, viii, 388-389). 4 The results of a previous study of the relationship between age an metabolism (Harris and Benedict,1 pp. 107-127) have shown that there a gradual and practically linear decrease in metabolism with age durin the period of adult life. The annual rate of decrease amounts to about 7.1 calories (per 24 hrs.) per year in men and 2.29 calories (per 24 hrs.) per ye£ in women. Correction for body size by expressing the results in calorii per kilo of weight gives a rate of decrease of 0.112 calorie in men and 0.15 calorie in women. If the results are expressed in calories per square meti of body surface area as estimated by the Du Bois height-weight chart, tl decrease for men is 3.60 calories and for women 2.96 calories per 24 hrs. < life. The change due to age is not, therefore, large and cannot be assume to be an important factor for subjects observed during a short period time only. 6 Benedict, F. G., J. Biol. Chem., 1915, xx, 290-295. 6 This conclusion was based on a study of the difference between tl highest and the lowest daily basal metabolism constant expressed as percentage of the minimum value as a base. The study showed that t differences varied greatly from subject to subject. In one case the ma: mum and minimum oxygen consumption varied as widely as 31.3 per ce J. A. Harris and F. G. Benedict 259 The purpose of the present paper is threefold: 1. To obtain some measure of the variability of the basal metab- lism of the normal individual. 2. To consider the relationship between the length of time over hich the observations extend and the variation in the metabol- im of the individual. 3. To consider the most suitable method for determining the opulation mean from measurements on a series of individuals. II. PRESENTATION OF RESULTS. 1. Variation of Metabolism in the Individual. , For a certain number of men investigated at the Nutrition Lab- I'atory the number of days on which measurements were made is itfficiently large (20 or more) to justify the calculation of statis- •3al constants for the individual subjects. These appear in Tables I to III. The constants indicate that individuals are differentiated among lemselves with respect to basal metabolism even when expressed i calories per kilo of body weight or calories per square meter of kly surface area as estimated by the Du Bois height-weight tart.7 Furthermore it is clear that the metabolism of each individual sbject is to a considerable degree variable. This is shown by te rather wide range between the maximum and minimum daily Rtabolism for each individual as shown in these tables. These rages are expressed as percentages of the minimum value found i the tables. It is also evident in the absolute variabilities as othe minimum value. In another case it varied only 3.5 percent. While i'vas pointed out that it was hardly correct to obtain an average value for t; oxygen consumption for individuals with such wide differences in the tie covered by the observations, an average value was determined in the asence of any better available method, and found to be 13.9 per cent. 7 Since a discussion of the differentiation of individuals with respect to b;al metabolism is not a primary purpose of this paper the subject is not p-sued farther. The statement above may be verified by taking differ- e.'es between the various constants and comparing them with their prob- ae errors. It is to be noted that these constants are uncorrected for a>, and that the age differences will, in general, tend to increase slightly tl differentiation of the subjects. 260 Basal Metabolism in Men given in terms of the standard deviations (S. D.). Expressir the total amount of variation as measured in terms of the stam ard deviation as a percentage of the means we have the relatii 100 S.D: variabilities expressed as coefficients of variation ( C.V. = Mean TABLE I. Statistical Constants for Basal Metabolism in Eleven Men. Total calories per 24 hrs. No. and individual. a Q Mini mum. Maxi mum. Per centage range. Mean. Standard deviation. Coefl cien of va atioi 47. F. P. R.... 20 1,446 1,684 16.5 1,540. 0±11. 2 74.6±8.0 4. 45. K. H. A.... 25 1,505 1,765 17.3 1,648. 3± 9.2 68.2±6.5 4. 96. A. J. O.... 25 1,679 1,804 7.4 1,741. 5± 4.5 33.5±3.2 1. 41. C. B. S.... 26 1,592 1,785 12.1 1,699. 2± 6.5 49.0±4.6 2. 61. J. K. M.... 27 1,458 1,650 13.2 1,546. 6± 6.6 51.2±4.7 3. 54. H. H. A.... 28 1,327 1,686 27.1 1,488. 3±10. 3 80.7±7.3 5. 66. L. E. E.... 31 1,596 1,848 15.8 1,705. 6± 7.9 64.9±5.6 3. 59. H. L. H. .. 35 1,548 1,890 22.1 1,694. 4± 9.2 80.4±6.5 4. 70. H. F. T.... 41 1,205 1,514 25.6 1,350. 4± 7.7 73.1±5.4 5. 9. M. A. M... 53 1,562 1,917 22.7 1,696. 0± 6.9 74.7±4.9 4. 48. J. J. C 53 1,511 1,740 15.2 1,583. 8± 4.4 47.3±3.1 3. TABLE II. Statistical Constants for Basal Metabolism in Eleven Men. No. and individual. 1 Q Calories per kg. Mini mum. Maxi mum. Per centage range. Mean. Standard deviation. Coef eiei of va atio 4.£ 47. F. P. R.... 20 22.1 25.7 16.3 23.65^0.16 1.08±0.12 45. K. H. A.... 25 22.8 27.1 18.4 24.84±0.15 1.10±0.10 4.4 96. A. J. O.... 25 23.3 26.6 14.2 25.13±0.11 0.81±0.08 3.S 41. C. B. S.... 26 21.9 25.4 16.0 23.92±0.11 0.81±0.08 3.4 61. J. K. M.... 27 24.5 27.4 11.8 25. 63 ±0.09 0.70±0.06 2.. 64. H. H. A.... 28 22.2 26.9 21.2 23.89±0.14 1.10±0.10 4.( 66. L. E. E.... 31 26.8 31.5 17.5 28.47±0.14 1.15±0.10 4.( 59. H. L. H.... 35 25.8 31.5 22.1 28.05±0.16 1.39±0.11 4.1 70. H. F. T.... 41 21.1 26.0 23.2 23. 35 ±0.12 1.18±0.09 5.( 9. M. A. M... 53 23.8 28.5 19.7 25.72±0.10 1.04±0.07 4.'( 48. J. J. C 53 22.6 26.7 18.1 24.39±0.07 0.81 ±0.05 8.S J. A. Harris and F. G. Benedict 261 sVe note that the coefficients for total calories range from 1.9 to \A per cent with a general average of 3.97. Those for calories »er kilo of body weight range from 2.8 to 5.1 per cent with a •eneral average of 4.40, and those for calories per square meter f body surface from 2.3 to 5.3 per cent with a general average f 3.95. The suggestion will naturally arise that the variation in basal letabolism in these longer periods is due merely to the uniform ecline in metabolic activity characteristic of adult life. TABLE III. Statistical Constants for Basal Metabolism in Eleven Men. No. and individual. >> oS Q Calories per square meter. Mini mum. Maxi mum. Per centage range. Mean. Standard deviation. Coeffi cient of vari ation. h F. P. R. . . . 20 808. 936 15.8 864.0±6.1 40.8±4.3 4.7 ;. K. H. A.... 25 814 954 17.2 885.6±5.0 36.9±3.5 4.2 i. A. J. 0.... 25 879 970 10.4 927.2±2.9 21. 5 ±2.0 2.3 I. C. B. S.... 26 834 947 13.5 898.2±3.6 27.6=<=2.6 3.1 j. J. K. M.... 27 851 948 11.4 897.4±3.5 26.7±2.5 3.0 . H. H. A.... 28 804 998 24.1 884.3±5.6 43.9±4.0 5.0 i. L. E. E.... 31 917 1,074 17.1 980.5±4.7 38.6±3.3 3.9 . H. L. H.... 35 905 1,105 22.1 986.5±5.4 46.9±3.8 4.8 X H. F. T. . . . 41 700 870 24.3 779.2±4.3 40.9±3.0 5.3 . M. A. M... 53 863 1,042 20.7 935.2±3.6 39.0±2.6 4.2 . J. J. C 53 840 956 13.8 883.8±2.4 26.3±1.7 3.0 Evidence that this is not the case will be adduced in the follow- g section in which it will be shown that for periods of not more tan 10 or 15 days the magnitude of the variation in metabolism : positively correlated with the duration of the period over tiich the observations extended. We have, furthermore, applied i correction for age8 to the measurements of three of the indi- 'duals with results as given in Table IV. The standard Aviations and the coefficients of variation are practically the same iter correction for age as for the original observations. The isult shows clearly that age is not a primary factor underlying fe variations. 8 Calculations from unpublished data. 262 Basal Metabolism in Men TABLE IV. Comparison of Basal Metabolism Constants Corrected and Uncorrected J Age. Subject and range. Constant uncorrected for age. Constant corrected for age. Differen in constan 88. T. M. C., range = 1,624. Standard deviation 54 04 53 27 0 'i Coefficient of variation 4 18 4 12 —0 ( 59. H. L. H., range = 905. Standard deviation 80 39 82 07 4-1 ( Coefficient of variation 4 74 4 84 4-0 1 48. J. J. C., range = 819. Standard deviation 47 27 47 15 — 0 ' Coefficient of variation 2 98 2 98 ±0 ( 2. The Time Factor in the Variation of the Metabolism of the Individual. In the preceding section we dealt with the problem of the van! bility within the individual on the basis of data for a few mij upon whom more extensive series of measurements had bei made. By the application of other methods it is possible to pi ii the analysis somewhat farther. While the ultimate purpose of studies of variation in the metr-j olism constants of the same individual should be to detenu* something of the proximate causes underlying these variatio , it is worth while to obtain some general idea of the amount f variation which may be expected to occur in the individual subj t with a lapse of time.9 9 In the first discussion of this subject (Benedict,5 p. 292) the sirce method of range of variation in metabolism led to the following conclusi : "A general inspection of the data will show that, as a rule, the greai t variations were found with the subjects studied over the longest perk ;. While it is hardly correct to obtain an average value for the oxygen consul - tion for so many different individuals with such wide differences in the t fi covered by the experiments, yet such a value has been found and shows t t on the basis of these observations there may be an average variatior f 13.9 per cent in the basal metabolism, when measured in the post-absorpi e condition and with complete muscular repose, during a period of two y( s or, in the majority of cases, considerably less. With no attempt to anal e the causes of these differences, it is sufficient here simply to call attenln to their magnitude." J. A. Harris and F. G. Benedict 263 If the metabolism of the individual changes from time to time rrespective of changes in bodily dimensions it would seem reason- ible to presume that these changes would be greater for more videly separated periods. Thus the observations made on a single lay can be reasonably regarded as based upon a subject in prac- ically stationary physical and physiological conditions. Those aade at widely separated dates more probably represent the indi- ddual in somewhat different physiological states. Thus while he active protoplasmic mass is probably essentially identical in he two cases (if the periods are not too widely separated) the inknown stimulus to metabolic activity may differ to a consid- rable extent from one period to the other. As a measure of variation of the metabolism of the individual ve have adopted the standard deviation10 of the measurements of ach subject. As a measure of time covered by the observation re have taken the actual number of days, including the days pon which the measurements were made, i.e. (Tz + 1) — TI, /here TI and Tz are the times of the first and last measurements, "hus if the metabolism of an individual were measured on July and 2 the range would be 2 days. If three observations were lade, one on July 1, one on July 10, and one on September 3 of he same year, the range would be 65 days. Correlating between le range in days and the standard deviation of total calories per 4 hours we have for 101 individuals r = +0.276 ±0.062, -£- = 4.45 LT The coefficient measuring the relationship between range in ays and the standard deviation of calories per square meter as itimated by the Du Bois height-weight chart, which will be the, nly approximation to the body surface used, is r = +0.254±0.063, -£- = 4.03 Er The correction between the range of days over which the experi- ients extended and the standard deviation of calories per kilo of ody weight is r = +0.248 ±0.063, • - = 3.94 Er 10 The coefficient of variation might have been used with equal propriety. 266 Basal Metabolism in Men TABLE V. Correlation between Duration of Period of Observation and the Stand Deviation of Basal Metabolism in Calories per Kg. per 24 Hrs. Range. No. of subjects. Correlation. Mean standard deviation for whole range. Mean standai deviation individl addec r ± Er T Jr days 2-5 19 +0.509 ±0.115 4.43 0.463 2-10 32 +0.398±0.100 3.98 0.544 0.66 2-15 37 +0.297±0.101 2.94 0.555 0.62 2-20 42 +0.343 ±0.092 3.73 0.591 0.85 2-30 49 +0.232 ±0.091 2.55 0.599 0.64 2-50 59 +0.139±O.OS6 1.62 0.605 0.63 2-125 73 +0.266±0.073 3.64 0.648 0.82 2-160 81 +0.344±0.066 5.21 0.679 0.96 2-240 86 +0.363 ±0.063 5.76 0.697 0.97 2-360 90 +0.370±0.061 6.07 0.709 0.97 2-370 91 +0.327 ±0.063 5.19 0.708 0.58 2-380 92 +0.337±0.062 5.44 0.712 1.05 2^15 93 +0.349±0.061 5.72 0.716 1.09 2^25 94 +0.334±0.062 5.39 0.717 0.81 2^30 95 +0.314±0.062 5.06 0.717 0.70 2-600 96 +0.280±0.063 4.44 0.717 0.70 2-775 97 +0.297±0.063 4.71 0.721 1.14 2-800 98 +0.245±0.064 3.83 0.720 0.57 2-820 99 +0.231±0.064 3.61 0.720 0.80 2-905 100 +0.2SO±0.062 4.52 0.727 1.3S 2-1,624 101 +0.248±0.063 3.94 0.729 0.91 TABLE VI. Correlation between Duration of Period of Observation and the Stand Deviation of Basal Metabolism in Calories per Kg. per 24 Hrs. Range. No. of subjects. Correlation. r-* r days 332-1 ,624 12 +0.116±0.192 0.60 236-1 ,624 16 +0.018 ±0.169 0.11 159-1 ,624 21 -0.067±0.147 0.46 131-1 ,624 28 -0.014±0.127 0.11 121-1 ,624 31 +0.007±0.121 o.oe 85-1 ,624 37 +0.020±0.111 0.18 51-1 ,624 42 +0.062±0.104 0.60 J. A. Harris and F. G. Benedict 267 •-1,624 days) are positive in sign, as are two of the other four efficients. There is, therefore, a suggestion of positive corre- liion in the longer time groups. .It is clear from the magnitude o; these correlation coefficients that, as suggested above, the s^ndard deviations do not steadily increase with the lapse of T1AHGE IN UflfS FIG. 1. Abscissae represent maximum range in days; ordinates show endard deviations of daily means in the individual or correlations be- tsen range of time covered by observations and standard deviation of dily metabolism. Solid dots and line represent correlation coefficients; ccles and solid line represent the mean standard deviations for the indi- vluals of each group for which the correlations were computed; circles ai broken line represent the mean standard deviation of the individuals aded to each preceding group to form the group upon which the correla- tn coefficient is based. Because of the great variation in the length of the priods no attempt has been made to represent abscissae on a uniform scale. 268 Basal Metabolism in Men time. This may be shown to be the case by determining th average values of the standard deviations of the metabolism ( the groups of individuals for whom the correlations in Table1 were calculated. These means have been calculated for th groups of 19 to 101 subjects with the range indicated in Table ' and for the individuals added to each group to give the next wide range group. These mean standard deviations are shown in th last two columns of Table V. The first series is represented i Fig. 1 by the circles connected by continuous lines while the sec ond is shown by the circles connected by broken lines. Th wide variability of the latter averages is attributable to the ver small number of individuals added in the longer range periods.1 Both series of means show that the standard deviation at firs increases rapidly as the length of the period becomes longer bu the rate of increase becomes smaller as the periods over whicl the observations extend increase in length. The last paragraph on page 264, written as it stands befor the calculation of the constants in this table, is therefore full; substantiated by the available data for individuals who have bee studied over longer periods of time. 8. The Statistical Constants for Basal Metabolism in Man. A primary requisite for continual progress in the investigatio of human metabolism under various special conditions, e.g. c exercise, rationing, or disease, is the determination of some stanc ard which may serve as a basis of comparison.15 Such a cor stant, based upon a considerable series of individuals and designe to serve as a standard of comparison, may be conveniently desij nated as a population constant. The average value of the basal metabolism constant has gene:' ally served this purpose, whether expressed in actual calori( per unit of time uncorrected for the influence of body mass, i calories per kilo of body weight, or in calories per square met( 14 In the twelve groups in which the range is wider than 2-360 days tl positions of the circles represent the standard deviations for single ind viduals only, not means. 15 The general principles underlying the establishment of control seri have been discussed elsewhere (Harris and Benedict,1 pp. 223-227; Harris and Benedict,3 p. 385). J. A. Harris and F. G. Benedict 269 * »f body surface area as estimated by some one of the various brmulas which have been proposed for this purpose. When observations for a number of days are available, and •/hen it is desirable to define the basal metabolism of the indi- idual more precisely than can be done as the result of experimen- ation for 1 day, the question naturally arises whether the aver- ge of the daily means or the minimum daily mean shall be used o represent the basal metabolism of the individual. The exact lethod of calculating the average and the standard deviation herefore requires consideration.16 In a preceding publication1 we used the average of the daily leans for the determination of the population constant. Our rotocols of data17 show these values and indicate the number of ays and the total number of periods upon which they were based. : One of our helpfully critical correspondents has suggested that . may be quite improper to lump together and treat as of equal alue basal metabolism constants for individual subjects some of hich rest upon an observation for only a single day while others epend upon many days measurements. This criticism has probably also occurred to others. It seems ssirable, therefore, to consider the problem of the best method : deducing a constant for a series of individuals — a population mstant — from the experimental readings. There are seven possible ways of determining the statistical mstants of a series of metabolism measurements some of which .ist upon work for but a single day while others depend upon iveral days observation. A. The average of the daily averages may serve as the units presenting the individuals. If the measured metabolism is variable it seems illogical, as our ^•respondent suggests, to treat the constant obtained from an oservation for a single day as equal in value to that deduced from :number of days observation. The selected constant may, there- :re, be (1) used only once in the calculation of the statistical "nstant for the population; (2) may be weighted with the num- 16 While we have elsewhere proposed the use of multiple prediction equa- tins for calculating the basal energy requirements, the consideration of ie most suitable method for the determination of the statistical constants 1 represent the individual is pertinent, since the calculation of these equa- ims involves the determination of the means and standard deviations. 17 Harris and Benedict,1 Tables A to D. 270 Basal Metabolism in Men her of days observation; or, (3) weighted with the square root o the number of days observation. B. The minimum value of the daily averages, i.e. the constan for the single day giving the lowest average, may be used. This method has for its justification a physiological consideratioi By definition the basal metabolism is the catabolism in the at sence of muscular activity and the stimulatory influence of re cently ingested food. Since these are the most potent factors L determining the superbasal metabolism of the individual, th basal metabolism is, practically speaking, synonymous with th minimum metabolism. It is possible, therefore, to consider tha the absolute minimum for any individual should be taken as th true basal value. If the mean of all the daily averages of meas urements made upon an individual is used as a measure of th basal metabolism a value somewhat higher than the absolut minimum is obtained and we admit that the individual may fa below his own basal value. Against this method is to b urged the criticism that the lowest value may be really subbas* because of errors of measurement. This criticism is in large pai met by the concordance of the results for the two or more perioc upon which the daily averages are almost invariably basec These minimum values may, like the individual means, be (*. used only once in the calculation of the statistical constant ft the population; (5) may be weighted with the number of daj observation; or (6) weighted with the square root of the numb* of days observation. C. (7) The constants may be computed directly from the who series of daily means available. The first group (1 to 3) may be conveniently designated as tlr method of individual means, the second group as the method of i dividual minima, and the third group as the method of daily mean Table VII gives the statistical constants for the daily (24 hour heat production of the 136 men18 for whom data (individual mean. are given in the protocols of our former publication.19 18 The 103 women considered in our volume were not studied over period sufficiently long to make it worth while to calculate weighted co stants comparable with those for men. 19 In the full revision of the data for the 863 individual periods a f< ] minor inaccuracies, of no practical importance for the purposes of o earlier volume, were found in trtie fundamental protocols. The unweight constants have, therefore, been recalculated for the purposes of tl paper. o iC -•f O3 ' "o A e5 S CM 03 co ^ . 'i'S'S o • jj d CO d t- O O-2 *'^ 1 1 ' ~~cs ~~*& CO K> CO S § * * s cS T-H 00 1C ?• CO 11 "c.2 •2 •• CM 41 CM 41 T-H CO h CO *G H 1C CM • T— 1 CO s d 41 CM CO CM 41 5 8 d 1C T-H CO CO CO cd CO 1 03 1 S 1 03 1 Sfi|.gg II r- CO T-H CO CO g d 1 2 T-H 1 CO d 1 CO O3 co 00 GO CM s CO J5 o T-H ^^ T~^ 1 1:1 Is d 4) d 41 OJ T-H CM d 4J ^*™ ^^ «5 ' 'CO i-H I> T-H d 41 i d 41 rH 11 O3 CO T-H 00 CO T— 1 o 41 CM d 41 T~< 1C • t— i-H T-H d 02 TJ CM ^ • d 1 CM d 1 CM o' 1 O3 CO CO CM T-H 1 T-I T-H § CM T-H GO T-H d i ,2 d 41 T-H O3 d 41 d "H CO CM £d d d 41 O3 d 06 o d o' 41 o oo d 41 ^ 03 • pQ O co d S t^" D ^^ ^•^ . . 1C CM 1C CM d 1C CM d 1C CM O B^AB 1C CO i CO CM 8 CO o"^'§ 2 C^l T— 1 T-H d CM' d T— ( T-H 1 0-3 >'^ '""' 1 1 1 co CO (M CO § 00 ^ T-H s GO j^ rH CO d I>- T-H 12 a 41 41 "S ^ 41 rH 41 co o 41 7 g 1C 11 41 T-H o 8 CO • 1C T-H O3 CO T— 1 1 8 O3 t^ CO CO CO 1 d (M T-H CO 1C T-H 5 CM' O3 CM I 1C T-H CM 1 CO co S 8 T-H CO CO CM CO~ T-H CO T-H d CO 03 1C d 1C d T-H 41 7 7 •* w H oo oo 41 7 s co 7 7 g5 pi d 0 CO O3 3 >c d o 0 CO 8^; T-H £c ^_ rn" r-' o CO £• co I 00 CM 1 GO CM CO^ 7 ^L 1 ^v 1 ,_! ,—1 T-H T-H ' f> *> • T5 t-i o : g*8 ~ d L. Unweighted* 1. Weighted wil the squa -^ *° 2§ o i 0 83 60 S o — ;g ^ g § Y^ a S S^~T g* S ^ IS g-o Q Q PH '5 -o ° ^ a ^ m bC <» ^ Cl? -f^» ""^ ^ CO £ ,X> !t3 co JE S a Percentage difference . 4. Based on dai observatio Difference (4)-(l).... Diff./^diff. • Percentage difference. 271 272 Basal Metabolism in Men Considering first the mean total daily heat production, whic is the fundamental constant for the establishment of a st'andar value, we note that the mean obtained by weighting is somewhe lower than that secured by giving each individual equal weigh irrespective of the number of days on which observations wei made. The differences are, however, of a low order of magnitude i compared with the average heat production of 1,631 calorie The heat production is on the average 13.54 calories lower whe the constants are weighted with the square root of the number « days and 28.38 calories lower when the constants are weighte with the number of days, or based upon the constants for the ind • vidual days.20 These differences are between total daily heat productions (ui weighted) of about 1,631 calories. Thus they are relatively sma only 0.83 and 1.76 per cent21 by the two methods of weightin The differences are not merely relatively small as compared wii the total heat production but are in all cases less than twice ; large as the probable errors of the differences.22 Turning now to the results for heat production per kilo of boc weight, we have the comparisons set forth in the second sectk of Table VII. The means show a slight but wholly insignificant increase calories per kilo as a result of weighting with the square root of number of days, or with the number of days, or by using the d averages in calculating the constants. Finally consider the results for calories per 24 hours per es mated square meter of body surface. The heat production is 3.43 calories lower when weighted 1 the square root of the number of days observation and 8.88 c: ories lower when weighted with the number of days, than wh calculated from the daily averages. The differences are re! 20 The means calculated in these two ways should be identical. T slight difference is due to the number of significant figures retained in t calculations. 21 Percentage differences have been computed by using the average the two means compared as a base. !2 The probable errors have in all cases been based on the actual, i the weighted, number of individuals as N. J. A. Harris and F. G. Benedict 273 ,vely small, being less than 1 per cent in the three comparisons. 11 differences are less than twice as large as their probable errors. It is clear from the foregoing constants that practically it is nmaterial whether the population means are calculated from the aver- ges of the individual subjects, from the averages weighted with the umber of days, or with the square root of the number of days, or hether they are determined directly from the daily observations.23 From Table VII it appears that the standard deviations obtained y weighting the individual means with the square root of the umber of days or with the number of days are lower than those ilculated without weighting. We now have to consider the constants deduced from the mini- mm values of the daily metabolism. The results are given in 'able VIII. Limiting our attention for the moment to a com- arison of these constants among themselves we note that, in •hatever units measured, the mean metabolism calculated by -eighting with the square root of the number of days is always »wer than the constant obtained without weighting. When the linima for the individuals are weighted with the number of ays instead of with the square root of the number of days the ifference between the weighted and the unweighted value is even reater, amounting to —69.6 calories of total daily heat produc- on, -0.579 calories per kilo, and —32.03 calories per square leter of surface area. These differences correspond to relative ifferences of 4.49, 2.35, and 3.63 per cent of the unweighted con- •,ants. They show that if an absolute minimum, i.e. the one single ay with the lowest average of metabolism measurements, for each idividual is adopted, the constants for a population will depend to considerable extent upon the number of days observation for each idividual. Table IX compares the percentage change in the population Dnstant due to weighting when the population constant is calcu- ited from means and from minima. For all three units of metab- 23 While this is the result for the large series of data in hand the calcu- .tion of the population constant from daily observations by weighting ith the number of days is not to be generally recommended since in series i which the number of individuals is small the population average may be )o greatly influenced by repeated observations on one or a few intensively udied individuals. j^ ^j.5 d t^ O CO CO CO OS t^ OS CN GO •* CO O T}< Tfl OS t^ OO fg 8_§ g-^ d r-I d t>- co' d co t^ d CO O 5 1-1 1 1 1 8 O i-H 1> §S 0? ^ ** co cc C> C5 1-H GO '^ CO ^ CO «£, e 1 6 a Standard deviation. CO t>^ OS CN OS t^ CN CN O O (P r* *o CO i> i 1-H i-H 1 8 CO odd I GO i ^ 8 CO O CO O T-I C5 O O CN CN d 1 *-j t^» r^» CN CN CO fl ^ -H 8 O f— t>- . os eg r» i— i CO t^ CO CO CO | J J3 1 g § 1 CO OS GO os os co l^ O GO i— i CN CO i-H i-H r—( IO O O o t-~ co CO GO CO "5 "5 73 £ 9 d 2 g 1-H n JJ _M i-H CO O OS i-H CO Tt< 1-H O 0> odd li (i jj O CO 11 11 71 ^ SX O GO i-H CO CO lO M M (1 CD CN CN CO CS . l>- OS t^- OS •g V C**i iO h>J t>» CO ^^ CN GO CO *« 8 t^i & O I-H GO 1-H i-H >O •**< i— 1 CN CM i cd co' cs 8 «-2.2d co co »o lO 1-H CN 1-H CO O ^ o t« t> a d 0 § C3-.2 1-H CN O GO OS O t^* t** C5 v> S a 0-3 > i-H i-H 1 1 1 e "5 CN OS O CD l> OS 1-H i-H OS OS OS CN O O i— i Igl 'e 1 1> O 1-H CD i -1 •« « 0 1-H d d d ^ fl •« fe gS OS !>. GO • ! CN CN CO •ti il -H 5> 1-H CN i-H • •1 i- H Ifc O2 T3 ^ CO OS ° (N S S 8 ° ° OS 00 OS O GO CO r*( 8 J« 1-H i-H 1 IN CN O 1 •* GO' co 0 0 | 8 o 3! !>• O ^ GO OS CN CN GO CO os co _)_ C3 jg*0 i • Jo os ^ lO iO O co co co CN CO ^ ^ cp'S'n o CN (N O os os d Is* t^" ^D 'e 0-3 > i-H ,-H | 1 1 GO CS •2 "s (^ « II "2 c' EJ 11 « > — (U 02-3 GO" oo I-H 1-H 1O •H -H -H °. ^H 10 T* O 0 CO CO i-H co d odd •« -H -H 3 S o o o o d CN CN CO -H -H -H ^ §t^- CO O GO GO o to' . i-H OS CN •< 8 CO CO -* CD^ »O^ i 1-H 1-H IO "HH O CN CN _|_ lO 00 CD CN OS CN OS GO _|_ g ""3 O 5 5G S£3 t-i ference. ries per § .9 S s » „ S 3"J!l|j O - 93 o3 »H .2 >- •g fi< Q Q PH ' O 'cS *•" S 2 • o ?=H Q Q PH -3 02 tn ^] | , p^ £ E^ 0 0 276 J. A, Harris and F. G. Benedict 277 The fact that the average metabolism is lower when it is cal- clated from individual minima than when it is computed from ilividual means furnishes no argument in favor of either of te methods of computing the metabolism constant. Conclu- g>ns in regard to this point must be drawn from the results for vighting discussed aboVe, and from a consideration of the varia- lities. From Table X we note that in whatever units heat production i expressed, the variation in the population metabolism (meas- i3d in either the absolute terms of the standard deviation or in ts relative terms of the coefficient of variation) is lower when the iiividual means are employed than when individual minima are usd as a basis for calculating the population constants. If the securing of a constant with the lowest probable error is ce of the goals to be attained, the method of means is, therefore, t be preferred over the method of minima. III. SUMMARY. In all special investigations in human calorimetry some stand- al constant measuring the metabolism of the normal individual cist be used as a basis of comparison. The selection of this cistant presents a problem of considerable difficulty from three ales. The first is that of the physiological conditions under which the bsal metabolism of the individual shall be measured ; the second isthat of the unit in which the caloric output of the individual sill be expressed ; the third is that of the method by which the svtistical constants for the standard series shall be obtained. Basal metabolism measurements are generally made in two or nire periods, with the subject in the postabsorptive state and in cnplete muscular repose, on the same day. Experimental piods which show evidence of muscular activity or of faulty tihnique in the analyses are discarded. So called minimum priods are utilized for obtaining a mean for the day. This may b designated as the daily mean. It may be reasonably assumed that the results of the several piods of measurement on a given day stand in the relation of dplicate, triplicate, etc. analyses, and that it is not necessary to THE WAVERLY PRE BALTIMORE. U S. A. ON THE OSMOTIC CONCENTRATION OF THE TISSUE FLUIDS OF PHANEROGAMIC EPIPHYTES J. ARTHUR HARRIS Reprinted from the AMERICAN JOURNAL OF BOTANY, 5: 49O-5°6. November, 1918, ON THE OSMOTIC CONCENTRATION OF THE TISSUE FLUIDS OF PHANEROGAMIC EPIPHYTES [Reprinted from the AMERICAN JOURNAL OF BOTANY, 5: 490-506, November, 1918.] ON THE OSMOTIC CONCENTRATION OF THE TISSUE FLUIDS OF PHANEROGAMIC EPIPHYTES1 J. ARTHUR HARRIS INTRODUCTORY REMARKS The purpose of this paper, which is one of a series dealing with the problem of the physico-chemical properties of vegetable saps in relation to environmental factors and to geographical distribution, is to present the results of three series of determinations of the osmotic concentration of the tissue fluids of phanerogamic epiphytes, and to compare them briefly and in a preliminary way with available data for the osmotic concentrations found in the sap of terrestrial vegetation. Notwithstanding the enthusiastic interest aroused in the mind of the botanical traveler by the remarkable range of form and the obvious physiological peculiarities of the Orchidaceae, Bromeliaceae, and other epiphytic forms so characteristic of tropical vegetation, our knowledge, in quantitative terms, of the physiology of these organisms is exceed ingly meager. Since I hope on another occasion to discuss epiphytism in greater detail, I shall not in this place review the general literature. MATERIALS AND METHODS In this paper I have meant to include only those species which may unquestionably be considered typical epiphytes. It was for this reason that a few determinations made on plants which may be either terres trial or epiphytic were included by Mr. Lawrence and myself in our paper on the Jamaican montane rain forest vegetation (191 70). In some instances it is extremely difficult to determine just which species shall be regarded as epiphytes. Our data are given in detail, and any botanist who chooses may arrange them differently. The methods employed in the present study are those sufficiently described in our earlier discussion of the parasitic and the terrestrial vegetation of the Blue Mountains (Harris and Lawrence, 1916, 19170). 1 This study was made possible by the Department of Botanical Research and the Department of Experimental Evolution of the Carnegie Institution of Wash ington. 490 CONCENTRATION OF TISSUE FLUIDS OF EPIPHYTES 49 1 The determinations here recorded were secured in three periods of field work, the first in Jamaica in 1915, the second and third in southern Florida in 1916 and 1917. In the first period I had the advantage of the co-operation of Mr. John V. Lawrence, who remained on the island for some time longer than I was able to do, and to whom I am indebted for a large part of the work on Jamaican forms. In the third period Mr. Charles W. Crane rendered most efficient service in several phases of the work. The determinations were carried out in the Tropical Laboratory at Cinchona, Jamaica, and in the Subtropical Laboratory of the United States Department of Agriculture at Miami, Florida. I have to thank Mr. William Harris, F.L.S., and the members of the British Association Committee for the use of the Laboratory at Cinchona, and am much indebted to Dr. David Fairchild, Agricultural Explorer, and to Mr. Edward Simmonds, in charge of the Plant Introduction Garden at Miami, for the use of the laboratory and other favors. All the species were determined in the herbarium of the New York Botanical Garden. In addition, I am indebted to Dr. Small for various courtesies in the field work. PRESENTATION OF DATA The following protocol gives the individual determinations for the several species in terms of freezing point lowering, A , corrected for undercooling, and osmotic concentration in atmospheres as determined from a published table (Harris and Gortner, 1914). The averages, designated by bars for each species, are given at the extreme right. When only a single determination is available it has of necessity served to represent the species in place of the average. In the Bromeliaceae an attempt has been made to arrange the forms in a rough series from the most typical tank forms to those departing most widely from the type in which water storage in the bases of the leaves is possible. Ultimately I hope our determinations will cover a range of forms sufficiently wide and be numerous enough to justify consideration of the problem of the relationship between sap properties and morphological structure in this fascinating family of plants. It has not seemed feasible to attempt any logical classification of the Orchidaceae, and they are merely alphabetically arranged for each of the regions. All the Jamaican montane rain forest determinations were made in 1915. Hence the year is omitted when dates are cited. In the case of 492 J- ARTHUR HARRIS the Florida determinations, the year as well as the day of the month has been given. BROMELIACEAE Guzmannia Sintensii (Baker) Mez A = 0.31, P = 3.8 Montane Rain Forest, Leeward Slopes, Feb. 24, A = 0.31, P = 3.7; Ridges, Feb. 9, A = 0.34, P = 4.1; Mar. 9, A = 0.45, P = 5.5; Jim Crow Peak, Feb. 17, A = 0.25, P = 3.0; Feb. 17, A = 0.28, P = 3.4; Windward Slopes and Ravines, Feb. 13, A = 0.25, P = 3.0; Feb. 13, A = 0.23, P = 2.8; Feb. 20, A = 0.28, P = 3.3; Mar. 13, A = 0.44, P = 5-3. Guzmannia capituligera (Griseb.) Mez (?) A = 0.44, P = 5.2 Montane Rain Forest, Leeward Slopes, Feb. i82, A = 0.46, P = 5.5; Windward Slopes and Ravines, Feb. 22, A = 0.41, P = 4.9. Guzmannia monostachya (L.) Rusby A = 0.46, P = 5.6 Subtropical Florida. Sykes Hammock, Jan. 27, 1916, A = 0.42, P = 5.1; Mar. 16, 1917, A = 0.50, P = 6.0. Catopsis Berteroniana (Schult.) Mez A = 0.46, P = 5.6 Subtropical Florida. Hattie Bauer Hammock, Mar. 19, 1917, A = 0.46, P = 5.5; Mar. 19, 1917, A = 0.42, P = 5.0; Royal Palm Hammock, Mar. 3, 1916, A = 0.50, P = 6.0; Feb. 21, 1917, A = 0.48, P — 5-7; Small Hammock between Florida City and Biscayne Bay, Feb. 17, 1917, A = 0.46, P = 5.6. Tillandsia utriculata L. A = 0.43, P = 5.2 Subtropical Florida. Hattie Bauer Hammock, Mar. 16, 1917, A = 0.43, P = 5.2; Mar. 19, 1917, A = 0.45, P = 5.4; Royal Palm Hammock, Mar. 4, 1916, A = 0.42, P =5.1; Mar. 3, 1916, A = 0.33, P = 4.0; Small Hammock near Royal Palm Hammock, Feb. 23, 1917, A = 0.43, P = 5.2; Bryan Hammock, Feb. 13, 1917, A = 0.37, P = 4.5; Palm and Live Oak Hammock, Peninsula, near the Narrows, Indian River, Apr. i, 1917, A = 0.44, P = 5.3; on dwarfed Rhizophora Mangle, near Biscayne Bay, Feb. 17, 1917, A = 0.40, P = 4.8; Feb. 17, 1917, A = 0.57, P = 6.9; Feb. 17, 1917, A = 0.39, P = 4.7; Feb. 17, 1917, A = 0.34, P = 4.1; Orange Grove, Miami, Feb. 10, 1917, A = 0.58, P = 6.9. 2 These determinations are for the older, outer leaves. Sap from the younger leaves gave A = 0.35, P = 4.2. CONCENTRATION OF TISSUE FLUIDS OF EPIPHYTES 493 Tillandsia Valenzuelana A. Rich. A =0.36, P = 4.3 Subtropical Florida. Royal Palm Hammock, Jan. 29, 1916, A = 0.35, P = 4.2; Jan. 29, 1916, A = 0.36, P = 4.3; Feb. 23, 1917, A = 0.34, P = 4.0; Small Hammock near Royal Palm Hammock, Feb. 23, 1917, A = 0.41, P = 4.9; Bryan Hammock, Feb. 13, 1917, A = 0.32, P = 3.9; Brickell Hammock, Mar. 9, 1917, A = 0.38 P = 4-5- Tillandsia incurva Griseb. (?) A = 0.25, P = T. o Montane Rain Forest, Ridges, Feb. 18, A = 0.28, P = 3.3; Wind ward Slopes and Ravines, Mar. 2, A = 0.22, P = 2.7. Tillandsia fasciculata Swartz A = 0.39, P = 4 6 Subtropical Florida. Hattie Bauer Hammock, Mar. 16, 1917, A = 0.36, P = 4.3; Mar. 19, 1917, A = 0.33, P = 3.9; Royal Palm Hammock, Mar. 4, 1916, A = 0.40, P = 4.8; Feb. 27, 1917, A = 0.41, P = 5.0; Small Pineland Hammock, near Royal Palm Hammock, Mar. 4, 1916, A = 0.44, P = 5.3; Sykes Hammock, Jan. 27, 1916,' A = 0.40, P = 4.8; Bryan Hammock, Feb. 13, 1917, A = 0.31, P = 3.7; Small Hammock near Royal Palm Hammock, Feb. 23, 1917, A = 0.43, P = 5.2; Murden Hammock, Jan. 28, 1916, A = 0.45, P = 5.4; Small Hammock between Biscayne Bay and Florida City, Feb. 17, 1917, A = 0.32, P = 3.9. Tillandsia aloifolia Hook. Subtropical Florida. On dwarfed Khizophora Mangle near Bis cayne Bay, Feb. 17, 1917, A = 0.43, P = 5.1. Tillandsia Balbisiana Schult. A = 0.46 P = =5 5 Subtropical Florida. Hattie Bauer Hammock, Mar. 19, 1917, A = 0.53, P = 6.4; Royal Palm Hammock, Jan. 29, 1916, A = 0.40, = 4-8; Mar. 3, 1916, A = 0.39, P = 4.7; Feb. 23, 1917, A = 0.47, • = 5.7; Small Hammock near Royal Palm Hammock, Feb. 23, 1917, A = 0.49, P = 6.0; Bryan Hammock, Feb. 13, 1917, A = 0.38, P =4.6; on dwarfed Rhizophora Mangle near Biscayne Bay, Feb. 29, 1916, A = 0.50, P = 6.0; Feb. 17, 1917, A = 0.51, P = 6.1. Tillandsia tenuifolia L. ^ = o ^2 p = c i Subtropical Florida. Royal Palm Hammock, Jan. 29, 1916, \ = 0.38, P = 4.6; Feb. 21, 1917, A = 0.45, P = 5.4; Sykes Ham- nock, Jan. 27, 1916, A = 0.46, P = 5.5; Mar. 15, 1917, A = 0.45, P = 5.5; Bryan Hammock, Feb. 13, 1917, A = 0.37, P = 4.4. 494 J- ARTHUR HARRIS Tillandsia recurvata L. A = 0.49, P = 5-8 Subtropical Florida. Royal Palm Hammock, Mar. 3, 1916, A = 0.52, P = 6.2; Feb. 23, 1917, A = 0.45, P = 54. Dendropogon usneoides (L.) Raf. A = 0.75, P = 9.0 Subtropical Florida. Hattie Bauer Hammock, Mar. 19, 1917. A = 0.62, P = 7.5; Royal Palm Hammock, Mar. 3, 1916, A = 0.86, P = 10.4; Bryan Hammock, Feb. 13, 1917. A = 0.50, P = 6.0; Palm and Live Oak Hammock, the Peninsula near the Narrows, Indian River, Apr. I, 1917, A = 1.32, P = 15.8; Sykes Hammock, Mar. 15, I9I7> A = 0.57, P = 6.8; Orange Grove, Miami, Mar. 6, 1916, A = 0.7o, P = 8.4; Feb. 9, 1917. A = 0.65, P = 7-9- ORCHIDACEAE Epidendrum imbricatum Lindl. Montane Rain Forest, Windward Slopes and Ravines, Feb. 13, A = 0.30, P = 3.6. Lepanthes ovalis (Swartz) Fawc. & Rendle Montane Rain Forest, Leeward Ravines, Mar. 18, A = 0.35, P = 4.2. Lepanthes divaricata Fawc. & Rendle A = 0.20, P = 2.4 Montane Rain Forest, Ridges, Feb. 9, A = 0.19, P = 2.3; Mar. 9, A = 0.27, P = 3.3; Jim Crow Peak, Feb. 17, A = 0.16, P = 1.9; Windward Slopes and Ravines, Feb. 20, A = 0.19, P = 2.3; Feb. 24, A = 0.18, P = 2.2; Mar. 4, A = 0.20, P = 2.4. Octadesmia montana (Swartz) Benth. A = 0.44, P = 5-3 Montane Rain Forest, Jim Crow Peak, Feb. 17, A = 0.41, P = 5.0; Windward Slopes and Ravines, Feb. 20, A = 0.46, P = 5.5. Pleurothallis racemiflora (Swartz) Lindl. Montane Rain Forest, Leeward Ravines, Mar. 11, A = 0.21, P = 2.6. SteUs micrantha Swartz A = 0.22, P Montane Rain Forest, Ridges, Feb. 9, A = 0.23, P = 2.7; Wind ward Slopes and Ravines, Feb. 4, A = 0.24, P = 2.9; Feb. 13, A = 0.20, P = 2.4; Feb. 20, A = 0.21, P = 2.5. Stelis ophioglossoides Swartz Montane Rain Forest, Jim Crow Peak, Feb. 17, A = 0.22, P = 2.7. CONCENTRATION OF TISSUE FLUIDS OF EPIPHYTES 495 Anacheilium cochleatum (L.) Hoffmannsegg A = 0.43, P = 5.2 Subtropical Florida. Hattie Bauer Hammock, Jan. 28, 1916* A = 0.44, P = 5.3; Royal Palm Hammock, Jan. 29, 1916, A = 0.41, P = 5.0. Auliza nocturna (L.) Small A = 0.42, P = 5.0 Subtropical Florida. Hattie Bauer Hammock, Jan. 28, 1916* A = 0.46, P = 5.5; Mar. 16, 1917, A = 0.47, P = 5.7; Mar. 19, 1917, A = 0.52, P = 6.3; Royal Palm Hammock, Jan. 29, 1916, A = 0.38, P = 4.5; Feb. 21, 1917, A — 0.29, P = 3. 5; Small Pineland Hammock, near Royal Palm Hammock, Mar. 3, 1916, A = 0.41, P = 4.9; Bryan Hammock, Feb. 13, 1917, A = 0.40, P = 4.8; Feb. 13, 1917, A = 0.39, P = 4-6. Encyclia tampense (Lindl.) Small A = 0.48, P = 5.8 Subtropical Florida. Hattie Bauer Hammock, Jan. 28, 1916, A = 0.48, P = 5.8; Mar. 16, 1917, A = 0.50, P = 6.1; Mar. 19, 1917, A = 0.51, P = 6.2; Royal Palm Hammock, Jan. 29, 1916, A = 0.44, P = 5.3; Brickell Hammock, Mar. 22, 1917, A = 0.49, P = 5.9; Mar. 24, 1917, A = 0.40, P = 4.8; Bryan Hammock, Feb. 13, 1917, A = 0.45, P = 5.4; Palm and Live Oak Hammock, Peninsula, near the Narrows, Indian River, Apr. i, 1917, A = 0.62, P = 7.4; Small Ham mock near Royal Palm Hammock, Feb. 23, 1917, A = 0.47, P = 5.6. Macradenia lutescens R. Br. A = 0.51, P = 6.1 Subtropical Florida. Royal Palm Hammock, Jan. 29, 1916, A = 0.53, P = 6.4; Feb. 21, 1917, A = 0.48, P = 5.7. Polystachya minuta (Aubl.) Britton Subtropical Florida. Bryan Hammock, Feb. 13, 1917, A = 0.50, P = 6.o.3 Spathiger rigidus (Jacq.) Small A = 0.38, P = 4.5 Subtropical Florida. Hattie Bauer Hammock, Jan. 28, 1916, A = 0.47, P = 5.7; Mar. 16, 1917, A = 0.36, P = 4.4; Mar. 19, 1917, A = 0.42, P = 5.0; Royal Palm Hammock, Jan. 29, 1916, A = 0.35, 3 Sample from Hattie Bauer Hammock obtained January 28, 1916, and one from the Brickell Hammock, March 22, 1917, were so mucilaginous that no deter mination could be made. The juice of the sample from the Bryan Hammock was also highly mucilaginous and could not be filtered. Until verification this deter mination must be taken as only approximate. 496 J. ARTHUR HARRIS P = 4.2; Jan. 29, 1916, A = 0.31, P = 3.7; Mar. 3, 1916, A = 0.40, P = 4.8; Feb. 21, 1917, A = 0.32, P = 3.9. Vanilla Eggersii Rolfe Subtropical Florida. Brickell Hammock, Feb. 14, 1916, A = 0.24, P = 2.9. This determination is of course based on sap from the stems. PlPERACEAE Peperomia basellifolia H.B.K. A = 0.35, P = 4.2 Montane Rain Forest, Windward Slopes and Ravines, Feb. 20, A = 0.40, P = 4.8; Feb. 24, A = 0.35, P = 4.2; Mar. 4, A = 0.33, P = 3.9; Mar. 13, A = 0.31, P = 3.7. Peperomia crassicaulis Fawc. & Rendle A = 0.40, P= 4.9 Montane Rain Forest, Ridges, Feb. 18, A = 0.40, P = 4.8; Mar. 9, A = 0.44, P = 5.2; Mar. 13, A = 0.42, P = 5.1; Mar. 16, A = 0.46, p = 5.6; Windward Slopes and Ravines, Mar. 4, A = 0.30, P = 3.6. Peperomia magnolia-folia (Jacq.) A. Dietr. A = 0.38, P = 4.6 Subtropical Florida, Royal Palm Hammock, Jan. 29, 1916, A = 0.38, P = 4.6; Small Hammock near Royal Palm Hammock, Feb. 23, 1917, A = 0.39, P =4.7; Bryan Hammock, Feb. 13, 1917, A = 0.37, P = 4.5; Feb. 13, 1917, A = 0.35, P = 4.2; Sykes Hammock, Jan. 27, 1916, A = 0.41, P = 4.9. Peperomia Myrtillus Miquel A = 0.36, P = 4.3 Montane Rain Forest, Leeward Ravines, Mar. n, A = 0.35, P = 4.2; Windward Slopes and Ravines, Mar. 13, A = 0.36, P = 4.4. Peperomia quadrifolia (L.) H.B.K. Montane Rain Forest, Leeward Ravines, Mar. 11, A = 0.39, P = 4.6. Peperomia septemnervis Ruiz & Pav. A = 0.31, P = 3-7 Montane Rain Forest, Leeward Ravines, Mar. n, A = 0.33, P = 3.9; Windward Slopes and Ravines, Feb. 13, A = 0.31, P = 3-7 1 Feb. 13, A = 0.30, P = 3.6. GESNERACEAE Columned hirsuta Swartz A = 0.36, P = 4-3 Montane Rain Forest, Leewaro. Ravines, Feb. 26, A = 0.40, P = 4.8; Windward Slopes and Ravines, Feb. 13, A = 0.33, P = 4-05 Feb. 20, A = 0.34, P = 4-1 ; Feb. 22, A = 0.33, P = 4.0; Feb .22, CONCENTRATION OF TISSUE FLUIDS OF EPIPHYTES 497 A = 0.32, P = 3.9; Feb. 24, A = 0.36, P = 4.4; Mar. 2, A = 0.37, P = 4.5; Mar. 4, A = 0.38, P = 4.5; Mar. 13, A = 0.40, P = 4.8. ANALYSIS OF DATA In this paper I shall limit discussion of the data presented to a comparison of the constants of the epiphytes among themselves and with the values which have already been obtained for terrestrial forms in various habitats. Even these comparisons must be limited by the still unorganized condition of our data for several important habitats. Since, however, it will be many months before all of these data can be fully analyzed and ready for discussion, it has seemed proper to place the data which have been obtained for epiphytes during the past three years on record in a form which will enable other physiologists and phytogeographers to use them. Consider first of all the relative magnitudes of the osmotic con centrations found in the epiphytic plants of the two regions considered. The results, grouped by families, are shown in table I. The constants in this table are the averages of species means, not of species determinations (except when only one determination is availa ble for a species), for each family. While the species means which are based upon a large number of determinations are somewhat more trustworthy than those which are based upon only two or three readings, or upon only a single collection, the general mean for the habitat is certainly more representative when calculated in this way than if the habitat average had been computed directly from the individual constants, thus weighting the species with the numbers of collections of each which happened to be made. TABLE i Comparison of Osmotic Concentrations in Jamaican and Floridian Epiphytes Jamaica Florida Difference Bromeliaceae ;A = 0.333, P = 4.00 A = 0.464, P = 5-57'A = + 0.131, Orchidaceae . 2 genera, 3 species A = 0.276, P = 3.32 5 genera, 7 species A = 0.362, P = 4.34 Peperomia only, 5 species 4 genera, 10 species A = 0.421, P = 5.06 7 genera, 7 species A = 0.380, P = 4.58 Peperomia magnolia- folia only P = + 1-57 A = + 0.145, P = + 1-74 A = + 0.018, P = + 0.24 Piperaceae - 0.350, r 4-33 Columnea hirsuta only _ No representative. 498 J. ARTHUR HARRIS The table brings out clearly two facts: 1. That in all four families and in both Jamaica and Florida, the osmotic concentration of epiphytic forms is extremely low. 2. That for the three groups represented in both regions the os motic concentration of the epiphytes (chiefly from the hammocks) of subtropical Florida is higher than that demonstrated in the Jamaican rain forest. The average difference is 1.57 atmospheres higher for the Bromeliaceae,4 1.74 atmospheres higher for the Orchidaceae, and o. 24 atmospheres higher for the single species of Peperomia. The comparison may be made somewhat more analytically on the basis of the means for the genera. The constants in table 2 are averages of the species means of each of the genera. TABLE 2 Genera of Jamaican and Floridian Epiphytes Arranged in the Order of the Average Osmotic Concentration of Their Species Jamaica Florida Genus P P Genus Pleurothallis 2 S7 Stelis 2 6S Tillandsia •3 OO 2.90 Vanilla Lepanthes 1 28 Epidendrum ^ S6 Columnea A -I-I Peperomia A T.A Guzmannia A AQ Octadesmia 5 2S 4-52 4-58 4-97 5-09 5-15 Spathiger Peperomia Auliza Tillandsia Anacheilium 5-55 ' 5-56 5.83 6.00 6.05 8-97 Guzmannia Catopsis Encyclia Polystachya Macradenia Dendropogon 4 That the higher value for Floridian Bromeliaceae is not primarily due to the inclusion of Dendropogon usneoides (= Tillandsia usneoides) is shown by the fact that if this species be omitted from the Florida series, the remaining 9 species average A = 0.433, P = 5.19, which are respectively o.ioo and 1.19 greater than the Jamaican average. CONCENTRATION OF TISSUE FLUIDS OF EPIPHYTES 499 It is clear at a glance that with the exception of the stem-succulent Vanilla in the Floridian and of Octadesmia montana in the Jamaican constants, the two series do not overlap in the average (generic) mag nitude of their constants. With the exceptions noted, the Jamaican (rain forest) genera range from 2.57 to 4.49 atmospheres, whereas the Floridian genera range from 4.52 to 8. 97 atmospheres. Instead of limiting our comparisons between the two regions to means, the individual determinations may be seriated according to their magnitude and the frequency distributions compared. This has the advantage of giving a general view of the range of variation in the individual constants, but the disadvantage from the standpoint of exact comparison that certain species are far more extensively repre sented than others'. The frequency distributions are given in table 3. TABLE 3 Frequency Distributions of Osmotic Concentration Determinations in Jamaican and Floridian Epiphytes Osmotic Orchidaceae Bromeliaceae in Atmospheres Jamaica Florida Jamaica Florida I-5-I-9 I _ 2.0-2.4 5 2.5-2.9 5 I 2 — 3.0-34 I 5 3-5-3-9 I 3 I 4 4.0-4.4 I 2 I 7 4-5-4-9 6 I n 5.0-54 I 5 I H 5-5-5-9 I 7 2 6 6.0-6.4 5 7 6.5-6.9 — — . 2 7-0-7-4 I — 16 30 13 51 Because of the unusually high values found in the Spanish moss (Dendropogon usneoides) it has been omitted from this table. Not withstanding this fact, the Floridian Bromeliaceae as well as the Orchidaceae show distinctly higher minima and maxima than the Jamaican forms. The distinction between the two regions is not as clearly shown by the distribution of the individual determinations as by the generic means, since individual determinations must be ex pected to show much wider variation than averages. 5OO J. ARTHUR HARRIS I now turn to the relative magnitude of the osmotic concentration of terrestrial and epiphytic plants. Since in a number of series of determinations we have found a differentiation in the sap properties of ligneous and herbaceous plants,5 I shall compare epiphytic Orchidaceae, Bromeliaceae, and Piperaceae primarily with terrestrial herbaceous plants. Unfortunately the several hundreds of determinations from the various coastal, pineland, hammock, and Everglade habitats of Sub tropical Florida are as yet unclassified, and it will probably require some time before the results from this highly interesting region are discussed in detail. The averages for the various groups of epiphytes from Jamaica and from Subtropical Florida have been given in table i . The average freezing-point lowering of the saps ranges from 0.276° to 0.464°, less than two tenths of one degree. In terms of osmotic concentration the values lie between 3.3 and 5.6 atmospheres, a range of less than two and one third atmospheres. The only extensive series of averages for herbaceous terrestrial vegetation are those for the Arizona deserts made by Harris, Lawrence, and Gortner (1916), and the first Long Island series, by Harris, Lawrence, and Gortner, as yet unpublished, and the Jamaican montane rain forest series which will be treated in greater detail below. For the Long Island habitats the preliminary average values are : Average Con- Habitat centration. P Beaches, coastal sand dunes, and marshes ............... 13-62 Dryer woods and open fields ........................... 10.04 Permanently moist localities ........................... 9-27 All habitats Note that the epiphytic forms show a sap concentration about one third to one half as great. For the Arizona desert (vernal) flora the averages for herbaceous plants are : 6 For averages for divers growth forms from the Arizona deserts see Harris, Lawrence, and Gortner (1916). Averages for Long Island and Jamaican habitats are given by Harris and Lawrence (19170). Some general comparisons are made by Harris (1917). CONCENTRATION OF TISSUE FLUIDS OF EPIPHYTES 501 Habitat Average Con centration, P Rocky slopes I5-94 Canyons 13-33 Arroyos 12-99 Bajada slopes 20.53 Salt spots 23.57 All habitats 15-15 These values are (roughly speaking) from 4 to 7 times as large as those for the epiphytic families. For the Jamaican series, and unfortunately only for the Jamaican series, it is possible at this time to compare the averages for epiphytic and terrestrial forms from the same habitat. Table 4 gives the averages of the species means for each habitat for the Orchidaceae and Bromeliaceae and for the genus Peperomia of TABLE 4 Comparison of Osmotic Concentration of Epiphytic Plants with that of Terrestrial Herbaceous Plants in the Montane Rain Forest Orchidaceae Bromeliaceae Piperaceae Habitats Average for Average Difference Average Difference Average Difference Terrestrial for and for Epiphy and for and Herbs Epiphytic Relative tic Brome Relative Epiphytic Relative Orchidaceae Value liaceae Value Piperaceae Value Ruinate of the leeward slopes A=o.8l2 A =0.385 -0.427 P=9.77 — P=4.6o -5-17 O = i7) (»=2) 47-i% Leeward ravines A =0.628 A =0.280 -0.348 A =0.357 — O.27I -P = 7-59 P = 3-40 -4.19 — P = 4-23 — 3-36 (n = i3) (n=2) 44-8% (n = 3) 55-7% Ridges and peaks A=o.7i8 A =0.267 —0.451 A =0.305 —0.413 A =0.43 1 —0.287 P = 8.63 P=3.22 -5-41 -4-98 P = 5.I9 -3-44 (» = 8) (n=4) 37-3% (n=2) 42.3% (w = i) 60. i % Windward slopes and ravines A =0.627 A=O.2Q2 —0.335 A =0.310 —0.317 A =0.330 -0.297 P = 7-52 p = 3.5o —4.02 ^ = 3-73 -3-79 P = 3.98 -3-54 (« = i5) («=4) 46-5% (w = 3) 49-6% (n=4) 52.9% All habitats A =0.700 A =0.280 —0.420 A =0.330 -0.370 A =0.353 -0-347 P = 8.43 ^ = 3-37 -5.06 P=3-96 -4-47 P=4-23 —4.20 (« = 53) (« = 10) 40.0% (w = 7) 47-0% (w = 8) 50-2% 5O2 J. ARTHUR HARRIS the Piperaceae. The number under each of the averages is the number of species, not the number of determinations, upon which it is based. The averages for terrestrial herbaceous species are those already published (Harris and Lawrence, 19170). The general mean for the region has been computed by averaging the species means for the individual habitats. Thus if a species occurs in both the Leeward Ravines and the Ridge Forest it is counted twice, whereas the species which occur in one of these habitats only will be counted but once. Thus the numbers of the species given for all habitats is the number of species weighted with the number of the sub-habitats in which they occur.6 The comparison between the epiphytic and the terrestrial her baceous forms has been made in two ways. First, the actual differ ences in the average depression of the freezing point and in the average calculated osmotic concentration have been determined and are given with their signs. Second, the average values of P of the epiphytes have been expressed as a percentage of the value for terrestrial herbs.7 An examination of the nine comparisons between the epiphytic and terrestrial herbs of the four individual habitats shows that the con centration is in every instance lower for the epiphytic forms. The averages are roughly 4.0 to 5.4 atmospheres lower in the Orchidaceae, 3.8 to 5.2 atmospheres lower in the Bromeliaceae, and 3.4 to 3.6 atmo spheres lower in Peperomia of the Piperaceae.8 There now remains for consideration only the half shrubby ges- neraceous epiphyte Columnea hirsuta. One determination from the Leeward Ravines gives A = 0.395, P = 4-76. Eight constants from the Windward Slopes and Ravine average A = 0.354, P = 4-28. If these be compared with the averages for herbaceous vegetation from the same habitats, differences in P of —2.83 for the Leeward Ravine determination and of —3.24 for the Windward habitats are secured. 6 This method of computing the average has both advantages and disadvantages. For present purposes it is quite adequate. 7 Practically the same percentages are secured by using the average values of freezing-point lowering, but since the relationship between A and P is not strictly linear the results are not exactly identical. 8 Comparisons with the herbaceous plants of the regions as a whole show a concentration 5.1 atmospheres lower for Orchidaceae, 4.5 atmospheres lower for Bromeliaceae, and 4.2 atmospheres lower for Peperomia of the Piperaceae. The averages for the whole region is obtained by weighting those of the individual habitats with the number of species examined. CONCENTRATION OF TISSUE FLUIDS OF EPIPHYTES 503 If the comparison be made with the ligneous terrestrial vegetation, the differences are —6.07 for the Leeward and —5.45 for the Windward habitats. In relative terms, the osmotic concentrations of the sap of the epiphytic Orchidaceae is only 37.3 to 46.5 percent as high as that of the terrestrial herbs of the same habitat, the constants for the Bromeli- aceae range from 42.3 to 49.6 percent of the comparable values for terrestrial herbs, while the determinations based on Peperomia range from 52.9 to 60. i percent of those for the non-epiphytic herbs of the same habitats. Columnea shows a concentration of 56.9 percent of that of herbaceous plants in the Windward habitats and 62.7 percent of that of herbaceous plants in the Leeward habitats. If compared with ligneous terrestrial vegetation it shows a concentration of 44.0 percent in the Windward and of 44.0 percent in the Leeward habits. Summarizing the results of this comparison : the osmotic concentra tion of the fluids of the epiphytic Orchidaceae, Bromeliaceae, Piper- aceae, and Gesneraceae of the montane rain forest of Jamaica is roughly speaking only 37.3 to 62.7 percent as high as that of the terrestrial plants of the same region. The averages for herbaceous forms include, as already explained, a few determinations based on species which may occur on the ground or as epiphytes. They also include those based on a few ferns and fern allies. The removal of these constants might change slightly the actual values of the difference in the table. Since the forms which have been classified as terrestrial but may occur as epiphytes are characterized by lower osmotic concentration than the vegetation as a whole, the re moval of these species from the list of herbaceous plants would make the differences demonstrated between terrestrial and epiphytic vege tation even larger. The exclusion of the few determinations for terrestrial ferns and fern allies could be justified only on the assump tion that they are sensibly differentiated in their sap properties from flowering plants. There is, at present, no basis for such an assumption. The low concentration of the sap of epiphytic Phanerogams may perhaps be most clearly brought out by comparing it with that of the ligneous species upon which they may occur. Table 5 gives the differences and relative concentrations for the Jamaican materials. Epiphytic Orchidaceae show from 28 to 36 percent, the epiphytic Bromeliaceae from 32 to 38 percent, the epiphytic Piperaceae from 39 to 45 percent, and the epiphytic Gesneraceae about 44 percent 504 J. ARTHUR HARRIS of the osmotic concentration exhibited by the foliage of the ligneous forms upon which they find lodgment. Of course these figures are only approximations, which will be somewhat modified by further work, but they are based on sufficient data to justify the conclusion that the epiphytic species of the rain forest are characterized by a concentration of about one third to one half that of the ligneous terres trial species. TABLE 5 Comparison of Osmotic Concentration of Epiphytic Forms -with that of Ligneous Terrestrial Species in the Montane Rain Forest Habitats Average for Ligneous Plants Difference and Relative Value Orchidaceae Bromeli- aceae Piperaceae Gesneraceae Ruinate of the leeward slopes. . . Leeward ravines I3-05 (n = 4o) 10.83 (n=32) 11.54 (»=36) 9-73 (n = 28) ~7"$ 31-4% -8.32 27-9% — 6.23 36.0% -8-45 35-2% -7.89 3i-6% — 6.00 38.3% -6.60 39-1% -6.35 45-0% -5-75 40-9% — 6.07 44.0% -5-45 44.0% Ridges and peaks . Windward slopes and ravines . . . All habitats " 11.44 (n = i36) -8.07 29-5% -7.48 34-6% -7.21 37-0% -7.11 37-8% In passing it may be worth while to point out that these results have an important bearing upon theories of the origin of parasitism. The suggestion has been made that epiphytism is the first stage in the evolution of parasitism in the flowering plants. But all of these most typical epiphytes are characterized by very low os motic concentration in comparison with the ligneous species of the same region, whereas the Loranthaceae of these forests have been shown (Harris and Lawrence, 1916) to have generally higher concentra tion of their tissue fluids than their hosts. Similar relationships have been found to exist in desert Loranthaceae (Harris, 1918). Theoretically one of the best methods of comparison would be to lay side by side constants for terrestrial and epiphytic members of the same family. Unfortunately I have not been able to secure terrestrial Orchidaceae from subtropical Florida. Determinations have been published (Harris and Lawrence, 191 ya) for Jamaican species. Epi- dendrum verrucosum, which we included in our first paper because we always found it growing on the ground, although Fawcett and Rendle CONCENTRATION OF TISSUE FLUIDS OF EPIPHYTES 505 record itjis occurring "on trees, rocks, and dry banks," gives on the average A = 0.51, p = 6.1 in the Leeward ravines and A = 0.55, P = 6.6 in the ruinate. Prescottia stachyoides from the windward ravines and slopes gave an average depression of A = 0.52, or an average concentration in atmospheres of P = 6.3. All of these values are distinctly, and in many cases very much, greater than those obtained from the individual species of epiphytic Orchidaceae. For comparison with the epiphytic Peperomia we have only Peperomia stellata, which we collected in Jamaica only as a terrestrial herb. It gave the following values: Leeward ravines, A = 0.43, P = 5.2 Ilidge Forest, A = 0.45, P = 5.4 Leeward habitats, A = 0.42, P = 5.1 These values are slightly higher than the averages for any of the epiphytic species from the rain forest. As far as I am aware, the only determination of osmotic concen tration of the tissue fluids of any bromeliad hitherto made is that for Bromelia Pinguim, which Mr. Lawrence and I (19176) found growing as a terrestrial plant in the Jamaican coastal deserts. This gave A = 0.63, P = 7.6. This is a value higher than any of those recorded in this paper with the exception of those for Dendropogon itsneoides. It is, however, extremely low for such a habitat as the Jamaican Coastal Deserts. With regard to two species which Mr. Lawrence and I treated with the terrestrial vegetation but which others have observed growing as air plants, the following points may be noted. The woody-stemmed Blakea trinervia, which may be rooted in the soil or, accordmg to Shreye, grown as an epiphyte, has a concentration measured by^ = 0.58, P = 6.9, as compared with the general average of A = 0.81, P = 9.7 for the ligneous species of the windward habitats in which it occurs. Tradescantia multiflora, which we included with terrestrial vege tation in our earlier paper, but which may also occur as an epiphyte, gave in a single determination_A = o.^^P = 4.7. This is far lower than the general averages of A = 6.3, p = 7.6 for the herbs of the Leeward ravines. 506 J. ARTHUR HARRIS CONCLUSIONS The osmotic concentration of the tissue fluids of epiphytic Brome- liaceae, Orchidaceae, Piperaceae, and Gesneraceae is far lower than that of terrestrial vegetation. In the Jamaican montane rain forest where direct comparisons for individual habitats are possible, the epiphytes show from 37 to 60 per cent of the concentration characteristic of herbaceous terrestrial vegetation, and from 28 to 45 percent of the concentration of ligneous terrestrial vegetation. In the Bromeliaceae, Orchidaceae, and Peperomia of the Piper aceae, the osmotic concentration of the species of the Jamaican mon tane rain forest is lower than that of the species of the hammocks of subtropical Florida. At some future time I hope to deal with the problem of the osmotic concentration of cryptogamic epiphytes and to obtain data on the inorganic and organic constituents of the fluids of epiphytes which will justify further discussion of the physiology of these ecologically remarkable forms. LITERATURE CITED Harris, J. A. 1917. Physical chemistry in the service of phytogeography. Science, n. ser. 46: 25-30. . 1918. On the osmotic concentration of the tissue fluids of desert Loran- thaceae. Mem. Torrey Club 17: 307-315. Harris, J. A., and Gortner, R. A. 1914. Note on the calculation of the osmotic pressure of expressed vegetable saps from the depression of the freezing point, with a table for the values of P for A = .001° to A = 2.999°. Amer. Journ. Bot. i: 75-78. Harris, J. A., and Lawrence, J. V. 1916. On the osmotic pressure of the tissue fluids of Jamaican Loranthaceae parasitic on various hosts. Amer. Journ. Bot. 3: 438-455. Diag. 1-2. . 19170. The osmotic concentration of the tissue fluids of Jamaican montane rain forest vegetation. Amer. Journ. Bot. 4: 268-298. . 19176. Cryoscopic determinations on tissue fluids of plants of Jamaican coastal deserts. Bot. Gaz. 64: 285-305. . With the co-operation of R. A. Gortner. 1916. The cryoscopic constants of expressed vegetable saps as related to local conditions in the Arizona deserts. Physiol. Res. 2: 1-49. [Reprinted from SCIENCE, N. S., Vol. LIL, 1351, Pages 494-495, November 19, 1920] ON THE RELATIONSHIP BETWEEN FREEZING POINT LOWERING, A, AND SPECIFIC ELECTRICAL CONDUCTIVITY, K, OF PLANT TISSUE FLUIDS THE problem of the contribution of noii- electrolytes, of undissociated molecules of electrolytes, and of dissociated ions of electro lytes to the depression of the freezing point, A, in terms of which osmotic concentration is usually measured, is one of considerable bio logical importance. We desire to know, for example, whether an observed difference in the osmotic concentration of the tissue fluids of a species growing in two different habitats is due primarily to differences in the quanti ties of electrolytes absorbed from the medium or to differences in the quantities of organic substances elaborated. The same question naturally arises when one is comparing the osmotic concentration of the tissue fluids of different species in the same habitat. In the mixed solutions with which the biol ogist has to deal the problem presents serious difficulties. In certain cases some progress may be made by determining the correlation between the freezing point depression, A, and the specific electrical conductivity, K. As a specific illustration we may take the relationship between osmotic concentration and electrical conductivity in a series of plant species growing in the non-halophytic habitats of the north shore of 'Long Island.1 In a series of 19 species of trees, 36 species of shrubs, and 162 species of herbs both A and 1 Protocols of data and full details are given in a paper in press in the Journal of Physical Chem istry. K are highly variable. The coefficients of variation, i.e., 100 a/m, where tr is the stand ard deviation and m the means are: A K Trees 21.46 28.49 Shrubs 18.46 28.03 Trees and shrubs . . . 20.20 28.27 Herbs 23.46 25.33 Our problem is to determine whether higher values of K are associated with higher values of A, or whether within each of these growth forms2 these two constants of the solu tion are essentially independent. Determining the correlation coefficients by the usual product moment method we have the following measures of relationship be tween the magnitudes of K and A in the various series. For trees, # = 19, r = + 0.127 ±.152 For shrubs, N = 3Q, r = — 0.079 =fc .112 For trees and shrubs, N = 55, r = -f 0.022 =fc .091 For herbs, N = 162, r = + 0.150 ± .052 For ligneous plants the correlations be tween A and K are low and statistically in significant in comparison with their probable errors. The coefficient for shrubs is actually negative in sign. That for trees and shrubs together is sensibly zero. The coefficient for herbaceous plants is also low but may indicate a slight relationship between the two con stants, higher values of A being associated with higher values of K and vice versa. 2 It is necessary to separate the growth forms, since, as shown in detail elsewhere (Harris, Gort- ner and Lawrence, loc. cit.)} the growth forms are highly differentiated with respect to both A and K. The actual means are: A Ky. io» Trees 1.292 11,213 Shrubs 1.177 10,770 Trees and shrubs . . 1.217 10,923 Herbs 0.846 14,308 3 These results show that, in the vegetation of the glacial moraines of Long Island at least, there is practically no relationship be tween the concentration of ionized electro lytes and of total solutes (molecules and ions) in the leaf tissue fluids.3 J. ARTHUR HARRIS, EOSS AlKEN GORTNER, JOHN V. LAWRENCE Reprinted from the Proceedings of the Society for Experimental Biology and Medi cine, 1920, xviii, pp. 95-97. 44 (1626) The specific electrical conductivity of the tissue fluids of desert Loranthaceae. By J. ARTHUR HARRIS and A. T. VALENTINE. [From the Station for Experimental Evolution, Cold Spring Harbor, L.I.} MacDougal .and Cannon1 and MacDougal2 suggested some years ago that the osmotic concentration of the tissue fluids of the two organisms is one of the fundamental variables in the relationship between plant parasite and host. Senn3 has pub lished one plasmolytic determination indicating higher concen tration in a Viscum than in the leaves of the host tree and has secured similar results with other phanerogamic parasites. In the Jamaican montane rain-forest the concentration of the tissue fluids of the parasitic Loranthaceae is in general higher than those of the host.4 The same relationship has been found to obtain in desert Loranthaceae.5 As far as we are aware the relative electrolyte contents of the tissue fluids of parasite and host have not been determined heretofore. In August, 1920, we had the opportunity while carrying out work for the U. S. Department of Agriculture at Sacaton, Arizona to measure the specific electrical conductivity, K, as well as the osmotic concentration in atmospheres, P, calculated from the freezing point lowering, A, of the expressed sap of the leaves of the host trees and of the stems of the leafless Phoradendron cali- fornicum parasitic on the leguminous trees Acacia greggii and 1 MacDougal and Cannon, Pub. Cam. Inst. Wash., 1910, No. cxxix, P. 3, 25-49. 2 MacDougal, Bot. Gaz., 1911, Hi, 249-260; Bull. Torr. Bot. Club, 1911, xxviii, 54-55. 473-480. 3 Senn, Verhandl. Naturf. Ges. in Basel, 1913, xc, 179-183. 4 Harris and Lawrence, Amer. Jour. Bot., 1916, iii, 438-455. 'Harris, Mem. Torr. Bot. Club, 1918, xvii, 307-315. SCIENTIFIC PROCEEDINGS (in). Olneya tesota and of the leaves of the leafy P. cockerellii parasitic on Populus wislizeni, Salix wrightii and Fraxinus attenuate,. Sap was extracted after antecedent freezing of the tissues in an ice and salt mixture1 to facilitate extraction2 and the constants determined on the centrifuged sap. Table i shows the average values of A and of P as determined from a published table.3 TABLE I. FREEZING POINT LOWERING A, AND OSMOTIC CONCENTRATION, P. A P Parasite and Host. Para site. Host. Differ ence. Para site. Host. Differ ence. P. Californicum on Acacia greggii 2.8l 2.21 +O.6O 33-66 26.57 + 7.09 on Olneya tesota 2.25 2.IO +O.I5 26.98 25.24 + 1.74 P. Cockerellii on Populus wislizeni 1.02 1.84 +0.08 27. 0"! 22.04 + I.OI on Salix wrightii 2.08 1.74 +0.34 24.98 20.88 +4.IO on Fraxinus attenuata 2.20 I.p6 +0.24 26.47 23-47 +3-00 For each comparison the osmotic concentration of the tissue fluids of the parasite is higher than that of the host. Thus the results of earlier investigations in Jamaica and Arizona are confirmed. TABLE II. SPECIFIC ELECTRICAL CONDUCTIVITY, K X io8, AND THE RATIO OF X TO A, K/A X 10*. K K/A Parasite and Host. Para site. Host. Differ- cnct. Para site. Host. Differ ence. P. Californicum on Acacia greggii 2242 1509 + 733 831 682 + 149 on Olneya tesota 2471 2192 + 279 IIO3 1052 + 51 P. Cockerellii on Populus wislizeni 306l 1990 + 1071 1598 1094 + 504 on Salix wrightii 3IOI 1582 + 1519 1488 908 +580 on Fraxinus attenuata 2399 1461 + 938 1091 749 +342 The constants for specific electrical conductivity and for the ratio of electrical conductivity to freezing point lowering appear 1 Gortner and Harris, PI. World, 1914, xvii, 49-53. 2Dixon and Atkins, Sci. Proc. Roy. Dublin Soc., 1913, N. S., xiii, 422-423; Gortner, Lawrence and Harris, Biochem. Bull., 1916, v, 139-142. 1 Harris and Gortner, Amer. Jour. Bot., 1914, i, 75-78. TISSUE FLUIDS OF DESERT LORANTHACE^E. 3 in Table II. This shows that electrical conductivity, like freezing- point lowering, and the ratio K/& is higher in parasite than in host. Thus it appears that there is some mechanism not as yet determined by which the mistletoe accumulates and retains in solution larger quantities of dissociated salts or organic acids than does the host. It is possible that higher transpiration from the parasite might result in the accumulation in a purely mechanical manner of larger amounts of salts from the transpiration stream, but this is merely a suggestion requiring further investigation. ON THE DIFFERENTIATION OF THE LEAF TISSUE FLUIDS OF LIGNEOUS AND HERBACEOUS PLANTS WITH RESPECT TO OSMOTIC CONCENTRATION AND ELECTRICAL CONDUCTIVITY. BY J. ARTHUR HARRIS, ROSS AIKEN GORTNER, AND JOHN V. LAWRENCE. [Reprinted from THE JOURNAL OF GENERAL PHYSIOLOGY, January 20, 1921, VoL iii, No. 3, pp. 343-345.] [Reprinted from THE JOURNAL OF GENERAL PHYSIOLOGY, January 20, 1921, Vol. iii, No. 3, pp. 343-345.] ON THE DIFFERENTIATION OF THE LEAF TISSUE FLUIDS OF LIGNEOUS AND HERBACEOUS PLANTS WITH RESPECT TO OSMOTIC CONCENTRATION AND ELEC TRICAL CONDUCTIVITY * BY J. ARTHUR HARRIS, ROSS AIKEN GORTNER, AND JOHN V. LAWRENCE. (From the Department of Experimental Evolution and the Department of Botanical Research, the Carnegie Institution of Washington, Washington.) (Received for publication, October 30, 1920.) The existence of a differentiation of ligneous and herbaceous plants with respect to the magnitude of the osmotic concentration of the tissue fluids was first demonstrated in a strictly quantitative manner by work on the sap of the plants of the spring flora of the Arizona deserts1 in the neighborhood of the Desert Botanical Laboratory, and on the terrestrial vegetation of the Jamaican montane rain forest.2 These studies, in two geographically widely separated and climati cally dissimilar regions, and an extensive series of unpublished obser vations demonstrate that the leaf tissue fluids of ligneous plants are characterized by an osmotic concentration materially higher than that of herbaceous forms. The magnitude of the specific electrical conductivity, K, of the fluids must now be considered in comparison with osmotic concen tration as measured by the freezing point lowering, A, for a series of plant species on which both of these constants were determined. The determinations here considered were made on the north shore of Long Island during the spring and summer of 1914 and 1915. Leaf * Studies carried out by the cooperation of the Department of Experimental Evolution and the Department of Botanical Research of the Carnegie Institution of Washington. The results will be published in full in the Journal of Physical Chemistry. 1 Harris, J. A., Lawrence, J. V., and Gortner, R. A., Phys. Researches, 1916, ii, 1. 1 Harris, J. A., and Lawrence, J. V., Am. J. Bot., 1917, iv, 268. 343 WAVERLY PRESS THE WILLIAMS & WILEMS COMPANY BALTIMORE, U. S. A. THE OSMOTIC CONCENTRATION AND ELECTRICAL CONDUCTIVITY OF THE TIS SUE FLUIDS OF LIGNEOUS AND HERBACEOUS PLANTS BY J. ARTHUR HARRIS, ROSS AIKEN GORTNER AND JOHN V. LAWRENCE (Reprinted from the Journal of Physical Chemistry, Vol. 25, pp. 122-146, Ftbruary, 192 J.) THE OSMOTIC CONCENTRATION AND ELECTRICAL CONDUCTIVITY OF THE TISSUE FLUIDS OF LIGNEOUS AND HERBACEOUS PLANTS1 BY J. ARTHUR HARRIS, ROSS A1KEN GORTNER AND JOHN V. LAWRENCE I. The Osmotic Concentration of the Leaf Tissue Fluids of Herbaceous and Ligneous Plants An examination of earlier literature on the osmotic con centration of plant tissue fluids shows various suggestions of a difference in the osmotic concentration of the leaf fluids of herbaceous and ligneous plants. As early as 1911 Fitting2 noted from his plasmolytic studies on desert plants that the lowest osmotic pressures are found in annuals and the highest in shrubs. The existence of a differentiation of ligneous and her baceous plants with respect to the magnitude of the osmotic concentration of their tissue fluids was first demonstrated in a strictly quantitative manner by work on the sap of the plants of the spring flora of the Arizona deserts3 in the neighborhood of the Desert Botanical Laboratory. Because of the strongly contrasted environmental conditions in these southwestern deserts the growth forms are sharply differentiated. Follow ing as closely as possible Thornber's classification of the growth forms,4 thereby obviating any possible question of personal equation in the classification of the plants, we find the results for freezing point lowering given in Table I.5 1 Studies carried out by the co-operation of the Department of Experi mental Evolution and the Department of Botanical Research of the Carnegie Institution of Washington. 2 H. Fitting: Zeit. Bot., 3, 209-275 (1911). 3 J. Arthur Harris, J. V. Lawrence and R. A. Gortner: Phys. Res., 2, 1-49 (1916). 4 J. J. Thornber: Pub. Carnegie Inst. Wash., No. 113, pp. 103-112 (1909). 6 Harris, Lawrence and Gortner: Loc. cit., pp. 45-46. The averages in the table are averages of species determinations, not of species means. Osmotic Concentration and Electrical Conductivity, Etc. 123 cn cn o3 el O ^0 t^- t^* O cu O _N a T)- co >O CN % 'C * H M M IH ID CU 5 w *C c _g cn 3 cn +j O O. cn •*-> oo O O 0*0 ^o O oo ON 03 cn O cu 03 £ if cn cn "S ~ fi cn O •c a ^O CN ^O ON jd 03 In . OO ON ^O f^* ^ ^^ 03 Y*T a **^ •d CN M l-l I-H HH E 1 'c? PQ CU i cn en 5"1 cn i cS cn cu a t^» M 10 ON •o O !-H o -4-J 14-H j , O cu ^ cn " cn GO r^ ^j- CN Q jd j^1 M M HI M bo , +J ^ cn 8 B| 1 |l cn t~-« >o O ^1- ^ 5i E 0 . vo *~* 10 ON CH V"! OO O 1-1 O *5H i£5 C £ ^O s U bC« ts 'N £ 1 o O O oo >o fi C •c cu t^ OO CN f^ Tj- CO HH O HH hH M M §g cu o O • CU *-* CU d 'o cn Q to c CU bo Average Freezing Growth form Trees and shrubs Dwarf and half si Perennial herbs Winter annuals tual and Percenta w cn rt ^ IO w , 3 03 ON too O CN ON CO •** M CN M O 00 3 CO cn "o a cn ON 0 vo O t>« O f~^- ON I-H ON 00 O i! rO ro 1-1 M 00 w u a |^>fc CO 00 10 C/3 ON CN O -i O OS I-H IO t^ 00 ro CN CN M O CN 'c? pq tn 0) I vO CO 10 00 HH >O CN CN I-H " IO t^ CO •<*• ^J- ^ M l-l l-l O ^ O CN cn O ^ 10 ^r CO O o r^ M O CN 03 M l-l W O ^O O o >o M 0 I-H Q ^- o CO O E K M HH hH O "0 CN CU o cn r*j .Si CJ ;H tn 'G cn H cu - oi 5 •"-' 00 ON !>• N T}- w CS 6 6 o 6'vo 3 J3 CN 0 3 «4-c O Tl t/"1 W W* ^o to r^* 00 *O 5 cs ^ O CN '3 E.-s ll 6 00 VO 6 6 hH M- 0 — si •a ON CN OJ M l-c VI OS 0) fi'l 0) ~ 8 OO 1-1 O oo M 6 CN Tj- O "o £ | h4 (N G*§ 03 0) -M 0 a en C OJ § OJ PH a y o en 'o •8 ft C OJ *T3 1 13 -t-> o < Growth 'o OJ tft Ligneous sp< Herbaceous Difference Percentage < 126 J. A. Harris, R. A. Gartner and J. V. Lawrence dissimilar regions (and by extensive unpublished series) that the leaf tissue fluids of ligneous plants are characterized by an osmotic concentration materially higher than that of her baceous forms. The magnitude of the specific electrical conductivity of the fluids must next be considered in comparison with osmotic concentration as measured by the freezing point lowering. II. The Osmotic Concentration and Specific Electrical Conductivity of the Leaf Tissue Fluids of Herbaceous and Ligneous Plants of a Mesophytic Flora The determinations here considered were made on the north shore of Long Island during 1914 and 1915. Leaf tissue was collected in large test tubes. After freezing in an ice-salt mixture1 to render the tissue permeable, as has been shown to be necessary by Dixon and Atkins2 and by our selves.3 The sap was extracted as completely as possible by pressure, cleared by centrifuging and the freezing point lower ing, A, was determined in the usual manner. Correction was made for the ice separating on undercooling by the for mula A = 0.0125 u A', where u is the undercooling and A' the observed freezing point lowering in degrees. The specific electrical conductivity, K, of the sap was measured at 30° C in a Freas conductivity cell, standardized against N/io KC1, which has a specific conductivity 0.01412 reciprocal ohms at 30°, by means of the ordinary meter bridge wire and resistance box of the physiological laboratory. All determinations were made with as great care as possi ble, but there are many possible sources of error, and some selection of the constants to be used in the present paper seems 1 R. A. Gortner and J. Arthur Harris: Plant World, 17, 49-53 (19*4)- 2 H. H. Dixon and W. R. G. Atkins: Proc. Roy. Soc. Dublin, 13, 422- 433 (1913)- Also in Notes Bot. Sch. Trin. Coll., Dublin, 2, 154-172 (1913). 3 R. A. Gortner, J. V. Lawrence and J. Arthur Harris: Biochem. Bull., 5, 139-142, pi. i (1916). Osmotic Concentration and Electrical Conductivity, Etc. 127 desirable. To avoid weighting the species upon which more than a single determination had been made, species averages are used whenever possible. These were determined as fol lows.* The whole of the data which had been accumulated at various times during the two years were arranged together by species and all determinations which seemed obviously open to criticism were thrown out. The determinations for each species were then averaged and the deviation of each determina tion from the average for the species was calculated. All numbers which showed a deviation of more than ±20 per cent for either A, K, or */ A, were discarded, and a new aver age with deviations < =»= 20 percent determined from the remainder. The inclusion of determinations differing from the average by as much as ±20 percent might at first seem to represent great laxness of selection. One must remember, however, that these variations represent more than the errors of experimental measurement. They include all the differ ences due to seasonal and environmental influence as well as the errors of random sampling in the collection of the tis sues. Thus the limits chosen probably represent rather stringent instead of lax selection. The detailed data are shown in Table IV. Determining the usual statistical constants from the protocols of measurements we have the accompanying re sults (Table V) for the three growth forms, and for a com bination of the two groups of ligneous plants. The constants in Table V show that the mean freezing point lowering of the leaf tissue is greater, although perhaps not significantly greater in comparison with its probable error, in arborescent than in shrubby species. The tissue fluids of both trees and shrubs are characterized by a far greater freezing point lowering than those of herbaceous plants. The differences between trees and herbs, shrubs and herbs, and all ligneous plants and herbs are everal times as large as the probable error of the difference and hence un questionably significant. 128 J. A. Harris, R. A. Gartner and J. V. Lawrence TABLE IV Protocols of Determinations1 Constants for Trees A K X I06 K/A X io8 Acer rubrum (2) 1.132 6585 7325 Aesculus Hippocastanum 0.722 10398 14401 Ailanthus glandulosa i .480 15546 10504 Alnus rugosa (2) 1.368 9393 6863 Betula lenta 1.464 11080 7589 Betula lutea I .221 10737 8833' Cynoxylon floridum (3) I . 119 12264 10957 Diospyros virginiana (2) 1.385 8586 6242 Gleditsia triacanthos (2) 1.250 11348 9083 Juglans cinerea 1.478 11802 Son Padus virginiana (2) 1-754 8183 4659 Quercus coccinea 1.487 17287 11015 Quercus palustris 1.780 9871 5586 Quercus Prinus 1-655 12518 7568 Robinia Pseudacacia (3) i .006 14364 14337 Salix alba vitellina 1.178 16513 14017 Tilia americana (2) i . 107 13814 12600 Vitis aestivalis i .071 6107 5702 Vitis labrusca 0.892 6657 7463 Constants for Shrubs Amorpha fruticosa i . 104 IOO63 9H5 Ampelopsis Veitchii 0.863 11460 13279 Aronia atropurpurea 1.165 IOI40 8703 Azalea nudiflora (3) 0.998 10696 IO7OI Benzoin aestivale (4) i . 104 H755 10744 Berberis vulgaris 1-555 9OOI 5788 Berberis vulgaris purpurea 1-598 8563 5358 Clethra alnifolia (3) 0.786 II075 I4II9 Comptonia peregrina I .211 8018 662O Cornus alternifolia 1.205 II886 9863 Epigaea repens 1.085 9526 8779 Gaylussacia frondosa I.3IO 8777 6700 Hibiscus Syriacus (2) I . 1 2O I73I7 15499 Lonicera tatarica 1.644 II979 7286 Myrica carolinensis (2) I-I35 8619 7578 1 Species are grouped primarily according to growth forms, as discussed in the paper. For convenience of reference they are alphabetically arranged under each growth form. The number in parentheses shows the number of individual determinations averaged to obtain the species constant. Those without numbers represent one determination only. Osmotic Concentration and Electrical Conductivity, Etc. 1 29 TABLE IV (Continued) Constants for Shrubs (continued) A K X I06 K/A X io« Parthenocissus quinquefolia 0-943 8426 8935 Prunus sp. (2) i-SH 18084 I2I04 Rhus glabra (3) 1.286 12131 9475 Rosa virginiana 1.043 10190 9769 Rubus argu tus (2) 1.199 11456 9483 Rubus hispidus 0.818 11841 H475 Sambucus canadensis (6) 1.065 15583 14670 Srnilax rotundifolia 1-237 11466 9269 Solanum Dulcamara (4) 0.914 17327 19146 Sorbaria sorbifolia (2) 1.297 16119 12453 Toxicodendron Toxicodendron i-i35 10190 8977 Toxicodendron Vernix i-39i 9989 7181 Uva-ursi Uva-ursi i. 218 5856 4809 Vaccinium angustifolium 0.965 8449 8755 Vaccinium atlanticum 1.366 5896 43i6 Vaccinium corymbosum 1.561 8038 5H9 Vaccinium vacillans 0.948 6768 7139 Viburnum acerifolium (3) 1-057 13153 12429 Viburnum cassinoides 1.300 7467 5743 Viburnum dentatum (2) i .272 11052 8899 Xolisma ligustrina (2) 0.977 9355 9730 Constants for Herbs Achillea lanulosa 0.815 16645 20423 Achillea Millefolium 0.738 13622 18457 Agrimonia gryposepala (3) 0.861 14508 16899 Agrimonia sp. (2) 0.875 13726 15726 Alsine media (4) 0.605 16388 27185 Ambrosia elatior 0.807 22250 27571 Ambrosia trifida 0-754 20072 26620 Anaphalis margaritacea (2) 0.940 19785 21140 Antenarria plantaginifolia 0-743 16987 22862 Anthemis Cotula 0.604 15671 25945 Aralia nudicaulis 1.386 9515 6865 Asclepias pulchra 0-593 13703 23116 Asparagus officinalis 1-545 i8795 12165 Aster macrophyllus (2) 0.646 17075 27124 Aureolaria Pedicularia i .41 1 I9I95 13603 Aureolaria villosa 1.174 16179 13781 Baptisia tinctoria (3) i .016 7832 7752 Barbarea Barbarea (4) 0.785 I7I33 21983 Barbarea stricta (2) 0-795 16038 20181 Brassica juncea (2) 0.728 15836 21787 130 /. A. Harris, R. A. Gortner and J. V. Lawrence TABLE IV (Continued) Constants for Herbs (continued) A K X I0« K/A X io( Bra'ssica napus 0.803 17897 22287 Brassica nigra 0.789 19257 24407 Cardamine pennsylvanica (2) 0.670 18141 27083 Carex scoparia 1 .017 16447 16172 Chelidonium majus (4) 1 .000 "345 "347 Chenop odium album 0.991 24054 24272 Chenopodium sp. 0.936 26845 28680 Chimaphila maculata 0.984 6349 6452 Chrysanthemum Leucanthemum (2) 0.967 15770 16305 Chrysopsis mariana (2) 0.806 14850 18447 Cichorium Intybus (3) 0.796 18711 23496 Cimicifuga racemosa 0.937 15235 16259 Circaea lutetiana (4) 0.489 10397 21363 Commelina communis 0.422 12176 28861 Convallaria majalis 0.829 12574 15167 Convulvulus arvensis 0.937 18272 19500 Crocanthemum canadense 0.741 8732 11784 Daucus Carota (2) I -143 20394 17836 Deringa canadensis (2) 0-934 21182 22810 Dianthus Armeria i .009 19038 18868 Erechtites hieracifolia 0.506 12422 24549 Erigeron annuus (3) 0.808 14070 17427 Erigeron ramosus I-I53 JQ355 8981 Eupatorium perfoliatum 0-583 13457 23082 Eupatorium trifoliatum 0-813 20372 25057 Euthamia graminifolia (2) 0.936 14846 15926 Euthamia tenuifolia 0.721 H.936 20730 Fagopyrum Fagopyrum 0.540 13198 24440 Fragaria vesca americana i .098 9384 8546 Fragaria virginiana 0.998 12828 12853 Galinsoga parviflora (2) 0.601 16392 27329 Galium Aparine (5) 0.722 12486 *7365 Geranium maculatum (5) 0.768 9922 13000 Geranium pusillum 0.789 17400 22053 Geranium rotundifolium 0.888 17829 20077 Geum canadense (2) i . 192 19014 16128 Gratiola aurea 0.618 12518 20255 Hemerocallis fulva 0.940 9459 10062 Hieracium sp. 0.783 15990 20421 Hypericum mutilum 0.865 "599 13409 Hypericum perforatum (3) i .002 12181 12239 Hypericum punctatum 0-833 !2473 M973 Impatiens biflora (5) 0.518 11784 22857 lonactis linariifolius 0.881 13566 15398 Osmotic Concentration and Electrical Conductivity, Etc. 131 TABLE IV (Continued} Constants for Herbs (continued) A K X I06 K/A X io6 Lactuca virosa 0.681 18264 26819 Lappula virginiana 0.644 15546 24139 Lathyrus latifolius (2) 0.942 10562 11219 Leontodon Taraxacum 0.707 13622 19267 Leonurus Cardiaca (4) 0.903 18654 20769 Lepti!on canadense (2) 0.810 H509 17957 Lespedeza capitata 0.946 12323 13026 Lespedeza frutescens !-035 7315 7067 Lespedeza hirta (2) 0.794 9734 12271 Lespedeza violacea 0.984 10834 IIOIO Lespedeza virginica 0.836 10566 12638 Linaria canadensis (3) 0.580 !Q495 18167 Linaria Linaria (2) 0.847 10232 12088 Lychnis a1ba 0-793 20680 26078 Lychnis dioica 0.711 18126 25493 Lycopodium obscurum 0.874 7928 9070 Lycopus sessilifolius 0.625 16120 25792 Lycopus virginicus (2) 0.538 J3554 25234 Lysimachia Nummularia (2) 0.747 12907 17397 Lysimachia quadrifolia (3) 0.634 11070 17660 Lysimachia terrestris 0.717 9076 12658 Medeola virginiana (2) 0-833 J3543 16371 Medicago lupulina i. 068 12371 11583 Melampyrum lineare (2) i . 164 15427 13248 Melilotus alba 1.119 10358 9256 Mentha citrata 0-751 13352 17807 Monarda didyma (2) 0.694 13636 19649 Monarda fistulosa 1-037 J2574 12125 Nepeta Cataria 0.724 15740 21740 Nepeta hederacea (2) 0.650 12805 19743 Oenothera muricata 0.711 11284 15885 Oenothera Oakesiana 0.726 12181 16778 Ornithogalum umbellatum 0.713 9268 12998 Osmunda regal 's 1.180 15925 J3495 Panicum clandestinum 0.764 14877 J9535 Persicaria Hydropiper 0.707 12225 17291 Persicaria Persicaria 0.607 11321 18650 Persicaria punctata 0.586 12473 21285 Phlox paniculata 0-737 14755 2OO2O Physalis heterophylla 0.704 I5I75 21555 Phytolacca decandra 0.726 14063 19370 Plantago lanceo!ata 0.867 13622 I5711 Plantago media 0-775 18500 23870 132 J. A. Harris, R. A. Gartner and J . V. Lawrence TABLE IV (Continued) Constants for Herbs (continued) A K X I06 ic/A X io« Plantago Rugelii 0.789 18192 23057 Polygonatuni commutatum i .014 10920 10769 Polygonum aviculara 0-593 H373 19178 Portulaca oleracea (2) 0.598 15962 26713 Potentilla canadensis 0-935 12225 13074 Potentilla monspeliensis 1.050 18205 17338 Prunella vulgaris 0.638 9740 15266 Pteridium aquilinum i -555 15671 10077 Ranunculus abortivus 1.231 10876 8835 Ranunculus bulbosus (2) i .016 12397 12203 Ranunculus recurvatus (2) 0.998 10574 10690 Ranunculus sceleratus 0.941 17264 18346 Ranunculus septentrionalis i .026 13677 13330 Rudbeckia hirta (2) 0.863 16616 19311 Rumex Acetosella (2) 0-531 8273 15596 Rumex crispus (2) 0.657 17085 25976 Rumex hastatulus 0.563 11883 21106 Rumex obtusifolius (3) 0.706 15227 21602 Saponaria officinalis 0-970 9780 10082 Scirpus polyphyllus 0.894 16968 18991 Scrophularia leporella (2) 0.834 *4553 I/54I Sedum purpureum (2) 0.471 4061 8707 vSericocarpus asteroides (4) 0.703 12302 J7549 Silene latifolia 0.872 21469 24620 Sinapis arvensis 0.888 18264 20567 Sisymbrium Nasturtium-aquaticum (2) 0.652 17274 26513 Sisymbrium sp. 0.803 18960 23611 Solidago altissima 0-959 15423 ' 16090 Sol dago bicolor 0.815 14231 17461 Solidago juncea (3) 1.074 14710 i378i Solidago odora 0,911 15546 17064 Solidago rugosa i . 126 J3Q37 11580 Solidago sp. 0.984 15483 15734 Spathyema foetida (2) 1.039 16424 15871 Specularia perfoliata 0.792 14756 18631 Tanacetum vulgare (2) 0.972 16164 16645 Thalictrum dioicum 0.988 14233 1 4406 Tovara virginiana (2) 0.451 9703 21991 Tridentalis americana 0.844 12471 14776 Trientalis borealis (2) 0.899 12194 13679 Trifolium agrarium 0.949 8323 8770 Trillium cernuum (2) i .022 18054 17748 Unifolium canadense (4) i .002 "655 11650 Osmotic Concentration and Electrical Conductivity, Etc. 133 TABLE IV (Continued) Constants for Herbs (continued) A K X I06 K/A X io6 Urtica gracilis i-i75 17213 14656 Uvularia perfoliata 0-833 12372 14852 Vagnera racemosa (8) i .041 12313 Il88o Veratrum viride (2) 0.845 14073 I675I Verbascum Blattaria 0.812 13512 16640 Verbena urticifolia (5) 0.831 12651 15342 Veronica officinalis (2) 0.929 13730 14767 Vicia Cracca 0.875 12225 I397I V ola cucullata (2) 0.715 10030 14234 Viola pa'Iens 0.763 12225 16022 Washingtonia longistylis 1.123 19195 17092 Xanthoxalis corniculata 0.796 2 1 469 26971 Expressing the differences in percentages of the constants for ligneous forms, we note that the value for trees and shrubs is 30.46 percent higher than that of herbaceous plants. These results are, therefore, in excellent agreement with those found in the Arizona deserts and in the Jamaican rain forest. The constants set forth in Table VI show that the specific electrical conductivity for shrubs is slightly lower than that for trees. The difference is, however, smaller than its proba ble error. The differences between the conductivities of the leaf tissue fluids of trees and herbs, shrubs and herbs, and all ligneous species and herbs, are several times as large as their probable errors and show that the conductivity is distinctly higher in herbaceous than in ligneous plants. The constants for the ratio of electrical conductivity to freezing point lowering, K/ A, appear in Table VII. The entries in this table show that the ratio of conduc tivity to freezing point lowering is lower in trees than in shrubs, although the difference cannot be considered significant in comparison with its probable error. The ratio of conduc tivity to freezing point depression is much smaller in both trees and shrubs than it is in herbs. The ratios (X iofi) are 134 J- A. Harris, R. A. Gartner and J. V. Lawrence ID CM CO 1C PO CM « 3 rt- "o •^- 1000 PO o\o r ^O ll •H 4i 41 -H 41 4i 4 4 ll ^.^g g^-g ^ J « U i— i CO PO O PO CM I* n PO CM i-1 | CM CS "b D ^> .2 °-> CT CO ^ O" PO^ 2 £• X ^ a 0 0 O O 0 O C ^ m '> o o o o o o c D O C OJ rtl •^J- CM rj- CM M rj- ( N CM c O O O O O O < DO W W fe . o o o o o o 3 O pq (^ «§ c! U 4 « -H -B •« -IH ^ ^ ^ 1 v> s _ lO^O M Tj- f^» -| r^ & CN t^» ^ r^*- \o lo -1 O c/2 "S O\ t^+ HH HH ^ T^ •o r^ 03 CN t-i HH CS 00 TJ- •o PO g 0! HH M O M O' O DO ^ C , - i_ i W 0 + +- O . 03 13 t/} C j > 10 o •^ II v!5 ^ o3 ~v 13 -i-> C^ CM Z PO -o o c/T CM K ^^ ^ ? M + ~^ -t-< II -^"^ II ^'^ ^s^ W Hy D T7-( D * Jl*r D OJ 0 0 C C U 1* r/r ^^ w 01 ^ ^ - - ^j r3 ^ flj -^ ^ Q_> Q £ a S £ qj }Q } 5 ta {H c/} Q H ffi C (• 5'p I-H CN CN CO M vO O POO w w O O PO^J-i-i Cs O !CO CN o 2 row TJ-~ ~ r^N « _tt>-j ~H4l"n~n~n"n"n"T1 11 "4- O - COCO OGO »C PO cs cs CM CS _|_ CS CS_j 1 1 *b X r-" V- .2 O O ""> C^O ic >O C £ .2 -l-> b .£ -o •H-H-H-fl-H-HilTl •4-J "d C o u 1 a M O !— ' O O ^ O U O 03 o 'C £ ^\ f^ ^^\ QO O1^ PO GO ^ w ^t" PO ^O CS *•* ^O PO P 1C S3 ^^1^1^^^^^ •£ M t^ "^t" CS C ^ PO G< cx H-I o 1 c ^ PO PO p 09 03 t/> 1C C O II r O II ^ 13 ^Z 'fo'ro _o X S ^—S**+~Ss* _ ™ CM ^ 1/1 Ox « "§ ^ ~o3 M u ^Jc x>-^'^r •• CO || ^-< I/! || ^-^^-^^ ^H ^ * ^ *~7 ^ ^ i s r" C ^^ ("" r* f f-< - C tl CCS 011)03 - l> D C ..r n t. ,, '~r. u u > aj3jti S^t^Jiu {-(!/}C;-i^QCf 1-1 CM CS PO Osmotic Concentration and Electrical Conductivity, Etc. 135 X be C •c 0) w Si w ^ « *?! cu W o 1 a C/2 *o o o !•! '3 ,2 o ^ a CN O oo r^ ON CN i-i ££r S&.£^+ (S VO 1-1 O O 00 (N 10 O *O ON CN ON r^ oo ^t" i . - — ON CN ro t^. r^ OO ^1" ON O 10 Th <*3^O i/o>-i CN ON ON I ON r^ 00 00 00 Q w CN CN 136 J. A. Harris, R. A. Gortner and J. V. Lawrence 9092 : 17674 in the case of trees and herbs and 9529 : 17674 in the case of shrubs and herbs. Since the ratio does not differ significantly in trees and shrubs it is quite proper to combine them. The average value of K/ A X io6 in all ligneous plants is 9378 =»= 292 as compared with 17674 =*= 282 in herbs. Thus the ratio K/ A is about 90 percent higher in herbaceous than in ligneous plants. It seems desirable from the physiological side to deter mine whether conductivity or osmotic concentration is more nearly a constant for the species of a region. Furthermore, it is of interest to determine whether either of the three physico- chemical constants considered is significantly more variable in one class of plants (trees, shrubs, or herbs) than another. Comparison of the variability of electrical conductivity and of osmotic pressure can only be made by means of the relative variation constants. The differences in the coeffi cients of variation of K and A for the three growth forms are given in Table VIII. TABLE VIII Difference in Coefficients of Variation of Electrical Conductivity and Freezing Point Lowering Growth form Difference C. V._ — C. Trees Shrubs Trees and Shrubs Herbs 7.03 ± 4.16 9-57 dh 2.84 8.07 =*= 2.38 1.87 ± 1.36 The comparison shows that for each of the growth forms investigated the variability of electrical conductivity from species to species is greater than that of osmotic concentra tion. The differences are conspicuously greater in ligneous plants (in which the conductivity is on the average small as compared with the osmotic concentration) than in herbaceous species in which the electrical conductivity is both absolutely and relatively much larger. As a matter of fact, the varia- Osmotic Concentration and Electrical Conductivity, Etc. 137 bility of K and of A cannot be asserted to be significantly different in herbaceous species. Turning to the question of the relative variability of the physico-chemical constants in the different growth forms we note that the variability of the freezing point lowering of trees is numerically greater than that of shrubs as measured by both standard deviation and coefficient of variation. The difference in the variability of the two groups of ligneous forms is not, however, sufficiently large to be considered significant in comparison with its probable error. The standard devia tion of A in herbaceous forms is lower than that in either trees or shrubs. The average osmotic concentrations, as measured by A, is also lower in these forms. In consequence the relative variability as measured by the coefficient of varia tion is higher in herbaceous species. The variability from species to species of the electrical conductivity does not differ, as far as the data now available show, in the two groups of ligneous plants. The standard deviations of the conductivities of herbaceous plants are higher than those of ligneous species, but since the average conductivities are also higher, their relative variabilities as measured by the coefficient of variation are somewhat lower. Finally, the results of the ratio K/ A show that the standard deviations are far higher in herbaceous than in ligneous plants. The mean value of the ratio is also far higher, and as a result the coefficients of variation of ligneous species are higher. Taking the results for variability as a whole, they seem to indicate that there is little difference between ligneous and herbaceous forms. The foregoing results show clearly that the osmotic con centration is higher while the electrical conductivity is lower in the tissue fluids of ligneous than in those of herbaceous species. The results for freezing point lowering are drawn from three climatically highly dissimilar regions. While those for electrical conductivity are based on determinations from one region only, they represent two years work. 138 /. A. Harris, R. A. Gartner and J. V. Lawrence (« . JS M w w *j* " j C7^ O O^ t^ *$- ^H o u G OOC^fN^C^S^^r^ r? ^1 ffi -»-> G O »Q -a O O X C x 03 JD l^i ^^^"^^^^^; <. u. O 3 o 03 i ^r^^-OtoiOTi-aNThcNvo be G 03 u l-'GOO\Tj-|-IH-IVOI^«Tj-CN •^-POO'-'OGOGOlOMlOt^. T3 ^ % lassified t/1 JC ^^ <^) r^ ^O ^i~ ro O GO ^ O O r^ rt Tf ir)00 | vO r *M~ f^ ^^ ^O lO CS IO ^ f^* ^~ ON O ^O ON t^** u U VI .Si 'o g Z$?2^z?^ £ 5 £ 8 K w22"J2"S?J?t?^ 2" ^ "0 M X t- tn 03^ C/5 3 CJ.X •^lOCN CN CN O< OOO rOTJ-CN t^O lOCNOOO 1-1 •rj-f^LOCN C C-C>CNOOi-iCO Tj-OO CN O \ "8 u "8 T3 n _ C 3 e C3 U 9 '^•'O^d'O'^C O ^hGO fOr~~- C ^ CN r^« CN GO P— < ON O ^ O^ o V ^ CO •g V) f^- "^t" ^ O O O^ GO r^ 3 H O5 O^Cs^ GO^r^l'^g ri bC OS 2 ^ -^ "^ ^t* t^^ c ^o *o o^ CN 10 oo *•* ^t* r^* > 4 1 ^" 10 ^C r^* GO ON O *•* CN f^ r^ T^- u"} S^Q t-N. Osmotic Concentration and Electrical Conductivity, Etc. 139 C en c3 ,Q en 3 l/l O t^ oo OO CS O oo & O^OOOOOOOOOOOh-iOOO CXDOO^O NOO f*5 O O ^ 1^" oc r^ « (N i— IO 00 « w h- O "0 O 00 140 J. A. Harris, R. A. Gartner and J. V. Lawrence While the materials are rather too meagre for exhaustive statistical analysis they have been classified according to the magnitude of A and the average value of K and of K/ A for each class of A has been determined. The results are presented in Tables IX and X.1 Diagram i , which shows by the position of the two means 16 Diagram i Average values of specific electrical conductivity, K, of leaf tissue fluids of ligneous and herbaceous species classified according to freezing point de pression, A. on the scale for A the conspicuous differentiation of ligneous and herbaceous plants for this constant, also brings out clearly the fact that for each grade of A the ligneous forms have a lower electrical conductivity than the herbaceous species. The mean values for K for the two growth forms lie 1 The class interval of A has been selected to represent 5 percent of the molecular lowering taken as A = 1.86. Osmotic Concentration and Electrical Conductivity, Etc. 1 4 1 at the points where the straight lines fitted to the means intersect the verticals representing the mean values of the freezing point lowering. Diagram 2 Average osmotic concentration, in terms of freezing point lowering, of leaf tissue fluids of ligneous and herbaceous species classified according to specific electrical conductivity, K X io6. The mean values of A for various grades of K are shown in Table X and represented graphically in Diagram 2. The differentiation of ligneous and herbaceous forms with respect 144 J ' • A- Harris, R. A. Gartner and J . V. Lawrence For trees: r = +o. 127 =t= o. 152, K X io6 = 9322 + 1464 A A = i . 1685 + 0.00001102 K X io6 For shrubs : r = — 0.079 ="= o. 112, K X io6 = 12059 — IO95 -^ A = i .2385 — 0.00000567 K X io6 For trees and shrubs: r = +0.022 ± 0.091, K X io6 = 10591 + 273 A A = i . 1985 + 0.00000153 K X io6 For herbs : r = +o. 150 ± 0.052, K X io6 = 11997 + 2730-^ A = 0.7293 + 0.00000819 K X io6 The correlations between the freezing point lowering and the electrical conductivity of the sap of ligneous plants are of a very low order and statistically insignificant in comparison with their probable errors. The value for shrubs is actually negative in sign. That for trees and shrubs together is sensi bly zero. The coefficient for herbaceous plants is also low, but may indicate a slight relationship between the two con stants, higher values of A being associated with higher values of K and vice versa. These results show that, in the vegetation of the glacial moraines of Long Island at least, there is practically no rela tionship between the concentration of ionized electrolytes and of total solutes (molecules and ions) in the leaf tissue fluids. If there be little relationship between the magnitudes of K and A one might expect the value of the ratio */ A to de crease as A becomes larger and to increase as * increases in magnitude. This is shown in Diagrams 3 and 4 to be the case. The explanation of the lower conductivity of the tissue fluids of ligneous plants presents a problem for future investi gation. It may be suggested that the arborescent forms are ex posed to greater insolation, and in consequence show greater photosynthetic activity. A fragment of evidence in this Osmotic Concentration and Electrical Conductivity, Etc. 145 direction is furnished by the fact that A increases while the value K/A decreases with height in arborescent plants.1 Diagram 4 Mean ratio of electrical conductivity to freezing point depression, «/ A, in leaf tissue fluids of ligneous and herbaceous species classified according to electrical conductivity, K. Summary Studies in the Arizona deserts, in the Jamaican montane 1 J. Arthur Harris, R. A. Gortner and John V. Lawrence: Bull. Torr. Bot. Club, 44, 267-286 (191?)- 146 J. A. Harris, R. A. Gartner and J. V. Lawrence rain forest, and in the mesophytic habitats of the north shore of Long Island, have shown that the osmotic concentration, as measured by the cryoscopic method, is far higher in the leaf tissue fluids of ligneous than of herbaceous species. A large series of determinations in the various non- halophytic habitats of the north shore of Long Island shows that the specific electrical conductivity of the expressed leaf tissue fluids of ligneous species is lower than that of herbaceous species. This shows that while the concentration of ionized electrolytes is lower in ligneous than in herbaceous forms, the reverse is true for total solutes. Because of the wide geographic range and the great diversity of conditions (xerophytic, mesophytic and hygro- phytic) under which the investigations on osmotic concentra tion were carried out, there can be no reasonable doubt but that the differentiation of ligneous and herbaceous plants with respect to the magnitude of their osmotic concentration (A) is a general biological law. Until confirmed by investigations in other regions presenting different conditions for plant growth1 the results for conductivity cannot be asserted to be of universal validity. The Carnegie Institution of Washington 1 These investigations are now in progress. Reprinted from the Proceedings of the Society for Experimental Biology and Medicine, 1921, xviii, pp. 106-109. 50 (1632) Maximum values of osmotic concentration in plant tissue fluids . By J. ARTHUR HARRIS, R. A. GORTNER, W. F. HOFMANN, and A. T. VALENTINE. [From the Carnegie Station for Experimental Evolution, Cold Spring Harbor, N. Y., and the University of Minnesota, St. Paul, Minnesota.] The observations of a number of botanists have shown that extremely high concentrations may characterize plant tissue fluids, especially when the plants1 occur in a highly saline sub stratum. To Fitting2 belongs the credit of first demonstrating that extremely high osmotic concentrations are found in some desert plants,3 although Drabble and Lake4 and Drabble and Drabble5 had preceded him in showing the fundamental relation ship between environmental conditions and the osmotic con centration of plant tissue fluids. As early as 1902 Cavara reported cryoscopic determinations on saps of high concentration6 and in 1905 gave results in full7 for a large series of determinations made at Cagliari. His maxi mum values were found in the sap of halophytes growing in locali ties where the concentration of the soil solution progressed with the advance of the season. He reports freezing point depressions of 7.25° in Obione portulacoides , 7.48° in Salicornia fruticosa, and 7.25° to 8.50° in Halocnemum strobilaceum. His determinations were, however, made on sap extracted without the antecedent treatment necessary to render the tissues permeable as has been 1 Our present observations apply to the tissue fluids of flowering plants only. No attempt is made here to discuss the concentrations found in such lower organisms as those studied by G. J. Peirce (Pub. Carn. Inst. Wash., 1914, No. 193, p. 47-69) or G. Senn (Verh. Schw. Naturf. Ges., 1911, xciv). 2 H. Fitting, Zeitschr. /. Bot., 1911, iii, 209-275. 3 Fitting found a number of species of plants in the North-African deserts, the leaf cells of which were not plasmolyzed by 3 gram molecular KNOa solution. The oretically potassium nitrate of this concentration should be the equivalent of about 100 atmospheres. The technical difficulties of applying the plasmolytic method are such as to lead one to question its value as a means of investigating in a quantitative manner the unusually high concentrations found in desert plants. * E. Drabble and H. Lake, New Phytologist, 1905, viii, 189. 6 E. Drabble and H. Drabble, Biochem. Jour., 1907, ii, 117. ' F. Cavara, Rendic. Congr. Bot. Palermo, 1902, 66. 7 F. Cavara, Contrib. Biol. Veg., 1905, iv, 41-84. 2 SCIENTIFIC PROCEEDINGS (112). shown to be necessary by Dixon and Atkins8 and others.9 His constants are, therefore, as pointed out by Atkins,10 probably sub- maximum because of incomplete extraction. Work on the spring flora of the Arizona deserts11 was probably carried out in a manner to obviate the objections to the preceding studies. In this series the maximum concentrations were found in Atriplex canescens, a shrub of the salt spots, in which A = 5.65, P = 67.5, and in Mortonia scabrella, a small shrub of the mesa- like slopes, for which one determination gave A = 4.78, P = 57.2. Concentrations of about fifty atmospheres have been demon strated in the leaf tissue fluids of more or less sclerophyllous trees Capparis ferruginea and Guaiacum officinale and in those of the succulent-leaved halophytic half shrub Batis maritima of the saline coastal flats of Jamaica.12 Cryoscopic studies on mangrove vegetation13 have indicated maximum concentrations of about fifty atmospheres in Avicennia nitida, although two questionable determinations indicated seventy atmospheres. Using plasmo- lytic methods, von Faber14 reports concentrations ranging from 24 to 72 atmospheres in East Indian species of the mangrove asso ciation. During the summer of 1920, while engaged in field operations in collaboration with the Department of Agriculture in the Great Salt Lake region, we had the opportunity of making several hundred determinations of the osmotic concentration of plant tissue fluids by the cryoscopic method. These measurements were made on sap extracted after freezing of the tissues15 and with such care as to render the results reasonably free from criticism. Such a series, based on species which have for ages been subject to the influence of the highly saline substratum afforded by the s H. H. Dixon and W. R. G. Atkins, Proc. Roy. Dublin Soc., 1913, N. S., xiii, 422-433. 9 R. A. Gortner, J. V. Lawrence, and J. Arthur Harris, Biochem. Bull., 1916, v, 139-142, pi. i. 10 W. R. G. Atkins, "Some Recent Researches in Plant Physiology," London, 1916, 94. 11 J. Arthur Harris, J. V. Lawrence, and R. A. Gortner, Phys. Res., 1916, ii, 1-49. 12 J. Arthur Harris and J. V. Lawrence, Bot. Gaz., 1917, Ixiv, 285-305. 13 J. Arthur Harris and J. V. Lawrence, Biol. Bull., 1917, xxxii, 202-211. 14 F. C. von Faber, Ber. Deutch. Bot. Ges., 1913, xxxi, 277-281. 16 R. A. Gortner and J. Arthur Harris, PI. World, 1914, xvii, 49-53. OSMOTIC CONCENTRATION IN PLANT TISSUE FLUIDS. 3 bed of the ancient Lake Bonneville, should furnish some indication of the maximum concentration16 to be found in the leaf tissue fluids of flowering plants. While high concentrations were demonstrated in a number of species, the highest was found in the typical salt desert half-shrub A triplex confertifoUa. It alone will be considered. Two collections made on the rocky cliffs of Stansbury Island, Great Salt Lake, on July 14 gave freezing point depressions of 6.96° and 7.97°. If we may use the formula of Lewis,17 upon which published tables of osmotic concentration have been based,18 these depressions indicate osmotic pressures of 82.9 and 94.7 atmos pheres respectively. The highest concentrations were found in plants growing on the low ridges in the salt-flats19 along the southern shore of Great Salt Lake. A determination on material collected July 16 gave A = 6.22, P = 74.2. On July 1 8 a determination on plants in about the same type of locality gave A = 10.00, P = 118.5. Finally, on July 27 a determination made in this locality on the leaves of this species indicated a freezing point lowering of 13.0°. The equation used would indicate a concentration of 153.1 atmospheres.20 These determinations show that concentrations measured by a depression of 13.0°, presumably the equivalent of 153 atmospheres, maybe found in the tissue fluids of apparently normal leaves. 16 A difficulty in work on the leaves of desert plants lies in the fact that the maximum concentrations must be expected during the periods of more extreme drought. During such periods the saps may become concentrated by desiccation merely. We know very little concerning the functional activities of such leaves or whether they are retained after the beginning of a period of more adequate mois ture. There is, therefore, the possibility that leaves which are too desiccated to be longer functional may be utilized for determinations and indicate concentrations which are really larger than those in which the metabolic processes of the cells may be normally carried on. We believe that except as specifically indicated, the con centrations here recorded were determined on leaves in fairly normal condition. 17 G. N. Lewis, Journ. Amer. Chem. Soc., 1908, xxx, 668-683. 18 J. Arthur Harris and R. A. Gortner, Amer. Jour. Bot., 1914, i, 75-78; Harris, Amer. Jour. Bot., 1915, ii, 418-419. 19 T. H. Kearney, L. J. Briggs, H. L. Shantz, J. W. McLane, and R. L. Piemisel, Jour. Agr. Res., 1914, i, 365-417, pi. 52-58. JOA sample from Atriplex nuttallii showed a freezing point lowering of about 14.4°, indicating a concentration of 169.3 atmospheres. The leaves appeared more dried than those of Atriplex confertifoUa, and we are inclined to await further measure ments before accepting this constant. Reprinted from the Proceedings of the Society for Experimental Biology and Medi cine, 1919, xvi, pp. 134-136. 75 (1450) The transformation of the plant ovule into an ovary. By J. ARTHUR HARRIS. [From the Station for Experimental Evolution, Carnegie Institution of Washington, Cold Spring Harbor, N. Y.] In plants there is a rather wide capacity for the development of organs of various kinds from primordia normally destined to produce quite different structures. For example, leaves may replace petals, stamens or carpels; petals may occur in the place of stamens or carpels. The transformation of stamens into carpels is a well-known phenomenon. Furthermore, the continued development of a growing point the activity of which is usually terminated by the formation of some highly specialized organ, such as the flower or fruit, is quite familiar to those concerned with problems of variation. Among these morphological abnormalities the continued meristematic activity of the axis which is normally terminated by the formation of the ovary is of very rare occurrence. It is, how ever, regularly found, although in a small and variable percentage of the cases, in one of the passion flowers, Passiflora gracilis. Here prolification of the fruit consists in the formation of series of carpels, which may or may not be ovuliferous, within the normal fruit. The mass of accessory carpels thus formed may be so large as to rupture the fruit wall. While the occurrence of prolification may be regarded as a heritable characteristic in P. gracilis the abnormality is of rela tively rare occurrence. Physico-chemical factors must, therefore, determine the occurrence of prolification in certain fruits and its absence from others.1 1 A prolonged effort to demonstrate the nature of these factors has been incon clusive. Subsequent studies have not substantiated in all cases the position taken by Gortner and Harris (Bull. Torr. Bot. Club, 1913, XL., 27). Studies on the os motic concentration and the electrical conductivity of the fluids of the proliferous mass and of the wall have been given by Harris, Gortner and Lawrence, Biochem. Bull., 1915, iv., 52. SCIENTIFIC PROCEEDINGS (100). If the formation of the basal prolification be due to the presence of special formative substances, one might occasionally expect to find the formation of carpellary tissue from other primordia. The only primordia normally developed subsequent to the carpels themselves are the ovules, which are borne on the carpellary margins. To test this point, and to secure materials for other investiga tions, a series of dissections was begun in 1908. Those which were made from 1908 to 1915 are summarized in the accompanying table. The results show that in the series of 568,098 dissections which have been made of fruits grown under a rather wide variety of conditions, basal prolification occurred 18,921 times, or in 3.330 per cent, of the fruits. Placental prolification occurred only 224 times or in .039 per cent, of the cases. Basal and placental prolification occurred in 18 of the 568,098 fruits. While the occurrence of basal prolification presents a number of interesting morphological problems it does not seem to have the physiological significance of placental prolification. In the first case we have merely the continuation of activity of an axis which normally ceases with the laying down of the whorl of carpels forming the normal fruit. In the second case we have an entire transformation of a primordium. The primordium which should develop into an ovule forms instead a carpel, i. e., one of the units of which the normal ovary is built up. I am inclined to consider that this result is due to the local influence of special formative materials. Experi ment. Without Prolifica Basal Prolifica Placental Prolifica Basal and Placental Prolifica Total Placental Prolifica Total Fruits. Percentage Placental Prolifica tion. tion. tion. tion. tion. tion. 1908 20,104 446 20,550 1909 116,821 4,622 30 30 121,473 .024 I9II 30,105 873 9 9 30,987 .029 1912 10,487 441 I I 10,929 .009 1913 123,216 4.458 I? 3 20 127,694 .015 1914 180,516 7.143 144 6 ISO 187,809 .079 IQIS 67,686 938 23 9 32 68,656 .046 Total . . 548.935 18,921 224 18 242 568,098 .042 Reprinted from the Proceedings of the Society for Experimental Biology and Medicine, 1921, xviii, pp. 4-5. 2 (1584) Formulae for the determination of the correlations of size and of growth increments in the developing organism. By J. ARTHUR HARRIS. [From the Station for Experimental Evolution, Cold Spring Harbor, L. I.] In the analysis of the growth of the higher organism it is essential to obtain definite measures of the interrelationship between certain measured magnitudes. Those which require consideration are the following: (i) The correlations between the actual size of the organism at the various stages1 of growth. (2) The correlations between growth increments of the organism during the several growth periods. (3) The correlations between the size of the organism at any stage and any or all subsequent growth increments. The labor of determining these correlations by ordinary methods is excessive. If the first set of correlations (i) be deter mined by taking all moments about o as origin,2 we may solve problems (2)-(3) as follows. Problem 2. — To determine the correlations between growth increments from the moments and product moments of size at the several growth stages. Let w, x, y, z be the dimensions of the organism at growth stages p, q, r, s. The growth increment during the intervals q-p, r-q, s-r will then be ipq = x-w, iqr = y-x, irs = z-y. 1 Growth stage denotes any given moment of time at which series of organisms of the same age are measured. During development it is, therefore, synonymous with age. The absolute size of the organism or any of its parts at a given growth stage is the only character of the organism available for consideration. Growth period denotes the period of time elapsing between the 5th and the s + nth growth stage, where 5 is any growth stage. Growth increment denotes the increase in size during any such period. 1 Harris, J. Arthur, Amer. Nat., 1910, xliv, 693-699- SCIENTIFIC PROCEEDINGS (109). The moments 2(x), S(*2), S(y), S(;y2),---, and the product moments S(m), S(wy), • • • , 2(yz) are available for the correlations between size, which are required on their own account (Problem i). The constants for growth increments are given by well-known formulae ipq = x-w, etc., and similarly for o^r, o-,;, The product moment for any two growth increments, say ipq and irs, is In the special case in which three consecutive stages, say w, x, y, are involved we write Problem j. — To determine the correlation between the size of the organism at any stage and any growth increment. The notation of problem (2) may be used. The physical constants for the growth stages and growth increments have been given. The product moments are - SO2), — 2(wy), etc. Illustrations of applicability will be given elsewhere. [Reprinted from BIOLOGICAL BULLETIN, Vol. XL., No. 5, May, 1921.] INTER-PERIODIC CORRELATION IN THE ANALYSIS OF GROWTH. J. ARTHUR HARRIS AND H. S. REED, STATION FOR EXPERIMENTAL EVOLUTION, COLD SPRING HARBOR, LONG ISLAND. I. INTRODUCTORY. In the literature of growth, mathematical equations to describe changes in the actual size of the organism, or changes in the growth rate, are finding continuously widening applications. One has merely to refer to the papers by Robertson, Miyake, Moeser, Ostwald, Reed and Holland (1919), and Reed (I92O)1 for illus trations. The criticism usually directed against such work is that in the higher organism, growth is a highly complex process, and that in consequence it cannot be represented mathematically. It is be cause of the very fact that growth is a complex process that mathematical analysis of the experimental data is necessary. Corollary to this must be the recognition of the fact that sines growth is not a simple process, no one mathematical formula will be adequate for full description2 and no one method adequate for complete analysis. Our purpose in the present note is to illustrate on a series of data collected by one of us (1919) the application of inter-periodic correlation coefficients to certain phases of the problem of growth. Before passing to the analysis, which is the special purpose of this paper, definition of the terms which will be used and a note 1 Citations of literature may be traced from Reed's paper. 2 Those who consider the possible adequacy of a single equation take the ground that if it be possible to represent the growth of an organism by a simple equation, it may be by virtue of the fact that during growth the various (often conflicting external) factors which affect the living substance are inte grated by the organism. 243 J. ARTHUR HARRIS AND H. S. REED. on the nature of the data on which the statistical methods are illustrated are in order. By growth stage we mean any given moment of time at which a series of organisms are measured. It is, therefore, synonymous with age during the growth period. The absolute size of the organism or of one or more of its parts a.t a given growth stage is the only character of the organism available for consideration. By growth period we understand the period of time elapsing between the sth and the j + ;/th growth stage. The increase in size during any such period we shall designate as a growth increment. By relative growth increment, /,-«, we understand the ratio of the growth increment, r, to the absolute size of the individual at stage, r, where r and s are any two successive stages. Turning now to the question of the original data as given in Table I. of Reed's (1919) publication we note from a study of the physical constants for absolute size in Tables I. and II. that there is an increase in the mean height of the plants up to the //th day. TABLE I. STATISTICAL CONSTANTS FOR SIZE AT VARIOUS GROWTH STAGES. Growth Stage. Mean. Standard Deviation. Coefficient of Variation. 17.931 1.617 9.0 14 36.328 4.786 13-2 21 67.845 8.932 13-2 28 97.672 I4.673 15.0 35 130.724 19.174 14-7 42 168.707 24.801 14.7 49 205.397 32.760 16.0 56 229.672 37.842 16.5 63 247.345 42.574 17.2 70 251.776 43-433 17-3 77 253.810 43.767 17.2 The increase from the 63d to the 7oth and from the /oth to the 77th day is relatively slight, being only 4.43 cm. or 1.79 per cent, of the height for the 63d day in the first case and only 2.03 cm. or 0.81 per cent, of the value for the 7Oth day in the second case. The difference between the 84th day and the 77th day is negli gible. In view of the fact that there is no appreciable growth in INTER-PERIODIC CORRELATION. 245 the sense in which the term is used here between the 77th and the 84th day, this period will be left entirely out of account in the calculation of the correlations for the following discussions. Furthermore by considering the constants for growth incre ments as shown in Table II., we note that the coefficients of varia- TABLE II. STATISTICAL CONSTANTS FOR GROWTH INCREMENTS FOR VARIOUS GROWTH PERIODS. Growth Period. Mean Increment. Standard Deviation. Coefficient of Variation. 7 to 14 l8."?97 3.764 2O.5 14 to 21 •2J.CI7 5.164 16.4 21 to 28 29.827 7.907 26.5 28 to 35 33.052 7.505 22.7 35 to 42 37.983 11.578 30.5 42 to 49 . 36.690 14.266 38.9 49 to 56 24.276 16.540 68.1 56 to 63 17.672 13.803 78.1 63 to 70 4.431 4.713 106.4 70 to 77 2.034 5.096 250.5 tion for growth increments from the 63d to the 77th day are abnormally great. This may be in part due to biological causes, but it is doubtless due to a considerable extent to the relatively large error of measurement when the increment is very small in comparison with the size of the organism. If this be true, we should expect the correlations for actual size for the 63d to the 84th day to be about the same as those for the immediately preced ing growth stages, but the correlations for growth increments may be expected to be of little value. The problems which may be considered will be presented and discussed seriatim. II. ANALYSIS OF DATA. PROBLEM I. The correlation between the absolute size of the organisms at its several periods of development. When examined at an early stage of development, organisms are found to differ among themselves in size. The same is found to be the case when the same series is measured at a later growth stage or at maturity. In the biological analysis of the phenomenon of growth a prob- 246 J. ARTHUR HARRIS AND H. S. REED. lem of great importance is that of the causes which bring about the differences in size observable at any stage of development, or after growth has entirely ceased. Are individuals which are found to be small at maturity those which were small initially and have remained so from the beginning, or may the growth rate of an individual change during the course of its development to such an extent that it may vary its position in the series under investi gation from time to time? That the latter is to some extent the case we know from general observations on human children. The problem to be solved is that of the quantitative magnitude of the relationship between the size of the individual at different stages of development. The nature of the biological problems to be investigated has been stated in earlier work, and an attempt has been made to solve them by grouping plants according to quintile (Pearl and Surface, 1915) or quartile (Reed, 1919) position in the culture to which they belong and ascertaining the quartile or quintile in which they fall at different stages of growth. This method has the disadvantage that all the individuals, whatever their size, are lumped together in four or five groups. In this method of treatment, small differences between two indi viduals are, therefore, given as much significance as large ones, providing they are large enough to throw the two individuals into different quartiles or quintiles. An alternative method, which will completely obviate this dif ficulty, is to determine the correlation between the sizes of the individual at different periods of growth. The possible correla tions between the absolute size of the individuals in the u dif ferent stages of growth of the Helianthus plants are shown in Table III. The coefficients in this table can be best understood by first ex amining those for the relationships between the sizes of the plants near the period of maturity, and then passing to the relationships between the sizes of the plants at earlier stages. Considering first of all the coefficients in the lower right-hand corner of the table, we note that all the coefficients are very high, denoting practically perfect correlation. This is the relationship which wrould be expected for a period when the organism has INTER-PERIODIC CORRELATION. 247 G U 40 a •H'g -H lJM Tl- _ i^!Tl'OTlMTlo\ 00 d\ ^ -stot—oooooooo MTj-Ot-OOOOOOOOOO _ roTl ro"tlvo OOO\« I— OO OO 00 CO OO 00 248 J. ARTHUR HARRIS AND H. S. REED. practically attained its adult size and in which there is relatively little change from one week to another. As we follow the correlations between the later periods and preceding periods back, we note that there is a regular decrease in the values of the correlation coefficients. This may be best shown by summarizing the results graphically in diagram i. In the graph the correlation of the size of the organism at each 1, 14 2.1 28 35 42 49 56 OF PLAA/T (STAGE) DIAGRAM i. 70 growth stage with its size at every antecedent growth stage (shown at the bottom of the diagram) is shown on the scale of correlation at the left by points marking the magnitude of the correlations for each of the growth stages. The pitch of the lines connecting the points for the I4th to the 77th growth stage shows the rapid decrease in the magnitude of the correlations as the stages be come more widely separated in time. l< | ' MI'I'KLATION. 249 The same type of diagram may be used to show the relation ship between the size at early and at later growth stages. Dia gram 2 shows the distribution of the magnitudes of the correla tions for sizes of the individuals at the ;th to the ;oth day (stage) and the size at subsequent growth stages. From these lines it is clear that the correlations between size 28 35 AGE 63 DIAGRAM a. at antecedent and subsequent periods decrease as the periods be come more widely separated in time. This is true wit! ception for every period which furnishes evident question. The coefficients are, however, positive in sign throughout, tl ni-esting (though in some cases not proving) that throughout its growth period the size of the plant bears some relation when first measured. This result is in agreement wit. 25O J. ARTHUR HARRIS AND H. S. REED. findings of Webber (1920) in regard to the growth of Citrus stock. PROBLEM 2. The correlation between the growth increments of the organism during the several growth periods. Our second problem is to determine whether there is a corre lation in growth increments as well as in actual size of the or ganism. We shall thus answer the question whether the organism which grows more rapidly than the average during one growth period will grow more rapidly than the average in other growth periods and whether the organism which lags behind the average in its rate of growth during one growth period will also lag be hind during other growth periods. Little has heretofore been done towards the statistical treat ment of growth increments. This is probably in part due to the arithmetical difficulties of computing the constants for incre ments, but if the moments and product moments be taken about zero as origin in computing the coefficients required under Prob lem i above, the calculations for growth increments are easily made by the use of formulae given elsewhere (Harris, 1920). The symmetrical table showing the relationship between the actual growth increments for all of the combinations of growth periods appears as Table IV. This table shows positive and sta tistically significant correlation coefficients for closely associated periods throughout the season up to and including the period for the 63d to the 7oth day. The coefficients for the period from the 7oth to the 77th day cannot in general be considered statis tically significant in comparison with their probable errors. Examining these results in a little greater detail, we note that the nine coefficients showing the relationship between the growth increments of successive weeks (the constants bordering the diag onal cell of the symmetrical table of constants) are all positive in sign and with the exception of the last (showing the relationship between the growth of the period from the 63d to 7oth and that between the 7Oth to 77th day) all are statistically significant. The eight coefficients measuring the correlations between the growth increments of weekly periods which are separated by one week are also without exception positive, but are lower in magnitude and less certainly statistically significant. For periods more INTER-PERIODIC CORRELATION. 251 t~- oo c\ vO oo oo o\ § 00 o -H U4i lo-H W -tl a-H S -H 5-H J?-H 1 1 1 1 1 + + + + o. w £ § s § f R | oo 00 o o VO 0 6 J °| ifil SS ^J IS 15 s oo ° O 1 1 1 i 1 I + + + I/! G M 0 OO o CO 0 oo O oo 0 00 o oc o O O 00 o s 0 •H oi-H w -M S -H fo-H "R-H o -H t-~ "H c 3\-H S PM * I ° 2 M 2" M ^ w<§ 0 % "° £ ro *° < ' oo N s H + + I 1 + + + + + £ O M J o H eg r ON oo q o oo o o oo q oo oo o i^~ 0 ^. oo q q oo o < K W H 9 1 + r r + + 1 | ^ cs °' H H x f 1 ? % Z § | s DURING 1 Period. o * •« i IM+! f M "H f + + ^ + + w _M \£ O Tl C f + (/) •£ H -S * s CC O oo o OO O o o ro O oo 0 oo 0 OO O oc 0 INCREMI G o H] 1* + + + 5 41 + + + f f THE GROWTH o 00 c2 c + oo q + VO q 4- § 0 o 4 + 00 q + oo q l' oo o s-ti r 0 q f oo q r 3NS BETWEEN 03 o q + q + a in q o + oo q M + 00 o o r oo o f OO q r OO 0 M -H 04 f oo q 0 r CORRELATI 0 q •« o + q\ IT) O o + oo q M ^ H \o M f oo q M "H O + oo q t— "H o r oo o jj f > Tl »r> 5^6 0 f o 10 o + oo q + oo o + OO q r oo q \ oo q f oo q + 00 q f oo o r E T3 _0 V o o o o o 0 0 O 0 o £ J N 5 % ^. OS <3 ro o 252 J. ARTHUR HARRIS AND H. S. REED. widely separated in time the correlations are in part positive and in part negative in sign. Thus from the results as a whole it appears that the incre ments of successive periods are generally positive and fairly highly correlated when the periods show actual growth incre ments. Thus the zone of coefficients lying along the diagonal cell are positive and generally fairly high. When the periods are separated by any considerable length of time the coefficients are generally insignificant in magnitude and may, as a matter of fact, be either positive or negative in sign. The relationship may be brought out by determining the aver ages of the correlation coefficients, with regard to sign, for the increments of periods separated by various lengths of time. The results are as follows. Period of Separation Number of Correlations Average (Weeks). Averaged. Correlation. 0 9 + .5009 1 8 + .2240 2 7 —.0334 3 6 —.1236 4 5 —.1640 5 4 —.1033 6 3 — .0077 7 2 —.0585 8 i — .1360 If we disregard the cases in which there are less than five co efficients to be averaged, we note a steady decrease in the magni tude of the correlation coefficient. Periods of growth which are successive or separated by only one week have positively corre lated growth increments. Periods which are more widely separ ated show negative correlations of the increments. The relationship between the coefficients in Table IV. may be clarified by diagram 3 which shows the relationship between four of the ten growth increments and each of the other ten incre ments. The increments selected as a " first variable " in the cor relation are the first, fourth, seventh, and tenth. This has the advantage of representing the first and the last growth incre ment, and of leaving undrawn no more than two successive incre ments. The figures are aligned according to the ten increments representing the " second variable " of the correlation. INTER-PERIODIC CORRELATION. 253 + •60 + •40 + •20 k CO ao £ PfR/OJJ 770/4 , k PER 101 28 JO 35 •+•60 I ^ ' « S • +-40 1 • + •20 ~ s; - ^0 J --•20 • - -40 — + •40 + •20 •00 -•20 PfRIOJ] 70 TO 77 7 14 21 28 35 42 49 56 63 70 77 254 J- ARTHUR HARRIS AND H. S. REED. The graphs for the first, fourth and seventh increment show clearly the shift in the position of the maximum positive corre lation from the earlier to the later periods as the " first variable " is chosen from the later periods. The same is shown less clearly by the correlations for the tenth increment, but there the coeffi cients are very small, presumably because growth has practically ceased. It is clear, therefore, that plants which are growing more rapidly during any period of development will grow more rapidly during a closely associated subsequent period of development but that there is little or no relationship, or even a negative relation ship, between the rate of growth of the organisms studied at con siderably separated periods of time. Since the correlations for absolute growth increments are so small for all except successive periods of time, it seems unneces sary to deal at present with the relative growth increments, i.e., with the growth increments expressed as a fraction of the size of the organisms at the beginning of the growth period. PROBLEM 3. The correlation between the absolute size of the organism at given stages of development and subsequent growth increments. In the higher plant organism rate of growth at any period must be supposed to depend to some extent upon plastic ma terials synthesized by the more nearly mature portions of the same individual. Thus one might expect to find a relationship between the actual size of the organism at any stage of growth and the rate at which the organism increases in size during a sub sequent period. We have determined the possible correlations between the ab solute size of the organism at different periods and the growth increment of the organism during subsequent growth periods. The coefficients are presented in Table V. This shows positive correlation between the actual size of the organism at every stage of development from the 7th to the 7oth day and the increase in the size of the organism during the following week. The mag nitude of the correlation is of the order ^ = 0.45 to r = o.6o for the 7th, I4th, 2ist, and 28th day. For these growth stages the correlation between actual size and the subsequent growth incre- INTER-PERIODIC CORRELATION. 255 -H 2"+i£+!^+i£Ti S-Ti § » $» g>M£6 3-M^ H H HI O M H r r r + "H oo Tl O Tl O r + '+! 2 H IJOOIJOOIJ TloOTloTI + + _LJ O 11 O JJ O Tl 00 Tl u-> Tl O\ u 256 J. ARTHUR HARRIS AND H. S. REED. ment is clearly significant in comparison with its probable error. The coefficients are lower for the 35th and the 42d day, but are probably statistically trustworthy. Beyond this period there seems to be no relationship between the size of the organism and its growth rate in an immediately following period. For the first two stages of growth measured, the 7th and the I4th day, there may be a significant correlation of the order r = -)- .285 between size and growth increments during the sec ond following week. The coefficient of correlation between size and the increment in the second week following is also positive for the 2ist and 28th day, but neither of these values may be considered statis tically significant in comparison with its probable error. Finally for the first stage (seventh day) there may be a significant cor relation between absolute size and growth increments during the third week following (r=-f-.239 for increment for 2ist to 28th day). Other than this the coefficients are for the most part sta tistically insignificant in comparison with their probable error. Summarizing the preceding statements as a basis for further analysis, we note that for the first six growth stages (7th to 42d day) there is a significant positive correlation between the size of the organism at the given stage and the growth increment of the following week. For the first two growth stages (and possibly in the third where r/Er=i.jj} there is a significant correlation between the size of the organism and the growth increment in the second subsequent week. Finally, for the first stage only, there is a significant positive correlation between size and growth increment in the third subsequent week. Disregarding these 9 coefficients and the 4 positive but not sig nificant correlations between the sizes at the several growth stages and the growth increments of the following week, we may note the following facts concerning the remaining 42 coefficients. Of these 42 coefficients 36 are negative while only 6 are posi tive in sign. Of the 6 positive coefficients only that between actual size on the 2ist day and growth increment between the 28th and 35th day (already considered above) is as large as its probable error. Of the 36 negative coefficients 18 are larger than INTER-PERIODIC CORRELATION. 257 their probable error, and 5 of these are over twice as large as their probable error. There is, therefore, clear evidence that the subsequent growth of the higher plant organism is measurably conditioned by its size. In general the larger individuals grow more rapidly in im mediately subsequent periods, but somewhat more slowly than the average in more distant subsequent periods. While a detailed discussion of the relation of these results to the theory that growth may be satisfactorily described by the curve of an autocatylic reaction falls quite outside the scope of this paper, it must be noted that negative correlations between actual size at a given stage and the growth increments of certain subsequent growth periods might be expected. As Reed and Holland (1919) have pointed out the plants attained about half their final height at about the thirty-fourth day. From this time on the increments were decreasing. Plants which had attained more than the average size at this period would, therefore, of necessity, make smaller average increase in size in later periods. The number of individuals measured is not sufficiently large to carry the analysis farther. III. RECAPITULATION. The purpose of this paper has been to illustrate on the basis of a specific series of data the value of the inter-periodic correlation coefficient in the analysis of the phenomena of growth. The analysis shows that in the case of a series of Helianthus plants the actual size of the individual at any stage of develop ment is closely correlated with its size at other closely associated stages of development. The magnitude of the correlation rapidly diminishes as the growth stages become more widely separated in time. Thus the final size of the organism is but to a slight extent determined by its initial size. The correlation between successive growth increments is posi tive in sign and statistically significant, with the general average of r = .5oi. The correlation for increments of weekly periods separated by one week is on the average only about ^ = .225. For periods more widely separated than this the correlation be tween growth increments is on the average negative in sign. 258 J. ARTHUR HARRIS AND II. S. REED. Thus plants which are growing more rapidly during one period of development will grow more rapidly during a closely asso ciated period, but there is little or no relationship between the growth increments of more widely separated periods. The growth increment of the organism is positively corre lated with its size at an immediately preceding stage. In the early stages of growth, the growth increments of two or even three subsequent periods are positively correlated with the initial size of the organism. LITERATURE CITED. Harris, J. Arthur. '20 Formulae for the Calculation of the Correlations of Size and of Growth Increments in the Developing Organism. Proc. Soc. Exp. Biol. and Med. In press. Pearl, R., and Surface, F. M. '15 Growth and Variation in Maize. Zeitschr. Indukt. Abst. u. Verer- bungslehre, 14: 97-203. Reed, H. S. '19 Growth and variability in Helianthus. Amer. Jour. Bot., 252-271. '19 The Growth Rate of an Annual Plant, Helianthus. Proc. Nat. Acid. Sci., 5: 135-144. Reed, H. S. '20 The Nature of the Growth Rate. Jour. Gen. Physiol., 2: 545-561. Webber, H. J. '20 Selection of Stocks in Citrus propagation. Bull. Univ. Calif. Coll. Agr., [Reprinted from SCIENCE, N. 8., Vol. LII1., No. 1576, Pages 460-462, May 13, NOTES ON THE OCCURRENCE OF GAMMERUS LIMNAEUS SMITH IN A SALINE HABITAT THE capacities of various organisms for withstanding relatively wide ranges of environ mental conditions has received considerable attention at the hands of physiologists and students of animal behavior, and is a problem which must ultimately be considered in greater detail by ecologists, students of geo graphic distribution and organic evolution. The purpose of this note is merely to call attention to the occurrence of Gammerus limnaeus Smith,1 normally a fresh water2 1 We are indebted to Mr. Waldo L. Schmitt, as sociate curator of marine invertebrates in the U. S. National Museum, for the determination of the species. The specimens are in the National Mu seum. 2 The key to the taxonomic and distributional literature is furnished by Weckel's paper on the fresh water Amphiopoda of North America (Proc. U. 8. Nat. Mus., 32: 42-44, 1907), and individual citations need not be given here. The species was first dredged in Lake Superior. It has been taken near Long's Peak, Colorado, at an elevation of 9,000 feet; from a cool spring, Fire Hole Basin; from Shoshone Falls, Idaho; Flathead Lake, Mon tana; and from the Yellowstone National Park. It is reported from Fort Wingate, N. M., and from the Wasatch Mountains and Salt Lake City, Utah. It is impossible to determine from the records whether all the localities were fresh water habitats, but that it is typically a fresh water form can ad mit of no possible doubt. It has been taken from the stomachs of trout from brooks near Marquette, Mich. species, in a peculiar and rather saline habitat.3 In the summer of 1920 the writers visited the Ice Spring Craters lava field of the Sevier Desert in the ancient Lake Bonneville basin described in detail by Gilbert.4 On climbing down into the old lava vent5 of the Terrace crater we were surprised to find a small crustacean abundant in the small pool of clear water at the bottom. It was noted that a number of the animals were very slightly pigmented, apparently indicating that in the semi-darkness of the pool they were approach ing cave conditions. In all instances, how ever, the eyes were fully pigmented. The presence of the Gammerus led to the assump tion that the water was non-saline and we were preparing to replenish our water bag when taste showed it to be distinctly brackish. A sample of the water was therefore taken in a clean Mason fruit jar from which it was afterwards transferred to citrate bottles for shipment to the laboratory. The water had a freezing point lowering of 0.410° C., indi cating an osmotic concentration of 4.94 atmospheres and an electrical conductivity of .0138 reciprocal ohm. The hydrogen ion con centration of the water (determined electro- metrically) was CH = 0.409 X 10'7 = PH7 -388. Analysis showed the following composition. s The genus Gammerus has species which occur in more or less saline coastal habitats and in non- saline inland waters. * Gilbert, G. K., "Survey West of the 100th Meridian," Vol. 3, pp. 136-144; also "Lake Bonneville," Monographs U. S. GeoL Survey, I., pp. 320-325, 1890. 6 The lava vent is a circular tube, at one side of the wide crater, about 12 feet in diameter inclined 10° or 15° from the vertical. It can be explored /or about 25 feet when progress is stopped by water. Grams per Liter Total solids (at 110°).. 8.5666 Total solids (at 210°) . . 8.1467 Total solids (ignited) e.. 7.6400 COy none HOO37 0.2187 Mineral Analysis Per Cent, of Grams Total Solids per Liter (Ignited) SiO2 0.0720 0.94 FeAAlA 0.0030 0.04 Ca 0.3305 4.33 Mg 0.2560 3.35 Na 1.9750 25.85 K 0.3050 3.99 Ol 3.4120 44.66 SO4 . , 1.3260 17.36 CO3s 0.1075 1.41 Total 777870 10L93 Hypothetical Inorganic Composition of the Solution Per Cent. Grams per Liter of Total Na^SiQ., 0.1460 1.84 Ca(HCO3)2 0.2913 3.68 CaSO< 0.8780 11.08 MgSO4 0.8855 11.18 MgCl2 0.3023 3.81 KC1 0.5875 7.42 NaCl» 4.8330 60.99 Total 7T9236 166700 « There was apparently considerable organic mat ter in solution. This could easily be derived from bat 'guano which was observed on the lava ledges surrounding the pool. 7 Carbonates and bicarbonates were determined by the titrametric method proposed by Scales (SCIENCE, N. S., 51, p. 214, 1920). s Calculated from bicarbonate data according to the formula 2RHCO3 + heat = BjCOs + C02 + H2O. 9 An average value based on NaCI contents of 4.8790 gr. calculated from residual Na and 4.7870 calculated from residual Cl. The difference of 0.092 gram per liter is within experimental error when one remembers that the above calculations are The Terrace crater, and indeed all of the craters of the Ice Spring Craters group, is un questionably post-Bonneville in origin. There is no trace of wave work on the outer slopes of the craters such as are so conspicuous on Pavant Butte to the north, and neither lacus trine sediments nor evidences of subaqueous erosion appear on the surface of the evidently recent lava fields as they do on the Fumarole Butte lava field to the northwest. The depth of the vent of the Terrace crater is 260 feet below its general rim and 220 feet below the sill of the last outflow. The prob lem of the original introduction of Gammerus into the small pool of water occupying the bottom of this crater is that of the transpor tation of small crustacean species or their eggs in general. The point of physiological interest is the occurrence of this species, hitherto reported from non-saline waters, in water of this concentration. ROSS AlKEN GORTNER, Division of Agricultural Biochemistry, Uni versity of Minnesota, J. ARTHUR HARRIS, Station for Experimental Evolution, Car negie Institution of Washington purely empirical and also when one considers that in some instances the actual analytical values, and consequently accompanying experimental errors, were multiplied by 50 to bring the calculation to a liter basis. Reprinted for private circulation from THE BOTANICAL GAZETTE, Vol. LXVI, No. 3, September 1918 SECONDARY PARASITISM IN PHORADENDRON BROWN'S' illustration of Phoradendron californicum parasitic on P. flavescens2 has a twofold interest. First, it records a case of secondary parasitism which seems to be very rare indeed. It has never, so far as I am aware, been noted by workers at the Desert Botanical Laboratory, a number of whom have been especially interested in parasitism. For the most part P. macrophyllum and P. californicum 'occur on quite different hosts.3 Second, the case is of interest physiologically, as BROWN suggests, in its relation to osmotic and other physical phenomena. HARRIS and LAWRENCE, in their study of the sap properties of Jamaican montane rain forest Loranthaceae,4 find that in these forms the sap extracted from the green stems of the leafless species shows lower osmotic concentration than that from the foliar tissues of the leafy forms. Thus in working with 7 species of Loranthaceae they found average values of the freezing point lowering of 1.153°, I-I7^°, and 1.177° in the leafless species as compared with i .305°, i .347°, i .400°, and 1.650° in 1 BROWN, J. G., Mistletoe vs. mistletoe. Box. GAZ. 65:193. jig. /. 1918. 2 This is presumably P. macrophyllum Cockerell, the P. flavescens macrophyllum of ENGLEMANN and of some subsequent workers, or one of its varieties. The host here, as Professor BROWN has kindly written me, was a Fraxinus. 3 TRELEASE (The genus Phoradendron, p. 14, Urbana. 1916) notes that P. cali fornicum, while occurring exclusively on angiosperms, belongs to a group, the "Pauci- florae," which with this and one other exception is limited to coniferous hosts. 4 HARRIS, J. ARTHUR, and LAWRENCE, J. V., On the osmotic pressure of the tissue fluids of Jamaican Loranthaceae parasitic on various hosts. Amer. Jour. Bot. 3:438-455. 1916. 275 276 KOTAMCAL GAZETTE [SEPTEMBER the leaves of the leafy forms. If the same is true of desert Loranthaceae, the relationship between leafless and leafy parasite observed by BROWN is just the reverse of what might be expected if successful parasitism were dependent upon higher osmotic concentration in the tissue fluids of the parasite. As pointed out elsewhere, however, the technical difficulties in the comparison of the tissue fluids of the stems and leaves by the methods as yet available for field work are rather great. In the leafless forms there is danger of including a considerable amount of fluids from woody conducting tissue not at all comparable with that of the green tissue which may be taken to be physiologically homologous with the leaf tissue of the leaves of the tree or of the leafy Loranthaceae. Furthermore, such work as has been done on the rather difficult problem of the physico- chemical properties of the tissue fluids of desert Loranthaceae5 is insuffi cient to show that the osmotic concentration is lower in the leafless desert forms. Furthermore, the concentration of the sap of desert forms seems to vary rather widely, and even if the average concentration of the fluids of P. californicum were lower than that of P. macrophylhtm, it is quite possible that the individual secondary parasite, P. californicum, had a higher concentration than its individual P. macrophyllum host.6 So far as I am aware, the only direct determination of osmotic con centration in primary and secondary parasitism in the Loranthaceae is that by HARRIS and LAWRENCE (loc. clt.) on the Jamaican broad- leaved Phthirusa parvifolia parasitic upon the leafless Dendrophthora gracilis, which is in turn parasitic upon a tree, Cyrilla racemi flora. The sap properties stand in the following relationship: Cyrilla raccmijlora, A = 1.1 8, P=i4.2; Dendrophthora gracilis (on Cyrilla racemiflora), A = 1.26, P=i5.2; Phthirusa parvifolia (on Dendrophthora gracilis), A =1.49, P=IJ.C). Osmotic concentration increases from the host to the primary parasite and from the primary parasite to the secondary one. Note also that the observed secondary parasitism is the leafy P. parvi folia with an average depression of i .347° upon the leafless D. gracilis with an average depression of i . 176°. — J. ARTHUR HARRIS. Cold Spring Harbor, N.Y. 5 HARRIS, J. ARTHUR, On the osmotic concentration of the tissue fluids of desert Loranthaceae. Mem. Torr. Bot. Club 17:307-315. 1918. 6 1 have individual determinations on P. californicum which indicate higher con centration than some found in P. macro phyllum. The great difficulty of comparing the sap properties of the two forms lies in the fact that, in the neighborhood of Tucson at least, they occur in the main on different hosts and for the most part in slightly different local habitats. THE INTERRELATIONSHIP OF THE NUMBER OF STAMENS AND PISTILS IN THE FLOWERS OF FICARIA. J. ARTHUR HARRIS. [Reprinted from BIOLOGICAL BULLETIN, Vol. XXXIV, No. i, January, 1918] [Reprinted from BIOLOGICAL BULLETIN, Vol. XXXIV., No. i, January. 1918.] THE INTERRELATIONSHIP OF THE NUMBER OF STAMENS AND PISTILS IN THE FLOWERS OF FICARIA. J. ARTHUR HARRIS. I. INTRODUCTORY REMARKS. A survey of the rapidly increasing literature must convince anyone that the problem of the factors which determine the sex of the organism is one of such complexity that it cannot be solved 'on the basis of any one kind of material or by any one method of research. In the flowering plants the same individual may produce both eggs and sperm. The relative numbers of egg and sperm pro ducing organs may vary from individual to individual, or from flower to flower within the individual. It is reasonable to assume that definite genetic, morphogenetic or physiological factors underlie these variations. Any success ful attempt to determine these factors and to measure their influence is just as truly a contribution to the wide problem of the physiology of sex as the more conventional breeding experi ments and studies on the morphology of the germ cells. The purpose of this paper is to point out certain hitherto unrecognized relationships between the number of sporophylls in the flower of the ranunculaceous genus Ficaria. Heretofore those who have investigated the problem of the relationship between the number of stamens and pistils in the flower have been content to merely determine the correlation between the number of the two kinds of spore-bearing organs. Positive correlations of this kind should arise as the resultant of any sets of environmental factors which tend to increase both the number of stamens and the number of pistils in certain of the plants or individual flowers and to limit the number of both of these organs in others. Morphogenetically and physiologically it seems of far greater importance to inquire whether the relative 7 J. ARTHUR HARRIS. proportion of the two types of spore bearing organs is correlated with the total number of sporophylls, which in lieu of any better character may serve as a measure of the total influence of in trinsic and extrinsic factors influencing degree of development. Several years ago Professor Pearson and I (Harris, '09) showed that problems of this kind can be approached by determining the correlation between the total organs laid down and the deviation of the number of a particular kind from the probable number on the assumption that the proportion of the particular kind is independent of the total number. The statistical method may of course be applied to experi mental data or to series of determinations made on organisms developing under natural conditions. As yet experimental series are not available. In a former paper ('16) I showed that in the inflorescences of both Arisarum vulgar e and A. proboscidium there is a significant negative correlation between the total number of flowers and the deviation of the number of staminate flowers from their probable number on the theory of proportional distribution. Thus the male flowers while absolutely more numerous in the inflorescences with larger total numbers of flowers are relatively less numerous than in the inflorescences with smaller total num bers of flowers. Or, conversely, the larger inflorescences tend to produce a larger proportion of pistillate flowers. In this paper the same analytical methods will be applied to the problem of the relationship of the number of stamens and the number of pistils to the total number of stamens and pistils produced by the flower. II. MATERIALS. The materials upon which the coefficients discussed in this paper are based have been tabled and the chief biometric con stants deduced by competent statisticians. The special methods upon which the conclusions of this paper are based were not, however, available at the time their calculations were made. The results are, therefore, quite new. The series employed are the following: 1-2. A series of 283 countings of number of stamens and NUMBER OF STAMENS AND PISTILS IN FICARIA. pistils of Ficaria verna from Trogen and another series of 80 countings from Gais, published by Ludwig ('01). Statistical constants for both of these series have been deduced and pub lished by Dr. Alice Lee ('02). 3-4. A series of 268 early and 373 late flowers of Ficaria ranunculoides collected by MacLeod ('99) and discussed by W. F. R. Weldon ('01). 5-8. Four series of Ficaria ranunculoides collected by Galton, Weldon, Pearson ('03) and others, in Italy, Guernsey and Eng land. III. PRESENTATION OF DATA. The means and variabilities of number of stamens and pistils per flower have been given in the papers cited. The only point which requires discussion in this place is the relative variability of the number of the two types of sporophylls. This is shown in Table I. TABLE I. RELATIVE VARIABILITIES IN NUMBER OF STAMENS AND NUMBER OF PISTILS IN Ficaria. Series. Number of Flowers. Coefficient of Variation for Pistils. Coefficient of Variation for Stamens. Differences Switzerland — Trogen, I 287 T« ^8 Gais, II 80 4.04 Belgium — Early, III 268 H-55 Late, IV 777 97 Sn 14,07 T£ Af\ 9-25 Italy, V 9-43 Guernsey, VI •23 England — • Dorset, VII. . . SO? yf, -,0 9-38 Surrey, VIII 500 27.19 17.32 9-54 9.87 The number of pistils is consistently more variable than the number of stamens. Other workers have shown that there is a correlation of medium intensity between the number of stamens and the number of pistils per flower. Their constants, all of which have been rechecked in the course of this work, are shown in Table II. I have also added the linear regression equations showing the rate of increase in mean number of pistils associated with an increase in the number of stamens and the rate of increase in 10 J. ARTHUR HARRIS. TABLE II. CORRELATION BETWEEN NUMBER OF STAMENS AND PISTILS IN Ficaria AND RE GRESSION EQUATIONS FOR STAMENS AND PISTILS. Series. Number of Flowers. Correlation Stamens and Pistils. Ratio of Correlation to Probable Error r/£r. Regression Line. Switzerland — Trogen 283 .530 ± .029 18.27 S = 11.708 + .645 P Gais 80 .388 ± .064 6.06 P S = 4.461 + .4295 = 19.075 + .262 P Belgium — Early 268 .507 ± .031 16.^=; P s 4.403 + .575-S = 18 197 + 489 P Late 373 •749 ± .015 49-93 P s 3.427 + .5255 = 9.006 + .729 P Italy 624 •439 ± .022 19.95 P s = ~ 1-593 + .769^ = I9-3I3 4~ -4i8P Guernsey 520 • 534 ± .021 25.4^? P s = 5.409 + .4605 — 18 302 -f- 404 P England — Dorset 505 .669 ± .017 39-35 P S = 4.160 + .707 5 = 20.369 + .535 P Surrey 500 .660 ± .017 38.82 P s = - 1-333 + .8355 = 19.091 + .588 P P = — .860 + .741 5 mean number of stamens associated with an increase in number of pistils per flower. The regression of the number of stamens on the number of pistils and of the number of pistils on the number of stamens is shown for three of the larger series in Figs. 1-3. The empirical means for the Italian series, Diagram i, do not conform very satisfactorily to the lines given by the equations. Better agreements between actual and theoretical means could hardly be found (in series of data no larger than these) than in the Guernsey and Surrey series represented in Figs. 2 and 3. The main purpose of the present paper is to present the results of the determination of the relationship between the total number of sporophylls and the number of stamens and pistils. The correlations between the total number of sporophylls and the number of stamens and pistils are shown in Table III. As is to be expected the correlations between total sporophylls and number of stamens and pistils are high. The constants showing the relationship between the total number of sporophylls and the deviation of the number of NUMBER OF STAMENS AND PISTILS IN FICARIA. II 8 A? /2 /4 /6 /8 20 22 24 26 28 30 32 34 36 38 4-0 42 FIG. i. Average numbers of stamens in flowers with various numbers of pistils and average numbers of pistils in flowers with various numbers of stamens. Empirical and smoothed values. Italian series. TABLE III. CORRELATION BETWEEN TOTAL SPOROPHYLLS AND NUMBER OF STAMENS AND PISTILS AND BETWEEN TOTAL SPOROPHYLLS AND DEVIATION OF THE NUMBER OF STAMENS AND PISTILS FROM THEIR PROBABLE VALUE. Series. Correlation Between Sporophylls and Stamens. r»,-1 r/£r. Correlation Between Sporophylls and Pistils. -V I. II. III. IV. V. VI. VII. VIII. .pOI ± .008 •755 ± -032 .862 ± .on .933 ± -005 .840 ± .O08 .836 ± .009 .892 ± .027 .900 ± .006 - .139 ±-039 - .548 ± .053 - .378 ± .035 - .477 ±-027 - .354 ±.024 - .433 ± .024 - .487 ± .023 - .463 ± -024 3-52 10.37 10.69 17-74 14.99 18.04 21-37 19.64 .845 ± .012 .896 ± .015 .873 ± .010 .936 ± .004 .855 ± .007 .9IO ± .005 .932 ± .004 .921 ± .005 +.139 ±.039 +.548 ± .053 +.378 ±.035 +.477 ±.027 +.354 ±.024 +.433 ± -024 +.487 ±.023 +.463 ± -024 1 Correlation between sporophylls and deviation of stamens from their probable value. 2 Correlation between sporophylls and deviation of pistils from their probable value. 12 J. ARTHUR HARRIS. macro- and the number of microsporophylls from their probable value are the coefficients of critical value. These are also given in Table III. The correlations for stamens and pistils are necessarily equal in magnitude but opposite in sign. They show that the number of pistils is relatively larger in the flowers with larger numbers of sporophylls. The results are consistent in sign throughout. All of the correlations except that for the series from Trogen may be considered certainly significant in comparison with their probable errors. While the constants for certain of the series differ significantly, the results are (considering the relatively small numbers and the very wide geographical distribution of the material) very con sistent. Five of the eight series differ from r = ± .50 by less than twice their probable error. Of the other three series, only Professor Ludwig's Trogen material is very aberrant. For two of the series I have determined the standard devia- /6 /? 20 22 2.4 2? 28 30 32 3,4 3ff 38 40 42 4,4- 4,6 FIG. 2. Empirical means and regression straight lines for regression of stamens on pistils and pistils on stamens. Guernsey series. NUMBER OF STAMENS AND PISTILS IN FICARIA. /4 , /j? 20 22 24 26 2? 3tO 32 3,4- 36 38 40 42 44 46 FIG. 3. Explanation as in Figs, i and 2. English series. tion of the deviation of the number of stamens (or pistils) from their probable value by a formula to be published shortly ('17). They are : For Bordighera,