THE DECENNIAL PUBLICATIONS OF THE UNIVERSITY OF CHICAGO THE DECENNIAL PUBLICATIONS ISSUED IN COMMEMORATION OF THE COMPLETION OF THE FIRST TEN YEARS OF THE UNIVERSITY'S EXISTENCE AUTHORIZED BY THE BOARD OF TRUSTEES ON THE RECOMMENDATION OF THE PRESIDENT AND SENATE EDITED BY A COMMITTEE APPOINTED BY THE SENATE EDWARD CAPPS STARR WILLARD CUTTING ROLLIN D. SALISBURY JAMES ROWLAND ANGELL WILLIAM I. THOMAS SHAILER MATHEWS CARL DARLING BUCK FREDERIC IVES CARPENTER OSKAR BOLZA JULIUS STIEGLITZ JACQUES LOEB .•.*f THESE VOLUMES ARE DEDICATED TO THE MEN AND WOMEN OF OUR TIME AND COUNTRY WHO BY WISE AND GENEROUS GIVING HAVE ENCOURAGED THE SEARCH AFTER TRUTH IN ALL DEPARTMENTS OF KNOWLEDGE INVESTIGATIONS THE UNIVERSITY OF CHICAGO FOUNDED BT JOHN D. BOCKEFELLEB INVESTIGATIONS EEPEESENTING THE DEPAETMENTS ZOOLOGY ANATOMY PHYSIOLOGY NEUROLOGY BOTANY PATHOLOGY BACTERIOLOGY THE DECENNIAL PUBLICATIONS FIRST SERIES VOLUME X CHICAGO THE UNIVERSITY OF CHICAGO PRESS 1903 Copyright 1903 BY THE UNIVERSITY OF CHICAGO CONTENTS I. On the Production and Suppression of Muscular Twitchings and Hypersensitiveness op the Skin by Electrolytes - - - 1 By Jacques Loeb, Professor and Head of the Department of Physi- ology II. On a Formula for Determining the Weight of the Central Ner- vous System of the Frog from the Weight and Length of its Entire Body ----__-__ 15 By Henry H. Donaldson, Professor and Head of the Department of Neurology III. The Development of the Colors and Color Patterns of Coleop- tera, with Observations upon the Development of Color in Other Orders of Insects (with Plates I-III) . _ . 31 By William Lawrence Tower, Assistant in Embryology IV. The Artificial Production of Spores in Monas by a Keduction OF the Temperature - - - -- - --71 By Arthur W. Greeley, Assistant in Physiology V. The Self-Purification of Streams ___-_- 79 By Edwin Oakes Jordan, Associate Professor of Bacteriology VI. The Lecithans : Their Function in the Life of the Cell ~ 91 By Waldemar Koch, Assistant in Pharmacology VII. A Contribution to the Physical Analysis of the Phenomena of Absorption of Liquids by Animal Tissues - - - - 103 By Ralph Waldo Webster, Assistant in Physiological Chemistry VIII. The Distribution of Blood-Vessels in the Labyrinth of the Ear of Sus Scrofa Domesticus (with Plates V-XII) _ . - 135 By George E. Shambaugh, Instructor in Anatomy of the Ear, Nose, and Throat n 127055 X Contents IX. The Animal Ecology of the Cold Spring Sand Spit, with Remarks ON the Theory op Adaptation _--_-. 155 By Charles Benedict Davenport, Associate Professor of Zoology and Embryology X. The Finer Structure of the Neurones in the Nervous System of the White Rat (with Plates XIII, XIV) - - - - 177 By Shinkishi Hatai, Research Assistant in Neurology XI. The Phylogeny of Angiosperms - 191 By John Merle Coulter, Professor and Head of the Department of Botany XII. Studies in Fat Necrosis - - - 197 By H. Gideon Wells, Instructor in Pathology XIII. Oogenesis in Saprolegnia (with Plates XV, XVI) - - - 225 By Bradley Moore Davis, Assistant Professor of Botany [Hull Botanical Laboratory] XIV. The Early Development of Lepidosteus Osseus (with Plates XVII, XVIII) ---------- 259 By Albert Chadncey Eycleshymer, Assistant Professor of Anatomy XV. The Structure of the Glands of Brunner (with Plates XIX- XXIV) 277 By Robert Russell Bensley, Assistant Professor of Anatomy XVI. Mitosis in Pellia (with Plates XXV-XXVII) - - - - 327 By Charles Joseph Chamberlain, Instructor in Morphology and Cytology XVII. A Description of the Brains and Spinal Cord of Two Brothers Dead of Hereditary Ataxia. (Cases XVIII and XX of the Series in the Family Described by Dr. Sanger Brown); (with plates XXVIII-XXXIX) -------- 347 By Lewellys Franklin Barker, Professor and Head of the Depart- ment of Anatomy. With an Introduction by Dr. Sanger Brown WEIGHT OF THE CENTRAL NERVOUS SYSTEM OF THE FROG \- ON A FORMULA FOR DETERMINING THE WEIGHT OF THE CENTRAL NERYOUS SYSTEM OF THE FROG FROM THE WEIGHT AND LENGTH OF ITS ENTIRE BODY Henry H. Donaldson As THE living substance which constitutes the animal body becomes differen- tiated into distinct tissues, the animal as a whole becomes more highly organized. The fundamental tissues which are thus formed — namely, the epithelial, connective, muscular, and nervous — are distinguished by the fact that each of them exhibits one or more of the general characteristics of protoplasm developed to a greater or less degree, whereas other of the characteristics are much less evident or apparently entirely lacking. The combined activities of these differentiated tissues are exhibited in the life-history of the entire animal. For the understanding of such an animal it is important to know the proportions of the several tissues present in any instance, and whether we study the animal from the standpoint of the number and size of the cell elements which constitute each tissue, or from the more general standpoint of the weight of modified living substance possessing the peculiar physiological characteristics of the tissue, the animal could be described in terms of the analysis, that is, in quantitative terms of the several systems of tissues which compose it. Thus, when tested in this way, animals like the dog, rabbit, and cat are found to be dissimilar in their make-up, and a snake, for example, has a different tissue com- position from a frog. To determine that these animals are thus differently constituted is merely a first step, and is naturally followed by the attempt to determine whether there are any laws governing the quantitative relations of these tissues either in the animal series or in the same animal during its life-cycle. If it could be shown that one system varies in a definite relation to any or all the others, we should have made a further step toward a comprehensive knowledge of the animal examined ; and it is believed that the facts here to be presented constitute such a step. The following paper describes the weight relations of the central nervous system (brain and spinal cord combined) of the frog, to the tissues constituting the rest of the body. The connection of this investigation with work already done along similar lines can be stated very briefly. An attempt by Snell (1892) to correlate the increase in the weight of the encepha- lon with some change in the remainder of the body led him to conclude that among mammals and birds the weight of the encephalon increased in proportion to the area of the body, when animals of different sizes, but otherwise similar, were compared. 17 'i Weight of the Central Nervous System of the Frog DuBois (1898) took up this conclusion of Snell and elaborated it (for mammals alone), making a more careful analysis of the conditions underlying the calculation, and finally giving a formula for the relative weight of the encephalon in mammals, which is very satisfactory, and which differs but slightly from the formula given by Snell. The study of the work of Snell and DuBois led me to attempt the extension of their results. Their formulae apply to the relative weights of the encephala in mature mammals, so that, in order to get the absolute value, the weight of one of the pair of encephala must be known. They do not discuss the increase of the encephalon in weight in the same mammal during its growing period, nor do they extend their observations to other classes of vertebrates or to the entire central nervous system. In the present instance we have sought to determine whether we could obtain a formula which would express the weight of the entire central nervous system at any time during the growing period of an animal, and in this instance have chosen the frog. For the study of this problem there were available in the laboratory records on two species of frogs, the bullfrog and leopard frog. It may be noted in passing that for a study of this kind the frog presents certain advantageous peculiarities, as it exhibits only a comparatively slight alteration in the bodily proportions during growth. Like other vertebrates, its increase in length is most rapid during the earlier portion of the growing period, and later, the increase in length becoming slow, the body enlarges at right angles to its long axis, and the animal becomes thicker. Nevertheless, the weight relations between the muscles of the legs and the remainder of the body remain nearly constant (Donaldson, 1898; Donaldson and Schoemaker, 1900), and in this respect the frog shows but very slight changes in proportion. In the foregoing characters the two species which have been examined, the bull- frog [Rana catesbiana) and the leopard frog [Rana virescens), were nearly alike. For each species the series of observations was extensive, comprising data on the body weight and length, and also on the weight and length of the brain and spinal cord, together with other measurements not needed for this investigation (Donaldson, 1898; Donaldson and Schoemaker, 1900). On looking at the curve previously published, for the weights of the brain and spinal cord arranged according to the body-weight (Donaldson and Schoemaker, 1900, p. 117), it appeared that the weights for the central nervous system (brain and spinal cord combined) were so related as to suggest a logarithmic curve, and this suggestion was at once tested.' The trial was made by forming a curve depending on the logarithms of the body- 1 In a paper entitled " Zur Anthropologie des Riicken- the body-weights of the dogs examined, and find that it markes" (Coi-resp.-Bl. d. deutsch. Anthrop. Gesellsch., No. gives a much flatter curve than that based on the weights 10,1895), Ranke presents observations on the weight of the of the spinal cords. In this instance, therefore, a logarith- spinal cord in dogs of different body-weights. He suggests mic relationship between the nervous system (spinal cord) that the curve which illustrates his Tabelle 3 has the form and the rest of the body does not appear, but, so far as I am of a logarithmic curve, but does not test the suggestion. aware, this is the first record of the suggestion that such a I have determined the curve formed by the logarithms of relationship might exist. 18 Henky H. Donaldson weights. To raise these logarithms to the value of the observed weights of the central nervous system they required to be multiplied by a constant factor. It was found that the factor which gave a correct value for the smallest frog was too small for all of the succeeding cases, the resulting numbers falling more and more below the observed numbers as the frog became larger. In order, therefore, to make the curve based on the calculated weights fit with that based on the weights observed, there was needed a second factor, the value of which should steadily increase as the body- weights of the frogs became heavier. Such a factor was found in the length of the frog, which increases rather rapidly at first and more slowly later. The unmodified lengths showed, however, too rapid an increase in the course of the series, but various trials revealed that the fourth root of the lengths gave a set of numbers which could be satisfactorily used. It was found, then, that the number obtained by multiplying the logarithm of the body-weight by the fourth root of the length of the body was always a nearly constant fraction of the observed weight of the central nervous system. In the case of the bullfrog the fraction thus obtained was one-thirtieth of the observed weight, while in the case of the leopard frog it was one twenty-eighth. It could, therefore, be made equal to the observed weight by multiplying it by a constant factor having the value of the denominator of the fraction. In this manner a formula was developed as follows : C.N.S. = (Log W X i/L) C. Here the weight of the central nervous system [C.N.S.), in milligrams, is made equal to the logarithm of W, the body-weight, expressed in grams, multiplied by the fourth root of L, the length of the body, in millimeters, the product of these factors being raised to the value of the observed weight of the central nervous system by multiplying by a constant, C. This constant, in the case of the bullfrog, has the value of 30, and, in the case of the leopard frog, the value of 28. To illustrate the application of this formula, we may take as an example the first record. No. 6, in Table I, p. 7. Here W, the weight of the body, is 5,02 grams, and L, the length of the body, is 93 millimeters. As this is a bullfrog, the value of the constant C is 30. Thus : C.N.S. = (Log W X l^Z) 30 = (0.7007 X 3.105)30 = (2.17) 30 = 65.1 = 65 milligrams. The calculated weight of the central nervous system is therefore 65 milligrams. The observed value was 62 milligrams ; thus the calculated exceeded the observed value by 4.8 per cent. In like manner the weight of the central nervous system was calculated in each of the cases entered in the table. While the formula applies to all the cases which are presented in the tables given in this paper, it does not apply to all the cases in the original tables (Donaldson, 1898, pp. 328-30; Donaldson and Schoemaker, 1900, pp. 120, 121), and its validity can, therefore, be seriously questioned, unless we are able to show that those cases to which it does not apply are capable either of 19 6 Weight of the Central Nervous System of the Frog explanation or correction. The formula is constructed so as to express the normal changes in the weight and length of body as related to the weight of the central nervous system — changes which are taking place as the frog grows larger. But it remains to be determined, first, how early in the history of the frog the formula can be applied, and, second, whether sex, season, and nutritive conditions are able to affect the result ; the nutritive condition including not only those changes which may occur from day to day, but those which occur from spring to autumn. Repeated examination shows that the formula does not apply to frogs until they have attained a body -weight of approximately 5 grams. For example, in a bullfrog with a body- weight of 3.53 grams the observed weight of the central nervous system was 56 milligrams, whereas the calculated weight was only 49 milligrams. A similar result is obtained when the test is applied to the leopard frogs under 5 grams of body- weight; hence, for frogs of this size, the calculated weight of the central nervous system is too small. The failure of the formula to apply to the smallest frogs is probably due to the precocious enlargement of the central nervous system — a character of all young verte- brates, and one still evident in frogs when less than 5 grams in weight. We conclude, therefore, that the relations found in the mature frogs are not established until they have attained a body-weight above 5 grams. From this point on the formula applies to all normal specimens. For the consideration of other sources of error it will be most advantageous to examine the two species of frogs separately. We begin with the bullfrogs. The original table for the bullfrogs (Donaldson, 1898) contains fifty-two cases. The first five cases (Nos. 1-5) are from frogs below 5 grams in body weight, and for this reason are excluded. Among the remaining forty-seven cases, six (Nos. 7, 32, 34, 37, 40, 47 in the original table) are marked "dry," which means that through drying their body-weight had been reduced below the normal. These also are excluded. No. 9 in this table is plainly abnormal, as is seen by comparing the body- weight with the length (body-weight, 8.75 grams; length, 127 millimeters), and for this reason is also excluded. For the foregoing exclusions no explanation is required, as, under the circumstances, one could not expect the formula to apply to them. There are, however, six more cases to be excluded, namely Nos. 10, 11, 43, because the body weight had been increased by the absorption of water ; and Nos. 45, 48, and 49, because long captivity had produced a loss of weight through starvation. The absorption of water by frogs whose vitality is much reduced is a familiar reaction, and the effects of starvation have been reported in earlier observations from this laboratory (Donaldson and Schoemaker, 1900, p. 112). In this series no correction for season is required, as the records are all from July and August frogs, and hence comprise midsummer frogs only. The final table contains, therefore, thirty-four records of approximately normal frogs to which the formula had been applied. These are presented in Table I. 20 O'" THE Henry H. Donaldson vr TABLE I Containing thirty-four records from bullfrogs (based on Table VII, Donaldson, 1898). This table shows in successive columns the original tabular number, the sex, body-weight, length, and the observed and calculated weights of the central nervous system in milligrams. The last two col- umns show the percentage deviation of the calculated from the observed weights of the central nervous system; the percentages being computed on the observed values as the standard. Tabtilae Number Sex Body Weight of Central, Ner- vous System in Milligrams Percentage Deviation of Calculated from Observed Weights Weight in Grams Length in Millimeters Observed Calculated Deficiency Excess 6 Male 5.02 93 62 65 4.8 8 Male 5.38 95 72 68 5.5 12 Male 11.37 125 108 106 1.8 13 Female 13.77 136 116 115 0.8 U Female 16.03 145 122 125 2.4 15 Male 20.33 159 144 139 3.4 16 Male 27. a3 167 153 155 1.3 17 Female 27.51 173 170 157 7.6 18 Male 32.95 184 165 168 1.8 19 Female 36.32 182 163 172 5.5 20 Female 37.46 188 185 175 5.4 21 Male 49.50 192 181 189 4.4 22 Female 49.82 202 187 192 2.6 23 Female 50.43 203 200 193 3.5 24 Male 51.77 200 201 193 3.4 25 Female 58.46 210 184 202 9.7 26 Female 60.12 211 205 203 1.9 27 Female 66.67 218 215 210 2.3 28 Female 73.05 231 212 218 2.8 29 Male 76.69 231 233 220 5.5 30 Male 87.05 231 223 227 1.7 31 Male 98.00 240 226 235 3.9 33 Male 144.50 280 255 265 3.9 35 Male 146.70 284 273 267 1.4 36 Female 146.90 275 279 265 5.0 38 Female 169.50 275 262 272 3.4 39 Male 184.60 284 287 275 4.1 41 . Male 191.76 313 290 287 1.0 42 Male 199.10 312 299 290 3.0 44 Male 212.50 304 306 292 4.5 46 Female 225.20 303 305 294 3.6 50 Male 244.60 313 292 301 3.0 51 Female 272.10 340 306 314 2.2 52 Male 313.00 343 321 322 0.3 A\ ^erage 212 211 3.8 3.0 1 Difference, 1 milligram; percentage, 0.4. 21 8 Weight of the Central Nervous System of the Frog This table gives the original tabular number, sex, body-weight (without ovaries in the case of the females), length from tip of nose to tip of longest toe, observed and calculated weights of the central nervous system, together with the percentage by which the calculated departs from the observed weight; the observed weight being always considered as the standard. The conditions under which these measurements were made are given in full in an earlier paper (Donaldson, 1898, pp. 323 ff. ). In the foregoing table the records in each case are for single observations. When the averages of the weights of the central nervous system, observed and calculated, are determined, it is seen that the average of the observed weights is 212, while that of the calculated is 211, thus giving a difference of only 0.4: per cent. That this small difference is the expression of discrepancies that are only slight is indicated by the fact that, if the entire series of records be divided into three groups, formed respect- ively by the first eleven, second eleven, and last twelve, and the difference in the average values of the observed and calculated weights be taken for each group, we obtain the percentage differences given in the following table: TABLE II To show the average percentage differences in the values of the observed and calculated weights of the central nervous system in three groups, formed from the records in Table I. Qkoup Tabulae Numbers Number of Records Percentage Difference ; the Observed Values Being Taken as the Standard Deficiency Excess A B C 6-21 22-a3 35-52 11 11 12 0.6 1.0 0.8 It is thus seen that the percentage difference between the averages does not in any group exceed 1 per cent, and consequently we may infer that, if the records were based on averages of eleven or more individuals for each entry, the agreement of the observed and calculated values would be well within 1 per cent. Another method of testing these results is by determining the relation of the per- centage differences calculated for the individual cases. On enumerating the cases in which the calculated values are in excess, it is found that they are just seventeen, or one-half the total number of records, thus leaving seventeen cases where the calculated values are below those observed. Table I shows that the average value of the per- centage deviations exhibiting deficiency is 3.8 per cent., while for those in excess it is 3.0 per cent. The plus and minus percentage deviations, therefore, nearly balance, as they should do if they depended on accidental causes. We see, therefore, that the formula gives results very close to those observed. On 22 Henry H. Donaldson looking at the curve (Fig. 1) we note that the calculated weights vary less from frog to frog than do those observed, and it thus happens that the line joining the dots which mark the calculated weights threads its way between the crosses which indicate the observed weights. Thus the weight of the central nervous system as calculated is less irregular than that directly observed. Before commenting further on these results the observations on Bana virescens will be presented. In the case of Rana virescens the original table contained thirty- six records (Donaldson and Schoemaker, 1900, p. 120). Of these, Nos. 1, 2, 3 are at once excluded as being below the 5-gram limit. Of the remaining 83, one. No. 16, through some error, has a body-weight too small for its length (27.19 grams body- weight; 195 millimeters length), and four more, Nos. 33, 34, 35, 36, all of them spring frogs, have body weights which are manifestly too small, as is shown by the relation of these records in the curve already presented (Donaldson and Schoemaker, 1900, Chart I, p. 117). As there are no data for correcting these last four records, they are excluded from the series here used. After these removals there remain twenty -eight records taken at different times from April 14 to September 15. Some unpublished work on the seasonal change in the nervous system of the frog shows that in frogs of the same body-weight the weight of the central nervous system is subject to a rhyth- mic change, thus altering according to the season of the year. During the past twelve months observations have been carried on in this labora- tory with a view to following this change in some detail, and at present we have at hand data which enable us to correct the weight of the central nervous system in these frogs in the early and late season so as to make the observations taken at those times comparable with the records from midsummer frogs. To standardize these early and late records which appear in Table IV, corrections have been made in twelve instances in accordance with a fixed scale. This scale is based on the following observations: It appears that frogs of a given body weight, just after they emerge at the end of March or the first of April, have a relatively small weight of central nervous system. TABLE III Showing the corrections made in the spring and autumn frogs, the weight of whose central nervous system appears in Table IV. No. in Date Percentage No. in Percentage Table IV Correction Table IV Correction 31 April 14 +4 23 June 5 -5 17 April 19 +4 26 June 5 -5 13 May 21 -1 10 June 9 -5 28 May 21 -1 29 September 10 +3 5 May 31 -2 30 September 12 +3 9 June 3 -5 22 September 15 +3 23 10 Weight of the Central Nervous System of the Frog This increases from 9 per cent, to 10 per cent, between the time of emergence and the first ten days of June, when it reaches a maximum. In undergoing this change the frog passes the midsummer weight about May 15. From this maximum the weight table IV Containing twenty-eight records from leopard frogs (based on Table VII, Donaldson and Schoemaker, 1900). This table shows in successive columns the original tabular number, the sex, body-weight, length, and the observed and calculated weights of the central nervous system in milligrams. The last two columns show the percentage deviation of the calculated from the observed weights of the central nervous system; the percentages being computed on the observed values as the standard. Tabular Sex Body Weight of Central Ner- vous System in Milligrams Percentage Deviation of Calculated from Observed Weights Weight in Grams Length in Millimeters Observed Calculated Deficiency Excess 4 Female 5.06 102 68 63 7.3 5 Female 7.85 124 82(c) 84 2.4 6 Female 10.90 136 103 99 3.9 7 Female 11.41 139 99 102 3.0 8 Male 12.30 141 106 105 0.9 9 Female 14.85 153 116(c) 115 0.8 10 Male 16.26 164 122 (c) 121 0.8 11 Male 16.31 160 121 121 0.0 0.0 12 Male 17.13 166 122 124 1.6 13' Male 19.91 160 131 (c) 129 1.5 14 Female 20.35 162 130 131 0.7 15 Male 23.45 168 134 138 2.9 17 Male 27.42 172 142 (c) 146 2.8 18 Female 29.40 185 143 152 6.2 19 Female 30.45 179 141 152 7.8 20 Female 33.96 172 152 155 1.9 21 Male 36.03 198 171 164 4.0 22 Male 38.16 200 161 (c) 166 3.1 23 Female 42.54 215 177 (c) 175 1.1 24 Female 44.75 208 188 175 6.9 25 Male 45.37 205 174 176 1.1 26 Female 46.00 216 179 (c) 178 0.5 27 Female 47.58 206 191 178 6.8 28 Female 48.33 220 174 (c) 182 4.6 29 Female 52.55 206 180(c) 182 1.1 30 Female 55.25 215 186 (c) 187 0.5 31 Female 61.10 226 193 (c) 194 0.5 33 Female 70.98 239 213 204 4.2 Av erage 146 146 2.9 2.5 Difference, 0 milligram; percentage, 0.0, 24 Henky H. Donaldson 11 drops rather rapidly, about 5 per cent., to the end of June. In July and August it remains, with slight fluctuations, comparatively, constant, and at the beginning of September falls off from 2 per cent, to 4 per cent, as the frogs enter upon hibernation. These observations of course apply strictly only to frogs subjected to the climatic con- ditions found in Chicago and the neighborhood within a radius of one hundred miles. In the preceding Table III we have indicated the tabular number of the frog, the weight of whose nervous system has been corrected, the date at which the initial observation was made, and the amount of the correction. The correction is entered in this table as a percentage of the observed weight, the -|- sign indicating that the amount was added and the sign — that it was subtracted. In Table IV the observed weight of the nervous system which is there given for these cases is the corrected weight, and the fact that it is a corrected weight is indi- cated by the small letter (c) which follows the entry. The other records in Table IV are from frogs killed in July and August, and are therefore classed as midsummer frogs. It will be recalled that in the case of Rana virescens the formula for calculating the weight of the central nervous system is the same as that for the bullfrog, except that the constant, C, is 28 instead of 30. The formula reads, therefore: C.N.S. = (Log T^ X f/L) 28. It is with this formula that the calculations appearing in Table IV have been made. The construction of Table IV is similar to that of Table I. On applying to the records in Table IV the same tests as were used in the case of the bullfrog. Table I, we obtain results which are in some respects more satisfac- tory. It will be seen that the average weight of the central nervous system as calcu- lated is exactly equal to the average weight observed. Further, if we divide the twenty-eight records into three groups of nine, nine, and ten, respectively, indicating the groups as A, B, and C, then the percentage differences for each group are seen to be also small — Table V. TABLE V To show the average percentage differences in the values of the observed and calculated weights of the central nervous system in three groups, formed from Table IV. Group Tabulae Number Number of Records Percentage Difference ; the Observed Values Being Taken as the Standard Deficiency Excess A B C 4-12 13-22 23-33 9 9 10 0.5 1.3 2.0 This shows a maximum deviation for Group B of 2 per cent., but it seems probable that a series of records based on averages would coincide more closely than this. On 25 12 Weight of the Central Nervous System of the Frog examining in the leopard frog the percentage deviations, we find in one case (No. 11) exact coincidence, in twelve cases the calculated value is deficient, and in fifteen cases it is in excess. The average value of the deficiencies is 2.9 per cent., and of the excesses 2.5 per cent. These nearly balance, and point therefore to accidental causes as the source of the deviations. These results for the leopard frog show that the curves fit somewhat better than in the case of the bullfrog, but the difference is not large nor significant. The state- ments that were made concerning the relations of the curves showing the observed and calculated weights in the bullfrog are also true for the corresponding curves based on the leopard frog. It will be seen (Fig. 1) that in order to get the curves for the two species on the same chart, where they might be compared without being confused, the records for the leopard frog have been shifted 50 grams to the right. This enables us to see the approximate parallelism between the two curves, despite the fact that the leopard frog is differently shaped from the bullfrog, being somewhat more slender and having the relative weight of its trunk slightly less than that of the bullfrog (Donaldson, 1898, p. 334, Table IX; Donaldson and Schoemaker, 1900, p. 124, Table VIII). This slight difference in construction probably accounts for the necessity of using a smaller constant in the formula employed for the leopard frog, since the weight of the central nervous system would most probably be closely correlated with the development of the trunk. It is interesting to note, before leaving these records, that there is appar- ently no modification of the formula necessary for sex, in the case of either species. If we select the females from Table I, for the bullfrog, we find that they represent sixteen cases, or nearly one-half the number in the table. Arranging the records according to the tabular number, we have the percentage deviation for each case as given in Table I. TABLE VI Showing the percentage deviation for the female bullfrogs entered in Table I. Percentage Deviation Tabclae Number Percentage Deviation Deficiency, (7) Records Excess, (9) Records Deficiency, (7) Records Excess, (9) Records 13 14 17 19 20 22 23 25 2.4 5.5 2.6 9.7 0.8 7.6 5.4 2.5 26 27 28 35 36 38 46 51 2 3 2 8 4 2 1.9 2.3 1.4 5.0 3.6 Average deficiency, 4.1 per cent.; average excess, 3.4 per cent. 26 Henry H. Donaldson 13 On comparing the averages for the percentage deviations in these two columns we find the average for the excess 3.4 per cent., while that for the deficiencies is 4.1 per cent. — results practically the same as those obtained for both sexes in Table I. TABLE VII Showing the percentage deviation for the female leopard frogs entered in Table III. Percentage Deviation Tabular Number Percentage Deviation Tabular Number Deficiency, (10) Records Excess, (8) Records Deficiency, (10) Records Excess, (8) Records 4 5 6 7 9 14 18 19 20 2.4 3.0 0.7 6.2 7.8 1.9 7 3 0 3 9 8 23 24 26 27 28 29 30 31 33 4.6 1.1 0.5 0.5 1.1 6.9 0.5 6.8 4.2 Average deficiency, 2.9 per cent.; average excess, 3.9 per cent. In this case the results are similar to those found in the female bullfrogs, except that the larger average percentage is on the excess side. From these observations we conclude that in normal summer frogs of both sexes it is possible to calculate, with a high degree of accuracy, by the formulae here employed, the absolute weights of the central nervous system. Should others be inclined to test the correctness of these results by repeating the observations, it will be necessary carefully to avoid the sources of error which have been here enumerated, namely, the limitations of small size, the effect of season in the spring and autumn, and of the nutritive condition of the frog, as represented by starva- tion on the one hand, and the abnormal absorption of water or of drying on the other. With these results in hand it is natural to seek for an interpretation of the formula which has been given in order to correlate it in detail with the changes which we know are going on in the central nervous system of the animals under examination. In the first place, the changes in the central nervous system, which the formula expresses, must take departure from the conditions which are present in the smallest frogs exam- ined. In such a frog the central nervous system is composed of the supporting struc- tures, neuroglia and ependyma, together with the blood and lymph vessels, and the nerve cells. These last form by far the greatest part of the substance. The nerve cells, or neurones, may be divided into those which are immature and those already 27 14 Weight of the Central Nervous System of the Frog matured, in the sense that these latter have sent out both kinds of branches, dendrites and axone, and that the axone has acquired a medullary sheath. As the frog grows larger the nervous system increases in weight. Concerning the method of this increase the following statements can be made: First, there is no cell division in either the supporting tissues or the nervous tissues at this time ; hence the increase in weight is due to the enlargement of cell elements which are already present in the system. In the case of the neurones already developed and function- ally active, this enlargement means an increase in the volume of the cell bodies, in the number and size of the dendrites, and in the length and diameter of the axone and its medullary sheath. In the case of the undeveloped neurones, it means a rather rapid acquisition of the branches and medullary sheath, to be followed by the slower changes just described above. In general, these changes tend to increase the com- plexity of the entire system, but, so far as they represent a mere lengthening of the connecting axones and a mere increase in their diameter, the added weight does not necessarily imply the increase in complexity, but only a passive adaptation of the system to the increasing size of the cavities in which it is contained. The formula which we have employed indicates that where the body-weight is expressed by numbers increasing in geometrical progression, the weight of the central nervous system is expressed by numbers increasing in arithmetical progression, these latter being multiplied by a factor derived from the length of the entire animal. Certainly this factor, depending on the length of the frog, is to be associated with the increase in the length of the brain and cord, but no satisfactory interrelation between this factor and this part of the growth process has been established. We are compelled, therefore, at this time to be content with pointing out the entire series of events which the formula expresses, without attempting to correlate any portion of the formula with any special part of the growth change. SUMMARY The formulsB here presented apply to the two species of frog: R. cateshiana, the bullfrog, and R. virescens, the leopard frog. The best results are obtained when frogs taken in midsummer (months of July and August) are alone used. The frog must be in normal condition and have a body-weight of 5 grams or more. When these conditions are fulfilled, then the weight in milligrams of the central nervous system [C.N.S.) of the bullfrog can be determined with a high degree of accuracy by the formula C.N.S. = (Log W X f/L) 30, where W is the weight of the frog in grams, L the entire length in millimeters, and 30 a constant peculiar to the species. In the same way the weight of the central nervous system [C.N.S.) in milligrams can be determined for the leopard frog by the formula 28 i Henky H. Donaldson 15 C.N.S. = (Log W X 1^ i) 28. This formula is similar to that for the bullfrog, except as regards the constant, which for the leopard frog is 28. BIBLIOGRAPHY Donaldson, H. H., 1898. " Observations on the Weight and Length of the Central Nervous System and of the Legs in Bull-Frogs of Different Sizes." Journal of Comparative Neurology, VIII (1898), pp. 314-35. Donaldson, H. H., and Schoemakeb, D. M., 1900. "Observations on the Weight and Length of the Central Nervous System and of the Legs in Frogs of Different Sizes (Rana virescens brachycephala — Cope)." Journal of Comparative Neurology, X (1900), pp. 109-32. DuBois, E., 1898. " Ueber die Abhangigkeit des Hirngewichtes von der Korpergrosse bei den Saugethieren," Archiv fur Anthropologie, XXV (1898), pp. 1-32. Snell, O., 1892. "Die Abhangigkeit des Hirngewichtes von dem Korpergewicht und den geistigen Fahigkeiten." Archiv fiir Psychiatrie und Nervenkrankheiten, XXIII (1892), pp. 436^6. EXPLANATION OF FIGURE I For this figure the data in Tables I and IV have been employed, and the accuracy of the figure can be tested by comparison with the tables. The divisions on the base line indicate grams of body- weight; the divisions on the ordi- nates, milligrams of weight of the central nervous system. The observed weight of the central nervous system in milligrams is marked by + on the line of the ordinate above the point on the base line corresponding to the body-weight of the frog from which the central nervous system was taken. The calculated weight of the central nervous system is marked on the same ordinate line by a black dot (.). So far as it could be done without confusion, the (.) black dots indicat- ing the calculated weights have been joined by a line, to better indicate their general relation to the observed records. The whole chart for the leopard frog has been shifted in the figure along the base line 50 grams to the right ; hence all the body- weights in this chart are to be reduced by 50 grams from the weight indicated by their position. In plotting the records, the indications (. and +) have been placed exactly where they belong except in those cases where exact placing would cause them to overlap. In such instances the displacement necessary for clearness has been distributed among the several records. In no case, however, does this displacement modify in any essential feature the char- acter of the chart. 29 l6 Weight of the Central Nervous System of the Fro( Fig. 1. Weight of Brain and Spinal Cord in Summer Frogs OBSERVED. • CALCULATED. MGMS. - ^^ -^? 300 - ;.^-^*^' Bull Frog 250 - y^ * 200 - < / : */• ■ • *;/* Leopakd Frog ♦ .' • .;-f- / + • ISO • ■ / X lOO f 1 • 50 - ■ BODY WEIGHT. O 1 1 L_ 1 1 1 1 1 1 t 1 1 _J 1 1 1 1 L__J 1 \ 1 1 i 1 1 1 1__J 1 1 1 CMS. 50 100 150 300 250 300 30 14 DAY USE RETURN TO DESK FROM WHICH BORROWED LOAN DEPT. This book is due on the last date stamped below, or on the date to which renewed. Renewed books are subject to immediate recalL I JUN24 1966 8?^ JOKlQ^^^ R^P APR 30 1968 15 RFCEIVED "MAY 7TO-ibAM LOASV r^'-'^T. MAY 211960 9 5 K..T.:T'D TO TKWni SCIENCES LIB. JUN 3 1969 RECPl-D , ^R 5 19748 » LD 21A-60m-10,'65 (F77638l0)476B General Library University of California Berkeley 4 c .. I f*^" •«a-.^ ''ST