## ABSTRACT

The rate of growth of the chick embryo depends upon an inherent growth rate, probably identical for all breeds. This rate is modified during incubation in direct proportion to a function of egg size. The increments in wet weight of the embryo are proportional to a function of the weight of the yolk sac, from the time of establishment of the circulation to the time of the changes preparatory to hatching. Both function and proportionality are probably identical for all breeds of chicken, regardless of egg size.

The growth in weight of the allantois and the yolk sac have been measured quantitatively for the first time. The weight of the allantois in eggs of different sizes is roughly proportional to the two-thirds power of egg weight after the first three or four days of its growth. During the initial period of its development the relative size is apparently independent of breed, egg size, or embryo weight. The yolk-sac weight in eggs of different sizes is roughly proportional to the circumference of the yolk after a similar initial period of independent growth.

Inclusion of the living material in the embryonic membranes in calculations of the rate of physiological processes of the embryo indicates that they are probably of the same order of magnitude throughout the incubation period rather than of sharply decreasing magnitude as supposed by some previous workers.

## INTRODUCTION

The author has shown in a previous paper (Byerly, 1930 *b*) that chick embryos of different breeds differ little in size when developed in eggs of the same size. Henderson (1930) found no consistent differences in embryo weights in breeds normally producing standard-weight eggs as adults. The present paper contains data on the growth of embryos of breeds producing eggs very different in size and of embryos in eggs of widely different sizes produced by the same breed.

These data indicate that there is one inherent growth rate for chick embryos of all breeds, regardless of the size of the egg. This inherent growth rate is modified in direct proportion to differences in the immediately available food supply. The immediately available food supply is proportional to a function of the weight of the yolk sac.

The growth of the embryonic membranes has been measured quantitatively for the first time, and an estimate of the amount of living material in these membranes made. When physiological processes, *e*.*g*. oxygen consumption and material burned for maintenance, are calculated per unit weight of the embryo plus the estimated living material in the membranes, they are found to be of the same order of magnitude throughout the incubation period. This is directly counter to the conception of sharply decreasing rates of these processes with time, presented in the literature.

## EXPERIMENTAL PROCEDURE

The basic data are presented in Tables I, III, VI and X. The weights of 2752 embryos and the membranes of most of them were obtained. This material was obtained from eight sources. The largest group consisted of embryos and membranes from eggs of standard market size^{1}. These eggs were chiefly from single-comb Rhode Island Red and single-comb White Leghorn flocks ; some eggs from several other breeds were included. A large portion of the data on embryo weight in eggs secured from this group was included in an earlier paper (Byerly, 1930 *b*). The embryos from all eggs of standard size are summarised in the present paper as a basis for comparison with embryos from smaller and larger eggs from the other sources. This has been deemed permissible because it was shown in the paper cited that differences due to breed are small and appear only during the latter half of the incubation period in eggs of the same size.

The second group of data consists of measurements of embryos and membranes from small eggs, mostly pullets’ eggs, which averaged about 43 gm. in weight. These eggs were from birds of breeds normally expected to lay standard-weight eggs as adults, chiefly single-comb Rhode Island Reds and single-comb White Leghorns.

The third group consists of measurements of Bantam embryos and their membranes. The Bantam eggs used averaged about 30 gm. The fourth group consists of measurements of embryos from eggs secured from the mating of *F*_{1} individuals from a cross of a Rose-comb Black Bantam male on Barred Plymouth Rock females. The average weight of the eggs was about 40 gm. The fifth group was obtained from eggs from *F*_{1} birds from the reciprocal cross, Barred Plymouth Rock male × Rose-comb Black Bantam female. These eggs averaged about 45 gm. each. The sixth group of data consists of but four embryos. They were developed in Barred Plymouth Rock eggs fertilised by Bantam sperm. This cross involves transfer of the sperm in a pipette. Fertility was very low; consequently, the very small amount of data. The eggs used averaged about 53 gm.

The seventh and eighth groups of data represent measurements of embryos which developed in double-yolked eggs from birds of breeds normally laying eggs of standard weight. The former group consists of embryos and membranes from those eggs in which only one embryo developed, the latter group of twin embryos and membranes. These double-yolked eggs averaged about 80 gm. in weight.

Errors of measurement must be considered in evaluation of the data. Indeed, the unavoidable errors in measuring the weight of the embryo during the first three days of development and in weighing the membranes at any period have probably deterred other workers from the task. However, even approximately accurate measurements are infinitely better than guesses. Errors of measurement are probably greatest in the case of the yolk sac. Two sources of error must be considered in this connection. Some yolk adheres to the yolk sac. The amount is relatively greater from the tenth to the eighteenth day of incubation than during the rest of the period, because the yolk is relatively less hydrated during that period. The yolk sacs were washed vigorously before they were weighed to remove as much of the adherent yolk as practicable. The second source of error lies in the fact that the yolk sac ingests considerable amounts of yolk that no amount of washing can remove. This yolk is non-living, of course, and must be eliminated in estimating the amount of living material in the yolk sac. An estimate of the amount of this ingested yolk is given under the discussion of embryonic metabolism.

Weights of the allantois vary rather widely during the periods of its maximum weight, which occur at about the ninth to the eleventh and the eighteenth to the twenty-first days. The allantoia are very turgid during these periods and exude liquid and thus lose weight rapidly on standing for even a short period.

Errors in weighing the embryo arise through the presence of adherent liquid. This may amount to a relatively large portion of the apparent weight of the embryo during the first two days of incubation.

Weighings were made to fourth place accuracy. Single specimens or groups were weighed, depending on embryo age and press of work in the laboratory.

The statistical estimate of error is the probable error. The number of weighings rather than the number of specimens was used in its determination. All curves were fitted by method of least squares unless otherwise stated. The coefficient of deviation, used in comparing goodness of fit, is that used by Titus and Hendricks (1930), and is simply the square root of the mean of the squares of the deviations of the observed from the calculated values in per cent, of the calculated values^{1}.

All the eggs used were produced and incubated at the U.S. Animal Husbandry Experiment Farm, Beltsville, Maryland. They were stored at room temperature for not more than a week and incubated in a Newtown Mammoth incubator. The temperature of incubation was 39-2 ± 0-2° C., as registered by a-thermometer lying on the upper surface of the eggs. The temperature of the lower surface of the eggs is somewhat lower than that of the upper surface in the type of incubator used. Seasonal variations in temperature affect somewhat the temperature of the lower egg surface. This probably accounts for part of the excess in size shown by some of the embryos from the eggs of *F*_{1} matings among the offspring of the Rose-comb Black Bantam—Barred Plymouth Rock crosses during the first half of the incubation period. These eggs were incubated, for the most part, during May, June and July. Most of the Bantam data were collected earlier in the spring, the pullets’ egg data in the fall, and the other data in the spring, summer and fall.

## GROWTH OF THE YOLK SAC

Changes in wet weight of the yolk sacs with time are shown in Table I for all classes of embryos. The growth of the yolk sacs of the first five classes is shown graphically in Fig. 1. The weights of the yolk sacs in the standard eggs are apparently no heavier than those in any of the other groups of eggs prior to the sixth day of incubation. From the sixth day on, the weights of the yolk sacs in the standard eggs become relatively heavier, surpassing all of the others by the middle of the incubation period.

The curves in Fig. 1 all show two ascending sigmoid segments and a final descending segment. The first segment extends from the beginning of the incubation period to the ninth or tenth day. During this period the yolk sac grows peripherally until it almost completely surrounds the yolk. The yolk itself increases rapidly in size during the first four days of incubation due to absorption of water from the albumen. The yolk sac is of approximately constant thickness during this process of yolk inclosure. The second segment of the curves extends from the end of the first segment to the fifteenth or sixteenth day of incubation. The yolk decreases in size during this period due to the excretion of water into the allantois. Possibly this fact accounts for the initiation of a new mode of growth of the yolk sac: the formation of radiating lamellae which invade the yolk. These lamellae are much deeper in the peripheral portion of the yolk sac than in the central. The third segment of the curves extends from the fifteenth or sixteenth day to hatching time. The size of both yolk and yolk sac decreases. The yolk becomes slightly more hydrated and finally both are drawn into the body^{1}.

The data represented in Table I and Fig. 1 show that yolk-sac weight, at any point in the incubation period after the first six days, varies directly with egg weight, except in case of the double-yolked eggs. This is as expected, for yolk-sac weight, at least the maximum weight, must be a function of yolk weight rather than of the weight of the entire egg, and the yolks of double-yolked eggs are of only normal size. Table II gives the approximate mean weight of the yolks in each of the classes for which there are most data. It seemed at first that the most probable relationship between the weights of the yolk sacs would be a direct proportion to the two-thirds power of yolk weight, since this is a measure of yolk surface. This was tried and found wanting. The probable reason is that the relative thickness of the yolk sac is similar to that of one of the layers of an onion, thick equatorially and thin at the poles, especially after the middle of the incubation period. The yolk-sac lamellae formed during the latter half of the incubation period are limited to the peripheral portion of the yolk sac. With this fact in mind, the author calculated the circumferences of the yolks and compared their relative values with the relative values for the yolk sacs. These are presented in Table II. The values are fairly close in the case of the Bantams and the *F*_{1} from the Bantam male × Barred Plymouth Rock female eggs. The eggs from the *F*_{1} from the reciprocal cross, and from the pullets’ eggs show yolk sacs too heavy to fit this relationship, but the amount of data is relatively small compared with the data for Bantam and for standard eggs. Values for the Bantam yolk sac calculated from the weights of the standard egg yolk sac, with the observed values, are given in Fig. 2. The fit, as judged by the coefficient of deviation, is satisfactory when one takes into account the errors of measurement involved.

The values for dry weight of the yolk sac and for per cent, dry weight are given in Table IX, and Figs. 8 and 9. The curve for dry weight shows the same three segments described for the wet weight curve. The curve for per cent, dry weight shows great variability, due at least in part to the washing before weighing. The per cent, dry weight appears to decrease somewhat during the first three or four days of incubation. It begins to increase again about the eighth to the tenth day and is maximum from the eleventh to the fourteenth days, subsequently decreasing somewhat.

The only previous work found on the growth in weight of the yolk sac is that of Fangauf (1928) who published data on the weight of the yolk sac from day to day as per cent, of egg weight. His data are not comparable to those in this paper, as obviously they have been greatly smoothed and the original observations were not published.

The growth of the yolk sac is only partially dependent on the presence of an embryo. Blastoderms comparable in size with those bearing embryos of two to three days of incubation are often found with no trace of embryo present. Byerly (1926, 1930 *a*) has found that at least a part of the yolk sac, especially the peripheral growing region, may live and grow several days after the death of the embryo.

## GROWTH OF THE ALLANTOIS

The data for wet weight of the allantois are given in Table III. The curves in Fig. 3 show the smoothed values for the five groups for which data were obtained for the greater part of the incubation period (smoothed as for Fig. 1).

The allantois appears on the fourth day of incubation and increases very rapidly in wet weight till it reaches a maximum about the tenth day. The wet weight then decreases till about the fifteenth day and subsequently increases to a second maximum prior to hatching time. During the periods of maximum wet weight, ninth to the eleventh and eighteenth to the twentieth days, the allantois is usually turgid and edematous in appearance.

Table IV gives the ratios between the weights of the allantola of the Bantam group and the weights of the allantoia of five of the other groups. Murray (1925 i) showed egg surface to be proportional to the two-thirds power of egg weight. These ratios are very close to the ratios between the two-thirds power of the egg weights except for the “single embryo in double-yolked egg” class. This last ratio is lower than expected due to the fact, discussed later, that a single embryo developing in a double-yolked egg is proportional in size to a function of the size of a single yolk to about the eighteenth day of incubation. This leaves a relatively large amount of water and much of the second yolk to be absorbed through the allantois during the last three days of incubation. It will be noted in Table III that one allantois in such an egg reached the relatively enormous weight of 7-7 gm. on the nineteenth day of incubation. This allantois was extremely turgid and had absorbed most of the second yolk.

In the case of the allantois, as with yolk sac, the first few days of its development gave no indication of limitation by either breed or egg size. The limitations of egg size become apparent by the eighth day of incubation.

Dry weight of the allantois is shown in Table X and Fig. 8. Changes in per cent, dry weight are given in Table X and Fig. 9. Only one period of maximum dry weight exists and this falls on about the fourteenth day, in the interval between the two periods of maximum wet weight. The per cent, dry weight is about 8 on the fourth day, drops to less than 5 on the seventh and eighth, rises to a maximum of about 12 on the thirteenth and fourteenth days, then decreases to about 5 at hatching time. Thus the maximum per cent, dry weight coincides with maximum absolute dry weight. About 100 mg. of dry matter are lost in the allantois at hatching time.

## GROWTH OF THE EMBRYO

The data for wet weight of the embryo for all groups of embryos studied are given in Table V. The weights for the early days of incubation, especially for the embryos from standard eggs, are greater than those given by Schmalhausen (1927), Murray (1925 *a*) and Romanoff (1929); less than those given by Fiske and Boyden (1926), and about the same as those given by Lamson and Edmond (1914). These differences are due, no doubt, to slight differences in temperature during storage and incubation.

Three general opinions as to the nature of the growth curve of the chick embryo have been expressed and supported during the past few years ; perhaps it is more accurate to say two opinions and a compromise between them. Brody (1927) plotted the data then available in the literature on arith.-log. paper, so that logarithm embryo wet weight was plotted against time. The slope of such a curve expresses the relative rate of growth in this mode of plotting. Brody showed that three or more straight lines, with fairly sharp breaks between them, gave a good fit to the data points, as judged by the eye. Such straight lines indicate that the relative rate of growth is constant during the period covered by each of them. Brody argued at some length to justify the fact that he used no mathematical test for goodness of fit, nor any but an inspection method of fitting. It has been stated by Gray (1928 *a*) in criticism of Brody’s method of plotting that any curve may be fitted by a sufficient number of sufficiently short straight lines. It may be added that the eye as a judge of goodness of fit is an inadequate comparator. Brody supposes that the breaks between successive periods of constant relative rate are caused by metamorphoses of the embryo.

*a*) has expressed an opposing view. He states that the weight of the embryo, at any time from the fifth to the nineteenth day, the period covered by his study, can be expressed by a simple exponential equation of the type in which

*Y*equals wet weight of the embryo,

*X*incubation time, and

*a*and

*b*are the parameters which he determined by the graphic method. He ascribed the breaks Brody found in the curve to errors of sampling, though his own curve showed two such breaks.

The position of Schmalhausen (1927) is intermediate between that of Brody and that of Murray. He describes the curve as a parabola but recognises the presence of systematic deviations corresponding, at least roughly, with the metamorphoses postulated by Brody. He has shown that segments of many growth curves approach a parabola in form. MacDowell, Allen and MacDowell (1927) have shown that a better fit is obtained with this type of curve when the starting-point used is that time at which the first rudiment of the embryo is discernible. Their own data were for the growth of the mouse embryo. MacDowell, Gates and MacDowell (1930) have shown, for the suckling period in the development of the mouse, that the curve also approaches a parabola as the food supply approaches *ad libitum* consumption.

The present data for the first six groups of embryos are plotted in Fig. 4. The method of plotting is that suggested by MacDowell, Allen and MacDowell (1927). Logarithm embryo weight in tenth milligrams is plotted against logarithm incubation time in tenths of days minus five-tenths of a day^{1}. It should be understood that the author does not state that the embryo proper first becomes discernible at exactly 0-5 day incubation. This is the value used by MacDowell, Allen and MacDowell for the chick and seems as good as any other as a conventional period.

*Y*= embryo weight, measured in tenths of a milligram;

*X*= incubation time less 0-5 day, measured in tenths of a day;

*R—*the reciprocal of the logarithm of the egg weight in gm. ;

*A, B*and

*C*are the parameters determined in the manner stated above.

Now, obviously, if the parameters of this equation are determined by using any one of the six sets of data, the quantity (—*BR*—C) has the same value as (—*b*) in equation (2). If, on the other hand, the parameters of equation (3) are determined by using all six sets of data, considered as a single set, as good a fit should be expected as is obtained by determining the parameters of equation (2) for each individual set of data, only if the assumptions implied in formulating equation (3) are essentially correct. These assumptions are : that the slope of the curve for each set of data is identical with that for every other set of data and thus that the relative rates of growth of all classes of embryos are identical, and that the limiting effect of egg size in each case is proportional to a function of the logarithm of egg weight in grams. The curves from the two equations very nearly coincide for the four best sets of data. The coefficients of deviation given in Table V are almost as good for the curves from equation (3) as those from equation (2).

The values determined for the parameters for each of the equations for each of the six sets of data are given in Table V. The values of parameter *A* in equation (2) vary but little from one set of data to another, whereas the values of *b* in equation (2) vary more.

The embryo weights in grams for each of the eight sets of data are given in Table VI.

The constant *b* in equation (2) is theoretically equal to logarithm embryo weight after the lapse of one unit time, in this case at 0-6 day incubation, since unit time is 0.1 day and zero time is 0.5 day. It is not possible to ascertain whether or not this is true. The data in Tables I, III and VI for the wet weight of the yolk sac, the allantois and the embryo, respectively, show a considerable amount of independent variation during their early development. For example, the standard-egg embryo is heavier than the Bantam embryo from the fourth to sixth days of incubation, whereas the reverse is true with respect to the allantoia. The standard-egg embryos weighed on the third day were heavier than the others weighed on that day ; this has increased importance, since a fair number of embryos was examined in five of the groups. It should be particularly emphasised that differences between standardegg embryos and those in pullets’ eggs are discernible just as early as those between Bantam and standard-egg embryos. The author (Byerly, 1930 *b*) probably attached somewhat too *little* importance to the effect of egg size on embryo size during the first days of incubation. Possibly the effect of egg size on embryo size appears as soon as the circulation is established or soon thereafter, apparently by the third day of incubation, and certainly by the seventh.

It is entirely possible, of course, that differences are present at 0-6 day incubation, as required by theory. This would mean that the embryonic anlage was proportional in size to a function of egg size or that the rate of cell division was proportional to a function of egg size. The latter seems hardly possible, since differences in embryo size are apparent as soon in eggs of different size from the same breed as in eggs of different size from breeds widely different in body size; because for single-comb Rhode Island Reds and single-comb White Leghorns, Byerly (1930*b*) and Henderson (1930) for Cornish and single-comb White Leghorns, showed that there is little or no effect of breed on embryo size during the early days of incubation in eggs of the same size. The data indicate that differences are probably imposed on embryos of the same size by differences in available food supply. This hypothesis satisfies the facts now available. It is not certainly proved, but is at least sufficient until facts inconsistent with it appear.

It has been pointed out that *b* in equation (2) is equivalent to the quantity *(—BR—C*) in equation (3) when determined from any one set of data. *R* in this quantity was assigned the value of the reciprocal of the logarithm of egg weight in grams simply because it was found by the hoary process of trial and error that this function of egg weight gave the quantity approximately correct values for all sets of data. This function has no apparent rational significance, but it will be shown later that a rational value may be substituted for it.

The constant *a* in equation (2) is equivalent to *A* in equation (3) ; it defines the slope of the curve and therefore the relative rate of growth, as has been stated. It was assumed that the slope of all the curves was the same in fitting equation (3) to the six sets of data considered as one set. The relative rate of growth on successive days of the incubation period is given for each of the eight sets of data, in Table VII.

Values for relative rate for a particular day are subject to considerable variation just as is an increment curve. Average relative rates and averages of the relative rates for successive days in per cent, of the relative rates for embryos in standard eggs are given for the third to the seventeenth day and eighteenth to the twentieth day periods at the bottom of Table VII. The average values for the third to seventeenth day period are practically identical ; the eighteenth to twentieth day period show average values roughly proportional to egg size.

The three-day values are used as a starting-point because a fairly large number of embryos was examined in each of five of the classes on that day, because the earlier values do not show that the embryos in standard eggs were heavier than the embryos in other classes of eggs before that time, and because the hypothesis that food supply is responsible for differences in embryo size requires equal size of embryos of all classes before the circulation is established. The data show a sharp diminution of relative rate on the eighteenth day of incubation in four of the five sets of data which show values for that period. This break undoubtedly has a rational basis. It has been shown that the yolk sac diminishes in size during the last days of incubation. The changes preparatory to hatching begin at that time. The most important of these from the present standpoint is the removal of the amniotic and allantoic fluids. This is accomplished in part by swallowing and probably in part by absorption through the allantois. The amount of material to be removed is directly proportional to egg weight, or very close to such a proportion. During the last three days the embryo changes from a proportionality in size to logarithm egg size to a direct proportionality to egg size (Jull and Heywang, 1930). This is especially striking in the case of the single embryos in double-yolked eggs. These embryos are little or no larger at eighteen days than standard-egg embryos, but at hatching time they are proportional in size to egg size. One such embryo weighed 57 gm., without the yolk, at hatching time as compared with an average weight of about 35-9 for the standard-egg embryos.

Perhaps it should be emphasised once more that a parabola gives only an approximate fit to the growth curve of the chick embryo. The deviations in Fig. 3 are systematic. The standard-egg data give the best fit to a straight line, plotted logarithmically against log time. This is probably due to the fact that selection for large egg size has been carried on through many generations in the breeds which now produce eggs of standard size. According to Hays (1929), the weight of the egg of *Gallus bankiva*, probably ancestral to the domestic fowl, is only about 40 gm. The increase in egg size would account for the better fit of the data to a straight line of the logarithms of embryo weight of embryos in standard eggs plotted against logarithm time for the last three days of the incubation period.

It should be possible to express the growth of the embryo in terms of its membranes and time if the postulate that the absolute rate of growth of the embryo is limited by food supply is correct, and if the efficiency of the membranes bears an approximately constant ratio to some function of membrane weight. This may, in fact, be done as is shown in Table VIII and Fig. 5.

*Y =*daily increment in wet weight of the embryo,

*X =*daily wet weight of the yolk sac, and

*A*and

*B*are parameters determined by method of least squares.

The values of the parameters *A* and *B* determined from each of the sets of data are given in Table VIII. Three of the four sets yield almost identical values; the parameters determined from the fourth set are somewhat lower. Table VI shows that on the thirteenth day a single embryo was weighed in this set and that this weight was only a trifle heavier than that recorded for the twelfth day. By smoothing the twelfth and thirteenth day increments to correct for this grossly variant observation, the second values for the parameters *A* and *B* given in Table VIII for this set of data were obtained. These values are practically identical with the values for the other three sets. This means that the efficiency of the yolk sac is constant throughout at least the greater portion of the incubation period, and that the efficiency of the yolk sacs is the same for all classes of embryos considered.

The calculated and observed values of the daily increments in wet weight of the standard-egg embryos are plotted in Fig. 5 against incubation time. The variations are rather large, but only become systematic after the eighteenth day when the embryo is rapidly becoming dependent on other means of food getting, and from the fifth to the ninth day period during which food material must be supplied for the rapidly growing allantois. Increment curves are notoriously variable, and it has already been pointed out that gross errors exist in measurements of the yolk sac.

*E =*embryo weight in mg.,

*YS =*yolk sac weight in mg.,

*T*= incubation time in days,

*A, B*and

*C*the parameters, was fitted to the Bantam-egg and standardegg data and to the six sets of data plotted in Fig. 3 considered as a single set, by the method of least squares. The values of the parameters of equation (5), determined as stated, are given in the upper portion of Table IX. The lower portion of Table IX presents the values of the parameters of equation (6) determined from each of the four sets of data which are most nearly complete. Equation (6) is in which

*E*= embryo weight in mg.,

*YS =*yolk sac weight in mg.,

*Al =*allantois weight in mg.,

*T =*incubation time in days,

*A, B, C*and

*D*are the parameters determined by method of least squares, using each of the four most complete sets of data. Comparison of the coefficients of deviation for equations (5) and (6) show that equation (6) gives a better fit. This is also demonstrated in Fig. 6 for the Bantam data.

*AEY*= the combined weight of allantois, embryo and yolk sac in mg.,

*YS =*weight of the yolk sac in mg.,

*Al*= weight of the allantois in mg.,

*T*= incubation time in days,

*A, B*and

*C*are the parameters determined by method of least squares from the standard egg data.

Since material absorbed is used by all these structures, it is reasonable that this equation should give a better fit than the others. Other equations including the same terms probably may be devised which would describe the data more accurately and more rationally. Material absorbed but used for maintenance has been ignored because of the difficulty of translating from terms of O_{2} consumed, CO_{2} produced or solids disappearing to a basis of wet material absorbed. There is no *a priori* reason to expect that the increments are proportional to the product of a power of yolk-sac weight by a power of allantois weight, as is assumed in equations (6) and (7). It seems more probable that increments would be proportional to the sum of a fraction of a power of yolk-sac weight plus a fraction of a power of allantois weight, since they may have widely differing efficiencies. To devise and fit such equations would involve a very laborious series of approximations. On the other hand, equation (7) may be the correct form; from an empirical standpoint, it is reasonably satisfactory (Fig. 7).

It is distinctly realised that the principle of proportional growth advanced by Robb (1929 *b*) may also serve as a limiting factor in the growth of the embryonic membranes, that is, that body size determines membrane size, rather than that membrane size determines body size. It is perhaps better to avoid that point since the facts in either case support the assumption that the ultimate limiting factor is food supply.

There is one striking feature of equations (5), (6) and (7). This is the parameter *B* in equation (5) and the parameter *C* in equations (6) and (7), which is identical with *B* of equation (5). This parameter multiplied by too × *s*, the natural logarithm of 10, 2-30259, expresses the rate of growth in per cent, relative to the functions of membrane weight defined by parameter *A* of equation (5) and parameters *A* and *B* of equations (6) and (7). It has been demonstrated in Table VIII and Fig. 5, that the daily increments in weight are proportional to a function of membrane weight, and that the function and proportionality are probably identical for all the sets of data. The parameter *B* of equation (5) and *C* of equations (6) and (7) express the same fact. The values of parameter *C*, equation (6), given in the lower portion of Table IX, are especially striking when converted to a per cent, basis as the range is only from 18-6 to 20-2 per cent. The value of the parameter *A* in equation (5) and of parameters *A* and *B* in equations (6) and (7) are somewhat more variable, but are probably actually identical from one set of data to another, varying only because of observational errors in the data for membrane weight.

It has been shown that the chick embryo has an inherent relative rate of growth which is unaffected by breed or egg size from the time the circulation is established to the time of changes prior to hatching. The absolute rate of growth is limited by a function of egg size which is approximately proportional to the reciprocal of the logarithm of egg size in grams.

The data in Table II for the relative weights of the yolk sacs of embryos from the several groups show that yolk-sac weight, an approximate measure of the available food supply, is roughly proportional to yolk circumference. The relative values for logarithm egg weight in grams are also given in Table II. They are sufficiently close to identity with the relative values for yolk-sac circumference to permit the substitution of the latter in equation (3). The substitution has not been made because of the labour involved and because a better value including an estimate of the rôle of the allantois as an absorptive agent, and an estimate of the amount of wet material used for maintenance may eventually be found. Further, logarithm egg weight is a vastly more convenient value for the worker who may care to check these results than yolk-sac circumference, which involves a series of calculations.

## DRY WEIGHT OF THE EMBRYO

The data for the dry weight and for changes in per cent, dry weight are given in Table X, and are plotted in Figs. 8 and 9.

The data are very similar to those of Murray (1925 *b*). The curve for increase in dry weight is rather flat up to the middle of the incubation period, when it rises abruptly. During the last day or two of incubation, the slope again diminishes. This is probably due to the relatively large amount of fluid that must be disposed of in the standard egg before the chick can hatch. The only measurements of dry weight are those for standard-egg embryos and their membranes (Fig. 8).

The curve for per cent, dry weight shows an initial value of about 15 per cent, which drops to less than 7 per cent, with the establishment of the circulation. The portion of the curve corresponding to the period covered by Murray’s data is very similar to his except that the nineteenth day value shows a drop probably due to the ingestion of amniotic and allantoic fluids (Fig. 9).

## GENERAL SIGNIFICANCE OF HYPOTHESIS OF LIMITING RÔLE OF FOOD SUPPLY

MacDowell, Gates and MacDowell (1930), have shown that as the food supply of the sucking mouse is increased, its growth curve approaches more and more closely the parabola in form. The same thing is true for the chick embryo. It has been shown that it is only in the standard and single embryo in double-yolked egg groups that there is no sharp drop in growth rate during the last three days of the incubation period. Gray (1928 *a*) showed that the rate of growth of the embryo of *Salmo fario* is proportional to its own size and to the amount of yolk in the yolk sac, at a particular temperature. He admits the probable advantage of using some function of the yolk sac as a measure of food supply rather than the total amount of yolk present. He found it difficult to see a reason for food supply restricting growth rate, when the amount of food was very great in proportion to the amount of the material in the embryo. This may be explained by the fact brought out in the present paper, that the growth of the yolk sac itself is determined by the amount of food present, but is dependent on diameter (or circumference) rather than on volume of yolk present. The present data confirms his observation that the specific growth rate of the embryo decreases because there is a reduction in the rate at which the tissues are supplied with raw material for building new tissues.

Gray (1928 b) gives a critical review of the requirements of rational growth curves. The author of this paper believes that he has only shown that the available data do not require a more complex hypothesis than the one presented. Under standard incubation conditions, the wet weight of the chick embryo from the time of establishment of the circulation to the changes preparatory to hatching is proportional to a function of time and to available food supply. There is some evidence that this is also true for mammalian embryos. Bluhm (1929) compiled a great deal of birth-weight data for the albino mouse and found negative correlation between litter size and birth weight, positive correlation between maternal body size and birth weight of young not to be explained by genetic constitution. It would be very interesting to know whether the efficiency of the digestive tract of the animal after birth or hatching is also constant. Robb (1929 *a*) observed that the ratio of the weight of the gut contents of the rabbit to body weight decreases as the rabbit matures. Latimer (1924) found that the ratio of digestive tract weight to body weight decreases with increasing body weight in the chicken. If the efficiency of the digestive tract is constant, the widening ratio between its weight and that of the whole body must serve as one of the immediate causes of the decrease in relative rate of growth with age.

Fig. 10 shows feed consumption plotted against digestive tract weight in the case of the chicken. This is the only available measure of the efficiency of the digestive tract at successive ages for the same birds. The interval between each two successive points of each set of data represents the change in two weeks’ time. The amount of food eaten is clearly proportional to the weight of the digestive tract for the first eight weeks after hatching (Fig. 10).

The data for feed consumption were taken from Titus, McNally and Hilberg (1930), and Titus and Godfrey (1931). The data for digestive tract weight were read from the curve given by Latimer (1924) for White Leghorns of weights corresponding to the observed weights of the birds in the experiments of Titus *et al*. Each set of feed consumption data was for *ad libitum* consumption of a uniform diet.

The first significant deviation from a straight line relationship, for the data examined, is the next observation after the major inflection in the curve for body weight plotted against age. This inflection corresponds approximately with the onset of puberty. It marks the close of the “self-accelerated” phase of growth (cf. Brody, 1927). Appetite apparently decreases with the beginning of the endocrine changes of puberty. Whether there is a causal relationship or mere coincidence is not apparent. It seems reasonable to conclude that the immediately available food supply, which is controlled by the size of the food-absorbing mechanism, is a factor causing steady reduction in the relative rate of growth prior to the major inflection in the growth curve for the chicken. It is of course realised that there may be some mechanism in the organism itself which controls the growth of the digestive tract according to Robb’s (1929*b*) principle of proportional growth.

## RATE OF PHYSIOLOGICAL PROCESSES

The rates of the various metabolic processes of the embryo, as given in the literature, are based solely on the weight of the embryo. Murray (1926) admits that an error may be involved in the omission of the embryonic membranes in the computation of such processes, but assumes that such an error would be constant or negligible. In order to estimate the error involved by neglect of the embryonic membranes, estimates have been made of the absolute and relative weights of the living material in the membranes throughout the incubation period on both dry and wet basis for the standard-egg data.

The calculated weights of the living material in the yolk sac are given in Table XI

The following scheme was used to obtain an approximation of the amounts of yolk and protoplasm present. It was assumed that the per cent, dry weight of the protoplasm in the yolk sac paralleled that in the embryo. The included yolk was assumed to contain 50 per cent, dry matter, the approximate value for fresh yolk. The amount of protoplasm in the yolk sacs was then computed from their observed wet weights and per cent, dry weights. The allantois observed weights were assumed to consist of living material. The relative amount of the total living material in the egg comprised by each, the allantois, the embryo, and the yolk sac, is given in Figs. 11 *a* and 11 *b* for the wet and dry basis respectively.

The calculated values for the yolk sac are probably conservative for the period during which the weight of the yolk sac is greatest relative to embryo weight, *i*.*e*. before the middle of the incubation period. The per cent, dry weight of the yolk-sac protoplasm is surely not much below the 6 per cent, shown by the embryo during this period. The living material of the yolk sac comprises a very much greater portion of the living material in the egg during the first few days of incubation than during the later portion. The allantois is relatively heaviest about the tenth day of incubation. Prior to the middle of the incubation period, non-inclusion of the weight of living material in the membranes in computing physiological processes of the embryo may involve an error of from 50 to *95* per cent. During the latter half of the incubation period the error involved would gradually decrease to about 10 per cent.

Figs. 11 *a* and 11 *b* demonstrate Murray’s (1926) assumption that to ignore the embryonic membranes introduced a constant or a negligible error in computations of physiological processes, is far from correct.

The curve for relative weight of the yolk sac is very similar to the curve for relative rate of growth of the embryo. It has been shown that the increments in wet weight are proportional to the wet weight of the yolk sac and that decrease in relative rate of growth of the embryo were caused by decrease in the available food supply and need not imply any other limiting factor than food. Before metabolic processes can be calculated on a correct basis, the relative rates of metabolism of membranes and embryo must be known. Dr Joseph Needham of Cambridge informs me that he is undertaking such determinations.

*Y =*amount of solids disappearing during one day,

*W*= total wet weight of living material in the egg at the end of that day,

*A*= a constant, obtained by solving the equation, in which the several terms are as noted for equation (8). The data for amount of solids disappearing were taken from Murray (1926). Murray’s data for solids disappearing yield a value of about 26 mg. per gm. wet weight of embryo on the sixth day. The value on the nineteenth day is about 10 mg. per gm., a drop of over 60 per cent. The third process illustrated in Fig. 12 is the rate of absorption of dry matter per unit wet weight of living material in the egg. The rate is of the same order of magnitude from the third to the seventeenth days. Murray’s (Zoe.

*cit.*) data yield similar values for this process, calculated in terms of embryo weight.

The other physiological processes of the embryo would show similar changes from the published curves if treated in the same manner. Neither those given nor any other can be accepted as valid until the relative metabolism of embryo and membranes, respectively, is determined.

## Acknowledgments

The author gratefully acknowledges much helpful advice and criticism from Mr H. W. Titus and Mr W. A. Hendricks.

## References

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*Mo. Agr. Exp. Sta. Res. Bull.*

*Anat. Rec.*

*Conference papers, 4th World’s Poultry Congress,*Sec. A

*Journ. Morph, and Physiol.*

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*Salmo fario.”*

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*Journ. Agr. Res.*

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*Journ. Gen. Physiol.*

*Journ. Gen. Physiol.*

*Journ. Gen. Physiol.*

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*Arch.f. Entw.-mech. d. Org.*

*Conference papers, 4th World’s Poultry Congress,*Sec. B, 285-293

*Poultry Science*

^{1}

The term “standard” is used in this paper to designate the eggs of *approximate* standard size, average about 60 gm., *not* the exact standard weight, 56-6 gm.

^{1}

*W*—observed value,

*W*

_{o}—calculated value, and

*N*= number of observed values (cf. Titus and Hendricks, 1930, p. 289).

^{1}

See Romanoff (1930) for detailed account of changes in hydration of the yolk.

^{1}

*Y*= yolk-sac weight on a given day of the incubation period for a given set of data;

*X*= yolk-sac weight on a given day of the incubation period for the standard egg data;

*A*= a parameter determined from the data by method of least squares.

This weights the later, heavier values, which was deemed proper because these values should show the limiting effects of yolk size more than the values during the first days of incubation. They would be less affected by slight temperature variations also.

^{1}

These units were used to avoid negative logarithms and for no other reason.