On Growth and Form

Then choosing two values out of the above experimental series This first approximation might be considerably improved by taking account of all the experimental values, two only of which we have as yet made use of; but even as it is, we see by Fig. 26 that it 1s in very fair accordance with the actual results of observation, within those particular linuts of temperature to which the experiment is confined. For an experiment on Lupinus albus, quoted by Asa Gray%, I have worked out the corresponding coefficient, but a little more carefully. Its value I find to be 1-16, or very nearly identical with that we have just found for the maize; and the correspondence between the calculated curve and the actual observations is now a close one.

Fig. 26. Relation of rate of growth to temperature in Maize. Observed values (after K6ppen), and calculated curve. Since the above paragraphs were written, new data have come to hand. Miss I. Leitch has made careful observations of the rate of growth of rootlets of the Pea; and I have attempted a further analysis of her principal results. In Fig. 27 are shewn the mean rates of growth (based on about a hundred experiments) at some thirty-four different temperatures between 0-8° and 29-3°, each experiment lasting rather less than twenty-four hours. Working out the mean temperature coefficient for a great many combinations of these values, I obtain a value of 1-092 per C.°, or 2-41 for an interval of 10°, and a mean value for the whole series showing a rate of growth of just about 1 mm. per hour at a temperature of 20°. My curve in Fig. 27 is drawn from these determinations; and it will be seen that, while it is by no means exact at the lower temperatures, and will of course fail us altogether at very high

+ Leitch, I., Some Experiments on the Influence of Temperature on the Rate of Growth in Pisum sativum, Ann. of Botany, Xxx, pp. 25-46, 1916. (Cf. especially Table III, p. 45.) temperatures, yet it serves as a very satisfactory guide to the relations between rate and temperature within the ordinary limits of healthy growth. Miss Leitch holds that the curve is not a van’t Hoff curve; and this, in strict accuracy, we need not dispute. But the phenomenon seems to me to be one into which the van’t Hoff ratio enters largely, though doubtless combined with other factors which we cannot at present determine or eliminate.

Fig. 27. Relation of rate of growth to temperature in rootlets of Pea. (From Miss I. Leitch’s data.) While the above results conform fairly well to the law of the temperature coefficient, it is evident that the imbibition of water plays so large a part in the process of elongation of the root or stem that the phenomenon is rather a physical than a chemical one: and on this account, as Blackman has remarked, the data commonly given for the rate of growth in plants are apt to be

irregular, and sometimes (we might even say) misleading*. The fact also, which we have already learned, that the elongation of a shoot tends to proceed by jerks, rather than smoothly, is another indication that the phenomenon is not purely and simply a chemical one. We have abundant illustrations, however, among animals, in which we may study the temperature coefficient under circumstances where, though the phenomenon is always complicated by osmotic factors, true metabolic growth or chemical combination plays a larger role. Thus Mlle. Maltaux and Professor Massart + have studied the rate of division in a certain flagellate, Chilomonas paramoecium, and found the process to take 29 minutes at 15° C., 12 at 25°, and only 5 minutes at 35°C. These velocities are in the ratio of | : 2-4: 5-76, which ratio corresponds precisely to a temperature coefficient of 2-4 for each rise of 10°, or about 1-092 for each degree centigrade.

By means of this principle we may throw light on the apparently complicated results of many experiments. For instance, Fig. 28 is an illustration, which has been often copied, of O. Hertwig’s work on the effect of temperature on the rate of development of the tadpole. From inspection of this diagram, we see that the time taken to attain certain stages of development (denoted by the numbers ITI-VIT) was as follows, at 20° and at 10° C., respectively.

{t Hertwig, O., Einfluss der Temperatur auf die Entwicklung von Rana fusca und R. esculenta, Arch. f. mikrosk. Anat. U1, p. 319, 1898. Cf. also Bialaszewicz, K., Beitrige z. Kenntniss d. Wachsthumsvorginge bei Amphibienembryonen, Bull. Acad. Sci. de Cracovie, p. 783, 1908; Abstr. in Arch. f. Entwicklungsmech. xxvin, p. 160, 1909. jeee Pech a/c ne eae iy OAR 2 Bae eae ey AA UES BRER SaaS ie! Fig. 28. Diagram shewing time taken (in days), at various temperatures (°C.), to reach certain stages of development in the Frog: viz. I, gastrula; II, medullary plate; III, closure of medullary folds; IV, tail-bud; V, tail and gills; VI, tail-fin; VII, operculum beginning; VIII, do. closing; IX, first appearance of hind-legs. (From Jenkinson, after O. Hertwig, 1898.)

We may then put our equation again in the simple form, ih 9 919 That is to say, between the intervals of 10° and 20°C., if it take m days, at a certain given temperature, for a certain stage of development to be attained, it will take m x 1-128” days, when the temperature is » degrees less, for the same stage to be arrived at. Fig. 29. Calculated values, corresponding to preceding figure. Fig. 29 is calculated throughout from this value; and it will be seen that it is extremely concordant with the original diagram, as regards all the stages of development and the whole range of temperatures shewn: in spite of the fact that the coefficient on which it is based was derived by an easy method from a very few points in the original curves.

Karl Peter*, experimenting chiefly on echinoderm eggs, and also making use of Hertwig’s experiments on young tadpoles, gives the normal temperature coefficients for intervals of 10° C. (commonly written Q,9) as follows. These values are not only concordant, but are evidently of the same order of magnitude as the temperature-coefficient in ordinary chemical reactions. Peter has also discovered the very interesting fact that the temperature-coefficient alters with age, usually but not always becoming smaller as age increases.

Sphaerechinus; Segmentation @!° = 2-29, Later stages me 0s Kchinus ; Segmentation Ae Dea) Later stages a 3208: Rana; Segmentation i 223, Later stages » oo. Furthermore, the temperature coefficient varies with the temperature, diminishing as the temperature rises,—a rule which van't Hoff has shewn to hold in ordinary chemical operations. Thus, in Rana the temperature coefficient at low temperatures may be as high as 5-6: which is just another way of saying that at low temperatures development is exceptionally retarded.

In certain fish, such as plaice and haddock, I and others have found clear evidence that the ascending curve of growth is subject to seasonal interruptions, the rate during the winter months being always slower than in the months of summer: it is as though we superimposed a periodic, annual, sine-curve upon the continuous curve of growth. And further, as growth itself grows less and less from year to year, so will the difference between the winter and the summer rate also grow less and less. The fluctuation in rate

* Der Grad der Beschleunigung tierischer Entwickelung durch erhdhte Temperatur, A. f. Hntw. Mech. xx, p. 130, 1905. More recently, Bialaszewicz has determined the coefficient for the rate of segmentation in Rana as being 2-4 per 10°C. will represent a vibration which is gradually dying out; the amplitude of the sine-curve will gradually diminish till it disappears ; in short, our phenomenon is simply expressed by what is known as a “damped sine-curve.” Exactly the same thing occurs in man, though neither in his case nor in that of the fish have we sufficient data for its complete illustration.

We can demonstrate the fact, however, in the case of man by the help of certain very interesting measurements which have been recorded by Daffner*, of the height of German cadets, measured at half-yearly intervals. Growth in height of German military Cadets, in half-yearly periods. (Daffner.) In the accompanying diagram (Fig. 30) the half-yearly increments are set forth, from the above table, and it will be seen that they form two even and entirely separate series. The curve joing up each series of points is an acceleration-curve; and the comparison of the two curves gives a clear view of the relative rates of growth during winter and summer, and the fluctuation which these velocities undergo during the years in question. The dotted line represents, approximately, the acceleration-curve in its continuous fluctuation of alternate seasonal decrease and increase.

In the case of trees, the seasonal fluctuations of growth} admit * Das Wachstum des Menschen, p. 329, 1902. + The diurnal periodicity is beautifully shewn in the case of the Hop by Joh. Schmidt (C. R. du Laboratoire de Carlsberg, x, pp. 235-248, Copenhague, 1913). of easy determination, and it is a point of considerable interest to compare the phenomenon in evergreen and in deciduous trees. I happen to have no measurements at hand with which to make this comparison in the case of our native trees, but from a paper by Mr Charles E. Hall* I have compiled certain mean values for growth in the climate of Uruguay.

Fig. 30. Half-yearly increments of growth, in cadets of various ages. (From Daffner’s data.) Mean monthly wncrease in Girth of Evergreen and Deciduous Trees, at San Jorge, Uruguay. (After C. BE. Hall.) Values expressed as percentages of total annual increase. The measurements taken were those of the girth of the tree, in mm., at three feet from the ground. The evergreens included species of Pinus, Eucalyptus and Acacia; the deciduous trees included Quercus, Populus, Robinia and Melia. I have merely taken mean values for these two groups, and expressed the monthly values as percentages of the mean annual increase. The result (as shewn by Fig. 31) is very much what we might have expected. Th» growth of the deciduous trees is completely arrested in winter-time, and the arrest is all but complete over

a considerable period of time; moreover, during the warm season, the monthly values are regularly graded (approximately in a sine-curve) with a clear maximum (in the southern hemisphere) about the month of December. In the evergreen trees, on the other hand, the amplitude of the periodic wave is very much less; there is a notable amount of growth all the year round, and, while there is a marked diminution in rate during the coldest months, there is a tendency towards equality over a considerable

Fig. 31. Periodic annual fluctuation in rate of growth of trees (in the southern hemisphere). part of the warmer season. It is probable that some of the species examined, and especially the pines, were definitely retarded in growth, either by a temperature above their optimum, or by deficiency of moisture, during the hottest period of the year; with the result that the seasonal curve in our diagram has (as it were) its region of maximum cut off. In the case of trees, the seasonal periodicity of growth is so well marked that we are entitled to make use of the phenomenon in a converse way, and to draw deductions as to variations in

climate during past years from the record of varying rates of growth which the tree, by the thickness of its annual rings, has preserved for us. Mr A. E. Douglass, of the University of Arizona, has made a careful study of this question*, and I have received (through Professor H. H. Turner of Oxford) some measurements of the average width of the successive annual rings in “‘yellow pine,’ 500 years old, from Arizona, in which trees the annual rings are very clearly distinguished. From the year 1391 to 1518, the mean of two trees was used; from 1519 to 1912, the mean of five; and the means of these, and sometimes of larger numbers, were found to be very concordant. A correction was applied by drawing a long, nearly straight line through the curve for the whole period, which line was assumed to represent the slowly diminishing mean width of ring accompanying the increase of size, or age, of the tree; and the actual growth as measured was equated with this diminishing mean. The figures used give, accordingly, the ratio of the actual growth in each year to the mean growth corresponding to the age or magnitude of the tree at that epoch.

It was at once manifest that the rate of growth so determined shewed a tendency to fluctuate in a long period of between 100 and 200 years. I then smoothed in groups of 100 (according to Gauss’s method) the yearly values, so that each number thus found represented the mean annual increase during a century: that is to say, the value ascribed to the year 1500 represented the average annual growth during the whole period between 1450 and 1550, and soon. These values give us a curve of beautiful and surprising smoothness, from which we seem compelled to draw the direct conclusion that the climate of Arizona, during the last 500 years, has fluctuated -with a regular periodicity of almost precisely 150 years. Here again we should be left in doubt (so far as these

* T had not received, when this was written, Mr Douglass’s paper, On a method of estimating Rainfall by the Growth of Trees, Bull. Amer. Geograph. Soc. XLv1, pp. 321-335, 1914. Mr Douglass does not fail to notice the long period here described; but he lays more stress on the occurrence of shorter cycles (of 11, 21 and 33 years), well known to meteorologists. Mr Douglass is inclined (and I think rightly) to correlate the variations in growth directly with fluctuations in rainfall. that is to say with alternate periods of moisture and aridity; but he points out that the temperature curves (and also the sunspot curves) are markedly similar.

‘OI6GT-OI8I “2'¥ 0F OGFI-OGET “A°V WoIT ‘(sporsad avad-jO] UI poeygoows) seer, vuoOZIIy FO YAMOAS Fo oye UT UOTyeNJony powed-SuoyT “ZE “Sip observations go) whether the essential factor be a fluctuation of temperature or an alternation of moisture and aridity; but the character of the Arizona climate, and the known facts of recent years, encourage the belief that the latter is the more direct and more important factor. It has been often remarked that our common European trees, such for instance as the elm or the cherry, tend to have larger leaves the further north we go; but in this case the phenomenon is to be ascribed rather to the longer hours of daylight than to any difference of temperature*. The point is a physiological one, and consequently of little importance to us here+; the main point for the morphologist is the very simple one that physical or climatic conditions have greatly influenced the rate of growth. The case is analogous to the direct influence of temperature in modifying the colouration of organisms, such as certain butterflies. Now if temperature affects the rate of growth in strict uniformity, alike in all directions and in all parts or organs, its direct effect must be limited to the production of local races or varieties differing from one another in actual magnitude, as the Siberian goldfinch or bullfinch, for instance, differ from our own. But if there be even ever so little of a discriminating action in the enhancement of growth by temperature, such that it accelerates the growth of one tissue or one organ more than another, then it is evident that it must at once lead to an actual difference of racial, or even * specific’ form.

It is not to be doubted that the various factors of climate have some such discriminating influence. The leaves of our northern trees may themselves be an instance of it; and we have, * Tt may well be that the effect is not due to light after all; but to increased absorption of heat by the soil, as a result of the long hours of exposure to the sun. + On growth in relation to light, see Davenport, Exp. Morphology, 11, ch. xvii. In some cases (as in the roots of Peas), exposure to light seems to have no effect on growth; in other cases, as in diatoms (according to Whipple’s experiments, quoted by Davenport, 0, p. 423), the effect of light on growth or multiplication is well-marked, measurable, and apparently capable of expression by a logarithmic formula. The discrepancy would seem to arise from the fact that, while lightenergy always tends to be absorbed by the chlorophyll of the plant, converted into chemical energy, and stored in the shape of starch or other reserve materials, the actual rate of growth depends on the rate at which these reserves are drawn on: and this is another matter, in which light-energy is no longer directly concerned.

probably, a still better instance of it in the case of Alpine plants *, whose general habit is dwarfed, though their floral organs suffer little or no reduction. The subject, however, has been little investigated, and great as its theoretic importance would be to us, we must meanwhile leave it alone. The curves of growth which we have now been studying ~ represent phenomena which have at least a two-fold interest, morphological and physiological. To the morphologist, who recognises that form is a “function” of growth, the important facts are mainly these: (1) that the rate of growth is an orderly phenomenon, with general features common to very various organisms, while each particular organism has its own characteristic phenomena, or “specific constants”; (2) that rate of growth varies with temperature, that is to say with season and with climate, and with various other physical factors, external and internal; (3) that it varies in different parts of the body, and according to various directions or axes: such variations being definitely correlated with one another, and thus giving rise to the characteristic proportions, or form, of the organism, and to the changes in form which it undergoes in the course of its development. But to the physiologist, the phenomenon suggests many other important considerations, and throws much light on the very nature of growth itself, as a manifestation of chemical and physical energies.

To be content to shew that a certain rate of growth occurs in a certain organism under certain conditions, or to speak of the phenomenon as a “reaction” of the living organism to its environment or to certain stimuli, would be but an example of that “lack of particularity +” in regard to the actual mechanism of physical cause and effect with which we are apt in biology to be too easily satisfied. But in the case of rate of growth we pass somewhat

* Cf. for instance, Nageli’s classical account of the effect of change of habitat on Alpine and other plants: Sitzwngsber. Baier. Akad. Wiss. 1865, pp. 228-284. 7 Cf. Blackman, F. F., Presidential Address in Botany, Brit. Ass. Dublin, 1908. The fact was first enunciated by Baudrimont and St Ange, Recherches sur le développement du foetus, Mém. Acad. Sci. xt, p. 469, 1851. beyond these limitations; for the affinity with certain types of chemical reaction is plain, and has been recognised by a great number of physiologists. ;

A large part of the phenomenon of growth, both in animals and still more conspicuously in plants, is associated with “turgor,” that is to say, is dependent on osmotic conditions; in other words, the velocity of growth depends in great measure (as we have already seen, p. 113) on the amount of water taken up into the living cells, as well as on the actual amount of chemical metabolism performed by them*. Of the chemical phenomena which result in the actual increase of protoplasm we shall speak presently, but the réle of water in growth deserves also a passing word, even in our morphological enquiry.

It has been shewn by Loeb that in Cerianthus or Tubularia, for instance, the cells in order to grow must be turgescent; and this turgescence is only possible so long as the salt water in which the cells lie does not overstep a certain limit of concentration. The limit, in the case of Tubularia, is passed when the salt amounts to about 5:4 per cent. Sea-water contains some 3-0 to 3-5 p.c. of salts; but it is when the salinity falls much below this normal, to about 2-2 p.c., that Tubularia exhibits its maximal turgescence, and maximal growth. A further dilution is said to act as a poison to the animal. Loeb has also shewn jf that in certain eggs (e.g. those of the little fish Fundulus) an increasing concentration of the sea-water (leading to a diminishing “water-content” of the egg) retards the rate of segmentation and at length renders segmentation impossible; though nuclear division, by the way, goes on for some time longer.

Among many other observations of the same kind, those of Bialaszewiezt, on the early growth of the frog, are notable. He shews that the growth of the embryo while still within the vitelline membrane depends wholly on the absorption of water; that whether rate of growth be fast or slow (in accordance with temperature) the quantity of water absorbed is constant; and that successive changes of form correspond to definite quantities - of water absorbed. The solid residue, as Davenport has also shewn, may actually and notably diminish, while the embryo organism is increasing rapidly in bulk and weight.

On the other hand, in later stages and especially in the higher animals, the percentage of water tends to diminish. This has been shewn by Davenport in the frog, by Potts in the chick, and particularly by Fehling in the case of man*. Fehling’s results are epitomised as follows: ; And the following illustrate Davenport's results for the frog: To such phenomena of osmotic balance as the above, or in other words to the dependence of growth on the uptake of water, Héber + and also Loeb are inclined to refer the modifications of form which certain phyllopod crustacea undergo, when the highly saline waters which they inhabit are further concentrated, or are abnormally diluted. Their growth, according to Schmankewitsch, is retarded by increase of concentration, so that the individuals from the more saline waters appear stunted and dwarfish; and they become altered or transformed in other ways, which for the most part suggest “degeneration,” or a failure to attain full and perfect ‘development. Important physiological changes also ensue. The rate of multiplication is increased, and parthenogenetic reproduction is encouraged. Male individuals become plentiful in the less saline waters, and here the females bring forth

t Schmankewitsch has made other interesting observations on change of size and form, after some generations, in relation to change of density; e.g. in the flagellate infusorian Anisonema acinus, Biitschli (Z. f. w. Z. xxix, p. 429, 1877). their young alive; males disappear altogether in the more concentrated brines, and then the females lay eggs, which, however, only begin to develop when the salinity is somewhat reduced. The best-known case is the little “brine-shrimp,” Artemia salina, found, in one form or another, all the world over, and first discovered more than a century and a half ago in the salt-pans at Lymington. Among many allied forms, one, A. milhauseniv, inhabits the natron-lakes of Egypt and Arabia, where, under the name of “loul,” or “Fezzan-worm,” it is eaten by the Arabs*. This fact is interesting, because it indicates (and investigation has apparently confirmed) that the tissues of the creature are not impregnated with salt, as is the medium in which it lives. The fluids of the body, the mliew interne (as Claude Bernard called them +), are no more salt than are those of any ordinary crustacean or other animal, but contain only some 0:8 per cent. of NaClt, while the milew externe may contain 10, 20, or more per cent. of this and other salts; which is as much as to say that the skin, or body-wall, of the creature acts as a “semi-permeable membrane,” through which the dissolved salts are not permitted to diffuse, though water passes through freely: until a statical equilibrium (doubtless of a complex kind) is at length attained. Among the structural changes which result from increased concentration of the brine (partly during the life-time of the individual, but more markedly during the short season which suffices for the development of three or four, or perhaps more, successive generations), it 1s found that the tail comes to bear fewer and fewer bristles, and the tail-fins themselves tend at last to disappear; these changes corresponding to what have been