A similar result, excepting the sudden closure, may be obtained with the stomata of Fouquieria splendens, and in an even more marked degree than

in those of Verbena. They not only open widely, but the guard-cells frequently separate from each other at one or both ends, enlarge greatly, and become tilted with reference to the epidermis. This enlargement and the distortion which accompanies it appears to be due, not to the swelling of the starch-grains, but of the thickened cellwalls, as these changes are often quite as great, even if the starch is in small amount or is absent from the stoma.

The behavior of the stomata of Galtonia was induced by Leitgeb by killing with iodine vapor and chloroform, and the opening under these reagents was quite as marked as in my fig. 9, which shows the forms assumed by stomata on treatment with strong potassium hydrate. It would seem, however, that the immediate cause of the opening is not

the same as in the case here recorded.

PART I.

TRANSPIRATION AND STOMATAL MOVEMENT.

The problem here considered has, as I conceive it, two aspects:

(1) The degree of correlation between the normal rates of transpiration and the normal changes in the size of the stomatal openings. There is, however, a logical difficulty to be encountered in that, even should a close correlation be shown to occur, it would remain unproved that the movements of the stomata were immediately related, in the causal sense, to the rise and fall of transpiration rate. This must be fully reckoned with in attributing a regulatory function to the stomata, for, unless marked quantitative differences between the functions of the chloroplasts of the chlorenchyma and those of the stomata exist, it would be quite possible that the photosynthetic activity of the chlorenchyma and of the guard-cells would run parallel without a necessary causal relation between stomatal movements and changes in transpiration rate. That such a causal relation exists is to be doubted from the consideration that the stomata, in very many cases at least, have a greater capacity for the outward diffusion of water-vapor than actually has been found to occur (Brown & Escombe, 1900) and this may be true at any given diffusion capacity of the stomata, depending upon their dimensions. (2) Since, in the final analysis, light, above all other factors, influences stomatal movement, and since also appropriate illumination is the condition par excellence under which photosynthesis takes place, if the supposed causal relation under consideration exists, wide and sudden changes in the degree of illumination should be accompanied by changes in transpiration rate, and these, at the same time, by corresponding changes in the diffusion capacity of the stomatal openings.

If such changes of transpiration rate occur unaccompanied by stomatal movement, the answer to the problem is clear. If, however, any changes in the stomata occur, due consideration must be given, in the interpretation of the data, to the law of diffusion through a perforated septum as formulated by Brown & Escombe (loc. cit.), whose study of the static diffusion of gases through membranes perforated by minute openings led them to the surprising result that the rate of diffusion through such openings is much greater than would at first be expected.

31

Diaphragms perforated at regular intervals with holes 0.38 mm. in diameter may be so arranged as to produce but little obstructive influence on the diffusive flow of a gas when the total area of the apertures amounts only to about 10 per cent of the area of the septum, and that nearly 40 per cent of the full diffusive flow may be maintained when the number of the apertures is so far reduced as to represent an area of only 1.26 per cent of the full area of the septum.

The structure of a typical herbaceous leaf illustrates in a striking manner all the physical properties of a multiperforate septum.' * Regarded from this point of view, it is shown that the stomatic openings and their adjuncts constitute even a more perfect piece of mechanism than is required [italicizing mine] for the supply of carbon dioxid for the physiological needs of the plant, and instead of expressing surprise at the comparatively large amount of the gas which an assimilating leaf can take in from the air, we must in future wonder that the intake is not greater than it actually is.

The large amounts of water-vapor which pass out of the leaf by transpiration are well within the limits of diffusion.

276 1730

The authors, assuming circular openings† in the application of their mathematical deductions, stated that the maximum observed rate of transpiration for a plant of Helianthus was one-sixth of the possible rate or 73% c. c. per square meter per hour, in view of the number of stomata and their distribution.

It will be of interest to compare the leaves of Helianthus and of Fouquieria splendens with respect to the physical conditions which are related to stomatal diffusive capacity. Brown & Escombe found that in Helianthus there are 33,000 stomata per square centimeter of leaf surface. The area of the pore was calculated to be 0.0000908 square millimeter, which is equal to the area of a circle of 0.0107 millimeter diameter. The depth of the pore is o.014 millimeter. In Fouquieria splendens there are 188 (=320) per square millimeter, or 32,000 per square centimeter of leaf. The depth of the stomatal pore is 9 to 15 micra. Their areas in various conditions were found by making careful drawings to scale of openings of different dimensions on standard ruled paper. The figures so obtained (figs. 2 and 5) were cut out and

160

160

*In their longer paper (1900 a) Brown & Escombe say that the perforations, if 8 or 9 diameters apart, do not interfere with each other, in which case they act as separate tubes; and this condition is approximated in the leaf.

Of areas equal to those of the elliptical stomata, since the evaporation from an elliptical surface is equal to that from a circular surface of the same area (Stefan). The area of a stoma

was taken to be

length breadth

X

2

2

×π (=1,65) as sufficiently close.

Since, however, the openings are not true ellipses (fig. 2) and are sometimes (Verbena) quite aberrant (fig. 5), the area may perhaps better be deduced empirically, at least in many cases.

This comparison does not extend to the form of the intercellular spaces, which are narrower, it is quite probable, in Fouquieria. It will be evident, however, that this does not vitiate the comparison, since, in spite of the small intercellular spaces, the maximum transpiration rate is fully as great as in Helianthus. The probable greater thickness of the leaves of Fouquieria may tend to offset the shorter transverse dimensions of the intercellular spaces by their greater extent. (Bergen, 1904.)

weighed, the weight being compared to that of the whole piece. The measurements are presented in table 17.

It will be seen that the largest areas here used, those of pores with dimensions 6 by 19.5 and 9 by 16 micra, are fully as great as the area obtained for the stomatal pore of Helianthus. The largest possible pore dimensions, which do not exceed 10 by 20 micra, give us an area of 157.5 square micra, equal to a circle of a diameter of 14.24 micra, quite in excess of the stoma of Helianthus. TABLE 17.-Measurements of stomatal pores, and areas determined by the method of proportional areas of weighing and by computation, together with the diameters of circles of equal areas.

The depth of the Fouquieria pore-tube is from 9 to 15 micra; so it may be concluded that, aside from slight differences possible in the form of the tube (fig. 3), the diffusion capacity of the stomata of Fouquieria is certainly not inferior to that of Helianthus stomata. How far the geometrical form of the area may modify the calculation we can not say, but, as in the case of the poretube, it may be assumed to be but little. Since the stomata of both plants conform closely to a very common type of this apparatus, the main results of the comparison will not be vitiated by the trifling differences which must of course exist.

By means of a potometer experiment, the maximum rate of transpiration for a Fouquieria shoot 27 cm. long, having a leaf surface of 299 sq. cm., was found to be 312 c.c. per square meter per hour,* a rate between one-sixth and one-fifth the stomatal diffusion capacity of Helianthus and, on the basis of the above comparison, approximately that of the Fouquieria leaf.

*It should be noted that due caution has been exercised in obtaining this rate, allowance having been made for the probable inaccuracy of the potometer method. The rate without the correction was 390 c.c. per square meter per hour. By weighing (vide ante) a correction for absorbtion of 10 per cent was determined to be necessary during the earlier hours of the experimental period. In order to be well within the truth a correction equal to the volume of the twig used has been applied. This correction proved to be about 20 per cent. The average rate per hour for 24 hours was found to be about 90 c.c. per square meter per hour, this being a high rate for a xerophyte. As has been shown, however, the leaves under consideration are not markedly xerophytic.

1

The diffusion capacity of the stomata considered as openings with no depth varies directly with the linear dimensions* which are derived, for purposes of computation, by comparing the stomata with circles of equal area. The actual rate of diffusion through stomata will depend upon the length of the tube, the gradation of density of the water-vapor between the surface of the cells of chlorenchyma, and the outer air, modified by air-currents.†

It seems clear from Brown & Escombe's experiments (cf., p. 259, fig. 6) that there exists such a gradation of density, from which it follows that under conditions of rapid transpiration the vapor-pressure within the leaf-cavities is less than when a low rate occurs, assuming the evaporation capacity of the cells to be constant. As in the case of CO2, the pressure of the water-vapor within the leaf, though much greater, must vary with the size of the stomatal pores, but here the relative humidity without is a very variable factor and will therefore modify the rate of transpiration independently of the pores.

It is also to be noted that the evaporating capacity of the surface of the chlorenchyma cells of the leaf is less than that of the pure water, so that the cell-walls tend to hold back the water. This, combined with a high relative humidity, would produce a high vapor-pressure within the leaf and a low rate of transpiration, even though the stomata are widely open. A low vapor-pressure within the leaf would follow on a low relative humidity, so that with open or partially open‡ stomata the rate of transpiration may be high, but because of the incapacity of the cells to give up water-vapor, the capacity of the stomata to allow its escape may not be made full use of. If this argument be sound we should expect that the rate of transpiration will vary independently of the size of the stomatal openings.

This view is borne out by the facts obtained during the progress of this investigation. As an illustration experiment 54 will serve, the full data of which are given beyond. In this the transpiration rate was found to be, at 9h15m a.m., 216 grams, and at 11h15m a. m. 221 grams per hour per square meter of leaf. At 9h15m a.m., the stomata were open, and measurements showed that the average width to be 6.5 micra and the average length 14 micra. The average area, by computation, was 71.66 sq. micra, and the

*This Brown & Escombe inferred from experiments with openings with diameters 40 to 2000 times the diameter of the stomata.

Increase beyond a slight movement of air will not make the increase of outward diffusion of water-vapor greater, because this slight movement will be sufficient to remove the density shells. The ratio between diffusion in still and moving air in a Helianthus leaf is 1 to 1.23 (Brown & Escombe, 1905. p. 65). In 1904 experiments were conducted to determine the effect of wind upon the transpiration in ocotillo, with a result which practically substantiates Brown & Escombe's figures. There are no such great differences as are commonly supposed to occur. (For ratios of diffusive capacity in still and moving air see table 18.)

The diameters of stomata might be reduced to from one-fifteenth to one-twentieth of their length, and still allow a sufficient amount of CO2 to pass for maximum assimilation, provided the absorption was perfect [italicizing mine]. (Brown & Escombe, loc. cit.)