SEPTEMBER 14, 1899] 
NATURE 
481 
favourable conditions it is quite possible, during assimilation, to | 
obtain an intake of atmospheric carbon dioxide into this leaf | 
at the rate of 700 c.c. per square metre per hour (measured at | 
o” and 760 mm.), corresponding to an average linear velocity of 
the carbon dioxide molecules of 3°8 centimetres per minute, 
supposing the intake to be distributed evenly over the whole | 
of the lower leaf surface. This velocity is almost exactly one- 
half of that at which carbon dioxide will enter a freely exposed 
surface of a solution of caustic alkali, But if the intake of the 
gas is confined to the stomatic openings of the leaf, its velocity 
of ingress must be very much greater than this. 
We have carefully determined the number of stomata occurring 
on a given area of this particular leaf, and also the dimensions of 
| 
ard 
ai 
When a shallow vessel containing a solution of caustic alkali 
is completely covered, the air above the liquid is very speedily 
deprived of the whole of its carbon dioxide. If we now imagine 
a hole to be made in the cover of the vessel, carbon dioxide 
will enter the air space by free diffusion, and its amount can be 
very accurately determined by subsequent titration in the manner 
I have previously referred to. The time occupied by the experi- 
ment and the dimensions of the aperture being known, we can 
express the results in actual amounts of carbon dioxide passing 
through unit area of aperture in unit of time; or, since the 
| tension of that gas in the outer air is known, we can express the 
average rate of the carbon dioxide molecules across the aperture 
in terms of actual measurement, say centimetres per minute. 
We have made a very large number of 
experiments of this kind, using, in the first 
instance, dishes of about 9 cm. in diameter, 
and varying the size of the holes in the 
cover, the air space over the absorbent 
liquid being always the same. 
The accompanying curve, Fig. 1, illus- 
trates the effect which a gradually de- 
creasing orifice has on the rate of diffusion 
of atmospheric carbon dioxide under these 
conditions. The diameters of the orifice 
in millimetres are given on the abscissa 
i 
s 
line, and the rates of diffusion through 
equal areas of the apertures are taken as 
ordinates, the rate of absorption in the 
open dish under similar conditions being 
40 45 SO 55 60 65 70 
Fic. 1. 
the openings, and find that the total area of the openings, sup- 
posing them to be dilated to the fullest possible extent, amounts 
to just under one fer cent. of the leaf surface. It follows from 
this that the average velocity of the atmospheric carbon dioxide 
in passing through these openings must be 380 centzmetres per 
minute, that is to say, just 7/¢y times greater than into a freely 
exposed absorbent surface of alkali. In other words, supposing 
every one of the stomatic openings of this leafcould be filled up 
with a solution of caustic alkali, the absorbent power of the leaf 
as a whole would only be =}; of what it actually is when assimi- 
lating. 
These are some of the consequences which flow from an 
acceptance of the hypothesis of stomatic exchange, and it 
appeared to be impossible to accept that hypothesis unreservedly 
without some collateral evidence that these comparatively high 
75 
velocities of diffusion are physically possible when dealing with 
such low gradients of tension as must necessarily exist when 
the highest amount of carbon dioxide does not exceed ‘03 per 
cent. 
The well-known general law expressing the rate of the 
spontaneous intermixture of two gases when there is no inter- 
vening septum was, as every one knows, established by 
Graham, and the more elaborate investigations of Loschmidt 
many years later served to confirm the general accuracy of this 
law, and to show that, within very narrow limits, the diffusion 
constant varies in different gases inversely as the square roots 
of their densities. 
But a mere knowledge of the diffusion constants of air and 
carbon dioxide does not, as far as I can see, materially assist us 
in the particular case we have under consideration. In order 
to gain some idea of what is actually possible in the way of 
stomatic diffusion in an assimilating leaf, we must know some- 
thing of the actual rate at which atmospheric carbon dioxide 
can be made to pass into a small chamber containing air at the 
outside tension, but in which the carbon dioxide is kept down 
almost to the vanishing point by some rapid process of absorp- 
tion ; and we must also determine the influence of varying the 
size of the aperture through which the diffusion takes place. 
Our attempts to answer these questions experimentally have 
led us into a long investigation, which promises to be of wider 
interest than we had first imagined. I only propose to give on 
this occasion a general account of the results so far as they 
affect the physical question of the intake of carbon dioxide into 
the plant. 
NO. 1559, VOL. 60] 
taken as unity. 
It will be seen that in the first instance 
a gradual reduction of the diameter of the 
opening is accompanied by a very regular 
increase in the rate of passage of the 
carbon dioxide until a diameter of about 
50 mm. is reached ; that is to say, up toa 
point at which about two-thirds of the area of the dish is 
covered. A further progressive diminution in the size of the 
aperture makes comparatively little difference in the diffusion 
rate until we reach about 20 mm., beyond which the curve 
again begins to rise, increasing rapidly in steepness as the 
apertures become smaller. 
The experiments with open dishes are too crude for a study 
of the influence of very small apertures, so for this part of our 
work we constructed a special form of apparatus which has 
enabled us to determine the relative rates of diffusion through 
orifices in thin metal plates ranging down to I mm. in diameter. 
16 18 20 22. 2422M, 
/é 
Fic. 2. 
I have plotted the results of such a series of experiments (see 
Fig. 2), showing the relative rates of diffusion of atmospheric 
carbon dioxide through equal areas of apertures between 
20 mm. and I mm. in diameter, under constant conditions, and 
it will be noticed how very steep the curve becomes after 
diameters of 5 or 6 mm. are reached. 
The speed at which the diffusion of atmospheric carbon 
dioxide takes place through unit area of an orifice of I mm. in 
diameter is just sixteen times as fast as it is through unit area of 
an aperture of 20 mm. ; and since we know that the rate of 
passage in the latter case is two and a half times greater than 
