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monise so closely with the twigs to which they cling that REPORT OF THE CARNEGIE INSTITUTION, it is difficult to see where one begins and the other ends. Fig. i illustrates this insect in the attitude in which it was

1904.' resting before being captured. Another interesting insect from Ceylon is one of the IN Nature for January 7, 1904, a list was given of the

awards made by the Carnegie trustees for the prosecution moths, Eurybrachis westwoodii. The fore wings of this of inquiries in various scientific directions. The third year insect are marked in a mottled pattern of green, grey and book, just published by the board of trustees, contains brown, the hind wings being white, with deep claret- reports upon most of these researches, but the time is far coloured marks near their base, and when it is on the wing too short to gather in the full harvest, which may hereafter the moth is an attractive-looking creature. But its appear- be expected, from so lavish and, presumably, judicious exance alters when it is at rest, with the mottled wings folded penditure. There is abundant evidence that many wellover the back. In Fig. 2 it is shown with the wings known men, engaged in every department of science, have expanded as it appears when flying, and below is a piece been enabled to attack problems which must otherwise have of bark with the same insect resting upon it, where been neglected, or pursued with inadequate material and less it was discovered by the keen sight of the collector-a energy. Beyond this general fact, the present volume does clever capture, as will be admitted when it is noticed how

not, in most instances, enable us to estimate the results. excellently the wings and bark harmonise, and how they The balance sheet attached shows that the trust is in a very seem almost to merge one into the other.

flourishing condition, and that 267,000 dollars have been There is found in Madagascar a small beetle 'which, provided for inquiries, which the management discuss under looked at apart from its natural surroundings, has nothing the three heads of large, special, and minor grants. specially interesting about it except that it is a conspicu- Under the division of large grants, we have a description ous, rugged-looking, pure white and black insect, about

of the station erected, or adapted, for the study of experithree-quarters of an inch long. It feeds upon a species of mental evolution at Cold Spring Harbour, some twelve fungus, which grows upon the bark of trees in mixed cream miles from New York. Plans of the building are given, and and black coloured patches. The beetle is shown at the a full account of the opening ceremony, at which Dr. Hugo

de Vries gave a scientific address. The objects sought to be gained by such an institution are typical of the uses of the trust, and legitimately appeal to a liberal consideration. The investigations must be long continued, the results may be doubtful or negative, and it is a research which no individual or institution is likely to undertake on a scale sufficiently broad to produce decisive results.

Another far-reaching scheme, the Marine Biological Laboratory at Dry Tortugas, Florida, under the care of Dr. H. G. Mayer, is quite in its first stages of development, but one whose usefulness may be confidently predicted in due time. The buildings that have been erected consist of a main laboratory, 100 feet long, one story high, and with special arrangements for keeping the building cool in the hot weather of those latitudes. A feature in the construction of the laboratory and of the smaller buildings connected with it, is that all are made portable, so that they can easily be removed from their present site and erected elsewhere if thought desirable. Attached to the station is a sea-going vessel of light draft, fifty-seven feet over all, and sixteen feet beam, with a 20 h.p. naphtha engine. There is sufficient accommodation for seven men on board, and the vessel is specially designed to dredge in depths of 500 fathoms or less. Among other projects for which large grants have been made is the subject of economics, whose many subdivisions include, among others, population and immigration, mining and manufactures, banking and finance, social legislation and the labour movement, &c. Reports on all these subjects have been added, showing the scope of the

respective inquiries and the progress that has been made. FIG. 3.- Lithinus nigrocristatus (Madagascar). The upper figures show Historical research and terrestrial magnetism are the re

beetle and bark separately, and in the lower figure the beetle is on the bark.

maining two subjects which come under the division now

being considered. On the latter subiect we have some of the top of Fig. 3, and beneath it a piece of twig with the

results of the discussion of the magnetic disturbance obfungus growing upon it. At the bottom of the same illus

served during the eruption of Mont Pelée, which are of tration the same piece of fungus-covered twig is shown,

special interest, since the inquiry discloses the fact that in but here the beetle is resting right in the middle of the

certain respects the disturbance resembled those storms which fungus, effectually concealed amongst the vegetation upon

are believed to be of cosmic origin. which it feeds.

The Transcaspian archæological expedition and geoThe paper is very fully illustrated by more than two

physical research are the subjects of special grants. The hundred figures of the insects described, with the localities

former is under the charge of Prof. Pumpelly, who left in which they were taken, covering the whole subject America in December, 1903, and began excavations in the treated by Mr. Sykes.

following March, first attacking Anau, in Turkestan. By Exception is taken to the use of the words “imago " and means of excavations in tumuli and by shafts sunk in the "imagine,” introduced by Linnæus, as representing the

city of Anau, the exploring party has traversed some 170 final stage of insect metamorphosis, and “matura

feet of the accumulations of successive generations of (maturo = to ripen) is suggested and employed as a sub

peoples, extending from recent times, through the iron and stitute, conforming conveniently with the accepted terms

bronze civilisations, and some 45 feet deep into the stone for the earlier stages-larva and pupa. The word

age. Among the objects of this investigation is the hope "mimicry" is also adversely criticised, as implying con

of throwing some light on the source of our domestic scious resemblance, which is not known to exist, and

animals. “simulism,” simulation," "simulating,” are

sub

The reports on the subjects of the so-called smaller grants stituted “as being at once expressive, explanatory and

cannot be particularly referred to here. The inquiries cover euphonious, and free from the inference of designed and

i Carnegie Institution of Washington. Year Book, No. 3, 1904. (Washcognitive resemblance."

ington : Published by the Institution, 1905.)

[graphic]
[graphic]

the whole ground of physical science, and are in many spontaneous liberation of energy
instances of the greatest importance, but generally have conceivably raise its temperature
reference to definite researches undertaken by individuals minute, provided there were no sim
not calling for wide cooperation. A list of papers, prepared radiation, conduction and convectio
possibly to pave the way for future applications, is added, in air, and internal vaporisation of wal.
which are discussed the conditions of solar research at of loss, of course, become opera
Mount Wilson, by Prof. Hale: the southern observatory temperature of the leaf exceeds tha
project, by Prof. Boss; fundamental problems of geology, We shall see presently that the ther
by T. C. Chamberlin; plans for obtaining subterranean leaf in still air is 0.015 calorie per
temperatures, by G. K. Gilbert; magnetic survey of the leaf-surface per minute, for a differenc
Pacific Ocean, by L. A. Bauer ; and geological research in 1° C. between the leaf and its surrou
Eastern Asia, by B. Willis.

temperature of the leaf, under the co
cannot exceed that of its surroundings

0.00582/2 X 0.015=0°:019 THE RECEPTION AND UTILISATION OF But this is assuming that transpiration ha ENERGY BY A GREEN LEAF!

ance, which is certainly not the case, so

temperature difference of oo.019 C. will THE subject of my lecture is derived from the series of

reduced. papers laid before the society to-day by my colleagues

The main point which I wish to bring out h and myself, dealing with some of the physiological pro

the thermometric disturbances due to the proce cesses of green leaves. In giving an account of some of

spiration are very small, so small, in fact, that these investigations I shall dwell mainly on their relation

be neglected in considering the large disturbano to the energetics of the leaf, and shall endeavour to show

by other causes. how the leaf behaves under various conditions when re

Let us now suppose our leaf to be placed garded from the point of view of the exchange of energy

same conditions as before, but in air which is between itself and its surroundings.

saturated with aqueous vapour for the temperatus: One of the problems which we attempted to solve was

The conditions are manifestly unstable owi: to draw up a revenue and expenditure account” of

excess of the partial pressure of the water vapo energy for a green leaf, showing the proportion of the

saturated air of the interspaces of the leaf ove incident energy absorbed, the amount of this absorbed

the vapour in the unsaturated air outside. energy which is used up for the internal work of the leaf,

The diffusion-potential thus set up will result. and the proportion which is dissipated by re-radiation and

vapour passing outwards through the stomata, the losses due to the convective and conductive properties

temperature of the leaf will fall. This fall will of the surrounding air under varying wind-velocities.

until the gradient of temperature between the sum Of these various factors, the one I have last mentioned, and the leaf is sufficiently steep to allow energ which presupposes a knowledge of the thermal emissivity

into the leaf from without at a rate just sufficien of the leaf-surface, presented by far the greatest difficulty ; duce the work of vaporisation, at which point but during the past year Dr. W. E. Wilson and I have

thermal state will be established which will rem been able to devise a suitable method for determining the

stant so long as other conditions are unaltered. thermal emissivity of a leaf-surface in absolute units, so will then have assumed a temperature t', which that our story is now fairly complete.

case will be lower than that of its surroundings. The discussion of the thermal relations of a leaf to its

Now it is manifest that when this steady therm surroundings will be simplified if we first consider the case

dition has been attained, the amount of water va of a leaf when it is shielded from solar radiation. We

per unit of area of the leaf in unit of time mase will assume that a detached leaf, freely supplied with

measure of the energy flowing into the lear water, is placed in an enclosure the walls of which are

gradient of temperature represented by t-t', non-reflective and are maintained, along with the enclosed

vided we determine the amount of water lost by air, at a perfectly uniform temperature t. We will further

and the temperature difference between the leai assume that the air is saturated with water-vapour. Under these conditions the system would remain in

surroundings under the steady conditions, we have

data necessary for finding the coefficient of thermal equilibrium if it were not for the respiratory pro- emissivity of the leaf-surface in absolute units, that cesses going on within the leaf-cells. These are exothermic

say, the rate at which a leaf-surface will emit or in their final result, so that the state of complete thermal

energy from its surroundings in still air for a diffe, equilibrium can only be attained when the temperature of tenperature of 1° C. of the leaf has risen to a point t', somewhat higher than Following out this idea, Dr. Wilson and I have suc t. The magnitude of the difference t' t, representing the fully determined the constants of thermal emissivity er maximal thermometric disturbance between the leaf and leaves of different kinds, both under " still-air "conditions its surroundings, will depend on three main factors :

and in air-currents of determinate velocity. The rdte (1) On the rate of evolution of the heat of respiration. are interesting from several points of view, since amu

(2) On the rate at which this heat is dissipated by the other things they enable us to estimate the rate at thermal emissivity of the leaf-surface, and,

the excess of solar radiant energy falling on a (3) On the magnitude of the slight rise of partial dissipated by mere contact with the air moving pressure of the water-vapour in the interspaces of the leaf, ordinary wind-velocity, and they also give us, under which gives rise to a certain amount of diffusion of water- conditions, a means of deducing the actual rate of vapour through the stomata. The rate of evolution of the heat of respiration can be

piration from mere observations of temperature-differe

Before proceeding to show more in detail the mana deduced with sufficient exactness from the amount of which the thermal emissivity of a leaf is determined carbon dioxide liberated per unit area of the leaf-lamina in will turn for a moment to the magnitude of the differ unit of time, since there is evidence that the carbon of temperature between a leaf and its surroundings: dioxide proceeds from the oxidation of a carbohydrate with may be expected from a given rate of transpiration a hea of combustion which cannot be far removed from will assume that the leaf of a sunflower, transpiring 3760 calories per gram. Taking the concrete example of the unsaturated air of the enclosure, when the a leaf of the sunflower respiring at the rate of 0.70 c.c. thermal condition is attained, is losing water at the of carbon dioxide per square decimetre per hour, it can of 0.5 gram per square decimetre per hour, or o cho be shown that the heat of respiration in this case amounts

gram per square centimetre per minute. to about 0.00582 calorie per square centimetre of leaf- The heat required to vaporise this amount of lamina per minute. From the known weight of a square 20° C. is 0.0000833 X 592.6=0.04938 calorie, which, centimetre of the leaf-lamina, and its specific heat, this theory of exchanges, must represent the amount of

1 The Bakerian lecture, delivered at the Royal Society, March 23, by entering and leaving a square centimetre of the Dr. Horace T. Brown, F.R.S.

lamina per minute. The thermal emissivity of this

a

con

40

ttelianthus

Liriodendror tulipifera

is 0.015 calorie per square centimetre of leaf-surface per velocity. The results of two such experiments with leaves minute, for a temperature gradient of 1° C., so that the of Liriodendron tulipifera and Helianthus multiflorus are temperature difference t-t' will be represented by

given in the figure. It will be seen that the effect of the

cooling or heating due to the air is a linear function of 0.04938/2 X0.015=1°:64 C.

the velocity, the coefficient of thermal emissivity of the For the simultaneous determination of the temperature leaf-surface increasing at the rate of 0.017 calorie per difference t-t' and the amount of water transpired, we square centimetre per minute for an increased velocity of employed two differential platinum-resistance thermometers

the air current of 100 metres per minute. This effect of each consisting of about 2-4 metres of fine wire arranged moving air in dissipating the excess of radiant energy in a mica and ebonite plate so as to form a flat grid, falling on a leaf is a very important fact in the economy against the two sides of which two similar leaves were of some plants in which transpiration is reduced to lightly pressed and held in position by ebonite frames minimum, and it is one of nature's means for preventing furnished with cross-threads of silk. The two leaf-laminæ the rise of temperature in strongly insolated plants from were thus in close apposition to the resistance-coils, which reaching a dangerous point. were favourably placed for rapidly acquiring the mean

We must now turn our attention to the thermal relations temperature of the leaves, which were supplied with water of a leaf to its surroundings when it is receiving direct from two small tubes attached to the frames. A definite

solar radiation, and here again, for the purpose of simplifyarea of leaf-surface was exposed, amounting in each case

ing my argument, I must ask you to imagine an ideal set to 1394 square centimetres. The loss of the water of of conditions under which a healthy leaf, well supplied transpiration was determined by weighing the apparatus

with water, is exposed to sunlight of constant intensity, at suitable intervals.

and that there is no variation in the temperature, humidity, The difference in temperature between the two coils was

or degree of movement of the surrounding air, or in the determined by means of a Callendar's recorder. Instead

dimensions of the leaf stomata. of determining the difference of temperature between the

As in the previous case, a state of thermal equilibrium leaf and the surrounding air, it was found more

will be speedily established between the leaf and its venient to clothe both coils with leaves, but to arrange

environment, when the simultaneous loss and gain of them in such a manner as to produce differential transpira

energy will just balance.

When this condition is attained, let R represent the tion between the two pairs, a result which can in most

total radiation falling on cases be brought about by arranging one pair of leaves

I square centimetre of the leaf with their dorsal sides turned to the platinum coils, and the other pair with their dorsal sides facing outwards. Owing to the comparatively rapid thermal adjustment which takes place, the results are not affected by the gradual closing of the leaf stomata during an experiment, provided the record is correctly integrated so as to give the mean difference of temperature. From this mean difference of temperature between the two pairs of leaves, and the differential transpiration corresponding to this, the thermal emissivity of the leaves is readily calculable.

As an example, we may take an experiment with the leaves of Liriodendron tulipifera, in which the experiment lasted 129 minutes. The difference in the amount of water transpired by the two pairs of leaves was 0.510 gram, and the mean temperature difference was 1°:41 C. Taking the latent heat of water at 593.6 calories, it follows that 0-510 x 593-6 = 302.7 represents in calories the excess of energy which must have entered the cooler pair of leaves from their surroundings, an excess which is conditioned

Air velocities in metres per minute. solely by the temperature gradient of 19:41 representing the difference of temperature between the two sets of Fig. 1.-Influence of moving air on the thermal emissivity of leaves. leaves. The surface area of the leaves exposed was 139.4 square centimetres, so that the thermal emissivity of a square centimetre of leaf-surface per minute for a 1° C.

in one minute, and, further, let the " coefficient of absorp

tion of the leaf for this radiation be represented by a ; temperature gradient will be

then Ra will represent the radiant energy absorbed per 302.7/129 X 139.4X1:41=0.01194 calorie.

square centimetre of leaf-lamina per minute. As examples of the extent to which the thermal emis

At this stage it is of some interest to give absolute sivities of leaves of various plants differ, the following

values to R and a in order to see what would be the may be given. They represent the emissivity under con

thermometric effect produced on a leaf by ordinary sunditions of still air :

shine in default of there being some ready means of dis

sipating the absorbed energy. Thermal Emissivity of Leaves of Various Species of

If we denote the mass of a square centimetre of the Plants, under Still-air Conditions.

leaf-lamina by m, and its specific heat by s, then on the

above assumption the rise of temperature of the lamina
Therma emissivity in calories
per sq. cm. of leaf-surface for a

per minute will be represented by Ra/ms.
Species of Plant
1° C. excess of temperature

Let R=0.8 calorie per square centimetre per minute,
Per minute Per second

which represents the intensity of ordinary summer Liriodendron tulipifera (a) 0.0119 0.000199

shine in these latitudes. (b)

Let a, the coefficient of absorption, be 0.78, a value

0.0127 Helianthus multiflorus

0.0150 0-000249

which is determinable by a method presently to be deTropoeolum majus

0.0142 0-000237

scribed ; further, let the mass, m, of a square centimetre Tilia euro poea

0.0159
0.000266 of leaf be 0.020 gram, and its specific heat s=0.879, then

the rise of temperature of the leaf under the conditions l'nder ordinary outdoor conditions we never have to deal postulated will be at the rate of with perfectly still air, and the inquiry had therefore to

0-8 X 0-78/0.02 X 0-879=35° 4 C. per minute, be extended to the influence of moving air currents on the thermal emissivity of leaves.

a result which would be speedily fatal to the leaf. This was investigated by observing the differential The dissipation of the absorbed energy necessary to keep temperature and differential transpiration when the two the temperature of the leaf within working limits is propairs of leaves were placed in a shaft through which a vided for, on the one hand, by the internal work of the current of air was passed having a definite and steady | leaf, consisting mainly of the vaporisation of water, and

Emissivity in calories per sq. c.m. per minute for

po Temp. Grcess 1006.

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to a less extent of the endothermic process of photo- readily convertible into water-gram
synthesis, and on the other hand by the losses due to cident on unit area of surface in uni.
thermal emissivity, which even in still air are consider- a mean value of R.
able, and may assume large dimensions if the air is in The proportions of the radiant en

spectively absorbed and transmitted
First, as regards the energy used in internal work, that were determined with the same insen
portion which produces the vaporisation of water, and in steady sunlight the amount of radi
which I will denote by W, is determinable from the weight the radiometer with and without the
of water lost by a given area of the leaf in a given time, leaf. This gives a measure of the con
and from the known latent heat of water-vapour. On the tion of the leaf a with a close approach to
other hand, the amount of the absorbed energy which is neglect the amount of reflected radiation,
used up in the photosynthetic process, and which I will small in cases of perpendicular incidence.
denote by w, is deducible from the actual amount of The coefficient of absorption, as might be ex
carbon dioxide which enters the leaf, on the legitimate considerably with leaves of different species
assumption that the synthesised product is a carbohydrate, shown in the following table, and there are
the heat of formation of which is approximately known. individual differences in leaves of the same plan
The generalised form of the thermal equation of a leaf

Coefficients of Absorption (a) and Transmission which is receiving solar radiation, and has acquired

the Radiant Energy of Sunlight for Lean a state of thermal equilibrium, may therefore be repre

Coefficient of sented by Ra=(W+w)Fr.

absorption When Ra is greater than W+w, that is to say, when the energy absorbed by the leaf in a given time is more

Helianthus annuus

0 686 than sufficient to perform the whole of the internal work, Polygonum Weyrichii... 0647 r is a positive quantity, and represents in absolute units Polygonum Sachalinense

0.69! the sum of the losses due to radiation and convective cool- Petasites officinalis

0.728 ing, and it is the only portion of R which can produce Silphium terebrinthaceum 0.699 a rise of temperature in the leaf.

Arctium majus

0.728 Provided we know the thermal emissivity of the par

Verbascum 'olympicum 0.758 ticular leaf which we are using, the actual rise of tempera- Senecio grandifolius

0.774 ture of the leaf-lamina above its surroundings can be de

In the generalised thermal equation the value to termined from r; for ife is taken to represent the

senting the amount of energy expended in photosyesis emissivity, then the temperature difference between the

measures the effective internal work of a useful leaf and its environment, that is to say, t' - t, will be

structive kind, for the due performance of which leat r/2e.

may be said to exist, and the relation which the tears On the other hand, when Ra is less than W+w, that

to the total energy flowing into the leaf gives an mair is to say, when the absorbed radiant energy is insufficient of the true economic coefficient when the leaf is ded to perform the whole of the internal work, r is a negative as a thermodynamic engine. quantity, and the excess amount of energy requisite to

In the five or six years during which these research perform the internal work must be drawn from the

occupied Mr. Escombe and myself at the Jodrell Lorasurroundings of the leaf; in other words, when thermal

atory, a large share of our attention was given to deterequilibrium is established the temperature of the leaf under

mining the best means of estimating the rate of pantothese conditions must be below that of its surroundings. synthesis in green leaves exposed to sunlight in air conHere again, however, the thermometric difference expressed taining, the normal amount of carbon dioxide. by t-t' will be r/2e.

At the time we commenced our experiments the only The true measure of the photosynthetic work effected by

practical method was a gravimetric one introduced by suitable radiation is, strictly speaking, not given exactly Sachs, by which the amount of material assimilated by a by the amount of atmospheric carbon dioxide absorbed by

leaf in a given time is deduced from variations in the the leaf, but by this amount plus the small amount of

dry weight of known areas of the leal-lamina. Cnfor carbon dioxide which would have been evolved by re

tunately, we found that the errors to which this method spiration if photosynthesis had been in abeyance. This is is liable tend on the whole too much in one direction, a correction which has to be taken into account in certain

and their sum, which frequently exceeds the value we are special cases, but it does not affect the generalised thermal

trying to estimate, is swept into the final result. equation I have given, since the heat of respiration is The method which we finally adopted was one base! opposite in sign to that of the heat of re-formation of the

on the measurement of the intake of carbon dioxide at a carbohydrate, and these values, representing a concurrent

partial pressure somewhere near that at which it exists gain and loss of energy by the leaf, must exactly balance in normal air, i.e. 3/10,000 of an atmosphere, each other if the carbohydrates standing at the two ends It is evident that such experiments must be conduried of the reversed process are identical, and if they are not on a relatively large scale, both as regards the area of identical the difference in their thermal relations must be leaf-surface exposed and the volume of air passed over it. so small as to be inappreciable.

(The nature and disposition of the apparatus were shorn Before proceeding to show how these general views can

in a diagram on the screen.) be applied to the construction of a revenue and expenditure The leaf, which, if desired, may still remain attached to account of energy for a leaf, I must briefly refer to the its plant, is enclosed in a glazed case through which mode in which the various factors have been determined.

stream of air is drawn by water-pump, We have already considered the manner in which the volume of the air being measured by a suitable thermal emissivity of the leaf e is determined, a value

Between the leaf-case and the meter there which is all-important in considering the temperature of is a Reiset's absorption-tube filled with a solution ! the leaf, and I have also sufficiently indicated how we caustic soda, which ensures the complete absorption of the can determine the work of transpiration, and consequently carbon dioxide remaining after the air has passed through the value of W.

the case. R, the intensity of the solar radiation falling on the leaf-surface, was measured by means of a specially con- allows of a simultaneous determination of the car structed Callendar's radiometer, the coils of which were dioxide in the air before it passes over the lear, and the enclosed in a flat rectangular case mounted on an adjust- difference between these values measures the carbon diosic able stand so that the orientation of the receiving surfaces taken up by the leaf. Tnis is referred to unit area of the could be made to correspond with that of the leaf under leaf by measuring, by means of a planimeter, the area, ay experiment. The radiometer was connected with the photographic impression of the lamina on positive Callendar's recorder furnished with a planimeter which paper. automatically integrated the curve recorded on the drum. A very delicate method was used for titrating the

The constants for the instrument were determined for absorbed carbon dioxide in the alkali, and when all proper us by Prof. Gallendar, and the planimeter readings were precautions are taken the errors of experiment arr smell.

a

meter.

the the duplication of the meter and absorption, apparatu

a

R

and with certain modifications there is practically no limit will give some idea of the values of the economic coto the scale on which the experiments can be conducted. efficient ordinarily met with :It is evident that with this apparatus the mean carbon

The Economic Coefficient of Leaves of Polygonum dioxide content of the air in contact with the leaf must be

Weyrichii under Various Degrees of Insolation. somewhat less than that of the entering air, so that a

Radiant energy falling correction of some kind is necessary in order to obtain

on 1 sq. cm. of leaf per an estimate of the rate of assimilation under free-air con

minute, in calories

Economic coefficient ditions. This is afforded by the fact, established early in

W/R X 100

0.612 our work, that when all other conditions are the same,

0.42 the rate of assimilation by the leaf is directly proportional

0.194

1.59

0.150 to the partial pressure of the carbon dioxide, provided this

1.66 does not exceed five or six times that of the carbon dioxide

0.143

1.32 of normal air.

Turning once more to the generalised thermal equation In deducing the amount of energy used up in the photosynthetic work from the amount of carbon dioxide absorbed

Ra=(W+w) Fr, by the leaf, we have assumed, as we are entitled to do, that we must not lose sight of the fact that this represents a the product of assimilation is a carbohydrate. If the par- set of conditions in which all the determining factors, both ticular form of carbohydrate is known, the amount which internal and external, remain constant for a sufficient time corresponds to a definite mass of carbon dioxide absorbed to allow of the attainment of steady thermal equilibrium by the leaf is of course determinable ; and, further, the between the leaf and its surroundings. energy used up in synthesising this amount of carbohydrate In practice this ideal state is never attainable. In the will be represented by its heat of combustion.

first place the incidence of solar radiation is subject to No sensible error will be introduced into this calculation rapid oscillations of considerable magnitude, even under by selecting one of the carbohydrates existing in a leaf in the most fair-weather conditions, and every variation of preference to another. We have based our calculations on this kind necessarily alters the value of Ra, the energy the assumption that we have to deal with a hexose having absorbed by the leaf, and will produce its effect on r, on a heat of combustion of 3760 calories per gram. On this which the temperature of the leaf depends. This, again, basis the assimilation of 1 c.c. of carbon dioxide corre- will influence the amount of water-vaporisation, and so sponds to the absorption of 5.02 water-gram-units of affect the value of w. In addition to this, complex disenergy; hence by multiplying this value by the number turbances may be introduced by the automatic opening or of c.c. of carbon dioxide assimilated per unit area of leaf closing of the stomata, by variations in the hygrometric in unit of time we obtain the value of w for the generalised state of the air, and, perhaps more important than all, thermal equation.

by changes in the velocity of the air blowing over the leaf, In using the apparatus I have just described we found, which will alter its rate of emission. amongst other things, that the actual rate of photo- With all these varying factors acting and reacting on synthesis induced in a leaf which is bathed by ordinary air each other in endless complexity, it will be readily underremains practically constant within very wide limits of in- stood that under natural open-air conditions the thermal solation. This is due to the fact that the special rays which relation of a leaf to its surroundings must be undergoing produce photosynthesis are present in solar radiation of constant re-adjustment, and that the point of thermal even moderate intensity far in excess of the demands of the equilibrium must change from moment to moment with assimilatory centres for dealing with the atmospheric every passing cloud, with every gust of wind, and with carbon dioxide which reaches them by the process of each change of inclination of the leaf-lamina to the indiffusion. The proof of this is afforded in the first place cident radiation. by the enhanced assimilatory effect which is produced by In the absence of means for instantaneously recording increasing the partial pressure of the carbon dioxide in all these variations, it is manifestly impossible to deterthe air surrounding the leaf, and, secondly, by the fact that mine the thermal conditions for any particular moment of we can reduce the intensity of ordinary summer sunlight time, and perhaps there would be no special advantage in to a very considerable extent by using revolving radial-doing this even if it were possible. It is, however, quite sectors placed in front of the leaf, without sensibly affect- practicable to determine the mean values of the varying ing the rate of photosynthesis.

factors and the average effects which they produce during It follows from this that the economic coefficient of the a period of time, say of several hours' duration, and we leaf, which is the ratio of the energy utilised for photo- can then introduce these mean values into our equation, synthesis to the total radiation falling on the leaf, must which will thus give us all the information we require. necessarily increase with diminished insolation, until a I will now proceed to illustrate the application of these point is reached at which practically the whole of the general principles by the consideration of a few concrete special rays which are active in producing assimilation are examples. utilised. At this point the economic coefficient of the leaf The first is that of a leaf of the sunflower, in which the must be at a maximum with respect to a given partial experiment lasted for about four hours. The results are pressure of carbon dioxide; in other words, the leaf re- expressed in water-gram-units (calories), and the units of garded as a thermodynamic engine is then working with area and of time are the square centimetre and the minute the least possible waste of energy.

respectively. . In order to illustrate this I will take the case of a leaf The conditions were such that the total solar radiation under the influence of moderate sunlight of an intensity absorbed by the leaf was in excess of that required to of 0-50 calorie per square centimetre per minute, and perform the internal work of transpiration and photoassimilating at the rate of 2.07 c.c. of carbon dioxide per synthesis; in other words, Ra was greater than W+W. square decimetre per hour. This corresponds to

an

Hencewas a positive quantity, and the temperature of economic coefficient of 0.34 per cent. On gradually the leaf was consequently somewhat higher than that of diminishing by suitable means the radiation falling on the its environment. leaf, it was found possible to reduce it to 1/12 of the original amount before any appreciable difference in the

CASE A.-Leaf of Helianthus annuus. rate of assimilation was observed. The economic co

Total solar radiation

R=0'2569 calorie. efficient was thereby raised to the maximum of a little Coefficient of absorption, a=0.686,... solar more than 40 per cent. This 4 per cent. will also energy intercepted,

Razo'I762 approximately measure the proportion of the special grade Water vaporised=0000209 gram, .. W, of energy in the original radiation which is capable of

the internal work of vaporisation inducing photosynthesis.

0.000209 x 592 6 ...

Oʻ1243 It is, however, only under very exceptional conditions Rate of photosynthesis=0'000355 c.c.CO2, that we can obtain anything like this maximal “ duty hence w, absorption of energy due to from the leaf.

assimilation=0'000355 * 5 02

0'0017 The following table, showing the results with leaves of

Ra = W + Polygonum Weyrichii under varying degrees of insolation,

0:1762=0*1243+0'0017 +0.0502

W

+

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