March 30, 1905] 



NATURE 



525 



and with certain modifications there is practically no limit 

 to the scale on which the experiments can be conducted. 



It is evident that with this apparatus the mean carbon- 

 dioxide content of the air in contact with the leaf must be 

 somewhat less than that of the entering air, so that a 

 correction of some kind is necessary in order to obtain ' 

 an estimate of the rate of assimilation under free-air con- 

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

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

 the rate of assimilation by the leaf is directly proportional 

 to the partial pressure of the carbon dioxide, provided this 

 does not exceed five or si.\ times that of the carbon dioxide 

 of normal air. 



In deducing the amount of energy used up in the photo- 

 synthetic work from the amount of carbon dioxide absorbed 

 by the leaf, we have assumed, as we are entitled to do, that 

 the product of assimilation is a carbohydrate. If the par- 

 ticular form of carbohydrate is known, the amount which 

 corresponds to a definite mass of carbon dioxide absorbed 

 by the leaf is of course determinable ; and, further, the 

 energy used up in synthesising this amount of carbohydrate 

 will be represented by its heat of combustion. 



-Vo sensible error will be introduced into this calculation 

 by selecting one of the carbohydrates existing in a leaf in 

 ^preference to another. We have based our calculations on 

 the assumption that we have to deal with a hexose having 

 a heat of combustion of 3760 calories per gram. On this 

 basis the assimilation of 1 c.c. of carbon dioxide corre- 

 sponds to the absorption of 5-02 water-gram-units of 

 energy; hence by multiplying this value by the number 

 of c.c. of carbon dioxide assimilated per unit area of leaf 

 in unit of time we obtain the value of w for the generalised 

 thermal equation. 



In using the apparatus I have just described we found, 

 amongst other things, that the actual rate of photo- 

 synthesis induced in a leaf which is bathed by ordinary air 

 remains practically constant within very wide limits of in- 

 solation. This is due to the fact that the special rays which 

 produce photosynthesis are present in solar radiation of 

 even moderate intensity far in excess of the demands of the 

 assimilatory centres for dealing with the atmospheric 

 carbon dioxide which reaches them by the process of 

 diffusion. The proof of this is afforded in the first place 

 by the enhanced assimilatory effect which is produced by 

 increasing the partial pressure of the carbon dioxide in 

 the air surrounding the leaf, and, secondly, by the fact that 

 we can reduce the intensity of ordinary summer sunlight 

 to a very considerable extent by using revolving radial- 

 sectors placed in front of the leaf, without sensibly affect- 

 ing the rate of photosynthesis. 



It follows from this that the economic coefficient of the 

 leaf, which is the ratio of the energy utilised for photo- 

 synthesis to the total radiation falling on the leaf, must 

 necessarily increase with diminished insolation, until a 

 point is reached at which practically the whole of the 

 special rays which are active in producing assimilation are 

 utilised. At this point the economic coefficient of the leaf 

 must be at a maximum with respect to a given partial 

 pressure of carbon dioxide ; in other words, the leaf re- 

 garded as a thermodynamic engine is then working with 

 the least possible waste of energy. 



In order to illustrate this I will take the case of a leaf 

 under the influence of moderate sunlight of an intensity 

 of 0-50 calorie per square centimetre per minute, and 

 assimilating at the rate of 2 07 c.c. of carbon dioxide per 

 square decimetre per hour. This corresponds to an 

 economic coefficient of 034 per cent. On gradually 

 diminishing by' suitable means the radiation falling on the 

 leaf, it was found possible to reduce it to 1/12 of the 

 original amount before any appreciable difference in the 

 rate of assimilation was observed. The economic co- 

 efficient was thereby raised to the maximum of a little 

 more than 40 per cent. This 4 per cent, will also 

 approximately measure the proportion of the special grade 

 of energy in the original radiation which is capable of 

 inducing photosynthesis. 



It is, however, only under very exceptional conditions 

 that we can obtain anything like this maximal " duty " 

 from the leaf. 



The following table, showing the results with leaves of 

 Polygonum Weyrichii under varying degrees of insolation, 



NO. Ji:>48, VOL. 7 l] 



will give some idea of the values of the economic co- 

 efficient ordinarily met with :^ 



The Economic Coefficient of Leaves of Polygonum 

 Weyrichii under Various Degrees of Insolation. 

 Radiant energy falling 

 on t sq. cm. of leaf per 



minute, in calories Economic coefficient 



R «//R X 100 



0612 ... ... ... ... ... 042 



0194 i-sg 



0150 ... ... ... ... ... 1-66 



0143 132 



Turning once more to the generalised thermal equation 

 Ra = (W+w)+r, 

 we must not lose sight of the fact that this represents a 

 set of conditions in which all the determining factors, both 

 internal and external, remain constant for a sufficient time 

 to allow of the attainment of steady thermal equilibrium 

 between the leaf and its surroundings. 



In practice this ideal state is never attainable. In the 

 first place the incidence of solar radiation is subject to 

 rapid oscillations of considerable magnitude, even under 

 the most fair-weather conditions, and every variation of 

 this kind necessarily alters the value of Ra, the energy 

 absorbed by the leaf, and will produce its effect on r, on 

 which the temperature of the leaf depends. This, again, 

 will infiuence the amount of water-vaporisation, and so 

 affect the value of W. In addition to this, complex dis- 

 turbances may be introduced by the automatic opening or 

 closing of the stomata, by variations in the hygrometric 

 state of the air, and, perhaps more important than all, 

 by changes in the velocity of the air blowing over the leaf, 

 which will alter its rate of emission. 



With all these varying factors acting and reacting on 

 each other in endless complexity, it will be readily under- 

 stood that under natural open-air conditions the thermal 

 relation of a leaf to its surroundings must be undergoing 

 constant re-adjustment, and that the point of thermal 

 equilibrium must change from moment to moment with 

 every passing cloud, with every gust of wind, and with 

 each change of inclination of the leaf-lamina to the in- 

 cident radiation. 



In the absence of means for instantaneously recording 

 all these variations, it is manifestly impossible to deter- 

 mine the thermal conditions for any particular moment of 

 time, and perhaps there would be no special advantage in 

 doing this even if it were possible. It is, however, quite 

 practicable to determine the mean values of the varying 

 factors and the average effects which they produce during 

 a period of time, say of several hours' duration, and we 

 can then introduce these mean values into our equation, 

 which will thus give us all the information we require. 



I will now proceed to illustrate the application of these 

 general principles by the consideration of a few concrete 

 examples. 



The first is that of a leaf of the sunflower, in which the 

 experiment lasted for about four hours. The results are 

 expressed in water-gram-units (calories), and the units of 

 area and of time are the square centimetre and the minute 

 respectively. 



The conditions were such that the total solar radiation 

 absorbed by the leaf was in excess of that required to 

 perform the internal work of transpiration and photo- 

 synthesis; in other words, Ra was greater than W-|-ju. 

 Hence r was a positive quantity, and the temperature of 

 the leaf was consequently somewhat higher than that of 

 its environment. 



Case A. — Leaf of Helianthus annuus. 

 Total solar radiation ... ... ... R=0'2569 calorie. 



Coefficient of absorption, a = o'686, .•. solar 



energy intercepted, ... ... ... Ra = oi762 ,, 



Water vaporised = 0000209 gram,.'. W, 

 the internal work of vaporisation = 



0000209x5926 01243 ,, 



Rate of photosynthesis = 0'000355 c.c.COj, 

 hence w, absorption of energy due to 

 assimilation = 0000355 X 5 02 ... = 00017 .. 



Ro = W + 5t/ + r 

 O"i762 = o'i243 + oooi7 + oo502 



