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and alcohol first showed a rise in respiration followed by a
smooth decline to zero ; at the death point the evolution of
carbon dioxide was not markedly smaller, and it may be con-
siderably greater, than the normal rate in living tissue. But
this post mortem respiration is not shown in all instances :
Palladin observed that the evolution of carbon dioxide from
finely ground wheat is less than from the living intact grains.

He also made a comparative study of the effects of various
poisons on the evolution of carbon dioxide from living and

* Palladin : " Ber. deut. hot. Gesells.," 1905, 23, 340 ; 1906, 24, 97.
f Haas : " Bot. Gas.," 1919, 67, 347.


dead tissues : quinine hydrochloride in a "09 per cent solution
gave a threefold increase in the output of carbon dioxide from
living stem apices of the broad bean but was without effect on
killed apices ; a dose of I per cent gave the same increased
yield from the live stems and reduced the evolution of carbon
dioxide from the dead. Arbutin in a I to 2 per cent solution
depressed the respiration of wheat seedlings to a greater degree
in dead than in live seedlings. Palladin looks upon the in-
creased output of carbon dioxide in living tissues following
poisoning as being due to the reaction of the protoplasm
against the poison employed. In such living tissues the poison
does not result in a change in the amount of peroxide ; in
killed tissues, on the other hand, the decreased output of carbon
dioxide is accompanied by a reduction in the amount of per-
oxidase, which presumably is destroyed by the poison.*

With regard to that aspect of respiration associated with
enzymes more directly connected with the protoplasm, Pal-
ladin f adopts the view not uncommonly held J that the pro-
cess is anaerobic and is essentially the same phenomenon as
alcoholic fermentation. It has been mentioned that a supply
of respirable material, of which sugar is a prominent material, is
an important conditioning factor governing the respiration rate.

Of the enzymes able to effect the decomposition of sugar,
zymase is the most prominent ; to what extent other enzymes,
more especially those associated with respiration in the narrower
sense, are operative is a subject for further investigation.
Zymase has been described as being of widespread occurrence.
The successive stages in the reduction are not known, where-
fore agreement regarding the nature of the complete reaction
has not been reached. Palladin considers that there is in the
first instance a reaction between the sugar and water which
leads to the formation of carbon dioxide, which is thus of
anaerobic origin, and hydrogen. But hydrogen as such is not
one of the gaseous waste products, wherefore it must be fixed
as quickly as it is formed. Here, Palladin's respiration pig-
ments are operative : they exist in the plant in the form of

* Palladin : " Jahrb. Wiss. Bot.," 1910, 47, 431.
f Palladin " Zeit. Garungs. Physiol.," 1912, I, 91. :

JBach and Batelli : " Compt. rend.," 1903, 136, 1357; Godlewski and
Polzeniusz : " Bull. Int. Acad. Sci. Cracovie," 1897, 267; 1901, 277.


prochromogens, which may be glucosidal in nature ; these pro-
chromogens are converted by enzyme action into chromogens.
The chromogens are oxidized by peroxidase into respiratory
pigment, which oxidation, according to Combes,* is accom-
panied by an increase in the respiration intensity. These
respiration pigments are the hydrogen acceptors and act in
the same way as does the methylene blue in the experiments
previously mentioned (p. 64) : they combine with the hydro-
gen to reform the chromogen ; the chromogen in turn and by
the aid of oxidase combines with atmospheric oxygen to form
water, which is thus of aerobic origin, and respiration pigment.

It will be observed that the views of Palladin and Wieland
are in accordance in their regarding hydration an initial change
in the oxidation of an aldehyde or a sugar. But to what ex-
tent Palladin's ideas regarding the cycle of changes involved
in the complete respiratory process are accepted is a matter
for individual judgment. His thesis is bound up with Bach
and Chodat's hypothesis, the tenability of which is discounted
by the observations of other investigators. The respiratory
chromogens may act in the way outlined ; but to what extent
their operation is universal is very doubtful. The existence of
phases, expressed in the different origins of carbon dioxide,
appears to be well supported by the facts, as also is the initial
hydration phase in certain oxidations. Finally, the occurrence
of a fermentation stage in the respiration cycle is a strong pro-
bability if not a completely proven fact.

With regard to the consumption of fats and proteins in
respiratory processes, there is but little precise information.
Oparinf has examined chlorogenic acid, C 32 H 38 O 19 , which he
has found to occur in over a hundred different plants, and finds
it to be a substance which readily oxidizes in the air, losing
4 atoms of hydrogen and forming a green pigment. The
latter can act as a hydrogen acceptor and so act as an oxidiz-
ing agent. The calcium salt of the fully oxidized acid is re-
presented by the formula CaC 32 H 32 O 19 + 2H 2 O, whilst the
salt of the unoxidized acid has the formula CaC 22 H 36 O 19 +
2H 2 O. Chlorogenic acid is more particularly active in the

* Combes: " Rev. gen. Bot.," 1910, 22, 177.

fOparin: " Biochem. Zeitsch.," 1921, 124, 90; Gorter : " Annalen d.
Chemie.," 1908, 359, 217.


oxidation of natural amino acids, peptides and peptones
giving origin to ammonia, carbon dioxide, and an alde-

R . CH . NH 2 . COOH + O -> R . CHO + NH 3 + CO 2

The process is accelerated by the presence of certain reagents
such as phosphoric acid. Chlorogenic acid would therefore
appear to be a respiratory pigment in the sense used by

The chemical changes involved in the destruction of re-
spirable material, must be to a large extent conjectural until
precise knowledge is available of the relatively simple enzymic
and the more complicated protoplasmic agencies employed,
and of their mode of attack. For this reason it is desirable on
the present occasion merely to give a brief statement of the
more obvious possibilities.

If the essential part of respiration, that concomitant with
life in distinction to that post mortem, is essentially anaerobic
and there is much to be said for the thesis then a sequence
of chemical changes similar to, if not identical with, alcoholic
respiration is indicated. Unfortunately agreement regarding
the stages in this sequence has not been reached,* although
the views of Neuberg and Reinfurth appear to be well sup-
ported by the facts of laboratory experiment. According to
these views, glucose is converted into glyceric acid and di-
hydroxyacetone, each of which yields methyl glyoxal which in
turn gives origin to pyruvic acid. The pyruvic acid by the
action of carboxylase gives rise to carbon dioxide and to acetic
aldehyde, from which ethyl alcohol results. Alcohol is an end
product of anaerobic respiration and its fate depends on whether
or not an aerobic phase follows. In the presence of oxygen,
the alcohol is oxidized to carbon dioxide and water, or it may
be used up in the synthesis of protein, since by oxidation it can
give origin to acetic acid which is employable in the formation
of amino acids. To what extent these intermediate products
obtain in the plant is not known and again it must be men-
tioned that the plant is not a test tube. Indications of the
sequence may possibly be obtained from animal sources and in
their respiration glucuronic acid occurs and also lactic acid

*Vol. I., p. 382.


which accumulates in fatigued muscle. Lactic acid, either as
such or combined in the form of a salt, has been considered an
intermediate product in alcoholic fermentation, and Stoklasa
and Chokensky * state that they have isolated a zymase which
converts sugar into lactic acid accompanied by a lactacidase
which resolves the acid into alcohol and carbon dioxide. The
evidence, however, for lactic acid being an intermediate pro-
duct is inconclusive and in animal physiology the facts would
appear to warrant the statement that lactic acid has its origin,
at any rate in part, from protein.

With regard to glucuronic acid, Spoehr has succeeded in
isolating it from certain Cactaceae, the only plants so far in
which it has been recorded.

The depth of our ignorance of this important aspect of
respiration is obvious : and until all the possible successive
stages in the dissociation of fats, carbohydrates and proteins,
all of which are respirable, are known, it is impossible to trace
the sequence obtaining in the living organism.

* Stoklasa and Chokensky : " Ber. deut. hot. Gesells.," 1907, 25, 122.


THE term growth not infrequently is used to imply mere increase
of the plant or plant member in various directions with little
or no attempt to correlate or to analyse these and other related
expressions of the activity of the organism. Thus increase in
surface is not necessarily growth : a pound pat of butter may
be spread over a number of slices of bread whereby its area is
increased but not its mass. An etiolated seedling may show
a much greater length of internode than its fellow of the same
age grown under normal conditions : but the comparison of
the dry weights of the two will show no increase in mass in the
etiolated example.

From considerations such as these, the conclusion is
reached that growth is properly speaking an expression of the
metabolism of the organism ; it is, to use F. F. Blackman's
phrase, the finished product of the metabolic loom. It is this
aspect which will mainly be considered on the present

Metabolism has two sides, debit and credit : if the anabolic
processes are more intense than the catabolic, growth will
result ; if the catabolic processes are in the ascendent, decretion
obtains. From this it follows that the sure index of growth
is increase in dry weight, the credit balance of the two opposite
activities. Thus Boysen-Jensen * found that under maximum
illumination the carbon assimilation of Sinapis, a sun plant,
was 6 mgs. of carbon dioxide per 50 sq. cm. of leaf surface per
hour at 20 C., whilst the respiration at the same temperature
and for the same units of surface and time was -8 mg. of
carbon dioxide. This means that for an average plant of
Sinapis, the amount of dry matter made in a day in July is

* Boysen-Jensen : " Bot. Tidsskr.," 1918, 36, 219.


60 mgs. whilst the loss of dry matter due to respiratory pro-
cesses is 14 mgs., leaving a balance of 46 mgs., which is equi-
valent to 1 6 -5 per cent, of the dry weight of the plant. A
similar relation is shown by Oxalis, a shade plant, but the
amounts are much smaller; -8 mg of carbon dioxide being
assimilated per 50 sq. cm. per hour at 20 C, whilst the loss
due to respiration is ! 5 mg. at the same temperature for the
same units.

A disposal to go further may be evinced and to select
the number or weight of offspring as being the true
measure of a naturally growing organism's growth, since the
selfish needs of the parent are thereby eliminated. For
obvious reasons such a measure is impracticable except in
special cases where reproduction takes place with extreme
rapidity, as for instance in bacteria, or where crop yield in re-
sponse to methods of cultivation is required.

The employment of the dry weight method has a disad-
vantage in that it forbids the study of progressive change in
one and the same member, since to find the dry weight,
the plant or plant member must be killed. For this reason
other indices sometimes must be employed. Thus change in
the size and area of leaves in certain investigations serve as a
reliable measure, a fact which becomes evident when it is
realized that an increase in the size of a leaf, or of the entire
chlorenchyma system of the plant, means an increase in the
plant's factory and all that this connotes. Thus Johnston *
found that the total dryweight and total leaf-area of the buck-
wheat ran on parallel lines during the season February to
October, the greatest rapidity of growth occurring in the
summer months.

In further illustration the observations of Briggs, Kidd, and
West,f based on the investigations of Kreusler and others on
the maize, may be considered. Briggs, Kidd, and West analyse
the growth of the maize in terms of dry weight, leaf area, and
time, and employ the relative growth rate and the leaf area
ratio. The relative growth rate curve is the weekly percentage
increase in dry weight plotted against time, and the leaf area

* Johnston: "Johns Hopkins Univ. Circ.," 1917, 211.

f Briggs, Kidd and West: "Ann. Appl. Biol.," 1920, 7, 103, 202.



ratio curve is the leaf area in square centimetres per gram of
dry weight plotted against time.

The growth rate of the maize varies much in magnitude at
different periods of its life. This is expressed in a generalized
form in Fig. 7.

The early seedling stage is shown by the portion ab, and
is characterized by a decretion owing to the young leaves being
in a low phase of carbon assimilation activity, and providing less
material than is consumed in respiratory processes, an observa-
tion which confirms the results of Irving and of Briggs. The
phase be corresponds to the morphological development of the

FIG. 7. The continuous line represents growth rate and the broken line leaf area
per unit dry weight.

plant during which the leaf area per unit dry weight increases
to a maximum. Finally the phase cd is the latter part of the
plant's life and includes the formation of the flower and the seed.
This portion shows two secondary maxima at e and f which
are respectively coincident with the appearance of the male and
female inflorescences and each is preceded by a minimum, g
and h, which corresponds to the early stages of flower develop-
ment at which epoch there is a marked increase in respiration

The incidence of the maxima is dependent on environmental
conditions operating not at the time but at a previous stage in
the life of the plant.


The fact that the curve for leaf area per unit dry weight
corresponds with the growth rate curve indicates the close
physiological connexion between the relative growth rate and
carbon assimilating area per unit of dry weight (Fig. 7). The
correspondence, however, is not precise ; instead of showing
a definite type of variation, as does the relative growth rate,
the leaf area per unit dry weight curve fluctuates about a mean
value. These fluctuations are due to the conditioning factors
of growth of which factors temperature is amongst the most
significant. The importance of leaf area in the economy of the
higher plant is so obvious that no elaboration of the statement
is required. The growth in area of the leaves of the cucumber
has been closely studied by Gregory* and may be alluded to at
this stage in that it introduces some aspects of growth which
properly belong to a general consideration. But before this is
done, the " grand period of growth " must be recalled to memory.
As is well known, Sachs used this expression to designate the
period through which the plant, or plant member, exhibits its
sequence of growth rates. Thus the growth rate of the first
internode of Phaseolus multiflorus is at first slow, then quickens
to a maximum, after which a decrease in the rate to zero obtains,
which point is coincident with the attainment of maturity.
The sequence is illustrated in Fig. 8 which is based on Sachs's

The grand period of growth does not include an analysis
of the fluctuations in the rate during the periods between the
measurements; thus the growth rate between the third and
fourth day is the summation of the growth during that period.
Priestley and Evershed f in their study on the root growth of
Tradescantia and tomato, based on the increase in dry and wet
weights of the roots produced on cuttings, find the curves ob-
tained are a sequence of these grand period curves which are
a series of S curves, a type which is very common in graphs
illustrating growth phenomena (see Fig. 9). The time of
transition from one S curve to the next coincides with the time
of appearance of a crop of roots of a subordinate branch order.

Gregory found that the growth in length, in breadth, and
in area of the leaves of Cucumis sativus show a grand period

* Gregory: "Ann. Bot.," 1921, 35, 93.

t Priestley and Evershed : Id., 1922, 36, 225.



of growth when grown under natural conditions ; but when
continuously illuminated by electric light, a method some-
times adopted by market gardeners to secure early crops, the
rate of increase falls from the first measurement of area. The
curves of increase in linear dimensions and in area can be







Temp. 12 75 -13 75 C

Time in days

5 6 7 8 9 10

FIG. 8.

represented by the formula of an autocatalytic reaction.* The
increase in area of the total leaf surface varies with the season of
the year : in March and June in daylight, the rate of increase
is proportional to the area existing at that time, that is, the
growth follows a compound interest law ; but during December
a detrimental factor intervenes so that the rate of increase,

* This term is explained on p. 113.


although still proportional to the extant leaf area, is not
maintained but falls away in time. When grown under

artificial light,
B * * * * results compar-

52 ? ' able to those

50 - grown in day-

48[- %ht during December

obtain. The detrimental

, * factor is hard to formu-

late: in December the



' ^



24 . conditions which indicate that res-

piration was intensified whilst carbon

* low light intensity and the low

temperature militate against
photosynthetic activity and
thus the amount of available
food may be adversely affected.
When grown under artificial
light, the energy value of the illumi-
nant was about equal to winter sun-
shine, but the temperature of the
greenhouse was that of the summer,

assimilation was depressed.

In this consideration mention has
been made of the law of compound



15 1- interest and of the law of autocata-

lytic reactions.

V. H. Blackman * has drawn
attention to the fact that in many
natural phenomena the rate of change

of some quantity is proportional to
the quantity itself. This is the law
of compound interest ; money left to

3l_ accumulate at

57911 13 15 17 19 21 23 25 compound in-
Atfe in days terest increases

to an amount

FIG. 9. Growth of the fruit of Cucurbita pepo ; . . . ob- ^ e ma gnitude
served value, x x x calculated value.

* Blackman : " Ann. Bot.," 1919, 33, 353 ; " New Phytol.," 1920, 19, 97. See
also Kidd, West and Briggs : Id,, 88.


of which depends on the initial capital, the rate of interest
and the time the money is accumulating ; the dry weight of an
annual plant depends upon the dry weight of the food reserves
in the seed, the percentage increase in the dry weight over the
selected period, and the time during which the plant is in-
creasing in weight. This may be represented by the equation

Where W l is the final weight, W the initial weight, r the
average rate of interest, t time, and e the base of natural

The rate of interest is obviously of first rate importance
and if constant the final weight will vary directly as the initial
weight, wherefore a large seed, with more initial capital, will
give a much larger plant than a small seed, with a relatively
smaller initial capital.

From considerations such as these Blackman arrives at the
conception that the rate of increase observed in the plant is
the index of efficiency of the plant, a conception which gives
a useful basis for comparison but which is not a constant
since it is the average of a number of rates which may show
variations through a wide range, for it is affected by the external
conditions. The rate of increase is highest in the early stages
of growth and falls with the inception of the reproductive

The laws governing autocatalytic reactions are the logical
outcome of the laws of monomolecular reactions.* An auto-
catalytic reaction is one in which one of the products of dis-
sociation of the original material acts as a catalyst on the
material which is obviously decreased in amount as the reaction
proceeds. Thus a solution of methyl acetate undergoes auto-
dissociation into methyl alcohol and acetic acid ; of these
products the acetic acid catalyses the methyl acetate so that
the rapidity of the reaction is continually accelerated, owing to
diminishing amount of methyl acetate, and the increasing
amount of acetic acid, until the whole of the substrate is dis-

From his study of the growth of various organisms,

*Vol. I., p. 363.
VOL. II. 8


Robertson * concludes that in any particular growth cycle,
either of an organism or of a member of an organism, the
maximum increase in volume or in weight in a unit of time
occurs when the total growth due to the cycle is half completed.
Such a cycle of growth conforms to the formula

A - x"

where x is the amount of growth in weight or volume which
has been attained in time t. A is the total amount of growth
attained during the cycle, K is a constant and t is the time at
which growth is half completed. These relations are such as
would be expected to hold good were growth the expression
of an autocatalytic chemical reaction, and the growth of the
organism should, from the hypothesis, remain constant, having
once attained its maximum. But the contrary obtains, in old
age and senescence a loss of weight occurs ; this is supposed
to be due to the action of secondary factors which are imposed
on the phenomena of growth itself.

An inspection of Robertson's figures, for example those
given for the oat,f or for Cucurbita, shows differences between
the observed and calculated growth values of varying magni-
tude, and these differences when expressed in percentages
sometimes appear too large to support the thesis ; but when
the observed and the calculated values are expressed in the
form of a curve (Fig. 9) their incidence is sufficiently close
to give support to the thesis, especially when allowance is
made for the experimental errors.

To what extent and in what degree growth processes may
be correlated with this law is uncertain. The observations of
Gregory show that the curves of increase in the area of the
leaf surface of cucumber plants are of the S form and can be
represented by the formula of such a reaction. In the earlier
stages of growth this increase also is in accordance with a law
of compound interest. There is thus a choice between the
two expressions : the compound interest law is a conception
rather than a physiological constant, but even so Gregory con-
siders it to have the advantage over the law of autocatalytic

* Robertson : "Arch. Entwicklungsmech. Org.," 1908, 25, 581.
[Id., 26, 108.


reactions in that it is independent of hypothetical mechanisms
of growth. For it is obvious that if growth is an expression
of the activity of some catalytic agent, that agent must be
sought out ; according to Robertson * the lipoids may sub-
serve the required function. With regard to other observations
in this aspect of the subject, the work of Reed and Holland,!
who found that the rate of growth of the sunflower closely
approximates the course of an autocatalytic reaction, may be
mentioned. Reed J also observed that the rate of increase in
the height of walnut and pear trees showed growth cycles
throughout the growing season. In each cycle the growth
rate corresponded to an autocatalytic reaction.

Returning to the terms in which increase in growth may
be expressed, allusion has been made to offspring especially of
unicellular organisms in which the unit grows to a certain size
and then divides. The yeast plant may be selected in illus-
tration, more especially as a consideration of its reproduction
rate will introduce other aspects of the subject of growth.

A young yeast cell on being placed in a suitable medium
increases to a certain size, the magnitude of which depends to
no small extent upon the osmotic strength of the medium,

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