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radiation and vital phenomena

RADIATION AND VITAL
PHENOMENA

PROEFSCHRIFT

TER VERKRIJGING VAN DEN GRAAD VAN
DOCTOR IN DE WIS- EN NATUURKUNDE
AAN DE RIJKS-UNIVËRSITEIT TE UTRECHT,
OP GEZAG VAN DEN RECTOR-MAGNIFICUS
Dr. J. A. C. VAN LEEUWEN. HOOGLEERAAR
IN DE FACULTEIT DER GODGELEERDHEID.
VOLGENS BESLUIT VAN DEN SENAAT DER
UNIVERSITEIT. TEGEN DE BEDENKINGEN
VAN DE FACULTEIT TE VERDEDIGEN OP
DINSDAG DEN IPEN OCTOBER. 192L DES
NAMIDDAGS TE VIJF UUR. DOOR

LOURENS GERHARD MARINUS
BAAS BECKING

GEBOREN TE DEVENTER

DRUKKERIJ F. W. HAJER - UTRECHT - 1921

va;\'": •
f ^

■ \'\'\'"VJ Vf .

y

" %

aan mijne moeder

ëk

-. -Vw -:

V?- - . \'

liE

f\'r\'s •

Hooggeleerde Weevers, vóór alles is het aan U dat
ik een woord van oprechten dank wil richten. Uw onder-
wijs heeft de verdere richting van mijn studie bepaald.

Elk Uwer, Hoogleeraren in de Plant- en Dierkunde aan
deze Universiteit, is een karakteristieke factor in mijne op-
leiding geweest.

Hooggeleerde N ierstra sz, gij toonde mij de kracht van
de intuitie en de spot, twee niet te onderschatten factoren
van het wetenschappelijk onderzoek, waar de laatste afbreekt
dat wat de eerste te veel heeft uitgebouwd.

Hooggeleerde Jordan, ook Uw invloed op mijn ont-
wikkehng is meer in de richting van het denken zelve dan
op de verrijking van feitenkennis gericht geweest. De wijs-
geerige grond van de biologie zal daardoor steeds mijn leven-
dige belangstelling bezitten.

Ook aan U, Hooggeleerde Westerdijk ben ik veel
verplicht, ofschoon ik slechts korten tijd het voorrecht heb
gehad onder Uw leiding te werken. Uw krachtig voorbeeld
heeft steeds mijn eerbied afgedwongen.

Hooggeleerde Pulle, het werk eertijds onder Uw leiding
verricht is voor mij een aansporing geweest om tijdens mijn
verblijf in het buitenland de embryologie der Eusporangiaten
tot onderwerp van onderzoek te maken. Uw vriendelijke
hulp zal mij steeds in herinnering blijven.

Hooggeleerde Went, Hooggeachte Promotor! Moge
het feit dat ik de eerst mogelijke gelegenheid heb aange-
grepen om naar Nederland terug te keeren teneinde onder
Uw leiding te promoveeren, genoegzaam uitdrukken welke
gevoelens mij jegens U bezielen.

..." -.j ■ - - F ■ - •

ï^ifonH

(mMiiyu\'-^^Ki ■ yf^^i -i^ir ^^

i

\'I

I

I

f:

INTRODUCTION

Energy Radiation is known to have a powerful effect on the
balance jj^gjjy reactions, chemical and physical, which accompany
processes^ possibly constitute — the phenomenon called life.

The maintenance of life on this planet is entirely depen-
dant on a iight-reaction; the synthesis of carbohydrates in
the green leaf. The oxygen supply of the tissues in higher
animals, that most important function of the haemoglobin,
is influenced by radiation.

Zwaardemaker\'), in a scries of papers on physiological
energetics, points out that the general form of the first law
of thermodynamics; total energy equals heat exchange minus
external labour, has no explicit physiological meaning. In
order to obtain a more serviceable form of the first law he
analyzes the total energy change in its different components;
the last factor in this series being the radiant energy. This
radiant energy can not be neglected in the equation, especially
in the energy balance of green plants, and Zwaardemaker
goes as far as to remark that:

"Eine wirklich biologische Energetik hätte sogar letztere der Reihe
von Energieformen (i. e. radiant energy) als erstes Glied an die Spitze
1 zu stellen. Leider befindet sich das theoretische Studium hier noch

i ganz Im Anfang und dürfen wir In unseren Formeln die Llchtenergle

nur pro memoria führen".

Since all vital energy can be derived from radiant energy
it. seems unwarranted to exclude, or even to mention "pro
memoria" this form of energy. In this paper radiation will
be considered as a factor in the energy balance of the
organism.

Statement A living cell is an energy transformer. The diversity of
of the its intricate mechanism allows for many different energy
problem, transformations. The transformations in which chemical and
thermal energies are concerned can be studied with the help
of thermodynamics and thermochemistry. A study on such
processes has been carried out in several cases.

The transformations in which radiant energy is concerned
are imperfectly known. A complete energy balance for the
radiant energy of a physiological reaction has never been
worked out.

Inasmuch as a living cell can be compared with a
closed opaque container it may be assumed that a certain
amount of heat radiation of any frequency is always present
within the cell. Therefore every chemical reaction takes
place in a bath of radiation.

Heat, the effect of molecular movement; radiation, the
effect of electronic movement are coexisting phenomena accom-
panying every chemical (and physiological) reaction.

It is not improbable that in this bath of heat radiation
there is radiation of a certain frequency, which frequency
shows a definite relation to an electronic frequency within
the chemical system. According to the principle of resonance,
the chemical system would be influenced in that case by the
radiation of that frequency.

Now Perrin^) advocates the idea that the radiant energy
is the cause of the combination and dissociation of the mole-
cules in every chemical reaction. The immediate consequence
of this hypothesis would be that vital phenomena were

caused by radiation.

Aware of the fact fhat Perrin\'s hypothesis has been the

subject of severe criticism, his i\'dea will be taken nevertheless
as a working hypothesis and it will be assumed that every
physiological reaction is influenced, and possibly caused, by
radiation. Every physiological reaction is accompanied by an
absorption as well as by an emission of radiation.

On this basis it will be tried to derive, at least partly,
the. energy balance of certain physiological processes. It
must be kept in mind that the deductions from this unproven
hypothesis are to be considered as a preliminary attempt to
connect radiation-phenomena with thermodynamics. No claim
will be made as to the absolute value of the statements
expressed in the following chapters.

\') Zwaardemakcr. Ergcb. d. Phys. V, 108, 1906.
2) Pcrrin. Ann. de Phys. XI. 31, 1919,

SYMBOLS

The symbols used in this paper are the usual letters. In a
few cases, however, the symbols used by Arrhenius. Nernst
and Perrin disagree. Therefore a list of the symbols used in
this paper will be given below.

CONSTANTS

h = Planck\'s constant = 6,415 . 10"^\'\' ergs/sec.
a = Radiation constant = 7,28 .10

k = Boltzmann constant = 1,34.10"^^ ergs/sec^ degree,
N = Avogrado constant = 6,8 . lO^^.
R = gas constant = N . /c.

&7r h

S = Perrin s constant =

c = velocity of light in a vacuum = 3. 10\'° c.M./sec.
p = modification constant for Perrin equation = 0.27.

VARIABLES

A = wavelength of light in 10"^ c.M.

V = frequency of light in vibrations/sec.

K = equilibrium constant.

K, and Kg = reaction velocities.

u = energy change p. molecule during a reaction.

U = N.u ergs (Q of Einstein, W of Perrin).

^ « A U

A = ^ ; A =

W= work done bij a system (A of Nernst).
q = energy change inside a system during a reaction.
Q = temperature coefficient.
T = temperature.
t = time.

N. B. Quotation jnarks point to the end of the chapter.

CHAPTER I
THEORETICAL CONSIDERATIONS

Black Assuming that temperature radiation must be thc cause
radiation, ^jf reactions it can be expected that this radiation is deter-
mineable by Wien\'s law. according to which the wavelength
of the maximum radiation intensity is inversionally proporti-
onal to temperature

%

a.T = 0.294 c.M. degree

at "physiological temperatures" (plm. 300° abs.) the maximum
will be situated in the infrared at

0.294 _ o «

löcr - ^

This maximum is also easily determineable by the lumino-
sity equations of Planck\'). Because of thc fact that these
equations will be used as a starting point for further deductions
some of their properties will be considered here. The lumi-
nosity referring to wavelength can be expressed by equation

E =£1^.-—ergs/c.M». sec.
[ekxT _ij

For different values of this equation reduces to sim-

pier forms.

when < 1 this form approaches

K A 1

c h

ekxT - 1 4- -—— and the original equation:
k X 1

E = ^ ^^ ergs/c.M®. sec.

A

c h

However, when ^^^ > 1, and. accordingly, e ^ ^ T is

large compared with 1, the luminosity equation reduces to

- ^ ^

E = Sl± e ^ A T ergs/c.M^ sec.
X

Fig I shows similar approximation formulae and their
range of applicabiUty as compared with the general relation.
Immediately above the maximum the approximation formula
coincides practically with the general equation.

For physiological purposes we always have to use small
values of A and T (low temperature, supra optimal frequencies).
It will be seen at which place the maximum value of E in
the equation

c h

E = e ^ ^ T is situated.

Differentiation with respect to A gives

/ SJ}- u ^ ^ \\
5E 5 Ve kxTe )

or, tor Amax. J

5 A 2 c h

A« . e^

^; = 0 At T = 300 abs.

kxH

3 . 10\'°.6.145 .
1.34 . 10"\'^3. 10^

Amax. — 9.6 (A.

The behaviour of the equation for the luminosity frequen-
cies is entirely analogous to that of the luminosity refer-
ring to wavelengths.

K = A^ --------ergs C.M2. sec.

c^ / h V

reduces to

Jt ^ Tf /? f

K = for small values of and to

h u

f 2 f, Jj

K = —ii- e for large values of , ^^ . as is the

c\' «A

case in physiological reactions. The maximum of this last
equation is situated at 16 ^c« in the infrared.

As the luminosity equations serve for both emission and
absorption it can be expected to find most of the chemical
and physiological reactions excited by infrared light. The light
emitted or absorbed during the reaction must belong also to
the infrared region. In most physiological reactions, however,
no infrared light seems to play a part. The light of the
firefly is "cold" light. Its emission spectrum lacks the infra
red part (Langley 6 Very; Langley; Ives 2)).

v. Gulik") found for chlorophyll an absorption maximum
at 3.4 (x. If^this maximum should be situated at the position
of the maximum black radiation it would correspond to a
heat radiation of 800° abs! It is clear that the luminosity

equations as such are not very well applicable on physiolo-
gical processes.

Theory of Perrin assumes that

"toute reaction chimique est provoquée par une radiation lumineuse;
sa vitesse est déterminée par 1 intensité dc cette radiation et nc dépend
de la température que dans la mesure où cette intensité en dépend."

The consequences of this assumption will be derived in
diflFerent ways.

A reaction velocity K^ is assumed to be a function of
a light intensity I:

The proportion of two light intensities at different tempera-
tures T, and Tj (T^ > T,) will be

^ = = ■ (1)

or

h p ( I 1 \\
/n Q = -f^ l^T, - %)•

This equation will hold for the reaction velocities if K] is
directly proportional to I. If K| is proportional to a power
of I [as is the case in absorption of light] equation (1) will
change into

h V f I 1 \\
Q = e^ A- VT, -T,; (2)

or

/n Q = p _ ^ in which p < I and a constant.

Both cases have been found experimentally. (1) Seems to
hold in certain cases of photochemical cquilibruim where reac-
tion velocity is directly proportional to luminosity (Trautz^)).

Equation (2) applies to the cases where the reaction velocity
is proportional to the quantity of hght absorbed (Plotnikow

In(l) and (2) Q is the acceleration of the reaction by the
increase in temperature of (Tg—T,) degrees. Q can also be
derived without using Planck\'s equations in connection with
Perrin\'s hypothesis. The equation of Gibbs—van \'t Hofl

= ^ in which K is thc equili-
brium constant can be modified into

^^ = in which K, is a velocity

constant (Arrhenius approximation). Integration gives us the
proportion of two such velocity constants at different tempe-
ratures (assuming A to be constant)

dln Kl = A

/n Q = A

Combination of (1) and (3) gives

A ^ ^
k

Combination of (2) and (3) gives
A = p —7—

This is a logical result, in harmony with the quantum
theory. The energy per molecule being quantumized we can

write u = const, h v, and, because A = = ~ we get,

by simple substitution equation (5).

Perrin\'s starting point is also the temperature equation
of Arrhenius. For a certain frequency v the intensity of supra
maximal radiation depends on T proportional to

h V

S . e ^ . This gives

^ ^ and the equation (4).

N.B. Langmuir®) crltisizcs Perrin\'s attempt to combine luminosity
and dissociation heat. The similarity between the Arrhenius\' equation
and the Planclt equation is. according to Langmuir, due fo the fact
that both are probabiUty equations. This may be the case, but still
their relation may hold true because of the fact that the probabilities
are, in both cases, taken from comparable elements (energy quantities).
The similarity between the two equations was, long before Perrin,
pointed out by E. Rasch"), who, nevertheless, reached no applicable
deductions.

In the following pages the quotient between two reaction
velocities at different temperatures. Q, wil be used. This
number has the advantage of a quotient: common discrepan-
cies in numerator and denominator will disappear. Besides
this it is easily determineable experimentally.

Equation (2) can be written:

h V /Ta — TA

1 n - n /T2 -

In Q-p —

/

and most determinations being carried out at temperature
intervals of 10°;

, ^ h V / 10 \\

in wavelengths;

10.6,415.10""\' 3.10\'

1,34 .10"^\' 2,3 . Ti . (Ti 10). log Q

_L43__

^ ^ 2,3 _ , , p. From (3) we get
— - T, (T, 10) log Q,o

1 43

X = p - ... (6) and from the foregoing;

___6^2____/-V

^ ^ Ti (Ti 10) log Q.o
In the analogous Perrin equation p = 1 and we get

and for the temperature coefficient

6,2

A =

Ti (Ti 4- 10) log Q,„

It must be remarked that Perrin\'s equations are only rigidly trae
for black radiation, where any absorption or emission of radiation
is counterbalanced by emission and absorption in surrounding sheaths.

Perrin\'s optimum black radiation, for which Perrin\'s equations

THEORY IS hold, is, at physiological temperatures, situated at about 10 ^

inade* in the infrared. Between 290—300" abs.
quate.

, ^ 6,2.1,0.10^ ^

♦ log Qio =--------------- or

^ 290.300

Q,o = 1.18

This temperature coefficient is of the order of the thermal
acceleration of photechemical processes; reactions accelerated
by the visible light! The absolute values as derived from
Perrin\'s equations don\'t hold for photochemical processes,

Langmuir has calculated the available energy for such a

1,43

photochemical reaction with the aid of A = —, The dis-

sociationheat of phosfine, corresponds, according te Perrin,
at 948" abs, with an exciting wave of 392 fj, [jt,. The mea-
sured reaction velocity constant at this temperature proved
to be 1,2 . 10"^ The required energy to keep up this velocity
is 4,65. 10\'"\' ergs/c.M®. sec. The total energy radiated from
a black body of 948® abs, with a wavelength less than
400 iJL(M is 1,3. 10"® ergs/c.M2. ggc. This is only 4 . 10~\'° of
the amount of energy required to cause the reaction in
1 c,M\'. of phosfine.

"In other words, a black body at 948" abs. radiates so little energy
in the neighborhood of 392 xm that this^ energy would only bc
sufficient to activate molecuIcs of phosphine in a layer having a
thickness not greater than 3, 10 c.M. even if all the radiation
were absorbed within this layer",

Lewis has calculated the velocities of the same reaction
at the same temperature. On the assumption of a quantumizcd
emission and continuous absorption (Planck) the discrepancy
reaches the value of 10\'^. On the assumption of a quantu-
mizcd emission and absorption (Einstein) the discrepancy
factor is reduced to plm. 10.

Still, black body radiation is not sii(ficient to account for
the energy requirements of systems bathed in this radiation.

It has been shown before that heat radiation at physio-
logical temperatures docs not correspond with the position
of the exciting frequency in different cases where these fre-
quencies are known experimentally.

Harvey^) remarks that organisms emit visible radiation much below
the temperature of heat radiation of corresponding frequency. He
confuses, however, in his statements the Boltzmann law and Wien\'s law.

Langmuir has apphed the principle of the exciting wave
on many reactions, the calculated values, however, show no
coincidence with actual absorption bands for the compounds.
Langmuir holds that this fact disproves Perrin\'s theory enti-
rely. It is more probable, however, that it only demonstrates
the inadequacy of the equation

1,43

A = ——^

There are more reasons for this fact. In the first place, a
reaction will be considered which is photochemically sensitive
to violet light. From equation (1) Q can be calculated. This
proves to be a number in the neighborhood of fifty at room
temperature. This means that this reaction will be explosive.
Now there are many colourless compounds which react
photochemically on violet rays. The vast majority of these
substances, however, is not explosive. Lindemann has poin-
ted out this fact, and Perrin himself remarks:

"Toulours au voisinage de la température ordinaire considérons
l\'action d\'une lumière visible, d\'un violet par exemple. 11 vient

= 50. Si donc une réaction est assez prodigieusement sensible

Ksofl

ù\' la lumière violette pour être déjà notablement provoquée par ce
qu\'il y a de lumière violette dans une enceinte opaque à la tempé-
rature ordinaire, elle sera explosive si du moins elle est exother-
mique. Car 20» C. suffiront déjà pour multiplier la vitesse par 2500,
ct la température s\'élévant forcément par le progrès de la réaction,
la vitesse ira s\' accélérant de plus cn plus".

It is dear that Perrin\'s equation, the black radiation
equation, gives no satisfactory expression of the experimental
results. This was a priori evident, because it is the infrared
part of the spectrum his equations deal with. Cane sugar
inversion will be accelerated, according to Perrin.-by a
wavelength of 1.12 tx, rays which are utterly inactive on this
reaction !

An application of equation (2). on the other hand, may
lead to a preliminary estimate of p. because in

Q and v for a certain reaction being known, p can be cal-
culated. It will be seen later that as an average of all deter-
minations p = 0,27.

Substituting this value for Q,o 1,5—3; which are the normal
temperature coefficients at room temperature, v varies from
the extreme red to the extreme violet of the visible spectrum.

Similar results arc obtained by Richardson and Compton for
the mean energy of emitted photo-electrons from metal surfaces

Env = Kav {V—Vo)

in which

Kav < /i . about 2,46,10"^^
in average. This would give

p < 1 , about 0,38.

Possible \') The equations which arc better applicable are derived
Causks of on the assumption that a reaction velocity is proportional to
I\'ancy" ^ po^er of the intensity. This statement, which shows a
superficial analogy to thc so-called Schwartzschild law, cannot
imply the assumption of an absorption unless it is not appli-
cable on heat radiation. In heat radiation any absorption
should be balanced bij emission in a surrounding layer. It is
rather doubtful if an equation, originally derived for black
radiation may, by simple multiplication with a constant become
adapted to other conditions.

There is, however, quantitative evidence in this direction.
Einstein\'s photochemical theory has recently been modified
by Ornstein & Burger"). These authors have been able to
derive a condition, which approaches closely to what is called
in this paper "the modified Petrin equation". Ornstein & Burger

have considered the conditions of a binary reaction, accele-
rated by light in both ways

(1.2) (1) (2) at T" abs.

The energy per molecule N]2 be s. Nj and N2 be e\'.
Statistical mechanics gives, according to the Maxwell-Boltz-
mann law, for the equilibrium condition

N,2 e

in which

R T

e = — , p = quotient of the a priori

possibilities of the system.

Now Ni2 —> Nl N2 is only accelerated by radiation,
no spontaneous dissociation taking place.

Nj N2—> Ni2 may be caused by both collision and
radiation. The velocity of dissociation is:

Bj . 3 . Ni2 in which ^ = density of radiation,

B| is a constant.

The velocity of association is:

(by collision) A2. Nj . Nj (by radition) B2. ^ . N, . N2.
Equilibrium gives:

Bl. Ni2 . 5 = A2. Nj . N.2 B2. N, . N2. ^ or

5 = A2 or

A2

----N

B.  B2 Now, according to

\' N1N2

f\'-f

Ni2_ _ 0 . Substitution gives

N1N2

s\'-s

Bl p e ^ -B^

If 0 increases, <5 increases as the first power of T. Aj
only increases as (kinetic theory of gases). Therefore

at fl 00, 5 00;

Bj p — Bj = o , and, all these factors being constant;

S =

f\'-f

e ^ — 1 or, substituting Planck\'s
value for the radiation density

£ —f

& z h v^ e ^ -1

^^/B. =-c3— .

0

-1

For T = o, Aj will be zero and it is necessary that in
this case h v > e\'—£ , or

The chemical active frequency must be situated above
a certain frequency which is aequivalent to the reaction heat
per molecule. This limiting frequency is given by the Einstein
equation

fo =

For f\'—£ we can write u, dissociation energy per molecule.
Now because

h V > —£. it follows that
h V \'> u or

h V ^ u «1. U A

> -r or -j- being equal to -— = A
K K K R,

> A .... (8)

If V be assumed a definite frequency, it follows that

A p , in which p < 1.....

This is obviously equation (6)

The Ornstein—Burger equation, however, gives only a

partly solution of the problem. According to these authors

any frequency v > v^^ will be active. There will be occasion

to consider this fact more closely in the next chapter.

Ornstein\'s deductions have given a theoretical explanation

of the factor p in the equations derived in the preceding

paragraphs. They are of no help, however, in determining

the absolute magnitude of this factor.

A similar idea, a litde more restricted however, has

been developed bij Tolman\' Tolman assumes an active

region of frequencies, which is limited at both sides, (not.

as Ornstein finds, at one side).

Prof. Dr. H. A. Lorentz has had the kindness to point out to me
the relation between Perrin\'s and Tolman\'? theories. Dr. Lorentz\'s
remarks will bc translated almost literally In the following lines:

"According to Perrin a photochemical reaction may be caused
by a frequency v, and the velocity of this reaction proportinal to
the energy of the "black radiation" at the corresponding temperature.
According to Planck the energy of black radiation belonging to the
frequencies v and t> -f ^^^ (P- c-M-^) is

S z hv\'\' 1 ,
--- - - d V (a)

and (neglecting the factor d r) Perrin puts therefore K proportional to

e

in which, for a certain v, S will be a constant; indépendant of
temperature; hence (b) shows K as a function of T.
Neglecting the term —1

— hv

K = S e ^^ ,ot

dln Y. h V

dT kT\'

Now Tolman assumes that thc reaction may bc caused by all
frequencies within a spectral region of larger or smaller dimensions.
This region may bc devided into infinitely small parts, corresponding
to interval d v. For each interval the radiant energy is given by
equation (a) and each interval will cause a proportional reaction
velocity Ky.

In this connection it must bc mentioned that Tolman does not
derive thc proportionality of Ky to thc energy of black\' radiation
for thc corresponding frequency interval from his theoretical conslde-
dcrations. He assumes, as Perrin docs, this proportionality to exist.

Assuming thc radiation of frequency i» (energy 1 per unit volume)
to causc a reaction velocity Kp. we get for a black radiation of
Intensity (a) a reaction velocity of:

8 TT hv^ 1 ^ ,

K., du

c3 hvjkT

e —1

and, totally

K

The factor Ky stands for thc "sensibility" of the system for rays
of the frequency v. This sensibility will be maximal for rays of a
certain frequency and will drop o£f more or less steeply at both

sides. The integral in (d) must be extended over the entire active
spectral region where K^ > 0. This factor K^ plays the same part
as S in Perrin\'s equation (b). Assuming K^ to be indépendant of
temperature, equation (d) can be changed so that an equation will
be obtained analogous to Perrin\'s equation (c). Neglecting the term
hvlkH

— 1 in{e —1), (d) will change into;

hvlkT

In this equation e depends on T. The differential quotient

of this factor with respect to T is

h V

hv ^ kT

u « A 3 -hvjkT
AJ\'^ . e K à, (g)

d T I k T^

Putting, at a certain temperature:

- ,3 -hvIkT

® e K = f i^) • wc can write for (f)

,3

K= f{v) dv (h)

and for (g)

±L AjLf I,) dv \' (i)

dT kT^ \' \'

When we plot v against f (v), a certain area will represent inte-
gral (h). Integral (I) will be represented by an area outside of which

ƒ (p) = 0; the limiting curve of this area can be obtained by mul-
tiplying each ordinate of curve (h) with . This factor is no

constant, but increases with increasing v. The maximum in the curve
(i) will therefore be shifted to the region of the higher frequencies.

will be the largest in the upper limiting frepuency (j^j:

the smallest in the lower limiting frequency
hv^

area (i) < area (h) X jj : but that
h v

area (i) > area (h) X \'

Therefore:

d K

kT\' A:T2

and there must exist a frequency v somewhere between v and v
that satisfies the condition

t\\

din K h V

(k)

dT kT^

in which V will be not far from Pfn^x. \'n K = ƒ (f).

Perrin\'s equation is therefore valid over an entire range
of frequencies. There will be an average active frequency
representing this region and which can be expressed by the
Perrin equation. In order to apply this equation, however,
the reaction velocity as a function of the frequency must be
known. The average frequency v\' will be situated in the neigh-
borhood of the maximum of this function.

Tolman\'s theory leaves the position of v\' undetermined.
It may be said that this v\' > v*, the lower frequency limit,
and which is the frequency found by the original Perrin

equation. About the size of the factor p these equations
are silent.

Prof. Dr. D. L. Webster called my attention to the
fact that in the case of an external light source, which is
true for the majority of photochemical reactions, the tempe-
ratures T, and Tg in the equations have no definite meaning,
because one could as well substitute the temperature of the
emitter as well as that of the absorber. • The uncertainty of
these factors may also contribute to the discrepancy between
Perrin\'s equations and the actual experimental data. Sum-
marizing it may be said that Perrin\'s equation

A = only gives a lower limit

of active frequencies. That the equations as derived by
Ornstein & Tolman give evidence that the active radiation
must be of higher frequency. Tolman\'s deductions point to a
definite maximal activity, while, according to Ornstein all
frequencies > v will be found active.

\') Planck. Heat Radiation. London, 191-1.

2) Harvey. The Nature of Animal Light. Philadelphia, 1919.

3) Trautz. Zt. Phys. Chem. LIII. 1905.
Plotnikow. Photochemie. Leipsic. 1910.

») Langmuir. Phil. Mag. XL. 1920.

\') Rasch, in Sheppard, Photochemistry. London, 1912.

•) Lindemann. Phil. Mag. XXXVIIl. 1919.

«) Richardson 6 Compton. Phil. Mag. XXIV. 575, 1912.

») Ornstein 5 Burger. Proc. Roy. Ac. Amst. XXIX. 1920.

") Tolman, Journ. Am. Chem. Soc. 1921.

") Gullik. v. Ann. der Phys. XLVI. 1916.

CHAPTER II

EXCITING FREQUENCIES AND TEMPERATURE
COEFFICIENT.

Equation (7)

6.2___

^ = P Ti (Ti J0) log Q

expresses.\'at a\'Jgiven temperature. A = ƒ (Q,o). In the first
place the real meaning of this fact will be considered.

Exciting Perrin calls A the exciting wavelength. In Chapter I it
EQUency. j^gg jjggjj shown that according to Ornstein & Burger A may
have any value as long as it suffices

A = ƒ (p.. Qio) in which p < 1 .

As\'soon as p ~ 1 ; the original Perrin equation is reobtained,
in which A is the limiting wavelength. This idea is similar
to that expressed by Richardson \') in his theory of photo-
electric emission in which there is a limiting frequency below
which no photo-electric emission takes place. The emission
intensity plotted against frequency shows a curve with its
convex side turned towards the frequency-axis.- It is doubtful
if such curves exist in chemical and physiological reactions.
For. when the colour-sensibility of a photographic plate, the
eye. or some other substance is considered, it can easily be
seen that there is no definite limiting wavelength, no discon-

tinuity in the curve which fades out gradually in the region
of the longer waves. This state of things may be compared
with the equations of Tolman, in which the reaction velocity
is dependent on the frequency in the same way as the radia-
tion density in Planck\'s equations. In photo-electricity such
curves are known for the so-called selective photo-electric
effect, which reaches its maximum at a certain critical wave-
length. Pohl ô Pringsheim^) have shown that the photo-electric
activity depends on the angle at which the light is incident
on the surface, and on the orientation of the plane of pola-
risation. When the light falls normally on the surface, the
electric vector is parallel to the surface, and the photo-electric
activity increases continuously as te wavelength decreases.
But when the light is incident at an angle with the normal,
the electric vector which is parallel to the plane of incidence
produces a maximum effect for a particular wavelength. This
maximum is taken to indicate a resonance phenomenon. The
position of light sensitive organs in relation to incident radia-
tion (transverse phototropism of the euphotometric leaf etc.)
may have something to do with this fact. As every photo-
chemical process starts with electron emission there is evidence
that the distinction between normal and selective effect may
hold triie for these processes.

Because Perrin considers chemical reactions as resonance
phenomena, the selective effect must play the most important
part in these cases. The negative outcome of Ursprung\'s
experiments on photo-electric emission of green leaves do
not indicate that such emission is absent. The emitted electron
may react again before it leaves thc system (see Bodenstein
theory of photochemical reaction in Chapter III of this paper).
Another fact in favour of the connection between photo-
chemical and photo-electric processes is Richardson\'s eqiiation
for the in^uence of temperature on electron emission which
shows a close relation to Perrin\'s equation (7).

The exciting frequency will, therefore, be considered as
an average frequency, situated in the neighborhood of the
maximum of a selective photo-chemical process.

Tempe- The temperature coefficient will be defined as the propor-
coEFpf between two reaction velocities of this reaction at two
cient temperatures, van \'t HofF has introduced the expression Qiq
in physical chemistry. This temperature coefficient for 10" C.
difference lies, at room temperature, usually between 2 and 3.
This statement of van \'t HofF has caused much confusion.
Usually it is assumed that, if a reaction is not 2—3 times
accelerated by a temperature increase of 10" C., this reaction
is not taking place according to van \'t HofF\'s "law".

Now equation (3)

can be written

10^

It is clear that when T = o Qio ~ ^ and that when
T= 00 Qio = 1 . It is evident
also that in the range of physiological temperatures (T =
273-303) Q,u will decrease. .

Krogh^) seems to think that the Qio is a rigid constant. Patter®)
tries to explain the decrease of the Qm by a complex system of
processes, each with a certain definite Qio- This is unnecessary.

Cohen Stuart") has derived an expression for this decrease,
assuming a certain reaction velocity to be a linear function
of the temperature. This assumption leads him to the following
connection

(Q,o — 1) T = constant.

This formula does not apply. Within the range of physio-
logical temperatures Qjo varies usually 30—50%, therefore

(Qio - 1) still more. T varies from 273®-303° abs. little more
than 10%. This change carmot compensate the large variation
in the Q. In order to compare the applicability of this equa-
tion and

the constant will be calculated from an actual set of experi-
mental data by both methods. The reaction time of photo-
tropic response in Avena is a temperature function. This
temperature function is studied by Miss de Vries The
constant from Cohen-Stuart\'s equation (= c) as well as A will
be calculated

Columm 7 proves to be constant. Therefore equation (3)
holds.

Analyzing the Q,o in its components; two reaction-velocities,
it may be asked if the reaction velocities themselves can be
analyzed further. For a reaction velocity a similar equation
as Ohm\'s law seems to hold

chemical resistance (ƒ)

velocity of reaction =

q -illjl

U.O-

Chemical force ƒ is a function of the free energy; very
little is known about chemical resistance, except that it is

greatly demmished by rise of temperature. Factors as internal
friction etc., undoubtedly have something to do with chemical

resistance, and are perhaps directly proportional to this factor.

f\'

For aqueons solutions — is small, and, in order to make

= 2—3, there must be an increase in the free energy

of the system. But for protoplasmatic processes, where — ,

the thermal coefficient of an emulsoid, is very large, the free
energy must decrease in order to keep Q,o in the range of
known experimental values. Generally spoken it can be said
that there are Qio\'s chiefly related to a) reaction velocities,
b) chemical forces or c), chemical resistances. .

^^ Qie rela- Longitudinal growth of plants and animals ; retinal current
«^EaS reaction times are different factors connected with reaction

Velocity! velocities. Reaction time is a good index for reaction velocity,
in asmuch the velocity constant can be represented by

a" — j:" a. being available- and
X. decomposed amount.

When the reaction is practically finished the .reaction
velocity is inversionally proportional to the reaction time, as
in that case the equation limits to

c

f

The intensity of an electric current can be compared directly
with a velocity. And it is clear that thc Q of congitudinal
growth, being the Q of a reaction rate belongs to this group.

^^ qio rela- Heat-, light- and electron emission, heat-, light- and electron
^"eISIcI^ absorption belong to this group. As these processe^i\'take place
force*! mostly at surfaces, the resistance does not change very much

with temperature and-^ will bc small. The small Q,o for many

of these cases has been explained is this way (diffusion theory
of Nernst).

c) chemical is a function of the internal friction of a system. The internal
resistance, friction of an emulsoid changes quite perceptibly with the
temperature. The rate of the protoplasmic current, a velocity
is so much influenced by temperature that it seems to be
dépendant on the internal friction only. The change in the
free energy of the system d f must, accordingly, be almost
nil. The long latency times (praesentationtime or refractory
period) of many physiological reactions are probably connected
with internal frictions.

d) other In most of the physiological reactions the origin of the
cases. Q^^ jg obscure. qio of respiration or assimilation, measured
by the amounts of carbondioxide given off or absorbed are
made up of many factors. Only when the intake or output
is constant during a long period of time it is warranted to
assume the velocity to be proportional to the amount of COj.
Another complex case is the time required for seeds to ger-
minate at different temperatures. Here the Q|o of absorption,
viscosity, respiration and all kind of enzym actions play a
role. The same can be said about the Qm of the time needed
for laI^\'ae to develop (Krogh) or for ants .to walk a certain
distance (Shapley).

There are several cases In which equation (3) is not applicable.
Instead of decreassing continuonsly with increassing temperature, an
initial increase may be observed in certain cases, as the saponification
of esters. Several explanations of this fact have been attempted, but
the real cause of this curions phenomenon is not known as yet. In
many reactions Q|o decreases very rapidly and becomes < 1 j which
means that the reaction velocity decreases with increasing temperature.
The so-called optimum reactions in physiology, and the reactions
the influencc of temperature on catalytic activity of metal soles belong
to this group. The theory of limiting factors, as proposed by
Blackman (8) has given an explanation for this fact. In optimum
curves it is no longer warranted to assume a temperature relation
with one variable; a second variable, the observation time, comes in.
Only when, at a given temperature, the intensity is indépendant of
the observation time, the van \'t Hoff law is directly applicable.

When the intensity varies with the observation time, Blackman
suggests that an extrapolation to the observationtime = zero may
lead to the construction of the van \'t HofF curve in this case. An
actual extrapolation was carried ont for a set of experimental data
on plant respiration. The results will be published in a separate paper.
It will only be pointed out here that the extrapolated curve can be
represented by a van \'t HofF curve.

In this paper cave will be taken to exclude all Q,o\'s
situated at abnormally hich temperatures.

Exciting For a certain temperature interval dT
\'^\'^EQuencv

At room temperature it may be expected to find the

violet ... , high

■ ^^^ sensitized reactions to have a temperature coeffi-
cient. According to equation (6)

1.43

in which A is assumed to be constant. This is not always
the case.

T, Tj In Qio is not always constant.

If it is constant the reaction will be sensitized by the
same wavelength at different temperatures. These reactions
will be called stenophotic {srsvcg = narrow). In other cases
Qio decreases too fast to be balanced entirely by the increase
of T, Tj. a will decrease, and the exciting frequency will
shift to the red end of the spectrum. If this shift is conside-
rable the reaction will be called euryphotic [eupCi; = broad).
The broad absorption bands of many coloured compounds
may provide the means to resist the action of this shift.

An absorption band be expected to shift to the red with
increasing temperature. Appreciable results have been ob-

tained with solutions of chlorophyll, aurine und eosine. also
with potassium permanganate. The amount of the possible
shift cannot, however, be calculated by the equations deve-
loped in Chapter I, as A is assumed to be constant.

1) Richardson. Phil. Mag. XXIII. 615. 1912.

2) Pohl 6 Pringsheim. B. D. Phys. Ges. XII. 215. 1910.

3) Ursprung. Ber. D. Bot. Ges. XXXVI 1918.

Krogh. The Respiratory Exchange of Animals and Man. Londen 1916.
\') Pütter. Ztschr. Allg. Physiol. XVl, 574, 1914.
«) Cohen-Stuart. Proc. Roy. Ac. Amst. 1912.

de Vries. Rec. Trav. Bot. Néerl. XI. 1914.
8) Blackman. Ann. Bot. XIX. 281. 1905.

CHAPTER III

THE MAGNITUDE OF THE TEMPERATURE
COEFFICIENT

A. Low Temperature Coefficient

Photo- It has been assumed by different authors that photoche-
^^OCESSE^ mica! processes have a small Q,o. It is assumed generally
that in "photochemical" processes the temperature coefficient
is much lower than in "chemical" or "physical" processes.
Bayliss \') remarks that ;

"This follows from the fact that the rate of the photochemical
change depends on that of the absorption of the light, which varies
only slightly with temperature".

Apart from the fact that the rate of photochemical change
is in many cases not dependant on that of the light absorp-
tion, it is a dangerous thing to ascribe the size af the Q,o
to the same cause in all cases. Different other authors, as
e. g. Tolman and Bodenstein^) hold a different opinion as
that expressed above. Nernst holds that the low Q,o is
caused by diffusion. Recently this idea has been opposed by
Hccht^) for thc bleaching of the visual purple in the light.
So it can be seen that there is no unanimous opinion about
the direct cause of the size of the Q,o in photochemical
processes. In this paper photochemical reactions will be
considered as photoelectric in their nature and the conce-

quencis of this idea will be considered. Allen 4) has developed
a photo electric theory of the photographic plate, in which
he assumes the silver halides to shoot off an electron from
one of the outer (valency) rings, because, according to
Richardson, the photo-electric processes take place in the
outer rings. If. moreofer, a ringstructure, similar to the Bohr
atom, is assumed to represent the structure of the substance
^ it is clear that it will take less labour to remove an
electron from a distant ring than to remove an electron which
circulates nearer to the nucleus. The labour to remove such
an electron is the equivalent of the dissociation heat of the

reaction. This is U = and. according to equation (3)

this labour must, at a certain temperature interval be propor-
tional to In Q,o. Therefore it can be expected that large
atoms and atom-aggregates possess a smaller Q,o for their
photo-chemical reactions than small atoms or atom aggre-
gates. As the accurate determination of these small thermal
coefficients is very difficult it is impossible to test this result
quantitatively. It will therefore be tested only if. in general,
the simpler compounds (as measured by atomic — and
molecular weight) will have a smaller photochemical Q,o as
the heavier atoms or compounds. From the book of Plotni-
kov. as well as from the article of Bodenstein and others
the following data were obtained:

Subsequently the correlation coefficient between molecular
weight and Q,o was determined in the usual way and found
to be /• = 0.84 ± 0.05; which is strong negative correlation.
Several reactions could not be treated because of the incer-
tainty of the Q,o or the uncertainty of the molecular weight.
Aware of the fact that the molecular weight is a poor index
for the number of electron-rings, it is clear that heavy atom-
aggregates or heavy atoms will have more rings as light ones.

M, Bodenstein has given a general photochemical theory,
derived from equilibrium considerations. This theory holds
that the first phase of light action (absorption) is photoelectric.
A valency electron rs shot off. The "primary" reaction takes
place in the remaining positive nucleus, the "secundary"
reactions are caused by the photoelectron.

The primary reactions are caused by a small number of quanta.
The secundary reactions are more complicated. In the latter reactions
the same quantum may act this way on a large number of molecules.

Prof. Dr. H. A. Lorentz was so kind to call my attention to the
fact that Tolman still holds another opinion about the temperature
coefficient of photochemical reactions. In his theory Tolman introduces
the "sensibility" factor K^ : a reaction velocity belonging to a frequency
range d^,. This factor is probably a temperature function: the internal
condition of the molecules may change during the reaction, and this
may cause a change in the "sensibility" for certain frequencies. This
also makes it clear, why a temperature shift of an exciting frequency

is possible. Tolman has derived the K,-T relation for black radiation

by means of statistical mechanics.

There are cases, however, in which the crucial point is the sens,-

bilitu of the molecules only. It is possible to imagine a photochemical

reacLn starting not under the influence of black radiation o its
environment: but under the influence of a contrôlable external light
source. Keeping this light constant, it is possible to change the

temperature of the illuminated object. Tolman remarks about this case
"As far as the author knows, this is the first theoretical treatment
of the temperature coefficient of photochemical reactions."

Catalysts. From the Arrhenius equation:

dlrxK\' ^ A
dT T2

it is possible, with the aid of equation (5) to substitute

p for A. The reaction be acceleratcd or retarded by a
^ k

catalyst and its reaction velocity be K\'.
For the uninfluenced reaction

dlnK-

For the influenced reaction at the same T;

dlnK\' hV

dT"" = P fc T2
dlnK\'_

If a reaction is ^^{j^y catalyzed, the exciting light

red

frequency will shift to the en^l of the spectrum.

Now V is inversionally proportional to In Qiq. From this
it can be concluded that:

if a reaction is catalyzed, the temperature

decrease

coefficient will -----

mcrease

Perrin\'s theory therefore gives an explanation of the fact, observed
by Winther^), that the decomposition of thc so-called Edcr oxalate
solution by light is catalyzed by Fc CI3 and that, the more thc reaction
is catalyzed, thc more the optimum activity shifts to thc red end of
thc spectrum.

Dhar«) found that, with a great many reactions, the temperature

decreased , , ,, negatively

coefficient was ^^^ as this reaction was catalyzed.

Therefore the second causc of the infra normal temperature
coefficient may be catalysis.

Changes Temperature has little or no influence on the change in
internal internal friction of suspensoids. As far as we arc aware, no
priction. ij^po^tant physiological reactions exist where this factor can
play a role, as nearly all physiological reactions can be con-
sidered as emulsoid systems.

Heat Heat radiation intensity at physiological temperatures has
■Radiation, gijo a small Qio- As the optimum frequency in this case is an
infrared radiation it can better be treated in the next group
of reactions, which are also characterized by a small tempe-
rature coefficient.

Red Equation (7)

Sensitive 5 2

^hactions. ^ = \'\'l^(t, 10)logq7

shows the relation between an optimal exciting light wave
and the temperature-coefficient of a certain reaction at certain

temperature. In chapter I it has been shown that, at room
temperature, there is a corresponding variation of A (visible
spectrum) and Qio (average values) if p = 0,27.

Ti may be taken between 0"—30° C.. as higher tempe-
ratures imply the influence of hmiting factors. The determi-
• nation of the Q,o. especially in older investigations, has often
been carried out in a very inaccurate way. The majority of
experimental values had to be rejected for this reason. It may
be asked if equation (7) expresses satisfactorily the results
in cases where both optimal exciting frequency and tempe-
rature coefficient are known.

Photo- The initial process, the intake of carbon dioxide, is
synthesis, notably influenced by light and by temperature. Recent
investigations of Ursprung (I.c.) have confirmed the view
held by the earlier authors: the optimum frequency for the
activity of the assimilation is situated near the optical axis
of the red absorption band of the green leaf. The tempera-
ture influence has been studied by Blackman and Miss Matthei \')
and recently by Warburg

As the results of the latter author confirm those of
Blackman, there is evidence that the values for the Qio are
trustworthy.

Blackman\'s value ^ = 2,05 gives

K\'

0,27.6,2
283. 293.0,312

lO-\' c.M.

2,95
= 644 (Cija.

^ =\' is probably a little too small, because of the limiting

1-67 ,,

A = —----------------- C.M.

\' 303. 263 .0,256

= 734 ^^

According to equation (7) the exciting frequency for C O2
assimilation is situated at the red end of the spectrum. The
average frequency between 10—30\'\' C. = 689 fx [x. probably
a little too high, because of the influence of the limiting

c ^\'30

factors on — - .

K 20

This value is close to that for the maximum absorption
in the green leaf (678 (x [i) and to that for the assimilation
maximum.

Lonqitu- The action of red and infrared light on longitudinal

Q growth has recently again been demonstrated by Klebs®).

•^OWTH, influence has been observed by different authors on

different plants. According to these facts the process can be
expected to have a low temperature coefficient. This is
actually the case, as an investigation of Miss Talma\'")
shows. The growth velocity of Lepidium sativum can be
assumed to be proportional to a reaction velocity. The most

constant series of data = 1.81 will be used.

K ,7

, = - .....c,M.

290.300.0.257

= 750 (xfx, or about the red limit of the

visible spectrum.

Supra- In chapter II it has been pointed out that, at supra-

•tSeTa\' temperatures, the temperature coefficient will decrease

tures, and become abnormally small.

;0nclusi0n Contrary to the prevaiUng opinion that the cause of a
for small g^^j^jj temperature coefficient is either hght absorption or
rature diffusion, it has been shown that there are many other in-
coeffi- stances, as; the size of the reacting molecule or atom, the
cients. temperature, the sensibility to low frequency radiation etc..
wich may cause the Q,o to be small.

B. High temperature coefficients.

As it has been pointed out in chapter II. high temperature
coefficients are typical for processes connected with changes
in the internal friction (viscosity) of emulsoi\'ds.

The viscosity of colophonium in terpineol. for example, decreases
92.10» to 4,8. 10\' units from 7.1« C. - 11,8° C.

v. Schroeder") found a decrease in the viscosity of gelatin
from 31° 0.^21" C. from 13,76 to 1,42 units. According
to equation (7) this high coefficient would point to an exciting
wavelength in the ultraviolet, situated at

^ _ _ 1,67
294 . 304 . log

\\ = 200 (Xfz.

In this chapter it will be tried to jarove that reactions
with a high temperature coefficient absorb U. V. light and
are sensitized by it.

Internal Friction is a very important factor in protoplasmatic
friction, processes, in as much it determines the rate of the plasmatic
current and many enzymatic reactions. In this chapter coagu-
lation, heat destruction, oxydation of haemoglobin and proto-
plasmic current will serve as examples.

v. Schroeder\'s value for the viscosity of gelatin pointed

to an exiting light wave of plm. 200 ^ ^ . We can, therefore,
expect, if equation (7) holds true, that proteins absorb quite
generally the ultraviolet part of the spectrum, and that their
reactions are excited by the ultraviolet light.

Now Soret \'2) found that, nearly all proteins absorb about
the same region in the ultraviolet. The work of Hertel
has shown that the inactivation of enzymes and toxins is

caused by ultraviolet waves.

*

coaqula- Chick and Martin\'^) found an enormous Q,o for the
^tion and coagulation of haemoglobin. It has been shown by Bovie
Truct^on that haemoglobin can be coagulated by ultraviolet light.

" Dreyer & Hansen\'") coagulated different proteins in the

ultraviolet.

The values, published by Tammann "\'). on heat destruction
of emulsin. are still classical examples of high temperature
coefficients.

14 7

Tammann found between 65° and 75° C. a Q,o of
According to (7) this would point to

, = _ . C.M.

338.348.0.712

X = 202 fj^H\'.

Hertel (I.e.) Green\'") and Schmidt-Nielsen"\') have
destroyed and inactivated enzymes by U - V light of short
wavelength.

In this conncction it is Interesting to see that dyphteria-toxln Is
destroyed by the U - V light while the antitoxin is not affected.
Similar antagonisms will be treated in chapter IV.

pROTO- Already Vclten^») has published data on protoplasmic
cutf""^ current. Between O^-IO« C. he found for the rate of this
• current in cells of Nitella Q.o = 9.33. Accordingly;

40
1.67

A = ------c.M.

273 . 283 . log 9.33

X = 225 iJ,iJL.

This reaction is markedly affected by hght; the optimum
reaction can be expected in that region which the protoplasm
absorbs.This is, according to V. Henri^\') between 240-214 fM (x.

Oxidation From the data of Barcroft and Hill 22) the Q,o of reaction
of haemo- velocities can be exterpolated; giving analogous results for
globin. ^^^ series of experiments.

Q26 = 5.0 Q^ = 4.7

16 30

Corresponding to

c.M.

2S9.299 Jog 5.0
a = 284 ^/tA and

1,67

A =

303.313. log 4.7
\\ = 27&

Now oxyhaemoglobin posesses a strong U-V absorption,
whchhas an optimum at 275 (Dh^r^)"). And the third
link in the chain gives Hertel (I.e.). who finds oxyhaemoglobin
to become reduced by the magnesiumline 280 ij. [a (2803 Ao).

conclu- High temperature coefficients are invariably connected
sions for with a) changes in internal friction,
high tem- jjv mj^g yjQlgj absorption.

perature v tt. • 1 •

coeffi- c) Ultra violet excitation.

cient A variety of causes, as for the low temperature coefficients,
could not be traced. The modified Perrin equation (7) expresses
satisfactorily the actual state of affairs. The results can bc
tabulated as follows:

N. B. The excitability of protoplasm is greatly affected by the
ultraviolet. Still the initial phase of this process is not influenced
by temperature. The probable reason of this fact will be traced in
the next chapter.

C Normal temperature coefpcients.

Photo- Avena sativa has been the object of many investigations
tropic both on the spectral sensibility and temperature coefficients
\'^^^Sts process. Blaauw^") has found the spectral position of

\' the optimum sensibility at 467 fx [x . The temperature coëffi-
ciënt of the phototropic reation time has been studied by
Miss de Vries (I.e.). It has been shown in chapter 11 that
the A in Arrhenius\' equation remains practically constant
throughout a wide range of temperatures. Equation (7) gives
for the exciting frequencies;

It may be remarked in this connection that in Avena the
yellow colour of the coleoptile may be the cause of the blue-

violet absorption.

If the determination had been carried out in two decimal places
instead of one, no doubt the approximation would have been
closer.

Retinal Again it will be tried to find three sets of data. The
processes, purple of the rods is bleached by hght. de Haas") found a
maximum absorption for the visual purple of fishes at 540 ^ fi,
of mammals at 500 f^ fM . This is probably the place of the
maximum action; Piper") found the the maximum retinal

current of the frogs eye at 544 [u, f/, •

Hecht (1. c.) could find no temperature influence on the bleaching
of the visual purple. Here again is an example of a series of
processes, of which the initial process is not influenced by tempe-
rature (see next chapter).

The Qio of the retinal current has been determined by
Riedel") for the Cray fish between 0^30" C. Equation (7)

=--------C.M.

273. 283./o0 2,5

A = 537 /x/x.

Hecht (I.e.) studied phototropic responce in Mya. Thc
temperature coefficient of the latent period Q^\'/io = 2,4

. = _- C.M.

283.293./op 2,4 .

X = 525

CoNCLU- The equation (7):

6,2

T, (T, 10) /op Q,o

seems to hold in a good many cases. About twenty different
temperature coefficients yielded values for A which are in
agreement with the experimental data. In the case of low
temperature coefficients the relation is not so clear.

Fia. H. Shows three spectra.

I shows the calculated exciting frequencies for

a) photosynthesis.

b) retinal processes.

c) phototropic response.

d) haemoglobin oxidation.

e) protoplasmic current.

\'DO C.

II shows the absorption maxima for the media, in which
these processes take place.

III shows the optimal spectral activity for the different
processes. The value at c. 467 fj, f^ is calculated from
data of Miss Hurd^®).

A satisfactory agreement between the three spectra is evident.

300 ^ ^ 2qo

rr

i^ca

n

ur

m

e- 200
IT

1) Bayliss. General Physiology. London. 1918.

2) Bodenstein. Ztschr. Phys. Chem. LXXXV. 1913.

3) Hecht. ]. Gen. Phys. III. 1921.

4) Allen. Photo Electricity. London. 1913.
fi) Winther. Ztschr. Wiss. Phot. 1908.

6) Dhar. Ann. de Chira. IX. 1919.

7) Blackman & Matthei. Phil. Trans. XCCVII. 1904.

8) Warburg. Bioch. Ztschr. CX. 1919.

9) Klebs. Abh. Ak. Heidelberg. Math. Nat. Kl. 1914.
<») Talma. Rec. Trav. Bot. Néerl. XV. 1918.

»\') V. Schröder. Ztschr. Phys. Chem. XLV. 1903.

\'2) Soret. Cited from Müller: Oppenheimer\'s Handbuch. Bd. I. 664.

13) Hertel. Ztsch. Allg. Phys. V. 1905.

14) Chick & Martin. ]. Phys. XL. 1910.

Bovie. Cited from Müller; Oppenheimer\'s Handb. Bd. 1. 664.
1«) Dreyer & Hansen. C. R. CXLV. 1907.
•7) Tammann. Ztschr. Phys. Chem. XVllI. 1895.
18) Green. Trans. Roy. Soc. CLXXXVllI. 1897.
1«) Schmidt—Nielsen. Ztschr. Physiol. Chem. LX. 1909.

20) Velten. Cited in Cohen Stuart. I.e.

21) Henri. Etudes de photochimie biologiques. Paris. 1912.

22) Barcroft & Hill. Bioch. Jrnl. VII. 1913.

23) Dhéré. Soc. Biol. 1909.

2<) Blaauw. Rec. Trav. Bot. Néerl. V. 1909.

25) de Haas. Cited from Zwaardemaker. Physiologie. Haarlem. 1921.
28) Piper. Arch. Phys. V. 1911.

27) Riedel. Cited from Zwaardemaker. Physiologic. Haarlem. 1921.
2») Hurd. Bot. Gaz. LXIX. 1920.

CHAPTER IV
RADIATION AND REVERSIBLE REACTIONS.

Intro- An endothermic reaction will be considered, which takes
AUCTION, pjg^^ under absorption of a light quantum h v . Now there
are two possibilities. Either the entire quantum h v is used in
the reaction, or the quantum hv is "degraded" to a quantum
hv\',\\n which h v\' < h v . The same idea can be applied
on exothermic reactions; either an entire quantum hv is
emitted, or the quantum h v\' is absorbed and "promoted" to
hv, in which h v > h v\' . The absorbed or emitted energy
in the above cases will be h ( v—v\' ) ergs.

Perrin expresses this idea as follows;

"Toute réaction implique deux mouvements inverses d\'énergie rayon-
nante. sav. absorption de la lumière qui la provoque, et émission de
la lumière qui la renverserait".

Or A v±^A\' V\'.

"Toute énergie dc réaction se mésure par l\'excès dc la fréquence
absorbée sur la fréquence rayonnée".

Or hv — hv\'.

This statement enables us to derive a reaction heat in
terms of frequencies. This reaction heat is for one molecule

h {v-v\') .

for a gramme molecule

N . h {v—v\') ergs or

4,3 . {v — v\' ) ergs or

1.0. 10"\'" {v — v\') calories
in which v corresponds to

AA

ph \' (5)

The idea of two frequencies becomes more clear when illustrated
by Ostwald\'s metastable-photochemical equilibrium. A wedge shaped
block rests on one of its rectangular planes. On tipping this block
over at first energy is required to raise the centre of gravity till it
is situated perpendicularly above the line of support, than it will be
lowered till the block lies on its next rectangular plane. The loss in
potential energy may be larger in each turn than the amount of
spent energy. If the energy be expressed hy hv. equation (10) can
be obtained immediately and it becomes clear why different frequencies
may play a role.

Ornstein 6 Burger found, and their results are in agreement
with many photochemical data, that the active radiation has
a frequency v which is larger than the

[energy of bound molecules — energy of dissociated molecules]

h .....

and in the case of the lower limit of the active frequency

h Vo = e\'—e ,

this frequency is directly proportional to the difference of
energies in the bound-and the dissociated molecules, in other
words, proportional ^o the reaction heat. Inasmuch the reaction
heat is a fixed quantily e\' and s can be written hv\' and hv
respectively\'and the lower energy limit becomes

± h {v—v\') which is equation (10)

This being a lower limit the Perrin equation must be
modified in

U = N.p.h {v-v\') or

U = 0.27.10~\'° [v-vf) calories (10)

Reversal Now, if a system of two exciting frequencies exits, the
light, reaction heat can be calculated. In a "dark" reaction the limiting
frequency will be low. In that case v\' — v will be maximal.
According to Perrin\'s idea, there are no real "dark" reactions.
This dualistic point of view, as proposed by Trautz (1. c.) and
Bodenstein (1. c.) becomes superfluous and reactions of the type

A light B

B in dark —> A can be written
A t; A\' t.\'

It was known long ago that opposite parts of the spectrum may
have opposite effects (Luther\')). The latent image of a photographic
plate is destroyed by infrared radiation (Millochau ^j). Stobbe\'s ful-
gides^) are a very striking example of this reversible action. The
bleaching of the visual purple by light is counteracted in thc dark
(Kühne*)). Ba-Pt-cyanure becomes brown in x-rays, bleached again
by visible light. Guaiacum becomes green in the light, but is bleached
in the dark.

A powerful antagonism between the red end and the blue
end of the spectrum exists in the case of plant growth (Klebs I.e.).
While the long waves stimulate longitudinal growth and
inhibit cell division, the short waves stimulate cell division
and inhibit longitudinal growth.

As in the dark reaction a large value of h{v\'—v) might
be expected, the Qio must be large — in the light reaction
thc Qio must be small.

This is actually the case, as the following table shows.

The difference in Qio\'s can be accounted for thermo-
dynamically. Considering a reactionisochore

d In K _ A
>r — H"

dT

The reaction is reversible, one reaction velocity
being Kj : the other Kj .

K, X

K

1 .t

Now K = dlnK^—dlnKi

Q,

InK = In -pr , between t and T
U2

Qi T — t

/n - ± A .

If A is positive, Qi > Q»
......negative; Qi < Q^.

With the help of equations (10) and (11) it will now be
tried to investigate the influence of radiation on physiological
reactions. The Perrin hypothesis in its general form

A p ^ A p\'

implies an emission of radiation, either as fluorescence or
luminescence, in every chemical reaction.

\') Luther. Zeitschr. Phys. Chem. LIII, 1905.

2) Millochau. C. R. CXLllI, 1906.

3) Stobbe. Lieb. Ann. 359, 1908.

*) Kühne. Physiol. Lab. Heidelberg. Ill, 1878.
\') Weigert. Ztschr. Phys. Chem. LXXXV, 1913.
•) Vrânek. Ztschr. f. Elektroch. XXIll, 1917.

CHAPTER V

RADIATION AND PHYSIOLOGICAL REACTIONS.

Physiological reactions vary from comparatively simple
processes — as protoplasmic movements and vacuole pulso-
tions to the complex phenomena as growth, assimilation. There
are. however, general laws which govern both simple and
complicated phenomena; the principles of thermodynamics.

Notwithstanding the many criticisms on the applicability of the
second law of thermodynamics there is no reason to raise serious doubts
as to its applicability on physiological systems (Zwaardemaker l) ).

In the preceding chapters it has been tried to modify and
extend the hypothesis of Perrin, which advocates the importance
of radiation as the cause of combination and dissociation of
molecules. One easily measurable factor, the temperature
coefficient, has given certain clues as to the nature of the
influencing radiation.

There is evidence that radiation influences a good many
physiological reactions. It is unlikely, however, that is causes
these reactions. Organisms in caverns or deep sea are only
reached by heat radiation of a low energy value, unsufflcient
to account for the energy changes within the system. The
same is the case for cells inside the organism. It is. however,
possible that in the case of heat radiation there is sufficient
energy available to initiate the destruction of a mestastable
equilibrium (comp. the wedge-shaped blok in the preceding
chapter).

In certain cases, part of the work is done by the radiant
energy.

The equilibrium of a radiation system would involve
absorption as well as emission of light. This emission has only
been studied in the range of the visible spectrum. It is possible
that, in the majority of cases, thé emission will be of an
infra red character and has sofar escaped attention. Up till
this time, it is mainly the high frequency radiation that has
called the attention of the investigators. Especially the specific
action of the ultra violet rays on the living cells has been
the subject of many investigations.

The Perrin theory requires in many cases an exciting
ultra violet frequency. This radiation, when emitted, will be
absorbed immediately by the surrounding protoplasm; as proto-
plasm possesses broad absorption bands in the ultra violet.
This occurrence of ultra violet frequencies in living tissues has
been assumed also by von Tappeiner and his school to account
for certain peculiarities in the action of sensitizing dyes on
the organism. It is not difficult to ascribe this role to a great
many natural pigments.

Tlic fact that thc cfFcct of radioactive metals as well as radioactive
emission on thc heart can bc modified by fluorescent dyes may have
some conncction with Tappeincr\'s assumptions (Zwaardemaker ).

It seems to us that the chief justification of Perrin\'s hypothesis
lies in the fact that it will prove to bc an excellent working
hypothesis: which calls the attention to a great many possi-
bilities which, hitterto, have remained unnoticed.

\'ERsible a complex scries reaction as underlies most physiological
CTioNS. phenomena may be considered as excited or inhibited by
different frequencies, corresponding to different temperature
coefficients. The temperature coefficients of these subsequent
reactions may either express the magnitudes of the cxciting
frequencies, or they may express the relation between two
exciting frequencies.

As the Einstein equation U = N /z y expresses the relation
between light frequency and energy; the Perrin equation
U = N /i (v—v) between frequency surplus and energy.

The Einstein equation may be compared with an expression of
the combustion heat, the Perrin equation with the expression of a
reaction heat. Only when f\'is sufBciently small both equations express
the same thing.

Now for a complex series reaction the whole process of
radiation exchange can be examplified as follows.

U = ±^Nhi: {v — v\') {v\' — v\')-h{v\' — V")

Exothermic
reaction

Absorption
spectrum

V" Frequency

In this schematical representation the energy change in
one reaction A U takes place between two frequencies, c. g.\'
u and v\'. In the exothermic process v is the initial optimal
frequency absorbed by the system, usually an ultra violet wave.

A U ergs is liberated when h v is degraded to h v\' in
other words, there is fluorescence or luminescence of a fre-
quency range with the average v\' . This same frequency can
initiate a second jump in potential energy, degrading to v\'.
This wil go on, and if the process is brought to an end by
the 3\'\' energy jump, a frequency average v*\', very often an
infra red frequency, will be emitted. The endothermic reaction
will go the other way; in this case with an initial absorption
of v", a final emission of v.

This schematical representation suggests absorption and
emission spectra of the reaction systems in which absorption
bands are emission bands and in which Stoke\'s law (frequency

of fluorescent light is smaller than the frequency of the
exciting light) doesn\'t seem to hold. Such spectra exist in the
living cell.

V. Henri has recently developed a formula which shows a
connection between the different absorption bands of many complex
organic dyes. The absorption spectra consist of equidistant bands;
obeying the formula

p = i>o na mb, n and m being Integers.

This gives

t) — Vo = na mb, or according to Perrin the equidi-
stance of the bands expresses:

d U — na mb, the energy jumps being the same be-
tween two arbitrarily chosen bands.

Henri remarks that vq usually possesses a strong fluorescence,
corresponding to the lowest energy level in the Perrin equation (10).

A series reaction will have different Qio\'s for the different
processes and these values will differ considerably when the
energy changes in the different stages of the process will
bc very unequal. In physiological processes there are several
instances known in which the initial temperature coefficient
is very small. This may point to the destruction of a meta-
stable equilibrium. (Retinal processes, sensibihty of protoplasm).
The theoretical spectrum of this reaction will be:

V V

The system takes in hv, and changes this into hv\'.
Energy/oss is p N/i (v\'—v) p . gram-molecule, corresponding
to a small Q,o {v—v is small). The system degrades hv\'
into h Vq .

Energy gain is p N /i (v\' —Vq) p . gram-molecule, corres-
ponding to a larger Qio.(f\'—i^J is larger).

The considerations developed in the above pages will

now be applied on different physiological reactions. This
influence of radiation will considered on

(1) Oxidation, respiration, hght emission.

(2) Carbon dioxide assimilation.

(3) Enzym action.

Oxidation, Luther s) remarks that nearly every photochemical reaction
respiration has the nature of an oxidation or a reduction. Therefore
radiation seems to be a powerful agent in changing the
emission, potential, either in a chemical or physiological

medium. Some authors (Hertel I.e.) hold that the reactions
in a certain part of the spectrum are either oxidations or
reductions. In the light of the developed theory this would
seem untenable, as, for a certain frequency v all rays
V ndv must induce a higher, all rays v—n dv a lower
oxidation potential. The experimental evidence shows that
the ultraviolet can induce both reductions (methylene blue)
and oxidations (sugars etc.). Generally, however, it is clear
that, if v—ndv induces an oxidation potential which is
much lower than v. v—ndv will be shifted considerably to
the red end of the spectrum, and it can be said that the
violet end of the spectrum is more liable to cause oxidation,
the red end to cause reduction. It will be seen that the two
important physological reductions are caused by the red end
of the spectrum.

The equilibrium Haemoglobin Oxyhaemoglobin.

The reaction Hb O^H b is exothermic in the lungs

and gills, exothermic in the tissues; accompanied by oxidation
and reduction respectively. The thermal coefficient for the
oxidation is very high. -The theoretical position of the average
exciting wavelength for this dissociation is situated at about
280 /x^ f a value quite close to the ultraviolet absorption
band of the haemoglobin (275 /x) and the maximum of the
actual reaction as found by experiment (280 /x/x).

It may be asked now if it is possible to calculate the

average frequency of the Ught which will be emitted during
this reacton. if this reaction is thought to be sensitized by
280 fjt,f^.

In order to carry out this calculation the reaction heat
of the system Hb —> O^H b must be known. The values
of du Bois Reymond®) and Barcroft 6 Hih®); plm. 28 K.G.
calories, will be taken.

In Equation (10)

U = 0.27 {v—V)

U . 10-\'"
0.27

p- = 1.07.10"\'\'-1.04. 10-\'®

p\' = 3. 10"\'\' . corresponding to a wave-
lenght of about 10 /x.

This means that, according to the modified Perrin theory,
the exothermic reaction H b —> QtH b will emit infrared
radiation; the endothermic reaction O^H b —> Hb will be
excited by this radiation.

Now this excitation occurs. Hartridge and Hill^) have
found that the system H b O^H b is sensitive to infrared
light. The equihbruim constant changing in this light from

K

K to

20

According to them, the labour done by the light is. per
gramme molecule (formula of Nernst)

RT /n 20 ergs or

2.3.6.8.1.34.1.3.3,1 = j 97 K.G. cal.

4.27

Hartridge & Hill find 1,85 calories, because of the N of Avogadro,
which they take to be 6,5. 10^ instead of the more recent value
6,8.1023.

Now, according to Ornstein & Burger the chemical active
frequency gives

hv > e\'-e .

In this case the active radiation must have a frequency
higher than

1,97.103.4.27.10\'

V =------------or

h.N

V > 1,94. 10\'3

corresponding to a wavelength of 15 /i.

The consequence of Hartridge & Hill\'s data is therefore
that any ware shorter than \\5 fi will be active so sensitize
the reaction Q^H b —► H b.

This is about the place calculated from the Perrin equa-
tion (7) and about the optimum of the heat radiation at
the body temperature of poikilothermic animals.

Now this would mean a remarkable coincidence, the
more so because the values of Hartridge & Hill seem very
trustworthy.

Unfortunately this is not the case with the experimental
values of Barcroft & Hill for the reaction heat. According to
these authors this reaction heat will be about 28 calories.
Now there are other investigations which give much smaller
values. (Berthelot 8), Torup»), Camis\'"), Meyerhof")). The
average value from their work is 13,6 calories (10,8-15 cal).
According to (7)

p\' = v -

v\' = 1,07. 10^"^— 0,5. lO\'\'^

= 0,57 . 10^®

corresponding to a wavelength of plm 530 fz [j,, in the neigh-
borhood of the maxima of absorption of C^fi b in the visible
part of the spectrum (540 tx fx).

The energy jump from this place to the infrared maximum
is also 13,6 calories. It is therefore possible that most of the
authors have measured the energy jumps between 275 (jt, fjt,
and 540 pt ju or between 540 fx /x and 10 ^ , both corresponding
to the intake of one molecule of oxygen.

The reaction haemoglobin oxyhaemoglobin may be.

therefore, compared to a dark light equilibrium, as in

the case of the photo-polymerisation of anthracene. The position
of the main absorption bands as calculated by the Perrin
equation is in agreement with the actual facts.

Oxidations. In order to acconnt for the exciting frequencies outside
the visible spectrum, the existence of a fluorescent substance
has been assumed by von Tappeiner and his school. Recently
Noack\'-) has developed a theory in which the Palladin
system peroxydase — oxygenase is replaced by fluorescent
substance — M n-salt. In thc light of the theory developed in
in the preceding chapters his ideas can be interpreted as follows.

The fluorescent substance changes the incident light into
photochemically active light, which action is catalyzed by the
M n-salt. Noach has worked with the colour changes in press
juices from Aloe and Vicia. It is possible that in these com-
plex solutions the M n-salt was already present. Therefore his
experiments were repeated, using phenoles instead of press
juices. 1 % Pyrogallol, pyrocathechin and hydrochinon proved
to react in a similar way as the press juices; their oxidation
was accelerated by eosin in thc light. Addition of M n-salt
had no effect on the hydrochinon; it accelerated the eosin-light
oxidation of pyrocathechin and pyrogallol. No effect could
bc traced on 1 7. phloroglucin, 0.5Vo o-cresole and a saturated
solution of tyrosin. One cannot expect the different phenoles
to react in the same way with the same sensitizer, as they
possess a different light absorption. As far as the evidence

goes the oxidation of phenoles is influenced by light and
optical sensitizers, and as these phenoles can be compared to
a Palladin system, there is no reason to assume that respiration
would prove indépendant of radiation.

Lumines- According to modern theories, luminescence is only a
cence. prolonged fluorescence. In organisms, this luminescence is
caused by an oxidation (Dubois The production of this light
is not accompanied by a measurable caloric effect. (Harvey I.e.).
The three last sentences enable us

a) to apply the equation of Perrin

A v:^ A\' v.

b) to connect lumniescence and oxidations,

c) to predict that

U = 0,27 . (v—V)

will be very small. Accordingly v—v\' will be very small and,
approximately, v = V , or the exciting frequency for reduction
is equal to the exciting frequency for oxidation. This oxida-
tion is,\' according to Dubois and Harvey:

luciferin —> oxyluciferin ,

a phenole derivative. Therefore the wavelength of the light
emitted during this reaction may give us, according to (7),
a clue as to the thermal acceleration of this oxidation process.
It will be seen if the thermal accelerations of other oxidations
in vegetable and animal cells are comparable to these calcu-
lated data. The value for the maximum wavelength for the
emitted hght in animals is by

while the values for plants show a considerable shift to the
higher frequencies;

Bacteria........ 505 ^

Bacteria........525

Bacteria.......

Agaricus melleus.....

Xylaria hypoxylon ....

AVERAGE......512

For these values we can calculate the corresponding Q|o
at room temperature (15-250). following:

log Q,o = 0.39/0.23. A. Ti.Tj.
This gives for animal light;

and for plant light;

These calculated values for the temperature coefficient are
of the same order as the known coefficient for other oxidation
processes, as the following table shows;

If these values arc true, the energy change during such a reaction
can be calculated, on the assumption that there is a direct connection
between respiration (or pact of the respiration) and light emission.

This proves to be about 10 gram-calories, a quantity too small
to detect, as luciferin must have a rather high molecular weight.

The C O2 assimilation of the green leaf.

In \' the case of haemoglobin oxidation it has been seen
that the hght energy of an ultraviolet quantum corresponds
to plm. 30 K.G. calories p. gramme-molecule. These values
were sufficient to account for the energy changes in the
haemoglobin, they are deficient to account for the increase
in energy that takes place during the process of photo-
synthesis in the green leaf. Even the simplest possible product,
formaldehyde, requires 137 K.G. calories per gramme-molecule.
External illumination, however, may provide several light
quanta per molecule before the first product of photosyn-
thesis is formed. Light of very different wavelength is ablfr
to initiate this process, provided that it is absorbed.

According to recent investigations a strong red fluores-
cence takes place inside the chloroplastids (Stern ). The

maximum red absorption in the leaf is also a maximum of
fluorescence. This may point, according to Perrin\'s theory,
to a series of processes. The first process may be initiated
at higher frequency and absorbing this hght, emitting radia-
tion of about 678 fxijt,\', the other process absorbing light of
678 (Jt. fx, and emitting an infra-red group of frequencies.
And, since Ursprung (l,c.) has shown that the infrared
radiation may cause photosynthesis it is possible that the
infrared emission may take place at different parts of the
infrared spectrum.

A series process, as it has been shown in the first para-
graph of this chapter, implies, as a consequence of Perrin\'s
theory, a series of absorption bands.

It suggests a series of equidistant bands, as expressed by
Henri\'s formula

v=Vo-{-na mb.

The values of Willstätter for the chlorophyll spectrum
and the rather scanty data for the infra red (v. Gulik) and
ultra violet (Ursprung) absorption may be related by the
expression

V = 8,9. 1013 &,9. 1013
as the following table shows;

The deviations may partly be caused by the uncertainty in the
determination of the determination of the optical axes of the bands.

y _ 8.9.10^3 corresponds to about 2,5 K.G. calories;
or, for the whole chlorophyll spectrum the energy jump is
about 20 K.G. calories. It may be that Willstätters assump-
tion, an initial reaction of the chlorophyll with the carbon
dioxide will lead to a small value for the reaction heat of
photosynthesis. The experimental data are as yet too scanty
to allow similar deductions as in the case of the reduction
of the oxihaemoglobin.

Light One conclusion, however, may be drawn in connection
emmission ^ith Perrin\'s theory. Inasmuch as the green leaf absorbs
green leaf during photosynthesis, there is evidence that

light of about this frequency will be emitted during the reverse
process; respiration.

This would mean, essentially, nothing else as a prolonged fluores-
cence.

Immediately after photosynthesis a green leaf can be brought
into a dark room.

The light emitted can be shown by an image made on a
photographic plate.

Care must be taken that the leaf is not in direct contact
with the sensitive emulsion as different chemical compounds
cause a. reduction of the silver emulsion. We name here;
carbon dioxide, formic acid, different ethereal oils, hydrogen
peroxide.

A leaf in immediate contact with a photographic plate
gives a visible image within 18 hours exposure,-as I was
able to verify on leaves of Tropaeolum, Escholtzia. Salix and
many others. Ursprung & Gockel have not been able to get
any image through a glass plate from Primula and Pinns leaves
after seven days exposure with an orthochromatic plate.

Scheminsky, however, mentions that radiation, emitted by
fermenting beans is able to penetrate through a glass plate.

In order to make the obstacle for the emitted light as small
as possible 2 inch coverslides were used of homogeneous
texture and thickness. Wratten panchromatic plates were used.
The results were entirely negative with Salix, Lonicera and
Malva leaves. Even after a four days exposure no trace of
an image could be observed. With Tropaeolum, however, a
distinct image was obtained within 18 hours. This same result
could not be obtained by using "Seed 23" plates.

Nor could it, till now, be repeated. This failure is probably due
to the fact that the emission takes place at the limit of the sensibility
for the Wratten emulsion. The experiments will be continued with
other sensitized emulsions.

Sugar It is obvious that the final product of photosynthesis cannot
\'^version, jjg starch as this can be formed, independently from light,
only by increasing the concentration of sugars in the cell.
There is considerable evidence that the first product is sugar
and we will take cane sugar as the end product of photo-
synthesis (Brown and Morris). The leaf must be able to invert
and synthesize cane sugar under the influence of the visible
light. Now the experiments show the result that cane sugar
[^cannot be inverted bij U-V. light down to 200 /x . .

Now, according to Perrin\'s equation (9), a catalyzer will
influence the position of this frequency. Positive catalysis will
lower the active frequency. Therefore there is evidence to
assume that the addition of a catalyzer will sensitize the sugar
solutions for visible rays. The experiments of Winther (1. c.)
have shown that iron is a powerful photochemical catalyzer.
It remained therefore to be investigated whether addition of
iron salts could cause cane sugar inversion. The experiments,
carried out in the Californian sunlight have shown that after
18 hours of sunlight more than 80% of a 0.5 N cane sugar
solution become inverted by rather small amounts (\'/2%) of
iron. Ten Erlcnmeyer flasks were prepared as follows:

FLASK

A and A\' ..... ; sterilized A in direct. A\' in diffuse

light.

100 cc. 0 . 5 N

cane sugar

25 cc. 10 7o FeSO^

B and B\'

100 cc. 0 . 5 N

cane sugar

25 cc. 10 7o Mn SO\'

C and C

100 cc. 0 . 5 N
cane sugar
25 cc. 10 7o Mg SO^

\'.....;

100 cc. 0 . 5 N
cane sugar
no additions

E. F. G, controls, like A. B. and C. but kept in absolute
darkness.

After ten hours illumination the controls gave a rotation
(Schidt-Haensch Polarimeter).

19.89° average.

The flask, iron sunhght gave .
,. iron diffuse light . .
„ manganese sunlight .

diffuse light
„ magnesium sunlight .

„ diffuse light
„ no addition, sunlight.
„ „ ,. subdued light 20.08°
controls dark..... 19.98°

Manganese and magnesium proved to be ineffective. An
important deduction can be made from this. If we assume the
reaction invert sugar—> cane sugar to be principally rever^-
sible. we can expect the plant to use a photocatalyzer to
effect this reaction. This would lead us to believe that in the
chloroplasid a catalyzer would act in a similar way as our
iron catalyzer with the in vitro experiments. Now, Moore
has established the presence of inorganic iron compounds in
the chloroplastids. He has been able to show the catalytic and
synthetic action of iron on several compounds.

From equation (9) it will be seen that the temperature
coefficient of a positively catalyzed reaction decreases. There-
fore, the factor A in equation (3) will be decreased also.
Now Euler and Laurin have determined the A for hydrogen
ion- and for enzymatic cane sugar inversion, finding for A
25,600 and 9,400 respectively. The A is considerably decreased
and corresponds now to a wavelength in the visible spectrum

(415 (j^f^).

\') Zwaardemaker. Ergeb. Phys. XII. 1912.

Î) V. Tappciner. Die sensibilisierende Wirkung fluoreszierender Substanzen.

Lelpslc. 1907.
3) Zwaardemaker. Arch. Nóerl. V. 1921.
<) Henri, cited by Llffschütz. Ztsch. Phys. Chem. 1921.
s) Barcroft & Hill. Journ. Phys. XXXIX. 1909.
0) du Bois Reymond. Arch. Phys. 1914.

7) Hartrldge Ö Hill, journ. Phys. XLVIII. 1914.

8) Berthelot. C. R. 109. 778.

0) Torup. Hammarsten Festschrift. 1906.
<») Camls. Bioch. Ztrbl. VII. 1908.

11) Meyerhof. Pflüg. Arch. CXLVI. 1912.

12) Noack. Ztschr. f. Bot. 1920.

\'3) Dubois. La Vie et la Lumlnlire. Paris. 1916.
><) Stern. Ztschr. f. Bot. 1921.

IS) Willstatter. Untersuchungen ueb. Chlorophyll. Berlin. 1913.
\'") Ursprung 6 Gockel. Ber. D. Bot. Ges. XXXVl. 1918.
") Moore. Proc. Roy. Soc. 87 B. 1914.
Euler. Óhemle der Enzyme. Berlin. 1921.

CONCLUDING REMARKS

Summarising the contents of this paper is not very well
possible, the statements being made in a condensed form
already.

The writer only wishes to emphasize once more that he
is perfectly aware of the many shortcomings of his work.
A short criticism on the preceding paper will make this clear.

1. The fundamental basis of this paper, the theory of
lean Perrin. is by no means a stable and recognized
structure.

2. The quantitative changes in the original Perrin equation
are entirely arbitrary.

3. The theory is incomplete, inasfar as it has ignored
the large field opened by the heat theorem of Nernst.

4. There is a considerable disproportion between theory
and experiment.

The. apparently, succesfull application of the theory, however,
seems to justify the opinion that the Perrin theory will prove
to be a convenient working hypothesis.

It enables the experimentator to synthesize a vast group
of. hitherto disconnected, facts.

«

The writer is very much indebted to Dr. Harlow Shapley.
Dr. David L. Webster. Dr. H. A. Lorentz and Dr. L. S. Ornstein
for inspiration and criticism.

He is also under great obligation to Dr. F. A. F. C.Went.
whose constant help enabled him to carry out this research.

EQUATIONS DERIVED IN THE PRECEDING
CHAPTERS.

, ^ h V (l 1\\

In Q =~ - yJ

/nQ = A
h p

A =

h V

A = p

k
1.43

A = p

6.2

Tl (Tl 10) log Q

h V

> A

V tf log K

v\' "c/logK,

U = 0.27. 10"\'" {v-v\')

/n = ± A (T; -

\' • • - - --\'liti.iiM.ii

■fe- ::

■ t

t

I

f\'

« B\' ■

STELLINGEN

I

Het levend protoplasma kan doorlaatbaar zijn voor
enzymen.

II

Bij de quantitatieve bepaling van enzymwerking
dient de latentietijd in aanmerking genomen te worden.

III

In de prikkelphysiologie dient dè meterkaars-secunde
vervangen te worden door de erg per secunde voor
monochromatisch licht.

IV

Bij vrije paring treedt na eenige generaties een
vaste numerieke verhouding op tusschen de eigen-
schappen eener populatie.

V

De proeven van Calvin Bridges zijn bewijzend
voor dc chromosoomhypothese der erfelijkheid.

VI

Het genus Botrychium dient in drieën gesplitst te
worden.

De Stelairtheorie is van geen waarde bij phyloge-
netische beschouwingen.

VIII

Het voorkomen van bepaalde planten wijst op be-
paalde samensteihng van den bodem, echter niet op
een bepaalde geologische formatie.

IX

Tumoren kunnen worden veroorzaakt door injecties
van hypotonische oplossingen.

X

De leerproeven genomen door Buitendijk op hoogere
dieren zijn methodisch onverdedigbaar.

XI

Palaeospondylus gunni Traq. is waarschijnlijk een
larvale vorm, bijvoorbeeld van Coccosteus.

XII

Het eiland Terschelling is geheel van alluvialen
óorsprong.

XIII

Het vraagstuk der internationale uitwisseling van
studenten cn hoogleeraren dient krachtig ter hand ge-
nomen te worden.

Sr:

; V •\'

•V • , • - ■ - •

, ... • •

. :: : ^ V V

. H \' •

• .\'•\'if\'

\'\' r.

r

•ti.^\'ir^,-,-■.

V

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