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FOR. THE PROFLE 
FOR EDVCATION 
FOR SCIENGE 


LIBRARY 
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THE AMERICAN MUSEUM 
OF 


NATURAL HISTORY 


HANOI CED 
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KON CPAN 


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KONINKLIJKE AKADEMIE 
VAN WETENSCHAPPEN 
-- TE AMSTERDAM =-:- 


BROCEEDINGS OF THE 
SEC TION GE SCIENCES 


5.06(49.2)AS5 
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VOLUME XXIII 
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JOHANNES MULLER :—: AMSTERDAM 
FEBRUARY 1921 : 


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(Translated from: Verslagen van de Gewone Vergaderingen der 
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KONINKLIJKE AKADEMIE VAN WETENSCHAPPEN 
TE AMSTERDAM. 


FrOCeeDINGs 


VOLUME XXIII 
Nani: 


President: Prof. H. A. LORENTZ. 
Secretary: Prof. P. ZEEMAN. 


(Translated from: “Verslag van de gewone vergaderingen der Wis- en 
Natuurkundige Afdeeling,” Vol. XXVIII and XXIX). 


CONTENTS. 


GUSTAV STIASNY: “Ueber westindische Tornarien nebst einer Uebersicht über die bisher bekannten 
tentaculaten Tornarien”. (Communicated by Prof. J. BOEKE), p. 2. (Mit 2 Tafeln). 

H. O. ANTONIUS: “Bemerkungen über einige Säugetierschädel von Sardinien”. (Communicated by 
Prof. J. F. VAN BEMMELEN). p. 37. 

NIL RATAN DHAR: “Catalysis — Part VII — Temperature Coefficient of Physiological processes”. 
(Communicated by Prof. ERNST COHEN), p. 44. 

ARNAUD DENJOY: “Sur une classe de fonctions admettant une dérivée seconde généralisée” p.50. 

C. B. BIEZENO, “Graphical Determination of the Moments of Transition of an Elastically Supported, 
Statically Indeterminate Beam”. Il. (Communicated by Prof. J. CARDINAAL), p. 60. 

J. BOESEKEN and CHR. VAN LOON: “On the determination of the configuration of cyclic cis and 
trans diols and the rearrangements of atoms and groups of atoms during chemical reactions”, 
p. 69. 

F. M. JAEGER: “On some Condensation-products of Aromatic Aldehydes and Amines”, p. 74. 

F. M. JAEGER and G. BERGER: “The Photochemical Decomposition of Potassium-cobaltioxalate 
and its Catalysis by Neutral Salts”, p. 84. 

F. M. JAEGER and J. H. DE BOER: “Colloidal Sulphurcompounds of Ruthenium”, p. 95. 

L. BOLK: “On the Index cephalicus and the absolute Dimensions of the Head of the Population 
of Holland”, p. 103. (With one plate). 

J. BRAMSON: “Experimental proof for the active dilatation of cross-striated muscle-tissue’, (Com- 
municated by Prof. G. VAN RIJNBERK), p. 111. 

J. J. VAN LOGHEM: “Identity of the blood-digestive and gelatine-liquefying bacterial actions”. (Com- 
municated by Prof. C. EYKMAN), p. 115. 

N. H. KOLKMEIJER: “Remark on the possible existence of binding rings in diamond”. (Communica- 
ted by Prof. H. KAMERLINGH ONNES), p. 120. 

. F. GOUDRIAAN: “The aluminates of sodium. Equilibriums in the system NagO—Al,0,—H,O. (Com- 
municated by Prof. J. BOESEKEN), p. 129. 

J. TRESLING: “Derivation of a formula for the temperature dependence of the velocity constants 
in gas reactions from a special image of the process”. (Communicated by Prof. H. A. LORENTZ), 
p 143. 

H. I. WATERMAN and J. GROOT: “The influence of different substances on the decomposition of 
_monoses by an aikali and on the inversion of cane sugar by hydrochloric acid”. (Communicated 
by Prof. J. BOESEKEN), p. 149. : 

P. EHRENFEST and V. TRKAL: “Deduction of the dissociation-equilibrium from the theory of quanta 
and a calculation of the chemical constant based on this”, p. 162. 

H. HULSHOF: “The osmotic pressure, regarded as a capillary phenomenon”. (Communicated by Prof. 
H. A. LORENTZ), p. 184. 

S. A. ARENDSEN HEIN: “Technical experiences in the breeding of Tenebrio molitor”. (Communi- 
cated by Prof. J. W. MOLL), p. 193. 


Proceedings Royal Acad. Amsterdam. Vol. X XIII. 


Zoology. — “Ueber westindische Tornarien nebst einer Uebersicht 
über die bisher bekannten tentaculaten Tornarien’’. By Dr. 
Gustav Stiasny. (Communicated by Prof. J. Boeke). (Mit 2 
Tafeln und 3 Textfiguren). 


(Communicated at the meeting of June 26, 1920). 


I. Das Material. 


In einigen schönen Planktonproben, welche von Prof. Dr. Boeke 
1905 in Hollindisch Westindien gesammelt und die mir von Prof. 
Dr.’ Max WeBeER zum Studium überlassen wurden, fanden sich zahl- 
reiche Entwicklungsstadien von Enteropneusten, die in der vorliegenden 
Mitteilung näher besprochen werden sollen. ‘Es handelt sich dabei 
nicht um neue bisher unbekannte Tornarien, sondern die in den 
Proben enthaltenen Enteropneustenlarven konnten mit ziemlicher 
Sicherheit mit Tornarien identificiert werden, die bereits in den 
Gewässern der Bahamas Inseln gefunden worden sind. Aus Hollün- 
disch Westindien waren bisher Enteropneustenlarven nicht bekannt. 
Die untersuchten Tornarien gehören zweierlei Species an und konnten 
in verschiedenen Entwicklungsstadien beobachtet werden, die zum 
Teil noch nicht oder nicht genau bekannt sind. So war es möglich, 
die Angaben in der Literatur tiber die Entwicklung dieser beiden 
Formen in mancher Hinsicht zu ergänzen. Die Etiquetten der Plank- 
tonproben tragen folgende Aufschriften : 


1. Plankton 1905, Saba, West-Indië, Gough Bay, Dr. BoEkKE, 
waarn. 37. 

2. Plankton, West-Indie, 1905, Dr. Borkr, Cove Bay, waarn. 36. 

3. Plankton, 25/VII. 1905, Saba, West-Indië, Dr. Boeke, waarn. 32. 


4. Plankton, Aruba, West-Indië, Pays bank, Aug. 1905, Dr. BOEKE 
0—30 vaam. 


Insgesammt fanden sich über 300 Exemplare von Tornarien, 
darunter eine kleine, nur in wenigen Exemplaren vorhandene, und 
eine grosse häufige Form. Die kleinere ist identisch mit der soge- 
napnten Limini-Tornaria, die grössere mit der sogenannten Bahamas- 
Tornaria Morgans. 


3 
II. Die westindischen Tornarien.. 


a. Die Bimini Tornaria (Tornaria Weldoni). 
(Tafel [). 


Ueber die Bimini Tornaria’’, welche ich zu Ehren ihres ersten 
Auffinders Tornarta Weldoni benenne, liegen Angaben von WrELpoN 
(A) und Morean (4) vor. WerpoN und nach ihm Morean fanden 
diese kleine Form gemeinsam mit der grossen Bahamas Tornaria 
auf North Bimini Island, auf dem Westrande der grossen Bahamas 
Bank, gegeniiber dem Siidende von Florida. Da sie nunmehr auch 
bei Saba und Aruba nachgewiesen ist, diirfte sie wohl im ganzen 
westindischen Archipel einheimisch sein, doch ist sie ziemlich selten. 
Wepon beschreibt (le) einige vorgeschrittene Entwicklungsstadien, 
die zum Teil bereits der Metamorphose angehören oder ihr unmittelbar 
vorausgehen, Stadien, die etwa der fig. 6 auf Taf I. entsprechen 
und z. T. bereits die für das erwachsene Tier so charakteristische 
Dreiteilung des Körpers in Rüssel-, Kragen- und Rumpfregion auf- 
weisen. Da Wetpon sich lediglich auf Abbildung und Beschreibung 
einiger Schnittpraeparate beschränkt und den äusseren Habitus seiner 
Form nur mit wenigen Worten andeutet, lasst sich nicht mit Sicher- 
heit, wohl aber mit grosser Wahrscheinlichkeit, behaupten, dass die 
von ihm beschriebenen Entwicklungsstadien zur Banini-Tornaria 
Morean’s gehören. Er spricht nämlich von einer grossen und kleinen 
Form, die von MorGaN später an derselben Lokalität wiedergefunden 
und von diesem Forscher mit den Namen Bahamas- und Bimini 
Tornaria bezeiehnet wurden. Auch in meinen Planktonproben kamen 
die beiden Larven nebeneinander vor. 

Mor@an hat einige Jahre später (4) ein jüngeres Entwicklungsstadium 
derselben kleinen Form genauer untersucht. Er bildet auf Taf. I. 
fig. 12 (4) ein Stadium ab, das etwa der Tornaria Krohni des 
Balanoglossus clavigerus aus dem Mittelmeer entspricht und gibt die 
Unterschiede desselben gegenüber der Bahamas Tornaria an, so 
dass die Wiedererkennung dieser Species in den Planktonproben 
möglich war. 

Nach Morgan sind für die Bimini Tornaria charakteristisch: 1. 
geringere Grösse, 2. ein kleiner Unterschied im Verlaufe des longi- 
tudinalen Wimperbandes, 3. Bau und Zahl der Tentakel, 4. Bau 
der Apicalplatte, 5. die dem Darm anliegenden Coelome, Vergleiche 
darüber die Ausführungen auf S. 28/29, sowie die Synopsis auf S. 31 

Während Morgan nur ein einziges Exemplar zur Verfügung stand, 
bilden die von Prof. Borkn gesammelten Exemplare eine Serie ver- 


schiedener Entwicklungsstadien, einen Ausschnitt aus der Entwicklung 
1* 


4 


eines noch nicht festgestellten Enteropneusten. Das in Fig. 4 auf 
Taf. I dargestellte Stadium stellt den Höhepunkt larvaler Entwick- 
lung dar, indem es alle typischen Larvencharaktere in voller Ent- 
faltung zeigt. Es entspricht etwa einem älteren Zornaria Krohnii 
Stadium des Balanoglossus clavigerus aus dem Mittelmeere und ist 
etwa gleich alt mit dem von Morgan abgebildeten Stadium (Taf. I. 
fig. 12, 4). Dieses und die in Fig. 1—3, Taf. 1, dargestellten jiingeren 
Stadien gehören jener Periode der Larvenentwicklung an, die ich in 
meinen Arbeiten (13, 14, 15) als Periode der progressiven Entwick- 
lung bezeichnet habe, während Stadium 5 bereits der regressiven 
Entwicklung, das Stadium 6 der Metamorphose angehört. In den 
erwdlinten Arbeiten habe ich ausgefiihrt, dass die erstere Periode 
charakterisiert ist, durch continuirliche Zunahme der Körpergrösse 
und des Blastocoels, durch Reduction des specifischen Gewichtes, 
Durchsichtigkeit und fortschreitende Ausbildung des Wimperkranzes, 
Coeloms und Herzblase; die 2. Periode, in welcher keinerlei neue 
Organe angelegt werden, gekennzeichnet durch Grössenabnahme, 
zunehmende Undurchsichtigkeit, Reduction des Blastocoels, Zunahme 
des specitischen Gewichtes bis zur Aufgabe der pelagonee™ Lebens- 
weise, und zum Kintritt der Metamorphose. 

In der unter (15) erwähnten Arbeit habe ich in Textfig. C. auf 
Seite 263 ein Schema des Verlaufes des longitudinalen Wimper- 
kranzes fiir die Zornaria Krohnii aus dem Mittelmeer gegeben. Ich 
gebe in Textfigur 1 ein gleiches Schema des entsprechenden Stadiums 
der Bimini-Tornaria. Ein Vergleich der beiden Schemata, so wie 
mit dem in Textfig. 2 dargestellten zeigt augenfallig die Unterschiede. 


Praeoralfeld IDEE alfel A RIN ak ot Praeo ralfeld 
oralfeld. Dorsal Tentakel rd 
| 
: Ventratsattel 
Ventralsatlel : Untere Dorsalloben 
Venttal Laterallobus DORSAL Laterallobus Vertral 


Textfigur 1. Schematische Darstellung des Verlaufes des longitudinalen Wimper- 
bandes der ausgebildeten Tornaria Weldoni. 


An Hand dieses Schemas lässt sich mit Hilfe der SpENGEL’schen 
Nomenclatur (3) der Verlauf der longitudinalen Wimperschnur der 
Tornaria Weldoni (Bimini Tornaria) kurz charakterisieren : 


5 


1. Prae- und Postoralfeld ziemlich breit, breiter als die Sättel. 
Loben verbaltnismassig schmal. 

2. 4—6 Tentakel (tentakelartig ausgebildete „seeundäre Loben” 
an jedem der oberen Dorsalloben, so bezeichnet nach dem Vorgange 
Spencers bei Tornaria Grenacheri (8); eigentlich sind es die Dorsal- 
sättel, welche die Tentakel tragen. Vergl. darüber meine Ausfiih- 
rungen auf p. 15/16). Die Tentakel sind kurz und breit, mehr 
stummelförmig, 

3. Oralfeld schmal, stark gekriimmt, Ventralsattel hoch. 

4. Untere Dorsalloben sehr lang und schmal, mit fast parallel 
verlaufenden Wimperschnüren, die dorsal fast zusammenstossen, ohne 
Tentakel. 

5. Lateralloben tief, mit schmaler Oeffnung, ohne Tentakel. 

6. An der Scheitelplatte legen sich prae- und postorale Wimper- 
kränze parallel aneinander und verschmelzen. 

Von den übrigen Merkmalen sei hier noch hervorgehoben, dass 
das Analfeld stark vorgewölbt, der circuläre primäre Wimperkranz 
kräftig entwickelt, der secundäre Wimperkranz rings um den Anus 
schwach ausgebildet ist und dass die Coelome dem Darm anliegen. 
Betrachten wir nun die einzelnen Entwicklungsstadien etwas genauer, 

Tafel I, Fig. 1. Dorsalansicht eines Stadiums der progressiven 
Entwicklung etwa einem etwas vorgeschrittenen Tornaria Miilleri- 
Stadium (13, 14, 15) vergleichbar). Dorsalfeld breit, Dorsalloben mit 
je 3 breiten tentakelartigen secundären Loben, weitere in Ausbildung 
begriffen; untere Dorsalloben sehr lang und schmal. Links oberhalb 
des primären circularen Wimperkranzes der eine Laterallobus (der 
andere ist verdeckt), secundarer circularer Wimperring ganz schwach. 
Analfeld mässig vorgewölbt. Im Innern: Mitteldarm cylindrisch, 
Enddarm kurz, kegelförmig. Eichelcoelom geräumig. (Kichelporus 
und Herzblase nicht beobachtet). Das eine der beiden Rumpfcoelome 
als rundliches Bläschen zwischen Mittel- und Enddarm. 

Fig. 2. Ansicht schräg von oben eines etwa gleichaltrigen Sta- 
diums mit 3 kurzen Tentakeln an den Dorsalloben und weiteren 
in Ausbildung begriffenen. Am Apex legen sich prae- und postorale 
Wimperkranze parallel an einander und verschmelzen. Lateralloben 
tief, Ventralband breit. Im Innern: Ein Coelomsäckchen als breite 
Platte dem Mitteldarm anliegend, an der Grenze zwischen Mittel- 
und Enddarm. 

Fig. 3. Oralansicht eines etwas älteren Stadiums, das noch der 
progressiven Entwicklung angehört. Etwas grösser als das vorher- 
gehende. Der longitudinale Wimperkranz wieder etwas complicierter, 
mit 4 Tentakeln an den Dorsalloben. Sehr deutlich das schmale - 


6 


hufeisenformige Oralfeld mit der trichterförmigen Mundöffnung und 
der hohe schlanke Ventralsattel zu sehen. ~Ventralband breit mit 
beiderseitigen tiefen Lateralloben. Im Imnern: der 3 teilige Darm. 
Dem Mitteldarm liegt das plattenformige Rumpfcoelom *) an, das 
denselben zu umwachsen beginnt. Unterhalb der Apicalplatte der 
glashelle Strang, an dem das Eichelcoelom befestigt ist. 

Fig. 4. stellt die typische Tornaria Weldoni in ihrer vollen Ent- 
wieklung dar, mit allen Larvencharakteren ausgestattet, den Höhe- 
punkt der Larvenentwieklung. (Dorsalansicht). Die Larve hat das 
Maximum der Körpergrösse, ca 2'/, m.m., erreicht. Der Verlauf des 
longitudinalen Wimperkranzes hat durch Ausbildung von 6 Tentakeln 
an jedem Dorsallobus, sowie durch die tiefen Lateralloben den 
höchsten Grad von Compliciertheit erlangt. Untere Dorsalloben sehr 
lang und sehmal. Seheitelplatte entsteht durch Verschmelzung der 
sich parallel aneinanderlegenden prae- und postoralen Wimperkränze. 
Cireulärer Wimperkranz breit und kraftig, secundärer Wimperkring 
ganz fein und schmal. 

Im Innern: Zu beiden Seiten des Mitteldarmes 2 Paare von Coe- 
lomsäckchen als längliche oder rundliche Bläschen, dem Darm 
angelagert. Die mehr dem Enddarm zu gelegenen die Rumpfcoelome, 
die gegen die Scheitelplatte zu liegenden (in der Abbildung von den 
Tentakeln etwas verdeckt) die Kragencoelome. Das Eichelcoelom als 
langer schmaler kegelf6rmiger Sack, dem Mitteldarm aufliegend 
mündet durch den Kichelporus in der Mitte des Dorsalfeldes nach 
aussen. Durch einen ziemlich dicken Strang mit dem Apex verbun- 
den. Herzblase nicht beobachtet. 

Dieses Stadium entspricht dem von Morgan in seiner Figur 12 
dargestellten, das eine Seitenansicht darstellt. Es ist das ,, Tornaria 
Krohnii-Stadium” der Tornaria Weldoni. 

Fig 5. stellt ein Stadium dar, das bereits der regressiven Entwick- 
lung angehort. Es ist gekennzeichnet durch geringere Körpergrösse 
gedrungenere Gestalt, geringere Durchsichtigkeit, Rückbildung der 
tentakelartigen Bildungen. Es sind deren jetzt nur mehr drei an 
jedem Dorsallobus vorhanden. Dieses Stadium ist dunkler, undurch- 
sichtiger als das sonst ähnliche in tig. 1 abgebildete Stadium der 
progressiven Entwicklung, zeigt jedoch das Analfeld stärker vorge- 
wölbt, kegelformig ausgebildet, die Lateralloben sind nicht mehr so 
tief, der circuläre Wimperring ist breiter, der secundäre circulare 
Wimperring ist geschwunden. Im Innern das mächtig entwickelte 
Eichelcoelom, das dem Darm aufgelagert ist und rechts ausmündet. 


') Nach SpenGeL vielleicht richtiger als ‚„Kragen-Rumpfcoelom” zu bezeichnen. 


7 


Die Coelome konnten an diesen undurchsichtigen Entwieklungs- 
stadien nicht mit Sicherheit beobachtet werden. 

Fig. 6 zeigt ein Stadium nach der Metamorphose. Es ist noch 
viel kleiner als das vorige, misst circa 1'/, mm. und ist fast undurch- 
sichtig. Der Körper zerfällt bereits in die 3 für das erwachsene Tier 
so charakteristischen Teile: Rüssel-, Kragen, Rumpfregion. Der 
keulenförmige Rüssel ist durch eine tiefe Ringfurche von der Kra- 
genregion abgesetzt. 

Die Kragenregion ist sehr breit und trägt in ihrer Mitte den in 
Rüekbildung begriffenen ecireulären Wimperkranz. Das Analfeld ist 
wie im vorhergehenden Stadium kegelförmig vorgewölbt. 

Der Tentakelapparat des longitudinalen Wimperkranzes, die 
Lateralloben etc. ist bereits ganz geschwunden. 

Im Inneren kann man, wenn man das Objekt zwischen Deckglas 
und Objektträger mit der Nadel etwas quetscht, im Rüssel das riesig 
grosse Hicheleoelom sehen, das fast den ganzen Innerraum des 
Rüssels ausfüllt. Auch die Contour des Mittel- und Enddarms tritt 
noch einigermassen hervor. 


Da mir nur wenige in Formol conservierte Exemplare zur Ver- 
fügung standen und es unter den gegenwärtigen Verhältnissen mir 
nicht möglich ist, Schnittpraeparate anzufertigen, waren der Unter- 
suchung von vorneherein enge Grenzen gezogen. So musste auf die 
Feststellung der Art und Weise der Entstehung des Coeloms, des 
Herzens etc. verzichtet werden, auch wurde in die Abbildungen 
nur das eingezeichnet, was tatsächlich beobachtet werden konnte, 
ohne Ergänzungen nach Schnittpraeparaten und olne zu schema- 
tisieren. 

Auch die vorliegenden Stadien stellen keine geschlossene Reihe 
von Entwicklungsstadien dar. So fehlt das wichtige ,,eingekerbte 
Stadium”, das ich bei Balanoglossus clavigerus beschrieben habe, 
und das seinen Platz zwischen dem in fig. 5 und 6 abgebildeten 
Stadien finden müsste (14,15). 

Da aber von dieser Form mit Sicherheit nur das einzige von 
Morean abgebildete und geschilderte Stadium bekannt ist, glaube 
ich doch, dass diese kurzen Angaben einen kleinen Fortschritt in 
der Kenntnis der Entwicklung dieser Form bedeuten. 


Zum Schlusse ergibt sich natürlich die Frage, zu welchem adulten 
Tiere die Zornaria Weldoni gehört. WerLpoNn und Morean konnten 
natürlich nichts sicheres darüber aussagen. Auch zur Zeit ist dies 
noch nicht möglich, aber eine Vermutung lässt sich doch äussern. 


8 


SPENGEL (3) hat auf Grund von Material, das er von WeLpoN von 
den Bahamas erhielt, einen Enteropneusten beschrieben, den er 
Ptychodera (Chlamydothorax) bahamensis nannte. Es ist dies eine 
auffallend kleine Form von ca 7'/, em Lange, von der gleichen 
Lokalität stammend wie die Bimini Tornaria, die ja auch sehr klein 
ist. Ich halte es daher für nicht ausgeschlossen, dass Ptychodera 
bahamensis SpeNGuL die adulte Form der Tornaria Weldoni darstellt. 
Mit Sicherheit wird sich dies natürlich erst dann feststellen lassen, 
wenn aus den Kiern von Ptychodera bahamensis die Tornaria Wel- 
dont gezüchtet worden. 


b. Die Bahamas Tornaria (Tornaria Morgani). 
(Tafel II). 


WerpoN (1) fand vorgeschrittene Entwicklungstadien einer grossen 
tentaculaten Tornaria bei Nassau, New Providence, Bahamas Bank, 
über welche er nur einige ganz beiläufige Bemerkungen macht. 
Morean (2) beschrieb einige Jahre später unter der Bezeichnung 
, Nassau Tornaria” Entwicklungsstadien einer von der gleichen 
Lokalitat stammenden, mit derjenigen WeLDons offenbar identischen 
Tornaria mit langen Tentakeln, von der er Detailschilderungen des 
Verlaufs des dorsalen Wimperbandes, des Tentakelapparates und 
der Scheitelplatte gibt (2, Taf XXIV, fig. 10—12). Die Coelome wurden 
dabei nicht beobachtet. Die wichtigsten Angaben über die ,, bahamas 
Tornaria’ sind in seiner grossen Arbeit (4) enthalten, in welcher 
er einen grossen Teil der Entwieklung und Metamorphose derselben 
tentaculaten Tornaria bis zur Umwandlung in das benthonische Tier 
beschreibt. Das Material für seine Untersuchung fand Morean in den 
Gewässern von Bimini-Island, Bahamas Bank (s. o. p. 2) zugleich 
mit der kleinen Lornaria Weldoni. Seine Beschreibung passt so genau 
auf die mir vorliegenden grossen Tornarien von Aruba und Saba, 
dass an der Identität beider Formen, trotz geringer Abweichungen, 
kein Zweifel sein kann. Es ist also wohl auch anzunehmen, dass 
diese von mir als „Zornarta Morgan’ bezeichnete Tornaria im 
ganzen westindisehen Archipel verbreitet ist. Die Angaben Moraans 
finden bei der Besprechung der einzelnen Organsysteme ihre 
gebührende Berücksichtigung. 

Wie von der Pornarta Weldoni liegt auch von der Tornaria 
Morgan, der grossen Bahamas Tornaria, eine Reihe von Entwick- 
lungsstadien vor, die einen Ausschnitt aus der Entwicklung darstellen, 
umfassend die 7. Morgani in ihrer höchsten Entwicklung (etwa dem 
Tornaria Krohnii-Stadium entsprechend) bis zum sogenannten 
,eingekerbten” Stadium. Die Serie umfasst gerade jene Stadien, die 


> 


9 


zwischen den MorGaN’schen Stadien III und IV liegen (Taf. I, fig. 
3 u. 4, 4) und von dem genannten Forscher nur ganz nebenbei be- 
schrieben wurden, so dass sie eine Ergänzung zu denselben darstellt. 

Infolge der Gréssenabnahme, zunehmender Undurchsichtigkeit, 
Sehwindens der Tentakel, und immer stärkerer Ausbildung der Coe- 
lome gehören die meisten Stadien mit Ausnahme des 1. Stadiums 
(Taf. II, fig. 7, 8), das den Héhepunkt der pelagischen Entwicklung 
und die typisch ausgebildete Tornaria Morgani mit allen Larven- 
charakteren zeigt, jener Periode der Entwicklung an, die ich in 
meinen Studien über die Entwieklung des Balanoglossus clavigerus 
(14, 15), vom morphologischen Standpunkte aus als ,,regressw’’ be- 
zeichnet habe. 

Bevor ich auf die Besprechung der einzelnen Stadien naher eingehe, 
sei bemerkt, dass das mir vorliegende Material in Formol conserviert, 
daher — bei meist vortrefflicher Erhaltung — doch mehr oder minder 
deformiert war. Daher die etwas unregelmässige Form der Kragen- 
region in fig. 7 u. 8. auf Taf. I]. Es wurde dabei, wie bei den übrigen 
Figuren, auf naturgetreue Darstellung Wert gelegt und möglichst 
jener von SpenceL (9, p. 123) beobachtete Vorgang der Schematisie- 
rung vermieden. Auch wurde in die Figuren nur das eingezeichnet, 
was tatsächlich gesehen wurde. 

Tafel Il, Fig. 7 und 8. stellen die Tornaria Morgani in 
typischer Ausbildung dar. An Hand des in Textfig. 2 dargestellten 


"Yay Wy \ 


VENTRAL DORSAL : VENTRAL 
Textfigur 2. Schematische Darstellung des Verlaufes des longitudinalen Wimper- 
bandes der ausgebildeten Tornaria Morgani. 

Schemas lässt sich der Verlauf des longitudinalen Wimperbandes mit 

seinen specifischen Eigentümlichkeiten gut erkennen : 
1. Dorsale und ventrale obere Loben mit 20—25 Tentakeln wee oF 
2. Ventralsattel hoch und schmal. 


1) In dem obigen Schema wurden versehentlich zuviele Tentakel eingezeichnet. 


10 


3. Die postorale (ventrale) Wimperschnur geht beim Oesophagen 
apicalwärts über die praeorale (dorsale) hinaus, überschreitet also 
die Mittellinie in einem höheren Niveau als die erstere. 

4. Kein unterer Dorsallobus vorhanden, daher das Dorsalfeld 
sehr breit. 

5. Laterallobus mit circa 5—10 Tentakeln besetzt. 


Wendet man dieses Schema auf die Figuren Moreans (4, Taf. I, 
1, 2, 3, an so findet man eine gute Uebereinstimmung, bis etwa 
auf die Zahl der Tentakel und die Form des Ventralsattels. 

Die Hohe dieser Stadien ist cirea 5—6 mm., die Breite (Dureh- 
messer des primären circulären Wimperrings) beträgt 4—4'/, mm., 
die Larve ist also etwas höher als breit, etwas grösser als die 
Exemplare Morgans. _ 

‘af. Ll. Fig. 7. Seitenansicht der Tornaria morgant *). Dieses 
Stadium wurde von Morean (4) so ausführlich geschildert, dass ich 
hier nur die Unterschiede zwischen dieser Abbildung mit derjenigen 
Moreans (4, Taf. I tig. 3) besprechen will. Die Tentakel scheinen 
etwas länger, weniger steif zu sein. Das Analfeld ist nicht so flach, 
sondern deutlich vorgewölbt. Die Scheitelplatte ist meist eingezogen, 
daher nur angedeutet. Ihr Bau stimmt mit den Angaben Morgans 
(2 und 4) sowie Spencers (3) bei Tornaria Grenacheri recht gut 
überein. Der wichtigste Unterschied betrifft das Coelom. Dasselbe 
wurde anfangs von Morean gänzlich übersehen (2 pag. 431) und so 
wird es wohl jedem Untersucher wegen der von der normalen 
gänzlich abweichenden Lage des Coeloms ergehen. (3, p. 432). 
MorGan konnte dasselbe nur auf Schnitten nachweisen und ist es 
daher in seine Abbildung nicht eingezeichnet. In Fig. 7 auf Taf. II 
sieht man das Rumpfcoelom als schmalen lang ausgezogenen Ring 
den ganzen Körper umgebend und dem primären circulären Wim- 
perring dicht anliegend. Es sind zwei ringförmige schmale Scheiben. - 
SPENGEL beschreibt das Coelom bei 7. Grenacheri in ganz alnlicher 
Weise als sehr lang ausgezogene der Epidermis anliegende Schläuche 
(3, p. 432) nur mit dem Unterschiede, dass bei seiner Form die 
Coelome in der Gegend des Laterallobus einen langen dünnen Fort- 
satz nach oben entsenden, was bei 7. Morgani nicht der Fall ist. 
Hier sind die Figuren Morgans (4, Taf. III, fig. 29, 30, 31) für 
den Vergleich von Wichtigkeit, -die sämmtlich Schnittpraeparate 
darstellen. Alle zeigen das Rumpfeoelom in Verbindung mit dem 
Ektoderm unmittelbar dem circulären Wimperring anliegend „atta- 


1) In fig. 7, 8 u. 9 ist der circulére Wimperring nicht eingezeichnet, um das 
Coelom deutlicher hervortreten lassen zu können. 


11 


ched to the inner surface of the circular band”, stets weit vom 
Darm entfernt. In fig. 29 ist auch das Kragencoelom mit dargestellt, 
welches ich auf meinen ungeschnittenen Exemplaren nicht auffinden 
konnte und das vielleicht erst etwas später zur Ausbildung gelangt. 
(Vergl. die Bemerkung unten auf S. 240). 

Fig. 8 stellt ein anderes etwas grösseres Exemplar in Dorsal- 
ansicht dar. Scheitelplatte eingezogen, Analfeld eine ganz flache 
Scheibe. Etwas unterhalb der Mitte ist der lange schmale Ausfüh- 
rungsgang des ,,Wassersackes” sichtbar, der ziemlich tief in einer 
halbmondförmigen Vertiefung mündet. Oberhalb des Porus die Herz- 
blase mit der Rüsseldrüse. Die beiden Rumpfcoelome verlaufen ganz 
entsprechend dem in Fig. 7 dargestellten Stadium innerhalb des cir- 
culären Wimperrings, demselben eng anliegend. Hier sieht man auch, 
was Morean in Fig. 23 auf Taf. IV, Spencer in Fig. 59 Taf. 23 
dargestellt hat: dass die beiderseitigen Rumpfcoelome unterhalb des 
Hydroporus sich einander nähern, ohne jedoch mit einander zu ver- 
schmelzen („these do not meet in the middle line”). Doch ist hier 
gegenüber der Beschreibung Spencers ein Unterschied, indem die 
Coelome bei seiner Form sich zuletzt etwas aufrichten und der linke 
in der Nahe des Kichelporus, der rechte in entsprechendem Abstande 
vom blinden Zipfel des ,,Wassersackes” endigt. Dagegen stimmen 
die Verhältnisse auf der Ventralseite, Spencers Fig. 60 Taf. 23, 
sehr gut, denn auch hier nähern sich in beiden Fallen die Coelome, 
ohne in einander überzugehen. 

Stadium Fig. 9. Seitenansicht eines etwas älteren Stadiums der 
regressiven Entwicklung. Die Larve ist kleiner, ca 4'/,—5 mm. hoch, 
undurchsichtiger, die Kragenregion sehr breit, wulstartig verdickt, 
das Analfeld ziemlich stark vorgewölbt, die Tentakel an den Loben 
kiirzer und dicker. Im Innern der 3-teilige Darm und das dem (nicht 
gezeichneten) ecirculären Wimperring dicht anliegende ringformige 
Rumpfcoelom. An der Berührungsstelle mit dem Ektoderm ist es ein 
wenig umgebogen, erscheint daher etwas dunkler, springt nach innen 
etwas vor, als ganz flache Scheibe. 

Stadium Fig. 10. Dorsalansicht eines etwas älteren Stadiums als 
das vorhergehende. Die Epidermis ist bereits recht undurchsichtig 
geworden, die Tentakel sind sehr viel kürzer, nur mehr stummel- 
formig ausgebildet. Der ,,Wassersack” ist eine mächtige Blase 
geworden. Am Darme sind bereits in der Nähe des Oesophagus die 
Anlagen der ersten Kiemenspalten zu sehen. Sie treten als paarige 
Aussackungen der endoblastischen Darmwand auf, als halbkugelige 
Protuberanzen, wie von Morean geschildert (4, p. 42). Die Coelome 
sind in Toto-Praeparaten fast nicht. zu sehen, da sie durch den 


12 


breiten circularen Wimperkranz verdeckt werden, dem sie eng 
anliegen. Dass sie bereits vorhanden und sehr mächtig entwickelt 
sind, kann man auf Zupfpraeparaten der gleichen Stadien sehr deut- 
lich erkennen. (Vergl. Textf. 3 u. die Ausf. S. 230/231). 

Stadium fig. 11. entspricht etwa dem MorcaN’schen Stadium IV 
(4, Pl. I, fig. 4) und meinem eingekerbten Stadium (15, Taf. 6, 
Fig. 6 u. 7). Die Tentakel sind bereits völlig geschwunden, die Dorsal- 
und Ventralloben ganz glatt, die Lateralloben sind verwischt. Die 
Kragenregion breit, wulstartig, ähnlieh, wie bei dem in fig. 9 anf 
Taf. Il dargestellten Stadium, das Analfeld sehr stark vorgewölbt. 
In der Mitte des Körpers ist bereits die für dieses Stadium so 
charakteristische _ ringförmige HKinschniirung oder Einkerbung zu 
sehen. Im Innern der Darm und der grosse Wassersack (Eichel- 
coelom); in der Kragenregion sind die Kragen- und Rumpfcoelome 
zu sehen. Man sieht in der Figur 11 oberhalb des grossen circulären 
Wimperrings die etwas dunkler gehaltenen Rumpfcoelome, oberhalb, 
d. h. in Wirklichkeit innerhalb derselben, die gleichfalls schon stark 
ausgebildeten Kragencoelome. Diese springen diaphragmaartig ins 
Innere vor, stets concentrisch den äussern Rumpfeoelomen und den- 
selben dicht anliegend verlaufend. Besser ist dies natürlich auf 
Zupfpraeparaten zu sehen. (Vergl. Erläuterungen zu Textf. 3). Auf 
Zupfpraeparaten lassen sich in diesem bereits sehr undurehsichtigen 
Stadium auch 2 Paar Kiemenspaltenanlagen als ‘halbkugelige Vor- 
wölbungen zu beiden Seiten des Oesophagus erkennen. 

Stadium fig. 12. Dieses kleinste bereits ganz undurchsichtige leicht 
rotlich-braunlich gefarbte Stadium halte ich für das älteste, vorge- 
schrittenste. Es scheint der Metamorphose unmittelbar vorauszugehen. 
Vor allem fällt die sehr stark vorgewölbte Analplatte und die tiefe 
Ringfurche auf, ferner die in voller Auflösung befindliche longitudi- 
nale Wimperschnur der Rüsselregion. Es scheint hier ein „vollstän- 
diger Zerfall ganzer Bezirke des Hautepithels” (12) und Auflösung 
des longitudinalen Wimperkranzes in einzelne mehr oder minder 
vertikal zur Längsachse stehende Stücke stattzufinden, die stellen weise 
noch gewellten Verlauf zeigen (Schrumpfung ?). Im Innern ist mit Mühe 
der Darm und die grosse Wasserblase (Eicheleoelom) zu sehen. Coelome 
und Kiemenspaltenanlagen sind in Totopraeparaten nicht zu erkennen. 

Textf. 3 stellt ein Totalpraeparat im optischen Schnitte dar. Die 
undurchsichtige Epidermis des Analfeldes ist mittels feiner Nadeln 
abgetragen, so dass dasselbe von einem ganz durchsichtigen uhrglas- 
formigen Häutchen bedeckt ist, durch welches hindurch man das 
ganze Innere der Larve beobachten kann. Es ist ein dem Stadium 
10 entsprechendes Objekt dargestellt. 


13 


Ganz peripher der grosse Wimperkranz, im Bilde nur angedeutet. 
Ihm anliegend die paarigen Rumpfeoelome, welche in der Sagittal- 
achse sich nähern. Dieselben 
zeigen peripher jederseits einen 
verdickten schlauchartigen Halb- 
ring mit deutlichem dünnen 
Lumen, der sich nach innen zu 
als solide Platte fortsetzt, was 
der fig. 30, Taf. IV Moreans 
mit dem Unterschiede entspricht, 
dass bei Morean gerade um- 
gekehrt der innere Teil des 
Rumpfeoeloms das Lumen zeigt. 
Während in den jüngeren 
Stadien, die in Fig. 7 u. 8 dar- 
gestellt sind, nur der periphere 
Textfigur 3. Optischer Schmitt durch ein schlauchartige Teil zu beobach- 
Total-praeparat (Stadium fig. 10) von Tor- ten ist, finden sich bei etwas 
naria Morgan. Die Larve ist so orientiert, ajteren Stadien, Fig. 9 u. 10, 
dass die Apikalplatte zu unterst, der After 
zu oberst ist, sie steht also gleichsam auf 


dem Kopfe. | Wassersack, 2 Herzblase und 
Rüsseldrüse, 8 Darm, etwas oberhalb des neren Teile des Rumpfcoeloms 
Bildeentrums der After, 4 Sporne („Zügel- scheinen in der Sagittalachse 
stücke”), 5 Rumpfcoelome, 6 Kragencoelome, mit einander beiderseits zu 
7 Oesophagus. 


wie etwa hier, plattenförmige 
Fortsätze im Innere. Diese in- 


verschmelzen, während die peri- 
pheren getrennt bleiben. Apicalwärts vom Rumpfeoelom, im Bilde 
innerhalb, liegen die mächtig entwickelten Kragencoelome, welche 
als breite diaphragmaartige Platten ausgebildet sind und vom 
Rumpfeoelom durch eine deutlich erkennbare schmale concentrische 
durchsichtige Zone getrennt sind. Sie sind in meinen Stadien riesig 
gross, ganz breite weit ins Innere vorspringende Scheiben, so dass 
es fast unbegreiflich erscheint, wieso sie von Moran, der ganz 
entsprechende Stadien vor sich hatte, entweder gänzlich übersehen 
werden konnten oder auf den Schnitt-praeparaten (4, Taf IV Fig. 
29 u. 35) nur so klein ausgebildet sind. Die beiderseitigen Kragen- 
coelome- vereinigen sich in der Sagittalachse und scheinen dort 
Mesenterien zu bilden, an denen sich auch die Rumpfcoelome 
anheften. In der Gegend des Oesophagus legen sich die Kragen- 
coelome an den Oesophagus an. An vier Stellen, etwa den äusseren 
tentakeltragenden Loben entsprechend, sieht man Verdickungen im 
Coelom, von denen apikalwarts in manchen Fallen Fortsätze 
auszugehen schienen, doch war mir dies in anderen Fallen wieder 


14 


zweifelhaft, und konnte dies mit Sicherheit nicht festgestellt werden. 

Weiter ins Innere fortschreitend ist in der Abbildung das nicht 
mehr so geräumige Blastocoel, ziemlich dunkel gehalten, dargestellt. 
Es folgt das grosse muskulöse Hicheleoelom (1), dem der Darm auf- 
liegt (3). Herzblase und Rüsseldrüse (2) deutlich zu sehen. Der drei- 
teilige Darm erscheint stark verkürzt, der After ganz oben, im Bilde 
oberhalb des Centrums, der Oesophagus in der Tiefe, in einem 
ziemlich scharfen Winkel abgebogen (7). Sehr deutlich sieht man 
hier beiderseits des Darmes, dem Wassersack aufliegend, die Zügel- 
stücke, ,Sporne’ (4). Dieselben inserieren einerseits ziemlich nahe am 
Oesophagus als breite anscheinend muskulöse Bander, ziehen dann 
bogenförmig, sich immer mehr fadenförmig verdiinnend, beiderseits 
zu einer ziemlich weit ins Innere vorspringenden verdickten Stelle des 
Kragencoeloms, wo sie angeheftet sind. Diese ,Sporne’ sind auch 
von Morean und SPENGEL beobachtet worden. Besonders bei der 
SpeNGer/’schen ,, Zornaria Grenacheri” (38, Taf. 23 fig. 60) sind sie 
sehr stark ausgebildet. Die Insertionsstelle dieser Sporen ist nach 
beiden Autoren nicht sicher. Nach Spence, endigen sie beiderseits 
„in einem bald kleineren, bald grösseren Häufchen von Zellen”. 

Damit glaube ich alles geschildert zu haben, was an derartigen 
Totalpraeparaten zu sehen ist. Schnitte konnten vorläufig nicht 
gemacht werden. Es ist daher vielleicht nicht alles richtig gedeutet, 
was ich beobachtet habe‘). 

Hier anschliessend nur einige Bemerkungen über die Scheitelplatte 
in den Stadien 7 u. 9. Taf. Il. Bei den meisten Larven ist die 
Scheitelplatte stark eingezogen und undeutlich, oder gar nicht zu 
sehen, ebenso die Augen, an denen niemals Pigment beobachtet werden 
konnte. In der einen oder anderen Larve konnten jedoch die Ver- 
hiltnisse an der Scheitelplatte, Verlauf der Wimperschniire ete., gut 
erkannt werden. Im allgemeinen entspricht die Darstellung und 
Beschreibung Moraans in seinen beiden Arbeiten (2 u. 4) sehr gut. 
Besonders hebe ich hier die fig. 10 in Moreans erster Arbeit (2) 
hervor, in welcher Abbildung jedoch leider die Augen nicht einge- 
zeichnet sind. Auch die Angaben SprneErs (3) über die Scheitelplatte 
seiner als „Tornaria Grenacheri”’ bezeichneten Form zeigen durch 
ihre Uebereinstimmung die nahe Verwandschaft derselben mit Zornaria 
Morgani. Ich füge nur hinzu, dass im Centrum der Apikalplatte 
ein kleiner dunklerer Fleck zu sehen ist, innerhalb dessen sich eine 
kleine lichte Grube (,,Wimperorgan SPENGEILS? 3, p. 394) befindet. 


1) Zusatz bei der Korrektur. Seitdem dies geschrieben wurde, bin ich in den 
Besitz vorzüglicher Schnittpraeparate durch diese Stadien gelangt. Ich behalte mir 
vor, darauf bei anderer Gelegenheit zurückzukommen. 


15 


Quer über die Apikalplatte verläuft eine seichte Rinne. Die breite 
Apikalplatte selbst hat etwa die Form eines Rechtecks, dessen 
Längsseiten von den parallel zu einander verlaufenden tentakellosen 
Wimperschnüren eingenommen werden. Die prae- u. postoralen 
Wimperschnüre scheinen nicht auseinander zu fallen (Moran 2, p. 
11), sondern, dort, wo in der Mitte des Rechtecks die quere zu den 
kurzen Seiten des Rechtecks parallele Rinne verläuft, gehen die beider- 
seitigen Wimperschnüre in einander uber, deren Tentakel gegen den 
Apex zu immer kleiner geworden und hier endlich ganz ge- 
schwunden sind. : 

Zum Schlusse ergibt sich naturgemäss auch hier die Frage: Zu 
welchem adulten Enteropneusten gehört die Tornaria Morgani? Leider 
lässt sich dieselbe vorläufig ebensowenig mit Sicherheit beantworten, 
als dies bei der Lornaria Weldoni und bei allen übrigen tentaculaten 
Tornarien der Fall ist. WeweLpoN und Morean sagen diesbezüglich 
nichts. Wirnney (6) spricht anlässlich der Beschreibung seiner neuen 
species Ptychodera biminiensis auf p. 288 folgende Ansicht aus: 
„Fhis is presumably the species whose Zornaria-development was 
deseribed by Morean’’, wohl deshalb, weil diese Enteropneustenform 
von der gleichen Lokalität stammt. Kin weiterer Beweis für seine 
Behauptung wird von Wirrey nicht beigebracht, doch ist. seine 
Annahme wohl richtig. Mit voller Sicherheit wird sich die Zusammen- 
gehorigkeit. der Tornaria Morgani mit Ptychodera biminiensis natürlich 
erst nach Ziichtung dieser Larve aus deren Hiern behaupten lassen. 
Am Schlusse seiner Beschreibung fiigt WiLrey, (6, p. 294) noch hinzu: 
„As at least two kinds of Tornarta have been recorded from the 
West Indies it is important to note that so far as known all the 
Enteropneusta inhabiting the shores of these islands belong to 
the family of the Ptychoderidae.” 


UI. Aritische Uebersicht über die bisher bekannten tentaculaten 
Tornarien. 
A. Kritik der Species. 

Im Anschlusse an diese Darstellung gebe ich im folgenden eine 
Revision der bisher beschriebenen tentaculaten Tornarien. SPENGEL 
hat, da sich unter den verschiedenen, in seiner grossen Monographie 
falschlich zu einer einzigen Species „Tornaria Grenacheri’”’ zusam- 
mengezogenen Tornarien eine grössere Anzahl wohl charakterisierter 
Arten erkennen lassen, eine Uebersicht derselben für nötig gehalten, 
eine solche in Aussicht gestellt, doch ist dieselbe bis nun nicht 
erschienen (9). Wiruey schreibt mit vollem Rechte (6, p. 185): ,,No 
doubt the differences between the Tornariae of some species are very 


16 


trifling, but it is a great mistake to imagine that all tentaculated 
Tornariae belong to one species”. 

Es ist ganz richtig, wenn SPeNGeL schreibt (9, p. 127.), dass ,,weder 
die besondere Ausbildung der Tentakel noch ihre Zahl zur Charak- 
terisierung der meisten tentaculaten Tornarienformen brauchbare 
Merkmale zu bieten scheint”, doch sind es nicht nur „Eigentüm- 
lichkeiten gewisser Loben, an die sich vorzugsweise die Unterschiede 
knüpfen”, sondern, wie ich hinzufüge auch eine ganze Reihe anderer 
Merkmale wie z. B. die Grösse, Beschaffenheit des Analfeldes, Bau 
der Scheitelplatte, Augen, Pigment, Sporne, vor allem jedoch die 
Lage und Entstehungsweise des Coeloms, (Vergl. die Synopsis der 
tentaculaten Tornarien 5. 249), die zu einer genaueren Charakteri- 
sierung der verschiedenen Tornarien dienen können. 

Bezüglich des longitudinalen Wimperbandes der tentaculaten Tor- 
narien möchte ich nur bemerken, dass der Verlauf desselben im 
Prinzipe, trotz der grossen Compliciertheit gegenüber den nicht ten- 
taculaten, doch im grossen und ganzen der gleiche ist, wie bei den 
letzteren. Nie ist das longitudinale Wimperband unterbrochen, sondern 
stets continuirlich. Man kann wohl sagen, dass soferne nach Angabe 
WiuLers bei der Tornaria von New Britain (Pornaria Wimvi) die 
Wimperschnur eine Unterbrechnung zeigen soll, dies höchstwahr- 
scheinlich auf einen Beobachtungsfehler dieser höchst schwierig 
feststellbaren Verhältnisse zurück zu führen ist. Es gilt also ganz 
im allgemeinen das Schema des Verlaufs der longitudinalen W im- 
perschnur auch für alle tentaculaten Tornarien, wie ich dasselbe 
in meiner Arbeit (15) über die Entwicklung des Balanoglossus clavi- 
gerus fiir das Tornaria Krohnii-Stadium dieses Enteropneusten 
gegeben habe. (15, p. 263., Textf. C.). Es lässt sich daher aach in 
allen Fällen die Spenarrsche Nomenclatur (Loben, Sättel, Ventral- 
band ete.) gut und zweekmässig anwenden. Natürlich hat jedoch 
jede einzelne Tornariaspecies einen ihr eigentiimlichen Verlauf der 
longitudinalen Wimperschnur mit specifischen Unterschieden, die 
sich jedoch alle auf das gemeinsame Schema zwanglos zurückführen 
lassen. (Vergl. Textf. 1 u. 2 mit der genannten Abbildung). 

Beziiglich der ,,Tentakel” sei noch eine mehr nebensächliche Be- 
merkung gestattet, da hier die Spencetsche Nomenclatur zu Missver- 
standnissen Anlass geben könnte. SPeNGEL bezeichnet die Fortsätze 
des Oralfeldes in die benachbarten Felder mit einem der Beschreibung 
der Ammoniten entnommenen Ausdruck als ,,Loben’’, die in das 
Oralfeld hineinragenden Fortsätze der anderen Felder als ,,Sattel” 
(3, p. 373). Bei der Beschreibung seiner „Tornaria grenacherv” (3, 
p. 379/89) schreibt SpeNaer: „Die Compliciertheit des Wimperappa- 


Hee 


rates beruht auf der Entwicklung von je 25—30 und mehr secun- 
därer Loben... Alle diese seeundären Loben sind bei der ausge- 
bildeten Larve sehr lang und schmal und haben ganz das Aussehen 
von kleinen Tentakeln, wie sie denn auch von Wetpown als solche 
beschrieben worden sind’. Im Sibogawerk (9, p. 124) schreibt dieser 
Forscher: „Bei allen (tentaculaten Tornarien) sind bekanntlich die 
scheinbaren Tentakel nichts als zahlreiche enge und sehr tiefe 
Buchten der im übrigen ihre normale Anordnung zeigenden Wimper- 
schnüre”’. — Danach waren die Tentakel als „secundäre Loben”’ 
aufzufassen, also als Nebenverzweigungen der Fortsätze des Oral- 
feldes in die anderen Felder, die von entsprechenden Windungen 
der Wimperschnüre begleitet sind, also die tiefliegenden Buchten 
der Loben des Oralfeldes, zwischen den hochliegenden Teilen der 
Sattel. Von Rrerrer und Morean wird übereinstimmend angegeben, 
dass die Tentakel ziemlich stark von der Oberfläche wegstehen 
„hanging freely like a fringe from the surface of the larva”, (4, p. 
429) was ich nur bestätigen kann. Spencer selbst-(3, p. 380) erwähnt 
die Aehnlichkeit der tentaculaten Tornarien mit einer Rippenqualle. 
Auch kommt den Tentakeln mehr oder minder Bewegungsfähigkeit 
zu (8, p. 175). Die tiefliegenden Fortsdtze des Oralfeldes, die Buchten 
der Loben (SprNamr) können doch nicht von der Oberfliche wegstehen 
oder fransenartig herabhäüngen und sich bewegen. Die Tentakel sind 
eben nicht Ausbuchtungen der Loben, sondern Ausbuchtungen der 
Sdttel, denn nach Zuermi’s Handbuch *) sind die vorspringenden Teile 
die „Sättel”, die zurückgebogenen Buchten die „Loben”. 


In der folgenden Besprechung wurden die meisten Tornarien mit 
neuen Namen bezeichnet. Der Vorschlag SPuNerrs (3), die Tornarien 
mit dem Namen jenes Autors zu benennen, der sie zuerst be- 
schrieben hat, erweist sich als nicht immer durchführbar, da z. B. 
SPENGEL selbst und WeLDoN mehrere Tornarien beschrieben haben. 
Es wurden daher die verschiedenen Species mit den Namen jener 
Autoren belegt, die an ihrer Auffindung oder Beschreibung einen 
wesentlichen Anteil haben. 


Tornarta Grenachert SPENGEL. 


Unter dem Namen ,,Vornaria grenacherv’ beschreibt SpPeNarr (3, 
p. 378 ff.) eine Tornaria, die Professor GRENACHER bei den Cap Ver- 
dischen Inseln gesammelt hat und halt dieselbe für identisch mit 
anderen Tornaria-Exemplaren, die von Cutercnia auf der Falrt des 


1) Zire KARL A., Handbuch der Palaeontologie 1. Abth. Palaeozoologie II, Bd. 


Mollusca und Arthropoda. 
2 


Proceedings Royal Acad. Amsterdam. Vol. XXIII. 


18 


„Vettor Pisani’ im Stillen Ozean, zwischen den Sandwich- und den 
Marshall-Inseln gesammelt wurden. 

Auch die von WeLponN, Brooks und Morean bei den Bahamas 
gefundene Form halt Spencer mit den genannten für identisch, sowie 
eine von Driesen und HerBsr bei Ceylon nachgewiesene Tornaria. 
„Sollte sich wirklich die völlige Identität dieser sämmtlichen Torna- 
rien erweisen, so wiirde denselben eine, wenn ich so sagen darf, 
circumterrane Verbreitung zukommen.” 

Dieser von SPENGEL geäusserte Zweifel an der Identitat der ge- 
nannten Tornarien verschiedener Provenienz erweist sich nur zu be- 
gründet. Wirnrey (6, p. 285) bemerkt dazu, das SPENGEL unter 
dem Namen „7. Grenacherv”’ Tornarien vereinigt, die sicher nicht 
identisch sind. 

Im Sibogawerk gibt Spencer selbst zu (9, p. 124), dass er „die 
tentakulaten Tornarien fälschlich zu einer einzigen Form, der 7. 
Grenacheri, zusammengezogen hat, während sich einige wohl 
charakterisierte Arten unter ihnen erkennen lassen”. 

Tatsächlich ergibt eine Prüfung seiner Darstellung in seiner grossen 
Monographie (Le), dass dieser Forscher tatsächlich hier mindestens 
zwei verschiedene Tornarien unter dem Namen ,,T. Grenacheri” ver- 
einigt hat. 

Vor allem besteht zwischen der Tornaria GRENACHERS und der- 
jenigen Cuiercnias ein beträchtlicher Grössenunterschied. Die grössten 
von GrenacHer beobachteten Exemplare, erreichen 5—9 m.m. Hohe, 
das grösste von CHiercHTA gesammelte dagegen nur 5 m.m. Höhe. 

Auf Grund seiner Abbildungen (3, Taf. 22, fig. 11 —13) welche 
nicht nach den GRreENACHERSChen capverdischen, sondern nach den 
von CHteRCHIA gesammelten pacifischen Formen gezeichnet sind, lässt 
sich mit Sicherheit sagen, dass die Crrercnia’sche Tornaria nicht 
identisch ist mit der grossen Bahamas Tornarta WerLpoN’s und 
MoraanN’s. Allerdings sind beide Tornarien sehr ähnlich und Wizer 
sagt mit Recht (9, p. 285) ‚‚no doubt the differences between the 
Tornariae of some species are very trifling’, doch hat die Cuiercura’sche 
Tornaria ziemlich tiefe untere Dorsalloben, welche bei der Bahamas 
Tornaria gänzlich fehlen (was Spencer übersehen zu haben scheint), 
auch erreicht die letzere nicht die Grösse der ersteren. (Vergl. damit 
S. 249). SprnNarrs Beschreibung lässt diesbeziiglich keine Schlüsse 
zu, denn er spricht stets ganz allgemein über ,, Zornaria Grenacherv”, 
da er ja alle tentaculaten Formen für identisch halt und auch nicht 
sagt, ob seine jeweiligen Angaben die GRENACHER’sche oder CHIERCHIA’- 
sche Form betreffen. Nur in der Figurenerklärung von Tafel 22 
erwähnt er bei Fig. 11—13 „Tornaria Grenacheri aus dem Stillen 


19 


Ozean, ausgebildete Form”, woraus hervorgeht, dass diese Figuren die 
Cuirrcnra’sche Tornaria darstellen. Auch scheint es, dass SPENGEL 
von GRENACBER nur Abbildungen, keinerlei Material, von der capver- 
dischen Tornaria erhielt, während dies bei der Tornaria CHtrrcuIas 
wohl der Fall war. Danach waren dann alle Detailangaben über 
Coelomverhältnisse, Herzblase, Darm, Wimperkranz eic., die in 
Spenari’s Monographie verstreut sind, auf die Tornaria CHirRCHTAS 
und nicht auf die GRERNACHER’sche zu beziehen. 

Auch die Angaben Spencers über die Entwicklungsstadien der 
‚Vornaria Grenacherv’ sind mit einiger Vorsicht aufzunehmen, denn 
es scheint auch hier keinem Zweifel zu unterliegen, dass er Ent- 
wicklungsstadien verschiedener Tornarien in Verbindung gebracht hat, 
die mit einander nichts zu tun haben. 

Durch die vortreffliche Schilderung der Entwicklung der grossen 
Bahamas Tornaria durch Morgan sind die Jugendstadien dieser Form 
zum Teil wenigstens bekannt (4, Taf. J, Fig. 1 u. 2). Sie sehen 
durchaus nicht so aus wie die Zornaria Krohnii des Mittelmeeres, 
sondern haben, obwohl viel kleiner, doch schon ganz den Habitus 
der tentaculaten Formen mit langen fingerformigen Tentakeln, die 
allerdings geringer an Zahl sind als bei den ,,ausgebildeten’”’. 

SPENGEL schreibt nun von seiner „Tornaria Grenachert’, dass 
,,Professor GRENACHERI einige jiingere Entwicklungsstadien seiner 
Larve beobachtet und gezeichnet hat, von denen eines fast genau 
die Tornaria Krohnit repraesentiert”, fiigt jedoch hinzu; „Es ist 
allerdings nicht ganz ausgeschlossen, dass dieses vermeintliche Jugend- 
stadium der T. g. wirklich eine Tornaria Krohnii ist, da ja recht 
wohl bei S. Vincente beide Arten neben einander vorkommen können, 
wie bei Neapel 7. Krohnii neben 7. Müllert und T. dubia... Diese 
Möglichkeit muss ich zugeben.” 

SPENGEL hält es also selbst für gar nicht ausgeschlossen, dass hier 
eine Vermengung von Entwicklungsstadien zweier verschiedener 
Tornarien vorliegen kann. 

_ Kine weitere Nachprüfung dieser SprNaer’schen resp. GRENACHER’ 
schen Angabe ist nicht möglich. 

Wohl möglich ist aber eine kritische Untersuchung der folgenden 
Bemerkungen SPrNaeLs, welche die WerrpoN’sche Bahamas Tornaria 
betreffen. 

, Wass indessen jüngere Exemplare der 7. Grenacheri in der 
Gestaltung ihres Wimperapparates tatsächlich von der 7. Krohnii 
kaum zu unterscheiden sind, ersehe ich aus dem reichlichen Material 
der ersteren Form, das Mr. WerponN mir in liebenswürdigster Weise 
zur Verfügung gestellt hat”. Nun hat WrLpoN, wie aus seiner kurzen 

2% 


20 


Mitteilung (1) hervorgeht, auf den Bahamas zwei verschiedene Tor- 
narien beobachtet, eine kleinere, welche von Morgan später Bimini 
Tornaria genannt wurde, und eine grössere, von Morean als Bahamas 
Tornaria bezeichnet. Es ist also wieder unsicher, was für Entwick- 
lungsstadien SPENGEL von WerpoN erhielt, solche von der Bimini- 
oder solche von der Bahamas Tornaria. Wertipon beschreibt in der 
genannten Arbeit (1) ausschliesslich ältere Stadien, die sich schon der 
Metamorphose nähern, die jungen Entwicklungstadien der Bimini 
Tornaria waren zur Zeit, da SpeNaer seine Arbeit schrieb, nicht 
bekannt. Aus der Morean’schen Abbildung 4, Taf. 1, fig. 12 geht 
jedoch hervor, dass es sich um eine tentaculate Form mit tentakel- 
losem Laterallobus handelt, was auch durch das mir vorliegende 
übereinstimmende Material bestätigt wird. Dass die jüngeren Stadien 
der Bahamas Tornaria (T. Morgani) ganz anders aussehen, wie 
Tornaria Krohnu, geht aus der Morean’schen Beschreibung deutlich 
hervor (4, Taf. I, fig. 1 u. 2). Die Angabe Sprnaers stimmt also 
weder für die eine, noch für die andre Form Wetpons. SPENGEL 
fährt dann fort: „Die jüngste endlich der von Herrn Prof. GRENACHER 
abgebildeten Larven gleicht wesentlich einer 7. Miülleri, indem die 
primären Loben, mit Ausnahme der Lateralloben, ausgebildet sind, 
secundäre aber noch gänzlich fehlen. Wir würden demnach im 
Entwicklungsgang der 7. Grenacheri zwei Stufen erkennen, welche 
die Endstadien der Yornaria Müllert und Krohnii entsprechen”. 
Darauf wäre einzuwenden, dass von keiner einzigen tentaculaten 
Form mit Sicherheit ein der 7. Müllert entsprechendes Entwicklungs- 
stadium bekannt ist ohne seeundäre Loben, da das jüngste bekannte 
Entwicklungsstadium einer tentaculaten Tornaria, dasjenige von 
Morean in Fig. 2 auf Taf. I. abgebildete und genau beschriebene, 
bereits Tentakeln trägt. 

Da also von keiner tentaculaten Tornaria ein tentakelloses der 
Tornaria Mülleri entsprechendes Stadium bekannt ist, erweist sich 
SPENGELS Schlussfolgerung als voreilig oder jeder Grundlage entbehrend. 

Vielmehr ist anzunehmen, dass die Tornaria Mülleri-Stadien 
GRENACHERS als jüngere Stadien jener Zornaria Krohnii GRENACHERS, 
welche auf der gleichen Lokalität gefunden wurden, aufzufassen sind, 
die mit der Yornaria Grenachert nichts gemeinsam haben, als das 
Vorkommen auf einer derselben Lokalität, denn nach SPeNGeL selbst 
(3, p. 376) sdurchläuft ja die Fornaria Krohnit ein im wesentlichen 
der 7. Miillert gleichendes Entwicklungsstadium”’. 

Auch ist es nach den Beobachtungen MorGANs, sowie meinen 
eigenen, höchst wahrscheinlich, dass sowohl die Bimini- als auch die 
Bahamas Tornaria sehr frühzeitig den Habitus der Tentaculaten 


21 


zeigen. Von Interesse wäre es natürlich zu wissen, was fiir Tornarien 
WerDoN an SPENGEL gesandt hat, denn von den Bahamas ist eine 
Tornaria Krohnii nicht bekannt. Ich komme also zum Ergebnis, 
dass Spencen unter der Bezeichnung 7. Grenacheri mindestens zwei 
Formen vereinigt hat, die Entwicklungsstadien verschiedener Enterop- 
neusten darstellen. 

Die von den Capverdischen Inseln stammende „7. Grenacherv’, 
die Spence wohl nur nach Zeichnungen und Angaben GRENACHERS 
kannte, ist nicht identisch mit der Tornaria Curercuias aus dem 
Pacific, die SPENGEL genau untersucht hat. 

Möglich ist, das die Grunacuer’sche Larve, über welche wir nun 
fast gar nichts wissen, da fast sämmtliche Angaben SPeENGeELs auf die 
Tornaria Cutercuias zu beziehen sind — ausser einer Aehnlichkeit 
beider Formen — identisch ist mit der Bahamas Tornaria Morgans. 
Die räumlich so getrennten Faunengebiete der Capverden und Bahamas 
sind ja durch den Golfstrom in direkter Verbindung. Es wiirde nur 
die grosse Entfernung dagegen sprechen. Hier ist jedoch die Auffindung 
von Tornarien durch die Planktonexpedition fern vom Festlande oder 
Inseln im Atlantik von Interesse. HeNsEN schreibt in seinem grossen 
Werke „Das Leben im Ozean nach Zählung seiner Bewohner” 
10) auf p. 254, dass mit dem grossen Vertikalnetze eine Anzahl 
Balanoglossus Larven 300 Seemeilen östlich von Fernando und 780 
Seemeilen westlich von Ascension gefangen wurden. „Dies sind Entfer- 
nungen die der Südaequatorial-Strom kaum in 40 Tagen von Ascension 
durchlaufen hätte und die gegen ihn von Fernando aus nicht durchmessen 
werden können. Auf den Stationen zwischen dem Fundort und Ascen- 
sion traten diese Larven auch nicht auf”. Die weitere Bemerkung 
Hensens: „Die Möglichkeit, dass die Larven, die übrigens recht 
häufig waren, aus grossen Tiefen stammen, ist nicht abzuweisen’’, 
bezieht sich wohl nur auf die gleichzeitig mit den Balanoglossus- 
Larven besprochenen Echinodermenlarven, denn bisher ist von keiner 
einzigen Enteropneustenform, die als typische Litoraltiere gelten, 
Aufenthalt in der Tiefsee nachgewiesen. 

Die grosse Entfernung der Fundstellen wäre also kein Hindernis. 
Auch ist aus meinen Arbeiten (14, 15) über die Entwicklung des 
Balanoglossus bekannt, dass die Larvenentwicklung unter normalen 
Verhältnissen mehrere Wochen dauert, jedoch unter abnormen, wenn 
die Larven durch Strömungen verschleppt werden, natürlich länger. 
Fiir die Möglichkeit der Identitat der Capverdischen und grossen 
Bahamas Tornaria spricht endlich noch eine Bemerkung SPENGELS, 
der erwähnt, dass bei seinen yermeintlichen Jugendstadien der 7. 
Grenacheri „der Wassersack schon eine bedeutende Ausdehnung erfah- 


22 


ren hat.” Auch erwahnt er eine briefliche Mitteilung GRENACHERS an 
ihn, dass es GRENACHER in Erstaunen gesetzt habe, dass ,,das Wasser- 
gefässystem und seine Adnexe (i.c. Herzblase, Eichelkieme) bei an- 
scheinend ziemlich gleichweit ausgebildeten Exemplaren so ungemein 
verschieden entwickelt sich vorfanden.” Derartige Schwankungen in 
der Entwicklung einzelner Organe sind bei aus ihrer urspriinglichen 
Umgebung verschleppten Entwicklungsstadien durchaus nichts unge- 
wöhnliches und durch den Wechsel der physikalisch-chemischen 
Bedingungen des Mediums leicht zu erklären. 

Die Spenaer’sche ,,Zornaria Grenachert’’ umfasst also 1. die Tor- 
naria Grenachers von den Capverdischen Inseln, 2. die von Driuscx 
und HerBsr bei Ceylon gefangenen Tornarien, 3. die Tornaria 
Chierchias aus dem Pacific. 


Grenachers Tornaria von den Cap Verden. 
(Tornaria Grenachert Spengel). 


Von der durch GRRNACHER gesammelten Tornaria ist nach den 
obigen Ausführungen mit Sicherheit nur Folgendes bekannt. Sie ist 
eine tentaculate Form, ist als solche der Zornaria Chierchiai und 
Tornaria Morgani ähnlich. Ihre Höhe ist 5—9 min, sie ist also die 
grösste bekannte Tornaria. Sie stammt von St. Vincente. Möglicher- 
weise identisch mit Fornaria Morgani von den Bahamas. 


Driesch und Herbst's Tornaria von Ceylon. 
(Tornaria Sp. ?) 


Ueber diese Tornaria ist nur bekannt, was SPENGEL in 3 Zeilen 
mitteilt (3, p. 379). „In allerjiingster Zeit habe ich 2 Larven, die ich 
nach dusserlicher Untersuchung nicht von Tornaria Grenacheri unter- 
scheiden kann, durch die Giite der Herren Docs. H. Driesen und 
C. Herssr erhalten, die sie bei Ceylon gefangen haben”. Daraus geht 
nur hervor, dass es sich um eine der 7. Grenacheri jedenfalls sehr 
ähnliche tentaculate Form handelt. Weitere Angaben fehlen. 


Chierchias Tornaria aus dem Pacific. 
(Tornaria Chierchiai). 
Unter 18° N., 175° W., zwischen den Sandwich- und den Mars- 
hall-Inseln. 
Grésse: Höhe (Augenpol-After) 5 m.m. 
Durchmesser Bi ie, 


Aussere Merkmale: obere dorsale und ventrale Loben mit je 
25—30 und mehr secundéren Loben besetzt. 


23 


Dorsale Sättel breiter als ventrale. 

Ventralsattel hoch und schmal. 

Ventralband breit. 

Lateralloben schmal mit 8 Tentakeln besetzt, untere Dorsalloben 
circa doppelt so tief wie die Lateralloben, ohne Tentakel. 

Analfeld flach mit breitem primären circulären Wimperkranz und 
schmalen seeundären Wimperkranz; Hichelporus tief liegend. 

Scheitelplatte eine breite lanagestreckte rechteckige Figur, die quer 
auf dem oberen Körperpol gelegen ist. Wimperschniire verhalten 
sich in der Hauptsache wie bei 7. Miller und Krohnit, mit dem 
Unterschiede, dass infolge der Breite der Scheitelplatte die Wimper- 
schnüre längs die Ränder derselben eine Strecke weit ziemlich 
parallel mit einander verlaufen. 

Augen liegen ganz nahe an einen der beiden Wimperschnüre 
(ventral oder dorsal?), haben complicierteren Bau als bei der Mittel- 
meerform. 

Pigmentierung stark entwickelt. Dichte Reihe rotbrauner Flecken 
längs des oberen Randes des primären Wimperringes, zerstreute 
Pigmentflecken längs der Wimperschnüre, sehr grosse sternförmige 
Zellen unter dem Prae- und Postoralfeld. 

Innere Organe: [in den Habitusbildern nicht eingezeichnet, aber 
aus guten Detaildarstellungen zu erkennen). Dreiteiliger Darm, 
Oesophagus und Enddarm kurz. Mitteldarm ein eylindrisches Rohr, 
6 mal so lang als breit, Wassersack im wesentlichen wie bei 7’. 
Miillern und Krohn. Sporne (,,ziigelartige Fäden”) symmetrisch 
entwickelt, eine grosse Strecke lang hohl. 

Coelom. Kragencoelome ') liegen unmittelbar der Epidermis an als 
ein Paar sehr lang ausgezogener, daher in longitudinaler Richtung 
nur sehr schmaler Schläuche. Auf der ventralen Seite nur ein kurzes 
Stück von einander entfernt. „Von hier zog ein jeder in horizontaler 
Richtung in seinem Verlauf der postoralen Wimperschnur folgend 
rings um den Körper herum, bis auf die dorsale Fläche, um sich 
zuletzt etwas aufzurichten und, der linke in der Nahe des Eichel- 
porus, der rechte in entsprechendem Abstande vom blinden Zipfel 
des ,,Wassersackes” zu endigen. Jeder entsandte ferner in der Gegend 


1) SPENGEL sagt anfangs nicht, von welchen Coelomen die Rede ist. Erst aus 
den letzten Sätzen auf p. 432, sowie aus der Bemerkung auf p. 433: „Ganz anders 
verhalten sich die Rumpfcoelome”, geht mit einiger Sicherheit hervor, dass er mit 
den fraglichen Bildungen die Kragencoelome gemeint hat. Ich halte sie jedoch 
auf Grund der Angaben Morgans und meiner Beobachtungen für die Rumpf- 
coelome. (S. o. 8. 228/9). Die wirklichen Kragencoelome, die erst 
später angelegt werden, scheint SpenaeL nicht gesehen zu haben. 


24 


des Laterallobus einen langen dünnen Fortsatz nach oben. Wo er 
endigt, habe ich nicht beobachtet”’. 

Die Rumpfeoelome liegen dem circumanalen Wimperring hart an. 
, Ueber ihre ventrale und dorsale Begrenzung habe ich keine Beob- 
achtungen angestellt *).” 

Entwicklung: nur 1 Stadium bekannt, (etwa einer älteren Tornaria 
Krohnii entsprechend), alle weiteren Angaben unsicher. 

Fundort: Pacifischer Ozean. 

Bemerkung: Die Tornaria Chierchiat unterscheidet sich durch 
folgende Merkmale von der Tornaria Morgant (Bahamas Tornaria): 
sie besitzt etwas mehr, jedoch kiirzere Tentakeln an den oberen 
Dorsalloben, unterer Dorsallobus ziemlich tief (Morgant hat keinen), 
der Mitteldarm ist viel länger, sie hat viel Pigment. Beide Formen 
haben jedoch die Grösse, das Coelom fern vom Darm, dem grossen 
Wimperring oder dem Ektoderm anliegend, gemeinsam, ferner den 
Bau der Scheitelplatte und der Augen. 


Ritters Tornaria von Californien. 
(Tornaria ritteri Spengel). 


1. Beschreibung im Zoolog. Anz. Bd. 17, p. 24—30. Fig. 1. 
Grüsse (des conservierten Exemplars) Höhe: 1,9 mm. 
Grösste Breite: 1,33. ,, 

Aussere Merkmale: Obere dorsale Loben mit 2—4, obere ventrale 
Loben mit 6 Tentakeln besetzt. Tentakel kurz, dick, stummelförmig. 

Veutralsattel: nicht hoch, breit. 

Oralfeld sehr breit. 

Unterer Dorsallobus? 

Laterallobus ziemlich breit, analwärts, an der Mündungsstelle enge, 
mit 1 Paar Tentakeln besetzt. 

Scheitelplatte wie bei der New England Tornaria Moreans (2, 
Dat, XXIV tera), 

Augen weiter von einander entfernt als bei der Bahamas Tornaria 
Moraans. 

Innere Organe: Weder aus der Beschreibung noch aus fig. 1 
etwas beziiglich Magen und Coelome zu ersehen. Als Besonderheit 
wird nur erwähnt, dass die ersten Anlagen der Kiemenspalten nicht 
vor Eintritt der Metamorphose auftreten. Ferner wird ein Band 


s 


1) Was für Bildungen Spence für ,Rumpfeoelome” halt, ist schon wegen ihrer 
ganz ungewöhnlichen Lage am circumanalen (doch wohl dem secundären ?) 
Wimperring ganz zweifelhaft. In Abb. 118 Taf. 25 allerdings sind sie dem Haupt- 
wimperring (primären Wimperring) anliegend dargestelll! 


25 


hoher cylindrischer Epithelzellen am Grunde des Oesophagus genau 
beschrieben und funktionell als Endostyl gedeutet. 

Entwicklung: nur 1 Stadium bekannt. 

Fundort: Avalon, Island of Santa Catalina, Southern California. 


2. Beschreibung in University Calif. Publ. Zool. Vol. 1. 
1904, p. 171 —203. Pl. XVII—XIX. insbes. fig. 1 u. 2. 
Grösse (der lebenden Tornaria,. Höhe: 2.07—2.32 mm. 
Grösste Breite: 1.08—2.07 _,, 


Aussere Merkmale: obere dorsale und ventrale Loben mit 6—8 
Tentakeln, ferner 3 Tentakel auf dem schmalen Verbindungsstiick 
(isthmus) zwischen beiden. Tentakel langer, abstehend. 

Unterer Dorsallobus ? 

Laterallobus laut Abbildung ohne Tentakel [Laut Beschreibung 
mit 1 Paar Tentakel s.u.| Ventralsattel hoch. 

Scheitelplatte ? Augen ? 

Die Larve ist relativ breit im Verhältnis zu ihrer Höhe. Das 
Vorderende flach, die Analscheibe vorgewölbt. „The diameter of the 
body increases rapidly from the oral field backwards to the ciliary 
girdle so that the sides form an angle much less than a right 
angle with the plane of this circle.” (5, p 174/5). 

Secundärer Wimperkranz vorhanden. 

Innere Organe: In fig. 2 auf Taf. XVII, ist der 3 teilige Darm 
eingezeichnet, an welchem der fast kugelige sehr grosse Magen 


auffällt. 
Die weiteren Angaben betreffen das Ektoderm, das Blastocoel, 


das Magenepithel in verschiedenen Entwicklungsstadien u. kommen 
für die Charakterisierung dieser Tornarienform kaum in Betracht. 

Entwicklung: nur 1 Stadium wird genauer beschrieben, von den 
älteren Stadien einige histologische Details angegeben. 

Fundort: der gleiche, wie unter (1) angegeben. 

Bemerkung: Beide Beschreibungen sind ungenau und stimmen 
in einigen Punkten nicht überein. 
__Ungenau sind sie, weil sie keinerlei Angaben über einige für 
die Charakterisierung der Tornarien wichtige Merkmale wie z. B. 
Dorsalloben, Coelom etc. enthalten. Wenn es auch denkbar ist, dass 
die Rumpf- und Kragencoelome in den geschilderten Stadien noch 
nicht ausgebildet waren — was ich jedoch nach den Erfahrungen 
bei den übrigen Tornarien für unwahrscheinlich halte — so ist doch 
bei so vorgeschrittenen Stadien mit so gut ausgebildeten Tentakeln 
das Eicheleoelom und die Herzblase etc. schon angelegt, doch fehlt 
auch hierüber jede Angabe. 


26 


Nicht übereinstimmen beide Beschreibungen : 

1. in der Grösse. 

2. in der Anzahl Beschaffenheit der Tentakel auf den Dorsalloben. 

3. in der Form des Ventralsattels. 

4. in der Beschaffenheit des Laterallobus. 

Ich glaube hier nur auf den letzten Punkt eingehen zu müssen. 
In seiner 1. Mitteilung im Zool. Anz. bildet Ritter in Fig. 1 im 
Laterallobus ein Paar Tentakel bei /' ab. ,,[n the narrow neck of 
this loop there appears to be the anlage of a single pair of proces- 
ses like those found in the preoral portion of the band”. Die weitere 
Bemerkung: „so far I am aware this loop does not exist in any 
other Tornaria’”’ ist durch die späteren Untersuchungen der übrigen 
Tornarien überholt, wo sich regelmässig ein derartiger Laterallobus, 
mit oder ohne Tentakel, vorfindet. 

In seiner 2. Mitteilung schreibt er p. 175: ,,A single pair of ten- 
tacles somewhat shorter than the longest ones of the series above 
described is present at the narrowest part of the lateral lobe’. Dies 
stimmt nun wieder nicht mit seiner Fig. 2 u. 3 auf Taf. XVII. 
Wenn man diese Abbildungen betrachtet, ohne auf die Beschreibung 
Riieksicht zu nehmen, wird man wohl sagen müssen, dass die 
Lateralloben der dargestellten Tornaria tentakellos sind. Nun fasst 
Ritter aber hier offenbar die beiden Zipfel des ventralen Wimper- 
bandes an der Miindungsstelle des Latterallobus als Tentakel auf, 
was er im ersteren Falle, bei der in Abb. 1. im Zool. Anz. darge- 
stellten Form, augenscheinlich nicht tut. Halten wir auch in diesem 
Falle den gleichen Vorgang ein, so wäre hier der Laterallobus mit 
2 Tentakelpaaren ausgestattet. Was ist also richtig? 

Es ist wohl zweifellos, dass in beiden Fällen ein und dieselbe 
Tornarien-Form vorlag, da sie ja von demselben Autor an derselben 
Lokalität in verschiedenen Jahren beobachtet wurde. Doch ist dieselbe 
ungenau beschrieben. : 


Tornaria Sibogae SPENGEL. 
(Tornaria Spengeli). 


Grösse: Höhe 2,5—3 mon. 

Grösste Breite im Wimperring 2 mm. 

Aussere Merkmale: Dorsale und ventrale obere Loben mit circa 
20 Tentakeln besetzt. 

Hoher schmaler Ventralsattel. 

Tiefer enger tentakelloser unterer Laterallobus. 

(Unterer) Dorsallobus tentakellos und etwa doppelt so tief wie der 
Laterallobus. 


27 


Scheitelplatte quer verbreitert (?) 

Augen in typischer Lage zwischen dorsaler und ventraler Area. 

Analfeld : etwas vorgewölbt. 

Innere Organe: Darm: Magen langgestreckt, erheblich seitlich 
zusammengedriickt. (Schrumpfung ?) 

Coelom : Die Rumpfcoelome liegen nicht dem Epithel des Wimper- 
rings an, sondern sind dem Darm sehr gendhert, wo dicht über thnen 
die Kragencoelome sich befinden. Beide Paare sind schon so weit 
entwickelt, dass sie auf der dorsalen wie der ventralen Seite nicht 
mehr weit von einander entfernt sind. Das muskulöse Eichelcoelom 
geht nach hinten in einen rechten Blindsack aus, während sich der 
entsprechende linke Teil in die unpaare Eichelpforte mit dem Porus 
fortsetzt. 

Entwicklung: nur eine Entwicklungsstufe bekannt (etwa einer 
älteren Zornaria Krohnit entsprechend). 

Fundort: Siboga-Stationen 144, 165, 185, sämmtlieh im Gebiet 
der Molukken, etwa zwischen Damar und Mysol. 

Bemerkung : Das Material, welches Spence. vorlag, war in Formol 
conserviert und mangelhaft erhalten. Daher seine unsicheren Angaben 
über die Augen, Scheitelplatte, Darm, daher konnte den Abbildungen 
(9, p. 123, fig. S, T, U) nicht ein einzelnes Exemplar zugrunde 
gelegt werden, sondern dieselben sind „schematische Ansichten nach 
mittels Zeichenapparat entworfenen Skizzen”. 


Willeys Tornaria von New Britain. 
(Tornaria Willeyi). 


Grosse: ? [Ausser der Angabe, dass die Figuren bei 12 facher 
Vergrösserung gezeichnet sind, wird nichts darüber bemerkt |. 

Aussere Merkmale: Obere dorsale Loben mit circa 24, obere 
ventrale Loben mit circa 18 Tentakeln besetzt. 

Ventralsattel sehr niedrig, flach. 

Laterallobus breit mit circa 10 Tentakeln besetzt, unterer Dorsal- 
lobus eine schmale tentakellose. Rinne (>). 

Ventralband (spätere Kragenregion) sehr breit. 

Circulärer grosser Wimperkranz verhältnismässig klein. 

Scheitelplatte? Analfeld mässig vorgewölbt. 

Augen legen nicht in typischer Lage, sondern wnerhalb der ven- 
tralen Area. (?) 
' Innere Organe: Darm sehr klein und schmal, Eichelcoelom sehr 
gross, muskulös, Eichelporus tief gelegen. 
_ Coelome ? 


28 


Herzblase /\ förmig. 

Sporne ? 

Entwicklung: nur 1 Stadium bekannt. 

Fundort: Blanche Bay and off the small coral islands (Pigeon 
Island), New Britain. 

Bemerkung: Von Wurer’s Tornaria liegt eigentlich keine Beschrei- 
bung vor, sondern die wesentlichen Merkmale — soweit dieselben 
von Wirrey festgestellt wurden — sind nur aus seiner sehr ober- 
flächlichen Vergleichung mit der Tornaria Grenacheri SPENGELS und 
aus seinen 4 Abbildungen fig. 7, p. 286 zu erkennen. 

„Among the external points of difference between my Tornaria 
and the 7. grenacheri figured by SpeNeeL may be mentioned those 
connected with the position of the eyes and the inferior dorsal lobe 
of the ciliated band. (Textfig. 4). In my Tornaria there is no such 
sharply defined lobe, but a groove passes continuously round from 
the lateral lobe of the ciliated band across the dorsal middle line. 
This groove is overhung by the anterior body of the Tornaria and 
appears in fresh surface view as a little more than a line. In 
Moraans Tornaria the dorsal edge of the lateral lobe is entire there 
being no inferior dorsal lobe proceeding from it”. 

Das ist WiLLEy’s ganze Beschreibung”. 

Der Verlauf der Wimperschnur wäre also ganz anders wie bei 
allen übrigen Tornarien, worauf SPENGEL bereits aufmerksam gemacht 
hat (9, p. 125). Während die Wimperschnur bei allen bekannten 
Tornarien continuirlich ist, wäre der Verlauf desselben bei der 
Wirrer’schen Tornaria unterbrochen. „Ich muss daher annehmen’”’, 
schreibt SPeNGEL (l.e.) „dass Winrey’s Beschreibung in diesem für 
die Charakterisierung einer Tornaria wichtigen Punkte ungenau ist.” 
Ich stimine SPENGEL darin vollkommen bei und bin der Meinung, 
dass der abweichende Befund Wirrer’s nur auf einen Beobachtungs- 
feller zurückzuführen ist. 

Was die Augen betrifft, so schreibt Winey in der Figurenerkla- 
rung: „The eyes in (tig. D) are seen to lie within the limits of the 
ventral area bordered by the ciliated band. In other species they 
tend to lie centrally between the dorsal and ventral area.” Dies 
stimmt allerdings fiir seine Figur D, betrachten wir jedoch seine Figuren 
A und B so sind in denselben die Augen ganz typisch am Apex 
eingezeichnet, je ein Auge zu beiden Seiten des das Eichelcoelom 
mit der Scheitelplatte verbindenden elastischen Stranges (am) wie 
bei allen übrigen Tornarien. Ich muss daher Witney’s Angaben 
betreffs der Augen gleichfalls fiir unsicher halten, ebenso seine 
Bemerkung betreffs des Pericards (,,note its /\-shape’’). 


29 


In Warrey’s Beschreibung sind endlich Angaben über die Grosse 
und die Coelome nicht enthalten, sowie die 4 Figuren augenschein- 
lich in verschiedenen Maasstabe gezeichnet. 

Im ganzen also eine sehr ungenaue Beschreibung, die sehr wesent- 
liche Merkmale unberücksichtigt lässt und sicher unrichtige Angaben 
enthalt. 

Dennoch scheint hier eine von der Vornaria Sibogae SPENGEL’s 
verschiedene Form vorzuliegen, da sie sich von ihr durch den sehr 
niedrigen Ventralsattel, die tiefe lage des Hichelporus, und den mit 
10 Tentakeln besetzten Laterallobus unterscheidet (Spanext). Ich fiige 
noch bei, dass bei Tornaria Wirreyr das Praeoralfeld viel breiter, 
der ecirculäre primaire Wimperkranz verhältnissmässig viel schwächer 
ausgebildet, das Analfeld und der Magen viel kleiner ist. Ferner 
liegt der Hydroporus bei Tornaria Wurevr links, bei 7. Szbogae 
rechts von der Herzblase; die Herzblase ist bei 7. Sibogae rundlich, 
bei Wi.iey’s Form hat sie die Gestalt eines /\. 


Weldons Kleine Tornaria von Bimini Island 
(Bahamas Bank). 


Moreans ,,Bimine’ Tornaria. 
(Tornaria Weldoni). 


Grüsse: Klein, etwas mehr als halb so gross wie die ,, Bahamas” 
Tornaria Moreans (nach der Abbildung Taf. I. fig. 3). 


Aussere Merkmale: obere dorsale Loben mit 5, ventrale Loben mit 
6 kurzen Tentakeln besetzt. 

Untere Dorsalloben ? 

Lateralloben breit, tentakellos. 

Ventralsattel niedrig, ziemlich brett. 

Ventralband nicht sehr breit. 

Analfeld jlach. 

Secundärer Wimperring ? 

Scheitelplatte? Verlauf der Wimperschniire nicht wie bei der grossen 
Bahamas Tornaria sondern mehr wie bei der New England Tornaria, 
indem dieselben in der Region der Augen nicht parallel laufen, 
sondern convergieren und dort verschwinden. 

Innere Organe: 3 teiliger Darm. 

Rumpf- und Kragencoelome dem Darm anliegend. Wassersack gut 
ausgebildet, mit der Apikalplatte durch einen contractilen Faden 
verbunden, durch den Eichelporus nach aussen miindend. 

Entwicklung: Von dieser kleinen Tornaria sind ausser diesem, etwa 


30 


einer älteren Vornaria Krohnii entsprechendem Stadium Moraans, noch 
ältere Stadien durch Werrvon bekannt, die unmittelbar der Metamorphose 
vorangehen oder derselben bereits angehören. Ausser der geringen 
Grösse (0.8 mm. hoch, 0.4 mm. breit) zeigen diese älteren Stadien 
nichts characteristisches, fiir diese Form besonders eigentiimliches. 

Fundort: Bimini Island, Bahamas, [| Aruba, Saba |. 

Bemerkung: Die obigen Angaben beruhen grössten Teils auf der 
schönen Abbildung Morgans (4, Taf. I, fig. 12), denn er beschreibt 
die Bimini Tornaria nicht, sondern hebt nur ihre Unterschiede 
gegenüber die viel grösseren Bahamas Tornaria hervor. Im allge- 
meinen haben beide Formen denselben Habitus. Die Tornaria Wel- 
dont ist jedoch viel kleiner, hat einen etwas anderen Verlauf des 
Wimperkranzes (?), geringere Anzahl von Tentakelchen, kürzere 
Tentakelchen, eine anders gebaute Apikalplatte, tentakellose Lateral- 
loben und dem Darm anliegende Coelome. 

Bezüglich des Verlaufes der Wimperschnur schreibt Morean 
(p. 25) folgendes: „The course followed by the anterior ciliated 
band differs from the Bahamas Tornaria in these respects: The lower 
horizontal limb of the anterior band does not turn forward at the middle 
of the side of the larva but continues toward the dorsal! surface. 
Before reaching the mid-dorsal line it turns back again (on each 
side) to follow a parallel line as far as the middle of the side of 
the larva. Then it turns forward along the middle lateral area. The 
course of the band after this follows the path characteristic for 
Tornaria”’. 

Ich bin mir nicht recht klar darüber geworden, was mit dieser 
Beschreibung gemeint ist. Ich glaube dieselbe so zu verstehen, dass 
Moraans Bimini-Tornaria ziemlich lange untere Dorsalloben besitzen 
soll — was aus der Abbildung der in Seitenansicht dargestellten 
Larve nicht ersichtlich ist — die bei der Bahamas-Tornaria fehlen. 

Gegenüber der Beschreibung Morgans ergeben sich bei meinen 
Tornarien Weldoni von Saba und Aruba folgende Unterschiede: 

1. Untere Dorsalloben sehr tief (vielleicht entfallt dies). 

2. Ventralsattel hoch. 

3. Analfeld vorgewölbt. 

4. Secundärer circulärer Wimperring. 

5. Bau der Scheitelplatte. 

Trotz dieser Abweichungen beider Formen von einander halte 
ich dieselben doch fiir identisch. 

Von der ebenfalls kleinen Zornaria ritteri unterscheidet sich die 
Tornaria Weldoni dureh die ganz andere Körperform, die flache 
Analscheibe, den tentakellosen Laterallobus und das starke Pigment. 


31 


Weldons grosse Tornaria von Nassau, New Providence. Bahama Bank. 
Moreans Bahamas Tornaria von North Bimini, Bahamas. 
Id Al . ‘ 
(Tornaria Morgan). 


Grösse: Höhe 4—4'/, mm. [jüngstes Stadium 1'/, mm. hoch, 
etwas weniger breit|. 

Aussere Merkmale: obere dorsale und ventrale Loben mit circa 
25 Tentakeln besetzt. 

Ventralsattel nicht hoch. 

Kein unterer dorsaler Lobus vorhanden. Laterallobus tief, mit ca 
10 Tentakeln besetzt. 

Analfeld eine ganz flache Scheibe. Secundärer Wimperkranz nur 
auf Schnitten nachweisbar. 

Apicalplatte: ‚In the apical plate the anterior ciliated band breaks 
into four free ends, not united across from right to left and those 
on one side running parallel to one another’. 

Augen compliciert gebaut. 

Pigmentflecke in der circumoralen Area im Schwinden (bei jün- 
geren Stadien stark ausgebildet). 

Innere Organe: 3 teiliger Darm, relativ klein, Magen schmal. 

Wassersack gross, mit Hydroporus, durch elastischen Strang mit 
Apicalplatte verbunden. 

Coelome: Rumpf- und Kragencoelome nur auf Schnitten gesehen, 
stets entfernt vom Darm, in der Nähe des circulären Wimperkranzes 
oder des Ektoderms. Sporne gross. 

Entwicklung: ältere Stadien der Metamorphose von WELDon, 
jüngere Stadien mit ca. 8 Tentakeln ohne Coelom bis einschliesslich 
der Metamorphose von Morean beobachtet. 

Fundort: Bimini, Nassau, Bahamas, (Aruba, Saba) Die Tornaria 
Morgani von Aruba und Saba unterscheidet sich von der typischen 
T. Morgani durch folgende Merkmale : 

1. durch die Grösse, (5—6 mm). 

2. Tentakel etwas linger, etwas geringer an Zahl. 

3. Ventralsattel hoch und schmal. 

4. Analfeld nicht so hoch. 


C. Geographische Verbreitung der tentaculaten Tornarien. 


SPENGEL, der allerdings, mit einigem Zweifel, simmtliche tentacu- 
late Tornarien fiir einer einzigen Art angehörig betrachtet hat (38, p. 
379), — ein Irrtum, den er später selbst zugegeben hat (im Sibo- 
gawerk 9, p. 124) —, schreibt ihnen circumterrane Verbreitung zu. 
Nachdem sich jedoch unter denselben eine ganze Anzahl wohl cha- 


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33 


rakterisierter Arten unterscheiden lässt, erweist sich diese Annahme 
als irrtiimlich und mit der Unrichtigkeit der Praemissen sind natiir- 
lich auch die Schlussfolgerungen und Combinationen, die VANHOFFEN 
an die angebliche circumterrane Verbreitung der einen Tornaria 
species gekniipft hat, gegenstandslos geworden. (7, p. 86, sowie 
Naturw. Wochenschr. Bd. XII, N°. 51, S 618). Nehmen wir die 
beiden tentakulaten Tornarien von der Westafrikanischen Kiiste und 
den Gewässern von Ceylon, über die wir ausser einigen Andeutungen 
SPENGELS fast gar nichts näheres wissen, als tatsächlich existierend 
an, so ergibt sich, dass alle tentaculaten Tornarien nur in den war- 
men tropischen oder subtropischen Meeren vorkommen. Nur aus dem 
romanischen Mittelmeer sind bisher keine tentaculaten Tornarien 
bekannt geworden. Auch in den kalten Meeren sind tentaculate 
Formen nicht nachgewiesen. Die tentacnlaten Tornarien sind aiso 
echte Warmwasserformen, die im Litoral aller warmen Meere ihr 
Verbreitungsgebiet haben. 


D. Verwandtschaft der tentaculaten Tornarien unter einander. 


Von keiner einzigen tentaculaten Tornaria lässt sich zur Zeit mit 
Sicherheit angeben, zu welchem erwachsenen Tiere sie gehört. Da 
überdies die Mehrzahl der Tornarienspecies nur unvollkommen 
bekannt ist, kann man vorläufig über verwandtschaftliche Beziehun- 
gen derselben untereinander nur wenig sagen. Fiir die Beurteilung 
der Verwandschaft sind die Coelomverhältnisse von ausschlaggeben- 
der Bedeutung. In dieser Hinsicht können unter den tentaculaten 
Tornarien zwei Gruppen unterschieden werden: solche mit dem 
Darm anliegendem Coelom und solche bei denen dasselbe weit ent- 
fernt vom Darme peripher am Wimperring oder dem Ektoderm 
anliegend ausgebildet ist. 

Zur ersteren Gruppe gehören Tornarta Spengeli und Weldont, zur 2. 
Gruppe 7. Chierchiat und Morgan. Die übrigen Formen lassen sich 
vorläufig noch nicht in diese Gruppen einteilen, da die Coelom- 
-verhiltnisse bei ihnen nicht näher bekannt sind. 

Die verschiedene Lage der Coelomsickehen in beiden Fallen macht 
eine verschiedene Entstehungsweise derselben wahrscheinlich. 

Bei 7. Spengeli und Weldoni, welche die Coelomsäckchen in ganz 
gleicher Lage haben wie die Tornaria Krohnit des Mittelmeeres, diirften 
dieselben auch in gleicher Weise entstehen, nämlich durch Abselinii- 
rung von dem Darme. 

Bei 7. Morgani und Chierchiai ist dagegen die Entstehung der 
Coelomsiackehen aus Mesenchymzellen anzunehmen. 

3 


Proceedings Royal Acad. Amsterdam. Vol. XXIII. 


34 


In der ersten Gruppe entstehen die Coelomsäekehen entodermal, 
bei der zweiten sind sie mesenchymatischen Ursprungs. 

Tornaria Morgant und Chierchiat, welche auch in anderen Merk- 
malen mit einander iibereinstimmen, sind jedenfalls nahe verwandte 
Formen. 

Weiteres lässt sich vorläufig über die Verwandschaft der tenta- 
culaten Tornarien untereinander nicht sagen. 


7 


Für die Ueberlassung der schönen, vortrefflich conservierten Plank- 
tonproben erlaube ich mir H. Prof. Dr. Max Weser meinen besten 
Dank zu sagen. Herrn Universitätszeichner Arorr Kasper, Wien, 
der die Abbildungen nach meinen Skizzen und Angaben an Hand 
des Originalmateriales ausfiihrte, sage ich auch an dieser Stelle 
meinen besten Dank. 


IV. Replik auf einige Bemerkungen SPENGELS. 


Ich beniitze diese Gelegenheit, um auf einige Bemerkungen SPEN- 
GELS, enthalten in seinem Referat (16, p. 55—57) über meine vor- 
läufige Mitteilung (13), zuriickzukommen. 

Zunächst erklärt sich Spenern mit den von mir gebrauchten 
Bezeichnungen, ,,Zornaria Miilleri-Stadium” und ,, Tormaria Krohnit- 
Stadium” an Stelle seiner ,, Tornaria Miiller’”’ und ,, Tornaria Krohn’ 
nicht einverstanden, in dem sich seine Bezeichnungen auf ,,die voll 
entwickelten pelagischen Larven”, nicht auf ,,Durchgangsstadien” 
beziehen. Ferner sei für Tornaria Miillert die Tatsache charakteris- 
tisch, dass ,,ibr Wimperapparat auf dieser Stufe stehen bleibt und 
keine Seeundär- und keine Lateralloben bildet, wie es bei Tornaria 
Krohnii geschieht, die eben in ihrem fertigen Stadium von der 
fertigen 7. Mülleri verschieden ist”. 

Demgegenüber muss ich neuerdings erklären, dass ich meine 
Bezeichnungsweise aufrechthalte. 

Die adriatische Pornaria Miilleri und Krohnit gehören in den 
Entwicklungskreis eines Tieres, des Balanoglossus clavigerus, was 
ich durch Züehtung nachgewiesen habe (14, 15). Nach SPENGEL 
gehört die Neapler Vornaria Miilleri und die Tornaria Krohni nicht 
in den Entwicklungskreis desselben, sondern zweier verschiedener 
Enteropneusten. Nun habe ich aber durch Vergleich der Gra- 
denser und Neapler Larven mit grosser Wahrscheinlichkeit feststel- 
len können, dass sie identisch sind. 

Die von Spence, behauptete geringere Entwicklung der Secundar- 
loben bei der adriatischen Form kommt gegeniiber der weit gehenden 


35 

Uebereinstimmung in anatomischer Hinsicht, (vergl. meine Ausfith- 
rungen (15, p. 281/281)) wohl kaum als specifisches Unterscheidungs- 
merkmal in Betracht. Dass der Gradenser Balanoglossus eine von 
clavigerus verschiedene Art ist, wäre ja möglich, ist aber noch zu 
beweisen. Aus der Identität der adriatischen und Neapler Tornarien 
ergibt sich als logische Consequenz, dass auch die Neapler Formen 
zu einander gehören u. z. zu Balanoglossus clavigerus, der ja gleich- 
falls in der Umgebung Neapels nachgewiesen ist. 

Ausser Balanoglossus (Ptychodera) clavigerus ist von Neapel und 
Umgebung nur Ptychodera minuta Kow. bekannt, die wahrscheinlich 
die von SpeNemL als Tornaria dubia beschriebene Larve hat. Es 
sprechen also alle Umstände fiir meine Auffassung. 

Die übrigen Bemängelungen Sprneerssind von geringerer Wichtigkeit. 

Es ist richtig, dass die Bezeichnung des analen Teiles der Tornaria 
durch mich als „rückwärtig”’ zu beanstanden ist. Aber auch MorGAN 
spricht wiederholt in gleichem Sinne von ,,backwards” und es ist 
fraglich, ob die von SpencEL gewählte Bezeichnung ,,unterer’’, ,,oberer” 
Teil passender und klarer ist. Jedenfalls dürfte doch jeder Leser wissen, 
welche Körperpartie gemeint war und das ist doch die Hauptsache. 

Dass die erste Coelomanlage richtiger als ,,Kragen-Rumpfeoelom” zu 
bezeichnen wäre, da sich die Kragencoelome von derselben abschnüren, 
während ich die erste Coelomanlage als ,,Rumpfcoelom” bezeichnet 
habe, gebe ich ohne weiteres zu. 


Leiden, Ende April 1920. 


LITERATUUR VERZEICHNIS. 


1. 1887. WerpoNn W. F. R., Preliminary note on a Balanoglossus-Larva from 
the Bahamas. Proceedings Roy. Soc. London. Vol. XLII. 

2. 1891. Mora@an, T. H., The growth and development of Tornaria. Journal of 
Morphology, Boston, Vol. V. 

3. 1893. SpPENGEL, I. W., Die Enteropneusten des Golfes von Neapel, Fauna 
und Flora des Golfes v. Neapei. 18. Monographie, Berlin 
- 4, 1894. Moraan T. H, The development of Balanoglossus. Journ. of Morphol., 
Boston, Vol. IX. 

5. 1894. Rirrer Wu. E., On a new Balanoglossus Larva from the coast of 
California and its possession of an endostyle. Zool. Anz. XVII. Jahrg. Leipzig. 

6. 1899. WittEy ARTHUR, Zoological Results. 16. Enteropneusta from the South 
Pacific, with notes on the west Indian species, Cambridge. 

7. 1903. VANHÖFFEN Ernst, Die craspedoten Medusen der deutschen Tiefsee 
Expedition 1898—1899. [. Trachymedusen. 

8. 1904. Rirrer Wu. E., and B. M. Davis, Studies on the ecology, morphology 
and speciology of the young of some enteropneusta of Western North America. 
Univ. Calif. Publ. Zool. Vol. 1. 

: 3% 


36 


9. 1907. Spenaet I. W., Studien über die Enteropneusten der Siboga Expedition. 
26. Monogr. Leiden. 

10. 1911. Hensen Victor. Das Leben im Ozean nach Zählung seiner Bewohner. 
Ergeb. d. Planktonexp. Bd. V. O. Kiel, Leipzig. 

11. 1911. Srrasny Gusrav, Ueber adriatische Tornaria- und Actinotrocha- 
Larven. Sitz. Ber. Akad. Wien. 120. Bd. Wien. 

12. 1913. SpeneeL I. W., Enteropneusta. In: Handwörterb. der Naturwissen- 
schaften. 3. Bd. Jena. 

13. 1913. Sriasyy Gustav, Studien über die Entwicklung von Balanoglossus 
clavigerus D. Ch. (Vorläufige Mitteilung). Zool. Anz. 42. Bd. Leipzig. ; 

14. 1914. ——, Studien über die Entwicklung der Balanoglossus clavigerus 
Delle Chiaje. I. Die Entwicklung der Tornaria. Zeitschr. f. wiss. Zool. 110. Bd. 
Leipzig. 

15. 1914. ——, Studien über die Entwicklung des Balanoglossus clavigerus Delle 
Chiaje Il. Darstellung der weiteren Entwicklung bis zur Metamorphose. Mitt. Zool. 
Stat. Neapel 22. Bd. NO. 8. Berlin. ; 

16. 1915. Spencer I. W., Referat über die unter 13. erwibnte Arbeit. Zentralbl. 
f. Zoologie Bd. 5. Leipzig u. Berlin. 7 


TAFELERKLARUNG. 


Tafel I. stellt Entwicklungsstadien von Tornaria Weldoni dar. 
Tafel I, stellt Entwicklungsstadien von Tornaria Morgani dar. 


Die einzelnen Figuren werden im Texte erläutert. 


TORNARIA WE 


Proc. Royal Acad. Amsterdam Vol. 


_G. STIASNY: WEBER WESTINDISCHE TORNARIEN | Tar. H. 
TORNARIA MORGANI. 


Proc. Royal Acad. Amsterdam Vol. XXIII 


Zoology. — “Bemerkungen itber einige Stinyetierschiidel von Sardinien.” 
By Dr. H. O. Antonius. (Communicated by Prof. J. F. van 
BEMMELEN). 


(Communicated at the meeting of June 26, 1920). 


Das Zoologische Laboratorium der Universität Groningen bezog 
im Jahre 1911 durch einen Herrn GrRTANNER eine Serie von 
Säugetierschädeln aus Sardinien, die z. t. Haustieren, z. t. aber wilden 
Formen angehören. Die ersteren sollen in anderem Zusammenhang 
gewürdigt werden, über drei der letzteren aber möchte ich in 
folgendem einige Bemerkungen machen, weil sie mir besonderes 
Interesse zu verdienen scheinen. 

Handelt es sich bei ihnen doch um jene merkwürdigen Formen, 
die durch ihre geringe, hinter jener der festländischen Verwandten 
weit zurückbleibende Grösse die Aufmerksamkeit seit langem auf 
sich gezogen und viel zu der Entstehung der Schlagworte, „Insel- 
zwerg, Inselkiimmerer”’ u.s. w. beigetragen haben. Zwei der Schädel 
gehören dem Rothirsche (Cervus elaphus corsicanus Erxl.), einer 
einem zwerghaften Individuum des europäischen Wildschweines 
(Sus scrofa L.) an. Ich gebe in den nebenstehenden Tabellen die 
wichtigsten Masse aller drei Schädel, neben jenen des Schweines 
— aus weiter unten ersichtlichen Griinden — auch noch die eines 
indischen Wildschweinschädels der Vittatus-Gruppe. 

Für die Hirsche stand mir zur Zeit der Untersuchung kein 
Schadel eines erwachsenen festländischen Verwandten zur Verfügung, 
so dass ich auf direkte Massvergleichung verzichten muss. Immerhin 
fällt gegenüber dem Typus des mitteleuropäischen Rothirsches, wie 
er mir durch frühere Untersuchungen an rezentem und prähistori- 
schem Materiale sehr geläufig ist, sofort die viel geringere Grösse 
auf, die jene eines starken Damhirsches nicht viel übertrifft, weiterhin 
aber auch gewisse Abweichungen in den Proportionen. Die Schädel 
sind nicht nur im ganzen kleiner, sondern namentlich im Facialteile 
viel kürzer, während die Breitendimensionen, insbesondere jene des 
Cranialteiles, von der allgemeinen Verkleinerung viel weniger betroffen 
erscheinen. Mit anderen Worten: sie entfernen sich in ihrem morpho- 
logischen Bild bedeutend weniger vom juvenilen Schädel, als solche 
der grossen europäischen Rothirschrassen oder gar solche der ost- 
europäisch-vorderasiatischen Marale: sie sind auf einem frühen 
Entwicklungsstadium stehen geblieben. Hievon abgesehen zeigen sie 


38 


keine besonderen morphologischen Verschiedenheiten. Caninen sind 
bei beiden Geschlechtern entwickelt, das Backenzalngebiss muss im 
Verhältnis zur geringen Gesamtgrösse sehr stark genannt werden, ist 
also von der allgemeinen Grössenreduktion nicht in gleichem Masse 
betroffen worden. 

Der Schweineschädel gehört einem weiblichen Individuum an, das 
jedenfalls erwachsen gewesen ist, denn der letzte Molar steht nahezu 
voll in Usur. Die Gesamtform, insbesondere aber die schräge Stellung 
des Hinterhauptes ist die gleiche wie beim gewöhnlichen mittel- 
europäischen Wildschwein, obwohl das Profil vor den Augen leicht 
konkav, die Stirnfläche über denselben aber in querer Richtung 
schwach konvex erscheint: offenbar auch eine Erinnerung an ein 
ontogenetisch friiheres Entwicklungsstadium. Ain interessantesten ist 
das Tränenbein, weil es ganz ausgesprochen den langen, niedrigen 
Typus des echten Sus scrofa zeigt und keinerlei Anklänge an die 
kürzere und höhere Form der Vittatus-Gruppe aufweist. Auch die 
verhältnismässig geringe Grösse und namentlich schmale Form des 
letzten Molaren ist ganz Scrofa-artig und verschieden von dem Typus 
des verglichenen Vittatus-Schädels. Die Backenzahnreihen liegen genau 
parallel, ohne also nach vorne zu divergieren, was ebenfalls einen 
gewissen Unterschied gegeniiber Sus vittatus ergibt. Die Eckzähne 
sind infolge des weiblichen Geschlechtes klein, die für das männliche 
Geschlecht charakteristischen Unterschiede zwischen Sus scrofa und 
vittatus daher nicht zu konstatieren. Es erweist sich also dieser 
Schädel als solcher eines Wildschweines der Sus scrofa-Gruppe, ohne 
irgendwelche Anklänge an Sus vittatus. Dies ist deshalb interessant, 
weil auf Sardinien zwei dem Schädelbau nach verschiedene Wild- 
schweintypen auftreten, eine gewöhnlich grössere von Scrofa-Habitus 
und eine kleinere mit engeren Beziehungen zu Sus vittatus. Der 
vorliegende Schädel beweist nun, dass auch die Scrofa-Rasse Sardiniens 
gelegentlich in ausgesprochenem Zwergwuchs auftritt. Das Vorkommen 
zweier verschiedener Wildschweine auf Sardinien glaubte noch 
C. Kerrer*) so auffassen zu müssen, dass nur die eine (Sus scrofa) 
ursprünglich wild, die andere dagegen aus entlaufenen Hausschweinen 
asiatischer Abstammung entstanden sei. Heute wissen wir durch die 
Untersuchungen S. Urmanskys ®), dass Wildschweine mit engeren 
Beziehungen zum indischen Sus vittatus viel weiter nach Westen 
verbreitet sind, als man friiher angenommen hatte: mindestens bis 
Bosnien. Wahrscheinlich sind die nordafrikanischen Wildschweine, 


}) Abstammung der ältesten Haustiere, Zürich 1902. 
2) Mitteilungen d. landwirtsch. Lehrkanzeln a. d. K. K. Hochsch. f. Bodenkultur, 
Wien 1913. 


—s 


39 


über die bisher bedauerlich wenig Untersuchungen vorliegen, auch 
nichts anderes als derartige Uebergangsformen zwischen Sus scrofa 
und dem eigentlichen Sus vittatus, wie sie ULMANsKy aus Bosnien 
nachgewiesen hat. Das Vorkommen zweier verschiedenen Typen auf 
dem immerhin kleinen Areal von Sardinien ist mit der Lage dieser 
Insel zwischen zwei Kontinenten leicht zu erklären : gelegentlich der 
ohne Zweifel wiederholt eingetretenen Landverbindungen konnten 
von Norden wie von Süden Formen einwandern. Zu ersteren gehören 
neben Sus serofa vor allem der Rothirseh und der Muflon, zu letzteren 
neben dem Vittatus-ähnlichen Wildschweine die sardinische Wildkatze. 

Die Untersuchung der vorstehend erwälinten zwerghaften Schädel 
war mir deshalb besonders interessant, weil sie mir Gelegenheit bot zu 
neuerlicher Beschäftigung mit der schon einmal von mir behandelten 
Frage der ,,insularen Zwergformen” unter den Säugetieren '). Hs ist 
ja eine in der modernen Zoologie weit verbreitete Ansicht, dass grosse 
Säugetiere auf Inseln kleinere Lokalrassen bilden, als solche das 
benachbarte Festland bewohnen. Leider konnte ich nicht feststellen, 
wer diese Ansicht zuerst geäussert hat; am schärfsten ausgedrückt 
wurde sie wohl von H. Simrotu, der in seiner ,,Pendulationstheorie”’ 
geradezu von einem „Gesetz der biologischen Abhängigkeit zwischen 
der Körpergrösse eines Tieres und des Areals, auf dem es lebt”, 
spricht. Ich habe schon vor Jahren betont, dass es ein solches Gesetz” 
m. E. nicht gibt, dass es vielmehr ein — allerdings menschlich 
durchaus begreiflicher — Beobachtungsfehler ist, wenn wir nach 
Prägung eines bestimmten Schlagwortes nur alle jene Fälle in 
unserem eigenen Bewusstsein registrieren, die ihm zu entsprechen 
scheinen, während die gegenteiligen uns gar nicht oder doch nur bei 
spezieller Beschäftigung mit der Frage zum Bewusstsein kommen. 
Ganz abgesehen von dem Verhalten der Reptilien und fluglosen Vögel, 
die bekanntlich gerade auf Inseln sehr grosse Formen erreicht haben, 
lassen sich auch unter den Säugetieren selbst so viele Fälle anführen, 
die dem fraglichen „Gesetz widersprechen, dass dieses fast ebensoviele 
-Ausnahmen aufweisen würde. Ich erinnere — um nur einige anzu- 
führen! — an die mächtigen Esel von Malta und Pantelleria, ein 
richtiges Gegenstiick zu dem Standardbeispiel der Shetlandponies, an 
den Riesenbären von Kadiak, die grösste Form der Braunbärengruppe, 
an den Canis antarcticus der Falklandsinseln, der seine festländischen 
Verwandten, die sogen. Azarafüchse, an Grösse weit übertrifft. Damit 
soll natürlich nicht das häutige Vorkommen von Zwergformen auch 
auf Inseln bestritten, sondern nur behauptet werden, dass sie ihre 


+) Verhandl. Zool. Bot. Gesellsch. Wien, 1913. 


40 


Entstehung nicht einem mehr oder minder mystischen ,,Naturgesetz’ 
verdanken, sondern genau den gleichen durchaus realen Umstanden 
wie auf dem Festlande: eine Verschlechterung der Lebensbedingungen 
wird auf dem Festlande ebenso zu einem Riickgang in der Grössen- 
entwieklung fiihren, wie auf einer Insel und dem Leben auf kleinen 
Inseln mag nur insoweit noch eine besondere Bedeutung für eine 
solche Grössenreduktion beizumessen sein, als es eine Abwanderung 
verhindert. Dieser Umstand kann eine Rolle gespielt haben bei der 
Entstehung der quartären Zwergelefanten in den Mittelmeerländern. 
Aber sogar in diesem Falle ist der Einfluss des Insellebens, so denkbar 
er an und fiir sich auch ware, nicht ganz sicher. Denn gerade auf 
Malta kam auch, wie Knochenfunde beweisen, der riesige Hlefas 
antiquus vor und das gegenseitige Altersverhältnis beider Typen auf 
der Insel seheint mir nicht über jeden Zweifel erhaben festgesetzt. 
Aber sei dem wie immer — für Hirsch und Wildschwein müssen 
wir jedenfalls andere Ursachen annehmen, die zu der auffälligen 
Grössenreduktion gefiihrt haben. Ich glaube, dass diese bei beiden 
Formen nicht auf ganz gleiche, aber doch auf alinliche Umstände 
zurückzuführen ist. 

Was zunächst den sardinischen Rothirsch anbetrifft, so ist es eine auffäl- 
lige Tatsache für jeden, ‘der nicht nut rezentes, sondern auch subfossiles 
Material untersucht, dass die ganze europäische Gruppe der Edelbirsche 
sich seit der Pfahlbauzeit in auffallendem Grössenrückgang befindet- 
Edelhirsche, wie sie Rurtimeyer') beschrieben hat, von der Grösse 
des Riesenhirsches oder eines starken Pferdes, sucht man heute auch 
in den besten ungarischen oder ostpreussischen Jagdrevieren vergebens, 
und in den ehemals kaiserlichen Gehegen in Niederösterreich erlegte 
noch Kaiser Josef II. (1780-1790) Hirsche, die die Grösse starker 
Wapitis erreicht, wenn nicht übertroffen haben, wie die erhaltenen 
Geweihe beweisen, während heute auch die stärksten Hirsche jener 
Gegenden weit hinter diesem Masse zurückbleiben. Je weiter nach 
Süden und Südwesten wir die Gruppe verfolgen, umso auffälliger 
wird dieser Riickgang: spanische und italienische Hirsche, die zur 
internationalen Jagdausstellung nach Wien gesandt wurden, also für 
ihre Heimat jedenfalls stark waren, nahmen sich neben dem Durch- 
schnitt ihrer mitteleuropäischen Verwandten wahrhaft kläglich aus! 
Auch der festländisch nordafrikanische Hirsch (C. elaphus barbarus 
Benn.) steht an Grosse hinter diesen weit zurück, obwohl er immerhin 
noeh grösser ist als der sardinische. 

Dass dieser allgemeine Grössenrückgang der europäischen Rothirsche 
seine Ursache in einer Verschlechterung der Lebensbedingungen haben 

1) Fauna der Pfahlbauten, Basel 1861, 


41 


muss, halte ich für sicher. Worin diese zu suchen ist, dafür gibt 
uns eben die auffallende Degeneration der südeuropäischen Hirsche 
einen Anhaltspunkt: es ist der Riickgang des europäischen Waldes 
in seiner urspriinglichen Form, der in Südeuropa fast ganz ver- 
schwunden, bezw. in Macchie verwandelt ist, während er in Mittel- 
europa nur sehr vereinzelt seinen alten Habitus bewahrt, meist aber 
in den des Kulturforstes geändert hat. Dass sich viele, aber nicht 
alle Hirsche von Korsika und Sardinien durch sehr kurze, stämmige 
Beine auszeichnen, diirfte eine Folge des Lebens auf steilem felsigen 
Terrain sein; jedenfalls trägt auch diese Higentiimlichkeit viel dazu 
bei, die Tiere kleiner erscheinen zu lassen. Im Gewichte diirfte 
zwischen einem Durchselnittshirsch von Sardinien und einem normalen 
Berberhirsch kein nennenswerter Unterschied sein. 

Aehnlich dürften die Ursachen gewesen sein, die zur Grössenreduktion 
der Schweine führten. Auch in diesem Falle haben wir einen allge- 
meinen Riickgang zu beobachten, aber er wird vielfach aufgehoben 
durch die Neigung der Wildschweine, einzelne Riesenindividuen 
hervorzubringen, ferner durch thre ausserordentlich rasche Reaktion 
auf Veränderung der Futterverhältnisse — eine Reaktion, die sich 
naturgemäss ebenso gut in allgemeiner Grössenzunahme als auch im 
Gegenteile äussern kann. Es ist eine in Wildschwein-reichen 
Gegenden jedem erfahrenen Jäger bekannte Tatsache, dass einige 
aufeinander folgende Jahre mit besseren Eichel-oder Buchel-Ernten 
auch eine Zunahme der Wildschweine an Zahl und Grosse hervorrufen. 
Wenn wir also die Zwerghaftigkeit des sardinischen Wildschweines 
in der Hauptsache auf die gleiche Ursache zurückzuführen haben 
werden, wie jene der Rothirsche, so mag nebenher auch noch die 
rasche Degeneration, mit der gerade die Schweine auf nahe Inzucht 
reagieren, mitgewirkt haben. Andrerseits wird durch die oben 
angeführte rasche Grössenzunahme bei besseren Futterverhaltmissen 
auch das gelegentliche Vorkommen einzelner grösserer Individuen 
erklärt, wie solche C. KerruuerR erwähnt. Interessant wäre es, über 
die geographische Verbreitung beider auf der Insel festgestellten 
Schweinetypen etwas zu erfahren. Hierüber könnten aber nur sorg- 
fältige systematische Aufsammlungen, wie sie bisher nicht vorliegen, 
Aufklärung bringen. 

Zusammenfassend wiederhole ich, dass wir m. E. weder den 
Rothirsch noch das Wildschwein von Sardinien kurzerhand als 
, Inselkiimmerer’, „Inselzwerg”’, u.s.w. erklären können, dass vielmehr 
bei beiden die vorhandene Grössenreduktion auf andere, mit der 
Isolation gar nicht oder nur sehr indirekt zusammenhangende Ursachen 
zurückzuführen ist. 


42 


Herrn Prof. J. F. van BEMMELEN bin ich fiir die Erlaubnis zur 
Untersuchung der Schädel zu Dank verpflichtet. 


TABELEE 1: 


Hirsche: .¢ Nr. XXVI der Sammlung, von Villagrande, Ogliastra, Sard., 7. IX, 1909. 
M; fast in voler Usur, Incisivgebiss vollstandig gewechselt, Gabelgeweih. 
2 Nr. XXV der Sammlung, von Arzana, Ogliastra, Sard., 11. VII. 1910. 

Ms; eben im Durchbruch, I, gewechselt. 


d Q 
Scheitel länge (von der Mitte der Hinterhauptschuppe zum 
Vorderrand der Pmx) 308 276 
Basilarlange 274 246 
Lange von der Mitte der Hinterhauptschuppe zum 
Hinterrand der Orbita 122 110 
Lange vom Vorderrand der Orbita zum Vorderrand der Pmx | 170 153 
» der Nasalnaht 95 83 
„ vom Gaumenrand zum Vorderrand der Pmx 178 158 
„ der Backenzahnreihe TOR a = 
„ vom vordersten Pm zum C 48 50 
„ des Lacrymale (obere Naht) 50 48 
„ der Orbita 45 41 
Hohen) 5 43 40 
Grösste Breite des Craniums 80 80 
5 8 an den Orbiten 130 118 
Breite an den Gehöröffnungen 88 80 
she GAN er 53 44 
Höhe des Foramen magnum 24 25 
Breite » A n 21 25 
Höhe des „Rosenstocks” (,,pedicel’”’) 28 a 
Umfang der „Rose” („burr”) ca 120 — 
Höhe der ,Stange” (,beam”) 367, 365 — 
„Auslage” (distance „tip to tip”) 3717 — 


aen tn ui a. 6 i ip 


43 


TABELLE 2. 
Schweine: 9, Nr. XLV der Sammlung, Gairo, Ogliastra, Sard., 12. VII. 08 
9, Nr. XLVII der Sammlung, annähernd gleichaltriger typischer Sus 


vittatus-Schädel aus Ostindien. 
LE al 


Sard. Ind. 
Basilarlange 235 268 
Profillange (Hinterhauptschuppe: Spitze der Nas.) 269 320 
Lange vom Hinterrand des Gaumens zum Vorderrand 
des Pmx 162 196 
Lange der Backenzahnreihe 90 110 
i. vom vordersten Pm zum Vorderrand d. Pmx 69 91 
é » Vorderrand der Orbita zum Vorderrandd.Pmx 172 208 
nd der Nasalia (Naht) 127 158 
Grösste Breite an den Jochbogen 114 136 
Breite der Hinterhauptschuppe 54 66 
Grösste Breite über den Orbiten 83 85 
Geringste „ 5 i es 62 61 
Breite am Hinterrand der Alveolen von M, | 39 39 
Fi » Vorderrand ,, 4, a PY 33 38 
Höhe vom Foramen magnum zur Hinterhauptschuppe 87 102 
» von der Spitze der Proc. jug. zur 9 128 150 
„ des Jochbogens 30 41 
» des Tränenbeins 20 26 
Lange „ st an der oberen Naht 48 46 
ze rs Dn nent Unterens 24 25 
Höhe des Foramen magnum 25 21 
Breite „ Pr A 19 22 
Lange des Unterkiefers vom Gelenk zur Spitze der 
Inc.-Alveole 209 237 
_ Hohe des Unterkiefers vom Gelenk zur Tischplatte 86 103 
Grösste Breite des Unterkiefers in der gegend des M, 71 88 
Lange der Backenzahnreihe 86 114 
» des M; im Oberkiefer 24 30 
Le hennen Unterkteter 26 38 
Breite „ „ „ Oberkiefer 15 21 
2 » yw » Unterkiefer 13 18 


Zoolog. Laboratorium der Universität. 
Groningen, Ende Juni 1920. 


Chemistry. — “Catalysis — Part VIL — Temperature Coefficient 
of Physiological processes’. By Dr. Ni Ratan Duar. (Com- 
municated by Prof. Ernst Conen). 


(Communicated at the meeting of May 29, 1920). 


In this article it is proposed to subject to critical examination the 
results obtained with regard to the effect of temperature on physio- 
logical processes. Before proceeding to the consideration of these 
reactions I shall briefly state the results obtained in the case of 
purely chemical reactions and then try to show how far these rela- 
tions are applicable to physiological changes. 

In homogeneous medium the following general results have been 
obtained. 

a. The higher the order of the reaction, the smaller is the coefficient 
of temperature, in other words, unimolecular reactions have higher 
temperature coefficients than polymolecular reactions under identical 
conditions. | 

6. The greater the velocity of a reaction the smaller is the temp- 
erature coefficient. . . 

c. The temperature coefficient of a positively catalysed reaction 
is smaller than that of the uncatalysed reaction and the greater the 
concentration of the catalyst the greater is the fall in the temperature 
coefficient. 

In the case of negative catalysis, a reaction which is catalysed 
(negatively), has a higher temperature coefficient than the uncatal- 
ysed reaction. In this case, the greater the concentration of the 
catalyst the greater is the increase in the temperature coefficient. 

In the case of heterogeneous reactions, the following points have 
been established : 

a. Diffusion is the guiding factor in the velocity of heterogeneous 
reactions. 

6. With heterogeneous catalysts which cause reaction between 
the substance in question to take place with practically infinite 
velocity, the actual rate of reaction will be determined solely with 
which the substance is diffused to the surface of the catalyst. 

c. If the heterogeneous velocity is that of the diffusion process, 
one will always get a unimolecular coefficient for the reaction in 
question, independent of the actual order of the more rapid chem- 


45 


ical reaction, which accompanies the diffusion process. Hence it 
is useless to try and determine the order of a heterogeneous 
reaction, from the velocity with which it proceeds. 

d. The temperature coefficients of heterogeneous reactions are 
small, (viz, about 1.2 for a 10° rise). 

In this connection it is interesting to note that photo-chemical 
reactions have small temperature coefficients (viz. about 1.1 for a 
10° rise). | 

Now I shall diseuss the results obtained in physiological proces- 
ses with regard to the influence of temperature on them. 

The relation between the temperature and the velocity of respir- 
ation has been studied during the last few years both for plants 
and animals. The principal object of these investigations has been 
to find out whether respiration can be considered as a chemical 
process. 

From the researches of CLAUSEN (Landwirt. Jahrbuch Bd. 19 1890), 
BrLACKMAN (Annals of Botany 1905, 19, 288), Kuprr (Rec. Trav. 
Bot. Néerl. 1910, 7, 181) LrHeNBAUER (Physilogical researches N°. 5, 
Avausr 1914), Miss Lerrscn (Annals of Botany January 1916), Miss 
SAUNDERS (private communication) and others we find that the 
temperature coefficients of plant processes generally lie between 2 
and 3 for a 10° rise of temperature. 

Brown and Worry (Proc. Roy. Soc. 1912, 85 B, 546) have 
shown that the temperature coefficient of the velocity of absorption 
of water by different seeds is about 2 for a 10° rise. If the values 
of the velocity coefficients are calculated from their results, we see 
that they follow the unimolecular formula. 

The researches of Vetny and Water (Proc. Roy. Soc. 1910, 
82 B) show that the ArrHeENius formula can be applied to the 
influence of temperature on the velocity of the action of drugs on 
muscles. 

Very large number of experiments have been made on the 
influence of temperature upon metabolism both in cold-blooded and 
in warm-blooded animals. But comparatively few of them have been 
made under standard conditions. In most cases animals have been 
free to move about and even in cases where they have been tied, 
muscular movements have not been prevented or muscular tone 
abolished. In these conditions a fundamental difference has been 
observed between the effects of temperature upon cold-blooded and 
upon warm-blooded animals. In cold blooded-animals the respiratory 
exchange almost always rises with increasing temperature, but 
generally irregularly and toa very different degree in different animals. 


46 


In the case of bees Marre PARHON (Ann. des Se. nat. Zoo. Sér., 
9, 9, 1—58) finds that the temperature in the cluster of bees inside 
the hives shows a very striking constancy throughout the year. 

In intact warm-blooded animals, a fall in the surrounding temp- 
erature regularly causes an increase in the respiratory exchange 
thanks to the mechanism of ‘Chemical heat regulation”. 

In all the experiments so far mentioned both on cold-blooded and 
on warm-blooded animals we have to do with two distinct effects 
of temperature, viz. one upon the central nervous system causing 
variation in the innervation of different organs and especially of the 
muscles and one upon the tissues themselves influencing the reaction 
velocity of the metabolic processes. 

In the warm-blooded animals the action of low temperature on 
the skin produces reflexly innervation of the muscles resulting either 
in movements or in increase of tone. 

In the cold-blooded animals the processes in the central nervous 
system | itself are probably acted upon, and increased muscular 
activity is produced by increasing temperature except in the cluster 
of bees which in the aggregate reacts against the temperature some- 
what after the fashion of a warm-blooded animal. 

When the influence of temperature on the metabolic process is 
to be studied, the nervous influence must be excluded, and the 
experiments must be made under standard conditions. 

It has been found repeatedly both on man and on animals that 
even a slight increase in body temperature over the normal produces 
an increase in the standard metabolism. 

It follows from the experiments of Kroc (Biochem. Zeit. 1914, 
62, 266) and others that the velocity of catabolic reactions increases 
in all animals with rising temperature up to a maximum at and 
above which temperature has deleterious effect upon the organism. 
The maximum temperature probably differs considerably for different 
animals, but very few determinations have been made so far. 

The more rigorously standard conditions are maintaind, the more 
regular is the influence of temperature observed. 

Crick and Martin (Journal of Physiol. 45, 40) find that the coag- 
ulation of haemoglobin by heat has the temperature coefficient 13.8 
for the elevation of 10°, whilst in the case of albumen it is higher. 
In this connection it is interesting to note that Von ScHRORDER (Zeit. 
Phys. Chem. 1903, 45, 75) has found that a solution of gelatine 
has a viscosity of 13.76 at 21° C. and 1.42 at 31° C. i. e. about 
10 times less with an elevation of 10°. 

The results obtained by Cuick and Martin show that the temper- 


Gan: _n — 


47 


ature coefficient of coagulation of proteins by water is an exceedingly 
high one compared with effect of temperature on most chemical 
reactions. In the majority of instances the reaction velocity is increased 
about 1.1 times for 1° C. i. e. 2 to 3 times for a rise of temperature 
of 10°. Even the biological processes of germination of seeds, respira- 
tion of plants and growth of bacteria fall within this range. 

On the other hand many reactions in which complex protein bodies 
are concerned have been shown to possess high temperature coefficients 
which are comparable with those obtained for heat coagulation. The 
destruction of emulsin by heat has according to TamMmann (Zeit. 
Phys. Chem. 1895) a temperature coefficient of about 7.14 for a 10° 
rise between 60° and 70°. Bavyriss (1908) found the action of 
trypsin to be hastened 5—3 times for some germs in accordance 
with a logarithmic law. Baitinev (1902) found the disinfection of 
anthrax spores by steam to take place from 9 to 11 times more 
quickly by raising the temperature 10° and the law of ARRHENIUS 
is equally applicable to his results. 

Cuick and Martin (loc. cit) have shown that the disinfection of 
vegetative forms of bacteria with phenol and other coal-tar derivatives 
has a temperature coefficient of 8 to 10 for a 10° rise of temperature. 

On the other hand the disinfection by Silver Nitrate and Mercurie 
Chloride has a much lower coefficient and that is about 2. 

The high temperature coefficient for the coagulation of egg albumen 
has a counterpart in that for the velocity of destruction by hot 
water of the haemolysins in vibriolysins, tetanolysin and goat serum. 

MapseN and his collaborators found the influence of temperature to 
be in accordance with the law of ARRHeNius and the velocity of 
this reaction to be doubled if the temperature were raised 1° C. 
They also showed that the action of hot water upon some agglutinins 
to be similarly influenced by temperature. 

This marked influence of temperature is extremely useful for men 
and animals. When a toxin enters the system, the temperature of 
the body rises by two or three degrees and we get the phenomenon 
of fever and the poison is destroyed about 10 or 20 times more 
quickly at this fever temperature. 

Hartrivgs (Jour. of Physiol. 1912, Vol. XLIV, 34) finds the temp- 
erature coefficient for heat coagulation to be as great as 726 for a 
10° rise for some protein matter. In this connection it is interesting 
to note that the decomposition of sulphur trioxide by heat has 419 
for its temperature coefficient for a 10° rise at about 30°. 

Watson (Jour. Hygiene 1908, 8, 536) applying Ostwatp’s isolation 
method to Miss Cuick’s results finds that in the disinfection of certain 


48 


bacteria with phenol, the molecules (MN) of phenol reacting with 
those of the bacterial constituent are in the proportion of 5.5 to 1. 
As regards the metallic salts the same law holds good for disinfee- 
tion by silver nitrate and the molecules (V) of silver nitrate reacting 
with those of bacterial constituents are in the proportion of 1:1. 
In the case of Mercurie chloride, however, the above relation between 
the concentration of disinfectant and the average velocity of disin- 
fection is maintained only if the former is expressed in terms of 
the corresponding concentration of mercuric ions. Under these cir- 
cumstances, MN has the value 4.9 for anthrax spores and 3.8 for 
paratyphosus. But the temperature coefficient of the disinfection by 
phenol is very high, though the reaction is approximately hepta- 
molecular. On the other hand, in the case of silver nitrate the 
reaction is approximately bimolecular and the temperature coefficient 
is small viz. 2 for a 10° rise. These results are contrary to our 
experience in ordinary chemical reactions, where the greater the 
order of a reaction the smaller is the coefficient of temperature. 

Kanitz (Temperature und Lebensvorgänge,, 1915), Snyper (Amer. 
Jour. of Physiol. 22, 1908, 309), Conen Sruart (Proc. K. Akad. 
Wetensch. Amsterdam, 1912, 20, 1270), Péirrer (Zeit. Allg. Physiol 
1914, 16, 617) and others have tried to represent the influence of 
temperature on physiological processes by the rule of van ’T Horr, 
but it is not very important whether the temperature coefficient has 
the value 2 or 3, the important point to establish is whether the 
formula of ArrueEntus (Zeit. Phys. Chem. 1889, 4, 226) or the formula 
of Harcourt and Esson (Phil. Trans series A Vol. 186, 817 (1895), 
Vol. 212, 187, (1912), which is applicable to ordinary chemical 
reactions, is also applicable to physiological processes. 

BrACKMAN (Annals of Botany 1905, 19, 281) has accepted the 
validity of the van ’t Horr rule and has found the value 2.1 between 
9° and 19°. He has assumed that this value of the temperature 
coefficient remains constant at higher temperatures; this assumption 
is contrary to our experience in ordinary chemical reactions, the 
temperature coefficient for a 10° rise becomes smaller as the temperature 
rises. This falling off of the temperature coefficient with increase of 
temperature is also expected from the Arruenius formula. Evidently 
the conclusions of BrACKMAN would have been more correct had he 
accepted the ARRHENIUS formula. 

Looking at the whole problem from a broad point of view it 
seems that temperature has two effects on vital processes: — (a) the 
increase of the velocity of the chemical reaction involved in the 
physiological changes, (b) the destruction of the living cells. 


49 


At low temperatures the first effect is predominant since the harmful 
effect does not begin to play its part. 

Thus the problem for us is to investigate the effect of temperature 
on vital processes at low temperatures that is, before the harmful 
effect on the living cells has begun and we shall probably see the 
same quantitative laws which are applicable in the domain of ordinary 
chemical reactions im vitro are also applicable to vital processes 
taking place in nature. 

Enzymes and colloids reign supreme in life processes and the 
BROWNIAN movement of these particles does away with the diffusion 
layer characteristic of heterogeneous reactions and makes them analogous 
to positively catalysed reactions taking place in homogeneous medium 
and hence we expect to find the same laws governing both ordinary 
chemical reactions and life processes, compare Drar, Proc. Akad. 
Wetensch. (1919). 

In conclusion I suggest that it is desirable to study the problem 
of acclimatization scientifically from the point of view of the influence 
of temperature on life processes. 


SUM A ROY: 


a. Physiological processes take place mostly in heterogeneous 
medium. The Brownian movement of the colloidal particles present 
in the reacting substances does away with the diffusion layer 
characteristic of heterogeneous reactions and makes the physiological 
reactions similar to positively catalysed reactions taking place in 
homogeneous medium. Consequently the temperature coefficients of 
physiological processes instead of being small (Viz. about 1.2) are 
generally greater than 2 for a 10° rise. 

6. The spontaneous destruction of certain toxins is highly influenced 
by temperature and this fact is extremely useful to the human body 
because in the phenomenon of fever the poison is killed very rapidly. 

c. Before the destructive effect of temperature begins to set in, 
the ARRHENIUS formula connecting temperature and velocity is generally 
applicable to physiological processes. 


Chemical Laboratory, Muir Central college, 
Allahabad (India). 


Proceedings Royal Acad. Amsterdam. Vol. X XIII. 


Chemistry. — “Sur une classe de fonctions admettant une dérivée 
seconde généralisée’. By Prof. Arnaup DenJov. 


(Communicated at the meeting at May 29, 1920). 


Considérons une série trigonometrique partout convergente 


SO) =a,d A, 4,4 ---+ 404+...) ne 
ou A, = an cos nO + b, sin nO; a,, dy, 6, étant indépendants 
de 4. Soit B, = — b„ cos nO + a, sin nd. Intégrons terme a terme 
la série (1), et posons: 


B,, 
POB tt Braden es ae 


en tout point 6 où la série du second membre converge. Aux points 
où cette série diverge, nous dirons que p (6) n'existe pas. C'est 
quelconque, indépendant de 4. Intégrant une fois de plus, nous trouvons: 


An 
POE + 00+ C—4,—... == 
n 
C' étant, comme C, indépendant de 6. 
RieEMANN a montré que la fonction continue #(0)admet 7 (@) pour 
dérivée seconde généralisée, c'est-à-dire que, si 
F(O + u) + F(O—u) — 2 F(A) 


u* 


R (0, u) = 


on a f (0) = lim R (Gu), quel que soit 9 indépendant de w. 
u—0 

Nous nous proposons dans cette note d’étudier les propriétés dif- 
férentielles du premier ordre de la fonetion / (6). Il est bien connu 
que, si # (A) possède au point 0, une dérivée #' (O,), la série (2) 
converge au même point et l’on a g (6,) = FH” (6,). La réciproque 
est exacte. Donec, p (0) et la dérivée de / existent ou non simulta- 
nément, et coincident chaque fois qu'elles existent. 

Posons 

F(O +) — F(0) 


u 


O.(G, 4) = 


On montre que: 
Q|9, (1,0 ae C +- B, . + =) 


tend vers O avee wu, si 2 wu) reste compris entre deux nombres 


51 


positifs indépendants de u. Les propriétés différentielles du premier 
ordre de F(A) et le mode de convergence ou de divergence de la 
série (2) sont ainsi étroitement liés. 

n étant choisi comme il vient d’étre dit, la différence 


: B. 
Q10 + wnt] — (4+ COHB +...4—) 
tend aussi vers O avec wu, uniformeément dans le champ: O quelconque, 


1 , : 
u, A, = bornes. Enfin, si p, + p, +....—-+ p, = 0, l'expression 


Po QIO, ul +p, QIO Hu, wy dj ul +... + pr Qld + ure, Au] 
tend wniformément vers O avec w dans le champ: @ quelconque, 
r r , pales | 
ee lp eS tip: | Salo). 2 
0 0 0 old: | 
tous bornés (u, — 0, 4, = 1). 
lia demonstration se fait en remarquant que, si Wa,’ + 6,7 = o,, 
on tend vers 0, d’apres la convergence de la série (1). Done, si 
g(m) wi (n) 
on m* n i 
les coefficients w (7), w' (7), w" (n) tendent vers O quand n croit. 


On a: 


> ¢(n) =n 0) . Emp (m) =n’ w'(n) , 


Am (O + u) = An (0) cos mu + B,, (0) sin mu. 
D'où 
An [O + (2+) vl — An [0 + u] = A (0) |cos mp HA u —cos mu ul + 
+ B(6) [sin m (u + 2) u — sin mu ul. 
Si m <n, nous transformons les coefficients de A, (0) et B, (0) 
par les eni 


(@—«) 


cos B — cos a= are iat <1 


sin B — sin a = (3 — a) k age af = ap “| (OO 


Si m>n, nous remplacons les mémes coefficients par 20, 2)’ 
mee 0. 0 <1. 

Les résultats énoncés paraissent alors en évidence. aye leur forme 
Peis simple’ (p, = — p, = 15, p, = 0, p, =. = 0), la propriété 
que Q[O,ul— Q[6, ul tend wniformément vers O avec u, dans le 


] , ki \ 
champ: 4 queleonque, à et 5 bornes, donne lieu a la remarque 


suivante. 


4* 


52 


Soit d un nombre dérivé (extreme ou médian)*) de F' au point 0. 
Il existe alors une suite de nombres de même signe h,, h,,...., hn,.... 
tendant vers O et tels que: tm Q[6,h,|=d. Soit « un nombre 


n @ 
superieur a 1, aussi grand que nous le voudrons, indépendant 
de n. Considérons ensemble £ forme des intervalles 7, et 7, ainsi 


ee ee ; Arles 
détinis: %, est l'intervalle 6 + | à 0 Halh,l; 7, est Vintervalle 
a 
: | Aen | ae : „ek 
6—«a|h,| a 0 — . 6 est évidemment un point limite de ZL. 
a 


Or, quelle que soit la facon dont un point t—= 0 + h tende vers 0 
sans quitter 4, Q[O,h] tend vers d. 

Nous disons alors que /'(6) admet au point 6 une dérivée spéciale 
a H, egale a d. 

La propriété étant exacte quel que soit « invariable, il est possible 
de choisir « croissant indéfiniment avec n, assez lentement pour que 
la propriété subsiste sur l'ensemble Hu ainsi obtenu. Done, 

Si d est un nombre dérivé extréme ou médian de EF (0), d est la 
derivée de F'(@) speciale à un ensemble Ea dont lépaisseur supérieure 
au point 6 est 1 bilateralement *). 


hy, . , . 
Supposons que le rapport — — soit borné indépendamment de n 
Un 41 


Ny 
(mais non de 4). Alors, si 1 < | “+ 
in 


< |, choisissons a >V J, et 


1) On appelle nombre dérivé de F l'une quelconque des valeurs limites d de 
F (0 + u) — F(A) 
u 
demeurant fixe. d est un nombre dérivé droit si uw > 0, gauche si u < 0. d est 
un dérivé extreme, soit supérieur, soit infériewr, si d est Pune des limites extrémes, 
soit la plus grande, soit la plus petite, de Q(6,w) quand w tend vers 0, avec un 

signe déterminé. 

Tout nombre compris entre les dérivés extremes de #’ pour un côté donné, est 
appelé nombre dérivé médian pour le même côté. 

2) Soit m(x) la mesure de la partie d'un ensemble donné / comprise entre un 
point fixe a et un point queleonque x. m (x) a le signe de x -a, à moins d'être 
nul. On appelle épaisseur supérieure droite, épaisseur inférieure droite, epaisseur 
supcrieure gauche, épaisseur inférieure gauche de EF en un point 2%, les nombres 
dérivés de même qualification respective de la fonction m(x) en x). Ges nombres 
dérivés appartiennent au segment (0,1), (c'est à dire à l'ensemble des nombres « 
tels que O<u <1). On dit que EF possède en Xp) une épaisseur (sous-entendu 
bilatérale) ou une épaisseur droite, ou une épaisseur gauche égales à A en 2%, Si 
m(xc) admet en x le nombre A respectivement pour dérivée (ordinaire, bilatérale) 
ou pour derivée droite ou pour dérivée gauche. On sait que les points de H ot ZE 
n'a pas lépaisseur 1 forment un ensemble de mesure nulle LEBESGUE). 


=(Q(6,u) quand w tend vers O avec un signe invariable, 6 


53 


construisons comme il a été dit plus haut les intervalles ¢,, 4 
Quelque soit », in et 7,41 Ont une partie commune, et il en est de 
même de 7', et de #41. ensemble / formé des 7, et des /'„ contient 
tout Vintervalle 0 — a lh,| à O + a lh,|, sauf le point 4. Done 


/ 
+ 


F(6) admet d pour dérivee (ordinaire, ou générale) aw point U. 


En nous placant a un autre point de vue, il nous sera possible 
d’étendre et de préciser les propriétés connues de l'ensemble # où 
existe gp (6). 

Considérons la courbe I représentant géométriquement #'(6). 6 est 
porté en abscisse, (0) en ordonnée. Soit M le point (7,/). Pour 
une valeur déterminée de 4, la fonction FR (4,u) est continue en w, 
quel que soit w, pourvu que lon pose hk (4,0) = / (0). Soit w (0) le 
maximum de | & (6,w)| pour toutes les valeurs de u. D'après 
Q[O, ul — Q[O, —u] 

, 


u 


(Or 


nous avons, quel que soit u: 


|Q(G, u) —Q(O, — u) | CA) |u|. 


U 1 
Oo O+K, O+A- <A, 6+H-24. 


FIG, 2 


Done les points M' et M" d’abscisses respectives 6 + wet 4 — u sont 
sensiblement alignés avec le point M. Les deux droites MM', MM' 
ont des pentes d’autant plus voisines lune de l'autre que |u| est 
plus petit (Fig. 1). 

Done de la position de M' d’abscisse 6 + u, nous déduirons avec 
une certaine approximation connue, la position de J/' d’abscisse 6 — u. 
Sur laxe des 4, nous pouvons considérer 6 — uw comme l'image de 
04u par rapport au point 6, regardé comme réfléchissant. JZ" 
est sensiblement le symétrique de J’ par rapport a M. 

Considérons maintenant deux points M et M, de la courbe I, 
ayant pour abscisses 0,0 Jk. Soit A un nombre supérieur a 


54 


w(A) et à w(O +k). Désignons par J/, un autre point de la courbe, 
et soit 6+ k son abscisse. 

Formons sur l’axe des Ó, les images du point 6 + 4, par une 
succession de réflexions alternées sur les points-miroirs (0, 4 + &,). 
Nous obtenons, selon que la premiere reflexion a lieu sur 9 ou sur 
0 + k,, deux suites de points-images: | 

0 —k, OLEL 2k, Ohh, Ok ae 
et 
O—k+2k,, Otk—2k, AO—k+4k, A+k—4kh,,... 

Les points représentatifs de /# pour ces deux suites d’abscisses, 
seront, avec une certaine approximation que notre objet est d’étudier, 
1° dans le premier cas, le symétrique MW’ de M, par rapport a M, 
puis le symétrique M" de M’ par rapport a M,, puis le symétrique 
de M" par rapport a M,, et ainsi de suite, 2° dans le second cas, 
le symétrique M’, de M, par rapport a M,, puis le symétrique JZ", 
de M’, par rapport a M, ete. 

Dans ce qui suit, nous ne restreindrons pas la portée de nos 


conclusions en considérant uniquement les points-images déduits de 


6+ par un nombre pair de reflexions sur le couple (6,4 + 4). 
Ces points-images ont pour abscisses des nombres en progression 
arithmétique de raison 2k,, formant la suite 0 4 4+ 2mk,, m etant 
un entier de signe quelconque. Un tel point-image est obtenu par 
m| réflexions doubles de 4 4% surle couple (0,0 + £,), la première 
réflexion se faisant sur 6 ou sur 0 + k,, selon que m est positif ou 
négatif. Exprimons les ordonnées des points de la courbe TI corres- 
pondant aux points-images: 0 + Jk + 2mk,. 

Nous avons par hypothèse, quel que soit u: 
F(O 4u) + F(@—u) = 2 F(A) + dA? dk 
F(O@—uj + FO4+2k4+y)=2F(O+4h) + oA(lu dk) dd" <1 

D'où: 
F (94 u]—F[0 + 2k, + u]=— 2[F(O+k,) —FO)] + dA [+ (uth) 

Supposons d’abord mm positif. Donnons a wu successivement les 
valeurs k,k + 2h,,...,4 +2(m—1)&,. Il vient: 

F [OH] — F(O42mk, +h = — 2m[F (6 +k) — F(O] + dAu, 
avec 

wk? H(k HA) +... [e+ (2m — 1k]. 

Supposons m négatif et égal a —m’. Dans la relation précédente, 
nous remplacons m par m’ et & par & — 2m’k,. Il vient: 

F (0+k) — F (042mk, +h) = — 2m [F (0 +k) — FCO] + A0, 
avec 

w, = (k—k)? +... + (k + Qmk,)*. 


55 


Les deux formules coincident independamment de 7, sauf par 
les coefficients w et w‚. Si m=O, on a w=w, = 0. 
Nous écrivons ainsi la relation générale: 
FO+H—F(0) FO + 2mk, +h —F(O) mk, +h 
k nie 2m k, SE rear a f 


PO +h) — FO -2mk, © 
k 


| 


k, k 
w’ étant w ou w, selon que m est positif ou negatif. Posons 
k + 2m k, =! 
k' — 2m k, 
7 — u, TL ns, 
Il vient: 


QIO k= QT + QIO ke + dA. 


Soit =r suppose au moins égal a 1, et es défini par 


1 


k 
1} 0. 
k 
Nous choisirons l'image k’ d’abord de maniere que u soit positif 
et » non négatif. D'après u + »—1, cette condition sera 
0< en Hi 


Done m a le signe de —e, si m #0, et en outre 2)m)< r. Done, 


sie=+1, — r2m<0, w'=w, =k? |(1— =) bot (1+ amy [eine 


(fa 


| 2m—1\? 
Sie 11,7 >2m>0, wom I +(1-*)}+. -(1 ) |eeme 
r 


7 


Done, dans tous les cas, 


6AM peut être remplacé par 2dmk4. 


La substitution est exacte même pour m= 0. 

La condition u >> 0, montre que k’ et & sont de même signe. Parmi 
toutes les images 0+ k + 2mk, de 6 + k, situées du même côté de 
0 que 6+ k, choisissons celle qui, sans être intérieure a l'intervalle 
0 —k,, 0 +k, est la plus voisine de 6. 

Nous appellerons ce point 0 +k’ Pimage-réduite propre a 0 
du point 0 + par rapport au couple (9, 6+ 4,). La distance de 
deux images consécutives obtenue par une suite de réflexions doubles 
sur le couple (6, 0 +k) étant 2k,, k’ verifie les conditions 


56 


[ASR I< 3 
/ 


qui, jointes aux formules 4’ =k + 2mh, et a la condition — > 0, 


k, | 


déterminent completement 4’. En effet, soit p l’entier non négatit 
déterminé par les conditions 
2p +1<r< 2p-+ 3. 
Net ki 
D’apres Een eravec & =1, me < Oet r > 2lm|, on a: en =r-2|m|. 
1 1 
D'où 1 <r—2|m| <3 et enfin lm) = p,m = — pe. 
0 4 hk’ étant lVimage-reduite caractérisée comme il est dit, nous 
ie k 
trouvons finalement, en utilisant 2 [| Lr El la formule: 
1 


k: 
QO HD =O kut Qk)» + dn A WANEN 


avec 0? <1, si teed d= 0.61 £ Se 


ath: 


k 
Il est essentiel de noter que 0c u= mn O<», utr 


propriétés et la formule (4) seraient conservées si £° était remplacé par l'un 
quelconque des termes de la série £ + 2 qk, compris entre k et £’. Mais il 


/ 


est essentiel pour la suite, que le rapport soit compris entre deux 


k 
G 
nombres positifs fixes. J] nous sera commode d’avoir choisi pour 
jouer ce role les nombres 1 et 3. 

Considérons maintenant une suite h,, /,,...,4,,... de nombres de 
signes queleonques, décroissant en modules et tendant vers 0, tels 
enfin que p[@-+h,|< A, A étant indépendant de n, avec en outre 
w (0) < A. 

Cette hypothèse sur les A, ne serait d’ailleurs pas rigoureusement 
indispensable pour valider le raisonnement et la conclusion ci-apres. 

En effet, désignons par w{@,1] le maximum de |& (9, «| pour 
ju! <4, O demeurant fixe. Le raisonnement subsiste alors moyennant 
la simple hypothèse 


ww [Ó SE Anti, 3 [An |] A, 

Soit h un nombre dont la valeur absolue est au moins égalea A, 
Soit A/ Vimage-réduite, propre a 6, du point @+ / par rapport 
au couple (0,0 + h,). On a: 

he 
Q[O, h] = Q{O, HIN + QIO hl, + us A 
1 


avec 


57 


Te ay are oe ae ae eg ET oP a 
Transformons de même Q[6,h’| et Q[O,h‚l grace a V+ h,. 
Soient respectivement 9+ h’’ et 0 Jh’, les images-réduites 

propres a 6, des points 6+’, 0 +h, par rapport au couple 
(0,0 + h,). On a: 


ji 
QI, A) = QIO "Ie" + QIO le" + OA 
be 


pe 
Q[d, h,| = Q [9, hi] u, zi Q [Ó, hl Ds =F dn A 


avec 
0 a a", u : 0 < pl, v a" ae ES a at v ae 
Done 
bi = ae : hist 
Q[A,h| = Q[A,h"] A" + QO, AIA, + Q[O, hl A, HJA EN + rh | 
1 3 
avec 
ea yA SA AND A pe, 
Done 


0< 2", ea. 0<a, eha Aes 
Entin d'après n° <9 h,?, 4’ +4, =1, le coefficient de 0 A peut 


bte h? he 
se remplacer a fortiori par 90 A | — + a 


JA] Il 
La méthode de transformation de Q[0,h| est évidente. Nous 
definissons la suite h, h’, h’’, … h®), … par cette condition que 


6+ A” est limage-réduite propre a 0 de@+h"—" par rapport 
au couple (9,0 + h,). De même, h‚® n’existant pas pour 7 < pet 
he) étant égal a A, par convention, la suite h,‚®, constituée de 
nombres de mêmes signes, sera définie, pour 2 > p, par la condi- 
tion que 9 +4 h," est limage-réduite propre a 6, de 9+/,"—") 
par rapport au couple (0,0 + h,). On aura des relations telles que 
les suivantes : 
| An | < | Ap) | << 3 | An |, 
quel que soit p< n; 
er) ig 


Q[0, hor] = Q[0, A] wp + QA, An] vp) +} DA 


hy 
avec 
OS® j OS Pi; Diens le, hh ij 
1 t 8, BREA , a” —1 
_ Le coefficient de Ò,m A peut a fortiori être remplacé par ae 
. tn 


Cette relation permet de justifier par récurrence la formule 
Q(0, h) = Q [9, hm] An) is 20 ii Q [9, hyo] ay”) | 200 t Q [0 ‘a hn| And | 
hl ne = (5) 


Pere. ena 


+904] 


58 


avec la condition qu’aucun des 2,” n’est négatif et que leur 
somme pour p=0,1...,m est 1. . 
[AC = 2), M= Jl. 


Utilisons maintenant la propriété de la convergence uniforme 
pro} 8 


if 
vers 0 de la différence Q[A,2u] — Q[O, u] quand 2 et + sont bornés, 


u tendant vers 0. 
Soit e(«) le maximum de la valeur absolue de cette différence, 
quand 1 < |A <3, lul <a, 9 queleonque. Alors, 
Q[0, AMM] = Q[O, ha] + dine [ | An |]. 
Les A, étant non négatifs, on a: 
SADE SENS 
Done 


QO, h|=Q [A hl 4de [nl] +90a[ 4... ped. . (6) 


Supposons que la série 


soit absolument convergente. 
n+1 


Nous allons déduire immédiatement de la formule (6) que Q[4, hl] 
tend vers une limite quand / tend vers 0. 
Soit en effet m lentier défini par 


| hm | <a | h | < | hig 4 |. 
Nous appliquons la formule (6) a la suite 2, hn, Ani, .- «> Pm: 
Dans le coefficient de 90 A, nous remplacons h? par h’,,_1, et nous 
2 


re: 
ajoutons tous les termes marquants de la serie er Nous obte- 
A” 


nons a fortiori: | 
je h,? 
Q (9, h] = Q(A hmty] + dell mtg |] +9 dA x at (7) 
Soit h’ un nombre quelconque inférieur en valeur absolue a h,,_; et q 
assez grand pour que |A, << |h’|. Nous trouvons, en faisant croitre q : 


De hes 
| Q[@, A) —Q(0,h)|<184 Ee. 
m—1 anti | 


Sous la seule condition: || et |h’| << |A). 

Done Q[6,h| tend vers une limite quand h tend vers 0. (4) 
possède une derivee au point 6. Soit p (@) sa valeur. Ona, en faisant 
croitre q indéfiniment dans la formule (7) pour |h| < 2a\h,). 


hh? oo hr? 
Q(0,1) = (0) + da] 7492 |. | 
on! m nt | 


2 
n 


/ inl 


En résumé, si |h,| tend vers O en deeroissant, si la serie 


a eee 


59 


Et + uw) + Flu) — 2F (db) 
ur : 

ou t= O+h, restent bornés pour toute valeur réelle de u et pour 

toute valeur entière de n (positif), sous ces conditions suf fisantes, 

F(O) possède une dérivée au point 9. 


est absolument convergente, si les nombres- 


hy 
Un cas particulier remarquable est celui où la suite Tae est bornee. 
Uut 
hn 


2, et si nous 
ht = < 


supprimons dans la suite les termes oe Ang, la nouvelle suite 


Soit 


<a, a étant indépendant de n. Si 


obtenue h,,’ satisfait a la condition 


< 2a. |h| étant compris 


En 
entre |h»—;| et ||, nous considérons ia Bute tims Vink. arty. Sb, 
conservant son premier terme, nous la réduisons de proche en proche, 
en y supprimant, au fur et a mesure que nous en rencontrons un 
dans la suite parcourue dans son ordre naturel, tout terme superieur 
en valeur absolue a la moitié du dernier terme conserve. 

Dans la suite restante, h, h',,h',...,h'4,... le rapport de chaque 
terme au suivant est inférieur en valeur absolue a 2 @. La série 


AN | 


——— est convergente, d'après: 
| Sere 
13 
ls a ECP 
|J n+1 | 
On a: 
- LOE ed < Za | hl fees Ses de ‘ 4 | 20e || 
IRA 1 ah = Ais SS 500 || = all, 
LA, | 1 Ant: | 2 2” 
Done, dans le cas où le rapport est inferieur en valeur ab- 
In +1 


solue à un nombre a indépendant de n, et où te rapport | R (t,u)) est 
borne par A quels que soient u reel et t=O+h, ou t=Ö, 
F(6) possède une dérivée ~p (A) au point 0, et on a la formule 


Q[O, h]—=p(0) + 20daAh, pour |h| << 2alh, |. (61) . . . (9) 


Mathematics. “Graphical Determination of the Moments of Transition 
of an Elastically Supported, Statically Indeterminate Beam’’. IL. 
By Prof. C. B. Biezeno. (Communicated by Prof. J. CARDINAAL). 


(Communicated at the meeting of December 29, 1917). 


12. In quite the same way as it has been attempted in § 8 to 
prepare a transition from the case of three points of support to that 
of four, it might now be tried to use the construction just found 
for the treatment of the beam on five points of support, by cutting 
it above its last point of support but one and charging it there by 
a moment of 0,1,2,... metretons. We are, however, arrested by 
two difficulties. In the first place the amount of drawing required 
becomes so extensive, that it is impossible to avoid mistakes. In 
the second place, however, an obstacle arises which has not yet 
been able to manifest itself in the case of the beam on three or 
four points of support. 

When the beam has been cut above the fourth point of support, 
it is among others necessary to construct a link-polygon for the left- 
hand part on four points of support after applying a moment of 
transition of one metreton above the last point of support. 

In the construction, however, of this link-polygon the beam on 
four points of support is again cut above the third point of support. 
Consequently this will be charged besides by the given forces acting 


Ì 
on ABC, by a force of, ton, directed upward and originating from 


the introduced unit couple Mp. 
Of course a similar thing happened in the case of the beam on 
four points of support above the second point of support. But there 


UL : 
the ascent 7 of the second point of support, due to the extra force, 


was known, because the remaining lefthand part of the beam was 
only supported at two points. Here the ascent of the third point of 
support is not known, as the unaltered lefthand part of the beam 
is itself statically indeterminate. 

And although it would of course be possible by the aid of $$ 3—7 
to determine the ascent which the righthand end of the beam ABC 
supported at three points, would be subject to in consequence of a 


61 


„force acting at this extremity, the execution of the required con- 
struction would only increase the difficulty mentioned at the begin- 
ning of this §. 

Yet all the auxiliaries for a fit construction of the elastic link- 
polygon of a beam on five or more points of support have been 
provided, as will appear from the following. 


13. Beam on more than four points of support. 

Let the beam on n points of support A, B. C,... U, V, W,- be 
given, and let it for the present be required to determine the descent 
and the inclination at the last point of support W, when the beam 
is successively charged at W by a unit force and a unit moment. 
Then the experience gained in the preceding $$ leads to the expec- 
tation that the quantities in question only depend upon the corre- 


sponding ones for the beam A, B, C,... U, V, i.e. upon the descent 
and the inclination which will appear at the last point of support 
of the beam A, 5,C,...U,V, when in V a unit force, resp. a 


unit moment, acts. 

Let us suppose these latter quantities, which may be indicated by 
To Pn—2, hs Gn—2, for a moment to be known, and let us attempt 
to derive from them the ys, Pa—1, OE Pea required. In deter- 
mining each of these quantities we might again use the introduction. 
of different moments of transition My above V. 

For each moment of transition My it would be necessary to 
determine the situation of the point W in two ways: 

1. by the aid of the equations of equilibrium of the field V W 
to the right, supposed to be free, by means of which a point W 
is found; . 

2. by means of an elastic link-polygon belonging to the beam 
A, B, C,... U, V, W, which gives a point W. 

If then the series of points W and W should appear to be similar, 
it would be possible to construct their double point, i.e. the extreme 
point of the link-polygon determining the required quantities. 

If the line of action described really causes y,—1, Pnr—1, Veer 
ie to be found, we must accordingly attempt to determine the 
corresponding quantities of the beam ABC...UV on (n—1) points 
of support. 

But this would be possible if under the same conditions of charge 
the inclination and descent were known for the beam ABC... UD 
on (2-2) points of support. 

On arguing further in this way, we are driven back to the beam 


62 


on two points of support, and it is therefore necessary first to find 
the quantities in question for this beam. 


14a. With a view to this let us consider the freely supported 
beam AB charged at its right end by a force of one ton (fig. 3a). 
The descent B Bt) =y, as well as the angle of inclination g, is 


Fig. 3a. 


Fig. 35. 
') In order to distinguish it from a moment of transition, a unit charge acting 
in a point of support B,C... is indicated by indices 17 or 1M placed under the 
letters B,C... according as it represents a force or a couple. 


63 


immediately known, as the point A remains in its place and AB 
remains straight. *) 


145. If the end B is charged by a moment of 1 metreton, the point 
A rises by an amount AA;y, while the point B descends by an 


amount 55. As the sides A17 3,,, and 3, B must cut a segment 
iM 1M 


of known length from /, the former, hence also the latter, is known. 
B 


Consequently the angle of inclination (7,) and the descent (y,) at 
B can also for this charge be found in a very simple way. 


15a. We can now proceed to the treatment of the beam ABC 
charged at its extremity C by 1 ton. 
If the beam is cut above B, the point C descends by an amount 


CC=u. The beam AB remains uncharged. The construction of 
017 


the elastic link-polygon furnishes therefore the straight line ALC; 
the point C coincides with C. 
017 
If then a moment of transition of 1 metreton is introduced at B, 


{ 
the point C rises by an amount C C= so that C is known. 
0,17 it by Cis i LP 
No more does the construction of C by the aid of the elastic 
i We 
link-polygon give rise to difficulties. The introduction of the moment 
of 1 metreton above B will cause the point of support B to des- 


= 1 
eend by an amount B B=y, + —y,, while the side III] B assu- 
re Ey Va? 


mes an angle of inclination Dy -+ ma 
The side III, B IV‚r (indicated in fig. 30 by the line P, B) 
tives gn 
can therefore be drawn, hence, also the side ,IV,7,C, since this side 


17 
together with III, ‚IV‚r must cut a segment of known length 
from /p. 
It is clear that the sides IIL, xIVi7 belonging to the different 
moments of transition J/g—.w metretons, pass through one fixed 


point P, on AB, because the descents of the point B as well as 
x 17" 


the angles of inclination of the side ,III, „IV‚r increase in propor- 


1) The angles of inclination 9 are replaced in the usual way by their tangents. 
These tangents are read in fig. 34 on perpendiculars drawn at distance one to 
the right of the different points of support. 


64 
tion to a. The series of points B" and ,1V;7 being moreover simi- 
ogi USE 


lar, also the joins B’ ,1Vir xC of corresponding points of these 
nei He 

series pass through one fixed point Q,, likewise situated on the 

line ABC. 


The series of points C and C are therefore similar. 
seal fe Sell: 
Their double point at finite distance supplies the point C, while 
a 


the line C Q, determines the angle of inclination in question. 
AWD 


155. Also in the case of a charge of 1 metreton at C the beam 
is cut above B. In this case, however, the elastic support of B is 


1 
charged by a force of 7 ton. Consequently the point B rises by an 


if ie 
amount > i and the beam AB assumes at 5 an angle of inclina- 


| 
tion EP If for ABC a link-polygon is drawn on the supposition 


M,z=0, the side III, IVi Vis (indicated in the diagram by 


BC"), hence also the side Vim C, is fixed. 
01M 01M 0,11 


— 1 
The point C, conjugated to C lies — below C. 
0,1M om L 


Now a second construction would be necessary for a moment of 
transition Mp==1 metretons in order to construct, in addition to 
the pair of points C, C just found, a second, which would make 

0,1 01M 


possible the determination of the double point of the series C and 
x1 M 


C. The situation of this double point, however, depends exclusively 
x1 ‘ 


Geul 
_ 01M 11M Gane 
upon the ratio “Gq, which in its turn only depends upon the 


01.7 11M 
situation of the centres of rotation that appear to exist for the 


sides IIx, xlViag and IVi, xVlijg and of which in the diagram 
only that of the sides ,1Via, xVlij has been indicated as Q’s 
According to the reasoning of § 7 however, these points must lie 
perpendicularly above the points P, and Q,. 
The ratio in question has therefore already been found (fig. 3a) 


Cee 

Ss foar 3 ’ Ar 

in the ratio “~~~. Hence the double point C, when once C and 
nel Op 1M 01M 


IE phy 


eS 


65 


~C are known, can immediately be determined as well as the corre- 
01M 


sponding point C”. 
1M 
The side .1Viy.Vl;,, must lie along the line joining this point to 


Q’,, so that the point .VI,y, can be constructed. Then .VI,y C can 
. 4M 


be drawn, by means of which y, and p,‚ are found. 


16. In quite the same way as Yar Var Par P, have been determined 


out of y,, 41, Pr, p, also Yar Yor Par Py CAN be bond out of y, ya, Par Py 
and in general 4, Uns Pn Pn Out of ys, Une Mii TR 

Any new quadruple of unknowns belonging to a following point 
of support, requires the drawing after a fixed precept of only six 
lines. 


Although for completeness’ sake the construction of the point C 
AM 


has been discussed, it will not be necessary to execute it in reality. 


For the theorem of Maxwerr teaches that y,=y,, so that C is 
LM 


directly determined. 


17. By the aid of the quantities y, p, y and gp, to be found accord- 
ing to the §§ 14 and 15, the construction of the elastic link-polygon 
of the arbitrarily charged beam can now be executed in the way 
as has been indicated in fig. 35 for a beam on 5 points of support. 

The charge is again applied in the middle of the fields, and 
amounts for the successive fields resp. to 3, 1'/,, 1'/, and 3 tons. 

First the descents A A, B B, CC... of the points of support are 


00 000 09 
determined which appear when the beam is cut above all the points 


of support. 
Then the point C is determined over which the beam ABC con- 


sidered as a al must pass. 
_ This point is determined exclusively by the aid of the link-polygon 
A’, C conjugating the point ie to the point C. For we can omit 


000 000 
the construction of the for aie: gon A’... B...C because itis only 
01 10 10 


used to determine two points C and C the situation of which gives 
100 100 


the ratio of the pieces into which the distance C C is divided by 
00 000 


the point in question C. This ratio, however, is already fixed in 
‚0 


5 
Proceedings Royal Acad. Amsterdam. Vol. XXIII. 


66 


TON 
fig. 3a by oe for a reason mentioned before. 
or uT 
In an analogous way by the aid of the link-polygon A. um vay D 


0 00 
the endpoint ne is determined for the beam ABCD onse as a 


whole. Of this polygon, belonging to the moment of transition 
Mc=0, the side Q", C VIII and therewith VIII D is determined. 


Os O7 0 0 0 .00 


The situation of the double point ee of the series of points D and 
yO 


D, which appear through the Hitesdheee of various moments of 

yO 

transition Mc and of which only the points D and D are known, 
00 „00 


DD 
is again found with the ratio ait which appeared already in 


Oli it 


fig. 3a. 
Finally Ë is determined by the aid of the link-polygon Q,” 2 Bie L, 


of which i extreme point E forms together wie a pair Ean 
„0 


of the series BE and #. The ratio in which the fra. E E must 
Z O38 


be divided by ine required point #, has also been found already in 


Br 
fig. 3a by the ratio == by the introduction of a moment of 1 
4) 1 
metreton above D. be 
The endpoint Z of the link-polygon in question is therefore fixed, 
so that no more is necessary than to construct the polygon itself. 


In the first place the side # XI can be drawn through Q',, then 
XIX D" through Q",, XIX through P,’ and IX VIII through D". 


The last side cuts with VIII VII from /g a piece of known length; 
hence VIII VII ean also be drawn. This side cuts dg," in a point 
Q,'", which enables us to determine the point P,’ through which 
the aie VII VI is to be drawn. 

While the supposition was made that no moment of transition 
existed in D, the sides VI VII and VII VIII on the introduction 
of various moments of transition Mc had to rotate round fixed points 
P and Q, which were determined as the intersections of the lines 
lp, and /g, with Q," C. But the moment of transition in D influ- 

‚0 


67 
ences the situation of the point C. According to § 15 this point 
0 


a Dees. 

rises by an amount C C=-—~y,, in consequence of which the line 
00 He a 

. . 4 


6) as which in absence of Mp contained the centres of rotation 


of the ‘tides VI VII and VII VIII, must be replaced by the line 
ie 4 Now the point Q,"" of en line is already determined as 


a 


the Becton of lg,” with the side VIII VII, so that P,', through 
which VII VI must pass, can be found as the intersection of Q," Q," 
with /p,. 

After VII VI we can draw VI V through C", V VI being again 


determined by the known segment which VI. V and V IV must 
cut from lp. 

Now V IV determines again on /g," a point Q,"" through which 
the line A’, Q,” can be drawn, which intersects /p, in the point 
P,’ of the side IV III. The completion of the link-polygon does not 


present any difficulties. 


" wm 


18. It appears from the preceding considerations, as was indeed 
already noted in § 2, that with the beam on five points of support 
the subject mentioned in the title of this paper has been treated 
generally, save for the restrictions made, that the fieldlengths of the 
beam as well as the coefficients of stiffness of the elastic supports 
are supposed to be equal. 

These restrictions, however, do not affect the general soundness 
of the construction. 

If for instance the fieldlengths AB and BC (fig. 1) were unequal, 
the sides II III and IV V would indeed not meet on /g, but at 
any rate on a perpendicular dividing the distance dr /rv into pieces 
which are inversely proportional to the fieldlengths AB and BC. 

Neither is the inequality of the coefficients of stiffness of the 
springs essential. If e.g. for the beam ABC with the fieldlengths 
AB=L, and BC=L, the coefficients of stiffness of the springs 
are a, 8, y, the extra descents of the springs which appear when 
the beam is cut above B in consequence of the introduction of a 


moment of transition of 1 metreton, will be oa te —+ 
sf 

; eee ft , | 

instead of EE oS = This alters indeed the values of the 


segments A’, A’, BB, ,C,C, but not essentially the construction 
0 1 


itself. 
5* 


68 


When the beam is not prismatic as was assumed in $ 1, but has 
a variable cross-section, the diagrams of bending moment can be 
reduced in the way already indicated by Monk. 


19. Lines of influence. 

By the aid of the construction given in the preceding $$ the lines 
of influence for the moments of transition of a statically indeter- 
minate elastically supported beam can now also be constructed 
graphically. In order to determine for instance the line of influence 
for the moment of transition above the pt point of support, we 
need only construct the elastic line giving the position of the beam 
on being cut above the p'' point of support and charged in the 
arising cross-section by a moment of transition of 1 metreton. For 
each of the pieces into which the beam is divided, the moments of 
transition — hence the diagram of bending moment — can be 
determined as described, after which the elastic line can be drawn in 
the known way. 


Chemistry. — On the determination of the configuration of cyclic 
cis and trans diols and the rearrangements of atoms and 
groups of atoms during chemical reactions’. By Prof. J. BöESEKEN 
and Car. van Loon. 


(Communicated at the meeting of June 28, 1919) 


In former communications in which the configuration of the 
hydrindene diols was discussed, we called attention to the fact that 
indene oxide, when being hydrated, may yield the cis diol as well as 
the trans diol. In the meantime we ascertained that the quantities 
formed of these diols depend on the reaction of the medium, the 
formation of the trans compound is favoured by alkaline media. 

Considering the probable situation of the atoms in indene oxide, 
the generation of trans diol deserves close attention ; one might expect 
the cis compound: 


OH OH 


H 
ip H 


Now it was of high importance to determine the configuration of 
the two diols with ful! certainty. Unfortunately the classic method, 
by testing the resolvability into optical antipodes, is of no avail 
here as both diols are asymmetric and consequently resolvable, so that 
another method had to be looked for. 

We have already proved that of the two diols only one increases 
the conductivity of boric acid and we have deemed ourselves justified 
in assigning to this diol the cis configuration — rightly, as will be 
proved below. 

[Here I may take it to be known, that the increase of the acid 
properties of boric acid by a number of substances, is due to the 
formation of complex dissociable compounds ; these are formed especially 
if two hydroxy] groups are situated “favourably” in regard to boric acid. | 

As this sole argument depends on the efficiency of the boric acid 
method, it called for a confirmation which could be given by our 
investigation on the cyclapentane diols. 


70 


For here we can verify the boric acid method by the classic one, 
as only the trans diol is not identical with its mirror image and 
consequently resolvable into optical antipodes. 


We shall not enter here into details about the preparation of these 
diols; suffice it to state, that the one diol was prepared by hydrating 
cyclopentene oxide, while the other was obtained from cyclopentene 
by oxydation with KMnQ,. 

The properties of the diols are as follows: 


m. p. of the | m. p. of the 
mp. bp. diphenyl di-p. nitro- 
urethane benzoate. 


C;H,(OH), from C5Hg andKMnO,| 29°—-30°.| 123.9°/29 205° 117°—118° 
C;H,(OH), from C;HgO and H20 54°.5—55° | 136°/21.5 P54 a 145° 


| 

In order to establish with certainty which of these two glycols 
was the cis and which the trans diol, they were treated with /-menthyl- 
isocyanate, in doing which the first one produced one single di-l- 
menthyl-urethane, while the highmelting diol yielded a mixture of 
di-l-menthylurethanes differing very much as regards rotatory power. 


Without isolating and saponifying these urethanes, we can draw the 


conclusion that here the urethanes of the trans diol were formed viz 
d-trans-cyclopentane-diol-di-l-menthyl-urethane and Ltrans-cyclopentane- 
diol-l-menthyl-urethane. 

From this however one must not conclude without further conside- 
ration that the diol with the higher melting point was in fact the 
trans diol. During the reaction of l-menthylisocyanate a sort of Walden 
inversion might have taken place 

However acloser inspection renders this improbable in a high degree. 

As we set forth in our last communication such an inversion is 
only to be expected when the reaction takes place at the atom which 
governs the configuration. 

This is not the case here: 

= C—O—H + RNCO = C—O —CO 
rs * 
RNH 
as the reaction takes place by detaching the O—H-linkage and so 
the typical C-atom is left alone’). 


1) It is for this reason that we have not applied other methods for the resolution 
into optical antipodes (c.q. esterification with active acids), because then the entire 
OH-group may be eliminated, in which case the C-atom determining the asymmetry 
is attached. 


—_—— pen 


71 


We may therefore conclude with great certainty that the isomer 
with the higher melting point is the trans diol, the one with the 
lower melting point the cis diol. 


Then the conduct of the two diols in relation to boric acid was studied. 

In effect it was found that the cis diol considerably augmented 
the conductivity of boric acid while the trans diol caused a small 
depreciation. 

The boric acid method therefore proves to yield a positive result 
only in the case of the OH-groups being situated near to each other. 

So now we can say with complete certainty that hydrindene diol 
(see former communication) m.p. 108°, which increases the conductivity 
of borie acid, is cis-hydrindene diol, while the one with the high 
melting point (159°) is the trans isomer without any doubt. The last 
substance exercises a small decrease of conductivity of borie acid. 

By a communication of E. Fiscnrr (B. 28, 1146, 2496 (1895) on 


the ready formation of cyclic additional compounds of polyaleohols 
with aldehydes and ketones, one of us (Cur. vAN Loon.) has been 


incited tostart an investigation about the conduct of these stereoisomeric 
diols in regard to acetone. . 
Here five- (or six) membered rings are formed of the following type : 


-—C—O 

| CCH). 
Bs ple ea 

Though not certain, it is however highly probable that with this 
condensation the decisive C-atoms are left alone so that here too a 
rearrangement in the sense of the WatLbDEN inversion is out of the 
question. 

With surprising ease the expected condensation product was formed 
from cis hydrindene diol as well as from cis cyclopentane diol, while 
the trans-compounds under the same circumstances [the diols were 
set apart for 24 hours with a twenty-fold quantity of pure acetone 
containing 1"/, HCl] reinained absolutely unchanged. 

We immediately made use of this method to have the configuration 
of the cyclohexane diols fixed. 


These two compounds were obtained 

1. by the action of potassium hydroxide on cyclohexene iodhydrin 
according to Brune, during which action the oxide may be regarded 
as an intermediate product. — This diol melting at 104° was taken 
for the cis diol by Bruner, because it originated from the oxide. 


72 


2. by oxidation of cyclohexene with KMnO,, by which a compound 
is formed melting at 99° and which was taken for the trans diol. 

However as this last compound according to experiments executed 
by H. G. Derx, quantitatively yielded an acetone compound, we must 
assign to it the cis configuration ; the diol, melting at 104°, did not react. 

Curiously enough both exercise a small negative influence on the 
conductivity of boric acid, so that in this case the acetone method 
is more reliable than the boric acid method. 

We must however observe that the classic method, based on the 
action of an active isocyanate has not yet been applied. 


So with the eyclopentane diols the configuration has been determined 
in three ways entirely independent of each other; the reliability of 
the borie acid method has been greatly exhanced by this. A close 
study will have to be made of the acetone method. It has the great 
advantage of quickly leading to the purpose; however its drawback 
is, that under the influence of the condensation reagent (HCI) inversions 
are not impossible. 

The determination of the configuration of the cyclic 1-2-diols has 
brought to light the remarkable fact that by the addition of water 
to the oxides not only the expected cis diol is formed, but besides 
and sometimes exclusively the trans-isomer. 

Therefore, if the oxide has a configuration in which the oxygen 
atom lies ontside the plane of the cyclopentane ring, which configu- 
ration in regard to the distribution of matter is the most probable 
one, then the opening of the three-membered ring must have been 
accompanied by an inversion. 

It is remarkable that this inversion with the symmetrical oxides 
of cyclopentene and cyclohexene is almost complete and that under 
all circumstances; on the other side with the asymmetrical indene 
oxide the inversion is dependent on the reaction of the medium. 

A very weak alkaline reaction reduces the quantity of cis diol, 
which is the principal product in acid medium, to zero. 

Attention may be drawn to the fact, that with the reaction in 
alkaline medium, 8 hydrindone (or a condensation product there-of) 
is always formed, so that the alkali seems to loosen the a-CO-linking. 


Indeenoxyd B-hydrindon 


73 


As exactly in this case trans diol is formed and a Walden inversion 
cannot otherwise take place but at the atom which determines the 
stereoisomerism, it is very probable that the change of the configuration 
takes place at the a-C-atom. 


A second observation may finally be made about the oxidation 
of cyclopentene and cyclohexene by KMnO,. Thereby, principally at 
least, the cis diols appear to be formed. From this it follows that 
the oxides cannot be the intermediate products, as these would pass 
into trans diols under the circumstances of the experiment. 


Perhaps the favoured production of ‘the cis diols by KMnO, is 
related to the formation of complex compounds of trivalent manganese. 
For on the one side it appeared that oxidation of oxalic acid by 
KMnO, also commences with the formation of these manganese 
compounds, while on the other side it was found that the «-hydroxy- 
acids are very liable to forming complex manganese compounds. In 
these compounds the hydroxyl groups are favourably situated, as 
was shown by the determination of the conductivity of mixtures 
with boric acid. Then we should have to admit here that the possibility 
of the formation of these complex compounds with cis-diols would 
exercise an influence leading to their production. 

However in that case a tendency to further oxidation of the cis 
diols is to be anticipated, just as the w-hydroxy acids are easily 
attached by mangani hydroxide. 

This would then explain the very poor yields not surpassing 20°/, : 
a closer examination however will have to clear up this matter. 


Chemistry. — “On some Condensation-products of Aromatic Alde- 
hydes and Amines.” By Prof. F. M. Jageur. 


(Communicated at the meeting of May 29, 1920). 


$ 1. Although, according to Hantzscn’s and Werner’s theoretical 
views, the existence of stereoisomeric forms should be possible in the 
case of condensation-products of aromatic aldehydes and amines of 
‘the type: R,—CH = N—R,, yet it had appeared impossible during 
a long time to find with certainty’) cases of such isomerism with 
these so-called “bases of Scuirr’. In 1906, however, ANSELMINO”) 
described some eases, where substances of this kind were met with 
in two different crystalline modifications, which at the same time 
appeared to be strongly different in colour, being red and yellow. 
The author concluded from his investigations that no true 
dimorphism in the common sense of the word was present here, 
but that rather a chemical #somerism had to be supposed. The 
arguments brought to the fore by him for demonstrating that neither 
enantiotropic, nor monotropic relations whatsoever between the 
crystalforms of the red and yellow modifications of o-oxy-m-methyl 
benzylidene-aniline should be present, can, however, in our opinion 
hardly be estimated to be convincing. It seems notwithstanding this 
to be true, that the deviating chemical character of the yellow and 
the red forms, of which the last reacts much more easily with 
reagents attacking the HO-groups of the molecule, points in this 
case really to a chemical isomerism, in which to the red modification 
must then be attributed probably the ¢rans-configuration, in the sense 
of WeRNER’s theory. 

In the light of the interpretations given of the more recent in vesti- 
gations of crystals by means of RönrGurrays, the question about the 
discrimination between cases of “physical”, in contrast with “chemical” 
isomerism, seems to have no longer any real significance, at least 
for solid matter: undoubtedly each modification of polymorphous 
substances will in the solid state also possess a definite spatial con- 
figuration differing from that of the other modification ; and probably 
this difference will, at least partially, be preserved in the state of 


1) A. HantzscH and O. Scuwas, Ber. d. d. Chem. Gec., 34, 892, (1901). 
3) O. AnseLMINO, Ber. d. d Chem. Ges. 38, 3989, (1906); 40, 3465, (1907). 


75 


solution, and almost certainly in the molten mass. But only, if such 
differences be really stated in the liquid phases to a measurable 


Fig. 1. 

degree, it appears rational to speak of two kinds of chemical molecules. 

However, disregarding for a moment their chemical isomerism, 
from a crystallographical point of view, the red and yellow 
modifications of the base mentioned, seem, in our opinion, to be 
related as true enantiotropic forms, as e.g. is the case with mono- 
elinie and rhombic sulphur. The zrreversibility observed by ANsELMINO 
is evidently only an apparent one, caused by intensive retardation 
phenomena: the transition-temperature: yellow = red, is 34° C., 
while the meltingpoint of the red modification is found to be 74° C. 
and that of the (metastable) yellow form 70° C. By this interpretation 
all relations existing between the red and yellow forms, as observed 


by ANSELMINO, may be explained in an unambiguous way. 


§ 2. With respect to the erystallographical properties of these 
compounds, in the first place the numbers relating to the derivatives 
already obtained by ANseLMINo, may be recorded in the following. 
They were already obtained by us in 1906, but by special circum- 
stances their publication has been postponed till now. 

The condensation-product of p-homosalicylaldehyde (from p-cresol) 
and aniline: 0o-oxy-m-methyl-benzylidene-aniline : 


occurs in two forms, of which the one is yellow, the other red, and 
which were studied already formerly by H. Trause and F. SCHMELING ') 


1) F. ScrweLinNg, Diss. Greiswald, (1905), p. 56, 58. 


76 


in detail. The yellow (metastable) modification, melting at 70° C., 
is rhombie-bipyramidal, with the parameters: a:b:c=0,3732:1: 
:0,4228, and the forms: {010}; {011}; {101}; {102}. Its bire- 
fringency is of positive character; the optical axial plane is parallel 
to {100}. The crystals show a cleavability parallel to {100} and 
{010}; their specifie gravity at 17° C. is: dso = 1,248, from which 
the equivalent-volume is calculated at: 169,75, and the topical para- 
meters at: 7: pw: w = 3,8269: 10,2471 : 4,3322. 

The red modification, which melts at 74° C., and to which the 
yellow form changes at 34° C., is monoclinic-prismatic. The para- 
meters published by the author do not agree with those calculated 
from his angular values: they are really : 

a:b6:c = 0,2362 : 1 : 0,6579; 
B= 7498, 

if the same angles be used as by the author mentioned. The occur- 
ring forms have the symbols: {010}, {001}, {110}, and {O11}. The 
optical axial plane of these strongly pleochroitic, negatively bire- 
fringent erystals is perpendicular to {010}; the cleavage occurs 
parallel to {001} and {010}. The specific weight of the erystals is: 
1,263 at 17° C.; the equivalent-volume is therefore: 167,06, and 
the topical parameters are calculated at: x: y: w = 2,4511 : 10,3770: 
:6,8271. The transition of the yellow into the red crystals occurs 
in such a way, that the two modifications are rigorously orientated 
with respect to each other in two different ways, the faces of {010} 
of the two forms remaining always parallel to each other; — a fact 
clearly demonstrating the intimate relation of their internal structures. 
It is worth remarking here, that the dimensions in the direction 
of the b-axes in both modifications appear to be almost the same 
(namely: 10,3, as topical parameter), while the intergrowth of the 
a- and g-erystals parallel to {010} occurs in such a way that either 
the c-axis of the one modification coincides with the c-axis of the 
other, or the a- and c-axes of the crystals appear to be interchanged, 
although in these directions the topical parameters do not show a 
direct relation to each other. 


§ 3. II. o-Methoxy-m-methyl-benzylidene-aniline. 


This substance, which has the composition : 
CH; 


CH=N—C,H; 
OCH, 


77 


was obtained from the foregoing by means of methylsulphate at 40° C. 
It melts at 70° C., and erystallizes from ligroin in beautiful, pale 
yellow, transparent crystals. 


Fig. 2. o-Methoxy-m-methyl-benzylidene-aniline. 
Monoclinic-prismatic. 
abs = 12792 0121 0509: 
B 76 IFE 
Forms observed: c= {001}, large and lustrous ; m= {110}, yielding 
good reflexes, like g = {011} also; 7 = 101}, small, but well deter- 
minable. The aspect of the crystals is tabular parallel {O01}. 


Angular values: Observed: Calculated: 
erg = (O01); (OL AI AD — 
em = (O01)-(110) —*~ St 54 — 
m:m = (410) : (410) =* 102 31 = 
c:r =(001):(101)= 44 22 4427 


No distinct cleavage was found. 

The specifie weight of the erystals at 16° C. was: 1,166; the 
molecular volume is therefore: 192,96, and the topical parameters 
are: %: pw: w = 6,7561 : 5,2813 : 5.5502. The form-analogy with the 
red modification of the foregoing substance is undeniable. 


§ 4. III. o-Oxy-m-methyl-«-anilido-ethylbenzene. 


This compound, which melts at 90° C., was obtained from the 


first by means of two molecules of methylmagnesium-iodide in 
boiling etheric solution, and subsequent decomposition of the product 
with water. It has the formula: 


CH, 
en 
< 


OH 


78 


and crystallizes from ligroin in very small, colourless, and almost 
rectangular plates. 


Monoelinie-prismatic. 
azo? e= 02682: 1707254, 
B = 85° 47’. 

Forms observed: 6 = {010}, predominant; 
m = {110} and a= {100}, well reflecting. In 
the zone of g={011}, s = {012} and c= {001}, 
the angular measurements ordinarily are not 
so accurate as in the other zones; commonly 
g = {011} is the best developed. The aspect of 
the crystals is that of thin plates parallel to 
{010}. 


Fig. 3. 0-Oxy-m-methyl-a- 
anilido-ethylbenzene. 


Angular values: Observed : Calculated : 
bm {O10 110) tT DE Ay? ze 
b:q = (010): (011) —* 54 7 Bs 


dig =—14 OO) = (01a en 35 — 
afc. = (100) MOOR — Sh te Soo 
sg == (O12) 101d) En 56 Hb) 
s:s =(012):(012)= 40 34 39 464 
mig =D) (O1ll=— — 78 0 71 56 
m: a= (110) (100) —- A 584 14 583 

A cleavage exists parallel to {001}. 

The specifie weight of the erystals at 17° C. is: 1,107; the 
equivalent-volume therefore: 205,06. The topical parameters are: 
vp: o = 2:73192-10,1861 -. 7.3890. 

On {010} the extinction-angle is 43° with respect to the direction 
of the c-axis in the quadrant behind. Probably the optical axial 
plane is parallel to {010}. 


§ 5. IV. o-Methoxy-m-methyl-«-anilido-ethylbenzene. 

This substance was obtained from the corresponding benzylidene- 
aniline by means of methylmagnesium-iodide and subsequent decom- 
position by water. | 

The compound, which has the formula: 

Oy 

Bes 

| Pe 
OCH, 


79 


melts at 78° C., and crystallizes from ligroin in big, colourless, 
strongly refracting crystals of tabular or prismatic aspect. Ordinarily 


Fig. 4. o-Methoxy-m-methyl-a-anilido-ethylbenzene. 


they manifest curved faces, exact measurements thus being rather 
difficult. 
Rhombic-bipyramidal. 
a: b=0,3301-; 1. 
Forms observed: c= {001} predominant; a={100} and 6—=}010}, 
yielding good reflections; m= {110}, small, but lustrous. 


Angular values : Observed: Calculated: 
am, = OO (HOL 18-16 — 
bemi Op — AE 71° 44’ 


All other angles are 90°. 

A good cleavage was found parallel to {100} and {010}. 

The optical axial plane is {100}, with the b-axis as first bisector. 
The angle of the optical axes is very small, with extraordinarily 
strong dispersion: @ >v; the apparent angle of the axes in oil 
(n = 1,54) was about 48° for the red, and about 25° for the violet 
rays. On {001} corrosion-figures were obtained of rectangular form, 
in agreement. with the adopted crystallographical symmetry. 

At 16°C. the specific of the crystals was: 1,098; the equivalent- 
volume therefore, being: 219,49. | 


§ 6. V. 0o-Oxy-benzylidene-aniline. ') 


This compound, having the formula: 


C} 
oN 


OH 


CH=N—C, H; 


1) Conf. also: L. Duparc, Ann. d. Chemie, 266, 140 (1891); here & is taken 
as {001}, the axial ratio, therefore becoming: c’: b’: a’ = 4,586:1: 2, 1922. (In 
Duparc’s paper a: 0 is erroneously taken ten times too small, and the a- and c- 
axes are interchanged. The crystals are identical with ours. 


80 


and melting at 50°,5 C., was obtained from salicylaldehyde and aniline. 

The substance is dimorphous: il occurs in a less stable rhombic 
a-modification, and in a monoclinic #-form, which is obtained in 
most cases; both modifications are yellow. 


1. a-Modification. 


Fig. 5. 0-Oxy-benzylidene-aniline. 
(a-Modification). 
From ligroin this modification erystallizes in most cases in the 
form of big, yellow, almost always opaque and flattened bipyramids. 


Rhombic-bipyramidal. 
a:6:¢= 0,4729: 1: 0,2188. 


Forms observed: 0 = §111}, big, but badly reflecting; 6 = {010}, 
small, yielding good reflexes. The crystals obtained from a solution 
in methyl-alcohol showed also a prism m = {130}, the faces of which 
gave good images. 

Angular values: Observed: Calculated : 
0:0 = (111): (111) = * 22°28)" — 
0:0 — (111): A11) = * 48 39 — 
0:0 = (111): (111) = 125 55 125°47" 
Obd) (O10) = an HAEG 78 46 
mb = (130) (010) =S - 3459), <35 41 

No distinct cleavage was found. 

The specifie weight of these crystals was: 1,087 at 16° C.; the » 
equivalent-volume is thus: 181,23, and the topical parameters are 
calculated at: 7: Wp: @ = 5,7005: 12,0539 : 2,6375. 


2. 8-Modification. 


The crystals of the a-modification are easily transformed into those 
of the B-form by reerystallisation. If, however, the long needles of 
the 8-modification thus obtained, are again recrystallized from methyl- 
alcohol, they are again changed into the bipyramids of the a-form. 


81 


Strongly refracting, yellow needles. 


Monoelinie-prismatic. 


a: 


Forms observed: m= {110}, large and lus- 
trous; a={100}, narrower; c = {001}, well 
developed. Moreover, again a negative pyramid 
and a doma are observed, which, however, 
cannot be determined more precisely. It is for 
this reason, that the occurring face c was taken 
as {001}, although this form represents certainly 
not a basal face, but a horizontal prism. 

Angular values: Observed: alculated : 
mm (110) : (100) —* 47°15’ — 
Bee (100): (001) =* 26 21 — 
Pe (110):(001 == 52 40 52925’ 


6 == 2, 40411, 
f= 267 2k" 


No distinct cleavability was observed. Fig. 6. 0-Oxy-benzylidene- 
The specific weight of the crystals was: aniline. (@-Modification). 


1,184 at 17° C. 


; the molecular volume is, therefore, 166,38. 


§ 7. VI. «-Anilido-ethyl-anisol. 


This compound was prepared from the just mentioned by means 


Fig. 7. Anilido- 
ethyi-anisol. 


of methylmagnesium-iodide, ete. It has the formula: 


& 


J, CMCHs) -NH—CoHs 
OCH; 
and melts at 46° C. 
From ligroin badly developed, strongly refracting 
needles are deposited, which allow only approxi- 
mate measurements. 


Rhombic-bipyramidal. 
fi. De == 0884-0 A0 
Forms observed: t = {110}, m = {320}, p = {210}, 
and m= {520}, all about equally narrow, and 
yielding multiple reflexes; q — {011}, smaller, and 
badly reflecting. The aspect of the crystals is elon- 


gated in the direction of the c-axis. 
6 


Proceedings Royal Acad. Amsterdam. Vol. XXIII. 


82 


Angular values : Observed : Calculated : 


t:¢ == (110): (110) =* 97° 4’ _ 
q:q == (011): (011) =* 49 51 me 


t:m=(110:(320) —= 11 12 11° 0’ 
mizp == (920): (210) =S 6 22 6 37 
Pin = (210) 4920) = 8 40 8 31 


A distinet cleavability was not stated. 

The specific weight of the crystals was: 1,141 at 18° C.; the 
equivalent-volume is thus: 176,16, and the topical axial ratios are 
calenlated at %: a: w = 6,6649: 7,5395 : 3,5059. 


§ 8. VII. p-Methoxy-benzal-aniline (Anisai-aniline). 


This substance, which melts at 63° C., and 
possesses the constitution: 
OCH; 


CH=N—C,H; 
was obtained from anisaldehyde and aniline. 
- It crystallizes from ligroin in colourless, well 


developed, very transparent crystals, having the 
odour of anisol. 


Monochnic-prismatie. 


a:b:¢==1,5745 : 1: 0,8063; 
B= 65°21’ 


Forms observed: c= {001}, well developed 
and yielding splendid reflexes; q = {011}, 
r —{201}, and o = {211}, givingall sharp mirror- 
images; m—{110} and a=$100}, somewhat nar- 
rower, but well measurable. The form a is often 
absent, or only developed with a single face, 
while o and + are often very narrow. The aspect of the crystals 
is that of thick prisms with an elongation parallel to the c-axis. 
They are generally well built. 


Fig. 8. Methoxy-benzal- 
aniline. 


83 


Angular values : Observed: Calculated : 
650, = (O01) (TOO i="). Go oe — 
Gd Oil). (sb. LE a 
n:m = (110): (110) =* 110 64 — 


1 
c:r =(001):(201)= 58 304 58° 234 
o:r —=(211):(201) = 33 574 33 51 
m:q = (110):(011) = 47 18 ATi 221 
o:m=(211):(110) = 44 7 43 54 
ee nt == (OOle: (11 Oy 76 4 76 104 
m:q = (110):(011)=: 73 3 Tay 2k 
& 


Perfect cleavable parallel to {001}. . 

An apparently second modification was, on more detailed inves- 
tigation, really identical with the one described. However, yet 
another, truly polymorphic modification was observed *), crystallizing 
in extremely thin, unmeasurable, small plates with normal extinc- 
tion; they are first deposited from solutions, but are rapidly changed 
into the crystals described in the above. 

The needles here investigated, have oblique extinction: on m 
at an angle of 224° with the direction of the c-axis. 

The specific weight of the crystals at 17° C. was: 1,165; the 
equivalent-volume is thus: 181,11. 

Topical parameters: 7%: wy: w = 8,4931 : 5.3942 : 4.3494. 


We are occupied with tentatives to obtain condensation -products 
of other aldehydes and amines of the aromatic series, with the 
purpose to find other cases of polymorphism or isomerism with 
bases of this kind. Perhaps we shall be able to return to this 
question within a not too remote future. 

Laboratory for Inorganic and Physical 
Groningen, May 1920. Chemistry of the University. — 


') H. Orr, Monatshefte f. Chemie, 26, 340 (1905). 


Chemistry. — “The Photochemical Decomposition of Potassium- 
cobaltiovalate and its Catalysis by Neutral Salts” by Prof. 
F. M. Jagger and G. Bereer. | 


(Communicated at the meeting of May 29, 1920). 


§ 1. With the intention of studying the photochemical action of 
dextro- and laevogyratory circularly polarized light upon both optical 
antipodes') of potassiwm-cobalti-ovalate: K, {Co (C,O,),} + 3 H,O, and 
with the purpose of proving the probable difference in speed of 
reaction with each component, if attacked by circularly polarized 
light of opposite direction, — we started a series of experiments, 
which were of a preliminary character as regards the specific 
peculiarities of the photochemical process itself. 

Simultaneously we tried to find out, if it would be possible to 
regulate the speed of reaction by the addition of certain substances to 
the solution in such a way that the velocity became as favourable as 
possible to the purpose aimed at on starting these experiments. We give 
already here a review of the results obtained, which must be con- 
sidered as the foundation of further investigations, because we found 
some remarkable facts, which in their turn might be of interest as 
startingpoints to some other research-work of a more general character. 

If all details are, for the moment, left aside, we can say that the 
photochemical decomposition of the complex potassium-cobalti-oxalate 
occurs in a way fully analogous to that observed in the case of 
the corresponding ferric salt of analogous constitution : in our case, 
carbondiowide is split off, and a pink coloured precipitate of cobalto- 
oxalate: CoC,O, is formed, while a gradually increasing quantity 
of potassium-ovalate goes into solution; this last salt may, for a 
small part, combine with some cobalto-ovalate formed, into a com- 
plex salt of the constitution: A,}Co(C,O,),}, which, however, is 
almost completely dissociated in its components. 

The reaction may principally be formulated in the following way : 

2 {CoC,0,}, K, = 2 CoC,O, + 3 KCO, + 2 CO; 


1) EF. M. Jaraer, Receuil des Trav. des Chim. d. Pays-Bas, 38, 247 —256, (1919); 
idem, Lectures on the Principle of Symmetry and its Applications in All 
Natural Sciences, 2nd Edit., Amsterdam, (1920), p. 216, 249, 250, 317. 


85 


or, — if the electrolytic dissociation of these salts is taken into 
account, perhaps better by the relations : 


2 {Co(C,O,),}" = 2 {Co(C,0,),}" + C,0," + 2 CO,, 

and FCO. One Cortes GION. 

$ 2. The photochemical reaction mentioned was, for the first lime, 
studied systematically in 1917 by Vranek'), under conditions of 
experiment very widely differing from ours. This author studied 
extremely dilute solutions of the salt, with concentrations ranging 
from 0,01 to 0,0001 mol. per Liter, and experimented always 
with very small volumes of the solution, — conditions made necessary 
by the optical method followed by him in this investigation. 
Nevertheless, the measurements were carried out with much care and 
a precision as great as possible, yet the results obtained give the 
impression that the reaction is in reality much more complicated 
than the author himself seems to believe. For, on the one hand, he 
thinks it probable with respect to the numbers obtained, that the 
reaction is a bimolecular one, in agreement with the ionic equation 
suggested above; but his absorption-measurements do not give any 
numbers, which might be looked upon as true reaction-‘‘constants”’, 
and it can be easily seen, that they do not agree really either 
with a monomolecular or with a d:molecular process, so that it 
were better to speak in this case of an accelerated bimolecular, 
or of a retarded monomolecular reaction. By spectrophotometric 
observation, he was, moreover, able to demonstrate, that the eme- 
raldgreen solutions have two principal absorption-maxima, for 

— 4260 A.U., and for == 6050 A. U. respectively ; and he stated, 
that the reaction goes on in darkness as well, light-radiation 
therefore chiefly acting as an accelerator. The temperature-coefticient 
of the dark reaction appeared to be rather great (4,56), but that of 
the photocatalysis, on the contrary, very small; finally an appre- 
ciable BrcQurrer-effect through the total volume of liquid is mani- 
fested, as soon as it is exposed to the light, which fact could be 
demonstrated by means of measurements of the electromotive force 
produced in mixed solutions of cobalto- and cobalti-salt with respect 
to a normal calomel-electrode, if the solutions are brought from 
the dark into the neighbourhood of a source of light. Vranexk 
could state as disturbing factors: 1. the slight solubility of the 
cobalto-oxalate formed in the solution of potassiwm-ovalate; 2. the 
retarding action exerted on the photocatalytic process by the potas- 
situm-oxalate formed in the reaction, — which influence, however, 


1) J. Vranek, Zeits. f. Elektrochem., 23, 336, (1917). 


86 


appeared to diminish gradually with inereasing concentration of the 
catalyst; and 3. the tendency of cobalto-oxalate to form supersa- 
turated solutions *), instead of precipitating normally. Finally there 
is again a disturbing effect, because of the subsequent photochemical 
decomposition of the ovalate-ion and its transformation into a for- 
mate-ion, which reaction, as BerrHeror and GAUDECHON ”) had already 
demonstrated formerly, oecurs chiefly under the influence of rays of 
small wave-lengths. All the different effects mentioned manifest their 
special influence in a more or less sensible degree, and they prove 
sufficiently, how very complicated indeed the whole mechanism of the 
process is. 

The author could, however, not find a catalysing action by 
addition of acids, such as hydrochloric or sulphuric, under the 
conditions of his experiments *). 

$ 3. In contrast to those of VraNek, our experiments were 
executed with much more concentrated solutions of the complex salt, 
while, after many trials, finally the direct gravimetric determination 
of the cobalto-oralate generated was adopted as method of analysis; 
the cobalto-salt was determined as metallic cobalt, after reduction in 
a current of dry hydrogen. Even in the case of very concentrated 
solutions, the error resulting from the solubility of the precipitate 
in the solution containing potassium-ovalate, appeared to be small 
enough to neglect it in comparison with the other incertitudes of 
the experiment: in the most unfavourable circumstances the deviations 
caused by this factor did not surpass 1,5 °/,. 

The dark green liquid was kept in a vessel of transparent quartz, 
surrounded by a quartz-mantle of greater diameter; in the space 
between the cylinders a current of water was continually passed, 
which was kept at an almost constant temperature by means of a 
metallic spiral-tube, placed in a thermostat; the temperature varied 
in our experiments between 21° and 23° C. As source of light a 
quartz-lamp (HERAKUS) was used, which was placed always at ex- 
actly the same distance (140 m.m.), and which sent its rays into 
the solution not before its current had reached a constant and 
always identical intensity, and also its radiating power had become 
constant. All the conditions of the experiments were, for the rest, 
in all cases as constant as possible; e.g. the volume of the 
solution was always the same, namely 50 ccm. Because also the 


1) Sr. Deakin, M. Scorr and B. D. SreeLe, Zeits. f. phys. Ghemie, 69, 126, (1909). 

2) D. BerrHeLot and H. GAUDECHON, Compt. rend. de l'Acad. d. Sc. Paris 
152, 162, (1911). 

3) J. VRANEK, loco cit, p. 350, 


87 


crystallised complex salt is decomposed very slowly, when preserved 
in darkness, the preparation used in our first experiments contained 
a very small quantity of the cobalto-salt; so that, after its quantity 
had been determined accurately, the necessary, and only very small 
correction of the results made necessary by it, was applied in the 
first series of measurements. The degree of accuracy of the method 
of analysis was tested beforehand by experiments with mixed solutions 
of known composition, and it was found really sufficiently great. 
The solutions were continually stirred by means of a current of 
nitrogen, regulated at about four bubbles every second ; later-on stirring 
was brought about by a current of carbon diowide, after it was found, 
that the reaction was not influenced by it in any respect. It is necessary 
to perform the analysis of the solutions in darkness, and to filter 
the precipitate as rapidly as possible, to wash it immediately, and 
to carry out all necessary manipulations in rapid succession. As long 
as the mother-liquor is adhering to the precipitate, all access of 
light must be carefully prevented, as well as all considerable increase 
of temperature. . 

In a first series of determinations, we thus obtained the following data: 


eee pd 
minutes: | in 50 ccm: | found: decomposed: 
223 | 60 ‘| 0.7247 Gr: 0. 0634 Gr. 73.349, 
22.2 60 | _0.9709 0. 0665 Bl.4l | 
Bae ee gy oN. d.2124 0. 0695 | 48.05 | 
ee 60s | 1, 4655 0, 9694 | 39.70 | 
21.7 60 1. 7021 0. 0686 | 38.78 | 
21.9 60 1. 9434 0. 0699 | 30. 16 


Taking into account the unavoidable uncertainties, which always 
remain in the study of so highly complicated a reaction as this, 
and attributing only a moderate value to the small increase which 
the first four numbers apparently show with respect to each other, — 
it must be evident from these results, that the quantities of the 
salt decomposed within identical intervals of time are approximately 
independent of the initial concentration, and chiefly determined by 
the amount of light-energy absorbed during that time. The reaction- 
order is evidently zero, — a fact which may be used as an argument 
on behalf of the view, that the process is of a purely photocatalytic 


88 


character. It might be expected that also a true proportionality would 
exist between the time of exposure and the amount of decomposed 
substance, if the initial concentrations were the same in all cases. 
However, experience only partially confirms this conclusion; at least 
we found, for instance, the following data in a series of experiments: 


rime of Ex- | ‚Corr. Weight o of Corr. Weight o of | | percentawe | 
Temper posure in | the Cobalti-Salt | the metallic Co.' of the Salt 
in °C. | minutes: in 50 ccm.: found: decomposed: 
| 
2392 0. 0803 Gr. 0. 0310 Gr. 26. 4 0/6 
23.9 0. 9017 0. 0357 33. 2 
24 0. 9902 0.0511 44,7 
| 


This divergence becomes somewhat intelligible if we remember 
that the medium is continually changing chemically and physically 
during the reaction; therefore, because it changes gradually as well 
in absorptive power as in concentration of the cobalti-salt or potas- 
sium-oxalate, the action of the light in 60 minutes e.g., can not be 
equivalent to twice the action in 30 minutes, ete. On the contrary, 
there is rather a cause for astonishment at the fact that the results 
of the first series of experiments were really so regular, while the 
initial concentrations in these experiments differed so appreciably 
from each other, and thus the same was true for the absorptive 
power of the solutions used. It may be, that the slight increase of 
the first four numbers mentioned above, finds its explanation also in 
this particular circumstance. 


§ 4. Afterwards the experiments described above were again 
repeated, and now a specially purified salt, free from all cobalto- 
ovalate was made use off. It was freshly prepared and immediately 
used in the experiments, in which a lamp of somewhat smaller 
intensity was applied as source of light. For the numbers obtained, 
see the table on the following page. 

From these measurements it appears that the speed of reaction is 
relatively greater with the smaller, than it is with the greater con- 
centrations; that also in the most favourable circumstances disturbing 
influences seem to play a rôle, which have as a consequence some 
uncertainties of the analysis; and that, at least with respect to the 
last four numbers, the total decomposition may be supposed as in- 
dependent of the original concentration. It must be remarked, that 


89 


emer Bel toe we ot maar St 
in °C, : | minutes: | 50 ccm : lic Co. found: | gecomposed: 
22° + 1° 6 | 0. 150 0. 0567 | ie", 
id. eo | 1. 000 0.0546 45.8 
id. iel 1. 250 0.0411 Tan 
id. 60 | 1.500 0. 0475 | 26. 5 
id. 60 1. 750 | 0.0429 20.5 
id. 60 2. 000 0, 0465 19.5 


the mean decomposition in 60 minutes (ca. 0,0445 Gr. Co) is here only 
about *, of that formerly observed, — which may be chiefly caused 
by the fact, that the intensity of radiation of the quartz-lamp was 
a smaller one than formerly, and by asomewhat modified form of the 
vessels employed. All these measurements have, therefore, not an 
absolute, but merely a relative significance. 


§ 5. Results mutually agreeing much better, however, were obtained 
in the study of the influence, which the addition of certain electro- 
lytes to the solution has upon the photocatalysis under consideration. 
For it had soon become evident by preliminary experiments, that, 
— in contrast to VRANEK’s negative results of the addition of acids, 
— a remarkably strong influence on the speed of reaction could be 
observed, if neutral salts were added to the concentrated solutions of 
the cobalti-salt used by us. An addition of alcohol had, however, no 
appreciable effect; but solutions of neutral salts, if added to the 
photosensitive solution, have immediately a very distinct influence, 
when the salts of strong bases and acids are used for this purpose. 

Such acatalytic influence of salt-solutions on photochemical reactions 
has, indeed, been found already by some other authors, e.g. by 
JORISSEN and RricHer*) in the case of the photochemical oxydation 
of solutions of owalic acid by free oxygen, and by Rororr®) in the 
case of Eprr’s solution: the last mentioned investigator found even 
one case which seems to be of the same type as those described here. 

Subsequently the influence was studied by us, which resulted from 
the addition of varying quantities of potassiwm, sodium, and hthiwm 
chlorides ;. in a second series of determinations the analogous influence 


1) W. P. JorissEN and L. Tu. Reicuer, Zeits. f. phys. Chemie, 31, 142, (1899). 
*) M. Rororr, Zeits. f. phys. Chemie, 18, 327, (1894). 


90 


of magnesium, beryllium, and ferric chlorides was investigated. The 
choice of such salts is limited by the condition, that only salts of 
such cations can be used, whose ovalates are easily soluble. For in 
the case of only slight solubility of those oxalates, a part of tie 
cation added would gradually be removed from the solution by 
precipitation with the potasstum oxalate set free during the reaction. 
However, these investigations may be extended eventually by the 
use of ammonium, rubidium, and caesium salts, while, on the other 
hand, a wide variation of all kinds of anions wil be possible 
here. 

In all experiments the same volume of solution (50 cem) was used, 
containing 0,0607 grammol. of the (anhydrous) complex salt per 
Liter. Moreover, the whole experimental arrangement was in all 
cases accurately the same, while the time of exposure was always 


Souentiye oh Ue Complex Salt 
decomprsed abten OY minutes 


m 


204: 
CD 
sf CS 
20; \ 
15 
10% 
$ 
e Concentration of the Cerobyles 


_ 025:050 O25 ts 20 25 3.0 35 40 ol. i . pik y, 


91 


I. 50 ccm. of a 0,0607 mol. solution of K3 {Co(C,0,)3' ; KCI as catalyst; 


| time of exposure = 60 minutes; temperature = 21° + 1° C. 


3 pele Kit: | 
Weight of KCI; Concentration | : o It} P 
in Eh i se Equiv, bid iene tence pee LG | Ee 
50 ccm. : per Liter: found: in Gr.: | posed: 
0 | 0 0.0648 Gr. 0.4833 Gr. | 36.17 % 
1. 864 0. 50 0. 0696 0.5196 38. 89 
3. 728 1.00 0. 0771 0. 5756 43. 08 
7. 456 2. 00 0. 0935 0. 6981 52. 24 
11. 184 3. 00 0. 0856 0. 6391 | 47. 83 
14. 912 4, 00 0.0781 | 0.5832 43. 64 


II. Conditions the same as before; NaCl as catalyst: 


0 | 0 0. 0648 0. 4833 36. 17 % 
3. 658 1. 252 0. 0792 0. 5913 44, 25 
5. 487 1. 878 0. 0946 | 0. 7063 52. 85 
7.316 2. 504 0. 0783 | 0. 5846 43. 715 

| | 
9.145 3. 128 | 0.0752 | 0.5614 42. 02 

| | 


III. Conditions the same as before; LiCl as catalyst. 


0 0 0. 0648 | 0.4833 36.17 % 

1. 153 |. 0. 543 0. 0816 | 0.6092 45. 59 

2. 306 | 1. 086 0. 0962 | 057482 53. 75 

6. 918 3. 258 0. 0827 ; 0.6174 46. 21 

9. 224 4, 344 0. 0685 0.5114 | 38. 27 
11. 530 0. 0609 0. 4547 34. 03 


IV. Conditions the same as before; MgCl, as catalyst. 


1. 829 0. 626 0. 0715 0. 5338 39, 95 


0 0 0. 0648 0, 4833 36. 17 % 
| 0. 299 0. 125 0. 0930 0. 6943 51. 96 
| 0. 599 0. 251 0. 0988 0. 7376 55. 20 
| 1, 198 0. 503 0, 1113 0. 8310 62. 19 
| 2. 396 1. 006 0. 0983 0. 7339 54 92 
| 4792 2. 012 0. 0567 0. 4233 31.68 
1.188 | 3. 018 0. 0041 0. 0306 2. 29 


92 


60 minutes. The temperature was 21° + 1° C.; the concentrations 
of the solutions of salts used were consecutively varied from 0,1 
normal to full saturation. The complex salt used was carefully 
purified and did not contain any appreciable amount of cobalto-oxalate; 
moreover, the solutions were stirred by the aid of a current of 
carbondioxide, after it had been demonstrated, that this gas had no 
influence upon the speed of reaction. 

Above we have given a review of the results obtained, while in fig. 1 
these data are reproduced in graphs, in which the equivalent-con- 
centrations of the electrolytes added are used as abscissae, while 
the percentages of the original salt transformed, are taken as 
ordinates in it. 

The determinations with BeCl, and Fe,Cl, are somewhat less 
accurate, as a consequence of secondary influences, as e.g. the strong 
hydrolysis of the berylliumsalt, and perhaps the formation of complex 
compounds in the case of the ferric salt; by these factors the image may 
be somewhat less definite. The data obtained in these cases follow here : 


V. Conditions the same as before; BeClg as catalyst. | 
: F . f Sal 
vin Grams in | ofBeChin | Veeken ene | cn 
50 ccm.: Equiv. p. Liter: found: in Gr.: posed: 
0 0 0. 0648 0. 4833 36.17 % 
0. 009 0, 004 0. 0383 0. 2859 21. 40 
0. 023 0.011 0. 0536 0. 4002 29. 95 
0. 045 0. 023 | 0. 0511 0. 3815 28. 55 
0. 090 0.045 | 0.0404 0. 3016 22.57 
0. 180 0. 090 | 0. 0332 0. 2479 18. 55 
VI. Conditions the same as before; FeCl, as catalyst. 
0 0 | 0. 0648 0. 4833 36. 17 % 
0. 035 0.013 | 0.0614 0. 4584 34. 31 
0. 087 0. 032 0.0798 0, 5958 44, 59 
| 0.119 0. 045 | 0. 0859 0. 6413 48. 10 
| 0. 174 0. 065 0.0585 0. 4368 32. 69 
1.044 0. 390 | 0, 0348 0. 2576 19. 28 


$ 6. In these series of observations evidestly we cannot speak of 
real reaction-constants: the data available do agree neither with the 
supposition of a monomolecular, nor of a bimolecular reaction-form. 


93 


But all curves of Fig. 1 manifest a clear and obvious analogy of 
shape: they rise evidently all to a steeper or flatter maximum, 
and then decline more or less rapidly. The addition of all these 
electrolytes thus involves an acceleration of the photochemical 
reaction in the case of smaller concentrations of them, which, 
however, reaches a maaimum at a certain concentration, charac- 
teristic of each salt, and which subsequently again diminishes. 
In some cases this diminution may even change into a retardation 
of the process') at concentrations, which are not even so very high ; 
and finally in the case of MgCl,, for instance, the reaction may 
be stopped even completely by it! 

Another very remarkable fact is, that the maxima are situated at 
smaller concentrations, as the valency of the cation, te. its electrostatic 
charge, is greater: for the divalent My-ion this maximum approaches 
much nearer to the ordinate-axis, than for the monovalent ions of 
the. alkali-metals, while the maximum of the curve of the trivalent 
Fe-ion is situated in the immediate vicinity of the Y-axis. The nearer 
these maxima approach the ordinate-axis, the more steeply the 
curves will appear to decline after passing the maximum. However, 
not only the electric charges of the ions, but also their specific 
properties appear to play a part in this: thus, for instance, the 
three maxima of the curves of the alkali-metals do not coincide, 
although their charges are the same; but they approach the Y-axis 
the more closely, the smaller is the atomic weight of these elements. 
The respective concentrations of the solutions of these three electro- 
lytes, at which the maxima are reached, are, if graphically inter- 
polated, — for LiCl, NaCl, and KCl respectively: 1,65 N. equiv., 
1,88 N. equiv, and 1,96 N. equiv.; these concentrations may e.g. 
be considered as approximatively proportional (1: 1,14: 1,18) to the 
logarithms of the ionic velocities at 18° C. of the three kinds of ions, 
being here about: 1: 1,06: 1,17. Of course, we emphasize, that no 
especial significance should be attributed to such relations as suggested 
here, because the number of data is yet too small, and their accuracy 
not sufficiently great. But attention may be drawn to the fact only 
that the specific properties of the ions play also a rôle in this, and 


1) It may be remarked here, that Jorissen and REICHER (loco cit), as well 
as Rororr, found instances of positive and negative photocatalysis under the 
influence of neutral salts, however, without making a general supposition about 
the possible shape of the respective curves. In ROLOFF’s paper one case is mene 
tioned, which is in full agreement with the data obtained by us, namely, where he 
used ANO, as a catalyst, and found a maximum of its action at a certain con- 
centration. 


94 


that the characteristics of the added salts in this photocatalysis are 
evidently intimately connected witb the electric charges of the ions 
and with their mutual electrostatic actions upon each other. 

If the relations found here, should indeed appear to be generally 
valid after the investigations have been extended over a much 
greater number of cases of photocatalysis, it would perhaps appear to 
be possible to give a theoretical explanation of all these peculiarities 
and more particularly of the occurrence of a maximal catalysis by salts, 
starting with the views about the nature of strong electrolytes and their 
abnormal behaviour, as developed in recent times by BJerrum }), 
Grosn *), Noyes *), and others; which views in every case, however, 
would involve a complete break with the electrolytic dissociation- 
theory of ARRHENIUS, at present still almost universally adopted. 

Perhaps one of us will return to this question again in future, 
after a more detailed experimental investigation of this kind has 
been made. 

Laboratory for Inorganic and Physical Chemistry 
of the University. 

Groningen, May 1920. 


1) N. BJERRUM, Zeits. f. Elektrochemie, 24, 321, (1918); Zeits. f. anorg. Chem. 
109, 275, (1919). 

*) |. C. GHosH, Journ. Chem. Soc. London, 113. 449, 627, 707, (1918). 

3) A. A. Noyes and Mc. Innes, Journ. Amer. Chem. Soc. 42, 239, (1920). 


Chemistry. — ‘Colloidal Sulphurcompounds of Ruthenium’. By 
Prof. F. M. Jancer and J. H. pr Boer. 


(Communicated in the meeting of May 29, 1920). 


§ 1. It was for the first time during the process of recovering 
ruthenium from residues, that we observed some phenomena 
indicating the existence of colloidal sulphur-compounds of that metal. 
The properties of the colloidal solutions thus obtained, appeared to 
be sufficiently interesting, to study the phenomena more in detail. 
The results of this investigation are accordingly summarized in the 
following paper. 

If a solution of freshly prepared ammoniwm-sulphide be added to 
a hot solution of some salt of tetravalent rutheniwm'), be it to the 
HO 
ro ED Bn: 
a brownish black precipitate of Rus, will be formed, which does 
not manifest any especially remarkable properties. Totally different, 
however, is the behaviour of these substances with respect to each 
other, if the experiment is carried out at lower temperatures, e. g. 
at O° C.: under these circumstances a dark, greenish black precipi- 
tate is formed, while a dark green colloidal solution appears at the 
same time. This solution is very unstable: it rapidly becomes turbid, 
depositing greenish black flakes of the same kind as the original 
precipitate. For the green solution is nothing but a colloidal 
solution of the original precipitate, produced by the addition of 
ammonium-sulphide; it shows the TrNparr-effect, and its dispersed 
particles appear to carry a negative electric charge, as follows from 
the electric cataphoresis of the solution. On being put into contact 
with the air for some hours, the solution is completely flocculated, 
and the supernatant liquid then shows only the yellow colour of 
the ammonium-polysulphides. The green solution is much more stable, 
if first strongly diluted with water; but even in these circum- 
stances it appears to be flocculated completely after twenty-four 
hours. Neither an addition of gum arabic, nor that of gelatine, can 
increase the stability of the colloidal solution. 


sulphate: Ru (SO,),, or to a complex salt *) like: | Ru 


1) U. Anrony and A. Lucuess1, Gazz. Chim. It. 28, (II), 139, (1898). 
2) A. Werner, Ber. d.d. chem. Ges., 40, 2621, (1907). 


96 


$ 2. If now the flocculated solution is quietly left standing during 
a couple of days, its colour becomes gradually pale pink; and after 
standing somewhat longer, finally a more or less intense reddish 
violet solution is obtained, while at the bottom of the vessel a preci- 
pitate of finely divided sulphur has accumulated. An analogous 
phenomenon is observed, when one tries to subject the original, dark 
green solution to dialysis: also in that case a pink solution is finally 
obtained after the flocculation of the original green one. This new 
red solution, into which the original green liquid is transformed, 
also appears to be a colloidal solution: both the original and the 
red liquid exhibit the Tynparr-effect and on being examined with 
the ultra-microscope they both show the characteristic structure and 
the Brownian motion of true colloidal solutions. The stability of the 
red solution appears, however, to be much greater than that of the 
dark green solution mentioned before. 

Soon it became evident that for the change of the unstable green 
solution into the much stabler red solution, the presence of the free 
oxygen of the air is essential; that, in other words, an oxydation- 
process goes on, in which the greenish black precipitate originally 
formed is gradually dissolving under continuous absorption of oxygen, 
while a red colloidal solution is formed by it. This chain of 
events could be illustrated, leaving no doubt whatever about its 
truth, by the following series of experiments : 


a. Greenish black ruthenium-sulphide freshly precipitated at O° C. 
was first washed with icy-cold water, and subsequently dried 
after washing it with absolute alcohol and ether. Immediately it 
was mixed with water and shaken in a stoppered bottle; a suspen- 
sion is formed of an originally bluish hue, the upper layer of which 
is, however, already after one and a half hour converted into a 
pale pink liquid. After a day the colour turns reddish violet, while 
the quantity of the precipitate is gradually diminished, the longer 
the contact of the different substances lasts. Simultaneously a slight 
precipitate of sulphur is deposited on the bottom of the flask. 

b. At O° C. freshly precipitated greenish black sulphide, treated 
as described above, was vigorously shaken with water, and a conti- 
nuous current of pure air sucked through the liquid. Soon the 
solution turns reddish violet; after some days the original precipitate 
has completely disappeared, while some finely divided sulphur only 
remains, which can be easily removed by filtering. This is one of 
the best modes of preparing the red colloidal solutions. 


c. On being exposed to the air for a long time, the dry greenish- 


97 


black sulphide gradually changes its colour, being converted into a 
reddish, dark coloured mass, which gives immediately the red solu- 
tion, if shaken with water. 


d. A piece of filter-paper soaked in the green colloidal solution, 
becomes very rapidly violet on being exposed to the air. If the 
oxygen of the air is first removed, no change of colour appears ; 
the precipitate generated in flocculating the green solution gives, 
however, automatically the reddish violet liquid, when exposed to the 
atmosphere. 


e. Whilst AwS,, precipitated from hot solutions is simply attacked 
by nitric acid (spec. grav.: 1,4) and oxydized to a brown solution, 
the greenish black sulphide is attacked by the same acid extremely 
vigorously, almost explosively: a red violet solution is formed, while, 
moreover, some sulphur is precipitated at the same time. The red- 
violet solution is, also after neutralisation of the acid in excess, slowly 
oxydized further, when in contact with the air; finally the solution 
becomes completely colourless, and the slightly acid liquid thus 
obtained appears to contain a sulphate. Not even a preliminary 
dilution of the red-violet liquid with water can prevent this oxydation 
to sulphate. The presence of mere traces of the unstable greenish 
black sulphide may be proved by this reaction of oxydizing the 
supernatant liquid by means of nitric acid’); and it is in this way, 
that we can demonstrate the fact, that the sulphides precipitated 
from ruthenium solutions by ammonium sulphide between 0° U. and 
boiling-temperature, are really mixtures of stable RuS, and the 
unstable greenish black sulphide, here described. It suffices to shake 
the precipitate simply with water, and to add strong nitric acid to 
this suspension: the red colour will then appear immediately. 

§ 3. Because the new sulphide appeared to lose its characteristic 
properties, if heated even to only 110° C., it was necessary, under 
exclusion of the oxygen of the air as much as possible, to prepare 
it always at dower temperatures; also it must be rigorcusly purified 
for the purpose of analysis. In the process of precipitation, free sulphur 
is moreover always formed, — a fact also noticeable?) in working 
with other ruthenium sulphides, — and therefore necessitating repeated 


') Already other investigators have occasionally had an opportunity to observe a 
pink coloration of the solutions obtained in their studies on ruthenium sulphides , 
without any attempt at an explanation of the said phenomenon, it was e.g. men- 
tioned by Antony and A. LucuHsssi, loco cit 30, (II), 540, (1900). 

2) C. Ciaus, Ann. der Chem. u. Pharm., 59, 245, (1846); U. Anrony and A. 

Lucuess!, Gazz. Chim. Ital. 30, (II), 539, (1900). 
7 
Proceedings Royal Acad. Amsterdam. Vol XXIII. 


98 


extraction of the product by carbon disulphide at low temperatures. 
The substance was, therefore, rapidly put into a small ERLENMEYER- 
tlask, carbon bisulphide was poured upon it, the air driven out by 
carbon dioxide, and the flask shaken for some time at room-temperature. 
This treatment was repeated several times, till no sulphur was any more 
extracted ; the carbon bisulphide was then washed out by a mixture of 
dry alcohol and ether, the product finally washed with absolute ether 
and carefully dried in an atmosphere of carbon dioxide. For the 
purpose of analysis a weighed quantity was put into a Rosr- 
crucible, which in its turn was hung inside a nickel crucible, and 
carefully roasted with access of the air; afterwards it was ignited 
in a current of dry hydrogen. All the determinations were made by 
means of a micro-balance. 

Analysis: 12,33 m.Gr. of the greenish black sulphide gave 4,26 
m.Gr. Ru; calculated for RuS,: 34,69°/, Ru; found: 34,55 °/, Ru. 

Because in the oxydation of this sulphide, as will be demonstrated 
below, there is formed a substance containing four atoms of sulphur, 
while simultaneously sulphur is set free, this high content of sulphur 
is perfectly in agreement with the whole chemical behaviour of the 
greenish black sulphide’), which has the character of a ruthenium 
persulphide. 

§ 4. We must now first review the properties of the red-violet 
solution, which is formed by oxydation of the green solution described 
above. Its refractive index appeared to be practically identical with that 
of pure water; moreover, besides the TyNparr-effeet and the Brownian 
movement, it manifests in a particularly beautiful way the phenomenon 
of electric cataphoresis: the dispersed particles possess, in contra- 
distinction to those of the green colloidal solution, a positive charge. 
Although the solution is very stable, and may even be concentrated 
on the water-bath without coagulation, it can be flocculated by 
the addition of electrolytes, — be it only slowly. The pure solution 
was mixed with a small quantity of solutions of NH,C/, CaCl, 
Fe, Cl,, KySO, and Na,HPO,. Already after a day some precipitate 
was formed from each of these liquids, and the intensity of their 
colour diminished. If more of the electrolytes be added, the precipitate 
formed first again disappears, but after twenty-four hours a certain — 
quantity is again deposited. After a couple of days the colour of the 
liquid has completely disappeared, and all of the dispersoid has been 
flocculated. Most rapidly this takes place, when phosphate is added, 

') It may be remarked here, moreover, that on heating this sulphide at the 


open air at 120° C., also SO» is formed; the sulphur seems to be partially more 
loosely bound than the remaining part of it. 


99 


the electrostatic charge of the anions, therefore, being decisive here, — 
a fact, which is in agreement with the stated positive charge of the 
dispersed particles. Such experiments were also carried out with a 
more concentrated solution, CaCl, being added to it. After one day 
already there appeared a precipitate, the colour of the solution being 
violet; after two days more precipitate was formed, while the colour 
became bluish violet; after five days the colour was dark bluish 
violet; after a fortnight it was similar and only a relatively small 
amount of precipitate was formed. In no case the colloidal solution 
was flocculated completely, it, therefore, appearing to be extremely 
stable. This follows also from the behaviour of the liquid, while being 
concentrated on the waterbath: even the last drops retain their bluish 
violet colour, and the amorphous reddish violet powder, which is conti- 
nually deposited at the surface-border of the liquid, may be redissolved 
immediately into a colloidal solution of the same kind as the original 
liquid. This reversibility of the colloid corresponds also here with a 
smaller sensitiveness to electrolytes. On complete evaporation a violet 
and a grey powder are obtained; only the violet one is reversible. If 
heated for some time, it turns grey, afterwards black, and then it 
can no longer be dissolved. After being dried at 110° C. until the 
weight has become constant, the powder is black and possesses a 
metallic lustre. 

Of this product the content of ruthenium was determined in the 
way formerly described, and by the aid of the micro-balance. 

Analysis: 17,23 mGr. of the powder contain 4,55 mGr. Ru. The 
amount of sulphur was determined by volumetric analysis: a solution, 
the rutheniwmeontent of which was accurately known, was oxydized 
by a solution of potassium-permanganate of known strength, and 
the amount of sulphate afterwards estimated as BaSO,. Such solu- 
tions were prepared from a known weight of the pure greenish 
black sulphide by oxydation of its solution by means of an air current. 

Analysis: A quantity of the solution containing 2,40 mGr. ruthe- 
nium, gave 21,4 mGr. BaSO,, corresponding with 2,93 mGr. sulphur, 
this being 32,18°/,. Therefore 41,42 °/, of owygen is present, cor- 
responding with the formula: RwS,O,,, which was afterwards con- 
firmed by other tests. 


Calculated for RuS,O,, : Observed : 
Ru: 26,16 °/, 96,40 */, 
S: 32,82 °/, 32,18 
O: 41,02%, 41,49 °/, 


The oxydation of the solution to ruthenium sulphate and free sulphuric 


acid can, therefore, be expressed by the equation: 
7% 


100 
RuS,O,, +40 = Ru(SO,), + 2S0,, 


which was completely checked and confirmed by the deter- 
mination of the oxygen liberated from the permanganate used and 
absorbed by the substance, as well as by the quantitative measurement 
of the amount of sulphuric acid formed. For this latter quantity is 
equal to the total amount of acid found, minus the acid added for 
the volumetric analysis, plus the quantity of acid used during the 
titration with KMnO,. 

Analysis: A quantity of the colloidal solution, containing 2,30 
mGr. of ruthenium (= 0,0225 milli-mol. Rw) was titrated with 10 


1 
ecm. of a 35 normal solution of sulphuric acid and 4,9 eem. KMn0, 


of 0,09 normal, — if a normal solution be calculated as one con- 
taining 0,4 mol p. Liter, equivalent to 0,09 mGr. atom  p. cem. 
Therefore, totally 0,0882 mGr. O, corresponding with 40 to 1 Ru 
were used. As there are used at the same time 2,65 cem. H,SO, 
of the strength mentioned above in this reaction, 7,385 ccm. sulphuric 
acid remain. As 38 eem. of +; normal NaQOH-solution were 
necessary in the subsequent titration, and for 7,85 ecm. H,SO, 
only 29,4 of this MaOH-solution were necessary, it follows tbat 
0,043 milli-mol. H,SO, are formed in the reaction by oxydation of 
the sulphur. For every atom fw there are thus formed 2 molecules 
A,SO,, which data, with respect to the quantity of O absorbed in 
the process, demonstrate clearly the correctness of the equation just 
mentioned. . 

§ 5. Thus, while the original greenish black sulphide appeared 
to be RuwS,, this is transformed by vigorous absorption of atmospheric 
oxygen into the reddish violet compound RuwS,O,,, with simultaneous 
splitting-off of free sulphur, according to the equation: 


RuS, + 50, = RuS,O,, + 28, 
while the compound formed is afterwards further oxydized by the 
potassium permanganate according to the equution: 


RuS,O,, + 40 = Ru(SO,), + 2H,Q,. 


The red colloid is, therefore, by no means to be considered as 
the final oxydation-product of the greenish black sulphide, but it 
represents an intermediate stage on the way leading finally to 
ruthenium sulphate. This fact too could be contirmed by special reactions : 

a. Strong mitric acid oxydizes the red coloured solution at low 
temperatures slowly, but on heating more rapidly, to a solution 
which appears to contain free sulphuric acid. 

b. A solution of potassium permanganate makes the colour of the 


101 


colloidal solution and that of the permanganate rapidly disappear, 
while in the liquid SO,-ion becomes demonstrable. 

ce. Addition of H,O, and some diluted acid soon makes the colour 
of the solution disappear, while sulphate is formed. 

d. The red-violet powder obtained by evaporation from the 
solution, prepared by oxydation of the original green solution by 
the air, no longer gives a reddish violet colloidal solution, after 
being exposed to the air for three weeks; it gives a slightly greenish 
solution of acid reaction, containing a perceptible amount of SO,-ion. 

These different reactions prove undoubtedly, that the violet RwS,O,, 
is an intermediate product, which by further absorption of oxygen 
is transformed into the sulphate: Ru(SO,),. The compound has the 
composition of a normal rudheniumsalt ofpyrosulphurous acid : H,S,O,, 
and more particularly, of a pyrosulphite of tetravalent ruthenium. 
In this way the pyrosulphite appears as an intermediate product 
in the oxydation-process of ruthentum-persulphide to rutheninm- 
sulphate; most remarkable in it is, moreover, the colloidal nature 
of this intermediary rutheniwm-pyrosulphite, the dispersed particles 
of which bear at the same time an electrostatic charge of opposite 
algebraic sign to those in the colloidal solution of the original 
persulphide. 

Some other reactions of the colloidal pyrosulphite may be of 
interest here: 

a. The colloidal solution of the salt is rapidly decolourized by 
strong sulphuric acid. 

b. Hydrochloric acid, especially in higher concentrations and at 
higher temperatures, has the same effect, while sulphuric acid is 
formed simultaneously. | 

e. Sodium hydroxide (1:3) slowly decolourized the solution, but at 
higher temperatures even a more dilute solution does this rapidly. 

d. On addition of mercurous nitrate, the violet colour disappears 
immediately; a brown turbidity appears, and, after some hours, a 
brownish black precipitate is formed, which is probably a sulphide 
of mercury. 

e. Ammonium sulphide does not give a precipitate, but makes 
the colour disappear; su/phurdioxide, however, has no appre- 
ciable effect. 

f. A solution of sever nitrate turns the colour slowly into a brown 
one, and a brownish black precipitate is gradually formed, which 
is soluble in ammonia. 

g- On boiling the colloidal solution with sodiwm carbonate, the 
colour is rapidly changed into a pale green one. 


102 


h. A concentrated violet solution turns blue on addition of a dilute 
acid; but after neutralizing with a base, the red-violet colour is 
restored; etc. 


SUMMARY. 


In the above we were able to demonstrate, that the product 
of the precipitation of a salt of tetravalent ruthenium by 
ammonium sulphide differs with the temperature: at 100° C., 
brownish black RwS, is formed besides free sulphur, but at 0° C. 
greenish black RuS, is formed, which has the character of an 
irreversible colloidal substance, and which in the presence of 
ammonium sulphide in excess, gives a beautiful green, but unstable 
colloidal solution. At intermediate temperatures mixtures of both 
sulphides are formed besides free sulphur. 

The dark green sulphide and the green colloidal solution of Rw5S,, 
the particles of which are negatively charged, rapidly absorbs free 
oxygen, and is transformed into a reddish violet solution of the 
reversible colloidal rwtheniwn-pyrosulphite: RuwS,O,,, the particles 
of which bear a positive electrostatic charge. This salt is, in its turn, 
changed by oxygen (air, nitric acid, permanganate) into rutheniwm 
sulphate and free sulphuric acid. The properties and reactions of 
these different products were investigated on general lines. 


Laboratory for Inorganic and Physical 
Chemistry of the University. 
Groningen, May 1920. 


Anatomy. — “On the Index cephalicus and the absolute Dimensions 
of the Head of the Population of Holland’ By Prof. L. Boux. 


(Communicated at the meeting of March 27, 1920). 


For a general anthropological characterization of a people or a 
race, one is generally restricted to the three following characteristics : 
the degree of pigmentation, the length of the body and the propor- 
tion of the greatest length of the head or skull to the greatest 
breadth, expressed in a proportionate number, the so-called Index 
cephalicus. 

100 breadth 

length 

as the length always surpasses the breadth, the Index cephalicus 
will always be expressed by a number smaller than 100. When 
the Index cephalicus rises above 80, the head is called brachycephalic; 
when it falls below 75, the term dolichoeephalie is applied to it. 
Indices between 75 and 80 are characterized as mesocephalic. 
The Index cephalicus — being a proportionate number — does not 
teach us anything about the real dimensions of the bead or skull, 
every value of the Index may occur with larger and smaller skulls 
and heads. 

Some time ago I communicated the result of very extensive 
investigations on the two first mentioned anthropological charac- 
teristics — the degree of pigmentation and the length of the body, 
so that I may assume a sufficient knowledge of this physical dis- 
position of our population. Until now this was not the case with 
the third characteristic — the Index cephalicus — because it is not 
„so easy to obtain data for this in sufficient number, as for the 
characteristics mentioned before. It is true that I previously 
communicated data *) on the Index cephalicus, but these were based 
ona comparatively small number of measurements and so they must 
be considered as provisional communications only. 

I have gradually gathered a number of data, in my opinion suffi- 
cient, to te able to construct a reliable image of the Index cephalicus 


This is calculated according to the formula ‚and 


1) De Bevolking van Nederland in hare anthropologische samenstelling, in 
“GauLée, Het Boerenhuis in Nederland en zijn Bewoners", Utrecht 1909. 


104 


of the Dutch population, taken as a whole. To obtain this, it was 
of course necessary to gather the measurements of the heads of a 
sufficient number of people out of every province, and besides, from 
as many as possible different parts of the province. The result of 
my investigations is, that the data of 9975 male inhabitants of 
Holland are at my disposal, which are divided according to the 
provinces as follows: 

Groningen 290, Friesland 768, Drente 460, Overijsel 467, Noord- 
Holland 1326, Zuid-Holland 1495, Gelderland 1379, Utrecht 430, 
Zeeland 1243, Noord-Brabant 883, Limburg 1243. These numbers, 
though rather different, may be considered sufficient for the stating 
of the provincial averages. 

In the anthropological literature one is used, with reference to 
the head, to restrict oneself to communicating the average value of 
the Index cephalicus of some group of population and the statistic 
of the different values from which the average of the index is derived. 

But, as I said before, the Index cephalicus is a proportionate 
number, and so it does not teach us anything about the absolute 
measurements of the head or skull. Yet I think that the absolute 
dimensions of the head, from an anthropological point of view 
deserve more notice than they do now, because they give, after all, 
an idea of the size of the head, as is the case with the length of 
the body. In fixing the sum of the average length and breadth of 
the head of a certain group of the population, one bas a datum, which 
though insufficient, is approximately a standard for the size of the 
head. And this standard is even more reliable than the contour of 
the head, as, by fixing the latter, the varying thickness of the hair 
is included individually. My opinion is, that the sum of the breadth 
and the length of the heads is a rather reliable datum, to answer 
the question by comparison, whether the heads of the inhabitants 
of the different provinces are about the same size, or whether they 
differ in this respect. | worked out my data in this direction and here 
I give the result of my investigations. 

These results are given on the map, added to this article. Two 
numbers are placed in every province. The number placed in the 
northern part of the province teaches us the average Index cepha- 
licus of the persons measured; the southern cipher denotes the sum 
of the average absolute length and breadth of the heads of these 
persons. So both these numbers are provincial averages. This does 
not apply however to the numbers in the provinces of Noord- and 
Zuid-Holland. The numbers mentioned here only refer to the people 
measured in these provinces, after deduction of those living in 


ank 


L BOLK: „On the Inc 


Population 


L. BOLK: „On the Index cephalicus and the absolute Dimensions of the Head of the 


Population of Holland”. 


84,2 
348 


Proceedings Royal Academy, Amsterdam. Vol. XXIII. 


105 


Amsterdam and Rotterdam. The averages of these will be mentioned 
separately, and this will give an explanation why they were excluded 
from the calculation of the provincial averages. 

Let us consider first the Index cephalicus. The following tables 
show the value of the Index cephalicus in the different provinces. 


Province | denice “people 
Groningen 81.2 290 
Drenthe at) 460 
Overijsel 81.4 467 
Friesland 80.4 168 
N. Holland 80.5 136 
Utrecht 80.5 | 430 
Gelderland | 80.4 1379 
Z. Holland | 19.6 1239 
Zeeland | 80.8 | 1243 
N. Brabant | 81.5 883 
Limburg | 80.6 1234 
Amsterdam 79 590 
Rotterdam 19.2 256 


In this table are mentioned also the numbers related to Amsterdam 
and Rotterdam, these data will be referred to later on. From the 
table mentioned above, it appears that taking the small geographical 
extension of our country into consideration, the Index cephalicus 
is rather variable, as it oscillates between the two extremes 79.6 
(Z. Holland) and 81.5 (N. Brabant). 

On. comparing the provincial averages with each other, one cannot 
help noticing a certain regularity in the variability. The three 
northern provinces: Groningen, Drenthe and Overijsel form more or 
less one group, in which the Index cephalicus attains the value of 
81 or surpasses it even. 

One might add to this north-eastern territory the so-called Achter- 
hoek of Gelderland of which 313 persons are measured with an 
average Index cephalicus of 81.1. This north-eastern part of our 
population forms, as is generally known, linguistically and ethnolo- 


106 


gically a more homogeneous part, it is the Saxon element of our 
population, which distinguishes itself by a higher Index cephalicus. 

A second group ineludes the provinces of Friesland, N.-Holland, 
Utrecht, Gelderland and Z.-Holland, in which the Index cephalicus 
is strikingly equivalent, with the exception of Zuid-Holland, in which 
a relatively strong decline occurs, The average would be lower for 
Gelderland too, if the population of the “Achterhoek” — with its 
own Index of 81.1 — had been left out of consideration. 

In the second group the Index cephalicus reaches its highest point 
in 80.5; consequently the population of these provinces is a little 
more long-headed than that of the north-eastern part of our country. 
This is most evident in the province of Zuid-Holland, in which the 
inhabitants have the smallest degree of round-headedness. 

The part of our country meant here, is that one, in which the 
Frisian element of our population predominates and which is charac- 
teristically different from the Saxon element by a larger degree of 
long-headedness. 

The three southern provinces, which, according to my investi- 
gations, as regards the pigmentation of the population, form a unity, 
are not uniform as regards the Index cephalicus. The index reaches 
its highest point, viz. 81.5 in N.-Brabant, from which it appears, 
that here the most round-headed part of our population lives. Lim- 
burg and Zeeland agree, with only a slight difference, and are 
nearer to the proportion, occurring in the Western provinces. In 
connection with the high degree of pigmentation these facts point 
to the population being very mixed. However, this is easy to point 
out for the province of Zeeland. While the Index cephalicus amounts 
to 80.08 for the whole of the province, it falls to 79.9 with 
respect to Walcheren. The population of the most western part of 
Zeeland has a more long-headed type than the people living in the 
eastern part. This phenomenon is not unique. In the provinces of 
Noord- and Zuid-Holland the people, living in the villages on the 
coast and on the edge of the dunes have a longer and narrower 
head than the people living more inland. 

About this fact, I said before, that the populations of Amsterdam 
and Rotterdam were left out of account for the caleulation of the 
Index cephalicus of the provinces of Noord- and Zuid-Holland. I did 
this on purpose, because the inhabitants of these towns have a 
lower average index than the population living in the country. And 
because the number of those citizens measured, does not form an 
unimportant part of the whole population of the province, the value 
of the provincial average would be influenced too much by tbe 


107 


town average. That was the reason why I did not take these citizens 
into consideration, in fixing the provincial average. 

The difference between the indices of the population of the two 
towns and of the province in which these towns are situated, are 
apparent from the foregoing and from the following table. 


NoordHolland \ in the country 80.5 


( Amsterdam (ee 
in the country 79.6 
Zuid-Holland Rotterdam 79.2 


A comparison of these indices teaches us that the people of both 
these big towns have a relatively narrower head than the people 
living in the country, surrounding these towns. This fact is not new, 
it has been well-known for a long time that in general the population 
of a town belongs to a more long-headed type than the people 
living in the country, this rule holds good also for the towns of 
Amsterdam and Rotterdam. 

As far as I had a sufficient number of data at my disposal, I 
sought, in how far this rule could be applied to towns of a smaller 
size. This fact is proved by the following data for the towns of 
Utrecht, Arnhem and Haarlem. 


Utrecht (province) 80.5 
Utrecht (town) Gel 


Gelderland 80.4 
Arnhem 79.4 
N. Holland 80.5 
Haarlem 79.4 


Adding to these data those, mentioned above for Amsterdam and 
Rotterdam, it is obvious that in the towns mentioned above, the 
Index cephalicus oscillates between 79 and 79.4, and this is com- 
paratively far below the provincial averages. The citizen has, as 
regards the proportions of his head, a type of his own, opposed to 
the rural people and this type occurs already in towns of a relatively 
small extent. We only state this fact without going farther into the 
importance or into the theories, based on this fact. 

Let us consider now the second group of numbers, which are 
marked in the provinces on the map added to this article and which 
refer to the absolute measurements of the head. The number indicates 
the sum of the greatest length and greatest breadth of the head. 


108 


These numbers are useful to a certain extent to give an approximate 
answer to the question whether on an average the head of some 
part of our population is larger or smaller than that of the 
remaining part. 

The results for the different provinces are laid down in the following 
table. For every province the average greatest length, breadth, and 
the sum of the two values is expressed in millimeters. The data of 
Amsterdam and Rotterdam are left out of consideration, because of 
the fixing of the provincial average, these will be communicated 
separately. 


Province Length Breadth Total 


Groningen 192 | 156 348 

Friesland 190.6 | 153.4 344 

Drenthe 192 | 155.6 347.6 
Overijsel 191.4 155.9 347.3 
N. Holland 190 153.— 343. — 
Z. Holland 191.2 152.3 343.5 
Utrecht 190.3 153.2 343.5 
Gelderland 191.7 154.2 345.9 
Zeeland 190.4 154.— | 344.4 
N. Brabant 189.2 154.2 | 343.4 
Limburg 191.7 154.5 | 346.2 


On comparing the data in the last row, we are struck first by the 
fact that the difference between the highest and lowest value is 
remarkably small. The lowest value was found in Noord-Holland, 
where the sum of the average length and breadth of the head amounts 
to 343 mm., while Groningen with 348 mm. is the highest in the 
series. The largest difference amounts only to 5 mm. This difference 
is so small that one would feel inclined to consider it unimportant. But 
a look at the map convinces us that a certain regularity in the 
differences of the provincial averages cannoi be denied. On comparing 
the data on the map, it is evident, that without any exception, the 
eastern provinces indicate a higher sum-average than the western 
provinces. To say it differently: though the increase is small, it is 
yet unmistakable that in the direction of the eastern frontier of our 
country the heads are larger as far as this size may be expressed 


109 


by the sum of the length and the breadth of the head. This may 
appear from the following table, in which the eastern and the 
western-provinces are ranged side by side. 


Noord-Holland 343 Groningen 348 

Zuid-Holland 343.5 Drenthe 347.6 
Utrecht 343.5 Overijsel 347.3 
Zeeland 344.4 Limburg 346.2 


To the second series might be added the Achterhoek of Gelder- 
land with an average of 346.2. 

In my opinion the contrast between the two series is too regular 
for not having any significance. On looking for any connection with 
the ethnological elements of our population, it appears that the 
average is smaller, where the Frisian element is represented, while 
the Saxon element has a higher average, In this respect the diffe- 
rence between the population of Friesland (344 mm) and Groningen 
(348 mm.) is very evident. 

From the following table it appears that the breadth as well as 
the length of the head of the eastern population exceeds those of 
the western population. 

Average breadth of the head. 


Groningen 192 Friesland 190.6 
Drenthe 192 N.-Holland 190.— 
Overijsel 191.4 Z.-Holland 191.2 


Utrecht 190.3 
Averaye length of the head. 


Groningen 156 Friesland 153.4 
Drenthe 155.6 N.-Holland 153. 
Overijsel 155.9 Z.-Holland 152.3 


Utrecht 153.2 

Though both the dimensions of the north-eastern population are 
larger, the difference between the breadths is greater than that of the 
lengths. Consequently the people living in the east of our country 
have rounder heads and a greater Index cephalicus than those 
living in the western provinces. 

The last question to be answered is: how does the population of 
the two large towns stand in proportion to the people living in 
the country, surrounding these towns, with reference to the absolute 
measurements ? 

Concerning Amsterdam, the following averages were fixed: Length 
of the head 191.5, breadth of the head 151.3. 

On comparing these numbers with those of the province of N.- 


110 


Holland (190 resp. 153) it appears that the population of Amsterdam 
has longer and narrower heads than the rural population. 

This is the cause of the Index cephalicus of the population of 
the town being so much lower (79) than the Index cephalicus of 
the rural people (80.5). 

In Rotterdam I found the following averages: Length 190, breadth 
150.5. On comparing these measurements with those of the country, 
it appears that both breadth and length are smaller. 

The same peculiarity may be applied to the people living in the 
towns of Utrecht and Arnhem, as is evident from the following data: 


Utrecht Length Breadth 
Province 190.3 153.2 
town of Utrecht 190 150.6 
Gelderland 

Province gs J ahs 154.2 
Arnhem 190.— 151.5 


As regards the towns of Rotterdam, Utrecht and Arnhem, the 
head is shorter and narrower, in fact smaller, than that of the 
people living in the country, surrounding these towns. As the diffe- 
rences between the breadth-dimensions are larger than those between 
the length-dimensions, the Index cephalicus of the inhabitants of the 
town is smaller than the Index cephalicus of the rural people. 


Physiology. — “Kvperimental proof for the active dilatation of 
cross-striated muscle-tissue’. By J. BRAMSON. (Communicated 
by Prof. G. van RIJNBERK). (After experiments made in the 
Physiological Laboratory of the University of Amsterdam). 


(Communicated at the meeting of January 31, 1920). 


We are accustomed to observe that a muscle, after contraction, 
regains its original length by mechanical influences from without. 
So in situ, by contraction or tonus of antagonists, and outside the 
body by gravitation, eventually by weights, stretching the muscle. 

In 1871 Luciani’) discussed the question whether dilatation of a 
muscle was an active process. He wanted to explain the diastole of 
the heart partly by the active dilatation of the myocard. 

We need not be surprised in the least that tissue dilates actively, 
when we only think of the formation of pseudopodies in the case 
of amoebes and leucocytes. 

But it was not thought possible however that cross-striated muscle 
tissue could regain its original length by its own force, because a 
muscle, put on mercury, does not lengthen again after contraction. 

In 1900 Kaiser *) pointed out that the frog’s sartorius lengthens 
again actively on mercury, when oiled. He thought he had proved 
the active dilatation by this. 

To this however an objection was raised, not without reason, 
that every particle of the muscle, owing to gravitation tries to place 
itself as low as possible and yields to this impulse, as soon as the 
contraction of the muscle ceases. It expands on the mercury as 
much as possible and thus it becomes longer again. 

Consequently the problem acquired a different aspect. The muscle 
had to lengthen itself, while it was withdrawn from the gravitation. 
This is possible by bringing it into a liquid of the same specific 
weight as the muscle has, viz. of 1,041. 

The difficulties, connected with this, are very great. A salt- or 
sugar-solution of specific weight is not isotonic. Even a raffinose 


1) L. Lucranr. Dell’ attività della diastole cardiaca. Rivista clinica Bologna. 
2) K. Karser. Ueber die Wiederausdehnung des kontrahirten Muskels. Centralbl. für 
Phys. XIV p. 195, 


112 


solution of this specific weight still causes a depression of the 
freezing-point A = — 0,59° C. Ureum penetrates quickly into the 
muscle and makes it soon heavier. Most of the other organic com- 
pounds, which are heavier than water are little soluble, have strong 
viscosity (albumen), are more or less poisonous, irritating or 
anaesthetic. 

I used a mixture of chloroform and benzene of a specific weight 
of 1,041, in which the muscle could be suspended, and I noticed 
several times very distinctly that the muscle lengthened itself again 
after the contraction. As chloroform and benzene are both very 
strong poisons, one is able to observe the muscle only for several 
minutes in this medium. 

] think I may ascribe the fact that these poisons do not affect 
the muscle immediately, to a capillary layer of Ringer’s that wets 
the muscle and through which both the liquids diffuse only slowly. 

Attempts to take a photograph of this phenomenon have not 
yielded beautiful results, owing to little secondary movements of 
the muscle (streams in the liquid through the contraction-push ete.). 
A cinematographic photo would give better results in this respect. 

Looking out for a better recording method, I thought I might be able 
to apply the graphic method, generally used in the muscle physiology, 
though this seemed very doubtful, taking into consideration the 
extremely inconsiderable energy of the dilatation. 

Yet by using an instrument of a minimal mass and friction I 
succeeded in recording a curve (Fig. 1). One sees on this figure a 
fragment of a curve. The upper row are curves of simple muscle 
shocks in Ringer’s liquid, the two following rows are curves of 
tetani in the same liquid. The 4* row is a curve of tetani in a 
mixture of chloroform and benzene. The five lower rows are simple 
shocks in this mixture. All the curves are of the same muscle. The 
steep part of the curve is the contraction, the dilatation is very 
clearly perceptible, but much slower. 

A considerable improvement has been made in this method of 
registration by Professor VAN RIJNBERK, who suggested to me the 
principle of a very useful instrument. It consists of a glass tube, 
with a hole in the side, over which an extremely thin membrane 
of rubber is stretched. A needle is stuck through it, which writes 
with one end on a sooted drum, placed horizontally and with the 
other end is stuck in the Achilles tendon of the frog’s gastrocnemius. 
The other end of the muscle is attached to a hook, which serves 
at the same time for one stimulus-electrode. It pierces a cork, which 
shuts off the tube on one side. Each of these stopcorks is perforated 


113 


by a glasstube through which the apparatus can be quickly filled 
with a liquid (Fig. 2). 


Fig. 1. Myograms of a suspended frog’s gastrocnemius (real size). 


Fig. 2. Apparatus used for the recording of the reproduced myograms 
in fig. 1 (l/, of the real size). 


From the preceding communication we may conclude that the 
dilatation occurs with so much force that it is able to overcome 
the friction of the writing-needle over the drum. 

I put the question to myself whether the muscle would be able 
to lengthen itself in opposition to the gravitation. This led me on 
to two new proofs: 

When we do not put the muscle into chloroform and benzene, 

8 

Proceedings Royal Acad. Amsterdam. Vol. XXIII. 


114 


but into a Ringer’s solution, then it will bulge between the two 
points A and ZB on which it is hung, the apparatus being held 
horizontally. It is easy to understand that the gravitation brings the 
two points A and B closer to each other, but can never make them 
diverge. Consequently the gravitation will act against the dilatation. 
Notwithstanding this the muscle lengthens itself again. Owing to 
this observation we are able to record curves without the stretching 
weights, which always deform the curve, while we need not use the 
poisonous chloroform-benzene mixture. 

When it was once stated that a muscle is able to lengthen itself 
in Opposition to the gravitation, I tried if it would even be able to 
raise its own weight. I succeeded actually in seeing a muscle, placed 
vertically, fastened at the lower end, lengthen itself after contrac- 
tion. This fact had been observed some days before, but without my 
knowledge, by Dr. Bakers and Mr. Prakken, in this Laboratory. 

It being proved that cross-striated muscle tissue dilates actively, 
two new points of view have been opened : 

1. We are able to record curves, excluding all the forces which 
could deform it. | 

2. With the aid of this technique it will probably be possible to 
find a solution to the problem, raised by the result of my experiments. 
The question is: what intramuscular forces cause this dilatation and 
through which are they influenced? The dilatation may be caused 
by the perimysium externum, the sarcolemma, the sarcoplasma or 
by the fibrils. 

l can state at all events, that the perimysium externum is not able 
to cause the dilatation only by itself (by its elasticity), for even a 
fragment of muscle tissue, cut out by me, actually lengthened itself 
again. The sarcolemma, which is a homogeneous elastine-membrane, 
has a tendency to diminish its surface, in other words: to take the 
globular shape. 

Consequently it will never be able to lengthen the muscle. 


December 19th 1919. 


Physiology. — ‘“‘Jdentity of the blood-digestive and gelatine-liquefying 
bacterial actions.” By Prof. J. J. van Logurm. (Communicated 
by Prof. C. Eykmav.) 


(Communicated at the meeting of March 27, 1920). 


In investigations on the determination of the so-called specific El- 
Torvibrios with regard to choleravibrios, I obtained as a result of 
more general importance a sharper definition of the idea ‘‘haemo- 
lysis” *). By admitting that the changes in the blood, caused by 
bacteria, may be of different nature, I suggested to understand by 
haemolysis only the causing of oxyhaemoglobin to come out from the 
red blood corpuscles; I opposed to this the digestion of blood elements 
by bacteria, which I indicated as haemo-digestion. 

Investigations by others (Grine’*) Lowy’) Fru‘), Kraus‘), Sopnie 
WorLMANN®) have taught us the practical significance of these for 
the distinction of choleravibrios. _BAERTHLEIN °) pointed out the 
necessity of a right distinction of these ideas, also in the case of 
other bacteria, whereas SNapprr*) — in connection with his inves- 
tigations on the decomposition of oxyhaemoglobin in the alimentary 
canal — has occupied himself with the nature of the digestion. 

The following illustrates the latter problem. 


Some time ago already, I put the question whether the haemo- 
digestive quality of the choleravibrio is identical with its collolytic 
capacity and I mentioned several facts which pointed to this 
possibility. 

1. Both the qualities are transient and their decline runs parallel 
in a certain strain. 

2. The processes of the haemodigestion and of the gelatine-lique- 


1) Centralbl. f. Bakt. Ie Abt. Orig., vol. 57, 1911; vol. 67, 1913 and vol. 70, 
1913; Ned. Tijdschr. v. Geneeskunde, 1915, II, p. 22. 

2) Indian Journal of medical research, vol. 2, 1914. 

5) Centralblatt f. Bakt., 1, Orig., vol. 75, 1915, 

4) Geneeskundig Tijdschr. v. Nederlandsch Indië, vol. 53, 1913. 

5) Die Cholera asiatica und die Cholera nostras, 1914 (with Busson). 

6) Wiener klinische Wochenschrift 1917, 
~ 7) Centralbl. f. Bakt., I, Orig., vol. 74, 1914. 

8) Ned. Tijdschr. v. Geneeskunde 1918, I, 1911. 

ge 


116 


faction are both checked by the appearance of the acid in the 
nutrient medium. 

3. The virtual gelatine-liquefaction-halo, which one can construct 
by means of EiJKMAN’s gelatine-stripe method *), is, it is true, not 
congruent with the haemodigestion-halo in the blood-agar plate; 
but on the oxyhaemoglobin plate the halos come very nearly together. 

4. The strains that are strongly haemodigestive consume casein 
also intensely; the identity of the casein-digestive and the gelatine- 
liquefying ferment has been made. very plausible by Etykman, by 
means of the gelatine-stripe method. 

SNAPPER’s discovery that the digestion of blood has a much quicker 
process in blood-bile-agar than in blood-agar, incited me to put my 
hypothesis, stated before, to the test and to enlarge my investigations 
on the decomposition of oxyhaemoglobin by other bacteria as well. 

I want to refer to the fact that the origin of the greenish and 
clear halo round the colonies of a haemodigestive choleravibrio on 
the blood-agar plate is actually based on transformation of the 
oxyhaemoglobin (SNAPPER entered into the details of this to confirm 
my previous spectroscopic research): first haematine-like bodies ori- 
ginate, which are decomposed in the course of the experiment. 

This. is also obvious in the decrease of the greenish colour near 
the stripe-culture, while the pyridin-chromogen reaction takes place 
slower at that point than at a greater distance from the culture. 

On oxyhaemoglobin plates on which, as I pointed out before, the 
process of the digestion of the oxyhaemoglobin is to be seen clearly 
with the naked eye by the zones of different colour, it is possible 
too to indicate the further decomposition of haematin by means of 
pyridin and sulphurammonium. On the blood-bile-agar plate the 
cholera vibrio is sustained in the digestion of the oxyhaemoglobin. 

By the action of the bile on the blood, the haemoglobin has not 
only come out (as is the case in the oxyhaemoglobin plate), but has 
been transformed into haematin-like substances besides. The process 
of decomposition is progressing already considerably when the cholera 
vibrio begins to influence it, which is revealed in the quick forma- 
tion of a broad clearly transparent and colourless halo round the 


1) The gelatine stripe method is executed by bringing, by means of a platinum- 
loop, stripes of liquefied gelatine close to the culture on the agar plate. The 
gelatine becomes solid at an ordinary temperature; so it is possible to trace how 
far the gelatine stripe (after some time at 22° C. e.g.) disappears from the 
culture by the action of a ferment. 

The figures in this text show how one may construct the gelatine liquefying 
halo in this way. (In Fig. 1 e.g. the white dotted line). 


117 


stripe-culture as an expression of its haemodigestive power. Even 
choleravibrios that influence the blood-agar-plate exceedingly slowly, 
are able to form a halo on the blood-bile plate. I tried this halo- 
formation of the choleravibrio on the blood-bile-agar plate by means 
of the gelatine-stripe method and compared this one with the halos 
on blood plates and casein plates. 

The result of these experiments which I made with several new 
and old cholera strains of a very divergent haemodigestive character, 
is shown half schematically in the following figures. 


ed 


( 


! 
! 
I 
1 
i 
t 
! 
! 
i 
1 
t 
| 
\ 
\ 
\ 


Nn tee 


J 


Fig. 1. Fig. 2. 


Fig. 1. The virtual (white dotted) gelatine-liquefying halo lies 
considerably beyond the halo of the haemodigestion on the blood- 
agar plate. 

Fig. 2. The zones approach each other very clearly on the oxy- 
haemoglobin plate; in some cases (as is shown on the figure) there 
is already an indication of transformation of the oxyhaemoglobin, 
whose line of demarcation is congruent with the halo of the gela- 
tine-liquefaction. 

Fig. 3. The halos of further oxyhaemoglobin transformation and 
gelatine-liquefaction are quite congruent on the blood-bile-agar plate, 
a condition which agrees with that on the casein plate. (Fig. 4). 

By this fact the identity of the oxyhaemoglobin-digestive, casein- 
digestive and gelatine-liquefying ferment of the cholera vibrio is 
confirmed. 

There is this profitable difference between the blood-bile-agar plate 
and the blood-agar plate, that the process of haemolysis does not 
take place in the former. 


118 


In this way | was able to compare haemodigestion and gelatine- 
liquefaction within the group of Proteus-bacteria. 

All the Proteusstrains which | have at my disposal (e.g. some 
indol-producing representatives of Bacteriwm vulgare Hauseri, Pro- 


Fig. 3. Fig. 4. 


teus X,, of Wem and Ferix producing indo] as well and several 
representatives of the Bacterium anindologenes distinguished by me 
as a separate species) are haemolytic, that is to say, they form a 
halo of blood-agar and cause the oxyhaemoglobin to come out from 
tbe blood-broth. 

They do not all liquefy gelatine. The an-indologenic strain Pneu- 
maturia, which liquefied gelatine strongly 16 years ago, lost this 
power long ago. This strain is the only one forming no halo on the 
blood-bile agar plate. Other facts may be added to this argument 
for the conception that also within the Proteus group, oxyhaemo- 
globin-digestion and gelatine-liquefacting are caused by the same 
ferment: only the non-haemodigestive Proteus-strain does not digest 
the casein, as the others do and the liquefaction halos, constructed 
by means of the gelatine-stripe method are congruent with the halos 
of haemodigestion on the blood-bile plate. 


Moreover I mention the experiments on B. prodigiosus, a gelatine- 
liquefying coccus from the air, B. anthracis, Vibrio dunbar, all of 
them haemodigestive and liquefying the gelatine, opposed to 5. typhi, 
coli, B. paratyphi A. and B., B. pseudo-tuberculosis rodentium, 
B. dysenteriae SuiGa and Fiexner, which do not form a halo on the 


119 


blood-bile plate and do not cause the gelatine to liquefy. Both these 
results are in favour of the identity of the actions in question. 


I want to make one more remark; as l pointed out before, some- 
times one sees in an organism, of which the casein balo and the 
gelatine halo cover each other entirely on a nutrient medium, that 
their congruence has disappeared on another nutrient medium. 

; When glycerine has been added to the casein plate, on which 
the cholera vibrio is inoculated, the virtual halo of liquefaction 
will remain at some distance within the halo of casein-digestion. 

So I observed also that the halo of gelatine-liquefaction in a 
strongly haemodigestive coccus, isolated from the air, is a little larger 
than the halo of the haemodigestion (on the blood-bile plate). The 
above-mentioned experimental experience teaches us that this does 
not contain an argument against the identity of the haemodigestive 
and collolytic bacterial action. 

I conclude by remarking that these experiments teach us that 
the blood-bile plate as well as the casein plate may serve for the 
substitution of the broth-gelatine in determining bacteria. This is 
an advantage while working in tropical littorals, where the use of 
the nutrient media is subject to difficulties owing to the high tem- 
perature of the air. 


Amsterdam, Institute of tropical hygiene, department 
Mareb 1920. of the Colonial Institute. 


Physics. — “Remark on the possible. existence of binding rings in 
diamond.” Communication N°. 4 from the Laboratory of 
Physics and Physical Chemistry of the Veterinary College at 
Utrecht. By Dr. N. H. KorkKMEIJER. (Communicated on behalf 
of Prof. W. H. Kersom, Director of the Laboratory, by Prof. 
H. KAMERLINGH ONNES). 


(Communicated at the meeting of January 31, 1920). 


§ 1. Some years ago Drpise and ScHERRER*) investigated, whether 
the assumption of the existence of “binding rings” of 2 electrons each 
between the carbon-‘‘ions” in diamond, was in accordance with the 
intensities of the beams of X-rays, reflected by some planes of the 
lattice as calculated on Braae’s pattern. 

For some time I have doubted however, whether the conclusion 
of DrBije and ScHeRRER, that the mentioned binding rings in diamond 
do not exist, might be regarded as right. In their calculation 
Degije and SCHERRER use an approximating representation, treating 
the two electrons of each binding ring as coinciding in their 
mutual centre of mass. Now I found, that the introduction of this 
simplification may be of great influence on the results obtained. 

These considerations induced me to calculate the relative intensities 
of the lines in the Röntgenogram obtained by the method of DeBije 
and ScHerrer and that without neglecting the real positions of the 
electrons in the binding rings. The comparison of these calculations 
with the observed intensities might give the solution of the question, 
whether these intensities are in agreement with the assumption of 
the binding rings. Eventually it might also enable us to deduce the 
radius of the binding rings. Proceeding in this way I found that 
without making new assumptions the conclusion of DeBĲE and 
ScHERRER must be accepted. At the same time however I got the 
impression, that the observations at our disposition on diamond only 
do not permit the drawing of a definite conclusion. This is evident, 
as the reflection of the X-rays is effected not only by the eventual 
binding electrons, but also by the electrons circulating about the 
nucleus (and perhaps even more or less by the eventual electrons 


1) P. Degise and P. Scuerrer, Physik. ZS. 19 (1918) p. 476. 


121 


within the nucleus). Moreover the structure-pattern of the crystal 
is not the only factor that influences the intensities of the RÖNTGEN- 
beams reflected by the different planes, but there are more factors 
viz. the polarisation — the number of planes — the temperature- 
and the summation-factor calculated for this case by Desur and 
SCHERRER. 

I therefore thought it better to wait with my conclusion till 1 had 
finished the measurements on other elements with diamond-structure. 
As such Si, Ti and grey Sn‘) in the first place came into con- 
sideration °). By these measurements I hoped to be able to separate 
better the different influencing factors. 

As however in these Proceedings XXII p. 536 Cosrrr has 
treated the question of the binding rings, my considerations and 
calculations may be already of some interest, especially as in some 
principal points and in the conclusion they do not agree with Cosrer’s 
paper. When my measurements on this subject are finished I hope 
to come back to the question. 


§ 2. In the main DeBije and Scuerrer base their declining con- 
clusion on the fact, that the line (222) that fails on the photos, 
should be one of the most intensive according to the simplified 
model. This is directly evident from fig. 1 taking the distribution of 
the particles over the planes into consideration. Here the full lines 
indicate the relative positions of the planes (111) or (222) of the 
nuclei with the inner Bour-circles concentrated in them. The broken 
lines represent the binding rings concentrated in their centre. 

2 When however the approximation is 
used no longer, each plane a remains 
plens! DA} _unchanged, each plane b is split up into 
| «Ay 6 planes that oscillate. 

is When we want to investigate how this 
influences the structure-factor, we must 
know the simultaneous positions of the pairs of electrons of the 
different rings. 

When we wish thereby to take into consideration the symmetry 
of the point-system, where now moving elements occur, the sym- 


DIE Vee. 


metry-elements which could be called “axis of rotation’, “‘screw-axis” 


1) A. J. Bur and N. H. KorkMeEweEr. These Communications NO. 2b. These 
Proceedings 27 (1918) p. 359. 

2) Rightly CosTER remarks (These Proc. XXII p. 541) that also measurements 
on Ge would be of interest. 


122 


and “plane of symmetry” are no more sufficient. Besides the position 
of the particles it is necessary to take also into consideration the 
time. For moving point-systems we may then introduce as analogous to 
the screw-axis a time-axis of rotation with n periods, with the meaning 


that the system becomes equal to and similarly placed with itself 
° 


after a momentaneous rotation of in a definite sense round 


n 
that axis, followed by a certain time-interval. It is apparent that 


the above mentioned moving system can have such axes, namely 
° 


ternary ones. According to the sense of rotation of the time 


n 
Alf 2 2 
interval in question is then en period of the electrons. For 


the configuration of the electrons in the binding rings then only the 
following possibility remains: 

1st Looking from a nucleus the sense of circulation in the four 
surrounding rings is the same; 

2nd. Consider a plane through two of the lines connecting one 
nueleus with the four surrounding nuclei. When an electron of the 
ring round one of these lines passes this plane, this is also passed 
by an electron of the ring round the other line and that in the 
opposite direction. In this case the electrons in parallel rings have 
the same phase, in non parallel ones the phases are connected by 
a simple relation. 

Now introducing into the discussion of the time-space-symmetry 
as analogue of a plane- and centre- of symmetry, a reversal-plane 
resp. centre of symmetry viz. a plane (centre), which acts momen- 
taneously as a mirror for the point system, while also at a definite 
moment all velocities are reversed’), the above discussed system 
has also three quaternary reversal mirror-axes of rotation and six 
reversal-planes of symmetry. 


$ 3. Now we can easily prove that the radius of the binding 
rings may be chosen in such a way that the structure-factor for the 
plane (222) will be nearly O at every moment and not a maximum, 
as was obtained by D. and Scu. with their approximation. 


1) This proceeding is analogous to the operation of reflection by a plane or a 
centre, where resp. one or three coordinates change their sign, while the time 
must be kept constant. This is evident when the reversal of all velocities is regarded 
as the “changing of the sign of the time at a certain moment” or as the “reflection 
of the time in a definite moment”. In connection with this is also the assumption 
of a definite sense of rotation for a time-axis of rotation. 


123 


In fig. 2 a and the full lines have the same meaning as in fig. 1. 
The nucleus Q is surrounded by 4 nuclei, one of which is P. 
R is another one and S and 7’ have not been drawn. Let QS and 
QT rotate about PQ until they coincide with QR. Then the binding 
rings about QR, QS and QT coincide too. The above mentioned 
relation between the phases is now so, that in those coinciding 
rings the pairs of electrons form a regular hexagon. The positions 
of the planes 6' and 6" into which the planes 6 of fig. 1 are split 
up are not changed by this rotation. In fig. 2 the phase has been 
chosen in such a way that those 6 planes form pairs that coincide 
and so give the three planes 6’ and 6", the construction of which 
needs no further explanation. In reality the hexagon pgqrstu is 
perpendicularto QR and at equal distances from Q and R. In the 
fig. it has been represented as shifted downwards and clapped down 
on the plane of drawing by a rotation about a diameter perpen- 
dicular to QR. The hexagon ABCD EF is the projection of the 
former on a plane perpendicular to the plane of drawing through 
PQ and clapped down on this plane by a rotation about this line. 

When now the radius of the rings has been chosen so, that 
6" falls halfway between 4' and a, the structure factor of (222) in 
the phase represented in the figure will become zero. From the 

ENE i 1 
construction it is evident that the radius must be chosen ee 245 
times the distance between two nuclei. It is found that in that 


124 


case the value of that factor remains small also for other phases, 
especially when the radius has been chosen a little greater. This 
would meet the chief objection of D. and Scu. to the binding rings 
as has also been shown by Coster with a somewhat different way 
of representation. 


§ 4. For the calculation of the intensities of the other reflected 
beams I proceeded in the following way : 

As a consequence of the smallness of the remaining inner ring of 
two electrons (of one quantum probably for each electron) compared 
with the binding rings (that are perhaps of two quanta for each 
electron) I assumed in the calculation of the intensities of the 
other lines the radius of the first ring to be zero and that 
ring to give then a “diminishing-factor”, analogous to that of D. 
and Sca. *), while also for nucleus + ring a temperature-factor had 
to be assumed. All this was comprised into the ‘“diffraction-factor” 
A(< 2) for nucleus + ring. In the same way the factor B (on) 
referring to each of the binding electrons comprised also the tem- 
perature factor of these electrons. 


; 8 
Replacing 76 by v we find then at the moment ¢ for */, of 
the structure-factor for unmixed triplets 


A A Zr 
stg == 


5 (blebs) HE ús 
+ Be | cos 4 "|i cos wt +h,cos (wr a. =) +h, c(t + 5) | == 
5 (hatha) OE An 
+e cos Zul h, cos wt—h, cos | wt + — | — h, cos | wt + — | | + 
1 2 ate 3 
(ith) In An 
+e cos $ | - h,cos wt Hoof of 4- =) h, cos (w + =) + 


> (hh) on Ar 
+e cos } v - h,cos wt—h,cos (wr == =)+ h, cos (ot Er |. 


In this expression we may substitute the unmixed indices-triplets 
of the lines that were to be seen on a photo of D. and Scn., take 
the modulus-square, multiply this by dt, integrate this over a period 


1) P. DeBise and P. ScHERRER, l.c. 


125 


9 
and finally divide it by 2E, In this way a measure for the inten- 
W 


sity of the lines is obtained. The squares and products of cosines 
obtained in this calculation were transformed into a sum of cosines. 
le 


— and 


Thus we find the following expressions, while further | Sous 


| Ons. fa 


duly got the value 0. 


TRE B: 

: ze EFA anar J,(20) H3B°I (3) + (3A BY/2-3B)J,(v) 

Hel! =A? LAB} 2B°J, (v /12)—6B*T,(20) +4 ABU, (v 8) 4A BJ,(0) 

Boel pares, 42, (Av) +2 BS (VV 13) + BS (vy 12) + 2B, (oy 7) + 
+ (ABY/2-+ 3B9 (20) + (BY—2ABY2)J,(0//3)—(ABY2+ BY)J,(0) 

se = A? + 8B? } 8B? J, (4x) — 8AB J, (20) 

RIE o's) adn jon! : B 

itl A" 2B + BJ (0/28) + B° (0/20) + = J,(40)-2 BJ (0/13) 


BA 
— B*J,(3v) +(2ABV/2+2B°)J, e+ —4By2)J (20) +4 By/2d,(v) 
ISreal? 
64 
where J,() represents a Bessrr-function of order 0. 


—§ BY +4 3 BJ, (4v) + 3B J, (vf/12) + 9B J, (20) 


Bv trials I found that is small, when v is in the neigh- 


1 
bourhood of 1,63 or when 7 is about 5.79 times the distance of the 


nuclei (comp. the result obtained from fig. 2). This value is of the 
order of magnitude that would correspond to a ring with two 
1 

quanta for each electron, namely | 194 times the distance of the nu- 
clei. Supposing that the ring has exactly two quanta we obtain the 
following expressions : 

Sak 

ee , A? — 1,16 AB 4 0,67 B 


S 2 
| ge — A? — 1,84 AB + 6,18 B 


126 


a — } A? + 0,62 AB + 1,62 B 
Sool” gs 4 2,41 AB + 6,99 B? 
En ’ “10; 

[Sissi 2 2 
21 = 4 At + 0,98 AB + 1,69 B 
[Ssst , 
ie 0,16 B 


The rather small intensity found in this way for the line refer- 
ring to the plane (222) seemed not irreconcilable with the obser- 
vations. 


$ 5. Before the calculation and the observation can be compared 
we must multiply the expressions found in $ 4 by the polarisation- 
factor, the plane number-factor, and the modified summation-factor. 
Just as well we can equalize the above expressions with the inten- 
sities obtained by Derpijr and ScHerRER corrected for the absorption 
in the rod and after division by the product of the three factors. 
In this way we obtain the following equations where k is a 
proportionality factor 


A? — 2,32 AB + 1,34 B? = 2391 k for (111) 
A? — 1,84 AB + 6,18 B? = 913k » (022) 
A? + 1,24 AB 4 3,24 BX= 610k he 
A? + 2,41 AB + 6,99 Bt= 483% » (004) 


A’? + 1,96 AB + 3,38 B? —= 446& *) waa (ite) 


A must decrease here: firstly exponentially with H?—=h,?+-h,*?+A,? 
by the heat motion. As coefficient of H? in the exponent of e we 
chose one of the values given by Desir and ScHeRRER le, viz. the 
largest one, that which is derived on the assumption of the exist- 
ence of a zero energy and which appeared to have the greatest 
advantage for the assumption of binding rings. Secondly A must 
decrease with H? because of the two remaining electrons acting as 
“sphere of electrons”. 

For the sake of simplicity I supposed that the action of these 


') In the table on p. 481 of the cited paper of D. and Sch. there evidently 
occur some typographical errors. In column 6 2,04 must be about 4.02, 11.56 
about 6 and in column 7 13 must be about 22. 


127 


two electrons might be regarded as that of a sphere over the whole 
surface of which the electrons circulate uniformly. The formula for 
270 


i 


a < 5 
the diminishing-factor then becomes PE , where vis the radius 


mo 


a 
of the spherical surface in question and a the edge of the elemen- 
tary cube, so that we must put for A: 

2n 


sin ae 
A — 2 e—4,5. 10-3 H? i ‘ 
a 

For the electrons of the binding rings we have only to attend to 
the heat motion. Thus I replaced B by e-”, 

When we compare the righthand sides of the equations, that of the 
first, viz. that for (111), is exceedingly large. When however 
we compare the left hand sides, the terms containing B show that 
in the equation for (111) this left hand side will become smaller 
than the left hand sides of the other equations. This difficulty will 
however not be met with, when a’ is chosen so great, that the 
terms with B may be neglected. This comes about to the same as 
the ascribing of the decreasing of the line intensity with H*, observed 
by DerBijr and SCarrreR, only to the circulation of the two remain- 
ing electrons about the nucleus. I calculated that for the radius 
of the spherical surface over which as a mean these electrons may 
be regarded to move, the value 0.075a had then to be chosen. This 
is about thrice the radius of the Bonr-ring (one-quantum for each 
electron) about the nucleus. This would not be an improbable value 
of the radius of that sphere. Then however we must take a’ at 
least equal to 0,6 in order to find somewhat fitting solutions of the 

2 nr? 


a? 


equations. When we put a? = (r = mean deviation by the 


„heat motion) r should thus become somewhat smaller than 0,2 a 
and such a great deviation seems to-be in contradiction with recent 
conceptions on the specific heat of solid bodies, to which the elec- 
trons contribute to a small degree only. We may lower the a-value 
wanted by taking for the radius of the electronic sphere about the 
nucleus 4 or 5 times instead of 3 times the radius of a ring of 
one quantum; then however this radius becomes improbably large 
and «’ remains still too large. *) 


y In my opinion Coster |.c. would also have met with these difficulties when 


128 


Summarizing, I am inclined to reject with DeBije and SCHERRER 
the existence of the binding rings in diamond as long at least as 
no other assumptions give us another insight into this question. Mean- 
while investigations (comp. § 1) on other tetra-valent elements, 
perhaps also on solid hydrogen are desirable in order to obtain 
more detailed indications on the configuration of the electrons in 
the electronic sphere. 


only he had continued his calculation so far that a direct comparison with the 
experimental data had been possible. 


Chemistry. — “The aluminates of sodium. Kquilibriums in the 
system Na,O—Al,O,—H,0O”. By Dr. F. Gouprraan. (Communi- 
cated by Prof. J. BöESEKEN). 


(Communicated at the meeting of April 23, 1920). 


Introduction. 

In a preceding paper’) a survey was given of the equilibriums 
that may arise at 30° in the system: Na,O—ZnO—H,O. Among 
other things the range of existence of the zincate of sodium and the 
stability-relation between ZnO and zinchydroxide were determined 
in this paper. In view of our still very slight and incomplete know- 
ledge concerning the corresponding compounds of other metals, it 
was now tried also to determine similar equilibriums of some of 
these metals. The following will give a brief survey of the results 
obtained in the system: Na,0—Al,0,—H,0. 

Although the existence of aluminates has long been suspected and 
in nature some even seem to occur in a crystallized state in some 
minerals (e.g. the spinels), not a single exact datum regarding these 
bodies is to be found in the literature. To be sure it is known that 
also in elaborating the mineral bauxite by treating it with soda, 
aluminium is fixed as an aluminate, but we are by no means 
acquainted either with the composition or with the stability of these 
compounds. It is true that several investigations have been made in 
this direction, but in none of these the solid phases have been 
isolated. The compositions that are therefore given to the aluminates 
have been determined in a more or less indirect way and serious 
objections may always be raised to the methods applied in doing so. 
Therefore it is not wonderful that the results are often in serious 
mutual contradiction. A short summary of the knowledge obtained 
up till now about the aluminates, from which this will further 
appear, is the following: 

Cavazzi*) first suspected the existence of these compounds and 
ascribed to them formulae like: NaAlO, on the ground of his obser- 
vation that 1 gram-atom Al will dissolve in 1 gram-molecule NaOH. 


1) Proceedings XXII, 179 (1919). 
*) Gazz. chim. ital. 15, 205 (1885). 


Proceedings Royal Acad. Amsterdam. Vol. XXIII. 


130 


Similar observations were made by Prescorr’) and Lyre’). A long 
time afterwards an investigation was made into the value of the 
molecular-weight of the sodium compound by Noyes and Wrraner ®), 
on the basis of the lowering of freezing-point which would occur in 
dissolving Al in NaOH. As however no perceptible lowering in the 
freezing-point took place and therefore the number of particles before 
and after the dissolution had to be equal, they determined upon the 
composition: NaAlO,; this compound was supposed to be divided 
into two ions and so to form just as many particles as the original 
NaOH molecules. It need not be demonstrated any further that this 
reasoning is uncommonly weak and little suitable as a powerful 
argument in favour of the composition NaAlO,. 

Herz‘) ascribes the composition: Na,AlO, and K,AIO, to the 
Al 
3 
equal to 1 : 1. On the ground of similar experiments Woop ’*) on 
the other hand again arrives at the composition: NaAlO,; although 
from his figures the proportion NaOH: Al,O, often proves much 
larger than would agree with this composition. 

Hantzscn *) performed some conductivity measurements in alumi- 
nate solutions of various concentrations and concludes from these 
that the aluminates behave like salts of mono-basie acids. With such 
salts, which are even hydrolized to a great extent in fairly concen- 
trated solutions forming partly colloidal Al(OH),, the conductivity- 
method entirely loses its value. We are not even sure of the nature 
of the ions present. Hanrzscu’s observations therefore cannot teach 
us anything of the composition of these salts. 

Finally we may still mention that SiapE’) tried to find out the 
composition by applying the law of mass action to aluminate solu- 
tions that are in equilibrium with Al(QH),. His reasoning does not 
hold exactly, because in diluted solutions the solubility of Al(OH), 
is extremely slight, so that small observation errors become of 
very great influence on the final result. In the strong NaOH solutions 
of comparatively large viscosity, in which the solubility can be 
measured very well, it becomes inadmissible to apply the law of 


aluminates, because in solution he found the proportion Na: 


1) Journ. Amer. Chem. Soc. 2, 27. 

2) Chem. News 51, 109 (1885). 

3) Zeitschr. f. phys. Chem. 15, 694 (1894). 
4) Zeitschr. f. anorg. Chem. 25, 155 (1900). 
6) Journ. Chem. Soc. 93, 411 (1908). 

6) Zeitschr. f. anorg. Chem. 30, 296 (1902). 
7) Zeitschr. f. Elektroch. 17, 261 (1910). 


131 


mass action. A proper equilibrium-constant is therefore not to be 
expected. 

The only exact datum concerning the composition of the alumi- 
nates is the melting-diagram of the system: CaQ—AI,O, determined 
by Snurprerp and Rankin‘). From this diagram there proved to be 
four compounds between these components. 


The modifications in which alummiumhydroaide may occur. 

In a similar way as described in the preceding paper, I tried 
to determine the solubility-curves (p and 7 constant) in this system. 
Also here the determinations were executed at 30,0° C. The NaOH 
used had been prepared from sodium, the water had been distilled 
and boiled immediately before use. The aluminiumhydroxide was 
prepared in various ways, for it is known that according to the 
preparation this compound shows different properties. The products 
used had been prepared as follows: 

A. Aluminiumhydrowide. 

Product a was obtained by precipitating an aluminium salt (sul- 
phate or chloride) with the required quantity of ammonia. The very 
voluminous, gelatinous precipitate was consequently sucked out and 
completely washed out, which took a long time. The gellous mass 
obtained in this way was dried at 1300—140°; after that it made 
the impression of a shrivelled up gellous mass and was very hard 
and glassy. Such a product does not possess a constant composition, 
the water-percentage varies according to the duration of heating. 
In the case of the product used, the time of heating had been chosen 
in such a way that the composition agreed as much as possible 
with Al(OH),. The water-percentage amounted to: 33,81 °/, (theore- 
tically for AKOH), to....34,57°/,). The particles of this product 
display no or hardly any perceptible swelling even after having 
been shaken a long time with distilled water. If however they are 
in contact with NaOH-solutions stronger than + 2 normal, they 
again swell very rapidly into a very voluminous product. This 
phenomenon renders the reaching of equilibrium particularly difficult : 
the swollen particles settle down very slowly. 

Product 8. In quite a different state aluminiumhydroxide can be 
obtained by issuing from the solution of an aluminate. If we gradu- 
ally decrease the alkalinity by carefully adding a diluted, weak 
acid (introducing CO, e.g.), then the hydroxide precipitates in a very 
compact, crystalline-looking form. Indications for the existence of 


1) Zeitschr. f. anorg. Chem. 68, 370 (1910). 
gx 


132 


this form are to be found with various investigators '); VAN BEMMELEN 
ascribes to this product the formula: Al,O,3H,O; later on it was 
once, more examined by Russ’). The latter arrives at the same for- 
mula and finds that the separation will take place the sooner and 
the more completely as the proportion Na,O: Al,O, in the solution 
more closely approaches the value: 1,24: 1. 

The most suitable preparation of this form of the hydroxide 
appeared to me the following. To a solution of 25 Grs. of NaOH 
in 110 em? of water, 13,5 Grs. of aluminium are added in small 
quantities at a time. When the reaction is finished, the solution 
is quickly filtered and after that left open to the air for some days. 
Soon already the hydroxide begins to precipitate and as under the 
continued influence of the CO, from the air the OH'-ions eoncen- 
tration decreases, the quantity of hydroxide gradually increases. 
finally the product is filtered and completely washed out; it displays 
absorption of tons in a much smaller degree than product a, so 
that the purifying is greatly facilitated. Russ mentions that his 
product, even at a 500 fold magnification, did not distinetly prove 
crystalline; nor was this the case with the product obtained by 
me. At a 600 fold magnification a distinet crystalline structure was 
not perceptible. Therefore the opinion of former investigators, that 
here we have a crystalline form of the hydroxide, is premature 


as yet. 
Analysis of the product, after drying at 110° to constant weight, 
yielded: 34,29°/, H,O.... 65,62 °/, Al,O,, corresponding with 


the composition: Al,O,. 3 H,O. Carbonic acid could not be indi- 
cated, so that the at first not improbable supposition, that perhaps 
basic carbonates of aluminium would have arisen, was not con- 
firmed. When strongly magnified, the product also made a perfectly 
homogeneous impression, even when brought into prolonged 
contact with water, the particles do not show any swelling and 
do not alter externally. To their behaviour with regard to NaOH 
solutions, we shall revert later on, when treating the equilibriums. 
We may still remark that the particles are finer, more sandy and 
more compact as we cause the separation of the hydroxide to take 
place more slowly and gradually. If, for instance, we suddenly 


') Bonsporrr. Pogg. Ann. 27, 275 (1834). 
Becqueret. Compt. rend. 67, 1061 (1868); 79, 82 (1874). 
Kraemer. Archif. pharm. [2], 79, 268 (1854). 
Van BEMMELEN. Rec. trav. chim. Pays-bas. 7, 75 (1888). 


*) Zeitschr. f. anorg. Chem. 41, 216 (1904). 


133 


lead a current of CO, into the aluminate solution, the precipitate 
is perceptibly more floecose and the particles are coarser than if 
we cause if to arise by a prolonged exposure to the air. 

Product y. A very remarkable and, so far as I know. in the 
literature not yet described form of the hydroxide, arose as follows: 
The dessiccated particles of product «, which have quite the outward 
aspect of a shrivelled up gellous mass, do not swell in pure water, 
in concentrated NaOH-solutions they swell very rapidly. On being 
shaken a long time with diluted NaOH-solutions, they not only 
were found to give nos welling, but even to pass into « fine crystallized 
product. This transition succeeds best if the concentration of the 
lye is between 0,5 and 2,0 normal, while they are continually 
shaken vigorously. It usually took a few months before the tran- 
sition had taken place completely. It can best be watched micros- 
copically; the original aspect: gelatinous, very irregularly formed 
particles of varions sizes, disappears in the long run and in their 
place we observe: bar-shaped crystals very regular in shape and 
size. No doubt we bere have a crystallized phase: at a 600 fold 
magnification the crystals could be distinctly observed. Their length 
amounted to 8—20 wu, their width + 3 u, they are faintly double- 
refractive. 

The remarkable phenomenon is especially that we have here a 
direct transition from the gelatinous state into the crystalline state, 
of which no examples have been stated with any certainty as yet. 
Where we see that, dependent on the OH’-ions concentration, the 
gelatinous mass of aluminiumhydroxide crystallizes or swells to 
amorphous particles, this pleads very strongly in favour of the 
gradual transition of the crystallized and the amorphous state of 
matter. This has been suspected on the ground of various phenomena, 
but the direct experimental proof is still wanting. The systematical 
study of the crystallization and swelling of such bodies as aluminium- 
hydroxide may probably improve our insight into this transition 
Anyhow the swelling of aluminiumhydroxide as a function of the 
H: and OH’-ions concentration is remarkable and a further study 
about this is in progress. 

On using the product y, close attention should always be paid 
that it no longer contains any gelatinous particles of product a, 
as these possess a greater solubility in lyes, so that in this case we 
should not measure the exact solubility of 7. A microscopical control 
of the form y was therefore applied with all following determinations. 

Analysis of the product yielded: 34,35 °/, H,O - 65,52 °/, Al,O,, 
so corresponding with Al,O,.3H,O (after drying at 100—110)). 


134 


B. Aluminiumowide. 

The three products of Al,O, that received consideration had 
respectively been obtained by careful, not too long heating at 300°—400° 
of the products a, 8 and y. Long heating was avoided, because this 
makes the oxide very indifferent, so that it delays the reaching of 
equilibrium, nay, may even render it impossible. Taken in the 
same order, in the following these produets will be indicated as 
On esand)5 

Product d, which had been obtained out of «, still made quite 
the impression of a shrivelled up, gelatinous mass; in NaOH-solutions 
the particles again proved capable of swelling or crystallizing dependent 
on the concentration. 

The particles of product € microscopically displayed entirely the 
same aspect as those of 98. The crystals of y proved to alter on 
heating; the oxide § was not distinctly crystalline. 


The equilibriums of aluminiumhydroxide with NaOH-solutions 
of various concentrations. 


The determination of these equilibriums yielded very great diffi- 
culties. The cause of this is partly the occurrence of the hydroxide 
in various forms, partly also the viscosity of the solutions on great 
NaOH concentration. Owing to this, we are in the first place com- 
pelled with each determination to carefully state what solid phase 
is present in the state of equilibrium, which is very often impossible 
by adirect way. In many cases the rest method is applied. Further 
we should continually control whether the values found really hold 
good for the state of equilibrium, in other words whether this state 
has perfectly arisen. This takes a long time, especially in the more 
concentrated solutions; many determinations could only yield repro- 
ducible figures after having been shaken in the thermostat for 2 or 
3 months. The depositing of the solid phases also requiring much 
time, this is the reason that the whole investigation takes up a 
very long time. 

A survey of the determinations performed is to be found in fig. 1 
and table I. The curves J, I] and III in fig. | refer to determinations 
performed with the products «a, 8 and y respectively. In fig. IT 
(page 140) they are indicated by CF, BE and AD. In the third 
column are indicated the solid phases which, when the experiments 
are performed, were added to the NaOH-solutions; in the tenth 
column those which proved present after reaching the equilibrium. 
As will be proved, some equilibriums must be considered metastable, 


135 


Let us first consider the equilibriums of the gelatinous hydroxide 
(a) with NaOH-solutions of various concentrations. In the more con- 
centrated solutions the particles swell very much and show a solu- 


ie 


bility that is considerably greater than that of the other forms of 
the hydroxide. Although in diluted solutions crystallization to product 
y arises very slowly, the rapidity of this transition is so slight, that 
after one or two months we still entirely measure the solubility of 
the gelatinous particles «. Most of the determinations performed with 
product « therefore form together the curve I; some that greatly 
deviate from this curve (see Nos. 10 and 11) have not been analysed 
till after a considerably longer time than the others. A considerable 
percentage of « had consequently been converted into y. Yet these 
points 10 and 11 are still situated far above curve III, which 
represents the solubility of y. This phenomenon requires our special 
attention, for if between the solid phases to which curves I and III 
refer, no continuous transition was possible, we then might expect 
to remain on curve I as long as the gelatinous phase was present 
and a subsequent sudden decline to curve III. The phenomenon 
observed here may have various causes: 

a. There is a continuous transition between the solid phases of 
curves I and Ill; between these curves we must imagine quite a 


136 


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139 


series of other curves relating to these continuously varying phases. 

b. If we imagine the conversion of « into y to come about, 
because primarily the a@ particles dissolve and y crystallizes from 
this solution, then it is possible that these two processes take place 
with very unequal rapidity. If the crystallization came about very 
rapidly in proportion to the solution of a, the values situated between 
curve I and curve [Il would be reached. 

As we said before however, the crystallization takes place extremely 
slowly, whereas the solution of the particles of product a happens 
more rapidly. Therefore explanation 6 does not hold true and as 
most probably it will not be easy to find a more plausible explanation, 
I believe I may best interpret the experiment by accepting a continuous 
transition between the solid phases that coexist on curves I and III 
with the solutions. For curve II this solid phase is the erystallized 
aluminiumhydroxide Al,O,.3H,O as microscopical examination as 
well as analysis of the rests prove. If we consider the rests of the 
points situated on curve I (Nos. 1—11) it then appears that the lines 
that unite solutions and accessory rests, do not display a mutual 
point of intersection inside the triangle. The gelatinous phase that 
coexists along curve [ by the side of the solutions, must therefore be a 
product of varying composition, rich in water and which besides 
(see analysis) has absorbed a certain quantity of alkali. Of course 
curve I is quite metastable with regard to curve ILI, but can be 
determined very well owing to the slight rapidity of transition. 

If we now survey the determinations performed with product g, 
it appears that they form curve II, which is situated between I and 
UI (fig. II, curve BE); besides the particles swell strongly in the 
more concentrated solutions, not appreciably in the diluted solutions. 
In any case we must therefore consider the form @ as metastable 
with regard to y; even though, in spite of numerous attempts I have 
not succeeded in experimentally realizing the transition By. Funda- 
mentally product 8 has nothing remarkable, it is but one of the 
many forms between I and III, which forms are all metastable as 
regards the crystallized hydroxide y. As to aspect, gis already much 
more like product y than a; this too pleads in favour of the 
continuous transition of the forms into each other. 


The equilibriums of Al, O, with NaOH-solutions of various 
concentrations. 

The determinations performed with the products d, ¢ and & dis- 
tinctly indicate that af 30° A/,O, is metastable as regards Al,O, .3H,0. 
The solutions in which product £ was added as a solid phase, give 


140 


values that fall on curve III with satisfactory accuracy; the bar- 
shaped crystals of y too proved to be present in the state of equi- 
librium. Consequently § has been hydrated and converted into y. 
In pure water this hydration takes place only very slowly; in the 
lye-solutions however much more quickly. The cause of this is 
probably that in the latter solutions the Al,O, dissolves primarily 
and the hydroxide separates from this solution. 

The determinations with the products © and « are about situated 
on the curves I and II; this too shows that the hydration takes 
place very rapidly in proportion to the stabilisation to product y. 
Besides it shows that the differences between the product a, @ and 
y have not disappeared after the heating, in other words that also 
Al,O, exists in various forms. All however are metastable at 30° 
as regards the trihydrate. 


CUO, 


ALO; 34,0 


Y¥%ay0. 302,03. 16H,0. 


2,03. 10,0 


10 Tie a0 


141 


The equilibriums along AG; the sodiumaluminate: 4 Na,O. 
GALO,.16 1,0, 

When alumiumhydroxide is dissolved in ever more concentrated 
solutions of NaOH, the sodiumaluminate from the above-mentioned 
formula crystallizes; curve AG in fig. If represents the solubility- 
curve of this salt. The compound crystallizes very well in diamond- 
shaped crystals; the equilibriums are reached much more easily than 
the others. The composition of the aluminate has in the first place 
been deduced from the results of the rest analyses. In the second 
place the wet salt was sucked out without the access of air, dried 
without the removal of the adhering mother-lye and analysed 
afterwards. The result was: 30,1 °/, Na,O; 37,1 °/, Al,O, (theoretically 
for the composition above-mentioned: 29,5 °/, Na,O; 36,4 °/, Al,Q,). 
As the salt forms very strongly incongruent solutions, a complete 
removal of the mother-lye is practically impossible. Taking this into 
consideration, the composition found corresponds very satisfactorily 
with our formula. The solubility-curve AG has as stable ends: on 
the one side A, the triple-point: Al,O,.3H,O + 4Na,O.3 Al,O,. 
16H,O + solution; on the other side G the triple-point: 4 Na,O. 
3AI,0,. 16 H,O + 4Na,O. Al,O, . 10 H,O + solution. The metastable 
part ABC of the curve AG is partly determined; on this a series 
of metastable triple-points are situated, of which B and C, both 
indicating the coexistence of the aluminate with gelatinous hydroxide, 
are determined. 


The equilibriums along GH; the sodiwmaluminate 4 Na,O. 
MeO 10 HO. 

To AG is joined the curve GH relating to a second compound, 
an aluminate of the composition: 4 Na,0. Al,O,. 10 H,O. Like 
the former compound it is well crystallized in needle-shaped 
crystals, which are very hygroscopical. Isolation of the pure salt 
yielded the same difficalties as have been described with the other 

aluminate. This too was sucked out with all precautions and quickly 
dried on porous earthenware. Analysis of the product thus obtained 
yielded: 47,6°/, Na,O; 18,1 °/, Al,O, (theoretically for the above- 
mentioned composition 46,8°/, Na,O; 19,3°/, Al,O,). Analysis of 
the rests also indicate this composition: 4 Na,O. Al,O, .10H,0. 

If to this solid salt we add a very slight quantity of water or 
diluted sodium lye, it must partly be converted into the other alu- 
minate: 4 Na,0.8 Al,O,, 16H,O, while tbe solution gets the com- 
position G (see fig. ID). This conversion could very well be stated 
by microscope. 


142 


The stable end of the solubility-curve GH, the triple-point H 
indicates the coexistence: 4 Na,O. Al,O,.10H,O + NaOH. H,O + 
solution. 


The equilibriums along HK. 

As last curve of the solubility-isotherm the curve HK is joined 
to GH indicating the solutions coexisting with the monohydrate of 
sodium-hydroxide. As the triple-point AH is situated near: 0,1 °/, 
Al,O,, so very closely on the Na,O-axis, the curve HK is very 
short. Therefore only the end points Mand XK have been determined. 


SUMMARY. 


1. At 30° two stable aluminates arise in the system Na,O— 
Al,O,—H,O: viz. 4 Na,0. 3 Al,O,. [6 H,O and 4 Na,O. Al,O,. 10 HO: 
Both of those form strongly incongruently saturated solutions, in 
other words they are decomposed by water and by diluted NaOH 
solutions. In fig. Il we may see below what concentration-limit 
the NaOH-solution will cause this decomposition. 

2. According to the preparation aluminiumhydroxide may be 
obtained in different forms. Under special circumstances it arises as 
a erystellized hydrate of the composition: Al,O,.3H,0. 

3. The gelatinous hydroxide must be considered as a metastable 
phase of variable composition. It absorbs variable quantities of alkali. 

4. Most probably there is a continuous transition between these 
gelatinous hydroxides and the crystallized hydrate. 

5. Aluminiumoxide is metastable at 30° as regards the hydrate. 

6. The swelling that the dessiccated particles of the hydroxide 
and oxide display, is very much dependent on the alkalinity of the 
solution. 


Delft, Inorganic and physical-chemical Laboratory 
April 1920. of the Technical University. 


Physics. — “Derivation of a formula for the temperature depend- 
ence of the velocity constants in gas reactions from a special 
image of the process.” By Dr. J. Trestine. (Communicated 
by Prof. H. A. Lorentz). 


(Communicated in the meeting of March 27, 1920). 


Using a definite image of the dissociation Bo.tzMann derived a 
formula for the equilibrium constant in gas reactions. By means of 
a similar image we only need a short calculation to find the tem- 
perature dependence of the velocity constants in gas reactions. 

As to the dissociation let us e.g. consider that of /, into / + /. 
We have then the following image of the dissociation : 

A iodine atom be a centre of force. It will act on a neighbouring 
atom only then when their distance lies between a and a + da. 
We call a sphere with radius a the attraction sphere of the atom. 

The action will be thus that at the passage of the layer da the 
potential energy will decrease from O to w (p being a negative 
quantity). Pairs of atoms, the mutual distance of which is less than 
a, will be regarded as /,-molecules. 

From the kinetic theory of gases we know the number 7, of 
simple atoms and the number 7», of pairs, we may expect in the 
gas viz: 

n, — Ae—hme’ du dv dw de dy dz 
Ny == Ate-hmldhet) hb du dv dwda dy dz du do dw'da' dy’ dz' 
where 
1 
IT 

A is defined by the total quantity of iodine. 

Each pair the atoms of which lie in their mutual spheres of 
attraction forms a molecule. Let us now arbitrarily choose in each 
molecule one atom as the “first one” and the other as the “second 
one’. We then see that the number of molecules n,, the first atom 
of which lies in an element de dy dz du dv dw, while the second one 
is situated in the element da’ dy’ dz’ du’ dv’ dw’, is given by the 
half of n,*) viz: 


DRE 


Co Ue ys: eae Cea ut: 9? SE we, 


1) E.g. Jeans. The Dynamical Theory of Gases. 2nd Kd. pg. 92 s.q.q., pg. 211 s.q.q. 
4) Prof. Lorentz called my attention to this factor '/g. 


144 


n, == 4 Ate—hm(c-+e)—2ht da dy de du dv dw da' dy' dz’ du! du' dw' 
Introducing the coordinates of the centre of mass and the relative 
coordinates for a pair, viz: 


X,=} (e+ 2) CIC; X,=a'—«2 etc. 
E=}t(u+u) ele a=u—u etc. 


and putting 
sy est a+ et y= V’ Ke HF 492) ee 
we find for n, 
n, = 4 Ate hm? d5 dy do dX.dY.dZ, e—thmV—2ht da dB dy 4a r? dr 
The number of atoms per unit of volume is found by integration 
of n, over u,v,w and by division by dw dy dz. As always further 
on we think namely of a diluted gas and thus find: 


a) 


The number of molecules per unit of volume is found in the 


same way from 7,, namely 


5 ge | BENS EN ; 
ees a 2hm hm AE 


where w has been written for the volume of the sphere of attraction. 
We thus find for the dissociation constant A the formula 
p 


YP ze 2 
K=— =} we * =} we Ja 
v, 


Passing to the velocity constants we may use the following con- 
siderations. A number of iodine molecules per unit of volume will 
dissociate spontaneously with a velocity proportional to the number 
of molecules, thus 

dv, 
fis 178 

The atoms will associate spontaneously with a velocity proportional 

to the number of pair of atoms. By this the number of molecules 


will increase, thus 


dv, E 
En — ie Vv, 
In the stationary state we must have therefore 
wm, | de 
kvij=kr ae —=——z 
pie ies 


The value of K has been found above. 
Accepting the image of the dissociation we evidently can also 


145 


easily calculate the velocity constant Kk. To find this we have to 
know which fraction of thé molecules dissociates per unit of time 
or of how many of the molecules one constituent leaves the sphere 
of attraction of the other one per unit of time. 

Consider a surface element do of the sphere of attraction. 

The number of atoms that passes this surface element of the 
sphere of attraction of the other atom per unit of time in outward 
direction is 


1 Are—2hm(? AS dy do dX. dY, dZ, fo e—thmV*—2ht = da dB dy do 


where v, represents the component of the relative velocity in the 


direction perpendicular to the surface. 
Let us take for the a-direction the direction of the normal, then 


we can write for the number in question 
4 Ate—2hmC? JS dy d§ dX. dY, dZ, fe eahmV*—2hb dedsdydo. (2) 


The integration limits for @, 8 and y are defined in the following 


way. 
The equations of motion of the two atoms are: 
d'r ( dE ; 
Mm zp (r etc. 
"ae : 
= v'—x 
Ss Sa (oe elc. 
mm €) 


When w(r) represents the potential energy of the two atoms, 
when their distance is 7, we have 


By subtraction we find the equation of the relative motion 
du HE Dn 
m—_=agpi{r)—  . ELC. 
dt ; r 


Multiplying these 3 equations respectively by «, 8 and y and 
taking their sum, we find the equation ot energy 


dee, En yee 
7 a 


wh 


dt Or \r dt 
so that 
im(?+ 2+ y)+2p=—C. 
As to the action of the sphere of attraction we shall use the 
image of a hard layer against the inside of which the atoms can 


impinge. As long as the velocity is small, the impulses are elastic. 
10 


Proceedings Royal Acad. Amsterdam. Vol. XXIII. 


146 


The layer will however not be able to resist a strong normal 
impulse. When the radial relative component a is great enough, the 
two internally colliding particles may leave each other’s sphere of 
attraction. Here also the tangential velocity component will not 
change. The normal component on the contrary will. 

The quantity }ma?-+2y will therefore have the same value 
before and after the impulse. 

We thus must take for 2 and y the integration limits — oo and 
+ oo and for aa positive value that satisfies } ma* + 2y = 0, and + op. 

With these limits the integration with respect to «,@ and y gives 


in (2) a factor 
TE ARNE 
Abr 


Let us write S for the surface of the layer. The surface in (21) 
gives a factor S. 
The integration with respect to §, 4, ¢ a factor 


x \% 
2 hm 


Thus we finally find for the number of molecules dissociating 
per unit of time and per unit of volume ' 


aa NE mw \% S 
a 2 \ hm 2 hm x 


Dividing this by the number of molecules (1) per unit of volume, 
we find the following value for the velocity constant 
p —- = 
S 1 Ss — kT 
hk, eth - — e kI ze Gan (ZI) 
V2nhm ©@ am 


while from (/) and (J/) we find for &, 


kT 
4 =15|% = a ap 
JEM 


Of course the £, can be found in the same way as &,. 

Thus far we have supposed, that every impulse is followed by 
a combination. The meaning of k,v,* is therefore the number of 
collisions per unit of time and volume. We find for it’) 

kT 
kv = oes —- 
m 


in agreement with (///). 


k 
This gives therefore a verification of the equation K = = 
1 


» Eg. BOLTZMANN, Vorl. über Gastheorie I, pag. 69. 


147 


For the logarithms of the constants we have thus the temperature 
functions : 


w w 

lg K= — Sea ee ee CE 

gE ip es (Z') 

w kT S 

lg ky =a te a een he 

k1 nm w 

kT S 

be Ke hl see er ed ae EEL) 
mm 2 


Prof. F. E. C. Scurrrer, whom I showed the above calculation, 
drew my attention to the fact that a formula as (///') will not be 
valid as long as it does not contain a term of the form a More- 
over he felt inclined to suppose that often two atoms, when they 
approach each other and impinge, do not always combine to a mole- 
cule, but only under certain conditions e. g. when the relative velocity 
of the particles surpasses a certain value. 

The image needs only a few alterations to fit the opinion of Mr. 
SCHEFFER and to give us more general formulae than (/Z/') and (//7/'). 

In order to make that an atom will only then enter the sphere 
of attraction of another atom when the relative velocity sur- 
passes a certain amount, we have simply to assume just at the 
outside of the attraction layer still a thin layer in which the 
forces between the atoms are repulsive ones. An atom coming from 
the outside, approaching another atom and having passed the out- 
ward layer will have gained an energy w,. It will however only 
be able to pass this layer when its kinetic energy was great enough. 
On its further way after having passed the inner layer, it will have 
gained a negative amount yw, of energy. 

Now we can repeat the above calculation. 

(4) and (/’) remain valid when only we put w= wy, + y,. 

To find the fraction of the molecules dissociating per unit of time 
and of volume, we have only to extend the integration in (2) with 
respect to a from a value of « satisfying 4 hma* + 2hw, —O0toa=oa. 

The result is a formula like II when we replace in this w by y,. 
The third formula may be obtained either again by division or directly. 

The three formulae thus found are 


htt, @ 

lg K = — en er ZI A 7 
ab, bi Sires 

lok, == + 4la—-+tlg— .... (ZL) 
nT am w 

we, kT S " 

ik = —— si ye a 3: 2 VN 

g 2 TSE A 2 In a= g 9 ( ) 


LOE 


148 


(/’’} satisfus the well known thermo-dynamie relation 
dlgK _ Q 
dt nr 

Hemptinne and Brkaert') have observed a velocity constant for 
the reaction (C,H,),N + C,H,B, — (C,H,), NB,. 

Here they found a dependence on the temperature which can 
be represented by a formula as (///"), but not by one as (//7’). 

The same holds for a reaction investigated by von HaLBAN’). KRÜGER *) 
proceeds in a calculation as we did in the first part of this paper; 
he thus finds temperature functions as in (/'), (//'), (///'). His model 
is therefore too limited. The purpose of this paper is to show how 
this may easily be avoided by inventing a somewhat wider model. 

Krüerer however thought the idea absolutely to be rejected, that 
for a combination a certain minimal velocity should be required *). 

Of course 1 do not pretend that in any case a formula as (/1") 
or (///") will hold. To be able to calculate a right formula, we 
must of course know the mechanism and as, even for the most 
simple dissociation, for that of hydrogen this is not the case, we 
shall have to content ourselves with an image. 

When van DER Waats derives his equation of state considering 
the molecules as perfectly elastic particles, he uses an image certainly 
not corresponding with reality. But still Boar is of opinion that Bd, 
may be compared approximately with the radius of a ring. Just as 
well as nobody will deny the quantitative insight given us by the 
considerations of vaN DER Waats, notwithstanding the special image, 
I think that the above formulae when they shall have been suffi- 
ciently tested by the experiment, will also give to some extent a 
quantitative insight into this phenomenon. 

The above considerations have of course no relation to the 
theory of quanta. The specific heat corresponds to that with 6 degrees 
of liberty. 


Physical Laboratory, Delft. 


1) Hemprinne und Bekaert, Zeitschr. f. physik. Chem. 28, 236 (1898) 

2) Hans von HALBAN ib. LXXVII 6. p. 731—733. 

8) F. Kriiger, Göttinger Nachrichten, 1908, pag 318 seq. 

4) See further: K. F. HerzreLp, “Zur Theorie der Reaktionsgeschwindigkeiten” 
Ann. der Phys. 59, p. 635, 


Chemistry. — “The influence of different substances on the decom 
position of monoses by an alkah and on the inversion of cane 
sugar by hydrochloric acid.” By Prot. H. 1. Waterman and J. Groor. 
(Communicated by Prof. J. BörsEKEN.) 


(Communicated at the meeting of January 31, 1920). 


When the strength of the acid and of the alkali, from which the 
salt is formed, are known as well as the nature of the ions, we 
ean calculate the percentage of the hydrolysis. The decomposition 
of monoses by an alkali can be controlled polarimetrically, so that 
this method as well as the often used inversion of cane sugar gives 
us a sensitive means to determine the percentage of the hydrolysis.’) 

Applying the law of mass-action to the electrolytic dissociation- 
equilibria that occur in such a solution, we can calculate the hydro- 
lysis. Using 
[B] [C, H, O”] 

[C, H, OH] 
and assuming the bydrolysis to be weak and the non hydrolized 
sodium-phenolate to be perfectly dissociated, we find for 4, N sodium- 
phenolate solution, [OH’] = rather more than 3.103, 7) 

When the hydrolysis of the sodium-phenolate in a + N solution 


10 
were perfect, then [OH’| would be 10-1. From this we learn, that 


=1,3.10- and [H][OH'] =1,2.10-"4 


Kabaal ei 


100 
of the sodium-phenolate only ne 3.10? = 3. Ui vies. hydrolized. 


For more diluted solutions the percentage of this hydrolysis is higher. 
For ;4, N potassium-phenolate at 25° the hydrolysis is 3,1 °/,.°) 

_ These results are in agreement with the experiments on phenol, 
which taught that in an alkalie medium phenol practically behaves 
like a monobasic acid. 

In this way the hydrolysis of many of the compositions treated 
up till now in the above mentioned investigations could be calculated 
when only enough data were at our disposition with regard to the 
strength of the respective acids and bases expressed in the well- 
known units. 


1) H. I. WarerMAN, These Proceedings XX (1917) p. 88, 382, 581. 
2) J. WaLKER, Introduction to physical chemistry 1919, p. 330 and 336. 


150 


A condition for the ealeulation is, that the nature of the ions 
and in general the constitution of the used compositions are known. 
When this is not the case the method of investigation followed 
by us may still give some indications. Before applying this method 
to the investigation of the acid or alkalic properties of organic dyes, 
we investigated a number of intermediate products. The investigation 
was also extended over several more or less strongly coloured sub- 
stances. It was found possible to take away the colour just before 
the polarimetric measurements by means of norit or of bone-coal 
without lessening the accuracy of the method. In other cases alcohol 
was added sometimes. This changed somewhat the nature of the 
medium, but several compositions that could not be investigated 
owing to their weak solubility, could now be treated. 

Most of the investigated compositions were obtained from KaAnr- 
BAUM at Adlershof (near Berlin). When this is not the case it will 
be mentioned. As further different solutions were primarily coloured 
we paid little attention to the intensity of the darkening caused 
by the action of the hydroxylions on the glucose. The obtained 
analysis numbers will be given here only partly, elsewhere completely. 

The naphtyl-amines. The melting-point of the used «-naphtyl-amine 
was 50°, that of the B-naphtyl-amine 112°. Hydrochloric compounds 
of these amines too were used. The experiment in an alkalic medium 
taught that neither «- nor g-naphtyl-amine bound an alkali, so that 
they do not influence the decomposition of a glucose in alkalic 
solution. In hydrochloric solution the amines in question behaved 
approximately as monovalent bases. 


Ortho-phtalic-acid Cinnamic-acid 


ri me == AN ’ 
| mt M.W.—166 , | En 


— COOH M.W. 148 
NL NF 
Ortho-coumaric-acid a-naphtoic-acid 
—OH COOH 
f= OHSSCH—- COOH ERSTEN 
eed M.W. = 164 ge | op ee 


NS 
a-oxynaphtoic-acid 
OH 
ON 
Nae 


The melting-point of the investigated ortho-phalic-acid was 200°, 


Bd 


MW. = 188 


ry. or 


151 


while for this substance is given e.g. 203°; a titration of the acid 
with + N. KOH and phenolphtalein as indicator gave the per- 
centage 99,8. 

The melting-point of the cinnamic-acid that was present in the 
laboratory was 133°, of the ortho-coumaric-acid 205°. The «-naph- 
toic-acid and the a-oxy-naphtoïc-acid melted respectively at 159° 
and at 187°. 

It was found, that in diluted alcoholic solutions these compounds 
practically did not hinder the inversion of cane sugar (Table 1); 
Table IV refers to the naphtoïc-acid. From the tables II and III 
we see, that in alkalic solution the behaviour of ortho-phtalic-acid 
is dibasic, of «-naphtoïc-acid monobasic, of cinnamic-acid monobasic 
and finally of coumaric-acid dibasic. : 

This might have been expected from the above given structural 
formulae. 

We further investigated: a-naphtol (M.W. 144, melting-point 96°), 
B-naphtol (M.W. 144, melting-point 122°), 2.3. oxy-naphtoic-acid 
(melting-point 217°) $ 


ANN on 


\/_/ COOH 
and B-naphtoic-acid (melting-point 165°, M.W. 172). 


From the experiments made with a nearly 50 °/,-alcoholic solution 
we learned, that «- and g-naphtol, «-naphtoic-acid and 2.3. oxy- 
naphtoic-acid practically do not influence the inversion of cane sugar 
by hydrochloric-acid (Table IV). 

The behaviour of «- and g-naphtol in alkalic solution was approxi- 
mately monobasic just as of 8-naphtoic-acid ; the 2.3. ovynaphtoic-acid 
behaved in an alkalic medium as a monobasic acid; this was also 
the case with the 1.2. oxynaphtoic-acid (Tables V and VI). 

In the same way as has been done for the salicylic-acid, 
led by analogous experiments), we are now inclined to assume 
also for the mentioned oxynaphtoic-acids, at least in alkalic media, 
a “ketoformula’, e.g. as follows : 


M.W. = 188 


O 
| 
EE C 
EET Rs) VV ZH 
ee ER ENZ 
2. 3. oxynaphtoic-acid 1. 2. oxynaphtoic-acid 
(ketoformula) (ketoformula) 


_1) H. I. Waterman, These Proc, XX, 581 (1917). 


152 


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158 


Similar ketoformulae for the 2.3 oxynaphtoïc-acid are already 
found in the literature *). 
Further we investigated still : 
SCHÄFFER-salt, G-salt, 
SO*Na 
pee DAP RE 


ieee | 
BO ONG es 


M.W. = 246 M.W. = 348 
and also 
sodium p. phenol sulphonate. 


gon: 

The sodium 2.6. naphtol sulphonate has been investigated as 
technical SCHÄFFER-salt and also as a purified one prepared in the 
laboratory by sulphonation of g-naphtol. 

To determine the percentage of the technical product this was 
titrated by means of diazotated p. nitraniline according to the 
method in use in the technical control-stations of the dye-manufac- 
turies*). In this way we found the percentage 76.4. The purified 
preparation when dried gave a loss in weight of 11,4°/,. In the 
dried substance we made a sulphate-ash-determination. Having made 
the calcutation for Na, we found from this 9,1 °/,. (Theor. 9.35 °/,). 

From the observations combined in table VII we see, that 4 
milligram-molecules of the pure ScHAFFER-salt bind just as much 
alkali as the corresponding quantity of the technical product. 


88,6 
If the pure salt behaved as a monobasic-acid, just can 49,55 cm 


N. KOH would have been found. In reality we find 3,7 em* 0,93 
N. KOH = 3,4cem’N. As the titration gave for the percentage of 
the technical product 76,4, it is probable, that the technical product 
in question is made impure by substances which can bind alkali, 
but which under the circumstances of the titration with diazo-solu- 
tions, cannot form colours. As might be expected the ScHärrer-salt 
could not bind an acid in a hydrochloric medium. 


1) R. Mörvau, Berichte d. Deutsch Chem. Gesellsch. 28, 3100 (1895); 
M. ScHépr, Idem 29, 265 (1896); F. Friepr, Sitzungsber. der Akad. der 
Wissenschaften, Mathematisch-Naturwissensch. Klasse, Wien, 119, 731(1910). 
4) R. Mörvau and H. Bucrerer, Farbenchemisches Praktikum. 


EE ———— ee ee 


159 


‘you 
jo suvouw Aq 
painojovap aq 0} 
pey Áayy ssul 
-pea ay} a10j9g 
*u90.13 YSIUMOIG 
painojoo SEM 
J uornjos 94} 
ajtya ‘aus 
-onjjonjg e oAeS 
H worjnjos au} 
apixoipAy-winis 
-sejod ay} UM 
‘poppe SEM IEX 
-je oY} Sutjooo 
JoyjySuneoy Aq 
poAjossip 319M 
saguejsqns UL 


‘syJe wo] 


‘mmm mm 


| | | sinoy 
90+) eet) esr | go+ | 6'0 + | MEIS Gage ZE En Zo + Airey 
| | -0} JV 
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5 yy3ua[ aqng) 
| sinoy | saaisap ‘A Ul 
ee eee ase Or | or a eI Slee alee ee pre ses eae eet one 
JIyW NBS BIO 

| | | | | | | nee 
Bee Te ledee jn Meh | Te) re eet | See LEENE ae et 

| | | | | | | Jo 

(ogg ainyesoduia}) Jejsowloyy 94} UI paoerd eld QOL 0} SUI JUV | 
| "N an Sena: 
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yes yes 
-YAAABHIS | -UAAABHIS 
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186 v86 
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| | | ; | 
M | I H | 5 | d a q > d Yv 


‘yeyye ue Aq asoonis JO uonrsodwosap ay} uo ([e91UYI)) HES- 


TA ATAVL 


Jageyos Jo pue (paytind) yes-1ayRYIS JO gouanyuy 


160 


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=G'I'Z! you | | JOUW (wp z 
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= 81 ‘4 | you Jayy | S2048ep A UI 
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00 0 pou | JFV 
‘aqn} wp Z B Ul 
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uea yng ‘UOIJeN | 
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TIA ATAVL 


161 


The percentage of the sodium 2.6.8 naphtol disulphonate (G- 
salt) was determined in an analogous way as that of the Scuärrer-salt 
by means of diazotated para-nitraline. The result was 82 °/,. 

For the sodium para phenolsulphonate (technical product) we 
also found 82°/,. The percentage for the dry substance was 87 °/,. 
In reality the percentage of sodium in the dry substance (calculated 
11,7 °/,) was 11,3 "/, (determined with the sulphate-ash method). 

The results with G-salt and sodium para phenolsulphonate in 
alkalie solution are to be found in table VIII. From these investiga- 
tions we see, that 7 milligrammolecules of the technical G-salt 
have bound 6 cm* KOH (0,92 N.) = 5,5 em* N. potassiumhydroxide. 

When we suppose that because of the formula 

SO,Na 
Oa: 
has Noa 
the G-salt behaves like a monobasic acid and at the same time that 
the admixtures, such as the inorganic salts, have no influence 
and that admixtures as other g-naphtolsulphonates have the same 
influence as the G-salt, we should conclude to a percentage of 
> 100 i.e. of nearly 80°/, of constituents that can be bound 
to dyes. 

By titration with diazotated paranitroaniline was found 82 °/,, 
so that in fact it is nearly sure, that in an alkalie solution the 
G-salt behaves like a monobasic acid. 

In an analogous way we may deduce from the observations that 


in alkalie solution the sodium para phenolsulphonate behaves as 
a monobasic acid. 


Delft, Jan. 1920. Laboratory of Chemical Technology Delft. 


len 
Proceedings Royal Acad. Amsterdam. Vol. XXIII. 


Physics. — “Deduction of the dissociation-equilibrium from the 
theory of quanta and a calculation of the chemical constant 
based on this.” By Prof. P. Enrunrest and V. Trkat. 


(Communicated at the meeting of February 28, 1920). 
Introduction. 


Nernst’s theorem, the theory of the specific heat of solids, of the 
vapour-pressure and of the dissociation-equilibrium must have their 
common root in the general foundations of statistical mechanies and 
in the quantum-hypothesis. O. Stern’) and H. TrrropE’) have shown 
how from Nernst’s theorem by means of EINSTEIN’s formula for the 
specific heat of solids and a vapour-pressure formula for high tem- 
peratures (derived kinetically) the chemical constants (hence also 
the dissociation-equilibrium) may be calculated. Notwithstanding the 
great advantages of this method a desire must be felt to calculate 
the chemical constants and the dissociation-equilibrium more directly 
by considering the hot gases themselves, without the use of a cycle 
consisting of a condensation, cooling of the crystals to the absolute 
zero, chemical transformation at 7’=0, heating of the new erystals 
and evaporation at the high temperature. 

This desire explains the fact, that even after the publication of 
STERN’s paper (1913) attempts have been made again and again to 
improve the earlier methods of calculating the chemical constants 
as given by O. Sackur*) in 1911-1913 and H. Terrope*) in 1912. 
These consist in considering a gas of N equal molecules in a volume 
V at the temperature 7’, calculating statistically by means of some 
formulation of the quantum-hypothesis the “thermodynamic proba- 
bility W” and by comparing r log W with the thermodynamic 
entropy of the gas fixing the indeterminate constant in the entropy. 
It is not an aecident that it is always the same point that remains 
obscure in these theories’), viz, how an expression of the form V—% 


1) O. Srern, Phys. Ztschr. 14 (1913), p. 629. 

2) N. Terrope. Verslag Kon. Ak. v. Wetensch., Amsterdam 28 (II), (1915), 
p. 1110. Proceedings Amsterdam 17 (1915), p. 1167. [henceforth to be quoted as 
‘“TInd paper’’|. 

3) O. SACKUR. Ann. d. Phys. 36 (1911), p. 958 ; 40 (1913), p. 67; Nernst-Festschrift 
(1912), p. 405. 

+) H. Terrope. Ann. d. Phys. 38 (1912), p. 434. [to be quoted as “I st paper”’). 


165 


_(Sackur) or (NI)! (Terrropr I) can be forced into the “thermody- 
namic probability W” in order to obtain an admissible value for 
the entropy. The law of dependence on N can only be satisfactorily 
settled by utilizing a process in which N changes reversibly and then 
comparing the ratios of the probability with the corresponding differ- 
ences of entropy. 

If condensation and evaporation (Stern and Terroper II) are not 
to be used, and the whole process is to be carried out with gases, 
it will be necessary to work with a gas-mixture and change the 
mamversvoy;- molecules N,, N,,..... N; of the various gases by dis- 
sociation. 

Remembering the real object of the calculation of the chemical 
constants, viz the deduction of the dissociation-equilibrium, the follow- 
ing formulation of the problem is finally arrived at: Consider 
X, Y,Z,.... atoms of different elements contained in a volume VV 
and possessing an energy /. These atoms can unite to molecules 
of different kinds in a large number of different ways. Determine 
by means of the quantum theory directly, which of the various states 
of dissociation possesses relatively the greatest probability. 

This problem is to be solved by methods belonging to statistical 
mechanics and the quantum-theory which will be set forth in § 2 
and § 4. On comparing the dissociation-equations arrived at in this 
manner with the corresponding thermodynamical equations values 
are obtained for the expressions containing the chemical constants 
which occur in the latter (§ 6). 

Our method: removes, as we hope, any remaining obscurities as 
regards the occurrence of N,! N,!.... This could only be accom- 
plished, as it appeared to us, by not stopping at the numbers of 
the molecules in the combinatory computations, but by going down 
to the atoms. This is the only way of obtaining a solid common 
basis for the computation of the relative probability of different 
states of dissociation (variations of the numbers of molecules N,, 
N,,...N;), viz. the phase-space of 6(X + Y + Z) dimensions (§ 4). 

The introduction into the combinatory calculation of this refinement, 
viz. the consideration of the atoms, confirms a result already attained 
by Terropr (ID): the factor which depends on the permutation of 
the atoms of the same kind 

MIX LZ! 


ING PN las ING ASG, +" Ostia 


(comp. e.g. (18) 


1) Comp. § 9. 
4) Comp. § 8. 


11* 


164 


contains” not only the expression V,/ N,/... N;/, but also the 
“symmetry-numbers” of the molecules 6,, 6,,..., 6; (comp. e.g. (6) 
$ 3). These, therefore, influence the dissociation-equilibrium (comp. $ 8). 

Accordingly the numerical vulue of the chemical constant of a 
molecule should depend not only on its mass and moment of inertia, 
but also on the “symmetry-number” of the molecule. 

The question whether any of the cases of dissociation-equilibrium 
or evaporation which have been investigated numerically, speak in 
favour of or against this modification, we shall leave to others who 
are more familiar with the experimental side of the question. 


§ 1. Fully excited and non-excited degrees of freedom. 


The thermodynamic theory of the dissociation-equilibrium considers 
the molecules as having constant specific heats in the range in question, 
i.e. possible changes of the specific heats are left out of account in 
the calculations. If they were taken into account, the expressions for 
the entropy and energy of the gasmixture would not have the special 
form, which is essential for the definition of the “chemical constant” *). 

In a kinetical theory of the dissociation-equilibrium analogous 
assumptions or approximations must therefore be admitted, if a 
kinetie interpretation of the chemical constant is aimed at. 

We shall make the following assumption in our calculations: 

I. The translational motions of the molecules as also their rotations *) 
(with the exception of those referred to under II) will be considered 
entirely free from any limitations depending upon quanta *) (“fully 
excited degrees of freedom”). 

Il. On the other hand the following motions will be assumed 
to be absent ‘) (“non-excited degrees of freedom): 

a. The rotation of di-atomic molecules about the axis of symmetry 
and all rotation of mon-atomic molecules. 


1) Compare the expressions for the energy and entropy in § 5 and in M. PLANCK, 
Thermodynamik §§ 237 — 241. 

2) We therefore exclude for the special object of our theory these cases, in which 
a rotation happens to be in the intermediate state of being “partially excited”, as 
these would introduce a variable specific heat (Comp. Nernst. Theor. u. exp. 
Grundlagen d. neuen Wärmesatzes, p. 136 bottom p. 137 top). 

3) Le. we approximate for these degrees of freedom all summations over succes- 


sive quanta-steps by the corresponding f fan dp; comp. “addit notes 1”. 


4) ie. for these degrees of freedom we confine ourselves in our calculation of 
the sum to the lowest quantum-stage. 


165 


6. Internal motions of the atoms in the molecule *). 

Note. In accordance with Pranck’s first quantum-theory we have 
provisionally assumed the lowest quantum-grade to be that of no 
quanta. N. Bonr’s investigations (On the Quantum Theory of line- 
spectra (Part ID, D. Kgl. Danske Vidensk. Selsk. Skrifter, Natur- 
vidensk. og mathem. Afd., 8. Raekke N. 1, Kgbenhavn, 1918) show, 
that probably in many cases the stage with the quantum-number 1 
must be taken as the lowest possible. The corresponding modifications 
might easily be introduced in the theory (and also specially the 
contribution of the kinetic side by side with the potential energy). 


§ 2. The phase-space of a molecule (u-space). 
The u-weight {u}. 


If a molecule consists of §, , § atoms of say three different 
chemical elements, its ‘‘phase” may be determined by means of 
6(S Hu 45) cartesian co-ordinates and momenta, i.e. by a point 
in a 6(§-+ 4-+ 5)-dimensional ‘“u-space”’ (phase-space of the mole- 
cule). In consequence of the assumptions IIa and 115 of the previous 
section, however, as long as the molecule is not dissociated, its 
phase-point (“u-point’) is confined to a portion of the u-space, namely 
to a 2X6, 2 <5 or 2 X 3-dimensional region according as the 
molecule is poly-atomic, di-atomie or monatomic. 

Considering for a moment the case of a poly-atomic molecule 
(EH + < atoms), this sub-space may be described af follows: 
owing to the rigidity of the molecule the 3(§ + 1 +5) cartesian 
co-ordinates of the atoms may be expressed by 6 co-ordinates 
Gi» Ya ++ Go, Which fix the position and orientation of the molecule. 
Similarly the cartesian momenta are determined by the six momenta 
Py» Ps -+-Pe Corresponding to the q,...g,. If in accordance with 
assumption I of the previous section we imagine the quantities 
g,---pP, to vary continuously within any arbitrary limits, the 
“u-point’ describes inside the 6 (& + n +5) dimensional u-space a 


1) This assumption underlies so far all derivations of the chemical constants 
for di-or monatomic molecules; for the theories never go beyond ,,rigid’’ molecules. 
This assumption seems more extra-ordinary in the present theory, in which the dis- 
sociation of the molecules is directly considered. Indeed, the molecules must first be 
gradually loosened, before they can dissociate. Still our method of calculating agrees 
with the following assumption: either every internal degree of freedom of the 
molecule is on its lowest quantum-grade, or the molecule is completely dissociated. 
This is of course only meant as an approximation in the calculation, similar to 
what is done in the thermodynamic derivations, where the variable contribution to 
the specific heat is neglected which would be due to a loosening of the molecules. 


166 


portion of a “surface” of 12 dimensions and the quantities q,. .p, 
play the part of curvilinear parameters on this surface. 

We define!) the following expression as the ‘“u-weight” {u} of 
this region: 


oy = h3 E+4+5)—6 a À fan re dg, dp, >. . UP a 


where the integration is to be extended over the region in question. 

In future applications ($ 4) the molecule will have to pass through 
the total volume V of a vessel and similarly through all possible 
orientations. Accordingly, integrating with respect to the co-ordinates 
q, we have 


fu} = Get —8 dar Barf. (dp, … dp, Scr EN 


The corresponding expressions for di- and mon-atomic molecules 
are as follows 


e= tds VA. | fap, dp .. a 


at weet 80. fa fdpy dps ann 


In (8) EH n=? and in (4) =1, but we have left the power 
of h in its above form in order to obtain the formulae in our 
calculations later on as symmetrical as possible ($ 4). 


§ 3. The constitution of the gas-mixture. 


In a vessel of volume V X, Y, Z atoms of say 3 different chemical 
elements (atomic masses mz, m,, mz) may be introduced. These 
molecules can associate to molecules in a number of different ways. 
At a special moment let there be present j different kinds of mole- 
cules; a molecule of the kind 2 may consist of &;,1;,5; atoms and 
may possess the following mass, moments of inertia and potential 
energy respectively : 

Mi; B Oo Ris Gs, a Se 

The arbitrary constant contained in 4;, we shall fix by the follow- 
ing rule: we shall ascribe to the atoms a potential energy 0, when 
they are completely separated from each other; y; is therefore a 
negative quantity, viz. equal to the negative work which the atoms 
give off, in uniting to form the molecule. 

It may happen that, owing to the special distribution of similar 
atoms in a molecule, the latter possesses more than one completely 


) Comp. the illustration of this definition by means of a special simple case 
n addit. notes I. 


RM MN 


167 


equivalent rotational orientation; its number may be called the 


ByMMetry-numer Gp) er er, (GO) 


of the molecule. (For instance for J, 6 would be=2, for CH, 
(methane) 6 = 12). 

Finally we shall call /; the number of fully-excited degrees of 
freedom of the molecule; therefore 

Tee Oat as a 

according as the molecule in question contains one, two or more 
atoms. 

The numbers of the molecules of different kinds V,, V,,.... Ny, 
have to ey the Snol 


= MEX, =i, SNZ RE ao) 


Le. with varying degree a dissociation Hie numbers “Ni. Ns 
change, as also the total number of molecules 


j 
NEEM. © 


but not the numbers of the atoms. 
The total energy of-the gas-mixture is given by the equation 
HSK le Ne Koda volt Me Sheene ene 60) 
where K stands for the total kinetic energy of all the molecules. 
In the thermodynamic calculation of the dissociation-equilibrium 
(§ 6) we shall use “molar” instead of molecular quantities. Calling 
Avoerabo’s number 
NE eene nee mera CL 
we have the following relations for the number of gram-molecules 
ni, for the potential and kinetic energies pro gram-molecule (5%, Ci, T) 
and for the specific heat (Ci) respectively 
„et bei tn = Gane a (12) 
where 
(13) 


hence 
Tei Ee Nie te UN 


§ 4. The phase-space of the gas (y-space). The v-weight {+}. 


The most general “phase” of our system may be represented by 
the 6(X+ Y-+Z) cartesian co-ordinates and momenta of the 


168 


X+ Y+Z) atoms, and therefore by a ‘“y-point” in a 6(X+ Y+Z)- 
dimensional “y-space”’. To a given condition of dissociation (N,, N,....Vj) 
of the gas-mixture, owing to the assumptions II ($ 1), a sub-space 
corresponds of 2 # dimensions, where 


ai] 
FE Nifi sve to ow 
1 


fr as before being equal to 3, 5, or 6 according as the index 7 
refers to molecules of one, two or more atoms (comp. eq (7). 

We must now consider more in detail the structure of this 
sub-space. 

Consider an individual “phase” of the system (any point y, of 
the y-space); the X + Y-+ Z atoms, which we shall provisionally 
think of as being individualized by numbers attached to them, are 
associated to MN molecules, which we shall also suppose to be indivi- 
dually numbered. The total energy of the system then also possesses 
a definite value 4. We now apply to the phase of the system 
changes of two types (A) and (4)'), which both leave the dissocia- 
tion (N,, NV,,..., Ns) and the total energy unchanged. 

Changes of type [A]. Starting from the initial phase y, we make 
the molecules independently of each other, pass through the total 
volume V7?) and all possible rotational orientations, and also make 
them assume successively all possible velocities of translation and 
rotation, which are in accordance with the original total energy. 

While in this manner the y-point starting from y, describes a 
region (A,) of the y space, the u-points of the various individual 


molecules — each in its own u-space — describe the regions which 


were discussed in § 2. In the classical theory the “y-volume” is 
obtained in cases of this kind by taking the product of the corre- 
sponding “gp-volumes”’. Analogously we shall here define the y- i: 
fvi4) of the region just mentioned by the relation 


Thee nn 
1 


where for {u;} we have to take the expressions (4), (3), or (2) of 
§ 2 according to whether 7 corresponds to a molecule of one, two 
or more atoms. The limits of the integrations over the momenta 
See Rene in (16) are determined by the fact, that on account of 


I) Comp. the somewhat similar discussion in P. and T. EHRENFEST, Math. Enc. 
Bd. IV. Art.432, § 12 6. 

2) The volume-correction which is due to the finite dimensions of the molecules 
is left out of account. 


a 


169 


the prescribed total energy / and dissociation N,, V,,...N; the 
total kinetic energy 


Koa Shy SNe eats” Rye eee 


is also fixed (comp. (10) in $ 3 and the computations further on in § 6. 

Changes of type [B]. By the mutual permutations of simi/ar- 
atoms starting from a given y-point new y-points arise *). In connec- 
tion with the X/Y/Z! possible permutations of the individual atoms 
of the same kind a set of X/Y/Z! different y-points in the y-space 
will be seen to belong together and all these points give the gas 
the same / and the same dissociation (V,, N,,...). 

In order to reach the total y-region which agrees with y, in the 
quantities NM and N,, N,,...N; we must combine the changes of 
the two types [A] and [4], in such a manner, however, that no 
portion of the region is counted twice. 

It may be proved, that including the region (A,) altogether 9 
identical regions (A,), (A,),... Aw, are obtained, in this manner, where 

f ED BVA 


p = - E ke A (1 8) ) 
Mi ! N, (ie Nj If on 6 Ns atd. of 


We shall give a few short indications as regards the proof of this statement. 
For this purpose we introduce the notion of “internal” permutation. 

A permutation of the atoms will be called internal, if the result may also be 
obtained by translations and rotations of the rigid molecules. 

Simple instances. 1. Two molecules of the same kind are made to exchange 
their position and orientation by translation and rotation. 2. A molecule of symme- 
try-number ci (comp. eq. (6) ) is made to pass from one orientation to another 
equivalent one 5). 3. The same operations are carried out at the same time 
with a number of molecules. 

An internal permutation carries the phase-point of the system say from 7’ to 
/; but here the following circumstance must be remembered: y’ is still inside 


1) Since each individual atom has six co-ordinate axes of the y space referring 
to it. Thus when two atoms of the system are exchanged, nearly all co-ordinates 
of the point remain unchanged, only 12 co-ordinates exchanging their values 
two by two. ; 

2) BoLTZMANN in his well-known paper: ‘Ueber das Arbeitsquantum, welches bei 
chemischen Verbindungen gewonnen werden kann,” [Wied. Ann. 22 (1884), p. 39. 
Wisschensch, Abh. III, p. 71] has determined a similar combinatory quantity. But 
in comparing the quantity Z in his equation (3) with our , the difference should 
be noted which is referred to in the next note 3. 

3) In a molecule of the constitution ABA, therefore, the permutation of the two 
A atoms is an internal one, in a molecule of the form AAB it is not. With 
BOLTZMANN the latter permutation would also have to be regarded as internal. 
This difference is due to the fact that with him the changes of type [A] form a 
wider class than with us and contain all exchanges of similar atoms inside the 
same molecule. 


170 


the plase-region (A’), which is formed from y’ by the changes of type [A] A’) 
(that is what the word “internal” is meant to express). 
Taking any phase-point y as starting point, there are always 
D = Ni! Nyt... Np hoo... oN oe 


internal permutations 3) and all y-points reached in that way lie inside one and the 
same 4-region. 

It will therefore be clear, that, if from the original phase y, by an operation 
[A] we produce the phase-region A,, and if we then apply the X/ Y! Z! operations 
of type [B] to every point of the region (A,), we donot obtain X! Y!Z! regions 
similar to (Aj), but altogether only ‘8 (eq. (18) ), since the X/Y/Z! permutations 
of the atoms divide into § groups of 9. internal permutations each. 


Combining (16) and (18) we obtain for the total y-weight of all 
the phases, which belong to given values of V, Hand N,, N,... Ny 
the expression : 

ALYAZ! MN Na N. 

7 A SNN wot} tb +. tess 7 (20) 

NN SONG Gy Ore 0e 


The expressions {u;} contain the integrals with respect to the 
momenta of all possible motions of translation and rotation of the 
molecules which have still to be computed. 

The total kinetic energy of the molecules is fixed by equation 
(17); the integration is to be taken over all the values of the 
momenta which are compatible with it. Calling these momenta for 
a moment p,,p,...pr, } being given by equation (15), we have 
the following relation between these quantities : 

Pf 
2 Ar 
where A,,A,,..., Ap represent the various molecular masses or 
moments of inertia 

Mis Ee Ordi - ; Mj, BOB. 
according to the index (comp. (5) in § 3). 

The multiple integrals with i to the momenta give together 
the surface of the “ellipsoid” (21). Neglecting numbers of the order 1 
as compared with the large number F’, we a use for it the following 
approximation °). 


== 


‚+ =K zn 


') For the operations [A] include all possible translations and rotations of the 
molecules, hence also those, which may replace our internal permutations 

*) The centres of gravity of the Ni molecules of type i may mutually exchange 
their Nj positions and moreover each of these molecules can choose among the 
ci equivalent orientations. 

*) The volume I of a sphere of radius R in a space of F dimensions and its 


171 


“() 
at (a 
2 

If we now include the remaining factor in the expressions {u;} 
(comp. eq. (2), (8), (4) in $ 2), having regard to the meaning of the 
quantities A,, A,,..., Ar, the expression (20) for {y} becomes as 
follows: 


(ERR RA Ae taat. oe (AH) 


ATEN ZEN ae 1 
by) — — <= AEE $Z) VN. 
N,! NL. alle N;! 0, “te 4 ee G7 el r (=) | 
. . (24) 
a ON. 
WEKE. (ak ji, 
1 
where 
ai'=47.2nVM;? P;QR; for poly-atomic molecules | 
ai = Ar WM; P,? ede if za (25) 


a;" V Mi’ PE) mon- ” ” 
the quantities f;, # and N being defined by equations (7) $ 3, (15) 
§ 4 and (9) § 3. 


§ 5. log {y} and the entropy for an arbitrary degree of dissociation 


Nn Net N;). 


Using Srirring’s formula log {y} assumes the following approximate 
form 


F en 
log fy} = [+ N log V + log K+ FlogV 2n+  N;(logai’—filog h—log 55) 


ie F 
EN ND (wg) Ne Tat 


or 


surface O (i.e. the differential coefficient of IJ with respect to R) are respectively 
[comp. say P. H. Scroure, Mehr-dimensionale Geometrie, Bd. IJ, (Sammlung Schubert, 
Leipzig 1905); J. H. Jeans, The Dynamica! Theory of Gases, § 46]: 


1 Be 1 wat 
ieee YY RP RF, SO Marr REL 


Ge) 0) 


It is in accordance with the usual approximations of the kinetic theory (/ very 
large as compared with 1), if we put log J and log O equal to each other, since for 
instance, if we-use STIRLING’s approximation, expressions are obtained for these 
quantities, which coincide completely, if we do not make any difference between 
F and F—1. We have used a similar approximation with regard to the ellipsoid. 


172 


log{yi{j=1I+ 2 Ni tu V +e log K + tog aj | 


P fF 
— = Ni [log Ni — 1} — = | u RRS |. ra 
where 
1 =log [X! VIZ! BANE), . 3) ae 
log ai! = log ai! — f; logh — log ai + filog V 2m . . . (29) 
therefore 
a! TW 2a 
a; = — | an TAN 
Oi h 


If there are 7,, %,,..., 7; gram-molecules of ideal gases of different 
kinds in the volume V at the temperature 7’, the entropy and energy 


of the mixture are given by the expressions: 


7 
Sne OT A ey | | 
i as (oa 

= 24+ En; (Rlog V+ Cilog T -+ x) — RZ nj log n;' 
EEn (Gil +b). ne 


{2 is a quantity which is independent of V’,7’ and the numbers 
ni, but may depend on the numbers of gram-atoms of the different 
kinds of atoms in the system (say wv, y, 2) 7), 6; is the potential energy 
of a molecule of the kind 7 as compared with the condition of complete 
dissociation, which is taken as the zero of potential energy, and 
C; the specific heat at constant volume. 


§ 6. Comparison of the kinetic and the thermodynamic calculations 
of the dissociation-equilibrium. The resulting values of the 
chemical constants. 


We now introduce the following axiom: With given numbers of 
atoms X, Y, Z, volume V and total energy E the dissociation- 
equilibrium is characterized by these values of the numbers of molecules 
N,, N,,..., Nj, for which log fy} vs a maximum. 


1) It may be noted, that, when all the numbers of atoms and molecules, the volume 


K 
V and the total kinetic energy are doubled, the numerical values of log log in 


the expression for Sy? remain the same and the value of the sums is therefore 
also doubled, whereas I increases to more than twice its value on account of 
X! Y! Z! Comp. § 9. 

2) In the theory as usually given (comp. say M. PLANCK, Thermo-dynamik. 4 Aufl. 
§ 237) © is left out. Incomparing the entropy with the “logarithm of the probability” 
this becomes the source of great obscurity (comp § 9). 


oe 


173 


Let 
iN i= vd or Sn=ridq. - . ee ees 

represent any possible) chemical reaction in the system, i.e. a 
reaction which is compatible with the given numbers of atoms 
NX, Y, Z;¥,,¥,,..., 0; are certain positive or negative whole numbers, 
which give the numbers of the molecules which are formed or 
disappear in the elementary reaction ’). 

The kinetic and thermodynamic deductions of the dissociation- 
equilibrium may now be given side by side: 


(kinetic) | (thermodynamic) 
dog iy }== 0. (84) OS Sa Oa Vee oo ee) 
BEI M= id 0 (85) | 0 inten bn 
JE=d(K+ >My) =O (36)| DE=S Tn (CT +b)=0 (36) 


Substitution of the expressions (26), (31) § 5 for log (y) and S 
and further development of the maximum-problems lead to 


1 
> rilog N; = (logV) ZE vit = vilog aj! | Evilogn;=(log VY = vit Erie OR) 


AS Di ae! (ft) Se ee 
— — > jy TS | ——— 3 0b; + (log 7). — 2 vi Ci 
Be ae Jo |e EON ) 


In (37’) we shall express V in the pressure p of the gas-mixture 
by means of the equation 
pV Fe Sara oe cs ig Se LO) 
Further in (87) we shall put 


7 
Kar, prEN .. . . (899) 


1) In general more than one reaction is possible between the molecules of the 
mixture each characterized by a special set of values of the numbers 
RAV ee, vj. 

In order to establish the dissociation-equilibrium completely, and to obtain the 
necessary number of equations between the equilibrium concentrations, all the 
different reactions [variations] have to be taken in succession [Comp. M. PLANCK, 
Thermodynamik § 247]. 

2) M. Puanck, Thermodynamik § 244 

3) Properly speaking these two equations must be taken as giving definitions of 
the quantities p and 7: the phase-region in the ‘‘y-space’’ which corresponds to 
the prescribed values of V, E and Nj, Nz, .. . Nj contains beside MAxWELL- 
BoLTZMANN states, others which deviate strongly from those and for which 
therefore in themselves the conceptions of “pressure and temperature of the gas” 
have no meaning at all. However, the very great majority of the phase-points of 
this region are of the MAXWEeLL-BOLTZMANN-type of distribution or closely 
resembling ones, and for those the relations (39) hold with the ordinary meaning 

of the quantities p and 7. 


174 
and instead of the numbers MN; (n;) we shall introduce the ‘con- 
centrations” 
N; nj 
¢= — ee fee ee a are (40) 
NHN... Nj ny tnt... tH 
This gives 
2p, log G OND = vj log e; = — (log p) Xr; 
1 1 
sl j/—— 2 vy; | — 2 pi; («; HRlog R—C;— Rh 
FE 8 oop ON ga ad ae yet (41 


+ (log rT) = vi (5 + ) 


i 


1 
RT =v; b;+(log Tym vil C;+R) | 


On comparing (41') with (41) and in view of (12) to (14) $ 3, 
we obtain for the ‘“‘chemical constants” 


aim HRlog RiB a . J 
following equation 
1 i 
mja Sp; log ein (4 + 1) logr). . .. ae 
R 2 
or 
5 San 44 
R Vag EVH de 
where 


[Mi 
ot; = log a;' + 


hence by (30) and (25) 


(5 +1) bar oe: er 


EEA rae iat 
a, — log Ee if VM; P; Q; R; (55) r | 


t 


Mf = 
a; — log = VM? P? 


„Oi 


d 


h 


(GE) | — 


for poly-atomic, di-atomic and mon-atomie molecules respectively. 


§ 7. Remarks on additional contributions of the atoms to the 
chemical constant of the molecule which remain indeterminate. 


Molecules of the kind as considered here may undergo a large 
number of different chemical reactions, each characterized by a 


'!) The term with Jog r is derived from log r T in equation (41). 


tin >» OS 


175 


different set. of numbers »,,»,, ..,v,;'). Each time we obtain a cor- 
responding equation for the chemical constants of these molecules 


1 
RN ee ab ne grea EAA) 


It will be seen, however, that the quantities a; are not complete- 
ly determined by these relations. For every chemical reaction which 
is possible the corresponding numbers »,,r,,...,rjs have to satisfy 
the relations: 

0, Evs n= 90; = Bye 0 ee a 

Therefore: for every chemical reaction the corresponding equation 
(47) will be satisfied by putting 

aj E 

meae EEN 8) 
with completely arbitrary values of the numbers u,v, w, that is to 
say: the chemical constant of a molecule is completely determined but 
for certain additive constants, which the several atoms bring with 
them into the molecule and carry away, with them in chemical reac- 
tions”). In the determination of the dissociation-equilibrium these 
arbitrary constants drop out, since in that case, as we have seen, 
we only deal with 2p; q;. 


§ 8. The influence on the dissociation-equilibrium of the 
“symmetry-numbers” o; of the molecules. 


The part played by the symmetry-numbers in the dissociation- 
equilibrium may be elucidated by a typical example. 

Let the chemical elements A and B be able to form the following 
kinds of molecules 2 

1) Comp. not 1 in § 6. 

2) Obviousiy the entropy-constants Ki; have exactly the same degree of determi- 
nateness and indeterminateness. The same indeterminateness remains, when the 
chemical constants are derived by means of the vapour-pressure equation (comp. 
“additional notes” III), and also, if following BotrzmaNn one would make use of 
_ the equation 


St — Sr [log y*} — log} vi] 


For also the numbers of molecules N,* No*, ... Ni* and Ny, No, ... M 
occurring in this equation have again to satisfy relations of the form. 
N;* N; a7 4 0 (comp. (33) § 6). 


in order that the change may be compatible with the number of atoms 1, Y, Z, 
present. We do not think that BorrzMANN's equation can be replaced by an 
assumption of the form. 

S=rlog}y} 


on grounds which will be set forth in § 9. 


176 


A, B, AAB ABA 2% ve iN 


the concentrations, moments of inertia, potential-energies and sym- 
metry-numbers being as follows 


€, €, Cs 
ove oib govern 
(51) 
0 0 ús x, big 
1 l 1 2 


The two reactions 
AABZA LB and ABA ZAL B . eS 
give dissociation-equations of the following form 


GPe TE 


since all the quantities are the same in the two cases with the 
exception of P, A P,y, Ax, and o, 0, (G is supposed to contain 
the quantities which are common to the two cases). 

If therefore for instance approximately P, = P, and 4, ==, we 
should have 


—s=2, » wae, 1 


or the concentration of the unsymmetrical molecules is about twice 
that of the symmetrical molecules. 


§ 9. Critical remarks on some allied deductions of the 
chemical constants. 


Whereas BorrTZMANN in his theory uses the equation 


SS =p oF 3. 0 
throughout, PLanck and many others following him replace it by 
the relation 

S= Plog Wo. Pee? re 

It was obviously Nernst’s theorem that first started this pre- 
ference of (60) over (59), as on the one hand it provided a natural 
zero-condition for the calculation of S and on the other a natural 
common unit for the estimation of W, viz. any condition of the 
system al 2 — 0: 

In the majority of calculations of the chemical constants a special 
obscurity remains as to the way in which the “thermodynamic 
probability” of a gas depends on the number of molecules. 

We shall try to explain in a few words, how this obscurity is 


sa 


connected with the use of equation (60)*): it is generally assumed 
as self-evident, that the entropy of a gas is to be taken twice as 
large, if the number of molecules and the volume are both doubled. 
Now it is certainly true, that the increase of the entropy in a given 
process in a gas of twice the number of molecules is twice as large 
as the corresponding increase in the original gas. But what is the 
meaning of taking the entropy itself twice as large and thereby 
settling the entropy-difference between the doubled and the original 
gas? By what reversible process is the double quantity of gas to 
be generated from the original quantity? Without that the entropy- 


d 
difference f = cannot be clearly defined. On account of equation 


(60) one is then confronted with the difficult problem of choosing 
the definitions in such a manner that the “thermodynamic proba- 
bility, of the double quantity of a gas is equal to the square of 
the “thermodynamic probability of the single quantity. ?) 

In order to remove this obscurity it is necessary to return to 
BoLTZMANN’s equation (59) and to apply it to a reversible process 
in which the numbers of the molecules change. 

We shall now go a little more fully into the relation in which 
our theory stands to others which are closely allied to it. ® Special 
interest attaches to the manner, in which in the various theories 
the terms MNilog N are produced. In our theory they originate in 
the combinatory factor: 

See hy NIE 61) 
: NANOS oo Nf 0 GE) A Ge REN ae i 

If instead of a gas-mixture, as in our case, a single gas of mon- 

atomic *) molecules is considered, this factor ) reduces to 
== aes a 
X/ 


(62) 


1) O. SrerN, quite recently remarks: “The difficulty in this deduction lies in 
the introduction of the quantity N, which is done in a very arbitrary manner”. 
(Z. f. Elektroch. 25 (1919), p. 79 at the top on the right). 

2) Comp. our remarks in notes (1) and (2) § 5 with regard to the quantities 
Q and I, which in our theory occur in the entropy and in log} y §. 

3) As regards the theories of Lenz (Vorträge der Wolfskehl-Stiftung 1913 in 
Göttingen, Teubner 1914, p. 125) and Kressom (Phys. Ztschr. 14 (1918), p.212), 
who apply Desue’s method for solids to gases, we may refer to papers by H. 
A. Lorentz (Versl. Kon. Ak. v. Wet. Amst. 23 (1) (1914) p. 515, § 6 — Proceedings 
Amsterdam 19, (1917) p. 737) and O. Stern (Ztschr. für Elektrochemie, 25 (1919), 
79 section C towards the end), where these theories are discussed. 

The same holds for a gas with more atoms in the molecule, if ¢ = 1. 


12 
Proceedings Royal Acad. Amsterdam. Vol. XXIII. 


178 


The question, therefore, is how those authors, who confined 
themselves to the consideration of a single gas, were able to obtain 
a “thermodynamic probability”, the logarithm of which yields an 
admissible entropy-equation, in other words, how do they manage, 
that the entropy does not contain a term of the form 


~ 


V 
RlogV. but. Blogs on % nn 
Ni 


1. ©. Sackur') reaches the desired result by a special method ot 
“quanticising” the motion of the gas-molecules: we may express it 
by saying, that he quanticises, as if each molecule were separately 

esa 
contained in a cell of volume We 

i 

2. M. Puanck’) similarly only obtains the term (63) in the correct 
form by dividing the phase-space of the molecules (u-space) into an 
increasing number of “elementary” portions, as the number of mole- 


cules is larger (G == Ng). The justification of this procedure and 
the fixing of g he considers to be open problems’), 


3. H. Terropr [1st Paper]|‘) attaches a factor to the expres- 


1 

N;! 
sion for the “thermodynamic probability”, 7 order that its logarithm 
may show the law of dependence on N which is needed in the entropy. 


But he does not justify this procedure on combinatory grounds *). 


1) O. Sackur, Annalen d. Physik, 40, p. 76 (1915). 

2) M. Pranck, Wärmestrahlung, 2 Aufl. § 126, § 133. 

3) M. Prancx, Theorie der Wärmestrahlung, 2 Aufl. p, 131; also M. PrancKk 
Vorträge der Wolfskeh!-Stiftung 1918 in Göttingen (Teubner 1914) p. 7; Phys. 
Zeitschr. 14 (1913), p. 258. In a later paper (Sitzber. d. Preuss. Akad., Berlin, 
1916, p. 653 —667) PranckK once more returns to the problem; here he takes in- 
to account the permutability of the molecules, but he does not himself look upon 
this discussion as giving a combinatory justification of his assumption as to the 
“elementary regions”. 

4) H. Terrope, Ann- d. Phys. 88, p. 434 (1912). 

5) H. A. Lorentz, (Versl. Kon. Ak. v. Wetensch. Amsterdam 28 (1) (1914, p. 
515, — Proceedings Amsterdam 19. (1917), p. 737), at the end of section 5 draws 
attention to this. H. Trrrope in his 2nd paper, where he gives the new deduction 
by means of the process of evaporation, à propos of Lorenrz’s remark in an 
appendix once more returns to his previous deduction. But again he explains — only 
more fully — that the division by the factor Ni! is required, in order that the 
entropy may show the desired law of dependence on Ni. P. ScHERRER, Gött. 
Nachr. 1916, p. 154 in following the same procedure simply refers to J. W. Griess, 
Statistical Mechanics without any further comment. 


nie mir A 


an re te medi Ch tC 


mg 
ADDITIONAL NOTES. 


I. Elucidation of the choice of the u- and y-weight: fu} and }y}. 
(Note to sections 2, 4). 


The definitions of {u} and fy} may be elucidated by a simple 
example. Consider first a PrLANCK-resonator. According to the theory 
of quanta its phase q,p must lie either at ¢g=p—O or on one of 
Pianck’s ellipses e =hv, 2hv,... Now two consecutive ellipses are 
known to enclose a ring whose area is 


ffaap=r. SU DA BEDEA EN SOA TOOL) 


The classical theory would admit all the points of the plane and 
ascribe to any portion «of it a “weight” equal to its area sil dq dp. 


It therefore seems natural in the statistical calculations of the 
quantum-theory to ascribe a weight A to each of the ellipses, % 
particular also to the point q=p=O. Since in all statistical 
calculations it is ultimalely only the relative weight that matters, 
the essential thing about this assumption is, that the same weight 
is ascribed to all the ellipses, which moreover is independent of the 
nature of the resonator (say its »). }) 

The choice of h itself as the weight in question has the following 
advantage in connection with (64): if in the y,p plane any portion 
is considered which contains a large number of ellipses, the total 
weight of all the ellipses inside this region coincides with its area 
owing to (64). ’) 

Let us next consider a material point elastically connected to a 
given position of equilibrium, say anisotropically. Its principal 
vibrations may be parallel to the co-ordinates q,, q,, 7s, its frequencies 
being supposed very different 


EEE ee dN Le G2 1. oy Sos meme) 


1) The choice of the weight must be subjected to certain limitations, in order 
that the statistical theory may not get into contradiction with the IInd law of 
thermodynamics. Comp. P. Exrenrest, Phys. Zeitschr. 15 (1914), p. 657; Ann. de 
Phys. 51 (1916), p. 340, § 8 — Versl. Kon. Ak. v. Wetensch. Amsterdam 25 (1) 
(1916), p. 423, § 8 — Proceedings Amsterdam 19 (2 part.) (1917), p. 576, § 8. — 
The above choice is in accordance with the limiting conditions in question. 

2) Hence for sufficiently high temperatures we shall have approximately 


ea) En ae ad 
She Tmf [ap dye "1 
0 


12" 


180 


The g-point of the system in the six-dimensional u-space (q,, . . . p‚) 
is then limited by the quantum-hypothesis in the following manner: 
its projection on the plane g,, p, must fall on one of the Pranck- 
ellipses; similarly the projections on the planes q,, p, and q,, p,, 
If the total energy EH is contained between 0 and a moderate value, 
we see by (65) that g,,p, may still fall on a large number of diffe- 
rent ellipses; (since for this degree of freedom the energy-stages 
&, = 0, hv,,2hv,,... follow each other closely), g,,p, on the other 
hand only on a few ellipses, whereas q;,p, is possibly completely 
confined to the position g, = p, = 9. 

If the limitation which is due to the quantum-hypothesis did not 
exist, the “weight” to be given to a given region in the u-space 
would according to BorrzMANN simply be its volume 


eae dp. TLE GN 


To each region, whose three projections are three PLanck-ellipses, 
we assign the weight 
RE DN 
The joint weight of all phases which the u-point can assume, 
when the energy is subjected to an upper limit, will then be 
fyizc SSS... ee 
nn 7% 
where the summations are to be extended over all the quantum- 
numbers which the first, second and third degree of freedom can 
assume. With a moderate upper limit for the energy t, as we saw 
would be able to rise to high values, and the corresponding sum 


may accordingly be replaced by {fea dp,; t, on the other hand 


would be confined to zero and the corresponding sum reduce to the 
first member /. Hence 


eee [ta dey (EIA -. 


According as the upper limit for the energy is made to rise or 
fall (i.e. the second degree of freedom is made to pass from the 
state of being half-excited to that of full excitation or non-excitation) 
(69) changes into 


gen ld dp, da dp zt … far, dp, . (70) 
Lr fs op, neren far dp, ee 


or 


ate t—“‘“SCS:;~‘<‘;..”.”;”tt 


181 


Evidently of all the original degrees of freedom only those remain 
in the power of h, which are not excited. The other factors h are as 
it were absorbed by the intregrals. 


Il. Calculation relating to § 6. 
We found [eq. (27) § 5]. 


og by} = 2 Ni lg vg K + tog a | | 


al ne ck | 
EN aha 


If this expression is varied, having regard to 
dr 0; dN; = 00: dE = dK + = ws dN; 0,4 (73) 
the last equation provided with a multiplier (— 6) being added to 
the variation of log fy}, we obtain: 


0 =dlog}y}— 4 an END 4 zen lg V+ log K + ve 
F (74) 
— JQ Zr; log Ni — ( 7) 00: = Vi Te dK — dQ. Eri: 
1 
The condition that the co-efficient of JA disappears, gives: 
F 
= end 


that for dQ 
5 fee eee 
ear, log. IN; — > v; ard log K + log ai — 519-5 — 0 „| (76) 
or by (75) after a small reduction 
Si 


2K F 
eee Fi + log di — OK x Cea) 


=> Dilog_N; = > vi | to V+ 


gemd 


The thermodynamical calculation is entirely similar. 


Ill. Deduction of the vapour-pressure formula for very low temperatures. 


The equilibrium of evaporation at very low temperatures may be 
deduced by the same means as that of dissociation. If again there 
are X, Y, Z atoms in a volume V, which, however, may now be 
associated in N poly-atomic molecules of one kind, of composition 
&,7,¢, mass and moment of inertia M, P,Q, R and symmetry- 
number o, N of these may be present in the form of vapour 


182 


‘potential energy — Ny) and N’ condensed to a crystal (potential 
energy = N’y’). 

For the vapour molecules we make again the assumptions I and 
IL of section I. As regards the atoms in the erystal our assumption 
will be, that 

Ill. In the calculations the motions of the atoms in the crystal 
are to be ignored *). 

The {y} weight of the condition (N‚N’) is then found to be 


OAL AVAL 1 path fake fee! | 
ya (XL Y4Z)-6NVN, (VW 2 Kn)®N (42.2nV M* POR), (78 
re ETT ren) m)eN (4rr,27 QR), (78) 
where 


K=E—S(Ny IN!) ee = eee 
On the other hand the entropy and energy of the system are 
given by the equations 
oe V 
S=2+ni\C log T + Rlog—+ x) Han's, « « (80)*) 
n 
B=al(CT $0) 4 Ad... 7 re 
The condition of equilibrium is given by 
Slog tyj=—0.. 2. .5 so 
with the conditions 
dio dix), JN 4 dN. = On (83) 
This yields an equation for NV’ as a function of V and K; sub- 
stituting 
al 
Ron nr VEN. 
he 
we find 


log p= —** 4 blog T + a - «> 
zs 


where « has the same meaning as @, in (46). The corresponding 
thermodynamic calculation gives 


1) This assumption is again meant not as a physical hypothesis, but as an 
approximation in the calculations. (Comp. note 5, 8 1). It comes to neglecting 


i dT for the solid (comp. M. Pranck, Thermodynamik, 4 Aufl., § 288, comp. 


0 
(270) in the thermodynamic deduction of the vapour-pressure formula for low 
temperatures. 

2) Properly speaking the last term should be #/s’; but with PrancK we neglect 


183 


b—b' 

RT 
where for shortness we have put 

“— Cp + RlogR=a mA 

The comparison of (85) and (86) produces the equation 


a-—s 


RS vanen 
Ben ee 


logp = — 


a § 4 

ra hg 
or for molecules of different kinds 

di aed 

Pe opp 


Nernst’s theorem requires for every chemical reaction r,, », .. 


which is possible the relation 
28 og =, 
which is satisfied by 
Si Siw eee Serge! 
where w’v’w’ remain perfectly arbitrary. 


(86) 


(87) 


(38) 


(89) 


Da 


(90) 


(91) 


Evidently the chemical constant as calculated by means of the 
vapour-pressure formula and Nernst’s theorem contains similar inde- 
terminate contributions by the atoms as in our deduction from the 


dissociation-equilibrium. 


Physics. — “The osmotic pressure, regarded as a capillary pheno- 
menon’”. By H. Hursnor. (Communicated by Prof. H. A. Lorentz). 


(Communicated at the meeting of March 27, 1920). 


In this paper an attempt will be made to give an explanation of the 
osmotic pressure by regarding this pressure as the consequence of 
capillary actions. Though some difficulties remain, in my opinion 
a trial in this direction might be made. In a former communication 
(these Proceedings January 1900) the surface tension has been defined. 
To that end we supposed at a point of the passage layer fluid- 
vapour the influence of the attraction in different directions to have 
different values. Now we shall base our considerations on the same 
suppositions. For a plane in the direction of the passage layer p, is 
the whole force per unit of surface (pressure) exerted by the matter 
on one side of the plane on that on the other side. It consists of 
the attraction q, and what may be called the thermic pressure 1, 
so that 


Di a! EE o. 
For a surface element perpendicular to the passage layer we can 
also speak of the total force exerted by the part of the system on 
one side on the part on the other side. Let us call this p, and let 


us write g, for the attraction between the two parts and & for the 


thermic pressure. Then we have: 


ben 
Instead of the attraction g, and g, we may also consider the 
molecular pressure J/,’ and M,’; q, = M,’ and q, = M,’; in homo- 


a 
geneous phases g—= M’ =ao?= —. The thermic pressure 9 = 
v 


MRT 


a will be supposed to have in all directions a value equal to 


that in a homogeneous phase of the density at the point in question. 
Pao = Ps +} M, =p+M=d. 

The index 1 refers to the direction perpendicular to the passage 
layer, the index 2 to a direction in this layer; as to gravity we 
assume that it only causes the layers to be horizontal; the height 
h is measured upward perpendicular to the passage layer. Differen- 


185 
tiating the different quantities with respect to h and taking into 
consideration that p, has a constant value, we obtain: 
dM,' = dp, + dM = dp + dM'. 


Omitting the constant we can write for the energy at the height / 


c‚d'o c, d‘o 
laa Bd 
where e= Splitting this energy into a part €, corresponding to 
the homogeneous phase and a part €”, we may write 

eze He 
Now the stationary equilibrium demands that both in the homo- 
geneous phase and in the passage layers fluid-vapour and fluid- 
solid wall 
&é—1y + pv uM 
has a constant value. Here p, represents therefore the pressure in 
the direction of the passage layer; in the homogeneous phase it has 
the same value as the constant pressure in the vessel. The equation 
expresses that layers lying in each other’s neighbourhood will exchange 
the same number of particles in the same time. 
The change of the attraction (molecular pressure) in the direction 
of h from point to point is: 
dM,' = — 29 de = — 20 (de + de") = 2a9 dg—2o de". 
This follows from the value of 
2 2 
M,' = ag’-+-¢,0 =< — ; (5) 
in conneetion with 


€ = & — ag — = 
dp + dM'= dp + 2uo do 
and so — 2ode"= dp or — 2de'"=rdp, whence oe Jode". 


For e— ty + p‚v=—=uM we may write & He’ —ru tpv 
+ (p.—p)v=uWM. By differentiation we find vdp de" +-d (p‚—p)v=0, 
as de — td + pdv=0; this is evident when we regard the unit 
of mass (as homogeneous phase) as having first had the volume v 
at the height A and afterwards the volume v + dv at the height 
h + dh. For the passage from one state into the other we have: 


tdy = de’ + pdv. 
As further vdp= — 2de", we have — de"+ d(p,—p)v=0 and so 


186 


&' = (p,—p)v of pe =p; =p. 
Now we find: 


PiP, = — GF + fzo de" = og" — fre do. 


Therefore 
dp, = #'do — ode", 
for which we may always write: 
dp, = edo — ode. 
Still it may be remarked, that when the condition of the thermo- 


: Wu ance 
dynamic theory that f— — — dh shall be a minimum, is satisfied 


v 
(the integration has here to be extended over the whole depth of 
the passage layer), one element of this integral is just equal to 
Pers p = ob and ME 

Suppose, we had started from the definition of the molecular 
pressure in the direction of the bounding layer that it was equal 
to — ge (with omission of the constant). Then this would evidently 
have led us to a value of the surface tension in agreement with 
the thermodynamic theory, which is a proof of the validity of the 
definition. But then we can at once write down the differential 
equation for the surface tension. For from 

Pi =p, = MM SM; 
it follows directly that 
— dp, = — doe + 20de = — edo + ode. 

When a fluid is in contact with a solid wall, the molecular 
pressure and therefore also the external pressure in the perpendicular 
to the passage layer will generally be different from the pressure 
in the direction of this layer. The action of the solid wall on the 
fluid at the wall influences the molecular pressure of the fluid at 
the wall. External forces like gravity, a magnetic or electric force 
will directly influenee the external pressure. As also in this case 
the molecular pressure in the direction of the passage layer M,’ may 
be represented by — ge and as JM, = — 2ede, we have here likewise: 


d(p, — p,) = — dp, = — doe + 20de = ode — edo. 

The calculation of the value of the molecular pressure of the fluid 
at the wall presents great difficulties, because the calculation is 
based upon the continuous division of the matter. In the immediate 
neighbourhood of the wall e.g. the value of the molecular pressure 
in the direction of the wall will be caused by the attraction 
of the wall and of the fluid, but in the case of equal spheres of 
action the contribution of the two will be due to unequal volumes. The 


tt, oo le es Pee 


187 


difference of these volumes will be intimately connected with the 
dimensions of the molecule. Moreover, except with regard to the 
attraction, a solid wali impenetrable for the particles is quite difte- 
rent from a fluid wall formed by the particles themselves. 


Let us consider avery much diluted solution e. g. a solution of sugar 
in water, the vapour phase of which does therefore not contain the 
solved substance. The concentration zw will then decrease in the 
passage layer from w, in the homogeneous solution to zero at the 
vapour -side. In the passage layer near the solid wall too the concen- 
tration will change and in very different cases a similar change of 
the concentration must occur as in the passage of fluid to vapour, 
viz. from wz, to zero in the layer next to the solid body. Now 
it is important to consider what will happen to the pressure 
p, (in the direction of the surface layer) especially in the layer 
next to the solid wall in which the concentration will be regarded 
as zero, when the concentration within the solution is increased 
from wz, to 2,-+dzx,. Here therefore we have not to do with 
the change in the total surface tension of the solution when 


in contact with the solid wall fi, —p,) dh, but only with the change 


of p, in the layer next to the wall. When the concentration is 
increased by de,, the potential of the solvent decreases. For when 
we have the solution under the pressure of the saturated vapour, 
the thermodynamic potential of the vapour decreases by va dp, when 
dp is written for the decrease of the vapour pressure and va for the 
specific vapour volume. In the uppermost layer of the passage layer next 
to the vapour the decrease of the thermodynamic potential is 
vadp, =vadp, as here too dp, —=dp. Also in the layer next to 
the solid wall the thermodynamic potential will decrease by the 
same amount. This decrease may be due for the greater part to 
a decrease of p, in the immediate neighbourhood of this wall, 
where just as in the vapour no dissolved matter is- present, so 
that a change of w can have no influence, as here x is zero. 
This is a tempting supposition, as in this case vadp would be equal 
to vdp,, when v represents the specifie fluid volume of the pure 
solvent near the wall. However this may be, it is certain that p, 
will change at the wall when the concentration is altered. 

Let us consider two glass vessels, both filled with the same diluted 
solution of sugar in water of exactly the same concentration. The 
vessels should be connected by a tube part of which is so narrow that 
no sugar molecules can pass through it, as their distance from the 


188 


wall cannot not be great enough. This part therefore contains only 
the outer layer of the passage layer. In this case the pressure p, 
close to the wall and in the direction of the wall will be the same 
everywhere both in the vessels and in the tube. Now when in the 
vessel on the left the concentration is increased by an amount Az,, 
then in every part of the left vessel as far as the narrowing of the 
tube, the pressure along the wall will have diminished by an amount 
Ap,; the equilibrium is destroyed, in the narrow part we now have 
a fall of pressure, which will cause a current of pure water through 
the narrow part from right to left. By preventing the solution in 
the left vessel from occupying a greater volume, the equilibrium 
will be established again by the displacement of some water. Owing 
to this the pressure in the left vessel will increase everywhere in 
all directions by the constant amount Ap,, so that the pressure 
along the wall in this vessel will again become p,, and the equili- 
brium will be established again. This increase of pressure Ap, is 
what is usually called the osmotic pressure, the over-pressure in the 
left vessel. Now when in the right vessel no sugar is present, so 
that in the left vessel there is already an osmotic pressure corre- 
sponding to the small concentration 2,, we may say, that the 
decrease of the pressure p, along the wall caused by an increase 
de, of tbe concentration is equal to the increase of the osmotie 
pressure due to the capillary action. 


7 


M 
From the experiment we know that Ap, = ———Aaz,, where Ap, 
v 


has been written for the osmotic pressure. When Ap, represents the 


MRT 
change of pressure along the wall, we may write —Ap, = Az. 
v 
In this last relation v is the volume of M, grams of pure solvent under 


if 


Se ee dv 
the pressure of the vessel. We may write for it: v'—2, (=) , where 
P 


/ 


v’ is the volume occupied by M, (1—.) grams of the first component 
and by M,a grams of the second under the same pressure. 
In the equation 

vA p, = — MRT Aa, 


the right hand side represents also the change of the thermodynamic 
potential, when the concentration increases by Aw,, while the pres- 
sure remains constant. The theory of vaN DER Waars namely gives 
for the value of this potential in the homogeneous solution 


a] dy, 
uM = MRT log(1—z«,) + us, — «, | — }. 
dz, Jp 


189 


Here is 


ay, 


uz, = pv — | pdv’' = pv — MRT log (v' — bo) — —. 


v' 
du M MRT ee 
ee ait 
de, Jp 1e, RE p 
and as we confine ourselves to very diluted solutions 


du M 
== RL 
de, p 


We find therefore the relation 
vA p= At M: 


The value of the thermodynamic potential of the solvent at the 
wall, where we take «= zero, may be represented by 

et + p,v—uM. 

For a change of the value of uM therefore we have the relation 

de —tdy + p,dv + vdp, = duM. 

When this explanation of the origin of the osmotic pressure is right 
then vdp, = duM. And asthe only change the state of the bounding 
layer in the immediate neighbourhood of the wall can undergo by an 
increase of the concentration of the homogeneous solution by dz, 
is a change in density, we must have for any such change 


de — tdy + p,dv = 0. 


But this consequence is in perfect correspondence with the ther- 
modynamic theory of capillarity. 

Let us consider an element of the outer layer and let us expand it, 
without changing its thickness, in the direction of the wall, so that 
v becomes v + dv. The external work done at the expense of the 
supplied heat is p,dv and not p,dv. The supplied heat is tdy, so 
that we have: 

tdyn =p, dv + de. 

In fact this equation is nothing but the well-known equation from 

the theory of capillarity : 
de = tdy — p, dv + ods, 


when we do not apply it to the layers as a whole, but to only 
one of the layers. 

As our conclusion is right, we may evidently also treat the 
problem in another way viz. by assuming that we have 


duM = vdp, 


190 


for an isothermic change in the outer bounding layers where we 
may suppose no sugar to be present. 

Let us further assume that in the homogeneous diluted solution 
the quantity uM for the water has another form but always the 
same value as for the outer layer that consists of pure water (or 
in the vapour phase without sugar, that is in coexistence with the 
solution). This uM in the homogeneous solution is a function of 
x, and p,; 


(5 E) MRT (Ge: ) (55) (5) *) 
=== = ai - and =U 4) a5 5 
da, A 1—2, da,* Jr dp, J x, da Pi 


when we increase the concentration of the sugar solution by de, 
while the pressure p, remains constant, uJ/ in the solution changes 
by — MRTdz,, and in the outmost sugarless layer near the wall by 
vdp,. From this it follows vdp, — — MRTdz,. When we admit 
that osmotic pressure appears this will have the value 

MRT de, 


v 


dn 


Here it may be remarked, that by admitting the osmotic pressure, 
the pressure will in all directions increase by the amount dp,. In 
the outer bounding layer the pressure p, thus gets its original value 
again. The total change of p, because of the two changes of state 
is therefore zero. 

The same is therefore the case with uM in the outer bounding 
layer as duM=vdp,. Also for the total change of wJ/ in the homo- 
geneous solution, so that 


duM duM 
(5 ) aa (5 jan =0, 
da, Jp, dp, Ja 


where Ap, = Ap,. By means of this relation Honpius Bor.prnen derived 
the formula of the osmotic pressure from thermodynamic considerations. 

The decrease of pressure in the layer at the solid wall may be 
compared with the decrease of vapour pressure. When the solved 
substance occurs neither in the vapour phase nor in the outmost 
layer at the solid wall, there will always be a decrease of vapour pressure 
and of the pressure at the wall in the direction of this wall according 
to the simple laws for very diluted solutions. To a definite solved 
substance in a definite solvent a wall will be semipermeable, when 
the pores in this wall are so narrow that only the solvent substance 
can enterinto them and not the solved substance. Itis evident that changes 
of temperature and pressure can also have influence on the semipermeabi- 


1) See Dr. G. Honprus Boupinau. Thesis. Amsterdam 1893. 


191 


lity. The layer of ferrocyancopper in the porous pot will generally stop 
the wide pores. The pores through which neither coppersulfate nor 
potassium ferrocyanide can pass, remain open, but we may expect 
that between the ferrocyancopper formed and the wall of the porous 
pot holes narrow enough will remain and moreover that in the layer 
of ferrocyancopper there will remain narrow holes fit for the 
semipermeability. Where this layer is formed, the concentration 
of the two solutions locally decreases considerably, so that probably 
the layer will not be continuous, leaving holes narrow enough 
for semipermeability. 

Also when the concentration of the solution near the wall is not 
zero, or when the pores are somewhat too wide osmotic phenomena 
may occur. Then, however, the simple law will no longer be valid ; 
the semipermeability will not be perfect and by pressing the solution 
we shall not obtain the pure solvent through the pores, but a solution, 
though perhaps of lower concentration than the one under the 
pressure. . 

The decrease of the melting point may illustrate the above 
considerations, also because we have indications here, that at a solid 
wall the concentration of a solution can be zero. Let us consider 
the solution at such a temperature that there is also ice present in 
the sugar solution. The ice is separated from the solution by a layer 
of pure water, in which the pressure close to the wall is p,. When 
the solution is frozen, generally pure water on the surface of the ice 
is frozen. This indicates that probably in the layer surrounding the 
vee the solved substance does not occur. Now when under constant 
pressure the concentration «, is increased by de,, the pressure p, 
changes by such an amount that vdp, = — MRTde,, where v is 
therefore the specific volume of the water next to the ice. Now the 
solid wall is a wall of ice, which must be in thermodynamic equi- 
librium with the water. When however the equilibrium is destroyed 
not directly between the ice and the solution, but between the ice 
and the layer of pure water surrounding the ice, in which layer 
the pressure p, along the ice surface and therefore also the difference 
in pressure p,-—p, is changed, only a change of temperature can 
restore the equilibrium, can cause that the two phases in contact 
regain their coexisting equilibrium. A change of the temperature dt, 
will change the potentials of the water and of the ice by —1, dt 
and —y dt. As —nydt is at the same time the total change of the 
thermodynamic potential of the ice, we shall have 


— Hi; dt = — Nw dt + v dp 


192 


À 
As further 10 — ny mk where 2 represents the melting heat, this 


relation becomes 
dp, 2h 
dt vt’ 
dp, is negative. We have thus a sinking of the melting point and 
there is no osmotic pressure. The osmotic action appears only when 
after having prevented the volume from increasing we bring, the whole 
system into semipermeable connexion with a solution of the original 


concentration «, and under the pressure of the system. The pressure 


in this whole system increases everywhere and in all directions by 


an amount just equal to — dp, (a positive amount). Except for the 
sign the formula for the sinking of the melting point therefore 
becomes the same, or, when dp is written for the increase of the 
osmotic pressure, 


- 


Zoology. — “Technical experiences in the breeding of Tenebrio 


molitor’. By S. A. ARENDSEN Hern. (Communicated by Prof. 
JW Morr). 


(Communicated at the meeting of April 23, 1920). 


Studies on variation in Tenebrio molitor, of which the results are 
published in the Journal of Genetics, gave occasion to make some 
observations with respect to the practice of the breeding of this 
insect. Though these facts are not very suitable for being treated in 
a genetical periodical, as they deal especially with technical particulars, 
1 thought their publication to be of some value for those who wish 
to experiment with this beetle. 


CON TENTS: 


1. Choice of the culture vessels. 

2. The food. 

3. The number of moults of the larva. 

4. The infection with Tyroglyphus farinae 

5. The gathering of Pupae and beetles. 

6. The gathering of the Eggs. 

7. The mortality. a. amongst the Eggs. 
b. - „ Larvae. 

DE se » Pupae, 


1. Choice of the culture vessels. 


Larvae. For the culture of larvae, glass erystallizing jars are 
preferable to any other kind. From these jars with their perpendi- 
‘cular slippery wall the larvae cannot escape. 

Porcelain pots with perpendicular smooth walls also give satis- 
faction. Tin boxes with lids not fitting too close (for the air circulation) 
are serviceable only when the inner wall is perfectly smooth (not 
varnished or painted), without any rust-stains, solder or rough con- 
necting seam, so that the larvae lack any support in crawling up 
the wall. 

The fulfilment of these conditions is of great importance when the 
perfect purity of the cultures is aimed at. Close attention should 

. 13 

Proceedings Royal Acad. Amsterdam. Vol XXIII. 


194 


be paid to these conditions in order to preclude unpleasant surprises. 
Glass jars guarantee against any disappointment. 

As the larvae thrive better when the layer of food is not too 
thick, the quantity of larvae that can be accommodated in a vessel 
depends on the size of the bottom rather than on the capacity. As 
a minimum about 20 sq. centimetres (3 or 4 sq. inches) should be 
available for every 100 larvae. 

For a quick growth and early pupation the food is to be renewed 
at set times. The need of a renewal becomes clear from the crumbly 
powdery state into which the scaly structure of the bran has passed. 

The renewal is brought about most effectively by sieving. 


— 


A suitable form of sieve is found among the common kitchen 
utensils (cf. sketch). The material is usually tin, the inner side and 
bottom smooth, the latter (no wire-sieve) perforated with round holes 
of 2 or 3 millimetres diameter according to the size of the larvae. 

By shaking the sieve horizontally and quickly, the larvae remain 
in a horizontal position, have no opportunity of erecting themselves 
and are left behind on the bottom, even when their thickness is 
smaller than the diameter of the holes. 

In less than no time a large culture of some thousands of larvae 
can be separated from the bran and provided with fresh food. 

For cultures of which the larvae are very small yet, very fine 
wire-sieves should be used. This practice should, however, be stopped 
as soon as possible as the food, defiled by faeces, is not sufficiently 
cleared by these fine sieves. 

The larvae jars were covered with a glass plate. By glueing two 
strips of thick cardboard firmly on this plate, an interstice is left 
between the rim of the jar and the glass plate through which opening 
an adequate air-circulation can take place. If these cardboard strips 
are laid loose, and if by shoving away or removing the jar, such 
a strip falls with one end into it, the larvae immediately utilise it 
as a bridge to escape, and before one thinks of it, the jar is empty. 


2. The Food. 


Relying on the statement occurring here and there in the literature 
(FRENzEL p. 298) on this subject to the effect that bran should be 
a sufficient food for larvae, bran was given at the outset. Their 
growth, however, was not satisfactory. Then a substance containing 


aia ay | 


= amp 


195 


more fat, in the form of rusk, was added by way of trial. According 
to the number of larvae one or more whole rusks were put in the 
larvae jars. The creatures took them with eagerness. For comparison 
some other jars were provided with some slices of peat. Also under 
these, the larvae gather up and they make large passages in the 
peat. It is not probable that the peat should serve them for food. 
After this experience the following comparative experiments were made. 
Six jars were provided with: 


Meer only bran . .- . See ee AN RER la 
N°. 2 bran on a layer of iat Pe ic and ee EO Me HT 
N*. 3 only meal (flour). . . EC a aes, ETE 
N°. 4 meal (flour) on a layer of LE BNN SI a CME 
an th Pus once eo ar Rat elke oe (BR): 
N°. 6 meal (flour) with rusk . . (M.R.). 


In each jar 300 eggs were placed in iet same hand (May 27— 
June 21 1915). Down to February 10, 1916 included, the following 
numbers of pupae were collected: 


TABLEVE 
| Number of! Pupae Number of 
Number | End | Larvae collected till, Pupaein Per- 
of jar. 7" | obtained Febr. 10.1916) cent. of the 
from 300eggs incl. larvae. 
1 B. 250 0 — 
2 B. P. 112 0 — 
3 M. 247 3 1.2 0, 
4 M. P 192 13 67 
5 Bake. 206 43 208 
6 M. R 225 36 168 
| | 


From the foregoing figures, though provisional, the following 
_eonclusions may be drawn. 

1. An exclusive nutrition of bran is inadequate to a normal growth 
of the larvae. 

2. An exclusive nutrition of meal is better than bran alone. 

3. An addition of rusk to meal or bran promotes the development 
of the larvae considerably. 

4. An addition of rusk gives a better result to bran than to meal; 
the pupation is 4 per cent higher. 

This provisional result was again tested in the following manner. 


13* 


196 


% 2 148 L18¢ I oy = = . u+d+qd og qz 
| an = 0 
%> OF 6S OGS Ig ie c= > d+q rae ad 
9161 
. Oz Iludy uo 
Je € 911 6096 € Ie = =) alee co: fae +9 =e Ut W 86 qe 
%o FET €9 116% | 22 IP = es lode == GE dn W 86 DE 
— OLI SORE) ee == el te = — | “over = EEE rd gl 
% 9S — — |L SI — 0 — 0 q cel vi 
el ZI 1 Ol | 6 8 L 9 q A z I 
| 
pead | Suir] Pee) Sulit) ret 9161 9161 9161 
9EAJBT OOI | BAe] ad 1e}0], | 8 Aine |og iudv | 8 Aine | 0g idv 9161 OF 4994 | zef yo 
uO BAIET 9161 8 Áinf uo ‚9161 oz [idyuo uo | uo uo uo poo uo deAIeT | Jaquiny 
o Ayyezsopw | ‘i ' o Jaquin 
=o ee egen EAIET Sulureway IBAILT AU} JO %/y [B}0, : aN 
‘ll ATAVL 


:ul palouze3 oedng 


197 


On the 10 of February 1916 the larvae of N°. 1 (B) and N°. 
3 (M) were sieved, and each group was divided into two halves of 
an equal number of larvae. The same process was applied to N°. 2 
(B.P.) on April 20, 1916. 

The 6 groups of larvae were put in separate jars. To 3 of these 
(half of each group) rusk was added; the 3 other jars kept the old 
food without rusk. 

On April 20, 1916, ie. 69 days after the above-mentioned 
division, the pupae collected from the sub-groups of N°. 1 were 
counted, and on July 8, 1916, ie. 48 days after the division, the 
pupae of the sub-groups of N°. 3. The group N°. 2 had not yet 
yielded any pupae. The remaining living larvae were weighed on 
a chemical balance. The result of this is shown in the following 
tabular statement. 

Here too, the four conclusions drawn from the first experiment 
(Table I) may be maintained unabated. That the addition of rusk 
to meal is very effective is manifest, not only from the more 
numerous pupation (80°/, more), but also from the absolute weight 
of the remaining larvae, which for M + R is nearly twice as great 
as for M alone. The enormous difference in the mortality of the 
larvae is also remarkable. 


_Until-now the rusks had always been added unbroken. 

A special reason gave occasion to putting the question whether 
rusk would operate as favourably if reduced to dust and mixed 
with the bran. Indeed, from former experiments (not undertaken 
for food purposes) the experience had been made that larvae fed 
exclusively on pulverised rusk (rusk meal), do not grow, and many 
die. The increase of the body weight of the larvae fed on rusk 
alone amounted to 48°/, in 43 days with a mortality of the larvae 
of 38°/,, whereas the figures for the larvae fed on bran appeared 
to be 117°/, with a mortality of only 1.5 °/,. 

The food experiments were therefore continued with the following 
modifications. The 118 larvae which remained on the 20‘ of April 
1916 of experiment N°. 1a. (cf. Table I], column 7), i.e. larvae fed 
exclusively on bran, were again divided into two equal halves, each 
of 59 larvae. With one of these halves the old way of feeding 
(only bran) was kept up, the other half received bran ++ ruskmeal. 

On the 8 of July 1916 the larvae of both groups were removed 
and weighed on a chemical balance. Pupae were not gathered from 
these groups between April 20 and Juli 8. (Table III). 

The result obtained was as follows. 


198 
TABLE III. 
: a Remaining : Weight of — 
ieee ot Larvae Mortality of Larvae 

arvae Food on July 8 | Larvae on | in milligrams 
on ai eee EO 

. De 100 Larvae Per 
April 20 Living | Dead Total | i aren 

N°.1a1 59 B (ue A 13 %, | 2565 50 

N°. la | | 
N°. la2 59 B + Ruskm., 59 0 — 8114 137 


It is obvious that the additional food administered in the form of 
pulverised (ground) rusk has operated very favourably, and in general 
no less than in the experiments with unbroken rusks. (Table 11). 

So far the experiments on the influence of rusk (fat) as additional food. 

Now the question had to be settled whether bran, or bolted meal 
(flour) either with or without the addition of rusk, is of equal 
nutritive value to the larvae. 

For this purpose it is necessary to revert to the jars N°. 4 (M.P.) 
N°. 5 (B.R.) and N°. 6 (M.R.) mentioned in Table I. 

From these groups the following numbers of pupae had already 
been gathered on the Febr. 10, 1916 (as stated in Table J) 

from N°. 4 (M.P.) 13 pupae. 
N° DABR kare 
N°. OMR Sb, 

The collecting of pupae was continued till July 8. Then the 
experiments were closed, the collected pupae counted, the mortality 
of the larvae figured out, and the remaining larvae weighed. This 
yielded the following results, also ineluding those of experiment 
N°. 2a (of Table II), which may serve for comparison. 


TABLE IV. 
| }os | WY be = . 
cok e= oq | Remaining So | Weight of the 
28 | g | & b= & | Pupae gathered Larvae <-> |Larvae in mgr. 
SE SAS | 229 ae 
£ 7 L S Y aD le 0/, of th ef | Sg Per 
3 & sE 5 Total. Loe paneer — 58 Total. |geen 
| | | 
5 (tab. 1) (B. R. | 206 149 | A24 |-53 | 25 9.) GO 
6 (tab. 1) |M.R| 225 | 118 | 52, | 50 57 | 25, | 5859 | 117 
2a (tab. II) B.P.| 52 0 | de 31 | 21 | 40, | 1850 | 59 
4 (tab. I) MP. 192 zo| 20 Pii | 142 1°44? SS 
| . 1 


From the above figures it is evident that bran with rusk a 
additional food had a much more favourable effect than meal + rusk ; 


eee 


——— - 


199 


the pupation is 20°/, higher, the mortality of the larvae is equal, 
the weight of the remaining larvae is 38 milligrams per larva more. 

This result could not be expected when at the outset it appeared 
(cf. Table I) that to meal and bran without any addition, meal 
was preferable; the addition of rusk shows the opposite, and this 
with rather strongly telling figures. It is probably only the fat and 
the albumin of the rusk that have operated so favourably. 

Especially fat is only seantily found in bran and meal (+ 1.6°/,), 
whereas the rusk used contained 8.9 °/,. 

Summarizing the results of these nutrition experiments, they may 
be worded thus: 

1. Exclusive meal food is preferable to exclusive bran food. 

2. Rusk as additional food to meal as well as to bran always 
has a very favourable influence on the growth and the quicker 
development (pupation) of the larvae; this holds good for rusk in 
an unbroken or a ground state alike. 

3. The most favourable results (more pupae, and low mortality 
and high weight of the larvae) were obtained by a mixed nutrition 
of bran + rusk. 

4. Ground rusk as exclusive food for larvae is perfectly unsuitable. 
The mortality is considerable, the increase in weight small, the 
pupation is stopped. 

5. The addition of slices of peat to meal or bran has no influence 
on the growth of the larvae, and is worthless as food. Peat seems 
to have a directly or indirectly noxious effect; the mortality is 
abnormally high. 


3. The number of moults. 


In the literature (BkEHM p. 128; Friscu vol. III p. 1; SALING p. 
2/8; Sturm p. 21/22) it is always stated, that the larva moults 
four times, and that after the fourth moult the pupa appears. 
Apparently this statement has never been controlled, for a simple 
experiment would immediately have shown, that it is false. 

A larva was put in each one of a series of numbered small pots 
filled with fit food. The larvae were at most one or two days old, 
and still white in colour. 

At fixed times these pots were searched for moults. The first mone 
are only to be found by carefully. spreading out the food, and 
examining it with a lens. Notwithstanding a close inspection they 
sometimes escape notice, because they are often no longer intact, and 
broken up into smaller fragments, so that they are no longer to be 
recognized as moults. 


200 


Therefore the number of moults, given hereafter, is one or two 
moults more rather than less. When the larvae bave grown larger 
and already show a distinct brown colour, these moults are easier 
to find; generally they lie on the surface of the food then. 

The investigation gave the following result. During the first period 
of strong growth a moult may be expected every fortnight ; afterwards 
this regularity ceases. 

N°. 1 gave 11 moults; larval period 400 days; died without pupation. 

N°. 2 gave 12 moults; larval period 194 days; normal pupation. 

N°. 3 gave 10 moults; larval period 194 days; normal pupation. 

N°. 4 gave 16 moults; larval period 405 days; normal pupation. 

Larva N°. 5 gave 16 moults; larval period 376 days. 

The investigation was repeated once more with 8 larvae, all of 
the same mother and of the same age. 


Number of gathered moults from Larva 
Dates of the gathering. 


N°. 1 | Ne. 2| N°. 3| N°. 4 NO, 5 | N°. 6 Ne. 7/N°. 8 
9th of November 1918 !) | | 

28th ; ‘ alae at Ok ne 1 2 1 
13th December Ri NS ON | 1 ER en 1 1 
29th 3 a eije 0 An? 0 1 1 1 2 
th Janwary gig: oT aurea et Sjeont ese eet 
31th ; 5 ce | 1 1 1 1 1 1 
14th February . | Beale BL A ae | 1 1 1 1 
28th EL E | 1 1 1 1 dwi 1 0 
14th March i ee ace OI ag 1 
SOES 9 a | 1 as a | 1 1 2 
13th April > Vaal esters | 1) On 
30th, 7 | iiss NI 1| oa en 
14th May À | 1 1 12)} 1 om | 1 1 

GI GAT ane eee | | 
Total of moults | 13 | 12 14 11 13 15 | | 13 

Duration of larval period | / 
in days. 187 | 187 | 209 | 187 | 187 | 187 | 187 | 187 


') Date of the just emerging larva. 
2) 26th May 1919. 


201 


The dates, on which the moults were gathered are also noted in 
the list before. 


4. Infection by Tyroglyphus farinae. 


Tyroglyphus farinae is a small mite strongly flattened dorsoventrally, 
about 0.4 millimetres long. The eggs of this mite seem always to 
be present in meal or bran, to develop only under definite circum- 
stances, of which moisture seems to be the most important factor. 

If the conditions of life are favourable to this mite, the multipli- 
cation may be so enormous that the whole layer of bran or meal 
seems to have changed into a homogeneous mass of Tyroglyphus. 

It is true that this mite does not infest the larva, still the growth 
of the larvae is considerably injured by the withdrawal of food. The 
development of the pupae gathered from a jar infected with Tyro- 
glyphus, also suffers great disturbances by this mite. 

In close little heaps it nestles between and behind the legs, wings 
and antennae, and causes deformities of these organs in the later 
emerging beetles. 

The researches with respect to Tenebrio were started in the spring 
of 1915 and continued without any incubators throughout the summer. 
The mite first made its appearance in 6 cultures at the same time, 
and that in jars which had been purposely placed in very damp 
surroundings; the development and multiplication of the mite in these 
jars was so intense that these cultures had to be done away with. 
Later on a similar experience was made with several other cultures 
standing free in the laboratory, when a spell of humid weather 
came. At first there seemed to be no better means than insulating 
these vessels from the rest. The necessity of this insulation to prevent 
all the cultures from being infected within a short time, is apparent 
from the fact that the infection passes from one jar to another in 
spite of their being covered with a glass plate, lying directly on the 
rim. The mite crawls up the wall of the glass, and tries to get out 
between the rim and the covering glass plate in which it generally 
succeeds, as there is always an interstice wide enough to allow its 
flat body to pass through. 

Then an expedient was tried, which was efficacious so far as to 
prevent an infection from passing from vessel to vessel, even if 
they stand uncovered side by side. 

At about 2 centimeters below the rim a ring of vaseline was 
applied inside. 

Through this greasy substance the mite cannot get and the infection 


202 


remains limited to the jar in question, especially if the vaseline 
ring is thickened from time to time. 

But restricting the extention of the infection is but an indirect 
measure against the evil, which may sometimes assume large 
dimensions, when its appearance must also be accounted for by the 
bad quality of the meal or the bran used. The experiences in this 
matter were at the outset so disappointing as to almost discourage 
any further investigations. So it stands to reason that with great 
satisfaction the experience was made that all at once everything 
changed for the better from the moment when the cultures were 
transferred into incubators with a temperature of + 25° Celsius. 

It sometimes occurred, it is true, that here and there the mite 
appeared (especially in humid weather), but by a general application 
of the vaseline ring, a sooner sieving and renewal of the food and 
an occasional raising of the temperature to 28°, the situation could 
be kept under control, so much so that Tyroglyphus farinae was 
no longer a formidable enemy. 


5. The Gathering of Pupae and Beetles. 


When the pupae make their appearance, they should be removed. 
Even if one does not wish to sort them into males and females, one 
has better not wait (for various reasons) until the beetles emerge. 

When the layer of bran is not too thick the pupae work them- 
selves up to the surface, either wholly, or partially, so that only 
the distal end of the abdomen sticks out above the bran layer. The 
sidelong broadened lateral edges of the segments 5 to 11 incl. 
(Fig. III) are provided with 3 or 4 sharp stings and wonderfully 
adapted to render this working up possible easily and quickly. 
That these broadened lateral edges with their stings are only 
serviceable in the pupae stage is apparent from the fact that this 
edge with the stings is cast off together with the pupal skin and 
does not return in the beetle. At a temperature in the incubator of 
25° ©, the larvae jars may, after the last gathering of pupae, stand 
7 days, before they require to be inspected on pupae again. At the 
temperature mentioned the development from pupa to beetle takes 
about 9—12 days. 

The pupae collected were put in deep saucers of a diameter of 
abt. 138 ¢.m., the bottom of which was covered with a patch of 
black sateen. As soon as the beetles emerge they crawl, shunning 
the light, under the patch or the curled-up borders of it. The number 
of cast moults that remain on the sateen, denotes the number of 
beetles that keep in the shade somewhere. 


— a i. 


i i it nn i me 


203 


If the beetles need not be gathered daily, a piece of rusk should 
be laid under the patch. If no food is offered them in time, they 
eat the pupae. 

The pupae dishes were covered with a glass plate reaching beyond 
the rim. In this way they may be piled up in the incubators, while 
any escape of the beetles is precluded. 


6. Gathering the Eggs. 


The collecting of the eggs was a matter of no small importance 
for the obtaining of a large posterity. The difficulties that were 
expected, did not occur; the problem was solved in quite a satis- 
factory manner. The beetles emerged in the pupae dishes are trans- 
ferred to the beetleboxes in which the production of eggs is awaited. 

The beetles were kept in tin boxes with smooth walls and pro- 
vided with a cover closing not too hermetically. The bottom of the 
boxes is covered with a patch of black sateen, in which a few holes 
have been cut to let the beetles through, which hide by preference 
under the patch. On the top of the sateen small pieces of a woolly 
material are scattered. The choice of the quality of this material 
(egg patches) on which the eggs are deposited, is very important. 
On this point the beetles are very particular and will not at all, 
or only in a small number, deposit their eggs if the stuff is not 
woolly or thready enough, so that the ¥ cannot attach the eggs on 
it. If the stuff is too thready, the eggs are laid so deep in the tissue 
that they are difficult to discover. Also Sanine records this peculiar 
habit of the beetles of depositing their eggs on a woolly material. 
The egg patches had a size of about 1 or 1'/,¢.m’. These small 
patches are preferable, for various practical reasons, to those of 
larger dimensions. 

As food for the beetles, pieces of rusk were used, soaked with 
a few drops of milk, or fresh cut pieces of potato. Of the latter the 
_ beetles eat all but nothing; yet they greedily fall to them, probably 
attracted by the humidity of the food. 

The food is put under the sateen, in which the holes serve for 
passages to reach the egg-patches, while the sateen, to some extent, 
prevents the egg-patches from being defiled by the faeces of the 
beetles. The egg-patches are transferred, with the eggs clinging to 
them, into a jar in which beforehand a thin layer of food has been 
brought for the coming young larvae. 

In a temperature of 25° C. the hatching of the eggs takes about 
8 or 10 days. 


204 


When from a culture a sufficient number of eggs had been 
gathered the egg-patches were still kept in the incubator 20 days 
after the last gathering. One is quite certain then that all the eggs 
capable of development have been hatched. The egg-patches are 
removed, some fresh food added in the larvae jar and this is left 
to itself in the incubator for some time. 

Like the pupae, the eggs were gathered only once a week. 


When a large number of beetles is kept together in one box, the 
harvest of eggs is often too small.in proportion to the number of 
beetles. If those same beetles are distributed over a series of small 
pots, the harvest of eggs increases considerably. 

This fact is illustrated by the following case. 

In a box of 21 «10 cm. were 88 beetles; from these were 
obtained respectively 131—148—181 and 121 eggs in the last 4 
gatherings. After distributing these 88 beetles over 8 little pots, the 
next harvest of eggs increased to 468, the 22¢ to 560 eggs, i.e. 
more than four times the last harvest of the preceding series. 


7. Mortality. 


The mortality among the eggs, larvae and pupae is as a rule 
considerable; low mortality figures are exceptions. 

a. Among the eggs. In the 6 nutrition experiments mentioned on 
page 195 there were in each jar an equal number of eggs (viz. 300), 
all of the same origin. The difference between this figure and the 
number of young larvae (living + dead) which were counted at a 
definite point of time, denotes the number of not-hatehed eggs. 

To each 100 eggs laid out, the mortality in those 6 cultures 
amounted. 


Hor Nes ato 6 27, 
eee et Se 55 
se. Gn eels, 
oe ORNE ss, 


” ” Hy) +) 24.6 > 


On an average 28.2 °/, 


The figures diverge rather much, whereas a special cause cannot 
be pointed out. At first arose the thought of errors in the counting 
which was carried out by spreading the bran very carefully, bit 
by bit. 


205 


The larvae were, indeed. counted only about a month after they had 
been transferred from the egg-patches to the food, and being very 
small, some might have been overlooked. 

To verify this method of spreading, the egg-patches, in four 
other trials, were deposited in empty dishes (not provided with 
food), and the newly hatched larvae counted and removed. Any 
overlooking of the larvae was precluded in this manner. The result 
of these four experiments was as follows. 


Eggs Larvae Not hatched eggs. 
NP. ool 
deposited. | obtained. Total. in %/, 
1 15 | 65 | 10 13.3 0/0 
2 ac all BIOS (Zilte 
3 | 191 136 55 28.7 „ 
4 108 Tous Men 305 „ 
Totals and mean 491 381 110 22.4 0/0 


Here, too, there is little if any agreement among the mortality 
figures: The result of these experiments gave no occasion for giving 
up as unreliable the previous method of carefully spreading the 
bran in small quantities. This is why this proceeding has always 
been followed in the subsequent fixing of the mortality figures; also 
because one acquires such a dexterity in it that an overlooking of 
the larvae becomes all but impossible. 

In the first two years the mortality of the eggs of nearly all cul- 
tures was determined. The following averages were then obtained. 


Eggs Larvae Mortality of eggs. 
Year of experiment. f a eA 
deposited. | obtained. | Tota). in 0/6 
1915— 1916 16451 11986 4465 | 27! % 
1916—1917 66517 38861 21656 | 415 , 
Totals and averages in 82968 50847 | 32121 38.7 0/, 
the 2 years. 


The abnormally high mortality figure of the experimental year 
1916—1917 as compared with 1915—1916, is striking. For this no 
definite cause can be assigned, except perhaps temperature intluences, 


206 


as the harvest of the eggs of the year 1915—1916 took place in the 
spring and the summer, and that of the succeeding year in the autumn 
and the winter. The room was heated, it is true, and, with a single 
exception, the cultures were transferred into the incubator, but both 
the former and the latter were done only when the cold became 
unpleasant. In the experiment year 1917—1918 the winter was 
severe, with long continued frosty weather. The following experience 
was obtained. 

A small series of cultures, which could not be accommodated in 
the incubator, stood free in the laboratory. In the daytime the room 
was heated, and during the frost it was heated slightly at night 
too, so that the minimum temperature was never below 7° C. This 
is known with perfect certainty as the temperature of the room and 
the incubators was regularly noted down 3 times a day. From these 
notes it appeared that the temperature in the early morning and 
late at night never sank below 7° C. 

If one assumes, to be certain, that the temperature, at a given 
moment may have gone down to 5° C. before the thermometer 
indicated this sinking, it may be stated as a fact that this tempera- 
ture is already deadly to the eggs. In the above-mentioned series of 
cultures the mortality was so high that only a few eggs were hatched. 

From two jars, each of which contained 1250 eggs, not a single 
larva was got from one of them, and only two larvae from the other, 
even after the eggs, which still looked rather normal, had been kept 
in the incubator for a long time. This great sensitiveness of the eggs 
to low temperatures, was not further studied. On another occasion 
this circumstance will be reverted to. These observations have been 
recorded only to point out that the abnormal mortality of the year 
19i16—1917 may possibly be connected with temperature influences. 


The 66517 eggs experimented on in that year were distributed 
over 5 series of 101 separate cultures in total. 

In one series of 7 cultures 24500 eggs had been put, and in 4 
series 42017 eggs in 94 cultures. 

The average mortality of the first series with 7 cultures amounted 
to 53.7°/. For that of the 4 other series the figures were 


2nd series of 7 cultures 8500 eggs with 32.2°/, dead 
SNC" hee seal) 3 4661 „ > OS ee 
AO vanen An in 21472 „ zt Aedes 
Oth. 2 svet eee 5 7384 „ ze OO SLATE 


Total — 94 cultures 42017 eggs with 34.4°/, dead. 


—_ ss CUM 


207 


If one leaves the abnormal high mortality of 53.7 °/, of the first 
series out of consideration, the average egg mortality over the two 
experiment years of 58468 eggs becomes 32.4 °/). 

As the outcome one may therefore assume that, in general, only 
2/3 of the number of eggs are hatched. 


b. The mortality among the larvae. 


As has been said, the cause of the egg mortality is still uncer- 
tain; that of the larvae mortality gives more positive indications. 
Fortunately epidemics have not appeared up till now. So they cannot 
have played a part in the mortality figures mentioned below. The 
larvae gnaw at each other’s bodies and perhaps they sometimes eat 
each other up entirely; this cannibalism is, to be sure, the main 
cause of the larvae mortality. 

A small percentage not gnawed at, died of unknown causes. 

The larvae mortality in the experiments years 1915/1916 and 
1916/1917 was: 


Number of Lar- Dead Larvae Morta- 
_ Year of experiment. \vae the culture ' lity in 100 
wot. “Larvae. =<) 
was begun with, larvae. 
1915—1916 11986 | 3655 30.4 0/0 
1916 — 1917 11294 1983 iy ea 
Totals and average. 23280 | 5638 24.2 Ofo 
| | 


Here the opposite case to that of the egg-mortality presents itself, 
viz. the first experiment year shows a considerably bigher mortality 
figure than in the second year. 

A factor that may have influenced this lies in the circumstance 
that an addition of thin fresh cut slices of potato or carrot scattered 
on the food (enhancing the humidity) had a specially favourable 
effect, not only on the growth and development of the larvae, but 
particularly on the mortality of the pupae. With regard to this, 
convincing figures will be submitted when the pupae mortality will 
be treated. 

In consequence of the results obtained in the early part of 1917, 
the addition of slices of potato was started late, when a large part 
of the total number of pupae obtained of that experiment year had 
been already gathered. By this the late gathered pupae (together 


208 


with the larvae) profited by this addition, but, of course, not the 
pupae that had been then collected already. Hence the pupae-mor- 
tality of 1916/1917 is still very high and even higher than of 
1915/1916. Now, the connection (alluded to above) that may exist 
between the mortality figures of larvae and pupae appears from the 
following. When one allows a number of counted larvae to pupate 
in a glass jar, and after some time adds the pupae gathered + 
the dead larvae + the remaining living larvae, the sum total is, as 
a rule, smaller than the number of larvae with which the culture 
was started. As an escaping of larvae from the glass jars does not 
occur (we never found any larvae crawling about in the incubator 
since the use of glass jars), the lacking larvae cannot but have been 
eaten up. This eating-up most probably took place not in the larval 
but in the pupal state, when the newly emerged body is still soft. 
The annihilation of these still soft pupae has then been executed in 
a much more radical manner than in the larvae gnawed at, while 
by the white colour the fragments of these pupae are much more 
difficult to find back than the relatively bigger remains of the brown 
larval bodies. This practically estimates the mortality figure of the 
larvae too high, and that of the pupae too low. This circumstance 
applies more specially to the year 1915/1916 than to 1916/1917, 
because in the latter year, as has been mentioned, a part of the 
larvae were already provided with slices of potato. 

This expedient promoted the growth of the larvae and an earlier 
pupation, and strongly diminished the mutilation of the pupae; in 
consequence the figure of the larvae mortality (by the manner of 
fixing this figure) had then to decrease. 

Now although these influences have, no doubt, asserted themselves, 
they were not of such a nature as to satisfactorily account for the 
great difference of the larvae mortality in these two years. Similar 
great differences appear also between the cultures (of one series) 
that have been exposed to equal exterior influences of food and 
temperature, and disagree only in one point, viz. in the time when 
the eggs were deposited, and in the number of these. 


c. The mortality among the pupae. 


The mortality among the pupae appears in the same way as among 
the larvae, viz. by gnawing-off, and by an unknown cause by which 
they dry up or, by way of rare exception, become black, and the 
body remains soft. 

Besides these pupae eaten at, also others are found, not dead but 
wounded. The humour that has flowed from the wound is then 


ment ee ag wi, Rae 


209 


- mixed with the bran and dried up into a lump. Such wounded 
pupae do not develop into beetles, but die sooner or later in pro- 
portion as the wound occurs on more or less vital organs. 

The cause of these injuries is alike a beginning of gnawing by 
the larvae, from which the young pupa has been able to withdraw, 
as it always reacts to mechanic stimulation with vehement move- 
ments. 

The gnawing away may, especially in young pupae, be so far 
advanced that only small remainders of the chitin-shell are found 
back. 

Between these extremes one finds many intermediate stages of 
mutilation. 


With this, the mortality among the pupae is not yet at an end. 

The pupa has still a critical period to pass through, viz. the time 
shortly before casting the pupal moult. Some unknown disturbance 
or other during the metamorphosis either occasions its death, or 
prevents a normal beetle from emerging. 

The disturbance usually manifests itself in that the wings are 
defective, or are not perfectly developed, and that the pupal moult 
in the distal part of the body is not removed. The legs are mostly 
developed so far that these pseudo-beetles can utilize them yet. They 
are wretched animals, which crawl about needy and invalid, and 
die after a short time. 

They have been mentioned separately as “half beetles’ in ourmorta- 
lity lists. The mortality of pupae gathered in the years 1915/1916—- 
1916/1917 and 1917 is shown in the table below. 


Pupae Of the a aaa Mortality of Pupae in 9p. 
athered. as | as as SEE} 
5 pupae | halfbeetles| pupae | halfbeetles Total 
1915—1916 8331 1269 150 15.2 %/ | 1.8 0 17 0/0 
1916—1917 28138 9355 1665 33.2 5. 30° 5 
1917 8135 1617 201 LOSS | 24 i 22 
Eee. | + 78 Ns 28 ee 
Total and averages | 44604 12241 | 2016 27.4 0/0 4,5 0/9 31.9 0/9 


More than once already I had been struck by the fact that if I 
laid big pieces of rusk, soaked with water, in the larvae jar, the 
larvae greedily eat of them. This fact led me to the supposition 

14 

Proceedings Royal Acad. Amsterdam. Vol. XXIII. 


210 


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211 


that the mutilating of the pupae by the larvae was perhaps brought 
about by want of humidity, given the circumstance that the food 
in the incubator dried up more and more, until it got crumbly and 
was renewed. 

I first put out a feeler by laying large thin slices of fresh beet- 
roots on the top of the food in a few jars. The outcome was a 
surprise. The harvest from these jars provided with slices of beet- 
root was not only greater, but the eating of pupae had diminished 
in a striking way. Then the following course was taken. 

Two jars were provided with fresh food. In each an equal quan- 
tity of larvae was put. One of these jars got 8 slices of beetroot 
or carrot, the other none. From these two jars 6 harvests of pupae 
were taken. The results are shown in the tabular scheme before 
and speak clearly enough. 

One will see a considerable decrease of the deathrate in each 
harvest. The decrease is slightest in the 2ed and the 5 harvest. 
Now it appears from notes made, that in the periods between 
January 10 and 17 and between Jan. 30 and Febr. 6 i.e. between 
the 1st and 2rd and the 4h and 5 harvests no carrot had been 
added, because the bran still felt very humid to the touch from the 
previous time. 

This after-effect of the humidity of the previous addition of slices 
is yet so great as to diminish the deathrate in both cases, in the 
AED /,, in the 2ad by 25 °/,. 

This experiment was repeated on another quantity of larvae, of 
which in the two jars an equal number was again deposited. Here, 
too, the result was again in favour of the jar with slices, of which 
the mortality was 20°/, less than in that without carrot (of Experi- 
ment IJ). It is also remarkable that in both experiments the total 
number of gathered pupae is larger, which clearly indicates that 
the growth of the larvae is very much furthered by the humidity. 


I was not quite convinced and started a third trial. 

I then reversed the state of humidity for the larvae at every turn 
after a number of harvests. Two jars were each provided with 
exactly 1000 larvae. In order to be sure that these larvae were in 
the same stage of development, they were weighed beforehand. The 
weights were the same for each group, viz. 110 grammes. The 
vessels got the same weight of food; one of them got 8 slices be- 
sides, the other none. 

When the food in the jar with slices was consumed earlier than 
that in the other (which always occurred in all series of experi- 


212 


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213 


-ments and which fact should be particularly noted), both were pro- 
vided with fresh food to keep the circumstances as equal as possi- 
ble. Five days elapsed between two successive harvests; during all 
the time of the experiment the jars remained in the incubator. 

The result of the first 5 harvests is shown in the table on page 212. 

As the table shows, the average deathrate in the jar without 
slices was about 17°/, higher than in the one with slices, The food 
was renewed twice, viz. on April 12 and 21. In both eases the 
food with slices had already become so crumbly that it had to be 
removed. Uuder ordinary circumstances, the renewal of the food of 
the other vessel (the one without slices) would not have been neces- 
sary. As has been said already, this case occurred repeatedly in all 
series experimented on. At the end of the 5 harvest the larvae 
were sieved and counted to verify all figures. 


Jar A. Experiment III a. without slices) 
Number of larvae the culture was started with... 1000 


on the sieve were left . . . . 642 larvae 
living + dead pupae gathered. . 321 „ 
dead larvae af 4s, 
total 1000 
Jar B. (Experiment III a with slices). 
Number of larvae the culture was started with... 1000 
on the sieve were left . . . . 629 larvae 
living + dead pupae gathered. . 343 „ 
dead larvae 28 5 
total 1000 


The subsequent series of harvests were dealt with as follows. 

The slices of potato were added to those larvae that had never 
enjoyed them, i.e. to the 642 larvae of jar A. The 629 larvae of 
jar B, which had always had slices hitherto, had to do without 
this addition. 

The figures of the harvest of this series are given in the table 
on the following page. 

With the exception of the 1st and the 6'» harvest the mortality 
figure for the jar without slices was considerably higher again in 
each successive harvest. That the lt harvest should be an exception 
to it could not but be expected. The larvae had, indeed, in the former 
harvest, profited from humid surroundings, and the after-effeet of this 
manifested itself in the next harvest in spite of the changed condition. 
The 5°/, lower deathrate in the jar without slices does not therefore 


214 


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215 


form an exception, but on the contrary, confirms the rule that the 
addition of slices caused a strong regression of the death rate of the pupae. 

The exception of the 6" harvest had been brought about by the 
circumstance that in consequence of the excessive humidity in the 
jar with slices, the food had clotted and grown quite mouldy. 

The wall of the jar was covered with big drops of water. 

The 7 dead pupae gathered had not been gnawed at, indeed, but 
were black. Here the too much of a good thing, had apparently 
produced a reverse effect. The food of the jar under discussion had 
to be renewed for that reason, and this was done in both vessels, 
again for the sake of the uniformity of circumstances. 

Notwithstanding these two exceptions the average mortality of the 
9 harvests had fallen by 24°/, for the jar with slices after all. 

At the close of the 9th harvest of the above trial series IIId, the 
larvae were sieved and counted to verify the figures obtained, with 
the following result: 


Jar A. (Experiment IIb without slices). 


Number of larvae this series was started with. . . 629 
On the sieve were left . . . . . 398 larvae 
Living + dead pupae ee en € 20D 
Dead larvae... RT NE 26 
Total 629 
Jar B. (Experiment IIIb with shces). 
Number of larvae this series was started with. . . 642 
On the sieve were left . . . . . 418 larvae 
Living + dead pupae pees ee 209 
Dead larvae .- . . Lenn 22 
Total 1.2. el eae 


More individuals accounted for than there were at the outset i 


The verification of jar B shows an excess of 7 individuals. 

How the error has arisen, is not known. As a rule such a veri- 
fication shows a deficit, as the remains of a number of individuals 
are not found back. The mistake, however, if it has been made by 
inaccurate counting, cannot raise the deathrate, but rather lowers it, 
so that one need not care about it any further. For the 3rd harvest 
series the slice-food was again reversed. 

The 418 slice-larvae of Jar B no longer got any slices; the 398 
of jar A, which had not had any slices in the 2rd harvest series, 
were provided with them now. The result of this 3rd series, with 
a summary of the three series together is given on page 216 


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Without slices. | With slices. 
mF Ee Ee 
Number | Dead pupae gathered ~ E Number| Dead pupae gathered = 5 
Bee Total | Unin- | muti- = ee Total | Unin-| muti- el 
harvest | dead | jured | lated ES harvest dead | jured | lated ES 
Ist 28 11 17 Ist 15 15 0 
2nd 16 5 11 2nd 6 6 0 
3rd 18 1 17 3rd 3 3 0 
4th 12 3 9 4th 2 2 0 
5th 4 1 3 5th 0 | = — 
7). eS |T Tot and | 
average. 18 21 57 13 0/o \|average.| 26 26 0 none 
6th 2 0 a | 6th 2 2 0 
7th 8 2 6 7th 2 0 2 
8th 16 0 16 8th 0 — — 
Qth 6 1 5 Oth | 0 
10th 8 4 4 10th | 1 0 
Lith Sel 2 3 11th if di 130 
12th is | *y 12 12th | 4 0 
13th 5 2 3 13th 1 1 0 
14th 3 1 2 14th 1 1 0 
Tot. and Tot. and 
average. 65 12 53 | 81.5% ||average.| 16 14 2. | 12.5 0/0 
15th aa ae Loth alge 
16th 3 1 2 16th 3 1 2 
17th 5 0 5 17th | 0 1 
18th 3 1 4 18th 0 = as 
19th 1 0 | 19th 1 1 0 
20th 2 1 1 20th 0 — — 
Tot. and | Tot. and 
average. 18 4 14 | 77.7 J ||average. 11 5 6 54.5 9/9 
Gerner. Gener. 
tot. and, 161 37 124 | 77 0% tot. and| 53 45 8 15 0/0 
average. average. 


218 


Here too, the after-effect in the 1“. harvest is again clearly 
observed. Properly speaking, it might be expected that this after- 
effect should be continued in a few harvests more, as the slice- 
larvae, after the 2°¢ harvest series, looked so much bigger and more 
vigorous than those of the dry jar. As a matter of fact the longer 
duration of the after-effect under discussion (in this as well as in 
the previous trial series) clearly finds expression in the circumstance 
that the differences of the deathrates between the two trial jars ever 
increase up to the 4" harvest. So, if as a final result it is stated 
that the mortality figure in the slice-jar has fallen by 18.5 °/,, this 
figure is certainly not flattered, but estimated too low, a good deal 
too low if one considers carefully the figures and the circumstances 
under which they were obtained. 


The supposition mentioned on page 211 that the gnawing of the 
pupae might be a consequence of the larvae’s need of humidity is 
corroborated by comparing the numbers of dead pupae mutilated or 
not, harvested from the two jars. 

From thetable on the former page it is seen that in the jar without slices 
77°/, of the dead pupae were eaten at, and by far most of them 
very strongly, whereas in the slice-jar this figure was only 15 °/, 
and even then so slightly that often doubt arose as to whether or 
not they had to be noted down as “eaten at”. 

The determination of the average mortality among the eggs, larvae, 
and pupae was to me of this practical signification that once I knew 
this, the approximate quantity of eggs for a given culture could be 
fixed, in order to get at my disposal a desired number of beetles. 
The outlay of too large a number of eggs was a needless labour 
and waste of time, leaving apart the drawbacks connected with it. 

The labour spent on the fixing of these figures in the first three 
years of experiment, has been amply rewarded by the use made of 
them. The average deathrate of eggs + larvae + pupae to each 100 
eggs laid out amounts to the considerable figure of about 58 °/,. 


LITERATURE. 

1. Breum. Tierleben. Insekten. 

2. FRENZEL. Ueber Bau und Thitigkeit des Verdauungskanals der Larve des 
Tenebrio molitor Berl. Entom. Zeitsch. Bd. XXVI. 1882. 

3. Frisco, J. L. Beschreibung von allerlei Ins. in Deutschland 1720. 

4. SALING, TH. Zur Kenntnis der Entwickelung der Keimdrüsen von Tenebrio 
molitor. Inaugural Dissert. Marburg 1906. 

5. Sturm, JAKOB. Deutschlands Fauna in Abbildungen uud Beschreibungen. 
V. Insekten. Kafer. 

Utrecht, February 1920. 


KONINKLIJKE AKADEMIE VAN WETENSCHAPPEN 
TE AMSTERDAM. 


PROCEEDINGS 


VOLUME XxXIill 
Nes, 2 and 3. 


President: Prof. H. A. LORENTZ. 
Secretary: Prof. P. ZEEMAN. 


(Translated from: “Verslag van de gewone vergaderingen der Wis- en 
Natuurkundige Afdeeling," Vols. XXVIII and XXIX). 


CONTENTS. 


ARNAUD DENJOY : “Sur une propriété de séries trigonométriques”, p. 220. 

L. E. J. BROUWER: “Ueber eineindeutige, stetige Transformationen von Flächen in sich” (Siebente 
Mitteilung), p. 232. 

P. GILBERT RAHM: “Einwirkung sehr niederer Temperaturen auf die Moosfauna”. (Communicated by 
Prof. H. KAMERLI?.GH ONNES), p. 235. 

J. BOESEKEN, W. F. BRANDSMA and H. A. J. SCHOUTISSEN: “The velocity of the diazotisation reaction 
as a contribution to the problem of substitution in the benzene nucleus”, p. 249. 

J. J. VAN LAAR: “On the Critical Quantities of Mercury in Connection with the Increase of the 
Molecular Attraction on Dissociation of the Double Molecules”. I. (Communicated by Prof. 
H. A LORENTZ), p, 267. 

J. J. VAN LAAR: “On the Critical Quantities in the Case of Association, when the Molecular 
Attraction is Considerably Increased on Dissociation of the Molecules to the Isolated Atoms, 
also in Connection with the Critical Quantities of Mercury”. II. (Communicated by Prof. H. A. 
LORENTZ), p. 282. 

NIL RATAN DHAR, A. K. DATTA and D. N. BHATTACHARYA: “Catalysis”. VIII. (Communicated by 
Prof. ERNST COHEN), p. 299. 

NIL RATAN DHAR: “Catalysis. IX. Thermal and photochemical reactions”. (Communicated by 
Prof. ERNST COHEN), p. 308. 

NIL RATAN DHAR: “Catalysis. X. Explanation of some abnormally large and small temperature coef- 
ficients”. (Communicated by Prof. ERNST COHEN’, p. 313. 

S. DE BOER: “On Fibrillation of the Heart”. (First part). (Communicated by Prof. I. K. A. WERTHEIM 
SALOMONSON), p. 319. 

S. DE BOER: “On Fibrillation of the Heart. (Part. II.) On the Relation between Fibrillation of the 
Heart and “Gehäufte” Extra-systoles”. (Communicated by Prof.I.K. A. WERTHEIM SALOMONSON), 
p. 329. 

LUCIE W. SCHUT: “Factors which are of importance for the habit-formation of birds. I Visual sensa- 
tions”. (Communicated by Prof. G. VAN RIJNBERK), p. 338. 

F. M. JAEGER “Two Isomeric Chloro-Tetracetyl-d-Fructoses”, p. 342. 

F. M. JAEGER: “On the Crystalforms of some Substituted Amides of Para-Toluenesulphonic Acid”, p. 347. 

J. F. VAN BEMMELEN: “The colour-markings on the body of Lepidoptera, compared to those of their 
larvae and pupae, and to those of their wings”, p. 363. 

L. HAMBURGER: “On Centres of Luminescence and Variations of the Gas Pressure in Spectrum 
Tubes at Electrical Discharges”. (Communicated by Prof. H. A. LORENTZ). p. 379. 

G. A. F. MOLENGRAAFF and MAX WEBER: “On the Relation between the Pleistocene Glacial Period 
and the Origin of the Sunda Sea (Java and South China-Sea), and its Influence on the 
Distribution of Coralreefs and on the Land- and Freshwater Fauna”, p. 395. (Met twee platen). 

G. A. F. MOLENGRAAFF: “On the Geological position of the Oil-fields of the Dutch East-Indies”, p. 440. 

M. W. WOERDEMAN: “On a human ovary with a large number of abnormal follicles and the genetic 
significance of this deviation”. (Communicated by Prof. J. BOEKE), p. 448, 


15 
Proceedings Royal Acad. Amsterdam. Vol. X XIII. 


Analyse mathématique. — “Sur une propricté de séries trigono- 
metriques.” By Prof. Arnaup Denvoy. 


(Communicated at the meeting of June 26, 1920). 


Dans une Note que j'ai eu l’honneur de présenter a |’ Académie 
dans sa dernière séance, j'ai démontré une propriété dont je vais 
rappeler l’énoncé, et qui appartient a une certaine classe de fonctions 
F(0) admettant une dérivée seconde généralisée f(A). 

Posons 
Q (4, ene seat at A) 

u 
F(O + u) + F(O—u) — 2F (0) 


u’ 


On a Q(O,u) = Q(0 + u, — u) et uR (Ou) = Q (0,4) — ÙUO— u). 
Par hypothèse (4,27) tend vers f(@) quand wu tend vers 0, 9 restant 
invariable (condition A). 

Nous désignons par y(4) le maximum de | A(4,w)| pour toutes les 
valeurs de w,@ gardant une valeur indépendante de w. 4 étant un 
nowbre positif quelconque, w(4,7) désignera le maximum de | A(4,w)| 
pour |u| << 9. 

Les fonctions #'(6) auxquelles s’applique le theoreme démontré 
dans ma précédente note, satisfont non seulement a la condition de 
posséder une dérivée seconde généralisée, mais encore a la suivante: 

La différence Q\9,2u) —Q(4,u) tend vers O avec u, unifor- 


R(A, u) = 


i. 
mément dans tout champ: @ quelconque, |\4| + il < r, r étant indé- 


pendant de @, de u et de 4 (condition B). 
Ces propriétés de (4) sont en particulier vérifiées si f(A) est la 
somme d'une série trigonométrique partout convergente. Si l'on pose 


{Ose EAT A 

avec A, =a, cosn@ + b, sin nd (a,, an, 6, indépendants de 6), on a 
a, A, 

F@=36 + COHC A ee B 


(C, C’ indépendants de 6). 
Et si y(@) désigne, quand elle existe, la dérivée de (8), 


B, 
PAO) = OE A tn 


221 


avec 
B, Zi Di COS n@ + An sin n@. 


Les points 6 de convergence de la série et d’existence de la 
dérivée sont les mémes, avec égalité de la dérivée et de la série en 
ces points. Cela posé, nous avons démontré la proposition suivante: 
le | 
hn +4) 
lument convergente, si w(A+h,) et w(A) sont inférieurs ad A 
mdépendant den, la fonction F'(t) possède pour t = 6 une dérivée yO). 


fide 4 


in 44] 
den, et si |h| [22 |h,|, on a 


Q (4, h) =p (A) + 20da Ah (0? iiet eid Kl) 


Enfin, si \h| <1, A peut être remplacé par la borne supérieure 
des nombres W(O, 1), w (0 + h, 1) pour |hy| Zn. 

L’hypothese faite sur y n’implique pas l'existence de la dérivée 
seconde généraliste de /(@). La démonstration exige la condition (B). 
_ De la formule (9) nous déduirons certaines propriétés différenti- 
elles de #'(4) en nous aidant du théoreme de Barre sur les fonctions 
limites de fonetions continues. 

THEOREME. Si P est un ensemble parfait (continu ou discontinu), 
ensemble K des points de P au voisinage desquels w (0), supposé 
find, est non borné sur P, cet ensemble est non dense sur P.*) 

Voici le sens de cet énoncé. Nous disons qu’une fonction g(0) n'est 
pas bornée sur P, au voisinage d'un point 6,, s’il est possible de 
déterminer une suite 9, de points situés sur P, tendant vers 9, quand 
n croit, et tels que |g(9,)| croisse indéfiniment. 6, appartient à P 
puisque P, étant parfait, contient ses points limites. 


Si |h,| tend vers O. en décroissant, si la série est abso: 


St en outre le rapport est inferieur ad a indépendant 


1) Je rappelle qu'un ensemble est dit fermé s'il contient tous ses points limites, 
dense en lui-même s’il admet chacun de ses points pour point limite, parfait 
sil est à la fois fermé et dense en lui-même. 

On appelle portion de P tout ensemble parfait 5 contenu dans P et renfermant 
tous les points de P compris entre les extrémités de 5. 

On dit que ensemble EZ est partout dense sur l'ensemble parfait P, si toute 
portion de P contient des points de £.E est dit dense sur P, s'il est partout 
dense sur une portion au moins de P.£ est dit non dense sur P, si dans toute 
portion de P il en existe une autre où H n'a pas de points. Si (HZ, P) désigne 
l'ensemble commun a Z et à P,E est partout dense, est dense, ou est non dense 
sur P, selon que le dérivé de (EZ, P), — c'est-à-dire l'ensemble des points limites 
de (HZ, P) — ou bien coincide avec P, ou bien contient une portion de P, ou 
bien n’en contient aucune. 


15* 


222 


On peut encore dire que, quelque soit MN, dans toute portion de 
P contenant 6,, existe un point Oy où \g(Ay)| > N. 

Si au voisinage d'un point 6, de P, wid) n’est pas bornée sur P, 
oscillation *) de y(@) sur P au point 6, est infinie. Et réciproquement 
d’ailleurs. 

Or, M. Batre a montré que si une fonction W(O) est limite de 
fonctions continues, l'ensemble A(a) des points de P où Vosecillation 
de y(@) sur P? surpasse un nombre positif « donné est non dense 
sur P. A fortiori, ensemble AK des points où l'oscillation de y(@) 
est infinie, est-il non dense sur P. 

Voici la démonstration de Barrw dans ce cas particulier. 

Soit A l'ensemble des points de P au voisinage desquels w(4) n’est 
pas borné. A est évidemment fermé. Si A n’était pas non dense 
sur P, il existerait une portion P, de P qui serait contenue dans K. 
Nous définissons simultanément: une suite de points 6,,..., On,..-, 
situés sur P,, une suite de segments?) s,,5,,..-, le segment s, 
étant intérieur a s,_; et contenant lui-même 6, à son intérieur, et 
une suite de nombres w,, par cette regle récurrente: s, est un segment 
quelconque contenant des points de P,.s,—1 étant supposé obtenu, 
nous définissons comme il suit 6,,s,, u». y(A) étant non borné sur 
P,, au voisinage de tout point de /,, il existe sur P,, intérieurement 


A Spi, un point 6, où y(A,) > 2n. D’apres w(A7) = maz. | R(G, , u) 
nur 


il existe un nombre w, non nul tel que |R(6,,u„)|>>n. R(O,u) 
étant continue par rapport a 6 si u #0, on peut entourer 6, d'un 
segment s, intérieur a s,—1, inférieur en longueur a 1/,s,-4 et en 
tout point 6 duquel | R(G,2,)| > n. 

Il existe un point @ (et un seul, puisque s, tend vers 0 en lon- 
gueur) intérieur à tous les segments s,.6’ est la limite unique des 
points @,. Done, @ est sur P,. Or, @ appartenant a s, quelque 
soit n, la suite | R(@’,u,)| eroit indéfiniment avec mn, ce qui est con- 
traire a l'existence de y(@’). | 

Done MK est non dense sur P. Dans toute portion de P il en 
existe une autre où AK n’a pas de points et sur laquelle, par suite, 
(uA) est bornée. Cette conclusion exige seulement que, pour chaque 
valeur de @, les limites d’indétermination de A(6,w) pour u= 0 


ki 


') L'oscillation de f sur un ensemble Q en un point limite 6, de Q, est l’écart 
des valeurs limites extrêmes de f (6) quand 4 tend vers 6 sans quitter Q. (6 peut 
coincider une infinité de fois avec 6, si 6) appartientà Q) Si f supposée finie en 
tout point et en particulier au point 4, est non bornée sur Q au voisinage de 6p, 
oscillation de f sur Q en 4, est évidemment infinie. 

3) Je distingue le segment afl (ensemble « < x < 2) del’intervalle af (ensemble 
a <r <8). 


223 


soient finies et non pas (condition A) toujours égales et finies. 

Si F vérifie la condition (A), on montre par un raisonnement analogue 
au précédent, que st en tout point de P, | f(@)| est inférieur à un 
nombre fixe C, on peut trouver un nombre positif y tel que, si (On) 
est le maximum de | R(O.u)| pour |u| <y, il existe une portion P, de 
P en tout point de laquelle w6,r) < C. L'hypothèse opposée, que 
toute portion de P contient, quelque soit 7, des points 6 où y(4,1) > C, 
entraine | 7(6,|>C en certains points de P. Toute portion de P 
donne lieu au même énoncé que P lui-méme. 

„Nous allons appliquer les propositions précédentes a diverses 
catégories d’ensembles parfaits P, en supposont que F vérifie les 
conditions (A) et (B). 

Prenons d’abord pour P un segment continu «3. [ensemble 
K relatif à P est non dense sur P. Done, dans tout segment S 
situé sur ag, existe un segment s’, ou a’p’, où K ne possède aucun 
point. Alors, pour tous les points de s’, w(@) est inférieur a un 
même nombre 4.0 et O-+h étant deux nombres quelconques 
= D’aprés w (6) et w(O HA) << A, F 
a une dérivée au point @. De plus, d'après la formule (9) où a = 2 (et 
dont la démonstration se simplifierait extrémement avec les valeurs 


intérieurs a s’, posons hy, = 


considérees de h,), 


h) — F(6 
Q (A, een : ( Pas + 40) Ah. 


En échangeant les rôles de 6 et de 6 +h, on trouve 


F (6) — F (6 
Q(p +h —h= at] a 96 FA) + 400'Ah. (9, 0 < 1), 


pO + h)— p(0) 
h 

Done la fonction p(6) est continue sur s’ et a ses nombres dérivés 
bornés. Elle possède, sauf éventuellement sur un ensemble de 
‘mesure nulle de valeurs de @ comprises entre @’ et 8’, une dérivée 
qui, constituant pour / une dérivée seconde, ne saurait être autre 
que f (0). 

Nous obtenons done ce premier résultat important: 

1°. L’ensemble des points de non existence ou de discontinuité de 
la dérivée de F(O), est non dense sur le continu. 

2°. L’ensemble des points autour desquels p (0), dérivée de F(O), 
existe et est continue, et en lesquels y (A) a pour dérivée f (9), cet 
ensemble est partout dense sur le continu. 


est borné sur lintervalle a’p’. 


Par conséquent 


224 


Je dis que l'ensemble des points où F(A) ne possède pas de 
dérivée est de mesure nulle. 

En effet, supposons que cet ensemble ait une mesure positive 
(qu’il soit épats)*). Il contient done un ensemble parfait épais en 
lui-même P. Il existe.une portion de P, soit P,, où w (A) est borné. 
Or P, étant épais, contient des points où son épaisseur est égale 
a 1. Soit 4, un de ces points. Il existe un nombre positif n, tel 
que, dans tout intervalle contenant @, et de longueur inférieure a y, 
Pensemble P, possède une épaisseur moyenne supérieure a */, 

a 
Qu+i 
positive. Done P, possède des points dans cet intervalle. Soit@ +h, 


hn 
Pun deux. La suite A, vérifie la condition 1 << < 4et w(O+h,) 


‚fen H1 

est inférieur, quel que soit n, au maximum fini de w(9) sur P. 

Le théorème général s'applique. Done, contrairement a notre 
hypothèse, /’(@) possède une dérivée en 6. | 

Done, Pensemble EH des points où F’(O) n'eviste pas, ensemble 
coincidant avec celui où la série (2) diverge, cet ensemble est de 
mesure nulle, résultat déjà connu et démontré en particulier par 
M. Fatou, mais que nous établissons sans recours a l'intégration. 

Considérons l'ensemble /, où y (A) existe. Je dis que p (A) possède 
une dérivée approvimative *) égale a f(A) en tout point de E, sauf 
éventuellement sur un ensemble de mesure nulle *). 

On montre d’abord par un type de raisonnement que j'ai indiqué 


. A 1 > 
Done, dans l’intervalle 6, + à 0, + an” la mesure de P, ést 


1) Je dis qu'un ensemble E est épais si sa mesure est positive; qu'il est épais 
dans un intervalle ab, si les points de EZ intérieurs 4 ab forment un ensemble 
de mesure positive; épais en un point, sil est épais dans tout intervalle contenant 
ce point; épais en lui-même, sil est épais en chacun de ses points. Si les points 
de EH compris entre a et b (a <b) forment un ensemble de mesure m(b)—m(a), 

m(b)—m(a) 

le rapport Supe ¥ 
L’épaisseur de E en un point x est la limite, si elle existe, de l’épaisseur moyenne 
de # sur un intervalle contenant x) et tendant indifféremment vers 0 en longueur 
(voir ma note de la précédente séance pour les cas où l'épaisseur n'existe pas). 
?) On dit que p (4) possède une dérivée approximative A en un point 9, (où p 


: : ; 6)— 96 
est définie) si le quotient (2) — (60) tend vers A, quand 4 tend vers 6, en se dépla- 


En 
gant indifféremment sur un ensemble (où ¢ est supposé défini) dont l’épaisseur en 6, 
est égale à 1. (M. KiNrcHiNE emploie dans le même sens lexpression de dérivée 
asymptotique). 

8) „Sur un ensemble contenu dans E, et de même mesure que lui’ s'exprime 
par la locution „presque partout sur Zj” de M. Lregesqve ou par celle.ci „sur une 
pleine épaisseur de £,”’ que j'ai proposée. 


s'appelle l’épwisseur moyenne de E sur l'intervalle ab. 


225 


ailleurs (Bull. de la Soc. Math. de Fr., 1915) que, si p (0) n’admet 
pas en 6, la dérivée approximative f (0), il existe un nombre positif 
d(@,) ou d, tel que l'ensemble e(d,) des points 6 vérifiant 
| IG ae) 
ae) 
possède en 0, une épaisseur supérieure positive, pour un côté au moins. 

Si le théoreme énoncé était inexact, l'ensemble H des points 
6, précédents anrait une mesure positive. 

Nous pouvons évidemment supposer que la fonction d(6,) de 4, est 
mesurable [il suffit pour cela que d(O,) soit par exemple la moitié 
de la borne supérieure stricte des nombres d tels que l'épaisseur 
supérieure en 4, de l'ensemble e(d) soit positive]. Soit H, l'ensemble 
des 6, tels que nd(0,) > 1. 

H est la réunion des H,. Done l'un au moins des A, a une 
mesure positive. Il existe done un nombre positif d, tel que l'ensemble 
H’ des 9, vérifiant d(O,) > d a une mesure positive. 

H’ contient un ensemble parfait Q épais en lui-même. 

F(A) étant limite de fonctions continues est ponctuellement discontinue 
sur Q (Barre). Si petit que soit d’, l'ensemble des points de Q où 
Yoscillation de f(9) sur Q est au moins égale a d’, cet ensemble est non 


d 
dense sur Q. Prenons d’ = 191° Il existe une portion Q, de Q en tout 


point de laquelle l’oscillation de f sur Q (done aussi sur Q,) est inférienre 

a d’. Done, si 9, est un point particulier de Q,, il existe un intervalle 

2 contenant 4, et tel qu’en chaque point 6 de Q situé sur le segment 2, 

d 

LO SONG 

Soit Q, la portion de Q, déterminée par l’intervalle 7. (Q, est 

Yensemble parfait situé sur le segment t et coïncidant avec Q, dans 
Pintervalle 2). 

Chacun, sauf le dernier, des ensembles B HOES OQ» Qeeon- 

tient le suivant. Done, en tout point de Q,, g(@) existe (puisque Q, 


. d d 
est dans ZE), /(@) est compris entre f(0,) — 91 et IOs) + For 


(dernière condition de Q,), et y(@) possède, en tout point 6, de Q,, 
et sur tout ensemble w(@,) d’épaisseur 1 en 4,, un nombre dérivé 
spécial a w(A,) et différant de f(0) de plus de d en valeur absolue 
(puisque Q, est dans H’). 


6 
Considérons #,(0)= F(A) — 9 S4,)- Cette fonction continue possede 
en tout point de Q, la dérivée p,(0) = 4(A) — 6 f\9,). F(A) possède 


226 
en tout point la dérivée seconde généralisée /, (A) = f (0) — f (0). 
d d 
4) est compris, sur Q,, entre ——— et ——. D'autre part, les nombres 
Ade pris, sur Q, jai *' 491 utre par ibr 

dérivés de ~,(A) sont ceux de ~(A) diminuês de /(4,). Done, p‚(9) 
dérivée de F'(@) existe en tout point de Q, et possède, quels que 
soient le point 6, de Q, et ensemble w(4,) ayant l'épaisseur 1 en 
6,, au moins un nombre dérivé spécial a w(A,) et differant de f(A 
d’au moins d en valeur absolue. Ce nombre dérivé vaut done au 


. 


l 
D'après | £,(0)| at quel que soit 9 sur Q,, il est possible de 


d 
trouver un nombre s’ >0, tel que l'ensemble w‚(0, s’) << —— 121 contienne 


une portion K de Q,.w,(,s’) est par définition le maximum de 


RO, 0 BEEN Nara ed a 2F, (A) pour 0 <= | au | Zal 


u 


L’ensemble parfait K jouit en résumé des propriétés suivantes: 
1° K a une mesure positive (K étant portion de Q,, épais en 
lui-méme). 
2° Il existe une-fonction (4) et un nombre positif s’ tel que la 
d 
fonction w, (0, s’) relative a F’, est, en tout point de K, inférieure a —— Ta" 
3° F,(0) possède en tout point de K une dérivée générale 
(ordinaire) g,(6). 
Quel que soit 9, sur K, et ensemble w(d,) d’épaisseur 1 en 


6,, p‚(O) possède en 4, un RE dérivé spécial à w(A,) et dont 


la valeur absolue surpasse a 


Nous allons montrer l’incompatibilité de ces conditions simultanées. 
L’ensemble des points de K où K a l'épaisseur 1, a même mesure 
que K, done une mesure positive. L’ensemble j(s) des points 6, de 
K tels que, dans tout intervalle contenant 6, et de longueur inférieure 


. ld . A 5 
a s(> 0), lépaisseur de A soit supérieure a—, cet ensemble a une 
6 


mesure positive dès que s est assez petit, et cette mesure tend vers 

celle de AK quand s tend vers 0. Supposons s << s’ et j(s) épais. 

Soit 4, un point où j(s) a lui-même l'épaisseur 1. Je dis que, si 
#0) (95) 


a ses limites d’indétermi- 
0—6, 


6 tend vers 4, sans quitter j(s), 


227 


! 120 120 deet 
nation comprises entre — —— d et ——d, ce qui est incompatible avec 
121 121 
la 4e condition ci-dessus; car l’épaisseur de j(s) en 4, est 1. 
Supposons |6 —0,|<s, 6 et 6, étant sur j(s). Puisque K a une 


épaisseur supérieure a — dans tout intervalle contenant 6 ou 6, et 


- Ol ox 


de longueur inférieure a s, nous pouvons trouver sur A deux suites 
de nombres 0+ hn, 0, + A, de manière que 


n Ln 
ie —k = O6,—6, 22E ot ac en SNG 
ht ken 
d 
D’apres w(0’,s) << zor oe! que soit 6’ sur K, on a done (a=3): 


d 
ge (4, G. = 6) Pf, (6) + ee (6, ET 6) 
et de même 
d 
Q, (A5 0 — 6.) —= fp) (,) + 60 J! za = G3): 


D’apres l’égalité des premiers membres de ces deux relations 


p,‚ (6) — p‚ (4,) ie 
a0 OO Oe 1). 
agi Me ee, 
Cette relation est exacte quels que soient @ et 4, sur 7(s), si 
lB—0,|<s. Done les nombres dérivés de p, (6) au point 6,, spécia- 


lement a j (s), sont inférieurs a d en valeur absolue, ce qui est 
oppose a l’hypothese 4. 

En résumé, l'ensemble des points où F'(@) ne possède pas une 
dérivée ordinaire ~(9) est de mesure nulle. Soit E cet ensemble, et 
E, son complémentaire. La fonction 9(9), définie seulement sur Ey, 
possède une derivée approximative egale a f(@), sauf éventuellement 


en des points formant un ensemble de mesure nulle. 


Soit maintenant P un ensemble parfait discontinu quelconque, 
situé sur l’axe des 6. Soit M un point de P. Ajoutons a P son 
symétrique par rapport à M. Nous obtenons un ensemble parfait 
discontinu P(M), symétrique par rapport a J. M est done un point 
de seconde espèce (ou limite des deux cdtés) de P(M). Pour chacun 
des intervalles contigus 7 de P(M) formons le rapport /(z) des distances 
respectives & M de l’extrémité de 7 la plus éloignée et de l'extrémité 
de 7 la plus rapprochée de J. 

1d est borné indépendamment de z et de M, si la distance de 2 


228 


a M surpasse un nombre donné. Quand # tend vers MV, / (i) possède 
une plus grande limite 2(M/) que nous appellerons indice de Pen M. 
L’indice est un nombre au moins égal a 1 et peut être infini, 
méme en tout point de P. 

6 étant labscisse de M, Vindice A(M) peut encore être ainsi 
caractérisé (s'il est fini). Si petit que soit e positif, il existe une suite 
de points 0 + Ah, situés sur P, tendant vers Met tels que, pour toute 


hn 
valeur den, 1 < es <4(M) He. Il n'existe pas de suite ana- 


——| < A(M) —«. 
Anti 

En tout point (sauf peut-être aux points extrêmes) d’une portion 
P, de P, Vindice de P, et celui de P coincident. 

Si P est épais, 4 (17) = 1 en tous les points M où l’épaisseur de 
P est 1. Mais, même si P est épais en lui-même, l'indice 4 (JZ) peut 
être infini en certains points, et même en un ensemble dense de 
points de P. 

On montre, selon un type de raisonnement maintes fois rencontré 
(voir par exemple, le Premier Théoreme des nombres dérivés, 
Journal de Jordan, 1916) les propositions suivantes: 


logue telle que 1 << 


1. Si Pensemble-des points M où 2(M)= = est partout dense sur 
P, cet ensemble est un résiduel de P. De même pour l'ensemble 
MM Sta > 1 

2. Si P possède en chacun de ses points un indice fini, l'ensemble 
K des points de P au voisinage desquels cet indice est non borné, 
K est non dense sur P. 

3. Si Pindice de P est en tout point inférieur à un nombre fixe 
a > 1, il existe un nombre 7 positif et une portion P, de P, tels 
que, 1° si 4 est quelconque sur P,, 2° si 6’ est quelconque à la 
fois sur P et dans l'intervalle A—n, 0 + ny, il ea un nombre 


6’’ situé sur P et vérifiant les inégalités 1 < a ZU 

Car l’inexactitude de cette conclusion entrainerait sur un résiduel 
de P, linégalité A(M)> «. 

La proposition precedente peut être appliquée a toute portion = de 
P. Les portions P, pour lesquelles existe un nombre 1 sont done 
partout denses sur P. 


L'application de ces remarques a l'étude de F'(0) est immédiate. 
Il est évident qu'en tout point de P où [indice est fini et autour 
duquel, sur P, w(A) est borné, p(0) existe. Donec: 


229 


Si l'ensemble des points de P où l'indice de P est fini, est partout 
dense sur P, Pensemble E, des points d existence de p (6) est partout 
dense sur P. 

Nous retrouvons comme cas particulier le théorème que l'ensemble 
E‚ des points d'existence de ~ (A) est partout dense sur tout ensemble 
épais, eten conséquence, que 4, complémentairede ‚est de mesurenulle, 

Si un ensemble parfait P possède en chacun de ses points un indice 
fini, ensemble des points où (9) n'eviste pas, ou est discontinue 
sur P, ou possède spécialement à P au moins un nombre dérivé 
infini, cet ensemble est non dense sur P. 

De plus, l'ensemble des points où (9) est dérivable spécialement 
a P et où sa deérivée spéciale à P est égale a f(9), cet ensemble est 
partout dense sur P. 

Comme exemple particulierement simple d’ensemble dont l’indice 
est partout fini, nous citerons l'ensemble parfait classique de Cantor, 
obtenu en retranchant d'un segment continu lintervalle occupant 
le tiers médian de ce segment, puis en recommencant l'opération 
sur chacun des deux segments conservés et en la répétant indéfini- 
ment. 4(//) est pour cet ensemble P, au plus égal a $ en tout 
point. Dans le cas le plus général, a eaiste sur P, un ensemble 
fermé non dense K,, tel que sur toute portion de P, sans points 
communs avec K, HF’ (0)=(Q) existe, est continue et doude spéciale- 
ment à P, de nombres dérivés finis; de plus, en tous les points d'un 
ensemble partout dense sur P,, p(@) admet f (0) pour deérivée spéciale a P,. 

Soit P un ensemble parfait quelconque, M un de ses points, 0 
labscisse de MM, P(M) l'ensemble parfait obtenu comme il a été 
dit plus haut. 

Pour chaque intervalle vours(O< r< s) contiguà P(M) et pour lequel 
(id) > 2 (on pourrait remplacer 2 par tout autre nombre indépendant 


N 2 


Rie \ 5 . , 

superieur a 1), formons le rapport eet —= 4 (2) du carre “de la 
r—- 

distance a M de l'extrémité s de 7z la plus éloignée de M, a la 
distance à M de l’extrémité + de 7 la plus proche de M. 

Il est aisé de voir que si la série uw (2) est convergente, il est pos- 
sible de déterminer une suite Ó + h, située sur P et telle que la 

2 


série soit convergente. La réciproque est évidente. Nous dirons 


hn4a 
que P est normal ou anormal en M selon que la série u (2) relative 
a M est convergente ou divergente. 
Toute portion de P contenant M entre ses extrémités est, en méme 
temps que P, normale ou anormale en M. 


230 


On montre sans peine que, si un ensemble P est normal en chacun 
de ses points, il existe, si petit que soit le nombre positif donné s, 
un nombre positif 4 et une portion P, de P, tels que, pour toute 
valeur de @ située sur P, et quelque soit 6’ sur P entre 6—y et 
0 + 1, il est possible de trouver une suite 6+h=—6’,O0+h,,..., 


heh edig haa 
0 + h. ., de points situés sur P et tels que la série ree ih, + 
by Uy 
fi . . MD as 
+...+—— +... ait une somme inférieure a s. 
antal 


De là résulte que, st wn ensemble parfait P est normal en chacun 
de ses points, l'ensemble des points de P ou p(0) est non existante 
ou discontinue sur P, cet ensemble est non dense sur P. 

Considérons un ensemble parfait P dont la construction satisfait’ 
aux conditions suivantes. Soient &,,?,,-.., Bn... une suite de nom- 
bres positifs inférieurs à '/,, el o, un segment quelconque. A la pre- 
mière opération, nous retranchons de 5, un intervaile, de manière 
qu’il subsiste sur v, deux segments 5, ayant chacun une longueur 
supérieure a 8,5, A la seconde opération, nous extrayons de chaque 
segment o, un intervalle, de facon que chacun des deux segments 
restants surpasse ce même segment o, multiplié par p,...A la n° 
fois, nous opérons sur 2" segments o, conservés a la suite de l'opé- 
ration précédente. De chacun de ces segments, extrayons un inter- 
valle de manière que chacun des deux segments 6,4; restants sur- 
passe le segment o, d'où il est extrait, multiplié par @,. Et ainsi 
indéfiniment. 

1°. Si la plus petite limite de 8, pour 7 infini est positive, et 
égale a u, P possède en chacun de ses points un indice au plus 


a 1p" 
egal a a= aa 
a 
2°. Si Oni = 6, 8,, P est normal ou anormal en chacun de ses 
e poe B, Bs CS [ar . 
points, selon que la série Tt ee est convergente ou divergente. 
n+1 


Si done §,==2-*", P est normal ou anormal selon que k < 2 ou 
que k < 2. 

L’ensemble E des points de non existence de (0) est, nous 
avons vu, non dense sur le continu. ll se décompose en un 
ensemble non dense sur tout ensemble parfait (ou clairsemé) G, et 
un ensemble dense en lui-même G. Soit HW le dérivé de G. I est 
parfait et G est partout dense sur JZ. MI est anormal en tous les 
poins de G, sauf éventuellement en certains points formant un 
ensemble g non dense sur 1, 


231 


On peut montrer par des méthodes analogues aux précédentes, le 
résultat suivant. 

Toute fonction F (6) doude d'une dérivée seconde généralisée f (6) 
(condition A) possède (indépendamment de la condition #) les 
propriétés ci-apres : 

L’ ensemble E de non existence de la dérivée F’(9)= (9) est non 
dense sur le continu. E est de mesure nulle. Les points où 7 () 
existe, sans posséder f{(9) pour dérivée exacte ou approximative, forment 
un ensemble de mesure nulle. 

Sur tout ensemble dont P l'indice est en chaque point inférieur à 2, 
1° il existe une portion P, où (9) existe, est continue, douée de 
nombres dérivés spéciaux a P finis, 2° p(0) admet en un ensemble 
de valeurs de 9 partout dense sur P, la fonction f(9) pour derivée 
spéciale a P. 


Mathematics. — “Ueber eineindeutige, stetige Transformationen von 
Flächen in sich’ (siebente Mitteilung’)). By Prof. L. E. J. 
Brouwer. 


(Communicated at the meeting of June 26, 1920). 


Im folgenden gebe ich die Charakterisierung aller Klassen von 
eindeutigen stetigen Abbildungen einer beliebig vorgegebenen end- 
lichfach zusammenhängenden Fläche u auf eine beliebig vorgegebene, 
endlichfach zusammenhängende Fläche u’. 

Sei O ein Punkt von u, # die Gruppe der geschlossenen stetigen 
Kurven von u durch O (welche in bezug auf F nur dann als 
verschieden betrachtet werden, wenn sie sich nicht mittels stetiger 
Modifizierung unter Festhaltung von O ineinander überführen lassen), 
N eine ,,Normalbasis’ von F, welche aus den, falls u zweiseitig 
ist, der Fundamentalrelation 


—1 gl —1 —1 poe 
ate ts aa ( a aan 2 == 
Le a, Os a, Cees n n—tI EE gel Ca 


und, falls w einseitig ist, der Fundamentalrelation 
1 


1 y2 2 2 ae 
Cler POMEL, C ; oe == 
a, 2 n—1 oF fee peas 


genügenden Kurven a,,d,,... Ann (die wir in dieser Reihenfolge 


1) Vgl. diese Proceedings XI, S. 788; XII, S. 286; XIII, S. 767; XIV, S. 300; 
XV, S. 352; XXII, S. 811. Hinsichtlich der fiinften dieser Mitteilungen kann 
bemerkt werden, dass der dortige Beweis auch unabhängig vom LüROTH-CLEBSCH- 
schen Theorem gefiihrt werden kann, nämlich so: a.a.0. S. 357 Z. 21 wählen 
wir auf «’ eine solche einfache geschlossene Kurve k, welche ein alle Bildpunkte 
von Rändern und Verzweigungspunkten der g, sowie alle nirgends dichten Bilder 
von g, enthaltendes Gebiet g begrenzt, und ziehen k+g stetig zusammen in einen 
Punkt P von g. Die durch diese stetige Kontraktion von k + g bestimmte stetige 
Aenderung von «, führt zu einer ,,primitiven Abbildung «, von u auf w'”, für 
welche die ausserhalb voneinander gelegenen Innengebiete G, einer endlichen Zahl 
einander nicht treffender einfacher geschlossener Kurven von w je eineindeutig mit 
dem Grade +1 auf die punktierte Fläche «’ und der Rest von w auf den Punkt P 
abgebildet wird. Sodann führen wir mittels wiederholter stetiger Verschmelzungen, 
jedesmal von einem durch ~, mit dem Grade + 1 und einem durch «, mit dem 
Grade — 1 abgebildeten G, , x, in eine „homogen-primitive Abbildung %q VON u 
auf w’” über, deren Gebiete G, entweder alle mit dem Grade + 1 oder alle mit 
dem Grade — 1 abgebildet werden. Dass alie homogen-primitiven Abbildungen 
neten Grades von « auf «’ zur selben Klasse gehören, leuchtet unmittelbar ein, 

In der sechsten Mitteilung ist S. 814 Fussnote *) statt Math. Annalen 81 zu 
lesen Math. Annalen 82. 


233 


geordnet denken) besteht, O’ ein Punkt von w', G die Gruppe der 
geschlossenen Kurven von u’ durch O’, M eine Normalbasis von G, 
welche aus den Kurven 5,,...b, bestebt. 

Zu einer eindeutigen stetigen Abbildung o von u auf wu’, welche 
O in O’, mithin jedes a, in ein Kurve a’, durch O’ überführt, gehört 
ein ,, 7ransformations formelsystem” 

Bp (Oy aye, Or)-() — Aal A Mm), oi | 2 CAN 
wo die p Produkte darstellen. 


Ist 4 (6,...6,) ein willkürliches Element von G, so gehört das 

Formelsystem 

Di Seep (P — KEE Ni) ae a (A) 
welches wir zu (1) dhnlich nennen werden, ebenfalls zu O in O' 
überführenden Abbildungen von « auf u' als Transformationsformel- 
system und zwar können diese innerhalb der Klasse von ogewahlt werden. 
Andererseits gehört zu jeder O in O' überführenden Abbildung von 
uw auf w, welche zur Klasse von o gehört, ein zu (1) ähnliches 
Transformationsformelsystem. 

Somit bestimmt jede Klasse von Abbildungen von u auf w' (zu 
welcher ja immer QO in O! überführende Abbildungen gehören) eine 
Menge von untereinander ahnlichen Transformationsformelsystemen. 
Diese Menge werden wir als das formale Bild der Klasse 
bezeichnen, so dass unsere Aufgabe in der Ermittelung der Bedin- 
gungen besteht, unter denen zwei dasselbe formale Bild besitzende 
Abbildungsklassen von u auf w' identisch sind. 

Um die Lösung dieser Aufgabe formulieren zu können, konstruieren 
wir auf w ein der Normalbasis MN entsprechendes, in O zusammen- 
hängendes kanonisches Rückkehrschnittsystem R, durch welches also 
gu in eine schlichte Fläche fr, deren Grenze g in R liegt, dabei 
übrigens einzelne Segmente von / der Fundamentalrelation ent- 
sprechend zweimal durchlaufen kann, und m je von einem Flächen- 
rande 7, und einer zu FR gehörigen, 7, umschliessenden ,,Rand- 
schlinge” s, begrenzteu Zylinderflächen C,(»—1,2,...m) zerlegt 
wird. Weiter wählen wir auf pw’, im Falle dass diese Fläche eine 
projektive Ebene ist, eine gerade Linie / durch O' und auf / 
einen Umlaufssinn 4. Im Falle dass pw’ eine projektive Ebene ist, 
werden wir sodann eine Abbildung eine Normalabbildung nennen, 
wenn sie jeden zu F# gehörigen Riickkehrschnitt entweder in O/ 
oder eineindeutig in /, und zwar das erste Mal, dass er in g 
auftritt, mit dem Umlaufssinne 2 transformiert. 

Die Lösung der gestellten Aufgabe gestaltet sich nunmehr folgen- 
dermassen : 


234 


Zu einem formalen Bilde B gehört nur eine einzige Klasse: 

1°. wenn die universelle Ueberlagerungsfläche von w offen ist. 

2°. wenn die universelle Ueberlagerungsflache von v' geschlossen, w 
aber offen ist. 

3°. wenn tw den Zusammenhang der projektiven Ebene besitzt, w 
einseitig und geschlossen ist, wenigstens ein einseitiger Rückkehrschnitt 
von U zweiseitig abgebildet wird und eine, mithin alle zu B gehörigen 
Abbildungen ungerade sind. 

Zu einem formalen Bilde B gehören zwei Klassen: 

1°. wenn Ww den Zusammenhang der Kugel besitzt und  einseitig 
und geschlossen ist. Das entsprechende Kriterium besteht in der Paritat 
der zugehérigen Abbildungen. 

2°. wenn & den Zusammenhang der projektiven Ebene besitzt, u 
zweiseitig und geschlossen ist und wenigstens ein Rückkehrschnitt von 
u einseitig abgebildet wird. Das entsprechende Kriterium besteht in der 
Parität der auf der zweiseitigen Verdoppelung von W gemessenen Grade 
der zugehörigen Normalabbildungen. 

3°, wenn w den Zusammenhang der projektiven Ebene besitzt, u 
einseitig und geschlossen ist, wenigstens ein einseitiger Rickkehrschnitt 
von  zweiseitig abgebildet wird und eine, mithin alle zu B gehérigen 
Abbildungen gerade sind. Das entsprechende Kriterium besteht in der 
Paritat der auf der zweiseitigen Verdoppelung von ' gemessenen Inhalte 
der zugehörigen Normalabbildungen. 

Zu einem formalen Bilde B gehören unendlichviele Klassen: 

1°. wenn v' den Zusammenhang der Kugel besitzt und  zweiseitig 
und geschlossen ist. Das entsprechende Kriterium besteht im Grade 
der zugehörigen Abbildungen. | 

2°. wenn w den Zusammenhang der projektiven Ebene besitzt, u 
zweiseitig und geschlossen ist und alle Rückkehrschnitte von # zweiseitig 
abgebildet werden. Das entsprechende Kriterium besteht im absoluten 
Werte des zugehörigen auf der zweiseitigen Verdoppelung von u 
gemessenen Abbildungsgrades. 

3°. wenn w' den Zusammenhang der projektiven Ebene besitzt, w 
einseitig und geschlossen ist und alle einseitigen Rückkehrschnitte von 
u einseitig abgebildet werden. Das entsprechende Kriterium besteht im 
absoluten Werte der Grade der zugehörigen Abbildungen der zwetseitigen 
Verdoppelung von w auf die zweiseitige Verdoppelung von we 


Kryo-Biology. — “Hinwirkung sehr niederer Temperaturen auf die 
Moosfauna”. By P. Givpert Raum (at Maria Laach). (Versuche 
im physikalischem Laboratorium der Universität Leiden und 
der kryologisch-biologischen Versuchsstation des Niederländi- 
schen Kälte-Vereins, Leiden Communications Suppl. N°. 435). 
(Communicated by Prof. H. KAMERLINGH ONNrs). 


(Communicated at the meeting of June 26, 1920). 


Als ,,Moosfauna” im allgemeinen bezeichne ich nach dem Vorschlag 
Fr. Heinis (ef. ,,Systematik und Biologie der moosbewobnenden Rhi- 
zopoden, Rotatorien und Tardigraden der Umgebung von Basel mit 
Berücksichtigung der übrigen Schweiz”. Archiv für Hydrobiologie 
und Planktonkunde. Stuttgart 1910. Bd. V. Heft 2, p. 91) „die Ge- 
samtheit der in den Moos = resp. Flechtenrasen vorkommenden 
Tiere’. Diese Definition umfasst sowohl die: 

I. Bryophilen Formen, d.h. solche, die in den Moosrasen „ihre 
Existenzbedingung”’ finden. [cf. Ricurers, F. Die Fauna der Moos- 
rasen des Gaussberges und einiger siidlicher Inseln’’. Deutsche Siid- 
polar-Expedition 1901—1908, Berlin 1907. (Zoologie), p. 292]. Ihre 
Nahrung können die lebende Moospflanze, organischer Detritus, und 
andere Tiere sein. [cf. Heinis le.p. 91]. 

Il. Bryorene Formen, d.h. solche, die entweder nur während 
einer bestimmten Entwicklungsperiode im Moose leben oder zufällig 
im Moosrasen gefunden werden. 

Zur ersten Gruppe gehören Protozoen, Rotatorien, Nematoden, 
Tardigraden und Gamasiden. : 

Zur zweiten Gruppe rechnet Heinis [le. p. 91]. Larven von Lauf- 
und Rüsselkäfern, Fliegenlarven, Myriopoden, Arachniden, Mol- 
lusken ete. 

In der folgenden Arbeit findet der Hauptsache nach nur die Moos- 
fauna im engeren Sinne Beriicksichtigung, vor aliem die Gruppen 
der Tardigraden (Bärtierchen), Nematoden (Fadenwürmer), und Rota- 
torien (Rädertierchen). 

Da diese Tiere in grossen Mengen die Moosrasen der kalten Zone 
bewohnen, müssen sie auch eine grosse Anpassungsfahigkeit an 
niedere Temperaturen besitzen. 

16 

Proceedings Royal Acad. Amsterdam, Vol. XXIII. 


236 


Prof. F. Ricntrers, der beriihmte Altmeister der Moosfauna, unter- 
suchte Bryum-Rasen vom Gaussberg, in dem — 41° C. gemessen 
wurde. [Rricnrers Le.) Ueberhaupt scheinen die Moose der kälteren 
Gegenden das Dorado der Moosfauna zu sein, während die Tropen 
nach den Angaben Murrays und Rrcurers relativ arm an Moos- 
bewohnern im engeren Sinne sind. 

Von diesem Gesichtspunkte ausgehend stellte ich im Oktober und 
November 1919 im chemischen und physikalischen Institut der 
Bonner Universität mit Tieren der oben genannten Moosfauna einige. 
Temperaturversuche an. Eine kurze Zusammenfassung der Ergebnisse 
ist in den Sitzungsberichten der Niederrheinischen Gesellschaft fiir 
Natur- und Heilkunde zu Bonn 1920 (1919) p. 21—23 veröffentlicht. 

Es zeigte sich, dass verschiedene Gruppen von Tieren, die die 
Fähigkeit besitzen, mit den Moosen auszutrocknen und nach dem 
Anfeuchten des Mooses wiederaufzuleben, im trockenen sogenannten 
asphyktischen Zustand sehr tiefe Temperaturen ertragen können. 
Temperaturen von c. —183° C., die mittels flüssiger Luft erzielt 
wurden, überstanden die Versuchstiere, Tardigraden, Rotatorien und 
verschiedene Arten von Nematoden schadlos 26 Stunden lang. 

Da ich in Bonn keine Gelegenheit hatte, noch tiefere Tempera- 
turen herzustellen, wandte ich mich an den Leiter des Kryogenen 
Instituts, Herrn Prof. Dr. KameriincH Onnis, mit der Bitte, mir zu 
gestatien, in seinem weltberiihmten Institut einige Versuche mit 
fliissigem Wasserstoff, wenn möglich auch mit flüssigem Helium, 
ausführen zu dürfen. Herr Prof. Dr. KAMERLINGH Onnes_ schrieb 
mir gütigst zurück, dass mir so viel flüssiger Wasserstoff zur Ver- 
fügung stehe, als ich zu meinen Versuchen benötige. Ich erhielt 
sogar die freundliche Zusage, mit flüssigem Helium arbeiten zu 
dürfen, falls nach den Versuchen mit lüssigem Wasserstoff sich 
dazu die Notwendigkeit ergebe. 


I. Versuch mit fliissiger Luft. 


Da ich in Leiden auch über beliebige Mengen flüssiger Luft ver- 
fügen konnte, bat ich den Conservator des kryogenen Instituts, Herrn 
Dr. CROMMEIIN, zunächst einen Versuch mit fliissiger Luft der sich 
auf einige Tage erstrecken sollte, ausführen zu dürfen. Die Moos- 
proben wurden in leichtes Papier eingehillt in einem Gazebeutel, 
der mittels einer Bleikugel beschwert war, sofort in ein bereitste- 
hendes Bad von flüssiger Luft getaucht. Die Tiere befanden sich in 
den lufttrockenen Moosen im asphyktischen Zustand. Der Versuch 
dauerte 125 Stunden. 


237 


Nach dem Wiederanfeuchten bald nach dem Versuch erwachten 
fast sdmtliche Tiere in verhältnismässig kurzer Zeit. Die folgende 
Tabelle soll eine Uebersicht über die Versuchstiere, die Dauer ihres 
Trockenschlafes und die Zeit ihres Wiederaufwachens geben. 


TABELLE I. 
Bad in fliissiger Luft. 
Dauer: 125 Stunden. 
Zeit: 11. II. 1920 bis 16. II. 1920. 
Temperatur: c. —190° C. 


Wiedererwachen. 
Moosart. Track 
Be Rotatorien. Tardigraden. | Nematoden. 
A. Grimmia spec. | Adineta bar- | Macrobiotus | Piectus rhizo- 
von einem Stroh- bata Jans. Die | Hufelandi C.} philus De Man. 
dach aus Ameron- 8 Tage. I, in 16 Min. | Schultze. DerI| Der |. juv. in 33 
gen. | in“19 Minuten, | Minuten, sen. in 
| andere in 32M. | 46 Minuten. 
B. Tortula ruralis Callidina con- 


Ehrh. von einer Gar- stricta Duj. Die 
tenmauer aus Hon- 16 Tage. | I. in 5 Minuten. | 
nef a. Rhein. | 


E: Racomitrium Gen.? spec. ? Plectus parieti- 
spec. bei Scheve- 5 Tage, | Das I. inc. 20 | nus Bast. Der I. 
ningen an den 86 | Minuten. | in 70 Minuten. 


Dünen. 


Wurden die Moosproben nach dem Kälteexperiment längere Zeit 
aufbewahrt, ehe sie angefeuchtet wurden, so erwachten die Tiere 
gewöhnlich etwas später. Eine allgemeine für alle Tierarten gültige 
Regel liess sich mit Sicherheit noch nicht ableiten. 3 Monate später 
wurde z. B eine Probe von A untersucht und nach dem Wieder- 
anfeuchten erwachte ein Rotator fast genau zu der in Tabelle | 
angegebenen Zeit, eller noch ein bis 2 Minuten früher. Die Rotato- 
rien von C brauchten indes volle 2 Stunden, bis sie nach dreimonat- 
lichem Trockenschlaf ihre volle Lebenstätigkeit wiedererlangten. 
2 Eechinieus-Arten (gepanzerte Tardigraden) erwachten nach mehr 
als dreimonatlichem Trockenschlaf in B nicht mehr. Die Kälte 
hierfür verantwortlich zu machen, scheint mehr als fraglich, wie 
aus spätern Versuchen klar hervorgeht. Eber könnte man sagen, 
dass diese Tiere schon vorher durch das Austrocknen geschädigt 
wurden. Denn die Fahigkeit der Versuchstiere wiederholt auszu- 
trocknen und wiederaufzuwachen, ist nicht unbegrenzt. 

16* 


238 


11]. Versuch mit fliissigem Wasserstof}. 


TABELLE IL 
Dauer: 26 Stunden. 
Zeit: 10,01 bis 12511, 1920. 
Temperatur: —253° C. 


| | Wiedererwachen. 
Trekken | We kiss Ne Aas 
Moose. | | 
| schlaf. _ Rotatorien. — Tardigraden. | Nematoden. 
| | | | 
| Adineta bar- | Macrobiotus | Plectus rhizo- 
A. wie I. 8 Tage. bataJans.inc. Hufelandi C. | philus De Man 
_ 15-20Minuten. | Schultze in 20 | 25 Minuten. 
| | Minuten. 
| | Callidina con- 
B. wie I. 16 Tage. \ stricta Duj. in 
3 Minuten. 
‚In 18 Minuten | 
ein Rotifer 
Giswiesl 5 Tage. spec.? Callidi- 


na brauchten 
| mehr. 
Vergleicht man Tabelle I und II, so findet man kaum bedeutende 
Unterschiede. Als Regel scheint festzustehen, dass Rotatorien am 
schnellsten nach dem Wiederanfeuchten zum Leben zuriickkehren ; 
es folgen die Tardigraden und zuletzt die Nematoden. Ferner scheint 
ein ganz kurzer Trockenschlaf mit folgendem kalten Bad auf das 
Wiedererwachen verzögernd zu wirken. Man vergleiche z. B das 
über Rotatorien Gesagte in Tabelle L und II. 


Ill. Versuch mit flüssigem Helium. 


Da Herr Prof. Dr. KAMERLINGH Onnes durch Krankheit verhindert 
war, während meines Aufenthaltes in Leiden flüssiges Heltum herzu- 
stellen, bat ich Herrn Conservator Dr. CROMMELIN, die Versuche für 
mich auszuführen, sobald sich eine Gelegenheit dazu biete. Herr Prof. 
Dr. KaMERLINGH ONNmps besass die grosse Freundlichheit, die Versuche 
selber zu leiten. Die Moose wurden dann sofort nach dem kalten 
Bad mir zur Untersuchung nach Bonn gesandt. 

Dem Briefe des Herrn Prof. Dr. KAMERLINGH Onnes vom 16. III. 
1920 entnehme ich folgendes: 

„Am 10. II] 1920 12" wurden die Moose lufttroeken in den Helium- 
Apparat gebracht. Dieser wurde dann — was fiir die Helium- 
verflüssigung nötig ist — luftleer gepumpt, blieb 24 Stunden luftleer 
bei gewObnlicher Temperatur stehen, wurde sodann mit Heliumgas 


239 


bei gewohnlicher Temperatur gefüllt und langsam 2 Grad pro Minute 
abgekühlt bis —150° C. Es wurde sodann das Präparat mit flüssigem 
Helium iiberschiittet und blieb in demselben von 1" bis 8u, 45m, 
Während 2 Stunden wurde die Temperatur auf 1°,22 K erniedrigt”. 


TABELLE III. 


Dauer: 73/4, Stunden vgl. auch das im vorigen Abschnitt Gesagte. 
Zeit: 10. III — 11. II im Vacuum, 11, III 12h — 8h, 45m im fliissigen Helium. 
Temperatur: — 269° C bis — 271,88° C. 

1. Fir Moos B. erste Untersuchung 21. III. 1920. 


| Wiedererwachen. 
Er Untersuchung. jt TT SR STV 
Rotatorien. Tardigraden. Bemerkungen. 
| En ENE 
21. III. 1920. 1. Callidina nach | Echiniscus trifi- | Nach 8 Stunden 
91 Minuten. lis (neue Art) waren fast alle 
sen. nach 23 Min. | Tiere munter. 
| juv. ”» 31 ” 
24. II. 1920. Alle lebend. | Fast alle lebend. 
26. III. 1920. | om is 7 noch lebend. 
28. III. 1920. rf * _ Einige schlüpften 
‚aus den Eiern. 
dee IV. 1920, ĳ ‘es | Zahl d. lebenden 
| Tiere nimmt ab. 
12. IV. 1920. ei c ‚Nur einer lebend. 
14. IV. 1920. | Einige lebten. | Alle tot. 


2. Fiir Moos B zweite Untersuchung. 
Am 28. IV. 1920. 104,45m morgens eine neue Probe angefeuchtet. 


Wiedererwachen. 


Tag der Untersuchung. 


Echiniscus trifilis n. spec. nn 


28. IV. 1920. 10h,45m, | In einer Stunde war der erste | Nach einer Stunde und 
‚alte Echiniscus erwacht; es ‚ 13 Minuten erste Bewe- 
‚folgte einer von mittlerer « gung. 


Grösse. 
29. IV. 10h morgens | Noch ein alter munter. sehr lebhatft. 
29. IV. 2h,5m, | Auch ein junger erwacht. ï 5 


| 


29, IV.) 5h: | Viele alte und junge erwacht. ra 5 


: 240 


Dann alles von neuem eintrocknen lassen. 


Wiedererwachen. 


Tag der Untersuchung 
Echiniscus trifilis non spec. | Milnesium tardigradum. 


En Se ee ee 


4. V. 11h,2m morgens. 


Bis 6 
. Niches 
Men, 
Che 
6. V. 4h,47m. Ein junger ausdem Eigeschlüpft 
ZN | Alles tot. Alles tot. 


Parallelversuch, um zu prüfen, ob die Schäden beim Wieder- 
eintroeknen nach dem kalten Bad auf das Kälteexperiment zurück- 
zuführen sind oder ob die Versuchstiere überhaupt ein mehrmaliges 
Wiedereintrocknen nicht schadlos ertragen können. 

Denis Lance schreibt in seinen Theses présentées a la Faculté des 
sciences de Paris pour obtenir le grade de docteur des sciences 
naturelles, Paris 1896, ,,9 bis 14 mal kann man die Tiere — gemeint 
sind Bärentierchen (Macrobioten) — austrocknen lassen. Die Zeit, die 
zur Wiederaufnahme der Lebenstatigkeit erforderlich ist, wächst mit 
der Zahl der Austroeknungen”. Ich muss gestehen, dass es mir noch 
nie gelang, Tardigraden spec. Eehiniscus-Arten öfters als 5 bis 7 
Mal auszutrocknen. Freilich hangt es auch ganz von dem Grad und 
der Dauer der Austrocknung ab. Macrobioten ertragen mehr als die 
gepanzerten Echiniscus-Arten. Rotatorien sind am widerstandsfahigsten. 


TABELLE IV. 


Parallelversuch mit Moos B, das nur lufttrocken seit 23. I. 1920 aufbewahrt 
worden war. 


Wiedererwachen. 
Tag der Untersuchung 
und Stunde d. Anfeuchten.| Callidina Milnesium tardi- “ae ae 
spec.? gradum Doy. Echiniscus trifilis. 
7. V. 1920, 4h,49m, | 5h,14m, also in 5h,14m, also in 
| 25 Minut. | 25 Minut. 
7. V. 1920. 54,41m, | 64,00m, also in | 64, 13m, also in | 6h, 03m, also in 
| 19 Minut. 32 Minut. | 22 Minut. 
Dann alles eintrocknen lassen. 8. V. 8h abends trocken. 
10. V. 1920. 9,244 mor- | 9,50h3jungeschon | c.?/4 114 erwacht. | Nur einer 9,50h mit- 


gens. sehr munter. telgross, alleandern 
| schienentot. 


241 


Alles eintrocknen lassen. 11. V. 114 abends alles trocken. 


14. V. 1920. 8,354 mor- | 9,13h d. erste. c. 9,30h. 10h abends war 
gens. 9,15h 3 Stück. ‚ einer aus dem Ei 
| geschliipft. 


15. V. 1920, 84 mor- | Alle lebhaft. | Sehr munter. _ Auch ein grösse- 
gens. | | rer erwacht, ein 

| alter bewegte 
sich auf Anstoss 
mit der Pinzette. 


Alles eintrocknen lassen. 16. V. mittags trocken. 


| | 
17. V. 1920. 8,35h mor- | 8,50heine erwacht.| tot? | Alle scheinen tot. 
gens. | 
| 


sehr lebhaft. | tot. Einerwachsener u. 


11,30h morgens. 
ein kleiner munter. 


Vergleicht man die Tabellen mit einander, so wird man wohl sagen 
dürfen, dass das kalte Bad (besser wohl die durch das kalte Bad 
bewirkte Austrocknung) den Echiniscus Arten schädlich war. *) 


TABELLE V. 


Bad in flüssigem Helium mit Moosart C. Allgemeine Bemerkungen s. p. 4—5. 
Erste Untersuchung. 


Dauer: s. p. 4—5. 
Zeit: s. p. 4—5. 
Temperatur: s. p. 4—5. 


Tag d. Untersuchung u. | Rotator Callidi Macrobiotus Hufe- Nematode 
or Callidina. | ‘ 
d. Anteuchtens. mae ken | landi. Plectus parietinus. 
21. III. 10,52h morgens. | 11,374, also in| 11,49h, also in 58 
45 M. | Min. 12,104 ein 
| junger. 
22. III. 10,30h morgens. | sehr munter. | Einer war sehr | lebhaft. 
munter. Zeit des 
Erwachens unbe- | 
stimt. | 


In der folgenden Tabelle soll die Lebensdauer der einzelnen in 
Tabelle V angefiibrten Tiere verfolgt werden. 


1) Anmerkung: Nach der Drucklegung wurden die in Tabelle IV mitgeteilten 
Untersuchungen fortgeselzt. Ich liefs die Tiere noch zweimai eintrocknen. Echiniscen 
und Rotatorien erwachten auch noch nach der letzten, also 6 Austrocknungs- 
peririode. Die Versuche werden fortgesetzt. 


eee ERE TET EN EE PE SE TET SEITE OL Le OE TED 


242 


Datum. Callidina. Macrobiotus. Plectus. 
| 
225 TIE ‚Sehr munter StirbtamAbend.|} 2 kleine sehr 
2-stiek. munter. 
24: TIT: > » » » 
26. III. » » » » 
Ein grosserPlec- 
tus parietinus 
Bast 06 mm 
gross doch nicht 
| geschlechtsreif. 
| Bei der Bestim- 
mung leider ge- 
tötet, 
27. Ill. (Ors. aes | Ein junger noch 
lebhaft. 
Zell » » 
29. III. | 2 Nematoden 
| sehr lebendig. 
| | 
30. III. | Einer lebhaft. 
(Ze any oe 15 rage SS 
9, IV. Einer sehr Ieb-| Sehr munter, |2 sehr lebhaft. | 
‘haft. wohl geschlüpft. 
10. IV. » » lebt noch Nur einer noch! 
| lebhaft. | 
Ii IVA Nur auf Anstoss 
hin erfolgt Be- 
wegung des | 
Kopfes. | 
14. IV. | tot. tot. | 


tot. 


| starb _ aber 
‚nach Uberführung 


Bemerkungen. 


Es erscheinen in 
der Schale Proto- 
zoen von ganz cha- 
rakteristischer Ge- 
stalt, die ich noch 
in keinem anderen 
Moos beobachtet 


habe. Die Tiere 
schwimmen leb- 
haft umher. Ob 


nachträglich hin- 
eingekommen, 
bleibt fraglich. 
Mehrere Milben 
erwachten nicht 
mehr. 


| Viele Protozoen. 


| Protozoennehmen 


ab. 


Junger Echiniscus 
trifilis lebte, 
bald 


in ein bes. Gefäss. 


Viele kleine Proto- 


‚zoen. 


Zweite Untersuchung v. Moos C. 


Tag der Untersuchung | Rotatorien. Calli- (Nematoden. Plectus 

bzw. des Anfeuchtens. | dina. spec.? parietinus. Bemerkungen. 

29. IV. 8,454 morgens. | 9,53h eine sehr , Nur ein junger Die merkwiirdigen 
lebhaft. erwachte, 2 alte |Protozoen s. oben 


M. 


erwachten bis 10 


nicht mehr. 


erscheinen wieder, 


also doch nicht 


nachträglich hinein- 
gekommen. 


243 
IV. Versuch. Bad in flissigem Wassersto ff. 


Um zu erproben, wie die Versuchstiere sich verhalten, wenn sie 
bereits völlig aus dem Troekenschlaf erwacht und im Wasser ihre 
Bewegungen aufgenommen haben und dann einfrieren, wurden 
bereits im verflossenen Winter im Bonner Chemischen Institut Ver- 
suche angestellt. Hine Kältemischung von —81° C., die mehrere 
Stunden einwirkte, überstanden bei langsamen Einfrieren fast alle 
Versuchstiere. Selbst die Kälte der flüssigen Luft schadete den Tieren 
nicht, wenn man die Kälte anfangs langsam einwirken liess '). Liess 
man aber das Wasser, in dem sich die Tiere befanden, plötzlich 
einfrieren, so war der Prozentsatz der Tiere, die nach dem Auftau- 
en lebten, sehr gering. Im Kryogenen Institut der Universitat Leiden 
wurden folgende Versuche ausgefiihrt: 

1. 2 Moosproben „wurden zuerst angefeuchtet und eingewickelt 
in ein bischen Gaze und am 20. Marz 1920 von 10° bis 4" /ang- 
sam abgekühlt im Dampf von flüssiger Luft. Sodann wurden sie 
eingetaucht in flüssige Luft. Sie blieben darin bis 12. Marz 11°. 
(Also c. 2 Tage). Dann wurden sie aus der fliissigen Luft genom- 
men und gleich in flüssigen Wasserstoff gebracht und blieben hierin 
bis 13. Marz 10°, 30m. (Also c. 1 Tag). Darnach sind sie schnell 
auf gewöhnliche Temperatur gekommen”. Aus dem Brief des Herrn 
Prof. Dr. KAMERLINGH ONNEsS an mich vom 16. III. 1920. 

Herrn Dr. DrooGrever Fortuyn hatte ich vor meiner Abreise aus 
Leiden gebeten, einen Teil dieser Proben nach dem Auftauen an 
Ort und Stelle zu untersuchen. Er hatte die grosse Freundlichkeit, 
mir über das Ergebnis am 13. III. 1920 zu berichten. „In der lang- 
sam abgekühlten Probe belebte sich schon nach 12 Minuten ein 
Nematode, welcher kraftige Bewegungen machte. Nach 20 Minuten 
belebte sich der erste Tardigrade, bald von vielen andern gefolgt’’. 

Die Proben wurden mir dann lufttrocken zugesandt. Das Ergeb- 
nis der Untersuchung sei in folgender Tabelle mitgeteilt. 


1) Anmerkung: Liess man die Tiere im Wasser nochmals einfrieren, so waren 
die meisten nach dem Auftauen tot. Also hatte das kalte Bad doch die Wider- 
slandskraft geschädigt. Es tiberstanden nur Rotatorien. Es kam bei diesem Versuch 
nur die Kaltemischung von — 81° C, zur Verwendung. 


244 


TABELLE VI. 
Moosprobe A. 


Dauer: 1 Tag in fl. Wasserstoff, 2 Tage fl. Luft. 


Zeit: 10. III. 1920 bis 13 III. 1920. 
Temperatur: — 253° C. bzw. — 192° C, 


Tag der 
Untersuchung. 


24. III. 5,35h 
abends. 


10,054 abends 


25. III. 9,45h 
morgens. 


21, NE 25k 
morgens. 


28. HE 


29.111. 8h mor- 
gens 


10h abends. 


30. III. 14 mit- 
tags. 


6h abends. 
Sil II 
1—7. IV. 


1, IV. 3,15h | 
mittags. 
8. IV. 


9. IV. 9h mor- 
gens. 


10. IV. 9,15 
abends. 


LC Ye 


12. IV. 


14, IV. 


Callidina 


russeola Zel. | 


5,45h also in 10 
Minuten mit- 
telgross. 


sehr lebhaft 
schwimmend. 


2-3 sehr leb- | 


haft. 


| Macrobiotus 
Hufelandi. 


| 6,20h ziemlich 
| lebhaft dunkel 
pigmentiert. 


Einer am Er- 
wachen, auch 
dunkel __—pig- 
mentiert. 


Nur einer noch 
| lebhaft. 


| tot. 


| 


Ein kleiner,wohl 


geschliipft. 
| 
Ein alter nimmt’ 


| die Bewegung | 


wieder auf. 


Alter tot. 


Ein alter lebhaft.| 


| Auch kleiner, 
‚wohl geschliipft. 


> » » 


Der kleine sehr 
lebhaft. 


Milnesium 


‚ tardigradum. | 


2 Stück noch 


schlafend. 


| Einer bewegte 


sich auf An- 
stoss. 


‚tot. 


alter sehr | 


Plectus 
rhizophilus. 


Noch schlafend. 


sehr lebhaft. 


2 kleine lebhaft. 


» » 


Dazu ein alter. 


| alle lebhaft 


| 


munter. 


2 junge lebhaft. 


Alterer erwacht. 


Bemerkungen. 


Protozoen 
treten auf. 


245 


| 
ne Rotator. | Macrobioten. | Nematoden. Bemerkungen. 
; | | 
26. IV. ‚ mehrere sehr 3 kleine, wohl | Der alte sehr 
‚ Jebhaft. | geschlipft. munter. 
28. IV. 5 î 3 sehr munter. pe ‘5 
1 V.11,30h mor-| 5 d | rc ss Dazu noch 2 
gens. | jüngere. 
De V, ” ” ” ” ” ” 
6. V. han ae Nur einen leb- 
| haft gesehen. 
8. V. 8,55h mor- 5 Pi Einer sehr mun- Einer lebhaft. 
gens. | ter Macrob. echi- 
| nogenitus Rich- 
| ters. 
9,404 morgens. “4 ES | 3 ziemlich er- | Eine lebende Mil- 
wachsen, mun- | be, wohl nach- 
| ter. träglich hineinge- 
| | kommen oder ge- 
10. V. | i: F ein erwachsener| Ein grosser be- schläpft? ? 
'Hufelandi leb-| wegte sich nur 
haft. | auf Anstoss. 
AV träge Bewegun- Ein Hufelandi Alle tot 
‚gungen auf An- mittelgross, 
| stoss. ‚dunkel, lebhaft, 
| | | 
14. V. Alles schien tot. 


Moosprobe A. 2. Untersuchung. 


Tag der Untersuchung, 


5. V. 5,40h abends. 


6. V. 8,30h morgens. 


7. V. 81 morgens. 


Rotator. 


9,40h 2 kleine sehr 
lebhaft, wohl lange 
vorher erwacht. 


| sehr lebhaft. 


schien alles tot. 
Moosprobe B. desselben Versuchs. 


Macrobiotus. 


6,30h ein Hufelandi 
lebhaft. 


noch einer erwacht. 


Nematoden. 


9 40h, 
wegte 
wenig. 


Einer be- 
sich ein 


Datum des Anfeuchtens 
und der Untersuchung. | 


24, III. 5,38 abends. 


| 
| 
| 9,555 erste am Er-, 
wachen. | 


10h mehrere leb- | 
| haft. | 


| Rotatorien. 
Callidina. 


Echiniscus trifilis 
non spec. 


Bemerkungen. 


246 


Datum der Untersuchung. Rotatorien. Echiniscus. Bemerkungen. 
| | 
25. III. 1920. lebhaft. | alle tot. 
27. Ill. bis 30. III. ‘ | 
31. III. 10h morgens. 4 Einer schlüpftaus | Viele Protozoen 
‚dem Ei. erscheinen. * 
1. IV. bis 14, IV. A ‚starb bald. 
14 IV. 10,20h morgens. | rs | Einer geschliipft, | Protozoen vermeh- 


| 0,150 mm. gross. | ren sich sehr stark. 


Die Eier der Eehinisei scheinen also bei weitem widerstandsfähiger 
zu sein wie die Tiere selbst. Es erwachte überhaupt kein erwachsener 
Echiniscus. 

2. Ein zweiter Versuch wurde mit Moosproben gemacht, die 
vorher angefeuchtet und dann plötzlich in flüssige Luft und in fliissigen 
Wasserstof} getaucht wurden. Herr Prof. Dr. KAMERLINGH ONNrs 
schrieb mir darüber am 13 III 1920: „Diese Probe wurde zuerst 
angefeuchtet und in Gaze eingewickelt und sodann 10 Marz 11> 
plötzlieh in flüssige Luft gebracht und blieb darin bis 12 Marz 
11" (also 2 volle Tage). Sodann wurde sie wie die vorige in flüssigen 
Wasserstoff getaucht und blieb darin bis 13 HIL. 10,380” (also fast 
einen Tag.) 

Herr Dr. DROOGLEEVER Fortuyn untersuchte auch von dieser Probe 
gleich nach dem Auftauen einen Teil und fand alles tot ,,wenigstens 
war nach 2 Stunden und 20 Minuten keine Bewegung sichtbar”. 
Brief vom 13 III, 1920. 

Der übrige Teil der Probe wurde mir dann lufttroeken zugesandt. 
Das Ergebnis einer genaueren und längeren Untersuchung sei in 
folgender Tabelle mitgeteilt: p. 511. 

Von den Moosproben waren A und B zusammengeschiittet worden. 

In einem andern Gefäss derselben Probe, die auch am 24. III 
angefeuchtet war, bemerkte ich erst am 8. IV eine Adineta lebhaft 
umherschwimmend. Vielleicht war das Tier inzwischen geschlüpft. 
Es lebte noch am 6. V. An diesem Tage bemerkte ich noch einen 
Rotifer lebhaft umherschwimmend *). 

Auf meine Anfrage hin teilte mir Herr Conservator Dr. CROMMELIN 
mit, dass die Moose 1 bis 1'/, Stunden vor dem Kälte-experiment 


1) Anmerkung: Rotatorien lebten noch am 25. [X. 1920. Aus den Eiern 
schlüpften viele Macrobioten. 


247 


angefeuchtet wurden. Es ist also wohl ausgeschlossen anzunehmen, 
dass sich Callidina russeola Zel. beim Einfrieren noch im asphyk- 
tischen Zustand befand. Am 27. V waren sehr viele Rotatorien und 
einige Macrobioten geschliipft. 


TABELLE VII. 
Dauer: 3 Tage. 
Zeit: 10. III. 1920 bis 13. III. 1920. 
Temperatur: — 253° C. bezw. — 192° C. s. vorher. 
nm _ = u ann mn an == SSSa Seg. 


Datum der Untersuchung. Rotatorien. : Bemerkungen. 


24. Ill. 10,554 morgens. | Erst 4,555 eine grosse Calli- | Viele tote Echiniscen, 
| dina russeola Zel. am Erwa- | Macrobioten, Rotatorien 
chen. und Nematoden. 


10,155 abends. sehr lebhaft, sich ausstreckend 
und schwimmend. 


25. III. bis 15. IV. Meist sehr lebhaft, nur abends 
> in Ruhe. 
16. IV. 9h abends. Bewegt sich nur auf Anstoss. 
25. IV. Nur langsame trage Bewe- 
gungen. 
21. IV. Bewegungen sehr träge. 
28. IV. ‘ 5 ie Das Tier war am Schlusse 
ZiemlichabeSmagen, ob- 
. wohl ihm Detritus zur 
29. IV. reagiert kaum noch. | Verfügung stand. 
1 MV: tot. 


Also ist kaum eine Schädigung durch das kalte Bad festzustellen. 
Die Tiere leben auch sonst nicht länger. 

Zusammenfassung der bisherigen Ergebnisse. 

I. Die Tiere der Moosrasen können im asphyktischen Zustand 
Temperaturen von — 271,8° C. mehrere Stunden ertragen. (Tardi- 
graden, Nematoden und Rotatorien). Protozoen scheinen auch diese 
Temperaturen zu überstehen, bedürfen aber noch einer sorgfältigen 
Nachprüfung. Temperaturen von — 192° C. wurden 5 Tage lang 
schadlos ertragen. Auch die Eier dieser Tiere werden nicht geschädigt. 

Il. Ein ganz kurzer Trockenschlaf mit folgendem kalten Bad 
scheint auf das Wiedererwachen verzögernd zu wirken. 

HI. Am schnellsten erwachen Rotatorien; es folgen die Tardi- 
graden und zuletzt die Nematoden. 


248 


IV. Durch die Kälte scheint die Fahigkeit der Echiniscus Arten, 
òftere Anstrocknungsperioden zu überstehen, gemindert zu werden. 

V. Lässt man die Tiere im wachen Zustand in Wasser langsam 
einfrieren, so ertragen die meisten die Temperatur — 253° C. 24 
Stunden schadlos. Eine Ausnahme scheinen die Echiniscen zu machen. 

VI. Lässt man die Tiere im wachen Zustand in Wasser plötzlich 
einfrieren, so sterben die meisten in extremer Kälte. Nur Rotatorien 
können schadlos überstehen und die Eier der Macrobioten. 

VII. Handelt es sich in den ersten Fallen, wo die Tiere im 
asphyktischen Zustand die tiefen Temperaturen ertragen, nur um 
eine Schädigung der Kälte als Wasserentziehung, die dem Austrock- 
nen gleichkommt, (s. Pürrrr, vergleichende Physiologie, Jena 1911, 
p. 385), so liegen die beiden zuletzt berichteten Fälle N°. V u. VI, 
doeh wesentlich anders. Hier könnte auch noch eine ‚mechanische 
Zertrümmerung der Plasmastruktur’ in Betracht kommen. 

Wirkt die Kälte langsam ein, so wäre es vielleicht möglich daran 
zu denken, dass die Kälte als Reiz wirkt, (sowie die beginnende 
Austrocknung des Mooses) in den asphyktischen Zustand überzugehen. 
Bei Fall VI scheint indes diese Erklärung nicht zuzutreffen. 


Zum Schluss habe ich allen Herrn vom Kryogenen Institut zu 
danken, die am Zustandekommen der Versuche mitwirkten. In 
erster Linie herzl. Dank dem Leiter des Instituts, Herrn Prof. Dr. 
KAMERLINGH OnneEs, der meinen Arbeiten so grosses Interesse ent- 
gegenbrachte und mir so grosses Entgegenkommen bewies. Herzlichen 
Dank auch dem Herrn Conservator Dr. CroMMEIJN, Herrn Dr. 
DroogreEvER Fortuyn, die mich mit Rat und Tat unterstützten, nicht 
zu vergessen Herr Mechaniker Fiim, der das Material bereitwilligst 
herstellte, und Herr Stud. Derarz, der mir beim Untersuchen half. 


Chemistry. — “The velocity of the diazotisation reaction as a contri- 
bution to the problem of substituiion in the benzene nucleus.” 
By Prof. J. BörseKeN, W. F. Branpsma and H. A. J. SCHOUTISSEN. 


(Communicated at the meeting of February 28, 1920). 


1. In regard to the problem of tbe substitution in benzene, the 
question has been considered whether only the group already present 
is decisive as to the place where the group newly introduced is to 
come or whether the nature of that new group too plays an 
important part. 

Supposing the last alternative to be right, one of us *) has projected 
the following scheme of the subsequent stages during the substitution, 
by which at the same time the answer was given to the question 
why in one case meta-, in another case para- and ortho-derivatives 
are formed by preference. 

If the acting molecule has an inclination to combine with group 
X of the benzene derivative C,H,X, then two courses may be taken: 

a. The acting molecule combines or reacts with this group; then 
no substitution in the nucleus takes place. 

6. The acting molecule has some inclination to combine with 
group X, which inclination however only tends to effect a shifting 
of affinity (electrones). In this case a change of condition will take 
place in the benzene nucleus, designated by him as a ‘“chinoid 
shifting of the affinities’, and which consists of an accumulation of 
attraction at the para and at one of the ortho places. 

If the acting molecule has no inclination to combine with group 
X, then no preference will be shown for ortho- and para-substitution 
and substitution of the meta H-atoms is sooner to be expected. 

The stress in these considerations is therefore laid on the affinity 
between the molecule to be introduced and the group already present ; 
an experimental illustration and eventually ‘a comfirmation of this 
theory may be expected, if quantitative data can be acquired on 
this reciprocal effect. When e.g. we could determine the rate of 


1) BOESEKEN: Koolwaterstoffen Il, (Hydrocarbons II, edited by WALTMAN, Delft) 
page 125 —127 and 134—137. See also these Proc. of March 30, 1912, 


250. 


eraction of an entering molecule with group X, then one could 
immediately trace the influence on this reaction velocity of the 
situation and of the nature of different groups in the benzene nucleus. 

If e.g. a group X directs substituents to the para- and ortho-place, 
it is to be expected that the rate of reaction mentioned above will 
be the most modified by groups already present in the ortho- or 
para-position and less by groups in the meta-position. 

If on the other hand we had a group X directing to the meta 
place, then the reverse would have to be expected if for the rest 
the acting molecule and the circumstances are the same. 

To this end we have in the first place selected the diazotisation 
reaction, viz. the rate of reaction of the NH, group with HNO,, 
partly as the NH, group directs to para and ortho in a very pronounced 
way, partly because HNO, will show a great similarity in its nature 
with HNO,, the reagent examined most fully by HorurmaN and 
his pupils. 

In this case one will have to take into consideration that the 
velocity of the diazotisation may also depend on the basicity of the 
“amine. For instance it is not at all out of the question that the 
reaction exclusively takes place between the free amine and free 
nitrous acid. Then this reaction will be the quickest with the weakest 
bases because their salts are hydrolysed in the highest degree. Now 
if the meta substituted amines are stronger bases than the para- 
and ortho-substituted ones, then the first mentioned would show a 
smaller rate of diazotisation than the last. As however the basicity 
can be deduced from data independent of the rate of diazotisation, 
its influence can be brought into account. 


2. About the rate of diazotisation of different substituted amines 
we meet with but a few investigations. 

The first studies go back to the research of Hanrzscn and SCHUMANN’). 
They estimated after different periods the quantity of unchanged 
nitrite by the reaction of Trommsporr (with zine iodide-amylum 
solution). As will appear later on, this method is too liable to errors 
to use it for determining the rates of diazotisation. Hanrzscx operated 
as follows: 

He mixed at 0° 500c.c. of a solution of the amine (*/,,, N. amine 
hydrochloride + '/,,, N. HCl) with 500 ec. */,,. N. nitrite solution; 
after 30 minutes he made the first determination. 5 cylinders each 
with 3¢.c. zine iodide-amylum solution and 1 e.e. H,SO, were filled 


1) Ber. 32, 1691 (1899). 


251 


up with water to 100 c.c. Simultaneously he brought in one of the 
cylinders 1 c.c. of a 0.001 N. nitrite solution and in the other four 
cylinders different quantities, accurately measured, of the liquid in 
the reaction vessel. The development of colour was then compared. 
However the colour does not appear instantaneously and therefore 
he did not compare the colour till after 15 minutes, though it still 
increases for some hours. 

It is clear, that in analysing each sample the diazotisation is not 
directly stopped; he allows the colour to develop in acid medium; 
the diazotisation continues and that with increased intensity because 
zine salts are still present, which notably accelerate the diazotisation’). 
Thus considerable errors are made. In this way it was of course 
impossible to Hanrzscu to examine the course of the diazotisation in 
the first stages of the reaction. At the same time it should be pointed 
out that his observations, as he diazotised in a weakly acidified 
solution will moreover be influenced by the formation of diazo-amino- 
compounds, which disturbance will vary according to the nature of 
the amine. 

The conclusions drawn by Hanrtzscu are as follows: 

1st. The rate of diazotisation is extremely great. 

2nd, Amines (aniline, p-toluidine, m-xylidine, p-bromaniline, p-nitro- 
aniline) are diazotised at equal rates (he ascribes differences to in- 
accuracies in his method) and he concludes from this that the 
presence of “negative” groups in the amine does not influence the 
rate of diazotisation. 

3rd, The rate of diazotisation is increased by the first excess of 
acid; however an excess of more than 1 mol. exersises no percei- 
vable influence on the velocity any more. 

4th, The diazotisation reaction is bimolecular and answers to the 
relation : 

1 wv 
i 
at a—w 

SCHUMANN °) has tried to affirm these results in another way. From 
the fall of electrical conductivity during the diazotisation, occasioned 
by the consumption of hydrochloric and of nitrous acid, he deduced 
the rate of the diazo reaction for some amines. In doing this he 
assumed the substituted aniline-hydrochlorides to have the same 
affinity constant, and the conductivity of the substituted diazonium 
salts to be the same*). Here some affinity constants follow: 


1) DLR. P. 171024, 172446, 175593. 
*) Ber. 33. 527. (1900). 
5) Ber. 28 1739 (1895). 
1% 
Proceedings Royal Acad. Amsterdam. Vol. X XIII. 


252 


hydrochlorides of: temperature 4 
aniline 25° 2.44 X 105 
p. anisidine . 8.08 « 10-6 
p. bromaniline AS 1.14 Xx 10-4 
p. chloraniline 258 8.56 « 10-5 
m. nitroaniline . 3.01 X 10-3 
0. 2 a a Bit 
p. 4 es 5 958% 1053 
m. toluidine 5 1:82 1078 
0 7 ss 3.45 X 10-5 
p. re 4 1:58’ 108 


He executed his determinations at 20° and the result was libera- 

tion of nitrogen and formation of free HCI: 
RN,Cl + H,O— ROH + HCI + N,. 

At the same time, as he could only work in a weakly acidified 
medium, formation of diazo-amino-compounds (especially at 20°) will 
take place. As SCHUMANN himself states, this amounts to several 
percentages in the case of p-bromaniline. Therefore also this method 
will not yield reliable results. 

After them Tassiur *) occupied himself with the study of the 
diazotisation reaction. He follows the progress of the diazotisation by 
determining after different periods the quantity of diazonium salt 
formed. This diazonium salt namely may be-coupled in weakly 
alcaline medium with ScHAFFER’s salt. 

Then he measures the solutions coloured from red to orange with 
the spectrophotometer of Féry in the green-blue part of the spectrum 
comprised between the marks 180 and 200 of the micrometer, 
(sodium line at 50) corresponding with 4, = 4500 and 2, = 4300. 
He sums up his results in the following conclusions: 

1. The diazo reaction is bimolecular. 

2. Increase of the quantity of acid does not increase the rate of 
diazotisation of aniline. 

3. The diazotisation of sulphanilie acid goes quicker when the 
concentration both of nitrite and amine is raised. 

4. The diazotisation of sulphanilic acid is accelerated by an 
excess of nitrite. 

5. The stability of the diazo solutions may be mutually com- 
pared by the help of his method. 

We cannot refrain from subjecting his treatise. (Bull. Soe. Chim. 
Jan. 1920) which gives a review of his researches, to criticism. 


253 


To begin with, in the first series of his experiments, which are 
meant to prove that the diazotisation reaction is bimolecular, he 
uses a nitrite solution containing 0,20 gr. in 1 L., that is a 0.0029 
normal solution, whereas theoretically (assuming the nitrite to be 
100 °/,) it should have been 0.0025 normal. This is too high by 
about 13°/,. As even the technically pure nitrite is 96 °/,, he always 
works with an excess of the nitrite in respect to the amine. Espe- 
cially his last determinations will therefore become erroneous. 

Casually we may point out that he finds after integration of 

ae = K (a—x)’ that: A= 5 : Elie 
dt ; t 100—2 

2 v 

100 ¢°100—z" 


while of course this ought to be K= So he finds 


K a hundred times too great. 

Further his determinations do not make the impression of being 
very accurate. He can read his spectrophotometer only to */, scale 
division. For the different amines a half scale division however can 
cause great divergences when we calculate in percentages. As appears 
from the table below, this may give rise to errors from 1'/,—11°/,. 


for aniline are |, 
i. p. toluidine cla) ee 
‘ 0. . lande 
sf m. xylidine Jeje 
x 0. anisidine See's 
Ë p- » Dele le 
»  p. nitraniline 3'/, °/ 
0. ‘i LO 
5 m. 55 HE naj 


The reaction constant of the diazotisation is calculated by Tassrr.ry 
‚rather arbitrarily. For instance for p-toluidine he derives it from a 
determination made after 45 minutes, however if considerably deviates 
from the K’s which we calculated from his determinations relating 
to other periods. If he had taken the average K, the agreement 
between the found percentage of inverted amine and the one cal- 
culated, would have been much better. 

He was more fortunate for p-anisidine. He found 0.142 for K 
after 30 minutes, while the average of the first four determinations 
gives K = 0.143. (See page 254). 

7 


[After | ivericd x | ie calcu- | K average x calculated cen 
lo. | lated by us | with K=0.060 K = 0.0695 

Zish beth Alle eer iv | | 10 | 12.2 
TN 0.076 | RR sf 
a0. Ven ds. 020 64 | “eee 

| 45 73 [o.oo] 0.065 = 73 | 76 
Gee vol vake 0.076 eer: | 80.5 
15 84 0.00 | 5 Ten 
90 | 8 0.064 hha. | 86 | 
300 | 100 ns 94 SE 


Now we have come to a diseussion of his results on the influence 
of an excess of acid on the diazotisation of aniline. 

TassiLy couples 10 c.c. of the diazonium solution, the acidity of 
which has been mentioned above, with 10 ec. of the ScHAFFER’s 
salt solution (containing 3 gr. of ScHArrer’s salt and 3 gr. of NaOH 
per liter). As a second experiment he couples 10 c.c. of a diazonium 
solution containing much more acid, with 10 c.c. of the same solution 
of ScHArrer’s salt. Now this diazonium solution contains per liter: 


100 ec. of the amine solution used, makes 0.21 gr. HCI 
moreover  #00''e.& 5 °/- HCl... Sier 
Total 5.21 gr. HCI 
The solution of ScHärrer’s salt contains 3 gr. NaOH per L., which 
ze = 2.74 gr. HCl. 

So the excess of HCl amounts to 2.47 gr. and consequently the 
coupling takes place in a solution, containing 1.235 gr. HCl per 
Liter; the diazotisation therefore can continue and the quantity of 
inverted amine will be found greater than was in fact diazotised at 
the moment the sample was drawn. From this we conclude that 
his experiments in regard to the influences of an excess of HCI on 
that rate of the diazotisation of aniline cannot be exact. 

As to his experiments on the influence of the concentrations of 
nitrite and amine together, as well as of each apart, on the course 
of the diazotisation of sulphanilic acid, we must call attention to 
the fact that Tassitiy tries to diazotise sulphanilic acid with sodium 
nitrite without the presence of HCI and that without a catalyser. 
He thinks he studies a quantitative diazotisation in doing this. As we 


therefore can neutralise 


255 


did not know examples from literature in which diazotisation in 
this way proceeds quantitatively, we have subjected his experiments 
to an examination. To this end we worked as follows : 

100 ee. */,5, N sulphanilie acid sol. were poured into a beaker, 
placed in melting ice. As a second liquid, a nitrite sol. was used, 
containing */,,,, gram-molecule NaNO, (controlled with KMnO,) per 
400 ee. Before the experiment was made both solutions were cooled 
to 0°; then they were mixed while being well stirred. After 90 minutes 
(TassiLLy finds 100 °/, amine inverted after 20 minutes already) we 
coupled 5 ec. of this solution with 5 ce. of the ScHArrnr’s salt 
solution as used by him. Then as much strong HCl was poured 
into the reaction vessel as was necessary to liberate the nitrous 
acid from the nitrite and to bind the amine. After 20 ‘minutes we 
again took 5 ee. and coupled them with the same ScHAFFER’s salt 
solution (5 ee). After 12 hours the colour was compared with that 
of experiment n°. 1 in the colorimeter (see next page); the colours 
were related approximately as 30: 100. So we may conclude that 
the diazotisation when HCI is absent, does not become complete. 
It is evident that because of this, his conelusions sub 3 and 4, 
based on his researches on sulphanilic acid have no great value. 

We see from the preceding that from the researches made till 
now, nothing can be deduced but that the diazotisation reaction 
proceeds quickly and is bimolecular. In spite of the -imperfections 
of Tassi_iy’s research, we thought we could follow his method if 
only we took care: 

1. that the diazotisations were executed under entirely equal 
circumstances. To this end care was taken that at all times a con- 
siderable excess of HCI, in every case the same, was present. 

2. that when adding ScHArrer’s salt, a sufficient quantity of 
alkali was present in order to stop the diazotisation with certainty. 

3. that the determinations were accurately performed. 

We attained this by making use of a simple colorimeter accord- 
ing to Worrr, after having ascertained that the resulting azo dyes 
complied with Brrr’s law in the dilutions used by us and that the 
estimations were not disturbed by the presence of amine not yet 
inverted. We proceeded as follows: 

In a beaker, placed in melting ice 100 ec. '/,,, N. amine hydro- 
chloride were poured, containing at the same time 5 c.c. HCI (spec. 
gr. 1.19) per Liter, in order to prevent the formation of diazo amide 
compounds and to set free HNO,. As the second liquid a nitrite 
solution was taken, which contained ‘/,,,, gram. mol. NaNO in 
400 c.c. (controlled with KMnQ,). Before the beginning of the experi- 


256 


ment both solutions were cooled to 0°; then they were mixed while 
being well stirred. So in 0.5 L. are present one millimol of amine, 
one millimol of NaNO, and about 6 millimol HCl. 

After different periods 5 c.c. samples were drawn with a pipette, 
which had been cooled to O° and coupled with 5 c¢.c. of a ScHAFFER’s 
salt solution (8 gr. of ScHArrer’s salt + 3 gr. of NaOH per L.); 
then an excess of alkali is present, so that the diazo reaction is 
brought to a stand-still. We executed the coupling reaction at 0° in 
order to evade every decomposition of diazonium compound. 

From determinations performed in the laboratory for Physical 
Chemistry of the Technical High School here at Delft, we knew, 
that at O°, even after 6 hours, we need not fear decomposition of 
the diazonium-compounds; this disturbance appears only at 20°. 
Below we cite some affinity-constants for these reactions, in which 
N, is split off: 


For aniline K3oe = 0.0064 K350= 0.0124 Kie = 0.0248 
te p. nitraniline Kase — 0.000869 Kige — 0.00136 
»  Sulphanilie acid Kygge= 0.0083  K51.7= 0.0078 Ks57= 0.0108 


From the coloured solutions, thus obtained after coupling, again 
5 ee. were measured and diluted to 500 ee. (with higher concen- 
trations Beer’s law did not hold good). Assuming the last sample 
taken after about 6 hours to represent 100°/,, we compared this 
standard solution in a colorimeter with the colours obtained from 
the samples after 2, 4, 6, 10 ete. minutes. In this way we could 
directly read the percentage of inverted amine. 

Finally it should be observed that we used distilled water for all 
our experiments, as water from the main possessed too much colour 
of its own. 

Below we give same numerical data. 


Average: 0.0928 


No. Rear nlite apne | 100 K. | No. After min.:) peer 
1. Aniline. | 2. m. Xylidine. 
1 2 17.4 Bios | il ek 28.8 
2 4 28.9 0.102 | 2 6 35.2 
3 r 36.0 0.094 = eae 42.0 | 
4 8 43.4 gol 4e 10 - | dee 
5 ie) a8 0.091 5 | 15 55.7 
6 is. leen 02090 6 | 20 63.0 | 
1 20 63.8 0.089 genes 12.5 
Bf 30 1.9 | 0.085 || 8 | 53 81.5 
9 60 85.9 | 0.102 || 9 | 989 ge 
10 105 alst ú: 1000 TD enne 34 | 
| 170 | e48 | 0.107 |u | 240 | 100.0 | 
12 | 260 100.0 | ee | 345 | 100.0 | 
Pee saa |=00.0) | = | | 
Average: 0.0965 Average: 
3. o. toluidine. 4. p. toluidine. 
| | i 
1 Mea) 18:2 0.102 1 5 26.5 
2 7 42.1 0.104 2 10 38.8 
3 12 52.0 0.090 3 15 51.2 
4 17 60.3 | 0.089 4 20, | 57.1 
5 22 65.9 0.088 Bee eRsÛ | 65.0 
6 30 73.6 | 0.093 6 40 | 12.5 
7 45 80.6 0.092 7 55 71.9 
8 60 83.3 0.083 8 70 80.9 
9 80 88.0 0.092 9 | 100 88.7 
10 | 110 91.3 0.095 10 | 130 91.7 
11 | 180 Bi che — ||| ee O72 
12 | 320 100.0 | — || 12 | 20 | 985 
13 360 oo |} = 138320 | - 4000 
| 14 | 360 100.0 


100 K. 


0.0886 


Average: 0.0687 


No. en min. (amine | 100 K. No. After min. ne aes 100 K. 
5. m-toluidine. 6. o-chloraniline. 
1 lek oet 0.135 EA MNM A 0.492 
2 4 | 36.0 | 0.141 elites On en 0.526 
3 ge ggg DAENS Le 71.0 0.478 
4 (0 el S6.Ro || <0 abet 4 13 | 86.0 0.473 
5 CRN NE 0.129 || 5 18 89.0 | 0.456 
6 25 76.5 0.130 6 26 | 98.5 | 0.474 
1 40 84.9 0.141 1 35 | 94.4 | 0.482 
8 4 | 93.2 0.146 8 50 96.8 1 
9 | 164 | 97.0 = 9 | 6 05 | = 
10 | 258 | 100.0 ns 1080 | 100.0 || 
u 380 | 100.0 sas (1 | 147. a) 1080 ES 
12 | 360. | 1000. | 
Average: 0.137 Average: 0.483 
7. p-chloraniline. 8. m-chloraniline. 
1 1 13.8 0.159 arl a | ssl Gn 
2 gee ne 0.161 Balu: 68 45.5 0.140 
Ba A B ore 0.161 3 8 51.6 | 0.14 
4 7 51.4 0.151 4 10 59.5 | 0.147 
5 Bt gph 6225 0.151 5 15 | 66.6 0.135 
6 15 | 69.2 0.150 6 20 12.5 0.132 
7 25 79.0 0.150 7 30 79.6 0.130 
8 45 87.0 0.149 8 GOD 0.122 
9 60 90.1 0.152 ot A20 | 924 = 
10 90 93.1 0.150 10 | 210 | 98.4 Be 
u a1 | 97.0 0.153 11 300 | 100.0 — 
12 | 271 100.0 5 12 | 360 100.0 2 
13 | 360 100.0 = | 


Average: 0.153 


Average: 0.135 


259 


No. \Aftermin: “i) Steg, 100 K. | No. After min.: verted. 100K. 

9. o-bromaniline. | 10. p. bromaniline. 

| | | 

De 12 48.28 | > 0405 OH ASB EN 28 0.130 
B 4 64.2 0.448 BUD Cet. aes 0.132 
ai 6 72.8 | 0.445 8 9 | 53.6 0.128 
4 8 71.9 | 0.440 Bih 12 vt 60.4 0.127 
Bey io vn stee). 0.440 BEG un 67.7 0.124 
BR as Dir verb ola BRD 25 Welk 461 0.128 
ee 20° 1e 901 | 0455 | 7 40 84.0 0.131 
6) . 30 93.2 0.456 8 55 88.3 0.137 
9 eyed. OF. 1 be. 9 | 121 94.0 0.129 
10 | 105 BU Me formes 180 95.7 0.124 
MR are ooo en oe ve 240 100.0 = 
el) aso tooo) — || 12 ao} 1000 = 
Average: 0.450 | Average: 0.129 

11. m. bromaniline. | 12. o-iodaniline. 
1 oel at's osn | ed 2 za | 0.445 
2 ai atc 0.154 | 2 4 62.8 | 0.422 
3 Gy, |) 47.8 | 0,137 | 3 TE 510 ge 0:48 
4 De EE HEL ee jo ee 96.0 ') 6.53 
5 zes 61.2 8) ob140 | 5 17 91.0 = 
6 16 68.0 | 0.133 | 6 27 G5." Bt! 
7 | 20 We-72-2° 8)" 0.130 | 4 45 Orig A 
a | 32 | e22 | 0.143 8 85 | 996 | — 
9 | 45 86.8 | 0.146 qian ee soe ol 
10 115 | 95.0 0;165' || 108 2E ca a a Je 
Bied 0.1L Gre OS ti aren AD 10070 ON AS 
Beke 300° odio Ut Ian | 00.0; ONG 

Gabe) Amst Âl 400:0° |S 2 I | | 
Average: 0.142 Average: 0.453 


260 


ST EA ES 


| : ‚| 0/9 amine | Pei | . | O/g amine 
No. (Attert inverted. 100 K. No. After min.: inverted. | 100 K. 


1} 


13. p-iodaniline. 14. m. iodaniline. 


! 21/, 29.3 2 Fula ote 23.4 | 0.488 
2 41, 42.7 0.165 | 2 A lar 318 0.152 
3 6 49.0 0.160 3 7 50.7 0.147 
4 10 58.9 0.143 4 10 59.5 0.147 
5 15 69.3 0.150 5 15 ole 000 Gn 
6 30 81.0 0.142 6 20 16.0 | 0.158 
7 45 86.5 0.142 || Hijo 30 ido BLD 0.151 
8 75 91.9 0.151 | 8) 45 87.1 0.150 
9 | 152 8.0 | — | 9-| 110 96.9 bh ae 
10 | 255 10010) | 10 | 178 93.0 4; ee 
11 360 100.0 _ Be at pe pees 100.0 | — 
12 | 400 100.0 aise vn 
Average: 0. 1505 Average: 0.1515 
15. Orthanilic acid. | 16. Sulfanilic acid. 
1 1 52.1 1.09 1 i ae noes 0.241 
2 2 65.1 0.93 2 2 33.0 | 0.246 
3 5 | 83.6 1.02 3 4 49.5 | 0.245 
4 7 87.6 | 1.01 || 4 6 els 59:6 0) ieee 
Bel 13 0.10 92-0 0.89 | 5 8 66.5 0.248 
6 \ 106 96.3 0.93 6 11 73.1 0.247 
ee 97.2 0.81 1 15 | 78.9 | 0.249 
8 | 58 98.1 0.89 8 25 | 86.1 -) ame 
9 | 180 99.5 11 duro AE 0.251 
10 | 240 ~~ 100.0 a 10 | 120 97.1 0.279 
11 300 100.0 | — 11 270 | 100.0 | — 
12 | 360 100.0 a 12 | 320 100.0 dr == 


Average: 0.966 Average: 0.247 


261 


. | . | 
No. After min. BO Sune IFoo RK. ND: Alter min, EERE Ter 


inverted. |. | inverted. 
17. Metanilic acid. | 18. Anthranilic acid. 
1 2 17.5 0.106 1 1 | 63.9 Lm 
a 5 33.4 0.100 2 2 | 11.2 1.70 
3 12 58.0 0.115 3 | 4 | 86.8 1.64 
4 ie hee 75.0 0.111 Ke 6; |. SE 
5 45 | 82.4 0.14 | 5 | 9 | 988 1.68 
6 60 | 86.1 Ertan | sheer Nis |} 06.50 | ine 
mi -90 | 90:4 0.105 gn 20 NN Ak 
8 | 114 | 92.6 0.109 8 | 30 | 100.0 — 
9 187 | 96.9 =S 60 100.0 | — 
fet 240 | ‘ooi — | 0 | 120 100.0 a 
1 | 300 | 1000 | — | u | 240 og ne 
B 360. oer 1000 — i 12 360. | = °100.02- | — 
Average: 0.107 | | Average: 1.761 
19. p-amidobenzoic acid. 1 20. m-amidobenzoic acid. 
1 Bi 56.2. | 0.570 | hee ned «305 0.145 
2 daat 671 | 0.510 ee ef | 50.0 | 0.138 
3 gekeoe 0.507 | Mand | 66.5 | 0.142 
‘ped fOrnd A,-5\84.5 0.506 | Ee zelle 1534 | 0.125 
5 15 88.3 0.503 | 5 38 82.6 | 0.173 
6 22 92.1 | 0.530 6 63 ioe. 
7 55 97.1 zE i 137 de 
Bao 122 99.5 =S ee 
9 ideen 400.0 = 9 255 100.0 = 
10 230 100.0 = 10 300 100.0 | — 
11 | 300 100.0 — || tt | 360 100.0 | — 
12 360 | 100.0 0 1} 
Average: 0.521 | Average: 0.145 


262 


iy fl 0/, amine | 
No. kad invented en 100 K. 


21. m-nitraniline. 


1 11), 57.0 1.06 
2 gi | 82.5 1.12 
3 6 | 87.5 1.19 
4 8 | 90.6 1.12 
5 10 91.8 1.04 
6 15 94.0 1.21 
7 20 96.2 (1.41) 
8 30 97.7 (1.83) 
deM eds LB En ES 
rohe 160 ike 25.4. hj eee 
1 95 | 100.0 = 
12 120 100.0 = 


Average: 1.13 


The following table contains a survey of the average values of 
the constants, while the graphs 1—-6 reproduce some of the series 
of observations. 


Velocity-constants of the diazo reaction: 100 K, 


C,H,NH, = 0.0965 o #p. (CH), C,H, NO = 0.0868 
o-CH;CsHyNH, = 0.0928 | o-CICsH,NH, = 0.483 | o-BrC,H,NH, = 0.450 
p- ni =0.0687 | p- i, =O153 pos » = 0.129 
m- i =0.137 | m- , =0.135 | m- , = 0.142 
o-I1,CgH4NHg = 0.453 | o-SO;HCgHyNH, = 0.966 Oo COOHC,HyNH2 = 176 
p- Ë =0.151 | p- 5 = 0.247 | p- 5 = 0.521 
Izer eh =0.1505 | m- 2 =0.107  m- 8 = 0.145 


From the results of our first series of experiments we have been 
able to draw the following conclusions: 

1. In coneordance with the researches cited above, the diazo 
reaction proved to be bimolecular under the given circumstances. 

2. When a group has been introduced into aniline, it will espe- 
cially influence the diazotisation velocity, if it is situated in the 
ortho-place; in the paraderivative the influence is less strong, in 
the meta-derivative it is commonly feeble (fig. 1, 2 and 3). 


— 0/, amine diazotised. 


— 0/, amine diazotisised. 


c) 


60 


20 40 


—> Time in minutes 


1. m-toluidine 
EKO a 
3. p- ” 

Fig. 2. 


20 40 


—> Time in minutes 


1. o-chloraniline 
2. p- ” 
3. m- 5 


— 0/, amine diazotized. 


20 0 


— Time in minutes 
1. o-amidobenzoic acid 


2. D- ” „ 
9. m- fi 5 


3. As appears from the figures 4, 5 and 6, the velocity of diazo- 
tisation increases with the negativeness of the substituent. 
Fig. 4. 


— 0/, amine diazotized. 


— Time in minutes. 
anthranilic acid 
orthanilic acid 
0-iodaniline 
o-bromaniline 
o-chloraniline 
aniline 
o-toluidine 


Oper E 


50 
5 
keb} 
ui 
= 
© 
Es <0 
2 
keb) 
a 
By ‘a 
3 
aS 
o 
‘i 20 40 60 80 io no 
—> Time in minutes 
1. m-nitraniline 
9. m-iodaniline 
m-bromaniline 
3 m-chloraniline 
“_) m-toluidine 
m-amidobenzoic acid 
metanilic acid 
5. m-xylidine 
Fig. 6. 
5 
keb) 
wm 
i= 
© 
N 
& 
ze) 
o 
a 
el 
G5) 
So 
o 


—» Time in minutes. 
1. p-amidobenzoic acid 
2. sulfanilie acid 


34 P ivdaniline 

j } p-chloraniline 
4, -bromaniline 
5. p-toluidine 


266 | 


We hope to collect further information by subsequent series of 
experiments (which have already been commenced) in which 
in the first place attention will be paid to the basicity of the amines. 

The last communication of Tasstnty (Bull. Soc. Chim. January 
1920) led us to the publication of these first results. 


Lab. for Organic Chemistry of the 
Technical High School. 


Delft, February 1920. 


Physics. — “On the Critical Quantities of Mercury in Connection 
with the Increase of the Molecular Attraction on Dissociation 
of the Double Molecules.” 1. By Dr. J. J. van Laar. (Com- 
municated by Prof. H. A. Lorentz). 


(Communicated at the meeting of May 29, 1920). 


1. Already twice I published‘) discussions of the critical quan- 
tities of mercury. Starting from the fundamental value 6, = 150.105 
holding for 1 gr. atom Hg (calculated from the densities of the 
solid halogen compounds) and the valueVa,=11.10—? derived from 
it (in connection with the critical temperatures of the said compounds), 
I calculated for mercury, assuming — what is confirmed in different 
ways — that this substance is quite or almost quite bi-molecular 
at 7, (cf. among others loc. cit. p. 9): 

Te = 1260° abs. (= 987° C.); pe == 192 atm. 

From determinations of the vapour pressure the pressure corre- 
sponding to 7’—1260° abs. was calculated < 204 atm. (loc. cit. 
p. 14). When 7, and p are both assumed to be unknown, the 
same vapour-pressure observations, on assumption of V a-=2>11.10-, 
yield for 7, the value 1242° abs., p, becoming = 187 atm. (loc. 
ene p. 15). 

In the second of the cited papers 1 made use of CorLARDFAU and 
Rivizrr’s later vapour pressure observations (1900), which go up to 
Se With be 149.105, Wa, = 107410" (for 1 Gr. atom. 
likewise determined from these observations), I now calculated (loc. 
cit. p. 144): 

Tr 472° abs. (—= 899° Chips 180 atin., 
while for D, about 3,8 was found. Through a simple calculation 1 
got at the same time the certainty that mercury is practically quite 
bi-molecular at 7, (ef. loc. cit. p. 139—140). 

The same value 6. =149.10-5 follows also from the limiting 
density 14,46 at the absolute zero, when 1,2 is assumed for the 
(reduced) coefficient of direction of the “theoretical” straight dia- 
meter. [I determined before 6,=120.10—5 per Gr. atom. for mercury 
itself, starting from D, = 3,77, calculated by Gupsere (le. p. 8)]. 


1) Cf. among others These Proc. 19, p. 6 (1916); 20, p. 138 (1917). Also Zeitschr. 
fir anorg. Chemie 104, p. 84 and 126 (1918). 
18 
Proceedings Royal Acad. Amsterdam. Vol. XXIII. 


268 


2. It appeared, however, more and more that the critical tem- 
perature of mercury lies much higher than 900° or 1000° C. 

Traupe and Tricaner found no critical phenomena at 1000° ©.. 
and Happen ') calculated 7’, = 1370° abs. (= 1097° C.), p. = 456 atm, 
from different observations. This would, therefore, be only 100° 
higher than my first estimation. W. C. Menzies *) came to 1275° C. 
(675 atm.), while it became clear from KÖNIGsBERGER’s experiments *) 
that the long sought critical temperature must lie above 1400° C. 
(1000 atm.). At + 1200° U. the meniscus becomes flat; only the 
liquid is luminous. Below 1400° C. there are seen small glowing 
drops, which rise from the liquid and fall back into it, or dissolve 
in the not-luminous vapour. At 1400° C. the emission of light of 
the liquid rapidly ‘diminishes, and the critical temperature seems to 
be near. 

Then followed Miss J. Bunper’s experiments“) giving determinations 
of density of liquid and vapour up to 1400° C. At 1400° C. the 
vapour was still quite transparent; “the distance of the mercury 
atoms, therefore, is still so great that the electron cannot yet detach 
itself from the atom, and can, therefore, not yet take charge of the 
conduction of the electricity.” At 1500° C. (one observation) ° 
there was still liquid mercury present. 

When the observed densities are represented in a 7'v-diagram, 
we arrive through graphical interpolation at 7, = 1400° C. about, 
or slightly higher, hence about 1700° abs. (1427° C.), whilst p, must 
be at the least 1100 atm. For the critical density about 4,15 is found. 


(GuLDBERG calculated 3,8). 


3. It is the question if this high critical temperature of + 1700° 
abs. can be theoretically justified. For this purpose it is required, 
as we shall see, to modify the values of 6, and Wa, for 1 Gr. atom 
of mercury somewhat. Instead of 10°6,=150 the lower value of 
about 120 must be assumed for it, while instead of 107” a.— 11 
it is necessary to assume 10 (hence 10*a,= 100 instead of 121). 

That at such a high temperature as 1700° abs. the values of a 


1) Ann. der Ph. (4) 13 (1904), p. 340 and 620. 

2) Am. Chem. Soc. 35 (1913), p. 1065. 

3) Chem. Zg. 36 (1912), p. 1321. Cf. also RorinJANz and SucHopskI, Ann. Inst. 
Pol. P. le Grand 23 (1915), p. 668. 

4) Physik. Zeitschr. 16 (1915), p. 246; 19 (1918), p. 410. 

6) Neither KÖNIGSBERGER, nor Miss BENDER state clearly in what way their 
observations of the temperature have been made. This remains in my opinion the 
weak point. 


269 


and 6 will be smaller than those which have been determined at the 
critical temperatures of the mercury-halogenides (which temperatures 
lie in the neighbourhood of 1000° abs.) is, indeed, to be expected. 
For it is known that 6 and a decrease with increasing temperature. 
But there is still something else required. If such a high critical 
temperature and pressure is to be reached, the double molecules 
must be dissociated at 7. to a slight amount. As at this dissociation 
the value of a is greatly increased (10°/a, becomes 40 per Gram- 
atom of the isolated atoms as against 10 in the double molecules), 
the calculation (which we shall give in the second part of this paper) 
shows that, even in case of a slight degree of this dissociation, in 
the formula a pretty large factor will appear for 7’. on account of 
the large value of da/dx, which will increase the value of 7. by 
abont 30°/,, and can consequently raise the value of p. to more 
than four times the amount of the original value (Cf. also § 8). 
Hence it is not because in consequence of this slight degree of 
dissociation «w the value of a, itself is appreciably increased, and 
consequently 7, and pe (which are both proportional to a,) are 
likewise increased in the same degree (for this the increase of a, at 
so slight a degree of dissociation is much too small) — but because 
in consequence of this dissociation, tz connection with the very high 
value of da/dx, the formula which expresses 7, in a, obtains a 
factor that is a function of « and da/de, and through which 7, is 
increased by the said amount of e.g. 30°/,, even though the disso- 
ciation of the double molecules is only slight. And im consequence 
of this factor in 7, the formula for 
Tedd g dc 


Vick be be 


Pe == 


will undergo such a modification that p‚ is not increased by 30 °/,, 
but by more than 300 °/. | 

Thus the extraordinary circumstances connected with the critical 
temperature and pressure of mercury have induced me to extend 
my former theory concerning the critical quantities on association *) 
for the special very important case that a is considerably increased 


1) Arch. Teyler (2) 11, 3e Partie (1908), p. 1—96; These Proc. 17 (1914), p. 598 
We remind the reader that the mere fact of the dissociation at Te (hence Ab and 
A@=0) causes the values of 7 and pc to increase considerably. Thus we found 
for x=!1/, already an increase of 10,6%, for Tc; for x="/g of 11,5 °/), and for c=?/, 
of 9,9°/, (for «=O and « =1 the factor is of course = 1), Le. for ideal snbstances. 
For “ordinary’ substances and for the cases that in the association e.g. Ab is 
not = 0, these amounts are considerably increased. And as regards pc, these 


or 


270 


in consequence of the dissociation of the double molecules. According 
to my recent investigations, this case is met with everywhere where 
the dissociation (as for He,) leads to free atoms, for which the 
increased attractions of valency are so enormously much greater 
than for the compounds *). 


4, Vapour Pressures and Values of the Vapour Densities D,. 


We shall start with the treatment of the experimental material 
known at present. To supplement this, it is however necessary 
approximately to know the values of D, (the density of the saturate 
vapour). But for this purpose first the values of the vapour pressures 
must be known insapproximation. 

When the critical temperature is -assumed°—= 1427° U. = 1700° 
abs., and p,==1100 atm., then follows from the known formula 


Pe Ï 
lon == 
: a uC ) 
at 100°, 200°, 300°, 500°, 700° and 880° C., where p resp. = 0,28 mm., 
17,2 mm., 246 mm., 8 atm., 50 atm. and 162 atm.’): 


f= 1582.4, 81. 1,80... 178i, BOD: 


increases become resp. 47,7, 54,3 and 47,6 0/, for ideal substances with the same 
values of x. Hence already on an average 50 °/, between 2 =!/; and x = 2/s, 
which amount is still considerably increased for ordinary substances, and for the 
case that /b is not = 0. 

But when besides ,@ is so enormously large as in mercury e.g. (formerly we 
always supposed Aa =O, because we had only to do with substances that do not 
appear as isolated atoms with the so greatly increased attractions of valency), Te 
and especially pc is increased in a still much greater degree, even though the 
value of x be only slight. 

1) These Proc. 18 —21; especially 21 (1918), p. 644. Cf. also Z. f. anorg. Ch. 
104, 56 —156 (1918) and J. d. Ch. Ph. 16 (1918), p. 411. 

2) pe = 1150 atm. instead of 1100 atm. would give 1,83 for the first value of 
f, 1,80 for the last, which would render the almost constant course of this quantity 
still slightly better. The more pc is assumed to be below 1100 atm., the greater 
the unjustifiable decrease of the f-values on rise of the temperature. The value of 
1100 atm. is therefore to be regarded as a minimum, and pe will sooner be found 
somewhat greater than this amount than smaller. We remind that the course of 
the values of f is a strict criterion for the determination of the critical pressure. 
For in the neighbourhood of the critical temperature these values always increase 
on rise of temperature; for ordinary substances there is a minimum at about 
T=3/, Te; for substances as He, Hy, etc., where a continually decreases instead 
of increasing at falling temperature, f will also continue to decrease from 7, to lower 
temperatures, without passing through a minimum. (Cf. also Recueil des Tr. Ch., 
N°. Bland 5 of 1920), 


271 


With f,,=1,8 (f=414)') and p-=1100 atm. the following 
values are further calculated for the temperatures above 880° C. 
oge 10009 P1000 1200°sFIS00e > 14005 T LAZ NE 
pre Wil 274 410 581 187 1029, 1100 atm. 
We can now easily calculate the values of D', from the subjoined 
values of the vapour pressures, on the supposition that the vapour 
is and remains monatomic, and besides continues to follow the laws 
of the ideal gases. 


| a | ome | See 
100° C. 0,28 mm. | 0,000 ©  — = 
gone et? ah 0,0001 = a 
250° TAs ae 0,0005 = = 
300° 246 0,0014 En = 
350° ionen 0,0034 38 fa 
400° 2,06 atm. | —_0,0076 ns = 
500° 8,01" 0,0253 a = 
600° 223°, 0,0624 = ae 
700° KORE ae 0,126 En x 
g00° 1025 0,232 = = 
900° igs 5 0,356 Ls = 
1000° zal ie 0,526 0,55 1,05 
11002 Ee 0,730 0,80 1,10 
1200° ET wih 0,964 1,15 1,19 
1300° Pe, 1,222 1,65 peas 
1400° leden |. 1503 2,60 1,73 
T= 1427° 1100 = p, | 1,581 (4,15) =D, 2,62 


The “found” values of D, have been graphically- interpolated 
from the following values of D,, determined by Miss BENDER. 
£0502 1210°. 1280° 1295 MES 0Re aso" C; 
D010 1,15 1,35 1,65 190 2,50 


1) It appears from this value of f that — at least at temperatures below 
10009 CG. — mercury behaves almost as an ideal substance (for them fe = 4, and 
f <4 below T). 


272 


The “calculated” values of D, have been determined from v, = 


RT 
= RT: p tor 1 Gr-atom, henee wr THS 22415 em’ for 1 Gr., 
when p is given in atm. and R=1: 2738.1. Hence we have: 
p 200,64 Ps 200,64 


D', == X a = 


ie 
Le == K ——_ = — 2,444, 
on ae tae 2D 82,08. 2 X 


It appears from the value at 1000° that at this temperature the 
vapour is still mon-atomic, and the deviation from the law of Borre 
is still very slight. The deviation increases more and more, and 
close to the critical temperature the vapour will be almost bi-molecular 
like the liquid. As D(calc): D(found) is about 2,6 at 7, the 
deviation from the law of MariortE would be there about 2,6 : 2=—=1,3. 
In an ideal substance s = 2,67; in an ordinary substance s = 3,8 
to 4+. We see therefore, that the normal value of s is very consider- 
ably decreased in consequence of the greatly increased value of p‚ 
through the small dissociation of the double molecules at 7,. Also 
the values of v, and 7, are modified by this, but not in the same 
degree as p‚. The result is accordiugly that, whereas p, is more than 
four times greater than the normal value in case of non-dissociation 
of the double molecules, s will be about 3 times smaller than the 


normal value 3,8 to 4, i.e. 1,3. 
We shall discuss this more at length in ó 8. 


5. The values of D, and D, + D,. 


We now proceed to the values of D,, i.e. those of the liquid 
densities. At the same temperatures (to which three more tempe- 
ratures below 100° C. have been added) the following values are 
found. The “found” values of D, + D, (see table following page) 
have been obtained by addition of the above found values of D, to 
those of D,. 

The “found” liquid densities D, above 350° C. are graphically 
interpolated from the following values determined by Miss Brenner. 

500° 600° 800° 900° 1000° 1100° 1130° 1200° 1270° 1320°C. 
DD, = 12,5) 12,15: 11,6511,15;, 10,55 1050. 79:40 TPS eon aoe 7,8 

As regards the “calculated” values of D, + D,, they were calcu- 

lated from O° to 350° from 


D, + D, = 13,5956 —0,0024507 t + 0,0,2089#2, . . . (a) 


in which the coefficients of ¢ and t° were calculated from the 
observations at 150° and 300° C. The calculated and the found 


273 


t D, (found) D, (found) et | D, + Ds (calc.) 
(trip.) — 38°,85 C. | 13,6902 a 13,6902 «13,6911 
oe | 13,5956 | a |_ 135956 | 13,5056 
50° 13,4733 Ee | 4134133 | 13,4736 
100° | 13,3524 | ia | 13,3524 | 13,3526 
150° 13,2327 | = | 13,2327 13,2327 
200° 13.1139 __(0,0001) | 13,1140 13,1138 
250° 12,9957 (00005) | 129962 \__ 12,9960 
300° 12,8778 (0,0014) | 12,8792 || 128792 
350° 12,7640 | (00034 «12,7674. «12,7635 
400° 12,65 (0,008) 12,66 12,66 
500° | 12,425 (0,025) 12,45 het OAS 
600° | 12,18 oost!) 122 | 12,24 
700° | 11,90 (0,13) 12,03 12,03 
800° 11,60 (0,23) 11,83 11,80 
900° be (0,36) 11,51 11,48 
1000° 10,55 0,55 | 11,10 11,12 
11009 | 9,90 | 080 | 1070), |) 10,69 
1200° ie 900 0 on 1015 10,15 
13000 | 7,80 bs! aes | 9,45 | 9,46 
1400° | 6,00 2,60 | 8,60 8,58 
14270 | @5)=D, | 415) =D, | (30) | 830 


values are in good concordance with each other; at 350° a small 
deviation begins to appear. At — 38°,85 the deviation is still exceed- 
ingly slight. The fictitious value D, at the absolute zero ({ == —273°,1 
is found = 14,2804 = 14,28 (if the mercury were still liquid then). 

For temperatures above 350° C. another term must be added to 
the above formula. As this formula yields somewhat too small values . 
from 400° to about 835°, and on the other hand to an ever increas- 
ing degree too large values above 835°, the term 


4 bes Nn als 
16,4.10—6 (zo) 8,35 a 100 6 tae Shoe sees is : (6) 


274 


has been added to (a) from 400°.) The calculation teaches that the 
deviations from the found values are least, when the exponent of 
the first factor (viz. ¢:100) amounts to 4, and that of the second 
factor to */,. Every modification in one of the exponents immediately 
gives not only greater, but much greater deviations. *) Here follows 
a survey of the values of the two parts (a) and (6), from 400° C. 


(a) (6) 

400° C. | 12,6486 + 0,0112 = 12,6598 = 12,66 
500° 12,4225 + 0,0230 = 12,4455 = 12,45 
600° 12,2004 + 0,0376 = 12,2380 = 12,24 
700° 11,9825 + 0,0490 = 12,0305 = 12,03 
800° 11,7687 + 0,0334 = 11,8021 = 11,80 
900° 11,5592 — 0,0807 = 11,4785 = 11,48 
1000° _ | 11,3538 — 0,2290 = 11,1248 = 11,12 
11009 _ | 11,1526 — 0,4598 = 10,6928 = 10,69 
1200° _ | 10,9557 — 0,8063 = 10,1494 = 10,15 
1300° 10,7627 — 1,3050 = 9,4577 = 9,46 
1400° | 10,5740 — 1,9985 = 85755 = 8,58 

= 8,30 


1427° | 10,5238 — 2,2254 = 8,2084 


The first table shows clearly that the thus calculated values are 
in perfect concordance with the found values. As we have calculated 
the coefficient 16,4.10-® of the correction term (6) exclusively from 
observations up to 1300° (inclusive), the agreement at 1400° C. is 
the more valuable. We may, therefore, safely assume the calculated 
value 8,30: 2—= 4,15 to be accurate for the critical density. 


6. The Value of D,—D, near T, and that of y at different 
Temperatures. 


We have another means to control the approximate correctness 
of the values of D, and D, e.g. above 900°, and of that of the 


1) Below 400° the correction term (b) is no longer valid. For 300° it would 
yield + 0,0041; for 200° + 0,0009 and for 100° + 0,00006, which values are 
too great. 

*) We point out that the exponent %3 is assumed not to influence the sign of 
8,35 — t/jo9, so that this remains negative for ¢ > 835°. 


275 


assumed critical temperature (1427° C.), viz. in the empirical Jaw 
that below 7, (not immediately below T,, however, where 


D—D,:..V1—m), the equation 

i) ks En 
holds in approximation, so that (D,—D,)* is proportional to 1—m, 
ie. to 7,—T (n=T: T.). Now we get the following table 


1000° | 1100° 1200° | = 1300° 1400° 


D-D;= | 10,0 Od | Areas 6,15 (3,40) 
(D:—D,)3= | 1000 754 484 233 (39) 


so that the four first values of (D,—D,)* are roughly to each other 
as 4:3:2:1, which would give the value 1400° C. for 7%. 

The corresponding values of (D,—WD,)? are to each other as 
100: 83:62:38 (:11,6), ie. as 5:4:3:2 about, which would point 
to T,=1500°C. And as (except close to 7.) the B~-law is sooner 
fulfilled than the P~-law, 7, will lie nearer to 1400° than to 
1500° — in concordance, therefore, with our assumption (1427°). 
A critical temperature higher than 1500°, as would follow from a 
few values recorded by Miss Benprr, is in my opinion in conflict 
with her own observations concerning D, and D,. When the two 
last values of (D,—D,)*, viz. 38 and 11,6 are taken as criterion of 
the ~-law, holding theoretically near 7, then the value of about 
1440° C. would follow from this for 7. 

Let us now examine the (reduced) coefficient of direction of the 
so-called straight diameter. For the total course between the absolute 
zero and the critical temperature evidently 2 (1Q—y) = 14,28:4,15= 
= 3,44 is found, hence 1+ y—1,72, y=0,72. But this amount 
can only be assigned to the last piece between 1000° C. and 77, 
where — in consequence of the increasing association in the vapour- 
phase — the straight diameter after its almost linear course between 
— 40° and + 1000° C. suddenly begins to show an appreciable 
curvature towards the side of the large volumes. 

As regards the said part below 1000° (where the vapour phase 
is still absolutely without influence), we find there e.g. between 0° 
and 300° C.: 

13,5956—12,8792 1700 


iio ETC. eS VEA 


300 4,15 


== 0,9782, 


hence y = 0,489 = 0,49. 


276 


And between O° and 1000° C.: 


13,5956 —11,1248 1700 
oy= Sf ee 
1000 4,15 


hence y = 0,506 = 0,51, almost equal to the value between 0° and 


300° C. The value y=0,5 is that which is due to “ideal” sub- 
stances with a and 6 invariable (chiefly 6 no function of v). We 
saw above that below 1000°C. also the value of f (viz. 4,1) points 


to the quasi-ideal behaviour of mercury at those comparatively lower 
temperatures. 


7. General Formulae for v,, T., p,. and s. 


When wv, is the critical volume (expressed in normal units) of 
1 Gr. atom, then. 


__ 200,64 
rt Aen 
hence with D= 4,15: 
200,64 
ve = rbe = — (002157 ~~ ae (1) 


AAT eN 


Accordingly the value cf 6. with given D, will only depend on 
yr. If e.g. r= 2, then 5, would be —= 108.105, but if r should be 
=— 1,8, 6. would become = 120.105. 


8 a! 
For 7, holds the relation RT, = X0, hence 
Ve 
: 
RT) a oe ee Ee 
Ales 


in which a, and 6, refer to 1 Gr. atom (200,6 Gr. mercury), so 
that in reality a', =n?a, and b'.=n6,, when n = 2: (1 +2) repre- 
sents the factor of association *). 

In normal cases (n—=1 or 2) @ is a factor somewhat smaller 
than unity, which we before represented by 2. (If e.g, r= 2, we 
find for 2 the value *7/,,, whilst for ideal substances (r = 3) 4 
becomes = 1). 


1) From 1 single molecule (or atom) = !/, double molecule */3 (1—a) + '/. (22) = 
ly (1 ++) molecules arise on dissociation of the double molecule. These molecules 
occupy the molecular volume b, (leaving contraction out of account; this has been 
reckoned with in the factor 6), so that every molecule on an average occupies thé 
volume 0b’. = be: '/, (1 + x) =b-*X2:(1 +2). If the degree of dissociation x of 
the double molecules = 0, then n = 2: (1 + x) = 2, hence bc = 2b, (all the molecules 
are then double molecules). And when «= 1 (all the molecules single), then” = 1 
and b’, = be. And the same thing holds with regard to Va and v. 


277 


But in all cases of association (n > 1 <2) @ will be a function 
of x, and besides of the contractions Ab and Aya, if they exist. 
As we stated above, this factor can become pretty large, e.g. 1,3. 


BT, aie . . 
Pron), ———— anai —, after substitution of the above-mentioned 
Ve Ve 
Maloe of 27, and of Vv, = nv De nb a= Hd, we find for ps: 
j “Gs, 84 21 Fe ee! ac 3 
ome ea oe ee 75 eet enc 


when besides 7}, is substituted for v. Then with »=2 the factor ar 
Be Oe en We eae ati bm 
nx) just as 


becomes therefore = 


1 
0, the factor of RT, — i.e. in the normal cases (n = 1 and 2). And 
8 27 
if then r=8, in which 6=1, then a becomes also = IT ie 


But for n>1< 2 a will again be a function of z, Ad and 
Ava, and in general much greater than @. If e.g. 6 = 1,363 (see 
§ 8), r=2, then a becomes — 10,91—6,75 = 4,16, so that a is 
more than three times as great as 6. The critical pressure will then be 


28 
416 = 4,3 times greater than the normal value for 7= 2, when 


there is no association, in which case a = 6 ==". 1). 
From (1), (2) and (3) the following equation follows now further 
Wit ve = 2ve— n X roe: 


RTS 8256 
gh ee EN 
PeVe 1 a 
in which s’ =s:n (where s refers, therefore, to v. per Gr. atom). 
Now we do not find rs’ = 8 as in normal cases — but 
0 | 
re =S AEN oe een 
IU 


in which 6: can be '/, in some cases (see above). In consequence 
of this s’ may be reduced from 4 (the normal value for r= 2) to 
4:3=1,3, ie. to the third of this normal value. (See the table in 


80 rat) 
1) We found before that in normal cases 6 =z. Then 6 See Aah from 
r— r 
2, : : . : 
which A=6= ce Ca When in this (l +): is substituted for r, in 
:(r—1) — 


which y represents the reduced coefficient of direction of the straight line between 


8y—1\y+1 
derived by me, yielding A=1 for r=3(y =0,5) and A = 27/9. for r = 2 (y = 1). 


27 2 
De and !/, Dy in a D,T7-diagram, we find back A= ( u ) , the formula 


278 


§ 4, in which we found for D, (found): D, (Mariorrr) the value 
2,62 : 2 = 1,31, when n is practically — 2 at 7. The great decrease 
of s’ is, therefore, almost exclusively owing to the exceedingly great 
increase of p. with comparatively little changed value of 7’, and of 
Ve. (the latter in consequence of a slight modification in the value 
of 7). 


8. Calculation of 46 and z, and of a. and b, from the 
given Values of Tp, and v.,. 


If 7, = 1700. (abs.), p, = 1100 (atm), and: », Son 
according to (1), we find for s/ =s:n the value (cf. also the table 
in $ +; on the supposition, therefore, that n at 7’, is not far from 2): 

1700 : 273,1 
* = 1100 X 215,7.10-5 
From (4e) follows for 0, the coefficient of RT, from 
84 


-3=1312 .”. > a 


the value 
07 27 s' 
6= we ee 


1 1 rs 
en ( -=) sr — 1) 
aoe ee y—l 


With s’ 1,312 we find from this the following values for dif- 
ferent values of r. 
r=2 io 1,8 157 1,6 1,5 
0—1,368 1,317 1,260- 1,194 -1,108 1,005 
The factor 4 becomes, therefore, smaller as » is assumed smaller, 
which also follows immediately from the formula (0), if only 7< 3,05, 
which is of course always the case. It also appears from (6) that 
6 becomes smaller, if 2 should be < 2, for then s’ = s:n becomes 
greater. 
Then is found for the factor z at pc: 


86 27 
SSS See oe (c) 
rs rs 
r—] 
yielding 
ae 1,9 KB lee? 6 mes 


wv =4156 4.9965 LIGA ATL ET 
Hence the factor a increases with decreasing 7, as long as r 
remains >1,74 (a = 4,277). For smaller values of a decreases 
again. 


279 


As@=1,36 is rather great, r=v,: 5. will probably lie in the 
„neighbourhood of 1,8 or 1,7 for mercury at the critical tempera- 
ture |as we shall see from the theoretical concluding part of this 
paper, this decrease is also a consequence of the degree of disso- 
ciation, however small, of the double molecules at 7, as soon as 
Aa is great). Then @ is 1,2 or 1,25 and a in the neighbourhood 
of its maximum value 4,28. 

Let us now examine the values of a, and 5, corresponding to 
the assumed critical data 7, =1700° abs., p‚ = 1100 atm., v, = 215,7. 
10-5) for different values of r. 


8 27 27 
From R7T.v,.= aa nrda-. X< 6 follows ac= 5 RT wvenr a= a X 
X 134,38.10-4:n7r6,s0 that 10* a, = 226,6: #0, when n—= 2. 


With regard to 6. we have simply be =ve:r; hence 10° be= 215,7:r. 
This gives the following values of a. and 6,. 


SS SS 


| r= | 2 ou ae ks 1,7 gine 
| | 
105 b. = 1079) tel), dl 119,8 126,9 134,8 ie 143,8 
104 a, = 83,13 90,57 99,91 111,9 121,8 | 1503 
102 Va, = 9,12 | 9,52 10,00 10,58 11,30 | 12,26 
We see from this that with »=1,8— in harmony with the 


slight degree of dissociation corresponding to the increased critical 
‚ pressure and temperature — the values 10°b, = 120, 10*a, = 100 (per 
Gr.atom) are about corresponding. Wa is then somewhat smaller 
than the value determined from the mercury halogenides at about 
mou C., viz. 10:.10—*instead of 11°. 10-2: 

By the aid of these values of a, and 6, we shall now calculate 
back the values of 7, and p. by way of check on two suppositions. 

In the first place that mercury were not dissociated at the critical 
temperature, i.e. consisted merely of double molecules (x = 0, n = 2). 
If we then suppose that 7 = 2, we should get in this case ve == rbe = 2 Xx 


8 
pot 9-9. 10-9 == 339.6. 105 (per Gr.-atom).Further RT, = a KOBE 


BON LOE 2 

198. 10-5 5 05 \ 38 28’ 
hence 7 = 4,766, 7, = 1302° abs. The following equation is then 
found for pe: ced 


‚as = 4 = 27/28 corresponds to r = 2 (see above); 


280 


1 99 O1, kO A WZ 
Des 57 ie 143,5. 105 pd 28 = 248,6 = 249 afm: 

With the now assumed values of a, and b. these would be the 
values of the critical temperature and pressure of perfectly undis- 
sociated Hg, at the critical point. They would give for 

4,766 
—_—_______________ — 4,00, 
248,6X479,2.10-5 al 
which value properly corresponds to r= 2. 

The equation of state is, of course, also identically satisfied. For 
dn ARE 
De is calculate 574,1.10-8 
: (Pe + Gc/V-?) becomes: 


8 SHI. pete With, = 24, the values == 


= 1740 atm., so that v'—é'..= RT: 


4,766 
(2300-1198) JOP 
248,6 + 1740,3 
i.e. 239,6 . 10-5 = 239,6. 10-5. 


We may state here that a,/v,” is also properly =(f.—1) pe = Ip. 
because /, = 8 corresponds to r= 2. 

But all these values are totally changed, when only, in the second 
place, the slightest dissociation of the double molecules exists at 7, 
(which we shall further develop theoretically in the second part of 
this paper). 

Let us suppose for convenience that then m remains = 2 (a will 
possibly be 0,01, so that strictly speaking n= 2:(1+ 2) would 
become 1,98, but in the calculation of 6 and a above we have also 
left n=), and further that in this case in consequence of the 
slight dissociation at 7, the value of » would have become 1,8 
instead of 2 (this too will be further elucidated in the second part); 
then v, becomes == 1,8  119,8* . 10—5 — 215,7.10—5. Further with 
6 = 1,260 and a = 4,268 (see above) RT = 6,228, 7 — 1700 abs., 
pe = 1100 atm., al! of them being the values from which we have 
started for the calculation of the factors 6 and a, and which will 

6,228 
1100 x 481,4.10-5 


give back the value 1,312 for s’ = 
28 
Accordingly the value of 7. has become 27 xXx 1,26 == 1,31-times 


28 
greater, that of p‚ 57 X 4,268 = 4,43-times greater, and that of s’ 


3,05-times smaller. 
The equation of state becomes in this case: 


281 


2 (215,7—119,8) Teenie eae on 192. 0 STINO, 
| 1100 4+ 2147 

Now a,/v.2 is no longer = 7 p-, but only slightly less than 2p,. 

In the above discussion we have always supposed m in the neigh- 
bourhood of 2. It might, however, be asked, how high e.g. 7, might 
become, if n was in the neighbourhood of 1. As )/a- would then be 
— 40.10—? (increased attraction of the isolated atoms) instead of 11 a 
10.10—-*, we should get (6 remaining = 120. 10-5): 

8  1600.10-4 


T, = 278,1 X — A—_—__.. = 80,92 4 X 133,8 = 10000° r 
c 97 190.10~6 X about 0° abs 


whereas in reality 7, will certainly not be far from 1700° abs. 
Total dissociation of Hg, into Hy + Hg is, therefore, impossible at 
the critical point. Only a value of 2 in the neighbourhood of 0 (n 
in that of 2) can represent the critical quantities as determined 
experimentally. 

In this first paper we have only specified the experimental data 
known at present more closely, and drawn from them all the conse- 
quences to which these data gave occasion. /f really v = 216. 10-#, 
T,=1700° abs. and p, = 1100 atm. — and there is no longer 
any doubt that this will appear to be the case approximately — 
then belong to the values of 7 mentioned in § 8 the values of 6 and 
a placed under them, viz. the factors for RT, and p, in consequence 
of the small degree of association at 7, in connection with the very 
great value of Ay/a. And this on the strength of the relations derived 
in § 7, which are of general validity. 

But this is only the foundation of our real task. To supplement 
our former theory of the critical quantities on association, we must 
now examine theoretically what follows, in the case of such great 


a d 
values of Aj/a on dissociation, from 7 (amd f= 0, and derive 
0) LU 


the relations which are valid for 7 = v,: 6, and also for 6, the factor 
ot. all in function of the degree of dissociation z and of Aya. 
Then the value of zr, the factor of p., is known at the same time. 

And then we shall also be able, on account of the found 
formulae for r and @, to define more closely the values of them; 
which was not yet entirely possible in this paper, because the choice 
between different values of 7 had still remained open. 

La Tour pres Vevey, spring 1920. To be continued. 


I state with pleasure that the execution also of this work has 
been greatly facilitated by the aid of the Van ’r Horr-fund, for which 
] express my thanks to the -board. 


Physics. — “On the Critical Quantities in the Case of Association, 
when the Molecular Attraction is considerably Increased on 
Dissociation of the Molecules to the Isolated Atoms, also in 
Connection with the Critical Quuntities of Mercury’. II. (Con- 
clusion). By Dr. J. J. van Laar. (Communicated by Prof. H. A. 
LORENTZ). 


(Communicated at the meeting of June 26, 1920). 


§ 9. General Relation for the Degree of Dissociation x 
of the Double Molecules. 


If Z is the thermodynamic potential of the mixture of double and 
single molecules, then it may assumed to be known that’) 


Zn Gant. — fp ae + pe + RT (n, log n, + n, log n,), 


when n, and n, represent the number of molecules resp. of the 
single and the double molecules, and C, and C, are given by 
C,=— hk, T (log T—1) + (,), — T (51), 
C,= —k, T (log T—1) + ©), — T @,). 

In this &, and &, are the capacities of heat at infinitely large 
constant volume, (e,), and (e,), the constants of energy, (s,), and (s,), 
the constants of entropy of the components. 

With equilibrium between the two components we have: 


u =D Os es, ee 
OZ 
when u, and uw, represent the two molecular potentials (viz. g, =a 
i 
0Z 
and fi, == or) of the components. [u,‚ refers, therefore, in mercury 
n, 
to 200,6 Gr., uw, on the other hand to 2 x 200,6 Gr. he Now 
0 
= = 4. RT (1 + log (n,+n,)) + RT log c, | 


u, = C, — : + RT(L + log (n, + n,)) + RT loge, 


as 6.2. Ee (n, logn, +n, log n,)=1 + log (n‚ dn) + log —_—-=1+ 


ms ER 


1) Cf. among others Arch. Teyrer (2) 11, gième Partie, p. 1—97 (1908). 


283 


+ log (n, + n,) + loge,, while w has been written for [ pao—po 
Hence (a) becomes: 


dw 1ldw R ET 
(C,—'/, C) zes | +4 RT (1+ log(n, +2,)) + HRT log —=0. 
On, 2 On, e. 
Further evidently n, ='/, X 2w =«, n, = '/, (1--2), because from 
1 single molecule ='/, double molecule arise '/,(1—.x) double 


molecules and '/, < 2a single molecules. 


N Ow ae dn, ee dn, Ow 10 ee | 
yom: ~ On, dn, —~ On, 2 On,’ Ban a 
dw ¢,” 
(OC) — = + 4 RT (1 + log 4 Cl + a)) + RT bog + —0, 
« on 
1.€. 
dw 
100, Deed de 
a ar tr tte). @ 
a He) RT 
From pm tE EN follows for w = [dope [in which 
es wy 


a 


in pd xv must be kept constant, because in the original equation 


for Z (which holds for any mixture, whether in equilibrium or not) 
the later possible state of equilibrium of the components, given by 
(a), must not be taken into account, so that n, and n,, hence « 
remain constant]: 


w= 4(14+ 2) RT | ba _5) fs 55 hen 


(a=konst.) 


In general 6 is still a function of v, hence inf pao the part 


IS Ey will be represented by {| ear: 2,5 = log (v—b) Seas 


[We may point out that in the assumed equation of state i 
quantities », a, and 5 of the mixture refer to simple molecular 
quantities (eg. 200,6 Gr. mercury). For with v’ =nv, b’ = nb, 
a’ =n’a, in which vn is the degree of association 2:(1 + 2), the 


a. JE 
original equation TENT (ef. the first part of this paper) 
passes into the given equation. If e.g. '/, (2) simple and */, (1—z) 
double molecules arise from 1 single —'/, double molecule, then 

19 


Proceedings Royal Acad. Amsterdam. Vol. XXIII, 


284 


b= xb, +'/,(1—2x)b, — when 6, represents the co-volume of 1 
single molecule and 6, that of 1 double molecule — which quantity 
refers, therefore, to the original single-molecular quantity. But 6’ 
refers to the molecular quantity, which on an average yields 1 
molecule after the association, and which is 2: (1 + 2) times greater 
than the single-molecular quantity. [i.e. at «=O (exclusively double 
molecules) twice greater; at «1 (exclusively single molecules) 
once greater; etc]. For from the original single molecule there have 
been formed '/, (1 + #) new molecules, so that every new molecule 
corresponds averagely to 2: (1 + ) original single molecules]. 


dw 
We can now compute ae As 6 is a function of v (through 6, and 
av 


6,) and of a, and also v a function of « on account of the equation 
of state v= f(p, 7,.x,a, 6), in which also a and 6 are functions of 
a, we have: 


d F et a Ves L Ade /( Ob \ adn 0b L (0b\ dv 00 
=I es je ale (Ge il i se zE), | 


| db 

$ = db dv 

when is written for {= dv, aud because evidently 
v—b v—b 


x=const. x=const. 


Lea ae hr GL 

(5 BE in 8 ence 
d 1 dv 1 /0b 00 
(ew Pr at 6 )= gash ce GE G3) 


00 
For the further calculation of El the quantity @ must be 


known, i.e. 6 in function of v. When we assume for this the 
approximate relation derived by me before *): 

v—b b 

PE 


in which 8 is a coefficient that depends on the nature of the 


substance, then (5) a ek 3) bo, ahah Bu vb) 


easily follows 


dv Ne IE 
from: = BE ae In consequence of this @ becomes: 
= pe ee et 5 See fl eee: + Jen 
Br (v—b,) (Bv + (1—B) b,) Bot (pe, eee 


x—=const 


1) See Recueil des Trav. Chim. N°. 3 and 5 of 1920. 


285 
i.e. 


Frog et) 


1 en 
Le 


which properly becomes =O for }=1 (ideal substances, where 6 
is independent of v). 
For this may also be written, because (see above) pv + (1—8)b, = 


pe Oa 
=o 
0 log — = log v + tog (eb) ek FP lg — bg = 
Now v= aie hence v—b, =r and @ becomes: 
=> log = Plog at log (b—b,) slab +logb, log(1—8).") 


Thus we find for & =}: 


oo is Ob 11 /e6\ 1 708, 
Gar (EE) EE); 


or also: 
00 bog — db bo/a—b 0b, 
== b (b— nll b, (b—b,) (5 é 
Now v—b = 6 (b— = (°e/2—b) (see the note), hence finally: 
(5. ihe 0b ies 0b 
J=s3(x)- b,v—b (re): 
For . (log (v—b) + 6) may therefore simply be written 
Me be 1 0) 1 deh ae A 
a b, v—b (=): ob da neo 
0b 
= 20), HI) )y we have (S*) = (bo). — 1 (2) 


which quantity we shall represent by Ad,. This is accord- 
ingly the increase of volume, when */, double molecule passes 
into 1 single molecule. From the above given expression 


For as 0, 


db : : Belo) 
1 = lee, zn == Me 
ln 4 Je 5 we might at once have substituted v — b=b 1-6 


Be: from the above given expression for v) for v — b, and 


— Bb lj, |p uy pene 
im Bae =e +) db = i —1) log Ob) ~ 3 log b 


might have been written, but then the constant term (i.e. constant with regard 
to v) logby, essential for the differentiation with respect to x, would have been 
wanting, and 4 would not have become =O for @ =1 (the integral is indefinite). 


19 


de, 
for w we now find for — 


dev 


0 RT ilone oi) ND ee eee 
de — ; ai aa ae v—b dx bh, v—b a 
ade. Ada dv 


Syne ae de 


U ie 
In this all the terms with — are eliminated in consequence of 


da 
the equation of state, and we keep: 
1 dw : b Ab, 1 da 


EEE Wi Ale Ee ~ 
Rode PE a ae Pee RTs de 


With regard to the quantity a, the following equation may be 
given: 
Yaa Va, +'/,(l—e) Va,='/, Va, + ella —'/, Va)=!l, Va, +aeÂVa, 
when Wa, refers to one single molecule and px, to one double 
molecule, and Aja represents the cncrease of the attraction, when 
'/, double molecule passes into 1 single molecule (atom). As for 
mercury '/, Va, 18 about =10-.. 10-2. and Vg, about=40 
Aya has there the exceedingly high value 30. 10-?, i.e. Apa three 
times the value of Wa, 

Hence from a= (Wa) follows 4/7, = 2 Wa. Ap/a, and thus the 
equation (6) becomes finally : 


1 nS 1 v—b b Ab 2a. Ava 

—| SS SS iy) Ee eles. ae 

2 Cp EE TE) © | 2 ( TO wip RTv () 
sr C.- C, 


when wecombine — — —1— log 2 to one constant (tempera- 


ET 
ture nen) C,, and write for c, and c, resp. c, =#:'/, =e) 
and = = '"/, | (1—2): ye “hs (1 + 2) 

It is now this last equation “aha serves as basis for the determi- 
nation of the degree of dissociation 7 of the double molecules, i. e. 


for the determination of the quantity = which will occur in the 
Uv 


3 2 

expressions for“? and on In the equation mentioned the quantity 
Ab, will probably be always exceedingly small, and may be neglect- 
ed in most cases, whereas on the contrary in this special case, 
where the dissociation of the double molecules Hg, leads to tsolated 
atoms Hg, Ay/a will possess. a very large value, which quite governs 
the modification of the critical quantities. 


287 


dx 
§ 10. Determination of (=). 
U/t 


Let us now differentiate the relation (c), ie. a= f(v,7) at T 
constant with respect to v, again taking into account that 6= f (wv‚x) 


and a= f(x). We then get: 
0b Ob\ da 
oee 
de 


BEES Balder pet 
NER 1 do 2e 
i IG + areal he 4 
| 5g "142 dv 


| Ab de ; (Le) Ab, 2a. kn Awa)’ da 
B(v—b,) dv | B dv \v—b RTv? | RTv dv’ 


1 ba wil 
because ———_ TEEN can also be written for Ren j (see $ 9). As further 


5 = (5). (5 en 3) b, te fie 
=) ahd ba =z In (see $ 9), 


we get: 
1 Ce dal Ab, dx 
Bir ays ei ey gee ae tea ae 
da 
Tenpin | 
ed A b, de (1+2) Ab, dv 2Yahya (Aa) da 
B (vw —b,) do te (vb) RTv? RTv dv’ 
or also 
Melle) Ab, (1+2)(4b,)% 24 ya) 
a (1-- 2?) BEEN Beb RTs sld 
sl baal l(d+2)Ab, 2Va.A wa 
Sb Saat): RTv’ 


When to obviate unnecessary complications in what follows, we 
disregard all the terms with Ab, — which may the sooner be 
done, as at the limiting volume v, = 6, the volume of :/, double 
molecule will probably be equal to that of 1 single molecule, and 
as besides Aj/a is very large with regard to Ab, — we thus get: 


ll 2V¥a.AYa 


(F)= 2 v—b RTv 
dok 1+ %/,e(l—#) 2(Aa) 
x (1—a?) RTv 


288 


vee ee (1 ova oe 
Te cs = v RTv 


da 
Ee vb A) Sl EET a 


—b 
; v(t ya. Ava) 
Vv 
Gebs (Q—«) RTv — 4a (le) (A Va 
because 1 + '/, 2 (1—x): (1+) is = 1—'/, «. If we put for brevity: 


we have finally : 


dar: il x (le) (RTv—4a A) 
dv), v—b (2—a) RTv—4x (1—a) A? 


(1) 


When A =O, or may be neglected, as in all cases of dissociation 
which do not eventuate in isolated atoms, then (5) = en nj 
dv}, v—b I--« 
the already known expression, which is always positive, and which 
becomes =O for z=0O and «= 1. 
But if A is large, as with Hg, — 2 Hg, then in consequence 


of RTv—4eh=RT0—4°—* ya. AVa=o| RIAS | 
5 v Va 


the quantity 4/7, can become negative at lower temperatures or 
comparatively small values of v. In mercury, where Va = */, Va, + 
+a.A Vais = (10+ 302r).10-, Aa: Va willapproach 30:10 = 3 
with small values of «, so that then the transition from positive to 


av—b 


negative is reached, when R7’= If v = ve, then with 


Ve = 1,86,, and a about =*/, a,b =*/, be, this temperature will 


0,75 a-1,8—0,75 35a, 


be given by RT? =12 x —— And as in mer- 


AB ibaa LER 
cury. Alias ~ = “>< 2x (about 1,25) = a, (compare the first part 
in these Proc), 7’ becomes about = "*/,, Zi, 

T~ 4 T, (at v =v), 
so that with a volume =v, the quantity ?/g, becomes positive 


again only above about 6700° abs. 


289 


Hence @/j, is always negative at 
the critical temperature itself, when 
Awa has such a high value as in 
mercury and similar substances. Then 
the degree of dissociation of the double 
molecules Hg, decreases when the 
volume becomes greater, instead of 
increasing — as it generally does. 

As a(v—b):v’? (a and b assumed 
constant) has its maximum value at 
v = 26, the transition temperature for 

veo oe V->co values of v both about < 26 and 

> 26 will be lower than that (7) at 
v = 26, which latter will be only little higher than that at v = ve 
(about 4 7) *). See fig. 1. 

The decrease of x with increasing volume is of course accounted 
for in this way, that on increase of the degree of dissociation « with 
increasing volume also a becomes greater. But this causes the volume 
to decrease again, in which the decrease in the end exceeds the 
original increase. 

At high temperature the pressure will be comparatively great, 
so that then, in consequence of an increase of a, p + “%/,2 will be 
increased little; v—5, hence also v, will then be lowered compara- 
tively little. For this reason 4*/q will always be positive at high 


1) The righthand branch of the transition curve (dotted in the figure) will get 
more to the left, and 7, possibly slightly lower than would follow from the above 
calculation, because then x can no more be assumed near 0. The intersection with the 
vapour branch of the saturation curve takes place at 7’ = about 0,8 T¢. For 


from pv ='/,(1-+2) RT andp =p eb) where 4,14 is the vapour pressure 
factor f = 1,8 X 2,303 and m = T: Te, follows pe ve © = Ig (1 + 2) MRT. When 
x is put approximately =1/,, then ne” “* becomes = 5/4, ms. (with v = nve and 
RTe:peve = 8). Now in mercury s = 2,62 (see the cited first part), so that finally 
n = 1,965 m ef l4(L/m— 1) (saturation curve). This must now be combined with 


In this Va = 30.102, while Va becomes = 25,10-2 


v v Wa 


with «= 1/,. When at the point of intersection a is put about = 11/4 ac, b =1!/4 be, 


= Lb 20 
Org Semen laabe | with ye Ea RT. == == (see 
: NVe NVe OT be 
; 1,8n—1'/, oe . . 
above) m = 2,5 ——__—— (transition curve). Both equations are satisfied by 


n 
m = 0,778, n = 4,99 (point of intersection), so that this will lie at about 
T=08 7, where v = bve. 


290 


temperatures (higher than the critical transition temperature 7;,=47;, 
in Hg). The same thing is also the case with great values of », 
for then @/,2 has only slight influence by the side of p. 

As regards the values of v near b, here too “*/g, will always be 
positive, because v cannot become smaller than 6, and « not smaller 
than 0. In consequence of the increase of a the volume will 
indeed become somewhat smaller; but this decrease can only be 
exceedingly small, as v is already almost = 6. 

Remark. In the equation (c) the constant C will contain the 
term (1/, (é3)>—(@))): RY = —Q,: RT (on account of (*/, C,—C,): RY), 
in which Q, represents the — always positive — heat of dissocia- 
tion (see § 9), while @ contains the term (1/2 — 1) log (v — 6) (for 


v—b=(v—b,) Xx B%/y,); hence #:W1-—a? will have the form 
Wa.AVa\ 

k wb)" De { ar anes ): pa in which & will contain ex- 
ponentially eae rb nor 7. If, therefore, the term with AVa 
is smaller than Q,, then 2 will shae O exponentially at 7=0 
vb. (If the term with Ap/a should be larger than Q,, ee 
approaches 0 exponentially). Hence according to (1) the differential 
quotient 42/7, will approach exponentially to O at any rate at 7==0, 
y=, as it contains the factor «(1—w«) : (v—b). If, however, 7 is 
> 0, everything depends at v—6 on the exponent of v—b, which 
will evidently be '/.;—1. In ‘ideal’ substances, where 8 = 1, this 
exponent is negative, hence 4/7, approaches to oo. But for “ordinary” 
substances, in which !/g, ranges between a little more than 2 and 
a little more than 4 (according as, in view of the factor 1: a oc- 
curring in 8, the temperature is higher or lower), the exponent in 
question will be positive, and @*/g, will thus approach 0. 


L 
§ 11. The Differential Quotient (5) and the Value of RT. 
t 


de) RT 


Al : 5 a |. 
From the equation of state p= ae follows : 


‘r) WRT (de) 1), +a) RT (, (00 DD (de 
& 1 v—b & (vb) ( a Gr Ge). 5; 


06 
Putting again (5 = Ab=0, just as before Ab, and writing 
G/]y 


291 


6’ tor ies , we get: 
Òv / 


dp EE du heads | da. Aa BDE ted 
dv), 2\dv/, | v—b v? (v—b) v 


Now substituting for 4/7, its value from (1), we find: 


(5) 1 #(1—2) RTv—4ah = da A | 


dv}, 2 vb (2—e) RTv Aar (le) A*| vb v(v—b) 
if, (1e) RT Qa 
=~ ~ 25 y = 
(v—b)? ( on v? 


writing simply « ’/,, for Va (see $ 10) and A for Aya; hence also: 
dp 1 a (l—a) (RTv—4ea A) 
(5 Nt 2 (v— mn RTv—4e (1—«) A: 
This must now be =O at the critical point; thus we have: 

@ (1—a) (RTv—4ah)? = [(2—#) RT v— Aw (1—a) APT [(1 Hw) RTv) 16!) — 40°], 
i.e. after some reduction and division of the two members by RTv: 
a (le) RTv — 8e (1\—a) aA = (2e) (14 2) RTv (15!) — 4 (2—2) a? — 

— 4 a (l1—2#’) (1—0’) A’, 


(la) RTv (1 re | 


and from this: 
(2—w) a? — Za (l—a) a A Ha (lr?) (lb!) LZ? 


Re en 
ld Lane 6) 
for which we may also write: 
== (ls (LAME De (A 
En aA had ee 


NER ab) 2 (2) 
This is, therefore, already the expression for R7,, expressed in 
Ve, be, ete. As a check may serve that at A =O this-passes into 
4(2—a)a*® 4(2—.2#)a, (ve — bo) 
Nv, zi N we 
our former expression (Arch. Teyler loc. cit.), derived for the case 
that there does not take place any change in the molecular attrac- 
tion in consequence of the dissociation of the double molecules. 
. If also x= 1 (all the molecules single), then becomes 
Za. (Web) 2 (r—l)’ a 
Si MOE rile re be 
as we also found before. (Cf. among others These Proc. Vol. XVI, 
p.45, and Ibid, p.810). In this the value of r=v,:6, can 


Kle 


RD 


qd? 
of course not be determined until we have also put (4 )= 0. 
Dart 


8 ite 
In ideal substances 6', = 0,7 = 3, hence RT, = 27 a In ordinary 
Yeo 


292 


substances, where b'‚ approaches '/, and r approaches 2, RT, becomes 
ag 8 a, 
28 bo 
We will now first substitute the found value of RT, in (4), in 
order to determine the value of @/,, at the critical point. If we 
write for brevity: 
a—(ltae)(l—b')A=A; (2-2) a—a(l—2)A=B 
(2—z) (1+ 2) (1—6) — (le) = 2 — (2—2) (142) b' = NY" 


we get, after substitution of 


; both known expressions. 


AB 
a Lee Oe he oe . pet (26) 


in 


(Z)= a (lr) RTv aA 


the equation 


Se (1—z2) AB: N 
(= tvb (2—a) a A + (2—2) AB: Ne (la) A?) 


In this (2—«)« A — a (l—e) A? = BA, hence also 


(F __ # (1l—a) A __#(l—a)A 
== bb NASA) oe eee 


because NA + (2—r) A is evidently = B. Hence we have now for 


dx 
(=) at the critical point the exceedingly simple expression 
t 


(= )= w(l1—a#)A alle) a—(1+e)(1—6) 4 
dv ede Ben v—be (2—a#) a—a (l—x) | 6) 


in which 2, 6’, a, and A all refer to Te. 

It is self-evident that it is unnecessary to derive an expression 
for p., as it follows immediately from the equation of state after 
substitution of the obtained value of RT. (Compare the first paper). 


§12. The Second Differential Quotient (2 and the Value 


OL == bee. 


As we observed already above, we cannot determine the final 
expression for RT, until also v, has been expressed in 6,. But for 
this the knowledge of the second differential quotient is required, 
which must again be put = 0 at the critical point. 


293 


d, ; 
As (5) — 0 is identical with the expression (2) or (2b) derived 
wat 


d? 
from it, <P) — 0 is identical aly —|1/,RTv — (« A+ =) |=°. 
dv’ t dv 


When we take (2) instead of (26), 
RTv N = (2—2) a? — 2 # (1—a) a A Ha (le?) (I—D') A? 


should be differentiated with respect to v(7’ constant); which yields, 


06 
when again, as in $11, (Ge) =A bd is put =0, so that 6 is only 
“yy 


a function of v: 


PRIN} Ni) = 20-0) ade ( 7) Qu (1—w) a'A 4-2 (21 aca 


After multiplication by v and substitution for '/, RTv of its value 
(26), we get: 


AB eet ENE 
(aa + =) (xn + & (l—r) (2 «—1) a | b BT (2—w) (L Hz) b ‚) = 


dx 


dv 


= 2a'v B—v (5 =) | «2-220 tye + (807-1 JL-H)A" [-a(L-st od 
{ 


For from N= 2-— (2—.) (1 4-2) 6’ follows N’ = —(2—.x)(1-++-2) 6" 4- 
di di >(1—2) A 
+ (2% — 1) 0’ (=). hence N’v becomes with (Z)= ae 


Vv 
which is written down above. Further (2—w) a—v (1—e) A has 
been replaced by B. 


dre d (v—b ey i — 
Kor a == |= va) we find — 
der dUN ev t v 


a ial = ava(S “). hence 


A ) | 
av=a (3 (1) teln Baa (1-0) («B-o(-0) Ad ) , 


so that we find: 


AB Uae 
(«a+ 5) (yv + & (1—2) (2 «—1) a b 5) = 


2 EE (Na A+AB) — #(1—a«) N | = 


294 


v a B—a(l —e) AA 
=2B| a—— (1—b!) — BET 
yp—b B 


— & (l—e) ze fs a jo (2a—l)a A + (82?—1) (1—0’) a]. 
v—b B 
When now for brevity C is written for 
NaA + AB = (2—2) a? —2e (l—e) aA + a (le?) (1-6) A? 
(according to (2) and (26)), then 


AC 
Cc 1—2) (2e—1) merker adt. ) a Ble = 


v ) A 

| = 2Ba — (Lb) — 2 C—w (l—a) — B la”? — ete, |, 

because a B—a(1—2«) AA is =C and (2—a’) C—a(1i—«) NA’? = BE 
Hence we have also: 


B: v q C 
3C—(1+a)— b"v=2aB es (1—6')— (le) - —| (2a@-—1)b'— Ne — ete.) 
N v—b Bv_b| 


For (2e—1)6’C + N (a? — etc.) may be written 5? (1 — 6’) — 
— A*(a’— os hence we have: 


(1+ #)B: pl TE En 
ore = 2aB— (1-8) «(1 “EB meh N si 


Before proceeding, we shall apply a control-calculation to this 
equation. When A is =O, then A becomes =a, B= (2—a)a, 
C = (2—a)a’, so that then (a) passes into 


(1 +) Em ", 


3 (2) a? —- N == 2 (24-2) a? DE (1—b') — | 
a(l—a) v (2—2«)' a? ef — a (w°— 4% + 2) 
ean N 
i.e. after division by (2—«#) «*: 
(la) (2-2) - (1-b')—(#?- 4a +2): (2-2)? 
—- — "y= 2 — b' l— ; 
N dende = (1- Je (1-2) — ar N | 


in which NV = (2—a) (14e) (1— 6’) —a (1a) = 2—(2— 2) (1+ a) 6’. 


This gives: 
bv 1 v x (1—.x) (1—’) 
3 — — — = 2(1—b' 
1—}' x (l—e) v—b | ( N * 
(2a) (1+) 0-5) 


w (1—a) ((2—a)?—2) | 
(2-20)? N 


or 


295 


r | v(l—e 2 (Coa Gee 
- b"'y Bebi ots x) ( —é) 4 
1--b'1—t v—b (2—a)* 2 — (2—r) (1 4 2) b 
In ideal substances, where 6’ =0,6"—0O, the equation would 
become: 
an Ks « (le) v 8 — 9w IL da’ 
v—b oe x)? ee (2—: v)? 


identical with what we have already derived. (Arch. Trrrer and 
these Proc; loc. cit). 
Mer Osor 1 we get: 
EE ee 
=o! v—bh 


and this too is a known result (These Proc., loc. cit), which with 
ieee 
Dr Or *b' = Oe reduces to 3=2 = Les Ve be 
Yv— 


We shail now reduce the above equation (a) still somewhat. 
When we divide by (2 —a)e’, we get the following form (see below 


for the meaning oft): 
1 
(1p. (2- ee 


si Zelle) A el I-a?)(1-B) AY] pags |, AE 
oe A HEE Laden 
| | ‚De nnee 
is _b') (rn) i a Sc 
Tib 2—a a 2—-«% je (La) A 
Sg 


(2—2) oles x) (L—B’) (1 DE) 


uv (l-a 2 w?-4a42 AN? 
ae ee ee) (2-2) (I- ne serie bi 


A v Aa 
i hiel == 8 . 
in which — En When we now put 
A «ls S40 Tas € aa 
(l+.21—s)—=o0 ; aw eis : ae) = t. 
at 2e «a (2— wx) (le) (1—6)) 
so that o = toe, the above becomes: 
| (I—o)? bv 
3 (1 — 2 = 
ete 
—_4rJ-2 
op gg 
1—o ce 5). (1—b') 


b')) 2 (1—o) — a (1—a) 1—o  (2—#)(14+-2)(1—b'(1—1) 


or 


296 


Ee b"v 
3 (1 + ze (e-—2)) — ae 
—r 1— ia 
vo 1_d4y 4-2 
69) 80-0) — 2h oy — 5 tt 04 | 
ais (2—a)? (1 —b') 
AV A 
When further mg is put, then — en hence — bd 
Va a v—b v—b 
A 1—0’ bv 
tn I ith — —— = 
«x 1—b)= zn = ce AE) so that with TE, 8 and 


mm Oe 1 1 ze ) = & 
aes ae a (TRE ay Nee 


1— ro)’ 
B (1 + re (e—2)) + = Se 
Q c 
SS —— | ae ap mee 6 ; 
re Jaret — oef | -@ 
when — (g—1l) is Er for 1—e, because gy is always > 1. 


In this latter equation g = 7 (1 4+ 2) (1—b’) X nd being in direct 


connection with 7==ve:b, the principal unknown quantity; ie 
it expresses @ (hence 7 = ve: be) in 6’, 6" (or 9), x’) and the para- 


60,="/,V a+ 


moe 
IE 
+ xvAy/a. For mercury p is therefore ES Bess because then 


1 + 3x 
Ave Yar 302 10> 
With small values of « r is very slight; then p is in the neigh- 
bourhood of 3, and w in that of 1:2 (l—b’). 


Aa 
meter p = A being in connection with 


When we now express also the values of RT, and (5) ‚ found 


te 
in § 11, in the auxiliary unknowns assumed just now, we may 
write for (2) in the first place: 


4 (2—#7)a*(1l+te(e—2)) 2 2 (ve—b,)*ae 1+ ty (c= 


Rl Qa) (14 2) (8) Rae te 1) 


Le. 

2 2(rl)'a 5 Trel (o—2) (5) 
lta (oe: EE 
in which Wa,='/, Va, He Ava="!/, Va, (1 + 382), whilst 7 = v¢: be 
is determined by (4). 

And in the second place we may write for (3): 


Rt = 


1) The value of x at the critical point will be determined by (c), and depends 
besides on 7. and ve also on the constants of energy and entropy (contained in €. 


297 


(5) PE (Le) x) 1—e 2 

dv EME eee qe lr’ ree oe 
(ay: (tl + ®) 4 NEE 

in which g=w( +2 =, i+ Sr ken (see 


above). In mercury, where den 1—e will, therefore, always be 
negative at 7’, hence also de/,. 


_$ 18. Calculation of some Numerical Values. 


The value of x being always very small at 7, we way write 
approximately for (4), when 1—r—1 and 1 rn is put: 


3(1+-1e(9—2)) + B(L—T0)'= leen (1—ry)? —w (v1)? | 


and from this follows for r ee ‚when wis small (see abov °)); 


2 (1—b’)’ 


20 
ee — (848 (1—ro)*) 
ied EN 


ST 
gate Delen ig En ee 


gezo Site] 


Spe) (lt) + =e“) 


With very small values of « also 1 — rg can be put =1, and 
we have approximately: 
ko nh 
he em On ed 
> (Se 


ple) — (el) + wel)" 

With small « we way write 1: 2(1—d’) for w. Now o is large 
(6 or 7), and it can easily be calculated that in the denominator 
the two first terms may be neglected by the side of w (e—1)’, provided 
the latter is provided with a factor about 1,35. When we also write 


ontor 1, — ee 


—1 
7) zat Ee =| becomes O at « = O (tx = 0) and or is 


then = we get: 


298 
2d 
Ts - RE —-~—~, hence T(o—l)? — 3 (1—b))d. 
1.85 See 
2 (1—d) 
Now 1+ +1(g — 1)? may be written for the factor (1 + ro (o—2)): 
(1—r) in (5) for small values of rt, which in view of the above 
3 (1—b')d 
ee 


approximated relation becomes 1 + 
Now o=3 (1—0’) = for small values of rv. This being about 6, 
T— 
2,5 (1—6’) = may be put for e—1, so that we get approximately 
pe 


Dd bed : 
Tsai —0 for the factor in question. Hence the factor @ in 
t Uy 


p 2 eer : 
R T=; TE X 6, referred to in the first part of this paper, 
will evidently according to (5), when for d its value is substituted, 


amount to: 


Cee Eeklo Std 

1 Sek PB 5 oP 2 (i= be 
holding for very small values for «. Only a small value of 7, e.g. 
r=1,5, satisfies this. If has then become =O, and 6’ ='/,, @ 
becomes 


2 
e=! tm |er 


while with r=1,5 (see the first part of this Paper in these Proceedings, 
$8, p. 278) 9 should be exactly =1. Possibly @ is not small enough 
to justify the above approximations and the neglect of certain values, 
and then it is possible that r > 1,5 drops out. But the calculations 
get very intricate then. 

At any rate the formulae (4), (5), and (6) contain the full solution 
of the problem put by us. 


La Tour près Vevey, spring 1920. 


Chemistry. — “Catalysis” VIII. By Nu. Ratan Duar (with A. K. 
Datta and D. N. BHATTACHARYA). (Communicated by Prof. 
Ernst COHEN). 


(Communicated at the meeting of September 25, 1920). 
a. Reaction between silver nitrate and ferrous-ammonium sulphate. 


I tried to determine the kinetics of the reaction between ferrous 
ammonium sulphate and silver nitrate. The reaction seems to be 
very rapid. 

When */,, silver nitrate and N/,, ferrous ammonium sulphate are 
mixed at 25°, a bimolecular velocity coefficient of 0.0007 is obtained, 
but unfortunately this coefficient falls off as the chemical reaction 
proceeds. Since the metallic silver formed reacts on the ferric salt 
produced and we get an equilibrium of this nature 


2 Ag + Fe, (SO), = Ag,SO, + 2 FeSO, 
Ag + Fe (NO), = AgNO, + Fe (NO), 


Fet+) (Agt 
ik | eae: aoe at equilibrium = 0:128 


(ef. Noyks en Braun, Jour. Amer. Chem. Soc. 1912, 34, 1016) the 
reaction between ferrous ammonium sulphate and silver nitrate is 
rapid even at 0° and has a small value for its temperature coefficient. 

The reaction is markedly accelerated by acids; nitric, sulphuric, 
citric, tartaric, and acetic acids have been tried; the greater the 
concentration of hydrogen ions, the greater is the velocity. This 
catalytic activity may be utilised in determining the concentration 
of hydrogen ions. 

Magnetic force has practically no effect on this reaction. It is 
extremely sensitive to the influence of dirt ete. 

Potassium nitrate appreciably retards the reaction, so do manganese 
salts very markedly. 

Carbonic acid markedly accelerates the reaction. Boric acid is 
practically witbout any influence. So is phenol, which is probably 
slightly retarding in its effect. Glucose markedly accelerates the 
reaction. This is a case of induced reaction. A mixture of excess of 
silver nitrate and very little of ferrous ammonium sulphate was 
prepared and divided into equal parts, to one of which glucose was 
20 

Proceedings Royal Acad. Amsterdam. Vol XXIII. . 


300 


added, whilst the other was left as it is; in a short time, more 
silver was deposited in the tube containing glucose, though a neutral 
solution of glucose cannot reduce silver nitrate. This is another case 
of an induced reaction already studied. (DHar, Trans. Chem. Soe. 
1917, 111, 690). 

Summary: a. The reaction between silver nitrate and ferrous 
ammonium in dilute solutions is bimolecular. The reaction is very 
rapid even at O° and the temperature coefficient has a small value. 

6. When the chemical change has proceeded up to a certain 
extent, an equilibrium is set up: 

Ag ain Fe (NO), = AgNO, == Ke (NO). 

c. Acids accelerate this change; in case of nitric, sulphuric, citric, 
tartaric acetic acids, the greater the concentration of H’ ions, the 
greater is the acceleration. Carbonic acid markedly accelerates, whilst 
boric acid and phenol are without action. Manganese sulphate and 
potassium nitrate are retarders. 

d. A neutral solution of glucose cannot reduce silver nitrate at 
about 20°; the reaction between ferrous ammonium sulphate and 
silver nitrate induces the chemical change between glucose and 
silver nitrate. 


b. Oxidation of sodium sulphite by atmospheric oxygen. 


Lurner (Zeit. phys. Chem. 19038, 45, 662) advanced the idea that 
negative catalysis cannot take place in a reaction which is entirely 
free from positive catalysts and the phenomenon is really due to 
the destruction or otherwise rendering latent of these positive catalysts. 
Tirorr (ibid. 1903, 45, 641) as a result of his studies of the combined 
effect of positive and negative eatalysors on the rate of oxidation of 
sodium sulphite lends his support to Lurner’s theory. The effect of 
negative catalysts on this reaction was first studied by BieeLow (ibid. 
1898, 26, 493), who found the oxidation of the salt in aqueous 
solution to be greatly retarded by the presence of minute quantities 
of benzaldehyde, iso-butyl alcohol, glycerol, phenol etc. BierLow also 
demonstrated that the effect of negative catalyst is not on the rate 
of solution of oxygen, but on the rate of the reaction between the 
sulphite and oxygen. A few years later Tirorr substantiated BieeLow’s 
results and in addition studied the simultaneous effect produced by 
copper sulphate, a powerful accelerator and manitol a strong retarder. 
He found that these two substances do not exert any additive effect 
but influence each other. Youre (Jour. Amer. Chem. Soc. 1901, 23, 
119; 24, 1902, 297) found that small quantities of certain alkaloids 


301 


greatly retard this oxidation, specially if this solution is alkaline, 
and the inhibitory effect of sucrose, invert sugar, asparatic acid, etc., 
have been noted by SairLanD (Zeit. Ver. Zuckerind. 1913, 68, 1035). 
In 1912, we conducted some experiments on this line. From prelim- 
inary experiments it was observed that the velocity of the reactions 
depends greatly on the quality of the water used. Ordinary distilled 
water was found quite inefficient as it contained sufficient dissolved 
salts and gases to affect the course of the reactions materially. 
Freshly prepared conductivity water obtained according to the method 
of Jones and Mackay (Zeit. Phys. Chem. 1897, 22, 237) was always 
used. The salts used were purified by reerystallisation from con- 
ductivity water and dissolved in the same water in resistance glass 
bottles. Well steamed Jena flasks were used as vessels in which the 
reaction took place. In short every care was taken to ensure purity. 
But in spite of all this care, it was found that velocity coefficients 
of the reactions carried out under identical conditions but on different 
days and even at different times on the same day were slightly 
different. Trrorr also found similar results. The explanation is 
probably that the reaction is so susceptible to external conditions, 
that even the slight variation of circumstances that is inevitable 
when we carry out the same reaction at two different times are sufficient 
to affect the results. It is therefore clear that our comparison of the 
results tried on different days or with different concentration of the 
same catalyst, cannot give an accurate idea of their relative effect. 
To remove this difficulty, at least partially, we carried out a blank 
experiment in which no catalyst was added, simultaneously with 
the main one. Two similar ERLENMEYER flasks of capacity 150 c.c. 
were arranged side by side. A detinite volume of sulphite was put 
in each flask. The catalyst was added in one flask. The course of 
the reaction was determined and their coefficients calculated. The 
ratio of these two coefficients gives the measure of the catalytic 
effect of the substance under consideration. In this way it was found 
that the ratio between the coefficients of two similar pair of reactions 
carried out on different days were almost the same, though their 
absolute velocities varied appreciably. The flasks were exposed to 
the atmosphere whose oxygen served as the oxidising agent. 


N 
About fan iodine and thio sulphate solutions were used as titration 


liquids. A definite volume of the sulphite solution is pipetted in a 
flask containing an excess of standard iodine and the excess of 
iodine was titrated back with the standard thio sulphate. 


The temperature of the experiments was about 30° C. 
20* 


302 


Substance Concentration ba 
Cane sugar 0:2 N 0:09 
a 31> 10-2 N 0°17 
4 6-1 10-3 N 0:47 
is 94% 10-4 N 063 
- 3°17 X 10-5 N 0°89 
Lactose 0:15 N 0:084 
a 31 10-2 N 0:15 
a 94 10-4 N 0:55 
ù 31 105N 0:85 
Glucose 01 _N 0 22 
sd 110-3 N 0°75 
5 2 10-3] N 0-83 


| 


It will be evident from the above results that cane sugar, lactose, 
and glucose are very strong retarders. Cane sugar and lactose have 
almost similar effects, though lactose is slightly stronger in its effect. 

it appears probable that sugars as a class will act as negative 
catalysts. It has been found that the sparingly soluble volatile sub- 
stances like camphor and menthol have marked negative effect while 
naphthalene, anthracene etc. have no catalytic effect. 

The effect of several organic acids and their salts were also 
investigated. (See Table next page). 

It is very peculiar that the weak acids like acetic, propionic, 
cacodylic ete. have comparatively small retarding effects. Their sodium 
salts also.exert practically the same effect. On the other hand comp- 
aratively strong acids like oxalic, salicylic, benzoic ete. exert much 
greater retarding effect, and their salts too exert the same effect as 
the acids. Moreover it is found that the sodium salts of stronger 
inorganic acid have no marked effect. 

We have found that hydroquinone has a very great negative 
effect on this reaction. For the same concentration, it exerts the 
greatest negative catalytic effect amongst the negative catalysts in- 
vestigated up till now. We tried to determine the temperature co- 
elficient of this heterogeneous reaction and see whether this becomes 
greater in presence of the powerful negative catalyst hydroquinone. 
Unlike most other heterogeneous reactions, we found that the temp- 


303 


mmm 


Substance Concentration Ke 
Oxalic acid 20 ION 029 
” 310-4 N 0:56 
5 310-5 N 0:90 
Benzoic acid LA><10-3 0°25 
5 2104 058 
= 5 X 10-5 0°83 
Cacodylic acid 02 N 0°75 
» ‘O1 _N 0:94 
Sodium benzoate 1X 10-3 0:19 
ze 07> 10-3 0:25 
- 15.< 10-4 0-70 
5 1D 10-5 0-90 
Potassium oxalate 1x 10-3 N 0°29 
5 VO IOA IN 0:80 
pe 2 10-5 0:96 
Sodium salicylate 1 >< 10-3 0:23 
" 15 XX 10-4 0°73 
” 1 >< 10-5 095 
Sodium citrate 1 x 10-3 0:14 
pd 1X 10-5 0:85 
Sodium acetate 3 103 0:73 
Fe tlie 0°85 
Sodium propionate 3>< 10-4 0:74 
» 1X 10-3 0 89 
Sodium butyrate 3X10 3 0:74 
a 1 >< 1053 0°85 


erature coefficient is about 2 (between 25°-—40°) and it does not 
appreciably change in presence of hydroquinone (Duar, Proc. Akad, 
Wet. Arnsterdam 1919, 21, 1042). It has been found that so long 
as about one third of the substance is oxidised, the unimolecular 
velocity coefficient remains practically constant, but as the oxidation 
proceeds further, the velocity coefficient increases rapidly, and hence 


304 


it becomes very difficult to determine the temperature coefficient 
accurately. It appears therefore that the reaction is auto-catalytic. 


Maruews and his colleagues (Jour. Phys. chem. 1913, 17, 211; 
Jour. Amer. chem. Soc. 1917, 39, 635) found that ultraviolet light 
markedly accelerates this reaction, and also established the fact that 
this is not a case of auto-oxidation. For this reaction, they could 
not find a positive catalyst; copper sulphate, which is known to be 
a powerful catalyst under ordinary conditions exerted no appreciable 
effect in ultra-violet light. On the other hand the negative catalysts 
like hydroquinone, phenol etc. exerted a retarding effect in presence 
of ultra-violet light. So it appears that there are very few positive 
catalysts, but very many negative ones for this reaction when carried 
out in light or darkness. 

The explanation of the negative catalytic effect of organic sub- 
stances in general on this reaction is this: 

The reaction consists in the oxidation of SO, radical into SO,, 
and the sulphite ion is the active agent. It is well known that several 
organic substances form complexes with sulphurous acid and sulph- 
ites; these complexes are stable so far as oxidation is concerned 
and hence the organie substances act as negative catalysts by dimin- 
ishing the concentration of sulphite ion by combining with it. 


In foregoing papers I have proved that the phenomenon of nega- 
tive catalysis is very common, whilst there are very few positive 
catalysts. According to Lutuer’s view a negative catalyst must have 
a positive catalyst as its counterpart, but this is not probable since 
there are so few positive catalysts and so many negative ones. 
Hence it appears that LurHer’s view which emphasises that nega- 
tive catalysis cannot take place in a reaction which is entirely free 
from positive catalysts, is not substantiated by experimental evidence. 


Summary. 


a. Cane sugar, lactose, glucose, camphor, and menthol are nega- 
tive catalysts, whilst naphthalene, and anthracene are without action 
on the oxidation of sodium sulphite. 

b. The weak organic acids and their sodium salts exert practic- 
ally the same effect. Benzoic, oxalic, salicylic acids and their sodium 
salts exert greater negative effect than the weak acids and their 
salts. It is very peculiar that the acid and its salt should exert the 
same effect. 

c. The temperature coefficient of the reaction is about 2 and it 


305 


does not change appreciably in presence of the strong negative 
catalyst hydroquinone. 

d. The phenomenon of negative catalysis is very common in 
oxidation reactions. LutuEr’s view which emphasises that negative 
catalysis cannot take place in a reaction which is entirely free from 
positive catalysts, is not substantiated by experimental evidence. 

e. The organic substances act as negative catalysts by diminishing 
the concentration of the sulphite ion, which is the active agent in 
this oxidation; the diminution in concentration of sulphite ion is 
caused by the formation of a stable complex of the sulfite and the 
organic substance; this complex is not oxidized as readily as the 
sulphite ion. 


c. Catalytic activity of the undissociated acid. 


In recent years the question of acid catalysis has entered into a 
new period; and as a result of the accumulation of new observa- 
tions and of increased exactitude in the measurement of the velocity 
of reactions, evidence has been obtained in support of the view that 
the catalysing power of an acid is not entirely due to the hydrogen 
ion, but that the undissociated acid also contributes to the observed effect. 

This investigation had for its object the determination of the 
function of the undissociated parts of oxalie and pierie acids in the 
hydrolysis of methyl acetate. 

The experiments were all conducted at 45°. Dry pure potassium 
oxalate and sodium picrate were added in different quantities to 
diminish the ionisation of the respective acids. The former salt was 
crystallised from Merck’s pure sample, and the latter was prepared 
from pure materials and purified by repeated crystallisations. 

The following summary of results is obtained *) 

Oxalic acid. 


Conc. of acid. | Conc. of KgC,0, ao K, 
05 N | ~- - 0:00091 
5 ‘0038 N 13°16 0:00065 
5 ‘0114 N 4:38 0:00044 
i ‘0174 N 2-37 0:00042 
” ‘0278 N 1:79 0:00038 
ï 0590 N | 1°02 0:00011 


1) The experiments described here were finished in 1913. 


306 


Pieric acid. 


EE em EERE ETE LP ESE ES ET 


Cones era: | sil GLE aa Cone Ky 
03 N la = 0-00135 
: 0:0031 N 9°67 0:00139 
3 0:0050 N 6.00 0.00141 
; 0:0513 N 0:58 0-00173 
8 0:0778 N 0:38 0-00160 
: 0-1161 N 0:25 0-00153 
ki 0:1597_N 0-18 0.00134 
: 03066 N 0:09 0:00122 


It will be evident from the foregoing tables that the velocity 
coefficients do not decrease proportionally with the decrease in the 
concentration of the hydrogen ions. In the case of oxalic acid the 
velocity coefficients fall off with the concentration of potassium 
oxalate; whilst in the case of picric acid the addition of sodium 
picrate produces at first an increase in the velocity coefficient and 
then when the concentration of sodium picrate reaches the value of 
0-159 N, the velocity coefficients begin to fall off. This is explicable 
on the assumption that even undissociated acids are catalytically 
active in the hydrolysis of esters. But in view of the work of 
Wa.pen (Jour. Amer. Chem. Soc. 1912, 35, 1649) on the measure- 
ment of the di-electric constants of solutions, a different interpretation 
of these results is possible. WALDEN has shown with non-aqueous 
solutions that the di-electric constant and the ionising power of a 
solvent are enormously increased when electrolyts are dissolved in 
it. Naturally the degree of ionisation of the dissolved acid and along 
with it the concentration of hydrogen ions are also increased. Thus 
by the addition of salts of the same acids, there are two effects: 

1. The diminution of hydrogen ions due to the increase of the 
common negative ion. 

2. The increase in the concentration of the hydrogen ions due to 
the greater ionisation of the acid caused by the increase in the 
di-electric constant of the solvent. 

It is evident that these two effects counteract each other. 

In the case of potassium oxalate the first effect preponderates 
over the second and hence the velocity coefficient falls off with the 
concentration of potassium oxalate, whilst in the case of picric acid 


307 


the second effect predominates over the first and the velocity coeffi- 
cient instead of decreasing, increases with the concentration of 
sodium picrate. 

Moreover WarpeN has shown that there are two types of salts 
with regard to their effects on the di-electric constant of the solvent. 
He has observed that N(CH,),Cl markedly increases the di-electric 
constant of the solvent, whilst CH,NH,HCI affects this constant to 
a very slight extent. It is quite possible that even in aqueous solution 
salts like potassium oxalate, sodium acetate, etc. do not increase 
appreciably the ionising power of the solvent and the velocity of 
the reaction in its presence does not increase. In this way we can 
explain the negative effect of potassium oxalate and positive effect 
of sodium picrate on ester hydrolysis from the point of view of the 
change of the di-electric constant of the solvent due to the dissolution 
of electrolytes. 


SUMMARY. 


a. The hydrolysis of methyl acetate was investigated in presence 
of oxalic acid and pierie acid and sodium picrate. In the former case, 
the velocity coefficient falls off, whilst in the case of picric acid, 
the velocity coefficient increases with the concentration of sodium 
picrate up to a certain extent and then decreases with the increase 
of the concentration of sodium picrate. 

6. An explanation of these results is suggested on the basis of the 
increase of the di-electric constant and ionising power of the solvent 
observed by Watprn when salts are dissolved in it. 


Chemical Laboratory Muir Central College, 
Allahabad, India. 


Chemistry. — “Catalysis. IX. Thermal and photochemical reactions” 
By Nit Ratan Duar. (Communicated by Prof. Ernst COHEN). 


(Communicated at the meeting of September 25, 1920). 


In a foregoing paper (Duar, Trans. Chem. Soc. 1917 111, 707) 
it was shown that the temperature coefficient of the oxidation of 
potassium oxalate by iodine has the value 7.2 for a 10° rise in the 
dark and this reaction is extremely sensitive to light. 

It occurred to me that all reactions which have high temperature 
coefficients should be sensitive to light. 

[ have shown previously that most uni-molecular reactions have 
high temperature coefficients and | investigated the effect of tropical 
sunlight on several of these reactions, and the following results were 
obtained. 

Ammonium nitrite decomposes fairly readily at about 33° in 
sunlight, whilst at 33° in the dark there is hardly any decomposition. 
The temperature coefficient for a 10° rise in the dark is about 4.5 
(ARNDT, Zeit. Phys. Chem. 1901, 39, 64). 

The intramolecular transformation of acetyl chloranilide to para- 
chloracetanilide has the temperature coefficient 3.2 in the dark. 
(Riverr, Zeit. Phys. Chem. 1913, 82, 201) and Branxsma (Ree. trav. 
Pays. 1903, 22, 290) has shown that the change is sensitive to light. 

Similarly the pseudo-unimolecular reactions, the hydrolysis of 
cane sugar and the decomposition of potassium persulphate, are highly 
influenced by light. An aqueous solution of cane sugar when exposed 
for several days to tropical sunlight, becomes converted into the 
invert sugars. 

Green and Masson (Trans. Chem. Soc. 1910, 97, 2083) have 
shown that potassium persulphate is slowly decomposed by water 
according to the following equation 

KS: Od HO oe ASO): 
This reaction has the temperature coefficient 5 in the dark. I found 
that the reaction is very sensitive to light and the oxygen given off 
in 24 hours in sunlight is practically equal to that produced in 
about 15 days in the dark at 27°. 

The decompositions of the sulfine bases and the tetraammonium 
compounds studied by Von Hasan have high temperature coefficients 


309 


and these reactions when investigated would show great sensitiveness 
to light (Zeit. Phys. Chem. 1909, 67, 129). 

Cain and Nicorr (Jour. Chem. Soc. 1903, 83, 470) have proved 
that the decomposition of the diazo salts has the value of about 5 
for their temperature coefficients and it is well known that diazo 
salts are sensitive to light. 

PENDLEBURY and Srwarp (Proc. Roy. Soc. 1889, 95, 396) have 
shown that the reaction between KCIO, KI and HCI has the temper- 
ature coefficient of about 4 in the dark and I have found that the 
reaction is very sensitive to light. 

I have already shown (Trans. Chem. Soc. 1917, 111, 707) that 
the oxidations of sodium formate by mercuric chloride and by iodine 
has 4.05 for their temperature coefficient. These two reactions are 
also very sensitive to light (Duar, Proc. Akad. Wet. Amsterdam 
1916, 24, 1324). 

I have shown that light markedly accelerates the reaction between 
iodine and oxalates and now I have tried to find out which part 
of the spectrum is active in this reaction. For this I exposed five 
small tubes containing a mixture of potassium oxalate and iodine 
in a spectrum obtained from a carbon are-light. It was found that 
the iodine disappeared first in the tube held in the indigo portion 
near the violet end of the spectrum. Then that of the tube held in 
the blue region. The chemical change took place almost simultane- 
ously in the tubes held in the green and violet portions of the 
spectrum and the colour of the tube in the red end was the last 
to disappear. 

A mixture of mercuric chloride and potassium oxalate undergoes 
the following change in sunlight: 


2HeCl, + K,C,0, = 2KCl + 2CO, + 2HgCl. 


This decomposition can also be induced by lights obtained from a 
carbon arc, quartz mercury vapour lamp, and an arc obtained by 
passing alternating current in electrodes made of thorium and 
zirconium oxides. I have repeatedly observed that in tropical sunlight, 
a solution of ammonium cupric oxalate decomposes readily in glass 
vessels with the separation of metallic copper and evolution of 
carbon dioxide; but it was found impossible to bring forth this 
change by light obtained from the carbon arc or the thorium and 
zirconium oxides arc. 

] have found that uranium nitrate markedly accelerates the photo- 
chemical decomposition of a mixture of mercuric chloride and potas- 
sium oxalate, but chromates having the same yellow colour as the 


310 


uranium salt exert a markedly negative effect. Matuews and Weeks 
(Journ. Amer. Chem. Soc. 1917, 39, 635) have shown that uranium 
nitrate is also a positive catalyst in the photochemical oxidation of 
sodinm sulphite. Moreover, it is wellknown that uranium salts mark- 
edly help the photochemical decomposition of organic acids (e.g.), 
oxalic, formic, lactic ete. Hence it appears that a uranium salt is 
a positive catalyst of great generality in photochemical reactions. 

I have observed that manganese sulphate exerts a negative effect 
in the photochemical decomposition of a mixture of mercuric chloride 
and potassium oxalate. It has already been shown that manganese 
salts act as a negative catalyst in the reactions between phosphorous 
and chromic acids, formic and chromic acids, mercuric chloride and 
sodium formate, iodine and sodium formate, silver nitrate and sodium 
formate, silver nitrate and ferrousammonium sulphate, ete. So it 
seems that a manganese salt is a negative catalyst for light and 
dark reactions alike. 

I have also observed the effects of the different parts of the 
spectrum on several other photochemical reactions by passing ordinary 
sunlight through different solutions and exposing the reacting sub- 
stances to the filtered lights thus obtained and the results obtained 
are summarised below: 


(1) HgCl, +(NH,),C,0, — 
(2) I, + (NH), CO, — 
(3) FeCl, + (NH),C,0, — 
(4) Pyrogallol and Pyrogallate 
+ 0, => 
(5) Hydroquinone + O, — | practically uniform acceleration in 
(6) Cu,Cl, (ammoniacaloracid) ( different parts 
Hd 0, => 
(7) Decomposition of H,S — 
(8) Quinine acid sulphate + Blue and violet slightly more active 
H,Cr,O, — J) than the red. 


Violet and ultra-violet more active 
Oene than red. 


Blue, violet and ultra-violet more 
active than the red and infra-red. 


In a remarkable article Perrin (Annales de Physique 1919, t. XI, 1) 
has enunciated the following hypothesis: 

“All chemical reactions are provoked by light radiations. Their 
velocities are determined by the intensity of the light radiations and 
depend on temperature to such an extent as the light intensity 
depends on temperature”. By applying the idea of the emissive 
power of perfectly black bodies and its relation to temperature, 


311 


Perrin has deduced the following equation connecting the velocity 
coefficient and the temperature: 


7] 


2.3dlog,, k = ev eas where &£ = velocity coefficient, v = wave- 
‘ [2 


length of the activating radiation and 7’= absolute temperature. 
From his calculations, it is seen that the wavelengths which are 
active in bringing forth the ordinary chemical changes vary from 
2.56 to 0.8 microns. It is also seen that a reaction which is highly 
sensitive to the influence of temperature, has a small value for its 
activating wavelength, that is, a reaction of this type would be most 
sensitive to violet and ultraviolet end of the spectrum. From Prrrin’s 
calculations it is seen that the reaction between K,C,O, and I,, which 
has the high temperature coefficient of 7.2 in the dark, has 0.8 
micron for the wavelength of its activating radiation. In other words, 
this reaction would be most sensitive to light near the red end of 
the spectrum. But it is experimentally shown that this reaction is 
not sensitive to the indigo part near the violet end of the spectrum. 
My own experiments on several photochemical reactions have shown 
that the blue and violet portions of the spectrum are most active 
so far as chemical effects are concerned. Although the hypothesis 
of Prrrt is still of a qualitative nature, it is a highly suggestive 
one and my experiments give this hypothesis a sort of general 
support. 

I have tried to prove experimentally that reactions, which are 
most sensitive to the influence of temperature, are also most sensi- 
tive to.the influence of light. In a foregoing paper, | have advanced 
the hypothesis that temperature and light affect a chemical change 
in a similar way. The experimental evidence brought forward in 
this article, as well as Prrrin’s hypothesis that all chemical changes 
are induced by radiations, give additional confirmation to my hypo- 
thesis regarding the identity of effects of temperature and light on 
chemical reactions. 


Summary: 


a. Evidence has been brought forward in support of the view 
that reactions, having large temperature coefficients, are sensitive to 
light. Hence for a chemical reaction, sensitiveness to the influence 
of temperature and sensitiveness to light radiations go hand in hand. 

b. The indigo part near the violet end of the spectrum is most 
active in the reaction between K,C,O, and I,; blue and violet parts 
more active than the red in the following cases: 


312 


(NH,),C,0, ae HgCl,, (NH,),C,0, = FeCl,, HO; a KMnO, 
and Quinine bisulphate + H,Cr,O,. 

c. Uranium salts are general positive catalysts in photochemical 
reactions, whilst manganese salts are general negative catalysts in 
light and dark reactions alike. 

d. Prrrin’s hypothesis that all chemical reactions are induced by 
radiations support the view that the effects of temperature and of 
light on chemical reactions are of an identical nature. 

e. A solution of ammonium cupric oxalate decomposes with the 
separation of metallic copper and evolution of CO, in tropical sunlight, 
but not in carbon-are-light or the zirconium + thorium oxides-are- 
light. 

Chemical Laboratory, Muir Central College, 
Allahabad, India. 


Chemistry. — “Catalysis. X. Explanation of some abnormally large 
and small temperature coefficients’. By Nm Ratan Duar. 
(Communicated by Prof. Ernst COHEN). 


(Communicated at the meeting of September 25, 1920). 


SKRABAL (Monatsh. 1914, 35, 1157) has shown that the velocity 
of formation of iodate from iodine and iodide in a mixture of 


: 8 5 5 ky 10 
sodium carbonate and sodium bicarbonate solutions has —1’° —45. 
it 
When a similar reaction was effected in sodium acetate solution, 
the temperature coefficient is 2. 


The velocity of decomposition of iodate in a mixture of acetic 


bt 


fs : , ky 0 
acid and sodium acetate solution has a Sia a The same reaction 
t 


in a mixture of disodium and monosodium phosphates gives a 
temperature coefficient 1.26; in a mixture of KF and HF, the 
temperature coefficient has the value 0.9 to 1.04 and a mixture of 
sodium sulphate and sodium hydrogen sulphate leads to the value 
of 0.85. 

SKRABAL remarks that the temperature coefficient must necessarily 
undergo a change when the substances, which affect the time 
equation, are transformed into complexes. The relationship between 
the temperature coefficient T of the original reaction and T’, that 
of the reaction between the complex substances is governed by the 
formula, 

oT — e10/RT (T + 10) (MQ) + nQy HH xq1 + Vda Hoer) 
in which Q and q represent the heat changes of the complex 
reaction and the sum (m-+n-+....+x+y-+....) indicates the 
order of the reaction. This formula indicates that a great variability 
of T is to be expected from reactions of the higher orders. 

In a foregoing paper (Annales de Chimie et de physique 1919, 
t. XI, 130) I have definitely proved that this conclusion of SKRABAL, 
which states that the temperature coefficients of polymolecular 
reactions are, in general, greater than those of unimolecular ones, 
is not supported by experimental evidence. 

SKRABAL investigated these two polymolecular reactions: 

31,+60H’=51’+10',+3H,0 and 
10'",+51+6H =31,+ 38,0. 


314 


He has shown that the second reaction has a temperature coefficient 
less than unity (about 0.83) in presence of sodium sulphate and 
sodium bisulphate (Zeit. Elektrochem. 1915, 21, 461). 

As these results are rather peculiar, it was thought worth while 
to re-investigate some of these cases. 

A dilute solution of iodie acid was prepared and potassium iodide 
added to this solution. The reaction is very rapid and it is practically 
impossible to determine its temperature coefficient; when the two 
sotutions are mixed at O°, iodine immediately separates. The mixture 
is divided into two parts, one of the two tubes is put into ice and 
the other heated to boiling. Now the hot tube is cooled and brought 
to the same temperature as the other and the colour of the two 
tubes compared. Generally it is very difficult to find any difference 
“in the two tubes. Sometimes the heated seems more pale probably 
due to the volatilisation of iodine when the tube is heated. Conse- 
quently the temperature coefficient without any sulphate is practically 
unity. 

Similar experiments were made in presence of concentrated solu- 
tions of sodium sulphate and magnesium sulphate. In presence of 
these sulphates, a mixture of iodie acid and potassium iodide liberates 
slightly less iodine at a high temperature than at ordinary temperat- 
ures, hence a slight negative effect, of increase of temperature on 
the velocity of the reaction between iodic acid and potassium iodide, 
is observed. 

On the other hand, potassium sulphate, potash alum, manganese 
sulphate etc. are quite ineffective in changing the temperature coef- 
ficient of the reaction between iodie acid and potassium iodide. The 
behaviour of potassium sulphate is different from that of sodium 
sulphate, since a saturated solution of sodium sulphate is richer in 
SO," ions than a saturated solution of potassium sulphate at the 
same temperature. The temperature coefficient of the reaction between 
iodie acid and potassium iodide in presence of the above sulphates 
is practically unity. 

Ammonium and zine sulphates behave differently and in their 
presence the temperature coefficient becomes greater than unity. 
Marked difference is noticeable in the two tubes; the tube, which 
is heated, contains much more free iodine than the tube kept at O°. 

The explanation of this behaviour is connected with the phenom- 
enon of hydrolysis. The sulphates of sodium, magnesium etc. are 
very slightly alkaline, since the basic portions in these salts are 
stronger than the acid portion. At higher temperatures more OH’- 
ions are produced, since temperature greatly increases the amount 


315 


of hydrolysis, and these OH’-ions react on the iodine which is set 
free re-forming iodide and iodate: 

Hence at the higher temperatures, less iodine seems to be formed 
from the mixture of iodic acid and potassium iodide in presence of 
concentrated sodium or magnesium sulphate. 

On the other hand, solutions of zine and ammonium sulphates 
produce H'-ions due to hydrolysis and these H'-ions are very active 
in liberating iodine according to the following equation: 

10'",+5’+6H =31,4+3H,0. 

Moreover, I have repeatedly observed that addition of acids pro- 
duces more iodine, from a mixture of iodie acid and potassium 
iodide, than in the absence of acids. ‘ 

Hence the abnormal effect of temperature on the velocity of the 
reaction between iodie acid and potassium iodide in presence of 
sodium sulphate ascribed by SkraBaL to complex formation, is really 
due to secondary changes produced by the interaction of the products 
of the hydrolysis on the reacting substances. 

A similar explanation is applicable to the small temperaturé coef- 
ficients obtained in the reaction between iodic acid and potéssium 
iodide in presence of sodium acetate, sodium phosphate and potas- 
sium fluoride; because all these salts are alkaline due to hydrolysis, 

The reaction between iodic acid and potassium iodide is extremely 
rapid even at O°. The reactions between KI and K,S,O, and KI 
and H,O, have smaller velocities than that between HIO, and KI. 
These two reactions have temperature coefficients greater than unity. 
Experiments were made on the effect of concentrated MgSO, solution 
on the influence of temperature on the reactions between HI and 
K,S,0, and HI and H‚O,. Even in presence of MgSO,, these two 
reactions have temperature coefficients greater than unity. The hot 
tubes contain much more iodine than the cold ones. 

In this connection, it is interesting to observe that the solubility 
of iodine in KI or HI is greatly diminished by the presence of MeSO 

HCl does not produce an increase in the amount of iodine libe- 
rated in the following cases: 

(a) K,S,0, + KI, (6) K,S,0, + HI, (c) Ferric nitrate + KI. 
In the following cases, HCI markedly increases the amount of iodine 
(a) H,O, + KI, (6) H,O, + HI, (c) HIO, + KI, (d) HIO, + HI, 
(e) H,Cr,O, + HI, (7) K,Fe (CN), + KI, (9) HNO, + KI. 

The last two reactions have temperature coefficients greater than 
unity even in presence of HCl. 

21 

Proceedings Royal Acad. Amsterdam. Vol. XXIII. 


316 


The displacement of iodine even in very dilute solutions of Kl 
by chlorine or by bromine is very rapid and almost instantaneous 
even at 0°. The temperature coefficient is practically unity. 

The liberation of iodine from KI,KMnO, and H,SO, is almost 
instantaneous even at 0°. The temperature coefficient is practically unity. 

The liberation of iodine from KI-+ KCIO, and H,SO, or HCI, 
Kl + KBrO + H,SO, or HCI has a measurable velocity and temp- 
erature has a marked influence on these reactions, but KIO, + KI 
+ HCl or H,SO, liberates iodine at once and no effect of temperat- 
ure could be detected. 

The reactions between iodine and sodium thiosulphate, and iodine 
and sulphite are extremely rapid even at O°. There is hardly any 
possibility of measuring the velocity of the reactions concerned. 

In a foregoing paper (Jour. Chem. Soc. 1917, 111, 707) I have 
shown that the oxidation of oxalic acid by chromic acid has the 
temperature coefficient 1.95, but in presence of Na,SO,, MgsO, and 
NaF’, the temperature coefficient goes down to 1.63, 1.61 and 1.59 
respectively. The explanation seems to me to be the same as in the 
SKRABAL reactions. The reaction between oxalic acid and chromic 
acid is accelerated by H' ions. Sodinm sulphate, sodium fluoride ete. 
are hydrolysed to a much greater extent at a higher temperature 
‘than at the ordinary temperature and the OH’ ions produced at 
the high temperature neutralize the H’ ions existing in the solution 
and hence the actual velocity of the reaction does not rise so high 
as it should have been if there were no increased hydrolysis and 
consequent generation of OH’ ions at these temperatures. In other 
words, the effect of temperature is partly neutralized. 

Exactly similar results were obtained by Harcourt and Esson 
(Phil. Trans. 186 A, 1895, 817) in the reaction between HI and 
H,O,. They obtained the value 1.4 for the temperature coefficient 
of the above reaction in presence of NaHCO,, whilst in presence of 
HCI, H,SO, ete, the temperature coefficient is 2.1; Harcourt and 
Esson could not account for this discrepancy. The explanation is 
the same as that of the SkraBaL reaction. Sodium bicarbonate is 
alkaline in aquoeus solution and it produces OH’ ions in a greater 
quantity at higher temperatures than at ordinary temperatures and 
these OH’ ions react on the iodine which is produced, forming 
iodide and iodate. Hence at the higher temperatures less iodine seems 
to be formed. In other words, the effect of temperature is partly 
neutralized and we get the small value (1.4) for the temperature 
coefficient of the reaction between HI and H,O, in presence of 
NaHCO,. 


317 


On the other hand, SKRABAL got the value 45 for the temperature 
coefficient of the reaction 31, + 60H’ = 5I’ + 10', + 3H,O, in 
presence of sodium carbonate and bicarbonate. Here the hydrolysis 
of the salts produce OH’ ions which are active in the change and 
helps the effect of temperature. The increase of temperature increases 
the hydrolysis and hence the OH’ ions are also increased and the 
velocity of the reaction is increased due to this effect in addition to 
the usual effect of temperature increasing the velocity of the reaction. 
In other words, the effect of temperature is intensified. 

Hence the abnormally large effect of temperature is explained. 


Summary : 


a. A dilute solution of iodic acid and potassium iodide react very 
rapidly even at 0°. The temperature coefficient cannot be exactly 
determined and is probably equal to unity. 

6. In presence of sodium and magnesium sulphates slightly less 
iodine is liberated from iodie acid and potassium iodide at higher 
than at lower temperatures. The explanation is that at higher temper- 
atures more OH’ ions are produced due to increased hydrolysis of 
sodium or magnesium sulphate and these OH’ ions react on the 
iodine which is forming and thus regenerate iodide and iodate. 
Hence in presence of Na,SO,, the temperature effect is partly 
counter-acted. 

c. Manganese sulphate, potassium sulphate, alum ete. have no 
action, whilst in presence of ammonium and zine sulphates, the 
temperature coefficient of the reaction between iodie acid and 
potassium iodide becomes greater than unity. Solutions of zine and 
ammonium sulphates produce more H’ ions at higher temperatures 
and these ions are very active in liberating iodine from iodic acid 
and potassium iodide. 

d. A similar explanation is applicable to the small temperature 
coefficients obtained in the reactions between 1. iodic acid and 
potassium iodide in presence of sodium acetate, sodium phosphate, 
potassium fluoride etc., 2. chromic acid and oxalic acid in presence 
of sodium sulphate, magnesium sulphate, sodium fluoride ete., 
3. hydrogen peroxide and hydrogen iodide in presence of sodium 
bicarbonate. 

e. Abnormally large values of temperature coefficient for the 
reaction 31, + 60H’ — 5I’ + 10’, + 3H,O, in presence of Na,CO, 
and NaHCO,, are also due to hydrolysis of the carbonates. 

f. The following reactions have measurable velocities and their 

21* 


318 


temperature coefficients are greater than unity even in presence of 
MgsO, or HCI: 
(1) KI + K,S,0O,, (2) KI + K,Fe (CN),, (3) KI + HNO, 
On the other hand, the following reactions are almost instantaneous 
even at O° and their temperature coefficients are about unity: 
(1) KI + H,SO, + KMnO, (2) KI + Br, (3) KI + Cl. 


Chemical Laboratory, Muir Central College, 
Allahabad, India. 


Physiology. — “On Fibrillation of the Heart’. (First part). By 
Dr. 5. pr Boer. (Communicated by Prof. I. K. A. Wertneim 
SALOMONSON). 


(Communicated at the meeting of March 27, 1920). 


i; 


It had struck me as early as 1914 that a single induction-shock 
applied to the ventricle repeatedly engenders fibrillation of this 
chamber of the heart. [ did not study this phenomenon any further, 
since at that time I was studying the eiectrograms of the extra- 
systoles and of the postcompensatory systoles. 

When, however, I continued my alternation-experiments with the 
bled frog’s heart through extra-stimulation, I noticed the above 
phenomenon so frequently that [ felt called upon to study the rela- 
tions, under which this fibrillation took place, more closely. It now 
appeared that fibrillation of the ventricle occurred after a single 
induction shock only when this was applied directly after the close 
of the refractory stage which always accompanies the systole imme- 
diately preceding. This is clearly illustrated by the curves of fig. 1, 
which were registered') half an hour after the bleeding of a sus- 
pended frog’s heart. In the upper row of curves an induction shock 
was given to the base of the ventricle at 1 a short time after the 
close of the refractory stage. 

Fibrillation of the ventricle was the result which manifested 
itself in the string-curve by totally differing detlections, whose tempo 
was very irregular. Similar results were achieved at 2, 6, and 8. 

We notice that the post-undulatory pause, after fibrillation excited 
in 6, may also be lacking (after 2). After 3 an extra systole is 
interpolated by the extra-stimulus, a phenomenon that may occur 
with a slow heart-beat, as has been first shown by TrenDELENBURG. 
In this case the stimulus was administered at a much later period 
of the ventricle (towards the close of the T-detlection), so that a 
fully co-ordinated extra-systole was the result. In the same way a 
complete extrasystole is generated at 7, because here also the stimulus 


1) In this and the following registrations a non-polarizable electrode was placed 
on the auricles and one on the apex of the ventricle. The tension of the string 
was in all experiments such that 1 mV. yielded a deflection of 1!,. mm. 


320 


+ 


321 


was applied later. Not a single exception to this did I find in a 
large number of experiments with more than 100 frogs. 

While fibrillation of the ventricle could be generated only by one 
induction-shock at the very commencement of the excitable period, l 
movarwbly obtained a fully co-ordinated extrasystole, when the stimulus 
was applied at a later stage of the excitable period with the same 
force and at the same spot. 

To the brief delirium, originating at 4 after the extra-stimulus I 
shall revert lower down. 

Fig. 2 shows that during an experiment the metabolic condition 
of the ventricular muscle must deteriorate considerably before delirium 
can be brought about. In the upper row a stimulus was twice 
administered to the base of the ventricle 15 minutes after the bleeding 
(at | in the beginning, at 2 in the middle of the descending branch 
of the 7-deflection). In both cases a complete extra-systole of the 
ventricle appeared. The second row of curves was registered a quarter 
of an hour after the bleeding and now at 3a little before the middle 
of the descending branch of the 7-deflection an extra stimulus is given 
to the base of the ventricle. Although the stimulus was now applied 
later than at 1, ventricular fibrillation now follows. Now that the 
general condition of the ventricular muscle is grown worse in a 
quarter of an hour, the stimulus on the ventricle must be applied 
still later to generate an extra-systole. It is obvious that the electric 
deflections are again very irregular. Shortly after this registration 
this fibrillation stopped spontaneously. When a few minutes after- 
wards I applied again a stimulus to the ventricle, a permanent 
fibrillation of the ventricle ensued, which | registered for 14 hours 
(see Fig. 3). I regret that the commencement of the fibrillation was 
not registered. The top curves were photographed 5 minutes after 
the beginning of the delirium. We see that now the deflections, as 
in fig. 2, are irregular. The 2°¢ row was registered */, hour after 
the commencement of the fibrillation. Now the curves present a 
totally different aspect. A certain regularity in the deflections 
can be observed. Every time three smaller deflections occur between 
two larger ones, but each of four successive deflections is different 
from the others and the tempo is irregular. But these groups of 4 
deflections recur continually. The bottom curves were taken 14 hours 
after the commencement of the fibrillation. Though the deflections 
are slightly altered the regularity of the delirium remains. In both 
registrations the two successive, equal deflections are at the same 
distance from each other. In the suspension-curves the regular 
deflections of the auricular contractions may be observed (in the 


322 


Kid KEA KAK KT Et Ad 
dl Reins 


323 


TENT TERRE ind 


AvA vn ne awed vn 


vt 


WR N Ni 


324 


lower registration the suspension-curve is slightly interfered with by 
a momentary movement of the frog). Also through inspection I 
noticed that the auricles continued beating during the fibrillation. 

I also possess the registration of two more frog’s hearts that kept 
fibrillating after a stimulus. Here also the deflections of the string 
were initially irregular and here also they became more regular 
afterwards. In these registrations large and small deflections were 
alternating and the auricles continued beating regularly. 


Significance of the experimental results obtained for an 
explanation of ventricular fibrillation. 


Before accounting for ventricular fibrillation in a way different 
from all previous interpretations, [I will just summarize the main 
results of this investigation. It should be remembered that the ven- 
triele can only be made to fibrillate by an extra-stimulus if this 
stimulus is applied directly after the close of the refractory stage. 
Fibrillation never appears when the stimulus is given later with the 
same force and at the same spot; if it is, it will result in an ordi- 
nary extrasystole. 

To these facts I attach great value. So the ventricle will begin 
to fibrillate after an extra-stimulus only when its metabolic condition 
is bad. This condition is still bad at the beginning of the excitable 
period, because in so short an interval after the termination of the 
preceding systole the ventricular muscle has not been able to recover 
itself. From this bad metabolic condition of the ventricle it follows: 

1. That the contractility of the ventricular muscle is bad. After 
an extra-stimulus there is a brief small contraction. This brief extra- 
contraction is accompanied by a brief refractory stage. 

2. That the conduetivity of the excitation through the ventricle 
is slight. 

These two circumstances are conclusive for the origin of the deli- 
rium. These conditions are quite different when the stimulus is 
applied at a later period. Then the metabolic condition is much 
better, because after the preceding systole the ventricle has had 
more time for recovery. Consequently the contractility and the con- 
ductivity are much better; then the excitation passes rapidly through 
the ventricle and a properly co-ordinated extra-systole results from 
the stimulus. 

In order to fully understand the origin of the delirium, we must 
first consider the brief delirium, since in some of our experiments 
the delirium was only of very short duration and consisted of 2 or 


325 


3 deflections in the mechanogram and in the electrogram. This is 
instanced in Fig. 1 (2"d row of curves at 4). Here we see after the 
electric stimulus 3 small deflections in the suspension-curve (a, 6 
and c) with which electric deflections correspond. Now what does 
this mean? When looking at 2 or 3 deflections, we observe a phe- 
nomenon formerly described by me as deformed ventricular systoles 
and which is known in the literature by the name of ventricular 
peristalsis. Similar deformed systoles also occur after digitalis poison- 
ing'). We illustrate this by a series of curves registered from a 
frog’s heart 25 minutes after a subcutaneous injection in the thigh 
of 14 drops of digitalis dialysate (Fig. 4). The first ventricular curve 
of the figure consists of two parts; first the suspension curve rises 
up to a certain point and at the beginning of the dilatation line a 
second rise begins. This form of the curve owes its origin to the 
circumstance that first a part of the ventricular muscle begins to 
contract; subsequently, owing to the bad metabolic condition the rest 
of the muscle comes into action with a prolonged latent stage; this 
causes a retarded contraction. 

The electrogram. registered at the same time fully confirms this 
statement. The third ventricular curve of the figure presents a break 
in the ascending branch and is, therefore, also deformed. During 
these deformed ventricular systoles the whole muscle is indeed made 
to contract, but in 2 or 3 tempos. The same is the case with the 
brief delirium. After the extra stimulus which affects the ventricle 
at a moment when the recovery of the muscle is still unsatisfactory, 
part of the ventricle begins to contract. The proceeding “Erregung” 
imparts contraction to the following portion only after a long lasting 
latent stage, so that the “Erregung’”’ passes through the ventricie in 
two stages. The brief delirium, then, is nothing but a deformed 
fractionated extrasystole. 

Now upon this basis we can readily conceive the origin of the 
longer fibrillation in our experiments. As set forth heretofore, the 
refractory stage of the contraction, generated at the outset of the 
excitable period, is shortened. This shortening is of great moment 
for the lengthening of the delirium. When the “Erregung”’, after 
an extra-stimulus, has gone through the ventricle in stages, the time 
of such a circulation is lengthened considerably. Now when the 
excitation wave reaches the starting point again, it begins to contract 
again, because the short refractory stage of the preceding contraction 
has already come to a close. Again the “Erregung”’ proceeds through 


1) Arch. Neêrl. de Physiologie. Tom. III, p. 69, 1918. 


326 


“i 
bbe. 


ic 


327 


the ventricle and again by jerks. Thus the excitation wave keeps on 
circulating through the ventricle like an ignis fatuus, and fibrillation 
is checked only when it strikes on a refractory region. Then 
the post-undulatory pause sets in, which however may also be 
absent. (Fig. 1 after 2 in the second row). 

After an extra-systole, elicited later in the excitable period, the 
excitation-wave does not begin a second course, because then it is 
checked by the refractory stage, which with this extra-systole is 
of longer duration. The same relations exist with the normal rhythmie 
systoles. If in this case the refractory stage were absent or much 
shorter, the excitation-wave would always continue its course in the 
closed muscular system of the ventricle, which would not be able 
to pulsate rhythmically under the influence of the sinus-impulses. 

According to my theory, therefore, fibrillation of the heart is 
brought about by a non-coördinated contraction, not as WINTENBERG 
conceived this; viz. that sundry sources. of contraction are function- 
ating independently; according to my theory the various regions of 
a ventricle contract successively and an “Erregung” being once 
elicited may pass through a ventricle several times running; the 
ventricular delirium consists of a string of fractionated ventricular 
systoles. For fibrillation two conditions must be fulfilled at the 
moment when it originates: 

1. The refractory stage must be shortened. 

2. The conductivity of the stimulus through the ventricle must 
be insufficient. Both conditions are fulfilled in my experiments. 
Directly after the close of the refractory stage the metabolic condition 
of the ventricle is bad, contractility is slight, so the refractory stage, 
accompanying a contraction, is short; moreover the conductivity 
through the ventricle is insufficient. 

WiINTERBERG and Rorpercer believed that the only essential con- 
dition for the origin of fibrillation was a much shortened refractionary 
stage. This is true if only conductivity is also bad. Only then will 
the phenomenon come forth. 

Now the question arises, why after digitalis poisoning of the 


1) Incessant fibrillation may succeed when the “Erregung”’ after one circulation 
always arrives at the starting point again at a moment when the recovery is still 
insufficient. Thus the excitation-wave may be emprisoned in a ventricle and every 
time renew its course. Especially when (as in Fig. 3) the delirium becomes regular; 
then the chance of a spontaneous termination is little, as, when the excitation-wave 
has gone through the ventricle some times in succession in the same way, this 
may be repeated every time without the “Erregung” being checked by a refractory 
region. 


328 


frog’s heart deformed ventricular systoles are generated, whereas it 
never brings about fibrillation of the ventricle. This finds an expla- 
nation in the fact that after digitalis poisoning (in a toxic dosis *)) 
the refractory stage of the ventricle is lengthened instead of shortened. 
Conductivity is then bad, however, so that a single deformed ventri- 
cular systole can arise, but the “Hrregung” cannot pass through 
the ventricle a second time. 


1) When speaking of digitalis-poisoning in a toxic dosis, 1 mean a dosage that 
lengthens the refractory stage and retards conductivity. 


Physiology. — “On fibrillation of the Heart. (Part. II). On the 
Relation between Fibrillation of the Heart and “Gehüufte” 
Eetra-systoles”. By Dr. S. pr Borr. (Communicated by Prof. 
I. K. A. WeRTHEIM SALOMONSON). 


(Communicated at the meeting of March 27, 1920). 


IT 


It is remarkable that while clinicians already suspected a relation 
between fibrillation and “gehäufte” extra-systoles, both abnormal 
cardiac actions could be generated under precisely the same conditions 
in the frog’s heart. Such was the case in some of our experiments 
when at: the close of the refractory stage of the ventricle we observed 
-a series of systoles of this chamber instead of fibrillation after the 
application of an induction shock. 

This phenomenon is illustrated in the three figures which we will 
now describe : . 

In fig. 1 are shown the suspension curves and electrograms of a 
bled frog’s heart *). At 1 on the summit of the negative 7-deflection 
an induction shock is applied on the base of the ventricle. This 
evokes an extra-contraction of the ventricle, which is represented in 
the string-curve by a ventricular electrogram of which the A-deflection 
is broadened, and at the same time the magnitude of the negative 
T-deflection is increased. Previous investigations made by me went 
to show that a broadening of the R-deflection and a change of the 
T-deflection in a negative sense resulted from a slowing of the 
conduction of the excitation through the ventricle. In the experiment 
before us, the reason why after the administration of the induction 
shock the conduction of the excitation is slowed, is that the refractory 
stage of the preceding systole had come to a close a short time 
before. The metabolic condition of the ventricle was consequently 
still bad. A second result from this bad metabolic condition is the 
bad contractility of the ventricular muscle. The extra-systole 
revealing itself after the stimulus, is small (as may be read from the 


1) In every figure the electrograms were taken by placing a non-polarizable 
electrode at the apex and one on the auricles. The tension of the string was such 
that the interpolation of 1 mV. caused a deflection of the string of 1!/, mm. 
Time was registered in !/; seconds. 


330 


suspension-curve). It is accompanied by a brief refractory stage. 
During this extra-systole we have, then, on the one side a slackened 
conduction of the excitation through the ventricle and on the other 


a brief refractory stage. 


Fig. 1. 


331 


These two factors contribute to the origin of “gehaufte” extrasystoles. 
The excitation-wave, it is true, bas not traversed the ventricle in stages, 
but the time required for a circuit, has nevertheless increased. The 
refractory stage being shortened, the excitation-wave performs again 
its circuit through the ventricle, because when it has arrived at the 
starting point, the ventricle has at that spot become excitable again 
after the shortened refractory stage. The second time the excitation-wave 
again traverses the ventricle slowly and again the contraction is of 
short duration. In this way the excitation-wave may move round the 
ventricle several times running and engender a series of reduced 
ventricular systoles. 

The electrograms imaging this process show the indicated character- 
istics of a slackened conduction of the excitation-wave '). After the first 
extrastimulus three “gehäufte” extrasystoles revealed themselves. 
During these three extra-systoles we see in the electrogram-curve 
one P-deflection (P;) preceding the next P by exactly one periodic 
interval. It would seem, then, that during these “gehäufte’” systoles 
of the ventricle the periodicity is not disturbed. At 2 the stimulus 
is repeated on the apex of the negative 7-deflection and again three 
“gehäufte” extrasystoles *) are generated. Now also the pulsations of 
the auricle are undisturbed. 

The curves of Fig. 2 are derived from the same frog’s heart. At 
1 an induction shock was applied to the base of the ventricle towards 
the close of the 7-deflection, which resulted in three “gehäufte” 
extra-systoles. At 2 the stimulus was renewed at the same time of 
the ventricular period, which produced a curve illustrating a ming- 
ling of irregular fibrillation and ‘“gehaufte’ extrasystoles. The 
first curve after the stimulus is a distinct extrasystole (as can be 
concluded from the deflections of the string, which show an &-deflection 
and an intense negative 7-deflection). Subsequently the electric curve 
becomes very irregular and at the close two distinct extrasystoles 
appear again, each with an R-and 7-deflection. When the ventricular 
base is stimulated again at 3, two extrasystoles are evolved. 

Fig. 3 shows the curves of another frog’s heart. 

The electrograms of the normal rhythmic ventricular systoles 


1) The influence of the rate of conduction upon the form of the ventricular 
electrogram is discussed by me extensively in Pfliiger’s Arch. Bd. 173, Seite 78, 
1918 and Arch. Néerl. de Physiologie, tome III (1918) p. 7. 

2) It will be seen that the duration of the pause after the ‘“‘gehiufte” extra. 
systoles is very different sometimes, as appears from the figures. The time of the 
post-undulatory pause may also be very different. I purpose to revert to these 
facts in a later communication. 


22 


Proceedings Royal Acad. Amsterdam. Vol. XXIII. 


332 


negative 


as is always distinctly the case 


corresponding 


large 


and 


broad? R-deflections 
discern 


exhibit “= 


Here we 


T-deflections. 


in each ventricular 


wave 


with slow conduction of the excitation 


il 


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DEE } 
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H i 1 Hi 


4 05 DA ad ON IN B! i iid | 
Pelee rei yee, Phi ddd] RN 


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333 


electrogram as a sign of persisting basal negativity the heel of 
SamosLorr (marked by an A in the figure) cut into the retarded 
apical negativity. 

At 1 the base of the ventricle receives an induction shock a 
little after the apex of the negative 7-deflection. Four connected 
extra-systoles are evoked by it. From the accompanying ventricular 
electrograms it is evident that the conduction of the excitation wave 
through the ventricle is considerably slowed with each extrasystole. 
We infer this from the marked broadening of the R-deflections and 
the considerable change of the 7-deflections in a negative sense. 
The heel of SamoJLorF is clearly observable in each electrogram. 
When at the same moment of the ventricular period the base of 
the ventricle is again stimulated at 2, five connected extrasystoles 
of the ventricle will appear. Again during each extrasystole a con- 
siderable slowing of the conduction is conspicuous and may readily 
be read from the electrograms. At 3, however, an extra-stimulus 
touches the base of the ventricle much later, viz. a short time after 
the 7-deflection. Now only one extrasystole of the ventricle appears. 
During this extrasystole the rate at which the excitation wave is con- 
ducted through the ventricle is very likely slower than during the 
periodic ventricular svstoles, but decidedly not so slow as with the 
preceding ‘“‘gehdufte’” extrasystoles ’). 

The f-deflection is not nearly so broad as in the ventricular 
electrograms of the “‘gehaufte”’ extra-systoles. 

We also see at a glance the far slower conduction of the excita- 
tion wave during the “gehäufte” extrasystoles, for if we look at the Zi- 
deflections of the electrograms, it strikes us that the ascending lines 
are very clearly visible during the “gehäufte” systoles, while both 
during the periodic ventricular systoles and during the extrasystole 
at 3 they are reproduced by much thinner lines’). This implies that 
during the ‘‘gehaufte” extrasystoles the excitation wave is transmitted at 
a much slower rate from the starting point through the base of 
the ventricle than during the periodic ventricular systoles and the 
extrasystole at 3. It is evident, therefore, that during the extra- 


1) If we wish to compare the rate of the conduction of the excitation wave, it is 
evident that we can cumpare the extrasystole at 3 only with the first systoles of the 
“gehäufte” ventricle-systoles, for only with them the stimulus starts from a definite 
point i.e. the same point of the surface of the ventricle (viz. where the stimulant 
electrode stands). 

*) In the electrograms of frogs’ hearts it usually appears also, when the con- 
duction of excilation has been slackened, that the descending line of the R-deflec- 
tion is very steep or rather steep. In that. case the ascending line of the R deflec- 
_tion is less steep. 


22* 


334 : 


systole at 3 the rate of the conduction of excitation wave is not nearly so 
much diminished as with the first systole of the “gehäufte” ventri- 
cular systoles. Besides, the duration of the electrogram of the extra- 
systole at 3 is longer than that of the first electrograms of the 
“gehäufte”” extra-systoles. The quicker conduction as well as the 
longer duration of the ventricle-electrogram, i.e. the longer duration 
of the refractory stage, contribute to the fact that after the stimulus 
at 3 only one extrasystole reveals itself. After the quicker conduc- 
tion the excitation wave is checked by the longer refractory stage. 

We see then that the same rule holds for the origin of ‘““gehaufte” extra- 
systoles and for that of ventricular fibrillation. When the stimulus 
meets the ventricle directly after the close of the refractory stage, 
the “gehaufte” extra-systoles can come forth. But when in a frog’s 
heart that exhibits “gehaufte”’ systoles after being given an electric 
stimulus directly after the close of the refractory stage, the stimulus 
is applied at a later time of the ventricle period at the same spot 
and with the same force, one single extrasystole will appear. 

It appears therefore that the ‘“gehäufte’” extrasystoles originate 
only when the metabolic condition of the ventricle is bad, and con- 
sequently the excitation wave is conducted slowly through the ventricle. 
At the moment when the metabolic condition of the ventricle is bad, 
a stimulus will also evolve a brief extrasystole with a brief  refrac- 
tory stage. The appearance of the “gehäufte” extrasystoles, there- 
fore, is aided as well by the slow conduction of excitation as by 
the short duration of the refractory stage. Then after the first 
course through the ventricle which is of long duration, the excitation 
wave can go round once more, because the starting point has become 
excitable again at that moment. This may be repeated several times. 
The conditions for the origin of the “gehaufte’ extra-systoles are 
therefore the same as for the origin of ventricular fibrillation. The 
mechanism of the processes at work in the ventricular muscle during 
fibrillation and the “gehéufte’ extrasystoles, displays only differences 
in degree. In the case of both deviations from the normal rhythm 
the conduction of excitation wave has largely slackened and the duration 
of the refractory stage has decreased with its appearance. In the case 
of delirium cordis the excitation wave passes through the ventricle so 
slowly that every time different muscular areas of the ventricle are 
made to contract, so that the excitation wave proceeds through the 
ventricle slowly and by jerks. This leads to fractionated ventricular 
systoles, which are linked together for the time of the delirium. During 
the “gehéufte’’ extrasystoles, however, the refractory stage is. also 
shortened at the moment of its origin, but now the excitation spreads 


335 


through the ventricle, slowly indeed, but undisturbed i.e. without 
shocks. This produces co-ordinated contractions of the ventricular 
muscle *). 

The relationship between cardiac fibrillation and “gehdufte” extra- 
systoles may also appear from the fact that these forms are inter- 
changeable: ‘‘gehaufte’” extrasystoles may pass into ventricular 
fibrillation and conversely ventricular fibrillation may pass into 
“oehdufte’ extrasystoles. I will confine myself here by reproducing 
only an instance of the latter transition forms. 

Fig. 4 gives the suspension curves and the electrograms of a 
froe’s heart after bleeding. At 1 an electric stimulus reaches the 
ventricular base a little past the summit of the 7-deflection. This 
induces ventricular fibrillation, ending in an extra-systole. During 
this fibrillation the auricles continue their pulsations regularly and 
are delineated in the suspension-curve as slight elevations (marked 
by the letter A). The appearance of an extrasystole at the termina- 
tion of a fibrillation of the ventricle is a common phenomenon. 
Anyhow my curves frequently bore this out. 

After the preceding discussion this can be readily accounted for. 
I also often observed that fibrillation ended in a strong rise of the 
suspension-curve, which is illustrated in the curves of the first part 
of this communication and in my paper in Pfliigers’ Archiv *). This 
marked rise at the end of the fibrillation curve points to a contrac- 
tion of a rather large area of the heart muscles as the final phase 
of fibrillation. Upon this the excitation will readily rebound. The 
same explanation holds for the extrasystole with which fibrillation 
often concludes. After the extrasystole a prolonged pause appears 
and after this the normal rhythm ensues. I wish to draw attention 
to one more particular. Between the fibrillation and the extrasystole 
a small negative deflection occurs (indicated by an arrow). 

It is impossible to say for sure how this deflection has originated. 
It may be that after the fibrillation a retrograde excitation conduc- 
tion has given rise to an auricular contraction, which at that moment 
coincides in the suspension-curve with the extrasystole curve. Then 


) It stands to reason that in the case of this strongly retarded conduction of 
the excitation every ventricular contraction of the “gehäufte” extrasystoles is no 
of necessity a contraction of the whole ventricular muscle. No doubt partia] 
asystoles especially of the ventricular apex will occur during various “gehäufte” 
extrasystoles. So much anyhow appears from the figures reproduced by me. Of 
several “gehäufte” extrasystoles of these figures the negative T-deflections are 
smaller than may be anticipated from the considerably retarded conduction. It is 
most probably brought about by the partial apex-asystole. 

2) Pfliigers Archiv. Bd. 178. Seite 1. 


336 


we should recognize a negative P-deflection, since the excitation 

wave proceeded in a retrograde direction through the auricles. 
Secondly it may be imagined that this negative deflection is gene- 

rated by a bulbus-contraction, We notice these bulbus electrograms 


Ta Ta AY 


1 co | | 

| : i & 

: 5 HEL 

a | | schi 

s i | me 
Up 


\t i 
Ke Ii EE IE / | 
j di A el i a 


a en 


ee 
Tea 


Fig. 4 


337 


during the ventricular electrograms of the periodic ventricular systoles 
and also during the electrograms of some “gehäufte’” extrasystoles 
(indicated in the figure by ab). Then the excitation wave would 
appear to have spread after the fibrillation over the bulbus arteriosus. 

At 2 the ventricular base is stimulated again a little past the 
summit of the 7-deflection. Again ventricular fibrillation is the con- 
sequence, while the auricles continue to pulsate in the undisturbed 
rhythm. After a short time, however, fibrillation passes into five 
“pehaufte’ extrasystoles, followed by a prolonged pause '). 

Subsequently the normal rhythm recovers itself. In what manner 
this transition occurs will be further examined by me. It has already 
appeared that the one process in the ventricle is liable to merge 
into the other, but also that this transition can occur indirectly. 
This will be recorded afterwards. 

We see then that ventricular fibrillation and ‘“gehdufte”’ extrasy- 
stoles, which are of the same genesis, may even pass into one 
another. It has thus been proved experimentally that the two rhythm- 
disturbances are closely allied. This conception has been advocated 
already by clinicians as WeNCKEBACH and Lewis. 


1) It is remarkable that this pause is of a longer duration than the one after 
the single extrasystole with which the previous fibrillation concluded. The post- 
extra-systolic pause then is very different as to duration (see also figs 1, 2 and 3) 
just as the post-undulatory pause, which may even fail altogether. To this | purpose 
to revert in a later publication. 


Physiology. — ‘Factors which are of vmportance for the habit- 
formation of birds. I. Visual sensations” *). By Miss Lucin W. 
Scuut. (Communicated by Prof. G. van RIJNBERK.) 


(Communicated at the meeting of June 26, 1920). 


Introduction. - 


In 1918) Buisrenpijk described experiments on habit-formation 
in birds. He found that a siskin very soon learns to look for food 
in a seed-box, where the food is hidden from sight by a flap. When 
this box is placed amongst similar, but empty ones, the bird invariably 
will go to the filled box, provided it is always kept in the same place 
amongst the others. The habit formed in this way was not forgotten, 
even after the bird having been taken for months to other surround- 
ings, for on itsreturn. placed in front of the same boxes, the bird at 
once flew to its old box for food. 


Control and corroboration of ButsTENDIIK’s results. 


I repeated the experiments made by Buistenpijk and arrived at 
the same results as he did. The birds I selected for the experiments 
were the siskin (Fringilla spinus, 3 specimens), the redcap (Fringilla 
carduelis, 2 specimens), the paradise widow (Steganura paradisea, 2 
specimens) and the Napoleon weaver (Pyromelana afra, 2 specimens). 
It is surprising how rapidly all these birds, but above all the siskin, 
learned to push their heads under the flap of the food-box. The siskins 
accomplished the task at the first trial, within fifteen minutes. The 
others took a little longer, the experiment having to be repeated 
regularly for a few days in succession. If, further, I replenished one 
particular box, placed amongst four similar ones, from the very 
beginning, as the rule was, the birds were equally quick in learning 
to look for food in that special box and rarely tipped up the flaps 
of the other boxes. Buirenpijk believes that the fixed place the 
feeding-box takes amongst the others, is the ruling element in this case. 


1) Afler experiments made in the physiological Laboratory of the University of 
Amsterdam. 

2) F.J. J. BuwrenDijK. Proeven over gewoontevorming hij dieren. Amsterdam 
1918. 


339 


1 can: corroborate this in principal. In a great number of expe- 
riments taken with a siskin I endeavoured to remove every possible 
mark which might have led the bird to the right box. To this 
purpose I covered the frontside of the boxes, as also the bottom of 
the cage in front of them with strips of cardboard, which were 
constantly renewed. Husks of the eaten seed were carefully cleared 
away each time and the flaps of the boxes were renewed each time, 
in order that the bird might not be able to tell it by scratches it 
might have made with its beak. In spite of these precautions, the 
bird, once having learned that its food was placed in oue particular 
box, rarely lifted the flap of another by mistake. As a positive 
proof, in connection with the supposition that the birds were led by 
other characteristics than the fixed place of the food box, I relate 
the following experiment: When the siskin had duly learned to go 
for its food to one particular box, I took a second cage, in all respects 
similar to the one in which the experiments had been made. This cage 
was perfectly new and the siskin had never been in it before. 
To this cage I had four new foodboxes attached, exactly like the 
four which up till that moment had been used for the experiments. 
The siskin had never eaten from these boxes, nor had they ever 
contained any seed. I now removed the siskin for ashort time, on different 
days, from cage 1 to cage 2. No seed had been put into any of 
the boxes in order to avoid that the bird should smell the seed behind the 
flaps. It was evident that the bird felt strange in its new cage; it 
flew about continually, coming up close to the food boxes, without 
however lifting up any of the flaps. After it had quieted down a 
little, the bird, though it certainly made more mistakes in its new 
cage than in the usual experimental cage, nevertheless sometimes imme- 
diately after leaving cage 1 for cage 2, flew to the right box and tipped 
up the flap. 

From this series of experiments I believe I am justified in forming 
the conclusion that the place the food-box takes is undoubtedly of 
great significance in the formation of habits. At the same time 
however [ thought it possible that other impressions contributed 
to the result as well. 1 therefore decided to find out in how far it 
_ was possible to train the birds by means of another factor of impressions. 


Other factors which may assist in forming a habit. 


I have endeavoured to eliminate the factor of place entirely from 
the series of experiments, which I will now proceed to give. This 
was done by filling a different box with food each time, and thus 


340 


preventing the bird from becoming accustomed to a fixed spot for 
its food-box (for this purpose [ employed siskins exclusively). I 
now however gave the food-box a visible mark, to distinguish it 
from the empty ones. 

1. First of all, I pasted black paper over the flap of the food 
box, the remaining ones being of bright tin. In a few minutes 
the bird had learned that the seed was behind the black flap. And 
in an astonishing short space of time a bird that has first been 
trained to look for the seed box, according to its position, seems to 
have forgotten this and it learns that the seed is behind the black 
flap. By repeatedly hanging this in front of another box, the bird 
is literally taught to fly after this black flap and exclusively or almost 
so, to tip up this flap to look for its food *). 

2. In a second series of experiments the flap of the food-box 
was pasted over with a blue paper. The flaps of the remaining 
empty boxes were also pasted over with blue paper, with blue of 
a different shade however. The result was that in a relatively sbort 
space of time the bird had learned again to go for its food to the 
box with the flap pasted over with blue of a particular shade, dis- 
tinguishing it from the remaining flaps. The difference was scarcely 
perceptible: in a series of experiments | used blue N°. 1186 of the 
well-known coloured papers of Baumann for the empty boxes, and 
N°. 1187 for the food box (food-colour)?), this difference is barely 
perceptible to the human eye. (1187 is the merest shade darker). 

3. A series of controls was still taken with green papers of dif- 
ferent shades. It appeared that the siskin distinguished as food colour 
N°. 985 from green N°. 984, from BauMmann’s scale. 

4. In a subsequent series of experiments I selected an extremely 
small token of distinction for the food box. The flaps of all four 
boxes were pasted over with white paper, but on the flap of the 
food box a small round black dise was stuck in the centre. 

Here again it was observed that it was comparatively easy by 
hanging the flap with the black food-token before another box each 
time, to teach the siskin, to look for its food exclusively behind 
the flap with the black disc. 


1) In fact the bird had by no means forgotten the first learned token of locality. 
| will revert to this point in the exhaustive paper to be issued soon. For the rest, 
experiments were frequently made with blank specimen, (empty boxes), to prevent 

nse of smell interfering. 
+ %) As is known, birds according to Hess do not see spectral colours further 
than the line of demarcation between green and blue. The difference detected 
must therefore be due to a difference in the shade. 


341 


5. Encouraged by the result of the series of experiments de- 
scribed so far, I resolved on employing a more subtle mark of 
distinction. I again employed white flaps for my purpose. The 
empty boxes had a black square, the food box a black disc of about 
the same size. The result of this series of experiments was not suf- 
ficiently convincing. Nevertheless I had the impression, when the 
siskin went to the box with the round disc, that this was not always 
entirely a matter of chance. 


SUMMARY. 


1. The result of my experiments is in corroboration with those 
of Buyrenpijk, that the place a food-box takes in the midst of other 
(empty) boxes, is of great importance for teaching birds to form 
the habit of eating from that box. 

2. In addition there are however numerous other visual factors 
which may tend to develop this habit. 


Chemistry. — “Two ILsomeric Chloro- Tetracetyl-d-Fructoses’”’. By 
Prof. F. M. Jarcer. 


(Communicated at the meeting of June 26, 1920). 


$ 1. Some time ago Dr. D. H. Brauns observed that, when phos- 
phorus pentachloride at low temperatures acts upon B-tetracetyl- 
fructose dissolved in dry chloroform, under differently chosen cireum- 
stances, tvo compounds are formed in the reaction, which both have 
the composition of a chloro-tetracetyl-fructose, but which differ 
considerably in properties. The one isomeride: a-chloro-tetracetyl-d- 
Fructose, melts at 83° C., and has a specific rotation of [el == 
160°,9 (the maximum value measured in chloroform-solution); it is 
produced only, if aluminiumchloride be added to the reaction-mixture 
as a catalyst. Contradictory to what one might perhaps expect 
beforehand from this mode of preparation, this @-derivative appears 
to be unstable to such a degree, that it is decomposed into an impure 
B-tetracetyl-fructose and an acid liquid within twenty-four hours, if 
exposed to the air at room-temperature. Only if preserved in the 
dark in an ice-box at a temperature of O° C,, it appeared possible 
to recrystallize the substance repeatedly from dry ether, if moisture 
be excluded as carefully as possible; even then, however, the decom- 
position mentioned above finally sets in. On the other hand, the other 
isomeride: 3-chloro-tetracetyl-d- fructose, which is produced under the 
same circumstances, if only no catalyst be added to the -mixture, 
appears to be a very stable substance in comparison with the labile 
a-derivative, and may be recrystallized from most of the organic 
solvents, without being changed to any appreciable degree. It melts 
at 108°C., and has, in chloroform-solution, a specific rotation of 
[ei 4502 While the «-compound has an intensely bitter 
taste, the g-derivative tastes only feebly bitter, and it is considerably 
more soluble in most solvents than the a-isomeride. The 8-compound 
is also not absolutely stable: when repeatedly recrystallized from 
absolute alcohol, the formation of ethylacetate can be observed; and 
when solutions in commercial benzine are slowly evaporated at 
18° C., the crystals obtained appear to be slightly coloured pink, 
while the mother-liquid also assumes a gradually increasing violet 
or even brown colour. In comparison with the ¢-compound, however, 
it can be considered to be “stable”; as far as known, these two 


343 


isomerides cannot be transformed directly into each other. A 0,1 
normal solution of NaOH causes all the chlorine to be split-off 
from the «-derivative within five hours at 0°C.; the g-derivative, 
however, does not liberate its chlorine under the same circumstances. 
The determinations of carbon, hydrogen, and chlorine (Carius), 
and those of the molecular weight, gave with both substances the 
same results, all agreeing with the composition of a chlorotetracetyl- 


fructose: C,H,O(C,H, O,), Ci. 


$ 2. In connection with the measurements of the isomeric @- and 
B-pentacetyl-*), and tetracetyl-d-fructoses*) formerly made by the 
author, it appeared of interest to study these two isomerides also 
from a crystallographical point of view, and to compare them with 
each other, as well as with the derivatives mentioned above. Chiefly 
with respect to the instability of the a-derivative, it was necessary, 
therefore, to prepare both isomeric substances once more, and imme- 
diately to measure the crystals eventually obtainable under favour- 
able circumstances. This was possible to me by Mr. Braun’s kind 
assistance, who placed a quantity of the 9-tetracetyl-derivative already 
described at my disposal, as well as his notes about the method of 
preparation of the chloro-derivatives. | wish to express to him also 
here my sincere thanks for his interest and help. 

The preparation, especially of the «-compound, must be carefully 
supervised; it is not so easy as it might perhaps appear to be. 
More particularly, the tetracetyl-fructose used must be free from acid, 
and the reagents applied may not contain moisture, nor may appre- 
ciable changes of temperature occur during the reaction. It is desir- 
able to work very rapidly: therefore, the evaporation of the solutions 
must take place under a glass bell-jar connected with a drying 
apparatus by blowing over the surfaces air carefully dried with 
calciumchloride. The e«-compound can best be recrystallized from 
dry ether in the ice-box at 0°C., and in darkness, moisture being 
carefully excluded. The same precautions should be taken in preparing 
the B-isomeride; but the substance may be recrystallized in the usual 
way at roomtemperature. Purification of the 8-compound can best 
be done by recrystallizing it from boiling absolute alcohol; to obtain 
beautiful and measurable crystals, the substance is dissolved in pure 
benzene, or in a mixture of chloroform and benzene, from which 
it is deposited on slow evaporation in big, transparent, prismatic 

1, F. M. JazeeR Proceed. R. Acad. of Sciences, Amsterdam, 20, 280, (1918). 


*) EF. M. Jazcer. Proceed. R. Acad. of Sciences, Amsterdam, 10, 563, (1903); 
Zeits. f. Kryst. und Miner., 45, 539, (1908). 


344 


crystals, possessing about the same refractive index as the remaining 
mother-liquor, and, therefore, being almost invisible in it. 

Preparation of «-Chloro-tetracetyl-d- Fructose. 

30 Grams of freshly recrystallized and carefully dried (-letracetylfructose are 
dissolved in 90 ccm. dry chloroform in a glass bottle with ground stopper; the 
solution is cooled to 0° C. by means of ice. Now first 7,5 grams of finely powdered, 
dry Al,Cl, is added, and afterwards 19 grams of dry phosphoruspentachloride. 
When all is at 0° C., the vessel is removed from the ice bath, and the mixture 
is left at room-temperature for 30 minutes, while il is stirred from time to time 
and while an opportunity is given to the vapours of the hydrochloric acid formed 
and to those of the chloroform to escape. Then the bottle is placed once more 
into the ice, the contents of it, after being cooled rapidly, brought into a separating 
funnel, and the liquor rapidly washed with a solution of sodium-bicarbonate cooled 
with pieces of ice; finally it is again washed with some ice-water. The chloroform- 
solution is subsequently dried by means of coarsely grained anhydrous CaCl,, 
and the dry solution, after being filtered, rapidly evaporated in a wide crystallisa- 
tion-dish by means of a strong current of dry air, under a glass bell connected 
with drying apparatus. The very viscous mother-liquor gets finally crystallized; 
crusts of solid matter are deposited, which are put upon a hard filter, rapidly 
sucked-off, the crystals pressed between sheets of filterpaper, and dissolved in dry 
ether. In the ice-box colourless needles or thicker prisms were gradually deposited from 
the solution, which, if suited for measurements, must be investigated immediately. 
All necessary precautions being taken, the reaction yields about 60—65°/, of the 
theoretical quantity. 

Preparation of (-chloro-tetracetyl-d-fructose. The preparation of this isomeride 
occurs just in the same way as that of the a-derivative, only no xx 
Al,Cl, being added to the solution. After the chloroform has 
been evaporated, a small quantity of absolute alcoliol is added, 
by which immediately an aggregation of colourless needles is 
formed, which is treated as described above and then. repeat- 
edly recrystallized from boiling absolute alcohol. Measurable 
crystals are best obtained from benzene; the substance crystallizes 
in short, thick prisms, the a-isomeride (from ether) in more tiny, 
colourless needles. In both cases a yield of about the same 
percentage may be obtained. 


oe ee ee oe 


$ 3. a-Chloro-tetracetyl-d-fructose (mpt. 83°C.) 
crystallizes from dry ether at O° C. in the shape of 
small colourless and transparent needles, the end-faces 
of which are often only rudimentarily developed. 

They are rhombic, most probably bisphenoïdical, with 
the parameters: a: 6: c = 0,9759 :1:0,3284. 

Forms observed: a ={100}, narrow, but broader 
than 6 = {010}, which form generally is present only 
with a single, extremely narrow plane; m = ;110}, Fig. 1. 
large and lustrous, commonly yielding multiple reflexes; %-Chlorotetra- 
r= 101}, giving sharp mirror-images. In the zône acetyl-d-fructose. 


' 
1 
' 
‘ 
' 
' 
t 
1 
' 
‘ 
‘ 
' 
' 
' 
1 
1 
1 
' 
1 


2 


345 


of the c-axis the angular values are mostly oscillating, the reflexes 
being multiple; with very thin individuals, however, exact measure- 
ments could be made. The aspect of the crystals is that of prisms 
elongated in the direction of the c-axis. No distinct cleavage was 
found. The prism-faces (110) and (110) were much more lustrous 
and yielded much sharper images than the faces (110) and (110), 
which ordinarily were somewhat curved and duller. 


Angular Values: Observed: Calculated: 
):(110) =* 44 18 = 
ya(101)=*) 37 12 = 


):(010) = 45 44 45°42’ 
):(110)= 91 28 91 24 
LON 1124 71 24 
PO Vine 10 76 1845 
(Op = Te 76 18}/s 


The crystals are positively birefringent. 
The optical axial plane is {001}; on the 
prism-faces, just at the border of the field, 
the emergence of an optical axis is obser- 
vable. The dispersion bas a rhombic charac- 
ter, with 9 >v. The aspect of the crystals 
is very much like that of the B-derivative. 


§ 4. p-Chloro-tetracetyl-d-fructose 
(mpt.: 108° C.) erystallizes from benzene 


U 

' 
' 
' 
‘ 
' 
‘ 
| 
1 
' 
1 
' 
| 
- “~ 


in the shape of large, clear, very lustrous 
and short prismatic crystals, which with 
exception of their smaller development in 
the direction of the c-axis, show an un- 


Fig 2 (-Chloro-tetracetyl- 5 ; 
: Et Nh deniable analogy with the erystals of the 


a-compound. 
Big, colourless crystals, yielding, however, ordinarily multiple 
. reflections, and imperfectly built. 


Rhombic-bisphenoïdical. 
20762157478: 1 OM EL2: 


Forms observed: a =—={100} and m=={110}, well developed and 
giving sharp images; r == {101}, large, eminently reflecting; once a 
positive bisphenoid, probably {523}. and very subordinate, was 
observed, difficultly measurable. 


346 


The aspect is short prismatic in the direction of the c-axis, oc- 
casionally also isometrically developed. 


Angular Values: 


a:m = (100) 

or — (110) 
m:m = (110) 
r:r.= (101) 
r:m = (101) 
o:m = (523) 
o:o = (523) 
0:0 =(523) 


No distinct cleavage was 


Observed : 
(110) =*% 60° 13e 
(101) =*- 67 51% 
( 


:(110)= 59 33 
(Ole 44 AT 
(110) = 79° 10 
: (110) =ca.50 56 


) 
: (523) =ca. 48 50 
(S= VIT 30 


observed. 


Calculated: 


50935! 
44 17 
19 1 
5] 51 
49 124, 
17530 


§ 5. There is evidently no distinct form-analogy present between the 
two isomeric chloro-tetracetyl-d-fructoses, in contradiction to what was 
formerly stated in the case of both a- and g-pentacetyl-d-fructoses. 
The substitution of a Cl-atom for hydrogen, has evidently, however, 
not a lowering of the degree of symmetry of the original substances 
as a consequence, all four acetyl-derivatives being rhombic-bispheno- 
idical. However, from the results obtained, it appears still to be 
impossible to demonstrate a more intimate analogy of the erystal- 
forms of the «- and g-derivatives of this series and that studied 


formerly. 


Laboratory for Inorganic and Physical Chemistry 
of the University of Groningen. 


Chemistry. — “On the Crystalforms of some Substituted Amides 
of Para-Toluenesulphonic Acid.” By Prof. EF. M. Jararm. 


(Communicated at the meeting of June 26, 1920). 


§ 1. In the following the results are communicated of an inves- 
tigation concerning the crystallographical properties of a series of 
substituted amides derived from p-toluene-sulphonic acid *), already 
prepared by Prof. Van Rompuren in 1902. These preparations, which 
in general occur in beautiful crystals, were ceded to me a long 
time ago by the said chemist for the purpose indicated; but the 
results of these measurements have not been published hitherto. 

To colleague van RompurGn’s benevolence [| am indebted also for 
some still lacking data on the specific weight of several of these 
substances. 

In the text occasionally attention has been drawn to some regu- 
larities of the erystalforms of these derivatives, which, from a che- 
mical standpoint, are closely related to each other; a review of the 
numerical data is, moreover, added to this paper at the end. Distinet 
relations in the erystalforms of these derivatives have, however, not 
been found in great number, notwithstanding their close chemical 
relationship. 


§ 2. I. Nitro-p-Toluene-sulpho-amide. 


This substance, which melts at 141° C., erystallizes from ethyl- 
alcohol in big, very transparent crystals, which often possess curved 


Fig. 1. Nitro-p-Toluene-sulpho-amide. 


1) Cf. also: P. van Rompurau, Proceed. Acad. of Sciences Amsterdam, Februari, 
(1902). 
23 
Proceedings Royal Acad. Amsterdam Vol. XXIII. 


348 


faces, making the measurements rather difficult. From ethylacetate 
we obtained occasionally also great, hexagonally bounded, tabular 
individuals. The most exact measurements were made with very 
small, almost colourless crystals, showing very constant angular values. 

Although they belong, according to their optical properties, to the 
monoclinic system, their angle 8, however, does not differ from 90°. 


Monoclinic-prismatic ; pseudo-rhombic. 
dere = 1,2289 esa he 11812. 
p== 900. 


Forms Observed: gq = {012}, predominant and yielding perfect 
reflexes; r= {101}, large and strongly reflecting ; m = {110}, smaller, 
but well developed and lustrous; 6 = {010}, narrow and dull, often 
absent; o = {212}, well developed and lustrous; a= {100}, very 
small and dull, but at least measurable; finally an extremely small 
pyramid a = {711} (2) was observed, which, however, was mostly 
absent and very badly reflecting. The aspect of the crystals is thick- 
prismatic parallel to g, with elongation in the direction of the a-axis; 
however, the crystals are often most irregularly distorted. Ordinarily 
r is present only with a single face. 

Angular Values: Observed: Calculated: 


qa: F=—(012) (101) = DI ZE — 

m:q=(110):(012) =*. 66 46 — 

q:q¢=(012):(012)= 61 3 61° 8’ 
q: b= (012): (010) =" 59°29 59 26 
q: (012):(100)= “90 "0 90 0 
0:0 =(212):(212)= 46 42 46 8 
o:q=(212):(012)= 39 34% 39 37 
o:q=(212):(012) = 67 59 68 10 
m:o = (110) (212);=" 45 2 45 4 
O27 = (212) (101), 4 23-4 
m:q=(110):(011)= 66 50 66 46 
ax = (100 (Ten WS 48 19.3 


There is a distinct cleavage parallel to {010}. 

Although the angle 8 does not differ appreciably, the optical pro- 
perties prove, however, that the compound has monoclinic symmetry : 
on {012} the extinction-angle is about 23° with respect to the a-axis; 
in the same way the extinction-angle on {010} is about 42° with 
respect to the a-axis. The optical axial plane is probably parallel 
to {010}. 


349 


The specific weight of the crystals at 15° C. is: 1,612; the equi- 
valent-volume is therefore: 133,99. The topical parameters are cal- 
culated to: y: wp: w = 5,5537 : 4,5194: 5,3383. 


§ 3. Comparing the axial ratio with the parameters of the three 
isomeric tolwene-sulphonamides themselves, their form-relationship 
becomes very clear, if only the interpretation is made somewhat 
deviating from that given in the literature *). 

Adopting the symbols of the different combination-forms, as given 
by WeriBuLL, we can give the following survey of the modified data: 


Ortho-toluene-sulphonamide ; mpt: 156°,3 C. ata e—= 1 000e 1 0532. 
Tetragonal-bipyramidal. Ao. 
p = {110}; v= {111}; o = {113}; u = {313}. 


Meta-toluene-sulphonamide; mpt: 108° C. a:6:c = 1,0453: 1 : 1,0333 ; 
Monoclinic-prismatic; pseudo-tetragonal. B = 88°27'/2’. 
a = {100}; b = {010}; m={210}:0 = f112};s = {112}; =f122};r = 102). 


Para-toluene-sulphonamide ; mpt: 137°,5 C. a:b:c=1,2016: 1: 0,9364; 
Monoclinic-prismatic. P= 81°29. 
b = {010}; p = {011}; o= {312}; v = {310}; r = {302}. 


Nitro-p-toluene-sulphonamide, mpt: 141°C. a: bse == 12089: heel 1812 
Monoclinic-prismatic; pseudo-rhombic. P= 002: 


= eee 


§ 4. II. p-Toluene-sulpho-methylamide. 


This substance, which has the formula: 


and which melts at 76° (., crystallizes from alcohol in the form of 
very thin, transparent, colourless, rectangular little plates. 


1) M. WerBuLL, Zeit. f. Kryst. u. Miner. 15, 251. (1889); O. Müaeer, Diss. 
Göttingen, (1879), p. 15; cf. also: K. WaALLIN and P. Krason, Ber. d. d. Chem. 
Ges, 12, 1851. (1879). The crystals were obtained from alcohol or water. On the 
binary melting point-curve of o- and p- toluenesulphonamide, cf. P. V. Mc. Km, 
Journ. Chem. Soc. London, 118, 799. (1918). 

23% 


350 


Fig. 2. p-Toluene-sulpho-methylamide. 


Rhombic-bipyramidal. 
a:6:¢=1,0358 : 1 : 2,6074. 


The crystals represent evidently pseudo-tetragonal limiting forms; 
also optically they approach to tetragonal symmetry. 

Observed Forms: c = {001}, very lustrous, predominant, giving 
splendid reflexes; = {101}, and g = {011}, almost equally broad, 
well reflecting; o = 121}, small, dull, and difficult to measure 
accurately. The aspect of the erystals is thin tabular parallel to {001}, 
often with a slight elongation in the direction of the b-axis. 


Angular values: Observed: Calculated: 
c: 7 = (001): (101) =* 68°20' == 
c:q= (001): (011) =* 69 1 = 
r:r=(101):(101)= 43 20 43°20’ 
q:q=(011):O011)= 41 58 41 58 
c:o =(001):(121)= 80 25 80 12 
0:0 = (121): (2h < 18-10 18 36 


Cleavage parallel to {001}. 

The plane of the optical axes is {100}, c being 1* bisector. The 
apparent axial angle is very small, the crystals approaching also in 
this respect to uniaxity. 

The specific gravity of the erystals at room-temperature was: 
dye = 1,340; the molecular volume is therefore: 138,06, and the 
topical parameters become: %: w: wo = 3,0442 :3,7113: 9 Ore 


§ 5. III. Nitro-p-Toluenesulpho-methyl-amide. 


This compound is derived from the first by substitution of a 
bydrogen-atom of the NH,-group by CH,. From ethylacetate the 
substance crystallizes in beautiful, pale yellow prisms, and melts at 
91° C. The crystals are generally dull and not easily measurable. 

Monoclinic-prismatie. 
a:b 2c = 0d: 1 -.0,3948- 
f= 86°404. 


351 


Forms Observed: im = {110}, the largest developed of all forms; 
a = {100}, narrow, and r = {101} yet smaller; 
0 = }111}, small, but yielding good reflexes. 

The aspect of the crystals is that of long 
needles or prisms parallel to the c-axis. 


Angular Values: Observed: Calculated’ 

m:a = (110): (100) =* 469241/2’ = 

0:0 =(111): (111) =* 71 52 = 

m:o = (110): (111) =* 78 18 == 
m:o=(110):(411)= 49 35 492391/0/ 
m:m=(110):(110) = 87 11 87 11 
c:m= (001) : (110) = — 87 42!/ 
meo (101): (11) = 35 58 35 56 


Perfectly cleavable parallel to {101}. 
As the crystals were in every case dull and 
curvi-planed, more exact measurements appeared 


Fig. 3. Nitro-p-toluene- 
almost illusory. sulpho-methyl amide. 
The extinction on a was normally, on m obliquely orientated with 
respect to the edge a: m. 
The specific weight of the crystals was: 1,485 at 16° C.; the 
equivalent-volume is, therefore: 154,21, and the topical axes are 
calculated at: y: : w = 7,5664: 7,1910: 2.8390. 


§ 6. IV. p-Toluene-sulpho-methylnitramide. 
This compound, which possesses the structure: 


CH; 


Za 
Sige 


SO, - Near 


and melts at 60° C., crystallizes 
from a mixture of ligroin and 
ether in almost colourless flat 
needles, or in thick, short prisms. 
They are well built and give 
good reflexes. 


Monoclinic-prismatic. 
Hebe == 1,3210 : 1: 0,6892 ; 
Seer sy Ne 


Fig. 4. p-T'oluene sulpho-ethylnitramide. 


352 


Forms Observed: q = {011}, large and very lustrous; a = {100}, 
large, mostly with one rudimentary face, but yielding good reflexes ; 
b= {010}, narrower, sometimes curved; r= {101}, great and lustrous ; 
m == {110}, perfectly reflecting; w= {111}, mostly narrow, but in 
the needle-shaped individuals as large as am, while 7 is here lacking 
in most cases; finally 0 = {311}, often well developed. The aspect 
of the erystals is thick prismatic, with a slight elongation parallel 
to the a-axis; rarely needles parallel to the same axis. 


Angular values: Observed: Calculated: 

q:q= (011): (O11) =* 67959! 2e 

g: a= (011): (100);—* 780-9 == 
a:m=(100): (110) =* 52 14% — 
g:6b6=(011):(010)= 56°0 56210 
a:r= (100):(101)= 53 14 53.21 
ger == (OL) S00 sal 14 41 9 
b:m= (010): (110) = 37 44 37 45! 
a:w=(100):(111)= 74 49 Tyee 
wee MD Ollie 25.08 24 49 
a:o=(100):(311)= 40 50 40 58 
ong = (311)... 5e 1 58 53 


No distinct cleavage was found. 

The extinetion-angle on {010} is 31° with respect to the a-axis. 

The specific weight of the crystals is: 1,454 at room-temperature; 
the equivalent-volume is thus: 165,06, and the topical axes are 
calculated at: x: W:w = 7,5309 : 5,7009 : 3,9291. 


§ 7. V. p-Toluene-sulpho-ethylamide. 
This compound, which melts at 64° C., has the structure: 


CH, 
2 
SO,NH(C3H5) 

It crystallizes from a mixture of absolute alcohol and ether in 
colourless, parallelogram-shaped, thin plates, or small prismatic crystals. 
The solutions have a tendency to supersaturation. 

Triclinic-pedial 
a:6:c=0,6481 : 1: 0,4136; 
oa 173 A= TS 
BOS 2 BS VSB 
y = 102°55}3; CG = 102 


353 


Fig. 5. p-Toluene-sulpho-ethylamide. 
Forms observed: r = {101} and v = {101}, large and very lustrous, 
mostly predominant, the crystals therefore being often tabular parallel 


to these planes; t= {101}, also lustrous, somewhat smaller than r 
and v; s={101}, smaller than ¢, and showing commonly a fine 
striation parallel to the edge s:v; a={100! and a’ {100}, narrow, 
but well reflecting; m= {110}, large, always showing a striation 
parallel to the edge m:r; p=}110}, n= {110}, and A = 110), 
large and highly lustrous; o = {121} and 2= {121}, very narrow 
and badly reflecting, 2 generally striated parallel to m:v; probably 
again g = {011}, very small and commonly not measurable. The 
aspect of the crystals is tabular parallel to r, or thick prismatic 
towards the c-axis. A cleavage occurs parallel to {101}. 


Angular Values: Observed: Calculated: 
ar = (100); (101) =" “58254: = 
a:s =(100):(101)=* 56 14 ee 
a: p= (00): (LO —*. amet ae 
a:m= (100): (110) =* 29 23 = 
r:p = (101): (110) =* 58 17 Px 
zr = (101). (101) = ~ 658 65°12’ 
s:v=(101):(101)\= 65 10 65 12 
s:p=(101):(110)= 70 40 70 24 
s:m=(101):(110) = 56 39 56 37 
sim (101):(110) = - 68°24 68 35!/ 
ap A20) — SRR 518 


On all faces the optical extinetion occurs obliquely with respect 
to the borders: on 7 about 46° with respect to the edge r:p; on 
p about 36°, on a about 43°, on m about 34° with respect to the 
direction of the c-axis. On r and p is the emergence of an optical 
axis observable, excentrically in the field of the microscope. 


354 


The specific gravity of the crystals is 1,307 ; the equivalent-volume 
therefore: 152,26, and the topical parameters become: 7: y:w = 
= 4,6805 : 8,4202 : 3,4825. 


S 8. VI. p-Toluene-sulpho-diethylamide. 


This compound having the structure: 
CH, 
SO.—N(C.H; ha H 
and melting at 59° C., erystallizes from a 
mixture ef absolute aleohol and ethylacetate in 
the shape of thin, colourless, hexagonally border- 


ed little plates, or in somewhat thicker tabular, 
and often opaque crystals. 


Monoclinic-prismatic. 
a:b>e=1,0149 31 :0,6763% 
ff OA Fig. 6. p-Toluene- 
sulpho- diethylamide. 
Observed Forms: a= {100}, predominant and very lustrous; 
o = {111}, g = {011}, m = 3110}, p = {120}, all about equally broad 
and yielding splendid reflexes; = {101}, very lustrous, well developed; 


w = {111}, somewhat narrower than o, but yielding also sharp images; 
n = {210}, and 6 = {010}, extremely narrow, often absent and giving 
feeble retlexes. The crystals are well built, and allow exact measure- 
ments. Their aspect is tabular parallel to « and elongated in the 
direction of the c-axis. The crystals are very brittle. 


Angular values: Observed: Calculated: 
a:o= (100): (111) =* 49°40’ Ss 
a:q = (100): (011) =* 74 57 = 
a:r = (100):(101) =* 44 17% — 
org (Ue (Olpe 2517 25017’ « 
dee (Olle (182 18 32 20 
Bee (111)5, (LOOS 245 72 42}/s 
= (ll): (10E 25-15 Ps ee 


(LEO) =F 43. 58/2 43 59/2 


) 
) 
010):(111)= 64 45 64 43 
) 
):(120) = 18 34 18 32!/ 


355 


Angular values : Observed: Calculated: 
pb: b= (120): (010) = 27 23 PM Was) 
b= om= (O10):(110) =. 746-2 46 O's 
a:n=(100):(210)= 26 9 25 46 
n:m= (210) (110) =... 17 59 18 13% 
a: p= (100):(120) =... 62 31 62 37 


No distinct cleavage was found. 

The optical axial plane is {010}. Very strong, inclined dispersion, 
with 9 < v; on {100} one axis emerges excentrically in the field of 
the microscope. 

The specific weight of the crystals at 15° C. was: 1,230; the 
equivalent-volume is therefore: 184,55, and the topical parameters are 
calculated to: y: py: w = 6,6611 : 6,5633 : 4,4381. 


§ 9. VIL. p-Toluene-sulpho-ethylnitramide. 


This substance, which has the configuration : 


CH; 


: (CgH5) 

SONS NO») 
erystallizes from ether in big, colourless erystals, or in hexagonally- 
shaped tables. It melts at 69° C. 


Monoelinie-prismatic. 

mee — 1.017821: 1,1005; 

a= 88" 11") 

Forms Observed: c = $001}, 
strongly predominant and lustrous ; 
a = {100}, sometimes large, often 
also narrower, but always yielding 
sharp reflexes; m = {130}, well 
developed, but often with curved 
faces and somewhat dull; 7 = 


{203}, well reflecting, often absent ; 
w = {133}, extremely narrow, in Wig. 7. p-Toluene-sulpho-ethylnitramide. 
most cases absent, and only approximately measurable. The aspect 
of the crystals is either short prismatic with an elongation parallel 


to the b-axis, or thin lamellar parallel to {001}. 


356 


Angular Values: Observed: Calculated: 
a:¢ = (100)=(001) =" BESI = 
a:m= (100) : (130) =* 71 51% — 
a:r = (100): (203) =* 55 25 = 
c:r = (001): (203)= 36 24 36 24 
m:m= (130): (130) = 36 27 36 17 
c: w= (001) : (133) 50 8 49 29 
m: w= (130):(133)= 40 58 4175 
e:m= (001): (130) = + 89 24 89 26 


Very perfectly cleavable parallel to {O01}. 

On a and ec the extinction is normally orientated, but often of 
undulatory character, as the result of geometrical anomalies in the 
structure of the crystals. 

The specific gravity of the crystals was 1,450; the equivalent- 
volume is therefore: 168,27, and the topical parameters become: 
x4: W:@ = 5,4115 : 53169 : 5,8513. 


§ 10. VIII. Nitro-p-Toluene-sulpho-ethylnitramide. 


This substance, which melts at 76° C., can only rarely be obtained 
in measurable crystals. Those here investigated were deposited from 
a hot saturated solution in carbon tetrachloride by very slow eva- 
poration. 

Thin, yellow, 
with hemimorphie development (fig. 


very lustrous and transparent plates, 
8). 


commonly 


Fig. 8. Nitro-p-Toluene-sulpho-ethyl-nitramide. 


Monoclinic, probably sphenoidical. 

a:b:c=0,4812 :1: 0.8766; 
tene 

¢ = {001}, 


reflexes, 


Forms Observed: 
aera 


predominant, and very lustrous, o = 
ideal often with only a single plane; 
a = {100}, giving good mirror-images; 6 = {010}, often absent, but 
otherwise well reflecting: {705}, very narrow, often totally 
absent. The crystals often show oscillatory angular values, principally 
in the zone of the orthodiagonal, and multiple reflexes. The aspect 
ig tabular parallel to {001}, and strongly elongated towards the 


b-axis. 


yielding 


357 


Angular values: Observed: Calculated: 
é:a@ = (001): (100) =* 85? 5) — 
c:o0=(001):(111)=* 67 16 = 
aso (dOr (181). + SaR 21 = 
ce: = (000) (705) = 64 42 64°23’ 

r: a= (705) : (100) = 20 16 20 42 
6: b= (001): (010) = 89 52 90 0 
a. = (1 P1205) — _ sti 54 24 


No distinct cleavage was found. 

The optical axial plane is parallel to {010}; on c and a both an 
optical axis emerges excentrically. 

The specific weight of the crystals is: 1,555; the equivalent-volume 
therefore: 156,91, and the topical parameters are calculated at: 
X:W:w == 3,4652 : 7,2001 : 6,3119. 


§ 11. IX. p-Toluene-sulpho-benzylamide. 


Structure: 
CH; 
(a 


$0, -NH—C,H; 


From a mixture of ether and alcohol the compound crystallizes 
in large, colourless crystals with varying aspect. It melts at 113°C. 
The crystals are well built and allow exact measurements. 


Fig. 9. p-Toluene-sulpho-benzylamide. 


Trichinic-pinacordal. 


aob<¢ = 09718 HROS 


A=83°32’' . @=63°24)’. 
B=90°56’ . gd. 
C— Jno EE CE 


Forms Observed : a = {100}, and c = {001}, large and very lustrous ; 
in most cases a is somewhat larger thanc; w= {111} and o == {lii}, 


358 


large, lustrous, and about equally well developed ; 6 = {010}, narrow, 
somewhat dull, commonly with only a single face, often totally 
asent;).2 == 1 li, small, dull, but well measurable. The aspect of 
the erystals is ordinarily prismatic parallel the 6-axis. 


Angular values: Observed: Calculated: 
aio = (100) 700) == -89° 4’ — 
c:o=(001): (Ill) =* 47 33 er 
c:w= (001): (111) =* 55 47 = 
gro (OO (Ll 59 A => 
a:w= (100): (111) See 51e 12% — 
o:w=(111):(111)= 66 45% 66°50!/2/ 
o:b==(111):(010) = 55 38% 55 46 
b:w= (010): (111) = 57 33% 57 23!/ 
x: a= (111): (100) 57 38 57 38 
bin = (010): (111) =. … 62, 50 62 42}/2 
oe id) ee 2 77 53 
x:e=(111):(01)= 54 24% 54 34 


No distinct cleavability was observed. 
. The extinction on a and ec was oblique with respect to the 
edge a:c. . 

The specifie weight of the crystals was: 1,313 at 17°C.; the 
equivalent-volume is thus: 198,78, and the topical parameters become: 
{2 == 59,9793 :6,1150 70 40eF. 


S 12. X. Nitro-p-Toluene-sulpho-benzylnitramide. 


This compound, melting at 153° C., crystallizes from ethylacetate 
in small, very lustrous, colourless crystals. They often show some- 
what oscillatory angular values; the faces of {001} are, moreover, 
often curved. Exact measurements were, however, possible. 


Fig. 10. Nitro-p-Tolwene-sulpho-benzylnitramide. 


359 


Triclinic-pinacoidal. 

a obkre= 1,800 dE 0: 
A= 9b at! Med 
B= 101203! EEE 
EBT -) a= She 

Forms Observed: c= $CO1}, large and lustrous, sometimes a little 
curved; a = {100}, narrower, but very lustrous; m= {i10! and 
o = {ll}, almost equally well developed, and yielding good reflexes; 
s = {011}, small, but well measurable; this form is often absent. 
Further sometimes again: = }101!, very narrow. The aspect of 
the erystals is tabular, thin plates parallel to c, and often elongated 
in the direction of the b-axis. 


Angular values: Observed: Calculated: 

axe k0OR NGO 7898 — 

c:o= (001): (111) =* 62 28% 

a:m= (100): (110) =* 79 13 a 
c:m= (001): (110) =* 77 25 ™ 
o:m= (111): (110) =* 54 10% = 
a:0=(100):(111)= 56 48%» 56°47’ 
o:s=(111):(11)= 44 19% 44 10 
ss a= (Olt): (00)= - 79.8 79 1% 
a:r==(100): (101) = 59 16 59 7 
r:c={(l01):(001)= 42 6 42 15 
Sve — (Obl) (008) = — 50 52 


No distinct cleavage was observed. 

On {001} the extinction-angle is 8° with respect to the edge a: c. 
In convergent polarized light one hyperbola is visible at the border 
of the field. 

The specific gravity of the crystals is: 1,530 at 17° C.; the equi- 
valent-volume is therefore: 229,54, and the topical parameters are 
calculated at: %: :w = 8,6739 : 4,7934 : 6,2983. 


§ 13. XI. p-Toluene-sulpho-piperidide. 


Structure: 
CH; 


SO... NCsHio 


This substance, which melts at 98° C., was obtained from ether 
in the form of large, flat, colourless, very lustrous crystals of ree- 


360 


tangular shape. They are well built, beautifully translucid, and 
allow very accurate measurements. 


Fig. 11. p-Toluene-sulpho-piperidide. 
Rhombic-bipyramidal 
a:6:¢= 0,7474: 1: 0.3790. 
Forms Observed: a= }100}, predominant and yielding good reflexes ; 
m = {110} and 5= {010}, large and very lustrous; p= {120}, very 
narrow; r= {101}, large and giving good reflexes. 


Angular Values: Observed: Caleulated : 
a:m= (100): (110) =* 36946!/2’ — 
a:r = (100): (101) =* 63 6% = 
m: p = (110):(120) = 19 23% 19°26}/2’ 
p:6=(120):(010)= 33 50 33 47 
r:r=(101):(101)= 53 46% 53 46%/s 


No distinct cleavage was found. 

The optical axial plane is {001}, with the b-axis as first bisector; 
the dispersion, of rhombic character, is very appreciable: 6 << v. The 
apparent axial angle is only small. 

The specific weight of the crystals is: 1,281 at 15° C.; the equi- 
valent-volume therefore: 186,57, and the topical axes become: 
4: p:@ = 6,5029: 8,7005 : 3,2967. 


§ 14. XII. Nitro-p-Toluene-sulpho-piperidide. 


The substance melts at 108° C., and crystallizes from ethylacetate 
in splendid large, somewhat pale yellowish, translucid, very lustrous 
erystals. They are well built, and allow good measurements. 


361 


Monoclinic-prismatic. 
a:h:-c = 0,7466: 1 :1,5713. 
B= 8 397 

Forms observed: c= {001}, 
predominant ; m= {110}, large 
and lustrous, shows sometimes 
a fine striation parallel to the | .* 
edges m:c; o= {111}, and : 
w = {111}, about equally large, 
but a little bit narrower than 
m; r= {101}, well reflecting ; 


s= {101}, somewhat smaller Fig. 12. Nitro-p-Toluene sulpho-piperidide. 
than 7, often absent ; ¢= {ok}, extremely narrow and not measurable 
only rarely present; b = {010}, small and narrow, dull; q = {011} 
clearly developed, yielding good reflexes. The aspect is often isome- 
metrical, or somewhat flattened parallel to {001}. 


Angular Values: Observed: Calculated: 
erm = (001) (111) =* _ T7911" = 
bro (Lr (UI 71 224 ae 
mic (110) (O01) —* 80552 = 
e:7r =(001):(101)= 55 28 55°34?/s’ 
rs = (101): (101)="" 501342. 5016's 
se (01): (001)= = 7401 74 9 
cog — (00E O11 Er SOEST 57 0% 
beg — 010) Olt) — 333 32 59!/s 
Oise (101) =" "35 35 41% 
m:m=(110):(110) = 72 22 72 24/2 
e:o = (001): 011)= 61°20 61 13% 
o:m=(111):(110)= 19 30 19 8 
meio = (LO (LI = 21574 21 57 
m:b =(110):(010) = 53 49 53 47% 


Very perfectly cleavable parallel to {001}, distinctly parallel to 
{110}. On {O01} diagonal extinction. 

The specific weight of the crystals at 15° C. was: 1,384; the 
equivalent-volume is therefore: 205,20, and the topical parameters 
become: Xi Wio= 4,2031 : 5,6259 : 8,8455. 


‘ 
. 


§ 15. 


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Zoology. “The colour-markings on the body of Lepidoptera, compared 
to those of their larvae and pupae, and to those of their 
wings’. By Prof. J. F. van BEMMELEN. 


(Communicated at the meeting of January 31, 1920). 


In former communications I have expressed my conviction, that 
originally an intimate connection must have existed between the 
colonr-markings of caterpillar, pupa and butterfly of the same species, 
all three being only varieties of one and the same archaic form. 
Consequently the few cases, in which this connection is evident at 
first sight, should not be considered as mere casualities, but as 
resulting from the preservation of the primitive condition. SCHIERBEEK, 
who chiefly studied the setal pattern of the youngest instars of cater- 
pillars, but also gave his attention to the colour-markings of a few 
older caterpillars, and to pupae, has fully corroborated my views. 
De Meyere on the contrary, in his paper: Zur Zeichnung des Insecten- 
im besonderen des Dipteren- und Lepidopterenflügels, 1916, has 
expressed his doubts about them, where he says on p. 181: “In 
my opinion the striking difference between the pupal- and the 
imaginal markings precisely shows that they have had an inde- 
pendent origin, and have followed different ways: — just as we 
found it in nearly related Diptera, we here see it in different stages 
of the same animal”. 

And further on: 

“According to my view the colour-markings of the pupa of 
diurnal Lepidoptera are as much of recent origin as their frequently 
grotesque shape and their very varying mode of fixation. The same 
might apply to pupal markings in comparison to those of caterpillars”. 

In his second paper: Zur Evolution der Zeichnung bei den holo- 
metabolen Insecten, he writes on p. 70: 

“IT consider the striking colour-markings of many butterfly-pupae 
as a secondary feature in these organisms, exposed to light as they 
are. In a similar manner the pupa of Abraxas grossulariata, which 
settles unhidden in shrubs, shows special coloration. VAN BEMMELEN’s 
assertion, that this Geometrid should show a primitive coloration in 
all instars, does not seem right to me, at least in regard to the 
pupa... . The pupa of Abr. sylvata, which hibernates in the earth, 
is quite dark; without doubt in this case, the older condition. The 
real primitive condition I believe to occur in the light-brown 

24 

Proceedings Royal Acad. Amsterdam. Vol. XXIII. 


364 


pupae of many Micro’s, of Hepialids, Limacodids ete., all these being 
very like the pupae of Neuroptera’. 

As I already pointed out in my paper on the primary character 
of the Pupal pattern in Butterflies (Proc. K. Akademie van Weten- 
schappen 1918) I feel justified in fully maintaining my views. 

I now wish to discuss somewhat in detail, a few examples of 
similarity between larva, pupa and imago, chosen from the family 
of Sphingids. It is true that up till now I have not been able to 
investigate the subject in full, as I have not yet got acquainted with 
the younger larval instars by personal inspection, nor found occasion 
to study the development of the colour-pattern inside the pupal 
sheath. The comparison of the markings in some nearly-interrelated 
species of caterpillars in a full-grown state, as well amongst themselves 
as with those of their imagines, and in a few cases also with marked 
pupae, gives us such a number of striking proofs of original unity, that 
I consider my assertion satisfactorily backed by evidence. I therefore 
believe it worth-while to direct the attention of entomologists to 
this highly promising subject, especially so, because a complete in- 
sight into the course of evolution of the larval, ny mphal and imaginal 
colour-patterns of a tolerably vast number of species can only be 
obtained by cooperation of a great many competent investigators. 

From times remote the wing-markings of butterflies have attracted 
the curiosity and admiration of men, but to those of the body proper 
only in exceptional cases a little attention has been given, and then 
still from a purily descriptive point of view. Intercomparison of the 
colour-markings on the bodies of related species, or investigation of 
the similarity between the design on the body and that on the wings 
has hardly ever been tried; only when a striking resemblance 
between the two latter exists, is this sometimes made mention of, 
but only as a casual remark. 

Yet it is evident, that when comparing the imago with its cater- 
pillar, only the markings of the body need be minded, and that the 
same applies to the pupa, though in a minor degree, as in the latter 
only the upperside of the forewing is exposed to view, while on the 
contrary part of the lateral body-wall is hidden beneath the wing-sheath. 

When moreover we wish to study the connections between the 
markings on the wings and those on the body, it seems desirable 
first to realise the exact nature of the wings. Now these organs may 
be considered as lateral folds of the dorsal skin of the meso- and 
metathorax, near to and dorsally of the line of stigmata (though 
these openings are obliterated in the said segments of the thorax). Con- 
sequently each wing consists of a dorsal and a ventral lamella of 


365 


the skin, which along the wing-border fold over into each other. 
When we imagine this fold to become repressed up to the first 
initial rudiment of its evolution, then these lamellae do not extend 
horizontally along parallel planes in contact with each other, but 
quite the contrary lie in one and the same dorsoventral plane. 
When in applying this mode of representation of the wing we look 
at it from the side, it is seen projected on the lateral body-wall, 
and so each wing can be drawn as a sexangle, which by its hori- 
zontal diagonal is divided into a dorsal half (the upper wing-surface) 
and a ventral one (the underside of the wing): the diagonal itself 
representing the wing-border. That by this projection-method the 
wing-field appears extremely small in relation to the dimensions of 
the body, need not according to my view be considered as a real 
objection against it. For the relation in size between wings and 
body in different species of Lepidoptera varies between very wide 
limits, and in the females provided with rudimentary wings of 
sundry species it even approaches the schematic condition described. 
Likewise during the pupal stage of almost all kinds of Lepidoptera 
the wings are far smaller than after the emersion from the nymphal 
sheath. 

This projection of both wing-surfaces upon the dorso-ventral 
plane sharply draws our attention to the fact that markings, which 
on the wall of the body stretch in an oro-aboral direction, will run 
in a so-called transversal one over the wing-surface, i. e. from the 
anterior towards the posterior wing-border. The dorso-ventral com- 
ponents of the pattern on the contrary will traverse the wing-field 
from root to external margin (commonly called longitudinally). In 
the same way this method can give support to the belief, that the 
pattern of the upper surface need not originally have been identical 
with that of the underside, as they correspond to different, though 
neighbouring areas of the sidewall of the body. 

Finally this way of representing the wings as projected on the body 
highly facilitates and accentuates the comparison with the caterpillar. 
To get a pure comparison with the pupa however, we are obliged 
somewhat to modify the position and the size of the sheath of the 
forewing, which involves the formation of an empty space towards 
the side of the abdomen, corresponding to the place where the hind- 
wing would have been situated, when this were visible on the pupa. 

In order to insert the real wing-pattern into these schematic 
sexangles, we have to project it upon them. To do this, we must 
turn the wing obliquely up- or downwards and draw a contracted 
image of its colour-pattern on the perpendicular plane of projection. 

24* 


366 


Moreover it is desirable to apply this same method of projection to 
the dorsal and ventral body-wall, in such a sense that the circum- 
ference of the figure no longer corresponds to that of the sideview 
of the animal, but roughly forms a trapezium, the upper- and under- 
side of which represent the median dorsal and ventral lines, or better 
still, stretch a little over them. This can also be expressed in such 
a way, that the body becomes compressed from left to right, thereby 
erowing higher in the dorsoventral direction, a condition so often 
shown in reality by squeezed specimens. As to the position of the 
wing-sexangles in regard to each other, I am of opinion that 
they should “be placed in one and the same horizontal body-axis, 
the one behind the other, instead of the anterior margin of the 
hindwing passing beneath the posterior one of the forewing. In size 
the two wings may be represented alike. The arguments for both these 
assumptions can be found in the wings of Hepialids. 

Consecutively the following points should be attended to in the 
investigation : 

a. comparison of the markings of the thoracal with those of the 
abdominal rings in one and the same individual, therefore in the 
caterpillar with its different instars, in the pupa, and in the imago. 

b. comparison of the colour-pattern of all these stages, to each 
other in the same species. 

c. comparison of kindred species in their successive stages with 
each other. 

For each of these comparisons an example may be given. 

Of the few Sphingid-caterpillars which were at my disposition, I 
choose the fullgrown larva of Protoparce convolvuli (scil. the brown 
variety) as a fit object for comparison of thoracal with abdominal 
markings. For in this species the relation of the one to the other 
can be very clearly observed, and in doing so, we are impressed 
by the fact that the first seem to bear a more prisnitive character 
than the second. For on the thorax the obliquely ascending lateral 
bars, which are so characteristic of the abdominal segments of these 
as of so many other Sphingid caterpillars, are absent. The pattern 
is restricted to longitudinal light and dark stripes, which in their 
turn are evidently composed of rows of spots, whose number cor- 
responds to that of the annuli or secondary rings, which enter into 
the composition of each body-segment of the caterpillar. The number 
of these annuli is constant, eight for each segment of the abdomen, 
except the posterior two; it is likewise diminished in the thoracal 
ones, probably an effect of reduction. On each annulus one row of 
light spots on a dark ground is seen. The relative size of the single 


367 


spots determines the impression they call forth, either of a light or 
of a dark party of the caterpillar-skin. While light spots on the same 
level on successive annuli arrange themselves to light longitudinal 
stripes, small spots on the contrary appear as light specks in a dark 
band. Here and there these specks totally vanish, a larger black 
spot being the result. So the prothorax shows no other ornamen- 
tation than a pair of big epistigmal dark blotches on its flanks, 
passing in a caudal direction into the dark longitudinal strokes, which 
on the abdominal segments periodically become transected by the 
oblique light stripes. On meso- and metathorax a light brownish-yellow 
median dorsal stripe is present, flanked at some distance by light 
subdorsal stripes, separated from the firstnamed by dark bands, which 
in the anterior part of eacb segment bear the character of dark spots. 

Beneath the jline of the stigmata runs a very broad light streak, 
over the roots of the legs two dark longitudinal lines are seen. 

All these markings are found again on the abdominal segments, 
but in a modified, more complicated condition. The dorsal stripe 
passes uninterruptedly from thorax to abdomen in the form of 
a light band, slightly contracting in the middle of each segment, 
while at its anterior margin a pair of yellowish-white spots, sepa- 
rated by a small dark stripe, contribute to render the first annulus of 
each abdominal segment more conspicuous. But in the first place this 
effect is reached by the two sharply drawn brownish-black spots at the 
lateral side of the just-mentioned light dorsal maculae, and by the clear 
white specks, which in their turn flank the outer side of these maculae. 

This series of alternately light and dark spots on the first annulus 
evidently only consists of nothing more than highly conspicuous 
links in the prolongation of the above mentioned three light and two 
dark lines that run over the dorsal side of the thoracal segment. 
It is therefore in harmony with this fact, when we remark that 
from each of the black blocks a dark streak runs on in a caudal 
direction. These streaks converge towards the centre of the segment, 
in harmony with the median light dorsal streak, whieh narrows in 
the middle of each abdominal ring, while towards the back end of 
the segment the streaks again diverge. Consequently the dorsal stria 
broadens towards the latter margin and so forms a triangular area, 
which somehow assumes the character of an independent spot; this 
aspect being heightened by the repetition, in the centre of the segment, 
of the small black stripe in the middle line on the first annulus. 

Looking from the lateral side, the similarity between thoracal 
and abdominal designs likewise strikes us, but at the same time we 
remark the deviation of the latter from the original condition, in 


368 


consequence of the differentiation of the oblique light stripes which 
ascend in a dorso-caudal direction, and are accompanied along 
their dorsal border by an obscuration of the brown-black ground- 
colour (called ‘“dunkle Grundierung”’ by v. Voss). At their posterior 
top these oblique light stripes exactly pass into the above-mentioned 
white subdorsal spots, in the same way as their accompanying dark 
seams join the black specks, which themselves run on into the dark 
subdorsal lines. A similar broadening and obscuration of the seam, 
as is caused by these specks at the dorsal end of the oblique stripes, 
is also found at their ventral beginning, on the level of the stigma. 
The latter however is situated at the back side of the light oblique 
stria (on the suture between the 3 and 4 annulus), while the 
mentioned dark spot lies before it on the 2 annulus. Still further 
forward to the front side, the corresponding part of the first annulus 
also bears a pair of dark maculae (praestigmal spots). The stigma 
itself is likewise coloured dark. In advance of the stigma the dark 
diagonal stria is still continued in a ventral direction over the poste- 
rior four annuli of the foregoing segment, and reaches the ventral 
border of the broad light substigmal band, where it joins the horizon- 
tal undulating line over the base of the false legs. 

Now in this brown variety of convolvuli we see at once that all these 
spots and stripes are nothing else but more or less differentiated 
parts of the general ground-pattern, which exclusively consists of 
rows of light maculae on a dark ground, keeping rigorously to the 
annuli, and therefore repeated eight times on the succeeding abdominal 
segments. In each row the number of maculae is large, yet tolerably 
constant, viz. + 13 at either side of the median line. 

The above described black spots are formed by the blending of 
dark stripes separating the white specks, the light blotches on the 
contrary by the obliteration of one or more of these stripes. 

Likewise the light diagonal stripes are built up by an obliquely 
rising series of eight light maculae that have increased a little in 
size, the dark seam in the same way by a similar gradation of 
black cubes, lying dorsally to these light maculae. 

Comparing the brown with the green variety, we remark that 
the latter has got nothing left of the entire ground-pattern but the 
larger dark maculae: the subdorsal, the epistigmal, the prostigmal, 
the stigmal and the hypostigmal or the basal spot. Of these the 
epistigma! spot still betrays its original character as a part of the 
dark seam along the diagonal stria by its obliquely extended shape 
in a dorso-caudal direction, pointing so to say to the subdorsal stripe 
of the following segment. 


369 


On the metathorax of the green variety the subdorsal spots are 
present in double number, on the metathorax in single. 

Comparing the larval design to that of the imago, we may here 
remark in parentheses, that the last-mentioned pair of spots also 
occurs on the caterpillar of atropos and here maintains itself as the 
eye-spots of the cranium-image. 

The collection Katiensacn also contains a halfgrown convolvuli- 
caterpillar, I therefore found occasion to compare this with the 
fullgrown larva, and thus could convince myself that the light sub- 
dorsal maculae of the latter really are the remnants of a complete 
subdorsal line, originally stretching over the whole series of the 
body-segments, in the same way as the substigmal line. On the 
abdominal segments however it is periodically broken by the diagonal 
striae which, though rather inconspicuous, are yet present in complete 
order, and which, before each stigma, meet the segments of 
the substigmal line, thereby forming a triangular spot on each body-ring. 
But the chief difference between this halfgrown caterpillar and the 
fullgrown one is its uniform dark ground-colour, sharply contrasting 
with numerous small white oval knobs, which stand arranged in 
several rows on the eight annuli. On the above-mentioned light 
longitudinal lines these knobs occur in the same way. They do not 
make the impression of standing in any relation either to the dark 
or to the light specks, their own hue in fact is a much clearer 
white than that of the latter. So we can only suppose, that at the 
last moult they disappear, to be replaced by the (tolerably regular) 
white spots in the dark ground-colour. 

When we pass from the caterpillar of convolvuli to that of atropos 
and digustri, the design of these latter two is seen to correspond to 
that of the first in all such instances, as can be considered as secon- 
dary modifications of the original pattern; those parts of it on the 
contrary, which in convolvuli are found in the least modified condi- 
tion, having nearly vanished in the other two species. The same 
may be said of the thorax: here the process has led to total absence 
of pattern in atropos and ligustii. Upon the abdominal segments on 
the contrary the pattern is the same for all three, only differing in 
shades and in completeness. 

These facts undoubtedly offer new and valuable arguments for the 
supposition, that the absence of pattern is a consequence of obliteration ; 
the two latter species therefore having suffered stronger regression 
from the original condition than convolvult. 

Still in another instance the lastnamed species seems to show the 
more primitive conditions, viz. in the simple and few colours that 


370 


enter into the composition of the pattern: darkbrown and diluted 
yellow. It is true that these colours only maintain themselves in the 
older instars of the larval period, as originally the caterpillar is 
green. So when we should ascribe a general applicability to the 
rule that the colours and markings of the younger stages invariably 
represent more original conditions than those of the later, we should 
be obliged to suppose that the brown colour had arisen from the 
green one. But though this rule can be applied in many cases, it 
by no means may be considered as of universal validity. Especially 
in insects I am of opinion that everywhere the green colour is a 
secondary modification of other shades, which lie farther to the red 
side of the spectrum, as I have already tried to demonstrate in my 
paper on the genus Charagia among Hepialids. 

In convolvuli therefore the change from green to brown should 
be considered as a reversion to more primitive conditions, and in 
connection with this supposition we might regard the green 
colour in ligustri, and to a certain extent also in atropos, 
as due to secondary modification’). Possibly this change in the 
general shade might be brought in connection with the reduction 
of the original design, which on the thorax has led to complete, on 
the abdomen to partial obliteration, and moreover on the latter has 
called forth a greater contrast between the uniformised green ground- 
colour and the very obvious pink and white oblique striae. 

As a hint that in convolvuli the brown caterpillar has best retained 
the original character, we may also regard, that in this species the 
connection of the markings with the every where occurring subdivision 
of the body-segments in a series of eight annuli or subsegments is 
most conspicuous. But likewise in the other two species it is obvious 
that the diagonal striae (pink and white in fgustr, pink and yellow 
in atropos) are composed of a step-like series of dark and light 
blocks of colour. With regard to this feature, those of the firstmen- 
tioned species strike us by the peculiarity, that in the forward 
prolongation of the diagonal striae on the foregoing segment a row 
of three or four white specks occurs, growing smaller from behind 
forward. In this anterior prolongation of the white striae the blending 
of the specks, which enter into their composition, has not yet taken place. 

In the green caterpillar of atropos another proof is seen for the asser- 
tion, that more extensive striae, bands and fields of colour are the result 
of the blending of smaller spots arranged in transverse rows. For 


1) This species also possesses a brown variety of the caterpillar, and this, as well 
as that of convolvuli, shows a more complete and primitive pattern than the 
green one. 


371 


on the bluish dorsal stripe as well as on the neighbouring yellow 
subdorsal bands and the pink-red oblique lateral bands, we find 
groups of knobs, which evidently are regularly arranged on both 
sides of the median line, in eight transverse rows, which correspond 
to the annuli composing each segment, the number of the wharts 
in the blue diminishing from before backwards in the ratio of three 
to two to one. Hach knob carries a hair, or at least was originally 
provided with one. On the pink bands the knobs have the same 
hue as the band itself, only a little deeper, in the yellow and the 
blue on the contrary they retain that same pink colour of their 
own. On the anterior row of each segment, where the number of 
wharts in the blue reaches its maximum (3 or 4 at each side of 
the median line) the wine-red colour even extends around the two 
lateral tubercles, and embraces them in one larger deep-red blotch. 
Surveying the whole of the segments, these blotches are seen arranged 
to both sides of the median line in a series marking the subdorsal 
line; this series can be retraced in convolvuli, in the form of 
the rows of dark subdorsal spots described before, which rows are 
in immediate contact with similar ranges of clear yellow-white 
maculae, nearer to the dorsal line, the latter itself being marked 
by dark stripes (8, one behind the other, on each segment). 

When now we pass to the survey of the body-markings of the 
imagines and begin with the abdominal segments of convolvuli, we 
here again meet the dorsal line as a series of little black stripes. 
To both sides of this the subdorsal. design is arranged as a sequence 
of grey areas touching the dorso-lateral colour-markings with a 
special convexly-curved borderline. These fields themselves are com- 
posed on each abdominal ring of three transverse bands: a narrow 
anterior one of white, and two much broader ones behind, the first 
pink, the second jet-black. This set of three transverse bands is 
repeated seven times: .at the end comes one segment with only a black 
dorsal stripe. The ventral border of this lateral pattern forms an 
almost straight line, situated at a certain distance above the row of 
stigmata. The intervening epistigmal seam is coloured less conspi- 
cuously in the same way as the entire hypostigmal ventral surface; 
yet it is possible to distinguish darker sets of hairbundles, which 
associate with the red and black bands, and a row of white bushes 
of hair stretching right above the stigmata. 

Though as mentioned, the ventral side shows no vividly coloured 
pattern, this uniformity of hue is precisely the cause, that a set of 
two dark spots in the ventral middleline, at the front-border of the 
fourth and the fifth abdominal segment, is highly conspicuous. 


372 


In my opinion the transverse markings of the dorsolateral fields 
might be ascribed to the original distribution of the colour in dorso- 
ventral bars, corresponding to the eight annuli which enter into 
the composition of each segment; probably the white represents the 
first annulus, the pink area the following four, the black the poste- 
rior three, but in convolvuli the limits of the single rings are indis- 
tinct. As we shall see, this division can really be traced in imagines 
of other Sphingids. 

Now comparing this pattern of the abdomen to that of the thorax, 
we remark that the grey ground-colour along the dorsal side of 
the latter, provided with three darker longitudinal striae on both 
sides of the middle-line, evidently may be considered as a broadening 
of the dorsal markings of the abdomen. Over the root of the wings 
runs a greyish-white streak of long, soft hairs, forming a continuation 
of the white transversal markings of the abdominal segments, 
especially of their dorsal part, which on the second segment already 
has the shape of an isolated round white blotch. This light stripe 
over the wing-root (epipterygial stripe) should probably not be 
considered the homologon of the white subdorsal line on the thorax 
of the caterpillar. 

In the third place an evident connection exists between the markings 
on the upperside of the hindwing and those on the dorsal side of 
the body, as well of the thorax as of the abdomen. The said wing- 
design consists of dark spots arranged in bands on a lighter ground. 
These bands apparently stand perpendicularly to the longitudinal axis 
of the body, thereby agreeing in position with the anterior three 
black transversal rings on the abdomen. As a matter of fact however 
they are not transverse but longitudinal bands, because they run 
from the anterior towards the posterior border of the wing, the 
apparent transverse position only being a consequence of the round- 
ing off and reduction of the hindwings, which in Sphingids has 
taken place in an extreme degree. 

When as described before, the hindwings are projected upon the 
lateral walls of the thorax, the dark bands may be drawn on the 
wing-fields as longitudinal lines, viz: in an oro-eaudal direction. In 
this way the similarity with the lateral design of the abdomen, 
which at first aspect is so striking, withdraws to the background, 
or, rather, is reduced to its real proportions. 

Indeed, as well as the design on the annuli of the thoracal segments 
of the convolvuli-caterpillar, that on the wings is seen to consist of 
dorso-ventral rows of alternately dark and light spots, which are 
arranged in longitudinal chains, by their situation at the same level 


373 


upon the succeeding annuli. It is true that the surface of the wing 
is not divided into regular annuli in the same way as the body-wall, 
yet also its surface becomes parcelled into so-called cells by means 
of the venous system, this division showing a considerable amount 
of similarity to the first-mentioned division in annuli. One even 
might feel tempted to ascribe a certain importance to the fact, that 
in the neighbourhood of the wing-root the number of internervural 
cells is equivalent to that of the annuli of the larval segments, when 
the original number of veins in the proximal area of the wing is 
taken to be eight, (costa, subeosta, radius, medius, cubitus and three anals). 

Comparing the body-design of the convolvuli-imago to that of the 
corresponding stages of Ligustri and atropos, the similarity is obvious 
on first view, and not less striking than that of the wing-patterns. 
But entering into details, which at first sight might seem to be 
trifles without deeper meaning, a few curious features may be 
remarked, which draw the original similarity with the caterpillars 
into stronger evidence. So in ligustrt the contrast between the light 
areas on both sides of the black median dorsal line and the enlarged 
dorsal tops of the black transversal bars, is sharper than in convol- 
vuli, these broadened black tops, protracted as they are towards 
the head-side, producing the impression of a sequence of dark sub- 
dorsal spots separated by the lateral emergencies of the front-corners 
of the lightbrown subdorsal fields, in a higher degree than is the 
case in the lastnamed species. 

Likewise in ligustr, the white lateral transversal stripes along the 
frontborder of the segments are lacking, or to express it more 
correctly, the white is replaced by black, which coalesces with that 
along the back-border of the foregoing segment, the black between 
the first and the second abdominal segment being restricted to a 
subdorsal blotch. Moreover the ventral ends of the black and of the 
red transversal bands are obliquely truncated, which calls forth the 
impression of a zig-zag-line, running at a certain distance above the 
series ‘of the stigmata, which line corresponds to the system of 
diagonal stripes on the abdominal segments of the caterpillar. _ 

At the ventral side the design has remained unaltered in a much 
higher degree than in convolvuli, the dark ventral line stretching 
over the whole of the segments. At both sides of this line light areas are 
found,which at the level of the stigmata are marked off by a dark festooned 
line. On the thorax the resemblance with convolvuli is striking, and 
especially the light epipterygial band is drawn with peculiar sharpness. 

The similarity in design between the abdominal segments and the 
hindwings is still more obvious than is the case with convolvuli, 


374 


because in /igustri the groundeolour of the hindwings plays into a 
rose-red hue, especially in the neighbourbood of the wing-root, this 
red even running over into the root of the forewings. The black 
wingbands lie more exactly in the prolongation of those of the anterior 
abdominal segments and show fewer traces of their origin by the 
coalescence of a row of intervenous spots. 

All the above-mentioned resemblances are equally found in atropos, 
only the hues and the variegations being different. When we start 
from the abdomen, the dorsal stripe on its back corresponds to that 
of the caterpillar as well in the V-shape of its segments as in its 
blue shade. The rose-red colour of convolvuli and ligustri is replaced 
by stark-yellow and the dorsal borderlines between the yellow lateral 
areas on the abdomen and the blue dorsal patches run in the same oblique 
direction as the lateral sides of the V-shaped elements of the dorsal 
design in the caterpillar. At the ventral side of the abdomen the 
black design along the frontborder of the segments, at least of the 
anterior ones, is well developed, and shows well-marked enlargements 
along the hypostigmal and subventral lines, pointing to the presence 
of series of spots at those levels. 

As well as in /igustri the light (in atropos yellow) hue of the lateral 
walls of the metathorax is continned not only on the hindwings, but 
also on the root of the forewings, though it does not reach the 
front-margin of these latter. 

The cranial design on the dorsal side of meso- and metathorax may 
be easily traced back to sets of dark spots on a light ground: two 
pairs of these spots standing on the meta-, one on the mesothorax, 
just as is found in the caterpillar, and in the same way in the 
imagines of many other Sphingids as well as in those of other 
Heterocerous families. The contour of the skull-image corresponds to 
the dorsal or medial dark longitudinal thoracal line, which forms the 
borderline of the median area of the thorax, in the same way as in 
convolvuli and ligustrt. The more ventral or lateral thoracal-line is 
likewise present in atropos, and next to it also the epipterygial light 
streak, though here this latter does not show the grey shade of 
convolvuli or the white of Ligustri; but a dark bluish grey, which 
of course renders it much less conspicuous. 

Lastly comparing the three stages of Chaerocampa celerio, as well 
with each other as with the corresponding stages of the three above- 
mentioned Sphingids, we meet again with all the already remarked 
peculiarities, but here they are in some regards more complete and 
better pronounced, in other points more original, in still other on the 
contrary more modified, either in a higher degree or in a different way. 


375 


E.g. in the fullgrown caterpillar the contrast between thorax and 
abdomen is of the same nature and as strikingly pronounced as in 
that of convolvuli. The dorsal stripe is only marked by a thin but 
sharply drawn black line, extending all along the thorax, but on the 
abdomen only covering the anterior three segments. The light subdorsal 
and epistigmal lines on the contrary are well developed on the 
thoracal segments, the first runs up to the big ocellus-spot on the 
first abdominal ring, this. spot, as WuwisMANN’s investigations have 
proved, differentiating itself in the course of development of the 
caterpillar from the anterior part of the subdorsal line on this segment, 
while at the same time the posterior part obliterates. 

The second eye-spot is formed in the same way. In the specimen 
at my disposal this spot was much bigger and more purely circular 
at the left side of the body than at the right. On the latter side 
however the spot consisted of two parts, lying immediately behind 
each other, and so betrayed its real nature asa part of the subdorsal 
line still better than at the opposite side. 

On the next abduminal segment traces of the light subdorsal line 
ean still be detected, and likewise of dark spots immediately above 
it on the level of the first annulus. Above the stigmata of the 
abdomen dark diagonal striae run upward, bordered at their ventral 
side by light stripes: proving that the common motive of design of 
the Sphingid caterpillars is present also bere. These striae and stripes, 
though occupying the whole length of the segments, yet figuratively 
speaking seem to be drawn on a back-ground of light spots and 
dark siripes, which themselves are strictly bound to the division of 
the segments into annuli. 

Moreover a contrast exists between the dorsal and the ventral side. 
On the first we meet at every annulus with a row of small black 
stripes, between which the ground-colour is lighter and therefore 
makes the impression of clear spots separated by black lines. This 
part of the design shows a great similarity with the annuli-markings 
of the full-grown convolvuli-caterpillar. 

At the ventral side on the contrary each annulus carries a row 
of white lentiform knobs, constituting the basal cushions of short 
setae. On the level of the epistigmal area the knobs pass into the 
light spots, evidently tbe latter occupy the same place as the former, 
at least the knobs diminish in size and conspicuousness towards the 
dorsal side. This feature therefore confirms the assertion that the 
colour-pattern of the fullgrown convolvuli-caterpillar may be derived 
from the condition before the last eedysis, by supposing the knobs 
to fall ont and to become replaced by the light spots. It also deserves 


376 


attention, that in ce/erio the knobs have maintained themselves at 
the ventral side of the caterpillar, in atropos on the contrary at 
the dorsal surface, while in ligustri they are totally absent, probably 
an effect of obliteration. 

These rows of knobs, standing regularly arranged along the annuli, 
probably represent the same feature as the chagrination of the larval 
skin, mentioned for many Sphingid-caterpillars by Weismann and 
Voss, these investigators however having paid no special attention 
to this feature. When studying the figures, which the latter author 
gives for the younger instars of the Smerinthus-caterpillars e.g. the 
yellowish-green variety of JS. ocellatus, (fig. 22, III stage and 23, 
III stage), we find distinct indications of these light spots arranged 
in a dorso-ventral row on the annuli. Judging from older tigures of 
Ceratoma amyntor and Pogocolon nessus, the rows of setiferous 
knobs here run regularly from the dorsal to the ventral side of all 
the segments, those of the thorax as well as those-of the abdomen. 

Now comparing the caterpillar of celerto with the body of the 
moth, the correspondence in design in many regards is still more 
striking than in the before-mentioned species of Sphingids. For on 
the dorsal side of the abdomen of the imago the markings consist 
of alternating light and dark longitudinal lines, and these lines are 
seen to be composed of a chain of coloured patches, which on every 
segment clearly show the division into annuli, just as on the body 
of the caterpillar. On the first and the last annulus of each segment 
the design is developed best: silvery-white spots in the dorsal median 
line and subdorsal stripes marking the anterior and the posterior 
border of the anterior abdominal segments. Along either side of the 
median line (which behind the mentioned white spot carries a series 
of black stripes), dark bands run in a longitudinal direction; these 
as well as the median stripe are prolonged over the thorax. To the 
lateral side of these three dark bands a silvery stripe is formed, the 
homologue of the subdorsal line, and over the root of the wing we 
again meet the light epipterygial stripe which runs on to the head 
above the eye, and shows a great similarity to the epistigmal stripe 
of the caterpillar. But on the abdominal segments we are likewise 
able to distinguish stigmal, hypostigmal, subventral and ventral 
longitudinal bands, and we also see that the epistigmal, the subdor- 
sal and the dorsal bands are characterized by the occurrence of 
silvery-white bushes of hairs. Using a magnifying glass for more 
minute observation, each of these stripes is seen to be again com- 
posed of lighter and darker bushes and groups of specks, the whole 
circumference from the dorsal to the ventral median line therefore 


377 


showing no less than 27 ecolour-patches varying in hue. E.g. the 
brownish-black bands to either side of the dorsal median stripe are 
by no means uniformly coloured, but show a mosaic of black 
and light seales. These bands pass on to the thorax almost unmodified. 
Especially the continuation of the subdorsal stripe on the thorax is 
striking, as the white bushes, which characterize this stripe on the 
abdomen, are also seen on the thorax. The epipterygial stripe 
evidently represents the prolongation of the epistigmal line, this line 
being likewise marked by yellowish-white busbes. Behind the eye 
the subdorsal and the epipterygial stripe unite into one. 

But traces of the diagonal stripes may, I believe, also be detected, 
at least in some specimens, in the shape of dark and light oblique 
bands on the sides of each segment, above the stigma. Those features 
which in celerto are either absent or very indistinct, are un- 
mistakably present in other species, e.g. alecto. About the wing- 
design of celerio we still want to remark that the considerable diffe- 
rence between the upper surface of the fore- and that of the hind- 
wing, in contrast to the nearly perfect similarity of both wings at 
their underside, probably points to the fact, that the upperside has 
become secondarily modified to an important degree. Now it is 
remarkable that at this side the forewings, in hues as well as in 
design, show greater similarity to the dorsal side of the thorax 
and abdomen than does the hindwing, notwithstanding the fact that 
on the first-named the V-diagonal design (as I have called it) is 
strongly expressed. Moreover this design, with regard to the direction 
of the diagonal-line, possesses a striking similarity to the oblique 
markings on the abdominal rings of the caterpillar. This similarity 
especially enters into evidence, when the wing is projected in the 
above-described way on the lateral wall of tbe thorax. 

In conclusion I wish to say a few words about the design of the 
pupae, which in Sphingids, as already mentioned in a foregoing 
paper, has been preserved more or less, especially in the group of 
the Chaerocampinae. It consists of dark blotches on a lighter ground: 
shape and size of these blotches is rather irregular, yet it is clear 
that they are arranged in rows, corresponding to the dorsal, sub- 
dorsal, epistigmal, stigmal, hy postigmal, subventral and ventral lines of 
the caterpillars and imagines. In a few specimens, which J found oceasion 
to investigate (amongst which was one of unknown derivation, the 
species therefore remaining uncertain to me) the number of these 
rows of spots is-much higher, which leads to astriking resemblance 
with the design of imagines, especially celerio. Though I could not 
yet find leisure to study in details the similarity between caterpillar 


378 


and imago (eventually also pupa) of other forms than the Sphingids, [ feel 
convinced, that it may be proved for a great many Lepidoptera, e.g. 
Saturnidae and many Bombycidae, and certainly also for Geometridae. 

From the above mentioned observations I feel justified in making 
the following deductions : 

The markings on the body of caterpillars, pupae and imagines 
follow the same rule as those on the wings of the latter. Conse- 
quently the original design is regular, simple, limited to each segment 
separately, complete, uniform over the whole extent of the segment, 
bound to the dispersal of the setae over its surface, and to the 
division of the latter into secondary rings or annuli. The colour, 
in which this pattern is executed, may differ, and is of no account 
as to its real character. Yet there exists a certain connection 
between different hues: green for instance always appearing as a 
secondary modification of other shades, especially brown, grey or yellow. 

Modifications of the original pattern take place in a similar way 
and after the same rules as those on the wings. Through the accen- 
tuation of a contrast in shades between neighbouring spots, which 
originally were similarly coloured, a richer gamma of hues may be 
produced. Vertical, horizontal and oblique lines are formed by coa- 
lescence of rows of primary spots; maculae, eye-spots, bands and 
areas result from the accrescence of spots and (or) their blending with 
others in their vicinity. Finally the whole bulk of the separate 
spots may merge into one general shade. 

Attention should also be paid to the fact, that in the same way 
as the front-seam of both wings is often marked in a different and 
stronger way than the rest of the surface (especially at the under- 
side), the first annulus of each segment likewise surpasses the rest 
of the annuli in sharpness of design and coloration. 

However restricted the material for my investigations may have 
been, it has convinced me still more of the validity of my 
assumption, that a primary relation exists between the colour-design 
of caterpillar, pupa and imago, the pattern of the imaginal instar often 
showing a more primitive type than that of the fullgrown caterpillar. 

The contrast between thoracal and abdominal pattern, which 
already in the younger instars of the caterpillar manifests itself in 
the different distribution of the setae (comp. J. T. Oupemans and A. 
SCHIERBEEK), maintains itself as well in the later instars by differen- 
ces in colour and design, occurring in the great majority of cater- 
pillars. An identical design on thorax and abdomen. is probably the 
result of secondary change. 

Groningen, January 1920. 


Physics. — “On Centres of Luminescence and Variations of the 
Gas Pressure in Spectrum Tubes at Electrical Discharges.” 
By L. HAMBURGER. (Communicated by Prof. H. A? Lorentz). 


(Communicated at the meeting of April 23, 1920). 
1. Zntroduction. 


Three years ago’) we published the results of some observations, 
in which among others the fact was stated that when discharges are 
sent through a spectrum tube, variations of the gas pressure may 
occur at the anode and the cathode. 

They owe their existence to the difference in properties of positive 
and negative ions. As J, Stark *) already observed, the difference existing 
between the two kinds of ions gives rise to the two following effects: 

a. The appearance of phenomena connected with the electrical 
wind (in general the electrostriction). 

6. Mass transportation by means of the electric current. 


The object of this paper is among other things to examine which 
of these two effects, which are in connection with each other, as 
they both rest on the difference in properties of the ions, has a greater 
part in the observed variations of the gas pressure. In connection 
with this the centres of electro-luminescence will then be considered. 


2. Klectrostriction. 


A Duteh physicist D. Bos*) has already made an extensive study 
of this. He finds for gases such slight variations of volume, resp. of 
pressure, (loc. cit. p. 92 et seq.), that it is clear that with the pressure 
effects observed by us — to an amount of 30°/, and more of the 
total pressure — electrostriction cannot have had an appreciable 
direct influence. . 

In the case of discharges through a spectrum tube the phenomena 
of the electrical wind connected with electrostriction may be considered 
as a consequence of the friction between the ions and the neutral 
gas molecules. It is clear that the electrical pressure will be the 
greater as the difference in properties of the positive and negative 
ions is greater. As we already mentioned, this electrical pressure is 
of an entirely different order of magnitnde than the variations of the 
gas pressure observed by us. 


1) L. HAMBURGER, Diss. Delft 1917. These Proc. 20, 1045 (1917). 
2) J. STARK. BoLTZMANN-Festschrift 1904. 
3) Diss. Groningen 1880. 


25 
Proceedings Royal Acad. Amsterdam. Vol. XXIII. 


380 


3. Mass Transportation by means of the Electric Current. 


The discharge of the ions taking place at the electrodes, 1owever, 
gives rise to a state which may be considered as an accumulation 
of what was discussed before. 

To the existing difference in properties of the oppositely charged 
ions corresponds to a certain extent the difference between the gas 
molecules formed from them by the discharge at the electrodes. 
Though the direct influence of the difference of the ions on the gas 
pressure is slight, the influence on the gas pressure assumes quite 
different proportions when it is kept in view that constantly the 
electrically charged particles withdraw from the ion-conditions. 
Resting on the same primary basis as the electrical wind, this 
accumulation leads to the effect that manifests itself much more 
strongly: mass-transportation by means of the electric current. 

In general on discharge of the ions taking place at the electrodes, 
another number of gas molecules will be liberated at the cathode 
than at the anode. 

[n consequence of this a constantly increasing difference of pressure 
would be found in the two parts of the tube, if not another counter- 
acting effect made itself felt. It is, indeed, clear that, when a difference 
in pressure occurs through the application of the electric field, the 
gas molecules will oppose this, and try to annihilate the difference 
in pressure by diffusion in the opposite sense. The resulting difference 
of pressure then corresponds to a stationary state, in which an equal 
number of molecules are brought back to the path of the current 
through diffusion, as new ones — in ion-form — are conducted to 
the electrodes by means of the electric current. 

Already J. Srark (loc. cit.) has carried out a few preliminary 
calculations on this line of thought. As at the time, however, the 
aerodynamic laws for greatly diluted gases had not yet been developed, 
his calculations are based on unsubstantiated grounds. Thus he arbi- 
trarily assumes that after ten seconds the diffusion would make 
equilibrium with the mass transportation brought about by the current. 
Already A. WennNerLT and J. FRANK’) tried to find a firmer foundation 
for their calculation. In their experiments, just as in those by STARK, 
the circumstances under which the experiments were carried out, 
were chosen so that the carriers of the negative electricity were 
present only in the form of electrons. In what follows we shall 
extend the cases to be considered over a somewhat wider region. 
Let us, however, first examine on what conditions the diffusion under 


1) Verh. d. D. phys. Ges. 12, 444 (1910). 


381 


consideration could take place in our experiments, in which it be 
assumed for the present that the so highly “electritied” state of the 
gas has no influence on the diffusion-laws. 


4. Diffusion. 


In the mathematical treatment of this problem it should be borne 
in mind that in GeissLer-tubes we have to do with a rarefied gas- 
atmosphere, and that the cathode and the anode space, between 
which differences of pressure occur, are kept separated by a capillary 
tube. Besides distinction should be made between the cases in which 
the free length of path of the gas particles 7s comparable with the 
dimensions of the capillary and those in which it is not. 

For air at room temperature and a pressure of p baryes') the 
free length of path is y= 8,67/p cm. When we have e.g. a gas 
pressure of 0,1 mm. Hg = 133 baryes, then 


I. Lanemurr?) has derived that the equations holding for velocities 
of transfusion for gases in tubes whose diameter is not more than 
21/, times larger than the free length of path of the gas particles, 
are practically the same as those for which the free length of path 
of the molecules is large with respect to the tube-diameter. 

It is now the question whether in the experiments described in 
the author’s thesis for the doctorate the circumstances were such 
that always the free length of path of the molecules was greater 
than two fifths of the capillary diameter. 

The pressure effects have been found by us down to a gas 
pressure of 0.087 mm. Then at room temperature: 

__ 100 
A= 0.65 a7 = 0,74 mm. 
which is about */, of the capillary diameter of the discharging 
apparatus used. 

In reality, however, the gas diffusing back through the capillary, 
is not at room-temperature, even apart from the high “electrical” 
temperature®) of the particles subjected to the discharge. With the 
applied current densities the quartz capillary appeared to get heated 
even with air-cooling. When suddenly the current is cut ont, so 
that the luminescence of the illuminating gas column is eliminated, 
it appears that with the very great current strengths previously used 

1) Dyne/cm?. 

*) Gen. El. Rev. 1916 p. 1062. 

3) Cf. J. Stark, Ann. d. Phys. (4) 14, 506 (1904). 

25% 


382 


the outer wall of the capillary is even glowing hot. Also in view 
of the estimations of other observers, it cannot be considered much 
too high, when we put the “mean temperature” of the gas at e.g. 
Tavs = 3000°. Although with constant density the free length of path 
must be considered independent of the gas pressure (comp. e.g. 
L. BotrzMann’)), it should be borne in mind on the other hand 
that in our experiments as a consequence of the higher temperature 
of the gas in the capillary, the density of the gas present there is 
a fraction of that which the gas would possess at the pressure 
indicated by the manometer at room temperature. 

If eg. for p=0.087 mm. the value of 2 at room temperature 
would already lie below the above indicated limit determined by 
Lanemuir, under the circumstances of the high gas-temperature in the 
capillary this is not the case; i.e. for almost all the measured pres- 
sure-effects (cf. diss.) the conditions of the experiment have always 
been so that 2 had a sufficient value in comparison with the capillary 
diameter to enable us to apply the diffusion formulae that refer to 
highly rarefied gases (on the assumption that the electric state of 
the gas does not influence the diffusion laws). 

When M. Kyupsen’s theory?) is accepted, the velocity of transfusion 
q of a gas per second measured at a pressure of 1 barye through 
a tube under circumstances in which À is large with respect to the 
diameter D of the tube is, aecording to Irvine LaNGMuIR®), determined by: 

4h 8 
VERE al - 2s) 
(in which M/ == mol. weight p, —p, the difference of pressure, and L the 
length of the capillary). When À is small with respeet to D, the formula 
II D'p 
9 = 198 yp (PsP) - 2. + 3s 


q, = 3809 


must be taken, in which also g, is based on a volume measurement at a 
pressure of 1 barye and 7 represents the coefficient of friction of the gas: 
If we wanted to apply formula (2) to our observations, we should 
at least have to fill in the value of 4 for high temperatures. 
For simplicity’s sake, however, we fill in the value of 4 for air 
at room temperature, viz. 181.10-° C.G.S. units. Further on we 
shall state results which enable us to make our choice between 


equations 1 and 2. Then formula 2) becomes: 
4 


D 
7; = 136 Ti -?p pop.) . 5 - A . 5 . (3) 


1) Vorlesungen über Gastheorie 1910 p. 70—71, footnote. 
2) Ann. d. Phys. (4) 28, 76 and 999 (1909). 
3) Gen. Electr. Rev. 19, 1063 (1916). 


383 


5. Calculation of the Pressure- Effect. 


a. It is seen that only circumstances are dealt with in which 2 
is “sufficiently” great with respect to D. In the thus restricted category 
two cases should, however, be distinguished: 

I. The gas pressure is higher than 0,1 mm., and the discharge 
takes place at comparatively low potential differences. 

Il. The gas’ pressure is lower than 0,1 mm., and the discharge 
takes place at high potential differences. This category has been 
treated by Stark, WeEuNerLT and Frank, and will be left out of conside- 
ration here. The pressure effects belonging to this are very slight, 
and of opposite sign to those found under I. 

When the gas pressure is higher than 0,1 mm., and the potential 
of discharge is slight, both the positively and the negatively charged 
particles may be considered to be at least partially loaded with matter. 
Let us suppose for a moment that all the charged particles are in 
this case. 

Let us consider the conduction of electricity through a gas, that 
contains only univalent ions, in a cube the sides of which are 1 cm. 
long, the direction of the current being parallel to one of the sides. 
When in this cube the direction of the electromotive force be taken 
as x-axis of a system of coordinates, then with a potential difference 
v between the end-planes, a positively charged particle undergoes 
an acceleration expressed by the known equation of motion: 

dz 
B 

(In this e is the charge, m, the mass of the positive ion). The 
electrie force acts undisturbed on the charged particle during a time 
which elapses between two collisions. Be À, the mean free length 
of path, and c, the mean velocity of the positive ion, this time is 
a 

By integration of the equation of motion, taking the value of t 
into account, summation of the components of velocity for all posi- 
tively charged particles n, per volume unit, the formula 

n,eVdpy 


on an average — tT — 


2m, Cy 
is found’) for the number of positive ions that passes per second 
through the cross-section of the conductor. 
Likewise follows from the theory of the conduction of electricity 
through gases for the number of negative ions: 


') Cf. eq. G. Jäcer. Theor. Phys. IV. Samml. G. 8 57, 61. 


384 


n‚eVÀ, 

“2m Cn 

When on discharge every positive ion gives a, gas molecules, 

and every negative ion a, gas molecules, it is seen that at the 

cathode per unit of time the number of gas molecules plus ions 
will be diminished by: 


Nn eV Anas n, eV Ja, 


(4) 
pp 


whereas at the anode a corresponding increase of gas molecules 
will take place. 

Hence it is seen that as was already stated in the author’s thesis 
for the doctorate, the differences of pressure must depend on the number, 
mass, charge and mobility of the positive and the negative ions. 

The supposition made here that only univalent ions would occur, 
does not answer to reality. Many kinds of ions will be found side 
by side, and at different places of the path of the current the con- 
dition differs. The current conduction is very complicated in its 
nature. We pointed this out already before *) in connection with the 
destructive action of the discharge on the particles affected by it. 
It is, therefore, to say the least of it, very hazardous to draw far 
reaching conclusions from the measured pressure effects with regard 
to the nature of the bearers of the electricity. It will always be 
necessary to take also other methods into account, e.g. those which 
have been followed with such fruitful results by J. J. THomson, 
J. Stark and others. 

It is, however, possible to demonstrate, that, as regards the order 
of magnitude of the calculated results, the view must be valid that 
the mass-transportation by means of the electric current must be 
chiefly responsible for the observed pressure effects. 

Thus considered there can be no objection to taking a single 
simplified case as a subject of further consideration, in which as 
gas nitrogen may be chosen. 

b. Let us assume that per unit of time an equal number of posi- 
tive, univalent nitrogen-ions leave the capillary space on one side 
as negative univalent nitrogen ions on the other side, and let us 
suppose that on discharge per negative ion one gas-molecule is sup- 
plied, whereas at the cathode two positive ions are required for this. 

A gram-molecule of an ion (= 22400 eem.) considered as gas 


under normal conditions cedes 96540 coulombs on neutralisation. 


A milli-ampere t orts second aoa ccm. of gas unde 
MAI -AI re trans ki CEasc n ————_—__—_ — - 1 Yr 
P Boe eel 96540.1000 6 


1) L. HAMBURGER. Chem. Weekblad 15, 982 (1918). 


385 


normal conditions = 0.28.10? eem. or ata pressure of p. mm of mercury. 


760 
— ,0,23.10-3 cm. gas. 
P 
According to the supposition the current is conveyed half by 


negative particles, half by positive particles. Hence taking into con- 
sideration what was assumed above 


760 
— .0,23.10—-3 ccm. 
ade 
is liberated on discharge per m.A. at tbe anode, and: 


760 
ae 0,23. 10-3. 4 ccm. of “neutral” gas 
p 


at the cathode. 


760 
Hence ae 0,23. 0-3 eem. more at the anode than at the cathode, 
P 


or when the strength of the current is A. milli-ampere: 
760 
yg lll Sd ee Ae hae AE) 
4p 
A stationary state will occur when through the diffusion an equal 
amount is carried back from anode to cathode. Let us think the 
current cut out for a moment with given difference of pressure 
and all the ions re-combined to neutral molecules. Then the gas 
must flow black through the capillary. Let us apply for this purpose 
formula (1), which under these circumstances ') passes into: 


JD 
9, — 38090 a Mee) ee Pr eae eee (5) 
When the stationary state prevails, we get’): 
A Cas 2,0,, 10—-4== 36090 ae 7 
don ek : ry ‘ 7 P/P i ; ( ) 
dD 
= 38090 . — . Ap, when p,—p, = Ap is put’). 


L 
Let the pressure of the gas be p = Bd = 0.15 mm. = 200 baryes, 


D=0.2 em, L = 5em. 
A = 400 mA., then: 


400 . 700 88090. 10-3 
lg ge Ape 
4. 0,15 5.200 


1) Assumed is 7'= 28008. (water-cooled capillary wall). 

2) pmm represent the pressure expressed in millimeters of mercury, pp that in bareys. 

3) A factor 1/pp has been added in the second member of this equation, because 
in equation 3 (resp. 6) qj (resp. dy) is measured by the product of volume and 
pressure (expressed in baryes), whereas from equation 5 a volume results at a 
pressure p, 


386 


5.760.400. 200, 2,3 . 104 

“P= 15380908. 10-54 

This amount for Ap is considerably greater than the experimen- 
tally found value (viz. about [0.08| mm.) with the substituted value 
of p. That the calculation gives a result that deviates from the value 
determined experimentally was only to be expected, seeing the 
arbitrary character of the suppositions. When e.g. in the beginning 
of § 5 sub 6 we had changed our assumptions in that sense that 
on discharge of the positive ions not 50°/,, but only 15°/, less 
molecules are formed, then on transition of the negative ions into 
the “neutral” gas state, we should have found for the calculated 
pressure effect a value of [0.087] mm., which practically would have 


— 335,5 baryes — [0,29 mm. | 


been in agreement with the empirically found value. 

c. However even the supposition that an equal number of negative 
and of positive ions take part in the conveyance of the current, will 
not correspond with reality. As will be shown presently, we should, 
bowever, have arrived at similar results, when it had e.g. been 
assumed that per positive ion an equal number of gas molecules 
are formed on discharge as per negative ion, but that a much greater 
part of the current-conveyance takes place by the negative ions 
than by the positive ones '). 

There is, indeed, a certain ground for the supposition that a 
greater part of the current conveyance takes place through the 
negative ions than through the positive ones. 

In the paper cited by us (BoLtzmann-Festschrift 1904) Stark already 
used the formula V,=1,37 X V, for air, when the positive and 
the negative ions are ‘“molecule-ions’, in which formula V, and 
V, are the different specific velocities of the negative and the posi- 
tive ions. Also Ratner (Phil. Mag. (6) 32, 441, 1916) uses this 
value for normal cases, pointing out, however, that on change of 
the gas pressure and of the electric force, this quantity does not 
remain constant. When we assume the value 1,3 for the ratio 
V5 
Vp 
negative ions, and for 43,5 °/, through the positive ions 


100 
a | 
(Ga = ) 


Among the circumstances described in this § 5 under c we find 


, the current conveyance takes place for 56,5 °/, through the 


') It is further plausible that the too high result is owing to the fact that also 
in the pressure region considered here for a great part free electrons will reach 
the anode. This will be further discussed presently. 


387 


that in consequence of the current transportation an increase of 


760 
A — .0,23.10-%.0,565 takes place at the anode, whereas at the 
Pp 


760 
anode the quantity of gas is diminished by A ——.0,23 .10-%.0.485 
E 


through the current transportation. 
760 


Hence there remains an increase at the anode of A— . 0,23 . 
his. 0.13. 4 

In the same way at the cathode a decrease is found of 
A i Oto. 10 O18: 

The difference between anode and cathode, therefore, becomes: 


760 she 760 
A — . 0,23. 10-3 . 0,26 —= A—.2,3.10-4. 1,04, 
p 4p 


which is practically the same as formula 5 of p. 385. 

In many cases the point of issue given here will be preferable 
to the supposition formulated in the beginning of § 5 under 6. 

It is, however, clear that under definite circumstances negative 
ions resp. electrons may act as attraction nuclei. We may refer e.g. 
to the condensation experiments of Witson in a nearly related case. 
Then it might very well happen that through the discharge of the 
negatively charged particles a great number of molecules is liberated 
at the anode. 

d. Application of equation 3 yields entirely different results. 
Combination of this equation with (5) gives: 


A 760 Ty 
- 2,82. 10-4= 136 — pp .(p,—p,)/p, + - . (8) 
Pon L 
Substituting the same numerical values as above we have: 
400 760 1G Al eee 2.102 A 
EA Os 5.200 Ps 


A p = 2700 baryes =| 2,0 mm. |, 


which value is so many times greater than the observation in this 
pressure region, that it must be looked upon as of an entirely different 
order of magnitude. 

Besides, the experiments teach that it is contradictory to reality that 
the pressure effect should be in inverse ratio to the gas pressure, as 
would ensue from formula 8. In reality within a pressure area lying 
between 0,2 and 0,5 mm. the value of Ap appears experimentally 
to vary little, if at all, with p, which is in harmony with formula 7. 
Hence formula 8 should be rejected. Apart from the reasons set 


388 


forth inter alia in the next paragraph, formula 7 is therefore to be 
preferred. 

e. It should now also be pointed out that it follows from equation 
7 that Ap is proportional to the strength of the current, which as 
was already stated by us (ef. Thesis for the doctorate) has also been 
established experimentally for nitrogen. 

It may, however, happen that with higher current densities there 
appear other bearers, as e.g. is very probable for argon. It is to be 
regretted that sufficient quantitative data are wanting about the 
dependence of the pressure effect on the current density in this gas. 

In general it may be said a priori that the pressure effect cannot 
be a simple function of the gas pressure, because, as is known, 
other bearers will occur for important variations of the pressure. 
One and the same supposition will not always serve our purpose. 
With very low pressures and with high potential differences electrons, 
instead of charged atoms or molecules, can be discharged at the 
electrodes to such an important degree, that the pressure effect even 
reverses its sign (STARK, WeHNELT and Frank loc. cit’). In this sense 
we have distinguished two categories on page 383. 

As was already stated at the end of § 5 under a the preceding 
calculations have, indeed, only been given to show that the difference 
in properties of the positive and negative ions can actually give rise 
to important pressure effects, which are of an entirely different order 
of magnitude than those which should be considered as ensuing 
directly from the electric wind. It is, therefore, necessary to point 
out here, apart from the criticism given in the following paragrapb, 
that in general the phenomena met with, are very complicated, 
especially for high gas pressures. We should, therefore, not be very 
optimistic with regard to a satisfactory, mathematical treatment of 
this subject. 


6. Criticism; Modification of. the Physical View. 


Both equation 7 and equation 8 have been obtained by combi- 
nation of equation 5 with equations of diffusion. We remind that 
in § 5 under 6 it was given by way of supposition: “Let us think 
the current cut out for a moment with given difference of pressure, 
and all the ions re-combined to neutral molecules. Then the gas 
must flow back through the capillary.” After this the diffusion laws 
are applied. 

In reality, however, the measurements are made, while the current 
has not been cut out. 

Then exceedingly important processes take place in the capillary 


389 


tube through which the gas flows. We are not justified in accepting 
the diffusion formulae 6 or 3 there without reservation. On the 
contrary. On similar grounds as before on another occasion we 
rejected any thermodynamic calculation of electro-chemical gas-reac- 
tions on principle, we cannot unconditionally accept the application 
of the normal diffusion formulae here. For brevity we refer to the 
part dealing with this point of the cited paper. *) 

It seems, however, not devoid of interest, to demonstrate some 
points also in a direct way. 


60 ZA 
We stated already that —-.2,3.10-4 ccm. of univalent ions 


are transported per mili-ampere. 

When we substitute in this e.g. A—= 435 mA p=0,76 mm., it 
would follow that also in the stationary state 96 eem. (reduced to 
room-temperature) of gas flowed per second from the capillary, though 
the capacity of the whole capillary is only 0,2 ecm.; moreover it 
should be considered that the gas in the capillary possesses a very 
high temperature, hence a very slight density. This is untenable. 
Though from the fact that the pressure effect at the anode (for the 
given value of p) corresponds to an increase of pressure, we must 
conclude that at the anode a considerable quantity of charged atoms 
and molecules is discharged, we must certainly derive from the 
just given numerical example that the conduction of electricity in 
the luminous column takes place in a very important degree by 
free electrons, which are charged partially 
with matter (see figure) when entering the 
spherical space A. Further divested of any 
mathematical garment, the physical view 
arrived at must really deviate from that 
which led to the combination of equation 
(5) with the diffusion-equations. 

The application of the ordinary diffusion 
laws referring to the reflux of gas through CD now appears to be 
very questionable indeed. For the gas-molecules, which have partly 
originated through the discharge of ions at the anode, and are going 
to leave the space A for C, will for the greater part be scattered 
and charged by the electrons rushing from CD, after which they are 
again subjected to the electric field. 

When it is finally assumed that for pressures ranging between 
0,4 and 1 mm. no great variations in the bearers of the electricity 


1) L. HAMBURGER. Chem. Weekblad 16, 664 (1919). 


390 
take place, the slight variability of Ap with the gas-pressure, which 
has been observed in this region for different gases, becomes expli- 
cable also in this way (cf. e.g. Diss. p. 92). 

The increase of Ap with the current density is also easy to see. 
For in the case that the nature of the bearers is not modified with 
the current density which may be assumed with a single excep- 
tion (argon) for the region examined experimentally, the following 
formula may be substituted for formula 5: 


1 100% 
I= AEO rn 

a p 
in which at constant gas pressure and not greatly varying tension 
a is a constant whose value is many times the unit. Putting: 

760 

—.2,32.10-4=b) 

oP 


(9) becomes 
gb oo) ois = oe. nnn 
We can also say something further about the diffusion: Both 
formula (1), and formula (2) show that the diffusion varies directly 
with Ap. In connection with the electrical conditions it must also 
be a function of variables of electric nature. The only motive force 
for the diffusion is, however, Ap; therefore the reflux must always 
be proportional to it. Hence may be written: 
g = Bp op yy, na) - aes eel 
As soon as a few more cem. of the greatly rarefied gas have 
entered the anode space, the stationary state sets in. 
Combination of (11) with (10) gives: 
ba. = Bape las yf: =.) 
or 
A p= Agi Oy). sf a a 


through which the proportionality of Ap with A finds expression. 
7. The Centres of Luminescense. 


a. Making use of the obtained experimental measurements regarding 
the intensity of light-emission of gases and mixtures of gases at 
electrical discharges, we have devoted some attention in our Thesis 
for the Doctorate to the consideration of the mechanism of electro- 
luminescence. Also in connection with the pressure-effect studied more 
fully tere, we will consider some points somewhat more closely. 

Let us first remind of this that the objective measurements of 
intensity taught that the intensity of the emission of light of a gas 
is in direct ratio to the supplied energy, if not on change of the 


391 


electric variables a change in the character of the centres of light- 
emission takes place. 

After J. Srark had already derived this theoretically for slight 
optical thickness (Ann. d. Phys. (4) 14, 506, (1904) ), C. D. Cuup 
has returned to this subject in some papers (Phil. Mag. (6) 27, 278 
(14); Phys. Rev. (2) 15, 33 (’20) ). 

From the fact itself that the quantity of emitted light 1s approxi- 
mately proportional to the current strength, follows that in principle 
the emission of light is owing neither to ionisation, nor to recombina- 
tion (after previous ionisation). It is known that it has been made 
experimentally probable, that emission of light can take place also 
without ionisation. It is, indeed, in agreement with the theory of 
Bour c.s, which states that radiation takes place when an electron 
crosses from a path that lies more on the outside to one that lies 
more on the inside of the atom, to which the supposition may be added 
that in most cases of electric discharge the electron that changes from 
one path to another, bas never been entirely separated from the nucleus. 

Cuip shows that if the emission of light were owing to the 
recombination of ions, this emission would have to be approximately 
proportional to the second power of the current strength, and the 
same thing would hold, when ionisation was considered as the 
cause of the light emission. While the number of recombinations 
resulting from complete ionisation depends on the product of positive 
_ and negative ions, and is, therefore, proportional to the second power 
of the electrons present, the number of partial ionisations’) depends 
only on the number of electrons present that gives rise to the partial 
ionisation. Consequently this is proportional to the first power of 
the electrons present. 

The previous calculations’) have taught that free electrons are really 
present in the luminous column in great numbers, and that they 
bring about the current conveyance in a preponderating degree. This 
proves that the current is approximately proportional to the number 
of electrons present. The number of partial ionisations is proportional 
to the latter, from which the proportionality of the light-emission 
to the current strength follows directly. For it will readily be seen 
that the number of recombinations ensuing from partial ionisation 
is in direct ratio to the number of partial ionisations. 

6. It is clear that a more accurate knowledge of what takes place 
with mixtures of gases, can give us a clearer insight with regard to 

') Let by partial ionisation be understood the increase of the distance of one 


of the electrons from the atomic nucleus, without it breaking away from it. 
2) Cf § 5c. note and § 6. 


392 


the centres of the light emission on electric discharges also for simple 
gases. In consideration of previous researches on collisions of electrons 
with gas molecules Frank and Hertz defined a theoretical view about 
mixtures of gases more closely, assuming that in electro-positive and in 
the rare gases the electrons collide elastically with the gas molecules, 
so long as the energy does not exceed that amount that corresponds 
with the ionisation-potential. They derive that with mixtures 
of gases the light-emission takes place preponderantly through the 
gas with the slightest ionisation-potential. Indeed, in many cases 
this theory appears qualitatively to harmonize with experience. 
Already in our Thesis we drew attention to the deviation in mixtures 
of argon and mercury, and in the Zeitschrift für wissenschaftliche 
Photographie (18, 43, (18)) we pointed out that our experimental result 
in the field of spectral intensity contirms the opinion that for mercury the 
determination of the potential of ionisation at 10 Volts is preferable to 
the value given earlier by others (5 Volts). We have, however, also drawn 
attention in our ‘Thesis’ to objections to the theory of Frank and 
Hertz, among other things on the ground of the fact that light-emis- 
sion can also take place without ionisation. Indeed, Frank and Hertz 
themselves have published a modification of the theory in question in 
connection with Bour’s results (Phys. Zeitschr. 20, 132 (19). 

The necessity of this modification follows particularly from the 
fact that also with values lying below the ionisation-potential 
electric discharges through gases can take place. Accordingly FRANK 
and Hertz abandoned their view of the perfectly elastic collision, 
and like Cuinp, they assumed in agreement with Bonr’s theory, that 
when an atom collides with an electron, and the energy of the 
latter is sufficient, one of the electrons of the atom can pass from 
its path to one lying more on the outside. It is now conceivable 
that a return to the normal path takes place with light-emission, 
but also that before this happens, the injured atom again collides 
with another electron, so that a further change of path takes place 
ete. etc, till at last the partial ionisation can have changed into a 
complete ionisation. 

c. So it is seen here that the optical phenomena compel us to 
assume dislocated atoms. Even in case of a rare gas multifarious 
particles will occur in the path of discharge according as the disloca- 
tion of the atoms takes place to a greater or less degree. When 
we have to do with molecules, i.e. with atom complexes, the ques- 
tion will be much more complicated. For of each of the atoms in 
the molecule one of the electrons in the “outer path” of the atom 
in question can be in an abnormal condition. To this complicated 


393 


state of the innumerable kinds of dislocated molecules corresponds 
the enormous complexity of the molecular specira. 

This is of importance for the chemist. The fact in itself that the 
determination of the chemical and optical properties is attributed 
to the electrons of the “outer shell’, shows clearly the great im- 
portance for the chemist to know the laws that govern the optical 
properties, because this must give him a clearer insight in the laws 
controlling the chemical properties. But besides H. J. Prins ') pointed 
out already in 1912 that the same factors that influence the chemi- 
cal properties, influence the catalytical properties in an analogous 
way. We think we are justified in concluding from this that the 
outer electrons also determine the catalytical properties *). Now it 
is exceedingly remarkable that it appeared necessary for the expli- 
cation of the catalytical phenomena to introduce the conception of 
dislocated molecules, resp. atoms, (J. BÖESEKEN) *) long before the above 
results had been established in optical region. Hence we meet with 
a proof for the existence of dislocated states in two widely diver- 
gent regions. It seems to us that this train of reasoning is of im- 
portance for the further substantiation of the theory of catalysis, as 
given above. 

d. In connection with what precedes it is also necessary to devote 
some attention to the law of displacement enunciated by W. Kossrr 
and A. SommErFELD (Berichte der Deutsche phys. Ges. 21, 244, 1919), 
which states that the spark spectrum of every element has the same 
character as the arc-spectrum of the element which precedes it in 
the periodic system. As early as 1916 W. Kossen (Ann. d. Phys. 
(4) 49, 229, 1916) had found a connection between molecule-for- 
mation and atomic structure, in which among others as basis the 
assumption was accepted that the elements from every vertical row 
of the periodic system are characterized by the same definite num- 
ber of outmost electrons, which number, rising to the number of 
8, is every time J more than that of the preceding vertical row. 

When through ionisation an electron is withdrawn from the atom, 
- it shifts with regard to its optical behaviour, which as we saw is 
determined by the outmost electrons, to the preceding vertical row. 

This view teaches us that also on complete ionisation the light- 
emission is chiefly determined by the rest of the atom ion that 
is left behind, and not by the return of the removed electron to the ion. 


1) Thesis Delft 1912. Journ. f. prakt. Chem. 89 (1914). 

2) Cf. also L. HAMBURGER. Chem. Weekblad 16 (1919). 
A. EB. LAcoMBLÉ, Zeitschr. f. phys. Chem. 98, 269 (719). 

3) Cf. eg. J. BörseKeEN, These Proceedings 1914. 


394 


e. And this forms in our opinion the connecting link to the view 
recently set forth by J. J. Tuomson, according to which he assumes 
that electro-luminescence radiation chiefly takes place with recom- 
bination of free electrons with ions (Phil. Mag. 37, 419, 1919) *). 

It seems to me that after the above remarks some difficulties 
would have to be removed if this view is to be maintained. But it zs 
clear that particularly when radiation is excited by a strong external 
electric source of energy, ions must appear, and to these rests them- 
selves the strong emission of light is, in fact, chiefly owing. 

That on combination of the ion with an electron a great distur- 
bance in the molecule takes place, which likewise gives rise to 
light-emission of the different “erregte” states, is clear. That such 
an emission of light takes place in case of the return we have dis- 
cussed, has experimentally been made very probable by P. LeENARD 
for the region of phosphorescence. 


8. Summary. 


As a summary we may give the following conclusions from some 
results of the author’s Thesis for the Doctorate and the preceding 
calculations : 

1. The observed pressure effects are chiefly owing to the difference 
in the number of molecules that arises on the discharge of the 
positive and negative ions at anode and cathode. In direct sense 
the electric wind plays only a very subordinate part. The extent 
of the pressure differences varies with number, mass, charge, mobility 
of the positive and the negative ions. Hence the dependence on the 
electric variables, the gas pressure, the nature of the gas. 

It appears possible to come to a physical interpretation of the 
factors, leading to the pressure effect (Ap), the consequences of which 
are also in harmony with the dependence of Ap on different. variables. 

2. There occur positive and negative ions charged with mass in 
the luminous positive column, and also electrons in a considerable 
degree. The current-conveyance is chiefly brought about by the latter. 

3. The conclusions under 1 and 2 form in the region of electro- 
luminescence experimentally and logically a support for the theories 
and views of Cuirp, Frank, and Hertz, and to a certain extent to 
those of THomson as indicated above. 

4. The outer electrons of the atom determine the catalytic proper- 
ties. The right of existence of the assumption of dislocated states in 
the theory of catalysis is optically confirmed. 

Dordrecht, March 1920. 


1) Cf. also Engineering 107, 410 (1919). 


Geology. — “On the Relation between the Pleistocene Glacial Period 
and- the Origin of the Sunda Sea (Java- and South China- 
Sea), and its Influence on the Distribution of Coralreefs 
and on the Land- and Freshwater Fauna”. By Prof. G. A. F. 
MoOLENGRAAFF and Prof. Max Wesrr. 


(Communicated at the meeting of November 29, 1919). 
I. GEOLOGICAL PART by G. A. F. MorENGRAAFF. 
The continental shelves and the agents at work in their formation. 


It is a well-known fact that continents are encircled over large 
distances by shallow seas deepening gradually down to about 100 
fathoms. Farther seaward this depth progresses more rapidly, until 
the average ocean-depth is attained. 

The floors of those shallow seas are together known by the com- 
prehensive name of “the continental shelf”. The total area of this 
shelf is according to Murray about 25 million km.*. 

In most textbooks the way in which the continental shelves ori- 
ginate is seldom explained, and their existence is generally put 
forward without comment as something quite natural. Moreover 
in the European geological literature the problem of their origin 
belongs to the more or less neglected subjects. This is the more 
remarkable since the existence or the non-existence of shelves and 
the manner in which they develop is apt to throw much light upon 
the geological history of the region concerned. 

Shelves must arise along the borders of every continent as long 
as its position relative to the sea-level remains constant; then the 
shelf is built up and enlarged by the sediments transported to the 
sea through the various denuding agents ') which act upon the land ®). 
The more denudation progresses, the more it becomes obvious that the 


1) Including the action of the surf, i.e. the abrasion at the coasts, and the 
formation of the plane of abrasion. . 

2) As long as the position of the land relative to the sea remains stable, the 
area of the shelf will grow towards the sea. Towards the land, however it will 
lose ground, because the peneplain not only broadens towards the land with 
increasing denudation, but also in some degree encroaches upon the shelf through 
accretion. 
26 
Proceedings Royal Acad. Amsterdam. Vol. XXIII. 


396 


circum-continental shelf is the submarine prolongation of the pene- 
plain above the sea-level '). The seaward growth of the shelf comes 
to an end only as soon as the continent concerned will have been 
eroded to about its base-level, i.e. has become a perfect peneplain. 

Of the latter no instance can be pointed out, because the process 
of shelf-formation is repeatedly (though with intervals of thousands 
of years, we may nevertheless use this word geologically) modified 
by relative movements of land and sea. 

To get a clear insight into the influence of these movements on 
shelf-formation, it will be convenient to apply the term gradation- 
plane to the plane which comprises the combined peneplain and 
shelf. The shelf is the submerged portion of the gradation-plane, 
whereas the peneplain represents its emerged portion. 

Now it is obvious that the mode of development of the shelf depends 
on: 

1. the mode of development of the entire gradation-plane ; 

2. the extent to which the gradation-plane has been submerged ; 

3. the position of the gradation-plane. 

First of all the growth of the shelf keeps pace with that of the 
entire gradation-plane, but besides this it also increases or decreases 
according to a larger or smaller portion of the gradation-plane being 
covered by the sea. Finally the area of the shelf also depends on 
the position of the gradation-plane; in case orogenetic movements 
cause it to shift from its original position (gently sloping towards 
the sea) to another, say, a more inclined one, the depth of the 
water on the shelf will, during these movements, increase seaward 
and the consequence will be that the sediments, which are transported 
from the Jand towards the sea, will become incompetent to fill up 
the entire available space; consequently the newly formed beds will 
not reach the sea-level and very little sediment will be left to build 
up these beds and thus to extend the shelf farther seaward. 

The above-mentioned three conditions lead to the following con- 
clusions : 

1st. Diastrophism will in the first instance, nearly always check 
the outgrowth of the shelf, because it generally steepens the slope of 
the existing surfaces both above and below the sea-level, consequently 
also that of the gradation-plane. Initially it will give rise to 
steep coasts with poorly developed deep-lying shelves or none at 


1) CHAMBERLIN unites denudation of the land and the growth of the shelf into 
one larger process called by him gradation. 

T. C. CHAMBERLIN Diastrophism and the formative processes. Il. Journal of 
Geology XXI. p. 528, 1913. 


397 


all. Very often, however, diastrophism introduces a new cycle of 
erosion, and consequently revives the process of denudation, resulting 
in the long run in intensified gradation and in growth of the con- 
tinental shelf. 

A lapse of time succeeding a period of strong diastrophism 
will, for regions affected by this process, be characterized 
by potent denudation, active sedimentation and a corresponding 
strong development of the gradation-plane, consequently also of 
the continental shelf. 

2nd. Negative movement of the coastline, i.e. uplift of the land 
or lowering of the sea-level will, as a direct consequence, narrow 
the continental shelf, or cause it to disappear altogether, expanding 
the emerged portion of the gradation-plane at the cost of the sub- 
marine portion. But, on the other hand, such a movement will in- 
vigorate the erosion by lowering the baselevel and will, there- 
fore, in the long run promote the growth of the continental shelf 
indirectly. 

3rd, Positive movement of the coastline, i.e. subsidence of the 
land or rise of the sea-level, will eo ipso broaden the continental 
shelf by expansion of the submerged portion of the gradation-plane 
at the cost of the emerged portion, although in the long run its growth 
will be slackened on account of the baselevel being raised. Even in 
case, at the commencement of such a positive movement, the terres- 
trial portion of the gradation-plane is little developed, or wanting, 
circumstances are imaginable in which the shelf will grow to a 
large extent. This will occur during a very slow but prolonged rise 
of the sea-level. In this case the sea, even if the land should offer a 
strong resistance, will be able to conquer a vast territory, to destroy 
the land down to the plane of abrasion, and to incorporate the 
latter with the shelf. A small island may be altogether truncated 
and converted into a very shallow submarine bank, probably gently 
inclining towards the side where the influx of the sea came from 
i.e. from where the prevailing winds were blowing. 

It stands to reason that, during a positive movement, the above 
extension of the continental shelf will be more rapid and far-reaching 
in case this movement has been preceded by a period of stability 
of the land, in other words by a period of peneplanation. For in 
that case the sea needs not gradually destroy and clear away 
the land in order to form a plane of abrasion and to incorporate 
it into the shelf; on the contrary, it finds a peneplain ready made, 
i.e. a vast area of low land easy to invade and to convert into 
a shelf. 

. 26% 


398 

This will hold all the more when the period of stability is preceded 
by one of diastrophism, since in that case the processes of pene- 
tration and sedimentation being invigorated, the shelf and the 
adjacent peneplain will be strongly developed *) the moment that 
the transgression of the sea sets in, resulting in optimal conditions 
for the extension of the continental shelf. 

Whereas at present in regions, far removed from each other con- 
spicuously large shelves occur, the question arises whether perhaps 
such optimal conditions for the expansion of continental shelves 
have existed in recent geological time. 

This question will be answered here in the affirmative. 

First of all the conditions for shelf-building are favourable now, 
because the Pleistocene and the Holocene are periods in which the 
processes of denudation and sedimentation (consequently also those 
of gradation and shelf-growth) are very active’), owing to the 
orogenetic movements in tertiary time, which are not yet abated in 
our time. Besides this there is one more condition that has been 
favourable to the extremely wide expansion of the present-day shelves. 
It is that after the close of the pleistocene glacial period a large 
part of the earth’s surface has been invaded by the sea. This 
transgression commenced, as appears from the above, at a moment 
that the shelves and the adjoining peneplains had already been 
strongly developed in consequence of the late-tertiary orogenetic 
movements. The object of this paper is to demonstrate, for one of 
the largest shelves of the earth, that it owes its origin to the optimal 
conditions for shelf-formation, which appeared after the close of and 
in consequence of the pleistocene glacial period. 


Influence of the pleistocene glacial period on the position of the sea-level. 


What has been the influence of the glacial period on the general 
position of the sea-level ? 

In the Pleistocene age (the so-called ice-age) the ice-caps of considerable 
thickness and extent, which then covered a vast portion of the land 


1) Isostatic upheavals of continents will, at least initially, also counteract the 
seaward accretion of shelves. The plastic movement of the continents towards the 
sea (continental creep, vide T. C. CHAMBERLIN l.c. p. 585, 1913), on the other hand, 
promotes the development of the shelves. These two factors will be neglected in 
this paper, because their influence can only be negligibly small as compared with 
other influences in the region to be discussed here, viz. the East Indian Archipelago. 
2) BARRELL in his interesting study on “Rhythms in denudation” considers the 
present time as one in the history of our Earth, in which the rate of the continental 
denudation process is very high. J. BARRELL “Rhythms and the Measurements of 
Geological Time”. Bull. of the Geol. Soc. of America XXVIII, p. 775, 1917. 


399 


in high latitudes in and about the polar regions, and to a smaller 
degree also the large snowfields and glaciers in the mountains outside 
these polar regions, must have abstracted large quantities of water 
from the oceans. Owing to this the water in the oceans must in 
the early pleistocene period have sunk relatively to the land. 

After the close of the ice-age i.e. at the end of the pleistocene 
period, the ice-caps in the higher latitudes dwindled down to their 
present state. 

The melting of these ice-caps caused the water to return to the oceans, 
so that the latter have now almost regained the level they had before 
the beginning of the pleistocene period. This implies that, from the end 
of the pleistocene period up to the present day the sea-level along all 
the coasts of tropical regions must have risen relatively to the land. 
Everywhere in the tropical regions the sea must, therefore, have 
encroached upon the land, and where this land rose only slightly 
above the sea-level, the horizontal extent of territory invaded by the 
sea since the close of the pleistocene period must have been considerable. 
_Prnck’) has given us a clear exposition of the influence of the 
pleistocene ice-age (in other ice-ages the same must have taken place) 
on the sea-level as early as 1882. Opinions may differ about the 
degree of oscillation of the sealevel. Observant of some of the 
accessory circumstances which render the problem more intricate, 
calculations have been made by Crom?) in 1875, by Penck in 1882 
and by Dary in 1910 and 1915. Penck in that year arrived at the 
conclusion that in the pleistocene period the sea-level in tropical regions 
must have been 100 m.*®) lower than at present. Afterwards, in 1894 *) 
accepting an average thickness of the ice-caps of 1000 m., be arrived 
at the figure of 150 m., which figure had been mentioned also by 
Von Dryearski in 1887. Daty*), who also assumed that the maximal 


1) A. Penck “Schwankungen des Meerespiegels”. Jahrb. der geogr. Ges. zu 
München VII, 1882, p. 47. In the main PENcK’s statement seems to me undeniable. 
It may be called a theory rather than an hypothesis. 

2) J. Crorr. Climate and time, Londen 1875. 

3) PENCK arrived at this figure (lc. p. 67) on the supposition that in 
the pleistocene age the phenomenon of glaciation was not restricted to one hemisphere 
only, but affected both hemispheres simultaneously, a statement which we endorse 
here. — In case in the pleistocene age the powerful glaciation had been restricted 
to the northern hemisphere only, the position of the general sea-level would, 
according to PENCK, (lc. p. 29) then have been at least 50, and at most 66!/, m. 
lower than at present. 

*) A. Penck. Morphologie der Erdoberfläche Il. p. 660, 1894. 

5) R. A. Daty. Pleistocene glaciations and the coral reef problem. Amer. Journal 
of Science XXX. p. 300, 1910 and The glacial-control theory of coral reefs. Proc. 
of the Amer. Acad. of Arts and Sciences LI, p. 173, 1915, 


400 


development of the ice-caps in the pleistocene age was attained 
simultaneously all over the earth, and that their average thickness 
amounted to 1100 m., estimated that, since the close of the pleistocene 
ice-age the sea-level has been raised by an amount ranging between 
23 and 129 m., most probably between 50 and 60 m. 

Certain accessory factors render the problem more intricate, as 
has been stated above. There are in fact still other phenomena that 
may give rise to changes in the relative position between land and 
sea and thus engender movements which either run parallel, or in 
an opposite direction to the above-mentioned. 

Among these phenomena the following have something to do 
with the glacial period : | 

1. fluetuations of the sea-level, caused by the fact that, the more 
the ice-caps grow, the more their attractive power upon the water 
of the oceans will increase, while the same will decrease again on 
the melting of the ice. This modifies the position of the sea-level all 
over the earth, but this modification is of some consequence only in 
the immediate neighbourhood of the ice-caps and there manifests 
itself by a rise of the sea-level. The corresponding sinking of the 
sea-level everywhere else on the earth, which will be most manifest 
in the regions farthest removed from the glaciated areas, is not con- 
siderable; the assumption is admissible that, during the maximal 
glaciation in the pleistocene age in the tropical seas, i.e. in the 
East-Indian Archipelago, it amounted to 10 m. or about 5 fathoms 
at most *). 

2. Fluctuations of the sea-level caused by the water being driven 
back into the oceans by the ice. In the polar regions the water of 
the sea is driven back from the coast over some distance by the 


1) This figure we borrow from Daty’s “Glacial Control Theory of Coral Reefs” 
p. 174. Daty has derived it from calculations given in R. S. Woopwarp’s “On 
the Form and Position of the Sealevel’’. Bull. 48 of the U.S. Geol. Survey 1888. 
Here, however, we do not find discussed (see note p, 78) the results obtained by 
E. von Dry@auski in “Die Geoidformation der Eiszeit’’. (Zeitsch. der Ges. für 
Erdk. XXII p. 169, 1887). In this paper von DRyGALSKY brings back to due 
dimensions the attractive influence on the sea-level of the ice-caps, accumulated in 
the ice-age on continental landmasses, which influence had been overrated hy 
Penck. It deserves attention that all these calculations have been made more or 
less based on the theory of Crorr, who held that during the glacial period only 
one of the hemispheres had been intensely glaciated, the other hardly or not at 
all (J. Crorr ‘Climate and Time” especially Chapt. 23 London 1875). It will be 
useful to make new calculations of the influence of the attraction of land-ice on 
the general form of the sea-level, based on the now generally accepted hypo- 
thesis that during the ice-age the glaciers and ice-caps have been all over the 
earth larger then now. 


401 


land ice, which is moving seaward. This repulse was more intense 
in the ice-age than now. Von Dryeaiski believes that in the ice-age 
the general sea-level must in consequence of this phenomenon alone 
have been raised 6 m. ’). 

3. Fluctuations of the sea-level, caused by elastic downward move- 
ments of the earth’s crust under the weight of the accreting land-ice, 
succeeded on melting, with some retardation, by contrary movements 
of about equal amount. These important movements are restricted 
to the regions that were covered by the land-ice, as has been proved 
principally by repeated careful researches in North-America’); they 
cannot have exerted a powerful influence upon the height of the sea- 
level, except in the glaciated regions and their immediate vicinity. In 
tropical regions these movements will only have resulted in a slight 
lowering of the sea-level, during the period of growth, and by a 
corresponding rise of the sea-level during and after the retreat. 

Iu tropical regions, therefore, as appears from the foregoing, all 
these additional influences are so little effective that the main pheno- 
menon cannot be largely modified by it. 

Careful consideration of all the calculations that came to my 
knowledge, justifies, I think, the assumption that the collective result 
of all the above-named influences, which, as already observed, partly 
co-operate, and partly counteract each other, has been that during 
the periods of maximal expansion of the ice-caps in pleistocene time, 
the sea-level in tropical regions (viz. the regions farthest removed 
from the large centra of ice-accumulation) must have been at least 
40 fathoms (72 m.) lower than at the present day. Daty *) estimated 
this figure at 33—38 fathoms, or 60—70 m. 

The relations between land and sea, however, are also influenced 
by crustal movements which are quite independent of the glaciation. 
I refer first of all to orogenetic movements of the land, generating 
apparent movements of the sea-level, manifesting themselves in shifts 
of the coast-line, which are not infrequently considerable. They 
occur all over the earth, but exclusively in tectonically active regions. 

Finally the relations between land and sea are still modified 
continually everywhere by shifting of the shore-line, consequent 
on the growth of alluvial deposits, derived from the land by the 
destructive and transporting action of water and wind, secondly by 
the continuous process of filling-up of the ocean-basins by sediments and 


1) E. von DRYGALSKI l.c. p. 199. 

2) Vide: H. E. FarrcuarLp. Postglacial uplift of Northern America. Bull. of the 
Geol. Soc. of Amer. XXIX, p. 187, 1918. 

GER Aj DALY-lesp. 74, LOT: 


402 


thirdly by isostatic uplift of the land, which latter considerably 
retards the effect of denudation. For the present I will leave those 
phenomena out of consideration, because they cannot materially 
have affected the oscillations of the sea-level dealt with in this paper. 
The validity of the above theory can hardly be called in question, 
anyhow not if we assume that in the glacial period ice-masses of 
considerable thickness, on an average 1000—1200 m., were accu- 
mulated over a vast extent on the land in polar regions. Thus far, 
however, its validity has not been tested for considerable areas of the 
earth’s surface by the relations observable at present along the coasts. 
In tropical regions these tests will be simpler and must yield 
more precise results than outside the tropics. For outside the trop- 
ies, especially in the regions bordering immediately on the regions 
glaciated in the ice-age, the phenomenon of shifts of the sealevel, 
depending on the greater or smaller extent of the polar ice-caps, is 
rendered indistinct through the interference of the above-named influ- 
ences, which are very operative outside the tropics, and on the 
contrary are hardly perceptible in the tropical regions ‘). 
Furthermore, such a test can be effectual only in regions not 
affected by tectonic movements since the close of the Pliocene. 
There is, therefore, a reasonable chance of the possibility to trace and 
to discriminate the displacements of the shorelines, caused by the 


') This does not mean to say that the oscillations of the sealevel in consequence 
of the pleistocene ice-age are not distinguishable in temperate zones. [t will be 
more difficult to identify the phenomenon there, since it has first to be severed 
from the additional influences mentioned above, whose magnitude relative to that 
of the main phenomenon, is nol sufficiently known. On the other hand, there is 
a factor that could be utilized in the neighbourhood of the glaciated regions, viz. 
the fact that there the consecutive glacial and interglacial periods will manifest 
themselves through variations in the marine fauna. At the commencement of the 
glacial period the first approach of the ice in the northern hemisphere will 
have revealed itself by the introduction of arctic types into the marine fauna. We 
know that this is noticeable in the latter part of the pliocene period in England 
and in Holland, and that, therefore, the assertion that the ice-age commenced 
already in what is generally called “Upper Pliocene’, is not unfounded. In tropical 
regions, on the contrary, the allernate interglacial and glacial times wiil presumably 
not have exerted an appreciable influence upon the fauna, so that in this respect 
the researches in tropical climes will have to do without a factor that is available 
outside the tropics. Taking everything into consideration the shift of the coast-line 
consequent on the alternate growth and melting of the polar ice-caps, will prove 
to be so much more regular and less modified through other influences in the 
tropical regions than elsewhere that a critical examination in the tropical regions 
is far preferable to one in the temperate zones, at all events a far as the main 
features of the phenomenon are concerned. 


“On the Relation between the Pleistocene Glacial Period and the Origin of the Sunda Sea (Java- and South China-Sea), 


. A. F. NGRAAFF and M. WEBER: x 
Bret oe and on its Influence on the Distribution of Coral-reefs and on the Land- and Freshwater Fauna. 


CELEB ES 
SEA 


Djam Bi 


Moest 
Toe 


8 a! ae NEA 


INDIAN ee RO 


ONSEN! 


stratt 
Soenda 


40 fathom line, also coastline of Soenda-land 


----- Hypothetical boundary of the stable portion of Soenda- land 


== 


Fig. 1. Sketch-map of the East-Indian Archipelago showing the Sunda-shelf and the Sahul-shelf. 


Seale 1 : 12.500.000. 
Proceedings Royal Acad. Amsterdam. Vol. XXIII. 


403 


variations of the extent of the glaciated areas in and after the 
pleistocene period, with certainty in tropical regions, especially in 
those that have maintained their stability ever since the commence- 
ment of the Pleistocene. 

In the following pages we purpose to consider the relations be- 
tween land and sea, the submarine topography and the distribution of 
the coral-reefs in a portion of the East-Indian Archipelago, in con- 
nection with the pleistocene ice-age. 


The stable and the unstable part of the Hast-Indian Archipelago. 


In the East-Indian Archipelago we distinguish two strongly con- 
trasting portions, one with ‘an exeeptionally uniform and undisturbed 
submarine topography and another with a strikingly complicated 
submarine relief. Both areas are indicated on the accompanying 
sketchmap (Fig. 1). To the former belong the Sunda Sea and the 
Sahul Bank, to the latter all the other seas of the Hast-Indian 
Archipelago. 

It deserves notice that this contrast has already been observed by 
W. Hare as early as 1845'). He termed the Sunda shelf the Great 
Asiatic Bank and the Sahulbank the Great Australian Bank. He 
noticed the unvarying mean depth of the sea above those banks, 
estimated by him at 30 fathoms and called attention to the fact that 
the character of the land and the coasts surrounding these banks is 
very similar and differs largely from that of the other regions in 
the Indian Archipelago. 


1) W. EARLE. On the Physical Structure and Arrangement of the islands of 
the Indian Archipelago. Journ. Royal Geogr. Soc. XV. p. 358, 1845. 

EARLE says l.c. pag. 359: 
These banks, which extend from the continents of Asia and Australia, form very 
remarkable features in the geography of this part of the world, and, as such, are 
deserving of more attention than has hitherto been bestowed upon them, since 
it will be found that all the countries lying upon these banks partake of the 
character of the continents to which they are attached; while those which are 
situated on the deep sea which separates them, are all of comparatively recent 
volcanic formation, with the exception of a few small coral islands, which, in all 
probability, are constructed upon the summits of submerged volcanoes. The depth 
of water on these banks averages about 30 fathoms, deepening rapidly as the 
edge is approached, and shoaling gradually towards the land. It will be seen that 
the one [ have termed the Great Asiatic Bank extends into the Archipelago from 
the south-eastern extreme of Asia to a distance of nearly 1000 miles, in fact to 
within 50 miles of Celebes, and I| strongly suspect that it will be found to extend 
to the south-western extremity of that island also; but as there is a space of 
nearly 30 miles across which no soundings have been carried, | have preferred 
reducing the bank to the limits for which we have actual data. 


404 


VeRBERK, in his report on the Moluccas '), was the first to contrast 
these two tracts geologically. On the basis of somewhat different 
geological conceptions the present author’) did the same in 1912. 

Thus the latest geological history of the Hast-Indian Archipelago 
teaches us that the two first-named shallow seas or shelves form 
parts of larger tracts, which have recently, anyhow after the 
Pliocene, maintained their stability and, putting it geologically, have 
behaved “‘continentally”, whereas all the others belong to unstable 
portions or geosynclines, which were orogenetically active in the 
same time. 

It thus appears that in the East-Indian Archipelago adjoining 
portions of the earth’s crust have behaved very differently in recent 
times; in the stable portions the consequences of the oscillations of the 
sea-level in connection with the ice-age will be easily distinguishable 
and unmodified; in the unstable or active portions these oscillations 
must have occurred just as well, but their traces will be distinguishable 
only where they have not been effaced or modified too much by 
the influence of diastrophism, or in other words by the orogenetic 
movements of the land. This is a very favourable circumstance, as 
it enables us to test the theory concerned, in different ways. 


How the Sunda Sea originated. 


In the year 1916 the author briefly pointed out the probability 
of a causal relation between the origin of the above-named remarkable 
shallow seas of quiet submarine topography and constant depth, 
and the pleistocene ice-periods*), and has put forward his view 
that both the Sunda Sea, and the Sahul Bank originated from 
the submersion of a low land by the rise of the sea-level in con- 
sequence of the melting of the great ice-caps of the pleistocene 
ice-age. 


') R. D. M. VERBEEK. Molukken verslag. Geol. verkenningstochten in het 
oostelijke gedeelte van den Ned. O.-I. Archipel. Jaarb. v.h. Mijnwezen XXXVII. 
p. 797, 1908. 

2) G. A. F. MOLENGRAAFF. On recent crustal movements in the island of 
Timor and their bearing on the geological history of the East-Indian Archipelago. 
These Proceedings Vol. XV, 1, p. 282, 1912. ) 

3) G. A. F. MOLENGRAAFF. The coral-reef problem and isostasy. These 
Proceedings Vol. XIX. p. 612, 1916. 

N. Wina Easton followed a similar line of reasoning when discussing the 
origin of the tin-deposits in the Dutch East-Indies. Vide: “Het ontstaan der tinerts- 
beddingen in Indië, Weekblad de Ingenieur, 12 Maart 1919. 


405 


The name of Sunda Sea is proposed here for the shallow sea between 
Malacea, Sumatra and Java on tbe one side and Borneo on the other 
side, which embraces the whole of the Java Sea and the southernmost 
portion of the China Sea. At present no one collective name 
used for these various seas, but geographically as well as genetically 
they form one indivisible whole. NrierMEYER *) applied the name of 
Sunda Shelf?) to the floor of the shallow sea between Sumatra, 
Java and Borneo, already in 1911. I agree with him, but I apply 
the name to the entire shelf which has derived its origin from the 
submersion of the majority of the peneplanized portions of the 
Sunda Land. (to be defined later on). 

The way in which the low land originated may be conceived as 
follows : 

Before the beginning of the pleistocene period, i.e. towards the 
termination of the Pliocene, what we now call the Sunda Sea was 
presumably taken up by rather low land, or by a group of islands. 
We may imagine a partly developed peneplain, covered here and 
there by a shallow sea *). 

At the commencement of the pleistocene period the sea retreated 
in consequence of the growth of the ice-caps and thus one continuous 
tract of land was formed, the Sunda Land, uniting the present islands 
of Sumatra, Borneo and Java. It was not a high land, but on an 
average it stood at least 70 m. above the sealevel. 

In the pleistocene age followed a period of prolonged erosion, 
which had become particularly active by the lowering of the 
base-level. Owing to this the pre-existing imperfect peneplain was 
greatly enlarged and perfected. Only these areas, which offered 
great resistance against erosion protruded as hills, so-called monad- 
nocks, from the great plain. This large peneplain was bounded 
on the south, the southwest and the west by the partly volcanic, 
partly non-volcanic mountain-ranges of Java and Sumatra, on the 
north and north-east by the granitie nucleus, the high sandstone- 
tableland, and the mountain-ranges of Borneo. In this broad peneplain 
probably all the water that flowed down from those two mountainous 
regions in opposite directions, collected into a few large streams. One 
of those streams must have flowed through the region where the present 


1) J. FE. NiermMever. Barrière-riffen en atollen in den Oost-Indischen archipel. 
Tijdschr. Kon. Ned. Aardr. Gen. 2. XXVIII p. 880, 1911. 

%) KRUmMMEL calls this bank the Borneo-Java shelf. Its extent is estimated by 
him at 1.850000 km? the depth of the sea at 50—100 m. Vide O. KRrüMMEL, 
Hndb. der Ozeanographie I p. 113, 1907. 

3) This supposition is not in contradiction with the known geological data. 


406 


Java Sea extends, and, while draining the peneplain towards east- 
southeast, must have emptied into the most southern part of Strait 
Macasser. It is probable, that the vast peneplain was drained towards 
the north and north-north-east by another stream in the direction 
of the China Sea. 

The hydrographic basin of those two streams must have been very 
large, viz. about 1.285.000 km?. So, when taking an annual rainfall 
as great as occurs at present’), viz. 2,7 metres, they must have 
carried about 1156 cubic kilometres of water to the sea annually, 
i.e. about double the amount discharged by the Mississippi (552 km?) 
in whose basin, which is much larger (3.225.400 km*), the rainfall 
is much less considerable, averaging somewhat more than 52 c.m. 

Presumably these streams, in spite of their little varying level, 
will, on account of their large mass of water, have cut their beds 
deep into the peneplain. Considering what takes place in other rivers 
in this respect, it will be safe to assume that the beds of those rivers 
in their lower course, must have been at least 10—15 m. deep. 

After the close of the glacial period the sea-level gradually began 
to rise again as the ice-masses in the higher latitudes began to melt 
down. Then all circumstances combined to bring about optimal 
conditions for shelf-formation in Sunda Land. Diastrophism in tertiary 
time had inaugurated a period of active erosion and consequently of 
rapid development of the plane of gradation; the retreat of the sea 
at the beginning of the ice-period had operated in the same way 
through lowering of the base-level; inhibiting influences on shelf- 
formation had not oceurred in Sunda Land, whieh had remained 
stable ever since the tertiary period; all this had co-operated to 
give rise to a plane of gradation, chiefly as a peneplain, of extra- 
ordinary dimensions. Vast tracts of land were now easily invaded 
by the rising sea and converted into a shelf. The Sunda-peneplain 
was overflowed, until the present average depth of 50 m. was reached. 
Thus originated the present Sunda Sea and the Sunda shelf, the lar- 
gest and one of the most remarkable shelves of the world. 

The iarger streams were drowned and dismembered, all their 
tributaries becoming independent rivers, now flowing into the Sunda 
Sea. Several of the monadnocks were surrounded by the sea and 
converted into islands, as Bangka, Billiton, Singkep, the Karimata- 
islands, the Karimun-djawa islands, Bawean, the Arends-islands, 
Great- and Little-Salembouw, and numerous other small islands. 

This is of course a much simplified conception of what has hap- 


') The volume of water discharged into the sea is taken to be !/z of the total 
rainfall in the riverbasin, which rough estimate is permissible in this instance. 


407 


pened in reality. The ice-age has not been one single cold period, 
but a succession of colder glacial periods alternating with milder 
interglacial periods. Consequently the ice-caps more than once have 
grown to a large extent and have melted again. Thus we may sur- 
mise that during the first glacial period the Sunda-peneplain, which 
probably already pre-existed in an imperfect state, has recommenced 
to develop, that it has been covered by the sea during the first 
interglacial period, that during the second glacial time it was ren- 
dered more perfect, that it was flooded again during the second 
interglacial time and so on, until the last glacial period saw the 
peneplain in such a state of perfection as is now illustrated by the 
floor of the Sunda shelf-sea. 

Many pecularities of the Sunda Sea and its surrounding coasts are 
in keeping with this conception or are sufficiently explained by it. 

However, before dwelling on these peculiarities the following two 
questions must be answered: 

1. how far did the pleistoeene Sunda Land extend? and 2. what 
were its boundaries ? 


The Pleistocene Sunda Land. 


There is one answer for these two questions: the Sunda Land 
is that portion of the western half of the Hast-Indian Archipelago 
which emerged from the sea during the maxima of glaciation in the 
pleistocene age. We take this Sunda Land to have been covered 
gradually by the sea to a depth of 72 m. from the last maximum 
up to the present day. 

The Sunda Land consisted of Java and Madura, Sumatra, Borneo, 
Malacca, and the present sea with its islands round these countries 
to a depth of 40 fathoms (72 m.) as is represented on the map (Fig. 1). 
All that has been said, however, applies only to that part of the 
Sunda Land which has been stable or orogenetically inactive since 
the Pleistocene. The present isobath of 40 fathoms during the last 
maximum of glaciationin the pleistocene age, gives the ancient coast- 
line for that part. In order to ascertain the extent of the stable conti- 
nental part of the Sunda Land it is, therefore, required to know as well 
the boundary between the land that has been orogenetically inactive 
since the close of the Pliocene, and the land that has been active. On 
the sketch-map this boundary has been indicated tentatively by an 
interrupted line. What lies within this line is the stable part of 
Sunda Land, to be ealled Sunda-iand proper. 

To this stable Sunda Land belongs in the first place the entire 


408 


Sunda Shelf, then also Borneo, probably with the exception of the 
northern part, Malacca and the eastern coastal region of Sumatra, 
and perhaps here and there a strip of the northern coast of Java 
and Madura. All the land bordering on the Indian Ocean, which 
belongs to the Malay geosyncline, does not belong to this Sunda 
Land in the strict sense of the term. Evidently this region of tectonic 
activity is the prolongation of the folds of the western portion of 
the Birma-are, still one of the regions of the earth where the oro- 
genetic activity is very great. It is not possible to fix the precise 
boundary between the stable and the unstable portion of the former 
Sunda Land; very likely there is no firm line of demarcation, | am 
inclined to class the volcanic regions, which are characterized by 
rocks of the Atlantic type, such as the Muriah, the Lurus and the 
Ringgit, under the stable region, because the Bawean-Islands with 
their Atlantic rocks certainly belong to it and because the voleanoes 
of the Malay geosyncline, like those of nearly all other geosyn- 
clines on the earth, have yielded exclusively rocks of the Pacific 
type. Doing so, however, the boundary-line between the stable and 
the unstable region must inevitably be drawn in such a way that 
the two regions encroach upon each other in Eastern Java. Perhaps 
the two relations are represented accurately in this way. The Sibbalds 
Bank, the Kalukalukuang Bank, the Laars Banks, the Bril, the Pater- 
noster Islands and the Postiljon-Islands, now all coral-islands, and 
perhaps also the Spermonde Shelf and part of South Celebes formed, 
as I believe, in pleistocene time islands that belonged to the stable 
Sunda Land. 

Now, what peculiarities are known of the present Sunda Sea, its 
islands and its shores? 


The Present Sunda Sea. 


a. General topoyraphy of the floor of the Sunda Sea and of the 
adjacent shores. 

The Sunda Sea has a strikingly uniform depth, averaging 40—45 
in., seldom exceeding 50 m. The shallowest part is that where the 
islands of Bangka and Billiton are situated. A depth of more than 20 
fathoms is the exception there. 

Excepting some gullies, larger depths than 28 fathoms (50 m.) 
are found only in the farthest eastern part, where the depth gradu- 
ally increases towards the much deeper Macassar Strait, and also in 
the northern part towards the deeper basin of the China Sea and 
finally in the neighbourhood of Sunda Strait. The most striking 
characteristic of the Sunda Shelf-sea, therefore, is its equal depth, 


409 


the almost perfect evenness of its bottom. This is the very sub- 
marine relief that would have originated, if this sea had been formed 
by the submersion of a large peneplain. The particularities of this 
relief may be explained assuming that this peneplain discharged 
its water towards the Bali Sea and the China Sea, and that a bay, 
from the present Sunda Strait encroached for some distance on it. 

For some hundreds of kilometers landward the surface of 
Borneo is only slightly undulating and the same is the case in the 
coastal region of Eastern Sumatra and on the islands in the Sunda Sea, 
as Bangka, Billiton, Singkep ete. The greater part of all this land 
partakes of the character of a peneplain *), rising only little above 
the sea-level, here and there with some gently sloping hills, consisting 
of rocks, which possess a more powerful resistance against erosion, 
emerging from the lower territory. This description applies less to the 
coastal fringe of Java, on which island voleanic activity repeatedly 
modified its sculpture and raised its level. 

The slightly undulating floor of the Sunda Sea is continued, as it 
were, on the surrounding land. Along the coast of West-Borneo a 
retreat of tbe sea to a depth of no more than 10 fathoms would 
join numerous islands to the coast and enlarge the still existing 
peneplain of West-Borneo with its peculiar, gently sloping monad- 
nocks, without affording any feature in the landscape to enable us 
to tell the old land from the new. 

All the islands in the Sunda Sea, as e.g. Billiton and Singkep, 
present so clearly the type of regions which on account of the existence 
of cores of hard resisting rocks were less subject to erosion than 
their surroundings, that spontaneously the idea forces itself upon us 
to join West-Borneo to Bangka, Billiton, ete., and to consider the 
whole tract of the Sunda Sea as a submerged peneplain, from which 
the present islands rose up as monadnocks, when in the pleistocene 
age the sea-level was lower. 

b. Character of the bottom’ of the Sunda Sea. 

The floor of the Sunda Sea about which little is known, appears 
„to be very muddy; the large majority of the soundings, performed 
in this sea, show that the bottom consists of silt or mud, whereas 
shells or coral-fragments are rarely reported. This can hardly be 
accounted for in a shallow sea like the Sunda Sea, by the influence 
of the rivers flowing into it now. Indeed, they transport a large 
amount of silt to that sea to a large distance from the coast, but 


1) Strictly speaking all that territory makes up that portion of the large pleisto- 
cene peneplain which has not yet been overflowed by the sea. 


410 


most likely nowhere beyond 60 km. from it. In February 1894 I 
found at flood-tide before the estuary of the Kapuwas in West 
Borneo the extreme limit of the muddy river-water as far as 50 km. 
from the shore). When considering that the muddy fresh water, 
wedging out seaward very slowly, floats on the specifically heavier 
seawater, and that in seawater the sedimentation proceeds about ten 
times quicker than in fresh water, we may be sure that silt does not 
settle down much farther than those 50—60 km. from the coast. 

When we also bear in mind that, among the rivers, debouching 
into the Sunda Sea, the Kapuwas and the Barito are the largest and 
richest in silt, we feel justified in saying that the limit of silt-deposit 
in the Sunda Sea lies at present between the coast-line and a 
distance about 60 k.m. from the coast. 

The charts of this sea show *) however, that the bottom all over 
the Sunda Sea consists of silt, i.e. as far as 100 km. or more from 
the nearest coast. 

When considering the Sunda Sea to be a peneplain, it is easy to 
understand that the sea, when it gradually flooded that plain 
received then much silt from the many rivers discharging their waters 
into the growing sea, this silt being deposited there at great though 
gradually diminishing distances from the present coast. 

The silt or mud, which nearly all the soundings in the Sunda Sea 
have proved to be the principal constituent of the bottom, may be 
looked upon as a sediment carried down chiefly by the former big 
streams before and during the long period of gradual submergence 
of the pleistocene peneplain. 

c. No traces of upheaval. 

The shores of the islands surrounding the Sunda Sea or emerging 
from it, show no traces of upheaval worth mentioning. If we con- 
sider that in regions where reef-building corals live (as is the case 
with the Sunda Sea, though, when compared with the sea-basins of 
the Moluceas it is poor in reef-builders) every upheaval of the land 
(or subsidence of the sea-level) is almost invariably manifested by 
the emersion and preservation — for a long time at least — of 
reefs, i.e. by so-called elevated coral-reefs, it is obvious that the 
absence of those features nearly everywhere along the coasts of the 
Sunda Sea, warrants the conclusion that in the most recent geolo- 


1) This limit is at the utmost 62 kilometers from the shore. 

*) Since this paper was read new invesligations have been made on the nature 
of the deposits on the floor of the Java Sea They have proved that only in the 
southern half these deposits consist of mud, in the northern half on the contrary 
they consist of sand and sandy loam. 


411 


B Sea-tin workings in drowned river-beds at 
the coast of the island of Singkep. 


(il Tin-deposits now worked out. 
Scale 1 : 50.000. 


Fig. 2. After a sketchmap in possession of the Direction of the Singkep Tin Company. 


gical time no negative shifts of the shore-line of any consequence 
have occurred there. 

d. Traces of subsidence; drowned and sunken rivers. 

On the contrary there are indications of subsidence of these coasts, 
or, which comes to the same in our argument, of rise of the sea-level. 

The way in which the large muddy rivers of Sumatra and of 
Borneo debouch into the sea, is peculiar. The absence of deltas, as 
well as their wide funnel-shaped mouths — very conspicuous with 
the Sampit — and the great depths in the lower courses of the 
rivers point to positive shifts of the coast-line. 

Only one of them, the Kapuwas, which carries more sediment 
than any of the others, has formed a delta, which, however, hardly 
protrudes from the coast-line into the sea. 

Furthermore, the traces of the rivers of the Sunda-peneplain, 

27 

Proceedings Royal Acad. Amsterdam. Vol XXill. 


412 


which have been dismembered and drowned through the rise of the 
sea-level, are clearly noticeable in the floor of the Sunda shelf-sea. 
The exploitation of tin-ore on the island of Singkep has revealed 
the existence of such drowned rivers (see Fig. 2). It has become 
evident that the tin-ore deposited by the running water in the 
deepest parts of the alluvium of the Dabo and other rivers, is 
still found at a considerable distance from the shore, and that the 
channels of the Dabo and of other rivers are traceable up to about 
1500 m. from the coast. In one of those rivers, the Djangkang, the 
lowermost tin-bearing part of the fluviatile alluvium worked at 
present lies at about 17 m. below the sea-level. The stream-deposits 
at a distance of 1300 m. from the shore are about 10 m. thick, 
while the sea above them has a depth of 7 m. The exploitation of 
this so-called sea-tin near the island of Singkep has distinctly shown 
the existence of the submarine prolongation of a number of river- 
valleys. 

This phenomenon can be readily accounted for when accepting 
subsidence of land or rise of the sea-level. I consider the presumption 
admissible, that also in the neighbourhood of other tin-islands in the 
Sunda Sea, as e.g. near Banca and Billiton, the existence of similar 
tin-deposits below the sea-level in the channels of drowned rivers 
could be proved. Just as near the island of Singkep, the exploitation 
of the sea-tin might probably prove to be of great economical 
importance there as well. 

The gullies of the sunken rivers need not always be found extended 
into the sea, they may still be situated in the land, but then at such 
a low level, that with the present base-level of denudation (the sea- 
level)they could not possibly have been eroded so far by the water. 
The exploitation of the stream-tin, in Banca as well as in Billiton, 
has revealed the existence of such abnormally deep valleys. VERBEEK ') 
records several instances, of which I will mention the following: 

In Banca, the pleistocene bed of the Krasak-river in the district 
of Pangkalpinang, which is eroded at least 16 m. below the bed of 
the present course; the ancient bed of the Pandji-river in the district 
of Blinju, lying 9.25 m. below the present bed and not much less 
below the sea-level; the ancient bed of the Liat-river in the distriet 
of Sungeiliat, the lower course of which lies 13—19 m. below its 
present bed and about as much below the sea-level; 

in Billiton the ancient bed of the Sidjuk-river, which near mine 


1) R. D. M. VerBeek, Geol. Beschr. van Bangka en Billiton. Jaarb. van het 
Mynw. XXVI, p. 143—156, 1897. 


413 


No. 30 is 6—11 m. deeper than the present bed; an affluent of the 
Munsang in the district of Manggar, whose bed is filled up with 
deposits down to a deph of 5 m.; several old river-gullies near 
Manggar, in which the lowermost deposits, containing the tin-ore, 
have been worked near mine No. 30, at a depth no less than 
6 '/, m. below the present sea-level. 

In connection with the occurrence of these sunken and drowned 
stream-tinore deposits some remarks may be added about the influence 
of the surf on the unconsolidated freshwater-deposits during the rise 
of the sea-level, i.e. the submersion of the Sunda-peneplain. Although 
in that very shallow sea with hardly ‘perceptible tides the action 
of the surf will not have been able to alter considerably the con- 
figuration of the sea-bottom, the incoherent bottom-deposits will 
no doubt have been modified more or less. As to the tin-islands, 
I believe that in the period of rise of the sea after the Pleistocene 
as well as during the periods of slight fluctuations of the sea-level 
in recent and subrecent times, both the stream-tinore deposits and 
the eluvial tin-deposits may have been modified more or less by the 
seawater, and especially as to the latter, may have been concentrated 
during this process. Instances of such modified deposits are, in my 
opinion, the tin-ore deposits which occur a little above the present 
sea-level in the island of Singkep along the beach to the west of the 
village of Dabo. They are, however, worked out now. (See fig. 2) *). 

In the islands of Singkep, Billiton and Banca only comparatively 
small rivers rising on the hills of the ancient Sunda Land are con- 
cerned in the process just described. But we may reasonably expect 
as well that the courses of the larger streams draining the Sunda Land, 
which had cut their beds into the Sunda-peneplain, will not yet be 
entirely obliterated, although they were partly silted up when that 
plain was gradually submerged in consequence of the rise of the 
sea-level. If so, it must be possible to reconstruct their former courses 
from the isobathic lines in the present Sunda Sea. 

However, the isobaths, as they are indicated on the charts, have 
been calculated from a limited number of soundings, at the very least 
rather more than a kilometer apart one from the other’). Moreover, 


1) A summary of discussions on the way in which tin-ore deposits originate and 
on the part played in this process by the seawater, may be found in an article 
which appeared when this paper was passing through the press, entitled: J. Rugs 
“Ontstaan der alluviale tinerts-afzettingen van Banka en Billiton”. De Ingenieur 
85e Jaarg. p. 21, 1920. 

*) This holds good for these areas which have been fairly well explored bathy- 
metrically, only few parts of the East Indian Archipelago being so well surveyed. 


2E 


414 


these soundings have been carried out on behalf of the navigation, 
consequently with the object to discover and to map the shallow 
parts rather than the deeper portions of the seas concerned. 

Now when consulting the published charts *) and the original sheets 
one can, indeed, gather from them something (though not much) 
about the course of the larger rivers in the pleistocene Sunda-peneplain. 
First of all it appears that in this peneplain the chief watershed 
ran between the Bali Sea and the China Sea from Sumatra across 
the present islands of Banea, Billiton, through Karimata-strait, and 
further on across the Karimata-islands towards Borneo. It may 
be called the Karimata-divide. Again, from the trace of the 
isobath of 40 fathoms we conclude that from the China Sea a bay 
(see Fig. 1) eut deep into the land between the islands of Great- 
Natuna and Subi. At its entrance this bay is wide, but it narrows 
towards the south and passes into a large stream, which, coming 
from the south, empties itself into it. That main river flowed west 
of the Tambelan-islands and closely past the Badas-island and can 
be traced towards the south almost as far as Pedjantan-island. 

This large river, which drained the whole. Sunda-peneplain 
north of the Karimata-divide, presumably received on the right 
the Kapuwas and the Sambas as principal tributaries and on the 
left the Musi and the Djambi, which, however, may have united 
before they had reached the main stream. The submarine course of 
the Kapuwas is feebly indicated by a gully which is the direct 
prolongation of the Pungur-branch, while the ancient bed of the 
Musi is represented straight along the north-west coast of Banca by a 
gully with depths of 20—25 fathoms. On the existing charts the 
Kapuwas gully cannot be traced beyond Datu-island, the Musi-gully 
no farther than the meridian of the northern extremity of Banca, 
so the data, borrowed from the charts, render it just probable that 
the Kapuwas and the Musi did empty themselves into the main 
stream in the way indicated on map N°. 1. They do not afford 
conclusive evidence ”). 


1) The charts which have been published, give only some of the soundings; their 
whole number is to be found on the original sheets which are kept in the depart- 
ment of hydrography of the Navy. 

1 take this opportunity of acknowledging my indebtedness to the Director of 
that Department, Captain Puarr, for his kindness in granting me perusal of these 
original sheets. 

2) After this paper has been read Mr. H. M. van Weer, then commander of the 
surveying-vessel Brak, has been able to compile another chart with lines of equal 
depths from fresh data then available. From that map the powerful riversystem which 


415 


It has not been ascertained as yet in what direction the Indragiri 
and the Kampar reached the main stream; the only warrantable 
conclusion from what we know of the present submarine topography, 
is that from Singapore Strait a gully stretched eastward towards 
the Victory and Barren Islands, which thence may be traced to 
the main stream. 

The water of the Siak-river and probably also part of the water 
of the Kampar-river discharged itself through Malacca Strait, where 
the isobath of 40 fathoms points to the presence of a deep bay 
from the northwest, into which the rivers of a part of Malacca and 
North-Sumatra at that time emptied themselves. 

At the coast of the Bali Sea the Sunda Land was similarly indented 
to the north of the Kangean-islands by a deep bay. This bay received 
a large river, of which the isobaths of 40 fathoms and, more upstream 
those of 37 and 35 fathoms, enable us to trace more or less the 
course over a distance of about 350 km., from a point to the north 
of the Karimun djawa-islands in eastern direction along Bawean 
and then south-eastward to the East Bay mentioned before. 

This large stream was formed by the, confluence of the rivers of 
the portion of Sunda Land situated south of the Karimata-divide. 
It may be presumed that on the left it received the waters of the 
Kumai, the Sampit, the Katingan, the Kahajan, the Kapuwas Murung, 
and the Barito. A portion of the drowned Sampit-river, to a length 
of 65 km., is distinctly indicated by the isobath of LO fathoms. It 
is likely that the Kahajan and the Kapuwas Murung united not far 
to the south of their present mouths and then discharged about 60 km. 
lower down into the Barito. The Barito very likely flowed in the 
Sunda peneplain in southern direction west of the Arends Islands 
and Great Salembouw, and then discharged into the great Kast Bay. 
Nothing more can be deduced from the existing charts about the 
course of these drowned rivers. 

It may be surmised that at some distance from the north coast 
of the present island of Java also a large stream existed, which no 
doubt must have been fed by many affluents taking their rise on 
the mountainland of Java. 

Finally the trace of a large river, which drained part of Sunda 
Land in he direction of Strait Sunda, may be seen in a narrow, 
deep trough, now from 30-40 fathoms below the sea-level, which is 
strikingly similar to the part of a drowned river broadening towards 


drained the portion of the former Sunda Land north of the Karimata-divide, 
by the aid of the isobathic curves, can be reconstructed with a tolerable degree 
of accuracy. 


416 


the sea; it runs just to the south of the Hoorn-Islands and of 
Pajang-island, and may be traced thence over a distance of 70 km. 
in north-northeastern direction with an approximately uniform depth 
of 30 fathoms. 

Data are wanting as yet to determine the further course of this 
stream and its branches. 


e. Traces of revived erosion in pleistocene time. 

Among the large rivers of Borneo there are some which possess 
terraces there where the low land passes into the upland. These 
rivers have cut themselves a bed into gravel formerly deposited by 
themselves. This must have taken place at a time when the erosive 
power of the rivers was stronger than at present, for now they 
have filled up their beds again, for the greater part, with finer 
deposits, sand and silt. These ancient gravel terraces have been 
observed by me at the Kapuwas near Sintang, a little above the 
confluence of this river with the Melawi and at the Katingan along 
its right bank, at and somewhat downstream from the place where 
it receives the Samba’). As late as the year 1894 gold was washed 
near Sintang from the gravel of these terraces. I feel inclined to 
think that the gravel of these terraces has been deposited in the 
late pliocene time and even in the beginning of the Pleistocene, 
when in Borneo denudation was not nearly so far advanced as it 
is at the present day. The origin of the terraces may readily be 
accounted for if we assume that during the glacial period the base- 
level of denudation was lowered about 75 m; this caused the fall 
of the rivers to become greater and the erosive power to be increased, 
and enabled the rivers to cut deep gullies into their own gravel 
deposits, which later on became broad valleys during the alternate 
periods of increased and decreased erosion corresponding to the 
successive glacial and interglacial periods. 

At present the base-level of denudation is about as high as it was 
at the commencement of the Pleistocene just before the ice-age, but the 
island of Borneo having been meanwhile much denuded and eroded and 
thus having attained a stage of mature erosion, the rivers can only carry 
sand and silt at those places, where formerly gravel was deposited. The 
broad pleistocene valleys cut into the gravel terraces, consequently are 
now gradually filled up with sand and silt. Precisely such old 
gravel-terraces are found in the middle- and the upper-course of 


1) G.A. F. MOLENGRAAFF. Geological explorations in Central Borneo p. 17—20 
and p. 388, Leiden 1902. Geol. Verkenningstochten in Centraal Borneo p. 19—21 
and p. 409—410, Leiden 1900. 


417 


several rivers in Sumatra; they are presumably also of pleistocene 
age and are due to the same causes as those of the rivers in Borneo, 
but, since the mountainland of Sumatra does not belong to the stable 
part of the Sunda Land, it may very well be that orogenetic move- 
ments have contributed to the origin of these terraces as well. 


The distribution of Coral-reefs and their mode of development ; 
the Great Sunda barrier-reef. 


The distribution of coral-reefs in the Sunda Sea strikes us as being 
peculiar. First of all it is remarkable that in the Sunda Sea, which at 
the first glance appears to be situated very favourably for the devel- 
opment of corals, coral-reefs are poorly developed. Along the 
coasts of Borneo as well as along those of Sumatra and Java coral- 
reefs have developed so little that they are rarely marked on the 
hydrographic maps. Off the coasts it is just the same; there coral- 
reefs are equally rare. This is easy to understand if we consider that 
at its origin the Sunda Sea, as described above, must have expanded 
very rapidly, but that its depth, in the beginning, must have been 
very small; moreover, its salt-content was slight and its silt-content 
large, so that it cannot have afforded then favourable circumstances 
for the rapid spreading of reef-building corals. 

An exception is formed only by the extreme marginal regions 
of the Sunda shelf-sea, where it borders on those seas, from 
where the water came that overflowed the former Sunda-peneplain. 
The marginal region I have in mind comprises first the archipelago 
to which the Natuna-islands belong, where well-developed fringing- 
reefs occur and also some detached coral-islands are found rising 
above the sea-level; secondly the archipelago of the ‘‘Duizend-eilanden”’ 
to the north-east of Strait Sunda, and lastly the Borneo Bank in the 
extreme east of the Sunda Sea. Apparently the Sunda Sea, which was 
originally very shallow and turbid, and rendered brackish by fresh 
water, was gradually stocked with corals from those three sides 
when it got deeper, clearer and salter; this process is perhaps still 
in progress. 

Another question which claims our attention still more is the 
following: did reefs exist along the shores of the pleistocene Sunda 
Land, and if so, what became of them during the post-pleistocene 
submersion of the land? Have the fringing-reefs perhaps developed 
into reefs remote from the shore, into barrier-reefs, in the manner 
expounded for the first time by Darwin in his classical work on 
the origin of barrier-reefs and atolls? The shores here referred to, 


418 


are marked on the map (Fig. 1) by the 40-fathom line in the China 
Sea, in the Strait Sunda and towards the east between the coast of 
Borneo and the southern part of Strait Macassar. 

From the deeper isobaths e.g. those of 100 and 200 m., it appears 
that from the coast of the former Sunda Land in pleistocene time a 
large shelf extended into the southern portion of the China Sea. On 
this shelf the depth of the sea increased very slowly and the sea-water 
was probably muddy, large rivers from the Sunda Land carrying 
their sediments into it, as may still be inferred from the character 
of the present bottom-deposits. The conditions for the development of 
shore-reefs, therefore, were unfavourable here. Hence one cannot be 
surprised to find now-a-days reefs rising from the ancient coast-line 
only here and there from a depth of 40 fathoms nearly up to the 
level of the sea. Nevertheless, it is a striking fact, that the only coral 
islands, now found in the South-China Sea, fairly follow the course 
of the 40-fathoms contour line drawn on our map, i.e. the probable 
coast-line of the submerged Sunda Land. 

It is difficult to say whether or no along such a peculiar coast 
as the upper part of Sunda Bay must have been, the conditions for 
the forming of coral-reefs were favourable. As observed above, as 
early as in the pleistocene period the Sunda Bay cut deep into Sunda 
Land and was formed right to the south of the present Hoorn-islands and 
Pajung-island into adeep gully, which passed into a wide estuary of 
a stream coming from the north-east. 

It is decidedly remarkable, though, that the area to the north-east 
of Sunda Strait, formerly the upper part of the Sunda Bay, contrary 
to all other parts of the Java Sea, abounds in true coral-reefs, which 
rise clear of the land from a depth of 20 fathoms or more, up to 
or near the level of the sea. Many of them, especially those rising 
up from a low depth, are most likely young and were generated 
by the union of small patches of corals, developed independently 
on loose rocks, as has been shown by Sruirrr*). In shallow water, 
e.g. of a depth of 12 fathoms new coral islands even now continue 
to grow up from the bottom. However, with regard to those islands 
of the group of ‘“Duizend-eilanden”, which rise from a depth of 40 
fathoms and more, as e.g. Pajung-island and others, I ascribe their 
origin to upward growth of reefs that had already been developed 
“in the ancient Sunda Bay at the shore of the pleistocene Sunda Land 
before its submersion. 


1) C. Pu. Sturrer. Einiges über die Entstehung der Korallenriffe in der Javasee 
und Branntweinsbai, und über neue Korallenbildung bei Krakatau. Nat. Tijdschr. 
voor Ned. Indié XLIX p. 365 et seq. 1889. 


419 


At the former eastern coast of Sunda Land the relations are much 
clearer and less disputable. Here the stable Sunda Land borders on 
the unstable area of the sea of the Moluccas, more especially on the 
Strait of Macassar, one of the many deep-sea troughs that are still 
getting deeper and deeper, while other parts, the present islands, 
are still rising. In the pleistocene age this area between Borneo and 
Celebes was subsiding, and consequently the conditions for the 
development of a shelf on the east coast of Sunda Land at that 
time were unfavourable. The subsiding sea-floor brought the sedi- 
ments, supplied by Sunda Land, down to such deep levels that 
shelf-formation was out of the question. The Sunda Land was thus 
bounded on the east by a deep sea, the present Macassar Strait, and 
its coast must have been steep on that side. There was no shelf. 
Thus ideal conditions for the growth of corals were realized: a deep 
sea, decidedly with clear and salt water, a strong surf, and a fairly 
steep, partly rocky shore. No. wonder that along this coast a fringing- 
reef flourished well. 

And what can be seen now? 

On the most northern margin of the Sunda-shelf, the so-called 
Borneo Bank, stands a reef (Fig 3) rising as a narrow wall, inter- 
rupted in many places, from a depth of 70 to 90 m. to the 
surface of the sea, or nearly so. From this reef towards the land 
the depth of the sea decreases only very slowly from 70 m. down- 
ward; towards the sea, the Strait of Macassar, the depth increases very 
rapidly, in some places precipitously to 200 m. and more. A 
depth of about 1000 m. is found at a distance of some kilometers 
from this reef. This reef stands on the margin of the pleistocene 
Sunda Land; in pleistocene time, before the melting of the ice-caps 
in high latitudes, it was a fringing-reef attached to its shore and 
gradually as the Sunda-peneplain was being submerged by the sea, 
the corals were building the reef up. Nowadays it is a true barrier- 
reef, grown up round the disappearing Sunda Land in the manner 
as DARWIN supposes barrier-reefs to have developed generally. 

Only this reef does not at first sight make the impression of a 
barrier-reef, because the land to which it belongs, has been flooded, 
in relation to the depth of the water, to such an exceptionally great 
distance. On close examination of the course of this reef, which may 
be termed the Great Sunda barrier-reef, it appears to begin at the 
Ambungi-reef, which belongs to the “Kleine Paternoster-eilanden’’. 
This small group of coral-islands, extending in east-westerly direction 
from Tandjong Aru to about 75 km. from the coast of Borneo, is 
perhaps to be considered as the most northern limit of the Sunda- 


420 


shelf on the east coast of Borneo. The coral-island of Ambungi lies 
about 120 km. to the south of the mouth of the Kutei-river. Our 
barrier-reef runs from the Ambungi coral-island in southeastern 
direction to a point opposite to and at the same latitude of Tand- 
jong Ongkona on the coast of Celebes. There the reef is at a distance 
of 230 km. from the present coast of Borneo, but only 44 km. 
from that of Celebes. To the west of the reef, towards Borneo, the 
depth of the sea is very uniform, and nowhere exceeds 75 m.; on 
the east of the reef, towards Celebes, the depth of the sea increases 
abruptly to 200 m., from there rapidly to 1000 and somewhat 
further to 2385 metres. From this point the reef proceeds first 
towards the south-west, then towards the south-south-west to about 
5°40' southern latitude. 

A well-nigh continuous portion of the reef, which at ebb-tide is 
laid bare in many places, lies between 4°'20 and 5°30’ southern latitude. 
It is known on the charts as the Laurel-reefs. The total length of 
the Sunda barrier-reef from Ambungi to 5°40' southern latitude is about 
500 km. The reef cannot be traced on the charts beyond 5°40’, 
but about 100 km. farther south it reappears again in the Kwong- 
Eng reef aud may even be traced along a number of coral islands 
as far as the Kangeang islands, marking here again the extreme 
limit of the Sunda Shelf, i.e. of the submerged Sunda Land. 

The gap of over 100 km. in the reef faces the entrance to a large 
inlet or bay, the Kast Bay, into which, in all likelihood, the large stream 
(or streams) discharged itself, which drained the Sunda Land in the 
pleistocene period in the direction of the most southern portion 
of Macassar Strait. This readily accounts for the absence of reefs there. 

According to the sea-charts the Great barrier-reef *) is interrupted 
in many places and only occasionally reaches the surface of the 
sea; in most places it is found a little below the surface and only 
to the southwest of the Laurel-reefs its depth increases gradually. 
Probably on account of the insufficient salt-content of the water the 
conditions for the upgrowth of the former fringing-reefs were less 
favourable here than more towards the north in Strait Macassar. 


1) NIERMEYER (lc. p. 884 and Chart XIII No. 2) has already considered and 
described a portion of this great reef as a barrier-reef, but I think that he failed 
to see the relation between the genesis of the Borneo Bank and of this barrier-reef. 
Regarding the part of the reef that does not reach the surface of the sea between 
the Laurel reefs and the ‘Kleine Paternoster-eilanden’’, he puts the question: “Isa 
reef building itself up here from the seabottom?’’ My answer is obviously in the 
affirmative, but [ conceive this building-up as having taken place not from a depth 
of 200 m., but from a depth of 75 to 90 m. simultaneously with the gradual 
rise of the sea-level after the glacial period. Let it also be stated here, that I do 


421 


The atolls and allied coral-islands, resting on truncated and 
submerged islands formerly belonging to the Sunda Land. 


The southernmost, shallowest portion of Strait Macassar is sepa- 
rated on the north from the deeper part of that strait by two groups 
of coral-islands named the Kalu Kalakuang-islands and the Laars 
shoals and again on the south-east from the Flores Sea, by two 
other groups of coral-islands and atolls’), viz. the Paternoster- and 
the Postiljon-islands (Fig. 3). As to their structure they display a 
striking similarity. 

1. The group of the Kalu Kalukwang islands. All of them are 
coral-islands. Most of them are rooted on the rim of a bank, which 
is rather flat, and lies on an average 20, nowhere more than 40 fathoms 
below the sea-level. Three soundings indicating depths of resp. 66, 
90, and more than 100 fathoms, point to a division of the bank 
into two parts by a narrow deep strait. 

All around the bank, which lies about 40 fathoms deep, the sea 
rapidly increases in depth from the edge of the bank. Upon this 
edge a coral-reef has grown up, which has been interrupted in many 
places. On the northern half of the bank this reef reaches the 
surface of the sea in many places; on the southern half this is 
not the case. Independent of the marginal reef, there arise here and 
there reef-structures from the upper surface of the bank as well, 
reaching the surface of the sea in some places. On the extreme northern 
part of the bank the reef-structures are arranged in the shape 
of a ring, thus forming a “faro” or atollon. The Kalu Kalukuang 
islands make up a composite atoll, the ring not being com- 
pletely closed, but, especially in the southern parts, being broken over 


not quite endorse the pronouncement made in the same paper on page 881: “no shelf, 
no barrier-reef.” Even the reverse sometimes appears to be true, as no barrier- 
reef was formed along the Sunda Land in the South China Sea in spite of the 
presence of an extensive shelf, whereas in Strait Macassar, where a shelf was 
absent, a perfect barrier-reef has been developed. No more can | share the writer’s 
opinion (p. 893) that the mode of development of barrier-reefs in the East-Indian 
Archipelago affords “fresh evidence to disprove Darwin’s theory according to which 
barrier-reefs have taken their origin from fringing reefs”. In my opinion Darwin’s 
theory is supported by the mode of development of these reefs, which can only 
strengthen my conviction that ‘‘without subsidence of the lard or rise of the 
sea level strengthen my conviction (which comes to the same) no true barrier- 
reefs and no atolls can originate”. 

') Our knowledge of these coral-islands is still very insufficient. Renewed surveying 
may yield surprising results, as was the case with the latest survey of the islands 
of the Tukang besi group in the year 1916 and of the atoll of the Zandbuis-banks 
in the year 1910. 


122 


large distances. In structure the atoll bears a close resemblance to 
the composite atolls of the Maldive Archipelago, e.g. the Miladdum- 
madula-atoll'), whose ring rising from the edge of the bank, which 
lies about 20—25 fathoms below the sealevel, is interrupted in very 
many places and also keeps below the sea-level over large distances. 
Only the shape of this Miladdummadula-atoll is drawn-out more in 
one direction than that of the Kalu Kalukuang atoll, the dimensions 
of the former being 146 X 31 km., those of the latter 98 X 58 km. 

2. The Postiljon- and the Paternoster-islands. The deseription 
given of the Kalu Kalukuang-islands applies, in the main, also to 
these islands. They consist of three submarine banks with a depth 
varying from 17 to 40 fathoms. From the first bank, whose largest 
dimensions are, 140 « 50 km. two groups of reef-structures rise 
up to, or nearly up to the sea-level. They have chiefly grown up 
from the edge of the bank and are arranged in the shape of a 
ring and constitute the composite double-atoll of the Postiljon- 
islands. This double-atoll is made up of the southwestern Sarasa- 
atoll and the north-eastern Sabalana-atoll. Some of the reef-islands 
of the first atoll are again disposed into a ringlike arrangement, 
the Sapuka-faro. The north-eastern Sabalana-atoll is characterized, 
westward as well as eastward, by a remarkable projection or 
horn, towards the west the Bankawang-atollon, towards the east 
the Sabalana-atollon. The southwestern Sarasa-atoll might be looked 
upon as a very large faro or atollon, belonging to the entire Sabalana- 
atoll, in which case the term double-atoll could be relinquished. 

The second bank, that of the Paternoster-islands, covering 115 x 26 
km., of similar depth to the other, also bears, especially on its edge, 
which lies at a depth of about 40 fathoms, numerous coral-islands, 
arranged in the form of a wreath, and drawn out in one direction. 
Together they present a not typically developed atoll. 

A little to the south of the Paternoster-islands lies a group of 
coral-islands whose beautiful atoll-shape became known by the hydro- 
graphical survey made by the surveying vessel Lombok in the year 
1910. They form a nearly continuous ring consisting of three islets called 
the Zandbuis-Banks, Maria Reigersbergen and Huzaar. The lagoon is 
about 100 fathoms deep. 

I presume that in the pleistocene age all these banks formed islands 
that belonged to Sunda Land, but had already been separated from it 
by subsidences in connection with the formation of the basins of 
the Bali Sea and Macassar Strait. The formation of these deep seas 


1) A. Acassiz. The coral reefs of the Maldives. Mem. Mus. Comp. Zool. 
Harvard College XXIX p. 83 and Pl. 1—3, 1903. 


423 


was indicative of the orogenetic movements that are still in opera- 
tion in the eastern part of the archipelago. It appears then, that 
already before the commencement of the Pleistocene the unstable 
Kast here encroached upon the stable West. Now, what is the history of 
these islands, the Kalukuang-, the Paternoster- and the Postiljon- 
islands? Initially they were raised at least 72 m. relatively to the 
sea-level, just as the entire Sunda Land. It is not known, but it is 
presumable that these islands, before the sea-level began to sink, 
were protected against the destructive effect of the surf, by fringing- 
reefs, and, accepting DarY’s opinion expounded in his glacial-control 
theory *) we may conceive that in pleistocene time they were entirely 
abraded by the breakers and converted into banks of shallow depth. 
Day believes that the abrasion and the truncation took place chiefly 
during the maxima of glaciation, i.e. the periods of lowest sea-level, 
through destruction by wave-action. It would appear to me that 
the abrasion and the truncation must have been especially 
strong and progressing during the periods of transition from glacial 
to interglacial, i.e. during periods of slow and prolonged rise of the 
sea-level. At the beginning of every interglacial period the abrasion 
and the truncation of the islands, which every time were penepla- 
nized more intensely, was brought nearer to completion, so that at 
last, at the conclusion of the Pleistocene, the islands were completely 
truncated and were reduced to submarine banks, which consequent 
on the final rise of the sea-level after the close of the glacial period, 
were covered by the sea to a depth of more than 72 m. The coast- 
reefs, which happened still to exist at the close of the Pleistocene 
and the reef-structures which were generated here and there during ~ 
the last submersion, grew up gradually with the rising of the water 
and were converted into atolls and atoll-like coral-islands, such as 
are found at the present day. . 

3. The Spermonde Bank. 

Accepting the Kalukuang-, the Paternoster-, and the Postiljon- 
islands to have been portions of the Sunda Land, which have developed 
into coral-islands, one is easily led to suppose the large shelf on the 
west coast of South-Celebes, which bears the group of coral-islands 
known as the Spermonde Archipelago, to have been likewise closely 
related to the Sunda Land. The Borneo Bank and the Spermonde Bank 
have many things in common; both are on an average 50 and at 


1) R. A. Davy. Pleistocene glaciation and the coral reef problem. Amer. 
Journal of Science XXX p. 297, 1910; Origin of the coral reefs. Science 
Conspectus I p. 120, 1911; The glacial-control theory of coral reefs. Proc. of the 
Amer. Acad. of Arts and Sciences LI p. 157, 1915. 


424 


most 75 m. below the sea-level; on the edge of the Spermonde Bank 
a barrier-reef has developed, which as to distinctness, is not inferior 
to the Great Sunda Barrier-reef, while the Spermonde Shelf, like the 
Borneo Bank is studded with a great number of reef-structures, which 
occasionally reach the surface of the sea. The Spermonde Shelf termi- 
nates abruptly at 4°16’ south latitude and the Spermonde Barrier-reef, 
which can be traced, although with interruptions, towards the north 
over a distance of 230 km., as a row of coral-islands, here gets 
attached to the coast-reefs; more to the north the coast of Celebes 
possesses only insignificant fringing-reefs. 

It seems as if the history of the west-coast of South-Celebes in 
recent geological time has been similar to that of Sunda Land, 
contrary to the other parts of Celebes. 

4. The Laars Banks and the atoll Bril. 

The coral-islands, known as the Laars Banks and the atoll Bril, 
situated in the channel connecting the Strait of Macassar with the Flores 
Sea, warrant the assumption that this strait has become deeper in 
post-pleistocene time. The Laars Banks constitute together a composite 
atoll. The reef-structures form a ring with large gaps. They rest on 
a base which lies more than 100 fathoms deep, but is for the rest 
almost entirely unexplored. In the northern part the reefs have 
grouped themselves into a separate ring or ‘‘faro”, which atollon is 
charted under the name of Laars-islands. The coral-islands of the 
Laars Banks have presumably originated in the same way as 
those of the Kalu Kalukuang Bank; it would seem then that formerly 
the Laars Bank was located at the same depth as the Kalu Kalukuang-, 
or the Paternoster-bank and like the latter belonged in the beginning 
of the Pleistocene as an island to Sunda Land. After the Pleistocene, 
however, the bank on which the Laars-atoll rested, subsided with 
the deepening of the water that unites Strait Macassar with the Flores 
Sea, and the coral-formations could only here and there, by upward 
growth maintain their position at or near the surface of the sea. 
The origin of the atoll Brill may be explained in the same way as 
that of the Laars-atoll. | am also inclined to believe that the Zand- 
buis-atoll and its lagoon with depths of more than 100 fathoms is 
founded on a bank which has subsided as late as the post-pleistocene 
time. 


Oscillations of the sea-level in recent and subrecent time. 


From the position of the terminal moraines and from other 
peculiarities of the territories that have been evacuated at the final 


425 


retreat of the pleistocene ice-caps, it has been possible to conclude 
that this retreat did not proceed continuously, but was interrupted 
by periods of stability and probably also of temporarily renewed 
growth of the ice. In historical times the same thing took place; the 
glaciers of the Alps were from the Roman era down to the last 
decades of the 16' century smaller than at this day, subsequently 
their area increased rapidly, and they generally remained more 
strongly developed than is the case now until about 1850; after this 
date they have almost continually decreased, but they are not by 
far so small now as, say, in the year 1570. These facts concerning 
the extension of the Alpine glaciers in historical times, points at least 
to one very marked oscillation, viz. slight extension between + 50 
A. D. and 1570; greater extension from 1570 to 1850 and once 
more less extension after 1850, which decrease is still continuing 
There is no reason for surmising that these fluctuations should not 
have manifested themselves in a similar way on all glaciated areas 
of the earth, and if this is the case they must have been reflected 
by corresponding slight oscillations of the sea-level. It may be 
accepted, ‘therefore, that also at the coasts of the Sunda Sea 
something of such oscillations will be visible. Indeed, from 
some geologically well-known parts of the Sunda Sea phenomena 
have been observed which point to a slightly higher sea-level in recent 
geological time. Verbeek records that at the coasts of Billiton’) and 
on the surrounding islands here and there elevated coralreefs are found, 
which, however, do not lie higher than 1 or 2 meters above high- 
tide level, and are often covered by coral-débris and sea-sand. According 
to Verbeek the same occurs on the island of Banca’), while he 
adds also for this island that he knows of no places where coral- 
reefs are upheaved more than 1 or 2 meters above high-tide level. 
The position of these coral-reefs (the sea-sand proves nothing, as it 
may have been blown up by the wind there) proves that in 
comparatively recent time a slight oscillation of the sea-level has taken 
place, during which time the sea-level must have stood 2 meters, or 
somewhat more, higher than now. CoRNETS Dm Groot’) believes that 
after the Tertiary the whole island of Billiton was uplifted some 
meters, because sea-shells have been found there of late-pleistocene 


1) R. D. M. VERBEEK. Geol. beschrijving van Bangka en Billiton. Jaarb van 
het Mijnwezen XXVI, 1897 pg. 81. 


5) R. D. M. VERBEEK. l.c. pg. 62. 


3) Corn. DE Groot. Herinneringen aan Blitong. ’s Gravenhage 1887, p. 200. 
208 and especially p. 470 — 478. 


426 


(or recent) date’) in the stream-tin deposits in the mine Ditjang No. 8 
in the district Tandjong Pandang, not far from the present beach. 
Still, from De Groot’s description we are unable to infer whether 
or no this bed of stream-tin-ore (Kaksa) lies above the mean sea-level 
of this day, while VerBeek reports that, most probably, it lies rather 
below the present sea-level. In 1911 -I found a precisely similar 
deposit of recent shells in the Kaksa of the Merante-mine in the 
district of Linggang. This mine is not far from the coast and the 
bed of shells occurs about 8 meters below the surface. Though 
the exact height of the surface is not known, we may safely say 
that this bed, at any rate, does not lie above, but below mean 
sea-level. VERBEFK’) states the occurrence of just such shell-beds not 
only in the localities mentioned above, but also in mine No. 30 to 
the east of Manggar and in mine No. 1 in the district of Linggang, 
and adds that they are situated about at the present sea-level. 

In connection with what has been said, I think that these occurrences 
of shells of very recent date, do not entitle us to draw conclusions 
about a possible slight uprise of the island with reference to the 
sea-level. > 

In the tectonically unstable portion of the Sunda Land, to which 
the greater part of Sumatra and Java belongs, various diastrophie 
movements are known to have occurred in pleistocene and post- 
pleistocene time. It is not my object to mention them or to 
discuss the way in which they originated. 


The Sahul Bank. 


The Sahul Bank is the submerged portion of a flat land, probably 
a peneplain that belonged to a large country of which in pleistocene 
time Australia, New-Guinea, the Aru-islands and some neighbouring 
islands formed a part. After the close of the pleistocene glacial period 
this low-lying land has been flooded consequent on the general 
rise of the sea-level. This flooded portion is the present Sahul Shelf 
(Fig. 1), which now lies on an average about 50 m. below the 
sea-level just about as deep as the Sunda Shelf. 


1) Martin has examinated these shells and comes to the conclusion “that the 
fauna in question belongs to a very recent past” and ‘‘that the fauna agrees with 
that of the sea surrounding the island of Blitong.” See K. MARTIN. On a posttertiary 
fauna from the stream-tin-deposits of Blitong. Notes from the Leyden Museum 
Vol. HI p. 17 and 19, 1881. 


3) R. D. M. VERBEEK l.c. pg. 170. 


427 


I have not been able to collect sufficient data to unravel the 
geological history of this shelf. Suffice it to say that the rivers of 
Northwest Australia now emptying themselves into the Sahul Shelf-sea 
show the characteristics of drowned rivers. The fjordlike lower 
course of the Prince Regent River presents a typical example of a 
submerged or drowned valley. 


Conclusions. 


The conditions for shelf-building in pleistocene time were very 
favourable and reached an optimum in tropical regions at the close 
of the Pleistocene. 

In tropical regions the sea-level stood in pleistocene time during 
the maxima of glaciation, at least 40 fathoms (72 m.) lower than 
at this day. 

Malacca, Sumatra, Java, and Borneo were united into one continuous 
land, the Sunda Land. 

In that Sunda Land the vast Sunda-peneplain has been developed 
into great perfection in the pleistocene age during the periods of 
low sea-level. 

After the close of the pleistocene glacial period submersion of the 
Sunda-peneplain gave origin to the Sunda Sea and the Sunda Shelf, 
during optimal conditions for shelf-building. 

The Great Sunda-barrier-reef originated by upward growth of the 
coast-reefs of the pleistocene Sunda Land during the period of general 
rise of the sea-level, which succeeded the ice-age. 

The atolls and the atolliform coral-islands in the southernmost 
part of Strait Macassar have originated chiefly in the way which 
Darry in his glacial control theory puts forth as the typical mode of 
origin of coral-islands. 


POs: Tf SC Relea: 


After the above communication had been concluded an article by 
L. J. C. van Es*) reached me which treats of a subject, in many 
respects related to my own. I am not in a position to discuss 
here fully the conclusions arrived at by van Es, and to compare 
them with my own. I only wish to refer to some points treated 
in the summary of this article, which, for the rest, contains many 
interesting details. Van Es imagines the island of Borneo to be 
united with Sumatra, and Sumatra also with Java and Malacca, 


1) L. J. C. van Es. De voorhistorische verhoudingen van land en zee in den 
Oost-Indischen archipel en de invloed daarvan op de verspreiding der diersoorten, 
Jaarb. van het Mijnwezen XLV p. 255. 1918. 
28 


Proceedings Royal Acad. Amsterdam. Vol. XXIII. 


428 


in late-pliocene time. The chart accompanying his paper gives his 
idea of the distribution of land and sea at that time. On that map 
also the courses of drowned rivers in that extensive late-pliocene 
and early-quaternary land are indicated, derived by the author from 
several of the isobaths in the present Java- and South-China Sea. 
He imagines in pleistocene time a subsidence of the land and a 
consequent transgression of the sea to have occurred beyond the 
present coastline. During that time barrier-reefs originated by up- 
growth of the coast-reefs along the late-pliocene and early-quaternary 
coastline and also atolls arose, where small islands occurred. During 
the post-pleistocene time van Es assumes upheaval of the land 
and corresponding retreat of the sea. He conceives the upheaval, 
just as the preceding subsidence, to have been irregular, and most 
pronounced where previous earth-movements had been strongest. 

The chief differences between his opinion and mine are: 

1st. in pleistocene time van Es assumes subsidence of the land 
relatively to the sea-level, where I assume upheaval, whereas during 
the post-pleistocene time he admits upheaval where [ assume sub- 
sidence of the land relatively to the sea-level. 

2d. van Es ascribes all shiftings of the coastline, the pre-pleisto- 
cene as well as the pleistocene and the post-pleistocene to orogenetic 
movements, whereas I claim the greater influence in pleistocene and 
in post-pleistocene time for oscillations of the sea-level in connection 
with the ice-age. 

3rd, van Es does not distinguish between the stable and the un- 
stable portions of the East-Indian Archipelago, i.e. between the two 
areas which, at any rate ever since the beginning of the Pleistocene, 
have been stable or unstable, whereas it is my opinion that only 
the great stability (which implies the total absence of earth-movements) 
of the greater part of the ancient Sunda Land can account for the 
remarkably uniform character of the present Sunda Sea and for the 
distribution and the mode of development of the coral-reefs in that 
part of the Archipelago. 


Il. BIOLOGICAL PART by Max Weger. 


The theory of the subsidence of the Ocean-waters in the pleisto- 
cene ice-period and its geological and hydrographical consequences, 
so well expounded in the preceding pages by Professor MOLENGRAAFF, 
also concerns in many ways the biological sciences, first of all the 
faunistics and the zoo-geography of the Indo-Australian Archipelago, 
to what extent also the phyto-geography, lam not competent to judge. 


429 


It has long since been accepted by Zoo-geographers that in the 
latest Tertiary Sumatra, Java, Borneo and the intervening islands 
must have been interconnected by land, and must have been united 
with the peninsula of Malacca, consequently also with the Asiatic 
continent. 

Only on the basis of this assumption could the faunistie unifor- 
mity of these islands be interpreted. 

The faunistic differences, which also exist, are of two kinds. 
Some of them would have been brought about also if the vast land- 
complex that extended from the West-point of Sumatra to Macassar 
Strait — the Sunda Land of MorwNGRAAFF — had never been broken 
up into the present parts, simply on account of its vast extent and 
the difference in conditions of life as the immediate result. For others 
an explanation was found in the longer or shorter duration of the 
continuity of the now separated parts. It had been assumed, for 
instance, that Java first lost its connection with Borneo and Suma- 
tra, while Sumatra remained longest united with the Asiatic continent. 

The questions how this connection by land was brought about, 
and how it was broken up afterwards, led to various hypotheses, 
which were most often ad hoc and devised by zoologists and had no 
geological foundation. It is remarkable that we do not find among 
them what we will simply call CrorL and Prnck’s theory, in which 
Prenck set forth the influence of the pleistocene ice-period on the 
ocean-level, in a comprehensive demonstration based on figures. 
Still, this theory would have afforded a sound interpretation of the 
recent changes of land and sea, required by Zoogeography for the 
facts observed. Nevertheless up to the present day it entirely escaped 
the notice of the Zoogeographers, who were engaged in the nume- 
rous problems regarding the Indo-Australian Archipelago. 

This is all the more regrettable as, conversely, the zoogeography 
of the Archipelago could have yielded evidence to substantiate the 
validity of the Crorr-Penek theory. In its turn it could then have 
shown again that it can afford data to prove geological hypotheses, 
and thus be subservient to the geologist, who is always occupied with 
problems bearing on the younger and the youngest history of our 
earth. 

The fact that the Crour-PrNekK theory meets the requirements of 
zoogeography in a masterly way, speaks well for its validity. 

But more cogent proofs of this validity might be given by zoogeo- 
graphy: one of them I will discuss here. 

The supposed subsidence of the Java- and the South China-sea of 
70 m. must also have affected the existing riversystems. That influence 

28* 


430 


was of no moment for the Westcoast of Sumatra and the South 
coast of Java. Here, as appears from the chart on page 4i1, the 
coast became only a few kilometers broader, the rivers lengthening 
in correspondence with it, which of course had no bearing on their 
fauna. On the other hand, that influence must have been very great 
elsewhere. A river discharging itself into the Java-, or the South 
China Sea, had to cut its way, when these seas were dried up, 
into the new land, in order to find a new outlet in the retiring sea; 
it had to receive newly formed affluents, which had to drain the 
newly shaped land. But, what is of still greater importance, is that 
two rivers, which are now separated, were mutually combined or 
formed part of a larger river-system. 

Geology teaches us how the riversystem of Holland and Germany 
in the recent past differed from what they are now. How eg. the 
Thames was a branch of the Rhine, how the Seheldt flowed in a 
different direction, how a large stream, which flowed through Germany 
from East to West, united the now separated Vistula, Elb and Weser. 

In such a way the Mussi of Hast Sumatra may have been an 
affluent of a large river debouching into the China Sea, which also 
may have received the Kapuwas, discharging itself at the West coast 
of Borneo and presumably also continental Asiatic affluents. May be 
another river system emptied itself through Sunda Strait into the 
Indie, and transported besides the rainwater that fell on the land 
of the dry Java Sea, also the water of the rivers that in former 
times discharged themselves into it. 

If there is a nucleus of truth in these speculations, we may suppose 
that some of it must be visible in the present-day fauna. 

Let us suppose that the Kapuwas of West-Borneo formed, in the 
pleistocene, part of a riversystem, to which also belonged the Mussi 
of Sumatra. This would have occasioned an interchange of the 
fauna and mutual enrichment. But then this must be noticeable in 
a considerable faunistic similarity of these rivers that are now separated 
and have each an embouchure of their own. 

The Mahakkam (Kutei) of the East coast of Borneo must behave 
quite differently. 

This large stream, flowing into Macassar Strait was in no way 
affected by a decrease of 70 m. in the depth of this strait, whose 
depth amounts to some 1000 meters. It remained what it was, 
though its lower course was lengthened by several kilometers; no 
supply of water from other rivers, neither a change, nor an enrichment 
of its fauna could be expected. 

The soundness of this reasoning, therefore, would be best testified 


431 


by a comparative investigation of the Kapuwas and the Mahakkam. 
Material for comparison could be procured by the fish-fauna, this 
being best known. 

In selecting our fish-material we had to shift critically, and to 
make many restrictions. We had to exclude marine immigrants, 
indeed all so-called anadromous and catadromous fishes; secondly all 
fishes living in brackish water; only those species could be used for 
which seawater is an insurmountable barrier. For when at the close 
of the ice-period, which for the sake of convenience we will con- 
sider to have been a continuous period, the water resulting from 
the melting ice and snow gradually raised the level of the oceans, 
the seawater in the neighbourhood of the large river-mouths of 
Borneo and Sumatra will have been of a brackish nature prior to 
the present condition of the sea. At that time it was, then, possible 
for fish that could stand brackish water, to migrate from one river 
into another. That possibility disappeared only when the definitive 
salinity was established permanently. 

After this shifting our working-material consisted only of two 
species of Notopterus, one Scleropages, 17 genera of Siluroids with 
39 and 37 genera of Cyprinoids with 100 species, altogether 56 
genera with 142 species. 

The reliability of our results will increase with the extent of our 
material. We will, therefore, lay stress on the full significance of 
the number of 142 species. It appears from the fact that the number 
of true freshwater fishes, in the restriction given above, which excludes 
marine immigrants, amounts to only 60 species for the vast land- 
complex that comprises the Netherlands, Belgium, Germany and the 
Danubian countries as far as the Black Sea. 

We have tabulated below our material taken from the Kapuwas 
and the Mahakkam, and have added those species that occur also in 
the rivers flowing into the Java Sea at the South Coast of Borneo. 
The table also contains those species that are found in East Sumatra, 
in Java and in rivers of the Asiatic continent (Malacca and Siam). 

From this we see that of the 142 species only 52 are common 
to both rivers. Of the 90 remaining species 23 belong to the Mahakkam 
and 67 to the Kapuwas. Of the 67 species that do not occur in the 
Mahakkam 55 (82°/,) are represented also in other rivers, viz. 75 °/, 
in the rivers of East-Sumatra. Only 12 species (1,8 °/,) are restricted 
to the Kapuwas, or are known from neighbouring rivers, also flowing 
into the South China Sea. | 

On the other hand the Mahakkam possesses 23 species which the 
Kapuwas lacks. But of these 23 species 17 (74°/,) are indigenous 


Notopterus chitala (H.B.) 


Notopterus borneensis Blkr. 


Scleropages formosus (Müll. & Schl.) | 


Silurichthys phaiosoma (Blkr.) 
Wallago leerii Blkr. 

Wallago miostoma Vaill. 
Belodontichthys dinema (Blkr.) 
Silurodes hypophthalmus (Blkr.) 
Silurodes eugeneiatus (Vaill.) 
Hemisilurus chaperi (Vaill.) 
Hemisilurus heterorhynchus (Blkr.) 
Hemisilurus scleronema Blkr. 
Cryptopterus macrocephalus(Blkr.) 
Cryptopterus bicirrhis (C.V.) 
Cryptopterus lais (Blkr.) 
Cryptopterus cryptopterus (Blkr.) 
Cryptopterus limpok (Blkr.) 
Cryptopterus apogon (Blkr.) 
Cryptopterus micronema (Blkr.) 
Chaca chaca (Ham. Buch.) 


Pseudeutropius brachypopterus 
(Blkr 


Lais hexanema (Blkr.) 
Pangasius nasutus Blkr. 
Pangasius polyuranodon Bikr. 
Pangasius nieuwenhuisi (Popta) 
Pangasius micronema Blkr. 
Glyptosternum majus (Blgr.) 


Bagarius bagarius (Ham. Buch.) 


Kapuwas. 


bik ee Sp BE SP dE 


+++t+ td kt + 


+ + 


Mahakkam. 


oa 


+ 


Je RO 


South Borneo. 


dok + 


gj 


dk tet 


+ 


+ + + + + 4+ East Sumatra. 


tt + 


a 4 4 


' 
= 


+ + + 


West Sumatra. 


Java. 


=Siam) 


Continent. 
Malacca; S 


(M= 


a 


433 


Macrones nigriceps (C.V.) 
Macrones. micracanthus (Blkr.) 
Macrones - wolffi -(Blkr.) 

Macrones nemurus (C.V.) 
Macrones planiceps (C.V.) 
Bagrichthys hypselopterus (Blkr.) 
_Bagroides melapterus Blkr. 
Leiocassis fuscus Popta 
Leiocassis mahakamensis Vaill. 
Leiocassis stenomus (C.V.) 
Leiocassis poecilopterus (C.V.) 
Leiocassis micropogon (Blkr.) 
Leiocassis vaillanti Reg. 
Breitensteinia insignis Steind. 
Gastromyzon borneensis Gthr. 
Gastromyzon nieuwenhuisi (Popta) 
Homaloptera wassinki Blkr. 
Homaloptera ophiolepis Blkr. 
Homaloptera orthogoniata Vaill. 
Homaloptera tate regani Popta 
Parhomaloptera microstoma (Blgr.) 
Botia macracanthus (Blkr.) 

Botia hymenophysa (Blkr.) 
Acanthopsis choirorhynchus (Blkr.) 


Lepidocephalus pallens (Vaill.) 


Acanthophthalmus lorentzi M. Web. 
& de Bfrt. 


Acanthophthalmus kuhli (C.V.) 


Acanthophthalmus borneensis Blgr. 


Eren x 
or 
SIN dn i is ell ale 
+ | +|+)+]+ 
+/+] +) + M.S. 
+} +]+4+]+4 IMS 
+ | + +/+])/+)™ 
+ + 
+ +) + S. 
+ 
+} + + + 
+ + + 
- + M. 
ip 
- + 
+ + 
oh 
+ | + + + 
+ + + 
+ + 
+ 
— 
+/+)]4+)4) + 
tt + + [SM 
+: |) eae ete a uote 
+ 
+ 
+ + + |M 
+ : 


Mahakkam. 


South Borneo. 


East Sumatra. 


West Sumatra. 


Java. 


Continent. 


Saevwv_« _—a—xKX«KwxKxr<—e_e_eeeeeooo 


Acanthophthalmus anguillaris Vaill. 
Elxis obesus (Vaill.) 

Vaillantella euepipterus (Vaill.) 
Nemachilus longipectoralis Popta 
Nemachilus fasciatus (C.V.) 

Chela oxygastroides (Blkr.) 

Chela hypophthalmus Blkr. 

Chela oxygaster (C.V.) 


Marcrochirichthys macrochirus 
(C.V.) 


Rasborichthys helfrichi (Blkr.) 
Rasbora argyrotaenia (Blkr.) 
Rasbora vaillanti Popta 
Rasbora volzi Popta 

Rasbora trilineata Steind. 
Rasbora kalochroma (Blkr.) 
Rasbora einthoveni (Blkr.) 


Rasbora lateristriata var. suma- 
trana (Blkr.) 


Rasbora lateristriata var. elegans 
Volz. 


Rasbora lateristriata var. trifasci- 
ata Popta 


Luciosoma trinema (Blkr.) 

Luciosoma setigerum (C.V.) 
Luciosoma spilopleura Blkr. 
Leptobarbus hoevenii (Blkr.) 


Leptobarbus melanopterus M. Web. 
& de Birt. 


Leptobarbus melanotaenia Blgr. 


Rohteichthys microlepis (Blkr.) 


ae Cek at dek 


+ 


+ +++ + + + 


+ 


+ 


+++ 4 


++ +4 


G. A. F. MOLENGRAAFF and M. WEBER: “On the Relation between the Pleistocene Glacial Period and the Origin of the Sunda Sea 
(Java- and South China-Sea), and on its Influence on the Distribution of Coral-reefs and on the Land- and Freshwater Fauna.” 


CHART OF THE CORAL ISLANDS IN MACASSAR STRAIT 


Fig. 3. 
Scale: 1: 2.000.000. 


ua „ze 0 
_ A 


STi 
Sg. ee 
NN ‘wet 
= 
. 
e 
° 
| 
| Aurora « 
’ 
i 
Sibbalds bank 
Kwong Eng 


PANINI 


== 


“en 
ay 


a ae 


+ © Ambeengi Jl 


Paternosrer ae 


ZOE Ee < 
v, . 
s cal 


A Zandbuis 


Hsen) S OEM Oe 
U2 Ce a 


Kaloe Kaloekoeang 


ry 


Bangkawa “ 
nge Rn ah 


AAO 8 


banks 


Ces 


O 


ae Sr, za 
OR es 


nn 


116” 
Solid line 
Dotted line . 
Black 


Oblique stripes 


20° 

. Coast. 
Isobathic curve of 40 fathoms or 72 meters. 
Coral-formations, projecting above the water or lying from 0 to 5 fathoms below sea-level 
Coraltormations, lying between 5 and 20 fathoms below sea-level. 


435 


ede ; 
Seen eee Me a = 
SIS jg ë 8 
a | wu 2 
Amblyrhynchichthys truncatus 
(Bikr.) — a a. Sh 
Amblyrhynchichthys altus Vaill. + 
Albulichthys albuloides (Blkr.) a a — 
Dangila ocellata (Heck.) + — aa + 
Dangila fasciata Bikr. -- + 
Dangila cuvieri C.V. + + Se > M. 
Dangila sumatrana Blkr. a — 
Dangila festiva (Heck.) == | oh 
Barynotus microlepis (Blkr.) + -+ + 
Thynnichthys vaillanti M. Web. & 
de Bfrt. JL 
Thynnichthys polylepis Blkr. + a. 
Osteochilus borneensis (Blkr.) + + 
Osteochilus melanopleura (Blkr.) a + + 
Osteochilus kelabau Popta + 
Osteochilus schlegeli (Blkr.) + 4 + + 3: 
Osteochilus kahajanensis (Blkr.) + -+ a + 
Osteochilus repang Popta st 
Osteochilus vittatus (C.V.) — oo +e ao + + M. 
Osteochilus hasselti (C.V.) aL +. + os + |M.S 
Osteochilus kappeni (Blkr.) + + 
. Osteochilus brevicauda M. Web. 
& de Birt. ty 
Hampala macrolepidota (C.V.) + + + + ae == Fe 
Hampala ampalong (Blkr.) + + 
Hampala bimaculata (Popta) sE 
Labeobarbus tambroides Blkr. a a + + + 
Labeobarbus douronensis (C.V.) + + + + == 
Cyclocheilichthys heteronema(Blkr.) | + M. 


436 


Cyclocheilichthys janthochir (Blkr.) 
Cyclocheilichthys apogon (C.V.) 
Cyclocheilichthys repasson (Blkr.) 
Cyclocheilichthys lineatus (Popta) 
Cyclocheilichthys armatus (C.V.) 
Cyclocheilichthys siaja Blkr. 
Puntius schwanefeldi (Blkr.) 
Puntius lateristriga C.V. 

Puntius tetrazona (Blkr.) 

Puntius fasciatus (Blkr.) 

Puntius binotatus (C.V.) 

Puntius anchisporus (Vaill.) 
Puntius sumatranus (Blkr.) 
Puntius bramoides (C.V.) 

Puntius collingwoodi (Gthr.) 
Puntius bulu (Blkr.) 

Puntius waandersi (Blkr.) 

Puntius nini M. Web. & de Birt. 
Balantiocheilus melanopterus(Blkr.) 
Barbichthys laevis C.V. 


Labeo (Morulius) chrysophekadion 
(Bikr.) 


Labeo (Labeo) rohitoides (Blkr.) 
Labeo (Labeo) pleurotaenia (Blkr.) 


Schismatorhynchus heterorhynchus 
(Bikr.) 


Tylognathus hispidus (C.V.) 
‘Tylognathus bo Popta 
Tylognathus falcifer (C.V.) 


Kapuwas. 


tet. dk + 


+ ++ + 


++ ++ 


+ 


Mahakkam. 


+ + 


South Borneo. 


+ + 


East Sumatra. 


+ + 


West Sumatra. 


fe 


Java. 


+ + 


Continent. 


M.S. 


akk oa hats 
dele E Ange |. Z 
Sheen re Se ae 
kee eles eee Pels 
£)/2/3)4)3 ö 
an | s 
Gyrinocheilus pustulosus Vaill. + + 
Paracrossochilus vittatus (Blgr.) — — 
Discognathus borneensis Vaill. 5 +0 
Epalzeorhynchus kallopterus Blkr. | -+ ; + + 
Crossochilus oblongus (C.V.) a. + 3 + + + M 
Crossochilus cobitis (Blkr.) + + ; ; + + | 
| 


to the Mahakkam or other neighbouring rivers flowing into Macassar 
Strait. Of the 6 remaining species only 3 (13 °/,) occur also in East 
Sumatran rivers, while 3 other species are distributed over a wider 
range 

When studying the well-defined genera it appears that of the 53 
genera inhabiting the Kapuwas 20 (38°/,) are lacking in the Mahak- 
kam. It strikes us, however, that of these 20 genera as many as 
18 are represented in the East Sumatran rivers. On the other hand, 
the Mahakkam possesses only 36 genera, 33 of which are also found 
in the Kapuwas, only 3 are wanting there, but they are not known 
to exist elsewhere, and are for the present to be considered as 
autochtonous. 

We conclude, therefore, that the Kapuwas does not owe its far 
greater abundance of fish to autochtonous forms, but to such as 
occur also in Kast Sumatra. They point to a former connection with 
Kast Sumatran rivers, which, as alluded to above, finds an explanation 
in the Crorr-PrNcK theory. This constitutes the great difference 
between the Kapuwas and the Mahakkam, though their sources are 
lying only at a few hours’ distance from each other. 

If my reasoning is correct, it must be so also for other groups of 
animals whose distribution underwent some change, anyhow in the 
pleistocene, not only for freshwater-, but also for land-animals. 
For the latter, the land of the Java- and the South China Sea, when 
laid bare, procured apparently the bridges required by zoogeography 
for emigration and immigration of animals. 

Fundamentally this is quite correct; still even such evidence as 


435 


can be brought forward is not so cogent as in the case of the fish- 
fauna of the Kapuwas and the Mahakkam. W hen studying the problem, 
difficulties will crop up. 

First of all the elements constituting a fauna are not of the same 
age. Older and younger strata occur with various possibilities of 
distribution. 

Besides this historical factor, there are also various biological 
factors of different nature: Even though a species be induced to 
migrate to other quarters and may, by doing so, possibly enlarge 
its habitat, it can avail itself of this opportunity only when the 
conditions of life in the new abode meet the requirements of the 
species. — Furthermore, the question arises whether perhaps other 
influences in the ice-period affected the countries concerned or part 
of them. The fauna of Java e.g. has ever afforded special difficulties 
for the zoogeographers. It has already been alluded to in this paper 
that Java has long since been supposed to have behaved differently 
from Sumatra and Borneo, and consequently, also differs in its fauna. 
An attempt to account for this has been made by assuming that 
Java was the first of the islands to detach itself from the land- 
complex that united them. — But the faunistic peculiarities of Java 
may also have resulted from the occurrences consequent on the 
formation of the enormous range of volcanoes that runs through the 
island from West to Hast; the products of their eruptions (ashes, 
mudstreams, and the like) may also have influenced the fauna 
directly, or indirectly by modifying the climate (through intercepting 
the sunlight by the suspended dust of ashes scattered through the 
air, or by profuse rainfall). 

Such questions will encumber the application of the CROLL-PENCK 
theory to the study of the distribution of animals in the Indo-Austra- 
lian Archipelago, but a good many of these problems will admit of. 
solution. For this theory offers a welcome basis for a number of 
hypotheses regarding former land-connections between the now 
separated islands, brought forward by zoogeographers to explain the 
facts observed. Moreover it clarifies our ideas with regard to the 
time at which the supposed land-connections originated. 

The Great Sunda Islands have been discussed above. 

But Penck’s theory also throws a new light upon the eastern half 
of the Archipelago. Here the distribution of animals led to the 
hypotbesis that New-Guinea, together with the Aru Islands, Waigeu 
and the neighbouring smaller islands, formed one land-mass, that 
was connected with North Australia. 

Those lands are now separated by shallow straits and a shallow 


439 


sea that covers the Sahul-bank. This bank is laid bare when the 
sealevel sinks + 70 m. 

In various writings I have tried to show that this condition was 
brought about in the pliocene and that the present status of land 
and water was developed in the pleistocene *). 

Also P. and F. Sarasin assume, in their wellknown work on 
Celebes, a pliocene “Festlands-epoche” for the Archipelago, and 
R. D. M. Verserk wrote that at this day, and presumably ever 
since the Pliocene New-Guinea was separated from Australia by a 
shallow sea. Other writers (e.g. Heprey and Marrarws) seem to be 
satistied in referring this occurrence to the “late Tertiary”. 

It was generally supposed that the process consisted in more or 
less local upheaval or subsidence of land or sea. Instead of these 
rather unfounded surmises, born of the wish to be able to dispose 
of land-connections, necessary for the zoogeographical theories, the 
Croni-Penck theory gives us a general view, yielding an actual 
basis. However, with this the supposed positive or negative sub- 
sidence is at the same time shifted from the Pliocene to the Pleisto- 
cene. This again lends support to our statement that the facts 
observed by Zoology speak for the validity of the CROLL-PrNCK 
theory. 


1) A short survey of these speculations will soon be published in the Sitzungs- 
berichte d. Heidelberger Akademie der Wissenschaften. 


Geology. — “On the Geological position of the Oil-fields of the 
Dutch East-Indies.” By Prof. G. A. F. MoOLENGRAAFF. 


(Communicated at the meeting of June 26, 1920). 


Experience has taught that the majority of the large oil-fields 
have originated in long enduring geosynclines, where these are 
marginal areas of sedimentation along the coasts of continents. *) 
In those geosynclinal belts, which are characterized by a long con- 
tinued subsidence of the soil, the organic matter in the sediments, i.e. 
the remains of animal and vegetable organisms may, as the subsidence 
of the soil proceeds, successively be covered by layers of fine sedi- 
ments. Thus, being shut off from water and air these organic remains 
may escape from destruction by oxydation. They may then be 
accumulated to a considerable thickness. As long as in such a geo- 
synclinal coastal belt, subsidence prevails over sedimentation, the 
area remains covered by the sea; if, however, sedimentation gets 
the better of subsidence, the area may become land. 

In the first case petroleum or allied hydrocarbons may be ulti- 
mately formed in the subsiding area; in the second case coal or 
allied substances may finally be found. A slow and gradual sub- 
sidence, the area meanwhile remaining all the time either low land 
‚or shallow sea, affords the most suitable conditions for the accumu- 
lation of such fossil fuels. Through the shifting of the equilibrium 
between the processes of subsidence of the soil and sedimentation, 
as well as through epirogenetic movements of land and sea relative 
to each other, every geosynclinal area may during its long life be land 
at one time and sea at another. Thus in the same geosyncline an 
accumulation of coal may take place at one time, and of petroleum 
at another; consequently in one and the same geosyncline coalbeds 


1) Among the recent publications bearing on this subject the following deserve 
special attention: M. R. Daty, Geosynclines and petroliferous deposits. Trans. 
Amer. Inst. of Min. Eng. LVII, p. 1054, 1918 and the discussion on it, ibid. 
p. 1065. W. F. Jones, The relation of oil-pools to ancient shorelines. Econ. Geol. 
XV, p. 81, 1920 and the discussion on it, ibid p. 350. 


441 


and oilbeds may') occur alternately from the surface downward. 

Broadly speaking the filling in such a geosyncline may be said 
to begin, as a rule, with the deposition of marine sediments with 
a monotonous microfauna, later and only when these sediments 
have attained a considerable thickness, they are overlaid by deposits 
of brackish-water, of fresh-water and perhaps by terrestrian deposits 
which will or will not alternate one with the other and possibly 
also with marine deposits. 

Experience has also taught that in such marginal geosynclines 
during their long life folds may originate more or less parallel to 
the shore-line of the continent and at some distance from the shore. 
These folds may cause one or more rows of islands or a more or 
less continuous strip of land to emerge from the sea. Not seldom in 
such a case the folding process is attended with volcanic activity. 
The result may be that the portion of the geosyncline immediately 
bordering the continental shore, gets separated from the deeper ocean 
by a row of islands or a more continuous strip of land consisting of 
a system of one or more folded mountain-chains, which may even 
shut the inner portion of the geosyncline off completely, thus con- 
verting it perhaps into a freshwater lake for some time. It is evident 
that then the materials for sedimentation will be transported to the 
geosynclinal receptacle from two quarters, viz. from the continent 
and from the strip of land or mountain-range newly emerged from 
the sea, whereas prior to the folding the geosynclinal belt received 
its sediments from one side only, viz. from the pre-existing continent. 
In the case of violent volcanic action in the said strip of land, 
voleanie material will perhaps from that moment play a prominent 
part among the sediments which continue to accumulate in the 
geosyncline. 

Finally experience has also taught that the geosyncline, which 
tends to get filled up completely, now that it has become narrower and 
receives sediments from two sides, mostly undergoes itself gentle 
folding. It is well known that this folding brings about a position 
„of the strata, which is of prime importance for the working of 
oil-fields. 

The outlines of the geological history of the largest and best known 
oil-fields of the world are similar to those described just now. 
Among the numerous instances only two, the oil-fields of Pennsyl- 


~ 1) Particular stress must be laid on the word “may”, because it is possible 
that during the development of a geosyncline the conditions for the origin and 
accumulation of coal, of petroleum or of both are never quite fulfilled; in that 
case the geosyncline will remain sterile. 


442 


vania and those of Argentina, may be mentioned: in the Pennsylvanian 
geosyncline, which has originated as a belt marginal to the then 
North-American continent (the archaean Canadian shield built out 
southward), the sedimentation, as well as the folding of the Appal- 
achians (Appellachia), which separated the inner portion of the geo- 
syneline from the Ocean to the south-east, reached its maximum of 
intensity in Pennsylvanian time, and closed in Permian time; the 
oil-fields in the Andine portion of Argentina are marginal to the 
ancient South-American continent, which, in geological structure, 
exhibits striking similarity to South-Africa and the so-called Gon- 
dwana-land. The sedimentation in that geosyncline occurred in 
Jurassic and in Cretaceous time, while the folding which was attended 
by intense volcanic activity and gave rise to the Andes, terminated 
in Tertiary time. As a third instance the oil-fields of Venezuela may 
be quoted. As soon as one considers this mode of development of 
an oil-field to be the typical one, such a field must show the following 
features (see fig. 1): 

1. a geosynclinal coastal belt G (fig. 1), being the depository of 
the sediments in which the hydrocarbons originate. The position of 
this belt will indicate in a rough way the original shore-line of 

2. the continental area ZL, from which the terrigenous material 
is derived, which gradually has been accumulated in the marginal 
geosyncline. This area may also be called the ancient continental 
area or the primary area of denudation, because it existed already 
as a landmass before the geosyncline had originated. 

3. the sea or ocean S, which, reckoning from the continent, lies 
on the other side of the geosyncline. 

In the geosynclinal belt one can distinguish : 

a. The portion near the land G, consisting of sediments deposited 
in a shallow sea or on a low land. These deposits consist preponderantly 
of terrigenous materials (limestones are rare) and contain coal-, or 
oil-beds or both. They are folded generally not very strongly during 
the last period of the orogenetic phase, which terminated a long era 
in the still longer life of the geosyncline. 

6. The portion G, more remote from the land in which the 
sediments, for a great part marls and limestones, were deposited 
farther away from the shore of the continent than in the portion 
G,. Generally this portion has been folded in a period of the oro- 
genetic phase prior to the folding of the portion G,. In that case 
the anticlinal parts of the folds had already emerged from the sea 
as rows of islands or more or less continuous strips of land or may 
be as lofty folded mountain-chains, whilst in G, the subsidence 


443 


of the soil and the sedimentation was still in progress. The belt G, 
generally has been upheaved, folded and compressed to a stronger 
degree than the belt G,. 

The folding of the belt G, is not seldom accompanied by voleanic 
activity causing the sediments in this area to be for the greater 
part composed of voleanic material. This area G, might, in contra- 
distinction to Z, also be called the secondary area of denudation. 

$$ eee 


L Continental 
Area of denudation 


EE ET et Se a 


G Coal and 


Geosynclinal Petroleum 


coastal belt 

G A EEE ee TEE VTi ed 

Folded mountain 
chains, often 


Area of Sedimentation G, F vol 
seat of volcanic 


activity 


ET I EN A ea cl al a a 


Fig. 1. 
Our object in writing this paper is to discuss how far the position 
of the oil-fields of the Dutch East-Indies, fits in with the scheme 
sketched above. 


The location of these oil-fields is marked on the accompany ing 
sketchmap') (Fig. 2). They are situated along the north-east coast of 
Sumatra, along the north coast of Java and along the east coast of 
Borneo. The sediments of which those oil-fields consist, have been 
deposited in the geosynclines in Tertiary, especially in Neogene time. 


1) In compiling this sketchmap two authorities on the Australasian oil-fields 
Kein and Rurren kindly have procured me some valuable data. 


29 
Proceedings Royal Acad. Amsterdam. Vol. XXIII. 


444 


There is in the Dutch East-Indies another oil-field of little impor- 
tance in the island of Ceram, which probably dates from Mesozoic 
time. Its age, however, has not been quite proved. Another oil-field 
again, genetically closely connected with the Tertiary terranes men- 
tioned above, is found in the East-Indian Archipelago outside of the 
Dutch possessions. It is the Tertiary oil-field situated in British North- 
Borneo and Serawak along the coast of the China Sea. 

These latter territories will here be left out of consideration. 


[. Kast- Borneo. 


The geosynclinal belt G lies at the east coast of Borneo, along 
the strait of Macassar. 


kig. 2. 
Black vertical lining: Neogene geosynclinal deposits, in which the occurrence of 
petroleum has not yet been established. 
Solid black: Oilfields in Neogene geosynclinal deposits. 
Dots: The dotted area represents the Sunda shelf; together with 
Malacca, Sumatra, Java and Borneo it indicates the 
largest extension of the Sunda Land in Pleistocene time. 


The continental or primary area of denudation ZL is Borneo, the 
sea S is the Strait of Macassar, and between these two the Tertiary geo- 


445 


synclinal belt G is located, which has now been folded and converted 
into land for the greater part. The belts G, and G, gradually pass 
one into the other. The seaward strip (@, is richer in lime- 
stones than G,, which lies more landward, as has been shown by 
Rurren. In G, no, volcanic action has taken place. According to 
Rutten the deposits in the Tertiary geosyncline of Kast-Borneo attain 
a thickness of about 5500 m. and comprise the entire Miocene, 
perhaps even a part of the Oligocene, and the Pliocene. Beds of 
lignite as well as beds of petroleum occur in this geosyncline. 
Rurten, from the differences in facies of the deposits, and before 
him VerBeeK concluded that the N.S.-shoreline of Kutei existed already 
in the Old-Miocene, and that at that time the Strait of Macassar had 
already been formed as a more or less deep trough. The oil-field of East- 
Borneo thus has been developed in a geosyncline, which lay between 
Borneo, a part of Sunda Land being the denudation-area from which it 
derived its sediments, and Macassar Strait being the adjoining oceanic 
area. This conception is accepted only provisionally, and some stress 
may be laid on the point that the geological position of Celebes relative 
to this geosyncline and to the Strait of Maccassar is not explained by it. 


II. Sumatra and Java. 


The geosynelinal belt G, to which the present oil-tields are con- 
fined (see map fig. 2) lies along the north-east and the eastcoast 
of Sumatra and the north coast of Java, bordering the Java Sea, the 
South China Sea and Malacca Strait. It is of Tertiary, Neogene age 
and the belt G,, which contains petroleum and lignite in many 
places, is now slightly folded and the major portion has become 
land. Towards the ocean follows the adjoining belt G,, which had 
already been folded and converted into a mountain-chain, whilst 
subsidence still continued in the portion G, of the geosyncline, and 
the process of sedimentation was still in progress there. The moun- 
tains of Sumatra, which I will designate here by the collective name 
of Barissan Mountains, represent one geanticline, and the row of the 
Mentawei-islands and others west of Sumatra represent another 
geanticline in these folded mountain-chains. More to the west follows 
the sea S, in this case the Indian Ocean. In the belt G, intense and 
prolonged volcanie activity has taken place in Sumatra as well as 
in Java; this activity commenced as early as the Old-Miocene. In 
the Miocene already volcanoes rose, presumably as a row of islands 
above the sea-level, for from that time andesitic material is found 
in the geosynclinal deposits of the belt G,. But, where has one to 
look for the primary area of denudation £ from which these geo- 

. 29% 


446 


synelinal troughs of Sumatra partly, and of Java entirely have derived 
the non-voleanie material now found deposited in them? 

Where, in other words, is to be found the continental area L, to 
whose shores these geosynclines were marginal ? 

This continental area L lay to the north-eastward; it is the 
neogene Sunda Land, the greater part of which had been overflowed 
by the sea after the close of the ice-age. The part of Sunda Land 
which is now submerged is indicated by the dotted area in 
the sketch map Fig. 2, the contours of which have been derived from 
the present isobath of 40 fathoms. The dotted portion, however, 
does not represent its extent in Neogene time, but the largest extent 
which it reached only in Pleistocene time. 

It appears, thus, that the geosynclines in which the three large 
oil-fields of the Duteh East-Indies, to wit those of Java, of Sumatra 
and of Borneo, have originated, during their development were 
marginal to one and the same continental area of denudation, the Sunda 
Land. This marginal position is now only noticeable in the Kutei- 
oilfield, of East-Borneo, because Borneo is the only portion of the 
former neogene Sunda-continent which still emerges from the sea as 
a small continental area. In order to understand the original relations 
between the area of denudation and its marginal geosynclinal belts, 
we must imagine the now overflowed portion of the neogene Sunda 
Land, viz. the JavaSea and the South China Sea, to be united again 
with Borneo, thus forming one continuous land. The assumption is 
admissible that originally the geosynclinal deposits constituted an 
entirely or almost entirely uninterrupted belt round the neogene 
Sunda Land. This is not the case now in the oil-fields hitherto known. 
The four oilbearing terranes, that of North-Sumatra, that of Djambi- 
Palembang, that of East-Java and that of East-Borneo are separated by 
large intervals. In Central-Sumatra, in the gap between the first- 
mentioned two territories, the geosynclinal deposits are present and 
petroleum may also occur in them, but, if so, presumably only ata 
great depth and overlaid by younger, posttertiary mostly volcanic 
deposits of considerable thickness. The same probability holds for 
the Lampong districts in the extreme south-east of Sumatra. 

There is good reason to expect the occurrence of petroleum in 
deposits of the neogene geosyncline along the north coast of Java 
to the west of the peninsula of Japara, i.e. in the gap between 
the East-Sumatra- and the KEast-Java-oilfields. Here, however, the 
petroliferous strata will be overlaid, besides by more recent sediments 
of unknown thickness, also by the sea to a depth of 50 metres at 
the utmost. 


447 


The rapid improvements in the methods of boring will in the 
near future probably enable to prove conclusively which portions 
are still in existence of the deposits of petroleum and lignite which 
have originated in the far-extending geosynclinal trough marginal to 
the neogene Sunda-land. 


CONCLUSIONS, 


1. The three large petroleum-fields of Sumatra, Java and East- 
Borneo have originated in a similar way in neogene time in geo- 
synclinal belts, marginal to the former Sunda Land, which after the 
close of the Pleistocene age for the greater part has been overflowed 
by the sea. | 

2. It may reasonably be accepted that, along the north-coast of 
West-Java, oilfields may occur below the surface of the sea over- 
laid by younger deposits down to a depth not established as yet. 
These oil-fields are closely connected to and fill the gap between 
those of East-Sumatra and East-Java. 

3. It is improbable that in the eastern part of the East-Indian 
Archipelago '), more especially in the volcanic Lesser Sunda-islands, 
however much their geological structure may resemble that of Java, 
neogene lignite- or petroleam-deposits will be found, because one of 
the conditions for their genesis has not been fulfilled there, namely 
the presence of a geosynclinal belt of sedimentation, marginal to a 
continental area of denudation. 

4. The opinion, enunciated by VerBrek ®) and Rurren*), that 
the Strait of Macassar had already been formed as a deep depression 
in Old-Miocene time, is supported by the way in which the oil- 
fields occur. 

5. The fact that in Neogene time a continuous, or nearly con- 
tinuous, geosynclinal area (which was folded afterwards) extended 
in a semicircle along the coast of the continental Sunda Land, makes 
it doubtful whether Have and P. Sarasin are right in considering 
the Hast-Indian Archipelago as the area where the Alpine and the 
circum-Pacific orogenetic systems meet or are interlaced. 

This fact rather points to the conclusion, that it would be prefe- 
rable to distinguish between a circum-Asiatic and an Australo-Pacific 
orogenetic system as those, which may be surmised to meet or to 
be interlaced in the East-Indian Archipelago. 


1) With the exception of New Guinea and the adjacent islands. 

9) R. D. M. Verpeex, Rapport sur les Moluques. Jaarboek van het Mijnwezen 
XXXVII, p. 823. Batavia 1908. 

5) L. Rurren, Modifications of the facies of the Tertiary formations of East Kutei. 
These proceedings. Vol. XIX, p. 728, 1917. 


Anatomy. — “On a human ovary with a large number of abnormal 
follicles and the genetic significance of this deviation.” By 
M. W. Worrpeman. (Communicated by Prof. J. Boeke). 


(Communicated at the meeting of June 26, 1920). 


Last year, at the course of microscopic anatomy, sections of a 
human ovary, which had many peculiarities, were distributed among 
the students. | made a series of sections of 10u of that part of the 
ovary, that had not yet been cut into sections, in order to make an 
extensive study of the peculiarities found. After my examination of 
the preparations and. the study of the very extensive literature, I 
think I am justified in adding another communication to that literature. 

The origin of the preparation could not be traced. In the collection 
of materials of our laboratory it was only mentioned as “human 
ovary”, without any further explanation. As it was not possible to 
make out, which of my predecessors had added the preparation to 
the collection, I am ignorant of the age of the individual, from 
which the organ was taken. It was fixed very. well in formaline 
and was imbedded in paraffine. At a microscopic examination it 
was evident that there were a great many folliculi vesiculosi of DE 
GraaF and a great many atretical follicles. At some places, I think 
I noticed some luteine cells. This is a sign that ovulation has taken 
place. Besides, the measurements of the organ in question and the 
comparison with ovaria of babies make it plausible that the ovary 
is from a mature -individual. But this is only a hypothesis. 

For in 1739 already, VartisNerus described the presence of ripe 
vesicles in a newly-born infant and according to E. Rvxer (1906) 
this phenomenon would appear regularly. The egg-cells would even 
be fit for fecundation and ovulation would take place. If this were 
true, the presence of large vesicles and ovulation phenomena would 
not prove that the individual was mature. But as KAppeni and Herz 
examined more than 200 ovaria of newly-born animals, in which 
they found large vesicles, but never saw the slightest trace of 
ovulation, we should not accept without further evidence that ovula- 
tion takes place with babies. Whatever the case may be, it is very 


449 


probable that the individual, of which the ovary will be described 
here, is a mature woman. The preparation bad several characteristics. 
First of all, it had a great number of ingrowths of the germinal 
epithelium, which covers the total organ as a single layer of cubic 
cells. These ingrowths are small tubes with a cylindrical round 
lumen, which is surrounded by a small number of bright, cubic cells. 

The nuclei of the ceils are lying almost in the centre of the 
cells. All the cells have about the same appearance. Most of the 
tubes are unbifurcated, only a few bifurcate. They generally do not 
proceed radially (towards the centre of the ovary), but very often 
they bend back under the germinal epithelium and proceed more 
or less parallel to the surface. Consequently one sees many rings of 
the epithelium under the germinal epithelium (transverse sections of 
tubes) in the sections. They are lying in the tunica albuginea and 
end, as far as I could see, blind. In the usual text-books of histology 
and microscopic anatomy these ingrowths of the germinal epithe- 
lium are not mentioned. But, in the text-books of veterinarian 
histology or those of embryology the occurrence of similar ingrowths 
in some animals and in human foetuses are mentioned. They are 
called “Keimschlauche” or ‘invaginations épithéliales”. 1 will describe 
them here as “ingrowths of germinal epithelium”, because a wrong 
idea of their genesis adheres to the name of “Keimschlauche’’. 

In the second place the ovary showed a large number: of cellular 
cords within the stroma. These cords are elongated and surrounded 
by a thin membrane of connective tissue and consist of very bright, 
regularly arranged, cylindrical cells (see fig. 1a). If they had a lumen, 
they would be exactly like glandular tubes. They have different 
names in the literature. The most usual one is ‘“Markstrange” 
(cordons médullaires). Therefore, I will call them in future “medullar 
cords.” The third and most obvious characteristic of the examined 
preparation is however the presence of a great number of abnormal 
eggfollicles. In many places, one sees the eggcells lying in groups 
and surrounded by a number of folliclecells, formed into, what is 
generally called “eggnests”. Besides these egenests ') in which I found 
as many as 9 eggcells, there were also vesicles (folliculi vesiculosi) 
with more than one eggcell. In those vesicles a large number of 
eumuli oophori, instead of a single one, occur (see fig. 1c and fig. 3). 
The greatest number I found was five. But beside the eggcells, 
which are lying in a real cumulus oophorus, one sometimes finds 
rudimentary eggcells in the vesicle. 


1) Eggball and eggnest may be used alternatively. 


450 


Rigs: 


a. Medullar cord. 
b. So-called eggball follicle. 
c. So-called Schlauchfollicle. 


Follicles with more than one eggeell are not unknown in man, 
however. The limit seems to be three. In some animals vesicles are 


Fig. 2. 


So-called Eggballfollicle. 


found with numerous eggeells, this is 
even a normal phenomenon. The human 
ovary described here is already important 
owing to the rather large number of 
eggeells; it gains in importance on tracing 
tbe origin of the abnormal vesicles. 
The former conception of the genesis 
of the ovary was (briefly) the following: 
From the germinal epithelium cellular 
cords penetrate into the ovary (occasion- 
ally they have rather the character of 
tubes or wedges). These so-called “Strange” 
or‘Schlauche’ of VALENTINPFLUGER Contain 
the primordial eggs and the future follicle 


cells. Gradually, connective tissue penetrates through these cords, 
destroys their connection with the germinal epithelium and divides 


them into cell-groups. 


These cellgroups (Eggballs, WALDEYER) contain a number of egg- 
cells and many follicle cells. Afterwards, every eggcell is surrounded 
by a single coat of folliclecells and the eggnests divide into a number 


451 


of eggcells, covered in this way (which are now called ‘‘primary 
follicles’). The ingrowths of the germinal epithelium are looked 


ín & 
NE ee iens Ot bee 
Ee ee bee 


Fig. 3. Atypical follicle. 


upon as the rests of tubes of Prrücer, originating from the germinal 
epithelium (ScuMaLtz in ELLENBERGER's Handbuch d. vergl. Mikrosk. 
Anat. der Haustiere, Bnd. 2, 1911). Consequently the name of 
“Keimschliuche” is given to those ingrowths. The medullary cords 
are also looked upon as rests of the proliferations of the germinal 
epithelium, viz. of the eggtubes of Prrücer. If the eggnests have 
been divided into primary follicles, vesicles, containing more than 
one eggcell would develop. According to Henin (1895) there is a 
‘struggle between the connective tissue and the epithelium in the 
ovary, which generally ends in the victory of the connective tissue. 
If this is not the case, the division of eggnests into primary follicles, 
does not, or insufficiently, take place and afterwards a vesicle with 
more than one eggcell may originate. According to SCHOTTLAENDER 
(1893) there is a regular relation between the growth of the con- 
nective tissue and the germinal epithelium. A disturbance in that 
regularity is the cause of the origin of the atypical vesicles. In later 
years, owing to a closer examination, a clearer insight was obtained 


452 


into the histiogenesis of the ovary. The excellent researches of Corrr 
(Acad. Dissertation, Leiden 1898) and of von Winiwarter (Archives 
de Biologie, Tome XVII, 1900) may be mentioned here. As not all 
the embryological textbooks give the same representation of the 
development, I follow the report, which Bünrer gives in Hurtwie’s 
Handbuch (1906). 

The ovary develops like the testis, from a special part of the 
posterior coelomic wall, in which the epithelium proliferates and 
forms a ridge (the so-called Genital-leiste or genital ridge). The line 
of demarcation between the epithelium of the ridge and the embry- 
onic connective tissue is vague. The sexual cells become visible 
afterwards in the epithelium. Generally the line of demarcation 
between epithelium and mesenchyme becomes also clearer. It is 
irregular. The epithelium penetrates actually with fringe-like ingrowths 
into the mesenchyme. Those ingrowths are called “epithelial cords’ 
(ALLEN calls them sex-cords). Sexual cells occur in these epithelial 
cords by the side of undifferentiated epithelium cells. An epithelial 
proliferation arises from the cranial part of the genital ridge, growing 
soon inwardly. Corr calls this mass the “reteblastem’’. When after- 
wards the genital ridge is tied off more and more, a small body, 
hanging on the posterior coelomic wall, originates (the undifferentiated 
sexual gland). There, where it is still connected with the backwall 
of the coelome, the ‘“‘reteblastem” lies, from which a number of 
cords arise, which grow into the direction of the pronephros, as well 
as towards the centre of the sexual gland (rete cords). The sexual 
gland consists of a cortical layer, which is nothing but the epithelium 
of the genital ridge (Str. germinativum or epithelial layer) and an 
inner mesenchyme mass (Str. medullare). The germinal cords penetrate 
from the cortical layer into the Str. medullare. Sexual cells occur 
in the so-called rete-cords and especially in the germinal cords. 

From this stage of development differentiation occurs between the 
development of the male and the female sexual gland. 

The convoluted seminiferous tubules arise from the germinal cords, 
during the development of the testis, the tubules of the rete testis 
from the rete cords. 

During the development of the ovary a thin layer of connective 
tissue (primary tunica albuginea) is formed between the cortical and 
the medullary layer. This tunica albuginea lets the epithelial cords 
pass at many places. A lumen is found, specially in the rete cords, 
less often in the germinal cords. The rete cords are also connected 
with the duct of the pronephros. Processes of development occur 
here, quite homologous to those, taking place in the testis. In the 


453 


primary albuginea, germinal cords and rete-blastem, we have to see 
the homologon of the testis anlage in man. 

But in a female body, processes of development take place in the 
cortical layer besides. Proliferation of the epithelium has taken place 
here regularly, (in the mean time). The connective tissue of the 
primary albuginea penetrates into the cortical layer and the cortical 
epithelium penetrates in many places through the primary albuginea, 
so that the line of demarcation between cortical layer and medullary 
layer is again a very vague one. In consequence of the interweaving 
of the cortical layer and the connective tissue, epithelial cords and 
epithelial balls develop (not very distinct in man) from which 
finally the primary follicles arise by further proliferation of the 
connective tissue. 

A complete epithelial layer remains finally at the surface of the 
ovary (germinal epithelium). The germinal epithelium still forms in- 
growths, but they contain very seldom primordial eggs. In any case, 
they have nothing to do with the ovogenesis and with the eggtubes 
of Priiicur. The name of “Keimschläuche” is in my opinion less 
desirable. I should prefer the neutral name of “invaginations épi- 
théliales” (von Winiwarter). They generally disappear later on. The 
germinal cords and the rete cords become rudimentary. The germinal 
cords grow into epithelial cords, lying in the medullary layer. 
Consequently they are generally called “medullary cords”. A number 
of tubules are left from the rete cords. They are lined with cubical 
epithelium and lie in the hilus ovarii or even in the mesovarium. 
Some medullary cords are still connected with the rete. The rete 
itself may still be attached to the rests of the pronephros (epoophoron). 

In the ovary described here (at least in the part I could examine) 
I did not find rests of the rete, but the ingrowths of the germinal 
epithelium and the medullary cords were present. With respect to 
the ingrowths of the germinal epithelium, the following may be 
said. They are probably a regular phenomenon in the ovaries of 
human foetuses. After birth they generally seem to disappear soon. 
A few communications on these ingrowths in infant ovaries are 
not very clear (cf. ScHOTTLAENDER. Archiv für mikrosk. Anatomie. 
Bd. 41, 1893). They occur more frequently in young animals and 
they are even regularly found in adult dogs. (ScumaLtz). From a 
figure in the book of ScnmaLtz we may conclude that they are 
considerably larger in the dog’s than in the human ovary, I de- 
scribe here. 

There is a great deal of literature on the medullary cords, which 
von Winiwarrer and Bönrer cite principally. It is evident that they 


454 


are observed by many investigators in all kinds of animals during 
the development of the ovary. They generally break up into pri- 
mary follicles before birth (Coert, von Winitwartrer). Then the un- 
differentiated cells of the cords form the follicular epithelium for 
the eggeells in the cords. If the medullary cords do not break up 
into primary follicles before, they certainly do so shortly after birth. 
Bünrer could not find them in the rabbit a few days after birth, 
though Coerr and Winiwartrr described them in the embryos of 
this animal. As von Winiwartrer found them even 6 weeks after 
birth in the rabbit, it is evident, that we must take into conside- 
ration large individual differences. They seem to appear very regu- 
larly in the mature ovaries of carnivores and insectivores. SCHMALTZ 
mentions them as a regular phenomenon in the dog’s ovary and 
less regular in the cat’s. 

Harz, Bonnier, PALADINO, VAN WINIWARTER, COERT and WIcHSER 
found them in human embryos. RieLANDER (1904) found them in a 
girl of only a few weeks old. They consist of clear, protoplasmatic 
cells by a thin, structureless membrane. This agrees remarkably 
well with what I saw, but is different from what SCHMALTZ saw in 
the dog’s ovary. The latter describes the cords as groups of granular 
cells with round nuclei, which sometimes surround a small lumen. 
In newly-born infants egg-cells occur besides (BUHLER). Kerper and 
Marr, (Handbuch der Entwickelungsgeschichte d. Menschen 1911) 
mention that the medullary cords are rather often found in the first 
years of life, but only seldom in the ovary of adult women. Bünrer 
saw them in a girl of 2 years old, but not in older ovaries. The 
preparation described here is interesting, because it contains very 
clearly embryonic rests (ingrowths of germinal epithelium and 
medullary cords). The appearance of these rests is not so rare that 
it would justify this communication. I think, however, I can point 
out a connection between the presence of the medullary cords and 
the appearance of the numerous atypical vesicles. 

While studying the sections of a medullary cord in the series 
(fig. 4) one perceives that egg-cells still occur in the medullary cords 
(cf. section 4 in fig. 4 and fig. 16), but one can see at the same 
time that the medullary cord is able to swell at a certain spot and 
is transformed there into a vesicle, in which often more than one 
egg-cell occur. 

It is obvious in the series that the medullary cord, after swelling 
and developing into a vesicle, afterwards regains its former appear- 
ance. This is an indication that the medullary cord of fig. 4 is 
not one that is accidentally connected with a vesicle, but that the 


455 


vesicle (Graafian follicle) is a modified part of the medullary cord. 
In fig. 1c we have a beautiful example of a vesicle, which is 


Fig. 4. 16 sections from a series of 80 (each of 10 u). 


merely a swollen part of a medullary cord. A rest of this cord is 
still seen attached to the vesicle. Though less clear the vesicle of 
fig. 3 shows such a rest. By these observations, I am convinced that 
a great number of atypical vesicles in the preparation, described 
here, originated owing to a proliferation of the epithelium in parts 
of the medullary cords. Afterwards those cells are vacuolised and 
a vesicle is formed. The remaining cells form a cumulus oophorus 
round the egg-cells, which originally occurred in the modified part 
of the medullary cord. As there are also groups of egg-cells, as 
reproduced in fig. 2, which must be looked upon as egg-balls, it is 


456 


not possible that all the atypical vesicles arise from the medullary 
cords but that also a great number originates in such egg-balls. I 
said already before that egg-cells are found in the medullary cords 
in embryos and also in newly-born infants. The fact that the medul- 
lary cords and the egg-nests originate from the same epithelium, 
explains this phenomenon sufficiently’). But all the investigators 
have found that those cords afterwards break up into primary follicles. 

ScuMattz calls the eggcells, occurring in the medullary cords, 
strayed (verirrte) elements and supposes that they are reduced after- 
wards. In the case of dog, cat and other animals, in which the 
medullary cords remain, ScHMALTz does not mention the occurrence 
of eggcells in those cords or their metamorphosis into vesicles. 

The vesicle formation described before, I did not find mentioned 
anywhere, not even in the texi-books of pathological anatomy. 

Probably ScHorrLAENDER (Archiv. f. mikrosk. Anatomie, 1893) 
found the same thing in man, as described before, but he explains 
them differently. There is only one text-book of histology (the anti- 
quated book by Bönm and Daviporr) which, according to the 
representation of ScHOTTLAENDER, tells something more of the atypical 
vesicles than the other text-books I consulted. 

ScHOTTLAENDER distinguishes ‘‘Kiballenfollikel” and “Sehlauch- 
follikel”. He calls the follicles, reproduced in fig. 2 and 3 eggball- 
follicles and those reproduced in fig. 1e and fig. 4 “‘Schlauchfollikel”. 
According to him the origin of eggballfollicles is due to the fact 
that the eggballs are not broken up into primary follicles, owing to 
insufficient development of the connective tissue. 

He thinks that the ‘‘Schlauchfollikel” develop from the tubes of 
Priiicur made free. (In his opinion the “Pflügersche Schläuche” are 
flattened and elongated eggballs). Undoubtedly ScnorrLAENDER has 
seen in the human ovary vesicles, which were more or less modified 
cords and he described about the same phenomenon I saw. In the 
atypical follicles of fig. 4 and 1c however, I cannot see tubes of 
Pricer, made free, partly because they do not occur in man 
according to Bünrer, KerBer and Marr) and partly, because the 
investigation has taught us, that they are parts of epithelial strands, 
which undoubtedly must be looked upon as medullary cords. 

Like SCHOTTLAENDER, I should prefer to distinguish two types of 
atypical vesicles: viz. ‘“‘ballfollicles’ and ‘“cordfollicles”. Probably, 
they both originate, owing to an insufficient anlage and develop- 


1) It must nol be left unmentioned that vAN DEN BROEK (1895) thinks there is 
a connection between the medullary cords and the mesonephros and GIANNELLI 
(1915) thinks they originate in the stroma ovaril. 


457 


ment of the ovarian connective tissue; the first because the normal 
rupture of eggnests into primary follicles failed to take place, and 
the last, because no primary follicles developed from the medullary 
cords. If this be true, the two kinds have also a different phylogenetic 
significance. The cord follicles arise from that part of the ovary 
which ought to be considered as the rudiments of the male part of 
the original hermaphroditic, sexual gland (Cf. Keren and Marr, Hand- 
buch d. Entwicklungsgesch. d. Menschen, part I, fig. 8). The ball- 
follicles are developed from the female part. Though the sexual 
cells in the rudimentary male part (the medullary cords) undergo 
exactly the same changes as the eggcells and afterwards actually 
lie in the real ‘vesicles’, it is yet possible that they are different 
from those developing in the female part of the sexual gland, (though 
this is of course not necessary). 

One might imagine that they will never develop into eggcells, fit 
for fecundation, and that the vesicles, containing such cells, become 
atretical. 

The follicles in the dog have generally more than one eggcell, 
but according to ScHMALTz the larger vesicles contain as a rule only 
one eggeell, and consequently Scnmaurz says the “mehreiigen Folli- 
kel” seem to disappear. According to Bonner (Lehrb. d. Entwick- 
lungsgeschichte, 1918) in multiparous animals, two or more eggcells 
are discharged at the ovulation. Bumm (Grundrisz der Geburtshilfe, 
12% Ed. p. 292), mentioning that STRASSMANN found in a human 
ovary two eggcells in nearly all the follicles, and even in the ovary 
of a woman, who died, while giving birth to twins, writes: ‘Da 
man bei Frauen, die nach Zwillingsgeburt starben oft nur em cor- 
pus luteum nachweisen konnte, scheint die Entstehung der Zwillings- 
gravidität aus zwei Hiern eves Follikels nicht einmal ein besonders 
seltener Modus zu sein”. Also, according to Keir. and Manu, vesi- 
cles with more than one eggcell may be the cause of twin gravi- 
dity. So it is very probable, that a number of follicles, with more 
than one eggcell, come to maturity and ovulation. But I wonder, 
are these not egenest follicles ? 

The following consideration led me to this conclusion: In an 
ovary of an infant of + months old, of which [ examined a 
series of sections, I found a great number of rather large folliculi 
vesiculosi and only some rests of medullary cords. Medullary cords 
are only seldom found in the calf (Mac Leop), on the other hand 
Hutz and Kapprniu found that shortly after birth, and even a short 
time before, a large number of well-developed Graafian follicles 
occur. This led me to the supposition whether these follicles, already 


458 


present at birth, could not have originated from the medullary cords. 
Afterwards it appeared that this idea was not a new one. ScHorr- 
LAENDER already is of the opinion, that most of the Graafian folli- 
cles of infants are eggnest- or Schlauch follicles, that is to say, 
follicles I described before as ball- and cordfollicles. 

I recapitulate: Burner accepts that the Graafian follicles, present 
at birth in man, become mature and that ovulation takes place 
already in infants. On the other hand Herrz and KAppeii never 
saw any trace of ovulation in 200 ovaria of newly-born animals, 
in which they saw however many very large follicles *). I think 
the wisest is to accept (for the present) that the large Graafian follicles 
present at birth, do not develop, but are absorbed. 

According to this idea, the follicles, with an abnormal number of 
eggeells, in adults, would not be cordfollicles, but ballfollicles. And 
these would be important for the origin of plurigravidity. We ought 
to point out besides that several authors talk of ‘“Hauptei’”’ and 
“Nebenei’’. That is to say that in a follicle with more than one eggcell 
one of them were to develop well and the others were to be reduced. 

As rudimentary eggcells were often present in the atypical Graafian 
follicles observed by me, the possibility is not excluded that, owing 
to reduction of a number of eggcells from the atypical follicles, 
normal ones finally originate. 

In a few words I will answer the interesting question whether a 
formation of new eggcells takes place in the medullary cords. I did 
not find anything that points to this fact. I can only say that I 
found in the ovary of a child of 4 months, which did not show 
any pathological deviation, primordial eggs in the germinal epithelium 
and also proliferations of this epithelium in which primordial eggs 
occur. This corroborates WALDEYER’s opinion and that of other 
investigators, that the formation of primary follicles still continues 
after birth, an opinion, which according to CUNNINGHAM and ROBINSON 
is based on observations in pathological cases. 


SUMMARY. 


1. In a probably adult human ovary were found: a. ingrowths 
of the germinal epithelium, which do not contain eggcells (the name 


1) In a series of sections of the ovary of a young porpoise (Phocaena communis) 
I found only primary follicles. Clear medullary cords were absent, neither did I see 
secondary follicles. It is an open question whether 1. probably weakly developed 
medullary cords have been present, which do not give rise to vesicles. shortly 
before or after birth or 2 the follicles formed at birth, have all been reduced I 
did not find traces of that reduction. 


459 


of Keimschläuche is less preferable) 5. medullary cords which contain 
egecells and at some places swell and develop into vesicles, c. a 
great number of follicles with more than one eggcell. 

2. The atypical follicles are of twofold nature: there are ball- and 
cord follicles. 

3. In the normal development of the ovary, owing to proliferation 
of the connective tissue, the eggballs and medullary cords divide into 
primary follicles, shortly before or soon after birth. In the preparation, 
described before, the development of the connective tissue was 
apparently insufficient. 

4. It is possible that the large follicles occurring in old foetusus 
and in infants arise from the medullary cords. This is possible, 
because larger parts of the medullary cords develop into vesicles, 
but these may also originate from the primary follicles, which in 
normal circumstances originate from the medullary cords. 

It is doubtful whether the opinion of Runer (that these vesicles 
contain eggcells fit for fecundation) is right, taking into consideration 
the genesis (medullary cord is homologous with the seminiferous 
tubules) and considering all we know on this subject in animals. 
The formation of vesicles from the medullary cords in the above- 
mentioned preparation, points to a disturbance in the development 
(a process, normally taking place at a very early age, found in an adult). 

5. Normal vesicles may be developed from atypical ones by 
reduction of all the cells (Nebeneier) except one (Hauptei). 

6. It is impossible to state whether the eggball or the cord follicle, 
or both can give rise to plurigravidity. In this case one ought to 
know whether the cord follicles are actually ripening to maturity. 


Amsterdam. Histological Laboratory. 


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KONINKLIJKE AKADEMIE VAN WETENSCHAPPEN 
TE AMSTERDAM. 


PROCEEDINGS 


VOLUME XXIII 
Ne, 4. 


President: Prof. H. A. LORENTZ. 
Secretary: Prof. P. ZEEMAN. 


(Translated from: ‘Verslag van de gewone vergaderingen der Wis— en 


Natuurkundige Afdeeling, Vols, XXVIII and XXIX). 


CONTENTS. 


JAN DE VRIES: “An Involutory Transformation of the Rays of Space which is defined by two Involutory 
Homologies”, p. 462. 

JAN DE VRIES: “An Involution of Rays defined by a Congruence of REYE and an Involutory 
Homology”, p. 466. 

TH. WEEVERS: “On the Calcifuge Plants of the Inland Dunes of the Island of Goeree”. (Communicated 
by Prof. F. A. F. C. WENT), p. 475. 

R. MAGNUS and U. G. BIJLSMA: “On the Pharmacological Action of Isoamylhydrocuprein (eukupin) 
and Isoctyl hydrocuprein (vuzin)”, p. 481. 

W. STORM VAN LEEUWEN and J. ZEYDNER: “On Adsorption of Poisons by Constituents of the 
Animal Body. II. The Adsorbent Power of Rabbit’s Serum for Atropin”. (Communicated by Prof. 
R. MAGNUS), p. 486. 

L. RUTTEN: “On the Occurrence of Halimeda in Old-Miocene Coastreefs of East-Borneo”, p. 506. 

A. DE KLEYN: “On the Effect of Tonic Labyrinthine and Cervical Reflexes upon the Eye-muscles”. 
(Communicated by Prof. R. MAGNUS), p. 509. 

W.H. JULIUS and P. H. VAN CITTERT: “The General Relativity Theory and the Solar Spectrum”, p. 522. 

S. DE BOER: “On Fibrillation of the Heart. (Part. III). Ventricular Fibrillation and “Gehäufte” 
Extrasystoles of the Ventricle excited by the “Erregung” consequent on an Artificial Auricular 
Systole”. (Communicated by Prof. I. K. A. WERTHEIM SALOMONSON), p. 533. 

S. DE BOER: “On the Artificial Extra-pause of the Ventricle of the Frog’s Heart”. (Communicated 
by Prof. W. EINTHOVEN), p. 542. 

S. DE BOER: “On Artificial and Spontaneous Changes of Rhythm in the Bled Frog’s Heart”. (Com- 
municated by Prof. W. EINTHOVEN), p. 552. 

H. A. BROUWER: “Crystallization and Resorption in the Magma of the Volcano Ruang. (Sangi Islands)”. 
(Communicated by Prof. G. A. F. MOLENGRAAFF), p. 561. 

H. A. BROUWER: “Fractures and Faults near the Surface of Moving Geanticlines”. I. (Communicated 
by Prof. G. A. F. MOLENGRAAFF), p. 570. 

CLARA ZOLLIKOFER: “Ueber die tropistische Wirkung von rotem Licht auf Dunkelpflanzen von 
Avena sativa’. (Communicated by Prof. F. A. F. C. WENT), p. 577. 

J. WOLFF: “On the Theorem of Picard”. (Communicated by Prof. L. E. J. BROUWER), p. 585. 

W. VAN DER WOUDE: “On the Motion of a Fixed System”. (Communicated by Prof. J. CARDINAAL), 


p. 589. 

J. E. W. IHLE and G J. VAN OORDT: “On the larval development of Oxyuris equi (Schrank)”. (Communi- 
cated by Prof. C. PH. SLUITER), p. 603. 

I. K. A. WERTHEIM SALOMONSON: “The Limit of Sensitiveness of the String-galvanometer”. (2d Com- 
munication), p. 613. 

H. C. BURGER: “The Process of Solidification as a Problem of Conduction of Heat”. (Communicated 
by Prof. W. H. JULIUS), p. 616. 

W. STORM VAN LEEUWEN and Miss C. VAN DEN BROEKE: “A Quantitative Inquiry into the Antogonism 
Pilocarpin-Atropin on the Surviving Cat-gut”. (Communicated by Prof. R. MAGNUS), p. 628. 

B. VAN DEX POL Jr.: “Discontinuities in the Magnetisation”. (Communicated by Prof. H. A. LORENTZ), 
p. 637. 

N. H. KOLKMEIJER, J. M. BIJVOET and A. KARSSEN: “Investigation by means of X-rays of the crystal- 
structure of sodium-chlorate and sodium-bromate”. (Communicated by Prof. H. KAMERLINGH 
ONNES), p. 644. : 

H. ZWAARDEMAKER: “On the adsorption of odorous molecules to the surface of solids”, p. 654. 

H. ZWAARDEMAKER and H. ZEEHUISEN: “On Spray-electricity of Solutions of Electrolytes”, p. 658. 

W. KOSTER Dz.: “On the Theory of Hysteresis according to VOLTERRA”. (Communicated by Prof. 
W. H, JULIUS), p. 663. 


Proceedings Royal Acad. Amsterdam. Vol. XXIII. 


Mathematics. — “An Involutory Transformation of the Rays of 
Space which is defined by two Involutory Homologies.” By 
Prof. JAN DE VRIES. 


(Communicated at the meeting of February 22, 1919). 


1. In a plane « I consider the involutory homology (central colli 
neation) which has A for centre and a for axis, in a plane 9 a 
similar involution with centre B and axis 4. If P,P’ is a pair of 
the first involution, Q, Q’ a pair of the second, | associate the rays 
1= PQ and tt =P’Q. In this way arises an involution in the 
rays of space, which will be ‘investigated in what follows. 

When PQ and P’Q’ intersect in a point M, the pair Q,Q’ is the 
central projection of P,P’ out of M as centre. By means of this 
projection the pairs of the involution [«] lying on p= PP’ are 
transformed into the pairs of an involution situated on ¢= QQ’; 
the latter has one pair in common with the involution which is 
defined on q by the homology [8]. Consequently through M passes 
one pair of rays tf’. 

Along AB two rays ¢ and tf coincide. Also the straight lines 
through A to the points of 6, and through ZB to the points of a are 
double rays of the involution (¢, 2’). The rest of the double rays 
form the bilinear congruence which has a and 5 as directrices. 


2. Let ¢. be a straight line in @; each of its points can be con- 
sidered as its passage P, while its passage Q lies on the straight 
line c= af. If Cz is the point that in [@] corresponds to C=Q 
and ¢', the image of ¢, in [«l, the involution (¢, 2’) associates to t, 
all the rays ¢ of the plain pencil which has C's as vertex and lies 
in the plane (Cat). All the rays tz are therefore singular. 

When tf, revolves round C, ¢, describes a plane pencil round the 
point Cx which in the homology [¢] corresponds to C. The plane 
pencils (¢’) corresponding to ¢, belong to the sheaf [Cs]; their planes 
pass through the straight line C,Cs. 

When C describes the straight line c, Cz describes the straight 
line ez, which in [2] is associated to c. Hence to the singular rays 
t, are associated the rays / of the aval linear complex ez which 
has c; as a directrix. 


463 


Analogously the rays of the axial complex |c.| are associated to 
the singular rays tz; to each ray f2 correspond the rays ¢’ of a plane 
pencil belonging to |cz\. 

The intersection of the complexes |cal and |cg| is a bilinear con- 
gruence of which the rays are associated to the ray t=c. The 
straight line c is therefore a principal ray; indeed, we can consider 
two arbitrary points of c as passages P and Q. 

All the rays ¢ through a point P= Q=C of c are associated to 
the ray ¢’ joining P’ Q’; hence also ¢’ is a principal ray. When C 
moves along c, P’ and Q’ describe two projective ranges of points 
on c, and ca; P’Q’ describes a scroll (c)’.. The quadratic scroll (c)’ 
consists therefore of principal rays, each of which is associated to 
the rays of a star [C']. 


3. When ¢, revolves round a point 7, Cz moves along cs and 
the plane pencil with Cs as vertex of which the rays ?¢’ ent the 
line ¢', in [a] associated to tf, defines a congruence. The range of 
points which C, describes on cg, is projective to the plane pencil 
T') described by f,; when it is projected out of any point M on 
a, there will be two rays f„ which pass through the projection of 
the corresponding point Cz. Through M pass therefore two rays of 
the congruence. Any plane u contains one point Cs and also the 
passage of the corresponding ray ¢., hence one ray ¢’ of the con- 
gruence. The plane pencil (tz) is accordingly represented by a con- 
gruence (2,1). . 

As the ray 7” Cs in each of its positions belongs to the (2,1), 
(T" Cà) is one of the singular planes of the congruence. Also « is 
a singular plane, for it contains the plane pencil the vertex of which 
lies in the point of intersection C=C of c and 6. 


4. lf t describes a plane pencil (7’,t) in the plane t, its passages 
P and Q describe projective ranges on the straight lines p = er and 
q=8r. But then also the ranges of points which the homologous 
points P’ and Q’ describe on p’ and q’, are projective, so that P’ Q’ 
describes a quadratic scroll. Accordingly in the transformation (1, ¢’) 
the image of a plane pencil is in general a quadratic scroll. 

If ¢ describes a field of rays uw, the passages P and Q remain on 
the straight lines p=au and g= yu; P’ and Q’ lie in this case 
on the homologous straight lines p’ and q’. The jield of rays is 
therefore represented by a bilinear congruence. 

The ray ?¢’ in uw joins the points pp’ and qq’; it is therefore a 
double ray of the involution. 

a0* 


464 


When ¢ belongs to the sheaf [M |, the passages Pand Q form two 
projective fields. As in this case also P’ and Q’ correspond in 
projective fields, we find for the image of the sheaf a congruence (3,1), 

Of the three rays which this congruence sends through an arbitrary 
point, two are associated to each other in the involution (¢, t’), 
while the third is a double ray (§ 1). The ray ¢ which it has in 
an arbitrary plane u, is the image of the ray ¢ which the (1,1) asso- 
ciated to mu, sends through M. 

As the sheaf [M/] contains the plane pencil of which the rays inter- 
sect the straight line c, the scroll (c)* belongs to the image (3,1) of 
the sheaf. 

The sheaf [Jf] contains a plane pencil óf rays ¢ intersecting cg. 
This defines on the intersection m of the plane (Mc,) with « a range 
of points (P’). Any homologous point P’ defines with the point C 
corresponding to Cs one ray ¢,. Any plane pencil (t) with vertex C 
contains therefore one ray corresponding to a ray of the axial 
complex [ez] belonging to [M]. But also the line c belongs to the 
congruence (3,1), it being the image of the transversal through M 
to c, and cz. Consequently the images ¢, of the rays of the plane 
pencil in (Mes) envelop a conic. From this appears that « and B 
belong to the singular planes of the congruence (8,1); in other 
words, « and 8 are osculating planes of the twisted cubics of which 
the axes (intersections of two osculating planes) form the (3,1). 


5. The rays ¢ resting on the straight lines d, and d, and also 
on cg, form a quadratic scroll; their passages / lie therefore on a 
conic J?. The corresponding points 7?’ form on a conic d’* a range 
of points projective to the range of the points C,, hence also to the 
range of the points C. Consequently the ray ¢’ envelops a curve of 
the third class. Through a point N/ of « pass four lines ?¢’, the 
images of rays ¢ of the bilinear congruence with directrices d,, d,, 
namely three rays t, and besides the ray associated to the ray which 
the point MN sends to the (1, 1). 

The bilinear congruence representing the field of rays (ul, has 
two rays in common with the (1,1) mentioned above; the image 
of the latter has therefore two rays in the plane u. Consequently 
a bilinear congruence is represented by a congruence (4, 2). 

The latter has « and 8 as singular planes of the third class. 

The rays sent by the (4,2) through a point M/, are the images 
of the rays which the (1,1) has in common with the image (3, 1) 
of the sheaf {M7}. 

The images of two bilinear congruences have among others the 


465 


scroll (c)* in common; for any sheaf [|C] furnishes one ray for each of 
the two (1, 1). 


6. The aval complex with axis d is transformed by the trans- 
formation (tt) into a quadratic complex {t’}?; indeed, to the two 
rays of the scroll (#)* representing the plane pencil (¢’), correspond 
two rays of the image-complex lying in the plane pencil (¢’). 

As [d] singles out one ray out of each plane pencil of singular 
rays, (dj? contains the two fields of rays [a] and [8]. Two congru- 
ences {4} have besides those two congruences (0,1) one more con- 
gruence (4,2) in common; from this appears again that a bilinear 
congruence is transformed into a (4, 2). 

The image (3,1) of a sheaf [|M] has four rays in common with 
the image (1,1) of the field (u). One of them belongs to the scroll 
(c)? and is associated to any ray that the corresponding sheaf { C'} has in 
common with [J/| and [u]. Another coincides with c; for [JZ] and 
lu] send each one ray to c, and ca. 

The straight line through J/ and the point Cy, in u belongs to a 
plane pencil that is associated to a definite ray ..; as also contains 
a ray of this plane pencil, the image-congruences (3,1) and (1,1) 
have this ray (¢,)in common. Analogously they have a ray tin common. 

The images of two fields of rays |u| and [u*] have two rays in 
common. One of them is the image of the straight line uu*, the 
other is the line c; this is associated to the two transversals of c, _ 
and cg in w and in u*. 

The image (1,1) of the field [u| has six rays in common with 
the image (4, 2) of a bilinear congruence with directrices d,, d,. To 
them belongs the ray of the scroll (c)? associated to the sheaf of 
which the vertex lies in the point (c,). They have twice the line c 
in common, for two transversals of cz and ca rest also on d, and d,, 
while one straight line of u rests on c,, cg. The transversal through 
the point (wcs) to d,,d, belongs to a plane pencil which has also 
one ray in wu; to both of them corresponds the same line ¢,. Analo- 
-gously the image-congruences have a straight line és in common. 
The sixth common ray is the image of the transversal of d, and d, in u. 


Mathematics. — “An Involution of Rays defined by a Congruence 
of Rue and an Involutory Homology’. By Prof. Jan pe Vrtus. 


(Communicated at the meeting of February 22, 1919). 


1. In the plane « an involutory homology [@] is given having A 
for centre, a for axis. Let further be given the bilinear congruence 
[B°] of twisted cubies which pass through the five principal points 
By (k=1, 2, 3,4, 5). An arbitrary straight line ¢ is a bisecant of one 
8; to its intersection P with @ a point P’ in [a] is associated; the 
bisecant ¢’ of B* passing through P’ be associated to ¢; in this way 
an involution (¢, ¢’) arises in the rays of space. All straight lines through 
the point A or through a point A* of the axis a are evidently double 
rays of the involution. 

Any straight line s, through B, is singular for the congruence as 
it is a bisecant of all 8° lying on the quadratic cone (,)? with 
vertex B, which can be passed through the other four points B 
and the straight line s,. The line s, is also singular for (¢, ¢’); for, 
to s,=B,P are associated all the bisecants ¢’ through P’ to the 
oo: curves B? of (B). These curves define an involution /’ on the 
intersection «? of (B,)* with a; the straight lines carrying the pairs 
of this Z* envelop a conic; in « lie therefore two of the rays f, 
associated to s,. Consequently to the singular ray s, the rays of a 
cone (P')? are associated. 

The cone (B) contains the four degenerate figures consisting of 
a straight line B, 5; and a conic 8? in the plane Bin of the. points 
B,, Bn, Bn. It does not contain, however, a figure with 6,,= 5,B, 
as a component; therefore the cone (P’)? can only cut 6,, in B, 
and B,. The figure consisting of 6,, and a conic in the plane 8,,,, 
sends a bisecant through P’, which cuts 6,, outside 5, and B,; 
hence the cone (P’)? does not pass through #,, but through the 
other four points Bx. 

If we make the passage P of s, describe the conic a’, P’ describes 
likewise a conic, @?, which cuts «? in two points on a. The cone 
(P’)? belonging to s,, describes in this case a system with base 
points B,, B,, B,, B,, the vertices of which lie on a’. The genera- 
trices ¢’ of these cones form a congruence of rays. 


467 


2. The rays ¢’ associated to the rays s, of the sheaf [B,|, form 
a complex. In order to be able to determine the order of this com- 
plex, I consider a plane pencil of rays ¢’ with vertex 7, of which 
the plane rt has with the plane « the straight line p in common. 
The 6? which has one of these rays t/ as a bisecant, is projected 
out of B, in the conic «°; this conic defines on the straight line p 
homologous with p’, two points P* which may be associated to the 
passage /” of ¢’ and ‘also to the point P homologous with P’. In- 
versely a point P* of p defines by means of the straight line 5, P* 
a cone (B), hence a conic a’, and the homologous conic «°° 
yields on p’ two points /”; the corresponding points P may be 
associated to P*. As P* coincides four times with P, the plane 
pencil (7, rt) contains four rays /’, each associated to a singular ray s,. 

To each of the five sheaves [B] corresponds therefore a complex of 
the fourth order. The complex curve in the plane u has the passage 
p’ =au as a double tangent. For the curve 8° which has p’ as a 
chord, is projected out of B, in a conic a’, and the intersections of 
a’ with the line p define two rays s,, both associated to p. 

To a singular ray s,= 5,P’ a cone (P*) of rays ¢ is associated, 
which among others passes through B, and accordingly has the 
generatrix B,P in common with the cone (B,)’ defined by s,= B, P. 
Any ray s, belongs therefore to the complex {?’}*, corresponding to 
the sheaf [B,]. This complex has in other words the four principal 
points br (k F 1). 

If P’ lies on the intersection p's, Of Bes; With @, hence P on 
the homologous straight line p,,,; to the singular ray B,P the plane 
pencil (7, 8,,,) is associated, in this case a component of the cone 
(P’)?. The planes Bx, (4, l,m F1) are therefore principal planes of 
the complex {4}. 

Also a is a principal plane. For the ray fx in a is a bisecant of 
a B? and this is projected out of B, into an «° cutting the homo- 
logous ray f, in two points P for which the point P’ lies on ?’,. 

That B, is not a principal point appears in this way. The cones 
(B) form a pencil and cut therefore « in a pencil (a’). This is 
projective with the homologous pencil («/?) and the two pencils 
produce a figure of tbe fourth order. As two corresponding conics 
intersect each other on a, this figure consists of the straight line u 
and a cubic that is invariant with regard to the homology [e]. 
Any two points P, P’ of this curve furnish two associated singular 
rays t,t’, while the points of the axis a furnish a plane pencil of 
double rays through B,. The complex-cone of B, consists therefore 
of a plane pencil.and a cubical cone. 


468 


3. Any straight line of the plane 9, is a singular bisecant for 
the congruence (98°, but at the same time a singular ray for (t,t). 
Indeed, 8,,, contains a pencil of conics #6’, each forming with the 
straight line 6,, a figure belonging to [8°]. The straight line ¢ of 
8,,, is a bisecant of each of these figures, hence it is associated to 
the bisecants £ which they send through the point P/ associated to 
the passage P of t. The plane pencils (¢’) in this way associated to 
the rays ¢ of the field [f,,,|, form evidently a bilinear congruence 
of which 6,, and the straight line p’,,, (homologous with the passage 
Piss Of Boss) are the directrices. But also the rays ¢ of this congru- 
ence are singular, for to a ray with passage P’ are associated the 
rays of a plane pencil with vertex in P. 

There are therefore ten fields of singular rays, each belonging to 
a bilinear congruence of singular rays. 


4. Any ray t, of a is singular; for any of its points may be 
considered as its passage, consequently also any point of ¢, as the 
passage P’ of a ray tf; this ray is a bisecant of the curve # cutting 
i, twice. For this reason the rays ¢ of the scroll (t)*, the locus of 
the bisecants of the §*® resting on the straight line fx, are associated 
to the singular ray 4 

When ¢, passes through A, hence coincides with #,, (t’)* degene- 
rates into the two quadratic cones which project the corresponding 
curve B® out of its intersections with ¢,. 

The scrolls (¢')* form a complex. In order to determine its order 
I consider the surface ® produced by the curves f* having the 
rays { of a plane pencil (7, r) as bisecants. To it belong ten figures, 
each composed of a straight line 6;; and a conic cutting it. The 
intersection of ® with g8,,, consists therefore of the straight lines 
b,., Dis Das and the conie connected with 6,,; consequently ® is a 
surface of the fifth order. 

The locus of the pairs of points defined by the curves p* of ® 
on the rays f, is evidently a curve tf with a double point 7. 
The plane rt has with ®° the curve rt‘ and also a straight line / 
in common; hence ®° is at the same time the locus of the curves 
8° intersecting the line /. 

Now let (J/,u) be an arbitrary plane pencil and u the curve 
analogous to t*, therefore the locus of the pairs of points in which 
the rays m of (M, u) are twice intersected by curves 8°. The curve 
u°, along which the surface ®° is cut by u, has with the curve u' 
the passages of the ten straight lines 6;; in common; but every ray 
m resting on one of these straight lines, cuts u‘ and u* in different 


469 


points, because bz, is connected to different conics by the two plane 
pencils (¢) and (m). The other ten points of intersection of the two 
curves lie in pairs collinear with Ms; the plane pencil (m) contains 
therefore five bisecants of curves 83° lying on ®*. In other words, 
the bisecants of the curves a* which have each a bisecant in common 
with a given plane pencil, form a complex of the fifth order. 

Now let p’ be the passage of the plane rt, p the homologous straight 
line. To every point P of p corresponds a point P/ of p’. The curve 
8° having the ray ¢ = TP’ as a chord, defines in « three bisecants 
t,, which cut p in three points P*. The complex {z}* of the bisecants 
of the curves 3° which have the rays ¢’ of the plane pencil (7) 
as chords, sends five straight lines wv through the point P*; to 
this point correspond consequently five rays ¢’ and therefore five 
points P. Whenever a point P* coincides with a bomologous point 
P, P carries a ray ts to which a ray through P’ is connected. 
The singular rays of the field [t,| are, accordingly, represented by the 
rays of a complex of the eighth order. 

The cone ( P’)? associated (§ 1) to the ray s; = Bz P, contains two 
rays t, Hach ray of the sheaf {| 4;| can, therefore, be considered 
_twice as a ray of the complex {¢’}*. Consequently this complex has 
the points B, as double principal points. 

Each straight line ¢’ in a is associated to two rays t,. For, if t’ is a 
chord Q'Q" of a B® cutting « besides in Q’, it appears that ¢’ 
is associated to each of the two rays Q'Q", QQ". The line ¢’, homo- 
logous with QQ'=t, in [ea], cuts ¢’ in a point P’ of which the 
homologous point P lies on Q'Q". Hence a is a double cardinal 
plane of the complex |}. 


5. There are still other sengular rays. The curve g° passing through 
a point /”/ of a, sends a bisecant s through the homologous point 
P. To the ray s are associated all the rays # of the quadratic cone 
which projects 83° out of P/. The rays s form a congruence, the 
corresponding rays ¢’ a complex. 

Any ray ¢’ of the plane pencil (7,1) is a chord of a 8°, and the 
pairs of points of intersection form the curve rf considered before. 
This curve defines on the straight line et four points P’; the plane 
pencil contains therefore four rays of the complex {t’}. The singular 
rays s are accordingly associated to the rays of a complex of the 
fourth order. 

This complex has the points Br as principal points and the plane 
a as a principal plane; any line ¢, is a generatrix of two cones 
(t°), and belongs therefore twice to the complex. 


470 


The congruence [s| has singular points of the second order in A 
and in every point A* of the straight line a. The generatrices of 
each of these cones are associated to each other and at the same 
time they are donble rays of the involution; these cones belong 
apparently also to the complex {/’}*. The generatrices of the cones 
the vertices of which lie on a, are combined to la congruence 
(4,2). 

Each ray ¢, represents two rays s; indeed, if P’ and P’, are the 
points that ¢ has in common with the curve 8? of which ¢, is a 
chord, t« is a singular ray for each of the homologous points Pand 
P,. If a ray s is to lie in @ without passing through A, it must 
contain the points P" and P" where the 8? through P’ intersects 
the plane. If P’ describes the ray m through A, p’ = P" P" revolves 
round a point M; for the groups (P’, P", P'’) form polar triangles 
with regard to a definite conic. The plane pencil (p’) is apparently 
projective with the range of points (?) on m; therefore p’ passes 
twice through the corresponding point P and is then a ray s. Con- 
sequently « is a singular plane of the fourth order for the congru- 
ence [s|. As a point of « carries besides one ray s that does not lie 
in a, the sheaf-degree (order) of s is equal to five. ; 

In order to be able to determine the field-degree (the class) of [s], 
I assume a plane u. Let P be a point of the straight line p= au; 
the curves 28° cutting the rays ¢ of the plane pencil (Pu) twice, 
form the surface ®° considered in $ 4, and therefore define on the 
line p' five points Q’, consequently on p the homologous points Q 
which may be associated to P. Inversely a point Q yields a point 
Q’ and the curve #* through Q’ cuts u in three points, determines 
therefore in u three chords ¢ and consequently three points P. When- 
ever Q coincides with P, there passes through P a singular ray s, 
the corresponding cone (¢')? of which has its vertex in the homologous 
point P'. The field-degree amounts therefore to eight. The singular 
rays s form a congruence (5,8). 

The points B, are singular for [s]. This appears when we consi- 
der the rays s belonging to a plane pencil (Bz, u); let p be the 
intersection of u with «, P a point of p. The curves 9’ intersecting 
B P, are projected out of A, into the conic «@ and on p’ this conic 
defines two points Q’, which may be associated to P’. Inversely 
the 8° through Q’ intersects the plane u in two more points, defines 
accordingly two points P, and through them also two points P’. 
As apparently Q’ coincides four times with P’, the plane pencil 
(Br, u) contains four rays s. Bx is, therefore, a singular point of the 
fourth order for the congruence [s]. 


471 


6. The ten straight lines bj, = Br Bi are principal rays for the 
involution (¢, ¢’). For bp, is a bisecant of all the curves 6’, hence it 
is associated to all the bisecants through the point P’7/ which is 
homologous with the passage Py of buu. 

The sheaf | Py] is therefore associated to the principal ray bx. 

A plane pencil (7) contains ten rays ¢, each resting on astraight 
line }d,; and-on a conic Bom connected to it. The corresponding 
ray U’ rests also on dy. 

Further four rays t belong to the complex {é*, which in the 
involution (¢,¢') is associated to the sheaf [27 |. Consequently the image 
of the plane pencil (4 has quadruple points in Bz and in Bj, so 
that nine rays ¢’ rest on bj. A plane pencil is therefore transformed 
into a scroll of the ninth order. The plane pencil contains eight rays 
of the complex {t’}*; in @ lie therefore eight rays ¢, of the ruled 
surface (£)°. Besides « contains the straight line p’, homologous with 
the passage p of the plane rt, and a directrix of the ruled surface. 


7. A sheaf with vertex M is represented by a congruence of rays 
[¢’]. Let N be an arbitrary point, u the bisecant through AN to the 
curve 8? which cuts the straight line MP twice. The passage Q 
of w corresponds in a birational correspondence to the point P’ 
which through the homology is associated to P. 

When Q moves along a straight line q, so that u describes a 
plane pencil, the bisecants ¢ (§ 4) of the corresponding curves 8° 
form a complex {f}°. The complex-cone of M intersects a along a 
curve «? and the homologous curve a’® contains the points P’ asso- 
ciated to the points Q of q. The correspondence between Q and P’ 
is, therefore, of the fifth order; consequently Q coincides seven times 
with P’. Through MN pass therefore seven rays ¢t’ of the image of 
the sheaf [M |. 

The sheaf has with its image the ray MA and the rays of the plane 
pencil (M‚,a) in common; hence M is a singular point of the image. 

Let u be a plane intersecting « along the line p’. The curves ? 
which have the rays ¢’ of the plane pencil (P’‚u) as bisecants, have 
five of their bisecants ¢ in the plane (Mp) and these define on p 
five points Q, which may be associated to the point P. Inversely 
a point Q yields three rays ¢’ in wu, which are bisecants of the p* 
having MQ as a chord. To Q three points P’, consequently also 
three points P, are associated. Whenever a point Q coincides with 
a corresponding point P, the ray ¢’ associated to t= MQ, lies in 
u; the field-degree of the congruence [¢’] amounts therefore to eight. 

The image of a sheaf is accordingly a congruence (7,8). 


472 


The sheaf contains a transversal of the straight lines bj, and Paas 
the congruence (7,8) has therefore in each of the ten planes 8u & 
plane pencil. These planes are accordingly singular for (7,8). 

The complex {4*, associated to the sheaf | Bj] has with [M] a 
cone (£)* in common; to this corresponds a cone (s;)‘; for to the 
intersection «* of a and the former cone, in the homology [ea] a 
curve «’* is associated and this curve contains the passages of the 
corresponding rays sj. Hence the congruence (7,8) has singular points 
of the fourth order in the jive points B. 

Through .W pass five singular rays s; accordingly (7,8) has five 
singular points of the second order in the plane «. 

The plane « is singular for the congruence (7,8), for the complex 
{t’}, conjugated to the field of rays [te], has a cone (¢’)* in common 
with [Af]. If a ray ¢ revolves round P, the bisecants u of the 
curves 6? which have the rays ¢, as chords, form a complex fu}®. 
Through MZ passes one bisecant u of the 4* corresponding to ¢,; its 
passage Q may be joined to P’ and the straight line P’Q—= q may 
be associated to the ray ¢’, homologous with ¢,. Inversely the plane 
(Mq) contains five chords wu, belonging to five different curves g*, 
each defining a ray ¢, through P, so that five rays ¢’, are associated 
to the ray gq. Through M pass therefore siv rays u, each correspond- 
ing in the involution (¢¢’) to a ray ¢t, of the plane pencil (Pa). 
Consequently «@ is a singular plane of the sixth order for the con- 
gruence (7,8). 

This congruence contains the ten rays by; for these correspond 
to the rays MP’). 


8. Now I shall consider the image of a jield of rays. The plane 
u contains ($ 7) eight rays ¢ associated to eight rays ¢’ through a 
point /. The image of the field of rays [u] has therefore the sheaf- 
degree eight. 

Let p be an arbitrary plane, P’ the intersection of p with the 
straight line p’ homologous to the straight line p — «u. The complex 
of the chords of the curves 8° which have each a ray of the plane 
pencil (P,u) as a bisecant, has five rays ¢’ in the plane pencil (P’,¢)- 
The plane p contains accordingly five rays of the image of [u]. 

Hence a field of rays is represented by a congruence (8, 5). 

The points Bx are singular for this (8,5). For the plane pencil 
(P, u) contains four rays of the complex {t¢'},‘; two of them coincide 
with p, the other two correspond to the ray BP’. The plane pencil 
(Bj, p') belongs therefore twice to (8, 5). 

The field [u] contains one ray of the field [,,,] and one ray of 


473 


the congruence (1,1) having 6,, and p’,,, as directrices. Hence the 
congruence (8,5) contains ten plane pencils (P, Brun) and ten plane 
pencils in planes through the straight lines bs. 

The plane pencil (P,u) contains eight rays of the complex {4}; 
the corresponding rays ¢, passing through the point P’, the rays 
in « belonging to (8,5) form a system with index eight. a is there- 
fore a singular plane of the eighth order. 


9. Let A’ be the image of a bilinear congruence 4. The image 
of the sheaf [|M] has 15 rays in common with 4, hence [J/] contains 
15 rays of dA’. Analogously a field [|u|] appears to contain 13 rays 
af A’. 

The image of a congruence (1,1) is therefore a congruence (15,13). 

This congruence contains the ten principal rays bz/, for the point 
P’;; has one ray in the (1,1). 

The complex {¢},* associated to Bx, has a scroll of the eighth order 
in common with a (1,1). To its intersection with a corresponds in 
[a] a curve a°, containing the passages of the rays sp in the image 
of the (1,1). The congruence (15,13) has, therefore, the points Bz as 
singular points of the order eight. 

I now consider the plane pencil (P?,«@) and the homologous plane 
pencil (P’, a). The curve 8° which has a ray ¢, of the former as a 
chord, has four bisecants « in the congruence (1,1); their passages 
Q joined to 7?” furnish four rays g, whieh may be associated to the 
ray fe A ray q separates from (1,1) a quadratic seroll and this 
_seroll has ten rays « in common with the complex {w}> belonging 
to the plane pencil (P, 4) (§ 4). To q are therefore associated ten 
rays tz; whenever two associated rays q and f„ coincide, there 
rests on ¢, a chord of a 8° that meets f, twice. From this follows 
that the plane « is a singular plane of the order fourteen for the 
congruence (15,13). 

To the ray which a (1,1) has in the plane ~,,,, corresponds a 
plane pencil, the plane of which passes through 6,,; to each of the 
two rays of (1,1) resting on 6,, and p’,,,, a plane pencil in the 
plane #8,,, is associated. The congruence (15,13) contains consequently 
twenty plane pencils in the planes Bxim and ten plane pencils in planes 
through the straight lines bs. 


10. The image of an axial complex with directrix d is a complea 
of the ninth order. For d intersects nine rays of the scroll (£)° which 
is the image of a plane pencil. 

Two generatrices of the cone (P/)' associated to a ray sp, cut 


474 


the directrix d; consequently Bj is a double principal point of the 
complex }7'}’. 

The plane pencil which is the image of a ray in §,,,, bas one 
ray in the axial complex; hence the complex {¢'}’ contains the ten 
fields |Biim|. It contains also the ten bilinear congruences with the 
directrices 641, P'mnr- 

Of the scroll (£)* representing a ray ¢,, four rays rest on d; the 
complex {£}’ contains therefore the field {t,|, which has to be 
counted four times. 

The quadratic cone associated to a singular ray s (§ 5), has two 
generatrices in common with the axial complex; hence the con- 
gruence (5,8) of the rays s belongs twice to {7'}’. 


Botany. — “On the Caleifuge Plants of the Inland Dunes of the 
Island of Goeree”. By Dr. Tu. Weevers. (Communicated by 
Prof. Went). 


(Communicated at the meeting of May 29, 1920). 


The broom, Sarothamnus vulgaris Wimm, occurs in the island of 
Goeree within a sharply defined area. This fact first induced me 
to examine the flora of the grounds where the broom occurs and 
where it does not; afterwards I was led to study that flora in con- 
nection with the nature of the soil. 

This research concerned especially the interior of the island, known 
as the “Oude Land van Diepenhorst’, which is bounded by the 
Western-Dunes in the West and the Central- and Eastern-Dunes in 
the Hast, the latter bordering on the young Sea-dnnes; the old center 
being for the rest surrounded by polders. Lori *) had already looked 
upon this center as the old inland-dunes; the small calcium-content 
of the sandy soil, less than 0.07 °/, CaCO, ’) lends support to this 
~ conception. 

Yet these inland-dunes cannot be put on a par with the inland- 
dunes to be found north of the Meuse. From data derived from 
borings, performed’) with a view to the construction of a tramway 
and to the watersupply of the island, it appeared to me that under 
the layers of sand are always found bands of bog-, and clay-soil, 
whose upper edge lies 1 m. below A. P. (Amsterdam water-mark), 
the lower edge from 2 to 5 m. below it, approximately at the same 
level where these layers are found also in the other parts of the 
island of Goeree and Overflakkee and likewise in Zeeland. So the 
inland dunes of Goeree are overlying peat-, and clay-layers of the 
old “haff”, as in Belgium, and not the old “Schoorwal”. But the 
Goeree inland-dunes are poor in calcium unlike most of the Belgian 
dunes, which are calcium-rich. Consequently their flora bears a marked 
resemblance to that of the few calcium-poor districts found in Zee- 
land and in Belgium, and termed by Massart *), in agreement with 
Ruror ®), the ‘dunes internes’”’ and “sable a Cardium’”’. 

DJ. Lorié, Arch. du Musée Teyler. Vol. III. 1892. 

2) Cf. Jeswier, Entwicklungsgeschichte der Flora der holländischen Diinen. 

5) These data were procured through the kindness of Dr. J. T. Sreenuuis. 

t) J. Massart, Essai de geographie bot. des districts litt. et alluv. de la Belgique 
Recueil Inst. bot. L. Errera, T. VII. 1908. 

5) A. Rurot, Bulletin de la société de géologie, paleontologie et d’hydrologie 1906. 


476 


Still, the formation in Goeree differs from that assumed by Massart ; 
archeological findings below the layers of sand proved that they 
must have been deposited there later than + 200 A. D.'), and 
probably they are an aeolian formation from more westerly and 
lixiviated older dunes, in the manner advocated by Jrswrer (I.c.) with 
regard to the grounds north of the Meuse. It appears, indeed, that 
their calcium-content does not increase even down to a rather great 
depth (+ 1 m.); and amounts in the Oude Land van Diepenhorst 
only to 0,018°/, CaCO,. I will not enlarge upon the matter, but 
will only add that the calcium-content in the Oude Land van Die- 
penhorst, is lowest (less than, 0,02 °/,)*); in the Western-, and the 
Central-dunes slightly higher (+ 0,1 °/,), while towards the coast it 
rises to + 1°/,. Now, while the grounds of the inland-dunes con- 
sist entirely of sand, and possess a psammitic flora in the sense of 
Drnde, the vegetation of the meadows in the Land van Diepenhorst 
is of quite a different nature from that of the ‘“Meent’’-meadows in 
the Western- and the Central-dunes. In the former we find every- 
where Sarothamnus vulgaris and occasionally Erica tetralix and Cal- 
luna vulgaris; in the latter all three are absent. This difference 
cannot be referred to the meadows being fed down, or to more or 
less manuring by the grazing cattle, these factors being the same 
for either territory; so we may readily correlate this difference in 
flora with the greater or smaller calcium-content of the soil, since 
the broom as well as leather and erica are considered to be calcifuge. 

The problem of calcifuge and calcicole plants is an intricate one 
and not by far solved; consequently it has given rise to an 
extensive literature, of which only the principal points can be dealt 
with in the present paper. In our case, however, there is the ad- 
vantage, that some factors, which in other cases are of vital im- 
portance, may be readily eliminated here. This refers especially to 
the physical factors, such as structure of the soil, size of the grains 
and in this connection the aqueousness of the soil, and the sensiti- 
vity to the sun’s rays. 

Researches by Tuurman’), and afterwards by Gr. Kraus*) have 
pointed out the great significance of these factors, especially. for 


1) | feel greatly indebted to Prof. Horwerpa for imparting to me the age of 
the objects found. 

9) Our method of determining Ca was the same as that used by Jeswiet (Lc). 
We confined ourselves to determining only the content of the Ca-compounds that 
could easily be attacked, i.e of those which are of interest for plant-food. 

3) THuRMAN, Essai de phytostatique appliqué à la chaîne du Jura. 1849. 

4) Gr. Kraus, Boden und Klima auf kleinstem Raum. 1911. 


477 


mountainous regions. They afford an explanation why a plant 
shuns calcium in one place and tolerates it in another; a sort of 
rivalry between allied species may also come into play here, as 
Náerrr has demonstrated with the familiar instance of Achillea 
atrata and Achillea moschata. 

In Goeree, however, none of these factors exist. The soil of both 
territories is sand, the grains being approximately of the same size, 
and the humus-content is low; in the sunlight the temperature does 
not differ materially in corresponding places; yet the drier grounds 
of the Land van Diepenhorst contain the plants under consideration, 
those of the Western-, and Central-dunes do not. Nor can the con- 
centration of the groundwater be the conclusive factor *), although 
generally speaking Gora’s classification, which lays special stress 
upon the contrasting characters of the colloidal and crystalloidal 
constituents of the soil, has many advantages. The xerophytic broom 
grows on the dry grounds of the Land van Diepenhorst; on the 
other hand it shuns the dry, as well as the moister sandy grounds 
of the Central dunes. In the former the concentration of the ground- 
water might be somewhat higher, and more stable on account of 
the slightly increased caleium-content, in the latter this is decidedly 
not the case, but both are pergeloid in Gora’s classification. Nevertheless 
it is obvious that the edaphic factors exert some influence here. 

The plant is capable of taking up considerable quanta even from 
a soil that contains very little calcium, thus the calcifuge Castanea 
vesca has on diluvial soil (calcium-content + 0.3 °/,) 45 °/, calcium 
in the ashes of the leaves, in those of the wood as much as 73°/,. 

The caleium-content of calcifuge plants is, however, mostly very 
low as may be demonstrated in a simple way with Motiscn’s *) 
reaction; formation of the double-salt Gaylussite by means of a 
10 °/, Na,CO,-solution. 

Calcifuge plants of the peat-moor, such as Drosera spec., Orchis 
maculata, Narthecium ossifragum, Gentiana pneumonanthe, Pingui- 
cula vulgaris, Molinia coerulea, Sphagnum spec. then yield a very 
faint reaction, Sarothamnus vulgaris likewise. From quantitative deter- 
minations [ gathered that the ash-content of this latter plant amounted 
to +16°/, of the dry weight, the calcium-content of the ashes 
=0.0°/,, that is 0.5°/,, of the dry weight. We see, then, that, 
though the ash-content of a plant and also the amount of calcium 
in the ash varies largely with the nature of the soil on which it 


1) G. Gora. Saggi di una teoria osmotica del edafismo. Ann. di Bot. VIII 1918. 


2) H. Morrscr, Beiträge zur Mikrochemie der Pflanze. Ber. d. Bot. Ges. 1916. 
31 


Proceedings Royal Acad. Amsterdam. Vol. XXIII. 


478 


erows'), this constitutes a striking contrast with the Trifolium pra- 
tense occurring in the Central dunes, which has a calcium-content 
of 2.5°/, of the dry weight, i.e. 50 times the value found for Saro- 
thamnus. Next I wish to call attention to the fact that in many 
cases CaCO, exerts a noxious influence on the calcifuge plants, e.g. 
the Castanea vesca. This is a familiar fact with respect to peat-moor 
plants, to such mycotrophes as Calluna and Erica, and is perhaps 
owing to the influence of calcium-salts on the mycorrhiza. Since 
our knowledge of the entire metabolism of these mycotrophes is still 
insufficient, I prefer to leave it out of consideration here and will 
discuss the deleterious effect on Sarothamnus*). Experiments by 
Massart (l.c.) undertaken at Coxyde showed the noxiousness of the 
calcium-rich soil of the recent dunes to this plant, but the nature 
of the bad effect could not be well made out. For Sphagnum spec, 
the case is better. Experiments by Paur*) evidenced that solutions 
of as little as 0.01—-0.03°/, CaCO, are deleterious to these plants, 
which are much less sensitive to CaSO,-solutions. In that case it 
can hardly be supposed that the noxious influence of the Ca-ions, 
as such, play the principal part. *) 

This leads us -gradatim to consideration of the reaction of the 
nutrient-medium, which in the latter two cases differs with an 
addition of CaCO, or of CaSQO,. 

When 150 germs of dry sandy soil was shaken up with 50 ec. 
of distilled water and the fluid was filtered off after 24 hrs., the 
filtrate presented, in the case of the sandy soil of the sea-dunes 
(caleium-content 2 or 3°/,) a distinct alkaline reaction with lacmoid-, 
and rosolic acid solution, also a weaker alkaline reaction in the case 
of the soil of the Central- and the western dunes (calcium-content 
0,1—1,0°/). On the contrary tbe reaction was neutral or faintly 
acid in samples of sand from the “Oude Land van Diepenhorst” (cal- 
cium-content 0,01—0,02 °/,), where Sarothammus, Calluna and Erica 
occur. Would it then be possible perhaps to find a clue to the problem 
in this direction? Pavr (le) carried out an inquiry into the occur- 
rence of Sphagnum in the peat-moors of Bavaria, which also pointed 
in this direction; some cases of plant-diseases did so too *). At any 


1) In weak specimens of the calcifuge Castanea vesca, grown on a soil richer 
in calcium, a higher calcium-content is found than in the healthy specimens of a 
calcium-poor soil. 

2) Influence of the calcium-richer soil on the root-tubercles, in other words on 
the N-intake is not likely. On the calcium-richer soil the other Papilionacea, also 
have tubercles; likewise there is N-manuring by the grazing cattle in both cases. 

3) Paur, Mitt, kgf. bayr. Moorkulturanstalt, 1908. 

4) The mostly calcifuge lupin is sensitive to CaSQ,. 

5) e.g. the oat-disease of the “Veenkolonie” and the Hooghalen-disease of rye. 


479 


rate it is evident that a difference in reaction of the groundwater 
yields quite another nutrient medium; by more calcium the decom- 
posing effect of the acids is abolished. As is obvious, it is the roots 
that undergo the deleterious influence of additional calcium, which 
is proved by the fact that the Castanea vesca, when grafted upon 
the oak, also thrives in calcium-richer soils. 

However, although this influence of the reaction of the ground- 
water is of great moment, it cannot be the only causative factor. 
This is supported by the cases in which two kinds of soil exhibit 
a similar reaction, and nevertheless possess distinctly differing vege- 
tation with identical physical factors but non-identical calcium-content. 
Cases in point are. the inland-dunes, such as the Central-dunes of 
Goeree on the one side and the sea-dunes on the other. In Goeree 
Orchis morio, Seleranthus perennis and others shun the seadunes 
(calcium-content from 2 to 3°/,). They are however indigenous to 
the Central-dunes (calcium-content 0,1—1 °/,). It is also supported 
by the fact that lupin, which is mostly calcifuge, undergoes the 
noxious influence of CaSO,-manure. In conclusion I, therefore, 
point to the antagonism of the bivalent Ca-ions and the univalent 
Potassium-, and Sodium-ions. Zoological researches by Lop’) and 
afterwards botanical experiments by van OsrTERHOUT*®) (e.g. with 
plantroots) have shown that the salts of the univalent as well as 
those of the bivalent metals, taken separately, have a toxic effect, 
which, however, is neutralised by a definite concentration of the 
others. 

Their effect on the permeability of the protoplasm is such that in 
Na-salts the permeability increases till death approaches; that in Ca-salts 
alone it first decreases in order to increase again after a certain 
minimum has been reached, till ultimately death sets in also, and 
permeability is constant, exosmosis complete *). On the other hand 
solutions of Na-, and Ca-salts in a certain ratio (e.g. 95,24 NaCl 
and 4,76 CaCl,) in experiments with Laminaria‘) do not affect the 
normal permeability at all, and render normal growth possible, which 
led van Ostpruovt (Le.) to hypothetical speculations about the action 
on the protoplasm, which cannot be gone into here. 

It is a fact, however, that excess of either salt (in casu Ca) can 


1) LoeB, Am. Journ. Physiology. Vol. 3. 1900. 

2) W. J. v. OsteRHOUT, Jahrb. f. Wiss. Botanik Bd. XLVI, 1908, On the 
importance of physiologically balanced solutions for plants. Botan. Gazette 44. 1907. 

3) TH. Weevers, Betrachtungen und Untersuchungen über die Nekrobiose und 
die letale Chloroformeinwirkung. Rec. des trav. bot. néerl. Vol. IX. 1912. 

4) W.J. v. OsrerHour, Antagonism and Permeability. Science Vol. XLV. 1917. 

ar i 


480 


he toxic, as eg. was shown by van OstERHOUT’s soil-experiments. 
Addition of CaCl,-solutions to the otherwise fairly favourable soil 
was injurious to the cultivated plants; addition of KCl-solutions was 
not. Van Ostrruovr interprets this by pointing out that through the 
addition of Caleium the relation of the two metals departs more 
and more from the optimal whereas it approximates the optimal 
relation through the addition of Potassium. 

Reverting to our broom we see that relative to the soil of the 
Land van Diepenhorst the calcium-content of the soil of the Central- 
dunes rises from 0.015 °/, to 0.90°/,, i.e. + 60 times the original 
value. On the contrary there is no appreciable total increment of 
the potassium-, and the sodium-salt-content: in the Central-dunes 
this was 0.08 °/,, in the Land van Diepenhorst 0.06 °/,. 

The relation in the Western and Central-dunes has been largely 
modified, so that the equilibrium for the true calcifuge plants, such 
as Sarothamuus, has been disturbed. The view is favoured by the 
fact that calcifuge-plants, such as Castanea vesca, can be cultivated 
in caleium-rich soil, provided the soil is of itself potassium-rich *), 
or potassiuin is added to it, ScHiMPER*) maintained that calcium 
inhibited the absorption of ironsalts, and that addition of ironsalt- 
solution to calcium-rich soil removed the excited chlorosis. By others, 
among whom SIDORINK®), this was however refuted and ascribed to 
the alkalinity of the nutrient solution that had been used. 

For Magnesium Lonw‘*) asserted that a certain ratio of Ca and 
Mg is required for a satisfactory development, which, however, has 
been negatived by Russian and American writers*) on the science of 
manuring. 

With the method for soil-examination adopted by me I found in 
both soils only traces of magnesium; I, therefore, refrain from giving 
my opinion about this question, which may be solved through 
subsequent experiments, which I purpose to perform with the Saro- 
thamnus by cultivating it on caleium-richer soil to which various 
salts will be added. This however is a time-consuming undertaking ; 
for the time being experiments with water-cultures of buck-wheat 
were indicative of the great importance of the antagonism of the 
salts of univalent and bivalent metals in the problem of calcifuge plants. 


1) ARNOLD ENGLER, Ber. Schweizer. bot. Ges. 1901. 

2) ScHiMPer, Pflanzengeographie. 1908. 

3) Srporin. Ergebn. Landw. Stat. Moskou 1916.. 

4) Loew. Bull. Agric. Coll. Tokyo 1902. Die Lehre vom Kalkfactor. Berlin 1914, 

5) A. Dosarenxo Journ. f. experim. Landwirtschaft 1903, F. A. Warr Journ. 
agr. research 1916. 


Physiology. — “On the Pharmacological Action of Lsoamylhydro- 
cuprem (eukupin) and Isoctyl hydrocuprein (vuziny’ By Prof. 
R. Maenus and U. G. Bisa. 


(Communicated at the meeting of April 23, 1920). 


Of late years especially three compounds out of a series of hydro- 
cuprein-derivatives, which had been examined by Morcsnrorn and 
his pupils on their antiseptic action in vitro and in vivo, have been 
applied in therapeutics. These researchers had namely discovered 
that the alkylated hydrocuprein-derivatives were strong antiseptics 
every member of this series having a specific affinity for certain 
micro-organisms. 

Thus ethylhydrocuprein counteracted especially pneumococci; 
isoamylhydrocuprein antagonized diphteria bacilli, bacilli of malig- 
nant edema and pyogenous cocci; isoctyl bydrocuprein neutralized 
the effect of bacilli of malignant edema and pyogenous cocci still 
more than isoamylhydrocuprein did (in vitro; in vivo they showed 
little difference). These three substances were given the commercial 
names, respectively of optochin, eukupin and vuzin. 

As most commonly happens with the products of chemo-terapeu- 
tie researches, also these three substances were applied to patients 
or to men under suspicion of being infected, before pharmacological 
examination had sufficiently established their effects upon the mam- 
mal. Indeed, with respect to optochin inquiries were made later on, 
but hardly anything was effected in this direction for eukupin and 
vuzin. In order to meet this deficiency as far as possible, we have 
examined pharmacologically the double-hydrochlorie acid salts of the 
latter two substances, which were put at our disposal through the 
kindness of Prof. Morcrnrorn (Berlin). Before long these experiments 
will be published’) in extenso in another place; for the present we 
are able to give a concise report of our results, in which eukupin 
and vuzin stand for the double hydrochloric acid salts. 

1. The pharmacological action of eukupin and vuzin (in the cases 
examined) agrees for the most part with that of quinine. 

2. Eukupinae bihydrochloridum is soluble in distilled water to 


1) For the bibliography we refer also to this detailed publication. 


482 


5°/,, vuzinal bihydrochloridum to 1°/, (5°/, solutions are clear again, 
concentrations between these values are turbid). In a physiological 
common-salt solution, Ringer-, or Tyrode-solution, turbidity practically 
exists in every concentration. 

In serum eukupin-biHCl dissolves to 1:14000, vuzin-biHCI 
to 1: 20000. When the solutions in serum are made to foam, the 
two substances are collected in a higher concentration in the foam 
than in the liquid. The foaming is diminished by the addition of 
much alkaloid-salt. 

3. With subcutaneous injection the fatal dose for white mice per 
ke. body-weight is for eukupin: 300 mgr. and for vuzin: 200 mgr. 
So the toxicity of either substance, administered subeutaneously, is 
for mice two- or three-times greater than that of quinine. 

The subcutaneous fatal dose for cats per kg. body weight, amounts 
to from 25 to 50 mgr. of eukupin, 200 mgr. of vuzin. 

4. With slow intravenous injection the fatal dosage per kg. cat 
varies with the concentration of the alkaloid salt: in a 1°/, solution 
it amounts per kg. cat to about 13 mer. of eukupin and about 
15 mgr. of vuzin; in 1°/,, solution per kg. cat to 70 mer. of eukupin 
(in one experiment, in which vagi intact); and 40-—120 mgr. of 
vuzin (vagi intact or cut). 

In the case of rabbits the intravenous fatal dosis of eukupin (in 
1*/,,-solution) seemed to vary with the Nn.-vagi being unimpaired 
or cut through: it was per kg. rabbit with unimpaired vagi about 
13 mgr, with vagi cut about 60 mgr. It appears from this that in the 
rabbit eukupin acts upon the vagus-center. 

5. After subcutaneous injection of eukupin and vuzin cats die 
under a progressively increasing sopor. Large doses of eukupin cause 
a marked fall of temperature. 

6. Subcutaneous injection of concentrated solutions (5°/,) of the 
two alkaloid-salts brings about local necrosis of the skin and the 
subcutaneous connective tissue. 

7. Cleansed sheep’s blood-corpuseles suspended in Ringer’s solution, 
were hemolyzed through eukupin in a concentration of about 1 : 5000 
through vuzin in a concentration of about 1 : 10000. 

The number of red blood-corpuscles per mm* plays some influence 
upon the required concentration of the alkoloidsalts. 

In the presence of serum the concentration of both substances, 
required for hemolysis, is about 1 : 1000. 

8. Kukupin and Vuzin in 1 °/,-solution convert oxyhemoglobin 
into a brown colouring substance, which in an acid as well as in 
an alkalin solution shows in the absorption-spectrum spectroscopically 


483 


as well as spectrographically a line in orange, right to the left of 
D, while the violet portion of the spectrum is shortened. The sub- 
stance formed is decidedly not methemoglobin and not hematin. 

9. On the frog’s heart at the Straub-cannula eukupin acts with 
certainty deleteriously in a concentration of 1: 50.000 Gn Rtnerr); 
vuzin does so in a concentration of 1: 150.000 (in Rinerr). Hither 
substance, in concentrations of 1:10.000 and higher, produces a 
standstill of the heart, eukupin a diastolic, vuzin a systolic standstill. 

Serum, and red blood-corpuscles diminish the action of both sub- 
stances on the frog’s heart. 

The cardiac muscle deprives the solutions of both substances. 

The lesions to the frog’s heart are little or not reversible. 

10. The isolated mammalian heart perfused after LANGENDOKFF is 
brought to a systolic standstill by either substance in concentrations 
of 1: 10.000 in RiNeer’s-solution. 

A solution of the two salts in undiluted mammalian blood lessens 
their activity. 

The lesion to the heart cannot be restored by washing out with 
RinGeEr’s solution, very little with blood. 

11. Eukupin causes the peripheral vessels of cold- and warm- 
blooded animals, separated from the central nervous system, to 
distend (smallest concentration 1 : 20.000); vuzin has under the same 
conditions a constrictive influence (smallest concentration 1 :10.000). 

12. Kukupin and vuzin most often constrict the pneumonic 
vessels; quinine and quinidin distend them (smallest concentration 
about 1 : 20.000). 

18. Eukupin and vuzin do not manifest a distinct action on the 
coronary vessels in the rabbit's heart perfused withRine@rr’s solution after 
LANGENDORFF. Kukupin widens the coronary vessels of the cat’s heart 
perfused with blood after LANGENDORFF (vuzin not examined), 

In the Starling-preparation (dog) modified after Dussnr DE BarENNE 
eukupin (1: 90.000 in blood) caused a marked distension of the 
coronary vessels, vuzin (1 : 60.000 in blood) a smaller. 

14. Intravenous injection of eukupin and vuzin causes lowering 
of the bloodpressure in cats and rabbits, in which process the 
following factors play a part: 

a. weakening of the heart-muscle ; 

b. distension of the coronary vessels (after eukupin stronger than 
after vuzin) ; 

c. distension of the peripheral vessels (permanent after eukupin, 
transient after vuzin); 

d. constriction of the bloodvessels of the lungs. 


484 


The bloodpressure regains entirely or partially the original height 
through the following factors: 

a. lessening of the concentration in the blood; 

b. increase of the output; 

c. constriction of the peripheral vessels after the initial distension 
through vuzin. 

15. Intravenous injection of vuzin lessens the action of intravenous 
adrenalin-injection on the rise of the blood-pressure; ultimately these 
injections do not yield any appreciable result. 

16. Intravenous injection of vuzin lessens the effect of faradic 
vagus-stimulation on the heart. 

17. In tbe isolated cat’s lung perfused with undiluted blood vuzin 
causes constriction of the bronchi; eukupin, quinine and quinidin 
cause distension of the bronchial tubes (concentrations about 1 : 20,000). 

18. Eukupin, vuzin and quinine nearly always inhibit the action 
of the isolated small intestine of the cat and the rabbit, they rarely 
stimulate it. The effect of quinine can be washed out; that of eukupin 
and vuzin can not. 

19. Eukupin, vuzin and quinine exerted in our experiments only an 
inhibitory influence upon the isolated uterus of the cat and the rabbit. 
Neither the quinine, nor the eukupin-action appeared to be reversible. 

20. On application in 1 °/,,-solution for one minute to the rabbit’s 
cornea eukupin and vuzin produce a transient total anaesthesia. 
1 °/,-solutions are very deleterious to the cornea. 

21. When given in a 1°/,,-solution, eukupin and vuzin bring 
about an interruption of the conduction in the sensitive ischiadicus- 
fibers of the frog (local application). 

22. In a 1°/,-solution both salts cause a total interruption of the 
conduction in the N. ischiadicus of the frog (local application). This 
effect can be washed out in the case of either substance. 

23. Eukupin and vuzin, injected intravenously in non-fatal dosis, 
do not influence the centres of the spinal cord of rabbits. 

24. Eukupin elicits stimulation of the vagus-center in rabbits; 
vuzin does not affect the vagus-center in cats. (Compare N°. 4). 

25. On intravenous administration both alkaloid salts produce 
stimulation of the respiratory center in cats and rabbits. 

26. When the hindlegs of the frog in the Laewen-Trendelenburg 
preparation are perfused with eukupin and vuzin in Ringer’s solution 
in small doses the result is increased lassitude, in larger doses 
decreased excitability of the muscles. In this process indirect excita- 
bility is influenced more than the direct. Quinine has a similar action. 
The action of vuzin is strongest, that of eukupin is weaker, that of 


485 


quinine is weakest. In the strongest concentrations the three salts 
cause a total rigidity of the muscles. The action is only sparingly 
reversible through washing with Ringer’s solution, a little more after 
‘quinine than after the other substances. 

27. In the normal rabbit vuzin, injected subcutaneously in doses 
of 50 mgr. per k.g., causes a temporary fall of the temperature. 
Eukupin, on the other hand in the same dosage has no effect on 
the temperature of the normal rabbit. 

28. After fever has been excited by injection of coliendotoxins + 
killed bacterium coli, both substances, like quinine, in a dosis of 25 
mgr. per k.g. lower the temperature in the rabbit. 

29. After subcutaneous and intramuscular injection eukupin and 
vuzin are resorbed only very slowly. Rests are found at the place 
of injection even after four days. 

Of an intravenous injection of vuzin, in almost fatal dosis, about 
'/, is still retained by the blood after 35 min., the rest is almost 
entirely to be found again in heart, liver, kidneys, adrenals, brains, 
spinal cord and muscles. After 24 hours only traces are to be found 
in these organs. Also with this intravenous injection no vuzin was 
found in the urine. 

Thus it appears that vuzin is destroyed rapidly after intravenous 
injection. 

30. In detibrinated blood vuzin is distributed over bloodcorpuscles 
and serum in such a way that in the corpuscles the concentration 
is from 7.7 to 16.6 times as high as in the serum. 

31. Various organs (heart, liver, muscles) in vitro largely detach 
eukupin and vuzin from their solutions in Tyrode. 

In vitro no abolition of the two salts by the named organs was 
demonstrable. 

32. After subcutaneous injection of doses that just failed to be 
fatal neither of the alkaloids could be demonstrated in the urine of 
the cat and the rabbit. 

33. The growth of Micrococcus tetragenus in 1°/, glucose-broth is 
inhibited by eukupin in a concentration of about 1: 150.000, by 
vuzin in a concentration of 1: 300.000 or 1 : 500.000. 

34. The antiseptic action of solutions of the two alkaloid-salts 
decreases largely after some days’ standing. 

35. Likewise the antiseptic action of the two substances decreases 
largely through dissolving in a physiological common-salt solution. 

36. The presence of red blood-corpuscles in the fluid culture 
medium weakens the antiseptic influence of eukupin and of vuzin. 

Pharmacogical Institute of the Utrecht University. 


Physiology. — “On Adsorption of Poisons by Constituents of the 
Animal Body. Wl. The Adsorbent Power of Rabbit's Serum 
for Atropin”. By Prof. W. Storm van LEEUWEN and J. ZEYDNER. 
(Communicated by Prof. R. Magnus). 


(Communicated at the meeting of June 26, 1920). 


In previous publications STORM VAN Leeuwen’) and ErrLAND and 
STORM VAN Leeuwen’) have demonstrated that in the serum and in 
the tissues of various animals there are substances capable of 
inactivating alkaloids. At the same time they were able to show, 
that this inactivation is not brought about by chemical destruction, but 
through a physical adsorption of the alkaloid by certain components 
of the serum or by animal tissues. In these earlier publications it 
has already been deemed probable, that inactivation of atropin by 
rabbit’s serum is not: brought about chiefly through a chemical 
decomposition, but very likely also through a physical adsorption. 
It has been our purpose in this paper to ascertain in how far this 
supposition is true. 

The natural resistance of rabbits to atropin has already frequently 
been investigated experimentally. 


HecKeEL 5) fed rabbits exclusively with solanea without mydriasis occurring in 
these animals; they remained quite healthy and procreated even a numerous offspring, 
which finally would not eat anything but solanea. Neither in the urine, nor in the 
faeces of the animals did he find atropin either by a chemical or a physical 
method (instilling into the rabbit’s eye). When the rabbits, fed in this way, were 
killed and their flesh was given to cats and dogs, these animals did not present 
any phenomena of atropin-poisoning. From this he concluded that the poison had 
been decomposed in the blood of the rabbits. 

HERMANN showed afterwards that the resistance of rabbits to atropin did not 
depend upon an augmented excretion of the poison, because it appeared that after 
ligation of the arteria renalis, the atropin-resistance of rabbits did not decrease. 


1) W. Srorm van Leeuwen. Sur l'existence dans le corps des animaux de 
substances fixant les alcaloides. Arch. Néerl. de Physiol. Tome 2 p. 650, 1918. 

4) L. EerLanp and W. Srorm van Leeuwen. On Adsorption of Poisons by 
Constituents of the Animal Body. L. The adsorbent power of serum and brain- 
substance of Cocain. Proceedings Royal Acad. Vol. XXII, p. 831. 

5) Hecker. De linfluence des solanées vireuses en général et de la Belladonna 
en particulier. C.R. Acad. de Paris 80. 1875. p. 1608. 


487 


WILLBERG !) examined the resistance of several species of animals to atropin, 
and calculated how many times they were more insensitive than man. We subjoin 
some figures : 


Rabbuik!. +2). 242 „ 
White Mouse. . 162 „ 
Young dog... 124 , 
Full grown dog 194 „ 
Cap METENDE Hoe 


This also shows that the resistance does not depend mainly on the intensity of 
the metabolism of the animals, since the smallest animal examined is less resistant 
than a rabbit or a hen. 

According to some the age of the animals influences the resistance. A young 
individual should then be more resistant than a full-grown animal. WILLBERG 
proved this for dogs. With men also the same phenomenon is observed; for an 
adult 50 berries of atropa belladonna are not fatal, 40 berries will kill an old 
man. The fatal dosis for an adult is 0,01—0,06 gr. sulf atropini; an infant seems 
to tolerate 0,14 grms (BARBIER ”). 

KRASNAGORSKI 5) gave infants with exudalive diathesis, 0,85—2,5 mgr. sulf 
atropini per day during a month without recognizing mydriasis or acceleration 
of the pulse-rate. He ascribes the greater resistance to an increased vagotony in 
young individuals. 

CALMETTE*) injected 200 imgr. of sulf atr. intravenously into a rabbit, without 
establishing any toxic atropin-action. On the other hand an intracerebral injection 
of 2 mgrs induced death under convulsions and paralysis. 

This proves that when the poison is administered in the usual way it is 
rendered harmless before it reaches the brains, which CALMETTE attributed to 
phagocytosis. Several researchers however showed that in this respect his experi- 
ments were fallaceous and that no active part can be ascribed to the white 
blood-corpuscles. 

FLEISCHMANN 5) found that the detoxicating influence of rabbit’s serum can also 
be demonstrated in vitro. 

At the same time he discovered that the individual differences in resistance 
were proportional to the “Zerstörung’'-capacity of the serum. According to this 
experimenter this may be observed also in man: that children, idiots and im- 
beciles tolerate more atropin and hysterici only very little may, according to 
FLEISCHMANN, also be dependent upon the atropin-destroying power of their serum. 
He found that there were rabbits which were very sensitive to intravenous injec- 
tion of sulfas atropini and that also their serum in vitro did not possess any weaken- 
ing action. These were strumous rabbits from Bern, showing hyperthyroidism. 


1) Waurgere. Die nat. Resistenz einiger Tiere dem Atropin gegeniiber. Zeitschr. 
f. Bioch. 66. p. 398, 1914. 

2) Barprer. Sur deux cas d'intoxication par l'atropine. (Thése de Bordeaux 1910). 

3) KRASNAGORSKI. Exsudat. Diath. u. Vagotonie M. S. Kind. XII 1913, p. 138. 

4) Carmerre. Sur le mécanisme de l'immunité contre les alcaloïdes. Soc. Biol. 
Jub. band 1899. 

5) FLEISCHMANN. Atropine-Entgiftung durch Blut. Arch. f. exp. Path. 62, 1910, 
p. 518. 


488 


Resistance then would be related with the thyroid gland. Metzner ') denied this 
relation. Indeed, he found rabbits whose blood did not destroy atropin at all, but 
when examined macroscopically as well as microscopically, they were found to 
evince a great difference in the sizes of their thyroid glands. The place whence 
they originale seems to be a more important factor. Rabbits from Alsace und 
Leipzig are highly resistant, MerzNer’s laboratory animals from Basel and Bern 
very little. FLEISCHMANN ®*) partly retracted his statement, but he cannot disavow 
all relations between thyroid gland and resistance. In patients with morbus Base- 
dowi he found a stronger “Zerstérend” serum in 30°/) of the cases examined. 


It was established, therefore, that rabbit's blood could render large 
quantities of atropin harmless, but the way in which this is brought 
about is still an open question. Most researchers assume that the 
alkaloid is broken up into its components tropin and tropic acid, a 
simple chemical decomposition ; Mrtzner*) suspects an enzym splitting 
the atropin. DöBriN and FrriscHmanN*) also do not think this 
improbable. Hrrrrer and Fickewirta *) invariably found tropin in 
the urine of the laboratory animals, but could not establish it in 
the serum or the liver. 

Dixon, Ransom, and Hami..*) report that they do not assume a 
destruction of the alkaloids in the body, but that the alkaloid (in 
casu strychnin) is adsorbed and can readily be regained by solvents 
of alkaloids. According to them the intensity of the adsorption varies 
with the “colloidal nature” of the adsorbing substance. For aught we 
know, they have not proved this assertion. Still, they are right, as 
will appear lower down. However, the matter is not so simple as 
they imagine, for the fact that rabbit’s serum adsorbs so intensely 
and dog’s serum does not, cannot presumably be ascribed merely 
to the degree of its “colloidal nature.” 

When an animal after intravenous injection is very little sensitive 
to a poison the chief cause may be one of the following: 


1) MerzneR. Mitteilungen über Wirkung nnd Verhalten des Atropins im Orga- 
nismus. Arch. f. exp. Path. 68, 1912, p. 11—99. M. und HepinNGERr ueber die 
Beziehungen der Schilddr. zur Atropin-zerstérenden Kraft des Bl. Hetzelfde 69, 
1918, p. 272. 

2) FLEISCHMANN. DöBLiN und Fr. Zum Mechanismus der A. Entgift. durch BI. 
etc. Z.schr. f. Klin. Med. Bd. 77, p. 145, 1918. 

8) MerzNER. l.c. p. 155. 

4) DöBrin u. FrEISCHMANN. l.c. p. 149. 

5) HeEFFTER u. FrckewirtH. Ueber das Verhalten des A. im Organismus d. 
Kaninchens. Biochem Z.schr. 40, p. 45, 1912. 

6) Dixon und Ransom. Die elektive Wirkung v. Arzneien auf d. peripheren 
Nervensystem-Ergeb. der Physiol. 12, p. 773. 

Dixon und Hamitt. Secretion and action of drugs. Journ. of physiol. 38, 
p. 314, 1909. 


489 


1. the organs of the animal may not be sensitive to the poison. 
(StravuB') demonstrated not long ago that to this the resistanee of 
the rat to strophantin is to be ascribed). 

2. the poison may probably be destroyed chemically in the body. 

3. the poison may be made inactive in the body of the animal 
in another way. 

The first supposition will hardly apply to the case under consi- 
deration, because although the: rabbit possesses a great power of 
resistance to atropin, the organs of this animal are very sensitive 
to this poison. It has been proved by Van Liprn pr Jrunw’s*) expe- 
riments that the action of atropin upon the surviving small intestin 
of the rabbit is about ten times stronger than its action upon the 
catgut. Besides, as already mentioned, CaLmerrn showed that an 
intracerebral injection of two mgr. of atropin into a rabbit induces 
death instantly. 

As appears from the inquiries by FrrIsCHMANN, Metzner and others, 
the second supposition has come true. Rabbit's blood can decompose 
atropin in vitro, but this decomposition proceeds comparatively slowly, 
and consequently not on such a large scale as to enable us to 
establish from it the rabbit’s resistance to atropin, when this poison 
is injected directly into the circulation. 

These considerations tend to support the third supposition, and in 
the experiments to be described now we have been able to demon- 
strate the high adsorbent power of rabbit’s serum for atropin; still it 
does not decompose it. 

In order to demonstrate in these experiments the inhibitory influ- 
ence of rabbit’s serum, we needed an accurate method for a physi- 
ological determination of the values of atropin-solutions. To this end 
we adopted the method expounded by Storm van Leruwen and van 
DEN BROEKE in a previous publication’). Their procedure was as 
follows: a certain quantum of pilocarpin is added to a surviving 
piece of catgut and hereafter the amount of atropin was determined 
that is required to abolish almost entirely the contraction of the gut 
generated by the pilocarpin. This method yields satisfactory results, 


1) W. Srraus. Ueber die Resistenz der Ratten gegen K-strophanten. Arch. f. 
exp. Path. und Pharmak. Bd 84, p. 228, 1918. 

2) v. LiptH pe Jeupe. Quantitatieve onderzoekingen over het antagonisme van 
sulfas atropini tegenover hydrochloras pilocarpini, salicylas physostigmini en 
hydrochloras muscarini op overlevende darmen van zoogdieren. Dissertatie Utrecht 1916. 

3) Storm VAN LEEUWEN and VAN DEN BROEKE. A quantitative inquiry into the 
antagonism pilocarpin-atropin on the surviving cat-gut. Proceedings Roval Acad. 
Vol. XXVIII, p. 1158. 


490) 


if some precautions are taken which are amply discussed in the 
publication we bave cited. 

The following experiments were made according to this method. 

To the liquid containing a surviving gut (75 cc. of Tyrode 
solution) O,l mgr. of pilocarpin is added. After three minutes 0,0004 
mgr. of atropin is added to the liquid. As may be seen from fig. 
la this dosis of atropin is not sufficient to completely abolish the 
contraction of 0,1 mgr. of pilocarpin. After the atropin and the 
pilocarpin has been washed out, and the gut has been standing in 
fresh Tyrode solution for half an hour again 0,1 mgr. of pilocarpin 
is administered and three minutes afterwards 0,024 mgr. of atropin, 
that is 60 times the quantity given in the previous experiment. This 
atropin had been for 50 minutes in contact with fresh rabbit's serum. 
It will be seen that this quantum of atropin is able to abolish 
the action of pilocarpin; this dosis, then, has a stronger effect than 
the preceding one (fig. 16). 

In fig. 1e first 0,1 mgr. of pilocarpin is given; after this 0,012 
mer. of atropin i.e. thirty times the quantum of the first experiment. 
It is evident that this atropin-action agrees with that of fig. 1a 
Here also the atropin had been previously in contact with rabbit’s 
serum; namely, 1 mgr. of atropin had been added to 5 e.c. of fresh 
rabbit's serum. From these experiments it may therefore be concluded 
that through the contact with rabbit’s serum the action of the atropin 
had been weakened to such an extent that less than one thirtieth 
of the original action is left. 

In fig. 1d again 0,1 mgr. of pilocarpin is added to the gut, and 
three minutes later again 0,016 mgr. of atropin is given. This atropin 
has also previously been in contact with serum; its action is stronger 
than that of 0,0004 mgr. of atropin in fig. 1a. In fig. le again 0,1 
mgr. of pilocarpin is administered and then again the dose of 0,0004 
mgr. of atropin, which had also been given in fig. 1a. 

This experiment serves to show that the sensitivity of the gut has 
not altered considerably; as will be seen the action of 0,0004 mer. 
of atropin is now a little stronger than in fig. 1a. From these 
experiments we may therefore conclude that (see fig. 1d) through 
the contact of atropin with rabbit’s serum its action is reduced to 
one thirtieth, nay, almost to one fortieth. 

Now, in order to prove that this adsorption of atropin by rabbit’s 
serum is not a chemical destruction, but most likely a physical 
process, we proceeded as follows: the atropin-solution, which through 
the contact with rabbit’s serum had lost the greater part of its acti- 
vity, was treated with hydrochloric acid and alcohol, as has been 


491 


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described in the preceding communication for the adsorption of cocain 
by serum *). The alcohol was evaporated, the liquid neutralized and 


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made up to the original volume. Now we ascertained how much 
active atropin was present. The result can be seen in fig. 1 f—1h 
In fig. 1f and 1h every time 0.2 mgr. of pilocarpin is added to 
the gut and afterwards 0,0006 mgr. of atropin’). As will be seen 
from the figure after three minutes nearly the whole action of the 
pilocarpin has been abolished by the atropin. In fig. 1g again 0,2 
mgr. of pilocarpin is given, and after three minutes so much of the 
_atropin-containing liquid (serum + atropin treated with alcohol and 
hydrochloric acid) has been added, as corresponds to 0,001 mgr. 
atropin of the original serum-atropin mixture. It will be seen that 
its action is slightly stronger than that of 0,0006 mgr. of atropin, 
from which we deduce that through the treatment with alcohol 
if not all, yet nearly all the atropin has been recovered in full 
activity. 


1) L. EERLAND and W. STORM VAN LEEUWEN. l.c. 

2) The piece of gut used here was not the same as that of fig. la—e. 
32 

Proceedings Royal Acad. Amsterdam. Vol. XXIII. 


494 


We did not deem it necessary to show that all the atropin is recovered, be- 
cause — vide supra — most likely, already during the short contact of the 
atropin with rabbit’s serum a small part of the atropin has been destroyed 
chemically. With our method we could not expect to find again all the atropin, 
but what we could show was that the greater part of the atropin could be 
reclaimed in active form. 

This experiment also explains the phenomenon observed by CLOETTA!) and 
SCHINZ *), viz. that they found in their chemical determinations more atropin than 
could be demonstrated physiologically. Now, the chemical reaction (Vitali) consists 
also in extracting with alcohol and chloroform. Scuinz tried to explain it in this 
way that the atropin-molecule was destroyed so far that it could no more react 
biologically, but still gave the chemical reaction. 


The investigation above described was repeated in several other 
experiments, invariably with the same result. | 

In another experiment we astertained whether some further know- 
ledge could be obtained about the quantitative relations in the case 
of adsorption of atropin by rabbit's serum. For this purpose (see 
fig. 2) first 0,1 mgr. of pilocarpin was given and after three mi- 
nutes 0,0002 mer. of atropin; this could neutralize the pilocarpin- 
action almost entirely. In fig. 16 0,1 mgr. of pilocarpin is given 
and subsequently 0,008 mgr. of atropin, which had previously been 
in contact with rabbit’s serum; its action will be seen to be less 
than that of 0,0002 mgr. of atropin, given before, so that apparently 
through the serum the atropin-action had been reduced to ‘/,,. In 
fig. Je again 0,1 mgr. of pilocarpin is administered, then 0,0002 
mgr. of atropin; this could neutralize entirely the action of the 
pilocarpin, from which it appears that the sensitivity of the gut to 
atropin has certainly not diminished during the experiment. The 
atropin given in fig. 25 was taken from a solution which contained 
0.1 mgr. of atropin to 1 e.c. of fresh rabbit’s serum. 

In fig. 2d 0.05 mer. of pilocarpin was given to another piece of 
gut. Its action, as appears from the figure, could be almost entirely 
abolished by 0,0002 mgr. of atropin. In fig. 2e 0,05 mgr. of pilo- 
carpin was given and after this 0,008 mgr. of atropin; this atropin 
had been taken from a solution whieh contained 1 mgr. of atropin 
per c.c. of fresh rabbit’s serum, i.e. 10 times the quantum of the 
previous case. In fig. 17 again 0,0002 mgr. of atropin of the usual 
aqueous solution was given. This experiment then tends to show 
that also when a whole milligram of atropin is added to 1 c.c. of 
rabbit’s serum, the action of atropin is reduced to about ‘/,,. 


1) Croerra. Ueber Angewöhnung an Atropin. Arch. für exp. Path. 64, p. 432, 1911, 
2) ScHiNz Zur angeborenen und erworbenen Atropin Resistenz des Kaninchens. 
Arch. fiir exp. Path. 81 pg. 206. 1917, 


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It would be well to observe the quantitative values of adsorption 
for a large number of concentrations of atropin in rabbit’s serum; 
this however would be a difficult task also on account of the time- 
consuming technique; anyhow from the single experiment just de- 
scribed (similar experiments led to the same results) it appears that 
probably the relations obtained with the adsorption of pilocarpin by 
rabbit’s serum also hold good for the adsorption of atropin by serum; 
the said relations have been discussed by one of us in an earlier 
communication. *) 

It was there that we found nearly all the poison adsorbed when 
working with comparatively small quanta of the alkaloid; larger 
quantities produced a different effect. 

If, namely, in that experiment 10 mgr. of pilocarpin was added 
to 5 ec. of rabbit's serum, 9.5 mgr. were adsorbed, so that only 
0.5 mgr. was left in the solution; an addition of 20 mgr. of pilo- 
carpin yielded an adsorption of 18,5 mgr. of pilocarpin, so that 
only 1,25 mgr. remained. Larger doses however gave widely different 
results: e.g. an addition of 100 mgr. led to an adsorption of 28,5 mer., 
so that 72,5 mgr. was left in the solution. As said, such an extensive 
quantitative inquiry in this direction fur atropin, takes a great 
deal of time and is almost impracticable. The experiment recorded 
here, however, points to the probability of similar quantitative rela- 
tions for atropin to those for pilocarpin. 

In conducting these experiments we observed something that 
necessitated an extension of our investigation. We found that the 
serum of a rabbit, to which before death an injection of some c.c. 
of a peptone solution had been administered, had no or only little 
adsorbent power. It also appeared that rabbit’s blood, to which citras 
natricus had been added to prevent clotting, had only a very slight 
adsorbing power for atropin. 

We might reasonably infer from this that the substance from 
rabbit's serum which can adsorb atropin, is not present as such, but 
is generated only after clotting, so that no adsorption will take 
_ place when coagulation is prevented. In looking through the literature 
this supposition appeared to be improbable, because Mrrzner’) made 
his experiments with rabbit's blood to which hirudin had been added, 
and he does not mention that this addition lessens the adsorbent power. 

The supposition is also refuted by Dovon and Sarvonat*), who 


1) W. Storm van LEEUWEN. |. c. 

ke. 

5) Doyon et SARVONAT. Passage d'une nucléoproteide anticoagulante dans le 
sang. Soc. de Biol. 74. 1913, p. 78. 


498 


found that atropin generates a nucleoproteid in the blood which 
obviates clotting, while they also observed that the adsorbent 
power of serum in vitro runs parallel with the animal’s resistance 
to intravenous injections in vivo. This would be difficult of explana- 
tion if the adsorbing substance should originate only with coagulation. 

Another possibility to be considered is, that the presence of peptone 
or citrate might prevent the adsorption of atropin by rabbit’s serum, 
or — if it had already been accomplished — might loosen the 
atropin binding and this assumption is not without foundation, since 
GenGou') has stated that certain colloidal solutions, several sera; 
albumoses and also citrates can inhibit certain adsorptions. 

Citrates e.g. can counteract adsorption of colouring matter by 
animal charcoal, nay, they can substitute certain adsorptions by their 
own adsorption. We have examined this question in the following 
way (see Fig. 3). 

In fig. 3a 0,02 mgr. of pilocarpin is added to the gut and after 
three minutes 0,0002 mgr. of atropin, which undoes the pilocarpin- 
action almost entirely in three minutes. 

In fig. 36 the same dose of pilocarpin is added, but a different 
quantum of an atropin solution which was obtained in the following way : 

To rabbit’s serum some atropin was added and also a few drops 
of citras natricus. Of this liquid the quantity was taken that could 
be assumed to contain 0,001 mgr. of atropin, the effect of which 
is slightly weaker than 0,0002 mgr. in fig. 2a, so that at the very 
least the effect of the atropin is reduced to '/,. In fig. 3c 0,008 
mgr. of atropin is given, but this atropin is derived from a solution 
obtained by adding 1 mgr. of atropin to 1 c.c. of rabbit's serum, 
without the addition of citrate. A very strong adsorption of the 
atropin is now noticeable, for 0,008 mgr. of atropin in experiment 
3c is less active than 0,001 mer. in fig. 35, from which it is evident 
that citras natricus largely inhibits the adsorption of rabbit’s serum. 

To the solution of atropin in rabbit's serum, which is used in fig. 3c 
subsequeutly citras natricus is added by which the adsorption is 
distinctly diminished, for 0,008 mgr. of atropin is active again in 
tig. 3d, whereas the same dose in fig. 3c was inactive. After the 
addition of pilocarpin in fig. 3e again 0,0002 mgr. of atropin is 
given to show that the sensitivity of the gut to this poison was 
unchanged. 

Fig. 4 tends to show that the action of peptone is in this respect 


1) Genaovu. Contribution a |’étude de]’adhesion moleculaire et de son intervention 
dans diverses phénoménes biologiques. Arch. int. de physiol. VII 1908. 


499 


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0,0006 mgr. of atropin, which annuls the pilocarpin-action almost 
completely. In fig. 45 0.01 mgr. of pilocarpin is added and after 
this 0.0006 mgr. of atropin, which has been in contact with hen’s 
egewhite. Here there is no inhibition, as is shown clearly in the 


501 


figure. Fig. 4c illustrates the experiment in which again 0.01 mer. 
of pilocarpin is given and afterwards 0.024 mgr. of atropin, i.e. 40 
times as much as in the preceding experiment; this atropin, however, 
has been in contact with rabbit’s serum, and now it can distinctly 
be observed that the action of the atropin is again reduced to less 
than '/,,. In fig. 4d 0.0015 mgr. of atropin is administered, i.e. much 
less than in fig. 4c; this atropin has also been in contact with serum, 
but in this case a little peptone (Warre) had been previously added 
to it. It is manifest that now the atropin-action is not nearly reduced 
to '/,,, from which it becomes evident that the addition of peptone partly 
prevents the adsorption of atropin by rabbit’s serum. That an existing 
adsorption can be loosened by the peptone appears from fig. 4e, 
where 0.005 mgr. of atropin has been added. This dosis is active, 
at least much more active than 0,024 mgr. of atropin was in fig. tc 
and this dosis of 0.005 mgr. of atropin is taken from a solution, in 
which the atropin had first been adsorbed by rabbit’s serum, and 
subsequently a drop of 5°/, peptone-solution had been added. So 
through the influence of peptone the existing adsorption had been 
partly abolished. Fig. 4f again tends to show that 0.0006 mgr. of 
atropin is still active. This is a control-experiment. 

Little is known as yet about the nature of the adsorbing substances 
in rabbit-serum. DöBLIN and FrEISCHMANN') found that the substance 
cannot be heated above 60°, also that it can be refrigerated and 
thawed again and even desiccated. It does not pass through a 
_ chamberlandeandle. At the dialysis of the serum the albumin group 

appeared to adsorb, the globulin group did not. When salting out 
they found the same result. 

We have endeavoured to learn more about the nature of this 
substance; thus far with very little result. Plasma of rabbits as well 
as serum seems to have a great adsorbing power; the blood- 
corpuscles, when washed out and suspended in a physiological 
salt-solution do not adsorb atropin. We also saw that although rabbit’s 
serum is very active, that of cats, men, horses, cows and goats is 
little active. We happened to have the disposal of a qnantum of 
rabbit’s serum, which had been reserved in Professor VAN CALCAR's 
laboratory for nine years in a sealed up glass tube; this serum has 
still a high adsorbent power for atropin. 

Finally we also learnt from special experiments that lecithin does 
not adsorb atropin, which accords with Srorm van LEeEuWEN’s result 
with respect to pilocarpin and lecithin. It may very well be that 


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the adsorbing substances do not occur only in the blood of rabbits, 
but also in other parts of its body. We detected that brain-, and 
liver-substance of the rabbit had a rather strong adsorbent power. 
This adsorption also could be undone by extraction with alcohol. 
An adsorption of atropin by liver substance had also been found by 
v. OETTINGEN '), who established that the liver of frogs adsorps atropin 
very strongly. The serum of this animal has no adsorbent power, 
although the animal is very resistant to atropin. Crorrra had also 
shown already that the livers of the rabbit, the cat and the dog, in 
vitro, could destroy atropin. We found that the brainsubstance of 
the rabbit had a stronger adsorbent power than that of the cat. 

When asking what does the adsorbent power of rabbit’s serum 
signify for these animals, we may safely answer that it will be an 
important factor for the great resistant power of rabbits for atropin. 
It should be borne in mind, however, that in this way we shall 
never be able to solve the entire problem of resistance, for it may 
be that when atropin is administered to rabbits per os part of it is 
destroyed in the gut. Metzner *) found in his experiments that Bazel-, 
and Bern-rabbits have apparently little or none of these adsorptive 
substances in their serum, although they are highly imsensitive to 
atropin given per os. Moreover this resistance can still be increased 
through immunization. Lastly, on the basis of the experiments by 
FLEISCHMANN, Metzner, Herrrer and others it cannot be doubted that 
a chemical destruction of the atropin also comes into play. When, 
however, a poison is injected subcutaneously or intravenously, a 
chemical destruction will be too late to prevent an acute intoxication, 
as has been pointed out by us more than once. A physical adsorpt- 
ion, however, operates quickly, and may therefore be of use in this 
respect. 

It remains still to observe that, although in this and in previous 
papers “physical adsorption” is frequently contrasted with “chemical 
destruction”, we cannot say for sure that this adsorption is indeed 
a physical process. Doubtless in the processes alkaloids or other 
poisons are influenced by tissue-substances, so that they are much 
less active, but can be easily restored to full action with very simple 
means, such as treatment with alcohol, or boiling in water. When 


1) V. OrrtinGEN. Ueber d. Verhalten d. Atropine im Organismus des Frosches. 
Arch. f. exp. Path. 83. p. 381 1918. 

2) Merzner. Mitteilungen über Wirkung und Verhalten des Atropin im Organ. 
Arch. f. exp. Path. Bd, 68. pg. 110. 1912. 

MerzNeER und HeEpinGER Ueber die Beziehungen der Schilddrüse zur atropine- 
zerstörenden Kraft des Blutes. Ibid. Bd. 69. pg. 272. 1918. 


505 


considering the quantitative relations we see that — so far as we 
are able to observe this — in the case of this process about the 
same rules are followed that have been laid down by FREUNDLICH 
for the adsorption of dyes by animal charcoal. 


From the Pharmaco-therapeutical Institute of the 
Leyden University. 
June 1920. 


Palaeontology. — “On the Occurrence of Halimeda in Old- 
Miocene Coastreefs of Hast-Borneo”. By Dr. L. Rurren. 


(Communicated at the meeting of April 23, 1920). 


In arranging the collections of the Siboga-Expedition it appeared 
how widely the calcareous alga Halimeda of the order of the Siphoneae 
is spread on the coastreefs round the islands in the eastern part of 
the East-Indian archipelago. This organism is found at the coast of 
the Little-Sunda Islands, at several places of the coast of Celebes, 
around the Aru- and Kei-islands and in the Banda-Archipelago *). 

In connection with this fact it is remarkable that up to this day 
so little has become known of the occurrence of this alga, which 
is so well adapted to fossilization, in the tertiary, littoral deposits of 
the East-Indian Archipelago, which have so many features in common 
with the present coast-reefs: as e.g the corals, the lithothamnia and 
the foraminifera, which are the chief builders of recent reefs, are 
also met with in the tertiary coast-limestones. 

To my knowledge R. Scnupert’) is the only writer who has 
reported the occurrence of Halimeda in very young — probably 
quaternary — limestones of North- and Central-Celebes. 

Also out of the East-Indian Archipelago fossil-rests of Halimeda 
have been found very rarely. TH. Fucus ®) was the first to describe 
unquestionable fossils from the Eocene of GruirEnsTEIN ; the Halimeda, 
whose ‘branchlets’ were impressed in sandstone, so that only the 
external form had been preserved, bore a great, habitual resemblance 
to the alga still living. Slight morphological deviations led to the 
establishment of a new species of fossils: H. Saportae. 

In some limestones — “transition rocks between Miocene and 
recent” — of Christmas Island, south of Java, also traces of Halimeda *) 
were found. 


1) E. S. Barton. The genus Halimeda. Monograph LX of the Siboga-Expedition, 
1901. 

2) R. ScruBerT. Beitr. z. fossilen Foraminiferenfauna von Celebes. Jahrb. K.K. 
Geol. Reichsans. Wien. 62. 1912, p. 127—150. 

3) Tu. Fucus. Ueber eine fossile Halimeda aus dem eocänen Sandstein von 
Greifenstein. Sitz. Ber. Akad. der Wiss. Wien. Math. Natw. Cl. Abt. I. 103. 1894. 
p. 200—204. 

4) Gu. W. ANDREWS. A monograph of Christmas Island. 1900, p. 250, 275. 


507 


Lastly J. CHAPMAN ') recorded the occurrence of Halimeda in “Late 
Caenozoic reef-rock”’ of Malikolo, New Hebrides, and (reproduced a 
limestone), almost entirely composed of fragments of Halimeda. In 
other places Halimeda never seems to have occurred as a rock- 
builder *). 

It is a fact, therefore, that in Europe Halimeda is encountered in 
Tertiary rocks, while in East-Asia and in Australia it is found up 
to the present only in very late reef-deposits, which have been formed 
in the Quaternary or on the boundary between Quaternary and 
Tertiary. 

Some years ago [ found in Old Miocene marls, scattered largely 
to the west of Bontang, on the Kast coast of Borneo, small flat 
calcareous bodies, which were not determinable. A few years later 
I saw on the coast-reef north of Wahai, Central Ceram, plants of 
a green alga, whose elements very much resembled the Borneo 
fossils. The Wahai alga appeared to belong to Halimeda Opuntia 
Lam and the Bontang fossils seemed to possess all the external and 
the internal characteristics of the genus. While investigating the 
silt-material from Old-Miocene marls of other finding-places in East- 
Borneo, still more Halimede were detected, rare specimens in an 
Old-Miocene marl from Sg. Blakin on the West-side of the Balik 
Papanbay and very numerous specimens in an Oligo Miocene mar! 


Fig. 1. > 2,2. Halimeda cf. Opuntia Fig. 2. & 9 (longitudinal section). 
Lam. forma triloba. Old- Miocene mar]. Bontang. 


1) J. CHAPMAN. Australasian Fossils. 1914, p. 77. 
*) E. GARWoop. On the important part played by calcareous algae at certain 
geological horizons. The Geol. Magazine. (5). X. 1913. Nos. 10, 11, 12. 


508 


from the region where rises the Sg. Melawan, southern affluent of 
the Sg. Sekuran, about 35 k.m. north of Bontang. 

Also in Old-Mioeene Miogypsina-marl, to the south of the Bungalun- 
river; in J.ate-Miocene marl from Kari Orang and in Pliocene marls 
from Sungei Busu, southwest of Bontang. In all these finding-places 
Halimeda coincides with littoral Foraminifera and with Corals, which 
goes to show that the places where the Oligo-Miocene algae grew, 
were similar to those of the algae still living. 

There is no argument for classing the fossil Indian remainders 
as a new species. The isolated calcareous bodies (fig. 1) agree satis- 
factorily in size and outward form with those of H. Opuntia Lam. 
forma triloba, and also the internal structure (fig. 2) corresponds 
with the structure of this species, in that the central thallus-bundles 
branch off already at the base of the calearious bodies, and the 
branches run directly towards the extremities of the lobes, which 
are occasionally more or less distinct *). 


1) Cf. E. Askenasy. Algen der Gazelle-Exp. in die “Forschungsreise S. M. S. 
Gazelle” in den Jahren 1874—1876. IV. 1889, p. 11. 


Physiology. — “On the Effect of Tonic Labyrinthine and Cervical 
Reflexes upon the Eye-muscles’. By Dr. A. pe KrryN (Com- 
municated by Prof. R. Maanrts). 


(Communicated at the meeting of April 23, 1920). 


Recent researches performed in our Institute have shown that in 
various animals the tonus of the skeletal muscles varies, according 
to fixed laws with the position of the head, and that the reflexes 
which come into play here, may be divided into two groups: Tonic 
labyrinthine reflexes, which appear when the position of the head 
in space is changed, and tonic cervical reflexes which appear when 
the position of the head relative to the trunk is changed. Our object 
in this paper is to ascertain how far these reflexes can be demon- 
strated as well for the eye-muscles. 


[. Tonic labyrinth-refleves acting on the eye-muscles. 


Many times already tonic labyrinth-reflexes have been examined 
in man and in various animals; they are the so-called compensatory 
eye-positions. 

Some years ago an extensive quantitative investigation in rabbits 
was published in Pfliiger’s Archiv *). 

_ For further particulars we refer to this publication; we wish to 
lay stress once more on the following final results: 

a. With every position of the head in space we note a corre- 
sponding position of the eyes in the orbita. 

6. If the head is brought from one position into another, the eyes 
attain their new position in the orbita either by rotatory or by vertical 
-movements, or by both together; no data could be obtained for lateral 
movements in the direction of the palpebral aperture. 

_ Neither was Bensamins’*) more successful in his experiments with 
fishes. 

c. It is allowable to state generally that, if the head passes from 


1) J. v. p. Hoeve und A. pe Kreyn. Tonische Labyrinthreflexe auf die Augen. 
Pfliigers Archiv. fiir die ges. Physiologie. Bd. 169. S. 241. 1917. 

3) C. E. Bensamins. Contribution à la Connaissance des Réflexes toniques des 
muscles de l'oeil. Archives Néerlandaises. Tome II, 4e livraison, p. 536 (1918). 

j 33 

Proceedings Royal Acad. Amsterdam. Vol. XXIII. 


510 


one position to another, the eye performs such movements to attain 
its new position in the orbita that it, as it were, tries to retain its 
spatial position. The curves in the above-mentioned publication show 
with how little suecess. To this we shall revert later on. 

We still wish to insist emphatically that these tonic reflexes must 
be distinguished from the transient eye-movements which appear 
during or directly after the movement of the head. This distinction 
is often more or less overlooked in the literature. The compensatory — 
eye-positions are determined by tonic reflexes and vary only with the 
position of the head in space. The determined eye-position, therefore, 
continues, until this position of the head in space is changed. 

In all experiments on compensatory eye-movements due care should 
also be taken that during the experiment the position of the head 
relative to the trunk cannot change. 

That in the above researches we really had to do with labyrinth- 
reflexes could be readily proved, as they disappeared completely 
after bilateral labyrinthine extirpation. 


II. Tonic cervical reflexes acting on the eye-muscles. 


Very little is known in the literature about tonic cervical reflexes 
acting on the eye-muscles. BARANY *) is the only author who (in 1907) 
published an investigation which warranted the assumption of such 
reflexes. In experiments on rabbits, the head of the animal being 
fixed and the trunk being moved relatively to the head, round 
different axes, eye-movements were the result. The results, however, 
varied and the reflectory eye-movements also appeared to depend 
on the position of the head in space. Technical difficulties prevented 
him from ascertaining experimentally whether cervical reflexes come 
into play here. 

On a priori grounds it seems to me improbable that true cervical 
reflexes should fundamentally be varying according to the position 
of the head in space. 

The question, therefore, urges itself upon us whether in the case 
of Barany’s reflexes, we may have to do with a superposition of 
cervical and labyrinth reflexes. The same cervical veflexes may very 
well evoke different eye-movements, when these reflexes affect eyes 
which, in consequence of tonic labyrinth reflexes, take up another 
position in the orbita when the position of the head in space is 
altered. 


1) R. Barany. Augenbewegungen durch Thoraxbewegungen ausgelöst. Centralbl. 
f. Physiol. Bd. XX. 


511 


If, therefore, we wish to examine only the influence of tonic 
cervical reflexes on the eye-muscles, it is necessary to do so in 
animals without labyrinths, in which case the appearance of tonic 
labyrinth reflexes is precluded. 


A. Tonic cervical reflexes on the eyes in rabbits without labyrinths. 


This experiment was carried out with 6 rabbits. After bilateral 
extirpation of the labyrinth, by a method previously described in 
Priicrer’s Archiv ®), we waited some days, until the jerks 
consequent on the operation bad completely subsided. Subsequently 
the head was fixed and the trunk was moved on various axes. 
The eye-movements resulting from this process were carefully noted. 
The examination was performed for various positions of the head 
in space, and was to the following effect: 

a. After bilateral extirpation of the labyrinth the position of the 
head in space does not affect the nature of the tonic cervical reflexes: 
in different positions we found invariably the same reflexes. (These 
positions were: head with lower jaw down, with lower jaw up, 
with muzzle down, with muzzle up and both lateral positions). 

6. A special position of the eyes in the orbita answers to a special 
position of the trunk relative to the head. 

c. When the trunk is turned round various axes the eyes attain, 
through various movements, their new position in the orbita in the 
following ways: 

1. When the trunk is turned round its dorso-ventral axis, by 
movements in the direction of the palpebral aperture. The eye towards 
which the trunk is moved, moves towards the nose, the other eye 
towards the ear. 

2. When the trunk is turned round its frontal axis, by rotations. 
When the trunk is moved towards the skull, both eyes rotate with 
the upper pole in the direction of the nose; when the trunk is moved 
towards the lower jaw with the upper pole towards the ear. 

3. When the trunk is turned on its long axis, by vertical move- 
ments. The eye towards which the back of the animal is turned, 
moves downwards, the other eye upwards. 

As. could be anticipated, it appeared that the same reflexes occur 
when, instead of the trunk being moved relative to the head, the 
head is moved relative to the trunk. BarANY forgot this and was 
consequently sent on the wrong course in drawing his conclusions. 
To this we shall revert lower down. | 


1) Prrücers Archiv. Bd. 145, p, 549, 1912. 
ss” 


512 


Now, when moving the head relative to the trunk the same phe- 
nomena will be observed that appeared for the tonic labyrinth 
reflexes, namely: 

4. It may be generally stated that, when from a certain position 
relative to the trunk the head is brought into another position, the 
eye of animals deprived of their labyrinths will also perform such 
movements to attain its new position in the orbita, as to make it 
appear that it tries, as il were, to retain its position in space. 

However, these cervical reflexes are much less pronounced than 
the tonic labyrinth reflexes, previously described. Only cervical 
reflexes seem to play a part exclusively for the movements in the 
direction of the palpebral apertures. 

As stated before, neither in our researches in conjunction with 
v. D. Horve, nor in those made by BeNJAMINs could the influence of 
tonie labyrinth reflexes be demonstrated. It would seem, therefore, 
that when the head is moved in a horizontal plane, the compen- 
satory eye-positions in the rabbit can be evoked only by tonic 
cervical reflexes. 


B. Tonic cervical reflexes in the normal animal. 


In the above lines we have already alluded to the possibility that 
the cervical reflexes noted by Barany with various positions of the 
head of his laboratory animals, may find an explanation in a super- 
position of tonic labyrinth-, and tonic cervical reflexes. On further 
investigation this really proved to be the case. It would be irrelevant 
to pass all these reflexes in review. One instance may serve for all: 

BARANY then found that with fixed head and rotation of the trunk 
on its dorso-ventral axis the following phenomena could be observed : 
when the animal is examined in normal position with the head in 
horizontal position with the lower jaw down, the left eye will move 
towards the nose in the direction of the palpebral apertures, and the right 
eye towards the ear, as soon as the trunk is turned towards the left 
eye. When the trunk is turned towards the right eye, this eye will 
move towards the nose and the left eye towards the ear. If, how- 
ever, similar movements of the trunk are performed, with the head 
and the muzzle down, rotation of the trunk towards the left eye 
will result in a movement of the left eye approximately upwards 
(i.e. vertical to the palpebral aperture) and of the right eye approx- 
imately downwards. The explanation is easy, as is shown by the 
diagram in Fig. 1. Fig. 1a represents the position of the left eye 


513 


in pure ventral position of the animal, with horizontal mouth-fissure 
and symmetrical position of the head relative to the trunk. 

Now, when the trunk is moved on its dorso-ventral axis towards 
the left eye, this eye will move in the direction of the palpebral aperture 
towards the nose; the M. internus contracts and, as will be seen 
later on, at the same time a relaxation of the M. externus appears. 
This and a movement in the direction of the arrow educes a new 
position illustrated in Fig. 16. Now the head is brought into another 


Hig. I. 


position with the muzzle vertically downwards. When the position 
of the trunk is symmetrical with the head, we find, however, quite 
another position of the eye in the orbita. The tonic Jabyrinth-reflexes 
caused the eye to perform a marked rotatory movement with the 
upper pole in a direction towards the ear. (Fig. 1c). This, however, 
has also brought about a shifting of the insertions of the Mm inter- 
nus and externus in the orbita. Now when precisely the same move- 
ment with the trunk is performed as previously, again a contraction 
of the M. internus and a relaxation of the M. externus will obtain; 
the result from the movement of the eye relative to the orbita how- 
ever has become quite different. Now the eye does not move in the 
direction of the palpebral aperture (Fig. 1d), but about vertically to 
it; the left eye attains its new position by a movement anteriorly 
upwards (the right eye by one posteriorly downward). 

As said above, also other differences in the cervical reflexes with 
different position of the head in space, observed by Barany, could 
be accounted for by asuperposition of labyrinth- and cervical reflexes. 
Since the tonic labyrinth reflexes act now in one way, now in an 
Opposite way, or sometimes, as in the above example, act rather in 
conjunction with the tonic cervical reflexes, a seemingly irregular 
complex of reflexes is produced, which at first sight is difficult to 
disentangle. 


514 


C. Influence of severing the sensitive roots of N. cervicalis 
1 and 2 on the tonic cervical refleves on the eyes. 


As stated heretofore, Barany supposed his reflexes to be cervical 
reflexes, but difficulties with regard to the technique prevented him 
from demonstrating this. These difficulties were known also in our 
Institute. In experiments with cats and dogs previously published 
by Magnus and Storm van Luguwen’) the tonic cervical reflexes on 
the skeletal muscles were eliminated by severing the sensitive roots 
of the Nn cervicales 1, 2, and 8. This could be readily done with 
cats, but with rabbits it was extremely difficult. It is rather easy 
to get at the roots of cervicalis 1 by splitting the membrana atlanto- 
occipitalis. By the help of suitable focal illumination the sensitive fibers 
will be seen to run along freely, and with the aid of a hook they 
can be easily pulled through. If, as will sometimes happen, the 
operation causes hemorrhage from a vein somewhere about the 
fibers, the operation should be discontinued, as in that case there is 
no knowing whether it has been fully accomplished. The sensitive 
root of cervicalis 2 can be reached outside the spinal column; the 
section of this root is rather simple. The difficulties arise only with 
the effort to sever the sensitive root of cervicalis 3. This must be 
effected in the spinal column and in this process the hemorrhage is 
often so profuse that the animal succumbs already during the opera- 
tion. This was shown also by Maenus and Storm van LEEUWEN’s 
researches, in which the researchers succeeded only twice in keeping 
the animals alive after this operation. 

We did not think it proper to sacrifice again a large number of 
animals and first wished to study the cervical reflexes after severing 
the sensitive roots of cervicalis 1 and 2. The experiments were 
conducted in the following way: First bilateral extirpation of the 
labyrinth in order to completely eliminate the tonic labyrinth reflexes. 
After a few days the animals were examined closely for tonic cer- 
vical reflexes. Only of those animals that showed distinctly the tonic 
cervical reflexes on the eyes, the sensitive roots of C. 1 and 2 were 
cut through. This was to the following effect. 

In one animal the tonic cervical reflexes had quite disappeared 
after the sensitive roots of Nn cervical. 1 and 2 had been cut through ®). 


1) R. Maenus und W. Storm v. Leeuwen. Die akuten und die dauernden Folgen 
des Ausfalles der tonischen Hals- und Labyrinthreflexe. Pflügers Arch. 159. 157. 1914. 

2?) In one other animal the tonic reflexes could still be evoked in a small mea- 
sure. After section it appeared that on either side of the N cervicalis 1 a fibril 
was left behind. 


515 


In two animals they still existed, though very much weakened, 
Through section we ascertained the full accomplishment of the operation. 

From this it follows that the reflex curve for the tonic cervical 
reflexes runs mainly through the sensitive roots of Nn. cervicalis 
1 and 2, but that in some rabbits also the n. cervicalis 3 still contains 
centripetal fibers for these reflexes. 


D. The reciprocal innervation of the eye-muscles attending 
the tonic cervical reflexes. 


SHERRINGTON’S researches ') have tended to show that contractions 
of definite eye-muscles are attended with relaxation of the antago- 
nists. BartTELs’) was able to demonstrate the same for various 
forms of nystagmus. 

The tonic eye-reflexes seemed to us just the proper object to ascertain 
this for these reflexes and to register it graphically. 

Registration of the tonic labyrinth reflexes is very difficult, because 
the head must continually be brought into another position in space. 

With tonic cervical reflexes the matter is quite different: then the 
head is firmly fixed and the movements are carried out with the 
trunks. 

Our procedure was as follows: tracheotomy was performed in 
ether-narcosis, the carotids were ligated, the vagi cut. Then a prepa- 
ration was made of the Mm. internus and externus of one eye, a 
thread was fastened to the muscles at the place of insertion to the 
bulbus; subsequently the muscles were severed from the bulbus. 
After this the bulbus was extirpated together with the other eye- 
muscles; then the muscles were separately connected by the thread 
over a pulley to a lever, which enabled us to register the contractions 
on a Kymograph. The whole arrangement, as will be seen, was like 
the one described by Barters. During the experiment the ether- 
narcosis was continued, or, what was more satisfactory, it was stopped 
after the two cerebrum-hemispheres bad been removed (thalamus- 
animal after Manus). 

The graphical representation of such an experiment with a thala- 
mus-animal is seen in Fig. 2. The upper line registers the con- 
tractions of the M. rectus int.; the lower line of the M. rectus ext. 
of the left eye. 

1. We started from: Animal in ventral position, mouth-fissure 


1) SHERRINGTON. Proceedings Royal Society 53, 407. 
3) Bartets. Graefe’s Archiv. Mitteilung I—IV. 76, 77, 78 and 80. 


516 


horizontal, trunk symmetrical to the head (Normal position in the 
curve). 


Left eye 
Poe exh. vab. 
kJ stana| abun uw Sip. | dine Rea Maan en Og war ed 
normal Trunk turned normal position trunk turned normal position 
position to to 


Fig. 2. 


2. After this the trunk was moved as far as possible about its 
dorso-ventral axis, towards the left eye (trunk turned to O.S.). Here 
a distinct contraction of the M. internus and a distinct relaxation 
of the M. externus is noticeable. These new contractions persist as 
long as the trunk is kept in its new position. 

3. Trunk back again in its normal position. This causes a relax- 
ation of the M. internus and a contraction of the M. externus. 

4. Turning of the trunk on a dorso-ventral axis as far as possible 
towards the right eye (Trunk turned to D.O.). Here we observe a 
fresh relaxation of the M. internus and a contraction of the M. 
externus. Here also the tonic nature of the reflex is again distinctly 
noticeable. 

5. Trunk again in normal position; contraction of the M. internus 
and relaxation of the M. externus, so that the muscles are again in 
the state of contraction of the commencement of the experiment. 

About five similar experiments were carried out, with invariably 
the same result. Sometimes the contraction of the muscles was more 
visible than the relaxation. At other times the reverse. Sometimes 
both were equally distinct as in the experiment described. In one 
case only the relaxatien of both muscles could be distinctly made 
out. This of course depends upon the degree of tonicity of the muscles 
at the beginning of the experiment. 

From this we may, therefore, conclude that a reciprocal inner- 
vation of the eye-muscles can also be established for the tonic cervical 
reflexes, but likewise that the tonic nature of the cervical reflexes 
described above, is demonstrable through registration of the contrac- 
tions of antagonistic eye-muscles. 


517 


LIL. Combination of labyrinth- and cervical reflexes. 


When discussing the tonic labyrinth- and cervical reflexes sepa- 
rately we saw in both cases that when the head is brought from 
one position into another, the eyes make an effort to retain their 
position im space. 

It also appeared that this could neither be attained by the tonic 
labyrinth reflexes nor by the cervical reflexes, much less even by 
the latter than by the former. 

Now the question arises what a combination of labyrinth-, and 
cervical reflexes can bring about. Quantitative results in this research 
will be best afforded by eye-positions occurring when in a vertical 
plane the head is brought into different positions relative to the 
trunk (i.e. by raising and lowering the head). 

As said above, with a fixed trunk the tonic labyrinth reflexes 
can be examined alone by fixing the head also and by bringing the 
whole animal (so the head also) into different positions in space, in 
which process tonic cervical reflexes are precluded in consequence 
of the fixed position of the head relative to the trunk throughout 
the experiment. By changing the positions of the head relative to 
the trunk also tonic cervical reflexes can be examined separately, 
but then only with animals in which through previous bilateral 
extirpation of the labyrinths tonic labyrinth reflexes have been 
eliminated. 

When, bowever, of normal animals the head is brought into 
different positions relative to the trunk, we shall observe tonic laby- 
rinth reflexes because the position of the head in space changes, 
as well as tonic cervical reflexes, because the position of the head 
relative to the trunk is changed. 

This is shown in Fig. 3. 

After cocainization a cross is burned into the cornea. A little 
window is placed before the eye, as in our experiments on tonic 
labyrinth reflexes in conjunction with v. p. Horve. The rotatory 
movements can be established directly by taking a photograph of 
the eye with the window before it. 

In the curve 1 mm — 1° rotation. 

Fig. 3. The full line indicates the rotatory movements at the 
raising and the lowering of the head. 

The dotted line indicates the rotatory movements for the tonic 
labyrinth reflexes alone, determined in the way previously described 
with v. p. Hoeve. The hatched field shows the rotations for which 
the cervical reflexes alone are responsible. 


518 


Afterwards the sensitive roots of the Nn. cervicalis 1 and 2 were 
severed on both sides. 
Head vertically upwards. Head vertically upwards. 


o 10 20 30 40 50° 69 0 10 20 30 40 50 60 


Rotation 


iM 
pee 
5 
NE EEN 
me mn En IEEE 
EN ed eel 

NLT le 
li EN 
EENES, OEEEEEENDE 
MENSE. SPR ERTSE 


Rotation 


Os 10 20 35, Gok So) 60) | 0 0 10 20 30 40 50 60 70 
Head vertically downwards Head vertically downwards. 
Fig. 3. 


Fig. 3b shows that at the raising and the lowering of the head 
the rotations are approximately equal to those determined for the 
labyrinth reflexes alone. The hatched part of the curve (cervical 
reflexes), however, has not completely disappeared, so that also with 
this animal the Nn cerv. 3 still play a very weak part in the 
cervical reflexes. 

Let us look at Fig. 3a more closely : | 

Commencement of the experiment: 0°: animal in ventral position, 
mouth fissure horizontal. Lowering of the head: 

10° lowering of the head; rotation 10° 
20 9 Ee it ct 20° ete. 
70° B % Á % 70 

We see from this that when the head is lowered down to 70° below 
the horizontal, the position of the eye in space remains absolutely 
constant, the eye performs a rotation (with the upper pole in the 
direction of the ear) of as many degrees as the head is lowered 
under the horizontal. 

Raising of the head: 

10° raising; rotation 10° 
20° 1 ns PS? rete, 
60° + od 37° 


519 


From this we see that when the head is raised only 10° above 
the horizontal, the position of the eye in space remains constant. 
Then the eye deviates. 

With a view to the difficulties attending photographing the lowering 
and the raising of the head were carried out respectively only 70° 
below and 60° above the horizontal. 

In five other experiments the head was lowered to 90° and raised 
to 80° and the rotatory movements were determined by the naked 
eye with the aid of a protractor. 

Our constant experience was now that the eye persists in its position 
in space when the head is lowered 90° under the horizontal and when 
it is raised 10° above the horizontal. 

Now if we consider that in a normal posture of the rabbit, the 
head is bent down about 35°, it will be seen that, in daily life, the 
animal can bring the attitude of his head from this position in the 
vertical plane between the rather wide limits (downwards about 55° 
and upwards about 45°) into every other position, without any 
alteration in the eye-position in space, consequently also without 
any alteration of its field of vision. 

This fact has also received BARANY’s *) attention. He burned a line 
into the cornea and noted with the naked eye the position of this 
line when the head was moved in a vertical plane. He believes the 
reflexes to be exclusively labyrinth reflexes. Literally he says: “Ich 
bemerke, das während dieser ganzen Bewegungen des Kopfes die 
Stellung des Körpers unverändert horizontal belassen wurde. Das 
Tier ist also mit dem Körper festgehalten, der Kopf aber wird frei 
nach unten und oben bewegt. Wie wir später hören werden, haben 
Veränderungen der Körperstellung eine Veränderung der Augen- 
stellung zu Folge’. 

Further on a deseription is given of the movements, in which 
also the “Körperstellung” is changed and the cervical reflexes, found 
by BARANY and alluded to above, are discussed. 

This view of BARANY rests upon an error. The gist of the matter 
is not whether the “Körperstellung’”’ remains constant, but whether 
the posture of the body relative to the head remains the same. So 
if the head of an animal is inclined to the front, cervical reflexes 
are sure to ensue even when the trunk is fixed completely. This, 
indeed, is easy to demonstrate, as we said before, by performing 
the same movement of the head of rabbits without a labyrinth. 


1) R. Bárány. Nordisk Tidskrift för Oto-Rhino-Laryngologi. Bd. IL. N°. 4. 1917, 
p. 477. 


520 


The constancy of the field of vision with different positions of the 
head is owing to tonie labyrinth-, and cervical refleves combined and 
not to tonic labyrinth-reflexes alone. 

When the head is turned on the occipito-nasal axis, such combi- 
nations of labyrinth-, and cervical reflexes will occur, whereas on 
turning the head from the normal position on the dorso-ventral axis 
only cervical reflexes appear. | 


SUI hy 


1. In the rabbit the state of the tonus of the eye-muscles appears 
to depend on the position of the head; the same has previously 
been demonstrated for the skeletal muscles by WHILAND. 

2. The reflexes which control this tonicity can be divided into 
two groups: tonic labyrinth reflexes and tonic cervical reflexes. 

3. The tonic labyrinth reflexes can be examined separately by 
bringing the head into various positions in space; it is required 
that, throughout the experiment, the position of the head relative 
to the trunk does not change. 

4. The fixed laws governing the tonic labyrinth reflexes, were 
published formerly in Pfiiger’s Archiv. (v. p. Honve and Ds KreryN, 
Dr KreyN and Maarus). 

5. The cervical reflexes can be examined separately by bringing 
the trunk into various positions relative to the head or conversely 
the head into various positions relative to the trunk. This experiment 
can only be carried out with animals with both labyrinths extirpated, 
so that tonic labyrinth reflexes are precluded. 

6. For the isolated cervical reflexes the following conclusions were 
arrived at: 

a. To every position of the trunk relative to the head belongs 
a special position of the eyes in the orbita. 

b. In the case of rotations of the trunk about various axes the 
eyes reach their new position in the orbita through various move- 
ments, namely : 

a. through rolling movements when the trunk is turned on its 
frontal axis. Movements of the trunk towards the skull will make 
the eyes roll with the upper pole towards the nose; movement of 
the trunk towards the lower jaw will make the eyes roll with the 
upper pole towards the ear. 

8. When the trunk is turned on its long axis, through vertical 
movements, in which process the eye towards which the back of 
the animal is turned goes downwards, the other goes upwards. 


521 


y. When the trunk is turned on its dorso-ventral axis, through 
movements in the direction of the palpebral aperture, in which 
process the eye towards which the trunk is turned moves towards 
the nose, the other eye towards the ear. 

These compensatory eye-positions in the direction of the palbebral 
aperture could be shown only for the cervical reflexes and not for 
the labyrinth reflexes. 

7. The fact discovered by Barany in 1907 that in normal rabbits 
the eye-positions, occurring with a change of the position of the 
trunk relative to the head, vary with the position of the trunk in 
space may be ascribed to a superposition of tonic labyrinth-, and 
cervical reflexes appearing in BARANY’S experiments. 

8. In some rabbits the centripetal fibers for the reflex arch of the 
tonic cervical reflexes pass only through the sensitive roots of the 
Nn. cervicalis 1 and 2. In others also the sensitive roots of the 
Nn. cervicalis 3 exert some influence. 

9. With tonic cervical reflexes the eye-muscles are affected by a 
reciprocal innervation. This was observed for the M. Rectus internus 
and externus, when the trunk was turned on its dorso-ventral axis 
with the head fixed. Also the purely tonic character of the cervical 
reflexes is distinctly demonstrable here. 

10. It holds in general for the tonic labyrinth-, as well as for 
the tonic cervical reflexes that, when the position of the head relative 
to the trunk is changed, the eyes perform such movements in order 
to attain their new position in the orbita that they try, as it were, to 
retain their position in space. However this position is not attained 
either by the tonic labyrinth or by the tonic cervical reflexes alone. 

The effect of the combinations of the two kinds of reflexes, however, 
is that the rabbit can bring its head from its normal position (head 
lowered about 35° under the horizontal) into every position by raising 
or lowering its head within wide limits. This it can do without 
change of the position of its eyes in space, consequently without any 
alteration of the field of vision. 


Pharmacological Institute of the Utrecht University. 


Physics. — “The General Relativity Theory and the Solar Spectrum’. 
By Prof. W. H. Junius and Dr. P. H. van Cirrert. 


(Communicated at the meeting of May 29, 1920). 


Of the three crucial inferences drawn by Einstein from the general 
relativity theory, which should make it possible to decide whether 
that theory conforms more closely than the old ideas to the results 
of most subtile observation, two seem to have stood the test success- 
fully. As to the third deduction — a systematic displacement of the 
Fraunhofer lines towards the red — evidence is still wanting. 

This uncertainty is not due to the smallness of the expected effect. 
Displacements of Fraunhofer lines with respect to the corresponding 
lines in the spectra of terrestrial sources have been measured in 
abundance; they are similar in magnitude to the “gravitational shift” 
required by the relativity theory, the latter shift averaging ten times 


the unity (0,001 A) in which the measured displacements are gene- 
rally expressed. But the simple law which, according to the theory, 
should connect displacements with wave-lengths, does decidedly not 
show itself in the direct results of observation; the difficulty, indeed, 
lies in the fact that several other causes (such as motion in the line 
of sight, pressure, anomalous dispersion) may co-operate, each capable 
of producing displacements of the same order of magnitude. 

One should, therefore, attempt to group and analyze the obser- 
vational data in such a way, that all influences except the EINSTEIN 
effect are eliminated or accounted for. This can be done, at least up 
to a certain point, because the said causes of displacement act 
according to different laws. 

Attempts have already been made to exclude the effect of pressure. 
ScHWARZSCHILD'), EversHeD and Royps?), St. JonN®, GRrBE and 
Bacnem*) selected for the investigation lines of which it was known 
that, in the laboratory, they did not show any appreciable pressure 
effect. The results obtained by these observers do not agree. Accord- 


1) K. ScHWARZSCHILD, Berl. Ber. 1914, S. 1201. 

2) EVERSHED and Royps, Kodaikanal Bull. 39, 1914. 

3) Sr. Jon, Astroph. Journ. 46, 246, (1917); Mt. Wilson Contrib. NO. 138. 

4) GREBE and Bacuem, Verh. d. D. Phys. Ges. 21, 454 (1919); Zeitschr. f. 
Physik. 1, 51 (1920). 


523 


ing to Sr. Joun the observed displacements tell against the exist- 
ence of the Einstein effect, whereas Gresik and Bacnem conclude 
from their observations that the gravitational shift is in evidence 
both as regards direction and magnitude. The effect of radial motion 
has been taken into account in these investigations. 

None of the above observers has, however, considered the possibility 
that anomalous dispersion might influence the position of the lines. 

The object of the present investigation is to approach the problem 
from the point of view that Fraunhofer lines are in the main 
dispersion lines’). 

It is realized that this interpretation of the solar spectrum differs 
profoundly from the current notion that one is dealing with a mere 
absorption spectrum ; we are, therefore, justified in accepting it only 
if there are convincing reasons for so doing. 

One of these is for instance the fact thaf the said interpretation 
enables us to establish, without introducing additional hypotheses, 
a comprehensive system of explanations of a great variety of solar 
phenomena which, when explained on the basis of the ordinary 
supposition as to the nature of Fraunhofer lines, lead to several 
difficulties and unsatisfactory conceptions. 

The strongest support, however, for the new interpretation of the 
spectrum is found in certain general properties of the Fraunhofer 
lines, which are readily deduced from the supposition that the lines 
are in the main dispersion lines, but of which, from other points 
of view, no explanation whatever has as yet been offered. Such 
properties are: . 

1. The general displacements of the Fraunhofer lines towards 
the red are very different in magnitude (ranging indeed from 
+ 0,020 A to — 0,007 A), even when comparing lines of one and 
the same element, and bear no relation to the displacements by 
pressure as observed in the laboratory. (Cf. especially the publications 
by EvrrsneD and his collaborators, of the Kodaikanal Observatory). 


1) Attention has first been called to the existence of dispersion bands and 
dispersion lines by one of us in 1904: Proc. Acad. Amsterdam VII, 184, 140, 
323; Astroph. Journ. 21. 271, 278, 286 (1905). Further investigations, on this 
special type of spectral lines are to be found a.o. in these Proc. IX, 848 (1906) ; 
XII, 266 (1909); XIII, 2 (1910); Le Radium 7 (Oct. 1910); these Proc. XIII, 
881, 1263 (1911); The Observatory 37, 252 (1914); Astroph. Journ. 40, 1 (1914); 
43, 43 (1916); Arch. néerl. Serie III A, tome IV, 51, 150 (1917); tome V, 
116 (1918). 

Cf. also the inaugural dissertations by Dr. B. J. van per Praars (Utrecht, 1917, 
also published in Arch. néerl. série II] A, tome V, 132) and by Dr. P. H. van 
Cirrerr (Utrecht, 1919). 


524 


2. When the lines are classified according to intensity, then, 
within each intensity class, the amounts of displacement are ‘still 
widely different from line to line; but if for each intensity class 
the mean displacement is taken, those mean values appear to depend 
on intensity according to a peculiar law, predicted on the basis of 
the dispersion theory (these Proc. XIII, 10 (1910); Arch. néerl. III A, 
tome IV, p. 59, 1917). 

3. The amount of displacement of a Fraunhofer line depends on 
the presence of closely neighbouring lines. A companion on the red 
side reduces, a companion on the violet side augments the displace- 
ment of a line towards the red, as if the components of close pairs 
of lines repel each other. 

The way in which these three characteristic properties of the 
displacements of Fraunhofer lines may be deduced from the theory 
of dispersion lines, has been indicated by one of us in some of the 
above-mentioned publications (The Observatory 87, 252; Astroph. 
Journ. 40, 1; 48, 43; Arch. néerl. III A, tome V, 116). 

Recently we have once more rigorously inquired into the third 
point, because it supplies what is probably the most convincing test 
as to the correctness or otherwise of our interpretation of the solar 
spectrum. 


Fresh evidence in favour of the view that the distribution of the 
light in Fraunhofer lines is governed by anomalous dispersion. 


The assertion that neighbouring Fraunhofer lines might, by ano- 
malous dispersion, influence each other to an appreciable degree has 
been strongly opposed by EversHep, Larmor, and Sr. Jorn. The 
latter says a.o. “While anomalous refraction may produce sporadic 
effects under occasionally favourable density gradients in the solar 
atmosphere, the conclusion from investigations and observations at 
this observatory is that, within the present limit of precision of 
measurement, the positions of the Fraunhofer lines in the spectrum 
of the solar disk are not systematically affected by anomalous 
dispersion.” *) 

We ‘are able to prove, on the contrary, that from certain obser- 
vations made on Mount Wilson with excellent apparatus, much 
experience, great care, and perfect impartiality, the existence of the 
mutual influence in question may be derived with a probability of 
about 500 to 1. 


1) Cu. E. Sr. Jorn, Astroph. Journ. 46, 250 (1917); Mt. Wilson Contrib 
N°, 138, p. 2. 


525 


The complete data on which this conclusion is based will be 
published shortly. At present we only give a summary of the in- 
vestigation, because the result tends to show the necessity of admit- 
ting, when looking for evidence as to the Emsrein effect, that in the 
solar spectrum we are substantially dealing with dispersion lines. 

Adequate material for inquiring into the possible influence of 
neighbouring lines is to be found in W. S. Abas’ measurements 
of the displacements of 467 lines in the spectrum of the sun’s limb 
as compared with the spectrum of the centre of the disk.’) But for 
two or three exceptions these lines are, in the limb spectrum, shifted 
towards the red with respect to their positions in the centre spectrum. 
That in this phenomenon gravitation potential should play any 
perceptible part, is of course excluded. Evrrsuep has convincingly 
shown that these displacements can neither be due to pressure, 
whilst his alternative explanation based on the Doppler principle, 
requiring a specific repulsive force exerted by the earth on the solar 
gases’), appears inacceptable. There is, therefore, sufficient cause to 
seek another explanation of this class of line-shifts. We connect 
these displacements with our hypothesis that Fraunhofer lines are 
in the main dispersion bands, which, indeed, envelop the real ab- 
sorption lines (which are extremely narrow) in a generally asym- 
metrical way. 

If this interpretation is correct, the above mutual influence of 
neighbouring lines must appear, for the shape of the dispersion curve 
in the environment of an absorption line is modified by the presence 
of another absorption line. How that modification must influence 
the degree of asymmetry of the dispersion line has been explained 
in Astrophysical Journal 48, 50—53 (1916). 

In order to select from Apbams’ list those lines for which, from 
the point of view of the dispersion theory, an excess or a deficiency 
of displacement towards the red is to be expected, we proceed as 
follows. 

The columns A and A' of his table are covered with strips of 
„paper, so that the choice cannot be influenced by a knowledge of 
the observed displacements; then the environing region of each line 
of the table is inspected on the atlases of Row.anp and Hraes, in 
order to ascertain whether the line may be presumed to have an 
“effective” companion. Cases in which on either side of the line a 
nearly equally effective companion is suspected, are of course omitted, 
as the opposite influences would neutralize each other wholly or for 


1) W. S. Apaus, Astroph. Journ. 31, 30 (1910); Mt. Wilson Contrib. NO. 43. 
4) EversHED, Kodaikanal Bull. 39. 


34 
Proceedings Royal Acad. Amsterdam. Vol. XXIII. 


526 


the greater part. Wave-lengths and intensities of the influencing lines 
are taken from Rowranpb’s tables. 

As “effeetive’ we entered a line of intensity ¢ (Rowland scale) if 
its distance from the line under examination was d or less, corre- 
sponding values of 7 and d being: *) 


i d. 
0 and 1 0.1 A 
2, 3, 4 0.2 
561, 8 0.3 
9 and heigher 0.4 


In a few dubious cases the general aspect of a group of lines had 
to be taken into account in judging whether a certain line could 
reasonably be expected, from the point of view of the dispersion 
theory, to undergo onesided influence by its companions. Differences 
of opinion on such cases will always be possible; but every effort 
has been made to apply the test with the utmost care. For that 
purpose three observers have selected the lines, first independently, 
then after discussion in common. 

We found 26 lines having the effective companion on the red side, 
and 24 lines having it on the violet side. 

The diagram shows the result. We have first plotted, for succes- 
sive intervals of 100 A, the mean values of all limb-centre displace- 
ments measured by Apams; they lie on the zigzag line. The small 
crosses indicate the means for intervals of 300 Á *). The intermediate 
curve R gives the progressing of the mean limb-centre displacement 
with wave-length *). Finally the displacements of the 50 influenced 
lines were separately entered. The small circles refer to lines with 
companion on the red side, the full dots to lines with companion 
on the violet side. 


!) There is, of course, something arbitrary in this assumption; by altering a 
little the corresponding values of { and d the numerical results will also be slightly 
modified; but we have ascertained that the validity of the inference is not thereby 
affected. 

2) In drawing up the means we have omitted the 17 lines whose intensity is 
greater than 10, as such lines show abnormally small displacements owing to a 
cause which the dispersion theory reveals at once. 

5) An explanation of the anomaly occurring in this curve between A 5200 and 
A 6000 has been proposed by one of us (Cf. P. H. van Cirrert, inaugural 
dissertation p. 54, Utrecht 1919). 


527 


It is apparent at a glance that the circlets lie for the greater part 
below, the full dots above the curve A of the mean displacements. 


4000 4500 5000 5500 6000 


o 
R mean limb-centre displacements (Adams), 
o lines with companion on the red side, 
e lines with companion on the violet side, 
C mean centre-arc displacements (different observers), 
G gravitational displacement according to the general relativity theory. 


The average departure from the curve is — 0,0017 A for the 26 
circlets, + 0,0015 A for the 24 dots. 

Small as these departures are, yet they are most significant. 

To prove this we shall calculate what would have been the pro- 
bability of finding mean departures of this order of magnitude, if no 
systematic influence were at work. 

The 50 selected cases gave 21 points lying above, 29 points lying 
beneath the curve A of the general mean displacements. The sum 
of their positive departures was + 0,0472, that of their negative 
departures —0,0547; so the group, as a whole, gave a sum of 
— 0,0075 A, which involves that, on the average, the group lay 
0,0075 
250 
for the 450 lines. 

Taking the sum of all 50 departures (irrespective of signs) which 

34* 


—0,00015 A beneath the curve R of the general means 


528 


the displacements of the selected lines show with regard to their 
own mean: 

0,0472 + (21 X 0,00015) + 0,0547 — (29 < 0,00015) = 0,1007 A, 
it appears, that the average departure from that mean was 
0,1007 

50 

Suppose we made a non systematic, absolutely arbitrary choice 
of 26 cases out of our gronp, then the average departure of their 
arithmetic mean from the mean of the group would only be 

0,002 ° 
= = = £0, 0004A 
Vb 
to which corresponds a probable departure: 
r = 0,8453 4 — 0,00034 A. 

Our real selection, however, was not at random; we took 26 
lines with companion on the red side, and found an average depar- 
ture — (0,0017 — 0,00015) = — 0,00155 ie moreover 24 lines with 
companion on the violet side, giving an average departure + 0,0015 
+ 0,00015 = + 0,00165 A. 

In both cases the departures from the mean of the group are 
about 4,6 times as great as the probable departure 7 (in case of 
random choice) would have been. 

Now the probability for a departure to lie between — 4,6 7 and 
+ 4,6 r is given by 

zee e—? dt (in which 9 = hr = 0,477) 
een: 4 rn err 


0 
the value of this integral being 0,998'). So there is only 0,002 left 
for the probability that, by mere chance, the mean departure of 25 
values from the general mean should exceed those limits. 

On the basis of ADAMs’ measurements we find, therefore, a pro- 
bability of 500 to 1 that there really exists a mutual influence of 
Fraunhofer lines. An analogous treatment applied to the limb-centre 
displacements measured by HEvrersnep and Royps’) has yielded a 
similar result, which will be published later. *) 

It is necessary, however, also to consider how far this mutual 
influence may be due to systematic errors in the way we estimate 
the place of a line when there is another line very near. 


— 0,002 A. 


y= 


4,6¢ 


1) CHAUVENET, Spherical and practical astronomy, Vol. II, Table IX A. 
*) Eversuep and Royps, Kodaikanal Bull. 39. 
5) A subsequent perusal and combination of all the data at our disposal has 


brought the probability of non-existence of mutual influence down to 10-68 (Note 
added in Dec. 1920). 


529 


One should be mindful both of objective and subjective errors in 
this- connection. 

Let us imagine two lines, bright in the negative (dark in the 
original spectrum), which, if standing isolated, would each of them 
show symmetrical distribution of the light, but which are in fact 
situated so near one another that they partially overlap; then the 
maxima of intensity will (as an objective effect) be at a smaller distance 
from each other than the real centres of the lines. This would become 
obvious when the intensity in the system is recorded by means of the 
micro-photometer, supposing the real distance of the cores of the 
lines to be known. 

On the other hand one would be inclined to over-estimate the 
distance between the maxima owing to the contrasts being weakened 
in the intervening space. This is a subjectiwe effect. 

It is not easy to presume which of these two opposite influences 
predominates‘). As this is a problem of high importance whenever the 
exact distance between the components of close double lines has to 
be determined, it is at present being made a subject of special 
inquiry in the Utrecht physical laboratory. 

But whatever may be the result of that investigation, it can easily 
be shown that the mutual influence revealing itself in the above 
mentioned observations published by Apams and Kversuep and Royps, 
is almost independent of the errors of estimation here considered, 
and that the phenomenon cannot therefore be ascribed to such errors. 

Indeed, let us suppose that in the spectrum of the sun’s centre 
the exaggeration of the distance between the components of a certain 
pair of lines be due to an error of estimation. 

The distance be e.g. 0,3 A, the apparent exaggeration caused by 
this nearness 0,003 A. 

Let us next consider the same pair in the spectrum of the sun’s 
limb. There both components are perhaps slightly shifted with respect 
to their positions in the centre spectrum; but their distance can 
scarcely be altered thereby more than, say, 1°/, of its original value 
of 0,3 A. Consequently the influence which the proximity of the 


1) Sr. JorN considers the latter influence the most important, and supposes it 
to be the principal cause of the fact that in RowLAND’s wave-length tables the 
distances between the components of narrow pairs of lines are greater than they 
should be according to measurements made on Mt. Wilson. He therefore calls the 
differences “systematic errors” in RowLAND's wave-length determinations (Astroph. 
Journ. 44, 16 and 265 (1916); Mt. Wilson Contrib. N°. 120 and 123). This opinion 
was contested by one of us in a communication to the Amst. Akad. 25, 1245 
(1917). Cf. also; Archives néerland. Ill A, Tome V, 122—126 (1918). 


530 


lines may have on the estimation of their distance must be practically 
identical in the two spectra: the exaggeration of the distance in the 
limb spectrum would also be 0,003 A. A mutual influence depending 
on errors of estimation will not appear in the limb-centre differences. 
The well-established fact that neighbouring lines are nevertheless 
more distant in the spectrum of the limb than in the spectrum of 
the centre must therefore be a real phenomenon. 

The only way to explain this mutual repulsion of neighbouring 
lines seems to be the one indicated by the dispersion theory owing 
to which, moreover, the phenomenon was discovered. A powerful 
support is thus given to our contention that Fraunhofer lines have 
indeed to be considered as dispersion lines, enveloping the (much 
weaker and narrower) real absorption lines in a generally asym- 
metrical way. 


The observational data as yet available contradict the inference that 
the Fraunhofer lines should be displaced by gravitation. 


We shall now refer to the displacements of Fraunhofer lines in 
the spectrum of the central parts of the solar disk with respect to 
the corresponding lines in terrestrial are spectra. 

The laws of these displacements are less easily derived from direct 
observations than those of the limb-centre displacements, because in 
many cases the wave-lengths of the are lines have not yet been 
determined with sufficient precision. It has however been established 
beyond doubt that here again the same peculiarities appear: great 
variety in magnitude of the displacements; dependence on line-inten- 
sity; mutual influencing of the neighbouring lines). This agrees 
with the conception of Fraunhofer lines as dispersion lines; indeed, 
also the radiation coming from the centre of the disk has been 
weakened by anomalous dispersion on its way through thick layers 
of gas, and therefore shows dispersion lines in its spectrum. As a 
rule these dispersion lines will cover the cores of the lines asym- 
metrically. (Ihe positions of the cores are determined by the solar 
values of their proper frequencies). 

As the radiation from the centre of the disk has in general travelled 
along shorter paths through the refracting and scattering gaseous 


1) ArBreEcHT, Astroph. Journ. 41, 333 (95); 44, 1 (1916). Royps, who 
challenges ALBRECHT’s conclusions, yet finds himself that 17 lines with companion 


on the red side give a mean sun-are displacement towards the red of only 0,0032 A, 
whereas 30 lines with a violet companion give a displacement towards the red 


of 0,0079 A. (Kodaikanal Bull. 48). 


531 


layers than has the light from the limb, the asymmetry of the centre 
lines is smaller, as a rule, than the asymmetry of the limb lines; 
the difference manifests itself in the limb-centre displacements. 

Which are the greater displacements, those of the limb lines with 
respect to the centre lines, or those of the centre lines with respect 
to the positions of the solar proper frequencies? 

Supposing the solar and terrestrial frequencies to be identical 
(absence of Einstein effect), and exactly given by the positions of the 
are lines, the simple comparison of the average limb-centre displa- 
cements with the average centre-arc displacements would teach us 
that there is not much difference in magnitude between the said 
two categories of displacements. The second one gives a somewhat 
smaller mean, as will be shown further on. The great inequality of 
the displacements of different lines is also similar in both cases, and 
points to a common origin and nature of the two phenomena’). 
Moreover, various considerations regarding the constitution of the 
outer layers of the sun lend support to the inference, that the light 
from the central parts of the disk has had on the average not quite 
half as much opportunity to be refracted and scattered, as has the 
light coming towards us from the marginal parts. 

The deductions from the dispersion theory are therefore quite in 
harmony with the observed displacements towards the red (both 
limb-centre and centre-are shifts), if the terrestrial are lines really 
give us with great approximation the solar values of the proper 
frequencies. 

The following table contains a summary of the observational 
material we have used. The sun-are displacements given in the 
tables of GRrrBw and Bacnem (Verh. d. D. Phys. Ges. 21, 454, 1919), 
EversHep (Kodaikanal Bull. 36), Korps (Kod. Bull. 38), Eversnip 
and Royps (Kod. Bull. 39), 446 values in all, most of which are 
means derived from several observations, have been divided by us 
into three groups according to wave-length, and for each group 
(covering 800 A) the mean value dof the displacement has been taken. 

These three values of d are indicated by eross-bloeks in the 
diagram on page 527. The intermediate block-line C shows the 
general progression of the sun-are displacements with wave-length ; 
it remains below the curve F of the limb-centre displacements, as 
already remarked. 


1) It should be kept in mind 1. that with regard to the second category of 
observed displacements the uncertainty about the positions of many arc lines cannot 
be overlooked, and 2. that, according to the dispersion theory, a simple propor- 
tionality of the two categories is not to be expected. 


2 532 


a Number of lines. | 5 5 
| 
| | 
3650—4450 | | A} f 
I 287 | 0.0050 A 0.0081 A 
mean 4050 
4450—5250 | | 
Il. | | 118 | 0.0042 0.0097 
mean 4850 | | 
52506050 | 
Ill. 41 0.0065 0.0113 
mean 5650 | 


The foregoing should give the answer to the question whether the 
existence of a gravitational displacement as required by the general 
relativity theory is compatible with the observations. The numerical 
values deduced from that theory are indicated by d' in the table 
and by the double line G in the diagram. 

The ordinates of G refer to displacements of the cores of the 
solar lines with respect to the terrestrial lines. Taking into account 
that the observed Fraunhofer lines are dispersion lines, and, therefore, 
are generally displaced towards the red with respect to their cores, 
we see that, if the Eistum effect did exist, the total displacements 
of the Fraunhofer lines with respect to the terrestrial lines would 
group themselves around mean values ranging from 0,008 + 0,004 = 
0,012 A at 2 4000 to 0,012 + 0,006 = 0,018 A at 2 6000 (as shown 
by the broken line at the top of the diagram). 


These theoretical mean values average 0,010 A higher than those 


actually observed — a difference far too great to be attributed to 
accidental errors. 
It is of course possible — although not probable — that there 


exists an as yet entirely unknown cause of general displacement of 
Fraunhofer lines towards the violet, exactly balancing the gravitational 
displacement. One should also keep in mind the possibility that the 
are lines have failed as yet to make the terrestrial frequencies 
known with sufficient precision, and may prove to be systematically 


displaced towards the red by so much as 0,010 A. 


On the basis of our present knowledge, however, we are forced 
to conclude that the gravitational displacement does not exist. 


We feel greatly obliged to Dr. M. Minnarrt and Miss C. B. BLEEKER 
for their active collaboration in analyzing the data at our disposal. 


Utrecht, May 1920. Heliophysical Observatory. 


Physiology. — “On Fibrillation of the Heart.” (Part Ill). “Ven- 
tricular Fibrillation and “Gehiüufte” Extrasystoles of the Ven- 
tricle excited by the “Eriegung” consequent on an Artificial 
Auricular Systole.’ By Dr. S. pu Boer. (Communicated by 
Prof. WeRTHEIM SALOMONSON.) 


(Communicated at the meeting of April 23, 1920). 
IND 


In the first Part I have described experiments with the bled frog’s 
heart in which ventricular fibrillation was excited through the ad- 
ministration of a single inductionshock to the ventricle directly after 
the conclusion of the refractory stage. 

I have observed since, that a direct induction shock is unnecessary, 
as fibrillation occurs also when excitation affects the ventricle directly 
after the conclusion of the refractory stage. We can carry this into 
effect by administering an induction shock to the auricles of the 
bled frog’s heart at the beginning of their excitable period. After 
the auricular extrasystole thus excited, the excitation proceeds along 
the atrio-ventricular paths to the ventricle. This excitation can reach 
the ventricle directly after the close of the refractory stage, only 
when the shock is administered to the auricle as soon as possible. 
This is instanced by the following experiment. In fig. 1 the suspen- 
sion curves of the ventricle (V) and the auricles (A) of a frog’s 
heart are illustrated, 15 minutes after the bleeding. Between the 
curves of 1a and 15 two heart-periods have fallen out. At the 
deflection of the signal in fig. la the auricles received an induction- 
shock, a short time after the conclusion of the refractory stage. 
Hereby an extrasystole of the auricles was generated. The excitation 
then reaches the ventricles at the end of the diastole (i.e. at a moment 
when the refractory stage of the ventricle has been concluded for 
some time), so that a premature ventricular systole is the consequence. 
Subsequently the auricles and the ventricle resume the ordinary 
rhythm. 

In fig. 16, on the contrary, the auricles were stimulated at 1. in 
the beginning of the excitable period, by which an extrasystole of 
the auricles is engendered. After this the excitation reaches the 


534 


ventricle already in the middle of the diastole, i.e. directly after 
the conclusion of the refractory stage. Instead of a premature ven- 
tricular systole, an irregular fibrillation of this chamber ensues, 
which is followed by a short post-undulatory pause. During this 


PRIN PRON ON, ANBI SD ON 


fe Rg I Ef TEE LILO Dn 


Rig. 0. 
fibrillation the auricles maintain their regular pulsation: after the 
extrasystole of the auricles followed the ordinary compensatory pause 
and subsequently the auricles resumed their regular beat *). 

At 2 the auricles are again stimulated at the beginning of the 
excitable period. After this extrasystole of the auricles the ventricle 
readily resumes fibrillation after the conclusion of the a—v-interval. 

In this experiment the relations are much more intricate than in 
the experiments of the first paper, in which the ventricle was stimu- 
lated directly after the conclusion of the refractory stage, after which 
ventricular fibrillation ensued. After some trials I readily found this 
point and fibrillation could easily be excited. In the experiments we 
are describing now, this is not done so easily, which is readily un- 
derstood. 

First we have to fix the moment, when the refractory stage of 
the auricles terminates. But, this done, the success of the experiment 
depends on two more factors, viz: 

1 on the rate at which the excitation proceeds from the stimu- 
lated spot to the ventricle. 


1) The auricular curves have diminished during the ventricular fibrillation. This 
is on account of the altered mechanic relations of the registration consequent on 
the fibrillations of the ventricle. 


53D 


2 on the duration of the refractory stage of the ventricle. 

Only when these relations are such that the excitation reaches 
the ventricle directly after the conclusion of the refractory stage, 
will the ventricle begin to fibrillate. 

Usually the excitation reaches the ventricle after an auricular 
extrasystole too late for a ventricular fibrillation. To make the 
experiment succeed better one might lengthen the refractory stage 
by poisons (digitalis, veratrin, ete), through which the excitation 
might reach the ventricle after an auricular extrasystole more 
directly after conclusion of the refractory stage. However, as ap- 
peared from my first communication, it is just after digitalis poisoning 
that the lengthening of the refractory stage hinders the prolongation 
of fibrillation. 

We, therefore, abandon this artifice. I have now succeeded in 
modifying the relations in the non-poisoned bled frog’s heart in such 
a way that the experiment succeeds better. It is well known that 
the duration of the post-compensatory systole is longer than that of 
the periodic systoles. This longer duration coincides with a longer 
duration of the refractory stage, so that when in the commence- 
ment of the post-compensatory systole I administer an induction 
shock to the auricles as early as possible in the excitable period, 
the experiment may meet with a better success. Thus through 2z- 
direct stimulation I could indeed bring the ventricle to fibrillation 
with greater ease. This is instanced in fig. 2. In fig. 2a the auricles 
receive an induction-shock at the first deflection of the signal, which 
causes. on extrasystole of these chambers followed by a premature 
ventricular systole. Now the stimulus’ is repeated after the next 
auricular systole and this as early as possible in the excitable period. 
An extrasystole of the auricles ensues. 

The excitation conducted after this to the ventricle, makes the 
ventricle fibrillate for some time, during which the auricular curve 
displays some anomalies, caused no doubt by intercurrent retrogade 
_ excitations running from the ventricle to the auricles to be oecasion- 
ally incited to an extrasystole. At the fourth deflection of the signal 
the auricles are again stimulated during a post-compensatory systole, 
but now the stimulus affects the auricles a little later than the preceding 
time. Subsequently a brief fibrillation originates (we might also call 
this two extrasystoles — it is wise not to draw a sharp boundary 
line between the two deviations). 

The curves of fig. 26 were registered with an interval of some 
heart-periods after those of fig. 2¢. Here an induction shock affects 
the auricles at the second deflection of the signal, but this time rather 


536 


late in the excitable period. Accordingly after the auricular extra 
systole thus excited, the ventricle presents a premature systole. The 


experiment will succeed better when at the fourth deflection of the 
signal the shock is repeated during a post compensatory systole at 
an earlier moment. Now an extra-systole of the auricles originates 
in the beginning of the excitable period. The excitation reaching the 
ventricle after this, comes early enough to evoke a brief fibrillation. 
_As before, the auricles exhibit some anomalies. At the sixth deflection 
of the signal the auricles are once more stimulated during a post- 
compensatory systole. This time this stimulus affects the auricles a 
little earlier still than the preceding time. After this extra systole 
of the auricles the ventricle begins to fibrillate for a longer period 
under the influence of the excitation. During this fibrillation the 
auricles present anomalies similar to the preceding. 

In Fig. 3 the curves show that the contractility of the ventricle 
was still intense’), although through indirect stimulation the ventricle 
could be made to fibrillate. At 1 the auricles receive an induction 
shock, which gives rise to an extrasystole of the auricles. 

This is followed by a premature ventricular systole with the ordinary 
a—v-interval. At 2 the extra-stimulus is repeated directly after the 
postcompensatory sytole, which is succeeded by a small extra-systole 


') With all curves taken with double suspension, the ventricular curves were 
registered with a five-fold magnification. 


537 


of the auricles. When after this the excitation reaches the ventricle 
before the middle of the diastole, the refractory stage of the ventricle 


VS 


Lot mes An | 
LLLLLLLE LLL LLLLLLLLELLNLLLLLELLELLE LL 


Fig. °s. 


has just come to a close. Consequently the ventricle begins to 
fibrillate while the auricles revert to pulsating in the normal rhythm. 
At 4 a renewed shock is administered to the auricles after a post- 
compensatory systole as early as possible in the excitable period. 
Again a brief fibrillation of the ventricle ensues after the auricular 
extrasystole. 

The above experiments afford sufficient evidence to assert that the 
ventricle begins to fibrillate when an excitation reaches this chamber 
directly after the conclusion of the refractory stage. Lf, however, an 
excitation reaches the ventricle later, an ordinary premature systole 
is originated. 

It appears, then, that experimentally the ventricle can be made 
to fibrillate through an excitation, by a single shock to the auricles 
directly after the conclusion of the refractory stage. After the 
auricular extrasystole thus excited, the excitation proceeds to the 
ventricle and makes it fibrillate, when at least it reaches the ventricle 
directly after the conclusion of the refractory stage. If the excitation 
reaches the ventricle too early, te. during the refractory stage, an 
extra-pause of the ventricle will ensue, because the excitation rebounds 
on the still non-excitable ventricle. If however the excitation comes 
too late, a premature ventricular systole will appear. It is evident 
that the success of the experiment depends on the three following 
factors : 

|. on the moment at which the auricles are stimulated. Since the 
excitation reaches the ventricle almost always too late, it is desirable 
to stimulate the auricles as early as possible in the excitable period. 

2. on the time of conduction from the point at which the auricles 
are stimulated to the ventricle. 


3. on the duration of the refractory stage of the ventricle. 

Since the excitation reaches the ventricle almost always too late 
the experiment will generally be more successful during the post- 
compensatory systole, of which the refractory stage has been lengthened. 
Another favourable factor consists in the fact that during the post- 
compensatory systole the rate of the conduction of the excitation is 
increased, which facilitates otir endeavours to make the excitation 
reach the ventricle at the right moment. 

There are still more obstacles in the way of this experiment. I 
said before that the auricles should be excited as early as possible 
in the excitable period for the experiment to succeed. Now just 
then either auricular tibrillation or “gehäufte” auricular extra-systoles — 
arise') repeatedly after a shock, anyhow when the metabolic con- 
dition of the auricles is sufficiently bad. 

In these two cases the ventricle does not display any fibrillation, 
but quite another aspect, which we purpose to describe in another 
paper. If our experiment is to succeed the extra-stimulus must, there 
fore, be followed by asingle auricular systole. The excitation reaching 
the ventricle after this, can cause it to fibrillate. 

Now, since, in the suspended frog’s heart, the metabolic condition 
of the ventricle is impaired much sooner than that of the auricles, 
the ventricle will reach a condition in which it may be made to 
fibrillate, much sooner than the auricles. Consequently an early shock 
applied in this period to the auricles will yield an extrasystole ; 
when after this the excitation reaches the ventricle directly after the 
conclusion of the refractory stage, this chamber will begin to fibrillate. 

I must lay stress on the fact that a chamber can be brought to 
fibrillation through an excitation wave. This fact seems to me to be of 
some clinical significance, because when the human heart-beat is 
accelerated through a sudden bodily exercise i.e. when impulses are 
sent out at a quickened tempo from the pace-maker of the heart 
(sino-auricular node of Kerita-FLUcK), we can conceive an impulse 
to reach the auricles or the ventricle suddenly, directly after the 
conclusion of the refractory stage. The chamber concerned then may 
suddenly begin to fibrillate. 

From this and the first communication it is obvious, that the 
metabolic condition of the chamber concerned is decisive for the 
origin and the continuance of fibrillation, which can reveal itself 
only when this metabolic condition has been sufficiently impaired. 
My new experimental data can also throw more light upon the 


1) To be discussed in a subsequent publication. 


539 


origin of sudden heart-death (according to Hurine’s conception, which 
has been generally received, this death is caused by ventricular 
fibrillation). 


From my second communication it is evident that “gehaufte”’ 
ventricular extra-systoles may arise after direct excitation of the 
ventricle under conditions similar to those under which ventricular 
fibrillation is generated. Now the question arises whether “gehäufte”’ 
ventricular extra-systoles can also be brought about under the influ- 
ence of an excitation that originates from the auricles and reaches 
the ventricle directly after the conclusion of the refractory stage. In 
the curves of fig. 4 this question meets with an affirmative answer, 
they were taken with the string galvanometer 1'/, hours after the 
bleeding. A certain irregularity is exhibited by the tempo of the 
ventricular systoles, because not all sinus-impulses were followed by 
a ventricular systole. [ placed a P where the P-deflections of the 
electograms are visible in the curve. Now when measuring the 
intervals between the various P-deflections, we can easily realize 
the ventricular rhythm. | 


Intervals between the P-deflections. 


Time-units Time-units 
P'— Pp? = 26'/, PtP) = 26" |, 
PSP? _— 26°/, P— PRP —_— i eal 
BAE CS Tie P= Pe ay"), 


It appears, then, that the duration of the sinusperiods amounts to 
87/, time-units, so that between P! and P?, P? and P? and between 
P* and P* two P-deflections coincide every time with the ventri- 
cular electrograms. Between P* and P*, P® and P°, P* and P’ one 
P-deflection coincides every time with the ventricular electrograms. 

The P-R intervals lasted particularly long (on an average 7/, 
second). 

The stimulating electrode was placed against the auricles not far 
from the atrio-ventricular groove. 

During this registration the auricles receive twice an opening 
induction shock viz. at 1 and at 2. The moment at which the shock 
is administered, is marked by the deflection of the signal, interpolated 
in the primary circuit, upwards. The closing induction shocks were 
turned aside. At 1 the auricles receive an opening induction shock 
a little after the summit of the 7-deflection (in consequence of intru- 
ding current-loops the electrogram-curve shows a gap at the moment 


540 


of the shock). About */, of a second later the electrogram of the 


subsequent ventricular systole commences. 


oe a 


Serer 


be considered short, when com- 


pared with the long P—R-interval, is due to the short distance to 


This conduction time, which may 


541 
be covered by the excitation, owing to the fact that the stimulating 
electrode is placed close to the auriculoventricular groove '). 
Whereas after the stimulus applied at 1, the ventricle responds 
to the excitation by a single ventricular systole, the result is quite 
different after the stimulus administered at 2. This finds an expla- 
nation in the fact that here the induction shock affects the auricles 
a little earlier. Whereas at 1 the stimulus affects the auricles a little 
after the summit of the 7-deflection, at 2 it reaches the auricles 
a little before the summit of the 7-deflection. After an interval of 
*/, sec. the ventricle does not now respond to the excitation by a 
single systole, but by a series of five connected systoles. From the 
electrogram-curves it can be seen that between the various electro- 
grams the string does not remain in the position of rest or does so 
only for a short time. This “Häufung” of extrasystoles is due to 
the fact that the excitation reaches the ventricle somewhat sooner after 
the preceding ventricular systole than the preceding time. Now when 
looking more closely at the electrograms of the ‘‘gehaufte” ventri- 
cular systoles, it appears that they are all different (the 2.4 and the 
4th curve are most likely produced by partial systoles?)). We 
conclude, therefore, that the ventricle of the bled frog’s heart can 
respond after an artificial auricular extra-systole to the applied 
- excitation by a “Häufung” of extra-systoles, if only this excitation 
is applied early enough. An excitation that reaches the ventricle at 
a later moment produces a single premature ventricular systole. 
From the Pathological Laboratory of the 
April 1920. Amsterdam University. 


1) The deflection of the signal downwards is caused by a closure of the primary 
circuit; these closure shocks are turned aside, so that the ventricular systole, the 
electrogram of which commences somewhat later, cannot be engendered by this 
closure. The electrogram succeeds the preceding one after an interval of 101/, 
time units, so that it is retarded 1°’; time units, in consequence of the brief pre- 
ceding interval after the previons ventricular systole. 

So the ventricle pulsates in this registration in the halved rhythm, except that 
a bigeminal group has manifested itself here. After the two shocks this halved 
ventricular rhythm is disturbed artificially. 

2) It might also be supposed that the ventricle had been directly stimulated by 
current loops. However */; sec. is much too long for an electric latent time. So 
this supposition must be precluded. 


Proceedings Royal Acad. Amsterdam. Vol. XXIII. 


Physiology. — “On the Artificial Extra-pause of the Ventricle 
of the Frog's Heart.’ By Dr. S. pr Borr. (Communicated by 
Prof. W. EINTHOVEN). 


(Communicated at the meeting of June 26, 1920). 


DastrE and LANGENDORFE were the first to show that sometimes 
after applying an artificial stimulus to the auricles of the frog’s heart, 
a prolonged ventricular pause arises, which is not initiated by an 
extrasystole of the ventricle. ENGELMANN was in position to corroborate 
this experiment and to elucidate it. He pointed out that the experiment 
succeeds only when the stimulus is given to the auricles at the 
commencement of the ventricular systole, after which an extrasystole 
of the auricles will ensue. After this the excitation proceeds to the 
ventricle and reaches it before the close of the refractory stage, so 
that no ventricular systole follows. Only after the compensatory 
pause which succeeds the extrasystole of the auricles do the auricles 
and the ventricles resume their normal rhythm. This experiment, 
however, seldom succeeds. It is instanced in fig. 1. At 1 the auricles 
were given an induction shock *) at the commencement of the ven- 
tricular systole. After the auricular extrasystole evoked by this shock 
the excitation reached the ventricle during the refractory stage, so 
that no systole of this chamber arose. 

Not before the end of the compensatory pause of the auricles did 
an auricular systole arise again, followed by a ventricular systole. 

I have now been more successful in this experiment, by lengthen- 
ing the duration of the refractory stage of the ventricle. Then 
the excitation after the artificial extrasystole of the auricles will 
with greater certainty reach the ventricle still in the refractory 
stage. This lengthening of the refractory stage of the ventricle may 
be effected in different ways. First of all we know ever since 
LANGENDORFF wrote, that the duration of the posteompensatory sys- 
tole has increased. I now found that during the postcompensatory 
systole also the duration of the refractory stage has increased. It 


1) In all figures the closing of the primary circuit was indicated by a downward 
deflection of the signal. At the opening of the primary circuit an upward deflection 
of the signal was effected. In figs. 1, 2, 3, 4, and 6 the closing stimuli were shut 
off and consequently they did not reach the heart. 


543 


may be expected, therefore, that the experiment succeeds better 
during a postcompensatory systole. This may be seen from fig. 1, 
in which the auricles received a fresh stimulus during the post- 


Fig. 1. 
Fig. 2. 


compensatory systole at the second upward deflection of the signal, 
and hereafter followed another extrapause of the ventricle, which 
was not preceded by a premature ventricular systole. 


At 2 the auricles were again stimulated at the commence- 
35* 


544 


ment of -a ventricular systole. After the evoked extrasystole 
of the auricles the excitation reached the ventricle after the refractory 
stage, so that a premature ventricular systole ensued. When, how- 
ever, at the next upward deflection of the signal the stimulus is 
repeated at the commencement of the postcompensatory systole, the 
excitation after the extra auricular systole thus evoked, readily 
reaches the ventricle during the refractory stage. Now an extrapause 
of the ventricle follows. In this way it is easy to repeat the ex- 
periment during every following ventricular systole, which is broad- 
ened every time. At last it is even unnecessary to stimulate the 
auricles at the commencement of the ventricular systole, the last 
stimulus being given about the middle of the ventricular systole 
without diminishing the suecess of the experiment. This, indeed, is 
easily understood, if we look more carefully at the ventricular 
systoles of this artificial halved ventricular rhythm. We then observe 
that after the compensatory pause the postcompensatory systole is 
broader than the preceding ventricular systoles, and that every sue- 
ceeding systole surpasses its predecessor in broadness. We see then 
that the contractility of the ventricular muscle increases after every 
lengthened ventricular pause. This restoration of the ventricular 
muscle in the artificial halved rhythm involves an increase in dura- 
tion of the refractory stage from systole to systole. This is why 
ultimately the stimulus can be administered to the auricles later in 
the ventricular period, without interfering with the suecess of the 
experiment. After the last stimulus the ventricle resumes again the 
normal rhythm. *) 

In the second place we can lengthen the refractory stage of the 
ventricle by poisons, namely digitalis, veratrin, antiarin or barium- 
chloride and, by doing so, ensure success of our experiment. The 
curves of Fig. 2 refer to a frog’s heart that had been poisoned 
with bariumchloride. At every upward deflection of the signal the 
auricles receive an opening induction shock at the commencement 
of a ventricular systole. Every time there appears an extrasystole 
of the auricles and every time after this the excitation reaches the 
ventricle during the refractory stage, so that extrapauses of the ventricle 
originate, which are not preceded by premature ventricular systoles *). 


1) After poisoning with veratrin, digitalis, antiarin or barium-chloride, the halved 
rhythm of the ventricle can persist after one or more extra-pauses of the ventricle, 
without stimulating the heart any more. This also occurs after bleeding the non- 
poisoned frog’s heart. (See fig. 5). 

2) In a later stage of this intoxication the ventricle maintains its pulsation in 
the halved rhythm after such an artificial extrapause. 


545 


I have now detected that artificial extrapauses of the ventricle 
may be evoked in the frog’s heart in quite another manner. Whereas 
in the method described above, the prolongation of the refractory 
stage of the ventricle was the decisive factor, the following method 
is based on a principle unknown as yet in the physiology of the 
heart: When we place the stimulating electrode in the auriculo- 
ventricular groove, we can evoke under certain circumstances (pro- 
longed refractory stage of the ventricle), by the administration of. 
an extra-stimulus towards the close of the diastole of the ventricle, 
an extrapause of the ventricle, which is not preceded by an extra- 
systole of this chamber. | 

In our experiments described above we had to give the extra- 
stimulus at the beginning of the systole to obtain the desired result. 
When the stimulus was given a little later a premature ventricular 
systole succeeded the extrasystole of the auricles. 

It is obvious, then, that when a stimulus at the end of the dias- 
tole of the ventricle produces the same effect, it cannot be explained - 
in the same way. We shall therefore illustrate the latter experiment 
by some curves. In fig. 3 we see a reproduction of the suspension 
curves of a frog’s heart after veratrin poisoning. (The heart was 
left in situ and the circulation of the blood was left intact; some 
drops of 1°/, sol. acetas veratrini, had been injected into the dorsal 
lymphsac about 10 minutes before). At the first upward deflection 
of the signal an opening induction shock was given. After this we 
see an auricular systole represented in the suspension curve, which 
is not followed by a systole of the ventricle. Just as in the experi- 
ments described above, an extrapause of the ventricle follows after 
this auricular systole. At the next upward deflection the same expe- 
riment was repeated in the upper row of curves with the same 
result. Now when measuring the curve we find that the auricular 
systole, which appeared a short time after each of the two stimuli, 
follows after the commencement of the preceding auricular systole 
with an interval of a sinus period. We, therefore applied the extra- 
stimulus in the auriculo-ventricular groove a short time before the 
commencement of anormal periodic auricular systole. At that moment 
the ventricle was apparently still refractory, as there did not appear 
an extrasystole of the ventricle. The auricles, however, respond to 
the stimulus. The excitation now traverses the auricles from the 
auriculo-ventricular boundary in the direction of the sinus venosus. 

But simultaneously the periodic sinusimpulse traverses the auricles 
in an opposite direction. The two excitations meet and rebound. At 
that moment the auricular systole is accomplished under the influence 


546 


of two excitations, passing through the two chambers in opposite 
direction. The excitations clash against each other and are annibi- 
lated. Now we understand that the auricular systole succeeding the 
extra stimulus, originates partly under the influence of the periodic 


Fig. 3. 


\ 


sinus impulse and partly from the extra stimulus.') It is also clear 
that this auricular systole cannot in this case be followed by a 
ventricular systole. In the lower curves, registered a little later, 
this experiment is repeated with the same result at the first and 
the third upward deflection of the signal. At the second upward 
deflection of the signal the stimulus is given a little later, so that 
then an extrasystole of the ventricle appears. In fig. 4 are illustrated 
the suspensioncurves and the electrograms of a frog’s heart after 
antiavin poisoning. Initially the ventricle pulsated in halved rhythm, 
which at the first upward deflection of the signal was changed into 
the normal rhythm of twice the velocity. At the second upward 
deflection of the signal another inductionshock is administered in 
the auriculo-ventricular groove.?) We see from the stringcurve that 
this stimulus is administered a short time after the P-deflection. At 
this moment the ventricle is apparently still refractory, so that an 


') It goes without saying that it depends on the moment, at which the extra- 
stimulus is administered to which impulse the greater part of the auricular systole 
owes its origin. So, for instance, in Fig. 6 the two auricular systoles will arise 
for the greater part from the extra stimulus. 

*) The moment at which the extra stimulus is applied, is marked by the signal 
and may also be seen_from the stringcurve, which shows a small gap owing to 
a short swerving of the string. 


547 


extrasystole of the ventricle is not evoked '). The auricles, however, do 
respond to the stimulus, so that these are now traversed at the 


> 


út 


Fig. 4. 


[LC ELL Me Ld 


1) In the stringeurve we see directly after the stimulus, a small triangular 
deflection, which tells us that after all an extremely small part of the ventricle is 


548 


same time by an excitation in a retrograde direction. This excitation, 
which traverses the auricle after the extra stimulus, encounters in 
the auricles the periodic sinusimpulse, which was already on its 
way from the opposite side at the moment when the extra stimulus 
was given. Both excitations are then annihilated, so that no prema- 
ture ventricular systole can follow and an extrapause of the ventricle 
manifests itself. Hereafter the normal ventricular rhythm is trans- 
posed into the halved rhythm’). 

It is beyond doubt that in this case the greater part of the auri- 
cular systole is owing to the periodic sinusimpulse, because this 
impulse was already traversing the auricles at the moment when 
the extrastimulus was being administered. We have seen heretofore 
that at the moment when the extrastimulus in the auriculoventri- 
cular groove is administered, the ventricle must be refractory. To 
ensure success of this experiment it will be well to lengthen the 
refractory stage of the ventricle. 

In the two preceding experiments we have effected this lengthen- 
ing by veratrin-, or by antiarin-poisoning. We can now avail our- 
selves also of the fact that the refractory stage of the ventricle is 
lengthened by the postcompensatory systole. This is instanced in Fig. 5. 

It represents the suspension curves of the auricles (lower curves) 
and of the ventricles (upper curves) of a frog’s heart after bleeding. 
The stimulating electrode is applied in the auriculoventricular groove. 
At the downward deflection of the signal a closing shock is admi- 
nistered *). This gives rise to an extrasystole of the ventricle, which 
is followed by a compensatory pause. During the postcompensatory 
systole an opening shock is applied. Although this shock was admin- 
istered at the commencement of an auricular systole just as the 
previous shock, the result is quite different. The refractory stage of 


contracted. We are safe to conclude that the sinus impulse cannot rebound on 
this extremely small partial contraction, since, indeed, in the frog’s heart the 
auricles are interconnected with the ventricle all along the auriculo-ventricular 
groove (auriculo-ventricular funnel.) Similarly we see in fig. 3 a slight difference 
in the magnitude of the deflections of the suspension curve, after the four stimuli 
which initiate the extrapauses of the ventricle. Very likely also here an extremely 
small portion of the ventricle has been made to contract once or twice. 

') | need not enlarge upon these transpositions of rhythm and the changes they 
involve for the ventricle-electrograms. They were discussed by me in Koninklijke 
Akademie van Wetenschappen te Amsterdam Proceedings Vol. XX p. 696, 
Vol. | (1917) p. 271 and 502. Archives Neéerl. de Physiologie tome Ill (1918) 
p. 7 and 90. Pfliiger’s Archiv. Bd. 173, S. 78. 

%) In this figure the closing induction shocks are not shut off and are announced 
by a downward deflection of the signal 


49 


» systole, namely, is lengthened, so that at the 


moment when the stimulus is applied 


the postcompensatory 
and consequently 


, the ventricle is still refractory 


The auricles, however, 


auriculoventricular boundary, so 
traverses the auricles in retrograde 


xtrasystole. 


stimulus at the 


no e 


presents 


do respond to the 


excitation 
ie) 
of 
E 


an 


GENNER NENDE DEET 


FNS EML RY AAU a UNA 


that consequently 


550 


direction. This excitation encounters in the auricles the periodic 
sinusimpulse, so that both excitations are annihilated and no prema- 
ture ventricular systole can follow. After the extrapause of the ven- 
tricle, thus originating, the following systole of the ventricle is 
extended and broadened. Now because this systole engenders a 
prolonged refractory stage of the ventricle, the ventricle is caught 
in the halved-rhythm'). It is evident that the previously described 
experiments succeed only when the extra stimulus affects the auri- 
culoventricular groove at a special moment. 

If that moment coincides with the moment at which the periodic sinus- 
impulse enters the auricles, the experiment will succeed. Success will 
even be achieved when the extra stimulus is applied somewhat later 
or earlier. In fig. 4 e.g. at the second upward deflection of the signal, 
it was applied shortly after the /-deflection, therefore shortly after 
the periodic impulse had entered the auricles from the sinus venosus. 

In fig. 6 the experiment succeeded twice through extra stimuli 
which were applied shortly before the /-deflection in the auricu- 
loventricular groove. At the first upward deflection of the signal the 
extra stimulus was applied on the peak of the negative 7-deflection, 
i.e. still before the P-deflection would be registered *). The excitation 
then traverses the auricles in a retrograde direction and encounters 
the periodic sinusimpulse in the vicinity of the sinus venosus. The 
P-deflection, which otherwise would have revealed itself directly 
after the close of the 7-defleetion, does not appear now. The auri- 
cular systole is somewhat premature in this case and may still just 
be seen in the suspension curve in the last part of the ventricular 
diastole. It is obvious that this auricular systole is chiefly owing to 
the extra stimulus. 

At the second upward deflection of the signal the stimulus was 
applied a little before the peak of the 7-deflection. The result is similar 
to that with the previous stimulus viz. an extrapause of the ventricle. 

If the extra stimulus is applied much later or earlier than the 
moment at which the sinus impulse enters the auricles, no extrapause 
of the ventricle will follow. If later the extra stimulus will affect 
the ventricle after the refractory stage and an extrasystole of the 
ventricle will ensue, followed by a compensatory pause. This is 
illustrated in fig. 3, in the lower curves at the second upward 
deflection of the signal. 


1) These transpositions of rhythm in the bled frog’s heart will be discussed in 
the following communication. 

2) In the electrogram-curve we see the P-deflections appear directly after the 
close of the 7'-deflectiuns. 


55 | 

Conversely, when the stimulus is given much earlier, an extra- 
systole of the auricles is originated, after which a systole of the 
ventricle follows at a normal a —v interval. An instance of this case 
is given in fig. 6 at the third upward deflection of the signal. 

At the first and the second upward deflection of the signal the 
extrastimulus was applied at the peak of the 7 deflection ora short 
time before it, which resulted in an extrapause of the ventricle. At 
the third upward deflection of the signal, however, the extra stimulus 
was applied much earlier, viz. rather more than '/, second before 
the peak of the 7-deflection. It appears that the auricles respond 
already to the stimulus and present a complete extrasystole, but this 
retrograde excitation is not stayed in its course by the periodic 
sinusimpulse in the auricles. After this auricular extrasystole the 
excitation proceeds to the ventricle and induces it to contract. 

Success of the latter experiment depends upon various conditions : 

1. The extrastimulus is to affect the auricles after the refractory 
stage of these chambers. 

2. After the artificial extra-systole the excitation is to reach the 
ventricle after its refractory stage. 

3. The extra-stimulus is to be applied so early that the excitation 
which traverses the auricles after this stimulus in retrograde direction, 
does not encounter the next sinusimpulse in the auricle. 

Finally I wish to advert to the necessity of amplifying ENGEL- 
MANN’S interpretation of the constant deviation of the compensatory 
pause in connection with the present investigation. According to 
ENGELMANN the reason why, instead of the extrasystole normal periodic 
ventricular systole has fallen out, is because the periodic sinusimpulse 
reached the ventricle during the refractory stage of the extrasystole. 
The present research induces me to add that in some cases the 
periodic ventricular systole falls out because after the extra stimulus 
the excitation, which proceeds also in retrograde direction, clashes 
upon the periodic sinusimpulse, so that both excitations are annihilated. 

When we thus amplify the interpretation of the duration of the 
compensatory pause, a fact becomes clear to me that had been known 
to me long since, namely that when an extra stimulus is given to the 
ventricle, we see in some of the experiments, during the extrasystole 
a P-deflection expressed in the electrograms, in others we do not. 
If the P-deflection is absent it is obvious that the periodic sinus- 
impulse has not traversed the whole auricle, but has been stayed in 
its course by the excitation proceeding in retrograde direction, evoked 
by the extra stimulus. 


Physiology. — “On Artificial and Spontaneous Changes of Rhythm 
in the Bled Frog's Heart’. By Dr. S. pr Boer. (Communicated 
by Prof. W. EINTHOVEN). 


(Communicated at the meeting of June 26, 1920). 


When a frog’s heart has been deprived of blood and suspended, 
the rhythm of the ventricle is sometimes reduced to a halved rhythm, 
a phenomenon that may also be observed in the intact circulation 
of the blood after poisoning with veratrin, digitalis, antiarin or 
bariumchloride. 

The cause lies in the fact that under these conditions the duration 
of the refractory stage of the ventricle increases. This increase of 
the duration of the refractory stage is to be ascribed to a disturbance 
of the metabolic equipoise, so that at the commencement of every 
ventricular systole the ventricular muscle is not fully restored. What 
is still left over of the refractory stage we call the residual refractory 
stage. In every systole the periodic refractory stage is added to this, 
as a result of the contraction of the ventricular muscle. Consequently 
when the metabolic equipoise has been disturbed, the total refractory 
stage consists of the two components mentioned just now. It is clear 
that the disturbance of the metabolic equipoise after poisoning with 
veratrin, digitalis, antiarin and bariumchloride is caused by a reinforced 
energy of the ventricular muscle. After bleeding, however, this 
anomaly arises from the inadequate anabolic processes. 

As soon as the refractory stage lasts longer than a sinusperiod, 
the normal rhythm of the ventricle passes into a halved rhythm. 
(This may happen suddenly or more gradually along the path of 
group-formation) *). 

Before the halved rhythm reveals itself spontaneously, we can 
halve the rhythm of the ventricle artificially, as appears from the 
following considerations : 


the duration of the total refractory stage . 
We eall — - J 5 the relative 


the duration of a sinusperiod 
duration of the refractory stage. 


') A more extensive discussion of this question has been given by me in Archives 
Néerl. de Physiologie tome J (1917) pp. 534 —538. 


553 


When considering this fraction more carefully, we can say before- 
hand in what way the normal rhythm can be changed into a halved 
rhythm and the reverse, for if we take the relative duration of the 
refractory stage larger than J, the ventricle will pulsate with half 
the rhythm. If, on the contrary, we take it smaller than 1 the 
ventricle will beat in the normal rhythm, in which every sinus- 
impulse is followed by a systole of the ventricle. We can make the 
fraction greater than 1 by increasing the numerator or also by 
lessening the denominator. Now in the case of a heart of which 
the total refractory stage is lengthened and which still beats in the 
normal rhythm, we can indeed prolong the total refractory stage so 
much as to make it outlast the sinusperiod. So we can make the 
fraction greater than 1, as we have only to evoke an enlarged 
systole, whose refractory stage has been prolonged. 

Now such an enlarged systole is the postcompensatory systole. 
When, therefore, we have lengthened the refractory stage of a ven- 
tricle (through poisoning or through bleeding), we evoke an extra- 
systole or extrapause of the ventricle. After the compensatory pause 
or extrapause the next ventricular systole is enlarged, while its 
refractory stage has been lengthened. Therefore, the subsequent 
sinusimpulse will be checked by this prolonged refractory stage; 
again a prolonged pause ensues, and after this the next ventricular 
systole is again enlarged and has a prolonged refractory stage with 
all its consequences. Thus the ventricle is caught in the halved 
rhythm by the enlarged and broadened postcompensatory systole '). 
An increase of the duration of the refractory stage, i.e. an increase 
of the numerator of the above-mentioned fraction sufficed to bring 
about the ventricular halved rhythm. 

Another method producing the same result, is heating the sinus 
venosus, which will increase the frequency of the sinusimpulses and 
consequently decrease the duration of the sinusperiod. The denomi- 
nator of the fraction is diminished. When the ventricle pulsates in 
the halved rhythm, the relative duration of the refractory stage is 
greater than 1. The fraction may then be made smaller by decreas- 
ing the numerator or by increasing the denominator. 

The first may be effected by administering an extrastimulus to 
the ventricle during the diastole. Then an extrasystole of the ventricle 
originates, which lasts much shorter than the ventricular systole 
from the ventricular halved rhythm. Therefore, the duration of its 


1) Not every post-compensatory systole is followed by a ventricular halved-rhythm. 
This happens only when the refractory stage has been lengthened before by a 
disturbance of the metabolic equipoise. 


554 


refractory stage is shortened and consequently the subsequent sinus- 
impulse can elicit a ventricular systole. Owing to the short duration 
of the preceding ventricular pause this systole will also be short and 
accordingly will have only a short refractory stage. Therefore, here 
also the next sinusimpulse is followed by a systole of the ventricle. 
Thus the ventricular halved-rhythm is changed into the normal 
rhythm of double velocity. The extra stimulus during the halved- 
rhythm may, however, be administered towards the end of the pause 
instead of during the diastole. Then the next sinusimpulse reaches 
the ventricle during the diastole of the extrasystole and elicits a 
small ventricular systole. Whereas in the first case the normal ven- 
tricular rhythm was initiated by a small extrasystole, there now 
appears the normal rhythm under the influence of a sinusimpulse, which 
reaches the ventricle in the diastole of an extrasystole and, therefore, 
yields a small systole. In both cases it was a small ventricular systole 
with a short refractory stage, that made the normal rhythm possible. 

In the second place we can change the halved rhythm into the 
normal rhythm of twice its velocity by cooling the sinus venosus. 
Then the tempo of the sinusimpulse is slackened by which the 
sinusperiods are lengthened. We will elucidate some of the above 
artificial changes of rhythm by some results obtained in experiments 
with the bled frog’s heart. *) 

Let us first look at Fig. 5 of the previous publication.?) The 
stimulating electrode is applied in the auriculoventricular groove. 
At the downward deflection of the signal the ventricle receives a 
closing inductionshock, which engenders an extrasystole. At the end 
of the diastole of the posteompensatory systole which has been 
enlarged, an opening inductionshock is administered, which results 
in an extrapause of the ventricle. *) 

After the extrapause the first ventricular systole has increased 
still more in magnitude and in breadth, so that now the next sinus- 
impulse rebounds on the refractory stage. The subsequent prolonged 
ventricular pause again causes an enlarged ventricular systole with 
a prolonged refractory stage. 

Again the next sinusimpulse does not result in a ventricular 
systole. Thus the ventricle, pulsating in the halved rhythm through 
the prolonged refractory stage is, so to speak, caught in its own 


1) In all the figures of this publication the upper row represents the suspension- 
curves of the ventricle, the lower row the suspension curves of the auricles. 

4) S. pe Boer. On the artificial extrapause of the ventricle in the frog’s heart. 
These Proceedings p. 542. 

5) For the causes of this extrapause I refer to the previous publication. 


2 OLA 


PERN GN Te NS NaN Ny Ne IEN (cayed PAS ONS on 


VENI SAA IAEA ES iN SE ERPS SAR 


TAVAVAVAVAVAVAVAVA| An A A POT af FTO MA POE OE 


556 


rhythm. We can change this halved rhythm again into the normal 
rhythm of twice thé rapidity, by eliciting a small ventricular systole. 
This happens in Fig. 1 *)- 

At the downward deflection of the signal an auricular extra- 
systole was evoked, after which the excitation reached the ventricle 
during the- refractory “stage. Consequently the rhythm of the ven- 
tricle did not change here. However, at the upward deflection of 
the signal the stimulus was repeated towards the end of the pause. 
Now the auricles are. refractory, but the ventricle responds to the 
stimulus with an extrasystole. After this the periodic sinusimpulse 
reaches the ventricle towards the end of the diastole, so that a 
decreased systole of the ventricle ensues. This is accompanied by 
a short refractory stage so that also the subsequent sinusimpulse 
again results in a ventricular systole. In this way every sinusimpulse 
may be followed by a ventricular systole. 

Fig. 2 shows the suspension curves of a frog’s heart, 10 minutes 
after bleeding. The stimulating electrode is at the auricles. At the 
first downward deflection of the signal the auricles receive a closing 
shock, which results in an extrasystole of the auricles, followed by 
a compensatory pause. 

It is evident that the ventricular rhythm is influenced only in 
this way that the next systole of tne ventricle appears somewhat earlier. 

When, however, at the upward deflection of the signal the auri- 
cles receive the opening induction shock at an earlier moment of 
the auricular period, the result is quite different. After the thus 
excited extrasystole of the auricles, coinciding with the commence- 
ment of the ventricular systole, the excitation reaches the ventricle 
still in the latter’s refractory stage. 

After the compensatory pause of the auricles the next auricular 
systole is followed again by a ventricular systole. Thus arises 
an extrapause of the ventricle, followed by an enlarged and broad- 
ened systole. Of this the refractory stage is prolonged, so that the 
next auricular systole cannot be followed by a ventricular systole. 
Again a prolonged ventricular pause arises, which is again followed 
by an enlarged systole of the ventricle. 

Thus the ventricle is caught in the halved rhythm by only one 
stimulus administered to the auricles. At the second downward 
deflection of the signal the auricles receive a closing shock towards 
the close of the pause, which evokes an extrasystole of these 
chambers. After this the next ventricular systole commences earlier. 


1) Between fig. 5 of the previous publication and fig. 1 of this paper two 
ventricular systoles have not been reproduced. 


557 


The then following sinusimpulse reaches the ventricle towards the 
close of the diastole and may, therefore, be followed by a small 
ventricular systole. This small ventricular systole now yields a short 
refractory stage. Therefore the next auricular systole can be followed 
again by a ventricular systole, which, on account of the short 
durations of the preceding pause, is again small and short. For this 
reason the next auricular systole can again be followed by a ven- 
tricular systole. Thus by a single induction shock the halved rhythm 
of the ventricle is changed into the normal rhythm of twice the 
rapidity. 

Figs. 1 and 2 show us that we are able to change the halved 
rhythm into the normal one by means of a single induction shock. 
Now the question arises why the ventricle does not take up the 
normal rhythm spontaneously. From the fact that the halved rhythm 
can be changed into the normal, it, indeed, appears that the meta- 
bolic condition of the ventricular muscle enables the ventricle to 
beat with a double frequency. Still the ventricle persists in its halved 
rhythm, unless we administer a stimulus at the right moment. The 
cause must be looked for in the magnitude and the long duration 
of the ventricular systoles of the halved rhythm. Every second 
sinusimpulse rebounds on this prolonged refractory stage; the ven- 
tricle is caught in the halved rhythm and can escape from it only, 
when through: an extra stimulus a small ventricular systole is evoked 
directly or indirectly. 

When, however, the ventricle has been pulsating for some time 
in the halved rhythm, the ventricle gradually discards the residual 
refractory stage under the influence of the many prolonged ventri- 
cular pauses, so that the total refractory stage is shortened after 
all. In this way the normal ventricular rhythm may yet return 
spontaneously. This is illustrated in Fig. 3. 


Fig. 3. 
The curves of this figure originate from the same frog’s heart’ 
which procured the curves of fig. 2. 


36 
Proceedings Royal Acad. Amsterdam. Vol XXIII. 


When looking again at the ventricle-curves of fig. 5 of the pre- 
vious publication and of figs. 1, 2, and 3 of the present one we can 
state what follows: 

As soon as the normal ventricular rhythm is changed into the 
halved rhythm the magnitude and the duration of the ventricular 
systole increases. This increment then proceeds from systole to 
systole, so that the 10" systole of the halved-rhythm is much greater 
than the 5, which again in its turn is greater than the first. This 
increment of the magnitude of the ventricular systole is brought 
about by an increase of the maximum diastole and at the same time 
by an increase of the maximum systole. It will be seen, then, that 
the ventricular muscle recovers itself during the halved-rbythm and 
that this recovery proceeds under the influence of an increase of 
long ventricular pauses. The reverse will be observed after the 
change of the halved-rhythm into the normal. 

The ventricle is then in a good condition owing to the preceding 
halved-rhythm. Directly after the change into the normal rhythm, 
the magnitude of the ventricular systoles has decreased. But under 
the influence of the frequent recurrence of short ventricular pauses 
the magnitude of the ventricular systoles lessens more and more. 
This lessening regards the maximum diastole as well as the maximum 
systole. An intermediate form between the normal ventricular rhythm 
and the halved-rhythm is the ventricle-alternant. 

We can change the normal ventricular rhythm into the alternant 
and this again into the halved-rhythm, as illustrated in the following 
figures, derived from the same frog’s heart. The curves of figs. 4 
and 5 were taken after the bleeding. The ventricle was then pul- 
sating in the normal rhythm; at the first deflection of the signal 
the auricles received an induction shock resulting in an extrasystole 
of these chambers, which was followed by a small systole of the 
ventricle. At the second deflection of the signal again an auricular 
extrasystole was evoked in the beginning of the postcompensatory 
systole. Hereafter the excitation reaches the ventricle during the 
refractory stage, so that an extrapause of the ventricle ensued. Then 
the first ventricular systole is very much enlarged. This enlarged 
ventricular systole introduces an alternation of the ventricle. (Similarly 
in our previous experiments the halved-rhythm was brought about 
by an enlarged systole). After some time this alternation changes 
spontaneously into the normal ventricular rhythm with systoles of 
the same magnitude. 

At the third deflection of the signal again an extrasystole of the 
auricles is evoked, followed by a small ventricular systole. After the 


559 


enlarged postcompensatory systole again the ventricle-alternation arises. 
The curves of fig. 5 were taken about 1 minute after those of 

fig. 4. A short time before the alternation had been elicited experi- 

mentally. It still exists at the commencement of the figure. 


i 


sa 
= 
= 
=> 
= on 
S= 
= 
Ss 
= 
=, 


= 


= 


Fig. 4. 
Fig. 5. 


| 
5 


VAA A AAA 


At the first deflection of the signal the auricles are incited to an 
extrasystole by an induction shock in the beginning of a large ven- 
tricalar systole. After this extrasystole the excitation reaches the 
ventricle during the refractory stage, so that no ventricular systole 
follows; an extra pause of a ventricle does follow, however. After 
this extrapause the first ventricular systole is enlarged again, so 

36* 


560 


that the next sinusimpulse reaches the ventricle again during the 
refractory stage. Owing to this the next pause of the ventricle is 
again prolonged with the ordinary consequences. In this way the 
ventricular halved-rhythm is brought about artificially. 

At the second deflection of the signal again an extrasystole of the 
auricles is evoked in the beginning of a ventricular systole. Because 
hereafter the excitation reaches the ventricle during the refractory 
stage, the halved rhythm of course continues. 

At the third deflection of the signal, however, an extrasystole of 
the auricles is evoked after the termination of a ventricular systole. 
After this the excitation reaches the ventricle towards the end of 
the pause so that a premature ventricular systole follows. Now because 
this ventricular systole is premature, the next sinusimpulse reaches 
the ventricle after the close of the refractory stage, so that a small 
systole of the ventricle can follow. This systole is small on account 
of the short duration of the preceding pause and therefore causes 
a short refractory stage. For this reason also the following sinus- 
impulse is again responded to by a ventricular systole, which also 
is a small one again. In this way the normal rhythm of the ventricle 
is restored. 

In the above we have given some instances of changes of rhythm 
in the bled frog’s heart. We could enforce at will any given rhythm 
upon the ventricle by evoking one ventricular systole of a certain 
magnitude and duration. 


Geology. — “Crystallization and Resorption in the Magma of the 
Volcano Ruang. (Sangi Islands)” By Prof. H. A. Brouwer. 
(Communicated by Prof. G. A. F. MoreNGRAAFF). 


(Communicated at the meeting of January 31, 1920). 


The solid lava from the highest peaks of Ruang, representing the 
oldest visible voleanie products of the island, display microscopically 
a great resemblance to the lava and the dome of the eruption of 
1904, and to the products of the latest eruption '),*. They are 
all hypersthene augite andesites. The extensive rockmaterial which 
was collected by me in 1915 along the slopes of the volcano and 
which may originate from different eruptions, confirms this: nearly 
all the rocks, which were examined microscopically, are also hyper- 
sthene augite andesites; among them occur only few hypersthene 
augite amphibole andesites and a single olivine-bearing rock, viz 
an augite hypersthene amphibole olivine basalt. 

Amphibole and olivine thus appear to belong to the rare minera- 
logical constituents of the magma, which has risen to the surface, 
but the numerous xenoliths, encountered in the ejected products, 
enable us to judge of the crystallization products of the magma at 
greater depth. Especially the homoeogeneous xenoliths *) are very 
numerous. They are not merely mineralogical curiosities, but they 
also indicate what minerals at greater depths of the magma can 
crystallize and they fill up the gaps between the data that are 
obtainable only through the study of the effusive rocks. 

We subjoin a short description of the volcanic rocks of Ruang, 
together with the xenoliths found in them: 


I. Oldest volcanic products. 
Hypersthene augite andesites from the highest peaks of the island 
with phenocrysts of strongly zonary plagioclase, of hypersthene, augite 


1) M. Kopersere, Verslag van een onderzoek naar de uitbarstingen in 1904 op 
het vulkaaneiland Roeang bij Tangoelandang (Sangi- en Talaoet-eilanden). Jaarb. 
Mijnwezen 1909. Wet. Ged. p. 207 e. v. 

3) H. A. Brouwer, Het vulkaaneiland Roeang (Sangi-eilanden) na de eruptie 
van 1914. Tijdschr. Kon. Ned. Aardr. Gen. 1915. 

3) A. Lacrorx, Les enclaves des roches volcaniques, 


562 


aud ore in a groundmass of the same constituents with small quan- 
tities of glass. 


Il. Products of the eruption of 1904. 

Hypersthene augite andesites from the dome, which had gradually 
arisen in the crater after the eruption of 1904 and was exploded 
for the greater part at the eruption of 1914. Hypersthene augite 
andesites from the lava-flow, which has flowed down the southern 
slope into the sea. 


Xenoliths in these rocks. 

They are fine-, to coarsegrained, sometimes porphyritie rocks, 
generally rich in plagioclase and moreover containing one or more 
of the following minerals: hypersthene, augite, amphibole of varying 
colour and magnetite. Glass sometimes occurs and is enelosed within 
felspars, or occurs between the other constituents. The plagioclase of 
the xenoliths is, in contradistinction to that of the enclosing ande- 
sites, of a much less strongly zonary, or of homogeneous structure 
and belongs to basic mixtures with the composition of basic labra- 
dorite or bytownile. 

The following mineral-combinations may be distinguished: 

1. plagioclase, brown amphibole, little hypersthene, augite and 
magnetite. The brown amphibole has been resorbed more or less in 
various xenoliths and has sometimes disappeared completely. 

2. plagioclase, brown, faintly resorbed, amphibole with much 
hypersthene, augite and magnetite. 

3. plagioclase, completely resorbed brown and not resorbed light- 
green amphibole with little hypersthene, augite and magnetite. 

4. plagioclase, light-green amphibole, hypersthene, augite and 
magnetite. 

5. plagioclase, hypersthene, augite, magnetite and light-brown glass. 

6. plagioclase with little magnetite. 

7. fine-granular mixture of lath-shaped plagioclase, glass, magne- 
tite, and little pyroxene. 


ILI. Products of the eruption of 1914. 

A very considerable portion of the material that now covers the 
slopes of Ruang, dates no doubt from the latest eruption of the 
volcano. It is beyond doubt that among the products of the latest eruption 
are the blocks and bombs overlying the lava-flow of 1904, which are 
distinguished from all the other material emitted by their light-grey, 
fresh colour. These rocks are also pyroxene-andesites with both hy per- 
sthene and augite. 


563 


Nenoliths in these rocks. 

In many respects the xenoliths resemble those of the preceding. 
In a few also olivine was found in large quantities. 

We mention the following combinations: 

1. plagioclase, brown amphibole, hypersthene, augite and magnetite. 
The brown amphibole is invariably resorbed, sometimes completely. 
In the latter case only little hypersthene and augite is present in 
separate crystals, out of the resorption-rims. 

2. plagioclase and light-green amphibole. The amphibole is partially 
resorbed and changed into a mixture of augite and ore. 

3. plagioclase and greenish brown, all but non-resorbed amphibole, 
with little magnetite. 

4. plagioclase, hypersthene, augite, and magnetite. 

>. plagioclase with very little pyroxene. 

6. plagioclase, partially resorbed olivine, hypersthene (and augite), 
little ore and glass. From the enclosing rock vitreous veins intrude 
into the xenoliths. 


IV. The other volcanic products. 

Beyond the above-named rocks, which could be ascribed with 
certainty to a special eruption, a number of rocks were examined, 
the. majority of which will no doubt belong to the products of the 
two latest eruptions, but whose age cannot be established positively. 
In the main they are also hypersthene augite andesites, exceptionally 
amphibole-, and olivine-bearing rocks. Homoeogeneous xenoliths, 
isolated or enclosed by effusive rocks, are numerous; besides these 
we encountered also a few xenoliths of effusive rocks in effusive 
rocks, from which conclusions may be deduced about their relative 
age. 


a. Xenoliths of the hypersthene augite andesites. 

They are in the main medium-grained or porphyr itic holocrystal- 
line rocks; fine-crystalline xenoliths are the exception. 

1. large plagioclase-crystals with enclosed pyroxene, ore and glass. 

2. plagioclase and non-resorbed olivine. 

3. plagioclase, non-resorbed olivine and hypersthene. 

4. plagioclase, augite, hypersthene, brown amphibole, little olivine, 
ore and brown glass with few microlites. 

5. plagioclase, completely resorbed amphibole and very little brown 
glass. The resorption products of the amphibole consist of augite, 
hypersthene, and ore. 

6. fine-crystalline diabases and diabase-porphyrites, consisting of 


564 


plagioclase (also as phenocrysts if present), augite, hypersthene, 
and ore. 


b. Xenoliths of the augite amphibole hypersthene andesites. 

To these belong first of all some xenoliths of effusive rocks, viz. 

1. hypersthene augite andesite. 

2. Angite amphibole hypersthene andesite, which in its turn contains 
a xenolith of andesite, in which no dark minerals could be recog- 
nized. Also numerous holocrystalline, generally medium-grained xeno- 
liths, occur, viz. 

3. large plagioclase crystals. 

4. brown, or greenish-brown resorbed amphibole in large crystals, 
plagioclase, magnetite. 

5. plagioclase, brown, faintly resorbed, amphibole, little hyper- 
sthene, augite and light-brown glass. 

6. plagioclase, hypersthene, augite, and magnetite. 

7. hypersthene augite diabase porphyrite with much glass. 

8. fine-granular hypersthene augite diabase. 


c. Xenoliths of the augite hypersthene amphibole olivine basalts. 

In these rocks, which rarely occur among the collected material 
also medium-grained xenoliths were found, viz. 

1. plagioclase and brown amphibole. 


d. The other xenoliths. 

Some of these were found as detached fragments without enclosing 
rock, others were detached from the enclosing rock and formed 
separate specimens, so that only the microscopical composition of 
xenolith is known. Probably, however, the enclosing rocks are also 
mainly hypersthene augite andesites. In some xenoliths the composition 
of the central parts differs from that of the marginal zone, the dark 
minerals are accumulated in the central parts. 

The following mineral-combinations were examined: 

1. dark-brown amphibole in large angular and poikilitie non- 
resorbed crystals, plagioclase, little hypersthene, augite, and magnetite. 

2. green amphibole in large angular and poikilitie, non-resorbed 
crystals, plagioclase, little augite, and magnetite. 

3. plagioclase, augite, hypersthene, little, rather strongly resorbed 
brown amphibole, and magnetite. 

4. xenolith with concentration of the dark constituents in the 
central parts, viz. 

Central part: very much green amphibole, magnetite, little plagio- 
clase and little dark-coloured glass with microlites. 


565 


Margin: plagioclase with little green amphibole, ore, and light- 
brown glass without microlites. 

5. xenolith with concentration of the dark constituents in the 
central parts, i.e. 

Central part: almost exclusively brownish green amphibole with 
a margin of ore and very little plagioclase. 

Margin: much brownish green, amphibole with angular forms 
and rim of ore, plagioclase with more or less idiomorphic form, 
“magnetite and very little augite and hypersthene. 

6. plagioclase, much olivine, little hypersthene and brownish-green 
amphibole. 

7. plagioclase, brown, almost entirely resorbed amphibole and 
little glass. 


Phenomena of resorption. 


a. of olivine. There are numerous xenoliths, in which the olivine 
is quite fresh, without resorption rim, e.g. in olivine-rich xenoliths, 
which contain besides plagioclase and rather much glass, only little 
brownish-green amphibole and some hypersthene. Here the line of 
demarcation between plagioclase and olivine is generally very sharp, 
but sometimes we observe the brownish-green amphibole disposed 
round the olivine or a combination of small amphibole crystals and 
a mixture rich in glass, of which the latter also occurs sparingly 
among the chief constituents, intrudes into the olivine crystals. 
The amphibole is no doubt one of the last erystallization-products, 
and it may be that, before its formation, a slight resorption of the 
olivine has taken place, which however occurs only locally and can 
be brought about only by a small amount of residual magma. 

Pronounced resorption-phenomena are shown e.g. by the olivine 
of xenoliths in blocks which were thrown out during the eruption 
of 1914, and are now overlying the lava-flow of 1904. The boundary- 
line between plagioclase and olivine is nowhere sharp here, but the 
remainders of the olivine-crystals are encompassed by a zone of 
resorption against which the plagioclase is bordered in a curving 
and undefined way. Sometimes the original olivine has completely 
disappeared; it has been replaced by a mineral-aggregate, chiefly 
made up of hypersthene. If the olivine-erystals have been preserved 
in part, they are seen to be encompassed by a margin, in which 
a concentric structure can be established. Close to the olivine the 
margin mostly consists only of an aggregate of larger hypersthene- 
crystals, by the side of which there may occur a little augite. 


266 


Farther from the olivine follows a finely crystalline mixture of 
hypersthene (and augite?) with a variable quantity of plagioclase 
and more to the outside also ore; this is succeeded by a zone of 
the larger adjacent plagioclase-crystal, in which pyroxenes are scat- 
tered in an irregular way. 

We see, therefore, that from the magma which yielded these 
xenoliths, first plagioclase and olivine were crystallized, then the olivine 
had lost its stability and a resorption rim of hypersthene was formed, 
enclosed by a margin of hypersthene and ore with very little plagio- — 
clase, while the enclosed hypersthene of the larger plagioclase crystals 
go to show that these crystals continued to form during the erystal- 
lization of the hypersthene. The hypersthene belongs to the last 
erystallization-produets of the xenoliths and they originated partly 
at the cost of olivine. 

b. of the amphibole. Just like the olivine also the amphibole occurs 
entirely unmodified in various xenoliths, especially in the detached 
xenoliths not enclosed by the solid lava. In these xenoliths very 
often rather much glass was found between the crystallized consti- 
tuents. In the olivine-free xenoliths with non-resorbed amphibole 
much magnetite but no or hardly any pyroxene was sometimes 
encountered. The colour varies trom dark-brown to brownish-green 
and dark-, or light-green in the sections with highest absorption ; 
the pleochroism is considerable in the dark-coloured varieties. Gene- 
rally the amphibole is distinctly the last erystallization-produet with 
angular contours relative to the other constituents which are often 
enclosed. 

In the case of faint resorption the resorption-rim consists exclusively 
of a black ore-mass or of a combination of ore, pyroxene and plagio- 
clase. The first case is found e.g. in the amphiboles from the xeno- 
liths that are very rich in this mineral of a brown or greenish- 
brown colour and that do not contain any pyroxene, numerous 
specimens of which occur along the slopes of the voleano. However, 
also in pyroxene-rich xenoliths similar resorption-rims round the 
amphibole are found. In the enclosures from the lava-flow of 1904, 
which contain by the side of amphibole less pyroxene, the ore does 
not only encompass the amphiboles as a rim, but it also penetrates 
along the cleavage-cracks into the central parts of the crystals. The 
resorption-rims, in which besides ore also pyroxene and plagioclase 
occur, were observed in the xenoliths of the eruption-products of 
1914. They are large greenish-brown amphiboles, plagioclase and 
little ore. The plagioclases are sharply defined from the material of 
the resorption-rims, in which the pyroxene consists entirely or chiefly 


567 


of augite, while only some of the colourless constituents can with 
certainty be said to be plagioclase. Also with stronger resorption the 
amphibole changes into a mixture of the three named minerals. An 
enclosure of the lava flow of 1904, which chiefly consists of plagio- 
clase and brown amphibole with few large augite- and hypersthene 
crystals, shows around, and also in veins running through the 
amphiboles, a mixture of hypersthene, augite and plagioclase, which 
also occurs isolated in the parts of the amphibole that have not 
been altered completely. The margin round the amphiboles becomes 
very rich in ore in the outer rim, so that the three minerals are 
found here in a more zonary arrangement. 

Numerous xenoliths are characterized by completely resorbed 
amphiboles. Sometimes they consist entirely of a combination of very 
small ore-crystals. In others pyroxene (chiefly certainly augite) and 
also sometimes plagioclase occur in great quantity with the ore. 
They were found in xenoliths from the south-eastern part of the 
island, together with plagioclase and much light-brown glass without 
microlites. For the rest most of the xenoliths collected from the lava 
dome of 1904 are characterized by totally resorbed amphiboles, which 
contain besides plagioclase only little augite and hypersthene, just as 
is the case with a few xenoliths of the latest eruption-products 
(eruption of 1914). 


Origin of the xenoliths. 


The volcanic magma that has reached the earth’s surface during 
the several eruptions, presents a very constant mineralogical compo- 
sition; the lava (as a flow, or as a dome) as well as the loose vol- 
canie products are principally hypersthene augite andesites. The 
sporadic amphibole-crystals in some rocks are in part and perhaps 
all to be considered as xenoliths of one mineral only *). For xeno- 
liths, consisting of mineral-combinations, which also occur as pheno- 
erysts in the enclosing rocks with or without glass or a crystalline 
groundmass, we can find an explanation of their origin in segre- 
gation or more perfect crystallization during the intratellurie phase 
of the magma, which has produced the enclosing volcanic rock. The 
xenoliths into which glass veins have penetrated from the enclosing 
hypersthene augite andesite, may be completely solidified rocks that 
were carried along by the rising magma. 

However, a great many of these xenoliths contain amphibole, a 
mineral which, as a rule, does not occur either unmodified or resorbed 


1) Cf. also H. KorPerBera, |. c., p. 270. 


568 


among the phenocrysts of the voleanic rocks. This points to consider- 
able mineralogical differences between the volcanic rock and the 
xenoliths, which in this case, unlike the homoeogeneous xenoliths of 
the amphibole andesites from the Hifel, cannot be explained merely 
by segregation. 

We are safe to assume that in the lower parts of the voleano 
various mineral-combinations have been crystallized from the magma 
in various places. In the magma, which came to effusion at various 
epochs, the phenocrysts of the voleanic rock were crystallized in 
the intratelluric period. The magma that procured the numerous 
amphibole-bearing xenoliths, has more or less perfectly been crystal- 
lized, while fragments were carried along by the escaping magma. 
The occurrence of glass in some of these xenoliths proves that erys- 
tallization was not yet quite terminated when the effusion took place. 

The mostly non-resorbed condition of the amphibole in these glass- 
bearing xenoliths in loose volcanic products and not in solid lava 
indicates that the resorption of the amphibole has begun during the 
effusion and the enclosing by the magma of the hypersthene augite 
andesites. In the parts of the enclosing lava that have cooled down 
rapidly we generally find the amphibole unresorbed or only very 
little resorbed; in the lava that has cooled down slowly and in the 
dome we find it much more or completely resorbed. 

Hardly any differentiation of the magma in the lower regions 
of the voleano need be made; once more we point to the constant 
composition of the voleanic rocks of different eruptions. The am- 
phibole-bearing xenoliths represent the sometimes slightly more 
basic, dioritie equivalents of the andesitic effusive rocks. There 
are several indications that, in general, in a crystallizing magma, 
augite represents the stable phase at a higher, amphibole that at a 
lower temperature. Also, that the development of the complex amphi- 
bole-molecule is rendered possible only in the presence of gaseous 
components in the magma. The complex molecule, stable only under 
definite circumstances, is replaced by simpler combinations, when 
conditions are changing, e.g. through escaping of the gases and 
diminution of pressure, as proved by the widely spread resorption 
phenomena of the amphibole in volcanic rocks, which have been 
described heretofore. This resorption does not take place if the 
cooling occurs very rapidly; this accounts for its absence in the 
amphiboles of the xenoliths enclosed by loose voleanie products or 
which occur as isolated fragments in tuffs. 

The occurrence of olivine in some xenoliths also constitutes a 
mineralogical difference with the effusive rocks that enclose them. 


But here again the numerous resorption-phenomena demonstrate the 
instability of this mineral under circumstances different from those 
which prevailed during crystallization. The phenomenon may be 
compared with the corrosion-phenomena of rhombic pyroxene in 
xenoliths of basalts.') In similar rocks, which are more basie and 
richer in lime than the effusiva of Ruang, phenocrysts of rhombic 
pyroxene occur very rarely, nevertheless this mineral is found in 
xenoliths mostly in a corroded condition. The formation of ortho- 
silicate instead of metasilicate is, under otherwise similar conditions, 
dependent on the quantity of available silica, which can combine 
with Mg and Fe, but many instances are known in which olivine 
is crystallized in magmas, which contain enough silica to give 
origin to metasilicate (SiO,-rich basalts). The co-incidence of pyro- 
genetic quartz and olivine in the same rock has been explained 
by the action of the water-vapour present in the magma’) which 
has impeded the formation of the metasilicate. 

The xenoliths of various mineralogical composition and of different 
structures point to erystallizations which have taken place under 
various circumstances and very likely at widely different depths in 
the magma. The various types are connected by intermediate struc- 
tures. We can account for the great abundance of amphibole-bearing 
xenoliths and the striking contrast of the absence of amphibole- 
phenocrysts in the lava by assuming that the magma beneath Ruang 
was in its upper parts, before the commencement of the eruption, 
under pressure- and temperature-relations, in which first pyroxene 
and later on at a subsequent cooling amphibole could crystallize, while 
at greater depths the field of crystallization of the amphibole was 
not reached. At the commencement of the eruption the upper portions 
of the magma were crystaliized completely or for the greater part, 
while the magma with fewer and different crystalline constituents 
and with greater liquidity lay at a greater depth, which magma 
was effused at an eruption of the volcano as a hypersthene augite 
andesite and presented the fragments of its dioritie crust which had 
been solidified completely or partially, as xenoliths. 


1) A. Lacrorx, Les enclaves des roches volcaniques, p. 491. 
3) J. P. Ippines, Igneous Rocks. Vol. I. 1909, p. 142. 


Geology. — “Fractures and Faults near the Surface of Moving 
Geanticlines’. I. By Prof. H. A. Brouwer. (Communicated 
by Prof. G. A. F. MOLENGRAAEFF) 


(Communicated at the meeting of April 23, 1920). 


When erustal movements take place they generally cause strata 
at greater depth to fold, and to break near the surface. In the high 
continental mountain-ranges, as the Alps and the Himalaya, which 
have already very long been exposed to eroding influences, because 
they have already long been lifted above the sealevel, the ancient 
folding phenomenon is completely visible, and the anatomical 
structure has become visible in its broad outlines and in the smallest 
details. Conversely, in the sculpturing of the broad outlines erosion 
has long since obtained a paramount influence by the side of the 
mountain-building movements; whereas the trend of the first valleys 
depended on the first geanticlines that rose above the sealevel, these 
forms have since that epoch long been influenced by the collective 
action of mountain-building and erosion, in which process the 
relationship between the broad outlines of the tectonic and the shape 
of the surface has disappeared more and more. Where, however, 
the mountains rose up from deep seas and were exposed to eroding 
influences during a much shorter space of time, the outer form is 
not controlled in the first place by erosion, but by the crustal 
movements themselves. In contradistinction to the mountain-ranges 
of the continents the erosion of the tertiary mountain-ranges has 
laid bare here chiefly only their superficial parts; here there is no 
question of a “herrliche Entblészung des anatomischen Baues des 
Gebirges”.') But, on the other hand, the now visible external shape 
of the Alpine mountains is only “eine Ruinenbildung’, whereas in 
the recent mountains of the deep seas the main lines of the latest 
phase of mountain-building manifest themselves clearly in the shape 
at the surface, which will be shown in what follows. 


Origin of fractures and faults. 


The origin of fractures and faults is correlated with the occurrence 
of tensional and compressional stress; the developments of fractures 


1) Aue. Heim. Geologie der Schweiz. Band II, Lief. 1, 1919. S: 72: 


571 


may be accompanied by faulting. Without faulting an extension of 
the geanticlinal axis is obtained by gaping fractures, i.e. by a 
movement normal to the fault-planes; with faults without gaping 
an extension is obtained by a movement parallel to faultplanes, 
which must be inclined to the geanticlinal axis. Shortening of the 
geanticline is possible by faulting along fault-planes that do not 
gape and which are not vertical to the geanticlinal axis. Similar 
relations prevail for a lengthening or a shortening of a section of 
the geanticlinal surface with a plane vertical to the geanticlinal axis. 

In the case of more or less free horizontal movement, a length- 
ening of the geanticlines will reveal itself near the surface through 
the formation of transverse or diagonal fractures, which may be 
gaping ov along which faulting may occur. Every position of the 
fault-planes is possible; besides by the direction and the velocity of 
the movement, the position of the fault-planes is also controlled by 
a great many factors, e.g. by stratification, composition and distribu- 
tion of the rocks near the surface. However, it is above all the 
more or less horizontal transverse faults, the gaping transverse 
fractures, the more or less vertical longitudinal faults, and the 
gaping longitudinal fractures, that chiefly govern the morphological 
aspect of the earth’s surface, leaving out of consideration the local 
areas with strong bending of the geanticlinal axes. According with 
the nature of the rocks, insignificant fractures of various trend may 
occur everywhere near the surface of the moving geanticlines; we 
consider only those areas of the geanticlinal surface where the 
faults, through more or less equal position and more or less equal 
direction of movement, bring about considerable alterations in the 
broad outlines of the morphological structure. Indeed, near the 
surface of the geanticline, zones of constant lithological characters 
may generally be separated by planes, which are parallel to the 
geanticlinal axis. If these planes are more or less vertical, this will 
chiefly influence the distribution of the vertical longitudinal fractures 
and the longitudinal faults. If these planes are principally more or 
less horizontal, this will chiefly influence the distribution of the 
horizontal faults, along borizontal planes, but the latter faults do 
not in the first place govern the morphological structure, and are 
left aside in our speculation. Accordingly on the distribution of the 
transverse faults, which really govern the morphological structure, 
the lithological character of the geanticlines near the surface exerts 
only little influence (at least as regards merely the major structure 
considered by us). And if the said planes near the surface are 
principally more or less horizontal, either in their original position 


572 


or after overthrust-movements, the lithological character affects the 
development of the vertical longitudinal faults only very little, so 
that then again the morphological structure is governed principally 
by direction and velocity in different places of the moving geanticline. 
If the crust near the surface does not undergo the direct influence 
of the compressional stress, in the main only passive displacements 
will appear here. In forming a judgment of the genesis of fractures 
and faults this should be borne in mind. 

When in the following pages faults are spoken of, we presume 
it to be possible that monoclines occur, which are essentially allied 
to faults. 


Movement of the geanticlines. 


The movement of a geanticline can be broadly described by indi- 
cating in the first place how the projections of the geanticlinal axis 
on the horizontal plane and on a vertical plane approximately paral- 
lel to the part of the geanticlinal axis under consideration, are moving. 
When we then consider the section of the surface of the geanticline 
with a vertical plane at right angles to the geanticlinal axis, it is 
also a matter of importance how this section will move. In this 
communication we only consider the movement of the horizontal 
projection of the geanticlnal axis. 

The movement of a geanticline, which can move more or less 
freely in a horizontal direction, e.g. as a row of islands in the 
direction of the ocean, will show itself for the greater part in the 
movement of the horizontal projection. Extension by bending at 
greater depth, will perhaps be visible near the surface in more or 
less regularly distributed, more or less gaping transverse or diag- 
onal fractures and faults. Straits may occur at the place of such 
fractures. In the row of islands Sumatra-Java-Lombok-Flores, e. g. 
numerous transverse faults occur near Strait Sunda and nearly 
always the western portion is moved towards the South’). Along 
the fault-plane of the Tji-Tjatih near Sukabumi the displacement 
amounts to 4 k.m. at the very least, along the fractures of Sunda 


1) R. D. M. VerBeeK and R. Fennema. “Geologische Beschrijving van Java en 
Madoera” 1896 p. 539. L. J. C. van Es. “Geologische Overz. kaart v. d. Ned. 
Oost-Ind. Archipel. Toelichting bij Bld. XV. Jaarb. Mijnw. Verh. 1916 II p. 132 
sqq. The faults now visible have, at least in part, originated already in earlier 
times, during an earlier phase in the orogenetie process, under a load of sediments, 
and along many of them the movement may have stopped by this time. The 
morphological structure is now governed especially by the faults in the neigh- 
bourhood of Strait Sunda. 


573 


Strait, the western part of Java has been moved several tens of 
kilometers towards ‘the South in regard to South Sumatra. Where 
fractures are gaping it is not necessary, as has been said, for them 
to be inclined to the geanticlinal axis, in order to bring about an 
extension of the geanticline. It is possible that the gaping along 
transverse fractures has contributed to the origin of Sunda Strait 
and, as a matter of course the transverse movements will not pro- 
ceed horizontally, but will have had a vertical component, which 
is not expressed in the movement of the horizontal projection, our 
only object of inquiry. In the Jura mountains we know only move- 
ments along fault-planes without gaping, but here the movement, 
now visible after erosion, took place under an overlying load of 
sediments. The arrangement of the faults is harmonic here, and 
consequently shows its alliance with the flow at greater depth. 
Several factors near the surface, as the composition and the strati- 
fication of the rocks, exert a stronger action to disturb the harmonic 
structure. 

The horizontal movement of a geanticline, which proceeds in the 
direction of a continental ““Vorland”, depends on the shape and the 
distance of the “Vorland”. If the shape is irregular, considerable 
differences in velocity for neighbouring points of the horizontal 
projection of the geanticlinal axis may occur and considerable faulting 
movements may take place. 

The row of islands Timor-Tenimber islands afford an illustration 
of a geanticline moving in the direction of a “Vorland” with an 
irregular shape). The 200 m.-line of the Sahul shelf presents an 
abrupt right-angled bend south-east of the east point of Timor and 
a less abrupt bend south of the Island Jamdena of the Tenimber group. 

Opposite the “Vorland”, between the two bends, the islands of the 
Sermata and Babber group lie in irregular arrangement. The non- 
harmonie northern position of the island Kisser may e.g. be allied 
with transverse faults, right in the prolongation of the N.W—S.E 
part of the projecting angle of the 200 m.-line of the Sahul shelf. 
No doubt a number of younger and older faults and, fractures 
are to be found in and between these islands, and we find that 
elements of quite different geological composition lie side by side. 
So, for instance the island of Kisser bears, in geological composition, 
resemblance to the island of Letti; the rocks of these two islands, now 
most probably displaced relatively to each other, may have been 


1) H. A. Brouwer. On the Crustal Movements in the region of the curving 
row of islands in the Eastern part of the East-Indian Archipelago. Proc. Kon. Ak. 
ve Wet. XI ps. 7°74. 

37 

Proceedings Royal Acad. Amsterdam. Vol. XXill. 


574 


more connected originally. West-Moa, though just beside Letti, cannot 
be considered geologically as the prolongation of that island, and 
Kast-Moa, part from the young coral limestones, consists entirely 
of peridotite mountains, which are not found in West-Moa. The 
Island Luang consists of massive permian crinoid-limestones, not to 
be found in any of the other islands of the Sermata-group and are 
first met with in Timor, whereas the adjacent island of Sermata again 
seems to consist of totally different rocks, viz. phyllites and schistose 
diabase tuffs, such as also occur in Letti and in Kisser. Of course, 
these facts may be explained in part by an overthrust structure in 
the different islands. We still point to the northern situation of the 
island of Babber. 


A Cc. D, B, 
A, 


Fig. 1. Movement of a geanticline opposite re-entering angles of the 
“Vorland’’, as south-east of Timor. 


An example of considerable differences in velocity for adjacent 
points C and D of the horizontal projection of the geanticlinal axis 
is given in Fig. 1. 

The prolongation of the above-mentioned geanticline proceeds in 
a curve via Ceram and Buru. A very striking wregularity in the 
harmonic course of this portion of the geanticline is the narrow 
Manipa Strait, nearly 5000 m. deep between Ceram and Buru. The 
strike of the Tertiary mountain-range is, in West-Buru and in the 
greater part of Ceram, about N.W.—S.K. In West-Ceram and in the 
islands between Ceram and Buru N.E. strikes have been observed *). 
So the Tertiary mountain-range displays considerable curvatures from 
Ceram to Buru. 

We have pointed out before’) that the latest crustal movement 
in this region is considered by us to be a younger phase in the same 
process and an exact continuation of the Tertiary crustal movement. 
Of the Tertiary phase we only know the folds and overthrusts at 
greater depth, of the youngest phase only the fractured and faulted 
crust near the surface. We see, however, that the two phenomena are 


1) L. Rurren and W. Horz. De Geol. Exp. van Ceram 9e Verslag Tijdschr. 
Kon. Aardr. Gen. XXXVI 1919. 
*) H. A. Brouwer. On the Crustal Movements etc. l.c. 


575 


mutually complementary, and that the place of sudden curvature in 
the horizontal projection of the Tertiary folding-axes coincides with 
the considerable transverse dislocations of the present geanticlines *). 

One of the numerous changes which may thus originate in the 
horizontal projection is illustrated in fig. 2. 


Ftg. 2. One of the possible modes of genesis of deep transverse straits (such as 
Manipa Strait between Ceram and Buru). 


Suppose C, and D, of the horizontal projection to have reached 
C, and D, in a succeeding phase, then a rapid increase of opposed 
velocities will be engendered on either side of the point of intersec- 
tion, through which the breaking crust will reveal here in the first 
place considerable transverse faults and fractures. 

Let us imagine an ideal free horizontal movement without trans- 
formation of the geanticline, then all points will be displaced in 
horizontal direction with the same velocity. In case the free hori- 
zontal movement is counteracted, the places where considerable 
disruptions will occur near the surface, will be determined by the 
distribution of the velocities. 

The geanticline of the Timor-row of islands is situated at the 
island of Timor, opposite and near a fairly rectilinear part of the 200 
m.-line of the Sahul-shelf. The free horizontal movement is hereby 
counteracted in the same degree and there is no reason for expecting 
velocity-differences for adjacent points of the horizontal projection 
of the geanticlinal axis, so that important transverse faults and 
fractures do not occur. The central basin, however, that we now 
know to exist over the whole length of the Dutch portion of 
Timor and which is also found more towards the East, illustrates 
the occurrence of longitudinal disruptions, along which oppositely 
directed movements took place — at least for a considerable time 
during the development of the geanticline. 


1) These transverse movements may also have occurred in earlier. phases of 
mountain-building, but the present morphological structure is governed chiefly by 
the most recent movements along the same or other fault-planes and fractures 
of the same kind, which have taken over tlie task of the older ones. 


a 


576 
SUMMARY. 


1. From the shape of the rows of islands we may conclude that 
besides in a vertical direction they can also move largely in a 
horizontal direction. 

2. The geotectonic geology of ten dealt with as a part of descriptive 
geology, includes a number of problems which admit only a dynamic 
solution. 

3. Just as a glacier impresses us with the idea that it is perfectly 
quiescent, whereas the presence of crevasses can only be accounted 
for by velocity-differences of the movement, the much slower move- 
ment and the velocity-differences in the case of geanticlines can be 
demonstrated by the faults and fractures near the surface, and that 
especially there where erosion has exerted only little influence and 
only during a short period, as in the case of the geanticlines in 
deep seas. 


Botany. — “Ueber die tropistische Wirkung von rotem Licht auf 
Dunkelpflanzen von Avena sativa.’ By Miss Dr. Crara 
ZOLLIKOFER. (Communicated by Prof. F. A. F. C. Went). 


(Communicated at the meeting of October 30, 1920). 
§ 1. Einleitung. 


Die in den letzten Jahren allgemein gebräuchliche Verwendung 
von mässig starkem rotem Licht bei reizphysiologischen Arbeiten 
im Dtinkelzimmer galt bisher als völlig harmlos, insofern die 
Pflanzen demselben nicht zu lange ausgesetzt waren. Speziell für 
Avena sativa hatte BLaauw') eine äusserst geringe Empfindlichkeit 
für die schwächer brechbaren Strahlen bis ins Grün festgestellt. 
Nur bei 1'/,—2 stündiger Einwirkung von starkem rotem Licht 
beobachtete er schwache phototropische Kriimmungen. Voaer®) fand 
bei Dauerbeleuchtung mit schwachem rotem Licht eine geringere 
Endlänge der Avena-Koleoptilen und eine Erhöhung des Zuwachses 
in 24 Stunden, analog den Erscheinungen nach Hinwirkung von 
sehr schwachem weissem Licht. In beiden Fallen handelte es sich 
um beträchtliche Lichtmengen. Genauere Feststellungen, wie weit 
tatsachlich das im Dunkelzimmer verwendete rote Licht als photo- 
tropisch unwirksam betrachtet werden darf, liegen nicht vor. Diese 
Liicke sollen die nachstehenden Untersuchungen ausfüllen. Sie 
beziehen sich einerseits auf die Kinwirkung roten Lichtes auf das 
Längenwachstum der Koleoptile, anderseits auf phototropische 
Reaktionen. Es wurde versucht, durch genauere Bestimmung der 
verwendeten Lichtmengen die Grenze zu finden, oberhalb der die 
Wirkung des roten Lichtes nicht mehr unberiicksichtigt bleiben 
_darf, und einige Daten über den Verlauf der Reaktion zu gewinnen. 
Es handelt sich dabei, wie ausdrücklich betont sei, nicht um reines 
spektrales Rot, sondern um den Strahlenbezirk, den die im Dunkel- 
zimmer meist gebrauchten Ueberbirnen aus Rubinglas durchlassen. 

Die verwendete Lichtquelle war eine 100-kerzige Metallfadenlampe 
mit sehr dunkler Rubinglas-Ueberbirne der Ica—A.G., spektros- 


1) Braauw, A. H. Die Perzeption des Lichtes. Rec. trav. bot. néerl. V, 1909. 
3) Voer, E. Ueber den Einfluss des Lichts auf das Wachstum der Koleoptile 
von Avena sativa. Zeitschr. f, Bot. VII, 1915, 


578 


kopisch gepriift. Die spektroskopische Kontrolle ergab, dass tatsäch- 
lich nur ganz wenige Strahlen im Orange durchgelassen wurden. 
Es waren vereinzelte von der Wellenlänge 609—613 wu (Na-Linie 
A= 589 uu), etwas zahlreichere von 613—-623 uu; lichtstark war 
das Spektrum erst oberhalb 623 uu. 

Die photometrische Bestimmung der Lichtstärke bereitete einige 
Schwierigkeiten und kann deshalb nur angenäherte Genauigkeit 
beanspruchen. Einmal war infolge von Stromschwankungen im Netz 
die Lichtintensität nicht ganz konstant. Sodann lässt sich mit dem 
Weber’schen Photometer, das mir zur Verfügung stand, genau nur 
weisses oder wenig gefärbtes Licht messen Es gelang mir aber mit 
einiger Uebung, den Punkt gleicher Helligkeit mit dem weissen 
Vergleichslicht doch angenähert zu bestimmen. Das Mittel aus einer 
grösseren Zahl von Messungen ergab für meine Lampe die. über- 
raschend geringe Lichtstärke von 0,08 HK, also eine ganz enorme 
Abschwäechung durch das Rubinglas. Der mittlere Fehler beträgt 
dabei höchstens 10°/,, sodass dieser Wert unbedenklich als Grund- 
lage für die nachfolgenden Untersuchungen dienen kann, umsomehr 
als bisher überhaupt keine Zahlenangaben für rotes Licht vorliegen. 

Die Versuche wurden ausgeführt in einem Dunkelzimmer des 
Botanischen Laboratoriums in Utrecht mit konstanter Temperatur 
von 22,5° C. und einer relativen Luftfeuchtigkeit von 55—60 °/,. 
Als Objekt dienten Dunkelpflanzen von Avena sativa von einer 
Koleoptilenlänge von 15—35 mm, die 24—48 Stunden bereits in 
der konstanten Temperatur des Versuchsraums zugebracht hatten. 


4 


§ 2. Wachstumsreaktion nach Hinwirkung von rotem Licht. 


Die von Voer *) bei Avena nach Anwendung relativ grosser Licht- 
mengen beobachtete Wachstumsreaktion ist von Simrp?) auch für 
Beleuchtungen bis zu 10 MKS herab festgestellt worden. Eine ähn- 
liche Schwankung in der Zuwachsbewegung tritt auch auf, wenn 
voliständig dunket erzogene Pflanzen rotem Licht ausgesetzt werden, 
und zwar geniigen dazu schon sehr geringe Mengen. 

Ich beobachtete die Zuwachsbewegung stets an einer einzelnen 
Pflanze, die in einem Thermostaten mit Wassermantel von Zimmer- 
temperatur aufgestellt war. Die Temperatur in dessen Innenraum 
schwankte im Verlauf mehrerer Stunden um höchstens 0.2° C. Die 
Messung des Wachstums geschah alle 3 Minuten durch ein horizontal 


1) Voer, EB, l.c. 
*) Siere, H., Ueber den Einfluss geringer Lichtmengen auf die Zuwachsbewegung 
der Koleoptile von Avena sativa. Ber. d. Deutsch. Bot. Ges. XXXVII, 1919. 


eingebautes Mikroskop mit Mikrometer-Okular, in den ersten Ver- 
suchen bei 131 facher, später bei 71 facher Vergrösserung. Mit 
Hilfe eines Kathetometers konnte die Versuchspflanze rasch und 
prazis in der Vertikalen verschoben werden. Die Beleuchtung erfolgte 
in der von Braauw *) angegebenen Weise mittels 4 Spiegeln, durch 
welche das Licht allseitig horizontal auf die Pflanze geworfen wurde, 
während sie gegen direkt von oben einfallende Strahlen geschützt 
war. Ein fünftes, drehbares Spiegelchen warf das für die Ablesun- 
gen nötige Licht ins Mikroskop. Durch gut anschliessende Kappen 
aus schwarzem Papier konnten die 4 Seitenspiegel nach Bedarf 
verdunkelt werden. Der Weg des Lichtes von der Lampe bis zur 
Versuchspflanze betrug 45 cm., die von der Pflanze empfangene 
Intensität 0,4 MK. Zur Absorption der Warmestrahlen diente eine 
zwischengeschaltete Wasserschicht von 5 em. Dieke. Mit den Able- 
sungen wurde sofort nach der Einstellung im Thermostaten begonnen. 
Während derselben waren die Pflanzen 1—2 Minuten dem Licht 
ausgesetzt und erhielten bei allseitiger Belichtung 120—240 MKS. 
Von da an wurde für die Ablesungen alle 3 Minuten 10— 12 Sekun- 
den belichtet. Die Wirkung war eine deutliche, sofort einsetzende 
Wachstumsreaktion, die in Figur 1 graphisch dargestellt ist. Die 
Abszisse gibt die nach der Exposition verstrichene Zeit in Absehnitten 
von 3 Minuten. Als Ordinaten sind die Zuwachsgrössen in ~ pro 
Minute fiir das betreffende Intervall aufgetragen. 


0 CS a 
0 6 12 18 24-7030 “36 42° “Ag oat Loom Ge: AOR ZEI ZERSO 


Fig. 1. Reaktionsverlauf nach Anfangsbelichtung von 220 MKS 
(5 > 0,4 MK. 110 Sek.). 


Auf einen anfänglichen Wachstumsanstieg, der in der Mehrzahl 
der Fälle deutlich ausgeprägt war, folgt eine beträchtliche Verringe- 
rung der Wachstumsgeschwindigkeit bis zu einem Minimum, das 
meist rasch überschritten wurde, manchmal sich aber auch über 
mehrere Ablesungsintervalle erstreckte. Nach allmahlichem Anstieg 
bis ungefähr zur ursprünglichen Höhe wird dann das Wachstum 
annähernd konstant. Durchschnittlich lag das Anfangsmaximum nach 
9 Minuten und überschritt im Mittel um 27°/, die ursprüngliche 


1) Braauw, A. H., Licht und Wachstum I, Zeitschr. f. Bot. VI, 1914. 


580 


Wachstumsgeschwindigkeit; das Minimum lag nach 26—29 Minuten 
mit einem mittleren Betrag von 66°/, der Anfangsgesch windigkeit. 
Die Reaktion dauerte ungefähr eine Stunde. 

Eine ganz entsprechende Reaktion trat ein, wenn die 4 Seiten- 
spiegel verdunkelt waren und nur */, der vorigen Lichtmenge durch 
den Ablesespiegel einseitig zugeführt wurde. Maximum und Minimum 
lagen an der gleichen Stelle und erreichten ungefälr dieselbe Höhe. 
Auch die Reaktionsdauer war annähernd die gleiche; in einigen 
Fällen nur trat ein wellenförmiger Verlauf mit einem zweiten und 
dritten Maximum auf und erschien die Reaktion stark in die Länge 
gedehnt 

Diese Gleichartigkeit bei den zwei verschiedenen Lichtstärken liess 
zuerst vermuten, dass die ganze Wachstumsschwankung bedingt 
sein könnte durch die Uebertragung in den Thermostaten, obgleich 
Temperatur und Feuchtigkeit dort dieselben waren wie im übrigen 
Versuchsraum. Die Reaktion trat aber auch auf, wenn die Pflanzen 
vorher 2 Stunden vollstandig unbelichtet im Thermostaten zugebracht 
hatten. Anderseits blieb sie uus. wenn eine Pflanze für 10—12 
Minuten aus dem Thermostaten entfernt wurde, nachdem ihre Zu- 
wachsbewegung eine gleichmässige geworden war. Es kann also 


nicht die Uebertragung in den Thermostaten sein, die die Anderung 
in der Wachstumsgeschwindigkeit hervorruft, höchstens wird sie 
dadurch vielleicht etwas verstärkt. Es handelt sich offenbar um eine 
Lichtwachstumsreaktion mit ganz charakteristischem Verlauf. Die 
weitgehende Uebereinstimmung bei den beiden verwendeten Intensi- 
täten liegt wohl darin begründet, dass diese einander doch noch 
verhältnismässig nahe liegen. Wabhrscheinlich würden sich ‘bei 
Zuführung betrachtlich grösserer Lichtmengen eher Unterschiede 
ergeben. Dass der Reaktionsverlauf sich nicht mit SterP's *) Kurven 
deckt, ist nicht erstaunlich, nachdem diese Kurven für verschieden 
grosse Mengen von gemischtem Licht sich als so stark unter einander 
abweichend ergeben haben. Ebenso verständlich ist es, dass die 
Schwankungen in viel engeren Grenzen bleiben und die ganze 
Reaktion in kürzerer Zeit verläuft. Da sie unmittelbar einsetzt, ist 
sie in der Hauptsache wohl als Wirkung der Anfangsbeleuchtung 
aufzüfassen. In ihrem späteren Teil muss sie allerdings melr oder 
weniger stark beeinflusst werden durch die in Intervallen von 3 
Minuten sich wiederholenden kurzen Beleuchtungen. Ohne dieselben 
wäre vielleicht, Voer’s’*) Befunden entsprechend, eine Ueberschrei- 


I) SIGRP, Hse: 
3) Voer, E., |. c. 


581 


tung der anfänglichen Wachstumsgeschwindigkeit und langer an- 
haltende Wachstumsförderung zu erwarten, die nun aber durch die 
sich regelmässig wiederholenden Belichtungen herabgedrückt wird. 
Es wird durch diese allmählich eine bestimmte Höhe der Licht- 
stimmung erreicht, indem die Pflanze sich an die regelmässige 
Lichtzufuhr anpasst und zu einem gewissen Gleichgewichtszustand 
gelangt, der sich in der schliesslich erreichten Konstanz des 
Wachstums äussert. Bei Verdunklung von mindestens 20—30 Minuten 
sinkt die ,,Lichtstimmung” wieder so weit, dass erneute Belichtung 
wieder eine neue Wachstumsreak tion hervorrufen kann. Die Gewöhnung 
an eine bestimmte Lichtzufuhr ergibt sich auch daraus, dass Pflanzen 
nach 1—2 stündiger Beobachtung auf eine weitere Erhöhung der 
Lichtmenge durch eingeschaltete Dauerbeleuchtung von 20—30 
Minuten kaum mehr reagierten. Die Empfindlichkeit erscheint also 
merklich herabgesetzt. 


§ 3. Tropistische Reaktion auf rotes Licht. 


Einer Lichtwachstumsreaktion im Sinne der Braauw’schen Theorie 
mussten phototropische Kriimmungen oder doch deren Anfangsstadien 
entsprechen, falls die Lichtmengen einseitig zugeführt wurden. Tat- 
sächlich war bei einseitiger, nicht zu schwacher Belichtung die 
Wachstumsreaktion von deutlicher Asymmetrie der Koleoptilenspitze 
begleitet. Diese wurde bei Dauerbelichtung von 30 Minuten schon 
nach 15 Minuten mikroskopisch sichtbar, nach 75 Minuten auch 
makroskopisch deutlich. Nach einer Anfangsbelichtung von 4 Minuten 
und: darauf folgender Wachstumsbeobachtung kam es zur mikros- 
kopischen Asymmetrie nach 45 Minuten und bis zur makroskopischen 
Wahrnehmbarkeit derselben nach 1'/, Stunden. Die einseitige Be- 
liehtung wurde erreicht durch Verdunklung zweier Seitenspiegel und 
Einfügung eines weiteren Spiegels zwischen die beiden andern. Die 
zugeführte Lichtmenge (4 « 0,4 MK pro Sekunde einschliesslich des 
_Ablesespiegels)} betrug im letztern Fall immer noch etwa 600 MKS 
bis zum Eintritt einer mikroskopisch sichtbaren Spitzenasy mmetrie. 
Demgegenüber zeigten nar makroskopisch beobachtete Kontroll- 
pflanzen, denen eine bestimmte Lichtmenge in kurzer Zeit zugeführt 
wurde, dass schon viel kleinere Mengen genügten, um sogar deutliche 
Krümmungen hervorzurufen, besonders wenn auf dem Klinostaten 
die geotropische Gegeninduktion aufgehoben wurde. 

Zur genaueren Feststellung, bei welchen Mengen die phototropische 
Wirksamheit des roten Lichtes deutlich wird, benutzte ich Serien 
von 20—25 Keimlingen, die reihenweise in 20 cm langen Blech- 


582 


kästchen gezogen waren und nur makroskopisch beobachtet wurden. 
Zur Belichtung diente die gleiche Lampe. Die Kästchen wurden, in 
der Längsrichtung etwas schräg aufgestellt, damit die Pflanzen 
einander nicht beschatteten, in einem phototropischen Kasten mit 
Camera-Verschluss exponiert. Die mittlere Lichtstärke betrug bei den 
meisten Versuchen 0,24—0,35 MK; für die vorderste Pflanze war 
die Intensität je nach der Entfernung von der Lampe 2 bis 3 Mal 
so hoch als für die hinterste. Die kleinen Lichtmengen bis 135 MKS 
wurden in 1'/,—-7 Minuten zugeführt, die höheren in 20—30 Minuten, 
bzw. 1 Stunde. Nach der Exposition kamen die Pflanzen auf einen 
Prerrer’schen Klinostaten und rotierten im Dunkeln um die horizontale 
Achse, um die phototropische Reaktion rein zu erhalten. Die zur 
Kontrolle des Reaktionsverlaufes unerlässliche Verwendung von 
rotem Licht wurde aufs äusserste eingeschränkt und streng darauf 
geachtet, dass das Licht stets senkrecht zur Krümmungsrichtung 
einfiel, die Reaktion also nicht verstärken konnte. Die erste Beob- 
achtung machte ich nach Verlauf von 15 oder 20 Minuten, zu 
dem Zeitpunkt wo der sichtbare Reaktionsbeginn zu erwarten war, 
die folgenden in der Regel alle 10 Minuten. 

Die kleinste Lichtmenge, mit der in allen Fällen noch eine photo- 
tropische Reaktion, meist noch deutliche Krümmungen, erhalten 
wurden, betrug 15—30 MKS. Der Schwellenwert für die Erzielung 
einer makroskopisch sichtbaren Reaktion dürfte bei 8—10 MKS 
liegen. Mit dieser Lichtmenge wurden in mehreren Versuchen teils 
ganz schwache Krümmungen, teils noch deutliche Spitzenasymmetrie 


erhalten. 
Zum zeitlichen Verlauf der Reaktion gibt Tabelle 1 einige Daten. 
TABELEE 1: 
Reaktionsverlauf nach Reizung mit verschiedenen Mengen von rotem Licht. 
1. pos. Reaktion | 2 pos. Reaktion 
Lichtintensitat Dauer der| Lichtmenge | neg. Reaktion = 
. : Beginn Höhe cad ‘Asymetrie| Krüm- 
in HK Reizung in MKS ain P | nach Min. y mung 
nach Min. | nach Min. 
0,16—0,32 50 Sek. 8—16 15 20 | 30—40 — — 
Tet 94 Sek. 15 -30 20 30 | 40 50 60 
at 187 Sek. | 30—60 15 | 20 | 30—40 50... Pesan 
” 5 7 Min. 67—134 20 | 25—30 40—50 60—70 90 
0,32 — 0,89 20 Min. | 384—1068 | 15—20 25—30 | 45 55 60 
0,047—0,066 1 Std.  169—238 ? ee? 60 5 | =e 
| | 


983 


Die Reaktion zeigt eine weitgehende Gleichformigkeit fiir alle 
untersuchten Lichtmengen. Hine gewisse Ausnahmestellung nehmen 
nur einige Falle rein negativer Kriimmung ein. Nach 15—20 Minuten 
wird die erste positive Reaktion sichtbar, die in der Regel nicht über 
eine deutliche Spitzenasymmetrie hinausgeht. Ihr folgt eine sehr 
deutliche negative Spitzenasymmetrie, welche 30--40 Minuten nach 
Beginn der Reizung ihren Höhepunkt erreicht und abgelöst wird von 
der zweiten positiven Reaktion. Diese beginnt in der Regel 60—70 
Minuten nach der Induktion und führt dann bis zur Kriimmung. 
80—120 Minuten nach Reizbeginn fängt in der Regel der Rückgang 
der Kriimmung an. 

Eine Abhängigkeit der Reaktionszeit von der Reizmenge, wie sie 
Arisz') festgestellt hat, ist aus Tabelle 1 nicht zu ersehen. Sie besteht 
aber sicherlich in gewissen Grenzen auch für rotes Licht, denn bei 
ein und derselben Serie setzte meistens die Reaktion in der vorderen 
Hälfte um 5—-10 Minuten früher ein als in der hinteren. Ebenso 
nimmt die Stärke der Krümmung mit wachsender Lichtmenge zu. 
Dafür sollen in einer ausführlicheren Publikation Belege gegeben 
werden. Das Ausbleiben der negativen Kriimmung bei schwachen 
Intensitäten gilt dagegen für rotes Licht nicht. Eine allerdings rasch 
vorübergehende, aber vollständig deutliche negative Reaktion war 
stets festzustellen zwischen der ersten und zweiten positiven Reaktion. 
Wo die negative Reaktion als Zwischenstadium erschien, ging sie nie 
weiter als bis zur zweifellosen Spitzenasymmetrie. Kam es dagegen 
bis zur negativen Krümmung, so blieb die zweite positive Reaction 
aus. Im Widerstreit der beiden Bewegungen wurde also stets die eine 
ganz oder teilweise unterdriickt. Falle von rein negativer Reaktion 
kamen besonders bei kleinen Lichtmengen (15—60 MKS) vor. Die 
Bedingungen für ihr Auftreten bleiben noch näher zu untersuchen. 
Es mag hier daranf hingewiesen werden, dass CraRrK *) die negative 
Reaktion bei um so kleineren Lichtmengen auftreten sah, je geringer 
die Lichtintensität war. Demnach wäre es nicht überraschend, dass 
bei den äusserst niedrigen Intensitäten des roten Lichtes die negativen 
Krümmungen bei so kleinen Lichtmengen erscheinen. Da sie in meinen 
Versuchen sämtlich bei der Rotation auf dem Klinostaten auftraten, 
werden hier die von Arisz gegen CrLARK's Beobachtungen erhobenen 
Bedenken hinfällig. 

Als praktische Folgerung aus diesen Ergebnissen wird künftig noch 


1) Arisz, W. H. Untersuchungen über den Phototropismus. Rec trav. bot. 
néerl. XII, 1915. 

2) CLARK, O. L., Ueber negativen Phototropismus bei Avena sativa. Zeitschr. f. 
Bot. V. 1913: 


584 


grössere Vorsicht in der Verwendung von rotem Licht zu fordern 
sein. Auch andere Versuchsobjekte für Dunkelversuche werden erst 
auf ihre Empfindlichkeit dagegen untersucht werden müssen. Besonders 
wo es sich um Reaktionen in der Nahe der Schwellenwerte bandelt, 
wird die Möglichkeit phototropischer Induktion durch rotes Licht zu 
berücksichtigen- sein. Genauer als bisher müssen auch die roten 
Ueberbirnen nachgeprüft werden. Als ,,spektroskopisch geprüft”” sind 
sehr verschieden dunkle Rubingläser im Handel, und der Spektralbezirk, 
den die durchgelassenen Strahlen umfassen, erstreckt sich bei etwas 
helleren Gläsern merklich weiter ins Gelb hinein, 

Nach Biaavw’s*) Feststellung, dass sogar spektrales Rot tropistisch 
keineswegs ganz unwirksam ist, kann es nicht überraschen, dass 
sich auch mit rotem Licht ausgeprägte phototropische Reaktionen 
erzielen lassen. Unerwartet erscheinen nur die geringen, dafiir erfor- 
derlichen Lichtmengen. Wahrscheinlich liegen bei den eingangs zi- 
tierten Beobachtungen von BraAuw und Voer starke Ueberbelich- 
tungen vor. Arisz *®) hat die Menge weissen Lichtes, die die stärkste 
„Maximalkrümmung’” hervorruft, zwischen 100 und 137 MKS. 
gefunden. Es ist zu vermuten, dass sie für rotes Licht nicht höher, 
sondern eher niedriger liegen wird. Bei dazwischenliegenden Reiz- 
mengen würde sich vielleicht eine mehr oder weniger ausgedehnte 
Indifferenzzone ergeben. 

Das Auftreten einer charakteristischen Wachstumsreaktion nach 
allseitiger, wie nach einseitiger Bestrallung mit rotem Licht spricht 
für Braauw’s Auffassung der phototropischen Erscheinungen. Es ist 
zu vermuten, dass sich auch für diese Strahlen bis zu den kleinsten 
tropistisch wirksamen Mengen herab die Lichtwachstumsreaktion bei 
geeigneter Versuchsanordnung nachweisen liesse. f 


Utrecht, Oktober 1920. Botanisches Laboratorium. 


1 BLAAUW, A, Hi, £909 1. -c. 
a)" Anisz.” WGE, Whe. 


Mathematics. — “On the Theorem of Picard.” By Prof. J. Worer. 
(Communicated by Prof. L. E. J. Brouwer.) 


(Communicated at the meeting of June 26, 1920). 


The theorem of Picard on the conduct of a uniform analytical 
function in the neighbourhood of an isolated essentially singular 
point was proved in 1896 by Bore. without the use of the modular 
function.) By this a series of elementary proofs was opened for 
the celebrated theorem. In 1904 ScHorrky made the demonstration 
of Bore considerably stricter.®) He found an important theorem 
on holomorphic and meromorphic functions which are nowhere 
zero and nowhere 1, and on this he founded the elementary proof 
for the theorem of Picarv.*) After this Lanpavu discovered an ex- 
tension of the theorem used by Scuortky‘). The remarkable result 
is as follows: if f(z) ts holomorphic for |z| < R, if tt is there 
nowhere zero or 1, if further | f(O)| <p, then for |z| SOR, in which 
0 <1, we have | f(z)|<P(u, 4), where ® only depends on 6 and u. 
As Scrorrky did not possess this proposition, his reason- 
ing is here and there subtile. Elegant proofs of the theorem of 
Picarp were given in 1912 and 1913 by Monrrer, but they are 
founded on the consideration of the so-called normal families of 
functions.*) BerNays, who in 1911 quite simply brought forth the 
theorem of Lanpau out of that of Scnorrky’), gave in 1913 new 
derivations of LANDAU’s theorem, and investigated at the same time 
the function p (a), the upper limit for the radius of a circle, where 
the series f= a-+z-+a,z*-+.... converges and nowhere becomes 
zero or 1‘). 

1) Comptes rendus, May 11 1896, part 122, p. 1045—1048. 

2) Sitzungsber. der K. Pr. Ak. d. Wiss., 1904, p. 1244—1262. 

5) l. ce. p. 1255 sqq. 

4) Göttinger Nachrichten 1910, p. 309— 312. 

5) Annales de l'école normale, part 29 (1912), p. 512 and part 33 (1916) p. 251. 
Monte. gives here at the same time a simple proof of the theorem of LaANpau 
(part 33 (1916) p. 517.) 

6) See e.g. Sitz. ber. der K. Pr. Ak. d. Wiss. 1911, p. 597. 

Levy made this derivation still more simple in the Bulletin de la Soc. Math. de 
Fr., part 40 (1912) p. 25—39. It deserves to be mentioned that in 1907 Scuortxy 
(Sitz Ber. der K. Pr. Ak. d. Wiss. p. 823—840) gave two new proofs of the 
theorem of Picarp. They are, however, no more simple than the one of 1904. 

7) Vierteljahrschrift der Naturf. Ges., Zürich, 58 (1914), part 3, p. 203—238. 


586 


Here follows a proof for the theorem of Picarp, which is founded 
on the theorem of Lanpau and which is for the rest elementary. 
1. Let f(z) be holomorphic for \z << # and let it there become 


1 
nowhere 0 or 1, while 0 <|f(0)| <u. Then according to the theorem 


of LANDAU: 
pw SlfE)|Splw, for |z| SA. 

By p(u) we can understand the upper limit of | f(z) |, when 
zi <4, for the functions which satisfy the conditions mentioned. 
Then p(u) is a monotonely increasing function of u. We shall prove 
that p (u) increases at a slower rate than a certain power of u. Let 
in the first place u —e?'*, where & is a positive integer, and con- 
sider the function 

1 eh SS 
(2k + 2) ni 
in which for z=O the numerator is equal to the principal value 
of Log f{O). 4(2) is uniform and holomorphic for |z)|< R and 
there nowhere zero or 1, because f(2) 40 and 41. Further 
| Log | f(0)| | + = 
Ee) eN 
From er < | f(0)| < e?* follows | Log | f(0)\| < 2hkz, so that 2(0) <1. 
Now the theorem of LANDAU gives 


AO |< 


R 
HOEP Her, for |2/ <>, 
so that 


R 
| Log f (2) | <C (2k + 2) ap, for |z| Sg 


and 
eHDap < | f(z) | << AAD ep, 
We have therefore: 
p (ec?) < e2k+2)=p for ka positive integer. 
If u be an arbitrary number >1, we can find a positive integer 


k for which 
UI u < e2kr, 


p (u) < — (er) SektDrp Set up. 
For u >1 we have therefore 
gua... «1-16.10. ae 
in which @=e*? and: p'— Pp (1,4): 

2. Let us now consider a function #'(z), holomorphic in a certain 
neighbourhood @ of O(z=0) with the exception of O. Let there 
exist a neigbourhood of 0, 2’ < 2 in which F(z) #0 and F 1. 
We describe a circle inside 2’ with radius 2 g. 


Then 


587 
Then for |z| =e we have a certain number u for which 
1 
SP (ON 
u 


in which we may suppose u > 1. 

By applying the formula (1) to /(z) in the cireles having the 
different points of the circumference of the circle |z| =p as centres 
and @ as radii, we get: 


| F(z) | and | F(2)|-!<ame for |2|=£. 


a 


By applying the formula in the circles with the different points 
of the circumference of the circle | z | = Fas centres and 5 as radii, 


we find: 


| F(z) | and | (2) |-! <Ca(apr)yp = apt) wr? for | z | = 


Going on in this way we find 


v—l1 v—2 y 
pri(zylend|F(z)|-1<a? (Fe teel = 


y 


pl 1 4 


v Ë 
Ed! u la) for Ken 
We have therefore 
| F(z)|and| F(2)|'<e” for lijm 2 


Qo» 


in which 
1 


g == Log (ar 1) . 
3. Log | #(z)| is harmonical in 2, with the exception of O. 
For 0< |z|<o we have therefore, if we pul 2=re%: 


Log | F (2) |= A Logr + & (an cos nO + by sin nO) vr. 


Here me 
Qn ° 
ar de 
An +4, 7° = „je nO . Log | F (re) | dO 
JE 
0 
and 
1 i 
b, mbr = „je nO Log.) E (re), dO et a ne ate 
Ed 
0 


where 0< r<g. r is for the rest arbitrary. 


If we now put r =< there follows. from (2): 


588 


go?” 
and |rt 


2n von 
An + ay cm ee (3) 

These inequalities hold good, when we choose for v and n arbi- 
trary positive integers. If we take for » a fixed number, so that 
2" > p, there follows from (3) that | a_,| and | 6_,| are less than 
any positive amount. From this follows: 

Gn DL = 0, when 2” Sp: 

The expansion into a series of Log |F'(z)| contains therefore at 
most a finite number of terms with negative powers of 7. This holds 
also for the expansion into a series of the conjugate harmonical 


funetion 


9 2nv 


Arg. F (2) = AO + 2 (— bp cos nO + an sin nO) mm. 


For O< |z|<e we conclude that 
F(2) Sede. nn = ee 
in which w(z) does not have the point O as an essentially singular 
point; hence it has there either a pole or an accidental singularity. 
From (4) follows 
Of iw, OL . 
PG) Zz ee 
The function 1— F(z) satisfies the same conditions as /’(z). It 
is holomorphic in &, except in 0, and for |z| < 2¢ it is different 
from zero and 1. For this reason 
Pi BY vie 
F yl 7 eee OS leise = ae 
in which y(z) has the point either as a pole or as an accidental 
singularity. 


F(z)—1 


From (5) and (6) follows that TP has the point either as a 


| 2) 
pole or as an accidental singularity, so that the same holds 
for F'(z), whereby the theorem of Picarp has been proved. 

4. The non-essential extension of the theorem, which is as follows: 
“When F'(z) is meromorphic in a neighbourhood 2 of O with the 
exception of OQ and when in a neighbourhood of 0, 2’ < 2, il does 
not assume three values a, 6, and c, then F(z) is meromorphie in 
2”, appears directly, because the function 
F(z2)—a c—o 
‘F(z)—6b ee 
satisfies the same conditions as H’(z) above. 

Groningen, April 18, 1920. 


Pe (2) == 


Mathematics. — “On the Motion of a Fixed System”. By Prof. 
W. van per Woupr. (Communicated by Prof. J. CARDINAAL.) 


(Communicated at the meeting of September 25, 1920). 


§ 1. In the discussion of the motion of a plane system the atten- 
tion is usually directed to the locus of the points which at a given 
moment describe a point of inflexion of their paths and to the locus 
of the lines which in their motion at that moment touch their enve- 
lope at a cusp; these loci are indicated as the inflexional circle and 
the cuspidal circle. The starting point is here the so-called formula 
of Savary for the radius of curvature of the path of a point, resp. 
for the radius of curvature of the envelope of a curve (or a straight 
line) of the movable system. 

Such a discussion of the singularities in the motion of a fixed 
system in space is not very simple, the expressions for the curva- 
ture and the tortuosity of the path of a point are such that they 
do not invite further conclusions. As far as I know these singulari- 
ties are only dealt with in the well known book of ScHoENFLins ‘) ; 
he there draws attention to the remarkable relation between the 
points A of the movable system and the points A’ of fixed space 
when to each point A the point A’ is conjugated which is the 
centre of the sphere of curvature of A in its path, and to the fact 
that in the “inverse motion” A is the centre of the sphere of cur- 
vature of A’ in its path. 

I wish to reach these results in an entirely different way; I shall 
make use of the so-called method of the movable system of axes 
(triedre mobile), for the application of which to kinematics we can 
refer to the text-book of Koenies °). In the $$ 2, 3 I shall therefore 
repeat a few well known formulae. 


§ 2. By 7r(0,, X,, Y;,Z,) and’ 7, (0, X, Y,Z) we understand 
two equally orientated right angled systems of axes which move 
relatively to each other. The velocity relative to 7 of a point 


1) Dr. A. ScHornriies: Geometrie der Bewegung in synthetischer Darstellung. 
(Leipzig, Teubner, 1886). 
2) G. Koenis: Legons de Cinématique (Paris, HERMANN, 1897). 


38 
Proceedings Royal Acad. Amsterdam. Vol. XXIII. 


590 


Pe, y, 2) — i.e. a point with the coordinates «, y, z, relative to Ti, — 
is called the absolute velocity of P, the one relative to Ti the rela- 
tive velocity of P, the absolute velocity of a point coinciding with 
P and fixed to 7 the convection-velocity of P; they are resp. 


represented by va, Vr, Um- 


Then 
dx dy dz 
Orr == 4 Vey SH Ts Ure S TF 
‘ dien dt 2 dt 
dx \ 
Var = Una = Ure =S 5 ige hij di | 
dy 
Day = Vmy + Uy = N+ re — pz + he > oka) 
dz | 
Var = Omz — Uy z == 5 + PY — qe ss at 


where En, ¢, p,q,” have the known significations of components of 
the absolute velocity of the point O and components of the rotation 
axis when we suppose these two to be dissolved along 1X, OY, OZ. 


If Pis fixed to 7, we have 


da 
a sf ==) 
var ing Edge =rgin oo) Je 
In the following we shall as a rule indicate the absolute velocity 
of a point fixed to 7), by Um: 


If J, is the absolute acceleration of P(«, y, 2), we can express 
Jaz, Jay, Jaz in the following way. 

We choose an arbitrary fixed point P, (a,, y,, %,) i.e. fixed to Zy, 
and consider the segment ?, P, which is equal and parallel to and 
equally directed with the vector vq representing the absolute velocity 
of P; then according to its definition the absolute acceleration of P 
is equal in amount and direction to the absolute velocity of P,, 

AS &, + Var Vo + Yay: Zo + Vaz are the coordinates of P,: 


d 
Jax =§ + q (z, + Va) f (y, =F Va,y) an ze si Va,x) 3 
but the absolute velocity of the fixed point P, is equal to zero, hence 


dz, 
EH qz, 14 PN, 


so that 


dq dr OH dz dy diz 
Jon = 8, $28 attend) «© 


where 
Senn qgs— rn 


2H=(pe + gy + rz — (P+ Hr) (e+ 9 + 2"), 
with similar expressions for Ja, and Jaz 

We can also write (3) — formulae of Bour — as 

Jar = Im,x + 2(Ger,2—7 7, y) + Jr,2 (Corro.is). 
For a point fixed to 7 
Jac =In,z. 

If we understand by J the absolute acceleration of the second 
order of P(z,y,2z), ie. the vector of which the projections on the 
fixed axes are: 

eden 72) _ Dan ‚wm _ Wan 


J rd an — ’ LA — ’ 
ahs a ade al Spgs gat 
it appears in the same way that 
dJa,r 
Joe =— > + qJa,z — r Jay 
and more generally 
(n—1) 
n Ze zx n — 
EN (4) 


We call attention to is fact that for each value of » the ex- 


pressions for Jen Je zi are linear in a, y, z. 4 
Remark. The preceding formulae may be simplified by making 
the axis OZ coincide with the instantaneous screw-axis; in this case 


Enig 
§ 3. If we call the motion of 7, relative to 7 the direct motion, 
we understand by the “inverse motion” the motion of 7 relative 
to FT; here the convection-velocity is therefore the velocity relative 
to T„ of a point fixed to 7; we shall represent this velocity 
by vl. 
Let P(z, y, z) be fixed to 7;, then according to (19) 


i (i) () 
OE Vn, z + w= Um, y + Um, y = Ume + Um, z 
38* 


592 


or 


zat Pet (Oe (ee 
Um,x— — Pmzs Un,y == — Um, y. Um,z— TT Omz ee © © (5) 


§ 4. We now assume 7 to be connected with a fixed system. 

It is required in the first place: 

to find “the locus of the points describing a point of inflexion in 
their paths — i.e. their paths relative to 7,” 

The projection of the acceleration of a movable point on the 
binormal of its path is always equal to zero; if also the projection 
on the principal normal is to be zero, it is necessary and sufficient 
that the radius of curvature of the path be infinite’), in other words 
that the point deseribe a point of inflexion in its path. A point 
describes therefore a point of inflexion when the velocity and the 
acceleration are equally directed, hence when À can be determined, 
so that 

Jar — Ag, 2 = JanS ay = dae hogs =e 
or, because we consider only points fixed to 7, so that 
Jn, a — Auma = Jin, y naz Avm, y= Jm,z A Omz 0. 


From this we find — see (16) and (3) — 
AN a Se _ 4, (a) 
— , = ee 
A(2) A(a) A(a) | 

where A, (a), A,(2), A, (2) and A(2) are functions of the third 
degree in A. 

The locus is therefore a twisted cubic. 

If we make OZ coincide with the instantaneous screw-axis, 


we have 


Eg 


Ome == Omy 10, Ome =F, 
f Ing = Eta — yt ee! 
Jmy = "IH = 


A= (5) + (5) | 


1) Here it is assumed that the point moves; the cases where at the moment in 
consideration either the whole fixed system or a line of points is at rest, might 
be treated separately (with little difficulty). 


593 


while 4, and A, are functions of the second degree in 2 and only 
A, contains the tind degree of A (the latter on the supposition that 
neither § nor 7 is equal to zero). 

Hence x, y and z become only infinite for 2 = oo and that in such 
a way that 


AE 


ìzo 2 


lim 
A=n 


The locus of the points of inflexion is in general We. unless 5 or 
r is equal to zero) a twisted parabola, which is osculated by the plane 
at mfinity at the point at infinity of the screw-awis. 

In case r is equal to zero, the motion at the moment in cunside- 
ration is a pure translation; vr and wv, are in this case equal to 
zero; if P(«, y, z) is to describe a point of inflexion, it is necessary 
and sufficient that also Jr and J, are equal to zero. 

If the motion at the moment considered is a pure translation, the 
locus of the points describing a point of inflexion is a straight line: 
AE, 

ITR et | 


e|s 


dr d dr 
sg VM \ 
dt dt --dt 
If at the moment considered ¢=—0O, the motion is at that moment 
a pure rotation. The equations of the locus in question are in this 


case 


dq dp d§ 
dt dt dt 
d d d 
r?(a*® + ye bk en peen 


If the motion at the considered moment is a pure rotation, the 
locus in question is a parabola in a plane parallel to the axis of 
rotation; finally the following cases are excepted to this: 

dp dg de o,% a Seed 

Sidi ant de de 

of revolution through the axis. 
dp dq d& dy_ a 
Made dt dt dt 
axis of rotation no points which describe a point of inflexion in their 
paths. 


Z 0; the locus in question is a cylinder 


b = 0; there are besides the instantaneous 


§ 5. Let in the second place be required: 
the locus of the points the paths of which have at the moment 


considered a stationary plane of osculation. 


594 
We remind *) that the distance from the point (w + Az, y+ Ay, 
A 3 
zt Az) to the plane of osculation at P is equal to + (Geet e). 


1 1 ard 
where — and — represent the curvature and the tortuosity in Pand 


R iM 


e 
As? 


approaches to zero at the same time with As; a stationary plane 


of osculation appears therefore only when is equal to zero (i.e. 


1 
RT 
besides at the points of inflexion there, where the tortuosity is equal 
to zero). 

We calculate the projections see jen JP of the acceleration of 
the second order on the tangent, the principal normal and the binormal. 
If a, a,,@, are the cosines of the angles which these make with the 
fixed X,-axis, we find from: 

v? dv 
Jz == 0, R + Lara 
by the application of the formulae of FRENET—SERRET 


2 d dv v Sov ww ah v® 
De =al— —— Fa Se Te 
aU leet dt? __R? INR dt BR dt aOR 


Hence 
d'v v® Sv dv v' dR v? 
B, SOG Cart) EN VEREEN 
herma za 


Nd 

BL 
In the motion relative to /y of a fixed system connected with 
i bs is is therefore equal to zero in those points where the plane 
of osculation is stationary and inversely, because — at least in the 


general case — no points appear where v,, is equal to zero. 

The velocity being directed along the tangent and the acceleration 
(of the first order) lying in the plane of osculation, this plane is 
stationary at those points and at those points only where the velo- 
city, the acceleration and the acceleration of the second order lie in 


1) See e.g. L. P. EisENHART : Differential Geometry (Ginn and Co, Boston) p. 21, 
Ex. 10. If we lay the axes OX, OY, OZ along the tangent, the principal normal 
and the binormal at an ordinary point of the curve, this can be represented for 
sufficiently small values of s by: 


s* s4 Zn Meik s dR slr da? a 1 1 5 
BR ERG ITR GR de ZldeR RET IR 


s? stal dal Te dl 
AS he A burrie 
GRT „24M de BT T ds R i 


LZS 


595 


the same plane. For the locus in question we find therefore the 
surface represented by: 


Um,x Umy Um,z 

Im,z Tiny Jm, = 0. 
(2) (2) (2) 
mx my M,z 


The locus of the points the paths of which have at the considered 
moment a stationary plane of osculation, is a surface of the third 
order. 

In the same way we show that the locus of the points the paths 
of which have at the considered moment a contact of the fourth 
order with the plane of osculation, is represented by 


Um,ax Um, y Um, z 
Jina Jn, y Jm, 2 

(2) (2) (2) 
Ji Fin: y aa Zz 


Tat) Gms Sh 2 
i.e. to this locus belong the common points of the four surfaces of 
the third order of which the equations appear by successively omit- 
ting a ray out of the above-mentioned matrix. The required locus 
is therefore according to a well known theorem of the determinants 
the curve of intersection of 


Um, x Vin, y Un. z Um, x Um, y Un, z 

Jm, x Jm, y Jm, z == 0 and Jm, x Tmyy Im, z == 0 
(2) (2) (2) (3) (3) (3) 
m, X Jm, y Jm, 2 Jm, x Jm, y Jm, z 


provided we do not count the points defined by 


Um, x Un, y Vin, z 
Pee Jae diep 
Le. the cubic we found before as the locus of the points of inflexion. 
The common points of the four cubical surfaces form therefore a 
twisted curve of the sixth order. 

The locus of the points of which the paths at the considered moment 
have a contact of the fourth order with the plane of osculation, is 
a twisted curve of the sixth order. 


i=. 


§ 6. Let P(w,y,z) be a point of the fixed system connected to 
T, and P’ (w', y',z') the centre of the sphere of curvature of the 
path of P; in this case P’ has the characteristic property that the 


596 


normal plane in P coincides with the plane of osculation in P’ of 
the curve which is the locus of P’, when P describes its path. P’ 
lies therefore always in the normal plane of P, while the velocity 
and the acceleration of P’, which lie both in the plane of osculation 
of P’, hence in the normal plane of P, are perpendicular to tbe 
velocity of P. Hence 


(ee) Um, x + (y a y') ny + (z F. z') Un, 2 —= 9 | 
Umm Van! os Umy Va,y! a Um,z Vaz!’ = as Oi, 
Um, x Ja, z +} Um, y au hk Ym, z ee == ie 


where vo, must be determined out of (la), Jas) out of (3). 
If we write the first of these equations thus: 


(7) 


x' Om,z + y' Vin, y eeh Un, 2 == & Um, x + Y Om, y + vine 
and if we substitute in the second member the expressions for v,»,x, 
Om,y» Vmz from (15), we find 


a Vin, x + y' Um, y aa Z' on, 2 = Sa = ny = Sz ee (8a) 


We write the second of the equations (7): 


… da dy 
Um, x S+gz sant kl + “ae + Um, y nr — pz ae a Be 


ante 
+ Um,z C + py'—- 1e ie = 


and subtract from this - 


da! dy dz' 4: ’ dm, “ - dvn, ao F dvm,z ER 
Vn an aus Vin, y HE =< Un, z dt v di + y di z di = 
dg dn de 
md — = 3 


which appears from (8a) through differentiation. 
If we now keep in mind that: 


dum, x 


Im,2= 


r QUm,z — Ten, y 
it appears that 
! 1 ! ds dj nee ct we 
& Jin, x == YImy =e 2Jn, z= mi = zl bm ae =F SUm, x == Ym, y == GUm, z 
or 
2'In,x + Y'Jmzy + Im = Et + yt GE we +o yg EST eps (BB) 
where El) = — zn + 9S — ry 


If we finally write the third equation of (7) 


597 


Vina Tai Ie Qla,z! — MVa,y' oe: Um,y We + Maz’ — PVar' + 


dva,z' 
+ ee me 
and subtract from this the equation that results from the second of 
(7) by differentiation, it becomes in the first place apparent that 
we can replace the third of (7) by 

Var! I myx ar Vay! Jmy == Var! Jm == 
which can also be seen directly. 

For the locus of is the euspidal curve of the developable 
surface described by the polar axis (axis of curvature) of the path 
of P, which is always perpendicular to the plane of osculation in 
P, in which lie the velocity and the acceleration of P. 

We find therefore again 


Var! Oma + Vay’ Umy + Var! Un,z = 0 | 
Vax! Ime Bik Vay’ Jm,‚y zi var Jm,z a= 
If we now write the latter equation 
ide IA: 
Jinx § = fear a | ae tap + Jy UI + re 7 pe a We at 
| | t dz 
+ Jm,z 5 + py =~ Oe Je Fr =S 
and subtract from this the equation that is found from (85) through 
differentiation, we find 


Ne (2) eG) dé dy dh 
m Y dm m,z — 3 ra va St | 
ID UD + Jl (aat 


ze (s! ye Ja a z ) (8e) 


dr ÒH(S, 7,5) 
med +1 4 +2 —— 
dt" dt dt dt dt og 
(see for the meaning of H § 2). 
Through the three equations 
U Um, x aE Ymy ze Z Ome = §# + Ny + Sz 
' ! ! Sy (*) 
Imex + y'Jmy + #Jmz = 2S Ee |. (8) 
» (2 1 2 7 (2 ds „(i) 
ot J, =e y jen = al id 2s, — és v 
a cubical correspondence is defined between the points P (a, y, 2) 
P’ (a', y', 2’). Hence: 
there exists a cubical correspondence when a point P of the system 


598 


fixed to T,, and the centre P’ of the sphere of curvature which has 
a contact of the third order with the path of P relative to Ty, are 
conjugated to each other. 


§ 7. We directly find again the locus of the points the paths of 
which have at the considered moment a stationary plane of oscula- 
tion; they are those points P of which the conjugated points P’ 
lie at infinity, hence the points defined by 


Um, x Um, y Um, z 


Jm, x Jm, y Jm, z == 
Juz Jay Jm 
Now we require 
the locus of the points P the paths of which have with the circles 
of curvature a contact of the third order (i. e. four points in common). 
To such a point P not one single point P’, but a line of points 
P’ is conjugated; they form the singular points of the transfor- 
mation through which the points of the space (P) are transformed 
into those of the space (P’). This locus is therefore defined by: 


Um, x Un,y Vin, z = Er 


| 
(i | 
Im, Im,y Jin, z SI Pe Ei v | 


2 7 ds (3) 
Fim Jab Fee 328 67 En > & © 


In the same way as in $ 6 it appears that: 

The points of the system fixed to T,, the paths of which have with 
the circles of curvature a contact of the third order (four points in 
common), form a twisted curve of the sixth order. 


Let it also be required to find those points P of which the paths 
have at P a contact of the fourth order (five points in common) 
with the spheres of curvature. 

If a point P is to belong to this locus and if P’ is to be the 
centre of the sphere of curvature, we have’) 

Vq, x! = Va,y' = Va, = 0. 

The coördinates of P must therefore satisfy besides (8) also the 
equations resulting from them by differentiation and by the substi- 
tution of 

de, dy' 


OTN DERK 
es ee ee), ae (y + rv — pe), 


' See the concluding remark. 


599 


dz! ¢ 
aie = (6 77 192 )- 


If however we differentiate (8a) this substitution gives us only 
(86); from (86) results in the same way (8c); ea (8c) we find 


ef HJ HJM |E ns AG E— + © :)| 


or 
‚78 ‚73 ' 
Boe Ieee a ee re 


where the expressions for the coefficients A,, EO a! 13 obs are rather 
extensive, but easily calculated. 


For the required locus we find accordingly : 


Um,x Um,y Um,z = Sx 
I nize Jy J mn, z =o — = gl? 
2 2) 2 = ; =— 0 
co. Jy sie 3 Poe a = §2 aa 
3 3 3 
Dee ee ued A, nn ze x | 


The points P of the system fixed to T,, the paths of which relative 
to Te have with the spheres of curvature in P a contact of the fourth 
order, form a surface of the fourth order. 


§ 8. It is clear that we shall find the same results when we 
consider the singularities of the inverse motion; at present we men- 
tion especially that a cubical correspondence will exist when we 
conjugate at a given moment a point P’ of fixed space to the centre 
P of the sphere of curvature of the path that P’ describes relative- 
ly to 7. We shall discuss the latter cubical correspondence 
more closely. 

The condition that P’(«’,y’,z’) shall lie in the normal plane of 
the path of P(a,y, 2) relative to Tf is expressed by the first of the 
equations (7): 


(w 


#) Ome + (y'—y) Umy + (2'—2) Omz = 0. 
Now 
(t'— 2) vm + (Yy'—y) Uy + (2 —2) Ume = (wr) (8 + gz—ry) + 
+ (y'—y) (4 + ra—pz) + (2'— 2) (0 + py—ye) = 
(#'—a) (§ + gz'—ry') + (Wy) (n + ra'—pz') + (2'— 2) (b+ py'—ge'), 
hence according to (5) 


(2'— 2) ome HWI) omy + (2'—2) ms = (el) 


i We 
+ (y—y) wy: srilez7e ) Une 


600 
We can therefore also write (7): 
i) zel me oe 
(—2') vr aha) vp he ea vee =0.. 15.8 


that means, in the inverse motion P lies in the normal plane of the 
path of the point P’ fixed to 7’. 

Lf at any moment in the direct motion P’ lies in the normal plane 
of the path of the point P fixed to T,, then in the inverse motion 
P les in the normal plane of the path of the point P’ fixed to Ty. 


We have already seen that the condition for P’ to be the centre 
of the sphere of curvature of the path of P in the direct motion, 
is expressed by the equations (7) or (8); what are then the conditions 
for P to be the centre of the sphere of curvature of the path of 
P’ in the inverse motion? 

The equation of the normal plane of the path of P’ in the inverse 
motion is 


(Ke) omer + (Ly) omy + (Z—2) ome = 0; 2. (10) 


the centre of the sphere of curvature of the path of P’ is therefore 
defined by this equation and two more derived from it by differ- 
de’ dy’ “dz” 
dt’ dt’ dt 


entiation with respect to ¢; for the values must be taken 


which follow from 
Var! = Vay' = Var = 0 
for instance 
qa’ 
dt 
In order to express that P(w,y, z) is the centre in question, we 
must substitute 


= — 6 + gz! — ry). 


Kz an Say eee A 

But then (10) is transformed into (8a), and we have already seen 
that in the way indicated before the equations (86) and (8c) appear 
from (8a) ($ 7). Hence: 

If P’ is the centre of the sphere of curvature of the path of P 
in the direct motion, P is the centre of the sphere of curvature of 
the path of P’ in the inverse motion, in other words the cubical 
transformation is reversed together with the motion. 

We can go one step further. 

The locus of the points P fixed to 7’, the paths of which relative 
to 7’; — hence in the direct motion — have a contact of the fourth 
order ($ 7) with the spheres of curvature in P, is at any moment 


601 


a surface O,, of the fourth order (6 7); in the same way a surface 


0; of the fourth order will be the locus of the points P’ the paths 
of which in the inverse motion have a contact of the fourth order 
with the spheres of curvature in P’. 

The former of these surfaces was determined by joining to (8) 
the equation (8d), which results from (8c) through differentiation, 


dx’ dy’ dz’ 


when for F ‚— the values are substituted following from 
de i eas 


Var! = Vay’ = tar = 9 
Now we do not require O'y, but the locus of the points P that 
are the centres of the spheres of curvature which have with the 


path of a point P/ of O', in the inverse motion a contact of the 
fourth order. 
The normal plane of the path of P’ has for equation: 


NO= (X—2’) oy + (Y—y’') vy + (Z—z2') wee ==) tard LO) 
the centre of the sphere of curvature is found from: 


aN© ad NO 
NO) ooh A ag ee (11) 
dt dt? 


the condition that this sphere has with the path of P’ a contact 
of the fourth order is expressed by 


a Nl) 
hie oe as ee Wie ce 
de dy dz' 
while Bl oe zp we determined from 
Var! == Vay! = Var = 0 


The locus in question is then found by eliminating a’, y’', z' from 
(11) and (12). 
In the same way however -— for the first member of (10) is 


identical with that of (8) — we have produced the surface O,,; the 
locus in question is therefore Os 

In the direct motion a surface On of the fourth order is the locus 
of the points fixed to T„ the paths of which have jive points im 
common with the spheres of curvature; in the same way in the inverse 
motion a surface O'y of the fourth order is the locus of the points 
fixed to Ty the paths of which have five points in common with the 
spheres of curvature; the points of Om and O'y correspond in the 
two cubical correspondences, so that e.g. in the direct motion a point 


602 


P’ of Of is the centre of the sphere of curvature which has five 
points in common with the path of a point P of On. 


CONCLUDING REMARK. 


In § 7 we remarked: 

If a point P describes a twisted curve y and the point P’ the 
curve which is the locus of the centres of the spheres of curvature 
of y in P, the condition that such a sphere has with y a contact 
of the fourth order is expressed by putting the velocity of P’ equal 
to zero. 

We shall briefly indicate the proof of this proposition. 

If we represent y by the equation developed in § 5 (footnote), 
and the sphere of curvature by 

1 


d 
© + y? + 27 — 2 hy — 2 it ena 


we find for the condition for a contact of the fourth order 


A ed las eo Re 
ora aur rs tau 


and for the arc described by P’ (see e.g. Brancui-Lukat: Vorlesun- 
gen iiber Differential-Geometrie, I, zweite Auflage, p. 25) 


R d dR 
de = 0,3 bh = 7 dT ; 


ds ds 
From var = 0 follows d, = 0 as aT = o is excluded. Inversely 


: i | 
d, is only equal to zero, when vg,’ is equal to zero, as for 57 0 


4 


Vax becomes generally infinite and d, differs from zero. It would 
lead us too far if we entered further into this. 


Zoology. — “On the larval development of Oxyuris equi (Schrank)”. 
By J. HE. W. Inte and G. J. van Oorpr. (Communicated by 
Prof. SLuIrEr.) 


(Communicated at the meeting of May 29, 1920). 


The only treatise known to us‘) on the larval development of 
Oxyuris equi is the one by Rainumr and Henry (1903). In this 
article two different forms of larvae are described: 1. those, having 
a length of about 5—10.5 mm. and 2. those measuring 5—6 mm. 
The posterior extremity of the body differs in these two forms. In 
the former the anus is situated rather far from the posterior extre- 
mity, in the latter this distance is shorter. In neither forms gonads 
are formed as yet. 

On the ground of the above and also because the second form 
occurs less often, Rainier and Henry are of the opinion that the 
former represent female, the latter male larvae. In certain characters 
(the presence of cuticular rings, of rectal glands and of rectal muscles) 
they correspond to adult Oxyuris-specimens, in many others they 
differ. Both larval and adult Ozyuris live free in the colon and 
coecum of the horse. The larva found by the French authors “parait 
être simplement une forme larvaire de |’Oxyuris equi (Schrank), ou 
“mieux une forme immature, qu'une dernière mue doit amener a la 
forme adulte” (RaiLrier et Henry 1903, p. 137). When the number 
of moults of Oryuris corresponds to that of many other Nematodes, 
this is the fourth and latest moult, according to the investigations 
of Surat (1914). 

In the material, collected by the commission, charged with the 
Sclerostomiasis-inquiry in Holland, we found the larval forms, 
described by Raimrter and Henry in many specimens, taken from 
different horses. In order to judge of the correctness of the opinion 
of the French authors, holding that the imaginal Oxyuris originates 
from this larval form by a last moult, we had to look for moulting 
specimens in the first place. We succeeded in finding a good number 
of such specimens, and so we could make out with certainty that 


1) PerRoncito’s article: “Sviluppo degli Oxyuridi’, Giorn. Acc. Med. Torino. 
Vol. 6, 1903, was not seen by us. 


604 


Rairuet’s and Henry’s opinion is correct. A more detailed description. 
of the male and female larvae and of the anterior extremity of 


young imaginal and of moulting specimens of Oxyuris equi follows 
here. 


The larval form. 


The length of the smallest specimens, observed by us, is about 
2.8 mm.; the diameter of these specimens is + 250 u at the level 


. Hania at, 
je ZS PARE 
Ad Le ? ee feet, *. 
<= EEN x0 RO 
---- ent. A DAL des ere 


ee OO A kle 
. Oe 
musc. ee”, 
iid etc: 


Here leut, 


Fig. 2. 


Fig. 1. Posterior extremity of a female larva, viewed from right side. Total 


length 6.11 mm., catch N°. 37. TD: 


Fig. 2. Posterior extremity of a male larva, viewed from right side. Total 
length 4.93 mm., catch N°. 37. 120, 


605 


of the anterior part of the body, + I50 u in the middle of the 
body. So in the front part they are much thicker than more back- 
ward at the level of the middle part of the body. Later on this 
difference disappears: the straight truncated anterior extremity (fig. 3) 
of the almost cylindrical body is then even somewhat thinner than 
the middle part of the body, which has the appearance of the broken 
point of a pin. The posterior part of the body is tapered, represent- 
ing a sharp cuticular point in the male as well as in the female. 
In the male specimens of two different catches, in which a large 
number of larval, moulting and adult Oryuris occurs, this point bas 
a different length. In the one catch (No. 37) it is 230—300 u long, 
in the other (No. 42) 320—340 u. In these catches the length of 
the cuticular point of female larvae differs still more, however. In 
catch No. 37 it amounts to 140 —160 u, in catch No. 42 to 200—250 u. 

These differences in measurements we have also found in the 
length of the moulting male and female specimens. The male moult- 
ing larvae of catch No. 37 are 7.5—8 mm. long, those of No. 42 
only 5.6—6.4 mm. The lengths of the female moulting specimens 
are 10.25—I1 mm. and 7.5—9 mm. respectively. The adult speci- 
mens of these catches belong in the first case to the mastigodes-, 
in the second to the curvula-type. Perhaps the measurements stated 
support the opinion that Oxyuris equi (curvula) and Oxyuris masti- 
godes are independent species. 

As Rainier and Henry have remarked already, the male and the 
female larvae are distinguished by the difference in shape of the 
posterior end of the body. The distance of the anal opening from 
the posterior extremity (the cuticular point included) is much longer 
in the 9 than in the &. Figs. 1 and 2 explain this. The part of the 
body, situated between the anal opening and the cuticular point 
decreases strongly in thickness in the male, gradually in the female. 
The shape of the cuticular point is the same, but in the ¢ this point 
is somewhat longer than in the Q. For the measurements to compare 
the following table (see page 606). 

From this table it follows that the ratio between the lengths of 
the part of body situated between the anterior extremity and the 
anal opening and of that part situated between anal opening and 
cuticular point remains about the same during the growth of“ the 
larva and that in the ¢¢ it is almost half of that in the 22. 

The cuticular rings of the larvae differ in breadth. In the anterior 
part of the body they are broader than in the posterior part. 
In the smallest larvae the breadth amounts to about 16—28 u, 
in the largest larvae, just before the moulting stage, to + 60 u 

39 

Proceedings Royal Acad. Amsterdam. Vol. XXII. 


606 


| Ih ante- | Length anal | Ratio 

Cafe NB | vn er OE aber En @) 
in mm. (1) | (2) | (1) 

ed 3 4.54 4.16 | 0.38 0.09 
37 > 5.03 4.62 0.41 0.09 
42 > 3.13 2.77 0.36 0.13 
42 » 3.67 3.31 0.36 0.11 
42 > 3.8 3.4 0.4 0.12 
42 3 4.24 3.81 0.43 0.11 
37 9 4.6 3.8 0.8 0.21 
37 A 6.11 jn 1.11 0.24 
37 » 9.05 1.6 1.45 0.19 
37 > 10.7 8.8 1.9 0.22 
42 > 2.8 2.22 0.61 0.27 
42 > 3.67 B 0.6 0.20 
42 > 5.01 — 0.91 0.22 
42 » | 6.14 5.— 1.14 0.23 


(catch N°. 42) and + 75 u (eatch N°. 37). So the breadth of the rings 
increases with the age of the larvae. However, after moulting, the 
rings of the young Ovyuris-specimens are much narrower. 

The mouth-opening, situated terminally, is round (fig. 4a) and 
not hexagonal as is the case in adult specimens. According to Rarr- 
LET and Henry the mouth-margin is divided into twelve lobes. 
However, this could not be ascertained by us. The mouth-opening 
opens into a very short mouth-cavity (fig. 3). Behind the latter lies 
the pharynx (according to Martini’s nomenclature (1916), generally 
called oesophagus). In imaginal specimens (fig. 5) we can distinguish 
a corpus, an isthmus and a bulbus in the pharynx, according to 
Martini. In the larvae, the pharynx is still short and consists of two 
parts, which can be compared to the corpus and bulbus of the adult 
worm, as. will be evident from the following. 

The corpus pharyngis is about half cylindrical in shape in optical 
section (fig. 3, c.ph.w.). If we look at the pharynx in the direction 
of the longitudinal axis (fig. 4), we see that the corpus is triangular, 
the wall being bent inwards dorso-medially and latero-ventrally (fig. 
4,5). In the anterior part of the pharynx the lumen widens dorso- 


607 


laterally (c) and ventro-medially, and becomes narrower from this place 
backwards. Here the lumen becomes tri-radiate in transverse section 
through the presence of one large dorso-median and two latero- 
ventral thickenings of the wall, the pharyngeal sectors (e), this being 
the case in the pharynx of all adult Nematodes. On the three parts 


SIE 
Sa GE 
dees ET) SL 
in ----- muse 
SSE ET PEEN 
ict. 


LE es a 


Figs SD: 


Fig. 3. Anterior extremity of a larva, viewed from ventral side. @, total 
length 4.6 mm., catch N°. 37. << 120: 


of the pharyngeal wall (e), protruding inwards, we can observe different 

teeth close behind the mouth-cavity (fig. 4). On the dorsal wall a 

double tooth is situated medially; both latero-ventral walls possess 

two small teeth: the one being situated more dorsally, the other 

more ventrally. The two teeth, situated most ventrally, touch in the 

median line. In the larva, represented in fig. 3, the six pharyngeal 
39 


608 


teeth were not all distinetly visible; for this reason only the dorsal 
tooth and a lateral one are drawn. 


Fig. 4. 


Fig. 4. The mouth-cavity and the corpus pharyngis of a female larva, 
viewed from before. The dorsal side lies at the top of the figure. Note 
the teeth on the three pharyngeal sectors. The letters a—e of figs. 3 and 4 corre- 
spond. Catch Scl. 88. >X 250. 


The bulbus pharyngis follows after the corpus pharyngis; its lumen is 
also strongly narrowed and tri-radiate in transverse section. The nerve- 
ring surrounds the bulbus. In the preparations, rendered transparent 
in glycerin or creosote no distinct limit is visible between the nerve- 
ring and the muscles of the body-wall. To the left and to the right 
between the bulbus and these muscles the first two lateral cells 
(Martini 1916, p. 367) are to be found. At its posterior extremity 
the bulbus pharyngis possesses three valves, protruding into the wide 
lumen of the intestine. An oesophagus, composed of some cells in 
the adult Ovyuris, according to Martini, is not visible in our total 
preparations, as they are only rendered transparent and not stained. 

Gonads are not visible in the larva, according to RaArmmer and 
Henry. In our younger specimens they are not distinguishable either, 


609 


but in older larvae, on the point of moulting, we observe close behind 
the excretory pore, situated ventrally, a distinct uterus and vagina. 
To mention some measurements: in a larva with a total length of 
10.25 mm., the excretory pore lies 3 mm. from the anterior extre- 


Fig. 5. 
Fig. 5. Anterior extremity of a 2, having just moulted. Total length 9,2 mm., 

catch N° 42. XX 75. 

mity and the vagina 0.75 mm. more backwards; in a larva 9.2 

mm. long the excretory pore lies 2.7 mm. from the anterior end, 

the vagina 0.62 mm. more backwards, whereas in-a larva having 

a total length of 7 mm., in which the distance between excretory 


610 


pore and anterior extremity is 2.45 mm., a vagina is not yet visible. 

The moulted worm. 

The moulted immature Oryuris agrees in all respects with adult, 
full-grown specimens and is at once distinguishable from the larval 
form by the possession of a long stretched pharynx. Fig. 5 shows 
us a moulted, but not yet full-grown specimen, having a length of 
9.2 mm. (catch N°. 42). The hexagonal mouth-opening opens into 
a small mouth-cavity. In this cavity three obtuse teeth are visible, 
situated in the three sectors of the corpus pharyngis. Behind these 
teeth lies a circle of very pointed bristles. In fig. 5 these three teeth 
and the optical section of the bristle-circle are indicated. The corpus 
pharyngis gradually passes over into the isthmus, which is much 
narrower, this isthmus again into the bulbus, which is about equally 
thick as the corpus. The pharyngeal lumen is much narrowed and 
(ri-radiate in transverse section, as is also the case in the larval 
form. The posterior extremity of the bulbus also possesses three 
valves protruding into the lumen of the intestine. An oesophagus in 
Martini’s sense is not visible. The pharynx of ¢ and ¢ shows no 
differences. 

The moult. 

How does the pharynx of the form, just described, originate out 
of that of the larva (fig. 3)? Numerous moulting specimens enabled us 
to trace this and we could study the prolongation of the pharynx 
in particular. Moulting specimens can be at once recognized by the 
fact that beneath the old cuticle of which the rings are of a con- 
siderable breadth (60—75 u), the new cuticle with very narrow 
rings (+ 12 u) is visible. 

In specimens, on the very first act of moulting, the larval pharynx 
is still present without change. Then the part of the bulbus, lying 
immediately behind the corpus lengthens markedly, and forms the 
isthmus in this way. Originally the lateral cells lie to the left and 
to the right of the bulbus. During the lengthening of the bulbus 
they remain in their place. The corpus too lengthens a little, but not 
so markedly as the bulbus; and so the lateral cells come to lie near 
the transition of corpus and isthmus in moulted specimens (fig. 5). 
We possess a preparation of a stage, in which the longitudinal 
growth of the bulbus has just started, but where the corpus still 
has the larval shape. The first anlage of the isthmus has been formed 
already. So the corpus lengthens later than the bulbus, through the 
outgrowth of which the isthmus is probably wholly formed. The 
prolongation of the pharynx takes place quickly: the different stages, 
mentioned above, occur in specimens of about the same size. 


611 


A more advanced moulted stage is represented in fig. 6. Beneath 
the old cuticle, which encloses the body anteriorly the new cuticle 


ee Keut. 


Eene 


-~--- b.ph. 


-----].cut. 


Fig. 6. 

Fig. 6. Anterior extremity of a moulting female. Beneath the larval cuticle 
with broad rings the imaginal cuticle of the adult. The imaginal rings are so 
narrow that they could not be drawn at this low magnification (« 75). The 
released cuticular lining of the larval pharynx is visible. Total length 8.8 mm., 
catch N°. 42. 


is found. The cuticular covering of the mouth-cavity and of the 
corpus pharyngis of the larva is distinctly visible in front. Before 
the pharynx lies the imaginal mouth-cavity, in which one pharyngeal 
tooth is visible. Behind it lies the corpus pharyngis, gradually passing 
over into the isthmus, which again continues into the bulbus pharyngis. 

The front part of the body of moulting ¢* and 2° presents no 


612 


differences. As has been mentioned the moulting “% are smaller 
than the 2©. The very marked differences present in the posterior 
part of the body of dd and $2, also occur in the moulting {d' and 
22. In both the cuticular tail-point is thrown off together with the 
old cuticle. In preparations of the moulting °, we see the long tail, 
somewhat rounded at its extremity, beneath the old cuticle; the 
distance between the anus and the extremity of the tail is rather 
considerable here. In the moulting ~ however, this distance is small and 
here the posterior part of the body shows already all phenomena 
described in detail by Raimumrr 1883, Eurers 1899, and Jerke 1900. 


Zoological laboratory of the Veterinary College. 
Utrecht, May 1920. 


LITERATURE CITED. 


Enters, H. 1899. Zur Kenntnis der Anatomie und Biologie von Oxyuris curvula 
Rud. Arch. f. Naturg. Jhrg. 65. Bd. 1. 

Jerke, M. 1900. Zur Kenntnis der Oxyuren des Pferdes. Jen. Zeitschr. der 
Naturw. Bd. 35. 

Martini, E. 1916. Die Anatomie von Oxyuris curvula. Zeitschr. f. wiss. Zool. 
Bd. 116. 

Ramet, A. 1883. Note sur le male de l'Oxyure du cheval. Bull. Soc. Zool. de 
France. T. 8. 

Ramuet, A. 1917. L'Oxyurose des Equidés. Receuil de Med. Vétér. T. 98. 

Ratturt, A. et Henry, A. 1903. Une forme larvaire de |’Oxyure du cheval. 
Archives de Parasitologie. T. 7. . 

Seurat, L. G. 1914. Sur l'évolution des Nematodes parasites. Je congrès int. 
de Zool. Monaco. 


ABBREVIATIONS. 
an. = anal opening. 
C.0. = + mouth-cavity. 
cut. = imaginal cuticle. 
l.cut. = larval cuticle. 
c.p. = larval cuticular point. 
ent. = intestine. 
Ke: = lateral cells. 
mm. = margin of mouth. 
musc. = muscles of the body-wall. 
ur. = rectal muscles. 
n. = nerve-ring. 
c.ph. = corpus pharyngis. 
t.ph. = isthmus pharyngis. 
b.ph. = bulbus pharyngis. 
c.ph.w. = wall of the corpus pharyngis. 
vr: = rectum. 
rz. = rectal glands, 


v. = valves of the bulbus pharyngis. 


Physics. — “The Limit of Sensitiveness of the String-galvanometer’’. 
(2¢ communication). By Prof. J. K. A. WERTHEIM SALOMONSON. 


(Communicated at the meeting of June 26, 1920). 


In the meeting of June 26th 1918 I read a paper in which I showed, 
that the sensitiveness of the Einthoven-galvanometer was limited by 
the elasticity of the material of the string. At the same time I stated 
that the actual limit was never reached. The theoretical liminal 
value in every case was much smaller than the actually observed 
value, except with very thick strings. There seems to exist a simple 
cause for this fact. It is not only the elasticity of the perfectly 
velaxed string that causes the deviated string to resume its original 
form and position of rest after stopping the current through it, but 
also gravity. As the exact form of a deviating totally slackened 
string is not the same in every case, and cannot be exactly repre- 
sented by a formula, it is only possible to approximately calculate 
the influence of gravity. We can do this in the simplest way by 
assuming that the string is suspended in a homogeneous field of H 
gausses; that it bends in the point of suspension without any resi- 
stance or friction; that the lower current bearing connection is 
equally free from resistance, friction and mass; and finally that the 
string is straight and rigid and does not change its form. If the 
length of the string be /, the diameter d, the density of its material 
y and the gravitational constant g, the string is acted upon by a 
force p='/, 2d? lyg. As soon as the wire be deflected, its middle 
part being moved over a distance h, the force pulling the string 
back to its original position is 

psta@lyy Shad yhg , Perey s(t) 

If this force is in equilibrium with the current 2, we may put: 

Hl= tx diya 


or 
(gpa ad : (2) 
bad'yg 
In my former communication I found the formula: 
Fils 
n= -— (3) 


62 Ed* 


614 


for the deflection of the middle part of the totally relaxed ie” 
E being the elasticity modulus. 

Comparing the expressions 2) and 3) we see that variation of the 
diameter d — and as a matter of fact also of the length / — appears 
to have another influence with relation to the weight of the string 
than with relation to its elasticity. Halving the diameter should 
cause the sensitiveness to increase 4 times according to 2) and 16 
times according to 3). The significance of this is, that the two for- 
mulas should be combined in some way. Also we see that with 
thick strings the sensitiveness is principally limited by the elasticity 
of the material, whereas with very thin strings elasticity has little 
or no influence at all but it is the weight that counts. Finally there 
should be for any material a definite length and diameter with 
which the limiting influence of weight and elasticity are equal. This 
critical diameter can easily be calculated by equating 2) and 3). 
We find then: 


Be (2) 

With this formula table I can be calculated giving the critical 

value of the diameter (with a length of 10 and 5.6 centimeters) with 
which the influence of weight equals that of the elasticity. 


TABLE I. 
je | ‚_d with | d with 
98.1.106 | ” l= 10cm. | /=5.6 cm. 
Copper | 11000 | 8.9 8.2 u | 3.4 u 
Silver | 7500 10.5 10.8 » 4.5 » 
Gold | 7500 19.5 14.7 » 6.1 > 
Aluminium | 6750 | id 4.6 » 1.9 » 
Platinum 16500 lors 1032 en 
Silvered quartz | (6000) | (5.46) | 87» | 3.6% 
| | | 


The value for # used for silvered quartz does not take the 
silvering into account, which anyhow cannot possibly be of much 
importance. The figure given for the density is calculated from the 
weight divided by the volume in case of a silvering of a thickness 
which gives the highest possible normal sensitiveness (v. Theoretisches 
und Praktisches Zum Saitengalvanometer, Pfliigers’s Archiv. f. 
Physiologie V. 158 p, 107 1914). 


615 


With a silver wire of 10 cm. length and of a diameter of more 
than 10.8 u the sensitiveness is mainly limited by the elasticity ; 
with silver wires of the same length but thinner than 10.8 u, the 
weight of the wire is the most serious obstacle to increasing the 
sensitiveness of the instrument. With a wire of 21.6 u the elasticity 
is 4 times more important as a limiting factor than gravity. 

If the influence of the two limiting factors is taken together, we 
find for the deflection of the middle part of the string: 


TA 
6d Ez 
Des 


fp, = 


(5) 


‘/,a yg + 


if the string be totally relaxed and fixed on the support without 
any longitudinal or torsional tension. 

With this formula we can calculate the next table giving the 
deflection of a 10 em. string of 1 u in a field of 10.000 Gausses 
with a current of 10-1? Ampere and an enlargement of 1000 times. 


TABLE II. 
Copper | 0.72 mm 
Silver 0.62 » 
Gold | 0.34 » 
Aluminium | 2.20 » 
Platinum | 0.33 » 
Silvered quartz | Lakh >> 


In the same way I find for an aluminium string of 2 u and 56 
mm. length in a field of 18000 gausses a theoretical deflection of 
„57 mm., the magnification being 1000 fold. In my former commu- 
nication I stated that such a string had given me a deflection of 
.40 mm. If we had taken the elasticity as the limiting agent we 
ought to have expected a deflection of 1.20 mm. 

Doubtless we get a better approximation for the liminal sensitiveness 
of the string galvanometer by considering the influence of the weight 
of the string without neglecting its elasticity. 


Physics. — “The Process of Solidification as a Problem of 
Conduction of Heat’. By Dr. H. C. Burger. (Communicated 
by Prof. W. H. Jurros). 


(Communicated at the meeting of June 26, 1920). 


- § 4. Introduction. The equilibrium between two phases has been 
fully investigated experimentally and theoretically. Little, however, 
is known about the cases in which there is no equilibrium, but 
one phase is converted into another. In the first case the thermo- 
dynamic laws may serve as basis of all considerations; in the second 
case, however, such leading principles are entirely wanting. The 
researches on the dynamics of the conversion of phases are quite 
detached, and are often restricted to the collecting of empirical data 
the meaning of which is not quite clear. 

It would be ‘very desirable to develop a general theory of 
dynamics, which will have to inelude ‘thermodynamics’ as the 
special case of its statics. Whether this is possible from a purely 
phenomenological point of view, further experiment will have to 
teach. 

In what follows I have worked out a general method for the 
treatment of the special case of the solidification of a chemically 
simple substance. 

On transition of a supercooled melt into the solid condition the 
following processes should be sharply distinguished : 

1. The formation of particles of the solid phase in the supercooled 
liquid *). 

2. The further growth of each of these particles, and also the 
growth of a particle of the solid substance put into the Jiquid 
purposely *). 

Only the second point will be treated in this communication. In 
this the particularities which are in connection with the anisotropy 
of the solid substance will not be taken into account. In this way 
the problem is simplified, but at the same time the idea of accounting 
for the formation of the crystalline form is abandoned. 


1) G. Tammany, Zeitschr. f. phys. Chem. 25, p. 442, 1898. 
*) D. GERNEz, Compt. rend. 95, p. 1278, 1882. 
B. Moors, Zeitschr. f. Phys. Chem. 12, p. 545, 1893. 


617 


The question which should be posed when one wishes to examine 
the course of the process of solidification, is the following: 

Given a supercooled liquid, in which there are one or more pieces 
of the solid substance. At a definite moment the temperature is 
given as function of the place. Required to determine for every 
successive moment the temperature as function of the place and the 
velocity with which the boundary surface of the two phases moves 
in consequence of the solidification. 

When the general principles and methods that may serve to solve 
this problem, are known, all the cases that present themselves can 
in principle be treated by the aid of them. This treatment only 
requires the surmounting of mathematical difficulties. The theory 
must be developed for a particular case and compared with the 
experiments. As is the case in every phenomenological theory, certain 
constants or functions which are characteristic of the substance, 
remain undetermined a priori here too. Comparison of theory and 
observations makes us acquainted with these constants or functions. 

When the above mentioned questions are answered, it should be 
borne in mind that in a substance in which the temperature differs 
from point to point, conduction of heat takes place. The conduction 
should not be considered as accessory, for without transport of heat 
solidification cannot take place. 

In a substance moving with a velocity V the temperature @ satisfies 
a generalized differential equation of the conduction of heat 


00 : 
(Bra A Ed ae ate) A ag eae oe let) 


This equation contains the quantities c, @, and 2, (resp. specific 
heat, density, and conductivity of heat), which refer to the phase 
for which (1) holds. An equation of the shape of (1) exists for the 
solid as well as for the liquid phase. In these equations there occur 
constants which are characteristic only of one of the phases separately, 
and not for the heterogeneous reaction between the two phases. 

As in every problem of conduction of heat there are here too, by 
the side of the differential equation, boundary conditions which the 
temperature 6 must satisfy, viz.: 

1. At the boundary plane of two media the temperature is 
continuous. This refers both to the boundary surface of the solid 
and the liquid phase and to the surfaces along which each of the 
phases touches the wall of the vessel in which they are contained. 

2. At a boundary surface the normal component of the current 
of heat is continuous, when no generation of heat takes place at 


618 


the surface. If this ¢s the case, the normal components of the current 
of heat in the two substances at the two sides of the surface together 
lead off a quantity of heat equal to the generation of heat taking 
place at this surface. 

The boundary conditions 1 and 2, however, together with the equation 
(1) are not yet sufficient to determine the condition for every succes- 
sive moment. For one thing, the velocity with which the boundary 
surface of the solid phase moves is not known, hence it is not 
known either at a definite moment, at what surface the conditions 
1 and 2 are valid. The velocity of the boundary surface of the 
phases is directed from solid to liquid during the solidification. This 
velocity can only depend on the condition of the substance at this 
surface, hence on the nature of the substance and the temperature 
there. As third limit condition we get, therefore, the relation that 
must exist between the linear velocity of crystallisation (or solidi- 
fication) and the temperature at the boundary. 

When the value of a quantity in the solid phase is denoted by 
the index 1, and in the liquid phase by the index 2, and when pv 
is the normal at the boundary surface solid-liquid, we have at this 
boundary surface the conditions: 


Bd) rna 
‚ % „dine 2b 
a gaa text +. o> a 0 le 
r=fO%) oi. 2-2 2 


When vo, is the mass solidifying per unit of time and per unit 
of surface, ve,Q represents the difference of the normal-component 
of the current of heat on the two sides of the boundary surface, 
when Q represents the melting heat at the temperature @ prevailing — 
at this surface. 

The differential equation (1) with the boundary conditions (2) now 
determines the course of the process of solidification. (1) and (2) can, 
however, not be solved, when the function f, which is characteristic 
of the substance, is not known. It might be tried to make different 


suppositions about the relation between @ and wv, e.g. that @ is equal 
to the temperature of melting. Every supposition leads to a definite 
value of the temperature as function of place and time. Hach of 
these results might be compared with the observation, and in this 
way it might be found what relation there exists between 0 and v. 


1) A horizontal line indicates the value at the limit. 
2) Of course inversely 6 = ¢ (+). 


619 


As wea priori do not even know the form of the relation (2c), 
the following course is, however, to be preferred. A value is chosen 
for the velocity v'). When further v is considered as given, the 
temperature can be determined from (1), (2a), and (26), hence also 
the temperature 6 at the boundary. By causing the solidification to 
take place under different circumstances, different values of v can 
be obtained, and for each of these values the corresponding tempe- 


rature 9 can be calculated, and in this way the relation between 


v and 6 can be found. To check the theory, the temperature 6 may 
be determined experimentally, but this is not necessary in order to 
find the relation given by (2c) for a definite substance. 


§ 2. Theory of the solidification in a cylindrical tube. 

One of the simplest phenomena of solidification, which has also 
been studied most fully experimentally, is the crystallisation of a 
supercooled liquid in a cylindrical tube. 

Let the solid substance be in one part (A) of a straight tube, the 
supercooled liquid in the other part (B). The whole is surrounded 
by a space of constant temperature, which must also prevail in A 
and B within the tube at infinite distance from the boundary surface. 
This temperature must, of course, lie under the melting-point of the ° 
substance used, because else no solidification takes place *). 

The solidification now proceeds as follows. Heat is liberated at 
the boundary surface of the phases (heat of melting). It flows off 
on both sides through the solid substance and the liquid, and finally 
passes through the wall of the tube to the sphere of constant tem- 
perature. In every vertical section of the tube the temperature is 
highest in the axis of the cylinder and decreases towards the outside. 
This is also the case at the boundary surface of the phases. Hence 
the normal velocity at this surface cannot be the same every where, 
but must increase or decrease from within outward as the velocity 
of solidification v increases or decreases with diminishing temperature. 
Both cases may occur. The velocity v is, of course, zero at the 
melting-point, then increases with decreasing temperature, after which 
it begins to diminish again, as experience teaches, approaching asy mp- 
totically to zero at sufficiently low temperature. 

Let us suppose the temperature of the surrounding space to be 


1 The velocity v can be determined in a simple way experimentally, and can, 
therefore, conveniently be used as basis for the calculation. 

9) A process of melting, analogous to the process of solidification treated here, 
is impossible, because a liquid cam exist under its melting-point, but a solid 
substance cannot exist above its melting point. 


620 


only little under the melting-point of the substance, so that the velo- 
city of crystallisation increases with falling temperature. Then the 
velocity of the boundary surface must be smaller in the axis of the 
tube than at the periphery, i.e. this surface becomes concave towards 
the liquid. The form of the surface can, however, not remain 
unchanged during the increase; as the velocity in normal direction 
is smallest in the axis of the cylinder, and increases towards the 
outside, the curvature will always increase, as is easy to understand, 
and at last a hollow may even arise, which is shut off, and is then 
filled up. At the same time the more rapid growth has proceeded 
at the periphery, and the same thing is repeated. The growth will 
further not be symmetrical round the axis. When through a slight 
disturbance the substance grows somewhat more rapidly at a point 
of the circumference than at the other points, the surface gets here 
further from the places where the crystallisation takes chiefly place, 
i.e. at points where the temperature is lower and the rate of solidi- 
fication, therefore, greater. Consequently the growth in the considered 
point takes place still more rapidly. Hence the condition is unstable. 
A small accidental disturbance will have great influence on the form 
of the boundary surface, hence on the process of the solidification. 
In this case the solidification is a very irregular phenomenon, and 
a theoretical treatment of the problem proposed on p. 619 is 
impossible. 

This is, however, entirely different when the temperature of the 
surroundings, hence that of the tube, is chosen lower, so that the 
velocity of solidification becomes smaller with decreasing temperature, 
Then the normal velocity is greatest in the axis of the cylinder 
where the highest temperature prevails. The surface of the solid phase 
becomes, therefore, convex towards the liquid. This convex surface 
now begins to move parallel to the axis, and in this it assumes a 
very definite form. The normal velocity during this displacement is 
greatest in the axis, and decreases towards the periphery. This decrease 
must be such that in every point the velocity v has the value that 
according to (2c) corresponds to the temperature 6 prevailing there. 
‘here can, and will, arise a condition in which the boundary surface 
moves uniformly and with constant form parallel to the axis. Every 
disturbance in this condition will disappear again of its own accord. 
It is also easy to convince oneself that everything around the axis 
of the tube must be symmetrical. If this is not the case at a moment, 
the growth and conduction of heat takes place in such a way that 
the symmetry is restored. 

Though in this way one can see that the differential equation (1) 


621 


with the boundary conditions (2) perfectly determine the form of the 
boundary surface of the phases on solidification in a tube, this 
determination is attended by great mathematical difficulties. We shall, 
therefore, suppose for simplification that tbe surface of the solid phase 
is a plane at right angles to the axis of the tube’). The constant 
velocity v, with which this plane moves, is determined according to 
(2c) by the temperature 6 at this plane. 

When there shall actually arise a condition in which the boundary 
plane, preserving its shape, moves uniformly, the whole distribution 
of temperature also in solid and liquid phase will have to move. 
with it with this velocity, in other words, the temperature will only 
depend on the distance from the boundary surface. That a solution 
of (1) and (2) with this property actually exists, will now be shown. 

In the solid substance, where the matter is at rest, and the condition 
round the axis is symmetrical, the differential equation (1) assumes 


the form: 
oo; 6 ores = Ld 00, : 
ee rs oe fee | tad ts en (0) 
| } 
in which a, —— and £ is a coordinate, which is measured along 


Cg, 
the axis of the tube in the direction of the velocity v with which 
the boundary surface moves, and 7 the distance from the axis. 
On solidification contraction takes place. In consequence of this the 
liquid moves in a direction opposite to that of the positive &-axis 
with a constant velocity V, which in the densities y, and o, of the 


solid and the liquid phase can be expressed thus: 


V=— Gee v. 
0; 
Accordingly the differential equation holding in the liquid, becomes: 
00, OO! 108 DEE 0,—0, 906, r 
gf Ty EEM RED OTE ® 


_ When the temperature in the solid and the liquid phase is sup- 
posed only to depend on the distances w, resp. a, from the boun- 
dary surface, the differential quotients according to time may be 
expressed in those according to place: 
. PO nahin 06 (ee 

En Det lth de 


nn rn | 
Further: 


*) As in the cases that occur most frequently the velocity v depends only little 
on the temperature, the boundary surface will generally be only little curved. 

40 

Proceedings Royal Acad. Amsterdam. Vol. XXIII. 


622 


Den DrK) OE 
dE) de, resp. BE Tides) 


When (5) is substituted in the equations (3) and (4), and when 
in these equations the following form is written: 


4! Q, 
MSV Stee S= 
0, 
it is found that: 
1-8 00 
li . «2 
“= =a, han tral =) (6) 


dot MU ded IUD ADE ze 
AT A, es a 


Besides there are still the limit conditions (2a) and. (26), which 
are in this case: 


(Ods Odon * oo 


(sy sigs 00, iyi ee 


The liquid having a ate Mere v at the boundary surface, 
it is not self-evident that (26) may be applied unmodified. A closer 
examination, however, teaches that this is, indeed, the case, and 
that therefore (80) is correct ’). 

Besides the relations (6), (7), and (8) the temperatures must satisfy 
other conditions which hold at infinite distance and on the wall of 
the tube. The tube being in surroundings of constant temperature, 
this temperature in both phases must exist at infinite distance from 
the boundary surface, where the influence of the generated heat of 
melting is not felt. The zero-point of the temperature being arbitrary, 
the temperature of the surroundings is chosen for it, and thus the 
following conditions are obtained : 

(Omen = 9 3 (Ode 2°) oe 

It is less simple to take the influence of the wall of the tube 
into account. When one wants to solve the problem accurately, also 
a differential equation must be drawn up for the temperature in 
the wall of the tube, and this temperature must be brougbt in connec- 
tion with the temperature of the solid and the liquid substance in the 
tube by means of boundary conditions corresponding to (2a) and (20). 
At the outer surface of the wall the temperature must be zero, i.e 
equal to that of the surrounding space. 

To put this train of reasoning into practice, though not impossible 
in principle, would lead to very elaborate calculations. In the cases 


1) Compare also W. HERGESELL, Ann. de Phys. u. Chem. 15, 1882, p. 19. 


623 


that have been examined experimentally, the conduction of heat 
throngh the wall is very great, however, because the wall is not 
very thick, and consists of a substance (mostly glass) that conducts 
heat pretty well. Consequently the influence of the resistance to heat 
of the wall of the tube is slight, and the following approximation 
may be used. When the current of heat in the wall is supposed to 
be radial, and when d and A, represent the thickness resp. the 
conductivity of this wall, a quantity of heat given by: 
1,0 
a 
flows through the wall per unit of time and surface. 
In this @ is the temperature of the substance on the inner side 
of the wall of the tube. 
When a is the radius of the interior width of the tube, we get 
the boundary conditions: 


He CAN aes PON fy 
ae hm ag Tan. 


Both members of this equation express the current of heat per 
unit of time and surface. 

In order to solve the differential equation (6) with the conditions 
(8), (9) and (10), we seek a particular solution, which is a product 
of two factors, one that depends on 2, (X,), and one that depends 
on r (R). When we substitute: 

On NAR, 
in (6), we may write for this equation: 


PR, HR, dX, AX, 


dries dr a, dz, daz,” 
rR, ae Xe 
As in this relation the first member depends only on 7 and the 
second member only on w,, both members are constant, e.g. — C. 
Then the following equations are obtained for X, and R,: 
at dh 5 
EEn En dr. + C Ji B; . 5 Oy 7 . e (11a) 
aX v, dX 
ee wes OK Oene Sew eee aie VID) 
dr? a, dr 


The solution of (41a) which remains finite for 7 = 0, is the Brssur. 
function of order zero: 
Et = Se WE). ae econ eae 
40* 


624 


As 6, must satisfy (10) for all values of «,, this is also the case 
with each of the products XZ, of which 6, is built up, hence 
also with A,. When in (10) the value of AR, given by (12) is sub- 
stituted for 6,, we find: 


wee CI LVO ACTA 


When in this 


WEE 
and 
Àd 
Thon er ol vore 
3 


is put, this equation assumes the form: 
nil) =Te (Ei) on en 


This equation has an infinite number of roots, which ranged ac- 
cording to ascending value may be called: 


Se Eel sne eN Ev, kh 


They depend on the quantity y, defined by (13). 
To every root § belongs a value of the function A,. These fune- 
tions become: 


5) 
R= J,( ) eS 2 ni Con 


Like (11a), (116) has also two particular solutions, one of which 
becomes zero for 7, = ©, and the other infinite. In conneetion with 
(9) the former must be chosen. Apart from a constant factor, this 
solution is: 


Res 
Kea" eee. - ae 


p, is the positive root of the equation: 


(k) \3 
ule 2p, — = 0, 
a 


which is found by snele of (16) in (115), and replacement 
of C by: | 
int mj 


The value of p,@ i 


Tas aa 


(17) 


625 


The general solution of the problem must be composed of special 
solutions in the following way : 


6,= SAMS, 
k=1 


SEO eer Tc. setae Ne! 


The constants A,“ can only be determined in connection with the 
value of 0,. The expression given by (18) satisfies the boundary condition 
(10), which holds at the boundary surface of the solid substance and 
the wall of the tube, and is also in agreement with (9). 

The value of the temperature @, prevailing in the liquid is found 
in an analogous way. It is: 


2 yr & (hk) En MGR 

Ee Add lr HEEE 7 OET 

ll a 

The quantities $,%) are the roots of the equation: 
Ya se J, (5) — J, (54) ° : : : y } 2 (20) 
in which: 

1,8 (ai 
Un Za e . . e je . ° . . ) 


From §,) follows p,): 


‘J. Us | Ban a 
en a iaucastilriagedns 82) 


In conclusion the constants A,“ and A,® occurring in (18) and 
(19), must be determined from the conditions (8) at the boundary 
surface of the solid and the liquid phase. By the aid of (18) and 
(19) these conditions become: 


» & (k) Ee „& (k) 
Su ey ieee (23) 
—] ( a =i a 
ao r 8%) r Ek 
= A, (*) A, p,* Je + A ut) Ay i (k) J == 0, v,. (24) 
il a 


Both equations must hold for all values of r. 

The difficulty to find the constants A,’ and A,“ from (23) and 
(24), consists in this that in these equations tore oceur two series 
»< (%) 
Rees 


iis 5 s 
i These series 


of normal functions, viz. J, 


are, indeed, each in themselves orthogonal; but Ee functions of one 
series are not orthogonal to those of the other. The most symmetrical 
way would be to try and find normal functions belonging to the 
whole space, and not, as had been done up to now, either to space 
1 (solid substance) or to space 2 (liquid). There exists, however, a 
simple — though asymmetrical — method, which leads to the pur- 


626 


pose with comparatively little trouble. It is possible to develop the 
functions for one region into a series of normal functions of the 
other region. The following development is then obtained: 


r E,(h oo 


= di, 
(sil 


rE 


(25) 


The constants «a, form a twofold infinite system of values that 


a 


r 
do not depend on the variables —, but on the constants y, and y, 
a 


defined by (43) and (21). As we saw before, they depend on the 
dimensions of the tube used, and on the conductivity of the sub- 
stances that play a part in the problem. 

For the determination of «7 both members of (25) are multiplied 


oe. tb) 
by rd, SS 


| dr, and an integration is carried out with respect 


to r from zero to a. When for this purpose use is made of the 
known properties of the Busser functions, and of the equations (14) 
and (20), the following form is found: 


26, 8. (rr) Js 181 


ee : 26 
KT Gey? GON + ys? 6,0), (8,9) Ee 
By substitution of (25) in (23), we get: 

A,(*) = 2 au AGU) TR SL EEN (27) 


il 
If this relation between the coefficients A,% and A, is satisfied, 
(23) holds for all values of 7. 
Also in (24) all the occurring functions of r must be developed 
rie aa Opee . 
with respect to dn — (25) gives this develop- 


ment: we write for the second member of (24): 
= (k) 


ro 


Qe, v, = = BJ, | = 
k=1 a 


Fors 


e 
U 


(28) 


The coefficients 8, are found by multiplication of both members 


ea : 
by rd, = dr, and integration with respect to r from zero 
to a. Then follows from (20) and the properties of the Besser functions: 
2Q 0, v 
Bk Q N 1 1 Ys 5 i t ' ; : (29) 


HH 7,7 (So!) J, (6,%) 
When (25) and (28) are substituted in equation (24), it appears 
that this is identically satisfied when the following relations exist 
between the still unknown coefficients 4, and A,: 


627 


ANDES AOD am Bee 2 8 (30) 
lil 


When finally the constants A,“ are expressed in A,“ by the aid 
of (27), then follows from (30) : 


= AO alk (p, Od, + p, 2) = Be TN, 


=i 

The equations (31) are infinite in number and contain infinitely 
many unknowns A,”. As we have not used orthogonal normal 
functions, we do not find the coefficients A, expressed explicitly, 
but as solutions of a system of linear equations. Practically this is, 
however, not a very serious drawback. For the quantities aj. are 
small for &=J/; hence they differ only little from one if & = l. 
In the first of the equations (31) all the terms but one can be left 
out in the first member in first approximation. The value of A, 
thus found is substituted in the second equation, in which all the 
terms following the second, are left out. Thus an approximated 
value of A,®) is obtained from this equation. Proceeding in the 
same way, an approximation is found for all the values 4,0. Now 
_the calculation is repeated, but no terms are left out. The terms 
which were neglected in first approximation, are now replaced by 
the value which they appeared to have in first approximation. By 
this method of successive approximation, which quickly converges, 
the values of the coefficients A,” are found. The values of the 
constants A,“ (or 4,%) are then found from (27). 

The temperature 6, in the solid substance and 6, in the liquid 
is found by substitution of the values found of A,” and A, in 
(18) and (19); the problem we had proposed to ourselves, has, 
therefore, been solved. 

The above-developed theory becomes of importance when it leads 
to a clearer understanding of the result and the interpretation of 
observations. Experiments on solidification in a tube and their rela- 
tion to the theory will be found in a subsequent communication. 


Institute for Theoretical Physics. 
Utrecht, June 1920. 


Physiology. — “A Quantitative Inquiry into the Antogonism Pilo- 
carpin-Atropin on the Surviving Cat-qut’. By Prof. W. Storm 
VAN Leruwen and Miss C. van DEN BROEKE. (Communicated 
by Prof. R. Maenus). 


(Communicated at the meeting of April 23, 1920). 


At our Institute we often felt the want of a correct physiological 
determination of the strength of atropin-containing solutions. With 
one of the usual methods which is based on the property of atropin 
to restore pulsation after the muscarin-standstill of the frog’s heart 
our results proved unsatisfactory. We, therefore, endeavoured to find 
a method that should yield more reliable results, viz. by taking the 
antagonism of atropin on the action of pilocarpin on the surviving 
gut, as an index of atropin-action. 

Laborious investigations of this antagonism have been carried out 
by van Lipra pe Juupe'). His publication also contains complete 
references on this subject. 


He conducted his experiments as follows: The contractions of pieces of a rabbit's 
small intestine were recorded on a kymograph. The pieces of the intestine were 
suspensed in vessels of 15, 75 and 150 ce. The experimenter disposed of an appa- 
ratus that enabled him to work with twelve pieces at a time. The vessels were 
filled with Tyrode solution to which varying quantities of pilocarpin were added. 
As v. Lior De Jeupe used vessels of varying sizes he was able to vary in his 
experiments the dosis of pilocarpin and atropin, with or without varying at the 
same time the concentrations of these drugs. As soon as, in his experiments, the 
pilocarpin had produced a contraction of the isolated gut, every 20 seconds !/4 c.c 
of a definite atropin-solution was added. This was repeated until an atropin action 
was clearly noticeable. 

VAN LiptH DE JEUDE points to several errors to be guarded against in a similar 
investigation. The rate at which the oxygen bubbles through the vessels during 
the experiment, should not vary too much, since a strong current of oxygen causes 
the atropin to mix sooner, and consequently an antagonistic action to manifest 
itself sooner than a weak current will do. The concentration of the atropin-solution, 
of which always '/, c.c. is added, should be the same in all experiments, other- 
wise erroneous results will be obtained, etc. 


With due precaution v. Lipra bE Jeupe undertook a series of 


1) A. P. v. Lint pe Jeupe. Quantitatieve onderzoekingen over het antagonisme 
van sulfas atropini tegenover hydrochloras pilocarpini, salicylas physosligmini en 
hydrochloras muscarini (Griibler) op overlevende darmen van zoogdieren. Acad. 
Proefschrift. Utrecht, 1916. 


629 


careful experiments of which we here record the results that bear 
upon the question under consideration. 

The pilocarpin-action depends on the concentration of- the poison 
in the Tyrode solution, and is not dependent on the absolute amount 
of pilocarpin present in the solution. 

The atropin-action per se (inhibitory effect of small doses) depends 
rather on the absolute quantum than on the concentration of the 
poison in the solution. The concentration is decisive with large 
atropin-doses (12,5—150 mgr. to 75 cc. of liquid). 

According to v. Liprn pe Jeupe also the antogonism of atropin 
hinges upon the absolute quantity, and not upon the concentration 
of the poison in the solution. 

Furthermore, v. Liprn pe Jeupe found, that generally the atropin 
doses to be added, differed little with highly varying pilocarpin-doses 
and pilocarpin-concentrations. 

The only relation, found by him between the values of the two 
poisons, was that with a considerable rise of the pilocarpin-dosis 
(100 times the initial dosis), the atropin-dosis increased but little 
(3—5 times). Hereby the results published by Macnus in 1908 *) 
were confirmed, as Macnus also found that with a rise of the pilo- 
carpin dosis (up to 50 times), the atropin doses required for the 
antagonism did not augment — anyhow less than ten times. 

Although v. Liptx pr Jeupe’s method suited his purpose very 
well, it could not, as such, be utilized in cases concerning the physio- 
logical determination of atropin-containing solutions, because large 
individual differences occur in the reactions of the guts of various 
animals, nay, even in the reaction of different pieces of the gut of 
the same animal. For this reason we have modified the method by 
utilizing the familiar fact that the action of various poisons can be 
abolished by removing the drug-containing solution and substituting 
it by a fresh solution, so that the organ resumes ifs former con- 
dition and will react again in the same way on a similar quantum 
of poison. This enabled us to observe repeatedly the action of a 
poison on the same strip of intestine. This was also BARrGER and 
Dar’s?) method when they examined the action of various poisons 
upon the uterus. Nrukircu®) has demonstrated that the effect of pilo- 


-1) R. Maenus. Kann man den Angriffspunkt eines Giftes durch antagonistische 
Giftversuche bestimmen? Pfliigers Arch. B.-123. S. 99. 1908. 

2) G. Barger and H. H. Date. Chemical structure and sympathomimetic action 
of amines. Journal of physiology. Vol. XVI. 1910, page 19. 

3) P. Nevxiren. Pfliigers Arch. 147. 171. 1912. Physiologische Wertbestimmung 
am Dünndarm. Pflügers Arch. 147. 151. 1912. 


630 


carpin upon the surviving small intestine could also be washed out.. 
It was, therefore, incumbent on us to find out whether this was the 
case also for atropin. Originally we supposed this was not so, because 
v. LiprH pr Jeupr had stated that the atropin-action depended on 
the absolute quantity of atropin, and not, as is the case with most 
other poisons, on the concentration in which the poison is presented. 
We believed that the atropin-action could depend on the absolute 
quantity only then, if all or nearly all the atropin had been adsorbed 
from the liquid by the gut. Now we deemed it improbable that in 
that case the whole quantity of atropin could be washed out again. 
On further examination, however we found that the atropin action, 
like the pilocarpin-action, could, indeed, be abolished by washing 
out. This induced us to ascertain whether the atropin-action indeed 
depended only on the absolute quantity and not on the concentration. 

We will not delay the statement that also for atropin only the 
concentration of the poison was found to be conclusive. In this 
inquiry we made use of an apparatus differing from that of v. Lipts 
DE Jeupe. Also our technique differs considerably from bis. 


The fact was namely that — unlike v. Liprn pe Jeupe — we did not add 
to the gut pilocarpin only once and subsequently some drops of an atropin 
solution till the pilocarpin-action began to be neutralized; but, in order to ascer- 
tain in the same gut the action of several doses and concentrations of atropin, 
we wanted to be able to transfer the gut to different vesseis every time without 
breaking the contact between gut and lever. To this end we used an apparatus, 
that was already described on a previous occasion'). With this apparatus 
(fig. 1) the gut is not fastened to the bottom of the vessel, but to the bent arm 
of a glass rod, which reaches into the glass vessel The glass rod is attached to 
a metal bar, which also supports a lever for the registration of the contractions 
of the organ. The metal bar is movable in a vertical direction, in a meta! mantle, 
so that it can be moved upwards by a single motion of the hand which lifts the 
gut out of the solution without interfering with the contact between lever and gut. 
The glass vessel, in which the gut is contained, and which has a capacity of 
75 c.c. stands in a copper vessel, in which there is, moreover, a second glass 
vessel of 150 c.c. capacity. In this metal vessel there is also a thermoregulator, 
connected with a small burner under the vessel. The metal vessel and the burner 
under it are attached to a revolving disc. All is arranged in such a way that as 
soon as the bar, which supports the gut and the lever, is moved upwards, the 
metal vessel can be turned by a single motion of the hand, so that the gut, on 
being lowered, reaches the vessel of 150 c.c. where the poison is washed out. 
The removal from tlie one vessel into the other can be accomplished so quickly 
that the curve on the kymograph is hardly interrupted. So, if necessary, the whole 
washing process may be registered accurately. 


‘) W. Storm v. Leeuwen. Physiologische Waardebepaling van geneesmiddelen. 
Acad. Proefschr. Utrecht. 1919. 


651 


The contrivance just described is a part of the large apparatus represented in 
fig. 1, which consists of three metal vessels, mounted, together with their revol- 
ving disc, on a plank that can be moved to and fro, The gut can now be trans- 


Fig. 1. 
Apparatus for the registration of the movements of a surviving 
organ, provided with a simple arrangement for washing out the added 
poisons and for operating at various temperatures. 


ferred at will to each of the 6 vessels of the apparatus (this is also of importance 
when examining the action of poisons at a different temperature). 

Here, then, we have an arrangement of three vessels of 75 c.c. and three ves- 
sels of 150 c.c. to which the surviving gut can be transposed. One of the three 
metal vessels was displaced in some of the experiments by a large glass vessel 
containing 1300 c.c. of Tyrode solution and in which also a thermoregulator was 
placed and a tube through which the fluid was oxygenated. When the gut was 
put into this large vessel, the action of a definite dosis of atropin could be watched 
with a dilution twenty times stronger than when an equal dosis of atropin was 
examined in one of. the small vessels, which contained only 65 c.c. 


In a series of experiments we tried to ascertain whether the 
pilocarpin-action indeed depended only on the concentration. This 
appeared to be the case, so that in this respect we quite agree 
with v. LiptH Dr JEUDE and consequently our experiments pertinent 
to the matter in question may readily be left out. 

In another series we examined the question whether atropin can 
be washed out. 

This was to the following effect : 

Atropin-action is completely reversible, for when the gut is put 


632 


in a vessel containing pilocarpin, after this in a vessel with pilo- 
carpin + atropin, then again in pure Tyrode, and subsequently again 
in pilocarpin, the second dosis of pilocarpin will act in the same 
way as before, while this action can, just as the first time, again 
be arrested by atropin in the same way. This experiment may be 
repeated as often as six times, without interfering with the action 
of pilocarpin or atropin. The experiment just described also proved 
that, while the antagonism is being accomplished, only very little 
atropin is adsorbed by the gut, because the experiment (pilocarpin- 
action subsequently arrested by a minimal dosis of atropin) can be 
repeated six times without the necessity of a fresh solution in the 
vessel with pilocarpin + atropin. The fact that during the action of 
atropin only very small quantities of it are absorbed by the gut, 
renders it highly improbable that the atropin action should not 
depend on the conceniration, but on the absolute quantity, for this 
woald be possible only if during the antagonistic action the greater 
part of the atropin were adsorbed from the solution by the gut, 
whereas our experiments showed that the gut can take up only 
very small quantities of atropin. To settle the question whether the 
atropin-action depends on the absolute quantity or on the concen- 
tration, a new series of experiments was undertaken, in which vessels 
of 65 and of 1300 ec. were used, so that action of a certain dose 
of atropin could be examined in various concentrations. The result 
of one of these experiments was, for instance, the following : 0.01 mgr. 
of atropin in 65 ec. Tyrode solution produced a stronger action than 
0.15 mgr. of atropin in 1300 ce. of solution ; 0.03 mgr. of atropin 
in 65 cc. of Tyrode had a greater effect than 0.45 mgr. in 1300 ec, 
but as great an efiect as 0.6 mgr. of atropin in 1300 ce. of solution. 

From these experiments, and others that had been conducted in 
precisely the same way, we are, therefore, justified in concluding 
that the atropin action, like the pilocarpin action is completely 
dependent on the concentration and not on the absolute quantity of 
the poison. This result differs from v. Lipru pr Jrupe's, which is 
owing to the circumstance that our technique differs largely from 
his. Van LipruH pe Jeupr took a different piece of gut for every 
experiment. Besides this, v. Lipra pre Jrupe’s using very small 
vessels (15 ec.) led to many errors, as in this case it is not possible 
to fix a correct dosage — especially because the solution most often 
foams considerably. In the third place the way in which v. Laprn 
DE JUDE administers the atropin and his index of the antagonistic 
atropin-action differ from ours: Van Liprm De Jeupe added to the 
solution that contained the gut, first a definite quantity of pilocarpin 


633 


and when the stimulating influence of pilocarpin was distinctly 
noticeable, every time '/, cc. of a constant atropin-solution was 
instilled by drops, at intervals of 20 seconds, until a distinet atropin- 
action revealed itself. 

We first put the gut in the vessel containing 10 mgr. of pilo- 
carpin, left it there precisely 1'/, minutes, then transposed the gut 
to a vessel that contained, beyond the 10 mgr. of pilocarpin, also 
the quantity of atropin under examination, and watched for an arrest 
(after a definite time mostly 1—1'/, minutes) of the increase of 
tonus caused by the pilocarpin. This we assumed to be the case if 
the bases of the curves were again returned to the original level, 
no matter whether the ‘oscillatory movements” of the gut were still 
greater than before or were not. The criterion used by v. LiptH DE 
JEUDE, on the contrary was, whether or no, after the administration 
of the atropin, a distinet beginning of the fall of the curve could 
be observed, in other words v. Liprn pr Jreupr watched for the 
beginning of the antagonistic action, whereas we looked for the 
condition reached after a certain lapse of time. 


Van Lipra pr Jude had established in his publication, which we 
quoted several times in this paper, that with an increase of the 
pilocarpin-dosis (up to a 500-fold) the atropin-dosis required for the 
commencement of the antagonism augments but very little (83—5-fold). 
We knew from earlier investigations that the curve, indicating the 
ratio between the concentration and the action of pilocarpin, runs 
as is shown in fig. 2. In the beginning of the curve (a to c) small 


“uostod oy} jo uono y 


Concentration of the poison. 
Fig. 2. Scheme of a Concentration-Action curve. 


differences in concentration bring about a large difference in action; 
while with the higher concentrations the action increases only very 


634 


little when the concentration rises. We were naturally led to sus- 
pect that the small augmentation of the atropin-dosis, observed by 
vAN LiptH DR Jeupe with a rise of the pilocarpin-dosis, would take 
place at the very beginning of the concentration-action-curve, i. e. 
we suspected that with very small doses of pilocarpin, the increase 
of the atropin doses would be relatively large when the pilocarpin- 
concentration increases, while in the higher pilocarpin-concentrations 
the quantum of atropin necessary for the antagonism would be 
the same. 

In another series of experiments we have attempted to solve this 
problem. 

We used pieces of a cat's gut contained in vessels with 75 c.c. 
of Tyrode solution. At the commencement of the experiment, several 
times pilocarpin was added to these guts (and after this the pilo- 
carpin was washed out again) till the sensitiveness of the gut to this 
poison had become constant. This done, we ascertained how much 
atropin had to be added to arrest the pilocarpin action almost com- 
pletely after 3 minutes. 

In this procedure the intensity of the ‘oscillatory movements” 
was not regarded, but the pilocarpin-action was considered to be arrested, 
when the base of the curve had nearly resumed its normal niveau again. 
It became evident from these experiments that the quantum of 
atropin necessary for arrest of the pilocarpin-action does not depend 
on the quantity of the pilocarpin doses, but on the intensity of the 
action incited by the pilocarpin, that is to say, when at one moment 
in one and the same experiment a given dosis of pilocarpin exerts 
a weak action and has a stronger effect at another moment, then 
the quantum of atropin required in the first case will also be smaller 
than the one required in the second. The same holds both for the 
action of pilocarpin upon one and the same piece of gut, and upon 
different pieces. So, if at a given moment the sensitivity of the gut 
to pilocarpin, is such that 0.1 mgr. of pilocarpin produces a weak 
action, the quantity of atropin, required to arrest this action, will 
be equal to that, required to arrest the same weak pilocarpin-action 
if at another moment it is elicited by a dosis of pilocarpin as small as 
0.01 mgr. In all we have performed 33 experiments in this manner. 
When arranging these experiments so as to place all the cases of a weak 
pilocarpin action in one group, in another all the cases of a mode- 
rately strong pilocarpin-action, and lastly all the cases of a sub- 
maximal pilocarpin-action (corresponding with the point c of the 
concentration-action curve of fig. 2) in a third group, it appeared 
that the average quantum of atropin required for the antagonism 


635 


was for the three groups respectively 0.0005 mgr., 0.001 mgr., and 
0.0014 mgr. This implies that when the intensity of the pilocarpin- 
action rises from a to c of the concentration-action-curve, three 
times as much atropin is wanted as before. The quantum of pilo- 
carpin required for a definite intensity of action, did not modify 
the quantum of atropin which would afterwards be necessary to 
arrest the pilocarpin action. 


Now that it had been demonstrated that in the zone a to c of the 
concentration-action-curve the atropin-action depends on the intensity 
of the pilocarpin-action, we suspected that with still higher pilocarpin- 
concentration, the atropin-dosis required for the antagonism, would 
not increase any more. 

If this were so our results would tally completely with those of 
VAN Lipra pe Jrupe, notwithstanding the difference between his 
criteria and ours. Contrary to our expectation, however, it appeared 
that with a further rise of the piloearpin-dosis, also the atropin- 
dosis had to be largely augmented, anyhow if we stuck to our 
criteria. So the latter result differs from that of van LiptuH Dr JRUDE, 
which finds a satisfactory explanation in the different techniques. 
In addition it is just with the high pilocarpin-concentrations that 
the difference between the criteria applied by van Liptn br JEUDE 
and by us comes much more to the front than in the previous 
experiment. For after these very high pilocarpin-concentrations the 
interval of 3 minutes, after which the atropin-action was observed, 
is too “short. In the experiments with small amounts of pilocarpin 
we observed that, if after 3 minutes the pilocarpin action was not 
yet arrested by the atropin, the atropin action increases but little 
with a longer interval, so that three minutes proved to be the proper 
time after which the action of the atropin should be registered. 
It is not so with the very high pilocarpin-concentrations, here 
it occurs repeatedly that after 3 minutes only a very insig- 
nificant effect has been produced by the atropin, whereas after 4 or 
5 minutes it is sometimes complete. Now, since with high pilocarpin- 
concentrations the space of 3 minutes is doubtlessly too short, and 
with low pilocarpin doses it must not be made much longer (or the 
chances are that the pilocarpin-action decreases spontaneously, so 
that an atropin-action could be presumed where it did not really 
exist) our method is not trustworthy in comparing the antagonistic 
atropin-action of small and very large pilocarpin-quanta. This is why 
we have not continued our inquiry in that direction and are only 
able to record that with a strong increase of the pilocarpin dosis in 


636 


the zone c to d (and farther) of the CA-curve, the atropin-dosis is 
sure to increase still more, without our being able to procure ac- 
curate data on this head. 


CONCLUSIONS. 


I. In accordance with what has been found by v. Liptn pe JEUDE 
and others, the pilocarpin-action upon the surviving gut is entirely 
dependent on the concentration of the pilocarpin in the solution in 
which the gut is suspended. The pilocarpin-action is completely 
reversible. 

II. Contrary to van LiprH pe JRUDE’s assumption, also the anta- 
gonistie atropin-action depends entirely on the concentration and not 
on the absolute dosis of the poison present. 

The atropin-action is also completely reversible anyhow when the 
atropin dosage is not too large. A surviving piece of gut does not 
adsorb so much of the smallest active dosis of atropin present in 
the 75 c.c. of Tyrode solution, as to alter the atropin-concentration 
appreciably. 

III. With the relatively small quanta of pilocarpin (i.e. such as 
exert an action corresponding with the zône a—c of the C.-A-curve) 
the amount of atropin, required for the antagonism, does not depend 
on the quantum of pilocarpin administered, but chiefly on the actton 
exerted by that quantum. The quantity of atropin, necessary to 
arrest a sub-maximal pilocarpin-action is about three times larger 
than the quantity of atropin, required to exert antagonism on a 
pilocarpin dosis with only a slight action. With pilocarpin-doses 
with a maximal action, a strong rise of the doses is still accom- 
panied by a rise of the atropin-doses. The reason given above ren- 
dered it impossible for us to examine this phenomenon in detail. 


Utrecht. Pharmacological Institute of the University. 


Physics. — “Discontinuities in the Magnetisation”. By Dr. B. van 
DER Por Jr. (Communicated by Prof. H. A. Lorentz). 


(Communicated at the meeting of June 26, 1920). 


In a recent paper, “Zwei mit Hilfe der neuen Verstürker entdeckte 
Erscheinungen”’, in the Phys. Zeitschr., Sept. 1919, Prof. H. Bark- 
HAUSEN describes some experiments by which discontinuities in the 
magnetisation were made detectable by a telephone. To this end 
‚an iron rod was placed vertically in a small solenoid which was 
connected to a triode-amplifier. When a small permanent magnet 
was brought by hand near the iron rod, so that the latter became 
magnetised, a rustling sound in a telephone connected to the 
amplifier could be heard, which sound was due to the induction 
pulses caused by the discontinuities. 

Repeating and extending these experiments we observed some new 
phenomena, which may be described here briefly. 

At the outset it may be remarked, that the mentioned rustling 
was known already in the technics of wireless telegraphy where it 
was regarded as troublesome in the use of the magnetic detector of 
Marcon! *). 

In our experiments we used a so-called three-stage low-frequency 
amplifier, in which the energy-transport from triode to triode took 
place by means of small transformers. The terminals of the solenoid 
that contained the iron to be magnetised were connected with the 
filament and the grid of the first triode either directly or by means 
of a small transformer of suitable dimensions. 

The rustling in the telephone, due to the induction-pulses in the 
solenoid must primarily be caused by a discontinuous change of the 
total flux through the solenoid which accompanies the sudden changes 
of magnetisation-direction of molecule-groups or of iron-erystals. 
When in this phenomenon the magnetisation of the separate iron- 
crystals is reversed suddenly by the external field, we should expect 
that the change of the number of lines of force that are already 
present in the case of spontaneous magnetisation and which must 
describe in the air small curves near the surface of the iron, will be 
best observed by means of a solenoid fitting narrowly round the iron. 


1) Ecctes. Wireless Telegraphy and Telephony, 2nd Ed. p. 284, 285. 
41 
Proceedings Royal Acad. Amsterdam. Vol. XXIIL. 


638 


In order to try this two solenoids were wound, the first one fitting 
narrowly round the iron (1.104 windings of 0,1 m.m. copper wire, 
the second one with an inner diameter of 24 m.m. (1.7 . 104 windings 
of the same copper wire). The diameter of the soft-iron core was 
1,00 mm. Therefore the wider solenoid had an inner diameter 24 
times that of the core. 

The rod was magnetised longitudinally by means of a small 
permanent magnet that was slowly brought near the core with the 
hand. Using then the narrow solenoid we could hear some increase 
in the intensity of the rustling, but not to such a degree as might 
be expected from the conception that principally the number of 
lines of force in the immediate neighbourhood of the iron is changed 
discontinuously. 

This experiment leads therefore to the view that the magnetisation 
of long filaments of molecule-groups are reversed as a whole, and in 
such a way that the direction of such a group coincides with the 
external magnetomotive force. For only then induction-pulses are 
possible of the same order of magnitude in two solenoids one of which 
fits narrowly round the core, while the second has a diameter 
more than 20 times that of the iron core. The distance between the 
poles of the permanent magnet we used was 60 m.m. At both sides 
of the solenoids, the core could be touched by the poles. 

Generally an annealed soft-iron wire shows the discontinuities very 
well. Even an iron wire thick 0,1 m.m. (annealed beforehand in 
a hydrogen atmosphere) showed the phenomenon distinctly, only 
over a shorter distance of the movable magnet, which can be simply 
explained by the iron being sooner saturated. This is also in good 
agreement with the hypothesis of the existence of long iron filaments, 
which are discontinuously magnetised each as a whole. 

As still other ferro-magnetic substances than iron were investi- 
gated, we may already here compare the characteristic iron-noise 
with a long-stretched french “ch”, viz. a sound that consists of a 
very great number (for the present not yet to be estimated numeri- 
cally) of soft ticks of nearly equal intensity; only with a greater 
amplification some sharply defined crashes are audible. 

When now a soft-iron wire (diameter e.g. 1 m.m.) has been 
magnetised first by bringing the magnet within a small distance 
from it, and when afterwards this magnet is taken away again, the 
characteristic iron-sound is heard during both operations. A rema- 
nent magnetism will however still be in the wire. When thereupon, 
we draw with short pulls at the iron-wire, we hear in the telephone 
at each pull again the characteristic iron-sound. With short pulls this 


639 


may be repeated 5 or more times. When bv stretching the remanent 
magnetism has been destroyed, further stretching does not recall the 
sound. Exactly the same phenomenon is observed during small torsions 
after magnetisation of the wire and also during a short heating of 
the wire e. g. by touching the wire with a Bunsen-flame, each time 
during part of a second. The sound heard during stretching, torsion 
or heating has quite the same character as that observed during the 
magnetisation. We therefore conclude: the destruction of the remanent 
magnetism in soft-iron by stretching, torsion or heating gives rise to 
discontinuities analogous to those occurring during the magnetisation 
or demagnetisation. 

A strong circular magnetisation causes a superponed magnetisation- 
in longitudinal direction of the rod to take place without disconti- 
nuities. For the above mentioned 1 mm. thick soft-iron wire a current 
of 7 Amp. had to be sent through it to produce the circular mag- 
netisation before the sound vanished. During such an experiment the 
temperature of the wire is of course considerably higher and one 
might feel inclined to ascribe the failing of the discontinuities to 
the rise of temperature. However, immediately after the closing 
of the current of 7 Amp. the sound vanishes in the case of longi- 
tudinal magnetisation and immediately after the breaking of the 
current it reappeared. In both cases the change of temperature must 
be still small. These experiments therefore prove that it is the circular 
magnetisation that prevents the discontinuities in the longitudinal 
magnetisation taking place. 

An annealed iron wire shows further by this sensitive method of 
observation the following remarkable property. When the iron has 
received its remanent magnetism in the above described way, this 
may be destroyed under the characteristic iron sounds by bending 
the part of the rod within the solenoid alternately to the right and 
to the left. But when afterwards this bending is continued the 
characteristic sound remains audible though somewhat weaker. Also 
a freshly annealed wire that has not been magnetised before, shows 
this last phenomenon. This bending may be repeated indefinitely, 
always the sound is heard with the same intensity. Tbis experiment 
seems to be a proof for the theory of Weiss on the spontaneous 
magnetisation of iron crystals. We may not consider the phenomenon 
to be due to the presence of the terrestrial field; for a weak direct 
current through the solenoid compensating or increasing the field in 
the coil has no influence whatever. We might formulate an explanation 
in the following way: by the bending the mutual positions of the 
spontaneously magnetised crystals are changed and by reversing 

41* 


640 


their sign of magnetisation, intermediate positions of equilibrium are 
taken up by the erystals. The bending-back of the rod gives rise to the 
same phenomenon. 

Next cobalt was investigated. This material was at our disposal 
only in the form of cubi with edges of 9 mm. Ten of these cubi 
placed in a row and kept together by thin paper, formed a rod which 
could be lifted as a whole by our magnet. The total induction was 
therefore of the same order of magnitude as for the iron notwith- 
standing the thin air-layers between the separate cubi. Result: 
cobalt produces a sound of the same nature as that of iron but of 
smaller intensity. Without an amplifier the phenomenon is well detectable 
with iron, but hardly with cobalt. 

Nickel behaved differently. Even without amplifier separate ticks could 
be heard distinctly. With a three-stage triode-amplifier these ticks 
‘are very loud and remind one of explosions. The degree of purity of 
the nickel used was not known accurately. Perhaps small impurities 
influence this phenomenon. 

Electrolytic iron gives the characteristic soft-iron sound, but con- 
siderably weaker. 

The maximum intensity of sound was obtained by a 1.98 mm. 
thick nickel-steel wire. With the three-stage triode-amplifier the sound 
that is heard in the telephones during the magnetisation of nickel- 
steel can hardly be endured by the ear and, when the telephones 
are laid on the table, it was very well audible everywhere in a 
room of 7 7 m. and even outside. The sound of this material 
consists of a very great uumber of explosions quickly succeeding 
each other; this makes this nickel steel wire especially suitable for 
a further investigation of the discontinuities. 

In the experiments described above the continuous change of the 
tield was obtained in the same way as by BARKHAUSEN viz. by 
bringing a permanent magnet gradually nearer with the hand. The 
distinctness with which the phenomenon was observed in the case 
of nickel-steel allows a more accurate working-method. Hence we 
tried to produce a continuous change of the field by means of a 
gradually increasing current. 

Experimentally, however, it is not a simple matter to alter the 
intensity of the field by means of a current so gradually that, without 
iron, no sound is heard with a triode amplifier. Some experiments 
were made with a second solenoid placed inside the first and 
through which a current was sent that was also caused to flow through 
a very great selfinduction (a Rumkorj-magnet with short-circuited 
iron-core). When now a rod of nickel-steel was placed in the inner 


641 


solenoid, we heard during the exponential increase of the current after 
it was closed a very great number (not yet estimable numerically) 
of claps within a short interval. At the end, when the current 
had nearly reached its maximum value, some isolated discontinuous 
magnetisation-changes were distinctly audible. 

After that one single isolated discontinuity was thus observed, the 
variation of the intensity of the field by means of a current was 
no longer used and we returned to the movable permanent magnet. 
This time however the magnet was fixed to a support that was 
adjustable by means of a micrometer-screw. In this way the distance 
between the magnet and the nickel-steel rod which was to be 
magnetised, could be changed very continuously by turning a small 
handle. The magnet was fixed with the poles vertically above each 
other at the same height as the solenoid surrounding the nickel-steel 
rod, and at a distance from it of about 5 cm. By means of a second 
magnet, a remanent magnetism.was now given to the rod in such 
a sense that it was decreased by the approach of the micrometrically 
adjusted first magnet. By gradually changing the position of this first 
magnet the intensity of the field could be changed very slowly ina 
continuous way. In this way the discontinuous reversals of the 
magnetism of, in our opinion, long crystal groups may be investigated 
in greater detail and the discontinuities can be heard isolated. 

With the arrangement described above the following phenomenon 
was found. When the magnet was quickly brought 1 m.m. nearer 
to the nickel-steel rod, of course the described claps were heard. 
But also afterwards, when by keeping the magnet fixed in the new 
position, the field was thus kept constant, we could distinctly hear 
in the telephones still several discontinuous magnetisation changes. 
The last discontinuities were heard sometimes 7 seconds after the 
field had remained constant. 

The great intensity, with which in nickel-steel the general pheno- 
menon was detectable, enabled us to investigate the discontinuities 
in the magnetisation also galvanometrically. To this end the solenoid 
was connected directly (without amplifier) to a SieMeNs and HALSKE 
galvanometer, system resistance 300 Ohm. With the external connection 
of the instrument to the solenoid, it was not damped to such an 
extend as is the case with the Grassot-fluxmeter, where the deflection 
obtained by an induction-pulse, remains practically constant for minutes. 
A slowly creeping back after an induction pulse could not be avoided. 
But still, notwithstanding this insufficient damping, the ideal property of 
the flaxmeter was approximately obtained, in which the galvanometer coil 
always tries to take up such a position that the total flux through the 


642 


whole circuit (galvanometer-coil -+ solenoid) remains constant. 
When now the magnetisation of the nickel-steel were perfectly con- 
tinuous, the continuous approach of the magnet should give 
rise to a gradual increase of the galvanometer deflection, while this 
should remain approximately constant, when the field did not change 
any longer. The discontinuities that occur in reality in the induction 
during a continuous change of the field become manifest by the jumps 
of the galvanometer deflections. With a scale-distance of 4 m. we 
observed jumps from 5 to 7 m.m. (scale divisions) during perfectly 
continuous changes of the field. . 

Between these jumps small periods were observed during which the 
induction, as far as could be observed at least, increased continuously 
together with the magnetic force. 

When after the field had inereased for some time, which was 
accompanied by the discontinuities, the field was weakened again 
by taking the magnet away a certain distance (say a few m.m.) 
and afterwards again increased beyond the point first reached; 
then however no discontinuous changes in the magnetisation occur 
neither during the weakening nor during the increase up to the 
point where the field had reached the previous value. 

As soon however as this point is passed, the discontinuities are 
again observed with the same intensity as before. Compared with 
the intensity of the field the continuous increase and the preceding 
decrease of the induction are much slower than in the discontinuous 
region. The described phenomenon is represented schematically by 
fig. 1, where the curve was described in the direction of the arrows. 


Fig. 1. Fig. 2. 


643 


The detailed structure of the discontinuities in the induction as they 
have been observed with the galvanometer, is roughly indicated 
in fig. 2. It is seen that as a rule the value of B before making a 
jump, remains constant a little while. The smallness of the jumps 
and the insufficient damping of the galvanometer, however, rendered 
the observations very difficult. 

By connecting the solenoid round the nickel-steel rod both with 
the galvanometer and with the triode-amplifier, the stronger claps 
could be indentified with the greater jumps in the galvanometer 
deflections. The weaker claps however could not be observed 
galvanometrically. 

Finally the order of magnitude of the discontinuities in the induction 
was determined for nickel-steel. 

To that purpose a second coil (diameter 8,65 mm., one layer of 
50 windings of length 45 mm.) was placed inside the first solenoid. 
A pulse of the current of 40 milli-ampere was necessary to obtain 
a leap in the galvanometer deflection of the same order of 
magnitude as those observed during the magnetisation of the nickel- 


steel. The intensity of the field in the coil was therefore : 
50 


TRE 1, teonp. = Hs 15 0,04 = 0,56 Gauss. 


We thus find for the change of the flux through a winding of 
the solenoid 


0.865? 
aN 9 (5) 0,56 = 0,33 lines of force. 


When therefore we assume the conception above described of the 
change of sign of magnetisation of long filaments to be correct, we 
should find for the order of magnitude of the cross-section of such 
a fibre of the ferro-magnetic nickel-steel : 

0.33 
18000 
on the assumption of a maximum induction 18000 as for iron. 

Assuming: finally a cylindrical form we find for the diameter: 

0,05 mm., 
a not quite improbable value. These calculations are however to be 
regarded as preliminary; further investigations being indispensable 
to bring more clearness in this complicated phenomenon. 


= 1,83 10-2cem-- 


Physics. — “Investigation by means of X-rays of the erystal- 
structure of sodium-chlorate and sodium-bromate”. Communi- 
cation N°. 5 from the Laboratory of Physics and Physical 
Chemistry of the Veterinary College at Utrecht. By N. H. 
Korkmever, J. M. Brvowr and A. Karssen. (Communicated 
on behalf of Prof. W. H. Kersom, Director of the Laboratory, 
by Prof. KAMERLINGH ONNgsS). 


(Communicated at the meeting of May 29, 1920). 


§ 1. Jntroduction. For biological science every deepening of our 
insight into the nature of the chemical bindings of the element 
carbon, so important for the organic world, will be of great value. 
In connexion with the investigation of the structure of the modifications 
of the element carbon itself this point has already been in discussion *). 
Also the close connexion between the atoms of the group CO, 
that has been stated in calcite”) forms an important datum for the 
purpose. Therefore we originally intended to investigate the crystal- 
structure of other carbon-compounds. Sodium-carbonate and sodium- 
bydrocarbonate first came into consideration because of their 
importance for animal life. Considering however that we could 
expect to meet with great difficulties in these investigations especially 
in the calculations as a consequence of the erystal-water resp. the 
monoclinic erystal-system, we first investigated some substances with 
analogous structure, for which these difficulties were not to be 
expected. We chose sodium-chlorate and sodium-bromate both 
erystallizing in the cubic system. We also hoped that these substances 
might give us some indications on the remaining together of the 
atoms of the acid-radical. 


§ 2. Present knowledge on NaClO, and NaBrO,. In P. Grotu’s 
Chemical Crystallography, the erystalforms are described into which 
NaClO, and NabrO, can crystallize under different circumstances. 
When crystallized from solutions in water these substances give at 


1) P. DeBije and P. ScHERRER, Phys. ZS. 19, (1918) p. 476. 

D. Coster, These Proceedings, 28, (1919) p. 391. 

N. H. KoLKMEIJER. Comm. N°. 4; These Proceedings, 28, (1920) p. 767. 
2) W. H. and W. L. Bragg, X-Rays and Crystal-Structure. London, 1918. 


645 


roomtemperature cubic tetartohedral forms. Both of the chlorate and 
of the bromate two enantiomorphous forms occur. In connexion 
with this phenomenon the crystals themselves show rotation of the 
plane of polarisation for every direction of the rays, while the 
solutions are non-active. The polar ternary axes are electric axes. 
With regard to these properties we thought it desirable to determine 
the structure of these crystals. 

BECKENKAMP *) investigated already this structure theoretically ; his 
conclusions were however not confirmed by our investigations. 

W. H. and W. L. Brace’) simply mention, that in the crystals 
of sodium-chlorate the places of the sodium- and Cl-atoms differ 
very little from those in sodium-chloride. From the following it will 
be evident that on the whole we agree with this opinion. 

JararrR and Haca ®) took Lauxz-photograms of NaClO,; they did not 
derive details on the structure from them. 


§ 3. The apparatus used. This was equal to that, described 
in a preceding communication *). This time the finely powdered 
substance was divided as equally as possible by means of a little 
collodion on a glass rod (diameter + 0,1 mm.) in a layer less than 
0,5 mm. The rod was fixed to the lid of the camera; by means 
of this lid it could be turned about its length axis during the expo- 
sure in order to avoid the seratches on the interference fringes 
caused by greater crystal-particles, which hinders the determination 
of the intensities °). Because of the small depth of the layer the 
correction for the thickness of the rod, given in Communication 
N°. 2°), was now much smaller than it was then. The glass core 
of the rod gave no difficulties. 


§ 4. Calculation of the crystal-structure. In the tables I and II 
are to be found for the chlorate resp. the bromate in the columns 


1) Comp. J. BECKENKAMP, Z. f. anorg. u. allg. Chemie, 110, (1920) p. 290. 
*) W. H. and W. L. Brace, X-Rays and Crystal-Structure, London 1918. p. 178. 

5) F. M. JazGer. These Proceedings Vol. 17 (1915) p 1204. 

4) A. J. Bij and N. H. KorkMeijer, These Proceedings 21 (1918) p. 408. 
Communication NO, 1. 

5) That these scratches touch the interference fringes has been explained l.c. 
p. 407. This time some films taken without turning of the rod showed also inter- 
secting scratches; this intersecting can be explained in the indicated way when 
the height of the exposed part of the substance is taken into consideration. By 
decrease of this height the intersections vanished. 

6) A. J. Bir and N. H. Korkuemwer, These Proceedings, 21 (1918) p. 496, 
Comm. NO. 1. 


646 


TABLE :L 
Na Cl O 
Cu, -radiation Cu, -radiation 
Distances in S gi 8 
0.1 mmand | 10° sin? ; zi 
estimated eee Mei 
103 sin? — A 103 sin? — 
intensities | (corrected) | 2? Mg | Arhohg | Eh | NE | Allahs 
(calculated) | (calculated) 
1 2 3 4 5: 6 | 8 
dee Heike oie 0 a i eee 
90 f | 26 2 Al 110 
114 f | 41 3 41 es KE: 
121 vf 41 4 45 200 
132 s 56 4 55 | 200 5 56 210 
141 vs 69 5 69 210 6 67 211 
164 m 83 6 82 211 
221 
199 m 125 9 124 11 124 311 
300 
Bri) vé 139 10 138 310 
221% 152 11 151 311 14 Hej 321 
241 vi 180 13 179 320 
250 vs 193 14 193 321 | 
322 
218 f 234 17 234 | 
410 | 
296 vf 262 19 261 331 
431 
12e F 288 21 289 421 26 292 
510 
431 
| 353 m 358 26 358 | 
510 
| 


Na Br O, 


647 


TABLE Il. 


Distances in | 
0.1 mm and 
estimated 

intensities 


en 
od 


Cu, -radiation 


% 


Chg ean | 


103 sin? Z : 
2 5 5 
3 sin2 — 3sin2 — 
parreeteay egen) OU “|e ae gene Te din, 
(calculated) | (calculated) 
2, a 4, 5. 6. a 8. 
25 2 25 110 
39 3 39 111 
52 4 53 200 5 54 210 
64 5 66 210 6 65 211 
79 6 79 211 
221 
97 9 97 
300 
221 
119 9 119 
300 
152 14 151 321 
184 14 184 321 
322 
221 17 224 
410 
251 19 250 331 
431 
275 21 216 421 26 280 | 
510 
313 24 316 422 
431 
342 26 342 
510 


648 


1 the distance from the central part of the image on the film to 
the interference fringes, expressed in 0,1 mm. and the estimated 


= é ee 
intensities. In the columns 2 are given the values of 10° sin? — 


calculated from these data. In the ordinary way the numbers, refer- 
ring to B-lines, have been separated. In accordance with the cubic 
erystal-form of both substances it was then found that the values 


of 10°. sin? 9 of the a-lines possess a common factor viz. for the 


chlorate A, — 13,79 and for the bromate A, = 13,16. The columns 
3, 5, 6, and 8 contain derived from these the indices triplets (resp. 
the sums of their squares) of the lines; the columns 4 and 7 the 


values of 10° sin’ > calculated with the mentioned values of A. 


From the obtained values of A, we find, in connexion with the 

molecular weights, the densities (resp. 2,496 and 3,254), the number 

of Avocapro 6,062.107*) and the wave-length of the Cu, -radiation 
ey 


(1,537.10—8 ecm) for the number of molecules per elementary cell 
resp. 3,98 and 3,93. This number is therefore for both 4°). 
This gives for the edge of the elementary-cell 6,55.10-S and 

6,74.10 8 for chlorate and bromate resp. 

Then we investigated which grouping of these 4 Na-, 4 Ct resp. 
Br- and 12 O-particles in the cell fulfils the symmetry demands 
that can be derived from the erystal-forms (viz. three binary axes, 
four polar ternary axes, rotation of the plane of polarisation). The 
model obtained in the following way fulfils these demands (see fig. 1). 

Divide the cell into 8 cubes, draw in four of them that have 
only edges in common a cross-diagonal so that they do not 
intersect. Place on one of the diagonals arbitrarily a sodium- and a 
halogen-particle. The places of the other sodium- and halogen-par- 
ticles are then found directly by means of the ternary axes. 

Place one oxygen-particle arbitrarily, the places of the other ones 
follow then again. 

The described model cannot cover its mirror-image (see fig. 2) 
which is in agreement with the optical activity. 

For the calculation of the places of the atoms we chose as para- 
meters, one of the three equal rectangular coordinates of one of 
the sodium particles a (expressed in the side of the cell as unit), 
one of the three equal coordinates of one of the halogen particles 


1) The essential difference with the model given by BECKENKAMP (l.c. p. 300) 
is that there this number is 10 (or 2 in a cube with an edge of half the value), 
which is in contradiction with our film. 


649 


}— band the three coordinates p, q and 7 of one of the oxygen par- 
ticles. With the values a= 74, b=7,, p=}, Jin" WO 
found intensities of the lines which suffice both for the chlorate and 


for the bromate, as is shown by the tables III and IV. The possible 


650 


Na ClO, TABLE III. 
INTENSITY 
Planes Calculated 
Observed 
A B C D 
100 2 0 0 0 0 
110 f 137 146 55 5 
111 f 47 10 22 4 
200 5 }) 80 95 BT) 32 
210 vs 305 sdi 252 123 
211 m 114 139 80 44 
220 ze 0 gn 1 3 
221 54, 70 37, 24, 
| m L 5a | 70 et {24 
300 0 | o 0 0 
Ye at vi Baak 10 2 0 
| sait f 2) 18 22 13 9 
222 dui 8 1 2 0 
320 WE 12 he 4 1 
321 vs 147 194 115 73 
400 Se eae 4 3 5 
322 12 6 4 1 
f 53 68 39 21 
410 41 62 | 35) 26 
330 20 13, 7 1 
cf 25 26 14 10 
All 5 13 7 9 
331 vf 36 47 24 23 
420 ms 31 26 15 6 
421 £3) 34 22 12 11 
332 Ps 29 19 10 1 
422 en 1 6 1 1 
430 ë 5 2 0 
= 6 5 | 2 0 
500 0 0 0 0 
431 27 36 24 26 
| m (40 41 | 98 27 
| 510 13) 5 4) 1 


1) at the same time @-line of 210 vs. 2) at the same time #-line of 321 vs. 


3) at the same time g-line of 431 m. 


Na Br O3 TABLE IV. 
INTENSITY 
Planes Calculated 
Observed EE) 
A B € D 
100 2 Die 0 0 0 
110 fm 3716 301 228 97 
111 vi 216 261 155 88 
200 fm ') 179 197 143 100 
210 vs 864 881 643 409 
211 f 288 | 324 228 159 
220 = 3 9 9 16 
221, 149 179 107, 97 
vi [49 | 179 { 107 97 
300 0 0 0 0 
310 bid 53 91 54 46 
311 f2) 41 50 37 32 
222 = 23 32 19 16 
320 zy 36 61 32 33 
321 vs 303 411 338 260 
400 ee 11 19 15 1 
322 16 21 12 u 
vf 152 | 193 137 113 
410 136 172 125 102 
330 20 13 7 1 
ze (53 65 46 43 
411 33 | 52 39 42 
331 vf gan 115 85 73 
420 ae 46 43 30 19 
421 f 8) 43 33 43 59 
332 as 29 19 10 1 
422 vf 30 50 30 25 
430 19, 32 19 17 
es {19 32 19 17 
500: 0 0 0 0 
431 18, 144) 96 | 112, 
ae s 86 {154 \ 102 118 
510 8) 10 6 6 
| 


') at the same time #-line of 210 vs. 
3) at the same time #-line of 431 s. 


651 


2) at the same time #-line of 321 vs. 


652 


error in the value of 6 for the bromate is about 0,01 of the cell- 
edge, the accuracy of the other parameters is much smaller *). 

In the calculation of the intensities we have taken into consider- 
ation besides the structure factor’) only the number of planes and 
the Lorentz-factor. We thus have neglected the absorption in the 
rod, the temperature-factor and the polarisation-factor. This is allowed, 
when only we compare the intensities of very close neighbouring 
interference fringes. 

Starting from the assumption that the X-rays are deflected for 
the greater part by the electrons, we calculated the intensities under 
the following simplifying assumptions. 

Round the sodium point we place 10 electrons (monovalent positive 
ion)*); the weakening of the coöperation by mutual interference is 
neglected. Round the halogen particles we place in the cases A, B, 
C, and D of the columns 3, 4, 5, and 6 of the tables III and IV 
respectively 12,18, 12, and 10 electrons for the chlorate and 30, 36, 30, 
and 28 electrons for the bromate, while again the same neglections 
were made; in the same way for an oxygen particle resp. 10, 8, 
6, and 2 electrons. All this is based upon the following suppositions : 

in case A: pentavalent positive halogen-ions and bivalent negative 
oxygen atoms; 

in case B: monovalent negative halogen-ions and oxygen-atoms ; 

in case C: binding of oxygen in the halogenate-ion by a ring of 
four circulating electrons, of which two are derived from the oxygen- 
atom and two from the halogen-atom. The interference-effect by these 
binding-electrons has been neglected ; 

in case D: binding between halogen and oxygen, where the effect 
due to the total outer electron rings, to which the binding electrons 
belong, has been neglected. 

From the tables III and IV we see that the agreement between 
the calculated and observed intensities is good from which of these 
suppositions we may start. 


1) "This must be ascribed to the fact that the displacements of the Br-particles 
can only be very small when their influence on the interference-result shall be 
compensated by displacements of the other particles. This is the case to a much 
less degree for the Cl-particle because of its low atomic number. Therefore we 
cannot give a limit of the accuracy of the parameters either for this particle or 
for the O- and Na-particles. 

4) In the calculation of the structure-factor we took into consideration, that for 
planes with three unequal indices for the symmetry of these crystals this factor 
depends on the succession of the indices. Comp. W. H. and W. L. Bragg, Le 
p: Fol, 

3) P. DeBije and P. SCHERRER, Phys. ZS. 19 (1918), p. 474. 


653 


From the values found for the parameters it is evident that each 
time three oxygen-particles are lying close round each halogen- 
particle; the plane of the three oxygen-particles perpendicular to a 
ternary axis contains, approximately at least, the halogen-particle. 
The distance between the centres of a halogen- and one of those 
neighbouring oxygen-particles is about + of the parameter of the 
lattice !). The situation of the groups Nat and CIO, resp. BrO,— can 
be found from the NaCl-model by diminishing the distance between 
the opposite ions all by about # of their value. 

Finally we wish to express our indebtedness to Prof. Kersom for 
his kindness to place his laboratory at our disposal for this investi- 
gation and for his great interest and help. 


1) (Note, added during translation). Quantitatively these values are not in accord- 
ance with the data of Brage (Phil. Mag. (6) 40 (1920) p. 169. The distances of 
the centres of an O- and a Cl-atom or a Br-atom, which, according to Brace’s 
data ought to be 1.70.10—-8 and 1.84.10—8 respectively are found by us as 
0.910.10-8 and 0.937.10—8 respectively This discrepancy is not astonishing, 
seeing 1 that in note 1) of the preceding page some reserve is made about the 
accuracy of the parameters for the O-particles; 2 that Braaa expects a shortening 
of the distance in discussion in radicals in which there is strong binding. 

We thought it desirable however, to investigate this point nearer, with this 
aim new photos will be taken and discussed by two of us (B. and Kaj. The 
intensities of the lines with the smallest radii especially, lying in a dark part of 
the film, can perhaps be determined more accurately. when an antikathode is 
used, which gives a larger wavelength and when the radius of the camera is 
enlarged. 


42 
Proceedings Royal Acad. Amsterdam. Vol. XXIII. 


Physiology. — “On the adsorption of odorous molecules to the 
surface of solids.” By Prof. H. ZWAARDEMAKER. 


(Communicated at the meeting of February 22, 1920). 


In the meeting of 24 May 1907*) I pointed out that in many 
cases a prolonged and marked adsorption of odorous molecules to 
solid bodies takes place, as soon as their surfaces have come into 
contact with gases that are mixed with odorivectors*). The simple 
act of opening a bottle filled with valerianie acid suffices to cover 
all the objects in a large room with valerianic acid molecules, so 
that when rubbing their surfaces with a dry wad of cottonwool, 
the latter is sure to give off a smell of valerianic acid. Even the water 
in which glass objects are washed that were in such a room, 
distinctly betrays the presence of odorous matter in a subsequent 
spraying under overpressure of two atmospheres and when studying 
the vapour electricity ensuing from it. *) 

The occurrence of these adsorptions depends chiefly on the presence 
of a condensation layer of air and watervapour on all surfaces. *) 
Besides, there is a possibility of a direct adsorption to surfaces from 
which this condensation layer has been purposely removed. Finally 
adsorption may occur to electrically charged surfaces, which attract 
particularly the particles of opposite sign that are present in the air. 

We will call the various forms of adsorption to the surfaces of 
solid bodies adsorptions of the 18*, 2™¢ and 3td sort. 

Those of the first sort comprise nearly all common cases of ad- 
sorption of odorivectors to solid surfaces. 

Those of the second sort are very rare. Strictly speaking they 
occur only on cleansed surfaces of amber, sulphur or paraffin, on 
which the condensation layer may be missing, and which consequently 
are excellent insulators for static electricity. 


1) Kon. Akad. v. Wetensch., Amsterdam, Proc. June 29 1907. This investigation 
has afterwards been extended by J. HERMANIDES, see Onderz. Physiol. Lab. Utrecht 
(5) 1909 X. bl. 28. Also H. ZwAARDEMAKER in Tigerstedt’s Hdb. der Physiol. 
Method. Bd Ill, p. 49. CG. van Dam, Arch. neerl. de Physiol. t. 1. p. 664, 1917, 
A. Heyninx, Essai d’Olfactique physiologique, Bruxelles 1919, p. 82. 

2) A. HEYNINX, l.c, p. 19. 

3) H. ZWAARDEMAKER, Arch. neerl. de Physiol. t. 1. p. 347. 1917. 

4) Bunsen, Wiedemann’s Annalen, Bd 24, p. 321, 1885. 


655 


The adsorptions of the third sort manifest themselves, when emanation 
is adsorbed to objects that may be considered as having a negative 
electrical charge, and they can be brought forth in special experiments, 
when gases, containing gasions or condensation-droplets, are placed 
between condensator-plates. 

The adsorptions of the first sort occur everywhere in daily life. 
According to Gipss’ theorem’) all substances that lower the surface- 
tension of the fluid of which the layer is composed, attach them- 
selves to the condensation layer that covers every object. The con- 
densation layer consists mainly of water, and since all odorous sub- 
stances lower the surface-tension of water’), the adsorption of odori- 
vectors must occur in all cases. It is specially those odorous sub- 
stances that possess great surface-activity, which will be largely 
adsorbed. 

It seems that the sublayer has some influence on the composition 
of the adsorbed air-vapour-layer. It may be assumed that all sorts 
of oxidation-products and decomposition-products of the solid sub- 
layer, as well as substances that have been dissolved in it, will 
pass into the condensation-layer. On metals we may look for oxides, 
on glass for alkali, on ebonite for sulphuric acid. Quartz is also 
hygroscopic and colloid chemistry assigns a reaction to its surface. 
1 feel inclined to ascribe to these components dissolved in the con- 
densation-layer, the specific character which experience has taught 
us that belongs to the adsorption of odours by certain surfaces. 

By my method (transmission of air at the rate of 100 cubic em. 
per second through cylinders of different material with a lumen of 
0.8 cm., a measured quantity of odorivector being added to the air) 
the quantum of odorous matter in the air can be determined which 
has passed along the inner surface of the cylinders. 

To perform this we should take into account the odorimetrical 
coefficient of the olfactometer that served as source of smell, as 
well as the minimum perceptibile of the odorivector in absolute 
measure. Both are known for the cases published previously and 
from them A. Heyninx and myself have deduced the partial tension 
of the odorous gas that served as odorivector. 

T will report some of my results here: 

Pyridin was hardly adsorbed to glass though a large quantity of 
‘it was present in the air; valerianic acid, however, of which there 
was only a small amount in the transmitted air, was retained for 


1) J. WiLLarp Gisps, Thermodyn. Studien, Uebersetzt von W. OsrwarLp, Leipzig 
1892, S. 258. 


*) Acta otolaryngologica, Vol. 1, p. 54, 1918. 
, 42% 


656 


a very long time. Neither did pyridin attach itself to aluminium, to 
which seatol again was largely adsorbed, although there was much 
less of it in the air. Iso-amylacetate was adsorbed to iron and tin 
only for a short time; scatol again for a long period, in spite of 
the small difference in the partial density of the air. Porcelain, on 
the contrary, attracts iso-amylacetate more than any other substance, 
scatol least of all. 

When, as was the case just now, the adsorption of the first sort 
is ascribed entirely to the presence of the condensation-layer, the 
duration of the adsorption will be a function 1. of the lowering of 
the surface-tension of water together with what had already been 
dissolved in it; 2. of the solubility of the odorous matter in water; 
3. of the thickness of the condensation-layer; 4. of the volatility of 
the odorous matter from water. 

The possibility of this differentiation proves the existence of a 
specificity. 

As said already, there are some solids without a condensation- 
layer, or if they have any it seems to be so inappreciable that no 
ions are available to conduct the electricity so that they may serve as 
insulators for static electricity. For this purpose amber, paraffin 
solidum and sulphur are used. These substances are not moistened 
by water *), for when tracing a channel in these substances by means 
of a darning needle no water will appear in it. This is indeed the 
case with a certain number of other odorous substances. With the 
method previously described we were able to demonstrate that a 
rather considerable number of odorivectors added to the air that 
passes through a tube of amber, sulphur or paraffin, is adsorbed to 
the inner surface of such a tube. To amber e.g. borneol! scent is 
retained 1 inin., creosol 1 min., geraniol 8 min., vanillin 29 min., 
nitrobenzol 37 min. Broadly speaking bere also the different degree 
of adsorption must depend on the difference in the lowering of the 
surface tension of the solid surface. 


In the case of the first sort as well as in that of the second the 
odorous substance must at length be dissolved also in the lower 
layers. In the first case it is the condensation-layer that is saturated 
with odorous matter and finally imparts a small portion of the 
dissolved substance to the sublayer. In that way the odorous matter 
can be retained almost for ever and it appears that the adsorption 
continues also after removal of the condensation layer. This phenomenon 


1) Vide: R. S. WorLows & F. HATSCHEK, Surface Tension and Surface Energy, 
2nd edition, London 1919, p. 89. 


657 


is seen in glass after a short exposure to muscon; while of objects 
such as rubber gastubes it is known that they can hardly ever be 
freed from gassy smell or from vinegary smell after the trans- 
mission of acetic-acid gas. With adsorptions of the second sort the 
phenomenon also appears especially when we endeavour to retain 
odours in a space with paraffin-covered walls. | 
Odorivectors are also strongly adsorbed by paper, even when it 
has been made non-conductive by being heated for some minutes, 
which deprives it for some time of its condensation layer. Many 
remarkable instances occur in which one adsorption cancels another. 
Eugenol, resp. xylidin e.g. drive out allylaleohol, but the reverse 
does not take place. Here also surface-activity must be paramount. 
The application of electrical changes on the objects does not modify 
the adsorption relations of the 1st and 2rd sort, so far as I could 
ascertain. For the adsorption of the 3'¢ sort, however, they are 
conclusive. The latter do not exert an influence on the adsorption of 
smells, which, indeed, need not surprise us, since thus far odorous 
molecules in gaseous state have proved to be uncharged *). 


1) Hdb. d. Physiol. Methodik, Bd IIIf 1, p. 50, 1910, A. HEyNiNnx, Essai d’Olfac- 
tique physiol., Bruxelles 1919, p. 221. 


Physiology. — “On Spray-electricity of Solutions of Electrolytes’. 
By Prof. H. ZWAARDEMAKER and Dr. H. Zrenuisen. 


(Communicated at the meeting of April 23, 1920). 


Our experience regarding Spray-electricity of aqueous solutions 
has led to the following results *) 


| Charge imparted by the nebula per 


cc. of sprayed liquid in 10 10 
| Coulombs. 


Saturated solutions. 


Odorous substances (27 in numb.) onan average 81 (extremes 300 and 1) 


Saponins (22, soluble) lees eee By 9 16 cod iim 
Antipyretics ( 9, soluble) lie ight eeen 15 „ 2w) 
Alkaloids (11, soluble) ay is 2.9 ( ss CRS 


Perfectly pure water does not yield spray-electricity (fresh-distilled 
water); no more does Utrecht tap-water. Since, in subsequent expe- 
riments, with more sensitive apparatus also solutions of electrolytes 
proved to impart a weak charge, which may be positive, as well 
as negative, these solutions were examined more in detail. To this 
we were prompted all the more, since all groups of physiologically 
active substances mentioned above, gave only a positive charge, 
which got weaker with every following dilution, while ultimately 
there was no charge whatever. The strong positive charge of the 
substances is apparently correlated to their volatility, which mani- 
fests itself, as has been described before, in their odour, in the 
odour of the nebula formed in spraying, in the decrease of the 
charge in their solutions, when an air-current is sent through, in 
the camphor-phenomenon, exhibited by many, in their boiling-point, 
etc. In the case of pure odorous substances this correlation controls 
smell-intensity and electrifying power. Generally the substances giving 
a positive charge exert a lowering influence upon the surface tension 
of the boundary surface air-water. 


!) Proceedings 25 March 1916, 27 May 1916, 30 Sept. 1916, 23 Febr. 1918 
Arch. Neerl. de Physiol. t. 1, p. 847, 1917. 


659 


The negative charge must be ascribed to another cause. The 
slight, but distinct, negative charges of the concentrated anorganic 
salt-solutions cannot be correlated to the volatility of these salts, *) 
as the latter, though not totally absent, is extremely insignificant. 
The existence of a transition from positive to negative charges in 
the solutions of some organic salts, naturally compels us to assume 
two components of opposite sign, whose influence on the transmission 
of electricity to the receiving disc is different. When considering the 
ions, generated by dissociation, as the carriers of the electricity of 
positive and negative sign, the droplets which strike on the disc 
may be responsible. It is possible that this new charge is superposed 
on the charge given by the electricity of condensation drops. 

That the presence of electrolytical ions in the droplets must 
occasion a complication of spray-electricity is obvious, since Lenarp’s 
experience with regard to waterfall-electricity has thrown light upon 
the significance of the electric double-layer, present in the surface 
of the drops. The outmost layer is negative, the inmost layer is 
positive. We may be sure that the influence of the former is greater 
than that of the latter, at least when the droplets impinge on the 
disc without great force. *) Still, the number of ions in the droplets 
cannot be small. When the ions of the superficial Jayers impart a 
charge to the dise when impinging upon it, the effect will probably 
be as great for the positive as for the negative sign. 

So far as we could judge, the solutions of anorganic bases and 
acids did not vield a charge in a single concentration. We examined 
the bases: potassiumhydroxid, sodiumhydroxide, ammonia liquida and 
bariumhydroxide; the acids: hydrochloric acid, sulphuric acid, nitric 
acid, phosphoric acid, hypophosphoric acid and hydrobromic acid; 
only hydrochloric acid formed an exception’). Of hydrochloric acid 
the complete molecules are volatile, but take up such a low place 
in the homologous series that they cannot be expected to produce 
a charge. Possibly, when in a gaseous form, they can yield an 
extremely weak positive charge, which may compensate the nega- 
tive charge of the faintly impinging droplets. 


1) CG. ZENGHELIS: ‘‘Ueber die Verdampfung fester Körper bei gewöhnlicher 
Temperatur’’. Zeitschr. f. Physik. Gh. 50, 219 (1904); 57, 9 and 109 (1907). — 
Ca-sulphate, Ca-phosphate, and Ca-sulphite proved slightly volatile. 

2) H. ZWAARDEMAKER and F. Hoerwinp: “On Spray-Electricity and Waterfall- 
Electricity”. Proceedings Vol. XXII. p. 429. 

3) This acid gave a strong positive charge and possessed a rather penetrating 
odour; in contradistinction to HCl and HBr it is not caustic when inhaled, even 

in a concentrated solution. 


660 


Among the organic acids and salts we observed some that were 
electrifying. To this eategory belong the fatty acids, soluble in water, 
which have been discussed in a previous publication '). With strong- 
er concentrations the sign is found to be positive, with weaker 
Ones negative, with a definite concentration, of course, passing through 
zero. The behaviour of bezoic acid, salicylic acid and lactic acid is 
completely analogous ’). 

With citric acid and hippuric acid the charge is, indeed, always 
negative, but in the strongest solutions that can be made at room- 
temperature, it approaches the point of transition, i.e. the negative 
charge begins to decrease again, so that whenever still more con- 
centrated solutions of ammonia-salts can be made, a positive charge 
comes forth. If the solubility of citric acid and hippuric acid were 
still greater, the point of transition from the negative to the positive 
phase would, with these salts, also be reached or passed. 

In comparing the curves of hydrochloric acid, chlorammonia, 
benzoas ammonicus, and benzoic acid, a general view is obtained 
by means of the hypothesis that the influence of the anion contributes 
most to the charge of the drops in the nebula, because the anion 
lies most on the surface of the drops. In spraying, however, the 
disc takes a positive charge, especially when the large and volatile 
molecules have lost their superficial layer. 

When meanwhile, by the side of the complete molecules, ions 
make their appearance in the liquid, an algebraic sum of charges 
is the consequence of it. A positive charge, as alluded to just now 
combines with the negative, which is imparted by the anions on 
the surface of the drops. With increasing dilution the algebraic sum 
comes nearer to zero and the point of transition is even passed. 

So far as we can see, the cation does not play an important part 
in this process. = 

Resuming we found first of all that the negative charges of the 
strong solutions of the anorganic salt are extremely small; further, 
that the form and the intensity of the negative phases of the charges 
of benzoas natricus and benzoic acid are strikingly uniform and 
that even their points of transition coincide. 

It may be conceived, therefore, that although the cations and 
anions in these solutions are equal in number, the latter are driven 


1) H. ZWAARDEMAKER and H. ZeEHUIZEN: “On the Sign of the Electrical 
Phenomenon and the Influence of Lyotrope Series Observed in this Phenomenon”. 
Proceedings Vol. XXI. p. 417. 

*) Also lactic acid in concentrated solution gave a strong positive charge; lactates 
were not at our disposal. 


661 


to the surface, so that the influence of the anions is greater than 
that of the cations. This rising of the molecules to the surface is 
aided through the addition of cane-sugar, which will intensify the 
charges, because the positive and the negative ions are expelled 
with nearly the same force (the former somewhat more than the 
latter). On the other hand addition of salt weakens the negative 
charges; therefore, intensifies the positive charges. The lyotrope 
series are also of influence. 

The same considerations apply to the positive and the negative 
phases of the phenomenon in some terms of the fatty acid series: 
propionic acid, butyric acid, valerianic acid, and caproic acid. The 
greatest negative charges occur with caproic acid, the smallest with 
propionic acid. Their positive charges are extremely intensive, since 


Negative charges of some anorganic salts'), (in Coulombs X 10—10 
per cc. of sprayed solution). 


Concentrations of the solutions. 
NAMES. ; ; = 
3 n. n. Oa nr 03 Ol at: 
Lithium Chloride 0.13 | 0.11 0.10 0.08 0 
Na. Chloride | 0.13 | 0.10 | 0.09 | 0.09 0 
K. Chloride | 0.10 | 0.087 | 0.07 | 0.07 0 
Ammonium-Chloride 0.096 | 0.07 | 0.05 0 0 
K. Nitrate = =| gs68" eh m.055,| 0:04 |) 0 
K Bromide == 0.09 | 0.08 0.07 0.05 
K. Iodide — 0.09 | 0.08 0.07 0.04 
K. Phosphate — 0 | 0.07 0.08 0.08 
Na. Phosphate = — — 0.05 | 0.04 
Na. Nitrate — ~ | 05080 | avumes) ossa e 0 
Ammonium-Sulphate — 0.07 0.07 0.04 0.04 


we have to do with volatile entire molecules that lower the surface 
tension. 


1) The other substances examined: potassium-hydroxide, sodium-hydroxide, ammonia, 
baritum-hydroxide (bases), hydrochloric acid, nitric acid, sulphuric acid, phosphoric 
acid, hypophosphoric acid and hydrobromic acid, potassium- and sodiumsulphate, 
potassiumrhodanate, potassiumchlorate, sodiumfluoride, sodiumbicarbonate, sodium- 
biborate, magnesiumsulphate, potassiumpermanganate (salts), do not impart a charge. 


662 


For the positive charges we believe the entire molecules to be answer- 
able on account of their volatility and their surface-activity. The negative 
charges we believe to be evoked by the anions, which, conformably 
to Lunarp’s hypothesis regarding waterfall-electricity, are in the 
majority in the outer layers of the drops, when they impinge on 
the disc. 

Addition of sugar molecules drives the dissolved entire molecules, 
together with the ions of the discussed substances, to the surface. 


Physics. “On the Theory of Hysteresis according to VorrerRA”’. By 
Dr. W. Koster Dz. (Communicated by Prof. W. H. Junius). 


(Communicated at the meeting of June 26, 1920). 


§ 1. In chapter VI of his ‘‘Lecons sur les fonctions de lignes” 
Vourrrra treats elastic hysteresis. By the method developed by him 
there the equations expressing the components of the elastic tensions 
as functions of the quantities that determine the state of the elastic 
medium, are revised. In the classical theory of elasticity these 
equations have the general form: 

Component of tension = linear homogeneous combination of the 
quantities of deformation. (Law of Hooke). VoLTERRa substitutes for 
this relation the equation: 


t 
tin (t) Dihfrs Yrs (t) fz Wih/rs (tt) Yrs (t) dt. 
0 


In this ¢, represent the elastic tensions at the moment ¢, y‚s (4) 
representing the quantities of deformation at that moment and jy, (t) 
the same quantities at a variable moment r. Further the 6’s and 
the w’s are coefficients; VoLTERRA calls the w’s coefficients of heredity. 

We shall show in what follows that dissipation of energy may 
ensue from these suppositions of VorTERRA’s; i.e. in the case that 
his suppositions have physical meaning. 

We further point out that the idea on which VorrTErra’s hypothe- 
sis is founded, is that of distance action in time. For the contribu- 

t 
tions to this f= Witirs (tt) Yrs (©) dt are supplied by deformations y‚s, 
0 
which existed at moments t in the past. This distance action in time 
is somewhat unsatisfactory, we ought to be able to manage with- 
out it. If at a given moment the condition is completely determined, 
the principle of causality tells us, that what will follow is also 
entirely fixed. Only with a definite previous history there will be 
another deformation at a fixed point of time than when the 
previous history had been different. We shall later on try to deal 
with elastic hysteresis without assuming distance action in time. 


664 


§ 2. Let us now proceed to the treatment of linear elastic vibra- 
tion revised for hysteresis according to VorTERRA. 
Then the following equation holds for this movement : 


dx 


t 
ca ter = feed dr, 


(ee) 


Now VorrprraA shows that in general in case of elastic hysteresis 
W(t‚r) must be a function only of (t—t), though there are hereditary 
phenomena in which this need not be the case’). Disregarding the 
latter, we, therefore, write henceforth y(¢—r). The fact that w has 
this form, is, indeed, easy to understand; if it is assumed that for 
what ensues it is only of importance how long ago certain forces 
acted, and not at what absolute points of time this took place 
precisely, only the difference of time ¢—-r will appear, or in other 
words we imagine that the effect for what follows will be the same 
when we subject a certain previous history (with its consequence) 
to a translation in time. 

Let us now further assume in particular for w the form of the — 
function : 


t—T 


w(t—1t)=Ae 7%. 


in the above equation (1). The supposition is plausible, for the term 
t 


fe (rt) w (tr) dr 


—% 
accounts for the influence of the previous history on the condition 
at the moment {; or expressed more definitely : 

the element «x (rt) y (—rt) dr of that integral represents the contri- 


bution of the condition at the moment rt to the value of the accelera- 
ob ha 


da. shail 
tion at the moment ¢ (the term de in equation (1) ). It will be clear 
; 


that as the moment rt is longer ago with respect to ¢, this influence 
must be smaller; this is really in agreement with our supposition 
for w: 
bt 
y= A en EN 
for this becomes zero for t—rt — infinite, and increases with decreasing 
Lr. 
When we now work with this y, and solve the equation (1), we 
can at once derive 


Wass. Vouterra Lc. p. 114. 


dr de 1 d'r 4 dx a et 0 9 
ge iter Soha oh ham ar eit ak off Be 


being a linear differential equation of the Sd order with constant 


coefficients. When we substitute «= ert, we get for the solution of — 
p the third degree equation : 


1 a 
pt opt + ap + (2-4) =o 
q q 


Interesting from our point of view are only the cases of physical 
signitication, i.e. damped vibrations. In order to yield them it is 
necessary that this 3'¢ degree equation has one real negative root 
and two conjugate complex roots, the real part of which is negative '). 

Condition for this equation having one real and two conjugate 
complex roots is that its discriminant D is positive, hence D> 0, 
in which 

at A AG tte a' 


Dee EEE ple ce 
rt “) 


1) It is necessary to make a remark on the energy. 
The equation of § 2 


Ce. oe daz 
aa toa tte Aged. o> Oe AER alef) 


yields multiplied by = 


da dx ee dx 


TR 


+c (EE) + ane =0 


or 


da \? dx gend De dx d*x dx 
a) trl) =F (240 tia +4(F)).@ 


ae i 
What stands behind 5 must be the energy (only «> Aq can have signifi- 


cation). This term gives the potential energy on the supposition that there is an 
elastic potential 4 (~—Aq)x?, and then an elastic force (c<—Agq)x, which is not 
the case here. It seems to me that the interpretation will be as follows: the 
lefthand member gives the work done on the system, the righthand member 
the change of energy. How must this work done of the lefthand side be imagined? 


dx \?2 
In the first place the work — zal d a) done by a frictional force proportional 
dx : dix? 
to eA and then in the second place also the work — q Ee ‚ done by a force 


d°x Hen 
proportional to =a Then of course not only the potential energy that exists with 


regard to the force (~—Ag)x appears in the righthand member for the potential 


666 


Let us now try to find the condition that the real root is negative. 
Let us for this purpose follow the course of the values in the left- 
hand member. We put: 


a 


1 
mre emg) 


foryp = — % y= — 0 
a 
Ned eh y=—— A, 
q 
t 
If the real root must be negative, tens A must be positive or: 
q 
a> Ag ol. 8. Oe 


which also appears in the first remark on the energy below. 
Finally the condition that the real part mentioned must be nega- 
tive; it becomes: 


1 3 
Voss VD+4"—4Q—VD>0.. (LI) 


dsx 
energy, but also that with regard to the force q —. For I interpret the whole 
dt? 


lefthand member of the equation (1) as a set of forces that keep each other in 
equilibrium : 

dr : 

ae force of D'ALEMBERT for the motion 


Ch 
xq at frictional force 


(a—Aq) x quasi elastic force and 
On : 

q-—— another elastic force. 
dts 


A second remark should be made on the limiting cases. As point of issue we 
have equation (1) of § 2, in which 


bt 
RI Pien igs 
When we make q approach zero, and A approach oo, we get: 
t 0 


de HEEE RS 
tea q uae(yafe ads = + x(t) Aq 
calling lim Aq= Bf, we get: 


: Sn 
de + (e—8)2=0, 


the equation for the ordinary periodic motion. — This equation is, indeed, imme- 
diately found when we take equation (2), multiply both members by gq, and then 
substitute q =O and Aq= 8. 

Let us finally treat equation (1) of § 2 with the general U (t— 7) approximating 


in which: 


Summarizing: when the a, A, and g fulfil these conditions 1, II, 
and III, the hysteretical term, as VorLTERRA has assumed it, comes 
simply to damping of the vibrating motion. 

When we call the roots —p,, —p, £ q,?, the solution becomes: 

w= A,e mt + Ae —Patcosg,¢-+ A,e—Ptsng,t. . . (A) 

As regards initial conditions, 

c=, «= 0 
e.g. up to t=O (from t= — oo) by adaptation of the found solution 
(A) to these values. From the integral equation follows: 


t 
1 tr 


ae ——— 
ge time, fe de de 
— 6 
aa 

nme 0 asi eee 

PL 
and this value of ae must be used when we make A,, A,, and A, 
q 


by assuming the supposition that | ({—r) has only values differing from zero for 
values of t—r that are very small. 
When we put ¢ — Tr =S, our equation (1) reduces to: 


d*xz 


Te a= fvOreHe. @ 
0 


According to the equation mentioned : 
E = (Ey gE er yEee 
wat) d= + [Od |E Od 
0 0 0 
Let us now put: 
ao foo] 
[rouse m fewer 
0 0 
then we get after substitution in the equation (A): 
ie. a damped vibration. 


For & >a we have the damped exponential motion. 
As a special case also x= occurs in it. 


668 


conform to the border conditions. For «= f(t, r= g(t) we can 
proceed analogously. 

Leaving the particular form of y (¢—t) undetermined, we shall 
now further treat an example that might be tested by experiment, 
which might, therefore, give us an opportunity to find the form of 
yw. In this case it is easy to write down the condition on which 
VoLTERRA’s scheme comes to damping. 

For the example that we now choose, the equation (1) holds 
again, but now let a force zero act from {= —o tot=0; wand v 
are then zero; a force A further constant suddenly begins to act at 
t=0. For the motion after the moment zero now the following 
equation holds: 

a 
Aa ae fet ae KK 
0 


2», 


de 
Practically the term ee be omitted (that is to say, we shall 
a 


presently examine ‘exactly what is tacitly assumed here). There then 
remains 


t 
a x (t) ~{ w(t) yp (t—t) dt = K, 
0 


being a linear integral equation of the 2"¢ order. The solution of 
this becomes: 


Ks 1 1 +e 
wv (t) =—(' + ‚fo dr +affr (t) w (t—t,) dr, r+.) 
at a at 
0 0 0 


When we now assume that « is great with regard to the hyste- 
resis, we may neglect terms with higher powers of u in the deno- 
minator. We get in first appr ee 


K 1 
2) = =(1 +— | y(t) ir) EEE 
if 


dz 
Is it really allowed to omit the term —— from the equation (A) 


dt 2 
above? When by differentiating the just found solution «(¢) twice, 
. 


= ne 
we determine ae for this purpose, we see at once that the right- 


K 
hand member contains the factor —. Hence when this may be ne- 
a 


glected compared with the hysteretical term: 


669 


| v(t) yp (é—t) dr 
0 
a 
dt? 
Let us now examine in the solution (B) for «(t) when it represents 
a damped motion. A movement will be called damped when the 
limit of the velocity for {== is equal to zero. When we, there- 


from equation (A), may also really be omitted from equation (A). 


' dE Tee ‘ 
fore, first determine the aa from the solution (B) for a(t), we get 
a; 


at once as condition for damping: 
lim w(t) = 0°) 


jie 
lim yp") (t) = 0 
(=n 
The example chosen, i.e. the movement with which from {== — oo 


to ¢=— 0 a force acts equal to zero, and further « and x are zero, 
and then suddenly a. force A that is further constant, so that for 
the movement after the moment zero the equation (A) of p. 668 


is valid, may now also be treated in the special case that we 
att 


assume ws Ae 9 . Equation (A) then passes into: 
t 


Lt 


Las =| a (r) Ae 9 dt + Kk 


0 


aa 


dt? 


By differentiating with respect tot, and by eliminating the integral, 
I derive the equation: 


a a DS eles 
leer WE dn Elger Kran oe en (B) 

The lefthand member of this equation is exactly the same as the 
lefthand member of equation (2) p. 665. When for the moment I 
call this ZL, equation (8) of this page becomes 1 — K, and its general 
solution is obtained by adding to the general solution of L=0O a 
particular integral = K. This is directly found: 

K 


ed 


d 


Further the considerations about damping as they occurred in 
equation (2) on p. 665 now repeat themselves completely. Literally 
the same conditions are written down for damping. 


1) Compare further p. 671. 


43 
_ Proceedings Royal Acad. Amsterdam. Vol. XXIII. 


670 
As analogy to the solution (A) p. 668 we now get: 
K 
a—Aq : 


eA” Ae Poos gt + Age °° sin gat + (A) 
which must also again be adapted to the initial conditions. 

Finally also the remarks on the energy and on the limiting cases 
of the footnote on p. 665 and seq. may be repeated here. In 
the energy now another term appears, Aw, which represents the 
work done by the force A. And as regards the limiting movements, 
the same limiting movements also occur here again. 

And now I will again start from the integro-differential equation 


dx 
pramen. . = 


with general w and inquire into the condition on which this equation 
of vibration revised for hysteresis by VorTERRA, represents a damped 
movement. . 

First I state that there can always be given a point of time t 
so that the history of before this moment + may be neglected. On 
physical grounds the function w must be such that: 

lim w (t—r) = 0, 
t—t= © 

for the influence of what took place very long ago, must become 
small. Now this wy under the integral sign in the righthand member 
of (1) must, however, still be multiplied by a(x), the a at this moment 
tT in the past, and when it is very large the product e(t) (t—t) 
may not be neglected after all. Now | observe that the number of 
times that in the previous history an x(t) can occur lying above a 
definite « which may be chosen arbitrarily great, must be decidedly 
finite, for the simple reason that we have to do with a physical 
problem. And then I go so far back in time that I have passed 
this finite number. 

Now equation (1) reduces to: 


t 
dx 
aa + an = | @ (t)W(t—r) dr. 


0 
In Fonet. de |. p. 97—99 Vourrerra gives as solution of this 
equation : 
«aS, (t/a) + OS, (t/@) 


in which S, and S, are two transcendental functions of @ as follows: 


671 
S, (t/a) =t + fe t) S(t/a) dr 
0 


t 
S, (t/a) = 1 + fs (t/a) dr. 
0 
In this: 


S (t/a) =aF'!(t) + a? F@) (t) +... + ak FAY 
t Ei 
—FO@M=t +f a8, fw (S.) a5, 
0 0 


Fe) (t) = [Fo (6,) FO) GE) dé, 
0 


FO) () = ef Fl (8) FY) (t—£,) dé, 
0 


=d da je 
a (F)_, a (%):=0 


When now specially as moment zero a moment is chosen, at 


and further 


which the velocity ap DS Ze will also become zero, so that the 
( 
solution passes into: 


e= 68, (t/a) 
Now the condition for damping was: 


; da 
lm = 
t= dt" 
Here the equation becomes: 
dz 5 dS, yee 
zg ee 


Hence we get as conditions for damping: 
lim S (t/a) =0 
==) 

lim St) (t/a) = 0 
le) 

$ 3. After what we have seen in the preceding paragraphs about 

the linear system, I shall now proceed to demonstrate in general 


that there does not exist an elastic potential in VorLrerra’s hysteresis, 
so that dissipation of energy takes place. 
Starting from the equations of motion: 


vi) Ou Watn dbnl OLNE 
e(2—5) | a Tou pena OD 
TE, bed TELT Ee IRE 
(3) 


the relation has been derived (see e.g. RrEMANN-Wreger. Die part. 
diff. Gleich. der math. Physik. IL § 65): 

Work done by the forces of mass X, Y, and Z acting on the 
volume elements + work done by the surface pressures — change 
in kinetic energy — 


‘ OY,, dy. pn 
— SAA GSE eo \ 1 — ( 1 
fle Ot Tha Ot _| te ve 


Then follows from the second law of thermodynamics that: 


lt ; t O¥11 t Òy.s 1 
C ij za Ot 12 Ot 2+. | ae 


represents the potential energy gained in the time dt inside the space 
a in consequence of elastic tensions, so that we get 


Change in the potential energy = dT" = Zn dyn 
th 


Substituting in this the expressions for the tensions corrected for 
linear hysteresis according to VOLTERRA, we get: 
; 
dT = T(z days Yrs | Cyan + SL] DE wijs (et) yrs(©) dr] dyn 
th rs th 2 rs 
0 

Formerly the w’s were zero, and the reasoning ran: 

If there is to be an elastic potential 7”, the righthand member must 
be a total differential; this requires a set of fifteen equations, con- 
ditions of integrability in the 36 coefficients, viz. bij, = 6s ; when 
they were fulfilled, a function 7’ could be solved as elastic 


potential. 
We shall now prove that the conditions of integrability cannot 
be fulfilled. To this end we consider: 


th rs 


t 
aT! => i > bih|rs Vrs (t) In 5 Won [rs (tr) Yrs (7) dr } dyn . (J) 
"i rs 


Following Vouterra’s fundamental idea | divide the interval from 


1) The tih's are as always the elastic tensions, the yii’s the quantities of 
deformation. 


673 


zero to ¢ into n parts h,... h,; let the values of ¢ in the division 
points be respectively ¢,...¢,; then the equation (1) must be 
considered as limiting case of the following set of differential 
equations: 


dT'—_>S> bn, irs Yrs (t,) dy, A ie te (1) 
th rs 
= = | = KA sYrs (¢,) ale Wehirs (ty t1) Yrs (¢,) h,| dy ch ~ (2) 
th rs 
dT'— > > { bihjrs Yrs (¢;) = Ue Wi), [rs (t, t,) Yrs (t,)h, of ) 
the Ts (3) 


+ Wir frs (t, t.) Yrs (¢,) h,| AY ch ) 


at == = | = [bis Yrs (4) + Wih/rs (ty t,) Yrs (t,) h, a ) 
hor 
th s Sr (n) 
FU) [rs (tnt) Yrs (ty) Age AW frs (tn Enzi) Yrs (tn t)hn—1 ayn ) 
As is known, the conditions of integrability of (1) may be derived 
as follows: 
Call its solution 7” (yin (¢,)), then: 


or 
ME s 
th Oyu (t,) 


this must be identified with (1); which gives: 

GE Det, (t ) (A 
— Nhirs Yrs oe Sade, ERS). Gh PF. 

Oy: (¢,) rs : ) 


hence 
or’ : 
Se sh 
Oy:h OY rs 
in the same way: 
5 : 
Ty Ze Or sfchs 
Onda 


hence as was known: 
Ds brs the 
Integration of (A) then yields as usual 
Td = = bAjrs Yih Yrs 

Now we get to (2). What are here in the righthand member the 
independent variables? The idea is that now 7” is no longer only 
a function of y,;(t,), but also of y,s(t,); these latter must, therefore, 
be added to the others and considered as new independent variables ; 
the meaning of the differential of y,,, as it is in (2), is clear: it is 
dyin (t,). We get: 

Conditions of integrability : 

Call the solution again 


674 


T (Yen (t,) Yeh (t,)) 


ryt oT" 
CS ee — EE, ae Sr th —d t 3 
SE dy (t,) + = a va (ts) 
and this must be identified with (2); this theo 
OT Nes 
Òya (t,) hi 
on 


Oya (t,) == = [Oct frs ¥ rs (ts) + Whjrs (tats) Yrs(t,) Ay] 
Among the various conditions of integrability there must also 


occur: 
drin gl ON 


Oyeh(t,) Òyrs (£,)  Òrra (ts) Oyen (&) 
We get on the lefthand side: 
00 
OYrs (t,) 


=) 


On the righthand side: 


a ar’ a 

t,) Hy Ty = LOnsirs Yrs (ts Wrs'rs (to) X Yrslt) h‚] = 

OYA (t‚) Òyrs(t.) OVA (t‚) rs | y ( yet ( ) Y ( " 
= rap Let, 


Hence W „sen (t,t,) must be =O. Likewise all the y’s must drop 
out. We can also prove that in (3), where also the y‚ (¢,) appear 
as new independent variables Wijjs (¢;¢,) as well as Wijyrs (l‚t,) must 
drop out. All the yw’s must vanish. At the limit we get that Wij, (fr) 
must drop out, in other words: | 

The equation (J), in which the w’s do not drop out, can never 
be taken as the limit of a total differential equation Hence there is 
not to be found here a function of the present and earlier defor- 
mations, which acts as potential energy. 


Utrecht, June 1920. Institute for Theoretical Physics. 


KONINKLIJKE AKADEMIE VAN WETENSCHAPPEN 
TE AMSTERDAM. 


PROGGEDENGS 


VOLUME XX11I 
Ne. 5. 


President: Prof. H. A. LORENTZ. 
Secretary: Prof. P. ZEEMAN. 


(Translated from: ‘Verslag van de gewone vergaderingen der Wis- en 


Natuurkundige Afdeeling,’ Vols. XXVIII and XXIX). 


CONTENTS. 


F. M. JAEGER: “Some Remarks concerning the Röntgenograms obtained by means of Mica-Piles 
composed by crossed Lamellae”, p. 676. 

A. SMITS: “On the Validity of the Law of Partition for the Equilibrium between a Mixed-Crystal 
Phase and a Coexisting Liquid”. I. (Communicated by Prof. P. ZEEMAN), p. 679. 

A. SMITS and J. SPUYMAN: “The Thermo-electric Determination of Transition Points”. I. (Commu- 
nicated by Prof. P. ZEEMAN), p. 687. ; 

H. C. BURGER: “Observations of the Temperature during Solidification’. (Communicated by Prof. 
H. A. LORENTZ), p. 691. 

W. EINTHOVEN: “On the Observation and Representation of Thin Threads”, p. 705. 

A. PANNEKOEK: “The Distance of the Dark Nebulae in Taurus”. (Communicated by Prof. J. C. 
KAPTEYN), p. 707. 

A. PANNEKOEK: “Further Remarks on the Dark Nebulae in Taurus”. (Communicated by Prof. J. C. 
KAPTEYN), p. 720. 

G. HOLST and E. OOSTERHUIS: “The so-called cyanogen-bands”. (Communicated by Prof. H. KAMER- 
LINGH ONNES), p. 727. 

A. D. FOKKER: “The geodesic precession: a consequence of EINSTEIN’s theory of gravitation”. 
(Communicated by Prof. H. A. LORENTZ), p. 729. 

J. VERSLUYS und R. DEMOLL: “Die Verwandtschaft der Merostomata mit den Arachnida und den 
anderen Abteilungen der Arthropoda”. (Communicated by Prof. MAX WEBER), p. 739. 

A. A. HIJMANS VAN DEN BERGH and P. MULLER: “On Serum-lipochrome”, (Part II), p. 766. 

J. M. BURGERS: “On the resistance of fluids and vortex motion”. (Communicated by Prof. P. 
EHRENFEST), p. 774. 

P. E. VERKADE: “On the Action of Micro-organisms on Organic Compounds. II. The Solubility 
of some Organic Acids in Fatty Oils”. (Communicated by Prof. J. BOESEKEN), p. 783. 

H. C. BURGER and P. H. VAN CITTERT: “Measurements on the Intensity of Spectrum Lines by the 
Aid of the Echelon”. (Communicated by Prof. W. H. JULIUS), p. 790. 

K. W. RUTGERS: “Degenerations in Linear Systems of Prane Cubics”. (Communicated by Prof. 
JAN DE VRIES), p. 797. 

RASSA RIWLIN: “Photographic Absorption- and Extinction-Measurements. Contributions to the 
study of liquid crystals. V. Extinction-measurements”. (Communicated by Prof. W. H, JULIUS), 
p. 807. 

F. BERNSTEIN (Göttingen): “Die Integralgleichung der elliptischen Thetanullfunktion. Zweite Note: 
Allgemeine Losung”. (Communicated by Prof. L. E. J. BROUWER), p. 817. 


44 
Proceedings Royal Acad. Amsterdam. Vol. X XIII. 


Chemistry. — “Some Remarks concerning the Ronreunograms 
obtained by means of Mica-Piles composed by crossed 
Lamellae”’. By Prof. F. M. Jararr. 


(Communicated at the meeting of October 30, 1920). 


In a paper recently published *) on the RÖNTGEN-images obtained 
by means of a system of muica-lamellae crossing at definite angles gp, 
it was said in a Note on page 821, that the image obtained was 
evidently mot a mere superposition of the images which were 
obtained by means of each of the composing lamellae separately, 
but that the RÖNTGEN-rays, after passing the first lamella, were appa- 
rently influenced during their passage through the next one in such 
a way, that the final result differed noticeably from the combination 
of the single images turned with respect to each other through the 
angle p. This conclusion was founded in the first place on a com- 
parison of the stereographic projections of the composed photographie 
images with the image obtained by the nm times repeated superposi- 
tion of the stereographic projection of the diffraction-image 
produced by a single lamella; and, secondly, on the fact that in 
the final photograph a considerable number of the outer spots were 
absent, which in the image of the single lamella appeared with 
appreciable intensity. At the same time a systematical investigation 
of this phenomenon was planned, because it was in contradiction 
with the usual interpretation of the diffraction-phenomenon now 
generally adopted. 

At my request my colleague Haca was kind enough to make 
the necessary experiments in the Physical Laboratory of this Uni- 
versity; for his kindness and help I wish here to express my thanks 
once more. The result is, as will become clear in the following 
pages, that the conclusion mentioned in the Note on p. 821, cannot 
be considered as justified in its generality; and after these investi- 
gations we are compelled to acknowledge, that the images formerly 
obtained must really be considered to be, at least in their principal 
features, superpositions of the images of a single lamella, turned 
with respect to each other through angles p,‚ although certain devia- 
tions are certainly present, the causes of which will be explained 
further-on. 


1) F. M. JAEGER, Proceed. R. Acad. of Sciences Amsterdam, 22, 815, (1920). 


677 


The said experiments were executed by means of two very thin 
muscovite-lamellae, about 0,22 m.m. thick, which were obtained by 
cleavage from one and the same crystal, and which could be crossed 
with respect to each other at arbitrarily variable angles y. In all 
cases, in which the angles + were varied between O° and 60°, the 
RONTGENOgrams obtained appeared to be almost the complete super- 
positions of the images of the composing thin lamellae. From tbis 
result it became more and more probable, that the images formerly 
obtained might finally appear to be also such superpositions. For the 
purpose of investigating this more in detail, a negative was prepared 
from the original image of a single lamella, as reproduced in Fig. 1 of 
the Plate, and from this a number of equal diapositives were made 
on pieces of photographic film. These film-diapositives were now 
carefully piled-up at the angles p with respect to each other, in the 
same way as the lamellae in the mica-piles used formerly. The thus 
obtained combination was carefully compared in transmitted light 
with the original photos formerly obtained. Although some spots 
of the primary images did not coincide completely with other spots, 
also in these cases their mutual distances might be considered small 
enough to give together the final impression of one spot of greater 
intensity. If this be taken into account, the combined image is 
really in its principal features analogous to the photographic image 
of the mica-pile. However, there are certain deviations: some spots 
were lacking in the last photographs, which were visible in the 
film-image with rather great intensity; some spots were feebler than 
in the film-image, and generally the relative intensities of the spots 
were different from those in the image of the combined films. 

Partially, these deviations could be easily explained by the influ- 
ence of a selectwe absorption of some wave-lengths, as already stated 
in former cases, when the rays of the tungsten-anticathode of the 
Coolidge-tube pass through thicker layers of the crystalline medium. 
With the aid of a muscovite-crystal of 2,35 m.m. thickness it was 
possible, indeed, to prove that certain spots in the diffraction-image 
obtained with it, — e.g. the spot in the middle of the first circular 
row beneath the centre of Fig. 1 of the Plate, — were convin- 
cingly less intense than the corresponding spots in the image 
obtained with a 0,22 m.m. thick lamella of the same crystal; and 
exactly in those places also the spots were absent in the composed 
image of a mica-pile of circa 3,5 m.m. thickness. By intentional 
experiments, in which the time of exposure was regulated in such 
a way, that the influence of solarisation-phenomena of the most 
intensive spots was certainly excluded, it could be proved 

44* 


678 


beyond all doubt, that such a selective diminution of the 
intensities of some spots with respect to others really happened 
in cases where the ROnTGEN-rays had to pass through thicker layers 
of a crystalline medium. Undoubtedly this selective absorption is, at 
least partially, responsible for the abnormal intensity-relations in the 
composed photogram of the mica-piles, compared with the corre- 
sponding relations in the film-combination. However, a certain 
momentum for this appears also to be the strong veil on the back- 
ground of the photographic plate in the first case; a veil, which may 
in the final photos of the piles also be the cause of the absence 
of the outer and feebler spots of the image obtained with a single 
lamella, because the photographic plate could not be developed a 
sufficiently long time to make them appear upon it. This photographic 
veil is, therefore, also one of the causes of the misleading aspect 
of the photograms of the mica piles, so that they seem to be different 
from a true superposition of the images obtained with a single lamella. 
That besides this, also the use of the stereographical projections in- 
stead of the film-combination, formerly led us to a conclusion 
which is now acknowledged as erroneous, need not surprise us: 
for in the stereographical projections the intensity of the different 
spots was not measured photometrically, but estimated in a purely 
subjective manner, and in thus comparing different stereographical 
images with each other, properly incomparable intensities are checked 
with respect to each other. These circumstances may elucidate why 
the photographical images of the mica-piles were formerly not 
recognised as being mere superpositions of the single images com- 
posing them. However, the veil of the photographic plates is probably 
amongst all cooperating causes of greater influence than the unequal 
diminution of the intensities of the spots by selective absorption. In 
any case no truly new phenomenon is here present of a kind in- 
conceivable with respect to the generally adopted interpretation of 
diffraction-phenomena in crystals. 


Physical and Physico-chemical Laboratories of the Unwersity. 
Groningen, October 1920. 


Chemistry. — “On the Validity of the Law of Partition for the 
Equilibrium between a Mixed-Crystal Phase and a Coexisting 
Liquid’. 1. By Prof. A. Smits. (Communicated by Prof. 
P. ZEEMAN). 


(Communicated at the meeting of May 29, 1920). 


Since 1911 [ have more particularly been oecupied in researches 
which in connection with the theory of allotropy were undertaken 
with a view to the study of the solid state. 

These researches had led to views about the solid state which 
are incompatible with the image given by Braaa in view of the 
R6ntgen-spectra found by him. 

Mr. Scuerrer and myself') have pointed out that when a grouping 
of atoms is assumed in the lattice points of a crystal lattice, the 
bindings being disregarded in accordance with the valence, there 
arise great difficulties. On that occasion we gave a model solely 
with a view to indicating the direction in which in our opinion 
the solution should be sought, and it is clear that the question 
whether this model it serviceable or not, leaves the objections ad- 
vanced by us against BraGe’s representation, entirely intact. Our 
paper was written solely to set forth these objections. Our efforts 
are only tentative as yet, and it seems to me that the Röntgen 
investigation of the solid substance in its present state does not yet 
enable us to get to know the real internal condition. 

Nevertheless this investigation must be considered of the utmost 
importance, and the hope may be cherished that continuing in this 
direction one day the way will be found that leads to that which 
interests us most, viz. to the manner in which the chemical action 
in the solid substance is manifested. 

The objections to Brace’s conception will be fully discussed and 
snpplemented elsewhere; here I will, however, point out that it 
might be said that the objections for a definite group of compounds, 
viz. those that are built up of two elements and can split up into 
ions, might be partly obviated, when it was assumed that this 
dissociation in the solid state was a complete one. 

It is clear that then for this group of substances as KCl and 


1) These Proc. 19, 432 (1916). 


680 


NaCl ete. the difficulty with regard to the valence would disappear, 
but then there would be no atoms, but ions, in the lattice points, 
and a chemical binding would not occur. Accordingly, the 
replacement of the atoms by ions in Brage’s image would already 
be an important modification for the said substances in the right 
direction. 

Of late Desir’) has published results that seem to prove that 
this is really the case with LiF. 

It is hardly necessary to observe that for all other compounds, 
which are. built up of more than two elements, and yield compound 
ions, the valency must find expression, because also on complete 
dissociation in the solid state this compound ion must be present as 
a group. But also for a compound composed of two elements, as 
Hel,, the assumption of complete dissociation into ions cannot lead 
to a solution, because this does not account for the existence of 
internal equilibria. 

I will, however, not continue this train of reasoning any further 
here; it only served to call attention once more to the fact that 
from a chemical point of view, the action of the valency in the 
solid substance cannot be disregarded; hence it is clear that it is 
desirable to find other methods which may teach us something about 
the internal condition of the crystallized substance. 

Some years ago I had already formed the plan to examine whether 
Nernst’s law of partition is valid for the coexistence of a mixed 
crystal phase with a solution. 

It is clear that Nernst’s law of partition can only be valid for 
this case, when the ordinary thermodynamic considerations, which 
lead to this law in equilibria between a gas and a liquid phase or 
between two liquid phases, may also be applied to the solid sub- 
stance. This is the fundamental question ! 

Van ’t Horr’), who was the first to point out in 1890 that there 
are states which may be designated by the name of solid solutions, 
embraced the opinion that the theory of diluted liquid solutions 
might be applied to these states. 

BakHuis Roozesoom ®), who started his important experimental 
researches on mived crystals a year later, practically treated the 
mixed crystals thermodynamically already in the same way as the 
liquid solutions had been treated, and it might be said that the 
experiment has justified this procedure, as the derived types were 


1) Phys. Zeitschr. 19, 474 (1918). 
1) Z. f. Physik, Chem. 5, 322 (1890). 
3) Z. f. Physik. Chem. 8, 504 (1891). 


651 


actually found, and there thus appeared to exist a very close 
agreement between the equilibria of a solid with a liquid phase on 
one side, and two solid phases on the other side. 

Already a few years after these publications Fock ') undertook 
an investigation on the partition of a third substance between mixed 
crystals and solutions, but there was not found a constant value 
for the coefficient of partition in a single case. If, therefore, this 
investigation had not been open to criticism, the conclusion might 
have been drawn from it, that the law of partition cannot be 
applied here. 

Fock’s results did not carry conviction, however; 1. because he 
omitted to examine the equilibria in which the substance to which 
he wanted to apply the law of partition was present in small concen- 
trations; 2. as he underrated the difficulties to obtain a homogeneous 
mixed crystal phase. 

BeLiatr and Lusanna’*) and also RoramunD tried to determine the 
molecular size of the dissolved substance from the lowering of the 
transition point of KNO, by the application of Van ’r Horr’s well- 
known formula for the lowering of the freezing point, in which 
the heat of transition was then substituted for Q. 

RorHMUND *), however, soon saw, that this formula is not valid 
when mixed crystals are deposited, and for this case arrived at the 
formula: 


Ree 
Gs IG ree TROUT. Seat EY 
in which: 
M, = mol. weight of a solvent. 
x, == eoncentration of the first phase. 
Lp = Dn Seconde 


This formula is valid, and follows immediately from VAN DER 
Waars’s general equation for two-phase coexistence : 


dv | dn ’ 
Uo 2 (v,— @,) dp = In. ne, %,) |az == 
dx, /P.T. da, / P.T. 


era) ae 
ve vy de, Pae 


When the considered mixed crystals contain very little of the 


1) Z. f. phys. Chem. 12, 657 (1893) 
Z. f. Kryst. 28, 336 (1897). 
2) Atti de Reale Instituto Veneto [7] 26, 995 (1891). 
3) Z. f. phys. Chem. 24, 705 (1897). 


682 


second component, i.e. when 2, and a, are small, the above equa- 
tion may be simplitied, for in consequence of the small value of 
« we may then write: 


ie) i RT 
dx,*)/p.7T. 2, (1—«,) 


and when we neglect wz, by the side of 1, the coefficient of dz, 
becomes: 


When we now consider the equilibrium between a mixed crystal 
phase and a liquid, or between two mixed erystal phases at constant 
pressure, we get: 


il Vann 
(4,—7,) dT = — RT ——— dz, 
wv, 
and 7'(n, — 7,) being = — M, Q,, we get: 
ET 
MQ «, 
or 
(iig 
AT = —— x 
MQ (z, 1) 


This is RornMunp’s formula derived by another way. For the 
molecular lowering, i.e. for the lowering caused by 1 gr. mol. of 
the second component in 1000 gr. of the first the following equa- 
tion is obtained: 

NN OO 
de, 100005 z, 

From this it is seen that when the second phase is no mixed 
erystal, hence «, = O, this formula passes into that of Van 'r Horr. 

When we consider the lowering of the freezing point, brought 
about by addition of a second substance that forms mixed crystals 
with the first, only the second phase is a mixed crystal and the 
first a liquid. When we, however, direct our attention to a lowering 
of a transition point, the first phase is a mixed crystal, and in 
general the second will be so too, just as in the case of solidification. 
(Cf. the subjoined figure). 

It follows from the above relations that when we may treat 
diluted mixed crystal phases thermodynamically as diluted liquid 
solutions, the molecular size of the second substance present in the 
second phase in small concentration with regard to the molecular 
size of the same substance in the first phase, can be found from the 


683 


lowering of the point of solidification, and from that of the point of 
transition on analysis of the coexisting phases and on measurement 
of the thermal quantity Q. 

Roramunp, who examined the system CBr,—CCi,, has not succeeded 
in determining w, and z,. He could not 
observe the range of solidification, and 
only found the lowering of the point of 
solidification proportional to the total- 
concentration. Nor did he know the 
value of Q, so that he could not test 
formula (1). 

On the occasion of his examination of 
the system HgJ,— Hg Br,, Reivers’) used 
Rotamunn’s formula for the first time 
applying it to the lowering of the trans- 
ition point. 

As ReEINDERS’s research was not ex- 
pressly undertaken with a view to testing 

MG RornMUND’s formula, and as it was not 
accurate enough for this either, it can only be concluded from this part 
of his interesting treatise that probably Rorumunn’s formula will be 
confirmed here, and that when it is assumed that here really a 
definite conclusion can be reached with regard to a molecular size, 
it will lead to the result that the molecular size of mercury bromide 
is the same in the two mixed crystal phases. 

It follows from the foregoing that there was still a large lacuna, 
and that we were not at all able yet to say to what results the 
application of the let us say, limiting laws, to the equilibria with 
mixed crystals, lead. 

And because it is the study of the diluted mixed crystals that will 
be able in my opinion, to give us a deeper insight into the solid 
state, I resolved to set on foot a most careful inquiry into the 
question whether the law of partition also holds in case of coexistence 
with mixed crystal phases. 

It was to be foreseen that the investigation would be very difficult 
and laborious, for reliable results can only be expected when the 
mixed crystal is perfectly homogeneous, so that the internal concen- 
tration is the same as that of the surface. In order to bring this 
about it was necessary that the formation of the mixed crystals 
should take place exceedingly slowly amidst vigorous stirring. 


1) Zeitschr. f. physik Chem. 32, 494 (1900). 


684 


My first assistant, Mr. G. Meer, to whom I suggested this 
investigation as a subject for his thesis for the doctorate, has been 
so fortunate as to obtain results for the system dichlor-benzene- 
dibrom-benzene-aleohol that gave for the first time an indubitable 
answer to the question proposed here. On the side of dichlor-benzene 
the law of partition appeared to hold within the errors of observation 
for the distribution of dibrom-benzene between solution and mixed 

TABLE I. 
RESULTS ON THE SIDE OF DIBROMINE. 


ST A LTS ES, i TE ETE, 


bene per1000 ee hol ee ooo) K a Ks 2 a ner 

eee ‚cm? solution pre IGE | KS i CG: 
38.7 4.76 52.7 1.23 5.90 3 AT 
48.7 6.31 53.7 1.30 8.18 2.66 
54.8 6.71 54.2 1.23 8.21 . | oen 
55.0 6.64 saa | do 8.02 2.19 
51.6 8.12 55.8. |. tadl 11.44 | 2.45 
61.7 8.32 55.8 1.35 11.22 | 2.49 
15.3 9.47 56.7 1.26 11.91 | 1.60 
83.6 10.11 58.1 1.21 12.23 1.45 
100.2 13.69 59.2 1.37 18.70 1.36 
118.3 13.97 59.5 1.18 16.49 0.99 
123.7 16.83 64.0 1.36 22.81 | 1.09 
190.5 | 24.97 71.0 1.31 32.13 | 0.69 
286.3 | 38.9 ae | 149 40.29 0.41 
564.8 |. 42,95 87.5 0.76 3443 | 0s 


crystal, and the same thing was found for the distribution of dichlor- 
benzene on the dibromine side. Greater deviations were always found 
with greater concentrations, coming from both sides, as was, indeed, 
to be expected. This result was obtained on the assumption that the 
molecular size of dichlor- resp. dibrom-benzene is the same in the 
mixed erystal phase as that in the coexisting solution. 

The foregoing Table I gives a concise summary. 


C 
It follows from this table that only the quotient = yields a very 
S 


685 


little oscillating value, and as the second decimal value, though it 
has been given, is quite unreliable on account of the error of ana- 
lysis, we see that in spite of the experimental difficulties of the 
research, the oscillations in the values may be called slight beyond 
expection for the above quotient. Hence the obtained results show 
beyond doubt that this quotient in the concentration region examined 


TABLE Il. 
RESULTS ON THE DICHLORINE SIDE. wer 
Gr. dibrom-b.| Gr. dibrom-b. |, tal conc. K 10 K K.10 
per 1000 cm3 | per 1000 cms [PSE PE cy | yp Ce ier 
mixed crystal solution fran | Cs Cs C2 
29.58 1.713 142.7 5.85 9.92 19.6 
fede, <0 4.497 143.1 5.66 2.52 7.2 
19.18 4.496 1427 | 568 2.56 7.2 
103.7 5.785 141.1 5.58 3.23 5.4 
99.04 5.460 128.5 5,51 4.71 5.6 
155.0 8.521 139.7 5.50 4.68 3.5 
167.6 9.912 136.7 5.91 5.86 3.5 
170.8 | 9.599 137.1 5.62 5.40 3.3 
173.8 9.305 136.8 5.35 4.98 3.1 
ats 11.39 135.6 5.24 5.83 2.4 
265.5 14.24 135.6 5.36 1.64 2.0 
329.2 17.17 133.6 5.22 8.96 1.6 
385.0 20.01 132.5 5.20 10.40 1.4 
460.2 23.67 131.5 5.15 12.17 1.1 
491.7 A23 127.4 4.82 11.43 0.98 
506.4 Le 128.5 4.64 10.92 0.92 
507.3 24.28 125.4 4.79 11.62 0.94 
528.3 25.57 128.5 | 4.84 12.37 0,92 
643.7 28.22 125.4 4.38 12.37 0.68 
651.1 28.90 125.4 4.44 12.83 0.68 
676.9 26.09 125.4 3.89 10.06 0.57 
686.7 29.52 125.1 4.30 12,69 0.63 


686 


here, which extends in the saturate solution up to 0,231 gr. mol. 

per liter and in the mixed crystal phase up to 1.947 gr. mol. per 

liter, is really a constant quantity. With greater concentrations the 
C 

quotient = presents a course as was also to be expected; the quo- 
S 

tient then becomes smaller, as the latter value indicates. 

Now that this result had been obtained, it was of course supposed 
that also on the dichlorine side the law of partition would prove 
valid. Mr. Meyer’s investigation yielded results in concordance with 
this expectation, which are recorded in: Table II. (see p. 685). 


C 
Here too only the quotient a yields values that vary only within 
S 


the errors of analysis over a definite range of concentration, viz. 
up to a dibromine concentration in the solution of 0,04 gr. mol. 
and in the mixed crystal of 0.72 gr. mol. Hence we may conclude 
that this quotient, which has of course another value than the 
corresponding quotient on the di-bromine side, is in reality a constant 
quantity. 

The results given here are of great importance. They justify us in 
concluding that also for the diluted component in a diluted mixed 
crystal GiBBs’s paradox will prove to be valid, and that we may, 
therefore, write for the equilibrium between a mixed crystal phase 
and a saturate solution: 

RT na, + F(v ‘ DD, =—— pall in Es + Q(v. Ie 


In a subsequent communication we shall see what conclusions 
may be drawn from the value of the factor v with regard to the 
molecular size of the diluted component in the mixed crystal phase. 

Meanwhile Mr. Meyer is carrying on the investigation with other 
substances, among which also electrolytes. 

Laboratory of general and inorganic Chemistry 
of the University. 

Amsterdam, May 28, 1920. 


Chemistry. — “The Thermo-electric Determination of Transition 
Points”. 1. By Prof. A. Smits and J. Spurman. Communicated 
by Prof. P. Zeeman. 


(Communicated at the meeting of June 26, 1920). 


In 1912 the transition point of tetrogonal tin into rhombic tin 
was determined by means of very lengthy and laborious determina- 
tions. Small quantities of mercury accelerated this transformation, | 
but at the same time brought about a lowering of the transition 
point. Through extrapolaticn up to the quantity of mercury = 0 
200°.5 was found as transition temperature, the subsequent experi- 
ments with pure tin, which gave a great deal of difficulty, yielding 
+ 202°.8 in the end.) Though it has appeared that also in other 
cases mercury is a catalyst for the transition from one metal modi- 
fication to another, so that this expedient may often be successfully 
applied, it seemed very desirable to try and find another reliable 
and quicker method. 

That thermo-elements can only be used over a range of tempe- 
rature, within which no points of transition of the metals used 
occur, is known, and likewise the conclusion of the existence of a 
transition point was drawn before from a discontinuity of the change 
of the electomotive force with the temperature. 

Thus among others in the examination of the thermo-elements 
Niekel-Copper*) and Nickel-Lead*) a discontinuity was found between 
350° and 360°, which points to a transition point of Nickel, with 
which also the study of the magnetic and mechanic properties and 
also the investigation of the change of length carried out by JÄNECKE, *) 
is in agreement. Further BripGMAn °) investigated the thermo-electric 
force of thermo-elements under pressure; we may, accordingly, say 
that the thermo-element has been used already several times to 
discover a point of transition in one of the metals of the thermo-element. 

That, however, on rational application the thermo-electric method 


1) Smits and pe Leeuw, These Proc. Vol. XV, p. 676. 

2) Harrison, Phil. mag. 3, 192, 1902; Wiener Z. f. anorg. Chem. 83, 310 (1913). 
3) Proc. Roy. Soc. Edinburg, 8, 182 (1872—1873). 

4) Z. f. Electr. Chem. 9 (1919). 

5) Proc. Amer. Acad. 53, 269 (1918). 


688 


supplies us with a method pre-eminently fit to discover transition 
points in metals, both on account of its accuracy and quickness, 
this was not yet known. 

This we found in the following research, which was undertaken 
with a purpose to discover the above-mentioned transition point also 
by a thermo-electrie way. For this purpose we first examined what 
metal combined with tin promised a good result. For reasons which 
will further be set forth in the theoretical discussion of this method, 
iron was chosen as second metal. 

The investigation of the electro-motive force of this element at 
different temperatures gave the following result: 


IRON-TIN. 

eae 

Temperature E. F. in milli-Volts 
139.89 1.30 
146.8° 1.31 
172.4° 1.39 
183.59 1.46 
196.69 1.63 
199,20 1.69 
204 :0° 1.72 
208.4° 1.74 
212769 1.79 


after sudden cooling 


180.09 1.65 
180.09 1.59 
180.09 1.53 
180.09 1.46 
180.0° 1.43 
170.4° 1.38 


When we represent this result graphically, we get fig. 1, from 
which we see that the transition point appears very clearly, and 
lies at 200°.2, which result is in perfect harmony with the extra- 
polated value which followed from the dilatometer-examination of 


689 


mercury-containing tin. What was also very clearly to be seen here 
was this that, when a temperature lying above the melting-point of 
tin, was rapidly Jowered, the transformation failed to appear, and 
the metastable prolongation of the upper branch could be followed 


180 


COPPER-TIN. 
Temperature E. F, in milli-Volts 
158.0° 0.52 
183.0° 0.63 
198.0° 0.71 
218.8° 0.79 
210509 0.75 
207.09 0.74 
191.09 0.67 
181.09 0. 62 
153.09 0. 50 
150.29 0. 49 
202.09 0. 73 


690 


for some distance. If the temperature was then kept constant, the 
E.F. decreased till the stable branch was reached (see the points 
OE Or Es U, 4): 

In the second place tin was combined with copper, in which the 
following result was reached. 

When these results are again represented graphically, the transi- 
tion point of tin again makes its appearance at 200°.5, in agreement 
with what precedes, but less clearly here. This is seen in fig. 2. 


When in this way the reliability of this sensitive and rapid 
method had been proved, we applied it to ascertain whether 
in copper indications for a transition point could be observed in 
the neighbourhood of 70°. As is known, the dilatometrie investi- 
gation *) gave no indication at all, no more than BRIDGMAN’s researches. 

The result of this investigation will be discussed in a following paper. 


Laboratory of general and inorganic chemistry of 
the Amsterdam University. 
Amsterdam, May 23'd 1920. 


1) CoHEN, These Proc. Vol. XVI, p. 628. (1914). Z.f. phys. Chem. 87, 419 (1914). 


Physics. “Observations of the Temperature during Solidification’. By 
Dr. H. C. Burger. (Communicated by Prof. H. A. Lorentz). 


(Communicated at the meeting of June 26, 1920). 


1. When in a supercooled liquid in a cylindrical tube, a seed 
of the solid substance is inserted, the boundary plane of the solid 
substance moves with uniform velocity. This velocity (linear velocity 
of crystallisation) has been measured by many investigators as func- 
tion of the temperature of the surroundings (thermostat), in which 
the tube is placed. They have, however, not measured the temperature 
prevailing during the solidification in the two phases and at their 
boundary plane, though it is the measurement of this temperature 
that is of great importance for the true insight into the process of 
solidification. More than once the opinion has been expressed that 
at the boundary plane solid-liquid the meltingpoint-temperature would 
prevail *), but no grounds were adduced in support of this statement. 
As, however, appears from my observations this is not the case, at 
least not for the substance examined by me. | 

The small quantity of substance. hence the small quantity of heat 
which is generated, renders it necessary that the instrument with which 
the temperature is measured, should have a very small heat capacity. 
If this is not the case, the distribution of the temperature in the 
substance is disturbed by the insertion of the instrument to such a 
degree that the temperature that is observed, is by no means equal 
to the temperature that would prevail at the same place, when this 
was absent. Besides the measurement of the temperature must take 
place with an instrument that possesses slight inertia, because the 
temperature that is measured at a fixed point of the tube, rapidly 
changes with the time. The temperature further shonld be registered, 
because reading is impossible on account of the rapid variation. 

Consequently a temperature measurement must be chosen which 
is made by the aid of a thermo-element, which must have as small 
a mass as possible. The current supplied by this thermo-element in 
consequence of the rise of temperature in the tube, must be observed 
with a galvanometer, which is sufficiently rapid to follow the process 


1) W. HerGESELL, Ann. d. Phys. u. Chem, 15, 1882. p. 19. 
G. Tammany, Kristallisieren und Schmelzen, 1903, p. 135. 
45 
Proceedings Royal Acad. Amsterdam. Vol. XXIII. 


692 


of solidification withaut appreciable inertia. Having at my disposal 
instruments that fully met all imposed requirements *), I could venture 
to make an attempt to solve the problem proposed with a fair 
chance of success. 

The method of observation was as follows. Two small holes were 
bored in a glass tube at points which were diametrically opposed 
to each other. The thermo-element was put through these apertures. 
It consisted of termo-sheet tin of Dr. Morr, which had been rolled 
out for this research to a thickness as small as possible. The thermo- 
elements that were used in the final observations, had a thickness 
of 1.4 u. Strips of this material were cut about 0.1 mm. wide, one 
half of which consisted of manganin, the other of constantan. Such 
a strip was put through the openings made in the wall of the glass 
tube. Before cementing the thermo-element care should be taken 
that it was spread ont flat, normal to the axis of the tube, and 
further that the place where the metals were soldered together, was 
exactly in the centre of the tube. The cementing substance had to 
be proof to the substance with which the tube was filled (salol), 
and had to adhere to glass and metal. A mixture of water-glass 
and asbestos powder appeared to satisfy these requirements ®). 

Copper wires, which led to the galvanometer, were soldered to 
the extremities of the thermo-element, which projected outside the 
wall of the tube. The coil of the galvanometer had a very small 
moment of inertia, so that the instrument indicated quickly. In 
order to enhance the rapidity, the suspension-wires of the coil were 
chosen fairly thick. This, indeed, decreased the sensitivity, but it 
was nevertheless sufficient to enable us to measure accurately the 
rises of temperature that had to be observed. The time of adjustment 
of the galvanometer was about 0.07 sec. 

The glass tube was now filled with the melted substance, for which 
| have chosen salol. This substance offers some advantages, viz.: 

1. The rate of crystallisation is small, at most 3.68 mm. 
per minute. Consequently the conditions imposed on the method of 
measurement are not so great as with substances that crystallize 


1) It is with great pleasure that I express my indebtedness to Dr. W.J. H. Mou 
for the use of the unequalled combination of instruments of his own invention, 
without which the measurement of the rapid local temperature changes would 
certainly have been impossible. 

2) Between two observations the tube of salol had to be placed in hot water 
to melt the salol again. In order to protect the solidified mixture of asbestos and 
waterglass against the action of the hot water, it was covered on the outside 
with Canada balsam. 


693 


more quickly. The instruments are however sufficiently rapid to 
be also serviceable in case of more quickly crystallizing substances, 
though the accuracy will then, of course, be less. 

2. Salol can be supercooled very easily. Spontaneous crys- 
tallisation, without solid substance being purposely added to the 
supercooled liquid, can be almost entirely excluded. The spontaneous 
setting in of crystallisation only becomes troublesome with very 
strong supercooling (more than 40°). This is, however, only the 
case when the substance is kept sufficiently dry. A slight quantity 
of water immediately causes the formation of ‘seeds’ of the solid 
substance in different parts of the liquid. Observation is rendered 
impossible by this. 

3. The melting-point of salol is very conveniently situated (42° C.), 
so that the observations can be made in the neighbourhood of 
room temperature. 

The observation is now carried out in the following way. The 
crystallisation is started on the upper side’) of the liquid, which 
is in one leg of a U-shaped tube, by the introduction of a small 
quantity of the solid substance. For this purpose the tube is placed 
in a well-stirred thermostat filled with water. In this way the joints 
of the extremities of the thermo-element and the copper wires con- 
ducting the current to the galvanometer, are kept at the constant 
temperature of the water in the thermostat. Accordingly the galva- 
nometer indicates the difference of temperature of the joint in the 
axis of the cylindrical tube and the thermostat. The deflection of 
the galvanometer was photographically registered, so that the regis- 
tered curve enables us to see and measure at a glance how the 
temperature has changed at a definite point of the axis in course 
of time. 

The curve obtained, has however, still another meaning. During 
solidification, the boundary plane of the solid and the liquid 
phase moves with constant velocity and retains its form. This ren- 
ders it probable, that the distribution of the temperature in the solid 
substance and in the liquid will also move unchanged with this 
velocity. A theory of the process of solidification confirms this sup- 
position °). The temperature which is registered at a definite point as 


1) To avoid convection currents in the liquid, the crystallisation must proceed 
from above downward, and not inversely. The liquid has, indeed, the highest 
temperature at the surface of the solid phase, where the heat of fusion is liberated. 
If the hottest place of the liquid is at the top, convection currents through diffe- 
rence of temperature cannot occur. 

5 H. C. Bureer, These Proc. XXIII 1920, p. 616, further cited as loc. cit. 

45* 


694 


function of time, is also the distribution of temperature that prevails 
at a definite moment as function of place in the axis of the tube. 
This distribution of the temperature moves, as it were without 
changing with uniform velocity along the thermo-element, and the 
temperatures, existing simultaneously at the different points of the 
tube, are successively observed. 

In order to be able to derive the difference of temperature between 
the joint and the water in the thermostat, from the deviation of the 
galvanometer, the amount of the deviation corresponding with one 
degree, must also be known. For this purpose a current has been 
sent through the galvanometer circuit at the beginning and the end 
of every observation by an electromotive force of known value 
(2 «x 10-4 Volts) for some seconds. The deviation given by this 
current has also been registered. 

When the electromotive force of the thermo-element for one 
degree of temperature difference is known, the temperature may be 
derived by comparison of the deviations during the solidification and 
that which the known electromotive force has caused. A determi- 
nation of the electromotive force with thermo-sheet tin of the kind 
out of which the thermo-elements used had been cut, had as result 
that it amounted to 41.3 >< 10-® Volts’). 

As in these observations rapid variations of the temperature must 
be registered, the registering drum must rotate quickly. This being 
difficult to achieve with a clock-work provided with a balance, the 
balance was replaced by a flying-pinion. The objection to this way 
of propulsion, however, is that the movement of the registering 
drum is not uniform. For the determination of the temperature as 
function of the time from the temperature curves obtained, it was 
therefore necessary to place time signals on every curve. They 
were obtained as follows: a resistance was placed in the circuit 
of the Nernst lamp, which sends its light to the mirror of the gal- 
vanometer, and then in the registering drum. The extremities of 
the resistance were connected with a clock work, which every 10 
sec. effected a contact between them momentarily. In consequence 
of the diminished resistance the intensity of the lamp increased 
every 10 sec. for a short time; hence the registered line shows 
slightly thickened parts, which recur at intervals corresponding with 
this period. This method has the advantage that there are no gaps 
in the registered curve. 


1) This result is in perfect harmony with what others have found for unrolled 
material. 


695 


One of the registered lines is reproduced in Fig. 1°). 
The following pecularities are to be noticed with regard to this 


Fig. 1. 


line. On the lefthand side the line is horizontal and straight’). This 
means that the temperature was constant at the beginning of the 
observation. This constant temperature prevailed in the liquid which 
at first surrounded the thermo-element, and was equal to the tem- 
perature of the thermostat. The boundary of the solid phase was 
still too far off to heat the surroundings of the thermo-element 
through the heat of fusion liberated there. When the solid phase 
approaches the thermo-element, the temperature begins to rise, and 
the curve presents an ascending branch. When the boundary plane 
of the solid and the liquid phase has reached the thermo-element, 
the temperature is maximum; the curve presents a sharp point. 
Then the temperature is seen to fall again, and finally it reaches 
again a constant value on the righthand side of the figure, viz. the 
temperature of the thermostat. In this last stage of the process, the 
thermo-element is in the solid substance, and the surface of the 
phases is so far distant that the generation of heat taking place 
there, has no influence then. 

In this curve the maximum is of the greatest importance. It 
indicates the temperature of the boundary between the two phases. 
This temperature determines the velocity with which the boundary 
moves in the direction of the solid substance towards the liquid. 
The relation between the temperature at the boundary of the phases 
and the linear velocity of crystallisation depends on the nature of the 


1) The curve of fig. 1 was registered in 9 minutes. 

®) The break in the horizontal line is caused by a constant electromotive force, 
which enables us in the way described on p. 694 to find the temperature from 
the deviation of the galvanometer. 


696 


substance, and not on external circumstances. This is not the case 
with the further course of the curve. This course depends on the 
properties of the tube in which the crystallisation takes place, and 
can be calculated when the necessary data about the crystallizing 
substance and the tube are known’). 

As it is of importance to determine the accurate value of the 
temperature of the boundary, it is necessary to consider the sources 
of errors that may play a part in the measurement. 

The vertex of the registered curve in Fig. 1 is sharp, and makes 
the impression that phenomena of inertia have not played an im- 
portant part even in the quickest part of the process. This sharpness 
is, however, only apparent. When the quickness of the registering 
drum is increased, and the sensitiveness of the galvanometer dimi- 
nished, the top of the curve appears to be more or less rounded, 
as is seen in Fig. 2. 


Fig. 2. 


This rounding is not found in Fig. 1, because there the scale of 
the figure is smaller in horizontal direction, and larger in vertical 
direction than in Fig. 1. The cause of the rounding lies in the 
finite dimensions of the thermo-element. 

By extrapolation of the two branches of the curve, as is 
indicated by the dotted line in Fig. 2, an ideal curve may be traced, 
which would give the course of the deflection of the galvanometer, 
when the thermo-element was infinitely small and the galvanometer 
infinitely quick. That this extrapolation cannot lead to a much higher 
temperature than is shown in the figure, may appear from the 
following considerations and experiments’). 

1. The inertia of the galvanometer cannot give rise to an appre- 
ciable error. The temperature changes during its adjustment (0,07 sec.) 
by only a very small amount, even at the moment of its most 
rapid ascent or descent. 

2. As may be understood a priori, the breadth of the thermo- 


ble. 
4) This appears, however, most convincingly from the agreement between the 
calculated and the observed temperature (see p. 701). 


697 


element has only little influence on the observed temperature. Both 
the quantity of substance that is to be heated (metal of which the 
thermo-element consists) and the quantity of substance which directly 
causes the heating (salol), are about proportional to the width of the 
thermo-strip. The rise of the temperature will, therefore, not depend 
on this width. 

The width can, however, have influence on the rise of the 
temperature of the joint, because the heat which the thermo-strip 
leads off through the glass wall, is proportional to the width. As 
an approximate calculation teaches, this quantity of heat is, however, 
very small, and will, therefore, not appreciably influence the result 
of the measurement. 

Observations with thermo-elements of different widths (75 to 
200 u) have proved that the rise of temperature decreases slightly, 
when the width of the element increases. This influence of the 
breadth is very probably owing to a slight obliqueness of the 
thermo-strip. If this is exactly at right angles to the axis of the 
tube, it indicates the temperature in a plane that is at right angles 
to this axis, and in which the temperature depends but little on the 
place. If, however, the strip is placed obliquely, it indicates a mean 
temperature of different perpendicular sections of the tube. The 
thickness of the layer over which the temperature is averaged, is 
proportional to the width of the strip. In consequence of this the 
top of the curve, which strictly speaking, ought to be perfeetly 
sharp *), is rounded, and the more so, as the thermo-element is 
broader with the same obliqueness. [f the thermo-element is adjusted 
with great care, this error cannot reach a great amount either. 

3. The influence of the thickness of the thermo-element is more 
difficult to estimate a priori, than that of the breadth. It is self- 
evident that the rise of temperature measured with thick material, 
is smaller than that which is determined with thinner thermo- 
elements. Whether, however, the real temperature is sufficiently closely 
approximated when the thickness amounts to 5 u, as was the case 
in my first measurements, can only be decided when the influence 
of the thickness on the rise of temperature, is examined. For this 
reason I have repeated the measurement with the same tube and 
at the same temperature of the thermostat, with thermo-elements of 
different thicknesses, varying from 1.4 to 13 u. As was to be expected 
the rise of temperature decreased with increasing thickness of the 
thermo-element. The difference in temperature, however, amounted 


!) i. e. where the differential quotient of the temperature as function of the 
time, would have to be discontinuous. 


698 


only to some tenths of degrees for the thickest and the thinnest 
material. After this the measurements were carried out with thermo- 
elements of 1.4 u thickness. The temperature which these thin 
elements indicate, differs so little from that which would be found 
with an infinitely thin thermo-strip, that the remaining error may 
be neglected by the side of the other errors. 


2. We shall now proceed tu a discussion of the results of the 
measurements guided by the theory *). 

In order, however, to be able to apply the theory, and also to 
be able to calculate the temperature that has been observed, a 
number of quantities must be measured, which occur in the theory. 

These quantities are: 

1. The linear velocity of crystallisation of salol at different tempera- 
tures of the thermostat and in tubes of different internal and externa 
dimensions ; 

2. The specific heat of the solid substance and of the liquid; 

3. The melting-heat of salol; 

4. The density of the solid substance and of the liquid; 

5. The thermal conductivity of the solid substance and of the 
liquid ; *) 

6. The interior and exterior radius of the tube. 

The results of these measurements were the following: 

1. The linear velocity of crystallisation was determined in three 
different tubes, which have also been used for temperature observa- 
tions. The temperature of the thermostat ranged between about 0° 
to 29° C. Measurements of the velocity of crystallisation above a tem- 
perature of from 22° to 29°, dependent on the thickness of the tube, 
have no value. When we get too near the melting-point (42°), the 
crystallisation proceeds irregularly, and the velocity of crystallisation 
is not constant. It can be observed that the surface of the solid 
phase, which is convex and smooth and has a definite form at 
lower temperatures, becomes concave and irregular of form. Theory *) 
is able to account for this fact. 

The maximum velocity appeared to be 3.68 mm. a minute in- 
dependent of the bore of the tube‘). This value refers to pure salol. 


!) Loe. cit. 

2) | take great pleasure in expressing once more my hearty thanks to Miss A 
M. Hurrnacet for the trouble she has taken to measure these quantities. 

3) Loc. cit. 

4) The temperature of the thermostat at which this maximum occurred, does 
depend on the dimensions of the tube. 


„699 


Impurities diminish the maximum velocity of crystallisation. Therefore 
the substance has been recrystallized before it was used, till the 
velocity of crystallisation no longer varied. *) 

2. The determination of the specific heat took place in the usual 
way in a calorimeter filled with water. The liquid salol had been 
fused into a glass tube to prevent crystallisation of the supercooled 
substance. 

The values found were for solid substances and liquids resp. 

é; = 0:35 
Cs = Cain 

3. In order to measure the heat of fusion, a tube filled with 
melted supercooled salol was put in the calorimeter, and then left 
till the temperature had become constant. By placing a particle of 
the solid substance into the supercooled salol, crystallisation was 
started. The heat of fusion followed from the rise of temperature 
found. The former depends on the temperature, in this way. that 
the increase per degree is equal to the difference c, — c, = 0.02 of 
the specific heats of the Jiquid and the solid phase. For the end in 
view determination of the value of the heat of fusion at a tem- 
perature not lying too far under the melting-point e.g. 16°, will 
suffice. 

As this temperature the heat of fusion is found to be: 


Q = 18.2 cal. 


4. The density of the liquid was determined in the supercooled state 
by means of a pycnometer, and amounted at room-temperature to: 


vla 

_ The ratio of the densities of solid and liquid phase was found 
from the contraction on solidification in a cylindrical tube. 

The density of the solid substance appeared to be: 

0, = 1:289: : 

5. The conductivity was measured in comparison with that of 
glycerine. These relative measurements were carried out in the 
following way. 


1) Great care should be taken not to heat the substance tov much above its 
melting-point, because a change takes place at higher temperature, which greatly 
diminishes the velocity of crystallisation. This phenomenon can possibly explain 
why Tammann has found a smaller value (3.46 m.m. per minute) forthe maximum 
velocity of crystallisation. When the substance which has been changed by too 
great heating, is recrystallized several times with avoidance of temperatures 
above 100°, the rate of crystallisation decreases. For the sufficiently purified sub- 
stance the value of 3.68 m.m. a minute is always again found for the maximum 
velocity of crystallisation. 


700 


The substances with known and unknown conductivity respectively 
are placed between three parallel copper plates. The upmost plate is 
electrically heated, the downmost is cooled with water. The differences 
of temperature between the plates have been measured thermo- 
electrically. The ratio of the conductivity of the two substances is 
found from the differences of the temperature and the thicknesses 
of the layers. When for glycerine the value: 

AS 12.5105 
is taken for the conductivity, the following values are found for 
solid and liquid salol respectively : 

A, == OORD 

Ans 43555, 10-5. 

It is worthy of note here, that the difficulties which are met with 
in measurements of conductivity of heat are greater than those in the 
other measurements which have been mentioned in this paper. Errors 
should therefore, for the greater part be attributed to the measure- 
ments of the conductivity. 

6. The exterior diameter of the tubes used has been measured 
with a micrometer screw. The interior diameter is determined by 
weighing of a quantity of mercury, which has filled a known length 
of the tube. 

The conductivity of glass, which has also influence on the meas- 
ured temperature, has not been determined. For this quantity 
different values have, indeed, been found according to the kind of 
glass that was examined, but the influence of the thermal conduc- 
tivity in the glass wall is comparatively small, so that a mean value 
suffices. For this has been taken: 

1 = LSO: 

By the aid of the results of the said measurements, the tempera- 
ture on solidification in a definite tube can be numerically calculated. 
The measurements having been carried out in a point of the axis 
of the tube, » =O should be put in the formulae. The calculation 
has only been completely carried out for a single case. The compar- 
ison of theory and direct observation cannot yield new results, but 
only corroborate the correctness of theory and observations. 

The tube for which the calculation was made, has as bore: 


a= 0.88 mm. 
The thickness of the glass wall was: 
d= 0:91 nim: 


The temperature of the thermostat was 16° during the observations. 
At this temperature the velocity of crystallisation was maximum in 


Temperaluarsuerhooging 


701 


the tnbe used. Hence an error in the temperature of the thermostat 
has little influence on the rise of temperature in the solidifying 
substance. 

The rise of temperature is measured as function of the time. The 
velocity of erystallisation being known, the temperature in the tube 
is easy to find as function of the position because the distribution of 
temperature prevailing at one moment moves uniformly past the 
thermo-element. 


theorelische kromme 
0 te xX waargenomen COmfUerAlaUr sly GIng 


On 
° hd 
* 
° 
a 
e 
° 0 
Le Afstand tel het grensolaf: 
= eee 
-02 -O4 9 
Fig. 3. 


Every ten seconds a time signal is given in the registered curve. 
The temperature has been calculated at the moment of these signals, 
and this has been done besides at the intermediate moments, so that 
the temperature is known every five seconds. The values thus 
obtained are drawn on four curves (fig. 3) with different symbols. 
Also the calculated curve is reproduced in the same figure. The 
ordinate represents the rise of temperature, and the abscissa the 
distance in cm. to the boundary plane of the phases. The agreement 
of the measurements with the theoretical curve confirms the correct- 
ness of theory and observation. 

Even without a complete calculation of the theoretical distribution 
of the temperature, a few particularities met with in the measurement 
of the temperature, can be explained from the theory. 


702 


1. At the same temperature of the thermostat the temperature of 
the boundary of the phases (maximum temperature in the registered 
curve) is the higher as the interior diameter a of the tube used is 
greater. Measurements with tubes of which the bore a varied from 
0,45 to 2,8 mm. had the result that the rise of temperature of the 
surface of the solid phase was about proportional to a. 

This observed fact is in accordance with the theory *), as may 
appear in the following way. 

If the glass wall of the tube is not too thick, it may be supposed 
that ‘approximately the temperature for r= a, i.e. at the boundary 
plane of salol and glass, is equal to that of the surroundings. The 
values 5, and &,, which occur in the theory, then become equal 
to the roots of the Bessel function J,, hence independent ofa’). In 
the constants p, and p,® the terms containing v are still smaller 


rey} 
compared with the term =. When the terms containing v are negleet- 
ed, we have approximately : 
ET 

Also the constants az, and 8, are approximately independent of 
a, because this is the case with £#. 

When we confine ourselves to the first and greatest term of the 
series that gives the rise of temperature @ as function of the distance 
« to the boundary of the two phases, we find for the temperature 
at this boundary : 

j= ee 
Oi {p,%) A, + pi) Js Gi, (A, + A.) 

It appears from this formula that really @ is about proportional 
to the radius a of the bore of the tube used. 

2. The registered curves are asymmetrical. The ascending branch 
(temperature in the liquid phase) is steeper than the descending 
branch (temperature in the solid phase). This difference is the smaller 
as the velocity of crystallisation v is the smaller. 

Theory completely accounts for these observed facts. The greater 
or less steepness of the two branches of the curve depends on the 
quantities p‚®) and p,®. It appears from the formulae 17 and 22 that 
in consequence of the term before the root-sign: 


pi <p." 
The difference of p, and p, is the greater as v is greater. 


1) loc. cit. 
2) loc. cit. p- 9 ef. p. 10. 
3) £,%) and &,(*) differ but little. 


703 


When v is zero, we find: 


E(k) 
p‚® = p= 
a a 


’ 


in this case p‚® and p, are almost equal, and the registered curve 
must consist of two almost identical curves. 


As was stated before (p. 696), the velocity with which the boun- 


Aristallisatiesnelhetd tri re. Mper pir. 


Temp eratuur van het grensvlak der „asen 


e = 2 
10 15 20° 25° 30° 


Fig. 4. 


dary of the phases moves, will depend on the temperature, prevail- 
ing at that boundary plane. The aim of my investigation was, 
besides testing the theory of the problem of the conductivity of 
heat which we meet with in cases of solidification, the determination 
of the functional relation between velocity of crystallisation and 
boundary temperature. This relation is completely determined by 
the nature of the substance (salol), and does not depend on the 
peculiarities of the method of observation *. 


1) In fig. 4 the observations made with different tubes, are indicated by different 
symbols. 


704 


Every registered curve can serve for the determination of a point 
of the curve that indicates the relation between rate of crystallisa- 
tion and boundary temperature. The sum of the temperature of the 
thermostat and the rise of temperature following from the curve, 
gives the boundary temperature. The temperature of the thermostat 
and the dimensions of the tube determine the velocity of erystalli- 
sation, which can be derived from the results of the measurements 
carried out with this purpose (p. 698). 

In fig. 4 the abscissa is the temperature of the boundary plane 
of the phases and the ordinate the velocity of crystallisation. As 
appears from the figure, the temperature does not reach the melting- 
point (42°) in any of the measurements, but always remains far 
below it’). The observations yielding temperatures of the boundary 
above 29° are of no value in consequence of the phenomenon 
mentioned on p. 698, hence they have not been reproduecd in fig. 4. 
When one wants to determine the portion of the curve above 29°, 
another experimental method must be followed, in which the process 
of soliditication has a mathematically defined course also near the 
melting-point, and does not depend on accidental disturbances. 

I am greatly indebted to the instrument maker of the Physical 
Laboratory, Mr. G. KoorscriJN, for the trouble he has taken boring 
the holes in the tubes used by me. 


Institute for Theoretical Physics. 
Utrecht, June 1920. 


1) J. Perrin, Ann. de Phys. Tome XI, serie 9, p. 96. 1919. 


Physiology. — “On the Observation and: Representation of Thin 
Threads’. By Prof. W. EINTHOVEN. 


(Communicated at the meeting of September 25, 1920). 


A fall discussion of this subject will be published elsewhere; a 
few conclusions, however, may be given here. 

|. Threads of 0.1 to 0.2 u can easily be observed with the naked 
eye as light lines on a dark background. Without difficulty they 
can be shot or blown, fixed, transferred, put under the microscope, 
bombarded, and stretched out in the galvanometer. 

2. Any thread that can exist, however thin it may be, can be 
made ultra-microscopically visible, when we are only able to bring 
it under the microscope in an efficient way. When it is assumed 
that in case of uniform radiation of a thread the quantity of light 
reflected by it, decreases in direct ratio to its diameter, the dia- 
meter of the thinnest thread visible is calculated at 0,2 « 10-6 uu, 
By way of comparison it may be said that the diameter of a hydrogen 
molecule is about a million times larger. 

3. The power to see the thinnest dark thread against a light 
background with the unaided eye is not determined by the dimen- 
sions of the cones on the retina, but by the power to distinguish 
two degrees of brightness. Two luminous points or luminous lines 
which approach each other more and more are still observed sepa- 
rately when they are represented on the retina at a distance apart 
corresponding to the diameter of a cone at which they appear at a 
visual angle of 60”; a thread, however, can still be seen at an 
angle of 2". 

4. Every circumstance which renders the microscopic image of a 
dark thread against a light background less sharp, increases the 
apparent diameter of the thread. As no microscope comes up to 
ideal demands, it may, therefore, be assumed, that the results of 
the measurements made with this instrument either agree with 
reality or give too high values, so that the threads mentioned in 
this paper are really 0,1 or 0,2 w thick or thinner. 

5. The conditions to observe the thinnest dark thread against a 
light background with the microscope, and represent it, are different 
from those which hold for seeing two luminous points or lines separate 


706 


which approach each other more and more. If the aperture of the 
projection-objective is MN and the wave-length of the light 2, the 
distance of the still distinguishable points or lines is generally 
assumed to be: 
a 
‘2 aN 

which for N= 0,95 and 42= 0,6 u yields the value of 0,31 u for /. 
The central diffraction-discs, which are formed in the image of each 
of the two luminous points, overlap for the distance of the length 
of the radius of the discs. 

On the other hand a thread of 0,2 u is represented sharply defined 
and contrasted with an objective of the same aperture. The edges 
are so sharply drawn that a number of small unevennesses becomes 
separately visible. 

6. When the same thread is represented with an objective the 
aperture of which is 0,18, the image becomes, indeed, less sharply 
contrasted and less detinite, but it remains clear enough to be useful 
for many purposes. In this the central diffraction discs formed of a 
luminous point on one edge of the thread, and of one of an opposite 
point on the other edge overlap to an amount of P= 94°/, of the 
diameter of the discs. 

7. In the direct observation of threads without application of the 
microscope we found as maximum values of P.... 98,2°/, and 
98,5°/,. Probably equally great and even greater values of P can 
be reached in the case of microscopic representation. 

8. There is every reason to assume that with commercial objectives 
a serviceable image may still be obtained of a thread of 0,04 uw. 

At the meeting photos were, in fact, exhibited of a bombarded quartz 
thread, the diameter of which was to all probability of the said 
order of magnitude. 


Astronomy. — “The Distance of the Dark Nebulae in Taurus’’. 
By Dr. A. PANNEKOEK. (Communicated by Prof. J. C. Kaprryn). 


(Communicated at the meeting of Sept. 25, 1920). 


§ 1. Various investigations made in recent years, have demonstrated 
ever more clearly the existence of dark cosmic nebulae, that aborb 
and weaken the light of the stars behind them. Between the luminous 
patches and streams in the Galaxy, dark spots and cavities are seen, 
which were originally considered as empty spaces in thestar-filled galactic 
system. The improbability of these empty spaces extending as conic 
tubes through HerscHel’s lenticular star-system, with our sun as 
vertex, constituted one of the main arguments for the conception of 
the Galaxy as a ring of no great extension in depth. For a long 
time the possibility that they should originate by means of absorption 
has played no part in the theories concerning the structure of the 
universe. 

It is through the photographs of Max Worr and BARNARD that we 
first have become acquainted with numerous details scarcely allowing 
of any other interpretation. Small dark spots are to be seen in the 
midst of the luminous star clouds; long, dark, fantastically shaped 
lanes intersect the luminous parts, and are evidently connected with 
faintly luminous nebulae. Max Worr has repeatedly pointed out the 
existence of extensive absorbing nebulous masses, as one of the 
main causes that determine the aspect of the Galaxy. The galactic 
system is then to be considered as a mixture of dense starclouds, 
luminous nebulae and dark nebulous masses. 

In an investigation of some star-photographs in Aquila '), comprising 
the densest parts of a starcloud and also a black spot therein, 
_ the author of the present article found that in the black spot the 
densities of the stars from the 11" to the 15" magnitude were all 
smaller in the same proportion, compared with the cloud besides it; 
if the spot were caused by absorption, the absorbing substance should 
therefore not lie in the far depths of the starcloud, but a great deal 
nearer by, so that it was only accidentally projected against this 
luminous background. 


1) A. PANNEKOEK. Investigation of a galactic cloud in Aquila. Proceedings R. A. 

of S. Amsterdam, Vol. XXI, Nr. 10. (March 1919). 

46 
Proceedings Royal Acad. Amsterdam. Vol. XXIII. 


708 


That objects of this kind do not present themselves in the Galaxy 
alone, became evident from the investigations of BARNARD, who 
published a list of 182 mostly small, dark objects, *) which, though 
they were best discernible against the bright background of the 
Galaxy, are yet to be found also outside it, and which here and 
there are even directly visible by means of telescopes as intensely 
black spots. The wide extension of this absorbing substance became 
evident in yet another way, by an investigation of the generai 
distribution of the stars up to the 11' magnitude’). It was found 
here that around two places with a considerable deficiency of stars, 
in Taurus and Ophiuchus, as around two centres of obscuration, there 
are wide regions where the number of stars is below the normal. 
As this investigation was carried out by means of averages over 
extensive regions, it could only give a general image, which could 
be equally well explained by a certain distribution of the stars in 
space, as by the effect of an absorption. But it became evident that 
in the one kernel, in Taurus, the distribution of the density of the stars 
to the 14% magnitude was very irregular, and that the poorest 
regions were precisely those, where, according to BARNARD’s catalogue, 
a number of black objects have accumulated; this points to absorpt- 
ion as the most likely explanation of the general distribution of 
stars over the sky we had found. 

We get a still clearer image of the irregularities in the star- 
distribution in this Taurus-region by an investigation of Dyson and 
Metottre*) by means of the FRANKLIN-ADAMS plates, which show the 
stars up to magnitude 15,8. The counts proved that there are mainly 
three regions of strongest obscuration, the irregular shapes of which 
are visible on the adjoining chart: about 3520™ + 30° (S.W. of 
5 Persei), 4'30™ + 26° (between the Pleiades and Tauri) and 
5h20m + 25° (S.W. of 3 Tauri). By comparing «the numbers of stars 
of different sources, they come to the same conclusion, that these 
absorbing nebulous masses must be situated relatively near to us. 
“Thus, taking the area as a whole, we find the number of stars is 
about one fifth of the normal number whether we go down to 
magnitude 97,0, 11,0 or 14,0. This would seem to indicate, that 


1) E. E. BARNARD, On the dark markings of the sky. Astrophysical Journal 49, 
1. (Jan. 1919). 

2) A. PANNEKOEK, On the distribution of the stars of the 11th magnitude. 
Monthly Notices of R. A. S. 79, 333 (March 1919). 

8) Str F. W. Dyson and P. J. Merorre, The region of the sky between R.A, 
3h and 5h 30 m and N. Dec. 20° to 35°. Monthly Notices of R. A. S. 80. 3 
(Nov. 1919). 


709 


if the small density is caused by absorbing matter, the screen cannot 
be at a great distance, say not more than 200 or 300 parsecs at 
most.” (l.c. page 6). However, as the P. M. of the stars up to the 
9th magnitude in the dark regions are found to be no higher than 
elsewhere, so that no larger average distance is pointed out, this 
conclusion again becomes uncertain. For the present investigation, 
which proposes to ascertain more accurately the distance of these 
absorbing nebulae, the chart of star-counts adjoined to their treatise 
proved to be most useful. 


§ 2. In order to deduce from the star-densities the distance of 
an absorbing nebula, we must first theoretically investigate what is 
the influence of an absorbing screen on the number of stars of 
different magnitude. We suppose that the luminosity-function is 
known according to the formula of Kaprryn; for the logarithm of 
the star-density as function of the distance we likewise, according 
to the empirical data, assume a quadratic formula. We call 1 the 
magnitude, M/ the absolute magnitude of the stars, and introduce as 
modulus of the distance o —= 5 logr, where 9 =O for 7=0'1 is 
taken’): then 


1 1 
log p (M) = Const — —(M—M,)’ log A (e) = Const — ree)" 
at 
The number of stars of magnitude mm will be 
ys a 0,6 9 Se (m—My—p)? Aa 0,6 p — ED (m— My —p)? SRA ip 
A(m) =i A (o) 10 at do = fio a gr do 
1 
or log A (m) = Const — — pn — (0, + M, + 0,38°)} 


a? + B? 


| 1 
For the luminosity-function = eS ae and M,—9 was 
a 


assumed. For the zone between 6 = 20° and 40°, in which the 
Taurus-regions are situated, the following formula was deduced from 
the numbers of van RHIJN 


1 
log A(m) = Const +-0,630 m — 0,0118 m?= Const — ae (m— 27)? 


which is met by the values «*-+ 6? = 86, fp" —= 52, M,+ 0, = 11, 
o,— 2. These values will be used in the following calculations. 


If at the distance o, there is a screen, absorbing ¢ magnitudes, 


NS 1 
1) If we call absolute magnitude M the magnitude for zr =1.”"0, all p in this 
article should be increased by 5 and all M diminished by the same number. 


46* 


710 


then from the more remote stars we do not see those with 1/=m—e, 
but those with M= m—e—ge as stars of the magnitude m. The 
number of stars of this magnitude A’, will be 


1 ee 1 
0,6¢ — — (m—M,—p)* - 0,62 — —(m—M,—<«- Vy 
Amp tap tu % ‘ ig + f A (o) 10 ER ; ‘ de. 


These two integrals, taken between the limits + o , represent the 
numbers A, and A. If now we put 


(a? HB), — 0,3 at B* — 07 0,— B (Mo) 
ap Vat tf ap 

(a? + 8) 9, — 0,8 B" — 00, — B (m—M,—€) _ 
ap Va? +B? | oen 


1 


Ti oo 


1 1 : 
and a= [10 i= Y, D= [lof HS 
Valoge Valoge 


— 00 


Tg 


then 
Am = Yi Am + Ya Ame 

While the number 4,, is obtained from the combination of stars 
at all distances, by means of integration between oo of a function, 
proceeding according to the probability-curve, the number A’, is 
found from two such curves, belonging to 7 and m—e; from the 
first is taken a part between — oo and w, indicated by the fraction 
y, (the stars in front of the absorbing screen); of the second the 
part between x, and + oo, indicated by the fraction 7, (the stars 
behind the nebula). From the above numbers we find 

#2, = 0,220, — 1,53 — 0,132 (m—9) e,= «, + 0,132¢, 

By means of these formulae and a list of values of Am, corre- 
sponding to it, the values of A’, for different suppositions concerning 
o, and e were computed. To compare them more easily with the 
results of starcounts, we calculated from the A’, the Nien the 
total numbers of stars brighter than m + 3, and these were compared 
with the normal number Ns. The values log N—loq N', the 
logarithmic defect in starnumber, then forms the best measure for 
the influence of the absorbing nebula. These values have been united 
in the following table. 

From these values, which are graphically represented in our figure 
it appears: 

a. The influence of the absorption extends, slowly varying, over 
almost all magnitudes that are open to our investigation. This is 
especially a result of the great spreading of the luminosity-function. 


fp, = 4,25 () = 7,25 61 = 10,25 
m. = 3 
eo} Se e=4 | ¢=1 Se e=4 | 2=l Si e=4 
2 | | 
0,093 | 0,105 | 0,105 [0,006 | 0,006 | 0,006 

>| 135 155 158 | 012 013 013 

ae 221 226 | 021 023 023 

> | 939 301 311 | 035 039 039 

© | 20 396 417 | 057 | 064 065 [0,003 | 0,003 | 0,003 

TT 345 500 543 | 085 ~ 099 100 | 006 006 | 006 
° | 383 605 689 | 122 | 146 150 | O11 012 | 012 
"| 404 697 854 | 164 206 214 | 019 021 021 
mel doe fet. | 1,033 |= 210. | — 279 204 | 032 036 | 036 
Es 399 188 | 1,214 | 253 | 361 393 | 051 059 | 060 
= 382 780 | 1,375 | 289 | 448 509 | 075 091 093 
Ne ae 149 | 1,479 | 312 527 641 | 106 133 138 
ele 705 | 1,500 | 320 | 587 785 | 140 186 196 
Pel Bia 657 | 1,448 | 315 | 617 933 | 174 247 269 
2 286 605 | 1,354 | 295 | 610 | 1,060 | 200 | 308 | 350 
oe Sea | 560 | 1,254 | 277 | 586 | 1,153 | 224 313 | 452 
a 255 546 | 1,179 | 236 426 563 
k 233 | 500 | 1,140 | 235 456 | 676 
: 212 | 454 | 1,059 | 225 460 778 

| | 


6. For fainter stars the logarithmic defect strongly increases at 
first, until a maximum is reached (about proportional to the absorp- 
tion), and the values again decrease. This is due to the fact that 
for the faint magnitudes an ever greater majority of the stars lies 
behind the nebula, so that the logarithmic defect approaches ever 
more to the difference log Nn—log N,,-:; for fainter magnitudes, 
however, this difference decreases. 

c. For the bright stars, where the influence of the absorption 
begins to be felt, the logarithmic defect changes but little with the 
absorption-coefficient. The reason is that here the obscured stars 
behind the screen play hardly any part at all. The decrease in the 
number of stars is almost entirely a result of the falling off of the 


712 


more remote stars of the magnitude m. For increasing & the 
logarithmic defect approaches here to a limit-value (calculated from 


Se 

the unobscured stars before the screen only), as represented in the 
drawing by the heavy line (e = oo). 

d. For the bright magnitudes the value of the logarithmic defect 
depends mainly on the distance @9,, for the faint magnitudes it depends 
in the first place on the absorption-coefficient ¢ of the dark nebula. 
For increasing 9, the effect of one and the same absorption on the 
logarithmic defect decreases.. 

From this follows in the first place, tbat it will be difficult to 
apply this method in general. In the case of small black spots (like 
the trifid hole near y Aquilae) the defect can be ascertained over 
some magnitudes (e.g. from the 11'* to the 16 magnitude), 
but this range is too small to separate the two unknowns g, ande 
and to find both; the number of brighter stars is too small to allow 
of any deductions. As we require data over the most divergent 
magnitudes, this method can only be profitably applied to regions 
of such extent, that it gives us the disposal also over a sufficient 


material of bright stars. This is the case with the dark nebulae in 
Taurus. 


Big. d. 


§ 3. For the star-density NV’, the following sources have been used: 
a. The “Bonner Durchmusterung” up to the star-magnitudes 6,5, 
8,0 and 9,0 incl. (the total number up to 9,5 could not be used, on 


713 


account of the inequality and uncertainty of the limiting magnitude). 
The normal density AN, was adopted from the lists “Groningen 
Publications 18”; the argument, the limiting magnitude after the 
scale of Groningen 18, was taken, according to SELIGER, dependent 
on the star-density, and was for the lowest limit still corrected 
by 0,11, *') which gave 


6,56—0,023(D—0,7); 8,12—0,068(D—0,7); 9,36—0,246(D—0,7). 


On the average these limits in photometric scale are 6.6, 8.1 
and 9.4. ; 

6. Two of Kaprnyn’s “Selected Areas” come within this region: 
N°. 47 and N°. 48; N°. 48 is situated closer to the centre, but according to 
the chart of Dyson and Mrrorrr just outside a region with strong 
absorption; N°. 47, though more distant, comes just within the dark 
field S.W. from § Persei. In the ‘Durchmusterung of Selected 
Areas” ”) the numbers of stars were counted up to 12,0, 13,0, 14,0, 
15,0, and on Area 47 up to 16,0 (faintest stars 15,96 resp. 16,49). 

c. From the Dyson and Menorre chart, for every part of the 
region from 3) to 5"30m and 20° up to 35° we could draw the 
star-density per 100 square minutes on the FRANKLIN-ÂDAMS plates, 
already reduced to a common system. Regarding the limiting mag- 
nitude, for which these densities count, the authors say: ‘The 
limiting magnitude is not accurately fixed, but may be taken at 
about 15,8 and should be within 0™,25 of this figure” *). I have 
tried to control these data by making use of the three “Selected Areas” 
(47, 48, 49) falling within this region. To this end the log N’ for 
these places, as deduced from the Dyson and Merorrr chart, was 
compared to that of Kapreyn for m= 13, 14, 15 (and 16) and 
thus, through interpolation or extrapolation of the deviations from 
the normal /oy N the limiting magnitude was deduced, The values 
thus obtained are 16,02, 15,83 and 15,90: their average 15,9 has 
been adopted. For the rest a mistake of 0,1 in this value gives a 
mistake in the log N of 0.03 only. 

d. The data of the photographic “Carte du Ciel” cannot in gene- 
ral be used here. The great accidental irregularities in the limiting 
magnitude of the separate plates does not prevent the fixing of 
average densities and an average limiting magnitude, it is true, but 
in this case it is the separate plates that count, and these can be 


1) See with regard to this A. PANNEKOEK, Researches into the structure of the 
Galaxy. These Proceedings, Vol. XIII, p. 254. 

3) Annals of Harvard College Observatory. Vol. Cl. 

$) l. c. page. 4. 


714 


greatly divergent from the average. This difficulty disappears, if the 
accidental irregularities can be abolished by reduction to one system, 
which is feasible if a great number of plates are joined so as to 
partly cover one another. With chart-plates this does not happen 
anywhere; but it does in the case of the Paris catalogue-plates, of 
which the zones 22°, 23° and 24° have been published complete. 
As in this case the centres of the one zone concur with the corners 
of an adjoining zone, each plate has a quadrant in common with 
each of the 4 surrounding plates. In this way it was possible to 
reduce all the plates of these three zones between 3'16™ and 532m 
to their average. A few particulars regarding this reduction will 
be added here. 

Two consecutive plates a and 6 of the central zone (23°) can be 
joined together by a plate of the N-zone (24°) c, which has a qua- 
drant in common with both, and also by one of the S-zone (22°) d. 


A be 
pct 


If we call the quadrants 3 the density (6): density (a) = TA 


and likewise =" x = For the logarithmic difference in density of 
An 4 

every two consecutive plates of the central zone we get therefore 
two values, the concurrence of which gives a measure of the accu- 
rateness obtainable. We must bear in mind that the quadrants on 
the adjoining plates do not accurately concur, because of the con- 
vergence of the declination-circles, and because they stretch 65’ 
from the centre. The results obtained, starting with log d (3h24m) 
— log d(3'16™) and ending with log d(5'40™) — log d (5'32™) (in 
units of the 3rd decimal), are: 


from de N. plate +046 +070 —161 +030 +216 —240 +029 +369 —002 
from de S. plate +027 +106 —335 +233 +298 —535 —115 +490 —073 
adopted +036 +088 —248 +131 +257 —387 --040 +430 —037 

+639 —816 +807 —552 +359 +094 —529 +500 —165 

+469 —856 +637 —531 +382 4-168 —588 +451 —120 

+554 —836 +722 —541 +370 +131 —558 +476 — 142 


Herefrom for every plate of the middle-zone the deviations from 
a medium-value were deduced and from these numbers the same was 
found for the N- and the S-zone; these values, with contrary sign, 
give the logarithmic reduction for each plate, the logarithm of the 
factor, by which the number of stars on that plate is to be multiplied, 
in order to count for the same average limiting magnitude. They 
are in the sequence of decreasing R.A.: 


715 


—09 +10 +01 —17 +07 —05 —05 +17 —02 —04 +06 +18 —03 +07 +08 +02 +14 +37 
—14 ~28 +20 —36 --23+4 14—40 +32—51-+04 00443439 00 +26 439 +14+423 26 
05 —0T —12—05-=15 —16 — 17 —09 05 99-100 — 14 = 34 05 4-05 — 16-217 


If on each plate a systematic difference exists between the E. and 
W. side, this reduction will produce a systematic error, increasing 
with the R. A. because the ring is not closed; the accidental errors, 
also because we have but three zones, will be eliminated to only a 
very slight degree. All the same the very considerable jumps in the 
limiting magnitude will thus be practically neutralized. This is evident 
also from the regular course of the reduced numbers of stars, which 
now run nearly parallel with the course of density according to the 
FRANKLIN-ADAMs plates, which is not the case with the non-reduced 
numbers. These numbers for the separate quadrants are given in the 
following list; (for the middle rows it gives two values, the upper 
one of which is always taken from the N-plate): 


h h 
5 4 
5 N40 36 32 28 24 20 16 12 8 4 0 56 52 48 44 40 36°32 28 
5o 
147 7124 110.39 30 25 36 53 16 75 63 53 53 30 12- 13, 13° 25 


240 
134 120 138 73 29 28 40 2753 69 172 73 45 39 39 41 24 19 

151 130 124 142 71 30 27 39 2852 70171 75 49 36 40 41 27 17 
23° 

154 159 174 163 146 90 38 21 4652 83 79 74 46 52 58 54 51 31 
: 143 176 170 143 93 36 20 4852 85 78 75 51 48 60 49 55 28 
2° 
Le 184 151 159170116 49 34 41 48 58 58 57 70 55 61 35 47 49 
1 

4 aL 

ee 24 20 16 12 8 4 O 56 52 48 44 40 36 32 28 24 20 16 12 
oe 19 14 38 42 42 3831 68 75 123 107 154 80 60 72 76 63 80 

15 37 69 78 70 88 70 101 89 81 “11155 Ii 46 69. 50 71 ’60 
gi; 15 36 64 83 75 81 83 85 85 86 69174 79 41 68 51 70 58 71 

16 46 65 62 65 7456 68 68 67 78 83 56 44 51 49 66 71 47 
a 11 45 61 67 71 6866 57 65 71 69 93 63 40 51 51 67 73 
ne 54 30 39 33 41 43 48 66 76 83 74 83 43 36 42 54 61 40 
1 


These numbers must be multiplied by 12? : 13? to obtain the 
numbers per square degree. If we may assume, that the average 
limiting magnitude of these 55 plates corresponds to the average 
value for the entire sky, the limiting magnitude deduced from the 
entire zones 23°—24° by means of the tables of “Groningen 27”, 
viz. 12.20 must be used here. 


716 


§ 4. In this part of the sky eight regions, bounded by irregular 
polygones, were more closely examined: A and B comprise about 
the two darkest regions of absorption 3"20m + 34° and 430™ + 26°; 
C, D, E, and F lie to the North, the East and the South around 
B, and contain regions with few stars, that are partly darkely traced 
on the chart of Dyson and Me.orte; and G and H are richer 
regions with centra 3'40™ + 27° and 4h4m + 32°. For the regions 
E and F 21° and 25° were taken as limits of declination, in order 
that the Paris results might be used. For each of these fields the 
B. D. stars were counted and divided by the area (for /# 5 stars 
up to 6,5, 3 of 6,6—8,0 and 3 of 8,1—9.0 were subtracted as 
Hyades-stars). In the same manner the average density for Paris 
was calculated. For the FRANKLIN-ADAMs plates average values were 
calculated from the density-figures on the chart of D. and M. 


A B C D. E F Fe | H 
—— EE — 

surface. 28.3 | 266 | 210 | 295 | 240 | 368 | 399 | 462 
gal. lat. aje | 13e | ge | g° | go | tec | Stee 


—65 | 032} 023| 019] 0.20) 0.12] 0.19) 0.07) 0.30 
B.D. | | 
oer | -80| LO) 060] 105) 088} 067) 087) 093) 123 


square | — 9,0 3.82 2.03 | 2.86 3.29 3d 293 | 4.14) 5.07 
degree 


—9,5 | 10 6 10 8 15 u 1 Se 
Paris per sq. d. 40.4 36.1 
Fr.-A. p. 100 | 96 | 93 | 13 15 18 113 | 24 26 


log N’ (6,6) | 951 | 936| 928 | 9.30| 9.08] 928| 985| 948 

» (@1 | 0.04] 9718| 002| 9.94] 983| 9.94] 9,97 | 0.09 
_ @4 | ossl os) o46| os2|. 057| 047| 062] 070 
, (12,2) 1.61 | 1.56 | 
» (3,9) | 254} 252| 2617) 213| 281| 261) 294| 297 


log N'/N (6,6) | +0.14 | —0.09 | —0.22 | —0.20 | —0.42 | —0.14 | —0.52 | +-0.04 


» @1) JT 10|— 46] — 27 | = 35} — 44) B 16 
»  9)4)0.| — 17. | =] 57.| = 48) = 43 = B — 34.) — 11 
» (122) — 61 | — 58 | 

050 |— 4 | 4 2 46 2 


| | | | 
In these values for the logarithmic defect the following charac- 
teristics may be noted: 


ART 


a. The difference between the strongly and the slightly obscured 
regions is not noticeable at all with the bright D. M. stars up to 
6,5, and it is hardly noticeable with those up to the 8 magnitude; 
it is only with those up to the 9" that G and H differ considerably 
from the others. By the accidental uncertainty of the numbers the 
difference between the more or less obscured regions A— F’ is not 
clearly evident. 

b. The defect for the stars up to 15.9 is about as great as that 
for the stars up to 9.4, This corresponds to the results obtained by 
Dyson and Merorrr. 

c The Paris results for the fields Z and F' point to the fact that 
the logarithmic defect for the limiting magnitudes between 10 and 
15 is greater. 

If we take first the fields H and #, where the data are most 
complete, we see that their averages (— 0,28, — 0,35, — 0,34 
— 0,59, — 0.40 for the 5 magnitudes), represented on our figure by 
open circles, concur pretty well with a curve (dotted in the figure) 
answering to 6, —=5,5, e=1,5. The values of 9, between 4 and 6 
with an absorption «< 2 give a maximum for the logarithmic defect 
for m 12 a 13, so that in this case we shall find, that the defect in 
stars for the magnitudes between the 9 and the 15 does not 
fluctuate very much. 

This, however, is contradicted by the results of the ‘Selected 
Areas”. These could not be united with the former, because they 
comprise separate, smaller regions. The counts give the following results: 


b = —21° b= —12° 
Area 41 surf, = 3600/ Area 48 surf. — 1600’ 
Number| log N’ | log N'/y |Number| log MN | log NN 
| 
Oty 23.5) Ie, 36 —0.32 19 1.63 —0.15 
> 13.0 208 | vb —0.58 37 1.92 —0.25 
> 14.0 44 | 1.64 —0.73 72 221 | —031 
> 15.0 10 1.85 — 0.83 84 2.62 — 0.22 
| 
> 16.0 178 225 —0.75 | | 


From the first field, falling within the region A of strong absorp- 
tion, we find: 

d. In the Selected Area 47 a regular, strong increase of the defect 
from the 12th to the 15'® or 16 magnitude is shown. 


718 


Separately considered these values represented on our figure by 
crosses, especially if supplemented by the value for 9,4 of field A, 
can well be harmonized. with a curve for o, = 7,5 (in which case 
the decrease of 15m to 16™ is not real). But the result (d) is utterly 
opposed to the result (6); the numbers of stars in the S.A. demon- 
strate, that the defect in stars for 9,4 and 15,9 cannot be about 
equal, cannot have a maximum at 12" and afterwards decline. 

The contradiction does not lie simply in a difference between the 
FRANKLIN-ADAMS plates and the Selected Areas. The S.A. 47 com- 
prises only 1 square degree of strong absorption, in which the counts 
on the F.A. plate give a defect of 0,71, about the same therefore — 
and this is only natural, the limiting magnitude employed, viz. 15,9, 
having been deduced from these Selected Areas themselves. The 
case might be explained by the fact that there is a real difference 
in structure between S.A. 47 and region A on the one side, (the 
small values for A from 6,5 to 9,4 ie. the slight defect in B.D. 
stars would then be considered as real) and the other regions of 
absorption on the other side; that therefore A is caused by another 
nebula at a far greater distance. It may be questioned, however, 
whether the data are accurate enough to allow of such a conclusion. 
The values for the B.D. in A are based on a moderate number of 
stars only; the numbers of stars 12—14 in S.A. 47 are very small, 
so that accidental irregularities in the distribution play a great part; 
and the taking of averages for the F.A. plates from the irregularly 
distributed density-numbers is somewhat uncertain also. This proves 
once more, that as yet we dispose of much too small a number of 
data concerning the star-density for the fainter stars 10™—16™ over 
sufficiently extensive regions. 

Now, according to § 2, the determination of the distance of ab- 
sorbing nebulae depends mainly on the bright stars; the uncertainty 
in the numbers of the weaker magnitudes is of very little importance 
here. It is upon the data of the B.D. therefore that this determina- 
tion must almost exclusively be based. To avoid accidental mistakes, 
we will therefore unite these 8 fields 2 by 2 into groups, in the 
order of the NV’ (15,9). 

Also now the accidental uncertainties still give an irregular course. 
Between the three first groups A—F no marked difference presents 
itself for these magnitudes; therefore these have still been combined 
to a general average, to which the values in the last column apply 
and which are represented in the figure by-dots. The slight depend- 
ence on the absorption e can be taken into account in such a way, 
that corrections are introduced to reduce them to the limiting value 


ASB €=F cWaD=s G—H ABCDEF 


log N’/n (6,6) | +0,04 —0,18 —0,30 =6.15 —0,15 
EBDE 0,26 — 0,26 —0,39 —0,15 —0,30 
eee ek Ah ee Sy —0,41 kn 013 — 0,39 


for «=o; the figure shows that for e between 1 and 2 for these 
corrections the amounts 0,05 and 0.10 are to be adopted. 

From the limiting values thus obtained: 0,15 for m= 6,6, 0,35 
for m=8,1 and 0,49 for mn —= 9,4 the values of 9, can be directly 
deduced; we tind for it: o,=6,1; 5,5; 5,6.If we consider that 
differences of resp. 0,05 0,10 and 0,13 in these three limiting values 
mean a change in o, of 0.6, we may assume that the uncertainty 


of each of these values for @, remains below the unit. As the average 
we then find e, == 5,7 + 0,6, from which follows 


n— 0 ;0072 r = 140 parsecs 


where r probably lies between the limits 100 and 200 parsecs. The 
absorbing nebulae in Taurus therefore lie behind the Hyades at about 
a four times greater distance. They stretch on Dyson and Merorre’s 
chart over an extent of 30°, which is to say about 70 parsecs. The 
dimension of the oblong, strongly absorbing region A are about 9° 
by 3°, or 20 by 7 parsecs. BARNARD in his catalogue describes small 
black objects lying therein (and in the other region 4) of 1° (nr. 5 
and 18), 8’ (nr. 24) and 4’ (nr. 28) dimension; their linear dimens- 
ions are then 500000, 40000 and 30000 astronomical units. 


Astronomy. — “Further Remarks on the Dark Nebulae in Taurus”. 
By Dr. A. PANNEKOEK. (Communicated by Prof. J. C. Kapreyn). 


(Communicated at the meeting of October 30, 1920). 


§ 1. In a previous communication, assuming that the star-voids 
in Taurus are caused by absorbing nebulae, we have determined the 
distance of those nebulae at about 140 parsees. The light-absorption of a 
region with moderate absorption, for which data were availablealso 
for the 12% magnitude, proved to be 1 a 2 magnitudes; for the 
darkest regions A and 5 the average must then amount to about 
2 magnitudes, which is not in conflict with the logarithmic defect 
for 15,9; the blackest kernels therein have a far stronger absorption 
still. The existence of such extensive regions (the dimensions of A 
are 9° by 3°, that is to say 20 by 7 parsees; B is most irregular, 
but about equal in area) of which the absorption is known, allows 
us to draw some conclusions regarding the density and mass of these 
gas-clouds. 

We assume, therefore, the existence of such a gas-cloud in space, 
the molecules of which absorb the light through scattering. Lord 
Ray.eieH in his investigations on the cause of the blue colour of 
the sky, has deduced a formula for the absorption of the light through 
a medium containing small particles in suspension in which the 
suspended particles scatter the light to all sides *). Scuusrer pointed 
out, in 1909, that the extinction of the light in our atmosphere is 
to be- attributed almost exclusively to such scattering, where the 
molecules of air themselves play the part of scattering particles, 
whilst the selective absorption constitutes but a minor factor’). As 
the absorption in magnitudes is proportional to the density > thickness, 
and therefore to the number of molecules the ray of light meets, 
the density and mass of a cosmic gas-cloud can be determined 
through comparison with the data of the atmospheric extinction. 
ABBorr gives for Mount Wilson in the zenith a transmission-coeffi- 
cient 0.95, an absorption therefore of 0,056 magnitude, valid for a 
column of air of 6 km., in height, and a density of 0,0013. If for 
the thickness of the gas-cloud in Taurus (after the linear dimensions 


') Philosophical Magazine, 1899, page 379. 
*) Nature, 1909, page 97. 


721 


20 X 7) we take 10 parsecs (1 parsec is 3 x 105 km.), we 
find, with an absorption of 2 magnitudes, 10! for the density of 
the gas-cloud. The mass is independent of the thickness assumed ; 
per cm? diameter it is 2/0,056 weight of air-column on Mount 
Wilson = 25 kg, for an area of 150 square parsecs therefore 
M = 3,5 x 10 kg. As the mass of the sun is 2 x 10% kg, 
the mass of the gas-cloud is equal to about 2 > 10!° sunmasses. 

This can also be found directly, by means of the formula of 
Rayieian for the absorption-coefficient £: 

ae Ate) 
eN 
in which u is the refractive index, A the wave-length, N the number 
of particles (molecules) per cc. If we assume, that the gas-cloud 
consists of hydrogen, (which gives the smallest mass), with an 
ordinary pressure and density therefore u == 1,000143, NM = 2,7 « 10”, 
moet we take 2==5,5 <x 10-5 em, we get k = 2,7 « 10-8-or 
2,7 <x 10-3 for unit of thickness one km., which is equal to 
2,9 > 10 3 magnitudes, whilst a column of 1 em? width per km. 
length has a mass of 8,3 x 10-° kg. The mass of a column of 
1 cm?’ diameter in an absorbing gas-layer is therefore 2,9 « kg., 
if e is the absorption in magnitudes (for 4 = 550). From this we 
find for a mass of gas with an area of 150 square parsecs and 2 
magnitudes absorption 
M=8 X 10° kg. =4 X 10° sunmasses. 


The difference with the former result is due to the difference 
between hydrogen and air. 

According to Kapreyn and van Rayn’) the density of the stars 
in the vicinity of the sun is ‘/,, per cubic parsec, so that in a globe 
with a radius of 2600 parsecs there are 4 x 10° stars. If we take 
their average mass as equal to that of the sun, this one gas-cloud, 
(one third perhaps of all absorbing gas-clouds in that region) only 
140 parsecs distant, contains as much mass as all the stars within a 
globe extending 20 times further. Unless therefore this Taurus-cloud 
is unique for size and density, we may safely conclude that in the 
fixed stars only a small part of the world-substance is condensed. 


§ 2. The assumption, however, that at a distance 140 parsecs there be 
a gascloud of such great mass, leads to a few most remarkable con- 
sequences. The attraction of this mass on our solar system is not 


J.C. KAPTEIJN and P. J. van RHIN, On the distribution of the stars in 
space. Astrophysical Journal 52, 32. 


722 


imperceptible; it amounts to 5 « 10~® times the force which the 
sun exercises on the earth. It deserves notice that this force is alto- 
gether independent of the assumed distance of the gas-cloud. It 
depends only on the amount of its absorption, and its apparent area 
in the sky. If this area is s square degrees, and the absorption « 
magnitudes, the formula of Rarrweicn gives, in the above manner: 


Force = 107 es X attraction of the sun on the earth. 


If the absorption is «' for photographic rays, (4 = 440) then « = '/, « 
is to be taken. If therefore in various directions and at various 
distances there are such absorbing gas-clouds in space round us, 
the total influence on our solar system can be calculated from their 
apparent area and absorption. 

For the time being we will consider only the influence proceeding 
from the Taurus gas-clouds. The perturbating forces are imperceptible 
also in the case of the most distant planets. But the force on the 
solar system as a whole is so immense, that (with a speed of 19 
km., supposed about perpendicular on the force), it must move in 
a curved orbit with a radius of curvature of 4 X 10° astronomical 
units = 2 parsecs, and the direction of the apex in 3000 years 
must be modified 1° towards Taurus. Compared with the distance 
of 140 parsees this slight radius of curvature indicates that our 
solar system must move in an elongated ellipse with excentricity 
°°/, around the gas-cloud; in a period of 2 a 3 million years, that 
at the present time it is nearly in the apocentre, and that in the 
pericentre it has practically to go through the gas-cloud. Something 
similar holds good for the Hyades, which run at a distance of about 
100 parsecs from the gas-cloud, with a speed of 45 km. To run 
away and get free from the nebula in a hyperbolic orbit, their 
speed would have to exceed 270 km.; with their small speed 
however they are bound soon to precipitate towards the gas-cloud. 
Such a huge mass as calculated above, would render it a central 
body dominating all movements in this part of the universe, over 
many hundreds of parsecs. The speed of the stars would be enormous 
in the vicinity of the gas cloud; especially in the direction of Taurus 
therefore, we should observe great proper motions, far exceeding 
the usual values. 

Also without the assumption of such a great attracting mass, the 
proper motions in the regions of absorption must be above the 
normal, because for a certain magnitude (on account of the dropping- 
off of stars behind the absorbing screen) the average distance there 
is smaller than elsewhere. Making use of the formulae of the previous 


723 


communication we find for the average parallax of the stars of the 
magnitude m in front of the absorbing screen: 
PL 


1 
En i 0,40 — rn (m— My — ¢)?— Ee (e — po)? 
ie —— fro do. 


The same integral taken between the limits + so represents the 
normal value of A, zin. If we put, therefore 
we = 0,22 0, — 1,078 — 0,132 (m — 9) = a, + 0,452 


and 
% 
al 
ix loge AOS i dt=7; 
then 
ae Ys 
x ne 


The average proper motions are enlarged in the same proportion 
as the average parallaxes. For y,= 6,05, r=160 parsecs (this 
value has been taken, because it allowed us to use the numbers of 
the previously calculated tables), we get for 
nw ==. 0 ‘ 8 9 
mee 1 Ae CRE 2, 


Dyson and Merorrr in their article have already compiled the 
proper motions of the stars in the darkened regions of Taurus, and 
have established, that they are not greater than anywhere else. We 
find, indeed, for their average 0",044, whilst stars of that magnitude 
(1 of the 6, 1 of the 7, 5 of the 8", 9 of the 9 magnitude) 
at such a galactic latitude give a normal average of 0".041. For 
the small number of stars the negative conclusiveness of this result 
is not strong enough in itself to refute the existence of an absorbing 
nebula. Of a greater average speed, however, through the effect of 
a gigantic attractive mass, there is no trace. 


§ 3. The difficulties, and as yet unconfirmed consequences, result- 
ing from the assumption, that the star-voids in Taurus are caused 
by absorbing gas-masses, give rise to the question, as to whether 
no other explanation is possible. Barnarp has always emphasized 
the fact that not all dark spots and regions in the Galaxy are to 
be attributed to absorption, but that a great number of them are 
undoubtedly due to actually void space. In many cases the aspect 
; 47 

Proceedings Royal Acad. Amsterdam. Vol. XXIII. 


724 


furnishes an indication: the fantastically twisted and ramified shapes 
of the dark regions in their various gradations of blackness, which 
present themselves on the chart of Dyson and Merorre, and are 
even more marked on the photographs by BaRNARD !), are a strong 
indication to the existence of absorbing nebulae in these Taurus 
regions. This indication is corroborated, if we calculate the influence 
of actual star-voids in space on the number of stars of different 
magnitudes. 

We assume that in the line of sight the space from 7, to 7, = 1,585r, 
is completely empty (over a region from @, to 9, +1 therefore). 
In the integral, representing the number of stars A, of the magnitude 
m, the part between the limits o, and ge, + 1 is lacking, thus 

ro+0,22 
1 - 


Am == Aj, (: = == 10-2? dz ) 
V 2 log € 


To 
in which rz has the same signification as in the previous communi- 
cation. If we calculate these values for a certain value of o, (eg. 
0, = 6,95, whereby the falling-off of stars-becomes a maximum 
for m= 9), and from that the total numbers WV’,,41, and the loga- 
rithmic defect log N'/y, we find: 


m. | log N’/N m. | log N’'/n 

3 10 
—0,028 — 0,080 

Ad yj 11 
| — 040 — 069 

Bie 12 
— 055 — 056 

6 13 
— 069 — 043 

7 14 
— 080 — 031 

8 cel 15 

IEN | 16 
| — 086 — 014 

10 -| 17 


With a void, extending over a unity in 9, there is therefore a 
lack of 18°/, at the utmost in the total number of stars. To produce 
such a strong defect as observed in the Taurus regions, the void 


must extend over many unities in g. If such holes do not extend 


1) KE, E. BARNARD. On a nebulous groundwork in the constellation Taurus. 
Astrophysical Journal 25, 3. 


725 


further in tbe line of sight as perpendicularly to it, one unity in @ 
means a lateral dimension of 26°, and two unities in @ (a void 
therefore from 7, to 2,51 7,), a lateral extension over 50°. Hence, 
if we want to explain a clearly evident defect of stars (over 20 °/, 
for instance, log V'/y > 0,10) over a small area (below 10°) by real 
spatial voids in the star universe, we come to the hardly acceptable 
assumption of protracted, tubular cavities, all running in the direction 
of the line of sight. It is only in those places, where the stars do 
not extend equably alongside of the visual line, but are clustering 
into actual clouds and other objects, that real voids between them 
can play an important part in the aspect of the Galaxy. 

Thus, if we abide by the explanation through absorption, but 
without the enormous mass, the particles that cause the scattering 
must have a mass, smaller than hydrogen-molecules, thus they would 
have to be for the greater part free electrons. The question as to whether 
there really is absorption, could be settled by means of an investi- 
gation into the colours of the stars in the poor regions. The absorption 
through scattering is inversely proportional to 4‘, so that the stars 
behind the gas-cloud must be strongly reddened. For a number of 
nebulous stars, stars which are surrounded by visible nebulous halos, 
in Monoceros, Scorpio and Ophiuchus, Snares and HvBBrr have 
recently found’) that their colour is considerably more red than it 
should be according to their spectral type, that therefore their light 
is scattered and dimmed by the nebula through which they shine. 
On calculating what portion of the stars of each magnitude lies 
behind the gas-cloud, assuming for its distance once more 160 
parsecs (g, = 6,05), we get for 

ci whee) 6 7 8 9 10 11 12 
0,4°/, ee a hie a ole ele 31 “lle 50°/, 

It is only with stars fainter than the 12' magnitude, therefore, 
that the majority will show this reddening through absorption. As 
in the case of such faint stars a comparison with the spectral type 
is difficult to accomplish, it will not be feasible directly to determine 
the reddening with absolute certainty; it may be, however, that a 
statistic determination of the colour or the effective wave-length of 
the fainter classes will lead to a decision. 


Postscript. Professor pr Sitter has drawn my attention to the 
fact, that the absorption of a mass consisting of opaque particles 


') F. H. Seares and E P. Husste. The color of the nebulous stars. Astro- 
physical Journal, 52, 8 (July 1920). 
47* 


726 


surpasses so much the ‘absorption of an equal mass of scattering 
gas, that by assuming a dust-cloud instead of a gascloud, a moderate 
mass will suffice to account for the observed extinction. In this case 
the absorption does not depend on colour. If a reddening of the stars 
is observed, indicating an absorption through scattering, we may 
still find a moderate mass, if the gascloud is mixed with dust 
particles. This would be in harmony with the views of ARRHENIUS, 
who has found in his studies on cosmogony that the small particles 
in space, driven away by lightpressure, are caught and collected 
in the extensive world nebulae. 


Physics. — “The so-called cyanogen-bands’. By G. Horsr and 
E. Oostersuis. (Communicated by Prof. H. KAMERLINGH ONNes). 


(Communicated at the meeting of May 29, 1920). 


In photographing the nitrogen-spectrum one usually observes a 
number of bands, which were formerly ascribed to cyanogen’). 
The most prominent of these bands lie between 3855 and 3883 A. 
and between 4158 and 4216 A. In 1914 Grorrian and RUNGE?) 
made some experiments, from which they concluded, that these 
bands are due to nitrogen and should not be ascribed to cyanogen. 
Many later observers’) have considered this view to be the right one. 
We have made a new investigation on this point and came to 
the conclusion that these bands are not due to nitrogen, but to one 
of its compounds which condenses at a much higher temperature. 
In our experiment the discharge tube was a cylindrical glass tube 
with one electrode connected to a Tesla-transformator. The gas in 
: the tube was an argon-nitrogen- 
mixture containing about 15°/, 
of nitrogen. The gaspressure was 
1. about 55 cm. Under these cir- 
cumstances the spectrum shows 
no argon lines, only the nitro- 
2. genbands and the so-called 
“cyanogen-bands”. (Fig. 1). 
The bands 3855—3883 A 
3, can be seen at A, the bands 
4158—4216 A at B. 
In order to discriminate 
whether these bands are due to 
nitrogen or to cyanogen, we immerged the lower half of the discharge 
tube into a glass filled with liquid oxygen and so obtained the 
spectrum fig. 2. 


AEB, 


U See Kayser, Handbuch der Spectroskopie. Bd. 5. 

2) W. Grotrian and C. Runee. Phys. Z. S. 15, 545. 1914. 

8) W. Sreusine. Phys. Z. S. 20, 512. 1919. 

L. Greet und A. Bacuem. Verh. D. Phys. Ges. 21, 454. 1919 and Zeitsehr. f. 
Physik, 1, 51. 1920. 


728 


The so-called cyanogen-bands have completely disappeared; it 
follows that these bands do not belong to nitrogen, but to a much 
more easily condensable substance, probably cyanogen. ') 

This is in accordance with Steusine’s observations; the latter found 
no trace of the cyanogenbands in his experiments, where the presence 
of any carbon was excluded. *) 

Probably Grotrian and Runae's nitrogen was not completely free 
from carbon. This may be due to the fact that they purified their 
nitrogen by pyrogallicacid-solution; during this operation small 
quantities of carbon monoxide are usually developed. 


Eindhoven. Laboratory Philips’ Incandescent 
Lamp works Ltd. 


1) In some of our experiments we completely immersed the discharge-tube in 
liquid oxygen, the spectrogram being taken through the walls of the Dewarvessel. 
During the operation of the Tesla transformer the walls of the Dewarglass show 
the green fluorescence of cathode-rays. In one of our experiments however some 
gas was liberated in the space between the walls of the Dewarvessel, so that a 
red glow appeared, the radiation of which is superposed on that of the discharge- 
tube. The so-obtained spectrogram is shown in fig. 3. A peculiar phenomenon may 


be observed. Some of the cyanogen-bands, namely 3855, 3883 and 4168 A. come 
out very strongly, whereas the other ones are absent. So it is not impossible. 
that the cyanogen-bands are due to two different carriers. 

*) Simular results have been obtained by L. HAMBURGER, who also found no 
trace of the cyanogenbands in extremely pure nitrogen. Chem. Weekblad (15) 931 
1918. (Added in translation). 


Physics. — “The geodesic precession: a consequence of EINSTEIN’s 
theory of gravitation.” By Dr. A. D. Fokker. (Communicated 
by Prof. H. A. Lorentz). 


(Communicated at the meeting of October 30, 1920). 


It is well known at present what parallel displacement or geodesic 
translation means in non-euclidean space’). And we know also that 
a compass rigid, moving parallel to itself and completing a closed 
circuit, in consequence of the curvature of space, will not regain 
the same orientation which it had before: a certain rotation of 
curvature will become apparent. Now it occurred to ScrourenN that 
the earth’s axis of rotation — provided the earth were a sphere — 
should remain parallel to itself in the general geodesic sense during 
the motion of the earth round the sun. Thus, after a year, we must 
expect the earth’s axis to point to a slightly different point of the 
heavens according to the curvature of space produced by the sun’s 
gravitation. This affords an additional precession which superposes 
itself on the precessions due to other causes known in astronomy ’). 

The problem however is not so simple as it is put here. Though 
it can be proved that the axis of rotation will remain parallel to 
itself in the geodesic sense, yet in reality we have to consider the 
dragging of the earth’s axis along her four-dimensional helicoidal 
track through time-space and not a circuital displacement in the 
ecliptic at some definite instant. The problem should be put as one 
of four-dimensional geometry; it is a problem of mechanics, and 
not a problem of three-dimensional geometry. If this be done properly, 
then the result is that we are to expect a precession one and a 
half times the precession foreseen by ScHoureN, viz. 0.019 of a 
second of are per annum’). This will be shown in the present paper. 

The idea at the bottom of the argument is the following. Imagine 
that in order to describe motions taking place in the neighbourhood 
of the earth’s centre we choose axes such that the time is always 

1) Levi Crvrra, Rendic. Cere. Mat. Palermo, 42, p. 1, 1917; Scuouren, Direkte 
Analysis zur n. Relativitätstheorie, Verhandelingen Kon. Akad. v. Wetensch. Amster- 
dam, XII, no. 6, 1919; Wevr, Raum, Zeit, Materie, Berlin 1920, 3rd ed.; Cf. 
also an article of the present author in Proceedings Kon. Akad. v. Wetensch. 
Amsterdam, 21, p. 505, 1918. 

2) Scuouten, Proceedings Kon. Akad: v. Wetensch. Amsterdam, 21, p. 533, 1918; 
with appendix by De Sitter. 

3) Cf. also a paper by Kramers, Proc. Amsterdam, September 1920. 


730 


directed along the earth’s four-dimensional track and that the origin 
of space-axes falls along with the earth. Moreover, the original 
directions of these. space-axes at successive instants are to remain 
parallel to themselves in the general, or natural sense. If our axes 
of reference are chosen in this way, we may confidently expect the 
equations of motion to assume a particularly simple form: in fact, 
as a first approximation, when motions take place very near the 
origin (i.e. within a domain the two-dimensional cross-sections of 
which are small compared with the reciprocal of RigMANN’s measure 
of curvature) then this region may be considered to be homoloidal, 
that is, free particles are moving in straight lines under no force, 
and a top spinning round its axis of symmetry will keep its axis 
of rotation in a fixed direction relative to the axes of reference. As 
the latter are carried along the axis of time parallel to themselves, 
so it follows that the same is true for the axis of rotation. *) 

If we proceed to the second approximation, we find that free 
particles are subject first to forces which we know are the causes 
of the tides due to the sun’s action, and secondly, to forces depending 
on the velocity of the particle in a manner which in a certain 
respect resembles Corionis’ forces in a centrifugal field. The latter 
were called by Poincaré “forces centrifuges composées’’. Accordingly 
the new forces might be designed as compound tidal forces. 

In order to obtain the second approximation, it is necessary to 
specify our coördinates in greater detail. In every point-instant of 
the axis of time we draw all geodesic lines which are perpendicular 
to the time-track and we desire that these shall define space, three 
of them being chosen as the axes of space. For convenience sake 
the latter may be chosen perpendicular to each other. 

It will be seen that this space cannot coincide with space as 
defined by an observer who is at rest with the sun. The two spaces 
of reference intersect in a surface, which, in each point-instant of 
the earth’s helicoidal track contains the direction in the ecliptic 
perpendicular to the velocity and the direction perpendicular to the 


1) In much the same manner during the moon’s motion, as a first approximation, 
— apart from the sun’s perturbing forces, which arise in the second approxi” 
mation, — the plane of the orbit must keep its position unaltered relative to the 
falling axes of reference. This results in a motion of the nodes equal to the motion 
of these axes. De SirTeR, proceeding in a totally different manner, arrived at a 
nodal motion of 1”.91 per century, which is exactly the amount given above for 
the precession. (Monthly Notices R. A. S. 77, p. 172, 1916). A comparison with 
observation could only be made if the nodal motion, resulting from other causes 
and computed with Newron’s law of force, were known to one further decimal 
place than it is at present. (Dr Sitter, l.c.). 


731 


ecliptic. This involyes a complication in comparing the relative 
positions of the two sets of spatial axes of reference. In the case 
of a planet moving in a cireular orbit this difficulty is readily 
overcome. 

If then we compare the falling axes, before and after a year’s 
revolution, with axes fixed to the sun and directed to fixed points 
in the heavens, we find a precession to the amount stated above. 

As pointed out by De Sitter the difficulty in testing the predicted 
precession by a comparison with observation lies not so much in 
the limits of accuracy of observation as in the fact that owing to 
our ignorance of the true values of the earth’s principal moments 
of inertia we do not know with the precision required how much of 
the observed precession is accounted for by the actions of sun and 
moon according to Newton's law. 

We now proceed to the analytical treatment of the problem. 


The geodeste falling coordinates. 


Consider some point-instant in an arbitrary field of ee 
where the potentials are denoted by gas, (a,6=0, 1, 2, 3), x, being 
the time and zb, x, «@) space-coordinates. In the usual Say we 
write the symbols of CHRISTOFFEL : 


ab ab Odam Òg sn Ògao 
=> J gm Sgr. bi 5 ss : 
9 ES 7 E 2 dze | 


where ger are the algebraical complements of the gen. 

A vector Ve is displaced parallel to itself over an inter val dar, 
if its components decrease during the displacement according to the 
formula 


b 
ave is TED ge 


a 


In the point-instant considered: 2°, (a= 0,1, 2, 3), choose a vector 

of unit length having time-character A°,: 
= Jab Ae. Ao, = J 

and three other vectors of unit length, all perpendicular to the 

former and to one another: At, A*,, A*,, such that 
= Jap A*, A, = — 1; and 2 9,,A%A%=0 if 147. 

As in our argument the component of time and the components 
of space will be treated in a different way, we shall establish the 
rule that whenever a suffix is indicated by a Greek character, it 
will not be liable to take the value 0. 

We change variables by introducing the coordinates z' according 
to the following formulae: 


732 


bm 


a 


et — 2% — J Aa; zi—_ 4 & | Abi Am; 24 23 — 


—42{ 55)" — LL 
Own a a 3 


— $F Quy Ab, (Am, An, — AX, Am) 2H 2” 2% — 
— 1S Qty my Ao, (Am, Ar, — AX, Am) 2 2° a 
By Q%m, we have denoted the same form within brackets which 
is found in the foregoing line. Note the symmetry possessed by 
Qo in the suffixes 6 and m. If we put 
Ra mn zE Q™,mn Tia Q% nm ’ 
then Rn, is the same as a four-index symbol of Riemann: 


bn 
8 


| 4% Am; Any, zi 23 oie aes 


ms 
a 


RE mn = ‚ba, mn}, 
and for its covariant components we have the identities which will 
be used in the following: 


Rabd,mn == Roajmn == TT Rab‚nm = Rynn,at ’ 
and 
Rad,mn oF Rom,an mk Rina, bn =); 


We proceed to show that the above transformation actually affords 
the geodesic falling coordinates alluded to in the introduction. 

The axis of 2° coincides with a particle's track. Put every 2*=0, 
_and we get 
bm 


wt — et —= At 2°—} > Ab, Am, 2°2° — 4E Q%) mn ALAT, A" zz es oe 


As a second approximation, this is the equation for the geodesic 
line starting from the point-instant «*, with initial direction para- 
meters A‘, and where z° is the interval along the arc. Thus our 
time-axis is along a particle’s track. Denote the second member of 
this equation by &. 


The axes of space are everywhere geodesics, as far as the approxi- 
mation goes, and perpendicular among themselves and to the axes 
of time. For put z° =r and let the other coordinates vanish with 
the exception of one 2”; on rearranging terms we get 


ga — wt, — Et = Aa, z4 — 
—=|" 
a 


b 
—4 =| ij Ab, Am, z# 2# — § 3 Woman AO, A™, A", rz Ze 
a 


Ab, Am, zee — bk DB Qay mn Abn Am, A”, rra 


Dt + = Q% mn Ab, An, An, ze 2h 2h, 


733 


This is, to the second approximation, the equation for the geodesic 
starting from the point-instant #*, + 5“ with initial direction para- 
meters 


bm 


ke 


Ab, Am Ll 4 = Qs mn Ab, A AM, TT, 


a 
and where z’ is the interval measured along the arc. We notice 
that these parameters are the components of the wntt vector Aon 
translated geodesically from the origin of time along the timetrack, 
with an accuracy up to the second approximation. As a geodesic 
translation does not alter the mutual angles of the translated vectors, 
it follows that the axes of space and time remain perpendicular. 
In the same way it may be shown that every spatial radius, that 
Penne z,—r, 20 As, 20 As, 28) 4,s, with 2,7-- 4,7 1,71, 
is a geodesic, s being the interval along the are from the origin. 


The potentials g' in geodesical falling coordinates. 


We shall calculate the new values g';; by means of the trans- 

formation formula 
Jij = & Pai Pbj Jabs 
where 
Pa = Òvafdzt. 

In calculating the pa; the symmetry of Qs in the suffixes 5 
and m is of great use. [t enables us to arrange terms in a practical 
way. We get 


bm ek 
Pao = As, we >| Ab, A”; gue 4 D3; Qa anh Ab, Al; fj zi zl == 
a 


Ie 5 Ss OF ain Ab; (An; An, oe A”; Am) zi 2d, 
and for any u F0, we get 


bm rae 
Pap. === Ay Pr =| Ab, Am; zt eed 4 = Q%5 mn Ab, Ami A"; zt 2J EE 
a 


=f S065 mn Ab (Ars Artemia er 
— 14 FS Q% mn Abs (Arte A", — Ate Ami) 2° 27, 

In the second lines of both formulae we shall replace Q‚n by 
4 Renn. This is permitted because the bracket forms are skew- 
symmetrical in the suffices m and n. 

In the first lines we find exactly the components of the vectors 
A“; shifted geodesically from the origin to the point-instant denoted 
by 2%. Thus, as far as these parts of pq are concerned, the trans- 
formation formula 2 pa po; Jos gives 1, —1 or O for 2=j=0, 
I=j=u, or 147 respectively. We get 


734 


Goo = 1+ 0— § = Radnn AP, Abs (Amy AX, — Ans Am) zi zo. 

Obviously in the last term the value 0 for 7 contributes nothing 
to the sum. Because of the skew-symmetry of Rasim, in a and 6, | 
the value O can be disregarded also for 7, and the skew-symmetry 
im m and » allows us to write: 

Gop = 1+ J Ret AG Abr A”, Ae ze 27. 

Proceeding to g'o,, we get 

gon =O +0 — 4E Radmn Atn A (Am; An, — An; Am) ied — 
— 4E Rainn At, Abs (Am, AX, — An, Am,) 2F 2° — 
— sy E Rabynn A%, APs (AM: Ar — Ate Amy) 2° or. 

Taking #=0 in the first sum, this part cancels out against the 
second sum (skew-symmetry of Ray», in 4,5). The remaining part 
is taken together with the third sum, and we get 

go = 3E Robynn A% Ab, Am, An, 27 27. 
Finally for g',, we find: 
Jp = — Em + 0 — He & Radin [At, Ao, (Am An, — Anz Am) + 
+ At, Ao, (Am, Ar, — An, Am,)] 27 zt — 
— 42 Radmn (A% Abu + Aas Ab‚) (Am, An, — Att, Am) 2" 2%, 
where «,,=1 for «=r and ¢,,=0 for uv. Having regard to 
the skew-symmetries of Rasm, we reduce this expression to 
gu == — Em +4 = Rab,mn AS, Ao, Am, A”, 27 27. 
If we remember the transformation formnla for Ras mn: 
Bij,rs = = Pai Pdj Pmr Pns Ravn » 
we at once see that without lowering the degree of approximation, 
we may abridge the forms for gs into: 


g'00 == 1 a = R'2,0 Oe, 
910 == } pes: Rabe oe con 
Tig —— Eny + a ee) Rey Zo ie 


It must be noticed that these gravitation potentials depend no more 
on the time z°. The field in our geodesic falling coordinates is station- 
ary as far as our approximation goes. 

The R's are closely associated with RisMann’s measure of curvature. 
If only particles are considered moving so near the centre that the 
squares of the distances multiplied by the measure of curvature 
may be neglected altogether, then the g'ij may be considered to be 
constant and to have the homoloidal values 1, +1, —1, —1. 


Equations of motion for free particles in geodesical falling 
coordinates. 


We put forward the simplifying assumption that only particles 


735 


will be considered moving slowly relative to the falling axes and 
that the square of their velocities will be negligible compared with 
the square of the velocity of light, which, in our coordinates, is 
nearly unity. 

The equations of motion are 

| Pet y {iil dede 

dats: 18 a\ de ds” 

With the above assumption we may put dz°/ds = 1, and we need 
only consider combinations where 7 or j or both of them are 0. 
In the CrrrsrorreL symbols the differential coefficients of g' are not 
known beyond the first powers of the coordinates; therefore the 
reciprocals g may be taken to be 1, —1, —1, —1, and 0. This 


makes 
5 tod 
= a 
Calculating we find: 


00 
| | == TT = Roaor zr, 


| a 


ij 


a 


and 
+ PS (R'28,0r + Rer,0g EE R'ga,or Tei BR groe) 27, 


08 
ps 
= — & Raor 27 — & & (R'px,70 + Par,go + Rope) zt. 
The bracket vanishes by symmetry of the R's,,.0, thus 


0 
| ai =P Rau, or Zr 


a 


Finally the equations of motion for free particles become: 
d* z% 
dz,’ 


Here we can put 


daf 
=d Loe, or ME == = Rea, or pA 
dz 


0 


Pe, R'23,0r ZR 2w,, 
= R’310- SS 20, 
= R'12,or = 2, 
This brings the last term into the form 
— 2[w.v]. 

Interpreting the equation of motion we note that the first term 
in the right hand member accounts for the forces causing the tidal 
effects. The second member has the form of a Cortomisian force, 
but the peculiarity is that the rotation vector w figuring in it, is a 
linear function of the coordinates and thus on opposite sides of the 
planet has the opposite direction. It is conveniently called the 
compound tidal force. It might come into play when we consider 
the motions of a satellite. 


736 


Resuming, we can say that as a first approximation the equations 
of motion for free particles in the geodesic falling system are just 
the same as those in classical dynamics under no forces. When we 
have mutual forces between the particles, their effects on the motions 
will be quite the same as predicted by classical dynamics. In parti- 
cular, a spinning top will keep the direction of its axis of rotation 
unaltered relative to the axes of reference, i.e. our geodesic falling 
coordinates. Hence when referred to the original coordinates, the 
spinning top will for its axis of rotation show whatever precession 
the geodesical falling axes might exhibit. 

The same must be said for the plane of the orbit of a particle, 
moving under a central force. 

If the tidal forces are considered, their effect in changing the 
direction of the axis of rotation relative to the falling coordinates 
would be zero if the earth were of spherical shape. If not, the 
precession caused by them is to be taken in reference to the falling 
axes, and the precession of the latter will be superposed on the 
precession due to the tidal forces. 

The common tidal forces are but part of the second approximation. 
The remaining part is a compound tidal force at right angles and 
proportional to the velocity, proportional to the distance from the 
centre and, like the Coriomisian forces, may be determined as a (three- 
dimensional) vectorial product of the velocity into a vector which, 
by means of certain components of the KimMannian bivector-tensor 
of curvature, is a linear function of the radius vector from the 
centre. For the present we shall leave these forces aside, and turn 
to the question of how much the amount of the precesssion of the 
falling axes may be. 


The precession of the geodesic falling axes in the case of ‘a 
planet moving in a circular orbit. 


AS we pointed out already, a complication in finding the precession 
of the falling axes arises from the fact that the space of the falling 
axes makes some angle with space as defined by an observer who 
has his coordinates fixed to the sun. These spaces intersect in a 
plane perpendicular to the velocity. By confining ourselves to circular 
orbits, matters present themselves much less complicated. 

In each point-instant of the helicoidal track of the planet we draw 
four local axes: one coinciding with the direction of the track; a 
second in the direction away from the sun along a radius vector; 
a third perpendicular to the ecliptic; and the last one with a time 


737 


component and a component tangent to the circular orbit; in such 
a manner that these four directions will be all perpendicular to each 
other. Now, if the planet with the geodesical falling axes comes across 
some particular set of local axes, the axes of time, both the falling 
and the local, will coincide, and therefore the spaces of the falling 
and of the local axes too will be the same. Thus the position of 
the falling axes relative to the local ones can be stated and the 
positions before and after a revolution compared. 

The gravitational field of the sun is given by the form of the 
infinitesimal interval : 

B Saar 1s 
1 — afr 

In this field a circular motion is possible in the plane 6 = 3a, 

with “radius” A and with angular velocity 


dip/dt = w = Vark. 


—rd* —r* sint 6 dy’. 


Now, every where along the track define four vectors A“,,A*,,A%,,A%, 
as follows 


(0) (1) (2) (3) 
2R i “ 
Aa: a 0, 0, = ee 
2 R—8a R 2 R—3a 
Aa: 0: Vi—a/R, 0, 0, 
As: 0, 0, 1/R, 0, 


R 1 CMG ine 
As, : A si rel, 0, Pp LA ( aM, 
(R—a) (2 R—3a) R 2 R—3a 


It will be seen that these vectors are all of unit length and 
perpendicular to one another. They define the local axes. 

A set of these vectors in one particular point-instant can be taken 
as the starting vectors of the geodesic falling coordinates. To find 
the directions of the falling axes after a lapse of interval ds (com- 
ponents A“,ds) we need the values of CurisTorFEL’s symbols. These are, 
in coördinates ¢, 7, 0, p: 

01 


bos uw 
ON OR). 
00 — 11 — 22 33 
em ee SS | [=-(A-0), =~ (R-a) sin’ 0, 
1 Zot 1 2h (R—a) ( 1 1 
a fis Ë ve ai 1 
| Veet Re 
33 ; 23 cos @ bap ; 
= — sin 0 cos 0, | ==. The remaining symbols vanish. 
2 3 sin Ó 


738 


Now, if we calculate the geodesic increment along ds of the 
vector components: 


ETE, he Ab; Am, de, 
we find 
dAa, = 0, 
dA, = 0, 
but 
dAt, = — Va/2R*. At, ds, or = — w At, ds, 
and 


dA+, = +Va/2R*. At, ds, or = + w AY, ds. 

From this we infer that the falling axes of ZW, Z@), after the 
lapse of interval ds, as compared with the local axes reached after 
the interval, show a retrograde rotation of amount wds in the plane 
of these axes. Meantime the planet’s anomaly has increased by wdt. 
Thus, the two angular velocities are the same if the one is measured 
in ds and the other in dt. The ratio is 

ds — V(1—3a/2R). dt. 

In the circular planetary motion this will continue uniformly, and 
it follows that when the planet has completed a revolution, the 
falling axes will not yet have completed theirs if compared with 
the local axes passed by during their motion. At the instant the falling 
axes will have completed a revolution, the radius vector will make 


an angle of 
2R 
an Wm 


with the radius from which they started. Relative to this new radius 
everything will be in exactly the same position as it was in the 
beginning of the revolution, 

Neglecting higher powers of a/R we conclude that there is a 
precession which, per annum, amounts to the excess of the angle 
between the two radii ovef 2x, i.e. 


per annum. 
For the earth, it is 0.019 of a second of arc per annum. 


Zoology. — “Die Verwandtschaft der Merostomata mit den Arach- 
nida und den anderen Abteilungen der Arthropoda”. Von J. 
Verstuys und R. Demorr. (Communicated by Prof. WeBer). 


(Communicated at the meetings of Sept. 25, and October 30, 1920). 


ii 


Noch immer gehen die Ansichten über den phylogenetischen 
Zusammenhang der grossen Abteilungen der Arthropoden, der Ony- 
chophora, Myriapoda, Hexapoda, Arachnida und Crustacea erheblich 
auseinander. Und es ist vor Allem die verschiedene Beurteilung der 
Verwandtschaft der Merostomen mit den Arachniden, welche zu so 
sehr verschiedenen Auffassungen in diesen Fragen führt. 

Im Mittelpunkte der Erörterung steht der einzige lebende Vertreter 
der Merostomen, die Gattung Limulus. Diese Form lebt im Meere 
und atmet dureh Kiemen, welche anscheinend von Gliedmassen 
getragen werden. Dementsprechend warde das Tier zuerst den 
Crustaceen zugerechnet. Weitere Untersuchung schien diese Auf- 
fassung zu bestätigen; namentlich machte die Entdeckung grossen 
Eindruck, dass die junge Larve von Limu/us im Körperauf bau den 
Trilobiten, diesen alten, ausgestorbenen Vertretern der Crustaceen, 
ahnlich ist. Man sprach geradezu von einem Trilobiten-stadium in 
der Entwieklung von Limulus. 

Andrerseits hatte schon 1829 Srraus DÜRKHEIM mit grossem Nach- 
druck auf eine Blutsverwandtschaft von Lumulus mit den Arachniden 
hingewiesen. Ihn folgten einige andere Forscher, bis 1881 und den 
darauffolgenden Jahren Ray LANKESTER das Limudus-problem einer 
eingehenden Prüfung unterzog. Er wies dabei eine tatsächlich über- 
rasschende Uebereinstimmung im Baue von Limulus mit den Arach- 
niden nach, ganz besonders mit den Scorpioniden. LankustER zweifelte 
aber andrerseits nicht an der Verwandtschaft von Limudus mit den 
Trilobiten und anderen Crustaceen. Da Limulus im Vergleich zu 
den Crustaceen eine viel mehr spezialisierte Form ist, musste er 
annehmen, dass Limulus von den Trilobiten oder damit verwandten 
Crustaceen abstammt. Die Arachniden mussten dann wieder von 
Limulus oder dessen weniger spezialisierten vorfahren, den Gigan- 
tostraken, abstammen, wobei die Stammformen der Arachniden vom 
Meeresleben zum Landleben übergegangen waren. 

. 48 

Proceedings Royal Acad. Amsterdam. Vol. XXIII. 


740 


Diese Limulus-Theorie von Lankestrr ist sehr wichtig wegen 
ihrer Konsequenzen ; diese sind folgende: 

1. Da Limulus, und noch mehr die Gigantostraken im Baue 
besonders auffallend mit den Scorpioniden übereinstimmen, müssen 
die ältesten landbewohnenden Arachniden im wesentlichen den Bau 
der Scorpioniden aufgewiesen haben. Alle anderen Typen von Arach- 
niden müssen also von einer den Skorpioniden ähnlichen Stammform 
abgeleitet werden. 

2. Da es gänzlich ausgeschlossen ist, dass Formen wie die Myria- 
poda von Arachniden abstammen (erstere stehen auf viel niedrigerer 
Organisationsstufe), so müssen die Myriapoda und die damit nahe 
verwandten Hexapoda einen besonderen Stamm in der Entwicklung 
der Landarthropoden bilden. An dessen Anfang muss man die sehr 
primitiven Onychophora stellen. Die Arachnida bilden dann daneben 
einen zweiten Stamm der Landarthropoden, der aus den marinen 
Merostomen hervorging und an dessen Wurzel die Scorpioniden 
stehen. Es ist also eine notwendige Konsequenz der LANKEsTER’schen 
Limulus-Theorie, dass zweimal Landarthropoden entstanden sind. 
Auch ihre typischen eigenartigen Atmungsorgane, die Tracheen, 
waren dann zweimal gänzlich unabhängig von einander entstanden. 

Diese beiden Konsequenzen der Limulus-Theorie von LANKESTER 
sind von grosser Bedeutung. Es ist zu beachten, dass ein Tracheen- 
system durchaus nicht so einfach ist und eine zweimalige Entstehung 
schon sehr bemerkenswert ware. Und dann setzt die Ableitung der 
so verschiedenen, zum Teil so einfache Züge aufweisenden Typen 
der Arachniden von scorpioniden-ähnlichen Vorfahren eine erstaun- 
liche Plastizitat des Körperbaues, ganz eingreifende Umbildungen 
derselben, und vielfache Rückkehr zu ursprünglicherer Organisation 
voraus. Die Umbildungsfähigkeit einer schon komplizierteren Orga- 
nisation wird hier in eine überrasschende Beleuchtung gebracht. 


i. 


Priifen wir zunächst die Frage, wie weit die Uebereinstimmung 
im Baue bei den Merostomen und den Arachniden, namentlich den 
Scorpioniden, geht. 

LANKESTER versuchte (1881) den Nachweis zu erbringen, dass die 
Organisation von Limulus Segment fiir Segment und Organ fir 
Organ mit der des Scorpions iibereinstimmt. Und wenn wir auch 
betreffend der Auffassung einzelner Organe zu wesentlich andern 
Ansichten kommen miissen, so ist toch das Ergebnis einer neuen 


741 


Prüfung durchaus die Bestätigung der Lankestrer’schen Schluss- 
folgerung. 

Die äussere Gestalt von Limulus ist allerdings recht erheblich 
modifiziert (Fig. 1), es liegt Anpassung an eine im Sande des Meeres- 
bodens wühlenden Lebensweise vor. Aber die ausgestorbenen Vorfahren 


Fig. 1. Limulus, von der Dorsalseite gesehen. 
Circa Ys der nat. Grösze. Nach SHIPLEY, Cambridge 
Nat. Hist., vol. 4, 1909, p. 261, etwas verändert. 

Abd Abdomen; Cth Cephalothorax; F.A. Facetten- 
auge; L.A. Linsenauge; T Telson. 


- von Limulus, die Gigantostraken, sind den Scorpioniden in äusserer 
Gestallt, Segmentierung und den Gliedmassen ausserordentlich ähnlich 
(Fig. 2, 3). Die wesentlichsten Uebereinstimmung en sind folgende. 

Der Körper besteht aus einem Cephalothorax, einem Praeabdomen 
von 7 und einem Postabdomen von 5 Segmenten mit Telson. 

Der Cephalothorax ist aufgebaut aus 6 gut entwickelten glied- 
massentragenden Segmenten. Die Embryologie vom Scorpion und von 
Limulus lehrt uns, dass dazu vorne noch ein Kopflappen (Acron) 


und ein rudimentäres Praecheliceren-Segment kommen, hinten sich 
48% 


742 


ein zweites verkümmertes Segment, Praegenital-Segment, auschlieszt 
(vergl. Braver, 1895; KisHinoure, 1891 B; Kinestry, 1893; Parren 
und RepENnBAuGH, 1899; Hrymons, 1905). Das Praecheliceren-Segment 


Fig. 2. Ein Scorpionidenähnlicher Gigantostrake, 
Eusarcus scorpionis Grote & Pitt, von der Bauch- 
seite. Circa Ys der nat. Grösze. Nach CLARKE & 
RUEDEMANN, 1912, Vol. 2, Tab. 28. 

Blf. Blattfüsze; K.Pl. Kauplatten der Gliedmassen, 
den Mund umstellend; 7 Sg 7tes abdom. Segment 
(letztes präabdom. Segment = 1stes Segment ohne Blatt- 
fusz und Kiemer, mit normalem Sternit); 8 Sg 8tes 
abdom. Segment (erstes postabdominales Segment, 
mit ringförmigem Chitinpanzer); T Telson (Gift- 
stachel). 


ist sehr rudimentär; es bildet kein selbständiges Coelomsäckchen 
mehr, sondern das Coelomsäckchen des Cheliceren-Segments wächst 
von hinten her in das Praecheliceren-Segment hinein. 

Während das vorderste gliedmassentragende Segment bei den 
meisten Arthropoden Antennen trägt, fehlen diese bei den Arachni- 
den und Merostomen; die vordersten Gliedmassen sind hier als 


743 


Cheliceren ausgebildet, kurze, zwei oder dreigliedrige und meist 
scheerentragende Angriffswaffen. Es ist dies ein sehr auffallendes 
Merkmal, welches Merostomen und Arachniden vereinigt; gleiche 


î 
An 
N \\ 


m. | bt 


Adf 
- ak, 
Cent fy KPI 
3 Pl. 
eA 


| En 


N | 
NN Za of RES G2 D 
eee aN Det 

yy 


Gents 
sea EON 
- | Ses 


Fig. 3 Scorpion, Pandinus, von der Bauchseite. 
Original. %/ der nat. Grösse. 

K.Pl. Kauplatten; m Mund; S Stigmata; 7 Sg Ttes 
abdominales Segment (letztes praeabdom. Segment 
— tes Segment ohne Atmungsorgane); 8 Sg 8s abdom. 
Segment (erstes postabdom. Segment, mit ring- 
förmigem Chitinpanzer); St Sternite des 3ter—6ten 
abdom. Segmentes, welche die Tracheenlungen be- 
decken; T Telson (Giftstachel). 


744 


Verhältnisse finden wir nur noch bei den Pycnogoniden, einer Gruppe, 
die nach neuesten Untersuchungen (Wiren, 1918) walrscheinlich mit 
den Merostomen und Arachniden verwandt ist. Dass die Cheliceren _ 
bei Merostomen und Arachniden am gleichen Körpersegmente liegen, 
ist nicht fraglich. Das Segment folgt auf dem Acron und dem Prae- 
cheliceren-Segment und verschiedene Ubereinstimmungen in Einzel- 
heiten sprechen fiir diese Homologie. So tritt das Cheliceren-Segment 
in der Ontogenese später als die 5 anderen, gliedmassentragenden 
Segmente des Cephalothorax hervor und zwar trennt es sich dann 
vom vordersten Körperabschnitt ab. Auch liegt es zunächst postoral 
und verschiebt sich nachträglich nach vorne bis eine praeorale Lage 
erreicht ist. Die gleiche Verschiebung zeigt das zugehörige Cheliceren- 
ganglion. 

Typisch für die Arachniden ist es, dass die weiteren Gliedmaszen 
des Cephalothorax, 5 Paare, keine eigentlichen Mundteile bilden, 
sondern als lange, mehrgliedrige Gehfüsze, oder, wie besonders das 
vorderste dieser Paare, die Pedipalpen, anch als Tastorgane entwickelt 
sind. Nur nebenbei sind die vorderen Gliedmaszen auch als Mund- 
teile tätig, indem als Kauplatten dienende Vorsprünge der Coxae 
bei der Verarbeitung der Nahrung mitwirken. Mandibel oder Maxillen 
fehlen den Arachniden. Bei den Merostomen finden wir durchaus 
ähnliche Verhältnisse; zwar sind hier an den Coxae alter fünf 
Beinpaare Kauplatten entwickelt, aber im Uebrigen ist die Gestalt 
der Gliedmaszen von dieser Anpassung nicht beeinflusst worden. 
Im Einzelnen ist die Gliederung der Beine etwas verschieden, aber 
genaue Priifung zeigt hier doch auch viel Uebereinstimmung. Beim 
meeresbewobnenden (fossilen) Scorpioniden Palaeophonus nähern die 
Gliedmaszen sich der Gestaltung, die sie bei den Merostomen auf- 
weisen. . 

Auf die gutentwickelten Segmente des Cephalothorax folgt das ver- 
kümmerte Praegenitalsegment. Bei verschiedenen Arachniden ist es 
auch beim erwachsenen Tiere noch deutlich abgegrenzt als vorderstes 
abdominales Segment. Bei den erwachsenen Scorpioniden und Mero- 
stomen hat es durch Verwachsung mit dem Cephalothorax seine 
Selbständigkeit eingebüszt. 

Auch in der Segmentierung des Abdomen besteht zwischen den 
Scorpioniden und den primitiven Merostomen, den Gigantostraken, 
vollkommene Uebereinstimmung. Das Abdomen besteht aus 12 Seg- 
menten und dem postanalen Telson. Die Differenzierung in ein aus 
7 Segmenten bestehenden Praeabdomen mit getrennten Tergiten und 
Sterniten, und ein aus 5 Segmenten bestehenden Postabdomen, 
dessen Segmente von einem geschlossenen, einheitlichen Skeletring 


745 


umgeben sind, ist Scorpioniden und Gigantostraken gemeinsam. Das 
Telson schlieszlich ist beim Gigantostraken Husarcus scorpionis von 
der selben eigenartigen Form wie bei den Scorpioniden (vergl. 
Fig. 2 und 3); bei Hughmilleria zeigt es noch Aehnlichkeit damit. 
Der eigentiimliche Gebrauch des Telsons als Waffe (Giftstachel) 
dürfte daher den Scorpioniden und primitiven Gigantostraken ge- 
meinsam gewesen sein. Ebenso aber wohl auch die mit dieser Funk- 
tion des Telsons eng verkniipfte Ausbildung eines schlanken und 
sehr beweglichen Postabdomen. 

Uebereinstimming besteht auch in soweit als das Praeabdomen 
die Atmungsorgane tragt — bei den Scorpioniden an Segment 3 
bis 6 die Tracheenlungen, bei den Gigantostraken und Limu/us an 
Segment 2 bis 6 die Kiemen. Vergleichung der Kiemen von Limulus 
mit den Tracheenlungen der Scorpioniden und anderer Arachniden 
deckt im Bau eine in mehrerer Hinsicht auffallende Uebereinstimmung 
auf. In der Lage scheint zunächst in so weit ein erheblicher Unter- 
schied vorzuliegen, als die Kiemen der Merostomen an der Hinter- 
flache der Blattfiisse liegen, die Tracheenlungen der Arachniden an 
der Bauchseite im Innern des Körpers, bedeckt von den Sterniten 
der betreffenden Segmenten. Blattfiisse fehlen den Arachniden und 
der Unterschied wird dadurch anscheinend noch erheblicher. LANKESTER 
(1881, 1885), Kinesiuy (1885, 1893) und Mac Lop (1884) versuchten 
den Unterschied in der Lage zu erklären und die Atmungsorgane 
der Arachniden von den Kiemen von Liümulus abzuleiten. Prüfung 
der Verhältnisse zeigt aber, dass ein so erheblicher Unterschied, wie 
die genannten Autoren ihn hier zu finden glaubten, gar nicht vor- 
handen ist. Die Blattfüsse der Gigantostraken entsprechen durchaus 
den Sterniten am Praeabdomen der Scorpioniden (vergl. Fig. 2, 3); 
sie sind damit identisch und sind auch wiederholt als Sterniten be- 
zeichnet worden (u.a. von SarLE, 1903, p. 1093 und von Crarke &, 
RUEDEMANN in ihrer Monographie, 1912, p. 60, 65). Die Kiemen der 
Gigantostraken liegen aber genau so auf der inneren, dem Körper 
zugekehrten Seite dieser Sternite, wie die Tracheenlungen bei den 
Arachniden. In der Lage ist kein Unterscheid vorhanden. Nur liegen 
die Kiemen der Gigantostraken nicht in einem engen, nur durch 
ein Stigma geöffneten Raume, wie die Tracheenlungen, sondern in 
einem weiten Raume, der am hinteren und seitlichen Rande der 
Sterniten in offener Verbindung mit der Aussenwelt steht. Der 
Irrtam bei LANKESTER, KinesLey und Mac Lxop lag darin, dass sie 
in den Blattfüssen wahre Gliedmassen sahen, homolog den ty pischen 
Gliedmassen der Arthropoden. Bei den Gigantostraken ist es ohne 
weiteres klar dass dies nicht zutrifft, sondern dass es sich um Sternite 


746 


handelt, die beweglich sind. Dass die Blattfiisse von Limulus auch 
nur modifizierte Sternite sind (daneben vielleicht noch Reste von 
Gliedmaszen enthalten) ist bei ihrem mehr komplizierten Bau viel 
weniger einleuchtend, muss aber doch nach Analogie der bei den 
Gigantostraken vorliegenden Verhältnissen geschlossen werden (verg. 
die eingehendere Darlegung von Versivys, 1919). 

Scorpioniden und primitive Merostomen (Gigantostraken) zeigen 
also bis in Einzelheiten der Segmentierung durchaus gleichen Bau, 
gleiche Körperregionen, aus derselben Segmentzahl bestehend, und 
die gleichen rudimentären Segmente. Die Neuromerie, die alte Ver- 
hältnisse so zäh fest zu halten vermag, bringt keinen Hinweis auf 
irgend einen wesentlichen Unterschied in der Segmentierung, etwa 
durch auftreten rudimentärer Neuromere die nur der einen oder 
anderer der zwei Abteilungen eigen waren. Dass bei Limulus mit 
der Verkürzung des Abdomens einige hintere Segmente und Neuromere 
fehlen, ist nicht befremdend. Im Ban des Gehirns besteht sehr weit- 
gehende Uebereinstimmung (vergl. HOLMGREN, 1916, p. 107, ff.) 

Eine interessante Uebereinstimmung liegt weiter in dem Anftreten 
eines ähnlichen, im Cephalothorax liegenden inneren Skeletes, eines 
Endosternits, bei Lumulus und bei Arachniden. Es hat bei Limes 
auch Áhnlichkeit in der Form mit dem Endosternit speziell der 
Araneae und der Scorpione, sowohl in den Fortsätzen wie in der 
Bildung eines subneuralen Bogens, der das Zentralnervensystem ring- 
formig umspannt. 

Bei der Muskulatur ist das Auftreten eigentiimlicher dorsoventraler 
Muskeln von Bedeutung, die sich in segmentaler Anordnung von der 
dorsalen zur ventralen Körperwand im Abdomen (Praeabdomen) 
erstrecken. Besonders interessant sind die in der gleichen Körper- 
region liegenden venopericardialen Muskeln, welche von Limulus, 
Scorpioniden, Araneae und Pedipalpi bekannt sind; sie verbinden 
die Wand des Pericard mit dem des ventralen Blutsinus und sind 
unseres Wissens von anderen Arthropoden nicht bekannt (vergl. 
LANKESTER, Bennam & Buck, 1885). Auch die Muskulatur des Cephalo- 
thorax zeigt, im Zusammenhang mit dem Vorhandensein eines ähnlich 
geformten Endosternits eine gewisse Uebereinstimmung. Diese Áhnlich- 
keiten sind deshalb von einiger Bedeutung, weil entsprechend der 
ganz anderen Form des Hautskelettes erhebliche Unterschiede in der 
Muskulatur bei Limu/us und dem Scorpion zu erwarten sind, und 
in mancher Hinsicht auch vorliegen. BERNARD (1896, p. 395) sieht 
in diesen Unterschieden eine Schwierigkeit fiir die Annahme einer 
näheren Verwandschaft von Limulus mit den Arachniden, aber sie 
scheinen uns durchaus nicht erheblicher als sie bei der besonderen 


747 


Spezialisierung des Abdomens von Limudus zu erwarten sind. Die 
Unterschiede in der Muskulatur hätten nur dann in diesem Sinne 
Bedeutung gehabt, wenn sie bei ähnlichem Bau des Abdomens, also 
etwa in der Muskulatur der Scorpioniden und der uns in dieser 
Hinsicht als fossile Formen unbekannten Gigantostraken nachgewiesen 
waren. 

Am Darmkanal sind als Ähnlichkeiten, welche mit einer Verwant- 
schaft in Beziehung gebracht werden können, hervorzuheben das 
Vorhandensein mehrerer hinter einander liegender Mitteldarm-diver- 
tikel (sog. Leber), sowie ihre gleiche eigentiimliche Bildungsweise 
beim Embryo durch Einwuecherung von Mesodermsepta in die 
Dottermasse. Bei den Crustaceen entsteht der Hepatopankreas (Leber) 
dadurch, dass an einer Stelle des Mitteldarmes Divertikel hervor- 
wachsen. 

Auch die spate Anlage des Proetodaeums ist den Arachniden und 
Limulus gemeinsam. Wester (1913) wies weiter nach, dass die 
Chitinauskleidung des Darmkanals bei Limulus mit dem der Arach- 
niden übereinstimmt, indem ein erheblicher Abschnitt des Darmkanals 
ohne innere Chitinauskleidung bleibt; bei Crustaceen soweit unter- 
sucht, fand er immer den ganzen Darm von einem Chitinhäutchen 
ausgek leidet. 

LANKESTER (1881, p. 615; 1904, p. 196) hat auch verschiedene 
Uebereinstimmungen in Blutgefäszsystem hervorgehoben. Es bestehen 
hier zweifellos Ähnlichkeiten. Aber abgesehen von den schon erwähn- 
ten eigentümlichen venopericardialen Muskeln, die auf eine gleiche 
Besonderheit im Kreislaufe hinweisen, sind die andern Ueberein- 
stimmungen doch nicht derartig, dass sie nicht auch eine Folge 
konvergenter Umbildung sein könnten und sind demnach als Beweise 
fiir eine Verwandtschaft von Limulus mit dem Scorpion nicht von 
grossem Werte. Damit soll nicht verneint werden, dass diese Ueber- 
einstimmungen mit der Ansicht einer nahen Verwandtschaft dieser 
Tiere in schönstem Einklange stehen. 

Ebenso scheinen uns die — neben nicht unwesentlichen Unterschieden 
— vorhandenen Ahnlichkeiten im Baue der Coxaldrüsen den Scorpions 
und Limulus beurteilt werden zu miissen. Die Miindung der Coxal- 
drüsen an den Coxae des 5ter Gliedmassenpaares stimmt überein. 

Die Art der Follikelbildung in den Ovarien lässt Zimulus und die 
Arachniden als eine scharf umgrenzte Gruppe erscheinen, Die gleiche 
Organisation finden wir nur noch bei Peripatus und bei Myriapoden. 
Die Zusammengehörigkeit dieser Formen wird ferner durch die in 
den Hiern vorhandenen Dotterkerne bestätigt. 

Aus allen diesen Uebereinstimmungen muss unbedingt auf eine 


748 


Verwandtschaft von Limulus sowie der Gigantostraken mit den 
Arachniden geschlossen werden. Und diese Verwandtschaft muss 
eine sehr enge gewesen sein, da die Ahnlichkeit im Baue zwischen 
Gigantostraken und Scorpioniden nicht nur eine allgemeine, funda- 
mentale ist, sondern sich auch auf eine Reihe besonderer Anpassun- 
gen erstreckt. Konvergenz wird ausgeschlossen dadurch, dass die 
Voraussetzung dazu, ähnliche Lebensweise, schon durch den Unter- 
schied in Milieu (Meeres- und Landbewohner !) nicht gegeben ist. 
Dagegen spricht ‘auch die tiefere Uebereinstimmung im Baue vieler 
Organe, sowie das Fehlen aller wesentlichen Unterschiede sowohl 
im Bau wie in der Entwicklung, wie es doch erwartet werden 
miisste falls die Uebereinstimmungen nur auf Konvergenz beruhten. 
Wichtig ist auch, dass gerade unter den älteren Formen der Mero- 
stomen einige den Scorpioniden am ähnliehsten sind und die Unter- 
schiede in verschiedenen Entwicklungsreihen der Gigantostraken 
zunebmen, so innerhalb der Pterygotidae und bei den Xiphosura, 
bis bei der lebenden Limulus schlieszlich eine von den Scorpioniden 
recht verschiedene Gestalt erreicht worden ist. Die Ahnlichkeit im 
Bau der Merostomen und der Arachniden ist also keine Folge von 
Konvergenz, sondern eine Folge wahrer und enger Blutsverwandt- 
schaft. 

Wir pflichten also Straus Dürkneim und LANKESTER bei, dass die 
Merostomen mit den Arachniden nahe verwandt sind und mit diesen 
in einer Abteilung, einer Klasse, der Arthropoda gestellt werden 
müssen; sie zeigen alle wesentlichen Eigentümlichkeiten der Orga- 
uisation der Arachniden. Die Gigantostraken sind sogar mit den 
Scorpioniden offensichtlich viel enger verwandt, wie diese mit den 
Opilioniden, Acariden oder Solifugen. 


UI. 


Das Wesentlichste am Lomulus-problem ist aber nicht der Grad 
der Verwandtschaft der Merostomen mit den Arachniden, sondern 
die Beantwortung der Frage ob nun die Arachniden von den mee- 
resbewohnenden Merostomen abstammen oder umgekelrt diese aus 
landbewohnende Arachniden hervorgegangen sind. Erstere Auffassung 
ist die von LANKESTER und der Anhänger seiner Theorie. Sie bringt 
notwendigerweise mit sich die Auffassung, dass alle Arachniden von 
Formen abstammen, deren Organisation derjenigen der Scorpioniden 
äusserst nahe stand, im grossen und ganzen sogar damit identisch 
war. Sie allein auch zwingt uns die eigenartigen Konsequenzen 
der Limulus-Theorie anzunehmen, die S. 740 betout wurden. 
Ist dagegen die Auffassung richtig, dass die Merostomen von land- 


749 


bewohnenden Arachniden abstammen, dann bekommen wir ein sehr 
viel einfacheres Bild von der Verwandtschaft der groszen Gruppen 
der Arthropoden und von der Umbildung der Organisation innerhalb 
der Arachniden. Eine dritte Möglichkeit, besonders eine Ableitung 
der Gigantostraken und Scorpioniden von einer gemeinsamen, aber 
wesentlich einfacher und primitiver gebauten Stammform, gibt es 
nicht. Eine solche Auffassung ist zwar besonders in Bezug auf die 
Ableitung der Atmungsorgane der Arachniden ausgesprochen worden 
(vergl. Hrymons, 1905; Reuter, 1909; Kautscn, 1910), aber sie ist 
nicht haltbar. Gigantostraken wie Husarcus, Hughmilleria und Slimo- 
nia sind den Scorpioniden so ähnlich dass die gemeinsame Stamm- 
form dieser Tiere auch einen sehr scorpioniden-ähnlichen Bau aufge- 
wiesen haben muss; Scorpioniden-Habitus und hochdifferenzierte, 
den Tracheenlungen durchaus ähnliche Atmungsorgane müssen vor- 
handen gewesen sein (vergl. auch Kassranow, 1914, p. 208, und 
Vexstuys, 1919, p. 8, 9). Lankester hat denn auch richtig erkannt, 
dass die Stammform aller Arachniden nach seiner Theorie sehr 
scorpioniden-ähnlich gewesen sein musste (vergl. die Scbilderung 
dieser Stammform bei seinem Schüler Pocock, 1893, p. 2). 

Dass die Lankustrersche Limulus-Theorie bei der Ausarbeitung zu 
manche merkwiirdige und unwarscheinliche Konsequenz führt, ist 
aus den eigenen Arbeiten von LANKESTER's Schülern und Anhängern 
ersichtlich. Seine Theorie zwingt uns, anzunehmen, dass die Tracheen, 
die den meisten Arachniden zukommen, mit den Tracheen der Ony- 
chophora, Myriapoda und Hexapoda keinen genetischen Zusammen- 
hang bezitzen; wir werden weiter gezwungen anzunehmen, dass 
Tracheen sich innerhalb der Arachniden selbst mehrere Male gebildet 
haben und dabei dann noch teilweise aus Tracheenlungen, teilweise 
als Organe sui generis (vergl. Pocock, 1893, p. 17; Laurin, 1894, 
p. 46—47; Purcerr, 1909, p. 88; Vurstuys, 1919, p. 43 —4d). Es 
stellt sich sogar heraus, dass die Umbildung der Kiemen der Mero- 
stomen zu Tracheenlungen ùnabhängig von einander bei den Scor- 
pioniden einerseits und bei den übrigen pulmonaten Arachniden 
andrerseits stattgefunden haben müsste (Purcerr). Nimmt man mit 
LANKESTER an, dass die Blattfüsse der Merostomen echte Gliedmaszen 
seien (dies stimmt nicht; es sind, wie oben S. 745 dargelegt wurde, 
beweglich gewordene Sternite), so entsprechen ihnen die Pectines der 
Scorpione und die Spinnwarzen (jedenfalls die äusseren) der Araneae. 
Die Pectines werden dann aber bei den Pedipalpi von Tracheenlungen 
vertreten und die Spinnwarzen müssten bei ihrer Entstehung aus 
kiementragenden Blattfüssen ein Tracheenlungen-Stadium durchlaufen 
haben (Purcerr, 1909, p. 90)! 


750 


Und noch ein weiteres groszes Tatsachen-Material macht der 
LANKESTERSChen Theorie bedeutende Schwierigkeiten. Die Scorpioni- 
den, die nach Lankester als den Stammformen der Arachniden sehr 
nahe stehenden Formen auch den urspriinglichsten Bau aller Arach- 
niden aufweisen sollten, sind in mehreren wichtigen Punkten zweifellos 
weniger ursprünglich als verschiedene andere Arachniden. Es sind 
follgende Punkte hervorzuheben. 

1. Die Scorpioniden haben, ebenso wie die Merostomen, keine freien 
Segmente mehr am Cephalothorax. Bei den Solifugen (SORuNsEN, 
1914), den Palpigradi und den Schizonotidae aber sind die zwei hin- 
teren Thoraxsegmente frei vom cephalothoracalen Riickenschilde. 

2. Das Praegenital-Segment, welches bei den Scorpioniden und 
Merostomen gänzlich mit dem Cephalothorax verwachsen ist, ist bei 
anderen Arachniden noch selbständig, so bei den Palpigradi, bei 
den Schizonotidae und anderen Pedipalpi, bei den Pseudoscorpiones, 
und, allerdings nur schwach entwickelt, bei den Araneae (vergl. 
Borner, 1902A). 

3. Die Differenzierung in ein 7-gliedriges, breiteres Praeabdomen 
und ein schlankes, aus 5 Gliedern und einem Telson bestehendes 
Postabdomen, wie sie das Abdomen bei den Scorpioniden und eini- 
gen Gigantostraken aufweist, fehlt den andern Arachniden, anch 
solehen, wo das Abdomen deutlich aus einer gröszeren Zahl von 
Segmenten besteht (Solifugen, Pseudo-Scorpioniden und amblypygen 
Pedtpalpt). 

4. Verschiedene Arachniden, besonders die Palpigradi und der 
fossile Arachnide Sternarthron, zeigen sehr viel primitivere Verhält- 
nisse in Bezug auf die Sterna, indem auf jedem Gliedmaszenpaare, 
auch zwischen den Cheliceren, noch ein selbständiges Sternum ge- 
funden wird. Bei den Seorpioniden und Merostomen finden wir sehr 
weitgehende Verschmelzung und wohl auch Verschiebung der Sterna. 
Die Solifugen und Pedipalpi sind in diesem Punkte gleichfalls ur- 
spriinglicher wie die Scorpioniden. 

5. Das Endosternit weist bei den Palpigradi und den Schizonotidae 
viel primitivere Verhältnisse auf, als bei den Seorpioniden und 
Limulus. Bei den Solifugen fehlt ein eigentliches Endosternit und 
hier muss LANKEsTER Riickbildung annehmen; es wird hier aber funk- 
tionell vertreten von einem Paare vom Aussenskelet ausgehender 
Entapophysen; es liegen also auch hier viel einfachere und primi- 
tivere Verhältnisse vor, als beim Scorpion. 

6. Die Coxaldrüsen der Arachniden gestatten keine Ableitung von 
dem einen Drüsenpaare mit Mündung am Sten Segmente des Cepha- 
lothorax, welches beim Scorpion vorhanden ist. Es kommt bei ver- 


751 


schiedenen Ordnungen der Arachniden daneben oder ausschlieszlich 
ein Drüsenpaar im 3" Segmente des Cephalothorax vor, und die 
Solifugen und Palpigradi besitzen (nur) ein Coxaldrüsenpaar im 
2ten Segmente. Wir müssen diese Verhältnisse von einem primitiven 
Zustande ableiten, wo vollstandige Coxaldrüsen noch in den meisten 
(wohl 2ten bis 5'en oder gar 2'" bis 6ten) Segmenten des Cephalo- 
thorax vorhanden waren. Weder die Scorpioniden noch Zumulus 
können hier als Ausgangszustand dienen (vergl. Buxton, 1913, 
1917). 

7. Bei Sternarthron, Koenenia (Palpigradi) und den Solifugen ist 
die Mundöffnung völlig unabhängig von den Gliedmaszen; Kau- 
platten fehlen. Dies ist ein sehr urspriinglicher Zustand, der sich 
schwerlich, wie es Borner (1902, p. 436, 437) will, durch eine Art 
Atavismus erklären lässt. Die Aufnahme nur flüssiger Nahrung, 
kombiniert mit einer eigenartigen ,, Aussenverdauung” (BerTKav, 1884; 
vergl. BrRNARD, 1896, p. 363; Borner, 1904, p. 75; Jordan, 1913, 
p. 444), ein typischer Zustand der Arachniden, machte Kauwerkzeuge 
von vorne herein überflüssig. Wo diese jetzt auftreten, wie bei den 
Seorpioniden und den Merostomen, stellen sie gewiss einen Neuer- 
werb dar, womit auch eine zweifellos sekundäre Verlagerung des 
Mundes nach hinten verknüpft ist. Am meisten spezialisiert sind in 
dieser Hinsicht gerade die Merostomen. 

8. Auch die Augen der Scorpioniden können nicht den Ausgangs- 
punkt für diejenige aller Arachniden gebildet haben; sie sind dazu 
viel zu sehr spezialisiert im Vergleiche mit den Augen anderer 
Arachniden. 

Wir sehen aus dieser Zusammenstellung, wie das Urarachnid, 
welches die Lankrestersche Limulus-Theorie annehmen muss, mit 
seinem Scorpioniden-Bau, unmöglich das wirkliche Urarchnid gewesen 
sein kann. Hs zeigt nicht den passenden Bau des Cephalothorax, 
des Praegenitalsegmentes, des Abdomens, der Sterna, der Atmungs- 
organe, des Mundes, des Endosternits, der Coxaldriisen und der 
Augen! Die primitiveren Verhältnisse unter den Arachniden finden 
wir bei Formen, welche den Merostomen und Scorpioniden möglichst 
ferne stehen, bei den Solifugen, den Palpigradi und den Schizonotidae. 
Man muss hieraus unbedingt schliessen, dass wir mit der LANKEs- 
TER schen Auffassung von der Abstammung der Arachniden von den 
Merostomen nicht auf richtigem Wege sind. Dies hat viele Zoologen 
dazu geführt überhaupt an einer Verwandtschaft von Leumulus mit 
den Arachniden zu zweifeln. Doch steht diese fest begründet; falsch 
kann und muss aber die Auffassung LANKESTER's sein, dass die 
meeresbewohnenden Merostomen die Stammformen der landbewohnen- 


752 


den Arachniden seien, — auch die umgekehrte Ableitung ist denkbar 
und soll jetzt gepriift werden. 

Wir haben hier jedenfalls eine Anderung des Mediums vor uns, 
indem die Tiere entweder vom Meeresleben zum Landleben oder, 
wie wir jetzt besonders betrachten wollen, vom Landleben zum 
Meeresleben übergegangen sind. Dies konnte von grossem Einfluss 
auf den Bau einiger Organe gewesen sein. Es tritt die Frage in 
den Vordergrund ob wir nicht im Bau dieser Tiere Verhältnisse 
aufdecken können, die uns zeigen ob das Landleben oder das Wasser- 
leben den mehr ursprünglichen Zustand war. 

Hierbei denkt man zuerst an die Atmungsorgane, als diejenigen 
Organe, deren Bau am ersten vom Medium beeinflusst werden könnte. 
Die Homologie der Tracheenlungen mit den Kiemen der Merostomen 
kann nicht bestritten werden. Und wir finden hier tatsächlich 
Unterschiede im Bau, welche mit dem Medium im engsten Zusam- 
menhänge stehen (vergl. S. 007). Die eigenartigen Lamellen, die für 
die Atmungsorgane so typisch sind, liegen verschieden. Bei den 
Merostomen liegen sie ziemlich offen an der Hinterfläche der Blatt- 
füsse, sodass das Meereswasser sie frei umspült; die Lamellen sind 
gross und zahlreich (Limulus), damit eine genügend grosse Ober- 
fläche für den Gasaustausch mit dem immerhin sauerstoffarmeren 
Meereswasser gegeben sei. Bei den Arachniden sind die Lamellen 
viel kleiner und liegen verborgen in Höhlen, die durch eine enge 
Offnung, das Stigma, nach aussen miinden; sie sind dadurch gegen 
eintrocknen oder Verletzung durch Erdteilechen geschiitzt, die Luft 
hat doch geniigend Zutritt und die Oberfläche der Lamellen genügt 
fiir die Aufnahme von Sauerstoff aus der daran viel reicheren Luft. 
Der Zusammenhang von Bau und Medium ist also klar erkenntlich. 
Zur schnelleren Erneuerung des Atemwassers liegen die Kiemen 
der Merostomen auf den beweglichen Blattfüssen. 

Diese Blattfiisse entsprechen den Sterniten der Scorpione (vergl. 
S. 007 und Fig. 2, 3). Nun sind aber Sternite nichts anderes als 
Skeletplatten der Haut und als solche primar unbeweglich. Sie 
miissen bei den Gigantostraken also erst beweglich geworden sein 
und es muss dies ein sekundärer Zustand sein im Vergleich mit 
den unbeweglichen Sterniten der Scorpioniden. Aber die von unbe- 
weglichen Sterniten bedeckten, also nur durch ein enges Stigma 
zugänglichen und bei ihrer entsprechend inneren Lage auch nur 
verhältnissmässig kleinen Atmungsorgane können nur in der Luft 
Geniigendes geleistet haben; sie kénnen nur Tracheenlungen und 
niemals Kiemen gewesen sein. Die gemeinsamen Stammformen der 
Scorpioniden und Merostomen waren also durch Tracheenlungen 


753 


atmende Tiere, das heisst dundlebende Tiere. Mit dem Uebergang 
zum Meeresleben wurden die Atmungsorgane daran, also an die 
-vom sauerstoffarmeren und weniger beweglichen Medium gestellten 
Bedingungen angepasst durch Vergrösserung der Oberfläche der 
Lamellen und der Lungenhdhle selbst mit den, an den hinteren 
Rand der Sterniten liegenden, Stigmata. Dadurch wurden die Sternite 
mehr und mehr aus dem engen Zusammenhang mit dem iibrigen 
Körper gelöst und schliesslich zu den beweglichen, kiementragenden 
Chitinplatten, die wir bei den Gigantostraken und, etwas kompli- 
zierter gebaut, bei Limulus finden. Es spricht auch für die Richtig- 
keit dieser Auffassung, dass wir bei den Merostomen neben den 
Blattfiissen keine Sternite finden. 

Die Atmungsorgane und das Landleben der Scorpioniden sind 
also urspriinglicher als die Kiemen unddas Meeresleben der Merostomen! 

Empfindlich fiir eine Anderung des Mediums miissen vielfach auch 
die höheren Sinnesorgane sein. Bei den Merostomen und Scorpio- 
niden ist offenbar der Bau der Augen vom Medium beëiflusst wor- 
den; denn diese Sinsesorgane sind bei beiden recht verschieden 
gebaut (vergl. Demon, 1914; 1917). 

Limulus besitzt zwei paarige Augen, das Facettenauge und das 
Linsenauge, beide oben auf dem Kopfbrustschilde liegend (Fig. 1). 
Ersteres, obwohl kein typisches Facettenauge wie es die Crustacea 
und Merapoda aufweisen, funktioniert ähnlich, indem jedes der 
zahlreichen Omma oder Einzelaugen, woraus es aufgebaut ist, nur 
einen Punkt der Umgebung sieht und erst die Vereinigung aller 
dieser Punktbilder das Bild gibt, welches vom Tiere wahrgenom- 
men wird. Die Linsenaugen sind kleine, einfache Augen; wahr- 
scheinlich sind sie Hilfsaugen der Facettenaugen, 
womit sie das Gesichtsfeld ungefähr gemein 
haben. Sie dienen vielleicht dazu, die Entfer- 
nung der Objekte einzuschätzen, welche mit 
dem Facettenaugen gesehen werden. Denn ein 
Facettenauge wie das von Limulus, gestattet 
nur eine sehr mangelhafte Einschätzung der 
Entfernungen. Viele Insekten besitzen zu 

Fig. 4. Cephalothorax diesem Zwecke Hilfsaugen, die Ocellen (vergl. 
mit Augen eines Scor- Devo und SCHEURING, 1912). 
pions, Pandinus. Ori- B ; i 
Saal: nat: Grosze. Der Scorpion hat keine Facettenaugen, aber 

H.A. Hauptaugen; Oc. Statt deren beiderseits des Cephalothorax eine 
Ocellen. Gruppe von 2 bis 5 Hinzelaugen oder Ocellen, 

jedes ein einfach gebautes Linsenauge (Fig. 4). 


754 


Dazu kommt oben auf dem Cephalothorax noch ein Paar Einzel- 
augen, ebenfalls mit Linse, aber von erheblich komplizierterem 
Bau, die Hauptaugen. Man hat wegen der ähnlichen Lage diese | 
Hauptaugen mit den Linsenaugen von Limulus verglichen, aber 
nähere Untersuchung hat einen so prinzipiellen Unterschied im 
Bau aufgedeckt, dass eine Umbildung der Hauptaugen zu den 
Linsenaugen oder umgekehrt unmöglich erscheint (Demon, 1914, 
1917; bestätigt wurde dies durch. die wichtige Entdeckung von 
HormareN, 1916, p. 110, dass die Innervierung von verschiedenen 
Absehnitten des Gehirnes ausgeht). Denken wir uns nun, dass ein 
Tier mit den Augen von Limulus, wie sie soweit ersichtlich auch 
die Gigantostraken besaszen, zum Landleben überging. Die Facetten- 
augen würden dabei in ihrer Leistung kaum beinflusst werden, denn 
bei der eigenartigen Weise, worin beim Facettenauge das Bild aus 
Einzelpunktbildern aufgebaut wird, hat das Medium keinen Einfluss 
auf das entstehende Bild. Das einfache Linsenauge wirde wohl 
beeinträchtigt werden in seiner Leistung, indem das von der Linse 
entworfene Bild nicht mehr genan auf die Netzhaut projiziert werden 
würde; entweder wäre dies bei einem Hilfsauge der Facettenaugen 
nicht sehr wichtig und das Auge würde ohne grössere Umbildung 
noch genügend leisten können, oder aber es würde als bedeutungs- 
los rudimentär werden. Niemals aber hätte das Hauptauge des 
Scorpions daraus entstehen können. Eine erhebliche Umbildung der 
Augen erscheint also durch den Wechsel des Mediums nicht begründet 
und es liegt kein ersichtlicher Grund vor, weshalb die Augen von 
Limulus zu den Augen des Scorpions umgebildet worden waren. 
Die Aufteilung des Facettenauges in eine Gruppe von Einzelaugen, 
eine Umbildung, die eine Verschlechterung des Gesichtsvermögens 
bedeutet, bleibt unerklärt. Und unbeantwortet bleibt die Frage, wo 
das hochentwickelte Hauptauge des Scorpions plötzlich hergekommen 
sein könnte. Es gelingt nicht die von LaNkesrers Theorie verlangte 
Umbildung der Augen von Limulus in die des Scorpions aus dem 
Mediumwechsel heraus zu erklären, oder durch morphologische Daten 
wahrscheinlich zu machen. Stellen wir uns nun die Gegenfrage: 
welchen Einfluss köunte der Uebergang zum Wasserleben auf die 
Augen, auf das Sehen, des Scorpions ausüben? Bei den Hauptaugen 
würde, durch die viel geringere oder fehlende Brechung der Licht- 
strahlen an der convexen Vorderfläche der unbedeckten Linse, das 
Bild ziemlich weit hinter die Netzhaut fallen, sodass im Auge nur 
ein sehr undeutlicbes Bild entstehen würde. Das Tier würde mit 
seinen Hauptaugen nicht mehr sehr gut sehen können, und diese 
würden, wie alle nutzlosen Organe, zurückgebildet werden oder 


755 


ganz verschwinden. Die Anderung des Mediums würde also das 
Fehlen der Hauptaugen bei Limulus erklären *). 

Die gehäuften Seitenaugen des Scorpions sind ebenfalls Linsenaugen 
und jedes einzelne wiirde, genau wie bei den Hauptaugen, von der 


Anderung des Mediums in ibrer Leistung erheblich beeinträchtigt 
werden. Aber diese Augen arbeiten, soweit ersichtlich, beim Scorpion 
auch schon einigermaszen zusammen, wie die Ommata der Facetten- 
augen, und dabei ist es nicht so wesentlich, ob das Hinzelbild auf 
oder hinter die Netzhaut fallt; namentlich fiir das so wichtige Sehen 
von Bewegungen der umgebenden Objekte wäre die Gruppe von 
Ocellen noch brauchbar. 

Die Seitenaugen könnten also erhalten bleiben und zwar so, dass 
sie nur noch zusammen, wie Ommata, wirkten. Man kann sich 
recht gut vorstellen, das derart im Wechsel des Mediums der Anstosz 
zur Vermehrung und zum engeren Anschluss der Ocellen gegeben 
war und dabei musste aus den Ocellen des Scorpions ein eintaches 
Facettenauge entstehen. 

Das Linsenauge von Limulus ist offensichtlich aus einem der 
Seitenaugen des Scorpions hervorgegangen, das 
nicht in das Facetten-auge mit aufgenommen 
wurde. Wir kennen einen fossilen, im Meere 
lebenden Scorpion, Proscorpius osborni, der 
deutlich das Wegriicken eines dieser Augen 
von den anderen, nach der Mittellinie des Körpers 
zeigt, während das alte Hauptauge auch noch 
erkennbar ist (Fig. 5). 

Es kann also durch den Uebergang vom 

Fig. 5. Cephalothorax Landleben zum Meeresleben sowohl das Ver- 
mit Augen des marinen schwinden der Hauptaugen wie die Umbildung 
Scorpions Proscorpius der Seitenaugen zum Facettenauge (und einem 
pee) ach CLARKE Hilfsauge) erklärt werden. Auch die deutliche 
& RUEDEMANN, 1912, : ; - 
p. 389, Fig. 83. Tendenz der Linse sich abzuschnüren deutet 

H.A. Hauptaugen; Oc. darauf hin dass hier ein Auge vorliegt, das 
-Ocellen; Oc’ nach der erst auf dem Wege ist, sich dem Sehen im 
Medianlinie verschobe- Wasser anzupassen (Näheres s. Demon, 1914). 
nes Ocellenpaar. Aus der Gestaltung der Linse allein miisste 


1D Nach HOLMGREN wäre es bei Limulus als Lateralteil des Geruchsorganes 
vorhanden (1916, p. 111). Diese Auffassung ist irrig. Dieses sog. Geruchsorgan 
— vermutlich ist es ein funktionloses rudimentäres Auge, weiter nichts — 
wird von demselben optischen Ganglion innerviert wie das Fazettenauge 
von Limulus, hat also auch denselben Ursprung wie dieses (= Seitenaugen 
des Scorpions) (DEMOLL, 1914). 

49 
Proceedings Royal Acad. Amsterdam. Vol. XXIII. 


756 


man schon schliessen, dass die Entwickelung vom Landtier zum 
Wassertier führte und nicht umgekehrt. 

So sehen wir, dass die fiir den Wechsel des Mediums an erster 
Stelle empfindlichen Atmungsorgane und Augen uns auf die Frage, 


in welcher Richtung eine Anderung der Lebensweise stattgefunden 
haben muss, die Antwort geben: in der Richtung vom luand- zum 
Meeresleben, nicht, wie LANKESTER annahm, umgekehrt. 

Es ist auch zu betonen, dass bei einer Anderung des Mediums 
erst nachher die Anpassung folgen kann; ein Tier kann sich einem 
Milieu nicht anpassen, bevor es darin lebt. Falls die Scorpioniden 
von Meerestieren abstammten, müssten die Uebergangsformen Land- 
liere gewesen sein. Was finden wir nun in dieser Beziehung bei den 
Gigantostraken und den Scorpioniden? Wir kennen keine auf dem 
Lande lebenden und in der Umbildung zu Scorpioniden stehenden 
Gigantostraken, wie LANKESTER’s Theorie sie voraussetzen muss. 
Wohl aber kennen wir im Meere, in Küstengewässern und vermut- 
lich Delta-gebiete, aber jedenfalls im Wasser ') lebende Uebergangs- 
formen, marine Scorpioniden wie Palaeophonus und Proscorpio?), 
und Gigantostraken von seorpioniden-ähnlichem Habitus, wie Husarcus 
und Slimonia. Die Lankester’sche Theorie würde hier bedingen, 
dass die Scorpioniden-Organisation noch während des Meereslebens 
entstanden wäre und nachher dann die nahezu fertigen Scorpioniden 
aus Land gegangen waren. Dort hätte sich dann ihre Körpergestalt 
als so geeignet erwiesen (trotzdem sie unter ganz anderen Bedingungen 
im Wasser entstanden wäre), dass sie sich nahezu unverändert bis 
in die Jetztzeit erhalten konnte. Das heisst, die Anpassung sei vorher, 
im Meere erfolgt, nicht nach der Anderung der Lebensweise, auf 
dem Lande! 

Leiten wir dagegen die Merostomata von scorpioniden-ähnlichen 
Land-arachniden ab, dann hat zuerst die Anderung des Mediums 
stattgefunden und erst nachher schwand allmählich der typische 
Scorpioniden-Bau. Aus zum Strandleben im Meere oder in Delta- 
gebiete übergegangenen, dem neuen Medium erst wenig angepassten, 
primitiven Scorpioniden sind dann die scorpionidenähnlichen Gigan- 
tostraken entstanden (Eusarcus scorpionds, u.s.w.); älimahlich anderte — 
sich die Körpergestalt unter dem Einflusse der neuen Existenzbe- 


1) Vergl. O’CoNNELL (1916) und SCHUCHERT (1916). O'CONNELL meint sogar, 
dass die Gigantostraca Flussbewohner waren; die späteren Formen (Euryp- 
terus z. B.) waren aber wohl sicherlich marine Tiere. 

2) Es soll hiermit nicht gesagt sein, dass diese marinen Scorpioniden die 
direkten Stammformen der Merostomen sein müssen; aber sie zeigen, dass 
Scorpioniden zum Meeresleben übergegangen sind. 


757 


dingungen, passte sich der schwimmenden Lebensweise an (Ruderfiisse, 
Sehwanztlosse) oder änderte sich in Anpassung an die wühlende 
Lebensweise immer mehr, bis zuletzt Typen wie Hemiaspis und 
Limulus entstanden. *) 

Diese Umbildung, Anpassung, ist bei Zamu/us heute noch nicht 
ganz zum Abschluss gekommen; hinsichtlich der Augen befindet 
Limulus sich jetzt noch in einem Uebergangszustand, wobei allerlei 
noch in Umbildung steht. Dies geht hervor aus die Zahl und die 
Lage der rudimentären Augen und aus die Linsenform beim medialen 
Auge. Wir stellen also nochmals ausdrücklich fest: nicht der Skorpion, 
sondern /amulus hat eine Zeit tiefgreifender Umbildung des Baues 
hinter sich, welche vielleicht jetzt sogar noch nicht gänzlich abge- 
schlossen ist. 

Aus diesen Ausführungen geht wohl überzeugend hervor, dass 
eine Abstammung der Arachniden von den meeresbewohnenden 
Merostomen nicht angenommen werden kann, sondern dass letztere 
hervorgegangen sind aus landbewohnende Arachniden, welche primitive 
Scorpioniden waren. Nur mit dieser Auffassung steht im Einklang, 
dass nicht die Scorpioniden und Merostomen die primitivste Organi- 
sation innerhalb der Arachniden zeigen, sondern ganz andere Formen 
die Solifugen, Palpigradi und Schizonotidae; vergl. S. 750). 

Hine Schwierigkeit könnte dieser neuen Deutung nur noch ent- 
stehen, wenn eine Verwandtschaft der Merostomen mit Trilobiten 
oder anderen Crustaceen nachgewiesen wäre. LANKESTER hat diese 
angenommen und dies mag mit bestimmend fiir seine ganze Auf- 
fassung vom Limulus-Problem gewesen sein. Hällt man an dieser 
Auffassung fest, dann wird es allerdings schwer die Merostomen 
von Land-Arachniden abzuleiten, weil man dann auch annelimen 
muss, dass die Crustaceen von den Merostomen abstammen (man 
vergleiche Jaworowski, 1894, p. 66 ff, 74—75). Daran kann aber 
nicht gedacht werden, weil die Crustaceen zweifellos von viel ur- 
sprünglicher und ganz anders gebauten Arthropoden abgeleitet werden 
müssen, als die Merostomen es sind. Es ist nun aber ein Irrtum, 
eine direkte Verwandtschaft der Merostomen und Crustuceen als 
feststehend anzunehmen. Hine solche ist durchaus nicht erwiesen. 


Die geringen Áhnlichkeiten (die Kiemen!) sind als Konvergenzen zu 
deuten. Die Blattfüsse von Limulus, die durch ihren angeblichen 
Spaltfusstypus an die Crustaceen ankniipfen sollen, sind nur modi- 


1) Mit dieser Auffassung steht im Einklang, dass Limulus seine Eier hoch 
hinauf auf dem Strande ablegt, sodass sie nur teilweise vom Meereswasser 
bedeckt werden (IWANoFF, 1907; MONTGOMERY, 1909, p. 314). 


49% 


758 


fizierte Sternite und keine Gliedmassen. Bei den Gigantostraken 
zeigen sie noch keine Spur vom Spaltfusscharakter; dieser tritt erst 
bei dem geologisch so viel jüngeren Limulus hervor. Es handelt 
sich hier nur um Konvergenz, und dabei um eine gar nicht weit- 


getriebene Ahnlichkeit. Die Crustaceen, einschliesslich der Limulava 
(Warcorr, 1911, 1912; Crarke und Roepemann, 1912, p. 410) 
besitzen 2 Paar Antennen’), typische Mundteile (Mandibel, 2 Paar 
Maxillen) und Gliedmassen von deutlichem Spaltfusscharakter. In 
keiner Hinsicht ist irgend welche Uebereinstimmung in den Glied- 
maszen bemerkbar, welche als ein Zeichen einer Verwandtschaft 
der Limulava mit den Merostomen gedeutet werden könnte. Die 
Körpergliederung ist, wenn man der Segmentierung der einzelnen 
Abschnitte gebiihrend Rechnung trägt, auch eine andere; eine ge- 


legentliche, nur sehr oberflächliche Ahnlichkeit der Gestalt, wie sie 
unter den Arthropoden verschiedener Abteilungen bisweilen gefunden 
wird, hat mit Verwandtschaft gar nichts zu tun. Dies trifft besonders 
für die, nicht einmal grosse, Áhnlichkeit der Limudus-Larven mit 
einzelnen Trilobiten zu. 

Strabops, eine fossile Form aus dem Cambrium, der als ursprüng- 
lichster, noch nicht typischer Gigantostrake gedeutet wird (CLARKE 
& RurprMANN, 1912, p.152—155) zeigt mit den Gigantostraken eine 


gewisse Ahnlichkeit in der Körpergestalt, aber diese ist langst nicht 
vollkommen. Von den Gliedmaszen, die bei fossile Arthropoda doch 
ausschlaggebend sind für die Beurteilung der Verwandtschaft, ist 
nichts Brauchbares bekannt (es liegt nur ein Abdruck der Rücken- 
seite und von ganz kleinen Fragmenten der Gliedmaszen vor). Die 
Augen haben ganz andere Form wie bei den Gigantostraken; Lin- 
senaugen (Hilfsaugen) fehlen. Weiter fehlt jede Andeutung einer 
Differenzierung in Prae- und Postabdomen. Wir wissen nicht ob 
das reichlich kleine Kopfschild einen aus 6 Segmenten bestehenden 
Cephalothorax bedeckte, und ob der Abdomen Blattfüsse trug wie 
bei den Merostomen, oder Spaltfiisse wie bei Crustaceen. Die Ver- 
wandtschaft von Strabops ist denn auch durchaus problematisch und 
die Form lässt sich zu phylogenetischen Schlussfolgerungen keines- 
falls verwerten. 

So liegen in dieser Richtung Bedenken gegen die oben befür- 
wortete Abstammung der Merostomen von Landarachniden nicht 
vor. Niebts zwingt uns eine Verwandtschaft der Crustaceen (Trilo- 
biten und Limulava einbegriffen) mit den Merostomen anzunehmen. 


1, Die Trilobita besitzen an Stelle des 2ten Antennenpaares noch die 
ursprünglich gebauten Spaltfüsse 


759 


Die tiefgehenden Unterschiede im Bau sowie die zweifellose Ver- 
wandtschaff des Merostomen mit den Arachniden sprechen gegen 
eine direkte genetische Beziehung der Crustaceen mit den Merosto- 
men; diese anzunehmen führt zu der unhaltbaren Konsequenz, dass 
die Crustaceen von den Merostomen abstammen miissen. 

Wir können also an der Auffassung festhalten, dass die Mero- 
stomen von primitiven, landbewolnenden Scorpioniden abstammen. 
Nur dann kann für die Arachniden die Stammform angenommen 
werden, die tatsächlich die für diese notwendige Arthropodenorga- 
nisation zeigt in Bezug auf Körpergliederung (zwei freie Thorax- 
segmente, freies Praegenitalsegment, keine Gliederung in Prae- und 
Postabdomen), Sterna, Mundbildung (Mund frei von den Gliedmassen ; 
keine Kauplatten), Atmungsorgane (Tracheen, mit Stigmata in den 
meisten Körpersegmenten), Endosternit (zunächst noch fehlend) und 
Coxaldrüsen (mindestens in Segment 2 bis 5 des Cephalothorax) *). 
Auch die Augen gestatten es nicht vom Zustand der Scorpioniden 
auszugehen; wir müssen von einem eversen Augentypus ausgehen 
(Solifugen, Phalangiden, Acariden); daraus ging der inverse Augen- 
typus der Scorpioniden hervor. 

EV: 


Diese Auffassung von der Stammform der Arachniden ermöglicht 
es auch, Beziehungen zu den andereu Landarthropoden, namentlich 
zu den Onychophora und Myriapoden anzunehmen. Die Arachni- 
den können dann von den gleichen primitiven, durch Tracheen 
atmenden Landarthropoden abgeleitet werden, wie die Myriapoden 
und die aus letztere hervorgegangenen Hexapoden; alle tracheaten 
Arthropoden sind dann gemeinsamen Ursprunges. Dabei muss sich 
der zu den Arachniden führende Ast schon sehr früh abgezweigt 
haben. Die vordere Lage der Geschlechtsöffnung weist auf progo- 
neate Myriapoden hin, die exogene Hibildung auf diese und aut 
Peripatus (van Kampen, 1916). Das Fehlen eigentlicher Kauwerk- 
zeuge lässt die Stammformen der Arachniden in der Nahe der 
Onychophora vermuten *). Darauf weisen auch die Coxaldrüsen hin, 
die bei den Solifugen wie bei Peripatus als Speicheldrüsen funkti- 
onieren (vergl. Buxton, 1913, p. 258; 1917, p. 8, über Palpigradi 
p. 9). Und namentlich bedeutungsvoll ist die von HoLMGREN aufge- 
1 Vergleiche S. 750—751. 

2) Die Frage nach dem Verbleiben der Antennen bei den Arachniden 
lassen wir unerörtert, da dies uns zu weit führen würden; in Betracht kame 
als Antennen-Segment vor Allem das Praecheliceren-Segment (vergleiche 
HEYMONs, 1901, p. 148; CARPENTER, 1913, p. 342; KorscHeLT & HEIDER, 
1892, p. 636, und namentlich HOLMGREN, 1916, p. 76). 


760 


deckte weitgehende Uebereinstimmung im Bau des Gehirns. Wichtig 
ist der primar unsegmentierte Typus des Vorderhirns bei Onycho- 
phora, Arachniden und Limulus (und Polychaeta errantia) im Gegen- 
satz zum sekundär segmentierten Typus des Vorderhirns der übrigen 
Arthropoden (Crustacea, Myriapoda und Hexapoda), der von dem 
ersten Typus abgeleitet werden muss. Weiter haben die Onychophora, 
Arachnida und Limulus einen typisch gebauten Zentralkörper (ge- 
streifter Körper), sowie ein dem Vorderhirn sich direkt anschliessen- 
des Tritocerebrnm (HOLMGREN, 1916, p. 274, 275). Wir haben soweit 
ersichtlich als Ausgangsformen für den Stamm der Arachniden 
kiefernlose, in einiger Hinsicht noch Peripatus-ähnliche Formen mit 
gegliederten Extremitäten anzunehmen. Die Arachniden gingen von 
hier ihren eigenen Weg; sie bildeten keine Kiefer aus, ernährten 
sich in der Hauptsache von den mehr flüssigen, oder durch Fer- 
mente in situ verflüssigten, Bestandteile der von ihnen erbenteten Tiere. 

Es liegt kein Grund vor, direkte Beziehungen der Urarachniden 
zu den Crustaceen anzunehmen. Der Ursprung der letzteren ist viel- 
mehr in der Nahe jenes Hauptastes zu suchen der in den Hexapoda 
gipfelt. Hierfür spricht vor allem der ähnliche Bau des Gehirns 
(Hormeren 1916, p. 116) und der gleiche Bau der Facettenaugen. 
Zwar ist eine konvergente Ausbildung von diesem Augentypus mög- 
lich, denn er ist bei den Scutigeriden, bei den Strepsipteren und bei 
Hexapoda-Crustacea entstanden (vom doch recht unvollkommenen 
Facettenauge von Limulus sehen wir hier ab). Aber beim Facetten- 
auge der Hexapoda und Crustacea liegt eine so weitgehende Ueber- 
einstimmung in Bau vor (gleiche Zahl der die einzelnen Teile anf- 
bauenden Elemente, wie von Hesse und seinem Schüler ZIMMERMANN 
aufgedeckt wurde; ZiMMERMANN, 1918; vergl. auch LANKESTER, 1904A, 
p. 573), dasz wir einen gemeinsamen Ursprung dieses Facettenauges 
annehmen müssen '). 

Es hat sich demnach, nach unserer Ansicht, vom Stamme der 
Arthropoden zuerst der Ast der Arachniden abgezweigt unter Aus- 
bildung der Cheliceren und Verlust der Antennen, während die 
Insekten und Crustaceen zunächst noch einige Entwicklungs-Etap- 
pen gemeinsam hatten, die sich in verschiedener Hinsicht in ihrem 
Bau aussprechen. Die Stammformen der Crustaceen gingen dann 
zum Wasserleben über. 

Einen diphyletischen Ursprung der Arthropoden, wie ihn von 
Kennet (1891) befiirwortet und auch Kinestey (1894) in Erwagung 


1) Gegen einen monophyletischen Ursprung des Facettenauges der Crustacea 
und Hexapoda hat sich Mororr (1911) ausgesprochen. Seine Gründe scheinen 
uns nicht stichhaltig. 


761 


zieht, wobei sich die Crustaceen selbständig aus Anneliden-ähnliche 
marine Stammformen entwickelt haben sollten, können wir nicht 
annehmen. Die Uebereinstimmungen im Bau aller Arthropoden 
scheinen uns dies aus zu schliessen (vergl. Heer, 1914, p. 498— 
499). Die Crustaceen müssen dann aber von tracheaten Landarthro- 
poden abgeleitet werden. 

Vom zu den Arachniden fiihrenden Aste zweigten sich vermut- 
lich die Pyenogoniden ab, und zwar frühzeitig. Mit den Arachniden 


Hexapoda 
Myriapoda 
A 
> 
SS Crustacea 
6. 
SB 
Merostomata 


epodertAjf 


Pyenogonida 


Primitive 


Peripa tus Myriapoda 


vioydoyahug 


Annelida 
Fig. 6. Versuch eines Stammbaumes der Arthropoda. 


und Merostomen zusammen bilden sie eine grosse Abteilung der 
Arthropoden, die man nach dem fiir sie typischen Besitze von 
Cheliceren als Chelicerota bezeichnen kann (vergl. Heymons, 1901). 
Unsere Ansicht von der Verwandtschaft der grossen Abteilungen 
der Arthropoda ist in schematischer Form im beigefiigten Stamm- 


_ baum (Fig. 6) niedergelegt *). 


1) Unser Stammbaum unterscheidet sich namentlich dadurch vom neuen 
HOLMGREN’schen Stammbaum der Arthropoda (HOLMGREN 1916, p. 278, 
Schema 6), dass HOLMGREN oberhalb der Onychophora die marinen Trilobita 
einschaltet, während wir dort primitive landbewohnende Myriapoda anschliessen 
lassen. HOLMGREN’s Stammbaum beruht wesentlich auf seinen eigenen Unter- 
suchungen des Gehirns der Arthropoda. Das Gehirn der Trilobita ist näturlich 
unbekannt und hier liess HOLMGREN sich leiten von der Auffassung, dass die 
Merostomen von Trilobiten abstammen, eine Ansicht, die wir verwerfen. 
Sonst besteht aber sehr weitgehende Uebereinstimmung in den Stammbäumen. 


762 
SCHLUSZFOLGERUNGEN. 


1. Die Merostomen sind aus primitive Seorpioniden entstanden, 
die zum Wasserleben übergegangen waren. Sie gehören zu den 
Arachniden. 

2. Mit den Crustaceen sind die Merostomen nicht näher verwandt. 

3. Die Arachniden stammen von sehr urspriinglichen, den Ony- 
chophora nahestehenden Myriapoden ab. 

4. Nachher erst entstanden aus den Myriapoden die Crustacea 
und die Hexapoda. 

5. Die Tracheen der Arthropoda sind einheitlich im Ursprung; 
eine zwei- oder mehrmalige parallele Ausbildung derselben hat nicht 
stattgefunden. 


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764 


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765 


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Physiology. — “On Serum-lipochrome’’. (Part ID) By Prof. Hijmans 
v. D. BeraH and Dr. P. Murrer. 5 


(Communicated at the meeting of April 23, 1920). 


In 1890 von NoorpeN described a peculiar colour of the skin‘), 
observed in sufferers from diabetes, which he named xanthose’). 
Originally he suspected the colouring matter, causing xanthose, to 
be a product of hemoglobin. Afterwards he receded from this opinion 
and declared that the nature of the pigment was still unknown. 

In 1913, before having cognizance of v. NoorDEN’s communication, 
we*) had observed the same orange-like colour in several persons, 
especially in sufferers from diabetes, but also in other men. This 
coloration seemed always to be attended by an increase of the serum 
lipochrome. The assumption was warrantable that this peculiar colour, 
which does not differ in any way from v. NoorpEn’s xanthose, 
depends on the supernormal lipochrome-amount of the blood. Since 
that time several reports on this subject have been published. PALMER“) 
and his co-workers have demonstrated that in cows the carotin of 
blood-serum, body-fat, and milk-fat, in fowls the xanthophyll of blood- 
serum, body-fat, and egg-yolk, originate from the vegetable carotinoid, 
taken in with the food. Latterly also German researchers have pointed 
to the correlation of the human serum-lipochrome, with the food- 
lipochrome. 

In 1913 and 1914 Mr. Bere performed unplublished researches 
in the Laboratory of the Groningen clinic, which support this 
hy pothesis. 

Mr. Bere’s conclusions were the following: 

1. The amount of lipochrome of the blood corresponds with that 
of the diet. It diminished (the experiments were made on Mr. Berea 
himself) considerably, after an exclusive diet during 10 days of 
skimmedmilk, uncoloured flour and rice. After a mixed diet and many 
egos the amount of lipochrome rose higher than befure the commence- 
ment of the experiment. 

2. Fowls possess a high serum-lipochrome content. After giving 


1) Handb. d. Pathol. d. Stoffwechsels, Il, 290. 
2) Internat. Dermatol. Congress, Berlin, 1904. 
3) Deutsch. Arch. f. klin. Mediz. 1913, blz. 540. 
4) Journ. biol. Chem. 1914, 1915, 1916, 1919. 


767 


them for some time a lipochrome-poor diet, the lipochrome disappears 
completely from their serum. 

3. Cows, pasturing in the meadow, yield milk that is much richer 
in lipochrome than with stall-feeding (relationship of the colouring 
materials of the grass and those of the bloodserum). Also the blood- 
serum of these cows contains more lipochrome than that of stable-cows. 

These conclusions are completely in accordance with PALMER’s 
findings. 

When prosecuting our inquiry, it appeared to be necessary to 
determine quantitatively or to estimate the amount of lipochrome in 
bloodserum, plant-parts, and animal tissues. This we attempted to 
do colorimetrically. 

For comparison-liquid we used a '/,, °/, aqueous solution of potas- 
sium-bichromate; the lipochrome was invariably examined in an 
ether-solution. It is necessary for similar quantitative estimations to 
use always the same solvent, the colour of an equal quantity of a 
detinite lipochrome varying in different solvents. 

The determination of the lipochrome-content of bloodserum takes 
place in the following way: 

1 or 2 ee. serum is precipitated with the same volume of 96 °/, 
alcohol. The liquid is centrifuged, the precipitate extracted with 1 
resp. 2 ce. of ether. This yields an (impure) lipochrome solution in 
ether of the same concentration as in the original serum. 

When there is a high lipochrome content, the precipitate is once 
more extracted with an equal quantity of ether, after which the 
value must be multiplied by 2. 

When there is a large amount of bilirubin the ether-extract is 
washed with a few drops of very dilute sodium hydrate solution. 

With the aid of Herrice's colorimeter we made a comparison 
with the potassium-bichromate solution. 

The lipocbrome-content of parts of plants and of animal tissues 
was determined as follows: 

Parts of plants were boiled with alcohol, and subsequently extracted 
in a mortar with aleohol and ether, until the extract was colourless. 
The extract is filtered, then the colouring matter is, by the additiou 
of water, transferred to ether. With this operation other vegetable 
pigments remain in the lowermost dilute alcoholic layer. If necessary 
this layer is still extracted with ether, and the ether extracts are 
given a proper intensity of colour by evaporating them down with 
caution. By the addition of a few drops of absolute alcohol a clear 
ether-extract is obtained, of which the volume and the colour is 
determined. Let a be the parts of plants in grammes, 6 the amount 


768 


of the extract in c.c. and c the standard percentage of the tint, then 
cb 
100a 
if 1 gr. of the substance was completely extracted to 1 cc. of ether- 
extract, the content expresses how many times this tint is stronger 
than our standard-tint. 

Animal tissues are minced up and divided into two portions. Of 
one of them a water determination is made, by drying it with 
dried seasand on the waterbath to a constant weight. 

The other portion is rubbed with alcohol and ether and, as in 
the case of plants, the content is determined. The content of animal 
tissues was generally determined for 1 gr. dry substance. With fat 
a fat-determination is substituted for a water determination, so 
that in that case the content is determined for 1 grm. of pure fat. 

The determination of the lipochrome-content of carotin-like and 
xanthophyll-like pigment in some parts of plants yielded the following 
result (the values found represent quanta of pigment to 100 grms. 
of moist substance, the pigment solved in 100 cc. of ether. (See 
table I). 

In making these determinations we used only a rather rough 
method. Besides the lipochrome pigment the solutions also contained 
all sorts of impurities. Moreover, if in our experimentation, we start 
from small quantities of material, traces of lipochrome will be 
unobserved. If, in starting from 10 ecc. of cow’s serum, we find 
3 carotin and 0 xanthophyll, it is very well possible that, when 
working with large quantities of serum, traces of xanthophyll might 
still have been detected. 

While performing these determinations, we have assumed that 
both groups of lipochrome (carotin and xanthophyll) have in the 
same concentration the same colour and intensity of colour, which 
is regularly diminished through dilution. According to WILLSTATTER’s 
experience this statement is not right. With the considerable dilu- 
tions, used by us, we deemed it justifiable to neglect this error. 
The values found are mean values, those of the several samples of 
the same substance often differ very much. 

As said in a previous communication, we mean by carotin and 
xanthophyll the pigments that have a greater affinity either for 
petroleum-ether, or for methylalcohol, being well aware that this 
group may comprise various substances. 

In order to ascertain the influence of diet upon the serum-lipo- 
chrome, we determined in a dozen subjects the amount of this 
pigment first with the ordinary, mixed, hospital diet, and a second 


So we determined the tint as 


the formula for the content is 


769 


TABLE I. 
xanthophyll carotin total 

salad . 2.9 0.76 3.66 
carrots 0.0 2.5 2.5 
spinage . 15.3 4.4 19.7 
egg-yolk . 27.5 0.0 Pi] dhe 
egg-white 0.0 0.0 0.0 
cow’s serum . 0.0 3.0 3.0 
fowl’s serum . 3.0 0.0 3.0 
rice. es ie trace 
white bread trace trace 0.3 
brown bread . trace trace 0.27 
ordinary milk, 0.0 0.9 0.9 
butter-milk A, at the 

laboratory) . 0.0 trace 0.01—0.02 
butter. 0.0 Baik 2.1 
beef (lean) . 0.0 0.08 0.08 

» (fat) 0.0 0.16 0.16 
potatoes. 2 3 0.2—0.5 
cauliflower . is % 0.3 
maize . 6.7 1.6 8.3 
beetroots 0.0 0.0 0.0 


time after a fortnight’s diet which contained a large quantity of vege- 
tables and eggs. The results obtained have been tabulated in 


TABLE II. 
el ordinary | lipochrome- Fe ordinary | lipochrome-rich 
diet diet diet | diet 
R. 0.25 1.08 Kn. 0.19 0.70 
v. H. 0.17 0.45 v. B. | 0.41 0.92 
Kr. 0.42 1.34 Kr. 0.8 1.24 
IF 0.34 0.86 Be. th) 0282 0.74 
Wr. 0.21 0.54 af 0.2 0.96 
E 0.16 0.65 H. 0.08 0.4 
N. 0.21 0.42 the same 0.56; ACE 


770 


From this table it follows that a lipochrome-rich diet produces 
considerable increase of the serum-lipochrome. The great obstacles, 
impeding a control of the food used by patients in a common ward, 
are responsible for the fact that an accurate determination of the 
lipochrome taken up could not be made and that we had to be 
satisfied with an approximate evaluation. 

When comparing these figures with those obtained with sufferers 
from diabetes, it appears that the diet may be made greatly answer- 
able for the high values with this disease (See Table III). 

This tallies with the experience that, with sufferers from diabetes, 
sometimes normal values are obtained; on the other hand that a 
patient not suffering from diabetes, but accustomed to eat 7 eggs 
a day, had a lipochrome-content of 0,9. 

Both with the consumption of many eggs (xanthophyll) and with 
the taking of carrots (carotin) an increase of the lipochrome-content 
was produced. Therefore, as will also appear further on, man is 
able to take up both pigments, contrary to the cow and the fowl 
which take up respectively only carrotin and xanthophyll. 

Thus far the inquiry had shown that with a diet comprising many 
carotinoids the lipochrome-content of the bloodserum rises rather 


TABLE III. 


Serum-lipochrome in some sufferers from diabetes. 


| 
i; 1.3 4, 0.82 i 0.7 10. 0.72 13. 0.95 
2e 0.9 5. 0.95 8. 1.9 i: 13 14. 0.75 
3. 0.54 6. 0.8 8. 0.85 12. 0.9 15. 0.45 


| 
rapidly, and that it is lowered rather soon after a diet, which is 
poor in these pigments. We also wished to examine the lipochrome- 
content of other organs. 
The provisional answer is to be found in Table IV, from which 
we deduce the following conclusions: 


1. The lipochrome-content of the various tissues is very different. 
The blood is poorest in this pigment, also when calculating its 
relation upon the dry weight of the blood, in which the water- 
content of the blood may be put at about 80°/,. Richest in lipo- 
chrome is the adrenal; after this generally follows the liver, (in 
some cases the fat contained more pigment than the liver); after 
this comes fat and lastly the spleen. Of the latter two the one 
sometimes takes precedence of the other. 


771 
The large lipochrome-content of adrenal and liver proves that 
these organs do not owe their pigment simply to the deposition of 


the coloured body fat in their tissues. There must be some elective 
affinity of these tissues for the lipochrome. 


2. With a single exception (N°. 6) considerable amounts of pigment 
were found in the organs also in those cases in which no lipo- 
chrome could be demonstrated in the blood. We will give a single 
instance: in patient N°. 40 a rather high value was noted for the 
adrenal, whereas the blood was free from pigment. In other cases 
(N°. 3) low values are found in all tissues, in number 6 even next 
to nothing. No rule can be discovered for the relations of the lipo- 
chrome-content of the various tissues. 

According to the data at our disposal a slight lipochrome-value 
of the blood is to be attributed first of all to the use of lipochrome- 
poor food. Since we often find low blood-pigment values by the side 
of normal or high organ-values, the conclusion must be made that 
these organs (particularly the liver and the adrenal) pertinaciously 
hold fast the pigment when lipochrome-poor food is taken. 


3. It is impossible to detect a relationship between the nature of 
the diseases and the amount of lipochrome in the blood or in the 
tissues. The high values in the case of diabetes are accounted for 
by the peculiar diet. 


4. The rise of the pigment-content of the blood with a lipochrome- 
rich diet, and the fall with a pigment-poor diet, warrants the conclu- 
sion that the organism derives these pigments from the vegetable 
kingdom (directly or indirectly through the use of animal food, 
which also owes these lipochromes to the vegetable kingdom). The 
blood absorbs these pigments and deposits them in the tissues. 
We are still wholly ignorant of their fate there. It might be supposed 
that they are accumulated by the fat, the adrenal, and the spleen, 
ad infinitum. This, however, does not seem likely, as in that case 
_the lipochrome-masses in the tissues of elderly people, would amount 
to enormous values, considering the large quantities of lipochrome 
taken up every day. So far as we were enabled by our data, we 
have arranged our results according to age. The number of cases is 
too small to draw conclusions from. Still, the inference may be drawn 
that, broadly speaking, children under 10 years of age present lower 
values than elderly people. However, we have not been able to 
ascertain, whether the values rise regularly with age and there is 
no question of elderly people presenting excessive values. 


50 
Proceedings Royal Acad. Amsterdam. Vol. XXIII. 


TABLE IV. 
eee Se ee ee re ee reece ane re 


Lipochrome-content in 


7 > | SA = 
No. | 5 | & diagnosis 82 al |S8 52) se) 88 
4 63| E|/#e|g-|/=2| ae 
: 
te a 54 years | appendicitis, multipleabsc. inthe liver. | 0.38 15 | 2.0 | 19.0 
LN BE 8 , | meningitis t. b. c. 0 1.1 1.3 | 10.0 
3 d | 53 „ | cirrhosis hepat. Laénnec. insuff. mitral.) 0.07 121). 105 1 
4 & | 51, | acute myeloblastic leukemia. 0.11 1.3 19 | 19.5 
5 J 10 , | endocarditis acuta. 0.12 Fg) 22 | 12.6 
6 Q 8 >, a & Bece palmon: 0 0 0 0 
7 d 52 , | aortitis, stenosis ost. aortae, insuffi-| — 
cientia mitr. 0.09 1.3 2.4 | 28 
8 d 15 , | peritonitis tuberculosa. 0 5 3.9 1.3 
9 2 ? ? 023 leze 34 | 39 
10 ? Zia rt -D. Capulmon: ? 18 £ 11.5 
11 2) 81 , | myodegeneratio cordis. 0.14 2.7 4.3 | 22 
12 | ¢ | 61 ,, | nephrolithiasis, spondylitis sanata. | 0.04 | 2.1 ? 11.6 
13 ¢ |62 „ | insuffic. aortae, tabes dorsalis. 0.11 3.7 1.0 “1-20 
14 Q | Î t. b. c. pulmon. 0.412 |. 2,9 1: GEUR 35 | 3.7 
15 | @ |24 „ | volvulus, peritonitis. 2 35 | 4.7 | 41 10 14 
16 ag | ? diabetes. 018 | 09 | 48 | 83 is 5.4 
17 Q ? carcinoma ventriculi. 0.14 | 10 13.6 | 29 8.6 1.1 
18 2 ? coma diabeticum, paranephritis. ? 2 2.2. | 28 13 9 
19 d ? t. b. c. pulmon. ? 2 ? 18 ? 1.3 
201) “cs: ? sepsis, nephritis parenchymatosa. ? 3 4.2 | 31 6 1.2 
21 2 ? t. b. c. pulmon. 3 3 ? 7 4 1.6 
Zend 4 atrophic cirrhosis of the liver, sepsis. | ? 3.7 8.0 | 32 146 | 5 
23 d id diabetes, nephritis. 2 31°) 5.5. DA 148 | 14 
24 d is acute aleukaemic leukaemi. 
(aleukia). cs 2.6 3.6 | 52 12 2 
25 d ? nephritis chron., sepsis. dg 1.3 | 20 | 105 SEN 
26 d Ha t. b. c. pulmon. ie 2.1 40 | 96 | 44 1.1 
ol CE ? pneumonia crouposa. 7d 10 42 34 8 3 
28 Q (6 t. b. c. pulmon. ? 1.6.| 114-) 238 5 1.8 
29 Q ? diabetes. ? 4.2 1.5 | 29 10.5 | 63 
aoe 2 ? diabetes. fe 3 ig 14 44 | PPE 
31 | 2 2 gangraena pulmonum. ? ES] 8 6.1 1.5 
39e el 19 pleuritis tuberc., arteriosclerosis. 4 ? ? 22.6 {= 3i2-| 0 
33 d ie t. b. c. pulmon. fe 3.4 | 5.4 | 10 22 1.2 
34 Q 25 „ | phthisis. 0 225 2 20.6 9 2.3 
35 d 65 „ | tuberc. peritonei. 0 15 1.8 1 8.4 1.9 
36 | @ | 80 , | pneumonia crouposa. 018 6.7 is 27 10 3.1 
a. A 56 „ | pneumonia. 0.55 5a") oe 25 22 3.5 
38 d Il _„ | lung abscess. 0.14 2.2 | 3.0 "ae 8 2.2 
a9 |. aS 42 „ | ulcus ventriculi. 0 ? 6.0 | 38 9.7 5.5 
40 ie 13 _„ | phthisis. 0 ? 13.0 | 14.5 | 10 4.1 
41 2 54 „ | carcin. uteri. 0 ? 3.0 | 17.5 7.5 2.7 
42 of ? (Foetus). ? 2 yy trace! | 0.9 | O 
43 = 2 (Foetus). fe 0 0 — | + | trace! 


773 


We are consequently forced to assume that the lipochrome 
pigment leaves the body in one way or other, or that it is broken 
down to unknown substances. If then the pigment loses its colour 
or solubility in alcohol and ether, we cannot for the present follow 
its course further. Perhaps it is decomposed, and passes into a 
colourless modification, or it may lose its colonr throngh oxidation 
(as happens under the influence of light). 

We have not succeeded as yet in demonstrating lipochrome 
pigments in urine or in bile. 


50* 


Physics. — “On the resistance of fluids and vortex motion.” By 
Prof. J. M. Burerrs. (Communicated by Prof. P. EHRENFEST.) 


(Communicated at the meeting of September 25, 1920). 


§ 1. Introduction. 


Several writers have drawn the attention to the connection between 
the vortices, generated by a body moving in a viscous fluid, and the 
resistance the body experiences during its motion.') The purpose of 
this paper is an effort to formulate this connection. The resistance | 
couple being neglected, the investigation will be confined to the 
resistance force. 

The following assumptions are made: The motion of the body 
may be an arbitrary one. However, the time since the beginning 
of the motion must be finite and the velocity must always have a 
finite value, while a change of the volume of the body be excluded. 
The fluid is incompressible; it is unlimited and at great distances 
velocity and vorticity become zero according to formulae of the form 


a a 
kim oe — 3: mw 7 ae 
' R=0 Rey? R= Rei ( 
where J >0.?) The pressure approaches a constant value, for which 
zero is taken. 


1) See among others: 

O. ReynoLps, Scientific Papers I, p. 184. 

F. Antporny, Jahrb. d. Schiffbautechn. Gesellschaft 1904, 1905, 1909. 
Tu. v. KARMAN u. H. Rupacu, Physik. Zeitschrift 18, p. 49, 1912. 


9) In connection with the eharacter of the equations for the diffusion of vorticity 
for high values of R w will probably behave according to a formula of 
R? 


the type: exp. (- rl See in connection with this: C. W. Oseen, Acta Math. 


34, p. 222, 1911.) 

In the stationary motion of Srokes — which therefore does not suffice the 
above conditions — w decreases only proportional with R—?; in the motion 
according to the formulae of OsreNn and LamB w decreases as: 


(1 + &R) 


sin O 
li 
that is exponentially for 4 #0; while for 6=0: w—=o. (See H. Lamp, Hydrodynamics 

p. 599, Cambridge 1916). 


exp |— kR (1 — cos 0) }, 


775 


§ 2. Impulse of a vortex system. 

The impulse of a vortex system is defined as the impulse of a 
system of forces that instantaneously can generate the given vortex 
motion in the fluid from rest '). When the fluid is unlimited and when 
it does not contain any body, this impulse is given by the formula: 


B sl {fae dy der w ee EN 


ela SO hod Caan ee cn a, a ME 


(9 = density of the fluid; r is the radius vector of a point 2, y, z; 
w is the vorticity, defined by w=rotv; C; is the circulation 
round a vortex line; A; the surface enclosed by the line, regarded 
as a vector). *) 


§ 8. Elementary derivation of the formula for the resistance. 

Let us consider a body in an unlimited fluid; originally all be 
at rest. By forces acting on the body it is j set into motion; let us 
have for the moment é: 

f = resultant of the forces acting on the body; 

B= the eee or momentum of the body =o’ 2V, where y’ 
ig -the density, {2 the volume and V the velocity of the centre of 
mass of the body (the body being homogeneous) ; 

I= the impulse of the motion of the fluid. The time integral 
of f must be equal to the total impulse of the system, therefore: 


t 


framen Nad age es A. ORN) 


and 
dB dl 
=d. (5) 
dt dt 
When W is the “fluid resistance’, we have 
=— W Sees Sa! Go ek ee (ON 
i (6) 
and 
dl ; 
Wisent als i nd | ell ig ker 7 
de ER (7) 


1) See Kervin, Math. and Phys. Papers IV, p. 13 et seq. (1869). 

5) See H. Lams, Hydrodynamics p. 209. The formula has been proved there 
for a vortex system of finite dimensions; the integral, however, remains ety 
for an infinite system, when only condition (Ll) is satisfied. 


776 


In order to calculate I we substitute for the body a fluid mass 
with perfectly the same motion as the body. The impulse of this 
fluid mass is to that of the body as @ to eo’; the total impulse of 
the fluid becoines therefore: 


vBti=eQvtl. . . 


This quantity can be calculated by means of formula (3). When 
the body has a rotatory motion it must be remarked that the sub- 
stituted fluid mass will contain vortex lines which must be comprised 
in the general sum. When the motion is a pure translation, all 
vortex lines lie outside the body. We have therefore: 

eQV+I=SJ=e02 CA... 7S ae 
from which follows 
I=o 2 Ci RY. ..o. 
and 


d dV 
We (ZCA) 08 .... . Uy 


This formula is the connection searched between the resistance and 
the vortex motion in the fluid. 


dV 
For a uniform rectilinear motion of the body Pie so that (11) 
is simplified into: 


d 
Wer Gh). . « +e Shean 


§ 4. Proof of formula (11). 

In the same way as above the body is replaced by a fluid mass which 
has the same motion as the body and zero pressure’). Let the 
following forces be acting on the fluid: 

a. on the part that has been substituted for the body: the forces 


dy ‘ 
X; which have the value X;= eee fe: unit of volume (v is the 


velocity of the fluid); 

5. on a thin layer that is always there where the surface of the 
body would have been: the forces Xj ;, equal to the force exerted 
by an element of the surface of the body on the fluid (pressure 
and frictional forces taken together). 

Then the fluid will have just the right motion viz. the inner 


1) This means that the pressure has the same value as at infinity. 


che 


fluid will move with the prescribed velocity and with zero pressure; 
and the outer fluid moves in the same way and experiences the 
same pressure, as if the body were present. For the sake of 
continuity the forces XX ,; will also be treated as volume forces 
(with finite derivatives with respect to w, y, 2) acting on a very 
thin layer *). 

We now have: 


» 7 dV 
[fae ay dex = fff de dy de x, + f [ate dy de X= 9 + WOS 


When on the other side we put 


sE [ffasdyderxw . O13 NO AB 
ee ffe ana ae 15 
aa |p fee ELKE oi. ter Te ee (HO) 


where according to the well-known formula: 


we have 


Ow 
a ON V)v—e(v- V)wtpAw. . (16) 


(u is the coefficient of friction of the fluid). 

Substituting this in (15), we find by working out the integrals, 
that according to (1) (these conditions suffice for this) all terms 
vanish except that with X, so that: 


d © Es Ow a du d EX 
—_—=— ; =d TR r = 
os w dy zx 8 if edy de fr X ro 
4 dV 
=| ftearaermor g+ 5 de Os) 
C 


d dV 
W = 0.= ("Gi dy pe sens ATS) 
dt dt 


Therefore: 


which is in agreement with (11). 


§ 5. Remarks. 

I. Applying (15) and (16) not to an unlimited fluid, but to a 
fluid bounded by a fixed surface S, along which both w and its 
first derivatives are zero, we find 


1) This layer is not the boundary layer from the theory of PRANDTL; it must 
_ still be thin compared with the latter. Outside this layer no external forces act 
on the fluid. 

2) The place and therefore the radius vector r of each element dx dy dz are 
regarded as fixed; then we must take the local differential quotient of w. 


778 


1 en hd / 4 S 9 n . . . 19 


(w is the volume enclosed by S; n is a normal of unit length to 
dS). The friction has therefore no direct influence on J. 

This formula is related to that used by von Karman in the cal- 
culation of the resistance experienced by a cylinder’). 

Il. In § 3 and § 4 the moving body was replaced by a fluid 
mass with a system of forces Xj,X//. The forces Ky, are surface 
forces about which we supposed that they might be replaced by volume 
forces. This substitution will be considered more in details for the 
case of a body with a translatory motion; moreover we shall assume 
for the present that this motion is uniform, so that K;=0. 
dUn Ov, 
dn’ On 
sure p are on the contrary generally discontinuous. The normal 
component of the surface force F, is equal to the pressure p, of 
the fluid on the surface; the tangential component F, has the 


Along the surface v is continuous’), also ) and the pres- 


Ov; 5 . 
value: — u a Let us now consider two surfaces 6; and o,, the 
n 
0 


first just at the inside of the surface of the fluid that replaces the 
body, the second just outside it, so that their mutual distance 
e is small. Afterwards both surfaces must approach the surface 5, 
of the body. In this “transition layer’ we replace p and vw, by the 
continuously changing quantities p’ and »,’, so that on o; and o, 
p’, vr’ and the derivatives of v;’ up to the third order inclusive are 
equal to p, v‚, ete. (p’ and the derivatives of v;’ are zero along 6; ). 
Then the following volume forces are introduced: 


normal component: fn = an | 
n 
(20) 


tangential component : fi= —u aa 
n 


ad 


These forces are of the order «—!; integration over the depth of 
the layer gives: 


1) von KARMAN calculates the change of J from the change of the vortex 
system; by adding to this the surface integral he finds the resistance. 

2) See e.g. H. Lams, Hydrodynamics p. 572; O. Reynotps, Scientific Papers Il, 
p. 288. 

3) vi, Fi, etc. ought to be written as vectors (vi = v— n Vn); this has not been 
done here, 


779 


ff dre (Pp) Pu 
dn = EE: Gr | 
fre Tjele) 


which differs from #, and F, by an amount of the order «. 

Ill. Let us now suppose that during an element of time dt the 
forces f do not act. Then the motion takes place under the in- 
fluence of the frictional and the pressure forces; diffusion and con- 
vection of vortices take place, ete. The pressure and the frictional 
forces being all finite, the velocity v will only change by an amount 
of the order dt; 6, is displaced over a distance V dt and is not 
deformed. Along oi and o, v, however, will no longer have the 
value V. The impulse of the motion of the fluid will keep its value 
unaltered. 

In order to obtain the motion that would have existed when the 
forces f had worked, the following motions have to be superposed : 

a. Outside o, the distribution of the vortices is right, as in this 
region no forces are active; here we must therefore superpose 
an irrotational motion, the potential of which is defined by 

òg* 
On 

b. Inside 6; no vortices appear as along this surface Aw’ = 0. 
Therefore we must superpose here too an irrotational motion, so that 
everywhere v becomes equal to V; it is perfectly defined by the 
boundary condition for the normal component °). 

c. Between o; and o, a vortex layer must be generated connecting 
these two motions. The total intensity of this layer is given by: 


fetan=ax tue ET OER EB) 


== Vr ta. (AlONS OJ Ee ike (22) 


The structure of the layer must be thus that the impulse is equal 
to the time integral of the resultant of the forces /: 


da aff { de dy det Wa paden „erk HRA 


1) Strictly speaking the vorticity both outside ou and inside c; has been influenced 


by. the change of the distribution in the transition layer; this amount is of the 


1 
order: exp. = a} which has been neglected here. 
td t 

2) The intensity of the vorticity generated in the transition layer is determined by 
rot f; to this both f„ and f; will contribute. As ft has a maximum in the layer 


(along oi and ou ft =O or finite; in the middle of the layer f is of the order 


780 


IV. Accelerated or retarded motion. 

When the motion of the body is not uniform, a second system 
of forces must be exerted by the surface of the body on the fluid. 
Outside 5, these forces can only give rise to an irrotational motion 
the potential ~** of which is defined by: 


op** 
On 
and may therefore be calculated by the methods of hydrodynamics 
for ideal fluids '). 


Within o; all velocities increase together with dV and in the 
transition layer a vortex layer is generated of the intensity 


== (dV, (along optie poe 


[we dna x (9 ot — dv) 0 08 es OO 


On a possibly existing structure of this layer nothing can be 
said directly; the impulse must be equal to dt times the resultant 
of all extra forces that have acted on the fluid (both inside 6; and 
in the transition layer). We can partly (perhaps totally) calculate the 
impulse from the total intensity of the layer, which is given by 
(26); this part must agree with that which may be calculated from 


el), this force will give rise to a “vortex double layer”: a positive and a 
negative layer with intensities of the order <—2 per unit of volume at a distance 


of the order e; so that the intensity per unit of surface fran, and the im- 


pulse per unit of surface f rXw*dn are both finite. For the layer formed by fn 


this is generally not the case; this layer is simple and consists of lines circling 
round the body. 

This may be illustrated by the consideration of a disc moving in its own plane 
while its thickness approaches zero. Then the resultant of the pressure forces 
becomes zero, which must therefore also be the case with the impulse of the vortex 
motion generated by fx. The resultant of the frictional forces remains finite and is 
nearly independent of the thickness of the disc. Therefore the impulse of the 
transition layer cannot or can only partly be due to the fact that it consists of 
vortex lines surrounding the disc. It must have its impulse “in itself” viz. it must 
be a ‘double layer”. 


A double layer may be represented by w= ——. 55 = Born € =. (—; ae a the impulse 


+o 
has the value few da =2 AV vz, independent of t. 


e 
— @ 


") See eg. H. Lams, Hydrodynamics, Ch. V and VI. 


781 


the potential g** by the methods of classical hydrodynamics *). This 
part of the impulse is received back by an equal decrease of velo- 
city of the body *). 

Now III and [V may be combined: the discussion of III remains 
valid for a non uniform motion, when only we replace in (22) and 
(23) V by V + dV, the velocity of the body at the end of the 
element of time dt. 


§ 6. Summary. 

When a body in a fluid is brought into motion a vortex layer 
is generated at its surface. This layer diffuses into the fluid by the 
friction and is carried on by the current, is ‘“washed away”. At 
the surface new vorticity is generated, which diffuses again etc. 
The generation of each vortex layer demands a certain impulse and 
the sum of the impulses that must be produced per second, forms 
the resistance W experienced by the body. At a definite moment 
the total impulse of all vortices together is equal to the time inte- 
gral of W: 


t 


fwa =I@M=e2 CA —of2V; 


the impulse may be calculated from the products: 
| (circulation) . (surface) 
of the separate vortex lines. 

1) Example: For a sphere (radius =a) we have for òV =1 the potential 
p** =1 37-2 cos §. From this follows for the tangential velocity of the fluid 
along the surface: — 4sin 4, while the tangential velocity of the sphere itself is: 
+ sin 6, so that the intensity of the vortex layer is: 


—sin Ó. 
2 


The impulse of this layer is: 


. 3 
Ge CG; A; = | a dé. Be G- xa? sin? 0 = 2x va’. 
0 
An : 
Subtracting from this the amount OAs pa? for the impulse of the fluid sub- 
stituted for the sphere we find the well known value: 


An dt © 
3 ua je mr 


(LAMB, le. p. 116). 

2) For a non uniform motion this ““acceleration resistance’ may sometimes be 
separated from the total resistance; see G. Cook, An experimental determination 
of the inertia of a sphere, moving in a fluid, Phil. Mag. 89, p. 350, 1920. 


782 


Part of this impulse can be received back when the motion of 
the body is retarded; viz. the part given by classical hydrodynamics, 
for which may be put: 

(“apparent mass”). (velocity of the body). 

Of the rest a small part can be received back; the greater part, 
however, is lost. *) 

When we have to do with an tdeal fluid (absolutely without 
friction) these considerations need not be changed, when only we 
say that the vortices always remain in an infinitely thin layer at 
the surface of the body. They do not diffuse and are not washed away. 
The impulse therefore is always seated in this layer and has the 
value: 

(“apparent mass’’). (velocity of the body); 
this amount can be totally received back when the motion of the 
body is retarded. 

In order to obtain an “irreversible” resistance viz. to give an 
impulse to the fluid that cannot be received back, the vortex motion 
must come outside this layer, there must be diffusion of the vorticity, 
be it to a low degree. 


1) O. ReynoLps mentions the following simple experiment (Scientific Papers I, 
p. 188), which may be repeated easily: a body moving in a fluid is suddenly 
slopped; when directly afterwards it is released, it proceeds still a short distance 
in its original direction. The motion in the fluid present after the stopping has 
therefore still exerted a force on the body in the direction of the motion and has 
given back impulse to the body. 


Chemistry. — “On the Action of Micro-organisms on Organic 
Compounds. II. (The Solubility of some Organic Acids in 
‘atty Oils”). By P. E. VeRKADE. (Communicated by Prof. 
J. BOESEKEN). 


(Communicated at the meeting of Sept. 25, 1920). 


I. The foundations on which the OverroN-Meyer lipoid-theory 
(which, as Hans WINTERSTKIN®) has so justly observed, contains two 
intimately connected parts, which are yet very clearly to be distin- 
guished, viz. the theory of the elective permeability of the cell-wall, 
and the lpoid theory of narcosis) rests appear most clearly from 
the following quotations from one of Ovrrron’s publications *): 

“Ks fiel mir nämlich schon frühzeitig auf, dass alle solche 
Verbindungen, welche in Aether, fetten Oelen und abnlichen 
Lésungsmitteln leicht léslich sind, resp. leichter löslich sind als 
in Wasser, denn hierauf kommt es hauptsächlieh an, durch den 
lebenden Protoplast mit grösster Schnelligkeit eindringen, während 
für solche Verbindungen, welche zwar in Wasser leicht, in Aethyl- 
aether oder fettem Oel gar nicht oder nur sehr wenig löslich sind, 
der Protoplast nicht merklich oder nur äusserst langsam durch- 
lässig ist.” 

And a little further: 

“Bei der weiteren Verfolgung des Gegenstandes zeigte es sich, 
dass, wenn man von einer relativ langsam eindringenden Verbin- 
dung ausgehend, solche Substitutionen an dem Molekiil vornimmt, 
dass die Löslichkeit in Aether, fettem Oel etc. zunimmt, die- 
jenige in Wasser aber abnimmt, zugleich die Sehnelligkeit des 
Durchtritts durch den lebenden Protoplast erhöht wird.” 

As fatty oil olive oil was exclusively used — at least as far as 
could be ascertained from the literature — probably because this 
oil is available in very good quality. 


1) First communication: VERKADE and SöHNGEN: Verslagen Kon. Akad. v. Weten- 
schappen 28, 359 (1919); Centralbl. f. Bakteriologie (2) 50, 81 (1920). 


2) Die Narkose (Berlin 1919). 
5) Vierteljahresschr. d. naturf. Gesellsch. Ziirich 44. 88 (1899). 


784 


OverTON ') tries to explain these facts by assuming: 

“dass die Grenzschichten des Protoplasts von einer Substanz 
imprägniert sind, deren Lösungsvermögen fiir verschiedene Verbin- 
dungen mit denjenigen eines fetten Oeles nahe übereinstimmt….” 

The permeability of the cell-wall to some compound resp. the 
nareotic action of this compound on the cell, would now be deter- 
mined by the distribution coefficient “plasma skin fatty substance” 
— water of this compound; as this distribution coefficient cannot 
be determined ®) by the experiment (at any rate not with any degree 
of certainty) (see below), the distribution coefficient olive ot/-water 
is used in its stead, in which it is then assumed that there exists 
a perfect parallelism — not to say proportionality — between these 
two distribution coefficients for different substances. 

Also Hans H. Meyer’), who at the same time came to a similar 
theory of narcosis quite independently of Overton, based his con- 
siderations on the distribution coefficient olive oil-water of the 
examined compounds. 


2. We bave now determined the solubility for three organic acids 
(benzoic acid, salicylic acid and cinnamic acid) at 25°.0 C. in a 
number of very carefully refined fatty oils. The results of these 


determinations — a fuller discussion of which will appear in the 
Centralbl. f. Bakteriologie — are recorded in the subjoined table: 
TABLE I. 


| Solubility in grams per 100 grams of oil. 


‘Cotton-seed oil. 


| Olive oil. Arachis oil I. | Arachis oil IL. 
cinnamic acid 1.29 1.44 1.62 1.42 
salicylic acid 2.43 2.55 2.82 2.39 
benzoic acid 3.96 4.22 4.78 3.98 
Cocoanut oil. | Linseed oil. Ricinus oil. 


cinnamic acid Pa 1.66 1558 
salicylic acid 3.18 3.42 14.81 
benzoic acid 4.98 4.27 14.70 


1) ibid. 


*) Vgl. OveRTON: Studien über die Narkose (Jena 1901) pag. 54, 69. 
3) Archiv. f. exper. Pathol. und Pharmacologie 42, 109 (1899); 46, 338 (1901) 
— Baum: ibid. 42, 119 (1899). 


785 


These data give occasion for a number of remarks and conclusions. 
a. In the first place it must strike us that the dissolving power 
of two samples of pure arachis oil) with regard to these acids 
appeared to be so very divergent. The difference amounts to: 
for cinnamic acid +14 °/, 
for salicylic acid +18 ,, > in the same direction’). 
for benzoic acid + 20 ,, 

The same thing appears on comparison of some of our data with 
those published by WAreRMAN®), though it should at once be stated 
that the latter determined the solubility by another and less accurate 
method than we. He found for the solubility in olive oil at 25°: 
of salicylic acid 2,59 gr. per 100 gr. of oil (hence 6.6 °/, more than 
we), of benzoic acid 4.33 gr. per 100 gr. of oil (hence 9.9 °/, more 
than we). 

It follows irrefutably from this that the solubility of some acid im 
a definite vil is by no means a constant, but that it varies with the 
inevitable oscillations in the constitution of this fatty oil. Undoubtedly 
this may be proved also for other substances than organic acids; 
we have only chosen these, because they can easily and accurately 
be determined by a titrimetric method. 

6. Of the six examined oils olive oil, cottonseed oil, arachisoil, 
and cocoanut oil agree with regard to their chemical constitution 
in so far that they all chiefly consist of glycerides of different acids 
of the fatty acid series, and of those of oleic acid and of linoleic acid. The 
differences consist chiefly in the different ratios in which these acids 
are present in the glycerides; thus cocoanut oil contains e.g. much 
trilaurine and trimyristine, on the other hand but little of glycerides 
of the unsaturated acids (the iodine number is accordingly very low); 
olive oil contains on the contrary very considerable quantities of 
these latter substances (in consequence of which the iodine-number 
is much greater) etc. 

As appears from table 1 we meet with a very different dissolving 
power with regard to the examined acids also in these closely allied 
oils. The difference between the highest and the lowest of the found 
solubilities is: 

by cinnamic acid + 37 °/, 
by salicylic acid + 33 °/, 
by benzoie acid + 26 °/, 


1) Cf. the extensive discussion in the Centralbl. f. Bakteriologie. 

3) Here and henceforth the meaning is: °/, of the lowest amount. 

8) Proefschrift Delft (1918) p. 79 et seq.; Centralbl. f. Bakteriologie 42, 639 
(1914) etc. 


786 


In table II are recorded the ratios of the solubilities of the three 
examined acids in each of these fatty oils, in which the solubility 
of cinnamic acid is always put — 1. As clearly appears from these 
values, there is no question of a proportionality of the solubilities 
(of the coefficients of distribution fatty oil-water); the oscillations 


TABLE II. 
DR VTT EE en men 
Olive oil. |Cotton-seed oil.;Arachis oil I.\Arachis oil II.;\Cocoanut oil. 
; es | | 
cinnamic acid | 1 1 1 1 
salicylic acid 1.88 ta rhe 1.74 1.68 1.80 
benzoic acid 3.07 2.93 2.95 2.80 2.81 


are even so considerable that the parallelism between the solubilities 
of the acids (hence also between the coefficients of distribution 
fatty oil-water) in the different oils becomes questionable. 

c. When we now consider linseed oil’), which has an entirely 
different constitution, as it consists for the greater part of glycerides 
of linoleic acid and isolinoleic acid, we see the ratios of solubility 
modified so radically and unaccountably that there is not even any 
question any longer of parallelism of the solubilities of our acids 
(or of the coefficients of distribution fatty oil-water). While e.g. 


TABLE III. 


CoN SE een en EE EEE I ETE EER SS RRS IE SE AE A EE ED 


Ratio of solubility. 


Linseed oil. Ricinus oil. 


cinnamic acid | 1 
salicylic acid 2.07 1.97 
benzoic acid 2.57 1.95 


cinnamic acid and benzoic acid are less soluble in linseed oil than 
in cocoanut oil, the solubility of salicylic acid is on the contrary 
greatest in the first oil. 

d. These facts make themselves felt much more strongly even in 
ricinus oil, consisting chiefly of glycerides of “ricinoleie acid” 
C,,H,,O,. This oil, indeed, occupies a place of its own: it is mis- 

\) It may be remarked here that such a strongly drying oil can of course | 


present no resemblance at all with any lipoids of the cell-wall. We examined 
also this oil, however, as it represents quite a type apart. 


787 


cible in all proportions with alcohol, and very sparingly soluble in 
petroleum ether. The solubility of all three acids in this oil is consi- 
derably greater than that in any other of the examined oils (see 
Table I); it is particularly striking that the solubility of salicylic acid 
in this oul still slightly exceeds that of benzoic acid *). 

Let us now determine the coefficients of distribution of the three 
acids between olive oil, resp. ricinus oil and water by the aid of 
the following solubilities of the acids in water: 

cinnamic acid 0.0546 gr. per 100 gr. water °) 

salicylic acid 0.223 „ OW De aR es 

Beneden Me eins, Miller pele cn LOO raad) 
Then we find: 


TABLE IV. 
| D.C» = Er substance in 100 gr. of oil _ 
“~~ gr. substance in 100 gr. of water 
Olive oil. Ricinus oil. 
cinnamic acid 23.6 138 
salicylic acid 10.9 66.4 
benzoic acid 11.6 43.2 


According to Overton benzoic acid would, therefore penetrate 
somewhat more easily into the living cell than salicylic acid, and 
will therefore also act somewhat more strongly narcotically. If on 
the other hand we had assumed the solubility of the acids in ricinus 
oil as basis of our considerations, we should have arrived at the 
opposite conclusion that the plasma wall is considerably more perme- 
able to salicylic acid than to benzoic acid, and that therefore the 
former acid would be the strongest narcotic, resp. disinfectant. 

On comparison of the coefficients of distribution of the three acids 
between the other oils on one side and water on the other side, we 
come to analogous contradictions. We shall not enter into a discus- 
sion of these data here, as they do not open new points of view. 


3. From this numerical material the following important conclu-_ 
sion may be drawn: 


1) This is the more remarkable as ricinus oil consists of glycerides of oxy-acids, 
and salicylic acid is an oxybenzene carbonic acid. The well-known rule of solubility 
holds, therefore, here again. 

2) Jur. Meyer: Z. f. Elektrochemie 17, 978 (1911). 

3) This value is a mean of the most probable data, recorded in LANDOLT— 
BORNSTEIN—RortH tables. 

51 

Proceedings Royal Acad. Amsterdam. Vol XXIII. 


788 


Though we admit the validity of Overton’s conception concerning © 
the elective permeability of the cell-wall, and the narcotic action of 
all kinds of compounds on the cell as a consequence of the presence 
of a “plasma skin-fatty substance’, conclusions about the behaviour 
of certain compounds towards the cell can be drawn from the value of 
the coefficient of distribution olive oil-water only if this “plasma-skin- 
fatty substance” is in exceedingly close relation with olive oil. 

About this “plasma skin-fatty substance” we know next to nothing, 
but it may be said with almost absolute certainty that — if it exists 

the chemical constitution will be entirely different from that of 
olive oil. But then determinations of the coefficient of distribution 
olive oil-water are worthless for a decision of permeability problems. 
This also appears already from the literature. Already on a cursory 
examination of the values published by Overton’) and Baum’), it 
is seen that the coefficient of distribution olive oil-water, and the 
strength of the narcotic action, indeed, in general vary in the same 
direction, but that mostly there is no question at all of a propor- 
tionality or even of an approximate agreement in the order of magni- 
tude. Besides we have been able to demonstrate in our first commu- 
nication that the coefficient of distribution olive oil- water can by 
no means serve to account for the assimilability or non-assimilability 
of unsaturated organic acids by moulds. 

Now the reason of this is clear: the solubility of a substance in 
olive oil is entirely independent, is by no means in any connection 
with the solubihty in any other fatty oil. 


4. QOverton*) has expressed the following opinion about the 
structure of the “plasma skin-fatty substance” : 

“Nach vielem Nachdenken neige ich immer mehr zu der Ver- 
mutung, dass das Cholesterin*) oder eine Cholesterinartige Ver- 
bindung (etwa eine Cholesterinester), resp. ein Gemisch solcher 
Verbindungen die imprägnierenden Substanzen sein dürften. Es 
wäre übrigens sehr wohl denkbar, dass Lecithin und in gewissen 
Fallen fettes Oel ebenfalls beteiligt sind, indem das Cholesterin 
demselben etwelchen Schutz vor der Verseifung gewähren diirfte”’. 

It need no argument that if really the plasma skin was soaked 
with such a cholesterine-lecithine mixture (called ‘“‘lipoid” by Overton), 
hence with substances absolutely different in chemical constitution 
from fatty oils, the coefficient of distribution olive oil-water would 


1) Cf. Studien über die Narkose (Jena 1901) pag. 100 et seq. 
) loc. cit. 

5) Vierteljahresschr. d. naturf. Gesellsch. Ziirich 44, 88 (1899). 
4) Also phytosterin etc. are, of course, included in this. 


789 


not constitute any criterion for the behaviour of some compound or 
other towards the living cell, because this coefficient of distribution 
need not have any relation to that of the same compound between 
this “lipoid” and water. The more so, where also the physical 
properties of fatty oils and “lipoids” are wide apart; the latter are 
e.g. lyopbile colloids, swell with water (with the exception of 
cholesterine, ete, which for this reason is considered by Lorwe ') 
to belong to a separate class of ‘‘semi-lipoids’’), and give accordingly 
rise to entirely different circumstances. Overton”) has also felt this 
difficulty, and has already adduced arguments for it himself (which 
are, however, still open to criticism and have in fact already been 
called in question); though the commercial salts of basic aniline 
dyestuffs are almost or entirely insoluble in olive oil, they easily 
dissolve in molten cholesterine or in cholesterine dissolved in oil, 
and also in lecithine *). I have been able to confirm this once more 
myself for a number of dyestuffs. 


5. There would not have been any reason for this criticism of 
the lipoid theory for it has been opposed by numerous investi- 
gators, and may be considered as pretty well refuted —, if not of 
late WarrrMaN‘*) had again explicitly expressed the parallelism 
between the coefficients of distribution lipoid components-water and 
olive oil-water, and had tried by comparison of the last-mentioned 
coefficients of distribution to give an explanation of the greater or 
less facility with which these compounds are assimilated by Penzci- 
lium glaucum. From what we have communicated above it may 
appear that the good results which WATERMAN is said to have 
obtained in this attempt, should be ascribed to accidental circum- 
stances, and that in any case no general significance may be assigned 
to them. This is also confirmed by our researches *) on the assimi- 
lation of unsaturated acids by Penicillium glaucum and Aspergiilus 
niger contained in our first communication; even on the assumption 
that the lipoid solubility of these acids is comparable to that in 
olive oil, an explanation of the behaviour of these substances with 
regard to moulds is by no means possible. 

Laboratory of the Dutch Commercial University. 

Rotterdam, August 19. 1920. 

1) Biochem. Zeitschr. 42, 217 (1912). 

3) Jahrb. f. wissensch. Botanik 34, 669 (1900). 

3) Loewe (loc. cit.) has later carefully studied the behaviour of ‘“‘lipoids’” and 
“semilipoids” with regard to dyestuffs (methylene blue) and derived forcible 
arguments against the OveRToN-MEyYER theory from his results. 


4) Proefschrift Delft (1913); Centralbl. f. Bakteriologie 42, 639 (1914) etc. 
5) VERKADE and SönNaeen; loc. cit. 


oi? 


Physics. — “Measurements on the Intensity of Spectrum Lines by 
the Aid of the Echelon’. By Dr. H. C. Burerr and P. H. 
VAN Cittert. (Communicated by Prof. W. H. Junius). 


(Communicated at the meeting of September 25, 1920.) 


1. Introduction. When determining the intensities of spectrum 
lines, one is confronted by the following complication : what is directly 
observed is the relation of the intensities of the lines which exists 
at the place where the examined spectrum is formed by the spectrnm 
apparatus used. In general, however, this relation is not the same 
as the relation of the intensities of the lines in the light emitted 
by the examined source of light. In the echelon this is even far 
from being the case for very small differences of wave-length. 

When the intensity of the light that traverses the echelon in the 
direction of the optical axis, is /,, the intensity of the light 
leaving at an exit angle « with the axis is theoretically *) given by: 


oe eae 
fay ee 
(rie) 
(2 = wave-length, o = width of a step). 

The differences in direction of exit may have been caused both 
by a difference in wave-length and by a difference in position of 
the echelon, provided the echelon is placed about parallel to the 
optical axis. In fig. 1 the relation between intensity and position (i.e. 
angle a) of a spectrum line is graphically represented. At an angle of: 

a 

Dese . 
the intensity becomes zero, and assumes only small values outside 
this interval. The distance between two orders also amounts to 


0 , 


À 
«a. = — so that at the utmost two orders of one line in the central 
6 


part of the curve (fig. 1) can be observed with pretty great intensity. 
As appears directly from the figure, it may happen that the intenser 


1) Enc. d. Math. Wiss., Band Physik V, 21, 389. 
BALy-WaAcHSMUTH, Spektroskopie, 1908, 137. 


791 


of two lines seems the weaker, when it is in the neighbourhood 
of the minimum of the curve of intensity. These circumstances 


should be taken into account in determinations of the intensity with 
the echelon. This has not been done’) in former measurements’). 
The error caused by this, cannot be redressed by a small correction, 
but causes the relations of intensity found to be perfectly different 
from those that are present in incident light. 

The great importance of the function represented by (1) and fig. 1 
led us to test the theory by experiment before applying it to 
our measurements. For this purpose the intensities of the different 
orders of a spectrum line were measured (cf. fig. 1, spectrum line 
in four orders A, B, C, and D with intensities Aa, Bb, Cc, and Dd). 
Then the whole system of lines was slightly displaced by a small 
rotation of the echelon round an axis parallel to the effective sides, 
so that the lines assumed another position A’, B’, C’, D’, and the 
intensities A’a’, B’b’, C’c’, D’d’ were determined anew. When these 
measurements are repeated for some positions of the echelon, and 
when besides the position of every line with respect to a definite point 


1) The considered distribution of intensity has also influence on the observed 
position of the spectrum line when the centre of gravity or the maximum of inten- 
sity observed with the spectrum apparatus is understood by this. For a line within 


A 
the interval x) = — will be more greatly weakened on the outer side than on the 
o 


inner side, hence it will seem to be displaced towards the inside. A system of lines 
will, therefore, be compressed. The great divergency of the values, which different 
observers have found for the distances of the satellites of the green mercury line 
(cf. Nagaoka and Takamine, loc. cit.) is probably for the gredter part owing to this. 

8) NAGAOKA and TaKAMINE, Proc. of the Phys. Soc. of Londen 25, I, 1912. 
Tokyo Sûgaku-Buturigakkwai Kizi, 2e Serie, 7, I. 


792 


in the image plane is determined, the theory can be tested. As it 
appeared in preliminary observations that the temperature had 
influence on the position and the distribution of intensity *), care 
was taken that the surroundings of the echelon remained at constant 
temperature during the measurements. The measurements have been 
carried out with regard to three components of the green mercury 
line (A = 546,1 uu). 


2. The determination of the intensity. The intensity was determined 
by a photographic method. The method used, the description of 
which follows here, is analogous to that which Miss R. Riw1n *) 
applied for the determination of the absorption. 

In order to prevent complications in consequence of difference in 
time of exposure, kind of plate, development etc., all the spectra 
belonging together were photographed on one plate with the same 
time of exposure’). The blackening of the plate then depends 
exclusively on the intensity of the incident light. When the functional 
relation between blackening and intensity (curve of blackening) is 
known, the second quantity can be found from the first. As the 
components of the system of lines examined by us have only a very 
small difference in wave-length, a curve of blackening need be 
constructed only for one wave-length. 

To find this curve the following course was taken. The spectrum 
of the green mercury line was photographed with a definite position 
of the echelon. Then different light-reducers *), which weaken the 
light of the green mercury line in known ratio, were successively 
placed before the slit of the collimator, and with the same position 
of the echelon the spectrum was repeatedly photographed. 

To gauge the light-reducer, the light of the mercury lamp (Wes- 
TINGHOUSE CoopErR-Hrwitt, 220 V., 3.5 A) is concentrated by con- 
densers on a surface thermopile of Morr, which was connected with 
a galvanometer of Morr. Filters ensured that only the light of the 
wave-length 546,1 uu fell on the thermopile. The reducers were 
placed immediately before the thermopile. The ratio in which the 
light is weakened is found by division of the deviation of the gal- 


1) Phys. Zeitschr., 21, 16, 1920. 

2) These Proc. Vol. 23, p. 807. 

3) Paget, Orthochromatic, Extra Special Rapid plates were used. The development 
took place for about 10 minutes with a glycin developer. 

4) For reducing the light solutions of chromealum were used in different concen- 
trations in air tight vessels. To prevent turbidity a litlle sublimate was added. The 
vessels were gauged anew a few times with an interval of some weeks. No change 
could be perceived in the absorption. 


798 


vanometer with reducer before the thermopile, by that without 
reducer. By placing a concave lens before the reducers it was possible 
to modify the convergence of the beam of light. It appeared to have 
no influence within wide limits. 

Five reducers were used, which transmitted resp. 68.0, 46.8, 32,5, 
21,3 and 14.7 °/, of the incident light. 

The blackenings were determined with Morr’s microphotometer *). 
In the registered curves belonging to the unweakened system of 
lines and to the weakened system of lines obtained in the way 
described above, the maximum of one of the lines, e.g. of the 
intensest of the system, was found. The blackening of this point 
was plotted for the different spectra with respect to the intensity, 


— blackening. 


~D ee ec ' 
147 21,3 32.5 468 68,0 100 
— log I 

Fig. 2. 


in which, as is usual, the abscissa was taken proportional not to the 
intensity 7 itself, but to log 7. This gave the curve AB (fig. 2), in 
which the intensity of the considered line in the unweakened spectrum 
is put arbitrarily at 100, so that the intensities of the other five 
points have the values mentioned above. 

If for another (fainter) line we put the intensity in the unweakened 
spectrum again at 100, we get for this line the curve CD. The 


1) Verslag Kon. Akad. 27, 566, 1919. 


794 


intensity of the unweakened line, is, however, not 100, but smaller, 
and the diminished intensities are all of them smaller in the same 
ratio. Accordingly each of the points of CD must be displaced to 
points where the intensity is smaller in a definite ratio, the value 
of the blackening being retained. As the abscissa represents log i, 
this means a shifting of the points of CD of the same amount 
towards the left. The amount of this shifting is not known a priori, 
but must be chosen so that after the displacement to C’ D’ the 
points of CD lie as much as possible between those of AB. This 
process may be repeated for still fainter lines, and in this way a 
curve of blackening may be constructed ranging from the smallest 
to the greatest of the occurring intensities, and of which many points 
are fixed, though only six spectra with known ratios of intensities 
have been reproduced. 

By the aid of this curve of blackening the intensity at any point 
of another spectrum reproduced on the same plate, may be found. 


3. Determination of position. To determine the position a spectrum 
of comparison has been placed under every spectrum, except under 
that which served for the determination of the curve of blackening. 
These comparison-spectra were photographed at the same position 
of the echelon, so that a definite line of these spectra indicates a 
definite position ') in the image plane of the echelon. 

The position of a detinite line was measured by the determination 
of the distance from this line to a definite line of the comparison 
spectrum with a Zxiss comparator. It is sufficient to measure this 
distance for one line of the spectrum with the comparator, and 
determine the position of the other lines from their mutual distance. 
This is found from the registered curves of the spectra, when once 
the ratio has been determined of the distances of two correspond- 
ing points on the photographic plate and on the registering paper. 
This ratio is a characteristic constant of the micro-photometer. The 
order of magnitude of the error in the localisation was 0.5 °/, of 
the distance of two orders, which amounted to 2 mm. 


4. Results. No exact agreement can be expected on comparison 
of formula (1) with the observations. When the light traverses the 
echelon obliquely, this formula only holds in first approximation. 
In this case @ represents the angle of the light with the optical 


') By position and intensity of a line here and elsewhere the position and intensity 
of the maximum blackened part of the line should be understood. The error 
mentioned on p. 791, therefore, plays a part. 


795 


axis of collimator and eye-piece. That (1) does not represent the 
intensities accurately follows among others already from the fact 


À 
that the distance of two orders does not amount toa, =~, i. 6. is 
9 


not independent of the position of the echelon. This distance changes 
very appreciably on rotation of the echelon; it increases as the 
echelon moves further from the position, at which the light is 
parallel to the steps. The difference between the greatest and the 
smallest distance of the orders amounted to abont 10°/, of this 
distance. We have, however, not occupied ourselves more closely 
with these particularities, but confined ourselves to expressing all the 
distances as fraction of the distance of the orders in the spectrum 
in question. 

The measurements have been carried out with regard to three 
components of the green mercury line, namely on the so-called 
principal line and two satellites (84 = — 0,0242uu and 8A=—0,0078uu, 
Nac. and Tak. loc.cit.). In its different orders and with tbe different 
positions of the echelon each of these lines gives a series of points 
of a curve which indicates the relation of intensity and position. The 
three curves obtained in this way have been reduced to one and 
the same value of the maximum intensity, which is reached when 
the line is in the centre of the image plane.') Fig. 3 gives the 
observed point, in which . refers to the principal line, O and X 
resp. to the stronger and the weaker satellite. The uninterrupted 
curve represents the theoretical distribution of intensity. 


Fig. 3. 


The agreement is sufficient in the neighbourhood of the maximum. 


1) The observations show that really every line has its maximum at the same 
point of the image plane. . 


796 


Also the height of the weaker maxima on both sides is in harmony 
with the theory, when it is taken into consideration that the accuracy 
is not so great at these small intensities. A considerable deviation 
is observed in the neighbourhood of the position where the intensity 
becomes zero. Here the observed intensity is much greater than 
theory led us to expect. !) As the three lines examined have a very 
different intensity and yet present the same deviation from the 
theoretical curve, this deviation cannot be attributed to a systematic 
error in the determinations of the intensity. It is quite possible 
that the approximations in the theory mentioned before give rise, 
at least partially, to the lack of agreement between experiment and 
theory. When we confine ourselves, however, to the central part of 
the curve, the agreement is sufficient. For the derivation of the true 
intensities from the distribution of intensity in a line-spectrum ob- 
served by means of an echelon it will, therefore, be desirable 
that the lines to be compared lie in the central part of the image 
of diffraction. 
Institute for Theoretical Physics. Physical Laboratory. 
Utrecht, Sept. 1920. 


1) It is, however, also possible that the width of the real distribution of intensity 
is greater than that which follows from the distance of the orders. For the position 
where the intensity becomes zero, lies further from the centre than follows from 
the theory. 


Mathematics. — ‘“Degenerations in Linear Systems of Plane Cubies’’. 
By Prof. K. W. Rureers. (Communicated by Prof. JAN pe VRIES). 


(Communicated at the meeting of November 30, 1918). 


1. The number of curves with two double points in a net of 

plane curves is given by the formula: 

RDE 6 API DTE PS 
where D represents the number of free points of intersection of two 
elements of the net, o the number of base points, p the genus of 
the curves. 

For a net of plane cubics this is therefore the number of degene- 
rations into a conic and a straight line; in a net without base points 
the formula gives a number of 21; each single base point reduces 
the number given by the formula by one. 

If there are single base points the question can be raised in how 
many degenerations the straight line passes through two, through 
one, or through none of the base points. If we take one of the base 
points as an angular point (2, == 0, «‚ =0) of a triangle of coordi- 
nates and if we make the condition that the straight line «, = ma, 
must be a part of a cubic of the net, it is easily seen that 6 values 
are found for m, that therefore there generally pass through a single 
base point 6 straight lines, parts of degenerations. From this follows 
the solution of the problem in question. | 

Another solution is found in the following way. The net is defined 
by a curve c, and a pencil to which c, does not belong. If D is 
the number of free points of intersection of two curves of the net, 
c, must pass through 9—D base points A; of the pencil. The latter 
cuts c, in an involution y of order D. Now the following is clear: 

a. The number of degenerations into a straight line A; Az and a 
corresponding conic is 4 (9—VD) (8—-D). 

6. A straight line through one of the base points can form a 
degeneration with a conic through the remaining 8—D. Thesystem 


1) GAPORALI, „Sopra i sistemi lineari triplamente infiniti di curve algebriche 
piane’’, Collectanea mathematica in memoriam Chelini, p. 182. The letter NV 
stands there instead of D. 


798 


of conies through 8—D_ points cuts c, in an algebraical sequence 
of points get (order = D—2, dimension —= D—8). Whenever a 
group of these is contained in a group of y, a degeneration appears 
in the net. The number of times this happens is found from the 
formula 


where n indicates the order, r the dimension of g, im the order, 
v the index of y, d the number of double points (here d = 2D) ’). 

In this case we find accordingly z= D—2, in other words 
through each base point pass D—2 straight lines, parts of degene- 
rations. In all (9—D) (D—2). 

c. A straight line through none of the base points is completed 
by a conic through 9— D base points. The system of conics defined 
by these points cuts c, in a 95 3. By the aid of the same formulae 
we have z= } (D—2)(D—3), which represents the number of 
degenerations where the straight component does not pass through 
any of the base points. 

The total number of. degenerations is accordingly *) 

} (9—D) (8—D) + (9—D) (D—2) + 4 (D=2) D=3) 228 


2. From the preceding follows that in a net of cubics with 6 
base points A,....,A, through each base point there passes one 
straight line which is completed to a degeneration by a conic through 
the other 5. It is known that these 6 straight lines pass through 
one point P when 4,...., 4, lie on a conic c,. Besides (he degene- 
rations PA;-+ c, are in this case contained in the same pencil of 
the net. All the nets chosen from the complex (threefold infinite 
linear system) of cubics defined by A,...., A, have this property, 
hence also the net with the base points P,A,,...., 4,. The existence 
of the fundamental curve c, causes this property. 

We shall now investigate whether this singularity can also appear 
in nets where there is no fundamental conic. 


Let A,,....4, be the base points of a complex S, and let us 


curva algebrica’’, Atti del Reale Instituto Veneto, t. 67% p. 1323, (1908). 

2) ©. Segre, „Introduzione alla geometria sopra un ente algebrico semplice- 
mente infinito”; Annali di Matematica, Ser. Il, t. XXII, p. 41. 

3) That the number of degenerations amounts to 21, independently of the 
number of single base points, follows also from the considerations in the paper 
“On Nets of Algebraic Plane Curves” (JAN pe Vries, these Proceedings VII (2), p. 716. 


799 


the above mentioned property; then it is easily seen that every 
time (besides the point P) two of the 9 base points of the pencil 
containing the degenerations, must lie on the straight lines PA,,... PA). 

For arbitrary situations of A,,..., A, p is therefore at most equal 
to 4; for p=5 P must lie on one of the joins A; Ar. If for 
p44 A,,...,A, are the base points of S,, B,,..., B, the other base 
points of the pencil, lying on the straight lines PA;, a straight line 
PA, must be completed by a conic through A; A; 4, B; B, Bn 
(7,4,mfFk); the polar straight lines of P relative to these four 
conics coincide in a straight line 7 and all the non degenerate 
cubics of the pencil are cut by P4A,,..., PA, in points lying har- 
monically with respect to P and /, in other words all the cubics of 
the pencil have P as an inflexional point and have a common har- 
monical polar line |. *) 


3. We shall now investigate the case p=5 more closely. With 
a view to this we shall start from the system S, with 6 base 
points P, A,,...,A,, where P, A, and A, lie on the same straight 
line. Now it will be possible that S, contains nets without other 
base points, so that the degenerations formed by PA,, PA, and PA, 
together with completing conics belong to one pencil. The situation 
of the other base points 4,, B, B, on the straight lines PA,, PA,, 
PA, can be determined. 

For the system S, represents a cubic surface ® with a double 
point O; PA,, PA, and PA, correspond to 3 straight lines p,, p,, 
ps of ®, which do not pass through O; a net out of S, without other 
base points corresponds to the plane intersections of ®, with planes 
of a sheaf the vertex Q of which does not lie on @,; the pencil 
to which the degenerations PA,, PA,, PA, belong, is the image of 
the intersections with a pencil of planes in (Q), which must also 
contain the planes (Qp,), (Qp,) and (Qp,). The axis of this pencil 
of planes must therefore cut p,,p,,p,, in other words, Q lies on 
the quadratic scroll R, having p,, ps Pp; as directrices. 

Generatrices of R, are among others the straight line p of ®, 
represented by the point P in the plane, and the straight line q 


corresponding to the conic c, through A,,...., A, 
If we project all the generatrices of R, out of O, there appears 


1) S. Kantor, , Ueber gewisse Curvenbtische! dritter und vierter Ordnung”, 
Sitz. ber. Akad. d. Wiss. in Wien, Bd. LX XIX (1879). See also H. J. van Veen, 
„Eigenschappen van bundels van vlakke kubische krommen by algemeene en by 
bizondere ligging der basispunten’, Nieuw Archief voor Wiskunde, 2e reeks, dl. 
XII, 1918, p. 279. 


800 


a pencil of planes having the directrix through O as axis; all the 
curves of intersection of , with the planes of this pencil pass 
therefore through the same point S’ of @,. These intersections 
correspond in S, to conies through A,, A,,A, and the point S cor- 
responding to S', which point S lies on c, because S' is a point of q. 

The points B,, B,, B, are accordingly the intersections of the 
straight lines PA,, PA,, PA, with a conic of the pencil through 
S, A,, A,, A, 

In order to determine the point S, we remark that the directrices 
of R, cut the generatrices p and q in projective point ranges; three 
pairs of corresponding points are the intersections of p and q with 
Py Po Ps The directrix through QO and with it the point S’ are 
therefore found by determining the point of g corresponding to O. 

In the image of ®, the directions round P are therefore projec- 
tively conjugated to the points of c, and that in such a way that 
both the points of intersection B',, 5',, B', of these straight lines with 
, correspond to the directions PA,, PA,, PA, If we project the 
latter points out of A,, there appear round P and A, two perspec- 
tive pencils of rays of which the axis of perspectivity is found as 
the join of B’, and B’, If this cuts A, A, in S" the second point of 


C 


intersection of A,S" and c, is the required point S. 

Any point P of A,A, defines out of the fourfold infinite linear 
system S, through A,,..., A, an S, in which one point S has been 
constructed; to each point P of A, A, belongs therefore one point 
S, or one point S". 

Let us now try to find the number of points P belonging to one 
point S or S". When P varies, B’, and B’, describe an involution 
on c,; the envelope of B’,B’, is a conic k, touching c, in the points 
A, and A,*). Out of S" we can draw two tangents to this conic, 
which define two pairs of points on c,, hence two points P, and 
P, on A,A,. The relation between P and S is therefore a (2,1) 
correspondence. 

Now it is known from § 2 that the curves of the pencil contain- 
ing the degenerations PA, PA, PA, have all a point of inflexion 
in P and also a common harmonical polar line for the pole P. 
The harmonical polar lines of all such pencils out of S, must pass 
through the 4 harmonical point P’ to P with respect to A, and 
A,; also the polar straight lines of P relative to each of the conics 
of the pencil (S,A,,A,, A,) must pass through P’; P and P’ are 


ij R. Sturm, "Die Lehre von den geometrischen Verwandschaften” 3ter Band, 
S. 138. 


801 


the double points of the involution cut by this pencil into A, A, 
Also the degenerations in this pencil, as the pair of straight lines 
A, A, + SA,, cut a,, in a pair of points of this involution, in other 
words also these points lie harmonically with respect to P and P’. 
The point S", the intersection of A, A, and 4, S, can therefore be 
found by determining tbe fourth harmonical point to P,, (A, A,, A, A,) 
and P’. In this construction it is easily seen that if by means of 
P’ we had determined an S, out of S,, the same point S", hence 
the same point S, would have been found. 


The two points P, and P, corresponding to the same points S of c, 
lie therefore always harmonically with respect to A, and A,. 

Each conic of the pencil (A,, A,, A, S) defines on the straight lines 
P,A,, P,A,, P,A, three points and also on the straight lines P,A,, 
P,A,, P,A, three points, which form together with A,,....,A,, P 
nine base points of a pencil in which appear the degenerations P,A,,P,A,, 
P,A,, resp. P,A,, P,A,, P,4,, with completing conics and where all 
non degenerate curves have a point of inflexion in P, resp. P,. 


4. Out of a complex $,* with 5 base points A,,....,A, a point 
P of A, A, defines a net S, contained in the complex S,* with 
base points A,,.....A,,P. If in S, there is to be a pencil with 
the above mentioned properties, the failing three base points B,, B,, B, 
must be cut into PA,, PA,, PA, by aconic of the pencil (S, A,, A,, A,), 


where S is the point of theconic c, through A,,...., A, belonging 
to =S,". 

By $,° a biquadratie surface ®, with a double conic is represented *), 
where the cubics correspond to plane sections of ®,. The straight 
line A,A, is the image of one of the 16 straight lines of the surface ; 
the plane sections through this straight line p,, correspond to conics 
through 4A,,A,, A, and a fourth fixed point Q. This proves that 
the conic through S, A,, 4,, A, must also pass through Q and we 
must try to find the conic cutting PA,, PA,, and PA, in the points 
B, B, B, among the conies of the pencil with Q, 4,, A,, A, as 
, in a point S to which 
two points P on A,A, correspond. Each curve of the pencil arising 
in this way, must belong to S,°, hence also the degeneration PA, 
with the conic through A,, A,, A,, B,, A,, B, must be a curve of it. 

Now to each conic through A,, A,, 4,, A, corresponds one definite 
straight line through A,, detining a point P’ on A,A,. Between the 


base points. A conic &, of this pencil cuts c, 


1) See among others Sturm, Die Lehre von den geometrischen Verwandtschaften. 
áter Band, S. 309. 


802 


points P and P’ of A,A, there exists therefore a correspondence 
(2,1) with 3 coincidences, from which follows: 

On any straight line joining two of the five base points A,,...., A, 
of S,* lie three points P, so that the straight lines joining P to the 
three remaining base points, are parts of degenerations belonging to 
the same pencil. 


5. We can arrive at the same results in an entirely different way, 
where at the same time the relation between the points P appears. 
With a view to this we shall first prove an auxiliary proposition. 

We start from a net of cubics with base points P, A,,...., A, 
and suppose the degenerations formed by PA,,...., PA, with 
completing conics to belong to the same pencil. We know that 
through P there pass two more straight lines which together with 
two conics through A,,...., A, form also degenerations of the net. 

Let us take PA,A, for triangle of coordinates and let us put 
PA, =p, tt, + pt, =(pe)=90, PA, red a te (qe) =F 
A,A,=a,2,+0,0,+4,2,=(ar7)=—0, B,B,=b,2,+6,¢,4b,0,=(b2)=0, 

The conics through A,, B,, A,, B,, A,, B, and through A,, B,, 
A,, B,, A,, B, belong both to the pencil (px) (ga) + 4 (aa) (b2) = 0. 

For the former conic 4 must be chosen such that it passes through 
A,, for the latter such that it passes through A,. Hence 4 must be 
resp. equal to —p,g,:a,6, and —p,g,:a,6,. The former conic is 
completed to a degeneration by «, =O, the latter by a, = 0. 

The straight line (av) =O belongs to a conic through P, A,, A,, 
and has therefore the equation c,v,v, + c,a,7, + ¢,v,c, = 0. By these 
three curves the net: 

) 2, }a,b, (pe) (qe)-p‚g,(0e) (be) + A4, ja, be (pe) (Ge)—Pags (22) (be); 
+ A, (az) (c,2,0,+¢,2,0,+¢,c,2,) = 0 
is defined. 

By assuming #,=rx, and by putting the condition that these 
straight lines be parts of degenerations in the net, we find through 
the elimination of A,,4,,4, and through division by p, + p‚r and 
q, + 9,7” the equation 

b, : ¢,+ 6,7 ee 
a,(6,+5, r) Te b, (4,44, r) ’ a,C,7r ai (c, +¢, r) (a, +a, r) ae 

This equaticn defines therefore the two straight lines m and n 
which pass through P and are parts of degenerations. 


In the net is a curve which has a double point in P. For this 


A, = Sh A. =e pass hs and the nodal tangents are found 
P3929, ss), 
out of: 


0. 


803 


— 4 Ber + (— a, 6, ¢, —a, b,c, + a, 6, c,) r—a, be, = 0 ne =) 


this equation appears to be the sameas the equation for 7 found above. 

Our auxiliary proposition reads therefore: 

When in a net of cubics with five base points the lines joining 
one of them to the other four are parts of degenerations belonging 
to the same pencil, the two other straight lines through that base point 
also parts of degenerations, are the nodal tangents of the curve of 
the net that has a double point in that base point. 

Some consequences are easily derived from this proposition. 

All the curves of the pencil containing the degenerations have 
according to § 2 a point of inflexion in Panda common harmonica! 
polar line /. 

Any straight line through P, hence also m and n, is cut besides 
in P in two more points lying harmonically with respect to A and 
the point of intersection with /. There is therefore a curve of the 
pencil touching m, resp. mn, in the point (/,m) resp. (/,7), and a 
curve having m resp. n as inflexional tangent at P. 

By a complex of cubics S,‘ with four base points A,,..., A, a 
surface ®, of the 5 order with a double curve of the 5% order 
is represented.*) The point P corresponds to a point P’ of ®,, the 
pencil of curves containing the degenerations PA,,..., PA, to the 
intersections of ®, with a pencil of planes of which the axis passes 
through P; this axis cuts ®, in the points B',,..., B', corresponding 
to the points B,,..., 6, in the image. The straight line m corre- 
sponds to a plane cubic c,” (lying in a plane VV) through P. This 
c‚” has a double point in one of the points of intersection of V 
with the double curve o,. Any curve of #, lying in a plane of the 
pencil (P’, B;’) cuts cy in 2 more points on the same straight line 
through /’. As appears from the image it must happen once that 
these two points of intersection coincide in P’, in other words P’ 
is a point of inflexion for c,”. For the same reason P’ is also a 
point of inflexion for the plane cubic c,” represented by the straight 
‘line n. We find therefore: 

The points defining a net out of S,* where the joins of these points 
and the base points of the same system are parts of degenerations 
belonging to the same pencil, are the images of those points of ®, 
where two curves belonging to one of the five systems of plane cubics 
on this surface, have both a point of inflewion; or 


1) Gaporau, „Sulla superficie del quinto ordine dotata d'una curva doppia 
del quinto ordine", Annali di Matematica, Ser. Il, t. VIL, 1875, p. 149. 
52 


Proceedings Royal Acad. Amsterdam. Vol XXIII. 


B04 


These points are the images of those points of ®, where there 
passes through each of the principal tangents a plane containing a 
cubic of one of the systems of these curves. 

If we take into consideration that the intersection of ®, with 
the tangent plane at P’ is represented by the cubic that has a double 
point in P, we have here a new proof for the algebraically proved 
auxiliary proposition. 

The point of intersection of m with the common harmonical polar 
line / is the image of the point of contact Q’ witb the tangent 
drawn from P’ to c,”. The double point D’ of c, is represented 
as a pair of points on the straight line m, i.e. as the two points 
on m associated to the curve corresponding to the double curve 
o, of ®,. This pair of points is cut into m by a curve of the pencil 
and lies therefore harmonically with P and (/, m). 

Besides P’ c,” has 2 more points of inflexion, which lie with P’ 
on the same straight line; they are therefore cut into c,” by a curve 
of the pencil (P’,8,’). It appears from this that the corresponding 
points in the image lie also harmonically with respect to P and 
(/,m). The curves of the. net which have double points in these 
two points, must have m as one of the nodal tangents‘). The same 
holds for the straight line n. 


6. We return now to the complex $,* of cubics with 5 base 
points A,,...., A, and suppose that the point P has been construct- 
ed on A, A, in such a way that the straight lines PA,,...., PA, 
are parts of degenerations belonging to the same pencil. 

One of the other two straight lines, parts of degenerations through 
P, always coincides with A, A,; the other passes through a fixed 
point O. The curve which has a double point in P, splits up into 
A,A, and a conic through A,, A,, A,, P and a fixed point Q*). 

According to the above mentioned auxiliary proposition the last 
mentioned straight line through P touches this conic. 

If we suppose that in each point of intersection of A,A, with a 
conic of the pencil (A, 4, A, Q) the tangents to that conie are 
drawn, these straight lines envelop a curve of the 3" class *) to 


1) 3 points have therefore been found on the straight lines m and n, each of 
which straight lines is one of the nodal tangents of the curve of Sz having a 
double point there. Generally five of these points can be found on an arbitrary 
straight line. To the three points mentioned we can add here the two points of 
intersection of m or m with their corresponding conics. 

2) Sturm, l.c. S. 306. 

5) SPORER, , Ueber eine besondere mit dem Kegelschnittbüschel in Verbindung 
stehende Curve’, Zeitschrift für Mathematik und Physik, 38 Jahrgang, 1893, S. 34. 


805 


which envelope three tangents can be drawn out of QO; in other 
words three points P lie on A,A,, so that the tangent at P to the 
conic (P, A,, A,, A,, Q) passes through O, and thus we have arrived 
at the result already found in § 4. 


7. We shall now try to find the locus of the points S for which 
one of the nodal tangents to the curve of S, which has a double 
point in S, passes through the fixed point O. 

A point P of a straight line / is a double point of one curve of 
S,; this curve cuts / in one more point P’. Inversely P’ defines a 
net of cubics out of S, with six base points(A,,...,A,, P’). The 
locus of the double points of the curves of this net is of the 6*% 
order with double points in A,,..., A, and P’; it cuts / therefore 
besides in /’ in 4+ more points. Between P and P’ there exists a 
correspondence (1,4) with 5 coincidences, i.e. on any straight line | 
lie five points P, so that one of the nodal tangents of the curve 
which has a double point in P, coincides with 1. 

We can deduce from this that the envelope of the nodal tangents 
of those curves in S, which have double points in the points of the 
straight line /, is of the 7' class. 

For this reason 7 tangents can be drawn out of the point O to 
this curve belonging to’ /, so that it appears that there lie seven 
points on / where one of the nodal tangents is a straight line that 
can be considered as a part of a degeneration. 

However it is clear that also the two points of intersection of / 
with the conic (A,,..., A,) must be reckoned among these 7 points, 
so that the result is: 

The points that are double points of curves of S, where one of 
the nodal tangents is a part of a degeneration, lie on a curve of 
the 5th order. 

It is already known from § 5 that the points of this curve c, correspond 
to the points of inflexion of that system of plane cubics represented 
by S, on the surface of the 4" order ®, that corresponds to the 
straight lines through OQ. Each of these cubics has three points of 
inflexion, so that each straight line through O can cut the c, in 3 
points. The point OU is a double point of ¢,, the nodal tangents are 
the tangents at OQ to that curve of S, which has a double point in O. 

It appears further that the base points A,,...., A, are points of 
inflexion of c,; the tangents at the points of inflexion pass all through 0. 

Besides these, 4 single tangents can be drawn out of O to c,, 
namely the lines joining O to the four points A; corresponding to 


the pinch points of the represented surface ®,. 
52* 


806 


The double conic d, of gp, corresponds to a cubic c, through 
OV, A,,....,A,. The associated pairs of points, images of the points 
of d,, are the intersections of c, with the straight lines through O; 
in the four points of contact A; of the tangents drawn out of O to 
Ca, there coincide two associated points’); the curves on ®, corre- 


sponding to these straight lines, have one cusp, hence one point of 
inflexion. 


\ 


These four straight lines OK; touch c, at K and have besides 


one free point of intersection with c,. The curves c, and c, touch 
at the points K and have no points of intersection besides these and 
they points (ASA ene yA 

If we now determine the points of intersection of A; Az with this 
c,, we find three points which have already been found in § + and § 6. 


1) The associated points of cs define together only a net out of S;. See among 
others STURM, l.c. S. 309. 


, 


Physics. — “Photographic Absorption- and Eatinction- Measurements. 
Contributions to the study of liquid crystals. V. Evtinction- 
\ 


measurements”. ) By Miss Rassa Riwrin. (Communicated by 
Prof. W. H. Junius). 


(Communicated at the meeting of May 29, 1920). 


In this paper a photographie method will be explained for measuring 
absorption-spectra, and a preliminary application thereof to the 
examination of the extinetion of fluid erystals. The purpose of this 
research is: to look more closely into the way in which the extinc- 
tion depends quantitatively upon the wavelength and especially to 
trace in what degree the difference, which Dr. W. J. H. Morr and 
Prof. Dr. L. S. ORNsteiN found between the phases ex-solid and 
ex-fluid ®) in the ultra-red, exists too for visible light. 


1. The extinction (absorption or dispersion) of a substance can be 
measured by the following method. A pencil of parallel rays pro- 
ceeding from a constant source of light runs through the object. 
After passing through the substance a spectrograph disperses the 
light into a spectrum and this spectrum is photographed. After this 
we remove the substance and substitute it successively by a few 
screens which reduce the incident light to a known degree; the spectra 
obtained in this way are photographed each time. It would be 
obvious to try and find for each colour the screen which causes on 
the photographic plate the same blackening as the preparation. The 
faculty of transmission of the screen being known, that of the pre- 
paration for the considered wavelength is equal to it. Practically, 
however, this method — the looking for places of equal blackening — 
is inconvenient and therefore an interpolation method is substituted 
for it. For every definite wavelength namely the blackening is 
found out of the different screen-spectra, which are marked as a 
function of the intensity of light. By means of the blackening-curve, 
in this way experimentally constructed, the blackening of the substance 
for every wavelength immediately indicates the desired faculty of 


') Cf. YNevre BJÖRNSTHAL, Untersuchungen über Anisotrope Flüssigkeiten. Ann. 
der Phys. Bd. 56 (1918), p. 161. 
*) Proceedings Vol. XX NO. 2 p. 210. 


808 


transmission for the mentioned wavelength. We define the latter by 
superposing each spectrum by a He-spectrum. The exposition-time 
must be the same for all the spectra. The method used has the 
advantage that the absorption for all colours is measured at the 
same time, and that it is produced in all spectral areas under identie 
circumstances. 


2. We shall now further expose the details of our method. In 
the first place we want to illustrate the use of the screens and to 
indicate the method for measuring their faculty of transmission for 
different colours. From the blackening, measured on the photographie 
plate, the intensity of the incident light is generally calculated 
according to the approximation-formula of ScHWARZSCHILD 


z = blackening of the photographic plate 
z=log.].t? ¢ |] =intensity of the incident light 
t = exposition-time 


wherein p is a constant varying from plate to plate. In order to 
avoid the use of such an approximation, we worked out a method, 
which renders it possible, without using this law, to find the relation 
between the intensity of the incident light and the blackening which 
it produces on the photographic plate. 

This relation can be found for each plate separately in an ex- 
perimental way by constructing a blackening-scale on each plate. This 
scale is obtained by means of a series of spectra, which are reduced 
in a known degree; in order to reduce these spectra several screens 
are put in the way of the rays. The screens are subjected to the. 
following conditions : 

1st. they have to absorb the light for all the waves to the same 
degree, that means: not to show any selective absorption; or — in 
case they have got any — the absorption for each colour must be 
easily determinable; | 

2rd, the structure of the screens has to be so subtle that its image 
on the slit of the spectrograph does not disturb the regularity of 
the photographed spectrum *); 

3'4. finally it must be possible to get the screens in any desired 
degree of transmission. 

A uniformly blackened photographic plate fulfils all these con- 
ditions. A first experiment showed that it does not possess any 

1) Reducing the light-intensity by nicols turned out to be too inaccurate. A 
tissue disturbs the regularity of the spectrum. 


809 


absorption of importance in the visible sphere.*) This preliminary 
result gave rise to an extensive research of Mr. A. Drumens, which 
will be published in these proceedings. The plate proved to show a 
selective absorption, which may be greatly reduced under suitably 
chosen circumstances. The screens were therefore measured again 
by means of the method elaborated by Mr. Droumens, and at the 
discussion of our experiments the decrease in every region was _ 
observed. We made use of about ten photographic screens, whose 
faculty of transmission in, percentages were chosen according to a 
mathematic progression. In this way the most accurate results can 
be obtained; as the blackening is approximately proportional to the 
logarithm of the intensity, we obtain with this series of screens a 
regularly increasing table of blackenings. 


3. The blackening {of the photographed spectra was measured 
with the photometer of Dr. W. J. H. Motu’). We used the small 
and simple apparatus of the Institute for Theoretical Physics, which 
is suitable to determine the blackening for extensive spectral regions. 
The apparatus differs in some respects from the microphotometer 
described in these Proceedings by Dr. W. J. H. Morr; viz.: 

1st. The slit S, is left out (see l.c. p. 571, fig. 5) while the 
microscopic objective Q, produces an image of the incandescent 
spiral on the plate P; 

2d, The velocities of the photographie plate P and of the 
registration-cylinder A were regulated in such a way that a removal 
of the photographic plate over 10 cm. corresponded to a removal 
of the sensitive paper on the cylinder over half its length i.e. 
about 20 cm. 

Before and after each spectrum a piece of the clear unblackened 
plate passed through the way of the rays, and the deviation of the 
galvanometer reached its maximum. 

The dark Heliumlines, which are marked as notches in the un 


1) This first experiment showed the following result: 


Colour of the incident light. Faculty of transmission of the screen. 
Red 27.4 4 
Yellow 27.6 0/, 

Green 27.0 0/, 
Blue 25.6 "/o 
Violet 25.0 0/, 
Total visible spectrum 27.20/,. 


2) Dr. W. J. H. Morr, Een nieuwe registreerende microfotometer. Versl. Kon. 
A. v. W. XXVIII (1919), p. 566. 


810 


broken registrationlines serve to identify the wavelength in several 
points of the spectrum. 


4. The fitness of the above mentioned method: to measure propor- 
tions of lightintensities by means of the photographic plate, will 
depend in the first place on the uniformity of the plate itself and 
on the faults in its structure. The first condition of its fitness is the 
possibility to reproduce a blackening, obtained by a definite intensity 
and time, by lighting another spot of the plate under quite equal 
circumstances. Each sort of plate therefore, before its use, has to be 
submitted to the following test: a series of equal spectra, taken 
with constant intensity of light, with the same time of exposure, is 
constructed one beneath the other on one photographic plate. The 
spectra then are photometered perpendicularly to their longitude in 
several different places. For each spectrum separately the blackening 
may not vary by passing in this direction, which is stated by the 
deviation of the photometer remaining constant. Further the elevation 
of these constant pieces for the different spectra must be the same. 
If the plate is all right, the registration with the photometer must 
give an image where the blackened resp. the clear pieces are lying 
on two lines parallel to the line of zero-points. In this way the best 
suitable photographie plate: the Panchromatic of WRATTEN and Wrain- 
WRIGHT, was chosen. (Panchromatic to be able to continue the measu- 
ring of absorption as far as possible in the red). But this plate too 
proved to be far from perfect. An accurate measuring gave the result 
that the blackening in the spectra on the border of the plate is always 
greater than in the spectra produced in the middle of the plate. 
A similar result can be obtained by measuring the blackening at the 
borders and in the centre of a photographic plate which is lighted 
uniformly over its whole surface. This systematic fault *) was eli- 
minated as well as possible by repeating each spectrum at least twice 
on each plate at different distances from the centre *). 

In the second place the regularity of the photographed spectrum 
depends highly on the kind of developer. The conditions to put on 
the developer is that it produces an equal blackening without spots 


1) The Kodac factory was not able to give a good explanation of this pheno- 
menon; they think of a drying out of the borders. 

4) To obtain in our case as many spectra as possible on one single photographic 
plate, the lengths of the comparison-spectra on the side of the small wavelengths 
was reduced. The substance examined namely did not allow any light to pass 
beyond the wavelength A= 4700. One half of the photographic plate was there- 
fore covered, the other used, and vice-versa. So doing it is possible to take 
on one plate of 9 & 12 c.m. two rows of 15 spectra each. 


811 


or black stripes and without veil, while the contrast between the 
different blackenings appear as strong as possible. Glycin proves to 
come up to the requirements, if the proper conditions are chosen 
viz.: of the concentration of the developer, of the duration and the 
temperature of development. In fulfilling all these conditions a fine 
equal spectrum can be obtained with glycine, which — with respect 
to abundance of contrasts — is even preferable to the one produced 
by hydroquinone. 


5. The method nsed will be illustrated further with the measuring 
of the extinction of para-azoxyanisol. This substance was chosen in 
connection with the above mentioned research of Dr. W.J. H. Moun 
and Prof. Dr. L. S. Ornstein. For the phases: isotropic-liquid, 
ex-solid and ex-liquid the spectrum of absorption is determined. As 
these phases cannot exist at the temperature of the room the substance 
had to be heated and to be kept ata constant temperature. For this purpose 
we made use of a small electrical oven, consisting of a hollow 
brass cylinder, wrapped up with manganine-wire, through which a 
current was sent. By regulating this current each desired temperature 
may be obtained in the oven. A woollen mantle protected the wind- 
ings from changes in the temperature of the surroundings. In the 
middle of the cylinder the wrapping is interrupted over a length of 
1e.m., and there, diametrically opposite to each other, two perpen- 
dicular openings are bored, where a strip of copper K is fitted, 
carrying the glass cuvet with the substance. The small cuvet inclosing 
the preparation is constructed according to the principle of the 
numbering-chambers of Zriss: along the borders of a flat glass plate 
A, long narrow little beams of glass are stuck (height = 1,53 m.m) 
by means of water-glass mixed with asbestos. Great care is taken to 
make this glass-enclosure equally high throughout. For cover-glass 
we used a glass plate B of the same dimensions as A, carrying at 
the centre of the lower-side a small round piece of glass C (height 
= 0.90 m.m.). By pressing the borders of B close to the little beams 
_ on A, the distance between A and C, at the point where the sub- 
stance is to be examined, amounts to 0.63 m.m. 

On account of the high temperature necessary to melt the para- 
azoxyanisol it was quite difficult to find a glue which remains 
absolutely transparent under these conditions. The water-glass too, 
which was originally used to stick B to C, got opaque after some 
time. A solution of this difficulty was found by making a hole in 
the centre of the cover-glass B, so that C had to be fastened only 
at its borders. Between the two glass plates A and B in the middle 


812 


a little para-azoxyanisol is put and the plates are pressed together 
and to the strip of copper K by two steel springs. The strip of 
copper is heated on a little gas-flame, till the para-azoxyanisol is 
melted. By capillary forces the isotropic liquid is drawn to the 
narrowest part in the centre, where it absolutely fills the space 
between A and C, and even by placing K in a perpendicular position 
hardly moves down at all. Air-bubbles, if they are present, are moved 
to the border by tapping carefully. After that, K is pushed into 
the oven, which before is brought to the temperature desired. The 
phases ex-liquid and ex-solid are obtained by regulating the heating- 
current around the oven, without moving the cuvet from its place. 
With the preparation obtained in this way the above mentioned 
measurements are taken. 

The source of light was a small Nitra-lamp, for which a battery 
of accumulators provided the constant current; the perpendicular 
incandescent wire of this lamp is placed at the distance of the focus 
before a lens which provides a parallel beam of rays filling the 
Opening in the wall of the oven and penetrating the substance. At 
some distance behind the oven, in the centre of the parallel beam 
of rays the narrow slit of the spectrograph is placed, which may 
be closed by a little valve. The spectrum is photographed; the plate 
is put in a chassis which can be moved up and down, and renders: 
it possible to take several spectra on the same photographic plate. 


6. Each of the 30 spectra on the photographic plate is photometered 
in the length-direction; and out of the registered curves the blackening 
is calculated for the various colours. For this purpose the deviation 
of the galvanometer U is measured in definite points e.g. on the 
right side of each zero-point, while the situation of these points is 
fixed with respect to the He-line 2 = 4718. 

Suppose the maximum deviation of the galvanometer obtained 
through ‘the unlighted part of the plate to be U,, then the blackening 
is defined by the formula 

2 == log: Ue 
D 

For each spectrum the blackening in about 15 points is calculated 
and marked as function of the wavelength. By comparison of the 
curves for two or more spectra obtained in this way, which repre- 
sent the same state in various spots of the plate, their mutual 
concurrence shows the degree of reliability of the method used. 
The greatest deviations from the average values all appear to be 


813 


below 3°/, of the total blackening. In fig. 1, to begin at the top, the 
curves are represented corresponding to the absorption spectra 
respectively of the phases: isotropic-liquid, ex-solid and ex-liquid; 
four different photographs of the same spectrum of absorption on 
one plate provided the material for every one of these curves and 
are marked by four different signs. 


120. - ° ed 


“oO 


4713 


o o o fo) fe) o o 
ro) Pon o > o oO A 
+ = roy ~ oO t a 
© © ay wo o o o 


4980 
4790 


— blackening. 
5210 
5090 


— wavelength. Fig. 1. 


The difference in optical conduct between ex-solid and ex-liquid, 
found already for ultra-red rays, proves also to exist for the visible 
spectrum. In the same way the blackenings for the screens are 
explained in drawing. Out of the curves obtained in this way, for 
each definite wavelength the blackening is measured for the successive 
screens; and by means of the known faculty of transmission of the 
screens, marked as function of the light-intensity (fig. 2). 

For 15 different wavelengths the blackenings thus calculated are 
explained in drawing. The faculty of transmission of the screens being 
marked in percentages on logarithmic millimeter-paper, then the 
blackening drawn as function of log. I shows the well-known form of 
the blackening-curve witli the big rectilinear part in the middle. This 
straight part corresponds with blackenings for which the plate is not 
over- nor under-exposed, and the best proportion between time of 


814 


exposure and intensity of development is that, where the straight 
part of the blackening-curve is inclined to the absciss-axis in an angle 


6 
8 


5 


000, 10 


— blackenin 
oO 
5 


— faculty of transmission in °/o. Fig 2. 

of 45°. According to fig. 2 this inclination is too small in our blacken- 
ing-curve; so we had to expose the plate a little shorter and to 
develop it for a longer time. 


100% 


4790 Wbp 
4713 


oo 
a 
oO 
i 


6900 

6400 

6190 

5770 
5600 
5460 
5330 
5090 
4980 


—> faculty of transmission. 
$610 


| 5980 


— wavelength Fig. 3. 


815 


From the screen-spectra about 10 points are deduced for each 
blackening-curve; as these points have to lie on a tight curve, the 
faults in their situation may be partly neutralised by graphic inter- 
polation, which increases the reliability of the method. In order to 
determine the extinction for a fixed wavelength, the blackening for 
isotropic-liquid, ex-solid and ex-liquid is gathered in fig. 1 and these 
values transmitted on the blackening-eurve of the corresponding 
wavelength. The absciss of the diagram shows immediately the faculty 
of transmission in °/, for the corresponding phases: By means of 
the values thus obtained for the faculty of transmission the absorp- 
tion-curve is constructed for each of the three phases mentioned. In 
fig. 3 the absorption-curves are designed; to begin at the top re- 
spectively for the phases isotropic-liquid, ex-solid and ex-liquid. In 
both the marked series of points the experimental material is laid 
down of two separate preparations each photographed on a separate 
plate; the height of the substance in both cases was the same. 

Suppose now (what surely is not in accordance with the strong 
extinction found) that the relation between incident and transmitted 
light for this substance is given by the known formula of absorption : 


1, = intensity of the incident light 
—hd | / = intensity of the transmitted light 

h =coefficient of extinction 

d = height of the preparation 


ea le 


then we can calculate the quantity “Ad” for the various wave- 
lengths by means of fig. 3. According to the Theory of Dispersion, 
given by Dr. SPIJKERBOER in his dissertation, where it is proved 
that absorption- and extinction-coefficient are mutually additional, 
the obtained quantity “h”’ for each phase = the sum of dispersion- 
and absorption-coefficient. Supposing now that by approximation the 
real absorption-coefficient is the same for the three phases, we find 
in the difference: 

h isotropic — h ex-liquid = A, 
and h isotropic — h ex-solid = h,, 
the extinction-coefficient in its relationship to the wavelength for 
each of the two liquid-crystalline phases. 

In order to find out whether the obtained extinction coefficient is 
proportionate to a power of A, we constructed the curve log h as a 
function of log2. This curve proved not to be straight over its 
whole length, but by approximation could be seen as existing of 
two recti-linear pieces, which showed a different inclination for each 
liquid-erystalline phase 


816 


I feel it ineumbent upon me to tender my sincere thanks to 
Prof. Dr. L. S. Ornstein, under whose stimulating guidance | was 
able to make the above research; and to Dr. W.J. H. Morr and Dr. 
H. ©. Burger, whose continual interest and good advise have always 
been of great support to me. 


CONCLUSION. 


1. A method is described to measure the extinction in the photo- 
graphic way. This method is applied to liquid-crystalline phases. 

2. The two liquid-erystalline phases ex-solid and ex-liquid possess 
different extinction also in the visible spectrum. 


Utrecht, May 1920. Physical Laboratory, Institute for 
Theoretical Physics. 


Mathematics. — “Die Integralgleichung der elliptischen Thetanull- 
Junktion. Zweite Note: Allgemeine Lösung”. By Prof. F. Burn- 
STEIN at Göttingen. (Communicated by Prof. L. E. J. Brouwer). 


(Communicated at the meeting of November 27, 1920). 


In den ersten Note über diesen Gegenstand, die in den Berichten 
der Berliner Akademie ') erschienen ist, wurde gezeigt, dass die 
Thetanullfunktion *) 


B , en — ntt 
O,(0/int)=9, (irt) = Ze 


n= #0 


der Integralgleichung von VorrerraAschem Typus 
ET Tg ON ee 
genügt, wobei die „Faltung”’ &x1j definiert ist durch 


S(t) % 1 (t) =| § (rt) (t—r) dr ae (t—r) n (vt) dr. 
0 0 


Die im vorliegenden Fall uneigentlichen Integrale sind durch 


ae 


=o 


tim f bei reellem e >0O zu definieren, und der Integrationsweg muss 
€ 


im Existenzstreifen des Integranden 0< Rr < Rt verlaufen. 
Durch die ‘Substitution e—™—hA geht die Integralgleichung (1) 
über in folgende: 


1 1 1 
h\ dk dk $ dk 
ror) toffe frof-w=0. . @ 
h h h 


In Bezug auf diese wurde folgender Satz bewiesen : 
Turorem 1. Die einzige im Inneren des Hinheitskreises reguliire 


Lösung von (2) ist die Funktion f(h) = 1 + 2 S pet. 
1 


Hieraus ergibt sich fiir die Gleichung (1) das 
Truorem 1a. Die einzige Lösung von (1), die in der Halbebene 


1) Sitzungsberichte der preussischen Akademie der Wissenschaften XL, 21. Okt. 
1920, S. 735—747. 

2) Wir folgen der Bezeichnungsweise von WereRrsTRASS-H. A. ScHwarz, For- 
meln und Lehrsätze zum Gebrauche der elliptischen Functionen, 2. Ausgabe, 
Berlin 1893. 


818 
Rt >0 regulär, in jeder Halbebene Rt2 6, >0 beschriinkt ist und 


die Periode — 1 besitzt, ist die Thetanullfunktion J, (int). 
Jt 


Bevor wir ein allgemeineres Theorem über die Gleichung (1) formu- 
lieren, schicken wir folgende Verallgemeinerung der bekannten 
Larraceschen Transformation für den Fall uneigentlicher Integrabilität 
beim Nullpunkt voraus. 

Es sei ¢ (u) eine für u > 0 definierte reelle oder komplexe Funktion, 
die in jedem endlichen Intervall 0 <a <u<g eigentlich integrabel 
im Rremannschen Sinne ist. Ferner existiere für 0 < u, 


tn {0 (3) a (¢ >)... EN 
und 
Lim fe (a) a fiir, Rao . 
sodass also ’ 
f(s) = =o “@p (u) sed al pf ep (u) du 


fir o > 0, existiert a absolut konvergiert. Dann nennen wir /(s) 
die Larracesche Z'ransformierte von p(u) und bezeichnen sie kurz 
mit L(¢); p(u) selbst heisse die determinierende Funktion '). f(s) ist 
für o > 6, regulär und beliebig oft unter dem Integralzeichen 
differenzierbar, insbesondere ist 


— f'(s) re ug (u) du, 
0 


also 
Lu) Dn ne 
wobei rechts Differentiation nach s gemeint ist. 

Sind p (u) und w (u) zwei Funktionen, deren Larpracrsche Trans- 
formierte im obigen Sinne existieren, so ist, wenn in dem Faltungs- 
integral der Integrationsweg reell ist: 

L(y). Ly =L(p*y)?). . . 2... UD 


1) Vgl. N. H. Ase, Sur les fonctions génératrices et leurs déterminantes. 
(Euvres completes, t. Il, pp. 67—81. 

*) Wegen der oben gemachten Voraussetzung (d), dass g(w) und b(w) in den 
Nullpunkt hineinintegriert werden können, existiert die Faltungsfunktion 9 sk , da an 
jedem Ende des Integrationsintervalls eine der beiden Funktionen beschrankt bleibt. 


819 


Beweis : meee der absoluten Konvergenz der Integrale ist 


L(g). L (w) = fo “ep (u) du. fe Vwo) dv = [ pares ” »(u) 0) du dv, 


wo das ae ee den Bereich u 20, v 20 zu erstrecken 
ist. Wir setzen 

VE 1h 

D= t 


und haben nun das Integral 


4, ep (w—t) w(t) dw dt 


über den Winkelraum O<t¢<w zu erstrecken. Man kann es 
folgendermassen durch ein iteriertes Integral darstellen : 


ee) : w 
| ee dw fr (wt) W (2) dt, 
"0 0 


da das Integral nach w existiert und absolut konvergiert. Damit ist 


die Behauptung bewiesen. 
Offenbar gilt: 


ris ECE) 


Wir formulieren nun folgenden Satz: 

Trrorem 2. Sümtliche Lösungen der mit reellem Integrationsweg 
gebildeten Integralgleichung (1), die eine Larracrsche Transformierte 
besitzen *), sind in der Form 


n? - 
Fa BE 


U (lt) = et ae 
nt 


n=l 
enthalten, wo c jeden komplexen Wert bedeuten kann, und sind somt 
für kt>O regulire Funktionen von t. 
5 Jr ‘ ; 
Peel fir c—0 und e= 3 erhält man 9 ,(O/ia t) und «7 ,(O/2 x t). 
U(e/t) ist eine ganze transcendente Funktion von ec mit.der Periode x. 
Der in der Variablen c gerade Bestandteil von U(eft) ist gleich 
Pe D, (tettert). 


Beweis: Bezeichnen wir die Larracrsche Transformierte der 
Lösungsfunktion mit y =y(s) und wenden auf (1) die Japiacusche 


1) D. h. die Bedingungen a) und 6) erfüllen. Damit wird nur über das Verhalten 
der unbekannten Lösung längs der Achse des Reellen eine Voraussetzung gemacht. 

53 
Proceedings Roval Acad. Amsterdam. Vol. XXIII. 


820 


Transformation zu, so erhalten wir unter Benutzung der Rechen- 
regeln (I) bis (III) die Differentialgleichung : 


Blk Ae: 
yv + 2y trim amie ere Ee 
Setzt man 
s=—v und y(t) =n(t, 
also 
dl n 
Tm 
so geht (3) über in 
GED ] 
Bear ier ar 
oder 
En tn nisl . . . | ae 
Durch die Substitution 
iy =S «, also ty == 2 
erhalten wir: 
liz. . .). Lo 
Die allgemeine Lösung von (5) lautet: 
t=arctg$ + ¢' 
oder 
5 = tg (t—c¢) — — etg (t — 0). 
Folglich hat die Differentialgleichung (3) die allgemeine Lösung 
ax ctg (V — s—c) 
RR 


wo c eine beliebige komplexe Konstante ist. 

Jeder Lösung y der Differentialgleichung (3), die so beschaffen ist, 
dass sie eine determinierende Funktion besitzt, entspricht eine und 
nur eine Lösung der Integralgleichung (1); denn die determinierende 
Funktion ist, wenn sie überhaupt existiert, eindeutig bestimmt bis 
auf eine Nullfunktion'). Aus der Integralgleichung (1) aber geht 


1) Dieser Satz ist von Lercu (Sur un point de la théorie des fonctions généra- 
trices d'Abel; Acta Math. 27, pp. 339 —351 [pp. 345—347]) für beim Nullpunkt 
eigentlich integrable o(u) bewiesen worden. Der Beweis gilt aber auch bei uneigent. 


licher Integrabilität, da auch in diesem Falle die durch (verallgemeinerte) partielle 


oo 
» 


Integration gewonnene Umformung f (s) = eso feo" Fay wo seinen Wert 


i") 


821 


hervor, dass zwei Lösungen, die sich durch eine Nullfunktion unter- 
scheiden, identisch sind. 

Wir können nun sogleich zeigen, dass jedem y eine determinierende 
Funktion zugeordnet ist, indem wir dieselbe angeben. Es ist 


i ei(V—s—e) Heid 1 1 4g 28 (M 8 $8) 
(si so ee ae pe eae). 


y= — 


also fiir 
| 5 (Vs + ¢t) 


Sods tapas Be fai ee 


y= —(1 ete) Se —2n(V sci) 
Vs n=0 
1 =<, > Amste) rs S ie 
0 0 
wa, 1 0 BE a wae 
14236 ee ee 
F7 zl Ws 1 Vs 
—2nVs 
Zu der als Summenglied vorkommenden Funktion Pe können 


wir die determinierende Funktion angeben; es ist nämlich 
ae L ae fi >0 
EE ————e 4 fur ne 
Vs Vat ER 


wo für positive s und ¢ die Wurzeln positiv zu nehmen sind. Der 
Beweis ergibt sich aus der Formel *) 


1 26 

i wa — ua? 
—e u = fe cos 2. na da. 
Van JT 


0 
Mit ihr erhalten wir nämlich: 


n2 oo oO 
1 ab 2 — US _— ua? 
—e t ) = = fe du fe cos 2 na da. 
Vat JT 
0 0 


Fir Rs >>0 ist dieses Integral absolut konvergent, die Integrations- 
folge also vertauschbar. 


u 
bedeutet, für den das LAPLACE-integral existiert, und (4) = fee p(v)dv ist 


0 
legitim und (uw) — was bei dem LercHschen Beweise den Ausschlag gibt — 
stetig ist. 
1) Vgl. Rmemann-Weper, Die partiellen Differentialgleichungeu der mathemati- 
schen Physik, I, 4. Aufl. § 61, Formel (7). 


822 


D A 
L =— \ eos 3 na da fe aay du 


0 


8 


=) 
° 


8 


2 cos 2 na 
ar sJ-a? 
0 


da. 


1 ; 
Nach einer bekannten Formel') ist dies gleich we KS für 
s 


nr): 
In Bezug auf die oben für y erhaltene Summe behaupten wir 
nun: Es ist 


en) Ante oo 1 n 
Se get —2nei Sc 
=e CUED eect we ee aise p ). 
n==1 Vs n==l Vat 
In der Tat ist 
oo 1 n2 
e= — net pe 
1 V au 
0 
a oo 
={+f. 
0 a 


wo a > 0 ist. Ersetzen wir in den beiden uneigentlichen Integralen 
den Integranden durch seinen adsoluten Betrag und vertauschen das 
Integral mit der Summe, so ist das Ergebnis eine für V Rs > Ie 
konvergente Reihe; denn 


oo B { n? co =" 1 n? 
Elen PEE dus zj ee 
1 Vau 1 V mu 
a 0 
—2n V ks 
2nIe € 
1 V Rs 

n? 

: : : : = — 2 net ET 

Ferner ist die im Integranden stehende Reihe = e Vas 7 

1 TU 


_in jedem Teilintervall O0< e<u<a, baw. a Su<w< oo gleichmiissig 
konvergent. Die Reihenfolge von Summation und Integration ist also 


. 2 DE . : . 
wenigstens für W Rs > Ic vertauschbar’), womit sich die Behaup- 


1) Vgl. RrEMANN WEBER, |, c. § 19, Formel (3). 
*) Vgl. Bromwicu, An introduction to the theory of infinite series. London, 
1908, p. 453. Der dort gegebene Satz lautet: „Wenn Xf(x) in jedem festen 


823 


tung auch für den Konvergenzbereich R\s > Jc ergibt. Folglich ist 


1 — Bee Ea 
y= L( Et ay ee r). 
Vat 1 Vat 


Alle Lösungen der Integralgleichung (1), die eine LarLacrsche 
Transformierte besitzen, sind also in der Gestalt enthalten: 
n? 


— 2nci — — 
u 


1 ao 
7 


Pure 0, bzw. c= = erhält man die Funktionen &, (0/i x 0), 


1 ' 
bzw. , (O/izt) in der auf = transformierten Gestalt *). 


Der in c gerade Bestandteil von U (c/t) ist 


© n2 


1 Ik 
vj |! FBT Ecos Bre 
IU 


Nach der Transformationsformel der Thetafunktion *) 


9, (v/t) = [ie ni 9, (/- =) 
T Tt T 


We be ee Do, (Get/izt), 
womit Theorem 2 vollständig bewiesen ist. 


ist 


Intervall a <x <b, wo b beliebig ist, gleichmässig konvergiert und b(x) fiir alle 
endlichen Werte von z stetig ist, so ist 


fo (z) = fn («#) dz = = {woh (x) dx, 
0 0 


vorausgesetzt, dass entweder das Integral f | ¥ (x) | & | fn(x) | dx oder die Reihe 


a 
Dy) | \¥(a)| | fn (a) | dw konvergiert’’. Das Entsprechende gilt bei uneigentlichem 
a 


Integral mit endlichem Integrationsintervall. 
1) Vgl. Weterstrass-‘Scuwarkz, |. c. p. 46. 


: Pa 
ag : ä : 
2 - 7 ol ‘ 
‚ ALM ary Pgh * ek 
¢ as . 
: EN = i | 
a w ; =r - (es >. 
Ted ‚mr 7 
f ’ q 
5 i bad Loree bi Gin Eze! 
ps 7 Ke 
- - 
7 
ee j = 
. fi f 
5 
Pena ks 4 j CALI 4 GON 
> 
° (RAET Fiabe 
ee 
Md nj 
5 | 
car. ‘ 
' 
‘ : \ 
‘© 
= i) 
4 « 
j k ‘ 
» 
i 
é 
5 
~ 
| 
J 
| 


ANS 
i -- ie 
É É ‘ bf 
had “i ‘ P 8 
haar ad 


KONINKLIJKE AKADEMIE 
VAN WETENSCHAPPEN 


-- TE AMSTERDAM -:- 


S,ObU4@2SAS 


a 
~ 


PROCEEDINGS. OF THE 
SECTION OF SCIENCES 


VOLUME XXIII 
2e TSE PARE a 
SEAN | aay 


JOHANNES MULLER :—: AMSTERDAM 
: : FEBRUARY 1921 : 


ey ps 


ih 
va ie 
a 


(Translated from: Verslagen van de Ga Vergaderingen 
Natuurkundige Afdeeling DI. XXVII, XXVIII and X 


RUKKERIJ HOLLAND 
AMSTERDAM — 


, 


ie 


Os 


ea 


wre 
BE Er: 


Kin: 


100140083
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