FOR THE PEOPLE| FOR EDVCATION | FOR SCIENCE | LIBRARY OF | THE AMERICAN MUSEUM | OF NATURAL HISTORY te Cound at 2 ® JAR SEK KONINKLIJKE AKADEMIE VAN WETENSCHAPPEN -- TE AMSTERDAM -:- PROCEEDINGS OF THE SECTION OF SCIENCES VOLUME XXVI — (NGE In) = PUBLISHED BY “KONINKLIJKE AKADEMIE VAN WETENSCHAPPEN”, AMSTERDAM 1923 (Translated from: ,,Verslag van de Gewone Vergaderingen der Wis- en Natuurkundige Afdeeling” Vols. XXXI and XXXII). Lb -r043q0. ln U ONTENTS. Proceedings N°s. 1 and 2 Nes. 3 and 4 Nes. 5 and 6 NCES U enol fe NGS, Emma iO) - KONINKLIJKE AKADEMIE VAN WETENSCHAPPEN TE AMSTERDAM. Pige CeEOUNGS VOLUME XXVI Nes, 1 and 2. President: Prof. F. A. F. C. WENT, Secretary: Prof. L. BOLK. (Transiated from: “Verslag van de gewone vergaderingen der Wis- en Natuurkundige Afdeeling," Vols. XXXI and XXXII). CONTENTS, B. L. VAN DER WAERDEN: “Ueber das Komitantensystem zweier und dreier ternärer quadratischer Formen”. (Communicated by Prof. L. E. J. BROUWER), p. 2. EJNAR HERTZSPRUNG: “On the magnitude equation of OSTHOFF’s estimates of star-coulours”, p. 12. CHR VAN GELDEREN: „On the development of the shoulder-girdle and episternum in Reptiles”. (Communicated by Prof. L. BOLK), p. 15. P. H. HERMANS: “Provisional Communication on Boric Acid Compounds of some Organic Substances containing more than one Hydroxyl-Group. Boron as a Pentavalent Element”. (Communicated by Prof. J. BOESEKEN), p. 32. H. R. KRUYT and W. A. N. EGGINK: “The Electro-viscous Effect in Rubbersol”, p. 43. J. P. KUENEN +, T. VERSCHOYLE and A. TH. VAN URK: “Isotherms of di-atomic substances and their binary mixtures. XX. The critical curve of oxygen-nitrogen mixtures, the critical phenomena and some isotherms of two mixtures with 50% and 75%/ by volume of oxygen in the neighbourhood of the critical point”. (Communicated by Prof. H. KAMERLINGH ONNES), p. 49. Ky0zO KUDO: “Contributions to the knowledge of the brain of bony fishes’. (Communicated by Dr. C. U. ARIENS KAPPERS), p. 65. H. J. BACKER and J.H. DE BOER: “n.z-Sulfobutyric acid and its optically active components”. (Communicated by Prof. F. M. JAEGER), p. 79. H. J. BACKER: “The second dissociation constant of sulphoacetic and z-sulphopropionic acids” (Communicated by Prof. F. M. JAEGER), p. 83. H. BOSCHMA: “Experimental Budding in Fungia fungites”. (Communicated by Prof. C. PH. SLUITER) p. 88. (With one plate). J. BOESEKEN: “The Valency of Boron”, p. 97. W. H. KEESOM and J. DE SMEDT: “On the diffraction of Röntgen-rays in liquids” II. (Communicated by Prof. H. KAMERLINGH ONNES), p. 112. P. C. FLU: “On the Bacteriophage and the Self-purification of Water”, p. 116. Proceedings Royal Acad. Amsterdam. Vol. XX VI. Mathematics. — “Ueber das Komitantensystem zweier und dreier ternirer quadratischer Formen”. By B. L. van per Warden. (Communicated by Prof. L. E. J. BROUWER). (Communicated at the meeting of February 24, 1923). Ein volles Komitantensystem für zwei ternäre quadratische Formen (“Kegelschnitte’) ist aufgestellt worden von GORDAN, und findet sich bei Cregscen *). Ein solehes für 3 Kegelschnitte ist unabhängig voneinander von CIAMBERLINL®), von BakKER*) und von Fiscurr und MuMMELTER *) aufgestellt worden. Das CraMBERIANI’sche System besteht, wenn man die “identische’ Komitante w, hinzurechnet, aus 128 Formen, das Baker’sche aus 148, das FiscHeR— MumarurteR’sche aus 185 Formen. In der Tat sind 20 von den Baker’schen Formen mittels der Crampertini’schen Formen reduzibel (siehe $2), während SEBLIG®)-gezeigt hat, wie sich die FrscurrR— Mumuerrrer’schen Formen auf die CraMBERLINIschen veduzieren. Schliesshch rührt ein voll- ständiges Typensystem für eine unbeschränkte Anzahl Kegelschnitte (oder, was auf dasselbe hinauskommt, für 5 Kegelschnitte) her von Turnpuit.*), der daraus ein vollständiges Formensystem für 4 Kegel- schnitte ableitet, bestehend aus 784 Komitanten. Mein Zweck ist, zu zeigen: in $ 1, dass die 21 Formen von Gorpan irreduzibel sind, in § 2, dass von den 128 CramBeruini’schen Formen 6 reduzibel sind, in § 3, dass die übrigen 122 irreduzibel sind. Die Methode der Irreduzibilitätsbeweise beruht auf dem folgenden evidenten Prinzip: Soll eine Reduktionsformel fiir eine Komitante gelten, so muss sie auch dann noch gelten, wenn man die Ur- formen spezialisiert, z.B. sie miteinander identifiziert, oder auch statt der symbolischen Quadrate aj? wirkliche Quadrate v,? einführt. Ich werde dementsprechend in den $$ 1 und 3 alle apriori mög- lichen homogenen Reduktionsformeln für die betreffenden Komi- 1) CLEBSCH-LINDEMANN, Vorlesungen I, Abt. III § VIII, p. 291 (Leipzig 1876) ?) Giornale di Battaglini 24 (1886) p 141. ; 5) Trans. Camb. Phil. Soc., Vol. 15, Part I (1894) p. 62. *) Monatshefte fiir Mathematik und Physik 8 (1897), p. 97. 5) 7 = 5 4 a eo (LOLS) Wp R2I5 8) Proc. London Math. Soc. (2) 9 (1910) p. 81. 3 tanten (mit unbestimmten Koéffizienten) aufstellen und sodann, durch verschiedene Spezialisierungen und nachfolgende geometrische Be- trachtungen, deren Unmöglichkeit zeigen. Die ersten Ansätze zu Irreduzibilitatsbeweisen finden sich bei TurNBULL') er zeigt auf Grund der Identifizierung, dass gewisse Komitanten fiir 4 Kegelschnitte irreduzibel sind, vorausgesetzt dass gewisse Komitanten für 3 Kegelschnitte es sind. TurNBuur fügt hinzu, er sehe noch nicht ein, wie man sonst noch Irreduzibilitätsbeweise geben könnte. Die Bezeichnungen schliessen sich an CrrBscu und CraMBERLINI an, obzwar später bessere Methoden eingefübrt worden sind. Die Urformen heissen ES oe Ta Ser oie ee (=O rome Die Kontravarianten der einzelnen Urformen werden bezeichnet als MGD A Pes RUS. W. Von Baker iibernehme ich noch die folgenden Abkürzungen : u = ay bedeutet u, — «a, y, — 2, Ya, U.S.W. (vw. zy) = (vw y) = (vw ay) SS Vz Wy —Vy Wy. 8 A=0O bedeutet: A ist reduzibel zu einfacheren Formen (d. h Formen deren Gesamtgrad in allen Koeffizienten und Variabeln niedriger ist). A= B bedeutet: A= B+ reduzibele Glieder (bei Baker =). = oder = bedeutet: identisch gleich fiir alle Werte der u, «, Uik Wijs Air: Ich werde die folgenden Reduktions-/dentitditen verwenden *): (a) deayva=hae Uy ee 0 (b) (abv) ay be = } va (ay2) = } ve (ave) dual: (c) (a8y) vz we = 3,7 . b, (bew) =i) (d) a, by ay be = a," , by be May) (ape) = — } (apy) (apa) dual: (e) 9.92 vawe —= 0’ . vawg— az’ (bov) (bgw)= 0 ) Proc. London Math. Soc. (2) 9 (1910), p. 120. 2) CresscH—Linpemann, |, III, § Vill. Am übersichtlichsten findet man die Identitäten, sowie die Ableitung des Formensystems zweier Kegelschnitte, bei Grace and Youne, Algebra of Invariants, § 228. 1% 4 (f) a, bg a, bs = apbgards + $ (apy) (ars) =a,bga,bs+ 4 (apg) (ars) ™ dual: (g) pagar3ss = qeperasa + 2 a,*.(apq)(ars) = qgaparasg WO ,9,¥Y, 2.0, W, p,q, 7,8 beliebige Symbole sind. Dazu kommen die fundamentalen Identitiéten des ternaren Gebietes. Bemerkung. Man kann von einer jeden Identität zu der dualistisch entsprechenden übergehen, indem man jedes a durch «, jedes a’ durch a’, usw, jedes x durch uw, und umgekehrt, ersetzt, und sodann, wo nötig, durch Hinzufügung von Faktoren 4 a,°, $ a’.”, usw, die erhaltene Formel homogen macht. Denn wenn man a durch « ersetzt, so müsste man eigentlich « ersetzen durch a, definiert durch @,? = (a 84)’; es iSlwaberM(GrB AE de § 1. Zrreduzibilität des Systems fiir zwei Kegelschnitte. Ich werde das Gorpansche System hinschreiben, dabei aber von je zwei Formen, die durch Vertauschung der beiden Kegelschnitte in einander übergehen, nur eine behalten. In Klammern füge ich hinzu die 4 Grade der Komitanten in a; a’; u,v. Kine daneben- stehende Zahl bezeichnet die Anzahl der analogen Formen. Dualistisch gegenüberstehende Formen sind mit den entsprechenden Griechischen und Lateinischen Buchstaben benannt, oder auch durch obere Quer- striche unterschieden. Ur (OT Ns (HD) \ ngs (MUD) il ja S08 (10.02) 2 Ciz= (aa u) a’, ay ua (31.21) 2 JO re (20.20) 2 N,, =(a al 2) uy We! (22.21) 1 i Sao Oy (CUED il D= (a al a) ag tty dy (32.12) 2 Anti (30.00) 2 D,, =(aa'u) avd, uxt (33.30) 1 VAN = Bias (21.00) 2 NHN dd (EON) eee Bin Soro 2 Dd, =(aa #) (22.02) Die apriori möglichen homogenen Reduktionsformeln sind: (Ue JA == (7). Ni, =0 (2) FL, = 8 (8) Cie 0 (3) A,,,=0 (9) -N, = (4) 45.5.0 (10) ie aera (@) Iti SZ Alias oe (11) ee) (Oi Oe — ACA arta Anas Ja (12) eA ae Jetzt gehe ich daran, die Unmöglichkeit jeder dieser Formeln zu beweisen : (7) (9) (8) (10) (11) (12) 5 Aus der Geometrie des Kegelschnittes weiss man, dass (1) und (3) nicht gelten. (1) und (3) sind aber Spezialisierungen von (2) en (4). Daher können auch diese nicht gelten. Bi» = 0 stellt, bei variabelem z, die Gleichung der Polare ° des Pols’ von wv dar (Pol® bedeutet: Pol beziiglich /,, Pol’ bedeutet: Pol beziiglich f,). B12 ist somit nicht identisch Null. Auch fällt diese Polare nicht für jedes mit « selbst zusammen, es sei denn, dass die beiden Polarsystemen identisch seien; By» enthält also nicht allgemein den Faktor wz: (5) gilt nicht. In (6) spezialisiere man a,°—v;. Jede Form, welche ein Symbol « enthält, verschwindet dann. Das ergibt ®,,=0, A,,,— 9, A, #0,f, 0, und daher u—0. Ebenso beweist man 20. Aus (6) wird ®,,—0O. Die dazu duale Formel (2) gilt aber nicht, daher kann auch (6) nicht gelten. Die beiden Polaren des Punktes 2 seien: vaa nt aan Sie sind im Allgemeinen weder unbestimmt, noch miteinander identisch. Daher ist NV = wwu)=/=0, oder (7) gilt nicht. Die dualistische Betrachtung gilt fiir (9). Die Polare’ des Pols® von w sei Doi Weiter sei uv =y. Da v nicht mit 2 zusammenfallt (siehe unter (5)), so ist y nicht unbestimmt. Nun ist Cie = a, a, =/=0, oder (8) gilt nicht. Die dualistische Betrachtung ergibt, dass in (10) 240 sein muss. In (10) setze man a’,? —7,". Jede Form, welche ein Symbol a enthalt, verschwindet dann, und es wird P‚2 — 0, N,, 4 0, A,,, #0, und daher 2—0, in Widerspruch mit dem Vorher- gehenden. D,, stellt das Produkt der linken Seiten der Gleichungen der drei Seiten des den beiden Kegelschnitten gemeinsamen Polardreiecks dar, und kann somit nichtidentisch verschwinden Der dualistische Beweis gilt für A,,. § 2. Reduktion der Formen Mz und T; von CrauBERLNT. Es sei M'e3 = (aa! x) ayag Ug, ; M'32—(ad' z)a,ayuz uy. CIAMBERLINI hat bewiesen ‘) ‘) Giornale di Battaglini, 24, p. 150, a. 6 M'o3 M'32 = . ° . . . . . . (1) Um M’o, zu reduzieren, multipliziere man die Identitat (a a! «) a = (el a" x) az + (aa a) a + (aa a’) ay mit auw U, Das erste Glied rechts is reduzibel nach (a), weil es den Faktor az enthält; das zweite Glied enthalt den wirklichen Faktor u”. Also: = r Mo 5 = CMO te 5 (&) Ebenso — r M'30 S(O Gunn 55 5 2 - 5 (3) Man multipliziere weiter die Identität | a Ag! ay ae Gade | (Cac? Eed!) uz Yen We, mit (aa) 6". 6",. Die rechte Seite spaitet sich in zwei wirkliche Faktoren (a'au)? und (aaa) 6", 6",,, ist also =0. Bei der Entwick- lung der Determinante auf der linken Seite kann man die Glieder die den wirklichen Faktor w, enthalten, vernachlassigen; ebenso nach (a) die Glieder mit a.. Es bleibt rs —(al'an)b yb" 4 a a! dy Uz +-(a"an)b", by a! yay uw +-(a"'a yb" .b" 4! dz! ad’, w= (4) Das erste Glied wird umgeformt mittels (d): — (a'au)b', b yay au, = 4 (a"a’ au) (ad! @) dy Ue = fay ug (a! a! a) dy ua — Fau Ug" (a! a! a) dye va Das zweite Glied von (4) gibt ebenso (aa u) b', bazar Ug = — } (aa. au) (aa a’) aruw he Ay! ua (al era) dy Uz + Hag Uz" (a" a d)) dg Uz oder, da das zuletzt angeschriebene Glied den Reduzenten a, enthalt, = — ba ug(a" aa’) ay uw + 0. Das dritte Glied von (4) wird reduziert mittels (/): (a" au) 626" ay ay Uy = (b"au)a'gb" 4 aya", u, HF (aa, au) (a"a' &) ay ug * = (blau) blaar. ag aly Ug + Har (aa! &) ag. Ue? — a — blaauw (aa x) au =0+0+4 0 Damit wird die Gleichung (4) zu: ~] 4 eet ! Lag Ug (a"'a'a) dy Uz, — bauer (a"a'a) ar us — 4 ay Ue (dae) ay u = 0 oder, da das erste und dritte Glied einander gleich sind, ; (Gel e)anaznugiu, + 4 (do e)aratugd ig == 0 2.2 … (5) Aus (2), (3), (5) folgt: Mia ate OPEN ds 2. (6) Endlich folgt aus (1) und (6): 13 s Ki : Vianen A= AN AP oeh (7) und somit: die drei CraMBERLINLschen Formen Mo3 = M'o3 + M's2 3; M3, = M'31 +M3 ; M,,= M's + M's sind reduzibel. a Der andere reduzibele Typus des Ciamperiini’schen Systems ist: T, = (a da’) (aar) (Bee) us. Nach (e) ist in einer Komitante jedes « mit jedem 8 vertauschbar, daher : Tr r vrl ! ” ’ " ' pir ae ' " 1 Im t LAA 1 " te (a'a" u) a'g a’, b'g bz bz b'y = (a a" u) ag ag. b'g bg bz 6", = 0 Auf der linken Seite wenden wir (d) an auf die Faktoren a's b'4 r (a B 5a! u)(e Beja! bbr 0 4 a'wug(e! B a) aa, bbr — a'g Un! (@ B x) ag, 6" b"; —0. Im zweiten Gliede dieses Ausdruckes ergibt abermalige Vertaus- schung eines « mit einem einen wirklichen Faktor a”. Folglich ist das zweite Glied zu vernachlässigen. Auf das erste Glied wenden wir wiederum (d) an, jetzt auf die Faktoren a", 6", und finden (a aa’) (a a x) ua (a) Bx) = 0 oder Ebenso == Bx ==) 945 TON $ 3. Lrreduzibilitat des Systems fiir drei Kegelschnitte. - Mit Weglassung der Formen die nur von zwei der drei Kegel- schnitte abhängen, und der reduzibelen Formen M und T, besteht das CiamBertini’sche volle System für drei Kegelschnitte aus den folgenden Formen : Li SS HJ (111.00) 1 Vi —(arande)n(asanu)ar (SL) 2) Sh Stn dle Ga Gs (211.02) 3 Es U Ag! Wel Uc!" (122.20) 8 As CTA (222.00) 1 V, =(ed a!) (a a" x) u, (222.11) 2%) Pog = A AA AE Wa!" (123.11) 6% H =(a'a'u)(a' av) (aa u) (111.30) 1 DSC Es Te Oe (nt 03) meel Qo SED (211.10) 3 E33 = (a' a" ua’, ue dn (211821) 6%) T, =(aa'a')(aa'u) (ba u) by (211.21) 3 2 SGC) Ge Gin Oe (811.01) 3 OM Natan) ana (122.01) 3 — Me =a', a", ax [aa'u)a, + (ad u)a"z| (311.12) 3 E23 = (a! a" x) ay" ar uw (122.12) 6 1 EN CHAN a en (222.30) 1 Uo3 =(a' a! u) ay a, us Uy" (213.30) 6 °) H =(de" x) (a! a z) (a ct! x) (222.03) 1 Yo3 = (a! a! &) award z Ar (123.03) 6 5 =(ae' a!) u, aaan (32210) 3 G, =(aa'u) ar aar ar ae (133.10) 3 *) G, =(a'a'r) aya", de d'r (233.01) 37) Die Methode der Irreduzibilitätsbeweise ist dieselbe wie in $ 1. Die Formen L, V, 2, X, G, U, Y sind irreduzibel, denn waren sie reduzibel, so waren auch 4, B,N,C,D,D,A (s. $ 1), die aus 1) Die Summe der drei V ist, wie man sogleich sieht, = L. uz. 2) Die Summe der drei V-ist reduzibel. 5) Bei Crampertini heissen diese 6 Formen P, Ps Ps IL, TM, M3. 4) Bei Cramperuint heissen diese 6 Formen E33, Es), io, Eos, Pa, Ens- 5) Bei CraMBERLIN: heissen diese 6 Formen U»3 U3; Uy U'o3 U's, U'1o- 6) Die Formen G und G finden sich nicht in der Ciamberlinischen Tafel (a. a. O. (p. 153). Das ist aber offenbar ein Schreib- oder Druckfehler, denn auf S 145 ist die Form G genannt unter den “Forme con un determinante fattore”; bei den reduzibelen Formen p. 148 wird G nicht genannt (d.h. sie wird zu den “forme fundamentale” gerechnet); in der Tafel der “forme fundamentale” S. 153 wird sie nicht genannt, wohl aber mitgezählt, und in den geometrischen Anwendungen S. 157 taucht sie wieder auf. Vgl. SeeLic, Monatshefte f. Math. u. Phys. 29, p. 265, Fussnote 21. 7) Bei Baker finden sich ausserdem noch die Formen (810), (911), (1010), die reduzibel sind nach CrAMBERLINI (p. 151g, p. 149¢, p. 151 9). 9 den erstgenannten durch Identifizierung von 2 der 3 Kegelschnitte entstehen, reduzibel. $ Für die beiden Formen E23 und £3. findet man durch Specia- lisierung : (Bagli — C23 = irreduzibel ; ls reduzibel ; | 3,2 ie = reduzibel ; [32|i—3—= C32 = irreduzibel ; Daraus folgt: Es kann weder Z3, noch £32, noch auch eine lineare Kombination der beiden, reduzibel sein, denn sonst wäre auch eine der Formen C reduzibel. Die dualistische Betrachtung gilt für Ess und Ess: Für die übrigen Formen werde ich alle apriori möglichen homo- genen Reduktionsformeln aufstellen. Dabei ist folgendes zu beachten. Wenn eine Komitante A,, symmetrisch ist bezüglich der Formen jf, und f,, so kann man in einer Reduktionsformel für diese Komitante rechts die Indizes 2 und 3 überall vertauschen, ohne dass die Formel ihre Geltung verliert. Bildet man dann die halbe Summe der beiden Ausdrücke, so tallen alle alternierenden Glieder heraus, die sym- metrischen bleiben stehen, und die anderen Glieder bilden Gruppen von je zwei ahnlichen mit gleichen Koeffizienten. Ist hingegen A,, alternierend bez. 2 und 3, so kehren sich die Verhältnisse gerade um: man bildet die halbe Differenz, die symmetrischen Glieder heben sich weg, die alternierenden bleiben. usw. Diese beiden Fälle werden mit s (symmetrisch) und a (alternierend) bezeichnet. In den jetzt folgenden Formeln sind diese beiden Operationen bereits aus- gefiihrt; beispielsweise sind in der ersten Formel die letzten beiden Glieder mit gleichen Koefficienten versehen. (1)s Sa = Af, L ie u (7. ee 4% ll A,,,) (yr NE Anes ce Ae AN AS, 3) (Send Ae CAS Aran Aran eae Aaa Arse) (4)s V, = AP ug (A, Assa Arre Agaa) Ue VA 00 Aras toAurtoLV, 1) (5) Paz ALA 3 Ue Hu As Anon Ur HP A,,, Anso Ur Ho A,,,V,+04,,,V, (OP (7) F =0 (S) O10) (9)s T, = 4(He3 + £30) + u O, ur (10)s—M, = 2 (A, Nia — A,,; Na) (ita F =1.(0, fF, - OFF, OCP) +e La (12a H MAS ALTA) + ul 1) Das Glied 7 L(Vs +V3), das noch möglich wäre, ist gleich 7 Lux — LV, und somit in anderen Gliedern der Gleichung aufzunemen. 10 (UIN A OE (ARONA NON) (4)a 6, =2 LS 4+ w(S, A,,, + 2, 4,,,) Frl ees ey (6), (7). (6) und (7) gelten nicht, denn H und J stellen JACOBIANA und CaryryaNa des Biindels 2, f, +4, f, +4, f, dar’). (1). In (1) setze man a,? =v,” (kurz: a=v). Es verschwinden dann alle Ausdriicke die ein Symbol « enthalten. Daher S,, = 0, Ay3=0,; A,,,=0. Weiter ist dann f,=/=0, L=/=0. Daraus folgta 0; Zweitens walle man w in einem der 4 Sehnittpunkte von /, und /,. (1) wird dann S,, = 0. Geometrisch würde das bedeuten, dass die Tangenten in w zu f, and /, konjugiert sind bezüglich f was nicht immer der Fall ist, weil /, ganz beliebig. (nen (2) -setze «man a’ =v. Dannewird) 2 = 0) Se A= Ors Ope == 0, 434 S/= Oh Dastergibtp2 SOMEREN verläuft der Beweis dualistisch entsprehend zu (1). (3). In (3) setze man a@=v, a’=w. Das ergibt in derselben Weise wie bei den früheren Beweisen d—=0. Setzt man nur a’ = wv, so findet man u=—0. (3) wird damit 4= 0. Dualistisch müsste dann auch £ =O sein, was falsch ist. (4). In (4) setze man zuerst a =v, a’ =w, ad) =s. Dann findet man 0=A(vws)* ur + 0(v ws)? (ws u) vz - Da aber die Linien w und v unabhängig sind, müssen die Koeffi- zienten von wu, und ve einzeln verschwinden, somit 4=0, o= 0. Oder: V, enthält den Faktor w,. Daraus folgt aber dualistisch, dass auch V, den Faktor enthalten müsste, was nicht der Fall ist. (5). In (5) setze man a =v. Pos, A,,, und A,,, verschwinden dann. Nach Division durch A, erhält mar’: 0 = (aa" v)* uz Holava!)(wa' war + olava!)(a!eu) ve. Setzt man hier a =s, a =vw, so findet man eine lineare Abhan- gigkeit der drei Linien u.s.w. welche aber ganz beliebig sind. Das ist nur dann möglich, wenn alle Koeffizienten Null sind, also wenn A4=0, e=0, 50. Daraus folgt dass P den Faktor wz enthält. Setzt man in P aber ~a=v, so zerfällt P in zwei nichtverschwin- dende Faktoren, der eine linear in u, der andere in «x. Diese beiden Tatsachen sind unvereinbar. (8). Die zu (8) duale Formel 2—=0 gilt nicht, daher kann (8) auch nicht gelten. 1) Siehe CLEBSCH-LINDEMANN, a.a.0., oder besser BAKER, a a.0., wo man die geometrischen Untersuchungen von CLepscH, Rosanes, usw. über die Figur dreier Kegelschnitte zusammengestellt findet. 11 (9). In (9) setze man a=v. Die rechte Seite verschwindet, und man erhält (wa a')(a' wv) (a uv).v, —0 oder (wa! a!) (a“ uv) (a uv) —= 0 und somit: die beiden Polaren des Punktes uv bezüglich unde sehneiden sich auf v. Das ist aber offenbar nicht immer der Fall, da diese beiden Polaren nach Wahl der Linien w und v noch beliebig gewahlt werden können. (10) In (10) setze man a’ =v, a’ =w, und erhält va Wz lar (awu).vr + dz (av U). wy} = =A S02 .(awu) ay . wz + ws (av U) Ay « Ux |. Da diese Gleichung für jedes w gelten muss, so müssen die Koeffi- zienten van (avw) a, und (awu) a, jeder für sich Null sein. Folglich ware Ur Wx eh We —— AW Ur = 0 was, wegen der Unabhangigkeit der Linien w und v unmöglich ist. (141) In (11) setze man a=v, a =w, a'=s, und erhält u = 0. Setzt man nur av, a’=w, so findet man 2=0. (11) wird damit Y = 0; die dualistische Formel (7) gilt aber nicht, daher kann auch (11) nicht gelten. (12) In (12) setze man a =v, a’ =w, a’ =s, und erhaltu=0. Setzt man nur a@—v, so findet man 2—0. (12) wird damit H — 0. Die duale Formel gilt aber nicht, daher kann auch (12) nicht gelten: (13). In (13) setze man a'=v, a'=w, und findet 4=0. Setzt man nur a’ =v, so findet man » =O. (13) wird damit 7=0. Die dualistische Formel gilt aber nicht, daher kann auch (13) nicht gelten. (14). In (14) setze man a =v, und findet A(va'a")?. (e'a'e) ver var Hv boa (va'a") aly: Vy d'r + 047 (vala") a’z” vra} = 0. Jetzt wable man für v eine der gemeinsamen Tangenten von /, und f,. Dann ist vr =0, vr? =0, wa'a”) =/=0 (denn wa a")? ist nur dann Null, wenn v he beiden Kegelschnitte in harmonischen Punktpaaren schneidet), (a! a") vv,” =/=0 (denn diese Form ist nur dann identisch Null in w, wenn die Verbindingslinie der beiden Pole, oder Berührungspunkte von v, unbestimmt wird). Also 2—0. Nimmt man sodann für v eine beliebige Tangente von f,, die nicht zu- gleicherzeit Tangente von ve ist, so wird v,27 =O, vr’ 4 0, während man geometrisch leicht einsieht, dass (va'a") a’, v,,a'x=/=0. Also v=0. Jetzt ist die Formel (14) homogen in « und a; sie kann daher dualisiert werden ohne dass Faktoren 4 a,’ hinzutreten. Aus der Irreduzibilitat von G folgt dann ihre Unmöglichkeit. Astronomy. — “On the magnitude equation of Ostnorr’s estimates of star-coulours’. By Einar HeRTZSPRUNG. (Communicated at the meeting of February 24, 1923). In Annalen van de Sterrewacht te Leiden Vol. XIV, Part 1, p. 14; 1922 I have noticed an unexplained magnitude equation for the derived ¢,/T values of stars of the spectral classes AO, A2, A3 and A5. Now the ¢,/T values used le. depend for about 58 percent of the total weight on direct colourestimates. A redetermination of the magnitude equation of those estimates is therefore very desir- able. The opportunity for this is given by the new catalogue of Osrnorr (Specola Astronomica Vaticana Vol. VIII; 1916) extending his estimates with the 4 inch refractor one magnitude farther viz. to about 6™. A. card catalogue was made containing the hour of R. A., the degrees of declination, the spectrum of the new Draper Catalogue H.D. (taken from the Index Catalogue, Spec. Astr. Vat. IX; 1917), the magnitude to one tenth and the estimated colour. The cards were divided into groups according to spectrum. After some trial the subdivisions of spectral class were combined in the way as shown in Table 1. For each of the 6 combined groups corresponding values of mean magnitude and mean estimated colour are given. On the accompanying diagram the figures of Table 1 are represented graphically. The most striking fact is, that the estimated colour does not, as hitherto adopted *), increase continuously with decreasing apparent brightness but shows a maximum in the neighbourhood of 4™ or 5™. Especially for the white stars the decrease in estimated colour between 5™ and 6™ is very marked. This is nothing more, than should be expected from the known peculiarities in colourconcep- tion by the human eye. If the spectrum of the sun is made to in- crease in intensity starting just below the limit of visibility, the blue and green portion will appear first, but without showing any colour, until by still greater intensity the colours green and blue are 1) A. Pannekoek, Koninklijke Akademie van Wetenschappen te Amsterdam, Proceedings of the Meeting of Saturday October 27, 1906, and E. HeRtzsPRUNG, Zeitschr. für wiss. Photographie Bd, 5, 100; 1907. 13 seen. On the other hand the red end of the spectrum will appear red, as soon as it is perceived. By very great intensities the colours will again loose in saturation *). The magnitude equation found for Osrgorr’s colours is in accordance with these facts. Se Bb ea 2 = OS ee aS = GG GH = - on @ : io re TS WKE : 7 4 ot wm © al a = a & “os a Fr > © | Nn © a nN wo 7 SS Se De 1 OOP Or, ON NS, Oo oF Je 0 WM OW WM WM is) a = a © a pe SZ E « 06 = © S | oOo + 9 WM oO | é SS SSS SS = = | © 10. = 19 : iF = tS) Cr Soe Te | : = | N a Nn a | oF = & 0 + es Ne) . ° = | Sy TS OS Su 5 —— 4 o = & x > NN ©O MM FE ‘ Oo Em » © 5 am oO oOo OH WM 10 | Dt iL | | oOo - E- oo | aa) = RO t = 4 Te i ee ae = | faa) > < Oe =) st Seton LO LO ms | a4 10 ov } ls e rig CES Sn ee eee = a 0 0 0 NN NN A | i | | A, | ee x~ mo - oO © 4 w+ a 5 Ea+so + 6 == Ben 23 Ser = of 121 19 WM we © 5 5 Ld u . . < = eo = 1) MO NN GS SO En en 19 i le) le) Ye] = : . | 3 N x, . | Stiles 5 zi = < © 202 9 @ a 2 j = = OF A wm o FE 1 3 > NNN A - = = _ 5 Ke) ey Pel Va fe GS x= Che < Eom ON Wm O = | O7 oy + 12 10 WW WO F (sa) | == & maxtor OQ | OO ats ONO ee So i=. ed ~ — _ — _ == @ © MA oo om EF 0 nana = = a = m Ta} 2 he 5 é EN | Me Eos & Es Figure 1. i) ZS oe Ee ee = aot SF Wm WL = ono © © =—- a ow st 1) E.g. the wire of the electric lamp behind the darkroom glass, only letting red light through, appears yellow. 14 The results obtained are able to clear up the discrepancies cited above from Leiden Ann. XIV. At the same time they form an in- structive example of the unsafety of extrapolation, as just at about 5m, which was the limit of brightness of the stars concerned in Leiden Ann. XIV, the magnitude equation of the estimated colour changes its character. The above considerations rest on the assumption, that stars of the same spectrum do not show any systematic change of effective temperature with apparent magnitude. As long as we have no other reliable colourequivalents of these stars, this seems to be the most plausible supposition, which can be used. Anatomy. — “On the development of the shoulder-girdle and episternum in Reptiles’. By Car. van GELDEREN. (Communi- cated by Prof. L. Bork). (Communicated at the meeting of December 30, 1922). In comparative anatomy we distinguish in the primary shoulder- girdle of most Sauria the scapula and suprascapula, coracoid, epi- coracoid and procoracoid. Procoracoid and coracoid are usually homologised with the similarly-named portions of the shoulder- girdle of the Urodela and Anura. This was long ago contested by Görrer *). According to him there is nothing in the ontogenesis to justify such an independence being attributed to the so-called pro- coracoid of the Sauria, for he holds that all the parts of the ven- tral portion of the primary shoulder-girdle (in Cnemidophorus) develop from one massive formation. The procoracoid of the Sauria, therefore, he says, will not originate as a free cranio-ventral process of the coracoid, to unite with it ventro-medially into a ring, as Gottr found it in Anura, and as in comperative anatomy it is frequently termed with respect to the Sauria. Although such a development was observed at a later date by WikDERSHEIM ’), Broom *) and BoGoLsupski *) in a tew other Sauria also, no hand-or text-books (with the exception of that by WiIEDERSBEIM) make any reference to this. It is this which has led to the present article, treating of the development of the primary as well as the secondary shoulder- girdle (including episternum). In intimate connection with the question as to the ontogenesis of the episternum is another, namely, that of the development of the clavicula. And attention will also be devoted to this in the following lines. The episternum, for the first data of the development of which we have to thank RarnKe®), was seen by the latter to originate 1) A. Görre, Archiv. f. mikrosk. Anat. Bd. XIV, 1877. 2) R. WiepersHEIM, Das Gliedmaszenskelett der Wirbelthiere. Jena, 1892. 5) R. Broom, Trans. South. Afric. Philos. Soc. Vol. XVI, Pt. 4, 1906. 4) S. BocousuBskI, Zeitschr. f. Wissensch. Zool. Bd. 110, 1914. 5) H. Rarake, Ueber den Bau und die Entwickl. des Brustbeines der Saurier. Königsberg 1853. 16 unpaired between the medial ends of the claviculae. Görrr holds the opinion that, also on account of its paired formation, the epis- ternum develops from a part of the clavicular formation whieh is bent caudally. Moreover, in his opinion, the clavicle originates as a blastemic process of the primary shoulder-girdle. G&GENBAUER *), on the contrary holds that the connection of the clavicle and shoulder- girdle is a secondary one. Horrman *) observed the paired development of the episternum in the crocodile, and also on the basis of Görre’s researches, he speaks of a clavicular sternnm. WirDERSHEIM was not able to find any real genetic connection of the episternum with the clavicula either in Lacerta or in Crocodilus, although he sue- ceeded in recognizing the clavicula, the embryonal existence of which Görrr had already surmised in a rudimentary form. As regards the relation between the clavicula and the scapulo-coracoi- deum, WiepersHeiM shares GOTTE’s Opinion. SCHAUINSLAND *) did not find in Sphenodon any primary connection of episternum and clavi- cula in stadia where the medial portion of the latter contained no bone as yet. Besides a primary connection of clavicula and scapulo- coracoideum boGoLJuBski mentions a paired formation of the epister- num, in which the ossification takes place from paired centra. Of the genetic relations of clavicula and episternum he gives no details. None of the researchers ever found any cartilage in episternum and clavicula. Görre and WinpersHeim, however, describe a form of ossification which is strongly suggestive of the formation of perichon- dral bone round about a nucleus of cartilage. The bony clavicle, they say, first canaliculate and afterwards cylindrical, enclosing a soft medullar cord, just like a cartilaginous process. SCHAUINSLAND and BoGoLJsuBskI specially mention to have found no trace of such a peculiar ossification process. According to these writers the medullar cavity is produced by osteoklastic action. | had for my investigations seventeen embryos of the common lizard, lacerta agilis, all of which I prepared in cross-sections. (Section thickness 10 u). Further, the collection belonging to the Anatomic Laboratory contained a dozen series of Gongylus ocellatus and two of Ptychozoon homalocephalum. The direction in which sections were made in the thorax-region depended intimately upon the age of the embryos, namely, they were all made frontal on the jaw. This, with the slight curve in the region of the neck in the older 1) CG. GeGENBAUR, Untersuch. z. Vergleich. Anat. der Wirbelthiere. 2 Teil. Schultergiirtel. Leipzig 1865. 2) G. K. Horrmann, Niederl. Archiv. f. Zoologie, Bd. V, 1879. 8) H. ScHAUINSLAND, Archiv. f. Mikrosk. Anat. u. Entw.gesch. Bd. LVI, 1900. 17 ‘ embryos, was practically identical with frontal on the thorax. Ac- cording as the neck-curve was more pronounced in the younger embryos, the sections were made more transverse on the thorax. In the account of my observations | shall commence with Laeerta, as my material of this was the most complete. Fig. 1a shows the shoulder-girdle of Lacerta agilis spread out in one flat plane, whereby the sternum and episternum have been left in position in order to show the relative positions. Fig. 15 shows only the primary shoulder-girdle. Clavicwule fenerracee? B. Fig. 1. Sternum and clavicula shoulder-girdle of Lacerta agilis. The primary shoulder-girdle, i,e. the cartilaginous preformation, consists of a dorsal portion: the scapula and the non-ossifying large supra-scapula, and a ventral portion, viz. the coracoid, in which we usnally distinguish three parts: coracoideum, s. str., procoracoid and epicoracoid. They surround an oval opening, the fenestra coracoidea principalis (FÜrBRINGER) *). Besides this cranial to the fossa glenoidalis humeralis, there is generally another fine canal, through which the n. muse. sopracoracoidei runs. This canal will henceforth never be counted among the coracoidal fenestrae (many reptiles possess more than one fenestra!). The cranial border of the primary shoulder-girdle exhibits a deep incisura scapulo-procoracoidea which is bridged by a strand of connective tissue, lig. scapulo-procoracoideum. The cora- 1) M. FürBriNGer, Jenaische Zeitschr. Bd. 34, 1900. Proceedings Royal Acad. Amsterdam. Vol. XXVI. 18 / coideum is received diarthrotically in the suleus articularis coracoi- dalis sterni. The clavicula is connected syndesmotically with the suprascapula. Between the medial extremities of the claviculae the cranial point of the dagger-like episternum interposes. The latter lies mainly cranial to the sternum; a small part, however, lies ventral to the sternum and is quite separated from it by connective tissue. The youngest embryo that I was enabled to examine, Lacerta ag. D. (N. T.)*) about 22), possessed no shoulder-girdle yet. Only in the inarticulated epiphysal limbbud was a central blastema. Besides the primary shoulder-girdle, also the clavicle was lacking. In the embryo Lacerta ag. 5. (N. T. about 24) the central blastema of the superior limb has extended proximally as a blastematic form- ation of the shoulder-girdle as yet very difficult to define. There is no trace yet of the clavicula, The embryos Lacerta ag. E. and F. (N.T., about 26) contain a well defined shoulder-girdle which still consists entirely of dense mesenchyme. Any clavicular formation is still lacking. In the humeral formation there is already praechondrium. The line of demarcation of the cora- coid with respect to the growing sternal formation is much more obscure than it was in embryo S. Specially noteworthy is the fact that the formation of the shoulder-girdle, apart from the nerve-canal, one solid whole. Embryo Lacerta ag. I. (N.T. about 28) is clearly in a more advanced stage of development. Cartilage is found in the humerus, which passes over proximally into praechondrium of which also a part of the primary shoulder-girdle consists. The latter still forms one conti- nuous whole with the humerus. In this embryo the boundary of coracoid and sternal formations has almost disappeared, a transition stadium which will speedily be followed by the formation of the definite articular cavity. In the process of the primary girdle the praechon- drium occupies the caudal region; the rest is still compact mesen- chymatous, but quite homogeneous. From the cranial border of the seapulo-coracoideum, dorsal from the humerus-formation a blastematie spur proceeds. There is also a very small fragment of bone tissue to be seen, quite dorsally close the point of attachment to the primary shoulder-girdle. Lacerta ag. K. (N. T. about 29). The line of demarcation between coracoid and sternum is indicated (now permanently) by a loose mesenchymatous layer. There is an increase of praechondrium in 1) K. Perer, Normentafel Lacerta agilis. 19 the scapulo-coracoideum. That portion, however, which is still blastematic, has lost its homogeneity. (Compare the schemata of fig. 5.) A more compact cranial border can be plainly distinguished; the ventro-medial border is also more compact than the rest of the blastema. Further, a likewise denser strip of blastema connects the cranial border with the praechondral caudal portion. In these compacter regions there is no praechondrium however. The blaste- matie spur proceeding from the cranial scapular border has become slightly longer, as also the fragment of bone lying in it. It is from this process that the clavicle develops; we shall therefore henceforth term it the clavicular process. The connection of the seapulo-coracoid and the clavicular process will be evident from the two consecutive sections illustrated in fig. 2. The left section lies cranial to the right one. In the former the ventral outgrowth of the clavicular process can be seen; in the latter the connection with the scapulo-coracoideum. Coracoid. Pe a re SUS Hon ¥ zt , hy Manet 5, Med spinalis Fig. 2. Lacerta agilis K. Cross-section. The dark spot at the place where the clavicular-process goes out 2x 20 from the scapula shows the thickening of the cells against the bone fragment present in the following (not drawn) section. Embryo lacerta ag. G. (N. T. about 29) is distinguished from the former one by a piece of bone which has grown larger in a ventro- medial direction in the blastematic process of the clavicula, which has grown out in the same direction. The blastematie clavieular process of the scapulo-coracoid still reaches much further ventrally than the bone fragment. Embryo Lacerta ag. H. (N. T. about 30). Both the form and the histological differentiation of the formation of the parts of the skelet- on have undergone marked changes. The calcified cartilaginous diaphysis is surrounded by a covering of perichondral bone. The articulatio humeri is indicated by a layer of thick mesenchyme which lies between the cartilaginous proximal humerus extremity and the shoulder-girdle. Cartilage is found in the seapulo-coracoid in accordance with the position of the scapula and of the later coracoideum s. str., i.e. in the dorsal and ventro-caudal parts. The ventro-cranial half consists of praechondrium and blastema, « except that where, in the adult lizard, the epicoracoid, procoracoid and lig. scapulo procoracoideum are found, we find in this embryo prae- chondrium, and that at the place of the future fenestra principalis and of the membrana scapulo-procoracoidea, only thickened mesenchyme blastema is found. For the rest the scapulo has grown out in a dorsal direction as well as the coracoid has done in wider sense in a ventral direction. The clavicular-process has grown longer ventro- medially, especially the bony nucleus lying in it. Moreover it is also striking that caudal to the bony clavicle a compact blastema-mass has developed. The significance of this will become plain later. Embryo Lacerta ag. J. (N.T. about 31). The organs, the deve- lopment -of which are examined here, show no striking differences from embryo H. More cartilage is present in the scapulo-coracoid than before. The outline of the praechondrium against the blastema is more easily definable. The blastema, of which the bony clavicle occupies the cranial border, has increased in size but is still perfeetly homogeneous. It is distinctly loose of the coracoid lying underneath it (properly dorsal to it). The schemata of fig. 6 may now be compared. , Embryo Lacerta ag. L. (N.T. about 31). In this specimen many of the parts still praechondral in the former embryo have become cartilaginuos. The blastema, of which the bony clavicle occupies the cranial border, has increased in size, but is still homogeneous. The bony clavicle is now nearly as long as the clavicular blastema. 21 In the ventral medial line the clavicular-blastema of both sides are still distinctly separated. Those parts of the coracoid which were still blastematic in the former embryos have decreased in density and have become some- what lighter. (fenestra principalis and membr. scapulo-procoracoidea). The later lig. scapulo-procoracoideum has remained praechondral. Pro- and epicoracoid now consist of cartilage. Fig. 3 shows four sections taken from this series (not consecutive). Section a contains the procoracoid, the lig. seapulo-procoracoideum and the scapula; section 5 has already passed (more caudally) through the later membrana scapulo-procoracoidea; section ¢ contains also the thinner blastema which corresponds to the later fenestra principalis; section d finally contains only coracoideum s. str. (and scapula). f Fig. 3. Lacerta agilis L. Cross-section. Embryo Lacerta ag. N. (N.T. about 32). The entire definite coracoid in a wider sense is now present in cartilage. In the bridging over of the incisura scapulo-procoracoidea, the praechondrium has diminished while the blastema has increased. The thinning of the blastema corresponding to the membrana scapulo-procoracoidea and to the fenestra principalis, already seen in the preceding embryo, is continued here. The definite form of incisura and fenestra is clearly recognisable. In the blastema which joins the clavicula caudally a still slight central thinning can be seen. Simultaneously, in the unthinied, 22 medial and caudal boundaries of the thinned centrum, a small trace of bone-tissue is seen, at a place almost corresponding to the crossing-point of the detinite episternum. The blastematie medial ends of the claviculae are no longer sharply defined; and there is no connection yet between the two by way of the medial line. Embryo Lacerta ag. O. (N.T. about 32). The changes in the primary girdle are confined here to the non-cartilaginous portions. At the place of the incisura scapulo-procoracoidea and of the fenestra prineipalis the thinning of the tissue is fairly complete; the blastema once present has become nearly a membrane of connective tissue. In the cranial border of the membrana seapulo-procoracoidea a thicker strand is distinguishable, in which a few praechondrium insulae are lying, as the remains of a entirely praechondral bridging. In the retro-clavieular blastema the central thinning has proceeded further. Fig. 4 shows five partial illustrations of sections from this series. Hach has been drawn exactly to the medial plane. There was still loose mesenchyme between the right and left claviculae. In Fig. a the bony clavicula has been taken for the greater part lengthwise. In Fig. 6 only the thickened medial end of the clavicula is to be seen. Lateral to it comes a thinner blastematic region (thinned centre), still more laterally the cut caudal border. In Fig. c only the thinned centre with the caudal surrounding border medial and lateral to it has been reproduced. Of the clavicular bone no more traces are to be seen. Figs. d and e have been chosen caudal to the thinned centre. Fig. e, the most caudal, shows the last vestige of the retroclavicular blastema. Embryo Lacerta ag. M. (N.T. about 33). In this one the thinning into a connective tissue membrane has been fully accomplished at the place of the incisura scapulo-procoracoidea and of the fenestra principalis. Apart from a praechondral insula, the incisura bridging consists of a strand connective tissue, ligament. The central thinning of the blastema lying caudal to the bony clavicula has here, too, practically led to the formation of a connective-tissuemembrane. The bony episternum has grown in size. There is thus now one connected complex present, consisting of a thin bony episternal transverse bar (situated in the caudal boundary), from which a thin blastema bundle can be traced to a point ventral of the equal-sided sternal band and in which a still much thinner fragment of bone, (even broken perhaps locally) is found. Thus, for the first time, in this embryo a small piece of the episternum is met with ventral from the sternal formation. From the transverse bar a blastema bundle (likewise caudal border) runs in a lateral and cranial direction and i= Gloéeula- Precora cocd. Dunner _ —< fe centrum. Epccoracoid D. Caucdale- ad rand E. wet looper Epcsteraum. Fig. 4. Lacerta agilis cross-section. Dunner centrum = Thinner centre. Caudale rand = Caudal margin. Caudale uitlooper = Caudal process. 24 comes to insertion at the clavicula. Finally, the medial boundary forms a blastema strip, in which the half of the little cranial point of the episternum will develop later. The complex of clavicular and episternal formations is connected with that of the other half of the body at the level of clavicle and episternal transverse bar; the caudal processes are still separated. Embryo Lacerta ag. P. (N.T. about 33). In this embryo the sternal borders are already blended cranially. Apart from a com- mencement of calcifying cartilage, there is nothing to remark at the primary shoulder-girdle except the occurrence of a cartilaginous insula in the lig. scapulo-procoracoideum. The coracoidea have passed the medial line, and are thus partly overlapping each other. The central thinning in the episterno-clavicular blastema has com- pletely given place to the membrana-clavicularis. In the caudal border the episternal transverse bar has elongated, and its lateral extremity is attached by ligament to the clavicula. The episternum, now grown unpaired, has also acquired a cranial point which inter- poses itself between the two clavicles. In cross-sections it shows traces of paired formation, (deep medial groove on the dorsal side); the paired bony formation [ have not seen however. On the medial half of the clavicula a thick cranial border and a thinner caudal bone-plate can be distinguished, the latter being evidently an ossified portion of the claviculo-episternal membrane. In embryo Lacerta ag. Q. (N.T. about 33—34) the cranio-caudal measurement of the episternum has attained its definite relative size. Several cross-sections show a paired cranial episternal point. This duality is merely local however. Nevertheless I take it as a proof that also this part of the episternum is formed pairedly, in which case the whole bony episternum was originally paired. In the primary shoulder-girdle the calcification has extended. Regarding embryo Lacerta ag. R. (N.T. about 34—35), in which the portions of the bony skeleton discussed here have all attained their definite form, although on a small scale, there is nothing of note except that in the lig. scapulo-procoracoideum vestiges of cartilage are still to be found. When the scapulo-coracoideum passes into praechondrium and later into cartilage, a narrow strip of tissue remains between it and the bony clavicula at the blastema stage. We can now for the first time speak of a syndesmosis scapulo-clavicularis, although the connection between scapula and clavicula was already long present. Only with the histological differentiation of the scapulo-coracoideum is it possible to indicate the boundary region as syndesmosis. 25 Of Gongylus ocellatus I had eleven series at my disposal, but without any older stadia, such as P. Q. and R. of Lacerta. As I had neither a full-grown specimen nor a good illustration of the shoulder-girdle of Gongylus, L am forced to describe the full-grown shoulder-girdle from data taken from the literature on the subject. Of the primary shoulder-girdle the coracoid only contains a fenestra principalis (apart from the canalis nervi supracoracoidei), just as in Lacerta; and further the cranial border of the scapulo-coracoideum shows a deep hollow. The clavicula, viz. the thin medio-caudal portion, according to SIEBENROCK, has an extremely irregular border. Embryo Gongylus oe. T. possesses a blastematic shoulder-girdle continuous with the humerus. The diaphysis humeri already contains praechondrium. No trace of the clavicle is to be seen yet. The vaguely defined scapulo-coracoideum consists every where of blastema of equal denseness. The sternum lies at some distance from the coracoideum. Thus this embryo, as also Gongylus oc. G. which shows the same degree of development, corresponds to Lacerta ag. S. The embryos Gongylus oc. A and B are of very nearly the same age. | shall base my description on embryo A on account of its better preserved colouring. The humerus diaphysis contains cartilage, which passes proximally over into praechondrium. This continues into the scapulo-coracoideum, but is there limited to the region bordering on the humerus. For the rest the primary girdle is blaste- matic, only more sharply defined than in embryo T. At this stage the sternal formation (temporary) has practically become one blaste- matic continuum with the coracoid. From the cranial border of the scapula a blastematic clavicular process goes out in a ventral direction. In: the dorsal portion of it I found already a small fragment of bone tissue. The scapulo-coracoideum still forms one compact whole. This embryo thus agrees with Lacerta ag. I. Embryo Gongylus oc. D. (embryo C, represents the same stadium). As in Lacerta ag. embryo J., the scapulo-coracoideum is here largely cartilaginous (scapulo, coracoideum s. str.). Epicoracoid and proco- racoid are still praechondral. Two thinned blastemic parts have appeared; they correspond to the fenestra principalis and to the incisura scapulo-procoracoidea. The latter is closed by a ligament containing praechondrium. The clavicular blastema, as also the bony clavicula lying in it, have become longer (in a ventro-medial direc- tion). Between clavicula and the praechondral-cartilaginous scapula is a strip which is still blastematic, representing the syndesmosis claviculo-scapularis. In the next embryo of Gongylus oc. E. the thinner blastematic 26 parts in the primary girdle have given place to thin membranes of connective tissue, or, in other words, the fenestration is complete. The lig. seapulo-procoracoidijeum contains praechondrium which is connected with the cartilage of the girdle only by ligament. The bony tissue in the elavicular process has increased in extent. In the remaining older embryos there is but little that is new to be remarked about the seapulo-coracoideum, (inerease in size and commencement of calcification). The further development of the clavicular formation could not be traced. In the older embryos the latter appears in the ventral body-wall, and as it is but thinly covered with the skin, it is hardly possible in the frontally cut series to define the cell-thickening under the almost tangentially cut breast-skin from the blastemic clavicular formation. For the same reason the development of the episternum could not be traced in detail. In the oldest series a paired bony episternal formation was present. (Gongylus oc. E. and L.). The episternal formation of one half of the body has been demonstrated by me elsewhere. (Fig. 6) *). Ptychozoon homalochephalum. Embryo A is still very young, the diaphysis humeri contains no cartilage as yet. The shoulder-girdle formation is continuous with the humerus formation. The blastematie scapulo-coracoideum is still rather vaguely outlined. The mesenchyme thickening, of which it is formed, is quite homogeneous. Nothing is to be seen yet of the fenestra principalis which occurs in the adult scapulo-coracoid; nor of the incisura scapulo procoracoidea. The bony clavicle, or even the blastematic formation of it, is still lacking. Ptychozoon embryo B. Round the diaphysis-humeri lies a covering of perichondral bone. The primary shoulder-girdle shows cartilage. The more cranial portions are still praechondral (epicoracoid!). The fenestration of the first homogeneous compact coracoideum is already fairly complete. So the conditions correspond completely to those found in Lacerta J. and Gongylus D—E. From the cranial border of the scapulo-coracoideum the bony clavicula proceeds, connected with the scapula by syndesmosis. Joined to the clavicula, just as in Lacerta, is a retroclavicular blastema. Of the episternum no traces of bone are to be found yet. The examination of the embryos of Gongylus and Ptychozoon has thus led to the confirmation of most of the facts observed in Lacerta, namely the origin of the fenestra principalis and of the incisura scapulo-coracoidea by reduction of parts of an originally compact primary shoulder-girdle and also the primary connection of the 1) CH. VAN GELDEREN, Proceedings. Kon. Acad. v Wetensch. Vol. XXIV, 1922. 27 blastematic clavicular formation with the scapula-coracoid. Others again of the results found in Lacerta could not be further veritied, namely, the formation of each episternum half connected with the formation of the homolateral clavicula. After the casuistie description in the above lines, I shall now with the help of figs. 5 and 6 summarize the development of the skeleton parts. In Lacerta, as well as in Gongylus and Ptychozoon the cora- Clavieule. Oe: a pe \Coraccideum primitivum. Ligt ea \ Membe} ae Oe ee Clavicule Vg, Coracoid Fig. 5. Lacerta agilis. Schemata of the development of the coracoid. Clavicule Memb Pan cu fl epist-claviculg L DE eptst-claviculare Fig. 6. Lacerta agilis. Schemata of the development of the secondary shouider-girdle. 28 coideum in youthful stadia does not show a single trace of the fenestra principalis, and the region of the later incisura scapulo- procoracoidea still forms part of the homogeneous compact formation of the scapulo-coracoideum. When later a progressive histological differentiation occurs at the place where scapula, coracoideum s. str., epicoracoid and procoracoid will originate (formation of cartilage) this is accompanied by regressive changes at the place of the fenestra prineipalis and of the incisura scapulo-coracoidea, viz. a thinning of the blastema and finally reduction to a thin membrane of connective tissue. The cranial closing of the incisura does not occupy such a prominent place in these regressive changes. In the lig. scapulo- procoracoideum there are still cartilaginous insulae in the oldest embryos, which prove that this ligament is a reduced portion of the coracoid (in a wider sense). In fig. 5 the four schemata show the process of development of the coracoideum. The scapular end of the clavicle has not been hatched in each of the figures, and has been indicated in the same form. In the primary girdle hatching indicates blastema, praechondrium or connective tissue according as the hatehing is more or less close. Entire absence of hatching indicates cartilage. The ab origine present nerve-canal has been omitted. The figures require no further explanation. Thus genetically both the fenestra prineipalis and the incisura scapulo-coracoidea, i.e. the membranes which enclose them, are parts of the shoulder-girdle. The lig. scapulo-coracoideum is, as it were, a reduced procoracoid. As regards the episternum, in the youngest embryo in which a blastematie clavicular process was found, it was continuous with the primary shoulder-girdle. From which | deduce a genetic con- nection, in a sense that the clavicular blastema originates as a process of the scapulo-coracoid. It might still be opposed that the stadium in which this connection did not yet exist has not come into my hands, to which I might return that the bone in the blastematic clavicula first occurs dorsally and enlarges in a ventral direction, a symptom which, in my opinion, is strongly in favour of the genesis of the clavicula as a process of the scapulo-coracoideum. The further development of the clavicular blastema I shall describe shortly with the help of fig. 6. In illustration a, already a fairly large bony clavicula is seen to be present in the blastemie clavicular process. In illustration 5 this is not more than a strip of bone lying in the cranial border of a large, for the rest homogeneous, blastema. In illustration e a further differentiation in the said blastema has commenced. It consists now of a centrum poorer in cells and a denser mesenchymatous border. In the latter, which represents a 29 portion of the episternum, a commencement of bone appears. More- over, a thin caudally-direeted blastematic process has also appeared. Finally illustration d shows the state of the episternum just before the right and left parts blend to one unpaired episternum. One blastema thus gives rise to one clavicula + the half of the episternum, augmented by the membrana episterno-clavicularis lying between them, which is nothing else than the reduced centrum of the original homogeneous blastema and by the lig. episterno-claviculare, that lies in the lateral border of the membrane of the same name. If we now consider that of this joint process only that portion exists first from which the clavicula develops, | believe | may conclude that the episternum is pairedly formed from the clavicular processes. This manner of growth would imply that without the clavicle there would be no episternum, a state of matters as is seen in Rhipto- glossa. The conditions as found in adult crocodiles (an episternum but no clavicula) is explained by WiepersHein’s discovery, namely that embryos of crocodilus contain a rudimentary clavicula. Of the peculiar manner of ossification of the clavicula, as deseribed by Götrre and others, | could not find any trace. We have still to see what comparative anatomical conclusions may be drawn from the above. In the large comprehensive works upon comparative anatomy the opinion formulated by GRGENBAUR is expressed i.e. a great independence is ascribed to the cranial boundary of the fenestra principalis. This boundary, the procoracoid, is said to be the homologue of the similarly-named shoulder-girdle part of the Anura, Urodela and Chelonia. The procoracoid would thus oceur in two main types, viz. as cranio-ventral process of the coracoideum in Urodela and Chelonia, and as cranial border of a fenestra in Anura and Sauria. Sphenodon has no procoracoid. The publications of Görrr, WirpERSHEIM, Broom and BocorJugsKkr have not been able to bring about any change in this theory. Now the coracoideum (in a wider sense) of the Sauria occurs in very different forms viz. 1*t entirely withont fenestrae in Sphenodon and Chamaeleo; 2"¢ with one fenestra, which has been named fenestra principalis on account of its frequent occurrence _(FÜRBRINGER; ““Hauptfenster” _GEGENBAUR); 3° with, besides the fenestra principalis, one or two more ‘‘Nebenfenster’’. The latter are said to have no morphological value, whereas the ‚„Hauptfenster” has. Now we know from Görre that in Cnemido- phorus spec. (3' group: one principal and two minor fenestrae) all the fenestrae develop secondarily by regression of parts of the shoulder-girdle, or in other words, that the early-embryonal Saurian- 30 coracoid has the same form as that of Sphenodon. And, moreover, it follows from the above description of the development of the coracoid of the lizard, that the incisura scapulo-coracoidea has the same genesis as the dorsal fenestra of Cnemidophorus, save that in Lacerta the cranial border also is practically entirely reduced (except for the remains of cartilage). Thus also the coracoideum of Lacerta with one fenestra contains, although it seems somewhat paradoxial, a second, dorsal fenestra. Consequently the so-called procoracoid of the lizard is the sum of what is in multiple fenestrated coracoidea termed the procoracoid and mesocoracoid (mesocoracoid lies between fenestra principalis and dorsal ‘““Nebenfenster”). By the procoracoid in the order of Sauria are thus understood different parts of the girdle. This fact, as well as the development of the coracoid (taken in a wider sense), induce me to side with Görrr; the whole ventral portion of the primary shoulder-girdle of the Sauria, with or without fenestrae, corresponds merely to the coracoideum of the Urodela and Anura. Respecting the latter Görrp has already demonstrated that their shoulder-girdle (with one fenestra) does not acquire its definite form by fenestration, but that it passes through an Urodelan stage (Rana esculenta). The fact that the adult shoulder-girdle of Lacerta corresponds to that of e.g. Rana thus depends upon caeno-genesis. The different parts of the two shoulder-girdles are not homologous. The crocodilia, in which a procoracoid is lacking, will thus, like Sphenodon and Chainaeleo, possess a coracoid homologous with the whole pars coracoidea of the primary girdle of Lacerta. In short, as far as our knowledge extends at present (regarding Chelonia there are no genetic data) we are not obliged in the case of any reptile to assume a procoracoid that is homologous with the pro- coracoid of the Amphibia. GEGENBAUER postulated the homology of the episternum of the reptiles and mammals; the difference in the histological structure (reptilia : bone; mammals: cartilage or bone), and in the histogeny reptilia : desmal, and in mammals chondral ossification) was evidently no objection, although he did consider as an objection the fact that the episternum of the Sauria lies ventral and that of the mammalia cranial from the sternum. Another weak point in the theory of this homology is that the episternum of the mammals is generally held to be a clavicular sternum, i.e. that we see in this episternum a product of the claviculae, whereas most of the researchers who studied the episternum of the Reptilia did not succeed in establishing a genetic connection between the clavicle and episternum. 31 Only Görrr saw (in Cnemidophorus) the episternum commence as caudal process of the clavicle. Well then, the foregoing casuistic demonstration shows the genetic connection of the clavicula and episternum, even though this is not so simple in Lacerta as was described by Görre for Cnemidophorus. Herewith a new point of agreement with the episternum of the mammals has been found. Further, we have seen that the episternal halves lie at first quite eranially from the halves of the breast-bone. Only later, with the commencement of the longitudinal bar does a small portion of the episternum of the Sauria come to lie ventrally from the sternum. The different position of the episternum thus seems to exist but partially, and it oceurs secondarily. The only difficulty in homolog- izing the episterna of Reptilia and Mammalia is thus the histogenetic difference. And GaveP') has demonstrated that too much importance must not be attached to this in general. As for the clavicle, respecting the development of which my resear- ches confirmed its primary connection with the scapulo-coracoideum, I do not deem it advisable for the present to enter into the discussion which is being carried on as to its homology, although in the theory developed bij Görae (homology of the clavicle with the “Procoracoid” of the Amphibia, which he terms the clavicula) and of which WiepersHem,*) on the basis of his own investigations, proves himself an advocate (in the last edition of his “Vergleichende Anatomie” WiepersHeim has changed his opinion, for what reason I do not know) there is undoubtedly a certain attraction. SUMMARY. 1. Fenestrae in the shoulder-girdle of the Sauria develop secondar- illy, in a girdle of the type of Sphenodon. 2: The incisura scapulo-(projcoracoidea is likewise a fenestra of which the cranial border, except for some cartilaginous remains, is reduced to a ligament. 3. The clavicle originates as a blastematie process from the scapulo-coracoideum. +. The episternum proceeds from a paired formation. This formation is the product of the homolateral clavicular process. 5. As long as there are no data of the development of the girdle of Chelonia, there is nothing which obliges us to assume a proco- racoid in any reptile, homologous with that of the Amphibia. 1) E. Gavre, Kopfskelett in Hertwia’s Handbuch. Jena, 1905. 4) R. WiepeRSHEIM, Grundrisz d. Verg). Anat. d. Wirbelthiere. 4e Aufl. Jena 1898. Chemistry. — “Provisional Communication on Borie Acid Com- pounds of some Organic Substances containing more than one Hydroxyl-Group. Boron as a Pentavalent Klement.’ By y Y l } P. H. Hermans. (Communicated by Prof. J. BörsEKEN). (Communicated at the meeting of December 30, 1922). The behaviour of borie acid towards hydroxyl-containing organic substances is striking in many respects. The extra-ordinary ease and rapidity with which it forms esters of the type of B(OR), with the ordinary saturated alcohols, also when a catalyst is absent, is a totally unexpected property for a weak, and for the rest mono-basic acid such as boric acid, and in this respect it is unequalled. Sull more interesting is the action of boric acid on the aqueous solutions of miulti-valent alcohols and other substances rich in hydroxyl, such as some sugars. It has been known for a long time that these mixed solutions sometimes present a much greater hydrogen ion concentration than a solution of boric acid only. The alkaline reaction of a borax solution can even become an acid one by addition of substances such as mannite’). Also the influence of boric acid or borates on the optical rotatory power of such substances rich in hydroxyl, was early observed. Undoubtedly these phenomena point to compounds which boric acid forms with the substances mentioned above. Several investigators have expressed their opinion about the nature of these compounds’). Mostly it is assumed that acid boric acid esters are formed which possess a higher degree of acidity than free boric acid. Systematic attempts to find out more about these compounds through their isolation, have seldom been made, at least they have not been very successful. In 1869 Duvr*) described a series of salts of different boro-tartaric acids, which however present the apparance of glassy, non-crystallizing masses or amorphous precipitates, the individuality of which is open to doubt. The same principle applies to most of the boro-citrie acid 1) We will postpone the older and more recent literature on this subject to a fullowing publication. 3) Vierteljahrsschr. pr. Pharm. XVIII, 321. 33 salts described by Scueipe') in 1879 and 1880, with the exception however of a potassium salt, which was considered to have the formula C,,H,,K(BO),O0,,.2H,O, crystallizes beautifully, and to which we refer below’). Also among the salts of boro-salieylie acid described for the first time by Jarns in 1878*) there are some well-crystallised compounds. The first who inquired more systematically into the influence on the acidity of boric acid by hydroxyl-containing substances, was Maenanini, who published a series of papers on the influence which these substances have on the conductivity (and some other physical constants) of boric ‘acid solutions.*) The number of compounds examined by him is very large, and he pointed out the influence of the constitution in connection with ‘the occurrence or non occurrence of an increase of conductivity. He found a.o. that this was only observed in «-oxy acids, and not when the OH-group is somewhere else, it was found in aromatic o-oxy carbonic acids, not in the m- and p-isomers, it was found in o-diphenols, not in m- and p-diphenols. These researches have been continued and extended by BörSEKEN (and collaborators)*), who assumed, discovered, and worked out an influence of the steric configuration by the side of the constitional influence. In his hands the Magnanini “boric acid method’ became an im- portant instrument, not only for the determination of the constitution and configuration, but also for our stereo-chemical views in general. These results reached their acme in the application of the method to the sugars and their derivatives, the isomeric tartaric acids, and the saturated cyclic vic. diols. In his “Lagerung der Atome im Raume” Van ‘t Horr already expressed his opinion that in the compounds which are responsible for the phenomena in question, the boron atom might be part of a ring-system, and that this ring could close only when certain condi- 1) Russ. Zeitschr. f. Pharm. 18, 257, 289, 321; 19, 513. Pharm. Journ. and Trans. (3) 11, 389. 3) We have not yet been able to test entirely the records given by KLEIN in 1878 on mannite-boric acid salts of rather complicated constitution. Probably we have to do with not accurately defined substances also here. 3) Arch. der Pharm. (3) 12, 212. 4) Z. phys. Ch. 6, 58. Gazz. chim. Ital. 20, 441, 448, 453; 21, 134, 215; 22, 841; 23, 197. Acad. dei Lincei Rend. (4) 6a, 411, 457. 5) E.g. These Proc. Vol. XV, p. 216 (1912); Vol. XVIII, p. 1647, 1654 (1915); Vol. XXI, p. 80 (1918); Vol. XXIII, p. 69 (1920); Verslag van de gewone ver- gaderingen K. Akad. v. Wet. Amsterdam Dl. XXIX, p. 368, 924 (1921). Chem. Weekbl. 19, 207. Recueil 40, 354, 558. 3 Proceedings Royal Acad. Amsterdam. Vol. XXVI. 34 tions were fulfilled. The accompanying formula was the simplest, and was used by different investigators (see e.g. ABrGG's Handboek III pg. 43), and also served Bérsekun as a working-scheme. According to C—O this assumption one molecule of di-oxy-compound, di DE therefore, combines with one molecule of borie Nolo acid with loss of water to a cyclic compound, which would have stronger acid properties. Different investigators have supposed other relations as to the number of moleenles combining than these to account for the physico-chemical behaviour of the mixed boric acid-polyoxyderivative-solutions, but the grounds on which these suppositions were based, are generally uncertain, and often conflicting. Up till now nothing could be said with certainty about the general type on which the acid complexes are based. The observations agree with each other only in so far that these com- pounds are almost completely dissociated in aqueous solution, and that their formation is favoured by increase of the concentration of the components. It further appeared from different investigations that in some cases (a.o. with substances like mannite and dulcite); several compounds of different composition must be present in the solution, of which however, it can, not be ascertained which are the typically acid ones. In 1911 Fox and Gaver) deseribed the first compound of boric acid with a multi-valent aleohol which is well erystallized. From an alcoholic solution they obtained a mannito boric acid C,H,,0,B. They do not however, say, anything about the constitution. A second compound was described by Derx®), viz. the crystallized cis-eyclo heptane diol borie acid. He determined the boron content by titration O and gave the following formula based on that C,H,, 9 BOH HAO. We might consider the mannito borie acid in an analogous way as ON ziek (Ola rel Oene » Bou, H,O. Both alcohols increase the conductivity of O the boric acid in a high degree. There were, as we see, reasons to look upon these compounds as being the strong complex acids that bring about these phenomena. The impetus for making a new attempt to ascertain the nature of the strongly acid borie acid compounds was given by the following accidental discovery. The 2.4. dimethyl pentane 2.4. diol*) when reacting on borie acid (even in very diluted 1) Soc. 99, 1075. 2) Recueil 41, 340 (1922). 5) Obtained from CH,MgJ and diacetone alcohol. Mr. LANGEDIJK drew my attention to a new method of preparation, which renders this latter substance very easily accessible. (Apams, Organic Syntheses 1921, p. 45). 35 aqueous solutions) gives a beautifully crystallizing and only slightly soluble compound, to which the following formula must be assigned as a result of analysis and examination of properties: (CH,), =C —0 pee ee ae cH. \BOH Caleulated 53,16 9,17 6,90 NS ye Found 53,10 9,07 6,80 (CH), =C —O 53,27 9,12 6,95 The compound has an exceedingly great erystallizing power, melts not entirely sharply at 100—102°, is somewhat volatile, and has a pleasant odour strongly reminiscent of saffron. It is, however, by no means a strong acid, and like boric acid it hardly colours blue litmuspaper red, and in accordance with this the said diol (which is readily soluble in water) does not bring about any increase of conductivity of the boric acid, as was to be expected from such a 1.3 diol according to the data collected by BörsEKEN up till now. As a result of this I believed that the really stronger acid boro- complexes must possess another structure than had been assumed so far, and this was soon confirmed. I succeeded, though only after some more difficulties, in isolating analogous and likewise only exceedingly weakly acid boron-compounds of 2.4.dimethyl hexane 2.4.diol, 2.4.pentane diol, and pinacone, likewise diols which do not appreciably influence the conductivity of boric acid. In the case of tri-methylene glycol, ordinary glycol, and cis-1.2.cyelo hexane diol the existence of compounds could be shown, but attempts to isolate them in a pure state failed‘). It is probable that all the 1.2 and 1.3 diols are able to form such compounds with borie acid, that in many cases, however, they can be separated only with great difficulty, if at all, in consequence of unfavourable solubility conditions and similar difficulties. In aqueous solution they are partially split up into their components. The compound described first, at O° in 0,1 normal solution for 75°/,. The readiness with which this compound is obtained, is owing to its slight solubility in water (4,46 g. in 100 ee. solution at 25°), which is still smaller than that of boric acid. It dissolves in diluted alkalies, probably accompanied by formation of a potassium salt, which is, however, also dissociated, as pure diol is withdrawn from the solution by ether. The liquid free dio] is salted out by strong potassium hydroxide; the potassium salt itself could not be isolated as yet. In the cis. 1.2 eyclo hexane diol, however, the corresponding potassium salt is slightly soluble in an excess of strong potassium hydroxide, and crystallizes out, 1) I hope to discuss the details of the preparation in my doctor’s dissertation. 3* 36 before the limit of solubility of the free diol is reached. It can be obtained pure by sucking off and washing with alcohol of 96 °/,. It is a compound that was discovered already before by BorseKen and Van GirrEN') but which was not isolated and more closely examined then. The aqueous solution of this potassium salt has an alkaline reaction, and the potassium can be determined quantitatively by titration with methyl orange, which proves anew that the corresponding complex borie acid is an exceedingly weak acid. Besides this compound C,H,,0,BK, a dipotassium compound C,H,,0,BK was obtained from very strong potassium hydroxide. Under the same circumstances crystalline compounds can also be obtained from eis-1.2 hydridene diol, cis 1.2 eyelopentane diol, and cis-1.2 and cis 2.3 tetrahydronaphtalene diols. These compounds consist of potassium salts of either of the two types or of both, some of which could, however, not yet be obtained pure and free from potassium hydroxide being sometimes (0.a. in the case of hydridene diol) too easily soluble, both in water and in alcohol, so that they cannot be washed with one of these solvents. It is remarkable that in the di-potassium compound of cis-cyclo- hexane diol boric acid both potassium atoms can be titrated with methyl orange and HCI, but that in the corresponding compound of cis-cyclo pentane diol only one of the two potassium atoms can thus be titrated. We reserve a further discussion of this point till some future occasion. We may point out here that these compounds supply us with a method to separate isomer cis- and trans- cyclic 1.2 diols from each other, the latter not giving such compounds. For in many cases the beautiful method of separation with the aid of acetone compounds found by Van Loon’) is attended with important drawbacks, as has appeared from another investigation (to which I hope to refer later on. *) The fact that the formation of these cyclic and only exceedingly weakly acid compounds seems to be a general property of the 1.2 and 1.3 diols, leads to the conclusion that the more strongly acid boro-complexes, which arise in appreciable quantities only in poly 1) Recueil 39, 183 (1920). §) These Proc. Vol. XXIII p. 60 (1920), and proefschrift Delft p. 59; of BOESEKEN and Derx, Recueil 40, 519. 3) The new method of separation has already been sucessfully applied by Mr. MAAN to the methyl 1. cyclohexane 1.2 diols. The cis-diol was obtained in a much purer state than by the acetone method, as the action of acids is now fully eliminated. 37 ) oxy derivatives with “favourably” orientated OH-groups, belong to another group. In 1917 BörsrKenN (in collaboration with Oprern and Miss van Hareten, Recueil 37, 184) described several salts of pyro catechin boric acids of pretty complicated constitution. As the former had already for some time considered the analysis values found to be uncertain, and as the boric acid compounds described above appeared to be by no means particularly complex, there was suffi- cient occasion to subject the beautifully crystallized salts of pyro eatechin boric acid to a renewed investigation, the more so because pyro-catechin greatly increases the conductivity of boric acid, so that accordingly the other type of compounds might be expected here. This expectation was confirmed: the potassium salt appeared to possess the forumla C,,H,O,BK ’). The carbon was determined by the wet way according to the method of MeiseNHEIMER, the hydrogen according to a simplified method worked out by myself, about which more will be given later. The following values were found : C 54,28; 54,26 H 3,03 B 4,3 K 14,7 Calculated 54,14 3,00 4,1 14,7 The only plausible structure that answers to this is: ZZAN peas | Sooo SA | K The boron is here pentavalent, or has (according to WeRNER'’s nomenclature) the coordination value four, just as in the well-known compounds KBF, and Na[B(OC,H,(4|. The latter was obtained from NaOC,H, and boric acid triethyl ester *). The free dipyro catechin boric acid can be obtained by heating the anilin salt in a vacuum of some mm. Hg. at 100—120°, in which the aniline escapes quantitatively. Mr. Mrunennorr (who has under- taken a closer investigation of these derivatives at Prof. BörSEKEN's request), found that the acid obtained in this way can be prepared in perfectly pure condition by sublimation in vacuum at about 200°. The potassium salt described is very little soluble in cold water, and this solution gives an alkaline reaction, probably in consequence of the fact that a dissociation in pyrocatechin and potassiumborate (possibly first in pyro catechin and mono-pyro catechin borate) sets in. | | (potassium dipyrocatechinborate) 1 The erroneous constitution, given in the last-mentioned paper is owing, partly to anerror of caleulation that has crept in, partly to the fact that substances con- taining boron and being rich in CG, are not easily combustible. 2) Copeau C.r. 127, 721 (1898) e.g. Livio Campi, Acad. dei Lincei Rend (5), 23a, p. 244. 38 The potassium can, however, „ot be determined quantitatively by titration, from which it appears that we have to do here with an acid that is stronger than the mono diol boric acids described. Unchanged pyro catechin can again be withdrawn with ether from the aqueous solution. The other complexes stronger than boric acid are probably also built up according to the type of di-pyro catechin boric acid. So far, however, the separation of a derivative that probahly belongs to this type, has succeeded only in one diol of abiphatic character, i.e. in the cis-cyclo heptane 1.2 diol. This diol was first prepared by Derx from suberic acid; he ascertained that it increases the conductivity of boric acid in a great degree, and states that he has succeeded in separating a solid boric acid compound, the b-content of which agrees with the formula C,H,,: )>BOH.H,O'). As only 0.2 gramme of this diol were available (prepared by Derx), I have carried out the following experiments on micro-chemical scale under the microscope. With an almost saturated boric acid solution the diol gives rise to the formation of an oil which is only soluble in much water. *) This oil is probably the liquid diciseyeloheptanediolborie acid, from which more or less accidentally Drrx obtained the mono ciscyclo heptanediolborie acid as a solid substance. On addition of a little strong potassium hydroxide an aqueous suspension of this oil gives crystals of a potassium salt, while also a drop of aniline is dissolved with separation of beautiful erystal needles, which are, however, pretty readily soluble in water and other solvents. In connection with the small quantity of material available it was better to abandon the idea of an examination of the liquid compound itself, and to try and separate one of the salts. For this purpose I chose the aniline salt to avoid the possibility that with KOH, as with the other eyelie diols, a compound of the monotype would again crystallize ont. It might, however, be expected of aniline that it would give a crystallized salt only with a stronger acid. Only a few tenths of milligrammes of the aniline salt were obtained in a sufficiently pure condition with a melting-point of about 50°. Mr. H. GravesTsin was so kind as to take the execution 1) Proefschrift Delft and Recueil 48, 340 (1922). 2) As Mr. Derx communicated to me in a conversation, this oil was also obser- ved by him, but considered as an impurity. He has obtained the solid boric acid compound described by him in a small quantity from a pretty large quantity of this oil and through rather complicated manipulations. 39 of a micro-elementary analysis upon him. The combustion of this boron-containing coumpound requires, however, special preliminary experiments, and has not yet been accomplished; the results will be published later. A determination of the boron-content yielded the following results: 9,76 mgr. were dissolved with 1 gr. of pure mannite in LOecc. of water, and titrated with 0,0097 N barite water (under similar circumstances tested by pure boric acid) and phenol- ftalein as indicator. Consumed 2,60 ce. Calculated for C,,H,,0,NB OOB mtounde 20 k/b: To all probability we have here actually to do with diciscyclo- heptane diol boric acid aniline. In this compound the aniline is bound still more loosely than in aniline dipyro catechin boric acid. In vacuum at room temperature it already escapes, the remaining part becoming liquid. The liquid residue becomes solid again by the addition of aniline. Also on evaporation of the aqueous solution over concentrated sulphuric acid an oil remains behind, which becomes solid again by the addition of aniline. Beside a dish with pumice saturated with aniline the salt can, however, be regained unchanged by evaporation of the aqueous solution in vacuum. Di-ciscycloheptanediol-borie acid is, therefore probably a much weaker acid than dipyrocatechin-boric acid, and the great increase of conduetivity of borie acid by pyro-catechin must, therefore, be put to the account not only of the favourable orientation of the OH-groups, but also partially to the account of the acidifying influence of pyro- catechin as such. This admonishes to caution in making comparisons with regard to the orientation of the HO-groups between diols that are not very much a like in structure, exclusively on the ground of measurements of the conductivity. This point was, indeed, already foreseen by BörsEKEN, and was a.o. mentioned by van Loon?) and Lremprt *). That also the increase of conductivity caused by the «-oxy acids in the boric acid is probably to be attributed to the formation of complex acids built in an analogous way, we have been able to make plausible by showing that the analyses of the ScreiBe’s boro dicitrie acid potassium’) and of the zincous salt of Jans’ boro di- salicylic acid are in agreement with the formulae: 1) Proefschrift Delft, p. 56. 2) Recueil 39, 359. *) Also the free acid has been separated crystalline by ScHerBe and by me. It is, however, difficult to purify and dry. Scaetse’s analysis, which | have not yet checked, is in harmony with my view. 40 (HOOC . CH,), : O—C: (CH, . COOH) Nem OG EN C=0 2 and O O AD le eee EV a) Wea, Bea In the eis 1.2 tetrahydro naphthalene diol and the cis 1.2 hydrin- dene diol (both increasers of conductivity) the formation of an oil can also be observed in supersaturated solution by addition of boric acid. Aniline dissolves in these solutions, but a salt does not erys- tallize out. [ will state here that a further proof of the constitution ot these boron compounds can be furnished, if experiments to split one of the asymmetric derivatives e.g. boron dicitrie acid or nitro pyro catechin derivatives into optical antipodes, should be successful. It is, therefore, probable, that we shall have to see the derivates of an unknown acid ee Beal H in the more strongly acid boron complexes. The material described here may possibly be able to throw some light on the so far obscure constitution. of the boron acids. As a working hypothesis we will now assume what follows: 1. Maintaining the coordination value four for boron, the formula for meta-borie acid becomes: [O'-B: OJ H 2. The mono-basic ortho boric acid is considered as meta-boric acid being hydrated one-sidedly : HO Onos which can, however, pass into (is in equilibrium with) the genuine trihydroxyl boron B(OH),, from which the well-known esters B(OR), have been derived. The first form is present to a certain percentage particularly in aqueous solution, the second form especially in organic solvents such as alcohol. The volatility of boric acid might be ascribed, to the presence of B(OH),. 3. We start from the principle that a hydroxy] group bound to boron forms exceedingly easily an esterlike compound with alcohols. 41 This enables the |(HO),B:O] H present in water to form compounds with a number of glycols and @-oxy acids, of the following type: a ) > DIE ol H S60 Like boric acid these acids are very weak. 4. On the other side of the boron atom a compound can now be formed with a second molecule of diol or oxy acid with loss of water. Whether then a molecule of water is first admitted, may be left undecided for the present. The existence of dipotassium salts, to which we can assign the structure: sbo” Nok may possibly plead in favour of this, like the presence of an extra molecule of water in Derx’s solid mono cyclo heptane diol boric acid and Fox and GavGr’s mono mannite boric acid. A second molecule of dioxy compound is, however, received in diluted aqueous solution in appreciable quantities only when certain favourable conditions are realized, i.e. with a favourable steric situation of the hydroxyl groups in the diol or oxy acid. The tendency to the formation of a di-compound is, accordingly, smaller than that to the formation of the mono-derivatives, and the former seems, therefore, to be very sensitive to the value of the ring-tension in the ring to be formed. This fact constitutes the hypothetical found- ation of BéxsrKEN’s boric acid method. 5. It is known that the poly-boric acids whose presence must be assumed in alkaline solutions, are stronger acids than ortho-boric acid. Plausible structure formulae could not be drawn up for this large series of acids as yet on Ee basis ae trivalent boron. Possibly they too possess the grouping Bete ses . Maintaining the as- sumption that to each H-atom that can be replaced by metals belongs one pentavalent B-atom, the other B-atoms being trivalent, a structure schema may be constructed for a great number of poly boric acids. Tetra borix acid, which forms the foundation of borax, possesses e.g. the scheme: *) 1) In this connection it will be of importance to examine whether in the saponification of B(OR); by water the presence of a relatively stable intermediate product (RO),BOH can be shown. 2) This representation does not lay claim, of course, to be anything more than a scheme. 42 In conclusion it may still be mentioned that the question what place three remark- able “acid borie acid esters” described by Wout and NeuBerG!) and also the boric acid complexes’) found by Grin and NossowircH, occupy in this respect must still be made a subject of investi- gation. I may still be allowed to express my great indebtedness to Prof. BörsEKEN for the kind interest which he evinced in this investiga- tion carried out in his laboratory. Delft, December, 1922. Organic Lab. of the Technical Univ. 1) Ber 382, 3488 (1899). 2) Sitz. Ber der Akad. der Wiss. Wien M.N. Cl. 125, 2B, 171 (1916). Chemistry. — “The. Electro-viscous Effect in Rubbersol.” By Prof. H. R. Kruyt and W. A. N. Eeeinx. (Communicated at the meeting of January 27, 1922). 1. Researches on agarsol *) have taught that the relation *) between the charge of dispersed particles and the viscosity of the dispersed system manifests itself clearly in those sols in which the charge can be considerably modified without the colloid system as such being annihilated, i.e. in those systems of which the stability does not only depend on their charge, but in which also hydration (more general: solvation) protects the system. The conceptions about the stability of the lyophile sol may be applied throughout the territory of the emulsoids*), at least when water is taken as the substance in which the dispersion takes place. Our attention was, however, drawn by a remark on p. 570 of O. pe Vrirs’ Estate Rubber *), where it is stated that increase resp. decrease of the viscosity of a benzene rubber solution is brought about by shaking it with a few drops of a solution of alkali resp. of acid or salt. As it seems as if this is a question of an electro-viscous effect, we have examined what influence electrolytes have on the viscosity of solutions of rubber in benzene. 2. Sols were used prepared in the following way: 1 gr. of a certain crèpe-rubber was added to 300 em. of benzene, after 24 hours it was carefully shaken, and the sol was poured through a folded paper filter. Then benzene solutions of the electrolytes were made; the liquids which were to be examined viscosimetrically, were prepared by mixing a volume of sol with a volume of the solution of the electrolyte (resp. a volume of benzene, for the zero-standard) ; or as far as the measu- rement of rubberless liquids are concerned by diluting electrolyte solutions with benzene, as they were diluted with sol just before. At the 1) H. R. Krurr and H. G. pe Jone, Z. physik. Chem. 100, 250 (1922). 3) M. von SmorvenowskKi, Koll. Z. 18, 190 (1918). We prefer the term electro- viscous to quasi-viscous, which v. Smorucnowskr uses, but which may give rise to misunderstanding. 8) H. R. Krurr, Koll. Z. 31, 338 (1922). 4) Batavia 1920. 44 beginning and at the end of every series the electrolyte-free mixture was measured, and when there was a difference, a correction was applied to the intermediate values. The measurements have been performed in an OsrwaLp viscosimeter*) and at 25°. In the subjoined tables the concentrations given are end-concen- trations, the viscosity of benzene is put at 1.000, 5, is the viscosity of an electrolyte solution, 44. that of a rubber sol with equal electrolyte concentration. The relation of these quantities is given "ste Ne applied. under , after the said correction for the time reaction has been TABLE I. Influence of benzoic acid on the viscosity of rubbersols. — = - — EEF : : Conc. Benzoic acid Viscosity ; EES) Ke Ns + mMol p. L. benzene ie benzoic} rubber a3 benzoic ze acid A acid | ; corrected Ne 4s +e 0 | 1.000 1.698 1.698 6 =") 1.635 | 1.633 12 me) 1.601 1.598 24 —?) 1.584 1.577 48 1.010 1.565 1.552 96 1.018 1.559 1.533 | | 192 1.036 1.574 1,522 0 1.000 1.695 1.698 In fig. 1 these results are represented graphically. Corresponding determinations have been carried out with acetic acid, hydrochloric acid, sulphurie acid, sulphuretted hydrogen and mercury chloride. Essentially the resulis are the same, the viscosity reducing action alone is different; most for hydrochloric acid, in which already 1*/, mMol per litre reduces the viscosity from 1,573 to 1,486 Ammonia shows a very remarkable behaviour; the results are recorded in table II. 1) With observance of all precautions according to H. G. BungenBere pe Jone, Rec. Trav. chim. Pays Bas 48, 1 (1923). 2) Interpolated between the values for O and 48 mMol per |. 45 The viscosity of the NH,-benzene mixtures (j,.) did not appreciably differ from that of benzene. 7)ste 1.700; | Te Rubber sol | Benzoezuur 1650: 1.600 SSO 1500 ennn NE m Mol per Liter 100 200 Fig. 1. TABLE II. Influence of ammonia on the viscosity of rubbersols. Conc. ammonia Viscosity Nise mMol p. L. rubber + NHs Te Tste corrected 0 1.608 1.608 0.37 1.616 1.616 0.75 1.622 1.621 1.49 | 1.625 1.624 2.98 | 1.622 1.620 5.96 } 1.620 1.618 11.92 1.620 | 1.618 23.85 | 1.621 1.618 } It appears from this that the viscosity of the sols rises by addition of ammonia, reaches a maximum, and then descends. 3. The great change of viscosity by an added substance in so small a concentration as is the case with the acids, certainly makes the impression of an electro-viscous effect. 46 In fig. 2 a graphic representation is given of the results of all examined electrolytes, but only for concentrations below 6 mMol per litre. We have always taken the relative viscosity of the electroly te- 1,08 Change of viscosity in Rubber sols by added electrolytes, 1,00 - + + + 2 => ss mS m Mol per Liter. Se HCl > 0:95); Th | “> CH3COOH 0,90 CeHsCOOH | SOo 7 HCL 0.85 } | Fig. 2. ste —l free sol as unit, and then plotted the relation — as ordinates. i The behaviour of NH, is in striking agreement with this explana- tion: for it has appeared in all investigations on capillary-electric phenomena that alcalic substances give a higher potential to a negatively charged wall, lowering it again on further addition’). In harmony with this researches in this laboratory by Mr. Lier confirmed the occurrence of an increasing electro-viscosity by hydroxy] 1) See e.g. G. von Exissarror, Z. physik. Chem. 79, 385 (1912); R. Extis, Z. physik. Chem. 80, 597 (1912); H. R. Kruyr and A. E. van ARKEL, Koll. Z. 32, 29 (1923). 47 ions in casein, those by Dr. RUNGENBERG DE Jone did so in amylum *). Especially this positive effect is, therefore, a forcible argument in favour of our view. 4. Two objections may, however, be raised. The first is: is NH, and also is SO, in benzene an electrolyte’ For the formation of an OH-ion from NH,OH, resp. an H-ion from H,SO, the presence of water is required. If it is, however, calculated how much water is required with the very small concentrations in question, values are found which are only a small part of the solubility of water in benzene, a quantity that is certainly always present in benzene that has not been dried with particular precautions. A second objection might be supplied by the question whether the electrolytes in benzene are sufficiently dissociated to put these phenomena to their account. WatLpen’s?) investigations, however, may reassure us in this respect. Equal dissociation in two solvents is attained at dilutions that are to each other as the third powers of the dielectricity constants, i.e. for the relation bezene- water 4,7 > 10*. Hence the succession of the strengths is the same in two solvents. If now according to WarpeN the « is calculated for HCI in benzene, conc. 1 mMol per litre, taking into account that the constant from Osrwaip’s law of dilution varies proportional to the concentration of the undissociated molecules, the value e—0,32 is found. Here there is, therefore, a considerable ionisation. With a weak acid, as benzoic acid, the dissociation is, indeed, more greatly lowered by benzene than in the case that the substance is dissolved in water, but in the concentrations in question here, it is yet not less than */,,, of that in water. There is, however, a striking difference between the electro-viscous phenomena in water and those in benzene. In water the curves for cations of equal valency coincide, but this is not the case for our curves, though they all have the H-ion as discharging ion (with the exception of HgCl,). It makes the impression that the real H-ion concentration plays a part: for the anorganic acids discharge in the order of their strength. The two organic acids are, indeed, stronger than H,S, but organic anions always counteract the discharge through their greater absorbability, the aromatic ion more strongly than the aliphatic one, thus compensating its greater strength. The exceedingly *) Still unpublished; compare however for casein W. Pautt, Kolloidchemie der Eiweisskörper, 81 et seq. (Dresden-Leipzig 1920) and for amylum M. Samec Koll. Beih. 4, 132 (1913), 5, 141 (1914) ete. *) P. Warpen, Z. physik. Chem. 94, 363 (1920). 48 weakly ionized HgCl, has accordingly the smallest discharging power. 5. In conclusion we wish to draw attention to a consequence of the stated electro-viscous character of part’ of the viscosity in the rubbersol. It has often been tried to compare the quality of different samples of rubber by measuring the viscosity of benzene solutions of the same concentration. The choice of this property for a com- parison is not unlogical, as in the first instance the viscosity may be considered as a measure for the solvation, and this can be taken into account as a real colloid characteristic. Experience now actually teaches that there exists a certain correlation between the viscosity of the sol and the mechanie properties which determine the quality ; it is, however, no more than a vague correlation. It has, however, appeared above, that part of the viscosity is „of in connection with the solvation, but is of electric origin, and has, therefore, a perfectly casual character, dependent on the soluble components which accom- pany the rubber and which have no influence on the mechanic properties in these minimum concentrations. If it is, therefore, desired to detect a functional relation between viscosity and the properties of the quality of the rubber, it will be necessary to eliminate before- hand the electro-viscous effect by judicious addition of the electrolyte. We consider the knowledge of these electro-viscous phenomena of importance from the standpoint of pure colloid chemistry, because they open a way to the study of the electric relations in non- aqueous sols. Utrecht, van ’r Horr-laboratory, 1922. Physics. — ‘‘/sotherms of di-atomic substances and their binary mietures. XX. The critical curve of oaygen-nitrogen mixtures, the critical phenomena and some isotherms of two mixtures with 50°/, and 75°/, by volume of oxygen in the neighbourhood of the critical pomt.” By J. P. Kuenen t, T. Verscnorre and A. Tu. van Urk. Communication No. 161 from the Physical Laboratory at Leiden. (Dr. KaAMERLINGH Onnes, holding his deeply regretted friend in affectionate memory, is glad to perform the honourable task of presenting for the Proceedings a paper by the late Dr. Kurenen which was made almost ready for the press), (Communicated at the meeting of November 25th, 1922). $1. /ntroduction. This work is a continuation of that of KurNeN and Crark’), the investigations, however, being carried out in such a way as to allow of the construction of complete isotherms, which involved a slight modification of the apparatus then used. The mixtures on which measurements were made, contained respectively 50°/, and 75 °/, by volume of oxygen, and it was found that these gave sufficient data for the construction of the eritical curve. This was found to be almost a straight line, while both eritical constants proved to be an almost linear function of the composition. $2, Preparation of the mixtures. A simple mixing apparatus was employed, consisting essentially of a measuring-bulb of about a litre capacity, surrounded by a water-jacket and connected with an open manometer tube, in which the gases to be mixed were measured, and of a mixing bulb of some 2 litres capacity. Through 3-way taps the bulbs could be put in connection with each other, the source of gas, the piezometer to be filled, and a vacuum pump, as might be desired. In measuring the relative quantities of the gases to be mixed, the mercury was 1) J. P. Kuenen and A. L. Crark. These Proc. XIX (2) pg. 1088. (Febr. 1917.) Leiden Comm. N°. 1505. 4 Proceedings Royal Acad. Amsterdam. Vol. XXVI. 50 always brought to a mark on the stem below the measuring-bulb, when the pressure-difference was read with a cathetometer, allowing for the height of the barometer, while the temperature of the waterjacket was observed. The oxygen was prepared from pure potassium permanganate *) and the nitrogen from solutions of sodium nitrite and ammonium chloride’). In the preparation of nitrogen the air was first driven out by carbon dioxide ; to free the nitrogen from the remaining carbon it was frozen out in liquid oxygen boiling under reduced pressure, before being used. The first part of the evaporating nitrogen was pumped off, and the next part used to fill the apparatus; the residue was also removed. § 3. Apparatus. a. Piezometer. The usual type of piezometer used in the laboratory at Leiden was employed. The volume of the large reservoir was some 500 cm’. and that of the small reservoir about 1 em*. The form of the latter differed from that used in Comm. N°. 1506 as an other method of stirring was adopted, to avoid the difficulties mentioned there. It consisted of a capillary about 50 em. long C, with a bore of +0.2 mm., and a cylindrical bulb Z, about 10 em. long, which was carefully rounded at the lower end, so that the stirrer 7 con- tained within (a short length of iron wire enclosed in a glass tube) could reach the extreme end, thus avoiding any dead space. The bulb R was graduated; and, as its section and the volume of the stirrer were known by previous calibration, it was possible to estimate the volume of any liquid formed in it. The reservoir was calibrated as a whole after its construction had been completely finished. b. Manometer. Pressures were read on the closed hydrogen manometer M. 60*). For the arrangement of the pressure connections and of the piezo- meter, reference may be made to Comm. N°. 97a. (Plate I.) c. Cryostat. The cryostat contained, besides the small reservoir A two platinum resistance thermometers W for reading the temperature, a stirrer B for the cryostat liquid (in this case ethylene), and the usual auxiliary 1) H. Kamertingh Onnes, GC. Dorsman and G. Horst. Proc. XVII (2) pg. 950. (Dec. 1904). Leiden. Comm. N°. 145b. 2) These Proc. [X p. 754 (Dec. 1906). Leiden Comm. N°. 97a. . 51 capillary H, a simple helium thermometer’) for ascertaining the Fig. 1. mean temperature of the portion of the small reservoir capillary within the eryo- stat, but above the liquid, as well as the necessary tubes for the introduction and removal of the ethylene. The connections, required for the reg- ulation of the pressure within the cryo- stat may be seen in Plate I of Comm. N°-97a, The method of stirring the gaseous and liquid phases within the small reser- voir bulb was as follows: round the bulb was fitted a soft iron sheath, which could be moved vertically up and down by means of an electro-magnet # above the cryostat, in the same way as the liquid stirrer is worked.*) In the lowest position of the sheath m (which is of about the same length as the reservoir R, and about three times as long as the stirrer), the lower edge was at the level of the bottom of the bulb A: in the highest position of mm its lower edge was raised to fully two thirds of the height of the bulb A. In order to be able to obtain a clear view of the whole length of the bulb A, two slits were cut out of opposite sides of the sheath m, and the latter so arranged that these slits were in line with the clear strips in the silver surfaces of the vacuum-glasses. Round the outer glass a ring electro-magnet m was placed with the bottom surfaces slightly above the level of the top of the bulb £. By a correct adjustment of the current circulating through this and the weight of the iron sheath m, it was possible to raise and lower the latter, which carried the small stirrer 7 with 1) These Proc. IX pg. 754. (Dec. 1906). Leiden Comm. N°. 97a. 2) These Proc. XX (2) pg. 991 (June 1917). Leiden Comm. No, 152a (§ 3). 4* 52 it, so that the gas and liquid phases in the bulb could be stirred as required. *) § 4. Observations and precautions. Before commencing the work at low temperatures, isotherms were experimentally determined for the two mixtures at 20°, the calcu- lations being carried out on the lines of Comm. N°. 78. The values of the expansion coefficients for the mixtures het CS 20 samara ler Ai required in the caleulation of the isotherms were interpolated as ~ linear functions of the composition from the corresponding values of the pure gases, the error involved being negligible. These values were, in the case of oxygen, those found by KAMERLINGH ONNBs and HynpMan?) and, in the case of nitrogen, calculated from isotherms determined at O° and 20° by one of us, which are not yet published. These normal temperature isotherms were determined with small reservoirs += 5 em? volume. For greater certainty a second series of points were determined for the 75°/, oxygen mixture using the small reservoir of + 1 cem* of the piezometer used in the critical zone as a leak occurred during the first series, and consequently only the normal volume determined at the end could be used in the calculations. The agreement of this control is satisfactory. Isotherms were made over a range starting about 5 degrees above the temperature of the critical point of contact, and extending as low as the proportions of the piezometer allowed, i.e., 6 degrees below that temperature for the 50°/, mixture, and 2} degrees for the 75°/, mixture. The temperature intervals were in general some 2 degrees, but, in the neighbourhood of the zone, were reduced to ‘/,, degree or less. All observations were made with rising pressure, the importance of which fact is insisted on in Comm. 1505; and, after finishing any series, the pressure is completely released, and gas in the piezometer well mixed by successively raising the pressure to 10 atmospheres or so and lowering, before proceeding to a new series. When only one phase was present, the pressure steps were of the order 2—3 atmospheres, but, when two were present, and near the critical zone, they were reduced to a few tenths of an atmosphere and sometimes the raising was accomplished by even 1) A. van Erpik. Amsterdam Akad. Versl. Mei—Juni 1897. Leiden Comm. NO. 39. 4) These Proc. IV pg. 761. (Maart 1902). Leiden Comm. N°. 78. 53 smaller steps. As soon as two plases are present, the equilibrium becomes extremely sensitive to the smallest change in pressure or temperature, and therefore the quantities that determine the condi- tions of equilibrium must be kept as constant as possible. In the critical zone, an alteration of a hundredth of a degree in the tempe- rature will cause the mercury in the stem of the piezometer to rise or fall by millimeters. Although the end-points of condensation could be fairly accurately observed, provided the pressure-increases were made with extreme care the tendency of the liquid phase to remain out, despite vigorous stirring, did not allow of accurate observation 4.25 Vara 0,75 gy th , 0,00 90020 of the beginning-point. Both points were accordingly graphically taken from the isotherms by finding the intersection of the one- phase and two-phase portions of the latter. Even in this way only very approximate results can be obtained in the critical zone. The critical phenomena were well observed, both as regards the typical opalescence at and near the plait-point, and the process of OL00°0 CO; O5 SLO Fig. 3. 55 retrograde condensation, although the latter was limited to a range of 0.13 degree at most. As an illustration of the perfection to which the regulation of pressure and temperature has been brought in the Leiden Laboratory, the 50°/, mixture was maintained under the plait-point conditions tor over an hour, the blue opalescence being continually there, while an indefinite meniscus alternately appeared and disappeared in the middle of the bulb on stirring. From the results a p, v4 graph for each mixture is constructed, and the points of beginning and end condensation determined as previously stated: the border curve is drawn through these. It was found that the two-phase line during the period of observation is to all intents and purposes a straight line, although, in the case of the 50°/, mixture, the first points determined after condensation lie below this line on every isotherm. This can hardly be explained by any delay in the appea- rance of the liquid phase (which would give the reverse effect), and the deviation is far greater than any error of observation. The accuracy of the pressure determination is at least 1 in 5000); that of the temperature reading within 0.02 of a degree, while the probable observation error of the volumes is not greater than 1 in 2000 when one phase was present, and 1 in 200 when two phases were present — apart from a possible constant calibration error of 1 in 500. To eliminate the last error it would have been necessary to measure a few points of the isotherm of 20° C. of hydrogen with this piezometer, and to compare the results with the accurate isotherm of ScHaLKwyk. But as such accuracy was of little impor- tance in our case, this was not done. The results for the two mixtures are given below with: p — pressure in atmospheres. v4 = volume, expressed in the normal volume. V‚ = volume of liquid, expressed in volume of the small reservoir. 6 = temperature on the provisional intern. Kelvin scale, reduced by 273.09. The condensation points, as found from the p.v4 graphs, are plotted on a p‚t (t= 6) graph; the results of Kuren and Crark being included on the same graph. (Fig. 4). The vapour pressures of pure oxygen’) and nitrogen‘) are also plotted, and the critical 1) C. A. CrommeriN and Mej. E. J. Smip. These Proc. XVIII (1) pg. 472. Leiden. Comm. Leiden. N°. 146c. 3) H. Kameruinco Onnes, C. Dorsman and G. Houst. l.c. 3) C. A. Crommenin. These Proc. XVII (2) 959 (Dec. 1914.) Leiden Comm. N°. 145d. —150 —145 —140 EE — 130 IE 120 300 200 100 —140 —135 — 130 iB —125 or Fig. t 57 carve drawn tangential to the various border curves, touching those in the plait points. By plotting 7, the volume of the liquid against v4 a series of curves are obtained which clearly show the process of retrograde condensation in the case of the 50°/, mixture’). A peculiarity of the last mixture is that all the lines in this graph go through the point Vz; = half the volume of the small reservoir, which means that the corresponding line of constant division of volume is a line of constant v4, therefore in the pv diagram it runs parallel to the p-axis’). If a d4, ¢ graph is drawn, a diameter is obtained which is rectilinear (as for a pure substance), but which is strongly curved towards the temperature axis at the extreme end, though in this zone, the position of the point as found must be necessarily rather qualitative than quantitative. The plait-point constants were found to be: 50°/, O, Mixture. 15°/, O, Mixture. (series XIV. 4.) (series [X. 5.) p 41.90 45.89 (observed) Vs 0.00358 0.00336 (from p‚v4 graph) @ —132°.66 —125°.60 (observed) The critical point of contact constants were found to be: (series IX. 4.) (series X. 3). p 41.90 45.86 (from p,v4 graph) v4 0.00404 0.00375 (from d4,t graph) 0 —132°.53 — 1125°.53 (observed) For the critical point of contact temperature it was found that, at 0.01 of a degree above it no condensation was, of course, observed, and at 0.01 below there was a momentary, but very evident con- densation. 1) J. E. VerscnarreLT. These Proc. I. pg. 288 (Dec. 1898.) Leiden Comm. N°. 45. 2) Leiden Comm. Suppl. N°. 23, p. 51. Ene. Math. Wiss. V 10. 58 Results for the mixture 50 °/, 0,—50°), N,. Isotherm of 20° C. Point. p da Pua Point. Pp da Pun 1 34.24 32.39 1.0573 fll 52.34 49.82 1.0507 2 37.55 35.56 1.0561 8 46.25 43.91 1.0533 3 41.39 39.25 1.0548 9 | 41.12 38.99 1.0546 4 46.41 | 44.07 1.0531 10 | 37.28 35.28 1.0567 5 51.88 49.37 1 0508 IN! | 34.03 | 32.17 1.0579 6 51.85 | 49.35 1.0507 | 60 0.0020 30 40 50 60 70 80 90 Va 100 Isotherms at low temperature. Point; p Va Vr 6 Point) p VA Vr 6 I. 1 | 37.12 | 0.01080 —120°.76 |IV. 1 | 35.41 | 0.00882 —132°.06 2 | 44.81 00793 8 2 | 37.95 749 6 3 | 54.30 533 6 3 | 40.33 615 6 4 | 41.91 495 7 d „51 | 0.00 —125°.97 36.5 00994 125 42.67 308 6 43.23 721 7 : 6 | 44.17 290 6 3 | 49.95 481 8 7 52.44 239 6 4 | 56.13 322 7 IX. 1 | 35.08 | 0.00886 —132°.51 Ill. 1 | 35.65 | 0.00907 —130°.90 2u STi 151 Ì 2 | 38.38 711 0 XV. 1 | 39.03 670 2 3 | 41.03 639 89 IX. 3 | 40.34 584 1 4 | 43.16 513 91 XV. 2 | 41.02 532 2 5 | 44.35 418 0 3 | 41.60 458 2 6 | 45.26 345 0 IX. 4 | 41.90 404 3 1 | 46.73 295 0 5 | 42.13 369 0 8 | 50.18 261 0 } XV. 4 | 42.25 347 2 5 | 42.78 303 2 IX. 6 | 43.38 285 | XV. 6 | 46.60 253 2 1 | Point Pp Va Vr 5 Point Dp: | VA Vr 6 | | | | X. 1 41.84] 0.00410 0.051 |—132°.56 | VI. 4 | 41.69, 0.00306 1.000 1329.00 | | 2 | 41.89 403} 029 | 5 V. 6 | 42.16 284 3 3 41.93 395| 000 5 | XVI. 6 |43.13| 268 1 = a= | | 1 | 45.78 251 2 XII. 1 | 41.60) 0.00436 (0.042 —132°.61 | ____ ‘bi ee XI 1 141.62 433 046 | o | XVII. 1 | 34.52 | 0.00843 —134°.50 XIE. 2 | 41.77 406 | 107 0 2|35.89| 757) 2 | | : | XI. 2 |41.85 392/ 138 | 1 3 | 37.03) 680 l XII. 3 | 41.92 379 068 0 4 | 37.60 624 (0.030 y XI. 3 | 41.95 372) 000 1 5 |87.98} 574) 054 3 XI. 4|41.97/ 373) 000 0 638.41; 478) 177 2 EET x 7 | 38.58 442| 240 2 XIII. 1 | 41.46 | 0.00455 |0.000 —132°.64 | 8 | 38.80 390| 369 2 2/41.75| 399] 151 4 | 9 | 39.01 346 | 524 2 3 | 41.89 369 | 268 4 10 (39.14 318| 653 1 4 | 41.91 366| 186 | 4 11 | 39.33 271| 916 2 5 41.91 366) 000 4 | : 2 12 |39.40) 267] 978 3 XIV. 1 | 41.40 | 0.00455 |0.026 |—132°.67 13 | 39.46 263 |1.000 2 2 | 41.61 413| 123 7 14 140.15! 256 1 3 | 41.89 362} 350 7 15 | 42.64) 242 2 4 | 41.90 358! 430 6 16 | 44.25 237 2 V. 1 | 35.12| 0.00867 —133°.01 | XVIIL 1 | 33.21 | 0.00860 —135°.98 2 |31.58 728 1] VII. 1 |34.32 790 1 3 | 39.67 594 3 | XVIII. 2 | 34.85 733 0.002 8 XVI. 1 |39.92 514 3 | VII. 2 | 35.21 692| 037 1 VI. 1 | 40.62 499 |0.031 2 3 | 35.66 584| 101 3 XVI. 2 | 40.65 527 2 | XVII. 3 |35.82} .521| 175 7 V. 4 | 40.73 482| 54 | 1 4 | 36.14 459| 255 1 VL 2 |41.03 421 | 192 | O| VIL 4/36.60) 382] 408 1 XVI. 3 | 41.08 408| 235 2 | XVIIL 5 | 36.90 302) 677 1 VI. 3 |41.29 373| 356 |—132 .99 6 37.09 262\ 877 6 V. 5 | 41.34 358| 472 |—133°.03 | VII. 5 | 37.19 246) 990 2 XVI. 4 | 41.46 336| 648 2 6 | 37.56 242 |1.000 2 5 | 41.62 310 2 | XVII. 7 | 39.77 234 7 61 Point P Va Vr 6 XIX. 1 32.02 0. 00842 0.000 - 138°.02 2 32.31 755 048 2 3 | 32.57 684 082 2 4 | 32.78 621 | 123 2 5 32.98 564 165 2 6 33.16 514 219 1 ij 33.37 457 219 2 8 | 33.54 415 349 2 9 33.65 382 414 2 KO 38) 76) 355 480 2 u 33.84 | 331 540 2 12 | 33.99 293 663 | 13 | 34.11 263 792 | 14 34,16 253 843 1 15 | 34.24 230 | 1.000 2 WANE fl 27.69 0.000 —140°.95 2 28.99 0.00585 186 5 3 29.41 452 316 9) 4 29.85 322 544 4 5 30.09 227 901 6 Results for the mixture 75 °/, O,—25°/, N. Isotherm of 20° C. Point P da Pua Point P da Tl 51.68 49,49 1.0441 Il. 1 36.91 35.08 2 45.18 43.15 1.0471 2 42.90 40.89 3 40.12 38.20 1.0503 3 48.79 46.63 4 35.91 34.14 1.0520 4 56.40 54.08 5 32.69 31.01 1.0542 6 28.89 21.34 1.0564 Pva 1.0521 1.0492 | 1.0464 1.0429 62 Ísotherms at low temperature. | Point) p VA Vr 6 Point! p VA Vi 6 I. 1 | 33.93 | 0.01206 119°.95 | Il. 7 | 50.16} 0.00426 122° .47 1 | 35.00 1151 U 8 | 52.05 327 6 2 | 37.20 1045 5 9 | 54.15 280 6 3 | 39.31 0956 5 10 | 56.41 260 6 8 |39.55| 944| 6 ere TH. 1 | 32.71 | 0.01159 —125°.00 4|42.27| 835) 5 | 2 | 35.59 1006 | 0 5 | 45.54 715 4 3 | 38.40 0869 4.99 9 | 45.88 704 6 | 4 | 41.19 137 5.01 6 | 48.66 608 4 5 | 44.28 587 1 10 | 50.64 540 U 6 | 46.04 467 1 11 | 53.36 443 8 1 | 46.83 | 359 1 12 | 55.97 355 6 | 8 | 47.51 293 1 13 | 59.13 294 7 9 | 48.73 265 1 II. 1 | 33.29 | 0.01183 —122°.47 10 | 50.60 248 2 2 | 35.82 1055 6 3 | 38.60 0926 6 4 | 41.72 193 6 5 | 45.00 661 7 6 | 48.02 535 6 63 Point p | Va Vr 6 Point Pp Va Vr 6 VL 1 42.68, 0.01149 —125°.42 | VII. 6 | 45.65 | 0.00326 | 0.631 | —125°.73 2 35.97 0973 3 7 |45.70 307 | 1.000 4 3 | 39.30 813 2 8 46.19 277 | 3 4 |42.54| 657 2 IV. 1 | 32.53] 0.01143 | —125°.96 5 | 44.89 520 1 2/35.93| 0959 6 6 | 45.67 440 2 | | 3 39.41 789 8 | 7 | 45.93 382 2 4 | 42.37 641 7 8 | 46.14 346 3 5 | 43.68 561 7 | 9 | 46.59 294 2 6 | 44.67 474 | 0.000 7 10 | 47.95 261 | 2 | | 7 | 44.75 460| 025 6 | | X. 1 |45.89|0.00369 | 0.041 |—125°.53 8 | 44.91 415 | 142 6 | | | 2 | 45.90 345| 53 3 9 |45.15 361| 368 | 6 | 3 | 45.86 315 | 000 3 10 | 45.43 297} 901 6 11 (45.51) — 287| 1.000 6 IX. 1 45.49 0.00419 | 0.000 —125°.60 | x p 12 | 46.11 267 6 2 45.72 366| 236 0 | | 13 |48.83| 248 6 3 |45.81 347 = 0 4 | 45.85 333| 648 | 59 V. 1 |32.74| 0.01076 —127°.99 5 | 45.89 386 | 1.000, 60 2 (35.41| 0926 8.00 3 |38.10| _ 785 0 VIII 44. 89 | 0.00394 — 1250. | Hel | 250 4 | 40.19 663 0 2 | 45.36 433 | 0.000 4 5 | 40.89 609 | 0.000 7.99 3 | 45.46 408| 78 4 6 | 40.95 592| 020 9 4 | 45.59 378 3 i 7 | 41.14 529| 090 9 5 | 45.75 343| 455 4 8 | 41.38 462| 186 9 | 6 | 45.80 328| 682 4 9 | 41.55 409| 289 9 | 7 | 45.83 321 | 1.000 5 | 10 | 41.70 371| 389 8.00 VI. 1 | 44.43/0.00523) = |—125°.75 gh dg |e rl il lata es 3 12 | 42.04 288| 709 7.98 ENE Med A 13 | 42.19 244| 994 | 9 A eter zer en 2 14 | 42.28 242 1.000 9 EE Sl er 7 15 | 43.17 236 | 8.00 64 0.0020 40 60 80 100 Va In conclusion it is our pleasant duty to thank Miss H. VAN DER Horst and Mr. J. D. A. Boks for their careful regulation of the temperature, and Mr. L. Ovwerker« and Mr. C. F. L. KRAANEVELD for the technical skill with which they helped us during the whole course of the measurements. Anatomy. — “Contributions to the knowledge of the brain of bony fishes.’ By Prof. Kyozo Kupo, Mukden (Manchuria). (Com- municated by Dr. C. U. Ariëns Kappers). (Communicated at the meeting of January 27, 1923). L The Tr. olfactorio-opticus. Nits HOLMGREN found in Osmerus eperlanus with the CaJar-method, but also with methylene-blue colouring, a bundle which, long before the middle of the telencephalon, separates from the tr. olfactorius lateralis, then, following the suleus externus, extends as far as the opticus, into which it enters, and can be traced (in the opticus) for some distance towards the eye. He called the bundle tr. o/factorius lat. optict (op. cit p. 188). With Callionymus lyra he found a ‘similar bundle, but lying in the medial olfactory tract (l.c., p. 188, Anmerkung). 3 This discovery should be considered most remarkable. Being able to test and confirm the latter case (the fibres in the tr. olfactorius med.) with various Teleosts also by Weieert-preparations, I will deseribe it here more fully. With the WereerT-colouring these fibres, connecting the tr. olfacto- rius with the tr. opticus, seem fairly coarse; they are nearly always scattered and mixed only with the tr. olfactorius medialis, never with tr. olfactorius lateralis. In the bony fishes, which I examined they run always the same way. As these relations are the most distinet in Ammodytes tobianus, I take this fish as example. With this fish the tr. olfactorius med. consists of two sorts of medullary fibres, a thin one and a much coarser one. The fibres divide into three parts The pars dorsalis is that part of the tr. olfactorius med. that on a quite frontal level turns towards dorsal. It consists for the greater part of thin fibres that radiate in dorso-lateral direction and disappear rather soon, already on the level of commissura anterior. A few coarse fibres, however, also belonging to this portion, run further caudad, always following laterally the tr. olfacto-hypothalamicus med., but strongly contrasting with these by their coarseness. They cannot be traced accurately from the place where they medially 5 Proceedings Royal Acad. Amsterdam. Vol. XXVI. 66 pass the fibrae ansulatae of BrLionct, caudo-ventrally descending by and by with the accompanying tractus olf.-hypothal. med. These fibres form the dorsal group of the coarse olfactory fibres. The pars intermedia of the tr. olfact. med. consists half of the thinner, and half of the coarser fibres. The first form a small bundle and cross in the commissura anterior (the so-called comm. interbulbaris). The pars ventralis is formed by coarse fibres exclusively. They at first join to a bundle, but gradually they separate into several small bundles. These, together with the fibres from the pars intermedia form the ventral group of the coarse olfactory fibres. The bundles soon arrange in regular order dorso-ventrally in the praethalamus, thereby dorsally touching the tr. olfacto-hypothalamicus med., ven- trally the tr. opticus, into which they are taken up gradually (fig. 1). A few fibres that are in an exceptional dorsal position, enter into the just rising commissura minor. Epiphysis Parencephalon Tr. olf-hypoth. med. with the dors. group of the fibres in question. Telencephalon | A AA IN 34 AEN z\ Ventr. group (5 Ee AP, A) of the fibres {* 3} in question. Z| Br A Br. tecti ant. Tr. strio- Ca thal. : Br. tecti geniculatum ant. lat. genicula- tum lat. Sy Sy £ . A a s 5, J P t 1 cus\ Nucl. praeopt. SS Ke pars R magnocell. Fig. 1. Ammodytus tobianus. (Preparation of the Central Institute for Brain-rescarch, Amsterdam). With other bony fishes the course of these coarse olfactory fibres is nearly the same. Only the relation to the commissura minor (and to the fasciculus medialis n. optici) does not always exist, this being most distinct, besides in Ammodytes, with Rhombus, Hippocampus and Morone. I have been able to find these fibres with Catostomi, Percesoces, 67 Acanthopterygii and Plectognathi, but not with Malacopterygii, Osta- riophysi, Symbranchii and Haplomi. They probably are neither to be found with Anacanthini and Pediculati (at least not medullated). The quantity of the fibres varies according to the kind of fishes. It often is so small that the fibres can be easily counted. In any case the fibres are generally not very numerous. The ventral group is always superior in number to the dorsal, which I even cannot find in Solea and Cottus. With Callionymus lyra, the very bony fish that HonMeren examined, the matter is somewhat different. Inasfar as it may be judged by Wercert-Paw series these fishes show no tr. olfactorius lat. The tr. olfactorius med. is fairly coarse and is found as usual on the medio-ventral side of the frontal half of the brain. Caudally it soon descends a little ventrally already before the level of the commissura minor, and comes in touch with the opticus fibres and especially with those that arrive here from lateral. | think it fairly probable that fibres are being exchanged between these two tracts, that is to say that tr. olfactorius gives away a part of its fibres to the tr. opticus, but in exchange receives more fibres from the latter tract during its deseension (see below) and so becomes visibly coarser. The fibre tract now runs medially along the dorsal opticus root in a ventral direction.') More frontal a small part of the tr. olfactorius is separated from the chief bundle on the spot where this tract begins to descend in order to come into touch with the tr. opticus. This separated little bundle runs independently in the praethalamus also ventrad, about in the middle of the inner and outer surface of same, and finally joins again the principal bundle. *) When the thus formed olfacto-optie bundle has at last left the tr. opticus, it runs lateral, viz. between the tr. strio-thalamicus med. and the nucl. anterior thalami?*). More caudally it wedges between the nucl. praerotundus?*) and the tr. tubero-dorsalis of Gorpsrein. A little way back nerve cells begin to appear in the bundle and finally take up the area of the bundie nearly entirely. This nucleus takes its place quite superficially of the lateral surface of the hypo- thalamus, close above the lobus inferior (see fig. 87 of HoLMGREN’s 1) The formation of the very extensive tectum plate and accordingly the topo- graphy of the opticus roots are in this bony fish different from others. f) So with Callionymus nearly all medullary olfactory fibres seem to run as far as into the praethalamus. 5) I have not yet succeeded in identifying these nuclei free from objection with this fish. 5* 68 work, showing the nucleus in question, medial of “tr. olf. tect. sem”). The cells of this nucleus are small, From this nucleus proceeds a new fibre tract, running in*a curve in the torus semicireularis, parallel to and inward of the tr. isthmo- tectalis mihi (see below), yet it seems to end in the torus itself. That besides this, fibres should come from the said tract in the path of the tr. tecto-bulbaris or tr. tecto-isthmicus into the tectum, as HorMGREN seems to presume, is improbable to me’). As to the origin and the end of my coarse olfactory fibres, | am quite unable yet to say anything definite. That frontally they are connected with the bulbus olfactorius is undoubtedly sure, but their caudal destination remains quite uncertain. HolMGrEN seems to hold the opinion that his tr. olfactorius lat. optiei runs centrifugally in the optieus (le, p. 188). | myself am more inelined to believe that the fibres of the ventral group tend through the path of the commissura transversa towards the tectum or, less probable, towards the nuel. praerotundus of the other side, the spot where they penetrate into the optieus root just corresponding with the most frontal level of this commissure. This, however, is a mere supposition. It is harder still to say anything of the dorsal group of my fibres. Concerning the curious olfacto-optie bundle in Callionymus, it ean only be said that the part of tr. olfactorius med., that enters frontally into the opticus, corresponds fairly certainly with the ventral group of my fibres. But about the other part of the tract, the associating opticus fibres, the peculiar nucleus and the bundle originating from it, L cannot give an opinion, as — till now — I have not seen anything similar with the other bony fishes. Summarizing we find in the brain of the Teleosts a remarkable fibre system, connecting -the tr. olfactorius with the tr. opticus, consisting in the more primitive forms (Osmerus eperlanus) of thin fibres (that can only be exposed by the impregnation method) running in the tr. olfactorius lat, whereas in the more highly organised forms it has coarse, medullary fibres as components and is mixed between the fibres of the tr. olfactorius med. At the present I must be content with confirming HormGreN’s finding, leaving the arising questions to later investigations. Il. The Tr. tecto-praerotundus. I think [ have discovered in the brain of bony fishes a medul- 1) Hotmaren, namely in fig. 87 of his work, has indicated this newly forming fibre tract as „tr. olfacto-tectalis et semicircularis”, without further referring to it in the text. 69 lary fibre tract, not yet described as far as [ know, which probably connects the tectum with the nucleus praerotundus. This tract appears in transverse sections on the level where the fasciculus medialis nervi optici, swinging across the tr. strio-thalamieus, joins the lateral optieus root. It there appears as a bundle, running dorso-ventrally, medially along the dorsal optieus root. Dorsally it lies in separate bundles between the just-mentioned opticus root and those fibres that branch off (more frontally) from the tr. opticus, run dorsad in the post-habenular region and finally lateral into the deep medullary layer tectum. From these fibres (probably corresponding to the fibrae teetales n. optici of Krause) the tract is distinguished by the smaller caliber of its fibres and its steeper course. Somewhat more caudally it bends in a lateral direction and enters also into the deep medullary layer of the teetum. Ventrally it crosses with the fasciculus med. n. optici directly medially to the praetectal nucleus, then runs laterally down from the tr. strio-thalamicus, to finally join the fibres of the commissura transversa (see fig. 2). ‘ Often, however, it does not run laterally to the tr. strio-thalamicus but medially, together with the fasciculus med. n. optici towards medioventral, consequently in this case delusive of a commissura minor in the sense of Ariins Kappers (one-sided in a specimen of Nucl. / 1e tecto- praerot. mihi Br. tectí post. Br. tecti post. Comm. minor on : Comm. transv Tr. strio-thal. a ——— x Tr. tecto-praerot. mihi Comm. HERRICK ° A 5 Fasc. med. n. opt. ge Sn A (Comm. HERRICK failing here) Fig. 2. Mugil chelo. (Preparation of the Gentral Institute for Brain-research, Amsterdam). 70 Gasterosteus (see fig. 3), double-sided in a specimen each of Belone and Exocoetes). However, I want to consider this course as aberrating, for in another specimen of Gasterosteus and also of Exocoetus it runs laterally to the tr. strio-thalamicus, as with the other Teleosts. gangl. haben. { Fibrae tect. n. opt. Tr. tecto- ~~ praerot. mihi nd Nucl. praetect. Tr. tecto-praerot. mihi for- ming a part of the Comm. HERRICK Comm. HERRICK Fig. 3. Gasterosteus aculeatus. (Preparation of the Central Institute for Brain-research, Amsterdam). Ventrally it mixes, as mentioned, among the fibres of the com- missura transversa, in two ways. One time it runs nearly horizont- ally towards medial as the most caudal part of this commissure, close to the ventral periphery of the midbrain. Here it soon cannot be traced any further among the commissure fibres. Yet it seems plausible to me that here it crosses the medial line. This I find with Trutta, Syngnathus?*), Ammodytes?'), Mugil, Ophiocephalus, Morone, Osphremenus, Pleuronectes platessa?*), Rhombus, Hippo- glossus?*), Solea?)’), Cyelopterus, Agonus?*), Trachinus and Tetrodon. Another time it forms the most dorsal part of the commissura transversa and crosses directly under the ventricle. I was able to ascertain this course, besides in the cases where it is delusive of the commissura minor (Gasterosteus, Belone and Exocoetus), with }) The question-marks denote that with these Teleosts I do not find the matter quite clear. 71 Clupea??) and Pleuronectes limanda. Also with Gadidae this tract can easily be traced from the subventricular crossing as far as the deep medullary layer of the tectum. Franz has erroneously indicated this bundle in Gadus, in fig. 6 of his work, as “fibrae tect. n. opt.” The correctness of my observ- ation, however, can be tested not only in Gadus itself, but very easily in Lota and Motella. In fig. 24 of the same work Franz has called the same tract correctly “ascending decuss. transversa’” (the upper line of his reference, at the bottom, left hand). Although the exact way of origin and termination of this bundle is not yet clear to me, I should like to call it provisionally tr. tecto-praerotundus and introduce it under this name. Ill. Vr. isthmo-praetectalis. Franz deseribes the course of his tr. isthmo-opticus as follows (op. eit, p. 414): “a tract which, together with the opticus, first appears ventrally to the midbrain roof, ascends on the inside of the midbrain roof, reaches the torus semicircularis and here curves round to the ganglion isthmi — here often difficult to distinguish from the fibres of the commissura transversa. It may be possible that part of the fibres remains already in the torus semicircularis.” He further is of opimion, supported by experiments (on which fishes?) that tbe fibre tract arises undoubtedly from cells of the ganglion isthmi and sends its neurites centrifugally into the eye (iep: 485). My investigation confirms the presence of such a bundle and its caudal course, as described by Franz. I only want to remark that IT could not find this bundle with all bony fishes. A few fishes, such as Salmonids, Siluroids, Misgurnus, Sy mbranchidae, Esox, Ammo- dytes?*), Gadidae, Lophius?') and Tetrodontidae?’) seem not to possess such a fibre tract. Its further frontal course, however, is not as supposed by Franz, but different according to the Teleosts examined. Franz seems to be right, in so far as the bundle, after its character- istie curve in the torus semicircularis, gathers its fibres at the lateral basal ridge of the midbrain, then by bundles enters into the lateral opticus root and disappears from examination under the fibres of the latter, as is the case with Megalops (with all)*), Gastero- 1) The question-marks indicate here that the matter concerned is not quite clear in these fishes. 2) The brackets refer to the quantity of fibres, entering into the opticus root. 72 steids (few)*), Seombresocids (part)*), Mugil (the greater part) ’), Ophiocephalus (the greater part)®), Morone (greater part)’), Osphro- menus (part)®), Cottids?'), Cyclopterus?)*), Agonus?)') and Trachinus (with the smaller part of the fibres) *). On the other hand there are bony fishes in which the bundle in question can be distinctly followed as far as the frontal tectum section, as Clupea, Cyprinidae, Syngnathidae, Osphromenus, Pleuro- nectidae (Solea excepted) and Callionymus. I therefore will give here a minute description of the course of this fibre tract in some specimens of fishes. Just with Pleuronectes, where Franz believed to have his tr. isthmo- opticus fully established, we can clearly prove that the bundle in question actually enters frontally into the tectum, in the most super- ficial medullary fibre layer of it. The small bundles namely gather on the lateral surface of the midbrain to a roundish bundle that protrudes into the optic ventricle and then takes a wholly sagittal course. (see fig. 6 of Hippoglossoides). At first it runs ventrally to the bundles of tr. tecto-bulbaris and directly dorsal of the ventral point of the tectum plate. Some way more frontal it takes the shape of a curved medullary plate and encircles about half of the nucl. praetectalis from the lateral side. During this course its position corresponds to the bottom of the tectal furrow characteristic of this fish and, situated caudally deep inside, it frontally more and more approaches the outer surface; at last, quite frontal on the level of the geniculatum, it comes close under the molecular layer*) of the tectum. Till there it never touches the opticus root. Now part of the bundle radiates caudo-laterally of the geniculatum, towards medio- dorsal into the dorsal part of the tectum‘), whereas the other part runs further frontad and finally enters latero-ventrally into con- nection with the ventral part*) of the tectum, which extends a little further frontad than the dorsal one. At this radiation of the bundle I could quite clearly distinguish its small bundles from those of the brachium tecti (Karpers) and the optic root, and prove that the most superficial narrow layer of the so-called opticus fibre layer of the tectum consists of the little bundles of the fibre tract in question and the next much broader layer of medullary fibres (of the opticus 1) See note 1 p. 71. 2) See note 2 p. 71 8) This designation has its explanation in the above-mentioned treatise „On the torus longitudinalis etc”. 4) The frontal part of the tectum plate is divided into two parts by the afore- mentioned furrow. 73 fibre layer), separated from the first by a strand of grey substance, consists of the small bundles of the brachium tecti and the tr. opticus (see fig. 4). Also with Clupea, examined likewise by Franz and drawn by him in fig. 9 of his treatise, I could trace the fibre tract as one or two coarsefibred bundles above and partly through the lateral opticus root, lateral of the praetectal nucleus and the geniculatum, as far as in the upper fibre layer of the most frontal teetum (fig. 5). With the Cyprinidae its course is about the same as with Clupea. The small bundles gather medio-dorsally to the lateral root in one or two bundles, then run frontad, at first between the nucl. prae- tectalis and the lateral opticus root, then between the nucl. anterior thalami and the ganglion geniculatum. Here a part of the fibres branches off into the tectum, but the remainder runs, dorsally tothe geniculatum, further frontad, then turns medio-dorsad and finally also reaches the tectum. By the way I want to remark that with these Teleosts (Pleuro- nectids, Clupea and Cyprinids) the bundle in question is accompanied in its entire frontal course by the tr. geniculo-myelencephalicus of HOLMGREN. The two bundles, however, can easily be distinguished, the fibres of the first bundle being far coarser than those of the latter. With Osphromenus the bundle shows a peculiarity. Part of its fibres enter, as mentioned above, already caudally into the lateral opticus root. Here again I expected to be able to trace the small bundles through the complex of the opticus fibres right into the upper fibre layer of the tectum. The other part, however, turns in the subependymal layer gradually medio-dorsad, above the comm. horizontalis fibre group‘), and finally enters into the fibre system of the most medio-frontal tectum part. Therefore I am fully convinced that there is no doubt but the bundle in question, that is to say what Franz ealls tr. isthmo-opticus, does not run in the opticus to the eye, as Franz presumes, but to the frontal: tectum, and there becomes part of the opticus fibre layer. Also in those cases where the fibres concerned enter already caudal into the lateral opticus root, it may be assumed that we have the same state of affairs as I have been able to prove in Osphromenus. In the following | shall call the bundle provisionally tr. isthmo- tectalis, although the direction of its course (ascending or descending) is not have proved yet. 1) Complex of commissura horizontalis and tr. tecto-cerebellaris (cf. fig. 5). 74 This tr. isthmo-tectalis mihi was traced already fairly minutely by Marser, the sharp observer. He called it “the outer (back) layer of the stratum zonale’ of the torus semicircularis; but made it originate frontal in the corpus geniculatum externum (nucl. prae- tectalis of the authors) and terminate caudally between “numerous = 2 = = S Z A En Q ~ je) = 4 = as # S oO thane ~ = \ S / ttle KN @ 2 a Nenad MND, ie) 3 eo > = Ss 3 S 3 = ey = S ae = Ss rc . ~ S = = x = 5, § thea ~ = c iz 64 : n = ur i ke) > 3 ES a z ay vs 2 SS x ne < S ES 2 =, = 2 = = cy) = =| = = = s S SS ) 2 5 SS = ~H WwW 5 = - = uy i (Preparation of the Central Institute for Brainresearch Amsterdam.) 5 Kl) = Pe KS Ain 5 2 LAA bags SN NE 5 ee) | lk 4 = = da \ = EAT 8 „ON AN Wt > LU | en KN zw = GH 3 ES Da = = So 2 Re 2» 2 sd = 8 cS 5 S 4 me io small nerve cells chiefly in the caudal and upper part of the torus” (op. cit, p. 342—343 and 348), without yet having applied to the latter a special name (ganglion isthmi). Horizontalis fibre group Tr. istmo-tect. mihi Tr. geniculo-myelenceoh. HOLMGREN. Comm. transv. Tr. thalama-lob. j Fig. 5. Clupea harengus. (Preparation of the Central Institute for Brain research, Amsterdam After Mayser no authors had occupied themselves, as far as I know, with this interesting fibre bundle, till Franz discovered it again. Through the result of this investigation the relation between the tectum opticum and the ganglion isthmi with Teleosts gets closer. The connection is twofold, one time through the tr. tecto-isth- micus of Franz, another time through the tr. isthmo-tectalis of myself, and we may presume that the first leads tectofugal, the latter tectopetal. Although Mayser’s opinion that the bundle in question originates from the corpus geniculatum externum s. |. (ie. from nuel. prae- tectalis of the authors) cannot be confirmed by me as to the Cypri- noids (s. above), yet | saw in a specimen of Exocoetus a small part of the fibres of my tr. isthmo-tectalis end in the nucl. praetectalis, the other larger part running further frontad past this nucleus. The same I have been able to find with Cyclopterus, Trachinus, with some doubt also with the Gasterosteids, Syngnathidae, Belone and Solea. As just on the spot where these fibres should enter and end 76 in the nucl. praetectalis, the brachium tecti, whose fibres are as coarse as the others, leaves this nucleus, it is quite possible that a misinterpretation can arise. All the same [ can maintain this point as being quite certain, at least with Exocoetus. When this is the case, these fibres correspond with those of Carois from the nuel. praetectalis, of which he writes: “Les autres (fibres)*) descendent presque verticalement de la partie inférieure du noyau prétectal, se recourbent ensuite en arriere et se dirigent vers la région basale du méseneéphale” (op. cit, p. 97). But when he supposes “qu’elles doivent servir a établir des connexions entre le thalamus et la moelle spinale” (lc. p. 97—98), this remains a mere supposition, for according to my investigations we can say for certain that they are connected with in the ganglion isthmi and consequently form a @. isthmo-praetectalis, *) (or praetecto-isthmicus). IV. Pars praetectalis Comm. posterioris. The component part of the so-called “stratum zonale” of the torus semicireularis, (for convenience’ sake | here use this long abandoned nomenclature) is not at all exhausted with the above tr. isthmo- teetalis mihi and the commissura transversa. With most bony fishes there is namely a fibre connection between this stratum and the commissura posterior. One bundle from about the middle of this commissure runs latero-ventrally and at the same time frontad, joins the tr. isthmo-teetalis in the most caudal level of the nucl. praetectalis (fig. 6) or, if this is missing, directly the commissura transversa and then joins in the characteristic curved course of the torus semicireularis. To the first category, where there is a tr. isthmo- tectalis, belong the Gasterosteids, Belone, Mugil, Ophiocephalus, Morone, Osphromenus, Pleuronectids, Gobius, Cottus, Cyelopterus, Agonus, Trachinus and Callionymus, to the latter, where the tr. isthmo-tectalis is not present, belong Symbranchidae?, Esox, Ammo- dytes, Gadids, Solea, Lophius and Tetrodontidae. The fibres of the latter bundle are thinner than those of the tr. isthmo-tectalis. On the other hand there are fishes that have no such connection, e.g. Megalops?, Clupea, Cyprinoids, Syngnathidae, Exocoetus and Zoarces?. This bundle differs from the other components of the commissura posterior by its finer fibres and mostly also by its compactness. As to its position it is about in the middle of the commissure, in sagittal 1) Bracketed by myself. 2) Cf. also HormereN’s drawings of Callionymus: fig. 87, 88 and 89: Tr. ist praet. di as well as in dorso-ventral direction. In Weicrrt-preparations it often has a greyish colour, which makes me suppose that it consists of medullary as well as unmedullated fibres. Horizontalis fibre group Lam. comm, tecti Nucl. cort. Frivscu thin fibres ) fi comm.post. coar. sefibri EN Tr. isthmo- tect. mihi Comm. horiz. (pars inf.) Nucl. rot. Tr. parolf.-bulb. FRANZ Fig. 6. Hippoglossoides platessoides. (Preparation of Prof. RorHte’s Collection, Berlin.) Ariens Kappers in his work on Ganoids (op. cit., p. 475) has expressed the supposition that the middle part of the commissura posterior partly enters into a connection with the geniculatum (i.e. thé nuel. praet-ectalis of the authors), partly passes over this nucleus, bends backwards and ends in the tegmental region, just under the torus semicircularis. Also in his treatise on the brain of Chimaera (p. 158) and of late in his manual (p. 818) he considers it as highly probable that this “lateral part” of the commissura posterior originates in the geniculatum (i.e. in the nuel. praetectalis) of the one side and extends caudad on the other side (extremely clear with Pleuro- nectidae, as he emphasizes). HormereN calls the relative part of the commissura posterior after Epincer commissura praetectalis, but is also of opinion that it is “not excluded that praetectalis fibres, that were traced till in the 78 commissura posterior, may go on the other side to an other final station than in the nucleus praetectalis” (op. cit., p. 262). In my opinion one of the two formations is to be considered as the caudal destination of this bundle, viz. the torus semicireularis or the ganglion isthmi, tbe first with greater probability than the latter. About its frontal extremity I cannot express an opinion for the present, although the nucl. praetectalis of the other side seems to be the most probable. In any case further investigations on this point are most desirable. It is difficult yet to say anything about the relation of the bundle concerned, to the commissura praetectalis (or pars praetectalis of the commissura posterior) of Epincur. However, I have been able to state with a specimen of Leuciseus rutilis that, although with no other of the Cyprinoids which I examined, | could prove a well- marked fibre connection between the commissura posterior and the tr. isthmo-tectalis mihi or even the “stratum zonale” of the torus semicirculavis, with the said fish there existed a well characterized, closed commissura bundle between the nuclei praetectales of both sides. LITERATURE. ARIËNs Kappers, C. U., Untersuchungen über das Gehirn von Amia calva und Lepidosteus osseus. Abhandl. d. Senckenberg. Naturforsch. Gesellsch., Bd. 30, 1907. DERSELBE, Die vergl. Anatomie des Nervensystems der Wirbeltiere und des Men- schen. 2 Bde. Haarlem 1920/1921. Arréns KaPPers, C. U., und CARPENTER, F. W., Das Gehirn von Chimaera mon- strosa. Folia neurobiol., Bd. 5, 1911. Cators, E., Recherches sur |’histologie et l'anatomie microscopique de |’encéphale chez les poissons. Bull. scient. de la France et de la Belgique, tome 36. 1901. Franz, V., Beiträge zur Kenntnis des Mittelhirns und Zwischenhirns der Knochen- fische. Folia neurobiol., Bd. 6. 1912. GorpsrteiN, K., Untersuchungen über das Vorderhirn und Zwischenhirn einiger Knochenfische usw. Arch. f. mikroskop. Anat., Bd. 66, 1905. HOLMGREN, N., Zur Anatomie und Histologie des Vorder- und Zwischenhirns der Knochenfische. Acta zooi,, 1920. Krause, K., Experim. Untersuchungen über die Sehbahnen des Goldkarpfens. Arch. f. mikroskop. Anat., Bd. 51, 1898. Kyozo Kupo, Uber den Torus longitudinalis der Knochenfische. Anat. Anzeiger; Bud. 56, 1923. Mayser, P., Vergl. anat. Studien über das Gehirn der Knochenfische usw. Zeitschr. f. wiss. Zool., Bd. 36, 1881. ; Chemistry. — ‘“n.«-Su/fobutyric acid and its optically active com- ponents”. By Prof. H. J. Backerand J. H. pr Borr. (Communi- eated by Prof. F. M. Jagerr). (Communicated at the meeting of January 27, 1928). After it had been shown that e-sulphopropionie acid can be separated into its optically active components *), we tried to effect this resolution also for norm. e-sulphobutyrie acid. At the same time the occasion was taken to study this acid, which has been known already since 1875, but hitherto had not been obtained in a pure crystallised state. The acid is formed by direct suiphonation of n.e-butyrie acid or of butyric anhydride *). Just as in the case of the propionic acid, the sulphonic acid group is attached to the a-carbon atom, as proved by its relation to «- bromobutyric acid, of which the structure is fixed. HeEMILIAN caused the ester of this acid to react with ammonium- sulphite and we have applied this reaction to the free «-bromo- butyric acid; in both cases the same sulphobutyric acid was formed as by direct sulphonation. We also obtained the sulphobutyrie acid in a good yield (70 °/,) from ethylmalonic acid, which by sulphonation loses one molecule of carbon dioxyde. Besides, this formation may serve as an argument for the structure, the active hydrogen atom of the ethylmalonic acid having the greatest chance of being substituted by the sulphonic acid group. As a method of preparation we used the sulphonation of the carefully fractionated n. butyric acid with sulphur trioxyde. In the cold butyrylsulphurie acid is formed, which on heating passes into sulphobutyrie acid: C,H, .CH, CO, .SO,H > C,H, . CH (SO,H) . CO,H. The acid was separated in the form of its barium salt, which was purified by crystallisation, and from which sulphurie acid liberated again the organic acid. 1) FRANCHIMONT and Backer, These Proceedings 17, 653 (1914); Recueil d. trav. chim. 89, 751 (1920). 4) Hemitran, Ann. d. Chemie 176, 2 (1875). FRANCHIMONT, Recueil d. trav. chim. 7, 27 (1888). van Pesk1, Recueil 40, 736 (1921). 80 Sulphobutyrie acid was hitherto only known as a viscous liquid. We succeeded in obtaining the acid in the crystallised state by leaving a concentrated pure solution for a long time in vacuo over phosphorus pentoxide. The «-sulphobutyric acid forms colourless hard crystals. Like sulphoacetic and sulphopropionie acids it contains one molecule of water of crystallisation and is extremely hygroscopic. The melting point, determinated by the aid of a formely described apparatus‘), was found to be 660. Since sulphoacetic acid melts at 84—85° and sulphopropionie acid at 100.5°, we have here perhaps the beginning of an alternating series of melting points, as shown by the fatty acids. From sulphobutyrie acid we have prepared some salts with aromatic amines. The acid sulphobutyrate of aniline forms small glistening crystalline plates with the melting point 175°. The acid sulphobutyrate of p-toluidine, which is separated by ether from its aleoholie solution in the form of an ethergel, may be obtained as a white crystallised substance of the melting point 163°. The acid salts of p-anisidine and p-phenetidine were obtained in a crystallised state, but not pure and colourless. If these sulphobutyrates are heated with an excess of the corres- ponding amines, the carboxyl group is changed into amide through loss of water, the sulphonic acid group remaining combined with a molecule of the amine. In this way aniline formed the butyrandlide-a-sulphonie acid salt of aniline (C,H,) (CONHC,H,) CH .SO,H...NH,C,H which erystallises from water in concentrically grouped featherlike needles, occasionally 5 eM. in length, which melt at about 253°—256°. From the other above mentioned aromatic amines well crystal- lised amides were also obtained, viz. butyro-p-toluidide-a-sulfonic acid salt of p-toluidine, m.p. 260—263°, butyro-p-anisidide-e-sulfonic acid salt of p-anisidine m.p. 242°, butyro-p-phenetidide-a-sulfonic acid salt of p-phenetidine, m.p.264—266°. When heated with aromatic o-diamines, sulphobutyrie acid, just as sulphopropionic acid, loses two molecules of water and gives derivatives of benzimidazole. The sulphobutyrate of o-phenylenediamine, for instance, formed 1) Chem. Weekbl. 16, 1564 (1919). 81 on heating at 180° benzimidazole-2-propylsulphonic acid (1), whilst from the sulphobutyrate of 3,4-diaminotoluene was formed in the same way methylbenzimidazole-2-propylsulphonie acid (II). Al ~~ 1 CHO CH Gane ECHO Hier CCH & ae (1) These imidazoles were obtained as white crystalline substances. They are almost insoluble in the common solvents, have a very high melting point, and, notwithstanding the presence ofa sulphonic acid group, they do not combine with aromatic amines and they are not hygroscopic. All these properties indicate, that the sulphonic acid group forms an internal salt with the basic function of the imidazole (III) and they completely recall the properties of taurine, for which an analogous structure is assumed (LV). a SS CCH). CLA, (I CHACHA SE) Meee: HO,S $0,H. NH, With strong bases, such as baryta, these imidazolesulphonic acids give well erystallised salts. From the barium salt and copper sulphate a green solution is formed, which, however, decomposes immediately when heated and also when kept for a long time at the ordinary temperature, so that the copper salt could not be separated in a erystallised pure state. It deserves attention, that, in spite of many efforts, also no copper salt of taurine has been obtained. The resolution of racemic «-sulphobutyrie acid was attempted with the aid of strychnine, by reason of previous experience with sulphopropionic acid, and the attempt was successful. The acid strychnine salt of the d-acid is less soluble than the salt of the l-acid, just as in the case of sulphopropionic acid. After three or four erystallisations the acid strychnine salt of the d-sulphobutyrie acid is entirely free from the other component. It erystallises with two molecules of water in small glistening needles. On concentration, the first mother liquor slowly gives a crop of the acid strychnine salt of l-sulphobutyric acid, which by repeated crystallisation from alcohol is obtained in a pure state. Decomposition of the strychnine salts by baryta gives the barium salts of the active acids. These barium salts crystallise from water in long needles which contain 24 molecules of water, in contradistinction to the racemic barium salt, which separates in small glistening leaflets with two molecules of water of crystallisation. 6 Proceedings Royal Acad. Amsterdam. Vol. X XVI. 82 The direction of the rotation of the neutral barium salts is, as in the case of sulphopropionic acid, opposite to that of the free acids. The molecular rotatory power depends on the concentration; on dilution it rises a little. The barium salts, for instance, give in a 24°/, solution for sodium light a molecular rotation of 32.2° and in a 5°/, solution a rotation of 29.9°. In a 25°/, solution the presence of 10°/, of barium chloride lowers the molecular rotation to 29.3°. This indicates, that the rise of the molecular rotation on dilution may be ascribed to an increasing of the ionisation, a phenomenon, which is perhaps connected with the fact that the sign of rotation of the neutral salts is opposite to that of the free acids. The molecular rotation of the free salts for sodium light is 7.8°. The acid salts rotate the plane of polarisation in the same direction and to about the same amount as the free acids. In this respect also, the behaviour of sulphobutyrie acid is there- fore analogous to that of sulphopropionic acid. The investigation is being continued and will be published later in greater detail. Groningen. 13 Jan. 1923. Organic Chemical Laboratory of the University. Chemistry. — ‘The second dissociation constant of sulphoacetic and a-sulphopropionic acids.” By Prof. H. J. Backer. (Com- municated by Prof. F. M. JarGer). (Communicated at the meeting of January 27, 1923). The determination of the second dissociation constant of a dibasic acid H,A from the concentration of the hydrogen ions in the selution of an acid sali readily suggests itself. However, A. A. Nores*) has shown, that generally these data will not suffice. Suppose that the ionisation of the acid sodium salt (reaction I) is nearly complete, and that the concentration of the HA’ ions, which according to reaction II are partly split further, may be identified with the concentration of the acid salt dissolved, we must nevertheless remember that the number of hydrogen ions will decrease by combination with the ions HA’ (reaction II). NaHA Na +HA’ (I) HA’ HHA" (Il) HA’+HZH,A II) This last reaction will be especially noticeable, when the acid is weak, which is indeed the case with all organie acids examined in this respect. The sulphocarboxylie acids, however, are examples of strong dibasic acids, which at small dilutions are already well ionised. Therefore, we may expect, that the consumption of hydrogen ions for formation of the free acid will only have a small influence, so that from the concentration of the hydrogen ions the degree of dissociation of reaction I] may be determined, and further the dissociation constants. Noyes has given the following general formula for the acid salts of dibasie acids: ae tet) na: k, (c—H) k, and &, are the first and second dissociation constants of the acid, ¢ is the original concentration of the acid salt (in gram molecules per litre) and # is the concentration of hydrogen ions (in gram ions per litre). 1) Z. f. physik. Chemie 11, 495 (1893). 6* 84 If &, is large compared with c and H, we may write: EH — : c—H Now, this expression is identical with Osrwarp’s dilution law, k = a*/(1—a)v, as shown by substitution of «= H/e and v=1/e. This simplification will be permissible in the case of sulphoacetic and sulphopropionie acids, for which, in a previous paper’) the first dissociation constants were found to be 0.58 and 0.57 respectively. Now, the solutions of the acid salts of these compounds in various concentrations were compared, by the aid of indicators, at room temperature, with the buffer solutions of SÖRENSEN and of CLARK. In the following table v is the numbre of litres, containing 1 gram molecule of the acid salt, p is the hydrogen exponent (p = — logy H) H is the concentration of the bydrogen ions in gram ions per litre, « is the degree of dissociation of reaction II («= Hv) and the equilibrium constant derived therefrom is £, = «?/(1—a)v. v P H a ka Sulphoacetic acid 16 2.65 0.00224 0.0358 8-30 32 2.8 0.00158 0.0506 8.4 64 2.95 0.00112 0.0717 8.5 128 3.05 0.00089 0.114 HES 256 3.25 0.00056 0.143 9.4 512 3.4 0.00040 0.205 10.3 Sulphopropionic acid 16 Quid 0.00200 | 0.0320 6.6 X 10—5 32 2.85 0.00141 0.0451 6.7 64 3.0 0.00100 0.0640 6.8 128 3.2 0.00063 0.0806 jd) 256 3.4 0.00040 0.102 4.5 512 AOD 0.00028 0.144 4.7 The concordance of the constants at various dilutions is very satisfactory, as the indicator method does not allow a great accuracy. However, for great concentrations a correction might be made 1) These Proceedings 25, 359 (1922). 85 according to Noyes’ formula. For this the values of 4, must be multiplied by (4, +¢+ H)/ kh. This correction only affects the dilutions 16, 32 and 64. Thus, the following values are found: Pee Un B te 128) 256) 512 mean value. sulphoacetic acid KA SIS. 8.8 11.5 9.4 10.3 27 sulphopropionic acid 4, = 7.2 7.1 70 55 45 47 6.0 Little differences in the colorimetric determinations of p have in this method a great influence on the value of &,. In a simpler way the second dissociation constant of a dibasic acid may be measured by examining a mixture of a neutral and an acid salt *). If a” is the degree of dissociation of the neutral salt Na,A and «’ the degree of dissociation of the acid salt NaHA, then the second dissociation constant of the acid may be represented by : en ax Nae Al Since these degrees of dissociation for salts are not much smaller than 1, the factor «’/e may be neglected in a first approximation. For the sake of simplicity a solution was taken containing an equal number of molecules of the acid and of the neutral salt, so that £ = H, and this solution was examined at various dilutions. The concentration of hydrogen ions was again determined by means of the indicator method. In next table v is the number of litres containing one molecule of the neutral salt together with one molecule of the acid salt. The variations of the constant due to dilution are not consider- able, but it is remarkable that they are all in the same direction. By dilution the degree of acidity of the solution decreases. This behaviour indeed agrees with the theory, since for the sodium salt of a dibasic acid the dissociation on diluting increases more than for the sodium salt of a monobasic acid. Therefore the value of a@'/a’, which for infinite dilution must amount to 1, is smaller for the greater concentrations. The value of a” follows from the conductivity of the neutral sodium salt at various dilutions, published in the previous paper, and for « the above mentioned values may be taken. 1) In this way |. M. KotrHorr has measured the second dissociation constants of a number of dicarboxylic acids. (Der Gebrauch von Farbenindicatoren, p. 102). v p H=ks Sulphoacetic acid 32 4.0 10.0 Xx 10— 64 4.05 8.9 128 4.1 1.9 256 4.15 1.1 512 4.25 5.6 Sulphopropionic acid 32 4.25 A 64 4.3 5.0 128 4.35 4.5 256 4.4 4.0 512 4.4 4.0 When this correction is made, the following constants are found: VNO LEIDS RIS ORD mean value: sulphoacetic acid cS EON TES 6,77 ore 7.2 3 sulphopropionic acid 4, =4.8 44 41 8 4.2 In the preceding paper the second dissociation constants of both acids are calculated from measurements of the conductivity of the acid salts. ; In the present paper these constants have been obtained colorime- trically first from the py of the acid salt and then from the pa of mixtures of neutral and acid salts. The mean results of the various methods are collected in the following table. Methods Sulphoacetic acid Sulphopropionic acid I. Conductivity of acid ko = 1.4 10— RAND >< 10-5 salts. | II. Hydrogen ion con- a? 4.2 centration of mixtures of acid and neutral salts. Ill. Hydrogen ion concen- DoH 6.0 tration of acid salts. 87 In judging these figures it should be remembered, that each of the methods used here only gives approximative values, which is also evident from the deviations in each series of measurements. However, the order of magnitude is the same for the constants determined in various ways. Thus from this research we may conclude, that the second dissociation constant of sulphoacetie acid amounts to about 1 X 10-4 and that the constant of sulphopropionic acid is about one third smaller. Groningen, January 1923. Organic chemical laboratory of the University. Zoology. — “Kuperimental Budding in Fungia fungites”’. By Dr. H. Boscuma. (Communicated by Prof. C. Pa. Srurren). (Communicated at the meeting of January 27, 1923), A large number of the Fungiae to be found on coralreefs display anomalies mostly arising from the destruction of part of the living tissue. In many cases the destroyed stretches of living tissue are attacked by small algae, which penetrate to a considerable depth, and gradually spread into the living tissue. Such decaying spots of- ten stimulate the adjacent tissue, which consequently exhibits a more energetic growth-activity than usual. The result then is that some- thing like a raised rim arises on the border between the living and the defunct part. In many cases this greater activity is also mani- fested even in the formation of buds. In a prewious publication 1 discussed this budding in adult Fungiae *). Here I also pointed to the fact that algae-parasitism is one of the chief causes of budding in adult corals. Generally the destruction of only a small part of the living tissue suffices for the vicinity to be stimulated to a more energetic growth-activity. This induced me to endeavour to develop buds experimentally in Fungia fungites. My material for this experiment consisted of spe- cimens of Fungia fungites from the reef of the island of Edam near Batavia. The most normal corals devoid of buds or other anomalies were selected. To destroy part of the tissue a small piece of putty was pressed into the central region of the oral surface of some fifty specimens on the 18" and the 19 of August 1921. The putty was held fast on either side of the mouth by the septa. The corals were then restored to their original places. In this experiment, I expected the destruction of part of the central tissue to extend to the mouth in most of the specimens, as this would most likely bring about a strong reaction to the lesion, so that budding would soon ensue. True, the ingest of food would hereby be slightly impeded. But considering that Fungia feeds only partly on organisms other than zooxanthellae, and considering moreover 1) H. Boscuma, “On Budding and Coalescence of Buds in Fungia fungites and Fungia actiniformis.” Proceedings Kon. Ak. van Wetensch. Amsterdam. Vol. XXIV, 1922. 89 that the basal portions of the axial groove were not entirely covered, the impediment was not of a serious nature. This experimenting method was most suitable for achieving results in a short time. After the lapse of nearly four months the putty could still be seen unaltered as to shape, as a hardened substance above the mouth. Some corals had already developed buds. On the 11‘ of December 1921 five specimens were brought back, one of which (N°. 464) was preserved in formalin and the other four were left dry (N°. 460—463). The changes resulting from the experiment are summarized as follows : N°. 462. About one fifth of the upper surface is defunct. Beneath it buds have developed on the under surface, smaller ones at the margin, larger ones more towards the centre. ; N°. 463. Half of the upper surface is defunct. Only few septa in this destroyed part exhibit in the margin residues of living tissue. Portions of the margin of the under surface, under the defunct part of the upper surface, are also defunct. The rest is still covered with living tissue. On the upper surface some large buds and many small buds at the margin. (Fig. 1—3). N°. 464. Two opposite quarters of the upper surface devoid of living tissue. The destruction of the soft parts has extended round the margin of the coral, so that here also some portions are defunct. On the under surface a few large buds, a few smaller ones in the margin. N°. 460. On the upper surface the living tissue was quite lost, on the under surface only in some places at the margin. Here a few small buds are to be recognised, while in the more central part a few larger ones have developed. N°. 461. Upper surface quite defunct, under surface still covered with living tissue. In the margin of the under surface many small buds, in the centre a few larger ones. In all specimens a stretch of the tissue nearest to the putty first died away. This process progressed along the septa to the periphery so that the defunct part assumed the form of a sector of a circle. The decay of the living tissue now spread along the margin on the lower surface, the consequence of which was that the environing tissue was stimulated to greater activity and accordingly developed buds. At the living corals the larger buds, which were located at some distance from the margin, were most conspicuous. (Fig. 3). The diameter of the basal part of these buds varied from 2 to 12 mm. The mouth was invariably small and the height inconsiderable. The spines of the costae of the parent coral were often visible through the thin living portions of the bud. In these large buds the skeleton is still very incomplete. The theca and the first septa are only little developed; on the other hand the columella is already distinguishable in the form of a large number of irregular trabeculae. 90 In the smaller buds, which were generated principally in the marginal regions of the under surface the development of the skeleton can easily be traced, as the buds differ very much in age. They are of a much more regular structure than the larger ones. In the youngest buds, with a diameter of about 0.5 mm., nothing of the skeleton is visible except the theca, which appears as a thin wall, stretching obliquely upward and consequently looks like a truncated cone. (Textfig. a). Fig. a. X 45. Fig. b. X 45. Fig. c. X 45. The theca has no perforations, which come forth only in much older buds. Soon after this the first cycle of six septa spring up. They proceed from the theca further towards the centre of the bud. (Textfig. 6). The upper rim of the theca rises above the septa. The columella also develops in this phase as short projections in the basal parts of the bud. In buds of this size there are never more than six septa. They originate almost simultaneously, buds with a smaller number of septa occurring only very seldom. The number of similar buds with less than six septa is too small to ascertain whether the septa arise in a definite order. The next cycle of septa can only be observed in buds of about 1 m.m. in diameter. In them the septa of the first cycle have already considerably increased in size and in thickness, and are already provided with some dentations. (Textfig. c). Likewise the columella has grown larger in this stage. The septa of the second cycle are distinguishable at first sight from those of the first cycle by their being less developed and being shorter. The bud has now attained the length of the youngest stage described by Bourne’), DG. C. Bourne, On the Postembryonic Development of Fungia. Transact. Roy. Dublin Soc. Vol. V, 1893. 91 to which it bears great resemblance. The further development of these buds resembles that of the buds of an anthocormus. With the exception of the five specimens that were brought back in December 1921, the other Fungiae remained on the reef during nearly nine months. On the 2"¢ of September, when the experiment had been going on for more than a twelvemonth, the specimens that could still be found, were collected. The putty was still in the central part of the oral surface; in the majority of cases the form was unaltered. In most corals at least some part of the oral surface bad lost its living tissue, in a few cases only the plug of putty had caused little or hardly any change. The aspect of the Fungiae was now as follows: Nos. 507. 510, 519 and 520. The aspect of the corals was very normal, without defunct parts. No budding. N°, 518. Living tissue normal. The central parts of some septa have risen and have longer dentations. This is owing to the occurrence of new mouths by the side of the old mouth, as was easy to see in the two following specimens. NO. 509. No parts of the living tissue destroyed. The central extremities of many septa have grown higher in those places which were in contact with the putty and new mouths have been developed beside these elevations of the septa. The new mouths are now entirely surrounded by septa; on the one side by long regular ones (the original septa of the parent-coral) on the other side by higher parts of recent origin. These parts are somewhat irregular in shape; also the dentations are longer than those of the original septa. N°. 508. Covered all over with living tissue. On either side of the old mouth- fissure a few young buds had developed, whose mouths lay between the normal longer parts of the septa and the higher irregular parts that originated later on. (Fig. 5). This specimen is very much like N° 509, in which the young septa between the new mouths and the putty are also provided with long dentations. N°. 521. Few alterations. The living tissue has disappeared only from the central parts of some contiguous septa. Budding is absent. N°. 512. Some adjacent septa devoid of living tissue, further no alterations. No budding. N°. 506. Upper surface with two defunct parts, the larger of which covers nearly one fifth of the surface; the smaller part is a narrow streak from the mouth to the margin of the coral. The larger part of destroyed tissue overlaps the margin and covers a small portion of the under surface. At the margin two stemmed young buds have taken origin. The diameter of the disc is respectively 2,5 en 3 m.m. In the defunct part on the under surface there are a few smaller buds. NO 501. Almost half of the upper surface defunct, just as a smaller part of the under surface, especially the margin under the destroyed portion of the upper sur- face. On the boundary between the living and the destroyed part of the under surface, five buds have developed still completely encircled by living tissue of the mother-coral. They are very regular and distinctly stemmed. The diameter of the disc, which in all of them is already broader than the stem, amounts to 6, 7.5, 92 10.5, 8.5 and 6 m.m. In the defunct marginal part of the under surface there are some smaller younger buds (diameter 1 to 3m.m.), which, however, have lost their living parts. N°. 500. Along the shorter diameter of the corallum a broad band of the upper surface has lost its living tissue. In the living part some septa exhibit a more energetic growth of the central part; however, new mouths could not be distin- guished as yet. The parts of the margin of the under surface contiguous to the defunct part of the upper surface had lost their soft portions. In their vicinity buds had developed in the living tissue, five on one side and two on the other (Fig. 4). These buds are less regular in form than those of NP. 501. Their stages of development differ. The dimensions are: 138, 7.57, 4.5% 4, 6*5.b, 5 & 4, 13.5 X 8.5, and 10 7 m.m. They are fixed to the parent coral by a broad base, The septa of the youngest buds, which are still little developed, are distinguish- able from the spines of the costae of the mother-coral py their flattened shape. In the basal parts of most of these buds the spines of the mother-coral are still unaltered. In the destroyed part of the margin, with the five buds, a stemmed bud has developed (diameter of the dise 4.5 m.m., of the stem 3.5 m.m., height 3.5 m.m.). Besides these there are still remains of a number of smaller ones, whose living tissue has, however, disappeared. N°, 511. Only one third of the coral was covered by living tissue on the upper surface as well as on the lower surface. In the defunet portion of the lower surface a great many buds had arisen, most of which were still alive. The dia- meter of these buds ranges from | to 3 m.m. N°. 502. Of the upper surface only a small part of the margin was still covered with living tissue; of the under surface almost one fourth was still alive. In this part there are in the vinicity of the defunct region four large buds, only two of which possess well-developed septa. The dimensions are 10 X 7, 7X 6.5, 9.5 & 7.5. and 10>%9 mm. The buds are not yet stemmed, so that the basal parts of the septa are still fixed over their whole length to the skeleton of the mother-coral. The septa of the youngest buds are distinguishable from the spines of the costae of the mother-coral only by their flattened shape. Besides these large buds there are at the margin, now surrounded by the destroyed region, two stemmed buds with a disc, 3 and 2.5 m.m. in breadth. Moreover a few smaller ones are also visible in the marginal part N°. 514. Upper surface without living parts. However, the tissues of a fourth part had died off quite recently, the skeleton of this part still being little overgrown with algae and other organisms, in contradistinction to the remaining part. At the margin of the part that died off long ago some few young, stemmed buds have developed, which however, have likewise lost their living tissue. The under surface still possessed rests of living tissue beneath that portion of the upper surface, which kept alive longest. Then follows a broad edge from which nearly all soft parts had disappeared. Here some large buds have developed (diameter up to 6.5 m.m.). Little is to be seen as yet of the skeleton In the remaining part of the under surface, which had been defunct longer, the remains of many small buds are visible, none of which were alive any more. N°. 516. Upper surface devoid of living tissues in the margin a few short-stemmed young buds. Under surface still covered with living tissue. In the margin a few young buds of small dimensions, still completely encircled by living tissue of the parent-coral. N°. 513. Living tissues entirely disappeared from the upper surface; on the under 93 surface about one third defunct. In the marginal stretches, where the soft parts have disappeared, a few young buds, most of which are stemmed. Diameter of the disc of these buds up to 3 m.m. In the part of the under surface, which is still covered with living tissue, there occur a large number of buds in all stages of development. The size ranges between 0.5 and 3.5 m.m. The stages represented in the textfigures are also perceptible in many buds. N°. 505. The upper surface as well as the under surface without living tissue. At the margin some buds occur; the disc of the largest bud has a diameter of 7 m.m. On the under surface of the coral many young buds in different stages of development. N°. 517. This specimen happened to lie upside down. It had lost its living tissue on both sides. On the aboral surface (now the upper surface) no buds had formed, on the oral surface there are eight buds, some of which are already stemmed. The diameter of the disc of these buds varies from 2.5 to 5.5 m.m. It appears from the foregoing that the results are very different. In some cases the destruction of part of the living tissues had an influence only on the immediate vicinity, where the tissue was con- sequently bronght to greater activity. This appeared from the forma- tion of new mouths beside the old one which had got lost, and of small septa between the new mouths and the defunct part. Owing to the experiment a smaller or a greater part of the remaining living tissue of the Mungi had been destroyed. This process began invariably at central parts of one or more septa, i.e. beside the putty. When the central part of a septum has lost its living tissue, this process progresses towards the periphery and farther along the margin to the under surface of the coral. Of the decaying tissue some isolated parts keep alive and buds issue from them. At the margin of the mother coral these buds are small and of a regular shape; they develop like buds of an anthocormus. Regarding the development of the skeleton a few remarks may follow here. According to Bourne’) the twelve first septa of Fungia originate simultaneously, as is also the case with Astroides. In the former, however, the six septa of the first cycle come first and then those of the second. Since the development of the buds is so very regular and the older stages are quite similar to those of the buds of an anthocormus, it may be expected that the first stage of devel- opment of the skeleton of the young Fungiae, which arise from planulae, is similar to that of the youngest buds here described. Moreover the youngest stages of Fungia patella described by GARDINER®) possess no more than six septa, while the older stages 1) loc. cit. 8) J. STANLEY GARDINER, On the Postembryonic Development of Cycloseris. Willey’s Zoological Results. Pt. II, 1899. 94 bear a striking likeness to the young Fungiae, described by Bourne. Vauenan') also points out that it has not yet been proved that the first twelve septa of Fungia appear simultaneously. In the development of Caryophyllia®) there is one stage in which the skeleton agrees very much with the stage illustrated in Textfig. b. However, the preceding processes differ in the two corals; whereas in Caryophyllia the septa are formed prior to the theca, the reverse takes place in Mungia. In Caryophyllia, therefore, the septa have outgrown the theea much sooner than in Fungia. So while a great number of small buds appear at the margin, and several large ones on the under surface, the tissue is dying off by slow degrees. The result is a defunct specimen with a large number of living buds of different age. Many authors *) look upon such buds on defunet specimens of the same species as having originated from larvae. In a previous paper I advocated my view that these young Fungiae must be considered as buds *). My experiment yielded all sorts of intermediate stages between normal specimens and defunct ones with buds. The large buds that may arise on the aboral surface, are in their earliest phase so large already (up to 12 mm. in diameter) that it is a priori highly improbable that they should have been formed from larvae. Besides the lateral tissues of the bud are connected with those of the parent, while the basal living parts of the bud overlie the skeleton of the old coral, which results from the way in which the columella is formed in these buds. The trabeculae of their columella namely are generated between and on the unaltered spines of the costae of the parent coral. In the above description the young individuals, which resulted IT. WAvLAND VAUGHAN, Recent Madreporaria of the Hawaiian Islands and Laysan. Smithsonian Institution, U. S. Nat. Museum, Bull. 59. 1907. 3) G. von Kocu, Entwicklung von Caryophyllia cyathus. Mitt. Zool. Stat. Neapel, Bd. XII, 1897. (The stage alluded to is reproduced in Fig. 14). 8) S. SrurcHBury, An Account of the Mode of Growth of Young Corals of the Genus Fungia. Trans. Linn. Soc. London, Vol. XVI, 1833. H. N. Moseurey, Notes by a Naturalist on the Challenger. London, 1872. L. DöperLeiN, Die Korallengattung Fungia. Abh. der Senckenb. naturf. Ges. Bd. XXVII, 1902. Also the youngest stages of Fungia patella, described by GARDINER (loc. cit.) are probably buds of a specimen, of which the remaining part of the living tissue had been destroyed. 4) loc. cit. SavinteE Kent (The Great Barrier Reef of Australia. London, 1893) also deems it most probable that these young Fungia are buds, originating from the remains of the living tissue. 95 from the destruction of stretches of living tissue, have been called buds. Theoretically however, none of these individuals can be considered as buds. In budding the parent remains intact, the buds are generated through a local intensified growth at the body of the parent (DeeceNer *)). The animal, on which the young individuals grow, is now only a remnant of what it was before. The process of development of the young individuals under consideration, is rather to be defined as a fragmentation, as it has been termed by Korscnerr and Herper’). Small portions of the tissue of the body are apt to develop into new independent individuals. That these portions are not detached from the parent coral but remain fixed to the skeleton does not take away from the theoretical significance of separation. Korscuent and Heiper point to the fact that fragmentation is originally not a phenomenon of itself, but the effect of processes of fission or budding. The processes in Fungia, dealt with in this paper are undoubtedly related to budding. Sometimes daughter-individuals are found on the aboral surface of specimens, whose oral surface presents no anomalies. These daughter individuals are true buds. They have the same outward appearance and are attached to the parent-coral in the same way as the buds which were developed experimentally. Daughter- individuals can also be developed from that part of the living tissue of a mother-coral, which is contiguous to a small region of the margin of which the living tissue has been destroyed. The mother- coral will then remain alive, although it is slightly injured, and the young individuals, derived from a portion of the living tissues, are buds also in this case. The evidence produced shows that any part of the tissue may develop into a complete animal. This, however, occurs only when the interconnection between the living parts of the original animal ceases to exist in consequence of destruction of part of the tissue. The place where the young individuals develop is very different. They may arise at the top of the costae or between two costae or, when they are larger, on several costae together (Fig. 1). In corals that were inverted while the tissue was being destroyed, young individuals may develop between the septa and in the vicinity of the mouth, i.e. on the oral surface. 1) P. DEEGENER, Versuch zu einem System der Monogonie im Thierreiche. Zeit- schrift f. Wiss. Zoologie. Bd. 113, 1915. 2?) E. KorscueLr und K. Hermer, Lehrbuch der vergleichenden Entwicklungs- geschichte der wirbellosen Thiere. 1 u. 2 Aufl. Allgemeiner Theil. 4 Lief. 2 Hälfte. 1910. 96 Some of the experimental animals could have survived in a slightly altered form. They are the corals, in which new mouths had been formed round the destroyed central part of the oral surface. Most specimens however had altered their shape completely: the ultimate result would ever have been a defunct dise with a number of young living individuals, chiefly on the under surface and at the margin. The young individuals on the under surface were in unfavourable conditions for further development, although some were already rather large (Fig. 4). The young Fungiae at the marginal regions, would have developed into a stemmed specimen if the corals had remained on the reef, When their dise has grown to a certain size, it falls off and at the upper extremity of the stem a new disc forms. These young Fungiae, originated from the last living residues of a defunct specimen, develop further in the same way as young individuals do, which are generated from fertilized ova. Leyden, Jan. 1923. Zoological Laboratory of the University. a F , Al ANY Pate repo auiu tines vor were ubstance had a smaller conductivity, while it could be ascertained by determinations of the freezing-point that it had not entirely split up into its components in aqueous solutions. The discovery of this compound made a renewed investigation of the boro-pyro-catechates necessary. 1) Recueil 37, 184 (1917). *) Cf. These Proc. following communication. Proceedings Royal Acad. Amsterdam. Vol. X XVI. i oscHMA: “Experimental Budding in Fungia fungites”. ‚B = Plate I. Plate II. Fig. 1, Part vargin of the aboral surface of Fungia fungites No. 463 paris r Many small buds and a few larger, less regular ones. né parts re Magnified X5 Fig. 2, Other part of the margin of the aboral surface of the same specimen. Besides Skeleton, The Batutulis near Buitenzorg. Proceedings Royal Acad. Amsterdam. Vol. XXVL a few smaller buds also a large number of irregular elements of the Especially of the columella of larger buds, are observable. Magnified 5!) Photographs for figs 1 and 2 have been taken by Mr. G. F. Brey of Fig. 3. Lower surface of Fungia fungites No. 463 living. A number of large buds, whose living parts tissue of the lower surface. Natural Fig. 4, Lower surface of Fungia fungites No. 500. Buds in the living part adjacent to a portion of the margin where the soft parts have died off. are connected with the unaltered size. 4 Nat. size Fig. 5. The central portion of the oral surface of Fungia fungites No. 508. By the side of the plug of putty new mouths had been generated, which, towards the central part of the parent-coral, are encircled by raised portions of the old septa with larger dentations. 2/, nat, size. Chemistry. — “The Valency of Boron’. By Prof. J. BörseKEN. (Communicated at the meeting of December 30, 1922). As the complex organic boric acid compounds have gradually acquired a great significance for the determination of the compo- sition of a number of organic compounds and for the knowledge of the configuration and of the state of motion of the molecules in space, it was felt as a serious deficiency that the existence of these complex compounds had so far been exclusively derived by an indirect way, and that no compound had as yet been separated, the composition of which had been entirely made clear. Some years ago we had, indeed, succeeded *) in obtaining some well crystallized salts of pyrocatechol borie acid, but they seemed to be built up in such a complicated way that no accurate conception could be formed of their composition. Now it chanced that Mr. Hermans’), who was engaged in an investigation of the equilibria in the system glycol + acetone 2 glycol acetone + H,O, and also examined the behaviour of the glycols towards boric acid, obtained a compound that erystailized beautifully from tetra-methyl-propane-diol-1.3 and boric acid, which according to analysis and properties possessed the following cyclic composition : (CH,),C—O EIN CH. SBOH. N (CH,),C—O Against our expectation this compound, which had a delicate saffron odour, was hardly acid, at any rate less acid than boric acid itself, as a solution of this substance had a smaller conductivity, while it could be ascertained by determinations of the freezing-point that it had not entirely split up into its components in aqueous solutions. The discovery of this compound made a renewed investigation of the boro-pyro-catechates necessary. 1) Recueil 87, 184 (1917). 2) Cf. These Proc. following communication. Proceedings Royal Acad. Amsterdam. Vol. XXVI. 98 Mr. Hermans, who undertook this investigation (c.f. following com- munication) soon succeeded in clearing up the composition of these compounds. « The empirical formula KBO,(C,H,), applies to the beautifully crystallized potassium salt; the volatile ammonium salt is NH,BO,(C,H,),, aniline salt C,H,NH,HBO,(C,H,),, from which through careful heating in vacuum, the free acid HBO,(C,H,), (prepared and analysed by Mr. MruLennorr) was obtained. There are, accordingly, two pyrocatechol rests bound to the boron atom, in which an entirely new type of compounds originates, as the potassium salt hardly reacts alkalically, and, as has been known for a long time already, the relatively strong acid nature of the hydrogen derivative manifests itself in aqueous solution by increase of the conduetivity. In view of the empirical constitution and this modification of properties the below-given structural formula naturally suggests OON itself, in which we must imagine the | | | | anion of a relatively strong acid to have Rag | oes - arisen through binding of the fourth oxygen atom to the boron. The acid is partially hydrolysed by water, but can be sublimated undecomposed in anhydrous condition. Also in its spatial structure the anion will be an antipode to the kation of the ammonium compounds; the four O atoms will lie in the four angles of a tetrahedron, and the two benzene rings then are vertical to each other. The discovery of this type of boron compounds throws light on the composition of a great number of other boron compounds, and indirectly gives a powerful support to the recent considerations on the atomic structure in general. In this connection we must devote a few words to Lewis?) and Lanemuir’s?) atomic model. and to the natural system of elements according to KossrL ®). Very much simplified and somewhat modified *) these hypotheses come to what follows: The atom is assumed to be a positive nucleus surrounded by different shells of electrons, in which the number of electrons must 1) G. N. Lewis. Journ. Am. Ch. Soc. 38 762 (1916). 2) Irving Lanamuir ibid 41 868 (1919) and 42, 274 (1920), 3) Ann. der Physik 49 229 (1916). 4) | wish to state here emphatically that I apply these considerations exclusi- vely to the first period of the system, because | consider the atoms of the second period already to be too complicated to satisfy the simple postulates. 99 be equal to the excess of protones of the nucleus. The electrons which can more or less easily be shifted, and can even be removed, are found in the outer.shell, and also electrons of other atoms can penetrate into this outer shell. There is further a general tendency to gather eight electrons in this outer shell, because this represents most likely a very stable condition of equilibrium. We meet with this constellation in the noble gases, which do not possess chemical affinity. Only helium has only two electrons in its outer shell, and evidently forms an exceedingly stable whole with the nucleus. The mono-valent metals have only one electron in their outer shell, and will easily split this off, in this way getting into the condition of the nulli-valent element, which stands one place lower down as to its rank; the elements of the seventh group, the halogens, have seven electrons in the outer shell, and will have a tendency to add one electron, passing with it into the condition of the nulli- valent element, which is one place higher in rank. Thus an exceedingly stable substance of the type of Helium-Neon will be formed when Li and F are joined, with this difference that there exists a very strong electric field between these atoms, which is wanting in the noble gases. Kosser. has designated this kind of bonds by the name of hetero- polar, they exist between all metallic elements on one side and the non-metallic ones on the other side. When the electron of the metal has entered the shell of the non-metal, this has obtained for the metal-ion a same value as the seven already present ones, which means that the metal-ion is no longer bound to a definite place in the molecule; it can place itself opposite to each of the electrons present. When the number of electrons in the outer shell increases, resp. decreases, they no longer get so easily quite outside, resp. the power to absorb foreign electrons has diminished; then ensues an interpenetration of the two shells, in which one electron of each of the atoms joins to a pair in the mutual shell division. This is the homédopolar bond according to Kossen, in which the two atoms are bound to a very definite place. The hetero-polar or briefly polar bond gives rise to molecules which conduct the electric current e.g. in aqueous solution; the homöo- or non-polar bond is met with in substances that do not conduct the electric current. As a type of the first we may name the alkali-halogenides, as a type of the second the organic compounds, but also water, boron- trichloride ete. 7* 100 In the polar bond the atoms are thought separated, in the non- polar bond they penetrate into each other at definite places. There is still a third kind of bond, which comes near to the Fig. la. Fig. 10. Lithium fluoride. Water. non-polar bond, and is distinguished from it only in form, not in nature. It is seen from the symbol for water that the oxygen atom has still two pair of electrons in the outer shell. These endow this molecule with the power to combine with other molecules, and especially with those of which one of the atoms lacks a few elec- trons in the outer shell. ‘Thus we must imagine that metal atoms which have ceded their electrons to acid rests on the salt formation, can get saturated with water molecules, and thus form hydrated metal ions. This kind of non-polar bond is that which was supposed to come about through by-valencies, and which is explained from the tendency to collect eight (or sometimes more) electrons in the outer shell. It is easy to see that ammonia, though a saturated compound, can combine with a great number of substances owing to the free electrons in the outer shell. All these bonds are of quite the same nature as those that come about through the principal valencies. The penetration of these ammonia molecules into the metal atom often gives it a more pronounced electro-positive character. That this bond is really restricted to a definite place of the molecule, follows from MriseNHeEIMER’s investigation *), in which he has succeeded in splitting up methyl ethyl aniline oxide into its optical antipodes. The four non-polar bonds, among which that where the nitrogen with its free electrons, has Fig. 2. penetrated into the outer shell of the oxygen Ammonia. find a place in the angles of a tetrahedron. 1) Berichte 41, 3967 (1908). 101 We point out that the nitrogen here behaves as a tetra-valent substance, the oxygen as a univalent one. Ammonia, in spite of its having 8 electrons in its outer shell, Cone <= <> Fig. 3. A=phenyl, B = methyl, C=ethyl, Doxygen. Methyl ethyl phenyl ammonium oxide. ean bind certain definite other atoms non-polarly, provided there be also an atom present that the electron, which is now in excess (and is, therefore, expelled) can take up. This may also be expressed as follows: ammonia passes into the positive ion condition when forming a bond with a hydrogen atom, or in other words: ammonia can only receive a hydrogen ion, as it is saturated with electrons. Here the nitrogen does not become tetra-valent, but penta-valent. This fifth valency, however, has another character: it gives rise to a polar bond. ; It is this very power through which a = number of atoms, which to start with, have an electro-negative character, acquire the pro- perty of an alkali-metal; we need only mention 65) C)4) iodine and sulphur. = We may now apply these considerations to the boron atom, and examine in the first place Fig. 4. what is the nature of the bonds in the simple Ammoniumion. derivatives of this element. The halogen com- pounds are the most suitable to decide this question. 102 These have BX, as constitution and entirely possess the character of acid chlorides, and not of salts. The three electrons are, accord- ingly, not ceded, as even the fluorium atoms are non-polarly bound. In these compounds boron has only six electrons in the outer shell; in some respects they will, therefore, have an unsaturated character (Fig. 5). These halogen compounds can, indeed, become saturated in two ways. The first way, which has been known longest and has already been explained by Werner to a certain extent, refers to the adoption of a molecule HF. Then there is formed e.g. HBF,, a mono-basic acid. It may now be assumed that a fourth atom F becomes non- polarly bound, which, however, is not possible, as boron has no free electron left, unless at the same time an electron (of the H) is taken up, and consequently the group BF, passes into the negative ion-condition (Fig. 6). Fig. 5. Fig. 6. Borium fluoride. Borium fluor hydrogenic acid. lt may also be said that the polarly-bound HF-molecule enters the shell of the boron with two of the eleetrons of the fluorium atom, the whole BF,-group becoming a negative ion. For the H-ion it is entirely immaterial whether the ceded electron is attached to one of the four fluorium-atoms outside or inside the shell of the boron; as ion it has no fixed place in the molecule, and can wander all round the complex. In view of the mono-valency of fluorium and of the complex, boron may be assumed to be penta-valent with as much reason as the nitrogen in ammonium compounds. The second way in which boron fluoride can add to its electrons is: to combine with molecules of which there are two electrons 103 available in the outer shell of one of their atoms, without this giving necessarily rise to ionisation. Thus BF, forms stable compounds with PB, and with ammonia, Fig. 7. Boron fluoride ammonia. of which the latter can be distilled undecomposed. Their consti- tution may be represented by the above simplified symbol; the two electrons which the N of the ammonia has in excess have penetra- ted into the shell of the sphere of the boron, thus forming a non- polar bond. Both atoms have eight electrons in this shell, and are mutually saturated (Fig. 7). It is not subject to doubt that when different groups are substi- tuted for the H-atoms at the N, a substance is formed which can be split up into its optical antipodes *). As regards the valency of the boron, this may be put, like that of the nitrogen, at four, as there is no reason to assume the bond between the N and the B to be of another nature than between the B and the F (resp. between the N and the H). Let us now proceed to the complex boric acid compounds. The very weak, volatile boric acid itself is, at least for the greater part, a derivative of the tri-valent boron, in which all the bonds are non- polar. In aqueous solution a very small part will be a derivative +) It may cursorily be pointed out that the constitution of the addition products of AIC]; with a number of organic and inorganic compounds can be seen in entirely the same light. 104 of the penta-valent boron, in which one of the bonds is polar (see further). The non-acid complexes agree with this, the acid ones, which are formed with the poly-hydroxy compounds, the hydroxyl groups € C Fig. 9. Potassium boro pyro catechate. of which have a favourable position, are derivatives of the penta- valent element. Let us choose as an example potassium boro pyro catechate. The four oxygen atoms of the two pyro catechol rests are bound to the boron atom. This eannot take place, however, until one elec- tron of a metal or of an H-atom has been ceded to the complex. When this has once been accomplished, it is immaterial for the potassium (or H-) atom, where this electron is to be found in the complex; in view of the tetra-valency of the carbon, of the bi- valency of the oxygen, and of the mono-valency of the complex, the boron may here be assumed as penta-valent; one of these bonds is then polar (Fig. 9). The four non-polar bonds, just as in the carbon atom — will be erouped as a tetrahedron, so that we may already expect optical activity in mono-derivatives of the pyro-catechol, These complex 105 boric acid compounds always being more or less hydrolized in aqueous solution, the splitting up into optical antipodes will be difficult. In general the negative ion will be particularly easily formed: - 1. When the hydroxyl groups of the poly-alcohols have a favour- able situation. 2. When the organic rests bear an electro-negative character. 3. When the other atom easily cedes an electron. 1. The researches on the complex boric acid compounds of the last ten years have proved that the substances with a pronounced acid character from scarcely acid compounds are formed particularly easily, when the hydroxyl groups are situated in one plane with the C-atoms bound to them. It may be assumed that the first phase will be the formation of the derivative of the tri-valent boron. When this complex meets a second molecule of the organic com- pound, the unsaturateness of the boron will collaborate with the favourable constellation of the poly-alcohol to form the very stable derivative of the penta-valent boron. 2. When this favourable situation of the hydroxyl groups coin- cides with strongly electro-negative properties of the poly-oxy-com- pounds, as of @-hydroxy acids and aromatic ortho-hydroxy-acids, these penta-valent boric acid compounds will be exceedingly easily formed. Mr. Hermans has actually succeeded (cf. following commu- nication) in proving this for boro di-citrie acid, and in ascertaining the constitution of the already known boro di-salicylic acid zine from this point of view. 3. It was to be expected that especially the alkali-salts of these complex acids could be isolated, because the complexes are only realizable on adoption of an electron, and this is easily ceded by an alkali-metal. We meet here with the same influence which the metal atom in general exerts on the stability of the acid rest, which renders it possible to obtain salts of which the corresponding acid is unstable and even unknown. This latter circumstance renders it also desirable to write the metal atom by the side of the atom to which it has ceded the electron, though in reality the whole complex becomes a charge richer, and it therefore seems indifferent to a certain extent where this metal atom is placed, since as an ion it is not bound to a definite place *). 1) That this is not quite immaterial may appear from the different behaviour of AgNO, and KNO, resp. AgCN and KCN towards alkyl iodides, which will be discussed later. 106 We are now able to bring some order in the inorganic derivatives of boron. The volatile boric acid and its esters are, as was stated above, derivatives of tri-valent boron, and as such, somewhat unsaturated. It will try to supply the deficiency by complex formation. AUERBACH’sS investigations ') have brought to light that when an insufficient quantity of a base is distributed between boric acid and arsenic acid there is formed far more borate than was to be expected according to the dissociation constant of boric acid. Complexes must be formed which are much more strongly acid than boric acid in diluted aqueous solution. Hence in virtue of 3 the added bases cause the quantity of poly- boric acid ion to increase. This is corroborated by an investigation of P. Mürrer®), who could shake out but very little borie acid from a mixture of borate and borie acid with amy! aleohol, though the free acid is easily dissolved in it, evidently because the boric acid was bound with formation of poly-borates in consequence of the above-mentioned kation-action. These stronger poly-boric acids will be derivatives of penta-valent boron, and accordingly in the symbol a place may be assigned to the metal atoms which promote this phenomenon, next to the boron atom. The metaborates then have the composition M(BO,), borax has the ye 7 ON formula : OBC O BO, while potasstum penta borate Na Oo a KB,O, (see Hermans, following communication), which erystallizes OBO OBO NI OBO” | NOBO K beautifully from formie acid, possesses the constitution all assumed to be anhydrous. There are described a great number of poly-borates; on the con- dition that the number of penta-valent boron atoms be taken the same as the number of positive metal valencies, their configuration can be easily constructed. Boric acid anhydride is distinguished from boric acid by its slight 1) Zeitschr. anorg, Ch. 37 353. 2) Apeca Handbuch III. | p. 32 (1905). 107 volatility ; this furnishes a sufficient ground for assuming this sub- stance to be strongly polymerized. This may possibly be explained from the tendeney of the boron atoms of one molecule to form non-polar bonds with pairs of electrons of the oxygen atoms of other molecules. It is possible to form an idea of this polymer by imagining the anhydride molecules to be built up in columns, in which alternately the oxygen atoms have penetrated into the outer shells of the boron atoms, thus contributing to the completion of the ‘octet’. There are enough free atoms left at the oxygen atoms to render the easy hydration to boric acid comprehensible. The boro hydrogen compounds. From the place of the boron in the system it was to be expected that the affinity of the H should be slight. The interesting investigations by Srock and his pupils *) have really proved that these compounds are formed in very small quantities from magnesium boride, and are very unstable. At first B,H, and B,H,, were separated as gaseous boro-hydrogens, and later B,H, besides higher boro-hydrogens. Srock is of opinion that the boron must be assumed to be tetra-valent in these compounds. He, therefore, tried to prepare halogen boron compounds BX,, in which he did not succeed, which is, indeed, not astonishing in view of what precedes; such a combination can only be realized when at the same time an electron is added. The B,H, obtained by him is not necessarily a derivative of tetra-valent boron; the BH,, which would’ have to be formed in virtue of the tri-valency of the boron, is evidently so unstable that two molecules inter-penetrate, in which, however, one of the B-atoms must more or less change into the ion-condition. It is actually immediately adopted by KOH with formation of KBOH, (propably a mixture or combination of KBOH, and KBOH,) and H,. Accordingly it is a compound with tri- and penta-valent boron, which through this makes the impression of being a derivative of the tetra-valent element (see the symbol on the following page). Nor need the second gaseous boro-hydrogen B,H,, possess a tetra- valent boron. In this two BH,-groups can be bound to each other, each of them bearing a BH,-group, while besides two H-atoms have passed into the kation-condition, and the rest, therefore, forms a bi-valent anion. The B,H,, which is, moreover, the most stable boro- hydrogen *), can certainly, not consist exclusively of tetra-valent boron atoms. If it is assumed that one of the boron atoms is bound 1) Berichte 54 A 142-158 (1921). 2) Berichte 54 A 155 (1922). 108 to four BH,-groups, which at the same time has taken up an electron with H-nucleus, the relative sta- (> EEN bility and the fact that this boro- Gos) Cy, hydrogen dissolves in KOH without residue, evidently with formation Ch of a salt, has been explained in a satisfactory way. Its formula SN) is, therefore, H{[B(BH,),] with one (+) SZ penta-valent and four tri-valent boron atoms. In the boro-alkyl compounds transition of an H-atom into the Fig. 10. Borohydrogen. ion-condition is not possible: B(CH,), has been separated, and a polymerisation to {B(CH,),|, has not been observed — also boro- triphenyl was lately prepared. That the boro-alkyl compounds can combine with ammonia *) can be explained in entirely the same way as for BF, (ef. p. 103), there is Sufficient reason in these non-polarly bound molecules to assume the boron, just as the nitrogen, to be tetra-valent. Boro-nitrogen. BN. It has not been possible so far to melt, this substance, which forms a white powder and which is very resistant against the action of the air also at high temperature, for which reasons it has been proposed as material for fire proof recept- acles; it is very interesting as far as the considerations given here are concerned. In appearance the demand of the valency has been completely fulfilled, as the tri-valent nitrogen is combined with the tri-valent boron. When, however, the properties of nitrogen com- pounds of other light elements, as cyanogen gas, halogen nitrogen compounds, ete. are considered, boro-nitrogen must at any rate be assumed to be very far polymerized. When every nitrogen atom is supposed to be surrounded by three boron atoms, and these again each bound to three nitrogen atoms and so on, two electrons of every nitrogen atom femain available in the outer shell for a non-polar bond. Inversely every boron atom can be joined by a pair of electrons. This mutual saturation is here exceedingly probable, because then at the same time an exceptionally stable structure can be attained, viz. that of the carbon in diamond. The properties of boron nitrogen lead us at any rate to expect !) Berichte 54 B 531 (1922). The ammonia compound of boro-trimethyl is a volatile well-erystallizing compound, much more stable when exposed to the air than B(CH3) itself. 109 a very stable configuration. If attempts to bring it to crystallisation should succeed, a substance may be expected with a very high refractivity and very great hardness, and with a still more consider- able resistance against external influences than any amorphous product known so far. The difference with the way of binding of the carbon in diamond is this that one of the bonds at the moment of its formation is not quite equal to the other; when one considers, however, that this difference has vanished after the two elements have combined, so that it is impossible to decide which of the four was this particular bond, the expectation is the more justified that crystallized boro- nitrogen will have the character of diamond. It is seen that when represented in this way, the idea of the valency begins to diffuse. The boron is more than tri-valent with respect fo the nitrogen, because the element lacks something. And the nitrogen is more than tri-valent with regard to the boron, because in the simple compound this element has something too much. Combined they make, therefore, the impression of two tetra- valent elements. Hence the valency is replaced by Werner’s coor- dination value, to which a firmer foundation is given by these considerations. If it should appear, e.g. from the Röntgenogram, that the diamond structure is applicable to the crystallized boro-nitrogen, this proves at the same time that a distinction between principal- and by-valencies is not rational, and that polar and non-polar bonds should be sub- stituted for this, in which the non-polar bond is a connection between two atoms, which in consequence of mutual repulsion of some such bonds, has taken up a certain place in the molecule, whereas the polar bond forms a connection between one of the atoms and a rest, which will often consist of a multiple of atoms, but which, also when it consists of only one atom, is not fixed to a definite place of it. It is self-evident that in the first periods, in which the atoms are simply composed, the number of pairs of electrons will not be greater than four, and the coordination-value will not exceed this number. As the atoms get more complicated, the coordination-value can also increase; we see this already happen in the second period in aluminium, many compounds of which are known, in which this element is bound non-polarly to six atoms. With regard to the other boron compounds, I will still draw attention to additional compounds of the borie acid esters with 110 alcoholates, e.g. Na{B(OCH,),|, which entirely possess the character of salts in absolutely alcoholic solution — they are decomposed by water. The boron is non-polarly bound to the four mono-valent OCH,- groups, which is only possible through the complex having taken up one electron. A very interesting group of compounds has been found by W. Ditrany '). He found that when acetyl acetone-rests had substituted two chlorine-atoms in BCI, the third chlorine atom assumed the character of an anion, hence the rest of a kation. He rightly calls these substances boronium compounds: the considerations developed Fig. 11. Boron di-acetyl acetone chloride. above account satisfactorily for the phenomenon. The two acetyl acetone rests have as enol replaced two of the chlorine atoms of BCI,, and then are bound non-polarly to the boron atom. The favour- able situation of the C =O-groups with regard to the boron-atom now gives rise to the penetration of two electrons of each of the oxygen atoms into the outer shell of the boron, causing non-polar bonds; this is, however, only possible, when at the same time the third chlorine atom, which was at first non-polarly bound, passes into the (polarly-bound) anion state and the boron complex becomes a kation. 1) Annalen 433, 300 (1906). 111 There is certainly no need to state explicitly that only a sketch has been given in the above. It seemed, however, desirable to me to test Kossen’s and Lewis-Lanemuir’s hypotheses by the simplest atom that can be bound both polarly and non-polarly to other atoms, for it is to be expected here that the complex compounds will be built up in the least complicated way. Complications occur in the elements of the second period, e. g. Al, Si, and S, as appears from the existence of compounds as Na, AIF,, K, Si F, and the derivatives of the hexa-valent sulphur. In connection with the above it would have to-be assumed that these atoms try to bring together sr pairs of electrons in their outer shell, whieh then possibly might have to be ascribed to the intluence of the electrons of the first spherical shell on those of the second. Before this can be examined more closely, the phenomena referring to the simplest elements will first have to be more fully cleared up. In the case of boron it is, indeed clear, that as regards the formation of compounds pairs of electrons play an important part, and that especially the non-polar bond, i.e. the bond that does not conduct electrically, is brought about by such pairs. If it is further borne in mind that the latter kind of bonds is much less reactive than the former, itis natural to suppose that the difference between polar and non-polar bond consists in a greater closeness of the latter. The non-polar bond might be compared to an electro-magnet with a well-closed armature or a toroid, whereas in the polar bond the armature is removed or the toroid opened. A similar image might be applied to the action of catalysts, in which it is likewise assumed that closed bonds are opened, which gives rise to a greater chance of interaction when meeting other molecules. Delft, Dec. 1922. Physics. — “On the diffraction of Réntgen-rays in liquids”. MI. By Prof. W. H. Keesom and Prof. J. Dre Surpr. (Commu- nication N°. 12 from the Laboratory of Physics and Physical Chemistry of the Veterinary College). (Communicated by Prof. H. KAMERLINGH ONNKS). (Communicated at the meeting of January 27, 1923). - § 1. Introducton. The experiments on the diffraction of Röntgen- rays described in Comm. N°. 10 *) were all made with K,-rays of copper. No diffraction ring was observed caused by the interference of rays scattered by the separate atoms in the molecules. Fi, in the case of oxygen this might be ascribed to the circumstance, that the distance of the centres of the systems of electrons grouped round the atom nuclei is too smal! to give an interference ring with rays of that wave length (viz. smaller than 0.95 A for a= 1.54 A). Therefore it seemed desirable to repeat some of the experiments with rays of a shorter wave length. We have now made several observations with Ke-rays of molyb- denum (4= 0.71 A). § 2. For method and apparatus see Comm. N°. 10. The rays emitted by the molybdenum anticathode were filtered by 0.35 mm. zirconium. a § 3. Results of the observations on the principal diffraction ring. We now exposed liquid oxygen, argon and nitrogen, also water and carbonic disulphide. For oxygen, argon, water and nitrogen (investigated for the first time now) we found confirmed that the principal ring is due to neighbouring molecules, which we may consider to be distributed approximately as spheres packed together as closely as possible and filling up the space occupied by the liquid. This time we obtained a diffraction ring for carbonic disulphide 1) These Proceedings 25, 1922, p. 118. 113 too and this gave a deviating value for the distance between the diffracting particles. This is evident from the following table. Here p is again the half top angle of the cone formed by the diffracted Röntgen rays. M and d have been written for the molecular weight and density, while 7,72 a SSS Aar sin £ 2 denotes the distance between the diffracting particles. Here we again have made the assumption that the observed diffraction ring is due to the cooperation of arbitrarily orientated systems each of two particles at that distance from each other. TABLE 1. 9 oa Substance aes a 1.33 y, M (2 = 0.71 A) d | Oxygen (9 plates) 12.50° 4.0 A 4.0 A Argon (1 plate ) 13.0 3.85 4.1 Water galmt) 13.44 3.73 3.6 Nitrogen (1 De) 11.34 4.42 4.4 Carb. disulph. (1, +?) 13.23 3.8 5.2 Instead of formulating a special hypothesis on the deviating behaviour of CS, we prefer to postpone this until more substances showing a similar deviation have been investigated. The diffraction rings obtained now are sharper than the former ones, the liquids being radiated this time in a tube of 1 mm. diameter. § 4. Results of the observations on the second ring. On six plates of oxygen and on those of argon and nitrogen the second ring is distinctly measurable. The other plates do not show this ring, probably because the obtained films are less blackened. For argon too this ring is very weak. 8 Proceedings Royal Acad. Amsterdam. Vol. XXVI. 114 TABLE IL. 7) a Oxygen 19.52 2.57 A Argon 18.9 2.65 Nitrogen 17.0 2.95 These values of a show a striking agreement with the values obtained in Comm. N°. 6a') for the diameter of the molecule’) viz. for oxygen 6 = 2.65 A, for nitrogen 6 = 2.98 DE This supports the assumption made in Comm. N°. 10 that this diffraction ring should be due to the collaboration of two molecules touching each other. With this wave length we also found for water at the outside of the principal ring a rather uniform blackening, rather sharply bounded at p= 24°, which corresponds with a distance a= 2.1 A. § 5. For oxygen and nitrogen no diffraction by separate atoms in the molecule. On a well blackened film of oxygen and on that of argon we found indications of a third maximum of blackening, for oxygen at p = 29° and for argon at p = 30.5°. We do not pretend the existence of this third maximum to be doubtlessly fixed by these indications. We only draw the following conclusion: If this third maximum really exists, it also does so for argon, so that this maximum cannot be ascribed to the interference of rays that are scattered by the separate atoms in the molecules. Though on several films the principal diffraction ring is blackened very intensively. no trace of an interference figure of the separate atoms in the molecule was found in these experiments. Yet with the bere used wave length a diffraction ring would have been o obtained for a distance of the diffracting particles greater than 0,43 A*). For a partial verification of the above we made still an exposition 1) These Proceedings 23, 1920, p. 939. 2) In fact the smallest distance that is possible between the centres of two molecules in the gas. 3) According to the discussion of the band spectra the distances of the atom nuclei would be for oxygen and nitrogen resp. 0,85 and 1J2A: A. Eucken, ZS. f. Elektrochemie 26, p. 377, 1920. Comp. W. Lenz, Verh. D. physik. Ges. 21, p. 632, 1919. 115 with Cu-K, rays (9 mA, + 25 KV). Though this film is thoroughly blackened, only two rings have been obtained. It may be suggested, that the rings obtained in these experiments are all due to atoms that temporarily are arranged in a crystal lattice. The values for the diameters of these rings found in this Comm. exclude a cubical arrangement’). The data are not sufficient to know, whether those temporary arrangements might belong to a crystal structure from an other class of symmetry’). Meanwhile the fact that freezing takes place suddenly at a definite temperature and the possibility of undercooling do not seem to point in the direction of such temporary crystal arrangements. Lead by these considerations we have made still a plate of water at + 0,5° C. The obtained interference figure perfectly agreed with that found at room temperature. At the outward side of the nearly uniform blackening only the intensity proved to be somewhat greater. In this way a second ring develops itself there, an indication of the presence of more double molecules at those low temperatures. No indication was found of the presence of more or greater crystal groups. 1) Comp. Comm. N°. 10 p. 122, footnote 1. ?) Nitrogen and argon crystallise cubically: W. Want, Proc. Roy. Soc. A 87, p. 371, 1912; oxygen below the melting point first hexagonally: W. Want, Proc. Roy. Soc. A 88, p. 61, 1913. Bacteriology. — “On the Bacteriophage and the Sel/-purification of Water’, by Prof. P. C. Fro. (Communicated at the meeting of Dec. 30, 1922). In 1896 Hanktn') reported that the water of various rivers in India, i.a. the Yumna and the Ganges possesses the property of rapidly destroying cholera-vibriones. He was disposed to ascribe this property to a volatile substance, which be assumed to oceur in the water of the said rivers. Subsequent experimenters have demonstrated that all so-called surface-waters have the faculty of exterminating microbes, notably fortuitous pathogenic germs, at a rate depending on the nature of the water and the temperature of the environment. Emmericn, who studied this phenomenon, the so-called selfpuri- fication of water, believed that in this process the part of germicide must be assigned to protozoa (Rhizopods, Flagellates and Ciliates) which occur in every surface-water. This view was adhered to by nearly all inquirers,who had occupied themselves with the phenomenon. D’Héretie refers in his work “Le bactériophage, son rôle dans Pimmunité” to the phenomenon observed by Hankin which he thoroughly believes to be merely the effect of a bacteriophage pre- sent in the water. Now, we know that bacteriophages are inactivated at a tempera- ture above 75°C., and that Hankin could heat water of the said rivers in a closed vessel (a sealed-up glass tube) for half an hour up to 115°C, without depriving it of its bactericidal capacity. We also know that, on heating up the Yumna, and the Ganges-water during the same interval and up to the same temperature (but in an open vessel), it really lost its bactericidal capacity. Now, in view of these facts it will be difficult to side with D'Hérerve, although we must admit at the same time that protozoal action does not explain the phenomenon any better. Still, it cannot be denied that after p’HíÉrerre’s significant disco- very and after the establishment of the presence of bacteriophages attacking various germs in all sorts of surface-waters, in seawater and even in the effluent from septic-tanks and from oxidation-beds, 1) Annales de I’Instituut Pasteur Vol. X pag. 175 and 511. 117 an interpretation of the self-purification of water can hardly be afforded without reckoning with the bacteriophage. If a special inquiry in this direction were to show that bacterio- phages play a more prominent part in the process of self-puritication than has hitherto been assumed, we should not only have to revise and modify our conceptions of and our insight into this self-puri- fication of water and our views concerning the action of sand-filters and oxidation-beds, but also a broad field would be opened up for studying the biological cleansing of sewage. Like many others I also became convinced by my experimentation in India of the prominent part played by protozoa in the destruc- tion of micro-organisms in the surface-water. For this reason [ deemed it a matter of importance to ascertain: a. whether in surface-water, e.g. that in and about Leyden, bac- teriophage could be found, and whether the self-purification of that water was in any way due to bacteriophages that might occur in it. 6. whether in surface-water, polluted intentionally with a profusion of pathogenic micro-organisms, and allowed, to purify itself, bac- teriophages are to be observed that may have annihilated the germs. c. the influence which is played on the purification by substances that kill the protozoa but do not injure the bacteriophages. d. whether protozoa and bacteriophages combined may accelerate the process of self-purification. To this end the following experiments were performed: On the 2d of June 100 ec. of various samples of Leyden water were mixed every time with a concentrated broth. The mixture stood during 24 hours at 37°C. and was then filtered first through rock-meal and subsequently through a “bougie”. The filtrate was mixed in quantities of 0,5; 0,2; 0,1; and 0,05 e.c. with broth, which was afterwards inoculated with an 18-hour-old Flexner-culture. For an examination for bacteriophage a smear-culture was made on agartubes of the broth thus prepared. After an incubation of 24 hours at 37°C. an estimination was made for ‘‘phages’’. The result is that from the examined waters bacteriophages can be isolated that react especially to Flexner but also have an action on other intestinal bacteria. Thus the isolated bacteriophages annihilate all the Flexner, Y, and Shiga Kruse stocks of our collection. They also have an action on bacillus faecalis alealigenes, on a proteus and a proteus X 19, but do not act upon Typhus, Para- typhus A. and B. or Enteridite Gartner, neither on two coli-stocks of our collection. 118 Neither was any effect of the bacteriophages on cholera-vibriones at all apparent. This result could be expected, as it is known that from the dejecta of fowls and horses a nearly always highly active bacterio- phage antibacteria dysenteriae can be isolated and the surface-water in and about Leyden is being constantly polluted on a large seale by the excrements of a number of living beings, also by those of horses and fowls. Anyhow this inquiry teaches us that bacteriophage occurs in the surface-water of Leyden. On the 2d of June quantities of 5 Liters of various kinds of Leydenwater were infected every time with two loopfuls of a 24- hour-old cholera-culture. The infected water was placed in large glass receptacles in diffuse daylight at room temperature (15° C.). On the 21st of June we examined two quanta of 25 c.c. of water; in neither of those samples could cholera-vibriones be detected. Of every sample of 5 L. 25c¢.c. was examined for bacteriophages by mixing the water with '/,, of the volume of concentrated broth, and inoculating the mixture with a loopfal of an 18-hour-old cholera-culture. After an incubation of 24 hours at 37°C. the sample was exam- ined in the usual way for bacteriophage anticholera-vibriones. The result was negative. On the 24 of June three flasks were filled each with 0,5 L. of Rijnwater, in which, as our examination had proved, bacteriophage antibacteria dysenteriae was present. Flask I was inoculated with the whole cholera-culture of a sloped agar tube; flask Il in the same manner with typhus-bacilli; and flask II with Shiga-Kruse bacilli. The fluid of each of the three flasks became very turbid and was placed at room-temperature in diffuse daylight. On the fifth of July the fluid of each of the three flasks became lucid and was examined for bacteriophage in the ordinary way. In all the flasks we found bacteriophage antidysenteriae, which was present in the water already before the beginning of the experiment, but in the typhus-flask not any bacteriophage antityphus was found, no more than bacteriophage anticholera in the cholera-flask. The flask infected with Sbiga did not become lucid sooner than the one infected with typhus and cholera, which might have been 119 expected if a protozoal action had been assisted by the bacteriophage antidysenteriae present in the water. In each flask the number of protozoa increased already two days after the inoculation with the mass of bacteria. Their number was greatest one day before the contents of the flasks became Ineid, whereas it decreased after the clarification had been completed; some of them were transformed into cysts. Again a culture, equal to the one at the beginning of the experi- ment was transplanted into the flasks in which the typhus-bacteria and the cholera-vibriones had disappeared. The same was repeated twice when, after about ten days the contents bad clarified again. After each new infection the number of protozoa was augmented, as with the first, reached its maximum shortly before the clarifica- tion and decreased again after it. Every time a portion of the pro- tozoa were seen to turn into cysts. When the contents of the flasks had become quite clear again after the fourth infection, another examination was performed for bacteriophage antiiyphus abdominalis and anticholera vibriones. The result was absolutely negative. So these experiments go to show that large crowds of typhus- bacteria and cholera-vibriones may disappear without any inter- ference whatever of bacteriophages, from water into which they were introduced fortuitously or intentionally. Even in water containing a bacteriophage anti-bacteria-dysenteriae the B. dysenteriae do not disappear quicker than other bacteria not attacked by bacteriophage. It was nevertheless of interest to examine especially the influence of the presence or the absence of bacteriophage anti-shiga on the rate of disappearance of B. dysenteriae from the water. Two series of experiments were accordingly carried out. In the first series the fate of B. dysenteriae in unfiltered water was compared with that of the same bacilli in filtered water. Protozoa cannot pass through a filter impervious to bacteria, whereas the bacteriophage is let through. In the second series a comparison was made of the rapidity of the selfpurification process of bacteriophage containing water that was or was not mixed wit KCN. The results of these tests, which were every time the same, are reported below. Viietwater, which contains bacteriophage, was used for the inquiry. Part of it was filtered through a Berkefeld-filter. A control-experi- ment showed that this water is free from bacteria and protozoa. Part of the filtered, as well as the unfiltered water was infected 120 with another quantity of highly active bacteriophage (0,2 cc. to 10 ce. of liquid. The bacteriophage was still active in a dilution of 1010). Bacteriophage was superadded to demonstrate its influence still more conclusively than could be done with the bacteriophage already occurring in the Vlietwater. The subjoined table shows the details of the experimentand gives a survey of the results achieved: Experiment Lucid after how 3 Contents of the tube. begun many times 24 hrs. SNe eee Filtered Vlietwater 5 cc + Flexner 23,9, 22 ne 5 » —+Shiga Kruse 9 . After 12 < 24 hrs all K.B. !) still turbid, after the » next sojourn’ of A ‘s » + Flexner + Bacteriophage 0,1 5 > AX 24 hrs 28°C. all de pn „ + Shiga + Bact. 0,1 55 5 remain turbid. i 5 » -+K.B.-+ Bact. 0,1 a 43 Unfiltered Vlietwater 5 cc + Flexner 5 4 4 > 24 hrs lucid. 7 5 » -+ Shiga Kruse nd i 10240; 5 »” ” n + K. B. n ” 6 x 24 ” ” 4 „ + Flexner + 0,1 Bact. - pe 6x24 5 5 5 „ + Shiga + 0,1 Bact. fe 5 OD 240 5 7 ‘5 » +K. B.+0,1 Bact. r 2 6524.55 fs The tests of the 2ed series were conducted as follows: The fluid of two flasks, each holding 0,5 L. of bacteriophage- containing Vlietwater, was infected with such an amount of Flexner- culture as to render it quite turbid. To the fluid of one of the flasks 20 mgms of KCN was added, - after which the flask was well fitted with a rubber stopper. Both flasks were placed at room-temperature in diffuse daylight. After a week the fluid of the flask without KCN had become quite clear, whereas the KCN-flask still contained a turbid fluid. In the former a large number of protozoa were found, which were lacking in the latter. On the eleventh day of the experiment the KCN flask was also getting more lucid and protozoa were noticeable in it. After a fortnight the fluid in either flask was clear. 1) K.B. is a Flexnerstock resistant to any bacteriophage action. 121 The phenomenon exhibited in the KCN flask is to be interpreted by the fact that at the beginning of the experiment the KCN destroys the vegetative forms of the protozoa and consequently they are prevented from clearing away the germs present in the water. The cysts of the protozoa are not killed by KCN. After a week so much of the KCN has been decomposed through contingent chemical processes, that the cysts again grow into vegetative protozoa, which devour the Flexner bacilli, present in the water. CONCLUSIONS. When summarizing our results it must be concluded that the significance of the bacteriophage for the selfpuritication of water is no doubt only small. I for one did not succeed in establishing the slightest influence. The purification is effected in the absence of the bacteriophage, whereas its presence does not accelerate the process, nor render it more complete. The experiments again yield conclusive evidence for the prominent role played by protozoa in the self-purification of water. When, under such circumstances as the laboratory enables us to establish, we eliminate the protozoa, the self-purification of water is entirely arrested even though bacteriophage be added to the water. (From the Laboratory for Tropical Hygiene of the Leyden- University). = ae ANN i ay a 2 UL oa he E be herre Meade, sG 1 ri ys we rh 4 it Ay renate alte Aa ta: pie 4 We ible A7 Vv b . 48 fel rae lh ; ; ae st ’ Biel : = À stn Family: dn a iv Pays Sant Se i a EB. ni 7 Id verzet Shae vake skep ane … en Rhee fi. KONINKLIJKE AKADEMIE VAN WETENSCHAPPEN TE AMSTERDAM. PROCEEDINGS VOLUME XXVI Nes, 3 and 4. President: Prof. F. A. F. C. WENT. Secretary: Prof. L. BOLK. (Translated from: "Verslag van de gewone vergaderingen der Wis- en Natuurkundige Afdeeling," Vols. XXXI and XXXII). CONTENTS, JAN DE VRIES: “A Nuli System (1, 2, 3)”, p. 124. JAN DE VRIES: “A Congruence (1,0) of Twisted Cubics”, p. 126. JAN ae ee: za Representation of the Line Elements of a Plane on the Tangents of a Hyper- boloid” 1 C. U. ARIENS KAPPERS: “The ontogenetic development of the Corpus striatum in birds and a comparison with mammals and man”, p. 135. ~ H. A. BROUWER and L. F. DE BEAUFORT: “On Tertiary Marine Deposits with fossil-fishes from South Celebes”, p. 159 H. A. BROUWER: “Fractures and Faults near the Surface of Moving Geanticlines. III. The Horizontal Movement of the Central-Atlantic Ridge”, p. 167. J.M LANGE: “On stimulation in auxotonic movements”. (Communicated by Prof. J. C. SCHOUTE), p. 171. J. lonen “On the Points of Continuity of Functions” (Communicated by Prof. HENDRIK DE VRIES), J. WOLFF: “Inner Limiting Sets”. (Communicated by Prof. HENDRIK DE VRIES), p. 189. W. F. GISOLF: “On the Rocks of Doormantop in Central New Guinea”. (Communicated by Prof. G. A. F. MOLENGRAAFF), p. 191. I. SWEMLE and L. RUTTEN: “New Findings of Pliocene and Pleistocene Mammals in Noord-Brabant, and their Geological Significance”. (Communicated by Prof. G. A. F. MOLENGRAAFF), p. 199. M. J. BELINFANTE: “A Generalisation of MERTENS’ Theorem”. (Communicated by Prof. L. E. J. BROUWER), p. 203. M. J. BELINFANTE: “On a Generalisation of ERDER Theorem concerning Power Series”. (Com- municated by Prof. L. E. J. BROUWER), p H. I. WATERMAN and J. N. J. PERQUIN: Arena of Paraffin by the BERGIUS’ Method”. (Com- \ municated by, Prof. J. BOESEKEN), p. 226. ~ O. POSTHUMUS: “Contributions to our Knowledge of the Palaeontology of the Netherlands. I. Otoliths of Teleostei from the Oligocene and the Miocene of the Peel-district and of Winters- wijk”. (Communicated by Prof. J. C. SCHOUTE), p. 231. / O. POSTHUMUS: Ibid. IL. “On the Fauna of the Phosphatic Deposits in Twente. (Lower Oligocene)”. (Communicated by Prof. J. F. VAN BEMMELEN), p. 235. C. B. BIEZENO: “An application of the theory of integral equations on the determination of the elastic curve of a beam, elastically supported on its whole length”. (Communicated by Prof. C. KLUIJVER), p. 237. 1 DROSTE: “An application of the theory of integral equations on the determination of the elastic curve of a beam, elastically supported on its whole length’. (Communicated by Prof. J. C. KLUIJVER), p. 247. SMITS: “The Phenomenon of Electrical Supertension” III. (Communicated by Prof. P. ZEEMAN), . 259. Smits: “The Influence of Intensive Drying on Internal Conversion” I. (Communicated by Prof. P. ZEEMAN), p. 266. SMITS: “The System Sulphur Trioxide”. 1. (Communicated by Prof. P. ZEEMAN), p. 270. RUTTEN: “Geological data derived from the region of the “Bird's head” of New-Guinea”, p. 274. D. KLOOSTERMAN: “A theorem concerning power-series in an infinite number of variables, with an application to DIRICHLET's series”. (Communicated by Prof. J. C. ee p. 278. A. H. SCHREINEMAKERS: “In-, mono- and divariant equilibria”. XXIII, H. DIJKSTRA: “The Development of the Shoulder-blade in Man”. (Communicated by Prof. L. BOLK), on Emilee p. 297. IG: re ‘VAN OORDT: “Secondary sex-characters and testis of the ten-spined Stickleback (Gasterosteus pungitius L.)”. (Communicated by Prof. J. BOEKE), p. 309. Proceedings Royal Acad. Amsterdam. Vol. XX VI. Mathematics. — “A Null System (1, 2, 3).” By Prof. Jan pe Vrins. (Communicated at the meeting of February 24, 1923). the base points C,, Cj, C,, C,, C°) and the crossing straight lines a and 6. Through a point N there passes one curve o°; let r be the tangent at NM and ¢ the transversal of a and 6 through N. We conjugate prt to N as a null plane. The curves @° touching a plane r have their points of contact 1. We consider as given a congruence [o°] of twisted cubics with in a conic o°. The transversal ¢ lying in r, cuts gy? in the null points NDS and SN, tof: If » revolves round the straight line /, ¢ deseribes a seroll (£)* and oe? a cubic surface through /. The locus of N is accordingly a twisted curve 4°, which has evidently /, hence also a and 6, as trisecants. We have therefore a null system with the characteristic numbers re 2. The points Cy are singular; for Cy carries one straight line ¢ but oo’ straight lines 7. The null planes of Cy form a pencil of planes round ¢ as axis. Also the points A of a and B of 6 are singular. For each of them carries oo’ straight lines ¢ which are combined to a plane pencil. The null planes of each of these points form a pencil of which the axis lies in the tangent 7. These axes form two cubic serolls (7)*. Other singular points S can only arise through coincidence of the straight lines ¢ and 7. Now the tangents of the curves 9* form a complex of the 6" order and this complex has a scroll (m)'? in common with the bilinear congruence [t). On each straight line n there lies a point S to which any plane through n corresponds as null plane. As / is intersected by 12 straight lines n, the corresponding curve 4* contains 12 points S. 1) The principal properties of this congruence are to be found for instance in R. Sturm: Die Lehre von den geometrischen Verwandtschaften, Part IV, p. 470. 125 3. The null points of the planes passing through the point P, lie on a surface (P)*. For P is the null point of one definite plane of the sheaf and on a straight line / through P there lie the null points of three planes through /. The intersection of the surface (P)* and (Q)* consists of the curve 4° corresponding to PQ, the straight lines a« and 6, and a curve 5’ which is the locus of the singular points S and which passes evi- dently through the 5 base points Cy. Three surfaces (O)*, (P)* and (Q)* have in the first place the curve 65° in common. The points which they have further in common, are apparenfly the points of intersection of (Q)* with the curve 2° corresponding to PQ. To them there belong the 12 points S on 2° and the 28 points A and B on 4°; the remaining two are the null points of the plane OPQ. 4. Any plane a through a is singular; it contains a plane pencil (t) and each ray ¢ cuts the conic 0? (§ 1) in two null points. Analog- ously the planes 8 through 6 are singular. Also the ten planes o each containing three base points C, are singular. For in 6,,, there lies a pencil of conics of which each individual is combined with the straight line C, C, to a curve 9°; they cut the straight line ¢ in 6,,, in an involution of null points. The surface (P)* contains the conics «@ and 8° lying in the planes Pa and Pb, and the intersection p of these planes. The straight line p is singular in this respect that it is a null ray for each of its points. The singular null rays p form the bilinear congruence with the director lines a and 6. Also the ten straight lines CC) are singular; for through each point on such a straight line rz; there passes one straight line f, while 777 may be considered as a tangent. Q* Mathematics. — “A Congruence (1,0) of Twisted Cubics’’. By Prof. JAN DE Vries. (Communicated at the meeting of February 24, 1923). 1. The twisted cubics through four points C,, C,, C,, C, cutting the straight line 6 twice, form a linear congruence {9*|; for through any point there passes one o°. The base points C are the cardinal points, b is a cardinal chord. If d'is a chord of one of the 6°; d(C GC, C) OCH CONO The chords d form therefore a tetrahedral complex; a ray l not belonging to this complex, is not cut twice by any o°: the class of the congruence is zero. Together with Cx and 6 a chord d defines a hyperboloid; on this there lie om’ curves g*? and these define on d an involution; d is consequently a tangent to two curves. The tangents meeting at a point P, lie on the complex cone of P; their points of contact form a twisted curve of the 5 order, 0°, passing through P. 2. Let B, be the point of intersection of 5 with the plane Vin = C, C,C,. Each conic @° through the points CC, OC Bi is a component part of a degenerate o°; the transversal ¢, through C, vesting on b and g? is the second component part. The straight lines ¢, form the pencil of rays through C, in theplane C, 6. There are therefore four pencils of rays formed by singular straight lines. The pairs of lines of the pencil (e°) produce three figures each consisting of three straight lines, e.g. the combination of C, C,, C, B, and the straight line ¢, resting on C,C, There are evidently twelve figures consisting of three straight lines. 3. With a view to finding the order of the surface 4 formed by the o* cutting a straight line /, we determine the intersection of A with the plane y,,,. It consists of two conics of the pencil (07); the former cuts /, the latter is a component part of the 9° which is defined by the transversal through C, of band /. Hence 4 is a surface of the 4" order; the cardinal points C are apparently double points of A“. A o* not lying on 4“, can only cut this surface in the points C and on the cardinal chord 6; from this there follows that 6 is a double straight line. 127 On 4 there lie 9 straight lines and 8 conics. The straight lines resting on 4 and /, determine a representation of 4* on a plane. A straight line /, through a point C cuts 4* in two more points outside C’; from this follows that the 9* cutting /,, lie on a hyper- boloid; this is entirely defined by /,, 6 and Cy. Analogously the g' resting in a fixed point on 5 or on a straight line intersecting 4, form respectively a quadric cone or a hyperboloid. 4. A plane à through / cuts 4* along a curve 2’ which has a double point on 5. In each of the three points of intersection of 2° with /, 2 is touched by a v*. Hence the curves o° touching a plane d, have their points of contact on a curve 0°. Let B be a point of 6; the 9? through the five points B and C% touching d, form a surface of the 10% order with sextuple points in B and C;,'). There are accordingly 4° through B and Cx which have 5 as a chord; consequently 6 is quadruple on the locus 4 of the g° touching the plane d and belonging to the congruence (1,0). Also it appears that A has quadruple points in Cy. Accordingly an arbitrary 9° of the (1,0) has 24 points in common with A, i. e. A is a surface of the 8'" order. 5. A® has the curve of contact d° and a conic 0? in common with the plane 0. The curves d*° and do? touch each other in 3 points; there are therefore three curves o* which osculate the plane d. If revolves round /, d* describes a surface of the fourth order with the single straight line /. On the curve 9° cutting / in R, the pencil of planes (d) defines an involution; / is therefore cut by two tangents of 9?. Consequently through / there pass two planes in which R is a point of the “com- plementary” curve d°. Hence d° describes a surface of the fourth order with the double straight line /. Let us now consider the relation between the points P and Q which the curves d' and d? in a plane d have in common with /. Through P there passes one 9°; the tangent at P defines the plane d, hence two points Q. Through Q there pass two o°, hence two curves J’, and two planes d each containing a curve d*; six points P are therefore associated to Q. If two homologous points Pand Q coincide, there arises a double coincidence of the (6,2), for at that point a g* is osculated by the plane d. On / there lie therefore four points VV for which the plane of osculation » passes through /. 1) This is easily seen from the intersection of this surface with 323, which consists of 2 conics and 3 double straight lines. 128 6. If we consider N as the null-point of », there arises a null- system with the characteristic numbers @=1, B=3, y=4 ($5). If » continues to pass through a point P, the locus of MN con- sists of a surface (P)* and the four pencils of rays round the points Ci. in the planes Cyd (§ 2). If » revolves round the straight line /, » describes a curve 2’ and the four singular rays through Cx which rest on /. The surfaces (P)’ and (Q)* have in common the curve 2? corre- sponding to PQ, and the 18 singular straigth lines Cy Grand Cy Bj. With a o° (P)' has in common the 3 points of which the planes of osculation pass through P; the remaining 12 common points lie in the cardinal points C; these are therefore triple points of (P)*. The planes of osculation in Cz envelop accordingly a cone of the third class. Mathematics. — “4 Representation of the Line Elements of a Plane on the Tangents of a Hyperboloid.” By Prof. Jan pr Vries. (Communicated at the meeting of March 24, 1923). 1. In order to arrive at a representation of the Ime elements (P,/) of a plane «‚ we consider a hyperboloid H which touches « in A, and which cuts it along the straight lines a, and a,. Let R be the projection of P on H out of the point O of H, o the tangent plane at R, r the intersection of g with the plane O/; we consider r as the image of the line element formed by P and /. If, inversely, r is a tangent of H, R the point of contact, P the projection of Rk, / the projection of 7, the line element (/,/) has the tangent 7» for image '). We shall call the straight lines of H which cut each other in O, 6, and 6,; 6, cuts « in a point B, of a,, 6, passes through a point Bs of a. 2. If / passes through B, and P coincides with B,, R is the point of contact of the plane 5,/, and any tangent 7 lying in this plane, may be considered as the image (Bl. Hence (B,,/) is a singular element and its image is the plane pencil (7) round &. If l revolves round Z,, the plane pencil (7) describes the parabolic bilinear congruence with the directrix 4,, formed by the tangents which have their points of contact on 6,. Analogously the line ele- ments (Bl) are singular. If B is an arbitrary point of the straight line b= B,B,, R lies in O. The line element (B,5) is therefore also singular and is repre- sented by the plane pencil (0) of the straight lines that touch H in O and lie in the tangent plane w. Hence, inversely, any tangent o is singular, as it represents all elements (5,6). But at the sume time it is the image of all the elements of which the point P lies in the intersection of o with «, for r is projected out of O by any plane which contains 7. The 1) A fine representation of the line elements of x on the points of space may be found in the thesis of Dr. G. ScHAAKE. (Afbeeldingen van figuren op de punten eener lineaire ruimte, P. Noordhoff, 1922). 130 plane pencil (O,w) is accordingly the image of the null system MN (0,1), in which N lies on 6. Let g, be a straight line of MH cutting 6, and a, so that its projection I: passes through B,. As any point of g, may be considered as a point of contact R, P is an arbitrary point of g, and g, is the image of all line elements lying on g,. The straight lines of the serolls (g,) and (g,) are therefore singular tangents. 3. Let the symbol (A, 7) indicate a system of line elements (P,/) in which the points P lie on a curve of the order a and the straight lines / envelop a curve of the class 2. The image of a plane pencil (1,0) is apparently a plane pencil of tangents. If P lies in A, the plane pencil (7) coincides with the plane pencil (A,/). The plane pencils (B,, /) and (B,,/) are repre- sented by congruences (1,1) (cf. § 2). The image of a system (0,1) consists of the tangents of a conic 2 lying in the projecting plane of the fixed straight line /. A system (1,1) consists of the line elements of which P lies on a straight line c and / passes through a point D. If P moves on the straight line c, R describes a conic y? (through) and g envelops — the tangent cone which has the pole of the plane y of y? as vertex. The plane d= Ol revolves round d= OD and describes a pencil which is projective with the system of the tangent planes @ (index 2). The image lines 7 describe accordingly a cubic scroll of which d is the double directrix and y° a director curve. The intersection of this seroll (#)° and the plane y consists evidently of the conie y? and the tangent o which rests on c and is the image of the line element (B,5) belonging to (1,1). The points of intersection of y? with c lie on the straight lines a, and a,; the line elements to which they belong, are represented by the tangents of (7)? which, apart from o, rest on c. To (7) there belong two straight lines of H; they cut each other on d, and are the images of the line elements for which / passes through B, or B, 4. Let a system (A,x) be given. The curve (P; which is of the order x, is projected out of O by a cone of the same order, which cuts H along a curve (R) of the order 2% (with a double point in O). The polar plane of the point /, chosen at random, contains accordingly 2m points R; hence the tangent planes @ envelop a surface of the class 27. To each plane @ there corresponds one plane (O/); inversely to one plane Q/ (containing a points P) there 131 are conjugated a planes o. The planes O/ and the tangent planes e define on any straight line a correspondence with characteristic numbers Ar and 22. Through each coincidence there passes one image line 7; accordingly the system (A,2) is represented by a scroll of the order (A + 2) 2. A system (A, 2) contains 2A straight lines / passing through B, or through B, As each of them carries a line elements, the scroll contains 2A straight lines of the hyperboloid, each of which is a x-fold straight line of the scroll. The system (1,7) in which the points P form a curve (P) of the order a which has a x-fold point D and where all straight lines 1 meet in D, has to be examined separately. For here a plane Ol contains only (a—x) points P and defines therefore only (1—zx) planes o. The characteristic numbers of the correspondence between the points of a straight line are in this case (a—x) and 22, so that the system (1,~) is represented by a scroll of the order (82—x) on which the straight line OD is evidently 2a-fold. A system (1,2) of the kind in question is found in a null system N(u,v) which is the locus of the null points of the rays of a plane pencil round a point D. For this null curve is a curve of the order (u Hv) with a u-fold point D, so that the line elements form a system (1,u + r). 5. A null system N(u,v) is represented by a congruence of rays [vr]. The straight line a, is a null ray for v of its points Pand the straight line r representing (P,a,), coincides with a,. Hence a, and a, are v-fold rays of the congruence; the field-degree of [7] is accordingly 2p. Let Q be the central projection of the point #. The null curve of Q is projected by a cone of the order (u + vr) and this cone has 2u Hr) points AR in common with the conic which is the inter- section of H and the polar plane of £. From this follows that the sheaf-degree of the congruence is 2(u + v). The image of an N(u,v) is therefore a congruence (2u + 2», 2 vr). Accordingly a bilinear null system N(1,1) is represented by a congruence (4,2). The singular points S,, S,, S, define three points R,, R,, R, on H; these are the vertices of three plane pencils (r,), (r,), (",), representing the plane pencils round the points S, hence singular points of the congruence [7]. The line elements on the three singular straight lines s,=S,S,, s, and s, are represented by the tangents of three conics op? through O. Their planes 6; ure singular planes of the congruence. Also the plane o=R,R,R, is singular 132 for it contains one ray of each of the plane pencils (7%). All tangents of the conic o* along which H is intersected by 6, belong therefore to [r]. On o* there lies one point B,* of 6, and one point B,* of . These two points are also singular, for the tangent to oc’ at B,* is the image of the line element of M(1,1) that has its null point in B,; but this line element is represented by any ray of the plane pencil (r) round B,*. The null point of the straight line 6 is represented by the plane pencil (O,@); hence also O is a singular point of the congruence (4,2). 6. The enveloping cone with vertex F is the image of a system of op! line elements of which the points P lie on the conic 22, which is the central projection of the conic o° in the polar plane of F. The straight lines / pass through the projection Q of F. Any line lis the projection of a conic through O and contains therefore two points P, corresponding to the two points R of vy? in Ol. The cone round # has accordingly a system (1,2) for image. The conic 2? passes through B, and B, the point Q is to be counted double, being the class curve of /. If F describes the straight line f, the corresponding tangent cones form a congruence (2,2) with directriv f. The curves of contact 9? pass through the intersections S,*, S,* of H with the polar line of f, and rest on 6, and 5, Hence the curves z° form a pencil with the base points B, 5,,.S,, S,, which are sengular null points. Through a point P there passes one line /; for the corresponding point R carries one tangent r that rests on f and has the straight line 1= PQ for projection. A straight line / defines a point Q of the projection q of f, hence a point F, and through this there pass two tangents r to the conic in Ol. The congruence in question (2,2) is therefore represented by a null system N (1,2). The line f ents the tangent plane w =h,b, in a point F*, the projection S of which lies on 6 and is a singular null point because the tangent OS represents all line elements round S. The intersections #,* and /,* of f and H are singular for the congruence (2,2); their projections F, and F, on « are therefore singular null points. In this way the seven singular null points which N (1,2) must have '), are indicated. 1) Cf. e.g. my paper on plane linear null systems. These Proceedings Vol. XV p- 1165. 133 Through F,* there pass two straight lines g, and A, of H, through F,* two straight lines g, and A. These four lines form a skew quadrilateral; g, and g, cut each other in S,*, h, and h, in S,*; g, and A, rest on 6,, g, and h, on 6,. The projections ae ie: In he of these lines are evidently singular null rays and form a quadri- lateral which has the singular null points S,,S,; F‚,F,; B,,B, as angular points. For B, = lie B‚=g, hs vi =4, he Ee =, hu; Gigs, 8, —— he The plane Of cuts H along a conic, the tangents of which belong to [r]; hence the straight line q, (the projection of f) is a singular null ray. On q lie the singular null points F,,F, and S. But S is the intersection of a tangent 0, therefore also a point of the singular null ray b= B,B,. Accordingly the singular elements of NV (1,2) form the figure of the angular points, the diagonal points and the sides of a complete quadrangle. This null system is therefore of the same kind as the (1,2) which arises if to each straight line there are conjugated as null points its intersections with the conic in which it is transformed by an involutory quadratic correspondence.’) 7. Five tangents r define a linear complex A; this has a congruence (2,2) in common with the complex of the tangents of H. The represen- tation on @ is again a null system N (1,2); for a point P defines a point R and in @ there lies one ray of the plane pencil which in A has the null point of @ as vertex; and a line / defines on A a conic of which two tangents belong to the linear complex. This complex has two straight lines in common with each of the scrolls of H; they form a skew quadrilateral g, g, h,,, the angular points of which are singular points for the congruence (2,2). For in 4 the point g,g, is the null point of the plane e defined bij g, and g,, so that any tangent at that point belongs to both complexes. Consequently the points g, g,, Jala hoho, and h,g, are singular null points of the null system (1,2) in «. As g, and h, rest on 6,, g, and A, pass through B,; hence B, and B, are singular null points. Also here the six null points are the angular points of a complete quadrilateral the sides of which are singular null rays. The plane pencil (O,@) contains one ray of A which therefore also belongs to the congruence; its intersection S is the seventh singular point of N (1,2). As Slieson band B, and B, are singular, also 6 is a singular null ray. 1) The general null system (1,2) has no singular null rays (l.c. p. 1167). 134 8. With a complex of the n order, I, the complex {7} of the tangents has a congruence (2n,2n) in common which has for image a null system N (n, 2n). 1” has 2n straight lines in common with any scroll of H; hence the null system has 4n singular straight lines, 2n of which pass through B, and 2n through B,. B, and B, are therefore singular null points. The straight line 6 is evidently a singular null ray. Anatomy. — ‘The ontogenetic development of the Corpus striatum in birds and a comparison with mammals and man’. By Dr. C. U. Arrins Kapprrs. (Communicated at the meeting of November 25, 1922). In the last ten years the corpus striatum has been a centre of interest as well for anatomists as pathologists, the latter chiefly after the researches of Kinnier Wirson. There are however great differences in the intraventricular growths to which this name is given in different vertebrates. Though I shall deal here chiefly with the corpus striatum in birds, mammals and man, I will start with making some introductory remarks on the intraventricular growths in fishes since the same principle which we shall meet in the amniota is already observed here: viz. the fact that the so called striatal parts do not only arise from the base of the forebrain but also from the mantle. If one looks at the forebrain of a teleost or ganoid, it seems as if only the basal part of the forebrain consisted of nervous tissue, whereas the dorsal part merely consists of a choroid membrane. This however is only seemingly so. As a matter of fact, the two primordia generally observed in forebrains, the basal one and the dorsal one (from the latter of which the mantle arises), are both present also in embryo’s of Teleosts and Ganoids. Whereas however the dorsal part in other fishes enlarges in a mantle-like way, increasing chiefly in surface and folding inward, the mantle primordium in Teleosts developes in a quite different way. Instead of increasing in surface it increases in thickness, thus narrowing the ventricle of the forebrain in which it protrudes. This increase in thickness even goes so far that the pallial part bulges outward, pushing the dorsal wall latero-ventrally, in conse- quence of which the roof membrane is stretched and widely extended from left to right. Thus an everted pallium is formed in these fishes, in contrary to the inverted mantle of otber animals. This process of development is seen in all larvae of Teleosts, and clearly demonstrated by a study of Lepidosteus osseus (a bony ganoid) 136 of which I give here some pictures. In the first figure (Lepidosteus larva of 5 cM.), the limit between the basal primordium (from which the palaeostriatum arises), and the dorsal (pallial) primordium is indicated by a line, the dorsal point of which might even be drawn somewhat more laterally (to coincide with the fiss. endorrhinalis interna). The basal pot de repère of this line lies in the fissura endorrhinalis externa, only slightly indicated in this stage. The pallial part is very small in this stage. In a later stage, the pallial part however in- creases considerably. In fig. 2 and 31 have given transsections of a 10 eM. larva and a full grown animal (1.20 M long). These two latter figures represent a more frontal level than figure I, so that the olfactory bulb is cut, in order to show Fig. 1. Transverse : section of the forebrain the reader that here we have really to do with of a 5 c.M. larva of a pallial part, (p.), which however in these Lepidosteus. fishes does not grow like a real mantle, but N.b.=basalnucleus merely increases in thickness. The insertion of Gael ua peduneulans the roof membrane is at the place of the X in anterior. Be = : fig. 3, from which results that nearly all the mantle substance has an intraventricular position. Fig. 2. Transverse section of the Fig. 8. Transverse section of forebrain of a larva of Lepidosteus the forebrain of an adult Lepidosteus (10 ¢.M.). (right half) 2 = insertion of the p = pallium. roof membrane, p = nervous pal- lium. 137 This increase in thickness gives rise — a little more caudally than fig. 3 — to a large mass of nervous tissue, extending over tbe palaeostriatum (which itself is derived from the basal part) and therefore has been named by EDINGER epistriatum. Epincer himself thought that this epistriatum is an outgrowth of the striatum. | have however been able to show that it really is caused by a medial thickening of the pallium extending over the palaeo-striatum. Also by studying its fibre-connections — which appear to be homologous to the fibre connections of the selachian mantle — I have been able to show this homology.') Referring for further details concerning the Teleostean brain to the works of JOHNSTON *), SHELDON’), Van per Horst‘) and HormereN ‘), I will only call the attention to the fact that this epistriatum of fishes has chiefly primary olfactory functions, viz. that it receives chiefly fibres of the tr. olfactorius (fibrae bulbo-epistriaticae). In this sense it is a primary epistriatum. A primary epistriatum also developes in Amphibia but it remains very small there (receiving only tr. olfact. fibres from the bulbus accessorius °)) since the surface growth of the mantle is so consider- able in Amphibia. This primary epistriatum of Amphibia developes entirely independently from the palaeo-striatum or basal nucleus, in front of it, from the side wall of the forebrain. In Reptilia the primary epistriatum is superposed by a much larger secundary epistriatum or archistriatum i.e. by an ingrowth of the mantle which does not receive bulbo-epistriatic fibres but lobo-epistriatic, i.e. secundary olfactory fibres from the primary olfactory cortex (palaeocortex mihi; cortex praepiriformis BRODMANN). Notwithstanding its enormous development and intraventricular 1) The structure of the Teleostean and Selachian brain. Journ. of Comp. Neur. Vol. XVI, 1906. Zur vergleichenden Anatomie des Vorderhirns der Vertebraten, Anat. Anzeiger Bnd. XXX, 1907. *) The telencephalon of Ganoids and Teleosts. Journ. of Comp. Neur. Vol. XXI, 1911 and the Teleostean Forebrain, Anat. Record. 1912. 5) The olfactory tracts in Teleosts. Journ. of Comp. Neurology Vol. XXII, 1912. 4) The forebrain of the Symbranchidae. Proceedings of the Kon. Akademie v. Wetensch. Amsterdam, 1920. 5) Zur Anatomie und Histologie des Vorderhirns und Zwischenhirns der Knochen- fische, Acta Zoologica, Bnd. I, 1920. ©) Herrick. The morphology of the forebrain in Amphibia and Reptilia. Journ. of Comp. Neurol. Vol. XX, 1920. De Lance. Das Vorderhirn der Reptilien, fol. Neurob. Bnd. V, 1911. Ariens Kappers und Hammer. Das Zentral-Nervensystem des Ochsenfrosches (Rana Catesbyana) Psych. en Neur. Bladen 1918. 138 (hypopallial, Err. Smirn *) growth, extending far backward, where it is continuous with the piriform and ammoncortex, this archistri- atum keeps its contact with the olfactory area in front of the Foramen Monroi, near the primary “Anlage” of the epistriatum (nucl. tr. olfact. lateralis in Reptilia: Crossy *). One might be inclined to ask, how it is possible to ascribe this hypopallial growth to neurobiotaxis — as Ent. Smita does — if the majority of aferent fibres (tr. cortico-epistriaticus) comes from the periphery Such fibres indeed cannot account for this mode of growth. But the archi- striata (sec. epistr.) of both sides are connected by a very strong commissure, which thus provides them with medial impulsus and moreover it receives aferent fibres from the basimedial grey by the taenia terminalis fibres. Both systems must be made responsible for the medial intraventricylar growth of the archistriatum. Whilst this archistriatum which is thus derived from the innerside of the mantle (hypopalium Ex. Smirn®) forms the larger part of the intraventricular mass in Chelonia (where the paleaostriatum is but small) a new striate substance which is only very small in turtles, becomes evident in Lacertilia, Ophidia and Crocodilia: the neostriatum. Moreover the paleaostriatum, the original basal nucleus of the forebrain, enlarges considerably in these animals (palaeo- striatum augmentatum or mesostriatum). Whereas the palaeostriatum augmentatum is really an increase from the same matrix from which the palaeostriatum primitivum arises, and from its immediate surrounding (corresponding approximati- vely with the tuberculum parolfactorium) the neostriatum is an entirely new addition starting in Reptilia as I pointed out in 1908 *). It arises from two sources. 1°. from the base of the brain in front of the palaeostriatum and 2° from the latero-frontal mantle joining this region, as has been pointed out by Err. Smita (l.c). The palaeostriatum, but chiefly the neostriatum receives its stimuli from the tweenbrain and this may be the neurobiotactic cause of its intraventricular medio-caudally directed growth. The neostriatum together with the archistriatum (which is separated from it in Ophidia and Lacertilia by a deep fissure, the fiss. strio-archistriatica), is called hypopallium by Ett. Smirn, on account of their character as an ingrowth of the pallium. 1) Vida infra. 8) The forebrain of Alligator missisippensis, Journ. of Comp. Neur. Vol. 27, 1917. 3) A preliminary note upon the morphology of the corpus striatum. Journ. of Anat. (English), Vol. Lill, 1919. 4) Die Phylogenese des Rhinencephalons, des Corpus Striatum und der Vorderhirn- commissuren. Folia Neurobiologica Bnd. I, 1908. Weitere Mitteilung zur Phylogenese des Vorderhirnes und des Thalamus, Anat. Anzeiger Bnd. 1908. There is no doubt indeed that the neostriatum partly arises as such a hypopal- lial ingrowth in all the higher vertebrates, though its anlage is not limited to the mantle, but, also extends over the base of the bram in front of the palaeostriatum (immediately behind the anterior olfactory ventricle). Whilst the neo-striatum is separated from the archi-striatum by the fissura strio-archistriatica (see my book on the Comp. Anatomy of the brain, Vol. IL fig. 534), Etuior Situ has rightly pointed out that the boundary between the neo-striatum and palaeostriatum is chiefly indicated by blood vessels. | may add that besides a shallow groove may indicate this boundary line (also in Reptilia), which groove [ shall call fssura neo-palaeostriatica. I have now studied the ontogenetic development of the different parts of the striatum complex in birds, mammals and man, and shall give here a short review of if, leaving the archi-striatum further out of discussion, since its place in brain-anatomy as the homologue of the nucleus amygdalae of mammals is since long established. Starting than with birds | may remind that practically all anato- mists have accepted the division of the forebrain of these animals as given by EpiNGer in 1896. Underneath the pallium (in which the cortex is very primitive) and continuous with it, is the Ayperstriatum, forming the most dor- sal and most lateral part of the striate complex. This hyperstriatum is in most birds — not in all —, easily distinguished in two divisions, by a thin medullary lamella: the lamina medullaris hyperstriati. These divisions I shall call Ayperstriatum superius*), and Ayperstriatum inferius *). The hyperstriatum inferius in its lateral part shows a special field characterized by large cells, and richly provided with medullary fibres: the ecto-striatum of authors, which like the rest of the hyperstriatum is separated from the underlying meso-striatum (palaeo- striatum augmentatum) by the lamina medullaris dorsalis of authors, which | prefer to call lamina medullaris externa since it does not only form the dorsal but also the lateral boundary of the meso- striatum. This lamina medullaris externa is very richly provided with bloodvessels as is also observed by Hunter (Sydney) in the Kiwi. !) This was called by Scuroeper pars fronto-dorsalis hyperstriali. [t consists of the areae A.C. and D. of Rose’s (c.f. Scororeper: Der Faserverlauf in Vorderhirn’ des Hiihnes, Journ. of Pschych. und Neur. Bnd. 18, Erg. Heft 1912, and Rose ,,Die zytolectonische Gliederung des Vorderhirns der Végel’’. Ibidem Bnd. 21, 1914), 8) This corresponds with the areae G1, G2, G3 of Rose's and with the striatum parichale of Kalisher (Comp. Kalisher: Abhandl. der Akad. der Wissensch. Berlin. 1900, 1901. 1905). 10 Proceedings Royal Acad. Amsterdam. Vol. X XVI. 140 Besides the boundary of the mesostriatum and hyperstriatum in some birds is marked on the ventricular side by a slight groove, my fissura neo-palaeostriatica. In caudal direction the mesostriatum, which extends to the ven- tricular surface becomes smaller and smaller, thus exhibiting a sort of cauda, which follows for some distance the caudal pole of the hyperstriatum inferius, and may be called substantia palaeostriatica caudata (see fig. 11 and 12). In some large birds, like Pelicanus, the hyperstriatum and meso-striatum may be separated from each other — starting at the ventricular side — by an obtuse object without cutting, which probably is due to the medullary external lamella being so richly provided with bloodvessels. In the centre of the mesostriatum (or palaeostriatum augmentatum) the so called basal nucleus of authors (palaeostriatum primitivum) is found, a cluster of large cells, separated in front of the augmented part of the palaeostriatum by another lamella the lamina medullaris ventralis of authors, lamina medullaris interna mihi. The archistriatum or nucleus amygdalae of which | shall not speak here further is pushed backward and ventrally in birds by the enormous development of the hyperstriatum. Consequently the fissura strio-archistriatica, so conspicuous in Lacertilia and Ophidia, has become invisible in birds (as is already the case with Crocodiles). In order to study the embryonic development of these parts in birds, I made use of haematoxyline and silverseries of the chick of 4, 5, 54, 6, 7, 9 and 11 days of incubation and of an embryo of the ostrich some days before birth. In a five days embryo of a chick, we find in a transverse section made on the level of the foramen Monroi, four protrusions in the ventricle (fig 4). The lower protrusion a is the eminentia basimedialis which some sections more frontally continues in the septum. This forms the basi-medial grey substance and has not to do with the striate complex. The other three protrusions form parts of the so called striate complex. The protrusion 6 is the primordium of the palaeostriatum. Its centre (less dark in fig. 4), is the basal nucleus or palaeostriatum primitivum, which is augmented by the surrounding darker cells, the palaeostriatum augmentatum. This protrusion has only a small frontal extension (as is seen in the sagittal section, represented in fig. 5. It is chiefly confined to the level of the foramen Monroi and continues backward in the side wall of the recessus praeopticus (r.o. tig. 5). The protusion b is separated by a fissure (the fissura neo-palaeo-striatica) from the 141 tnberculum ec which is less protruding but continues further front- ally than 6, bending down more or less to the base of the brain. Fig. 4. Transverse section of the forebrain of a chickembryo of 5 days on the level of the foramen Monroi. b = primordium of the palaeostriatum, c— primordium of the hyperstriatum inferius, d = primordium of the hyperstriatum superius. For a see text. This protrusion c appears to be the primordium of the hyperstriatuim inferius. Caudally the groove which separates it from 6 fades away, the cells of ¢ extending over 4 (comp. also fig. 6). Dorsally from c, arising equally from the mantle is d, merely a thickening of the pallium in this stage which however appears to give rise to the hyperstriatum superius. Figure 6, representing a sagittal section, is taken from an embryo of six days of incubation. The section shows the relation of the hyperstriatum inferius c to the palaeostriatum augmentatum 6, which extends frontally to the triangular fissure, a part of the fissura „eo-palaeostriatica. It is further seen that c, the hyperstriatum inferius, arises on this level from the basal region in front of the palaeostriatum cor- responding with the tuberculum olfactorium (t. o.). The hy perstriatum inferius thus partly has a basal origin (partly because more laterally it is continuous also with the mantle as we already saw in the transverse section of fig. 4). 10* 142 Examining the same series on a more lateral level (fig. 7), we meet with the hyperstriatum superius d, and see that this arises Fig. 5. Sagittal section of the forebrain of a chickembryo of 5'/, days. b = primordium of the palaeostriatum. r 0.= wall of the recessus opticus. from the mantle only, i.e. from the brainwall above the small split that indicates the communication between the lateral ventricle and the olfactory ventricle (already in fig. 6 the frontal part of the pallium shows a thicke- ning at this place). In the last section of this series which I reproduce (fig. 8), all the parts of the striatum complex of birds are already visible in their mutual arrangement: the hyperstriatum superius (d.) forming the most dorsal part and extending over the rest, being continuous frontally with the pallium. Underneath it we find the hyperstriatum inferius c being in this Fig. 6 Sagittal section of the forebrain of a chickembryo of 6 days on a level lateral to fig. 5 t. p. = tuberculum parolfactorium, #0. = tubere. olfact. 6 = palaeostriatum augmentum, c— hyperstriatum inferius. (= mesostriatum). 143 section continuous with the most frontal part of the basis cerebri (more laterally with the mantle) and covering 6, the meso-striatum or palaeostriatum augmentatum, in which the lighter centre (richly provided with fibres) is the primitive palaeostriatum, the basal nucleus. If we now look at the figures of a 11 days embryo of the chick, we find that the chief alteration exhibited, is the enlargement of both parts of the hyperstriatum, which not only have increased in Fig. 7. Sagittal section of the forebrain of a chickembryo of 6 days. 6 = palaeostriatum augmentatum (= mesostriatum). c = hyperstriatum inferius. d = hyperstriatum superius. thickness (as appears from the fact that much less of the ventricle has remained free), but also has enlarged in medial direction. The latter fact is evident from a comparison of tigg. 9 and 6, which are taken on approximately corresponding levels (rather medial). Whereas in fig. 6 on this level nothing is as yet visible of the hyperstriatum, the latter is very clearly shown in fig. 9, as a result of its growth in medial direction, further extending into the ven- tricle. It also shows the division in hyperstriatum superius and inferius. In this figure we see moreover that the hyperstriatum superius is continuous only with the brainwall above the ventriculus, 144 being entirely derived from the mantle‘), not from the basal part of the brain. Olf. b. Fig. 8. Sagittal section of the forebrain of a chickembryo of 6 days (lateral to fig. 7) d = palaeostriatum augmentatum (= meso- striatum) c = hyperstriatum inferius, d = hyperstriatum superius. In fig. 9 only a small part of the palaeostriatum (b.) is seen, viz that part which is continuous with the recessus praeopticus. Fig. 10 is interesting to us because it shows that the hindpole of the striatum nearly only consists of hyperstriatum inferius (c), the lamina medullaris hyperstriati (in this stage of development) ending only little beyond the contact of hyperstriatum superius and pal- lium. In the same figure (but better in 11 and 12) is seen that the hyperstriatum. inferius is continuous with the base of the brain (whilst more laterally it is continuous in the pallium). Of the palaeostriatum besides the part that is continuous with the recessus opticus a frontal part is seen in fig. 10, seemingly separated from the hindpart by a recess of the ventricle. This is however only seemingly so, this aspect being caused by the fact 1) One might ask if the part called hyperstriatum superius here is not partly the ‘mediale Sagittal-Wulst” of the cortex with which the hyperstriatum superius in many birds (f.i. the Cacatua) coalesces. This however is not so here, though later the hyperstriatum superius continues in the medio-dorsal mantle, without showing any medullary limitation. 145 that the palaeostriatum following the lateral convexity of the brain is curved and not cut here in its entirely length. In fig. 11 this separation is smaller and in fig. 12 it has entirely disappeared. Fig. 9. Sagittal section (rather medial) of the forebrain of a chickembryo of 11 days. r. 0. = transition to the recessus opticus. b= posterior part of the mesostriatum or palaeostriatum. c = hyperstriatum inferius. d= hyperstriatum superius. P. < 6cM. Moreover in the same stone some scales of other fish-species occur, which I do not venture to de- termine. This shows, that fish-rests are probably abundant in these layers. A further exploration would certainly be worth while, and could give us more solid information about the age and the character of these deposits. Geology. — “Fractures and Faults near the Surface of Moving Geanticlines. U1. The Horizontal Movement of the Central- Atlantic Ridge’. By Prof. H. A. Brouwer. (Communicated at the meeting of January 27, 1928). Many explanations that have been given for tectonic structures are unsatisfactory on account of the geometrical treatment of the problems and a preference to vertical movements. The geometrical treatment draws attention to the change in position of parts of the earth’s crust, while the velocity of the movement receives no further consideration. Because of the predilection for vertical movements we often explain the observed facts by vertical movements, until it is proved that faulting must bave been effected in another direction. In regions, which are not accessible to direct observation, i.e. the parts of the earth’s crust covered by the sea, the existing mor- phology is explained by rising and by subsiding movements, while the factor time is neglected. Subsidence of continents and subsidence of “land-bridges’” are common expressions in geological literature. Velocity and direction of the movement are hardly or not at all considered in these inadequate interpretations of dynamic phenomena. The reason is obvious, the forces causing the movement are unknown, and the velocity of the movement cannot be measured. Another way of studying these problems is the comparative-tectonic method. Our object in this paper is to consider the results achieved by applying this method to the movement of a region, which is almost entirely covered by the sea, of which the morphology is known in broad outlines, and which is still moving, as we know from numerous earthquakes. It is the S-shaped ridge, of which the existence has been proved by numerous soundings and parts of which emerge from the sea, as e.g. the Azores and the islands of St. Paul and Tristan da Cunha. In previous papers’) we pointed to the significance of the bending-points of the horizontal projection of a geanticlinal axis for a judgment upon the horizontal movement of geanticlines. Transverse fractures, which may be more or less 1) These Proceedings XXIII, p. 570; XXV, p. 327, H. A. Brouwer. The horizontal movement of geanticlines and the fractures near their surface. Journ. of Geology. 1921, XXIX, p. 560—577. 168 gaping are the surface expression of velocity-differences in a horizontal direction; horizontal transverse faults prevail at greater depth, while with increasing plasticity deformation takes place without fracture- movements. If these tectonic zones of different depths are all visible at the surface, they enable us to trace the movement for a considerable Space of time, because then the different phases of the movement are observable. If the movements are still going on, the epicentra of earthquakes will be accumulated near the places with considerable velocity-differences and may be disposed along more or less transverse fractures. In this connection we point to the region in the neigh- bourhood of Sunda Strait between Java and Sumatra, to the earth- quake lines near the bending-point between the Alps and the Carpathian mountains, to Cook-strait between the Northern and the Southern island of New Zealand and to many others. A Ais En) arte Wis, ENT é Azoren : dhe iz ron EN = i 2 aye! . i AFRIKA yo py die we xl at age ir ietan ra da Cunha Zuid Amerika = South America. Romanche diep = Romanche Deep. Afrika = Africa Azoren = Azores Fig. 1. 2978 etc. Depths of the sea in meters on the Central-Atlantic Ridge. If a submarine ridge has a bending-point, the strongly curved shape of the ridge may have been developed from an originally simpler form by velocity-differences in a horizontal direction. Where the velocity-differences are greatest, the epicentra of earthquakes will be numerous, and from an accumulation of epicentra near a 169 bending point it may be concluded that velocity differences in a horizontal direction are a characteristic of the present movement. In the Central Atlantic Ridge there is a distinet bending-point between the island of St. Paul and the Romanche Deep, while quite close to it there is a zone of strong seismic activity. Further appli- cation of the comparative method would lead to the conclusion that the Central Atlantic Ridge is not only moving now, but has been moving for a long time, with velocity-differences in a horizontal direction. The tectonic structure of the ridge is not accessible to observation. However, there are indications that a further application of the comparative method is possible. The morphology is still little known, but the soundings have proved the existence of very great depths, viz. in the Romanche Deep, where a depth of 7370 m. has been sounded. This depth has been considered as a remarkable phenomenon for the Atlantic Ocean. The situation close to the bending-point points to an origin such as already previously suggested by us with regard to abnormally deep straits near the bending-points of rows of islands. Just as is the case in Manipa Strait between Ceram and Boeroe. The Romanche Deep can be explained by difference in velocity of horizontal movements for neighbouring parts of the ridge along the axis. We only find the results of the dijerences in velocity in a hori- zontal direction, the absolute horizontal movement cannot be inferred from the surface characters with the comparative method. We do not know whether the Central Atlantic Ridge originally had a more rectilinear form. Neither do we know whether the bending of the strong curve between the Azores and the island of St. Paul is still increasing, or whether the southern portion with Ascension and Tristan da Cunha is moving with less velocity than the northern in a western, or in an eastern direction, or whether it has become stationary now. Many widely different views have been brought forward concerning the origin of the Central Atlantic Ridge. Some authors*) look upon it as a rising geanticline, as a mountain range in statu nascendi. Up to now these authors never considered the horizontal movements, which as evidenced before often are much more important than the vertical movements in rising geanticlines. Another explanation’) has been afforded representing the ridge as the filling of an originally 1) E. Hava, Traité de Géologie I, 1907, p. 164. *) A. Wecenrr, Die Entstehung der Kontinente und Ozeane. 1922, p. 42. 170 narrow gaping fracture, which opened to the present Atlantic Ocean by horizontal movements of continental areas. In either view regarding the origin of the ridge the movements can take place with velocity-differences in a horizontal direction. Other explanations, such as the ridge being of volcanic origin or the highest parts of a subsided continent (horst), do not consider horizontal movements. Vertical movements may occur and may have occurred in some places perhaps in an upward, in other places in a downward direction, and varying at different periods, because no movement of the earth’s crust will have exactly a horizontal direction for a long time, just as it will never have exactly a vertical direction. The comparative method does not enable us to trace out the movement of the Central Atlantic Ridge down from its earliest development. It proves, however, that the simple explanations by upward and downward vertical movements, which have been suggested, cannot be maintained. Botany. — “On stimulation in auxotonic movements”. By Prof. J. M. Janse. (Communicated by Prof. J. C. Scnoure). (Communicated at the Meeting of January 27, 1923). Many movements (curvatures) of very different plant-organs are caused by a change in the speed of growth on one side of the organ; collectively they are often called ‘‘auxotonic’ movements. Various stimuli, among which those of gravitation and of light are by far the most important, may be the indirect cause of these movements; these stimuli are received locally and conducted to the growing zone in which the bending will afterwards take place. The theory hitherto generally accepted was that the normal vertical longitudinal growth was a separate phenomenon, and that, for instance, the gravitation-stimulus appeared only after the plant- organ had been given a different position. In a recently published paper’), I expressed as my opinion that, on the contrary, the normal length-growth is also due to the gravitation-stimulus which by an increased growth of the cells equally on all sides would cause, for instance, the vertical growth of the main-axis and of the radicle. In this position there would even be the maximal stimulation corresponding to their maximal speed of growth in this position, which is experimentally demonstrated. The experiments carried out by Wiesner, Moriscu *) and CzapekK *) speak in favour of this theory; they showed that after the tip of the radicle had been cut off, the rate of growth diminished appreciably within the next 24 hours; this dimination would undoubtedly have been still more apparent if the observations had been recorded also during the ensuing days, because the growth during the first day must still have been influ- enced by the stimulus received before the amputation of the tip. It is generally assumed that the stimulation by gravitation depends upon the pressure of the specifically heavier starch-grains (statoliths) upon the outer layer of the protoplast of certain cells (statocysts) ; 1) Reizwirkung bei Rektipetalität und bei senkrechtem Wachstum; Jahrbiicher für wissenschaftliche Botanik, 1922, Bd. 61, p. 590. *) Berichte d. d. bot. Gesellschaft, 1883, Bd. 1. p. 362. 5) Jahrb. fiir wiss. Botan., 1895, Bd. 27, p. 246. Poceedings Royal Acad. Amsterdam. Vol. XXVI. 172 such a stimulus, however, as has already been demonstrated by Noni, (Heterogene Induction, 1892), can be the cause of a move- ment only if the sensitiveness of this outer layer is unequal at different parts. As the vertical position, in the said organs, was regarded as the one in which no stimulation took place, it was supposed that the part adjoining the lowest transverse wall was not sensitive. If, however, also the longitudinal growth be indueed by the gravitation-stimulus, as we suppose here, that part would have to be on the contrary the most sensitive. However this may be, it is sure that there must always exist a certain connection between the position of the place of the greatest (or least) sensitiveness in the statocyst and the direction of normal growth of each organ, so that this, for instance in the cells of the vertically-growing stem, must be found at a different place to those of a horizontally-growing rhizome, etc. This ought to imply further that when an organ of itself changes its position, this should be preceded bv a shifting of the outer layer of the protoplast inside the cell. The supposition of such a shifting of the outer layer would, however, be inconsistent with the general assumption that this layer is immovable, an hypothesis, it is true, but one which for other reasons, e.g. the existence of the plas- modesms, might be called probable. This inconsistency suggests the query as to whether it is not more probable to assume that the excitable portion of the statocyst forms a separate organ of the cell, which might then lie between the outer layer and the granular protoplasm, but quite independent from the former. This protoplasmic part, which alone should be sensitive to the pressure of the starch-grains, might be termed the “static apparatus” and should be capable of shifting, consequent on some influence co The accompanying diagram represents, schematically, the 1 --K supposed position of the “static apparatus’ in the statocyst: Z = cellwall, H = outer layer, K = granular protoplasm, R = the static apparatus of which, M= the middle-field. The unequal thickness of the static apparatus in the drawing serves merely to indicate the local difference in sensitiveness ~R of this apparatus which should be greatest in the middle- field. from inside or outside, without the outer layer of the protoplast being involved in this movement. Moreover this apparatus should have to be most sensitive in the middle-field, while this sensitiveness 173 should diminish towards the edges as represented in the accompany- ing sketch. The apparatus need not be present in cells which are insensible to stimulation. The normal vertical position of the main axis and radicle would seem to imply that in these organs the middle-field lies against the basal transverse wall of the statocyst. But in a horizontally-growing rhizome, for instance, it ought to ly next to the lower longitudinal wall, for then only there would be maximal stimulus, accompanied by the maximum, equal all round, speed of growth, whereby the rhizome would keep its horizontal position. If now a certain shifting of the static apparatus is required to produce a new position of equilibrium, then inversely we might deduce from the changement in the position of equilibrium what shifting should have taken place in each separate case, but therefore it were necessary to know also in what part of the organ the static apparatus occurs. This shifting cannot be microscopically controlled, for the present at least, but if it should appear from the following lines that by assuming such a shifting we succeed in giving a simple explanation of widely different and often very complicated pheno- mena, this must favour our supposition of the presence of a movable excitable organ in the sensitive cell. It must be borne in mind, however, that it is therewith immaterial whether we think of an “static apparatus” as indicated above, or of the outer layer as a whole, provided this be but movable; in future we shall suppose the presence of a “‘static apparatus”. If it be possible by this means to explain why a plant-organ which has a certain position of equilibrium is able to keep this position during its growth, it does not, however explain the familiar phenomenon of an organ that is brought out of its equilibrium returning to this position, not only of its own accord, but also by shortest possible way; so a root, for instance, placed horizontally will curve downwards in a vertical plane until the tip points per- pendicularly again. That this movement is of great advantage for the later development of the plant is of course no sufficient expla- nation of its cause, especially since the preparations for the movement are made long before the utility of the bending could be perceived by the plant. We should have to ask, therefore, why it is that a part of the plant makes a useful movement and how it comes that the new position is acquired by the shortest way. This question which, as it seems to me, is proposed here for the first time so sharply, is connected so deeply with the more intimate life of the cell that it can not surprise that no entirely complete 12* 174 answer to it can be given yet, but nevertheless we can endeavour to arrive a step nearer at its solution. We shall confine ourselves now in the first place to the stimulus of gravitation. We have thus supposed that the statie apparatus of the statocyst lies in snch a position that the middle-field, which forms its most sensitive part, adjoins the lower wall of the cell when the organ is in equilibrium, whatever this position may be. When this position be changed, if, for instance, a root be placed horizontally, the starch- grains which shift under the influence of gravitation, come into contact with the less sensitive border of the apparatus; if then, after some time, the tip bends downward, the starch-grains, again shifting, will gradually come into contact with the more and more sensitive parts of the apparatus till, when the tip stands vertical, they will have reached the most excitable place again; thus we see that the curving downward is accompanied by a continual increase of the stimulus and that the speed of this increase will be greatest when bending takes place in a vertical plane. Could it be that this increase of the stimulus is the indirect cause of the bending and at the same time of the choice of the shortest way ? Of itself this “striving after the maximal stimulation’, as we might term it, cannot be regarded in the plant as the direct canse of any movement, although it might later on be of aid in explaining it; nevertheless cases are known in which there exists a rather direct connection between this striving after an ever stronger stimulus and the movements. So, for instance, in positive chemotaxis: if e.g. spermatozoides of ferns be placed in a weak solution of malic acid in which the con- centration is unequal at different places, they will move towards the place of the strongest concentration, i.e. in the direction of the increasing concentration or stimulation. It is known, regarding some of the senses of man and animals, such as the eye, the ear, and perhaps also of the static organ when the organism is at rest, that they adjust themselves automatically (reflectorily) to a stronger stimulus, i.e. that the same stimulus which causes the sense-perception also excites other nerves and through them certain muscles, which last thereby move the sense- organ in such a way that it receives then the strongest possible impres- sion; thus here too we have the case of a movement with the aim of increasing the stimulation. If such a comparison with the plants were entirely justified, which could not be decided at present, we 175 might go further and state that, because the sense-perception is wanting in the plants, their bending might be compared with the purely reflectory movements of animals. However, although it must be admitted that within the scope of physiology comparisons between plants and animals may be success- fully drawn in many cases (as is probable especially with regard to stimulation, for the reason that in both groups of living organisms one and the same relation appears to exist between stimulus-inten- sity and stimulus-effect: the law of Weger), this must be done always with the greatest caution. Bearing this in mind it nevertheless appears to me that the facts furnish us with sufficient reason to assume the striving on the part of the plant to receive the greatest possible stimulation by the quickest way as a supposition, just as we know this is the case with regard to positive chemotaxis. It must be left to later researches to reduce this striving after maximal stimulation to an actual cause of movement. With the aid of a number of examples taken from the different groups of auxotonic movements, I now wish to demonstrate very shortly how simple the explanation of these phenomena becomes when we set forth from the assumptions mentioned above. The different movements may be brought to certain groups according to the (supposed) position of the static apparatus and to the shifting which it should undergo. A. STIMULATION BY GRAVITATION. I. Stationary position of the static apparatus. a. In the first place the static apparatus might lie against the lowest transverse wall of the statocyst. This should be so in the case of the vertically-growing main-root and main-axis, where the, maximal, stimulus should be the cause of the vertical growth of both by the equal lengthening of the cells allround. If these same organs be placed in another position, e. g. horizont- ally, they will show positive (root) or negative (stem) geotropism. This we should now try to explain by the striving after a stronger stimulation. In the horizontal position the starch-grains press upon a part of the less sensitive border of the static apparatus; if they have to come into contact with the middle-field, the most sensitive part, the root will have to bend downwards, the stem, on the other hand, upwards. The explanation of these opposite movements requires therefore no new supposition; it follows from the circumstance that in the statoeyst the middle-field in the case of the root lies against the transverse wall which is turned away from the growing-zone 176 (where the bending occurs) and in the case of the stem against the one that is turned towards it. If in the centrifugal-experiment, the statolithes are moved outwards in the statocyst, then, for the same reason as given above, the stem must react by bending towards the centre, whereas the root will curve away from it. 4. Normal horizontally-growing plant-organs, such as rhizomes and some rootlets of epiphytes, can only maintain their position of equilibrium and continue growing in the same direction if the middle-field lies at the lowest longitudinal wall of the statocyst, for the same reason again that it is only in this position that the starch- grains will come in contact with this middle-field. Whether these organs also attain their quickest growth in this position has still to be investigated. c. Besides lying against the transverse and longitudinal walls, the middle-field might also lie between the two, i.e. slanting; in such eases the organ should also exhibit a slanting position of equilibrium, the size of the angle it makes with the perpendicular depending upon the position of the apparatus with regard to the axis of the statocyst. This would explain the fixed position which the lateral branches and lateral roots of the first order always assume, and which is so different in different plants (cf. e.g. Araucarut, the common foliage trees, Populus piramidalis). ll. Variable position of the static apparatus. Various organs of plants undergo a change in equilibrium during their normal development which could be ascribed now toa shifting of the apparatus at a certain moment, that is to say, if it can be demonstrated that gravitation-stimulus or longitudinal growth plays a part in the phenomenon. The shifting may take place either at a certain moment or be continuous; moreover it may occur autonomously or as a result of some outside cause. According to this we may distinguish the following cases: a. The position of the apparatus changes, autonomously, at a certain moment. During the germination of the seed of a twining plant the young stem is at first vertical, but very soon the summit assumes a more or less horizontal position and at the same time the twining com- mences. It is possible that this transition from negative to transversal geotropism were preceded by an autonomous displacement of the lee static apparatus, whereby the middle-field is shifted from the lowest transverse wall to one of the longitudinal walls; by the bending of the stem this longitudinal wall would then become the lowest of the statocyst. If the apparatus in the cell shifts over 90°, the new position of the stem-tip will become exactly horizontal; if, on the contrary, it moves less, the stem-tip will, as is often the case, assume a corres- ponding upward slope. Similar changes in position, as seen in many flowers before and after flowering, may be explained in an equally simple way. The flowers of Narcissus, for example, when in bud stand perfectly upright, but when about to open are practically horizontal, which again would point to a preceding shifting of the apparatus from the lower transverse wall to one of the longitudinal walls. In Agapanthus the same movement occurs, but goes farther on, because after fertilization the ovary bends still further downward; in this case a further shifting in the same direction should have taken place, by which ultimately the middle-field arrived at the apical trans- verse wall. In all these movements the bending is accompanied by a distinct growth of flower- and of fruit-stalk. Amputation of the flower-bud will prevent these movements, for which reason it is assumed that the statocysts are situated in the ovary. Other plants again exhibit the phenomenon that the peduncle which stands upright during bloom, after fertilization increases much in length and curves downward; this is most striking with those plants which bury their young fruit in the ground, e.g. Prifolium sublerraneum, Arachis, etc; here the shifting of the apparatus from the lowest transverse wall to the highest should take place in one phase. In all these cases the change of position of the static apparatus is clearly a result of a separate new stimulation which is either the growth of the flower or the process of fertilization. A shifting of the apparatus in a contrary sense should take place in those cases in which the tip of the sympodial rhizome bends vertically upwards for the purpose of producing leaves and flowers, because this upward curve would have to be preceded by a displace- ment from the lowest longitudinal wall to the basal transverse wall. The best known instance of a particular curvation is that of the flowerstalk of Papaver (to which those of the peduncles of the inflorescenses of Tussilago Farfara are closely connected), since there the movement has to take place before the flowering in one sense and after the fertilization in the opposite direction. VöcHrinG in 1882 succeeded in demonstrating that these movements are inti- 178 mately connected with the geotropic-stimulus both of the stalk and of the ovary, while the “rectipetality” should also play a part it. VocntiIngé gave the name of “rectipetality” to the phenomenon that a plant-organ, which has curved upon irritation, begins straight- ening itself out again as soon as the stimulation has ceased. This he regards as a separate quality of plant-organs since it further appeared that the straightening required no new stimulation. It seems to me, however, as | set forth also in my article quoted above, that rectipetality must be regarded rather as a consequence of the original stimulation which, being gradually conducted to the opposite side of the organ, causes a contrary curving. In Papaver the young flowerbud stands upright on a short and vertical peduncle; soon, however, the rapidly growing stalk makes a curve of 180°, so that the bud now hangs inverted. In this position the peduncle continues to grow which takes place at the bend, without however the curve increasing, owing to the simul- taneous tendency towards rectipetality, and so it seems as if the growth is limited entirely to the part below the bend. When the flower is fully formed, the bud rises again and this upright position is also retained by the fruit. Amputation of the ovary only (inside the bud before it is full- grown) checks the growth of the stem, which then stretches straight out as much as possible; the cessation in the growth should be regarded as a result of the cessation of the gravitation-stimulus in the ovary, the straightening of the stalk as caused by the “rectipe- tality” which is then the result of the stimulus received before the ovary was cut off. The peduncle as well as the bud is negatively geotropic; the statie apparatus should thus again be supposed to lie against the basal transverse wall and this position should remain unchanged in the peduncle. The reason that the growing stalk bends over at an angle of 180° should be attributed to a shifting of the static apparatus in the statocysts of the ovary from the lowest transverse wall to the uppermost, while the erecting of the full-grown bud later on should be preceded by the opposite movement in the same cells. This example shows well how simply these seemingly complicated movements can be explained upon our assumptions. A last group will comprise the epinastic and hyponastic movements which are so common in plagiotropic organs. These movements depend upon temporary inequalities in the speed of growth between the upper and lower surface of the organ (especially leaves), whereby the growth predominates now on one 179 side and then on the other. The reason of these cbanges in the speed of the growth is unknown, but, while a renewed research into these movements is highly desirable, it may be taken as fairly certain that, although all apparently similar, they are not so in reality, since they are evidently not all governed by the same stimuli. The influence of gravitation, for instance, can be demonstrated in many of them, so that for this reason and also because the movements depend entirely upon longitudinal growth, there is every reason to assume that statoeysts are also present in these organs. With respect to the place where they occur in leaves in general, not much is known, and it would therefore be useless to make further premises regarding the shifting of the static apparatus before sufficient data on this point have been obtained. Some movements, however, might already be explained in a similar way as above; so, for instance, the movements of the leaves in the unfolding buds of Aesculus; in the bud, and also as soon as it opens, the petiole and leaflets stand vertically upright, after which the leaflets make a downward bend of 180° at the joint (shifting of the apparatus from the basal to the apical transverse wall); finally the leaflets, as well as the petioles, take up an almost hori- zontal position (shifting of the apparatus in both to the undermost longitudinal wall). In connection with the above | may refer to the very important though apparently almost totally forgotten observations of HOFMEISTER *), from which it would seem that the lateral growth of the leaves in the bud is frequently influenced by their vertical position so that the half of the leaf pointing upwards in the bud will grow faster than that pointing downwards. If these observations be correct they would form a further indication that statocysts are also present in the leaves and would thus be able to exercise an influence upon the growth of the cells. This would agree with my view, expressed above, namely that the static apparatus also governs the normal growth in length. We shall return later to the consideration of the influence of gravitation upon the normal position of the leaves, as this also should be connected with the influence of the static apparatus (page 184). b. The position of the static apparatus is altered by external influences. Sometimes an external influence leads to a change in the position of organs, as, for instance, amputation of the main-axis. 1) Allgemeine Morphologie der Gewächse. 1868, § 25. 180 If the terminal bud or a part of the main-axis be cut off, the lower lateral bud or lateral shoot will develop more strongly than it would otherwise have done, and will at the same time bend upwards until it assumes the position entirely, or almost, of the main-axis; amputation thus causes an accelerated growth as well as strong geotropic bending. The absolute relation between the two, so striking here, is simply explained now by the circumstance that both are dependent upon stimulation of the static apparatus. If, for instance, the almost horizontal lateral axis of Araucaria, after amputation of the terminal bud, gradually assumes a vertical position, this might have been preceded by shifting of the apparatus from the lowest longitudinal wall to the basal transverse wall, i. e. a shifting in the direction of the wound. Tanar *) and NesrLer ’) now have demonstrated that the result of a wound is that in the neighbouring cells the protoplasm tends to accumulate in the direc- tion of the wound; if it be that the static apparatus had a share in this shifting, this alone could be a reason for the appearance of the negative-geotropic movement. It might be mentioned in this connection that, according to Ricutrger *), even a plant of so much more simple structure as Chara, shows the same phenomenon, namely, that after amputation of the terminal bud, the adjoining lateral branch grows out more quickly and bends sharply upwards. Amputation of the radicle has not the same effect upon the side- roots of the first order; Sacus*) has demonstrated that the lateral roots already present show no change in position, but that the after the amputation new formed lateral roots grow out in a more vertical direction, thus showing rather an influence upon the position of the apparatus in the newly formed cells instead of producing a shifting in those already present. c. The static apparatus changes its position continually. When the static apparatus is at rest in any organ, that organ assumes a certain position of equilibrium; in the case of a continual autonomic shifting, on the contrary, the organ will never arrive at a position of equilibrium and therefore never be at rest. Such ceaseless movements are known in the nutations and in the twining of plants. !) Sitzungsber. der K. Akad. der Wissensch., Wien, 1 Abt., 1884. Bd. 90, p. 25. 2) [bidem, 1898, Bd. 107, p. 708. 3) Flora, 1894, p. 416. 4) Arbeiten des botan. Inst. zu Würzburg, Bd. 1, p. 622. 181 The nutations are now considered to be movements which take place without any stimulations, but their explanation is still wanting. As they depend, however, entirely upon longitudinal growth, they will be considered here to be induced by the stimulus of gravitation. The least common case of nutation is seen in the peduncles of Allium Porrum which first hang over to one side, then straighten out and afterwards bend over to the other side, and soon. A slight displacement of the static apparatus might induce this movement; if, for instance, the middle-field lies against the basal transverse wall, the stalk, as we have seen, will assume a vertical position; should it then move slightly to one side, the stalk, in its effort to find the new equilibrium, would have to bend over to the same side; if the apparatus then moves back across the transverse wall and then shifts slightly to the opposite side the stalk would become straight and then also have to bend to that side, and so on. This autonomous shifting of the apparatus to and fro across the basa! transverse wall would thus be sufficient to cause indirectly the “swinging nutation’. Much more frequent is the “rotating nutation”, in which the tip of the stem moves as if over a conical surface; it may very well be imagined that this movement is brought about owing to the - apparatus, as in the preceding instance, lying somewhat to the side of the transverse wall but is now pushed round in a circle, as it were, though in such a way that the middle-field remains always at the same distance from the centre of the transverse wall. The stem would then again have to follow the whole movement, always making the same angle with the perpendicular. The more the apparatus shifts, and keeps aside from the transverse wall during the nutation, the greater will be the angle at the apex of the cone described by the tip of the stem. The twining movement was regarded by Sacus as being intimately connected with the rotating nutation, also because at that moment in both the influence of gravitation seemed to be excluded. Later on, however, it was demonstrated by Nor. that in the twining the effect of this stimulus showed itself as “lateral geotropism” where- by the gravitation stimulus brings forth the lateral movement of the apex by causing a difference in growth between the two opposite lateral sides of the stem. This lateral geotropism thus causes the apex of the stem to swing round, with the tip in a more or less horizontal position, while at the same time the tip twists round its own axis in the opposite 182 direction. It appears to me that these movements may also be explained by an autonomous shifting of the static apparatus. We have seen (page 6) that the tip of the young stem which at first is vertical soon afterwards assumes an almost horizontal position, after which it begins to twine; this was then explained by a shift- ing of the apparatus from the basal transverse wall to one of the longitudinal walls which then by the bending became the lowest. And if this apparatus were displaced now again in the statocyst, so that it goes round the cell, but always keeping at one of the longitudinal walls, this would cause the tip twisting aback and at the same time its rotating in the horizontal plane, since this twisting could not take place without a simultaneous and equally rapid rotation (one turn for each cirele described in the horizontal plane). This displacement should take place in the one direction in plants which twine to the left and in the opposite direction in plants which twine to the right. If the summit of the stem is not perfectly horizontal in rotating as often occurs, the apparatus should have to lie still at the longitudinal wall but somewhat shifted towards the basal transverse wall and should be carried round in this same position in the cell. It is worth noting in this connection that this displacement of the apparatus, and also the nature of the movement of the stem, agree largely with those described for the rotating nutation above-mentioned; for this reason, and because, in our opinion, both are to be regarded as dependent upon the gravitation-stimulus, the old supposition of Sacus is confirmed again, viz. that twining and rotating nutation are movements intimately connected with each other. The only differ- ence would consist in the size of the apical angle of the cone described by the tip of the stem (which in twining plants may be as much as 180°) and thus, with regard to the static apparatus, in the distance, which exists continually during the shifting between the middle-tield and the centre of the basal transverse wall. This discussion, though necessarily too short, may however suffice to show that with the help of our theory it is possible to give even a simple explanation of the lateral geotropism. A shifting of the apparatus back to the original position at the basal transverse wall would again lead to the negative geotropism wich causes the stem to raise itself when the twining ceases and by which the convolutions are pressed against the support. The twisting of the stem which can frequently be observed as an accompanying phenomenon and which probably also depends upon the gravitation, cannot be discussed here. 183 B Sarmunarion BY GRAVITATION AND LiGar. Many plant-organs curve under the influence of an unequal illumination, as this causes an unequality in the longitudinal growth at different sides of the organ (heliotropism). Since this depends thus entirely on increase in length, these movements must be regarded here as being brought about both by gravitation and by light. It is known that light can cause certain movements of protoplasm: the swarm-spores move towards light (positive phototaxis), whereby, according to the experiments of ENGELMANN, it is the uncoloured portion of the swarm-spore which receives the stimulus; if green cells are exposed to the light ‘after having been kept in the dark, the chlorophyl-grains undergo a definite change of position, but resume their original place when withdrawn from the light. These reasons would already be sufficient to assume that the position of the statie apparatus also can undergo the influence of light, but such an assumption will become still more probable when it can be shown by different examples that a similar shifting of the apparatus, i.e. towards the light, could furnish us with a rather simple explanation of very different familiar phenomena. a. Positive and negative heliotropism. In the vertical position of main-axis and radicle, as was said above, the middle-field of the static apparatus should lie against the basal transverse wall of the statocyst; if these organs receive light from the side, and the apparatus, as we have just supposed, moves towards the source of light, these organs can no longer be in rest, and they can find the new equilibrium, i.e. the starch- grains will come to rest again on the most sensitive middle-field of the apparatus, only if the stem moves towards the light, and the root on the contrary from the light; thus the familiar positive and negative heliotropic curvatures. If the plant is replaced in the dark the organs return to their vertical position, from which we should have to infer that after cessation of the light-stimulus, the apparatus of itself returns to their former place at the basal transverse wall. Consequeutly this is the same thing observed with the cblorophyl-grains in the above-mentioned cases, namely, that they are brought out of their position of equilibrium by light and return to it when replaced in the dark. PFEFFER ') considers this a matter of course. 6. It is known that certain rhizomes react to light in such a 1) Pflanzenphysiologie, 1904, Vol. 2, p. 780. 184 manner that when their tip receives the light they acquire positive- geotropism and bend downward; when the tip pierces the ground again and is thus no longer illumined, the transverse-geotropism reappears These movements too may be explained in the simplest way from our suppositions. In the normal rhizome, as we have seen (page 6), the static apparatus should lie against the lowest longi- indinal wall; if, under the influence of light, the apparatus is displaced again towards the source of the light, i.e. in the direction of the apical transverse wall, the tip will have to bend downwards in order that the starch-grains may again reach the middle-field, and this is just the movement that we see the rhizome make. When again in the dark the apparatus, and therefore the rhizome too, will resume its former position, as in the preceding case. c. The sleep-movements of leaves, as will be known, are influenced by light to such a degree that it was long believed that light alone was the cause of them. Later, however, exhaustive researches, in particular those of Prerrer, showed that gravitation has also a share in them. This has been most clearly demonstrated for instance in the experiment with Phaseolus, in which the petioles of the two first leaves were secured during the day in their normal position, so that only the leaflets could make the sleep-movement. When the plant was then turned upside down, the nyctitropie movement took place at night, but showed exactly the reverse of what in the normal position occurred, i.e. in the light the leaves now stood vertically upright, whereas in the dark they were spread out horizontally. Thus, with respect to gravitation the leaves moved in the same direction as before, with regard to light however in a manner exactly contrary to the normal way, from which it is evident that it was the gravitation in the first place which governed the nycti- tropic movement and determined the equilibrium of the leaf. As practically nothing is known regarding the position of the statocysts in the leaves (see page 179), it is still difficult to express here any opinion with respect to the eventual shifting which the statie apparatus might undergo here under the influence of light, the more so because there are so many varieties of nyctitropic movement. Important in this respect for an explanation in the sense as meant here, however, is the fact that it proved the pre- sence of the principal auxiliary, namely the static apparatus itself, in leaves which show sleep-movement. d. What has been written concerning the sleep-movements is really also applicable to the movements which cause the leaves to 185 assume their natural position; apparently they are influenced only by light, but here again the experiments of Prurrer have shown that gravitation plays an important part; f.i. many leaves when brought away from their normal position can return to it in the dark, which evidently can be effected only through the medium of the gravitation-stimulus. Here again the lack of data regarding the position of the statocysts in the leaves prevents us from prosecuting the research as to these movements in connection with our theory. C. Stimunation BY LIGHT ALONE. Auxotonic curves are seldom caused by the light-stimulus alone; the instance of this most fully investigated is that of the “trans- versal heliotropism”’, whereby certain leaves place themselves per- pendicular to the incident bundle of light. HABERLANDT *) endeavours to explain this movement by assuming that the middle-field of that portion of the outer layer that adjoins the lower wall of the sen- sitive epidermical cells is more sensitive to light than its sarround- ings. If now the leaf seeks to reach the desired position by the shortest way, this must be accompanied by the quickest increase in the intensity of the stimulus, exactly in the same way thus as was assumed above with respect to the stimulus of gravitation. The stimulation of an sensitive organ causes everywhere a cer- tain sensation or movement, whereby, however, the nature of the sensation or of the movement, is determined solely by the special properties of those parts of the organism which lie outsvde the perceiving sense-organ; consequently the nature of the stimulus can never excercise any influence whatever upon the effect that the organism shows. If this conelusion should hold good for the plant too, as is very probable from the nature of the case, and if we also bear in mind that all auxotonie movements mentioned are executed in the same way, it would follow that it is sufficient for the plant to possess only one single sensitive organ for all these movements, induced by gravitation, by light or by both. Therefore not even for transversal-heliotropism an exception should be made, for if we consider that a static apparatus without statoliths (starch-grains) could not be stimulated by gravitation but can never- theless remain sensitive to light, it might very well be possible 1) Die Lichtsinnesorgane der Laubblätter, 1905, p. 127. 186 that the mentioned apparatus of HABERLANDT, sensitive to light and in which the starcb-grains are always lacking, might be identical with our static apparatus (provided that in this case it should be unmovable), for both exercise exactly the same influence upon the growth-phenomena in the joints, ete. These expositions might serve to show that the hypothesis of the presence of a movable “static apparatus” in the statocyst affords Such a great advantage in the consideration and the grouping of the mentioned auxotonic movements, that it is entitled to be duly regarded as a working-hypothesis of sufficient foundation and further that there is probably in plants (and in animals ?) a general striving towards an increase of stimulation which might later serve to find a further explanation of how these appropiate movements be brought about. Leyden, January 23, 1923. Mathematics. — “On the Points of Continuity of Functions’. By Prof. J. Worrr. (Communicated by Prof. Henprik DE Vrins). (Communicated at the meeting of February 24, 1923). Let f(P) be a function of the coordinates of a point P in a space with an arbitrary number of dimensions. The points where f is continuous, form an imner limiting set, i.e. the intersection of an enumerable set of open sets of points @,, where we may assume that 2,4; is a part of 2, for any n. For the points, where the : i il function oscillates less than —, form an open set @, because the oscil- n lation is an upper semi-continuous function. The set of the points of continuity is the intersection of all 2,, n = 1, 2,3,.... Young *) has shown that to any inner limiting set # given in a linear interval, there belongs a function in that interval which is continuous in the points of E and discontinuous in any other point. We shall give here a simple proof, which is directly valid for spaces of any number of dimensions. 1. Let a set of points Z be given as the intersection of an enu- merable set of open sets 2,, where 2,4, is a part of (or coincides with) 2,,. We define f(P) for any point of space in the following way: in the first place f(P)—0 if P lies in EZ. Now let P be a point not lying in £, np the least value of n for which @, does not contain the point P. We put ' P) Î(P) = a Mot ot) where w(P) is the function which in the points of space of which all the coordinates are rational, is equal to 1, in any other point of space equal to —1. We may say that (1) holds also good for the points of Z, if there we assume 2p = 0. 2. Now we shall show, that f(P) is continuous in the points of E and discontinuous outside them. 1) W. H. Youne. Wiener Sitzungsber., vol 112, Abt. II, p. 1307. 13 Proceedings Royal Acad. Amsterdam. Vol. XXVI. 188 Let u$ first assume that P belongs to E. In this case f(P)=0. If e be an arbitrary positive number, we may choose the natural number » in such a way that HE RO) As P lies in 2, and 2, is open, there exists a region U round P which lies also in 2,. For any point Q of U we have therefore Ng > vr, so that according to (1) and (2) OI Se Hence f is continuous in any point of Z. Let us now assume P to lie in the complement of Z. If P is not an limiting-point of Lips it has a neighbourhood U which has no point in common with Lp point Q of U we have in this case ng — np. Hence | A(Q) | = | f(P)| As the points where / is positive as well as the points where / is negative, lie everywhere dense on U, the oscillation of f in P is equal to 2 | f(P) |. If however P is an limiting-point of 2 and whieh lies in Lpi: For any up» every neighbourhood U of P contains a part of 2,,. For any point of that part np > ng, hence 1 1 Np Np + 1 As the points Q for which the inequality (3) holds good, have P for a limiting-point, P is a point of discontinuity of 7. Herewith the theorem has been entirely proved. S(Q— f(P) |= (3) Mathematics. — “Inner Limiting Sets”. By Prof. J. Worer. (Communicated by Prof. Henprik pr Vriws). (Communicated at the meeting of February 24, 1923). Hopson has been the first to prove the following theorem: *) An enumerable set of points which has no part that is dense in itself, is an inner limiting set, i.e. the common part of an enumerable set of open sets each of which we may assume to contain the following one. Brouwer has given an extremely short proof, but just as Hopson he makes use of the transfinite ordinal numbers’). In the proof which follows here, no use is made of these numbers. 1. If EE... are inner limiting sets, if further each Zj, is a part of an open set 2%, while no two 2; have any points in common, also the sum #, + #,-+... is an inner limiting set. For we may write: JB, = Pin Pip osce 5 [Sty Docc which means that Zj is the set of points lying in @j: for every 7. The 2;; are open sets of which we may assume that they all lie in §2;. The set (rn een qe coda Se keker ee oen contains #,-++ E‚ +... but no point outside them, as 2;; 2), = 0 for k Al. Now the auxiliary theorem has been proved. 2. We call a set of points Z an inner limiting set in a point P if there exists an open set containing this point, so that the part of Z lying in this set is an inner limiting set. This holds also good for the part of # lying in an arbitrary open set which is a part of the above mentioned one. 3. If an enumerable set Z is an inner limiting set in each of its points, Z is an inner limiting set. We call the points of #: P,, P,,... 1) Proc. London M.S. (2) 2, p. 316—323. 4) These Proceedings, Vol. XVIII p. 48 (1915). ‘ 13% 190 Round P, as centre we take an interval /; (a quadrangle, a cube, ete. according to the number of dimensions of the space in which E is given), so that #/; is an inner limiting set, taking care that the boundary of Zp contains no point of Z, which is possible on account of # being enumerable. By J, we understand the open interval, by J; we shall indicate the closed one, by an accent, the complement of a set. Now E= El, + El, A) + El, (L) (1) +... From N° 1 there follows now immediately that # is an inner limiting set. 4. Let / be enumerable and not an inner limiting set. In this case according to N°. 3 the set D of the points # in which £ is not an inner limiting set, is not empty. Let P be a point of Dand [an interval with P as centre. H/ is according to N°. 2 not an inner limiting set, hence neither is #/—P; according to N°. 3, E1I—P contains a point Q in which #/—P is not an inner limiting set, hence # is not an inner limiting set in Q, so that Q lies in D. From this there follows that D is dense in itself and from that the theorem which was to be proved. Petrography. — “On the Rocks of Doormantop in Central New Guinew’. By W. F. Gisorr. (Communicated by Prof. G. A. F. MoLENGRAAFF). (Communicated at the meeting of February 24, 1923). During a causerie about New Guinea, delivered at Batavia, Dr. H. J. Lam of Buitenzorg, at a meeting of the “Koninklijke Natuur- kundige Vereeniging’, showed a sample of a roek from Doormantop, which directly engrossed my attention to such an extent that I asked him to leave it to me for examination. He readily did so. Afterwards he furnished me with more samples of the same material, for which kindness I hereby tender him my best thanks. The geol- ogist of the Mamberamo-expedition Dr. P. F. Husrecat, was staying in East-Java at that time, and was not in a position, within the first ten months, to send me any material. However, when asked, he did not object to an examination of the samples nor to public- ation of the results. I have much pleasure in thanking him also for his kindness. The first samples that came to hand, present a schistose structure, chiefly due to parallel bands of magnetite; they are of a dark green colour, with a thin light-brown non-detached weathered crust of a cavernous appearance, on either side a relatively considerable quantity of magnetite reveals itself in non-erystallized masses; the erosion has spared the magnetite, so that it projects '/, — 1 centim from the rock. A blow of a hammer made the rock split along the magnetite, thus effecting the first separation between the rock and the ore. Some slides were made of the part from which the magnetite had been removed as much as possible. Under the microscope the rock proved to consist of magnetite with fresh olivine and a colourless, lath-shaped mineral of moderate refringence and very weak birefringence. The structure is slightly varying, the olivine now encloses the colourless mineral, now it mingles with it as if they were crystallized out simultaneously; the magnetite encloses the colourless mineral and occurs xenomorphie in the aggregate olivine- unknown material. The magnetite is polarimagnetic. A little apatite presumably occurs. . 192 The olivine, which extinguishes undulatorily, but not to such a degree as is the case in most peridotites, looks very fresh and is absolutely free from weathering. The apparent weathering in the crust appears to be merely a brown colouring; serpentinization as an effect of atmospheric influence is absent. In another slide the refractive indices were, by the immersion-method, fixed at 1.66 and 1.70, after the Canada balsam had been carefully extracted by the use of xylol. The thickness of the slide was ’/,, mM. (measured by detaching the slide and fixing it with tallow vertically on the object glass): the highest interference-colour observed was green 3*¢ order, making y-« about 0.04, which agrees with the determination of the indices. The observation perpendicular to an optical axis in con- vergent light revealed on rotation of the table a slightly curving beam, at which the optically positive sign and a large axial angle could be established. Presumably one has to do here with a ferro- magnesium olivine with about 10°/, to 12°/, °/, iron-olivine and 90 ®/, to 87'/,°/, magnesium-olivine (See Dorrrer Handbuch der Mineral- chemie II, I p. 16). The colourless mineral, however, caused most trouble in its determination. Long as well as short laths occur; quadratic sections are lacking; the birefringence is low, sometimes next to zero; in one and the same lath the double refraction is not always the same, but varies, without attaining however, the so called ,,Pflock- structure”. All the laths show straight extinction; the elongation is invariably positive; cleavage lines run lengthwise through the crystal, especially in the middle and parallel to the outline. It was very difficult to obtain an interference figure. Therefore it was surmised that the mineral might belong to the melilite group, but this surmise proved to be untenable, as it was in no way supported by further microchemical and optical testing. For this reason I applied to Dr. Lam for more material. This additional supply enabled me to identify the mineral. The coverglass was taken from all the slides, which were rinsed repeatedly with xylol, in order to remove any trace of Canada-balsam from the margins of the slide before being examined by the immersion-method. The refractive index appeared to be 1.58. Being treated with hydrochloric acid and washed cautiously, gelatination ensued; when moistened with fuchsin and again washed carefully, the olivine as well as the unknown mineral under con- sideration appeared to be gelatinized. To make sure that the silex- gel of the olivine had not spread over the unknown mineral as well and might thereby be misleading, the whole procedure was repeated 193 and brought to light that the mineral under consideration gelatinized sooner than the olivine. In the liquid that had been collected micro- chemically the presence of calcium could not be detected. Finally each individual lath was examined conoscopically ; thus | succeeded in establishing in several of them that the mineral is biaxial, and that the axial plane is always perpendicular to the longer axis, the elongation being always positive. This is possible only if the mineral is developed into flakes perpendicular to the optical A-axis; it thus became more and more probable that the mineral could be rhombic. If so we must have to do with antigorite in its primary form. The idea of a secondary postmagmatic genesis should be dropped altogether, the antigorite laths traverse freely from one olivine- erystal into another; subsequently they form with them as it were a eutectic crystallization and ultimately become the predominant mineral (See the microphoto fig. 1 and 2). All this applies to the material rich in large magnetite masses. Other material, finer grained Fig. 1. Primary antigorite in olivine. 194 and poorer in large magnetite masses appeared to my surprise to be made up of the ordinary antigorite-serpentine with so-called olivine- Fig. 2. Same as fig. 1, in polarized light with crossed Nicols. rests. It appears to me that the cross-grained structure in those serpentines and the fine grain are caused by rapid crystallization. Also in these specimens the olivine is quite fresh. The sequence of cristallization as manifested in the slides is the following : Antigorite; antigorite-magnetite; antigorite-olivine-magnetite. To all appearance the latter combination is a eutecticum, although it is not impossible that the magnetite is resorbed later. Since the rock les near the surface, the conditions for serpenti- nization by meteoric agencies have been favourable. However, of this the rock does not present any recognizable trace. The question, therefore, urges itself upon us whether the serpentine might perhaps be always of a magmatic origin, at all events not a product of weathering. Now, as to the genesis of this rock we may broach the supposi- 195 tion (until the system H,O—Mg0-—-FeO —Fe,O,—SiO, shall be investigated) that the magma, from which this rock originated, crystallized under such a pressure that the gaseous components (notably watervapour) could not escape and consequently were taken up into the rock substance from the very beginning of the crystal- lization, thus occasioning a primary origin of serpentine. Putting it chemically *): the crystallization begins in the serpentine-field and terminates in a point serpentine-olivine (magnetite ?), which is per- haps located close to the connecting line olivine-serpentine (because Fe‚O, takes up only litlle space in an olivine-serpentine structure). In the case of eutecticum this point will be found on the same side as Fe,O,, and in that of resorption in the common field of serpentine-olivine. It may be suspected that in other peridotites, in which olivine crystallized first, the said pressure was less, so that, indeed, the gases could escape at the beginning of the crystallization, but were taken up again afterwards at the final crystallization, so that in similar cases serpentinization of olivine might be considered as an apomagmatie (hydrothermal) process. Expressing it chemically: the crystallization then begins in the olivine field; on increasing pressure the stability field of the olivine is subsequently left for that of the serpentine. The consequent segregation of magnetite is self-evident after what has been said before. Magnesium is also set free for the forming of periclase or picotite or magnesite. As the gases move upwards it is obvious that serpentinization will occur chiefly in the upper zones of peridotite-masses and on rents in the solidifying and consequently shrinking peridotite-masses. Krosion being a downward process, first the marginal portions are laid bare, so that in the field the serpentine will in many cases be found prior to the olivine, which fact, 1 think has lent support to the erroneous but current view that serpentine is a weathering product, After the foregoing had been written (August 1922), the chemical ’ analysis came to hand (Dec. 29). Of a sample freed as much as possible from magnetite an analysis was made at the Head Office of the Mining Department by Mr. A. TER BRAAKE and Mr. G. J. Waruy. The loss of water has been 1) To simplify matters it has been assumed that the serpentine and olivine are very definite compounds, which is not the case, of course. For the thermal- pressure-diagram of the five-substance-system a six or seven-dimensional space would have to be used, which would not facilitate the conception. 196 determined at 100° and at 200°, the latter temperature was maintained for three days, viz. until the weight remained constant. The result of the analysis is: SiO, 40.46 MeO 40.20 FeO 7.69 (determined as Fe,O,) ALO, 4.12 H,O (100°) 6.14 H,O (200°) 1.60 100.21 CaO, MnO, Cr,O0,, NiO are absent, as well as P,O,; no estima- tion could be made of K,O and Na,O, because in Java platinum chlorid at that time could not be obtained. In the determination of the iron-amount FeO and Fe,O, were not estimated separately ; it is likely, however, that they are both present. It is evident that the chemical analysis fully confirms the micro- scopical examination. : Judging from the analysis also pyroxene is probably present, either separately as in so many peridotites, or in solid solution with, or as a component of the serpentine. Presumably the latter is the case, since pyroxene has not been found in any of the slides. It must be remembered that DausrÉn') already succeeded in demonstrating that at a bigh temperature serpentine passes after melting into olivine + enstatite, while water escapes : H,Me,Si,O, = Mg,SiO, + MgSiO, + 2H,0. When leaving aside the watervapour, this case is merely a sub- division of the system MgO—SiO,, which has been examined by ANDERSEN and Bowen. Dauprét’s experience *) is in complete harmony with their results; so for instance from a mixture of the system Mg,SiO,—MgsiO, on cooling first Mg,SiO, crystallizes, which at 1557° begins to react with the solution, in consequence of which . MgSiO, is formed which is precipitated on the surface of the olivine; at the same time the solution becomes richer in silica, so that ultimately SiO, can be set free; as Dausriéx added magnesia he did not obtain cristobalite. In the light of later experiments his 1) Doerrer failed in this experiment. Still, it is worth while to peruse DauBRÉE's carefully described experiments. 3) Comptes Rendus 1866, I, p. 660. ISN observations are correct; e.g. ,,Des aiguilles d’enstatite y sont fréquemment disséminées ou en recouvrent la surface” (i.e. of the olivine, obtained through smelting of serpentine with the addition of magnesia) and again in case he did not add magnesia: „le (péridot) se montre en moindre proportion que dans les fusions faites en présence de la magnésie. Now since most peridotites (with the exception of dunites) consist of olivine and pyroxene, consequently of orthosilicate and metasili- cate, we may venture to bring the primary and the secondary serpentinization into one focus. For a general theoretical treatment of the case the knowledge of the thermal pressure-diagram of the system H,O—MgO—SiO, would be a first step.’) Needless to say, that this diagram will become very complicate owing to the great difference in volability of the components. From the foregoing it is evident, however, that under a pressure of one atmosphere serpentine is unstable; it would be worth while to repeat the experiment of DauBrÉr in watervapours of various tensions in order to establish the limit of stability of serpentine. Now if we are right in supposing that olivine and pyroxene are not stable at high pressure and in the presence of watervapour, but that they are transformed into serpentine, the former with liberation of MgO?) the latter with precipitation of silica, serpentinization may be accounted for as follows: 1. If the pressure is high enough serpentine crystallizes first from a magma, which is composed of x Mg,SiO,, y MgSiO,, 2H,O; at a lower pressure the crystallization begins with olivine. 2. When olivine and (or) pyroxene are segregrated, the volatile components congregate in the upper zone of the batholite, which may give rise to a high tension, in case they have no opportunity to escape; thus the field of stability of the olivine and (or) the pyroxene is abandoned, and that of serpentine is attained, after which ser- pentinization of olivine and pyroxene commences, occasionally with a residue of MgO (Fe,O,) or (and) silica; while in most cases MgO is present as magnesite. Already Davuprée acknowledged: „Rien ne prouve d’alleurs que Vhydratation qui s'est produite dans la transformation des roches de péridot en serpentine ait été opérée par les agents de la surface du globe”. 1) See e.g. H. E. Boeke, Grundlagen d. phys. chem. Petrographie, p. 179. 1) E.g. as magnesite, because the component carbondioxyde is always present. Many serpentine deposits in fact contain magnesite and quartz. 198 It scarcely needs to be pointed out that, under the influence of. the volatile components of a later intruded igneous rock, a peridotite mass may also be altered into serpentine. Let it be recalled here that a résumé of the olivine-serpentine problem has been brought forward by W. N. Benson (Origin of Serpentine, American Journal of Science 46 p. 693, 1918). It is to be regretted, however, that the problem has not been dealt with from a physico-chemical point of view. Finally I beg to use this opportunity to thank Mr. A. C. DE Jonen, Director of the Research Committee of the Mining Department, for his willingness to have the analysis and the slides made in his laboratory. From the above it may be inferred that many difficulties have stood in my way by the insufficiency of my laboratory-equipment. It is to be hoped that the Government of the Netherlands Hast Indies, which are so extremely rich in occurrences of beautiful rocks, may, at no distant date, take measures for the building of a well-equipped petrographic laboratory, Weltevreden, Aug./Dec. 1922. Palaeontology. — ‘New Findings of Pliocene and Pleistocene Mammals in Noord Brabant, and their Geological Signijicance”’. By I. Swemie and Prof. L. Rurren. (Communicated by Prof. G. A. F. MOLENGRAAFF). (Communicated at the meeting of February 24, 1923). In the past year the Geological Institute of Utrecht obtained, partly through mediation of the Geological Survey, partly from the Govern- ment Bureau for Watersupply, some remains of fossil mammals originating from the southern and the western part of Noord-Brabant, one of the southern provinces of Holland, a distriet which up to the present has yielded very little in this respect. As we know, representatives of the young-diluvial fauna have been found in some localities of Noord Brabant, e.g. Bos primigenius Boj. near Den Bosch, Elephas primigenius Blumenb. near Acht, Rhinoceros anti- quitatis Blum., in Hollandsch Diep. It is noteworthy, however, that in two places, near Oosterhout in the northwest, and near Wester- hoven in the south of the province, remains have been recognized of a pliocene fauna, viz. Elephas meridionalis Nesti, and Rhinoceros etruscus Fale *). Now, part of the remains, detected last year, have been derived from the zone between Oosterhout and Westerhoven. Three findings of mammals, belonging to the young diluvial fauna occurred in the vicinity of Esbeek 5.S.E. of Tilburg, viz. a molar from Elephas primigenius Blum., found by Mr. Sissinen on the premises of the clay-pit to the north of Esbeek, under a deposit of loam at a depth of three meters; three molars from Rhinoceros antiquitatis Blum, unearthed from a depth of 2} m. in peat-bearing layers of clay, during the construction of the lock in the Wilhelmina Canal near Diessen, when the canal was being dug, and a molar from Equus Caballus L., found during the construction of the same canal to the east of the Diessen-lock at a depth of 34 M. ’). The above fossils are not highly remarkable in themselves. The Molar from Elephas primigenius is a M III, sup. sin., on which 1) L. Rurren. Die Diluvialen Säugetiere der Niederlande, 1909. ?) Far more eastward, viz. near Breugel on the Dommel, a fragment of a horn of Bos Primigenius Boj. was found, with which the Utrecht Geol. Inst. was pre- sented last year. 200 — 194 x are still visible on 215 100 > 160 mM.'). The extre- mely thin lamellae and the slight thickness of the enamel prove conclusively thath the tooth is to be referred to El. primigenius; it is remarkable however, that the enamel bands are finely folded which oceurs only rarely in El. primigenius. The remains of Rli- noceros antiquitatis are three successive teeth, of one set of the right lower-jaw, viz. P3, M1, and M2. They are but little worn down and have therefore belonged to a young animal; they must undoubtedly be referred to Rh. antiquitatis; the very thick enamel, the distinet striae of the enamel bands, the deep depressions and the trifling convexity of the teeth, all point in the same direction, while for the rest the teeth are almost quite similar to a set pictured by J. Branpr?). The tooth from Equis caballus is also a M of the lower-jaw. From Oosterhout, however, where already previously teeth and bones from Elephas meridionalis Nesti *) had been found in a superficial layer of loam, in a locality not precisely indicated, remains of bones and fragments of teeth were also sent to us, that belonged to this species. They were met with at a depth of 34,75 M. below Amsterdam-level in the first of five borings executed for the Water-company of Western Noord-Brabant. The wells are situated to the left of the road from Breda to Oosterhout on the Vraggel moor. The bones from the well cannot be further determined, but a fragment of a tooth, most likely the posterior part of a M. 1 sup. sin. is distinetly indicative of Elephas meridionalis. It presents-3 x with a length of 74 and a breadth of 8-9 centims, while the height minus the root is about 8 cM. The fragment was not chewed down, but was sawn, in order to get an opportunity of studying its structure. Indicative of El. meridionalis are: 1° the extraordinary thickness of the lamellae, which appears already from the lamallae-formula ; 2° the extreme thickness of the enamel (up to 4 mM); 3° the large breadth and the small height of the tooth; 4° the way in which the chewing-figures originate, namely through fusion of the four annuli (see figure). Not only do we recognize in this fragment all the characteristics of El. meridionalis, but those characteristics even become prominent in the extraordinary thickness of the lamellae and the enamel. Dr. J. Sreennuis kindly wrote us that the Geological Survey 1) MET Pourie. Nova Acta Acad. Car. Leop. 53, p. 251. 2) J. BRANDT. Mém. Acad. St. Pétersbourg. 1849. T. XI. 1) L. Rurrey. Die Diluvialen Säugetiere der Niederlande. 1909. 201 parallelized the part of the bore in which the tooth-fragment had been found, with the clay of Tegelen, which may be referred to the youngest pliocene or the oldest pleistocene. The tooth-fragment { corroborates this parallelism, for of late Elephas meridionalis has also been found near Tegelen '). From the fact that the previous discoveries of El. meridionalis were made near Oosterhout in a loam-quarry, near the surface, it may be concluded that in this part of Noord Brabant the pliocene rises locally to the surface. In the Annexes 11 and 13 of the “Final Report of the Government Exploration of Minerals”, a fault running N. 40° W is marked West of Tilburg, which, however, in Annex !1 is drawn 2 KM. farther to the east than in Annex 13. To the north-east of this fault the soil has considerably subsided, as indicated on the sketch map; to the south-east the subsidence is less marked. When mapping the finding-places of the pliocene or the old pleistocene fauna (Westerhoven and Oosterhout), it will be noted that they fall to the east of the fault, as indicated in Annex 13, while Westerhoven would also lie within the trough, when assumung the course of the fault as marked in Annex 11. It is clear, however, that the pliocene can be expected near the surface only in the least subsided region, so that it is certain that the above-named fault — marked on the map only as a “suspected” fault — must be shifted more eastward. In that case, however, the locality of El. primigenius near Esbeek falls certainly to the west 1) S. RrcHARrz. Centralbl. f. Miner. Geol. u. Pal. 1921 p. 664—669; id. Stadt Gottes 1921/22. Heft III. 202 of the fault, and that of Rh. antiquitatis and Eg. callabus does so most probably, i.e. in the least subsided region. Two possibilities are then to be considered: in the first place near Diessen and Esbeek more recent diluvium may have overlapped the denuded pliocene and secondly the fault postulated in the above as a straight line, may proceed more irregularly, so that in reality Esbeek and Diessen come to lie east of it. — At all events it appears from the foregoing that the young fossil mammalian remains in this part of Noord Brabant, whose geology may give us still many surprises, are rather numerous and may be of use in unravelling the tectonic of this province. The previous discoveries near Westerhoven and Oosterhout as well as the recent ones near Esbeek and Diessen were made in super- ficial or nearly superficial loam deposits, which but for fossil findings, would surely be referred to the ‘“Argiles de la Campine '). It has already previously been pointed out that these loam-deposits may be of different ages; the palaeontological findings lend support to this hypothesis. 1) J. Lorié. Bull. Soc. Belge de Géol. XXI. 1907 p. 532—576. Mathematics. — “A Generalisation of Mertens’ Theorem”. By M. J. Berinrante. (Communicated by Prof. L. E. J. BROUWER). (Communicated at the meeting of February 24, 1923). The theory of infinite series, which so far chiefly consisted of convergent series, being extended to the so-called summable and asymptotic series, it is natural to generalize as much as possible the classical results about convergent series to these classes of series. For the well-known theorem of Mertens this has been done by Harpy (Bromwicu, Theory of Infinite Series, p. 284), who used Borrr’s method of summation. In the present paper we treat a somewhat different generalisation, whereby we are only concerned with Cresaró’s method of summation. The product or the product-series of the series OBES hae | Clit Urea oiee- Sioa is defined as the series c, + ¢,+.... where cj =a, bi + a, bit +.... + aib. Crsaró has proved: if two series are convergent, their product will be summable of order 1, and if two series are summable respectively of order p and q, their product will be summable of order (p+ q-+1)’). If we call a convergent series summable of order zero, then the first part of CesarÓ’s theorem is included in the second. Mertens’ theorem, which runs as follows: “If one of two convergent series converges absolutely, their product is convergent’ may now be stated thus: The product of a series which is absolutely convergent, by a series which is summable of order p is summable of order zero. In the first place we are led to the following generalisation: Theorem 1: The product of a series which is absolutely convergent, by a series which is summable of order p, is summable of order p. 1) BROMWICH. Theory of infinite series, § 125 pp. 314—316. 14 Proceedings Royal Acad. Amsterdam. Vol. X XVI. 204 Further we may ask for a condition, such that the product of a convergent series by a series which is summable of order p and satisfies the condition, will also be summable of order p. This can be seen from: Theorem 2: The product of a convergent series by a series which is summable of order p and whose mean-vahies of order pH are limited, is summable of order p. Finally we consider the product of two series, which are summable respectively of order p and q; then we are led to: Theorem 3: The product of a series which is summable of order p and whose mean-values of order p—l are limited, by a series which is summable of order q, is summable of order p+ q. If we call a series which is summable of order p (p21) and whose mean-values of order p—l are limited, jomnable of order p, and if we call an absolutely converging series joinable of order zero, then the above theorems are included in the following: Theorem: The product of a series which is joinable of order p, by a series which is summable of order q, is summable of order p+ : The proofs however will be given separately. For the sake of completeness we begin with the deduction of some well-known formulas. Let ai), x), .... 2, .... be un arbitrary sequence of complex 9 4 numbers; we define: TE ENE Oee (U) n 1 2 n ak) = al) all) is OO cast ene) n n We denote w by A® if a 1, whatever be 7. It is easy to 1 t verify that: age n (n—1)/(k—1)! We consider the series a, + a2 + .... and b, + 6.+.... with their product: c:+co+.... (where c,=a16,-+....-- a, bi), and we put: (3) D | RA A NE | (3a) A Biv ete Be n VAER SS ey ot ie. en | n 205 The quantities Sa; Ei and Wie are now also defined. The following identity will be satisfied for p—2721: )T Se) 719) = Sd Tati (yi) Ti SP TO 4 SPTO, HST = Sr) THF) +... + SHIT) (4) This follows by induction: SOT + SPT@ +... + SOTO = = SP) TO) + (PDF SPV) TO +... + (SPN +... + STD ie 7 Sp (TW) +…+ TW) + Sp) Ha TI de Tú) des 5 ak Se— 1) Tig) = = = SP—) TOT) aL Sp) TOT) se. + Sle) Tat, n UI n We also prove with induction: Wry) =S) TW) + SP) PD) + ...4 SUIT]. . . (5) n 1 n ì 2 n—l n 1 for we have by (5): Wotte Weta) + ie 4... Wiede) n n (oS Sip) Ti) +... SP Pa LSP TO Ht SPL TON 4... Str) Ta) B dt TOS ro. fee $ TO) +... + SOTO PY) ES PTUED oe SOT ie. (Ba) n Nr n Finally we deduce from : E Wott) = SOTO) + SOTO) 4+...4 SOTO). . © n n 2 n— n with the aid of SO) =d Has +... + an Wer) =n Tw) 1 (a, + ag) TP), + ...+ (ar + a +...+ a) Tp) =a, [TW + TP HH 1) ag (PO)... TO... and (P) or Wot ay T\ptD) t+ az er) Tee oe Gn Teti) be 1e RT) The n't mean-value of order p of the series a, + as +. respect- ively 6,-+6.-+.... is defined as S++) Tt p+) n rae ‘tively 8 AED respectively AGD If such a mean value of order p has a limit for „== we call the corresponding series summable of order p*). By a well-known 1) In our definition the first term of a series has the index 1 and not zero as is usually the case. 14* 206 theorem the summability of order p (and also the convergence) of a series implies the summability of order (p +7) if 721°). Proof of theorem 1. Suppose that the series a; + d2 +... is absolutely convergent (sum — s); let the series bi + be +... be summable of order p, or Tp) lim. Fete (Ga) n =, then we have to prove: W(p+1) lim. ——— = nae AOD Now we have: Wert) = ay TAD) Har TOY 4... Han Te) . . (7) n n | T +1) Put h, = ——— —t, then lim h, — 0. Substitution of Apt) n n= T P+1) = tA(p+1) + hy, AlptD) n n n in (7 gives: W(p+1) — n =a, Art ta APT) hypag Art) taz Alp) hj 1+. tan APT tan, Alpi) hy = t [ay AU+Y Has AVY HH ay AVY] + ar [ay Apt) h + az Apt) Eee Oy A(p+}) hi] . QE JSS A(p+}) -L az AQT) +...+ a Av+)| — == 1% [si Atp+}) + (se — si) APD a eee + (s, = ni) A{ptD] == == út (Apt) — ACP) + so (APD — Apt) SE en A(r+1)] = =t|s1 Alp) + 82 Alg) eis t= Sn Al?) = t[Si) A) + SH AP, oe ESS AP) =t[SP) A) + SW) AD +. SP) AW] n 2 n— n NR ee =t S(pt+), n JE S(p+1) lim ———-=t. lim. -"—- = 1. s fora, +a2 +... converges Hence HE VED tS SOAS 8 n n absolutely and is consequently summable of order p. 1) BROMWICH. l.c. (p. 312). 207 Q = ay APD hy Har AVEY hj HH an APHD hij an LAP) + Alp) +. AP] +ae hry —1| A?) +... + AD) | +... ahi Ar) = Alp) [ay hn aa hija de Han Mg] 4 AP [at Ii eo Han ha] +. + AW) ash, From fimh,=0 it is evident that MJ, may be chosen, so n= Bates My if 14,2 and lnv. My 0; putting o, = k=@ = |ay|+\a2|+...+ ]a,| and lim.o, =o, we have: nzo [QS AP [laa]. an] + [ae]. [nl +--+ + Jan). [all + +. AQ) (lau al He + lana [all + + AP. [aal ld < Alp) My (Jai) +laal + . + lanl] + Al) Ma (laa) + ..+Jan—1|]+ + Al) M,,\a1| 0 it is possible to calculate & so that My4; < = further let M be chosen so that M;< M, then we have, if n>4: QS ofA) Mi + .. + AW Me] He AR), +... + AM) SM GAP +... 4+ API] He [AVD — Art], Hence: | AGH) Alp) — Alp EBIT p M gede Î n Alp+t) | ee Art) ah A(p+1) n n n Ap) Lim . a= 0 for lim. AP) =o because AP) > AD =n. n= n=o0 Hence, if n is sufficiently great: Q EN id AOD) ~ FAs and since € is arbitrary lim .——— = ES AGA n Therefore : W (p+1) P+ @Q [2 lim. n . . SSS lim „zz et) n— 0 Ap) nzo A{ptD B WR: 6 SS EB oll n=0 Alpi) 208 Proof of theorem 2. Suppose that the series a1 + de +... converges to s, and that the series 6; + 62+... is summable of order p (sum = 2¢); further, let the mean-values of order (j—1) of the series b, + b, +... be limited. We have to prove: Wip) fn ADH) erk Put SO) =s, = 8 +h, then en hn =O and n=0 Wot) = SOTO) SOTO HH 90TH)... (6) = (6 +h) TH + (sh) TO +... 4+ (6 + hn) TY) =f TOE TP) Ft TOA THAT FHA TP =S fis De) TP), +...+ TOS sTO+) R Per) 40+) SS 5 AGH) Since the series 6, + 6, +... is summable of order p, we have: oe ae mo’ ADHD A Art T Sh, Tin) +h, TO) | oe. + hy TW. Since the mean-values of order (p—l) are limited, it is possible to find M so that: ae < M. Hence: |S| << MIA, | Ap Be |h,) A@), det [nl AP. NB) Put |4n| = H then we have by (4) WA [AD HALA, Ht APD = = HD AD) + HMA) | de oo dk HU) Ar = Hp AD + Hp AY + + ADA = HY) + AY) +... 4+ HY) = Her) The inequality (8) may now be written: | S| 0, we can calculate an integer 4 so that € al En further we can find u so that |A; | < u. Then, if n >> we have: | V | Ala, n 2 n— n n 1 == — (p [VLS e ACHEED + MuAGH) [AM +... + ADI e Alp+o+)) + Mp Ag+) Ant), n an u k n hence: |V| Apt) — MAG en Set ARTE n n Alp-+1) lg stelen. n ELT ek AQT) ntpl)! (21)! (pt)! Ate) (n=)! p! | (nt+p+q—))! n ’ fag! vt DI p! (n+p+q—l)! 5 (p +4)! f (nt+p—l)! pto)! 1 =p! Natptl-Df = ph Nat) 211 Hence we have if n is sufficiently great: een >, Arta) i Since e > 0 is arbitrary we have: li luis 0 see Aep+9+1) a Hence: Wipe) U V lime 2 — km li EES me AUTH) Tee ADD Pee Artrh Remark 1. K. Knopp?) ad S. Cuapman?) have limited the order of summability of the product of two series, which are summable of order p and q, by considering non-integral orders of summability. It may happen that the theorems proved above give more result, as is seen by the following example: The series 1 — 1 +1 —1 4... is summable of order 1 and its mean-values of order 0 are limited. Hence, applying theorem 3, we see that the product of this series by a series which is summable of order p, is summable of order (p + 1). Now the so-called index of summability of the series 1 — 1 +... is zero (see CHAPMAN, |. c.); the index of a series which is summable of order p, cannot exceed p: hence the index of the product cannot exceed p + 1, and there- fore we can only infer by Cuxapman’s theory that the product is summable of order p + 2. Remark 2. Harpy *) has also given the following extension of Mertens’ theorem which is totally different from the generalisations mentioned above, and which contains Mertens’ theorem as a special case: If Za, is absolutely convergent and bd, is a finitely oscillating series whose n‘ term tends to zero, then their product is a finitely oscillating series, and if the limits of oscillation of & 6, are 8, and 8, those of the product are s. 6, and s. 8,. ') Sitzungsberichte der Berliner Math. Gesellschaft 1907 (p. 1—12) 2) Proceedings of the London Mathematical Society, Ser. 2 Vol. 9 (p. 369— 409). 5) Proceedings of the London Mathematical Society, Ser. 2 Vol. 6 (p. 410—423). 212 Evidently the terms a; and b; are supposed to be real: therefore Mertens’ theorem is only a special case of this theorem when the terms of the series are real. It is however easy to see that Harpy’s proof is also valid for the following extension to series with complex terms: *) Theorem 4: If Za, converges absolutely to s, if bu + ba + ...+ by is limited and lim .b, = 0, then the product of the series Za; and n= 0 Sb; oscillates for n= a about the same region as the series s. Spe The functions p(n) and y(n) are said to oscillate about the same region if 2 tends to oo, if the following condition is satisfied: whatever be « >0O we can find two numbers je and a so that it is possible to calculate whatever be ”>gu a number m which satisfies the conditions: |g(n)—w(n)| Ze |n—m| a number n which satisfies the same conditions. Finally we prove the following theorem which is analogous to theorem 4 and which contains theorem 1 as a special case: Theorem 5: If Za, converges absolutely to s, if the mean-values of order p of &b, are limited and the mean-values of order (p A) (which we denote by UW) satisfy the condition: UP lam Lik n=o Nl then the mean-values of order p of the product-series oscillates about the same region as s. Ue+ as n tends to oo. Proof of theorem 4 Substituting p= 1 in formula (7), we have: Wn = A, th + Gy bnl Heee + Ont, Hence, if 1< k0, an integer 4 so that: € Sr é é then we have also |s—s,g| < a and |Q|==|an41 tn He + ant, | << 5 P= 4, ty Ht Or bna = a, (b, Hb) +... a4 (b, + + bn—k-+41) = (6, +6, +...+ Ont) . (e, + Ag dee. Jaz) + dns, + Onl Ss imke —k+1 Sk - = tre sh + Rals R= brs, +... + Oni She é We can find « so that |6,—74;| Sone ifn >; then we have 0 also [Ee if n> wp. Now sz tn—k = 8tn—k — (s—sk) . Inke € Since |(s—sz) . tnt Se (see above), we have if n> u: 2e € pas ene Ei and, since |Q| << 5 and w, =P + Q: |w, — s-tik| Ze. Hence we see that it is possible to calculate, whatever bee > 0, an integer « which satisfies the conditions. Proof of theorem 5. We have: Wet) = Tipsy a, Tek SE Kende @ Tip+1) afs so (TH) Hence, if10 we can find an integer & so that: € arg) dd Lip | Sg et Then |s—sr| < = and a fortiori: 214 |Q| e AGA oe [la goe = Sn PS [a TOP+") +. +a, Lal sar 1 Loy a (ESP) 5, a TE % ren oe —k+1 A Hence it follows from 1) — Tp) — (p) ( p) -. T(p) thes Te) Bel Te tee HO that kl Wp tees (p Ee 7) Eeten ETD Cte APF TT“ AlptD A(p+1) n n n It is evident that the absolute value of S is less than TO + [TW | HH [TP n— ia Age We now prove that we can find u > so that if r >u: (ele al ; de _ Zei Se then it follows that |,S| Le if n> u. T) For we have by hypothesis lim .———0 a : Se Ap) Api) idp—l T(?) Since AD = 5 we have fan ; Avy) = If n > u we have: | Wiet) Aas (AED — kart) S : Ë 5 and since |s —sk| < 3; our theorem is proved. Remark 3. A. RosenBLATT (Bulletin International de |’Academie des Sciences de Cracovie’, ser. A 1913 p. 612—620')) has proved the following theorem : 1) ROSENBLATT’s memoir not being accessible to me, the reference above is taken from an article of G. Doerscu, Mathematische Zeitschrift Bd. 11, p. 161—17d. 215 If Sa, is summable of order p +1 and its mean-values of order p are limited, if 6, is summable of order q + 1 and its mean- values of order q are limited, then the product-series is summable of order p + q+ 2. This theorem is an extension of Caucuy’s theorem that the product of two absolutely convergent series is convergent, analogous to the extension of Mertens’ theorem given in theorem 8, and, like Mratens’ theorem implies that of Caucny, so theorem 3 implies that of RosENBLATY. Mathematics. — “On a Generalisation of TauBer’s Theorem con- cerning Power Series”. By M. J. BeLINFANTE. (Communicated by Prof. L. E. J. Brouwer). (Communicated at the meeting of March 24, 1923). Introduction. In this paper we consider power series with complex coefficients, but for real values of the variable. We suppose them to converge if |v) <1, and we denote by «—1 that 2 approaches 1 by real values from below. Tauser has proved the following theorem '): If lim. nan =0 and lim. Za,a” =s, then S an converges to s. n= Ertl LmerLewoop ®) has shown: that the usual proof of this theorem proves more than is actually stated, and that the same proof applies to the theorem: ze . . . . . . . If + a,” oscillates finitely as & — 1, then the limits of oscillation 0 n co as no of Sa; are the same as the limits of oscillation of + a„a”. 0 0 In the present paper we give extensions of both theorems to the so-called mean-values of HOLDER. . $ 1 contains the proof mentioned above and a definition of the expression “oscillate about the same region’; in $ 2 the definition of Hörper’s mean-values and some necessary formula’s will be treated, while § 3 contains the generalizations of TauBer’s theorem. Get. Definition®). We say that f(x) oscillates for «—a, about the same region as g(7/) for y — y,, when the following conditions are satisfied : 1) Monatshefte fiir Math. u. Phys., 1897 Bd. 8, p. 273. 3) Proc. of the Lond. Math. Soc., 1911 Vol. 9, p. 436. 5) We always suppose that «x resp. y approaches 2 resp. 4) by real values from below. 217 primo: it is possible whatever be « >0 and 30 aad y0, we can calculate an integer u so that if » > u: € OSS ern. Sid vaan (I) zijn 9 — POAT Gia ~ nc OORD SA ‘ 5 Enh an| Ss (2) Now, if 0< «<1, we have: v—1 oo yv—1 y—1 © | 2 an — San a” | <| Sa, — Zane | + |Z a, x" | 0 0 0 0 v vl oo eS oleate ANDES cay a (8) 0 5 y—1 yv—1 vl | 2 a, (Le) | SZ | a, |. (lar) < (le). Enla, |. « (4) 0 0 0 ; 1 Substitution of «, = 1—— in (4) gives: Dv 1) Bromwicu, Theory of Infinite Series, p. 383. 218 v—1 1 yv—1 | Fa, (la) | << Enja, | 0 ki v oo Hence by (2) if » >u: y—1 [Zarda |< | iv 2} Substitution of (1) in Lana” gives: be 0 PS | SE tlr yv y n or a fortiori: oo in the last inequality we have: From (3), (5) and (6) we deduce: v—1 2 | 2 a, — Da, a |u and 2, =1—-, and it follows easily that both conditions of our definition are satisfied. § 2. If ¢,,¢,... is an arbitrary sequence of quantities, we define the so-called Hölder mean-values as follows *): ( ttt... Ht BC Te eee n Fm (k —1) Hem 1) (k) + He Ore (t) D= er (2 H, j= : (8) HDE DO el EE The following relations are easy to verify: PLH) rm it p= lg on 9) and 1) This definition differs slightly from the usual one, as the latter is given for a series Uj + Uy +... and not for a sequence. 219 He (ke) 35) Hn (t) = (n—1) - Ani (t) = Oy oo a UY) ‘Let SAG ee RA EO ew (IT) then we define: EOS (ices n> 5) 4. … (1) sts 25S) ite Re ws! ) (La) NEE OF 0. . . (13) From (10), (12) and (13) we deduce: Pe ES AMY lee oh Pal (14) Finally we define: C= Se A at ite MAA (15) | thus OOS EREN EE A Ke zl (DLT 1 We prove the following identities: *) (k+1) _(k) ott) ; PAN a Jakes I= ee 16 IE ; (16) ' 1 } P, (x) + (l—2). Y, (== = Pi (EPR er re ee (117) (le). (e)= S long: — on Joen 2... (18) 0 Proof of (16). By (14) we have: Bee eae oes a = Aerie ian) At ed IE en Sir aE 8 tas gly = 72. Ae a (n—1). ee Sei Saw Sn, hence: ) We tacitly assume that the power series 9, and op ; are convergent if —1<%x<-4+1; in our applications this will be the case. Proceedings Royal Acad. Amsterdam. Vol. XX VI. 220 Ue) (k) (1) er 02 ein On y Hi. [o Wed n : (k+1) Aj = = = iY = Are + za n Eel oe == 6; a + — an n Proof of (17) vp, @) + (le). p, (2) = id Zn ADE SE GEEN A= Aln Le rn A® Lal 0 Z k k k = 2 a" 4 (n+1). Aan" ye) = [pe AS Eej Anes 0 re i= ae gta Aa di == Ae An Di a 5 Saal ie = AX Di 0 U 0 IRS (kl) (k—1) mr » [An BE n—1 ] x es 1 = Te Pr-1 (x). a Proof of (18). (k) (k) (k) (1 = «) a Ly (x) == (1). [Ani = Ae | = 1. [An — An (k) (k)- - [on — On |. fore § 3. We prove the following extensions of TauBer’s theorem: Theorem 2. If lim.n. Lae Ayes = 0, and |sn| << c¢ whatever be nn an n, then ÊS ana") oscillates as «1 ‘about the same region ; (P) vp as Ay’ if No. 2 e 1) A! Theorem 3. §Lf lim.n. (ives Ae =0 and lim. oS Ori Se n=a Beas L . —1 then we have also: lim. APP = n= @ Proof of theorem 2. From the fact that sy is limited it is easy;to deduce that A® is 1) See remark 2 at the end of the article. Hence by (16) we conclude: lim. LHe Go” no noe tae (19) Now it is a well-known theorem that lim. Hi () =s implies n= lim. Bt) 0e) hence we deduce from (19) with the aid of (9): n= lim HST 0®) — HY (0 "tj = 0 n=—o from which we conclude: If dim. Hy” (o*) —0, we have also lim. Hit? (ad) == OE (20) nzo n—o By hypothesis we have: /im.n Al eA = 0 or by (13) n= lim. a” = 0: Hence by (19) dn lim. Hn (6? >) = 0 n=0 and applying (20) we get successively : lim. HO ro? | = 0 lim. H® [o? kl ==\()) nzo TEL Nou 0 eene ee WK) nzo Hörper has proved’) that if lim. AY (t) =h, then we have also: nzo wo lim. = CES) h. Sil In virtue of this theorem we have by (21): a Ei 4 lim. > mee — oe ae ==) Tl 0 ‘ or by (18): lim: (Va). pig, 4 (2) "0 p-i tl thus by (17): 1) See Bromwicu, Theory of Infinite Series, p. 383. *) Mathematische Annalen, Bd. 20 (1882), p. 535. Gye" 222 ee [ee pe) ren (0: Hence we infer that ppi) (e) and pp; , (e) oscillate about the same region as «—41. Repeating the argument for 7=1,2,..p, we see that ao a (P) = “al (p) Pe (x) EE = Cay ah and Py (z) = = [ : pn An or oscillate about the same region as a — 1. 5 ° (p) 7) : 5 By hypothesis we have lim. n [Af — 4 AP = =O; with the aid of n—a ; Sr 4) (P) : : theorem 1 we deduce that )(#) = > [An’—An—.]| 2” oscillates as 1 ) (p) (p) el about the same region as A” = s (4? vais | if moo. 1 a Combining these results we see that Za,” oscillates as 7—>1 1 about the same region as A,,'"?) as mo. Proof of theorem 3. - > . Ld 1 Lemma: If lim. Pp, ‚© = s and gr (a) + (l—) ¢, (©) = -9,,, @) r—>!1 = x ‘ then lim. gp, («)=s. r—>1 k Proof of the lemma: If we solve the differential equation we become: Pi (2) 9, Gen OL) (le)? Since dim. gra (e)==s, it is possible whatever be e>>0 to calculate Tl “a number §,<1 so that &<{e<1 implies: [p,_,@O ele 1 (x) P,_, (©) ~P,_, (#) kl k— ; k-1 (1 ) il : a } da == (1 av) 5 a x)? dx aa (1 nl w)? 0 51 Ei x zi AG ee) Pees ie == Se =a du —«2) | er ea + Be sues: = [ ae 1 iy ie Lim. [==0; therefore we can calculate a number & > &, so Ll 223 that |J|8, so that |///| < 2e if E kar 1 1 = 1) 12” Sn == — 23 Sf}: n 1 OH IN) OD) at) — 2 Gh nr =D Y Ie toen oral and proves the following theorem : ag) Da a jb seo Cage Ef thw Theorem C: The conditions lim. — vr» = Oand liam. Sana? =s no I Tl 1 e ea Tim. sn =s, and tak are each necessary for the existence of lim. s, =s, and taken toge- noo ther they are sufficient. (A) The mean-valuesjs, differ from Cusarò's or Hörper's mean-values, but in a second paper’) Kienast has shown the equivalence of his mean-values with those of Cresarò-HöLDeR. Remark 2. iva} We have tacitly assumed that Sa,w" converges if —1 @ il; J 8 1 This is however superfluous for our purpose as the condition 4 (p (p 5 : 5 KS lim. ny? Ali Zi — 0 implies the convergence of > az” pro- nzo l vided |a|’< 1. . (p) (p) ain Indeed from dian. n (ae = An = 0 we infer the absolute n= @ ; > (p) (p) n . convergence of ,(#) = > [An — Anje” provided |«| < 1. | Further we have by (17): pi, =#.y, (#) He (le) @); therefore the absolute convergence of (a), which implies the abso- lute convergence of gy’; (a), implies also the absolute convergence of gr—1(w). Repeating the argument we infer the absolute convergence a of p‚(#)= = a,2" provided |z|< 1. 1 Be) Proceedings of the Cambridge Phil. Soc., vol. 19 (1918), p. 129. 3) Proceedings of the Cambridge Phil. Soe., vol. 20 (1920), p. 74. Chemistry. — “Hydrogenation of Paraffin by the Bureaus’ Method”. By Prof. H. 1. Waterman and J. N. J. Perquin. (Communicated by Prof. J. BörsSEKEN). (Communicated at the meeting of February 24, 1923). In a previous communication on the hydrogenation by Brrarus’ method of mineral oils or allied products, different experiments were discussed, which were carried ont with heavy Borneo-asphalt-oil, distillation residue (pitch) of this oil, and with asphalt obtained by, distillation of Mexican crude oil’). The experiments in question, comprising both cracking- and ber- ginisation experiments, were executed in a vertical immovable auto- clave. That we have now chosen another material, technically perhaps of less importance for this purpose, is owing to the peculiar advan- tages which commercial paraffin offers for such experiments over other materials, as asphalt. Paraffin is much more easily analysed than asphalt, and this holds also for the products prepared out of paraffin, when they are compared with the corresponding substances formed in the treatment of asphalt. Thus paraffin yields products that are less strongly coloured than Mexican asphalt. For these experiments we had an autoclave at our disposal which could be shaken continuously *). The way of procedure was for the rest quite analogous to the earlier experiments; the arrangement of the apparatus is represented in fig. 1. The capacity of the autoclave was about 2500 em”, the heating took place by means of gas, in such way that the tempe- rature could be regulated accurately to a few degrees. The paraffin had a Sp. Gr. (15°/15°) of 0,913, the solidifying point (SHUKOFF method) was 50,6°, the bromine-value, (addition) determined by Mc. [rarer’s method *), was 0,5. 1) Congrés international des combustibles liquides, Paris, 9—15 Octobre 1922; Chimie et Industrie, numéro spécial, Mai 1923, p. 200. 3) Apparatus supplied by AnpreAs Horer, chief instrument-maker at the laboratory of Prof. Dr. Franz FrscHer, Kaiser Wilhelm Institut für Kohlenfor- schung, Milheim—Ruhr. 3) Journ. Am. Chem. Soc. 16, 275 (1894), 21, 1084 (1899), Journ. Soc. Chem. Ind. 19, 320 (1900); H. Beckurrs, Die Methoden der Massanalyse, Braunschweig 1913, p. 480. a 227 Practically the bromine value of the paraffin may, therefore, be neglected. The bromine-value determined according to Mc. Iuminey’s method, is obtained by subtracting the substituted bromine from the Fig. 1. 430° 42o 2 Koo |. 5 © re Pes © 0 2. H I > 38° oO 0 a, Í —— DUUR IN MN STe hd Go 12e 180 24o Overdruk = Pressure Duur in min, = Time in minutes Fig. 2. 228 total amount of the absorbed bromine. The remaining quantity gives a measure of the degree of unsaturation, and is expressed in percent- ages of weight of the weighed quantity. In every experiment 300 gr. of paraffin was taken, an equal weight of stones being put in the autoclave to promote a thorough mixing; the temperature was always 435°. Some of the results obtained are recorded in the table, and in fig. 2 an illustration is given of the variation of the pressure in the course of experiments 33 and 34. Though in experiment 33 the typical pressure curve according to Beraius given in our preceding communication is not obtained, probably on account of the high temperature, the difference from the cracking-pressure curves is nevertheless very striking. In all the other experiments recorded in the table the pressure curves obtained are analogous to those of 33 and 34. The oils obtained by the Beraivs’ process were coloured from yellow to red, and perfectly transparent, a small quantity of “carbon” was deposited on the bottom. The oils obtained in cracking were very dark of colour and pretty well opaque. Here too separation of some carbon is found. The small quantity of carbon which is deposited on the bottom, when the weight of carbon which had already been deposited on the stones is added, is so small, both in the cracking and in the Bereius’ method, that practically the paraffin may be assumed to have been entirely converted into oil and gas in both processes. In this we leave out of consideration experiments 35, 37, and 40, where the duration of the processes was still so short that the reaction produet had remained partially solid. Hence the product obtained had to be melted out in these experiments. It appears from the experiments made that, 1. observations can be obtained which can be perfectly reproduced (compare 35 and 37, and 46 and 48). 2. if the duration of the experiments is long enongh, the paraffin is practically quite converted into liquid oil and gas, both in the cracking and in the Berarus’ process. 3. the yield of gasoline does not differ much in the two processes. 4. there is a great difference in the nature of the residues left in the distillation of the oil obtained according to Enarer. Its specific gravity is always smaller in the Berginisation experiments than in the corresponding cracking experiments, which is a confirmation of corresponding experiments made by Berxeus. 5. lt appears from the final pressure, also in connection with the gas analysis (percentage of hydrogen), that actually considerable quantities of hydrogen are absorbed in the berginisation. EN COMPARISON OF BERGINISATION AND CRACKING AT + 435° C, ] on = £ = L Distillation of the obtained oil = 2s v5 5 NEE = according to ENGLER CLES: <= — = 0 ia an ore v 5 es u ApS 8 |fe2 | See | #5 | 28) Ss lsd.) 55 Br d S$ | 3ge sE fe | 83 | fe |< E | 2 | Weight % of the distilled oil. Sp. Gr. = fe ES 5 = Be BS 58 = E ER 6 Sp. G. Quantity |compar-| Hydrogen Cec bee, = wis w ~ H 5 E _ 5 Bar | 5 a Ss w SES 5 3 © to to || residue residue in Litres | ed with) percentage. at el nee A Sie E EE Sn Sn IE Loss?) | 15°/15°. Z v me sl Le 220° | 300° [> 3009 air = | chy) 60 60 40 ORS 37.5 2601)| 16.4 | 24.9 | 41.0 | 56.3 Peal 0.846 — 0.24 85.8 37 E 60 60 40 108.5} 37.5 | 272')| 16.1 | 22.8 | 37.9 | 59.0 Boll 0.854 — 0.20 89.5 © 36 3S 60 120 40 107 | 3) 272 19.0 | 36.6 | 56.6 | 38.7 4.7 0.835 — 0.37 74.6 33 5 60 180 40 117 30 256 20885 bleh Wwe |p 22 5c! Ono) 0.852 — 0.56 56.9 - U 46 JA 15 240 40 118 | 28 250 | 21.0 | 58.9 | 79.6 | 14.8 5.6 0.836 63 0.63 47.5 48 15 240 40 120 | 28 240 PAD KOOR MORZAN STE 7.0 0.838 62.5 0.63 46.5 40 80 60 Oa SOB sal) es EZLN 21565923). 0F | 39s ONO] 0.9 0.854 — 0.99 — 45 2 10 120 0 5 51.51< 4 BOR STORIONI KOI NRR 20 4.3 0.855 — 0.80 — ES 2 34 S 60 180 Of i Om dome P20 A18 ROOM eK ZO EON PND 6.0 0.900 — 1K) Pas) O 8 49 15 240 0 1E 12 1.5) 238 | 23.9 | 56.8 | 76.9 | 16.2 6.9 0.902 29 0.94 3.7 ') The product obtained was still solid and had to be melted out, which gave rise to extra losses of weight. 2) Belongs to the lowest fraction. 230 6. The bromine value caused by addition of the oils obtained by berginisation is lower than that of the corresponding cracking experiments. It is, however, very risky to draw general conclusions from this bromine value, for dissolved unsaturated gases can have a great influence on the halogen value. The example given here proves convincingly that a determination of the yield of oil and gas from a solid substance does not suffice to enable us to form a correct opinion on the process of Brr@ius. A comparative cracking experiment is required for this. Possible results refer only to the procedure followed, in this case to the periodic process, the temperature at the experimenting etc. It is self-evident that in practice processes that proceed continu- ously, will be preferred. It may, however, be considered to be an established fact that when Bereivs’ method of procedure is followed, important quantities of hydrogen added from the outside, are che- mically bound. After the scientific researches of SABATIER C.S. CON- cerning the hydrogenation of hydro carbonic vapours with catalyst and the technical hardening of fatty oils (NorMANN and others), this fact, combined with the absence of express addition of catalyst, may be considered as the third great discovery in the region of hydrogenation. Delft, Laboratory of Chemical Technology of the Technical- University. Palaeontology. — “Contributions to our Knowledge of the Palae- ontology of the Netherlands. 1. Otoliths of Teleostet from the Oligocene and the Miocene of the Peel-district and of Winters- wyk.” By O. Posrnumus. (Communicated by Prof. J. C. Scnourr). (Communicated at the meeting of February 24, 1923). As regards the fish-fauna of the tertiary deposits in the Nether- lands the occurrence has been reported of a number of Selachii in the Oligocene of South-Limburg >), and of the Miocene of East-Gelder- land *) and Overijssel *). No remains had as yet been found of Teleostei. We are in a position to form an idea of the fish-fauna in the North Sea of Miocene time, from a number of otoliths occurring in material obtained from borings, undertaken by the Government (Institute for the Geol. Exploration of the Netherlands) on the Southern Peelhurst, notably from boring 20 (Helden) of the Middle-Miocene (75.4—80.4 m.), from boring 21 (Swalmen) of the Upper-Oligocene (100—160 m.), and of the Middle-Miocene (75—100 m.); likewise in material originating from boring 22 (Liessel) also of Middle- Miocene date (LOO—190 m.). Moreover the test-boring U near Winterswijk, placed at my disposition some otoliths from the Septarian clay, and from the Middle- Miocene, laid bare in the bed of Slingerbeek near Winterswijk. The following specimens have been found‘): Oligocene. Middle-Oligocene (Septaria clay), Winterswijk. Otolithus (Seopelus) pulcher, Prochazka. 1) W. C. H. Sraring De bodem van Nederland, Ze deel, Haarlem, 1860, p. 282. 2) Ibid, p. 209, 210. 3) T. C. Winkuer. Catalogue systématique du Musée Teyler, 6me livr. 1867, p. 624. *) They will before long be figured and described in a more detailed memoir. 232 Upper-Oligocene, Swalmen. Otolithus (Dentex) nobilis, Koken. 55 (Percidarum) limburgensis, nov. spec. i (Trachinus) mutabilis, Koken. Ms (Trigla) Schuberti, nov. spec. i. (Scopelus) austriacus, Koken. A (Scopelus) pulcher, Prochazka. 5 (Gonostoma ?) parvulus, Koken. he (Gonostoma?) angustus, nov. spec. 5 (Fierasfer) nuntius, Koken. ce (Gadus) elegans, Koken. a (Merlangus) cognatus, Koken. Miocene. Middle-Miocene, Swalmen. Otolithus (Pereidarum) frequens, Koken. a (Trachinus) mutabilis, Koken. * (Trigla) rhombiens, Schubert. " (Gobius) aff. elegans, Prochazka. 33 (Ophidiidarum) semiglobosus, nov. spec. 5 (Ophidiidarum) swalmensis, nov. spec. S (Gonostoma?) parvulus, Koken. en (Solea) approximatus, Koken. a (Rhombus) rhenanus, Koken. a (incertae sedis) peelensis,. nov. spec. Middle-Miocene, Helden. Otolithus (Serranus) Noetlingi, Koken. 55 (Centropristis) integer, Schubert. is, (Dentex) nobilis, Koken. re Percidarum) acuminatus, nov. spec. En Trigla) Schuberti, nov. spec. on ‘Sciaenidarum) Staringi, nov. spec. 7 Gonostoma) aff. gracilis, Prochazka. os (Clupea) testis, Koken. ee Clupea) Priemi, nov. spec. % (Gadus) elegans, Koken. bs (Phycis) elongatus, nov. spec. 5 (incertae sedis) Mariae, Schubert. n (incertae sedis) peelensis, nov. spec. 233 Middle-Miocene, Liessel. Otolithus (Dentex) nobilis, Koken. (Percidarum) frequens, Koken. (Percidarum) Liesselensis, nov. spec. (Scopelus) austriacus, Koken. (Scopelus) pulcher, Prochazka. (Gonostoma?) parvulus, Koken. je (Clupea) testis, Koken. (Fierasfer) nuntius, Koken. (Gadus) elegans, Koken. (Merluccius) emarginatus, Koken. (Phyeis) elongatus, nov. spec. (Hymenocephalus) globosus, nov. spec. 5 (Hymenocephalus) medius, nov. spec. =; (Hymenocephalus) ovalis, nov. spec. ns (Hymenocephalus) Brinki, nov. spec. (Hymenocephalus) dubius, nov. spec. (Maerurus) pusillus, nov. spec. (Maerurus) ellipticus, Schubert. (Maerurus) debilis, nov. spec. Middle-Miocene, Winterswijk. Otolithus (Gadus) elegans, Koken. The fauna of the Upper-Oligoeene ot Swalmen is characterised by the absence of littoral forms; the fishes that occur, inhabit the deeper fand more open parts of the sea, as e.g. Dentex, especially in the upper water-layers, or the Scopelidae, especially at greater depth. {The depth may have been somewhere about 400 m. at a moderate distance from the shore. This tallies with the known data, as the Upper-Oligocene is represented in erosion-rests as far as the line Liege —Aachen—Cologne. From Middle-Miocene data are known from localities on the Southern Peelhurst, lying in one line, that is about straight and runs about $.E.—N.W. In the South-most of these three localities, near Swalmen, the genera Rhombus, Solea and Gobius are conspi- cuous. They are all littoral forms, and not met with in the material of Helden, about 20 km. farther, where, however, Clupea, Serranus, and Dentex oceur; these fishes we also find naar Liessel, about 18 km. farther in Noord-Brabant, where, however, Macruridae and Scopelideae predominate in the material. Judging from the remains of fishes Swalmen is not far from the ancient coastline; in the vicinity of 234 Helden the fauna resembles closely that of a moderately deep sea, while the remains of Macruridae, occurring in the material of Liessen, originate from deep-sea forms, so that here we have to assume a greater depth of about 1000 m. This conclusion is in accordance with the results of the inquiries of the Government Institute for the Geological Exploration of the Netherlands: the boundary-line between the continental and the marine Miocene runs about via Swalmen; the lignite formation occurs near Melick-Herkenbosch and Vlodrop, while in the profile of boring 21 the lowermost layers of the Miocene are marine, and the upper layers display a limnie facies. It seems to me that a closer inspection of material from the Groote Slenk, southwest of the Peelhurst, would be very interesting. The tertiary fauna of this region differs from the recent fauna of the North-Sea: on the one side forms occur that inhabit greater depths than those living in the North Sea at the present day, such as Scopelidae and Macruridae, which occasionally occur at high latitudes in the Atlantie Ocean; on the other side the tertiary fauna comprises genera such as Dentex, Centropristis and Serranus, now living at lower latitudes. In my judgment the occurrence of the latter points to a change of environment, which is to be aseribed either directly to a change of climate, or to other conditions, e.g. an altered direction of the oceanic currents. In conclusion I wish tot express my warm thanks to Prof. Dr. J. H. Bonnema for kindly placing at my disposal the material in the Geological-Mineralogical Institute of the State University of Groningen. / Palaeontology. — “Contributions to vur Knowledge of the Palae- ontology of the Netherlands”. Il. ““On the Fauna of the Phos- phatic Deposits in Twente. (Lower Oligocene)” By O. Posrnumus. (Communicated by Prof. J. F. van BEeMMELEN). (Communicated at the meeting of March 24, 1923). In examining a collection of fossils, derived from the phosphatic- nodulus-bearing deposits of the localities Ootmarsum and Rossum (between Oldenzaal and Denekamp) I came upon the following formations : Coeloma balticum Scarier, Zeitschrift der deutschen Geol. Ges. Bd. 31, 1879, p. 604, Pl. XVIII; one specimen. Myliobates toliapicus 1 Acassiz, Recherches sur des Poissons fossiles, vol. 3, 1843, p. 321, tab. 47, fig. 15—20; loose toothplates. Carcharodon angustidens a. Agassiz, Recherches etc., vol. 3, 1843, p. 255, tab. fig. 20—25, tab. 30, fig. 3: teeth. Notidanus primigenius L. Acassiz, Recherches ete., vol. 3, 1843, p. 218, tab. 27, fig. 4—8, 13—17; teeth. Oxyrhina Desori (L. AGassiz) Sismonpa, Memoria della Reale. Accademia delle Science de Torino, 2d series, t. X, 1849, p. 44, tab. II, fig. 7—16; teeth. Owvyrhina Desori L. Sismonpa mut. flandrica, M. Lerican, Mé- moires du Musée Royal d’histoire naturelle de Belgique, T. 5, p. 280, fig. 87; vertebrae. Odontaspis cuspidata L. Agassiz, Recherches etc. vol. 3, 1843, p. 294, tab. 37, fig. 43—49; teeth. Otodus obliquus L. AGassiz, Recherches ete., vol. 3, 1843, p. 267, tab. 31, tab. 36, fig. 22—27; teeth. Lamna spec., vertebrae. Phyllodus polyodus L. Agassiz, Recherches ete., vol. 2, 1843, p. 240, tab. 69a, fig. 6, 7; And in addition some fragments of bone, presumably from Cetacea. The phosphatic deposits are disposed in the profile as follows *): “Underlying the Middle-Oligocene Septarian clay are..... pale- green, very fine glauconite sands, probably referable to Lower- Oligocene, but seeming to belong to the Middle-Oligocene. At the basis of these sands a very typical conglomerate layer of loosened phosphorite nodules and shark’s teeth appears, as may be found e.g. in the eocene quarries at the southern base of Lonnekerberg in the neighbourhood of Rossum, between Oldenzaal and Denekamp, and in the hills north of Ootmarsum”. The phosphatic deposits 1) Eindverslag van de Ryksopsporing van Delfstoffen. Amsterdam, 1918, p. 114. 16 Proceedings Royal Acad. Amsterdam. Vol. XX VI. 236 therefore may be estimated to be of Lower-Oligocene date; at all events they must have been formed at the commencement of the Oligocene transgression. These formations are best compared with the Oligocene phosphatic deposits of the North-German Plain, of which those from Helmstedt have become familiar to us through the researches of Von KoENEN and H. B. Grinitz'). It appears that all the fossils found in Twente, except Oxyrphina Desori, are also to be found near Helmstedt, which proves that the two deposits are equivalent. This induces me to put forward some remarks about the forma- tion of phosphatic nodules. Most authors advocate the view that the more or less rounded shape of these bodies is to be attributed to transportation, which view is adhered to by recent observers, as shown by the “Eindrapport” from which we just now quoted a passage. We contend that the nodules, in many cases, are not rounded, but more or less irregular, nay, as STARING?) observes, they often seem to be made up of two or more rounded nodules. The shark’s teeth are in many cases enclosed in an approximately rounded phosphatic nodule: the portion that is sticking out, however, is not worn off at all, which fact clashes with the presumable genesis. H. B. Gwinrrz assumed the transport of the nodules to have taken place in the Recent Tertiary and based this view on the fact of their presence in the layers of Myliobates and of Lamna cuspidata, which he had examined, and which up to that time had been recognized only in the Pliocene. Now, this cannot apply to the Overijsel phosphatic deposits, in which these remains have also been met with, because the younger deposits of the Oligocene also occur here. The palaeontologieal argument that the rounded shape is attributable to rolling cannot be sustained. We are bound to assume that after the formations of the phosphate-concretions, the position of the deposits remained unaltered, which conception has been supported already by Dr. W. P. A. Jonker *) on other grounds. I wish to conclude by gratefully acknowledging my indebtedness to Mr. J. Berninx, Director of the Museum ‘Natura Docet’ at Denekamp, for granting me access to the fossils collected by him. 1) H. B. Geintrz, Die sogenannten Koproliethenlager von Helmstedt, Biidden- stedt und Schleweke bei Harzburg. Abhandlungen der Naturwiss. Geselschaft , Isis” in Dresden. 1883, p. 3— 14. H. B. Gerrrz, Ueber neue Funde in den Phosphatlagern von Helmstedt, Biid- denstedt und Schleweke. Isis, 1883, p. 37—46. 2) W. H. C. Srarina, De bodem van Nederland. 2e deel. Haarlem, 1860, p. 195. 3) W. P. A. Jonker, Het ontstaan van phosphorieten. Handelingen van het 17e Natuur- en Geneeskundig Congres, 1920, p. 94— 96. Mathematics. — ‘An application of the theory of integral equa- tions on the determination of the elastic curve of a beam, elastically supported on its whole length’. By Prof. C. B. Brezeno. (Communicated by Prof. J. C. Kiurver). (Communicated at the meeting of March 24, 1923). In his well-known treatise ,,Vorlesungen iiber Technische Mecha- nik” (Vol. III, § 48) Fépr1 describes a construction, by which the elastic curve of a beam, elastically supported on his whole length, might been approximated. If in the differential equation of this elastic curve Ely" +ky=q (Hl = coefficient of stiffness of the beam, / — coefficient of stiffness of the supporting ground, g = specific continuous loading) the function 4 where known, it would be possible to refind this function by integrating four times the expression fe This integration would graphically correspond to the construction of the elastic curve of a beam, which carries only well-known forces. It is obvious, therefore, first to make a supposition about the elastic curve — in such a way, of course, that the reaction-forces of the supporting ground will be in equilibrium with the external forces of the beam —, then to integrate graphically the expression ua and finally to controll, if the before-mentioned accordance takes place. „Im allgemeinen — such is the opinion of FérpL — wird man zunächst eine starke Abweichung in der Gestalt beider Kurven finden. Dann ändert man die zuerst gezeichnete Belastungsfläche so ab, dasz sich die Lastverteilung jetzt der Gestalt der gefundenen elastischen Linie nähert und wiederholt das Verfahren für diese zweite Annahme. Die Uebereinstimmung zwischen Belastungsfläche und zugehöriger elastischen Linie wird jetzt besser werden und nach mehrmaliger Wiederholung findet man mit hinreichender Genauig- keit die wirkliche Druckverteilung.” 16* 238 Certainly it will be possible, — under favourable conditions — to find in this way technical sufficient accordance between the supposed curve and the one, derivated from it; but generally the convergency of the described process is uncertain. In the following paper a convergent process will be given. 2. The equation Ely" +ky=g is transformed in gj + kel y = q' k q if —=k*, 6 TNT, Putting y"" =p (2) it becomes: gp (a) + xf ple) det = q' + Av? + Ba? + Cz + D 0 or, using the well-known relation f ple) da* Le p (s) ds *(e— s)° yy ple) +k 0 p(s) ds =q' + Az' + Ba? + Cr + D. A, B, C and D are constants of integration, which enable us to satisfy the following conditions: lee oy 0, Dr ie — ()) Bett Ot ORL 1 The former conditions imply, as is seen from the relation > Ab Sede (Cia JD fn that the coefficients A and B are zero. The coefficients C and D are determinated by the latter conditions. 3. According to VorLrerrA the solution of the integralequation ae ag y (s)ds = q' + Ce + D 239 may be written as: p (7) =p, (@) + kp, (@) + kK? py (e) + RPG (we) +... where f, (#2) =q + Ca + D n= gas 0 pn (x) == TT (p= fn—1 (s) ds, 0 This solution however can only graphically be used, if the coefficients C and D are known. Nevertheless this coefficients depend on the second and first integral of y (x) in a point which is different from zero. Therefore we cannot find them a priori. 4. To meet this difficulty, we introduce the function Xe) =g + Cor + Ds C, and D, being two constants, determinated by: | %e (©) dx = 0 0 l ue 2 de = 0. 0 By choosing C, and D, in this manner, we reach that 1°. C, and D, can easily be graphically found, and 2°. that the function g(a) = — [Oo ats as 0 satisfies at the point «—/ the conditions p‚' == 0, Q," == 0, or the conditions l l x fu mar =0, fte fn mae=e 0 0 0 240 x l l For: l x p', (omi fte fr (z) dx = a ® Xo (z) dx = 0. 0 0 0 0 If we should deduce the function vp, («) from g, (a), in the manner which Vorrrrra indicates, the second and third derivates of ~, (2) would not be zero at the point «—/. Therefore we define the function x oe dg Xi (x) ZT | ($= ho (s) ds se C, © +D,| 0 C, and D, being constants determinated by l lie (@) dx = 0 0 l fue ndi A0 0 In this way, the second and third derivates of x, (v) take at the points «=O and «e=! the prescribed values; on the other hand fore-fold integration of x, (~) gives rise to a function, the second and third derivates of which are at the point « = /also equal to zero. This being stated, we are lead to define the series of functions x, (7) =q + Cor + D, % (x) = — [Jar Xo (s) ds =i C, x ar D, | ta wo = [fs (w — He Xn (@) = == 7 B TT) 1 (3) ds + Cu 4D, | where the coefficients Ci and Di are bound by the conditions l [u@d=o 0 l fue). ar=0 0 Mn drt Ce D,| 241 and to put = ITB) Se 12 9a(@) a2 ee0e (9) dos This function satisfies formally the equation x ' («—s)' p(x) +k nn (s) ds =q' + Ca D . ! and the expression y, which follows from it: DCE DEN OEE Os Fran ke a k =— x, (z) — Ky, (2) — ky, (2)... satisfies formally the conditions, imposed at the ends « = 0 ande = /. For, substituting the expression g in the integral equation we obtain — provided that it be allowed to integrate term by term the series, which occurs under the sign of integration: Cx + D,— k(C, «+ D,) —k? (C, a+ D)—....=Ca+D. If the series, which appears in the first member of this equation, converges, there can be disposed of the constants C and D in such a manner, that the equation becomes an identity. Of course it would now be necessary to examine the convergency of the described process of iteration. For this investigation however we refer to the paper of Mr. J. Droste, which follows this. We will state here only, that conver-_ »]4 gency is sure, if a7 < 500, and go on to demonstrate in which manner the process can be graphically performed. 5. At the first place the system of forces, which loads the beam, is substituted by another load, changing linearly, (q, — ae + B), and which is statically equivalent with the first. This substitute load causes a sinking down of the beam, determi- nated by arg Ip Dean This y, can be considered as the first approximation of the required y, and can be brought in relation with the expression C,z + D,, which is defined in N°. 3. Indeed, «x + 3 satisfies the equations 242 l l JG + B) dx =fgde 0 l l J Gea fiers 0 on the contrary Cr + D, is defined by l 1 i fice | D,) de = — ide = (de 0 0 0 l l l [ce + D,). 2 da= feae Aven 0 0 0 It follows, that aa + 8B=— E/(C,x + D,), so that: az+B , Cat D, ET ek The load which really charges the beam differs from the substitute load by: Van ng 4=g ler Hp) =H + Cr + D)= Ely, (2). By adding this load (which is in equilibrium) to the load q,, we would regain the real conditions of loading. However, if we add the load g, the beam gets a deflexion y,, determinated by: Ely” = ET?, (2) Hence: na fReoden (es Gide Acct Bi Cee The second and third derivates of y, being zero for «= 0, it follows that 4, =0, B, =0. Choosing C, and D, so that: we identify y, and — x, (2). 243 At the same time, the forces, defined by Zy,, are in equilibrium. If the elastic ground were loaded with 4, it would obtain the the deflexion y,. In this case the beam and the ground would have the same shape. However the load on the ground can only arise from the beam. The deflexion y on the ground therefore involves necessarily a reaction-load —y, on the beam. This latter load gives rise to another deflexion y, of the beam, defined by: EIy,"" = — ky, =k YX, () Hence x disse | (Sn, (s) ds + Cr zin Dl 0 3! If we require again that the load £y,, which follows from y,, is in equilibrium, we find that: IST k' X, (x). From this, we deduce y, = — k?x,(x) and so on. Therefore, the terms of the series: C,«+ D ae En > —X, (w) — kX, (2) — kX, (©) represent elastic curves of a beam, which is loaded in a well- defined manner. 6. Fig. 1 illustrates the described construction in the case: 7/= 200 em., 6 = breath of the beam = 25 em., J = 5000 ecm‘, E = 100000 kg/em?; EI = 5 X 10° kg.em’, £= 5 kg/em?, k=—=bk=125 kg/em*. The load diagram has a parabolic form; the specific load at the ends of the beam is '/, of its value at the middle. The total load is 15000 kg. The scale of length in horizontal direction is n= 5 (l em — means 5 cm <—=). t The deflexion are 25 times enlarged; 1 cm. fn Wee em]. The linear load q,, which is statically equivalent to the given load q, will give a sinking down to the beam, which is: 15000 KG UTERO GA This sinking down is represented in figure 1a by 25 < 0,6 cm. = 15 cm.; and gives rise to the straight line y,. This line also 244 represents, when the scale is altered, the load q,; in this case 1 em. | eee nes 15000 kg. Si k en as Le N 7 bh must be interprete 200 X 15 em g/em (say m, kg/cm) Yo On this scale the parabolic load q has been drawn in fig. 1a, so that the load q—q., — Which determines the elastic curve y, — is represented in fig. 1a by the hatched area. In the well-known manner the elastic curve y,, which corresponds to the load g—q,, is constructed (see figures 16 and 1c with the corresponding pole figures 1 and 2). To determine the situation of the pole in the second pole figure, we make the following remarks. In figure 1a 1 cm. <—— represents 2 cm. ——; 1 cm. | represents m, kg/em. Therefore 1 cm? of fig. la represents nm, kg. Assuming now that in the first pole figure 1 cm. (whether ——~ or ) will represent m, em? of figure Îa (in the drawing m, is supposed to be 5) and that the first pole distance has a length of H, em (in the drawing 10 em), we see that 7, represents m,m,n/, kg. Hence | cm. | in fig. 15 represents m,m,n’?H, kg. cm. Consequently 245 : ; ‘ : emmen the unity of area in fig. 15 means in the next integration Ke units. . m,m,m,n'H, H, The second pole distance H, therefore represents TE units, if we suppose that 1 cm. of this distance represents m, cm? (in the drawing 10cm’) of the area in fig. 16. From all this it follows finally that 1 em. | in fig. 1¢ represents 4 m,m,m,n‘ HH, EI em. Now the elastic curves y, and y, must been drawn on the same scale; hence: m,m,m,n‘ H, H EI 1 EI H. a mnd 7 25 m, m, m, n* H, Ssi: = 12,8 em. The elastic curve y, once found, the drawing process is to be repeated so many times, that the last approximations may be neglected. By adding the different curves yy, y,.... we obtain the elastic curve y. The final result can be controlled as follows. We load the beam at the one side by the well-known external forces, at the other side by the continuous load ky, which follows from the elastic curve y. Then we construct the elastic curve y. If the result y were exact, the curves y and y must be identical. Fig. 1/,9, 4 shows, that a difference between the curves y and y cannot be observed. 7. Considering fig. 1, it appears that the ordinates of the curves y, and y, are proportional. If the factor of proportionality is called — wu, so that y, = — uy‚, it is easily seen that the ordinates of the curve y, can be written as — uy, and so on. The ordinates y,,y,,...Yn at any point can therefore been looked upon as terms of a geometrical series and the curve y can be obtained by adding y, to the sum of all the following approximations. Not only when the factor of proportionality u is <1, but also when « >1, it may occur that the described drawing process is useful to find the elastic curve. Supposing that the load — ky, gives rise to the deflexion — uyn there can be found a factor rv, such that the function vyn 246 satisfies the equation ly" + ky——ky,. Using the relation — EI py," = — ky,, we find the condition: kin == = kvyn == TT kun lu whence: SU y= —— a+ 1 We therefore can obtain the deflexion y of the beam by —=" adding oy yn to the sum of the curves y,, 7, .-- Yn, or by adding —u 1 (1 de | Un Dn yn to the sum y, + y, +... + Yn-t- u Thus we can stop the drawing of curves, as soon as two conse- cutive ones y, and vj are found, the ordinates of which are proportional. Though — generally — the above mentioned proportionality only appears exactly after an infinite number of iterations, it nevertheless will be approximately observed tolerably soon. Neglecting in such a case that part of the last found loading diagram which troubles the proportionality between its ordinates and those of the foregoing diagram, we can use the preceding remark, provided that 1° the neglected load diagram be insignificant, and 2" it gives no rise to following load diagrams which grow larger and larger. kis The second condition is satisfied when EIS 14600. The justification of this latter statement can be given most naturally by the aid of the deductions, given by Mr. Droste. We therefore refer to his paper. Mathematics. — “An application of the theory of integral equations on the determination of the elastic curve of a beam, elastically supported on its whole length’. By Dr. J. Droste. (Communi- cated by Prof. J. C. Kruiver). (Communicated at the meeting of March 24, 1923). 1. Under the same title and at the same time a paper’) of Mr. BirzrNo appears in these Proceedings. The question, suggested, in N°. 4 of that paper as to the validity of the process of iteration used in it, will be answered here. For that purpose we observe that the function of a, satisfying the differential equation 4 y — Ay=g (a br EEA leo el 1 mee ane (x) . (1) and the conditions at the ends of the interval, is a meromorphic function of 2. We might find it by means of the method of the variation of constants and then expand it in ascending powers of 2; the radius of convergence R of the power series that stands after the first term (containing At as a factor) might easily be calculated then. After this it will be necessary to investigate wether it agrees or not for 42=' with the series of paper I; it is only in the first case that the latter series will be valid for #<{ R. For the sake of this investigation, however, and also in order to get an idea of the proportionality of the functions %, («) (vid. I, 7), we prefer to use the method based upon the theory of the integral equation of FREDHOLM. 2. We construct a function of x, satisfying in the interval (0, /) both the equation 4 d'y det and the conditions y" = y'"= 0 at the ends, and being continuous as well as its first three derivates everywhere in (0,/) with the only exception of a saltus of the third derivate at the point 5: d°y | +0 ke = (j) da |: =o TAN Ot YS Soe te ER bd A. (2) 1) Referred to in the sequel as “paper I”. 248 This function we call K(w,§, 4); it represents the deflexion of the beam, loaded by a load 1, which is concentrated at the point §. Putting 4 = — gf the function 1 zE 15 {sinh OQ (a—§) — sin 0 (x—§)} (the upper sign for «<6§, the lower for «2 §) will satisfy all conditions excepted those at the ends. Assuming 1 USS Se 40° \sinh @ (a—8) — sin 9 (a—§)} + Q +A cosh 9 (w«—}) + Bsinhole— tl) + Ceose(w—$l) + Dein ole — 3), we may determine A, B, C and D in such a way that K(w, &, 4) satisfies the conditions at the ends. This gives 1 — Acosh} ol + Bsinh } ol + C cos } ol —D sin } ol — i }sinh OS +-sin 0§}, Q 1 2 2 — Asinh} ol+ Beosh 4 el—C sin 4 ol —D cos } ol = 40’ fcosh 08+ cos QS}, — Acosh 4 el—B sinh } ol + C cos Hol + Dsin} ol = 1 ~ { sink @ (I—&) + sin 0 (/—8)}, 40 — Asinh } el—B cosh $ pl —C sin } gl 4 D cos } ol = Sap {cosh @ (J—§) + cos @ (I—S)}. Adding the first and the third of these equations and also the second and the fourth we get two equations containing only A and C. Subtracting the third from the first and the fourth from the second we get two equations containing only B and D. In this way we obtain 1 — Acosh} ol + C cos} el= Dn {sinh 4 ol cosh e(§—4 ol) + sin $ ol cos e(E—41)}, Q 1 — Asinh}el— Csint ol= i {cosh 4 ol cosh 9 (§—4 1) + cos } gl cos p (541) }, ] . Bsinh } ol — Dsin} ol = Te {cosh 4 ol sinh o(S—} l) + cos 4 ol sin 0 (E—$ D}, 1 Bosh } ol — Dain} Ql = re { sinh 4 ol sinh 9 (§—4 1) — sin } gl sin o(S—}))}, 249 From these equations A, B, C and D are easily solved; putting A, (e) = cosh } yl sin } ol + sinh 4 ol cos 4 ol, A, (9) = cosh 4 ol sin § ol — sinh } gl cos 4 ol, we get — 40° A, (9)} Acosho (etl) + C cos 9 (v—}$ l)} = = (cosh } ol cos ol + sinh } ol sin } el) cosh 9 (a —} 1) cosh 9 (S— + cosh 9 (x—t4 l) cos g (S—} /) + cos 9 (a—} L) cosh (5 —} 1) + (cosh 4 ol cos 4 ol —sinh $ ol sin 4 ol) cos v (w—} 1) cos 9 (E—4 J), — 40° A, (0)} Bsinh 0 (rtl) + Dsing (e—-$)}= = (cosh 4 ol cos $ pl —sinh } gl sin 4 ol) sinh 9 (x —} 1) sinh ol E — $1) + sinh 9 (c—3 l) sino (§—} ) + sin 0 (a—} lL) sinh gp (§—3 l) + (cosh } ol cos $ ol + sinh 4 ol sin } gl) sin 0 (a—} 1) sing (S—$ U). We now have calculated the function A (z,8,2); it appears to be a function with the denominator 407 A, (e) A, (©). The values of À equating to zero this denominator are the characteristic numbers of the problem; as A (a, &,A) is symmetrical with respect to « and & that numbers will be all real. From this it follows that the cor- responding values of @ have an argument that is a multiple of +; it is easily proved to be an even multiple so that the values of o wil be real or purely imaginary and the corresponding values of 4 negative or zero. For that purpose we first write 1—cosh olcos ol for 24, (0) A,(e) and then substitute in it ed =a@+478; equating the real part to zero we get cosh a cosh B cos a cos B 4+- sinh a sinh B sin a sin B == 1, which is not satisfied by B= + a +0, for substituting 8 = + a@ in it we get sinh? a — sin? a, which is impossible for a 4 0. Therefore the values of @ are real or purely imaginary and the characteristic numbers are negative, except one which is zero. If @ be a root of A, (e)—0, also zg will be a root (and con- sequently — e and — 10); the same is true with respect to the roots of A, (ge) =90. We now call the positive roots of the equation toh p = — tg p, in the order of their magnitude p,,p,,.... and the positive roots of the equation toh p = tg p, ordered in the same way q,,q,,... Then the characteristic numbers will be 2 pn\* Zn Gil i ) ff 2) os Il Pes) 250 3. We will also calculate the characteristic functions. If p represents one of the numbers p, and g one of the numbers qg, we have to calculate the following limits: 2p\* 2q\4 lim of K (x, §, A), lim \ — ( 2 | K (a, §, 2), lim je’ (7) 20 peer ty U e>2g/l l ay 1 To none of the limits the term = FS | sinh @ (a —&) — sin g(x —§)} Q ACS ZN contributes. For the first of the limits we find immediately lim o* K (x, §, 2) = ze 41) (§ — 4 4). 20 l ip To the second only the term A cosh y (we — 4 l) + Ccoso (ae — $2) contributes. First we have jel ces = i) 1 CE) —49° A, (eye — Leosh p cos p and the numerator of the fraction we have found for A coshe (a—t l) + Cos e (a—} l) changes for gp = *?/; into 5 E cosh 2 p G- :) (os poop + sinh psinp) cosh 2p G i) + cos 2»( | -1) a + cos 20( — :) From cosh p sin p + sinh p cos p=0 we have ie E cosh 20( | — 1)+ (cosh p cosp—sinh p sinp) cos 2p G- 1) | , 4 cosh p cosh p cos p — sinh p sin p = ——— cos p , cos p cosh p cos p + sinh p sin p = ; cosh p and consequently the numerator becomes x coshp x cos p Ë ) Nen 2 } h2p| ——3 2p| —— jou zl P :) ae cos of i i) = 5 cosh (| 1 ) tom (| 4 In this way we find 9 4 lim Je" -(7) | Hua, E,a)= o—>2p/l l 251 i cosh ‘ 2»(F :) cos (5 - 1) cosh 2»(7- = = = a l cosh p cos p cosh p cos p | rs tol ee isc) S a” io 3 EN | On nh S74 In the same way AD lim Je" = prol! v3 sinh 2g aa sin 2g LA Ni 29 Jen t sin 2q Sia 4 1 AK at Lars l iy) RE Ss: A= — l sinh q sin g sinh q sin q Putting i cosh 2 Dn € — :) cos 2p,, (G- i) (U) = —,7 2, (es) = = ’ Po (# Vl Pale) vl | cosh py r COS Pn x x 3 | sinh 2 (| = :) sin 2qn GC — i) | = — (¢4—} eK Ge) j= aa 9 Beem tO TM enk qn i sin Qn (SR) the functions @, (x), W, (w) mn = 0,1, 2...) will be the orthogonal / 8 and normal characteristic numbers; ‘iby: satisfy equation (2), 2 being replaced by the corresponding characteristic number. Now drawing graphs of the functions y= tgv, y= tghe and y= tgha in one figure, it is easily seen that p, is an angle in the 2n-'® quadrant, and gq, an angle in the (22 + 1)-*" quadrant. For no p, and gq, converge to the middlepoints of the intervals. From this it follows that cos p, and simp, converge to +42 and it is easily seen that the absolute value of ~, (2) and w, (7) remains less than a number which is independent from w and n. Now as Fie eee no NN no N the two series occurring in OB tw OW OL nn) À n=1 A == (7Pnji)* AA (77 m(é EN) n=1 4 = (CAI) will be uniformly convergent and the right hand side therefore will be equal to K (a, &, 4). NASI iY Proceedings Royal Acad. Amsterdam. Vol. XX VI 252 4. We now suppose y to be the required solution of (1), viz. that solution for which y" = y'" =O in the points «=0 and «=/ and which is continuous in (0,/) as well as its first three derivates ; as to y'” it may have a saltus in a finite number of points aj, which will be the case if q' (x) has in the points a; discontinuities for which g' (a; +0) and q(ai —0) exist. The points a; and the value € divide the interval (0,7) into a number of subintervals; in the interior of each of them we have d ’ 1 À ' " wl 2 EE [y"" K(e, &, 4) —y K' (w, &,4) + y' K" (a, 8,2) —y K" (a, §, a = ax = y'" K (w, &, a) — y K'" (@, &, a): Integrating the equation over the subintervals, adding the results and regarding that y" = y" = K" (a, §, 4) = K'" (#,§,4)=0 forz=0 and «—/ and that y,y',y",y", K,K', K", K"' are continuous every- where except A’” in & we find l — y (5) = fis" (x) K (w, 5,2) — y (@) K'" (a, 5, A)} de 0 Replacing y'" by q'—ay from (1) and &'" by —aK from (2) we get l y (§) = | K (, &, a) q (2) de 0 or interchanging rv and § and observing the symmetry of K (2, &, a) with respect to w and & l ole 4b K (a, &. 2) q'(8 a8. 0 If the beam is not loaded by q(x), but by N loads Q;, concen- trated in the points §;, we have N ye) = E UK 5D where Q';= Q;/EI. If the beam bears both the load q(x) and the loads Q; we have l N vk EDI OEH E OKE ED. EE 0 From (4) it follows that y is a meromorphic function of à with the poles 0, — (2?,/))* and — (?9,/)*. This is easily seen from sub- 253 stituting (3) in (4) and integrating term by term, which is permitted, the series (3) being uniformly convergent. Expanding y in a series of ascending powers of 2 (the first term will in general contain A) the expansion will generally be con- vergent for |A <(??1/)*; only if the term with the denominator A + (#?4)))* cancels, the expansion will be valid for larger values of 2. In case the Q;’s are zero this occurs if g(x) be orthogonal to g, (x). We thus see that if the expansion of paper 1 be exact and if not by chance { {a (x) p‚ (we) da = 0 0 it converges only if 4 ray a) gh ea beh ai, CO) From (4) we deduce a formula which will be of use further on. Supposing the beam to bear only a load p(x) pro unit of length and to be in equilibrium, we will have l | [eta = ferme =0 0 a or which is the same 1 i fe (2) po @ de = fp (2) ap, (@) dx = 0. 0 0 Now from (4), in which q' (x) is to be replaced by p(x)/HJ and in which Q'; =0, we have l y (2) = | Tea, EA Me ae. where K(x, &, 2) arises from K (a, §, 4) by omitting in (3) the term with the denominator 4. Putting 2=0 K (w, 8,2) changes into K(o, 8) = = Ge) 5 Peelen (5) n=1 (?Pn/,)* n=1 (4m 1,)° tees ee 0) and we get l ye) = Fy [Kop Oa Perea e549) 0 254 This represents the deflection of the beam under the conditions that the beam be in equilibrium and that the ground be absent; it is such that l l fr@a= PNY) - ET ve (C3) 0 0 since ‘K(x, §) is orthogonal with respect to v(x) and y,(x). By the conditions (8) the deflection is perfectly determined and (7) repre- sents it. 5. We shall now prove that the series deduced from (4) agrees for 2=k’ with the series of paper |. Representing the iterations of K(x, &) by K,(a, §), Kw, §).... we get for |a| < (/;)* K (a, §, 4) = K (« B) —1 K, (@, &) +2° K, (2,8 .-., l ! l [Kt §, Aa) q' (§) ds = [Ke 5) q' (8) dE —À fr, (zE) (E)dE+.--, 0 ° 0 as is proved in the theory of integral equations. From this it follows that (4) for |A| < (%1//)* takes the form ve) = ye) +9, (©) +9, (@) + ---s- - + & where l l 1 Le pe = = |. (a) | @, (8) 9 (8) dE + w, (w) f he (&) 9 (8) dB + 0 0 N N +H) = AH) +H) F Gv (8)| l Ms 1 N n= ap [KIO op, >, WK 8, 0 l k 0 255 k . el) = pr ij K (x, 8) yn © dE, 0 Each of the functions y,(2), except v,(w), satisties (8). We shall now prove the terms yv, 4, ¥,,--- to be the same as the corresponding quantities of I, 5, from which it will follow that the series Yo ty, +.-.-- agrees with the series of I, 4. Indeed in the first place y,(z) is a linear function of 2; the function /y,(x) represents - the linear load ax + 8, which is defined in I, 5 and is statically equivalent to the given load. For we have l N kfm (x) , (x) dz =o, BAD d5 + EQ, 6), 0 0 ai 1 N fn Ondern fwd + = WE, 0 0 or substituting in it the expressions found for the functions ¢, («) and 1p, (0) fis (a) jie fr dE + = Q: Senin = fea ja} > = DE which proves the proposition. Omitting from (9) the deflexion y,, the remaining terms represent the remaining deflexion. This becomes y, for £=O and so y, represents the deflexion which the beam, if not supported by the ground, gets under the influence of the load that remains after subtraction of «2+ 8 from the given load. As besides y, («) satisfies (8), it is identical with the quantity y, of I, 5. The reaction of the ground, arising from the deflexion y,, represents a load — fy, of the beam; by this load the beam, if not supported by the ground, would get a deflexion, which we may calculate from (7) viz. l k — gf Kende 0 256 This represents the deflexion y, (a); it is seen to be the same as the quantity y, of I,5. In the same way we continue and so we may prove that (9) agrees term by term with the series of paper I. 7. In case the expansion do not converge, it may happen that the method of graphical integration, communicated in paper I, remains still valid (vid I, 7); this depends on the approximate proportionality of the functions y, (x) for large values of n. We shall prove this now; more exactly: we shall prove ek) no Un (2) where u is independent from w. Now K,(x,§) is represented by the absolutely and uniformly convergent series Palen en Wm lize (Ss). m=1 he where the quantities 4,, represent the numbers (2i/))* and (2%/;)* in the order of their magnitude and the functions w,,(#) are the corresponding normal orthogonal functions. Putting l fm Gd > ROA an RE 0 we get the absolutely and uniformly convergent series ES =P, © Yn (x) =(— nt zn (n == 1 2, OE x) n= ° m Supposing / to be the smallest value of m for which P,, 4 0, we can write k'yn—1 À Eh ei Un (@) = = j = |p, Wh (a) AF (* : y = ( nal En Um (x). Ant m=1 Ah+m The series in ate right hand member of this equation has an absolute value which is less than the sum of the series 25 hi Py Wm (2) |, m=1 Antm a quantity which is independent from n. From this and from : 2 h n ie || == || ==0) n=> AH we get 257 Qn h lim ———— y,, («) = Ph, wp (x Bee ea yet! («) (7) In this way we find chan. Yn+i (£) n k Kyr k' l date! @) lim ( i = n—>o Yn (a) an ro ri An? mn dale) rr! which proves the proposition; we see that k' u a ae Now, if in drawing the successive deflexions y,,7,,¥;,.... it is found that y,41:y, is sufficiently independent from z, it will be permitted occasionally to consider — Yn Yn == HUF. ty—i+— k' es ie A to be the deflexion y. For we have DL A entra (2) Yn u SAE nn de 5 + x gesl m= À 1 an m 1 ——, at Ge =f Fi ze = == Wn = -(— ay" i S En = oR (— J m=h 4m + m m=h Je 1 ien Ah = on m\z ra — kN! 1 2 == mn Ee) —— | i mah Am == k m=h Am An =F ke Am (Ah Se k') and as EN Wm (a ;) = Dy Sn ien hm ar K we get — — Nt 1 hp nn Yl —— 55 Pm Wm (& ca RIO 7 il m=h+ ( ) (5 Ne ) Jan + k Am (An SF k') \ Since m=h gives zero. If k' Angi, the series has zero as a limit for n — oo, which is easily seen by writing it in the form = Ni (0 À n—1 1 À Yn -Y=— ( ) = ‘Pe Wm (a) ( zt) | seh h Jr m=hA--1 Devs Jin ae k An On HE k 258 since the absolute values of the series occurring in the right hand member is less than the sum of the convergent series Ee | Bm Wm (a) | m=h+1 Am =F k' It thus appears that we may consider yn to be the required deflexion 4, supposed n be large enough and & <2. If g is, after h, the first value of m such that Pm #0, the condition Z'<. must been satisfied if we wish to replace y by yp for large values of n. Chemistry. — “The Phenomenon of Electrical Supertension.’ IL. *) By Prof. A. Smrrs. (Communicated by Prof. P. Zeeman.) (Communicated at the meeting of February 24, 1923.) In my book ‘Die Theorie der Allotropie’’*), and also in the preceding communications I have treated the electrical supertension only very briefly. Therefore I will discuss this important phenomenon somewhat more at length here. We imagine the case that a palladium or platinum electrode is made cathode. For the explanation of the phenomenon that will now 2H 46 Pa Fig. 1. appear, we shall make use of the /#, X-diagram, in which the ex- perimental electric potential of the electrodes is plotted as function ) These Proc. Vol. XXI No. 3, p. 375 (1918); Vol. XXI, No. 8, p. 1106 (1919). ®) JOHANN AMBROSIUS BARTH, Leipzig. 1921. English edition Lonamans, GREEN and Co. London 1922. French edition GaAuTHIER VILLARS. Paris. 1928. 260 of the concentration; on the assumption that the pressure (1 atm.), temperature, and total ion-concentration (metal ions + hydrogen ions) are constant. In the foregoing figure 1 hydrogen is taken for one electrode, and palladium for the other, but instead of the latter platinum might, of course, have been chosen just as well. Line bh indicates the potentials of the series of electrolytes that can coexist with different palladium phases. These phases of the palladium are different, because palladium dissolves the hydrogen in quantities which increase with the hydrogen-ion concentration of the electrolyte. Line bf indicates the potentials of the different palladium phases containing hydrogen’), which coexist with the different electrolytes. In our Z,X-figure the potential of the metal-phase can be read on the H-axis, but it is clear that on this axis also the potential of the electrolyte can be read, when we reverse the sign. The line ag represents the potentials of the different electrolytes coexisting with the gaseous hydrogen phases. These hydrogen phases consist of pure hydrogen, and lie, therefore, on the hydrogen axis. Accordingly the portion ak of the hydrogen axis gives the potentials of the hydrogen phases coexisting with the different electrolytes. The point of intersection c of the lines bh and ag represents the electrolyte which can coexist at the same time with the palladium phase (e) and with the hydrogen phase (d), so that it also shows the potential of this three-phase equilibrium. The situation of this point of intersection follows from the solubility products of hydrogen and palladium : *) Lp, = Gy =AV* == Era (GO LO mt: At the three-phase equilibrium (Or, = (9) ra from which follows: (Pa) Bs ay Ze lii(Hs)sisaput == 4, then) (2a) — 102x142. From this it is seen that the point e lies very much on one side, and that when a palladium electrode was immersed in a 1-N sulphuric 102 x —14.2 1) This line indicates the gross hydrogen concentrations, and gives, therefore, no information about the state in which the hydrogen is. 2) Compare with regard to the smallness of these products the remarks in “The Theory of Allotropy” in the chapter: “Small concentrations” p. 172. 261 acid solution, and the palladium was and remained in inner equilibrium, this metal would dissolve a little, till the palladium concentration of 10? '4? was reached, while a corresponding in- appreciable quantity of hydrogen would have been generated. In this it is assumed that both platinum and hydrogen continue to be in inner equilibrium, for the value used for Ly, agrees with the value for hydrogen in inner equilibrium, and we shall for the moment assume the value used for Lp, also to agree with the condition of inner equilibrium of Pd. Pd is, however, an inert metal, so that the solubility product of this metal will in reality have decreased through the slight attack, and the dissolving will have already stopped, before the palladium ion concentration 10? —15-2 has been reached *). For the sake of simplicity we shall, however, assume here that no disturbance of the Pd takes place, and that the three-phase equilibrium is established, in which the Pd-phase e coexists with the electrolyte c and with the hydrogen phase d at a pressure of one atmosphere. When now the Pd-electrode is made cathode, or in other words, when electrons are added to the Pd, hydrogen and palladium ions in the ratio of 1 : 10°*—'42 or practically only hydrogen ions will be separated at this electrode. It will now depend on the velocity with which the inner equilibrium 2H + 26¢2 He, sets in, if the hydrogen formed will coexist in a state of internal equilibrium or in a state of formation. In this condition the solubi- lityproduct of the hydrogen is greater, and the point that now denotes the coexisting hydrogen phase, will lie on a potential curve that lies at more negative values, and is represented by ag in fig. 2. We must, however, not forget that this line could only be realised when the state of formation of the hydrogen discussed just now could coexist unchanged in electro-motive equilibrium with a series of solutions. This is, however, not the case; only one point can be realised on this curve, and this is the point indicating the liquid layer that coexists with the hydrogen phase d', which is in a state of formation, and with the palladium phase e’. The heterogeneous equilibrium between the metal boundary layer and the hydrogen boundary layer, just as that with the liquid boundary layer, having been immediately established, the palladium boundary layer will also contain too many hydrogen ions and electrons, which means that also the hydrogen dissolved in this metal boundary layer, will be in a state of formation. 1) The potential + 0.82 V., from which the solubility product Lpa = 10?* —822 has been calculated, is most probably already a potential of a disturbed state of the metal palladium. 262 We may, of course, also start from the Pd, and say that only in the Pd-electrode to which electrons are added, and in which hydrogen ions dissolve, hydrogen is formed in a state of formation, and that afterwards gaseous hydrogen occurs in a state of formation, but this only implies a difference so far as the first moments are concerned, for when once electrolytic generation of hydrogen has set in, this oH 3E Fl Fig. 2. will occur in a state of formation at the same time in the gas phase and in the metal phase. It should be pointed out here that when we have a homogeneous phase, as the solid solution of hydrogen in palladium, the electrical potential of these two components with respeet to the coexisting electrolyte must be the same. This applies also to the solid solutions lying on the line be, but in the solid solution lying on this line there is equilibrium between hydrogen molecules, hydrogen ions, and electrons, whereas this is not the case in the Pd-boundary layer which coexists with hydrogen in a state of formation. This is, therefore, the reason that the Pd-phase e' coexisting with the hydrogen phase a', does not lie on the prolongation of the line be. The hydrogen dissolved in the Pd-phase e' is in the state of formation, and consequently this phase is richer in hydrogen ions and electrons than when the hydrogen is in inner equilibrium. The 263 potential of the dissolved hydrogen in e' is more strongly negative, and the same must, therefore, hold for the Pd. lt is now, however, the question in what way the potential of the palladium has under- gone this change. It is clear that the Pd must have become richer in Pd-ions and electrons. We have already seen that this phase has become richer in electrons through addition of hydrogen in a state of formation, so that only the question is still to be answered how the concentration of the Pd-ions can have been increased. This must have taken place through the reaction 2Hs + Pds — Pds + 2Hs in which, therefore, hydrogen ions have ceded their charge to Pd-atoms. We, therefore, come to the conclusion that the palladium boundary layer, which coexists with hydrogen in a state of formation, will possess too many hydrogen ions, palladinm ions and electrons, or in other words, that it will contain both hydrogen and palladium in a state of formation. If palladium could coexist in the same state of formation with a 1.N. solution of a palladium salt, the electric potential would, of course, possess a more strongly negative value than corresponds to point 6 in fig. 2. This more strongly negative potential is indicated by 0’. And when, therefore, the same state of formation of Pd could continue to exist also in contact with the whole series of solutions, the line b'e would indicate the solid solutions which can coexist with the electrolytes lying on the line 6'c’. The new three-phase equilibrium that is found when Pd is made cathode at a definite density of current, and in which hydrogen escapes in a state of formation, is denoted by the points d'c'e’. The line a'c'g' rising very little throughout the greater part of the concentration region, it is clear that the value of the negative potential in this new three-phase equilibrium would be equally great when the point c’ lay on the prolongation of the line be, and the point e on the prolongation of the line be, but as we demonstrated above, the points c’ and € belong to other lines than those that are mentioned here. It follows from these considerations that in the ease of electrolytic generation of hydrogen the state of formation of the hydrogen in the coexisting hydrogen and palladium phases are very closely related. This makes it clear that the cathode metal can exert influence on the degree of super-tension. The state of formation is a state of non-equilibrium, and the differ- ent cathode metals will, to a different degree, accelerate the con- version of this state of non-equilibrium in the direction of the inner 264 equilibrium. This is the reason why the so-called super-tension of hydrogen is different, when different metal cathodes are used. It is self-evident that when the state of formation of the hydrogen does not vanish too quickly, the hydrogen must possess an abnormally high conductivity for electricity immediately after the escape. This phenomenon was, indeed, found long ago‘), but it was tried to explain it in another way; it is, however, probable that this phe- nomenon is for the greater part to be attributed to the state of formation. The activity of the hydrogen dissolved in the metal phase, is in perfect harmony with the considerations given here. As regards the temperory variations of the super-tension, they will have to be explained by the slow change in constitution of the coexisting phases. The heterogeneous equilibrium between the boundary layers is established with great velocity, but the composition of the phases changes slowly, and this must be the reason that the three-phase equilibrium metal-electrolyte-hydrogen changes slowly. In conclusion I will still point out that analogous considerations, of course, apply to oxygen and other non-metals. As is discussed in “The Theory of Allotropy” p. 160 et seq, the extension of this theory to non-metals, necessitated the assumption that the atoms of all elements can split off and receive electrons.*) The difference between the solubilities of the positive and the negative ions in elements with pronounced metal- resp. metalloid character, is so great that for the explanation of the electro-motive behaviour as a rule only the positive or the negative ions need be taken into account. But as was also already stated the supposition mentioned must very certainly be used when the positive charges of non-metals with regard to electrolytes, and likewise the small electric conducti- vity of non-metals in electrically neutral condition, is to be explained. Further the said supposition is also required to make clear the formation of compounds between metals. ’) When we now return to the non-metals and choose oxygen as example, we have to consider the two following reactions: ONZ 20" + 2v, 9 and 0, + 27,0220" As v, = 2, the latter reaction may be written: On 40 = 20", 1) Becker. Jahrb. der Radioaktivität. 9, 52 (1912). 4) Theory of Allotropy p. 160. 265 The latter equation is sufficient to explain the electric super- tension of the oxygen. It was stated *) that in the case of anodic polarisation of an unattackable electrode or an inert metal the sepa- rated oxygen must relatively contain too few electrons and too few negative oxygen ions, so that oxygen in a state of formation or in other words oxygen in super-tension would have to possess an abnormally small electric conductivitly immediately after its formation, at least when no other phenomena neutralise this effect. When we have an inert metal, i.e. a metal that can be easily disturbed, and we make this anode, polarisation will take place. If the disturbance of the metal goes so far that oxygen is separated, then, the metal boundary layer being poor in ions and electrons, also the coexisting oxygen phase will be abnormally poor in elec- trons. Besides the other substances coexisting in the liquid, the metal boundary layer will also contain oxygen dissolved, and it is evident that the state of this oxygen, dissolved in the metal, will depend on the state of the oxygen in the coexisting oxygen layer. Laboratory for General and Inorganic Chemistry of the University. Amsterdam, Februari 1923. 1) Theory of Allotropy p. 164. Chemistry. — “The Influence of Intensive Drying on Internal Conversion”. 1. By Prof. A. Smrrs. (Communicated by Prof. P. ZrrMAN). (Communicated at the meeting of March 24, 1923). In December 1921 a communication was published in the 100th volume of the Z. f. physik. Chemie under the same title as is given above. In manuscript this communication was at first more extensive, for it also contained a possible explanation of the great influence found by Baker of intensive drying on the chemical reactivity of gases, and besides a discussion of the sa-ammoniae problem’). The reason why for the present | withheld this part was as follows. [ was at the time still in doubt whether in intensive drying it should be assumed that a fixation or a shifting of the inner equilibrium takes place. The results of Baker’s researches *) published then spoke greatly in favour of a shifting, but at first this assumption seemed open to objections, because it is then necessary to assume that the slightest trace of moisture can give rise to a great displacement of the inner equilibrium. Afterwards, when Baker had published*) a new series of experi- ments, it seemed nevertheless the most probable conclusion that here a shifting of the inner equilibrium takes place, which from a thermodynamic standpoint means that very much work is required to withdraw the last traces of water from a system. Accordingly I showed in the English and in the French edition of the Theory of Allotropy, in which I devoted a chapter to Bakrr’s experiments, that in my opinion intensive drying gives rise to a displacement of the internal equilibrium. Since then my own investi- gation, which L carried out with some of my pupils, has confirmed this supposition. A The explanation of the influence of intensive drying on reactivity, which I left unpublished so far, is exceedingly simple, for we 1) Also the influence of intensive drying on the properties of Sal ammoniac, becomes explicable, when this substance is assumed to contain two kinds of molecules, one of which is dissociable, and the other is not. 3) Trans. Chem. Soc. 51, 2339 (1903). 8) Trans. Chem. Soc. 121, 568 (1922). 267 have only to apply the theory of allotropy, i.e. we have to assume that every phase of these substances contains at least two different kinds of molecules, which are of course in inner equili- brium in the case of unary behaviour, to which we add the supo- sition that at least one of these kinds of molecules is chemically inactive. This is very well possible, since the mechanism of the transformation into another type of molecule will be an intirely different one from that of chemical action with other substances. To represent the case as simply as possible we can then assume that there are only two different kinds of molecules, one of which is active, the other inactive. When for ammonia we denote them by NH,a and NH,?, we have in each phase in the case of unary behaviour, the following inner equilibrium: NH, 2 NH,g HL My supposition was this that on intensive drving this inner equilibrium is shifted towards the inactive side, and in this case, completely, so that in the ammonia remains that only contains the inactive kind of molecules. I will just mention here that I emphatically pointed out before that the expression “different kinds of molecules” should be taken in its widest sense. It should comprise not only the isomer and polymer molecules, but also the electrically charged dissociation products, ions -++ electrons, and if stands to reason that in many cases the difference between the different kinds of molecules lies in a difference in the atomic structure. It is particularly the more recent views of atomic structure that have brought to light that between the different atoms very subtle differences are possible, which are e.g. in connection with a change of the quanta values of the valency-electron-paths, and this leads to kinds of molecules with more subtle differences than those which are assumed to exist between the ordinary isomers. The fact, however, remains that also these different kinds of molecules may be ranged under this category when the sense in which the idea “‘isomery”’ is taken, is very wide. During my investigation there appeared a publication by Bary and Duncan’), in which they communicate among other things that the rapidity at which gaseous ammonia, withdrawn from an iron cylindre with liquid ammonia, is decomposed by a platinum spiral heated at a definite temperature, is dependent on the velocity of evaporation of the liquid ammonia. On rapid evaporation ammonia gas 1) J. Chem. Soc. 121 en 122, 1008 (1922). 18 Proceedings Royal Acad. Amsterdam. Vol. X XVI. 268 was obtained of much smaller velocity of decomposition than on slow evaporation. BaLy and Duncan expressed the opinion that this difference is probably caused by this, that on rapid evaporation there is formed a gas phase rich in the kind of molecules that preponderate in the liquid phase, whereas on slow evaporation there has been a possi- bility for the conversion of this kind of molecules into another, of which the gas phase chiefly consists in ordinary circumstances. One kind of molecules, which chiefly occurs in liquid ammonia, would then be the inactive kind, and the other kind of molecules, of which the ordinary ammonia gas chiefly consists, the active one. They further pointed out that the existence of inactive and active kinds of molecules probably accounts for the chemical inactivity of the gas dried by Baker. So we see that in this paper Bary and Duncan already express the supposition at which I had also arrived, though 1 did not publish it because my investigation was not yet sufficiently advanced. Baty- Duncan’s results, however, are not very convincing, as BRISCOE ') observed, because they can also be explained in another way. He says: “It is known, that ordinary commercial ammonia, dried over lime, contains about | percent of water’), and that rapid, irreversible destillation, such as may occur by free discharge of gas from a cylinder of liquid, is a very effective means of separating the constituents even of a constant boiling mixture’), so that the gas thus obtained may well be considerably drier than that in real equilibrium with the cylinder liquid. Baty has found that the addition of water vapour to ordinary ammonia increases its reactivity, drying certainly decreases its reac- tivity, and so the greater dryness of the “inactive” form would appear to be capable of explaining the whole of the observations, including the “recovery” of the gas in cylinders on standing (by acquisition of the equillibrium content of water vapour) identity of slowly released cylinder gas with laboratory preparations dried by lime, recovery of inactive gas in the experimental tube, when the wire is heated at 200° (release of absorbed water from the wire or walls) and the increase in reactivity of “inactive” increase of temperature of the wire’. These remarks of Brrscor’s, which are very true in my opinion, deprive Baty’s published experiments for the present of all their ammonia with 1) Annual Reports of the Progress of Chemistry vol. 19 1922, p. 37. 2) Briscoe refers here to Wurre T. 121, 1688 (1922), but this must be a mistake for Wurrtre has not found this. 3) Mutuken J. Amer. Chem. Soc. 44, 2389 (1922). 269 cogency as a proof of the existence of an active and an inactive kind of molecules in ammonia. I wanted to test my supposition in another way and took, accord- ingly, an entirely different course. After having convinced myself that the pure P,O, which I prepared by Baker’s method, had really the same properties as that of Baker’), I began with some of my pupils an investigation of the influence of intensive drying on the point of transition, the melting-point, the vapour tension of the solid and liquid state, and the electrical resistance of the liquid phase of a great number of substances, and among them those substances, of which Baker found that the chemical activity disappeared by intensive drying, occupy a very particular place on account of the great importance of this phenomenon. Of this latter group first of all NH,, HCl, CO, and O, were taken in hand. In a following communication our results and the particulars of the experiments will be discussed. Laboratory of General and Inorg. Chemistry. of the University. Amsterdam, March 20% 1923. ') | became acquainted with this method through a private communication by Prof BAKER before it was published, which saved me a great deal of trouble and time. [ will avail myself of this apportunity to express my cordial thanks to Prof. Baker for his kindness. Se Chemistry. — “The System Sulphur Trivaide” 1. By Prof. A. Smits. (Communicated by Prof. P. Zeeman). (Communicated at the meeting of March 24, 1923). For some years the examination of sulphur trioxide has been on my programme, because I surmised that this substance would yield suitable material to test the theory of allotropy. As, however, other investigations had to go first, this examination could not be taken in hand until a short time ago. In the meantime Brertnoup') Le Branc with Rürrr*) published each a treatise on vapour tensions and melting-points of this sub- stance. Though these two papers will be discussed more at length later on, I will make here already a few remarks, and more parti- cularly in connection with the latter publication. The results published there prove with the greatest clearness that SO, is really a substance which not only can be used as a test of the above-mentioned theory, but which is so eminently fit for it that in this respect it is unequalled by any other. For the results obtained show that both the liquid and the solid phases of the SO, can behave as phases of more than one component, which without any doubt must be attributed to the complexity of this phase. This complexity is owing to the occurrence of different kinds of molecules in the same phase, which molecular-species are in internal equilibrium with each other in the case of unary behaviour. I emphatically pointed out on an earlier occasion that the term “different kinds of molecules” should be taken in as wide a sense as possible*). By them we should understand not only the isomer and the polymer molecules, but also the electrically charged disso- ciation products, ions + electrons, and it is self-evident, that in many cases the difference between molecular-species mentioned here lies in a difference between the atoms. It is in particular the more recent views on the atomic structure, that bring to light, that there are very subtle differences possible between the different atoms, which e.g. are in connection with a change of the quanta-values of the valency-electron-paths, and this leads to kinds of molecules with 1) Helvetica Chem. Acta 5, 513 (1922). 4) Ber. d. Sachs. Akad. v. Wiss. Leipzig 74, 106 (1922). 8) The theory of Allotropy p. 2. 271 more subtle differences than those, which are assumed between the ordinary isomers. Nevertheless when the idea of “isomery” is taken in a wider sense, also these different kinds of molecules may be classed under this category. We cannot say as yet what kinds of molecules occur in the diffe- rent phases of the pure SO,. The molecular size in the vapour phase agrees about with SO,, but it is very well possible that there occur isomer molecules of SO, at the same time, and it is also possible that there is also a polymer kind of molecules present in small concentration. The kinds of molecules that occur in the gas phase, will also be present in the liquid phase, hence according to the theory of allotropy also in the solid phase, though in a different proportion, when the idea molecular of conception is taken in a wide sense *). Up to now we have been completely in the dark as far as the internal state of solid SO, is concerned. The measurements of the surface tension can, indeed, extend our knowledge concerning the complexity of the liquid phase somewhat, but we still lack means to decide whether a unary solid phase is a mixed crystal in internal equilibrium or not. Contrary to Lr Branc’s opinion it is not possible to conclude to the molecular size of a substance in the solid state in a solvent from the found mol. weight of this substance. ?) With a view to supplementing our methods of research with those that make use of RénTGEN rays in the hope of learning something more in the end about the more delicate inner state of equili- brium in the solid phase, I instituted a department for the RÖNTGEN investigation of the solid substance in my laboratory some years ago. Though the way which I had decided to follow, leads to the typical allotropic substances, it seemed desirable first to examine some simple. but nevertheless very interesting, substances, in which results were to be expected which might be of great importance for getting a clearer insight into the nature of the chemical bond. Accordingly Messrs J. M. Bisvowr and A. Karssen bave studied Li, LiH, NaClO,, NaBrO,, in which it was possible to determine the structure and the binding of the particles on definite suppo- sitions.*) Now the investigation of Hgl, has been taken in hand, though we know that by means of this investigation we shall not be able to decide whether the solid phase in a mixed crystal. 1) Cf. “The Theory of Allotropy” p. 220. 3) Loc. cit. 8) Partly published in These Proc. 28, 644, 1365 (1921); 25, 27 (1922); Zeit- sehr. f. Physik. 14, 291 (1923). 272 The investigation by means of RÖNTGEN rays is by no means so powerful as it is often supposed to be. Thanks to the researches of Baknuis RoozeBoom and his pupils we have got to understand the bebaviour of the mixed erystal phases in binary systems to a great extent, but what does the RONTGEN investigation teach us about these mixed crystals ? Let us e.g. take the simple system KCI,KBr, a system of which we know that the solid components are homogeneously mixable in all proportions, and let us now suppose an arbitrary mixed crystal from this continuous series to be given to a RénTGEN analyst. If this investigator is under the impression that he has to do with a solid phase of a simple substance, he will interpret the intensities found in the usual way, and will find them in very good agreement with the image of the system that was supposed by him to be mono- componential. For the intensities can only serve as a test of an already assumed model, and as there are still so many factors that are not sufficiently accurately known in the interpretation of these intensities, and because besides there are nearly always some para- meters that have to be chosen so as to suit, a good agreement can be found, even when the supposition is erroneous. Partly in consequence of these circumstances, partly in conse- quence of the impossibility to give already now a sharp image of the complexity, as this has also been assumed by me for the solid phase, the ROnTGEN investigation, in its present stage of development, cannot serve as yet for a further elaboration of the theory of allotropy, and it will, no doubt, be still some years before the RöNrceN research will be able to throw new light on the inner equilibria, which have already been found in the solid state. All the same we have started the RöNrGeN study of the interesting Hgl,, because we wished in any case to ascertain if any changes occur in the ROnTGeN spectrum of these compounds in the temperature interval of 130—255°, and, if so, what changes, hoping that some conclusions may be drawn from this with some probability. I have thought it necessary to publish the above discussion, because a great many mistaken ideas still prevail in this region. When we now return to Le Branc's investigation, I will remark that he found, among other things, that on cooling of the supercooled liquid below 13.9° solidification suddenly sets in,‘ on which the vapour tension appeared to have risen, also after the temporary rise of temperature had disappeared. Hence at the same temperature the solid phase formed presented a higher pressure than the super- cooled liquid, and Le Branc thought this phenomenon comparable 273 with the action of oxygen on phosphorus, in which ozone and a phosphoro-oxygen compound was formed. This, statement shows very clearly the insuperable difficulty with which one is confronted, when with phenomena which so clearly point to the complex character of the phases, one yet continues to occupy the old standpoint. I will not treat the phenomena found in the examination of SO, more at length here, but leave the discussion of them to the following communication. Amsterdam, March 1923. Laboratory of General and Inorganic Chemistry of the University. Geology. -— “Geological data derived from the region of the “Bird's head” of New-Guinea’. By Prof. L. Rurren. (Communicated at the meeting of March 24, 1923). The great northwestern Peninsula of New-Guinea is one of the least known parts of the Indian Archipelago. In recent times some data concerning it have been published by R. D. M. VerBeeK in his “Molukken Verslag’’’), and C. E. A. Wicnmann, when journeying from the east coast to Horna, discovered a folded coal-bearing for- mation”) which proved to be of tertiary age *). In the last few years (between 1917 and 1921), however, explo- rations were made on a large scale in Northern New-Guinea and also in the “Birds head” for oil and coal, by the officers of the Mining Department in the Dutch East Indies. The results of these explorations have not been published as yet*), but some years ago I received from the Director of the Mining Department in the Dutch East-Indies a rather large collection of limestones and marls for examination. The study of this collection has been finished, but there would be little sense in expatiating on it here, a fortiori as a description will probably be published elsewhere. I] may be of interest though, to summarize the obtained results. Although we are not quite sure that all the rocks we examined, are of tertiary age, this may yet be assumed for the great majority. Now, when observing on the subjoined sketch-map the localities of ‘“Bird’s head” from which the examined rocks are derived, we realize at once that tertiary deposits have a wide distrbution in the north-west part of New-Guinea. However, eocene rocks seem to be scarce among the tertiary deposits, which is quite in keeping with what we know about the other parts of New-Guinea. They were found only in two regions: in the first place between the island of Rumberpon and Horna, where, in two localities, Nummulites- Alveolina limestone and Alveolina-Lacazina limestone have been 1) Jaarboek Mijnwezen Ned. Indié 1908. Wetensch. Gedeelte. 2) Nova Guinea. IV. 1917. 3) Nova Guinea. VI. 2. 1914. 4) [.C.0.-Commissie, The history and present state of scientific research in the Dutch East Indies. Geology. p. 28. 1923. 275 collected, as well as oligomiocene limestones; while Lacazina-lime- stones have been found near the Campong Horna; in the second Warmands. Www BES NW N-CGuinea. a Eoceen o Oud Neogeen. MU Jong Neogeen. NW Jndifforende Gesteenten, maart lertrarr. a JMlarune Ârkose. m Marmer « Oude. Schuler un lertrarr Eoceen = Eocene. Oud Neogeen = Older Neogene. Jong Neogeen j . = Younger Neogene. Indifferente Gesteenten, meest tertiair = Indifferent Rocks, mostly tertiary. Marine Arkose = Marine Arcose. Marmer = Marble. Oude Schist-materiaal in Tertiair © = Old Schist-material in Tertiary. place in the northwestern part of the “Bird's head”, where Laca- zina-limestones have been collected, at one locality. From this it is evident that eocene is only sparingly distributed; moreover it should be observed that the rocks of the two localities, where Lacazina alone is found, cannot on that account be referred to the eocene with absolute certainty, however probable this may be. From the region between Rumberpon (Amberpon) and Horna rocks have been described by me formerly that pointed to the boundary strata between eogene and neogene ‘). On the contrary limestones of littoral facies from the older neogene have been found in a large number of localities, characterized by the occurrence of Lepidocyclina, Miogypsina and Cyeloelypeus. Similar limestones from the region between Rumberpon and Horna and from the Andai-river near Menokwari, have been previously described. They now appear to occur to the west of Rumberpon in a broad zone, running north-south, and to extend farther south 1) Nova Guinea. VI. 2. 1914, 276 than Andai, while they can be recognized in a zone running all along the north coast of “the Bird's head” as far as the island of Batanta. I] will be seen at a glance that we have to do here with a comparativily narrow zone of older-neogene, which follows the east coast and the north coast of the “Bird’s head”. It may be that older-neogene still occurs also in the more western and southern region of “Bird's head”, but it is remarkable that among the numerous rocks from those regions that were examined by me, there was not a single one that could positively be referred to the older neogene. We shall see lower down that this is partly due to the facies of the discovered rocks being indifferent, to our having to do either with non-fossiliferous rocks or with rocks that have been deposited in a deeper sea, in which the fossils, so characteristic of the littoral older neogene, cannot be expected to occur. But beyond these also rocks occur repeatedly in the southern part of the “Bird's head’, that are of littoral facies, in which e.g. Lithothamnium, Operculina and Amphistegina, the companions of Lepidocyclina in the older neogene etc, occur, but in which the Foraminifera, which are characteristic of the older neogene, are lacking. In such cases we no doubt have to do with younger neogene which indeed is often borne out by the habitus of the rocks. As an instance we point to the basin of the Aer Beraur and of the Aer Klasaman, in which a series of rocks occur that are referable to the younger neogene. Another region of probably young-neogene rocks, partly with true littoral habitus, is situated North of lake Amaru. Between lake Amaru and the Aer Beraur a number of rocks have been found: globigerina marls, fine grained lime sandstones and the like, which are completely indif- ferent, so that nothing can be said about their age. The same applies to some rocks from the region south of lake Amaru. A long list of rock samples, collected in a west-east zone far north of lake Amaru, are undoubtedly referable to the neogene, but their fossils and their facies are not typical enough to say whether they belong to the older or to the younger neogene. In some rocks, however, doubtful Lepidocyclina were recognized; the others have been classed under the ‘indifferent rocks’. Lastly among the rocks from the basin of the Aer Sebjar there are some littoral limestones, in which no “older” forms are to be found, so that here also we have probably to do with younger neogene. On the other hand, a number of very fine grained lime sandstones and globigerina limes, collected east of Muturi-river have to be classed under the ‘indifferent rocks’. They may be of older-neogene age, because in the adjacent region towards the east (west of Rumberpon) a few transition rocks were 277 found among true littoral Lepidoeyelina-limes and Globigerina-limes. Lastly presumably young-neogene rocks are to be found to the North and West of Menokwari. Here Globigerina marls and loose limesands, occur, which indeed do not include typical fossils, but which on account of their quite young habitus are most likely to be reckoned to the younger neogene. This in fact agrees with the circumstance that some limestones in this region are of littoral facies but do not contain Lepidocyclina, Cyclocly peus or Miogy psina. Before this a description was published of limestones from the island of Manaswari, near Menakwari, that were considered to be younger- neogene *). Between the localities of old-neogene limes south of Menokwari and those west of Rumberpon are situated the high Arfak Moun- tains, which according to VerBewk *) and WicHMANN °) are composed of granular eruptive rocks, schists and slates. From the region of the Arfak mountains I received three rocks most likely tertiary and built up of detritus from the Arfak Mountains. They are coarse-grained arcoses of marine origin, which together with Corals also contain a very few Globigerina. The minerals represented here are much quartz, orthoclase, perthite and less plagioclase and biotite: apparently we have to do here with the detritus of acid granites. Coarse-grained detritus of old rocks occurs also frequently in the northern part of “the Bird’s head” in the rocks of tertiary age — notably in the old-neogene rocks. This goes to show that below, and perhaps also at the surface, there must evist a mountain range of older rocks. The localities marked on the map by an o are those where in the limestones transported fragments of quartzite and phyllite oecur. A rock from the basin of the Aer Sebjar contained grains of perthite and orthoclase, which remind us of the detritus rocks of the Arfak mountains. The future reports of the Mining Department will undoubtedly contain interesting information on these ‘‘older rocks” in the‘ Bird’s head’. 1) Nova Guinea. VI. 2. p. 29. 42. *) Nova Guinea IV. p. 97. 3) Tijdschr. Kon. Ned. Aardr. Gen. (2). 21. 1904. Mathematics. — “A theorem concerning power-series in an infinite number of variables, with an application to Dirrcnuer’s *) series” By H. D. KroosrerMaN. (Communicated by Prof. J. C. Kiuyver.) (Communicated at the meeting of March 24, 1923). $ 1. An important relation between the theory of DiricHLer’s series and the theory of power-series in an infinite number of variables (for abbreviation we shall write: power-series in an i. n. of v.) has been discovered by H. Bour’). Let 5 2 An 5 AE) Elek os. EO EN ot ern oe (U n=1 N° . . 4 1 1 be an ordinary Dinicuer’s series. Puts, = —, dige ee Mn 1 gs 3 3s 1 ? ; = ne … (where p,, is the m-th prime-number, and let » = pe pi says m where pn, Pno»--+ Pn, Are the different primes which divide 7. Then the series (1) can formally be written as a power-series in an i.n. of v., thus: n r 0 INE Ganon otame cad) 25 Gy GE OS os o == A= ny Pa ar c+ DB fete + TE Cagtata+ DE Cae, Wa tae, +... aijn: a,8—1,2,... ,8,/7—1,2,... a

8, in terms of (preferably as simple as possible) analytic properties of the function represented by (1). Let B be the abscissa of absolute convergence of (1), and D the lower limit of all numbers a, such that /(s) is regular and bounded for 6 >«. The absolute- convergence-problem will be solved, if the difference B— D is known. Bonr proves that B= D for any Diricuiet’s series that can be formally represented in one of the following forms: 1) A more detailed proof of the theorem will be published elsewhere. 2) Göttinger Nachrichten, 1913. 279 al os II m=1 zl (pl): or al AO s —2 = ; m=l l=1 (pl, )s or, what comes to the same thing, for any DiricHLer’s series for which the connected power-series in an i.n. of v. has one of the forms Blan, em JEG (Gp) to vee oren Bt) or a IPN Goo bos ng NE 10 SE OUCH) vg eer (3) where Q, (#,) (2 = 1, 2,....) is a power-series in «2, without a con- stant term. The equality 4 — D is a consequence of the theorem: < Gai td.) ). then b. it is absolutely convergent for |z,|< OG, where @ is an If: a. The series is bounded *) for |x, arbitrary positive number in the interval 0O<4< 145). Now, if we consider the power-series (2) and (3), we see that the variables z, occur to some extent separated from one another. This led Boar to the conjecture, that the equality b= D would hold for any Diricuier’s series, for which the variables in the con- nected power-series in an i.n. of v. do not occur too much mixed up. Confirmation of this conjecture is the purpose of the present com- 1) According to Hitpert (Wesen und Ziele einer Analysis der unendlich vielen unabhängigen Variabeln, Palermo Rendiconti, vol. 27, p. 67) a power-series in an i. n. of v. is defined to be bounded if: 1°. The power-series Pi (2%, %,...%m) (Abschnitte), that may be obtained from the power-series inan i.n. of v. by putting am 1 = %m+2 =...=0, are, for all values of m, absolutely convergent in the region |zj\< Gj, |a2| < Go, |am| < Gn. 20, There exists a number K, independent of m, such that, for every m, the inequality | Pm (ei, oem) SK holds in the region |2,| < Gi, |xol < Go,.... |am| < Gm. *) It is well known, that b follows from a for-any power-series in a finite number of variables. Originally Hinperr had assumed this also, as being self-evident, for an i. n. of v. But Bonr showed that this could not be true by constructing an example to the contrary. 280 munication. In fact it can be proved that B= D holds for any Diricaiet’s series that can formally be written in the form f (s) =p De m mi Il (pl ye where p is an arbitrary (non-constant) ') integral function. As a consequence of the relation, already mentioned above several times, the following theorem concerning power-series in an i. n. of v. is equivalent to this statement. Theorem. If p is an integral function and Q,(«,) (n=1,2,...) a formal’) power-series in 2,, without a constant term, and if the power-series in an i. n.of v. P(w,,2,,...-&m,-+-)J=(Q,(#,) + Q,(@) H.H Qn(am) + ....) is bounded for |z| < G,(n=1, 2,....), then it is absolutely convergent for |2,,) << OG,, if0<0<1. In the following pages an outline of the proof of this theorem will be given. §2. For the sake of simplicity we take G, = G, =....=G,= SiGe 1 butinaiG <1. Because the given power-series in an i.n. of v. is bounded, there exists a number A, not depending on m, such that (Qi) + Qs) ew 41 Qa (an) SE 2). The first part of the proof of the theorem of § 1 discusses the power-series Q,, (a) (n= 1,2,....). It is proved that it follows from (4) that all these power-series possess a certain region of conver- gence. Further research shows that two cases may occur: 1*. The functions Q, (#,) are all regular for |2,/ 1, all regular in their resp. circles |2,|< 1. For any function f(e), regular for jz <1, and for which /(0)=0, we now define a number 7 as follows: r is the radius of the largest circle, of which all points represent numbers assumed by f(z) in the circle KES 1. Let rv, (n =1, 2,...) be the corresponding quantity on for Q, («‚). Then we first prove, that the series > 7, converges. ul For this purpose we consider (4), valid for all sets of values of Hy, %,,.-.. Xm, Satisfying [onl < Gar ANA ten) vand ar fortzor2, for all satisfying |,|< 1. Because p(y) is an integral function, it is possible to choose a number £ so large, that the maximum value of (y)|, on the circle \yl—= L, is > K. Now suppose that, for some value of m, r,+r,+....+7, > L. Then the maximum value of lp (y)| on the cirele |yl=r, Ar, +... rm would be > K. Now if we let the variables z, (u — 1, 2,....m) describe their resp. cireles a, < 1, then Q, (w,) assumes all values satisfying |Q, (#,)| =7n. Hence y= Q, (@) + Q, (v,) +... + Qn (wm) assumes all values satisfying jy) =r, +r, +... + rn Therefore it would be possible to find a set of values w',,2',,.....2', such that PSs («',) iQ) + --- + Qn (en) = (1, + SS ae) ea where (7, +7, -+....—+7,)e represents that point of the circle y= Fr, +... Hr where |g (y)| assumes its maximum value. Therefore we should have | p (Q, («',) ofr Q, (z') in Pd Qn ('n)) | => K, contradictory to (4). Therefore the supposition r,+7,+...+7, >L can not be true. Since ZL is independent of m, this proves the a convergence of > rr n= We now apply the following theorem of Bour *): Let the function f(z) = = a, 2" (f (0) = 0) be regular for |z| <1. nl Let M(o) be the maximum value of | f()| on the circle |z|=o0 (O k Mo), where £ is a number which depends on g only (X is 1) Not yet published. 282 therefore the same for all functions satisfying the assumptions of the theorem). Hence, if M,„(e) is the maximum value of |Q, (w‚)| on the circle en "9 (1,2). wenhaven 1, Dik M, (v). Since we have proved that st r, is convergent, it now follows that the series © M,(e) n=1 n=1 converges also (for g <1). From this fact the theorem of $1 can be easily deduced. For let Q, (an) = > i. a (n=1,2,...). Then p=1 M,(e) (n= 1, 2, (n) | < 1 es 5 bn 2, Jes ). If o=6G (where @ is the constant of § 1), then it follows 1+0 that, if O0< 9 <1, (we take for example e = + | Hence the series oo ao = = | alr)| OP, n=1p=1 P is also convergent. This proves a fortiori the convergence of the given power-series in an i. n. of v. for w‚ <0=0G(n=1,2..,). It cannot be denied that the assumption, that ~ is an integral funetion, is somewhat unaesthetic. However, the author has not succeeded in dealing with the more general problem, where p is an arbitrary (purely formal) power-series. In any case the method described does not give the required result in the more general case. Copenhagen, November 1922. Chemistry. — ‘“/n-, mono- and divariant equilibria.” XXII. By Prof. F. A. H. SCHREINEMAKERS. (Communicated at the meeting of March 24, 1923). Equilibria of n components in n +1 phases, when the quantity of one of the components approaches to zero. The injluence of a new substance on an invariant equilibrium. (Continuation). We write the isovolumetrical reaction of an equilibrium #(«=0): Fla Fo OD. HO SOR) SO Savy=o. . WW and the isentropical reaction : eee te ee OREN (WEL OSR (VA >10.. (2) Consequently in reaction (1) are formed on addition of heat and in reaction (2) on increase of volume those phases, which have a negative reaction-coefficient. We have, therefore: = (ax) y = — a, &, —A, 2, — en = (ue) = — , 2, — py, 2, — When we subtract both reaction-equations (1) and (2) from one another, after having multiplied the first one with u, and the second one with 2, then we find the reaction: (#4, — 4,4) EH dn A) P+. >. =O. … (3) wherein the change of entropy is u, 2 (A H)y and the change of volume is —A, > (u Vr). As (3) represents the reaction, which may occur in the equilibrium (F,)= FE, + F,+..., we have dP\ ssw, 2 (AA)y i Ely Nae Alas (fe VOTERS ee 2) Pal LTP NO TENS Herein 5 indicates the direction of curve (#,) in the invariant C 1 point. In the same way we find: ne dl DEN (LV) en NUTR A, = (UV) As we are able to deduce from (1) and (2) also the direction of temperature and pressure of the different monovariant curves, the P,T-diagram is, therefore, quantitatively defined. Now we add to the equilibrium a new substance X, which occurs 19 Proceedings Royal Acad. Amsterdam. Vol. XXVI. 284 in the phases PF, F,... with the concentrations x,2,... In accor- dance with. (13) and (15 ) (XXII) we now have: > (AH — WV (dT) = 4,2, FA, +... = (As) = (uV aT Je …(dP): = — uti at. =E(ue)H. . (8) V IP iv) EG (5) —«u,(55) — 4 « (©) RT dP), dP), A fe (5) dm & ESD) RT IT RENT It follows from (8) and (9): dT ro {Re dT OAD dT (%),= > (wa) (oP), eli a from (7) and (10) it follows: dP fay Zk GME Ede dP - are. Ly aH (5). = (An); ee) = (Ax)y @) and from (7) and (8): = (u yer (F By, + Bs +... (13) SS (H)y dT ANN 4-Ajyay t+... From (7) we see that we are able to express (d7’), with the aid of the isovolumetrical reaction (1); it is apparent from (9) that, however, we cannot express (d7’), with the aid of the isentropical reaction (2) only, but that we must know also the directions of the monovariant curves (Ff) (fF)... of the equilibrium # («= 0). It appears from (8) that we are able to express (d/), with the aid of the isentropical reaction (2); we see, however, from (10) that we cannot define (dP), with the aid of the isovolumetrical reaction only but that we must know for this also again the directions of the curves (Pf) (F,)... The direction of the monovariant curve # can be defined, as is apparent from (13), with the aid of the isovolumetrical and isen- tropical reaction; it follows from (11) and (12) that it can also be defined with the aid of the directions of the curves (Ff) (F,).... and one of both reactions. When we add a new substance X which occurs in one of the phases only, f.i. in F, than we must put in (7)—(13) 2,=0 #,—0... As now & (Ax)y=— 4, x,, it follows from (12): dP _(dP 14 ==), ne EN 285 which follows of course immediately from (11). Consequently curve FE and (F,) have the same tangent in the invariant point. It follows from (7) and (8) that they go also in the same direction of tempe- rature and pressure, starting from this point. When viz. 2, is positive, then it follows from reaction (1) that curve (F) goes towards higher temperatures, starting from the invariant point. As it follows, however, from (7) that (d7), is then positive also, con- sequently curve ZE goes also towards higher 7. When 4, is negative, then the curves (#,) and F go both towards lower 7. It follows from (2) and (8) that both curves have also the same direction of pressure. In accordance with previous papers (Communication XXII) we, therefore, find: when the new substance occurs in the phase F, only, then curve # coincides with curve (4). When the new substance occurs in the phases #, and F, only, then (12) passes into: dP jk dP VEN er I= ir teer 1005) AD) pee Ka Na) a. RA aT) ; = x A wherein K=—. Hence it follows: Zi (PD — 2s dP aN ae in (a wap lar), Gr) «00 : 4 HEN dP For fixing the ideas we assume that | —, | is greater than | —, |. aE dT), Now we distinguish two cases. 1. 2, and 2, have the same sign. The following is apparent from iP (15) and (16). When A changes from O tot oo then =) increases dd fr (5 to om ae discontinuous. 2. 4, and 2, have opposite sign. When K changes from 0 to oo, then dl dP . : . ie ( | without becoming maximum, minimum or 2 dP ; ee : ( =| decreases without becoming maximum or minimum from C x BPN. } a till — oo, then it proceeds discontinuously towards + oo and C 1 } dP afterwards it decreases to | — |. dT), When À, and 4, are both positive, then, in accordance with reaction (1) both curves (#,) and (F,) go towards higher tempera- {Sj 286 tures starting from the invariant point; when 2, and 2, are both negative, then both curves go towards lower 7’; when A, and 2, have opposite sign, then both curves go, starting from the invariant point in Opposite direction of temperature. It follows from all this that the tangent to curve F is situated within the angle, which is formed by the curves (Ff) and (F,). [Of course we mean that angle wich is smaller than 180°]. As in the case of A =O (consequently «,—0) curve EF coincides with (/,) and in the case of K—o (consequently #, == 0) curve F coincides with (/’,) consequently the property follows, which we have deduced already in the previous communication also, viz: Curve £ is situated between the curves (F,) and (/) or in other words: in the region (H, F). Yet also we find, however: Curve HE is situated nearer curve (/,) in proportion as the con- centration of the new substance in the phase /’, is larger with respect to that in /,; curve U is situated nearer to curve (Ff) in proportion as the concentration of the new substance in the phase F, is greater with respect to that in F’. When the new substance occurs only in the phases F, F, and F,, then we find, in accordance with previous papers that curve # is situated in the region (£, #, F,). When one of the curves, fi. (/’,) is between the other two (/’,) and (F,) then curve MW is situated also between (/’,) and (/,). When, however, none of the three curves is situated between the other two, then curve # may go, starting from the invariant point in every arbitrary direction. Now we consider the binary equilibrium E(@@=0)=F+L1,4+1,46 we represent the composition, the entropy and the volume of F by y 1—y H and V Ley Ay and 7, L, „ 4. 1—y, H, and V, G ,, y, 1—y, A, and V, When we add a new substance Y, then we call its concentration in those phases xa, a, and «, In order to deduce the isovolumetrical and isentropical reaction we take two arbitrary reactions; for this we choose: 287 eine ee aE i) (AMR. 50 a 12) (LDL, AF HIG AVE Vi. jee eae (is) Herein is: AH=(1+a)H,—H—aH, A: H'= H+ bH,—(14 6)4d, AV =(1 + a) V, — V—al, A vVi=V4 6bV,—(1 +5) V, In (17) and (18) a and 6 may be as well positive as negative. It follows from (17) and (18) for the isovolumetrical reaction: (AVLAV’) F —(1+a) AV'L, + [aAV'— (148) AV] L,+0AV.G=0 Tia EY AA AUING AUT Naa aa a (19) and for the isentropical reaction : — (AH+AH') F+(1+a)AH'. L,— [aA H'—(1 +4548] L,— bd. G=0 0 LEENA Ee GVM ope (20) We now add to this equilibrium H («= 0) a new substance X, which occurs in the two liquids LZ, and ZL, only. With the aid of (19) and (20) it then follows from (7) and (8): M. (dT), = — (la) AV'. #, + [aA V' — (1b) AV] a, . (21) M .(dP), = — (1+a) AH’, «, + |aQH'— (1408) AA) a, . (22) wherein : Mis (EEA VEE ASTER It follows from (21) and (22): when we add to the equilibrium E(e=0) a new substance which occurs only in the two liquids, then the temperature as well as the pressure may be increased or decreased. We now shall assume that the four phases are situated with respect to one another, as on the line Y Z in fig. 1. Then we have: VN Ph > Ys. It follows from (17) and (18) for the determination of a and 6: ytay,=—(1+a)y, (1 + 6)y, =y + by, pee je 23) Yas Ya Vs so that a and 6 are positive. Further we assume that Hand L, and also that L, and L, are not situated very close to one another, so that a is neither very small nor very large. When F and L, and also L, and G are not situated very close to one another, then also b is not very small and not very large. As now AV’ is positive and very large with respect to AV, M is positive. Further we may distinguish the following cases. AH>0 DOVE ahH'- (1+)AH>0 AH>0 AVZ0 GA (th BA Fee AH>0 AVA ahA'—(1+s)AH<0 a) b) ¢) In each of the three cases, ficient of w, negative and of (dT), Z 0 when We > 288 ATi) wei | (24) aAVv'—(14+d)AV>0 A50 Am Vassr0 | (25) aQ vV'i—(1+b5)AV>0 IN 151 << MV) LV (26) ak WEE HA mentioned above, is in (21) the coef- xv, positive; consequently we have: (hay A We EA (27) As AV’ is very large with respect to AV it follows from this approximately with the aid of (23): wv N= (4T)z 20 when -2. 2 (28) vm yyy In the case, mentioned sub 6 in (22) the coefficients of a, and wz, are negative, so that (dP), is also negative; consequently the pressure is lowered. In order to examine more in detail the sign of (dP), we write for (22) MNP) = aya wherein: EGET l+a x, | N (29) a eae EREA a AH! H N=aÂAH'!—(l+4+b)AAH When we put herein the value of a from (23) then we may write for (29): AH! =) (GP). — |= Lr ln a —1 Uae 1 A = AH y U vy ( ) a When we consider the three cases a, 6 and c mentioned above, then we may write for (30): x, Hae a) anas tte. (31) %, YY b) (iP), =—| Zr. (32) vy Vn c) um. rate. (33) x, yn" 289 wherein 1, AK, 1+ K and 1—K are positive. In each of the three formula’s L and K have different values. In order to apply the above we take the figs. 1 and 2, wherein XY is a side of the components-triangle XYZ. The points FL, L, and G represent the four phases of the invariant binary equilibrium E(j«=0)=F+L,+ L,+ G. When we add a new substance X then the ternary equilibrium H= F+ L, + L, + G arises. The liquids ZL, and ZL, then proceed along the curves L,q,7, and L,q,7,; as the new substance is not volatile, G follows a part of the line XZ. When we add only a little of the new substance, then the liquids are represented by the points g, and q, in the immediate pf AT>o a) dpèo 6) ap 0 as is also indicated in the figure. It follows from (31)—(33): in case a is (dP), 20 ” ” De (dP), cv <0 ” ” ” (dP), <0 as is also indicated in fig. 1. In fig. 2 is: a, < vy OF apa Y—4Ys Yrs wv, Vn It follows from (28): (d7’), <0. From (31)—(38) it follows: (35) 290 in case a is (dP), <0 ed AE dn ” ” c ” (dP), 2 < 0 as is indicated also in fig. 2. In fig. 1 the pressure may as well increase as decrease in the case a; it is apparent from (31) that (dP), shall be positieve for large values of w,:w,. As L, (and consequently also q,) is the liquid which contains the most of the solid substance # we shall call L, (and consequently also q,) the concentrated and ZL, the diluted solution. We, therefore, find the following: when the threephases-triangle solid-liquid-liquid turns its concen- trated solution towards the side of the components-triangle (fig. 1) then the temperature increases and the pressure generally decreases ; only when the concentration of the new substance in the diluted liquid (consequently z,) is much larger than in the concentrated liquid consequently «,), then in the case a the pressure may incre- ase also. In fig. 2 in the case c the pressure may as: well increase as decrease; it appears from (33) that (dP), shall be positive for small values of 2,:2,. Consequently we find the following: when the threephases-triangle solid-liquid-liquid turns its concen- trated solution away from the side of the components-triangle (fig. 2) then the temperature decreases and generally the pressure also. Only when the concentration of the new substance is much larger in the concentrated solution (w,) than in the diluted solution (,), then in the case c the pressure may also increase. We may obtain the previous results also by using the P, 7-dia- gram of the equilibrium H(«=0). We may deduce this in the following way. ; The direction of temperature of the equilibrium (G) = F + L, + L, is defined by the sign of the coefficient of the phase Gin the isovo- lumetrical reaction (19). As 64V may be as well positive as negative, curve (G) may go, starting from the invariant point 7, as well towards higher as towards lower temperatures. The direction of pressure of the equilibrium (G) is defined by the sign of the coefficient of G in the isentropical reaction (20). As —b4H is negative in each of the cases a, 6 and ec, curve (G) proceeds, starting from the invariant point 4, towards higher pressures, As further, in accordance with (17): 291 TENE aL H ar) AV and AV is very small, curve (G) is ascending, starting from point 2 fast vertically. In figs 3 and 4 this curve is drawn vertically up- wards; the double arrow indicates that starting from 7, it may run either towards the right or to the left. , As the coefficient —(l + a)4V’ of the phase /, is negative in each of the cases a, 6 ande, in accordance with (19) curve (L,) = F + L, 4 G is going starting from point 7 towards lower pressures (figs 3 and 4). In the cases a and 6 the coefticient (1 + a) 4 H’ of phase L, is positive in equation (20) so that curve (L,) is going, starting from 2, towards lower pressures (fig. 3). In the case c is(1 + a) A H' negative and curve (L,) is going, therefore, starting from 7, towards higher pressures (tig. 4). This is in accordance also with that which follows from (18) viz. dP fe! A H' Ce) ny Consequently we have defined the direction of the curves (G) and (Z,); fig. 3 is true for the cases a and hb, fig. 4 for the case c. With the aid of (19) and (20) we should be able to determine also the position of the curves (/’) and (Z,) and then we could prove that the four curves are situated with respect to one another as in figs 3 and +. [Compare f. i. Communication XIII]. As we know, however, the situation of the curves (G) and (L,) we can find the position: of curves (F) and(Z,) much more easily by using the rule for the position of the four monovariant curves of a binary equili- brium [Compare Communication [| fig. 2]. In accordance with this rule we must meet, when we go, starting (Z) > & 292 from curve (G) in the direction of the hands of a clock towards curve (Z,) firstly curve (F) and afterwards curve (Z,). As further (G) and (#) must form a bundle and their prolongations must be situated between (£,) and (L,) and as the angle between two suc- ceeding curves, must be always smaller than 180°, hence follows for the curves (#’) and (Z,) a situation as in the figures 3 and 4. In fig. 3 curve (Z,) is drawn horizontally; starting from 2 it may run either upwards or downwards; this has been indicated by the double little arrow. When it goes upwards, starting from 27, then its prolongation must yet always be situated above curve (Z,). It appears from the coefficient of the phase Z, in reaction (20) that curve (Z,) must go in case a starting from 2 upwards and in case bh, starting from 7 downwards. This has also been indicated in fig. 3. As we know the P, 7-diagram of the equilibrium H(#=0) we can easily determine the situation of curve Z. It follows viz. from our general considerations in the beginning of this communication, that curve / must be situated between the curves (L,) and (Z,). For «,:2,=0 curve Z coincides with (/.,) for #,:x,=0 with curve (L,). When w,:«, changes from oo towards 0 than curve U moves in the direction of the hands of a clock from (Z,) towards (Z,). Firstly we now take the case a, so that we must imagine in fig. 3 curve (L,) to be drawn upwards starting from 7. When we do change now w,:2, from ao to 0, then it follows from the diffe- rent positions which curve E may obtain, that the following cases may occur: ((T);>0 and (dP),>0 (dT),>0 and (dP),<0 (T);<0 and (dP),<0 In case 6 we must image in fig. 3 curve (Z,) to be drawn down- wards starting from 7. When we do change x,:x, from oo to 0, then it follows from the situation of curve ME: (aly, ande (EP) 0 (AT), <0 and (dP),<0 In case c fig. 4 is true. When wv, :w, changes again from oo to 0, then it follows from the position of curve L: (dT), >0 and (dP),<0 (AT), <0 and (dP),<0 (AT), <0 and (dP),>0 We see that those deductions are in accordance with the previous ones and with the figs 1 and 2. 293 Our previous considerations are all valid in the supposition that the four phases /'L,L, and G are situated with respect to one another as is indicated in the figs 1—4. When the four phases are situated otherwise with respect to one another, the reader my deduce all in similar way. We now shall assume that the new substance is volatile, so that it occurs in the phases 4,4, and G with the concentrations Ti Edle We find with the aid of (7) and (19): M (dT), =— (la) AV'e, + [AAV, —(14B)AV]e, HbAV.e, (36) and with the aid of (8) and (20): M (AP), = — (la) AH'z, + [aAH' —(14-b)AH]e, + bAH-e, (87) wherein M=(AH.AV'—AH'.AV):RT so that the direction of temperature and pressure of curve F are defined by (36) and (37). As AV is very small in comparison with AV’ we may neglect in (36) the terms with OV as long as x, is not very large, then it follows with approximation : << (AT), 20 voor SZ... GB Cn ann Only for very great values of w, in comparison with x, and a, the term b64V..2, in (36) will be of great importance and will be approximately RNN Ie In (37) AH is not small in comparison with AH’ and the term bAH.z, will assert its influence already with values of 2, which are not too small. Consequently, in general the influence of the new substance on (aT), and (dP), will be larger in proportion as the new substance is more volatile and it will assert its influence sooner on (dP), than on (dT). RAE Vi Tees! (falar = ( ) (39) We may also deduce anything about the position of curve ZE with the aid of the general considerations at the beginning of this communication. Hence it follows viz that curve /# must be situated either between the curves (L,) and (L,) or between (L,) and (G) or between (Z,) and (G). As in the figs 3 and 4 the prolongation of each of those curves is situated between both the other curves, curve Z may go, therefore, starting from point 7 in every direction. 294 Consequently the temperature may as well increase as decrease, and the pressure may increase or decrease as well at rising as at falling temperature, dependent on the position of curve £. It follows from (12): when w, is extremely small with respect to w, and x, then curve / is situated between (G) and (L,); when wv, is extremely small with respect to 2, and w, then curve His situated between (G) and (L,); when w, is extremely small with respect to v, and rv, then curve FE is situated between (L,) and (L,); when w, is extremely large with respect to w, and a, then curve E is situated in the vicinity of L); when a, is extremely large with respect to 2, and z, then curve 4 is situated in the vicinity of (L,); when w, is extremely large with respect to «, and w, then curve les = Eis situated in the vicinity of (G). In each of those cases we can see at once from the figs 3 and + which signs (dT), and (dP), may have. When fi. x, is very small with respect to x, and x, then curve FE is situated between (L,) and (G); when now fig. 4 is valid then the pressure shall, therefore, always increase and the temperature shall decrease. In the special case only, when w, is still also extremely large with respect to w, and when at the same time AV > 0 [then curve (CG) proceeds, starting from 7, a little to the left | then the temperature may fall a little. When we add a new substance which is not volatile, but which forms mixed crystals with the solid substance #, then we have in figs. 3 and 4 the curves (#) (Z,) and (L,). It appears from the position of those curves with respect to one another that the previous considerations are also valid in this case. When we wish to calculate (dT), then, as is apparent from (19) we have to substitute in (36) b4V x, by(AV+AV") a. When we neglect again the terms with AV then we find: M (dT), = [a —(1+a) 2, Hao, A V' or: (40) (T= Ela Os H en In the figs 5 and 6 YZ represents a side of the components- triangle, FL, L, and G the four phases of the invariant binary equilibrium Z(r 0). When we add a new substance then the ternary equilibrium H= F+ L, + L, + G arises. The solid sub- 295 stance F’ and the liquids ZL, and L, then proceed along the curves Fqr, L,q,7, and L,q,7,. When we add only little of the new substance, then the 3 phases are represented by the points q q, and gq, Which we must imagine in the immediate vicinity of the side YZ. When we put ¢= 2 (y,—y,) —(y—y,)", + (y—y,)", and when we consider x and y as running coordinates, then ¢= 0 represents the equation of the straight line which goes in fig. 5 and 6 through g, and g, When the point g is situated on the line q,q, then ¢=0; the sign of (dT), is then determined by the terms which have been neglected in (40). When q is situated at the right side of the line q,g, (viz. when we go from g, towards q,) as in fig. 5, then ¢>>0; when q is situated at the left side of the line q,q,, as in fig. 6, then ¢< 0. Hence it follows, therefore, that in fig. 5 the temperature increases and in fig. 6 the temperature decreases, as is also indicated in both figures. Fig. 5. Fig. 6. Consequently we find the following: when we add to the invariant binary equilibrium # (v= 0) = =F+L,+ L, + G a substance which is not volatile and which forms mixed crystals with the solid substance #, then the temperature rises, when the threephases-triangle solid-liquid liquid turns its concentrated liquid towards the side of the com- ponents-triangle (fig. 5) the temperature falls when the threephases-triangle turns its con- centrated solution away from this side (fig. 6). Comparing fig. 1 with fig. 5 and fig. 2 with fig. 6, the reader will see that for the change of temperature the same rules are true, independent of the fact whether the new substance forms mixed crystals with F or not. 296 Finally we could still treat the general case that the new sub- stance forms not only mixed crystals with / but that it is volatile also. It follows from figs. 3 and 4, in connection with the theories discussed in the beginning of this communication that curve / can go in all directions, starting from point 7. In order to define (¢d7’), we must still include in (86) the term (AV-+AV"),; then we get again (40) approximately unless a, is extremely large. Consequently in this case also the figs. 5 and 6 remain valid, unless the threephases-triangle gq, q, becomes very narrow and the concentration of the new substance in the vapour is extremely large. (To be continued). Leiden, /norg. Chem. Lab. Anatomy. — “The Development of the Shoulder-blade in Man”. By O. H. Duxstra. (Communicated by Prof. L. Bork). (Communicated at the meeting of March 24, 1923). Unlike the development of the clavicula that of the scapula has received comparatively little attention. The textbooks of anatomy (CUNNINGHAM, GEGENBAUER, RAUBER— Korpsen, Merker, Porrter—Cuarpy, Tersrur) contain only general notions such as the information that the ossification of the shoulder-blade begins in the vicinity of the collum scapulae at the end of the second or in the beginning of the third month. Poirier and CHARPY speak of an incipient ossification between the 40% and 50‘ day. BARDELEBEN reports a periostal ossification (such as occurs with the bones of the cranial vault) beside and under the spina scapulae at the end of the 10% week. Bryce alone enters into more details in Quains’s Elements of Anatomy. According to his description the rudiment of the shoulder-blade is in the 6t® week entirely cartilaginous, proc. acromialis and proc. coracoïdeus are present, but the spina scapulae is wanting. (Nevertheless Bryce reproduces the diagram of Lewis’), in which a spina is really indicated). In the 8" week ossification begins with a centre near the collum scapulae, developing into a triangular plate, at whose upper margin the spina appears in the 3'¢ month as a low ridge. At birth coracoid and acromion, margo vertebralis and the margin of the spina are still made up of cartilage. This description by Bryce agrees fairly well with the one we find in Broman’s textbook of Embryology and in that of Keren and Marr, in which BarpreN deals with this subject. Broman, like Brycn, states that no spina is to be found at the cartila- ginous scapula. Nonetheless he reproduces the figure of Lewis, in which there is indeed a spina. KoOLLMANN, SCHENCK, Minot, Parker do not speak of the first development of the shoulder-blade and only dwell on stadia of advanced ossification. In Herrwie’s Entwickelungsgeschichte Braus and also Hertwie himself report a separate centre of ossification in the spina scapulae; according to the latter the spina in the neonatus still consists of cartilage sometimes; according to Körriker (quoted by Bape, Arch. f. mikr. Anat. LV) this is even always the case. 1) Am. Journ. Anat. Vol. 1. 1901—’02. 298 The most detailed report concerning the development of the shoulder- blade is that by Bryce and Broman. From their figures it is evident that they derive their data from Lewis, who published in the American Journal of Anatomy (Vol. 1 1901—’02) a minute description of the development of the arm in man. Broadly stated his data agree with those of Bryce, mentioned above. They differ, however, as to the spina scapulae. According to Lewis the spina probably takes origin in the upper margin of the scapula. This margo superior thickens and then splits into a medial and a lateral lip. The medial lip is the future margo superior, the lateral one is the first beginning of the spina scapulae. Haen *) deseribes a shoulder-blade of an embryo 17 mm. in length. The spina scapulae is absent, the proc. coracoideus is large, the proc. acromialis small. The latter statement cannot be reconciled with Lewis’s communication, which, on the contrary, speaks of a relatively large proc. acromialis. This review of the literature would not be complete without mentioning the interesting study by RurHerrorD*) who entered into many details of the development of the shoulder-blade. Like Luwis he constructed wax models of the skeleton of the shoulder-girdle, and La. found that the spina scapulae originates in very early ossi- fication of derivates of cartilage cells, situated between M. supra- and infraspinatus. From this review it is clear that our knowledge of the modus of development of the shoulder-blade in man is still limited. The shape in the initial stages of development is described differently. Contlieting views are held as to the genesis of the spina and from the contents of this paper it will be seen that these are not the only points of controversy. With a view to trace the development of the shoulder-blade in man, I constructed wax models of various stages of development. Fig. 1 represents the wax model of the shoulder-blade of the youngest embryo, 16 mm. in length. The scapula is drawn from the lateral side and from above. The reconstruction shows: 1°. that the shoulder-blade lies in a sagittal plane, so that the lower half is in contact with the three upper ribs. Processus acro- mialis and clavicula are not in contact as yet. 2°. that the processus coracoideus is large; the processus acro- mialis is relatively small. The joint-cavity rests chiefly on the processus coracoideus. j 1) Arch. f. Anat. u. Entwickel. Gesch. 1900. 3) Journal of Anatomy and Physiology 1914. 299 3°. There is no indication of a spina scapulae. The margo superior is neither thickened nor split into two labia. Fig. 1. Fig. 2. 4°. The margo superior is straight, so there is no incisura scapulae. 5°. For the rest the shape of the scapula fairly well agrees with that of an adult shoulder-blade. In reconstructing the scapulae of two monkey embryos (viz. Macacus cynomolgus 17 mm. in length, and Semnopithecus maurus) it became evident that, also in these primates, the embryonic shoulder-blade already in its first beginning resembles that of the adult. Here also a spina was absent. 6°. Close beneath the angulus superior we observe a well-defined fovea where a foramen is found in older stages of development. To this we shall revert when discussing the following stage. This stage is illustrated in fig. 2. It concerns the shonlder-blade of an embryo, 25 mm. in length. Also in this stage any indication of a spina scapulae or of a thickening of the margo superior is lacking. Nevertheless when compared with the first stage some modifications can be recognized. 1*. The shoulder-blade does not lie any more in a sagittal plane, but makes an angle with it, as is also the case with the adult. The joint-cavity lies at the level of the first rib. Acromion and clavicula have joined. 20 Proceedings Royal Acad. Amsterdam. Vol. XXVI. 300 2°. The processus coracoideus las comparatively decreased, the processus acromialis, on the other hand, has increased. It appears, then, that the processus coracoideus, which is phylogenetically the oldest part, is most strongly developed in the youngest stage, where- as the processus acromialis, which is phylogenetically younger, comes more to the fore in the older stages. The joint-cavity now lies for the greater part on the planum scapulae. 3°. The margo vertebralis consists of a shorter upper portion and a longer lower portion. They are at an obtuse angle to each other. 4°. The portion of the scapula from which afterwards the fossa supraspinata develops, makes an angle with the future subspinal portion. This deviation of the upper part, which also occurs in the adult shoulder-blade (since fossa supra- and infraspinata do not lie in one and the same plane), had not yet taken place in the 16 mm. embryo. 5°. In the cranial part of tbe shoulder blade a foramen oceurs under the angulus superior, which extends at the costal plane of the scapula as a groove along the margo superior in the direction of the joint-cavity. In fig. 3 we give a cross-section of this foramen, which is filled with connective tissue. The existence of this foramen is no doubt surprising; yet it was not entirely unknown, as already RurnerrorD has described it (1. ¢.). However, according to this author it proceeds in a groove, which reaches as far as the margo vertebralis. Now, in all the serial sections in whieh I also met with a groove as well as with the foramen, it proceeded along the margo superior in the direction of the joint-cavity. RurnerrorD explains this foramen as follows. He considers the part of the scapula, cranial to the foramen (resp. groove), as a separate piece of cartilage, which he terms praescapula, and which, according to his account, is connected by a strand of mesenchyma tissne with the sternal half of the clavicula. In this way he believes an inner shoulder-girdle to have developed, while he supposes the acromion-clavicula to build up the outer girdle. He adduces various arguments to prove this; however, they are weak. In my judgment the hypothesis is of no value, because a connection of the so-called praescapula with the sternal balf of the clavicula does not occur. At all events in my preparations I never found a cell-strand like the one described by RuTHErForD. This foramen is not present in all cases. Its development also differs with various individuals, as shown by the following data. I could establish its presence either as a true foramen, or as a deep groove in human embryos of the length of 16, 17.5, 18, 19.6, 21, 22, 25 (see fig. 3), 26, 27, 56, and 90 mm. On the other hand I did not 301 recognize it in embryos of 12, 18, 18, 24, 26, 40, 120 mm. From this it follows that it is not infrequently absent. In some embryos the portion of the planum scapulae cranial to the foramen, i.e. RoTHERFORD’s praescapula, made an angle with the rest of the planum, a fact that lends support to Ruraerrorb’s view, viz that it is really a separate piece Fig. 3. Homo 25 mm. transverse. Sc = Scapula; Acr = Processus acromialis. of cartilage. The foramen which, in young embryos, is situated rather closely to the margo superior, as observable in fig. 3, migrates in older embryos towards the margo vertebralis. Consequently Rurur- FoRD’s praescapula is relatively enlarged. Now it is an interesting fact that this foramen does not occur in any other mammal, neither in reptiles, nor in amphibians. At least 1 never detected any. The following embryos I have examined for the occurrence of this foramen. * Semnopithecus maurus 20 mm. (C. R.) Macacus cynomolgus 17 mm. (C. R.) Cercopithecus 2 stages. Sus scrofa N.T. (Keibel) 83—85, N.T. 88, N.T. 88, N.T. 91, 24 mm. (C. R.) 26 mm. (C. R.) In the last two embryos two foramina were recognized in the fossa infraspinata. It is not quite impossible that these foramina are analoga of the foramen in the human shoulder-blade. Bos taurus 21 mm. (C. R.) Ovis aries 19.5, 20.5, 21.5, 22.5, 23, 23.5, 26, 27, 29, 35, 45 mm. (C. R.) 20% 302 Canis familiaris 12, 12, 22, st mm. (C. R.) Sciurus vulgaris 12, 30 mm. (C. R.) Mus decumanus 11.5, 12, 13, Dn 13.2, 14.5, 16, 18, 20, 22 mm. (C. KR) Lepus cuniculus 17, 20 mm. (C. R.) Spermophillus citillus 15 mm. (C. R.) Rousettus amplexicaudatus 7.5, 10.5, 11, 11, 11.5, 12, 12, 14.5, ily, 1d ikke) Tame (Ole) Talpa europea 8.5, 9, 9, 10, 12, 13, 16.5, 20 mm. (C. R). Perameles obesula 50 mm. (C. R.) Perameles spec. 38 mm. (C. R.) Dasyurus viverrinus 19.6, 33, 36, 40, 53, 63 mm. (C. R.) Sminthopsis erassicaudatus 13, 25 mm. (C. R.) Phascalogale pennicillata 37 mm. (C. R.) Trichosurus vulpecula 32 mm. (C. R.) Didelphys cancrivora, 4 embryos of 25 mm. length. Lacerta agilis N. T. (Keibel) 117, 118, 120, 123, 123, 124, 125, 126. Calotes iubatus, length of the head 5'/, mm., 7 mm. Lagysoma 27.5 mm. Hemidactylus fren. length of the head 4.5 mm. Salamandra mac. 11, 13, 15, 16, 16, 24 mm. Pipa Americana, 12 mm. Rana . 2 embryos. So far as I am able to judge foramina in adult shoulder-blades occur only with Homo and with various Edentata, in which they are always formed by bridging of the Incisura scapulae, and with Delphinus delphis. In the latter the character of the foramen is not known. RurnerrorD (1. ¢.) has described it. A conceivable connection, that might exist between the praesca- pula of RurHerForD and the attachment of the clavicula (not only the sternal half of the clavicula, as RurHerrorp supposed) to the margo superior scapulae, as it occurs in reptiles, echidna and orni- thorynchus, could not be ascertained, since a connection of the praescapula of RuruerForD to the acromial part of the clavicula could not be detected either. It appears, then, that the foramen, present in the majority of human embryos in the cranial part of the shoulder-blade, does not occur in other vertebrates, (except in Delphinus delphis, which, however, is of such a pronounced specificity that this foramen cannot be looked upon as a homologue of that of man). Neither did I find any attachment of the praescapula of Rurnerrorp to any other 303 skeletal bone. The significance of this foramen is unknown as yet. As to the ossification of the seapula my experience proved it not to be so simple as is represented in the literature. The earliest ossification I observed in an embryo of 40 mm. I constructed a wax model (fig. 4) of the scapula of this embryo. 4 LAN SHA Dor AA B es "5 i 0) Hi 4 fee: Aar + Hy 4 LY \ | : MW \ AN = {iy Fig. 4. Fig. 5. Homo 40 mm. Transversal. Cor = Processus coracoideus; Hu = Humerus; Acr = Processus acromialis; Sc — Scapula. Like the preceding model this also is viewed from above and from the dorso-lateral side. What this reconstructed model shows us may follow here: The joint-cavity, lying at the level of the first rib, is now located almost entirely on the planum scapulae (as with the adult scapula). Of the spina not a trace is visible as yet, the margo supe- rior is not thickened. To the basis of the processus acromialis an area of closely packed mesenchyma is attached, which extends between the muscular tissue and separates the rudiment of Muse. supra-, and infraspinatus. This area of mesenchyma is cut in a cross section as represented in fig. 5. Behind the root of the processus acromialis begins a peri- chondrial ossification, which continues into this condensed mesen- chyma. This ossification is the first formation of the spina. We see, 304 therefore, that it is formed by a perichondrial ossification, for although no ossifying perichondrium is visible here, the fact that the bone is formed from the surrounding mesenchyma co-ossifying with carti- lage, established the character of the ossification. In fig. 5 we givea cross section of this first stage of the spina. I have not been able to recognize two centres of ossification in the cartilaginous scapula, described by RamBaup and ReNaLr (quoted by Porrier'), which, according to these authors, arise between the 40% and 50 day and fuse in the third month. In the scapula of an older embryo (56 mm. in length) this peri- chondrial ossification appears to be largely extended. The margo anterior scapulae is almost reached. The cartilage of the planum WAY Nd Ast Fig. 6. Homo 56 mM. Transversal. Hu — Humerus; Cl = Clavicula; Cor = Processus coracoideus; Acr = Processus acromialis; Sp = Spina scapulae; Sc = Scapula. scapulae, however, has been distinctly calcified over a considerable area already. The marked enlargement of the spina scapulae is shown in fig. 6. Besides the spina this figure also shows part of the foramen described above. The spina is formed by a growth of bone between 1) Poirier et Carey, Traité d’Anatomie humaine. 305 M. supra- and infraspinatus, between acromion and planum scapulae. It cannot be denied, however. that in the mesenchyma, in which this bone develops, very young cartilage-cells are noticeable here and there. These cells, however, have no intermediate matter as yet; they are little differentiated and it is difficult to distinguish them from the mesenchyma-cells. So it is evident that besides bone-cells also cartilage-cells develop in the mesenchyma. In an embryo of 90 mm. enchondrial as well as perichondrial ossification takes place, the boundary between the two being no Pl. Se. Fig. 7. Homo 90 mm. Margo Fig. 8. Homo 90 mm. Scapula trans- anterior scapulae transversal. versal Acr. = Processus acromialis J.c. = Joint-eavily. Pl. Sc. = Planum scapulae. longer perceivable. The peculiar character of the perichondrial ossi- fication along the margo anterior is remarkable. In the place of the formation of compact bone, which in other cases occurs with perichondrial ossification e.g. that of the long bones, we see here a bony framework encircled by mesenchyma. Fig. 7 shows a cross section through the margo anterior. The study of this object (embryo of 90 mm.) shows remarkable pecularities of the growth of the spina scapulae. In the mesenchyma between M. supra- and infraspinatus a distinet cartilage is now recognizable. It is quite independent of the other mass of cartilage 306 of the scapula. [t is younger than the remaining part of the shoulder- blade; nevertheless it has already calcified to some degree and forms bone of the spina. The cartilage has been cut in three different cross sections, as represented in the figures 8, 9 and 10. Fig. 8 illustrates a section through the scapula above the place of attachment of the processus acromialis. In the mesenchyma, which extends from the processus acromialis towards the margo vertebralis, lies the cartilage which is already partly calcified. In fig. 9 we give a section at a lower level. The processus acromialis attaches itself at this level to the planum scapulae. Here also we observe the cartilage of the spine, independ- ent of the remaining cartilage of the shoulder-blade. Fig. 10 shows a section through the scapula at the level of the lowest place of Fig. 9. Homo 90 m.m. Scapula trans- versal. Aer. = Processus acromialis. Pl. Sc. Pl. Sc. = Planum scapulae. Fig. 10. 90 m.m. Scapula transversal. C.= cartilage of the spine. Pl. Sc. = Planum scapulae. attachment of the spina. The young cartilage, which forms the spina, has here been cut over a large area. The cartilage will be seen to 307 be partly calcified, while bone has been formed, uniting with this calcified area. So while the first beginning of the spina is formed by perichon- drial bone in the mesenchyma between M. supra-, and infraspinatus, its further development is effected by chondrial bone, which origin- ates in the younger cartilage. This cartilage has been generated between the afore-said muscles by the same mesenchyma. A peculiar feature is still to be observed at the shoulder-blade of the embryo of 90 mm. Bone is developed at the margo superior as well enchondrially as perichondrially. In the mesenchyma that forms the perichondrial bone, and into which this bone extends over some distance, there are two cartilaginous nuclei, made up of the same young tissue from which the cartilage of the spina has been built up. Fig. 11 shows in cross section these nuclei, which are not in contact with the remaining cartilage of the shoulder-blade. These cartilage-islets appear to be already calcified and ossified here and there. It is impossible to draw a boundary-line between the bone formed in this process and the perichondrial bone of the scapula. This ossifying process, in which (besides the enchondrial ossification of the scapula) both perichondrial and chondrial ossification of a cartilage nucleus, situated outside the perichondrial bone, are present, agrees completely with the formation of the spina scapulae. This is striking, since the spina scapulae and the definitive margo superior are the two parts of the shoulder-blade, which are missing in the first rudiment of the cartilaginous scapula. This deficiency vertebral of the place destined for the future incisure, is indeed accounted for by the fact that the margo superior in young embryos is still straight and displays no incisure. The missing parts are apparently supplied by the perichondrial bone that reaches far into the mesenchyma, together with the bone formed by the afore- said cartilage-nuclei. At the shoulder-blade of an embryo of 120 mm: in length, in which the ossification had considerably advanced, the incisure was indeed present. Of course, the question arises, how the cartilage of the spina as well as the cartilage nuclei are further developing. In both places the cartilage is soon transformed completely into bone. In an embryo of 120 mm. only a very few remnants of the cartilage of the spina were still left. The rest had been ossified. After this the development of the shoulder-blade proceeds in the way described in the text-books of embryology. Now let us review once more the current opinions of the develop- ment of the spina scapulae. It will be seen, then, that however 308 divergent they may be, most of them cannot be deemed incorrect, when we bear in mind that they concern different stages. Fig. 11. Homo 90 m.m. Margo superior scapulae transversal. Rurnerrorp’s view of the very early ossi- fication of cartilaginous cells is no doubt correct, but holds good only for young stadia. Neither is the conception of Hertwie and Braus about a separate centre of ossification quite incorrect, since there is a stage in which an _ in- dependent cartilage is forming bone.BaRDELEBEN’s record about an ossification under and beside the spina cannot altogether be disqualified either, but it only applies to a brief stage of development. However, ossification like that of the bones of the cranial vault does not occur in the development of the shoulder-blade. In the neonatus a few cartilage may possibly sometimes be found at the spina (Bryce), but it is certain that the spina scapulae in the new-born child does not consist of cartilage. (K6LLIkER and HeErtwicg advocate the opposite view). Lewis’s conception, however, (doubling of the margo superior) is altogether wrong. The diagram borrowed from Lewis by Broman, Bryce and BARDEEN represents a faulty recon- struction of the shoulder-blade. Zoology. — “Secondary ser-characters and testis of the ten-spined Stickleback (Gasterosteus pungitius LJ)” By Dr. G. J. van Oorpr. (Communicated by Prof. J. Boeke). (Communicated at the meeting of March 24, 1923) It is generally known that the sex-glands strongly influence the so-called secondary sex-characters. This is apparent from the marked somatic and psychic differences, which e.g. Mammals or Birds, castrated at an early age, show, when compared with normal animals. At present it is generally accepted that in Vertebrates this effect, resulting from the gonads, takes place by internal secretion, that is by the influence of certain substances, which pass into the blood (“hormones’’). As the correlation between the secondary sex-characters and the gonads generally is most distinct in male Vertebrates, | will speak only of the formation of these hormones in the testis for convenience’ sake. Recently it has been especially attempted to ascertain, by which part of the male gonad these hormones are formed. The numerous investigators, treating this subject, chiefly hold the two following, contradictory opinions. According to Stimve (1922) and others these hormones are exclu- sively formed by the sexual cells, whereas Bouin and Ancer (1903), Sremacnh (1920), Lipscnürz (1919), Bascom (1923), their collaborators and others are of opinion that these hormones originate in the interstitial cells (Luypie’s cells), situated in the interstitium of the male gonad. According to Stimve these cells are only thropic ele- ments for the sperm cells. Consequently no value must be attached to the name ,,Puberty Gland’, which name was given to the col- lective Leypia’s cells by Sremacn and Lirscnürz. Up till now the investigators, when treating the subject above mentioned, have chiefly examined Mammals, Birds and Amphibia. For that reason I resolved to trace the changes in the testis at the appearance of the secondary sex-characters in a Fish, and so I chose the ten-spined Stickleback (Gasterosteus pungitius L.), which was easy to obtain. During breeding time, in spring, the males of this species possess 310 a number of secondary sex-characters (ef. Tirscnack 1922), of which the following are distinetly perceptible. In spring a very distinet black pigmentation (red in the three- spined species) can be observed at the throat and at the abdomen, which soon spreads over the rest of the body, so that the animals become dark-black, except for their pectoral spines. Outside breeding-time it is difficult to distinguish the males from the females: then both show dark spots on a pale green ground. Individual colour-differences occur. Every male makes a nest, in which the eggs are deposited. The material of which the nest consists (parts of waterplants ete.) is collected by the male and fastened by means of a secretion, formed by the kidney-tubules and Wolffian Duets (Trrscnack 1922, COURRIER 19226, both in Gasterosteus aculeatus 1..). This peculiar secretion occurs exclusively in the male during breeding time ; for that reason in spring the kidney strongly increases in size, the kidney-tubules and the Wolffian Ducts get a larger diameter and exercise a different function. The male guards his nest and drives off all intruders fiercely. When the eges have been deposited in the nest, they are at once fertilized. During the development of the eggs, the male takes care that they are constantly provided with oxygen by conducting fresh water to the nest with his pectoral fins. Sometimes, when eggs drop out of the nest, they are again collected by the male and taken back to the nest in his mouth. Whether the young are guarded by the male, after they have left the nest, in nature, is not known to me: care must be taken to separate the young, living in prison, from their father and the other inhabitants of the aquarium, as the young will otherwise be eaten. The aim of my investigation, begun in September 1922, was to trace the changes, occurring in the testes of the Stickleback at the appearance of the secondary sex-characters. So it was my intention to catch a number of Sticklebacks at fixed times during the winter and the sueceeding spring and to examine their sex-glands. At that time [ thought that nothing was known as yet about the relation between the secondary sex-characters and the testis of the Stickle- back, but it soon appeared to me that Courrier had already investi- gated the three-spined Stickleback (Gasterosteus aculeatus L.) and had published some papers, regarding this point (1922a, 19226). I therefore changed my original plan and resolved to trace what influence a rather high temperature, about the temperature of 311 ditehwater in spring (12°—20°C.), would have on the appearance of the secondary sex-characters and what changes would take place in the testes of these animals simultaneously. The sex-glands of control-animals, caught in nature, could serve at the same time to verify the results of Courrier. In this paper I will only communi- cate the results, obtained in animals, kept in a temperature of 12°—20° C. during last winter. In September and October 1922 I caught a large number of specimens of (rasterosteus pungitius L. at Rotterdam. They were kept in an aquarium of which the water was often renewed, and they were copiously fed with Chironomus-larvae. All the testes of the Sticklebacks, killed in autumn, contained a more or less large number of spermatozoa. The number of sperma- togonia is always small, the number of spermatocytes and sperma- tids varies in the different specimens. In all cases, examined by me, small groups of interstitial cells (Luypie’s cells) were present, close to the hilus or there where three or more tubules come together. In a few testes, in which the interstitium is somewhat wider, these cells are also situated between the seminiferous tubules. They were absent in none of the cases examined. In one specimen (n°. 6), a rather dark-coloured male, not showing the black pigmentation of males during breeding time, however, the interstitium is much wider than in the other males, caught at the same time. The number of interstitial cells is also larger in this specimen, while in the seminiferous tubules spermatozoa are almost exclusively found. Oblong connective tissue-nuclei are observed everywhere in the interstitium of the testes of animals, caught in autumn, blood-vessels are present, but they are not numerous; they are narrow and contain few blood-cells. This testis-structure is shown by animals, caught in September and the beginning of October, and which were kept in an aquarium of which the water then agreed in temperature with ditehwater. The testes of Sticklebacks, kept for two, three and even four months, i.e. till the end of January 1923, in a temperature of 12°—20° C., all increase in size and show the following structure. The spermatogenesis is very intensive. In all testes this process takes place from the exterior to the interior, i.e. the spermatozoa are situated as a rule more in the centre, the spermatogonia and spermatocytes more at the periphery of the gonad. The interstitium of such animals does not change; it remains narrow, the number 312 of Leypie’s cells is generally small and they are especially present near the hilus and there where three or more seminiferous tubules come together. Till the end of January it was difficult to distinguish the males from the females. In the last days of January, however, one of my specimens showed at throat and abdomen a faint black pigmentation, which soon increased strongly. Besides, this animal became very agressive and in the beginning of February he began to collect material for the nest. On the 14% or 15 of February the eggs were laid in the completed nest; (I cannot give the exact date, as the female was not seen in this nest). On the 16 of February this male was killed. The nuptial colours successively developed in the other males, which soon began to prepare their nests. After the eggs had been deposited in them, they were carefully guarded by the males, which constantly conducted fresh water to the nests. 3 On comparing the testes of animals killed in the end of Decem- ber or in January with the testes of these males, we see that the latter have greatly changed. The spermatogenesis has totally come to an end. The seminiferous tubules are entirely filled with a large number of spermatozoa. Moreover, at the periphery of the tubules small groups of sperma- tozoa are to be seen, the heads of which are directed to the wall and the tails to the centre of the tubules. The number of sperma- togonia and spermatocytes has strongly decreased. The interstitium is no longer narrow but is enlarged; the number of Lrypre’s cells has strongly increased ; the blood-vessels have become more numerous and larger. So we see that the high temperature of the water in winter favours the spermatogenesis and that consequently after four months a testis originates of which the seminiferous tubules practically contain spermatozoa exclusively. Then the secondary sex-characters distinctly develop, the interstitium is enlarged and the cells of LeypiG and the blood-vessels increase in number. So I have observed a coincidence of the occurrence of the second- ary sex-characters and the termination of the spermatogenesis, while simultaneously an enlargement of the interstitium with increase in number of the Leypie’s cells and of the bloodvessels takes place. This does not prove, however, that a correlation exists between these phenomena. According to Courrier (1922a, 19226) it does. This investigator observed in the three-spined Stickleback that after the spermato- 313 genesis the interstitium increases considerably in size. In it a strong augmentation of the number of Luypia’s cells and of the blood- vessels has taken place. According to Courrier the testes of Stickle- backs, caught in winter, only contain a few interstitial cells here and there. The spermatogenesis, which is very intensive in spring till the end of March, has no influence on the development of the secondary sex-characters. The latter occur not earlier than at the end of April, simultaneously with the strong development of the inter- stitial cells. As he, moreover, observes the same granules in the cells of LeypiG and in the bloodvessels, situated close to them, he assumes that the hormones which influence the development of the sex-characters are formed in the interstitial cells and pass from the ‘latter into the blood. In my opinion it might be that the granules, observed by Courrier, are transmitted by the blood to the inter- stitial cells. Courrier has also kept his fishes in water of 17° C. (19224 and 19226, p. 137) during a part of the winter. After two months and a half the structure of the seminiferous tubules of these animals resembles that of animals during breeding time i.e. they are entirely filled with spermatozoa and contain only a few spermatogonia, spermatocytes and cells of Serrorr. Changes in the interstitium have not occurred. Consequently, the secondary sex-characters have not developed in these animals. Courrier thinks, however (1922, in a note), on the ground of experiments, which were in progress at that time, that the interstitium would increase in size, when exposed longer to a high temperature and that consequently the sex-characters would also develop in these animals. I think I am justified to conclude from my investigations, de- scribed above, that the correlation of interstitial cells and secondary sex-characters is not so easy to establish. In the first place all testes of Gasterostevs possess a more or less large number of interstitial cells. These evidently do not cause the development of the secondary sex-characters. Here I must especially point to the male above described (N°. 6) of which the testes contain a wide interstitium with many Lerpie’s cells and of which the seminiforous tubules are entirely filled with spermatozoa. The secondary sex-characters had not developed in this animal, however. Among the testes of control-animals, caught in nature in winter, I also found some-of which the tubules almost exclusively contained spermatozoa and of which the interstitium with numerous interstitial cells is rather strongly developed. These animals, however, did not show sex-characters either. 314 In a very recent paper Cnrampy (C. R. Soe. de Biologie, Séance du 17 Février 1923) communicates that he has obtained Sticklebacks (aculeatus) with nuptial colours last winter and that in the testes of these animals he had not observed a well-developed interstitial tissue. As he has not found any interstitial cells in the testes of various species of fishes with distinct secondary sex-characters, Cuamry is of opinion that these cells have no influence on the development of those sex-characters and that the formation of the hormones responsible for the development of these characters would take place by means of the sexual cells. Finally, I will once more call attention to the fact that the testes, examined by me, in which the spermatogenesis has almost come to an end, possess a more strongly developed interstitium than testes, in which the spermatogenesis is still in full swing. Possibly this fact points to a correlation between spermatogenesis and interstitial cells. Whether the sex-hormones are formed in the seminiferous tubules as well, | cannot decide at this moment. Later on, when I have more material at my disposal, I hope to recur to this subject in a more detailed paper. Zoblogical Laboratory of the Veterinary College. Utrecht, March 1923. REFERENCES. Bascom, K. F. 1923. The interstitial cells of the gonads of cattle, with especial reference to their embryonic development and significance. Amer. Journal Anat., vol. 31. Bouin, P. et AnceL, P. 1903 Recherches sur les cellules interstitielles du testi- cule des Mammifères. Arch. de Zoöl. expér. et génér., 4de Série, T. 1. SN CHAMPY, CH. 1928. Observations sur les caractéres sexuels chez les Poissons. G. R. Soc. de Biol., T. 88, pag. 414. | Courrier, R. 1922a. Sur l’indépendence de la glande séminale et des caractères sexuels secondaires chez les Poissons. Etude expérimentale. C. R. Acad. des Sciences, T. 174, pag. 70. “Courrier, R. 19225. Etude préliminaire du déterminisme des caractères sexuels secondaires chez les Poissons. Arch. d'Anat., d'Hist. et d'Embryologie, T. 2. Lipscutirz, A. 1919. Die Pubertätsdrüse und ihre Wirkungen. Bern, Verlag von E. BrrcHer. STEINACH, E. 1920. Kiinstliche und natürliche Zwitterdrüsen und ihre analogen Wirkungen. Archiv f. Entw. Mech., Bd. 46. Streve, H. 1921. Entwickelung, Bau und Bedeutung der Keimdrüsenzwischenzellen. Ergebnisse der Anat. und Entwickelungsgeschichte, Bd. 23. \TitscHack, E. 1922. Die sekundären Geschlechtsmerkmale von Gasterosteus acu- leatus L. Zool. Jahrb. Abt. f. allg. Zoologie und Physiologie, Bd. 39. KONINKLIJKE AKADEMIE VAN WETENSCHAPPEN TE AMSTERDAM. PROCEEDINGS VOLUME XXVI Nes, 5 and 6. President: Prof. F. A. F. C. WENT. Secretary: Prof. L. BOLK. (Translated from: “Verslag van de gewone vergaderingen der Wis- en Natuurkundige Afdeeling,” Vol. XXXII). CONTENTS. J. C. KLUYVER: “On EULER’s Constant”, p. 316. J. P. WIBAUT and J. J. DIEKMANN: “Researches on the Addition of Water to Ethylene and Propylene”. (Communicated by Prof. A. F. HOLLEMAN), p. 321. W. H. JULIUS and M. MINNAERT: “The relation between the widening and the mutual influence of dispersion lines in the spectrum of the sun's limb”, p. 329. J. P. BANNIER: “Cytological investigations on Apogamy in some elementary species of Erophila verna”. (Communicated by Prof. F. A. F. C. WENT), p. 349. F. W. ‘I’. HUNGER: “On the nature and origin of the cocos-pearl”. (Communicated by Prof. G. VAN ITERSON Jr.), p. 357. TH. VALETON: “The genus Coptosapelta KORTH”. (Rubiaceae). (Communicated by Prof. J. W. MOLL), p. 361. D. TOLLENAAR: “Dark Growth-responses”. (Communicated by Prof. A. H. BLAAUW), p. 378. JAN DE VRIES: “Representation of a Tetrahedral Complex on the Points of Space”, p. 390. A. SMITS: “The Electromotive Behaviour of Magnesium’. Il. (Communicated by Prof. P. ZEEMAN), p. 395. D. S. FERNANDES: “A method of simultaneously studying the absorption of Og and the SEE of COs in respiration”. (Communicated by Prof. F. A. F. C. WENT), p. 408. H. J. HAMBURGER: “A new form of correlation between organs”, p. 420. J. P. WIBAUT and Miss ELISABETH DINGEMANSE: “The Synthesis of some Pyridylpyrroles”. (Com- municated by Prof. P. VAN ROMBURGH), p. 426. G. M. KRAAY and L. K. WOLFF: “The splitting of lipoids by Bacteria’. (First communication). (Communicated by Prof. C. EYKMAN), p. 436. \ J. B. ZWAARDEMAKER: “The Presence of Cardio-regulative Nerves in Petromyzon fluviatilis”. (Communicated by Prof. H. ZWAARDEMAKER), p. 438. W OD. COHEN: “The light Oxidation of Alcohol (III). The Photo-Catalytic Influence of some Series of Ketones on the light Oxidation of Ethyl Alcohol”. (Communicated by Prof. J. BOESEKEN), p. 443. M. }. BELINFANTE: “On Power Series of the Form: x?0— xP1 + xP2—..” (Communicated by Prof. L. E. J. BROUWER), p. 456. F. F. HAZELHOFF and Miss HELEEN WIERSMA: “On Subjective Rhythmisation', (Communicated by Prof. E. D. WIERSMA), p. 462. R. BRINKMAN and A. V. SZENT-GYORGYI: “Researches on the chemical causes of normal and patho- logical Haemolysis”. (Communicated by Prof. H. J. HAMBURGER), p. 470. L. HAMBURGER: “Nitrogen fixation by means of the cyanide-process and atomic structure”. (Com- municated by Prof. P. EHRENFEST), p. 480. F. D'HERELLE: “Culture du bactériophage sans intervention de bactéries vivantes”. (Présenté par Mr. le Prof. W. EINTHOVEN), p. 486. V. VAN STRAELEN: “Description de Crustacés décapodes nouveaux des terrains tertiaires de Borneo”. (Présenté par Mr. le Prof. H. A. BROUWER), p. 489. C. WINKLER: “A partial foetus removed from a child”, p. 493. Erratum, p. 496. Proceedings Royal Acad. Amsterdam. Vol. XX VI. Mathematics. — “On Eurer's Constant’. By Prof. J. C. Kivyver. (Communicated at the meeting of May 26, 1923). In calculating the value of HEurer’s constant C the summation formula or any other asymptotic series is used, and one term at least in the expansion is always a transcendental quantity. It would be preferable to represent Cas a convergent expression containing rational terms only, because such a representation of the number C perhaps eventually will furnish the means to establish its irrationality. As yet Vacca’s series *) ne of Mees! Sach \ api a Ng en A Cdn 1 Sere ab ener is the only result in the desired direction, and as a second | will add the proof that C—4 can be expanded in a convergent continued fraction 44 Wp 1 1 ALL dels aoe a. Yate the quantities a, being throughout positive and rational. Following Stie_tses’ method *) for converting an integral into a continued fraction, I consider the integral 1 J (z) aha NO == i . Brul’ de supposing z >>0. Expanding the integrand in powers of —, term-by- 2 term integration gives the divergent series the coefficients of which are determined by the equation 1) Q. J. Math, London, vol. XLI, p. 363. 2) Recherches sur les fractions continues. Oeuvres completes, II, p. 402. 317 ao 0 2 * p2h+1 Bi = h ee 1 = peewee ch =| uh f (u) du = Em | n= TE) 0 0 Hence cj, directly deduced from the Bernoullian number Bj, is a positive and rational quantity. In order to evaluate the integral J(z), we write ao Sekt udz emu Le ArVu 1 e—6rVu He 2m | + oe 4 du g—2mrV u El 0 0 and substituting in the remainder w= v’, we find co oo du e—2mnV u dv ve rv 1 de welig = 4 : utz eu] vitz etl 2n°mz 0 Hence we have a du k=0 a k=o il J (2) =| in € rk =| due tru > SE) k=1 ut hz 0 0 : Utz Jel zu" and, putting u=-——, we get 4x? a k=c0 9 n° v 1 1 MEN rl >>, ee == | el 2'dy Lee es kar v?* HAL x? ev—] v 2 ao oo ; ev ex1—_V 2) Sti 1 =f dv | — — dv = | | v ev—1 | +f v 2Vz , 7 ; =: I” l = — 5, (V2) + log (V2) — ’ 2V2 a result from which we deduce at once J/(1) = C—}. Now according to Stirites’ theory the integral J (z) can be converted formally in a continued fraction il vz Bebe Alte tp ole lt ot... le, lage” le, lave the quantities a, depending on the coéfficients c,,c,,c,,... of the Zs 318 divergent series. Following the general method we consider the determinants | CG, @& Ch EC ON ann Cn A c, Cs C, lots anions Cn+1 C, cy Cy wa cece Cn Vanin ACH Che | Aan |E; CF G7 foe peas Cutt |» | €n CnHl “n42+-. . C2n—1 Cn—1 Cn Cn4i+ +++ €2n—2 then we shall have WZ : Dn ZE ab: k= Bice : @. ars Gh : : Ak Are These general formulae give no insight in the numerical values Se ges Ars Bin of the quantities az, remembering however that cj, = es 242 obvions that they are rational and depending on the Bernoullian numbers only. Moreover they are positive, for considering the determinant [Cp Cp pte ++. Sp tin lep Cp42 Cp+3 see Gptm4+i D= lep+2 Cp+3 Cp+4 sees Cptm+2)5 | - á 5 A 5 . 5 e | le Opm Sptm+i1 &p+-m-+2 - «Cp with arbitrary indices p and m, we get 1 2 m 2 UNI 2 oe lu, w.... Us D= 7 Si rn In, 2 oe ae 0 0 . . . Bo, © 2 m Luin lee Um Hence D and in particular every determinant 27 is positive, there- fore the same conclusion holds for az. By direct calculation we get for the very first quantities a, rather irregular numerical values. We shall find 252 no 24072 5 ee = 12, Sn WT én cea 2480 a, 6" Fase TR Te RET REEN. but these results give no indication about the possible convergence of 319 the continued fraction. In order to prove this convergence for z > 0, we change f(%) into ] J () EE e2tVu__ eV u and applying StieLrJes’ method to the new integral ih r' An Tav N ] hae = ——— — 2) - — AEN Nanda tand LOG) ag © =f dee iW A ps OV ah ap we obtain the continued fraction 1 | 1 | 1 | 1 1 | se SRR la de See la’,z la’, la',z a, la 62 ith a’ - d a! ne N both the series Sa and WIEN Aon =S And Aon = =—_,. NOW Doth the series 209; anc ae an an 2n+1 ae 1 oo Ed's evidently, diverge, hence we infer that for z >>0 the new 0 continued fraction necessarily converges, and by the way we may 1 note for z =o the rather remarkable result JT bean: Comparing the functions f(u) and g(w) we have eh. 9 («) and accordingly everywhere in the range of integration LO on, gu) = therefore, again using SrieLTJES’ argument, we conclude to the inequalities 5 (a, Ha, +a',+.-.4-@'2n41) < (4,+4,+4,+..-+42 n41) << AGS a,+a,+...-+ Aoi)» en Ed otherwise written ls) CO 1 (rte oe ae 1 <16(1 +5 eed +59). 320 Consequently the lower limit of asz4, must be zero, and that CnH1 Cn agrees with the fact that tends to infinity, for StieLTsEs shewed that in that case no upper limit can be assigned to : Un An4+4 oo The principal conclusion, however, is that the series > dar 0 diverges, that therefore the continued fraction EN 2 la,2 el ERE dd dje ee | la,z la, la,z 8 6 converges except when z is real and negative, and that it is equal to the integral J(z). Thus then, putting z— 1, we have proved that C — } can be expanded in the continued fraction | eS ae + = SS 1 Sere la, la, la, fe la, | the quantities a, being rational and positive, whilst those of odd index have the lower limit zero. More or less we are inclined to believe that a fraction satisfying these conditions cannot represent a rational number, and so the expansion of C — } again suggests the conjecture that C must be irrational. The result obtained is of no. practical value; that after some reductions we have 6| 79| 2410) | 262445 5 * lag a Ape es ELSES C eee “ea is of small service in the evaluation of the constant, and though numerator and denominator of any convergent can be expressed in the Bernoullian numbers, in approximating the constant C other methods are to be preferred. Chemistry. — ‘Researches on the Addition of Water to Ethylene and Propylene”. (Preliminary Communication). By Dr. J. P. Wipaur and J. J. DieKMANN. (Communicated by Prof. A. F. HorLeMAN). (Communicated at the meeting of March 24, 1923). About two years ago experiments were carried out by one of us purposing to study the possibility of a direct addition of water to ethylene and propylene. The continuation of this investigation has been rendered possible by a liberal support granted me from the HooGrewerrr-fund. [ gladly avail myself of this opportunity to express my great indebtedness to the Board of Management of. the Hoocewerrr-fund for this help. Though these investigations have not yet been completed, it seems desirable to me in connection with a short notice in the ,,Cbhemiker Zeitung’ of Jan. 2ed 1923 (N°. 47, p. 7), in which H. W. Krrver describes similar researches, to publish a preliminary communication on the results obtained by us. J. P. Wieavr. § 1. The Action of Water-vapour on Ethylene and Propylene in the Presence of Catalysts. Since the investigations by [PATIEW, SENDERENS and SABATIER it has been known that at high temperature and in the gaseous condition ethyl-alcohol and some of its homologues can be decomposed in two ways: C HOH GH HO ns .ughe alike . covedhp H ©, A. OH =>, CH,C==0 + Ho esrueb. oidavel (iD: Both reactions are typical catalytic reactions, which only proceed readily in the presence of certain contact-substances. Anhydrous aluminiumsulphate and aluminiumoxide are typical catalysts that split off water (reaction I). Metals like copper and iron, especially in finely divided condition, are typical catalysts for the splitting off of hydrogen (reaction II). The range of temperature, in which particularly the first reaction 322 takes place, lies between 300—400°, dependent on the nature of the catalysing substance; when the temperature is raised to about 400° and higher, the formation of aldehyde becomes prominent even in the presence of substances like aluminium oxide and other catalysts that split off water. It is well known that reaction (II) is reversible — aldehydes can be smoothly reduced with molecular hydrogen over nickel — but nothing is known about the reversibility of reaction (1). In the extensive literature on the splitting up of alcohols into olefine and water, the question whether direct addition of water to the double bond in ethylene and propylene is actually possible, has never been examined. We have carried out a number of experiments to answer this question. A mixture of ethylene and water-vapour was led over different contact-substances at a temperature between 300° and 400°C. On use of aluminiumhydroxyde or of aluminium sulphate as catalysts, the reaction product contained acetaldehyde. We have proved the presence of acetaldehyde by the usual reactions (reduction of an ammoniacal solution of silver hydroxide); Scurrr’s reaction; reaction with nitro-prussidsodinm and piperidine aceording to Lewin) and also isolated as p-nitrophenylhydrazone. The quantities of acetaldehyde are very small; by far the greater part of the ethylene remains unchanged during the experiment. The quantity of acetal- dehyde amounted to from 0,2 to 0,4 °/, at 350°—360°, calculated to the quantity of ethylene. The presence of alcohol could not be verified '). In our opinion the formation of acetaldehyde must be explained in this way that primarily ethylaleohol is formed through addition of water to ethylene, and then acetaldehyde through splitting up of hydrogen. If this second reaction proceeds much more rapidly than the addition of water to the double bond, no alcohol will be found in the reaction product. As at 350°—360° ethyl-alcohol is almost quantitatively decomposed into ethylene and water (at this temperature, however, a little hydrogen is also formed) it is clear that only at a lower temperature the inverse reaction can take place in a considerable degree. We have, however, not succeeded in finding a catalyst that causes the addition of water to ethylene below 300°. We have proved by means of a separate experiment that no acetal- dehyde is’ formed from mixtures of dry ethylene with about 10°/, of air at 360° over aluminiumoxide. It, therefore, appears from 1) The analytical particulars will be given later. as also the full description of the arrangement of the experiments, 323 this that the formation of acetaldehyde is not the consequence of an oxidation of ethylene, e.g. according to the scheme H C,H, + O >CH,—CH, — CH,C=O DOE Hence the formation of acetaldehyde cannot have been caused by the possible presence of small quantities of air in the ethylene used. We are, therefore, of opinion that we are justified in concluding that a primary addition of water to. the double bond has taken place, and that the reaction: C,H,OH 2 C,H, + H,O may accordingly be considered as a reversible reaction. We have obtained perfectly analogous results with mixtures of propylene and water-vapour. At 350° and in the presence of alumi- niumbydroxide acetone was then formed in a quantity of from 0,2 to 0,3 °/, of the propylene. In our opinion the primary formation of isopropylalcohol by addition of water to propylene, must be assumed in this case. Afterwards the isopropylalcohol is transformed to acetone through the splitting off of hydrogen. Hence the direct addition of water proceeds analogously to the addition of hydriodie acid, in which likewise the isopropyl compound appears. Accordingly the rule of Markonikow remains valid also in this case. On the ground of these results it is probable that the addition of water to propylene and ethylene can take place under high pressure at temperatures far below 300°. We have, however, made no experiments in this direction. § 2. The Hydration of Ethylene and Propylene by Means of Acids. The syntheses of ethyl- and isopropylaleohol from ethylene and propylene by the formation of alkyl-sulphurie acid, and subsequent hydrolysis, by M. Berrarvor *) are among the classic syntheses of organic chemistry. Berrarror investigated the absorption of these olefines by pure sulphuric acid of 98—99°/, H,SO, at ordinary temperature. Afterwards the absorption of ethylene by sulphuric acid has been repeatedly studied. Particularly in the last few years several technical chemists have made experiments to absorb the ethylene from ') BerTHELoT: Chimie organique fondée sur la synthèse, p. 115. c.f. Ann. de Chimie et de Physique. (7), 4, 101 (1895). Bull. Soc. Chim. XI, 13. (1869). 324 coal-distillation gases by means of hot strong sulphuric acid (of 96 °/), and to obtain ethvlaleohol after dilution and distillation of the sulphuric acid *). With regard to the action of sulphuric acid on propylene, a process of CaRLETON-Erus ®) has become known. In this process the waste gases formed in the preparation of light hydrocarbons from heavy petroleum-distillates (cracking-process of Burton) are passed through sulphuric acid of 87°/,; the propylene present in these is said to be transformed into isopropylsulphuric acid. After dilution and distillation of the sulphuric acid isopropylalcohol is obtained. Systematic researches on the behaviour of ethylene and propylene towards acids of different concentrations have not been published. On the other hand there are many instances known, in which the addition of water to a double bond takes place under the influence of diluted acids. Geraniol absorbs two molecules of water when treated with 5°/, sulphuric acid. Burrerow *) found that isobutylene and heptylene were very slowly hydrated to the corresponding alcohols by means of diluted sulphurie acid and nitric acid at the ordinary temperature. It seemed interesting to us to examine how ethylene and propy- lene would behave towards acids of different concentrations. If ethylsulphurie acid can be obtained through the action of ethylene on diluted sulphuric acid at high temperature, there would be a possibility that afterwards the ethylsulphurie acid should be hydro- lized : (1) C,H, + H,S0, > C,H,HSO, (2) C,H,HSO, +-H,0 > ©,H,OH + H,0 If the two reactions proceeded rapidly enough, the experiment might be arranged so that the alcohol formed is immediately distilled off from the reaction liquid. Such a course of the reaction would then be practically an addition of water to ethylene, in which the question whether we have to do here with a direct addition or which an intermediary ') PRITZSCHE. Chemische Industrie 20, 266 (1897) and 21, 27 (1898); Tau and BERTELSMANN, Glück Auf 57, 189 (1921); Bury en OLLANDER: ,,Byproduct devel- opment in the [ron and Steel Industry”; Paper read before the Cleveland Institution of Engineers, 15 December 1919; cf. Tipman, Journ. Soc. Chem Ind. 40, 86 T (1921); pe Lorsy. Compt. Rend. Ac. d. Sc. Paris 170, 50 (1920); DAMIENS, DE Lorsy en Pierre, Eng. Pat. 180988 (1922). 2) Cf. Chemical and Metallurgical Engineering. Vol. 23, 1230 (1920). *) Lieb. Ann. 180, 245 (1876). 325 formation of ethylsulphuric acid, can be left undecided for the present. We have devised an apparatus, in which an ascending stream of gas came into intimate contact with the descending acid. ‘This washing apparatus, which is placed vertically was electrically heated by means of a coil of nichrome-wire so as to make it possible to keep the reaction temperature constant within narrow limits. The ethylene, which is led through the heated, diluted sulphuric acid will withdraw water-vapour from the liquid, for so far as it is not absorbed, which would cause the acid to become more con- centrated in the course of the experiment. To prevent this we have added water-vapour to it at the same time with the ethylene ; the partial tension of the water-vapour in the introduced gas-mixture was about the same as the water-vapour tension of the used sul- phurie acid at the temperature of the experiment. In this way the concentration of the sulphurie acid was kept about constant during the experiment. At the top of the apparatus there escaped, therefore, water-vapour, not absorbed ethylene, and alcohol vapour, if any was formed. It actually appeared possible to obtain alcohol from ethylene in this way. A mixture of ethylene and steam was washed with sulphuric acid of 65°/, H,SO, at a temperature of 150°—160°. After 5 litres of ethylene had been passed through in 5 hours’ time, the distillate contained 0,21 gr. of alcohol’), i.e. a conversion of about 2 °/,. Then the sulphuric acid used was strongly diluted and distilled out, and in this way 0,08 gr. of alcohol more was obtained. Hence a little ethylsulphuric acid was still present in the sulphuric acid after the experiment. This renders it probable that the ethylsulphuric acid is formed as an intermediate product, and that accordingly the formation of alcohol is the result of two successive reactions, as given above. , In a second similar experiment 4°/, of the ethylene that was passed through, was converted into ethylalcohol. With a mixture of sulphuric acid and water containing 55°/, H,SO, only 0.01 gramme of ethylalcohol was found in the distillate, when 5 litres of ethylene mixed with steam had been passed through at 140°. With sulphuric acid of 70°/, no alcohol was found in the dis- tillate, when three litres of ethylene had been passed through. After 1 The analysis took place by oxidizing the reaction liquid with chromic acid, in consequence of which the alcohol present was oxidized to acetaldehyde. This latter was determined colorimetrically. 326 dilution and distillation the sulphurie acid yielded, however, 0.32 gr. of alcohol, which was, therefore, present as ethylsulphuric acid. This corresponds with a conversion of 5 °/,. In these experiments most of the ethylene passed unchanged through the sulphuric acid; only a slight carbonisation took place. Though in principle it, therefore, appears possible to convert ethylene in this way into ethylaleohol, the yield was so small that: no practical significance can be assigned to these experiments. These researches are being continued with other acids and with salts, as aluminiumsulphate and others. § 3. Propylene and Sulphuric Acid. It is well known from Berrneror’s investigations that propylene is very rapidly absorbed at the ordinary temperature by sulpburic acid of 98—99°/,. We have first of all made some preliminary experiments on the action of sulphuric acid of different concen- trations on propylene. In a Hempet’s gas-pipette 100 ec propylene was placed together with the sulphuric acid to be examined. Sulphurie acid of 96°/, at once absorbs the propylene, also sul- phurie acid of 90°/, acts very rapidly on it; with acid of 85 °/, the propylene is absorbed after 20 minutes’ shaking, about an hour being required for this with acid of 80°/,. Also sulphuric acid of 75 °/, still absorbs propylene, but very slowly. We have further investigated the action of propylene on sulphuric acid of 96°/, at 0°, in which we carefully guarded against rise of temperature both during the absorption of the gas, and during the pouring out of the reaction product on ice. We have only succeeded in obtaining a small quantity of isopropylaleohol from the reaction product. Through the action of the sulpburic acid the bulk of the pro- pylene was changed into an oily liquid, which was unsaturated, and boiled within wide limits. It is, therefore, probable tbat higher unsaturated hydro-carbons are formed by the condensing action of the sulphuric acid. Bertne.or too states that such condensation products are formed, when rise of temperature takes place during the experiment. In our experiments with sulphuric acid of 96 °/, at O° the bulk of the propylene was always transformed into condensed and resinous products in spite of all our precautions. With sulphuric acid of 85°/, the absorption of propylene takes place very slowly at 10°. On further treatment 327 of the reaction product, chiefly condensation products were again obtained. We then examined the absorption of propylene by more diluted sulphuric acid at higher temperature. The experiments were arranged in the same way as was already described for ethylene. The mixture of propylene and steam was brought in contact in counter-current with sulphurie acid of definite concentration and definite temperature in the vertical washing-apparatus; 7.5 litres of propylene mixed with steam were passed in 4 hours through sulphurie acid of 55 °/, H,SO, at 140°. The distillate contained 0.25 gr. isopropyl alcohol, After dilution with water a distillate was obtained from the acid in which 0.27 gr. of isopropylaleohol ') was present. There was, therefore, evidently still isopropylsulphuric acid present in the acid. In all 2.6°/, of the total quantity of propylene was, accordingly, obtained as isopropyl alcohol. A much greater part of the propylene was, however, decomposed. Separation of carbon took place and formation of sulphur-dioxide. After the experiment 5,3 litres of the 7,5 litres of propylene was found back. Hence 9°/, of the consumed quantity of propylene was changed into isopropyl alcohol. An experiment with sulphuric acid of 45°/, H,SO, and at 125 —130° proceeded in the same way; 6 litres of propylene were passed through, 5 litres of them were obtained after the experiment. The yield of isopropyl! alcohol amounted to 0,2 gramme in the distillate and 0.1 gramme in the acid liquid, together 0,30. gr. Le. 10°/, of the consumed propylene. Here too a large part of the consumed propylene was carbonised. It therefore, appears from these experiments that the bydration of propylene by hot diluted sulphuric acid is possible. The reaction velocity, however, is small, which renders the yield small. Besides the sulphuric acid has a decomposing action on the propylene. If on the other hand the experiment is made with concentrated sul- phurie acid at low temperature, the propylene is quickly attacked, but chiefly transformed into condensation products. We have tried therefore the action of other acids. We first investigated the action of benzene sulphonic acid. 6 litres of pro- pylene with steam were passed through a concentrated solution of benzene sulphonic acid; in the aqueous distillate of this expe- riment we found 0,25 gr. isopropyl alcohol or about 1'/,°/, of the propylene. Hence in this case too the reaction proceeds slowly. 1) The analysis took place by oxidation to acetone, and colorimetric deter- mination of this substance. 328 The result of the experiments on the action of acids on ethylene and propylene can, therefore, be summarized as follows: It is pos- sible to obtain ethyl alcohol, resp. isopropyl! aleohol by one opera- tion from ethylene and propylene by means of mixtures of sulphuric acid and water at 130—150°. In this reactions the alkylsulphuric acids are probably formed as intermediate products. The yield of alcohols is, however, very small, and particularly with propylene, the hydro-carbon is decomposed in another way during the experiment. These investigations are being continued. Physics. — “The relation between the widening and the mutual mfluence of dispersion lines in the spectrum of the sun’s limb.” By Prof. W. H. Junius and Dr. M. Minnaekrr. (Communicated at the meeting of April 28, 1923). Introduction. The hypothesis that the darkness of Fraunhofer lines is mainly an effect of anomalous dispersion enables one to explain, at any rate qualitatively, a great many characteristics of the solar spectrum. It thus appears possible to formulate a theoretical connection — which has then of course to be verified quantitatively — between numerous phenomena that are less easily seen as inter-dependent if we consider them from the point of view of the unmodified classical absorption theory introduced by Krircnnorr. Such phenomena are e.g.: the general displacement of the solar lines towards the red, differing greatly in amount from line to line; the limb-centre dis- placements and their dependence on intensity and wave-lenght; the widening and the change of intensity of the lines as the limb is approached; the apparent mutual repulsion of neighbouring Fraun- hofer lines, generally greater at the limb than in the centre of the disk; the systematically curved shape of the lines of the spot- spectrum if the slit cuts the spot in a direction passing through the centre of the disk; the gradual increase of the distance between the components of the bright calcium lines H, and K, as the limb is approached; and varjous particulars of a more local character. We shall endeavour to express mathematically the connection which, according to the dispersion theory, should exist between a few of the above-mentioned phenomena, and then to investigate how far these quantitative relations agree with the results of measure- ments made on solar lines. It is evident that the absolute magnitude of the influence exercised by anomalous dispersion in the solar gases on the aspect of Fraun- hofer lines cannot be calculated directly so long as the refracting and scattering power of the sun is not otherwise known. Neither can this power be safely computed starting from line displacements only. It must be remembered, however, that a similar uncertainty prevails regarding the values given for temperatures, pressures, radial velocities, intensities of magnetic or electric fields, or grades of dissociation in the sun in so far as such values are derived from 330 spectral phenomena; in fact, such statements are always based on the doubtful assumption that the observed spectral phenomena are entirely due to the causes mentioned. There is, of course, no objection to introducing this assumption, — provided its hypothetical character be always kept in mind. With equal justification we may assume that Fraunhofer lines are mainly “dispersion lines”; the essential point will then be to examine whether the deductions from this hypothesis result in an adequate theory, covering a substantial proportion of observational data. In this paper we confine ourselves to showing that the dis- persion theory of the solar spectrum connects quantitatively two at first sight independent groups of observed phenomena, namely the well-established general widening of the Fraunhofer lines at the limb, and the increase, also at the limb, of the mutual influence of neighbouring lines. This relation proves to be independent of the unknown laws that govern the weakening of any given kind of light on its way through the solar gases; it enables us to indicate an upper limit of the mutual influence that may be expected, thus lending fresh support to our fundamental hypothesis. It will be shown, indeed, that the average value of the mutual influence as deduced from the dispersion theory is perfectly consistent with the actual observations. The dispersion lines which, according to our hypothesis, envelop the exceedingly narrow‘) true absorption lines of the solar spectrum arise from two dimming processes, viz.: irregular refraction and molecular scattering. For although light of any wave-length is sub- ject to refraction and scattering on its long way through selectively absorbing gases, it is well known that these causes of darkening specially affect waves in the immediate vicinity of absorption lines. As the two processes weaken the transmitted light according to different laws, we shall treat them separately. [. ON THE WEAKENING OF LIGHT IN PASSING THROUGH EXTENSIVE MASSES OF GAS. $ 1. Spreading of light by irregular ray-curving in a mixture of gases. Suppose we have in a given space a mixture of gases which, if they were each of them alone to fill the space, would show the absolute refractive indices 7,, n,.... ni... then, according to ex- 1) Our assumption that real absorption is restricted to very small ranges of wave-lengths is in harmony with views recently derived from the quantum theory by N. Bour (Zeitschr. f. Physik 13, 162, 1923). 331 periments of Biot and Araco (confirmed by modern observations), the refracting power of the mixture equals the sum of the refracting powers of the constituents: - n—1= 2 (n;—1). The condition is implied that the gases do not act on each other. We shall assume this law to be valid also in those spectral regions where one of the constituents causes anomalous dispersion, although no very accurate direct measurements concerning such cases are as yet available. (The exceedingly narrow regions of true absorption are not considered here). If the gaseous mass is very extensive and of unequal optical density, with irregular gradients in all directions, it will make every beam of light spread out like a bunch of feathers. According to ORNSTEIN and Zwrnicke') the rate of this kind of scattering is determined by ‘the average square of the spreading per unit of length” = to any short path / corresponds an angle « depending on the average value of the irregular density gradients, and proportional to n—1 of the mixture. The weakening of the transmitted light will therefore be a function of Se FG =1) ED en ie an) that has the property of increasing and decreasing with this quantity. A characteristic difference between scattering by irregular refraction, and molecular scattering, is, that in the latter process a considerable part of each beam passes straight, and a small part of it disperses in all directions, whereas in refractional scattering every beam itself widens like a plume. § 2. Scattering of light by the molecules of a gaseous mixture. If a beam of light of intensity /, has travelled a distance z through a medium containing iV scattering particles per cube cm, its intensity has diminished to / = /,e—"*, where, according to Ray.rieH, A has the value 32 2? (v—1)? ERE ZK In this expression v is explicitly stated to represent the refractive index of the medium as modified by the scattering particles against the unmodified medium’). Denoting the absolute index of the latter h 1) ORNSTEIN and ZERNICKE, These Proceedings, Vol. 21, p. 115 (1917). 4) RAyreiGH, Phil. Mag. 47, 375, 1899. — Scientific Papers IV, 400. 22 Proceedings Royal Acad. Amsterdam. Vol. XXVI. 332 by n, the absolute index of the modified medium by n', we have n' 2 32 n° | —-—1 n 3227 (n'—n)? 322° (n'—n)? SENS dear Ed me 3 At . hi because for thin gases we may put n?= 1. We shall take for granted that this expression for A remains valid in those regions of the spectrum where the scattering particles produce anomalous dispersion. It is precisely in those regions that h will assume considerable values. Now suppose there be a mixture consisting of N,, N,,...Nj,... scattering particles of the kinds 1,2,...7,... For each kind the mixture of the remaining kinds forms the “unmodified medium”, whilst the ‘modified medium” is the same in all cases, viz. the complete mixture. We are concerned, therefore, with a single quantity n' and several values m1), %2),..-7@,... Of n, if ng denotes the absolute refractive index of the mixture without the constituent 2. The scattering-coefficient 2 of the complete mixture will be the sum of the scattering-coefficients peculiar to the separate constituents, each in its proper medium: sant s (n'—n()” 3 13 N; This expression may be simplified because the above-mentioned law of Bror and AraGo requires, that n'—1 = (no)—l) + (n;—1) n; representing the absolute refractive index which the gas 7 would show if it were alone in the given space. We, therefore, have n'—nq) = nj—1, and may write: 32 2* _ (nj—1)? — = DE ° B Ni A beam of light, having travelled a long way through such a mixture of gases, will emerge with a loss of intensity expressible as a certain function of h which has the property of increasing and decreasing with 4. In regions of the spectrum sufficiently small to permit of neglecting the change of 2* in them, we see that now (n;—1)? Fait ae Market cana aie v is the variable quantity determining the loss of light. (Compare this expression (2) with the corresponding one (1) which applies to refractional scattering). kh, + hd... = 333 § 3. How anomalous refraction and anomalous scattering act in producing dispersion lines. It appears from the above remarks that the distribution of the intensity in a dispersion line is determined by two darkening laws which, it is true, depend on local circumstances (dimensions and shape of the source of light, condition of the medium, etc), and to that extent are unknown, but which we do know will change with wave-length in accordance with the functions (1) and (2). We shall first deal with the share which irregular refraction, and there- after with the share which molecular scattering has in the formation of dispersion lines. A. Imaginary pure refraction Lines. Imagine a selectively absorbing gaseous mixture, lacking the faculty of molecular scattering, but with many irregular gradients of density; let a beam of white light travel through that medium, and attention be confined to a small part of the spectrum where only one characteristic frequency, i.e. one ideally sharp absorption line, is in evidence. If the said line were absent, the mixture would, in this narrow range of wave-lenghts, show a refracting power n,—1 varying only very slowly with A, but to this will now be added the anomalous refracting power n,—1 of the constituent producing the absorption line, thus determining the resultant refracting power: n— 1 =(n, — 1)+ (n, — 1). The term (n,—-1) will, as a rule, preserve the same (generally positive) sign throughout the region considered, whereas (n,—1) is negative on the violet side of the line, positive on the red side. Light on the violet side of a line will be called V-light, on the red side f-light. All effects of refraction in a gaseous mixture are, therefore, on an average greater for R-light than for V-light, because they depend on (n—1)? or on the absolute value of n—41, i.e. on | (n‚—1) == (n,—1) |. Fig. la shows the course of n,—1 and n,—1 each separately ; Fig. 2a gives n—1 = (n,—1) + (n,—1); in Fig. 3a is represented the course of /n—1) = |(n,—1)-+ (n,—1)| which determines the distribution of the light in our “refraction line”. The sharp absorption line will thus be enveloped in an asymme- tric refraction line, whose “centre of gravity” is displaced towards the red if m,—1 has the positive sign. (The general displacement of the Fraunhofer lines towards the 22* 334 red, which increases on approaching the sun’s limb, may be con- sidered in connection with these inferences). Let us now imagine our small spectral region to contain two neighbouring sharp absorption lines, then we have n—l = (n,—1) + (n,—1) + (n,—1), where n,—1 is again assumed to be nearly constant, and the other two terms are strongly variable with A. In the region between the lines, (n,—1) and (n,—1) have opposite signs (cf. Fig. 1,6, where the three terms are represented separately). The resultant »—1 = / (A) Fig la Fig 16 ek = 0 Fig 2a | Fig 26 2(n,-1) Fig 3a | Fig 36 | |Z(n-1)| | 0 : Fig 4a Fig 4b expe) 0 - ~ - - — —- = Fig. la—4b. shows a point of inflexion there (Fig. 2,5); and, owing to the opposite signs of (n, —1) and (n,—1), the modulus |(m, —1)H(n,—1)+ +(n,—1)| is smaller than |(m,—1)-+ (n,—1)| in the left section, and smaller than \(n,—1) + (m,—1)) in the right section of the interval (ef. Fig. 3,5), so that on the two sides of the refraction lines that face each other the weakening of the light is less than it would be if the lines stood wide apart. The “centres of gravity” _ of two neighbouring refraction lines are, therefore, a little more 335 distant from each other than their cores, i.e. the true absorption lines: we observe an apparent repulsion. In Fig. 3 we see, moreover, that on the violet side of each line there appears a point where n—1=0. (If n,—1 were negative, such a point would be found on the red side of the line). Light of the corresponding wave-length would not be weakened by irregular refraction and should, therefore, show an intensity in the spectrum, surpassing the average intensity of regions clear from lines. JEWELL’) seems indeed to have observed casually such phenomena in the solar spectrum. It is not surprising, however, that similar places of greater brillancy are not very conspicuous there; for we can scarcely doubt that in the sun the proportion of the components of the mixture varies with depth, so that the values of 2 for which n—1i =O will not be the same on the entire paths of the beams. Moreover, the Fraunhofer lines are partly due to molecular scat- tering, and it will presently be shown that this process does not involve the appearance of such narrow regions of greater brillancy in the spectrum (at least not in the central parts of the solar disk). Both circumstances tend to obliterate the brighter places near refrac- tion lines. B. Imaginary pure scattering-lines. Now suppose the density of a gaseous mixture to be so uniform, that rays of light pass through it in straight lines, then the true absorption lines will yet be enveloped into dispersion lines, because for kinds of light belonging to the nearest environment of the distinctive frequenties the coefficient of molecular scattering has greater values. Let us analyse, indeed, how 32 n° _ (nj—1)? 3 A Ni varies with 2 in a narrow spectral region containing a single absorp- tion line of the constitnent 7. All terms of the sum but one may there be treated as constants, so that Sarma (ri 1): 344 N; This quantity varies with 2 in the manner represented in Fig. 4,0; the curve is symmetrical with respect to the absorption line, provided that the dispersion curve associated with the line has the regular D= Sl 1) Jewett, Astroph. Journ. III, 99, 1896. Cf. also: ABBor, The Sun, p. 115, where analogous observations of EVERSHED are mentioned in addition. 336 shape, and that the change of 2* in the small region may be neglected. The distribution of the light in the scattering line will then also be symmetrical; this we may infer without knowing the exact form of the law of darkening’). In contrast to what characterizes pure refraction lines, the sym- metry of pure scattering lines is not disturbed by the addition of a similar cause of weakening that is constant in the region considered. (The above expressions (1) and (2) explain this difference). Anomalous molecular scattering, or diffusion of light, cannot therefore have any share in the production of the general displace- ments of the solar lines towards the red’). Let us now consider the case that our small spectral region contains two absorption lines. The scattering coefficient will then take the form EN [es | | N; Nk ; 3220? 2 for we may replace the factor Or by the constant quantity p. Fig. 46 represents / as a function of 4. To this will correspond a darkening curve whose ordinates grow and decline with h. We see that in the interval between the absorption lines the superposition of their individual scattering effects must produce a greater increase of the darkening than outside the pair; so the centres of gravity of the two diffusion-lines will be a little less distant from each other than the absorption lines proper (apparent attraction). Summarizing the above qualitative results with a view to their application in the spectroscopy of celestial bodies, we may state: 1. The general but very unequal displacements of the Fraunhofer- lines towards the red can be explained by the properties of refraction lines, but not by those of diffusion lines. This also applies to the limb-centre displacements. 2. The mutual influence of neighbouring Fraunhofer lines, which increases, as a rule, from the centre towards the limb of the solar disk, may be the result of either scattering process; but irregular refraction causes apparent repulsion, molecular diffusion of light gives apparent attraction. 1) The Jaw of darkening through molecular scattering in the sun has been amply studied by J. SPIJKERBOER in a dissertation, published in Utrecht, 1917; cf also Arch. néerl. IIT A, 5, p. 1—115, 1918. 8) To this point our attention has first been drawn in a conversation with EINSTEIN. 337 Il. THE RELATION BETWEEN WIDTH AND MUTUAL INFLUENCE IN DISPERSION LINES AND IN FRAUNHOFER LINES. In this chapter formulae will be deduced expressing the connection between mutual influence and width of dispersion lines. If Fraunhofer lines are in the main dispersion lines, it will thus be possible, starting from data concerning the widening of the lines in the spectrum of the sun’s limb, to derive values for the probable increase of the mutual influence in passing from the centre to the limb. We may then compare these theoretical results with the data obtained from observations regarding limb-centre displacements of Fraunhofer lines. The respective shares which irregular refraction and molecular scattering may have in the production of the lines will again be treated separately. § 1. Refraction lines in the spectrum of the centre of the solar disk. The distribution of the luminosity in a refraction line depends on the values of |n—1|/— f(/). We owe to Roscupestwensky !) the most accurate measurements concerning the form of this function. He found that in region of the two yellow sodium lines SELLMEIER’s formula: an a,’ =1= Ns AEEA NE (dl : PLR wae ee Ne, represents the observations almost exactly. We shall suppose this formula to be applicable to the cases we are considering. If the difference between 2, and 2, is rather considerable and if we only pay attention to the surroundings of one of the lines, we may unite the latter two terms of (1) into a single, nearly constant refracting power (n,—1), and moreover put À + A4,—24. The ; fn One : C expression thus simplifies itself, if we write / for —, to: k valde Sia Bae DA ee (2) D= The intensity at any place in the spectrum depends on the absolute value |n—1|. On either side of the absorption line we mark the values of 4 where n—1 — + H (ef. Fig. 5), H being provisionally an arbitrary constant. These places in the spectrum will be called the ‘“‘H-boundaries” of the dispersion line; their distance (to be 1) RoscHDESTWENSKY, Anomale Dispersion im Natriumdampf. Ann. d. Phys. 39, 307, 1912. 338 indicated by 5) is the “H-width” of the line. So B signifies the width an observer would assign to the line if he estimated its Fig. 5a—6b. boundaries to be situated at the wave-lengths where the relative intensity has the value corresponding to H. (By “relative intensity” we understand the proportion between the intensity at the selected point of the dispersion line and the intensity in the surrounding continuous spectrum). Suppose the ““H-boundaries” of the line to be situated at ap and Ay, then we obtain from equation (2); k k pa Ay, = . AEs H—(n,—1) Be om A+ (n,— — Dj ED Re 4 Sc) eh gmeriae Os is or, inversely, expressing H in B, Hee Ey erm We may leave the negative value of the radical out of account. Now proceeding to the case of two neighbouring equally strong lines, we prefer to indicate the places in the spectrum by the quantity (SA (ef. Fig. 5,5) in which 2 represents the wave-length corresponding to the point halfway between the two absorption lines, so that this 339 middle-point becomes the zero in our scale of l-valnes. If the distance between the lines is 2A, we have in the new notation: 1, =A for the line on the red side, /, —— A for the line on the violet side, and we get, in analogy with (2), the relation n—1l= Ke + ‘ lln N nk ses et clas (8) Eh TE : For each of the lines we may again define two ‘/7-boundaries”, to be found by taking (6) equal to + H, wherein H has the value fixed by the relation (5). We consider the red-facing line of the pair. Its H-boundaries Ir and /y are found by substituting in (6) H for n—1, /r or ly for 7. We thus obtain, according as the + sign or the — sign is chosen: k ee BELT + H— (n,—!) 1 We H—(n,—))7? b Seana Raton B or Sy+Ty. (0) Similarly it follows, that the violet-facing component of our pair has for its H-boundaries Ue OF TENOR 1595p OP Ta TR (a) § 2. Refraction lines in the spectrum of the limb of the solar disk. Seen in the light of the dispersion theory, the widening of the Fraunhofer lines in the spectrum of the limb is due to the fact, that near the limb smaller values + H’ of n—1 are already suffi- cient for producing the same relative darkening, which in the central parts of the disk is only produced by the greater values + H. The H’-width, shown by the line at the limb, will be called B’. As a counterpart of (5) we now obtain the relation se al 1)? 8 gn Rat Mee 12h either (8) and, in the case of two limb-lines, as counterparts of (7) and (7a): k k: WENO we BOS pc 1 Ror’; EG a EH RAR or Sy LT’ (9) IR or LIS RET ER OF STE Jeg, (9a) $ 3. Theoretical possibility of a general solution of our problem. In principle, the formulae (5), (7), (8), and (9) embody a rather complete answer to the question how, on the basis of the dispersion 340 theory, the widening of the lines near the limb and the increase of their mutual influence must be connected. Indeed, if the distribu- tion of the relative intensity were established both for an isolated refraction line of the centre type and for the corresponding limb line, it would now be possible to plot the curve giving the distribu- tion of the light in a set of two neighbouring equal lines, and to examine how the asymmetry in it increases when passing from the centre to the limb of the disk. It would only be necessary to sub- stitute for B and B’ the values corresponding to relative intensities 0,9, 0,8, 0,7 ete., and then to calculate from (7) and (9) where the places of equal intensity ought to be found in the pair. *) For the present, however, the intensity curves are not sufficiently known; the observers of the solar spectrum provide us with the “visual widths” and the wave-lengths of the “centres of gravity” of the lines, quantities by no means free from subjectivity. Nevertheless we can draw from such observations some useful inferences concerning our problem. § 4. Limitation to what may be derived from already existing data. The average widening in the limb-spectrum of lines whose widths lie between 0,07 and 0,16 A was found by FaBry and Buisson *) to be 0,01 A. Although we do not know the exact value of the relative intensity at the places where their interference method made them estimate the “boundaries” of the line, there was yet in this way assigned a definite width to each line. (We have some reason to think that in the ordinary visual estimates of the width of a dark line the relative intensity at the borders is about 0,8. This statement reposes on extrapolation of an empirical formula by which, in an earlier investigation, we were able to represent the visual boundaries of bright lines on the photographie plate. Cf. Ann. d. Phys., 71, 59, 1923). Whilst under the influence of a neighbouring line these boundaries shift asymmetrically, the central parts of the dispersion line, with 1) If limb- and centre-lines have been photographed on one and the same plate (the centre spectra with shorter exposition so as to make the intensity of clear spaces equal in both centre and limbspectra) it is even possible to use the transparency values of the single lines directly for computing, by means of our formulae, the course of the transparency in pairs of lines occuring on the same plate. It is unnecessary then, first to translate the degrees of blackening into original intensities. 2) FABRY and Buisson, CG. R. 148, 1741, (1909); Astroph. Journ. 31, 97, (1910). 341 their greater darkness remain almost stationary. The point midway between the boundaries will, therefore, by its position depict all asymmetrical distortions of the dispersion line somewhat exaggerated in comparison with the “centre of gravity” instinctively used by the observer to identify the place of the line. If, therefore, we calculate the displacements of that midway point, we are sure to find upper limits for the displacements which, according to the dispersion theory, may be expected as the result of measurements. $ 5. The difference in mutual influence of refraction lines at the limb and in the centre of the disk. It is easily seen that the midway point Mp between the H- boundaries of the red-facing displaced refraction line is determined by the absciss ly =|, ((r+lv)='/,\Sr+Sv+Tr+Tyv) in the centre-spectrum, and by (10) Uy="/,Urtly='/,(Srt+tSv+T'r-+T'y) in the limb-spectrum, so that the amount of its displacement, when passing from centre to limb, is: Uu—ly="/, (S'r + S'y—Sae—Sy + T'r+ T'y-Tr—Ty)- (11) This expression contains side by side all the various systematic displacements of Fraunhofer lines which the dispersion theory fore- sees as consequences of irregular ray-curving. The first two terms give the general displacement of limb-lines against arc-lines; the third and fourth the general displacement of centre-lines against arc-lines*); the fifth and sixth term show the apparent repulsion of neighbouring lines in the limb-spectrum; the seventh and eighth the apparent repulsion in the centre-spectrum. At present we are especially interested in the increase which the apparent repulsions must undergo when passing from the centre to the limb, because we are in possession of a good many observational data concerning this phenomenon ’). For each component of a pair the said increase is represented by : TE lo! RL) which expression, after substituting the quantities determined by (9), (8), (7) and (5), becomes 1) Here are, of course, not included those displacements which the core-lines or true absorption lines may perhaps be subjected to as a result of radial velocities, pressure, or fields of force. Such displacements will simply have to be added to the phenomena we are considering. 8) Cf.: W. H. Junius, Mutual Influence etc., Astroph. Journ. 54, 92, 1921, and W. H. Junius and M. Minnaert, Ann. d Phys. 71, 50, Kayser-Festheft, 1923. 342 B : Ny 1 A? | 2 de (n,—1)?B? (n,—1)B Egt | E Be Wipers we | I A? a AE (4,--1)'B* | (n,— DB TB Ft Bt | (12) 1 4 ABN) Hey Gree n —1)B |? B ele _ 2 | pil a) > Ee n,—1)B 13%: Ve en ef | In order to estimate the numerical value of this expression we base ourselves on the result of observations of FaBry and Buisson, who found the widening at the limb to be approximately 0,010 A with lines varying from 0,07 to 0,16 A in width (mean width 0,11 A). The mean width of those other lines, taken from the observational materiai of Mount Wilson and Kodaikanal concerning limb-centre displacements, for which the existence of mutual influence has been stated *) by us in the above mentioned papers, amounts to 0,09 A. Taking these data into consideration, we have calculated the value of the expression (12) after substituting 6 — 0,100 A, B=B=O0010 A, (n,—1)B and, in succession, mp — tropes A tan du Om ihe Mesut 2A have then been plotted as ordinates against abscisses B (which, therefore, represent distances of the lines expressed in their width as unit). We so obtained the full drawn curves of Fig. 7 (p. 346). They represent (for a refraction line) by how many thousandth parts of an Ängström unit the middle point M'j between the boundaries of a limb-line is shifted in excess of the middle point My between the boundaries of the corresponding centre-line, in consequence of the presence of an equally strong neighbouring line, if this is situated at a distance equal to 3, 2, 1 times the estimated width of the lines. [t will be seen that the repulsion is already perceptible at a 1) W. H. Juus, Astroph. Journ. 54, 92, (1921); W. H. Junius and M. Minnaert, Ann. d. Phys. 71, 50, Kayser-Festheft, 1923. 343 rather great distance, and increases slowly to 0,004 A maximum. Obviously the value of nm, has only little influence on the result. As B' differs little from B, the radical quantities of (12) can be developed into rapidly converging series. It will then appear that as a first approximation the repulsion is proportional to the absolute value of the widening at the limb, ie. to B'—B, Accordingly, our curves are also valid for lines differing in width from those here considered, provided their widening at the limb has the value found by Fasry and Buisson. They are therefore applicable to the case of lines having the average type of those for which mutual influence has been observed. § 6. Diffusion-lines in the spectrum of the centre of the solar disk. The distribution of the intensity in a pure molecular scattering line (in the absence of irregular gradients of optical density) depends on the manner in which the scattering coefficient (cf. p. 335): 322" (nj;—1)? PN varies with À in the surrounding small part of the spectrum. And because even the variation of A‘ may be neglected there, the distri- bution is entirely governed by the nature of (ie) ERE NET MAO a function, obviously symmetrical with respect to the position of the absorption line. On either side of the latter we may again 2 mark a wave-length where (omitting the index 7) ae equals a certain — provisionally arbitrary — quantity L*. By these places in the spectrum we define the ‘‘Z-boundaries’, and by their distance the “L-width” of the diffusion line (Cf. Fig. 6, on p. 338). We now introduce the dispersion formula (2) of p. 337 and confine our attention to the case that there is only one single ab- sorption line, so that we may write k ape h=C+ n—1 = (13) Our two L-boundaries will be found by substituting in this equation n—1=+ LVN and À=dr or =Ay, which leads to k - k ARA pai, == ale na Aerin (412-5 R 1 LYN en | 1 LVN ( ) and makes the L-width of the diffusion line equal to from which follows Lan ns Pulte iaie Wi In case we are dealing with two neighbouring lines of equal +2 k strength (na is: equal value of Fr) at distance 2A from each other, it is convenient to indicate all places in the spectrum (like we did on p. 338) by a new system of abscisses: l=1—iy ee ee en. (10) Am representing the wave-length of the point midway between the absorption lines, where we place the zero of our scale of /-values. The abscisses of the two absorption lines are now — A and + 4. According to the equation = +h; of p. 335, and considering the smallness of the selected spectral region, the distribution of the (n,—1) rm (n,—1)? light in it will entirely depend on the quantity N, NS as a function of 4 or of /. Applying (13) and (16) we find (n,—1)* (Ae k,* k,” hk hk” 7 = = AT () 3 AT, ES = T P a5 7 (17) N, Ne). NOAR Naa) CLA NUE The ZL-boundaries of each of the components of the pair are k . Let us iN obtained by making (17) equal to L’ or, after (15), to consider the red-facing component. Its L-boundaries are situated at =/p and /=/y, and can be deduced from (17). According as the + or the — sign is taken, we obtain B 44? lr votives DAE el nod ars vnd a (USE The two negative values of the same radical quantities represent lr and ly of the violet-facing component of the pair. § 7. Diffusion lines in the spectrum of the limb of the solar disk. (n—1)* At the limb a smaller value £/* of — Fai will suffice to bring about the same degree of darkening that ZL? gave in the centre. The ‘Z'-boundaries’” determine a width B' through the relation 2k EEA in analogy with (15). We thus find for the borders 345 of the components of our pair of limb-lines nisi A sier os MOLEN § 8. The difference in mutual influence of diffusion lines at the limb and in the centre of the disk. In conformity with our procedure with the refraction lines, we are now going to determine also in the case of pure diffusion lines an upper limit for the apparent displacements which the components of a pair impart to each other. We therefore consider the point My, midway between the L-boundaries of one of the lines, defined by the absciss lu ='/, lr + ly) and will only have to compute how much this value differs from + A. But we are especially interested in the difference between the apparent displacements of a component in the limb-speetrum and of the same line in the centre-spectrum, i.e. in the quantity Uum lu=!/, UR + lv —lr—lyp). for which we find, after substituting (18) and (19), ee: ee Vi ABE UM — = — == = = ==: == Mg | B: sl B ait B B dT B 5 a sare AA =a Soa ld a BR (20) The numerical value of this expression has been calculated for four different widths of the lines, namely B — 0,050, 0,070, 0,100 and 0,200 A. We took B’ always to be = B+0,010 A, and 2 selected a number of distances A so as to have values of Be (as abscisses) suitably situated for plotting curves. The dotted curves in Fig. 7 show the result. All ordinates should be imagined negatwe, because in this case there proves to be an apparent attraction of the components. We notice that the effect is 346 less than 0,001 A so long as the distance exceeds twice the width of a line. On closer approach the lines rapidly grow very asym- 0010 A | \ L \ n ee Ie EEn Zn | B=q200 A AFSTOOTING BIJ BREKINGSLIJNEN | _--- AANTREKKING BIJ | VERSTROOIINGSLIJNEN | 4 : | \ B-qroo A iy 1 fi dt 4 i if LN 1 a | | | B-g070 A 4 Mise 0005 A i] i ki i Bret) _ eh sat, - 0 (B-0,050 A 5 & \ 2A=1B =2B metric; at distances smaller than about 1,5 times the width, the second term of (20) becomes imaginary and the formula impracticable. $ 9. Comparison of the theory with the results of observations on Fraunhofer lines. In the foregoing we have supposed, for simplicity’s sake, that the width of the true absorption lines could be neglected; but there are, of course, reasons for assigning a finite width to these cores of the Fraunhofer lines. Especially as far as very strong lines of the solar spectrum are concerned (which were not considered in the above), it would have been necessary, therefore, to base the calculations on a still closer approximation to the shape of the 347 dispersion curve. There is still another reason why strong lines — many of which lose their “wings” near the limb — require separate treatment, namely because for such lines, according as the limb is approached, it is indispensable to make due allowance for the spherical shape of the source of light when the consequences of diffusion, and particularly of irregular ray-curving, are inquired into. Indeed, looking almost tangentially towards the source, we are no longer allowed to assume that the darkness of the line increases 2 4 at 7 ; 5 a with — and with h, particularly not if n—1 has great values. Such l considerations suggest that in a further development of the theory it will be necessary to reckon with a different set of conditions and circumstances for different lines, especially very near the limb, where the Fraunhofer spectrum passes gradually into the chromospheric spectrum. The sharply differentiated structure visible in the chromosphere at times of excellent seeing indicates that, at least at a level only slightly outside the apparent edge of the disk, the gaseous medium must be highly transparent along the path of the nearly tangential rays, even for waves belonging to the very Fraunhofer lines. This proves that in those layers molecular scattering is unable to make the medium appear “foggy”, in other words: that anomalous irregular refraction plays a greater part there in determining the distribution of the light, than anomalous molecular scattering. We infer that probably with most Fraunhofer lines, also with the weaker ones, the darkness will depend to a greater extent on refraction than on molecular scattering — though it appears possible that the proportion between the respective influences differs from line to line. All this has to be taken in consideration when comparing our theoretical results with observational data. Fig. 7 shows the upper limits of the effects of mutual influence to be expected in the cases we discussed, if the lines were pure refraction- or pure diffusion- lines. In Fraunhofer lines the two processes are probably intermingled and the respective displacements opposed; but refraction is likely to have the advantage. We therefore may expect, e.g., if the distance between certain Fraunhofer lines lies between 1,5 and 3 times their width, that their mutual repulsion at the limb will exceed their repulsion in the centre by an amount certainly not greater than 0,002 A. Now, according to the above-mentioned observations of Mount Wilson and Kokaikanal, the examined effect has the average value 23 Proceedings Royal Acad. Amsterdam. Vol. X XVI. 348 0,00175 A, for pairs of lines whose average distance amounts to 1,7 times their mean width.’) This harmonizes, as regards order of magnitude, with the computed value. In the publication just referred to we have shown that the mutual repulsions which two equal, symmetrical lines seem to exercise on each other as a mere consequence of systematic (photographical or psychological) errors of measurement, only become appreciable when the distance between the lines sinks below 1,5 times their width, and that, therefore, only a fraction of the mutual influence observed with Fraunhofer lines, can be ascribed to such errors. The theoretical anticipation here advanced thus proves to be consistent with the observational material till now available; but for the present our conclusion cannot go beyond this, because the quantities involved in this investigation are near the limit of preci- sion attainable with existing means for measurement in the solar spectrum. Utrecht, April 1923. Heliophysical Institute. ') Cf. our article „Kritisches zu Deutungen des Sonnenspektrums”, Ann. d. Phys. 71, p. 50, 1923. Botany. — “Cytological investigations on Apogamy in some elemen- tary species of Erophila verna”’. By J. P. Bannter. (Commu- nicated by Prof. F. A. F. C. Went). (Communicated at the meeting of March 24, 1923). After Jorpas, in 1823 *), made his well-known communications concerning the constancy of the elementary species, and in particular those of Hrophila verna, this highly polymorphie species became not merely the classic type of absolute constancy of the elementary species, but also the subject of much experimental research. The best known work on this subject is that of Rosen on the formation of new sub-species by cross-fertilization. According to this writer the hybrids do not conform to the laws of Menper, but, after having formed a very heterogeneous F, remain constant in the F, and following generations *). The explanation of this can only be found by cytological research, accompanied by repeated efforts at hybridization. The investigations, the principal results of which so far obtained are given here below, were prompted by similar attempts at hybri- dization, carried out by Dr. J. P. Lorsy between two elementary species found near Bennebroek, and further cultivated constant by him, which, as they could not be identified with absolute certainty with any previously described sub-species, were christened Hrophila eochleoides and Erophila violaceo-petiolata. These experiments, however, were unsuccessful in so far as no hybrids resulted from a cross- fertilization, but all the offspring were like the mother plant, and remained constant in following generations. One plant only, at first regarded as a hybrid, was a very fine intermediary between the two aforesaid sub-species, but further cytological examination proved that it could not be a hybrid result of the applied cross-fertilization. The following generations of this 1) Arexis JoRDAN. Remarques sur le fait de l'existence en société, a l'état sauvage, des espèces végétales affines et sur autres faits relatifs à la question de espèce. Bull. Ass. franc. Avance. des Sciences Lyon 1873. 5) Ferix Rosen. Die Entstehung der elementaren Arten von Erophila verna. Beitr. z. Biol. d. Pfl. 1911. Bnd. X, p. 379—421. 23% 350 plant were perfectly constant. They all possessed quite the habitus of the intermediary form. That the plant in question cannot be a true hybrid, but had probably arisen from a seed of another ele- mentary species which cannot be discussed here, was however, only demonstrated with certainty by the examination of the generative nuclei. My thanks are due to Dr. Lorsy who, in the spring of 1921, gave me part of his material for the purpose of repeating the ex- periment of cross-fertilization, further cultivation of the plants, and cytological examination to ascertain the cause of the constancy. My own experiments in cross-fertilization also yielded only plants which were the same as the mother plant. The cultures of E. coch- leoides and of E. violaceo-petiolata, as well as those of the inter- mediate form which was first taken to be a hybrid, but which, since it appears that this is not the case, I will now term Zrophila confertifolia on account of its extremely close roset of leaves, remained perfectly constant in the years 1922 and 19237). The results of the attempts at eross-fertilization soon suggested to Dr. Lorsy the possi- bility of apomixy. This would not agree with the results obtained by Rosen, but if correct it might explain why his Hrophila’s remained constant in the F,. The following notes upon the results | obtained will prove that the supposition of apomixy was correct and that apogamy ’) played a part in the affair. As regards the methods, it must be remarked that the best pre- parations were obtained by fixing with chloroform-alcohol-acetie acid after Carnoy. The sections, after being imbedded into paraffin, were made with a ReinsoLnp-Ginray microtome to a thickness of 5 u. The colouring was done with HeIDENHAIN's haematoxylin. Like all elementary Mrophila species hitherto described, which were found together at the same place, the sub-species here treated exhibit, besides points of great difference, also a great similarity, which a very close systematic relation suggests. K. cochleoides is the smallest of the three, possesses short spatulate leaves, slightly narrower towards the base and only in the older stadia showing a shallow denticulation. The stalks are strong but not of great length. On the other hand £. confertifolia possesses longer and softer stalks 1) Although the plants have not yet flowered, the constancy can be proved with a fair degree of constancy from the young rosets. 3) ,Apogamy”’ is employed here in the definition of STRASBURGER, i.e. develop- ment of an unfertilazed diploide ovule; according to WINKLER this is a question of somatic parthenogenesis. 351 and its very close roset has larger leaves with a fairly broad base and which exhibit several deep dentata, while in /. violaceo-petio- lata all three characteristics are much more pronounced. Also the flower differs in form in the three subspecies. The cytological examination in the first place brought to light that the nuclei are extremely small; in young cells in rest they are but 24—34 u. Fig. 1—4. 1 Vegetative equatorial-plate before the division of Erophila cochleoides. 2 Idem of E. confertifolia. 3 Vegetative prophase of EF. violacea-petiolata ; 4 Segmentation of the chromosomes in a vegetative cell of HL. violaceo-petiolata n. = nucleolus (in all the figures). Magnification 1-2-3: 2200 X; id. 4: 1100 X. Vegetative cell-divisions were studied in stem-tips, of which a cross-section is usually found in the sections through the entire inflorescence. No abnormalities are seen in the vegetative divisions of E. cochleoides and of EL. confertifolia. HE. cochleoides possesses 12 (Fig. 1), EF. confertifolia 24 chromosomes (Fig. 2). They lie typi- cally in pairs, a feature which recurs in all the divisions and in 352 nearly all the stages studied. The chromosome pairs differ appreci- ably in size. The vegetative cells of /. violaceo-petiolata exhibit a peculiarity which seems to belong only to this subspecies and occurs but very rarely in the vegetable kingdom. The normal number of chromosomes (diploid) is here 12 (Fig. 3). This number, however, was very seldom found. In almost every case the numbers found were higher and invariably different, up to 100 and probably still higher. Only in distinetly early prophases could the number 12 be found with certainty, and in very late telophases, shortly before the period of rest commences, this number is again nearly reached. In this last stage the counting is a matter of great difficulty, as the nuclei are very small and the outline of the chromosomes indistinct. Finally there is a third stage in which the normal number occurs, namely, the stage of splitting and seperation of the chromosomes. Occasionally, however, the number 12 was clearly seen. In all other stages of division the chromosomes divide up into numerous chro- matie particles (Fig. 4). The longer the time is between the division stage and the resting stage, the larger is this number. How the transition from these stages and the metaphasic division-stage is accomplished could not be investigated. The formation of the embryosac takes place in all three elemen- tary species mainly in the same way. One large right-angled sub- epidermal cell immediately becomes an embryosac-mother-cell, without first forming a tapetal-cell. The embryosac grows considerably in size and the nucleus passes through a lengthy synapsis-stage. Finally it divides into two daughter-nuclei which do not divide again directly, but round off and like normal mitotic nuclei pass over into a res- ting-stage. A cell-wall is formed, and for a short time the two daughter-cells lie undivided. Then only does a second division take place in the two cells. Frequently the micropylar cell degenerates during this division; in other cases this takes place with the new- formed products from it. This division of the micropylar daughter- cell very often takes place in a transverse direction, whereas that of the chalazal daughter-cell always takes about the same direction as the first division of the embryosac-mother-cell. One of the four grand-daughter- or tetrad-cells, that is situated nearest to the chalaza, increases and becomes primary embryosac-cell. The other three tetrad- cells have usually degenerated by now and meet closely over the embryosac-cell. The development of the primary embryosac-cell to an embryosac probably takes place according to the normal plan; stages with 2 and 4 nuclei are frequently met with. The nuclei lying near the 353 micropyle in the latter stage form the egg-cell, synergidae and one of the polar nuclei. It was not possible to ascertain whether the division of the group lying towards the chalaza takes place in the normal way, as the antipodal cells degenerate very early, per- haps even during their formation. So much is certain, however, that one or more antipodal cells and a lower polar-nucleus are always formed, and the two polar nuclei speedily fuse together. The formation of pollen did not exhibit any special features in the cases under examination, but very typical tetrads are formed from the pollen-mother-cells. It was immediately seen, however, that the pollengrains which were formed were largely sterile. No division of the nucleus of a pollengrain was clearly observed, and artificial cultures of pollen were unsuccessful, although a considerable quan- tity of pollen was usually found on the ripe stigmas. From here the pollentubes penetrated to any depth only in a very few stigmas. In one single case did the pollentube reach the cavity of the ovule. Although in this way the chance of fecundation was augmented here, the ends of the pollentubes were not found in this embryosac any more then in any of the other preparations. A male nucleus was never in a single case to be found in this embryosac; the egg- cell invariably remains lying alone and after some time begins to enlarge of itself. Finally it begins to divide, after which the first embryo- and suspensor-cells are formed. The further development of the young embryo is quite normal. While this points to apogamy, it is only proved with absolute certainty from the behaviour of the nuclei in the embry osac-mother- cells. These commence to divide. like in so many other apogamous plants, according to the heterotypical scheme. Many synapsis- and Spireme-stages are observed. Instead of real gemini of chromosomes which totally or for the greater part fuse together, merely pseudo- diakinese-pairs are observed. The chromosomes approach each other, but remain at some distance from each other. After this the division has a homoiotypical character. Fig. 5 represents a telophase-stage of the division of the embryosac-mother-cell of K. cochleoides. In the uppermost micropylar daughter-céll the chromosomes are present in diploid number (12). The same number can also be counted in the chalazal daughter-nucleus, though less distinctly. The knife of the microtome had touched this nucleus, so that a few ends of chromo- somes are to be found in the adjoining section. The figure shows which fragments in the two cross-sections belong to each other. The telophase-stage of FE. confertifolia, which possesses vegetatively 24 chromosomes, is a still clearer and stronger proof of the apogamy, 3504 as is shown in Fig. 6. Here there are 24 chromosomes in both nuclei; they can be best counted in the micropylar nucleus. The fact, that the chromosomes after the division still lie so clearly in Fig. 5—9. 5. Daughter nuclei of the embryosac-mother-cell of ZE. cochleoides, on the left the chalazal nucleus, on the right the micropylar nucleus ; al—a?, cl—c? ete. fragments belonging to the same chromosome. 6. Idem of B. confertifolia. '7. Endosperm nucleus of 2. violaceo-petiolata. 8 One of the three sections through a pollen-mother-cell of E. violaceo-petiolata. 9. Formation of the tetrad nuclei in a reducing-division in a pollen-mother- cell of ZE. cochleoides. Magnification 5-6-8: 2200 X; id. 7: 1450 X; id 9%: 1100 X. 355 pairs, points to a very strong affinity which cannot be broken by the individual splitting. In the division of the embryosac-mother-cell and the pollen-mother- cell of the E. violaceo-petiolata we have the same phenomenon again as was also seen in vegetative cells, namely the segmentation of the chromosomes. It is remarkable, however, that here the chro- matic particles lie in pairs, as we find all the chromosomes in the two other subspecies in pseudo-gemini. Here too very large num- bers were found; approximately 50, 64, 70 and even as high as 130 or 140 were found. Fig. 8 represents such a stadium taken from a_pollen-mother-cell, which had been cut into three sections, only one of which is shown here. Nevertheless about 60 chromo- some particles can be counted. As the embryosac-mother-cell has exactly the same appearance and as here too the same phenomenon is seen directly after the division, it was impossible to find a pair of daughter nuclei with the diploid number to prove apogamy. Here, however, some very distinct endosperm-divisions lend assistance. As it was established that the polar-nuclei unite with each other in this apogamous plant also, the endosperm-nuclei must possess twice as many chromosomes as the embryosac-nuclei. Thus, to demonstrate apogamy this number would have to be 24, and that this is actu- ally the case is shown by fig. 7, which illustrates a cross-section through the middle of one spindle, looking in the direction of one of the poles. The ends of the 24 chromosomes can be clearly distinguished, while the attraction of some chromosomes by the poles can also be observed. Whereas in the divisions of the embryosac-mother-cell there is no reduction of the number of chromosomes, even though it has passed from the heterotypic phase to the homoiotypic very shortly before the division, the reducing division in the pollen-mother-cells occurs normally. During this division no peculiarity was observed in any of the cases examined other than the segmentation above-men- tioned in B. violaceo-peticlata. Fig. 9 represents 2 sections of the tetrad nuclei of a pollen-mother-cell of E. cochleoides, all of which form the reduced number of chromosomes. As has been said, however, the great majority of the pollen-grains produced from them are sterile. But even if there be fertile ones among them, they are not productive. Thus the most important conclusion arrived at was that apogamy occurs in these three elementary species of Hrophila, which explains the failure of the attempts at cross-fertilization. The experiments of Rosen have shown that not all subspecies are apogamous, or at 356 least they are not obligatory apogamous. The constancy of his new forms in the F, might find their explanation in apogamy. The intermediate hybrid formation in the F, and the singular appearance of the F, on the other band, are not explained, and in respect to this a special theory would have to be applied to explain the sudden occurrence of apogamy. Utrecht, March 1923. Botanical Laboratory. Botany. — “On the nature and origin of the cocos-pearl”. By Dr. F. W. T. Huneer. (Communicated by Prof. G. van IrERSON JR.). (Communicated at the meeting of March 24, 1923). In the endosperm cavity of the seed of Cocos nucifera a local calcareous formation is sometimes found to occur, to which the name of ‘cocos-pearl” has been given, and which must be looked upon as a highly remarkable and very rare phenomenon *). Such a cocoa-pearl has usually the form of a pear, or egg, some- times it is almost spherical and has a smooth surface, as a rule of a milky-white colour. Its chemical composition corresponds somewhat to that of the oyster-pearl, from which it differs, however, in appear- ance by the lack of the pearly sheen. Rumenius was the first to describe this caleareous formation as “calappites’ *), and for more than a century after him nothing was heard of this phenomenon, till at the Meeting of the Boston Society of Natural History on the Ist. of February 1860 ®), Mr. Frep. T. Busa presented a specimen of this cocos-pearl for chemical and micro- scopical examination. The research was entrusted to Dr. Bacon, who submitted his report on the subject at the Meeting of the same Society on 16th. May 1860 “). In 1866 Dr. Rieper, Ex-Resident of Menado, reported having found a pearl in a cocoanut he opened’). This was the first report by an eye-witness who had actually seen this phenomenon, apart from the many stories told by natives about it. Contrary to the statement of Bus to the effect that cocos-pearls “are said to be found free within the cavity of the cocoa-nut”, SkeaT’) reported in 1900 that they are “usually, if not always, found in the open eye or orifice at the base of the coeoa-nut”’. 1) F. W. T. Hunger, Cocos nucifera, 2nd Ed. pp. 243—250, Pl. LXVII (1920). *, E. Rumpuius, Herbarium Amboinense, Vol. I, pp. 21—23 (1741). Idem, D'Amboinsche Rariteitkamer, pp. 291- 292 (1741). 3) Proceedings of the Boston Soc. of Nat. Hist., Vol. VII, pp. 229 (1861). 4) Idem, Vol. VII, pp. 290—293 (1861). 5) Nature, Vol. XXXVI, pp. 157 (1887). 6) W. W. Skrar, Malay Magic, being an introduction to the folk-lore and popular religion on the Malay Peninsula, pp. 196 (1900). 358 No other data regarding this remarkable phenomenon exist, and at the present day we are still completely in the dark as to the nature and origin of such a cocos-pearl. On my last voyage to the Hast Indies for purposes of study, 1 resolved to endeavour to find out something further about the cocos- pearl and if possible solve the problem of its formation. At the same time I realised the utter futility of going to look for cocos- pearls in the Tropics on account of their extremely rare occurrence. In proof of this it may be mentioned that on a cocoa-nut estate, where approximately 3 million nuts have been opened annually for years, no such pearl has ever been found, although stories about them have led to their existence being suspected. | therefore directed my research to gathering as many authentic data as possible. On one of my voyages | met a native of British India who pos- sessed a very fine cocos-pearl. According to his own account he had seen with his own eyes this specimen inside an opened cocoa-nut which had been brought to him from Madras. He assured me solemnly that his pearl had been attached to the kernel of the cocoa-nut and exactly at the place where, in germination, the cotyledon forms a haustorium. Later on I also met with an Arab on whose cocoa-nut plantation in South Borneo a cocoa-nut had been gathered which, on being opened, proved to contain a pearl attached to the inside of it. He had dislodged the pearl from the kernel of the nut with his own hand. In this case also the pearl had been attached at exactly the same place as in the case first-mentioned. These two corroborative declarations of eye-witnesses, who had both seen a cocos-pearl still attached inside an opened cocoa-nut, furnished me with a preliminary guiding-thread and led me to sup- pose that the spot which they indicated would probably be the normal point of attachment of such a cocos-pearl. The normal germination process of the cocoa-nut begins by an enlargement of the embryo, whereby the cotyledon commences to grow inwards to an absorbing organ (haustorium), and thereby comes to protrude outside the endosperm and into the central cavity. Simultaneously with this, the plumule grows out and, breaking through the membranous operculum of the germinating pore, it pushes its way out through the hard shell. Proceeding from the provisional determination of the place of 359 attachment of the cocos-pearl, the following hypothesis could now be formed. Given that the germination, being in progress, is stopped by some cause or other, thus preventing the further development of the haustorium, it is conceivable that the haustorium in this state might become encrusted by the influence of the cocoa-nut milk, and that from this the completely petrified cocos-pearl would gradually be formed. It was now essential to find the reason for any such check in the process of germination and the accompanying solidification of the haustorium, and I wish now to submit the following remarks on this head. At the side where “the cocoa-nut has been attached to the stalk, three thin spots so-called germinating pores, or ‘eyes’, can be seen in the hard inner shell of the fruit. As a rule one of these holes, the so-called “‘porus pervius’’, is closed by a membrane, whereas the two other, the so-called ‘‘pori caeci’, are furnished with a hard tegument. In germination, the plumule pushes its way out through the porus pervius. By way of exception there may be, instead of three, two germi- nating pores, viz. one porus pervius and one porus caecus, and only very rarely will there be only a porus pervius with both pori caeci entirely absent. Nevertheless a cocoa-nut of this description can germinate in the usual way. It is a different case, however, when there is not even a porus pervius, the base of the inner shell showing no germinating pore at all, as occurs in extremely rare cases. Such a cocoa-nut is known in the Malay language as a ‘“kelapa boeta’’, or “klapa& boentet” in Javanese, which signifies a “blind cocoa-nut”’. As remarked above a cocoa-nut without germinating pores is a very great rarity, for which reason they are regarded by the Mahom- medans as sacred. The “kelapa boeta” is a talisman (tjimat) par excellence, and consequently it is very difficult to obtain a specimen. This meeting with the kelapa boeta furnished me with an instance of the way in which a normal germination is rendered impossible by nature, and I did my utmost to procure some specimens. I finally succeeded in collecting eight unopened “blind” cocoa-nuts from the Kast Indian Archipelago. Two of them came from South Borneo, one from Halmaheira, one from Ceram, one from the North of New Guinea, one from South New Guinea, one from the Arde Islands and one from the Tanimber Islands, all of which I have collected personally from these several places. 360 Most of the specimens were very old nuts; some, according to their owners, had been preserved for scores of years as family heirlooms. The first four ‘“boetas” which I opened produced nothing, but in the fifth I found a really beautiful pearl still attached to the kernel; the two next produced negative results again, and the eighth speci- men I have kept unopened. The nut which had contained the pearl, as shown in Fig. 1, had been purchased from an old native at Ritabel (Larat), one of the Tanimber Islands in the Moluceas, who informed me that it had been gathered but a short time before. This proved to have been the case, because the endosperm in it was quite normal, whereas in the other nuts the kernel was either very much dried up or had even partly become a mass of brown powder. The pearl was attached without the least trace of a stalk, being merely embedded in the endosperm (Fig. 2), and was quite easy to remove from the kernel. It lay exactly at the base of the nut, just under the spot where the germinating pores ought to have been, and thus agreed completely with the indications as given above. This discovery, in my opinion, warrants the inference that the cocos-pearl actually represents a calcified haustorium, which has been retained in the nut after the primary germination was checked, owing to the plumnle not being able to get through the shell on account of the porus pervius being lacking. As the inner shell of the kelapa boeta remains hermetically closed, the newly formed haustorium becomes encrusted under the influence of the cocoa-nut milk with calcium-salts, although it still remains unexplained why the cocos-pearl consists almost entirely of calcium carbonate, while neither the cocos-kernel nor the cocoa-nut milk contains any calcium carbonates. The belief that a Kelapa boeta invariably contains a cocos-pearl was sufficiently disproved by my experience that of seven specimens only one such formation was found in a “blind” cocoa-nut. On the other hand, it is probable, in my opinion, that it will be principally (or exclusively?) the kélapa boeta that contains the cocos-pearl. The nature and origin of the cocos-pearl as a calcareous plant germ might botanically be considered as analogous to a phe- nomenon seen in human and animal pathology in the petrifaction or mummification of the embryo, and termed Lithopaedion or Lithoterion respectively. Amsterdam, March 1923. F. W. T. HUNGER: “On the nature and origin of the cocos-pearl’’. Fig. 3. Cocos-pearl from fig. 2. nat. size. Fig. 1. Kelapa boeta Basis of a blind cocoanut, without germinating pores. : 3 nat. size. Fig. 2. Kelapa boeta Endosperm cavity with a cocos-pearl insite. 3/5 nat. size. Botany. — „The genus Coptosapelta Kortn”. (Rubiaceae). By Dr. Tu. VALETON. (Communicated by Prof. J. W. Morr). (Communicated at the meeting of April 28, 1923). § 1 In my paper on Lindeniopsis, a new sub-genus of Coptosa- pelta Kortn. (Proceedings of the Academy of Sciences of May 30, 1908) I gave a synopsis of the few species of the genus, known at that time. At my further study of the Rubiaceae of the Malay Archipelago and of New-Guinea, I again found a number of species not described at all or not in the right genus, in consequence of which this number has increased to 11. Besides it appeared from the research, that the existing diagnosis, already revised by me, could no more be applied to all species. For this reason I want to subject the chief characteristics of the genus of systematical interest to an investigation and subsequently to summarize the species known at the present time. § 2. Historical review. The genus was constituted by Kortuais (1851) on some fruiting branches of a liane, gathered by his colleague Dr. Minter on the sandy plains near Karrau (Southern and Eastern division of Borneo). He found them to belong to anew genus in the group of the Cinchoneae DecANDOLLE, of which there are but a few genera known in the Duteh Indies. As chief characteristics he considered the liane-like habit, the fruit splitting up in two cells, each of them splitting up again and the peltate seeds provided with a fringed wing, a combination of characteristics, not yet found in any genus. In naming the genus he apparently referred to the seeds. At least | think to recognise the words zonmtw, in the meaning of ,,Chopping” or „Hewing” (because of the notched wings) and szreaty shield. The significance of the connecting syllabe sa” is not clear to me. Probably the name originally ran: Coptospelta, a bad word-formation. As a specific name he used flavescens”, alluding to the yellowish tint the leaves get on drying. Korrnars’s specimen is lacking in the Dutch and Dutch-Indian Herbaria. It is not apparent either, that Mique, knew it (1856). It was however known to Hooker, when describing in 1876 a second species of the same genus, C. Grijithii Hook f. in Icones plantarum 362 tab. 1089, in which he quoted Korruats’s original and Borneo, Sumatra and Malacca as its native places. A short description of the species was afterwards given by Hooker in Hook. Flora indica ILI (1885) especially to distinguish this species from C. Grijithi. A little more detailed was Kine in Kine and GaMmBLe, Flora of the Mal. Peninsula (1903). The species however had not escaped the attention of either Warrien or Biome. The former published it in 1828 mistakenly as Stylocoryne macrophylla (= Webera macrophylla Roxs.), the latter took it for a new species of the same genus and gave a brief diagnosis of it in Brome, Bijdragen (1826), as Stylocoryne tomen- tosa, while Mique, gave a somewhat fuller description of the same species, gathered by ZorLLINGER in Tjikoja in Java (number and date unknown), in 1856 in Fl. Ind. bat.. as Stylocoryne ovata Miquer. A third species of this genus, in order of time of discovery, is the Coptosapelta Hammii (subgenus Lindeniopsis) 1 previously discussed. It was gathered by Ham in Billiton in 1907. At about the same time a fourth species was collected in the Philippine Islands and, by E. D. Merrit, described as Randia olaciformis and classed with the right genus by Ermer in 1912 (in Philippine Leaflets). A fifth species, already gathered by H. O. Forges in British New-Guinea in 1885—86, was described by Wernuam in 1917 (in Journ. of Botany). He classed it however with the genus Tarenna Garrrn. (= Styloco- ryne Wicut et Arnorr). Besides | found two Borneo species unde- - seribed in the Herbaria at Leyden and Berlin and three of New- Guinea, while finally an eleventh species was discovered, gathered bij the army surgeon JaNnowsky at the ‘“Geelvinkbaai’ in 1910. $ 3. Habit. Except the deviating species C. Hammii, above mentioned, a half-climbing shrub, all Coptosapelta-species hitherto known are lianes. To all of them the excellent description by Eimer of C. olaciformis (Phil. Leaflets V. p. 1856) is mainly appli- cable: “A looping treeclimber; stem two inches thick, very irregular, heavylooping, numerously branched toward the top and forming hanging masses; leaves coriaceous, descending, curved upon the upper deeper green surface, apex recurved; inflorescence from the longer samewhat drooping branches, erect. Of the species, gathered in German New-Guinea by LEDERMANN, is twice given “Liane mit beindickem Stamm’, once “Liane mit armdickem Stamm”. For C. Grijithii from Malacca as well as for the oldest species C. flavescens is given Liane’, to which Kune’s native collector adds: ”A handsome creeper, 30— 50 ft. high”. The 363 two species from Borneo first described here, were probably of a similar habit. Of Janowsky’s species is only said: ”10 Meters high”; the piece of branch or stem, about as thick-as a finger, gathered by him, shows a soft whitish strongly-lobed wood-cylinder with large vessels. § 4. Stem and buds. The rod-shaped twigs, as occurring in the herbaria, are nearly cylindrical (only in some species e.g. C. montana the utmost twigs are square), the nodes swollen and provided with an annular groove. As a rule only the flowering lateral and terminal branches are gathered, consequently but a few terminal buds, all of young specimens of C. flavescens and C. montana are present. These are wanting bud scales; they are formed by the two youngest leaflets, pressed together with the flat upper-surfaces, and are enclo- sed by the two rather small stipules only at the base. With the young growing twigs these very young leaflets are lanceolate and they consist more than half of a broad ” Vorlduferspitze’ rounded at the tip and certainly dark-green when alive (see RaciBorskt in Flora 1900), reminding us of Dvoscorea-species. Where there are axillary-buds, they are but a couple of mms. long, ovate, covered with long and dense hair. § 5. /ndument. All species have a coat consisting of single short appressed hairs, and long hairs lying flat but free at the top; the latter are soft, straight, colourless or rarely (in sieco) yellowish, usually thinly spread; on the young twigs and leaves, the inflore- scences and generally also the petioles, they are closer together, forming a soft, thin “tomentum”. On the full-grown leaves they are almost or totally absent in C. olaciformis, fuscescens and maluensis, where the twigs also grow bare in course of time. C. Grijithii, C. Beccarii and a hairy type of C. flavescens have a soft hairy covering, consisting of long curved hairs not close together. $ 6. Leaves: 1. Shape: In most species hitherto known, the almost exact elliptical shape of the lamina is characteristic for the average- leaf; i. e. a symmetry of the two halves with respect to the trans- verse as well as the longitudinal diameter of the leaf, apart from the frequently lengthened tip and wedge-shaped base. Hooker (1882) and Kine (1903) refer to it in their descriptions of C. Grigithii and C. flavescens, Merritn of C. olaciformis, WeRNHAM of C. hameliaeblasta. 24 Proceedings Royal Acad. Amsterdam. Vol. XXVI. 364 Of course the elliptical shape is not constant with any individual, but often passes into the ovate form or becomes oblong (in this case the symmetry is preserved), the leaf-base varies between rounded and wedge-shaped. Young plants of C. flavescens have lanceolate leaves. The few known leaves of C. Janowskii (a mountain-species) are likewise lanceolate and provided with a long dropping-point. C.-montana (a mountain-species from Borneo) has on several twigs elliptical and Oval leaves with rounded base, and lanceolate, acuminate leaves. C. Hammiu (the xerophilous species above-mentioned) has the tip ending in a very short bard mucro. For the rest the leaves of all species have a clearly marked acumen, sometimes very short. 2. The consistency of the leaf of old plants and twigs is thin- leathery, the colour of the upper-surface is glossy dark-green, of the lower surface lighter green with dark-green veins, in a dry condi- tion hard and in herbaria as a rule brittle. Of young plants (see above) they are much thinner, in sicco almost membranous (in vivo herbaceous). C. Janowskii (see above) has likewise thin ones. When drying the leaves always change their colour to yellow or yellow-green, more or less mixed with sepia-brown, the upper-surface is as a rule dark-brown or olive-brown 153—155 (Code des couleurs de KrincKsieK et Varerre). For C. olaciformis 183 —188 or 193, or paler 217 ; for C. Hammii 202—217, for C. flavescens the colour of the upper-surface frequently 114, of the lower-surface 153. 3. With respect to the diagnosis of the genus as well as the species the nervature of the leaves, though showing common char- acteristics for all species, is of some importance. The nervature of the leaves is penniform, and the secondary or lateral veins never start from the median nerve opposite to each other at the same level, their number being as a rule rather small, 2 or 3 or 4 on each side. In many species the secondary veins next to the tip do not start above the middle of the median nerve, so that the upper half of the leaf is mainly supplied by tertiary veins. Besides they start at unequal distances from each other and are closest to each other at the leaf-base, the /owest two (or sometimes one) starting close to or even from the leaf-base; in consequence of this they resemble triplinerved and trinerved leaves (/icus, Cinnamonum, Viburnum). There often starts from the leaf-base on one or both sides a secondary vein so thin, that it may be counted among the tertiary veins and may easily be overlooked; yet it follows in its course the stronger veins. After starting from the midrib these go upward in a wide curve till close to the edge, next about parallel with the edge towards the apex. The two foremost veins 365 end in the apex (acrodromous veins of ErriNGHAUSEN), the next run some way between the edge and the first pair and all or most of them end in the tertiary net without uniting. The secondary veins thus run parallel to the margin for a great length and most of the basal veins partly embrace the higher ones. A definition answering exactly to this nervature, | do not find in ErrincHausen. It forms a mixture of the common camptodromous, (bogenläufige) with the acrodromous (= spitzenläufige) nervature ; the term amplexidromous might be applied (see e.g. the figures of Thibaudia species (acrodromous) in v. E.’s work, besides Nectandra and other Lauraceae). The species with larger leaves C. flavescens, olaciformis, Beccarii have a somewhat greater number of veins (11—12), while the basal veins sometimes curve inward and unite with the preceding: schlingenläutige (brochidodromous) nervature. The number of secondary veins of the deviating species C. Hammit amounts to 12; in the rather small leaves they are more crowded and fairly equally divided over the length of the leaf, joining with a curve. This is an instance of regular brochidodromous nervature, but the leaf-base is pointed and the veins are ascendent and embrace each other upward from the base, so that the character of the genus is not quite lost. The tertiary nervature is always clearly visible and equally spread over the whole leaf; the horizontal connecting veins are usually prominent and form a delicate lattice- like reticulation. Leaf-impressions made with carbon-paper usually show only this net-work. 4. Regarded biologically the leaves of Coptosapelta jlavescens belong according to HanscirG (Phyllobiology, 1903, pag. 293) to the Myrtus- or Lawraceae-type with which he also classes the Cofjea- species together with numerous other Rubiaceae, among which Crossopteryz, an african genus closely allied to Coptosapelta. According to him these types are xerophilous. They belong to the periodically dry and moist regions along the Mediterranean from Spain to Palestine and also to tropical regions with similar climatological properties. As their characteristics he gives: Strongly cutinized epidermis, rectilinear polygonal or sometimes undulated epidermis-cells, stomata sunk, very glossy lamina usually bare, some- times grey- or white velvety, simple, narrow and entire or round, elliptical, oval and oblong, leathery and stiff’, as protection against strong insolation, excessive evaporation, adhesion of water, winter- temperature, etc. Without doubt many of these properties belong to C. jlavescens, occurring in the secondary woods of the first zone, a.0. in bamboo-woods between 200 and 500 meters, but only on 24% 366 adult old plants, the leaves of which are indeed rather like those of Coffea arabica. Also the tomentose leaves of C. Beceari and C. Griffithii belong to this type. On the other hand C. Janowskii and C. montana are both mountain-plants with narrower leaves and a long dropping-point, instances of Hanseire’s “jicus-type of the rain- woods’. To this type the young plants of the above-mentioned species also approach, in which the’ xerophilous habit does not much come to the fore. Here it is not only the danger of too strong evaporation, brought along by the succession of the monsoons, but no less the risk of the damage, caused by strong rainfall which prevails. Among the remaining species, of which C. maluensis does not grow higher than 200 meters above the sea-level, while the others occur at different levels in the mountains, various transitions between Hanseire’s Myrtus- and Ficus-type are found. An instance of real xerophilous habit is only given bij C. Hammii (Lindeniopsis) which as I previously mentioned should be classed with Scaimprr’s “Hartlaub formation”. § 7. Stipules. The usual shape of the stipules is that of a small triangular scale, which has often been lost with the full-grown twigs in the herbaria. At the back-side and along the edges it is covered with hairs, turned to the front, often longer than the stipule and sometimes covering it entirely. The variations in shape are usually due to differences in the ratio of width and length, which depends on the width of the node. Sometimes however they may be of use in the determination of the species. This is for instance the case with C. flavescens and C. olaciformis, which show a great resemblance on superficial contemplation of leaves and flowers and were considered identical by Merrit. Here, in numerous specimens examined by us, the stipules are quite sufficient to distinguish between the two species. C. flavescens has linear-lanceolate ones, rather abruptly passing into the broad base. They vary in length between 4 and 8 mms. and strike the eye in the herbaria because, at least in the dry specimens, the back-side is absolutely bare and the broad hairy edges show clearly. C. olaciformis has smaller stipules, usually only 2 mms., slightly longer than broad, in old condition hairless and swollen at the base. This description has been taken from a specimen, distributed by Merrit himself from Luzon (Ph. pl. 396) and classified as C. flavescens. It is also applicable to Ermer’s original specimen (see below § 11. Synonymy and relationships). 367 § 8. Inflorescence. In all species the inflorescence consists of axillary compound cymes or corymbs, starting from the leaf-axils near the top of the twigs. At the top they are closer together and often (by the reduction of the floral leaves) are combined to large terminal decussated panicles or thyrsi. Such terminal panicles also occur in other genera of the group of Cinchoneae, viz. on Cinchona and Ferdinandusa. In the descriptions of the genus (Hooknr—Scuumann— VALETON in Ie. bog.) there is wrongly spoken of ”thyrsi penduli”. Undoubtedly the panicles are erect in all cases (see Ermers’ description above, § 3), but the ends of the long branching twigs are drooping and proper flowering-branches start sideways from these. In good her- baria it may sometimes be observed how the flowering-branches form an almost right angle with the leaf-twigs. The extension and relative length of the axis determine the cha- racter of the inflorescences with respect to the species. First of all two types may be distinguished. The simplest case is C. Janowskit, a New-Guinea-Mountain-liane, where the axilary inflorescences have been reduced to single flowers and the terminal thyrsus to a simple closed raceme. The pedicels are rather long and about midway provided with two bracts. It is highly probable that on more luxuriant branches these bracts are fertile, forming forked cymes (dichasia). C. montana likewise has isolated flowers (uniflorous cymes) in the axils of poor flowering- branches and at the top a raceme of 5 flowers. A more luxuriant terminal twig, consisting of 6 internodia, has in the lower axils long-stalked closed racemes, bearing 5 flowers, in the following three-flowered cymes, while the top again forms a closed raceme with linear bracts. The twig of C. Hammii also ends in a raceme of 5—7 flowers, but with very short internodes and pedicels, so that the flowers, provided with long corollatubes, are close together and take the shape of an umbel. In the second type both the axillary and the terminal inflores- cences are compound, and the latter have the shape of corymbi or depressed (almost umbelliform) thyrsi in consequence of the decrease of length towards the apex of the internodes and peduncles; the axillary ones too are more or less corymbiform. Especially the relative length of the peduncles of the partial inflorescences, the number and density of the flowers, the number of internodes of the terminal panicles, determine the character of these species. C. olaciformis deviates most of the rest on account of the slight extension of the corymbi and the small number of flowers. The 368 axillary inflorescences are sbort-peduncled cymes with only 3—5 flowers, many times shorter than the leaves. The terminal thyrsi consist of but 2—3 internodes and cymes with few flowers and short peduncles, and are also shorter than the higher leaves. In the remaining species of this second type both the axillary and the terminal inflorescences are multiflorous much branched, corym- bous, with moderately long or very long stalks, while the terminal panicles may consist of 5 internodes. § 9. Flower and Seed. The calya is now cup-shaped, only superficially emarginate with 4—5 very short pointed teeth, now divided into nearly free sepals down to or almost down to the base, in which case the limb is not sharply separated from the ovary; in a third more frequent case cleft to the middle or a little farther. To characterise the genus it is therefore of no value, but of great value to determine the species. For all species mention should be made of the “intestinal gland papillae’, (Darmdriisen papillen: Sour- REDER), which are placed at the inside alternate with the lobes or teeth, and resemble those which the Rubiaceae always bear at the inside of the stipules and are sure to occur on their calyces more frequently than appears from literature The corolla which is contorted in aestivation, but without externally visible torsion, is trumpet-shaped and reminds us of species of Randia and Tarenna, having a quinquepartite limb and as in the case of Manda the relative lengths of tube and limb, though not always constant in the same individual, is when the average is considered, a means of distinguishing the species. The following average rations were found: Tube many times as long as the lobes (Lindenia-type), 3—6 cms. long: C. Hammii. Tube twice as long as the lobes: C. Janowski. Tube about the same length as the lobes or a little shorter: most of the species. Tube about half the length of the lobes: C. Grijfithii, C. fuscescens and C. lutescens. A peculiarity is, that the tube which is usnally cylindrical and equally wide along its whole length, shows a sudden inflation above the middle in two species, C. Grijithit and C. Janowsktt, which for the rest are farthest apart on account of the length of the corolla tube. The internal hairy covering of the corolla tube is also of some interest. Only in 3 species C. Hammi, C. olaciformis, C. flavescens, the interior of the corolla tube and the filaments are glabrous. In the other species, where the filaments are covered in front with long furry hairs directed downwards, this hairy covering continues 369 as projecting ridges along the inside of the tube, down to the middle or till close to the base. Between these ridges the inside is covered with soft crisp hair; the descriptions of the genus however are wrong, where they say: “Haux barbata” for the hairy covering of the faux (regarded as orifice of the tube) is lacking everywhere. When the limb is still closed, the corolla is externally entirely covered with thiek-velvety or short silky hair. The stamina have thin filiform filaments, which, as already observed, are congenitally attached to the corolla-tube, forming protuding ridges; the part projecting from the corolla is short and filiform, in some species hairless, in most of them covered with furry hair in front; the anthers are very narrow lanceolate and have a linear connective, coherent with the filament near the base at the backside; the long linear anthercells diverge more or less at the base, so that the base of the anther is retuse, or arrow-shaped as with C. flavescens, while the tip ends in a tapering point; the backside is covered with appressed hair, except in C. Hammit, where also the free filaments are almost lacking. The anthers hang more or less versatile from the corolla during the flowering and are curved up or contorted. The pistil is highly characteristic for this genus. The stigma is wedge-shaped or cylindrical (in Lindeniopsis club-shaped) not divided into lobes, and proportionately long. The style is straight and smooth and compressed sideways, and about as long as the corolla-tube, so that the stigma overtops the corolla far. The papillary surface I generally found covered with pollen. The ovary, covered with an annular disk, is regular, bilocular as in the whole group of Cinchoneae. Around a fleshy, cylindrica! axis, nearly filling the two ovary-cells, are the numerous anatro- pous, flat, peltate, erect, imbricate ovules. The fruit is globular or more or less oblong, compressed at right angles with the septum and has in a ripe condition a though, horny or thin parchment-like envelope, surrounded by a thin dry outer-integument. In very old fruits the outerlayer crumbles down and the horny valves come quite into view; in this respect there is some analogy with Bikkia (Condamineae). The splitting into valves is not perfectly regular. It begins with the separation of septum and axis, (loculicide dehiscence) at the top of the capsule, but next the septum itself splits, so that 4 cocci are formed open at the top and at the sides and connected at the base. This latter splitting however may fail to occur. During the splitting the fleshy placenta shrivels up, causing the numerous seeds to get gradually loose. 370 The seeds are flat, round or oblong with the hilum about in the middle (peltate) and surrounded by a membranous fringe-like notched wing, about as broad as the seed. For the distinction of species only differences in size are to be considered (except in Lindenvopsis where the edge of the wing is not fringed); C. olaciformis and C. maluensis have the smallest seeds; C. Grijithii the largest, as far as we know. As to the process of pollination it may only be surmised. The contorted movable projecting anthers and the long protruding stigma point at the probability of wind-pollination, but the prominent flowers scenting of elder and orange-blossom may point at a connection with insects. The possibility of self- and inter-pollination is corro- borated by the great mass of flowers and by the fact that (at least in the herbarium) the anthers are already open in the buds. § 10. The station: About the character of the locality in which the various species are found we only know as follows: C. flavescens was gathered by Korrnars on the barren sands along the river Karrau in Borneo; by Kine’s collector in bamboo-woods in Malacea 100—200 metres above the sea-level, by various collect- ors in Western Java at the foot of the mountains, on various spots in light secondary wood. C. maluensis at 40—100 meters above the sea-level in passable primeval forest, about 20—25 meters, high; the ground covered with foliage („Galerie wald’’ Scuimprr), with occasional low wood, mostly consisting of Pandanus and low feather-leaved palms (Camp Malu); idem with many tree-ferns and bamboo and Selaginella a metre high, as undergrowth (April-flusz): LEDERMANN. C. fuscescens in “Buschwald” changing into mountain-wood up to 1500 metres above the sea-level, few large trees, many epiphytes and moss, many glades, ground often overgrown. On steep rocky slopes (Felsspitze): LEDERMANN. C. lutescens in dense wood on hills, about 25 metres high, rather mossy; in the underwood many dwarf-fan-palms and lianes, Frey- cinetia, Araceae, Agathis, Pandanus: LEDERMANN. § 11. Relationships and synonymy. On account of the structure of ovary and fruit Coptasapelta belongs to the very natural tribe of Cinchoneae Hooker (Genera plant. II p. 11) among which 44 genera are reckoned. This tribe is divided into two subtribes: I. Mucinchoneae with a valvate aestivation. Il. Hillieae with an imbricate or twisted aestivation. 371 To the latter tribe Coptasapelta belongs, which genus in Genera plant. was placed among the former, a mistake already corrected by Kine and by SCHUMANN. The latter places (Pflanzenfam. IV, 4 p. 42 and 48) Coptasapelta immediately beside Crossopterya, an African genus, I could not examine, to which only one species or group of species belongs, living on the barren Campos of Abyssinia — till lower Guinea. On comparing the detailed description Oriver gives of this genus, | found, that nearly all more or less important characteristics given by O. are also applicable to Coptosapelta; only two are lacking, viz. Stigma clavatum bilobum and tubuscorollae graci- lis, limbus parvus. The important characteristic of the length of the stigma however is present. Lindeniopsis however has a stigma clavatum and a tubuscorollae gracilis, so that only the bilobular stigma forms an important difference. This points to a close relation between these two genera, especially between Crossopteryx and Lin- deniopsis, on account of the shrubby, xerophilous habit. The leaf-nervature of Crossopteryx is not fully deseribed, but the leaves have the same shape; they are larger than with most Copto- sapelta-species, but equal to those of C. flavescens. The close rela- tionship of the two genera cannot be doubted. I could not find any striking points of similarity with other genera of the tribe of Cinchoneae, of which but a small number of species occur in the old world. The most characteristic peculiarity, the structure of the stigma does not occur in any other genus of this tribe. Remarkable however is the resemblance of pistil and corolla in species of two genera, belonging to the bacciferous Rubiaceae with many ovules, viz. Tarenna GAERTN. (syn. Stylocoryne, syn. Webera), which has given rise to a peculiar synonymy. The name Stylocoryna, given in 1797 by CAvaNILLEs to a species from the Liu-tchiu-Archipelago, is formed from the words orvdos: pillar and xogvry: club, briefly denoting the structure of the pistil of Coptosapelta, as described above. Hooker referred this species to the genus Randia Linn., so that the characteristic generic name was lost. In 1834 Wienr brought it up again in the form of Stylocoryne (independent of Cavanilles?) for a plant from Ceylon new to him, viz. St. corymbosa Wiant, which again showed this peculiar shape of pistil. Neither could this name be kept, as the same species had previously been diagnosed by GARRTNER (in 1788) as Tarenna zeylanica, wich latter name of course enjoys the pre- ference. The first generic name however had been accepted by various authors (RoxBuren, BLUME, a.o.) and Brumm was the first to 372 apply it to Coptosapelta flavescens Kortu, discovered by v. Hasse. and himself in Java. He called it Stylocoryna tomentosa, while likewise Warricn, Mique. and later Merri. and WerRNHAM classed species of Coptosapelta either with Stylocoryne or with Randia (see above p. 2). Whether the great similarity in floral structure between two genera, belonging to different principal divisions of the family, also points to a natural relation, is still an open question. § 12. New description of the genus. Calya cup-shaped, quinquepartite, quinquelobate or quinquedentate, perennial, with axillar glands. Corolla, contorted in the bud, trumpet-shaped, tube varying in length, outside velvety or covered with sulky hair, inside bare or provided with furry ridges descending from the filaments, between those thinvelvety, straight or inflated above the middle, throat not bearded, lobes linear-oblong, obtuse. Stamina 5, inserted on the throat, filaments filiform, short, the front furry or bare, anthers thin, linear-lanceolate, tapering at the top, at the base twice-pointed, obtuse or arrow-shaped, near the base dorsifix, on the backside provided with two rows of hairs directed upwards (in Lindeniopsis bare). Dise small, annular. Ovary bilocular, style anceps, hairless, stigma entire, cylindrical or club-shaped, long, far overtopping the corolla (in one species square with hairy angles); placentas coherent to the septum, ovules numerous, ascendent, imbricate. Capsule more or less globular or oblong, bilocular, at the top loculicide bivalvular, later on quadripartite. Seeds small, peltate, imbricate; membranous, winged all round with fringy notched (in Lindeniopsis undulate) wing; endosperm fleshy, germ straight, root straight, directed downwards. Lianes or Shrubs (Lindeniopsis). Twigs velvety or bare, round or more or less square. Leaves opposite, thin-leathery, elliptical, lanceolate or oval, usually tapering with a rather abrupt acumen; usnally hairy on the underside. Leaf-nervature more or less acrodro- mous. Stipules small, interpetiolar, triangular. Flowers small or middle-sized, white or light yellow, in axillary closed racemes or trichotomous, branched cymes, united at the twig tops to many-flowered panicles. 373 § 13. Conspectus of the Species. I. Subgenus Lindeniopsis. Shrub. Seeds with a slightly crenate and undulated wing. Calyx-lobes longer than the ovary. Corolla tube long. Anthers hairless. 1. C. Hammii, Var. 1909. Leaves elliptical with short, acute, hard point; secondary veins 5—7 on each side, arcuately anastomosing (brochidodromous). Corolla hairless inside. Twigs sharply squared. Stipulae very small. Plant grey velvety all over, later on bare. Fruit oblong, length up to 30 mms. Distribution. Hitherto endemic in Billiton on sandy barren soil. Il. Subgenus Hu-Coptosapelta. Lianes Seeds with fringed wing. Calyx-lobes not longer than the ovary. Corolla tube not more than twice as long as the lobes. Backs of the anthers covered with long hair. 2. C. olaciformis (MERRILL), EtmeR 1913. Randia olaciformis, Merr. 1908. C. flavescens, Mrrr. (non KorrH.) 1909. Inside of corolla tube and filaments glabrous. Corolla lobes slightly longer than the tube. Inflorescences corymbose united to panicles at the tops of the twigs; cymes short-peduncled and few flowered. Flowers very small. Stipules small, triangular, no hairy edges. Leaves elliptical or oval, shortly acuminate, smaller than 100 mm. number of secondary veins 4—5 on each side, hairless when full- grown, colour in sicco pale greenish grey or olive grey. Width of fruit at most 6 mm., broader than long, calyx consisting of free oval lobes. Distribution. Hitherto endemic in the Philippines, in the following places: Mindanao, lake Lanao, camp. Keithly, Mrs. CrrMeNs n. 1220, 1907 (type); Mindanao, prov. of Agusan, in mt. Urdaneta, 700 M. above sea-level KLMER n. 18355 ?; Luzon, San Antonio, prov. Laguna, mt. Ramos Bur. of Science, Manila, n. 396! . 3. C. flavescens, KortH. 1851. Stylocoryna tomentosa Bl, Bijdr. 1826; Stylocoryne ovata, Mig. 1856; Stylocoryne (Webera) macrophylla, WALL non Roxs.; Coptosapelta macrophylla, K. Scuum. Inside of corolla tube and filaments glabrous. Inflorescences corymbose long- peduncled and dense flowered, united at the twig-tops to large thyrsus-shaped panicles. Leaves elliptical or oval or oblong. shortly acuminate, base as a rule broad, rounded, length 80—125 mm., number of secundary veins 4—5 on each side, colour in sicco usually olive-brown, undersurface of leaves, especially along the veins thinly covered with accumbent or crisp hair. Young twigs and in- florescences coated with dense, soft hair. Fruit obovate, sepals free, oval, erect. Stipules linear-lanceolate with broad base, hairy edges. Distribution: Malay peninsula, Burma, Western Java, Sumatra: Palem- bang, (Pretorius), 1837, in Herb. L B; Borneo S.E. Division, on sandy plains on the river Karrau (KORTHALS). 4. C. hameliaeblasta (Wernn.) VAL. nova comb. Tarenna hameliaeblasta 1) Fhis species being rather widely spread, differs rather in habit according to the place where it is found. For instance the specimens from the Malay peninsula (Kies collector 10384 and 10393) have stronger flowering-twigs and considerably greater leaves and flowers than the specimens from Java and Sumatra. The latter are again distinguished from the Javanese form by smaller, narrower leaves, in sicco coloured darker brown, covered with crisp hair on their undersides. Similar leaves also occur in a specimen from Malacca (MainGAy, 908). Kl | D) AN WAN yl Ne > Oi ) a PN x ISOs SAG G ; Lil Ii A Ál a( ‘ \ À reel ru. BEN D A vand, SS En: < AN SEL Ms) ‘i if id A ONREIN | Banse LANDING Wb | Ae Kah TAN WS bas deler rt Lo Ser A / Je" | 1 | 4 (7 é ee = maul las | Aa iy > wij 376 Wernu. Inside of the upper part of the corolla tube and the filaments densely hairy, the former not inflated. Corolla lobes about as long as the thin corolla tube. Axillary cymes longpeduncled and dense-flowered; terminal thyrsi many-flowered. Corolla tube (in sicco) covered with appressed whitish hairs. Calyx lobes about as long as the ovary, erect, curved outward. Leaves oblong or elliptical, with very short acumen. Secondary veins 3—4 on each side, sometimes with an additional thin basal vein; veins erect. Stipules very small, triangular, the edges covered with dense hair. Colour of the leaves in sicco yellow-olive-green. Stalks and inflorescences hirsute, leaf-veins at the backside with remote procumbent hairs. Distribution: British New-Guinea, Sogeri-region, 950 —1400 metres above sea level. (FORBES). 5. C maluensis, VAL. n. sp. Upper part of the corolla tube not inflated, hairy as are the filaments. Corolla lobes a little shorter or of equal length as the corolla tube. Axillary inflorescences with long stalks; terminal thyrsi with abundance of flowers. Flowers the smallest of the genus. Outside of corolla covered with short appressed hair. Calyx-limb divided for half its length, lobes oval, erect. Leaves usually broad, elliptical with 3—4 rarely 2 secondary veins on each side (together 5—7), acrodromous. Fruit crowned by the very small calyx-lobes. Underside of leaves with a very thin hairy covering near the edge, for the rest bare. Stipules pointed, with thin indument. Distribution: North-East New-Guinea, at 190—200 metres above sea level, in primeval wood. (LEDERMANN). 6. C. Beccarii, Val. n.sp. Upper part of corolla tube not inflated and at the inside covered with long and dense hairs, as are the filaments. Corolla grey velvety externally, lobes about as long as the corolla tube. Axillary inflorescences long-peduncled, thyrsus-shaped. Terminal thyrsi with abundance of flowers. Leaves broadly oblong, ending in a caudate acumen, large, with 3—4 secondary veins on each side. Petiole fairly long; underside of leaf covered with crisp soft hair. Distribution: Borneo (BEccaRi 2271). 7. C. fuscescens VAL n.sp. Upper part of the corolla tube not inflated, inside covered with dense hairs, as are the filaments. Corolla lobes twice as long as the tube. Axillary cymes long-stalked and repeatedly remotely branched; terminal thyrsi many-flowered, spreading. Outside of corolla tube covered with short silky hairs, lobes hairless. Calyx small, lobes detached nearly to the base. Leaves elliptical, glabrous. Usually 3 secondary veins, or in a single specimen 2, on each side. Stipules very small, obtuse, triangular, hairy, Distribution: Nord-East New-Guinea in mountain woods 600 —1500 metres above sea level, in the Kani and Torricelli mountains (ScHLEcHTER) on the Felsspitze at 1500 metres (LEDERMANN). 8. C. lutescens, VAL. n. sp. Flowers as in C. fuscescens, but a little larger. Leaves with 2 secondary veins on each side, in sicco greenish-ochreous-yellow. Distribution: North-East New-Guinea, on the Etappenberg at 850 m. in dense high wood (LEDERMANN). 9. C. Griffithii, Hooker. f. Upper part of corolla tube inflated, inside covered with long dense hairs, as are he filaments, lobes more than twice the length of the short wide tube. Axillary ane cymes rather many flowered; terminal thyrsi densely. Outside of corolla grey velvety all over. Calyx-hmb wide by cup-shaped, divided for half its length into broad lobes. Leaves elliptical, at the underside crisp hairs. Secondary veins 3—4 on each side. Distribution. Gathered in numerous places in the Mal. peninsula, in the low lands. 10. C. Janowskii, VAL, n. sp. Upper half of the corolla tube inflated, inside covered with long, dense hair, as are the filaments Corolla lobes half the length of the tube. Axillary flower- stalks with 1-3-5 flowers. Terminal inflorescences simple racemose. Flowers the largest in the genus. Outside of corolla-tube thin-velvety, lobes hairless. Calyx large, cup shaped, not incised, with short broad acute teeth. Leaves lanceolate, long-acuminate. Distribution: Northern New-Guinea. Jabi mountains. 11. C. montana, Korra. mse., in Herb. L. B. Flowers unknown. Fruits in the leaf axils isolated or in peduncled cymes of 3-5-flowers, forming simple closed racemes at the twig-tops. Calyx-lobes persistent on the fruit, only connected at the base, linear-subulate. Leaves lanceolate or elliptical, rather firm, with long tapering points and acute, obtuse or rounded base. Secondary veins 2-3 on each side. Stipules small, triangular, having long hairs. Stems, inflorescences and under sides of leaf-nerves thin-velvety, in sicco ochreous yellow. Fruit obovate oblong. Distribution. S.E. Borneo. Summit of the Sakoembang, 1000 metres above sea level. EXPLANATION OF THE FIGURES. Fig. 1 Coptosapelta montana; Leaf of an old plant. Fig. 2 af flavescens, flowering plant. Fig. 3 or an very young plant. Fig. 4 +3 montana; young fruiting plant. Fig. 5 5 hameliaeblasta. Fig. 6 5 olaciformis. Fig. 7 = Fig. 1. Fig. 8 and Fig. 9 Coptosapelta fuscescens. Fig. 10 zi flavescens, flowering plant Fig. 11 = Fig. 6. Fig. 12 er lutescens. Fig. 13 and Fig. 14 ,, maluensis. Fig. 15 3 Hammii. The figures have been obtained by carbon-impressions according to the method of Eimer D. Merrity. Fig. 4 is not retouched, only retraced with ink. The others have all been worked up by the designer with the aid of the original print and of the leaf; the tertiary vein system is consequently a little too promineut ! Botany. — „Dark growth-responses”’. By D. Torvenaar. (Commu- nicated by Prof. A. H. Braauw). (Communicated at the meeting of April 28, 1923). In our previous report on the light- and dark-adaptation of Phy- comyces nitens (Proc. Vol. XXIV Nos. 1, 2 and 3, 1921) the existence of the so-called ,,dark-growth-response’ was already proved in a great number of experiments. By dark-growth-response we under- stand the occurrence of a growth-response, when a sporangiophore of Phycomyces nitens adapted to light (by a four-sided illumination for hours at a stretch) is placed in the dark. It seemed worth while considering in how far this dark-growth-response of Phycomyces-nitens (the negative after-images of the human eye probably being in reality comparable) occurs in other organs. In this communication the results are mentioned concerning the dark-growth-responses of the sporangiophore of Phycomyces nitens, the hypocotyledons of Helianthus globosus, the coleoptiles of Avena sativa, the roots of Avena sativa and the roots of Sinapis alba. If possible the results have been compared with the light-growth- responses hitherto known. Method and accuracy of the results. In all experiments the preceding illumination was four-sided; the temperature being kept constant by means of the oil-thermostat, described in ,,Licht- und Wachstum 1”. In this way the temperature could be kept constant to 0.02° C. with moderate illuminations. It should be particularly kept in view, that the growth was as a rule only considered sufficiently constant, when it did not oscillate above 10°/,, i. 0. w. with an average rate of growth of 100 no rates higher than 105 or lower than 95 occurred. This enables us to ascertain responses of growth more than 5°/, above or below the average; responses of growth therefore of an acceleration or retar- dation of 10°/, we can ascertain with some certainty. We mention this in order to give the illustrations and reviews the value due to them, which could not be judged of without the full data — which we omit here with a view to space, but all of which will appear in the ‘“Mededeelingen der Landbouw-hoogeschool” this year. 379 As long as on account of insufficient constancy of the outward circumstances or through inward causes, the growth already greatly oscillates before the change in light-conditions, it may be easily understood that a response of growth due to this one factor cannot be accurately ascertained. As responses of growth of more than 50°/, are but rare, they are not demonstrable when the growth shows such variations beforehand. With the data in literature however this repeatedly occurs. We repeat, that for our reactions we only used organs, showing as a rule no oscillations of growth greater than 10 °/,. The figures subjoined all represent the response of individuals, approaching the average type as closely as possible. Only in the case of Phycomyces nitens a schematical figure of the process of reaction was given. Just as in most of the previous curves published by Braauw such figures, in which the reaction-type of a definite experimental series is composed, are mainly based on the so-called cardinal points, to be found in the reactions of all individuals. These cardinal points are: 1. the average-point of time, at which the response of growth begins ; 2. the average-time, at which the reaction reaches its first climax (either maximum or minimum of growth); 3. the average-rate of growth at that moment in percents of the original rate of growth; and next again the average time, at which eventually another maximum or minimum occurs and the average-rate of growth at that moment. Dark- and light-growth-responses of Phycomyces nitens. The light-growth-responses are known from the results of BLaauw, published in “Licht u. Wachstum III’ (Med. d. Landb. Hoogesch. 1918) p. 108. The cardinal points for some intensities follow : TABLE I. ; Maximum of response : À : Hise Ee = Final rate of Light-intensity | after beginning | after beginning | in °%o of the of exposure rate of growth growth of exposure in dark 1/8 MK. 8 Min. 9!/, Min. 141 0/9 102 % 1 n 51/, „ 9 ” 148 0 103 0/5 are Sl» 82 „ 152 % 111 % 64, PS 8 jn 174 9% 112 % 25 Proceedings Royal Acad. Amsterdam. Vol. XX YI. 380 At a temperature of about 17° C. some sporangiophores adapted to exposures to 1/512, 1/64, 8 and 64 M.K., were darkened, the growth-measuring being continued. The responses of growth, con- sisting in a retardation of growth were very characteristic. The cardinal points, computed from sets of 5—6 experiments are given in the subjoined table. TABLE II. Pp ie En Minimum of growth Adapted to | after beginning | after beginning | in %o of the of darkening | of darkening See 1/512 MK. | 10% Min. 12! Min. 89 % 1/64, 64; 1200 85 % 8 Dn 6 De 11 À 61 % 64 7 4} i 10 . 13 6 The reaction at 64 MK was observed in a great number of observations (19). From the results obtained a maximum after about 17 min. could be derived with a rate of growth of about 984°/, of the rate of growth in light; after that the oscillations get more and more indistinct and after 1*/,—2 hours the equilibrium for the growth has externally been reached. The rate of growth appears to have become 93°/, of the rate of growth in light, with a mean error of about 1 °/,. From comparison of the above reports the contrary reactions, brought about by making light and dark, are clearly perceptible. (See the figure). The dark- and light-growth-responses of hypocotyledons of Helianthus globosus. The light-growth-response of these organs is sufficiently known from “L.u.W. II”. It consists in a retardation of growth, making its first influence felt, when exposed to 1 MK after 8 min.; the minimum of 74°/, of the rate of growth in light appears after 27 —38 minutes, after which the growth reverts to its previous rate, at least in a slight number of observations it is after 3 hours not perceptibly different from the rate before exposure. 381 <5 20--— 49 60-80" 00MIN. 0 20 AO: ©. 60 80 100 MIN. EXPLANATION OF THE FIGURES. These figures have been arranged in twos, in such a way, that above the process of growth has been represented when the organ after having been in dark, was permanently exposed to light (7) below the organ made dark (J) after having been exposed for hours. The height. of the dotted space represents the rate of growth. In the case of Phycomyces the two growth-curves have been plotted according to the average progress of a number of individuals; the cardinal points are indicated by X For all the other organs the curves have been composed of the figures found for one of the individuals. The curve for the coleoptile of Avena sativa has been plotted after an individual reaction after KONINGSBERGER. How these curves have been plotted will be further discussed and explained in the more detailed publication. 25* 382 AVENA SATIVA (WORTEL) 0 RRT HELIANTHUS GLOBOSUS (HYPOCOTYL) 7 En 0 DE DRE EE 383 At 64 MK the first reaction already appears after about 34 min., the minimum amounting to 39°/,, after 20—25 min., while after that the rate of growth gradually reverts to its initial value. Finally at 512 MK the reaction-period is 34 minutes, the minimum, now 21°/,, appears after about half an hour and continues for a long time. Even some hours after the beginning of the exposure the rate of growth remains considerably below the rate in dark. Compare the figures subjoined. What reaction takes place, when we darken after these hypoco- tyledons have been mainly adapted to a constant illumination for 5—7 hours? The results of these experiments, made at about 20°C. have been briefly summarized in the subjoined table. TABLE III. | Maximum of response | i Beginning of Second Adapted to response after | After beginning in & of tne ; rate of grow i darkening Oene a ie Em maximum after 1 MK. 7's Min. 18's Min. 128 % 40 Min. 64 84: „ Kera 137 2% pe SIZE oe, 8% „ 18 Fe 15 18e — After about an hour and a half the growth had become settled again. As to the rate, putting together all data of 1,64 and 512 MK and comparing the rate of growth in light to the rate 1—2 hours after darkening, we find of the 14 results: a retardation of growth in 7, an acceleration in 6 and an unaltered rate in one, while an average acceleration of growth of 5 + 21°), may be computed. Therefore the chances for the existence of a lasting acceleration of growth may be called slight. On comparing the light- and dark-responses to each other (see figure!), we are again struck by the reverse process, though there is no perfect symmetry. In both cases the reaction is more marked for higher intensities (lower minima, resp. higher maxima). Upon the whole the dark-response is not so strong as the light. response. The reaction-period is longer, the change in growth less intense, the external equilibrium of growth sooner restored. 384 The light- and dark-growth-response of coleoptiles of Avena sativa. By means of the experiments of Vor, Simrp and KONINGSBERGER a light-growth-response has been ascertained. On application of 90 MK on 3 sides KONINGSBERGER finds a minimum of about 55°/, 85—40 minutes after the beginning of the exposure — next a maximum after about 65—70 minutes (about 80 "/, of the rate of growth in dark) — while after 90 minutes a second minimum occurs amounting to about 65—70°/, of the rate of growth in dark. The latter how- ever continues oscillating irregularly for hours together. In the figure the curve of the light-growth-response is taken from an individual of table 9 from KONINGSBERGER’s dissertation. What reaction oceurs, if we darken after the rate of growth has been in the main adapted to light for some hours? With Helianthus and Phycomyces darkening appeared to cause less intense changes of growth, than “Light”. If this should be the case with the coleoptiles of Avena sativa, there would be danger of this reaction finding no expression at all or but indistinctly, on account of the irregular growth of Avena, in consequence of occurring nutations. We have therefore tried to eliminate or restrict these impeding movements. Not only were a great number of Oat-races observed in this respect, but also conditions of more or less moist and hot cultivation were tried. In this way we have succeeded in finding an Oat-race called “Zwarte President” which when cultivated in a very dry soil but very rarely nutates inconveniently. As long as the coleoptiles secrete little or no drops of moisture, the growth was extraordinarily constant and frequently remained within the limits fixed by us: no more than 10°/, variation of growth. The tempe- rature at which the plants grew was about 22°C. In order to give a good idea of the results, obtained for this object, we decided to give the whole of its individual responses of growth in this commu- nication. Our preceding illumination was 4-sided with 64 MK.. which intensity deviates but little from that used by the above- mentioned investigators. The rate of growth has been given in microns per minute. *) N°. 1. Exposed beforehand for 44 hours at 21°,9 C. to 64 MK: 1) The small figures denote the time of observation, by which the beginning of darkening is again put at the full hour (60). 385 45 124 50 124 55 124 park! 0 125 5 124 10 124 15 124 20 13 25 16 30 13 35 12 40 104 45 9 50 10 55 105 1 hour 104 1.05 104 1 10 N°. 2. Exposed beforehand for 4 hours at 21°,9 C. to 64 MK. 51 20 54 20 57 20 park! 0 19 3 19 6 19 9 20 12 19 15 18 18 NSR 2 2 RANT SN SO RIMS ese Oil eere AIS "50 1953 18 56 18 1 hour 18 1.03 18 1.06. N°. 3. Evposed beforehand for 4 hours at 22°,2 C. to 64 MK.: ESAT END NR KOMO ANG RIN OPI DEN ANS 29: 18 29 zi Dn GL DG Lr WM BO) Die Why so DEL Shy Py ce DB) EEDE Di5sAo i st 2081 hour 26, 1.03.25) 1.06 25 1209" 25 1212: N°. 4. Exposed beforehand for 8 hours at 21°,9 C. to 64 MK.: 50 9 55 8 Dark! 0959 10 11 15 11 20 12 25 11 30 104 35 10 40 94 45 10 50 10 55 94 1 hour 94 1.05. N°. 5. Exposed beforehand for 6 hours at 22°,0 C. to 64 MK.: 40 9 45 9 50 9 55 9 Dark! 084 59 10 11 15°12} 20 14 25 12 Bom 35110) 40) 10) 45° 110'50'92 559 1 hour 971.059 9M1 101915 91:20. N°. 6. Exposed beforehand for 4 hours at 21°,1 C. to 64 MK: 45 26 48 24 51 25 54 25 57 25 Dark! 0 24 3 24 6 25 9 25 12 25 15 28 19 30 21 33 24 86 27 36 30 36 33 29 36 24 39 24 42 26 AAS 4825-51 20 542051) 20, de hour 2671.03 Aid 1,10; The occurring dark-growth-responses in the above cases yield the following averages for the cardinal points: Mene Lespouse A minimum in the rate of in % of the growth (except in No. 5) rate of growth | after beginning of darkening First response | after beginning | After beginning of darkening | of darkening in light 16 Min. + 23% Min. | 133 % + 42 Min. In some cases there is apparently a slight secondary maximum after 50—60 Min. (Nos. 2, 3, 4 and 6). Little may be concluded from these experiments with respect to the final rate of growth. It does not seem to deviate much from the rate in light. The above shows a distinct response of growth, again contrary to the light-growth-response. Again it is less intense than the light- growth-response; the former gives a slighter change of growth: the undulatory movement is less vehement (undulation of shorter duration with slighter amplitude). 386 In the averages KoNINGSBERGER's tables (4) of the light- and dark- growth-response a maximum occurring after darkening may indeed be found on pages 51, 52 and 53. It occurs after about 20—30 min., (circa 25 minutes), but also in connection with further experiments KONINGSBERGER does not consider these reactions as dark-growth- responses. In the cases, in which Voer observed the dark-growth-response, it lies averagely after 21—24 min., (averagely 22} min.), which is in accordance with our results. Simre finds his maximum averagely after 30$—35! min. (averagely 33 min.). But we should bear in mind, that this investigator did not change the exposure to 320 MK. to dark, but to a slighter illumination with .17.7 M.K. (pag. 699 and (following). Accordingly in our experiments both after a previous exposure of 6 and 8 hours, and of 4 and 43 hours, we found a dark-growth- response with the coleoptiles of Avena, contrary to the light-response of this organ. The Light- and Dark-growth-responses of the root of Sinapis alba. This organ being much less sensitive to light, | deemed it desirable to apply stronger illuminations, viz. of 3500 M.K. In spite of the insertion of a cooler with running water into the circuit, a gradual rise of temperature from 0°.5—1°.0 C. in the course of an hour could not be prevented. On darkening, a fall of temperature could be prevented by again putting the heating into operation. Then oscillations above 0°.05—0°.1 C. did not oceur. The roots were subjected to 4-sided illumination at 21°.5—22°.8C. for 3—5 hours. First the light-growth-response was determined, yielding the following averages : Ta, Minimum of growth oe Rate of growth EN after some hours in in % of the rate |lightin ofthe rate First response after making | after light of growth in dark jof growth in dark 31 Min. | 391s Min. | 19 % 88 % We observe a distinct response of growth. The retardation of growth is permanent in all cases also after the new external equi- librium of growth has been attained. 387 A subsequent darkening caused the following reaction : Fired response Maximum of response Rate of growth in after in % of the rate |dark in% oftherate alter darkening | of growth in light | of growth in light 30! Min. | 35!s Min. | 124 2% 113 2 Here too the contrast between light- and dark-response is found. Both are fairly equally marked. Meanwhile I have observed the dark-growth-response with an illuminating-power of 512 M.K. | found as an average of 7 experi- ments: Birseeres pause Maximum of response Rate of growth in after in % of the rate |darkin % ofthe rate after darkening | of growth in light | of growth in light 27 Min. | 36! Min. | MI 26 105 % Here we already approach the limit of the reactions still percept- ible, which also appeared from the fact, that a few plants no more gave a perceptible dark-growth-response. On subjecting these plants to an illumination of 512 M.K., there did not occur a light-growth- response either. The sensitiveness to light, found by Braauw (“L. u. W. III”) for Sinapis alba was greater. At the time there was even found a marked response at 64 M.K. with a minimum of 81 °/, and arate of growth after 2 hours of 91 °/,, an equally strong response, as the one found by us for 3500 M.K. To what causes this may be owing (older seed? other Sinapis alba race?) should be further investigated into and may become an indication for the deeper cause for sensitiveness to light. The behaviour of the tap root of Avena Sativa, with respect to light and dark. Braauw did not find a perceptible response with illuminating- powers of 64—500 M.K. I exposed to 3500 M.K. Even then no reaction occurred, or so slight a reaction, that it might as well be attributed to the slight rise of temperature. After a 3 hours exposure at a constant temperature of 20}°— 224° C. followed darkening. In not a single case there was a marked 388 response, i.e. the oscillations of growth remained of the size also occurring in constant circumstances (smaller than 10°/,). With a reservation as to the existence of such an exceedingly slight reac- tion, we may observe, that the lack of a light-growth-response goes together with the lack of a dark-growth-response. SUMMARY. 1. With the organs observed the occurrence of a lght-growth- response went together with a dark-growth-response, in the main con- trary to the former. 2. The lack of a light-growth-response (Avena-root) goes together with the lack of a dark-growth-response. This going together seems to hold good also individually (Sinapis-root 500 MK.). 3. With Phycomyces, Avena coleoptile and Helianthus-hypocotyledon the dark-growth-response is less intensive than the light-qrowth-response : the waves have smaller amplitude and are of shorter duration so that externally a constant rate of growth is sooner attained. It remains to be investigated into, whether the inward equilibrium is likewise sooner restored than the externally observable light- growth-response. Equilibrium in the inward processes indeed does not coincide with the appearance of a constant rate of growth to be judged by the observer (7). With regard to the word ‘dark-growth-response’, used for con- venience, sake, it should be borne in mind, that dark as such does not cause the response: dark itself is not a stimulus, but the modifi- cation in energy-supply, either when suddenly occurring (light-growth- response), or suddenly ceasing \dark-growth-response), respect. increasing or decreasing. It may be easily understood, that stoppage of energy-supply causes a slighter and shorter reaction in an organ, i.e. it sooner settles down than when energy is supplied. LITERATURE. l and 2. Braauw, A. H. Licht u. Waclistum I en II (Zeitschrift f. Bot. 1914, 6 und 1915, 7). 3. BLAAUW, A. H. Licht u. Wachstum III (Med. d. Landb. Hoogesch. 1918, 15). 4. KONINGSBERGER, V. J. Tropismus u. Wachstum (Dissertatie. Utrecht, 1922). 5. Srerp, H. Ein Beitrag zur Kerntniss des Einflusses des Lichts auf das Wach- stum der Koleoptile von Avena sativa (Zeitschr. f. Bot. 1918, 10). 6. Siere, H. Untersuchungen über die durch Licht und Dunkel hervorgerufen Wachstumsreaktionen bei der Koleoptile von Avena sativa (Eb. 1921, 13). 389 7. ToLLeNAAR, D. and Braauw, A. H. Light and Darkadaptation of a plant cell (Proc. Vol XXIV. Nos. 1, 2 and 3, 1921) 8. Voer, E. Ueber den Einflusz des Lichtes auf das Wachstum der Koleoptile von Avena sativa. (Zeitschrift f. Bot. 1915, 7). 9. Wepvers, Tu. „De werking van licht en zwaartekracht op Pellia epiphylla”. (Verslagen Kon. Akad. v. Wet. Deel XXX, 1922). Laboratory for Plant-physiological Research. Wageningen, April 1923. Mathematics. — ‘Representation of a Tetrahedral Complex on the Points of Space.” By Prof. Jan pr Vries. (Communicated at the meeting of April 28, 1923). 1. Let there be given a pencil of quadratic surfaces which has a twisted curve g‘ as base curve. The polar planes of a point P with respect to these surfaces pass through a straight line p, which we shall call the polar line of P. Through P there pass two bisecants of o°; the straight line p joins the points of these bisecants which are harmonically separated from P by of. If P lies in the vertex of one of the four cones belonging to the pencil, the polar line becomes indefinite; any straight line of the plane wx = O; On On may be considered in this case as a polar line. The complex of rays 7’ of the polar lines p is represented on the space of points {P}. The side 0, O; is represented in any of the points of the opposite side 0, On. If a straight line r is to belong to 7, its polar lines 7’ and r" with respect to the surfaces «° and 8? of the pencil, must cut each other. If the straight line r describes a plane pencil, 7’ and r" describe two projective plane pencils; the plane pencil (7) contains accordingly two rays for which r’ and r" cut each other. The complex 7’ is therefore quadratic ') and has four cardinal points 0; and four cardinal planes w;; hence it is tetrahedral. A point P of of is the image of the straight line p which touches o‘ at P. The scroll of the tangents of of is therefore represented in the points of o*. 2. If P describes a straight line 7, the polar planes of P with respect to a’ and 3? describe two projective pencils round the polar lines r’ and r". The polar line p describes accordingly a quadratic scroll (p)?; the conjugated scroll consists of the polar lines of r with respect to the quadratic surfaces through o*. The points of intersection of 7 with the cardinal planes , are the images of four 1) If the pencil is defined by Zas? =O and Lbhyx,* = 0, the polar planes of 4 4 the point y have axs and byys for coordinates. The coordinates of p are in this case Py = (d3b4—A, bs) yz yy etc. If we put a) a3 by by + dada bj bs = Cg,04, T is represented by Cj2,34 Pia P34 + Cass14 Pag Pis + C1524 Pan Pas = 0. 391 rays p, which pass through the cardinal points Oz. 7’ contains evidently * scrolls (p)’. If r is a ray of 7, r’ andr" cut each other, so that the projective pencils of polar planes produce a quadratic cone which has the point 7’7" as vertex. From this follows that the complex cones of T are represented by the point ranges (P) lying on complex rays. 3. The rays of 7’ which lie in a plane p (and which accordingly envelop the complex conic p*), are represented by the points P of a twisted curve which passes through the cardinal points O;. For the intersection of the planes p and wj is a tangent of ~’ and is represented in Q,. As wj can only contain the images points QO), On, On, the image of the system of the tangents of p?° is a twisted cubic g* circumscribed to the tetrahedron O, O, O, O,. 4. The complex 7’ cuts a linear complex A in a congruence (2,2) which has singular points in O,, singular planes in w,;. For O, is the vertex of a plane pencil belonging to both complexes, hence to (2,2). The polar lines p’ and p" of the rays of this plane pencil with respect to a and g* form two projective plane pencils in w; and these produce a conic cireumseribed to QO; On On. The image of the congruence (2,2) is therefore a quadratic surface $2* cireum- scribed to O, O, O, O,. As A does not generally contain any of the sides O0, $2? will not generally contain any of these sides either. ’) The o* surfages £2? are the images of o* congruences (2,2) contained in 7. To these belong a‘ axial (2,2) defined by the a‘ axial linear complexes. 5. The rays of 7’ belonging to two complexes 4, and 4,, form a scroll (p)* of the fourth order; this scroll belongs of course at the same time to all complexes 4 of the pencil defined by 4, and A,, hence also to both axial complexes of this pencil. Their axes are director lines of (p)* and moreover double director lines, for the complex cone of a point lying on one of these axes,:is cut twice by the other axis. =0, (2° has for equation 1) If A is defined by 2d Pay Be Cae! y,, = 0. Inversely the surface Ev, y, =9 is the image of the (2,2), which is defined 6 by the complex s/e Dmn =O. 6 Ck/ 392 The scroll (p)* is represented by the twisted curve o* which is the intersection of the two surfaces {2° that are the images of the congruences defined by A, and 4. If, the axes 7, and 7, of two axial complexes cut each other, the congruence (2,2) which these complexes have in common with 7, degenerates into the system of the complex rays p through the point R=r,r, and the complex rays in the plane e=7,7,. In connection with this the image surfaces (2* defined by 7,7, cut each other in the twisted curve o° representing the complex rays in ov, and in the polar line + of FR (the image of the complex cone of &); evidently 7 is one of the bisecants of 9’. If o° is an arbitrary twisted cubic cireumseribed to O,O,0,0,, there pass oo° surfaces 2* through e* of which any two have also in common a biseeant of o*; evidently they represent two axial complexes of which the axes cut each other, so that the corresponding (2,2) splits again up into a complex cone and a complex conic; the latter is represented by o°. 6. A conic (P)? has four points in common with the surface (2? belonging to an axial complex 4; it is accordingly the image of a rational scroll (p)'. Any ray s of 7’ lying in the plane of (P)’, contains two points of (/)*; the image S of s carries therefore two rays of (p)*. Hence the curve (S)*, representing the rays s, is the double curve of (p)*. If (P)* passes through O,, it is the image of a eubie scroll (p)° of which the double director line passes through O,; for the points of intersection of (/)* with w, are the images of two rays p through O,. If (P)? passes through O, and through Q,, it is the image of a quadratic scroll (p)*. Inversely a seroll (p)* has two rays in common with an axial complex; its image cuts accordingly the corresponding surface 2* outside Ox in two points. Hence this image is either a straight line ($ 2) or a conic through two cardinal points O. 7. The points P of a plane p represent the rays of a congruence |p|. The polar planes « and 3 of P with respect to two quadratic surfaces «? and 3? of the given pencil form two projective sheaves of planes ronnd the poles of p. Their intersections with a plane w form two projective fields of rays, hence pp contains three rays p= ag. The planes « through a point Q form a pencil; one plane of the corresponding pencil (8) passes through Q, hence Q carries one ray p. 393 The field of points [P] is therefore the image of a congruence (1,3). This consists of the chords of a twisted cubic 6* which passes through the points O; for the range of points (P) in wx is the image of the generatrices p of a quadratic cone which has O, for vertex. 8. If the twisted cubic (P)* passes through three cardinal points, it is the image of a cubic scroll (p)*. For an arbitrary surface ®* representing an axial complex cuts (/)* in three more points; on the axis of this complex there rest therefore three lines of the scroll. One pencil (#*) can be passed through (/)'; for through any four points of ¢P)* aw! ? can be passed, each of which contains seven points of (/)*. The corresponding complexes A form also a pencil; the axes of both axial complexes belonging to this pencil, cut all rays of the seroll and are therefore the director lines of the cubic scroll (p)°. If (P)* passes through two cardinal points, it is the image of a scroll of the fourth order. In this case one #* passes through (P)*: the seroll belongs to the congruence (2,2) which the corresponding complex A has in common with 7’; as it is rational, it has a double cubic. 9. A surface | P|" is the image of a congruence with sheaf degree n, for its intersections with a ray ¢ of 7’ are the images of n rays through the vertex of the complex cone represented by ¢ The jield degree of the congruence is generally 3 for each point of inter- section of |P] with the cubic g? representing the rays ¢ lying in a plane g, is the image of a ray of the congruence in gy. If { P|” passes sj times through O,, the field degree is evidently 3n— sg. A twisted curve (P)" is the image of a scroll of the Dre. for the image surface [P|’ of an axial complex cuts (P)" in 2n points, which are the images of as many rays ¢ cutting the axis of the complex. 10. If the base of a pencil of quadratic surfaces consists of a cubic 9’ and one of its chords, the polar lines of the points of space form a quadratic complex which is represented in the same way as the tetrahedral complex. We can always represent this pencil by a(w,*— 2, «,) + B(2,’—a«, ,) = 0. The polar planes of the point y relative to the cones « — 0 and 394 B=0O have for coordinates y,,—2y,,¥,,0 and 0, y,,—2y,,y,. The polar line of y is therefore represented by Nie as peed Ts, Lg Cire War en vet At, UI We vts yd Hence 4P as” = Pis Pas This complex has QO, and O, as cardinal points, w, and w, as cardinal planes. The complex cone of « touches 0,0, at O,, O,O, at O,. The polar line of y lies in the plane § if the equation $1 (2447s YY as) + Esala + Es Vaate + §, Cya uit) =O is satisfied by all values of «, and «,. From this follows that the complex rays in § are represented by the points of the cubic which is defined by the cones 25u HE Ea so 2E HEI = Sia (The chord O,O, does not belong to the image). The congruence (2,2) which the complex has in common with the axial complex with directrix a, — 0, 6, =O, has for image the quadratic surface the equation of which is (a,b) viva + [4(a,b,) + (a,b) Yas — (a,b) Hiv, + (0,6) Yao + + (a,b) 9,7 + a,b) ys” = 9, where (ab) = azbi—aibr. Chemistry. — “The Electromotive Behaviour of Magnesium’. 11°). By Prof. A. Smits. (Communicated by Prof. P. Zrrman). (Communicated at the meeting of March 24, 1923). Introduction. The fact that the rest potentials of magnesium and aluminium in aqueous solutions of their salts are too small negative has been the subject of frequent comment. An apparently succesful explanation was that which assumed the presence of a film of oxide on the metal. This was however due to a not sufficiently careful examination of the consequences of such a premise. This is especially true in the case of aluminium where it had been supposed, that the etched or even the polished metal was coated with a not porous film of oxide of molecular. thickness. Now a number of different investigations have proved with cer- tainty that if an etched or polished aluminium electrode is immersed in mereury above which there is an aqueous solution of the alu- minium salt, the aluminium immediately shows the potential of the mercury layer, whilst there was no indication of the penetration of a film of oxide *). It follows from these investigations that either a film of oxide does not hinder the passage of the electrons or there is no film at all. If the electrons only were going through an oxide layer we should expect the behaveour of a gas electrode. This is not in accordance with the fact. Consequently if the oxide film existed it would be penetrable for ions, but it is then manifest that we are dealing with a metal-electrode. Now it is possible that under certain circumstances the liquid in the liquid bounding layer is saturated with respect to the hydroxide of the metal. This could easily be proved by the fact, that in the formula OTS ede 1) The considerations applied here are explicated in the book “Theory of Allo- tropy”. Longmans, Green and Co. 1922. The first Communication appeared These Proc. Vol. XXII, 876 (1920). 2) See Zeitschr. f. Electr. Chem. 27, 523 (1921) and 28 (1922). 26 Proceedings Royal Acad. Amsterdam Vol. XXVI. 396 Lm (OH), OH)’ 0.058, Ly (OH'y (My) can be substituted by so that en, Brie AND 5 y 08 Lm (OH), ~ (4) or 0.058 Ti Ken EZ AO SEE CLM of 18 EGT KN Y °8 Lm (OH), (Hr) Ge From which it appears, that the electrode will behave as an oxygen or hydrogen one, but that the electromotive forces will show a constant difference. These considerations however are no help to us, for expression (1) which always holds good, requires the potential of the metal to be very negative, because the concentration of the metal ions in a saturated solution of Mg(OH), or Al(OH), is very small. The exact converse is observed. Ten years ago KistiAkowsky ') calculated the normal potentials neglecting the temperature coefficient in the formula of GiBBs-HELM- HonTz and found with Mn, Fe, Co, Cu and Cd differences between the calculated and experimentally found normal potentials of 10—60 m.V.; with Ni, Sn, Pb and Hg differences of 140—190 m.V.; with Ag he found diverences of 310 m.V., and with TI of 360 m.V., whilst the difference with Al was 460 m.V. and with Mg 900 m.V. As Kisriakowsky found the electromotive force which the caleu- lated for Mg and Al so much higher than that found experimentally, he simply assumed that at the two electrodes in the galvanic cell metal-electrolyte-lydrogen, the reactions Ms > My + 26, and 26, + 2Hr > H,, do not take place as in other cases, but the following: M, + 2 0H, > M (OH), + 26 and 291-980 >20H +H. It should be noticed that the remarkable assumption is made there, 1) Z. f. phys. Chem. 70, 206 (1910). 397 that a reaction which takes place at the hydrogen electrode is reversed when Mg is replaced by zinc. Kistiakowsky, however, rightly comes to the following conclusion : “Hieraus fogt unmittelbar, dass die Mg bzw. Al. Electroden die Eigenschaften von Gaselektrode besitzen mussen, d.h. ihr Ey, von der Metallionen-konzentration unabhängig, dafür aber von der H° und OH’-Konzentration abhängig sein muss; ausserdem muss es, wie bei Pt, von den reduzierenden Eigenschaften des Elektrolyten abhangen.” In this Kistakowsky, however, quite overlooked that the behaviour of an hydrogen electrode will also be found with any other metal, if tbe boundary liquid consists of a saturated solution of the metal hydroxide. Kistiakowsky, instead of measuring the Mg and H, potentials in the same solution by changing the Mg concentration, dipped his Mg electrode, besides in a solution of MgSO, and in a solution of MgCl,, in different other solutions, not containing Mg, and then obtained results, of course, from which no conclusions at all can be drawn. In his opinion, however, his results proved that the Mg- potential is independent of the Mgconcentration. Beck!) was the first to demonstrate in his Thesis for the Doctorate the invalidity of Kistiakowsky’s views; he has also shown experimentally that Mg never behaves as a hydrogen electrode. All the same electromotive behaviour of Mg in MgSO,-solutions of slight (Hy) was not yet cleared up, for it appeared to him that the difference in potential between the Mg and H electrodes in these solutions of small H’-concentration increases with the Mg-concen- tration. *) Breek found that the Mg electrode does not behave as a hydrogen electrode, but the Mg does not behave as a normal metal electrode either, for it was found that the Mg-electrode becomes more negative when the MgSO,-concentration increases. It further appeared that on increase of the H'-concentration the Mg-potential becomes more negative, and that it reaches a maximum negative value for every MgSO,-concentration at a definite H'-concentration. This maximum negative value varied with the MgSO,-concentration, at least qualitatively, in a normal way. 1) Rec. tray. chim. 41, 353 (1922). *) All the measurements were carried out by Beck in an atmosphere of very pure hydrogen, with vigorous stirring of the liquid, the Mg-electrode being at rest. If was found, that this way of stirring is much better than stirring by the electrode it self. 26* 398 The maximum negative potentials are however no equilibrium potentials, that follows already from this, that the potential of Mg activated by amalgation in a solution of 1 gr. mol of MgSO, per litre, is more negative, i.e. — 1.856 Volt. instead of —1.790 Volt, which value will also lie still below the real normal potential of equilibrium of Mg, as will be shown below. Magnesium. After this introduction we shall examine the metals Mg more closely. ; | The difficulties which are usually encountered in the study of the electromotive behaviour of magnesium and aluminium are owing to the fact that extraordinary phenomena appear when the usual methods of determining the equilibrium potential are applied to these strongly basic metals. For example, suppose that the Mg potential is — 1.86 Volt. Since the Me electrode develops hydrogen, this means that the above potential corresponds to the potential of the three phase equilibrium, magnesium (inner equilibrium) — hydrogen (by inner equilibrium) and the surrounded liquid layer. The liberation of gaseous hydrogen takes place because hydrogen ions from outside diffuse into the surrounding liquid layer and com- bine with the electrons. The above assumption holds for -Fe and Zn because it can be shown by calculation that the surrounding liquid layer can coexist with metal and hydrogen, the two latter in inner equilibrium. If however we take now strongly basic metals, we can see that the quotient — would be so large, that the electrolyte would (2H") become inconsistent. The question now arises: “Can the above negative potential (—1.86 Volt) be the potential of magnesium and unary hydrogen (that is to say hydrogen in inner equilibrium) with respect to the surround- ing liquid layer containing say 1 gr. ion Mg per litre.” 0.058 Applying the formula KE = — log. ta 2.8) and sub- stituting for E the value — 1.86 we can calculate that Lise — (Mg) (0, )* = 108% 16. If we consider that for hydrogen in inner equilibrium 1) The Theory of Allotropy p. 128. 399 L, = (i jr = 102% 48 ITT it will be seen, that for the surrounding liquid layer which is in electromotive equilibrium with magnesium and hydrogen the following formula holds good : MEL) Ee gren (A, Ly It is evident that this ratio is not realizable. If we chose (Mey) = 1 then CH) = 10°*32 and since (a (OH, = = 10—-" we have (OH) = 1018. If we take (Mgy) = 10+ then (HY) == 10-25 Ge (OH) = 1010, From the above figures it is seen that if magnesium is in such a state that the solubility product is 10°" with unary hydrogen and liquid because the surrounding liquid it can never coexist layer, required for this coexistence, cannot exist. A graphical representation of the above statement in Z,X diagram (fig. 1), is given by the point C. C lies so near one axis that any stable aqueous solution lies to the right of it. If we assume that the Fig. 1. solution into which the Mg electrode is dipped has the composition X then there are two limiting possibilities for the coexistence of 400 Fig. 3. 401 Meg, hydrogen and electrolyte. Between these limits the observable cases lie. One limit is indicated in fig. 2. Here the hydrogen is in inner equilibrium but that of the Mg is displaced to such an extent that the potential line of this metal has the position a, ¢,. At the other limit the Mg remains in inner equilibrium but the liberating hydrogen is in a state of formation so that its potential line has the position 6,c, in fig. 3. In the latter case the observed potential of the three phase equi- librium ac,e will practically correspond with the equilibrium poten- tial of Mg’). The observed cases lie between these limits. The above remarks concerning Mg with a potential of —1.86 V. also apply to Mg with a potential of —1.3 Volt. In this case 2x —26 (Mey) Ly. 2x 22 lee 110 and then —— = —"== 10 ‚so that if (Me) Mg (Hy le > L =1,(H)=10-* or (OH’) = 10°. Consequently when Mg of a potential of — 1.3 V. was liberating hydrogen in inner equilibrium from a solution of a Mg salt in which (Mgy) =1, then OH’ in the surrounding liquid layer would be 10°. This is practically also an impossibility. From the above it follows that the hydrogen which coexists with magnesium and the surrounding liquid must be in such a condition that the value of 1, is much greater than that corresponding to the inner .equilibrium. This statement arouses a suspicion to the precipitations of Mg- hydroxide in the surrounding liquid layer, but if this occurred the coexisting hydroged would be formed in a stronger state of formation than even in the case that the surrounding liquid is no longer saturated with respect to Mg(O8),. The solubility produet of Mg(OH), is about 10°” since the value we choose for Mg, is immaterial we will assume (Mg) — 1. In this case (OH) = dom If the Mg-electrode has the value Liv; = 10°* 73 we have already calculated that (Hy) = 10 anon (OH) = 10° which is quite im- possible for the solubility produet of Mg(OH), requires here (OH’) = 1) Here it must be remarked, that if hydrogen is being liberated the composi- tion of the bounding liquid layer will always lie more to the lef than that of the liquid outside. 402 It is therefor evident that the apparent svlubility product of hydrogen shows large deviations, from the value which would be expected when the hydrogen is in inner equilibrium. We will now calculate what the value of the solubility product of hydrogen must be in this case. In the pee we have manifestly employed a value for Ly, which 2x13.25 ,. A grt a ee is 10 times too small. The value of Li, for the hydrogen 2 which is being liberated, in the case under considerations, is therefore 10°*—** instead of 10°%—**. In other words this hydrogen has become so much more basic, that in respect to its electromotive behaveour it somewhat resembles zinc. If the OH-ion concentration in the surrounding liquid layer is lower than 10-°” then no precipitation of Mg(OH), will take place. If (OH) = 10 °° then 10 and electromotively the heden is beginning to resemble manganese. From the above considerations it follows that an approximation to the equilibrium potential of magnesium would only be possible if the hydrogen could appear in a stronger state of formation, for, as already has been demonstrated, an increase in the solubility produet of magnesium will always be accompanied by an increase in the solubility product for the hydrogen which is being liberated. This is not necessary the case with less basic metals. It is clear that the foregoing conclusions will also hold for aluminium and we will now examine the conditions under which we can measure the most active potentials of these metals. According to the theory of capillarity the change between two liquid phases or between a liquid and a gaseous phase is really an extremely sharp change in continuity. In the above case however we are dealing with random arrangements of particles in each phase. When we come to consider a metal and an electrolyte one has a definite structure and the other has not. We are however sure, that in this case also in the bounding layer there will be a very sharp transition, though with a discon- tinuity, and that consequently the coexisting phases will only show quantitative differences with respect to compositions. Now we make the assumption, that the parts, present in the metal bounding layer, in concentrations depending in the depth of the layer, in general will exert influence in the rapidity, with which the inner equilibrium is establishing in the bounding layer. Oxygen, nitric acid, nitrates, etc., are already known to exert a retarding influence on the establishment of internal equilibrium in 403 metals and the electromotive behaveour of Mg and Al now shows that their oxids and hydroxides may exert a similiar influence. In a solution of MgSO,, to which no acid is added, some Mg(OH), is in solution. If we dip a Mg-electrode into this solution then, besides other parts, present in the electrolyte, also Mg(OH), will solve in the metal bounding layer. This does not mean to say, that the Mg will lose any of its characterisiic properties such as the power to precipitate mercury from a solution but this small quantity of Mg(OH), seems to exert a retarding influence on the velocity with which the internal metallic equilibrium is established. A Me-electrode under the above conditions dissolves slowly, evolu- ting hydrogen, and shows too low a potential owing to the disturbance of the inner equilibrium. Addition of sulphuric acid however decreases hydrolysis, and with this the Mg(OH), concentration in the metallic surface and induces a change in the direction of the inner equili- brium of the metal, such that the potential becomes more strongly negative. This effect of adding acid is however twofold. On the one hand the concentration of the negative catalyst in the metal Mg(OH), is decreased, on the other hand direct attack at the metal is increased. This attack in cases where it is rapid, such as the one under con- siderations, always gives rise to disturbances and it might be expected, that the potential would first become more negative and finally would fall a little. This was found to be the case by the author and the GRUYTER and also by Beck. Beck's table XII p. 42 shows this quite plainly. This table sbows in addition that the differences between the Mg and the hydrogen potentials are not constant and that, whilst the hydrogen potential is becoming decreasingly negative, the magnesinm potential changes in the opposite direction. This means that Mg does not behave as a hydrogen electrode, which would be the case if the magnesium surface was unchanged and moreover was surrounded by a liquid layer saturated with respect to the Me(OH),. It is probable that this was the case with some solutions when the H-ion concentration was very low, merely with the vigorous stirring employed in these experiments. The certain conclusion from Brck’s experiments is that, whether the surrounding liquid layer was saturated with respect to Mg(OH), or not, the state of the Mg bounding layer was changing with the hydrogen concentration. By increasing the hydrogen concentration the magnesium bounding 404 layer became more basic that is to say the normal inner equilibrium tended to be established. Another phenomenon showed by Beck which has not yet been considered is that the potential of Mg in MgSO, solutions alone becomes more negative as the concentration increases. Up to the present it has always been observed that a metal dipped into dilute solutions of the corresponding sulphates or chlorides were more early disturbed than in concentrated solutions of the same salts. This was particularly the case with sulphates but also with chlori- des; the phenomenon was namely with chlorides also very distinct, though not so strong as in the case of sulphates. This was always ascribed to the strong catalytic effect of Cl ions and the less one of the SO,. Brck’s measurements now show us that with magnesium not in inner equilibrium, SO, ions has also a powerful effect. Although the highest potential shown in the last table (—1.816 V) is that of an active state of magnesium and the coexisting hydrogen must have been in a strong state of formation (strong overvoltage) yet this potential of Mg does not correspond with the inner equili- brium, for Mg containing small quantition of mercury shows a still higher negative voltage. This value was a maximum for 2 at 24°/, Hg. Now Beck found that the compound between Mg and Hg richest in the latter is Hg,Hg and that the electrolytes in equilibrium with the various amalgams are practically free from mercury. The influence therefore of the small quantity of mercury, under discussion on the Mg electrode can only he an activating one for the EK—X fig. on the Mg side must be as follows (fig. 4). From this will be seen that if the influence of small quantition of mercury has not an activating one, then the potential of the amalgamated magnesium would have been less negative than that of the pure metal. Thus activating by small quantities of mercury causes the true inner equilibrium to be approached more closely. Magnesium which has been activated by mercury showed a poten- tial of —-1.856 Volts when placed in a solution containing 1 gr. mol. of MgSO, per liter. Even this potential is below the equilibrium value owing to the disturbing effect, due to corrosion, but it is probable this is near the true equilibrium potential. It is evident, that the potential of pure magnesium in true inner equilibrium must be more negative than that of the not disturbed amalgam, containing 2 at °/, Hg., because the E—X diagram 405 (fig. 4) shows us, that such potential is rendered less negative by increasing mercury content. Fig. 4. Finally we must consider a remarkable phenomenon to which brief reference has already been made. If we add a little HgCl, in an aqueous solution of MgSO, or of MgCl, in which there is a magnesium electrode, there is an im- modiate fine deposit of metallic mercury on the electrode whose potential becomes /ess negative. As follows from the formula Mg, 2 Mg; + 29, me + wh and 2 4, + Her Her The precipitations of mercury proves that mercury ions penetrate the surrounding liquid layer and that these on arrival combine with electrons, thereby disturbing the heterogenous equilibrium with the result that electrons and magnesium ions enter the solution. It must also be observed that in consequence of the hydrolysis in the magnesium salt solution to which no acid has been added the magnesium electrode will contain dissolved Mg(OH), and will consequenty behave inertly, so that by sending ions and electrons into solution, the potential of magnesium will be altered in the direction of that of the noble metals. The experiment mentioned here is very important; it shows in the first place that the magnesium electrode notwithstanding its non 406 equilibrium state and the dissolved Mg(OH), has still retained its metallic properties. Still its properties have altered, for the precipitated mercury is not able to activate it at once. An apparent explanation, namely that the precipitated mercury does not dissolve in the magnesium, is not correct. For if we remove the magnesium electrode covered with fine mercury, prepared as above, wash it with distilled water and than dip it into pure MgSO, solution, the potential is at first less negative, but it becomes increasingly negative, so that after a few minutes it is stronger than that which attained before the negative electrode was coated with mercury. This is shown in the following table Mg-potential in relation to a Solution 1-N-calomel electrode 0,1 gr. mol. MgSO, p. liter | — 1.902 V. to 150 ccm. of the above men- tioned solution is added 5 ccm. of | a saturated solution of HgCl, | — 1.740 V. | The magnesium electrode was then washed with distilled water and dipped into a pure solution of MgSO4. 0.1 gr. mol. MgSO, p. Liter | — 1.898 V. — 1.956 V. after 5 minutes The above data show that the magnesium eleetrode, though its surface is strongly disturbed by corrosion, has dissolved some mercury. When we consider the great change brought about in a magnesium electrode by corrosion it is no wonder that its other properties, such as the power of dissolving mercury, are modified. The explanation of the results in the above table now is clear. The activating influence exerted by the small quantity of dissolved mercury is not sufficient to decrease the retardation, exercised by the Me(OH), in such a way, that the electrode becomes insensible to the corrosive action of water and sublimate. When this solution has been substituted by one of pure MgSO, the influence of the sublimate disappears and that of the small quantity of mereury becomes manifest. It might be supposed at first sight that in the experiment under consideration solid Mg(OH), depositing on the magnesium electrode might diminish tbe contact between the magnesium and the mercury, 407 the fact is however that the contact between the magnesium and the electrolyte is so good that mercury is separated over the whole surface in a finely divided state, even whilst hydrogen is being given off. At the same time it is clear, that if we wish to get a magnesium into as highly an active state as possible, it is desirable to make its surface as poor as possible in Mg(OH), by first immersing it in an acid solution and then amalgamating it. Magnesium, activated in this way, contains more dissolved mercury and even remains active in normal KOH, giving the high negative potential of —1.97 volts in relation to the hydrogen electrode on account of the low Mg-ionic concentration. In a solution containing 1 gr. mol. MgSO, per liter this electrode gave a potential of —1.85 V. in relation to the hydrogen electrode. Amalgamation experiments have also been studied in detail for Al and will be the subject of a next paper. Amsterdam, Febr. 1923. Laboratory for General and anorganic Chemistry of the University. Botany. — “A method of simultaneously studying the absorption of O, and the discharge of CO, in respiration.” By D. 8. Fernanpes. (Communicated by Prof. F. A. F. C. Went.) (Communicated at the meeting of May 26, 1923). Before entering into details, writer will briefly indicate, how the apparatus works and what precautions should be taken, illustrated by a simple diagram. (fig. |). Fig. 1. From p, a rubber sucking- and forcing pump, the air is pumped as the arrows indicate. The air enters the respiratory vessel v at the top, leaves it at the bottom and is dried in the wash-flask de which contains concentrated sulfuric acid. From d, passing through 409 the glass cock &, (k, is then closed) it reaches the absorptiontubes b,, 6, and 6,, containing baryta-water. On its way back the air passes through the wash-flask d,, containing sulfuric acid like d, and the control-baryta-tube e, after which it returns to p and recommences its circular course. In a subsequent observation 4, is closed and 4, opened, causing the CO, absorption to take place in the tubes b,, b, and b,. The 6 absorption-tubes are fixed to a copper frame with clips. In order to enable us to take more than two observations, without bringing too many tubes in the glass vessel filled with water, which serves as a thermostat, we should have two of these frames at our disposal. If one has served its purpose, the connecting parts 1 and 2 are turned up and rise above the water, where they may be loosened. The whole frame with the 6 baryta-tubes is raised out of the vessel and the other (the tubes of which are meanwhile cleaned and filled each with 100 c.c. baryta-water) is put in. This exchange of frames is brought about in less than a minute, but before taking further observations with the newly-inserted baryta-tubes, we should wait (according to the temperature in the thermostat) 10—15 mins. that the tubes and their contents may adopt the temperature of the thermostat. The apparatus works ventilating during this time in the following way: Cock k, is closed, while #, and #, are opened. If next the pump is set working, the air, leaving the vessel, can only pass through 4#,, while at k, air is sucked in, after having first been rid of CO, by means of wash-flasks containing strong KOH- solutions (not represented in the fig.). There is another advantage in the ventilating action of the apparatus. When in experiments of long duration the observations are stopped in the evening, the apparatus can continue to work ventilating the whole night. Conse- quently the objects are not subject to oscillations of temperature aud the next morning the experiment may at once be continued by opening &, and closing &, and &,. In experiments, lasting 10—12 hours, it saves a great deal of time, to put the plants into the apparatus the previous night, so that early in the morning the ex- periments can begin at once. After the ventilation during the night all CO, has been driven from the apparatus which may be demon- strated by blind experiments. When the outer-air is shut from the apparatus, and the pump is set working, there is immediately produced an effective pressure on the vessel, while the manometer m,, indicates a reduction of pressure. If next k, is opened, the air pressed in the vessel is blown off. On subsequent gradual closure of this cock, the pressure in the vessel 410 = 1. In the manometer m, the liquid is equally high in both limbs, whereas m, indicates a greater negative pressure than before. The broken equilibrium, generated by the action of the sucking-and forcing pump in the closed system is apparently shifted by the opening and closing of 4, in such a way, that in the respiratory- vessel (accordingly on the plants) no effective pressure can arise. As soon as there disappears O, from the closed system through respiration, m, will indicate it at once. When however an equal quantity. of O, is added at the same time, m, will remain at zero and the atmospheric pressure is preserved in the vessel. At O the oxygen, electrolytically produced in Z, enters the vessel. With the aid of the resistance w the O,-development can be increased from a minimum to a definite maximum. The intensity of the electrolytic process may be thus regulated, that the O,-production keeps pace with the O,-consumption. By inereasing or reducing the resistance this equilibrium is soon found and the manometer m, indicates whether this condition is preserved. [t may happen (for instance by rise or fall of the respi- ration-intensity), that for a moment there is a somewhat greater or smaller supply of O, to the apparatus. In this case the height of the manometer 7,, indicating as slight a difference as 0.1 cc.‚ may at once be restored by means of the resistance, so that irregularities in the O, supply, amounting to more than 0,1 ce. need not occur. The hydrogen simultaneously produced by the electrolysis in Z is collected in the burette du. After necessary corrections (in height of barometer, temperature, water-vapour tension and pressure of the water-column in the burette) the quantity of hydrogen received, divided by 2, denotes the volume O,, brought into the apparatus during the observation. The manometer m, renders some other services. When a solution of kalium-jodide (with some soluble amylum) is used, m, is a sensitive test for the existence of spores of ozon. In the presence of this gas for instance the germ-plants of Pisum sativum do not develop normally, so that it is desirable to prevent ozon from entering the respiratory-apparatus. Finally we have in the manometer m, a suitable test whether the desired temperature has been completely adopted by the whole apparatus as well as by the objects. If the observations are started before the whole has attained the desired temperature, the fluid will at onee rise in the open limb of m,, which signifies, that extension still takes place, while in consequence of the respiration (O, absorption) an immediate decrease of volume should appear. 411 For determining the period of preheating therefore m, is of practical interest. The watervapour carried along from the vessel is combined in d, so that dry air enters the baryta-tubes. The watervapour taken from the lye is absorbed in d,. By measuring the increase of volume in d, it may be found, how much water disappears from the lye and the titration standard may be corrected accordingly. This eva- poration from the baryta-tubes is very slight and amounted to cirea 2 ce. in experiments lasting 8 days, so that the correction may be left out without scruple. The manometer m, is filled with mercury and serves to indicate the pressure, to be surmounted by the sucking and forcing pump, needed to drive the air throngh the various liquids. A drop of paraffine-oil on the mercury in the closed limb, prevents the origin- ating of damaging mercury-vapours. On the rubber-pump p taps a flat hammer /, moved vertically by an electro-motor (not represented in the figure). This hammer may be mounted higher or lower in order to regulate the capacity of the pump and consequently the size of the bubbles. The speed of the motor may be increased or decreased by means of a resistance, with which the regulation of the number of bubbles is possible. Size and number of bubbles are of course material to a good CO,- absorption. For an equable distribution of the air, entering the vessel, the ebonite plates on which the plants lie, are brought into a slow rotary movement by an axis. Accumulation of CO, in the vessel (see further on) is excluded in this way. The suction of the air into and from the vessel, causes the liquid in m, to move up and down, which is not to be prevented. At an effective regulation of the pump this movement may be kept so slight, that it is no impediment. Indeed the motor may be stopped at any moment, to Convince oneself whether the manometer is really at zero. The whole apparatus is fixed to the inside of a copper frame and fits exactly in a glass vessel (contents about 45 L.), serving as a water-thermostat. Electrical heating enables us to keep the tempe- rature of the water constant to 0.03° C. The oscillations of tempe- rature in the apparatus itself are slighter than those in the thermostat, so that corrections relating to this, may be omitted. If the apparatus is immersed in the water of the thermostat, it may be easily tested with respect to air-tightness. For this purpose air is pumped into the apparatus through £, and one watches whether 27 Proceedings Royal Acad. Amsterdam. Vol. XXVI. 412 any bubbles rise from the water. When the connections are made with vacuum rubber-tube and glass to glass, leakages do not oceur. IT. Descriptions of the parts. a. Sucking- and foreing-pump (tig. 2). An air-tight pump, working for a long period without failing and having a sufficient capacity, is easily constructed. "The glass tubes 7 and w are connected by a piece of strong rubber-tube p (about 15 ems. long and 2*/, ems. wide). Each of the tubes 7 and « is provided with a valve, consisting of a piece of vacuum-tube (1 em. long) 1, to which the end of a piece of valve- tube 2 (about 3 ems. long) is glued on with solution. The other end of the valve-tube is tightly tied with a string at 3; in the valve-tube a straight lengthwise cut 4 is made, the two edges of which meet, when the pump does not work. To prevent these edges from sticking together afterwards, they have been rubbed in with taleum powder. The glass tubes / and v fit in the rubber-tube p, while the vacuumpieces 1 must also fit perfectly. How the pump works, when the hammer A taps on it, is clear from the fig. 2. b. The respiratory-vessel (fig. 3). As in Kuyprr’s research’) here too is made use of a copper cylinder 1. The experimental objects are on the ebonite plates ¢, fixed to an axis a,. In each of the plates ¢ 25 round holes are made in such a way, that germinating seeds of Pisum sativum cannot fall through. On the plates ¢, moist cotton-wool is put, on which the roots rest, in consequence of which there cannot occur a deficiency of water. The axis a, is enlarged at the top, provided 1) Kuyper J: Recueil des Travaux Botaniques Néerlandais. Vol. VII. 1910, pag. 1. 413 with 4 teeth ¢a, just fitting into the four teeth ta, belonging to a simular enlargement at the base of the axis a,. This steel axis a, passes through a copper case / (soldered to the cover), in which it | th vil ie B H i — ¢ 2 i i H H H H Á ; H H ) i A H Y A | | | | 2 my, H f i / H 4 H | | H : / vu i f x Ú Amite ss, J 4 f H 4 / men t i Lp 4 a | il D i A Za je A 4, be Fig. 3. fits exactly, but may be easily rotated. Round & there is a glass cylinder g, closed at the bottom by the india-rubber-ring 7. The axis a, is at the top tightly clasped in a copper tube &,, at the bottom of which the hollow metal cylinder c is fastened, and at the top the grooved wheel sv. By the oil in g the axis is closed 27* 414 off air-tight and leakage is impossible, because there never arise great differences Gf pressure in the vessel. In the middle of the loose part 6 there is a cavity, in which a, can rotate freely. When sn is slowly rotated by a motor, a, will transmit this movement by means of the teeth fa, and ta to a,, which causes the circulating air to be equably distributed over the whole vessel, in consequence of which the germplants are constantly surrounded by fresh air. The necessity of ventilation in a cylindrical respiratory vessel (dia- meter 15 cms., height 20 cms.) was immediately apparent from one of the many test experiments. At a constant temperature of 20° C. the O,-absorption caused in 50 mins. a height of 4 ems. on ‘the manometer m,. Next a quicker circulation of 10 mins. duration followed, causing an equal rise of the manometer as before in 50 mins. No other explanation of this could be found, but the occurrence of a CO,-accumulation in the vessel. This was supposed to be due to the fact, that the air entering at v/ passed by the easiest route through the vessel to the exit vu, taking with it only part of the CO,. When in consequence of a more rapid circulation part of the accumulated CO, disappeared, this explained a sudden greater rise of the manometer. As soon as the rotary movement of the respiring objects, prevented all CO,-accumulation in the vessel, there was indeed no abnormal rise of the manometer to be noticed. It needs no argument, that not only with a view to oxygen-supply and measurement, but also for other reasons, the CO, due to re- spiration, should be directly removed. With a CO,-accumulation in the vessel, a volumetric determination of the vanished quantity of QO, is no more possible. Besides in this case part of the plants gets into an atmosphere full of CO, and deficiency of O, will soon cause intramolecular respiration. It seems to me, that in the respiratory apparatus after the model given by Prrerrer and Dermer and used e.g. by Kuyper, little or no attention has been paid to the error which may be committed, when in a respiratory vessel as described in this paper, no perfect ventilation is provided for. The loose bottom 6 is provided with a marginal groove, containing a rubber-ring. The handle be bears in its middle a screw s, which, when turned up, presses on ve and by doing so presses the lower edge of the vessel tightly in the groove with rubber-ring. In the cover of the vessel is, besides the aperture o to admit oxygen, also a pierced rubber-cork through which a thermometer th passes. c. Fig. 4 gives a representation of the drying-tubes and the 415 controltube. Cock 1 serves for filling, coek 2 for emptying and cleaning. d. The absorption-tubes are fastened to a copper frame (fig. 5). As with a view to preversing a constant temperature ; the size of the thermostat cannot be chosen at will, straight absorption-tubes (length 25 ems., width 3 ems.) si are more suitable than Perrenkorgr or WINKLER-tubes. When baryta-water is chosen for combining with CO, (21 grammes of bariumhydroxyde + 3 grammes of barium- chloride in 1 L. of water), the absorption is only complete, when the air passes through 3 of those tubes (each containing 100 ee. lye). Each frame of 6 tubes therefore can only serve for two observations. The tubes end at the base in thin open pieces, which may be plugged by rubber stoppers. At the top they are closed by rubber- corks 3 ems. thick. In each cork there are three holes, Fig. 4. two of which serve for the inlet- and exhaust-tubes, while the third, which serves for filling can be plugged by a little massive glass bar. The tubes are connected with vaeuum-rubber 416 tube, just as all other connections in the apparatus are made. There was no sign of any CO, diffusion inward from the water of the thermostat through the rubber-connections and corks, nor of an Q,-absorption through the rubber. Blind experiments, lasting 24 hours gave no measurable change of titration standard of the lye at tempe- ratures between 20° and 30°C., while the manometer m, remained at zero throughout that time. e. The oxygen-supply and measurement. In order to prevent ozon-formation, a 10°/, natronsolution is to be preferred to diluted sulfurie acid for the electrolysis, In fig. 6 C is a glass eylinder with natron-lye in which the platina-eleetrodes p, and p, are placed. By means of thin platina- wire these electrodes are fastened by melting in the glass-tubes 1 and 2 respectively. The tubes 1 and 2 pass through caoutchouc- ‚Fig. 6. 417 corks, fitting exactly in the wider tubes w and z (open at the bottom) and are filled with some mercury. By means of a resistance we the intensity of the current can thus be regulated, that the amount of the electrolysis can reach the desired extent. Thus it is possible to keep the oxygen-development, occurring in the tube z at the electrode p,, in balance with the O,-consumption of the respiration. As a resistance (we) a glass basin with water, in which the electrodes w, and z,, is quite satisfactory for this purpose. By moving w,, which is fastened to a stand, along a sloping board, not only the distance w,—z, is made smaller or larger, but this electrode also goes more or less deep in the water. The O, formed in z is in open connection with the manometer m, and the respiratory-vessel. The tube z really is likewise a mano- meter, in which the lye will be equally high as in c, when the quantity of O, developed is equal to the quantity disappearing in the apparatus; m, however, as already mentioned, is necessary to control the ozon-formation. For receiving the hydrogen, formed at the electrode p, in the tube ww, the burette bu serves, which gives accurate readings to 0.1 ce. This burette ends at the top in a bent glass tube 3, provided with a glass cock & At the bottom the burette has a narrow aperture, while not far from this a lateral tube has been fitted on, forming a connection with the tube w. When the burette is placed in such a way, that the bottom aperture lies just below the water- level in the thermostat, it is impossible, that while water is flowing out, air is ascending in the burette at the same time. Filling the burette with water from the thermostat is done by closing 4, opening & and sucking at the tube 3. When after filling & is closed and &, open, the only reason why water should flow from the burette, is the formation of hydrogen in w, which rises in the full burette as bubbles. The formation of the first hydrogen-bubbles in the burette requires a little effective pressure, which is shown by the fall of the fluid in the tube w. This effective pressure, which remains constant during the emptying of the burette, should exist before the observations begin, lest the first reading should give a too small figure. This error is prevented, when some minutes before the experiment commences — when the apparatus still works ventilating — the electrolysis is made to take place, till the first bubbles vise in the burette. In case that, during one and the same observation, the burette is filled several times, the sucking up of the water should occur very slowly and equally, lest the hydrogen, which is in the connective-tube between 4, and the burette, should be sucked in 418 with it. If the water is sucked cautiously into the burette, the effective pressure once made is preserved in 2. Another error arises, when the burette is exposed to oscillations of temperature in the laboratory. In that case not only in w, but also in z and m, falls and rises occur, which are not due to ab- sorption of oxygen. This may be prevented by keeping the burette likewise at a constant temperature, which may be attained as follows. By means of a metal sucking- and forcing-pump zp (likewise fastened to the copper frame, to which the whole apparatus is fastened) water from the thermostat is pumped up with great rapidity into a wide glass cylinder wa, which contains the burette. The water enters wa at the bottom and is led back to the thermo- stat at the top through the tube af. Even at high temperature (50°, 55° C.), the temperature in the burette is kept equal to that of the water in the thermostat in this way. f. The regulation of the temperature principally corresponds to the one deseribed by Rurerrs') and Conen Stuart’) and is an imitation of apparatus, used in the van r Horr-laboratory at Utrecht. The heating-apparatus » (fig. 7) consists of a copper case, sur- mounted by a metal tube, rising above water. In v is paraffine-oil, electrically heated by a nickel-chrome-wire, wrapped round a piece of mica. Thermoregulator 7, stirring-apparatus 7 and v, are close together in an open glass cylinder c, resting on legs in the centre of the thermostat g. To prevent all influence of vibration in the height of the mereury, the thermoregulator is hung from the ceiling on a steel spiral-spring, according to the method Morr. The method described above gives no new principle, with respect to the CO,-determination. We have chosen the simple and always trustworthy baryta-method, which need not be further described here. On account of the insertion into a closed system, the various parts were subjected to some alterations in shape, which however have nothing to do with the principle of the baryta-method. The problem of oxygen-supply, ever yielding many difficulties, could be satisfactorily solved. Compared with the methods’) already existing, the following advantages and simplifications are achieved: 1) Rutgers, A. A. L., Recueil des Travaux Botaniques Néerlandais. Vol. IX, 1912, pag. |. 2) CoHEN Sruart, Recueil des Travaux Botaniques Néerlandais. Vol. XIX, Livraison 2. 1922. 3) Cf. Krom: “The respiration exchange of animals and man. LoNemans, Green and Co., London 1916”. 419 a. the decrease of pressure and oxygen-content in the apparatus is reduced to a minimum. 6. the place of the consumed QO, is at once taken by pure O,, without first passing a stop-valve, and may directly be controled. c. an oxygen-bomb or other reservoir may be omitted. The apparatus has been constructed by Mr. P. A. pr Bourne, amanuensis at the Botanical Laboratory at Utrecht. I am greatly indebted to him, not only for the way, in which he performed his task, but also for introducing some clever improvements. Utrecht, May 1923. Botanical Laboratory. Physiology. — “A new form of correlation between organs.” By Prof. H. J. HAMBURGER. (Communicated at the meeting of May 26, 1923). Thus far we were acquainted with two forms of cooperation between organs. As to the eldest known form, here the central hervous system plays an important role. If any one pricks my finger unexpectedly with a needle, | immediately withdraw my arm; a cooperation has taken place between the skin of the finger and the museles of the arm, and well by means of the spinal chord. Here we have to deal with a reflex. Some years ago we got acquainted with a second form of corre- lation between organs; this one is not effected by means of nerves, but here the bloodeurrent is the mediator of the cooperation. For instance, the glandula thyroidea produces substances, which are carried through the body by the bloodeurrent and influence the metabolism and growth of distant organs. That nerves here don’t play an essential role appears from the fact, that the glandula thyroidea still exerts its influence, even when it is detached from its nerves and transplanted to another part of the body. Now, in the last years experiments, performed in our laboratory, have clearly demonstrated a third new form) of correlation between organs. The starting point of these researches, carried out by Dr. R. Brinkman, Miss E. van Dam and Dr. L. JeNDRASSIK, was the following experiment of O. Loew: in Graz. The vagus nerve of an isolated frog’s heart, which is filled with a salt solution, is for some time stimulated so that the heart stops its beat. Then the content of the heart is removed and transferred into another frog’s heart, which was isolated in the same way. Then the well-known pharma- 1) See my lecture at the opening of the Biological Buildings of Me. Gill’s University in Montreal (Canada) in September 1922. See also: H. J. HAMBURGER. The increasing significance of permeability problems for the biological and medical sciences; the Charles E. Dohme Memorial Lectures. First Course, 10, 11, 12 October 1922, delivered in Baltimore; printed in: Bulletin of the Johns Hopkins Hospital, June 1923. 421 cologist saw, that the second heart often showed slower contractions. Experiments with the sympathetic nerve gave analogous results. Now the purpose of our experiments was in the first place to eontrol the results of Lonwi’s researches under more physiological conditions. In the vena cava of a frog A a glass tube is inserted and in this way a suitable saltsolution is conducted through the heart. A similar small tube is introduced into the aorta. Then we see, that the saltsolution will leave the heart in a rhythmical manner. If then the fluid, leaving the heart, is led to the vena cava of another frog B, the fluid will run through the heart B, and after leaving it by the aorta of this second frog, it may be taken up again by the vena cava of the first frog A. Thus we obtain a circulation of saltsolution through both frog’s hearts. This method of socalled “crossing circulation” was first introduced by Prof. J.C. HEMMETER. Now, if the sympathetic of the first frog A be stimulated electric- ally, causing acceleration of the heart beat of this frog, it can be observed that already after a few seconds, the heart rate of the second frog B is also quickened, although the sympathetic of this animal has not been stimulated. How to account for the acceleration of the second heart? Evidently in no other way than by assuming that in the first heart A, in virtue of permeability of course, sub- stances were liberated which had a similar effect upon the second heart as if this had been directly stimulated. I shall presently come back to the probable nature of these substances. How it is possible that substances, liberated by a physiological action of an organ, here the heart of the frog A, may also stimulate the same organ of the second animal B, [ shall not discuss here. It is sufficient to say, that there is an analogy between this case and the secretion of saliva. If we allow a salt solution to percolate through the salivary gland, as J. Demoor has demonstrated some years ago, no saliva is secreted. However it does occur if a small quantity of saliva is added to the saltsolution. The product formed during the activity of the salivary gland is, it seems, a stimulus again to further secretion of saliva. The substances, formed in the stomach during conversion of protein, excite gastric secretion. It is therefore not strange that the substances, liberated in the first heart during stimulation of the sympathetic, should have a stimulating action on the second heart. Dr. BRINKMAN and Miss van Dam made yet another experiment that in a still more convincing and striking manner demonstrates, that the transmission of stimuli can take place by means of fluids, 422 in other words that there exists a humoral transmission’), I say “in a still more convincing manner’, for by the just mentioned experiment the remark could be made, that with the movement of the second heart hydrodynamic influences might have played a rôle. For this reason for the second organ not the heart of the frog B was taken, but the stomach of this animal. It is well known that stimulation of the sympathetic nerve is followed not only by an acceleration of the heart beat, but also it slows, even inhibits the spontaneous movements of the stomach. Now the question arose: if the fluid of the stimulated heart of frog A is transferred into the arteria gastrica of the frog B, will it then cause the spontaneous movements of the stomach of this last frog to grow slower, even to stop? This proved to be the case, as the experiments of Dr. BRINKMAN and Miss van Dam showed us. In other words, on sympathetic stimulaiton of the first heart sub- stances were liberated which influenced the movements of the stomach in an inhibitive way. Analogical phenomena as occur in stimulating the sympathetic nerve could be observed by stimulation of the vagus nerve. As it is well known, stimulation of this nerve affects the rate of the heart beat and also influences the strength of the contractions of the stomach, but in an antagonistic sense. Stimulation of the vagus slows the heart, but causes the contractions of the stomach to become more powerful, contrary to what happens when the sympathetic nerve is stimulated. Now the experiment was repeated by crossing the circulation of the beart of the first frog with that of the stomach of the second frog; in other words, the salt solution coming from the heart of the first frog, is conducted to the stomach- circulation of the second frog. On stimulating the vagus of the first frog, the heart slows its beat and when the solution has passed through this heart and reached the stomach of the second frog, this organ shows typical vagal contractions, though the vagus of frog B has not been stimulated electrically. From this we may infer that stimulation of the vagus of the first frog sets free in its heart vagus-substances, which may cause the stomach of the second frog to contract, as if its own vagus nerve had been directly stimulated. We are therefore in presence of two kinds of substances liberated by the vagus and sympathetic nerve respectively, which may be called vagus- and sympathetic substances. IR. BRINKMAN und Frl. E. v. Dam, Pfliiger’s Archiv. Bd. 196, S. 166, 1922. 423 That really such substances exist, could be directly proved by the fact that the salt solution, leaving the heart after stimulation of the vagus, contains substances, which lower the surface-tension of the original salt solution, socalled capillary-active substances. On the other hand we find that the surface-tension of the salt solution, coming from the heart after the sympathetic nerve has been stimulated, is slightly increased"). Further it appeared that the vagus- and sympathicus-substances were able to neutralize each other in capillary- active sense, i. 0. w. they were able to neutralize each other’s influence on the surface-tension. I shall not euter here into further particulars. It is an established fact now, that as an effeet of stimulation of the vagus nerve, a liberation of vagus-substances takes place, and that on stimulating the sympathetic nerve, sympathetic-substances are set free. However the nature of these substances has not yet been determined ; perhaps, at least with the vagus-stimulation, we have to do with cholin- compounds, which cooperate with the potassium. As for the method to determine the surface-tension of very small quantities of fluids, we refer to two articles, which appeared last year?). There it is shown that a very simple apparatus will do for this purpose. By means of a torsion balance, well-known to the clinicians, the force is determined which is necessary to pull off a small platina-ring from the surface of the fluid which is to be examined. The experiments discussed here, give rise to many questions. So the clinician will think of the bearing of these results on the nature of vagotonia and sympathicotonia and will ask himself under whieh conditions an excess of vagus- and sympathicus-substances will exist in the circulation and influence different organs; and also he will put himself the question how it will be possible to make this surplus harmless for the body. The physiologist will ask himself whether the latent period and the after-effect in vagus-stimulation can be explained by the time, which is necessary for the liberating and the disappearing of the vagus-substances; further he wants to know whether the vagus- substances are specific for one and the same animal. And what will be of interest both for the physiologist and the clinician is the question: can we observe the same phenomena, seen in the frog, 1) See the article of Dr. BRINKMAN and Miss van Dam, in the Journal of Physiol., still to appear. 2) R. BRINKMAN und Fr]. E. van Dam. Münch. Med. Wochenschr. 1921. S. 1550. R. BRINKMAN, Arch. Néerl. d. Physiol. VII 1922, p. 258. R. BRINKMAN und Frl. E. van Dam VIII, 1923, p. 29. 424 also in warmblooded animals? With this question Dr. L. JENDRASSIK has occupied himself very recently. The results obtained untill yet, can be summarized in a few words. If the surviving heart of a rabbit is perfused with a suitable salt solution, and we stimulate the vagus nerve, then the liquid, leaving the stimulated heart is able to accelerate in a high degree the contractions of an isolated piece of gut, taken from the same animal. I cannot enter into these researches on this place. Dr. JENDRASSIK will describe them in a short time in the Biochemische Zeitschrift. Here we will only point out that the experiments proved, that on stimulation of the vagus nerve not only in the heart of coldblooded animals but also in those of warmblooded animals substances are produced, which are able to influence other organs in the very same way, as if the vagus of those organs were stimulated by an electrical current. Here the gut proved to be the most suitable object for the researches. Further I might draw the attention of the readers to three remark- able facts. In the first place it appeared that an extract of the atrium of a rabbit’s heart in saltsolution was also able to accelerate the contractions of the isolated piece of gut. This experiment was made in considering that it would be very probable, that the atrium still contained vagus-substances, which were formed there during the life of the animal. Secondly it appeared that if atropine, which, as is well known, inhibits the influence of vagus-stimulation, was added to the active extract, this was turned into an unactive one, i.o.w. then it had no more influence on ihe movements of the gut. In the third place it was found, that the extract of the ventricle- muscle of the heart has a sympathetic effect on the movements of the gut instead of a vagus-influence. The experiments on warmblooded animals described above, were all performed in a room of body temperature. Sau WM ALR: Thus far we have been acquainted with only two forms of correlation between organs, one, the eldest, established through interference of the central nervous system in cases where a quick response is needed (reflexes). The second form comes into play where slow processes are concerned; it may be exemplified by the intluence of the glandula thyroidea on metabolism and growth. For the formation of hormons the influence of the nervous system is not needed, neither for the transport by the bloodeurrent. In the third new form 425 of correlation the action is neither quick nor slow; it is to be seen at work where functions, holding the medium between these two, are concerned. The essential thing here is, that by nervous stimula- tion substances are set free, which are conducted to other parts of the body. There is much evidence to lead to the belief that the three forms may finally by reduced to one, but I cannot enter into this here. | have spoken about this possibility already in one of my Herrer-Lrorures, delivered in New-York in October 1922. It may be of importance to lay stress on the fact that the forma- tion of vagus- and sympathicus-substances is not only postulated, but that it is proved directly in a physico-chemical way. There is no doubt that an analogous correlation between organs as described here for heart and stomach and for heart and gut will be established also between other organs’). We face here a wide field of new researches; we are only in the beginning. May 1923. The Physiological Laboratory of the University of Groningen. 1) So it appeared very recently in our laboratory, that when stimulating the nervus vagus and the nervus sympathicus of the heart, substances are set free, which influence the Jwmen of the small urteries of another animal. (Note after the correction). Chemistry. — “The Synthesis of some Pyridylpyrroles.” By Dr. J. P. Wisaur and Miss ErisaBETH DINGEMANSE. (Communicated by Prof. P. van ROMBURGH.) (Communicated at the meeting of March 24, 1923.) In the course of the researches on the structure of the natural alkaloids, several of these vegetable bases have been prepared by synthesis. In other groups of vegetable substances, investigators have not only succeeded in building up the substances occurring in nature, but also closely allied bodies were obtained synthetically. In the group of the sugars, e.g., a number of monoses have been obtained which do not oceur in the vegetable kingdom, but which are isomeric with or closely related to the sugars found in nature. Our knowledge of the chemical and biochemical properties of the monoses dias been greatly improved by these synthetic researches. It seems not devoid of interest to try and build up an isomer of a natural alkaloid, in order to examine afterwards in what respect the iso- meric substance is distinguished from the natural alkaloid, especially with regard of physiological and biochemical properties. Keeping this end in view we will try to build up an isomer of nicotine. ‚In his synthesis of nicotine Picrer started from g-amino-pyridine; this substance was heated with mucic acid, through which N (g- pyridyl)-pyrrole (I) was obtained. At high temperature N (3-pyridyl) pyrrole undergoes an isomerisation, in which C (s-pyridyl)-pyrrole (II) is formed: CH CH = CH CH ore, a HCS eK | i EL No 20 nen | oi. \ch=cH erase nd HC N/CH HC NY CH H N N IT. Pictrt and Cr&pinux') give the above structure to this C (8-pyridyl) 1) Ber. d. deutsch. chem. Ges. 28, 1904 (1895). 427 pyrrole, in which it is, therefore, assumed that the pyridine nucleus is united at the «C atom of the pyrrole nucleus. In how far this assumption is justified, will be discussed after- avards. The preparation of these substances did not offer any special difficulty; on the other hand, the conversion of C (pyridyl) pyrrole (Il) into the methyl derivative, nicotyrine (III), was difficult to realize: a en a OGL. HZ \ nee He HEA von ba aa CH De HC JCH ENG XN CH, Ng CH, UI Iv. When it is tried to methylate the pyrrol derivative at the nitrogen atom by treating the potassium-compound with methyl-iodide, there is also a molecule of methyl iodide combined with the nitrogen atom of the pyridine nucleus, so that the iodine methylate of nicot- yrine is formed, from which afterwards methyl iodide must be split off. Prerer and Rotscny') have obtained but very little of the nicot- yrine by this method. For the continuation of his experiments Picrer has, therefore, made use of a nicotyrine preparation which was prepared by oxidation from nicotine (IV) by Brav’s method. A similar procedure is of course impossible in our case. In the end Picrer and Rorscuy have succeeded in reducing nicotyrine to nicotine by an indirect way through making use of iodine and bromine substitution products. Hence if this synthesis is repeated, starting from «-amino-pyridine, an isomer of the nicotine can be built up, in which the pyridine nucleus is substituted at the «-place. As a-amino-pyridine is at present an easily accessible substance, it seemed not impossible to obtain sufficient quantities of all the intermediate products, so that it may also be expected that it will be possible to prepare so much of the final product that its properties can be properly studied. § 2. The preparation of N-(a-pyridy!)-pyrrole. For the preparation of N-(@-pyridyl)-pyrrole we have heated 25 gr. of a-amino-pyridine with 28 gr. of mucie acid. First the salt of 1) Ber. d. deutsch. chem. Ges. 37, 1225 (1904). 28 Proceedings Royal Acad. Amsterdam. Vol. XXVI. 428 mucie acid with 2 mol. @-amino-pyridine is formed. At a tempera- ture of about 140° this salt begins to decompose: with separation of water and carbon dioxide the pyrrole derivative is formed while 1 mol. amino pyridine is split off. Hence a distillate is obtained which contains besides water, the required pyrrole derivative and amino pyridine. We have subjected the reaction product to fractio- nated distillation at 15 m.m. pressure. The first fraction of 104— 130° is chiefly «-amino pyridine: At 140—145° distills a liquid, of a slight yellow colour, which solidifies to a white crystalline mass on being cooled in ice. The melting-point of these erystalls is Went. This substance is N-a(pyridyl)-pyrrole, to which the following structure formula (V) applies. CH Ho7\ cH v HC =CH He Jo nt | NZ Nuc = CH nb The freshly distilled N-(«-pyridyl)-pyrrole is a colourless liquid, which, however, assumes a dark colour after some time. The boiling- point at 760 mm. lies at 260—261°. This substance is sparingly soluble in cold water, volatile with water vapour, and readily soluble in all organic solvents. A pine- chip moistened with hydroehloric acid is coloured red-violet by the vapour of N-(@-pyridyl)-pyrrole; with a hydrochlorie acid solution of dimethylaminobenzaldehyde there arises a red-violet colour, which later on changes into a dirty green. These colour reactions are considered as characteristic of pyrrol derivatives. By potassium permanganate this compound is rapidly oxidized already at the ordinary temperature. The values of 19.58°/, N and 19.34°/, N were found for the nitrogen percentage of this preparation, the calculated percentage for C,H‚N, being 19.44". We have prepared a picrate of this substance which melts at 143°. We obtained the iodine methylate of the N (a-pyridyl)-pyrrole by heating it in'a sealed tube at 100° with the calculated quantity of methyl iodide. The reaction product was recrystallised from aleohol: yellowish white prisms, melting- point 141°—142°. The isomeric N (s-pyridyl)-pyrrole prepared by Picrer and Crépreux has been described by these investigators as a liquid with 429 a boiling-point of 250.5—251° at 730 mm., which does not solidify at —10°. The yield of N (e@-pyridyl) pyrrole was in our experiments from 7 to 8 gr. out of 25 gr. of «-aminopyridine. We found, however, that there is formed another substance besides this pyrrole derivative in the reaction between mucic acid and amino pyridine. During the distillation of the reaction product a liquid went over at 170°— 190° and 15 mm., which erystallized at room temperature. After reerystallisation from aleohol this substance had a melting-point of 95°, and appeared to be «-'- dipyridyl amine. The formation of this compound during the heating of the mucic acid salt of amino pyridine seems to be analogous to the formation of diphenylamine from aniline and hydrochloric aniline. . We have actually obtained «-e-dipyridy! amine by heating equivalent quantities of e-amino pyridine and the bydrochloric acid salt of this base in a sealed tube for two hours at 300°. We hope to return to this reaction on another occasion. § 3. The conversion of N(a-pyridy!)-pyrrole ito two isomeric C (a-pyridyl)-pyrroles. It was found long ago by Ciamician') and his collaborators that the N-derivatives of pyrrole can be transformed into C-derivatives by the action of high temperatures. CramicraN and Magnacui’) heated N-acetyl pyrrole in a sealed tube at 250—280° and found that part of the starting material was changed into pyrryl methyl ketone: HC—CH HCS CH (hy fe HC CH = HC €.COCH; a NVA N. COCH, NH That the acetyl rest actually oecupies the «-position in the pyrrole nucleus, results from the observation that the bromation product of this pyrryl methyl ketone yields the imide of di-bromomaleic acid by oxidation with nitric acid *). Also some other pyrrole derivatives, in which an acylrest is combined with the nitrogen atom, were trans- formed into «-pyrrylketones on heating. It was found later by Picrer and his collaborators that N-methyl pyrrole, N-phenyl-pyrrole, and similar substituted derivatives of 1) Cf. Cramrcran. Ber. d. deutsch. chem, Ges. 37, 4200 (1904). 2) Ibid. 18, 1828 (1885). 3) Cramician and SiLBeR. ibid. 20, 2594 (1887). 28* 430 pyrrole can be transformed into C-derivatives by distillation throngh a red-hot tube. In all these intra-molecular arrangements only one C-derivative was found, whereas it would be theoretically possible that two isomeric pyrroles would be formed, since the hydrocarbon rest might be united at the «- or at the g-carbon atom of the pyrrole nucleus. From N-methyl! pyrrole the «-C-methyl pyrrole was obtained by Picter. The structure of «-C-methyl pyrrole had already been deter- mined by Zanetti, by converting this substanee into the dioxime of levulie aldehyde. Picter and Créprikux assume on grounds of analogy that in the C-phenyl pyrrole which they obtained from N-phenyl-pyrrole, the phenylgroup is united at the «carbon atom of the pyrrole nucleus, and that the same thing holds for the C-pyridyl pyrrole (ID), which they obtained from N-(pyridyl)- pyrrole (I). A direct experimental evidence, for this view was not given. As regards Prcrer and Crépirox’ B-pyridyl-e-pyrrole, the structure which these investigators assign to it, is undoubtedly supported by the fact that they have obtained nicotyrine (III) from this g-pyridyl pyrrole, as the structural formula ([V) of nicotine has been made very probable by Pinner’s researches. We found however that two isomeric C-pyridyl-pyroles are formed in the transformation of N(a@-pyridyl) pyrrole, one of which melts at 93° and the other at 132—132.5°. This reaction must be represented by the following scheme: CH HCZ\CH HC—CH shit be ™ CH aad N Sn HCZ\CH ay NH (0) EN SCH HON ZON \ da HC HC/Z\ CH ere ~ HO\/C————C—_CH N oll Cae HC CH Ww NH To which of our isomers formula VI applies and to which formula VII should be assigned, has not yet been established. It 431 will not be very easy to decide this point. In former researches it has been tacitly understood that in the transformation of a N-deri- vative of pyrrole in a C-derivative, it is always the «-compound that is formed. In consequence of our observations the validity of these conclusion has become doubtful. We shall now give a short description of our experiments on these reactions. In the first place we have determined the most favourable temperature for the transformation of N(e-pyridyl) pyrrole into the C(a-prridyl) pyrroles, as in Picter’s papers the reaction tempe- rature is only vaguely indicated as “heated to redness” or ‘faintly red-hot”. The best procedure appeared to be as follows: 25 gr. of N(a-pyridyl)pyrrole are distilled through a glass tube filled with pieces of pumice, which is heated at 670°—690° C. in an electrical oven. Part of the substance is decomposed, which shows itself in the formation of dense white vapours. The distillate consists of a black liquid, which soon solidifies at room temperature. This reaction product was distilled with steam, in which a white erystalline substance passed over, which was filtered off. This substance appeared to be very sparingly soluble in cold water. The erude product melted at 84°; after recrystallisation from a mixture of benzene and ligroine the melting-point is 90°. The yield of this substance was about 12 gr. The aqueous distillate contained only very little unchanged N(e-pyridyl) pyrrole. A second substance remained behind in the distillation flask, which is not volatile with water-vapour, and which after recrystallisation from hot water melts at 132—132.5°. Properties of the pyrridyl-pyrrole melting at 90°. This substance is obtained from benzene, to which some ligroine has been added, in hard, very shiny, colourless octobedrical crystals. We found 19,41 °/, for the nitrogen content; 19,44°/, was calculated for C,H,N,. This substance is readily soluble in alcohol, ether, chloroform acetone and benzene; less easily in hot water and ligroine, very little in petroleum ether. These solutions exhibit a blue fluorescence, except the aqueous and alcoholic solution. A solution of 3-pyridyl a-pyrrole also shows fluorescence according to Picret and Cripievx. Our pyrrole derivative does not give a colour reaction with a pine-chip moistened with hydrochloric acid; with a hydrochloric acid 432 solution of dimethyl-aminobenzaldehyde there appears, however, a red-violet colour. Metallic potassium acts on this substance: a potassium compound is formed, as is to be expected. For this purpose we dissolved the substance in toluene, and let the potassium act at the boiling tem- perature of the solution. At first the action proceeds pretty rapidly, but it soon slows down, so that the heating must be prolonged. The potassium compound was deposited as an insoluble yellow- brown powder. In order to ascertain the structure of the C-(«-pyridyl)-pyrrole, we have oxidized two grammes of this substance with potassium permanganate in sulphuric acid solution. The oxidation takes place very readily at the ordinary temperature. Out of the reaction product we have isolated the characteristic violet copper salt of picolinic acid, and from this salt we freed the picolinic acid itself by addition of sulphuretted hydrogen. The picolinic acid thus obtained was sublimated in order to purify it. The sublimated preparation melted at 134°.2, while we found 136°.8 for the melting-point of picolinie acid obtained by oxidation of picoline. The melting-point of the mixture of these two preparations was 132.5°—133°. The nitrogen percentage of our preparation that melted at 134.2, was 11.25 °/, (calculated for picolinie acid 11.38 °/,). In spite of the slightly too low melting-point there is no doubt of the identity of our prepara- tion; the characteristically crystallizing platinum salt had exactly the same appearance as the platinum salt of the picolinie acid prepared from picoline. It appears from this that in the pyrrole derivative melting at 90° the pyrrole nucleus is united to the «-C-atom of the pyridine nucleus. We have prepared a picrate from this pyridyl pyrrole, which was obtained after reerystallisation from alcohol as fine, yellow needles of the melting-point 227—228°. We have prepared the iodine methylate of the pyridyl! pyrrole melting at 90° by heating this pyrrole derivative in methyl alcoholic solution with an excess of methyl iodide at 100° for three hours. After evaporation of the solvent and of the superfluous methyl iodide the reaction product was recrystallized from methyl alcohol; in this way yellow-brown hard prism-shaped crystals were obtained, which melt at 148°. We found 9,6°/, for the nitrogen content, and 44.7 °/. for the iodine content. The calculated values for CHN, J are N: 9,73 °/,; J: 44,37 °/,. This substance has, therefore, been formed bv the addition of one molecule of methyl iodide; the group CHA is combined with the nitrogen atom of the pyridine nucleus. 433 Properties of the pyridyl-pyrrole melting at 132° 5. This substance, which as we already remarked, is not volatile with water vapour, and is separated in this way from the isomer melting at 90°, crystallizes from alcohol or benzene in leaves joined to rosettes; from hot water long needles are obtained. This base is readily soluble in alcohol, ether, acetone, chloroform, and benzene; not so easily in ligroine and hot water, very little soluble in low-boiling petroleum ether. As far as the solubility properties are concerned, there is, therefore, a close agreement with the isomer melting at 90°. The ethereal solution shows a blue fluorescence. We found 19,34°/, and 19,62 °/, for the nitrogen content (calculated for C,H,N,: 19,44°/, N). This base does not give a colour reaction with a pine-chip moistened with hydrochloric acid; with a hydro- chlorie acid solution of dimethylamino-benzaldehyde there appears, however, a cherry-red colour, which has changed into blueviolet after a day. That this substance, too, possesses a pyrrole nucleus, appears again from the behaviour towards metallic potassium. The base was dissolved in toluene and the calculated quantity of potassium was added. The potassium dissolves with vigorous generation of hydrogen; the reaction is much more rapid than with the isomer of melting- point of 90°. The potassium compound is deposited as a white powder. We have oxidized the pyridyl pyrrole of melting-point 182.5 in the same way with potassium permanganate in an acid solution, as we already described for the isomer of melting-point of 90°. From the pyridyl pyrrole melting at 132°.5 we likewise obtained picolinic acid, which melted at 136°.8 after sublimation, and was identical with the picolinie acid from picoline. It results from these experiments that the two substances that are formed from N-(«-pyridyl)-pyrrole, are two isomeric C-(a-pyridyl)- pyrroles, which are distinguished in this that the pyrrole-nucleus in one substance is substituted at the «-place, and in the other substance at the @-place, as is expressed in formulae (VI) and (VII). We may also mention that in this reaction chiefly the isomer melting at 90° is formed; the quantity of the isomer melting at 132°.5 is small. § 4. The methylation of the C-(a-pyridyl)-pyrole of melting-point 90°. The next step in the synthesis of a substance isomeric with nicotine is that the hydrogen atom of the imide group of the pyrrole-nucleus is replaced by the methyl rest. 434 The difficulties experienced by Picrer and Crépimux when they endeavoured to realize the reaction, were already pointed out in the introduction. We met with the same difficulties in our case. The potassium compound of the pyridyl pyrrole melting at 90° was heated with an excess of methyl iodide in a sealed tube at 100° for three hours. The reaction product was freed from superfluous excess of methyl iodide and solved in water. On evaporation of the aqueous solution crystals were separated, while potassium iodide was present in the mother liquor. These crystals were purified by recrystallisation from a small quantity of water. Yellow-brown crystals were obtained, inelting at 186°. Analysis gave 8.95 for the nitrogen percentage, and 42,55 for the iodine percentage. Calculated for C,,H,,N,1: Nitrogen 9,34 °/,, iodine 42.30 °/,. This substance is, therefore, the iodine methylate of C (a-pyridy!)- N-methyl-pyrrole: (CHI) N—C,H, .C,H,N . CH,. Just as in Prerer and CRÉPiROX’ experiments not only was the nitrogen atom of the pyrrole nucleus methylated, but also a molecule of methyl iodide had combined with the nitrogen atom of the pyridine-nucleus. This iodine methylate is easily soluble in water, sparingly in alcohol, very little soluble in the other usual organic solvents. In order to split off the group CH,I out of this compound, we have followed the method which Pricrer and Rorscuy') already applied, i.e. heating with quick lime. The jodine-methylate was mixed with quick lime, and slowly heated in a retort. Soon a liquid distilled over, which was received in ether, in order to separate it from a little of the unchanged methyl iodide compound, which had also been distilled over in a small quantity. After evaporation of the ethereal solution there was left a light yellow liquid; we have converted this base into the picrate, which melted at 143° after a double recrystallisation from alcohol, We found 18.19 for the nitrogen percentage of this sub- stance, while 18.09 °/, of nitrogen is calculated for the monopicrate of C (a-pyridyl)-N-methyl-pyrrole, We have, accordingly, very probably obtained the required methyl derivative, which must, therefore, be an isomer of nicotyrine. [t seems, however, possible to carry out the methylation of the C («-pyridyl) pyrrole in such a way that the C(a-pyridyl) N- methyl-pyrrole is obtained without the necessity of following the indirect way over the iodine methylate. jmke: 435 It had, indeed, already appeared that the addition of methyl iodide to the pyridyl pyrrole of melting point 90° only takes place at a higher temperature, whereas Picrer and CrÉPimux’ pyridyl pyrrole combines with methyl iodide already at the ordinary tem- perature. For this reason we have heated a mixture of pyridyl pyrrole potassium with methyl iodide in molecular quantities in a sealed tube at 50°. The reaction mixture was a solid mass, in which pyridyl] pyrrole potassium and the above mentioned methyl iodide compound of C-(pyridyl)-N-methyl-pyrrole were present. It was, however, possible to extract by means of ether a little of a yellow oil from this reaction mixture. This liquid was received in alcohol, and picric acid was added; a picrate crystallized out, which melted at 142° when it had been recrystallized out of alcohol, and appeared to be identical with the picrate of the C (a-pyridylj-N-methyl- pyrrole described above, as appeared from the melting point of the mixture of both preparations. We shall first of all set ourselves the task of preparing a larger quantity of this C(a-pyridyl)-N-methyl-pyrrole, and examining its properties closely. We shall further try to determine the structure of the two isomeric pyridyl pyrroles more exactly. A full communication of this investigation will appear in the Recueil des Travaux chimiques des Pays Bas. Organie-chemical Laboratory of the University. Amsterdam, March 1923. Bacteriology. — ‘The splitting of lipoids by Bacteria.” (First communication.) By G. M. Kraay and L. K. Worrr. (Communicated by Prof. C. Eykman.) (Communicated at the meeting of June 30, 1923). The splitting of fats by bacteria has often been investigated and the behaviour of the lipases has properly been recorded. However no literature dealing with the splitting of lipoides by bacteria is known to us. Also in general physiological chemistry little infor- mation is given concerning the splitting of lipoids (lecithin) by enzymes, apart from the beautiful researches by DerrzeNNe and Fourngau about the splitting of lecithin by serpent venom. In many respects we thought it of interest to investigate the action of bacteria on lipoids, the formation of strong blood poisons being possible, as DELBZENNE and FourNeav found as the result of the action of serpent venom on lecithin. We first tried to find out whether some fat- splitting bacteria are able to split lecithin and further if there exist among the non-fat-splitters some that will split lecithin. Considering our working method this; we mostly used plates with lecithin agar obtained by shaking up a small quantity of lecithin and ordinary nutrient agar (about 0.5 gram per 100 gr.) at about 50° C. If the lecithin is affected an area is formed all around the streeks of inoculation. It appears on microscopical examination that this area contains per surface unit more grains than are to by found anywhere else in the culture medium. Plates with yolk of egg cannot be used; the fat contents of yolk of egg cannot be used; the fat contents of yolk of egg makes one unable to distinguish lecithin-splitters from fat-splitters. Our results are summarized in the following table. Our conclusions based upon this table are: there exists fat-splitting bacteria unable to affect lecithin; lecithin-splitting bacteria unable to act upon fat, bacteria unable to act upon both fat and lecithin, and bacteria able to act upon both. (See table on p. 437). The latter bacillus, a very strong lecithin splitter, but quite unable to split fat has been isolated by us from brackish water; this bacillus resembles much the bac. piscium pyogenes described by MATZUSCHITA. 437 Splitting of fat lecithin bact. typhi == | ae ne coli en | Ke , dysenteriae Shiga Ze | ae » prodigiosus a ai » pyocyaneus + H » fluor. liquef. al a » proteus‘) an ga staphylocc. pyogenes ai. = spir. El Tor. EEn ap Dunbar | = aL » Cholerae En ee Bac. piscium pyogenes ? | — | =. We have not yet resolved the question, how the lecithin is broken down; we can only say that as a result of the splitting by the here above mentioned bacteria no hemolysines are formed. We could not find a link between hemolysis by bacteria and lipolysis or lipoidolysis; we found a staphylocc. which had lost its hemolytic property but not its lipolytic character and on the other hand one of our colistrains behaved hemolytic but was inactive on fat or lecithin, our bac. piscium pyogenes splitted lecithin but had no hemolytic action. No fatty acids could be titrated in broth containing splitted lecithin (B. piscium prog.). This result is in agreement with observations on the non-hemolytic action of the splitted lecithin, because if lecithin is splitted in such a manner that (unsaturated) fatty acids are formed, a hemolytic action must take place. We still want to mention that the power of splitting of the bacteria in the table, has been tried on cholesterol and lanoline, the latter was affected only by a staph. pyog., the former only by B. pyocyaneus. June 1923. Laboratory of hygiene of the University of Amsterdam. 1) One of our proteus strains affected fat. Physiology. — “The Presence of Cardio-regulative Nerves in Petro- myzon fluviatilis’. By J. B. Zwaarpumaker. (Communicated by Prof. H. ZWAARDEMAKER.) (Communicated at the meeting of March 24, 1923). In the 2rd edition of his “Physiologie des Kreislaufs” TiGeRSTEDT *) remarks that inhibitory cardiac nerves are present in nearly all vertebrates. Only among the ecyclostomata some exceptions are known, Greenn?) found that in Myxine electrical stimulation, starting from the brain, the spinal cord or the vagi did not affect the frequency of the heart-beat. Cartson *) corroborated this finding and tried to extend the investigation to another group of cyclostomata, viz. the petromyzonta. At first he could work only on the larval form, in which cardio-regulative nerves appeared to be absent. Afterwards he examined adult animals *). When, in these experiments, he applied an electrical stimulus to the medulla oblongata on the level of the vagus nucleus, he noted a brief standstill, which was followed by an accelerated rhythm. From this he concludes that “the central nervous system is connected with the heart by ordinary augmentor and probably also by inhibitory nerves” (l.c. p. 231). In the continuing volume of his ‘‘Vergleichende Anatomie der Myxinoiden” Jouwannes Méii.er makes mention of a connection between. N. sympathicus and cardiac nerves °). He also adds some remarks about the N. vagus, for which | think it better to refer to „the original work (le. p. 59 sqq.) The first experiments which I made myself to ascertain whether in petromyzon fluviatilis any influence is exerted by the central nervous system upon the hearts action, yielded a negative result, which was in accordance with GREENE and with the first set of experiments performed by Cartson*). However, | have been in a position to extend my research. In order to preclude 1) R. Treersrepr, Die Physiologie des Kreislaufs II p. 319. 2) Cu. W. GREENE, Amer. Journ. of Physiol. VI p. 318 1901. 8) A. J. Carson, Zeitschr. f. allg. Physiol. IV p. 259 1904. *) A. J. GARLSON, Amer. Journ. of Physiol. XVI p. 250 1906. 5) J. Mürrer, Fortsetzung der vergleichenden Anatomie der Myxinoiden p. 57, Berlin 1838. 6) J. B. ZWAARDEMAKER, Physiologendag Amsterdam Dec. 1922. 439 movements of the animal I eurarized it beforehand. Paralysis of the skeletal muscles can, in fishes, be effected only with very large doses'). For my animals | used 4 mgr. tubo curari of which, 2 mgr., injected intraperitoneally, was sufficient to paralyze a 220 gr-rat. after 7 minutes. This also plays an influence upon the vagus-function *), but this inconvenience could readily be obviated by the technique followed, because the synapses of the vagus are restored sooner than the motor innervation. After the injection the animal was let alone until no “Stellreflexe” were distinguishable any longer. Also the gills are completely motionless then. At that juncture the cerebrum is severed from the rest of the nervous system by an incision posteriorly along the eyes. After this the cerebrum and the spinal cord are laid bare down to the second gill-hole. Now a straight glass cannula is inserted into the Vena cava dextra, through which the animal, in ventral position, is perfused during some time with Rinewr’s fluid, containing 6'/, er. NaCl, 200 mgr. NaHCO,, 200 mgr. CaCl,, 200 mgr. KC) *). The surplus of curari is hereby gradually washed out. Through a window in the cartilagenous pericardium‘) the atrium is fixed to a lever beneath the animal. Now two thin platinum electrodes are fixed, so as to be well visible, at the level where stimulation produces the effect aimed at. With strongly curarized animals it sometimes takes rather a long time before any effect can be distinguished. At that moment, however, the animal is perfectly quiet, and the experimenter can be sure that only the movements of the heart are registered. In subsequent periods of the perfusion also the contraction of the gills can be distinguished. The electrodes are connected with the secondary coil of an inductorium of Dusois-Reymonp, provided with a Nerer-hammer. An accumulator is connected up in the hg. J. Scuirrer, Arch. f. Anat. u. Physiol. p. 453, 1868. b. J. Sremer, ibid 1875. c. Bout, Mon. Ber. d. Kg]. Preuss. Akad. d. Wissensch. Noy. 1875. d. J. Steiner, Das americanische Pfeilgift Curare p. 56. c. and d. After R. Borum’s article in Handbuch der experimentellen Phar- macologie II 1. Hälfte p. 183. *) R. Borum, |. c. p. 202. 8) J. B. ZWAARDEMAKER, Diss. Utrecht 1922. *) When the pericardium is being opened it all at once changes colour. Originally the heart is seen to loom vaguely through the transparent cartilaginous tissue with a bluish tint; after the opening the pericardium shows its own milkwhite colour, while the atrium now appears to lie at tbe bottom of the cavity. Apparently in the pericardium a negative pressure obtains, which of course is lost at the opening, so that the atrium partly collapses. 440 primary circuit. The Pfeilsignal, which was used sometimes (e.g. in the first figure), could not be placed in shunt, so it came in the primary circuit. The obtained coil-distances (C. d.) are smaller than when no signal is connected up. On stimulation we note a considerable acceleration shortly after the stimulus has been set up. If the stimulus continues a short time only (in fig. 1 5 seconds) the acceleration will be seen to disappear soon and to be substituted by a retardation ; in case the latter increases, the heart is brought to a standstill. After cessation of the negative chronotropic effect, Frome Accelerans-vagus effect. Petromyzon fluviatilis. Perfused with Rincer’s mixture. Stimulation for 5 seconds of medulla oblongata of the level of the exit of the N. vagus. C. d. 100. The tracings from above downward: record of atrium movement - , stimulus signal 5 „ time line 10 sec. a new rhythm appears, more rapid than the original. A little later it gives way to the old rhythm. In fig. 1 the rhythm prior to the stimulation is + 45 beats per minute, after the standstill the frequency amounts to 55. The action of side-currents upon the heartmuscle need not be taken into consideration in these experi- ments, because the effect appears only when. a sharply defined area in the medulla oblongata is stimulated and the effect is destroyed again by a slight displacement of the electrodes. Besides this a great influence is exerted by summation. A stimulus, for instance, that produces no effect after 5 seconds, causes a distinct standstill after a longer period. 441 When instead of presenting a short stimulus, the current is sent through permanently, at first a marked quickening of the rhythm will be noted, attended with a marked positive inotropic effect. This is apparently an accelerans effect. tig. 2. Petromyzon fluviatilis. Fatigue of accelerans and vagus through permanent stimulation from medulla oblongata. The stimulus starts at the first elevations. C. d. 143. This continues as far as the stroke. Time 10 see. When breaking the current during this period a standstill will rapidly ensue, which will disappear again directly after fresh stimu- lation. When, however, the current passes continuously, a slower rhythm will appear after some time spontaneously an fig. 2 + 30 seconds), while at the same time the height of the contractions diminishes gradually. It is the transition to a distinct vagus-effect. When this rhythm has also continued for some time (in fig. 2 about 1 min.), it will change into a rhythm that is only slightly quicker than the normal, or does not differ from it at all, and will persist unaltered after the breaking of the current. When perfusing the animal with a potassium-free uranium-con; taining, instead of a potassium-containing fluid we shall see that the phenomena are practically the same in the K-, and in the U-condition. First we see an acceleration, then a retardation, which in some cases is followed again by an acceleration. This, however, is never so pronounced as at the beginning of the stimulation. What has been said above goes to show that: 1. in Petromyzon fluviatilis cardio-regulative nerves are present. 2. with the technique employed after the removal of curari the excitability of the cardiac nerves returns sooner than that of the motor nerves. 3. in the curarized animal the latent period of the accelerans is shorter than that of the vagus. 442 4. with long-continued stimulation the accelerans-effect is notice- able before the vagus-effect. 5. with brief stimulation the vagus effect appears only after cessation of the stimulation. 6. after cessation of the vagus-action an acceleration will some- times follow, which is perhaps due to a longer after-effect of the accelerans-stimulation. Chemistry. — “The Light Oxidation of Alcohol (UI). The Photo- Catalytic Influence of some Series of Ketones on the light Oxidation of Ethyl Alcohol’. By W. D. Conen. (Communicated by Prof. J. BöesEKEN). (Communicated at the meeting of May 26, 1923). Introduction. A first communication on this subject appeared in these proceedings) already several years ago; a continuation of this was published by BörsrKeN*). In this paper the theoretical grounds on which these researches are founded, are set forth in extenso*), and we may, therefore, refer to this treatise for a study of them. It was now my purpose to examine what relation exists between the configuration of a ketone and its photo-catalytic influence on the oxidation of a definite alcohol, and for this reason I studied the influence of some series of ketones on the velocity of oxidation of ethyl alcohol, to be able, if possible to arrive at a conclusion with regard to the constitutive requirements which a ketone must satisfy to be able to act as a photo-catalyst under the circumstances specified later, which at the same time establishes its photo-chémical attackability. This question has, indeed, already been mentioned more than once before“), but the comparatively small regularity in the observed phenomena rendered an extension of the research in this direction very desirable. The light-thermostat. In the reaction : Light + Ketone + Alcohol + Oxygen = Ketone + Aldehyde + Water a certain quantity of oxygen disappears, and the rapidity with which the oxygen is absorbed, is under for the rest fixed circumstances, a measure for the photo-catalytic activity of the examined ketone. The light thermostat (fig. 1) consists of a copper trough, provided with two windows placed opposite each other in the longitudinal walls, which make a continual observation of the reaction vessel 1) BOESEKEN and CoHEN, These Proc. XVIII, p. 1640. 2) BOESEKEN, Rec. 40, 433 (1921). 5) Ibid, 437. 4) CoHeN, Rec. 39, 258 (1920). Chem. Weekblad 13, 902 (1916). 29 Proceedings Royal Acad. Amsterdam. Vol. XXVI. 444 possible, and a window in the bottom for the illumination. The thermostat rests on an iron framework, which has become an entirely 445 closed space by a cover of incombustible material. This space is divided in two by a vertical partition. On the left there are found two gas-burners connected with a thermo-regulator, and on the right there is adjusted a Heraeus quartz lamp. To work this the wall in the lefthand side of the framework is made like a door (drawn halfopen in the figure); in the front partition at the place of the incandescent body there is a ventilator which works by suction and serves to cool the lamp. The water in the thermostat can further be cooled by means of a cooling spiral, through which water flows under constant pressure, a screw stirrer ensuring thorough mixing in the trough; besides the windows, the vertical walls are insulated with felt. Ventilator and stirring apparatus are worked by separate regulatable motors. The temperature of the thermostat can be kept constant at 35 + 1/,,,°, which temperature has been chosen, because at this temperature the thermostat can be regulated most accurately. As reaction vessel I, at first, used the before described stirring- apparatus) (fig. 2); it possesses the drawback, however, that the surface of illumination is small, the accuracy of the measurement being seriously impaired by the rapid contamination of the mercury in the mercury feal. Therefore I tried to modify the reaction o vessel in such a way that also without intensive mixing of gas and liquid, an aleoholie liquid could be obtained, which remains saturated with oxygen, or contains at least such an excess of oxygen that there can be no question of measuring a velocity of diffusion instead of a velocity of reaction. This is possible when the thickness of the liquid layer is taken very small (about 1 mm.). According to fig. 8 a reaction vessel is then obtained, whieh chiefly consists of a flask with a perfectly flat bottom; the dimensions being such that 5 ce. of liquid give a_ thickness of layer of 5 mm. The neck is narrow and possesses a ground piece to which a bent capillary tube with tap can be attached. Near the bottom there is further a side tube with tap, through which the whole apparatus can be filled with oxygen. Besides there is a filling body in the flask, to make the gas-volume as small as_ possible in proportion to the surface of illumination; this considerably enhances the accuracy of the measurement. For definite purposes this filling body has been made to a second reaction vessel within the former; then an apparatus is obtained as is shown in fig. 4. By the aid of a narrow tube the reaction vessel is connected with the micromanometer. The lefthand leg of this has a capacity 1) These Proc. XVIII, p. 1642. 29% 446 of 1,5 ce. and is divided into 150 parts. Each space between two dividing lines represents, therefore, a capacity of 0.01 cc. The adjustment is obtained by moving the flask up and down by means of a hoisting apparatus, the position of the meniscus in the two Fig. 5. A 1 | Rigas: Fig 2. Ee 447 legs of the manometer being verified by a mirror behind it, on which horizontal lines are drawn at distances of 1.mm. When the apparatus has been properly cleaned and filled with distilled mercury, an accuracy of adjustment can be attained of 1 or 2 hundredths, which as well as the influence of the temperature lies within the limits of the error of observation. The calibration error of the apparatus was so small that it could be neglected. After having been weighted with a copper ring, the reaction vessel is placed on a glass table, which itself rests on the bottom plate of the thermostat. The table can be put in a horizontal position by means of three adjusting screws, through which the thin liquid layer entirely covers the bottom surface of the reaction vessel. After being lit the incandescent body of the lamp is always placed in a horizontal position; the lamp burns ata terminal voltage of 110 Volts and a series resistance of about 20 2 constant at 2,7 Amp./40 Volt. Lamp and reaction vessel are always at the same distance from each other; in my experiments the distance from the bottom side of the reaction vessel to the window was 20 mm., and from the upper side of the lamp to the window 25 mm.; taking into account the thickness of the glass, the mutual distance from lamp to object was about 50 mm. The measurements. a. The preparations. They were prepared for the greater part by myself or under my supervision, and purified as carefully as possible. As the way of preparing is known for all of them, we may refer for this to the records of the literature published on this subject. When it was possible, at least two preparations of different origin were examined, or the preparation was again recrystallized or distilled after the measurement; the values found were not considered as definitive until they were perfectly constant and reproducible; save for a single exception this was always the case. 6. As solvent, resp. liquid that is to be oxidized, was used absolute ethylalcohol, not because its being absolute was quite indispensable for the success of the reaction — for water is formed during the reaction — but in order to start always from a solution of constant proporties. In my, earlier investigations I had come to the conclusion that water would be a strong anti-catalyst, at least for the photo-chemical reduction’). At the time | did not yet know the photo-catalytie alcohol oxidation by molecular oxygen, nor that 1) Cowen Rec. 39, 244 (1920). 448 this reaction and the keton reduction were primarily the same, and that it is, therefore, illogical to assume that water would be an anti-catalyst in the ketone reduction. It has really appeared in a new investigation, that there would be no question at least of a considerable anti-catalytic action of water, but that the error made before, which has, unfortunately, already been adopted in the hand- books *), must be attributed to a wrong interpretation of the experiments made at the time. It seems to me of use to discuss this a little more at length. if it were only to point out how easily certain phenomena are overlooked in the study of a reaction. For at first | made my experiments on the photochemical ketone reduc- tion in such a way that I illuminated the 96°/, alcoholic solution in a thin layer in open flasks, but did not observe then anything of the crystallisation of the sparingly soluble pinacone already described by Cramicran®). This succeeded however without any difficulty when | used absolute alcohol — as CrAMICIAN also did —, and besides worked in closed apparatus, hence with exclusion of oxygen. I then drew the very plausible conclusion, which proved erroneous after- wards, that water would be a strong anti-catalyst, and quite overlooked the interesting photo-catalytie alcohol oxidation in which — the results of this paper are a convincing proof of this — aldehyde does appear, but no pinacone3), and which was not discovered until a few years later. c. In order to be able always to have a great excess of oxygen at our disposal, the reaction vessel after addition of 5 ec. of the solution to be examined, is filled with oxygen which is saturated with alcohol vapour in a washing bottle. Under these circumstances the solution always remains more than sufficiently saturated with oxygen; it is, however, without influence on the result of the measurements, if the gas in the reaction vessel is air or oxygen; for the sake of safety oxygen was, however, always taken. The measurements, the results of which are combined in the following table, extend chiefly over the following series of ketones: a. benzophenon and its hydration products in the nucleus, b. acetophenon and some alkyl-, and also phenyl substitution pro- duets in the CH,-group, c. the phenyl substitution products of acetone, d. the simplest aliphatic, aromatic, and fat aromatic «-g-diketones, e. some a-p-y-triketones. The figures over the horizontal division line indicate the molar 1) HouBeN— Weyn. Die Methoden der organischen Chemie 2te Aufl. (1922), Band Il pag. 983. „ °) Cramrcian and SinBer, Ber. 33 2911 (1900); 34 1530 (1901); 44 1288 (1911). 3) BöesEKEN and Couen, l.c. 449 concentration of the ketone, the values under it representing the oxygen absorption, expressed in ec. per hour. They are the mean of a great many mutually concordant observations. 1 3/4 Mo We Vy Nhe | '/30 | Ves (saturated) 10.30 |12.00| 12.00) 11.90) 9.00 | 5.60 | 3.65 | 2.28 1. Benzophenon. 1 Yo Wy Ve (saturated) 5.15 5.00 | 2.82 | 1.12 2. Phenylcyclohexylketone. 3. Dicyclohexylketone. Inactive in all concentrations. 2 1 YB Wy 4, Phenyl n. hexylketone. — 1.00 | 0.97 0.68 | 0.22 5. Di-n hexylketone. Inactive in all concentrations. 2 11, 1 “Ja Vy 6. Acetophenon. | 1.30 | 1.40 | 1.42 | 1.03 | 0.22 7. Propiophenon. 1.10 | 1.11 | 0.92 | 0.20 y/ U | Ms (saturated) 5.05 | 4.85 | 2.35 8 Phenylbenzylketone. AAG “ea 9. Diphenylacetophenon. Kea turated), 3.13 | 0.78 eee rpucnylacetophenon(e-Denepinacoline). Inactive. 11. Acetone. Inactive in all concentrations. 12. Monophenylacetone. 0.50 | 0.48 | 0.35 15. 16. 17. 18. 19. 20. Symm Diphenylacetone (dibenzylketone). 1.76 | 1.75 | 0.85 1 iy Asymm. Diphenylacetone. LEED 0.03 0.01 ay Triphenylacetone 1.1.2. eee 0.05 Z l/o Symm Tetraphenyl- (saturated) acetone !). 0.17 2 1 If, Phenylfurylketone. 0.07 | 0.10 | 0.10 Diacetyl. 4 3 2 1, 1 | 3/4 Vg Vy an at i 7 16.00 | 15.30 | 15.30) 15.10 | 14.90| 14.10} 10.60| 6.40 | 2.60 | 0.64 | 0.16 Ig 1/, (saturated) Benzil. 3.20 1.44 | 0.52 Acetylbenzoyl 2). 4 3 l/o 3 2 11/ 1 3/4 Vo 1, Is "6 8.60 | 11.70 | 12.90 | 12.60 | 12.80) 13.10) 10.80) 8.50 | 6.05 | 4.15 | 2.08 1) Prof. STAUDINGER, Zürich, had the kindness to send me a small quantity of this preparation. *) By illuminating an alcoholic solution of acetylbenzoyl in a sealed tube the corresponding photoreduction product can be very easily obtained. The substance consists of very fine colourless crystal needles, sparingly soluble in alcohol, and is perfectly stable at the air in dry condition. For the rest the compound is quite comparable with the corresponding reduction product of diacetyl (Comp. Chem. 451 Remark. After some time’s illumi- fae dead nation the absorption, which was 21. Furil. NESS | constant at first, descends to 0; in 2.80 this the ketone itself is attacked with decoloration of the liquid ; 2 1 Vy Vig 22. Benzfuril. 5.80 | 6.30 | 6.20 | 2.20 0.01 | 0.006 | 0.004 23. Terephtalophenon. (saturated) 2.80 | 3.55 | 3.45 0.1 0.01 24. Isophtalophenon. (saturated), 2.80 1.48 0.02 0.01 25. Phenanthrenequinone. GEEN Remark. Behaves like furil. 10.50 | 6.25 0.004 26. Anthraquinone. SCALE) 0.67 27. Camphorquinone. The activity varies with the origin of the preparations. Some five varied at 14, mol. from 0.19—0.43. With still lower concentrations, and also with very small ones the activity is practically not perceptible 28. Fluorenone. In all concentrations — also very small ones — inactive. 2 1 Yo 29. «-Hydrindon. 9.19 0.17 | 0.07 Weekbl. 13, 594 (1916); it melts amidst decomposition at 116°—124°. It is still uncertain whether the structure formula is: CsHs CeHs CH; CH; EE 5 or HO dieses ts tog 2s cao CH, CH, Cos Cal 452 30. @-Hydrindon. Is useless as a photocatalyst, as this substance itself is very readily attacked by oxygen in alcoholic solution. 1 "he 31. Indanedion 1.2. He ee — | 0.92 0.39 32. Pentanetriketone. Inactive. 33. Diphenyltriketone. Inactive. 34, Alloxane. Exceedingly slight activity. These data allow us to draw the following conclusions : a. The velocities of activation are independent of the concentration of the ketone (printed in bold type in the tables) within compara- tively wide limits, quite corresponding to the reduction velocities found before). This phenomenon does not, indeed, manifest itself in all the examined cases, but it should not be forgotten that the circumstances of the experiment necessitate a certain degree of activity and solubility of the ketone to reach the maximum velocity of activation. Clear examples in which the oxygen absorption remains constant within wide limits, are benzophenon, diacetyl, and benzoyl! acetyl (compare the graphical representations in fig. 5 and 6). We some- (imes see the activity diminish again in very high ketone concen- trations (20) or in the neighbourhood of the point of saturation (1), which must then be attributed to mutual disturbances of the ketone molecules’). The diminution of activity in lower concentrations must simply be accounted for by the absence of a sufficient quantity of activable ketone molecules, in which part of the available light is left unused. That really in the concentration region of the maximum activation all the photo-active light is absorbed by a layer only 1 mm. thick, | have been able to prove very clearly by means of the reaction vessel according to fig. 4, which can, therefore, be perfectly compared with the ‘mantle tubes” described formerly for the photo-chemical reduction. When e.g. an alcoholic (or a benzolic) solution of benzophenon in a concentration necessary for the maxi- mum activation is brought into the outer reaction vessel, a benzo- phenon solution in the inner reaction vessel appears to absorb no trace of oxygen; the absorption begins, however, to become imme- diately perceptible, as soon as the ketone concentration in the outer -) Conen, Rec. 39, 253 (1920). 2) Ibid.’p. 273. 453 vessel descends below the critical. In the region of maximum acti- vation all the photo active light is, therefore, arrested by a layer of 1 mm., and this takes place independent of the solvent used. These phenomena are in perfect harmony with what was found before in the ketone reduction. Corresponding experiments with diacetyl and benzoyl acetyl! lead to perfectly the same results. IT ee \ [. benzophenon Sis \ If. phenyleyclohexyl ketone; Fig. 5. s 4 \ Ill. phenyl. n. hexyl ketone / a 7 \ sé \ UL ee y 2 + — \ ao DATE \ IV. acetoph 20 \ phenon 5 4 TESS \ 5 » Fig. 6. Ss, . \ V. acetylbenzoyl \ DN is 4 DN 1 WI. diacetyl 5 1} AT FEET en : DNS it Vy 7 = conc. in mol. Fig. 5. | | ‘oe | | sj = 7 LE = i se a \ gen s See: $ tz} ad : 3 \ N Ss , ya \ | ay \ S 3 EN So \ 2 | © ‘| \ En | ol Pra 5 Ore sai \ | i \ L SS. 4 3 =z 7 6 conc. in mol. Fig. 6. : b. For the photo-activity of the mono-ketones the “aromatic”, character influence has been is in general decisive '), constitutive factors being of by the side of it. Thus the photo-activity of benzophenon reduced to about half its value, when one of the nuclei 1) Conen, Chem. Weekbl. 13, 902 (1916). 454 has been hydrated (2) (fig. 5), and it has quite disappeared in the dieyelohexyl ketone (3). That for the rest the cyclohexyl nucleus weakens the activity of the phenyl nucleus less than a purely aliphatic group, is proved by the much smaller activity of phenyl n. hexyl ketone (4) (fig. 5), which may be put on a line with the activity of acetophenon and propiophenon (6,7) (fig. 6). On intro- duction of C,H,-groups into the CH,-group of acetophenon, the activity at first greatly increases (8,9), suddenly becoming 0 in triphenyl acetone. It is, indeed, known that g-benzpinacoline lacks all the ketone characteristics. In the phenyl substitution products of acetone (quite inactive in themselves, just as di-n-hexyl keton (5, 11)), the introduction of only one phenyl group appears to make the compound photo-active (12). Of the higher phenyl! substitution pro- ducts, the molecules built symmetrically show the greatest activity (compare 13 and 16 with 14 and 15). c. The photo-activity of the «-8-di ketones is a much more general property, and bound neither to the specifically aliphatic or aromatic character, nor in particular to the more or less symmetrical struc- ture of the molecule. The introduction of a second C=O group has mostly a greatly strengthening influence on the photo-activity (compare 18 and 20 with 11 and 6), in which possible disturbing influences issuing from the rest of the molecule, are thrown into the background. In this connection it is e.g. interesting to point out that phenanthrene quinone (25), which is to be considered as a particularly ortho-substituted benzil, far exceeds all the examined ketones with regard to its relative activity, whereas fluorenon (28), which may be compared with it, is perfectly inactive. The opposite case presents itself in the comparison of benzil (19) with regard to benzophenon (1), where the di-ketone compared with the mono- ketone is less active. It may, however, be possible that in conse- quence of the slight solubility of benzil in alcohol the maximum activation concentration cannot be reached. Of great importance is also the activity of the a--di-ketones, which carry one or two furane-nuclei (21 and 22), which furnishes a new proof of the great resemblance in properties of the furane and benzol. derivatives. d. Thus we see that the phenyl and furyl groups do not exert a disturbing influence on each other in the «-g-di-ketone ; this influence is, however, evidently particularly strong in the corresponding mono-ketone, phenyl furyl ketone (17), which presents a very small activity. Here the above-mentioned influence of the symmetry of the molecule on the photo-activity of the mono-ketone is very 455 pronounced. This influence of the symmetry was already observed more than once in the photo-chemical reduction of the substitution products of benzophenon, but it had not been recognized as such *). To give a further support to this view it has been tried to make di-furyl ketone, as this compound would have to possess an activity equivalent to benzophenon. Unfortunately all attempts to obtain this substance have failed so far’), but in this connection attention may already be drawn to the much greater activity of terephtalophenon compared with isophtalophenon (23 and 24). e. A somewhat separate place among the «-g-diketones occupies camphorquinone, the activity of which is unexpectedly slight, and moreover not reproducible. The greater or smaller purity of the preparations seems to be of great influence. jf. a-Hydrindon (29) and indane dion 1.2. (81), considered as internal condensation products of resp. propiophenon (7) and acetyl benzoyl (20), present a greatly diminished activity. 3-Hydrindon cannot be used as object of comparison with mono-phenyl acetone on account of its great oxidisibility. g. The photo-activity of the examined «-p-y-tri-ketones is zero, or so small as to be negligible (32, 33, 34)*). This phenomenon must, without any doubt, be attributed to the paralysis of the middle C=O group caused by the solvent‘), through which the compound has practically quite lost its favourable properties of double «-g-di- ketone. °) Laboratory of Organic Chemistry of the Technical University. Delft, April 1923. 1) Compare. Conen, Rec. 39, 258 (1920). 2) FREUNDLER, Bl. (3) 17, 612 (1897). 3) Compare for the photo-chemical reduction of alloxane Ciamician and Silber, Ber. 36, 1581 (1903). 4) At first pentane tri-ketone and di-phenyl tri-ketone dissolve in absolute alcohol with a dark yellow colour, after standing some time the colour of the solution changes into light yellow, in which very probably alcohol addition „OH „OH products CH,—CO—C< t——-CO—CH, and (C,H;—CO—C< —W\CO—(G,H, NOCHE \ OCH; which are analogous to the hydrate, are formed. 5) Comp. SacuHs, Ber. 34, 3052 (1901); 35, 3311 (1902); Von PrcHMmANN, Ber. 23, 3380 (1890); WieLAND, Ber. 37, 1531 (1904); Brurz. Ber. 45, 3662 (1912). Mathematics. — “On Power Series of the Form: «Po — «Pi 4 wPs—..” By M. J. BELINFANTE. (Communicated by Prof. L. B. J. BROUWER.) (Communicated at the meeting of April 28, 1923). Introduction. It is a well-known theorem of Frosenius that if a, is summable of order 1, (te if lim. © gei zE et Sn n= n wo Ha, +... + an) then lim. 2 a, «"=s, provided «a approaches 1 1 == |S, where silk by real values from below (which we denote by «— 1).’) Under the same conditions we have: ?) oo lim. E a, an mm Pal = 8 provided p, ay) 1 Put p, = 2” and a, =(—1)"t', then we have: KJ Se St hie Sp lim, ans == n= 0 n ao while > a, an = « — a2? + a4 —a*+... oscillates between limits 1 at least as wide as 0,498 and 0,502, if «—+1'). Thus we are led to the question: what is the connexion between the exponent-series pp, pi, Ps, Ps ----- and the existence or non- existence of lim. (ao ar + aPa—...) Td | 1) Bromwicu, Theory of infinite series, p. 312. *) BromwicH, op. cit., p. 388. 3) Bromwicn, op. cit., p. 498 example 30. 457 Harpy‘) has investigated several particular exponent-series with particular methods that cannot be applied to other exponent-series, for instance the series of Fisonacctr: lo Ao Gy Saw The only general result Harpy could reach was the non-existence of a limit if: Pate CRT) OPEN ve ey Cl) but Harpy’s example quoted above (where p, = 2’), shows the non- existence of a limit notwithstanding the condition (2) is not satisfied. In the present paper another condition is given ($ 2), with the aid of a theorem of Lirti.nwoop which is treated in $ 1. el LirrLewoop has proved the following theorem: *) a oo Theorem 1. lf |na„l <<, and lim. Sa, 2°=s, then Sa, con- => 1 1 verges to s. For our purpose we want the following extension which has also been enunciated by LirrLewoop: *) Theorem 2. If the mean-values*) of order k-—1 of = a, are limited 00 and lim. Za, a" = s, then Za, ts summable of order k. tet dl LirrLewoop states that the proof of theorem 2 follows the lines of his proof of theorem 1. The latter being rather long and tedious, it seems not without interest to show that theorem 2 is an immediate consequence of theorem 1. Adopting the notation of our article “On a Generalisation of TauBur’s Theorem concerning Power Series” *), we have the follow- 5 5 k) : ing relations between the mean-values A.’ and the functions Gk: 1) Quarterly Journal, vol. 38, p. 269, 1907. 8) Proceedings of the London Mathematical Society Ser. 2, Vol. 9, p. 434—448, 1911. 3) Proc. of the Lond. Math. Soc. l.c., p. 448. *) For definitions of the mean-values of order p we refer to BRomwicu, op. cit., § 122, 123 and Lanpav, Darstellung und Begründung einiger neuerer Er- gebnisse der Funktionentheorie, § 5. 5) Proceedings Vol. XXVI (p. 216—225). 458 ao p= = [An — Aloe. 1 Pe (2) = 2a, 22 1 9, (2) Ha). D= @) ne in With the aid of (2) we have proved !) that lin . Bane" = s implies Lap ll lim. P, (2) =s. Tp Ì Now, if moreover: k k) ln. LA; jee AS] LC, ao 4 we have by theorem 1 that D[A®— AW | converges to s, i.e. : 1 ; k lim. AN ls nz or: La, is summable of order &. Since (k—1) (k—1) 2 ienie An n k-1 4h Ai zie A n= we infer from |A%—| << c: | A®| 1 + oy , then rn cL, fe) = a—er+er— .... does not tend to a limit as x1). Proof: We show that the series of coefficients of f(x) (which consists of the terms 1, (7,—7,—1) zeros, —1, (7,—7,—1) zeros, 1, and so on...) is „ot summable of the first order, i.e. that o, does not tend to a limit as no. Then it is impossible that f(w) should tend to a limit as «—1, for this implies by theorem 3 the existence of lim. on °). n= We show that 6, does not tend to a limit ifm — oo, by calculating two positive numbers y and 7 so that: Oe — Gi OM GD tide We have: sds, 4... Hsn na, + (n—l)a, +. + [n—(n—1)]a, D= == — a Ss : n n Beedle Nl ate ee le ee tT rap = rap Ty — Tg +73 — ee — Top Tap — Tp + 12p-2 — ---— 1 =1 + —— --— Py Ees see ee "2p Top ie r, 5 4 Since 1 <4, < 2 it follows that. m4: 2 7, k, and ry r4i— 12 (k,—1)r,. Substituting this in the expression for Ora, we have: 6, < ae (Ai—1) T2p—1 +- (ki—1) T2p—-3 H see + (arl) m1 ADT Tap zi kil rapt + rop—a Hs. HM We ka Pap - 1 1 Seep Sal RE Ps et eo Tr en : | ET el 1 ie jn ke ey a! A pe ko 1 atl E 1) We suppose 7) = 1. 8) The condition |s,\ ky 1 1 a i Ek gint te 1 il kept? > EK ko 1 1 1 hid kapt? il kip Or Fae pa > —1 =F Se 2p+1 2p ka ] ko 1 hes = tee „hl 2 Let ke mam ko 1 ka k2p 1 een 2 ES 2 Ls is kid 2 2 — 1 Put ——. —1=c, then it follows from k, > 1 + 4 >— he cas ib 2k, ks that c > 0. Hence we have: e+ 1 | 1 2 UE 2 Orap si Oron ZC = ; Since k, > 1 the second term is possible to calculate whatever m so that: Oren tt — Onde if tends to zero as poe; hence it be y between O and c an integer Pp > m. 461 Remark 1. a! : / r Of course it is sufficient that the relation 1 <4, gees ke n is only satisfied provided n> some finite number g, since the addition of a finite number of terms does not influence the existence or non-existence of a limit. Thus the function #—#? + a}? + x'—x'? +... does not tend to a limit as «—1 since 22 (yo 9 3 3 3 Vul a, SEZ = ifm >5 and 1 7 >1+ a(t 2) : 9 ba ei a 5 Tn ] ers 3 Remark 2. Strictly spoken we have proved theorem 2 only if the Hörper- mean-values are limited. Now the existence of a “Hölder-limit” of order / implies the existence of a “Cesaró-limit” of order 4 and vice-versa’); hence if we prove that the Hörper mean-values of order p are limited provided the Crsaró mean-values of the same order are limited, then our theorem is proved for both classes of mean-values. Now we have (see lanpau l.c.): (k ï + (k) EI =S JI lms 5 TC ) . . . . . . (1) (k) th Hú zat tl where H,” is the nth Hörper mean-value and C, is the nt Crsaró mean-value of order &, and: a pl wi + a2 +...+ a, 1 Ta ee ERE fal n P From (2) we deduce that | z;| <{e implies | 7} (e;) |