ee romain - | Hi i a OE Toronto Digitized by the Internet Archive in 2009 with funding from University of Toronto http://www.archive.org/details/p1 proceedingsofs17akad KONINKLIJKE AKADEMIE VAN WETENSCHAPPEN -- TE AMSTERDAM -:- peOckE DINGS OF THE SE CRON OF SCIENCES VOLUME XVII Pe Oe vy 1 Is JOHANNES MULLER :—: AMSTERDAM JUNE 1915 ek es KONINKLIJKE AKADEMIE VAN WETENSCHAPPEN -- TE AMSTERDAM -:- ER@ChReOUINGS OF THE SECBION OF SCIENCES VOLUME XVII (5) PART — )) JOHANNES MULLER :—: AMSTERDAM : DECEMBER 1914: : i ° r m Py 0 J £ a ; = 4 ly 0 ures ¥ Aj a Tin ievst eh fae : PA wn 7 ot Mine ‘ —_ a % iM < “~ x 1 ra fr .) >. q eq > ‘ - b (Translated from: Verslagen van de Gewone Vergaderingen der Wis- en. kundige Afdeeling van 30 Mei 1914 tot 28 November 1914. Dl. XXIL) CVOeNS EO, NG TS: —— Page Proceedings of the Meeting of May 30, LOUAT aera! 1 » > > > » June 27 @ oe uaetietr aes ido > tear > > September-26 >» . 9. =» 2 . = 467 > >» » > » October 31 > : coe ere oul! > > » > » November 28 > Rs. ec. OO CONTENTS. ABEL’s polynomia (On Hermrre’s and). 192. ABSORPTION LINES D, and Ds, (On the structure of the). 720. ATR-BLADDER (The physiology of the) of fishes. 1088. ALBUMINOUs FLUIDS (The identification of traces of bilirubin in). 807. ALKALIES (The coloration of some derivatives of Picrylmethylamide with). 647. aLLorropy (The) of cadmium. IT. 54, II. 122. [V. 688. V. 1050. — of zine. II. 59. ILL. 641. — of copper. II. 60. — of antimony. I. 645. — of lead. 1. 822. Note. 1055. — of potassium. I. 1115. — of bismuth. Il. 1236. — (The application of the theory of) to electromotive equilibria. IT. 37, IIT. 680. — (The metastability of metals in consequence of) and its significance for Chemistry, Phyics and Technics. 200. III. 926. LV. 1238. — (The metastable continuation of the mixed crystal series of pseudo-components in connection of the phenomenon). II. 672. ALMOND (Gummosis in the fruit of the) and the Peachalmond as a process of normal life. 810. amipEs of gz-oxyacids (Action of sodium-hypochlorite on). 1163. ammonra (On the interaction of) and methylamine on 2.3.4-trinitrodimethylaniline. 1034. ammonta-water (The system), 182. AMORPHOUS CARBON (The decoloration of fuchsin-solutions by). 1322. Anatomy. P. Réraic and C. U. Arrins Kappers: “Further contributions to our knowledge of the brain of Myxine glutinosa”. 2. — ©. Winker: “A case of occlusion of the arteria cerebelli posterior inferior”. 914. — J. Borke: “On the termination of the efferent nerves in plain muscle-cells, and its bearing on the sympathetic (accessory) innervation of the striated muscle- fibre”. 982. — J. Borke: “On the mode of attachment of the muscular fibre to its tendonfibres in the striated muscles of the vertebrates’. 989. — H. A. VERMEULEN: “The vagus area in Camelidae”. 1119. ANOMALIES (On SBELIGER’s hypothesis ubout the) in the motion of the inner planets, 23. ANTIBODIES (On the formation of) after injection of sensitized antigens. Il. 81S, 89 Proceedings Royal Acad, Amsterdam, Vol, XVII, ap CONTENTS. \NTIGENS (On the formation of antibodies after injection of sensitized). II. 318. antimony (The allotropy of). [. 645. APOPHYLLITE (On the real symmetry of cordierite and). 480. ARIENS KAPPERS (c. U.). v. Kappers (C. U. ARrENs). ARSENIC TRISULPHIDE soLs (The connection between the limit value and the concen- tration of). 1158. ARSENIOUS OXIDE (Compounds of). I. 1111. ARTERIA cerebelli posterior inferior (A case of occlusion of the). 914. Astronomy. J. Wouter Jr.: “On Seeiiaer’s hypothesis about the anomalies in the motion of the inner planets”. 23. — W. ve Srrrer: “Remarks on Mr. WotLtyEr’s paper concerning SRELIGER’s hypothesis”. 33. — W. ve Sitrer: “The figure of the planet Jupiter”. 1047. — W. vr Sirrer: “On the mean radius of the earth, the intensity of gravity and the moon’s parallax”. 1291. — W. ve Srrrer: “On isostasy, the moments of inertia and the compression of the earth”. 1295. — VW. pe Srrver: ‘The motions of the lunar perigee and node and the figure of the moon”. 1309. ATEN (A. H. Ww.) and A. Smivs. The application of the theory of allotropy to electro- motive equilibria. If. 37. III. 680. ATLANTIC OCEAN (On the relation between departures from the normal in the strength of the trade-winds of the) and those in the waterlevel and temperature in the Northern Kuropean seas. 1147. atomic Forces (The caleulation of the molecular dimensions from the supposition of the electric nature of the quasi-elastic). 877. BAA T (W. c. DB) and F,A, H. Scurernemakers. The system : copper sulphate, copper chlorid, potassium sulphate, potassium chlorid and water at 30° C. 533. — On the quaternary system KCl—CuCl,—BaClo—H,O. 781. — Compounds of the arsenious oxide. I. 1111. BACKER (H. J.) and A. P. N. Francurmont. The coloration of some derivatives of picrylmethylamide with alkalies. 647. — z-Sulpho-propionie acid and its resolution into optically active isomerides. 653. BAKHUYZEN (H.G. VAN DE SANDE). Comparison of the Dutch platinum- iridium Metre N°. 27 with the international Metre MM as derived from the measurements by the Duth Metre Commission in 1879 and 1880, and a prelimi- nary determination of the length of the measaring-bar of the French base apparatus in international metres. 311. ~- N. Witpeporr and J. W. Dteeertnk: “Comparison of the measuring bar used in the base measurement at Stroe with the Dutch Metre N® 27. 300. BASE MEASUREMENT (Comparison of the measuring bar used in the) at Stroe with the Dutch Metre No. 27. 300. BEEGER (N. G W. H.). On Hermrre’s and ABEL’s polynomia, 192. BENZENE DERTVATIVES (The replacement of substituents in). 1027, COP ND ky) Nat Ss. Lent BENZENES (The nitration of the mixed dihalogen), 846. BEIJERINCK (mM. w.). Gummosis in the fruit of the Almond and the Peachalmond as a process of normal life. 810. BILIRUBIN (The identification of traces of) in albuminous fluids. 807. BINARY MIXTURES (Isothermals of monatomic substances and their). XVI. 275. — (Isothermals of di-atomic substances and their). XV. 950. XVI. 959. BINARY SYSTEM (On unmixing in a) for which the three-phase pressure is greater than the sum of the vapour tensions of the two components, 834. BismutH (The allotropy of). II. 1236. BOEKE (J.). On the termination of the efferent nerves in plain muscle-cells and its bearing on the sympathetic (accessory) innervation-of the striated muscle-fibre. 982. — On the mode of attachment of the muscular fibre to its tendonfibres in the striated muscles of the vertebrates. 939. — presents a paper of Dr. A. B. Droocierver Forruyn: “The decoloration of fuchsin-solutions by amorphous carbon”. 1322. BOER (s. DE). On the heart-rhythm. 1075 IL. 1135. BOESEKEN (J.). On catalyse. 546. — and W. D. Coney. The reduction of aromatic ketones. II!. Contribution to the knowledge of the photochemical phenomena. 849. BOILING PoINTs (The influence of the hydration and of the deviations from the ideal gas-laws in aqueous solutions of salts on the solidifying and the). 1036, BOIs (H. DU). Modern electromagnets, especially for surgical and metalJurgic practice. 468. — The universality of the Zpeman-effect with respect to the Srark-ellect in canal- rays. 873. BOKHORST (s. c.) and A. Smits. On the vapour pressure lines in the system phos- phorus. Il. 678. III. 962. — Further particulars concerning the system phosphorus. 973. BOLK (4.) presents a paper of Dr. P. Rorate and Dr. C. U. Ariens Kapprrs: “Further contributions to our knowledge of the brain of Myxine glutinosa”. 2. — presents a paper of Dr. H. A. Vermeunen: “The vagus area in Camelidae”. 1119, BOSCH (J. C, VAN DEN) and Erns? Conen. The allotropy of antimony, I. 645. Botany. Miss Lucie C. Dover: “Euergy transformations during the germination of wheat-grains’’. 62. — M. W. Betertnck: “Gummosis in the fruit of the Almond and the Peachal- mond as a process of normal life”. 810, — C. E. B. Bremexame: “The mutual iufluence of phototropic and geotropic reactions in plants”. 1278. BratN of Myxine glutinosa (Further contributions to our knowledge of the). 2. uravats (The theoty of) (on errors in space) for polydimensional space with applications to correlation (Continuation). 150. BREMEKAMP (c. E. B.). On the mutual influence of phototropic and geotropic reactions in plants. 1278, 89* IV CONTENTS. BROUWER (u. A.). On the granitie area of Rokan (Middle-Sumatra) and on contact phenomena in the surrounding schists. 1190. BRUTIN (G, DB). A erystallized compound of isoprene with sulphur dioxide. 585. — and Ernst Couey. The metastability of the metals in consequence of allotropy, and its significance for Chemistry, Physies and Technics. III. 926. BiicHNER (x. u.) and L. K. Wotrr. On the behaviour of gels towards liquids and the vapours thereof. Il. 92. capmtum (The allotropy of). IL, 54. ILL. 122. IV. 638. V. 1050. CAMELIDAR (The vagus area in). 1119. cANAL-RAYS (The universality of the ZeeMAN-ellect with respect to the Srark-effect in). 873. CAPILLARY PREssURE (On the measurement of the) in a soap-bubble. 946, CAPILLARITY (Measurements on the) of liquid hydrogen. 528. caTALYSE (On). 546. CHEMICAL constanr (The) and the application of the quantumtheory by the method of the natural vibrations to the equation of state of an ideal monatomic gas. 20. Chemistry. A. Smivs and A. H. W. Aven: “The application of the theory of allotropy to electromotive equilibria”. IL. 37. ILI. 680. — E. Coney and W. D. Hetperman: “The allotropy of cadmium, IL. 54, IIT. 122. IV. 638. V. 1050. — FE. Commn and W. D. Hetprerman: “The allotropy of zine.” IT. 59. IIL. 641. — E. Conen and W. D. Herperman: “The allotropy of copper”. II. 60. — F. A. H. Scureremakers: “Equilibria in ternary systems’, XV, 70. XV1. 169. XVIT. 767. XVIII. 1260. — L. k. Worrr and EK. H. Biicuner: “On the behaviour of gels towards liquids, and the vapours thereof”. IL. 92. — A. Smrrs and 8. Postma: “The system ammonia-water’’. 182. — Ernst Conen: “The metastability of the metals in consequence of allotropy and its significance for Chemistry, Physics and Technics’. 200. — F. M. Janepr and Ant. Sirmex: “Studies in the field of Silicate-chemistry”. I}. 239. TIT. 251. — I. M. Jarcrr: “The temperature-coefticients of the free surface-energy of liquids at temperatures from —80° to 1650° C. I. 329. F. M. Jazerer and M. Surv, IT. 365. ILL. 386. F. M. Jananr and J. Kany, IV, 395. F. M. Janorr. V. 405. VI. 416. VII. 555. VIII. 571. — I. A. H. Scaremyemakers and Miss W. C. pg Baar: “The system: copper sulphate, copper chlorid, potassium sulphate, potassium chlorid and water at 30° C.” 533. — J. Borsrxen: “On catalyse”. 546. — G. pe Bruin: “A erystallized compound of isoprene with sulphur dioxide”, 585, — H. R, Kruyt: “Current potentials of electrolyte solutions”. 615. — H. R. Kruyt: “Electric charge and limit value of colloids”. 623. — Erxst Coney and J, C van pen Boscu: “The allotropy of antimony”. I, 645, CONTENTS. v Chemistry. A. P. N. Francurmontr and H. J. Backer: “The coloration of some deri- vatives of Picrylmethylamide with alkalies”. 647. — A. P.N. Francurmontr and H. J. Backrr: “2 Sulpho-propionic acid and its resolution into optically active isomerides”. 653. — A. Smits: “The metastable continuation of the mixed crystal series of pseudo- components in connection with the phenomenon allotropy”. [L. 672. — A. Smrrs and 8. C. Bokuorsr: “On the vapour pressure lines of the system phosphorus”. If. 678. — F, EH. C. Scugrrer;: “On gas equilibria and a test of Prof. v. p. Waats Jr.s formula”, I, 695, Lf. 1011. — W. Rernpers: “Equilibria in the system Pb-S-O, the roasting reaction process”. 703. — F. A. H. Sctretnemakers and Miss W. C. pe Baar: “On the quaternary system KCl-CuClo-BaCl2-H.0”. 781 — Ernst Conen and W, D, Heiperman: “The allotropy of lead’, 822. Note. 1055. — A. F. Houtemaw: “The nitration of the mixed dihalogenbenzenes”. $46. — J. Borsexen and W. D, Conen: “The reduction of aromatic ketones. III, Contri- bution to the knowledge of the photo-chemical phenomena”. 849. — Ernst Couen and G. ve Bruin; “The metastability of the metals in conse- quence of allotropy and its significance for Chemistry, Physics and Technics”. Ill. 926. — A Smits and 8S. ©. Bokuorst: “On the vapour pressure lines of the system phosphorus”. If. 678. I[f. 962. — A. Smits and 8, C, Bokuorst: “Further particulars concerning the system phosphorus”. 973. — A. F. Hotieman: “The replacement of substituents in benzene derivatives’. 1027. — P. van Romburcu and Miss D. W. Wensink: ‘On the interaction of ammonia and methylamine on 2.3,4.-trinitrodimethylaniline”. 1034. — C. H. Sturrer: “The influence of the hydration and of the deviations from the ideal gas-laws in aqueous solutions of salts on the solidifying and the boiling points”. 1036. — Miss Apa Prins: ‘On critical end-points and the system ethanenaphtalene”’. 1095. — F. A. H. Scursinemakers and Miss W. C. pt Baat: “Compounds of the arsenious oxyde”. L111. — Ernst Conen and 8. Wourr: “The allotropy of potassium”. I. 1115. — H. R. Kruyr and Jac. van per Spex: ‘The connection between the limit value and the concentration of arsenic trisulphide sols”, 1158. — R. A. Weerman: “Action of sodium hypochlorite on amides of z-oxyacids”’. 1163. — FE. M. Jarcer: “Researches on Pasteur’s principle of the connection between molecular and physical dissymmetry”. I. 1217. — Ernst Conen: “The allotropy of bismuth”. [I. 1236. — Ernsr Couen and W. D. HELpermMan: “The metastability of the metals in consequence of allotropy and its significance for Chemistry, Physics and Tech- nics”, IV, 1238. VI CONTENTS. Chemistry. A. W. k. pp Jone: “Action of sunlight on the cinnamie acids”. 1274. CINNAMIC aciDs (Action of sunlight on the). 1274. crncLes (Systems of) determined by a pencil of conics. 1107, COUEN (ERNST). The metastability of the metals in consequence of allotropy, and its significance for Chemistry, Physics and Technics, II. 200. — presents a paper of Dr. H. R. Kruyr: “Current potentials of electrolyte solutions”. 615. — presents a paper of Dr. H. R. Kruyt: “Electric charge and limit value of colloids”. 623, — presents a paper of Dr. H. R, Kruyr and Jac. vAN per Spek: “The connection between the limit value and the concentration of arsenic trisulphide sols”. 1158. — The allotropy of bismuth. IL. 1236. — and J. C. van pen Boscu. The allotropy of antimony. I. 645. — and G. pe Bruin. The metastability of the metals in consequence of allotropy and its significance for Chemistry, Physics and Technics. III. 926. — and W. D. Hexperman. The allotropy of Cadmium. IL. 54, ILL. 122. LV. 638. V. 1050. — The allotropy of zine. If. 59. ILI. 641. — ‘The allotropy of copper. IL. 60. — The allotropy of lead. I. 822. Note 1055. — The metastability of the metals in consequence of allotropy and its significance for Chemistry, Physics and Technics, IV. 1238. — and S. Wotrr. The allotropy of potassium. L. 1115. COMUEN (w. D.) and J. Borsnxen. The reduction of aromatic ketones. [II. Contri- bution to the knowledge of the photochemical phenomena. 849, coLLorps (Electrie charge and limit value of). 623. coLORATION (The) of some derivatives of Picrylmethylamide with alkalies. 647. coLtoyurs (On IresNeL’s coefficient for light of different). Ist part. 445. compound (A crystallized) of isoprene with sulphur dioxide. 585. COMPOUNDS of arsenious oxide. I. L111. CONCENTRATION (The connection between the limit value and the) of arsenic trisulphide sols. 1158. : CONGRUENCE (A bilinear) of rational twisted quinties. 1250. CONGRUENCES (Some particular bilinear) of twisted cubics. 1256. conics (Systems of circles determined by a pencil of). 1107. CONTACT=PHENOMENA (On the granitic area of Rokan (Middle Sumatra) and on) in the surrounding schists. 1190. coprer (The allotropy of). II. 60. — (Measurements on the specific heat of lead between 14° and 80° K. and of) between 15° and 22° K. 894. COPPER SULPHATE, Copper chlorid (The system :), potassium sulphate, potassium chlorid and water at 30°. 533. CORDIERTTE and Apophyllite (On the real symmetry of). 430, Gon Tren Ts. VIl CORRELATION (The theory of Bravats (on errors in space) for polydimensional space, with applications to) (Continuation). 150. CORRESPONDING sTATEs (Contribution to the theory of), 840. CRITICAL POINT (Vapour pressures of oxygen and) of oxygen and nitrogen. 950. CRITICAL QUANTITIES (A new relation between the) and on the unity of all substances in their thermic behaviour. 451. — (Some remarks on the values of the) in case of association. 598. CROMMELIN (ec. 4.) Isothermals of monatomic substances and their binary mix- tures. XVI. 275. — Isothermals of di-atomic substances and their binary mixtures. XVI, Vapour pressures of nitrogen between the critical point and the boiling point. 959. — E. Marutas and H. Kameruineu Oxnes. The rectilinear diameter of nitrogen, 953. CRYSTAL sERIFS (The metastable continuation of the mixed) of pseudo-components in connection with the phenomenon allotropy. LI. 672. crysTaLs (On a new phenomenon accompanying the diffraction of RONTGEN rays in birefringent). 1204. cue (The different ways of floating of an homogeneous). 224. cusres (Some particular bilinear congruences of twisted). 1256. curves (Characteristic numbers for nets of algebraic). 935. — (Characteristic numbers for a triply infinite system of algebraic plane). 1055, DECOLORATION (The) of fuchsin-solutions by amorphous carbon. 1322. DEEP reflexes (Exaggeration of). 885. pensity (On the manner in which the susceptibility of paramagnetic substances depends on the). 110. — (Accidental deviations of) and opalescence at the critical point of a single substance. 793. DIAMETER (The rectilinear) of nitrogen. 953. DIEPERINK (J. G.), N. Winpesorr and H. G. vaN DE SanpE Bakuuyzen. Com- parison of the measuring bar used in the base measurement at Stroe with the Dutch Metre N°. 27. 300. DIFFRACTION (On a new phenomenon accompanying the) of Rontgen rays in bire- fringent crystals. 1204. DIFFUSYON COEFFICIENT (The) of gases and the viscosity of gas-mixtures. 1068. DISCONTINUITIES (On apparent thermodynamic) in connection with the value of the quantity 2 for infinitely large volume. 605. DISSYMMETRY (Researches on PastTEUR’s principle of the connection between molecular and physical). I, 1217. DORSMAN (c.), H. KameruincH Onnes and G. Hoxsr. Isothermals of di-atomie substances and their binary mixtures. XV. Vapour pressures of oxygen and critica! point of oxygen and nitrogen, 950. DOYER (LUCIE c.). Energy transformations during the germination of wheat-grains. 62. DROOGLEEVER FORTUYN (a. B.). v. Fortuyn (A, B. DrooGieever). DROSTE (J.). On the field of a single centre in Ernsrein’s theory of gravi- tation. 998, VIII CONTENTS. varru (The mean radius of the), the intensity of gravity and the moon’s parallax. 1291. — (On isostasy, the moments of inertia and the compression of the). 1295. PHRENFeEST (P.) and H. KameRLINGH OnNes. Simplified deduction of the formula from the theory of combinations which PLaNck uses as the basis of his radiation- theory. 870. — On interference phenomena to be expected when RONTGEN rays pass through a di-atomie gas. 1184. — On the kinetic interpretation of the osmotic pressure. 1241. EWRENPEST (t.)—AvaNaSsJEWA, Contribution to the theory of corresponding states. 840. EINSTEIN’s theory of gravitation (On the field of a single centre in). 998. EINTHOVEN (On the theory of the string-galvanometer of). 784. ELASTIC DEFORMATION (On the lowering of the freezing point in consequence of an). 732. ELECTRIC CHARGE and limit value of colloids, 623, ELECTRODES (The effect of magnetisation of the) on the electromotive force. 745. ELECTROLYTE SOLUTIONS (Current potentials of) 615. ELECTROMAGNETS (Modern), especially for surgical and metallurgic practice. 468. ELECTROMETER (A new) specially arranged for radio-active investigations. 659. ELECTROMOTIVE FORCE (‘Lhe etlect of magnetisation of the electrodes on the). 745. ELIAS (G, J.). On the structure of the absorption lines D,; and Dy. 720. — On the lowering of the freezing point in consequence of an elastic deforma- tion, 732. — The etlect of magnetisation of the electrodes on the electromotive force. 745. END-POINTS (On critical) and the system ethane-naphtalene. 1095, ENERGY- SURFACE (Lhe temperature-coeflicients of the free) of liquids at temperatures from —80° C, to 1650° C. 1. 329. If. 365. IIL. 386. LV. 395. V. 405. VI. 416. WUE Gibias MANE. by7pl- ENERGY-TRANSFORMATIONS during the germination of wheat-grains. 62. ENTROPY CONSTANY (Theoretical determination of the) of gases and liquids. 1167, EQUATION OF sTaTE (The chemical constant and the application of the quantum theory by the method of the natural vibrations to the) of an ideal monatomic gas. 20. EQUILIBRIA (The application of the theory of allotropy to electromotive). Il. 37. III. 680. — in the system Pb—SO, the roasting reaction process. 703. -- in ternary systems. XV. 70. XVI. 169. XVII. 767. XVIII. 1260. ERRATUM. 944. L073. 1202. ERRORS IN sPACcE (The theory of Bravats, on) for polydimensional space with appli- cations to correlation. (Continuation). 150. FTHANE-naphtalene (On critical end-points and the system). 1095. EUROPEAN SEAS (On the relation between departures from the normal in the strength of the trade-winds in the Atlantic Ocean and those in the waterlevel and tem- perature in the Northern), 1147. BYKMAN (c,) presents a paper of Dr. L. K, Wourr: “On the formation of antibodies after injection of sensitized antigens”. IL, 318, CRO MN es ONT 8, IX FISHES (The physiology of the air-bladder of). 1088. FLOSTING (The different ways of) of an homogeneous cube. 224. FLoreEs (On the tin of the island of). 474. FOLMER (MISS H.). A new electrometer, specially arranged for radio-active investigations. 659. FONTAINE SCHLUITER (J. J. DE LA). v. ScHLuiter (J. J. pe LA Fonratne). FORTUYN (A. B. DROOGLEEVER). The decoloration of fuchsin-solutions by amorphous carbon, 1322. FRANCHIMONT (4. P. N.) presents a paper of Dr. R. A. WeerMAN: “Action of sodium hypochlorite on amides of g-oxyacids”. 1163. — and H. J. Backer. The coloration of some derivatives of Picrylmethylamide with alkalies, 647. — a-sulpho-propionie acid and its resolution into optically active isomerides. 653. FREEZING POINT (On the lowering of the) in connection of an elastic deformation. 732. FREQUENCIES (The treatment of) of directed quantities. 586, FRESNEL’s coefficient (On) for light of different colours. 445. FUCHSIN-SOLUTIONS (The decoloration of) by amorphous carbon. 1322. FuNcTIONS of HERMITE (On the). 1st part. 139. GALLE (ve. H.). On the relation between departures from the normai in the strength of the trade-winds of the Atlantic Ocean and those in the waterlevel and tem- perature in the Northern European seas. 1147. Gas (The chemical constant and the application of the quantum theory by the method of the natural vibrations to the equation of state of an ideal monatomic). 20. — (On interference phenomena to be expected when Rontgen rays pass through a di-atomic). 1184. Gass (The diffusion-coefficient of) and the viscosity of gas-mixtures. 1068. — (Tueoretical determination of the entropy constant of) and liquids. 1167. Gas EQuiLiBriaA (On) and a test of Prof. v. p. Waaus Jr.’s theorema.]. 695. IL. 1011. Gas-Laws (The influence of the hydration and of the deviations from the ideal) in aqueous solutions of salts on the solidifying and the boiling points. 1036. GaS-MINTURES (The diffusion-coefficient of gases and the viscosity of). 1068. GeELs (On the behaviour of) towards liquids and the vapours thereof. IT. 92. Geodesy. H. G. van De Sande Baknuyzen, N. WiLpEsorR and J. W. Dreperin«k : “Comparison of the measuring bar used in the base-measurement at Stroe, with the Dutch Metre N® 27”. 300. — H. G. van bE Sanpe Baxkauyzen: “Comparison of the platinum-iridium Metre No. 27 with the international Metre M as derived from the measurements by the Metre-Commission in 1879 and 1880, and a preliminary determination of the length of the measuring-bar of the French base-apparatus in international metres”. 311. Geology. H. A. Brouwer: “On the granitic area of Rokan (Middle-Sumatra) and on contact-phenomena in the surrounding schists’. 1190. Geophysics. J. P. van pDER Stok: “The treatment of frequencies of directed quanti- ties”. 586, 5 x CONTENTS. Geophysics. P. H. Ganié: “On the relation between departures from the normal in the strength of the trade-winds of the Atlantic Ocean and those in the waterlevel and temperature in the Northern European seas”. 1147. GroTROPIC REACTIONS (On the mutual influence of phototropic and) in plants. 1278. GERMINATION (Energy transformations during the) of wheat-grains. 62. GRANITIC AREA (On the) of Rokan (Middle-Sumatra) and on contact-phenomena in the surrounding schists. 1190. GRAVITATION (On the field of a single centre in Ernstetn’s theory of). 998. Gravity (The mean radius of the earth, the intensity of) and the moon’s parallax. 1291. GuMMosis in the fruit (of the Almond and the Peachalmond as a process of normal life. 810. I1AGA (H.) presents a paper of Miss H. J. Foumer: “A new electrometer, especi- ally arranged for radio-active investigations”. 659. — presents a paper of Prof. I. M. Jancer: “On a new phenomenon accompanying the diffraction of Réntgenrays in birefringent crystals”. 1204. — and F. M, Jarcer. On the real symmetry of cordierite and apophyllite. 430. HAMBURGER (H. J.) presents a paper of Dr. E, Laqueur: ‘On the survival of isolated mammalian organs with automatic function”. 270, — presents a paper of Prof. A. A. Hymans van pDeN Bercu and J. J. pe La FontaIne Scutuirer: “The identification of traces of bilirubin in albuminons fluids”. 807. — Phagocytes and respiratory centre, 1325. HEART-RHYTHM (On the). 1075. IT, 1135. WELDERMAN (Ww. D.) and Ernsr Conen. The allotropy of cadmium, IL. 54, ILL. 122. IV, 638. V. 1050. — The allotropy of zine. IL. 59. — The allotropy of copper. II. 60. — The allotropy of lead. 1. 822. Note. 1055. — The metastability of the metals in consequence of allotropy and its significance for Chemistry, Physics and Technics. LV. 1288. neLiuM (Further experiments with liquid), [. 12. 278. K. 283. L. 514. N.520. M. 760, HERMITE (On the functions of). 1st part. 139. — and ABEL’s polynomia (On). 192. oF (K) and H. Kamerurnen ONNEs, Further experiments with liquid helium. N. 520, HOLLEMAN (A. F.) presents a paper of Dr. L. K. Wourr and Dr. EK. H, Bicaner: “On the behaviour of gels towards liquids and the vapours thereof. IL. 92. — presents a paper of Prof. J. BoEsEKEN: “On catalyse”. 546. — The nitration of the mixed dihalogen benzenes. 846. — presents a paper of Prof. J. Borseken and W. D. Couen: “The reduction of aromatic ketones, II. Contribution to the kuowledge of the photochemical phenomena”. 849, — The replacement of substituents in benzene derivatives. 1027. a — presents a paper of Dr. C, H. Suurrer: “The influence of the hydration and CUGeN DORN T's; xl of the deviations from the ideal gaslaws in aqueous solutions of salis on the solidifying and the boiling points’. 1036. HOLLEMAN (A. F.) presents a paper of Miss ADA Prins: ,,On critical end-points and the system ethane-naphtalene’. 1095, noustT (G.) and H. KaMertinen Onnes. The measurement of very low temperatures. XXIV. The hydrogen and helium thermometers of constant volume down to the freezing point of hydrogen compared with each other and with the platinum- resistance thermometer, 501. — On the electrical resistance of pure metals. IX. 508. — Further experiments with liquid helium. M. 760. — H. Kameruncu OnnEs and C. Dorsman. Isothermals of di-atomie substances and their binary mixtures. XV. Vapour pressures of oxygen and critical point of oxygen and nitrogen. 950, HOOGEWERFF (s.) presents a paper of Prof, W. Remnpers: “Equilibria in the system Pb-S-O, the roasting reactionprocess. 703. HULSHOF (H.). On the thermodynamic potential as a kinetic quantity. Ist part. 85, HYDRATION (The influence of the) and of the deviations from the ideal gas-laws in aqueous Solutions of salts on the solidifying and the boiling points. 1036, HYDROGEN (Measurements of isotherms of) at 20° C. and 13.°5 C. 203. — (Measurements on the capillarity of liquid). 528. HYDROGEN ISOTHERMS (The) of 20° C. and of 15°.5 C, between 1 and 2200 atms. 217. Hydrostatics. D. J. Korrewec: “The different ways of floating of an homogeneous cube”. 224. HYMANS VAN DEN BERGH (a. a.) and J. J. DE wa Fonraine Scuuurrer. The identification of traces of bilirubin in albuminous fluids. 807. INERTIA (On isostasy, the moments of) and the compression of the earth, 1295. INNERVATION (On the termination of the eiferent nerves in plain muscle-cells and its bearing on the sympathetic (accessory) ) of the striated muscle-tibre, 982. INTEGRAL EQUATIONS (On some). 286, INTEGRAL-FORMULA (On an) of STIELTJEs. 829. INTERFERENCE-PHENOMENA (On) to be expected when Roéuntgen-rays pass through a di-atomic gas. 1184. INVOLUTION (A cubic) of the second class, 105. — (A triple) of the third class, 134. ISOMERIDES (g-Sulpho-propionic acid and its resolution into optically active). 653. 1soOPRENE (A crystallized compound of) with sulphur dioxide. 585. isostasy (On), the moments of inertia and the compression of the earth, 1295, ISOPHERMALS of di-atomic substances and their binary mixtures. XV. Vapour pressures of oxygen and critical point of oxygen and nitrogen. 950. XVI. Vapour-pressures of nitrogen between the critical point and the boiling point. 959. — of monatomic substances and their binary mixtures. XVI. 275. IsOTHERMS (The hydrogen) of 20° C. and of 15°95 C. between 1 and 2200 atms. 217. — of hydrogen (Measurements of) at 20° C. und 1595 ©, 208, XII CRONE DL EN DiS: JABGER (er. M.). The temperature-coeflicients of the free surface-energy of liquids at temperatures from —80° C. to 1650° C, I. 329. V. 405. VI. 416. VIT. 555. VHI. 571. — On a new phenomenon accompanying the diffraction of Rontgenrays in birefrin- gent crystals. 1204. — Researches on Pasreur’s principle of the connection between molecular and physical dissymmetry. I. 1217. — and H Haga. On the real symmetry of cordierite and apophyllite. 430. — and Juz. Kaun. The temperature coefficients of the free surface-energy of liquids at temperatures from —80° C. to 1650° C, LV. 395. — and Ant. Srmex. Studies in the field of silicate-chemistry, If. 239. IIL. 251. — and M. J, Suir. The temperature-coefficients of the free surface energy of liquids at temperatures from —80° C. to 1650° C. IT. 365. IIL. 386, JONG (A. W. kK. DE). Action of sunlight on the cinnamic acids. 1274. Jupiter (The figure of the planet), 1047. KAUN (JUL) and F. M. Jatcer, The temperature-coefficients of the free surface- energy of liquids at temperatures from —80° C. to 1650° C. LV. 395. KAMERLINGH ONNES (H.). vy. Onnes (H. KAaMERLINGH). KAPPERS (Cc. U. ARIENS) and P. Roratc. Further contributions to our know- ledge of the brain of Myxine glutinosa, 2. KAPTEYN (J. Cc.) presents a paper of Prof. M. J. van Uven: “The theory of Bravais (on errors in space) for polydimensional space, with applications to correlation”. Continuation. 150. KAPTEYN (w.). On the functions of Hermite. Lst part. 139. — presents a paper of Dr. N, G. W. H. Bescer: “On Hermire’s and ABEL’s polynomia”, 192. — On some integral equations. 286. — presents a paper of Prof. M. J. van Uven: “The theory of the combination of observations and the determination of the precision, illustrated by means of vectors’, 490. KEESOM (w. H.). The chemical constant and the application of the quantum theory by the method of the natural vibrations to the equation of state of an ideal monatomic gas. 20. — On the matter in which the susceptibility of paramagnetic substances depends on the density. 110. — and H. Kamerttncu Onves. The specific heat at low temperatures. I. Measure- ments on the specific heat of lead between 14° and 80° K. and of copper between 15° and 22° K, 894. KetToNES (The reduction of aromatic). III. Contribution to the knowledge of the photo- chemical phenomena. $49. KINETIC INTERPRETATION (On the) of the osmotic pressure. 1241. KINETIC QUANTITY (On the thermodynamic potential as a). 1st part. 85. KLUYVER (J. c.). On an integral formula of STIELTJES. 829. CONTENTS XI KOHNSTAMM (eH.) and kK, W. Watsrra. Measurements of isotherms of hydrogen at 20° C. and 159.5 C. 203. KORTEWEG (pb. J.). The different ways of floating of an homogeneous cube. 224, KRUYT (H. R.). Current potentials of electrolyte solutions. 615. — Electric charge and limit value of colloids. 623. — and Jac. van DER Spex. The connection between the limit value and the concentration of arsenic trisulphide sols, 1158. KUENEN (J. e.). On the measurement of the capillary pressure in a soap-bubble. 946. — The diffusion-coefficient of gases and the viscosity of gas-mixtures, 1068. KUIPER JR, (K.). Lhe physiology of the air-bladder of fishes. 1088. KUYPERS (H. A.) and H. KaweruincH OnNeEs. Measurements on the capillarity of liquid hydrogen. 528. LAAR (J. J. VAN). A new relation between the critical quantities and on the unity of all substances in their thermic behaviour. 451. — Some remarks on the values of the critical quantities in case of association. 598. — On apparent thermodynamic discontinuities in connection with the value of the quantity 4 for infinitely large volume. 606, — The calculation of the molecular dimensions from the supposition of the electric nature of the quasi-elastic atomic forces. 877. LAQUEUR (&). On the survival of isolated mammalian organs with automatic function. 270. LEAD (The allotropy of). I. 822. Note. 1055. — (Measurements on the specific heat of) between 14° and 80° k. and of copper between 15° and 22° K, 894. LIGHT (On FResNEL’s coefficient for) of different colours. 445. LIMIT VALUE (Electric charge and) of colloids. 623. — (The connection between the) and the concentration of arsenic trisulphide sols. 1158. 11auIps (On the behaviour of gels towards) and the vapours thereof. II, 92. — (Theoretical determination of the entropy constant of gases and). 1167. — (The temperature-coefficients of the free energy-surface of) at temperatures from —80° C. to 1650° C. I. 329. IL 365. ILL. 389. LV. 395. V. 405. VI. 416. VII. 556. VILL. 571. LORENTZ (H. A.) presents a paper of Dr. J. J. van Laar: “A new relation between the critical quantities and on the unity of all substances in their thermic behavtour’. 451. —- presents a paper of Dr. J. J. van Laan: “Some remarks on the values of the critical quantities in case of association’’. 598. — presents a paper of Dr. J. J. van Laan: “On apparent thermodynamic discon- tinuities in connection with the value of the quantity 4 for infinitely large volume”. 606, — presents a paper of Dr. G, J. Evras; “On the structure of the absorption lines D, and Ds”, 720. XIV CONTENTS. LORENZ (H. A.) presents a paper of Dr. G. J. Enias: “On the lowering of the freezing point in consequence of an elastic deformation”. 732. — presents a paper of Dr. G, J. Extras: “The effect of magnetisation of the elec- trodes on the electromotive force”. 745. — presents a paper of Dr. L. S. Ornstetn: “On the theory of the string galvano - meter of Er1ntHOVEN”. 784. — presents a paper of Dr. L. S. Ornstein and Dr. F. Zeentke: “Accidental deviations of density and opalescence at the critical point of a single sub- stance’. 793. — presents a paper of Mrs. T. Eurenrest —AranassJewa : “Contribution to the theory of corresponding states’. 840. — presents a paper of Dr. J. J. van Laan: “The caleulation jof the molecular dimensions from the supposition of the electric nature of the quasi-elastic atomic forces”. 877. — presents a paper of Mr, J. Droste: “On the field of a single centre in ErNsTern’s theory of gravitation”. 998. — presents of paper of Mr. H. Terrope: ‘Theoretical determination of the entropy constant of gases and liquids”. 1167. — presents a paper of Prof, P. Kurmnrest: “On interference-phenomena to be expected when R6NTGEN rays pass through a di-atomic gas”. 1184. — presents a paper of Prof. P. Eurenrest: “On the kinetic interpretation of the osmotic pressure”. 1241. LUNAR PERIGEE (The motions of the) and node and the figure of the moon. 1309. MAGNETISATION (‘The effect of) of the electrodes on the electromotive force. 745. MAMMALIAN ORGANS (On the survival of isolated) with automatic function. 270. Mathematics. Jan pe Vries: “A cubic involution of the second class”. 105. — Jan pve Vrigs: “A triple involution of the third class”. 134. — W. Kapreyn: “On the functions of Hermite”. 3th part. 139. — M. J. van Uven: “The theory of Bravats (on errors in space) for polydi- mensional space with applications to correlation”. (Continuation). 150. — M. J. van Uven: “Combination of observations with and without conditions and determination of the weights of the unknown quantities, derived from me- chanical principles”. 157. — N. G. W. H. Beraer: “On Hermrre’s and AsBet’s polymonia”. 192. — W. Kapreyrn: “On some integral equations”. 286. — M. J. van Uven: “The theory of the combination of observations and the determination of the precision, illustrated by means of vectors”. 490. — J. ©. Kivyver: “On an integral formula of Srievtses”. 829. —- JAN DE Vrizs: “Characteristic numbers for nets of algebraic curves”. 935, — Jan pe Vries: “Characteristic numbers for a triple infinite system of algebraic plane curves”. 1055. — Jan pr Varies: “Systems of circles determined by a pencil of conics”. 1107. — W. van per Woupe: “On Norner’s theorem”, 1245. — Jan pe Vries: “A bilinear congruence of rational twisted quintics”. 1250, CON TEN T §&. >A Mathematics. JAN pe Vries: “Some particular bilinear congruences of twisted cubics”. 1256. MATHIAS (£.), H. Kamertincu Onnes and C. A, Crommenin. The rectilinear diameter of nitrogen. 953. MEASUREMENT (The) of very low temperatures. XXIV. The hydrogen and helium. thermometers of constant volume, down to the freezing point of hydrogen compared with each other and with the platinum-resistance thermometer. 501. MEASUREMENTS On the capillarity of liquid hydrogen, 528. — of isotherms of hydrogen at 20° C. and 1595 C. 203. — on the specific heat of lead between 14° and 80° k. and of copper between 15° and 22° K. 894. MEASURING Bar (Comparison of the) used in the base measurement at Stroe with the Dutch Metre N® 27. 300. — (Comparison of the Dutch platinum-iridium Metre N®%, 27 with the international Metre M as derived from the measurements by the Dutch Metre-Commission in 1879 and 1880, and a preliminary determination of the length of the) of the French base-apparatus in international metres. 311. MECHANICAL PRINCIPLES (Combination of observations with and without conditions and determination of the weights of the unknown quantities derived from). 157. METALS (The metastability of) in consequence of allotropy, and its significance for Chemistry, Physies and Technics. 200. III. 926. 1V. 1238. — (On the electrical resistance of pure). IX. 508. METASTABILITY (The) of metals in consequence of allotropy and its significance for Chemistry, Physics and Technics. 200. III. 926. IV. 1238. METHYLAMINE (On the interaction of ammonia and) on 2. 3. 4.-trinitrodimethylaniline. 1034, METRE No. 27 (Comparison of the Dutch platinum-iridium) with the international metre M/ as derived from the measurements by the Dutch Metre-Commission in 1879 and 1880, and a preliminary determination of the length of the measu- ring bar of the French baseapparatus in international metres. 311. Mineralogy. H. Haca and I’. M, Jararer: “On the real symmetry of cordierite and apophyllite”. 430. — C. E, A. Wichmann: “On the tin of the island of Flores”, 474. MOLECULAR DIMENSIONS (The calculation of the) from the supposition of the electric nature of the quasi-elastic atomic forces, 877. MOLENGRAAFF (G. 4. F.) presents a paper of Dr. H. A. Brouwer: “On the granitic area of Rokan (Middle-Sumatra) and on contact-phenomena in the sur- rounding schists”. 1190. moon (The motions of the lunar perigee and node and the figure of the). 1309. MOON’S PARALLAX (The mean radius of the earth, the intensity of gravity and the), 1291. MUSCLE-CELLS (On the termination of the efferent nerves in plain) and its bearing - on the sympathetic (accessory) innervation of the striated muscle-fibre. 982. MUSCULAR FIBRE (On the mode of attachment of the) to its tendontibres in the striated muscles of the vertebrates, 989, XVI CONTENTS. MYXINE GLUTINOsA (Further contributions to our knowledge of the brain of). 2. NERVE-DISTRIBUTION (On the) in the trunk-dermatoma. 632. Nerves (On the termination of the efferent) in plain muscle cells and its bearing on the sympathetic (accessory) innervation of the striated muscle-fibre. 982. Nets (Characteristic numbers for) of algebraic curves. 935, NITRATION (The) of the mixed dihalogen benzenes. 846. NITROGEN (Vapour pressures of oxygen and critical point of oxygen and). 950. — (The rectilinear diameter of). 953. -—— (Vapour pressures of) between the critical point and the boiling point. 959. NOTHER’s theorem (On). 1245. occLusion (A case of) of the arteria cerebelli posterior inferior. 914. ONNES (HW. KAMERLINGH). Further experiments with liquid helium. J. 12. 278. K. 283. L. 514. — presents a paper of Dr. W. H, Kegsom: “The chemical constant and the appli- cation of the quantum-theory by the method of the natural vibrations to the equation of state of an ideal monatomic gas’. 20. — presents a paper of Dr, W. H. Kersom: “On the matter in which the suscep- tibility of paramagnetic substances depends on the density”. 110, — presents a paper of Dr. C. A. Crommezin: “Tsothermals of monatomic sub- stances and their binary mixtures”. XVI. 275. — presents a paper of Dr. C. A. Cromme in: “Isothermals of di-atomic substances and their binary mixtures”, XVI. 959. — C. Dorsman and G. Hotsr. Isothermals of di-atomic substances and their binary mixtures. XV. Vapour pressures of oxygen and critical point of oxygen and nitrogen. 950. — and P. Enerenrest. Simplified deduction of the formula from the theory of combinations which PLANoK uses as the basis of his radiation theory. 870. — and K. Hor. Further experiments with liquid helium, N. 520, — and G. Hotst. The measurement of very low temperatures. XXIV. The hydrogen and helium thermometers of constant volume down to the freezing point of hydrogen compared with each other and with the platinum-resistance thermo- meter. 501. — On the electrical resistance of pure metals. 1X. 508. — Further experiments with liquid helium, M. 760. —and W. H. Keresom. The specific heat at low temperatures. I. Measurements on the specific heat of lead between 14° and 80° Kk. and of copper between 15° and 22° K, 894. — and H. A. Kuypers. Measurements on the capillarity of liquid hydrogen. 528. — BE. Marutas and C. A. Crommenin. The rectilinear diameter of nitrogen. 953. OPALESCENCE (Accidental deviations of density and) at the critical point of a single substance. 793. ORNSTEIN (4. 8.). On the theory of the stringgalvanometer of ErNTHOVEN. 784. — and F. Zerntxe. Accidental deviations of density and opalescence at the critical point of a single substance. 793. CONTENTS Xvit OSMOTIC PRESSURE (On the kinetic interpretation of the). 1241. OXYGEN (Vapour pressures of) and critical point of oxygen and nitrogen. 950. PARAMAGNETIC SUBSTANCES (On the matter in which the susceptibility of) depends on the density. 110. PASTEUR’s principle (Researches on) of the connection between molecular and physical dissymmetry. I. 1217. PEACHALMOND (Gummosis in the fruit of the Almond and the) as a process of normal life. 810. 'Petrography. A. Wicumann: “On some rocks of the island of Taliabu (Sula islands). 226. PHAGOCYTES and respiratory centre. 1325. PHosPHORUs (On the vapour pressure lines of the system). Il. 678. IIL. 962. — (Further particulars concerning the system). 973. PHOTOCHEMICAL phenomena (Contribution to the knowledge of the). $49. PHOTOTROPIC and geotropic reactions (On the mutual inftuence of) in plants, 1278. Physics. H. Kamprimcu Onnes: “Further experiments with liquid helium”. J. 12. 278. K. 283. L. 514, N. 520. M. 760. — W. H. Kersom: “The chemical constant and the application of the quantum- theory by the method of the natural vibrations to the equation of state of an ideal monatomic gas”, 20. — H. Huusuor: “On the thermodynamic potential as a kinetic quantity”. 1st part. 85. -- W. H. Kexrsom: “On the manner in which the susceptibility of paramagnetic substances depends on the clensity”. 110. — Pu. Konnstamm and k. W. Watsrra: “Measurement of isotherms of hydrogen at 20° C. and 15° C.” 203. — K. W. Watstra: “The hydrogen isotherms of 20° C. and of 15°95 C. between 1 and 2200 atm.” 217. — C, A. Cromme.in: “‘Isothermals of monatomic substances and their binary mixtures”, XVI, 275. = P. Zeeman: ‘'FResNoL’s coefficient for light for different colours”. 1stpart. 445, = J. J. van Laar: “A new relation between the critical quantities and on the unity of all substances in their thermic behaviour’. 451. = H. vu Bois: “Modern electromagnets, especially for surgical and metallurgic practice”. 468, = H. Kamerninc Onnes and G, Horsr: “On the measurement of very low temperatures. XXIV. The hydrogen and helium thermometers of constant volume, down to the freezing-point of hydrogen compared with each other and with the platinum resistance thermometer’. 501. =— H. Kamerninau Onnus and G. Housr: “On the electrical resistance of pure metals ete.”. [X. 508. — H. Kamernrnen Onnus and H, A. Kuyerrs: ‘Measurements on the capillarity of liquid hydrogen”. 528) = J. J. van Laan: “Some remarks on the values of the critical quantities in case of association’’. 598. 90) Procéedings Royal Acad. Amsterdam. Vol. XVII, XVIII CONTENTS. Physics. J. J. van Laar: “On apparent thermodynamic discontinuities in connection with the value of the quantity 4 for infinitely large volume’’. 606. — Miss H. J. Foumpr: “A new electrometer, especially arranged for radio-active investigations”. 659. — G. J. Brras: “On the structure of the absorptionlines D,; and ),”. 720. — G. J. Evras: “The lowering of the freezing point in consequence of an elastic deformation”. 732. — G. ap Enras: “The effect of magnetisation of the electrodes on the electromotive force”. 745. — L. 8. Ornstern: “On the theory of the string-galvanometer of ErytHoven’’. 784. — L. 8. Ornsrern and F. Zernike: “Accidental deviations of density and opales- cense at the critical point of a single substance”. 793. — F. E. C. Scnerrer; “On unmixing in a binary system for which the three phase pressure is greater than the sum of the vapour tensions of the two compo- nents’. 834. — Mrs. T. Exrenrest—Aranasssewa: “Contribution to the theory of corresponding states”. 840. — P. Burenrest and H, KameruincuH Onnes: “Simplified deduction of the formula from the theory of combinations which PLANcK uses as the basis of his radiationtheory”. 870. — H. pu Bors: “The universality of the Zeeman-elfect with respect to the SrarK- effect in canal-rays”. 873. — J. J. van Laar: “The calculation of the molecular dimensions from the suppo- sition of the electric nature of the quasi-elastic atomic forces”, 877. — W. H. Kersom and H. Kameruineu Onnes: “The specific heat at low tempe- ratures. I. Measurements on the specific heat of lead between 14° and 80° K, and of copper between 15° and 22° K.” 894. — J. P. Kunnen: “On the measurement of the capillary pressure in a soap-bubble”. 946. — H. Kamertincu Onnes, C. Dorsman and G. Horst: “Isothermals of di-atomic substances and their binary mixtures. XV. Vapour pressures of oxygen and critical point of oxygen and nitrogen”. 950. — E. Mararas, H. Kameruincn Onneis and C, A. CromMEtiIn: “The rectilinear diameter of nitrogen”. 953. — ©, A. Crommeniy: “Isothermals of di-atomic substances and their binary mixs tures. XVI. Vapour pressures of nitrogen between the critical point and the boiling point”, 959, «- J, Droste: “On the field of a single centre in ErnsTEty’s theory of gravitation”, 998. «- J, P, Kusnex: “The diffusion coefficient of gases and the viscosity of gasa mixtures”. 1068, s H: Terropk: “Theoretical determination of the entropy constant of gases and liquids”. 1167. CROPNELS ENG TCS XIX Physics. P. Enrenrest: “On interference phenomena to be expected when Réntgen rays pass through a di-atomic gas’. 1184. _— F. M. Jazcer: “On a new phenomenon accompanying the diffraction of R6ntgen rays in birefringent crystals’. 1204. — P. Enrenrest: “On the kinetic interpretation of the osmotic pressure”. 1241. Physiology. ££. Laaueur: “On the survival of isolated mammalian organs with auto- matic function”. 270. —L. K. Wotrr: “On the formation of antibodies after injection of sentizised antigens”. II. 318. — G. van Risnperk: “On the nerve-distribution in the trunk-dermatoma’’. 632. — A. A. Hymans vAN DEN Bereu and J. J. pe ta Fontatne Scauurrur: “The identification of traces of bilirubin in albuminous fluids”. 807. — I. K. A. Werraetm Satomonson: “Exaggeration of deep reflexes”. 885. — S. pe Borer: “On the heart-rhythm”. 1075. If. 1135. — A. B. Droocierver Fortuyn: “The decoloration of fuchsin-solutions by amor- phous carbon”, 1322. — H. J. Hameurcer: “Phagocytes and respiratory centre”. 1525. PICRYLMETHYLAMIDE (The coloration of some derivatives of) with alkalies. 647. PLANCK (Simplified deduction of the formula from the theory of combinations which) uses as the basis for his radiation theory. 870. PLANET Jupiter (The figure of the). 1047. PLANETS (On SEELIGER’s hypothesis about the anomalies in the motion of the inner). 23. PLANTs (On the mutual influence of the phototropic and geotropic reactions in). 1278 poLyNoMIA (On Hermitre’s and ABEL’s). 192. PostTMA (s.) and A. Smits. The system Ammonia-water. 182. porass1uM (The allotropy of). I. 1115. POTASSIUM SULPHATE, potassium chlorid (The system: copper sulphate, copper chlorid) and water at 30°. 532. POTENTIAL (On the thermodynamic) as a kinetic quantity. Ist part, 85. POTENTIALS (Current) of electrolyte solutions. 615. PRECISION (The theory of the combination of observations and the determination of the), illustrated by means of vectors. 490. PRINS (Miss ADA). On critical end-points and the system ethane-naphtalene. 1095. PSEUDO-COMPONENTS (The metastable continuation of the mixed crystal series of) in connection with the phenomenon allotropy. I. 672. quantity 4 (On apparent thermodynamic discontinuities in connection with the value of the) for infinitely large volume. 606. QuaNnTUM-rtHEORY (The chemical constant and the application of the) by the method of the natural vibrations to the equation of state of an ideal monatomic gas). 20 QUATERNARY sysTEM KCl—CuClz2—BaCl,—H20 (On the). 781. auinrics (A bilinear congruence of rational twisted). 1250. RADIATION THEORY (Simplified deduction of the formula from the theory of combina- tions which PLancK uses as the basis for his). 870. XX CONTENTS RADIO-ACTIVE investigations (A new electrometer, specially arranged for). 659. REPLEXES (Exaggeration of deep). 885. REINDERS (w.). Equilibria in the system Pb-S-O, the roasting reaction process. 703. RESISTANCE (On the electrical) of pure metals. 1X. 508. RESPIRATORY CENTRE (Phagocytes and), 1325. ROASTING REACTION PROCESS (f{quilibria in the system Pb-S-O, the). 703. rocks (On some) of the island of Taliabu (Sula islands). 226. ROKAN (Middle-Sumatra) (On the granitic area of) and on contact phenomena in the surrounding schists, 1190. ROMBURGH (e. VAN) presents a paper of Prof. F. M. Jareer and Dr. Ant. SimEk: “Studies in the field of silicate-chemistry”. Il. 239. ILI. 251. — presents a paper of Prof. F. M. Jarcer: “The temperature-coefticients of the free surface-energy of liquids at temperatures from —S8U° to 1650° C.” I. 329. II. 365. ILI. 886. IV. 395. V. 405. VI. 416. VII. 555. VILL. 571. — presents a paper of Mr. G. pr Bruin: “A crystallized component of isoprene with sulphur dioxide”. 585. — presents a paper of Prof. F, M. Jazcrr: “Researches on Pasteur’s principle of the connection between molecular and physical dissymmetry”. I. 1217. — presents a paper of Dr. A. W. K. pg Jona: ‘Action of sunlight on the cin- namic acids’. 1274. — and Miss D, W. Weysinx. On the interaction of ammonia and methylamine on 2.3.4,-trinitrodimethylaniline. 1034. RONTGEN Rays (On interference phenomena to be expected when) pass through a di-atomic gas. 1184. — (On a new phenomenon accompanying the diffraction of) in birefringent crystals. 1204. ROTHIG (p.) and C. U. ArtENs Kappers. Further contributions to our knowledge of the brain of Myxine glutinosa. 2. RIJNBERK (G. VAN) On the nerve-distribution of the trunk-dermatoma. 6382. SALOMONSON (J. K. A. WERVHEIM). Hxaggeration of deep reflexes. 885. — presents a paper of Dr. S. p—E Boer: ‘On the heart-rhythm’. 1075. LI. 1135. saLts (The influence of the hydration and of the deviations from the ideal gas-laws in aqueous solutions of) on the solidifying and the boiling point. 1036. SANDE BAKHUYZEN (H. G VAN DE). vy. Bakauyzen (H. G. vaAN DE Sanpg), SCHEFFER (Ff. E. c.). On gas equilibria and a test of Prof. v. p. Waats-JR.’s theorema. I. 695. Il. 1011. — On unmixing in a binary system for which the three-phase pressure is greater than the sum of the vapour tensions of the two components. 834, SCHLUITER (J. J. DE LA FONTAINE) and A. A. HyMans VAN DEN BERGH. The identification of traces of bilirubin in albuminous fluids. 807. SCHREINEMAKERS (fF. A. H.). Equilibria in ternary systems. XV. 70. XVI. 169. XVII. 767. XVIII. 1260. — and Miss W. C. pe Baat. The system: copper sulphate, copper chlorid, potas- sium sulphate, potassium chlorid and water at 30° C. 533, CONTENTS. XXI SCHREINEMAKERS (Ff. A. H.) and Miss W. C. pe Baar. On the quaternary system KCl-CuClg-BaClo-H,C. 781. — Compounds of the arsenious oxide, I. 1111. 8EEL1GER’s hypothesis (On) about the anomalies in the motion of the inner planets. 23. — (Remarks on Mr. WoLtsEr’s paper concerning). 33. SILICATE-CHEMISTRY (Studies in the field of). If. 239. III. 251. SIMEK (anv) and F, M. Jazcpr. Studies in the field of silicate-chemistry. IT. 239, IIL. 251. SITTER (Ww. DE) presents a paper of Mr. J. Wouter oro: “On SEELIGER’s hypo- thesis about the anomalies in the motion of the inner planets”. 23. — Remarks on Mr. Woutyer’s paper concerning SrenicEr’s hypothesis. 33. — The figure of the planet Jupiter. 1047. — On the mean radius of the earth, the intensity of gravity and the moon’s parallax. 1291. — On isostasy, the moment of inertia and the compression of the earth. 1295. — The motions of the lunar perigee and node and the figure of the moon. 1309 sLUITER (c. H.). The influence of the hydration and of the deviations from the idenl gas-laws in aqueous solutions of salts on the solidifying and the boiling-point. 1036. smivt (m.) and F, M. Jancrer. The temperature-coefficients of the free-surface-energy of liquids at temperatures from —S0° C. to 1650° C. Il. 365. IIT, 381. i. sMits (a). The metastable continuation of the mixed crystal series of pseudo- components in connection with the phenomenon allotropy. II, 672. — and Aten (A. H. W.). The applicaticn cf tle theory of al’otropy to electro- motive equilibria. 11. 37. ILI. 680. — and 8S. C. Boxknorst. On the vapour pressure lines in the system phosphorus. {1 678. III, 962. — Further particulars concerning the system phosphorus, 973. — and 8, Postma. The system ammoniawater. 182. SOAP-BUBBLE (On the measurement of the capillary pressure in a). 946, SODIUM-HYPOCHLORITE (Action of) on amides of z-oxyacids. 1163. SPECIFIC HEAT (The) at low temperatures. [. Measurements on the specific heat of lead between 14° and 80° K. and of copper between 15° and 22° k, 894. SPEK (sac. VAN DER) and H. R. Kruyt. The connection between the limit value and the concentration of arsenic trisulphide sols. 1158, stakK-effect (The universality of the Zeeman-eflect with respect to the) in canal-rays. 873 sT1ELTJES (On an integral-formula of). 829. STOK (J. P. VAN DER). The treatment of frequencies of directed quantities. 586. — presents a paper of Mr. P. H. Ga11é: “On the relation between departures from the normal in the strength of the trade-winds in the Atlantic Ocean and those in the waterlevel and temperature in the Northern European seas.’ 1147. STRING-GALVANOMETER (On the the theory of the) of EintnHoven. 784. stRoE (Comparison of the measuring bar used in the base measurement at) with the Dutch Metre n° 27. 300. suBsTANCES (Isothermals of monatomic) and their binary mixtures. XVI. 275. — (Isothermals of di-atomic) and their binary mixtures, XV. 950, XVI, 959. NXIT CONTENTS. substances (A new relation between the critical quantities and on the unity of all) in their thermic behaviour. 451. suBsTItuENTS (The replacement of) in benzene derivatives. 1027. 4-SULPILO-PROPIONIC acrb and its resolution into optically active isomerides. 653. SULPHUR DIOXIDE (A erystallized compound of isoprene with). 585. SUNLIGHT (Action of) on the cinnamie acids. 1274. system PJ-S-O (Equilibria in the), the roasting reaction process. 703. — (The) copper sulphate, copper chlorid, potassium sulphate, potassium chlorid and water at 30° C. 533. — (Characteristic numbers for a triply infinite) of algebraic plane curves. 1055. — ammonia—water (The). 182. — ethane—naphthalene (On critical endpoints and the). 1095. — phosphorus (On the vapour pressure lines in the). IH. 678. [[L 962. — phosphorus (Further particulars concerning the). 973. vALIABU (Sula islands) (On some rocks of the island of). 226. TEMPERATURE (On the relation between departures from the normal in the strength of the trade-winds of the Atlantic Ocean and those in the waterlevel and) in the Northern European seas. 1147. TEMPERATURE-COEFFICIENTS (The) of the free energy surface of liquids at tempera- tures from —80° C. to 1650° C. I. 329. IL. 365. ILL 386. LV. 395. V. 405. VI. 416. VIL. 555. VIII. 571: TEMPERATURES (The measurement of very low). XXLV. The hydrogen and helium thermometers of constant volume down to the freezing point of hydrogen com. pared with each other and with the platinum-resistance thermometer. 501. — (The specific heat at low). [. Measurements on the specific heat of lead between 14° and 80° K. and of copper between 15° and 22° K. 894. TENDONFIBRES (On the mode of attachment of the muscular fibre to its) in the striated muscles of the vertebrates. 989. TERNARY sYSteMS ([quilibria in). XV. 70. XVL. 169. XVIL. 767. XVIII. 1260. TETRODE (u.). Theoretical determination of the entropy constant of gases and liquids. 1167. TuEORY of allotropy (The application of the) to electromotive equilibria. I. 37. UL 680. — of Bravats (The) (on errors in space) for polydimensional space with applica- tions to correlation. (Continuation). 150. — (The) of the combination of observations and the determination of the precision, illustrated by means of vectors. 490. i — of combinations (Simplified deduction of the formula from the) which Pranck uses as the basis of his radiation theory. 870. — of corresponding states (Contribution to the). 840. — of gravitation (On the field of a single centre in Etnsrety’s). 993. THERMOMETERS (The hydrogen and helium) of constant volume, down to the freezing point of hydrogen compared with each other, and with the platinum-resistan ce thermometer, 501. TUREE-PHASE PRESSURE (On unmixing in a binary system for which the) is greater than the sum of the vapour tensions of the two components. 834. CONTENTS. XXIII Tin (On the) of the island of Flores. 474. TRADE-WINDs (On the relation between departures from the normal in the strength of the) in the Atlantic Ocean and those in the waterlevel and temperature in the Northern European seas. 1147. TRINITRODIMETHYLANILINE (On the interaction of ammonia and methylamine on 2.3.4.-). 1034. TRUNK-DERMATOMA (On the nerve-distribution in the). 632. UNMIXING (On) in a binary system for which the three-phase pressure is greater than the sum of the vapour tensions of the two components. 83+. UVEN (M. J. VAN). The theory of Bravats (on errors in space) for polydimensional space with applications to correlation. (Continuation). 150. — Combination of observations with and without conditions and determination of the weights of the unknown quantities, derived from mechanical principles. 157. — The theory of the combination of observations ani the determination of the precision, illustrated by means of vectors. 490. VAGUS AREA (The) in Camelidae. 1119. VAPOUR PRESSURE LtNeés (On thie) in the system puosphorus. IL. 678. ILL. 962. VAPOUR PRESSURES of oxygen and critical point of oxygen and nitrogen. 950. — of nitrogen between the critical point and the boiling point. 959. VAPOUR TENSIONS (On unmixing in a binary system for which the three-phase pressure is greater than the sum of the) of the two components. 834. vectors (The theory of the combination of observations and the determination of the precision, illustrated by means of). 490. VERMEULEN (H. A.). The vagus area in Camelidae. 1119. VerTEBRATES (On the mode of attachment of the muscular fibre to its tendontibres in the striated muscles of the). 989. viscosity of gas-mixtures (The diffusion-coefticient of gases and the). 1068. VRIES (JAN DE). A cubic involution of the second class. 105. — A triple involution of the third class. 13+. — presents a paper of Prof. M. J. van Uven: “Combination of observations with and without conditions and determination of the weights of the unknown quantities, derived from mechanical principles’. 157. — Characteristic numbers for nets of algebraic curves. 935. — Characteristic numbers for a triple infinite system of algebraic plane curves. 1055. — Systems of circles determined hy a pencil of conics, 1107. — presents a paper of Dr. W. van per Wouve: “On Noraer’s theorem”. 1245. — A bilinear congruence of rational twisted quinties. 1250. — Some particular bilinear congruences of twisted cubics. 1256. WAALS (J. D. VAN DER) presents a paper of Prof. A. Smits and Dr. A. H. W, ATEN: “The application of the theory of allotropy to electromotive equilibria” I]. 37. ILI. 680, — presents a paper of Dr. H. Hunsuor: “On the thermodynamic potential as a kinetic quantity”, Ist. part. 85. — presents a paper of Prof. A. Smits and S. Posraa: ‘The system ammonia-water.”” 182, XALV CONTENTS. WAALS (J. D. VAN DER) presents a paper of Prof. Pu. Kounstamm and kK. W. Waustra: “Measurements of isotherms of hydrogen at 20° C. and 1525 C.” 203. — presents a paper of Mr. K. W. Waustra: “The hydrogen isotherms of 20° C. and of 15°.5 C. between 1 and 2200 atm.”, 217. — presents a paper of Prof. A. Smits: “The metastable continuation of the mixed erystal series of pseudo-components in connection with the phenomenon allotropy”. II. 672. — presents a paper of Prof. A. Sirs and S. C. Bokuorst: “The vapour pressure lines of the system phosphorus”. II. 678. IIT. 962. — presents a paper of Dr. F. E. ©. Scuerrer: ‘On gas equilibria and a test of Prof. vaN per Waats Jr.’s formula”. I. 695. IL. 1011. —— presents a paper of Dr. FB. E. C. Scnrrrer: “On unmixing in a binary system for which the three-phase pressure is greater than the sum of the vapour tensions of the components”. 834. — presents a paper of Prof. A. Smrvs and 8. ©. Boknorstr: “Further particulars concerning the system phosphorus”. 973. WAALS JR's theorema (On gas equilibria and a test of Prof.). L695. If, 1011. WALs@tRA (xk. w.). The hydrogen isotherms of 20° C. and of 15°5 C. between 1 and 2200 atm. 217. — and Pu. Kounstamm. Measurements of isotherms of hydrogen at 20° C, and 159.5 C, 2038. water (The system ammonia—), 182. — (The system: copper sulphate, copper chlorid, potassium sulphate, potassium chlorid and) at 30°, 533. WATERLEVEL (On the relation between departures from the normal in the strength of the trade-winds in the Atlantic ocean and those in the) and temperature in the Northern European seas. 1147. WEBER (MAX) presents a paper of Dr. K. Kuiper Jr.: “The physiology of the air-bladder of fishes’. 1088. WEERMAN (k. A.). Action of sodium hypochlorite on amides of ¢-oxyacids. 1163, weicuts (Combination of observations with and without conditions and determination of the) of the unknown quantities, derived from mechanical principles. 157. WENsINK (Miss pv. w.) and P. van RomBurcu. On the interaction of ammonia and methylamine on 2.3.4,-trinitrodimethylaniline. 1034. WENT (F. A. FP. C.) presents a paper of Miss Lucin C. Dover: “Energy transfor- mations during the germination of wheat-grains”. 62. — presents a paper of Dr, C. E. B. Bremexame: “On the mutual influence of phototropic and geotropic reactions in plants”. 1278. WERTHEIM SALOMONSON (I. K. A.) v. Sanomonson (I. K. A. WERTHEIM). WHBEAT-GRAINS (Energy transformations during the germination of). 62. WICHMANN (a.). On some rocks of the island of Taliabu (Sula islands). 226. — On the tin of the island of Flores. 474. WILDEBOER (N.), J. G. Drepertnx and H. G. vAN DE SanpE BaknuyzEN. Com- parison of the measuring bar used in the base measurement at Stroe with the Dutch Metre No. 27. 300. CONTENTS. XXV WINKLER (c.) presents a paper of Prof. G. van RignBerk : “On the nerve-distri- bution of the trunkdermatoma.” 632. — A ease of occlusion of the arteria cerebelli posterior inferior. 914. WoLFF (L, K.). On the formation of antibodies after injection of sensitized antigens. II. 318. — and E, H. Bicnner. On the behaviour of gels towards liquids and the vapours thereof. II. 92. WOLFF (s.) and Ernst Conen. The allotropy of potassium. I. 1115. WOLTJER JR. (J.). On Srevicer’s hypothesis about the anomalies in the motion of the inner planets. 23. WOUDE (Ww. VAN DER). On Noruer’s theorem. 1245. ZEEMAN (P.). On FRESNEL’s coefficient for light of different colours, 445. ZEEMAN-effect (The universality of the) with respect to the Srark-ellect in canal- rays. 873. ZERNIKE (f.) and L, S. Ornstein. Accidental deviations of density and opalescence at the critical point of a single substance. 793. zinc (The allotropy of). Il, 59. III. 641. Zoology. K. Kuiper Jr.; “The physiology of the air-bladder of fishes.” 1088. de | ie 9 KONINKLIKE AKADEMIE VAN WETENSCHAPPEN TE AMSTERDAM. PROCEEDINGS OF THE MEETING of Saturday May 30, 1914. Von XVII. IS President: Prof. H. A. Lorentz. Secretary: Prof. P. Zueman. (Translated from: Verslag van de gewone vergadering der Wis- en Natuurkundige Afdeeling van Zaterdag 30 Mei 1914, DI. XXII1). OOyaNy PROD INES P. Rérmie and C. U. Armys Karrrrs: “Further contributions to our knowledge of the brain of Myxine glutinosa’”. (Communieaied by Prof. L. Bork), p. 2. (With 2 pl.). H. Kamervincu Onnes: “Further experiments with liquid helium, J. The imitation of an AMPERE molecular current or of a permanent magnet by means of a supra-conductor”, p. 12. W. H. Kersom: “The chemical constant and the application of the quantum-theory by the method of the natural vibrations to the equation of state of an ideal monatomic gas’, (Communicated by Prof. H. Kamerrinon Onnes), p. 20. J. Wortses Jr.: “On Srericer’s hypothesis about the anomalies in the motion of the inner planets’. (Communicated by Prof. W. DE Sirrer), p, 23. W. be Sirrer: “Remarks on Mr. Wortser’s paper concerning SEELIGER’s hypothesis’, p. 33. A. Smits and A. H. W. Aten: “The application of the theory of allotropy to electromotive equilibria”. If. (Communicated by Prof. J. D. van per WaAats), p. 37. Ernst Conrn and W. D. Herperman: “The allotropy of Cadmium”. IT, p. 54. Ernst Conen and W. D. Herprerman: “The allotropy of Zine”. II, p. 59. Ernst Conen und W. D. Heriperman: “The allotropy of Copper. II, p. 60. Lucir C. Dover: “Energy transformations during the germination of wheat grains”. (Com- municated by Prof. F. A. F. C. Wenn), p. 62. F. A. H. Scuremvemakers: “Equilibria in ternary systems.” XV, p. 70. H. Hursnor: “On the thermodynamic potential as a kinetic quantity”. (First part). (Commu- nicated by Prof. J. D. van DER WAALS), p. 85. L. K. Worr and E. H. Biicuner: “On the behaviour of gels towards liquids and the vapours thereof”. (Communicated by Prof. A. F. Horiieman), p. 92. Jan DE Vries: “The quadruple involution of the cotangential points of a eubie pencil”, p. 102. Jan dE Vries: “A cubic involution of the second class”, p. 105. W. H. Kersom: “On the manner in which the susceptibility of paramagnetic substances depends on the density.” (Communicated by Prof. H. Kamertincu Onnes), p. 110 Ernst Conen and W. D, Herperman: “The allotropy of Cadmium IIL’, p. 122. Proceedings Royal Acad. Amsterdam. Vol. XVII. ») Anatomy. — ‘Further contributions to our knowledge of the brain of Myaine gluitinosa.” By P. Rorsic (Berlin) and C. U. Artins Kapprrs (Amsterdam). (Communicated by Prof. L. Bork). (Communicated in the meeting of March 28, 1914). The former of us has given a description of the motor roots and nucler in’ Myxine glutinosa and in some Amphibia in Vol. XVI of these Proceedings (p. 296). For Myxine the topography of the V—VIL nucleus and the spino- occipital column has been discussed, and mention was made of the absence of the eyemuscle-nuclei and the motor glossopharyngeus. For the discussion of the vagus roots reference was made to further researches not yet completed at that time, which we should accomplish in conjunction. It is known that the vagus of Myxine glutinosa has caused many difficulties, and before givine our own results we wish to review the opinions of former authors, because such a review clearly shows the points which give rise to different interpretations. It is obvious that in doing so we shall be obliged to deal again with other roots of the cranial nerves in Myxine. The first deseription of the central nervous system of Myxine elutinosa was given by Anpurs Rerzivs ?), who mentions three nerves of the Oblongata, the Vagus, a nerve of the labyrinth (Table VI le. Fig. 7), a cutaneous branch of this labyrinth nerve (Table VI, Fig. 8) and several branches of the V (p. 397, 400 and 401.) After A. Rerzivs, Jonannns MUier’*) gave an elaborate description of the origin and periferal course of the cranial nerves in Petromyzon, Bdellostoma and Myxine. For Myxine he gave a description of the Trigeminus, Facialis, Acusticus and Vagus (comp. Fig. 4, 4 and 6 on Table III |. ¢. 1888). It is interesting that he mentions a cutaneous branch of the VII (p. 195 Le. 1838), which still wants affirmation, specially since Miss Worrnineton *) could not find any but visceral sensory and Deere Rerztus, Beitrag zur Anatomie des Ader- und Nervensystems der Myxine Glutinosa (Lin.) (Aus d. Abhandlg. d. KGénigl. Sehwedischen Akademie der Wissen schaften Jahrgang 1822 H. 2) Meikel’s Archiv fiir Anatomie u. Physiologie 1826 S. 386—404. 2) J. Miitter, Ueb. d. eigentiimlichen Bau des Gehdérorgans bei den Cyclostomen, mit Bemerkungen itiber die ungleiche Ausbildung der Sinnesorgane bei den Myxinoiden Abhandlg. d. Kgl. Akad. d. Wissensch. Berlin 1837 (25. LV. 1836), und: Vergleichende Neurologie d. Myxinoiden, ibidem, 1888 (15. IL. 1838). 3) J. WortHiInaTon: Descriplve Anatomy of tbe Brain and cranial nerves of Buellostoma dombeyi (p. 169) Quart. Journ. Miser. Science Vol. 49, 1906. 3 motor fibres in the facial nerve of the American Myxinoid Bdello- stoma dombeyi. After Jou. Minter, Gusrar Rerzius') gave very valuable contri- butions which appeared abundantly illustrated in 1881 and 1893. It is just the excellent descriptions given by G. Rerzits that show how difficult the interpretation of this brain is, for G. Rerzius himself emphasizes at the end of his elaborate description of 1893 (p. 63) that — though he had been gathering the data concerning the brain of this animal for several years, he had not yet succeeded in obtaining a complete idea of its exact relations. G. Rerzius mentions, as did P. Rérmie in his contribution (1. ¢.), the absence of the trochlearis, oculomotorius and abducens. The most frontal nerve roots, according to him, are two trigeminal branches (p. 60 and Table 24, Fig. 1—3) each provided with a spindleshaped ganglion. Following on this he finds a small nerve without ganglion (a motor nerve consequently) which he considers to be — like Jon. Miitiwr — the facial nerve. Close to this nerve he finds a third ganglionated root, which he supposes to be a third trigeminus root and behind these the two roots of the oetavus occur whieh he had already described before (1881): the Ramus anterior and ramus posterior acustici. Mueh more backward the vagus roots appear without ganglion. Dorsally from these le, however, finds a small sensory root with an oval ganglion, which he considers to be a sensory vagus root (p. 99). After G. Rerzius Sanpers*) took up this subject. Since this work was not available for us, we can only quote from it what Hon has cited (Il. ¢. infra). According to this author Sanpprs found the V, VI, VIII and X nerves, but differs in so far from G. Rerztus that he considers some roots entering the brain behind the vagus of Rurzius still as vagus roots, whilst the latter mentions them as spino-occipital nerves. It is Sanprrs’ merit to have first given a detailed«deseription of the oblongata-nuclei, which he divides into two cellgroups of which one has an entirely central position near the dorsal raphe: “ganglia centralia’, and another near the perifery of the bulb: “ganglia latero- 1) G. Rerzius. Das Gehérorgan d. Wirheltiere Bd. I, Stockholm, 1881; Ueb. d. Hypophyse von Myxine Biolog. Untersuchg. Bd. Vi; Das Riickenmark yon Myxine Biolog. Untersuchg. N. F. Bd. W. 1891; Das Gehirn und das Auge von Myxine Biolog. Untersuchg. N. F. Bd. V 1893 2) Sanpers. Researches on the nervous system of Myxine glutinosa, 1894, Williams and Norgate, London. 4 ventralia”’, the latter of which extending ‘varying in size) from the entrance of the V to the X. In Geeenpaur’s Festschrift Fiirprincer') describes the spinal, oeci- pito-spinal and vagal roots (p. 616 et seq.) and gives a drawing of the roots of the American Myxinoid : Bdellostoma (Text figure 1). Acecord- ing to him the vagus leaves the brain with 1—4 rootlets (he draws 2) and possesses a prevailing motor character (p. 619). Fiirprincrr states that this also holds good for Myxine. He con- siders the glossopharyngeus — not mentioned by preceding authors — 1s represented by elements of the nervus pharyngeus X, although he states that a branchial sack innervated by the LX is failing im Myxinoids. In other words he grants the absence of an independent IX, but supposes that elements of it are included in the pharyngeus branch of the X. *) FirBRINGuR emphasizes that the spino-occipital roots are shifted in a frontal direction in Myxine. This holds good as well for his first sensory spino-occipital root as for his second spino-oceipital root. The first in his opinion enters the brain on the level of the ramus acusticus posterior, the second near the level of the vagus roots. FURBRINGER points cut that, in contrast to Myxine, in: Petromyzon the spino-oceipital roots are located on a fairly large distance behind the vagus roots. This difference between Myxine and Petromyzon, according to him, can be explained in two ways, either the first spino-occipital root of Myxine is lacking in Petromyzon, or the spino-oceipital roots are shifted forward in Myxine. Firprincer believes that the ') FiirBprineer, Ueber die spino-occipitalen Nerven der Selachier und Holoce- phalen und ihre vergleichende Morphologie. lestschrift fiir Gge@znBAuR Teil IIL 1897 p. 249-766. We do not deal here with the paper of Ransom and p’Arcy THompson (quoted by Fiirsrincer) because it contains very little on our subject. Compare: On the spinal and visceral nerves ef Cyclostomata. Zodlogischer Anzeiger No. IX, 1886 p. 421. *) We may add here that Miss WortHinGTon, to whom we owe such an excellent series of papers on the American Myxinoid Bdellostoma, considers this branch as a real IX (I. ¢ p. 172), “lying so close to the X that it is difficult to distinguish one from the other’. She also mentions that they have a common foramen and that (p. 173) “the glossopharyngeus runs in the same sheath with the vagus as far as the second branchial arch”. Consequently — as far as these points are concerning — the presence of a real glossopharyngeus is not very conspicuous either in Bdellostoma nor in Myxine — Since its periferal territory also is fairly well alrophied — (see the following pages) these arguments for the presence of a IX seem to be open to criticism, though in a very rudimentary way it may be present. o first is true, and that consequently the first sensory spino-occipital root of Myxine is lacking in the Lamprey. We may remark here that, in our opinion, FirBriNcer is mistaken when he considers the first root here mentioned as being a spino- occipital one. We are more inclined to believe that in Myxine the same relation is found asin Bdellostoma, for which Miss Worrninaron has pointed out that Firericer’s first spino-oce. root is the Acusticus b, i.e. a lateralis root. *) The topographical difference in the spino-occipital roots between Myxine and Petromyzon consequently is not so considerable as Fiir- BRINGER thought, since the spino-oecipital roots of Myxine do not reach as far frontally as the acusticus. Still there is a conspicuous frontai displacement of spino-occipital elements in Myxine, as appears from a comparison of Fig. 2 with Fig. 1. In our opinion the transitory region between oblongata and cervical cord is shifted in a frontal direction. The vago-spino-occipital region of the oblongata has approached the trigemino-facial region, the otic and postotie part of the bulb being reduced. This frontal shifting of the vago-spino-occipital region of the brain is acecompaniéd by a frontal displacement of the spino- occipital nucleus and roots, but the vagusroots (see fig. 2) are not so much displaced as their nucleus and remain behind, perhaps on account of their lying on the ear capsula. In consequence the spino-occipital and vagus roots have consider- ably approached and the vagusroots appear crowded together on the level of the caudal extremity of the nucleus, instead of being divided fairly regularly over the level of the whole nucleus as is the ease in Petromyzon. That the whole vago-spino-occipital region of the bulb has shifted frontally and not only the spino-occipital region, appears from the fact that the spino-oceipital column does not overlap the vagal column in Myxine more than in Petromyzon. ‘ As already said, this process is accompanied, if not partly caused, by a reduction of the acoustic region of the brain. That the acoustico- lateral system in Myxinoids is not very much developed results also from the researches of Ayrrs and WorTHINGTON *) (see further below). We shall now proceed to the description of the nuclear topography of the bulb and discuss at the same time the paper published by 1) Compare: Quarterly Journal of Microscopical Science Vo!. 49, 1906 p. 171 and 175. 2) Ayers and Worruinaron: The finer anatomy of the brain of Bdellostoma dombeyi I. The acustico-lateral system. American Journal of Anatomy vol. VIII, 1908. SS -Tl MM-lV &:8-V © VW &e-V BE-K ZZ -X- Bh Spor. P. ROTHIG (Berlin) and C. U. ARIENS KAPPERS (Amsterdam). Further contributions to our knowledge of the brain of Myxine glutinosa. frontal Nucl. X mot. Nucl. VII—V mot. Nucl. V mot. Fig 3. Myxine glutinosa Sagittal Section. Magn. 30 : 1. Nucl. V mof. Fig. 4. Myxine glutinosa Magn. 20 : 1. Frontal Section through the frontal part of the motor V nucleus. Nucl, V mot. Fig. 5. Myxine glutinosa. Magn. 20 : 1. Frontal Section through the middle part of the mot. V-nucl. (caudally from Fig. 4). Proceedings Royal Acad. Amsterdam. Vol. XVIL. P. ROTHIG (Berlin) and C. U. ARIENS KAPPERS (Amsterdam). Further contributions to our knowledge of the brain of Myxine glutinosa. Nucl. V-VIl mot. Nucl. V-VIl mot. Fig. 6. Myxine glutinosa. Magn. 20 : 1. Frontal Section through the mot. V—VIl-nucleus. Dorsal Spino-occipital rootfibres Nucl, VII mot. Nucl, X mot, Fig. 7. Fig. 8. Myxine glutinosa. Magn. 20: 1. Myxine glutinosa. Magn. 20: 1 Frontal Section through the mot. Vil nucl., Frontal Section through the mot. X nucl. caudally from Fig. 6. Dorsal.Sp no-occipital rootfibres Nucl, X mot. ee é 2 = Fig 9: Fig. 10. Frontal Section through the Nucl. X mot. Myxine glutinosa. Magn 20:1. Magen. 20:1 (caudally from Fig. 8). Frontal Section through the spino occip. column. Proceedings Royal Acad. Amsterdam. Vol. X VII 7 Hotm') on this subject in 1902, which is certainly the best de- scription as yet given of the motor nuclei in Myxine glutinosa. Horm points out that tie motor column ef the spinal cord (comp. our Fig. 10) can be traced frontally in the bulb. Laterally from it lies the posterior extremity of what Sanpers has called the lateral or latero-ventral cell group (comp. our. Fig. 9). Hotm divides this latero-central column of the bulb, which we shall call the viscero-motor column, into two divisions, a frontal and a caudal one. He again divides the frontal division into two, the caudal one into three subdivisions. We can only follow him in so far as we also divide the viscero- motor column into two divisions (see Fig. 2 and Fig. 3) of which however only the frontal one is again divided into two subdivisions. The caudal viscero-motor division, in our Opinion, is continuous (see Fig. 2 and 3 nucl. X mot.) and does not exhibit subdivisions. Apart from this column Ho_m mentions a group of cells located next the ventricle in the rostral part of the oblongata from which he thinks that a part of the motor trigeminus originates. Another part of the motor trigeminus should originate from a nucleus in the lateral part of the oblongata on the level of the acusticus ganglion. The nuclei of the trigeminus thus would be located at a fairly great distance from each other, one lying near the ventricle, the other near the perifery of the bulb. (Comp. lis Fig. 20 on Plate 21: NeIm.N V and Nell m.N Y). We do no agree with this description, nor with his statements concerning the motor facialis. Also the facialis — according to HoLm’s opinion — should have two nuclei (i.e. p. 389) and from his description it clearly appears that he considers our frontal motor V nucleus as a VII nucleus, for the axones of this nucleus — as shown in his drawings — (Fig. 21 Plate 21) constitute the most frontal root of the bulb. No doubt the two VII roots deseribed by Hom (VIIa and VI1I16) are V roots, since only this nerve leaves the bulb with two motor roots *), whereas the motor VII root is single and very small. Our opinion is confirmed by his description of the corresponding nuclei. The first Vil nucleus described by this author lies in the frontal part of the bulb near the perifery, and consists of large cells. His 1) J. EF. Hotm. The finer Anatomy of the nervous system of Myxine glutinosa. Morpholog. Jahrbuch Bnd. 23, 1902. *) This separation of the motor V in two roots is only visible near the en- trance. Soon after it they unite. 8 second V nucleus according to his description is located in the caudal elongation of the first, is not completely separated from it and consists of smaller cells, which description is perfectly in accordance with the two V nuclei (see Fig. 8) of which the second, con- sisting of smaller cells and not completely separated from the frontal nucleus, gives also rise to the VII root. (Comp. also Fig. 4—7). Like Hotm we were first inclined to consider the second (caudal) nucleus only as a VII nucleus, but a more scrutinous examination of the V fibres showed that in this nucleus also the second motor V root found its origin. Summarizing we state that the motor V nuclei mentioned by Horm are no motor V_ nuclei, and that of the two VII nuclei mentioned by this author the frontal one is a pure V_ nucleus, whilst the caudal more parvocellular one contains root cells of the V and VII. This union of motor V cells and VII cells is in perfect harmony with the condition found in Petromyzon (comp. Fig 1), where the motor VII cells also form the caudal continuation of the V nucleus and are a little smaller. Since we only wish to deal with the motor nuclei in this de- scription, we shall pass the acustico-lateral system, which for the American Myxinoid Bdellostoma dombeyi has been so minutely described by Ayers and Worrnineron *) and proceed to the motor X nucleus of Myxine. It is obvious that, without an examination of the periferal nervous system and its muscles, the question of the presence or absence of a motor glossopharyngeus cannot be settled. We can only state that our researches show a reduction of the number of root fibers of the motor X group, which in Myxine only consists of 3 of 4 rootlets, whereas in Petromyzon it contains together with the glossopharyngeus at least 5 rootlets. This combined with the fact that the posterior visceromotor column has suffered a reduction in its frontal part is in harmony with the opinion defended by Jounsron *) that the glossopharyngeus and perhaps even the first motor X root sensu strictiori are either very much reduced or absent. A comparison of Fig. 1a and 2a shows that this reduction is only probable for the frontal pole of the column, 1) Ayprs and WortHINGToN: They finer anatomy of the brain of Bdellostoma dombeyi. I. The acustico-lateral system. American Journal of Anatomy Vol. VIII, 1908. *) Jounsron: Note on the presence or absence of the glossopharyngeal nerve in Myxinoids. Anatomical Record Vol. Il, 1908, 2a. “u~ DC SOC Showing the reduction in the frontal part of the vagal column. since the overlapping of the caudal part of the vagal column and spino-occipital column, as well as the topography of the posterior extremity of the vagal column to the spino-occipital roots, are the same in both Petromyzon and Myxine. The reduction of the roots and of the frontal part of the vagal column in Myxine is also in harmony with Srockarpb’s observation that in Myxinoids, at least in its American form Bdellostoma, the branchial sacks behind the hyomandibular arch are atrophied. *) The vagal column begins fairly near the posterior extremity of the mixed V—VII nucleus, lying in a somewhat more dorsal position (Comp. Fig. 3,7 and 8). A few seattered cells lie between them, thus constituting a sort of broken link. The size of the vaguscells is considerably smaller than that of the frontal V nucleus, more like the cells of the mixed V—VII nucleus, specially the smaller caudal cells of the latter. In its frontal part.the vagus nucleus is rather small and the cells do not attain their largest size here. The nucleus as well as the cells attain their maximum development in the middle part. We have not been able however, to state a division of the nucleus in three parts as Hoxm did. 1) SrockarRD: The development of the Mouth and Gills in Bdellostoma Stouti. American Journal of Anatomy Vol. V 1906, specially p. 511 and fig. 35—3s6. Compare also for further knowledge of these animals : Ayers. Bdellostoma dombeyi. Woodshole lectures for 1893. WortTHINGTON. Centribution to our knowledge of the Myxinoids. American Naturalist Vol. 39, 1905. 10 On the other hand we agree with Hotm that the small ventro- lateral root that leaves the bulb in the posterior part of the vagal region and is considered by SanpErs to be a vagalroot, is certainly a spino-oceipital one (Cf. Hotm p. 395), as much on account of its position as on account of its central connection. — That the spino-occipital column extends for a short distance in the vagal region is a general feature in vertebrates and has been shown before to occur also in Myxine by Epinerr *) (I. ¢. p. 28). We also agree with Hoim that the dorsal sensory root entering on . this level is a sensory spino-occipital or spinal root and not a sensory Vagusroot, as results from the facts 1. that the size of its fibres corresponds with those of the sensory spinal rootfibres, 2. that the line of entrance and the ascending character of the fibres during their intramedullary course are the same as in the spinal sensory roots and 3. because they are joined by the latter during this course. Finally we wish to call attention to the fact that not only the topography of the uuelei, but also the general morphology of this brain shows the compression which the brain has suffered. Similar to the other ventricles of the brain the 4" ventricle is reduced to a minimum. This is complicated by the peculiarity that the caudal end of the midbrain (a cerebellum does not occur in this animal) protrudes a considerable distance between the dorsolateral walls of the oblongata and is so closely adjacent to it that ouly the pial membrane can follow it. Behind the caudal extremity of the midbrain the dorsolateral walls of the oblongata unite. One cannot speak here of a real calamus scriptorius caused by a widening of the ventricie itself. The lateral deviation of the walls takes place only under the influence of the midbrain, but the 4t ventricle itself remains a small split underneath it. The dotted arrow in figure 2 indicates the place of this pseudo-calamus. Since in this animal, with atrophic eyes, there is no question of an enlargement of the midbrain being the cause of this telescoping, the only reason of it can be found in the compression of the whole brain in its longitudinal axis, which is also exhibited by the approach of the vago-occipital part of the oblongata to the trigemino-facial part. This longitudinal compression probably finds its chief reason in the pressure exercised on the frontal part of the brain by the olfactory pit and dorsal lip, the influence of which on the form 1) Epryaur: Das Gehirn von Myxine glutinosa. Abhandlungen der Preussischen Akademie der Wiss. 1906. 11 ‘ of the brain in Cyclostomes is already mentioned by Scorr ‘) in Petromyzon. As stated above, the telescoping is the more obvious in the oblongata on account of the reduction in the acustico-lateral system of the bulb. Everything indeed shows that in Myxine we have to do with considerable secondary modifications. Also the topography of the motor nuclei is by no means a primi- tive one. The primitive location of the V, VII, and X nuclei in Cyclostomes is near the ventricular ependyma where the matrix of the nerve cells is, and where they are still found in Petromyzon. In Myxine, however, the V—VII nucleus has a ventro-lateral periferal position and the X nucleus a lateral periferal position, a condition that can only be caused by secondary influences originating in the functional reflectory relations of this animal. The influence which has caused this secondary position is certainly the considerable development of the descending sensory V, which has a dominating influence on the structures of the oblongata, an influence which is the more prevailing since the other sensory and reflectory paths are either atrophied or poorly developed in this animal. We know that in animals with a well-developed dorsal viscero-sensory nucleus the motor vagal column generally has a dorsal position, adjacent to its sensory grey (Selachians), which is still the case even in Petromyzon. On account of these facts we cannot agree with Hotm in his statement that Myxine has a more primitive character than Petro- myzon. Summarizing our results we conclude : In Myxine the eye-muscle nuclei are absent. The motor V nucleus is incompletely divided into two parts corce- sponding to the central division of the motor root into two parts. In the continuation of the caudal V nucleus also the motor VII cells are found, as is also the case in Petromyzon. These nuclei have a ventrolateral position very near the concomitating grey substance of the sensory root. A central V nucleus (Hotm) has not been found. The posterior viscero-motor column, and also the spino-occipital motor column has shifted considerably frontally. By the adjacency of the earecapsule this shifting could only be partly followed, by the motor X roots, which are crowded together on the earcapsula. ') Scorr. The embryology of Petromyzon. Journal of Morphology Vol. 1, 1887 12 The spino-oceipital roots have, however, followed the shifting of their nucleus and have come very near the vagus roots. The posterior viscero-motor column is considerably shortened at its frontal extremity, which most probably results from the absence or extreme reduction of the motor IX, and perhaps even of the frontal motor X root (JOHNSTON) in connection with the absence or reduction of the two posthyomandibular branchial sacks (Stock aRD). Physics. — “Further experiments with liquid helium. J. The imitation of an Ampbee molecular current or of a permanent magnet by means of a supra-conductor.” Communication N°. 1046 from the Physical Laboratory at Leiden. By Prof. H. KamErtinen OnnEs. (Communicated in the meeting of April 24, 1914). § 1. lntroduction. If a current is generated in a closed supracon- ductor, from which no other work is required than what is necessary to overcome the possible remaining micro-residual resistance of the conductor, it follows, from the small value that the micro-residual resistance can have at the most, that the current will continue for a considerable time after the electromotive force that set it in motion has ceased to work. The time of relaxation + in which the current decreases to e-!t of its value is given by the ratio of the self-induction Z and the resistance 7 of the circuit. When s r approaches zero, this period may rise to very high values. Whereas the time of relaxation is extremely small in ordinary cases (for the coil with which we are about to deal for instance, of the order of a hundredthousandth of a second) when the resistance in the supra- conducting condition becomes say 1,000,000 or even 1,000,000,000 times smaller it may increase so much, that the disappearance of the current can be observed ; it may even take place extremely slowly. From the moment that [ had found in mercury a supra-conductor at the lower temperatures which can be obtained with liquid helium, I was desirous to demonstrate the persistence of a current in a con- ductor of this kind, and amongst other things to take advantage of it in the further investigation of the microresidual resistance of the supra-conductor '). But it was only after the previous study of various 1) For the sake of brevily we use the word resistance here in the sense of quotient of potential difference and current strength. In supra-conductors (see Comm. No. 133) we can at present only speak of current and potential difference ; whether the relation between these two can be expressed by means of the concep- tion of specific resistance, has still to be investigated. (Comp. note 1 § 3), 13 problems, which were also of value for the knowledge of the con- ditions which had to be considered, that I arrived at the simple experiment which I am now able to deseribe, and whieh confirms what I have adduced in a convincing way. For this experiment a conductor was available whose constants, in so far as they were needed in designing the experiment, were known: I refer to the coil of lead wire Phx which has several times been mentioned in previous papers. A thousand turns of lead wire of ‘/,, sq. mm. in section are wound on a small brass tube of 8 mm. in diameter in a layer 1.1 em. thick and 1.1 em. lone. At the ordinary temperature the coil has a resistance of 734 2 and as the inductance is I milli-henries, the relaxation time may be put at about 1: 70000 of a second. The micro-residual resistance at 1°.8 Kk. had been found to be more than 2 > 10°° times smaller than the resistance at the ordinary temperature ; the relaxation time therefore must be at least of the order of a day. The limit to which the current may be raised before ordinary resistance is suddenly generated, had also been determined ; at 1°.8 K. this limit was 0.8 amp.; it is clear that a lower current than that is sufficient to make the coil into a powerful little magnet. Finally the threshold value of the magnetic field, below which no resistance is produced in the coil was known : at 1°.8 K. it had been found to be about 1000 gauss. It was ascer- tained (ef. § 3), that if was unnecessary to use a field of that strength to be able to make the experiment by means of generating a current by induction in the conductor. The conductor after having been tested as to its superconductivity had to be closed in itself in a supereon- duetive way. This was effected by fusing the ends of the lead wire together: in previous experiments it had been found, that this treat- ment did not lead to the production of ordinary resistance. In view of all the data I could be assured, that all the conditions necessary for the suecess of the experiment were fulfilled. § 2. Arrangement of the experiment. The coil was fitted up in the same eryostat which had served for the previous experiments with the plane of the windings vertieal in such a manner, that it could be raised and lowered, as well as turned round a vertical axis. Fig. 1 shows the arrangement diagrammatically. As the coil was closed the current in it was generated by induction. A large Wuiss-electromagnet, at hand for the experiments of Comm. N". 140d could be moved on casters towards the cryostat to a position in which the cryostat with the coil was in the interferrum, In order to obtain an unambiguous result it is advisable to be 14 able to test the magnetic condition of the coil while no other magneti¢e objects are in the neighbourhood; it is also necessary to prevent the induction currents which are generated when the field is produced and when it disappears from partly or completely neutralising each other (cf. § 4). . It can therefore be easily seen that the follow- ope ing procedure is advisable: the field is put on, while the coil is in the cryostat at the centre of - the interferrum, everything being prepared for || siphoning the liquid helium into the eryostat. | The current generated at the production of the field is then immediately dissipated by the ordinary | | resistance of the coi before the helium is poured over. Care is taken to keep the field below the threshold-value of the production of ordinary resistance, which holds for the temperature at which the experiment is going to be made. The coil is then cooled by letting in liquid helinm, the field remaining unchanged. In this manner a supra-conducting coil is obtained, closed in itself - without a current placed in the magnetic field. If the field is now put off and the apparatus which have produced it are removed, a current a will remain in the coil which is smaller than or in the limit equal to the threshold-value corre- sponding to the temperature of the coil. The presence of this current can be established by its magnetic action outside the cryostat. In order to obtain a strong current it is advisable te cool the coil as far down as possible, as thereby the threshold-value of the field to be used for the induction and the threshold-value of the current are both made as high as possible. Fer that reason the first experiment was made at a temperature of 1°.8 kK, the towest temperature which can be reached comparatively easily and maintained for a long time. § 3. Culeulation of the experiment. Assuming that the field diminishes proportionally to the time ¢ from //, to O and ealling J/ the magnetic potential of the coil in the field //, “will be constant during the period of the disappearance of the field and the equation’) !) Here is supposed that 7 is independent of 7 below the threshold value ip of 7. 15 with 70 at the beginning gives 1 dM — 3 EAM bites ). r dt ‘i and for small values. of and ?¢, as lone as J/ has not reached zero, With sufficient: approximation | 1 aM = (Fe) Ts it so that, if M/ reaches O while ¢ is still small, will be the final value of the current. In our experiment the constants were //, = 400, J/,= 1,26 10°, L=10', so that 2 could rise to 0,126 C.G.S. or 1.261) Amps. The current can therefore reach the threshold-value 0.5 Amp. even with a field of rather more than half the strength assumed in the caleulation (cf. one of the experiments in § 4). From the moment at whieh this value is reached ordinary resistance appears and i will be no longer small; the further increase of 7 above the threshold value zp follows a different law from below 7p. For an aecurate calculation of the process above 7p, it would be neeessary to take into account the complicated law of imerease of the resistance with the current beyond 7p. For our purpose it is sufficiently accurate to assume, that when 7p is exceeded by a small amount, the resistance becomes suddenly 7 of the order of magnitude above the vanishing point. dM .e In that case, a remaining the same as before, the current will aL aw \duw be able to rise by a small amount ¢—ip = — a whieh will soon yr dM be reached, will then become constant and, on J/ and ar becoming td zero, disappear again in a short time. In view of the value of J/ and r’ we may, if J/ does not change very rapidly, disregard <—7p, unless we intend an explanation of all the details of the experiment, We therefore come to the conclusion, that, J/, being sufficiently ') The more accurate data given here differ somewhat from those in the Duteh text. 16 large, the current (Fig. 2) on M diminishing to O will reach the threshold-value, belonging to the temperature of the experiment, and mp m by Fig 2. Fig. 3. after the induction being completed will continue, while only after a long time /# according to the relation in accordance with the large value of the time of relaxation — T an appreciable diminution of 7 will be observed. The ease, that the initial value of J/ is above the threshold-value of the production of resistance Mp, is represented in Fig. 3, which after the foregoing needs no special elucidation. The result is ap- parently again dependent on the threshold-value of the current (see also one of the experiments in § 4). As appears from the values given above an initial field much smaller than J/, was sufficient in our experiment. According to the above calculation it was to be expected, that the examination of the magnetic action of the coil could be per- formed with a simple compass-needle broughi near the eryostat. § 4. Details of the observations. The result proved the correctness of the discussion contained in the previous sections. The field was taken at 400 gauss. In 10 seconds it was reduced to 200 gauss and immediately afterwards the electromagnet was rolled away in 5 seconds. The compass-needle which was then placed beside the cryostat to the East of it on a level with the coil and ata distance 17 from it of 8 ems pointed almost at right angles') to the meridian. When the action on the magnet was compensated by means of a second coil placed on the other side (West) of it of about the same dimensions as the experimental coil and of 800 turns, it was found that the coil was carrying a current of about 0.5 to 0.6 amp. *). This was further confirmed by turning the coil and by moving the compass-needle to various positions about the cryostat *). During an hour the current was observed not to decrease perceptibly (as far as could be judged by the deviation of the needle with an accuracy of 10°/,). During the last half hour the coil was no longer at 1°.8 Kk. but at 4°.25 K. the temperature of helium boiling under normal atmospheric pressure. Undoubtedly even at this temperature the observation might bave been continued much longer without much diminution of the current. A coil cooled in liquid helium and provided with current at Leiden, might, if kept immersed in liquid helium, be conveyed to a considerable distance and there be used to demon- strate the permanent magnetic action of a supra-conductor carrying a current. | should have liked to show the phenomenon in this meeting (Kon. Acad. Amsterdam), in the same way as I brought liquid hydrogen here in 1906, but the appliances at my disposal do not yet allow the transportation of liquid helium. Whereas the experiment, so far as described, shows, that a current when started in a supra-conducting wire continues to flow, the process is immediately stopped as soon as ordinary resistance is generated in the circuit. When the coil is lifted out of the helium, the current is instantaneously destroyed. The temperature of the coil is thereby very quickly raised above the vanishing point of lead (6° K) and the very long relaxation-time is replaced by a very short one. Reimmersion of the coil, if not too soon after the lifting out, does not again produce magnetic action. If the experiment is made with the windings of the coil parallel to the field, no effect *) is to be expected. This expectation was in so far confirmed as only a slight effect was observed: this effect cau 1) The field of the earth being distorted by machinery the action of the latter was compensated by magnets and there resulted a weaker field (note added in the translation.) 2) [Calculated from the moment, comp. N®. 140d § 8, end. Added in the trans- lation}. The coil has a magnelic moment of about 180 C.G.S. and behaves as if the lead possessed remanent magnetisation of some 200 C.G.S. units. 8) On repeating the experiment at 4°.25 K. nearly 0.5 amp. was obtained; a later experiment with larger initial field at 2°.3 K. gave 0.7 amp. (see further down). ') Nearer consideration points to a small effect Comp. N°. 140c (Note added in the translation). Proceedings Royal Acad. Amsterdam. Vol. X VIL. 18 be sufficiently explained by assuming that the attempt to place the windings exactly parallel to the field had not sueceeded. *) If the initial value of the field is higher than the threshold-value, Mp the result is the same. Tlus case is represented in fig. 3. In one experiment the initial field was 5000 gauss and the observed magnetic moment corresponded to a current ¢ = 0.7 amp. If the field through the supraconducting coil is first put on and subsequently put off again by bringing the excited electromagnet to its position at the cryostat and then removing it, according to the above reasoning (disregarding the exceedingly slow diminution with the time) no resultant current ought to remain, if no account had to be taken of the threshold-value of the current. Indeed for Gre Sa! gale ; : the second period the relation 7—7,e ° = a holds, if ZL is 4 7 the current obtained in the ) 3 5 . 3 first period during the gene- ration of J/,. This case will be realized, if care is taken, that the threshold-value of -ig fa -==--b == 7 ~- = the current is not exceeded. 7 It is represented in fig. 4 by the lines which give the field J/5 and the current 7, as funetions of the time. If during the increase of M = the threshold-eurrent is reached, the current will not grow appreciably on further Fig. 4. rise of J/; from the moment, that the inerease of J/ stops, the current assumes the threshold-value and stays there, until J/ begins to decrease: it then begins to fall and becomes zero, before the field has disappeared; on the further diminution of the field, the current assumes the opposite sign and the resultant current will be that whieh has been formed at the moment that J/=0, if it remains below the threshold-value, or the threshold-current itself, if that is reached before J/ has disappeared. In the latter case the current will exceed the threshold-value by ') This expériment had been made some says before the main experiment, although it had not been the intention to make it with that position of the coil. So far it has not been repeated. At the moment of making this first communication it had not been repeated. [It has been repeated since; again a rest was found, (Note added in the translation. Comp, Gomm. N°. 140c)]. 19 a very small amount from the moment, that the threshold-value is reached, until J/ = 0. In fig. 4 this case is represented by the lines which give the relation between the field J/, and the current Za. An instance of the case represented by a is given by an experi- ment, in which the field brought to the eryostat was 400 gauss. A strong resultant current was observed as in the ease, when the coil was first free of current in the field of 400, was then made supra- conductive and was finally charged with current by the removal of the field. An instance approximately corresponding to case was obtained, when the same experiment as @ was carried out with a field of 190 gauss. Even in this case the compensation was not quite complete and a little more favourable. when the field was made to approach slowly, than with a rapid approach. With a rising field account has to be taken also of the compli- cation arising out of the influence of the field of the current itself on the threshold-values of the field and current. In fact this was not the only feature in the experiments which could not be fully explained yet: naturally as they were performed for the first time, the arrange- ments were still imperfect '). Taken together however they may be said to confirm the main experiment which shows that it is possible in a conductor without electromotive force or leads from outside *) to maintain a current permanently and thus approximately to imitate a permanent magnet or better a molecular current as imagined by AMPERE. The electrons once set in motion in the conductor continue their course practically undisturbed, the electrokinetic energy, represented by Maxwet1 by the mechanism of the rotating masses coupled to the current, retains its value, the rotating fly-wheels go on with their velocities unchanged, as long as no other than supraconductors come into play: the application of a small ordinary resistance however stops the mechanism instantaneously. Although the experi- ment mainly confirmed my deductions as to what had to be expected, 1) One of the first questions still to be answered is, what part a possible magnetisation of lead or brass may have played in the phenomena: so far no proof las been given, that this may be neglected. However, even now from the experiment, in which the windings were parallel to the lines of force, we may draw the conclusion, in view of the small amount of the action in that case, that the magnetisation of the material of the coil can only play a very subordinate part compared to the electromagnetism of the current, to which I have above ascribed the deviation of the compass-needle. *) It may be mentioned here, that it will be possible, by a change of tempera- ture of a small part of the conductor, to insert a resistance in the circuit which can be very delicately regulated without touching it. )%* 20 a deep impression is made by the very striking realisation which it gives of the mechanism imagined by MaxwrLi completed by the conception of electrons. It is obvious that the subject will lead to further discussions *) and plans, but in this paper 1 may be allowed to confine myself to the simple description of the experiment carried out. Physics. — “The chemical constant and the application of the quantum-theory by the method of the natural vibrations to the equation of state of an ideal monatomic gas.’ By Dr. W. 10 H. Kuvsom. Supplement N°. 364 to the Communications from the Physical Laboratory at Leiden. (Communicated by Prof. — H. IK AMERLINGH ONNws). - (Communicated in the meeting of March 28, 1914). § 1. In Suppl. N°. 33 (Dee. 1913) the expression for the entropy, S, of a gas was discussed, as it follows from the application of the quantum-theory to the molecular translatory motion by the method of the natural vibrations. Molecular rotations and intramolecular motions were not taken into account there. As was observed, the chemical constant is connected with the additive constant which occurs in the development of S for high temperatures. The object of this paper is to show that the value of the chemical constant, which in that manner is deduced from the expression for the entropy (an expression which had already been given by Trrropg), is in satisfactory agreement with values of this constant which correspond to the experimental data concerning vapour pressures of monatomic OAcaS gases. § 2. We shall confine ourselves in this paper to the consideration of monatomic gases. If for the energy distribution one of the tem- perature functions is assumed which occur in the quantum-theory, one may suppose that the molecular rotatory motion, particularly for the molecules of a monatomic gas, is in thermal equilibrium say with the translatory motion. If in particular that temperature function (given by Pranck) is assumed which implies a zero point energy, the molecular rotations in a monatomic gas also, at the temperatures at which they have been investigated, represent a con- siderable amount of energy in proportion to the molecular trans- 1) Compare also MAXWELL, Electricity and Magnetism Il, Ch. VL. 21 latory motions. The characteristic temperatures (@,, ef. Suppl. N°. 382), which according to that hypothesis govern the rotatory energy, are, however, owing to the small moment of inertia of the monatomic molecules, so high, that at the temperatures mentioned the energy of rotation of the molecules does not yet deviate appreciably from the corresponding zero point energy. The same applies to the motions within the atom. The contributions to the entropy due to these rotations of and motions within the atom may then be counted as zero. We limit ourselves to the temperature range within which this is the case’). We shall further assume that we are dealing with an cdeal monatomic gas, so that terms due to the influence of the real volume or of the mutual attraction of the molecules need not to be considered. The entropy of such a gas is then, on the basis of the hypot of Suppl. N°. 30a, determined by the expressions given in Suppl. N°. 33 § 2a. heses Q § 3. In the first place, as was already observed in Suppl. N°. 33 § 2af8, the introduction of the zero point energy makes no change in the value which is found for the chemical constant. Hence a comparison of the value calculated for this constant, e.g. with the value which was found by Sackur to agree with experimental data, cannot furnish a test between PLANck’s formula with or without zero point energy ’*). § 4. If the development of S for high temperatures: equation (14) Suppl. N°. 338, is written in the form S=C,4+ Nklnv + */, NklnT + 1 -+ terms of smaller order of magnitude () then C= Na(4 a Ina), Tera ees (2 1) According to measurements by Pier of the specific heat of argon, this tem- perature range extends for this gas to at least 2300° C. As Prof. Euysrein pointed out in a discussion, the investigation at high temperatures of the specific heat of a monatomic gas with high atomic weight, such as mercury, would be of great interest. 2) Prof. SOMMERFELD asks me to say, that he wishes the sentence: “Nebenbei sei bemerkt etc. on p. 139 of: Vortriige tiber die kinetische Theorie der Materie und der Elektrizitét,’” Leipzig und Berlin 1913, to be omitted. 22 From equation (13) of Suppl N°. 83 with equation (187) of Suppl. N’, 30a it follows that 3k? (42 7s (= saa (Gx) oh Oe re Krom these formulae. follows for the entropy constant C, = NE 4 a eee (aa) {- oo, ul On Re 9 Nh? \5Nk With the values V = 6.85.10** (according to Perrin), 4 = 1.21.10 1°, h kh (4) with WA = PR passes into = 4.86.10°"', which were accepted in Suppl. N°. 30a, equation 0, =n |= in M— 7.48) . se Sees If we take MiiiKan’s?) values V=6.06 .107, £=1.87 .10-“, h ; — 183.107 "", we find M — 7.285 (5b) | For the chemical constant Cyp, which is derived from C, by means of the relation *) é C, — 2.5R + R In Nk CAS ae Rint we find Oni = log M +- 3.60 Pee) el ee (6a) and in ¢.g.s. units Crus = 5 log M + seal SE SG (60) respectively. These values differ from those which Sackur has compared with the vapour pressures of mercury and argon and which he found fairly well confirmed, only by 0.85 and 0.28 respectively. This agreement may be called very satisfactory considering the uncertainty which yet exists with regard to several of the quantities used in that comparison on the one hand, and the approximate character of some of the hypotheses on which the deduction of the expression for the eninopy was founded on the other hand. 1) ne aa Miuurkan, Physik. ZS. 14 (1913), p. 796. 2) Gf. O. Sackur, Ann. d. Phys. (4) 40 (1913), p. 23 § 5. The relation (4) also follows from equation (19a) of the paper by SommurreLp (p. 134), quoted in note 2 p. 21, if@ occurring 10 there is put equal to ioe as has been supposed in the relations (3) and (4) given above, and if in SomMmrrELD’s expression /: is replaced by 4 A'). The latter change is connected with the fact, that in deriving the expressions given here the supposition was made that in considering the molecular translatory motion in an ideal monatomic gas we have to deal with energy elements of a magnitude } hy, as we tried to make probable in Suppl. N°, 30a § 2. The fact that in § 4 a satisfactory agreement with experimental data was obtained, may, if the validity of the other hypotheses is admitted as sufficiently approximate, be regarded as a confirmation of the above supposition concerning the magnitude of the energy elements. Astronomy. — “On Sevnicer’s hypothesis about the anomalies in the motion of the inner planets.” By J. Wourinr Jr. (Com- municated by Prof. W. pe Srrrer). (Communicated in the meeting of April 24, 1914). To explain the differences between observation and calculation in the secular perturbations of the elements of the four inner planets, SEELIGER *) worked out the hypothesis that these are caused by masses of matter, which by reflection of sunlight offer the aspect of the zodiacal light. He imagines these masses to have the form of a flat dise surrounding the sun and extending nearly in the direction of the orbital planes of the planets and reaching outside the orbit of the earth; the density of the matter within the dise has its greatest value in the proximity of the sun, though it is very small even there. For the calculation of the attraction of the mass of matter special hypotheses on its constitution are introduced; we imagine a number of very flattened ellipsoids of revolution with the sun at the centre, the inclinations of the equatorial planes to the orbital planes of the planets being small. It is evident that by the superposition of a number of such ellipsoids we get a flat dise within which the density varies 1) This confirms at the same time the fact, that the introduction of the zero point energy does not produce a change in the value of the entropy constant. 2) Das Zodiakallicht und die empirischen Glieder in der Bewegung der innern Planeten, Sitzungsberichte der Bayerischen Akademie, XXXVI 1906, 24 after a certain law from the centre outwards. SeenigEr arrived at the conelusion that two ellipsoids suffice, one of which is wholly contained within the orbit of Mercury, the other reaching outside the orbit of the earth. There appears to exist a certain liberty in choosing the values of the ellipticities and the quantities determining the position of the second ellipsoid. As quantities to be determined so as to account for the differences which are to be explained SrvLiceR introduces the densities of both ellipsoids, the inclination and the longitude of the ascending node of the equatorial plane of the first ellipsoid with reference to the ecliptic, and a quantity not con- nected with the attraction of the masses of matter, but relatiug to the deviation of the system of coordinates used in astronomy from a so called “inertial system”. Last year Prof. py Sirrek drew my attention to the necessity of festing Sepiicer’s hypothesis by calculating the influence of the masses admitted by Seeriger on the motion of the moon and the perturbation of the obliquity of the ecliptic, which Srerierr did not consider’). | performed the calculations and arrived at the conclusion that the perturbation of the ecliptic changes the sign of Nswcomp’s’) residual and makes its absolute value a little larger; further that the perturbations of the motion of the moon are insensible. I may be allowed to thank Prof. pr Srrrer for the introduction into this subject and the interest shown in its further development. — One could take the formulae required for the last mentioned purpose from Surnicur’s publication; I did not do so, but developed them anew. I give them here on account of small differences in derivation. First I shall give this derivation and the results; after that I shall do ihe same for the motion of the moon. I. Perturbations of the ecliptic. Let x,y,z be coordinates in a system the origin of which is at the centre of the ellipsoid, while the axis of rotation is the axis of z, kh? the constant of attraction, g the density of the ellipsoid, a, a and ¢ its axes, then the potential V at the point w, y,z is given by the expression : f= barge | 1.— = == ———y ‘ Vtu c+u/) (a+tuwye +u 1) See pe Sirrer, the secular variations of the elements of the four inner planets, Observatory, July 1913. 2) Astronomical Constants p. 110, No ur for a point outside the ellipsoid 4 is the positive root of the equation vty? ae P qa ee = 0; for a point inside A is zero. ata c aE Z* 77 we have: Putting V = k’nqa’c2 and #+y?'+2=r ae > 1 rT z*(a?—c’) du ae, =| ( atu “Sass, (7+ SE ana a " aa’ —c*) Ta) Gea) Perturbations caused by the jirst ellipsoid. I develop in powers of 27 =, § being a small quantity ; for that purpose we need (neglecting terms of the third order) : (= Ey An of du ks OS) hae (a* (a? +-u)? (c? +u)'l2 r—a* ?Q Pe (a?—c’)? 0c? es r(r?—a? + cy ile : I put r=a,(1+ 8) and develop the part of $2 independent of $ besides the coefficients of the different powers of § in powers of § Introducing the quantities : o.=f- = du C of du (a? +- eae @+ wu)” Vay : (a° + w)*(c? --u)"h a,*—a* ;2—a? a,?—a? a 2 A oe} a," —= a*— a’+c=p ax 7 we get >) y 5° 2 2 3° 2=C,—4/C, — str@rerarG) Oh —gats tile 1 1 1 NES _v—c* eA Anes A eas aMGachia Yate ach 6 Cee pp ost (- 9 —3y)s + 2 2 P a,"p Per z 27 1) SOLE Ns ae (Esa On ae Wace ar i= a a a ag ee 8 sla 1 JG Cu)a bh 2 Co Ie Let v be the true anomaly of the planet, y the angular distance between the ascending node of the equatorial plane of the ellipsoid on the orbital plane of the planet and the perihelion of the orbit 26 J ihe inclination of the equatorial plane to the orbital plane, then we have z= — a, (14+ §)sin(v + W) sin J S=a,?(1 4 §)? sin? (v + wy) sin? J. For the ecaleulation of the secular portion of the perturbative function we thus need the secular portions of §”, §? sin? (v + yw) and sin'(v-+ wp) for different values of p. I get (denoting the secular | portion by the letter S): mt é 4 é? Aye 3 bs 3 co Si 5 SS re Se sin? (v + w) =~ — Ge + gt ore 8 6 § sin® +m = pe(1—perrw) + Georre 2 1 1 1 S § sin? (v + yw) = rn é? (: — 5 008 2 v) =6 e* cos 2 wy @ za 3 1 A 538 , =— i — 0) S Z S §* sin? (v + w) = e* 6 are cos 2 W 3 1 S § sin? (v + pw) = e* ae: a S sin’ (v + py) = Substituting in the expression for £2 we find : ae e? 3 ee ée 1 1 ome Soars ae ae e ace ) > ( io. 6a aa P a : v—ec oe i 1 a A A 3 3 3 aa | at sin? J 15) Ci ap +e To ae Y— i C,a,7p* + v 3 5 j ‘ ae 9 ee) tyr CO8 SDI agate pn sae aa gat t+ go? 105 1 ee 3 25 35 ‘| 3 (w@’—c?)? ip = cos2y | — = 4 rie tn 39° ral Tete a sin Let 7, © and § be the inclination, the Ne: of the perihelion and the longitude of the ascending node of the orbital plane of the planet, /, and ® the inclination and the longitude of the node of the equatorial plane of the ellipsoid all with reference to a fixed fundamental plane, e.g. the ecliptic of a certain epoch ; then we have: sin J cos (W-— w + 9) = — cos J, sini -} sin J, cos i cos (§4 — P) sin J sin(w — & + QQ) = sin (84 — &) sin J. 27 E ; Ad Ee ; 0S OJ Ow Oy, From these expressions we can determine ag a Ope i the quantities required for the computation of the derivatives of 2 with regard to these elements. In view of the calculation of the perturbation of the obliquity of the ecliptic I do not use the elements 7 and {), but the elements p and gq thus defined : p=tanisin §% 7 = tani cos §% I get: ay Z ale 2, Seat) ) — = cost | cos? — sin (yw -— @) + sin? — sin (w — wo + 2Q) Op 2 2 { Oc ca ae 3? = e083 (wy — @) — sin* = cos ( — @ + 29) q Ow Shae =sin Ftan © eosieos Qt cosJeosi cos + cosy )-+sin? “ cos(tp- 0+29)) \ P mee, Pt ee Ree eerie aay eee See stn. eae tan Sie aac! cost} cos ee SO) ae 5 eintp-O+ 28) ; The differential equations for p and q are’): dp _ 1 OV dt na,2V 1—e*cos*i 99 dq l OV dt na,*V 1—e’?cos*i Op To verify these formulae I have used them for the computation of some of the perturbations of 7 and §), which are given by SEELIGER °). To compute the perturbation of the obliquity of the ecliptic I take: Sued V = — k*xqa’e (a*—c’) C,a,’ According to SeeiicEr’s data a= 0.2400, c = 0.0239, J=6°57'.0 I get C,=0.426; taking as unit of mass the mass of the sun, as unit of time the mean solar day I get log ¢ = 0.7119 — 5 and | find : ') TisspRAND, Traité de Mécanique Céleste I p. 171. , di : ete AG) ’ . : *) For Mercury I get: — =+0%.573; sini —-? — — (049; SEELIGER gives: li 1°), + 0.574 and — 0.049. For Venus I get: - = + 0".163; sin is. = + 0”.091; ¢ at SEELIGER: + 07.159 and + 0.088; the small difference is owing to the value I get for C; = 2.286, while from SsELIGER’s data follows Cy = 2.217. 28 OV 2) C. ain J au 0.5986-8 OS = — 53 3 ge 20 (—Ca O 8 108 — = od 5 y— ; ) mrga7e (a°—e 4, Sued C 3 [0.5 | 3 where the number within brackets is a logarithm. Further: 0d ; 0d ——— sn Bb; —=—cosD®; ©=—40°1'8; Op 0g therefore OJ 0d F~ = =- [0/8083 —1]; === — [0.88414] Op 0g therefore oR : OR ; ~—= 4 [0.4069—8]; — = + [0.48278]; Op 0q from which follows, taking as unit of time the century : Uy I P — + 9".065; — = — 0".054. dt dt Perturbations caused by the second eltipsord. Here the caleulation is much simpler. Introducing : ie) ioe) Ek du r= > du EB =f. du i =| (@+tu)Vcit u + =| (a? + u)? Vetu oJ (8 +a)? (2+ wu)" 0 0 0 we find: i 3 Ike 5 S2 = H,—a,*B, — 4, be — (a?—c?) a,°E, sin | Fide cos2yp As a verification I have here also computed the perturbations of the inclination and longitude of the node for some of the other planets *). To compute the perturbation of the obliquity of the ecliptic I take: sin? J V = — Faga’e (a? —c’) E,a,? oi According to Srenieer’s data a= 1.2235 and c= 0.2399; I get di slat a REO : 1) For Mereury I find: 7 = A060 sie a = — 0”.013; SEELIGER gives: € f s di d — 0.057 and — 0.016. For Venus I find: = -+ 0’.007; sinz =>) sills) d ¢ SEELIGER: + 0”.009 and + 0”.144; the results differ somewhat; however, cal- dS culating according to SEELIGER’s formulae, for Venus I find: siz 2 = -+ 0”. 154. 29 B, = 2.445, log g = 0.8582—9 ; OV oJ e = [0.3401—7] ae @ = 74°22! (1900.0), J = 7°15’; therefore OS A OS — — [0.98361]; — = — [0.48051]; Op 0g therefore V ry QoQ co] OV Ne » a = + [0.3237 —7]; ag = + [0.7706—8] ; from which, taking as unit of time the century, | get: dp A dq , — == + 0".125; — = — 0".447. ay t at Therefore the perturbation caused by both ellipsoids together is: dp " dq — = + 0".190; — = — 0".501. dt dt Let « be the obliquity of the ecliptic for the time ¢, ¢, the same for the time ¢,, ¢ and Q inclination and longitude of the node of the ecliptic for ¢ with reference to the ecliptic for ¢,, then: cos & = cos i cos &, — sini sin &, cos Sb, from which, differentiating, we get: de Cs ib We red ih) — sme dt = — smicosé, ae sin &, a (sin 2 cos S%) therefore for t= t,: de dq Gendt The perturbation of the obliquity of the ecliptic thus is = = — 0".507- cd The difference between observation and theory given by Nprwcoms is —0".22 + 0.18 (probable error); this thus becomes + 0".28. The addition to the planetary precession a is given by: da 1 dp a =— — = + 0".478. H. Perturbations of the motion of the moon. We shall now proceed to the formulae for the computation of the perturbation of the motion of the moon. As the perturbative foree in the motion of the moon we have to take the difference between the attractions of the ellipsoid on the moon and on the earth. Suppose a system of coordinates, the sun at the origin, the axis of z perpendicular to the eliptic; let a, y,2 be the coordinates 30 of the earth in this system, 7+ § y+, 2+ those of the moon, then the projections of the perturbative force on the three axes are given by the expressions: OV OV OV OV OV ove & ir, idee © er dy | & ee Oz The ratio of the distances sun-earth and earth-moon being very large, IL develop in powers of §, 7,6, neglecting second and higher powers. Then the expressions for the perturbative forees are: OV VE Ve Oy eV OV 02V, eV a ¥. Oa? SD dd cps Oxdz = dxdy if dy” tints oon dxdz a dy0z ts Oz? and one can introduce as the perturbative function the funetion parler et a ee eae ons eel oe a ea loss ak fen age , Sr sn det | bady |? dade Here for v2, y,2 are to be substituted their expressions in elliptic elements and then the secular portion of F is to be taken. Since the powers and products of §, 4,6, contain only the elements of the orbit of the moon, the coefficients on the contrary only the elements of the orbit of the earth we can take the secular portion of each separately and multiply these together. Besides the system just mentioned suppose another system a’, y/’, 2’, the sun also being at the origin, but the axis of 2’ perpendicular to the equatorial plane of the ellipsoid. Then we have z =asin Psind, — y cos PsinJ, + zcosJ,, therefore de! 02! dz! a = sin P sin J,; a = — cos sind; a COS eee Perturbations caused by the jirst ellipsoid V From the expression given for £2———-— we deduce, negleet- aga ing the terms having sin? J as a factor: 0 :. ~ du 42” Oia ay | (@tu(etuh | (apap bay 72 4uy dady (a? 2) (+A) oO 072 4u2' ot Ue geet! : du — (a°—c’?)— 2 (a?—c’?) sin D sin J, | - dede (@ Lay a) | pw? (puis 31 72 ae 2 du |! Ay? Oy? i 4 (a? +-u)? (c?+u)le — (a?+2)? (ce? +4)'b os) 072 Aye! ° = = (a7 —c¢7) + 2i(a? cos P re OyOz (a? A)? (c? +-a)*2 te Jase oN coe rie Se uy? u)? (c?-Lu)t2 Q du du <1 A OE ea ee) Oe (a? tu)? (c2 + up'e AC +u)? (c? + u)'h Substituting the elements of the oibit of the earth for a, y, 2 and neglecting the second and higher power of the excentricity I get: 72 2 C72 072 =— ere N) 2 0a? Ly °p Oy dady 0°2 = 2(a*—c?) : a a J, — 2 (a’—c’) C, sin B sin J, Owdz a, Pp 072 2'a? —¢?) ; : J aa _=— Tape cos D sin J, + 2(a?—c?) C,cos B sin J, inte 1 072 —_ == — 20, — 2(a?—c’) Cy. Let o be the radius vector, v the true anomaly, © the longitude of the perigee, §% the longitude of the node, 2 the inclination of the orbit of the moon, then we have : § = 0 [cos (v + © — §{Q) cos §}, — sin (v +0 — Sp) sin S% cost] 4 =0 [cos (v+- O—§h) sin [ + sin(v+O — Sb) cos Hh cos 7] $= osin(v+@—Jy) sini. 1 write these expressions thus: = 0 (A cos v + Basin v) gn y= 0 (Cocos v + Dsinv) = 0 (Leos v + F sin v), Vas A, B,C, D, FE, F being expressions not containing the true anomaly. For the formation of the required products we need the secular portion of 0° cos? v and 9? sin’? v; I get: So? cos? v=a',* (4 + 2e?) Sg? sin? v= ka’? (1—e’) a, being the semi-major axis of the lunar orbif. Thus we get expressions as : eee (ae 32 * 92 v a . v Neglecting terms hke ¢* svn* >, e* sin‘ we get: 2 2 — —— — —— sin® (1—cos2 {X) + e? + — cos 20 a, 2 4 4 4 i 3) le Fo me Sh io < — = — sin® isin2. 4+ — e? sin 20d es 4 a, EO ee rey, = — sure sin \% 4- e@ su s 20)— \/ )— — sin 73 5 sini sin 9) 1. ¢ hee in (2 \)) 9 oy Cf 1 =_ ~ = ve l i eC 2A) ee 3 5 ne — — —— sm" i(1 4+ cos2't) +e —— cos 2M Ge. 2 4 4 4 75 ye ie hy 5 £ 3 , ~~ — = sini cos () e* sin ————=COs(2@— a) cos Q, 1g 5 9 5 ‘ 9 ay, “ 2 a a a G le — == — sin* 4 a Te 2 Substituting in FR these expressions we get : Kagqate 1 a," 2 1 ey eel ees — “A -2C,a,?+—+ de? —C,a,* )+4sin" -—-C,(a°-c*)a,? R Cais zi P p 2 p : : 1 + 2(a?-—c?) sin J sin 2 cos ({i— ®) (2¢,— 4 j Pp The only perturbations to be considered are those of the longitude of the perigee and of the node. The differential equations required are : Ia 1 OR - dsl, 1 OR e— = - - sin 1 — == ——_ —. dt na,” Oe dt na," 07 One easily perceives that the last term in the expression for gives no sensible perturbation on account of the factor a*—c’, the as 6 : ‘ : value of whieh is about Te. and of the facet that $2 has a period ( of 18'/, years so that the coefficient we get by integration is about thirty times as small as would have been the case if {f had been absent. In the same way | omit the term (C,(a@’—c’*)a?, in the coeffi- cient of s7m>— and thus we have the following expression for FR: : <3 i f : I get C, = 0.678 ; — = 1.080 from which follows taking as unit PR of time the century : 30 Se arog: ©) ae Roh 33, dt dt - Perturbations caused by the second ellipsoid. I find: e2 d2 72 SSS SS SS SS I = Ox? Oy? a dwdy 2 Rpt ee : 072 Pay s —— == — 2 (a?—c’) E, sin B® sin J; ——— == 2(a? —c’) E, cos ® sinJ ; Oude ; Oy0z 5 072 == 2E, 2(a*—« a) Wee from which follows: R 1 a," k@mgase | 2.0," | == 2H ,a,” 3h ,a,*e? — EB, (a®*—c?*)a,* sin? 2 + 2(a?—c¢?) a,” E,,sin J sin t cos (\i — ?)|. Although the term @*—c* is not small, yet it is. allowed to omit the periodic term. I get H, = 0.684, LH, = 2.445 from which follows taking as unit of time the century : do ; di. is SSS (IMEI 9 SS (J dt dt Thus both ellipsoids together give : UE iio oe. dt dt both insensible amounts. Astronomy. — “Remarks on Myr. Wourier’s paper concerning Seenieer’s hypothesis.” By Prof. W. pe Srrrer. (Communicated in the meeting of April 24, 1914). SeeLiger’s explanation of Newcoms’s anomalies in the secular motions of the four inner planets consists of three parts, viz : a. The attraction of an ellipsoid entirely within the orbit of Mercury The light reflected by this ellipsoid is, on account of the neighbour- hood of the sun, invisible to us. 6. The attraction of an ellipsoid which inecloses the earth’s orbit. The light reflected by this ellipsoid appears to us as the zodiacal light. c. A rotation of the empirical system of co-ordinates with reference v0 Proceedings Royal Acad. Amsterdam. Vol. XVI 34 to the “Inertialsystem’’. This rotation is equivalent with a correction io the constant of precession. The value of this constant which is implied in Newcoms’s anomalies is that used in his first fundamental catalogue (Astr. Papers Vol I). In “The Observatory” for July 1913 I have shown that this constant requires a correction of + 1.24 (per century). Consequently, of SretiGer’s rotation 7 only the part r, =r—1".24 ean be considered as a real rotation. The position of the equatorial plane of the ellipsoid @ was deter- mined by Serricer from the equations of condition: he found it not much different from the sun's equator. For the ellipsoid 6 the sun’s equator was adopted as the equatorial plane. It is important to consider the part which is contributed by each of the three hypotheses towards the explanation of the anomalies: By the way in which Sernicer has published his results this is very easy. It then appears that the ellipsoid a is practically only necessary for the explanation of the anomaly in the motion of the perihelion of Mercury, and has very little influence on the other elements. Similarly the ellipsoid 6 affects almost exclusively the node of Venus. The rotation 7 of course has the same effect on all perihelia and nodes. In the following Table are given Newcoms’s anomalies together with the residuals which are left unexplained by Segicer’s hypothesis. In addition to Seriicer’s residuals I also give residuals which are derived: A. by rejecting the rotation 7,'), and C. by omitting the second ellipsoid. The constants implied in the three sets of residuals are thus SEELIGER g,=2.18 X10 ¢,=0:31 K 105% 77a ee A 2.42 0.93 0 C 2.03 0 + 6.85, where g, and g, are the densities of the two ellipsoids expressed in the sun’s density as unit. di Seeiicer did not compute the value of rr for the earth. The resi- dual given in the table is derived from the preceding paper by Mr. Wor Tder. From the table it appears that the residuals C are quite as satis- factory as those of Srxiicer. Consequently the ellipsoid 6 is not a 1) The residuals A have already been given im the above quoted paper in “The Observatory”. The density g, is there erroneously given as 0.37 instead of 0.93 (the correction to Seeticer’s value having been taken-as 0.2 limes this value, instead of 2.0). | have used the figures as published by SeeLiger. The small deviations found by Mr. WoLtsER are of no importance. : bys) necessary part of the explanation. Of the residuals A on the other hand there are, amongst the 10 quantities which were considered Mercury Venus | Earth | Mars de Fi NeEwcome | —0”.88 +0”.50 | --0/.21 +0”.31 | -++0/”.02 +0”.10 | +-0’.29 +0”.27 | | | | Newcoms | +8 .48 +0 .43| —0 .05 +0 .25/-+0 .10 +0 13) +0 .75 +0 35 dw Ci, —0 .01 | —0 10 | +0 .03 | +0 .16 “dt [/ 0 .00 0 .05 |+0 .18 0 52 Cc -—0 .02 |—o 12 —0 .04 | 0 .00 Newcoms |-++0 .61 +0 .52;+0 .60+0 17). ..... | 40 .03 +0 .22 |—o 04 +0 .02 ona Men area |—o .20 sin paels +0 .55 +0 .01 —0 .11 —O0 31 +0 .05 —0O .24 | NEWCOMB | +0 .38 +0 .80 | +0 .38 +0 33)—0O .22 +0 .27 | —0 .O1 +40 .20)| a (seni |—0 .14 ‘| +40 .21 (40 .28) |+40 .01 dt )4 =) 2 | +0 aN al He) +0 .05 & —0O .15 +0 .23 —0 17 —0 .01 by Srrnicger, 3 residuals exceeding their mean error. This in itself would not be sufficient to condemn the hypothesis, but the residual for the secular variation of the inclination of the ecliptic (+ 1'.18) is entirely inadmissible. We conclude therefore that the rotation 7, is a vital part of the explanation. The great influence of the ellipsoid 4 on the ecliptic is, of course, due to the large inclination of its equator. If this equator was e.g. supposed to coincide with the invariable plane of the solar system, instead of with the sun’s equator, this influence would be much smaller. It is impossible to decide a priori whether it will be found possible so to adjust the position of the equator and the density of this ellipsoid that it has the desired effect on the node of Venus without appreciably affecting the earth’s orbit. The motion of the node of the earth’s orbit is the planetary pre- cession. Calling this 4, we have, for t= t, 3* 36 ne dp =a where p is the quantity so called by Mr. Wortser. We thus find for the three hypotheses Ad. sine SEELIGER Ah = + 0".47 A +1 13 Cc +0 15 Newcoms did not include a deviation between observation and theory for this quantity. At the time of the publication of the “Astronomical Constants” (1895) it was of course entirely correct to consider a determination of the planetary precession from obser- vations as impossible. Since that time however very accurate invest-' igations of the precession have been executed by Nrwcoms himself (Astr. Papers, Vol. VIII) and by Boss (Astr. Journal, Vol. XVI, Nrs. 612 and 614). Now the precession in right-ascension depends on the planetary precession, but that in declination does not. We have m = lcos €—) n=lsine / being the lunisolar precession. Newcoms determined / from the right-ascensions and the declina- tions separately, and found a large difference in the results. If this were interpreted as a correction to the planetary precession, we should find A= 0747. Boss determined m and 2 separately, the latter both from right- ascensions and from declinations. From his results I find (applying the correction of the equinox Ae — + 0.30, adopted by both Boss and NEWCOMB) : Ah = + 0".85 + 0".22 The mean error does not contain the uncertainty of the correction Ae. Its true value probably is about = -+ 0".25. The mean error of the value of 42 derived from Nrwcome’s work is difficult to estimate; we may assume it to be equal to that of Boss. The mean of the two determinations would then be Aa = + 0".66 + 0".181). 1) Also L. Srruve (A. N. Vol. 159, page 383) finds a difference in the same sense. Neglecting the systematic correction », | find from his results Ar = + 0".93 + 0".80. The m. e. again is too small as it does not contain the effect of the uncertainty of the correction ». o7 Now it is certainly very remarkable that this correction is of the same sign and the same order of magnitude as the planetary preces- sion derived from the attraction of Srenicmr’s ellipsoids. It must however be kept in mind that it is very weil possible to explain the disere- paney between the determinations of the constant of precession from right-ascensions and from declinations (or from m and from 7) by the hypothesis of systematic proper motions of the stars. Thus Hoven and Haum (M. N. Vol. LXX page 586) have from the hypothesis of unequal distribution of the stars over the two streams derived a systematic difference which is equivalent (for Newcoms) ‘) to a correction Ai = + 07.56. As the effect of the attraction of SepricEr’s ellipsoids on the motion of the moon Mr. Wortser finds a secular motion of both the perigee and the node. Both of these are due chiefly to the inner ellipsoid and are thus not much altered if Seeticur’s hypothesis is replaced by either of the hypotheses A or C. We find dw ASG et SRELIGER a SL OTL SS = HN) dt dt A 4+. 2.04 135.30 C + 2 10 —-2 .06 All these quantities are well within the limits of uncertainty of the observed values. Chemistry. — “Vhe application of the theory of allotropy to electro- motive equilibria.” Ul. By Dr. A. Smits and Dr. A. H. W. ATEN. (A preliminary communication). (Communicated by Prof. J. D. VAN DER WAALS). (Communicated in the meeting of April 24, 1914). 1. In the first communication *) under the above title it has been demonstrated that the theory of allotropy applied to the electromotive equilibrium between metal and electrolyte, teaches that a metal that exhibits the phenomenon of allotropy and is therefore built up of different kinds of molecules immersed in an electrolyte, will emit different kind of ions. The different kinds of ions assumed by the theory of allotropy, need not be per se different in size, as was remarked before. They 1, For Struvn’s stars the correction would be + 0”.77. For Boss the corre- sponding computation has of course not been executed by HouaH and Hats. *) These Proc. Dec. 27, 1913, XVI. p. 699. 38 may be equal in size, but different in structure. There can, however, be another difference besides, viz. in electrical charge. In the preced- ing communication the molecule kinds J/ and J/, were assumed, and for simplicity’s sake the circumstance that part of these molecules are electrically charged also in the metal, was not mentioned. This circumstance need not be taken into account, because the electrical charge of the atom J/ in one ion JJ/,*) was put equal to that in the other ion (J2-*). If it had then been our intention to indicate the total equilibrium in the metal, we might have drawn up the following scheme : 2M@M°+602M=+60 (1) QV eo 2M Fe M, (4) from which follows that the system would then be pseudoquaternary. For an explanation of the electromotive disturbances of the equi- librium mentioned in the preceding communication, a consideration of the equilibrium (1) or (4) sufficed. Then equation (4) was chosen and 2M and M, were therefore called the pseudo components, though of course we might as well have taken 2M: + 66 and MM. + 60. Now it is clear that when in the metal ions of equal structure occur, but of different value, the scheme of equilibrium can be as follows. M-+202M-:-+30 (1) (2) XS [ Ly (3) . i The system is then pseudo ternary, but in most of the cases it will be sufficient to consider the pseudo binary system, indicated by equation (1), and assame MW: +20 and M--+30 as pseudo components. A similar equilibrium will have to be assumed, when the metal can go in solution with different valency under different circumstances. This case is probably of frequent occurrence. Of course the metal phase is already complex, when metal ions occur by the side of uncharged molecules, but this complexity does not suffice to explain the peculiar electromotive bebaviour of the metals, whereas schemes I and II are competent to do so. In connection with the foregoing considerations it could be shown that the unary electromotive equilibrium finds its proper place in the 4,2 figure of a pseudo system, which ean clearly appear under certain circumstances, when we namely sueceed in bringing the metal out of the state of internal equilibrium. Thus it was e.g. shown that when a metal is brought to solution by an electrolytic way, so when it is made into an anode, the internal equilibrium will be disturbed, and the metal will become superficially enobled, at least when the velocity of solution is greater than the velocity with which the internal equilibrium sets in. In this case therefore the dissolving metal will have to become positive with respect to an auxiliary electrode of the same metal which is superficially in internal equi- librium. If reversely the metal is made to deposit electrolytically, the reverse will take place, and the separating metal will be less noble and therefore negative with respect to the auxiliary electrode. The anodie disturbance of equilibrium being attended with a dimi- nution of the more active kinds of molecules, this process will bring about a diminution of the chemical activity. This is therefore the reason that this anodic state of disturbance is a more or less passive state of the metal. At the eathode the disturbance lies exactly in the other direction, and a more active state will be brought about. The degree in which a metal is thrown out of its state of equi- librium in case of electrolytic solution or deposition, will depend on the current density at constant temperature, and it was therefore of importance to study the discussed phenomenon at different current densities. What may be expected is this that the internal equilibrium will generally be able to maintain itself for very small current densities. Then the tension with respect to the auxiliary electrode will be zero, both when the metal is anode and cathode. With greater current densities the metal will get superficially more and more removed from the state of internal equilibrium on increase of the current density, and the tension with respect to the auxiliary elec- trodes will greatly increase. As the metal surface gets further removed from the state of internal equilibrium, so becomes more metastable, the velocity of reaction which tries to destroy the metastability, increases however in consequence of the change of concentration in the homogeneous phase; and we may therefore expect that the potential difference between metal and auxiliary electrode will vary with the current density in the way indicated in Fig. 1. When the velocity with which the internal equilibrium sets in, is small, the part a) will lie at exceedingly small current densities, and if the measurements are not exceedingly delicate, we shall get the impression that this piece is entirely wanting. lt is clear that the tension which is represented here as function 40 of the current density means the tension with respect to the auxiliary electrodes. This tension, which is also called polarisation tension, is Polarisation. Fig. 1. positive when the metal is anode, and negative, when it is used as cathode. Further this possibility was still to be foreseen that when the metal assumes internal equilibrium very slowly a distinct change of the potential difference would have to be demonstrated even after the current had been interrupted. Now it shonld be noted here that when a base metal has become noble during its use as anode, and the difference of potential between the metal and electrolyte has risen to the tension of liberation of the oxygen, at the anode two processes will begin to proceed side by side; besides the going in solution of the metal we get also the discharge of the OH’-ions and the possible formation of oxide skins, the influence of which should be examined. We get something of the same kind at the cathode. When viz. the difference of tension metal-electrolyte at the cathode has become ereater than the tension of liberation of the hydrogen, besides dis- charge of metal ions, also discharge of H’-ions will take place there. Method of Investigation. The measurement of the polarisation tensions took place in the following way (see Fig. 2). Two electrodes of the metal that is to be investigated, in the shape of wire or rods, were placed in a solution 41 of a salt of the metal, generally the nitrate. The two electrodes were connected by a variable resistance and an Amperemeter with a number of accumulators, so that the strength of the polarizing current is easily changed and measured. To measure the tension of polarisation at one of the electrodes a beakshaped bent glass tnbe was brought into the solution, whose capillary point was placed as close. as possible ‘against the polarized electrode. In this glass tube a third (auxiliary) electrode of the same metal was brought. This auxiliary electrode, which is currentless, exhibits the normal potential difference with respect to the solution. As there is no loss of tension in the liquid of the auxiliary electrode, and its point is close against the polarized electrode, the potential difference between the auxiliary electrode and the polarized electrode gives directly the deviation which the potential difference of the polarized electrode presents from the normal potential difference, so the polarisation tension. The measurement of this potential difference took place by reading the deviation which was obtained by con- necting the auxiliary electrode and the polarized electrode by means of a resistance of _ Fig. 2. some meg. ohms with a gal- vanometer. The value of the scalar divisions in Volts was determined by connecting the galvanometer with a normal element. Silver, Copper, Lead. 2. The investigation of different metals, undertaken in this direc- tion, has shown us that as was to be expected, they represent the most different types. There are metals which in contact with an electrolyte, assume internal equilibrium very quickly ; there are those that do so very slowly, and there are those that lie between these extremes. Beginning with the metals which quickly assume internal equili- brium, we may first mention the metals: sé/ver, copper and lead. The result of the investigation of these metals is found in the following tables. 4 be After the current had been interrupted, no potential difference with the auxiliary electrode was to be perceived. In the first column the current density is found expressed in milli- amperes per em*®. In the second column the potential difference with the auxiliary electrode is indicated in Volts, the metal serving as anode (anodic polarisation tension); and in the third column the same is given for the case that the metal served as cathode (cathodic polarisation tension) / AB Es Silver electrode immersed in 1/, N, Ag NO3-solution. l : = ne V-anode V-cathode 25 + 0.03 — 0.006 50 + 0.03 —— 0.012 100 + 0.04 — 0.014 200 + 0.05 — 0.015 300 + 0.05 — 0.016 400 + 0.06 — 0.018 750 + 0.09 — 0.020 It is seen from this table that the silver is not materially nobler during the solution, and not materially baser during the deposition than the auxiliary electrode, which is entirely in internal equilibrium. The polarisation is therefore exceedingly slight here, from which we may deduce that the metal silver very quickly assumes internal equilibrium. Under these circumstances it is of course out of the TABLE 2. Copper electrode in '/. N.Cu(NOs))-solution. | = = uae V-anode V-cathode 14 + 0.016 — 0.016 29 + 0.026 — 0.026 57 | + 0.032 — 0.035 114 + 0.048 — 0.063 171 + 0.048 — 0.082 930 + 0.050 — 0.088 43 question that a potential difference could sull be demonstrated after the current had been broken, which accordingly was by no means the case. For copper the following values were found. (See table 2 p. 42). This is, therefore, the same result as was obtained for silver, and lead behaves in an analogous way, as appears from the following table. TAB EES 3: Lead electrode in 1,.N.Pb(NO3)-solution. 2 — ne V-anode | V-cathode 36 + 0.010 — 0.006 140 + 0.033 — 0.010 280 -L 0.046 — 0.013 510 | + 0.082 — 0.017 1000 «=| «40.126 =| . — 0.020 | After the current had been interrupted no potential difference with the auxiliary electrode could be demonstrated. Nick ‘el ° 3. A splendid example for an internal equilibrium setting in very slowly is furnished by nickel, as appears from the following result. TABLE 4. Nickel electrode immersed in '/, N . Ni (NO3),-solution. 5 | V-anode V-cathode | ——. 21— | +1.61 — 0.95 ra Nigel hg Cine 4 SET GES ES ho 180 + | + 1.77 — 1.40 360 | +4 1.83 | 1166 540 | STEER |b eles yg Nickel shows therefore an enormous anodic and cathodic polarisa- tion, which we must ascribe to the very slow setting in of the internal equilibrium, the more so, as we found that even after the 44 current had been interrupted a great potential difference with the auxili- ary electrode could still be demonstrated viz. an anodic polarisation tension of 0,95 Volt. and a cathodic polarisation tension of 0,5 Volt. These tensions decreased with diminishing velocity to 0, as a proof that the metal assumes internal equilibrium by the aid of the electrolyte. As on account of the osvillations of the mirror of the galvanometer the said tensions could not be observed quickly enough after the current had been interrupted, the above values give the tensions some seconds after the interruption of the current. Immediately after the interruption they willhave been + 1,88 V resp. — 1,77 V. Hence nickel, used as anode, becomes superficially a metal nobler than platinum as we know it. Cadmium. 4. Cadmium is a metal lying between silver, copper, and lead on one side and nickel on the other side with regard to the velocity with which its internal equilibrium sets in. For this metal we found what follows; TABLE 65. Cadmium electrode in !/> N. Cd (NO3)o-solution. d | V-anode V-cathode 21 |) 220h093) | —n027 et Stats | — 0.186 144 | + 0.290 | — 0.220 286 | + 0.380 | = 0.220 428 | + 0.507 | — 0.220 Besides that the polarisation is smaller here than for nickel, it is noteworthy that while for nickel the anodic and cathodic polarisa- tion tension differ little, this difference becomes pretty considerable for cadmium, at least for large current densities. This peculiarity may be explained in a simple way by means of the A,z-figure given in the preceding communication. (See Fig. 3.") Suppose that with unary electromotive equilibrium at the given temperature the electrolyte 4 and the metal phase S coexist, then the 1) Here the potential difference of the metal with respect to the electrolyte has been given. 45 metal phase in case of anodic polarisation will move from S to 6, dA and over this range — is great. Ae In case of cathodic polarisation the metal phase moves from S§ upwards along the line SC, but here we see now that the quantity END ee : : = will continually decrease and can become very small in consequence of the ever increasing curvature of the line SC, which can be even a great deal more pronounced than has been drawn here. It now follows from the observations that the metal cadmium assumes internal equilibrium pretty rapidly, and in harmony with this is the fact that after the current had been broken the polarisa- tion had soon entirely vanished. It was besides noticed in this investigation that the metal which 46 Served as anode, was gradually covered with a skin of basic salt. It was, however, easy to demonstrate that this skin could not have caused the observed phenomena through increase of the resistance, for the phenomena remained the same also when this skin, which could be very easily removed, was taken away during the electro- lysis. Moreover it appeared that when this metal with skin was made to cathode, the cathodic polarisation was the same as in the absence of this skin. The formation of the skin is therefore a secon- dary phenomenon, as was also expected (see under 1). bismuth. 5. bismuth is a metal that very clearly seems to be catalytically influenced, as appears from the following table. TABLE 6. Bismuth in '/9 N Bi(NO,)-solution. 5 | V-anode | V-cathode 35 AE S02 a = 0802 G0) ie OROL en OF08 133 © |) St eDs050 le =aulov03 2600) | Zeal S14el =. 50803 The anodie polarisation presents this particularity that though it is exceedingly small up to a current density of 133 milli Amperes per cem*, as for silver, it becomes pretty considerable for a current density of 260 milli Ampeéres. Now it is worthy of note that the anodic polarisation was at first also small for a current density of 260, but if increased slowly, so that it amounted to + 1.14 volts after a few minutes. For smaller current densities, however, no rise of the polarisation tension took place in course of time. The explanation of the observed phenomenon is probably as follows. The Bismuth, which gets positively charged in the used solution, assumes internal equilibrium very quickly at first. At the greatest density of current, however, this internal equilibrium is no longer able to maintain itself, and then generation of oxygen seems to take place, which oxygen evidently exercises a negative, catalytic influence, which renders the metal still nobler. This phenomenon being attended with the formation Al of a white skin (probably of basie salt) we have again examined what influence this skin exercises on the phenomenon. For this pur- pose the current was suddenly reversed, after a thick layer of the basie salt had formed, in which however, only a cathodic polarisation of 0,18 Volt was observed as a proof that this skin, indeed, increased the resistance somewhat, as was expected, but that this could have been only of slight influence on the amount of the anodic polarisation tension’). What the negative catalytic influence here consists in, cannot be said with certainty, but as has been stated, it seems probable to us that the oxygen, dissolved in the metal to an exceed- ingly slight degree, retards the setting in of the internal equilibrium. Tron. 6. If we now proceed to the metal iron we meet again with phenomena, and very pronounced ones too, which in our opinion point to catalytic influences. We found the following result : TABLE i: Iron electrode immersed in !/) N.FeSO,-solution. 0 | V-anode 50 0.026 100 | 0.038 130 0.044 160 | 0.064 199 0.075 250 | 0.113 300 | 0.164 400 2.25 600 2.47 800 2.53 from which it appears that in this transition of a current density from 300 to 400 the iron has suddenly become very noble. This 1) For it ean hardly be assumed here that the skin offers a different resistance to currents of different direction. 4s phenomenon, whieh has been already often observed, and is called the becoming passive of iron, has not been accounted for in a satisfactory way. In the light of these new considerations the explanation, as was already observed, is not difficult.) The iron, which shows. this sudden increase of the anodic polarisation, is entirely free from so- called annealing colours and_ perfectly reflecting, so that an oxide skin is out of the question. If we, however, assume that the metal dissolves a little oxygen, and this oxygen retards in a high degree the setting in of the internal equilibrium, the sudden considerable enobling of the metal is explained in a simple way. Up to now it has been lost sight of too much that the pheno- menon of passivity, arisen by an electrolytic way, and that called into existence by a purely chemical way, must be explained from one and the same point of view. By a purely chemical way iron is made passive by being simply immersed in strong nitric acid for a few moments. If then the iron is put in a solution of copper sulphate, the copper does not deposit. By a shght shake, the appli- cation of a magnetic field ete. this passive state can, however, at once be destroyed, and the iron is covered with a coat of copper. If we consider the passive iron to be iron that is superficially very far from the state of internal equilibrium, in which super- ficially the easily reacting molecules are practically entirely wanting, and assume that this state can be maintained for some time on account of the negative catalytic action of oxygen under certain circumstances, which state, however, outside the cell, can be destroyed by vibrations, a magnetic field ete., the phenomenon of passivity of iron becomes less unintelligible. *) Returning to the experiment, we will show in the first place what was found when smaller current densities were worked with after the iron had become “passive” at higher current density. This table exhibits therefore the great difference between the passive and the active iron. As appears from the last table but one, the active iron yields a difference of tension with the auxiliary. electrode of 0,026 Volts for a density of current of 50; the passive iron yields a difference of tension of 2,18 Volts for the same current density. i) Suits, These Proc January 25, 1913, XVI. p. 191. 2) We have probably to do here with metal ions of different valency. (We shall return to this later on.) 49 ; TABLE 8. iron electrode, immersed in ''5 NFeSQO,-solution. ‘ V-anode | V-cathode 800 DOS 0 50 600 2.47 | 0.47 400 2.40 0.44 200 | 2.30 | 0.42 100 2.24 | 0.37 50 | 2.18 0.27 It is now remarkable that, as has also been found by others, contact with hydrogen can annihilate the passivity. When we reversed the current and made the passive anode the cathode for a moment, and then reversed the current again at a density of 400 m.A., the difference of tension with the auxiliary electrode amounted at first only to 0,12 Volt, but this tension rose at first rather slowly to 0,6 Volt and then rapidly to 2,27 Volts. It therefore appears from this experiment that hydrogen is a positive catalyst for the setting in of the internal equilibrium of iron. which also accounts for the fact that the cathodic polarisation, as appears from the last table, is extremely small in comparison with the anodic polarisation. The difference between anodic and cathodic polarisation is therefore so great here, because for the anodic polarisation a negative catalyst, and for the cathodic polarisa- tion a positive catalyst come into play. That for nickel the anodic and the cathodic polarisation are about the same proves that the oxygen and the hydrogen do not act noticeably catalytically on this metal. It should finally still be pointed out that when at the moment that the passive iron had veached an anodi¢ tension of polarisation of 2.27 Volts, the current was broken, still a tension of polarisation was observed of 1,07 Volts, which tension, however, pretty quickly fell to O. So it appeared just as for nickel that the iron without passage of the current soon assumes internal equilibrium by the aid of the electrolyte, and becomes active. We see from this that the hegative catalytic action is maintained by the current; when the current is broken the active iron above the liquid will, however, 4 Proceedings Royal Acad. Amsterdam. Vol. XVII. 50 promote the setting in of the internal equilibrium in the at first passive part, and this will be the explanation of the fact that the iron becomes active after the current has been broken. Also after the use of the iron electrodes as cathode the current was broken, and as was to be expected, the much smaller cathodic polarisation tension of + 0,15 appeared to run very rapidly back to 0. Aluminium. 7. As far as ifs electromotive behaviour is concerned, aluminium is undoubtedly one of the most interesting metals. For anodie pola- risation the current density decreased regularly, and the tension increased, as is shown in the following table. TAB EE V9: Aluminium electrode in !y NAlo (SO4)3-solution., ; L 0 V-anode 0.8 + 2.56 0,53 Ly 0,46 | + 3.84 0,36 = | ate ASD Accordingly we find anodie polarisation tensions of about 4 Volts for this metal already at very small current densities, which points to the fact that here a layer of great resistance must have been formed. Up to now it has been tried to explain this strong anodic polari- sation for aluminium by the formation of an insulating skin of Al,O,. With greater densities of current the anode is really covered with an oxide skin, and it is therefore natural to assume the formation of this skin also for smaller densities of current, and attribute the observed phenomenon to this skin of Al,O, with great resistance. There are however objections to adopting this explanation, for in our experiments no trace of annealing colours was to be observed, and the metal remained beautifully reflecting. To ascertain whether in our experiments a skin of great resistance had formed round the anode, we made the following experiment. The bottom of the vessel with the Al?(SO,), solution was covered with a layer of mercury, and the aluminium electrode was anodi- 51 éally polarized. When this electrode was now covered with a skin of great resistance, an immersion of one extremity of the aluminium electrode in the mereury should not exert any influence on the difference of tension between the aluminium anode and the auxiliary electrode. If, however, this skin does not exist, the aluminium elec- trode will get into contact with the mercury during the just described manipulation, and the said difference of tension will be modified. The result was that when during the anodic polarisation the aluminium anode was immersed in the mercury, and the current was then broken, the difference of tension with the auxiliary elec- trode was absolutely unchanged, which proved therefore that the aluminium electrode did not get in contact with the mercury, but was surrounded with a coat of electrolyte. This appeared to be no specifie property of the anode, for the same thing was observed after cathodic’ polarisation. An unpolarized Al-wice, immersed from the electrolyte in the mercury layer, immediately assumed the potential of the mercury, from which therefore follows that the gas layer on the aluminium retains the electrolyte with great force. In this way the question of the skin could therefore not he solved. What is remarkable is this that the skin formed during anodic polarisation, immediately seems to disappear again by cathodic polarisation. The assumption of a film of Al,Q, is attended with great difficulties, in the first place this oxide cannot be reduced under these circumstances by H in status nascens, and in the second place it appears, that nothing is to be perceived of this skin, at least with the naked eye, as no annealing colours are to be observed, and the metal remains clearly reflecting. It seems therefore not too hazardous to us to conclude in virtue of this that the skin cannot be an oxide layer, and the only thing left to us is to assume, as we did for iron, that the oxygen dissolves in the aluminium during anodie polarisation, and that this solution possesses a great electric resistance for aluminium. In this way we come to the assumption of a layer with great resistance, of which it is, however, to be understood, that it entirely disappears on cathodic polarisation to make room for a solution of hydrogen and aluminium. Accordingly this layer is metallic, and can amalgamate in course of time when in contact with mercury, through which the resistance disappears. The result at which we arrive is therefore this that the anodically measured tension is so extraordinarily great for aluminium, much greater than the liberation tension of O, can be here, because the dissolved oxygen not only retards the setting in of the internal equilibrium, but also a layer of great electric resistance is formed. 52 At greater current densities Al,O, can separate from this solution of oxygen in aluminium, but then the electrode is no longer reflect- ing, and it cannot be made reflecting again by cathodic polarisation. This layer of Al,O, can also possess a great resistance, but the primary feature of the phenomenon is in all cases the formation of a solution of oxygen in aluminium, which possesses a great resistance. If we now proceed to the description of the experiments with amalgamated aluminium, we will begin with stating that when in the just deseribed experiment the aluminium electrode was. raised ont of the mercury, after amalgamation had set in, and the lower opening of the auxiliary electrode was placed against the extremity of the aluminium wire, this part of the aluminium had undergone a great change, and had become negatively electrical with respect to the auxiliary electrode. The tension difference amounted to —0.9 Volt, and still increased slowly. At the place where the aluminium had been in contact with the mercury, it had therefore become much baser, and had visibly become somewhat amalgamated. That amalgamated aluminium is baser than the non-amalgamated metal, was known, but the exact value of this difference in tension was not met with in the literature. To determine this difference in tension, an aluminium electrode was amalgamated by immersion in a solution of HgCl,, after which this electrode was compared with the auxiliary electrode. We found that the amalgamated Al obtained in this way was still baser than the just mentioned Al, for the tension of this electrode with respect to the auxiliary electrode amounted now to —1.27 Volts. That the amalgamation for aluminium has a very particular effect follows moreover from this that amalgamated aluminium possesses a much greater chemical reactive power than the ordinary alumi- nium. Amalgamated aluminium immersed in water gives a very considerable generation of hydrogen, and it oxidizes so rapidly when exposed to the air that the metal is immediately covered with a layer of oxide, the liberated heat raising the temperature of the metal very noticeably. In consideration of all this it seems more than probable to us that the action of mercury is here positively catalytic, and that mer- cury therefore, when dissolving in aluminium, brings the metal in internal equilibrium, which condition corresponds to a greater con- centration of the simpler, so more reactive kinds of molecules. The anodic polarisation of the amalgamated state is almost as slight as for silver, as a proof that the internal equilibrium sets in 53 much more quickly here than for pure Al, but not yet so rapidly as for Ag. Amalgamated Aluminium. Lo leaned V-cathode 2 | + 0.03 5) |) 420.07), |) = 0:05 Ne a= ONS |= 0120 33 | +018 | --033 i a7), 0.34 1 | That the amalgamated aluminium goes into solution much more rapidly than the non-amalgamated aluminium also appears from what follows. If a new aluminium electrode is put in the just men- tioned mercury layer, which covers the bottom of the vessel with the Al,(SO,),-solution, this electrode assumes the mercury potential. The tension difference with the auxiliary electrode is then namely + 0,6 Volt, which tension difference is also found when a plati- num electrode is used instead of an aluminium electrode. If the same experiment is, however, made with an amalgamated Al-electrode, the tension difference with the auxiliary electrode is — 0,78 Volt. It follows from this that if the ordinary aluminium partially immer- sed in mercury, failed entirely to maintain its potential difference with respect to the electrolyte in consequence of too slow solution, the amalgamated aluminium does not quite succeed in this either, but it almost sueceeds, for instead of — 1,27 Volts its tension with respect to the auxiliary electrode has namely become — 0,78 Volt. lt is perhaps not superfluous to elucidate this phenomenon in a few words. With immersion of the aluminium electrode in the mer- cury a short circuited element aluminium-electrolyte-mercury is obtai- ned, in which the aluminium is the negative pole, and therefore sends ions into solution. If now the setting in of the internal equili- brium took place with great rapidity, the aluminium would be able to maintain its unary potential difference, and in this case the ten- sion of this electrode with respect to the auxiliary electrode would have remained — 1.27 Volts. Now we find —-0,78 Volt, proving that the state of internal equilibrium was disturbed to a certain extent after all, and the metal has become a little less base by dissolving. If, as was described, the same experiment is made with 54 ordinary aluminium, which is therefore an enobled state of aluminium, we get what fellows. The ordinary aluminium is at first the negative pole with respect to the mercury. It becomes, however, noble by the dissolving, and it is soon as noble as mercury. Nobler than mercury it can, howe- wer, not become then, since in this case, the current would be reversed, which would change the state of the aluminium again in the base direction. This is the reason that ordinary non-amalgamated aluminium immersed in mercury, assumes the potential of the mer- cury. This experiment can however not be continued for any length of time, because the aluminium in contact with mereury slowly amalgamates, as we have seen, in consequence of which finally also the part which is not in contact with the electrolyte, will become active, so that the same things will be observed as in case of well- amalgamated aluminium. In a following communication the investigation of the other metals will be treated, after which a critical summary will be given of the theories which have been proposed by others up to now as an ex- planation of some of the facts discussed here. SUMMARY. In the foregoing pages the theory of allotropy was applied to the electromotive behaviour of the metals Ag, Cu, Pb, Ni,Cd, Bi, Fe, Al. We have come to the conviction that the newly obtained point of view, as we hope to prove further, enables us to survey the widely divergent cases, and gives a deeper insight into the signifi- cance of the observed phenomena. Anorg. Chem. Lab. of the University. Amsterdam, April 23, 1914. Chemistry. — “The Allotropy of Cadmium.” Il. By Prof. Ernst Conen and W. D. HeELpEerMAN. (Communicated in the meeting of April 24, 1914). 1. In our first paper on this subject') we concluded from measure- ments with the pyknometer and the dilatometer that cadmium has a transition temperature at 64°.9 and that this metal as we have known it until now, is a metastable system in consequence of the very strongly marked retardation which accompanies the reversible 1!) These Proc. 16, 485 (1913). a) change of these allotropie modifications both below and above their transition points. As we pointed out in our papers on the allotropy of copper and zine, the possibility that there might be present at the same time more than two allotropie forms had to be taken into account. If this were the case, a variation in the previous thermal history might have an influence on the transition temperature. The samples which had given 64°.9 as their transition point (Vide § 11 of our first paper) only differed by the fact, that the second one had been in the dilatometer at 100° in contact with paraffin oil for 36 hours after having given 64°.9. At the end of this time the measurements were made, which are given in Table II. On continuing our investigations we got the impression that this difference in the thermal history of the samples might not have been large enough to determine whether a third modification can be formed. As a result of the following considerations we carried out some new experiments. 2. If in our sample A, (first paper) there had been present originally more than two modifications, it might be possible that the greater part of the modification(s) which is (are) stable at higher temperatures had been changed into the ;“-form, as the sample had been heated at 101°C. for 24 hours in contact with a solution of cadmium sulphate. In this case the heating at 100°, which followed the first experiment with the dilatometer, might have had no perceptible influence on the transition point which is in accordance with the results given in tables I and II. 3. We now varied the previous thermal history of A, very markedly. For this purpose the metal was taken out of the dilato- meter and chilled by throwing it into water. After this it was put into a new dilatometer without previously treating it with a solution of cadmium sulphate at 101°. The dilatometer was then kept at 70°.0; the temperature remained constant within 0.003 degrees. The meniscus fe// in 3°’, hours 143 mm. while we observed formerly (first. paper) a strongly marked increase of volume at the same temperature. 4. In order to control this result, we carried out the following experiment : A fresh quantity of the metal (‘‘KanLBaum’ — Berlin) weighing about 300 grams (A,) was melted and chilled. We then turned it into thin shavings on a lathe and put it into a dilatometer ; the bulb was filled up with paraffin oil and a quantity of small glass-beads. (Vide our first paper § 10). At no temperature between 50 and 100° (vide § 4 of our first paper) did any change occur. We then added 100 grams of the same material A, which had been in contact with a solution of cadmium sulphate (at 50°) during 12 hours. We now observed that the meniscus of the dilatometer fell 167 mm. in 54 hours at 50°.0 ped Ss Tw pa aia eee meter OO: This result is in perfect accordance with the observations of § 3. 5. The following experiments prove in a more quantitative way that the previous thermal history of the metal has an influence on the transition temperature. A fresh quantity of the metal (4) was divided into two parts [(K,)r and (K,)77| of 500 grams each. (Kj. was reduced into turnings on a lathe and immediately put into a dilatometer. At 69°.9 we observed a decrease of volume (456 mm.) in 257/, hours. (K,)j) was converted into turnings in the same way and kept for 5 days and nights at 100° in a solution of cadmium sulphate. After having it put into a dilatometer (bore of capillary tube 1 mm.) we made the following readings (Table 1). TABLE I. | Temperature. Dee euaee ae \ Hee orth sib Beat: is hours. , in mm. per hour 49.6 : — 100 | — 600 60.4 ; — 125 — 250 62.5 3 | ats ed 63.1 ; ae its) + 45 63.7 r + 83 | + 249 69.6 " | + 225 | + 2700 The transition point is 62°.8. 6. The metal was now kept at 100° in contact with a solution of cadmium sulphate for 7 days and nights. After this it was put 57 again into a dilatometer which was heated for 24 hours at 145°, then for 24 hours at 270° (that is only 50 degrees below the melting point of the metal). We only succeeded in ‘bringing it into motion” by heating it for 48 hours at 50° in a solution of cadmium sulphate. We then got the following results (Table IT): . TABLE Il. Duration of the Increase of the Temperature. observations in | pacueaee eae: level hours. : in mm. per hour ° 60.0 "Vo — 105 — 210 63.0 ES — Il — 33 63.5 | 1g — 8 | — 6 64.0 | 11g | at 22 | ae 18 | 69.0 | Vg + 58 | + 348 The transition point has been changed to 63°.4. 7. In this way we carried out a great many experiments with samples of different previous thermal history *). The extreme limits which were found for this (apparent) transition temperature were 69°.3 and 61°.3. 8. As it is almost impossible to fix the real transition point of the pure modifications in this way, we tried to prepare a sharply defined modification of cadmium avoiding high temperatures. For this purpose we electrolyzed an ammoniacal solution of cadmium sulphate between an electrode of platinum and one of pure cadmium. (40 Volt, 20—25 Ampere ; surface of the electrodes 26 em?*.). We kept the temperature of the solution below 40°, cooling the vessel with ice. The solution was kept homogeneous by a glass-stirrer (Wirt), which was kept in motion by a small motor. The cadmium which was formed at the electrode was washed with dilute sulphuric acid, then with water, alcohol, and ether. After this it was dried at 40°. 170 grams of this material were put into a dilatometer. As it is very finely divided, great care must be taken in order to remove the air from the dilatometer. We used a Garpr-pump for the purpose. 1) The details will be given in full in our paper in the Zeilschrift f. physik. Ghem, 58 The paraffin oil was boiled on this pump with finely divided ead- mium. If there had been formed during the electrolysis only one modification of cadmium, we might expect that no transformation would occur in the dilatometer, in consequence of the absence of germs of a second form. From our earlier experiments (first paper § 4) we know that even if a second modification were present the retardation may be very strongly marked. We found in our first experiment that neither at 50°, nor at 80°, nor at 100° did any change occur. After having removed the paraffin oil we washed the metal with ether and brought it into contact with a solution of cadmium sul- phate (12 hours at 100°; 48 hours at 50°). After this the dilato- meter gave the following results (Table III). TABLE II. Téaperatuze | Digaiontoties. | Ieease obievel | dnsecas Oh a | 71.0 | 34 — 351 — 468 94.8 | Yq He5132 + 528 70.5 | 53/4 — 267 = 5 70.5 | i | Bea | ny 6 60.0 24 | — 138 | — 6 70.0 | 11), a7 0 + 46 65.0 1p =) 853 | gs There is a change in the direction of motion of the meniscus at a constant temperature (7O°.5). The transition point is now between 65 and 70°. This change proves therefore that now (viz. after the treatment at 100° and 50° with a solution of cadmium sulphate) there are simultaneously present more than two modifications. 9. Finally it may be pointed out here that the pyknometer cannot be used to determine with exactness the density of the moditications of cadmium formed by electrolysis, as this material always includes constituents of the solution which has been electrolyzed. The water may be driven out by melting the metal; the salt will then flow on to the surface of the metal and may be washed away, but for exact determinations this material cannot be used. Utrecht, April 1914. van “tT Horr-Laboratory. 59 Chemistry. — “The allotropy of Zinc.” Il. By Prof. Erxsr Conny and W. D. HeLperMan. (Communicated in the meeting of April 24, 1914). 1. In our first paper on the allotropy of zine’) we called attention to the “atomized” metals which may be prepared by the new method of M. U. Scnoop of Zurich. We then pointed out that this method forms an ideal way of producing chilled metal. As a result of our investigations on the metastability of the metals as a consequence of allotropy we may expect that ‘‘atomized” zine will contain two or more allotropic forms at the same time. From a technical standpoint we thought it interesting to prove this more directly : if the “atomized” metal really contains two or more modifications at the same time, it will disintegrate in the long run when stabilisation occurs. 2. Mr. Scnoop supplied us with one kilo of zine, which had been “atomized” in the way described in our first paper on the subject. As the material is very finely divided one would expect that an eventual change would proceed in such a way that it could be measured easily. On the other hand much care must be taken to remove air from the very finely divided material after having brought it into the dilatometer. 3. About 750 grams of the metal and a small quantity of glass- beads which had been heated beforehand*) were put into a dilato- meter. The material had not been in contact with an electrolyte. The capillary (bore 1 mm.) was bent horizontally and put in connection with a GarpE pump. In order to remove the air as completely as possible the dilatometer remained in connection with the pump for 1—1'/, hours. After this the paraffin oil was filled in; it had been carefully boiled on the pump at 200° in contact with some “atomized” zine. In this way the instrument was made perfectly free of air as many experiments proved. 4. In a_ preliminary © of the metal occurs at 25°.0. We then carried out a fresh one, the experiment we found that a contraction “atomized” metal having been kept at 15° in a dry state for three 1) These Proc. 16, 565 (1913). *) These Proc., 16, 485 (§ 10) [1913]. 60 months. We used a_ special thermostat, which will be before long described. The temperature was determined by means of a BrckMANN thermometer. It remained constant within some thousandths of a degree. The results are shown in Table I, TAUB LE we Temperature 25°.00. Level of the meniscus (mm.) Time in hours | 0 526 I 425 22/, 252 2/3 219 112/5 181 A strongly marked contraction at constant temperature occurs. 5. As the metal contains a certain amount of zine oxide in consequence of its fine state of division, the question might arise whether the contraction observed may be attributed to some chemical reaction between the oxide and the paraffin oil. In order to investigate this point more closely we filled a dilato- meter (100 ec.) with zine oxide and the same paraffin oil we had used in the experiment described above. After having evacuated it at the GarpE pump we put it into a thermostat at 25°.00. The meniscus did not show any change in 24 hours. The contraction observed in our first experiment has consequently to be attributed to a change in the metal. We intend continuing our investigations on the different modifications of zine present in.the “atomized” metal. Utrecht, April 1914. vAN 't Horr-Laboratory. Chemistry. — “The allotropy of Copper’. UU. By Prof. Ernst Coney and W. D. Henperman. 1. We have also continued our investigations on the allotropy of copper in the direction indicated in our second paper on the allotropy of cadmium. The dilatometer had shown (§ 4 of our first paper) that there is a transition point at 71°.4. We used the same method described in our second communication on cadmium in order to determine if 61 this point changes by a change in the previous thermal history of the metal. 2. The sample the transition point of which had been fixed at 71°.7 ($6 of our first paper) had not been treated with an electrolyte. It was removed from the dilatometer, washed with ether and kept in contact for some days with a solution of copper sulphate. This material (Cu,,) then gave the following results: TABLE I. | Duration of Rise of level Rise of level Temperature. measufements in | ie a ae 61.7 ie | — 78 — 468 14.6 | lg | 4.225 41350 69.6 | Iq | 38 | — 152 72.1 tg | + 67 | + 402 70.3 | \poiassss [es 11.6 2/5 + 84 4. 126 70.8 | ip | Te aae | LL O7 10.6 1g | — 10 — si 70.7 | Big | 4. 36 fe The transition point has thus been altered from 71°.7 to 70°.65. 3. As far as the measurements we carried out with samples of very different previous thermal history are concerned, we only mention here that we found as upper limit of the transition tem- perature 71°.7, as lower one 69 .2. *) 4. We merely give here some details concerning a sample (Cuz) which had been made by mixing a certain weight of Cuyy (Transi- tion point 70°.65) with an equal anantity of the original material (Kupfer-KanLBaum, Elektrolyt, geraspelt), which as we were told when purchasing it, had heen melted after electrolysis. Curr had been at 50° for 10 days and nights in contact with paraffin oil. The results are given in table II. 1) The description of our experiments will be given in full in our paper in the Zeitschr. f. physik. Chem. 62 TABLE II. Rise of level Tempertre. | gpumienest, | Rita | co ee 68.0 21, = 5 | iG 75.0 11/2 + 46 | + 30 72.0 5/6 + 14 | Be iti 70.0 5, + 10 | Me sy 69.5 58 1-243 | Me 69.5 31 — 36 | =a At constant temperature (69°.5) the direction of motion of the meniscus has changed. This change proves that also in this case there are more than two modifications present at the same time. 5. How. extraordinarily marked the retardations are which may oceur, is shown by the behaviour of a sample Cury (comp. § 7 of our first paper); it was not possible to “bring it into motion” even after treating it with a solution of copper sulphate. However, it ought to be pointed out that there was no finely divided powder present, which was the case with the other samples we investigated. Utrecht, April 1914. van ‘t Horr-Laboratory. Botany. — “nergy transformations during the germination of wheat-grains’. By Luerm C. Dover. (Communicated by Prof. F. A. B.C. Went). (Communicated in the meeting of April 24, 1914). The reserve materials of seeds represent a large quantity of che- mical energy. In germination these substances are split into com- pounds with a much smaller number of atoms and partly by the process of respiration completely oxydized to carbon dioxide. In consequence of these exothermic processes a considerable quantity of energy is set free, which can be used for the various vital- processes. In order to obtain a conception of these transformations of energy during germination, | have made some observations on germinating 63 wheat-grains, on which I now wish to make a short preliminary communication. The germination of the wheat-grains under observation always took place at about 20° C. in the dark, there couid therefore be no energy taken up from without by assimilation of carbon dioxide ; all the energy needed for the processes of germination had therefore to be provided by means of the reserve materials. At the commencement of germination imbibition chiefly takes place, in this way heat is already liberated, therefore energy ; then there follow very soon a series of exothermic processes, in wheat- grains more especially decomposition of starch to sugars and com- plete oxydation of this material of respiration to carbon dioxide. The energy set free in this manner is now applied to various ends : 1st. for all kinds of synthetic processes by means of which plastic materials are formed for the growing plant, 2". for the production of osmotic pressure, 3". for the overcoming of internal and external resistances, and 4'>. energy is given offin the form of heat-radiation. The methods used to obtain an insight into these various energy- relations were the two following : 1s'. Determination of the heat of combustion before germination, and after the germination had been progressing for some time. 2-4. Determination of the quantity of heat produced during ger- mination. As regards the first point, it must be pointed out that the internal chemical energy during a certain length of germination must decrease; a measure of this loss can be found by determining the difference in the heat of combustion. The energy which will no longer be shown by this heat of combustion, is that which is utilized osmoti- cally, for overcoming resistances and which is lost by the giving out of heat. The energy, however, which is used up during germination for synthetic processes is again fixed as chemical energy and is indeed represented by the heat of combustion. The loss of energy, that is found by determinations of the heat of combustion, does not give therefore the total amount of energy, which has played a part during germination, for a considerable part of this energy has again been withdrawn from observation by the synthetic processes. The Brrtue.ot-bomb was used for determining the heat of com- bustion. In it a weighed quantity of wheat-grains, germinated or ungerminated and previously dried for a long time at 100°, were burnt; by the rise of temperature of the water in which the bom 64 was placed, in combination with the water-value of the respective parts, the amount of energy which was set free by combustion, could be caleulated. This heat of combustion was always calculated for the weight of 1 eram of ungerminated wheat (initial-weight) ; this was done in the case of both germinated and ungerminated wheat. In this way comparable values were obtained; the difference in heat of combustion after a definite period of germination gave therefore the loss of energy above referred to. Heat of combustion of wheat calculated per gram of the initial-weight, expressed in gram-calories. ee The germination took Average place at + 20° C. | | values | | | ————— ———————— . Ungerminated 3748 — 3774 — 3778 —3794—3797!)| 3778 Loss of energy ~ Sudtin; 0.6 Ist day After 1 day’s germin: 4 Me wewic 2nd day meet ay ” 3756—3793 3774 ) lise OE eigemrenpaies 3rd day Pog : 3740 3740} ? ; 94 4th day ye ey " 3653—3681—3682 —3707—3707 | 3686 j | ( Year O62 5th day ” 5 » ” 3594 3594 | ) ' OG). mentee 6th day ” 6 ” ” 3498 3498 180) eee Ith day ” 7 ” ” 3318 3318 | It is clear from these values, which were found for the heat of combustion, that the loss of energy during germination steadily increased. The loss of energy in the first two days was slight ; probably imbibition had chiefly taken place at this stage, whilst the chemical transformations had then only subsidiary importance. It can be further deduced from the figures that between the 2"4 and 38" day especially the loss of energy greatly increased, and after that continued to rise. If these values for the loss of energy after different lengths of vermination are summarized graphically, a curve is obtained, whieh begins almost horizontally, and rises more and more steeply. The loss of energy per hour per kilogram of initial-weight can be roughly ealeulated from the loss of energy during the different days. The loss of energy per gram of initial-weight was after two days 4 calories. 1) The figures are arranged in ascending values, and not chronologically. 65 During the 1s* and 2.4 days the loss of energy per hour per kilogram of g i 8. | $s 1000 the initial-weight was therefore roughly is = oom, cals LOOG The same for the 3'¢ day aie pq et ==141'7...;, 9 ” ” ” 4th ” ” S< 54 —= 2250 as We. 2 Bees Ol aes su Jn S833 |, ”? ” ” ” Gt ” ” << 96 — 4000 an ” ” ” ”» oh ” ory < 180 SS 7500 5 This amount of lost chemical energy corresponds therefore in all DO. probability to that which is applied to osmotic purposes, to the over- coming of resistances and to the evolution of heat. In a second series of observations | aiso attempted to determine directly the amount of heat that is given off. The principle, that underlay these determinations, was briefly as follows: air, saturated with water-vapour, which had been brought to a constant known temperature, was passed over germinating wheat-grains at a constant velocity ; these acted as a continuous source of heat; the air which passed over it therefore rose in temperature. If the difference of temperature between the air streaming in and out were measured, when the latter passed at a known rate, then in the ideal case when absolutely no other heat conduction took place, the amount of heat set free could be calculated from the known heat-capacity of the air. Moreover for this the space in which the seedlings were placed would have to be completely saturated with water-vapour ; if this were not so, evaporation would take place on germination, in whieh way heat would be withdrawn from the observation. The apparatus: with which | conducted these experiments consisted of a copper vessel placed in a waterbath of constant temperature. Through this copper vessel, in which a large number of germinating wheat-grains were placed, a current of air was directed at the rate of % litres per hour; the air had had for a large part of its course an opportunity to take up the constant temperature of the water. A set of thermal needles served to measure the difference between the tem- peratures of the air entering and leaving; the current resulting from this difference in temperature was led through a very sensitive mirror-galvanometer, whilst a spot of light was thrown by the mirror on a seale and so made it possible to compare accurately the deflections, The apparatus was for the most part composed of materials which 0 Proceedings Royal Acad. Amsterdam. Vol. XVII. bb conduct heat very easily, thus making the ideal case described above very far from being realised. If a source of heat were introduced into the vessel while a regu- lated stream of air was passed through, only a part of the heat liberated could be used to raise the air-temperature ; the remainder would pass into the surrounding water by conduction. It was to be expected that, when a definite source of heat was present, a maximum difference of temperature between the in- and out-sireaming air would arise after some time; with the given rate of passage of the air this difference of temperature caused by this source of heat, could not become greater. A calculation as to how ereat this maximum difference of temperature would be for different amounts of heat, would be very complicated, if not entirely impos- sible. For this reason the simplest way was to calibrate the apparatus by introducing a source of heat of known magnitude. For this purpose a manganin-wire was placed inside the apparatus over as wide an extent as possible, in the place where later the germinating wheat-grains were to be put. This wire formed a metallic contact with two copper rods which projected above the lid of the appara- tus. An electric current could be passed through the manganin-wire by connecting these rods with the two poles of an accumulator. The resistance of the manganin-wire was accurately determined, whilst a milliamperemeter, placed in the cireuit, served to measure the strength of the current. By taking the current from 1, 2, and 3 accumulators alternately, sources of heat of different magnitude could be introduced into the apparatus. When in this way a source of heat of known magnitude occupied the apparatus, air was passed through and at regular intervals the (double) deflection of the spot of hght on the scale was read till this ultimately remained constant and therefore had reached a maximum. These observations were conducted at temperatures of 20°, 30°, and 40° of the surrounding water, and also therefore of the entering cr. These calibration-experiments showed: 1st that the maximum deflection of the spot of light, or in other words the difference of temperature between the in- and out-going air was roughly in proportion to the source of heat which was placed in the apparatus, 2e¢ that this proportionality was maintained at a surrounding temperature of 20°, 30°, and 40°, 3" that the absolute magnitude of the deflection was independent of this temperature, 4'", that a deviation of 1 centimetre corresponded to a development of about 11.5 calories per hour. 67 As the apparatus was now calibrated it was possible conversely, by reading the deflection of the spot of light, to calculate the magnitude of any source of heat, which was in the apparatus. For such an unknown source of heat germinating wheat-grains were used. (The number of these was always 500). In the course of the experiments however it became plain that in this ease the deflection of the light spot could not be looked upon as showing exclusively the heat-evolution which took place in germination. For when 500 germinated wheat-grains, which had previously been killed by heating to 106°, were placed in the apparatus, then it was seen that the spot of light inevitably passed the zero; in various experiments of this kind a deflection of about 8 centimetres was always found. In order to ascertain whether the dead seedlings did not after all give off some heat possibly as a result of a continued enzyme- action, the apparatus was filled by way of control with quantities of filterpaper previously soaked in water. In this case there could be no question of heat-evolution by the filterpaper. Also with this arrangement of the experiments the spot of light invariably passed the zero, reaching finally a maximum deflection corresponding to that obtained when dead seedlings were placed in the apparatus. The extent of this deflection was independent of the temperature of the surrounding water (fixed at 25° and 35°), in other words, with this arrangement of the experiment there arose always a constant difference of temperature between the in- and out-going current of air. Since in these cases no direct evolution of heat by means of the substances used was possible, another cause for the rise of temperature in the experiment described had to be found. The most probable thing was that condensation of water-vapour must have taken place in some way and that the heat thus set free caused an increase of temperature in the out-going air and in consequence of this of the upper thermal needle. In the calibration-experiments the spot of light had remained at zero when there was no heat-source in the apparatus; the difference in conditions then and during the experiments just described was, that the space within was in the latter case for a great part filled with a completely imbibed mass. The many efforts made to eliminate this irregularity were practically without results; I was therefore compelled, in experimenting with living seedlings, to adopt a correction, the amount of which was experimentally fixed while theoretically it had to be left partly unexplained, Since it was therefore found that by filling the apparatus with 58 b8 very moist substances a difference in temperature between the two needles arose when the current of air passed through, it had to be assumed that this would be also the case when living seedlings were present. The deflection found in that case would have to be attributed partly to this physical cause, partly to generation of heat which actually took place in germination. It was therefore necessary to subtract from the deflection found in this arrangement the amount of deflection found in the experiments with dead seedlings, the remainder then being the measure of the heat generated in germination. This latter was observed at different temperatures and in different stages of germination. In consequence of the complications mentioned higher up the sources of error were relatively very numerous’ and. this was. especially noticeable in’ the few parallel-determinations which were carried out, so that in the values summarized in the table below an approximation to the amounts of heat given off must be expected rather than an exact measure thereof. These influences are proportionately very large in the lower values. Number of calories given off per hour calculated per kilogram of the initial weight. eee | | | | a. | On the 2nd} On the 3rd | On the 4th | On the 5th | On the 6th | On the 7th 5 day of | dayof | day of day of day of | day of f | germination) germination germination | germination | germination | germination | | | | 20° | 710 "2143 2790 | 2869 : : : St is | ates 25° 363 540 | 2938 2977 4341 3455 30° | | | 4999 «| = 6790 | 6313 Boe 752 7326 | 71575 | io MiMi se | - 40° | | 5689 6847 It appeared therefore from the values found that the generation of heat on the 2™¢ and 3° days was still small in comparison to that in later stages of germination. The generation of heat shows a great and sudden increase between the 3'¢ and 4 day and it is probable that it continued to increase slowly during the following 69 days, but the relatively small differences from the 4 to the 7! day justify the calculation of an average for this period of germination. Number of calories given off per hour calculated per kilogram of the initial weight. The generation of heat, therefore, surrounding temperature; by arise Temp. leery aa 5th day | 6th day | 7th day, Average 20° 2143 | 2790 | 2869 2601 | | harness | 25° | 2038 | 2977 | 4341 3428 | 3455 | 30° 4999 | 6790 | | 6034 6313 | | 35° 7326 | 7575 | 7450 ——— + — ~~ —~ 40° | 5689 | 6847 6268 | | | was much influenced by the of 10°, the quantity of heat evolved, increased to more than double. The generation of heat was diminished at 40°, a proof of the harmful influence of this temperature. | | Finally a comparison can be made between the number of calories pro kilogram of initial weight given off as heat and the loss of energy deduced from the heat of combustion. This comparison could only be made for a temperature of 20° because at this temperature germination had always taken place, so that the heat of combustion referred to processes at this temperature only, Loss of energy per hour per kilogram of the initial weight. At 20° By heat given off On the 2nd day | ' Calculated from the | heat of combustion 83 Cal. f4i7' . py oils 710 Ca. ee ee 4th 3 2143, Sy iw eOUnue 5 2790 , re pa Melos a en i pithien 2869 , 2250, 3833 4000 7500 70 The total amount of chemical energy which was set free in evermination was therefore always larger than the quantity of energy given off as heat to the surroundings. A part of the free energy which became available in the process of germination was therefore evidently used for other purposes (osmosis ete.) than for heat-evolu- tion only. This was however doubtful only on the second day, the evolution of heat on that day was not determined; the loss of energy, cal- culated from the heat of combustion, was however so small in this period that it is very possible that the evolution of heat at that moment was larger. If afterward it should appear that this is really the case, it would be very intelligible. For in the beginning of germination imbibition will principally take place so that in this case evolution of heat is not at all necessarily connected with chemical transformations. The results of this investigation may therefore be summarized as follows. The loss of energy calculated from the heat of combustion as well as the evolution of heat increase with the duration of germination. Both are small at the beginning of germination and greatly increase, chiefly on the 34 day. The evolution of heat is greatly dependent on the surrounding temperature. The optimum of beat-evolution is roughly 35°, The total loss of energy during germination at 20° exceeds the loss of energy by evolution of heat at the same temperature. Utrecht, 1914. Botanical Laboratory. Chemistry. — “Lyquwilibria in ternary systems XV”. By Prof. F: A. ,H. SCHREINEMAKERS. (Communicated in the meeting of April 24, 1914). In our previous considerations on saturationcurves under their own vapourpressure and on boilingpointeurves we have considered the veneral case that each on the three components is volatile and occurs consequently in the vapour. Now we shall assume that the vapour contains only one or two of the components. Although we may easily deduce all appearances occurring in this ease from the general case, we shall yet examine some points more in detail. The vapour contains only one component. We assume that of the components A, 6, and C' the first two are extreiaely little volatile, so that practically we can say that the vapour consists only of C. This shall e.g. be the ease when A and / are two salts and Ca solvent, as water, alcohol, benzene, ete. Theoretically the vapour consists always of A+ B+ C; the quantity of A and 4, however, is generally exceedingly small, compared with the quantity of C, so that the vapour consists prac- tically completely of C. When, however, we consider complexes in the immediate vicinity of the side AZ, circumstances change. A complex or a_ liquid situated on this side has viz. always a vapourpressure, although this is sometimes inmeasurably small; consequently there is also always a vapour, consisting only of A+ 45 without C. When we take a complex in the immediate vicinity of the side AZ, the quantity of C' in the vapour is, therefore, yet also exceedingly small in comparison with the quantity of A+ Sb. Considering equilibria, not situated in the vicinity of the side AB, we may, therefore, assume that the vapour consists only of C; when, however, these equilibria are situated in the immediate vicinity of the side AA, we must also take into consideration the volatility of A and # and we must consider the vapour as ternary. Considering only the oceurrence of liquid and gas, as we have formerly seen, three regions may occur, viz. the gasregion, the liquid-region and the region L—G. This last region is separated from the liquid-region by the liquid-curve and from the vapour-region by the vapourcurve. As long as the liquid-curve is not situated in the immediate vicinity of AZ, this last curve, as a definite vapour of the vapour- curve is in equilibrium with each liquid of the liquid-curve, will be situated in the immediate vicinity of the anglepoint C. Therefore, the gas-region is exceedingly small and is reduced, just as the gas- curve, practically to the point C. Consequently we distinguish within the triangle practically only two regions, which are separated by the liquid-curve, viz. the liquid-region and the region L—G ; the first reaches to the side AZ, the last to the anglepoint C. The conjugation- lines liquid-gas come together, therefore, practically all in the point C. When, however, the liquid-curve comes in the immediate vicinity of the side AA, so that there are liquids which contain only exceed- ingly little C, then in the corresponding vapours the quantity of A and & will be large with respect to C. The vapour-curve will 72 then also be sitnated further from the anglepoint C and closer to the side AB, so that also the vapour region is large. At a sufficient decrease of pressure or increase of temperature, the vapour-region shall even cover the whole components-triangle. Consequently it is absolutely necessary that we must distinguish the three regions, of which the movement, occurrence, and disappearance were already formerly treated. When the equilibrium “+ 2+ G occurs, we may now deduce this in the same way as it was done formerly for a ternary vapour. a) The solid substance is a ternary compound or a binary com- pound, which contains the volatile component C. For fixing the ideas we shall assume that in the triangle ABC of fig. 1 which is partly drawn, the point C’ represents water, /’an aqueous doublesalt, #4” and /” binary hydrates. In accordance with our previous general deductions we now find the following. The saturationcurves under their own vapour-pressure are circum- or exphased at temperatures below 7’, (7’,—= minimum meltingpoint of the solid substance under consideration). The corresponding vapour- curves are reduced to the point C. When these substances melt with Fig. 1, increase of velume, the points //, H’ and //’ are situated with respect to /, #”’ and F" as in fig. 1; when they melt with decrease of volume, these points are situated on the other side. 73 In fig. 1 different saturationcurves are completely or partly drawn ; the pressure increases along them in the direction of the arrows. Further it is apparent that along the saturationcurve of /’ the pressure is maximum or minimum in its points of intersection with the line CF; the point of maximumpressure is situated closest to C. On the curve bcdihg of fig: 1, which is only partly drawn, c is, therefore, a point of maximum-, 4 a point of minimumpressure. The pressure along a saturationcurve of the binary hydrate /” (or #'") is highest in the one and lowest in the other end, without being however in these terminating points maximum or minimum. On the curve abg/f of fig. 1 which is only partly drawn, the pressure in @ is the highest and in / the lowest. This is also in accordance with the rule, formerly deduced, that the pressure is maximum or minimum, when the phases /’, 4, and ( are situated on a straight line, but that this is no more the case when this line coincides with a side of the triangle. As the vapour has always the composition C here the point of maximum- and that of minimumpressure of the saturationcurve of / are, therefore, always situated on the line C#’; the saturationcurves of F’ and F" can, however, not have a point of maximum- or minimum-pressure. As we may obtain all solutions of the line Ch (CB and CA) by adding water to / (F” and F'") or removing water from /’ (/” and F'"), we shall call the solutions of Ch (CB and CA) pure solutions of # (#” and Ff"). Further we eall the solutions of C H/ (CH’ and CA") rich in water and those of Hh (H’B and H"A) solutions poor in water. Consequently in fig. 1 a, ¢ and e represent pure solutions rich in water and f, 4 and & pure solutions poor in water. We may express now the above in the following way : Of all solutions saturated at constant 7’ with a binary or ternary hydrate, the pure solution rich in water has the greatest and the pure solution poor in water the lowest vapourpressure. Therefore, the pressure increases along the saturationcurve from the pure solution poor in water towards the pure solution rich in water. When the solid substance is a ternary hydrate, the highest pressure is at the same time a maximum- and the lowest pressure also a minimum pressure, We see that this is in accordance with the direction of the arrows Vay jot Ale 6) The solid substance is the component A or / ora binary com- pound of A and £4; therefore, it does not contain the volatile com- ponent C. 7+ In fig. 2 some saturationcurves under their own vapourpressure of A (ak, blem,on) and of B (hi,g lfm, pn) are completely or partly drawn. When in one of the binary systems, e.g. in CB, there exists a point of maximumtemperature H’, then also there occur saturationcurves as the dotted curve gi. As long as we consider solutions, not situated in the vicinity of AB, the vapour region is represented by point C. When we consider, however, also solutions in the vicinity of A 4, the vapour region expands over the triangle. Consequently, when we de- duce the — saturationeurves under their own vapour-pres- sure, assuming that the vapour is represented by C, we may do this only for solutions, not situated in the vicinity of AB. For points of the curves in the vicinity of AL we take the case, treated already in communi- cation XIII that the vapour is ternary. The same applies, as H’ is situated in the vicinity of 5, also to the curves in the vicinity of H’. If follows from the deduction of the saturationcurves that the pressure, e.g. along a, continues to decrease from a; only in the vicinity of 2, a point of minimumpressure may perhaps be situated. As the pressure in 6 and consequently also in the minimum possibly occurring is exceedingly small and practically zero, we can say: along tae saturationcurve of a component the pressure increases from the solution free from water (4) towards the pure solution (q). The pressure of the solution free from water is practically zero. Let us now take a binary compound of A and # (for instanee an anhydric double-salt); it may be imagined in fig. 2 to be repre- sented by a point # on AL. When we leave out of account satura- tioncurves in the vicinity of #, we may say that the saturation- curves under their own vapourpressure have two terminatingpoints, both situated on AS. As the pressure is again very small in both the {terminatingpoints, it follows: along the saturationcurve of an anhydric doubdle-salt, the pressure increases from each of the solutions free from water towards the pure solution. c) The solid substance contains the volatile component C' only. This is for instance the case when an aqueous solution of two io salts is in equilibrium with ice; the saturation- or icecurve under its Own vapourpressure has then, as curve ed in fig. 2, one ter- ay minatingpoint on C A and one on C4. We find further: along an icecurve under its Own vapourpressure the pressure is the same in all points and it is equal to the pressure of sublimation of the ice. We may deduce the previous results also in the following way. As the vapour consists only of C, we equate, in order to find the conditions of equilibrium for the system /-+ 4+ G in (1) (Il) Zo—OLand 7v— 0. We then find: OZ Lb Z—3 Z IZ WA a eet and Z.-pe. apipey sr aa Fey se ee GL) y For the saturationcurve of / under its own vapourpressure we find : (Gop saa (Gist) O,j—— Giddens by (2) (art Bs\de+t(astBddy=—(A+tOdP .. .¢ which relations fellow also immediately from 8 (II) and 9 (II). In order that the pressure in a point of this curve should be maximum or minimum, dP must be = 0. This can be the case only, when COP SS MRS oe ee ere eo (GH) This means that the liquid is situated in the point of intersection of the curve with the line CF’, consequently, that the liquid is a pure solution of /’. Consequently we find: along a saturationcurve under its Own vapourpressure of a ternary substance, the pressure is maximum or minimum in the pure solutions. In order to examine for which of the two pure solutions the pressure is maximum and for which it is minimum, we add to the first part ef (2) still the expressions : 1 Or 108 1 Or Os snd : Ose SOL sy? 3’ pas +y = a 1 (stots I, 7) vdy +-— 2( 1 Lo 5, } ye. and to the first term of (38): 1 Or ac is ony ate Pedy 1 Ose me ee 3 Biv + | a da~ +- oy +- { a dudy +4 9 («5. + | 5.) dy? + . Now we subtract (2) from (3), after that (2) is multiplied by «& and (3) by w. Substituting further their values for A and ¢ " we find: 1 5 (rda* +- 2sdedy + tdy’) = [(e—a) V, + a V—avjdP. . (5) ra Representing the change of volume, when one quantity of vapour 76 arises at the reaction between the phases F, LZ and G, by AV, (5) passes into: 1 5 @(rde* 4 Asdady + tdy*) = (c—a) AV, X 0. Considering only the solutions of the line Ch, we can consider the system “+ L-+ G as binary. Imagining a P,7-diagram of this system, // is the point of maximum- temperature. From this it is apparent that AV, is negative between H and F, positive in the other points of the line Ch. From this it follows: : (e—a) AV, is negative in points between C and H, therefore for the solutions of /” rich in water. (a—a) QV, is positive in the other points of this line, therefore, for the solutions of /° poor in water. The same applies also when the point // is situated on the other side of Let us take now a pure solution rich in water of /’, for instance solution c of the fig. 1; as the first term of (6) is positive and (a—a) AV, is negative. it follows: dP is negative. This means that the pressure is a Maximum in ¢. When we take a pure solution poor in water of /’, for instance solution h of figure 1, (e—a)AV, is positive, therefore, the pressure is a minimum in h. In accordance with the previous considerations, we find, there- fore, that the pressure along the saturationcurve of a ternary com- pound is a minimum for the pure solution poor in water and a maximum for the pure solution rich in water. When the solid substance is a binary compound, as /” in fig. 1 or 3, we must equate «=O. (Of course 3 =O for the compound F’"). (2) and (3) pass now into: (wr + ys) dx + (as + yt)dy=-—CdP . . . 2) Bsda + pidy = —(A + @)\dR, 2 2 es) From this we find: Bu (rt — s*) da =[(as + yt)(A + C) —BC))dP . . . (9) From this it is apparent that dP? can never be zero or in other words: on the saturationcurve of a binary hydrate never a point of maximum- or of minimumpressure can occur. In the terminatingpoint of a saturationcurve on BC« =0; as j 7 Lim it while ¢ and s remain finite, it follows, when we & replace also A and C' by their values: Bee da — || — 8) Veep —yoee. s 2=. (10) Representing by AV, the change of volume, when one quantity of vapour arises at the reaction between the three phases (#”, L and (G), (10) passes into: BRL edec — (y — PB) A VeriOve b= gee eeeaNes. 6 (1h) For solutions between C and /” is y— <0, between /” and B is 1—gs>O0. Imagining a P,7-diagram of the binary system hr t+L+G, H’ is the point of maximum temperature; A’, is consequently negative between //’ and /”, positive in the other points of C4. From this it follows: (y — Bp) AV, is negative in points between C' and //’, therefore, for the solutions rich in water; (y—~) AV, is positive in points between //’ and #, therefore for the solutions of #” poor in water. From (11) it now follows: dP is negative for liquids on CH’, positive for liquids on H’. In accordance with our former results consequently we find: along the saturationcurve of a binary hydrate the pressure increases from the pure solution poor in water towards the pure solution rich in water. When /° is one of the components, which are not volatile, e.g. B in fig. 2, then a=O and B=1. From (11) then follows: RT .d«e =(y — NN AWA 5 CHE arama oo (12) We now imagine a P,7-diagram of the binary system B+ 1+G; this may have either a point of maximumtemperature //’ in the vicinity of the point 4 or not. When a similar point does not exist, AV, is always positive; when a similar point does exist, AV, is positive between C’ and #1’, negative between H’ and B. As we leave, however, here out of account points, situated in the vicinity of B, AV, is positive. As y—1 is always negative, it follows from (12) that dP is negative. In avcordance with our former results we find therefore: along the saturationcurve of a component the pressure decreases from the pure solution towards the solution free from water. When F is the volatile component, as for instance in the equili- brium tce+ L+G, then «=O and B=O. The second of the con- ditions of equilibrium (1) passes now into: Z =. This means that not a whole series of pressures belongs to a given temperature, but only one definite pressure, viz. the pressure of sublimation of the ice. Therefore we find again: along an icecurve under its own ke) Vapour pressure the pressure is the same in all points and equal to the pressure of sublimation of the ice. Now we shall consider the boilingpointcurves; in general the same applies to them as to the saturationecnrves under their own vapourpressure, which we have considered above. Now we assume that the curves in fig. 1 represent boilingpoint- curves; the point /7 no longer represents a point of maximum temperature, but a point of maximum pressure ; consequently it is always situated between C and #. This point of maximumpressure His always situated closer to C' than the point of maximum tem- perature /7; the same applies to the points #7’ and #" in the figs. 2 and 8. Wishing to indieate by arrows the direetion in which the temperature increases, we must give the opposite direction to the arrows in the figs. 1—3s. We saw before that on the side CB of fig. 2 a point of maxi- mumtemperature /7/’ may either occur or not; on this side, however, always a point of maximumpressure is situated. The same applies to the side C'A. We now find the following. a) of all solutions saturated under constant P with a binary or ternary hydrate, the pure solution rich in water has the lowest — and the pure solution poor in water the highest boilingpoint. There- fore, the boilingpoint inereases along the boilingpointeurve from the pure solution rich in water towards the pure solution poor in water. When the solid substance is a ternary hydrate, the highest boiling- point is at the same time a maximum- and the lowest at the same time a minimumboilingpoint. 6) along the boilingpointeurve of a component or of an anhydrie double-salt the boilingpoint increases from the pure solution. When the solid substance is an anhydrie double-salt, the boilingpoint of the pure solution is at the same time a minimum. c) along the curve of the solutions saturated with ice under a constant pressure the boilingpoint is the same in all the points and it is equal to the sublimationpoint of the ice. The icecurve under its Own vapourpressure of the temperature 7’ and the boilingpointeurve of the ice under the pressure P coincide, therefore, when / is the pressure of sublimation of the ice at the temperature 7. The following is amongst others apparent from what precedes. We take a pure solution of a solid substance (component, binary or ternary compound). Through this solution pass a saturationcurve Us) under its Own vapourpressire and a boilingpointcurve. Generally we now have: when the vapour pressure at a constant 7’ decreases (or increases) from the pure solution, the boilingpoint under a constant P will increase (or decrease). This, however, is no more the case for solutions between the point of maximumpressure and the point of maximumtemperature. The point of maximumpressure is situated viz. closer to the point C than the point of maximumfemperature. When we take a solution between these points, it is a solution rich in water with respect to the saturationcurve under its own vapourpressure, & solution poor in water, however, with respect to the boilingpointeurve. Consequently as well the pressure along the saturationcurve as the temperature along the boilingpointcurve will decrease from this solution. We may express the foregoing also in the following way: the vapourpressure (at constant 7’) and the boilingpoint (ander. constant P) change from a pure solution generally in opposite directions. When, however, the pure solution is situated between the point of maximumpressure and the point of maximumtemperature, then as well the vapourpressure as the boilingpoint decrease from this solution. Formerly we have already considered the saturationcurve under its Own vapourpressure of two solid substances (viz. the equilibrium P+ Fk’ + L+ G); now we shall discuss some points more in detail. It should be kept in niind in this ease that all deductions apply also now to points, which are not situated in the vicinity of AB. The deductions discussed already formerly apply to points in the vicinity of this line. Let us take the solution m of fig. 2 saturated with A+B, ihere- fore, the equilibrium A+ 6-+ Z,,-+ G. As the pressure increases from m towards ¢ and towards /, we may say: the solution saturated with two components has a smaller vapourpressure than the pure solution of each of the components separately. When we consider the solution p of fig. 2 saturated with ice +A and when we imagine curve np to be extended up to CA, it appears: the solution saturated with 7ce-+ A has a greater vapourpressure than the solution saturated with A—+ / and a smaller vapourpressure than the metastable pure solution of A. In the previous communication we have already discussed the curves zu, 2v,and zw; 2 represents the solutions of the equilibrium A+65+L+G, zw those. of the equilibrium tee + A+ L+ G and zv these of the equilibrium tce+ B+ + G, w and v are binary, < is the ternary eryohydric point under its own vapourpressure. 50 Let us now contemplate the solution m of fig. 3 saturated with the hydrates 7+ /”; it is apparent from the figure that solution m has a smaller vapourpressure than 7 or n. When we take however Cw wn eek aa Cc the solution 4, saturated with these hydrates, this has a larger vapourpressure than the solutions @ and ce. Curve pq represents the solutions of the equilibrium #4 #”-++-L-+G; point HZ is the point of maximumtemperature of this curve. In accordance with our previous definitions we call the liquids of branch pH vich in water and those of branch //q poor in water. We then may express what precedes in this way: the solution saturated with two components or with their hydrates has in the region rich in water always a smaller vapourpressure, in «he region poor in water always a greater vapourpressure than the pure solution of each of the substances separately. Let us now take a liquid saturated with a double salt and one of its limit-substances. [In fig. 1 the series of solutions saturated with /’ of curve bed is limited in 6 by the occurrence of F” and in d by the occurrence of /'". Therefore we shall call 7” and #" the limit-substances of the double-salt /’). Curve po represents the solutions of the equilibrium /’-+ 4” + L-+ G, curve og those of the equilibrium #” + F+ + G and curve o7 those of the equili- brum F"+F+4+2-+G. M and M’ are points of maximum- temperature of these curves. In accordance with previous definitions we call solutions of o//7 and oJ’ rich in water and those of Mg and J//7 poor in water. 81 The following is apparent from the direction of the arrows in how AP a. In the region of the liquids rich in water. When a doublesalt is soluble in water without decomposition, the solution saturated with this double-salt and with one of ifs limit-substances has a smaller vapourpressure than the pure solution of the doublesalt and also than that of the limit-substance. When a double-salt is decomposed by water, the solution saturated with this double-salt and one of its limit-substances has a smaller Vapour pressure than the pure solution of the limit-substanece. The solution saturated with double-salt and with the limit-substanee, which is not separated, has a smaller vapour-pressure than the solution, saturated with double-salt and with the limit-substance, which is separated. 6. In the region of the liquids poor in water the opposite takes place. As a special case a liquid can be saturated with two substances of such a composition, that one of these may be formed from the other by addition of water. They are represented then by two points /” and #”, which are situated with C on a straight line. In fig. 4 this line CF does not coincide with one side of the triangle. In this figure aec f is a saturationcurve under its Own vapourpressure of /’, curve bedf one of F’; the arrows indicate the direction, in) which the pressure increases. Both the Fig. 4. curves can be circum- or exphased and they either intersect or they do not. In fig. 4 they intersect in e and f/f, so that the equilibria #” + #” + L. + G and F+ Ff’ + Lr+G occur. Now we can prove that the vapour pressure of those two equilibria is the same, therefore P= Pr. When we remove viz. the liquid from both the equilibria, we retain r+ Fk’ +G. As between these three phases the reaction */’+G is possible, we can consider /’+ #” + G as a binary system. We then have two components in three phases, so that the equilibrium is monovariant. At each temperature /’+ /” +- G has, therefore, only one definite vapourpressure, from which immediately follows : ips ad ee 6 Proceedings Royal Acad. Amsterdam. Vol. XVII. 82 Curve gehfk in fig. 4 indicates the solution of the equilibrium FtrF+t+L+G; when in a P, 7-diagram we draw‘the curve r+ F’ + G@ (consequently the curve of inversion /Z /” -+ G) and eurve /} + 7” + L+ G, then they coincide. In fig. 5 the line CFF” coincides with the side BC of the triangle ; We assume viz. that the component B and its hydrate /” occur as solid substances; further we have also assumed that the component A occurs as solid substance. The curves be, fy and th are saturation- curves under their own vapourpressure of A, th and ef of B, ab and de of the hydrate /’; the arrows indicate again the direction in which the pressure increases. It is apparent from the figure that vz represents the solutions of the equilibrium A+ /+ L4G, cw those of A+B+L+4G B and zu those of b+ F+4+L-+4G. Consequently in 2 the invariant equili- w brium A+ 6+ F+ 2+ 4 occurs. ; Curve zu terminates on side BC in the quadruplepoint a with the phases B+ F+4 L+G of the binary system CB. When we remove the liquid LZ, from the equilibrium 5+ #7+21,+G occurring at the temperature 7, and C A underthe pressure /’., we retain the mono- (w) a variant binary equilibrium B+ 7G. Fig. 5 When we draw in a P,7-diagram the curve b+F+-G (therefore the curve of inversion / 2 5+-G) and curve B+ f+ L+G, these two curves coincide. We can say, therefore : the vapourpressure of a solution, saturated with a component and with its hydrate, is equal to the pressure of inversion of the hydrate (the pressure of the reaction 2 b-+ G). From the direction of the arrow on de it follows that the pressure in @ is smaller than in d. We can say, therefore : the solution saturated with a component and with one of its hydrates has a lower pressure than the pure solution of the hydrate, The same considerations apply also when two hydrates of a same component occur. We may summarise the previous results in the following way. Through each solution saturated with two solid substances go two saturationcurves; when we limit ourselves to the stable parts of 83 these curves, we may say that two saturationcurves proceed from such a solution. Then we may say : 1. The two solid substances are situated in opposition with respect to the line LG. a. The solution saturated with these substances is rich in water: The pressure increases from this solution along the two satura- tioncurves. 6b. The solution saturated with these substances is poor in water. The pressure decreases from this solution along the two saturation- curves. 2. The two solid substances are situated in conjunction with respect to the line LG. a. The solution saturated with these substances is rich in water. The pressure decreases from this solution along the saturation- curve of that solid substance which is situated closest to the line LG; the pressure increases along the other saturationcurve. 6. The solution saturated with these substances is poor in water. The same as sub 27.; we must take however the changes of pressure in opposite direction. 3. The two solid substances are situated on a straight line with the vapour. The pressure increases from the solution saturated with these sub- stances alone the saturationcurve of the substance with the largest amount of water, it decreases along the saturationcurve of the sub- stance with the smailest amount of water. We find examples of 1¢ in the equilibria : FAR +1,+G (fig 1), F+F"+014+4 (fig. 1), A+B+L,+G4 (figs. 1 and 2), #”+F"-+L,,4+G (tig. 3), A+ B+ ,4G4 (fig. 5) and F+A+L;/+G (fig. 5). We find examples of 1° in the equilibria: 7-+-/”’+-L,+4G (tig. Feu ae et Ga(fies 2) and. P42" by iG (fe. 3): An example of 2“ is found in the equilibrium /-+- /”+ L,+-G (tig. 1). We find examples of 3 in the equilibria: P+/”+21,.4-G (fig. 4), P+’ +Ljy+G (fig. 4) and B4+4+1,4 G (fig. 5). . We may deduce the above-mentioned rules also in the following way. We shall viz., while the temperature remains constant, change the volume of the system M+ /” + L4G, so that a reaction takes place between the phases and there remains at last a three- phase-equilibrium. As this reaction is determined by the position of the four points with respect to one another, we may immediately distinguish the above-mentioned cases 1, 2, and 3. When we eall 6* S4 the change of volume, when one quantity of vapour is formed at the reaction, AJV,, then AJ, is always positive, except when the liquid is represented by a point of the fourphase-curve between the point of maximumtemperature and the intersectingpoint of this curve with the line #/”.-When we now apply the rule: ‘the equilibria, which arise at increase (decrease) of volume, are stable under lower (higher) pressure’, we may easily refind the above-mentioned rules. When we take as an example fig. 38 in which the case sub 1 occurs, the equilibrium /” + /".+ L + G is represented by curve pq, Which intersects the line A’ 7" in WS; 7 is the point of maximum- temperature of this curve. Consequently 4’ is positive on pH and Sq, negative on //S; the solutions of p/ are rich in water, those of Hg poor in water. When we take a liquid rich in water, the reaction is: L2k+k’+4. AV,>0. 4th AG RP’ tL +G4 PAR +G. Retr’ E As the reaction proceeds from left to right with increase of volume (AV, >0), the equilibrium to the right of the vertical line occurs on decrease of pressure and the equilibria to the left of the vertical line oceur on increase of pressure. Therefore, from each point of branch pQ the equilibria /”-+ 1+ G and I'"+ L + G proceed towards higher pressures; consequently we find the rule 1¢. When we take a liquid poor in water, this is situated on /ZS or on Sq. When it is situated on /7S, the above-mentioned reaction applies also, but OV, <0. Therefore, from each point of branch HS the equilibria #’ + 1+ G and #'" + L + G@ proceed towards lower pressures; this is in accordance with rule 1%. When we take a solution of branch Sg, the reaction is: + FY’ S Lt G. AV, >0. M+R A LE Iv tL+G MAR’ AG | FP+AL+G As the reaction proceeds from left to right with increase of volume the equilibria to the right of the line oceur with increase of volume. In accordance with rule 1° we find, therefore, that the equilibria FtL+G and F"4+ L4G proceed from each point of the branch Sq towards lower pressures. Now we have deduced the rules 1¢ and 1? assuming that point #7 is situated on branch pS; we may act in a similar way when point H is situated on branch gS. In a similar way we can also deduce the rules 2 and 3. 85 Considering, instead of the saturationcurves the boiling point curves, the same applies to these in general. We must then replace on the fourphase-curve the point of maximumtemperature by the point of maximum pressure. In fig. 3 besides the point of maximum- temperature H, also the point of maximum-pressure Q is drawn. We imagine further that the saturationcurves are repiaced in the diagrams by boilingpointeurves. We then refind the rules 1, 2, and 3, with this difference, however, that increase of pressure must be replaced by decrease of the boilingpoint and decrease of pressure by increase of the boilingpoint. From each point of the four-phase curve proceed two saturation- curves and two boilingpointecurves. When this solution is to be considered as rich in water or as poor in water with respect to the saturationcurves, it is also the same with respect to the boiling- pointeurves. Only the solutions between the point of maximum- pressure and the point of maximumtemperature make an exception ; these are rich in water when we consider the saturationcurves, poor in water when we consider the boilingpointcurves. Now we find: from a solution saturated with two solid substances the vapour- pressure (along one of the saturationecurves) and the boilingpoint (along the corresponding boilingpointcurve) change generally in opposite direction. When, however, this solution is situated between the point of maximumpressure and the point of maximumtemperature, vapourpressure and boilingpoint change in the same direction. (To be continued). Physics. — “On the thermodynamic potential as a kinetic quantity”. (First part), By Dr. H. Hunsnor. (Communicated by Prof. J. D. VAN DER WAALS). (Communicated in the meeting of April 24, 1914). In a communication published in These Proc. Il p. 889 of Jan. 27 1900°) it has been set forth by me that in the capillary layer the molecular pressure must have a different value in different directions as a direct consequence of the attraction of the particles, whereas the thermic pressure (the sum of the molecular and the 1) I expressly call attention to this date, because some time after, this subject was treated in the same way by a writer who had informed me of his own accord that he was going to publish an article on this subject in the Zeitschrift fiir phys. Chemie, and that he should of course, cite my paper there, but who has failed to do so. 86 internal pressure) must be the same in all directions. Hence a condition oceurs in the capillary layer in which the external pressure in the direction of this layer p, has a quite different value from the pressure normal to this layer p, i.e. the pressure in the homogeneous vapour and liquid phases. In the surface a tension appeared to exist: fo. —p,)dh. The molecular pressure could be easily defined so that the surface tension was in agreement with the capillary energy determined by Prof. vAN per Waats by a thermodynamic way : fee —T,y + p,w—pM)dh, 1 : : : in which ge—=— and v is the volume for a molecular quantity of v MW grams and c, d*o Cy d‘o 2d 4) dh” The two integrals, which must be extended over the full height of the transition layer, are equal, and this is also the case with two p= (6) ao corresponding elements so that: o(e—T\y + p\v—uM) = p,— Pp, from which immediately follows e—T7 yn 4+ pv=ul. * As p,, the pressure in the direction of the capillary layer, has the same value in the homogeneous vapour and liquid phases as p,, it holds for the quantity e— TI, + pyv that i has a constant value both in the homogeneous vapour and liquid phase and in the capillary layer. This property leads us at once to expect that if will play an important part especially for kinetic considerations, and that it will express that the number of particles that two arbitrary phases will exchange in the same time, will be equally great. It will, in fact appear that this quantity makes the capillary layer accessible for the considerations developed by Prof. vax per Waats in his paper on the kinetic significance of the thermodynamical potential. Assuming that really in the direction of the capillary layer the pressure p, is different from the pressure p,, and besides entirely different in different layers, the neglect of this circumstance will make it impossible to derive the thermodynamic conditions of equilibrium for the capillary. layer from kinetic con- 87 siderations. A particle, namely, that begins a new path at some place, is subjected to the influence of the pressure p, prevailing there, and in the layer, where it terminates this path, it is subjected to the in general entirely different pressure p, of this layer. Van per Waals’ first equation runs: a a dmNu,? + pr, — — = 4mNu',? + pu» ——-. - . . (1) v v 1 2 The expression pv, — - = G = ) is for a monatomic fluid the 2 1 heat of evaporation for the molecular weight, «, -+ pr, —(#, + pr,). We shall now have to apply a modification to this equation, when the layers between which the interchange of particles takes place, are taken in the capillary layer. Here we shall have, as it were, an evaporation from a space under the pressure p, towards a space under the pressure p’,, and a condensation in opposed direction. Hence our first equation becomes : = ImNu,,? aL Cs d*9 1 Nu! an teat ' Cy d*o! 1) for all variations of @ and a, which satisty fg dh = constant and fe (1 — x) dh = constant, he found for the variation with respect to @ 89 f(ex)+o af —— a, M, (1-«) — uw, Mx — ¢,, (1-«) diet ae) c, (1-2) Gee — INS ry do ess M243 11 dh? 13 dh? d’o(1-«) Pou eer emi” 75 eee In this f(@z) is the free energy of a homogeneous phase with the w and o existing in /, and hence — MRT log (v—b,z) — ae 4+- MRT \(1—2z) log (1—«) + «@ log 2}. t . t v ‘ s of o an = pv The energy for M, grams of the first ee amounts to eh dc. (1—2) M.. dow é, = C,—a,, 9 (l—2) —4,, 9@ — 3 ¢, un Fe ie a and for J/, grams of the second component : % d°o(1—-2) d* ow &, = C, — a,,0(1—2) —a,, 0 e — $.¢,, ——>—__ — 36 2 dh* anes dh? We get therefore for our equations (1) for the first component : me. ELAN a A ig d* o(l—a ) dou 1m,Nu, ? + ——— — a,,90(1l—e# ox — te -—1¢, —_= et it o (1-2) 118 113 Le dit 219° apa tm, Nul, 2+ se Be Nie ni ay nme Ea OS Ney tan Ni. a @ )—a,,.9 & —3C; Sam 2 iis =e as AGE ian Bi eae ge dh? ; and for the other component: d’o(1-w) doa $m, Nu, Le SEO —z)—a, 29 — SACts aang — Im, Nu', * re n log ae es ee yb, of “URI from which then follows for the first Component in connection with Ge) sama yar) pe =n) note d*o(1-«) \T log =e +- 65) —4,,9 (1-2) -a,,0%-}¢,, 7 d* ow Ore Roce ; : Per } — 3Cr, dh? — MRP log jaa AG o'(1-a") wane (1-a')-a,,g'@ ik (3,) ?9'(1-z') d?9'x' a v — 3¢, dit aga Gays =e, — Tn, eg and for the een component : P 1? o(1-« \ — MRT log - Sow 242 a 4129 »(1-«) —a,, ow —3e paul ae x ox dh? dow Fa eS OE Pate a ; —4¢,,—,,— — MRT log—__ + = 40 1-0) — oh 0 dh a Ou d?o'(1-2') d?o'a' v 21g dhe San Cas dh? 5 Ty, + 5% 2a =o uM, . The expressions : 2 Vv é, — Ty, + 17, ae and é LU v — Ty, + .2, —=u,Y, & have a constant value throughout the vessel. For every component they give us the thermodynamic potential in its kinetical signification. 91 When we now write the value of w.J/,(1—.«)+ yu, Je, we tind for it, at the height of / with density y and concentration « — MRT SU rsdeiag MRT \(1 = x) log (1L—w) + wx log x} +- pv — azo — d*o0(1-«) ; dou ; d*o(1 x) = $og(1—2) ell a Ge 2 Oy gt ii ad’ ox ba VU, (l-«) +m «; for iT, ay == —— 0 Q Q The pressure p, can be expelled from this relation when we consider that p;-+ 4, (molecular pressure in the direction of the capillary layer) =p--a.e*, in which p represents the pressure belonging to an homogeneous phase of the same density and con- centration. In general M, = — 0 fe, — C, (A-—a) — Cyz} holds, in which ¢ = ¢, (1—w) + ¢,7, hence the energy for the quantity of the mixture M, —2) + M,x. Now: 4 d’o(1—z) &; = C, (l—a) + C,z — a9 — }¢,, (1-—«) dh? age +, d?9(1—-x) Pow are) dh? Ne dh? — $450 dh? hence ; Eola, do. SOE) dow i= $C, (1-2) dh? ¥ 4c,,(1- x) — dh? mat} 2 Oya? Ae 5p Qt dh? If this value of p, is introduced, the found relation passes into — MRT log (v —b,) + MRT \(1 —«) log (1—a) + «log x} + pv — arg — d° oe 2) d? ow d*o(1-«) Pox — ¢, (I-2) 72 —¢,, (1-2) dhe ks a dhe meas ae = = uw, (1—2) + u,M,« This relation, which we have derived by means of kinetic consider- ations only, is the first of the two conditions for the equilibrium determined by van Expik by a thermodynamic way. For the two homogeneous phases, which are in equilibrium with each other, the following form holds: —MRTlog(v-b,) + MRT}\(1—a)log(1-«) +- wloge} + pv-a,o=, VM, (1-2) +4, Mya or yw -}+ pv = "MY, (l1—2) + uM. As the kinetie theory teaches that the pressure in the two phases must be constant, it follows immediately from this that: yw — J, (1—2) — vw, Ma — Pr . v 9? Chemistry. — “On the behaviour of gels towards liquids and the vapours thereof.’ Il. By Dr. L. K. Wore and Dr. E. H. Bicuner. (Communicated by Prof. A. F. Honieman). (Communicated in the meeting of April 24, 1914). In continuing the experiments mentioned in our first communi- cation about this subject"), we hit upon two observations which have given us the key to the solution of the problem. Firstly it was found that, when leading saturated water vapour over gelatine which at the same temperature had swollen in water, the weight of the gelatine does not change; secondly it appeared that the amount of decrease with the experiments made in the previously described way — in desiceators according to VAN BreMMELEN — depended upon the size of the desiccator, and besides that in this way of experimenting pure water also lost in weight. These things found, we came to the following conception of von ScHROEDER’Ss phenomenon : 1. the state attained in water vapour is no equilibrium ; even though the quantity of water absorbed does not visibly increase for days and days, one must suppose an extremely slow absorption still to be taking place, at least if the experiment is made in the exact way which will be presently deseribed. However, it may be several years, before the true equilibrium is reached, which in liquid water appears within some days. So the so called vapourequilibrium is only a ‘false equilibrium”. 2. the curve which indicates the connection between the water content and the vapourtension, runs almost horizontally as soon as the point which represents the vapour equilibrium, is passed; the tension being taken as ordinate, the concentration as abscissa. 3. The observation formerly advanced by von ScHroepmur, BANCROFT, and also by us against the hypothesis mentioned under 1, viz. that. the watercontent of gelatine swollen in the liquid. decreased again in vapour, (from which was concluded that the ‘equilibrium’ was attained from two sides), is founded on an unsatisfactory way of experimenting. This conception seems to give a satisfactory explana- tion of the whole of the phenomena; we can support it by a great number of experiments. We shall now first of all treat the proof of the third thesis. As 1) These Proce. 15, 1078 (1912/18). 93 we doubted about the exactness of the method with desiceators, we made experiments in another way. We let a piece of gelatine swell under water until the equilibrium was attained, put it into a U- tube with ground stopeocks, hung this tube in a thermostat, and sucked a stream of air saturated with watervapour through it. In order to fully saturate the air with watervapour, we let it pass in extremely tine bubbles through four tubes of water which were also hanging in the thermostat. We made sure of the vapour really being saturated by placing a U-tube filled with water before the U-tube with gelatine, and by also weighing the former before and after the air had been led through. Nasi Is ke Time Weight of U-tube Weight of U-tube ++ water + gelatine | 30.130 | 30.779 | 24 hours | 30.127 30.781 | Temp. 19°.0 267". | 30.126 | 30.779 | (in thermostat) [Sin | 30.123 30.778 Hts wy tl 30.117 | 30.780 It will be seen, that the gelatine, coutrary to our former experi- ments, showed no decrease of weight: if was in equilibrium and it remained so, and there was not the slightest abnormality. Now which method, the old or the new one, is more reliable ? The answer cannot be dubious, for we succeeded in improving the old method to such an extent that if gives the same results as the new one. Formerly we used to place little dishes of gelatine in a ScHErBl.Er- desiccator, at the bottom of which was some water, and which stood in a room of a fairly constant temperature. In order to exclude the possibility that the water from the gelatine, under the influence of gravity, should distill to the water at the bottom, we have now, instead of pouring the water into the desiccator, placed a dish of water at the same level as that with gelatine. And, thinking of Foorr’s experiments mentioned in our first communication, we also weighed this dish, expecting, of course, that the water lost by th gelatine, should be found back here. However it appeared that both gelatine and water equally decreased in weight; (it is to be noticed that the desiccator was not evacuated). 94 DAB GE MI: Tt a Weight of dish ranean’ Weight of dish Time aaatar decrease + gelatine decrease 47.458 48.391 temp. 22° (room). 24 hours 47.238 .220 48.209 . 182 24k 47.031 207 48.009 . 200 Bs 45.868 163 47.863 . 146 a || 46.5067 | .301 47.525 -338 2nd experiment (three dishes of water). a time weightn9l decrease weight n°2 decrease weight n°3 decrease | | | 81.129 | | 64.399 | 45.888 | temp. 22° | | | (room). 24 hours 80.868 | 261 64.041 scien | heel eat 94 80.601 | 267 63.709 .332 45.291 | .300 We see from this that, in taking the experiment in this way, a dish of water decreases in weight 200 to 800 mG. in 24 hours, and that consequently the experiments thus made with gelatine, do not prove anything whatever. It is not quite easy to say where this water goes to. It might be thought that if serves to saturate the whole space of the desiccator with vapour; but for this a much smaller quantity suffices, 1 L. saturated watervapour of 22° only weighing 19 mG. Nor are differences of temperature probable, because the changes we have found always go in one direction, and because we cannot think why the water in the middle of the desiceator should always be warmer than the walls thereof. Besides the temperature in the room was rather high'), only varying within 0,5°, and so the dishes, after being weighed, would sooner enter colder than warmer. It was also controlled if a loss of weight occurred during the weighing and the preparations for it; by working quickly however, this loss could easily be kept under 1 mG. The only explanations left are, either the watervapour diffuses to the outside, passing through the layer of grease which is between the desiccator and the lid, or water is adsorbed at the great glass surface of the de- siccator. The latter explanation will be most probable, as in smaller 1) Except in two series of table IN), where the differences are equally great all the same. 95 IpAy Bybee eit: Small desiccator of FRESENIUS; temp. room 22°. : weight dish 1 |... weight dish2 | 4.00. Time -P water decrease - water decrease | | 33.798 21.409 | 48 hours) 33.745 053 21.382 | 0.027 Volume of the 48, 33.722 023 21.360 | .022 | desiccator: 700 c.c. dish 3 | dish 4 | + gelatine -++ water | | 31.584 27.566 24 hours) 31.573 O11 27.545 021 240s 31.561 012 27.527 O18 | 24) 4 B1549 eer O12 27.510 O17 120 , 31.505 044 | 27.471 039 water water | ——+ ae ee 31.621 27.834 24hours 31.605 016 27.819 O15 temp. room 14° 24 31.585 020 27.800 | .019 AN 31.565 020 Ditties e023 pee Ae Se i oa gelatine | | 27.764 | Qe | 72hours|) 27.741 .023 | 27.7159 018 temp. room 16°.5 48, 27.724 O17 27.739 .020 | Bell-jar in pail; temp. room 22°, EEE weight of weight of Time weighing-bottle decrease Time weighing-bottle decrease + gelatine -+- water 36.116 40.407 90 hours: 36.052 .064 5 hours 40.411 (-+.004) SOL. anal 36.026 026 48 , 40.250 161 18 | O17 Poth ge 40.122 . 128 » 36.009 Yb desiceators — model Fresenius — we found much smaller decreases, and as we also found a loss of weight when making the experiment differently. A glass bell-jar, in which was hanging a weighing-bottle with gelatine swollen in water, was partly placed ina pail of water, so that the gelatine remained some em. above the water surface. There can here be no question of diffusion to the outside. Yet the adsorption hypothesis is not without its difficulties; for in taking the above mentioned experiments the desiccator or the belljar were first well rinsed out and moistened with water, so that one should think the glass surface to be entirely covered with a layer of water. Perhaps the two last mentioned causes of decrease of weight are cooperating. Whatever may be the cause of decrease, we can distinctly see by this able that both water and swollen gelatine decrease. So if we wished to really confirm voN ScHroEDER’s observation, we first ought to have an arrangement with which water only does not diminish in weight. A series of experiments, undertaken in consequence of Foorr’s communieation which has been mentioned before several times, will illustrate how hard it is to make exact observations by the statical method. In a glass tube were two small tubes filled with water above one another, which had been weighed before. The tube was closed with a rubberstopper or it was sealed in the flame, and then placed in a thermostat; after two days the tube was opened, and the little tubes were quickly put in weighing bottles, and were weighed. PAS Bees EMV: | | “an himey ete lowet ‘decrease | Welg BtUBper | decrease | 22.098 24.000 48 hours 22.090 | -008 | 23.992 | 008 temp. 18°.0 48, 22.081 009 | 23.980 | .012 rubberstopper ond experiment. | 22.060 23.923 48, | 22.051 | .009 | 23.918 | .005 | id. id. 3rd experiment. 10.108 | | 36.289 | | AB 10.098 010 36.244 045 | sealed of So we again found a decrease of weight in all cases, be it less than with the experiments made before. As the amounts are so much smaller here, another circumstance, except the one of adsorption at the glass walls, must be taken into consideration, which, as we have found with the apparatus presently to be described, can account for differences to an amount of some mG.!) The tubes were opened outside the thermostat; the outer’ walls then cooled down a few degrees, while the inner tubes remained a litthke warmer. In those few moments a small quantity of water could distill to the wall of the great tube, and this may be the cause of the loss of weight. Now in order to exelude adsorption we have passed on to another arrangement. We had a cylindrical box made of brass (measures: diameter 7.5 em., height 7.5 em., volume 320 ¢.c.), which was closed by an exactly fitting brass lid that could be still more strongly fixed on by screws. Both the box and the lid were silvered at. the inside. The apparatus was entirely plunged into a thermostat, kept constant within O°.1. In this apparatus too we began with weighing- bottles, which only contained water; we again had to state a loss of weight. With these experiments the vessel was taken out of the thermostat, and was quickly unscrewed after which the weighine- bottles were taken out and weighed with their stoppers closed. When a closed weighing-bottle with water was placed in the vessel, the weight remained constant; when taking if out, some sheht moisture was to be seen against the stopper. A refrigeration evidently took place here, by a colder stream of air entering when the lid was taken off. In order to avoid this as much as possible, we placed the apparatus rather high in the thermostat; when it had to be opened we made the water run out of the thermostat through a siphon, so far that the lid appeared just above the watersurface. Meanwhile the screws were unscrewed so that the lid could be taken off as soon as it was above the waterlevel; in this way the whole kept the same temperature until the very last moment. The then obtained results were satisfactory (ep. table V), and we there- fore repeated our experiments with gelatine-water, agar-water, and celloidin-aleohol in this way. From these experiments we learn that gelatine, agar, and celloidin swollen in a liquid, do not undergo a loss of weight when placed in saturated vapour, if the experiment is made rigorously. The results with the celloidin-aleohol system are not so good as with the others, it is true, but the decrease which reached an amount of 1O0—200 ') The greater difference in the upper tube of the 5rd experiment is evidently due to the heating during the sealing process. Proceedings Royal Acad. Amsterdam. Vol. XVII 98 TAY BLEW. Temperature 19°.0; weighings every 24 hours. weight of weighing- |... | weight of weighing- bottle 1 -+- water decreas] bottle 2-+- water decreas 26.045 25.096 Ist series water | 26.033 .012 25.088 008 vessel opened outside the 26.025 008 25.081 007 thermostat | 26.012 013 25.069 .012 2nd series ; 2 rarer 25.772 27.837 vessel opened c ; 97 @ in the thermostat 25-1168 004 ay Eos 003 | weighing- bottle | + gelatine 20.136 The gelatine had been 90:13 wa swelling for a fortnight in Beit exaas Wess) ; | water at a temperature of Pate ae 20.135 0 19°.0, and had been dried gelatine with filter paper before the | 20.135 | 0 experiment. | 20.133 -002 (after 3>< 24 hours). | | | Temperature 21°.4. 24.575 | Mls arine Da AN | The agar had been swel- ALN | BOE | (+ -005) | ting for 8 days under water agar 24.582 | (+ .002) | at the same temperature, and had been dried as said above. | 24.581 | .001 | Temperature 21°.4 3 SEEEREEeaeiemeed NO, | NO, 2 No. 3 N°. 4 | | | | | | | | | 12.202 12.122 | | 12.389 | 11.310 | 5th series | | | | after celloidin- | 12.200 | .002 | 12.108 | .014 | 12.379 010 304 | .006 | 42 hours alcohol 12.095 | .013 | 12.370 Ne | 11.301 | AGO || ES Temperature 0°, | 12.248 12.115 | 12.397 | | | I | | 6th series) 12.255 | (+.007) | 12.113 | .002 | 12.399 | (+.002) | after 61 hours celloidin | 12.249 .006 | 12.109 | .004 | 12.396 20033] ins & | | 12.249 | 0 0 12.395 | S001) 24 > 12.109 | | { 99 mG. with the old method, has been reduced to some mG. only ; we must herewith remember that the vapour tension of alcohol is considerably greater than that of water. Therefore the 6" series of experiments was undertaken at 0°; according to our expectations the results were better than at 21.4°. The experiments communicated here have taken away every actual ground of existence from the opinion expressed first by von ScHRoEDER, viz. that here was a conflict with the second law of thermodynamies; the second law, as one might think, remains untouched. Of course the phenomenon of several substances swelling more in liquids than in vapours, remains; but we think this can be sufficiently explained by assuming that the absorption in vapour occurs extremely slowly in the end. We have also investigated if not totally swollen geiatine and celloidin placed in vapour, would absorb more water in our new apparatus, and would come to the real equilibrium. This appeared not to be the case; e.g. with gelatine of the following compositions: 1 gelatine to 26 parts of water (in weight); 1:24,2; 1:18,8; 1:15,8; 1:6,5, (the ‘false vapourequilibrium’” is about 1: 0.7) no change of weight was found for five days’). So it goes without saying that the absorption takes place exceedingly slowly. This is most probably connected with the fact that the vapour tension of gelatine (and numerous other substances) is already very near to that of pure water when they have only absorbed a rather small quantity of water*); consequently all the further water absorp- tion of any importance is only of slight inflaenee upon the vapour tension. Or in other terms, the difference of the vapourtension of pure water and of gelatine in “vapourequilibrium” is very small, and consequently the absorption velocity will also be very small. That it is yet very great in liquid water, may be easily explained from the density which is 50000 times greater. We just wish to state that the determinations meant here have ail been obtained by the statical method, the deficiency of which we have proved; a true opinion can only be possible if the experiments are taken along the dynamical way‘), and if the real equilibrium has been proved by placing the jellies alternately in vapour of higher and lower tension. The values given for the composition of the substances swollen in the vapour of pure water are never true ‘') These experiments were also made in the dynamical method with U-tubes, yielding the same result. ») Katz, these Proc. 18, 958 (1910/11). 5) Or m the apparatus described above. 100 equilibria; one ought to state the value which is attained in liquid water °). The explanation of the phenomenon becomes somewhat different, if we do not let the gelatine (ecelloidin) swell in pure water (alcohol) but in solutions. In case of the dissolved substance being volatile (example: celloidin-aleohol-water), the circumstances are exactly the same as above mentioned; but, if the substance is e.g. a salt, the thing changes. Von Scurogper has made some experiments about this question, and he ascertains that '/,,,,,,-"norm. sulphate solution already lowers the vapourtension of gelatine so much, that there is not even a decrease in vapour, but an increase. After the results deseribed above, voN ScurorpEr’s argument loses all weight, and his result is sure to be due to chance. . It is a fact we have repeatedly observed, that gelatine (celloidin) which had swollen in the vapour of a salt solution (NaCl in water, resp. HeCl, in alcohol) absorbs much more still, when brought ito the liquid; 1 Gr. celloidin e.g. gains 1,77 Gr. in weight in a solution of 4°/, sublimate in alcohol of 96°/,, whereas only 0.89 Gr. is absorbed in the vapour of aleohol, and consequently still less in the vapour of a solution in alcohol. The difference between the swelling in a pure liquid and in a solution finds its cause in a substance, when in the vapour of a solution, never being able to absorb anything but the solvent, as long as the dissolved substance is not volatile; when placed in the liquid itself, it also absorbs the dissolved substance. This is a wellknown fact about gelatine; we have ascertained by the experiments with celloidin mentioned above, that this substance too had not only absorbed alcohol, but also sublimate. So in these cases it is clear for other reasons, that a substance swollen in vapour, when brought into the liquid) phase, must still absorb more, and that the state attained in vapour is not a true equilibrium’). In vapour e.g. celloidin passes into celloidin + alcohol, until the vapour- tension of this phase has become equal to that of the liquid phase: alcohol + HgCl,. Now if one brings the celloidin phase under the liquid, the HgCl, diffuses into the celloidin; diminishes so to say the vapourtension of the alcohol which is contained therein, and consequently a furtber absorption of alcohol must take place. If we 1) Strictly speaking one must not speak of pure water, but of a saturated solution of gelatine, agar ete. in water; of course, the difference really is exceedingly minute. 2) Cf. Totman’s views, J. Amer. Chem. Soc. 35, 307 (1913). We have assumed with ToLMAN that every substance evaporates somewhat, no matter how little; if one objects to this, one must speak of an equilibrium which lies differently in consequence of passive resistances (GIBBS). 101 represent this by a figure, we obtain in the vapour a state @; and after this the state 6 is reached in the liquid along an exactly horizontal line, for the vapourtension remains absolutely the same ; only the composition of the celloidin changes. @ lies of course at a lower pressure than «@ in the figure, which stands for pure alcohol; in the latter ab’ is only approximately horizontal. iE : oy b 2 XK It is evident that in this case the greater absorption in the liquid must be connected with the solubility of the salt in the gelatine or celloidin. According to the colloid absorbing more salt, the difference between the vapour and the liquid equilibrium will be all the greater. We believe a closer study of this subject may probably bear fruit with a view to the knowledge of the behaviour of jellies in different solutions. We intend to start experiments about this with celloidin, which, as to stability, has great advantages over gelatine with which suchlike experiments have been made up to the present’). We do not consider skinpowder an ideal substance for this purpose either *). As a summary we think, we can say that the pretended conflict with the second law of thermodynamics has been put an end to, and that von Scurogper’s phenomenon in the principal case is due to a slowly coming equilibrium; one may expect it in all cases where the vapourtension already approaches the tension of the pure liquid very nearly, a long time before the equilibrium has been attained. If the liquid absorbed is a solution of a nonvolatile sub- stance, another explanation must be given. Path. Anat. and Inorg. Chem. Lab. University of Amsterdam. 1) HormeEIsTER, among others. *) Herzog and Apuor, Koll. Zeitschr. 2, Supplem. heft 2, (1908). 102 Mathematics. -- “The quidruple involution of the cotangential points ef a cubic pencil.” By Professor Jan pe Vries. (Communicated in the meeting of April 24, 1914). 1. We consider a pencil of cubies (v*), with the nine base-points 4,. On the curve gv’, passing through an arbitrary point P, lie three points P’,P",P", which have the tangential point’) in common with P; in this way the points of the plane may be arranged in qua- druples of an involution (P) of cotangential points. We shall suppose, that the pencil is general, consequently contains fivelve eurves with a node D,;. On such a curve dé all the groups of the (P*) consist of two cotangential points and the point D, which must be counted twice. Apparently the 12 points ) are the only coincidences of the involution; as the connector of the neighbouring points of D is quite indetinite, the coincidences have no detinite support. The points Dy are at the same time to be considered as singular points ; to each of them an involution of pairs P,P’ is associated, lying on the curve J),*, which has D, as node. 2. The nine base-points Br are also singular; to each point Lb, a triple involution of points 2”, P", P" is associated, lying on a curve B,, of which we are going to determine the order. To each curve g* we associate the line 6, which touches it in B; in consequence of which a projectivity arises between the pencil of rays (b) and the eubie pencil (*). The curve tr produced is the locus of the tangential points of B (tangential curve of B). The line 6, which touches a g* in £#, cuts it moreover in the tangential point of B; this is apparently the only point that 6 has in common with +r’ apart from B. So rt! has a triple point in By there ave three lines 6, which have in # three points in common with the corresponding curve g*; i.e. B is point of inflection of three curves g* Let us now consider the tangential curves rt‘, and t*,, belonging to b consequently have apart from the peints 4, three points in common ; , and #,. Both pass through the remaining seven base-points, so there are three curves g*, on which B, and 4, have the same tangential point. Hence it ensues that the singular curve 3, belonging io B,, has triple points in each of the remaining eight points Bb; it does not pass through 2B, because (/') has coincidences in D, 1) The ¢angential point of P is the intersection of 9% with the straight line touching it in P. L038 only. With an arbitrary g*, 3, has moreover in common the three points which form a quadruple with 4, ; consequently 27 points in all. So the triplets of (P') belonging to 4, lie on a curve of order nine, Which passes three times through each of the remaining base-points. We found that 5, and 4, belong to three quadruples; the three pairs, which those quadruples contain besides, belong to the singular curves 3,’ and ~#,°. They have moreover in the seven remaining points 5;, 63 points in common; the remaining 12 common points are found in the singular points Dy. 3. The locus of the points of inflection / of (~*) has triple points in Br, has therefore with an arbitrary v*, 9 x 3+ 9 = 36 points in common; it is consequently a curve of order twelve, v?. On a curve d* lie only 3 points of inflection ; we conclude from this, that v= has nodes in the twelve points DY, ; in each of those points «4 and d* have the same tangents. The points P’, P', P'", which have / as tangential point, lie in a straight line, the harmonic polar line h of I. So e* is the locus of the points, which in (77) are associated to dinear triplets. The curves p,° and <«* have in the singular poiits LB and D 8 x 37-12 x 2=96 points in common; on @,’ lie therefore 12 points 7, so that B, belongs to 12 linear triplets. From this it ensues by the way, that the involution (/*) lying on p,° has a curve of involution (p) of class twelve; tor the line p= P’P" will only pass ~ through B, if P" is a point of inflection, while P lies in 4,. As B, is point of inflection of three g*, (P*) has three linear triplets, consequently (p),, three triple tangents. The locus 2 of the linear triplets has, as was shown, 9 dodecuple points B; as g* bears nine points of inflection, therefore 9 linear triplets, it has with 4 9 >¢ 12-49 < 38=1385 points in common. Consequently the linear triplets lie on a curve 2". 4. We shall now consider the curve g, into which a straight line ¢ is transformed, if a point P of 7 is replaced by the points P’, which form a quadruple with ?; for the sake of brevity we shall speak of the transformation (P, P’). If we pay attention to the intersections of 7 with ?;” and with d,°, we arrive at the conclusion that @ has nonuple points in B, and triple points in Dy. It has therefore with a gy in 4, 81 points in common; further these curves cut moreover in the three triplets which correspond with the intersections of ? and 7. Consequently 9 is a curve of order thirty. 104 On an arbitrary straight line lie therefore fifteen pairs of cotangential poms. By the transformation (P, ?’), the curve 2", which contains the linear triplets, is transformed into a figure of order 1350. It consists of twice 2 itself, three times «, twelve times the curves B® and seven times the singular curves d*. For 2 x 45+3 «12+4+9x 12 < 91098; the points PD produce therefore a figure of order 252. From this it ensues that 4** has septup/e points in the 12 singular points D. The pairs P, P’, which are collinear with a point &, lie on a eurve «*, on which / is a triple point; the tangents in # go to the points of the triplet of the (P'), determined by /. The line HA, cuts p,’ in 9 points P, which form with 4; pairs of the (/*) ; hence e* has nonuple points in By. The locus of the pairs P", P", belonging to the pairs P, P’ of e'’, we shall indicate by «,. As # is collinear with 12 pairs of the involution (/*) lying on 2,°, B, is a dodecuple point of &,. On an arbitrary g* the cotangential points form three involutions of pairs and the supports of the pairs of each of those involutions envelop a curve of class three (curve of Cayiny). Consequently 1 is collinear with 9 pairs P, P' of ~’, and this curve contains 9 pairs of s. As the two curves in 4; have moreover 9 >< 12 points in common, consequently 126 points in all, e is a curve of order 42. The curves ¢** and B,° have in the points 5,(4==1)8 x9 3 points in common; moreover they meet in 9 points of #4, and in the 12 pairs P, P' mentioned above. The remaining 48 common points must lie in D,; so e* has quadruple points in the 12 singular points D. The curves «,‘? and 8° have in By (k==1)8 x 12 <3 inter sections; further they meet in the 9 pairs P", P", belonging to the 9 points P' lying on #B,, and in the 12 points P", belonging to the 12 pairs P, P’ of 3,°, which are collinear with 4. So they must have 60 intersections in Dj); &"* has consequently quintuple points in the 12 singular points D. The curves ¢,"* and «” have in Be 9X 123, in D,12K5K2 intersections, together 444; the remaining 60 lie in points of infleetion, of which the harmonic polar lines pass through /. In sueh a point of inflection /, «&,? will have a ¢rip/e point, for the corresponding 3, 80 that T appears three times as point of ¢&,. Consequently 4 bears 20 straight lines h: the harmonic polar lines of p* envelop a curve of polar line h contains a linear triplet, so three pairs of & class twenty. 105 Mathematics. — “A cubic involution of the second class.” By Prof. Jan pr Varins. (Communicated in the meeting of April 24, 1914). 1. By the class of a eubic involution in the plane we shall understand the number of pairs of points on an arbitrary straight line’). In a paper presented in the meeting of February 28", 1914 °*) I considered the cubic involutions of the jirs¢ class, and proved that they may be reduced to sév principally differing sorts. The triangles A, which have the triplets of an involution of the first class as vertices, belong at the same time to a cubic involution of lines; the sides of each 4 form one of its groups. The cubic involntions of the second class possess the characteristic quality of determining an involution of pairs i.e. an involutive birational correspondence of points. For, let Y, ¥’, X" be a group of an involution (X*°) of the second class; on the line X’ NX" lies another pair Y’, Y""; the point VY’, completing this pair into a triplet, is apparently involutively associated to XY. In the following sections I shall consider a definite (Y") of the second class and inquire into the associated involutive correspondence (\)’). 2. We start from a pencil of conies g? with the base-points A, B,, B,, B, and a pencil of cubies ¢° B,, CG. (h=1 to 6). The curves «* and y arbitrary point Y, intersect moreover in two points X’, X", which with the base-points B,, B,, *, which pass through an we associate to A. As the involutions /* and /*, which are determined on a Straight line by the pencils (4*) and (¥*), have two pairs X’, X" and ¥Y’, Y" in common, a cubic involution (X*) of the second class avises «here. The ten base-points are singular points, for they belong each to 1 0 point of one of the pencils. groups; on the other hand is a singular point certainly a base- The pairs of points which with the singular point A determine triangles of involution A, lie apparently on the curve «* of the pencil (~*), passing through A. As they are produced by the pencil (¢?), they form a central involution, i.e. the straight lines.« = X’X" pass through a point Lot a (opposite point of the quadruple AB,B,B,). Analogously the pairs \’, i] , which are associated to C),, lie on 1) This corresponds to the denomination introduced by Capora.i for involutive birational transformations. (Rend. Acc. Napoli, 1879, p. 212). *) “Cubic involutions in the plane”. These Proceedings vol. XVI, p. 974. 106 the conie y,2 passing through C,, which conic belongs to (y*); the straight lines v intersect in a point J/,, the centre of the /?. In order to find the loens of the pairs, corresponding to B,, we associate to each g* the gv, which touches it in B,. The pencils being projective on this account produce a curve of order five, B,°, which has a triple point in B,, nodes in B,, B, and passes through A and Cy. If the straight line «= X’Y" is associated to the straight + and) qos niineeemes correspondence (J, 1) arises between the “curve of involution” enveloped line, which touches the corresponding curves » by a and the pencil of rays B,; from this it ensues that (7) must be a rational curve. As no other lines w can pass through 5, but ihe tangents at 3,° in the triple point B,, (z) is a rational curve of the third class, has consequently a bitangent; on it lie two pairs of (X*). To the tangents of (2), belong the lines Ab, and AB,. There are three singular straight lines b; = ABg; each of them bears a /* of pairs Y', XY". The corresponding points X lie on the ine nO bens 8. The curve of coincidences (locus of the points X= X') has triple points in #; and passes through A and C;. With the singular curve y*, it has 10 intersections in A and Sz; as it touches it in C’, and at the same time contains the coincidences of the involution (X', X") lying on y?,, it is a curve of order seven’), which will be indicated by 47. It passes through the 12 nodes of (y*) and the 3 points (0; bin). As d@ has six points in common with g*, apart from By, and Ch, the involution /* of the A inscribed in g* possesses sev coincidences. In the same way it appears that the involutions 7? lying on «* and 8° possess four coincidences each. The supports of the coincidences envelop a curve (d) of class eight; for through A pass in the first place the lines dg, each bearing two coincidences, and which consequently are bitangents of (d) and further the tangent in A at «@*, which will touch (d) in A. 4. To the points Y of a straight line / correspond the pairs of points YY’ and XV" of a curve 2, which has in common with / the two pairs of the (.Y*) lying on /, besides the points of intersection of / and 6’; hence 2 is a curve of order eleven. By paying attention to the intersections of / with the singular curves a‘, B;°, and yj’, we see that 2'! passes three times through A, jive times through By and two times through C4. 1) This corresponds to this well known proposition : the locus of the points where a curve o” of a pencil is touched by a curve ¢” of a second pencil is a curve of order 2(m--n)—3. 107 On 2, XN’ and X" form a pair of an involution; of the straight lines v= NX’ X" six pass through A. Three of them are indicated by the intersections Y of / and «'; here ’ lies every time in A. The remaining three are the lines 6;; for each of them contains a pair X’, Y" corresponding to the point Y = (/b,,,,). The curve (x), enveloped by w is rational, because we can associate w to NX; it has therefore ten bitangents. As such a bitangent bears two pairs \’, X" and Y’, Y" it follows that the imvolution (X,Y) contains ten pairs on /, and consequently is of the tenth class. 5. Let a straight line / be revolved round a point HL; the pairs X', X" and Y', Y" lying on it describe then a curve «°, which passes twice through / and is touched there by the straight lines HE and HE". On EFA lie two points X' and Y", each forming with Ea pair of the (X"); so A is a node of ¢°. For the same reason é° has nodes in 4;; it also contains the points Ci. In consequence of the existence of 5 nodes, &° is of class 20, so that / lies on 16 of its tangents. Of these 8 contain each a coincidence of the (Y*); the remaining 8 are represented by four bitangents, being straight lines s, on which both pairs belonging to (X"*) have coincided. From this it ensues that the lines s envelop a curve (s), of the fourth class. Apparently the straight lines s, passing through A, are tangents to a’. In the same way the four tangents out of A, to pe° are the straight lines s, which may be drawn through By. ts and J’ have 16 points in 6 Apart from the singular points ¢ common; to them belong the 8 coincidences of which the supports d pass through #. The remaining 8 must be points Y’, coinciding with the corresponding point Y without ¢/’s passing through 4; i.e. they belong to the locus «, of the points Y, which complete the pairs lying on é* into groups of (.X°). As EF lies on three of the straight lines «= X'NX" belonging to br, By is a triple point of e,; analogously A and C; are simple points of that curve, so that the latter has 2+3<2<3+6= 26 6 intersections with ¢° in the singular points. Besides the 8 points of 7 y ' ny J’ indicated above they have moreover the points 4’, £” in common; so we conclude that «, must be a curve of the sivth order. To the intersections Y of ¢°, and / correspond lines w, which pass through HL; trom this it ensues again that v envelops a curve of the sixth class, when Y deseribes the straight line /. 6. If # is laid in C,, &° is replaced by the tigure composed of 1 | \ : > and a curve y,*, which has a node in C,, the singular conic y, and passes through the points A, 5;, C,. The two curves have apart 108 from A and Be two more points “’, 2" in common; the lines C, £', C, #" touch y,.in C, and are apparently the only possible lines s passing through C,; hence C, is a node on the curve (s),. The curve ¢." belonging to C, is represented by the figure com- posed of y,* and a curve *y,*, which has nodes in Ly. This may be found independently of what is mentioned above. The trans- formation replacing a point Y by the corresponding points X', X", transforms a straight line / into a curve y1', consequently the curve y,' into a figure of order 44. It consists of y,* itself (for this curve bears oo’ pairs X, X'), twice ,?, the curves a’, B;° 7,’ and twice the locus of Y"; the latter is therefore of order four. If # is brought into the centre J/, of the 7? lying on y,?, &° passes with node J/,. Of the latter 6 tangents pass through J/,, whereas this point lies on 2 tangents of y,?; from into y,? and a curve ,,* this it ensues anew that the lines d envelop a curve of the eighth ,' four points in common, which must form two pairs of the /?, and so determine two lines s, J/, too is a node of the curve (s),. If # lies’ in A, &° consists apparently of a@’*, and the three lines b.; whereas ¢,." is the figure composed of an @ and the three lines bun. For FE in T &* is replaced by the figure formed by a® and a class. As y,? apart from A and 4, has with u curve t*, also passing through 7’ and having with a@* besides the four points A, By. two more pairs collinear with 7’; consequently T is also a node of (s),. For Bb, «° consists of B,° and the line BA; «,° of B,° and B,B. 7. Passing on to the consideration of the involutive correspondence (X, 1”) we cause X to describe the straight line /, and we try to find the locus of the corresponding points Y. On each line X' X" lies a second pair J’, Y"; the curves ¢* and g*, which intersect in the points }', Y" we shall associate to each other. In order to determine the characteristic numbers of this correspondence, we consider the involutions /°, which are formed on a curve ¢ or g* by greups of (X*). The sides of the 4 described in a ¢ envelop a conic; among the 12 tangents, which this curve has in common with the curve of involution (wv), belonging to 4'' must be reckoned the two lines N\', X", for which X is one of the intersections of / and g*. The remaining JO contain each a pair Y', ""; consequently each g? is in the said correspondence associated to 10 curves gp’. The involution /* on a y* possesses a curve of involution of the third class; for 6, bears in the first place the line 6,, which contains 109 a pair of the 7*, then the lines joining B, to the two points, deter- mined by the y*, which touches y* in 5,. The intersections of / and g* procure three common tangents of (7), and (v),; there are consequently 15 straight lines, which bear a pair )”', Y"", so that the said correspondence associates 15 curves ¢° to y”. By means of this correspondence the points of a straight line + are arranged into a correspondence (30, 30). For to the gv? passing through a point R of 7 correspond the 30 intersections A’ of 7 with the 10 curves g* associated to g*; on the other hand the g* passing through =f’ procures 30 points A, by means of the corresponding 15 q’. The intersections of the corresponding curves form therefore a figure of order 60; it consists, however, of two parts: the locus of the pairs ¥’, ¥", which lie on the tangents of the («),, and the locus of the points Y. The former may also be produced by. the pencil (v*) and’ the system of rays (v),. To each y?, in virtue of the consideration men- tioned above, a number of ten straight lines is associated, which are each coupled to one yg’ only ; henee a (10,12) arises now on 7, so that the pairs of points ’, Y" are lying on a figure of order 22. For the points )” we find therefore a figure of order 38; it is composed of the three lines 4, and a curve of order 35. For to the intersection Y of / and 6,24, corresponds a pair XY’, VY" on AB,; but this line bears co! pairs ’,)"" and the corresponding points 7 of b,B, are all associated to V. Apart from these three lines the line / is transformed by means of the birational correspondence (X, Y) into a curve of order 35, 7**. It cuts / in 10 pairs_X, Y (§ 4) and in 15 coincidences Y= )’. There is consequently a curve of coincidences of order jifteen. The figure of order 22 found above 1 consists of the three lines 6; and a curve 4'', for to the conic (,, O,,) corresponds the tangent , of (),. 8. We shall now determine the fundamental curves which are associated to the fundamental points A, By, Ch. The curves of invo- lution (7), belonging to ¢,° and 3,° (§ 2) have 9 tangents in common, there are consequently 9 lines, for whieh lies in , and Vin £,. Therefore the fundaniental curve of 2, has nonuple points in 2, and B,. No other point VY of the line B,6, ean correspond to a point X lying in £,; the said curve is therefore of order 18. It has a nonuple point in 4 too and passes three times through each of the points A and C),; for through 7 or J/;, passes one line, bearing a pa ie, eof py and aspair YY" then 5, = X corresponds to a point Y lying in A or C4. of «@ or xy)”; through whien 110 The fundamental curve of A is apparently identical with the curve &" (§ 5) belonging to the point 7; we shall indicate it by a’. As «* has two pairs in common with t* (§ 6) A is a node of a’. That «® passes through the points Ci, and has triple points in Bz, ensues from the consideration of the lines 71, and of the tangents out of 7’ to the (xv), belonging to By. It appears analogously that the fundamental curve of C, has triple points in 4; and a node in C,; it passes through A and the remaining points C, and is of order six. This curve is at the same 6 time the «° belonging to J/,. We can now prove once more that the birational correspondence is of order 35. To the intersection Y of two lines /, corresponds . the point }’, which the two curves 4, apart from the fundamental points, have in common. As appears from what was mentioned above 2 passes 18 times through 4; and 6 times through A and Cy; from 1+ 3 187+ 7 6? = 1225 = #5? it appears now that 2 is a curve of order 35. Physics. — “On the manner in which the susceptibility of para- magnetic substances depends on the density.” By Dr. W. H. Knpsom Supplement N°. 36c¢ to the Communications from the Physical Laboratory at Leiden. Communicated by Prof. H. IKCAMERLINGH ONNES. (Communicated in the meeting of April 24, 1914). § 1. Introduction. In Suppl. N°. 32a (Oct. °13) an expression was developed for the molecular rotatory energy in a system of freely rotating molecules as a funétion of the temperature. This expression was introduced into the theories of Laneryin and Wrauiss, on the sup- position that, when the equipartition laws are deviated from, the statistics of the molecules under the action of an exterior directing field, in this ease a magnetic field, is determined by the value 2, of the rotatory energy in the same way as for equipartition it is by ‘kT. Wt then appeared that different experimental results can be re- presented very satisfactorily in that way '). 1) The expressions developed in the above-mentioned paper appear to be also suitable to give a quantitative representation (as far as observations are available) of the decrease of the temperature of the Curin-point by the addition of a dia- magnetic metal to a ferromagnetic one, with which it forms mixed crystals, on the supposition that the diamagnetic metal exerts no other influence than that the vautual action of the ferromagnetic molecules is lessened in consequence of the sale In the communication mentioned above the system of molecules increase of their distance, as regards the molecular field in particular according to the supposition mentioned further on in this note. In fig. 1 the points -++- repre- ~ Fig. 1. sent the temperature 7» of the Curte-point of alloys of nickel and copper as a funetion of the mass-composilion «x of nickel according to W. GuerTLer and G. Tammann, ZS anorg. Chem. 52 (1907), p. 25 [the quantity « introduced here is not to be confused with thal ef equation (4)|. The carve represents the results of the calculation. In this I started from equation (16) of Suppl. N°. 32a, applied to the nickel molecules Nnngu? = Uae oteeney Nes! Wem F, = c - (d) The equation which determimes the value of Te which cateeennaas to a given 112 was always‘) supposed to be contained in the same volume. and in the comparison with experimental data no account was taken of the influence which the relatively small changes of density connected with the temperature changes exert on the parameter (/,, which acenrs in the formulae of that communication, and which [ will call the characteristic zero-temperature. Since then the measurements by Prrrimr and Kaweriincu ONNEs *) coacerning the susceptibility of liquid mixtures of oxygen and nitro- gen have furnished very important data, which, when considered from the point of view taken in the paper quoted above, allow a conclusion as to the manner in which the characteristic zero-tempe- rature @, depends on the composition of those mixtures. If it is further assumed with Prrrmr and KamertmGcu Onnes, that to a’ first approximation the presence of the nitrogen molecules in these mixtures does not exert a direct influence on the statistical distri- bution of the orientations, nor on the magnetic noment of the oxygen molecules, so that it is only the changes in density of the oxygen, which determine the changes in the susceptibility, then those mea- surements furnish at the same time data for a discussion of the question how “, depends on the density. We will in the first place treat the question whether the results of the measurements by Perrier and Kamuriincn Onnxes mentioned above can be represented with the aid of the relations of Suppl. value of 2, may then be pul into the form: Ure Urel == ails ec, ec a . (c) «0 UyO1 Ota For nickel (7.1 = 633, G0,1 = 2100, cf. Suppl. N°. 32a § 4) awd 1,30. From UyO1 i ‘“ the value of can be derived, and then with “/) from (b) the value of 7c ae) 0 corresponding to «2 can be found. A continuation of the investigation of the magnetisation of alloys such as those mentioned above, particularly for compositions, for which the CuRt&-point lics below O° C., would be of great interest, on the one hand for putting the appli- cation of the quantum-theory to a test (according to this with such alloys the different cases indicated in Fig. 5 of Suppl. N’. 326 might be realised), on the other hand for increasing our knowledge of the molecular field [In the mean time | nave received an article by P. Watss, Ann. de physique (9) 1 (Febr. 1914) p. 134, in which is mentioned, that, with a view to the investigation of the molecular field, a series of measurements concerning alloys of nickel and copper has already been undertaken. (Added in correcting the proof of the Dutch edition)]. ') With the exception of the note added in Leiden Comm. : note 2, p. 6. *) ALB. Perrier and H. KAMeRLINGH ONNES. Comm. No. 139d (Febr. 714). 113 N°. 32a’). It is shown in § 2 that the answer is in the affirmative, in § 3 the same appears to be the case for the measurements con- cerning the susceptibility of liquid oxygen over a wider range of temperatures. § 4 contains the conclusion which follows from §§ 2 and 3. Finally in the following § § are treated the consequences concerning the dependence of 6, on the density, which follow from the results of those measurements *). § 2. The susceptibility of the liquid mixtures of oxygen and nitrogen and the application of the quantum-theory to paramagnetisin. As a preliminary to the question whether the results of the measurements by Prrrmr and KameriincH Onnes can be represented with the aid of the relations of Suppl N°. 32a, in so far as these are applicable to paramagnetic substances, the specific susceptibility of the oxygen in the mixtures (Table [, Comm. N*. 139d) was compared with the specific susceptibility for pure oxygen in the gaseous state at the same temperature, which would follow from the measurements by Weiss and Piccarp if Curim-LAnGrvin’s law remained valid down to that temperature (cf. tabie I, Comm. N°. 139d). This value we will call the equipartition value Zey. On the assumption mentioned in § 1, that the presence of the nitrogen molecules does not cause a change in the magnetic moment of the oxygen molecules, the (paramagnetic) specific susceptibility of the oxygen in the mixture is determined by Oostgruuis’s relation : nu Owmnmintre— gag Py (1) In this relation n represents the number of oxygen molecules in 1 gram of oxygen, uw is the magnetic moment of an oxygen molecule, w, the mean rotatory energy (about two axes 4 to the magnetic one) of a molecule of oxygen in the mixture at the tem- perature and density considered. According to LanGuvin nu? Xeq. = 3k" Division gives 1) For a detailed discussion of those measurements on the basis of the assump: tion of a negative molecular field, as well as a consideration of the other cir- cumstances which may have an influence, we refer to the paper by Perrier and KAMERLINGH ONNES quoted above. *) The principal results of this paper were already inserted in the translation of Comm. No. 139d; p. 915 note 2 8 Proceedings Royal Acad Amsterdam. Vol. XVII 114 eq. Ur ee es me et CD kT Xo, in mixture If for w, we assume the temperature function, developed in Suppl. N°. 32a, and determined by - (4) where 2 0 Ct —— g ké, ’ . : . . . . . . (5) : : Skip r at each value of « the mutually corresponding values of Ep ae r 0 can be calculated. The value of ae corresponding to the value of : / j 0 u/kT given by equation (3) can then be found by graphical inter- polation, after which @, immediately follows. From the data of Table [| Comm. N°. 139d by Perrier and KAMERLINGH ONNES the following values of 6, were in that way obtained : TAREE | Values of J, | Oi) vs Sehr aaie | | 2 | y \f=— 195.65|f = — 202.23) = — 208.84) Mean | A (= a 9.) pera) Gob! | | 1 | 0.7458 165 161 159 162 21.6 I | | » HW 04010 | 975 99.5 | 971 98.0 13.1 | WI | 02304 | 53.9 55.1 [61.0] 54.5 7.3 SIV: s|Dlas0ele we 250 EYE || SPAN 23.3 3.1 Vo 0.0801 7.55 10.6--} 91 1.2 | | | | From the fact, that the individual values of 6, vary irregularly about the mean values, the conclusion may be drawn that the obser- 115 vations can be represented with suflicient accuracy by the equations (1) and (4). This is confirmed by Table Il which gives. the values of xy calculated with the aid of the mean values of 4, given in table I. Table II also contains the deviations ( C' between observed and calculated values. IPAS ELE II Calculated specific susceptibilities of oxygen. Comparison with observed values. | +i | 4 | i l | t= — 202.23) O-C || t= — 208.84, O—C 0 |t=—195.65) O-C SS | ! ——— —— ——— 1 |o7458 |} 2962 |—17 3139, | 06)| 2345. | £20 eet hozofor! aa62) (|= 0.2\||" “s6l20 J 161) 300m - | 205 | : MM | 02304 | 3636 |+ 05) 3038 |—os|| 4292 | [—5.7)| |= 1 | 01380 | ~ 384.6 |— 10] 4188 | + 1.6 || 460.1 | —03 | |v /ooso | 3037 | +12/| | WP a yaiey alleen pe | Table II confirms the conclusion that the observations concerning the specific susceptibility of oxygen in the liquid mixtures of nitrogen and oxygen can be represented within the degree of accuracy of those observations by substituting the expression 4:7’ in Lanarvin’s theory by an expression for the molecular rotatory energy which is derived from the quantum-theory with the assumption of a zero- point energy *). These observations do not therefore furnish a decision between the assumption just mentioned and that, in which the expression £7" in LanGEvin’s theory is left unchanged, but the assumption of a negative molecular field is added, which was found by Perrine and Kamernincu Onnes (Comm. N°. 139d) to be in sufficient agreement with the observations. In the mean time it must be mentioned that on the assumption investigated in this paper the inclination of the y~1, 7- lines for the mixtures with small density of the oxygen approaches to the equipartition value for oxygen, which follows from the measure- 1) Dr. OostERHuts tells me, that calculations made in the way indicated above, but in which for a the expressioa is taken which was assumed by him in Suppl. N° 31, lead to the same result Cf. note 2 p. 915, Comm. N°. 139d 8* 116 ment by Wetss and Piccarb, whereas, as was found by Prrrier and KampriincH Onnes, on the assumption of a negative molecular field with unchanged molecular rotatory energy a correspondence of the inclinations can only be obtained by the aid of a new hypo- thesis (unless the difference in inclination should be ascribed to a systematic difference of experimental origin). § 3. The susceptibility of liquid oxygen and the application of the quantum-theory to paramagnetism. The susceptibility of liquid oxygen being measured over a considerably larger temperature range (from 65.°25 K. to 90.°1 K.: Kamertinch Onxes and Perrier, Comm. N°. 116; from 70.°2 kK. to 90°.1 K.: KAMERLINGH ONNuS and OosTERHUIS, Comm. N°. 132e), than was possible for the mixtures treated in § 2, - it is important to investigate whether the data which are available about liquid oxygen can be represented also with the aid of the relations (1) and (4). In table II] the corresponding data have been put together. As Perrier and Kamertincuo Onnns observe, account has to be taken of the change in density of liquid oxygen. For the reduction of 7, to the same density use was made of the result whieh will be derived in § 5 from the observations concerning the above mix- tures considered in connection with those concerning oxygen, viz. that at these large densities 7, is proportional to @”s. Tt AGB AE slita | Specific susceptibility of liquid oxygen (KAMERLINGH ONNES and PERRIER). | i | Keale.’ 1 | PI NEYR LOSE.) “ON TEC ore—=nio3. 3| O—-C | | Boal ey \with @, = 232. (ao | 4 (Gee) 64.25 | 284.9 | 232.5 | 1.267 229 282.6 + 2.3 70.86 | 271.4 | 232.7 | 1.235 | 233 | 271.7 70m | 77.44 | 259.6 | 231.3 | 1.204 | 238 | 261.3 =e | | | | 0h i Watt 22012 | 1.143 | 232 | 240.9 ALO i | i : | a mean 232, The agreement between observation and caleulation may be con- sidered sufficient. This conclusion is supported by the observations 117 of KAMERIINGH ONNES and OosTERHUIS: TABLE Ilo. Specific susceptibility of liquid oxygen (KAMERLINGH ONNES and OOSTERHUIS). oO 3 ii H.108 | Ao, = 232 (—~) epee OL=G 10.2 Pat | 232.65 272 8 Oe | | 79.1 258.1 297.4 | 258.8 Oa fe “O04 Se al 220.2 Dae. IL weleaie | i a> ae § 4. Conclusion. The data treated in §§ 2 and 3 lead to the following conclusion : The susceptibility of oxygen in liquid mixtures of oxygen and nitrogen as well as that of liquid oxygen can be represented within the degree of accuracy of the observations with the aid of the application of the quantum-theory to paramagnetism as expressed by equations (1) and (4). The agreement between observation and calculation (particularly if the susceptibility of liquid oxygen is also considered over the whole range of temperatures) is somewhat better with the application of the quantum-theory than with the introduction of a negative mole- cular field alone: indeed Perrier and KamernincH Onnes find it necessary for the mixtures of oxygen and nitrogen also to change the value of the Curtm-constant. Calculations made for liquid oxygen support this conclusion. Nevertheless it is quite possible that for liquid oxygen also if a changed Cvrin-constant is assumed just as good an agreement may be obtained by the introduction of a negative molecular field. § 5. Dependence of the characteristic zero-temperature on the density. Table 1V shows more particularly the manner in which /, depends on the density 9 of the oxygen. From the last column the conclusion may be drawn that for the , 4, 2 log 9, rs higher densities ——- approaches to #/,. For those densities we 7 0g Oo may therefore write as a limiting law: G00; smn pay etch) << evel ete te. (Ol) 0 118 TABLE IV. | | A log @, oO 4 ——— : sl) eAYogio San nn EE : 0.0801 Oneal | ss 0.1381 | 23.3 | \) eale66 0.2304 || 54.5 | | | | 1.06 0.4010 | 98.0 | 0.82 0.7458 | 162 | | Osan 12235 ea) N2S2 un | where a is a constant (for a definite substance, This dependence of O, on the density quite agrees with that, which in Suppl. N°. 30a was derived for the molecular translatory motions from the hypo- theses assumed there, cf equation (184) of that paper. This result can be interpreted as indicating, that the proportionality factor in the relation C= eh, (ef. Suppl. N°. 32a § 2), in whieh e¢ represents the velocity of the “rotational waves” considered in the paper mentioned, is independent not only of the temperature but also of the density, as aceording to Suppl. N°. 80a equation (7) is the case for the corresponding “translational waves”. In Fig. 2 the points indicated by small circles represent the values of 6, derived from the observations as a function of e. The curve 6—<— — Se pivese@o29) Sram | | | “| chosen so as to obtain agree- {| |} 6hcment for the higher valiies jor | | | | | | vy. This agreement is in fact | z4 | very good for @ >1, as results | from the fact that the two | curves do not intersect here at | a definite value of v, but coin- cide over a certain range of | densities. | | For values of @ smaller than 1 a deviation begins to show Fig. 2. itself; this deviation at first increases regularly in proceeding to lower values of 9. 119 It is natural to ascribe this agreement at higher, and this deviation at lower densities to the following’). At larger densities the rotations of the oxygen molecules are continually disturbed by collisions, or at least interactions with the other oxygen molecules, so that the periods of revolution of the oxygen molecules cannot play a part in the determination of the frequencies in the system which govern the distribution of energy. For those densities the frequencies are determined by the analysis according to Jnans of the molecular rotatory motions in the system into natural. vibrations; the relations given in Suppl. N°. 32a § 2 are then valid as approximations. At small densities, however, at which every molecule performs in the mean a certain number of revolutions before its rotation is disturbed by the collision (interaction) with another molecule, it is the numbers of revolutions of the individual molecules in the unit of time which govern the distribution of energy. These frecuencies are then determined at the limit by Etnstwin’s relation *). Uy = 4 LD (2x)? and are independent of the density. Between these two extremes a transition range lies. If (for 7’ = 85) the number of collisions, which an exygen molecule undergoes. in 1 sec. at e=1 (the molecular diameter 6 = 3.10—-8 derived from the viscosity), is compared with the number of revolutions per sec. (distance of the oxygen atoms being assumed = 0.7.10—%, derived from the moment of inertia calculated according to Hom‘) from O—1, which value was assumed according to Fig. 2 for oxygen in the gaseous state), one finds that in the mean the oxygen molecule makes 0.4 revolution between two successive collisions. It is, however, not necessary to assume that the number of times that the rotatory y motion is disturbed in a second, coincides with the number of times that this is the case with the translatory motion. Some room is thus left for an average number of revolutions between two successive disturbances of the rotatory motion other than the number just mentioned. But if we assume that the order of magnitude will not be essentially different, the result of the calculation mentioned above is such as to be quite consistent with the theory developed above that at g@=1 a transitional region begins in which the 1) Cf. the note quoted p. 112 note 1. *) Rapports conseil Solvay 1911, p. 433. 8) E. Hotm. Ann. d. Phys. (4) 42 (1913, p. 1319. The ¢ used by Houm corresponds to / in this paper. 120 frequencies of the individual molecules begin to play a part for the energy distribution. This theory involves that for smaller densities «, is no longer determined by the relations of Suppl. N°. 32a, equations (4) and (5) of this paper. Notwithstanding that, in consequence of the relative insensibility of the way in which w, depends on 7’ for the special assumption about the distribution of the frequencies (cf. Suppl. N°. 31 § 7 by Oosrprnuts), a good agreement may still be obtained by those relations with the observations considered in this paper, but then the values of 7,, which give such an agreement, do not have the meaning laid down by the theory in Suppl. N°. 32a, Meanwhile the part for the smaller densities (@ < 0.15) of the, @, ,o-curve of Fig. 2 may be given a simple meaning by supposing 15 the curve for this region to represent — A, if 4 is determined 2 by the fact that the u,,2-curve on the side of the high temperatures approaches asymptotically to uy kh (T + A). As according to the relations of Suppl. N°. 32a § 2 (ef. Suppl. 4 2) N°. 32) § 5) 0,=—A, the curve has also this meaning for o> 1. For a nearer interpretation of the intermediate region the theory will have to be further developed. On the side of the small densities the curve in Fig. 2 has been extrapolated (indicated by dots) to a part that terminates parallel to the c-axis, in agreement with the theory given above, that at small densities the frequencies of rotation are no longer dependent on the density. In this region of densities the rotatory energy is determined as in the simplified scheme of Estrin and Strrn or of OosTErauis, in which to all the molecules the same velocity of rotation was ascribed, or better in the more elaborate theory of Hotm'), in which the 1) &. Houm. Ann. d. Phys. (4) 42 (1913), p, 1311. This theory, in which in the system of rotating molecules all frequencies occur, and for the distr:bution of the molecules according to the frequencies, in a way analogous tc that which PLancKk in his recent theory followed for linear oscillators, the plane in which the condition of a molecule rotatimg about one axis is represented by the values of its azimuth and moment of momentum, is divided into regions of constant probability limited [aes ; 3 by energy curves 4=” ir 8 consistent with the resu’ts of ByerRum and EK. y. BaHR concerning the discontinuous character of absorption spectra in the infra-red of gases of not too high densities, if it is assumed that the absorption 121 distribution of the velocities of rotation over the molecules is taken into account. Resuming we may conclude, that the observations by PERRimR and KAMERLINGH ONNES concerning the susceptibility of liquid mixtures of oxygen and nitrogen, although they do not furnish an experimentum erucis between the theory of the negative molecular field and the application of the quantum-theory on paramagnetism, nevertheless fit without any constraint ') into the whole scheme which can be built up on the basis of this application. § 6. The results of the former § concerning the dependence of 6, on the density lead to ihe following inference regarding the influence of the rotatory motion on the external pressure. For those densities at which w, is determined by the equations (4) and (5), and at which 4, — 07s, the energy u, and also the entropy s, for the rotatory motion are represented by the same functions (only with another value of @,) as the corresponding quantities for the translatory motion in-an ideal gas. In that case the rotatory motion gives a contribution to the external pressure similar to that of the translatory motion. The ratio of this contribution, for one degree of freedom, to that which in an ideal gas is due to the translatory motion, approaches to 1 at increasing temperature *). At small densities, however, vz. in the region in which 6, does not depend on o, the rotatory motion does not give a contribution to the external pressure. This agrees with what has always been of radiation energy supplied from outside only occurs when the representative point has arrived at one of the limiting curves mentioned above (for instance in conse- quence of the probability of emission on reaching a limiting curve, cf. PLANCK, Theorie der Wiirmestralung, 2te Aufl., § 151, being changed by the presence of the radiation from outside) The observations by E. v. Baur, Verh d. D. physik. Ges. 1913, p. 1150, concerning hydrochloric acid seem to be mere favonrable to this view than to a distribution, in which, in the plane mentioned above, only the 1 hy ? z : 5 . energy curves | m+ >} > are covered with points, which is the assumption alluded to in the note quoted p. 112, note 1. 1) The views advanced in this § about the coming into the foregrond of the frequencies of rotation of the individual molécules are im fact, as will appear again in § 6, a necessary complement for small densities to the theory of Suppl. N°. 32a. *) I find that A. Wont, ZS. physik. Chem. 87 (1914). p. 9, by quite different considerations was also led to the suggestion that at large densities the molecular rotatory motion may give a contribution to the external pressure. (Note added in the translation). 122 derived for an ideal gas, e.g. from Borrzmann’s entropy principle, cf. Suppl. N°. 24a § 4, or from the virial theorem. Conversely it necessarily follows from this, that in Fig. 2 the 4,, e-curve at the small densities must change its direction to one parallel to the g-axis, as is clearly indicated by the point e = 0.08, In conclusion we will return for a moment to the assumption rigidly adhered to in this paper, zzz. that the presence of the nitrogen molecules does not exert any influence on the distribution of the rotatory energy of the oxygen molecules. The following mechanism would be in accordance with this supposition: the oxygen molecules behave at a collision (at least with the nitrogen molecules) as rigid smooth spheres, they carry a (magnetic) doublet (or have according to Suppl. N°. 324 § 7 a magnetic moment in consequence of a rotation about an axis of small moment of inertia with zero-point energy in the temperature region considered); the nitrogen moleeules have a_ structure such that they do not exert a directive force on the oxygen molecules. The object of this suggestion is, however, no other than to show that the assumption mentioned above is not an impossible one. Chemistry. — “Vhe Allotropy of Cadmium. IY’. By Prof. Ernst Conun and. W. D. Hertpprman. The electromotive behaviour of Cadmium. L. The dilatometric measurements made with cadmium which had been deposited electrolytically, had shown ') that this material is a modification which is not stable af room temperature. This corre- sponds with the result found by Ernst Conrn and E. GoLpscamipt *) in their investigations on the electrolysis of solutions of tin salts. When such a solution is electrolysed below 18° C. there is not formed grey tin as might be expected, but the modification whieh is metastable at this temperature is deposited. ~ In the following pages we give an abbreviated account on the investigations we have carried out in order to identify the product which is formed during the electrolysis of solutions of cadmium salts. 2. Some years ago Huxnrr*) deseribed “a low voltage standard cell”, represented by the following scheme : 1) These Proc. p. 54. 2) Zeitschr. f. physik, Chemie 50, 225 (1905). 8) Trans. Americ. Electrochem. Society 7, 358 (1905). 123 | Solution of cadmium sulphate | Cd-amaleam * | of arbitrary concentration 12.5°/, of Cd by weight The electromotive force of this combination is 0.0505 Volt at 25°.0. The reproducibility is about 0.5 millivolt. The cadmium elec- trode of this cell has to be electrolytically deposited, as Th. W. RicHarps and Lrwis') have proved, that only this kind of electrodes give a definite potential. Ernst Conn and Sinnien*), who used these cells in their piezochemical investigations also found that they are reproduceable. 3. Some points in the construction of such cells which play an important role in the experiments, to be described below, may be given here. (Fig. 1 A). Fig. |. The glass part is a thin walled tabe about 8—10 mm. in dia- meter, closed at one end and provided with a platinum wire; two ov three centimeters above the closed end is a platinum spiral, with its end fused through the side of the tube (the wires are thoroughly cleaned with aqua regia before filling the cell). In filling, the spiral is pressed to one side and some 0.5 cc. of 12.5 percent cadmium amalgam is brought into the lower part and melted (carefully avoid bringing the amalgam in contact with the 1) Zeitschr. f. physik. Chemie 28, 1 (1899). *) Zeitschr. f. physik, Chemie 67, 1 (1909). 124 platinum spiral). The spiral is then pressed down into a horizontal position. The tube is now filled up with a solution of cadmium sulphate of arbitrary concentration (the E. M. F. of the cell is in- dependent of the strength of the solution). In order to produce the cadmium electrode a current of 1 or 2 milliamp. (1 or 2 milligrams Cd per hour) is passed from the amal- vam to the platinum spiral. At least 18 milligrams must be depo- sited. The cell may then be sealed off. 4. We specially call attention to the following passage in HuLEtr’s paper: ‘‘The electromotive foree of these cells is high when the cadmium 1s freshly deposited, and the length of time required to. reach the normal value seems to depend on the thickness of the deposit. Air free cells and those saturated with Cd(OH), behave like ihe others and I have as yet no explanation of the high E. M. F. of newly constructed cells.” Our table I shows this decrease of potential of newly constructed cells. It amounts to about 1 millivolt. POA BLE i: Temperature 25°.0. E. M. F. in Volts. ee —— eng | | TO cds ee | | 5 > 2 After 1) After 2) After 3| After 4| After 5| After 7| After 8 sont ates ae i 5 5 day days days | days days days days = vo = | Eo z| £ a. | 0.05156 | 0.05105 | 0.05084 | 0.05078 | 0.05070 | 0.05065 | 0.05052 | 0.05052 | | b. | 0.05143 0.05099 | 0.05082 | 0.05076 | 0.05068 | 0.05067 | 0.05054 0.05056 | 0.05154 | 0.05103 | 0.05084 | 0.05076 | 0.05070 | 0.05067 0.05056 | 0.05058 0.05151 | 0.05099 | 0.05082 | 0.05076 | 0.05070 | 0.05067 | 0.05056 | 0.05056 | 0.05162 | 0.05113 | 0.05090 | 0.05084 | 0.05074 | 0.05070 | 0.05058 | 0.05058 S Ss ~ 5. These determinations and those to be described below were carried out by the PogecEnporrr compensation method. The resistances used had been checked by the Physikalisch-Technische Reichsanstalt at Charlottenburg-Berlin. The same was the case with the thermometers used. Our two standardelements (Weston) were put into a thermostat which was kept at 25°.0. We used as a zero instrument a Drsprez- p ArsonvaL galvanometer. It was mounted on a vibration free sus- 125 pension (Junius). The readings were made by means of a telescope and seale; 0.02 millivolt could easily be measured. 6. As it was:very important for us to get rid of this variation of KE. M. F. we tried to find its cause. We thought it might be found in the electromotive behaviour of the cadmium amalgams, which has been studied particularly by H. C. Bur’). Fig. 2 contains his results as far as they play a role in our in- vestigations. The curves represent the E. M.F. (ordinates) of cells which are constructed according to the following scheme: Millivolts At. °/) of cadmium. Fig. 2. Solution of cadmium sul- Cd-amalgam F ee a phate (765.4 er. Cd SO He, SO, — He x-at. Proc. 2 pel Gas +7: /, H,O per Litre) The abscissae represent atom per cents of cadmium. oy Zeitschr. f. physik. Chemie 41, 641 (1902). 126 From the drawing it can be seen that the E.M.F. of these cells at 25°.0 is independent of the concentration of the amalgam when its concentration lies between 9.0 and 24.4 at.percents (i.e. 5.9 and 15.4 percent by weight). As soon as the concentration decreases below 5.9°/, by weight (when we pass from the heterogeneous amalgams to the homogeneous, (c.f. Bi1’s paper Fig. 3) the E.M.F. varies with the amount of cadmium present in the amalgam, the potential against pure cadmium énereasing with decrease in the percentage of cadmium. 7. In the light of these facts the high E.M.F. of freshly construeted cells becomes intelligible. During electrolysis the cadmium which is deposited on the spiral is withdrawn from the upper layer of the 12.5°/, (or stronger) amal- eam, which was originally a two phase system. It is thus possible for this layer to become a monophase system and if this is the case the E.M.F. will increase when electrolysis is continued. After the formation of the cell its E.M.F. will then be too high. In the long run cadmium will diffuse to the upper layer: this becomes again a twophase system and the E.M.F. will decrease and finally becomes constant. 8. In order to check this supposition we carried out the following experiment: We put two platinum spirals into the A-shaped tube B (Fie. 1). into the right-side tube we put some 1°/, (by weight) ead- mium amalgam (99 parts by weight of mercury, 1 part of cadmium). This amalgam is a fluid monophase system at ordinary temperature. We filled the tubes with a dilute solution of cadmium sulphate (half saturated at 15° C.). After this the cell was formed in the way described above. (1 milliampere). After having deposited 20 or 25 milligrams of cadmium on the left-hand spiral, the capillary tube on the right was brought into connection with a waterpump in order to remove the amalgam. A number of small pieces of the 12.5°/, amalgatn were then substituted for this. These cells give at once an E.M.F. of 0.0503 Volt when they are put into a thermostat at 25°-0 C. It is evident that our assumption oc made above (§ 7) is correct. 9 All the cells we investigated have been produced in the way described ; it is now possible to measure their E.M.F. at onee with- out waiting for 8 to 14 days before their becoming constant. 10. Our dilatometric measurements with cadmium which had been 127 electrolytically deposited gave the result that this material only under- goes transformation at temperatures below 100°, if it has been in contact at 50° (400°) with a solution of cadmium sulphate. The probable and obvious conclusion is that by electrolysis we get exclusively s-cadmium, the modification which is stable at high temperatures. If this were the case, the y-cadmium would be trans- formed into p-cadmium at 100°, into @-cadmium at 50° in contact with the solution of the sulphate. If now the y-modification is really generated by electrolysis, (analogous to what happens with solutions of tin salts) the Hunerr cells which have been measured until now would contain this material as the negative electrode. If this modification happened to be transformed into the modifi- cation which is stable at ordinary temperatures and pressures (1 atm.), this would manifest itself by a decrease in the E.M.F. On the one hand we are working in this case under extraordi- narily favourable circumstances for stabilisation (change into the a-modification) as the, material formed electrolytically is in a very fine state of division and surrounded by an electrolyte, while the quantity which has to undergo transformation is so very small (20 or 30 milligrams), that the transformation, if if occurs, will be finished in a short space of time. On the other hand, and this is to be borne in mind in researches of this kind, the possibility exists that the transformation which has to take place spontaneously, may be suspended, if the metal depo- sited by electrolysis forms only one single modification, as the germs needed for transformation are then absent. 1i. That the stabilisation generally does not occur is shown by our dilatometrie observations as well as by many other facts i.e. by the experiments of W. Jancer,') Ernst Conen,*) Bun’) and Hunnrr,*) who all found the same E.M.F. (50 millivolt at 25° C.) for cells which were constructed according to the scheme: Cd | Solution of | Cd-amalgam electrolytically | cadmium ; 12,5 per cent deposited | sulphate | by weight. How obstinately the transformation may be delayed might also 1) Wied. Ann. 65, 106 (1898). *) Zeitschr. f. physik. Chemie 34, 612 (1900). 3) Zeitschr. f. physik. Chemie 41, 641 (1902). 4) Trans. Amer. Electrochem. Soc. 7%, 333 (1905). — 128 be inferred from Hunerr’s') words: “many of these cells are still in good order after five years.” This wonld be in perfect accordance with our own experiences : Crark-cells which contain ZnSO,.6H,O as solid depolariser preser- ved their E.M.F. for five years notwithstanding their having been standing at room temperature, i.e. 25 degrees below the transition point of ZnSO,.6H,O. As in the case of Hunter's cells they had been sealed up after formation. 12. On account of these observations it might be expected that even under circumstances favourable to a transformation (stabilisation) of the negative electrode only a certain number of Hurerr cells would show the transformation. On December 11'? 1913 we prepared three H.C. (N°. 1, 2 and 5) in the way described above (§ 3) at room temperature (80 mgr. Cd on the spirals). We then substituted a 12.5 percent cadmiumamalgam for the | percent. The E.M.F. was now 0.0503 Volt. After standing for two months at room temperature the cells were measured again on February 26% 1914. The E.M.F. of 1, 2 and 5 had deereased to 00475 Volt at 25°.0 ©. and this value remained unchanged. As might have been expected the E.M.F. had decreased by stabilisation of the cadmium. 13. We prepared two new cells (nos. 6 and 7) in the same way as 1, 2, and 5. Immediately after the preparation their E.M.F. were 0.04847 and 0.04795 Volt respectively. Some days later these values became constant: 0.04788 and 0.04778 Volt. Stabilisation had begun already during electrolysis. 14. In order to determine whether «cadmium is formed during electrolysis if, this modification is present on the spirals before electro- lysis begins, we shunted the cells 6 and 7 in a current of 1 milli- ampere. In this way we deposited upon the a-cadmium which was present, a fresh quantity of 30 mer. After formation we put a fresh (12.5 percent) amalgam into the cell, while a fresh solution of cadmium sulphate was also introduced. Subsequent to this treatment the E.M.F. at 25°.0C. was again 0.05026 Volt which proves that y-cadmium had been formed on the old layer of «-cadmium. 15. On continuing our experiments we found that on one oceasion 1. Trans. Amer. Electrochem. Soc. 15, 435 (1909). 129 cells of O.047 Volt E.M.F, on another, cells of 0.050 Volt E.MF, were obtained. As our dilatometric measurements had shown that stabilisation occurs with great velocity at 50°, we prepared cells (C and O) at 47°.9. The dilute amalgam was then taken out and an 8.5 percent (by weight) amalgam was put in, while a fresh solution of cadmium sulphate was used. We substituted an 8.5 per cent amalgam fora 12.5 percent as our intention was to measure these cells also at 0° C.; At this temperature the 12.5 percent amalgam is a monophase system and such a system must not be used. In this way we found at 25°.0 C. Cell C: 0.04745 Volt. Cell O: 0.05022 __,, The cadmium in cell © had thus been stabilised at 47°.9. 16. In order to check the results found up to this point we also determined the E. M. F. of our stable and metastable cells at 0° C, If the differences in E. M. F. at 25°.0 between the different cells were really to be ascribed to the presence of «cadmium (cell C) and y-eadmium (cell O) the difference which was at 25°.0 C. 2.8 millivolt ought to increase at 0° C. as we are at that temperature at a greater distance from the metastable transition point ¢-cadmium = y-cadmium. The measurements at 0° C. gave the following results: cell C: 0.05225 Volt. cell O: 0.05626 __,, While the difference was 2.8 millivolt at 25°.0 C. it has increased as might be expected to 4.0 millivolt at O° C. 17. Several phenomena which are described by Hunerr, but which are obscure until now may find an explanation in the light of our experiments. HuLerr says: “A number of cells were made with addition of Cd (OH), thinking this might make a more uniform cadmium deposit; also the air was completely removed from three before sealing, and in others the air was removed and the cell saturated with nitrogen and with hydrogen. All of these gave very variable results, but in each case only 10 milligrams of cadmium had been deposited on the spiral, and | have lately learned this is too little cadmium, since some cells prepared as above described, excepting that only 10 mg. of cadmium was deposited on each spiral, showed the same irregularities and tendency to constantly decreasing electromotive force. These cells were recently all discharged and then reversing 9 Proceedings Royal Acad. Amsterdam. Vol. XVII. 130 the current about 26 mg. of cadmium was deposited on each platinum spiral, and they seem to be all coming together nicely and to the value indicated by the old cells”. 18. Our observations agree perfectly with those of Hunerr but we have to add the following restrictions: A number of our cells in whieh only LO mgrs. of cadmium were deposited indicated imme- diately after formation an E. M.F. of 0.0502 Volt at 25°.0 which decreased during 2 days. Then it became constant: 0.047 Voit. Transformation into @-cadmium had consequently occurred; the faet that only a small quantity of cadmium is present causes the KH. M. F. fo reach very soon its definite lowest value. The phenomenon obser- ved by HuLrrr is therefore the quick stabilisation of y-cadmium. 19. Prof. Hunterr has been kind enough to communicate to us ihe following facts: “Twelve cells which had been sealed after formation remained unchanged from March 18" 1905 to May 7 1914, i.e. during 9 years. Their EK. M.F. has been during all this time 0,0505 Volt. The quantity of cadminm on the spirals varies between 3.7 and 13.7 mers. of cadmium”. 20. The decrease of E.M.F. which had been observed with cells which contain only 10 mers. of cadmium is consequently not to be ascribed to the minute quantity of metal’) deposited on the spirals; this quantity is much less in the cells which have been constant during 9 years. The reason of the decrease in E. M. F. of those cells is the transformation of y-cadmium into «-cadmium. 21. In order to check this conclusion we prepared a number of cells (at room temperature) whieh only contained 5 mers. of cadmium on the spirals. Some of these remained metastable (0.050 Volt) while others were transformed into the stable form (0.047 Volt) after some days. 22. Although the discussion of a number of questions must be delayed until a subsequent paper, we will mention here the behaviour of cadmium which has not been formed by electrolysis. In our second paper we stated that a piece of cadmium chosen at random which had been produced from the molten metal contains three modifications: «, B and y-cadmium. If such is the case, it might 1) OpprBEcK found [Wied. Ann. 31, 337 (1887)] that a layer of metal A of 2>10-® mm. suffices to give to a metal on which it has been deposited the potential of A. As the surface of the spirals in the H. C. was 0,28 cm? the layer of cadmium deposited is much thicker. 131 be expected that the potential of such a material against cadmium which has been formed by electrolysis should be zero. In erder to test this conclusion we carried out the following experiment: We prepared a certain quantity of electrolytic cadmium (Prep. A) (Comp. our second paper § 8) and determined (at 40°) the potential diffe- rence between this material in a solution of cadmium sulphate which was half-saturated at 15° C. and: 1. Cadmium, which we received from KAnLBaum (molten) in a finely divided state (Prep. B). 2. Cadmium which we had used in our dilatometric measurements ; in this material the presence of y-cadmium was presumed. (Prep. C). Making use of the small apparatus shown in Fig. 3 we first determined the potential difference between two samples of the same material, subsequently that between samples of different preparations. In this way we found: E.M.K. of A against A = 0.000037 Volt. a Be) eee B= 01000018) Volt: ~C ‘A C= 0.00000 — Volt. Be MEK A 3 3 = 0.090037 Volt. Ae) C0 0000377 Volt: From these measurements we see that y- cadmium is really present in our preparations, Fig. 3. as the dilatometer had shown. Utrecht, May 1914. van “T Horr- Laboratory. (July 3, 1914). KONINKLIJKE AKADEMIE VAN WETENSCHAPPEN TE AMSTERDAM. PROCEEDINGS OF THE MEETING of Saturday June 27, 1914. Vou. XVII. DEce — President: Prof. H. A. Lorentz. Secretary: Prof. P. Zeman. (Translated from: Verslag van de gewone vergadering der Wis- en Natuurkundige Afdeeling van Zaterdag 27 Juni 1914, DI. XXIII). COW EE anes Se JAN DE Vries: “A triple involution of the third class”, p. 134. W. Kapreyn: “On the functions of Heruirs.”’ (Third part), p. 139. M. J. van Uven: “The theory of Bravars (on errors in space) for polydimensional space, with applications to correlation.” (Continuation). (Communicated by Prof. J. C. Kavreyy), p- 150. M. J. van Uven: “Combination of observations with and without conditions and determination of the weights of the unknown quantities, derived from mechanical principles.” (Commu- nicated by Prof. JAN DE Vrigs), p. 157. F. A. H. Scurememaxers: “Equilibria in ternary systems.” XVI, p. 169. A. Smits and 8. Posrma: “The system ammonia-water”. (Communicated by Prof. J. D. van DER WAALS), p. 182. N. G. W. H. Brercer: “On Hermire’s and Apev’s polynomia.” (Communicated by Prof. W. Kapreyn), p. 192. Ernst Couen: “The metastability of the metals in consequence of allotropy and its signi- ficance for Chemistry, Physics and Technics’. II, p. 200. Pu. Konuystamm and K. W. Warsrra: “Measurements of isotherms of hydrogen at 2C° C, and 159.5 C.” (Communicated by Prof. J. D. van per Waats), p. 203. K. W. Watsrra: “The hydrogen isotherms of 20° C. and of 15.5 C. between 1 and 2200 atms.” (Communicated by Prof, J. D. van pER Waats), p. 217. D. J. Kortewec: “The different ways of floating of an homogeneous cube”, p, 224. A. Wicumann: “On some rocks of the island of Taliabu (Sula-Islands)”, p. 226. F. M. Jascer and A. Simex: “Studies in the Field of Silicate-Chemistry”. II. On the Lithi- umaluminiumsilicates whose composition corresponds to that of the Minerals Eucryptite and Spodumene, p. 239. Ibid ILI. On the Lithiumaluminiumsilicates, whose composition corresponds to that of the Minerals Eucryptite and Spodumene. (Continued), (Communi- cated by Prof. P. van RompurGn) p. 251. E. Laqueur: “On the survival of isolated mammalia: organs with automatic function”, (Com- municated by Prof.,H. J. HampBurGEr). p. 270. C. A, Crommetin: “Isothermals of monatomic substances and their binary mixture:. XVI. New determination of the vapour-pressures of solid argon down to —205%.” (Communi- cated by Prof. H. Kameriincu Onngs), p. 275. Il. KaMErRtINGH Onnes: “Further experiments with liquid helium. J. The imitation of an AmprRE molecular current or a permanent magnet by means of a supra-conductor”, (Cont.) p. 278. H. Kamertinen Onnes: “Further experiments with liquid helinm. K. Appearance of begin- ning paramagnetic saturation’, p. 283. 10 Proceedings Royal Acad. Amsterdam. Vol. XVII. 13 W. Karreyn: “On some integral equations”, p. 286. H. G. van pe Sanne Banunuyzen, N. Winpesorr and J. W. Diererinx: “Comparison of the measuring bar used in the base-measurement at Stroe with the Dutch Metre No, 27”, p. 300. ; ; Hi. G. van pe Sanpe Baxuvyzen: “Comparison of the Dutch platinum-iridium Metre No. 27 with the international Metre M, as derived from the measurements by the Dutch Metre- Commission in 1879 and 1880, and a preliminary determination of the length of the measuring-bar of the French base-apparatus in international Metres”, p. 311. L. K. Wotrr: “On the formation of antibodies alter injection of sensitized antigens”. 1, (Communicated by Prof. OC. Eyxman), p. 318. F. M. Jarcer: “The Temperature-coefticients of the free Surface-energy of Liquids at Tem- peratures from —80° to 16500 C. 1. Methods and Apparatus. (Communicated by Prof. P. van Romeuren). (With two plates), p. 329. F. M. Jarcer and M. J. Suir: Ibid If. “Measurements of some Aliphatic Derivatives,” p. 365. Ibid IIL. ‘Measurements of some Aromatic Derivatives.’ (Communicated by Prof. P. van RomeBurcn), p. 386. ¥. M. Jarcer and Jur. Kaun: Ibid IV. “Measurements of some Aliphatic and Aromatic \thers”. (Communicated by Prof. P. van Rompuren), p. 395. ? F. M. Jarcrer: Ibid V. “Measurements of homologous Aromatic Hydrocarbons and some of their Halogenderivatives”, p. 405. Ibid VI. “General Remarks”. (Communicated by Prof. P. van Rompuren), p. 416. H. Haca and F. M. Jarcer: “On the real Symmetry of Cordierite and Apophyllite’. (With two plates), p. 430. P. ZEEMAN: “FRESNEL p. 445. J.J. van Laan: “A new relation between the critical quantities, and on the unity of all substances in their thermic behaviour’. (Conclusion). (Communicated by Prof. H. A, Lorentz), p. 451. s coefficient for light of different colowrs”. (First part). (With one plate), Mathematics. — “A triple involution of the third class.” By Professor JAN DE VRiks. (Communicated in the meeting of May 30, 1914). 1. I consider the projective nets of conics represented by Qaz? + Mag? + aMaz = 0 and Ab.* + 16,2 + 26 — The points of intersection of corresponding conics form a quadruple involution *). On the straight line YZ, which we may represent by 2, = ey, + + 6z;, the two nets determine the pairs of points, indicated by YA (Q’ay?+ 296a,az+o7a.2) = 0 and A (9%,? +200b,b.+-0°b.*) = 0. 3 2 These equations produce the same pair of points, as soon as the relations Day? = +t LAby?, LAayaz =e Zhbybz,, Dda.* = x1 > hb,’. 3 3 3 3 3 8 are satisfied. By elimination of 4,2',4" we find from this system the relation | Ay’ —tby", AyQz—tbybz, az’—tb* |= 0. . = 4 (2) 1) This involution is an intersection of the linear congruence of elliptic twisted quartics, which I haye considered in my communication in vol. XIV, p. 1127 of these Proceedings. 135 trom which it appears that YZ contains three pairs of the involution ; the latter is consequently of the third class. 2. We shall now suppose that the two nets have a common base point 4; they produce then a triple involution of the third class. We choose the base point 4 for vertex QO, of a triangle of co-ordinates. Through QO, pass o ‘ conies of the first net, which are touched there by the corresponding conics. For we have the conditions Ss — > ‘ Sy) = SS Sr — 407 and 2 Na — t= be, 3 3 3 3 so that the parameters 4, 4,4” are connected by the relation aes aie Oued | 3 3 . | — — [=== OL ies Voeomas cle ectperttig(()) eid a =b,,4 3 3 Now we find from (1) | Ie Ie |) ea Ge iL ete. | | | 12 "2 | BE ose If we substitute these formulae 2, 4', 4" in (3), an equation of the eighth order will arise. The locus of the pairs Y', X" of the triple involution (Y*) associated to O,== A is therefore a curve of the eighth order, which we shall indicate by «&; A is a singular point of order eight. By (3) two projective systems with index two are separated from the two nets, which systems produce the curve «*. Their intersec- tions with the arbitrary straight line 7, are the coincidences of the (4,4), which the two systems determine on 7. If 7 is laid through A, the free points of intersection are connected by a (2,2); one of the 4 coincidences of this correspondence lies in A, because two homologous conics touch each other and 7 in A. Hence it appears that the s¢ngular curve a has a quintuple point in A. This corre- sponds to the fact that (V*) must be of the third class; the three pairs on a straight line 7 laid through A are formed by A with the ihree points in which 7+ is moreover cut by @*. The line «c= XX" envelops a curve of the fifth class; for of the system (x) only the lines which touch e* in A pass through A. 3. A is not the only singular point of (X*). The homologous conics intersecting in a point Y are determined by Ziha,? = 0 and Pi ie 3 3 If these equations are dependent, JY becomes a singular point. 10* 136 Through Y pass then two projective pencils of conics, which deter- mine a quartic represented by Qy> ax? bx? Ohare cnt re. ((24) or also by [B52 Gat Mast ie=Oh\ (212) 5 ees The singular points are determined by the relations Qy? ay" ay’ by? by? By [aoe Now the curves a,? 6,'? =a," b,? and a,’ 6,’? = ay’ 6,’ have apart from the point QO, (which is node on both) 12 points in common. To them belong the three points, which a,? =O and 6,7 = 0 have © in common apart from O,; they do not lie, however, on the curve ay" by"? = ay'" b,. There are therefore, besides the singular point A, nine more singular points By; the pairs of points, which form with ZB; groups of the involution (X*) lie on a curve {;*, so that By is a singular point of order four. The singular curve (;* is produced by two projective pencils with common base points A and ;; it has therefore nodes in these two points. From (4) and (5) it appears that this curve also passes through the remaining singular points. The straight lines 2, which contain the pairs X’,X’’ lying on s;', envelop a conic. As §,* passes through A twice, there are in (X*) two groups in which the pair A,45; occurs; so 5, belongs twice to a*. This singular curve has therefore besides its quintuple point A, nine more nodes Ey, is consequently of genus two and of class 18. On each of the 8 tangents of a*, passing through A, two pairs of the (X*) coincide; from this it ensues that the straight lines s on which two pairs have coincided, envelop a curve of class eight, which we indicate by (s),. 4. We can now determine the order « of the locus 4 of the pairs of points X’, Y’’, which form groups of the (X*) with the points Y of a straight line / As a* contains eight points of J, a passes eight times through A; analogously it has quadruple points in By. The w points of intersection of 2 with an other straight line /* are vertices of triangles of involution, of which a second vertex lies on J, so that the third vertex must be a common point of A and 4*. As these curves, besides in two vertices of the triangle determined by the point //* and the w points mentioned, can only intersect moreover in the singular points, we have tor the deter- 13% mination of 2, the relation 2? = «+ 2+ 87+9>< 4"; hence 15. The transformation (XY, X’), which replaces each point by the two points, which (X*) associates to it, transforms therefore a straight line into a curve of order fifteen with an octuple point and nine quadruple points. As 7 contains three pairs X,X’, which supply six intersections with 4’, the curve of coincidences Jd is of order nine. Apparently d* has a quintuple point in A and nodes in By. With a’, J’ has 56+ 9X 4=—66 intersections in A and B;; the remaining szv are coincidences of the involution of pairs lying on a@*. Analogously we find that /* has fowr coincidences on £;'. The supports d of the coincidences envelop a curve of the éenth class (d),,, which has a quintuple point in A. 5. The locus of the pairs X’, X’’, which are collinear with a point /, is a curve «*, passing twice through 7 where it is touched by the lines to the points “” and #”’, which form a triangle of invoJution with /. It is clear that e* will pass three times through A and twice through each point 4; it is consequently of class 30. To the 26 tangents of «°, passing through /, belong 10 lines d; the remaining ones are represented by 8 bitangents, which are straight lines s. If EF is brought in A, then «* passes into «*. For a point 2, &§ consists of ~,* and a curve ¢;‘, which passes through A and the points 4; and has a node in 4; The two curves have 14 inter- sections in the singular points; the remaining two are points /’ and i’, belonging to = B;,. The 6 tangents passing through 2, at es; are supports of coincidences; the curve (d),,, has 2, for node. The curve «* has with d*® 51 intersections in A and #;; of the remaining common points 10 lie in the coincidences mentioned above, of which the supports d pass through /. Consequently there lie on é* 11 coincidences Y= X’, of which the supports do not pass through /, whereas \’ and X’’ are collinear with /. These 11 points belong to the curve e,, which contains the points YX, for which the line «= X’X’’ passes through /#. The curves ¢«* and g also have ihe points 4” and /’’ in common, forming a triangle of involution with ££. As Z£ is collinear with 5 pairs of the /? lying on @* and with 2 pairs of the /* lying on Ly, &, passes five times through A and twice through #;. Consequently ¢° and «, have in all 3X5+9X2-+13=—64 points in common; the locus of X is therefore a curve «,*. 138 As EF is collinear with 5 pairs’) X’, X’’ of a’, and with two pairs of §2°, €* has a quintuple point in A and nodes in bg. If / is brought in A, &,° For £, &.° consisis of the curve 8,* and a curve *3,‘, which passes three times through A and once through the 8 points Bz. The intersections Y of «° with the straight line / determine 8 lines w= N’N’’ passing through /; we conelude from this that x envelops a curve of the eighth class (1), when X describes the straight line J. In confirmation of this result we observe that with the 8 intersections Y of / and «* correspond the 8 straight lines passing through A(X’’) to the associated points X’. As (/), must be rational, consequently possesses 21 dbitangents,. / contains 21 pairs Y,¥, for which the corresponding points X7,.X7’; coincides with a’. V’,¥” are collinear. 6. An arbitrary straight line contains three pairs (Y’, X"), (V7, 1"), (Z’,Z") of N*’; the corresponding points X, ’, Z apparently form a group of a new triple involution*), which we shall indicate by (XYZ); it appears to be of class 21. Apparently (XYZ) has singular points in A and B;. Let x be the order of the curve «, which contains the pairs }, 7, belonging to NA; let further y be the order of the corresponding curve b, belonging to Bg. Let the straight line 7 be described by a point 7, the associated pair X}” will then describe a curve 2, the order of which we shall indicate by z. If attention is paid to the points of intersection of 7 with @ and ~;, it will be seen that 2 must have an 2-fold point in A, a y-fold point in By. In order to determine the numbers a, y, 2, we may obtain three equations. We consider in the first place the intersections of the curves 4 and gw, which are determined by the straight lines /and m. To them belong the two points which form a triplet with dm, further z points Z, for which X lies on 7 and Y on m; the remaining intersections lie in the singular points. So we have the relation 2 2) ee ae? Esa 5 eee Let the curve «a® be described by 7, then the figure of order 82, 1) The curves g® and <-§ have 3X5+9X2X2=5!1 intersections in the singular points; they have 3 more points in common on FA; the remaining 10 intersections form 5 points A’,X” collinear with £. From this appears anew that the curve of involution z® is of class 5. *) This property is characteristic of the triple involutions of the ¢hird class. 135 which is described by the pair X, Y, will be the combination of twice a’, five times a® and twice Bx. Hence SSS Gas bye ste So og eS ea a 6 l(t) If Z deseribes the curve *3,*, the corresponding figure of order 4z consists of the curve @,*, of three times @*, and of the 8 curves Bw (k £1). Hence : AV EY) ote og a, Oe a Ose Gs) Out of (6), (7), (8) we find by elimination of « and y, 2? — Viz + 882 =0; so z is equal to 63 or 14. The second value, however, must be rejected ; for we have proved above, that (XYZ) is of the class 21, so that 7 has 42 points in common with 4 at the least. So we find the values z= 63, « = 40, i iis For the involution (YYZ), A is a singular point of order 40, B, a singular point of order 16. As 7 ana 4 besides the 21 pairs already mentioned can only have coincidences in common, the curve of coincidences (XYZ) is of order 21, Jd*’. Apparently a‘? has in A a 20-fold point, @,'° in Bz an eight-fold ‘point; in these points d** has the tangents in common with «* and 3;.°. If X is placed in A and Y in By, c= X' X" envelops a curve of the 5t class, y= Y'Y"" a conic; so there are 10 straight lines a=y. From this it ensues that the singular curve @*° has ten-fold points in B;. In a similar way we find that the curve (;"* has quadruple points in /,; it passes ten times through A, eight times through Dx. Mathematics. — “On the junctions of Hermite.” (Third part). By Prof. W. Kaprryn. - (Communicated in the meeting of May 30, 1914). 12. After having written the preceding pages, we met with two important, newly published papers, on the same subject. The first by Mr. H. Garsrtn: “Sur un développement @une fonction a variable réelle en série de polyndmes” (Bull. de la Soe. math. de France T. XLI p. 24), the second by Prof. K. Runer ‘Ueber eine besondere Art von Integralgleichungen” (Math. Ann, Bd. 75 p. 180). 140 In this section we will give their principal results though not altogether after their methods, and make some additional remarks. 13. Mr. Garprun considers the question of the expansion of a funetion between the limits @ and 6, in a series fe) = AM, (a) + A, (a) +. where 6 el Ls A, = — —= [e—“7 (a) My (a) da. 2°n!l Vax. ; a He finds that this expansion is possible when /(«) satisfies the conditions of Diricatrr between the limits a and J. This agrees with our result in Art. 7, the only difference being that our limits were —oo and +o. This difference however is not essential, for considering a function which has the value zero for all values a>a>b Art. 7 gives immediately the expansion of Mr. Garsrun. His proof rests on two interesting relations which may be easily deduced from the formulae in the first part of this paper. The first relation S Ay (#) Hp (@) ay alts Ay 43 (x) HT, (a) — H,, (x) Ay+1 (a) (29) Fp 2p! 2r+lp/ e—a may be establishedin this way. According to (5) we have 2xHy 2) Sas x 2nH,—1 (x v LT, (a) Jal +1 (%) + n 1 (x) (n> 0) 20H, (a) = Ap (a) 2nIT, - 1 (a) Multiplying these equations by H/,(a) and //,(2) we find by sub- tracting 2 (@ —a@) A, («) Hy (a) = Ani («) An (a) — An (#) An-1 (2) — 2n|H, (#) Hy—i (a) — Hp—1 (x) I, (@)). Hence, putting for m successively 0,1,2,..n, we get 1 | 2(¢-a)H,(«)H (a) = H,(x)H,(a)-A, (2), (a) (2(e-a)H, (@)H, («)=H, (a), (@)-H, (x) 1, (@)-2 |, (a) 41, (a)-H (x) 2, (a) | 2(r-a)H, (a), («) =H, (a) H (a) -H,(a)H,(«) - 4[H,(w)H, (a)-H, (w) 1, (@)] —— | 2a) Hy (0) H, (a) =H 4.1(0)H, (0) Hye) 4 Ce) —2n| H,(a)H, —\(a@)-H" (2) H, (a) |. \ 141 in question Multiplying these relations with the different factors written on the left, the addition of these products immediately gives the formula The second relation zx ales Ga Vals | ¢ A See ee OES ee co. (30) 1 27 nl 0 may be obtained by introducing (9) into the first member Thus we get T,(@)H,—-1(2) 1 27. nl eon" wo ioe} u2 eo ial —— nm f : —— = e 4 u®cos | vu — — J|du J e—’v —! sin wu | Qin 2 0 where NIT vv — =) dv . 2 1 wo yryr nm nx —2 cos{ wu — — }sin{| xv — = o 42". n! ( 2 ) ( 2 ) __ cos au sin xv eur iy sin wu COs VY %, urk+ly2k+l Fx ; Q2k (Qh) F ] Q2R+N(2h+ 1)/ uv uv uv uv cos au sin av (e2 +- e ® i sin xu cosav (e2—e 2 re v ( 2 ) v ( 2 ) Substituting this value, it is evident, according to the formulae of Art. 6, that all the terms of this sum vanish except only the term corresponding to —1. Hence = H,,(«) ay = @ = oe COS LU SIN LV — du dv jl Qn nl ae v 5 and because eb u? Ss Ji J e COBL DIGI —= Vor ean Ne ree Vn ence as (22) a 0 ea vp &, H,(a a ae 1 (coma sie er € dv. ae Qn, Rees v 0 If now we iply O and w, we hav multiply the equation (a) by dev and integrate between e 149 &® wu? x 7 4 Stn eu af fe du=V ax | e-* de, u 0 0 thus finally HF 5S Hr(e) Hn— Ce) == et f ee? da. 1 22 nl 0 14. ° Prof. Rune gives the solution of the integral equation TF =| K (2) p(w -- 2) de <.5,2 eee where /(w) and A(x) are given functions and g (x) is required, by means of Hermire’s functions. He assumes K (x) = e—* [a, H,(x) + a,H,(x) + a,H,(2) + ...] gp («) = e—** [b,H,(2) ++ b,H,(a) + b,H,(@) + J which gives a J) = Gn be fe Hf, (x) e"t+2? HH, (u + «) dz or, after some reductions : 4 u Wm oo “(Ve (a) — = (— 1)"anbn : — =e i ) VAR th ( ) ; (V2 yntn If now, the given function f(w) is expanded in this form | u u "(u) = = ats cs (v2) ar : (v2) sie u) = —e Cy C, — Cy a i V2 V2 (V2) we have from (31) c) =a bn 3 16; = 0,000), 4) Cy =, 0s 10 Ge Oraienere and it is evident that from these relations the coefficients 4 may be determined. If /(w) and g(x) were the given functions, the same relations would be sufficient to determine the function A (7). 15. The preceding reduction rests on the formula ie 1 ET +) = —— [A,(2) + C."A-a(a)7,(y) + Cy" Ap—0(w) H,(y)4+. . wer + C,,(y)) (32) 143 where C’ are the binomial coefficients. This relation may be obtained in the following way. According to Art. 8 Il we have . h? h® eens Th H, @) =le Dye (2) a 37 H, (<) ety ein ts) (p) and, expanding by Taytor’s theorem F(« +h, y + &) TA (a) ea ad l d e— (tk? —(y-+k)? et? +9? —er"-+7" | ev aey | e—y* al =) +e? ao ) | ai Y i ie Pads o 5 d is d ae et a e eye (eat ae [eee ey et : rary da? ‘ uF da \ dy ‘ By da? rs | - which may be written k? e— 2h 2h 1 AH (0) + Hy) +5 [A (0) 42110) (+H (0) where Putting now ¢ Seen (p) and k= no in.(g) we get V2 V2 e-(a+yhve—l? — 1 —h H, (=) as = IT, (=) ect . h easy i218 — | Va [| H, (x) + A, (y)] + jE EG) Roe Gy 4 Fy ee (V2)72/ : hn Comparing the coefficients of — im the second members we obtain nh. the required relation (31). Proceeding to the reduction of the integral a M ee] EH, (w) e~2? IT, (u +a) da we put, according to (2) qn Lith (wv) —— (— 1)m ev oe (e-2") dam then xD >in , M= ip) ron OM) whe? Hh, (u +2) de. dat Now, integrating by parts we have generally i44 in jin U fe a da=(— 1m firs dw + < ¢ Lym Lym + | oS V dU dm—2V qm—1 U | Seo iy da dx dxm—* dam—1 thus, assuming OG 6 =n) and introducing the limits —o and o = dm M =/e"= [e—utt? A, (uta)] da ain = (1)"fe-2 dutn —u+r)?) d — ) é damtn (e . ) v — (<1 fe —x2—(u-+xr)? et (u+-2) dz or, adopting —v uv V2 t= —— V2 See - N= ames ap ad Antn (ee) dg. V2 V2 Applying now the relation (32), it is evident that the integral reduces to the first term, thus (_D* pat An+n (v) V2 (VY Q)mn Uu Ue Tn, a7 (-1)" ~2 (ys) = -—— e = : VY 2 (Vv g)mtn 16. We will now compare the preceding solution of the integral- equation (81) with the formal solution given by Prof. K. ScHwarzscHILp Astr. Nachr. Bd. 185 N°. 4422). Putting MS or finally M Cer ey 18 Cae the equation fe (t.s) F'(s) ds = B(t) 0 takes the form 145 fA (e— (u+®)) F (e—*) e-* dx = B (e—*) or, assuming e—* F (e+) = K (a) A (e— (4) = o (uta) Ble) =f) {xe gp (u -+ «) dx = f(u). Now Scawarzscaitp multiplies this equation by e-’“ du and inte- grates between the limits —o and + o, thus [reo e—4u du =f ¢ (x) ae fy (uta) e—%u du = | K (ec) e* de fo (v) e—2” dv and puts 2 i ,2 . Tw = fro eudu thus F (4) = 5— fren e— Pu du aT —o 5 ier K (x) =z (a) e da x (2) = x I* (zie dx ast —D ~ Pye ‘ @p (v) = Paedy , Bo()= ml @p (v) e—?” dv therefore F(A) = 2aL (—-A) ® (A) or Ky) : 2x b(—1) LQ)= Multiplying again by e’*da and integrating between —o and + o this relation, he obtains ei a) K («) = — ——_—— et dj. 22.) b(—2) —o If now we compare this result with the preceding, we have 146 ee F(a)= xf eu du or u ar. 2 Ripe |e 5 a Wee F(a) 1 Ve ( — F NS (va) : b=— - CA Cy —— CF ae 5 du. on V2. ‘V2 (ar The general term in the series of the second member being u2 Se } . Pay) ‘eo Jens = fe 2 IT, Ga e—44 du = V 2 fe 0? FT, (v) e742 dy V2 —o —on it is obvious that for 2 = 24 the imaginary part and forn—=2k+1 the real part of this integral vanishes. Thus for m= 2h i v2 | e—* Ao}. (v) cos (A v V2) dv, where according to Art. 8 IL 2 = Tops 2p os (AvV2)—e ~ S(--1)P ——— Ae, (v cos (Av ) é =i ) 2302p)! 2) (v) thus 2k+1 2 a ea Pop — (=a) 2 Vaaric mmaate In the same way, we get 22 Poppy = — i(— 1k 241 Ve 7 ARH and therefore 32 Y eT s% eee iC) = DS Po}. SS Ps \ ) 2V 27 Ok 2k u 2k+1 2k-+1 2 2 Biers s | = 58 [2 (— Mk ow Ei S (1h conga PE]. In the same manner we find ® (2) = * [3S (1) bop 22!# — 2 S (—1)* borg BAH] Va and finally 147 2 LC a Shoot iS (—1) hoop 12H ar : ex dx. rf S(—1)bad* piste ee If now the conditions SUNS C100 a0) c, =a,b, —a,b, + a,),, are satisfied, A(z) must be reducible to e— [a HH, (x) + a, H, (v) + a, A, (x) +...) It is easy to show, that this is the case; for if the conditions are satisfied we have D(—1)Fenp2 + iS (—1 hong 22k 41 S(— yo! iS (— 1) EH a,?-+-a,2* ... —i(a,A—a,A*-+ ...) ——n Ob 0 thus NY ey iKe(2)\— BV= Oe [> —1) ao, 2-1 (-1)F aon) A2AF1] (cos Ax + isinaa)da “Va 2 2 1 aoe. = ——_ | e * [cos Av XS (—1)' ap 2k + sind x S (—1)F agp 4 2k+1] da. Va or, introducing (9) =} = Hoy, (x) e-? = Gade € 4 yok cos Aw da Vae 2 ae apes Hox.43 (x) e—? = -—— e A2K+1 sin Ax da Vw K(#)=e = [a, ‘Hi, («),+ «, A, (#).+.2, Hf, (z) +... 17. From the relation (32) another important result may be deduced. For multiplying by e—” dy and integrating between — o and o, this relation gives yH (224) 4 Va fe Jab (Se) a = (van ae+-y= aV 2 eS (V2 )rh or, putting fave H,(a)da = H,(z). —o@ Therefore, assuming 148 1 = @;(a) = a 2 H,(w) 22Y/nl x we obtain Q)rFl ( — —(Y—= ay?2 +23 Cs (G)) = Vv = | e a 3 ein Va thus, in the same way as in Art. 9 3 = 1 gee 24 By — — (a2—-—ary2+a3 A= (V2), K(z,c) = Va Boe ( 3 i m Here the value of the function A’ (@.«) is finite for wand @ + o. In the same manner as in Art. 9, therefore es L)Ppn)a K(«,e) == nl“) Pn)@) 0 an or e—(a2—2xa) 2+ Ce > H,(«) Hy(@) 1 3n+1 22 ni which may be verified by (9). 18. Now, according to the theory of the integral equations the determinant D(a) of the kernel A(v,¢) must vanish for the values 4=V2y41MmM=0,1,2..)). To examine this, we write D(a) in the form which is given by PLEMELJ ') Oe Pappa 3 Se = (sea a GaP SE on: D(a) 1 2 as where a, = | K(a,2)dz2, af K (eae, a,—|\K,(@ x)da,..-: K,(a,@) = [Kew Ky—1(y,@) dy (n =1,2.3...) and K,(v.a) = K (a.a) From K (vy), which may be written K (ay) — Agha 2kay—ly* 1) Monatshefte f. Math. und Phys. 1904 p 121. 149 the functions A,,(7y) which have the same form Ki, (xy) = Ane —hnax* + 2k, xy—lny’ , may be easily deduced, for ace K,(w.a) = AAy—1 fe (C+ hn) y? + 2(he + ky a@)y— (he? +1, 10° ) dy -@ and 2) 7 oa) 5 G2 fh gq \? : == =i j= = fe Sy 2gy—h dy ——/ On | é ( ) dy =o —o g—fh — ara =: ———— Vif Hence —h,v2+-2h,va—l,a@? A, é — ke? kkn—1 Re A —— == a? +2 : ca—| l4— ae a ee! = ( I+-hyn—1 Lt hy—1 i l+hy—1 = V; e Vit hn ‘ which gives APA = ke k kn— 1 u— —_— Vas hy=h— a a — ieee l,=l,-1— me : - Vhthy-1 la-hn—1 I+hy—-1 bt hy Now, we know 4 : h i k=/y 2,1 8 Jal SS oF OOS => ay — — Va Biv, 2 thus i. 5 2 5 A, == , kh ES — Se LS = V32 6 3 6 1 9 2V2, A, =——= », 4, S — , 4 = - z neers Via 14 7 14 1 17 4 17 : “ Wiba 3 and nH ee LA Bet A Eas ae Re ee Cn oon et Sk, This gives 11 Proceedings Royal Acad. Amsterdam. Vol. XVII. n+1 2S ~ as r? oy n+l i : Pp Penal ay ls QnA = fa (ez) dz = Veronad e af Cc =Ep 9 2a Constructing now, according to Wee an integral funetion 7(a), with the assigned zeros a= V2, 2=(V2)", 2 = (V2)... we obtain F@) = eG) (1 —— ,) F(9) n=0 (V2)n+1 or, assuming 7(0)=1, G@a=0, a= r f (a) = IT (1—AorH), Thus ic Tita aes PO AR sk he 70) Aa TS Ss and expanding the fractions of the second member Sep Se 2 =) OF 7@ eae ry +4 ee ete An eas Comparing this with D(A) Giese At+a,vo+. we see that /(4)= D(A), tor (0) = DO) =1 and a Srp — i's = : : p= aa ppt np 22 Mathematics. — “The theory of Bravais (on errors in space) for polydimensional space, with applications to correlation.” (Continuation). By Prof. M. J. van Uven. (Communicated by Prof. J. C. Kaprryn.) 1) (Communicated in the meeting of April 24, 1914). In the theory of correiation the mean values of the products aja% are to be considered; denoting these by 77, we have 1) The list of authors who have treated upon the same subject, may be supple- mented with: Cu. Mi. Scuots. Theorie des erreurs dans le plan et l’espace. Annales de |’Ecole Polytechnique de Delft, t IL (1886) p, 128. +n +o TT ae E : : —(b,.%"+ @it..+b ) : Vik = = =a UU € da, ..da n RP.) j= OX =—H To integrate in the first place over all the variables x except xv; and 2, comes to the same thing as to drop the g—2 linear relations x= Da; v;(/==7,4). Thus we start, as it were, only from 1 the two equations Bj = aziz + ajgve +... + ayers, Le = agiyvi + apgove +... + ager. and find therefore oo 2 ee pup +2 bi Ke jep + bpp’ eh?) | Yjik = LIL dajday , — oO U where E' == ES “ byy'; bik =p" Dik's Dick D’ yepresenting a determinant of the matrix Qj1y Aj2y +++ Aj | IE | | | cet 5 Qp2s +++ Akz | Besides i Ae Gia sss « Ofens Dy = aj, Aj2y 2 0 6 Ajay hence Day? pees TIS es bj; Sse = ES ap; ; oe = — EH Dajiapi; in. = E'S a5;7. By performing the integration we obtain for 1;% t =a ater bite = Aj Uk lik == ) 7! 9 Sy? . 5 z =v; Ma, — (bj j'aj? 4 2b ja jap ben’ 247) rire = Aji a vj dz ;* = — —. \n _ —@ —@ Now the correlation-coefficient 7;; of v; and a, is defined by the expression A hn 152 — V nj ;%Kk This correlation-coefficient can therefore also be written in the following form > ajl al i —— — > aj". > axl” or By Vik V Bj; Bre Introducing the coefficients «;;, we find > €/? aj] Akl rik = —————————————— et) VS ef ae ae We now will imagine the variable w to be connected with some cause Q;. To express our meaning more clearly: we suppose the quantity 2 to be built up of some variables w, viz. as the sum of these variables, in such a way, that in this sum the term wy 1s lacking if ; is not subject to the influence of the cause Q. So in the relation Vj = aj, U1 + ajzue +... + aju +... + Qjz Us we have aji=1, when Q does act upon aj, aji= 0, when Qi does not act upon 2j. s Thus in 2 e? aj? only those terms &,*s &*)++-&,? occur which (— correspond to the variables u,,, u,,,...Ur,, due to the causes Oe GOR Weise Qn, actually influencing «;; on the other hand those terms are lacking, which owe their existence to the causes not con- tributing to 2;. In the sum 2 €/?aj;@% Only those terms &’ occur, for which both il aji=1 and az=1, that is to say: the terms, which derive from the causes (Q), acting both upon a; and zx. e The expression 1j;, = > &aj,a,, therefore may be called the i-1 square of the mean value of those elements of «j and xk, which are due to the common causes. z,;, We may define the correlation-coefficient of the quantities 7; and av, in the following manner, proposed by Prof. J. C. Kaprnyn *). The correlation-coefficient rj. of x; and xp is that part of the square of the mean error common to «vj and aj, which is due to the common causes. Supposing every quantity w; to have the same mean error, or €; = €9 == ...=>=6& , we find for rz = aj) Ay) Hg Ni SS eT V Sa;)’. = ap? Now + a;,* apparently equals the number A; of the causes acting upon 2j, ay? the number NV; of the causes influencing x, and 2 aj, ax, the number N,;;, of the causes contributing both tov; and x,. Jt Ek J 5 ‘ k Thus, in the case of equal mean errors, we have in other words: for ¢,=6#,—=...=e«, the correlation-coefficient equals the quotient of the number of common causes, divided by the geometrical mean of the numbers of the causes, which act upon xv; and 2, resp. If both xz; and zz are subjected to an equal number (V; = V;,—.V) of causes, Vj, of which act both upon 2; and a, then Nyx No in other words: the correlation-coefficient is that part of the causes of x; (resp. 2%) which also contributes to zz (resp. 2;). i The expressions for the correlation-coefficients admit of a very simple geometrical illustration. Calling spherical simplex S, a (g-dimensional) 9-gon lyeg on a g-dimensional hypersphere (extension of the spherical triangle in 3-dimensional space) we may state that a spherical simplex |S. has 9 (e—1) as —— edges pj, = Pj Pr. Gsavertices) 2 er. =... 3P, and Pp Opposite to the vertex P; we find, in the (@—1)-dimensional linear space a;, the (curved) (¢—2)-dimensional face of S,, which contains the remaining e—1 vertices P; (j=|=2). Further we denote by 2a), the angle between the linear spaces x; and a; [consequently also between the (@—2)-dimensional faces 1) J. CG. Kapreyn. Definition of the correlation-coefficient; Monthly Notices of R. A. §., vol. 72 (1912), p. 518. 154 (Pi; Pa. se Pia Pha. PA and te Res en e ee Building the positive-definite determinant | 1 1 .€08)19) oh RCOSYPiS wy a= mismieenCOS OH om | | | cos P12; ] Te COSV0D3) uated i COSiDDD. r= cos Pig, COS P23 1 spn) eet SBCOS IS COS Pip , COSP2ap , COSPgo 3 - = - 1 | and representing by Cj, the minor of cos pyr, we have by the theory of the spherical simplexes : Ujk V Cy; Con cos Hj, = — Substituting big =H" bj = Gy Me C08 zk the quadratic form H in the expression for the probability W trans- forms to H = Bb 5; 0; + 2 Vd jK w; wp = ZV (qy aj)” + 2 > cos pju (95 %7) (Gk ee)- This form is positive-definitive, when r>0, or, in other words: when the arcs pj, are the edges of a o-dimensional spherical simplex. Furthermore P o ~ i —— GL 1 and i ° I V- 1 Y Bip = ——_~ XK Cite qj Qk whence Byy. Cir i — Z g - == — cos IT;x,. VBij Bex V Cjy Crt So, putting H in the form H = XJ (qj 2;)? + 2 = cos pjx (qj 7) (ge 2k); the ares pj; must be the edges of a 9-dimensional simplex and moreover: the correlation-coefficients are, but for the sign, equal to the cosines of the “opposite angles” IT;,. In the case of “errors in a plane” only a circle-biangle P,P, is to be considered. Then the are P,P, =p,, equals the angle J, 11515) included by the opposite spaces (straight lines, radii of the cirele) a, = OP, and x,=OP,, O being the centre of the circle. So, in the case of two variables x, and x, with the quadratic form JE Oe tie PAO Cy Ol a= Opt re we have to put bi, =" 3 b,, = 49; ’ bb. =H G2 COS Py 5s whence E = q,’ 9," sin* p,,- The correlation-coefficient 7, now takes the value 13 b 12 i —— 1 COS ——|——1C08, Da — —. DVGe Considering the errors in 3-dimensional space, the spherical simplex 13 2 is a spherical triangle P,P, 7. The quadratic form //, after being transformed, reads HH Gy? 749g %y +9 q © y $29.93 2g COSPy y $29,912 gi, COSP y +24, Jo iV COP, The opposite angle J/,, of the edge (or side) p,, now merely is the angle P, of the triangle. Denoting, for the present, the edges (or sides) by p,, Py, Ps» So that (eg 0 Tee 9 WS we have COR = —— COS Ti == —IC0Se and cos P, + cos P, cos P, ee ; COS Py, = C08 Py = = = =—- els, SUPE Spas V(1—r, ,?)(1—",,”) I= 1 — cos’ p,, — cos" p,, — cos” p,, + 2 cos p,, COS p,, COS P,, = 1 — cos’ p, — cos? p, — cos* p, + 2 cos p, cos p, COs ps. Putting further Pitptp=2s , P+P,+P,=28, we may reduce T to T= 4 sins . sin (s—p,) . sin (s—p,) . sin (s —p,) = 4 cos S. cos (S—P,) . cos (S—P,) . cos (S— =| 0 TEA JER Gp Lee The relation ajay Biz = — = —_ a 2 2H here involves Ons Of Be | by 5, Oss Jz Qs Sin® Pp, — = = Sao Sete : In = 97 2B QE: Now a — 4 cos 8. cos (S—P,) . cos (S—P,) . cos (S—P,) e — . . . 4 ; GOs 1 i Tee hence sin? P 1 i —e : x ’ 13 2[—4cos S . cos(S—P,) . cos(S—P,) . cos (S—P,) ~~ q,? Putting — 4cos 8. cos (S—P,) . cos (S—P,) . cos (S—P,) = Q, we obtain ae ae io = 2 2 ’ whence sin P, ho u V2Qn,, Further we find, after reduction, Q = 1 — cos’ P, — cos? P, — cos? P, — 2 cos P, vos P, cos P,, consequently rae i Pa + 2 Toa Tig Ties Finally (RS one oe Oba qa" Osa Q° = = etek Pain? Phen Plein 873,N1s%ssQ Introducing the mean errors 7,, 9, and 9, of 2, 7, and a,, Which satisfy the equations & —— Pt een Ub 4h 9 Ye = hee yy = han ’ we find sin P; ; : ee ee) ni V2Q 1 Psa e Ie . E and Tes Tis Tie 1 betel feat ih 9 723 ae =— ee — evel Je Geos. i eae ds, .05,.08,. Ps — (22)"2 1, 4,%,VQ 157 Mathematics. — “Combination of observations with and without conditions and determination of the weights of the unknown quantities, derived from mechanical principles. By Prof. M. J. van Uven. (Communicated by Prof. JAN pr Vaiss). (Communicated in the meeting of May 30, 1914). The theory of the combination of observations by the method oc Jeast squares has already been the object of numerous geometrical and mechanical illustrations. In the geometrical representations the leading part is usually played by vectors (L. von Scururka '), C. Ropricurz*)); the mechanical ones are taken partly from the theory of the ‘pedal barycentre” (Y. Vinuarceau *), M. p’Ocaene *) ), partly from the theory of elasticity (S. Finsrerwanper®) R. b’EmILIo‘), S. WeELnmIscH, PANTOFLICEK ’), F. J. W. Warrier’), M: WrsterGaarD *), G. ALBENGA ")). In the following paper we will try to develop a mechanical analogy of the solution of the equations furnished by observation, supposing that no conditions are added, as well as for the case that besides the approavimate equations of condition (called by us: 1) L. von Scururka. Eine vectoranalytische Interpretation der Formeln der Aus- gleichungsrechnung nach der Methode der kleinsten Quadrate. Archiv der Math. u. Physik, 3. Reihe Bd. 21 (1913), p. 293. 2) (C. Ropricurz. La compensacion de los Errores desde el punto de vista geo- metrico. Mexico, Soc. Cientif. “Antonio Alzate’, vol. 33 (1913—1914), p. 57. 3) Y. Vimrarceau. Transformations de |’astronomie nautique. Comptes Rendus, 1876 I, 531. 4) M. p’Ocaene. Sur la détermination géométrique du point le plus probable donné par un systéme de droites non convergentes. Comptes Rendus, 1892 1, p. 1415. Journal de l’Ecole Polytechn Cah. 63 (1893), p. 1. 5) S. Finsterwatper. Bemerkungen zur Analogie zwischen Aufgaben der Aus- eleichungsrechnung und solchen der Statik. Sitzungsber. der K. B. Akad. d. Wissensch. zu Miinchen, Bd. 33 (1903), p. 683. 6) R. p’Emito. Illustrazioni geometriche e meccaniche del principio det minimi quadrati. Atti d. R. Instituto Veneto di scienze, lettre ed arti, T. 62 (1902—1903), p. 363, 7) S. Wettscu. Fehlerausgleichung nach der Theorie des Gleichgewichts elasti- scher Systeme. Panroruicex. Fehlerausgleichung nach dem Prinzipe der kleinsten Deformationsarbeit. Oesterr. Wochenschrift f. d. 6ff. Baudienst, 1908, p. 425. 8) F. J. W. Wutepte. Prof. Bryan’s mean rate of increase. A mechanical illustration. The mathematical Gazette, vol. 3 (1905), p. 173. %) M. WesterGaarp. Statisk Fejludjaevning. Nyt Tidsskrift for Matematik, B, T. 21 (1910), pp. 1 and 25. 10) G. Atpenca. Compensazione grafica con la figura di errore (Punti determinati per intersezione). Atti d. R. Acead. d. Se. di Torino, T. 47 (1912), p. 377. 158 “equations of observation”) also rgorous equations of condition are given. Moreover, in either of these cases also the weights of the unknown quantities will be derived from mechanical considerations. The method here developed is founded on the staties of a point acted upon by elastic forces and is in principle closely related to the procedure of the last-mentioned mathematicians. To obtain general results, we will operate with an arbitrary number CV) of unknown quantities or variables, which are consi- dered as coordinates in -dimensional space. In order to render the results more palpable, we shall, at the end, recapitulate them for the case of two variables. I. To determine the V unknown quantities ii iy. Zoe: ou « (UND) the » (approximate) equations of condition or equations of observation aja -+ by + o2+...4-m=0 (CS Oa) are given, with the weights g; resp. In the sums, frequently occurring in the sequel, we will denote by > a summation over the coordinates 2, Up poor OY Over the corresponding quantities (for inst. their coefficients @;,b;,¢;,...) and by | | a summation over the m equations of observation, thus over 2 from 1) fom: Putting accordingly aj? + 6? +o? ... = Bia? and introducing aj bj Ci mM; oS VSae = Sat = Sas ANS bi see A we may write the equations of observation in the following form Vi=aet By tyet...+u=—0 G=1e 2) or V;=Zaje¢+ w= 0 (CSS thpo so): These equations have resp. the weights Pi=H > ai’. The equations V;=0 represent (V —1)-dimensional linear spaces; their normals have the direction cosines (aj, 3;, yi,-.-) resp. In consequence of the errors of observation, the approximate equations |; =O are incompatible; in other words: the n linear spaces 7;=0 do not meet in the same point. By substituting the coordinates w,y,z,... of an arbitrary point P in the expressions V;, the latter obtain the values v;, representing the distances of the point P to the spaces V;= 0. The distance from V;—=0O to P is to be considered as a vector »; with tensor v; and direction cosines a, Bi, yi,..- We now imagine a foree ¥; acting upon P (in V-dimensional space) in the direction of the normal »; (from P to V;=0) and the magnitude of which is proportional to the distance v; and a factor pi characteristic of the space V;. (The space V;=0, for instance, may be considered as the position of equilibrium of a space V;=7; passing through P by elastic flexion.) So the space V; acts upon P with the force $= — pity. All the spaces V;(¢=1,...n) combined consequently exert on P a resultant force, amounting to 5 = [oi — [pal This resultant force depends on the position of the point P. Hence we have in .V-dimensional space a vector-field 5. determined by the above equation. Now the question to be answercd, is: at which point Pare these forces §; in equilibrium? For this point P we have =A") or lp pasi|i—20 The “components” of this vector-equation in the directions of the axes are pore | 07 lor 87 0) perry 07s. Substituting for v; the expression V;= Sa;c-+- ui, we obtain [piai?] a + [piaiBi) y + [piaiyi] 2 +.-.-+ [pia cal === (l), [piGiai] « + [piBitly + [piBivile +--+ ipibiuil =. [piviei] « + [piyiBily + [piv le +--+ [piviu] = 9, . or by aj b; A Cj mj ; esas == ———_ , pi = = YS 8 SS SS EH HL MG =» VA OO V ai’ ar (ea [giai?] a + [giaibily + [giaic. ] 2 +--- + [gaimi]=0, [gibacle + [gibi*)y + [gible +.-- + [aibimiJ =O, [giccac |e + [gicrbily + [gia*]2 +--- + [giami] = 9, In this way the ‘normal equations” are found, 160 . The force §;= — piti has the potential Ui= piv? =tpiVirs for : OU; OV; (Fi)x = — —— = — pi Vi —— = — pivia; ete. Ow Oa The whole potential therefore amounts to U=[Uil= 3 [pivi'). As the equation V;= Sa2-+4=0 has the weight p;, the mean error of weight 1 is determined by hence At the point P satisfying the normal equations the potential and consequently also €° isa minimum. The “weight” of the distance v; was pi- This weight may be determined a posteriori, if we know the influence of the space V; alone acting upon any point. We then have but to divide the amount /; of the force §; by x. II. In order to find the weights of the unknown quantities, we now remove the origin by translation to the point P, which satisfies the normal equations. Calling the minimum potential U/,, denoting the new coordinates by w',y',2',... and introducing V;'=aye' t+ Biy + ye +... aie’, we obtain lp? Va) 2 (Ey 20 So U’ is the difference of potential existing between a point (v', y',2',...) and the minimum point P. The equation [p; V;"]=2U’ represents a quadratic (N — 1)- dimensiunal space &, closed (ellipsoidal) and having P as centre. This space is an equipotential space and at the same time the locus of the points of equal ¢. We shall call these spaces 2 briefly hyper- ellipsoids. The hyperellipsoids $2 are homothetic round P as centre of similitude. Introducing the principal axes as axes of the coordinates _X, Y, Z, ..., we obtain for £2 an equation of the form AX? BY? 2072 4... = 2107 The components of § in the directions of the principal axes are found to be au" ? aU’ E du! a eS — dX =—_— AX, Fy =>— Pia —— Deh 7 — ry; === UC We may therefore attribute these components to attractive forces of the spaces ¥ = 0, Y=0, Z=—0,... (principal diametral spaces), which are perpendicular to these spaces and proportional to the “principal weights’ A, B,C,... For a point on the principal axis of X holds xe —— AX 1, oH yi — Ol 7 108 rete: Consequently the principal weight A may be determined by dividing the force at a point of the principal axis of X by the distance Y of that point to the principal diametral space Y = 0. To determine the weight of another direction !, only those points are required, at which the direction of the force coincides with the direction |, i.e. the points the normals of which to the hyperellipsoids $2 have the direction 1. When dividing the amount of the force existing at such a point Q by the distance of the tangent space of Q to the centre P, the quotient found is equal to the weight of the given direction. So, in order to determine the weight g, of the direction of the original z’-axis (or of the w-axis), we only have to turn back to the coordinate system w,y7/',2',..., relatively to which the equipotential spaces have the equation WA 40 For a point Q(a’,y’,z',...) at which the normal to the equipotential space, passing through Q, is parallel to the w'-axis (or to the x-axis), we have Ffys—g0' , Fy=0 , Fy=0, ete or so pe our Ou! apr = 9 , eae : ape ete, hence [pia Vi] == gee! , [pir Vi'}=0 , [piyiVi'] =, ete, or Lpiai*] a + [piaisil y' + [piaivi] 2! +... = goa’, [piBia:]e' + [piBi7ly + lpi Bivile' +-...=0, [piy.ai |e’ + [piviBily' + (piyZ)]e' +... 9, or y! Dpa : 1 : eH [pia |— + [piaibi] — + [piaiys] —-+...—1=0, Ju 4 Jat ! ; | i zZ ’ [pi Bias] — + [pi Bi") if + [piBiye]—t+.-..+90=9, Ja Jad Jat It ea [piyees] — -[piviBi]— + [pivi*] — +--- -0=9, Ix Jar Ja or ] y! 2! Jgiai?] 7 all le [gia; b; | ——1 |= laiaic | es +...— 1 == (0) Ix Jar Jak 1 < Of Zz lgbier] + [9 8i*] — +. [gi bit] — 2 =-F 0 = 0; Ox et Dyk 1 y' ber 2 : [gicia;| == [eieib; = =— [gier=]) —— + - - = 0; Ix Jat Jat Yo aes 4 ag ble So — is apparently found as the first unknown quantity in the De “modified” normal equations, modified in this way, that the constant terms are replaced by — 1,0,0,... resp. Considering U (e.q. U;) as an (N + 1)" coordinate perpendicular to the N-dimensional space (v7, v, z,...), the equation Vii 20; represents a quadratic space of NV dimensions, built up of 0 (N—1)- dimensional linear generator-spaces, all parallel to (V;=0, U=0), the intersections of which with the planes perpendicular to (V;=0, U7=0) are congruent parabolae. The parameter of these congruent parabolae is —. pi The quadratic space pi Vi? =2U; will briefly be called a parabolic eee ; il cylindric space with parameter —. su Di The equation | pi V2) 2 U represents a quadratic space W of N dimensions, the centre of which is at (7 =o, and the intersections of which with the V-dimensional spaces U = const. are hyperellipsoids 2. Thus YW is the extension of the elliptic paraboloid. The point 7 of WY with minimum JU (U,), and hence closest to (7=0, which is called the swmmit of ¥% is projected on U=O in the point P, satisfying the normal equations. By displacing the system of coordinate axes (w, y, 2,...,U) (by translation) from O to 7, ¥ obtains the equation [pi V;"] = 2 U'=2(U—D)). By constructing the enveloping cylindric space, the vertex of which 163 coincides with the set of points of the space «—O at infinity, thus the tangent cylindric space, the generator-spaces of which are parallel to the z-axis, we find for this cylindric space the equation Onatha ——ay life Ree : Its parameter is —, or the reciprocal value of the weight of the Gx direction «. Ill. We now suppose, that the variables w, y,2,... must at the same time satisfy the following » rigorous equations of condition Day ee) 0 (Gisaa5, 2) Then the point P is constrained to the common (V—»)-dimensional space ® of intersection of the »(N—1)-dimensional spaces ®;. Now the point P, subjected to the elastic forces §;, is in equi- librium, when the resultant 4 = [6;| is perpendicular to ®. Let the normal at P to #; have the direction cosines O®; OP; 0’; Ow Oy Oz a! J eae a Se tc (98 ee 0@;\? ca (0D; \; ie SS > v>(5') a CG) v3(%) The normals at P to the spaces #; form a linear v-dimensional space. In this space % must lie, which means: § can be resolved in the directions of these normals, the wnit-vectors of which will be denoted by w So we have a — 5 = [9 wy] where | ]' signifies the summation over j from 14 to ». The components of this vector-equation are Lpivias |] + [99 as’! =0, [pe riBi] + Lay B=, [piri ye] + [qi vi']'=09, ete. or [piai*] x + [piarBily + {pieivi] = +--+. + [piaiui] + [gj ey] = 0 [piBiec] @ + [pibi*] y + [peBivi] 2 4- ©. - + [piBiwi] + lay 8;'T = 9, [piyi ag] @ +- pees Ny Yet Piva lee seer ‘ [piyier] + [aj v5) =, Q Putine a ee? ie ae a, G=UVV= » (y=1,..>) Ow , we may write the above equations in the form , OD; Ow =20) [giai*) @ + [giaidi]-y + [aiaic le 4+... + [giaimi] + [qi 164 0D; , [qi bai) @ + [oi bi*] y + [oi dici] 2 4-6 <. =E [ai bimi | + lay >, l=05 y 0; _, [meres ]@ + [oerbi]y + [oe] 2 +... + oem) + [y' 7 Y=0, These N equations serve, together with the » conditions ®; =0, to determine the NV variables 2, y, 2,... and the vy auxiliary quantities q;’- Now the solution of the problem is not represented by the centre of the hyperellipsoids £2, but by the point, in which the intersection space ® (space of conditions) is touched by an individual of the set of the hyperellipsoids 2. The analytieal treatment of the problem is simplified by taking the coordinates so small, that in the expressions ®; homogeneous linear forms suffice. The geometrical meaning of this is that a new origin O' (vy, Yo, Zo, --) IS Chosen in the space of conditions ® near the probable position of the required point. So the spaces ®; are replaced by their tangent spaces /;, and the space of conditions by its tangent space R&R of N—vr dimensions, intersection of the tangent spaces Lj. Denoting the coordinates obtained by translation to O’ by §, 9, §, «., so that e—.w2,+6,... and putting ae, + Biy, + Yiz%) + aah , axe, + by, + cz, +... + mj = mi; we find 2U =[pilaiw + iy + yi» + wi] = [pais + Bin + iS + + HH) putting aE + Bin + iS 4-... gi Vi, 20i= [pi Vi). The equations #; (x,y,z...) = 0 may now be written: (Pbjn Odd) (Day Ds (a5) Yurzo.- - | —— 5 ' ) ae C+...)/+..S0 Ow or, since O” is assumed in ®; =O, and higher powers of §, 7, &... are to be neglected, OD; OD; OD; io : Eee be 02 (y= ee) Ow Oy 02 or W,=a;§+86;n+y7/S$4+...=2a;5=0. (j=1,..-»). So the normal equations appear in the following form [viae?) § + [eae br] + (yeaie |S +.» + [gcaimi] + [ar oy!) = 9, [yi bias | § + [gobi] my + [ue bier]$ + -- + [ge dime] + Lay 2s! =% 165 lgccraz] § + [gecebs] y 4 Lore?) $+. + [oiceme] + ony lk 05 IV. To determine the weights of the directions a, y, z,..., we again begin by shifting the origin (by translation) from QO’ to the point P, satisfying the normal equations and |W’; = 0. a : . 7 Calling U, potential relatively to P, &’,9)’,6’,... the coordinates with respect to P, and putting finally the potential in P, (7—U,=U" the difference of as + Big py Se. vil, a St Bin! + yi G+... = Wy we find 20) lp Va 2h; Wei This equation represents the set of equipotential spaces 2. U/’=0 furnishes the byperellipsoid 2, touching ® (or 7?) in P. Now those points must be found at which the force can only be resolved into an (inactive) component perpendicular to FR and a component parallel to the «-axis. For such a point we have aU ‘i carts Feta [yee] — ges), al OU! r nr EE — a on et 0, U/ eu! : ee aie Cee Stare or Lpi Vir ac) -— [qpe3') = — [rye;']' + oe8', [pi Vi Bil — (q98;') = — [585], [pi Vi! vil — lays) = — Ura, or putting i) = == 8 [pias Vi'] + Lsjery''=a8', [pi 8! Vi'] + [553;'=0, [prvi Vi'l+1s;7;'I'= 0, ete. whence = Lpiai* |S + [pias Bil a! + [pieivi] § + ~~~ + [sjey'|’ = ge8', [pieiai]s’ + Lpeei*) a! + [reir 1S + -.- + [s78;']' = 9, [piy es + pivibi)a + [pixels 4 T=9, oo ae ey or Proceedings Royal Acad. Amsterdam. Vol. XVIL 166 Is 9s Ube 7 q eee [aiai?] - + [giajb; | - i + [gja; a See es) dé = 1 , | oS) $j [9% ba; }— + [9: b; 7] = + a be; | SS Roo oS | [tj + 0 == (i). gz Grs zs q | Js JSS 1 / 2 S 7) " lo:ciai |] — + [oie b; | oad + lai c*] Sqn 050 Sr 6 9A 10 ==10" 5 : the conditions ' 1 ' 7] ! o . aj +f 85) = ee ae (Gj = 5 5.0.9))s gs ges 98 also being satisfied. From the above NV -+ » equations with the V unknown quantities 1 9 C sos wy 1 .—=,——,... and the rv unknown quantities — , — can be solved. ge 98) eS 9:5 9 The method of solution of Hansen is found again by introducing SSS an <7 Gs $j ! es SS) S a] et) i) JES ), A —— 10) (== ono), [cag Ay ey" |'=1 , [he bs 4 [4y'8;''=0 5 [Ai ci JH-14;'y;']=0 , ete. (NV in number) the .V variables A,B, C,..., the m unknown quantities %; and the yr auxiliary quantities /;' can now be solved. 167 The weight of x is thus defined by 1 Ia — 9 =S = A It may also be found by the following ealeulation ke? a = [hia A] = ZA [hia;] = A [hia;] + B [kbs] + C [hier | 4 =A— A [ka — B[AB;] — C [h'7;J —... ll = Al = Gea) = Se 95 so that g, is also determined by 7a EA By considering the quantity U as (V + 1)" coordinate perpendi- cular to the N-dimensional space (7, y,z,...), the equation [p: Vi'?] — 2 [g; W;') = 20" represents the quadratic space ”. The origin of the coordinates §',7/,0,..U' now lies at the point S, the projection of which on U'=— U,(U=D) is the required point. Now this point S is not the summit of ¥. The linear space of conditions R of NM —» dimensions is now joined to the point U” = @ by an (NV —v- 1)-dimensional space R,, which passes through S and intersects the quadratic space ¥ in a 1 also has its centre in U’ =o, but is of fewer dimensions, viz. N + (N—-++1) — (N-++-1) = N —v. The quadratic space ¥, has its summit in S. We now have to determine the points Q in ¥,, at which the quadratic space ”, having the same character as Y, in that it ((v-+-1)-dimensional) spaces of normals are parallel to the a-axis. In such a point Q ¥, is also enveloped by a parabolic cylindrie space, the generator-spaces of which are parallel to the a-axis, and which therefore has an equation of the form gx §? = 2. U'. 1 Ya Its parameter is ao In other words: — is the parameter of the parabolie cylindric Ya space, which has its generator-spaces parallel to the a-axis and envelops the quadratic space ¥, . V. We conclude this paper with a short summary of the results for the ease of two variables w and y. 12* 168 The equations of observation are represented by the straight lines Vi;=aje + By + w=O (weight pi) @=1,...n). The point P(, y) is subjected to the force 6 = [di] = — [piri] in which », represents, in amount and direction, the distance of the line V;=0 to the point P. The point P remains at rest, if its coordinates satisfy the equations [pias] @ + [piaiBily + Lriecui] = 0, [piBiai]@ + [piBitly + [piBier] = 0. Denoting here the potential U7 by 2, we obtain [pi(ace + Biy + wi)?] = 22. This equation represents an elliptic paraboloid ¥, being the sum- surface of the parabolic cylinders pilare + Bry + fy)? = 2z;, which have the plan z—O as summit-tangent-plane along the gene- rator ae + By --+ wi 0, z= 0, and which are obtained by trans- lating the parabola lying in the normal plane of Vi= «je + 3:y 4+- a= 9, perpendicularly to V;=0. The parameter of this parabola is ok i The summit 7’ of the elliptic paraboloid ¥ ({p; V,*] = 22) is pro- jected on z—0O into the point P, satisfying the normal equations. By constructing the tangent cylinder, the vertex of which lies upon the «-axis at infinity, we obtain a parabolic cylinder, the perpendicular transverse section of which has a parameter equal to the reciprocal value of the weight g, of the variable a. There being only two variables, only one (rigorous) equation of condition &(v,y)—=0O may be added; (x,y) =O represents the curve to which the point ? is constrained. We now have to determine that particular ellipse of the homothetic set [p; Vi?]=const., which touches the curve @. The point of contact is the point P required. In #, near the probable position of P, the new origin O% is taken. We have thus only to operate with linear functions of the coordinates. So we really replace ® by its tangent R at P. The elliptic paraboloid 7 is cut by the vertical of P in the point S. The vertical plane &,, which intersects z=0O along R, pierces the paraboloid 4 along the parabola ’,, having Sas summit. We now construct the cylinder having its vertex at the point 169 at infinity of the «z-axis and having the parabola ¥, as directrix (ie.: enveloping the parabola ,). The parameter (of the perpen- dicular transverse section) of this cylinder is the reciprocal value of the weight g, of the variable z. The equipotential lines in 2=0O are the homothetic ellipses [pi Vi? | =const. Such an ellipse is the locus of the points of equal «. When the (rigorous) equation of condition is: «= ceonst.. the parabola , is parallel to the plane «=O. The tangent cylinder is then infinitely narrow ; its parameter is 0, the weight of « is infinite. Chemistry. — “Kquilibria in ternary systems. XVI. By Prof. F. A. H. ScHREINEMAKERS. (Communicated in the meeting of May 30, 1914). Now we shall consider the case that the vapour contains two components. We assume that of the components 4, 6, and C only the com- ponent 6 is exceedingly little volatile, so that practically we may say that the vapour consists only of A and C. This is for instance the case when B is a salt, which is not volatile, and when 4 and C are solvents, as water, alcohol, ete. Theoretically the vapour consists only of A+ £-+ C; herein the quantity of B is however exceedingly small in comparison with the quantity of A and C, so that the vapour consists practically totally of A and C. When, however, we consider complexes in the immediate vicinity of the point 5, the relations become otherwise. The solid or liquid substance has viz. always a vapour-pressure, although this is some- times immeasurably small; therefore, a vapour exists however, When we now take a Y which consists only of 4, without A and C. liquid or a complex in the immediate vicinity of point B, the quantity of 4 in the vapour is, then still also large and is not to be neglected in comparison with that of A and C. Consequently, when we consider equilibria, not situated in the vicinity of point 4, then we may assume that the vapour consists only of A and C; when these equilibria are situated, however, in the immediate vicinity of point 4, we must also take into consider- ation the volatility of 45 and we must consider the vapour as ternary. When we consider only the occurrence of liquid and gas, then, as we have formerly seen, three regions may occur, viz. the gas- region, the liquid-region and the region L—G. This last region is 170 separated by the liquid-curve from the liquid-region and by the vapourcurve from the vapour-region. As long as the liquideurve is not situated in the vicinity of point 6, the corresponding vapour- curve will be situated in the immediate vicinity of the side AC. Consequently the vapour-region is exceedingly small and is reduced just as the vapourcurve, practically to a part of — or to the whole side AC. Therefore we shall call this vapoureurve the straight vapourline of the region £— G in the following. Consequently we distinguish within the triangle practically only two regions, which are separated by the liquideurve, viz. the liquidregion and the region L—G:; the first reaches to the point B, the latter to the side AC. The conjugation-lines liquid-gas end, therefore, all practically on the side AC. When the liquideurve comes, however, in the immediate vicinity of point B, so that there are liquids, which contain only exceedingly little A and C, then the quantity of 46 in the corresponding vapours will no more be negligible with respect to A and C. The vapour- curve will then also be situated further from the side AC, so that also the vapour-region becomes larger. At sufficient decrease of pressure or increase of temperature the vapour-region will cover even the entire component-triangle. In that case we must, therefore, certainly distinguish between the three regions, of which the movement, occurrence and disappearance have been treated already previously. In order to deduce the equilibrium #'+ L+G, we may act now in the same way as we did before for a ternary vapour. We dis- tinguish the following cases. 1. The solid substance is a ternary compound. 2. The solid substance is a binary compound of two volatile components. 3. The solid substance is a binary compound of one volatile and one non-volatile component. 4. The solid substance is one of the components. 1. We consider firstly the case sub 1, viz. that the solid substance is a ternary compound; this is for instance the case with the compound Fe,Cl, . 2HCl.12H,0. Now we imagine for instance in fig. 7, 11, 12, or 13 (I) the component-triangle ABC to be drawn in such a way that the point F is situated within this triangle. Curve Mm can then again represent the saturationcurve under its own vapourpressure of F, val the corresponding vapourcurve J/,;m, is then, however, no more a curve situated within the triangle 46C, but it becomes a straight line, which is situated on one of the sides of the triangle. We shall call this line the straight vapourline of the compound /. When A and C' are the two volatile components, then this straight vapourline is situated on the side AC. As not a single liquid of curve J/m can be in equilibrium with a vapour, which consists of pure A or of pure (C, the points A and C’' can never be situated on the straight vapourline. From this foilows: the straight vapourline of the ternary compound /#’ covers only partly the side AC and in such a way that it covers neither A nor Bb. 2. The solid substance is a binary compound, of two volatile components. We take a binary compound F' of B and C (tig. 1) so that 5 and C' now represent the two volatile components and A the non-volatile component. In order to deduce the saturationeurve under its own vapour- pressure we may act again in the same way as we did before for the general case. For this we take a definite temperature 7’ and a pressure ? in such a way that no vapour can be formed and the isotherm consists only of the saturationcurve of /°. This is represented in fig. 1 by pq. At decrease of P the region L—G occurs; such a region is represented in fig. 1 by Cdee, with the liquid-curve de and the straight vapourline Ce,. The liquid’ e is in equilibrium with the vapour é,, the liquid @ with the vapour C and with each liquid of eurve ed a definite vapour of the straight vapourline Ce, is in equilibrium. We may distinguish three cases with respect to the occurrence of this region L—G. a. In the equilibrium L—G of the binary system BC a point of maximum-pressure occurs. The heterogeneous region L—G arises in a point of the side BC. b. In the equilibrium L—G of the binary system BC a point of minimum-pressure occurs; one heterogeneous region arises in 2 and one in C, which come together at decrease of P in a point of BC. ce. In the equilibrium L—G of the binary system SC’ neither a point of maximum- nor a point of minimumpressure occurs; the heterogeneous region arises in / or in C. Here we consider only the last case and we assume in this case that Cis more volatile than B; after this the reader can easily deduce the two other cases. At decrease of P the heterogeneous region arises, therefore, in the angu- lav point C’ (fig. 1) and it expands, while curve pg changes of course its form and position, over the triangle. Under a definite pressure the terminatingpoint e of the liquid- curve coincides with the termina- tingpoint p of the saturationcurve, under a definite other pressure e coincides with ¢. When e coincides with g, we may imagine in fig. 1 that the liquideurve is represented by qq’, d or by gqq',; in the latter case it intersects the curve qp, in the first case it is situated outside this curve. When e coincides with p, we may imagine that the liquideurve is represented either by p/ (fig. 1) or by a curve, not drawn in the figure, which intersects pq. Now we shall examine which of these cases may occur. To the equilibrium between a ternary liquid w, y, 1—a—y, and a binary vapour y,, 1—y, the conditions are true: ee 5 fans, : et! an Tin (y—y,) Ox = 4, anc Oy Oy, So te eS eee ) Let us firstly consider the region L—G in the immediate vicinity of the point C. As x,y, and y, are then infinitely small, we put: Z=U+RT2rlogx+ RT y logy and Z,= U,+ RT y, log y, The two conditions (1) pass then into: OU OU OU U—#«# — —y— — U, +4, SSR (@ + y—y,)=0 . (2) av Oy Oy, OU we OU, ; ’ — + RY logy=—+ RT logy, . . . . . (8) Oy Oy, Under a pressure Pe the region Z-G in fig. 1 consists only of the point C, and, therefore, «=0, y=O and y,=0O; then the unary equilibriam: liquid C+ vapour C oceurs. This is fixed by LZ=fZ, 011 U= U,, wherein: 2 = 057 = 0sande7y)— 10: Let in fig. 1 the region Cdee, make its appearance under a pres- sure Po + dP; the points e,, e, and d are then situated in the imme- Lio diate vicinity of C; now we equate «= §, y = and y, = 1. From (3) follows: 1 = ae cee a et Ae fe (4) wherein AK is a constant fixed by (8). When we assume, as in fig. 1, that Cis more volatile than 6, the point ¢, is situated between C and e and “J is, therefore, smaller than 1. Nowe we equates ()) == Po = dP vai ey — 7) andy, = 7. : as in the point C U= U, is satisfied, it follows, that: —RT[E+ y= y,) +[V—V,|dP=0 or E41 (—K) —— dPighs Seema) am (5) In the immediate vicinity of the angular point C (fig. 1) curve ed is, therefore, a straight small line. We find from (5) for the length of the parts Cd and Ce: V,--V : Via ——— dP and Ce= — —————dP. . . . (6) RI Ri (ea) As V,—V >0 and 1—K > 0, it follows from (6) that Cd and Ce are positive, when dP is negative. At decrease of pressure curve ed shifts therefore, within the triangle. From (6) follows :Cd: Ce=(1—A);: imoreeas: 1 — 7 — Coan Ce: we. find: Cd = eex In order to examine the lquideurves going through the points p and q (fig. 1) in the vicinity of these points, we put in (1): C= — Mie) ( UB Bed RI LRRD oa tc RB Stace oun WL) we then find: U—a ee —(y—y ee —RT«e—Z, =0 wae eaeies . (8) Ow Matar : Oy Oy: For the liquideurve of the region L-G we find from this: [er + (y—y,)s + RT] de + [as + (y—y,)t]dy=0 . . (9) For the direction of this liquideurve in its end on the side BC (therefore «= 0) we find: dy y—y_) s-— RI oh a Uae (10) da (y—y,) t When we call g the angle, which this tangent forms with the side BC (taken in the direction from 4 towards C), we have, when we imagine the componenttriangle rectangular in C: (y-—y,) ¢ Ch. ———— =5 (y—y,)8 + RI | (11) 174 For the saturationcurve under a constant pressure of /’, consequently for curve pq, we find: OZ 0Z Z—x - (8—y = (Ge R age 0 (file Z—a— + (8 Day oa (12) or after substitution of the value of Z from (7): [er + (y—B)s + RT] dx + [xs + (y—p)t]dy=0 . . (183) When we call wy the angle which forms the tangent in p or q with the side BC (taken in the direction from 8B towards C, we tind; gs EE (y—B) s+ RI Let us now consider these two tangents in the point p of fig. 1. In this point y—3< 0 and y—y, > 0. The denominators of (11) and (14) bave, therefore, either opposite sign or they are both positive, so that we may distinguish three cases. In each of these cases we find y < w; the liquidcurve of the region /.-G and the saturationcurve of / under a constant pressure are, therefore, situated in the vicinity of point p with respect to one another in the same way as the curves pf and pq in fig. 1. Curve pf can also no more intersect curve pg in its further course; we may see this also in the following way. At decrease of P the two curves must touch one another under a definite pressure P;, somewhere in a point / within the component- triangle; therefore imagining the liquideurve of this pressure P, to be represented by ed (fig. 1), we must imagine ed to be drawn 2 z ; : dy in such a Way that it touches pg in h. For this point nh trom (9) ax dy must be equal to ;_ from (13); then holds: aw ar + (y—y)s + RT ar + (y—3)s + RT 15 ast(y—y)t ws + (y—pa)e . 20a or a) veiw oo sg (1G) As y, indicates the vapour conjugated with liquid 4, (16) means: the liquid-curve of the region L—G and the saturationcurve under a constant pressure of /# touch one another in a point 4, when the vapour belonging to this liquid / is represented by the point /. As all vapours belonging to curve ed (fig. 1) are represented by 175 Ce,, and consequently no vapour exists of the composition /’, the curves ed and PY therefore, cannot touch one another. Let us now consider the tangents to the liquid-eurve and to the saturationcurve under a constant pressure in the point q (fig. 1); as the vapour, belonging to this liquid, may be represented either by a point q, situated between gq and F or by a point qg, between F and C, we must distinguish two cases. When the vapour is represented by g,, then we have y— 7 >0 and y— y, >0. As y—/??>y-— y,, the denominators of (11) and (14) have either the same sign or the denominator of (11) is positive, while that of (14) is negative. In each of these three cases we find g 0; in absolute value (y—/?)s is always smaller than (7 — y,)s. The denominators of (11) and (14) have, therefore, either the same sign or the denominator of (11) is negative, while that of (14) is positive. In each of these three cases we find ~ >y; the liquid-curve of the region L—G and the saturationcurve under a constant pressure of /’ are, therefore, situated in the vicinity of point q with respect to one another as the curves gp and qq’,- With the aid of the preceding considerations we may easily deduce now the saturationcurves under their own vapour-pressure of /’; for this we shall assume that the solid substance melts with increase of volume. We distinguish three cases. 1. The temperature is lower than the point of maximum-subli- mation 7x of the binary substance /. In a similar way as we have deduced the general case fig. 11 (I) we now find with the aid of fig. 1 for the saturationcurve under its Own vapourpressure a diagram as is drawn in fig. 2; in this figure a part only of the componenttriangle is drawn. Curve hacmbn is the saturationcurve under its own vapourpressure, h,a,¢c, FP, b,n, is the corresponding straight vapourline. In_ this figure are indicated the equilibria: #74 Ln + Gy,, M+ La + Ga; FLEL+ Ga, P+ In+ Ge F+ y+ Gy, and F+ L, +Gn,; Ln and £, ave binary liquids. As we have assumed that the temperature d is lower than the point of maximum-sublimation 7%, of the solid 176 substance #’, the vapour m, must be situated between #’ and x. Consequently we have here the case that the vapour, corresponding in fig. 1 with the liquid g, is represented by q,; the liquid-curve of the region L—G going through the point qg can, therefore, be represented by qq,’ (fig. 1). It follows from this position of gq,’ that on further decrease of pressure the liquideurve of the region L—G must touch curve pg ina point m (fig. 1); in fig. 2 this point of contact is also represented by m. Previously we have seen that the vapour corresponding with such a point of contact has the com- position #’; in fig. 2 m and F are joined for this reason by a conjugation-line. Fig. 2. It follows from this deduction that the pressure is a minimum in the point m of fig. 2 and increases from m in the direction of the arrows, consequently towards n and h. Further it is evident that the vapourpressure in / is higher than in 7. 2. The temperature is higher than the point of maximum subli- mation 7’~ and lower than the minimum-meltingpoint 7p of the substanee F. In a similar way as we have deduced the general case fig. 7 (I), we now tind with the aid of fig. 1 a diagram as fig. 3. Curve hachun is the saturationcurve under its own vapour-pressure, /, a,c, 6,1, 1s the corresponding straight vapour-line. As we have assumed that the temperature is higher than 7’_ but lower than 7'p, F must, as in fig. 3, be situated between n and n,. Therefore, here we have the case that the vapour, corresponding in fig. 1 with the liquid g, is represented by qg,; the liquid-curve of the region IL—G going through the point g may, therefore, be represented by qq‘. (tig. 1). It follows from this position of qq, that on further decrease of pressure the liquid- curve of the region L—G no more intersects curve PY: 177 From this deduction it follows that the pressure increases along curve /im in the direction of the arrows, therefore, from 2 towards h and that on this curve im neither a point of maximum- nor a point of minimumpressure occurs. 3. The temperature is higher than the minimum-meltingpoint 7’ and lower than the point of maximum-temperature 777 of the binary equilibrium #’+ 1 -+ G. In a similar way as we have deduced the general case fig. 12 (1) we now find for the saturationcurve nnder its Own vapour-pressure an exphased curve, in fig. 4 a similar curve is represented by the curve hn indicated by 5; the pressure in- creases in the direction of the arrow, consequently from n towards h. In fig. 4 the saturationcurves under their own vapour-pressure of F are drawn for several tempera- tures (7,—T,). When we take 7, and 7, lower than 7x, then a point of minimum-pressure must occur on the curves, indicated by 1 and 2. When we take 7’, between Tx and Ty and 7, between 7'x and 7’'y7, then the saturationcurves Fig. 4. under their own vapourpressure have a position as the curves /2 indicated by 4 and 5, on which no point of minimumpressure occurs. At 77 the saturationcurve disappears in a point A and the corresponding straight vapourline im a point //, (not drawn in the figure). On the saturationcurve of the temperatures 7’, and 7’, we find a point of minimum-pressure m, this pomt has disappeared on the saturationcurve of the temperature 7’, ; between these two temperatures we consequently find a temperature 7’, at which the point m coin- cides with the terminating point 2 of the saturationcurve under its own vapourpressure. As the vapour belonging to a point of minimum- pressure has always the composition /’, this case occurs when the liquid 2 can be in equilibrium with a vapour /” As then the binary equilibrium /’-+ £-++ vapour /# can occur this temperature 7%, : 178 consequently is the maximumtemperature of sublimation 7x of the substanee /’. Now we will deduce in another way the saturationcurves under their own vapour pressure of /. The conditions of equilibrium are: WA OZ OZ 07 07 a -— == fi - == 5 i =p} ah —C eS eres é iy; ae (y—/?) hoo: .—(y,—/?) Sg ae ae (17) These conditions follow also from the equations 1 (II) when we equate herein @ =O and «, =O and when we consider 7, as inde- pendent of «,. We put Z—= U- RT ailogm 0.) ee The three conditions (17) pass then into: U—a« ae — (y—/?) gu = tala 5 =O cee (19) Ow : Oy i Z,—(y 7) Oe eee Sock) Ls her a eae OD nA From this follows: far + (y—/?)s + RT| da + [as + (y—)¢#] i — ay av — | V—e on = (y—/?) rm =< ie. ers as ee (22) x Yy F hes , OV, ‘ : (y,—/*) t, dy, =| Vi\—(y.—") a =—wl|dP . . 7 4(23) ; i av. av. sdx + tdy—t, dy, = a ea en P . - ae (24) dy, dy With the aid of (23) we may also write tor (24,: ee OV (y,— 7) sdx + (y,—)tdy = i ; (y,—,;9) a oar (25) dy so that for the relation between da, dy, dy,, and dP we shall consider the equations (22), 23), and (25). In order to examine if a point of maximum- or of minimum- pressure is possible on the saturationcurve under its Own vapour- pressure, we take (23). From this follows ¢? =O when Gia 0 ss on Ae In order to examine if the pressure for this point is a maximum or a minimum, we develop (20) further into a series: when we equate herein y, = /7, we find: Wes) 1 (V,—2) Oe == = t dy,’ 5h FA nee ach Sere ne (27) < As V,—v and ¢, are both positive, it is apparent that the pressure is a minimum. In accordance with our previous considerations (see fig. 2) we find therefore: on the saturationcurve under its own vapourpressure of the solid substance /’ the pressure is a minimum in a point m, when the vapour corresponding with this liquid has the composition In order to examine the change of pressure along the saturation- curve in the vicinity of its extreme ends / and 7 (fig. 2, 3, and 4) we equate «=O; from (22) and (25) we then obtain: T oy [(y—-/?)s + RT] du + (y —B) t dy = [V—-(y—/?) ai —ydP . . (28) = Oy (y,—/?) sdx + (y,—B) t dy = [V,—(y.—,*) ar vyjdP. . (29) From this follows : (y, —/?) RTdx = [(y,—/?) V + (@—y) V, + Y¥—y,) ey] dP. (80) When AJ, is the change of volume, which occurs when between the three phases of the binary equilibrium #’'+ 4+ G a reaction oceurs, in which one quantity of vapour arises, then we may write for (30): py, RT Sa glean Silig ela wile tae ele (31) Now AJ, is always positive in the binary system / + ZL -+ G, except between the minimum-melting point 7 and the point of maximumtemperature 7'7, where AJ, is negative. In fig. 4 AV, is consequently negative for liquids between /’ and H, positive for all other liquids on the side BC. —y is positive, when the liquid is situated between # and C, negative when the liquid is situated between / and B (figs. 2—4). —y, is positive, when the vapour is situated between /’ and C, negative when the vapour is situated between /’ and B (figs 2—4). In the points A of figs. 2—4 is AV,>0, /’—y>0and /?—y,>0; from (31) follows therefore dP <0. From each of the points / the pressure must, therefore, decrease along the saturationcurves, we see that this is in accordance with the direction of the arrows in the vicinity of the points / (figs. 2 -4). In the point » of fig. 2 is AV, >0, 7—y <0 and (?—y, <0; from (81) follows, therefore dP <0. Consequently we find that 180 the pressure in fig. 2. must decrease from n along the saturations curve, which is in accordance with fig. 2. In the point 2 of figure 3 is AV, >0, P—y0; from (31) follows, therefore dP > 0. Consequently the pressure must increase from the point 2 in fig. 3 along the saturationcurve. which is in accordance with fig. 3. In the point 2 of curve 5 in fig. 4 is OV, <0, ;“—y > 0 and 8— 7, >0; from (31) follows, therefore dP>0. Consequently the pressure must increase from n along curve 5, which is in accordance with the direction of the arrows. We may summarise the above-mentioned results also in the following way: when to the binary equilibrium + 2-+-G (in which F’ is a compound of two volatile components) at a constant tempera- inre we add a substance, which is not volatile, then the pressure increases when the binary equilibrium is between the point of maximum-sablimation 7Z'~ and the point of maximum temperature 7; in all other cases the pressure decreases. In the consideration of the general case, that the vapour contains the three components (XI and XII) we have deduced that the saturationcurves under their own vapourpressure can disappear in two ways at increase of pressure. 1. The saturationcurve of the temperature 7’7 disappears in the point #7 on the side BC |fig. 5 (XD)]. 2. The saturationeurve of the temperature 77 touches the side BC in the point 7 and is further situated within the triangle ; at further increase of 7’ it forms a closed curve situated within the triangle, which disappears at 7’z in a point within the triangle | fig. 6 (XJ)]. In the case now under consideration, that the vapour consists only of B and C, only the case 1 oceurs; this has already been discussed above and is represented in fig. 4. It follows already immediately from the following that the case 2 cannot occur. On a closed saturationcurve under its Own vapourpressure a point of maximum- and a point of minimumpressure occurs. On the curves now under consideration only, as we saw before, a point of minimumpressure can occur, so that closed saturationcurves are impossible. We may deduce this also in the following way and we may prove at the same time these curves, just as in the general case, to be parabolas in the vicinity of 77. When we consider the binary equilibrium #’+ liquid AH + vapour, then «=O; we equate y=y,, y,=~y,., and the pressure = Py. To this equilibrium applies: Be NG) ee Ze We | (Of = (Y,—i?) = — G60 Z, - (fon ) - 50) Oy OY, (32) dU . OZ, dy e on, further we have: (Y:-0—/?) a =F (F—y,) V, =r [%o— Yao] v= 0 as (33) which condition we may also write: Wee U Va == V, = V = a (34) y—0 = Yr — [2 ee For a ternary equilibrium /’+ 4 + G, the liquid of which is situated in the vicinity of point //, the pressure is equal to Ba «, f= Ss, 7, 4 and 7, 7. 7,- The three equations (17) pass then, when we use the conditions (22) into: Ss RSI. Hy AYL=0 (85) RTE+[v-V] a+ 4r&? + 4tn?+-4 (5 dv oOoV [p—V,] a ate $e, LF =e 2 Gan a) Sd <5 5 OG: 4 (y,—/?) L, =? (36) iS ee va ae th sap kes os ot * (S18) Herein is: 2 OV Os Ot 0?V Ts EAR fey foo toe ES hE Wee yth Oy Ow ~ OY dyOP (38) 4 Os 3 0?V 07V a! Sam oe TE. Ov, ne ot, 0°V, OPA as 6 —=i fey a un —_— enc 3¢ fig Malka hag apt og eS (89) In (35) and o6 Y, and y)9 are replaced by y and y,; we shall do the same in the following equations. When we multiply (385) by y,— and (86) by y—@, then it follows with the aid of (37) that: (y,—B) RTS + 2 (y,—B) 7 & + § (y—B) ty’ —3 (y—B) t, 1," mitre dV ( 2) OV. Ov are UTES AF 2 (( UP) dP ts y ey) =e = i= ap +(y, —B)sSy—= ( ) From (36), (87), and (40) it follows that this can be satisfied by: 7, Of the order -, 4 of the order a and § of the order 2°. From (35), (86) and (37) then follows: OV OV, i —— |o and t.y, =(|u— a. . . (41) Oy Oy, Proceedings Royal Acad. Amsterdam. Vol. XVII. 182 Substituting these values in (40) we find: 2): (4. —=B) RLS ears. al A ose oe emer es) wherein a has the same value as in (21) (XII). From this it follows with the aid of the first relation (41) that: at 2 (y,— 8) RT § = —_.__7?. ... . (43) In the same way as in (XII) we find that we may write for this: j2 t® (y—B) (y,—y) — Sa (y—B) (1 —9) ao PRT == WW. és) d*l LP? curve going in fig. 4 through the point H is parabolically curved in this point and touches the side LC in this point. d?l As in this point y—-8<0, y,—y <0, y,—8< 0 and TP >; a § is always negative. From this it follows that this parabola has only the point 47 in common with the triangle and is further situated completely outside the triangle. Consequently only the point H vepresents a liquid; its other points have no meaning. wherein is fixed by (24) (XID. From this it follows that the (To be continued). Chemistry. — “The system Ammonia-water’. By Prof. A. Smits and S$. Postma. (Communicated by Prof. J. D. vy. p. Waats). (Communicated in the meeting of May 30, 1914). After the preliminary communication’) on this subject the inves- tigation of the system NH,-H,O has been continued in different directions, and it has now been completed. The continued research was directed in the first place to the accurate determination of the meltingpoint lines, corresponding with the pressure of one atmosphere. These determinations, which were now carried out by means of a gauged resistance thermo- 1) These Proc. XII, p. 186. 183 . meter’), as is in use in this laboratory *), gave the following result. } . <9 ) (Method of procedure : supercooling a little and then seeding). [initia eee Concentration point of par peut mixture solidifica- | ti tion cauon 100 mol. 9%) NH; | — 77.6°. 94.7 = 80.9" | 90.4 — 83.7 | 86.5 — 87.2 — 92.4 81.55 — 92.6 | — 92.5° 78.45 = 68 Tee 92.5: 73.5 — 82.2 | — 92.6 71.1 — 80.3 69.9 = TOT | 66.7 — 718.8 65.8 —— 18.9) 64.6 — 719.2 62.0 — 81.0 61.3 — 81.7 | — 86.0 60.7 — 82.3 iors 86.0 60.3 — 82.9 — 86.0 59.0 = 85,2) |= 8548 51.0 — 84.1 | — 8.8 53.0 — 80.2 50.2 — 79.1 50.1 — 79.0 | 49.3 == 719.0) | 43.9 | — 83.0 | 42.2 — 86.0 | 1) Gauging points were: melting ice 0°, melting mercury — 38.85°. Boiling CO, + alcohol — 78.34° + 0.20 (B—76). Boiling point of oxygen — 182.8° 4- 0.56 (B — 76). 2) Cf. pe Leeuw. Z.f. phys. Chem. 77, 603 (1911). : 13* 184 jneulritia| al = eee Concen- : Final point tration Point. oF of solidifi- mixture on cation 40.6 — 88.2) 39.8 = O07 | 39.1 == Ol7 35.75 =5 Ohi 34.5 — 100.3 34.0 — 96.7 | 32.6 == 789.24) 29.7 1492 | 28.7 = (F353:| 27.6 | 163i 26.55 | — 50.4 | 23.0 | — 43.5 20.2 | = 3440 17.9 | — 28.6 | | 4.46 | — 4.8 0:0) 9 0.0 | This result is expressed in Fig. 1. From this 7-X fig. follows : for the point of solidification of the compound 2 NH,.H,O0—78°.9. ra) ie a 5g - NH,.H,O—79°.0 Further the eutectic point of NH, + 2 NH,.H,O + IL appears to lie at 81.4°/, NH, and — 92.5°. a ss yf , of 2NH,.H,O-+-NH,.H,O-+ L appears to lie at 58.5 °/, NH, and — 86.0°. 3 . or ,» of NH,.H,O + H,O +L appears to le at 34.7 NH, and — 100.3°. Great difficulties were experienced in the case of the mixtures with less than 50°/, NH,, in consequence of the great viscosity of these mixtures at low temperature. Shortly after our just mentioned preliminary communication a treatise on the same subject by Rupert’) appeared in Journ. Am, Chem. Soc. 81 866 (Aug. 1909). 1) Buriher Goinammenien Journ. Am. Chem. Soc. 82. 748 (1910). 30) ~b0} ~100+ ee oe — re = = Ny 10 50 YW kD 60 Wiha 40 30 20 10 0 X Fig. 1. As point of solidification Ruprrt determines the point at which the crystals brought into the liquid no longer grow or disappear. He measures the temperature accurate down to 0°.5 with a verified toluol-thermometer. Below —- 100° he uses a thermo-element, tested by comparison with the toluol thermometer and with the boiling point of liquid air. He himself considers the determinations with this thermo-element insufficient, which tallies with our results, as by extrapolation about —125° may be derived from Rupurv’s investigation for the temperature of the eutectic point NH,.H,O + H,O + L, whereas this point lies certainly 24° higher according to Fig. 1. Leaving the region of concentration 80—40°/, out of account, the agreement between Ruprrt’s results and ours is fairly satisfactory. If we compare the principal points, we get what follows: 186 REET Oe | Observer NH; 2NH3.H_O | NH,.H:0 RUPERT. = 16220 se eo nO sale 28 2 | | | Smits, Postma | — 77.°6 | — 78.°8 79.°0 | Observer Eutecticum | Concentration Temperature RUPERT. NH; -+ 2NH3.H20 + L 81.2 mol. 9/9 NH3 — 94.°0 S. P. | F fe , VSIRS Leena — 92.50 | RUPERT. 2NH3.H,0 + NH3.H,0+L /|57.9 _, il — 87.0 | See 5 = Sholay ‘ — 85.9° NH; .H,O0 + H,0 + L not determined by RUPERT . ee . r 34.7mol.%)NH3|} — 100.3° It is at onee apparent from the determination of the melting-point diagram that the two chemical compounds, one with 2 mol. of NH, to 1 mol. of H,O, and the other with 1 mol. of NH, to 1 mol. of H,O are already considerably dissociated in liquid state at the temperature of solidification. Boiling-point lines. After centainty had been obtained in the way described here about the existence of two solid compounds between NH, and H,O, it was of importance to examine whether the existence of these compounds in the liquid state would also follow from the boiling- pomt lines observed at different pressures. These determinations, which were carried out with an apparatus as was used by Dr. pe Leruw’), yielded the result that there was no indication to be perceived that could point to the existence of compounds in the liquid. Hence it followed from this that at the observed boiling temperature the dissociation was already too strong, and that the investigation has therefore to be continued at still lower pressures. As the dynamic method is attended with all kinds of difficulties at low pressire, it was desirable to apply the statistic and not the dynamic method in the continuation of this investigation, and deter- mine the vapour pressure line of different mixtures of definite concentration, from which the boiling-point lines and the p-a-lines 1) ZA. phys. Chem. 77, 284 (1911). ee 187 might then be derived. This investigation, in which also the mixtures which had previously been investigated dynamically were verified, yielded the followimg result. The following mixtures were examined. 88,0 mol. °/, NH, 54,7 mol. °/, NH, Sng Se a Sib) eee oo Oe ek hi = 39:7" ae TA Cie ee A. 35.97) een 695 ee, 39:7. ae cn ee O35. Gi as, ae 62,7 ”? ” ” the results of which are expressed in fig. 2. These vapour pressure lines enable us to read the corresponding boiling temperature for a definite pressure (see table I), hence to indicate the boiling-pomt lines, and that with an accuracy down to tenths of degrees, and it is also possible to indicate the vapour tension of different mixtures for a definite temperature (see table II), hence to find the (pz)y-lines with an-accuracy of + 0,5 m.m. Hg. Fig. 3 contains the boiling-point curves, from which it appears 100 90 80 x Sstatisch Geng dynanr sch 70 Le 60 50 40 30 20 10 -30 -40 -00 Ty AV Bri E:T T-X- or boiling-point lines for different pressures. mol. % NH3 | fp = 50mm. | p= 100 mm. DAMEN SET p=380 mm. | P/=760 mm. 100 SE AIGEGN lk == 6122: || ==! 6liz4y pe 3.35 | ==, 4653) plik = =03a04 88.0 Seioe ale = Goro. ler S0tise | eesti 249.6)” N= °30.4 84.1 — 741 Geo ates en — 400g |=729)3 77.8 = 7.0) | = 6215) ||. = 563 i aI | == 40.5). | = 26-8 74.6 = 170.85 | = Gl! =054,0\5 | = derae ele ergant — 25.4 69.5 =ycs.6- 88 — 587 | 52.4 | = 438 | 2eae.gt || @= ong 66.3 — 66.4 — 56.4 = 50.20 | 4 — 34.0 = 199 62.7 63.6) |= 536 |} = 47.25 || — 48.6 | 230.9): = Sit 54.7 2G! earns ee © eens eas | poe 51.5 Seo 42.1 SES | Ewa. al KG a 39.7 mar SSeORn tee COLI Oye 19: G2m | 10-20 = Ike a 35.9 — 32.7 | —21.3 | —140 | — 44 | + 44 = 32.7 wey 8c g5|| =e 1G iG wel le me OF 250 =Peco.6510|| 15,914 a 25.6 aS eo Or ese fl) eee ode el ce ipe7s a Ps TABLE IL p-X-lines for different temperatures. ; Le t=—10° | t= — 65° | t= — 55° | t = — 45° | r= — 35° | t = — 30° | t= — 250 mol. °/) NH3 | pincm.Hg. Pp 7) 7) P p p — 100 8.25 11.75 22.6 | 40.95 | 69.95 pe eae 88.0 7.2 10.2 19.6 | 35.5 60.6 71.4 aa 84.1 6.7 9.6 18.5 | 33.4 57.3 73.6 = 71.8 5.8 46«| «8.4 1652) |). 12955 BO}pieleG5r0y a TAG) 15:3 (4a 14.9 | 27.4 47.2 61.0 | 77.4 69.5 | 4.58 6.5 12TH esos ee 40] 52.5 | 66.8 66.3 5 Sra ye os5) pale Waite Ona 20.5 | 36.0 46.9 | 59.7 eS fees (eel Asse page 922 17.25 | 30.55 39.9) | = Sg ee Disie lee 5h 10.6 19.4 25.1 | 33.55 Bie S eel see ane oil 1cGs 4.2 | 8.3 he abs 20.7 27.15 39.7 | = | 0.85 1.41 3.08 | 6.1 8.3 | 11.0 35.9 | = | oe + 1.1 2.15 4,35 | 5.9 | 7.95 Sie 8) Wee i OL Ie) Oi8 16 | 3.15 be ate | 6.45 Dotemie ese othe ye = 0.9 1.65 2.3 | 3.1 190 that even that corresponding to a pressure of 50 m.m. He. does not reveal anything about the existence ef compounds in the liquid phase; there is nothing to be detected here of a constriction at the place of the compounds, as was found by Dr. ArEn’) in his investiga- 110) gop CM Ha. = 90 30 io Suse ith +. NH; qa Fig. 4. tion of the system sulphur-chlorine, and by Dr. pr Lrruw’) in the system aldehyde-alcohol. Still more interesting is the consideration of the liquid lines of the (px)7-sections, which are represented in fig. 4 for the tempera- c mes ——= PH = SS a Re — die. 55°, —65°, and — 70°. *) 1) Z. f. phys. Chem. 54, 55, (1906). 2) loe. cit. 8) The vapour phases of the mixtures need not be investigated, as it appeared from a preliminary investigation that they practically consisted only of NH at the examined temperatures, as was indeed to be expected a priori. era eS? i & 191 We sce that at all the temperatures mentioned here these liquid lines exhibit the type of negative liquid lines’), as was met with by Konxstamm and van Daursen’) for the system ether-cnloroform, and by Grrtacn*) for water and glycerin, while as Baknuis RoozeBoom remarked, such a line may also be derived from the investigation carried out by ScHREmNEMAKERS*) for the system acetone-phenol. Nor do liquid lines of the (px)7-sections give the least indication of the existence of compounds in the liquid phase, and it is most remarkable that this even applies to the liquid lines corresponding to a temperature of — 70°, so only 9° above the temperature at which the compounds separate out of the liquid; an indubitable proof therefore that the compounds found undergo a dissociation in the liquid, much greater than would have been expected. To complete the investigation the most important lines of the P7- projection of the spacial figure were also determined, the result of which is expressed in fig. 5, in which the three-phase lines of the two compounds are very apparent. The difference in triple point pressure of the two compounds.amounts to +17 m.m. Hg. Finally also the. plaitpoint curve was partially. determined; as was to be expected this curve does not present any particularity either. Anorg. Chem. Laboratory of the University. Amsterdam, May, 1914. 1) Baxuuts Roozesoom. Die Heter. Gleichzew. Il 40 (1904). *) Verslagen d. Kon. Akad. v. Wet. 1901, 156. 3) Z. f. anal. Chem. 24, 106 (1885). 4) Z. f. phys. Chem. 39, 500 (1902), 192 Mathematics. — “On Hermite’s and Apri’s polynomia.” By N. G. W. H. Beverr. (Communicated by Prof. W. Kaprryy). (Communicated in the meeting of May 30, 1914). Prof. Kaprryn has deduced the following expansion ‘) : (a—b6x)? 1 spe =a Or H,( oe) ee > —_— ep Vy (1—6’) 0 2n on! (1) in which #, (2) represent the polynomia of Hermite. Let in this expansion «=O, then we find: 48 (2) 2x2 1 ie _ 2, 6H,(2)H,(0) VO—é6’) R erie anal Now it holds good for the polynomia of Hermite that: i ue Hon+1 (0) = 0 Hz, (0) = (— 1)" x > ae) On account of which the above relation passes into: 6272 os ix eo == \(= 1p , Hen() (4) V(1—6’) 0 22n. nl For the polynomia ¢, (7) of ABEL we know the expansion: x9 1 i= oo aay = San ety / > 6 ope If we replace in (4) 6? by 6 we find: 62:2 eae 18 eS (—1)" Hor(2) Vy (1—d) 0 222. mJ 1 If we multiply the first member of this relation by t——— and vy (1—6@) (2n)! 2] the second member by . Q2n (p!y2 04 a (n!) to the first member of (5). By equalizing the coefficient of 4” in the two second members, we find the following relation between the polynomia of ABeL and those of Hermite: 6”, the first member becomes equal yp (a= > | 1)jr-k (24)! — Ho, 9%(z) - (6) Q2n pe (k@—hE _. If we multiply both members o7 (6) by Hyp, —i (3) e—™ dx y These Proceedings. Vol. XVI, p. 1198 (22 193 and integrate between —o and + o, then we find by application of the well-known integrals : +a [eo (a) Ey, (a)\e—* dz == 0 moe n +a de (2) e—? da = 2" .m!i Yn: —on ae Qn—2i)M(2i! | in () Hon si(e) db = (=I) en Ss) ~] — Prof. Kaprayn deduces the following representation by means of an integral for HeRmirr’s polynomia ') : Cae eae wn e — 7 let @) = e *u cos { vu — — )du. n Va 9 J 0 If we substitute this expression in (6): ; ~=— 2h)! P(x’ )= : fe ae (S128 — y2n—2k eos (wu—(n—k) x) du 22a k—=0 (k!)?(n—hk)! or, if we work out the cosine ao u? ex? —— n (2k)! p : Gila") = — e 4 cosaudu + ~ ) urxn—k) , . (8) 221V/ ar, k=0 (k/)?(n—h)! 0 Now is 8 (2h)! = fe-wyhay 0 consequently f+ 2) 7 Db)! n 2(n—k) < Ss ess y2(n—k) — S ee : “ yy dy a > (k(n —h)! 0 (k/)?(n—b)! ves v » (9) 7° NOGA cant OE A ok ne 1 y 2k — y2n ul fn yi \2 = yen e—vdy = ae : —— e—Ydy 2S = == i 0 (kL)? (n—h)I \u mi o KILE u For AseL’s polynomia we have: : ens al n\ (y \2* a ue een, k u 1) lie. p. 1194 (9). so that we can write for (9) , oa yen y" €Yapn | ——, | du ni, w 0 Substituted in (8) we get the double integral io 2) 2 i 3) u 4 ex? as D(a?) = EL fe 42"+1 cos wud | e—ul ep, (—t?) dt 0 0 if we introduce y = wt. By substitution of «= 2y it passes into im i] a) . e—¥ yn) cos Danydy | ee Pri—t*)dt . . (10) 0 0 Now we make use of the relation *) also deduced by Prof. Kaprnyn Pilz?) = nl 70 n i t yo Prt) Bat = ea (11) (SED a) es vu 0 In (10) we substitute «= ¢ and then. multiply both members by 1 e—t dt 140 and integrate between O and o, then we get by making use of (11): ive} +e) a) D 3 tn 4 : ‘ 2yVt r ef : for y2n-l dy {e—20 Gn(—wu*) du ae gv" dt. A (1+¢t)"11 niV x, ‘ : : 1+t 0 0 0 0 According to a well-known integral in the theory of the integral- logarithm, 1s *) oo RD “cos 2ypt _ ( # cos 2yHa : ; | — dt==2 | SS hi, (e2)—ey li (e—2Y) : l+e consequently 2) Lo) Ae = us = dt= oi ey" y2n+ie—2u]7 (e21/) or Uli(e —2y)'dy i (1+) nlm, : : : : 0 0 (12) 5 fens) du.\- 0 | By summation from 7 =O to n= we find: 1) lc. XV, p. 1250 (14). 2) See for instance “Theorie des Integrallogarithmus Dr. Nietsen page 24. 195 oO ng ~ 4 BREA a icy tees : Sryelrve ears e—#" e—24lt, (e7Y) + e2yli(e—2Y) dy | e—2y"'du >’: : Gf i(-u’*) a QO 7! 0 10) Now is’): s am Pm (a) = e*J (2 az) m! 2) > —_— ) in which J, represents the function of BesskL of order zero. From this it ensues consequently that : yO 4 i — Va, yie—2li, (é 27) + yli(e »—2y) iy fe e—2yu J. y(2iuy) lu. i) As is known, oa) y2ny2n Jy (Quy) u=0 (n We so « ) yen Jie] roa) if 7 —2uy J, (Qiuy) du = + +— {- 2uyy2ndu= = ——— J e—% 22n dz — ot ive ~ aaa y(n!) 292n-+1 0 0 v ee eee ay y(n 3 22n1 * Introducing this we have en (eee & 2n)! 1 = — —— | [e—2v i, (ev) 4+. e2y li (e—2)] dy . 5 Vn no (n/)?220+1 0 or l oD af — | [e—2y li, (29) + ey li (e—2y)] dy . (03) 2n Me as 271 1 Meciine to an integral used before, is ao D 7 . DQ, fleom (e27) + e2yli(e—29) | dy=— :f tcostdt cen til 108 taretg =" dt . « Yas ) 0 Formula (18) may also be written as follows: 1 4 ij AR 2y F ; = — lim costarctg—dt . . (14 a (2n 1 Vz y=00 “¢ ! E = rest 0 n=0\ 2 J 2241 . . . an . . By multiplying formula (11) by ar and by summation from 2 = 0 ni fo n =oo we find: 1) These Proceedings XV, p 1246 (9). 196 et ey t n * e—! oOo at if OD) = 4) = J, (2V ct | Ie Ga 070 “lre) = ieee: 0 gs (0) Nike eres (2V at) 0 0 meat +(«—1)t ‘| aS nae fr nevend 0 or (15) In order to deduce some more relations from formula (11) we set to work as follows. In Dr. Nianp’s dissertation’) the following relation is deduced for ABen’s polynomia: n—1 = Gn (v=) = — = gx(e)- k=0 By summation of formula (11) from 2=0 to n—1: on n—1 tn ie n—l ,—t > = = n (t) dt Jere at a lee eae 0 or alae 1! ae ay lt FE A eu foams re Ok 0 0 or s t . aya | Ge 1 (t) dt fe py” al te ee 0 We integrate the second member partially : - | (l+¢+1 et et ei pet ces a Ore Fe) Tey 0 0 ety, (t) dt = (16) aya! oe = ——— +f Ta Gn (t) dt 4 (to Gn (t) dt . 0 0 Formula (16) passes into: Ae pr n n \d See =f Oe ee bias 0 or by application of (11): 1) Over een bijzondere soort van geheele functién. Utrecht. 1896 p, 19. 197 & t tn n a eH e—t___ dt= | e—'—____dt -++- | ——_—_q, (#) dt. fi (Ite 4 (ah Say ay 0 0 0 The first integral of the second member we convey to the first member, and we find: fe ae dt = we t) dt ae “(pay =farp el Se aa 0 0 If we apply the same process to this, and again to the result, ete., we find at last after m-fold appliance: na oO [ : tim : { et 5 e— ana —————(pal(t) dt ee 8) 7 (1 +4) J +o" ie ( 0 0 We can render this formula still more general by summation from 2 —0O to n= o after division by (—1)" m/; we get: iv 2) a fo fr Guat e—2t r= (|= ((a\@iig 6 6 6 6 (ale) | (i441 pg m) 0 0 We apply the process explained above to this again and by summation again after division by (—1)" m/ ete. we finally find: on trp Pn (¢) —kt ey, | aoe / a eee ; : ; ) Je (1+¢°+1 a [i (t+ kyr at (20) in which % and m represent positive integers. Of course a formula analogous to (12) may be deduced from this o 53 un a J Gay 0 \ (21) «2 ® 4 ie 2 > 0 da] > * > Fi 2 — ey yar Je—2ykli, (224!) + e2ykli(e 2k) dy fe- 24 Pn (—#*) dt. mY a _ ; 0 0 By summation, formula (18) is, however, found again. The formulae (4) and (5) may also be used in order to express the polynomia 2, in g’s. For this purpose we multiply the two members of (5) by 1 fire tetas 1 10:5 eee ii ec OT Las saat ap ae By equalizing the coefficient of G' in the second member of the I4 Proceedings Royal Acad. Amsterdam. Vol. XVIL. 198 equation, thus obtained, to the coefficient of 7’ in the second member of (4) we find: . eal n 1 1.8.5...(2k-8) : Hp,,(#)=(-1)" 22"! } pp(z?)- Se a Ts ORT aan Pn—K x") } (22) By means of this expression an integral may be deduced. For if we multiply both members by e— “ip (x) da after replacing 2? by « and if we then integrate between O and o, we find, using the following well-known formulae ') : wo fe m (x) Pn (vz) da = 0 m == x 0 a foro (cdo! - 0 ° l 1.5.5.. .(2n—2m— 3) =a ») Ho a) da = (-—1)"4+! 22n , SS, —— | é Pn (a) Foy (Y v) da ( 1) al nt (n m)! Dn—m 7 or after some reduction: : ni e— Pn (@?) Hon (x) ede —(— 1)"+12"-+-m—1 _____ 13.5... (2n —2m—8) (28) ys (n—m)! 0 maon—l. In the same way we find D . fe —2* Qn (&") Ho, (@) veda == (—1). 228-1 nr, 2a) vu 0 and —_ | e— @n—i- (a?) Hon (a) cde = (—1)s" 229 eee) 0 If we write formula (22) in this form: 1 £m) Ph Ve —2 kd Fo,, (x) — (—1)" 22n mI Y nv") 4 pn—1 (27) Pi (v7) we know that) fo 2) ox? ¥ Ci oh (Ge) == mae —40 KT (2e)//a)da. 0 !) Dr. Nistann’s Dissertation page 11. *) These Proceedings XV. p. 1247. 199 This we substitute: io 3) il! a Hp,(a) = (—1)”. 22" Indep, (w?)—3nlg,—1(@’)— — @t fe*F,2e/ee Dae 0 Ls n! Aha - iin We further introduce: & 3 (=) Sit 2 dt 0 and ta! @r—(2’) = ava is i) (2aVa)da . na” 1 fetentae 0 We find then: FF LIE [o-“Neavejtafet 23 ” ok tk 0 0 or ea, some reduction (—1)—! — Han (a) + 1! gy (0°) = Ee >. (26) = eee (2a a) da fe tt Weta ma | dt 2Y/ x : : 0 0 For «=0, the following identities arise from the formulae (6) U and (22): mi \> x, (24I(2n—2k) )! ni? n\k a) se ——— or — 22n — > ——— (27) a kP(n—h)!? (2n)/ ro ( 2n 2k and 9, n 9 F 5) (Caren Sealer aes aieel Claeee n! 2 p= k! ok or St Stee | ay nf? ve 2 ke=2 KI Qk (2n)! 14* 200 Chemistry. — “The metastability of the metals in consequence of allotropy and its significance for Chemistry, Physics, and Technics”. Il. By Prof. Ernst Conen. The specific heat of the metals 1. 1. In my first paper ') on this subject I called attention to the fact that the physical constants of the metals hitherto known, are to be considered as entirely fortuitous values which depend on the previous thermal history of the material used. In that paper I wrote with regard to the specific heat of the metals: Considering, for instance, the important part whieb the specific heats of the metals have played in chemistry and physics during the last few years, it is evident that a revision of these constants is wanted. 2. Reviewing the earlier literature dealing with this constant, I found that it contains already a number of data which prove unequi- vocally that the specific heat of the metals does indeed depend on their previous thermal history. Le Verrmr published in the year 1892 a paper *) “sur la chaleur spécifique des métaux”, in which he describes his measure- ments with copper, zine, lead, aluminium, and silver. The calorimetric determinations were carried out between O° and 1000° by the method of mixtures. The temperature of the metal at the moment at which it was brought into the calorimeter was determined by means of a Ln CHareLigr pyrometer. 3. Le Verrier stated that the mean specific heat remains as a rule constant till 200—3800°, after which it changes abruptly, as Pioncuon *) also found in the case of iron, nickel and cobalt. The variation of the total heat (i.e. the quantity of heat required to raise the temperature of 1 gr. of the substance from 0° to # C.) with the temperature is consequently to be represented by a curve with breaks and not by a continuous one. In the neighbourhood of these breaks the condition of the metals is not only a function of the temperature, but also of their previous thermal history. ‘) These Proc. 16, 632 (1912). 2) CG. R. 114, 907 (1892). 3) CG. R. 102, 675, 1454 (1886); 108, 1122 (1886). In full: Ann. de Chim. et de Phys. (6) 11, 33 (1887). 201 As a consequence of the retardations in the structural change (changements d’état) of the metal, a different value of the total heat is found on cooling from that on heating. If a certain piece of metal is cooled or heated repeatedly, differ- ent values for the total heat are found. If we start from a lower temperature and return to it after having overpassed the break in the curve of total heat, a closed and not a single curve is obtained. 4. This result is in complete harmony with the dilatometric and electromotive force measurements carried out by myself in collabor- ation with messrs. He_berMAN and MoksveLp, on copper, cadmium, zine and bismuth, measurements which led to the conelusion men- tioned above. 5. Le Verripr’s paper contains some interesting data which we shall now consider in connection with our dilatometrie and eleetro- motive force measurements. The curve representing the variation of the total heat of copper as a function of the temperature, consists of four parts. At 850° an absorption of 2 Cal. occurs; at 550° an absorption of 2 Cal.; while at 750°, 3.5 Cal. are absorbed. Thus, while our dilatometric measurements proved that there exist more than two modifications of copper, the same fact was noted a long time before by Lu Verripr, using a different method. The measurements of Le Verrigr which are summarized in table I, have, however, been quite overlooked hitherto. It may be pointed out here that the transition temperatures which can be deduced from Le Verrier’s determinations will generally be too high. This is a consequence of the retardation of the molecular changes, which were also observed by him. Fresh experiments with the pure modifications of the different metals will throw light upon this point. 6. From the determinations of Lu Verrier there follows also, that there exists a transition point for lead which has so far been unknown. Experiments in this direction are in progress in my laboratory. 7. The same may be said with regard to silver. 8. Aluminium shows, according to Ly Verripr, an absorption of 10 Cal. at 535°. It may be pointed out that Dirrensercer (Phys. Techn. Reichsanstalt at Charlottenburg—Berlin) proved ten years Temperature. 0—230° 220—250 250—300 O—110° 100—140 very variable 110—390 300—400 0—300° 300—530 202 DABBLE Mean spec. heat. Pb. 0.038 Almost nil. 0.0465 0.096 Total heat. 0.038 X t Almost constant. 8.15 + 0.0465 (#250) 0.096 « ¢ absorption of 0.8 Cal. in the neighbourhood of 110° 11.36 + 0.105 (¢ -110) . 0.105 31.4 + 0.122 (¢t- 300) 0.122 \ increases rapidly above 400° and ra amounts to 46 Cal. in the neigh- bourhood of 410° immediately before melting. Al. 0.22 0.22¢ 0.30 Te crystallization of the silicium | occurs at + 500° and the break 530—560 ? lies with Al which contains Si in the neighbourhood of this tempe- rature 65 + 0.30 (t-300) Absorption of 10 Cal. in the neighbourhood of 535° 139 ++ 0.46 (t-530) 540—S00 0.46 170 Cal. at + 600°; increases rapidly and exceeds 200 before melting (620°). Ag. O—260° 0.0565 0.0565 ¢ 260—660 0.075 14.7 + 0.075 (f—260) 44.7 + 0.066 (t-660) : : 62 Cal. at + 930, imme- 660 —900 0.066 diately below the melt- ing point. Cu. 0—360° 0.104 0.104 ¢ 320—380 0.104 Absorption of 2 Cal. at + 350° 360—580 0.125 37.2 + 0.125 (#360) 560—690 0.125 Absorption of 2 Cal. at + 580° 580—780 0.09 37 + 0.09 (¢—580) 740—800 0.09 Absorption of 3.5 Cal. at + 780° 780 —1000 0.118 eM N a aed 117 Cal. at + 1020°. 208 after Le Verrier that this metal is capable of existing in more than one allotropic modification and he found a transition temperature between 500 and 600°. I hope shortly to report on this point, in connexion also with a question which is important from a technical standpoint i.e. the disintegration of aluminium objects at room tem- perature, a disease which is the cause of a good many complaints in industrial circles as well as in daily life. 9. That others had never observed the phenomena described by Ly Verrier may be explained by the fact that they had not heated their preparations repeatedly to high temperatures, as he did. We have also observed during our dilatometric researches that such a transition point can be overpassed several hundreds of degrees without any effect. If on the contrary the metal is repeatedly cooled and heated the transition is “set going”. As the means of overcoming these retard- ations are now known we are able to avoid them. A systematic research in this direction is now possible and I hope to report shortly on it. Utrecht, June 1914. van “t Horr- Laboratory. Physics. — “Jleasurements of isotherms of hydragen at 20° C. and 15°.5 C.” By Prof. Pa. Konystamm and Dr. K. W. Watsrra. Van per Waats fund researches N°. 7. (Communicated by Prof. J. D. vaAN DER Waats). (Communicated in the meeting of April 24, 1914). § 1. Choice of the substance and the temperature. With the apparatus described in N’. 5 and 6 of this series we have made measurements of hydrogen isotherms at 20° C. and 15°.5 C. This choice was led by the following considerations. As we already set forth in the beginning of Communication N°. 5, one of the motives of our research was the desire to be able to make an accurate comparison with the results obtained by AmaGat. Our first intention was to determine anew AMAGAT’s air isotherms; then we were, however, checked by peculiar difficulties. Every time, namely, when a measuring tube was filled with air in the way described in the previous Communication, and was then left for 204 some hours at high pressure, (above 1500 atm.), it appeared to be unfit for accurate measurements after that time. When the apparatus was opened, the mercury appeared to be quite contaminated, the glass tube and the platinum contacts being also covered by a black substance. Though in view of AmaGat’s experiments it could hardly be supposed that this substance was mercury oxide, formed by the action of the oxygen on the mercury, experiments of various kinds made it impossible to assume another cause. The supposition that at high pressure amalgamation of the platinum took place, proved erroneous, for in the black substance no trace of another metal than mercury could be demonstrated. Also the humidity of the air proved to be entirely without influence. When it finally appeared that neither filling with hydrogen nor with nitrogen yielded any trace, we could not but conclude that we had really to do here with the same phenomenon that Kurnen and Rosson‘) and Kurrsom*) had observed when using closed air-manometers, namely that oxygen and mereury act on each other at pressures of about 100 atm. KiEsom, however, describes a slow action, which only after the lapse of months manifests itself clearly; whereas we could demonstrate the formation of mercury oxide with certainty already after a few hours on account of the so much higher pressures. How it is that neither in his determination of air-isotherms nor in that of oxygen AmaGaT was troubled by this action, we cannot explain. After we had once ascertained it, the use of oxygen and oxygen mixtures was of course excluded. We therefore resolved to begin with measurements of hydrogen, which is most easily obtained in very pure state. The choice of the temperature of our measure- ments was directed by the desire to obtain a direct comparison with AMAGAT’s Measurements on oue side, and a supplement to SCHALKWIJK’S very accurate measurements at low pressures on the other side. § 2. Filling of the apparatus with pure hydrogen. Most of our determinations have been made with hydrogen from the factory ‘Electro” at Amsterdam, which sells cylinders of com- pressed electrolytically prepared hydrogen. For the further purifi- cation and the filling of the apparatus with purified gas the arran- gement was used of which fig. 12 gives a schematic representation. It fits on to the most lefthand part of fig. 6 at /. 1) Phil. Mag. Jan. 1902, p. 150. *) Diss. p. 50—53. Thesis III. 205 A horizontal glass tibe «@ passes on the lefthand side into a vertical tube c via an emergency reservoir 4. The tube c ean be fastened to the Gaedepump by means of a glass spring and a ground joint piece. In the middle of the tube @ is a three-way-cock In order to fill the measuring tube with pure hydrogen, the cocks BE, D, and F’ are opened after the already mentioned operations (Comm. N°. 6, p. 828). The position of three-way-cock A is such that both sides of @ are in communication with d. The three-way- cock B shuts off the tube g at the top. Position I. The airjet or oil-pump is made to serve in the beginning, the Gaede-pump completing the evacuation. When the air is sufficiently rarefied, the cock /’ is closed, and the empty tubes m, p,q, and r are filled with hydrogen from the cylinder. The mercury, which in the tube s has risen to barometer height in the meantime, will deseend; the mereury difference in the tubes / and g still indicating the barometric height.’) Then the hardglass tube g is heated, till the platinum asbestos begins to glow. The cock # is slowly opened. And while the gas is flowing into the empty space & and further, the hydrogen tube is again opened, so that the pressure in the tubes in, pg, and + always remains + 1 atm. This is desirable because in case of too great rarefaction the glowing hardglass tube g indents, and soon gives way. The gas that flows through mm to the different tubes, is almost pure, for the oxygen, for so far as it is present in ihe electrolytic-factory hydrogen, is quite combined with hydrogen to water throngh the catalytic action of glowing platinum asbestos, 1) On account of an eventually too high pressure the tubes m, p, q, and r might burst now, if the open tube s with mercury safety valve had not been added. 207 and the water formed is entirely retained in the phosphorus pentoxide tube p. When the mercury in f and g is again at the same level, it may be assumed that everything is filled with hydrogen of one atmosphere. Now the cock / is again closed; / and the other tubes are again evacuated. An idea about the purity of the gas which was found in the tubes after the first filling, is now given by the discharges in the cathode ray tube e. As long as traces of oxygen still contaminate the hydrogen (i.e. with air — and the presence of the latter appears at the same time — the only possible con- tamination) the tube will be filled with red light. When pure hydrogen has filled the tubes, the light will exhibit the well-known rice-colour. An opinion may then be formed at the same time about the degree of rarefaction attained, and also about the closure of different cocks and couplings. The tubes are then again filled with purified hydrogen, and after another evacuation and filling the purity of the gas in all the tubes may be safely assumed to be sufficient. Then the cock VD is closed, the mereury bulb (see Comm. N°. 6 p. 828) is raised, and the pure hydrogen is in the first “pressure stage” \see p. 823). Now for a control the cock # was always closed once more, and the part of the tubes k, a, gy, d, f, and e was exhausted, to ascertain the purity of the gas with which we are going to work by means of the colour of the discharge light. If, what need not yet be done, (p. 830) it is desired first to determine the normal volume of the gas at + 1 atm., before it is brought into the first “pressure stage’, /’ must be closed before the last filling. The difference in height between the mercury levels in Z and ¢, and also the temperature of the thermostat must be deter- mined. The barometric height can be read with the siphon baro- meter /, g.*) But now the tube / must be in communication with the outer air. This may be effected by turning the cocks uf and B 90° in positive resp. negative direction (Position ID). Then the tube / gets into communication with the outer air via / and /. This remains the case with g. But to prevent the tubes d and 7 to get commu- nication with the outer air also the cock A must be turned, but in opposite direction. The determination of the normal volume in JV’ has, however, as said before, only sense when we wish to convey a quantity of gas quantitatively to the measuring tube, which has not yet been done. To ascertain whether sufficiently pure hydrogen was obtained in 1) By means of a cathetometer and the scalar divisions etched on the tubes. 208 this way, we made also a series of experiments with distilled hydrogen from the Leyden laboratory. The quantity of admixtures had been estimated at at the most by Prof. Kamuriinga Onnes. We 5000 oladly avail ourselves of this opportunity to express our indebtedness to Prof. Kamertincu Onnes for his kindness. In the filling with this gas the purification apparatus could safely be omitted ; the cylinder was therefore immediately connected with the tube m. The results of the measurements with this agreed within the limits of the errors of observation with the results obtained with the gas purified by us in the way described above. § 3. The measurements. How through the different “pressure stages” the gas is conveyed io the measuring tube, has already been described above. Also how the temperature is then kept constant. This is seen by the deviation of the galvanometer, inserted into the Wuratstonr bridge. To get a first idea the pressure at which the galvanometer needle deviates is read on the manometer, and a corresponding number of weights is placed on the rotating pressure gauge, after it has been brought in communication with the tubes. If the number of rotating weights is too great, some are taken off till the galvanometer needle has returned to its original zero position. At last a final condition is reached, in which the putting on of 50 grams on the rotating weights makes the needle deviate, while the needle returns to its position of equilibrium when this weight is removed. The accuracy with which the pressures are thus measured on the small and the large pressure balance generally amounts to this 25 erams up to 900 atmospheres. When the measurement is made with the small pressure balance, which goes up to 250 kg. per em*. the galvanometer needle may be made to deviate and return by putting on or taking away 10 grams, and even when the contacts are very clean with less. As, however, 25 gr. implies already an accuracy of 1 to 10.000, whieh is not reached on account of other sources of error, there is no sense in going so far in the determination of the pressure. We only mention the fact as a proof of the very great accuracy of the pressure balance for relative pressure measurements. When one pressure measurement has thus been made, the pressure is increased. The galvanometer needle, which now would continue to deviate, must again be brought back to zero, because now another resistance of the volume wire is measured, 209 Thus for every platinum contact in the measuring tube the pressure at the corresponding volume is determined. Then the pressure is diminished, so that two series of observations of the same results must be obtained, but one passed through at increasing, the other at decreasing pressure. The pressure differences at two corresponding observations of two such series rarely amounted to more than 50 grams. It must of course be continualiy verified whether the tem- perature differences inside and outside the measuring tube have disappeared. This has taken place when the resistance of the tem- perature wire (ef. Comm. 6 p. 833) has become constant. In the measurement of the highest pressures, so when the large “head” of the pressure balance is used, i.e. between 1200—2400 atinospheres, the accuracy of the pressure measurement becomes less, especially on aceount of the increasing viscosity of the mineral oil used as transmission liquid. Yet the error will certainly remain below '/J00- § 4. Determinations between 2 and 200 atms. As was already mentioned in Comm. 6 (p. 830) unforeseen diffi- culties prevented us from determining the normal volume of the quantity used in the apparatus itself. For the determination of the isotherm of 20° C. we could make use for the calculation of the normal volume of ScHALKWIJK’s measurements, as will become clear from the discussion of our results. Such data were wanting for 15°.5 ©, And in order to be able to carry out al! the same an accurate comparison with AMAGAT’s measurements, we have executed measure- ments at lower pressures at that very temperature. In this way a control was obtained whether the equation for low pressures derived from the measurements may be extrapolated. We shall return to these points when our results are discussed, and first give a description here of these measurements too. As we again wished to use a large quantity of gas, the iron vessel D used in the large apparatus was used as a pressure cylinder. We then could fill the piezometer with a quantity of gas of the order of magnitude of 1 liter at 1 atmosphere. The piezometer originally consists of two pieces. The upper part was as the upper reservoir of our ordinary measuring tubes. At the top at a (fig. 13) there are 4 etched lines to be used after the cleaning of the tube. Lower down there is a widening 4; under this a sealed in platinum wire c, and at last an etched scalar division d. This tube was connected with a capillary, and bent round. A_ platinum wire is sealed into the bent part. Here a current can enter, and 210 leave through the mereury at the wire sealed in higher. When we provide the side-tube with a scale, and fill everything with mereury, and place it in a waterbath, a very accurate gauging is again possible as described in Comm. 5 p. 766. We first gauge the dis- iances of the etehed lines, then the volume from these lines to the sealed in wire, and then from there to the etehed scalar division, and this division itself. a G Fig 13. Fig. 14. The large reservoir, which is to be sealed to this top piece is calibrated after this sealing, by tiling with mereury the volume from the scalar division on the top piece to the sealar division at the bottom on the bottom piece. We now know sufficiently accurately the volume from the etched lines to the sealed in wire, and from here to the sealar division under the large reservoir. The tube is now fused to at the upmost 211 line, and at the bottom a bent tube is added. The brass flanged tube i of the pressure cylinder had been previously cemented at ¢, and after a few drops of mereury have been brought into the large reservoir, the tube is evacuated and filled in a horizontal position. When the tube has been filled with pure hydrogen, it is put erect, and the drops of mercury shut off the gas from the outer air. Then the whole thing is placed in a waterbath of 15°.5, while the differ- ence in height of the mercury in the tubes / and g is read. As the volume up to the scalar divison, and the division itself too, has been gauged, we now know the volume of a definite quantity of hydrogen at about 1 atm. and the desired temperature. In order to determine the pressure accurately, the pressure of the outer air must of course also be determined, for which purpose the siphon barometer is again used (p. 205). We can further dispense with the side tube, for it only served to protect the mercury at the bottom of the tubes against the water. It is knocked off at g, and after the still remaining tube has been entirely filled with mercury, the whole arrangement is put in the pressure cylinder filled with mereury. The pressure cylinder is closed, and connected with the hydrostatic press, which connection is also in communication with the pressure balance. By means of a rubber stopper a glass cylinder provided with a side tube at the bottom and at the top is put round the projecting part, so that water of 15°.5 from a thermostat keeps the gas at the desired temperature. The current was closed on the iron pressure cylinder ; then it passed through the mercury, and. when the required height had been reached it passed further through the platinum wire. By means of the pressure balance the pressure at which the platinum wire is reached, hence the pressure at which the gas volume is diminished to the upper part, could be very accurately determined. § 5. Corrections. Some corrections should be applied to the experimental results obtained in the above described way. First of all in the gauging the volume is obtained in gr. of mercury of a definite temperature. To reduce these values to the accurate volume in em‘. two reduct- ions must be applied. A reduction should take place to em*. by dividing the value in gr. of mereury by the specific gravity of mercury at the temperatures of the gauging. The specific gravity of mereury according to the Tables of Lanponr and Bérnsrein was used for this- reduction. Further the compressibility of the glass of 212 the measuring tube should be takea into account. The gauging takes place at J atm.; during the measurement the tube is subjected to a pressure on all sides, in consequence of which the volume decreases. As the correction in question is only a small one, we have thought that for our first calculations it would suffice if we took the com- pressibility of our glass equal to the valne determined by AmaGat. We have therefore put the factor of compressibility at 22 x 10-7 and assumed this quantity to be constant between 1 and 2500 atms. Also to the values of the pressure read directly some corrections should be applied. The weights in kg. read on the pressure balance should first be reduced to ke. per em*. by taking the value of the effective area into account. In anticipation of the comparison of the small pressure balance with an open manometer of sufficient capa- city discussed in Comm. N°. 5 p. 759, we have assumed that the effective area of the small balance, the piston of which is as accurately as possible ground in at 1 em?*., really amounts to 1 em’. Since we wrote our first communication we have been greatly strengthened in the conviction that we cannot make great errors in this way, by the result of Grora Kuein’s research '). According to his investigations*) the error in consequence of the neglect of the difference between piston and cylinder sections for ScHArFER and BUDENBERG’s balance amounts to at most O.1°/,,, and the deviation of the indicated and the directly measured value of the difference of the two piston sections is 0.4°/,, in the case examined by him. Now the large pressure balance could be compared with the small pressure balance by méasuring the same point of the isotherm in the neighbourhood of 250 atms. first with the one, and then with the other. So the measuring tube with the galvanometer in connection with it ete. serves simply as a manoscope, to judge when in the use of the two balances the pressure is exactly equal. It then appeared from some observations carried out in this way that when the section of the small balance is put at = 1 em*., the section of the small head of the large balance must also be put at 1 em*. within the limits of the errors of observation. As at these pressures the errors of observation are very small as we saw above, and will certainly remain below 0,2°/,,, this result is a new confirmation of the great accuracy of the Scuirrer and BupeNnserG pressure balances, and it gives therefore a new support to the validity of the made supposition. In the same way a comparison was made between the small and 1) Untersuchung und Kritik von Hochdruckmessern. Berlin 1909. 2) sO! (Clty peel 213 the large head of the large pressure balance in the neighbourhood of 1200 atms. Instead of the theoretical numerical ratio +4, three measurements gave resp. the values 4,012, 4,015, 4,016, average 4,014. The weights when the large head is used, must therefore be multiplied by this value. The thus obtained value for the pressure in the head must now still be corrected for the excess of pressure of one atmosphere, and for the hydrostatic pressure difference between the head of the pressure balance and the measuring tube on account of the mercury and oi! columns. ‘These liquid columns were roughly measured, in which 1 em. of mercury more or less need not be considered ; nor need the oscillations of the barometer be taken into account. Finally the thus obtained pressure had to be reduced to atmospheres of 1,0336 kg. per cm*. In table T. The column under v, indicates the weighed volume in er. of mercury. g g 4; - 3 » Pkg the number of kg. on the pressure balance. Dy oe - pe the pressure, corrected for hydrostatic pressure difference in kg. per em’. 33 5 », p the corrected pressure in atmospheres. rn % » § the ratio of the volume at 1 atm. and at the measured pressure in consequence of the com- pressibility of the glass. Bv, the product of 8 and »,. ” > ” E *. , » the corrected volume in em*. 5) 3 » pv the product of p and v. TWIN NSS MG TE, IU 5), November 1912. E— 2025 CE —— —————— vg Pre Po p | > pug v Pr 67.1491 195.850 194,750 188.419 | 0.99959 | 67.1216 | 4.95473 | 933.57 55.0632 | 245.400 | 244.300 | 236.358 0.99948 | 55.0346 | 4.06250 960.26 45.4959 | 306.575 | 206.175 | 296.222 | 0.99935 | 45.4663 | 3.35620 994.18 | 37.3710 | 390.200 | 389.800 | 377.128 0.99917 37.3400 | 2.75633 | 1039.49 31.0962 | 494.550 | 494.150 | 478.086 0.99895 | 31.0636 | 2.29302 1096.26 27.4110 | 587.000 | 586.600 | 567.531 099875 | 27.3756 | 2.02087 1146.91 22.7296 | 769.500 | 769.100 744.098 | 0.99836 | 22.6923 1.67508 1246.42 19.3102 | 992.625 | 992.225 | 959.970 | 0.99789 19.2695 1.42242 1365.48 Proceedings Royal Acad. Amsterdam, Vol. XVII. 214 TABLE I. (Continued). November 21, 1912. t—20% Ys Pre | Pe p B Be, v | pv | 90.3267 130.200 129.100 124,903 0.99973 | 90.3019 | 6.66580 832.58 87.5019 134.700 133.600 129.257 0.99972 87.4774 | 6.45734 834.66 85.4277 138.250 137.150 132.692 0.99971 85.4029 | 6.30420 | 836.52 43.7526 | 292.925 | 292.525 | 283.016 | 0.99938 43.7255 | 3.22769 | 913.49 34.5011 391.600 391.200 | 378.483 | 0.99917 | 34.4725 | 2.54466 | 963.11 25.0070 | 599.600 | 599.200 | 579.721 | 0.99872 | 24.9750 | 1.84358 | 1068.76 December !!/;5, 1912. 6209) 60.4928 222.500 221.400 214.203 | 0.99953 | 60.4644 | 4.46331 956.05 58.0°61 233.000 231.900 | 224.361 0.99951 58.0676 4.28639 961.70 55.9451 243.350 242.250 234.375 0.99948 | 55.9160 | 4.12756 967.40 53.7822 254.700 253.600 245.356 0.99946 | 53.7532 | 3.96791 973.55 48.5533 286.400 | 286.000 276.703 | 0.99939 | 48.5237 | 3.58188 991.07 45.9361 306.000 305.600 295.665 | 0.99935 45.9062 | 3.38867 | 1001.91 42.9934 331.450 | 331.050 | 320.288 | 0.99929 | 42.9629 | 3.17140 1015.72 39.4220 | 368.750 368.350 | 356.376 | 0.99922 | 39.3913 | 2.90775 | 1036.25 35.8492 | 415.575 | 415.175 | 401.679 | 0.99912 | 35.8177 | 2.64396 | 1061.99 22.0889 | 814.000 | 813.600 | 787.152 | 0.99827 22.0507 1.62772 1281.24 February 10, 1913. 120% 65.7937 225.050 = 223.950 += 216.670 +=: 0.99952 —s«65.7621 = 4.85437 ~—- 1051.80 34.9813 485.200 484.800 469040 0.99897 34.9453 2.57956 1209.92 27.9749 660,000 659.600 638.158 0.99860 27.9357 | 2.06214 1315.97 21.3124 995.000 | 994.600 952268 0.99788 21.3470 1.57578 | 1516.32 20S Ug Pre Po. p p Ug 65.7937 | 220.200 219.100 | 211.929 | 099953 | 65.7628 | 34.9813 472.950 472.550 | 457.188 0.99899 | 34.9460 27.9749 | 641.825 641.425 | 620.574 | 0.99863 27.9366 21.3924 | 964.100 963.700 | 932.372 | 0.99795 | 21.3486 14.4836 487.750 1960.3 1896 6 0.99583 14.4232 February 13, 1913. C=20' 65.7937 196.850 195.750 | 189.391 | 0.99958 | 65.7661 34.9813 416.300 415.900 | 402.382 0.99911 34.9502 27.9149 558.800 558.400 | 540.251 | 0.99881 | 27.9416 | 14.4836 , 400.250 1609.1 | 1556.8 0.99658 | 14.4341 April 22/54, 1913. G— 7202. 36.1414 351.450 351.050 339.643 0.99925 —-10.7858 32.4244 402.700 402.300 389.221 0.99914 13.7748 21.1098 | 720.400 720.000 696.590 | 0.99847 17.2937 17.3297 | 980.000 | 979,600 | 947.755 0.99792 21,0775 13.8172 , 361.000 1451.5, 1404.3 0.99692 | 32.3965 10.8401 | 587.750 | 2361.7 | 2284.9 0.99497 36.1143 April 22/94, 1913, E— Nde.08 36.1414 345.900 | 345.500 | 334.272 | 0.99926 | 10.7864 32.4244 395.950 395.550 | 382.691 | 0.99916 | 12.0677 21.1098 708.200 | 707.800 684.791 | 0.99849 | 13.7753 17.3297 | 964.100 | 963.700 932.374 | 0.99795 | 17.2942 13.8172 | 355.750 | 1430.4 1383.9 0.99695 | 21.0779 121097 457.000 | 1836.9 1777.2 0.99609 | 32.3972 10.8401 580,250 2255.8 0.99504 36.1150 215 TABLE I. (Continued). 2331.6 | February !\/;2, 1913. 4.85443 | 2.57962 | 2.06220 | 1.57589 1.06468 4.85467 2.57993 2.06257 1.06548 2.6559 2.3914 1.5559 1.2765 1.0168 0.7962 2.6659 2.3914 1.5559 1.2766 1.0168 0.8904 0.7962 Pov 1029.03 1179.37 1279.75 1469.32 2019.27 919.42 1038.14 1114.30 1658.74 905.45 930.79 1083.89 1209.81 1427.89 1819.24 891.16 915.20 1065.47 1190.26 1407.15 1582.42 1796.07 15* TABLE I. (Continued). June 4, 1913, = ee he sae | Vg. Pre Po Pp p | pug | vb Pu a ee EEE eee eee ee 64.3346 | 141.800 140.700 156.13 | 0.99970 | 64.315 4.7476 646.28 | | | | 59.8154 153.475 152.375 147.42 0.99968 | 59.796 | 4.4140 | 650.71 27.1963 | 370.500 370.100 358.07 0.99921 | 27.714 2.0502 | 734.12 21.2326 | 524.750 | 524.350 507.30 | 0.99888 21.209 1.5656 | 794.23 16.2658 766.100 | 765.700 740.81 0.99837 16.239 1.1987 | 888.01 | | | | 12.1023 | 1236.000 | 1235.600 | 1195.4 0.99737 12.070 0.89097 | 1065.07 | In conclusion we give the two observations at 15°.5 for the deter- mination of the compressibility between 100 atmospheres and atmos- pheric pressure. The first column gives the pressure in atm., the second the volume in em*. the third the product pe. ABE we November 1913. [5 == Va\ea), 1.0384 | 484.6 503.19 97.91 5.4474 | 533.35 December 1913. as NSD | 1.0004 | 536.07 | 536:28 104.82 | 5.4474 570.99 Amsterdam. Physical Lab. of the University. PACE Physics. — ‘The hydrogen isotherms of 20° C. and of 15°.5 C. between 1 and 2200 atms.” By Dr. K. W. Watstra. Van per Waats’ fund researches N°. 8. (Communicated by Prof. J. D. van pER WAALS). (Communicated in the meeting of May 30, 1914). Tete er § 1. Agreement of the observations below 1000 atms. with SCHALKWUK’S csotherms. For each of the series of observations given in the preceding Communication we have determined an empiric equation of the form ; PV=a+6D+cD+d. As only series of observations below 1000 atms. can be represented by this equation with 4 virial coefficients, only these series come into consideration for the present. The obtained observation material above 1000 atms. will have to be considerably extended to enable us to calculate the following virial coefficients with the same certainty. If of the above equation we wish to determine a, }, c, and d, we get a number of equations equal to the number of obser- vations, and consequently then with 4 unknown quantities. To solve these equations according to the method of least squares is not feasible, as then the normal equations become practically identical, which may already be seen beforehand. We have been able to apply Prof. E. v. pb. SANDE Bakunuizen’s method successfully, which was also ie— 202: 5), November 1912. T=20°. 21 November 1912. P | PH(O) | PYO) (AC) P| PY(O)| PY (0) | (O¥(C) | | 959.97 1365.48 1365.48 0.00 579.72 1068.76 1068.76 0.00 744.10 | 1246.42 1246.43 | —0.01 378.48 963.11 963.11, 0.00 567.53 | 1146.91 1146.81 | +0.10 283.02 913.49 913.49 0.00 478.09 | 1096.26 | 1096.42 —0.16 132.69 | 836.52) 936.49| 0.03 371.13 1039.49 | 1039.49 0.00 129.26 | 834.66 834.66/ 0.00 296.22 | 994 18, 993.95| + 0.23 124.90 | 832.58 | 832.55] +0.03 236.36 | 960.26] 960.42] —0.16 PV =710.50 4311.45 D + 188.42 | 933.57] 933.56) +0.01 Bie OE inte 02D PV = 829.71 + 445.08 D + + 353.40 D2 + 197.28 D4. T=20?: N/;5 December 1912. Ti — 202% 10 February 1913. P| PV(O)| PY) | (O)(C) Pp | PY (OV PEG) Ae | | 787.15 | 1281.24 | 1281.25) —0.01 962.27 | 1516.32 | 1516.32 0.00 401.68 | 1061.99; 1062.00 —0.01 638.16 | 1315.97 | 1315.97, 0.00 256.38 | 1036.25 1036.21 0.04 469.04 1209.92 1209.92. 0.00 320.29 1015.72) 1015.76 —0.04 216.67 1051 80 | 1051.80. 0.00 295.67 | 1001.91 1001.81 +0.10 PV = 923.03 + 508.75 D + + 552.10 D2 + 296.55 D4. 276.70 | 991.07; 991.12; —0.05 245.36 | 973.55) 973.51) +0.04 234.38 | 967.40) 967.35) +0.05 224.36 | 961.70) 961.75) —0.05 214.20 956.05 956.11 —0.06 PV = 842.61 + 409.64 D + + 423.18 D2+ 191.36 D4. used at Leyden for the calculation of Amacat’s values at the time. (See Comm. 71). In how far we have succeeded in determining the empiric equations may appear from the following tables. We have placed there side by side P, ’V(O) — observed pressure and pressure 1.8573) the series of observations have now been reduced in agreement with each other. From these equations we calculate first the product PV for the densities 100, 200, 300, 400, and 500 for so far as the corresponding pressures lie in the region of observation of the series, and hence agreement may be expected. We then find : D100 | 200° | 300 | 400 +] 500 I | 1.1491 | 1.2429 | 1.3573 | 1.4961 —_ I | 1.1491 | 1.2428 | 1.3573 1.4963 | ‘1.6654 Il | = "1.2426 | 1.3573 “1.4959 | 1.6641 Wil is | 1.2423 | 1.3573 - 1.4963 1.6650 V | — | 1.2419 | 1.3573 | 1.4967 1.6653 VI | = | oe | 1.3573 | 1.4966 | 1.6644 Vit | a | 1.2430 | 1.3573 ae a ~j—.. = eae ee Mean 1.1491.) 1.2427 | 1.3573 | 1.4963 1.6648 Besides with the mutual agreement, we are struck here with the agreement of the mean values PV with those determined provisionally. We reproduce therefore this part of the table and place the mean values PV(M) by the side. D | PV(S) PVC) PV(M) | 100 | 1.1492 1.1486 i.1491 200 1.2457 (12427 | 1.2427 300 | 1.3621 | 1.3573 | 1.3573 400 1.4983 1.4963 1.4963 500 1.6544 1.6654 1.6648 It remained to draw up an equation which satisfies the last table of the mean values with a=1.07258 in accordance with SCHALKWIIk’s isotherm. This final equation drawn up for convenience with five virial coefficients, becomes: (). PV = 1.07258 + 0.0,6763D -+- 0.0,88215.D? 4 + 0.0,,66954.D* — 0.0, 151 D", 5 222 This equation not only represents all our observations as well as possible; but the agreement with ScHALKWIJK’s results appears to be even better than for the provisional calculation, which is seen from the following table. | | D | PV(S)| PV(F)| (F)-(S) D | PV(S)| PV(F)| (F)-(S) 1 1.0733 1.0733 0.0000 60 1.1162 | 1.1163 0.0001 | | | | 101.0794 1.0794 | 0.0000 70 | 1.1242 | 1.1242 | 0.0000 | | | 20. 1.0863 1.0864 +0.0001 80 1.1324 1.1324 0.0000 30 1,0935 | 1.0936 40.0001 90 1.1406 1.1406 0.000 40 1.1009 1.1010 | +0.0001 100 1.1492 1.1491 | — 0.0001 50 | 1.1085 | 1.1086 | +0.0001 The tinal equation may therefore be considered to represent the whole region of the isotherm below 1000 atms. The agreement with ScHaLkWik is perfect up to = 100, which corresponds with a pressure of 115 atms. Reversely it appears therefore that we may extrapolate up to +120 atms. from the equation at which ScHALKWIJK arrived from his observations from 8 to 60 atms., viz. PV =1.07258 + 0.0,6671 D + 0.06993 D?, At D= 200 or P=250 atms. the error which would then be made, becomes already 3 per 1000. For greater densities up to 2500 the number of virial coefficients 3 is too small. It must then be 4 at least. It will not do simply to add a 4" coeffi- cient to SCHALKWIJK’s equation, which appears from the deviations, which (see table) are now positive, now negative. § 2. Comparison of the observations at J5°.5 with Amagat’s. We have one series of observations with 4 data below 1000 atms. and three above it at our disposal. (See p. 215). An equation has been calculated from the 4 data below 1000 as a control of the observations at + 100 atms. (See preceding com- munication). To compare our data with those of AmagaT at 15°.4 we have calculated an empiric equation with 6 virial coefficients from 6 observations. In the seventh observation at 383 atms. we have then a control. P |PV (0)| PV(C)\ (OO 2255.8 | 1796.07) 1796.07 0.00 1777.2 | 1582.42) 1582.42; 0.00 1383.9 | 1407.15 1407.15 0.00 932.37 | 1190.26 | 1190.26 0.00 684.79 1065.47 1065.47 0.00 383.29 | 916.64) 916.66 —0.02 334.27 891.16 891.16 0.60 PV = 637.965 + 892.46 D = 735.72 D® + 1215.49 Dt — — 787.959 D® + 204.470 D*. With the value of PV at 700 atms. this equation is then reduced to: PV = 0.92967 + 0.0,18953 D — 0.0,22767 D? + 0.0,,79888 Dt — — 0.0,,10996 D® + 0.0,,60639 D*. The easiest way for the calculation is now to compare the pressures for the same volumes as Amacat. We then find: V | P(Am.) P(C) (C)-(Am ) 0.002234 | 700 700 0 0.002046 800 800.5 0.5 0.001895 | 900 904.7 4.7 0.001778 | 1000 | 1005.3 5.3 0.001685 | 1100 | 1101.8 1.8 0.001604 | 1200 | 1200.7 0.7 0.001533 | 1300 1301.6 1.6 0.001472 | 1400 | 1401.0 1.0 0.001418 | 1500 | 1500.9 | 0.9 0.001370 | 16c0 | 1601.1 | 1.1 0.001326 | 1700 | 1704.2 4.2 0.001288 | 1800 1804.2 4.2 0.0012545 1900 | 1902.6 2.6 0 0012225 2000 2008.0 8.0 0.001194 | 2100 | 2113.6 | 13.6 ; | .0011685 | 2200 2220025) 20 ee These deviations and especially the progressive ones above 2000 atms. cannot be explained from the temperature difference of 0°.1, among others on account of their irregularity. This would give a pressure difference of no more than 0.6 atm. at 2000 atms. For the rest the deviations are too large and too systematical to be con- sidered as accidental errors of observation. The most obvious explana- tion, a systematic error in the absolute pressure measurement made by Amagar or by us, cannot be accepted either, as it would yield a deviation proportional for large and for small pressures. Probably the same causes come into play, which also prevented agreement between AMaGaT and SCHALKWIJK’s observations. Amsterdam. Physical Laboratory of the Cuiversity Hydrostatics. — “The different ways of floating of an homogeneous cube.” By Prof. D. J. Korrewee. (Communicated in the meeting of May 30, 1914). This problem, whose treatment, however simple it may seem, offers considerable difficulties, was lately brought to a complete solution by Dr. P. Branpsen. If we limit ourselves to the cases in which the specific weight of the cube amounts to less than half of that of the liquid (which is allowed, because the other cases may be derived from it by inter- changing the floating and immersed parts) stable floating appears to be possible in four different possitions. In the jirst position four of the edges are vertical. It may be acquired for specific weights, expressed in that of the liquid, smaller 1 1 : L 1 than a Re Y 3= 0,211... For those smaller than e == (GG it is the only one possible. In the second position two of the faces are vertical, but the edges belonging to them are sloping. The surface section is consequently a rectangle. This manner of floating is possible between the specific weights 0,211 .... and O,25 In the third position the space-diagonal of the cube is vertical and the surface section a hexagon. It is possible between the limits : and : of the specific weight. For the limits themselves the cube ) a) is lifted or immersed just so far that the surface section, perpendi- cular to the space-diagonal, has passed into a triangle. Those limiting positions themselves are already unstable; consequently the stability 225 of this position disappears exactly there where for specific weights < — a hexagonal section becomes impossible on account of ARcHI- 6 2 MEDES’ Law. This third manner of floating was, probably for the first time, referred to in the ‘Mathematical Gazette” of Dee. 1908, Vol. 4, p. 338, Math. note N’. 285, in which note, however, the second one and the case now following was not referred to at all. In the fourth position one of the planes passing through two opposite parallel edges assumes the vertical direction. In this posi- tion one of these edges is partially immersed, the other one quite outside the liquid. In consequence of this the surface section is a pentagon for which the intersection of the liquid surface with the plane just mentioned is an axis of symmetry. Such ‘pentagonal’ floating can only exist, however, between narrow limits of density, viz. between the densities 0,226... and O,24... It should be observed that only the first and the second position gradually pass into each other; further that a completely unsymme- trical way of floating, in which neither one of the faces, nor one of the diagonal planes, nor a space-diagonal assumes the vertical position, cannot arise. One of the greatest difficulties connected with the problem consisted in the formal exclusion of such cases. It further appears that between definite limits of density, several positions, amounting at mosf to three, are possible for the same cube, viz., Below 0,166... the first position is the only possible. From 03166)... to. 0,211... the first and the third. From 0,211... to 0,226... the second and the third, From 0,226... to 0,24 ... (the limits of pentagonal floating) the second, the third and the fourth. From 0,24... to 0,25 the second and the third. Between 0,25 and 0,5 only the third. Strictly speaking one case in which one of the diagonal planes coincides with the liquid-level and the specific weight therefore anounts to exactly 0,5 ought to have been added to those mentioned above. Dr. Branpsen has indeed proved that stability exists in this case. Yet at the slightest alteration of the specific weight the adjacent positions of equilibrium become unstable, ei. those which arise by 226 lifting the eube a little or by immersing it in such a way that the diagonal plane mentioned remains parallel with the liquid-level. A paper by Dr. Branpsen in which the results described above are set forth and proved is going to appear in the “Nieuw Archief voor Wiskunde’ . Petrography. — “On some rocks of the Island of Taliabu (Sula Islands.) By Prof. Dr. A. WicHMANN. (Communicated in the meeting of May 30, 1914). After G. E. Rumpnivs had deseribed. towards the end of the 17th century, some jurassic fossils, originating from the east coast of Taliabu') it was not before the year 1899 that new geological inves- tigations were made again in the island mentioned above. It was R. D. M. Verseek who collected some rocks in some places of the north coast on the 4? and 5 of August and afterwards described them’). In November of the same year G. Bornm followed his example, and chose as point of departure of his investigations the findingplace mentioned by G. Rumpnivs, and afterwards continued his work over part of the south coast*). In December 1902, in January and especially during the months of October and November 1904 an extensive part of the southern part of Taliabu was surveyed by J. W. van Novunuys*). The large collection gathered by him was described by G. Born‘), in so far as regards the fossils. In the following lines the communication of an investigation of the rocks may find a place. 1) D’'Amboinsche Rariteitkamer. Amsterdam 1705, p.p. 253—255. 2) Voorloopig Verslag over eene geologische reis door het Oostelijk gedeelte van den Indischen Archipel in 1899. Batavia 1900, p.p. 9, 10, 46, 47. — Molukken- Verslag. Jaarboek van het Mijnwezen van Ned. Indié. 37. 1908. Wetensch. ged. Batavia 1908, p.p. 20—21, 107108, 221223. 3) Aus den Molukken. Zeitschr. d. D. geol. Ges. 54. 1902. p. 76. — Geologische Mitteilungen aus dem Indo-Australischen Archipel. N. Jahrb. f. Min. Beil. Bd. 27 1906, p.p. 385—395. — Beitriige zur Geologie von Niederlindisch-Indien. Palaeon- toeraphica. Suppl. 1V. Stuttgart. 1904, p.p. 6, 13—14. ) Maatschappij ter beverdering van het Natuurkundig Onderzoek der Neder- landsche Kolonién. Bulletin No. 48. 1905. — Bijdrage tot de kemnis van het eiland Taliaboe der Soela-groep (Moluksche Zee). Tijdschr K. Nederl. Aardrijksk. Genootsch. (2) 27. Leiden 1910, p.p. 945--976, 1173—1196. 5) Beitriige zur Geologie von Niederliindisch-Indien. Palaeontographica. Suppl. LV 1912, p.p. 123177. 227 Taliabu is a longitudinal island extending in the direction from East-West between 124°8’ and 124°41’ E. and 1°50’—2° S. Whilst the length amounts to 117 km., the width is no more than 387'/, km. A mountain range of an average height of 1000 to 1200 m. extends over its entire length. The formations of the northern part, hitherto little known, are restricted to old slate-rocks, quartzites, granite-porphyry and coral limestone, whiist on the southern part moreover extensive strata are found containing numerous fossils from the Jurassic system those of the Berriasien ineluded '). Among the eruptive rocks occurs especially much granite. Younger forma- tions play here likewise an inferior part, because the coral limestone is found only in the eastern half of the south-ecoast and no farther than cape Kona | Mantarara| ’). Granite. Van Novuvys already called the attention to the fact that the granites of Taliabu have much similarity with the granites deseribed by Verberk of the Banggai Islands, which are situated westward from the Sula Islands. They are characterized by the occurrence of dark red orthoclase, greenish dull white plagioclase, white quartz and black biotite*). Rocks in which the orthoclase is of a lighter colour are however not wanting in Taliabu. They are contrary to most granites of the Indian Archipelago, which as a rule are rich in plagioclase, to be regarded as normal biotite-granites, in which a more subordinate place is assigned to oligoclase. It appeared that mikrokline was always absent. The red colour of the ° orthoclase is caused by a finely distributed reddish brown substance, which disappears however as soon as the feldspar is altered into kaoline. Biotite is indeed always present, but sometimes very scarcely represented. It also occurs that by alteration it has been changed into chlorite, and then, at the same time, rutile-needles appear. Brown iron ore (limonite), in the shape of irregular flakes and aceu- 1) J. Antpure asserts (Versuch einer geologischen Darstellung der Insel Celebes. Geolog. und paleontolog Abhandl. herausgeg. von J. F. Pompecxi und F. yon Huens. N. F. 12. Jena 1913, page 110), that among others also Lias is found in Taliabu. Most likely he mistakes — he is not so very particular — this island for Misol. Further, he says, with regard to the demarcation strata of the Jurassic and the Cretaceous system, that they “allerdings nach neueren Untersuchungen der Trias angehéren’’, There can neither be question of this, as is clearly proved by G. Borum’s essay (Palaeontographica. Suppl. IV. 1904, pp. 1—46). Most likely Antpure has in this respect mistaken Taliabu for Buru. (Vide: Centralblatt f. Mineralogie 1909, p. 561; 1910, p. 161). 2) According to a communication of Mr. van Novnavys the coral limestone reaches only a height of + 10 m. 8) Molukken-Verslag, p. 218, 228 mulations along the fissures is rather widely spread as a product of alteration. Apatite and titanite occur only sporadically. Van Novnvys has already aequainted us with the finding-places of the granites.') In the western part of the island we must mention the territory of Lekitobi in’ the first place. The hill westward from the entrance to the lagoon, the hills of the island Kona in the lagoon and likewise Tandjunge Merah the red cape — at the east side are all composed of this rock. The second granite-territory was found on the upper course of the Wai fa, where it borders upon strongly folded phyllite. The third region is situated northward from the Wai Taha and extends in the N.E. till beyond the left bank of the Wai Kabuta. A fourth area occurs on the upper course of the Wai Najo, where it borders the strata of the Jurassic system. South of this river rises moreover a granite-hill on the coast in the neighbourhood of cape Pasturi. The erratics that were found, besides in the rivers mentioned above, also in others namely Wai Miha, Wai Kilo, Wai Ila, Langsa, Wai Tabana and Wai Kasia point to the fact that granite is widely spread over the interior. H. Bickine finally mentions a biotite-granite containing hornblende from the Wai Husu °). : The contactmetamorphical formations, which have been caused by the eruption of the granites, deserve attention however in the first place, especially because both old slates and jurassic sediments have been concerned in it. On the northside of the lagoon Lekitobi an andalusite-mica-rock is found as a rock. In the pink compact rock macroscopically only numerous silver-white laminae of muscovite can be detected which, also according to the microscopic examination, form also the chief con- stituent. Besides the aggregates of these colourless laminae there are also those of irregular grains of quartz. The elongated prisms of andalusite are already to be recognized by their relief, they are nearly colourless in the thin sections and show no perceptible pleochroism. Rather numerous are the fluid- inclusions which they contain. As an accessory constituent tourmaline is present in the form of little strongly pleochroitical prisms (O = yellow to greenish-brown, E almost colourless). Ore is irregularly scattered in the form of black grains, and occurs moreover as a fine dust 1) Bijdrage tot de kennis van het eilland Taliaboe, p. 949, 951, 963, 967, 971, 972, 1174, 1178, 1180, 1184, 1185, 1190, 1191, 1193—1195. 2) G. Bornm. Geologische Mittheilungen aus dem Ind. Australischen Archipel. Neues Jahrbuch fiir Min. Beil. Bd, 27. 1906 p. 93. 229 between the muscovite-laminae. As a product of alteration finally brown-iron-ore (limonite) is found. Andalusite-mica-schist. This hard, distinctly schistose, reddish-grey rock, in which the naked eye discerns only silvery muscovite-laminae, was found as a boulder only in the Wai Miha. In the thin sections the rock, of which quartz forms the principal constituent, shows a erystalloblastic structure. Numerous are likewise colourless laminae of muscovite, and besides those of a greenish mica. Andalusite is found in the form of colourless prisms stringed together and in grains, whilst prisms of tourmaline scarcely ever occur. Rutile forms dark- brownish red, very strongly refractory grains and knee-shaped twins. Mica-quartzite-schist. A boulder from the Wai Kabuta, a hard, grey and very fine-grained, distinctly stratified rock. Under the microscope we perceive that quartz, which is usually accompanied by muscovite, is the chief constituent, whilst in strata of a darker colour, but restricted to these, biotite is likewise freely spread. Moreover andalusite occurs in the form of aggregates of prisms, with numerous Ore-grains and further occasionally garnet, rutile, titanite and tourmaline. Mica-quartzite occurs among the boulders of the Betino, a left tributary river of the Wai Miha. In this fine-grained, reddish-grey rock numerous muscovite-laminae can be discerned by the naked eye. As appears from fig. I the quartz individuals do not exhibit, “Pflasterstructur’ under the microscope, but they engage into one another like teeth. Further it must be remarked that finely distributed 16 Proceedings Royal Acad. Amsterdam. Vol. XVII. 230 ironhydroxide has penetrated between the aggregates of muscovite. Though the rock does not contain andalusite, it is yet likely, that it belongs to the contactmetamorphie formations. Spotted clay slates such as Verbeek discovered ') in the isle of Labobo (Banggai Isles) were not found among the rocks of Taliabu. A group of rocks that have likewise been transformed by contact with granite, but belong to the Jurassic system, are of a quite different nature. Van Nounvys indicated already on his map a hornfelsmass in the region of the source of the Wai Najo, whilst for the rest he detected normal Jurassic sediments partly covered with alluvial sediments from the source of the river to its upper course. As appears from a subsequent investigation these hornfelshike masses belong to the calesilicate-rocks.*) Van Novnuys collected specimens of these in the Wai Najo and its right tributary, the Baja, and likewise in the Wai Tabana and the Langsa. They are all dense, very hard splintery and usually of a greenish-grey colour which, in some spots, changes into whitish and occasionally into dark crey. Some of those rocks as those of the Langsa consist of parallel strata sharply separated from one another, perceptible to the naked eye, and of a whitish- and blackish-grey colour. The epidote is a mineral, which, according to the microscopic examination, is never wanting, it is almost always represented by the optically-positive klinozoisite, which is usually colourless but oceasionally provided with a light-yellow tint. The always irregularly shaped grains can easily be recognized by their strongly refractory power and their other optical properties. Some parts of the /me- silicatehornfels originating from the Wai Najo consist chiefly of aggregates of this mineral, among which is found a_ colourless eroundmass that cannot be nearer defined and often contains infini- tesimal parts of dust. In other parts this groundmass forms the chief constituent of the rock, in which klinozoisite occurs then only in the form of isolated grains. Jesides the many and very little grains of klinozoisite in the lime-silicate hornfels found in the river Lanegsa, prisms of tourmaline and needles of rutile(?) were occasionally met with. According to the microscopic examination the difference between the light and the dark strata is only caused by the fact that the latter are rich in infinitesimal parts of dust. !) Molukken-Verslag, p. 219. 2) Bijdrage tot de kennis van het eiland ‘Taliaboe, p. 1190, 1193, 1194, map N°, XX. 9314 The composition of a cale-silicate-hornfels from the Wai Najo is, according to the analysis of Prof. Dr. M. Dirrricn of Heidelberg, as follows: SOO Aa ee remem BAe ow Soe 58) DEG Os ee co ea le tu A tte BOCAS ATO ar Oe ee Se ee ee C0) Pee AP es ae ee Ge EOL C0 ere 1 A Ce iC Oma etn ee ee I Foe 6,02 Mil Ore ear aey fo ees oh 5 POLS COD eee a ee OO) VIG ORE eee ae ne a ES By Oe pare ice eS ee, gee Tu Ses? OPT NG OMMe Penna cr wets ew ey, oh OR PAOD. Apts sh tei ie ee a 2 a hae Pe lee Me OR) Yo) COE Fee ee a ae) eee AOIGS PaO = (ind eredlOe\t et enw ee eames = (eI 7, 1GPO (@ver TIO? to 1A). 4 5s iew 100,40 The specific weight is 3.213. From the analysis it appears that the result of the chemical composition in consequence of the contact- metamorphosis of the Jurassic marls is the disappearance of CO’, which, as in other similar rocks, is found only in a very slight quantity. The water was likewise for the greater part evacuated. A modification of the composition with regard to the other con- stituents cannot be observed. The results of the analyses of the cale- silicate rocks vary greatly, which is not astonishing on account of the great variety of the sediments that gave occasion to their formation. The fact that the youngest strata of the Jurassic system in Taliabu were interspersed with granite and metamorphosed, is of great im- portance; its eruption can consequently not have taken place earlier than during the Cretaceous system. The occurrence of granite of mesozoic age was hitherto only stated or made probable in the Malay peninsula by J. b, ScriveNor*), in Sumatra by Auc. Tosier’*) and R. D. M. Verser’), 1) The Rocks of Pulau Ubin and Pulau Nanas (Singapore). Quart. Journ. Geolog. Soe. 66. London 1910. p. 429. — The Geologic History of the Malay Peninsula, Quart. Journ. Geolog. Soc. 69, London 1913, p. 351. 2) Voorloopige mededeeling over de geologie van de residentie Djambi. Jaarboek van het Minwezen in Ned. Indié 39. 1910. Batavia 1912, p. 18S—19. 3) Koloniaal-Aardrijkskundige Tentoonstelling. Amsterdam 1913. Catalogus, p. 76. 16% 232 their statements were a short time ago confirmed by W. Vortz’). On the contrary J. Antpure writes: “Was das Verhalten der Gesteine “der Tinomboformation| zum Granit betrifft, so ist es immerhin von “Bedeutung, dass woh! nahezu alle echten Granite des Indischen “Archipels, vor allem die Granite von Malakka, Sumatra, “und Bangka, ebenso die grosse Granitplatte von Siidwestborneo, “paldozoischen und zwar in den meisten Fillen nachweislich*) kar- “bonischen Alters sind.” *) Mr. AnLBuRG is prudent enough not to mention the names of his informants. Graniie-porphyry. Hitherto this rock has only been found as erratic rock, namely by R. D. M. Versexk on the north coast, near Cape Damar *), by G. Borum in the Wai Kadai (described by H. BicKtne °) and by J. W. van Novusuys in the Wai Ha, a tributary of the Wai Miha. The granite-porphyry of the latter finding-place contains a yellowish brown, fine crystalline groundmass, in which numerous grains and dihexaedrons of quartz are inclosed. The light-yellowish crystals of ortheclase — sometimes twins according to the law of Karlsbad — are dull and have caused the formation of scaly mus- covite, as appears from the microscopic examination. They are moreover filled up with finely distributed brown iron ore. The much less numerous twinned individuals of plagioclase have caused similar alteration as the orthoclase. The crystals of quartz are characterized by numerous fluid-inclusions. Sometimes the intrusion of the groundmass is perceived, but glassy inclosures are utterly wanting. Dark constituents were only exceptionally found, and if so, in an entirely decomposed condition. The previous occurrence of biotite however is unmistakable, as the shapes of the laminae are found back in the limonite into which they have changed. The feldspars which form a part of the groundmass as well as the porphyrie crystals have caused a transformation into muscovite. Quartz-porphyry was collected by G. Borum in the Wai Husu and examined by H. bBickine. In Van -Nounvys’s collection are two specimens from the boulders of the Wai Najo. One is characterized 1) Oberer Jura in West-Sumatra. Centralbl. f. Min. 1913, p. 757. — Stid-China und Nord-Sumatra. Mitteilungen des Ferd. y. Richthofen-Tages 1913. Berlin 1914, p. 37. 2) The italics are mine. 5) Versuch einer geologischen Darstellung der Insel Celebes. (Geolog. und palaeontologische Abh.dlg. von J. F. Pompeckr und Fr. Von Huens, N. F. 12. ane 1913, p. 28). ) Molukken-Verslag, p. 223. 5 G. Bornm. Neues aus dem Indo-Australischen Aretipel p. 391. 233 by a light brown groundmass, bearing great resemblance to the colour of chocolate, whilst that of the other specimen is yellowish brown. Microscopically the groundmass is like that of the porphyry from the Wai Husu microgranitic. The porphyrie erystals of quartz are bluish and attain a diameter of 2—4 mm. The flesh-coloured orthoclase crystals attain a length of about 1 em. Microscopically they are covered with a fine brown pigment and partly altered into an aggregate of little muscovite-scales. The groundmass is micro- granitic and consists of a fine aggregate of quartz and orthoclase. Syenite-porphyry. Only one specimen of this rock originating from the Wai Najo is present. With the naked eye only a few dark constituents can be detected in the grey to brownish dense ground-mass showing a somewhat violet tint, with the help of the magnifying glass likewise little rectangular sections of whitish grey feldspar can be discovered. From the microscopic examination it appears that they consist for the greater part of orthoclase, partly however also of plagioclase (oligoclase). The dark constituents are in the first place represented by green hornblende. The pleochroism is « = yellowish sreen, \=dark green, ¢—bluish green; ¢ >) Sa; ¢:¢ = 12°. Besides this biotite occurred frequently, which was however completely transformed into chlorite, whilst grains of ore and epidote were formed. Apatite is found in the shape of little thick prisms. The eroundmass is entirely crystalline and is composed of aggregates of particles of feldspar, among which a few little, angular grains of quartz occur. From the scarcity of porphyrie rocks in Taliabu may be deduced that originally they occurred only in the form of dikes. Diabase. ‘This kind of rock is likewise only represented by one specimen from the boulders of the Wai Kabuta. It is dull, greenish- grey and contains a few macroscopically observable dull-white erystals of feldspar. In thin sections the characteristic ophitic structure is to be observed, narrow and broader lath-shaped erystals of plagio- clase, between which the xenomorphic augites appear, which have undergone however partly an alteration into epidote. Grains of black ore are freely dispersed. On the fissures of the rock greenish-yellow epidotes have deposited themselves, which are accompanied by quartz. The oldest sediments found in Taliabu are represented — in so far as it is known — by phyllites, which have submitted to a very strong folding, as was already remarked by van Nounvys at the place mentioned. An extensive region is watered by the Wai Miha, i.e. from its source till it leaves the chasm between the Bapen Kudi and Bono Kedot6, whereupon it reappears again at Nali. In some spots 234 the rock contains strata and lenses of quartz and occasionally much pyrite‘). A second region that has not been thoroughly explored is found, according to the map, at the upper course of Wai Kabuta. Besides the finding-places mentioned above, van Nounuys mentions the river Langsa, but he remarks emphatically that the phyllites occur there only in boulders, but nowhere *) in the form of rocks. One of the specimens is composed of alternating thin, dark-coloured, almost black strata, and lighter brownish-grey strata more rich in quartz. From the microscopic examination it appears that biotite forms the chief constituent, occasionally accompanied by many grains of ore and fine black particles of dust and only few prisms of tour- maline and grains of titanite. The lighter strata consist chiefly of an ageregate of quartz grains among which are numerous little biotite- laminae. The rock is moreover penetrated in several directions by small veins of quartz, in which yellowish-green, wormshaped aggre- gates of little pleochroitical laminae of chlorite (helminth). Another phyllite is of a blackish-grey colour, dense and rather hard. In consequence of the decomposition of the rock such parts as are richer in quartz appear at the surface as knots. Microscopic- ally the little biotite-lamellae are irregularly spread over the quartz-mass, and sometimes closely compressed in accumulations. Sometimes a light 1) Bijdrage tot de kennis van het eiland Taliabu, pp. 958, 961, 1174—1176, 1187—1188. *) Page 1180. i) 35 sericitical mica occurs, and further prisms of tourmaline and ilmenite. The phyllites of the Wai Miha are usually softer than those of the Langsa, and the microscopic examination proves them to be different. Because thin dark, blackish-grey strata alternate with light ones that are rich in quartz, the folding can very distinetly be observed (fig. 2). The former are composed of closely compressed aggregates of light-green sericite, as a consequence of the folding the laminae were likewise bent. Little flakes of brown iron-ore (timonite) are abundantly spread. The lighter strata chiefly consist of aggregates of quartz, containing very few fluid inclusions. Further light greenish mica-lamellae are discerned, floating as it were in the quartzmass that is as clear as water. In other phyllites, besides grains of ore, many particles of carbon are spread and further prisms of tourmaline and needles of rutile. At the foot of Sangeang, situated on the upper-course of the Wai Miha, oceurs a black phyllite containing numerous hexaedrons of pyrite having a diameter of 2 mm., it has great resemblance with the rock collected by R. D. M. Verserk on the north coast in the neighbourhood of Cape Damar’). Under the microscope the eye distinguishes light strata containing much quartz, alternating with quite dark ones, which are filled with carbonaceous matter in sucha way that even the thin sections remain in some places opaque. It appears that the grains of quartz contain few and small fluid-inelu- sions. The rock moreover contains light-greenish laminae of sericite, needles. of rutile and If the quartz predominates a phyllitequartzite is formed. A similar rock is likewise found as a rock near the Wai Miha along the fissures — particles of limonite. and consists chiefly of whitish-grey quartz of a greasy appearance, interwoven with strata of phyllite. At last there is still a bowlder- phyllite in itself normal and containing small boulders of white quartzite and of siliceous limestone. The rock forms a counterpart of the boulder-clay slate described by E. KaLkwosky’). Near the upper course of the Wai Miha was found, besides the rocks described above, a waterworn specimen of clay slate which is strongly folded and apparently belongs to the same system of strata as phyllite. Microscopically it behaves as a common rooting- slate, contains as the latter numerous needles of rutile, a few prisms of tourmaline, and black widely distributed carbonaceous matter. 1) Molukken-Verslag, p. 223. 2) Uber Gerdllthonschiefer glacialen Ursprungs im Kulm des Frankenwaldes Zeitschr. d. D. geolog. Ges. 45. 1893, p. 69—86. 256 Van Novnvys moreover collected in the bed of the Wai Miha a phiyllite-breccia consisting of numerous angular, sometimes a little rounded fragments of phyllite having a diameter of at the utmost 3 cm. They are usually strongly altered, and have consequently given occasion to the formation of chloritic minerals. As appears from the microscopic examination the white quartz-cement is composed of some grains of quartz as clear as water, the angles of which engage into one another like teeth. In the neighbourhood of Cape Pasturi boulders were found of a hard, grey, distinctly strated quartzite, containing moreover a great number of small hexaedrons of pyrite. Under the microscope the eye discovers, beside the grains of quartz which are as clear as water, green lamellae of chlorite, little titanite and a few black erains of ore. For the present moment it is still impossible to determine the age of the strata of phyllite. It is certain that the folding they have been submitted to, has taken place before the deposit of the Jurassic sediments which show nothing of this nature. Petrographically some fragments are completely identical to some Cambrian rocks in the Ardennes, especially those belonging to the etage devillo-revinien. Much nearer to hand is a comparison with similar rocks of the continent of Australia. Whilst there the Cambrian sediments are chiefly represented by limestones, those of the Praecambrium contain not only similar rocks as those of Taliabu, but it appears that they are likewise strongly folded all over the continent. In the strata of the Jurassic system found in Taliabu, a few rocks are found which, also from a petrographical point of view, draw special attention. Van Novunvys reported already that S. E. from the mouth of the Wai Najo cliffs are found consisting of “iron-hard “dark rock having on the fracture entirely the appearance of con- “olutinated gun-powder. This reck contains belemnites, which are “however as a rule badly conserved, and are often cemented with “the inclosing rock. Moreover the rock behaves entirely like granite, “as it is split into steep perpendicular prisms divided into blocks “by cross-fissures. This rock likewise changes into another of a “lighter colour, in which on the weathering-planes reddish quartz- “orains are found.” *) The rock that is meant here, is a chloritic iron-odlite (chamosite) dull, of a deep blackish-green colour, and containing numerous small grains, which have indeed great resemblance with gun-powder. 1) Bydrage tot de kennis van het eiland Tahaboe, p. 1195. 237 As the colour makes us already suspect, in the thin sections under the microscope it is to be observed, that the rock is chiefly composed of fine dirty-green chloritie particles, which have been altered in the same way as those of the Chamoson-valley’). They contain a fine black dustlike matter, furtber pretty large grains of ore and moreover a few angular splinters of quartz. Some cavities are filled with erystals of calcite. As to the odlite-formations they distinguish themselves only from the other mass of rock by their structure. In the thin sections they are always of an elliptical or circular shape (diameter 0.08—0.6mm.) and consist of very thin green successive coats. The nucleus usually consists of a stranger body, as a rule of quartz, the grain of which occasionally becomes comparatively large (fig. 3). Though its shape may be ever so irregular the coats of the chamosite are always arranged in such a way that the unevennesses disappear, and the result is in the end a regular odlitic body. There are however likewise fragments of quartz in which every trace of a chamosite- edge is wanting. Exceptionally the fragment of the skeleton of a sponge serves as nucleus of an odlite. In consequence of an altera- tion the odlites change into a yellow- to red-brown mass. Formations of chamosite were also met with in other Jurassic sediments of the Najo-region. As van Nounvys has already remarked the chamosite-rock changes into another rock of a lighter colour ‘in which on the weathering-planes reddish quartz-grains are found”. The rock meant here, is a rather course sandstone, the quartz-grains of which have a diameter of 2 mm. The cement is of a greyish- green colour and effervesces strongly by treatment with hydrochloric acid. In thin sections one consequently perceives much calcite, partly in the shape of grains, in which the rhomboedrical cleavage is very obvious, for the greater part however in that of a fine scalish mass forming the real cement. The green chamosite is spread as in the above mentioned rocks, but odlites are only met with as a great 1) G.Scummr. Ueber die Mineralien der Kisenoolithe an der Windgille im Canton Uri. Zeitschr. f. Krystallographie. XI. 1886, p.598. — Geologisch-petrographische Mittheilungen. Neues Jahrb, f. Miner, Beil. Bd. 4. 1886, p. 395. 238 exception. Parts of the skeletons of sponges have also been changed into chamosite in these rocks. Another sandstone of the same finding-place is more compact and contains much less calcite. Microscopically it appears to consist of angular and rounded quartz-grains, the intervening spaces of which are filled with fragments of sponges, the skeleton parts of which have been altered into chamosite. Odlitic formations are scarce. In connection with the rocks described above attention must be paid to a Limestone that was found in the Wai Najo in bank- shaped flakes. The greenish grey fine-grained rock leaves at the solution in hydrochloric acid a green sandy residue which appears {o consist of quartz and chamosite, the latter at the same time as petrifaction-material of numerous skeletons of sponges. In the thin sections of the rock the grains of calcite show rhomboedrical cleavage and form partly also polysynthetic twins. They likewise enclose particles of chamosite. Odlitie formations are not rare, but in this case only the outer zone consists of chamosite, whilst the inner part is still caleite, in which the rhomboedric cleavage-planes of the neighbouring grains of calcite have found their immediate con- tinuation, so that they form with these one individual. The skeletons of the sponges have been metamorphosed into pure green chamosite, whilst the intervening spaces are filled with limpid calcite. Besides ihe constituents mentioned numerous quartz-grains are present. From the above it appears that the limestone contains the same constituents as the sandstones that contain chamosite, and that there exists only a quantitative difference. As regards the formation of odlites, there can be no doubt that they have come into existence in the still soft mass of rock during or after the sedimentation. In my opinion they have originally con- sisted of carbonate of lime. That chamosite is no original mineral is already proved by the metamorphosed parts of the skeletons of sponges. It remains still unexplained which chemical processes have operated to bring this metamorphosis about. E. R. Zarinski has given an excellent summary of the different theories regarding the formation of thuringite and chamosite'), but it appears that none can be regarded as valid. Finally a few annotations about crystallized minerals of Taliabu may follow: Pyrite occurs — as has already been mentioned — in the shape ‘') Untersuchungen tiber Thuringit und Chamosit aus Thiiringen und Umgebung. Neues Jahrb. f. Miner. Beil. Bd. 19. 1904, p. 79—82. 239 of cubic crystals in phyllites and quartzites of the Wai Miha region, whence also pseudomorploses of limonite originate. Quartz was found in limpid and dull-white crystals, attaining a length of 9 cm., found near Pela, situated between the Wai Miha and the Wai Ha. The shapes are the usual combinations of xf, Rand — R. Calcite. Elegant skalenhedrons 3 were found in a concretion, originating from the river Kempa, a tributary of the river Wai Miba, and likewise in a cavity of a geode with Macrocephalites. Small rhombohedrons are present in the cavity of the chamosite-rock in the neighbourhood of the mouth of the Wai Najo. Rhodochrosite occurs in the shape of small rhombohedrons on the walls of the air-chambers of a Macrocephalites from the Betino. Siderite was detected in a boulder of quartzite, originating from the upper-course of the Wai Miha, in the shape of yellowish rhom- tbohedrons. Brown rhombohedrons together with calcite were found in the chambers of an Ammonite from the Wai Galo. Barite. All the chambers of Macracephalites keewwenis G. Bown are sometimes filled with limpid barite in such a way that the whole mass forms one individual. Chemistry. — ‘Studies in the Field of Silicate-Chemistry.” 1. On the Lithiumaluminiumsilicates whose composition corresponds to that of the Minerals Eucryptite and Spodumene. By Prof. F. M. Jancer and Dr. Anr. Stwek. (Communicated by Prof. P. van RompBurGH). (Communicated in the meejing of May 30, 1914). § 1. In connection with the study of the ternary system, whose components are: Lithiwmovide, alumina and silica, it was necessary for us, to obtain the compounds, whose composition corresponds with that of the minerals ewcryptite and spodumene, in a perfectly pure state, and to investigate their characteristic properties. The third ternary compound, corresponding in its Composition with the mineral petalite, will be taken in account only afterwards, as for some reasons it is better to deal with it, when the experimental study of the ternary mixtures themselves shall have proceeded some-what further. The eucryptite: LiAlSiO, belongs to the series of silicates, whose other members are: nepheline, kaliophilite, ete. In nature the said compound occurs in the form of microscopical, hexagonal crystals, e. g. in the albite of Brancnmvittn (Conn.) ; albite and eucryptite both take their origin here from spodumene, decomposed by solving agents. 240 The spodumene LiAlSi,O, is a monoclinic lithiumpyroxene. The mineral is found in several places, in the form of colourless or feebly tinged, glassy crystals of prismatic habitus, or in the form of opaque, eryptocrystalline aggregations. The transparent or coloured varieties, which are strongly dichroitic, are used as a beloved precious stone ; they are: called: triphane, kunzite, hiddenite, ete. Their properties are mentioned further on. § 2. As was already pointed out, in a previous paper *) on lithiumsilicates, the synthesis of the pure compounds offered severe difficulties, caused by the volatilibility of the lithiumoxide at higher temperatures. The composition of the mixture is thus altered during the synthesis, and the quantities of all three components must there- fore afterwards be corrected, after being accurately determined by long and troublesome analysis. A relatively small loss of the lithiumoxide, is of considerable influence on the meltingpoint and other properties of the investigated compound, because of the very small molecular weight of the oxide. The analysis offered many difficulties: for notwithstanding all care and all arrangements’), it often happens, that some A/,O, is found in the silica, and some SO, in alumina, so that afterwards a controlling determination of these admixtures must be made, which takes a lot of time. The small amount of Li,O is furthermore hardly determinable under the colossal excess of Na,O in the liquid; therefore, being determined as the difference of 100°/, with the sum of the percentages for S’O, and A/,O,, all mistakes and inaccuracies of those determinations are summed up in the number for L7,0, so that the correction of the preparation after- wards, often depending on very slight differences in the amount of Li,OQ, is a hazardous and not very amusing task. So it takes much time to obtain products, which will not differ appreciably im their constants and properties from those to be expected for the true pure compounds, the criterium being given by the perfect identity of the products, prepared in several ways. § 3. Synthesis and Properties of the Pseudo-Kucryptite. The materials for this and other syntheses were the same, whose purity was before tested and described; the alumina used was also provided by Bakrr and ApaAmson. It was necessary to heat it for a long time in a platinum dish on the blaze, and often to stir the powder with a platinum-wire, to allow the watervapour and the nitrous gases, which the preparation evolved, to escape completely. The 1) FE. M. Jaeger and H. §. Knoosrer, these Proceedings p. 900, Febr. (1914). 241 heating was checked when the weight of the dish remained constant after repeated heatings. Analysis then showed, that an almost pure Al,O, (100°/,) was present; even no appreciable trace of iron could be demonstrated with the usual reagents. To point out the change of composition, taking place on heating mixtures of known composition during the melting of the mass, the numbers here following can serve very well: a mixture of 6,23 gram Li,CO,, 8,61 gram Al,O, and 10,16 gram SiO,, was melted in a closed platinum erucible in the Frrrcumr-furnace at 1500° C. After crystallisation, the mass was finely ground and sieved, melted again, and this process repeated three times. Instead of the expected composition /, the composition // was found by analysis to be: / IT SiO, A7,7°/, 48,6°/, Al, 0, 40,4°/, 40,9°/, Oe 11,9°/, 10,5°/, As there was thus 1,5°/, Lz,O0 too little, 0,055 gram Al,O, and 0,718 gram dry Li,CO, were added to 18,92 gram of the resulting product, and this mixture was then heated four times in platinum crucibles, by means of small resistance-furnaces, at 900° or 1000° C., the mass being finely ground and sieved after every melting. Then the preparation was again heated once at 1450°C. in a resistance-furnace. Analysis gave: Odserved : Calculated : SiO, 47,9°/, 47,7 °/, Al,0, 40,1 °/, 40,4°/, Li,O 12,0°/, 11,9°/, The deviation from the exact composition is so slighf, that this preparation could safely be used for the study of the properties of the compound, § 4. The meltingpoint of this preparation was determined several times by means of a calibrated thermoelement (N°. ///). The mean value of all readings was 14200 M.V. + 2 M.V.; as the correction of this element with respect to the standardelement, which was standardized by means of Sosman’s element G, was -— 12 M.V.; the meltingpoint of the substance, in terms of the Washington nitro- vengasthermometerscale, can be fixed at 1888° C. The heat-effect on melting is only small; as a result of that, on cooling down the molten mass, one finds a retardation of its erystal- lisation up to about 12840 M. V.; then crystallisation takes place while the temperature increases only to 1306° C. The point of 242 solidification therefore is found 80° or 90° below the true tempe- rature of equilibrium: solid = liquid, although the velocity of crys- tallisation can by no means be called very small. From this faet also the discrepancies in the data of different authors are to be explained : 1330° C. (Dirrier and Baio), 1807° C. (Ginsprre), etc. In this case also, the usual method of cooling appears to give no reliable results. A remarkable fact is the relatively appreciable cncrease of the volume of the molten mass on crystallisation; it is immediately observable by the deformation of the platinum-crucible. (fig. 1). That really this phenomenon is caused in this case by a volume-change like that of water into ice at the freezing- point, and that it need not be explai- = i. ned in the manner mentioned in the Fig. case of the spodumene, can be demon- Increase of the volume of molten ‘Strated by the determination’ of the Eueryptite on crystallisation. specitic gravities of the erystallized mass, and of that of the beautiful, colourless ‘glass’, obtained by suddenly chilling the liquid. The expansion seems to be about 3°/, of the original volume. § 5. The crystallized substance, obtained by slowly cooling the liquid, is opaque and greyish white. Microscopical investigation showed it to be a eryptocrystalline aggregation of irregularly shaped, erain-like crystals, which are so small, that even with an 800-times enlargement, they can hardly be seen; they possess a very weak birefringence. Greater pieces seem to be built up between crossed nicols by innumerable lighting points ; such aggregations always show an undulatory extinction. In no case erystals with determinable borders were found. As a ‘mean’ refractive-index the value: Ny = 1,531 + 0,002 was obtained. The specific gravity at 13°,6 C. was pyenometrically found to be: do 2,365, and at 25°, C: dy = 2,362 ; we used orthochlorotoluene (1,0825 at 25°,1 ©.) as immersion-liquid. As follows clearly from those values for the refraction of light and for the specific gravity, the natural eweryptite must be another modification of the compound Lz AlSiO, ; therefore we will distinguish the artificial silicate by the name: pseudo-eucryptite. *). 1) Ginspera (Zeits. f. anorg, Chem. 73. 291 (1911)) describes his preparation in the followmg manner: completely isotropous, uniaxial negative in convergent pola- vised light, with a birefringence smaller than that of nepheline. Weypera asserts to have obtained an “eueryptite” of rhombic symmetry, by the reaction of Li,SO, on kaoline in solution. Cf. also the experiments of Tuuaeurt, Zeits. f. anorg. Chemie 2. 116. (1892). 245 § 6. The glass, obtained by suddenly chilling the molten mass in mercury or cold water, is colourless, perfectly clear and exceed- ingly hard. It can be removed from the platinum-crucibles in an easier way than the crystallized mass, which fact is connected with the volume-change in crystallizing. The refractive index of the glass appeared to be: mp) = 1,541. We have prepared several glasses of varying chemical composition, all in the vicinity of the composition of the pure compound, with the purpose to measure accurately the refractive indices and the dispersion, in order to get information about the influence of the chemical composition on the optical behaviour of these glasses. They were ground in 18,99 /5 ha. C). i VesCompos:, 48.4°/- S71 Obs 39:39), Al. 0, > 1 i RO! Gt. Wavelength in Angle of Refractive Ne eet Oe Totalrejlection : Index: Li 6708 62°26’ 1,5484 0,0047 Na 5893 G2ebr ie 1.5437 | 0,0044 Tl 5850 61°47’ 1,5395 LUE Wavelength in Angle of Refractive aN INGE dee Totalrejlection : Index : li 6708 63°36" 1.5647 0,0048 Na 5893 Gave 1.5599 0,0039 fl 5390 62°58’ 1,5560 244 LV Wavelength in Angle of Refractive A: ICE Oa Totalrejlection : Index: li 6708 61°50’ 1,5400 0,0046 Na 5893 61°31’ 1,5354 0,0053 fh) 5350 Gie97 1,53801 It is difficult to deduce a simple relation of chemical composition and optical properties from these data. Generally speaking, an increase of the amount of 7,0 seems to cause an_ increase of the refractive power (except in JV), while a larger amount . of SO, appears just to diminish the refractive index, the exceptional case /V could be explained by the superposition of these two causes. This dependence of the quantities of the oxides present, appears to bear some connection with the relatively higher refractive power of the lithiumoxide, and the smaller one of the silica '). The pseudoeucryptite-glass is, with respect to the opaque, erystal- lized compound, a typical metastable phase: already on heating the glass during a very short time in a Bunsen-gasburner, the pieces of glass become primarily yellowish, then they become opaque, and finally they appear under the microscope wholly changed into the mentioned cryptocrystalline aggregation of birefringent grains. If heated only for ten minutes at 900°C., they are completely - changed, and the same occurs, on heating the finely powdered glass during some time with molten LiCl or LiF in a platinum crucible. The specific gravity of the pare pseudo-eucryptite-glass was deter- mined by means of the method of swimming, in a mixture of bromoform and benzene, at 13° C.; it was found to be : dy = 2,429. Thus both the refractive index and the density of the glass are somewhat higher than for the crystallized compound. § 7. Finally we have compared the artificial product with a natural eueryptite of BrancunviLLe (Conn.). The mineral, of which a thin section was prepared, looked as an aggregation of erypto- crystalline, homogeneously extinguishing fields: however, although they had superficially some analogy with the artificial product, they must be considered as composed of much larger crystals, showing apparently the kind of structure, somewhat similar to the so-called “schrift”-granite. Locally it is intermixed with a much more strongly 1) fF, M. Janeen and H. S. van Kuoosrer, these Proceedings, loco cit. (1914). 245 birefringent mineral; although the eucryptite is here generated from spodume. with deposition of albite, the properties of the inclusions did not agree with those of the two lastnamed minerals. The specific gravity was pycnometrically determined to be dyo = 2,667 at 25°C.; the available data show the composition not to be the proper one, the S’O,-amount being 0,6°/, too high and that of the LiV,z about 1°/, less than the theoretical value. The fig. 2 and 3 represent two microscopical preparations of the thin section between erossed nicols; in the fig. 3 the preparation is turned over 30° with respect to that in fig. 2; — this fact pointing to a trigonal twinfor- mation. Also the very peculiar structure of the crystals is shown in fig. 3. The refractive index was microscopically determined on : 2p = 1,545 + 0,002. A definite meltingpoint could not be fixed by the usual, 1 dynamical method; at about 1120° C. the mineral gradually changes into a viscous mass, which, on cooling, becomes a glass. The refrac- tive index of this glass appeared to be: np=1,506 + 0,001, it is thus evidently lower than that for the glass of psewdo-eucryptite. On being heated it is devitrified only slightly; there seems to be no doubt, that the natural mineral and its glass are other than the corresponding phases of the artificial product. As also never any indication of an oceurring inversion could be found, it is highly probable that eucryptite and pseudo-eucryptite are in relation of monotropic modifications to each other. § 8. Synthesis and properties of (?-Spodumene. The compound, ~ whose composition is: LiAlS7,0, was prepared 17 Proceedings Royal Acad. Amsterdam. Vol. X VIL. 246 by us in four different ways, just to get information on the final identity of such preparations: a. By melting together calculated quantities of Li,CO,, Al,O, and SiOQ,, repeating this manipulation a few times, after thoroughly erinding and sieving the crystallized masses. Analysis and correction were made as usual. b. By starting from pure Lz,S70,, Al,O, and SiO,. ce. From LiAlSiO, and Si). d. From LiA/O,, the lithiumaluminate, and S7O,. The four preparations, thus obtained, were used only for the definitive measurements after it had been proved by repeated ana- 2? lysis and correction, that their composition did correspond, within the limits of error, with that of the formula. AIl these experiments were made in electrically heated furnaces with oxidizing atmosphere ; the preparation of these substances took a long time, because of the volatibility of the 7,0, and the fact, that only small devia- tions in the content of 7,0 showed themselves of appreciable influence on the meltingpoint and properties of the compound. § 9. The purest preparation we got, was obtained from synthe- tical eueryptite by admixture of SvO,. Analysis gave the following data: I. 1 Caleulated : SiO, 64,39 °/, 64,438 °/, 64,6 °/, AlsOe 227,000), 27,66 °/, 27,4 °/, I1,O 8,05 °/, ieoies 80°75 The mass was kept during a longer time at a high temperature, to allow it to erystallize totally. Then the meltingpoint was deter- mined in the usual way, by means of thermoelement ///; we found : 14353 M. V. 14341 MM. V. Mean: 14347 J/. V. (without correction), if the rate of heating was about 65 M.V. pro minute. As the correction for the thermoelement was — 12 M. V. at this temperature, the meltingtemperature is 1400°C., in terms of the nitrogenthermometer. As a check the mellingpoint was now again determined by the statical method: very small quantities, wrapped in platinum folium were heated during a considerable time (from half an hour to one full hour) at a certain and accurately constant temperature, and then, after suddenly chilling *) in cold mereury, investigated by means of 1) F. M. Jareer, Kine Anleitung zur Ausfiihrung exakter physiko-chemischer Messungen bei héheren Temperaturen. Groningen, 1913, Seite 73, 74. 947 the’microscope. We found that after heating at 14340 M. V. (element IIT) the whole preparation was again crystalline, although it had the outward appearance of a glassy, half-opaque mass; but on heating at 14360 M. V., all had been changed into a real “glass”. The meltingtemperature therefore must be fixed at 14850 M. V. As the correction for the used quenching-system (vid. the determinations of the meltingpoint of natural spodumene of J/adagascar) was shown to be practically equal to zero, we can conclude from this, that the meltingpoint thus determined is in full agreement with that found by the dynamical method, and can be put at 1401°C.(G Th.). The crystallized product appeared to be identical with the /?-modification, later to be described, the refractive index was about: » = 1,521; the specific gravity at 25° C: dy = 2,411. 2. In a similar way the preparation, obtained from lithinmaluminate and SiO, was investigated; analysis gave the following data: I Il Calculated: StO, 64,80°/, 64,07°/, 64,6°/, AGO 2S Os fae 205092 2 e Li, O Cpa edie a liptess sali 8,0°/, This preparation therefore evidently can also be considered as a very good one; it contains ca. 0,4°/, 17,0 too little, and ca. 0,5"), Al, O, too much. Fig. 4. Artificial 6-spodumene, obtained from LiA/O, and Si0,; melted and slowly cooled. CX Nicols). 248 The meltingpoint, determined after the dynamical method (element IT]), was found: 14463 M. V. 14481 M. V. Mean 14472 M. V. = 10 M. V. (without correction) ; after correction, the meltingpoint can be fixed at 1410° + 1° C. (G.Th.). After the statical method, the meltingpoint was determined at 14450 M. V., corresponding to 1410°C. The small excess of A/,O, has evidently caused an ncrease of the meltingtemperature, of about 9°C. The erystallized product again was shown to be /?-spodumene (n= 1,519); a photograph of it, taken between crossed nicols is reproduced in fig. 4. 3. An analogous result was, in both ways, obtained with a pre- paration, prepared from Li,S/0,, Al,O, and SvO,. Analysis of this product gave the following data: ] II Caleulated : SiO, 64,7°/, 64,48°/, 64,6°/, Al,O, 28,4 °/, 28599) 2a ye 1,0 G95 Ce S076 The content of S/O, is here the right one, but the Ad,O, is 1°/, too high. The meltingpoint determinations gave as a mean value: 14456 M.V. (uncorr.) after the dynamical method, and about: 14450 M. V. after the statical method. The meltingpoint is therefore : 11092 (Ch(Gelhe): 4. Most deviating from the composition: Li AlSi,O,,. was a pre- paration, obtained from the melting together of £7,C0,, SiO, and Al,O,. Analysis gave the following numbers: I II Caleulated ; SiO, 64,44°/, 64,88°/, 64,6°/, Al.O,, J2T09/. SEAT Uh eno Ane Li,0 —*847 > S795 eS Sey) Evidently it contains about 0,21 °/, Z7,0 too mueh. After the first method the meltingpoint was found at 14552 M.V. (uneorr.), and after the statical method: 14550 M.V. The true melting- point can thus be put at: 1417° C. (G.Th.). § 10. Although in most eases perfectly colourless products were obtained, which evidently were identical to and independent of the particular manner of preparing them, and which all represented the 8-modification, —- we succeeded however in several cases in obtaining beautifully erystallized preparations, which locally or also totally were 249 tinged with a nice, reddish lilac hue; they were in most cases obtained by longer heating, somewhat below the meltingtemperature. The meltingpointdetermination with such an intensively coloured product, prepared from L7A/O, and SiO, and showing by analysis the following composition : I. Me Caleulated : S72, 64-92) o)s NEARY. F< Gd6/5 Al,O, 28,10°/, 27,94°/, 27,4 °/, ROTC OSS 29) SOR and thus evidently containing about 0,68°/, too much alumina, gave the following results (statical method) : After heating at 14660 M. V.: all glass. 14640 M. V.: all glass. 14600 M. V.: all glass. 14500 M. V.: all erystallized. 14560 M. V.: all crystallized. The meltingpoint is thus situated at 14580 M.V., corresponding with 1420° ©. (G.Th.). Such lilac coloured preparations present in most cases rather larger individuals of the 2-modification, which possess a tabular shape with appreciably stronger birefringence than the common erypto- crystalline masses, although the mean refractive index is the same. While commonly this birefringence varies between 0,001 and 0,008, it amounts in these preparations to about 0,007 ; the principal refrac- tive indices are about: 1,520 and 1,527. In convergent polarized light, at the border of the field an interference-image is partially visible, giving the impression of that of an uniaxial crystal. However on moving the table of the microscope, one can easily observe the curvature and even the hyperbolic form of the dark beams; undoubtedly an optically biaxial erystal with a very small axial angle, is present here; while the position of the first bisectrix and the character of the dispersion, point to monoclinic symmetry, with a strong tendency to tetragonal forms. This last pecularity can be deduced, — besides from the apparent uniaxity — from the fact, that rectangular plates are not rare, which possess an extinction under right angles or parallel to a diagonal, and a system of cleavage-directions under 45° with the optical sections. The specific gravity, like the refractive indices, does not differ appreciably from that of the common @-form, and was determined at 25° C.: d» = 2,401 + 0,008, measured with several preparations. We obtained these same apparently uniaxial plates, also from natural spodumenes by melting and slowly crystal- lizing; there is no doubt whatever about the fact, that these tabular 250 crystals are identical with the common g-form, which represents the stable form at the meltingpoint; the plates must be a peculiar kind of erystals of this g-modification. However we have till now not succeeded in giving a final explan- ation of the remarkable reddish-lilac colour of many of these pre- parations. It is quite sure, that it does not depend in any way on the admixture of certain metallic impurities, solved from the crucible- walls; on the contrary it appears to be connected with the macro- crystalline strueture of the preparations. The nearer the chemical composition came to the theoretical one, and the slower the crystal- lisation of the mass takes place, by heating during a long time at a temperature just below the meltingpoint, the more the appearance of the violet tinge seems to be probable. The same colour appears, if spodumene-powder or the pulverized “glass” of it, are brought into liquids of about the same refractive index (e. g. inta orthochlorotoluene, with n= 1,522); in that ease the wellknown phenomenon of the “monochromes” (CHRISTIANSEN) will appear. It is not impossible, that in our case the colour is produced in An analogous way by the presence of the tabular, very thin crystals amidst spodumene-glass, which possesses about the same refractive index (1,519) as the ecrystal-tables (1,520 till 1,527), or Yeversely ; these tables would be therefore quite invisible in the surrounding medium. It could be understood in this way also, why in the uncoloured mass in some cases locally smaller or larger pink spherolithes are produced, making the impression, as the molten mass were locally inoculated with germs of the violet substance. By means of the ultra-microscope we were able to show, that the preparation was not “optically empty”, as a great number of differ- ently coloured lightspots, which do not move however, could be observed; they are manifesting a structure of some particular kind, without it being possible to ascertain of what kind the imbedded particles are. § 11. As it follows from these investigations, in connection with the meltingpoint determinations of natural a-spodumene later to be described, that the chemically pure compound LiAlSi,0, has a meltingpoint considerably lower than the natural spodumene-minerals, — we made a series of investigations to find out, what admixtures of the natural spodumenes might canse the mentioned increase of the meltingpoint. Therefore to an artificial product, whose composition was: StOp Ie oder ALO; Dida fe Li,O 8,2) /6 we added successively in concentrations of 1 mol. percentage, the following chemically pure preparations : Observed and reduced Meltingpoints: 1. Jadeite: NaAlSi,O,, synthetical. elas SMe —— 382° 2. Leucite: KALSi,O,, synthetical, anhydrous. 14506 M.V. = 1414° 3. Lithtwmowide: Li,O. 14304 M:V. = 1397° 4. Alumina: Al,O,. 14585 M.V. = 1420° 5. Silica: SiO, (quartz). | 14530 M.V. = 1416° And in concentrations of 2 mol. pere.: | 6. Pseudowollastonite: CaSiO,, sy nthetical, 14357 M.V. = 1402° 7. Siliimannite: Al,SiO,, synthetical. 14593 M.V.=1421° Keeping in mind, that the pure substance melts at 1417° C. (G. Th.), we can deduce from these experiments, that : a. An excess of L7,0 lowers the meltingpoint of the compound LiAlSi,O,, while the influence of an excess of S’O, is somewhat uncertain, but seems to produce a slight increase. b. That a lowering of the meltingpoint is also produced by an excess of synthetical jadeite, leucite and pseudowollastonite, which can be considered as the principal admixtures of the natural kunzites and spodumenes. c. That on the contrary, an dncrease of the meltingpoint is produced by an excess of alumina and of alumosilicates, like e.g. pure sillimannite. In how far these facts, which of course will be studied more in detail, when the ternary system: Li, 0—A/,O,—Si0, is investigated completely, can be used for the explanation of the phenomena, observed in the case of the natural spodumenes, will be shown in the next paper. Groningen, May 1914. Laboratory of Inorganic Chemistry of the University. Chemistry. — ‘Studies in the Field of Silicate-Chemistry. UL. On the Lithiumaluminiumsilicates, whose composition corresponds to that of the Minerals Eucryptite and Spodumene”. By Prof. Dr. F. M. Janeer and Dr. Ant. Smek. ( Continued ). (Communicated by Prof. P. van Rompureu.) (Communicated in the meeting of May 30, 1914). § 12. For the purpose of comparison of the properties of the described artificial product with the mineral itself, we have inves- tigated a number of natural spodwmene-species in an analogous way. 252 We obtained a number of very pure funzites, and some good spodumenes: 1. An almost colourless, somewhat lac tinged, strongly dichroitie kunzite from Rincon in California. 2. A completely transparent, glassy, pale rose tinged kunzite from Suhatany-valley on Madagascar. 3. ,1aC. The refractive indices of the molten and solidified substance are considerably different from those of the original mineral. While tor the unmelted substance we found respectively: 2, = 1,658 + 0,008; — ARGE9H= = O1O03 Zande rie —1nGi-2) = 01003 2) for: the solidified mass we found an extremely feeble birefringence of about 0,001, and a mean refractive index of: 2p —= 1,518. The erystalpieces showed an irregular extinction, evidently by very complicated intergrowth of several individuals. On rapidly cooling, an isotropous glass was obtained, with a refractive index of m, = 1,517 + 0,001, being about the same as for the crystallized mass. The specific gravity was at 25°,2 C.: d,o = 2,388 + 0,003. When heated during a longer time at 1300° ©., it becomes erystalline; even at lower temperatures the glass gets soon opaque and like porcelain by devitrification; but glass and crystalline product obtained from it, evidently do not differ in their properties to any appreciable amount. Il. Kunzite of the Sahatany-valley on Madagascar. Big, clear and completely transparent crystals; they are dichroitie and tinged with a pale rose hue. Locally the environing rock-material is again discernible, as a rusty coloured, finely divided substance. The erystals were carefully cleaned from it; then they were ground and sieved, after which the investigation proceeded in the usual manner. As a mean value for a greater number of determinations, we found the meltingpoint at: 14683 +5 M.V.; as the correction of the thermoelement was —8M.V. at this temperature, we can adopt the value 14675 M.V. of the E.M.F. of the thermoelement at the ineltingpoint, corresponding with: 1428° C. (G. Th.); in this case the meltingpoint is also very sharp. Evidently this kunzite differs only slightly from the preceding mineral of Rincon. With respect to its chemical composition, we have some data, given by Lacroix’), who investigated colourless, 1) In a liquid of nm» = 1,670, composed of methylene-iodide and monobromo- naphtaline, the crystalpowder showed a very beautiful reddish-violet colour, just as some of CuristIANsen’s “monochromes”. The same phenomenon was observed fo1 the glass and the @-modification of artificial spodumene. 2) A. Lacroix, Minéralogie de la France et ses Colonies, [V, 775, (1910). 254 greenish-yellow and rose kunzites (triphane) from Maharitra on Madagascar; the lilac and rose kunzites of Ampasihatra are im- bedded in a kind of kaoline-earth, generated from the spodumene by decaying-processes. The green kunzites possess the greatest values of their refractive indices, however only little differing from the other ones, while the rose tinged erystals have a smaller, the colour- less ones yet smaller values for those constants. We found by means of the immersion-method n, = 1,658 and n, = 1,673, which values do not differ appreciably from the mean values: n, = 1,6588, n, =1,6645 and n, = 1,6750.') For the ana- lysis of the red and greenish crystals, the following data are given in literature; they are reproduced here for comparison with the composition of the Californian kunzite : rose cristals: | green cristals: SiOz :63,85% 9 CaO : 0,529) MnO : trace | SiO, :62,21%9 CaO :0,50% MnO : trace AlyOy:29,87%\y NagO: 0,98) Fe,03:0,15%) | AlzO3:29,79%) NaO: 1,03%y) Fe03: 2,489/g Li0 : 3,76%9 MgO :0,13°%/9 KoO :0,13%p Li,O : 4,02", MgO : trace K,O :0,212%p Residue : 0,37%. | Residue: 0,25%p. From these data results, that the quantity of S’O, in the rose crystals is about the same as for the pale rose kunzite of Rincon; but the content of A/,O, is much greater in the mineral of Mada- gascar, and thus the 2,0 appreciably less than in the American kunzite. The sum of those three constituents does not differ very much in all these cases: 97,5°/, for the kunzite of Madagascar, 95,2°/, for that from Rincon. The specific gravity of the rose species is about 3177: a value, only slightly different from the value, determined by us: d,e = 38,3801 + 0,005, at 25°,1 C. The refractive indices of the melted, feebly birefringent produet, were found to be n, = 1,518 and n, = 1,520; the birefringence is not greater than 0,002. At 25°,1 ©. the specific gravity of the melted and solidified sub- stance was determined: d,° = 2,373, when the preparation was heated during several hours at a constant temperature, just below the meltingpoint; under the microscope the obtained product then showed the typical aspect of the aggregates of scales, which are always found with the @-spodumene; they have a weak birefringence, and an irregular, often undulatory extinction. When «-spodumene was not melted before, but only kept at a constant temperature below the meltingpoint, the substance appeared to be wholly transformed into the same @-modification, with a specific gravity of: do = 2,376 at 1) Duparnc, Wunper et Sasor, Mém. de la Soc. physique de Geneve, 36, 402, (1910). 259 25°,1 C. In both cases the mean refractive index for sodiumlight was: ny = 1,518 + 0,001. From the molten mass therefore no other phase is deposited than the mentioned 8-modification. The fig. 5, 6, and 7 may give an impression of the manner, in which the transformation of the e-, into the /?-modification gradually occurs. In fig. 5 the original kunzite of J/adagascar is photographed between crossed nicols, when heated only during 2 hours at 975°C., and showing no trace yet of the @-form; in fig. 7 the same heating, but prolonged to 15 hours, has led to complete transformation of the erystals into the #-form. The fig. 6 represents the crystals, after 8 hours heating at 975° C.; they show a partial transformation, and the gradually occurring differentiation of the originally homogeneous crystals into an aggregation of the felty needles of the @-modification. Ill. Greenish-yellow Kunzite of Minas Geraés, Brasil. This kunzite appears also in the form of large, very transparent crystals, having a pale greenish or yellowish hue. This colour is caused by a content of /eO, which in melting the mineral, is con- verted into: Fe,0,; thus the solidified mass being always tinged with a reddish-brown colour. The analysis of this mineral ') gave the following data : SiO, : 63,3— 64,3°/, CAOr 02-00 Al,O,: 27,7—27,9°/, Na,O: 0,6—1,0 °/, 1,0, : i 7,4°/, FeO ° O12 WE This kunzite therefore is also relatively close in composition to that of Rincon, approaching in its content of L7,0 closer to the theoretical value; the sum of the principal constituents is 97,7 °/,. The meltingpoint of this mineral was determined five times; the results were, with thermoelement IV: 14643 M.V. 14646 M.V. 14650 M.V. 14639 M.V. 14646 M.V. Mean value: 14645 M.V.; after correction: 14637 M.V. (G. Th.) The meltingpoint, reduced on the nitrogengasthermometer, lies thus at 1425° C., i.e. about 3° C. lower than for the kunzite of Rincon. The specific gravity of the substance before melting, was deter- mined at 25°,1 C. to be: dy= 3,262; the data, given in literature for the specific gravity of natural crystals, vary between 3,16 and % 1) CG. Hintze, Handbuch der Mineralogie. 3,174. The refractive indices of the original substance were: 2, = 1,661 and n, = 1,669, with apparently a somewhat weaker birefringence as for the already deseribed kunzites. Fig. 5. Fig. 6. Kunzite of Madagascar, heated tor two hours Beginning of the transformation of z-spodumene at 960° CG. and not yet perceptibly transformed, (Madagascar), after being heated during eight hours (X Nicols). — - at 975° CG. (X Nicols). Fig. 7. Kunzite of Madagascar, completely transformed into the 6-form, after being heated at 975° C. (< Nicols). 257 After being melted however, the reddishbrown, crystalline product had _a specific gravity at 25°,1 C.: dy = 2,463, while the refractive indices of the feebly birefringent grains were found to be about 1,522 and 1,527. There is no doubt whatever about the fact, that the solidified product is again a modification absolutely different from the original kunzite; moreover it is evidently identical with the already mentioned @-spodumene. IV. Hiddenite from Alexander County, North Carolina, U.S.A. Long, needle-shaped, pale green crystals, and emerald-green crystal- fragments, which are transparent and dichroitic. The specific gravity of this mineral at 25°,1 C. was found to be: dy=3,295 + 0,002 ; the refractive indices were: n, = 1,664 and n, = 1,674. The data for the specific density, given in literature, vary between 3,152 and 3,189. Of a hiddenite from Alevander City, with specitic weight of: dy= 3,177, the analysis gave the following results : SUON 2. 63595.9/5 Pe Oraey lelve of. Al,O, : 26,58 °/, Na,O: 1,54 °/, iO G82), CaO: no trace. The sum of the principal constituents is here 97,35 °/,; the hue of the erystals is caused by the admixture of /eQ, which is oxydized in melting to Fv,O0,, giving a brownish-black or chocolate-brown colour to the solidified mass. Another hiddenite of the same locality, but of a paler colour, had: 64,35°/, SiO,, 28,10°/, A/,O,, and 7,05°/, Li,9, — consequently together: 99,5 °/, ; moreover: 0,25°/, LeO and only about 0,38°/, Na,O. The differences of the meltingpoints of these two kinds of hiddenite, were about 1° C. or less. In a series of observations, made with thermoelement IV, the melting- point was fonnd at 14565 M.V. + 410M. V.; after correction, this corresponds to 1418? + 41°C. , x.Th.). On cooling down the moiten mass, first an undercooling is observed to about 1255°C., if the temperature-fall was about 4° pro minute; then the temperature rose to 1262°C. during the solidification of the mass, being 150° C. lower than the real equilibrium-temperature. Another time we found an _undercooling to 1208°C., then solidification at 1214°C., — this being 204°C. lower than the true meltingpoint! Although this point of solidification is lower than that for the pure kunzites, it can have no essential signification whatever, being wholly dependent on the speed of cooling and other accidental circumstances. V. Spodumene of Somerd, Finland. A white, opaque eryptoerystalline and very hard mass. It was finely ground, and investigated in a manner, quite analogous to that for- merly described. The specific gravity at 25°,1 C. was : dy = 2,997 + 0.050; the refractive indices were about : 2, = 1,658 and n, = 1,669. With the thermoelement /J’ the meltingpoint was found at 14649 M.V. +5 M.V.; being, after correction, 1425° C. on the gasthermo- meter. Because of the inhomogeneity of the material, the meltingpoint is here not so sharply localized on the heatingeurves, as in the cases of the kunzites; on cooling the molten mass, solidification oeeurs in the neighbourhood of 1298° C. The substance solidified and heated for some hours below its meltingpoint, had a specific gravity at 25°,1 C. of: do = 2,398 ; the refractive indices were about: 1,510 and 1,518 for sodiumlight, just a little smaller than commonly with the -spodumene. The substance always shows very complicated aggregations of feebly extinguishing scales with undulatory extinction. If the original substance is not melted, but only heated during a longer time below its meltingpoint, the erystals are converted into the aggregations of the B-spodumene ; the specific gravity at 25°,1 C. was now: dy— 2,412 and the refractive indices about: 1,519. VI. Spodumene from Maine, U.S.A.; perhaps from Windhain. This mineral consists of long, opaque, prismatic crystals, looking Fig. 13. Dense #Spodumene of Someré, Finland. (X Nicols). 259 like porcelain, with predominant cleavage. The carefully selected material was finely pulverized, and investigated as described before. The specific gravity at 25°41 C. was: d= 3,154 + 0,002; the refractive indices were about: 7, = 1,656 and n, = 1,672. A micro- photograph of it between crossed nicols is reproduced in the fig. 13. The meltingpoint was determined several times with the thermo- element ///; the following results were obtained : 14669 + 13 M.V., being after correction: 1427° + 1° C. on the gasthermometer. Also in this case the meltingpoint is not quite so sharp as with the kun- zites, just because of the chemical inhomogeneity of the material. The obtained product had a specifie gravity : dyo = 2,336 at 25°,4 C.; the weakly birefringent, irregularly extinguishing scales, had refractive indices of about: 1,517 and 1,520; the birefringence is not greater than: 0,008. In fig. 8 a microphotograph between crossed nicols is given of the dense a-spodumene of Jaine; in fig. 9 the same preparation, molten and solidified into the 3-form is reproduced in the same way. ’ The strong analogy witb the image of fig. 4, representing an arti- ficial 3-spodumene, made from L7AlO, and LiQ,, is obvious. Another preparation was not melted, but only kept at a constant temperature of about 1200°C. for some hours. The original «@-form appeared to be totally converted into B-spodumene ; the volume of the mass had increased then in such a degree, that the platinum- Fig. 9. Dense z-Spodumene of Maine, between crossed 6-Spodumene obtained by melting and crystallization Nicols. of the z-modification (X Nicols). 260 erucible was wrecked during the process. The substance showed the typical granular strneture of the crystal converted into p-spodumene with undulatory extinction and a mean refractive index of: 1,518. Phe specific weight at 25°,7 C. was determined to be : dy = 2,309, and. tobe 2oi7, at ood: § 18. In all these experiments it was observed by us, that the platinumerueibles, in which the silicate was melted and solidified, showed a strong deformation, which increased every time that the experiment was repeated. As fig. 10 shows very clearly, this observed deformation is of such a kind, that it always appears as a dilatation, as if the silicate, like water, solidifies under a volume-expansion. The values obtained for the specific volumes of the erystals and of the g/ass, seem however to make this explanation rather improbable. We have tried by a series of systematic experiments to find out, ahen really this increase of the volume sets in, by measuring the diameter of the crucibles, after their contents had been subjected to different manipulations. In this way, we found, that by far the largest deformation of the crucibles took place, at the transformation of «, into 3-spodumene, which is accompanied by a volume-increase of about 30°),. When the substance is then melted once more, and again solidified, the deformation already present will be increased by the thermal expansion of the mass, and because the liquid substance is |o\3.b4 1|\2 Fig. 10. Deformation of the platinum crucibles after melting and solidification of the natural Spodumene. 0. Origmal form of the platinum-crucibles. 1. Pale yellow spodumene of Minas Geraés, Brasil. 2. Kunzite of Sahatany-valley, Madagascar. 3. Dense Spodumene of Someré, Finnland. 4. Kunzite of Rincon, California. Ww 61 enormously viscous, enclosed air-bubbles are hardly squeezed out, but will rather expand in the mass itself, while the surface of the liquid can change its height only with extreme slowness. In repeating snecessively the melting and solidifying of the substance a number of times, the deformation-effect will be gradually increased to such an extent that, as fig. 10, N°.2 shows clearly, at last the crucible bursts. The gradual lowering of the liquid surface in successive experimeuts can be seen in those crucibles; in such a manner it often happens, that with a strong deformation of the platinum vessels, when they finally look like inflated balloons, the junction of the thermoelement emerges at last out of the surface of the liquid mass, so that the heat- effects on the heating-curves get gradually worse and will finally disappear totally. § 14. To control the found meltingpoints, we have made a series of experiments to determine it once more (with the kunzite of Madagascar) by means of the quenching-method, which is to be de- scribed afterwards in connection with our experiments for fixing the temperature of beginning transformation. The quenching-system was first calibrated by means of meltingpoint-determinations, made by this statical method with lithiummetasilicate (1201°) and: diopside (139L°); the corrections to be applied to the measured temperatures appeared however to be practically zero. We found in successive experiments : Kunzite, heated during half an hour atl4600 M.V.and quenched in mercury: All crystallized 7 P » Fe PAO ENS 5 Pee ee eAlleolasce ” ” 2 Hp py LEOO MWS. 4 Js JN lbs: ” ” ” Be unr AONE ~ Sa aor alleclasss ” ” n Sut ay nee GSO en. ‘ ee i Glassand crystals. , . , PTE OOUIMEN Gear, F » » ? Allerystallized ” > > m3 wae 14690 M.V. ) > > ” : All glass. Thus, the meltingpoint was found to be 1428° C. (G. Th.), quite in accordance with the direct meltingpointdeterminations after the dynamical method. In these experiments we once obtained a product after longer heating on 14600 M.V., — just somewhat below the melting- point, — consisting of somewhat larger individuals. They appeared to be large, homogeneously extinguishing plates, whose birefringence was about 0,007, and with refractive indices of 1,518 and 1,519, like those of the 8-spodumene, obtained from artificial spodumene after melting and cooling. In convergent polarized light the same inter- ference-image as in the former case, was observed ; there can thus 18 Proceedings Royal Acad. Amsterdam. Vol. X VIL 262 hardly be any doubt, that the spodumene-modification, which is deposited from the liquid mass, is quite the same as that, which is discerned by us as 3-spodumene. There are no reasons to adopt the existence of a third modification, which on cooling should be con- verted into the 3-form, as occasionally has been done. § 15. Before describing our experiments with this compound with respect to the study of the transformations into the solid state, the determined values are once more recapitulated in the following table. From this table (next page) we can see, that in general the melting- temperatures of the natural kunzites are considerably higher than those for the synthetical products, and further we can, generally speaking, deduce, that the meltingpoint of the kunzites are decreasing at the same time with the increase of specific gravity. (The specific gravities of the two first mentioned kunzites differ too little to give any certain argument for this view). Of the two kinds of dense spodumenes however, the mineral of higher specific density seems to have the higher melting- point also, although in this case the meltingpoints are too close together, and are moreover not sufficiently sharp, to give any certain argument for an eventual rational relation between the two mentioned constants. § 16. Now we will proceed to the question, in what relation the different modifications of the compound LiALSi,O0, stand with respect to each other. That there are several of these modifications, can already be deduced from the mere fact, that the product o7 solidification of the natural spodumenes is quite different from the original substances. Our investigations moreover have taught us, that there are really only to modifications, which can be discerned as a- and @-spodumene. Of these two forms the @-modification is undoubtedly the one to be considered as the more stable form at temperatures in the immediate vicinity of the meltingpoint. The question, however, then rises im- mediately: in what relation are «- and #-spodumene to each other? Are they enantiotropic forms, like e.g. wollastonite and pseudo-wollasto- nite? Or are they monotropic modifications, as e.g. they are observed in some forms of the pentamorphic magnesiummetasilieate ? After numerous experiments in this direction, we have come to the opinion that both forms of spodumene must be considered as monotropic ones with respect to each other, and a-spodumene, i.e. all kunzites, hiddenites, spodumenes of nature, must be metastable phases of the compound with respect to the B-form at all temperatures below 263 cI F oLéPl ol + c92hI c8Ibl J9}aWOWIIY}Ses UOD on Ur sjurod3unjaw €1 + 199F1 €1 + PoOrl LGGPl LEoPl SLOPFI SLOrI (syUNW] A - 1OJDWIOULIIYYSeL)) > "Wa poyosio7 €1 + 69941 Z00°0 + #S1°¢ (uoneSei33e sult -leysAto1svu ‘anbedo ‘ssajinojo7) ‘JUIDWY WIOIY auauinpods asuaq SI + 299r! 0S0'0 + L66°Z (aulyeysAs9 | -o}dA19 ‘onbedo ‘a}1yM) puryulj | ‘o4au0S Wo auaunpods asuaq cocrl 200'0 + S62'¢ (quaiedsue.sy | | ‘u9013 ayed ‘usa18plesaula) BUL[OIR “"N | ‘(juno sapupxalp WoO apzluappipy cProrl Z00°0 + 292'¢ (quoi1edsuvs} ‘moyjeA-ysiuaeis aed [iseig ‘sapuan svuly WO.l ajisuny €89rl c00'0 + 102’ | Quasedsuv.y ‘aso1 ajed) 1eoses -PPeW Aa7]Da-duvjDYVS WIOIl ajiIsUuNnyY €89r1 | €00°0 + F0z'S Quosedsue.y ‘oe ‘ayed 10 ssayino[oD) | “BIUIOJeD ‘Wwoosuly WO. asuny CAW ‘Usoqur) Py : JUIWI|IOULIY} 9yy | JO “TWA PeAtasqO | Ayiaess oyioads > UISILIQ JO d0RTq puP ‘[eIOUIW ‘SHNAWNGOdS TWHNLVN AO SHILIAVYD OISIDAdS GNV SLNIOGDNILTAW AHL JO SISCONAS 1S* 264 1400° C. Therefore it is neither possible to indicate an “inversion- temperature’, below which the e-form, and above which the @-form would represent the more stable phase: at all temperatures below its meltingpoint, the @-spodumene is the only stable form of the compound LZ7AlS7,0,. Under what conditions the «-form was always eenerated in nature, while it was till now never obtained in the laboratory from “dry” molten mixtures, may preliminarily be put aside. The reason however, that the «-modification, once produced, has remained so, notwithstanding its metastability with respect to the 3-form, is to be ascribed to the enormous slowness, with which the transformation «— @ takes place. § 17. To give an idea of this phenomenon, we will describe here a series of experiments, made with the purpose to answer the question, at what lowest temperature the transformation @a— @- form again will ocenr with a velocity just observable? Preliminary ') experiments had taught us that a long and little prominent heat-effect was. observed between 900 and 1000° C., if a larger quantity of finely powdered «-spodumene was gradually heated; and the micros- copical investigation also taught us soon, that within the mentioned temperature-interval, a transformation is going on with observable velocity. We therefore made the following series of experiments by means of the already mentioned statical method. For it is evident, that just with reactions proceeding so enormously slowly, this method can be used with great suecess, because 7 permits us to keep the studied substances at a constant temperature during an arbitrarily long time; in this way one can be sure that the reaction is thus completely finished, while the sudden chilling of the preparation in cold mereury will fix the momentaneous state of it in a most effective way. - The following data were obtained by observations with the thermo- element 1V; because the thermoelement was not placed in the mass, lut beside it, the whole furnace-system needed to be especially calibrated for this series of experiments. The calibration of the used quenching-system was executed by means of meltingpoint-determinations after the statical method, with substances, whose meltingpoints in terms of the gasthermometer were !) Vide also : G. Tawmann, Krystallisieren und Schmelven, p, 114. Spodumene (d=3,17) was transformed gradually into a much less dense substance (d=2,94), by heating on a Bunysexbarner during ten hours. The new product was attacked much more rapidly by HF than the original cubstance. already accurately known before. Only in this way is it possible, to find out, what temperature really corresponds to that, indicated by the thermoelement placed in the furnace. For this purpose we have made use of the meltingpoints of two compounds: L7,Si0, and MBoO,; the Li,ScO, melts at a temperature of 11956 M.V. on our standard-elements, the second at a temperature, corresponding to an E.M.F. of 7822 M.V.'). In this way we observed: | T | LinSiO3. | LiBO>. | | | Heating during along | | ‘ Heating during a long J : : _ time at a temperature, — State of the chilled time at a temperature, | State of the chilled _ at which the E.M.F. of system : at which the E.M.F. of | system: | element IV was: | element IV was: 12060 M. V. All glass. | 7800 M. V. All glass. 120205, All glass. TmOOwn All crystals. 11980, All glass. | sors, Many crystals; a | | little glass. 11940, | Much glass, afew crystals | TO 5, | All crystals. 11930, All crystals | \| UTE 9 All glass. 11950 sy, All glass. } Thus, when the furnace-element indicates 11940 | The meltingpoint of the LiBO, is thus reached, | M.V., the meltingpoint of Zz-.SzO3 is reached;the || if the furnace-element indicates 7780 M.V.; there- _ correction of the indicated temperatures at 1201°C. | fore the correction at 845° C. is: +42 MV. _ to reduce them the nitrogenthermometer, is there- | fore + 16M.V. From both these data for 845°C. and for 1201° C., the correction for every intermediate temperature is found by intrapolation; for a temperature of e.g. 965° C., it is + 28 M. V.; ete. It is with this number, that the just mentioned temperature (in M. V.) needs to be augmented, to be reduced to the nitrogengasthermometer-scale. Having in this manner determined the temperature-correetions for the whole quenching-system within the range of temperature from 845° to 1201° C., we have chosen as an object for these experiments 1) With the thermoelement IV three series of experiments were made, with heating-rates of 30, 40 and 60 M.V. per half minute. lor the lithium-metaborate we found thus successively as mean values: 7786, 7778 and 7781 M.V., — which gives as probable value: 7782 +4 M.V. The correction of element IV was + 40 M.Y. at this temperature; the true meltingpoint thus being at 7822 M.V. = 845 C, (G. Th,). 266 the kunzite of Madagascar, and we tried to find in the described way the lowest temperature, at which a just discernible transform- ation of «¢— 3-form yet occurred. The reader may be put in mind, that the experiments 1—14 were made with a thermoelement, provided with a very thin protecting tube; in the experiment 14—20, this protecting tube was omitted, which appeared however to make no appreciable difference. | Indication of ther-| & | es Z \ moelement IV at) Ga | Soe No. | theconstanttem-|.EE | Des | Result of the Chilling: perature of healing Sf | 2S on | =I a= (=) (See ee wee Les | 6510 M. V. | 723° | 2 hours | Only «-modif.; no transformation. 2 6800, 750 oy = idem Sm S80 S05 a Oe idem | | 4 8450, COLA ee a idem ae | 9570, 1000 2 , | All s-spodumene. 6 | O500/ eu wie mousenieoian idem 7 9070 , | 957 CA No transformation; z-modification. 8 9220 ,, 970 he idem 9 9360 982 3 x ‘Partially transform.; «-, and #-form. | 10 70s s 966 _ Probably the same. | | 11 9280 , | 9715 Saar Partially 3-spodumene. 12 9280 ,, 975 ey = All ?-spodumene. yt} 9260 ,, 913 | 4", Probably partially 3-form. | 14 9260, O73 .aeiSua All 8-spodumene. | | | Tis) 9260 , | 973 | 855 | All s-spodumene. 16 |B) 9225 , 9170 | 8 , For the greater part: 3-form. Ya | | 17 |2& \o160 965 | 4 , | All «spodumene. ae | | 18 =e | 9200 ‘ 968 4 , Evidently partially g-form. 19 |S8foi70 965.5 | 4 , | Some -modification, many crystals eae | of «-spodumene. 20 9150, 964 | Was | No #-form; the transformation has | | not yet begun. | | | | | | In this case therefore an evident transformation has already taken place at 9170 M. V. (uncorr.), or at 9198 M. V. = 968°C. (G. Th.), 267 Similar experiments with the kunzite of Rimcon taught us, that this lemperature is situated somewhat higher, at about 995° C.; in all these cases however, only very long continued heating can lead toa complete transformation of the «-, into the 3-form. It is therefore quite evident, that at ordinary temperatures, and even at 400° or 500° C., the transformation-velocity of «-, into @-form must be practically equal to zero; thus the « and 3-spodumenes can be in immediate contact with each other, during an undetermined long time, without transformation taking place. The transition of «-, into @-form is accompanied by an enormous increase of specific volume: it is augmented from 0.81 to 0.41, being about 33°/, of the original value. It often occurred that the heated and transformed powder had risen over the borders of the platinum crucibles. In the described quenching-experiments, the trans- formation could often be stated already, when the used platinum folium had not yet been opened: it seemed to be inflated by the increase of volume of the enclosed preparation. Microscopically it is observed that the larger crystals of the «-form, in this transformation primarily get innumerable cracks and fissures; afterwards they change into opaque, no longer normally extinguishing aggregations of fine, felty, or even broader needles, whose extinction is @/most normally orientated on their longer direction; they ean be recognized by their weak birefringence, as well as by their low mean refractive index : 1,519. The microphotographs fig. 7 and 9 may give some impression of the aspect of the two modifications between crossed nicols. § 18. It may be expected, that the mentioned transformation- velocity will possibly be affected by some catalysers or by some fluxes in such a way, that it will show a discernible value already at considerably lower temperatures. Indeed we succeeded in proving, that on heating spodumene-glass with molten sodiumtungstate’) at temperatures between 850° and 920° C., after 32 hours a partial crystallization has begun, which however was complete only after 65 hours of heating. The ecrystal- mass had a refractive index of 1,523, and appeared to be no other thing than B-spodumene; the determined specific weight was at 25° C.: yo a Devise 1) The great difference between the specific gravities of the silicate and the molten tungstate, makes it necessary to use a platinum stirrer, to bring the silicate from the surface into the molten mass again and again. This stirrer was moved by means of a suitable electromotor-driven mechanism. 268 We then made similar experiments with @-spodumene (of Mann) in a mixture of 20°/, J/oO, and 80°/, sodiummolybdate at tempe- ratures below 650° C.; on heating during 122 hours on temperatures between 595° and 605° C., we obtained birefrmgent aggregates of felty needles of the @-modification, with often rectangular borders. The refractive index was 1,527, and while the aggregates of needles did not extinguish in any position between crossed nicols, the rectan- gular needles often showed a normally orientated extinetion. As in - ihe former ease, the product had also a pale lilac hue. Then we made the same experiment with a-spodumene (of /tincon); it was heated during 88 hours in the same mixtures at 595° to GO5° C. The small pieces of the «-form had got opaque and were converted at their borders or totally into the @-modification; the refractive Index was 1,519. More experiments were made, which all taught us, that from molten magmas, cooled under manifold varied circumstances, never was another thing produced, than either spodumene-‘“glass’, or B-spodumene; however we did not succeed in getting the a-form from dry magmas even a single time. As devitrification of spodumene- glass appears also never to give another phase than @-spodumene, — we are of opinion, that it may be considered as sufficiently proved, that the @-modification is the only stable modification below the melting point. The spodumenes of nature therefore certainly cannot be produced from dry magmas; they represent metastable forms of the compound, which are very probably generated from circulating solutions, that is by so-called “hydrothermal” synthesis; the natural forms of the compound only appear to be preserved by the enormously retarding factors, which prohibited the transfor- mation into the more stable €-form. Experiments are going on, with a purpose to produce the «-modification of the silicate by such hydrothermal synthesis. The results of these experiments will be discussed in a following paper. § 19. Finally we can here give some data, concerning the lithi- wmnaluminate: LiAlO,. This compound was prepared by heating in platinum crucibles the weighed, finely ground and well mixed com- ponents, — lithiumecarbonate being taken instead of L7,0, — in our resistance furnaces once at 900° C., then at 1200° C. After the resulting mass had been pulverized, the heating was repeated and these manipulations repeated four times. Analysis of the beautifully crystallized, homogeneous mass gave the following numbers; 269 Observed : Calculated : Al, O7: 76,8 °/, TOL Uae fe LEOr: 23,2 °/, 23,0 °/, 22,7 °/, 100,0 Although a small excess of 47,0 was still present, the substance could be considered as -practically pure Z7A/O,, — the more so, as on heating, a certain amount of Z7,0 always volatilizes gradually. A preparation, heated only shortly at 1600° C. contained, as ana- lysis showed us, only 19,34°/, Li,O and 80,65 °/, Al,O,; no further change had occurred than that the crystals of the original prepa- ration had got inuch larger dimensions, while preserving their gene- ral properties. At 1625° ©. the substance shows no trace of melting, but decomposes partially, by the volatibility of the Z7,0. The pla- tinum is strongly attacked, 27,0, being formed, and thus the alumi- nate cannot be heated at higher temperatures, without changing its composition. The meltingpoint can thus be hardly determined; the substance must have been changed a long time before already into Al,O,, with perhaps a slight admixture of some lithitumoxide. Even in a “hollow thermoelement”, we were not able to melt the substance, notwithstanding it being heated up to 625° C. Microscopically the aluminate shows large, round-edged, hexagonal or octogonal plates (fig. 12), with a relatively high birefringence Fig. 12. Crystals of Lithiumaluminaie. (X Nicols). 270 and high interference-colours between crossed nicols. The refrac- tive indices were determined toe be: n, =1,604 + 0,001; n, = 1,615 + 0,001 for sodiumlight; the birefringence was about: 0,012. No axial image could be observed. The specific gravity of the erys- tals at 25°,1 C. was: d,o = 2,554. In a following paper we hope to be able to give an account of the formation and the occurrence of the «-modification of the spo- dumene in nature, and to review the results so far obtained, also with respect to their geological significance. Laboratory for Inorganic Chemistry of the University. Groningen, May 1914. Physiology. — ‘On the survival of isolated mammalhan organs with automatic function.” By Dr. E. Laqunur. (Communicated by Prof. H. J. Hampurerr). (Communicated in the meeting of April 24, 1914). When studying the movements cf extirpated pieces of gut, I was struck by the following fact: a piece of gut which had contracted for 9 hours in a Tyrode-solution at 37°, to which oxygen had been added, and which had been left to itself at room-temperature, began to move again the next morning, after being heated and after a renewed addition of oxygen. However frequently such experiments with pieces of gut — in the way suggested by Magnus — have been carried out by various investigators, yet the possibility of keeping the gut alive for so long a period seems to be unknown. ~ Further researches show, however, that the automatic movements of such pieces of gut are of much longer duration than one day and one night. The longest period, as yet observed by me, runs to more than 3 weeks. As many as 21 days after the death of the individual the movements of the piece of gut could be observed. This time probably exceeds everything hitherto observed in this respect on mammalian organs working automatically. We may compare with this, for instance, how long after the death of the individual the beart can be made to contract. The heart is indeed the only automatic organ, as far as | know, on which experiments have been carried out in this direction. KuLIABKo, for instance, discovered that when the heart of a rabbit, after being kept for 44 hours after death in an ice-chest, was perfused with Lockn’s solution, contractions again manifested themselves. The heart 274 sometimes beat for several hours at a stretch; certain parts of the heart are even said to beat on the 3, the 5, and the 7" day after death. It is a well-known fact that, when at the obduction air can penetrate into the cavity of the chest, this may give rise to spontaneous contractions of the right atrium — the w/timm moriens Halleri ov vather Galent. Vunrran states that he has observed these contractions in the dog for 93'/, hours after death. Rovussnau main- tains that he has seen these movements in an executed woman, 29 hours after death. The human heart has also been made to contract independently after death. These attempts have never succeeded with adults when the individuals had been dead for more than 11 hours. (H. E. Herina). This could be done with the heart of a child 20 hours after death and in the case of a monkey as many as 53 hours after death. (KuntaBko, H&rtNa). ') Recently Carret and INnGrsrictsEN have stated that some tissues ean be kept alive for a long time after the death of the individual ; the tissues could even become differentiated under these circumstances. These experiments, however, have been taken partly with very small pieces of hardly differentiated tissues: this applies for instance to the muscle-cells of the embryonic chicken heart, contracting 104 days after the death of the animal. (Carrer). And partly they relate to parts of organs (bone and skin) where it is not so easy to determine whether the cells are living still. To ascertain this the “surviving” tissues must be transplanted on another animal. It must be taken into account, however, that these tissues may have permanently lost their independence. Only with the assistance of the normal tissues of the animal on which they were transplanted, they had regained life. With regard to the following experiments on the movements of isolated intestines, the investigations of MaGnus have shown. that automatic movements are only met with, when besides the musele- cell the nervous system of Awerbach’s plexus has retained its activity. The phenomenon is, therefore, of a complex nature. Intestines can be kept alive longer than usual (++ 12 hours) only when the periods of activity are alternated with long periods of rest. This can easily be done, as we know, by lowering the temperature. At body-temperature the isolated gut works itself, sit venia verbo, to death, within from 10 to 14 hours, 1) See the Summaries by O. Langenporr in Ergebnisse der Physiologie 1903 and 1900. 272 For various reasons the intestines of smaller animals, mouse, cavia, rabbit, were chiefly experimented upon. The method followed here keeps the intestines longer alive in proportion as they are thinner. In reality this method is a very primitive one. In the intestinal wall there is no longer any circulation and the metabolism is therefore restricted to the diffusion through the whole thickness of the wall. Hitherto I have not succeeded in keeping the gut alive in ftyrode- solution, a medium particularly fitted for intestine-experiments, for a longer period than 5 days. Pieces of intestine which no longer moved in the solution in which they had been placed immediately after the extirpation, began to move again when the solution was refreshed. This can easily be explained. The experiments carried out by collaborators of Magnus, WEINLAND and Nwuxirch have taught that when the intestine is placed in a liquid medium, substances are formed which stimulate the intestine. That an accumulation of these stimulating substances, besides the usual decom- position products, and more especially besides the bacterial decom- position products, unavoidable in intestine-experiments,should impair the activity of the intestine in the long run ean easily be understood. If the temperature of the pieces is kept particularly low (+ 3°), then the intestine keeps alive much longer than if the temperature remains but litthe under the limit at which activity still manifests itself. Pieces of ecavia gut in tyrode-solution at 15° were already dead on the 38" or 4% day. If the temperature of the tyrode-solution was + 3°, the gut died only on the 5% day. To keep the gut alive for a longer period a medium is required resembling more than tyrode-solution the normal body-fluids. For this purpose I took Aorse-serum’*), the serum of the small animals experimented upon not being obtainable in sufficient quantities. Since oxygen must bubble through the fluid in which the gut has been placed, a great quantity of froth is formed if serum is taken instead of tyrode-solution. This can be avoided, however, by pouring a thin layer of olive-oil on the serum. It might be assumed as probable that serum would prove a better medium than a salt- solution on the strength of the many experiences obtained with the surviving heart. (Wurre, Howni., Greex, Wanpen, with hearts of warmblooded animals, Guririm and Pike with hearts of mammals. *) 1) Horse-serum can be oblained by the method, described by HAMBURGER and often applied in his laboratory, | take this opportunity of again thanking my colleagues De Haan and Ouwewwen for the readiness with which they always provided me with horse serum, It is true, cases have been mentioned where a frog’s heart, which beat no longer in sheep serum and could no longer be stimulated mechanically, was made to contract again by Rtina@ur’s” solution (Waxprn). Yet the possibility is net excluded that in these cases the strange serum has gradually had a poisonous effect. Therefore I shall also leave it an open question if the time during which the eut keeps alive would not be longer still if, instead of horse-serum, serum of the same animal, if possible of the same individual, were used. The experiments of INGrBeiarseN with tissue-cultures in auto-, homo- and hetero-geneous sera have demonstrated the relative superiority of autogeneous serum to serum of other individuals of the same kind, and of these two sera to heterogeneous ones. INGr- BRIGTSEN has not used horse-serum; this seems to be a particularly indifferent medium. Numerous experiments have shown that this serum is a much better medium for the gut than tyrode-solution. The gut of a cavia, for instance, kept in tyrode-solution, was dead after 5 days; when kept in horse-serum another piece of the same gut still moved after 21 days. The experiments were carried out in the following manner. The animal, a cavia for instance, is killed by decapitation, + 20 em. behind the stomach a piece of the small intestine, long + 40 c.m. is cut out and divided in Tyrode-solution into 8 pieces long 4—6 c.m., called a—h. 4 of these (a, b, e, f,) were placed in Tyrode-solution, 4 others (¢, d, g, /) in horse-serum. Oxygen is led through the 8 glasses. The pieces a, e, ¢, g, are connected with a writing apparatus lo a cymographion (method of Magnus) To ¢ and g olive-oil is added. The movements of these 4 pieces having been registered at + 37°, they are slowly cooled down. Then the current of oxygen is stopped. The glasses a, e, and the reserve-experiments b, f, remain at room- temperature (+ 15°), the glasses c, g and the reserve-experiments d, h are exposed lo a temperature of + 3°. The pieces a7};, eT, ¢T\, and g7T, remain connected with the writing-apparatus or are removed with it. On the third day after the death of the cavia the pieces a, e, c, and g are connected wilh the cymographion whilst oxygen is led through, and are slowly heated to 40°. All the pieces move, but not so much as the first time except Sz, the movements of which have become greater. The fluid in all 8 glasses is refreshed after being cooled down and saturated with oxyen as on the first day. On the sixth day all are heated ete. just as on the third day. Piece 77; moves no longer now, not even after the Tyrode solution has been refreshed. The reserve piece “7); does not move either: therefore in Tyrode solution at + 15° the gut dies before the 4th day The three other pieces ¢7, °S);, and 9Ss still move, the first two less again than last time. On the 6th day everything is heated again etc. Piece e7; moves no longer, not even after the Tyrode-solution has been refreshed. Nor does the reserye-piece /7'; move: hence in Tyrode-solution at + 3 D174. the gut dies before ithe 6th day. Piece “S|; does not move either. On the other hand the reserve-piece 4S), is still in motion. Movements of 7Sg are still greater and have the same frequency as before. The three fluids are renewed etc. On the Sth day only “S; moves distinctly: hence in horse-serum at + 3° death before the 8th day On the 10, 13, 15, 17, 20, 22ud day 7S; moves distinctly, but the movements have become smaller. On the 25th day no movements. The reserve-piece 2S; got fresh serum for the last time on the 24nd day and is for the first time connected with the cymographion on the 27th day. It does not move; only its tension decreases when heated. Hence in horse-serum at 3° the intestine dies after the 22nd and before the 25th day. Hunan gut can also be kept alive for a comparatively long time ‘). A piece of colon, obtained after an operation, moved still after 86 hours. And an appendix, kept in horse-serum, described no straight line on the cymographion after as many as 6 days. There were slight but distinet contractions, which ceased when the intestine was cooled down to 25°. Finally I may mention that a human vas deferens was still alive in tyrode-solution after 30 hours. Summary. Isolated pieces of mammalian gut can be kept alive during a long time, much longer than the periods found hitherto for other auto- matic mammalian organs. For this purpose the medium in which the gut has been placed must occasionally be refreshed whilst it is of great importance that the temperature of the solutions should be low. In Tyrode-solution of 15° the gut dies after 3 days, at 3° after + 5 days, in horse-serum at 15° after + 7 days, at 3° after more than 21 days. Also pieces of human intestines still showed signs of life after they had lain for 6 days in horse-serum at + 14°. Groningen, April 1914. Physiological Laboratory. '!) I am indebted to Prof. Kocn for his kindness of providing me with pieces of human gut. 975 Physics. — ‘/sothermals of monatomic substances and their binary mintures. XVI. New determination of the vapour-pressures of solid argon down to — 205°’ Comm. N°. 140a from the Physical Laboratory at Leiden. By C. A. Crommenin. (Communicated by Prof. H. Kamernmen Ones). (Communicated in the meeting of March 28, 1914). The vapour-pressures of solid argon, which are communicated below, form an extension of and have partly to replace those published on a former occasion. ') The measurements were made in the usual vapour-pressure apparatus for low temperatures. *) The manometer on which the pressures were read was constructed after the model used by G. Hots for his measurements on ammonia and methyl-chloride to be published shortly: this form of manometer gives perfect security against leakage. The method of conducting the measurements gives no oceasion for special remarks: we refer the reader to the previous paper. It may be mentioned however, that the temperatures were measured with a gold-resistance thermometer, as below — 200° gold is preter- able to platinum. This thermometer was very carefully compared with the standard-platinum-thermometer Pty. I am indebted to Mr. P. G. Carn assistant in the physical Labo- ratory for the measurement and calculation of the temperatures and for the comparison of the two resistance-thermometers referred to. Table I contains the results of the observations and the deviations from the Rankru-Bose-formula : log Peoex. =arnB + bra T—! + erp T—-2 + dep T-3, with the following values for the coefficients agp + 6.6421 crg = — 0.677438 x 101 bea = — 3.7181 10? dre = + 0.280384 « 108 1) CG. A. Grommetin, Comm. Leiden. N°. 138¢c. The measurements were repeated because shortly after the publication doubt arose as to the accuracy of the determi- nations at the lowest temperatures (see note on p. 23 of Comm. N®. 138c). The new measurements showed this doubt to be justified, the observation at — 2069.04 being found altogether wrong and the one at — 179°.62 not very accurate. The remaining observations of Comm. N® 188¢ correspond well to those published here. The probable cause of the errors must be air having leaked into the argon at the low pressures: but [ cannot explain how it is that this was not noticed during the measurements. *) H. KamertinaH Onnes and C. BraaK, Comm. N°. 107a. bo ~f o> TABLE |. Vapour-pressures of solid argon. pat @ (Celsius | ia | Percentagerdeviations ig | Ne SN cae) TUT eee ee Ceyesee | | MCCAY: formula. | formula. | 26 Nov. | XXIII ~189.64 | 0.6554 | 49.78 | +0.20 | +1.33 | | XX |” 191/31 | 0:5175. "|" 39.30 ot oa XXVI 195.60 | 0.2749 | 20.88 | +0.35 Ss XXVII 197.25 | 0.2153 | 16.35 | 2.16 +0.15 28 Nov. XXVIII 200.97 | 0.1113 8.456 | —0.94 |) ==o029 XXIX | 202.21 | 0.08931 | 6.783 | —0.89 —1.49 XXX | 203.78 0.06740. 5.119 | —0.04 +0.59 XXXI 205.32 | 0.05043 | 3.830 | 10:36 [|p ="2:79 and from Nernst’s formula (treated simply as an empirical formula) A log Peoex. = 7 Se SUR es Ding Ps 5D xr i I («—p 2| p (@) = Pas = byl, - Od, se bef, ee e WOK 0 or, with the values of 6 from (9) =tlel, +¢4+¢%+-- 1] + $[e.7, tet, +¢,2%, + --] which by means of (5) may be written Therefore the solution may be put in this form 2g(w) — [2° fFE(@)| — 3 [fo] = — ofan Me me dp . (10) yo ee Differentiating 291 P= (v (8) Z, (e—8) a we obtain 2f(2) =r (8) (1,—1,] 48 29H 200 + fi (8){— 47, + 312,—J,] dp. Thus av ak a? TA. eee 227 Me)+ 2AM Bele) — [HOLL +L MP=24 (0) —8 (6G) e & 0 0 where 1 - 1 => flew = ec. eal, es... sf fe) dB 0 0 This gives the solution me =v se I (ie 24 (0) — [24f)(2)] —4[2/M(a)] =f jG)" aa fi (0) ap —p z—Pp U U i pc. By differentiating J(#) = Jv (B) Z, (eB) dB we obtain 247° (a) = {o(B) 21, + 1.) a8 292 27 (o) = 2 (0) + f(B)L— 51, + OL —A1, + La 0 Multiplying these equations respectively by 4, 5, 1 and adding we get ‘ [247 (@)J 4- 5[ 2277 (@)] + 4[ A(2)] = : v)| wi fu ee ue 8 = 2y (x) + 12f) (8) a = dg 0 where if tle 8) 6 fv) gy BL, EOL, + OT + e vU—t 0 == i(C, I. sp os Sp Oar ao) SF $ (cl, = cL, == ORI + -.-) ae a I (#—p) 4 7 , L(e7—B8),, = » {78 per dp + 2. WO ane 0 0) In this case therefore the solution takes the form 2y (a) — [24a] — 5 BVO) — 4 el = 48 oe fre Pa, (12) 4. Proceeding now to the general case, we may expect, A;{”) being constants, ly (w)-A,' P ) Paes AC )(x)} =A i Pp) [2P—1f pt \(x)] -A, (p)[2P—3 fP = 3)(x)} = Bs = (—1)?. 4p [vi 3) 0 I2,(«@—8) ee . (18) If p be even the last term in the first member is — AY [27 (w)], 2 and if p be odd it is ~ Able v)]. The second member now reduces to > (z—B 2pfutey™ vie ae = b, 1 Ta, bate ela ee 0 293 = $ [pile, + p4olo,pi + cp43lopte + . | +} [ep4itopte+e42lopt3t+¢,43lots + ---] thus zr z on (nc. t2(@—B) 1p P—! (re — p+l Ty 4i(a- 2p fate) a PP (ray ae Baas EA gyi = V3 (14) 0 0 Substituting this value in the equation (13) we see that g(x) may be expressed in differential coefficients of the function J(2) and two integrals. To determine the law of the coefficients A,(”), A,”, A\™, A,)... we put together the values for p=1, 2,...10 in the following table: p AO SAC VAG) | 2A) A VA) AG) 1 1 3 2 \ 4 a 1 5 4 4 1 6 8 5 1 7 13 4 6 1 8 19 iz 7 1 9 26 25 4 8 1 10 34 44 16 9 1 11 43 70 41 4 10 1 12 53 104 85 20 Examining this table we see that A,(P) = A\P-Y + AS p—®) A,r) = As ps) of A ip 2) A,(p) = A,(r—1) 4+ A,fp—2) (p even) OD) —— y—1) (p—2) __ (p— 2) AY, — is + Ape =4+ A (p odd) (p) =. Ay = 4 If therefore the coefficients of order p— 2 and p —1 are known those of order p may be found. To verify the results we may remark that if TAM=S, we must find Sp = Sp—2 aia Sp—1 . The resulting values of these coefficients are as follows 20 Proceedings Royal Acad. Amsterdam. Vol. XVII. 294 AK (p12 ed.22) A?) ==/)) + 2 — 1a -) 1 A= > (p?+p—4) (p=3.4.5...) rare Bye Ae) 31 (p—4) (p?+-p—6) (p=5.6.7...) . (15) eS 1 PORK 5 A fp) = ai (p—5) (p—6) (p?+p—8) (p=7.8.9...) 1 er (p—68) (p—T) (p—8) (p?+-p—10) (p=9.10.11..) | where the law of succession is evident. With these values the equa- tions (13) and (14) give the required solution. 4. To generalise the preceding results we will proceed to examine the more general integral equation. f(a) =[9(@)K(@—A)dB . . . . . . (16) J assuming that the functions f(z) and A(x) may be expanded in series _ of Brssex’s functions Se) = ¢,1,(@) + el .(w) + e,2,(@) + «. K(«) = a,l,(e) + a, f,(e) + a,1,(a) +... which is the case if these functions are finite and continuous from O to 2. If now —p (x) = b,L,(x) + b,1,(x) + 6,7,(x) + ... the second member reduces to x S355) yl. I, (8) L) (e—8) a8 = U 2S ayy pyle) — Lp-+943 1b Iptags — +] Thus, comparing the two members, we find = 10- » = 2a,b,+2a,), c, = 2 (a,—a,) b, 4+ 2a,b, + 24,6, c, = 2 (a,—a,) b, +2 (a,—a,) 6, + 2a,b,-+4 2a,, etc. Cat c which give ‘ 1 26, = —e, ay ob ee a, C, | 2b, = —_, Dx Ce Os) 1 4 Oc! 26,=>— 4, a, ¢, ay g,—4, a, ¢, a, 0 C; 1 fa a 0c 1 0 2b, =— ; a,’ |a,—a, a, i, Cs a,—a@, 4,—a, @, ¢, ete: Therefore g(v) may be written in this form ay 0 0 0 a, 00 ] a, 0 1 1 a, a, 00 24(«)= —e,?1,+ == (aie ee Cp hy OT ipee a, Gea anic. a, Gy \a,-a, a, a, 9 a,-a, &, Cy @,-@; @—a) a, ¢, ‘ a, 0 00 a, 0 0 1 Gace 1 1 a, ay 0 0. “tee ott gal PANEL Ul i It. a, |a, V| a, a |a,-a, a, a, Cy a,-a,a, 0 a,-@, a,-a, a, 0 ay 0 0 0 a 0 c, | iT 1 \4, a, ONG: = 0,/,+— iD a 311 GON ae 7 sche. a," a a,-a, a, a,0 \a,-a, a, 0) @,-4, a,-a, a, 0 0 1 1 a; ae, ADD) + > z J,+-. 0 |a,—a, a, a, 0 a, 4, a,-a, a, 0 or 20% 296 1 2¢(«) = lan (1,42, | c,l,+ “M :) 0 We 0 (c,2,+¢,2,+-¢,2,+ a) ke, 1 +s make a, 0| (¢,f,-+-¢,2,+¢,1 4.4 - -) : a,—a, a, 9 \d, 0 0 1 pie. Ol | + ar | (c,I,+¢,1,+¢1,+--) a, |a,-a,a, a,9 a,-a, a@,-a, a, 0} + ete. If now f(e)=eJ, + Cale aie Cas ci we have df pa am Sead ie SS Gye da = (c,1, 33 ty, =e o,f, a as -) thus, according to (5) c.J,tel, +¢/, +... = 0th frosts ap and by the same formula In—\(e@— 8) dp e,In + ¢Inpi + eslng2 + ++ = 0) {7 259 0 Introducing these values we have ee a ee ae where a. Oru eal Ea 1 | | anaes fee ala! 0| A, a,? Ci a, 0 | ie (17) |@,—Ay A, 0 | Remarking that nIn(a« —B) «—Bp this result we may write = $ [Znsl@—8) + Ing (eB) 497 2¢(2) = = 2 a aes Ane ae $ J@l—A AGS BAC er dg ar 0 : | (18) ASME rAnane—oa| 0 When the integral equation 2D («) = | W(8) K (« —8) dp 0 is given, we find by (18) eo = A, /,(«) + A,4(e) + 4,4,(2) + -- Therefore = = (A,+-A,42)4, pov) be expressed in function of wp. For LETTS a hey WI oma eo Pea fae aa) and, differentiating again ee a -B) A,I,(a) | AD, +A TD, +-.=4 = +29+-A,F,—A,7,—2 | w8)— a av a — Bp 0 thus x 2 Ged mal Ij(e—f) _, (Ay 4 Appa) = 475 + Bh + A, AL —2 | WG) 7 a3 : . assy e 0 5. We now proceed to give some applications of formula (18). First let the integral equauien be a=fu (3) I, (e—8) dB then Gy SS ly Gh = 0 So SW) hence A =I ARO AL ale A =A! 10) thus x 9 9 df % ) 5) 2p (e) = 2 + 4 (F(8) (22, (@—B) + 22, @—B)] 4B 0 or 998 = oli" f+ fan se —p which agrees with (2). Considering the integral equation z Ho) = [x (3) 1, ayaa 0 the formula (18) is not applicable because a, — 0. In this case and assuming a, =— 0, we have 1 2p) (@) = ae (Ql ORIEN 55) Ie as — Notre vom ae ee) a, aa ; a Oma tall 4s Gen0> (0,0 geri) where PY Di ce Ie er i oe . T, («—f) oy Be =e ~ = Gi tah $n = 2S r ff @) ee 0 I, esl, 4 pals 2 2) as c | oe == 4 —— + 27 — 2 f 7 (8B) ——_ c TO Sik dx? “oe fi Bp t . af —8) 2p (x) = B, se : afi (8) ee pe aah + B, 17 (8) 1 fe—8) 13 w—B 0 299 or —é) af i ‘ (@ +(2B,+B,)/—2 rf) oe a+ 2g (7)=4B, an? +2B, Ie ) a A RB +f me [(\B,4+B,)1,(e—p)+2B,1,+3B,1,+. Jade. 0 Now putting we have Bell Bi) 13). == 1 Bi == == eat 0 thus xr : Gap > fj.«—B 24(«)=4 de ok 2 K(8)- <> d3 e ( which agrees with (10). Finally let the integral equation to be solved be x ¢(@) cos (e—B) dg In this case thus i — Av —=0 , Ano 7 A= 0h, ALS Aes er eel peel and, according to (18) ie 24 (2) = 2 ay ence @)+ 80,4 87,4 °8/,+...] de 0 which, by means of the known relation Pia DT (aya Tey ee SS may be written or 300) Geodesy. —- “Comparison of te measuring bar used in the base- measurement at Stroe with the Dutch Metre No. 27”. By H. G. vy. p. Sanpe Baknuyzen, N. Winpesorr and J, W. Dinewrink. In the summer of 1918, the Government-Commission for Triangu- lation and Jevelling measured a base of about 4320 metres, under the direction of Prof. H. J. Hruvenmk, on the high road between Apeldoorn and Amersfoort, near the Railway-station Stroe. The measurements were made with the base-apparatus of the “Service géographique de Varmée” at Paris, which was lent through the courteous help of the Director of that service to the Government Commission by the French Government. The measuring bar of this apparatus is an H-shaped invar-bar_ of four metres length, provided with two very sharp end lines at the extremities, between whieh three intermediate lines are drawn, which divide the measuring bar into four parts, a, 6, ¢ and d, each one metre long. : Previous to the base measurement here, this measuring-bar had been compared several times with the métre international at Breteuil ; these comparisons had shown, that the length had undergone some slow changes, as is often the case with invar-bars; it was therefore important to determine the length shortly before and after the base- measurement. In April 1913 therefore a comparison was made at Breteuil, but as the comparator there had to undergo some repairs, the comparison could not be repeated in the autumn of 1918; it was therefore decided to compare the measuring bar in this country with one of the two Dateh platinum-iridium metres, viz. with No. 27, by means of the comparator which had been supplied by messrs. RepsoLp and Sons in 1867 with the base-apparatus for the triangulation in the East Indies, and which is now mounted in the geodetic buildings in Delft. From the experience gained in previous measurements we did not consider that sufficient accuracy could be obtained with this compa- rator, especially on account of the inferior quality of the microscopes ; on this account it was decided to order two new micrometer-miecros- copes from Zeiss (in Jena) which were delivered in the autumn of 1913, so that in December the comparator was ready for the comparison. We are very much indebted to Prof. Hruveninx, who arranged everything for the measurements and placed a room in the geodetie buildings, and an instrument-maker at our disposal for some weeks ; and further to the ‘Commission for the preservation of the stan- dards”, who allowed us the use of metre 27. 301 il Arrangement of the comparator. A complete description of the comparator can be found in Dr. J. A. C. Ouprmans, “Die Triangulation von Java, erste Abteiling”’ ; we may therefore confine ourselves here to a short account of the arrangement. A wooden case over four metres long inside, contains a long iron carrier, which can be moved upon rails from one side of the ease to the other, at right angles to the length. Upon this carrier the measuring bar and the metre with which it is to be compared, are placed parallel to each other, while the metre with the box in which it is placed can be moved along the carrier in the direction of its length, and can so in turn be placed opposite to each of the four parts a, 6, c, and d of the measuring rod. The wooden case is further provided with a strong iron frame to which the micrometer-microscopes are attached at a distance of exactly a metre and which can be moved upon rails, independently of the carrier, above the measuring bar and the metre. The first thing to do is to place the metre opposite the first part of the measuring bar, parallel to and at the same height as the bar, and to push the carrier upon which they both le as far as possible sideways across the case, until it touches a pair of correc- tion screws. If everything is properly arranged, the microscope frame upon its rails can then be placed so, that the two microscopes are just above the end lines of the metre, or the part a of the measuring bar. If the carrier is then moved to the other side of the case, where it similarly touches two screws, the microscopes will be directed just above the end lines of part a or of the metre. By focussing with the micrometers accurately upon the end lines of the metre and of part @ in both these positions, it is easy to find the difference in length between them, expressed in micro- meter-divisions. By subsequently placing the metre successively opposite to the portions 4, c, and ¢ of the measuring bar, and making the same observations, the data are procured, by which the length of the measuring bar can he determined in metres. : In order to be certain that in the successive measurements of portions a, 6, c, and d the microscopes were each time directed upon the same points of the division lines, small brass plates provided with a point in the middle were fixed on the middle of the bar near the division lines, in this way fixing a line along the middle of the measuring bar. The correction screws at the sides of the case, (against which the carrier moves up in ils sideways movements) were so adjusted, that these points came exactly under the fixed 802 horizontal wires in the two microscopes. As care was taken, that the moveable micrometer wires were parallel to the division lines, an influence of a small deviation of the point upon which the micros- copes are directed need not be feared. 2. Microscopes. At our request the microscopes were so con- structed, that on the obiective-side the course of the rays is tele- centric; they have a 30-fold magnification, and the illumination of the division lines is not sideways but central, by means of a prism with total reflection, which is placed behind the objective in the tube of the microscope, and occupies half of the field. The light from a small electric lamp falls through an opening in the tube of the microscope upon the dull face of the prism, is then reflected by the prism vertically downwards through the objective, falls upon the reflecting surface of the metre or the measuring bar, and is thus reflected vertically back into the microscope. With an electric lamp of a few candles the illumination was excellent, and the division lines were seen as very fine black lines. 3. Temperature. The exact determination of the temperatures of the metre and the measuring bar is a matter of great importance. In order to make the changes of temperature as small as possible we endeavoured, in the first place, to keep the temperature of the room as constant as possible. For this purpose the windows were covered with thick curtains, and the central heating was shut off. As only a small amount of heat was conveyed through the floor and walls, the temperature did not change much, and only rose a little from the presence of the observers, and the burning of a few gas lamps. All the metal parts of the comparator were shut off from the outside air by wood and other badly conducting material, outside which only the eye-pieces of the microscopes protruded ; the measur- ing bar was moreover entirely enclosed in a thick aluminium case and the metre in a brass box, in which there were only small openings for the reading of the division lines and the thermometers. The protection of the metre from the radiating heat was less effective than that of the measuring rod, so that in half of the measurements, during which the observer was on the side of the comparator nearest to the metre, it was found advisable to cover the outside wall of the comparator with a layer of badly conducting material, which gave a greater constancy of temperature. For the determination of the temperature of the metre and mea- suring bar, upon the horizontal faces on which the division lines are drawn a thermometer A was laid upon the metre, and on the measur- 303 ing bar two thermometers B and C, the last two about a metre from each extremity. Moreover there were placed in the comparator case a registering thermometer ), two thermometers // and F upon the outside of the aluminium case about above the thermometers B and C, and two thermometers G and #/ at the two extremities of the comparator, which were read through glass-covered openings in the end-walls. On the whole the temperature readings were of such a nature, that there is every reason to believe that the readings of the thermo- meters A, B and C may be taken as the temperatures of the metre and the measuring bar. 4. Programme of the measurements. It was arranged, that the measurements should be made by the two engineers of the Govern- ment Commission for triangulation and levelling, A. Winprsorr and J. W. Dieprrink, and a member of the commission, H. G. v. p. SANDE Baknuyzen. Each of these made a complete series of measurements. Mr. Witprsorr and Mr. Dirprrink arranged everything beforehand, so that (1) metre and measuring bar were parallel to each other and at the same level, (2) the micrometer wires were parallel to the division lines and showed no parallax with regard to the division lines, (8) in the extreme positions of the carrier the division lines of the metre and of the measuring bar appeared in the correct position in the field of the microseopes. In the adjustment of the level of metre and bar, so that no parallax could be detected of the micro- meter-wires with respect to the division-lines, the adjustment of one of the observers was always checked by a second or third. When the carrier had been placed in one of the extreme positions and the microscopes were therefore directed upon the end lines, say of the metre, the observer placed the micrometerwires of the left- hand microscope twice in succession upon the line, then took four readings with the right-hand microscope. and finally two with the left-hand one. In the middle of these eight readings the thermo- meter on the metre was read. The carrier was now brought into the other extreme position, so that portion a of the measuring bar came under the microscope. In the same way as for the metre, 8 readings were taken with the microscopes, and readings of the thermometers. The observer then returned to the metre, and in the same way took seven sets of observations in succession, alternately upon the metre and the selected portion of the measuring-bar, each consisting of 8 readings. A series of observations of this kind, which lasted about a quarter of an hour, we shall henceforth call an observation-series. 304 Hach of the three observers made two of these observation-series in succession. After these six series, the metre was turned round in its case, so that the mark which first showed on the left hand side now lay on the right hand side; and in the same way as at the beginning of the measurements, the position of the metre with regard to the measuring bar and the microscopes was then properly regulated. As the comparator case had to be opened for this, there was a disturb- ance in the equilibrium of the temperature. An hour or 1‘/, was therefore allowed to pass before fresh measurements were begun. As in the first position, each of the three observers then took two series of observations in this second position. For the determination of the temperature in the comparator, at - the beginning and at the end of the 6 series with the same position of the metre, the thermometers /, /’, G, and H were read. These readings served only to ascertain, whether disturbances of tempera- ture had oecurred in the comparator. In none of the series which were used for the determination of the length of the measuring bar was this the case; there was therefore no further use made of the readings of the thermometers 1, /, G, and H, any more than of the records of the registering thermometer. As in the computation of the results the differences of the readings of the right-hand and left-hand microscopes are used, the influence of a personal error of adjustment will disappear from the results, if both end lines, the micrometer wires and the optic images in the two microscopes are exactly alike. This complete equality however does not exist. The lines are, as far as can be seen, all equally fine and faultless, but the distance of the micrometer wires is smaller in the one microscope than in the other, so that the appearance of the line, when it is placed between the two micrometer wires, is different in the two microscopes. In order to eliminate the personal error arising from this, the observations would have to be repeated after exchanging the microscopes, or else with the microscopes in the same position, but the observer standing the second time on the other side of the comparator, so that the microscope which was first on his right hand, is now on his left. The latter method is simpler than the former, and had the further advantage (over the changing of the microscopes) that the observer, who first stood nearest to the measuring bar, is now nearest to the metre, and an irregular influence of the heat radiated by the observer will thus be also, at least partially, eliminated. On these grounds the observers, after they had compared each of 305 the 4 portions of the measuring bar with the metre, while standing on one side of the comparator, repeated the observations standing on the other side. To distinguish the observation-series from each other, we shall call those which were made while the observers were in their original position with respect to the comparator, A, those in which they were on the other side, £6, the series in which the mark on the metre lay to the right of the observer 7, that in which it was on the left 7, while the first of two identical series we shall call 1 and the second 2. For each portion of the measuring bar each observer therefore took 8 series of observations Ar,, Ar,, Al,, Al,, Br,, Br,, Bi,, Bl,. Care was taken, that when the first series was begun with the metre, the second identical series should begin with the measuring bar. 5. Runs and errors of the micrometer screws. For the purpose of determining any possible changes in the runs of the micrometer serews, the length of the millimetre divided into 10 marked on the measuring bar near the end lines was measured every day before and after the measurements, with both of the microscopes. From the results it appeared, that the value of the run, which was approxi- mately 200 micromillimetres, did not change perceptibly. As, however, it was not certain, that the millimetres on the measuring bar were of exactly the correct length, the absolute value of the run was afterwards determined by measuring out a distance of 1 centimetre divided into millimetres on a measuring rod of nickel-steel belonging to the Observatory in Leiden, supplied by the Société Genevoise, the errors of division of which had been accurately determined in Breteuil. For all the measurements the same value of the run is assumed, viz. 198.69 micromillimetres for the microscope marked I and 199.82 micromillimetres for the unmarked microscope. Moreover the periodic errors of the micrometer screws were determined in the observatory at Leiden, by measuring distances equal to a half and a third of a turn. The continuous errors were determined by measuring a larger distance, with portions of the serew situated symmetrically with respect to the zero. For micrometer | the correction formula of the readings in parts of the divided head, was found to be: 0.18 Sim (wu + 17°); the influence of the term dependent on the double of the reading was imperceptible. In the unmarked microscope no periodic errors could be detected by the observations. The continuous errors were imperceptible in both microscopes. 306 6. Reduction of the observations and results obtained. The micro- meter readings are all reduced with the above mentioned values for the run of the screws in micromms and for the periodic errors in micrometer I. The errors of thermometer 4570 belonging to the Dutch platinum- iridium metres, which was used for the temperature-determinations of metre No. 27, were determined by comparison with two thermo- meters standardized at Breteuil, and by separate determinations of the freezing point. It appeared, that between 0° and 30° the ther- mometer is free from errors, except the error of the freezing point, which was —0.48°. The determinations were made by Mr. H. C. Vorkers, lecturer at the Technical University at Delft. For the thermometers 153855 and 15356 belonging to the invar- bar both the errors of division and the correction for the zero are negligible. In the reduction of the length of the metre and the measuring- bar the following coefticients of expansion were used. For the metre the value communicated by Bosscua in his paper: ‘Relation des expériences qui ont servi a la construction de deux métres étalons en platine iridié, comparés directement avec le metre des archives” and which from 0° to ¢° gives an expansion for the metre in micromms of: 8.4327 ¢ + 0.00401 7’. For the measuring bar, the determination made at Breteuil was used, which gives for the expansion per metre in micromms; 1,6245 ¢ + 0.001065 ¢?. After the introduction of these reductions, the three observers obtained the following results for the lengths of the 4 portions of the measuring-bar, each about a metre in length, diminished by the length of N°. 27 both at the temperature of zero. These results are the mean of the observations of one series. Portion O—1. WILDEBOER DIEPERINK BAKHUYZEN Position A Position B Position A Position B Position A Position B 1, —29.70 —27.43 —26.65 —27.39 —27.93 — 26.40 l, 28.25 27.84 28.28 27.19 28.60 27.13 1, 29.25 28.39 28.85 27.94 29.89 27.96 iP 29.01 28.95 28.89 28.23 29.49 27.91 307 Portion 1—2. WILDEBOER DinPERINK BAKHUYZEN Position A Position B Position A Position B Position A Position B i, —99.31 —95.46 —98.59 —96.73 —97.96 —96.10 E 99.61 95.28 98.64 96.02 97,65 96.22 iP 98.82 95.338 97.95 96.99 97.30 95.69 ip 99.96 95.18 98.50 96.7 97.69 94.94 Portion 2—8. WILDEBOER DIrPERINK BAKHUYZEN Position A Position 6 Position 4 Position B Position A Position B Poe ee —— 12200) 12.2570) 1.23.64 2352) 199-95 i 22.25 122.22 122.26 123.00 12239 123.03 r 122.72 AO ioe, 121.18 121.04 122.85 1:23:35 7 122.00 121.46 120.75 122.24 121.96 122.83 Portion 3—4. WILDEBOER DIEPERINK BAKHUYZEN Position A Position B Position A Position B Position A Position B 1, —144.49 —14348 —143.28 —143.45 —144.09 —143.22 i 144.55 143.58 143.96 143.37 143.938 143.28 ry 144.91 144.00 144.09 143.69 145.10 144.57 r 143.70 144.08 143.98 143.65 144.44 143.48 In order to eliminate the effect of personal errors the means were now formed from the observation-series A and JB, those two series being combined in which the metre was in the same absolute position in space, not relatively to the observer, i.e. Al, with £r,, Al, with Sr,, Ar, with Bl, and Ar, with Bl,. In this manner the following results were obtained : WILDEBOER. Portion O—1 Portion 1—2 Portion 2—3 Portion 3—4 —29.04 —97.32 —122.24 —144.20 28.60 97.39 121.85 144.31 28.34 97.14 122.36 144.19 28.42 97.62 122.11 143.64 Mean 28.60 97.37 122.14 144.08 308 DIEPERINK. Portion O0—1 Portion 1—2 Portion 2—3 Portion 3—4 ——Ora9 9) 1187 —143.48 28.25 97.70 122.25 143.80 28.12 97.34 122.41 143.77 28.04 97.26 NSH 143.67 Mean 28.18 97.52 122,10 143.68 BakHUYZEN. Portion O—1 Portion 1—2 Portion 2—3 Portion 3—4 —27.94 — 96.82 — 108} 144033 28.25 96.29 122.61 143.70 28.14 96.70 122.90 144.16 28.29 97.45 122.49 143.86 Mean 28.16 96.82 122.86 144.01 If the sum is taken of the lengths of the 4 portions of the measuring-bar, we get for the length of the whole measuring bar at O°: Measuring bar = 4 x Metre 27—392.19 WILDEBOER 4 So Metre2 (=a Oras DIEPERINK ” 55 = 4 xX Metre.27— 391285 Mean for the three observers : Measuring bar = 4 « Metre 27—391’.84. BAKHUYZEN 7. Mean errors. The errors in a series of observations are caused by the pointing- and reading errors of the microscopes, the change in the distance of the microscopes, erroneous determinations of temperature and personal errors of observation. Owing to the excellent optical qualities of the microscopes and the fine sharp end lines, the errors in the reading and pointing of the microscopes are small. From the observations for the determination of the periodic screw-errors we found for the mean reading-error, from the mean of two observers, + 04,32: this error leads to a mean error of + 0,17 in one series of observations. The influence of other sources of error are difficult to determine separately. We shall therefore try to calculate their combined effect, in different ways, in order to find out, what systematic errors are to be feared, and how the series of observations are to be combined in order to obtain a result in which the effect of the systematic errors will be as far as possible eliminated. 309 In the first place it was investigated, whether there was a systematic difference in the results of a series of observations according to whether the microscope was pointed 8 times on the metre and 4 times on the measuring-bar, or 4 times on the metre and 3 times on the measuring-bar. For this purpose the mean was first formed of corresponding series in the positions A and #4, in which the number of times that the microscope was pointed on the metre and therefore also on the measuring bar, was the same. According to these averages the mean error of observation in micromms was: WILDEBOER DIgPERINK BAKHUYZUN Mean Ott 0.366 0.509 0.420 (I) After this the average was formed of corresponding series in A and & in which the aumber of times pointed on the metre and on the measuring bar was unequal; according to these averages the mean error of observation for a series was : WILDEBOER DinperiInk BAKHUYZEN Mean 0.496 0.330 0.440 0.428 (IT) From the agreement of the two means we may infer that there is no systematic difference in the series with 3 or with 4 pointings on the metre or measuring bar. It was next investigated, if there was a systematic difference in the results of series in which the metre was in a different position relatively to the observer, i.e. in the results of the series / and 7. This was done in two ways. 1. The differences were found of the corresponding series in Which the observer and the metre were in the same position in which differences the systematic error referred to plays no part. The mean error for a series 7 deduced from this is: WILDEBOER Divperink BAKHUYZEN Mean 0.450 0.346 0.492 0.434 . (IIT) After this the mean was formed of all the corresponding values found with the same position of the observer, in position / as well as position 7 of the metre. The deviations of all these values from their mean, in which the influence of the systematic error is present give the following values for the mean error of a series. WILDEBOER DiePERINK BAKHUYZEN Mean 0.454 0.594 0.636 0.564 (IV) 2. The means were found of an observation-series in position A and in a corresponding series in position B, in which the metre 24 Proceedings Royal Acad. Amsterdam. Vol. ¥ VII 310 Was in the reversed position relatively to the observer, i.e. 7 and /. In these averages the systematic error is thus eliminated. In this way the mean error of one series was found to be WILDEBOER Dinprrink BAKHUYZEN Mean 0.370 0.296 0.507 0.401 . (V) If on the other hand a series in position A was combined with one in 4, in which the metre was in the same position with regard to the observer, so that the systematic error was not eliminated in the mean, the mean error was found to be: WILDEBOER DinpuriInk BAKHUYZEN Mean 0.424 0.755 0.768 0.666 . (VI) Both the double sets of mean errors (III) and (IV), and (V) and (VI) show clearly, that there is a systematic difference in the results of the series r and /, or with different positions of the metre relatively to the observer. In order to remove the error, therefore, the mean of two corresponding series of observations must always be taken, in which the metre is in different positions with regard to the observer. We further computed the mean error from all the series of ob- servations for the same portion of the measuring-bar, without regard to the position of the metre or of the observer, in which therefore the influence is present both of the position of the metre and of the observer. First the mean errors were computed for each observer separately. This gave WILDEBORR DIuPeERINK BAKHUYZEN Mean 16222 0.805 0.955 1.009 , (VII) Finally the results of the series for the same portion of the measuring bar in all positions of the metre and of the observer for all three observers were averaged, and the mean error determined from the deviations of each of the results, which must therefore contain (1) the influence of the position of the metre (2) the influence of the position of the observer, (3) any other possible influence of the observer. The mean error was then found to be: 15002, 0, on te 2 Se ODL The difference of the mean errors (VII) and (IV) shows, that the position of the observer has a marked influence, on the other hand the agreement of the mean errors (VII) and (VIII) shows, that there does not appear to be an influence due to the observer other than that which depends upon the position of the metre and observer. We may further conclude from the values found, that if the two systematic errors mentioned are elimimated, the mean error of a oll series of observations is the mean of the values: 0.420 (1), 0.428 (IN), 0.434 (IIT) and 0.401 (V) therefore: m— a= O42 As the measurement of each portion of the measuring bar was obtained for each observer by taking the mean of 8 series of obser- vations, the mean error in the length of each portion measured by one observer is: 0#.421 ae Se ea V8 and as the whole measuring-bar consists of four portions, the mean error in the length of the bar for each observer is UPA (7 4 = SOK 298. If the value of this mean error is formed by comparing with each other the lengths of the measuring-bar according to each of the three observers, we obtain: = 0#2355. From the agreement of the last fwo values we may conclude, that in the results obtained the influence of the observer and of the position of the metre and the measnring-bar is eliminated, and that therefore, beyond the influence of the temperature determination and errors in the coefficient of expansion, the mean error in the length of the whole measuring-bar expressed in the length of metre 27, determined by one observer, is equal to : == (04.36. and is therefore for the mean of the three observers: 0.36 = — = 04205 V3 Geodesy. — “Comparison of the Dutch platinum-iridium Metre No. 27 with the international Metre M, as derived from the measurements by the Dutch Metre-Commission in 1879 and 1880, and a preliminary determination of the length of the measuring-bar of the French basc-apparatus in mternational Metres.” By Prof. H. G. van pe Sanpe BAKkHUYZEN. The main object of the measurements made by the Dutch Metre- Commission (BosscHa, OvuprMans and SramKart) at Paris in 1879 and 1880 was an accurate comparison of the two Dutch metres 19 and 27 with the Métre des Archives, the various papers published by Bosscna on the subject show, how very well this object was 214 3li2 attained. As we shall have to refer to these papers more than once we shall quote by volume and page from “Bosscua’s Verspreide geschriften” (B.’s collected papers) published in three volumes. The importance of a comparison of the Dutch metres with the International platinum-iridium metre kept in Paris was, however, not lost sight of by the Commission. It was probably by their request, that in the protocol drawn up of the handing over of the two metres by the French Section of the international Metre-Commission to the Duteh delegates BosscHa and OvupgEMANs it was specially stated : Cette remise est faite sous la réserve du droit qu’aura le Gonver- nement des Pays Bas de faire effectuer les comparaisons entre ces metres et le prototype du Bureau international des poids et mesures pour la determination de leurs equations a VPégard de ce metre. However, not only did the Dutch Commission leave open the possibility of obtaining a direct comparison with the international metre later on, but also by making determinations at Paris of the differences between the Dutch metres and metres which are in their turn connected to the International metre, they took care, that the relation between the lengths of our metres and the International metre can be calculated. Although all the observations which are required for these caleu- lations are fully communicated in Bosscna’s papers and only very simple caleulations are sufficient to obtain the relation in question, the results have not been published either by Bosscua himself or as far as I know by anybody else; and as they are needed in order to express the length of our base-line in international metres, I shall here shortly communicate them. The relation to the International metre is obtained not only through the metre des Archives A (see further down), but also through the two Metres /, and 20, both of the second alloy of Marrnry, of which .J/ is also made; in addition use is made of the two metres 23 and 27 both of the first alloy (metal du conservatoire). For the reduction of the difference of length of 23 and /, the difference of the coefficients of expansion of these two metres is reqnired, and I shall therefore try to derive its most probable value from the results communicated by Bosscna. In the first place we may conclude from BosscHa’s calculations, that the metres of the second alloy have all got the same coefficient of expansion (Vol. III, p. 74—76). The equality of the coetficients of expansion of the metres 1, 3, 12, and 13 of the first alloy is also demonstrated (Vol. I[l p. 77). According to Fizeau’s measure- ments the coefficients of expansion of the metres 19, 27, and 23 of the first alloy would also have very approximately the same value (Vol. Il, p. 314), whereas according to the measurements of the Dutch Commission the difference in expansion of the metres 19 and 23 is too small to be observable. (Vol. II, p. 314, 315). This is not quite in accordance with Fizwau’s results (Vol. II, p. 823) obtained at 12°, 42°, and 62°, as these give for 19 and 27 somewhat different values. but if the quadratic term is taken into account, the coeffi- cients of expansion at 40°, the mean temperature used by Fizvav in his measurements, would be according to his formulae 8’.74 for 49, and 8”.75 for 27, so that in connection with the equality men- tioned above of the expansion of the 4 first-named metres of the “metal du conservatoire” and the equality of the expansion of 19 and 23 found by the Dutch Commission it may be inferred, that all the metres of the first alloy have also the sume coefficient of expansion. The next question is, what the difference is between the coefficients of expansion of the first and second alloy. According to measurements by Brnorr and GuiLLaume with Metre 6 of the 2°¢ alloy the mean expansion between O and 20° per degree and per metre is 8’.617; according to measurements by Fizeau the mean of the same expansion for metres 19 and 2 the first alloy is 87.537, i. e. a difference of 0.408. It is necessary, © i however, to observe, that the two values were obtained by altogether different methods, that of Brenorr and GuiniaumE by ordinary measure- ments of length at different temperatures, that of Fizeau by his well-known interference-method. Against these we have the determinations of the differences in expansion of metre 6 of the 2°¢ and of metres 1, 3, 12, and 13 of the 1s* alloy (Vol. IIL p. 77) all from ordinary measurements of length at different temperatures. As the result of these 0”.02 is obtained as the average of the differences. Taking into account, that, where the methods of observation differ, systematic errors in the differences are possible, it seems to me probable, that the latter result is the more trustworthy. In the reduction of the Dutch metre 27 to the International metre the difference in length of metres 23 and 27 also plays a part. For this difference two values have been determined; in 1879 the Dutch Commission found 27 — 23 = 0.92 + 0*.031 (Vol. I, p. 297) and in 1880 the same commission found 27 —- 23 = 0.41 + 07.073 (Vol. If p. 334). Of the latter value no further use has been made by Bosscua; it seems to me, however, that it is preferable to use the mean of the two results, taking into account the respective weights. In that case the result is Reduction by means of I,. From several series of observations at a’ mean temperature of 16°.44, Tresca found (Vol. III, p. 14) 23 = J, + 14.24. Adding 0°.02 < 16.44 = 07.33 for the reduction to 0° the equation becomes 93 = 1, 1657, further 27 = 23-+ 0.84 (see above} and I, = M- 5.94 (Vol. Ill, p. 70), so that 27 = M+ 8.35. Reduction by means of 20. From three series of measurements one by Bosscua and two by Tresca, follows : 23 = 20 + 7#.19 (Vol. III, p. 24), further 7} ee 23 ais Or. can (see above) and Fol. Til, pesto} so that 27 = M 4 8.99. The mean of the two reductions is 27 = M+ 8+.67. If the 5 above mentioned different equations containing 4 unknown quantities, are taken as all equally accurate and if they are then solved by the method of least squares, obviously the same value for 27—JV is found, while the mean error of each of the equations is + 07.32, that of 27 — 17 =8".67 being + O?.45. A value for 27— J/ is also arrived at by using the comparisons with the “Metre des Archives’ A, viz. 27 = A+ 64.11 (Vol. II, p. 323), A=M-- 2.63 (Vol. Ill, p. 24). 70); Hence 27 —M+ 8.74. This result agrees very closely with the value found above. But, as it is largely based on the comparisons which have also served for calculating the previous result, no particular importance can be attached to the accordance. Considering the value of the mean error + 0.45 a direct comparison of 27 and WV would certainly seem to be desirable. If the length of the measuring bar of the French base-apparatus in terms of metre 27, as given in the previous note, is now expres- sed in International metres by means of the equation 27 = J/ + 87.67 the result is; L=4 M— 391-84 + 4 & 84.67 =4 M — 3574.16. The value of Z had been determined several times before at the “Bureau international des poids et mesures” at Breteuit; on these occasions the following values were obtained, leaving out the some- what uncertain correction for the “change in the molecular equilibrium”. 1903 March 4 M—277".6 Breteuil 1904 June —-373 .5 re 1907 February —-363 .7 is 1909 February. —356 .8 7 1909 December —358 .4 3 1910 December —— St ae - 1911 June 515) a) “ 1911 Sept.-October - 398 .4 ; 1913 April —348 .7 “ 1913-14 Dee.-January —357 .2 Delft. It appears from these numbers that during the first years up to 1909 the bar increased in length. From that year onwards the length seems to have remained practically unchanged; only in April 1913 a further very marked increase in length shows itself, of which, however, no trace is found in the measurement made by us. In view of this contradiction a new determination at Breteuil of the length of the measuring-bar is desirable; col. LALLEMAND, chief of the geodetic department of the Service géographique de l’armée, and Monsieur Bunorr, Director of the Bureau international des poids et mesures at Breteuil, have both promised to undertake this comparison shortly. Postscript. A few weeks after the meeting of our Academy I received from Monsieur benoit a letter in which he communicated the results of an elaborate investigation concerning the length of the bar of the French base apparatus. He and Monsieur Mauprer compared in the Bureau at Breteuil first that bar and three other ones each with the prototype and afterwards the four bars with one another. Benoit found as final result for the length of the French bar, with- out correction for the change in the molecular equilibrium: L, = 4 M — 3487.23 , almost exactly the same value as that found in April 1915. On the average the length determined at Breteuil is therefore 8’.7 greater than that determined at Delft. In order to find what may be the causes of that difference I 316 used the formula by which the length of the bar at zero is derived from the measurements. During the measurements at Breteuil the temperatures of the bar were, according to Brnorr’s statements, not very different from 15°. I bave not here at my disposal the data of the exaet values of the tem- peratures during the measurements at Delft, but I know that they presented no great deviations and, if I am not mistaken, the extreme differences from the mean, about 15°. were not greater than about two degrees. We can therefore combine the observations at Breteuil, and also those made at Delft each into a mean result, at a mean temperature, and we then obtain the following equation, in which the letters without a dash indicate the values determined at Breteuil, those with a dash the values determined at Delft: Lp=L tel, T=4l,+48t+S8 , p= +e'Lh | T’=41,'+48t-+S, L,— bhi eh, Fee Ll Poe AG 1) 468) ae In these formulae Z is the length of the bar, 7 its mean tem- perature during the measurements, « the adopted coéfficient of expansion of the bar, / the length of the comparison metre, ¢ its mean tem- perature, 3 the mean expansion of the metre for 1°, S the difference of the length of the bar and the fourfold of the length of the com- parison metre, determined by means of micrometrical measurements with the microscopes; 7’ and 0, as indices of LZ and / indicate the temperatures to which these lengths have been reduced. The differences of the temperatures 7’— 7” = AT and t—t = At, and also the differences in the adopted coefficients of expansion 8— p'=Ap are small, and for the value of the coefficient of ex- pansion «@ and e« the same value has been adopted in Breteuil and in Delft; the last of the three equations may therefore be put approximately into the following form: L,— LL, =4L=—aLAT+ 4Al 4 4pAt 4+ 4tAg+ S—S’. When A7’, At, Al, As and S—S’ have their exact values, AZ is zero; the value 8.7 for ASL found from the observations is there- fore only a funetion of the errors in those values, and putting on the first side of the formula AZ = 8’.7 the quantities on the second side represent those errors. We will consider each of the terms separately. 1. «LAT. T and 7” have been determined in the same manner by readings of the thermometers laid on the surface of the measur- ing bar within the thick aluminium case; the temperatures in both comparators were fairly constant, and the value of @ is small; eZ for O°. is about 07.7. In view of the great value of AZ, we may therefore neglect that term. 317 2. S-—S’. Taking into account the precision of the micro- metrical measurements and the small influence of the systematic errors in the measurements made at Delft, as appears from the values of the mean errors, that term may also be neglected in trying to explain the great value of AL. 3. 484¢. 43 is about 34” and Af is the difference in the errors of the mean temperatures of the metre, determined at Breteuil and at Delft. When we assume, that in the perfectly constructed comparator at Breteuil the error in the mean temperature of the metre was zero, the effect of an error of 0°,1 in the mean tempe- rature of the metre at Delft on its length is 3”,4, and in order to gel a positive value of AZ the temperature of the thermometer laid on the surface of the metre must be lower than the tempe- rature of the metre itself. During the measurements the temperature of the metre was slowly rising, it is therefore improbable, that the teimperature of the thermo- meter should be systematically lower than that of the metre, and it is difficult to explain the positive value of AZ, either totally or for the greater part by an error in Af. 4. 44/7. I cannot say, what is the real value of A/, the error of the difference I adopted between the length of metre N°. 27 and the International metre.. The mean error of the adopted value of 44/ is +1”.8. It is therefore possible that a part of the AZ may be accounted for by an error in the adopted difference, but it is improbable, that it should explain the whole value, 8%.7 of AZ. 5. 4t43. We can determine a fairly probable value of that term. According to a telegram from Monsieur Brnorr, the mean expan- sion for 1° between O° and 15°, used in the reduction of the measurements of the prototype, made of the second alloy, is 8’,662, the mean expansion per degree between the same limits adopted in my reductions of the length of N°. 27 made of the first alloy is 8’,493 ; the difference between the two is 04,169. As a_ result of direct comparisons, the mean difference of the expansion of the metres of the first and second alloy is 07,02, as I stated above. If we assume, that the coefficients of expansion of the metres of the second alloy are really equal and that it is the same with the metres of the first alloy, which assumption after the researches of Bosscna is very probable, the error 43 would be equal to 0.169 —(0.02 = 02,15. As ¢ is about 15°, the term 4¢Af is 9”, almosi equal to the value 87,7 found for AL. Although I do not pretend, that the assumptions made in order to explain the difference between the results obtained in Bbreteuil 318 and Delft are absolutely certain, still I believe that the probability is not small, that the difference between the assumed and the real coefficients of expansion of the prototype at Breteuil and the metre N°. 27, is for the greater part the cause of the value of AL. It remains absolutely uncertain, what the real coefficients of expansion of the metres are and also whether the coefficient of N°. 27, determined after Fizuavu’s method, merits greater or less confidence than that of the prototype deduced, as I believe, from direct measure- ments at different temperatures. But whatever it may be, it is of great importance, and it is in my opinion the chief result which may be deduced from my discussion, that when a direct comparison of the metre N°. 27 and the international metre shall be made, according to the right given to our government, it will not be confined to a comparison at a mean temperature, but that if possible, the absolute coefficient of expansion of our metre, and certainly the difference in expansion of N°. 27 and the prototype will also be determined. Lenk (Switzerland. Physiology. — “On the formation of antibodies after injection of sensitized antigens.” Il. By Dr. L. K. Worrr. (Communicated by Prof. C. Eyxmay.) I. As a continuation to my series of experiments given in the first communication, | have examined the immunisation power of a mixture of erythrocytes and specific serum with a surplus of amboceptor. It is generally stated in literature that this power is very slight or that it does not exist at all; in my two series of experiments I have also found very little or no formation of amboceptor. I shall communi- cate one of the series. Horsecorpuscles — specific rabbitserum */,,, strong. Binding power of 1 ecm. 5°/, blood + 7 doses. Mixture of 40 c.em. serum and 20 e.em. undiluted blood i. e. 20 doses amboceptor, so a great surplus. Rabbit 149, 73 and 76 each get 20¢.em. of the mixture intraperitoneal. x, ADS Oennavelecale =, - 6'/, ,, undiluted blood only % Titre after 1 day after 7 days after 12 days 149 Yi) weak ae Ear (i aif 1/,, weak 1/,, weak 76 “ie ‘/,, weak ha 179 7s ia “en 70 aa iNet Woon @ re “Laoo AGE weak, 319 / So with the rabbit 149 and 73 we do not find a trace of active immunisation, only of passive; rabbit 76 after 12 days shows a small (active) increase of titre. The controlling rabbits however have distinetly formed amboceptor. The second experiment with cattle corpuscles had a_ perfectly analogous course. With these experiments we cannot inject intra- venously; the animals which are intravenously injected with such a great quantity of serum and corpuscles die of anaphylaxis. II. I have now put to myself the question what happens with the sensitized corpuscles after the injection into the rabbit or cavia. Therefore | have for the time being confined myself to the sub- cutaneous resp. subconjunctive injection; the intravenous one is very difficult to follow, the progress of the peritoneal one it mostly known ; besides the subcutaneous is the only one that is to be considered with regard to man. I expected that in keeping with what happens in the peritoneum, viz. a solution of the sensitized red corpuscles in a short time, the corpuscles would also dissolve in the subeuta- neous tissue. I have taken the conjunctiva as the spot where to inject: there the phenomena are to be controlled better than any- where else, and one can easily cut out little pieces for microscopic examination. Well then: if we inject foreign corpuscles under the conjunctiva they are generally gone after one, and certainly so after two days. As they have no movement of their own, we must assume them to be led away along the lymphpaths a leading away by phago- eytes in such a short time is not to be assumed. It is however different if sensitized corpuscles are injected; these remain on the spot; they do not dissolve in any quantity worth mentioning, and if one microscopies the place after a longer or shorter space of time (after cutting out, fixing, embedding, and colouring) one will find an important number of leucocytes between the corpuscles. After 6 to 8 days only the corpuscles have generally disappeared; sometimes however they are still to be seen after 10 to 12 days. During the first few days one mostly finds polynuclear small leucocytes, later more great mononuclear ones. Now the question is how to explain this conduct. For this we must examine three things. Ist. How is it that the sensitized corpuscles which are injected subconjunctively do not dissolve, while those injected intraperiton- eally do. 2nd, Why do the sensitized corpuscles remain in the same place, whereas the normal ones are carried away. 320 3°'. What happens finally to the sensitized cells; what do the leucocytes do. Let us first answer the first question. Here we must ask at once if there is complement in the sub- cutaneous lymph. As far as I know H. Scuneiper’s') researches about this subjeet are the best; he found that the tissue lymph which is obtained by bringing a piece of cottonwool under the skin, and afterwards pressing if out, contains very little complement indeed. One always finds a littlke more complement than would really be the case if we had pure tissue lymph; a slight mixing with serum can of course hardly be avoided. It goes without saying that in this Way we cannot be certain to get a liquid, agreeing with the tissue lymph; the piece of cottonwool naturally works irritating; an inflammation arises. But the injection of the corpuscles also causes an inflammation, and as such these two processes are equal. I have also made some complement titrations to the guinea pig and rabbit, of subeutaneous fluids obtained in this way. For the solution of my haemolytic system I needed : 1/ I. Fresh guinea pig serum Hori Gitte Subcutaneous fluid “om Cxe lta. [I]. Fresh guinea pig serum eeGRC NN: Subcutaneous fluid Win (OsK0e Ul. Fresh rabbit serum Wf, CxO. Subeutaneous fluid 0,6 c.cm. no haemolysis ! Siowing fluid 0,6 c.cm. trace of ,, So we can affirm ScuNemeEr’s experiments and assume very little or no complement to exist in the subeutaneous cellular tissue ; and we need not be astonished about the sensitized corpuscles not dis- solving, when being injected subcutaneously. Now we must answer the second question. The sensitized cells remaining in the same place was supposed to be due to the agglu- tination which always accompanies the sensitizing. I did not succeed in obtaining an immune serum prepared in the usual way, which did not at the same time agglutinate. As I did not know any method to separate amboceptor and agglutinin when I started my experiments, | took another way to prove that the remaining of the bloodcells was owing to their being agelutinated and not to the sensitizing. | therefore agglutinated the bloodecells in a different way, and now found that clinically and histologically the same was to be seen after injecting these corpuscles as after injecting sensitized (and 1) Arch, f. Hygiene 70. p. 40 seq. 321 at the same time agglutinated) cells. In the first place T used a colloidal solution of SiQ, for it. All the red bloodcells I used (rabbit, guinea pig, horse, cattle, dog) were agglutinated by it, be it in various concentration. Only the SiO, had no effect; it caused neither swelling, nor leucocytosis. It had been prepared by saponifving Siliciumethylether (Itan_BauM) with greatly diluted hydrochloric acid. Colloidal SiO, prepared in a different way had the same effect. Now one might object against this experiment that the SiO, not only agglutinates the bloodcells, but that it also sensitizes them; for together with guinea pig serum ina great quantity, it can dissolve some kinds of blood. Therefore I took refuge to the vegetable agglutinins which are found in the bean, pea, lentil, and in the seeds of Datura Stramonium. In all these cases the result was the same: the bloodcells always remained there ; the conjunctiva also showed the wellknown bluish-red change of colour after some days, and histologically the image was always the sane. It goes without saying that with all those experiments the sterility was taken into consideration as much as possible. *). In order to make quite sure, however, that only sensitized and agglutinated corpuscles did not show the phenomenon, I examined some thirty rabbits out of my collection on haemolysin and agglu- tinin against sheep-erythrocytes, and I really found some sera which did contain baemolysin, but only little agglutinin. I repeated the experi- ments with these sera; but the results were not very distinct : there sometimes was a difference, but it was not big enough to draw a certain conclusion from it. This is because all the sera employed were rather weak (ambo- ceptor */;,—'/,9.) and so a rather big quantity of serum was necessary (+ 3 em.) to sensitize the cells. Normal rabbitserum generally con- taining some agglutinin, we did not sueceed in this way in obtaining a suspension of sheep-erythrocytes which are sensitized but little or not agglutinated. Yet I ean communicate one experiment which came out rather well: Serum rabbit 73 titre amboceptor ‘/,, very little agglutinin. cml tt! 87h o, oe srneanly a>, much iy » 100 1/, ecm. sheep-erythrocytes is digested with += 3 cem. serum 73, just as ‘/, ecem. with +3 ecm. serum 147. The suspensions are centrifuged and the corpuscles are taken up in 1 cem. saltsolution. Erythrocytes 73 are injected on the right, erythrocytes 147 on the 1) I did not use ricine because the poisonous qualities of this substance would have injured the image. 322 left under the conjunetiva of rabbit 172. The serum of this rabbit contains neither amboceptor nor ae in a noticeable quantity against sheep-erythrocytes. After one day there is a distinct difference. There is very little swelling and redness (+) on the left, but very strong swelling and bluish-red change of colour (+-+-++) on the right. The next day the difference is a little less, but still it is distinet. Consequently it was desireable to obtain a serum which sensitized strongly (at least ), but whick agglutinated little or not at all. As there was no question of a chemical separation — all the litera- ture tells us that all suchlike attempts lead to no result whatever — such serum had to be obtained in a different way. In the literature 1000 about the heterogenetical antibodies is mentioned that serum of a rabbit which had been in some way prepared in order to get hetero- genetical amboceptors against sheep-erythrocytes, would then contain no more agglutinins than are found in normal rabbitserum. My experiments in this direction have however not yet led to the desired result. One rabbit which was injected with pempeie had a serum with titre '/,,, against cattle-corpuscles, and a titre */, 999 against sheep-corpuscles. Hoa eet it very clearly contained agelutinins against the latter. The same thing appeared with two rabbits which had: been injected with horse-kidney extract. The titre against sheep- blood was ‘/,,, of both of them. Both distinctly contained agglutinins, if only little. The sheep-corpuscles treated with this serum remained for some days in the same place, after having been injected under the conjunctiva. So in this way I could not prove awith certainty that the agglu- tinin is the cause of the prepared corpuscles remaining under the conjunctiva, * 11. I will now mention some experiments which have been made in connection herewith, but which do not directly bear upon the subject mentioned in the title. | have asked myself whether the same difference as is mentioned above, is also found when non-prepared bloodeells are injected subconjunctively partly with prepared, partly with non-prepared animals, and whether here too the agglutinin was of any importance as to the remaining of the erythroeytes. And this has indeed appeared to be the case. Rabbits with serum containing amboceptor (and agglutinin) still show a strong swelling under the conjunctiva after one or two days after having been injected with the erythrocytes in question ) Note added during to the correction: Now | had more success with this experiment. The heterogenetical serum which | now used was '/aoo9 strong. oe (in my experiments they were horsecorpuscles), whereas the controlling animals showed hardly any swelling after one, and no swelling at all after two days. In accordance with this the tissue fluid (obtained in the above mentioned way with cottonwool) obtains amboceptor as well as agglutinin, if they are in the serum. Rabbit 160 immunized against cavia-erythrocytes. Serum agelutination '/,, amboceptor ‘/,, weak (+--+) fluid * oe * ay key aie Rabbit 192 immunized against horse-erythrocy tes. Serum agglutination */,, amboceptor jluid 3 1/7, weak ,, 1/,, nearly / /20 Rabbit 147 immunized against cattle-erythrocy tes. Serum agglutination ‘/, amboceptor */,, fluid 1 mie ms lee I have now investigated if it really is the agglutinin which deter- mines the difference. Rabbit 116 agglutination strong, amboceptor ', 100° Rabbit 148 » very weak, fe eee Both rabbits are subeonjunctively injected with '/, c.em. washed sheep-ery throcy tes. After one day there is a very strong bluishred swelling with 116, with 148 hardly any swelling; after 2 days still a strong swelling with 116, with 148 nearly all the blood has disappeared. A stronger proof is given by the rabbits that were injected with horsekidney extract’). Although the titre against sheepcorpuscles was not high here (with both */,,,) a great difference was stated with the controlling animal (titre also */,,,). After one day hardly any blood was to be seen with the first, contrary to the controlling-animal. 1 think these experiments are of some importance. For in the latest great report about the agelutination known to me, that by Patraur*), the author says on p. 515: Ob Agglutination auch im Organismus stattfindet erscheint recht zweifelhatft. At least I believe I have proved the haemagglutination to take place in the subcutaneous tissue. [| only want to insert bere that 1) These are the same animals as were mentioned above: their serum did contain agelutinin, but much less than the animals immunized in the ordinary way. That here we get no agglutinin effect, and that we did when mixing the serum with the bloodcells in vitro, may be explained by the fact that the agglu- tinin can pierce with so much more difficulty into the tissue fissures and reach the bloodcells than when a great quantily of serum in vitro ts directly added. 2) Kotte und Wasserman, lle Auflage, Il, p. 483—654. 324 the phenomena mentioned above belong to the department of local anaphylaxis (Phenomenon of Artuus). As far as 1 know they have not been studied as to the immunisation with bloodeells; they have with serum or bacteria. This really is only a question of name however: the essence of local anaphylaxis is still as unknown to us as that of general anaphylaxis. In any case we can see by the bloodcells that the disintegration of albumen is a very slow one; I do not wish to deny however, that part of the flood of leucocytes is owing to this disintegration. What has been stated somewhere else viz., a primary necrosis of the tissue and after that an infiltration of leucocytes '), I have never observed; I could sometimes also state a toxical influence of the injection out of an oedema of the cornea: but this happened very rarely. Then one should not directly compare the phenomena of subeutaneous injection with those of intracorneal injection (WESsSELY, von Sziny); in the latter ease the current of fluid is much slower, so that great differences can occur by this. It would however lead us too far if we entered into this more closely. We must now still treat of the third question: what happens to the sensitized (agglutinated) cells, and what do the leucocytes do in this process? I must first of all mention that 1 could not find any difference between histological images when injecting sensitized or only agglutinated bloodeells. ‘This, however, is in keeping with other experiments. For, there being a great difference in vitro between the phagocytosis of sensitized (opsonized) and nonsensitized cells, -— the former are phagocytated, the latter are not, when brought together with suitable leucocytes — one does not find back this difference in vivo when injecting the cells into the abdomen, previously injected with broth. AcHarp and Forx’*) some time ago tried to find the causes of this difference, but in vain. I did not succeed either*). We need not be astonished however, when finding the same conduct in the subcutaneous tissue as in the prepared abdomen. Are the erythrocytes now phagocytated? Notwithstanding my observing a great many preparations, I did not succeed in getting any certainty whatever about this in my histological sections; to form 1) H. Fucus und Metter, Z. f. Ophthalmologie. Bd. 87, p. 280. 2) AcwarpD and Forx Arch. de Medecine expérimentale et d’anatomie Patholo- gique, January 1914. 3) Prof pe Vries advised me to add to the mixture (foreign bloodcells, fresh serum (without opsonins) and leucocytes) scrapings of the peritoneum endothelium; with this | had no suecess either. 325 an opinion about it is, however, very difficult; leucocytes are always among a great number of red cells and the sections are always thicker than one red or white cell. Anyhow, it seems very probable to me that this must happen. For: 1. the red cells disappear atter 6—8 days. 2. in vitro they are easily phagocytated. 3. The subcutaneous cellflaid and the leucocyte extract do not contain an unspecific haemolysin (ScuNumwer: |. ¢.; this concerns polynucleous (mikrophages) as well as mononucleous cells (macrophages). I have tried after one or two days to cut out the swelling (after injecting the sensitized (agglutinated) cells), and then to spread them out on a coverglass: these preparations too gave bad images; princi- pally by the stickiness of the substance: I did not see a distinct phagocytosis. I have here always spoken about sensitized cells without wishing to form an opinion about the open question of identity between amboceptors and opsonins and tropins. (NEUPELD *) SaTSCHENSKO’’) ). The following experiment will show that there can be amboceptor as well as tropins in the subcutaneous cellular tissue. A piece of cottonwool was entered under the skin of the abdomen of a prepared rabbit (against sheep-erythrocytes) and the fluid was examined after some hours: in vitro it sirongly stimulated the phagocytosis of sheep-erytrocytes by rabbit-leucocy tes. As a summary we can draw the following conclusions: 1. When using red corpuscles loaded with amboceptor as antigen one should remove all surplus of serum. 2. Sensitized and agglutinated red corpuscles, when injected sub- cutaneously, remain in the same place for a long time; non-treated cells are soon led away. 3. This will most probably be the consequence of the agglutination, not of the sensitizing. The same happens to non-specific agglutination — also when it concerns the animal’s own cells. +. With prepared animals possessing agelutinin, the cells injected also remain in the place where they have been injected. So agglu- tination in vitro also takes place; this is not the case with animals which only possess amboceptors (opsonins) and no agglutinins. 5. The subcutaneous lymph contains very little or no complement, it does contain amboceptor, agglutinin, opsonin (tropin). The above will show my experiments not yet to be complete. They require to be completed as to the question to what “1) Arbeiten aus den Kaiscrl. Gesundh. Bd. 25, 27 en 28. *) Arch. Se. biol. St. Petersburg. XV, blz. 145 1910. a Proceedings Royal Acad. Amsterdam. Vol. XVIL. extent the immunizing power of red corpuscles loaded with antibodies is related to that of normal cells as to the tropin- and the agglutinin- content of the serum. We may suppose, also in consequence of the above mentioned experiments, that the content of antibodies of serum and subcutaneous lymph goes parallel and so we shall not investigate this point separately. IV. After the immunisation with sensitized erythrocytes the one with mixtures of serum and anti-serum comes next. I have not stated the amboceptortitre (to be stated by means of complement fixing) but the precipitincontent. Where the results do not differ much from the experiments with sensitized erythrocytes, 1 think I can suffice with only stating the precipitin. 7A Rabbits, injected intravenously with horseserum, 0,5 ¢.c.m. per ke. (made inactive). > Rabbit weight titre after 3days after 5 days after 7days after 12 ds. after 14 ds. 103 26007 3 =— of z Pa t= ae s} "oo hoo 104 2850 — lB ee =) \s | — NE EF Yoo weak — /r900 105 2830 i Ne a A 7 2 ¥ — 5 - Thooo » "/r000 106 1650 tS Zs vee z\ he x "hoo “/iooo Weak 107 2100 — a8 = pe SI Mio) weak Th o00 /B. Rabbits injected, intravenously with 0,5 ¢.em. horseserum (inactive) + 1 ccm. precip. serum ('/,,,,), after this mixture had stood for 1 hour. Rabbit weight titre aft. 3days after 5 days after 7 days aft. 12 days aft. 14 days 8 = 2150 — ges —(og “ho "hoo Yoo 109 2150 = 5 5 5 — E 5 ho Thooo Miooo a ee — ie 2 © et par = ae some . ‘hoo ‘A000 35 = at ys — ea te — (horse serum 5 a fellas /ho00 / 1000 112 9150 — et = s /ip Weak Mhogo weak 1/009 So here we do not see a distinct difference between the A and B group. Il A. Rabbits, injected intraperitoneally 0,4 cem. human serum >} * per kg. Rabbit Weight after 5 days aft. 7 ds. aft. 10 ds. aft. 12 ds. aft. 14 ds. 67 2150 — g ; “= tho 000 Mhonoo 78 2450 — 5 5 = hho hoo T/1o99 Weak 70 1900 — /s 5 = Vio ooo 1 0000 60 2320 — jog Wo? 1/00 1 000 M1000 76 1820 — a 1h hoo hoo 10000 II B. Rabbits injected similarly 0,4 eem per keg. + 3.6 cem. antiserum (‘/,,,, largely). The mixture had stood for 4 hours, a thick precipitate has been formed. O26 alt. 7 dss atte VONdss © Jatt) 12) ds. “aft. 14 ds: 9 =) or a 7 Rabbit Weight 2100 —— 5 \ - hoo “hooo 1000 114 3200 — (: 2) = = = “ho 113 2000 — /¢§ i ; = = et tho 112 2550 —_ (2 :| = =a “ooo "/igo Weak 7/Al 1600 pil = Te a 1h ooo 1/0000 After 17 days the titre already went back. Here we can see that, whereas of the series B three rabbits distinctly lag behind, two of them reach as high a titre as the A rabbits. Knowing (UsLENAUTH) that accidental failures in the preparation of precipitinholding sera are not to be avoided, I should not wish to draw any other conclusion from this than that a good formation of precipitins is also possible with mixtures of serum and antiserum. I have also taken the following series of experiments. III. Rabbit 140 1 c.cm. horseserum intraperitoneal. ee kG * 5 » + 1 cem antiserum (*/1000) » 142 - ‘ Sng crt, Sha ss e 99 33 An Wey SIMO! Gata Perio teas OO 7? este oe 7: 8 2 0 Diet! Ae i 42 5 x ad foter dy MES, es 48 3 93 Geeta OV ee Rabbits after 8 days 140 oe 116 ‘Tipo 4Wweak. 142 a epaiate Mn v9 Hitent 121 t/acus 8 piaaen 42 aetet 48 — So here too we find a rather important formation of antiserum with rabbits, which, with the serum, bad also got antiserum. IV. Rabbit 155 50 ¢.em. antiserum ‘/,,,, -- 2¢.cm. horseserum intraperil. per is6: 30, ‘ Fiat alae 57 10) | ‘ nae ‘ marissy On, 3 ia) a : meson dS. .. y ae ; i 328 Rabbit after 1*/, hour after 1 day after 3 days after 5 days contains — | » contains / contains / contains es se serum | horse serum horse serum horse serum dd - —\+++4¢—\) ++ + 156 Sie aby a ge ++ as, oy < — eee z 4? Pah ae shaRAE = aioe ++ 169 aes : after 7 days. aft. 10 ds. aft 12'ds. att. 4vdse Vath diadee contains horse serum 28 aos Sk <> 1/ 1) . 1 155 = + ailing BS 5 100 /1000 Ww. nee LOG Staats > IE a 3 > ‘L100 weak L100 WwW. “hres Si | 1/ oe) 1 9 1 157 — — fio a oa : ho Ww. KO 1/ Aes / 1 1/ 158 — staat 10 3 a /100 /100 /100 1G eee re a ee ve om Here too we also see some irregularity: (rabbit 157 immunizes somewhat less than the other, but even a mixture of 25 times more antiserum than serum still has immunizing: effect. I did not try if surplus of serum can do any harm when immunizing, for one then gets too great quantities so that it is hard to inject them: 50 ccm. serum is rather much for a rabbit. These experiments seem to be somewhat contrary to a communi- cation of Do6rr (report about Anaphylaxis, Kote unp WassrrM. Ile Aufl.), that the precipitate obtained by mixing serum and _ anti- serum, has no immunizing effect. But this is only a seeming contadiction. For, according to investigations e.g. by Wetsa and CHAPMANN’) this precipitate only contains traces of parts of the serum and it is almost exclusively formed out of the antiserum. Thus I have found that of a serum of a rabbit which was immunized against human serum (titre '/,,,.) 75 ecem. was necessary to form together with 1 cem. human serum (together till 150 cem.) a precipitate, so that in the above mentioned liquid no more human serum could be indicated with my antiserum (’/,,,,). 1 cem. being a very small dosis to immunize a rabbit, it is clear that not much can be expected in general from an injection of the precipitate’). I have now also examined the local effect of serum and antiserum. 1) Zeitsch. f. Immunitiitsf. 9, p. 517. 2) T here give up the question whether there is any human serum at all to be found in the precipitate, or whether it could be again removed by washing. 329 With this the antiserum and serum were always both inactive, so that we have nothing to do with any possible anaphylatoxin. If one again injects the mixture in which a precipitate has been formed subconjunctively, one will find a rather strong swelling the next few days, which at a morphological examination again seems to contain polynucleous cells. The controlling animals which had only been injected with serum, were normal again the next day. If one centrifuges the mixture, the above mentioned liquid is not found to cause a swelling, but the precipitate is. So we have here an analogous conduct as with the corpuscles’). I have now tried whether specific albumen precipitations did not show the same conduct, and for this I chose the precipitates of horseserum with colloidal He (OH), and S/O,. Both precipitates gave some swelling and ata morphological investigation polynucleous Jeucocytosis. This investigation must still be extended. If one injects a prepared animal with specific serum, one gets the same phenomenon: swelling and lencocytosis. This phenomenon is wellknown. I did not yet succeed in proving here as well that the precipitins hold the serum in its place’*), although | do think it likely, considering what goes before. For the time being I do not see a chance of preparing a serum which possesses amboceptor against foreign albumen, but no precipitin. Amsterdam. Path. Anat. Laboratory of the University. Chemistry. — “The Temperature-coefficients of the free Surface- energy of Liquids at Temperatures from —80° to 1650° C. 1. Methods and Apparatus. By Prof. Dr. F. M. Janeur. (Com- municated by Prof. P. van Rompuran). § 1. The purpose of the experiments here described was to en- deavour to ascertain the relation between the so-called “molecular a relation surface-energy” of molten salts and the temperature, which has hithertho been studied only in liquids, which possess no electrolytical conductivity. 1) The experiments are somewhat analogous to those about the local effect of the anaphylatoxin (fRiepBeRGER), but I always used serum that was made inactive, contrary to the investigators, into the anaphylatoxin. 2) That is to say subconjunctively. For the cornea other laws probably prevail; there the serum remains in the same place for rather a long time without there being any precipitins (WersseLy, von Sziny). 330 A probable relation founded upon the law of corresponding states, between the value of the temperature-coefficient of the expression : Ge) , and the degree of molecular association of a liquid was first suggested by Eérvés*), and later by Ramsay and Saietps*) and a number of others*). These observations appeared to prove, that the values of these coefiicients do not differ much from 2,2 Erg per degree C. for “normal” liquids, while for associated ones they are considerably less. In any event some definite knowledge of the dependence of the free surface-energy x upon the temperature will be of high importance for the consideration of all problems, relating to the internal state of liquids. It can hardly be supposed with any probability, that the law of corresponding states will be found to apply in the case of molten salts, because they are really electrolytes and more or less dissociated. Notwithstanding this, if the investigation should chance to reveal relations in any way analogous to those hitherto supposed to be characteristic of organic liquids, this fact must carefully be considered in estimating the significance of the theoretical speculations mentioned, and especially is this the case, where criteria are sought for judging about the molecular state of liquids in general. In fact, one can better hope to elucidate the influence of chemical constitution on characteristic properties in the case of molten salts, than in the ease of the much more complicated organic molecules. These and other considerations, some years ago (1910) suggested the development‘) of an experimental method, which should permit the study of the dependence of the molecular surface-energy upon iemperature, — even up to temperatures in the vicinity of 1650° C. 1) Kérvés, Wied. Ann. 27. 448. (1886); vAN DER WAALS, Zeits. f. phys. Chem. 13. 713. (1894). Erste. Ann. d Phys. 34. 165. (1911-) 2) RAMSAY and Surewps, Zeits. f. phys. Chemie 12. 483. (1893). 8) Vid.: Guyz and collaborators, Journ. de Chim. phys. 5. 81, 97. (1907); 9. 505 (1911); etc.; WaLpEen and Swinney, Zeits. f. phys. Ghem. 79, 700. (1912) 3ull. Acad. St. Pétersbourg, (1914) 405, ‘) Preliminary experiments of this kind were begun during my stay at the Geophysical Laboratory in Washington, (U.S. A.), in the winter 1910-1911, and I wish to express my thanks here once more to my friend Dr. A. L. Day for his kind assistance and most valuable advice in this matter. Through these preliminary experiments the availability of the method up to 1200° C. was clearly established by me, and it became quite clear, in what directions improvements were necessary. The further development was hindered by the building and equip- ment of the new Chemical Laboratory of the University of Groningen: not earlier than November 1913 could the first measurements of the present series be made. With the increase of the temperature of observation, the experimental difficulties of precision-measurements increase very rapidly : measure- ments, which at room-temperature are of the utmost simplicity, are often very difficult at 400° C., and commonly almost impossible above 1000° C. This fact explains, why it has not been possible until now, to communicate the results obtained, because only an extended experience could prove to us the reliability of the method used and the degree of accuracy obtainable. § 2. Of all the methods hithertho deseribed for the determination of surface-tensions, the one most used is the method of measuring the rise of the liquid in capillary tubes. Ramsay and Suipips and most of the investigators who have followed, have used this method. It can however hardly be denied, that the absolute values of x, obtained by different observers with the same liquids and at the same temperatures, show discrepancies of considerable magnitude. Commonly this lack of agreement is attributed rather to the unequal degree of chemical purity of the materials studied, than to the methods employed. In many of the cases, however the discrepancies were found with liquids, which can be obtained in a state of complete purity without extraordinary trouble; so that one is easily inclined to the belief that the method of measuring the capillary column includes some sources of error which are not yet sufficiently known. Possibly adhesion to the walls of the tubes plays a certain role in it, or perhaps the influence of the angle between liquid and solid material may be not completely negligible, as is ordinarily assumed. However there is a decisive argument against the use of the method of capillary ascension in the following investigations; the walls of the capillary tubes used, were ahvays damaged in a greater or less degree by the action of the molten salts. A microscopical examination of the walls of the tubes readily revealed this fact. The method cannot be employed therefore at temperatures, exceeding 400° C., because the liquids will always be contaminated and the results will be almost valueless. Furthermore, the method assumes, that a rather long column of liquid can be held throughout its full length at a constant and uniform temperature. At high temperatures this condi- . tion can searcely be fulfilled. The study of large platinum resistance- furnaces has shown convincingly, that even in a central furnace- tube of about 26¢.m. length and 4,5 ¢.m. diameter, with the heating- coil wound inside, the space of really constant temperature is scarcely 332 longer than 4 or 5 em.') Therefore it is absolutely essential in every method intended for exact measurement at high temperatures, that the working-space be reduced to dimensions as small as possible. With respect to the measurements of temperature under such con- ditions, the available methods will permit making them with an accuracy of 0°,1 C.,*) which is more than sufficient for the purpose. On the other hand, the necessary measurements of the surface-energy must be made in such a way, that the results will have the same degree of accuracy at the highest temperatures, which they possess at lower temperatures, while at the same time the liquid to be studied must be restricted to a space of one or two cubic centimeters. § 8. To fulfill these postulations, there is a method which can_ be used under certain conditions, which was first projected by M. Srvon, and later developed by Cantor, *) while it was successfully used afterwards for researches at lower temperatures by FrusTEt. *) It appeared to be possible to develop the technical procedure in such a way, that the method could be used, without any appreciable loss of accuracy, up to the highest temperatures, which can be measured with the platinum-platinumrhodium thermoelement. The principle of the method is the measurement of the maximum pressure HH, prevailing within a very small gas-bubble, which is slowly formed at the circular, knife-edge opening of a capillary tube immersed in the liquid perpendicular to its surface, just at the moment, when the gasbubble is about to burst. The sharp edge of the capillary tube eliminates the influence of the capillary angle. In this way absolute measurements of the surface-energy are possible in Ergs per em’., if the radius » of the tube, the specific gravity d of the liquid at the temperature of observation, and the depth of immersion 7 of the tube into the liquid, are known. To obtain the true value of //, the readings of the manometer require to be diminished by the hydrostatic pressure, corresponding to this depth of immersion 7. The method evidently can only give exact results, if the final state of the gasbubble represents a state of equilibrium, and is thus reached 1) BorromLEy, Journ. of the Chem. Soc. 83. 1421. (1903) ; Lorpnz and Kaurier, B. d. d. Chem. Ges. 41. 3727. (1908); Trauss, ibid. 24. 3074. (1891). Vide also: MoryLewsk1, Z. f. anorg. Chem. 38. 410. (1903). : *) F. M. JAgaer, Eine Anleitung zur Ausfiihrung exakter physiko-chemischer Messungen bei hoheren Temperaturen. (1913). p. 36, 43. 3) M. Smon, Ann. de Chim. et Phys. (3). 32. 5. (1851); Canror, Wied. Ann. 47. 399. (1892). 4) FeusTeL, Drude’s Ann. 16. 61. (1995); Forcu, ibid. 17, 744. (1905). Doo passing a series of mere equilibria; that is: the method required to be made practically a sfatic one, the final maximum-pressure being independent of the special way, in which the pressure in the growing gas-bubble is gradually augmented. Thus a very slow rise of pressure in the growing gas-bubble is necessary, and only in this way does it appear possible to eliminate the small differences of pressure in the long connecting tubes of the apparatus. For it is well known, that the adjustment of such small pressure-differences takes a considerable time, if the connecting tubes are relatively long. If the radius of the capillary tube is 7 (in em.), the specific gravity of the liquid d, and the observed maximum-pressure (in Dynes) is H, then the surface-energy x (in Erg. pro em’*.) is calculated from Cantor’s expression (loco cit.) : oh hat Dang am - 3 The last two terms of the second member of this equation are usually so small, that they can be neglected in comparison with the experimental errors, as being corrections of the secondary order. Nevertheless it has become clear, that a special correction requires to be applied to the values calculated in this manner, because of the fact, that in the theoretical deduction of this relation, a simpli- fication is used, which cannot be considered quite legitimate. We will advert to this correction lateron. (Vid.: VI; under general remarks). With this limitation extended experience in the use of the method leads to the conviction, that in the form it is used here, one ean obtain reliable and, within narrow limits, reproducible results. It has the advantage, that the surface-layer of the liquid is continually renewed, thus the often-observed and troublesome phenomenon of the alteration of this layer, need not be feared. Furthermore one can vary the flowing gas at will with the different liquids, to prevent eventual oxidations or reductions’). With these precautions the results can be considered as accurate at 1650° C. as at ordinary temperatures, if only no abnormally high viscosity is encountered in the liquids; for this will destroy to some extent the reliability of the measurements. The influence of the viscosity will be discussed lateron in more detail. Of all sources of error to be considered: inaccuracy in the 1) As long as the gas is indifferent, i.e. as long as it does not react with the liquid, the results will be quite comparable, because experience teaches, that the differences in the values of y, measured with different gases, are vanishingly small in comparison with the experimental errors. 304 measurements of 7, of d;, of the pressure H/, of the reduction-factor of the observed pressure on the manometer to mercury-pressure, of the measurement of temperature, of the depth 7, ete., — the last mentioned appeared to be the most significant. If all these errors are assumed to be cumulative, the total effect upon the reproducibility of the results, even at 1650° C. is still within about 1°/, of the true value of x, and at lower temperatures about 0.6 °/, of that value. With many molten salts, where // is very great and the viscosity very small, the percentage error appeared to be even less than this, not exceeding 0,4°/,. For our purpose this degree of accuracy may be considered a very satisfactory one considering the enormous difficulties of measurements at those extreme temperatures. lt is also question- able, whether it will be possible to exceed this accuracy at such high temperatures in the near future. And if this could be done, it is very problematical whether much would be gained for the purpose proposed. For experience teaches us, that at those extreme temperatures all compounds are in a state of more or less advanced dissociation, and it can hardly be of any significance to express the surface-energy yx of such compounds in tenths of Ergs, when the uncertainty in the values of x, caused by the inevitable admixture of the dissociation-products, will surely be larger than the correction-factors following from this increase in the accuracy of the measurements. § 4. In this and the following papers we will successively give an account: (1). Of the experimental arrangements and the manner of procedure, including some instances, illustrating the general adapta- bility of the method employed in different cases. (2). The results, obtained between .—80° and + 270° C. in the study of a great number of carboncompounds, in connection with their atomic constitution and the validity of E6érvés’ theoretical views. (3). The experiments made to determine the free surface-energy of molten salts, by means of the method here developed. In this connection we will also discuss more in detail the earlier attempts to solve the problem by the method of capillary ascension in glass-tubes. (4). Finally a discussion of the results obtained and a number of considerations of a more general kind will be given, which are suggested by the study and comparison of the data now available. § 5. Apparatus and Experimental Equipment. a. In all the measurements pure, dry nitrogen, free from oxygen, was used, because even at the highest temperatures this gas appeared 335 to be quite inert, and to attack neither the compounds studied, nor the thermo-elements. Carbondioxyde can be used as a furnace-atmos- phere up to relatively high temperatures, but is often not very suit- able to be bubbled through molten salts under these circumstances, because of its character as an anhydrous acid. Furthermore, at the highest temperatures a_ slight dissociation is always to be feared. At the same time the dry nitrogen permitted us to drive out the air from the glass bulbs at lower temperatures, and completely prevented the oxidation of the organie liquids studied. The nitrogen employed was prepared from a mixture of pure sodiumnitrite and ammoniumchloride, washed by distilled water, and collected in a gasometer D (fig. 1). It was led through a series of wash-bottles ¢, filled with an alkaline solution of pyrogailol, then through otbers, filled with concentrated sulphuric acid (4, and finally through a tube /, containing a large surface of freshly sublimed phosphorous-pentoxide. The dried gas was preserved in a collector W, closed with dry mercury. When needed, it was pushed on into a inetal reservoir NV by means of a movable mercury-holder 7. Any arbitrarily chosen pressure could be used which was then read on the mereury-manometer A. The stopcock / carries a micrometer, used in the regulation of the gas-current. In the study of the organic liqnids, this reservoir .V was placed in the oil-thermostate (’, with the glass-bulbs containing the liquids tod be investigated. In this way the nitrogen was pro-heated to the temperature of observation, thus preventing disturbances of temperature in the surface-layer of the 336 liquid due to the small gas-bubbles emerging from the ecapil- lary tube. The regulation of the velocity of flow of the gas was obtained by means of the stopcock /# already mentioned, in combination with two accurately adjustable pinch-cocks 6, which were inserted between the reservoir N and the apparatus 2, carrying the capillary tube and its adjustments. With this arrangement no undesirable cooling of the surface, nor any lack of adjustment of the gas-velocity need be feared as a considerable source of error. b. The apparatus R consists of an upright rod H (fig. 2a), about 1 meter high, and made of brass heavily plated with nickel. It rests on a heavy iron tripod fitted with three levelling screws. The vertical rod can be rotated about its axis by means of two gliding discs O at the foot of the pillar; they may be clamped fast when desired. In this way it is possible to bring the horizontal arm, bearing the adjusting arrangements and the movable counter-weight / into any desired azimuth, and to fix its position by means of the clamps at O and the collar at 7. With the aid of a handle provided with a vertical rack and pinion, this horizontal arm can be raised to any height and fixed there with proper clamps. This arm can also be moved horizontally, in order to vary its length. Moreover it appeared to be necessary to prevent a slight bending of the pillar A7 under ceriain circumstances, by means of three steel supports attached to H and to the iron tripod *). Just over #, it has at its end a rectangularly bent steel support, to which are attached the spiraltubes G’, made of gas-tight aluminium- tubes, nearly 3 millimeters wide, and also the similar tubes U, which however consist of much wider spirals. The latter form the continu- ation of the aluminiumtubes G, and their ends are firmly fastened to the horizontal beam, which is fixed in the laboratory just above the whole apparatus. The two sets of spiraltubes appeared to be necessary to ensure the desired mobility of the apparatus with regard to the manometer-connecting tubes, and also to render an effective operation of the adjusting devices possible. The great sensitiveness of the manometer makes it necessary, that all the connecting tubes of the instrument, as well as the spirals Gand U, should be wrapped with a thick layer of white flannel or asbestos, in order to avoid the disturbing influence of slight oscillations of temperature. !) In the construction of this apparatus the mechanics D. VonkK and A. VAN DER MB®ULEN, and the amanuensis J. J. FoukeErs, all of Groningen, have aided ina most practical and effective way. Prof. Dr. F. M. JAEGER. The Temperature-coefficients of the free Surface- energy of Liquids at Temperatures from —80° till 1650° C. I. Methods and Apparates. { 2 Poe mg Fig. 2a. Proceedings Royal Acad. Amsterdam. Vol XVII. oe ae eter The adjusting device FR is represented on a somewhat larger scale, in fig. 26; it is fixed in position over a resistance-furnace, and con- nected with the capillary tube made of the platinum- rhodium-alloy and the therro- element #. In this drawing the rectangular support with the spirals G are also plainly discernible, together with the hollow water-sereen ./, in which a current of cold water is continually — circulating. This adjusting device consists of two semi-circular parts about 40 em. in diameter. One part is permanently attached to the apparatus FR, the other can be fitted to it by means of pins and short tubes. The latter part has a circular elass- window, where upon the totally reflecting and movable (around a horizontal axis) prism /7 is placed. By means of this prism the be- haviour of the liquid in the furnace can be observed and controlled at every moment. At temperatures over 1000° C., coloured green glasses are Fig. 20, inserted in front of the prism. With the protection of the waterscreen / it proved possible, to use the manometer even at temperatures of 1650° C., without any disturbance from the heat-radiation of the furnace. The furnace 6 is a platinum- (or nichrome-) resistance furnace of the usual type ’); it has an inside wound heating-coil, and can be heated with a central tube of alundum inside, up to 1400° C., and without such a ; 1) F, M. JAEGER, Anleitung u.s.w. (1913). p. 36. 335 central tube, to about 1680° C. The platinum-erncible is borne upon a movable support of burned magnesite. which can be fixed to the iron support A at any elevation. The construction and arrangement of the part # of the adjusting device is elucidated more in detail in fig. 8a and 36, a giving the a. Fig. 3. b. external view from one side, / a section through it, in a plane, perpendicular to that of fig. 2a. The apparatus consists of two metal dises P, and P,, of which the dise P, with the tube S attached to it, can be moved horizont- ally round the hemi-spherical button Q, and by means of the screws A, and A, can be brought to any inclined position with respect to 6: B09 P,. Wf P, is turned in a horizontal direetion, the screws A, and A,, as well as the springs /’, and F,, (fixed at one end only) will glide along the upper dise P,, the whole upper part thus remaining in its original position. It appeared to be necessary to use a third serew B&B for the adjustment of the capillary tube. It is first completely loosened from P,, then after ?, and P, have been brought into the desired relative position, the screw / is turned so as to touch the dise P, slightly: in this way the relative position of the two plates is completely fixed. The tubes S and J}, (not shown in fig. 3a) are bent rectangularly upwards, and fitted, to the spiral tubes G. By this arrangement an undesirable motion of the apparatus (during the adjustment of the capillary tube), due to the influence of the stress and weight of the connecting-tubes, could be sufficienly prevented, while the mierometerscrew J/ at the same time remained in working condition. This serew J/, fitted with a drum WN and a seale D, serves to move the discs ?, and P, together through a known ver- tical distance. The serew has a pitch of 1 mm. exactly, the cireum- ference being divided into one hundred equal parts, it thus permits a vertical motion of 0,01 mm. to be measured at DY. This is more than sufficient, because experience proves, that no adjustment of the capillary tube in contact with the surface of the liquid, can be made with greater accuracy than about 0,1 mm. During this vertical motion the drum N and the micrometerscrew J/ remain in their original positions, because they can only move in a horizontal direction round the fixed part V of the apparatus. A vertical scale 7, provided with divisions for about 30 mm., is moved at the same time with the two dises P, and P,. In this way the number of revolutions of N can be read directly. Concerning the adjustment of the capillary tube with respect to the surface of the liquid, which can be made either visually, or with the aid of the manometer-readings, the neces- sary directions will be given below. § 6. It was soon found, that the adjustment of the slight diffe- rences of pressure in the long connecting-tubes happened so slowly, that considerable errors in the measurements must inevitably occur. For this reason all the capillary tubes, with which the apparatus was originally equipped, were replaced by 5 mm. gas-tight tubes. These tubes were made in part of lead, in part of aluminium ' ) and, 1) Also tubes of cellon, made by the Rheinisch-Westphdlische Sprengstoffe A.G. in Céln a/Rh., and which may be bent in hot water, can be recommended for such purposes. The material is gas-tight and fire-proof; however it is difficult to obtain it from the plant in any desired shape. 340 where neeessary, were wrapped with a thick layer of asbestos. A considerable time had to be spent, to get all connections completely free from leakage ; but when this was accomplished the indications of the manometer were so prompt as to be practically instantaneous. After this no errors from this source needed to be feared. The connection of the tubes occurred in the usual way, as with high-pressure apparatus; these connections appeared fo remain gas- tight, even after a longer use. § 7. For the measurement of the maximum pressures to be observed, originally a mercury-manometer of the type indicated by ScHEEL and Heusk') was used. The instrument had been modified in some details ; but it appeared not to be suitable for our work, because of the necessity of always reading tivo menisci, which was very troublesome with a pressure varying continually up to the moment, when the maximum was reached. This instrument therefore, which is very well adapted for static measurements, was only employed for the calibration of the manometer finally constructed. This second instrument was built on the principle of the manometer with two liquids. In the measurements of organic liquids, it was necessary to avoid any contamination of the connecting-tubes with the vapour of the manometer-liquids, so that only pure mercury could be used as one of the liquids in the manometer. For the second liquid we chose normal octane. This liquid is very thin, behaves very well in contact with glass-walls, and, if completely dry, appeared not to blacken the mercury-surface, even after long exposure. The vapourtension at 20° C. is only 10,45 mm., the viscosity at 238° C. is 0,0052 C.G.S., the surface-tension at 25° C. is 21,3 Erg. pro em?*., and the expansion- coefficient is O0,00t18. After repeated fractional distillation, its boiling- point was found to be 125° C. under 758 mm. pressure, and its specific gravity at 25° C. was: dy = 0,6985, i.e. about 19,38 times less than that of mercury at the same temperature. This last relation operates in the following way : Suppose the diameter of the wider tube (fig. 4) to be D, that of the capillary tube d and the mercury-meniscus to the right to be @ m.m. higher than to the left. Then the height of the octane-column to the left 1) ScugeL und Heuse, Ein heizbares Quecksilbermanometer fiir Drucke bis 100 m.M.; Mitt. aus d. Phys. Techn. Reichs-Anstalt, Zeits. f. Instr. 30, (2). 45, (1910). 341 . / . at wri ] ind > 1 * Side (c) 1s: — m.m., 1f e = ——- — 0.0516. Suppose 4p to be the increase é 19,38 of pressure (in m.m. mercury), necessaryon the right side, to sink the mercury-surface just 1 m.m. The mer- aed cury-surface on the left side, will then rise just 1 m.m., and the octane- column from ¢ to c’ (=Ahmm.), D over ; m.m. The difference of level ad of the two mercury-surfaces is now: (a—2) m.m., and the octane-column : a D : to the left =(-— 1+ i) mm. This é C corresponds to a mereury-column of: a D Dé —— {+ —)e={a—e+— |mm. & d d Therefore the necessary increase fost?) of pressure on the right side (= A p), is evidently : D (« —e+ 7°) — (a—2) m.m. = 2 + D Fig. 4. +3 Ge 1) m.m., and thus : € or: Soi The reciprocal of the expression between }} will be seen to be the “multiplication factor” /’ of the instrament. With small values of é, (2—e) will differ little from 2; therefore it is necessary to reduce d ‘ _ : p* much as possible and to make F' as large as possible. In our instrument these conditions were fulfilled in the following way: preliminary experiment gave d = 2,406 m.m’, and D = 1257,36 d Bee m.m’; thus p — 900191, and / becomes ea. 18. The reproducibility of the same pressure appeared to be possible within a limit of 23 Proceedings Royal Acad. Amsterdam. Vol. XVII. 342 O,1 m.m. octane, which corresponds to 0,005 m.m. mercury-pressure. The accuracy of the measurements was within the limits 0,05 and O,1°/,; it was greater than necessary in comparison with the magni- tude of the systematic errors of the method. The final form of the manometer, as it was used in all the measu- rements is shown in fig. 5. This final form resulted from a great number of experiments and numerous changes. The tube A is made from the best quality of hard-glass, and connects two bulbs B of ca. 39,9 mm. diameter with a volume of about 1380 cubie centi- meters ; they possess 1,2 mm. wall-thickness. The bulbs must carefully be chosen, and be completely cylindrical throughout their full length. As the height is about 110 mm., it is not easy to find tubes of the desired quality. The capillary tube must have an internal diameter of about 1,7 or 1,8 mm., and a wall-thiekness of about 2,5 mm., and must be suitable for precision-measurements and carefully TIAX “JOA ‘Wepsajsury ‘peoy [eAoy sBurpaa00.1 g ‘9 ‘SIT | 1M *‘sojvivddy puv spoujew ‘T “9D o0S91 II .08— wos soinjesodwmay ju spinbr] Jo Adsiaua-advJANGS 99IJ dy} JO S}UdIDYJa0I-2INjUJodWa_ eYL “YADAVS ‘W ‘Ad 40 J0Jd 343 calibrated. Its length is about 600 mm. Another tube D, of equai length, but about 7 mm. in diameter, serves as a connection to the gasapparatus. The capillary tube (bears at its top a silver tube EH, overlapping the tube C; it communicates with C by means of a silver capillary fube, and can eventually be easily removed. The tube C' is widened at its top-end to about 10 mm.. and con- nected with the silvertube in such a manner, that no dust of the room can contaminate the capillary tube €, while at the other end it communicates with a small reservoir &, partially filled with octane ; — this for the purpose of preventing, as far as possible, the evapora- tion of the liquid in C. For this reason F& is placed in the same thermostat as the manometer-tube. The connection of R with the atmosphere (or with the nitrogen) is made by means of an adjustable glass tube G, which opens into a very wide connecting tube leading to a large flask with three mouths, which is provided with dry caleiumoxide, with a small manometer, a tube with drying materials and with a connection to the nitrogen-holder. In the fig. 1 the octane- reservoir is indicated by C, the silver capillary tube by |S, the three- mouthed bottle by /. In the same way the manometer is indicated by w, the drying-tube by z,, and the connecting tubes by Qand H. The manometer is arranged in a glycerine-thermostat of the type usual in dilatometer-thermostats (KOunLER), however its construction has been varied in some particulars. The thermostats commonly sold are quite unsuitable for this purpose, because they commonly show leakage or will show it very soon; then they cannot be used for glycerine, which was chosen because of its refractive index and low volatility, because this liquid will dissolve the paste used in setting the glass- windows, within a short time. Two rectangular frames were there- fore made of brass, about 38 em. broad, and soldered to the thermo- stat. These frames were smoothed as perfectly as possible and possessed an inside furrow about 5 mm. deep and 1 em. broad, in which a layer of very thin rubber paste, fixed by a solution of rubber (in carbonbisulphide), held the two glasswindows fast. Then a second layer of plastic rubber was applied, and the second brass-frame was uniformly pressed against the former with some forty screws. The ther- mostat holds 22 kilos of glycerine, but even after long use it shows no leakage. By means of a toluene-regulator 7’ a spiral-stirrer J/ with motor A, and a pair of small burners 4, and 6,, the instrument is kept at 25°,1 C. +0°,1. Z is a thermometer, divided in 0°,1 C. The support # is suspended from the lid H by means of four movable rods /. The manometertube can then be brought into a vertical position by means of the screws s,, s,, s; and s,. Within 23* 344 the thermostat and just behind the capillary tube C a glass-scale V is introduced, which possesses a very accurate division in 0,2 mm., by means of very fine lines (38 microns) made by the Compagnie Genevoise. The scale is read with a telescope and ocular-micrometer by the same firm, and at a distance of about 2 Meters; the enlarge- ment is about 25. During the readings the motor A’ must be stopped for a moment, because even the slight vibrations are rather annoying. The thermostat is wrapped with felt except for the narrow opening needed for the readings. Behind the manometer a ground glass-plate is applied, which is illuminated by two long, tube-straight-filament incandescent-lamps, each of 50 candle power. Between the lamps and the thermostat, a watertank with glasswindows, is introduced, to prevent heat-radiation into the thermostat. With this mode of lighting the fine divisions and the octane-surface are seen very distinctly, without any observable parallax, against an illuminated background and readings can be made with extreme accuracy, with the aid of the movable cross-hair of the micrometer. However readings of less than O,1 mm. appeared to be unnecessary, because of the fact, that the mean oscillations in the successive determinations of H, were about + 0,05 mm. octane, the total uncertainty therefore being about 0,1 mm. octane-pressure, or about 0,005 m.m. mercury-pressure. § 8. To bring the capillary tube into a vertical position, a mer- curymirror was used: by means of the screws A, and A, (fig. 3d) the position of the capillary tube is altered until its mirrorimage will seem to be in a straight line with the tube; the position of P, and P, is then fixed by means of the screw B. The capillary tube itself was origimally made from purest, iridiumfree platinum ; this however appeared to be too soft, and so an alloy with 10°/, or 20°/, suitable capillary tubes for this purpose from the shops in trade. of rhodium was used afierwards. It is impossible to get any Therefore the rough capillary tube with its widened (ca. 6 mm.) upper part, was purveyed by Herarvs; the lower end was then carefully turned off on the lathe to a conical and sharp edge, which Was once more whetted on an oil-stone, if necessary. With some practice in this way the repairs of the damaged or worn capillary tubes can be accomplished within a relatively short time; and it proved to be possible to obtain a cross section of the tube, which in several directions did not deviate more than about 0,002 m.m. from a pure circular shape, while the rim of the lower end measured no more than 0,01 mun. The cross section was determined by means of a_ horizontal 345 microscope, provided with a micrometer of the movable-cross-hairty pe with divided ‘cylinder: the diameters were measured in ten or twelve directions, the squares of these numbers added, the total amount divided by the number of measured diameters, and the square root from this value considered as the true value for 27. With regard to the measurements to be made at extreme temperatures, and on account of the fact, that a whetting of the capillary tubes appeared to be necessary almost after every set of measurements, no tubes with a radius of less than 0.040 ¢c.m. were used during these investigations. The platinum-rhodium-tube ends at its upperside in a carefully smoothed, polished brass disc; the tube of the adjustment-apparatus R possesses just such a smoothed circular brass-plate. As a washer between the two discs, a very thin ring of mica is used ; the capillary tube is screwed against the end of the apparatus #&, and both tubes are then drawn together by the aid of two steel-keys, till the discs are firmly pressed against each other: in this way an absolutely gas-tight connection is obtained. This closure appears to be a very perfect one, and if it is often controlled, no leakage needs to be feared from this source. § 9. The temperature-measurements were made with our calibrated thermo-couples and compensator-equipment, in the way always used in this laboratory *). Originally it was planned to connect the platinum- wire of the thermocouple directly to the end of the platinum-rhodium- tube by means of the oxygen-flame; this tube then being considered as the positive end of the thus obtained thermo-couple. However the perfect isolation of the tube at very high temperatures appeared to be a serious obstacle; so the idea was abandoned, and the usual thermo-couples, provided with isolating Marquarpt-capillaries, was fixed to the platinum-rhodium-tube by means of fine platinum-wires ; at the other end they were connected with the ice-box J (fig. 2a). The wires of the element are bare over a distance of about 5 e¢.m. from the junction; this point lies in the same horizontal plane as the lower end of the capillary tube, thus being in immediate vicinity of its opening. Of course all platinum parts within the furnace (crucibles, coils, ete.) need to be made from iridiumfree platinum, to prevent contamination of the thermo-couples as much as possible. § 10. The adjustment of the capillary tube with respect to the 1) F. M. Jagger. Kine Anleitung u.s. w. (1913), vid. p. 16—24, 346 surface of the investigated liquid, can be made in the following way. The surface of the liquid is strongly illuminated, and now attenti- vely the moment is watched, when the capillary tube, while screwed downwards, will just make contact with its mirror-image, seen in the surface of the liquid. At temperatures above 500° C. ordinarily not, and above 1000° C. never, a special illumination of the surface is necessary: for the liquid radiates then sufficiently to make the obser- vation of the moment of contact a very accurate one. If the tem- perature however becomes 1400° or higher, it is often no longer possible to discern the end of the capillary tube from the surround- ings: in these cases the adjustment must be made by the aid of the manometer, as is further below described in some details. This visual method involves, even after sufficient practice an- uncertainty of about O.1 mm. in the case of organie liquids, which corresponds to ca. 0,006 to 0,008 mm. of mercury in the determi- nation of the maximumpressure /7. The percentage error of the obser- vation caused thereby, is about from 0,4 to 0,7°/,; this uncertainty in the adjustment of the capillary tube on the surface of the liquid, really appeared to be the chief source of the errors, as has been said, and is hardly or not to be avoided. However just at higher tempera- tures this and in the case of molten salts, where / is very great, the accuracy of the method is only slightly affected by this uncertainty. The other way of adjustment is this, that the capillary tube is approached quite near to the surface of the liquid; then carefully a flow of nitrogen is applied, and then, wlile the capillary tube is slowly lowered by means of the micrometer-screw, by observation of the manometer, just the moment is determined in which a sudden rise of pressure, caused by the contact of the tube with the surface of the liquid, is seey. In this way the proposed aim was also often attained ; but the uncertainty appeared to be here of the same order of magnitude, as in the case of the visual method. Furthermore it is necessary to ascertain that the small column of liquid, which often remains hanging in the capillary tube, if turned upwards, has no misleading influence on this observation ; first this column of liquid needs to be biown out by the aid of a sufficiently strong flow of nitrogen, before the contact with the liquid is made in the way just described. § 11. The manometer was originally calibrated by immediate comparison with a mercury-manometer, which was read by means of a cathetometer and a divided scale. The paralaxis appeared to be extremely small; the accurate adjustment of the mercury-surfaces was highly facilitated, by putting a half transparent and diffusely illuminated sereen behind the manometertube, on which screen black lines were drawn under an inclination of about 25° with the horizon in such a way, that their mirror-images in the mercury-surfaces were visible thereupon as a bundle of very fine and easily discern- ible dark lines. After the application of a certain excessive pressure to both manometers, two observers read siimultangously both instru- ments; the manometers were connected with each other by a short, very wide tube, sufficiently protected against temperature-oscillations. As an example of this calibration, the following series of obser- vations may be reproduced here in deta‘! : Mercury manometer. Octane-manometer (25° C.) Temperature: — Observed Pressure Rise of the octane column pressure : 02 C m m.m. 12,°4 7,00 6,99 124.8 12,°6 10,23 10,21 181,8 12,°9 12,45 12,43 220,8 112.23 9,13 914 162,2 12,°6 13,14 13512 235,3 13,°0 13,78 13,75 245,0 13,°4 12,44 122) 219,9 A rise of the octane over 1 m.m. is therefore equivalent to an excessive pressure of 0,0561 + 0,0003 m.m. mercury (=74,8+0,4 Dynes). After it was found, that our measurements of the free surface- -energy of purest water, were in so complete agreement with those ot VoLKMANN, Brunner, Worry, among others, we afterwards repeated this calibration in most cases by the accurate determination of x for pure water, at three or more temperatures. The factor of enlargement F of the manometer appeared after all to be only slowly variable : in Octobre 1913 e.g. it was: 17,91 in February 1914: 17,86; in June 1914: 18,10; ete. § 12. The molten salts to be studied were in most cases placed into crucibles of iridium-free platinum; for the organic liquids we used vessels of glass of the shape indicated in fig. 7. A eylindrical glass tube P with rounded bottom possesses a narrower neck at A; a wider glass cup A is fixed round it. A tube G, closed with a stopper A, which is firmly fixed round the platinum capillary tube, possesses a collateral tube 46, which ends into a drying tube G, which communicates with the free atmosphere at Z, and which is filled with odS quick line. The vessel P is cleaned, care- fully dried, and if possible several times washed out with the vapours of the boiling liquid V; —_ N then it is filled again with a fresh quantity of the liquid V’, while a layer of dry mereury is poured into IW. The tube is placed into the oil thermostat, and the capillary tube with C the part GBC fixed to it, is lowered then, till G makes contact with the surface of the mercury. If V has reached a constant tempe- rature, the capillary tube is further lowered by screwing it so far downwards, as is necessary Seok SA rr ye ps3 to bring it just in contact with the surface of the liquid. This enclosure by means of mer- cury insures a sufficient freedom of motion, while the Jiquid at the same time can be shut off from the air’), and the small bubbles of nitrogen, emerging from &, can freely escape at Cand Z,. All communications with the free atmosphere, which are present in the connect- ing tubes of fig. 1, are provided with drying apparatus, filled with dry caleium-oxide. § 18. All measurements now were made in such a way, that always the zero-point was controlled anew accurately, before and immediately after each reading of the manometer. One needs to ascertain first, that all connecting tubes (fig. 6) are free from leakage, and that a diminution of the speed of gas-flow has no influence any longer on the value of the maximum pressure H. After the highest point of the octane-column is reached the liquid falls suddenly back to a point, which depends upon the speed of gas-flow, and then it begins to rise again slowly ; ete. By experience one learns to estimate the reliability of the measurements, by the particular motion of the octane in the manometer ; finally the repro- ducibility of the value of H needs to be considered as the decisive criterion for answering the question, if the real pressure of equili- brium in the gas-bubble has been measured. Even when the speed of gas-flow is varied within certain limits, this value appears to be reproducible quite exactly. The influence of the variation of the depth of immersion 7 on the manometer-readings, can be found by 1) For if necessary, the air in the vessel P can be first substituted by a current of pure nitrogen. 349 repeated lowering of tue capillary tube over known distances by means of the micrometer-screw J (fig. da), and by repeating the readings of the manometer in every case. In all calculations we used the number 1383.2 Dynes as the equivalent of 1 m.m. mercury-pressure at 0° C.; the surface-enerey is expressed in Erg pro e.m.’. *) § 14. As an illustration of the general availability of the method at all temperatures between — 80°C. and + 1650°C., we will give here already some few instances, relating to: water, some colloidal solutions, some organic liquids, and some molten salts. The specific weights of the organic liquids were, after a pyenometrical control at 25°C., calculated for other temperatures from the thermic expan- sion-formulae, if they were already sufficiently and accurately known in litterature. In other eases the densities at 25°; 50°, and 75° C were pycnome- tricaily determined, and a quadratic relation with three constants was calculated from these observations ; this relation was used then afterwards for the determination of the other specific weights. In the case of the molten salts the specific weights must again be - determined by means of a method to be described later. To use the numbers for the densities with more than three decimals, has no real significance, because the experimental errors are always of an order so as to make the influence of more decimals of no importance. § 15. The curve (fig. 8) is evidently concave with respect to the tempe- rature-axis ; the temperature-coefficient of «is only small, and amounts to from 0,9 to 1,05 Erg. per 1° C. Furthermore in this diagram the corresponding curves are repro- duced for a colloidal solution of tron-oxide and for a colloidal solution of silicium-dioxride ; from both solutions the electrolytes were elimi- nated as far as possible by longer continued dialysation. It appears, that both curves are evidently situated somewhat above that for the pure solvent, although the deviations for 7 from the values for pure water are only very small. The temperature-coefti- cients are analogous to those for the solvent itself; however in the ease of the colloidal iron-oxyde it could be observed, that if such a solution was heated toa higher temperature, and if afterwards the determination of the surface-energy was repeated at the original 1) The result is after all the same, as when expressed in “Dynes pro c¢.m,”. 350 Ie Water: H,0. 0) eee ee ee Bo ese edad ea Surface: Sneeitie rie: HG — | | tension x in MERACe: | &c jin mm. mer-| . iEre. procm?,) gravity d).| Cnerey “in B~ Gat ere) Dynes | ea | is Erg. pro cm?., | PUN Ton SN ween OS Ese: 5) 2 | 0.4 | 2.593 3457 75.8.) 11.000. |) esaae 2 2.583 i 3444 13%) | 1.000 518.9 | 16.4 | 2.498 3330 | 73.0 0.999 502.1 ° | 18.4 2.488 3317 TPAST| 0.999 500.0 IP aay. 2.456 3275 TY 0.997 493.6 35 2.398 | 3197 70.0 0.994 483.1 37.8 | 2.383 | 3177 69.7 0.993 481.3 55 | 2.291 3055 66.9 0.986 464.3 74.2 | 2.178 | 2904 63.6 | 0.975 | 444.8 98.5 | 2.014 2688 58.9 0.960 415.8 99.9 | 2.004 2672 58.5 0.959 414.0 Molecular weight: 18.02. Radius of the Capillary tube: 0.04385 cm. Depth: 0.1 mm. The value of x at 20° C. is thus 72.6 Erg. pro cm.?; it is more probable, than the often accepted value: 75.') The here mentioned numbers are in full agreement with those of VOLKMANN 2) (1880), BRUNNER 8) (1847) and Wor.ey *) (1914); they differ however consi- derably from the values published by Ramsay and SHIELDS 5), | lower temperature, for x a value was found, somewhat different from the formerly observed one with a fresh solution. Thus, although the iron-oxide-solution remains ‘‘stable” until relatively higher temperature and in general does not coagulate on heating, it seems however yet to undergo some zrreversible change, which is manifested by the somewhat changed value of the free surface-energy. The described method is evidently also adapted for the investigation of colloidal solutions of different nature; it is planned to determine these values so highly important for the chemistry of the colloids in the case of a more extended series of colloidal substances. 1) FREUNDLICH, Kapillarchemie (1909), p. 28. 2) VoLKMANN, Wied. Ann. 11, 177, (1880); 17, 353, (1882); 58, 633, 644, (1894) ; 56, 457, (1895) ; 62, 507, (1897}; 66, 194, (1898). : 3) BRuNNER, Pogg. Ann. 70, 481, (1847). +4) Wor.EY, Journ. Chem. Soc. 105, 266, (1914). 5) The other points mentioned in the diagram, have the following significance : W=WenperG, Z. f. phys. Chem. 10, 34, (1892); S—=Sre, Diss. Berlin, (1887); .R=RayweicH, Phil. Mag. (5), 30, 386, (1890); Ss = Senris, Ann. de VUniv. Grenoble, 9, 1, (1887); H=PRocror Hatt, Phil. Mag. (5), 36. 385, (1893); M—=Macin, Wied. Ann. 25, 421, (1885). These data were obtained by very different methods; they are evidently appreciably deviating from each other. 351 § 16. Aliphatic Derwatives. II. ! ETHYLALCOHOL: C,H;.OH. o : 2} Maximum Pressure H Surface- ve, | Molecular gO = eee es tension 7 Specific | Surface- o We | rs eae lent saan oes ee in Erg. pro | gravity d,,| energy ” in S~ eae of 0° C. ae Dynes | cm?. pe pro cm?., — ———_ : — : : i = —79° 1.066 1421.2 30.6 | 0.886 | 426.2 —24 | 0.881 1174.5 25.2 0.820 | 369.6 0.1 0.825 | 1086.5 23.3 OF SOT = 3 345.4 25 0.746 995.7 ZS 0.786 321.4 35 0.724 965.2 20.6 0.777 313.1 55 0.667 889.2 19.1 0.759 | 294.9 74.5) 0.617 822.6 17.6 0.741 276.1 | Molecular weight: 46.05. Radius of the capillary tube: 0.04385 em. Depth: 01 mm. The alcohol was completely anhydrous and was therefore preserved in a bottle with drying-tube. At the boilingpoint (78°.4 C.) the | value of z is 17.0 Erg. pro cm*. The mean temperature-coefficient of » is only: 0.94 Erg. Il. Acetic Acip: CH,. COOH. | : | = Maximum Pressure H Surface- | ei | Molecular s S |-— | tension x | ppecitic | Surface- oOo || se | . Sulla ate ae | in Erg. pro | gravity d,,| energy ” in aco cury of 0° C. | in Dynes | em?. eal Erg. pro em?. = | | | | | * ) | : | = 26° | 0.943 | 1257.2 ON ele ate046 8) 400.7 34.6 0.914 | 1218.5 26.1 | 1.039 390.1 55 ORGA2 ile Sioa. eNO ed Oot 1/4 Ge aos 70 0.787 | 1049.3 22.4 | 1.010 | 341.2 98.5 | 0.691 | 921.3 19.7 0.987 | 304.7 Molecular weight: 60.03. Radius of the capillar tube: 0.04385 em. Depth: 0.1 mm. | By repeated freezing and distilling, the liquid was thoroughly purified; its boilingpoint was 118°.1 C. The temperature-coefficient is between 26° and 55° C.: 1.3 and preserves that value up to the boiling- point. At the last temperature the value of x is: 17.7 Erg. pro cm2?. 352 Specific Surface-energy in Ergs pro c.m2, 75 70 65 60 * Observat. of Vorkmann, and of BruNNER \ x © Observations of Wor.ry (1914) d © Observations of JancER (1913) és * Observat. with SiQ,-, and Fes O3esol. (1914) 55 eee 10° 0° 10° 20° 30° 40° 50° 60° 70 80° 90° 100° Temperature. Fig. 8. Surface-tensions of pure water and colloidal solutions at different temperatures. Although acetic acid doubtless is a gradually dissociating liquid, and in accordance with this manifests only a small temperature coefficient of uw, this last remains constant, contrary to the cases, where the curves appear to be concave or convex. z Maximum Pressure H Surface- Specifi | Molecular g° ! ——| tension z EERE Surface- oO . . Beg |e ‘ Si ike in Erg. pro gravity d,, energy » in s~ cury of 0° C. in Dynes em?. “| Erg pro cm?.) —19.9| 1.237 1649.2 35.5 1.095 985.3 0.7} 1.167 | 1555.8 332) 1.075 941.2 8.5 1.142 H 1523.2 32.9 1.068 928.4 2oE2 1.077 1435.9 31.0 1.050 | 884.8 34.5 1.044 1391.9 30.0 1.041 861.2 50.1 0.994 1325.2 28.5 1.025 | 826.6 69.2 0.920 1226.8 26.3 1.005 | 712.9 102 9.804 1071.8 23.0 0.969 692.5 124.5 0.723 963.9 20.6 0.945 | 630.7 144 0.660 880.2 18.8 0.924 584.3 148.7 0.649 866.4 18.5 0.919 | Silla 171 0.571 761.6 16.2 0.896 | 513.9 = ale Ns eee Par Molecular weight: 160.1. Radius of the capillar tube: 0.04385 em. | Depth: 0.1 mm. The compound boiled constantly at 1979.3 C.; at —50° C. it is solidified. At the boilingpoint the value of ~ is about: 13.7 Erg pro | em?,; the temperature-coefficient of » has as mean value: 2.52 Erg. § 17. Aromatic Derivatives. V. BENZENE: C,H. = Maximum Pressure gO ie : Bo a6 in mm. mer- Dv @ |leury of 0°C.; ™ ~~ ynes = (o} By | ASOT) 1436.7 9.5 1.055 | 1406.5 25.1 0.969 le ed2O1R9 35 0.920 1226.5 55 0.836 1114.6 74.6 0.757 1009.2 th Molecular weight: 78.05. Surface- tension 7% in Erg. pro cm?. WNMNONMWW =—-WOANOO DwAW1W 0 Depth: 0.1 mm. Although the mean value of the temperature-coefficient of » oscil- lates round 2.0 Erg., the dependence of » and ¢ is not a linear one: between 5° and 25° the coefficient is: 2.65; between 25° and 55° C.: 2.12; and between 55° and 75°: 1.95 Erg. At the boilingpoint (80.°5), | e value of % is: 20.7 Erg. Specific 895 .889 873 862 841 817 ooococoo Radius of the Capillar tube: 0.04385 cm. | gravity Ayo) Molecular Surface- energy in Erg. pro cm?. 607.7 596.6 553.8 530.3 487.8 451.4 ANISOL: CH,.O, C Hs. | @o | | Es Maxi ressur aS | Maximum Pressure H Sirfake: Specific Molecular 30 Near, ; ———| tension y in aon = jin mm. mer-| . Erg. proem2,) gravity d4o a eal 3" joury of 0°C. | me Dec | a 1 Erg. pro em?. | | 1 ] = = | |—-21° hss Ai) WIEEER G7 4 39.3 1.029 874.8 | 0.4 1306) | elAliad 37.3 1.010 840.6 25 1210) ee eee OS cyl 34.6 0.987 UNS) | 45 1137) eal lo l6eo: 32.5 0.970 15255) 7) 74.4 12022 4 i 136225, 29.1 0.942 | 687.0 | 90.8 O2962) ey 1282/52 27.4 0.927 653.9 | 110 0.875 1167.3 24.9 0.907 | 602.9 | 134.7 O65: 4) 102022 21.7 | 0.882 | 535.3 151 0.700 |} 932.9 19.8 | 0.865 494.8 | | | | | Molecular weight: 108.6. Radius of the Capillar tube: 0.04352 em. Depth: 0.1 mm. The boilingpoint was constant at 151.97 C.; at —50° the substance crystallizes to a beautiful, hard aggregate of crystals. The tempera- ture-coeflicient of » increases, just as in the case of water, with | increasing temperature: between —21° and 45° C, itis: 1.88; between | 45° and 90°.8 C. it is: ca. 2.14; between 91° and 151° its mean value is: 2.63. | VII. PHBNETOL: C,H;.0O.C,H;. | 5 _ | Maximum Pressure H | Surface- Molecular re -| tension x Specitic Surface- © | |e : B Rec as iM er |} naDyhes ‘s aid se ae a's nae ‘A zs 2 eaty of O° CC. : ike Pe) PXORC MS | | | = 21° 1.289 1718.5 36.8 1.006 902.1 0.3) 1.213 1617.7 34.6 0.986 859.6 25.2! 1.117 | 1489:0 31.8 0.962 803.1 45 1 OSes el S8an3 29.5 0.943 755.0 74.3} 0.931 | 124038 26.4 0.914 689.9 90.6| 028715) i e lGie3 24.8 0.899 655.3 | 110 0.813 1084.6 23.0 0.889 | 612.3 184.7 0.734 | 979.0 20.7 0.855 565.6 150.1 0.687 915.9 19.3 0.849 529.8 160.5) 0.651 868.6 18.3 0.839 506.3 Molecular weight: 122.1. Radius of the Capillar tube: 0.04352 ecm. | Depth: 0.1 mm. | The boilingpoint is constant at 168°; the substance solidifies at — 50° C. to an aggregate of long, colourless needles. The tempera- ture-coefficient of » can be considered as constant, its mean value being: 2.14 Erg. 355 VIL. AneTHoL: CHO. Csll,.CH:CH . CH (1.4) | 2 ae 2 ore ee | = : Maximum Pressure | Surface- en | Molecular | €° pew red OE Jl “tension 2 Wareeees Surface- | Be inmm.mer-| 5 py _ in Erg pro | gravity dyo| energy 4 in| 5 | cury of 0° C. | In yes | cm?. | Erg pro cm?,| hea i Int oa ail | mee: | "O47 1.267 | 1689.2 36.2 0.988 1021.8 "45.5 1.188 | 1583.8 33.9 0.969 969.1 ATByG)! 1.078 1438.4 30.7 0.944 893.0 “94.2 1.017 1355.7 28.9 0.927 850.9 115 0.929 1239.0 26.9 0.908 803.0 135.1 0.865 1153.4 25.0 0.890 756.4 160.9 0.787 1049.8 Dol 0.867 698.9 192.8 0.689 919.1 19.8 0.838 623.6 | 212.7 0.625 833.5 18.0 0.820 575.6 230 0.588 783.9 16.9 0.809 ~ 544.9 ei We see ett a inl eee PS [ee LEE a Molecular weight: 148.1. Radius of the Capillar tube: 0.04439 em.; in the with * indicated observations, the | radius was: 0.04352 em. Depth: 0.1 mm. The boilingpoint was constant at 230°.5 C.; the meltingpoint is: 2195 C. Between 25° and 75° C. the temperature-coefficient of » is about: 2.53; later on it becomes fairly constant: 2.25. At the boilingpoint the value of ~ is: 1.68 Erg pro cm’. IX GuasAcoL: CH,0.C 5H, . OH (1,2). oO 5 Maximum Pressure H | : Es : : Surface- | Specific | Molecular $0 tension yin | | SEO | Ss inmm.mer- . Erg. proem?.| gravity dy.) Cnerey “in | | 5° leuy of o°¢,| i Dynes | jis | + Erg. pro em?. | | | | 26° 1.377 1°36.4 43.3 | 1.128 994.0 45.5 1.302 1736.4 40.9 1.109 049.6 66.5 1.224 1632.4 38.4 1.088 | 902.9 86 1.156 1540.7 36.2 1.058 861.8 106 1.087 | 1449.1 34.0 1.048 819.7 |125 1.024 1365.8 32.0 1.029 780.9 Hi4GmeeeeKOcose) SNP ri26500) | 12086 |) sl eitoos), I") "7394 166 0.874 | 1166.0 27.2 | 0.988 682.1 1184 0.803 1070.2 24.9 | 0.970 632.1 206) oF 1027189, MIGRL COS TT asp 10,2253 0.948 | 574.8 | | | Molecular weight: 124.06. Radius of the Capillar tube: 0.04803 cm. Depth: 0.1 mm. The substance boils under 24 mm. pressure at 1069.5 C.; the melting- point is 32° C. The temperature-coefficient of » is between 26° and | 46° C.: 217; between 146° and 206° the curve is feebly convex to | the f#axis and the mean value of the coefficient is therefore about: 2.66 Erg. ae RESORCINE-MONOMETHYLETHER: C,H, (OH) . (OCHS) (1,3). EI é Maximum Pressure / 45 Molecular 5 | Surface- Specific Saree 50 a — | tension x in : = in mm. "| eravity d,.| energy in « BF mercury of | in Dynes | Erg pro cm?. era ace Erg’pro cm?, a —— - = : = —20° 2.622 | 3495.6 83.1 1.181 1850.1 OTF Pee lS6S6 een ee 211 el 51.6 1.161 1161.9 25.9] 1.462 1948.8 46.0 1.136 1051.0 45.9) 1.380 1840.5 43.4 1.119 1001.6 66.5) 1.318 1757.3 41.4 1.102 965.2 86.5 1.252 1669.7 39.3 1.082 927.5 107 1.196 1594.9 37.5 1.061 896.7 125 1.140 1519.9 35.7 1.044 862.9 146 1.075 1433.2 33.6 1.023 823.2 166 1.009 1345.0 31.5 1.003 782.0 184 0.956 1274.2 29.8 0.986 748.2 206 0.862 1149.4 26.8 0.965 682.6 | Radius of the Capillary tube: 0.04803 cm. Depth: 0.1 mm. Molecular weight: 124.06. Under 25mm. pressure, the compound has a boilingpoint of 144°C. The observations over 180° C. relate to the substance already slightly dissociated, as was seen from the brownish colour of the liquid. At —79° C. it becomes glassy, without indication of crystal- lisation. At 0° and — 20° ©. also, the viscosity of the liquid is still enormous. XI. eee Maximum Pressure H | Pant 3 Molecular SS 2 pera | : UT Ace Specific Surface- oS ; | ension % in : a, in mm. : i a energy / in £2 | mercury of | in Dynes | Erg pro cm?. gravity dao Erg pro em2. o | = a OOK? —22° 1.520 2026.5 44.3 1.104 1107.9 0 1.419 | 1892.3 41.3 1.084 1045.6 25 1.325 1766.2 38.6 1.064 989.4 45.3 1.250 1667.0 36.4 1.046 944.3 70.5) 1.166 1554.4 33.9 1.022 893.2 90.1 1.090 1453.2 31.7 1.004 844.6 116 1.007 1342.7 29.2 0.980 790.6 135.3 0.943 1257.0 27.3 0.963 TA7.9 *162.1 0.781 1041.0 24.4 0.939 679.8 *189.9| 0.700 932.8 21.8 0.914 618.4 *210 0.637 849.5 19.8 0.894 570.0 Molecular weight: 138.08. Radius of the Capillary tube: 0.04439 cm.; in the with * indicated observations the radius was: 0.04803 cm. Depth: 0.1 mm. The substance has a constant boilingpoint at 214°.5 C.; the liquid can be undercooled to — 76° C., and solidifies to a crystal-aggregate, wich melts at —52°C. At lower temperatures, as far as to 0° C., the temperature-coefticient of » is rather large: 2.83 Erg; later it is fairly constant, with the value: 2.25 Erg. HypRocHINON-DIMETHYLETHER: CyH, (OCH), (1, 4). g ; Maximum Pressure HH Surface- a0 tension x See in mm. in Erg g= | mercury of | in Dynes pro em. = 0° C. 66° 1.106 1474.5 34.7 86.5 1.031 1374.1 32.3 106 0.974 1299.2 30.5 126 0.909 1213.8 28.4 146 0.843 1124.4 26.4 166 0.775 1032.7 24.2 184 0.709 945.3 22a 206 0.628 837.0 19.5 Specific gravity d 40 1.036 1.008 0.990 0.976 0.957 0.938 0.921 0.901 Molecular Surface- energy » in Erg pro cm?, 905.4 858.3 820.3 dithle| 726.2 674.7 623.7 558.4 Molecular weight: 138.08. Radius of the Capillary tube: 0.04803 cm. Depth: 0.1 mm. The meltingpoint of the substance is at 56° C.; it boils under a pressure of 20 mm., at 109° C. On cooling first a glass is obtained, which gradually crystallizes in fine needles. Between 66° and 106° the temperature-coefficient of » is about: 2.11; between 106° and 166°, about: 2.46; and between 166° and 206° C., about: 2.88 Erg. The relating curve is therefore concave to the f-axis, § 18. Heterocyche Derivatives. XII. PyRIDINE C;H,N. g Maximum Pressure Surface- eas Molecular ay tension Sa Surface- Oo . . . a, in mm. in Erg avity d,,| energy in BF mercury of | in Dynes in em? ch eee Erg pro cm’, = ONC: —19 1.698 2263.8 48.9 1.078 827.8 —20.5 1.430 1906.5 41.1 1.018 722.9 0.1 1.329 1771.8 38.1 0.998 679.0 25 1.215 1619.8 34.9 0.975 631.8 35 Lol 1569.2 33.8 0.962 607.3 55 1.099 1465.2 31.5 0.942 583.4 14 1.022 1362.5 29.3 0.923 550s 92.5 0.960 1279.9 PACS: 0.904 523.5 Molecular weight: 75.09. Depth: 0.1 mm. The pyridine crystallizes readily at —52° C.; thus the measurements at —-79° C. relate to a strongly undercooled liquid, The curve, giving the dependence of » and ¢ is not quite regular. At the boilingpoint Proceedings Royal Acad, Amsterd am. Vol. XVII. Radius of the Capillary tube: 0.04385 cm. 358 XIV. o . EES Maximum Pressure H Surface- BY ia Molecular a tension , perie Surface- ere inmm. | in Erg gravity Ayo energy # | E er re of | in Dynes pro em?. in Erg —70° eiey || Uleil - 47.4 1.036 950.8 —20.7| 1.246 1661.5 | 39.2 0.986 812511) 0 | 1.165 1553.2 | 36.6 0.965 7169.7 25.8] 1.074 1432240) SB lod 0.940 721.2 46 0.999 1332.5 31.3 0.920 679.6 66.5) 0.928 1236.9 29.0 0.900 638.9 86.5 0.846 1128.5 26.4 0.881 590.0 106 OFIST 2) a s104953. 4) 24.6 0.862 557.8 126 0.718 957.7 22.5 | 0.842 518.2 2-PICOLINE: C;H, (CH) N. Molecular weight: 93.07. Radius of the Capillary tube: 0.04803. Depth: 0.1 mm. The liquid, which is boiling constantly at 1339.5 C., can be under- cooled as far as —74° C.; it solidifies at — 64° C. and melts there very rapidly. Between — 70° and — 21°, the temperature-coefficient is about: 2.83; afterwards the mean value remains about: 2.02 Erg. EV _CHINOLINE: CoH, - N. /3H3. o hee Maximum Pressure H L Surface- Molecular €° | ee MELONS LOT Specific Surface- | © | - ie baer a | in Erg. pro gravity d,.| energy » in a= ees of PO, in Dynes em?. = Erg. pro.cm*. es —21° 1.682 | 2242.4 49.1 | A124 | eGO RO 0 1.608 2143.8 47.0 | 1.108 1121.1 *24.8) 1.562 2082.5 | 44.7 | 1.089)- 9) 107826 *45.2) 1.486 1981.1 42.5 | 1.073 | 1035.6 *714.3 W319) 99 eel838 52 39.4 | 1.051 973.5 *94.7 1.303 1737.1 37.2 1.034 929.1 115 210) 3)" 61320) 9) 35.2 1.018 888.4 135.2 1.135 | 1513.8 | 33.0 1.002 841.7 160 1.047 | 1395.9 | 30.4 0.981 786.4 192.5 0.929 |} 1239.0 | 26.9 0.954 708.9 213 | 0:855, 113959 25.7 0.938 658.3 230 0.797 ° || 1063.3 = |) 23,0 0.924 619.2 Molecular weight: 129.07. Radius of the Capillary tube: 0.04439 em.; in the with * indicated observations, the radius was: 0.04352 em. Depth: 0.1 mm. The boilingpoint was constant at 233° C.; the liquid can be under- cooled as far as —50°, and then crystallizes, melting readily at —25° C, The temperature-coefficient of » increases with the temperature: between —21° and 45° C. it is: 1.92; between 45° and 115° C.: 2.10; between 115° and 230°: 2.33 Erg. At the boilingpoint the value of x is: 22.7 Erg. pro cm’. 359 Molecular Surface- Fig. 9. energy, in Erg pro c.m2. 7790 1160 7730 7100 7070 “80°-60°-40° -20° 0° 20° W* 60° 80° 100° 120° 140° 160° /S0° £00° 220° 240° Temperature 24* Some of the curves, which relate to these organic liquids, are reproduced here in the usual graphical way (fig. 9); the corresponding critical temperatures of the liquids, so far as they are known, are 360 mentioned and written between () behind the names of the substances investigated. 19. Salts of the Alkali-Metals. XVI. a ee | POTASSIUMCHLORIDE: ACl, lem eu eee = &| Maximum Pressure Surface- Molecular Ee ; Specitic ae ico} a = tension x re Surface- | a | {lure ° Be ° | in mm. mer- in Detieg fn re Pr | etevity idgo| PROTEUS '5 £| cury of 0°C.| J em’, Erg pro em?. ie ck | | | 799:5| 3.015 4019 | 95.8 1.509 1290.0 | 827.1 2.957 | 3942 94.0 1.492 1275.3 861.5 2.873 3830 91.3 1.470 1251.0 | 885.1 2.819 3758 89.7 1.456 1237.0 908.5) 2.768 3690 88.0 1.442 1221.3 | 941 2.697 3595 85.8 1.421 1202.6 | 986 2.582 3442 82.2 1.396 1165.8 1029 2.484 3311 79.1 — = 1054 | 2.425 3233 iliez _ os 1087.5 2.361 3147 1522 — — |1103.6 2.313 3083 USsa1l — — 11125 | Poel fe) 3033 72.5 — _ 1167 2.182 2909 69.6 — — Molecular weight: 74.56. Radius of the Capillary tube: 0.04736 em. at 15°C. The expansion-coefficient is here 0.0000083. Depth: 0.1 mm. The salt melts sharply at 771° C.; after four hours heating between 900° and 1100°, it solidifies at 769°C. It evaporates rapidly at 980°, at 1160° with great speed. Just as in the case of the other alkali- salts, the vapours are doubtlessly acid, while the solidified mass gives an alkaline reaction, if dissolved in water. The gradual dissociation lowers the value of the maximum pressure more and more, as is seen from repeated experiments after a longer heating 1100° C. As some illustrations of the changes caused by the commenced dissociation of the salt, the following measurements are given, which were made after a heating at 850° and 1150° C. during full four hours: | At 848° C. the maximumpressure was found to be 2.821 mm, mercury | 904 2.720 | ” . ” ” ” ” ” » ” S = ” ” ” 941 ” ” ” ” ” ” ” ” 2.645 ” n ” 956.5 » » ” ” ” ” 5 a) 2.615 ” ” ” 1037 ” ” ” ” ” ” yn 7” 2.455 ” ” All values are evidently lower than the previously observed ones, and at the lower temperatures, at which the observations were made after the longest heating of the salt, the decrease is most appreciable. 361 XVII. POTASSIUMBROMIDE: (Br. | Temperat. Maximum Pressure / Surface- LTC Cys | aueeenntan | ennennmnnann LENS LONI air in mm. (corr.) mercury of | in Dynes | Erg. pro cm?. 0° C. ° 775 2.102 3602 85.7 798 2.642 3522 83.8 826 2.585 3446 82.0 859 2.504 | 3338 79.5 886.5 2.450 | 3266 71.8 920 2.376 3167 75.4 Molecular weight 119.02. Radius of the Capillary tube : 0.04728 cm. at 15°C. Depth: 0.1 mm. The dissociation and splitting off of hydrogen- bromide and bromine is observed at 825° C. At 940° C. the evaporisation and dissociation of the salt have become so rapid, that measurements | at higher temperatures seemed to be without any real significance. XVIII. POTASSIUM IODIDE: AV. Temperat. Maximum Pressure H Surface- mya Ce tension x (corr. on in mm. in Erg G. Th.) mercury of | in Dynes pro cm?, 0° C. Sie ane meta nar a. 737 2.372 3162 15.2 164 2.274 3031 72.1 866 2.106 2807 66.8 873 2.097 2795 66.5 Molecular weight: 165.96. Radius of the Capillary tube: 0.04728 cm. at 15°C. Depth: 0.1—0.2 mm. The salt melts at ca. 700° C. Already at 750° C. it evaporates rather rapidly, and at 900° C. with dissociation into hydrogen-iodide and iodine. Meas- urements at higher temperatures can have hardly any significance. 812 2.183 2910 69.2 362 XIX. SoprumcuLoripn: NaCl. o a = E Maximum Pressure H Surface- bas me Molecular gOS st ANS tension haa Surface- o° : ; Be |; Ula in Erg. pro gravity d energy ” in ens aeee OG in Dynes em? 4 Erg. pro em?. Bias E 802.6 3.580 4772 113.8 1.554 1275.9 810.5 3.572 4762 113.5 1.549 1275.4 820.8 | 3.552 4735 112.9 1.543 1270.8 832 3.520 4692 111.9 any 1262.6 859 | 3.457 4608 109.9 1.523 1247.7 883.2 | 3.401 4534 | 108.2 — — 907.5 3.345 4459 | 106.4 — 930.6 3.285 4379 104.5 — — 960.5 3.227 4302 102.7 — 995.5 3.132 4175 99.7 — _ 1037 3.047 4062 97.0 —- — 1080 2.951 3934 94.0 — — 1122.3 2.864 3818 91.3 -— — 1171.8 2.761 3681 88.0 — = Moleculair weight: 58.46. Radius of the Capillary tube: 0.04736 cm. 15°RC Depth: 0.1 mm. at { The pure salt melts at 801° C. At 1080° it evaporates already rapidly, at 1150°C. very rapidly. The temperature-coefficient of « calculated in the few cases, where values of specific gravity were available, is very small: strong alkaline reaction; about 0.57 Erg. The solidified mass gives in water a rather reaction. the vapours of the heated salt have an acid SODIUMSULPHATE: Na,SO,. 2 a ‘ 55 2 SI Maximum Pressure H Saitate: oe oS = : Ey ° g tension yin BS g |inmm mer | in Dynes | Bre procm = 3 900 6.285 8379 194.8 945 6.247 8328 189.3 990 6.209 8278 188.2 1032 6.149 8197 186.5 1077 6.088 8116 184.7 Molecular weight: 142.07. Radius of the Capillary tube: 0.04512 em. Depth: 0.1 mm. The pure salt melts at 884° C. If heated to 1100° C. the solidified mass! gives in water a rather strong alkaline reaction, indicating a dissociation. Measurements at higher tempera- tures than 1100° C. thus seemed to be useless. XXI. SopDIUMMOLYBDATE: Na,Mo0,. | Oo : Bos Maximum Pressure H Satraee: ra E | tension x in S2)inmm.mer-| . i 2 5 cury of 0°C, | ™ Dyueaia pe rere eee | eeu rie i 698.5 6.091 8122 214.0 | 728.5} 5.975 7967 | 210.0 Tl 5.921 7893 208.1 777 5.828 7770 204.9 | 818.8 5.757 7675 | 202.4 | 858.5 5.657 1542 199.0 ; 903.8 5002 7401 | 195.4. | | 948 5.436 7247 191.4 989.5 5.330 7106 187.7 1035 5.224 6966 184.1 1078.5) 5.141 6854 | 181.2 /1121.5 5.070 6760 178.8 1171.5 4.998 | 6654 176.1 1212 4.947 6595 174.6 = Molecular weight: 206. Radius of the Capillary tube: | 0.05240 cm. Depth: 0.1 mm. The compound melts at 687° C. to a | _colourless liquid. = XXII | LITHIUMSULPHATE: Li,SO,. \o 5 Maximum Pressure // Surface- a H tension , |@29 6 ; . }259} in mm. in Erg a= mercury of | in Dynes pro em2, a 0° C. 860° 6.361 8481 223.8 873.5 6.342 8455 223.1 897 6.303 8403 221.8 923 6.256 8341 220.2 962.5) 6°169 8224 217.4 | 976.8) 6.146 8194 216.4 |1001.2 6.099 8132 214.8 1038.5 6.027 8035 212.3 | 1057 5.987 7982 211.0 |1074 5.953 71936 209.8 |1089.5 5.923 7897 208.8 1112 5.879 7838 207.3 1156.5 5.791 77120 204.2 1167.5 5.766 71687 203.4 1183.5 5.737 7649 202.4 1192.2 5.718 71624 201.8 1214 5.675 7566 200.3 Molecular weight: 109.94. Radius of the Capillary tube: 0.05240 em. at 16° C, Depth: 0.1 mm. The salt was prepared frompurest lithium- carbonate and sulfuric acid, carefully dried , and heated at 900° C.; it melts at 849° C. After being heated to 1200° C., the substance, shows an alkaline reaction with water. Also here it is of little significance, to pursue the measurements to higher temperatures. XXII. LITHIUMMETASILICATE: Li,SiO;. 5 : = Maximum Pressure 7 Surface- EOS ee eS tension oo | a . a. 8 in mm. in Erg 8 sues mercury of | in Dynes pro em2. a 2 O°RC: al SSS SS Ee = SSS ee —_ 1254° 11.82 15759 374.6 1380 11.29 15052 358.2 1421 Lee 14958 356.2 1479 11.11 14812 352.8 1550 10.97 14626 348.7 1601 10.90 14532 346.6 Molecular weight: 90.01. Radius of the Capillary tube: 0.04706 cm. Depth: 0.1—0,.2 mm. The analysed metasilicate was perfectly pure. It melts at 1201°C. The temperature-coefticient of » is very small. 365 § 20. In the case of Porassiumcunorate: ACUO,, the maximum pressure HH was 3,573 mm. mercury at 413°.5 C; at 448°.5 C. it was: 3,540 mm. The radius of the here used silver-capillary tube being: — 0.03460 em., the free surface-energy is calculated : At 413°.5 C. 7% = 82,4 Erg. pro cm’. At 443°.5 C. ¥ = 8156 Erp. proven: At the last mentioned temperature the salt commenced to decompose already distinctly, while O, was split off; at higher temperatures therefore the values of y appeared to increase gradually by the generation of AC/O, and KC7. It was not possible therefore to investigate the values of the temperature-coéfficients at higher temperatures; in every case however they seem to be rather small. With Stnvernirrate: AgNO,, the value of x is about 164 Erg. pro em*. at 280°C; at 410°C. it is about 153.8 Erg. In this case the temperature-coefficient is also in the neighbourhood of 0.6 or 0.9, — this being a rather small value too. § 21. It is not my intention, to discuss now already the here mentioned data, nor to add the remarks, which are suggested thereby. It is better to postpone that task, until the complete experimental material now available will be published. The given instances may however prove, that the question: how to measure the surface-tensions of liquids with great accuracy within a temperature-interval, from — 80° C. to 1650° C., may be considered now as completely solved. Groningen, May 1914. Laboratory of Inorganic Chemistry of the University. Chemistry. — “The Temperature-coefficients of the free Surface- energy of Liquids, at Temperatures from —80° to 1650° C”. II. Measurements of Some Aliphatic Derivatives. By Prof. Dr. F. M. Jagger and M. J. Suir. (Communicated by Prof. P. v. Rompuren). § 1. In what follows the data are reviewed, which were obtained by us in the study of a series of aliphatic derivatives after the method formerly described by one of us‘). With respect to the liquids here used, we can make the following general remarks. No product of commerce, not even the purest ob- 366 tainable, can be esteemed suitable for this kind of measurements: the small traces of humidity already, which even the best chemicals always contain, are sufficient to make the results unreliable. Most of the orga- nical liquids of commerce however seem to contain several admixtures, in small quantities or even larger quantities of water. We often obtained a first purification by distilling a small fraction from it, whose boiling point remained constant between 1° or 2° C. In several cases even this appeared not to be possible: in such case the preparation was dried during some days by means of anhydrous sodiumsulphate; then, if the special character of the substance did not forbid this, it was dried again during a long time by means of freshly sublimed phospherpentoxide, after which the fractional distillation was tried again. Commonly it appeared to be possible, ’ to separate from it a fraction, whose boiling point remained constant between 1° or 2° C. With some preparations we succeeded in drying them by means of metallic sodium. After very dry fractions, boiling within a few degrees, had been obtained in this way, they were once more distilled with a small flame only, or on the water-bath, under atmospheric or reduced (12—20 mm.) pressure; in this operation only the fraction, boiling within an interval of 1 C°., was used for further treatment. The liquid was then cooled during several hours in a closed vessel, by means of a mixture of salt and ice, or by a bath of, solid carbondioxide and alcohol. If it erystal- lized, a further purification was often possible by repeated freezing and decanting. Often a very thin layer of a solid substance (eventually of ice) was deposed at the walls of the vessel, the rest remaining liquid and transparent; the liquid portion was poured into a dry, clean vessel then, and the said operation repeated, till no solid layer any more appeared. [f however the phenomenon continued to appear, the liquid was treated again at least during a week with fresh phosphorpentoxide, and the freezing repeated again and again. Finally the purified liquid was distilled once more under atmospheric or reduced pressure; only the fraction, boiling within half a degree was collected then for the measurements. It is hardly necessary to mention, that hygroscopical liquids were preserved and treated in a suitable manner. The thus obtained liquid was commonly only a jvery small fraction (10°/, or 20°/,) of the original commer- cial preparation; it must be remarked, that the observed boiling- temperatures often differed appreciably from the data, given in the literature, and in several cases appeared to be dower than those; — which perhaps can be explained by the fact, that in the distil- lations, described in the literature, the liquid was heated éoo rapidly. In our experiments the speed of distillation often did not exceed about six drops every minute. In some cases, e.g. with ¢olwene, it was impossible to distil from the product of commerce a fraction, fulfilling all conditions; in such cases the substance was prepared in some other way, e.g. the mentioned toluene by dry distillation of purified calciumphenylacetate; ete. In the series of compounds described, several were taken from the collection of scientific prepa- rations of this laboratory; from these also only the small, constantly boiling fraction was used for our purpose. § 2. Notwithstanding the by no means negligible differences of the boilingpoints observed, the specific gravities of the liquids in most cases differed only slightly or not at all from the data, given in the literature. If this was the case, — and we always controlled this by some pycnometrical determinations at 25° C., — the specific gravities at other temperatures were calculated from the expansion- formulae eventually already determined. If the direct determination of d=’ did not agree with the number, given in literature, or if the expansion-formula was not known accurately enough, three specific gravities, e.g. at 25°, 50°, and 75° C. or at a higher temperature, were determined pycnometrically, and from these determinations an empirical equation of the second degree with respect to ¢, was calcu- lated. This is completely sufficient here, because the specific gravities were all abbreviated with three decimals: an account of the densities in more than three decimals, must be esteemed valueless here, with respect to the obtained accuracy of the measurements. With most liquids, the mean decrease of the specific weight for 1° C. does not differ largely from 0,001. For temperatures of — 70° and above 100° C. it was often necessary to extrapolate by the aid of the established empirical formulae ; although conscious of the uncertainties, which are always connected with such extrapolations, we are of opinion that we have not introduced here in this way errors of appre- ciable amount, because for these values such an error could manifest itself only in the third decimal place, and dilatation of the liquids occurs ordinarily in so regular a way, that the probability of heavy errors is thus highly diminished by this circumstance. Moreover another way was not available at this moment, if not with large sacrifice of time and labour. § 3. In the following the obtained results are collected in tables. For the value of 1mm. mercury at 0°C., 1333,2 Dynes (45°), was ealeulated, and this value was used in all further calculations; in the tables all numbers for x and u are adjusted by the necessary corrections. 368 The graphical diagrams relate to the variation of the so-called “molecular” surface-energy mu with the temperature; in the same diagram analogous, homologous compounds or such, related by simple substitutions, are put together; this will be of practical use for the comparative considerations later to be given, and allows a rapid review of the behaviour. For the construction of the diagrams, not the numbers of the tables, but those following directly from Cantor’s formula, are used; therefore the correction, necessary to derive the absolute value of 4 from these readings by diminution, are indicated on each curve in the diagrams. § 4. Aliphatic Derivatives. This series of measurements relates to the following aliphatic Molecular Surface Energy in Erg. pro cm?*, 7000 « 990 = ~ 940 x, ‘ 9/0 os Ne SSO \ \\ \ G50 NS ‘ 20 as 2 . e 790 Saw eR ak 760 Ss =2. 730 NG = ‘ ° 700 YE « 670 ee XN 640 4 x . « 610} , \ x . bs \ I8O x Xe a. . 5501. NS se xy Xe NS \ 5200, SO RK Pee? 490 Hs eee Sues co ease Te Cp 460 AS: SS SoS “SOSo See Sa ORS é 430 b. aS Stee SS “3556 Ss era! Ss, as Co. . ne ~ aa ’ 5 , 400 SS a ne =< ; ne 2 eee 5 ASS SNS 370 ee 2) Sc atid 340 Se Se [OSs SA -8 JII0 EE ote (ae. SB 280 SLPS, =a 250 “50° -60°-40° -20° O° 20° 40° 60° 80° 00° 120° 740° 160° 780° 200° 220°247° Temperature Fig. 1, 369 substances: norm. Propylalcohol; Isobutylalcohol; Diethylether ; Ethyl- formiate; Ethylchloroformiate; Ethylacetate, Methyl-, Ethyl-, and norm. Propyl-alcohol: C3H;. OH. = Maximum Pressure Surface- Specifi Molecular aS tension pecie Surface- Es in mm. mer-) _ in Erg. per gravityd,, | energy v in Bie cury of in Dynes: cm’. 4° | Erg. pro cm?, & OOK: ~76 1.170 1559.8 33.4 0.881 557.4 —21 0.924 1245.4 © 26.6 0.837 459.3 0 0.875 1167.3 24.9 0.820 435.9 25.5 0.807 1075.4 22.9 0.800 407.5 45 0.755 1006.4 21.4 0.784 386.0 74.5 0.679 905.3 19.2 0.759 353.9 90.6 0.638 850.2 18.0 0.746 335.6 | | Molecular weight: 60.06. Radius of the Capillary tube : 0.04352 cm. Depth: : 0.1 mm. The substance boils at 96°.7 C. constantly. Isobutyl-alcohol: (CH3). CH .CH,OH. v . a Maximum Pressure Surface ee Molecular so tension x Beeme Surface- a” jin mm. mer- in Erg. pro ravity d,,| energy » in EE | cury of in Dynes 2 Seat aes 2 2 he. y; cm’. Erg. pro cm’. —11.5 1.149 1531.8 33.0 0.885 631.5 —12 0.890 1186.5 25.5 0.828 510.1 0.3 0.853 1137.2 24.4 0.817 492.5 | 10.4 0.825 1099.9 23.6 0.807 483.9 | 25.1 0.783 1044.5 22.4 0.794 | 460 9 35.1 0.756 1008.0 21.6 0.785 447.7 49.7 0.723 963.9 20.6 0.771 432.2 69.6 0.670 893.8 19.1 0.753 407.0 101 0.594 791.9 16.9 0.731 367.4 Molecular weight: 74,08. Radius of the Capillary tube: 0.04385 cm. Depth: 0.1 mm. The compound boils at 106°.8 C. constantly; at the boilingpoint y has the value: ca. 16.5 Erg. pro cm’. 370 Tsobutyl-Isobutyrates; Acetone; Methylpropylcetone; Ethyl-Acetyloacetates Methyl-Methylacetyloacetate; thyl-Propylacetyloacetate; Methyl-, Ethyl-,. Diethylether: (CjH5)o O. ql Maximum Pressure 7 Surface- 2 Molecular SOP MAL. Be Et oes tension Specific Surface- ao in mm. | inErg. pro | gravity d,. | energy in ES mercury of in Dynes cm?. 4 Erg. pro cm? | 0° C. I-75" 0.990 1319.9 28.5 0.818 574.7 —20.5 0.748 997.2 21.5 0.758 456.2 0.2 0.670 893.8 19.2 0.735 415.8 10.9 0.628 837.2 17.9 0.723 392.0 2523 0.584 718.6 16.7 0.707 371.2 29.5 0.574 766.2 16.4 0.703 365.9 Molecular weight: 74.08. Radius of the Capillary tube: 0.04385 cm. Depth: 0.1 mm. The substance boils at 34.98 C. constantly; at the boilingpoint x is: 15.9 Erg. pro cm? IV. Acetone: CH;.CO.CH3. iS Maximum Pressure 1 Surface- . Molecular eS u a tension x Specific Surface- 2.0 in mm. in Erg. pro ity d energy » in §-= | mercury of | in Dynes | . cm2, agree es Erg. pro cm”. be OoRE EY, le oles 1647.8 35.6 0.917 565.5 —19.5 0.971 1295.6 27.9 0.845 468.0 Oe) 0.886 1181.3 25.4 0.818 435.4 11.4} 0.838 1117.4 24.0 0.803 416.5 25.5 0.786 1047.9 22.5 0.785 396.4 35 0.740 085.6 Ake 0.772 375.9 50.1 0.695 926.6 19.8 0.757 357.4 Molecular weight: 58.05. Radius of the Capillar tube: 0.04385 cm. Depth: 0.1 mm, The boiliagpoint is 56° C.; the value of y is there: 19.4 Erg. pro cm*. Eye! Propyl-, Butyl-, Tsobutyl-, and Amyl-Cyanoacetates; Tri-, and Tetra- chloro-methane; and Isobutylbromide. V. — Methylpropylcetone: CH3.CO.C,H;. = E ; Maximum Pressure | Surface- . Molecular ey tension ~ Specific | Surface- a. in mm. | in Erg. pro ity d,. | energy » in 5 P gravity s* menu of | in Dynes | em2, | 4° Erg. pro ae 74-2 1.240 1653=2)00 35.4 | 0.936 721.4 —20.5, 0.996 el 32729 28.3 | 0.872 604.6 0.3) 0.913 1217.8 26.0 | 0.852 564.1 25.5} 0.831 1107.6 | 23.6 0.826 22 45 0.762 1015.7 21.6 0.806 486.3 74.3 0.672 896.1 19.0 0.777 438.3 90.8 0.613 818.1 | URS 0.761 404.7 99.6 0.589 785.8 | 16.6 0.753 391.1 | | Molecular weight: 86.1. Radius of the Capillary tube: 0.04352 cm. Depth: 0.1 mm. The substance boils at 101.93 C. constantly. = =| VI. Ethylformiate: HCO. O(C2H;). v . Ele Maximum Pressure H | Surface- acan Molecular hes tension % peeitic Surface- on in mm. : > in Erg. pro | gravity do energy » in ‘= | mercury o in Dynes em?. Erg. pro cm2. 2 ee | ee 1605) 12289 1661.2 | 37.8 1.032 502.7 *—16.2 0.945 1259.9 28.5 0.958 398.3 baer aad 0.864 1151.9 26.0 0.938 368.5 24.9 0.802 | 1069.2 22.9 0.910 331.2 Sone 0.757 1009.6 21.9 0.899 319.3 49.2 | 0.718 957.2 | 20.5 0.879 303.4 be a Molecular weight: 50.0.5 Radius of the Capillary tube: 0.04408 cm.; in the observations, indicated by *, this radius was; R=0,04638 cm. Depth: 0.1 mm. After carefully drying, this ether boils at 54.93 C. constantly ; it remains a relatively thin liquid as far as —79° C. At the boiling- point , is 19.9 Erg. pro cm®*. 372 Molecular Surface- ee ; Bs Energy in Erg pro em?. Fig. 2. 80°-60°-40°-20° O° 20° 40° 60° 80° 700° 120° 740° 760°780° 200°22G° Temperature VII. Ethylchloroformiate: C/.CO.O(C:Hs). vo ° iB , Maximum Pressure H | Surface Bane Molecular See —EE -| tension pectic Surface Be in mm. mer-) in Erg. pro | gravity d,,| energy win ce cay ao in Dynes em? Erg. pro cm’. — 15.5 1.353 1803.8 42.4 1.278 819.0 - 21 1.046 1395.0 32.6 1.186 661.9 0) 0.951 1269.2 29.6 1.160 609.9 25 0.847 1129.2 26.2 1.127 550.3 45.3 0.774 1031.8 23.9 1.095 Sila 70.2 0.692 922.6 Dili, 1.050 466.8 84.8 0.643 857.8 19.8 1.022 443.9 Molecular weight: 108.49. Radius of the Capillary tube: 0.04803 cm. | Depth: 0.1 mm. | The compound boils at 91.°5 C. constantly; at this temperature x is 19.3 Erg. pro cm’. VIII. : Ethylacetate : CH,.CO.O(C)Hs). rs ] 5 : Maximum Pressure 1 Surface- Specifi Molecular e- tension z Beciuc Surface- a. jin mm. mer-) | in Erg. pro | gravity d,.| energy # in | a” ony ee | in Dynes cm?. Erg. pro cm’,) | S714 | 1.274 || “1698.5 36.6 1,016 716.8 —20 0.994 1325.2 28.4 | 0,949 582.1 0 0.892 1189.2 25.5 0,924 532.1 25.5 0.780 1039.9 22.2 | 0.893 473.8 34.7 0.744 992.5 21.2 0.881 | 456.6 55 0.679 897.2 19.1 0.856 419.3 70 0.623 838.5 17.8 0.829 399.2 Molecular weight: 88.06. Radius of the Capillary tube: 0.04385 em. Depth: 0.1 mrh. After very carefully drying and repeated distillation, this ether boils at 77.°1 C. constantly. It remains a thin liquid as far as —80° C. At the boilingpoint the value of z is: 17.2 Erg. pro cm’. 25 Proceedings Royal Acad. Amsterdam. Vol. XVII, IX. | ; | Methyl-Isobutyrate: (CH3), CH .CO.0O(CH5). o | : ae Maximum Pressure Surface- i Molecular so ie ee A BA ene Specific Surface- Bie | in mm. mer- | _ inErg. pro | gravity d,, | energy in | §- cury of in Dynes em2, 4° Erg. pro cm?, |e ONG: 73° | M.296 1728.0 37.1 0.995 813.1 21.5) 1.006 1341.9 28.7 0.936 655.1 0.5 0.903 1204.0 syotl 0.911 597.3 | 25.3) 0.805 1073.2 22.8 0.882 541.5 | 45 0.727 969.7 20.6 0.859 497.9 | 74.7 0.631 840.9 17.8 0.825 442.0 | 91.3) 0.589 785.8 16.6 0.806 418.6 Molecular weight: 102.08. The substance boils constantly at 91°.8 C. Radius of the Capillary tube: 0.04352 cm. Depth: 0.1 mm. X. Ethyl-Isobutyrate: (CH3). CH.CO.O(C,Hs). bol POs eS) ENE NS Maximum Pressure Surface- : Molecular ese ae we | tension x Specific Surface- | in mm. mer- | in Erg. pro gravity Ayo energy » in cury of in Dynes em?2, Erg. pro cm’, a ay je —— —— — = = — | 1.165 155352 i 33.3 0.976 805.4 0.940 1253.2 26.8 0.913 677.7 0.867 1155.9 24.6 0.891 632.3 0.779 1038.6 | 22.1 0.859 582.0 0.717 955.9 20.3 0.837 544.0 0.624 831.8 17.6 0.809 482.4 0.572 762.9 16.1 0.791 448.0 0.507 675.5 14.2 0.769 412.6 Molecular weight: 116.1. Radius of the Capillary tube: 0.04352 cm. Depth: 0.1 mm. The substance boils at 110.°2 C. constantly. At —76 C. it is again a thin liquid; it was only slightly turbid, probably by extremely fine crys tals. 375 XL. Isobutyl-Isobutyrate: (CH3),CH.CO.O(CH) .(CH . (CH3),). g ‘ Maximum Pressure Surface- +f Molecular e* — tension x SUE Surface- a. jin mm, mer-) in Erg. pro | gravity d energy in | ~ cary ot | in Dynes cm. =| 4° | Erg. pro cm’. ~16.5 1.182 1576.3 33.8 0.951 960.6 —21.3 0.927 1236.2 26.4 0.896 780.8 0 0.865 1S Sota 24.6 0.875 739.2 25.4 0.785 1047.8 | 22.3 0.850 683.1 45 0.731 974.3 20.7 0.830 644.2 74.7 0.638 850.2 18.0 0.801 573.6 91.1 0.596 795.0 16.8 0.784 543.1 109.2 0.545 726.1 15.3 0.766 502.3 134.5) 0.469 625.0 13.1 0.740 440.1 Molecular weight: 144.11. Radius of the Capillary tube: 0.04352 cm. Depth : 0.1 mm. The compound boils at 147.°2 C. constantly. XIL. Ethyl-Acetyloacetate: CH,;CO.CH,.CO.0O(C,Hs), & Maximum Pressure H Surface- | S if Molecular ES tension x | “Pectlic Surface- te ‘in tim. mers) in Erg, pro | gravity dy. energy ” in ce cary ct | in Dynes cm. | Et'g. pro cm’, == = a — oa se SSS —20°| 1.210 1612.8 3am) e070 900.7 1 1.133 1510.5 34.3 1.048 853.5 S25 ea ere Lets 1483.6 32.0 | 1.023 809.2 yaks) 1.069 1424.7 30.7 1.013 781.4 * 49.5, 1.024 | 1365.8 29.4 0.999 155.3 71 0.906 ae 201: Aten | 27.3 0.976 712.3 89 0.841 1121.2 25.3 0.958 668.4 e125 0.774 1031.9 211 0.923 587.7 MoS 0.675 900.2 18.9 0.896 522.1 =S1765") (05596 794.9 16.6 0.869 468.0 | =e Pale all 4 Molecular weight: 130.08. Radius of the Capillary tube: 0.04638 cm.; in the observations indicated by *, it was 0.04408 cm.; in those by **: 0.04352 cm. Depth: 0.1 mm. The substance boils at 179.°6 C. constantly. 25* Molecular Surface- energy in Erg pro cm2. 720) 690 . § 660 y Sete eS Tempe- -80°-60°-40° 20° O° 20° 40° 60° 80° 100° 120° 740° 160° 180° 200° 220° 240° 260" ature. Molecular Surface- energy in Erg pro cm’ 7020 Fig. 4. “80° -60°-40" -20° O° 20° 40° 60° 80° 100°120°740' 00180200 Temperature 377 XII Methyl-Acetylomethylacetate: CH;CO.CH(CH3).CO. 0(CHs3). a : Maximum Pressure | Surface- ie | Molecular | Sie eee | tension x | Specific Surface- are in mm. mer-| | | in Erg. pro | gravity d,,| energy “in bi ue in Dynes | cm?, as pro cm’, <1 | 1.477 | 1969.6 | 46.5 1.121 | 1106.2 —21 1.218 | 1623.8 | 38.3 1.071 939.3 0 1.137 1515s ees Bball 1.050 887.2 20e3 1.046 1395.0 32.8 1.024 828.9 45.5 0.985 1313.2 30.8 1.003 789.2 710.2 0.901 1201.2 28.1 0.977 | 732.7 85.2 0.856 1141.2 26.7 0.962 703.4 Lees OS 68 1024.4 23.9 | 0.930 | 644.0 138.2} 0.709 945.2 22.0 0.908 602.3 156 0.658 877.2 20.4 0.890 566.0 Molecular weight: 130.08. Radius of the Capillary tube: 0.04803 cm. Depth :0.1 mm. Under a pressure of 18 mm., the substance boils at 75.95 C.; in the at —71°C. very viscous liquid, the growing of the gas-bubbles took more than 60 seconds. The specific gravity at 25° C. is: Ayo = 1.0247; at 50°C.: 0.9991; at 75° C.: 0.9732. At © C.: Ayo= 1.0500—0,001006¢ —0.00000024 #. XIV. Ethyl-Propylacetyloacetate : CH3CO.CH(C3H;)CO . O(C)Hs). £ _ | Maximum Pressure H Sine | ato | Moteeular eo tension x Recinie | Surface- o - F y | ‘ Qa. jin mm. mer-| _ in Erg. pro | gravity d,,| energy “in =o cury of | in Dynes 2 aS) 2 2 °C. cm | Erg. procm ‘| ° | —76.2 1.430 | 1906.0 43.6 1.082 1280.1 —20 1.142 1522.2 34.8 1.007 1070.2 PAS) 1.058 | 1410.1 32.2 0.978 1011.3 i 2s) 1.018 | 1356.6 29.4 0.948 942.7 hs eta) 0.977 1302.2 | 28.2 | 0.934 913.2 ™* 49 0.929 ~ | 1238.7 | 26.8 | 0.916 | 879.2 70 0.818 | 1091.0 24.8 | OFSS0Uy ea 88las 90.5 0.763 | 1017.7 23.1 0.866 786.8 *125 0.714 951.5 2022 0.833 706.0 *143 0.669 | 891.5 | 18.9 | 0.816 669.7 *152.9| 0.641 854.8 | 18.1 0.806 6465 lala 0.576 7167.5 16.2 | 0.785 589.1 *200.5 0.507 676.4 14.2 0.764 525.8 Molecular weight: 172.13. Radius of the Capillary tube: 0.04638 cm.; | in the observations indicated by *, R | was 0.04352 cm.; in those indicated by ** it was 0.04408 cm. Depth: 0.1 mm. Under ordinary pressure the boiling point is 223.96 C. constantly ; notwithstanding the great viscosity of the liquid at —76° C., it was yet possible here to determine the value of z evidently very exactly, if the time of grow ofthe bubbles was sufficiently long (ca. 40 seconds). | a Ee ee eee ———— XV Methyl-Cyanoacetate: CN.CH2.CO.O(CH,). a | 3 : Maximum Pressure H Surface- : Molecular sot eee at. | tension x Specific Surface- Fe fe PRRs in Erg. gravity d,.| energy # in & | mercury of | in Dynes pro cm’. Erg pro cm» e 0° C. 6°| (2.424) | (3231.6) C41) ae 222 (1387.8) 16 pen tats 1923.2 43.9 1.140 861.2 1 1.362 1815.4 41.4 1.122 820.8 i= 25-5) 1.337 1783.0 38°6 1.096 me aitile! 50 | 1.184 1578).3' 14) 35.9 1.070 | 134.6 70.5) 1.116 1487.7 | 33.8 1.039 | 705.4 90 | 1.043 1390.8 | Set 1.028 666.2 * 124.5) 0.987 1315.8 28.0 0.994 601.8 * 153.1) 0.877 1169.2 24.8 0.965 543.7 * 176.5] 0.789 ae LOS 2ha Sy 22.3 0.942 496.8 Selo 0.713 Oo IRS Ira 20.1 0.921 454.6 Molecular weight: 99.05. Radius of the Capillary tube: 0.04638 cm.; in the observations indicated by *, R was: 0.04352 cm., in those with “, it was: 0.04408 cm. Depth: 0.1 mm. The carefully dried ether boils constantly at 203° C.; at — 76? C.the liquid is extremely viscous and gelatineous; although the time of formation of the gasbubbles was about 100 seconds, the viscosity in this case evidently diminishes the exactitude of the determinations of . The specific gravity 40 was at 25° C.: 1.0962; at 50° C.: 1.0698; at 75° C.: 1.0438; at £°: 40 = 1,1231—0,001086 ¢ +- 0,0000004 ¢?, XVI. Ethyl-Cyanoacetate: CN. CH,.CO.O(CjHs). ovo . | 5 . | Maximum Pressure H Surface- ate Molecular se = tension x Pecite Surface- a inmm.mer- | | in Erg. pro | gravity d,, | energy » in = cury of in Dynes cm? | Erg. pro cm?, ol 0? ‘G |-17° 1.313 1750.8 39.9 1.099 876.1 i) 1.245 1660.2 37.8 1.082 838.6 ieee) W222: 1628.8 35.2 1.056 7193.7 pareetaygs) 1.188 1583.5 34.2 1.046 776.1 49 1.083 1444.5 32.8 1.032 ible SD 71 1.016 1354.0 30.7 1.009 713.6 | 90 0.951 1267.8 28.7 0.990 675.6 mle 0.896 1194.8 25.4 0.955 612.4 P13 0.803 1070.8 ~ Bes 0.927 558.3 *176 0.727 969.7 20.5 0.904 512.7 * 201 | 0.651 868.6 18.3 0.879 466.3 Molecular weight: 113.07. Radius of the Capillary tube: 0.04638 cm.; in the observations indicated by *, R was 0.04352 cm.; in those by **, it was: 0.04408 cm. Depth: 0.1 mm. The compound boils at 206° C. constantly; at —76° C. it becomes glassy and crystallizes very slowly on heating. The crystals melt at about — 40° C. The specific gravity at 25° C. was: 1.0562; at 50°C: 1.0307; at 75° C.: 1.0052; at ¢-: A40 = 1.0817—0.00102 ¢, in general. O79 XVII. Propyl-Cyanoacetate: CN.CH,.CO.O(C3H)). E ; Maximum Pressure H | Surface- | j Molecular | So ae ee tension 7 Specific Surface- | Be inmm., mer aa in Erg. pro | gravity do | energy / in 3 cury of | in Dynes a) Erg. 2, 2 0c. cm rg. pro cm —16° 1.236 1647.3 37.5 | 1058; > 91259 0 1.184 | 1578.3 35.9 | 1.042 882.9 P25 1.164 1551.7 3350) 1.021 835.1 heels) 1.130 1506.5 | 32.5 1.011 815.5 hee 1.075 1433.8 | 31.0 0.996 786.0 ab! 0.961 1280.71, =} 29.1 0.976 747.6 | 114.5} 0.834 W225) 92522 0.933 667.1 2.5 0.858 | 1144.4 | 24.3 0.923 647.9 *152.5 0.780 1039.9 22.0 0.896 598.3 “176.1 0.701 934.6 | 19.7 0.872 546.0 *201 0.624 | 831.8 17.5 0.847 | 494.1 Molecular weight: 127.08. Radius of the Capillary tube: 0.04638 cm.; in the observations, indicated by *, the radius was: 0.04352 cm.; in those with “it was: 0.04408 cm. Depth: 0.1 mm. The substance boils at 216° C. constantly; at —79° it solidifies slowly to a crystal-aggregate, which melts at about — 39° C. The density d,. was at 25°C.: 1.0214; at 50° C.: 0.9973; at 75° C.: 0.9717. | at AG: 40 = 1,0424 —0.000962 ¢-+- 0,0000012 &. XVIII. Butyl-Cyanoacetate: CV.CH2.CO.O(C4Hb). vo . ae Maximum Pressure Surface- ey Molecular BY = — tension % Lo iay Surface- a _ jin mm. mer- in Erg. pro | gravity d energy v in E-= | cury of in Dynes 2 3 ce 2 2 0°'C. cm’. Erg. pro cm». ° —21.3 1.213 1617.5 35.2 1.041 928.8 0 1.159 1545.2 33.6 1.020 898.7 psa 1.117 1489.0 31.7 0.998 | 860.3 if 45.2 1.055 1406.2 29.9 0.978 822.5 im 14.9 0.975 1300.6 Alot 0.952 715.8 * 94. 0.924 1231.6 26.2 0.934 743.2 114.5 0.852 1135.3 24.6 0.915 707.4 135 0.797 1063.3 23.0 0.895 671.2 161.1 0.729 971.9 21.0 0.870 626.3 192.1 0.662 883.1 | 19.0 0.840 | 578.4 213.1 0.615 820.0 17.6 } -0.820! || ° 544.5 Molecular weight: 141.1. Radius of the Capillary tube : 0.04439 cm.; i in the observations indicated by * it was: 0.04352 cm. Depth: 0.1 mm. The ether boils at 230°.5 C. constantly; it can be cooled as far as —80° C., without crystallisation setting in. The specific gravity 40 is at 25° C.: 0,9978; at 50° C.: 0.9749; at 75° C.: 0.9518; at f° it is: d 40 = 1.0204—0.000904 ¢ +- 0.00000016 &. XIX. lsobutyl-Cyanoacetate : CN.CHp. CO. O(CHp. CH. (CHs3)s). uv . E : Maximum Pressure 7 Surface- 3 Molecular eS | Ae = tension Suen: Surface- o. jin mm. mer- in Erg. pro ravity d energy » in E= cury of in Dynes cm? 3 AS. Ete epro Gale = 0° C. ae ; ° —20.5 1.179 1572.4 34.2 1.033 907.1 0.3 1.122 1495.9 32.5 1.014 872.7 e225) 1.069 1424.6 30.3 0.990 826.7 pedo 1.013 1351.1 28a 0.971 793.3 * 74.8 0.934 1245.4 26.4 0.944 743.6 * 04.5 0.879 1174.6 24.9 0.925 710.9 | 115 0.811 1081.3 23.4 0.905 677.9 | 135.1 0.757 1009.2 21.8 0.886 640.5 161 0.686 914.6 19.7 0.862 589.5 191.8) 0.595 792.9 17.0 0.834 520.0 213 0.541 720.9 15.4 0.815 478.4 Molecular weight: 141.1. Radius of the Capillary tube: 0.04439 cm.; in the observations indicated by *, Rwas: 0.04352 cm, Depth: 0.1 mm. The compound boils at 223° C. constantly; it can be undercooled as far as —76° C,, and crystallizes then slowly into a crystalline aggregate, melting at about -—26? C. The specific gravity at 25’ C. was d,,. = 0.9903; at 50° C.: 0.9669; at 75° C.: 0.9441. At ¢° it is generally : Ayo = 1,0138—0,.000952 ¢ + 0.00000032 @. XX. Amyl-Cyanoacetate: CN .CH,.CO.O(C;H\). 5 Maximum Pressure Surface- Pes Molecular pho FS RE ae eee ad eet aa Specific Surface- Go i energy = en in Erg ravity d : E-= | mercury of | in Dynes pro cm?, ier IS Sy 18 a 0° C. pro cm’. a SSS SSS = — WSS SS ——————————————_SI ESSE —17:5| 1.080 1440.3 32.7 1.017 933.5 IS 1.029 1371.3 SI 1.001 897.2 ee Zee 1.028 1370.2 29.5 0.976 865.5 aD) 1.000 1333.2 28.7 0.966 847.9 69 | 0.880 1172.9 26.5 0.939 797.8 89 | 0.831 1108.3 25.0 0.920 763.0 plas) 0.807 1075.4 Poel 0.891 107.7 153 0.744 992.6 21.0 0.864 668.3 0.689 919.1 19.4 0.843 627.6 201 0.634 845.6 17.8 0.821 586.1 | Molecular weight: 155.11. Radius of the Capillary tube: 0.04638 cm.; in the observations indicated by *, R was 0.04352 cm.; in those with * it was: 0.04408 cm. Depth: 0.1 mm. The compound boils at 240°.2C.; at —76°C. it is a jelly, but does not crystallize. The specific gravity at 25° C. was: 40 = 0.9763 5 |) Yat 50>'G:: (0/9547; at 715° G2 O82, Ate itis: A4o = 1.0019—0.090061 z + 0.00000032 #. Molecular Surface Energy in Erg. pro cm’. Fig. 5. 4SO -50°60"-40"-20° 0° 20° 4W° 60° 80° 100" 120° 14° 160° 180" 200.220 }eMperature XXI. | Trichloromethane: CHCl. Maximum Pressure Surface- tension x | Molecular | Specific | Surface- | in mm. | in Erg. Se ee uP RCHCRY | mercury of | in Dynes | pro cm? | gravity “4°! in Erg. ! = | Temperature iba © (CG, OnE: | | pro em?2. —22 1.142 | 1523.4 | 32.5 1.555 | 587.5 0 | 1.050 1394.3 29.7 1.519 545.3 25 | 0.927 1236.0 | 26.2 1.476 490.4 35 | 0.881 |) Lae S 24.8 1.459 467.8 55 | 0.798 1063.9 22.4 1.425 429 .2 Molecular weight: 119.51. Radius of the Capillary tube: 0.04385 cm. | Depth; 0.1 mm. The trichloromethane was prepared from purest chloral, carefully | dried, at —79° C. several times frozen, and purified by repeated distillation. It boils constantly at 61°.2 C.; at this temperature, the value of x is: 21,8 Erg. pro cm?. 382 XXII. Tetrachloromethane: CCl. | | £ | Maximum Pressure H | Surface- aa Molecular go a = _____} tension x Becmc Surface- a. in mm. mer- E in Erg. pro | gravity d,.| energy “in | = | cury of | in Dynes cm?, 4° Erg. pro cm’, = | OG. —18° | 1.087 | 1450.4 | 30.9 1.659 633.0 0.1) 1.005 1340.9 28.5 1.632 590.2 25 | 0.899 1199.5 25.4 1.585 536.4 35 | 0.862 1149.4 | 24.3 1.560 518.6 55 0.793 1058.1 22.3 1.525 483.2 | 1 ie - ee. ase Molecular weight: 153.80. Radius of the Capillary tube: 0.04385 cm. Depth: 0.1 mm. Under reduced pressure (ca. 90 mm.) it boils at 26° C., and solidifies at — 60’ C. to a white crystalline mass. Under ordinary pressure, it boils constantly at 76°.4 C. At this temperature the value of x is about: 20.2 Erg. pro cm?*. —4 Molecular Surface-Energy in Erg pro em’. Fig. 6. 7020 990 960 aS 930 TAN PAO 900 NESS 8 YO a70 SEO RR oh Na NG ; ‘Sa, NRG? 750 ~S ‘WS 720 SSE RY a RES SENG 690 SS Oe Nah 660 GENS. SS 630 SNORE OS \ SSS aN 600 FSS NS Ye 570 Ns We Se 500 Se x > ? uN \’ 510| tx CancacHiale® WO, 480 AS 450 : aot SO OPI WO 20° YO” OF 80 100 120 M0 160 180 200 220° 200 260" “NPE rature 383 XXIIL Isobutylbromide: (CH3). CH . CH2B?). = 4 Maximum Pressure H Surface- Specif Molecular so : tension x | ~Pectlic Surface- os in mm, mer-| . inErg. pro | gravity dg. energy “in “ cury of in Dynes cm?. Eeonocotenall = One: ot = ] — =z = <== SS SSS SE —— = = = = = — L95” 1.227 1636.5 38.4 1bS85 ma eeS2166 —19.5 0.949 1265.9 29.5 1.314 653.7 0 0.874 1166.0. | 27.1 1.291 607.6 25.4 0.790 1053.5 24.4 1.259 556.3 44.4, 0.728 970.2 22.4 | 1.236 By eie} 69.9, 0.646 861.9 19.8 1.205 464.8 85.3 0.600 799.5 18.3 | 1.186 439.2 Molecular weight: 137.07. Radius of the Capillary tube : 0.04803 cm. Depth: 0.1 mm. The carefully dried compound boils very constantly at 90.°5 C.; at this temperature x is about 17.9 Erg. pro cm?. Molecular Surface- Energy in Erg pro cM?. Vig. 7, -§0°-60°-40° 20° O° 20° 40° 60° 80°10" Temperature | | | § 5. 384 Temperature-coefjicients of w of the here studied substances. norm. Propylalcohol. Isobutylalcohol. Temperature-interval: re in Erg. Temperature-interval: = in Erg. between —76° and —21° 1,78 between —71° and — 12° 2,3 —21° , +259 1,11 —12° ,, +101° 1,1 2 ap 91° 1,10 Diethylether. Ethylf ormiate. between —75° and —20° 2,16 between —76°,5 and —16° 1,72 —— 2) ae 0? 1,94 —16° ,, +25° 1,62 O20 ay. 29° 1,70 Zoe ss 35° 1,29 Se 54° 1,12 Ethylchloroformiate. Ethylacetate. between —75° and —21° 2,86 | between —74° and 0° 2,50 —21° , +25° 2,41 Og. 25° 2,37 Dock TOS 1,82 Dap 35° 1,86 WY 91° 1,70 GI? 5) 55° 1,78 55°u,. nis 1,30 Methyl-Isobutyrate. Ethyl-Isobutyrate. between —73° and —219,5 3,0 between —78° and +109? 2,15 —21° , 25° 2,4 ; Pao 45° 2,1 452), 91° 1,7 Isobutyl-Isobutyrate. Acetone. between —76° and — 21° 3:2 between —73° and —19°,5 1,81 —21° ,, +135° 2,18 —19° 5, =e 1,66 Oy 54° 1,57 Methylpropylcetone. Ethyl-Acetyloacetate. between —74° and 0° 2,13 between —20° and +-176° 2,19 2 5) g9° 1,73 Methyl-Methylacetyloacetate. Ethyl-Propylacetyloacetate. between —71° and —21° 3,39 between —76° and —20° 3,74 Al 0° 2,47 —20°,, +20° 2,84 WH 70° 2,18 beer. 70° 2,36 TOR! Sf 156° 1,94 TPs ies 2,24 12525 eee OSS 2,11 Then an increase: 2,37 to 2,68, occurs as a consequence of beginning dissociation. Methyl-Cyanoacetate. Ethyl-Cyanoacetate. between —76° and — 16? not measurable | between —-17° and +201° 1,88 independently of viscosity. —16° ,. +1979 1,90 Propyl-Cyanoacetate. | Butyl-Cyanoacetate. ete Ou. . Ou. Temperature-interval: ay in Erg. Temperature-interval: a in Erg. between —16° and +152? 1,88 ‘between —21° and 4213° 1,62 Then an increase: 2.13, under dissoci- ation and liberation of HCN. Isobutyl-Cyanoacetate. | Amyl-Cyanoacetate. between —20° and 0° 1,64 | between —17° and 4- 1° 2,0 Ps 1152 1,70 | 1 201° ca: 1,6 i taee 213° 2,0 Gradual decomposition, under liberation | of HCN. | Chloroform. Carbontetrachloride. between —22° and --55° 2,06 between —18° and 0° 2,6 Ore; 25° 1,95 25° 55° 1,75 Isobutylbromide. between —75° and —19° 3,0 alig2 9, -1-952 2,15 25°, = 699,9_—s—«2,08 70°, 90° 1,91 acy 0 Evidently only in some cases the coefficient 5, appears to be really constant; in most cases it decreases doubtless with a rise of tempe- rature. Where the inverse behaviour was stated, a decomposition of Oo the studied substance always seemed to occur. The value for - t is in the interval of ordinary temperatures relatively small for propyl- and isobutyl-alcohol and for the cetones; however in these cases it appears to be variable with the temperature in no higher degree 0 than in the cases, where the values of = do not differ largely from 2.0 Erg. Groningen, June 1914. Laboratory for Inorganic Chemistry of the University. 386 Chemistry. — “The Temperature-coefficients of the free Surface- energy of Liquids, at Temperatures from —80° to 1650° C. III. Measurements of some Aromatic Derivatives.” By Prof. Dr. F. M. Jarcer and M. J. Surv. (Communicated by Prof. P. vy. Rompuran). § 1. In continuation of our measurements of organic liquids, the data obtained in the study of a series of aromatic compounds, are reviewed here in tables, quite in the same way as in our former communications’). This series of substances includes the following terms: Nitrobenzene; ortho-Nitrotoluene ; Aniline; Dimethylaniline ; ortho- Toluidine; Thymol; Methyl-, Ethyl-, and Benzyl-Benzoates ; Salicylic Aldehyde ; Acetophenone, and the non-aromatic compound: e-Cam- pholenic Acid. With respect to the determination of the specific gravities and the purification of the studied substances, we can refer to the preceding communication; the diagrams also have the same significance, as indicated there. § 2. Aromatic Derivatives. 1. Nitrobenzene: C,H;(NO,). 5 Maximum Pressure 1 | Surface- | Rae Molecular | id | tension x | ~Pecic Surface- | Sey he in Erg. pro | ity d energy “in = in mm. mer-| ; | Sravity =~ cury of 0?C.| '" Dynes cm? 4 Erg. pro cim?. 5 1.538 | 2050.5 | 44.4 1.215 064.7 26.6 1.473 | 1965.8 | 42.5 1.197 932.7 | 34.9 1.448 | 1930.5 41.7 1.190 918.7 55.3 Lon 1827.8 | 39.5 1.171 879.7 70.8 1.314 1751.8 37.8 1.156 849.0 100 1.198 1596.0 34.4 1.125 786.8 110 1.156 1541.6 33.2 1.115 _ 163.9 126 1.089 1459.8 31.4 1.097 730.4 145.5 1.014 1351.9 29.0 1.075 683.7 W225 0.903 1204.0 25.8 1.042 621.0 Molecular weight: 123.06. Radius of the Capillary tube: 0.04385 cm. Depth: 0.1 mm. The nitrobenzene was carefully dried, several times frozen, and distilled; it boils at 209° C. constantly. At this temperature 7 = 21.2 Erg. pro cm? At O° C. it solidifies completely. The specific gravity at 25° C. is: d4. = 1.1988. 1) F. M. Jaraer and M. J. Sarr, Preceding communication, (1914), Il. Ortho-Nitrotoluene: CH; .C ,H,. (N02). (1) (2) © } Maximum Pressure // Surface 30 = _ tension x a | in mm. mer- in Erg. pro Es cury of in Dynes eat O2NG; 0.1 1.505 2006.8 43.3 9.6 1.465 1953.1 42.1 zo 1.416 1887.5 40.9 3438 1315 1833.1 39.7 * 49.3 1.257 1675.8 38.2 70 1.252 1669.4 35.8 101.6 1.132 1509.8 32.4 122.6 1.055 1406.5 30.1 144 0.971 1295.4 Qe 148.6 0.954 1272.4 27.2 170 0.864 1151.9 24.5 Molecular weight: 137.1. The compound boils at 218° C. constantly; the meltingpoint is — 4° C. At the boilingpoint, the value of x is about 18.1Erg. pro cm’. 0.04408 cm.; 0.04638 cm. Depth: 0.1 mm. Specific gravity a4, ee ee _ —_ Radius of the Capillary tube: 0.04385 cm.; in the observations, indicated by *, R was in these with Molecular Surface- energy » in Erg. pro cm>,| DOW bNWOWWH oo | it was: Il. Aniline : CgH;(N H2). E : Maximum Pressure H Surface- a ———| tension , Yo : lire! a in mm. | in Erg. pro ££ | mercury of in Dynes antl fe O3E (e) 0 1.573 2096.5 45.4 5.3 1.552 2069.8 44.8 26.2 1.473 1963.8 42.5 34.7 1.452 1935.8 41.8 54.8 1.371 1827.8 39.5 70 1.320 1759.8 38.0 100 1.190 1586.5 34.2 109.5 1.156 1541.6 382 126 1.089 1459.8 31.4 143 1.027 1369.2 29.4 148.8 0.998 1331.8 28.6 173.7 0.889 1185.8 25.4 Molecular weight: 93.04. _The liquid boils at 184° C. constantly. It is colourless, and only at higher temperatures it gets somewhat yellowish. At the boilingpoint, x is: 24.3 Erg. pro cm? Radius of the Capillary tube: 0.04385 cm. Depth: 0.1 mm | Specific gravity a4, Molecular Surface- energy / in Erg. pro cm’. IV. Dimethylaniline 5 CoHs 5 N(CH3)3. | wo 7 (ees Maximum Pressure Surface- ; Molecular HS) st sf | @tensionie Specific Surface- oo : | = z 4 energy » = eee in Erg. ravity d. : == | mercury of | in Dynes pro cm?, SEE By Erg. i= OPC, pro cm?. 26 | 1.165 1553.2 36.6 | 0.951 926.4 45.5 | 1.087 1449.1 34.1 0.935 873.0 | 66.5 1.018 S579) 31.9 0.917 827.3 | 86.5 | 0.959 | 1278.4 30.0 0.900 787.8 | 106 0.893 1190.8 271.9 0.884 741.5 125.8 0.831 1107.6 25.9 0.867 697.3 146 0.768 1024.4 23.9 0.850 652.0 166 9-709 945.3 22.0 0.832 608.8 184 0.650 866.1 20.1 0.817 | 563.0 Molecular weight: 421.11. i) Radius of the Capillary tube: 0.04803 cm. Depth: 0.1 mm. The liquid boils at 191° C. constantly; it solidifies easily and the crystals melt then at 0°.5 C. The value of x at the boilingpoint is about: 19.3 Erg. per cm?.. Molecular Surface-energy in Erg pro em’. Fig. 1. 7170 450 “S§0°-60°- 40° 20° O° 20° 40° 60° 80° 100°/20° 740° 160° 150° 200° 220° 389 V. Ortho-Toluidine: CH, .CgH,.(NH,) . (1) (2) | E ; Maximum Pressure 1 Surface- : Molecular aU z= se tension x Specific Surface- oe . . . &_ jin mm. mer- in Erg. pro | gravity d energy in Es cury of in Dynes ane. Se aa4e Erg. pro cm? 5 a: ‘ = ORNS | —20° 1.573 2098 .0 | 45.4 1.027 1005.8 0.6 1.492 1989.1 43.0 1.013 961.4 9.3 1.465 1953.1 42.2 1.006 947.9 25 1.403 1870.5 40.4 0.992 | )ikeyGE) 5 34.6 1.375 1833.1 39.6 0.985 902.1 | 50.1 1.310 | 1765.8 Sileu 0.973 | 865.8 | 70.5 1.234 | 1645.2 39,0 0.957 | 824.4 101.4 ielS3 151025 S285 | 0.933 767.6 123.2 1.043 1391.0 29.9 0.916 714.9 144 0.957 1277.0 27.4 | 0.899 663.3 149.5) 0.937 1249.8 26.8 0.895 650.8 172 0.831 | 1108.2 Zoe 0.877 583.3 Molecular weight: 107.09. Radius of the Capillary tube: 0.04385 cm. Depth: 0.1 mm. The ortho-toluidine boils at 197.4 C. constantly. It is perfectly colourless, but above 180° C. it gets gradually reddish brown. At the boilingpoint 7 = 19.9 Erg pro cm’. VI. Thymol : (CH;),CH. CsH;. OH(CH3). & Maximum Pressure H Surface- | eer Molecular | EO) 5 || ea ok ees tension z% Wael te Surface- | Vo 5 : : a jin mm. mer- in Erg. pro itv d energy / in 5 . gravity | E ¢ vary ot IPRS cm?, bk Erg. pro cm*: g° 1.176 | 1567.9 34.2 0.986 975.1 25 1.109 1478.5 32.2 0.968 929.4 45.7 1.054 1405.7 30.6 0,952 893.1 710.7 0.991 1321.9 28.6 0.933 846.0 | 90.1 0.943 1257.0 27.3 0.920 815.2 | 115 0.875 1156.6 ZOE 0.901. 766.0 135.3 0.825 1099.3 23.8 0.887 728.2 “160 0.703 935.9 21.9 0.867 680.3 )* 190.1 0.628 837.0 19.5 | 0.845 616.2 er 0.578 770.3 17.9 0.829 572.9 Molecular weight: 150.11. Radius of the Capillary tube: 004439 cm. ; in the determinations indicated by *, R was: 0.04803 cm. Depth: 0.1 mm. The substance melts at 51°.5 C., and boils at 231.°5 C. constantly ; it can be undercooled to a high degree. At the boilingpoint ~ is 16.6 Erg. The specific gravity at 24.°4 C. is 0.9639. Ww co Proceedings Royal Acad. Amsterdam. Vol. XVII. 390 VII. & Maximum Pressure 10) D0 7 | ES in mm. mer- sa AGS 2 cury of 0° C. y | | le? 1.405 1873.1 S25r1 1.306 1741.2 | 245) e222 1629.2 tas: || 1.110 1479.8 *04.5| 1.034 1378.7 115.2 0.946 1261.2 135.3] 0.875 1166.9 (160 | 0.791 1054.6 192.5 | 0.686 914.6 I | D Methylbenzoate: C,H,;.CO. O(CH;). Surface- tension x | in Erg. pro cm*. Specific gravity ayo Molecular Surface- energy “in |Erg. pro cm2, | —KMNMMMWWwWwFt | SCnanorhaA- ADWRhREADWS, epth: 0.1 mm. Molecular weight: 136.06. Radius of the Capillary tube: 0.04439 cm.; in the observations indicated by *, the | radius was: 0.04352 cm. The boilingpoint of the compound lies at 195.°2 C. The liquid can be undercooled as far as —21° C.; then it crystallizes, and the crystals / melt at about —15 C. Atthe boilingpointthe value of , is: 19.4 Erg. pro cm’. Specific gravity Ayo Molecular Surface- energy vin Erg. pro cm:. 1.081 1.066 1.047 1.032 1.009 0.995 0.980 0.964 0.945 0.921 0.914 1045.7 1001.3 947.7 904.3 833.8 782.1 738.5 694.6 624.7 554.9 539.7 adius of the Capillary tube: 0.04439 cm. ; in the observations indicated by * this VIL. | Ethylbenzoate: CyH;.CO. O(C:Hs). E J | Maximum Pressure H Surface- sos tension 7 Heese in Erg. per | Se ht - : | =.= jin mm. mer-| . f & jcury of 0° C.| in Dynes cm’. Pabete eat | | aw 550-51) Absssun| wuireses 39.0 | 0 | Lei) | 1694.1 | 37.0 | be ay | 1.213 1617.6 34.6 * 45.1) 1.148 1530.4 S2ai he ztey | 1.044 | 1392.4 29.7 * 04.4 0.972 | 1295.9 27.6 114.6 0.892 1189.4 25.8 | 135.4| 0.833 | 1110.6 24.0 160.2) 0.740 986.7 21e3 | 192.1] 0.649 | 865.0 18.6 | 200 0.628 | 838.0 18.0 —— — — = —< = | — Molecular weight: 150.08. R radius was: 0.04352 cm. | The compound boils at 210.°8 C. It can be undercooled as far as —79' C., and then slowly crystallizes to a white mass, which melts at —57? C. At the boilingpoint, z is 17.4 Erg. pro cm*. The great viscosity ofthe liquid at -70° C. makes accurate measurements impossible. 391 IX, Benzylbenzoate: CoHs CO _O(CH . CzHs). a ae 8) . ae Maximum Pressure 1 Surface- feline Molecular Bo. a =| satensionyy peene Surface- Be in mm. mer- | in Erg. pro | gravity d,, | energy ” in = cury of in Dynes 2. Erg. pro cm’. EB 0°C. Wee Be 51-8). 1.622 2162.4 | 47.4 1.153 1533.2 0 1.548 2063.5 45.2 1.136 1476.6 25 1.456 1941.9 42.5 oye) 1405.7 45 1.384 1851.8 | 40.5 1.099 135235 710.8 1.294 1725.8 37.6 1.078 1271.9 90.8 1.230 1640.0 35.8 1.062 Wn eli22se2 106.2 1.179 1572.4 34.3 1.042 1186.9 135.1 1.092 1455.2 Slei 1.027 1107.6 *159.9 0.949 1265.9 29.8 1.006 1055.6 “190 0.890 1186.7 27.9 0.982 1004.4 S215 0.849 1132.6 26.6 0.965 968.8 Molecular weight: 212.10. Radius of the Capillary tube: 0.04439 cm.; in the observations indicated by *, this radius was: 0.04803 cm. Depth: 0.1 mm. The substance boils constantly at 308°? C.; it can be undercooled as far as — 70? C., and then crystallizes. The meltingpoint is some- what higher than -++ 12° C. At the boilingpoint % is 22.6 Erg pro cm’. The density at 25” C. is: Ayo = 1.1151; at 502 C.: 1.0940; at 75° C.: 1.0724; at PC: Ayo= 1.1357 — 0.000814 ¢. ee X. Salicylic Aldehyde: C,H,.COH, | : p | Maximum Pressure H Surface- Specifi Molecular hag = oa tension x Decne Surface- | es in ae Wee ‘gras in eS pro | gravity dg. ety yn i 2 et cm? rg. pro cm*. 0 1.534 2045.5 44.8 1.176 989.4 25 1.443 | 1923.8 42.1 1.152 942.6 45.5 1.368 1823.8 39.9 1.132 903.9 70.7) 1.274 1698.6 STL 1.108 852.5 90.5 1.205 1606.5 35.0 1.090 813.1 116.2) 1.115 1486.8 32.4 1.066 764.0 135.4 1.053 1403.8 30.6 1.052 127.9 “160 0.896 1195.1 28.1 1.030 677.9 1909 0.796 1061.9 24.9 1.002 607.2 -- ——+-- a ——— ——— il — ——-~ = - —-—--— —~—— = — Molecular weight: 122.05. Radius of the Capillary tube: 0.04439 cm. ; in the with * indicated observations, this radius was: 0.04803 cm. Depth: 0.1 mm. The boilingpoint is constant at 192.°5 C.; the substance soon solidifies, and melts at —7> C. At 25° C. the specific gravity is: dy. = 1.1525; at 50 C.: 1.1282; at 75° C.: 1.1036. At ¢ in general: a4, = 1.1765— 0.000954 t—0.00000024 ¢?, At the boilingpoint, the value of x is: 25.4 Erg. pro cm?, 26* 392 XI. Acetophenone: CH;.CO. CgHs. ea ie, | E | Maximum Pressure 1 Surface- ent Molecular sO |= 2 at AA tension, Pecuic Surface- &° jin mm. mer. | in Erg. pro | gravity d,, | energy vin E-= | cury of | in Dynes cm’. ‘Erg. pro cm®. 24.8| 1.375 1833.6 40.1 1.024 963.5 44.7 Meo 1703.1 37.2 1.007 903.8 71 1.169 1558.9 34.0 0.984 839.1 90.3) 1.098 1464.2 31.9 0.967 796.3 117 1.017 1356.2 29.5 0.945 747.8 135.3) 0.966 1288.6 | 28.0 0.929 717.9 *160 0.824 1099.3 | 25.8 0.907 672.1 *189.9 0.750 999.4 | 23.4 0.881 621.5 *200 | 0.728 970.2 | 225i 0.872 607.1 “Molecular weight: 120.06. Radius of the Capillary tube: 0.04439 cm. in the observations indicated by *, the radius was: 0.04803 cm. Depth: 0.1 mm. The compound boils constantly at 201. 5 C.; and becomes solid at —20° C.; it melts at + 20°.5 C. At the boilingpoint the value of x is 22.6 Erg. pro cm*. The specific gravity at 25° C. is: ayo = 1.0236; at | 502 C.: 1.0026. XII. | (CH,).:C.CH.CH, COOH. | @-Campholenic Acid: |. >CHe (CH,).C: CH | . Nl al | oz 1 pa a . z E : Maximum Pressure H | Surface- | ane Molecular SS peste ie —| tension x peeilic Surface- a. — |in mm. mer- in Erg. pro | gravity d, | energy # in Wes eee Pe ate Os in Dynes cm’. Erg. pro cm’, ie = ole eOSIC a | Lane —19.8 (1.695) (2259.8) (52.6) | 1.030 (1598 .6) 1.177 1569.2 | 37.0 1.016 1114.1 25 1.077 1436.6 33.8 | 0.999 1029.4 45.4 1.019 1358.5 319 0.985 980.9 TOA Wscke |) 12D 29.8 | 0.969 926.6 85.3 0.915 1220.1 28.6 0.960 895.0 P| 0.846 | 1128.5 26 4 0.939 838.7 138.1} 0.805 1073-2 25.1 | 0.925 805.6 156 | 0.771 1027.9 | 24.0 | 0.913 771.5 2A 0:728 | 970.2 22.6 0.902 739.1 191.7 0.664 885.2 20.6 0.889 680.5 212 | 0.608 810.6 | 18.8 0.876 627.8 ————— - ae . a No ee ee eee ee Molecular weight: 168.13. Radius of the Capillary tube: 0.04803 cm. Depth: 01 mm. Under a pressure of 12 mm., the compound boils constantly at 153° C. Below 0° C. the liquid is extremely viscous; although the growing of the gas-bubbles lasted about 50 seconds, the measurements at —19°C. cannot be considered to be very reliable. The substance | solidifies at —79 C.; above 160°C. it gets yellow by aslowly proceed- | ing decomposition. — — Molecular Surface-energy in Erg pro cm? Fig. 2. I00 40°-20° O° 20° 40° 60° SO° 700° 720°740°760° 180° 209° 220° § 3. Values of the Temperature-coefficients of the molecular Surface-energy |. 394 Nitrobensene. 0 | Temperature-interval: a in Erg: t between 5° and 35° 1,53 SOC aml 1,93 TAI able 2.16 WDD ee 2,25 145099, else 2,31 Aniline. between 0°? and 35° 1,57 Sole OS 1,73 102 AS 2,16 o-Toluidine. between —20° and +-101° 1,98 LOC 144° 2,44 14420 WP? 2.85 Above 1602 a graduél decomposition with colouring of the liquid, sets in. Methylbensoate. between 0° and 25° 3,0 DOR MEADS 2,6 45° >= 192° 2,21 Bensylbenzoate. between —22° and -+-135° 2,70 135omer 160° 2,08 160°, 211¢ 1,66 Acetophenone. between 25° and 45° 2,99 RSD ee Ale 2,45 TEE, OS 2,19 90°, 160° 1,76 16025 7,7 #2002 1,61 o-Nitrotoluene. Ou Temperature-interval: va in Erg: t between 0°? and 25° 1,81 BRP 7 282 2,19 492 232 2,29 1232 8 4a 2,42 144° , 170° 2,82 Dimethylaniline. between 26° and 46° 2,12 AGS fyi 2,23 Thymol. between 0°? and 160° 1,83 16025 sez 2,09 Ethylbenszoate. between —20° and +200° 2,29 Salicylic Aldehyde. 0° and 160° 160° , 190° between 1,98 2,19 a-Campholenic Acid. between —19°,8 cannot be determined and 0° independently of the viscosity GF Aye 3,39 25°, «45° 2,42 45°, 85° 2,12 852 ele 1,76 117° ,:138° 1,59 Above 138° (decomposition) ca. 2,6 3esides some straight lines, there are found here several curves for the dependence of « and ¢, showing in contradistinction with the formerly deseribed ones, the shape of that of wuater. Groningen, June 1914. Laboratory for Inorganic Chemistry of the University. - 395 Chemistry. — “The Temperature-coefficients of the free Surface- energy of Liquids, at Temperatures from —80° to 1650° C.: IV. Measurements of some Aliphatic and Aromatic Ethe:s.” By Prof. F. M. Jagger and Jun. Kany. (Communicated by Prof. P. van Rompurau.) § 1. In this communication the results obtained in the measure- ments of the free surface-energy of a number of ethers, are recorded by us. With respect to the purification-methods and the determina- tion of the specific weights, we can refer to communication II of this series); also the arrangement of the data and the significance of the diagrams are completely the same as indicated before. This series includes the following aliphatic terms: Amylacetate ; Diethyl-Ovalate ; Diethylmalonate ; Diethylbromo- malonate; Diethyl-Ethylbenzylmalonate; Dimethyl and Diaethyltartrates; and the following aromatic substances : ortho-Nitroanisol; Methyl-, Ethyl-, and Phenyl-Salicylates ; Methyl- Cinnamylate. | | | I. Amylacetate: CH3.CO.0O(C;H,;). Semi, oe | Bir ee Maximum Pressure H | Surface. | : Molecular oe = tension x Specific | Surface- reecennl in Erg. pro i | energy “in in mm. mer-| .; : gravity d,. gy ! es cury of 0° C.| Ul TONES cm?. | : |Erg. pro cm?. | | | | : | a \ tie | | | | ; a ; SiN 1.099 1465.8 34.6 0.968 907.8 ir 4 0.915 1220.1 28.7 0.918 780.0 0 | 0.850 | 1132.6 26.6 0.896 734.9 25.8) 0.771 | 1028.6 24.1 | 0.869 679.5 | 46 | 0.712 | 949.4 22.2 | 0.847 636.8 66.5. 0.653 870.3 20.3 0.827 591.6 | 86.5) 0.600 | 799.5 18.6 0.808 550.5 106 0.549 7132.9 17.0 0.790 510.8 | 125 0.506 | 674.6 15.6 0.774 475.1 | 614.6 | 14.2 0.752 | 440.9 | | Molecular weight: 130.11. | Radius of the Capillary tube: 0.04803 cm. Depth: 0.1 mm. The boilingpoint of the carefully dried compound lies at 148.94 C.; | at this temperature x is 14.0 Erg. pro cm?®. 1) F. M. JAnGER and M. J. Suir, These Proc. (1914) p. 365. 396 II. Diethyl-Oxalate: (C2H;) 0.CO.CO. O(C)Hs5). | = | Maximum Pressure 1 Surface- , Molecular eee Reet a _ tension Specific Surface- a° jin mm, mer- | in Erg. pro | gravity d,. | energy » in E= cury of in Dynes | em?, Erg. pro cm?.. oat OAC | —20.7| Nt rizt | 1569.9 37.0 1.139 941.0 Om ha OU 1482.5 34.9 1.110 903.0 26 | 1.025 | 1366.5 32.1 1.074 848.8 | 46 om52 | «(1278.4 «| = 30.0 1.050 805.5 | 66.7, 0.896 1195.1 | 28.0 1.025 764.0 86.5 0.818 1091.0 25.5 1.001 706.8 106 | 0.768 1024.4 23.9 0.977 673.3 125) 9 0.717 955.9 22.2 0.954 635.4 145.5 0.650 866.6 | 20.1 0.930 581.1 166 0.568 15des 17.6 0.905 521.8 184 | 0.478 637.3 14.6 0.883 440.0 Molecular weight: 146.08. Radius of the Capillary tube: 0.04803 cm. Depth: 0.1 mm. The substance boils at 99.°5 C. constantly, under a pressure of about 12 mm. In solid carbondioxide and alcohol it soon solidifies, and melts at —41.°5 C. Above 160? C. the ether seems to decompose slowly. Ill. | Diethylmalonate: (C2H5) 0. CO.CH,.CO.O(C,Hs). = _ | Maximum Pressure H Sur face- : Molecular eS eee | at ensioney Specific Surface- oD ie) . . . a” |in mm. mer- _ in Erg. pro | gravity d energy » in |} ££ | cury of in Dynes em? AS Ere nco | 2 ole | ; g. pro cm’, = \—19.9) 1.237 1649.2 35.5 1.095 985.3 0.7 1.167 1555.8 | Oo, 1.075 941.2 8.5) 1.142 1523.2 32.9 1.068 928.4 | ayy 1.077 1435.9 31.0 1.050 884.8 | 34.5 1.044 1391.9 30.0 1.041 861.2 50.1) 0.994 132582) 28.5 1.025 826.6 | 69.2) 0.920 1226.8 26.3 1.005 7712.9 10204 0.804 1071.8 23.0 0.969 692.5 124.5 0.723 963.9 20.6 0.945 630.7 144 0.660 880.2 18.8 0.924 584.3 | 148.7) 0.649 866.4 18.5 0.919 571.1 tpl | 0.571 761.6 16.2 0.896 513.9 Molecular weight: 160.1. Depth: 0.1 mm. | Radius of the Capillary tube: 0.04385 cm. | The compound boils constantly at 197.°3 C.; after crystallisation, it melts at — 50° C. At 25° C. the specific gravity was 1.0518; at 50° C.: 1.0254. At the boilingpoint the value of x is: 13.7 Erg pro cm*. 397 IV. | Diethyl-Bromomalonate: (C2H;)O.CO.CHBr. CO. O(C2Hs). | | vu . | = _ | Maximum Pressure /7 | Surface- | ; Molecular | WO = —| tension x | SSE Surface- | oe inmm,mer- | _ in Erg. pro | gravity d4o energy / in ae cury of in Dynes | cm2, | \Erg. pro cm2,| fe (HKG; | —20.7 1.250 1666.5 | 39.1 1.464 1168.2 | 0 1.165 1553.2 36.4 1.436 | 1101.6 26 1.065 | 1419.9 33.2 | 1.401 1021.5 45.5 0.999 133259 Sel | © tess 968.9 66.6) 0.943 Zoe || 29.3 1.347 | 925.4 | 86.5 0.896 1195.1 27.8 1.320 890.0 106.5 0.853 1136.8 26.4 1.293 } 856.9 126 0.815 | 1086.8 25.3 1.266 | 832.8 | 146 OF780) Fa 103959 24.2 1240 807.7 i Molecular weight: 239.09. Radius of the Capillary tube: 04803 cm.; Depth: 0.1 mm. Under reduced pressure (ca. 20 mm.) the substance boils constantly at 121° C.; at —54> C. it becomes a jeily, but does not crystallize. Above 150° C. it begins to be tinged brownish, apparently by beginning deposition. The specific weight at 25°C. is: 1.4022; at 50° C.:: 1.3688; ato? 1Gr 13359 Ata Gs: Ago = 1.4361—0.001366 ¢-+ 0.0000004 #2, V. Diethyl-Ethylbenzylmalonate: (C2H5)O . CO. C(CpHs) (C7H;). CO. O(CoHs). EB Maximum Pressure 7 Surface- ; Molecular a a = tension + Specific Surface- ° . | : a. in mm. mer- in Erg. pro | gravity d energy v- in se cury of in Dynes wae - 2 2 0-°C. i Erg. pro cm2, fo} ] —20.2 (2.174) (2898 . 4) (68.8) 1.086 (2775.0) Ome 1.241 1654.5 | 39.0 1.072 | 1586.7 26 1.121 1494.9 35.2 1.052 1450.1 | 45.5) 1.050 1399.9 32.9 1.035 1370.2 66.6) 0.984 Sle 30.8 1.016 | 1298.7 86.7) 0.940 1253.4 | 29.4 | 1.001 1252.1 106 0.901 1201.2 28.1 | 0.986 1208.8 126 0.853 1136.8 | 26.6 | 0.971 | 1156.0 146 | 0.805 1073.2 2m } 0.956 1102.2 | 166 | 0.759 1011.9 23.6 0.941 1047.3 | 184 | 0.690 920.3 | 21.4 0.927 959.2 206.5) 0.637 849.5 | 19.7 0.911 893.3 Molecular weight: 278.18. | Radius of the Capillar tube: 0.04803 cm. Depth: 0.1 mm. Under 12 mm. pressure, the substance boils constantly at 189° C.; at — 79° C. the liquid becomes a feebly opalescent glass. Already at — 20° C. the viscosity is enormous, and at 0? C. again very great. The grow of the gas-bubbles at 0° C. lasted about 40 seconds. The specific gravity at 25°C. is: Ayo —HOpa ry at o0m Gor leOs22 ator Ges 1.0098. At ¢° C. in general: A4o = 1.0725 — 0.000746 t—0.0000012 ¢’. VI. Dimethyltartrate: (CH3)0.CO.CH(OH)CH(OH).CO.O(CH3). | & . Maximum Pressure 7 Surface- eer Molecular | os ie ae ae | tension PECMIC Surface- | a. |in mm. mer-| _ in Erg. pro | gravity dy. | energy # in | =~ aye | in Dynes cm? Erg. pro cm? 45° 1.490 1986.6 43.2 1.306 1144.6 | 70.7 1.405 1873.1 40.7 1.281 1092.2 90.7) 1.340 1786.5 38.8 1.261 1052.2 116.2) 1.255 1673.2 36.3 1235 998.2 135.5 1.200 1599.5 34.7 1:216 964.1 159.6 1.046 1395.0 o2em Vai key 920.7 "190 | 0.974 1299.2 30.4 sila 876.1 | 210.3 0.929 1238.5 28.9 1.131 842.7 | Molecular weight: 178.08. Radius of the Capillary tube: 0.04439 cm.; in the observations indicated with *, it was: 0.04803 cm. Depth: 0.1 mm. The compound boils under 12 mm. pressure, at 180° C. constantly ; at —79°? C. it becomes a glass, which crystallizes with extreme slowness; | the solid substance melts at + 48° C. Even at 25° C. the ether is so viscous, that no reliable measurements were possible. z VII. Diethyltartrate : = (C,Hs)O. CO. CH(OH). CH(OH). CO. O(C2Hs). E f Maximum Pressure Surface- Specifi Molecular ae |e ————e tension , Beane Surface- ein mm. mer-| _ in Erg. pro | gravity d,, | energy » in a cy | in Dynes cm?, Erg. pro cm?. 25° role 1755.5 37.6 1.210 1155.4 45.3 1.241 1654.4 35.4 1.191 1099.3 74.3) 1.134 1512.0 | aoe) 1.164 1018.5 91.1 1.082 | 1443.0 | 30.8 1.147 980.8 110.1) 1.024 I) 136429) 9) 29.1 1.129 936.5 134.7) 0.948 1263.8 26.9 1.105 878.2 | 150.1] 0.899 | 1199.4 | 25.5 1.091 839.6 | 160.3 0.872 | IG 24.7 1.081 818.2 | 192.7| 0.765 1019.9 22.0 1.050 743.1 212.7) 0.716 955.9 20.2 1.032 690.2 Molecular weight: 206.11. Radius of the Capillary tube: 0.04352 cm. Depth: 0.1 mm. Under circa 16 mm. pressure, the boilingpoint is 166.5 C. At —79° the liquid becomes glassy, and crystallizes very slowly at —20° C.: | only after 5 or 6 hours all has got crystalline. The meltingpoint is 15° C, At 0° and lower temperatures the liquid is too viscous, to make reliable measurements possible. 6 SM amMyedad ia], 0766 2007 OBL OW OU OF OL OP 09 04 .0F 0 OO O€L ORL OOL 0 Se OS? 6 ‘tuo oad Ban, ut AGaroua-ddVjANG aAVNoda[O]| shot aN IIA WI], 007 0H.0% OU Ot OL 09 009 OF OF O 02-04 - 09-089 - Ose O9€ 06E 064 OS% 08% Os One +,wu0 oad Bay Ut AS aaue VOVJANS Iv[NoIOI{ 400 VIII. ortho-Nitro-Anisol : Cs . . CgHy. re ( al | Ee | Maximum Pressure Surface- " Molecular ae | aa es — tension x Specific Surface- & | 01a 0? 1.613 | 2150.4 50.8 e273 1237.6 25.4 5S | 2048.8 48.4 1.247 | 1195.4 44.9) 1.480 1973.8 46.6 1.227 1165.1 70.1) 1.390 | 1853.0 43.7 1.202 1106.1 85.3 1.340 1786.4 42.1 1.187 1074.6 117 1.227 1635.8 38.4 1.156 997.6 138.2) 1.160 1546.5 36.3 1.135 947.3 | 156 1.109 | 1478.2 34.7 1.118 921.8 | 172 1.043 | 1390.8 | 32.6 1.102 874.4 191.5 0.968 1290.5 | 30.2 1.083 819.4 | A 0.850 S350 e ss) 26.5 | 1.062 728.8 —— a —- - -—— — = | — — — — Molecular weight: 153.07. Radius of the Capillary tube: 0.04803 cm. Depth: 0.1 mm. The substance boils constantly at 272’ C.; at 20° it solidifies, and melts at + 10° C. Above 165° C. a slow decomposition begins. The specific weight at 25° C. is: Ayo — 124712" at o0Rn CG. al 22s mat 75° C:: 1.1970: at ¢ generally: A4o= 1.2732—0.001052 t-+ 0.00000048 #2. IX. Methylsalicylate: C,;H,(OH).CO.OCH3 . ie ee (1) (2) vo | 4 5 ' Maximum Pressure Surface- 4 Molecular eg | = = tension Specific Surface- Bs | in mm. mer- | in Erg. pro | gravity d,, | energy ” in = cury of in Dynes cm?2. Erg. pro cm2. (een SPP —19:8| 1.518 2023.8 44.2 1.220 1102.9 0.3 1.436 1914.8 41.8 1.202 | 1053.4 gee Sie 1829.0 39.1 1.179 998.1 “45 1.303 1737.2 | Silo! 1.158 956.4 Rr aewll 1.193 1590.1 | 33.9 1.128 | 891.7 * 94 | 1.124 1498 2 31.9 1.110 | 848.3 114.5) 1.031 1374 2 29.8 1.092 | 801.2 13522 0.968 1290.5 27.9 1.073 758.4 | 160.5 0.867 1155.9 24.9 1.050 | 686.7 192.9 0.760 1013.7 21.8 1021-1) ) seieke 212.2 0.696 928.1 19.8 1.003 | 562.9 | Molecular weight: 152.06. Radius of the Capillary tube: 0.04439 cm.; in the observations, indicated by *, it was 0.04352 cm. Depth: 0.1 mm. The substance boils at 217.°6 C. constantly; it can be undercooled | as far as —50° C, and crystallizes to a solid mass, which melts at | —16° C. At the boilingpoint z is: 19.3 Erg. pro cm?. The density at | 25° C. is: dyo = 1.1787; at 50° C.: 1.1541; at 75° Ce l28opAtee Cr Ayo = 1.2023—0.000924 ¢ —0.0000008 ¢. 401 X. Ethylsalicylate: C;H,(OH) .CO.O(C,Hs) . (1) (2) lars ; | ety Maximum Pressure H | Surface- : _ Molecular | BS tension | SITES Surface- oe ‘in mm. mer-) | | in Erg. pro | gravity dao | energy » in E-= | cury of | in Dynes | aa Erg. pro cm?. | (1 (C, | — ——st = — _ = — — 0° 1.346 1794.5 39.1 1.154 * 25 1.275 | 1700.4 36.3 180, Were e451} 1.206 1608.5 34.3 1.110 | 966.7 |; a4. 1) 1.110 | 1479.8 SHES) 1.082 903.0 \* 94.3] 1.047 | 1395.9 29.7 1.063 | 861.6 } 115.1) 0.963 | 1284.1 27.8 1.043 816.7 135.2} 0.906 | 1207.4 26.1 1.024 716.2 159.8; 0.828 | 1103.8 23.8 1.001 118.6 193 OM7123)) |) © 96452") 2087 0.980 633.9 | 212.5 0.669 892.1 | 19.1 | 0.962 592.9 Molecular weight: 166.08. Radius of the Capillary tube: 0.0 ‘439 cm. in the observations, indicated with * it was: 0.04352 cm. Depth: 0.1 mm The substance boils at 231.°2 C. constantly; at —20° C. it solidifies and melts at ca. —10° C. At the boilingpoint y is 17.6 Erg pro cm?. The specific weight at 25° C is: 1.1298; at 50? C. : 1.1053; at 75° C.:1.0806. | At ¢@ it is calculated from: d4o = 1.1541—0.000968 ¢ -—0.00000016 7. | XI. Phenylsalicylate (Salol): C;H,;(OH) .CO.O(C Hs). | (1 | = _ | Maximum Pressure Z | Surface- | } WeMolccnlartl| hy —————— | tension z Specific | Surface- | &. |in mm. mer-| | in Erg pro | gravity d,. | energy 4 in | (ES cury of in Dynes 2 [aSean ey ac) 2 | J 2, Erg. 4 oe oc | | cm | rg. pro cm |—20-1| (2.613) (3482.8) | (76.5) 1.221 (2396.4) | 0 | 1.571 | 2095.1 45.7 | 1.202 1446.7 | 725) 1.485 1980.6 | 43.2 1.179 1385.2 | 45 1.419 S925 3 5 41.2 | 1.160 1305.1 TESS | 1035 EAT agk | 38.7 1.136 1272.0- | fe O0st) "4.272 © "|| ¥ 1605.8 36:8: 9/1120 122th tee} 116 1.193 1590.4 34.5 1.098 1160.0 | 135 1.132 | 1509.3 | 32.7 1.078 1130.3 S16085) 0.971 | 1295.0 30.3 | 1.055 1046.3 *189.8} 0.890 HTSO=i ee 27.7 1.026 974.5 \*211.6 0.846 1128.5 | 26.3 1.006 637.5 Molecular weight: 214.08. Radius of the Capillary tube: 0.04439 cm.; in the observations, indicated with * it was : 0.04803 cm | Depth: 0.1 mm. Under 12 mm. pressure, the salol boils at 173° C.; at —33° C. it crystallizes spontaneously, and melts at +42? C. It can be under- cooled to a very high degree, and possesses a small velocity of crys- tallisation. At 35 C. the specific gravity is: 1 1697; at 50 C.: 1.1553; ator 11330 402 Some other derivatives of aromatic phenoles: Anzsol, Phenetol, Anethol, Guajacol, Resorcine-Mono-, and Dimethylethers; Hydrochinon- Dimethylether have been described before by the first of us). The temperature-coefficients of these compounds are however also reviewed in the present communication, because they were not mentioned in the one referred to. (Vid. also the preceding communications.) Molecular Surface energy in Erg pro cm?. Fig. 3. 7220 7190 1160 1130 530 oe =20° O° 20° 40° 60° 80° 100° 120° 140°160" 180" 200° 220° Semperalure 1) F, M. Jarcer, These Proc., Comm. I. (1914) p. 354 seq. 403 XII, Methyl-Cinnamylate: CjH/,.CH:CH.CO.O(CH,). | 5 , Maximum Pressure H | Syurface- | - | Molecular ise = 3 —_| tension x Specific Surface- a jin mm. mer- in Erg. pro | gravity d,, energy » in eo cury of in Dynes | em?, | : Erg. pro cm?. Ee O2NE: | | | 45, HeS20r ee LIL S le | 38-1 AN | 7 1062 Ne anOs.2 71 1.230 1639.8 | 35.8 1.038 } 1038.1 | 90.6) 1.166 1554.5 | 33/69 | 1.020 | 994.5 | 116.2) 1.092 1455.2 Madi | 0.997 944.2 135.4) 1.024 136552555) 29.7 0.980 894.9 | *159.7} 0.868 ) sea | Palle! 0.958 | 829.0 | *190.5) 0.777 | 1035.9 | 24.2 | 0.930 | 155) )lenmn| *210.9 0.712 949.4 | Doel | 0.911 | 699.1 Molecular weight : 162.08. Radius of the Capillary tube : 0.04439 cm.; * in the observations, indicated by * it was: 0.04803 cm. Depth: 0.1 mm. point ~ is: 18.6 Erg. pro cm?. The specific gravity at 35°C. is: @4o = 1.0700; at 50° C.: 1.0573 at 75° C.: 1.0340. | | | The ether boils at 253.°5 C., and melts at 36.°5 C. At the boiling- | | § 3. Values of the Temperature-coefficients of the molecular surface-energy & of the studied compounds. Amylacetate. | Diethyl-Ozalate. Oe. Ou . Temperature-interval: ae in Erg: | Temperature-interval: ae in Erg: i | at between — 70°? and — 21° 2,59 | between — 20° and 0° 1,8 — 219 and -- 662 -2)14 0°? and 66° 2,02 66° and 106? 2,03 66° and 106° 2,2 106° and 148° 1,73 106° and 146°? 2,3 146° and 184° 3,6 | Above 146? a decomposition seems slowly to set in. Diethyvlmalonate. Diethylbromomalonate. between — 20? and + 171° 2,52 | between — 21° and 0° 3,20 } 0°? and 26° 3,08 | 26° and 46° 2,67 | 46> and 67° 2,04 67° and 86° 1,75 86° and 106° 1,63 106° and 126° 1,35 126° and 146° 1,23 404 Diethyl-Ethylbensylmalonate. Ou Temperature-interval: - in Erg: t between —20° and 0° cannot be deter- mined indepen- dently of the vis- cosity. OO wae 5,2 AN oy (HO 3,7 66° ,, 106° 2,25 106gm,, 126° 2,6 1262" 5, 146° 2 1462 wl OGSe- 2,15 166° ,, 206° 3,85 | Above 166° a slow decomposition begins | to make itself perceptible. o-Nitroanisol. between 0° and 45°? 1,61 45°, 172°? 2,29 | Wize loos 2,82 egy ee Pye) 4,45 Above 170°? a gradual decomposition | sets in, which proceeds very slowly. Ethylsalicylate. between 0° and 212° 2,23 Methylcinnamylate. between 45° and 210°,9 2,44 Phenetol. | between —12° and 0° 2,0 0? , 74°,3 2,29 74°, 160° 2,13 The curve is almost a straight line, | Om with sama Ot Guajacol. between 26° and 146° 2,17 1462, 2062 2,66 Dimethyltartrate. Ou Temperature-interval: x in Erg t between 45° and 117° 2,08 117°, 160° 1,71 160° ,, 210° 1,53 Diethyltartrate. between 25° and 74°,3 2,15 pen Pile 2,35 Methylsalicylate. 2,30 between —19,°8 and 212° Phenylsalicylate. (Salol). | between —20° and 211°,6 2,43 Anisol. | between —21° and -+45° 1,88 B52 91° 2,14 Co ole 2,63 Anethol. between 24°,7 and 75°,1 2,53 15 eo 2,25 Resorcine-Monomethylether. between —20° and O° cannot be deter- mined indepen- dently of the vis- cosity. QO 5 Base 4,3 26° OS 2,45 46° ,, 184° 1,82 184° ,, 206° 2,97 Above 184° a decomposition sets in slowly. 405 Resorcine-Dimethylether. Hydrochinon-Dimethylether. Ou Ou Temperature-interval: va in Erg: | Temperature-interval: x in Erg: t | OF between —22° and U° 2,83 between 66° and 106° 2,11 D2 Vo Poe 2,2 | 106° ,, 166° 2,46 166° ,, 206° 2,88 Up to 166°, this -tcurve coincides | practically with that of guajacol and of resorcine-dimethylether. Pyridine. | z-Picoline. between —79° and —20° 1,79 between —70° and — 20°77 2,83 —20° , +25° 2,04 —20°,7 , +126° 2,02 25o re 92° 1,60 Chinoline. | between —21° and +45°,2 1,92 45°, 115° 2,10 5 2302 2,33 § 5. Also tor these substances one can state, that a decom- position of the compound causes an extraordinarily rapid decrease age Ou of the values for x or « with inereasing temperature : a becomes much larger in such eases with rising temperature. Furthermore it can be seen from the cases of salo/, diethylbenzylmalonate, resorcine- monomethylether, etc., that an extraordinarily great viscosity of the liquid can appreciably diminish the accuracy of the measurements ; however the case of dimethyltartrate on the contrary proves, that sometimes reliable results can be obtained, even with very high values of the internal friction. Groningen, June 1914. Laboratory Inorganic Chemistry of the University. Chemistry. — “Vhe Temperature-coefficients of the free Surface- energy of Liquids, at Temperatures from —80° to 1650° C.; V. Measurements of homologous Aromatic Hydrocarbons and some of their Halogenderivatives’. By Prof. Dr. F. M. Janerr. (Communicated by Prof. P. van RompBvurGu.) § 1. In order to answer also the question of an eventual depend- ence between the chemical constitution of liqnids and the values of their free surface-energy and of its temperature-coefficient, in 27 Proceedings Royal Acad. Amsterdam. Vol. XVII. 406 this communication the results of the measurements are recorded, made with a series of homologous hydrocarbons and some of their halogen-derivatives. With respect to the methods of purification, the determination of the specific gravities, and the significance of the diagrams, we can refer to the previous communications. This series includes the following terms : Benzene; Toluene; para-Xylene; Mesitylene; Pseudocumene; Tri- i y phenylmethane; Chlorobenzene; Bromobenzene ; meta-Dichlorobenzene ; yara-Eluorobromobenzene; meta-Eliorotoluene; and para-Chlorotoluene. l For the purpose of comparison with benzene, also Cyclohevane was taken into account here; the data relating to benzene were’ already published in a former paper‘), but are repeated here once more for comparison with the other hydrocarbons. The obtained results are put together in tables, in the ordinary way. § 2. Aromatic Hydrocarbons and some Halogenderivatives. it Cyclohexane: CgHjo. = ; Maximum Pressure H Surface- ee Molecular | a = _ tension % pecific Surface- | Be in mm. mer-| in Erg. pro gravity d,, | energy in | ca euro in Dynes | cm? Erg. pro cm?. he U c : | eee \ as: s. | | | | a Fes | Ha? 0.830 | 1106.8 28.3 0.788 636.7 | 19 0.785 | 1046.5 26.7 0.778 605.9 124.6 | 0.755 1007.6 25.7 OR Seo 40 0.682 909.2 23m 0.768 BPA Pa = | | 58 0.601 | 801.2 20.3 0.744 474.6 | | 70 0.548 730.6 18.4 0.732 434.9 | | 80 0.504 | 671.6 16.9 0.723 402.7 Molecular weight: 84.1. Radius of the Capillary tube: 0.05240 cm. Depth: 0.1 mm. The liquid boils constantly at 80.°7 C.; at this temperature the value of x is: 167 Erg. pro cm®. Jt solidifies at 10 C.; the crystals melt at +8 C. The specific gravity at 25° C. is. 0.7733; at 35° C.: 0.7645; " | at 502707515 At tame, d4> = 0.7958—0.000913 ¢ + 0.00000053 #7, | 1!) FB. M. Jaccer and M. J. Smit; F. M. Jazarr and J. Kann; F. M. JAEGER, these Proc., Gemm. I, II, IV. (1914; 407 II. Benzene: CoHg. | E Maximum Pressure Z | Surface- idee Molccula®. | SS — _| tension x peeie Surface- |. jin mm. mer-) _ in Erg. pro | gravity d,, | energy » in ao CaS | in Dynes | cm?. | Erg. pro cm?. =a ———————— = = = = 5.4 1.077 1436.7 30.9 0.895 607.7 9.5 1.055 1406.5 30.2 0.889 596.6 owl 0.969 1291.9 | 27.7 | 0.873 553.8 35 0.920 1226.5 26.3 0.862 530.3 55 0.836 1114.6 |} 23.8 0.841 487.8 714.6 0.757 1009.2 21.6 0.817 451.4 Molecular weight: 78.05. Radius of the Capillary tube: 0.04385 cm. Depth: 0.1 mm. The compound was already formerly described !), and is here only mentioned for purpose of comparison. The boilingpoint is 80.5 C.; at this us ty DoE x is: 20.7 Erg. pro cm?. 1) JAEGER, These Proceedings, Comm. I. (1914). Tin Toluene: CH,. C,H;. 5 : Maximum Pressure /1 _ Surface- eee Molecular | oe = tension 7 Preemie Surface- | vo =) . a jin mm. mer- in Erg. pro | gravity d,, | energy # in | ES cury of in Dynes | em2 Ao 2 | & 0°C. Erg. pro cm? | | I—71 | 1.385 1946.5 | 43.7 | 0.956 918.1 —21 | 1.090 Ip 45325 7 34.3 0.905 | 747.6 | Om 1.006 1340.8 31.6 0.884 | 699.5 | 26 0.906 1207.16) 5} 28.4 0.860 640.3 46 0.831 1107.6 26.0 0.841 595.0 | 66.6 0.756 | 1007.7 | 23.6 0.823 547.9 | 86.5 0.693 924.4 21.6 0.803 509.7 | 106 0.637 849.5 19.8 0.783 475.2 | | INoteeurar Weishe: 92. 06. Radius of the Capillary tube: 0.04803 cm. Depth: 0.1 mm. The commercial toluene appeared always to manifest a turbidity of the liquid at — 22° and —79° C.; a solid substance in little quan- tities separated at the walls of the tube. The here used toluene there- fore was especially prepared by distillation of sodium phenylacetate; it was dried by means of phosphorpentoxide, and boils at 109.°4 C, Down to —20°C. it remains perfectly clear; at — 79° C. it shows, as e.g other hydrocarbons (pseudocumene) do, a slight turbidity, At ‘the peer z is ee es pro cm?, PHT fi para-Xylene: (CH,) .CgH,. (1) (CH3) . (4) | E 7 | Maximum Pressure /I Surface- go tension a. in mm. mer- ' in Erg. pro | e cury of in Dynes cm?2. = OFIG: a_| Zoe 0.928 1236.7 29.1 45.9 0.853 1137.2 26.7 66 0.774 1031.9 24.2 86.5 0.709 945.2 22.1 106 0.648 863.9 20.1 126 | 0.597 7194.6 18.5 Molecular weight: 106.08. Radius Depth: 0.1 mm. The substance boils at 136.°2 C. point z is about 181 Erg. pro cm?, Specific gravity d4o Molecular Surface- energy » in Erg. pro cm’, of the Capillary tube: 0.04803 em. and melts at 15°C. Atthe boiling At 20° the density is Ayo = 0.8611. V. Mesitylene: (C/Z,);.CgH,. (1-3-5-). = ‘ Maximum Pressure JI Surface- : Molecular we tension ~ Specific Surface- a in ua. mee ve | in Erg. Pro | gravity d4o energy in Thien y o in Dynes em?, Erg. pro cm?. coal | DXC. | = | — . — = ————— ee 20-8 1.141 ! 1521.1 32.6 0.897 | 853.2 hy OL. | 1.061 1415.4 30.3 | 0.880 803.2 25.5 0.972 1296.0 iles| 0.859 746.2 45.2| 0.907 1208.7 25.8 0.843 703.8 140i 0.807 1075.4 | 22.9 0.818 637.3 91.3 0.755 1006.4 21.4 0.804 602.5 110 0.700 933.0 19.8 0.788 565.0 134.5 0.631 841.0 17.8 0.768 516.7 150.5 0.585 Ula. | 16.5 0.754 484.8 160.5, 0.562 749.3 | 15.8 0.741 469.7 | | Molecular weight: 120.1. Depth: 01 mm. The compound boils at 162.°8 C. constantly. At —46° C. it soli- difies to an aggregate of long, silky needles. Radius of the Capillary tube: 0.04352 cm. VL. Pseudocumene: (C//3), . CgH; (1-2-4-). lia l Tr i z | 5 _| Maximum Pressure H | Surface- | cee le Molecular ig — —_ = | tension x pecilic | Surface- | rae ‘in mm. mer-) | in Erg. pro gravity d, | energy in | e= cury of in Dynes | cm. ‘ Erg. pro cm?. = 0G: | | = — 1 = = — ———— = SS SSS = Bo ee ag) aa 0.910 | 883.9 | 0 1.031 | Is74eiy |) 3274 0.893 850.5 26 0.953 1270.1 29.9 0.871 798 .0 46 | 0.890 1186.4 27.9 0.855 153.9 66.5 0.828 1103.5 25.9 0.839 708.8 86.5, 0.768 1024.4 24.0 0.823 665.2 105 0.725 966.1 | 22.6 0.807 634.7 125 0.656 | 874.5 20.4 0.792 | 580.1 145.9, 0.600 799.5 18.6 0.776 536.2 ; 166 0.525 699.6 | 16.2 0.760 473.5 Molecular weight: 120.1. Radius of the Capillary tube : 0.04803 cm. Depth: 0.1 mm. The substance boils at 168.°5 C. constantly. It solidifies at —79° C.; the meltingpoint is about —60° C. At the boilingpoint the value of z is 15.8 Erg. pro cm?. Molecular Surface- energy in Erg pro c m2. 960 450 -S0°-60°-Y0°-20° O° 20° 40° 60° 80° 700° 720° 140° 760° 780° Fig. 1. Temperature. Triphenylmethane: CH (C,H;);. 2) | 5 4 | Maximum Pressure /I Surface- ae _—_— | tension x | ae in mm. met : | in Erg. pro E--= | cury of in Dynes cm2, [ec | 0°C. —— = = SSS = SSS a | 138.4] 1.074 145254 pl) ones | 156 1.044 1391.9 32.8 | 7p 0.999 | 1332.5 31.3 ; ee Wesia) 1211.9 28.4 0.833 1110.5 26.0 Specifi Molecular peeric Surface- | gravity d45 energy » in | Erg. pro cm? 0.984 1330.5 0.971 1302.6 0.959 1257.1 0.942 1154.4 0.928 1067.4 , Molecular weight: 244.11. Radium of the Capillary tube’: 0.04803 cm. Depth: 0.1 mm. The meltingpoint of the compound is 92° C.; it is hardly possible to keep it in undercooled condition. Above 165° C. a slow decom- position begins; finally the liquid is coloured brown. The specific gravity 40 is at 95° C.: 1,017; at 100°: 1,013; at 125° C.: 0,994; at 150° C.: 0,975; it was determined by means of the hydrostatic balance. Ate ayo = 1,013 — 0,00076 (¢ — 100). VIII. Chlorobenzene: C,H, Cl. E Maximum Pressure H aU | So, | See a. jin mm. mer- Es cury of in Dynes om Ov o} —16 1.252 1668.8 0 1.184 1578.3 25 1.143 1524.5 rao 1.099 1465.5 | 50 | 0.980 1306.6 70.5) 0.893 1190.2 | 90 | 0.805 1079.0 \*102 0.807 | 1075.4 Stas 0.751 1001.8 = 12255 0.717 955.9 | Surface- | tension x in Erg. pro cm?, Specific gravity d 40 Molecular Surface- energy in Erg. pro cm?, es | Palio So HUW CAMCCO is) oO 144 128 101 090 -078 051 029 O16 -003 -995 as ee a completely crystallized. The compound boils at 131? C. Molecular weight: 112.5). Radius of the Capillary with the observations, indicated by *, R was 0.04352 cm.; with those: **, it was: 0.04408 cm. Depth: 0.1 mm. tube: 0.04638 cm.; constantly; at — 34.°5 C. it is 41] Ix. Bromobenzene: C,H, Br. = : Maximum Pressure | Surface- | aS — : tension i | 26 in mm. alee | in Erg ‘= | mercury 0 in Dynes ro cm?. & | One: ae ° | —17.5 1.394 | 1858.6 42.2 ee 1.309 |) 1746-4 | 39.6 ~25 1.267 | 1698.5 | 36.5 *35.6 1.229 | 1638.5 | SHge *49.8 1.172 156255 33.5 71.5 1.032 ISTEEO || 31.0 90.5) 0.953 | 1270.5 28.5 125.5) (0.875 1167.3 24.5 pal53 0.758 LOWER) 21.1 Depth : 0.1 mm. The compound boils constantly at 154° C. X. Molecular weight: 156.96. Radius of the Capillary tube: 0.04638 cm.; in the observations, indicated by * R was: 0.04408; in those by **, it was: 0.04352 cm. meta-Dichlorobenzene: C,H, Cl, (1-3-). The boilingpoint is at 172.55 C. constant; the liquid can be under- At = Maximum Pressure H | Surface- Molecular | = a | tension x Surface- ie in mm. | in Erg enerey 2 | —-= mercury of | in Dynes | pro cm2. in Erg DC. | pro cm?. —22 1.433 1910.3 41.6 956.8 0 1.328 1770.6 38.5 895.9 25 1.230 1640.0 35.6 840.0 44.9 1.156 1540.9 33.4 797.9 irl 1.061 1414.7 30.6 Ti2.2 | 90.7 0.993 13246 =| 28.6 700.2 | 116.4 0.912 1216.5 | 26.2 651.5 | 136 0.858 1144.4 24.6 619.0 “160 0.737 982.7 22.8 582.4 PIE dl ee é a ee | Molecular weight: 146.93. Radius of the Capillary tube: 0.04439 cm.; in the observation, indicated with *, the radius was: 0.04803 cm. Depth: 0.1 mm. cooled to a high degree, but once solidified, it melts at —19° C. the boilingpoint ~ is: 22.2Erg pro cm?. The specific gravity at 25°C. is: 1.2824; at 50°C.: 1.2543; at 75° C.: 1.2253; at f C.: 1.3096—0.00107 ¢ | —0.00000072 f. Molecular | Surface- | energy » in Erg pro cm?. } Molecular Surface- energy in Erg per c.m?*. 412 450 2 — Temperature. -40°20° 6° 20° 4b° 60° EI? 100° 120° 440° 60" 18D” Fig. 2. XI. | para-Fluorobromobenzene: C,H,. /. Br (1-4-). _——S ee ES : : ey £ | Maximum Pressure H | Surface- Molecular | ee ian Specific Surface- | &. jin mm. mer- | in Erg. pro | gravity d@,,| energy v in ears cury of in Dynes cm2, | Erg. pro cm?. = OG: | eines 1707.8 398 | 1.654 890.2 0 1.198 1597.2 37.2 1.626 841.5 25.5 1.106 1474.1 34.3 1.590 787.6 45.3 1.031 1374.1 31.9 1561 741.6 710 0.953 1270.1 29.4 1522 695.1 84.7| 0.906 1207.6 27.9 1.504 663.8 Hedi 0.810 1079.9 24.8 1.460 602.8 | 138 | 0.734 978.6 22.4 1.436 550.5 Molecular weight: 174.95. Radius of the Capillary tube: 0.04803 cm. Depth 0.1 mm. The boilingpoint is constant at 150° C.; the value of x there is: 21.2 Erg. pro cm’. The specific gravity at 25° C. is: Ayo = 1.5998; | tat 50Gs 15538; atwiocn Ga M5147) eAb eaiteis. @4o = 1.6257 —0.00135 | t—0.00000168 #2. oats 9 413 XU. meta-Fluorotoluene: CH,.Cs,H,.F . | (3) | ; : i Rests | — Maximum Pressure | Surface- Fal Molecular ig = 2 | tension ~ Specific | Surface- | &e jin mm. mer-| — | in Erg. pro | gravity d A energy / in | & | cury of in Dynes | cm?. oat Erg. pro cm2., is eed | | Ae oe as _ aE en | ie || Bessy 1782.5 42 | 1.097 909.0 —20.5 1.090 1453.3 34.2 1.041 764.7 0 1.006 1340.9 31.5 1.021 TNS: 25.4 0,906 1207.9 28.3 0,994 652.6 , 45.3 0.839 1118.5 26.2 0.973 612.8 | 70.2 0.760 1021.2 23.8 | 0.947 566.8 84.9 0.721 961.9 22.4 | 0.932 539.2 Erg. pro cm? Molecular weight: 110.06. Dept h: 0.1 mm. Radius of the Capillary tube: 0.04803 cm. The boilingpoint of the substance is 114°.5 C.; 7 is there: 20.2 The density at 25° C. is: d4> 1059942 o0P G: 0.9680; at 75°C.: 0.9420. At © it is calculated from: d4o= 1.0206— —0,00106 ¢ + 0.00000016 ?. Molecular weight: 126.51. Radius of the Capillary tube: 0.04439 cm.; in the observation, indicated by *, it was: 0.04803 c.m. Depth: 0.1 mm. The substance boils constantly at 162.5 C.; it solidifies at —22°C., | and melts at +7.°5 C. At the boilingpoint z is 20.1 Erg. pro cm?. XII. para-Chlorotoluene: CH3;.CgH,Cl . : (4) £ | Maximum Pressure H Surfaces Malecutar Se = — = tension SERENE | Surface- a. |inmm.mer-| _ | in Erg. pro | gravity d,| energy “in | | &= | cury of in Dynes | em?2, " *lErg. pro cm?, = (HG: 25) 1.137 1515.8 32.9 1.065 795.0 44.7 1.059 1410.2 30.6 1.045 748.8 71 0.959 1279.6 Plot 1.018 689.8 90.2 | 0.895 1193.2 25.8 0.999 650.6 | 116.1]. 0.813 1083.9 23.4 0.973 600.6 135.7 0.760 1013.8 21.8 0.953 567.3 *160 0.653 870.3 20.2 0.928 535.1 414 Molecular Surface-energy in Erg pro cm?. 7020 290 960 930 200 S70 450 -80°60-40"-20° O° 20° 40° 60° 80° 100° 120 ryo'réo' 760" ‘Temperature Fig. 3. § 8. Values of the Temperature-coefficients of the molecular Sur- Fface-energie & of the liquids here studied. Cyclohexane. | Benzene. ; Ou. . Ou. Temperature-interval: a in Erg: Temperature-interval: ae in Erg: Ot between 9 and 80° Be between 5°,4 and 25°,1 2,73 This value is remarkably great; the 25 » 0D 2,20 curve is almost a straight line however. 55 » 14,6 1,85 Toluene. para-Xylene. between —71°? and —21° 3,40 between 25°,5 and 45° 2,53 Ve 2 GAS 2,27 45286 2,43 Gili 86,5 1,90 86 » 106 2,21 86,5 , 109 1,76 106 7 126 1,71 415 Mesitylene. Pseudocumene. Temperature-interval: a in Erg: Temperature-interval: = in Erg: between —20°,8 and 0° 2,40 between —21° and 0° 1,60 0 lO 2,20 QO 2 2,00 15 » 110 2,06 20h an LAG 2,18 110 POO 1,97 146, «166 3,0 Triphenylmethane. Chlorobensene. between 138°,4 and 156°? 1.59 between —16° and +25° 2,20 156 = algal 3.03 2 50 2,42 gil ney! 4.46 SOE e122 2,60 194 » iz 4.83 Bromobengene. meta-Dichlorobengene. between —17,°5 and +125,°5 =.2,38 between —22° and 09° 2,79 1:25)50n,, 153 2,53 O) =) 224) 2,23 25 yo Anti Ol se 1,88 WG si SS 1,64 136, 160 1,51 para-Fluorobromobenzene. meta-Fluorotoluene. between —21° and 0°? 2,41 between —71° and —20°,5 2,85 OF} j 45 2,09 —20,5 , 0 2,49 ey py Lily 1.97 On, 25,4 2,38 lily EO) 2,49 25,45 45,3 1,99 45,3 84,9 1,85 para-Chlorotoluene. between 25° and 45° 2,33 45 ay HL 2,23 Tie wallG Lor | L1G, 160 1,49 | Especially the last mentioned four cases prove once more very Ou strikingly the fact, that re cannot be considered as a constant, but r t that it is itself a function of temperature: in most cases in such a way, that it will decrease with increasing temperature. With ch/oro- and bromobenzene however evidently just the reverse happens. In the same way benzene, toluene, p-vrylene and mesitylene belong to the first group of substances, while the isomeric psewdocwmene manifests on A Caen a the contrary an increase of — with rising temperature. The devia- tions of the linear decline are so great and in most cases so system- atical, that they can by no means be accounted for by experimental ae MOBY Fas errors; the variability of F with the temperature must therefore ° t be considered as an essential fact. Groningen, June 1914. Laboratory of Inorganic Chenustry of the University. 416 Chemistry. — “The Temperature-coéfficients of the free Surface- eneryy of Liquids, at Temperatures from — 80° to 1650°C: VI. General Remarks”. By Prof. Dr. F. M. Janexr. (Commu- nicated by Prof P. RompBuren). § 1. If we wish to use the results up to now obtained in the study of these more than seventy organic and about ten inorganic liquids, to draw some more general conclusions, the following remarks in this respect may find a place here. In the first place it is proved once more, that the free surface- also in the peculiar case of the electrolytically conducting, molten salts studied at very high temperatures, — always decreases with increasing temperature. This fact, an exception to which also within the temperature-interval hitherto investigated — has never been stated, must be esteemed in every respect quite in concordance with the views about the origin of such surface- tensions. It is immediately connected with the other fact, that a decrease of the molecular surface-layer must be accompanied by a heat-evolution, an increase of that layer however with a heat- energy of liquids, absorption, if the temperature is to remain constant. Furthermore this gradual diminution of % with increasing temperature is in full agreement with the continual levelling of the differences in properties between the liquid phase and its coexistent vapour, when the temperature is gradually rising: at the critical temperature the value of y must have become zero’). Of more importance for our purposes however are the following results : I. A linear dependence of y and ¢ appears in general noé to exist. 1] The observations prove the possibility ; of all the three imaginable principal spe- cies of y-é-curves: the type 1, with a concave shape towards the temperature- axis; the type 3 with a shape convex to that axis; and the rectilinear type 2. Besides there are found some rare cases of combinations of these three principal types. Characteristic for type N°. 1 is, that oh will inerease with rising tempe- at rature, while it decreases under those oO t circumstances on the curves of type 3; 1) The critical temperatures of the studied liquids, are as far as known, in the diagrams indicated between ( ), behind the names of the different substances. 417 only in the case N°. 2 this quotient remains really constant. It is now of importance to draw attention to the faet, that in contradiction with the hitherto prevailing views, the presence of type 2 on one side, and of types 1 and 3 on the other side, appears to be in no : s : : du é clear connection with the absolute value of the quotient a nor with the absolute values of x or w themselves. Il. In agreement with the results of previous investigators, it appears to be possible, although only in some arbitrary way, to divide the studied liquids into fo principal groups, with respect to du the value of —. In the first group A belong all liquids, whose at : , du quotients = really are very near to Eérvés’ “constant”: 2,27 Erg a pro every degree Celsius. However it must be said here, that only a F. a mean value of = evidently can be considered in these cases, and only over a sparely extended temperature-interval; for, just as we already mentioned sub I, these liquids will by no means always show a linear dependence of y and ¢, corresponding to the type 2, and therefore such a linear dependence may be supposed in most eases only for rather short parts of the curves in question. To this group A we can bring e.g.: a number of ethers, like Ethyl-Isobutyrate (2,15); Tsobutyl-Isobutyrate (2,18); Diethyl-Ovalate (2,26); Diethylmalonate (2,52); Diethyltartrate (2,35); Ethyl-Acety/o- acetate (2,19); further: Chloroform (2,06); Dimethylaniline (2,23); Phenetol (2,14); Anethol (2,25); Methylbenzoate (2,21); Ethylbenzoate (2,29); Methylsalicylate (2,30); Ethylsalicylate (2,23); Methylcinna- mylate (2,43); a-Picoline (2,02); ete. With most of these and analogous substances however, we can state a considerable increase of at /ower temperatures (type 3), and at for many of them a value in the vicinity of 2,27 may be accepted only within a very narrow range of temperatures, e.g. between 25° and 80° C. 45 ; du To the group £6 all liquids belong, whose quotients = show values appreciably lower than 2,27 Erg pro 1°C. To this group the following substances can be brought: Water (1,04); Ethylalcohol (0,94); Propylalcohol (1,10); Tsobutylaleohol (1,10); Acetone (1,6) ; Acetic Acid (1,3); Pyridine (1,6); ete. However with several of these 418 du, liquids the value ot ; increases much at the lower temperatures, at while to the other side many liquids of group A, which e. g. between Oe 25° and 80°C. show rather normal values of vo will have abnor- mally low values for it at the higher temperatures. As far as the not numerous determinations of the specific gravities make a con- clusion possible in this respect, to this group 4 can be brought also the molten salts of the alkali-metals: Sodzmehloride (0,6), Potrssium- chloride (0,64); ete. Furthermore the hitherto observed dependence of x and ¢ for: Sodiumsulfate, Sodiummolybdate, Sodiumtungstate, Sodiumphosphate ; Potassiumbromide, Potassiumiodide, Potassium- . phosphate, -molybdate, -tungstate ; Lithiumsulphate, Lithiummetaborate, Lithiummethasilicate ; ete. ete., -—— seems to prove, that also with Oe: these salts the values of 5 will appear to be remarkably small. Ot = § 2. The prevailable opinion is, that the liquids of the group B must differ from those of group A in this respect that they would be associated, while the liquids of group A would be normal ones. Regarding those liquids, which show an almost linear dependence of y% and ¢ (type 2), the “association-coefficient” x is then calculated 3 : 2,2 |2 from the expression: «= \— Ow I(r) a linear dependence can not be supposed, several other formulae are proposed"). After what has been said, however, it can hardly be quite sure, that such a calculation of the degree of association can be thought of as a step in the good direction. For among the substances of group A the greater number are of a kind, whose «-t-curves belong to types 1 or 3; type 3 can be thought moreover again to be in so far in agreement with the postulations of the theory, that - while in the cases, where such here at least exists the possibility that the curve will approach to the axis asymptotically in the vicinity of the critical temperature. If now however the supposition were right, that a decrease of 1) After vAN Der WAALS (Z. f. phys. 18. 716. (1894)) e. g., a relation of the : T \B form: wt = A{ 1 — —] , — in which B at the critical temperature should ot Vr have the value: 3/o, but im praxi appears to be: about 1,23, — would reproduce in many cases the dependence of y and / to a rather sufficient degree. 419 Ou the values for va indicated an augmenting degree of association, it would be very difficult to imagine, why the larger number of liquids just show u-teurves of the type 3: for from the gradual Ola suse : decrease of a with increasing temperature in these cases, we must ; 2 conclude, that the association of the liquid would increase for most liquids with a rise of temperature. But because by far the most dissociations are accompanied by a heat-absorption, the mentioned conclusion could surely be hardly put in concordance with the laws of the mobile equilibrium. With liquids, which will dissociate to a higher degree at higher temperatures, one had to expect on the contrary the progress of type L: water e.g. is such a liquid, showing a gradual dissociation of complex molecules into simpler ones at increasing temperatures, and the «-tcurve here really possesses ') the expected type 1. In the same way we observed some organic liquids (Diethyl-Ovalate; Ethyl-Propylacetyloacetate; Propyl-, and Isobutyl-Cyanoacetates ; — 0-Toluidine; Resorcine- Monomethylether ; Hydrochinondimethylether ; a-Campholenic Acid; ete.), for which a gradual dissociation or decomposition at higher temperatures could be stated, and for those we found also a faster increase of Oye a a than before, as soon as the temperature of beginning decomposition t was surpassed. In opposition therewith is the case of acetic acid, where a gradually proceeding depolymerisation with increasing temperature has been quite doubtlessly proved, and where notwithstanding u 0 this fact, the value of va remains constant within very wide limits of temperature. *) These facts seem after my opinion to make it very dubious, if Ou the increase or decrease of a with varying temperature can be esteemed : ying mot: ‘ , : { 1) From E6éryés’ observations one can deduce already immediately Pek t will increase with rising temperature in the case of water: he observes between 3° C. and 40°C. a coefficient: 1,59; between 40°C. and 100° C.: 1,80; between 100° ©. and 150° C.; 2,28; and between 150° and 210° C.; 227. ®) Also this fact can be already de jiuced from Eérvés’ observations: between l 91° and 107° GC. he finds for —:; 1,52; between 107° and 160° GC. also: 1,82; Ot between 160° and 280° C.; 1,38. 420 any longer to be connected directly with the degree of association of liquids? Son ae , On :; Mee § 3. The variations of 5 must in the first instance be dependent t on the way, in which the specific heat ¢ of a liquid, is connected with the magnitude S of the bordering layer of it. In general we 0c 077 . i shall have a relation: so Tas , from which follows, that x can Ox ° only be a linear function of 7’ in the case, when c is mdependent of |S. From our measurements however we must doubtlessly con- 2 ou that therefore ¢ must really be dependent upon S. This fact proves clude, that generally can not be supposed equal to zero, and. at the same time, that the specijic heat of the surface-layer must have another value than for the remaining part of the liquid. The surface-energy therefore cannot be completely of a potential nature, but partially it must be considered as being of kinetic origin. In what manner however it will vary with the state of proceeding polymerisation or depolymerisation of the liquid, we cannot tell in advance; and the same is the case mtatis mutandis with the depend- ence of g upon ¢. At the same time it is not superfluous in this connection to fix the attention upon the fact, that it cannot be permitted to make any definitive. statement") concerning a high degree of association uw in the case of molten salts, because the observed values of a are very small, and the w-teurves seem to approach in these cases much better to the rectilinear type 2. For the whole theoretical exposition of Eérvés cannot be applied to cases like the present one, where nobody can know a priori, if the law of corresponding states will be valid. It is just the question, if the measurements still to be made will permit us to draw general conclusions upon an analogous connection between the temperature-coefficients of the molecular surface-energy and the degree of association of such electrolytes? Such conclusions could only be esteemed sufficiently justified, if certain analogies in the behaviour of molten salts and of the organic liquids should be found; at this moment we are still far distant from the time, when we shall be able to give any definitive judgment upon this matter. 1) Vide e.g. the relating views of Watpen, Bull. of the Academy of Petrograde loco cit. 421 § 4. The rather appreciable differences of our results with respect to the variations of w and xy with the temperature, with those of other investigators, who bave principally worked after the method of capillary ascensions, have suggested to us to investigate in detail, if perhaps in our way of working certain factors could be present, which may cause systematical errors in any direction ? First it was noted, that besides the particular shape of the mentioned curves, also the absolute values of y, determined by us and already by Feusten, were generally somewhat higher, than those obtained with the same liquids by other experimenters and by other methods. Of course it is very well possible, that e.g. the lower values published by Ramsay and Suieips, and obtained by them by means of the method of capillary ascension, are caused by the fact, that the moistening of the glass-walls in their capillary tubes has been not so complete, as is supposed in the theory of the phenomenon. In that case the angle of contact gy will play again a role; and because the height of ascension ceteris paribus is proportional to the cosinus of the supplementary angle of y, there could thus really be found a cause, which would make their results appear smaller, than those obtained in our work. But moreover we were able to prove on the other side, that our values for z, calculated after Cantor’s theory, must surely appear somewhat higher, than they really are, because in praxi_ the conditions are not completely fulfilled, on which is based the deduction of the jinal formula between H, d; and 7 in Canror’s theory. Let us start with the somewhat more summary deduction of his formula by Frusre.’). From this deduction as it is found in the paper of this author, it can be seen, that the formula of Canror ean have only validity in the special case that the angle 6, which the tangent in every point of the sharp edge of the capillary tube drawn in any azimuth to the rotation-surface of the small gasbubble, makes with the horizontal surface of the liquid, — differs only slightly from 90°; in that case 6 = 90° —s, wherein « bas a very small value. Some years ago prof. Lorentz was so kind as to draw my attention to the fact, that this limiting supposition can be avoided, if one makes a few simple substitutions in the two formulae of FrusrTut ; 2x 1 —cosA0=r.d, ti ; i COs Oy and 1) R. Feusret, Ann. d. Phys. loe. cit. oc Proceedings Royal Acad. Amsterdam. Vol. XVII. ote d; . sin 6 y. di 2 H = —_____—_ + ——_— | ¢9s 9 + ———_—_}, cos G (1 — cos 6)? 3 sin @ 1 — cos A 2) él by putting: ¢g = — 3 and) —— Fe Where » is the radius of the rT . ht r.cdt capillary tube, and y and // are the known symbols. The mentioned formulae can by this substitution be changed into: 1 1 1 (= en p=gsn@ + ct 48 ie 4 cos 6 sin* (9/,) ; : 3 © sin O sin® (’/3) Table of Corresponding Values of 0, q and p 0 q p 0° ea) (co) 10 4399.4 793,94 20 292,60 100,080 30 61,717 30,86 40 23,850 15,33 45 16,458 15,21 50 12,192 12,06 55 9 588 9,995 60 8,000 8,660 65 7,098 7,862 70 6,753 7,546 710 31/43” 6,750 7,542 715 7,033 7,814 80 8,433 9,183 85 13,770 14,479 86 16,567 17,269 87 21,277 21,960 88 30,764 31,448 89 59,35 60.027 89°4 63,44 64,12 90 oe) co Now it is possible to calculate for a complete series of values of 6, the numbers p and g, and to plot them against each other with respect to rectangular coordinate-axes. If /7 is measured, and 7 and d, are known, p can be caleulated for every experiment, and from the diagram the corresponding value of qg (and therefore also of x) can be immediately found. The following table gives a survey of the corresponding values of p and q, for a series of angles 6 between OprandeoO 2s. From this table it is seen, that » and qg reach simultaneously a mininiun tor 6= 70° 31'43", and that Canror’s formula is properly only valid without appreciable error for values of ¢ between O° and 423 0°55'. The corresponding curve generally deviates only a little from a straight line; however we found that this deviation is yet sufficient, to make a correction necessary for all numbers, caleulated from Cantor’s formula. § 5. From a special case we can now see easily, that the cal- culation of the results in this way and from Cantor’s formula, w7// never cause an appreciable change in the general shape of the p-t- . . Ou curves, and therefore neither in the deduced values of =f the deviat- at ion of a linear relation between p and q is between 6= 70 31'43" and 90° only so slight, that a somewhat important deformation of the mentioned curves cannot be the result of this difference in com- putation. However there will be caused a parallellous shift of every curve, which will dininish the absolute values of % and w with a small amount. That this influence is not at all without importance in the cases hitherto investigated, may be proved in the following way. We choose for this purpose two extreme cases of the here studied liquids: diethylether, because the observed values of H are here the smallest, and e.g. a substance as resorcine-monomethylether, whose values for // belong to the rather great ones. The caleulation is made as follows: HZ in m.m. of mercury (O| C.) is multiplied by the specific weight of mercury, and this number divided by the product r.d,, (r being expressed in mm.). With the obtained value for p, the corresponding value of g is found from the table or the diagram; this divided by 2 and multiplied by the product 7? .d,, gives y% in mG. pro m.m; the number is reduced to Erg pro cm?, by multiplication with 9,806, Diethylether. yinErg. yinErg. winErg. win Erg. Us p J em. em.-?(Cantor) em.-2 em.-? (Cantor) MOL MOOLOD Ao, 28,9 574,7 582.8 =20°.5 30,60 29,89 21,5 PLS) 456,2 464,7 OF Deets) Da ats! AIG 19,6 415,8 424,5 1 SSR WOW ally) 18,4 392,0 402,9 EP DESI DSO0) AUT viel 3 74,2 380,0 292.6 25.30 2470 A6y4 16,8 365,9 374,8 The whole y-tcurve is thus parallellously shifted to an amount of — 0,4 Erg. 28* 424 Resorcine- Monomethylether. yin Ere. yin Erg. win Erg. win Ere. be P gq ems? em.?(Cantor) em.? cem.-?(Cantor) == 20° 62785 62520) -83; 83,9 1850,1 1867,9 OS Sees) SOB) = bul 52,4 1161,9 ORS 46° 34,91 34,30 43,4 44,2 1001,6 1020,1 NMOS aileils sil no) eC) 38,3 896,7 915,8 166° 2848 27,80 31,5 32,3 782,0 801,8 206° 25,29 24,60 26,8 27,6 682,6 703,0 Here is the y-d-ecurve shifted totally to an amount of —0O,8 Erg. This is the correction to be applied, and which was already indicated in our first communication’); it has been taken into account since in every case in all the tables. It may here be repeated once more, that although the absolute values of the surface-energy really have approached closer by it to the values formerly published, however the shape of the y-¢, or u-f-curves is not altered by it with respect to any particular feature. § 6. Another question to be answered with respect to the obtained experimental results, is this, if it may be considered as possible to determine the right values of 4, without being embarrassed there- with by the influence of the viscosity of the studied liquid? For just because the internal friction of liquids always increases rapidly at lower temperatures, and an extreme viscosity of the liquid, — even if the bubbling of the gas is executed with extreme slowness, — will cause, as we have seen, the maximum pressure /7 to appear too great from all kinds of disturbing effects, — the influence of this viscosity could perhaps be advanced as a cause of such a deformation of the y--curves, that they just would manifest a steeper temperature-gradient at the lower temperatures than at the higher. Therewith an explanation of the curves of type 3 would be given; but it must be here remarked already in advance, that such a cause could hardly be adopted for the presence of the curves of type 1, just because all viscosity-curves have themselves the shape of type 3. However there seem to be many reasons, not to attribute too higha value to this explanation of the curvature of the «-¢-lines, even not in the case of type 3. In the first place it must be remarked, that the curvature of the 1) I’. M, Jarcer, these Proc., Comm. I, (1914). 425 said curves does not run parallel to the variations of the viscosity with temperature. Most strikingly this can be seen in those substances where the curvature is so slight, that the curves can be considered to be straight lines: with ethylbenzoate, whose viscosity at 10° is about six times that of acetone, and in a temperature-interval of 50° decreases to two or three times that value, the y--curve is a straight line; with the tsobutylbromide, whose y-t-curve between O° and 85° ean be considered as a straight line, the viscosity decreases to less than half its original value (from 0,008 C.G.S. to 0,008 C.G.S.) ; etc. Neither does the curvature of the y-¢-lines seem to be inmediately connected with the absolute value of the viscosity : with acete acid, whose viscosity is about three times, with salicylic aldehyde, whose viscosity is four times, with pyridine, whose viscosity is about twice, with pheneto/, where it is circa three times as large as that of ethylalecohol, — in all these cases the curvature of the z-écurves is less than for the last mentioned liquid, because they are almost straight lines; and with the amine and nitrobenzene, whose viscosity is about eight or ten times as great, as that e.g. of the edhylformiate, the z-t-curves are even slightly convex. In many cases the y-¢-curves will show a more rapid and steeper curvature at the higher tempe- ratures, where the viscosity becomes smaller; and the part of the y-¢ curve between — 79° and O° is often almost a straight line. With .the ethylalcohol the viscosity is about three times as great as in the ease of ethylacetate or eihylformiate, but notwithstanding that, the y-t-curves show in all three cases about the same curvature. To be sure, we have met during our measurements numerous cases, where very clearly the impossibility was shown, to determine the surface-energy dependently of the viscosity. But this we observed only, where the viscosity reached such enormous magnitude, that the liquid became glassy or gelatineous, and did not or hardly move on reversing the vessel. Such cases we found in: methy/- cyanoacetate, methyl-methylacetyloacetate, diethylbromomalonate, cie- thylbenzylethylmalonate ; in undercooled dimethyl-, and diethyltartrate and a-campholenic acid, and very strikingly with salo/ and resorcine- monomethyl-, or dimethylethers. Even in these unfavourable cases we succeeded sometimes in making some good measurements ; but in most cases this appears to be impossible, which is shown by the fact, that even with so small a velocity of formation of the gas-bubbles as 50 to more than 209 seconds, it proved to be impossible to find a maximum pressure fl, which really is independent of the speed of the nitrogen- flow. 426 The behaviour of such extremely viscous liquids with respect to the gas-bubbles produced in them, is very variable and often very peculiar: in this ease the bubbles are hardly loosened from the capillary tube, in that case one observes a periodic increase and decrease of the gas-pressure, without a bursting of the bubbles occurring ; in another case a very large bubble is produced, which suddenly explodes into a great number of very small bubbles ; but in no case a maximum pressure can be measured, which is really independent of the speed of the gas-flow, proving that it corresponds to a real state of equilibrium of the gas-bubble. And this last men- tioned fact is so characteristic for all our other measurements : within rather wide limits one can vary the speed of nitrogen-jlow, when working with ordinary liquids, without a measurable change in the determined pressure H_ being observed. On the contrary we studied a long series of very thin liquids: e.g. ethylalcohol, diethylether, ethyl- formiate, ethylchloroformiate, acetone, methylpropylcetone, chloroform, ete., cooled to —-80°C., which notwithstanding the low temperatures gave very reliable values of //7; the occasional fact that the temperature is so low, can therefore neither be considered of high importanee for the abnormally high values of y and w observed. However it must be said in this connection, that E6rvés’ relation can no longer be considered as valid at temperatures, lower than about half the absolute critical temperature of the studied liquids. In this connection it is not superfluous to remark, that with liquids whose volatility is very great, and which therefore possess at higher temperatures a very considerable vapour-tension, there is often some difficulty in obtaining reliable values for 7, this maximum-pressure being apparently somewhat increased. However the right value can be deduced in such cases by often repeating the adjustment of the capillary tube, until a really reproducible value will be found. The influence of these abnormally high vapour-tensions cannot be of essential significance, if the measurements are controlled accurately and often carefully repeated. All arguments taken together, we think it really very improbable, that the changes in viscosity of the studied liquids could be argued as the chief cause of the observed curvature of the y-¢- or u-t-curves. But in cases of abnormally great values of the viscosity, the deter- mination seems doubtlessly no longer possible after this method in any exact way; however with liquids, whose viscosity comes e.g. very near to that of glycerine, or is even somewhat greater, such measurements are already quite reliable if only the formation of the gasbubbles takes place ewtremely slowly: in this way for 427 instance we found again reliable values with: déethylimalonate (—20 and butyl-, or tsobutyl-cyanoacetates (—22°). Therefore we think it right to draw the conclusion, that the non- linear dependence of 7 on the temperature, must be connected with the very nature of the surface-energy itself, and that it will manifest itself always, as soon the studied temperature-interval is only wide enough. We can also mention here the fact, that in the ease of molten salts, even at very high temperatures and with very small viscosities of these liquids, we observed just the same three types of y-t-curves: so with potassiwmiodide the type 3, with potassium- metaphosphate the type 1, with many others the rectilinear type 2, — without it being possible to indicate an immediate reason for it. Finally we can draw the attention to the fact, that notwithstanding the fact that these determinations range over a much smaller tem- perature-interval, some y-écurves of other experimenters (vide e.g. Guye and his collaborators) show, on better consideration, also clearly a deviation from the rectilinear type; for water this has moreover already been mentioned before. § 7. Finally it is bere the place to discuss some points connected with the relations between the magnitude of w and the chemical constituents of the studied liquids, in so far as we may draw con- clusions about it already with respect to the sparing experimental data. Moreover the investigations relating to this subject will be continued in this laboratory in a quite systemaucal way, because a great number of problems have risen in this respect, which only by collecting a more extended experimental material can be answered by generally acceptable views. The facts hitherto gathered are principally adapted, to bring the values of u in qualitative connect- ion with the homology of some analogous compounds, and with the substitution-relations between some organic derivatives. This can be executed best by comparison of the a-¢-diagrams, which were published in the successive communications. A. Homology. Of homologous series we can mention the following: Ethylalcohol. Bthylformiate. Ethylacetate. 1.) n.-Propylalcohol. *) Ethylacetate - *) Amylacet ate. Isobutylalcoho!. 428 Methylisobutyrate. Acetone. 6 Bthylacetyloacetate. 4.) Ethylisobutyrate. ’) Methylpropylcetone. *) Eiirylpropyloacetate. Tsobutylisobulyrate. Tsobuty!cyanoacetate. \ Diethyloxalate. Dimethyltartrate. Amylcyanoacetate. ae | Diethylmatonate. , | Diethyliartrate. Dutyleyanoacetate. *\ Propylcyanoacetate. | Ethylcyanoacetate. | Methyleyanoacetate. 10 | Trichloromethane. | Benzene. o \ Nitrobenzene. Aniline. "| Tetrachloromethane. Toluene. ~) 0-Nitrotoluene. ~” ) o-Toluidine. ll. p-Xylene. Mesitylene. | Pseudocumene. Anisol Resorcinemonomethylether. Methylbenzo ate. : | Phenetol. é | Resorcinedimethylether. 16. { Hthylbenzoate. Benzylbenzoate. Methylsalicylate. Pyridine. 17.) Ethylsalicylate. ‘) a-Picoline Phenylsalicylate. By such a comparison of the results obtained we can now derive the evidently general fact, that the values of the molecular surface energy at the same temperature increase in homologous series, if we come to terms of higher hydrocarbon-radicals. Although quantitative relations do not so. strikingly come to the foreground, it seems however to be clear, that the influence of the same increase in this respect, becomes smaller within the series, if the molecular weight of the compound increases; a fact, that must be thought also completely comprehensible. In most cases these rules hold, as the following instances may prove: The value of w is at the same temperature greater for isobutyl-alcohol, than for normal propylalcohol, and here again greater than with ethylalcohol; just so with ethylacetate greater than with ethylformiate, with amylacetate greater than with the corresponding ehylether; it is greater for isobuthyl-isobutyrate than for the ethylether, and here again greater than for methylisobutyrate ; with ethyl-propylacetyloacetate greater than for ethyl-acetyloacetate. In the series of the six cyanoacetates, the value of «is greatest with the amyl-ether, and decreases here regularly within the series till the methylether is reached, while the temperature-coefticients remain almost the same; the zsohuty/-ether however has another value for Ou - and values for uw, which are only partially greater than for the 429 propyl-ether: in this also a manifestation must be seen of the differ- ences between normal and ramified carbon-chains. In the same way the molecular surface-energy of diethyltartrate appears to be greater than of dimethyltartrate. In the series of aromatic hydrocarbons, the curves for pseudocumene and the isomeric mesitylene are situated highest; then follow successively: p-xylene, toluene, and benzene; in the same mw is greater for o-toluidine than for aniline, for o-nitrotoluene greater than for nitrobenzene; just so for phenetol greater than for anisol, for dimethylaniline greater than for aniline, and for a-picoline greater than for pyridine. The only exception to this rule hitherto found, is presented by the resorcine-monomethylether, which possesses a ereater molecular surface-energy than the corresponding dimethylether. The substitution by means of members of the aromatic series has an analogousinjluence as by those of the aliphatic series, but it is much more intensive: in the series of the benzoates, the value of u for the ethy/-ether is indeed, greater than for the methyl-derivative, but for the corresponding benzyl-ether it is excessively much greater; in the same way it is the case with methyl-, and ethylsalicylates and salol, and with methyl- propylcetone on one side, and acetophenone on the other. B. Relations of Substitution-derivatives. The conclusions, which in this respect can be drawn hitherto, can be summed up shortly in the following rules: 1. The substitution of H by halogens is accompanied by an inten- sive increase of the molecular surface-energy at the same temperatures; the injluence increases evidently with augmenting atomic weight of the halogen. So u for chlorotoluene is greater than for slorotolwene*), and here much greater than for todwene itself; for bromobenzene ai is greater than for chlorubenzene, and appreciably greater than for benzene; with the m-dich/lorobenzene it is greater than for /lworobromobenzene, showing that the specific influence of fluorine seems to be less than the difference between bromine and chlorine. In the same way the ralue for diethylbromomalonate is appreciably greater than for dietyl- malonate; for tetrachloromethane just so greater than for chloroform. 2. Vhe substitution of N-atoms for C-atoms, or of that of negative nitrogen containing radreals for a H-atom, is followed by a relatively great increase of the molecular surface-energy at the same temperatures. +) The relatively small differences caused by the structural isomerism of these compounds, is here neglected for the present; generally the pava-substitution seems to be of the highest, the meta-substitution of the smallest influence in this respect. We will discuss this peculavity afterwards by considering the results of a special set of measurements. 430 So yt is appreciably greater for o-nétroanisol, than for anisol; for o-nitrotoluene much greater than for ¢olwene; for nitrobenzene much greater than for benzene; for aniline and o-toluidine, much greater than for benzene ov toluene. Just so for pyridine appreciably greater than for benzene; ete. 3. The substitution of aromatic hydrocarbon-radicals instead of H-atoms makes the values of the molecular surface-energy also con- siderably greater. So the values for sa/o/ ave much greater than for the other salicylates; of benzylbenzoate it is much greater than of both the other benzoates; of acetophenone much greater than of démethylcetone or methylpropylcetone; of diethyl-benzyethylmalonate much greater than of diethylmalonate itself; ete. Only continued investigations in this direction can however, as has already been said, prove with more certainty, if these rules may be considered as general ones. Researches of this kind will be started in this laboratory within a short time. Laboratory for Inorganic Chemistry of the University. Groningen, June 1914. Mineralogy. —* On the real Symmetry of Cordierite and Apophyllte”. By Prof. H. Haca and Prof. F. M. Janerr. § 1. In continuation of our investigations!) on the symmetry of erystals, which can be discerned as mimetic or pseudosymmetrical, we will give in the following a review of the results obtained in our experiments relating to the cordierite (tolite; dichroite) and to the apophyllite (albine; ichthyophtalm). Of both kinds of silicates specimens of dijferent localities were at our disposal, — a fact, which hardly can be over-estimated in the study of ROnreEN-patterns, as will be proved below. We will describe in the following pages successively our observations with: a) Cordierite; b) Apophyllite. § 2. «a. Investigations on the true symmetry of Cordierite. Cordierite, asilicate of the chemical composition: H,( Mg, Fe), Al,Sz, ,0,,. belongs to those minerals, which lke the arragonite, imitate the habitus of hexagonal crystals by means of particular polysynthetical twinformations. In literature it is only mentioned, that it is “rhombic” 1) Haga and F. M. Jagcer, these Proceedings, XVI. p. 792. (1914). 431 (a: b:¢ =0,5871 :1:0,5585), but it is evidently unknown, to which symimetry-class of the three possible ones it belongs. Its pseudohexagonal habitus is obtained in two ways: a. by twin formation parallel to {110}, consisting in an intergrowing of ¢hree individuals in such a manner, that the faces of {110} will function as the apparent prism- faces of the pseudohexagonal combination; 4. by a twinning parallel to {130}, in which three_ individuals form either a threefold twin by contact, or a threefold one by imtergrowth, the faces of {110} being turned outward (fig. 1a). In crystals of the structure, described sub a, a plate cut perpendicularly to jOOL{, will appear to be divided into six sectors, of which every one is optically biaxial, the planes of the optical axes being situated in three successive sectors under 60° one to the other, while they are of course equally directed in every two diametrically opposite sectors. In crystals of the type 4 there will be either three sectors, in which the axial planes are orientated along the larger diagonal of the kite-shaped sectors (fig. 16,); or there appear six sectors, in which the axial planes are orientated perpendicularly to a diameter of the rhomboidal boundary of the whole complex (fig. 16,); in this last mentioned case the axial planes in two diametrically situated sectors will appear, as in the case sub a, orientated in the same direction. The considered possibilities are elucidated by some schematical drawings in fig. 1. (ii {ft) 10)’ 010) (iio) (iio) cs =f ane s™~ 5 oo) 9 (730) coe (130) f Sp (Seca | 2 | “ ev « | < y " (070) (20:) (e10) (o10)| e--0 >< e-e-@ | (0 (110)} % P \(ilo ’ | be EY 4 22 | Sal y e cc3o | (130) y /(190) (10 Atel SS eae , L POC ‘iio (0) ane (110)' (110) ——— “( 110) Sales SIL ~Y (100) 7 Single Cristal re £ b, Vig. 1. In most cases the boundaries of the sectors are not distinet; the different individuals on the contrary, will penetrate each other partially. The cleavage occurs parallel to {O10}, but it is not very distinctly pronounced. The optical axial plane is parallel to {LOO}; the c-axis is first biseetrix, and the dispersion is only weak: o>b>>c. The axial - plane was parallel to {100}; the c-axis was | del low White 4 (100) first biseetrix (a). The birefringence is about _ | 62 =. 05008, and of negative characters @treqes Dery Sight Lilac | IntensVutey of these plates we obtained a R6ONTGEN-pat- Fig. 2. tern, after they had been carefully orientated in the way formerly described by us.'). The distance of the photographic plate and the erystal was 45 mm., while the time of exposure varied between 1*/, and 2°/, hours respectively. In connection with the question of the orientation, attention must be drawn here once more to the fact, that deviations of the theoretically right orientation, even so slight that they cannot be controlled any more by means of optical test, will however always manifest themselves by a slight dissymmetry in the R6OnrGEN-pattern. For instance, the image obtained by radiation through {O01} in several experiments, appeared to be always un- syminetrical to a more or less degree, while by the optical test in any of these cases no appreciable deviation of the optical image and of the right orientation of the first bisectrix could be proved. Thus even the greatest attainable degree of precision in this orien- tation can never exclude the necessity, to acknowledge certain imperfectibilities of the expected symmetry of the obtained RONTGEN-patterns as of only secondary importance in the com- parison of these images. and to neglect them presently in drawing conclusions from the photographs. This point must always be con- sidered in all following discussions of the obtained results; without this restriction it simply appears absolutely impossible to draw any valuable conclusion from the results obtained by experiment. At the same occasion we wish further to remark, that the use of a phos- phorescent screen (species “Eresco”) behind the photographic plate 1) H. Haga and F. M. Jagaer, these Proc., loc. cit. (1914). TABLE I: Cordierite. 433 evidently often causes disturbances in two possible ways: (st. by increasing appreciably the dimensions of the central spot, because of the diffuse light-emission of the sereen; which fact may render some of the spots situated in the immediate vicinity’ of the central part invisible in the reproductions; and 2". because the impossi- bility of pressing the phosphorescent screen over its whole surface quite equally against the photographic plate, eventually will cause some differences in the intensities of the black spots, which apparently create an accidental dissymmetry in the obtained photograph. Also both these disturbing effects must be taken into account together with the above given arguments, to explain the inevitable imperfection of the ROnrGEN-radiograms, thus prepared. The R6énreen-patterns, which now are reproduced ‘in fig. 3, 4, and 9 of plate I, can teach us the following facts: A somewhat more accurate study of these photographs will immediately show, that the images obtained by radiation through the erystalplates {100} and {010}, possess only a dilaterc] symmetry: the molecular arrangement of the crystal, seen in the two directions perpendicular to these faces, can thus possess only one single plane of symmetry, in the first case perpendicular to {100}, in the last one perpendicular to {O10} and passing through the c-axis; by both images however it is proved indubitably, that axes of binary symmetry are completely absent. The image, obtained by radiation through the erystal in a direction perpen- dicular to {001} however, must be considered doubtlessly to be symme- trical with respect toa set of two symmetry-planes, perpendicular to each other ; of course the intersection of these two planes, being the c-axis, needs to be an aais of binary symmetry too. On Table / we have repro- duced a RonTGenogram of this ease, which shows some dissy mmetries by a very small error in the normal orientation; the distribution of spots of equal intensity however, etc., suggests the symme- trical nature of this radiogram with respect to the mentioned planes without any doubt. Of this same crystalplate we obtained some more radiograms, which were however not sufficiently intense for reproduction; they were somewhat more symmetrical than the pho- tograph reproduced here, which fact apparently was caused by a somewhat better adjustment of the crystalplate with respect to the Ronreen-tube. But an optical investigation of the crystal-plates in quite the same position as in which they were during the experiment, allowed no distinction of the orientation in the several cases: it must there- fore be considered a fact of mere chance, if one gets accidentally the right position of the plate, necessary to obtain a pattern, whose symmetry approaches the pure one with more or less perfection ; 434 and furthermore, as we already mentioned, the accidental situation of the phosphorescent screen will play in this question also a more or less important role. § 4. The obtained results were so surprising, that we thought it necessary to repeat the experiments of radiation through the plates parallel to {100} and {O10}, also with cordierites of other localities. 6. From a beautiful, pink eordierite of J/ount Lhity, Madagascar, which had no geometrically definite boundaries, two planeparallel plates were cut after {100} and {010} and about 1 m.m. thick. The plate parallel to {O10} was distinetly dichroitic : for vibrations in the directions of the axial plane it was lilaec-white, for those perpen- dicular to it intensively pink. On {100} the colour for vibrations: perpendicular to the c-axis was pink; for those parallel to it, the plate was almost white. In the same way two such plates were cut from a single, short. prismatic, chaleopyrite-covered cordierite-crystal of Bodenmais ; it was fixed upon an aggregate of chalcopyrite and sphalerite. The mentioned fo) plates were from 1,0 to 1,1 m.m. thick, and showed no distinet di- chroism: the plate parallel to }100} showed hardly any difference of colour for two perpendicular directions ; that parallel to {010} was for vibrations parallel to the c-axis yellowish-white, for those perpen- dicular te it however pink coloured. In a quite analogous way as described before, ROnrarNograms of these four crystal-plates were obtained. The fig. 6 and 7 give the photo- graphs for the erystal from Lodenmais, the figures 8 and 9 those for the crystal of Mount lbity *). From these ROnTGEN-patterns it can in the first instance immedia- tely be seen, that also with these crystalplates all radiograms are only symmetrical with respect to one single vertical plane, and that in these minerals also binary axes perpendicular to {100} or {010} appear to be absent. In connection with the results obtained with the other cordierite-plates, it is hardly possible to give any other explanation of this, than that the absence of both horizontal binary 1) The cordierites of /bity are somewhat richer in SiO;, Al,03, and MgO, than those of Bodenmais, but their content of iron-oxides is less ; the followimg analysis may give some idea of this: Ibity : 49.05 9/9 SiO, ; 33.08 /) Al,Og; 11.04 °/) MgO; 5.2%) FeO + Fe,Os ; 1.649/, HO. Bodenmais : 48.58 °/, SiQ,; 31.47%) Al,O3; 10.68°/) MgO; 4.90) FeO; 1,85/, FeO, ; 0.09 %/) CaO; 1.96%/, H,0. Vide also: Wutrine and Oppenueimer, Silz. B Heidelb. Akad. d. Wiss. Abt. A. N°. 10. (1914). 435 aves and of the horizontal symmetry-plane, is really characteristic of the molecular arrangement of the silicate. Founding our statement on these experiments, we must therefore draw the conclusion, that cordierite is an hemimorphic mineral, belonging to the rhombic-pyra- midal class (rhombic-hemimorphie class) of the rhombic system, just like calamine and struvite, ete. The threefold twinning-aggregations of the cordierite must thus be considered to be real pseudo-hevagonal, and no pseudo-trigonal mimetic forms. Because all possible space-lattices of the rhombic system, as deduced by Bravals, possess vertical and horizontal planes of symmetry, the molecular arrangement of cordierite can therefore by no means correspond to such a Bravats’ space-lattice. However the pseudo- hexagonal symmetry of the mineral, just as its prismatic twinforma- tions, seem to indicate with strong emphasis a structure-unit, which must be considered derived from the rectangular prism with rhombic base, whose angles will differ only slightly (ca. 25’) from 60° or 120°. The choice between the possible structures is hardly to be expected: after SCHOENFLIES’ theory e.g., there will be no less than 22 arrangements, which correspond to the hemimorphy of the rhombic system. (SCHOENFLIES, Krystallsysteme und Krystallstruktur, 1891, Sk ZSR)E j) 5. A second peculiarity of the obtained R6nrGEN-patterns is this, that notwithstanding their agreement with respect to their general symmetry, yet appreciable differences in the distribution of the black spots show themselves, if analogous crystalplates, but of different localities are compared. Even a superficial comparison of the figures 3, 6, and 8 of plate I to the one side, and of fig. 4, 7, and 9 to the other side, is able to manifest the great differences immediately. Doubtless all analogous images show a number of common spots ; but in every radiogram there are moreover new ones, while even homologous spots in the different photographs appear with such different relative intensities, that the total aspect of the figure becomes a quite different one by it. As these photographs were made all under precisely the same circumstances, we must conclude from this, that the symmetry of a species of minerals being evidently always the same, the number and the arrangement of its molecular reticular planes, just as their molecular densities, are however variab/e with the special conditions, which were prevailing during the formation of the crystals. With respect to the erterni/ form of the crystals, this is a fact which has long been known, and which can moreover readily be explained 436 by the different influences of the factors accompanying the formation of the crystals. But from our experiments it follows moreover, that the ¢nternal arrangement also, the molecular structure itself, must be considered as being variable with those evternal factors; thus to the different localities, where minerals are found not only the especial differences in habitus of the erystals must correspond, but also some variations of its internal structure. With respect to the great signi- ficance of this conclusion for the question about the constancy of mineral-species in general and about the velations between the external forces during the crystallisationprocess and the internal crystalline structure, — we must remark, that the correctness of our view will be established only — satisfactorily by a great number of such experiments, to be made with minerals of very different origin and accurately known chemical composition. For especially of many silicates, and also of cordierite, it is known, that they can be altered under the influence of chemical reagents’); and it is very well explicable, if such differences in internal structure, as we have stated here, were dependent upon such differences in chemical composition, instead of being attributed to the Variation of physical factors, whieh may have had a variation of the external forms as a consequence, however in the case of cordiriete, these variations in chemical composition are only small. Only numerous experiments in the direction indicated above, will enable us to decide in the alternative. § 6. We have tried to prove the hemimorphy of the cordierite, just as it follows doubtless from the described experiments, by verifying it again by means of the now usual physical methods. In the first instance we tried*) to reach our purpose by the aid of the wellknown method of corrosion-figures. The plates of cordierite, having been carefully cleaned by benzene, afterwards by alechol and ether, were submitted during a short moment to the action of a very dilute solution of hydrotlhuoric acid; later we made again such experiments by means of gaseous hydrofluoric acid and with dilute potassiumhydrate-sclutions. In the last mentioned ease, we were unable to get any well-shaped corrosion-figures; in the expe- riments with hydrofluoric acid however, we always got, even after ‘) Vide in this respect the paper of WuLrinG and OPPENHEIMER, just published in: Sitz. B. Heidelb. Akad. d. Wiss., Abt. A. N°. 10. (1914), p. 5 and 6; l,, OPPENHEIMER, Inaug. Diss. Heidelberg, 1914. *) In these experiments Dr. A. Siwek has willingly given us his esteemed assist- ance. 437 the shortest possible action and by means of very dilute solutions of the acid, a great number of corrosion-figures, which appeared to be elevations, instead of impressions in by far the most cases. They generally (fig. 10a, 6, c) did not have any well definiable shape, and were moreover quite irregularly distributed over the surface of the erystalplates*), only on {O01{ we succeeded sometimes in getting some extended rectangular forms, proving the presence of a binary axis and of two perpendicularly intersecting symmetry-planes. The corrosion-figures on {100} and {010}, and also on the prism {110} of the crystals from /bity and Bodenmais, proved clearly in every ease the absence of a horizontal plane of symmetry; they were however furthermore so abnormally shaped, that they could hardly he used for the control of the above deduced symmetry of the crystals. This case proves once more, that the method of corrosion- figures used, eventually can give unreliable results, either by the production of abnormal etching-figures or by a shape of the corrosion- figures, which cannot sufficiently exactly be defined. A second trial to determine the physical symmetry in this case, was based upon the idea, that because the principal axis c was of polar nature, it would be possible, that its ends would manifest opposite electrical changes on mechanical deformation or on heating. Although we are strongly convinced of the truth that a negative result can hardly be considered to be a decisive argument in this question, we have nevertheless spent a considerable time in en- deavouring to prove the polarity of the c-axis by means of Kunpt’s method of dust-figures. Although we were able to obtain on this oceasion e.g. the alternative red and yellow powdering of the vertical edges of prismatic quartz-crystals in a very satisfactory way, however all our numerous tentatives with plates of cordierite, as well with the pinacoidal as with the prismatic plates, remained without a positive result. In every case, if present, this piezo-, or pyro-electrical polarity of the c-axis appears to be only so feeble, that it seems ‘impossible to prove its existence in the described way with any certainty. It is a quite remarkable fact, which strongly corroborates the value of the new method that even where all crystallographic methods to find the smaller physical symmetry-differences of crystals used up to this date, are failing, the new method however appears to be quite able to elucidate the finer feature of symmetry of such crystals in so complete and persuading a way. Therefore an indubitable place 1) In these photographs, the crossed hairs in the field are parallel to the directions of optical extinction of the plates. 29 Proceedings Royal Acad, Amsterdam. Vol. XVII. 438 needs to be reserved in future to the method of RONtGENograms among all other crystallographical methods. At the same time however it is proved by the results obtained with minerals of different localities, how strictly necessary it properly must be considered, to build up the whole systematical mineralogy starting from this new point of view, and what surprising results are surely to be expected therefrom. We will now deseribe here the analogous experiments, made with apophyllite. § 7. Investigations relating to the Symmetry of Apophyllite. For our investigations of the symmetry of apophyllite, we had material at our disposal from the following localities: a. from . Paterson (U.S. A.); from Bergen Hill, Erie Railroad N.J.; ¢. from (ruanajato, in Mexico; d. trom Berufjord in Iceland. The apophyl- lites of American origin we will place opposite to that of Iceland as a typical group, because they manifest, as will seen below, some peculiarities in their molecular structure, which are not present in the /celand-mineral, and are substituted in it by other qualities. Apophyllite, a mineral with the chemical composition : KH,Ca,Si,O,, +45 H,O belongs to the important group of the remarkable zeo/ithic silicates ; they all contain water, and as was proved for many of them already, their vapourtension at constant temperature appears to be continually variable with their momentaneous content of water, — a behaviour quite opposite to that of hydrated salts in general. The explanation of this pbenomenon is commonly given in this way, — which is confirmed completely moreover by the physical properties of these silicates, — that the water is not combined with the silicate like the water of crystallisation, but that it is present, at least partially, either in solid solution or hold in the silicate-skeleton by absorption. Apophyllite is a typical representative of an optically anomalous or mimetic crystal: Brewster in 1819 already discovered the partition of the crystal-sections in numerous fields, and since that time the pseudo-tetragonal crystals of this mineral have often been the subject of research. For the explanation of this anomalous behaviour, two theories have been started: in 1877 by Matriarp, who supposed the erysials of apophyllite to be polysynthetic twinnings of perpendicularly crossed and penetrating monosymmetric lamellae, — the dimensions of the monosymmetric molecular-arrangement differing only slightly from those ofa tetragonal structure. The second- view, chiefly defended by ©. Kiri, explains the optical abnormalities as caused by internal 439 stresses, which in their turn are caused by an isomorphous mixture of optically positive and negative material '). The supposition of the existence of such positive and negative apophyllite-substances which is really confirmed in some cases by direct observation, must serve at the same time for the explanation of the very weak birefringence, and the so-called lewhocyclite-, and chromocyclite-phenomena. We will demonstrate in the following pages, that, — waiving tbe question, how far the last mentioned phenomena need to be explained by this intergrowth of optically positive and negative substances, -— in every case the method of the R6nrepn-radiation decides the alternative between the two views indubitably in favour of MALiLarD’s hypothesis. § 8. The American apophyllites used were all transparent, pearl- coloured crystals; they have a layer-strueture parallel to {001!, to which form also the direction of perfect cleavage is parallel. Without exception all these apophyllites are optically biaxial in convergent polarised light, with positive character of the birefringence. The apparent axial angle is only small, with a dispersion: 0 < v. By means of a gypsumplate giving the red colour of 1s* order, one sees, that numerous blue-, and orange-tinged, rectangularly bounded, very small fields are in juxta-, and superposition to each other, as in a mosaic; the crystal makes the impression of consisting of an innumerable quantity of perpendicularly very small lamellae, which evidently are distributed and superposed in very unequal number and in a rather irregular way. All these preparations give, if the ROnrarnrays are directed per- pendicularly to {O01}, the radiograms, which in Table // are repro- duced in the figures 1, 2, 3" and 4. Of all these radiograms it is again characteristic, that they possess a single plane of symmetry as unique symimetry-element ; it is placed in a vertical situation in all reproduced figures, and corresponds, as was found later, to a direction perpendicular to the axial plane of the optically biaxial individuals. The direction of this plane of symmetry can always rather easily be fixed on the original negatives by the particular aggregation of spots at the upper side of the image, which has the shape of a double pinnacle between the two very distinct circular garlands of spots there; and also by the facet, that it cuts symmetrically the group of the five very intense black spots, which in fig. 1, 8' and 4 are visible just beneath the centre: in fig. 2 these spots are invisible 1) The optical phenomena in basal sections of the optically positive apophyllites are (after Kooke) exactly analogous to those which would be produced in the originally uniaxial crystals, by stresses, working parallel to the edges (O01); (110). 29* 440 on the reproduetion, by the strong radiation of the phosphorescent screen and the enlargement of the central spot caused by it, but they were distinct on the original photographs. It is therefore doubtless, that these photographs can be considered to have brought the proof of the fact, that the pseudotetragonal c-axis of the apophyllite-crystals, is not even a binary axis; but that at best it can be compared with the vertical axis of a monosymmetric molecular arrangement: the original molecular structure of apophyllite is not of tetragonal, but of monoclinic symmetry. We once more emphasize in this connection the existence of the group of five intensive spots, just beneath the centre of the image. Indeed this garland of five spots, which correspond to five molecular planes, seems to be typical for all apophyllites of American origin ; it plays evidently in these silicates a preponderant role. As in literature there can be found some data, relating to the fact, that a heating to 270° C. would be able to expel a part of the water and to make the crystal tetragonal in reality, — we have studied ihe effect of such a heating at 270° to 300° C. by means of the heating-apparatus formerly described by us. And now it was found, that all spots disappear, but that the mentioned five intense spots are elongated like the fingers of a hand (tig. 36 on plate II). This fact could be explained by the supposition that the original sets of parallel molecular planes, by which the five intensive spots were produced, are changed during the deshydratation and heating gradually into the same number of now divergent molecular planes lying in five zones respectively. This would be possible, if the molecular planes, which are situated nearer to the crystal-surface, will lose their watermolecules sooner and more easily than those situated nearer the inner part of the crystal: the expelling of the water takes place namely very slowly and gradually, while the planes are rotating round their zone-axes continually during this deshydratation. It is possible, that an analogous, but far more irregular distortion of the positions of the molecular planes will be the cause of a gra- dually getting vaguer and finally of a disappearing of all other points and spots; if not the other explanation, namely that all these points correspond to the action of the zafermolecules alone, can be accepted. It will be only possible to give some stronger affirmation of this view, if more zeolithic silicate will be investigated in an analogous way. The fig. 34 is made, after the heated crystal being cooled down to the roomtemperature; it appears to be completely identical however with the image obtained at 300° C. within the furnace, and it is only reproduced here instead of the other, because the last mentioned 441 photograph was too pale. The resulting state of the heated apophy llite remains thus absolutely fixed on cooling; after the data given in literature, the water expelled at 260° C. will be only resorbed after about 3600 hours from an atmosphere of water vapour. Anticipating on our experiments with the apophyllite of Jceland, we can remark in this connection, that with this mineral, which did not show the five mentioned spots, there remained nothing at all on the photo- graphic plate, after the crystal was heated, except some feeble action on the places of the most intensive spots of the original image; they only proved, that the transformation by the heating was not yet completely finished. In no case we have therefore succeeded in proving, as before was done with the boracite, that the pseudotetra- gonal aggregation of monosymmetric material, above a certain tem- perature can be changed into the really higher symmetrical form : instead of such inversion, a change in the silicate-skeleton is pro- duced, which at least during the short interval of the experiment can be considered to be zrreversible, and which has nothing or not directly to do with the real transformation into a true tetragonal form. § 9. In opposition to these American crystals, the used apophyllite of Leeland must be discerned as a most beautiful, glassy, and perfectly clear crystal, which was determined to be a combination of sharp pyramid {111} and basal pinacoid {OO1{. The angles of the pyramid and of pyramid and basal pinacoid were variable within rather wide limits; they deviated from the angles commonly mentioned in literature by an amount of cirea 30' to 1°; yet the reflected images were splendid and quite sharp, this phenomenon too leading to the supposition, that the tetragonal symmetry could only be a mimetic one: {O01} : {t11} = 59°24’ to 60°13; in literature : 60°32’. 144} : {4171} ao : ‘5 : 58°56' Shea): fe == 74°38! to. 75°39" 3 BO add “rather oscillating’’. | From this crystal two planparallel plates were cut, the one parallel to {OOL}, the other to {100}. The plate parallel to {O01} between crossed nicols appeared to be not completely isotropous, but to possess an extremely weak birefringence, with the principal optical sections orientated perpen- dicularly to the edges (110) : (OO1). By means of a gypsum-lamella, giving the red of 1% order, it appeared to be divided into four sections, of which the diametrically 442 Opposed ones were tinged blue, while the other ones were orange. Every sector is optically biarial, with positive character; the axial plane is in every sector perpendicularly orientated upon the corre- sponding edge (110):(O0O1). The four quadrants were limited in the centre of the basal section by straight borders, corresponding with the edges of the psendo-tetragonal pyramid; in every sector the direction parallel to the corresponding edge (110): (O01) is that of smaller optical elasticity. The plate, which was cut parallel to {100}, showed on very strong enlargement and by the aid of a gypsum-plate with the red of Ist order, a very fine lamellar structure: the lamellae are super- posed parallel to the faces of the pyramidal, apparently tetragonal limiting forms, while also locally smaller or more extended fields can be discerned, in which the optical orientation appears to be different and in an orientation, evidently perpendicular with respect to each other. Of these plates the RONrGEN-patterns were obtained in the usual way: the fig. 5a, plate II represents the image, if the plate parallel to }OOL} is radiated through; it corresponds to the centre of the basal sections, where the four sections are tangent to each other; fig. 6 was obtained by radiation through one single sector, and fig. 56 represents the RON?rGENogram, correspondiug to a radiation through the plate, cut parallel to {100}. Although fig. 5@ appears to be approaching to a much higher degree to real tetragonal symmetry, it is easy to recognize in it the perpendicularly crossed partial figures of the photographs fig. 1—4, but without the formerly mentioned intensive five spots near the centre; and fig. 54 shows a symmetry with respect to two planes of symmetry, perpendicular to each other, and a binary axis. In fig. 6 it would again be possible to doubt this approach to tetragonal symmetry; however it seems to be present, and the figure allows, e.g. by direct comparison with fig. 4, to prove that in the radiograms of the /celand-apopliyllite doubtlessly several elements of the mono- symmetric American structures are present. From all these peculiarities it seems that we may conclude, that the image of the apophyllite from Iceland approaches only therefore more that of a real tetragonal crystal, because the intergrowth of the monoclinic lamellae is in this case much finer and more regular than in the American species; and with this doubtlessly the other facet is connected, that the Iceland-mineral looks so much clearer and within larger sectors more homogeneous, than the turbid-looking and opaque American apophy llites. 445 Finally we can here also fix the attention to the fact, that the RontGenograms of the apophyllites of different localities differ yet in their finer features, although they possess the same general symmetry. § 10. In our opinion these investigations have decided ‘without any doubt between the two prevailing theories for the explanation of the optical anomalies of apophyllite, i favour of MaLiarn’s hypothesis: not the tetragonal molecular structure, disturbed later by internal stresses, must be considered as the primary state of the mineral; but this state corresponds to an originally monoclinic molecular arrangement, which approaches very closely to a tetragonal one, and which reaches its pseudo-tetragonal character by the crossing and intergrowth of two such monosymmetric structures, by means of polysynthetic lamellar twinning, and a mutual penetration in directions, which make an angle of 90° with each other. POSTSCRIPT. Finally we will use this opportunity, to add here again a con- @ fe) ® ® Q ® (o) ® Q e 2 @ Oo 2 — + — —— — —— @Q— ——&) — ® (e} e = ® @ S e e ® ® ® @ @ Boracite at 300°. C. 444 struction-figure, relating {0 our paper on the symmetry of boracite ‘); this figure will reproduce the changes observed by us with this mineral before and after heating, in a ciearer way, than the not very satisfactory photographical reproductions given in that paper. In constructing this stereographical projection, Dr. L. S. Ornsrpin has given us again his kind assistance, for which we thank him here also once more. The change of the binary axis into the quaternary one, is proved by this figure again in a very striking manner, and it is easy to see, which reticular planes of the molecular structure have disappeared at higher temperature. At the same time we will correct some errors in the former paper, where on p. 797 the words “right” and “left” need to be interchanged several times, because the photographs are unhappily placed in reversed position, so that on comparison of the text and the figures, there is a confusion of right side, left side, and of horizontal and © 9 r) ® ® @ Te ) e® @ i) Ouike a oe a ® e ® 2) © @—_®- ® 1e) @ r) & ® ® ° So © e ® ® e © @ oe °® ® a2 Boracite at room-temperature. ') H. Haca and I’, M. Jan@er, these Proc. loco cit. 798 (1914). 445 vertical directions. The new figure in this paper has been adjusted in such a position, that it will correspond to the text of p. 797, if only the words vertical and horizontal (line 9 and 10 from beneath) are inter- changed on reading. Groningen, June 1914. Laboratories for Physics and for Inorganic Chemistry of the University. Physics. — “FRESNEL’s coefficient for light of different colours.” (First part). By Prof. P. Zeeman. One of the empirical foundations of the electrodynamics of moving bodies in the domain of optics is Fiznau’s celebrated experiment on the carrying along of the light waves by the motion of water. Let w be the velocity of water relative to an observer, then for him the velocity of light propagated in the water wauld be - CG. === sB07 u if the dynamical laws for the addition of velocities were perfectly general. In this equation a designs the index of refraction of water, c the velocity of light in vacuo, and we must take the upper or the lower sign, according as the light goes with or against the stream. Fiznau demonstrated that not the entire velocity w but only a fraction of it comes into action. This particular fraction appeared to be approxi- 1 mately equal to 1 — —, Frusnew’s coefficient. Hence we must write 3 ae in place of the above given formula: = c Cr SS SSC Joh is Joo antes Me ape (al) where 1 Sieelettee iii gd callie oy we For water ¢ is equal to seven-sixteenths. The extremely important role which the formulae (1) and (2) have had in the theory of aberration, in the development of Lorenrz’s electronic theory needs not to be exposed here, and it is hardly necessary to state that equation (1) is now regarded as a simple confirmation of Einsrrin’s theorem concerning the addition of velocities. I may be permitted however to point out the smallness of the 446 second term of formula (1). The velocity which we are able to obtain in a column of water transmitting light is of the order of magnitude of 5 metres per second. We have thus to find a difference ; 3108 : of velocity of 5 metres in 13 m., i.e. Of one part in fifty millions. This was done by Fizeav ') in one of the most ingenious experi- ments of the whole domain of physics. Fiznau divided a beam of light issuing from a line of light in the focus of an object-glass into two parallel beams. After traversing two parallel tubes these beams pass through a second lens, in the focus of which a silvered mirror is placed. After reflection the rays are returned to the object glass, interchanging their paths. Each ray thus passes through the two tubes. A system of interference fringes is formed in the focus of the first lens. If water is flowing in opposite directions in the two tubes, one of the interfering beams is always travelling with the current and the other against it. When the water is put in motion a shift of the central white band is observed: by reversing the direction of the current the shift is doubled. The ingenuity of the arrangement lies in the possibility of securing that the two beams traverse identical ways in opposite directions. Every change due for example to a variation of density or of tem- perature of the moving medium equally influences the two beams and is therefore automatically compensated. One can be sure that a shift of the system of interference fringes, observed when- reversing the direction of the current must be due to a change of the velocity of propagation of the light. The tubes used by Fizeau had a length of about 1,5 metres and an internal diameter of 5,3 m.m., whereas the velocity of the water was estimated at 7 metres. With white light the shift of the central band of the system of interference fringes observed by reversing the direction of flow was found from 19 rather concordant observations equal to 0,46 of the distance of two fringes; the value calculated with FRESNEL’s coefficient is 0,404. : The result is favourable to the theory of Fresnen. The amount of the shift is less than would correspond to the full velocity of ‘ ? ei: 1 the water and also agrees numerically with a coefficient 1——, if- ul the uncertainty of the observations is taken into account. ) H. Fizeau. Sur les hypotheses relatives a |’éther lumineux et sur une expérience qui parait démontrer que le mouvement des corps change la vitesse avec laquelle la lumiére se propage dans leur intérieur. Ann. de Chim. et de Phys. (3) 57 385, 1859. 447 Fiznau’s experiments, though made by a method which is theore- tically as simple as it is perfect, left some doubts as to their accu- racy, partly by reason of the remarkable conclusions as to relative motion of ether and matter to which they gave rise, and these doubts could only be removed by new experiments. 35 years after Fiznau’s first communication ') to the Académie des Sciences, Micuenson and Moriny*) repeated the experiment. They intended to remove some difticulties inherent to Fizeau’s method of observation and also, if possible, to measure accurately the fraction to be applied to the velocity of the water. Micurnson uses the prin- ciple of his interferometer and produces tmterference fringes of con- siderable width without reducing at the same time the intensity of the light. The arrangement is further the same as that used by Fizwau but performed with the considerable means, which American scientists have at their disposal for important scientific questions. The internal diameter of the tubes in the experiment of Michrtson and Moriey was 28 m.m. and in a first series the fotw/*) length of the tubes was 3 metres, in a second series a little more than 6 metres. From three series of experiments with awhile light Micuuson found results which if reduced to what they would be if the tube were 2 5 metres Jong and the velocity 1 metre per second, would be as follows: “Series 4A = double displacement if 0,1858 2 0,1838 3 0.1800” “The final weighted value of A for all the observations is 4 =0,1840. From this by substitution in the formula, we get «= 0,454 with a possible error of + 0,02”. For light of the wavelength of the D-lines we calculate 1 1 at — —, = 0,437. This agreement between theory and observation is u extremely satisfactory. A new formula for ¢ was given by Lorentz *) in 1895 viz.: 1) Comptes rendus 53, 349, 1851. 2) A. A. Micuetson and E. W. Mortey, Influence of motion of the medium on the velocity of light. Am. Journ. of Science (3) 31, 377, 1886. 8) Viz. the sum of the lengths of the ways in the moving medium, traversed by each of the interfering beams, or approximately twice the length of one of the tubes. 4) H. A. Lorentz Versuch einer Theorie dev electrischen und optischen Erschei- nungen in bewegten Kérpern, p. 101, 1895. See also Theory of Electrons p. 2¥0, 1 gn =1-- —-——4 Wome AEN oe © sale j uw uda (3) For the wavelength of the sodium lines this becomes: 0.451. We see, therefore, that the value deduced by formula (3) deviates more from the result of the observations than the value given by the simple formula (2). “Sollte es gelingen, was zwar schwierig, aber nicht unméglich scheint, experimentell zwischen den Gleichungen (8) und (2) zu entscheiden, und sollte sich dabei die erstere bewahren, so hatte man gleichsam die Dorrrer’sche Veranderung der Schwingungsdauer fiir eine kiinstlich erzeugte Geschwindigkeit beobachtet. Es ist ja nur unter Beriick- sichtigung dieser Veranderung, dass wir die Gleichung (3) abgeleitet haben’. 7) It seemed of some importance to repeat with light of different colours Fizeav’s experiment, now that the correspondence between theory and observation had become less brilliant, and in view of the fundamental importance of the experiment for the optics of moving bodies. From the point of view of the theory of relativity the formula (3) is easily proved, as has been pointed ont by Lave’), neglecting terms of the order sh Recently, however, again some doubt as to ; the exactness of Lorentz’s term has been expressed. I may refer here to a remark by Max B. Weinsrein*) in a recent publication and to a paper by G. Jaumann *). The last mentioned physicist gives an expression for the coefficient ¢, which for water does not differ much, but in other cases deviates very considerably from FREsNEL’s coefficient. The interference fringes were produced by the method of Micuerson. The method of observation introduced will be described later on. The incident ray s /a meets a slightly silvered plate at a. Here it divides into a reflected and a transmitted part. The reflected ray follows the path abcdea f, the transmitted one the path aedcbha f. These rays meeting in the focal plane of 7 have 1) Lorentz. Versuch u. s. w., 102. 2) M. Lauvs. Die Mitfiihrung des Lichtes durch bewegte Kérper nach dem Re- lativititsprinzip. Ann. d. Phys. 28, 989. 1907. 5) Max B. Wernsrery. Die Physik der bewegten Materie und die Relativitits- theorie. Leipzig. 1913, see note on p. 227 of his publication. ) G. Jaumann. Elektromagnetische Theorie. Sitzungsber. d. Kaiserl. Ak. der Wiss. Wien. mathem. naturw. Kl. 117, 379. 1908, especially p. 459. 449 pursued identical, not only equivalent, paths, at least inis is the case for that part of the system of interference fringes which in white light forms the centre of the central band. Fig. 1. In order to verify the formula (3) it is necessary that the light be monochromatic. Further it seems of immense advantage to have a water current which remains constant during a considerable time. For observations with violet light this even becomes strictly neces- sary, because visual observations are impossible with the violet mercury line (4358) used. MicueLson obtained a flow of water by filling a tank, connected with the apparatus; by means of large valves the current was made to flow in either direction through the tubes. “The flow lasted about three minutes, which gave time for a number of obseryations with the flow in alternating directions”. In view of my experiments the municipal authorities of Amsterdam permitted the connection of a pipe of 7.5 em. internal diameter to the main water conduit. There was no difficulty now photographing the violet system of interference fringes, though the time of expo- sition with one direction of flow was between 5 and 7 minutes. The pressure of the water proved to be very constant during a series of observations; the maximum velocity in the axis of the tubes, of 40 m.m. internal diameter and of a total length of 6 metres, was about 5,5 metres. : Before recording some details of my experiments, | may be per- 450 mitted to communicate the general result that for water there eaists a dispersion of Fresxwi’s coefficient and that formula (3) and there- fore the third term of Loruntz ts essentially correct. I wish to record here my thanks to Mr. W. pn Groot phil. nat. eand. and assistant in the physical laboratory for his assistance during my experiments with the final apparatus. The difficulties encountered in these experiments were only sur- mounted after two reconstructions of the apparatus. Great annoyance gave the inconstancy of the interference fringes, when the pressure of the water or the direction of flow were changed. Then not only the width of the interfereice bands, but the inclination of the fringes were undergoing uncontrollable variations. All these defects were perfectly eliminated by the use of wide tubes and by arranging the end plates in the manner indicated in Fig. 3. I am indebted to Mr. J. vAN Dpr Zwaat, instrumentmaker in the laboratory for his carefully carrying out my instructions and designs in the mechanical construction of the apparatus. In fig. 2A a side aspect, and in Fig. 2B a horizontal projection of the arrangement on a scale of about ‘/,," is given (see Plate). The interferometer is at the right side, at the left the rectangular prism is placed. The mounting of this prism is only sketched and was in reality more stable than might be inferred from the drawing. 451 Prism and interferometer were mounted on the piers cemented to the large brick pier of the laboratory. The tubes are entirely disconnected from the interferometer and mounted on a large iron [ girder; this girder is placed upon piers of freestone cemented to large plates of freestone fixed to the wooden laboratory floors. In this manner the adjustment of the interferometer cannot be disturbed by vibrations proceeding from the tubes. At the right of the horizontal projection the four large valves may be seen, by turning which the current was made to flow in either direction through the tube systems. The mountings containing the glass plates by which the tubes are closed are not given in the Plate. One of these mountings con- taining the plane parallel plates of glass is drawn to scale in Fig. 3 at one half of the natural size. The four plates of glass are by Hiteer, they are circular of 24 m.m. diameter and 10 m.m. thick ; in a second series of observations plates 7 m.m. thick have been used. The accuracy of parallelism of the plates is excellent; they are indeed cut from echelon plates.. The general plan adopted for the construction of the plate mountings is this: one can only be sure that no change will occur in the position of the plates during the course of an experiment, if this position is entirely dejinite. In order to attain this the glass plate rests upon the inner, accurately grinded, surface of the brass piece d. This piece d fits accurately into the conical inner part of a piece 4, itself rigidly screwed to the tube a. Parts d and 6 are connected by means of the counter nut c. The glassplate is held against d by the nut e. There is no objection to the presence at the zmszde between e and d of rings of hard india-rubber and of brass. (To be continued). Physics. — “A new relation between the critical quantities, and on the unity of all substances in their thermic behaviour.” (Con- clusion). By Dr. J. J. van Laar. (Communicated by Prof. H. A. LorRENTZ). (Communicated in the meeting of April 24, 1914). By way of supplement we shall add the calculation of three more isotherms he/ow the critical temperature, for which (loc. eit.) data are known from the unsaturated vapour region. If the p-values above T; were somewhat too high on the whole, now we shall find values which are much too low, lower even than #,, and therefore impos- sible. These deviating values can only be explained, when with low temperatures and large volumes association in the vapour is assumed, 452 For then, when R7 in the equation of state is made smaller by a factor <1, also v—/ will be smaller, hence 6 greater. In this way the too small /-values could therefore be raised to the normal amount. We shall see in the following paragraph that inside the region of coexistence the same phenomenon takes place: the 4-values in the vapour much too small (even large negative), the 4-values in the liquid phase normal and in harmony with the theory. Something particular takes therefore place for the large volumes: there is either association in the vapour, or the values of the pressure have been measured too small, or the values of the vapour densities too large. We shall presently return to this. Ff. Isotherm of —130°,38 = 142,71 absolute. Hence m=0,9473, 3,424 m = 3,244. p dy & | n €+5:n2 n— | B | | 12.773 27.394 0.2661 10.873 0.3084 10.518 | 0.355 | | | | | 28.878 77.821 0.6016 3.827 0.9430 3.440 } 0.387 | Mean 0.371 | Here we should have y = 0,727, 4, = 0,415, &, = #8, K 1,475 = 0,421. Hence the value of ”, found is too low. g. Isotherm of — 139°,62 = 133,47 abs. Here is m= 0,8860, 424 77 = 31034: p dy € n e+5:72 n— 11.986 28.122 0.2497 10.591 0.2943 10.308 || 0.283 14.586 35.573 0.3039 Sono 0.3752 8.085 0.287 Mean 0.285 With 7 = 133,47 corresponds y=0,719, 2, — 0411, 2,— Gee << 1,457 = 0,416. The found value of &,, viz. 0,285, is far below the theoretical value O,42. h. Isotherm of — 149°,.60 = 123,49 abs. For m is found m= 0;8197, so 3,424 m= 2.807. —— | 0.2323 | 10.206 | 0.2803 | 10.014 0.192 | 0.3341 8.401 0.195 | o tr a a > ioe) or vo} -I Mean 0.194 _ Here y=0,711, 4 =0,406, &,=8, X1,439 = 0,411; 0,19 again remains considerably below this. Combining the found values of &, in a table and comparing them with the theoretical values, we get the following survey. m | OS ele AS meets oie elt, OFemenl Ot | 0.95 0.89 0.82 0.49 0.46 0.435 0.43 0.43 0.42 0.42 0.41 | B, cale. | OF55) v0: SIN O45" 043i 0242 | 0.37? 0.28? 0.19? B, found As was already remarked above, the great deviation, especially below 7i.(m<1), mmst not be ascribed to the theory, but to the experiment, or to association in the vapour. For the found values of &, become, as we shall see, even negative, henee impossible, at still lower temperatures — while also yop, is continually fornd smaller than @j,,, which of course points to something particular in the vapour: either association, or inaccurate vapour- or volume determinations, in consequence of a systematic error. (Consult also g. of § 18 for a possible explanation.) 18. The region of coexistence. (Cf. Comm. 131 and These Proce. of Nov. 1913 (Comm. 138)). For the calculation of & from the given values of the coexisting vapour and liquid densities it is to be regretted that the vapour pressure observations (see also Comm. 115) have not been made at exactly the same temperatures as the density observations. This has rendered interpolations necessary, which of course impairs the perfect accuracy of the ¢, which will make its influence felt chietly on the #-values which are calculated from the vapour densities. In this connection we should not omit mentioning that the value of /, caleulated from the first observations of the vapour tensions (Comm. 115), is much too low, viz. 5,712, whereas the much better 30 Proceedings Royal Acad, Amsterdam, Vol. XVII, 454 value 7 > 5,933 follows from the values given in Comm. 1204 (see p. 10)’). We had even sufficient reasons (see § 17) to fix the value of 7’ at 6 (f could be still somewhat larger then). Rankine-Bosr’s interpolation formula (see These Proe. of Noy. 1913, or Comm. 188), namely c d b log pa + i Ser gives by differentiation : hence T 2,3 A ied ve Oo 61538,18 32293927 ~ Pas aca ity eae Wael eV Yop cesta 2 tp die OT To) a / T? But this formula, which is caleulated from all the observations of p (so also from those below — 140°,80), and corresponds pretty well with it, gives the value /;,= 5,628, which is much too low, at 7), (150,65), hence still lower than the value fj, = 5,712, given at the conelusion of Comm. 115, and ealeulated with / = — 524,3169, c= + 11343,28, d= 0. In virtue of this I think I have to recommend caution in the use of the values of p, at least in the neighbourhood of the eritical temperature. We shall now give the following survey of the values found for the densities 9, and 9, (Comm. 131), and also the corresponding values of p (Comm. 115, and These Proe. of Noy. 1913 or Comm. 138). — 125°.17 — 131°.54 —. 1359.51 —— 140°. 20 — 150°.76 — 161°.23 — 1759.39 — 183°.15 We have | calculated . 771289 .91499 .97385 .03456 .13851 22414 .32482 .37396 | from ~~ Jo l Vi 0.29534 0.19432 0.15994 0.12552 0.06785 0.03723 0.01457 0.00801 and o v2 | p=42.457 (for — 125°. 49) 35.846 ( >» — 129°.83) 29.264 (» —134°.72) 22.185 (» — 140°.80) 13.707 (» —150°.57) 7.4332 ( » — 161°.23) 1.3369 ( » — 183°.01) given in the following tables by means of 0; = 0,53078. the values of d, and d, 1) Slightly below 7%, at —125°,49, f = 2,577 K2,3026 = 5,933 was namely found, 455 @. t= —125°,17, hence T= 147,92, m= 0,9819, 3,424 m = 3,363. By means of linear interpolation p = 42,944 has been calculated, so «= 0,8947. 0.292 0.394 (Lig.) 1.376 0.421 (vapour) 0.687 1 11.50 P07 —l|° 2.443 d, = 1.4563 dy = 0.5564 As theoretically @ ranges from 0,42 to 0,29 (see above), both the values found can be correct. by = — 131° 54, P= 141,55. Hence m =0)9396, 3,424m= = 3,217. Linear interpolation, giving p= 38,545, «= 0,6989, would be too uncertain here, as —129°,8 differs too much from —131°,5. Van per Waats’ formula — log’ =f gives with /= 2,444") _ the value «= 0,6964. I | | | | d | n | e+5 ad? | n—£ B | l | d, = 1.7238 0.580 | 15.55 0.207 | 0.373 (lig) d, = 0.3661 Ques 1.367 | 2.354 | 0.377 (vapour) As £2 ranges from 0,42 to 0,29, the @-value in the vapour is too small. c. == —135°,51 = 137,58 abs. Hence m = 0,9132, 3,424 m=3,127. A linear interpolation gives p= 28,344, ¢=0,5905; van per Waats’ formula with f= 2,420 gives «= 0,5890. | j | =e = 7 TI d n e+5d2 | n—B } B | | | dy =1.8348 | 0.545 | 17.42 | 0.179 | 0.356 (4ig.) d, = 0.3013 3.319 1.043 | 2.998 | 0.321 (vapour) 1) The values of f have in each case been calculated by me from the vapour- pressure observations. 30* 456 The .2-value in the vapour begins to be smaller here than that in the liquid! d. t= —140°,20 = 132,89 abs. Hence m=: 0,8821, 3,424 m=3,020. For p we find through linear interpolation p= 22,795, ¢=0,4749; from — log’ «= ete. with f=2,415 on the other hand «= 0,4757. d n |) et5d2 | n— & d; = 1.9491 0.513 || 19:47 ety te | | | 0.358 (Lig.) | 0.230 (v.) | 48, should be about 0,42. Besides 0,23 is again < 0,36. @) $= —150°176 = 122533 abs.; Hence yn 0138120, 33404 7— = 2.780. Linear interpolation gives p = 13,595, « = 0,2832. d>—=0.2365 | 4.229 || 0.7553 | 3.999 1 e+5a2 | n—Z B | ) || || d, = 2.1450 0.466 || 23.29 | 0.119 | 0.347 (Lig) dy=0.1278 | 7.823 | 0.3649 | 7.619 | 0.204 (v.) | The value of @, is 0,41; 0,20 remains far below this. We moreover point out that also / of § 17 at t= — 149°,6 yielded a perfectly harmonious value for the vapour, viz. 0,19. The two series of observations, therefore, cover each other entirely. f. t= 161°,23 = 111,86 abs. From this m = 0,7425, 3,424 m = = 2,542. Linear interpolation gives p= 17,4332, «= 0,1549. d n We 52) n= G | B | || \| d; =2.3063 | 0.434 || 26.75 0.095 |, 0.339 (lig.) d>— 0.07014 | 14.257 | 0.1795 | 14.167 | 0.090(v.) | | | £2, begins to be more and more impossible. We point out that when f— 1 is iaken not =5, but e.g. =4,95, the value Bi,, does not appreciably change: 0,339 then becomes 0,338. But 2, would then become still smaller, viz. 0,07 instead of 0,092). If p=7,58 instead of = 7,43, so ¢ = 0,158 instead of = 0,155, we should also have found 0,34 for the value of g in the vapour, the same value at least as that for the liquid. (Also the ,assumption °, = 0,C366 instead of 0,0372 might lead to the desired purpose). vA¥ 457 g. 1=—175°,39 = 97,70 abs. Hence m = 0,6485, 3,424 m = 2;221. The value of « interpolated from —/og™ «= ete. with f= 2,322, gives ¢ = 0,05518. —— ——— ——- ——— d n € +5 @?2 n—P ie) d, = 2.4960 0.401 31.21 0.071 || 0.329(diq.) dy = 0.02745 | 36.43 0.05894 | 37.67 —1.24!(v.) Can the clue to the singular behaviour of the vapour perhaps be found in this that Crommenin has not determined the vapour densi- ties directly, but that he has calculated them from the law of BoyLE? With a too small value of » one naturally gets then a too slight value of @ from @ =n — (38,424 im: ¢). Then no association need of course be assumed in the vapour, and the impossible values of 2, below 7%. are at once accounted for. The found values of 2, would then be quite worthless. The question is therefore: where has CromMeLIn begun not to determine the given values of the vapour | density directly, but to ca/cuéate them from the (not yet valid) law of Borin ? *) he t= — 183° 15=6994 abs. Here m= 035970, 3.494 m = 2.044. From /og'*e= etc. we find the value «= 0,02742 (p = 1,3162) with f= 2,314. dy | a i etsa| ne | |B OS SF SS SSS SS ; d; = 2.589 | 0.386 || 33.53 | 0.061|| 0.325 (dig.) dp = 0.01509 66.26 |) 0.02856 | 71.87 | --5.31! (2) | | We point out that the liquid value duly decreases gradually, and is still higher than 8, = 0,29 at 7’ = 90 (absolute). So there is nothing impossible here °*). 1) Otherwise p= 2,78 would have to be taken here instead of 2,64, hence , e — 0,058 instead of 0,055; or else o; should be assumed somewhat smaller, in order to find at least the value 0,33 (that of the liquid) for 8 vapour’ 2) A rise of p to 1,44 instead of 1,32 (s to 0,030 instead of 0,0274) — or else a diminution of 03 from 0,0O8O ts 0,0075 — might reduce 6, to 0,33 here. The first supposition is impossible, for then the value of p at —183°,15 would be greater than at 183°,01, where 1,34 was found. But a diminution of g. by 6%/, in consequence of an erroneous calculation of e, (probably from the law of Boyte) is very well possible. 458 Summarizing, we get the following survey for the region of coexistence. m | 0.98 0.94 0.91 0.88 0.81 0.74 0.65 0.60 | Blig.| 039 0.37 0.37 0.36 0.35 0.34 0.33 0.325 Bo. | 0.42 0.38 0.32? 0.23? 0.202 0.09? —1.24? —5.3? At the lowest temperature, viz. t= 89,94 abs., y would be about 0,688, and 8, accordingly 0,393, 8, = 8, « 1,889 = 0,397, so that 8 ranges from about 0,40 to about 0,29. The liquid value 0,825 at n= 0,4 can be in harmony with this. In order to examine whether the values of Biiy. also agree quan- titatively with our theory, we will in the first place indicate for the different values of 7(m) the corresponding values of m and y (caleu- lated from 2y — 1 = 0,038 V 7). Besides the value of v: vy, =v: bd, = =n: 8, is given. (8, = 0,286). m | 0.98 0.94 0.91 0.88 0.81 0.74 0.65 0.60 0 n | 0.687 0.580 0.545 0.513 0.466 0.434 0.401 0.386 | 0.286 % 0.731 0.726 0.723 0.719 0.710 0.702 0.693 0.688 | 0.5 D:0) | 2.40 © 2.03 1:91" 1-79" 1.63 4.52) “1 -40mieiegs 1 hence p:jy| 1.33 1.245 1.215 1.18 ° 1.14 1.11 - 1.08 1.07 1 acalc.| 0.381 0.356 0.348 0.338 0.326 0.318 0.309 0.306 | 0.286 afound| 0.394 0.373 0.366 0.358 0.347 0. 39 0.329 0.325 | (0.305) The values 8:8, =6:6, have been calculated from the tables of § 16, viz. from those for y=0,75 and y=0,70. We have inter- polated for the values of y given in the above table. On an average the found values of 8 are 6°/, higher than the values ealeulated from our formula (30). If 8, = 0,30° were taken instead of 0,28°, the agreement would have been perfect. In connection with this it is remarkable that the dzjference between Bround ANd Beale, AaMounts almost constantly to 0,018 or 0,019. The course of the §-values is therefore perfectly identical with the course calculated from our formula; identity in the numerical values may be obtained by simple change of B, from 0,28° to 0,30°. 459 In fact, something is~ to be said in favour of this. In § 17 we namely calculated the value of @, from 2y = 6;:b,= &;: ?,, so that &, = &,: 27 = 0,429:1,5 became = 0,286. But in this it is assumed that the direction of the straight diameter remains the same down to the absolute zero point — which (as we already observed at the conclusion of § 14 (III p. 1051) cannot be the ease. On the contrary the coefficient of direction will approach to about 0,5 for all substances at low temperatures. It follows from this that the value of the liquid density at 7 =O, viz. @,, which is extrapolated from the direction of the so-called straight diameter (at the critical poit), will always be too great, hence v, too small, and also 6, =v, too small. Accordingly also the value of ?, = 6,: vz will be found too smali, when the inadmissible extrapolation is performed. The real value of &,, occurring in our formula (30) for b= /(v), will therefore be always greater than that which occurs in our relations found in I (which are valid aé the critical temperature). For the calculations of the real ,, in order to test our formula (30) by the observations, the calculation from &, = &,: 2; (which is based on this extrapolation) has therefore to be rejected. The above table need, therefore, give no occasion to conclude to any deviation with respect to the calculated and the found values of &; the more so as the course is perfectly the same, in consequence of the fact that in the relation (80) not 6, but b—b, occurs, so that through simple increase of 2 to 0,305 the found values of b—d,, resp. B—, will agree perfectly with the values of 8— 3, calculated . from our formula. Remark. We saw that the found values of 3, from the unsaturated gas state (§ 17) were all found too great for values of m>1; for values of m< 1 all too small i.e. larger or smaller than the values of p, or By caleulated from our formulae. Also in the region of coexistence (7 << 1) we found values for 3, which are all too small, nay even negative, hence impossible. Now the too small values may be easily accounted for either by association in the vapour at low temperatures, or through a faulty method of calculation of 8, from the law of Boynr (see above). But the too large values of By at m > 1 cannot be aecounted for in this way. It is, however, remarkable, that those too large values of 3, at m*/,, and /’ >4! Only for “ideal” substances, i.e. at the absolute zero point, can ) be independent of the volume. Other relations could’ also be derived, among others between the found values of 8, 2—p, and m'‘), but they may also be due to chance. We shall, therefore, no longer dwell upon them. 19. The characteristic function. It is known that for “ordinary” substances the value of the ee Pettey aa : characteristic” function @, 1. e. j—1 «¢ iS = 4 fi-—l1 did. ; é . m d&cocx. in which #=— —— is not constantly = 1 — as would have to e dm be the case, when a or } should either not depend on 7’ or only linearly — but with diminishing m inereases from 1 to about 1,4 at m=0,6, with about 1,5 as probable limiting value when m approaches to 0. See vAN pEk Waars, and also my Paper in These Proc. of 25 April 1912, p. 1099—1101, in which it appeared that g~ =1-+ 6,8 (1—m) can be put in the neighbourhood of the eritical point. (loc. eit. p. 1101). 1) When e.g. in the region of coexistence for the different values of m we write the corresponding values of n and n— f, viz. +0,23. i a appears to be about constant, 461 bavin¢ a For this it is however required that either —{ — ] = 6,8, or Om? \ an) i O20 : == {= | 6,9. (Cf. These Proc. of 3 Sept. 1913; p.56 and 57). Om? \ by. / 7. It is now certainly interesting fo consider how this will be for a substance as Argon, where yz is not 0,9, but 0,75. For the calculation of the values of / I bad to make use of RanktnE—Posr’s interpolation formula drawn up by Crommenin and treated already above (§ 18). This gives, indeed, the much too low value 5,628 instead of 6 for /;,, but 'as also the following values of J will possibly be too small in the same degree, there is a chance that the value of the ratio (f—1):(/,;—1) will not differ too much from reality. We then find the following table. | 147.92 | 0.9819 | 0.8047 | 0.8103 | 1.104 | 5.696 | 1.015 141.55 | 0.9396 | 0.6964 | 0.6311 | 137.58 | 0.9132 | 0.5890 | 0.5529 | 1.965 | 5.987 | 1.078 | 1.15 132.89 | 0.8821 | 0.4757 | 0.4609 | 1.032 | 6.137 | 1.110 | 1.15 122.33 | 0.8120 | 0.2832 | 0.4742 | 1.033 | 6.534 | 1.196 | 1.24 111.86 | 0.7425 | 0.1549 | 0.1618 | 0.957 | 7.047 | 1.307 | 1.25 97.70 | 0.6485 | 0.0552 | 0.0685 | 0.805 | 8.080 | 1.530 | 1.23 89.94 | 0.5970 | 0.0274 | 0.0391 | 0.702 | 8.945 | 1.717 | 1.21 It is certainly remarkable that it would follow from the found 04 : values of g that here too 4 would be about — 7, just as for me) I. Og ordinary substances as Fluorbenzene e.g. (see above). For (5 = k 2) = — ee = — 6,63 (whereas it is — 6,8 for C,H,F). But on this head little can be said with certainty, as we have too few observations in the immediate neighbourhood of 77, at our disposal. The limiting value for m—0,6 is now, however, much lower, namely about 1,23 against 1,41 for ordinary substances. Now for 462 C,H,F the value of yz, is = 0,95; hence 0,:b, = 2Y~ = 1,90, and (6, : 6. )e = 1,90 <1,06 = 2:01,> whereas) 72,01 — 1,42. Further for Argon k= 0,75, hence 0: 6,=1,50 and (6,:5,),=1,49 X 1,018 (See II, p. 986) = 1,516, whereas 1,516 =1,231. It follows from this that with great accuracy 9, =V bo: be = V By 2 sw ee. DD) may be written for the limiting value at low temperature of the characteristic function ¢. It is therefore again only for “ideal” substances (6 = const.) that (> = 1, and hence ¢ continully =1 from 7% (then = 0) to the absolute zero. but for all the other substances the value of gy will increase from 1 to a limiting value, which will depend on the degree of variability of 6. As according to (36) (b,—d,),: 6, = 2y’ — 1 = 0,041 V 7; (see IIL § 15), we have also : G, = VIS 004A ss We shall not enter any further into this subject, leaving it for a possible later discussion. In conclusion we shall just repeat what we have already remarked in I, p. 820, that the temperature dependence at extremely low temperatures, where the departures from the equipartition law make themselves felt, undergo a modification. But we shall not enter into this any further either, and we only mention that for Argon the departures from the said law fall entirely within the errors of ob- servation even at 90° absolute (the lowest temperature at which observations have been made). Besides, at those extremely low tem- peratures all substances will probably have passed into the solid state, and this state is controlled by other laws than the liquid and the gaseous state, for which our considerations exclusively hold. 20. Conclusion. Though there are still many questions to be answered, and many difficulties left, we may already conclude in virtue of the foregoing to this: 1. The quantity a of van per Waats’ equation of state seems within a large range not to depend on the density, so that the : a é molecular attraction can be represented by —, both in the gaseous y? and in the liquid state. *). 1) Cf. also the conclusions in a paper by Tyrer in the just published number of the Zeitschr. f. Ph. Ch. (87, Heft 2) p. 198. 463 2. Whether the quantity @ is also independent of the tempe- rature, cannot be stated with perfect certainty yet. For as I think I have fully set forth in my Communieations of These Proce. of 25 April 1912 (p. 1091 —1106) and particularly of 3 Sept. 1913 (44—59 , ae ; (One ; 0° the assumption of a darge value either of { — ] or of — k k or OL (see p. 56—57 loc. cit.) is necessary for the explanation of the course of the characteristic function g (see §19). And as, aceord- ing to the above, 6, is, indeed, variable with the temperature, but 2 probably not so much that —(r) gets the required value, besides t~/) i 6 possibly also @ might depend on the temperature. Only a separate investigation ean furnish certainty about this. 3. The quantity 4 depends both on v and on 7. The way in which 4 depends on v — which is expressed by a formula of the form (see I] p. 981 et seq., Ill p. 1048, formula (29)]| = j) xv y peel oie ; b,—b, Zi, in which «= (b—4,):(v—yv,), and n depends on the quantity y, which is in connection with 4,:4, — leads us to suspect that the variability of 6 is possibly chiefly a real change after all, caused by the action of the pressure p+ “/.2 and of the temperature, in an analogous way to that which van Der Waats had in mind when drawing up his “equation of state of the molecule’, with which the above expression shows a close resemblance. [ef. also I p. 980—-931 (23 April 1914)|. Particularly also with regard to the temperatare dependence, viz. [see HI p. 1051—1058, formulae (85) to (36)| b,—b 7 _* — 9y'_] — 0,047, this agreement is remarkable. But whereas vAN per WaAAtLs’ two exponents are different, our two exponents are the same and dependent on 7, i.e. on 7 so that m can vary from 3'/, (for y = 1) to © (for y='/,, ite. T=0), as has been set forth in II, p. 935. 4. It seems to be unnecessary to ascribe the change of / to “quasi association’. It might namely be assumed that the complex mole- cules possess another volume than the simple ones, and from this a relation b= /(v) might be calculated — according to the known thermodynamic relations which indicate the degree of complexity as function of v and 7. R7'is then however multiplied by another factor which depends on the degree of association. What van ver Waats has treated in that sense on p. 1076 of 464 his Paper in These Proc. of 25 Jan. 1913 (published March 13%), had then already been treated very fully in a series of four papers, written by me at Clarens 1911—1912 (On the variability of / ete. ; see These Proc. of 26 Oct., 22 Nov. 1911; 24 Jan., 22 Febr. 1912). That a good deal may be attained in this way can sufficiently appear from these Papers. That difficulties present themselves of the same nature as have been advanced by van perk Waats on p. 1076 at the bottom (loc. cit.), has also appeared at the end of the 4 Paper (p. 716 et seq.). In any case it is a kind of relief that according to all that proceeds the assumption of quasi association does not seem absolutely necessary. The change namely of 4 with v and 7’ can very well be explained by other influences. 5. That 6, gradually decreases with the temperature, so that b, would coincide with 6, at Z’—0, and accordingly the variability of 4 would have quite disappeared — in consequence of which we approach more and more to the ¢dea/ equation of state with constant 4, on approaching the absolute zero — this points to the invalidity of the kinetic assumption, that for very large volume (for b, only refers to /arge volumes) i.e. in ideal gas state, b, would be = 46,. For according to the well known kinetic derivation, 6, would then still be = 46, at the lowest temperatures, whereas it has clearly appeared that 4, approaches more and more to }, at low tempera- tures. Compare particularly Ill p. 1051, formula (85) and the sub- sequent eloquent table. 6. Thus after all it would prove true what I wrote in I p. 809 (These Proc. of 26 March 1914), that namely in v—é the quantity 6 always refers to the real volume of the molecules m and is not = 4m, as the kinetic theory would lead us to assume. And in this way the difficulty, which I emphatically pointed out in II, p. 925 (at the bottom)—926, would have naturally vanished. So it is getting more and more probable that the so-called quasi diminution of 4 does not exist, and that there remains only real diminution, which is represented by a formula of the form (29), as far as the dependence on v is concerned, and by a formula of the form (36), as far as the dependence on 7’ is concerned. Why the earlier kinetic assumption 6, = 4m is really a fiction, and what circumstance has been overlooked then — this I shall demonstrate in a separate Communication. It will then have become clear that only v—m, and not v—4in determines the thermic pressure -- which becomes already probable when the kinetic energy of the moving molecules is thought to be 465 uniformly absorbed by the surrounding medium (see p. 809 of I, already cited above). 7. Hence at bottom the whole thermic behaviour of a substance does not depend on/y on the two quantities @ and 6, which deter- mine the critical quantities, which in their turn govern the law of the corresponding states — in such a way that all the substances behave correspondingly when they are only considered in equal multiples or sub-divisions of their critical temperature and critical pressure, but also (and the deviations from the said law are governed by this) on the absolute height of the temperature, at which the substance is considered. According to (86) every substance passes namely through the different types — characterised by the variable ratio b,:,, from the type of the “ordinary” substances, where i b, is about 1,8 (y= 0,9) to the type of the ‘ideal’ substances, where },is—=06, (y='/,) — when we descend from the ordinary temperatures to the absolute zero point (see the tables in I, p. 819 and III p. 1052). The individuality of the different substances, which they continue to preserve within the region of the Law of the Corresponding States, is therefore entirely determined by the rea/ height of the (absolute) temperature. Hydrogen at 328° absolute (77’=107%) will e.g. on the whole (Law of Corresponding States) exhibit the same behaviour as Helium at 52° absolute (7’ also = 107%) — but H, will show a value of about 1,7 for the ratio 6,:4, at that higher temperature, while He at the same “corresponding” temperature shows a value of about 1,2 for that ratio. For ve: hr we shall find about 2,7 for Hydrogen and Helium at their critical temperatnre, while vz: 6, = 2,1 is found for an ordinary substance at its critical temperature. Ete. Ete. And this may suffice for the present. I hope to come back to some separate problems later on, which are still awaiting solution. I may mention: the temperature dependence of / (see I, p. 811), the change of direction of the “straight” diameter from 77, to very low temperatures (III p. 1051), the form of the vapour-pressure equation p= 7(7'), the dependence of the densities of liquid and vapour on the temperature (in connection with the problem of the direction of the straight diameter); and finally the course of the characteristic function in its dependence on 7. But the very first point that will be elucidated in a following Paper is the circumstance mentioned under 6 of the conclusions, that 4, cannot possibly be = 4m. Fontanivent sur Clarens, April 1914. (September 26, 1914.) ons KONINKLIJKE AKADEMIE VAN WETENSCHAPPEN TE AMSTERDAM. PROCEEDINGS OF THE MEETING of Saturday September 26, 1914. Vout. XVII. DGC = . President: Prof. H. A. Lorentz. Secretary: Prof. P. Zeeman. (Translated from: Verslag van de gewone vergadering der Wis- en Natuurkundige Afdeeling van Zaterdag 26 September 1914, Di. XXIII). (SSyany Bwaa AN, PRISE H. vu Bots: “Modern electromagnets, especially for surgical and metallurgic practice”, p. 468. A. Wicumann: “On the Tin of the island of Flores”, p. 474. M. J. van Uven: “The theory of the combination of observations and the determination of the precision, illustrated by means of vectors.’ (Communicated by Prof. W. Karrryy), p- 490. H. Kameriincu Onnes and G. Horsr: “On the measurement of very low temperatures. XXIV. The hydrogen and helium thermometers of constant volume, down to the freezing—point of hydrogen compared with each other, and with the platinum-resistance thermometer,” p. 501. E H. Kameriincu Onnes and G. Horsr: “On the electrical resistance of pure metals ete. 1X. The resistance of mercury, tin, cadmium, constantin and mapganin dowa to temperatures, obtainable with liquid hydrogen and with liquid helinm at its boiling point,” p. 508. H. Kamertiscn Onnes: “Further experiments with liquid heliam. L. The persistence of currents without electro-motive force in supra conducting cireuits’, p. 514. Hl. Kameriincu Onnes and K, Hor: “Further experiments with liquid helium N. Harr-effeet and the change of resistance in a magnetic field. X. Measurements on cudmiam, graphite, gold, silver, bismuth, lead, tin and nickel, at hydrogen- and helium-temperatures.” p. 520, H. Kameruingu Onnes and H, A. Kuyrers: “Measurements on the capillarity of liquid hydrogen,” p. 528. F, A. H. Scurememakers and Miss W. C. bE Baat: “The system: Copper sulphate, copper chlorid, potassium sulphate, potassium chlorid and water at 30°, p. 533. J. Borsexen: “The Catalyse.” (Communicated by Prof. A. F. Hlotteman), p. 546. F. M. Jagger: “Researches on the Temperature-coefficients of the free Surface-energy of Liquids between —80° to 1650° C. Vil. The specilic surface-energy of the molten Halogenides of the Alcali-metals”. p. 555. “Ibid VIL. The Specific Surface-energy of some Salts of the Alcali-metals’’, (Communicated by Prof. H. HaGa). p. 571. G. pe Brur: “A crystallized compound of isoprene with sulphur dioxide.” (Communicated by Prof. P. van Rompurcn), p. 585. J. P. van per Srox: “The treatment of frequencies of directed quantities. p. 586. J. J. van Laar: “Some remarks on the values of the critical quantities in case of asso- ciation.” (Communicated by Prof. H. A. Lorentz), p. 598. J. J. van Laar: “On apparent thermodynamic discontinuities, in connection with the value of the quantity J for infinitely large volume.” (Communicated by Prof. H. A. Lorenrz), p- 606. H. R. Kroyr: “Current Potentials of Electrolyte solutions.” (Communicated by Prof. Ernxsr Couen), p. 615. Hi. R. Kruyr: “Electric charge and*limit value of Colloids,” (Communicated by Prof Ernsy COHEN), p. 623. ol Proceedings Royal Acad. Amsterdam. Vol. XVIL. 468 Physics. — “Modern electromagnets, especially for surgical and metallurgic practice.’ By H. pu Bois. (Communication from the Bosscua-Laboratory). (Communicated in the meeting of May 30, 1914). Carrying-Magnets. The lifting-power of the famous steel magnets of Logrman and van WertrrEN, has for a long time belonged to the somewhat antiquated subjects. However, traction-electromagnets are now being much more used in different forms, especially for loading and transportation purposes. In general we may say, that for sueh magnets with armatures at a very small distance Maxwetw’s well-known law holds; accordingly B*/8Sa measures the carrying-power per unit cross-section of an almost closed magnetic circuit. Prof. TayLtor Jonus has entirely confirmed this by experiment in the Bosscua-Laboratory. The mag- netic balance as a measuring instrument is equally based upon this fundamental law. Electro-magnetic brakes on this principle are also being more and more used. Field-Magnets are of more interest for a variety of scientific and practical purposes. In these Proceedings a description was given of semicircular magnets’), one of which, weighing 350 kg., with an interferrum of 3 0,5 mm. gave a uniform field of 59 Kilogauss, while using only a few Kilowatts. With a cryomagnetic “immersion- armature’ in a liquid gas at low temperature this reduces to 45 Kilogauss. With the heaviest type weighing four times more (1400 kg.) we may cet. par. expect no larger increase than 10°/, , thus reaching 65 and 50 Kilogauss respectively. Until now these field values have not been superseded, no more than the Haarlem magnets were. For the investigation of several highly interesting problems they are absolutely necessary. With regard to so small a rise of the field however it requires dne consideration whether a further increase of the size of the magnets appears justifiable. For while the weight increases as the third power of the limear dimension, thus becoming quite unwieldy, the field rises logarithmically only, which means a great disadvantage. In fact for a given field we practically obtain only a larger interferrum. However convenient this may be, it is questionable whether it justifies the very high expense which gradually begins to surpass an average laboratory-budget. 1) H. pu Bors, These Proceedings 12 p. 189, 1909; 13 p. 386, 1910. 469 The results mentioned are partly due to concentration of the Ampere-turns near the air-gap and also to careful calculation and design of all details; the theory of polar armatures ') communicated to the Academy, contributed its share to the result. Intestinal magnets. Incidentically the formulae for attractory arma- tures were also given in the paper referred to. They show, that the attraction of saturated ferromagnetic particles is a maximum for cones with a semi-angle of 39°14’, and for prisms of 30°; for non- saturated ferromagnetic or for paramagnetic substances these angles are 42°11’, and 32°8’ respectively. According to the principle of Farapay and Kervin the attraction is determined by the gradient of the first [second] power of the intensity 9 of the field for the first [second] group of substances. Some time ago Prof. Payr*) proposed a magnetic diagnosis, prophylaxis and cure of peritoneal adhesions and similar deviations. For this purpose a ferromagnetic intestinal filling is introduced either per os or per rectum. Then magnetic force is applied from outside without the necessity of more or less dangerous laparotomy. At the request of this well-known surgeon I was glad to collaborate in the attempt towards a practical solution of this peculiar a¢traction-problem ; for a rational treatment of it the above-mentioned armature-theory is absolutely necessary. The existence of an indifferent intermediate zone and the necessity for exciting large attractive forces only beyond this, characterizes this particular question. The ordinary type has a core of high permeability (of 12 cm. thickness and 40 em. length). It is somewhat concave at one end and thus fits the average form of the human body. In the paper referred to the formula is given for 9, 05/dr and 0?.9/dx? on the «x-axis for the case of a segmental spherical armature and for that of a coneave paraboloid of revolution. For the latter case it was shown that a certain distance not before a maximum of the field was reached. In this “neutral” point the gradient is zero and therefore the attraction also vanishes; the latter then increases, reaches a maximum and de- creases again gradually. This distribution of the field is favoured by the higher magnetisation at the periphery of the core compared with that of the centre, which makes this case similar to that of hollow cores. In the outset I even used a core with a conical bore in order to allow an eventual radiologic transmission through it; this however proved later on to be practically unnecessary. A central a) H. vu Bois, These Proceedings 15 p. 330, 1912. *) E. Payr, Miinch. med. Wochenschr. 60 p. 2601, 1913. 31* +70 filling of the core with a substance of higher permeability might be made -to compensate the distribution of the field above described. - In our case however this very topography of the field is desired ; for it is within the peritoneum only and not in the surrounding layer (the thickness of which individually varies from 2 em. to 10 em. and even more) that an attraction may be usefully exerted. Towards its other end the core gradually becomes thicker and the end is formed by a flange in order to decrease the magnetic reluctance ; the counter-action of this pole compared with the attraction of the working pole is negligeable. The coils are wound with enamelled copper wire or with oxydized square aluminium wire the thickness of which increases by steps from the working pole towards the other end. This principle is well-known for galvanometers and has also found partial application in my semicircular magnets. The increased efficiency of the “polar windings” must necessarily cause a greater heating effect which may be counter-acted by water circulation. ; Until now this precaution proved unnecessary, the more so because too cold iron may cause undesirable vasomotoric reflexes of the patient. The front flange of the coils is conical, in order not to be in the way of the operator’s eyes and hands; it may be provided with a corrugated peripheric radiator. The use of alternating currents is not advisable; but a pulsating current may be caused by periodic short-circniting of the magnet, while a non-inductive resistance remains switched in the circuit. The relaxation-time is a few seconds; by exciting the polar coil only it may be diminished to a few tenths of a second; when pulsations are often to be applied, it is advisable to use a subdivided core. In order to reduce the weight as much as possible the core onght to be saturated only to */, or */,. A minimum total weight is obtained for a dimensional ratio’) between 3 and 4; then the power required is only little above its minimum value; it amounts at most to 4 K.-watt, for most operations it is considerably less; and con- sidering the short duration of an operation the energy consumed (K.-watt-hours) is but very small. The magnet weighs about 100 ke. and is suspended by a kind of crane above the operation table, in such a way that its 6 degrees of freedom may be disposed of, i. e. a displacement along the vertical and a rotation around it, and the same for two horizontal axes parallel to the body of the patient and normal to it. Below the patient the ROnrcEn-tube is placed, as 1) Calculated from the demagnetizing factors for short cores, as measured by S. P. Taompson and E. W. Moss, Proc. Phys. Soc. Lond, 21, p. 622, 1909. 471 far as possible from the magnet, in order to diminish its deviating action on the cathode rays'). In some cases the patient may be treated while standing, which is much simpler. Deep-seated intestines (7—20 em. under the skin) are treated without pole-shoes. For those lying nearer the skin, the following pole-shoes are used which may be made of a highly saturated, polished and nickeled, substance, such as ferrocobalt. 1. A “drawing-pole” in the form of a truncated cone with a semi- angle of 40°; the attraction is strongest in the apex of the cone. The contents of the intestines may be first drawn towards a par- ticular spot and then attracted towards the magnet. 2. A prismatic pole with a semi-angle of 32° for the treatment of longer intestinal sections. 3. An unsymmetric hoof-shaped “dragging-pole” for applying force parallel to the peritoneum. Starting from the above-mentioned principle it may be shown that a maximum gradient of §* is reached when the narrow pole front forms an angle « = 65°54’ = t7-1V5 with the direction of dragging. For a very long prism on the other hand it ought to be ¢ = 60° = tg—'!V3. In this way the best adapted shape of the pole-shoe may be determined, also fitting the cylindric core. For special purposes pole-shoes of various shapes may be designed. The forces used bere have often been measured with small iron test-spheres. The force component is 3 ‘ 0 r 04° Iie = vi) ’ An Ou 2 Ox v denoting the volume, 7 the radius, there being no question of saturation. This expression is quite independent of the nature of the substance if only this is not too weakly ferromagnetic. The force, expressed as a multiple of the weight G of the ,test-sphere will be greater, the smaller the density of the latter. The value f,/G—=1 corresponds to the case that at a certain distance under the magnet the sphere is just being prevented from falling down. Considering this, spheres were made of magnetite (/’,O, = ferroferrite = ferr. oxyd. oxydulat. nigrum.) which quite fulfilled my expectations. Best of all proved small spheres of 1 cm. diameter of /’,O,-powder mixed with a little mucilage and some light neutral powder; generally 1) The Rénreen-tube is moved by the foot of the operator. The deviation of the cathode-current is proportional to its own strength, the value of the field at that place and the sine of the angle between these two directions; these three quantities onght to have low values. An iron-clad Réyreey-tube might prove useful ; but sparking constitutes rather a dilficully. In some cases a compensating coil near the cathode rays may be arranged. 472 these were used as test-spheres. This substance which fulfils all magnetic conditions is also to be recommended from a clinical point of view; it is neither poisonous nor soluble; it does not rust nor causes hydrogen to develop; it is not resorbed and hardly irritates the mucuous membrane. It gives good R6NTGEN-contrasts, even without addition of bismuth carbonate and it is more satisfactory than ferram reductum pulverisatum; it is the principal ingredient of the emulsions, which are given per os or per anum, the prescriptions of which vary in practice. On this point and on the very satisfactory surgical results I need hardly give full details. The following will suffice *). The operative conditions were fulfilled and even surpassed. The practice gained with a number of patients led towards a reliable diagnosis of the normal or abnormal mobility of the intestines and of adhesions and their exact place. It was often managed to stretch and to raise them carefully either in the stage of fibrous adherence hat of lasting mutual connexion. Of course reliable © ihe results cannot be obtained until later. The treatment day lave a great effect on the position of the intestines or of their special sections; such a locomotion highly influences the peristaltic function; this ought to be especially the case with pulsating magnetic fields of smaller or greater frequency up to about 10 or 20 per second and of different form of pulsation-curve. The accelarated or retarded displacement of intestinal substance containing ferromagnetic ingredients ; the dragging of this into organs, which are too deeply seated to be reached in any other way, especially the appendix, with a view to radiologic diagnosis, the turning and loosening of intestinal slings remain subjects for further research. The principal advantages of this method are its localisation on a special part of the intestines, the precise regulation of the displace- inent, the easy dosing of the effect by regulating pole distance and current and the simultaneous radiologic examination. : In order to determine the topography of the field for various distan- ces and currents, it was fixed by iron filings, with or without pole- ‘oes und if necessary it was measured with a standardized test-coil. yuicing along the axis, from the start at the concave pole front uinimum of the field is first met, then a maximum. To these cor- respond theoretically a transverse maximum and minimum respecti- vely, and also an unstable and a stable zero-point of attraction. This is easily shown with a test-sphere in an axial glass tube, which is seen to remain suspended in that very point. With a plane pole front such singularities do not appear. ) See also E. Payr, Ber. D. chirurg. Congress, Berlin April 1914. 473 The attraction of a number of test-spheres or pills was measured under different circumstances with a spring-balance; its maximum was found at a distance of 4—5 em. and amounts up to 25-fold weight; the greatest “carrying distance” is 22 cm., for test cylinders even more. For a round drawing-pole the maximum was found at 2 or 3 cm. and reaches 50-fold weight; at distances greater than 7 cm. the attraction becomes smaller than that observed without the use of a pole-shoe. The coils were constructed in such a way that their purely electrodynamie attraction, which is determined by the square of the current, contributes considerably to the total force. With a dragging-pole a transverse force is obtained up to 25-fold weight at a distance of 2,5 cm. Though for our purpose the type described proved amply sufficient, it appears however interesting to study the properties of a similarly enlarged or reduced instrument. If the linear dimensions be n-fold the weight of the iron varies as n’*, that of the copper as n* (or as n*, depending on the mode of winding), tle kilowatts consumed as n (or respectively as n*), the attraction of non-saturated particles at a given distance however nearly as 7‘. This 4° power (in fact about the 3,7") is evidently very favourable, especially as compared with the above-mentioned very uneconomical logarithmic progression for field-magnets. We may safely predict that it will be possible to produce any necessary force with magnets which do not yet become unmanageable and the cost of which will hardly prove a serious obstacle in this case, where life and health of the patients may be at stake. Extracting magnets. In this way it ought to be possible to move about ferromagnetic probes brought into the body on purpose or to extract undesirable objects, such as steel bullet shells, broken needles or injection-syringes and various iron or nickel objects, which are daily met with in the surgery of accidents. Also an effect on other organs, less soft than the intestines may be thought of. It has long been known that all tissues are diamagnetic; Faraday already showed that this is also the case with blood; the iron atoms in haemoglobine are bound in such a way that no para- magnetism occurs, no more than e.g. for potassium ferrocyanide. Picker’) showed that a magnet repels the red blood globules relatively to the serum. It is moreover also known that the flow of diamagnetic liquids through tubes and their dropping may be con- 1) A. PLiicker, Pogg. Ann. 73 p. 576, 1848. A474 siderably influenced under special circumstances by very strong fields *). By putting 2 <4 the effect of reducing the dimensions is at once evident; this is interesting with a view to the design of the usual ophtalmic magnets which may also be improved by the above caleu- lations and experiences; the maximum distance in this case is not more than 2,5 em. A type is now being made of 8,5 em. diameter of core, serving the double purpose of an intestinal magnet of less strength than the above and at the same time of a very powerful ophtalmiec electromagnet. Ore separators have long been applied in metallurgy to separate unmagnetic from ferromagnetic or only paramagnetic powdered ove by the dry or the wet method. These apparatus are variously con- structed; the principal magnetic organ is however essential and common to them all and is a more or less finely ribbed polar arma- inve. The best cross-section for a definite mean size of the grains may be determined by means of the theory above-mentioned for a prism semi-angle between 30° and 32°8’. Mineralogy. — “On the Tin of the Island of Flores.” By Prof. Dr. A. WicHMAnNn. (Communicated in the meeting of June 27, 1914). During the last decenniams very contradictory answers were given to the question regarding the occurrence of tin-ore in the Isl and of Flores. The fact that the solution of this question does not only regard the interests of a mining-scientifical nature, but is likewise very interesting from a mineralogical and geological point of view may justify the attempt of elucidating this subject. In ihe first place we have to bring into remembrance the fact, that in the Sunda Islands the older geological formations gradually disappear if we move in that range of islands in an_ easterly direction, till — beginning from Bali — only neogenie and _pleisto- cenic sediments are found, and at the same time tertiary and _post- fertiary eruptive rocks with their tufas begin to play a predominant part. The question rises then: Does Flores make an exception to ‘iis rule and do we find in this island remains of ancient granite siocks, accompanied by deposits of tin, or are all the reports regarding the occurrence of this ore only of a legendary nature ? 1) QO. Lresknecut and A. P. Witts, Ann. d. Phys. 1 p. 183, 1900. W. J. pp Haas and P. Drapier, Ann, d Phys. 42 p. 677, 1915. 475 The first report originates from J. P. Freyss, who wrote on account of his information received in 1856 in Manggarai (West Flores). “In the mountains of Rokka at Sui Tui’) gold is found, whilst “Mount Aspana produces tin)”. In 1866 a resolution was taken by the Governor General L. A. J. W. Baron Storer van ps Berrie “to send a trustworthy funetionary “to the isle of Flores in order to investigate if on the south-coast “of this island in the neighbourhood of the village of Rokka tin “is found”. It is unknown whether the resolution (of January the 15 N°. 3) was ever put into execution *). Five years afterwards J. A. vAN per Cus fixed the attention to the fact, ‘‘that every year a rather considerable quantity of arm- “and leg-rings made of tin and of a rude construction was exported “from the district of Rokka, situated on the south-coast of the isle “of Flores’ *). The Indian Government having been requested to order the controller S$. Roos, established in the isle of Sumba, to make an investigation whether in reality tin occurred in Flores, a resolution was taken to this effect November the 13! 1871 N°. 3, and the Board of Directors of the Soeiety of Industry and Agricul- ture received a short time after from the above-mentioned functionary “a few specimens of tin-ore from Masara’. According to the investigation which was entrusted to C. br GaveERE, the mineral in question was pyrites*). In the mean time the Governor General Piwrer Mier had authorised, by resolution of April the 18% 1872 N°. 59, the resident of Timor to send an expert to Rokka “that he might convince bimself on the spot, in “how far tin-ore is dug up and melted there, and at the same time “to collect some specimens of ore and rocks” °). This investigation had neither any result, for, as was reported, the native chief’) — this was the expert — “had until now, on account of ill health and 1) The place is called Sui (manggaraish) or Tui (endehneish) and is situated on the west-side of the Aiméré bay. There can be no question of the occurrence of gold there, for behind that place rises the extinct vuleano Komba. 2) Reizen naar Mangarai en Lombok in 1854—56. Vydschr. voor Ind. Taal-, Land- en Volkenkunde. 9. Batavia 1860, p. 507. *) Koloniaal Verslag van 181, p. 29. 4) Tijdschr. voor Nijverheid en Landbouw in Ned. Ind. 16. Batavia 1871, p. 158-159. 5) Tydschrift voor Nijverheid en Landbouw in Ned. Ind. 17. Batavia 1572, p. 184. 21. 1877, p. 40—41. 6) As quoted 17. 1872, p. 385. 7) He proved afterwards to be an Arab who had settled in Sumba. (Koloniaal Verslag van 1591, p. 22). 476 “the unfavourable disposition of the population of the island, not “vet fulfilled the order given to him. ’) A short time after 5. Roos communicated the following inform- ation concerning tin. “The people of Rokka often sell on the shore “bracelets made of tin, but they do not allow anybody to visit “their village... The Endehnese admit as rather certain that much “tin-ore oceurs in the ground of Rokka, but for fear of being mur- “dered they dare not venture into this village; this was likewise “the reason why nobody, even for ample payment, would accom- “pany me thither, so that I had to desist from the journey: It is “however known to me that proas of Endeh and likewise Chinese “of Kupang and persons of other places from time to time come “there to trade with the natives i.e. they anchor at Wai Wau or “at Aimeré and carry on their trade on the shore with the people “of Mangarai and with the inhabitants of the mountains, the latter “offering for sale a trifle e.g. a parang or a pair of bracelets made “of tin to the merchants. The bracelets are heavy, of rude work- “manship, more than a hand broad and are worn above the elbow.” ?) According to J. G. F. Riepen the tin is collected in Liu and Langgi (read Langga) by the natives ‘fin a mysterious manner.” *) Hitherto there had only been question of the supposed occurrence of tin in the district of Rokka, but in 1877 F. C. Hnynen wrote : “according to reliable reperts a considerable quantity of tin is found “in the territory of the Rajah of Larantuka, somewhere in Flores... “the tin objects resembling silver gave lately to a traveller whom “we met in Flores, the conviction, that the tin there is of an excel- “lent quality.” *) A request made by L. P. pen Dekknr d.d. Kupang July 1s* 1882, but not granted, to obtain the permission of prospecting in Flores, tbe Solor and the Alor Islands fixed again the attention of Govern- went to the tin. The mandate of trying to obtain, if possible, some 1) Verslag omtrent het Miynwezen in Ned. Indié voor het jaar 1872. Jaarboek van het Minw. in Ned. Indié. Amsterdam 1873. I, p. 327. — Koloniaal Verslag over 1873, p. 260. — Two years afterwards it was reported however that, on account of the distrust of the population, it could not be ascertained whether the territory of Rokka was really rich in tin. (Koloniaal Verslag van 1875, p. 26). *) lets over Endeh. Tijdschr. voor Ind. T. L. en Vk. 24. Batavia 1877, p. 515. 8) The island cf Flores or Pulau Bunga [sic.!]. Revue coloniale internationale 1. Amsterdam 1886, p. 66. 4) Het ryk van Larantoeka op het eiland Flores. Studién op Godsdienstig, Wetenschappelik en Letterkundig Gebied. 8, No. 6. ’s Hertogenbosch 1876, p.34—35. A. JAcoBSEN described tin bracelets of East Flores (Reise in die Inselwelt des Banda-Meeres. Berlin 1896, p. 606—61). 477 of the tin objects originating from Rokka, given to the resident of Timor and to the magistrate of Larantuka was complied with. *) From the investigation made by H. Crermr it appeared that a tin bracelet contained lead, whilst a specimen of tin-ore was very ferruginous. *) The examination of some bullets led further to the result that they were not composed of tin, but chiefly of lead and zine with traces of tin, copper and iron. Should the “strongly ferruginous” ore be identical with the specimen “stroomtinerts van Oost-Flores”, mentioned in the catalogue of the Mineralogical Collection of the Office of the Department of Mines at Batavia under N°. 3302 and really contain tin, then it is certainly not originating from this territory, where in several places titaniferous iron-ore but no tin is found. In consequence of the resolution of the Governor General O. van Rens of August the 5 1887 N°. + the resident of Timor was authorised to order the magistrate E. F. Kurran to go to the district of Rokka, situated on the south-coast of this island, in order to obtain reliable evidence about the occurrence of grounds containing tin-ore in the interior of the isle of Flores.*) Kieran had supposed that he would reach his aim by choosing as place of issue the village of Nanga Lian in the district of Toa *) situated on the north-coast, where he landed the 12 of September. The 17 he marched to Nbai *) (about 8°34’ S., 121°10’ E.), he was however decidedly refused to go further to Soa and Poma, the supposed finding-places of the tin-ore. An inhabitant of the mountain of the village of Dora told, that at a few days’ walk distance in a place called Watam Kadjan, situated between Poma and Soa, specimens of native tin were collected in the ravines, when the rainy season was over, to make bracelets and other ornaments. After having returned to the coast on the 19% he continued his journey as far as Rium on the 20. The Rajah here, however, did not know anything about tin, nor was he inclined to procure an interpreter or a guide for the journey to the interior. Without having attained his end Kian returned home again to Kupang. 1) Verslag van het Mijnwezen in Ned.-Indié over het jaar 1882—83. Jaarboek van het Minwezen in Ned.-Ind. 12. 1884. Techn. en administr, ged, p. 376, 304. 2) Bydragen uit het scheikundig laboratorium van het hoofdbureau van het Mijn- wezen. Jaarboek van het Mijnw. 13. 1884. Wetensch. ged., p. 312. 3) Koloniaal Verslag van 1891, p. 23. 4) He had already paid a visit to this district in 1875. (en voetreis over het oostelijk deel van Flores. Tijdschr. v. Ind. T. L. en Vk. 34. 1891, p. 530—582. 5) Embai according to J. W. SroursEspuK.. 478 When in 1888 two applications for concession were made, one by A. Laneen, who had received from a Chinese a specimen of granite and likewise a specimen of tin-ore, said to be originating from “the river Aspana’, and a second by R. van pen Brorx') with 4 others, who requested to be allowed to explore 100000 bouws (!), the Governor General C. Prnakker Horpisk resolved to have an investigation made by an expert into the supposed abundance of tin-ore in Flores. By resolution of the 20 Sept. 1889 n°. 18 the mining-engineer of the Department of Mines C. J. van ScHEt.u was appointed leader of the expedition. Tie expedition left Batavia on the 15 Nov., and arrived the 30% next at Kupang. After the resident of Timor had ordered the magistrate E. F. Kieran to accompany the expedition, they left on the 3°¢ Dee. for Larantuka and afterwards to Endeh, where the assistant magistrate F. A. Broeman joined them. On the 10" they disembarked at Soa, situated on the westside of the Aiméré Bay, and a reconnoitring-expedition was undertaken in a north-eastern direction as far as the village of Foan, where however none of the inhabitants could be prevailed upon to accompany the expedition to Langga, “which village is said to be situated in the neighbourhood of the “tin-region”’. After their return. on the 11 December they went into bivouae which they left again on the 15%. After a 1O hours’ march in a north-eastern direction the mountain-ridge of Watu Loko was reached in the neighbourhood of Ekofeto. The next morning, a short time before their departure, they had to sustain an assault in which Van Scnette and Kieran were wounded by sword-thrusts. In a forced march the expedition drew back to the Aiméré Bay, which they left in the afternoon of the 17 to sail back to Kupang °). Krom the information he had obtained Van ScueLLE came to the couelusion “Ist that none of the Endehnese, who had visited the “eoast-region of Rokka and the neighbouring Mangarai knew anything “of an importation of tin under any form whatsever. 2°¢ that the “mountaineers of these regions with whom they came into contact “possess tin ornaments, and use likewise tin to make their fishing- 1) This gentleman undertook in 1889 a scientifie journey by order of the Kon. Nederl. Aardrijkskundig Genootschap Tie results obtained have however never been published. 2) Koloniaal Verslag van 1890, page 21. — Verslag van het Mijnwezen over het 4e kwartaal 1889, p. 11. — J. CG. van Scusie. Verslag van het onderzoek paar het voorkomen van tinertshoudende gronden op Flores. Extra-Byvoegsel der Javasche Courant. Batavia 1890, No. 10. — Tijdschr. voor Nederlandsch-Indié 1890. 2, p. 77 —79. — Tu. Posewrrz. Die niederliindisch-indische Zinnerzexpedition auf Flores. Das Ausland 64. Stuttgart 1891, p. 145—149. 479 “nets heavier; 3° that tin has little value for them and iron and “copper is valued higher by them; 4% that constantly as finding- “place of tin a special spot is indicated, situated northward from “Mount Roukka, and the natives possess there considerable quantities “of tin’ '). Further lhe asserted “that the idea formerly occasionally “suggested, that the tin that the people of Rokka possess, should “be imported or proceed from solder of petroleum- or other tins ‘must be rejected as utterly unfounded”. The summary of his considerations was: ‘ As far as the information “I obtained reaches, | must admit that the soil to the north of the “Mountain of Rokka is very rich in tin-ore...... Along a fissure “running probably from East to West along the South-coast of “Flores, the volcanic products have found a way and partly covered “the other formations. The region containing tin-ore is situated at “the frontier of the two formations, and we must admit, that the “older formation there is strongly impregnated with tin-ore, and that “by the desaggregation this comes free at the surface’. The favourable expectations raised by VAN ScHELLE’s report induced the Indian Government to send out a second expedition this time however supported by a strong military power. (Resolution of the 31st March 1890) ’). On the 11 May 1890 a detachment departed from Surabaya and arrived on the 14 in the Aimeére Bay, where on the left bank of the Wai Moké (Aiméré River) a bivouae was pitched. On the 8" July the well-known Watu Loko was occupied. On the 24% and 25 under protection of a strong patrol C. J. van Scretie made from this place in an eastern and north-eastern direction reconnoitring excursions to the supposed tin-region. Instead of grounds containing ore he found however crater-mountains, of which Kopo Lebo and Lebi Sega were ascended. On the 29! the patrol reached the top of Wolo Meré, 1650 feet high, and discovered that, as far as could be seen, it was of a voleanic nature. Atter this complete failure a last effort was ventured to reach the ‘“tin-region” from the district of Toa situated on the north-coast, where E. F. Krein had taken information in 1887. By resolution of 10% Sept. 1890, N°. 1 it was stipulated that vAN ScHELLE and 1) In reality more than a dozen places were mentioned. 2) Koloniaal Verslag van 1870, page 22., 1891, p. 2329. — Verslag van het Mijnwezen over het 2de kwartaal 1890, p. 16; dde kw. 1899, p. 12. — P. G. ScumipHAmEer. De expeditie naar Zuid-Flores. Indisch Militair Tijdschrift. 24. Batavia—'s Gravenhage 1893, p. 101—115 %7—218, 289-307, 315—404, 493—504, 25. 1894, p. 1—11. (tT to Wolorsfok / (o> PE INGASS 5) his companions were to leave the south-coast, to repair to the district mentioned above. In the mean time a division had arrived there on the 26" September, that transported their head-quarters to Nbai on the 27" October. When van Scue.Le had been obliged to leave the spot on account of ill-health, he was replaced by the overseer A. F. H. Heusch and along the river Koli they marched into the interior towards Mundé, but on this expedition likewise only voleanic formations were found.*) Inereasing cases of illness rendered a longer residence impossible, so that on the 23'¢ of November Nbai and on the 2°* of December Remang had to be evacuated. *) In the mean time information about the oceurrence of tin was gathered from other sides. J. W. Merersure on his march across Manggarai in 1890 did not see anywhere an object made of tin; only at Nanga Mborong he obtained a tin bracelet, which was said to originate from Anduwa to the W. of Wai Moké, where, as was said, the tin-ore was to be found. *) In the beginning of 1891 the controller J. F. Horpr was sent to the North-coast of Flores, in 1) According to P. G. ScHMIDHAMER Poré was the real finding-place of the tin (p. 404) and not Poma, Mundé and Soa (p. 500). *) Koloniaal Verslag van 1891, p. 26—29. — J. W. SroursEspiuK. Een mede- deeling over het eiland Flores. Tijdschr. K. Nederl. Aardr. Gen. (2) 8. 1891, p. 748—749, map N°. IV. 5) Dagboek van den controleur van Bima, J. W. MEERBURG, gehouden gedurende zijne reis door het binnenland van Manggarai. Tijdschr. y. Ind. T. L. en Vk. 36. Batavia 1893, p. 143, 148. 48] consequence of a report of ALBerT CoLrs') according to which the inhabitants of Potta bring tin to market. That information was not confirmed by him, on the contrary he was told that in the district of Dua to the South of Potta, tin, gold and even diamonds occurred.’) The last investigation took place in the end during the years 1910 and 1911 by J. J. Pannexork van Ruepen. In the second of his papers *) mentioned at the foot he says with regard to the occurrence of tin: ‘According to the reports of WichMann and VAN SCHELLE “there was sufficient foundation for the supposition that the tin that “was used by the population of Central Ngada was originating “from ore found in the district itself. *) As the presumable finding- “place the region to the North of voleano Inié Rié is indicated. On “the occasion of the expedition in North Ngada in 1890 a slight “quantity of fine cassiterite was collected near Torang. The investi- “gation L was charged with about the occurrence of tin-ore in these “regions could not yet be brought to an end on account of the un- “favourable political situation.” *) After the above historical explanation we shall now try to answer the question whether there is sufficient ground to admit that tin occurs in Flores. C.J. van Scuenie had answered the question affirm- atively and supported his answer by the 3 following hypotheses. 1st. nothing is known about the importation of tin objects, 2°¢ the }) CoLFs made a journey through Manggarai in 1880. In the description of his journey not a single word is said about the above communication (Het Journaal van ALBERT Cours. Batavia 1888, p. 71—72). ®) Verslag van de reis van den Controleur Horpt naar de noordkust van West- Flores. Tydschr. voor Ind. T. L. en Vk. 36. 1893, p. 281, 292. 8) Eenige geologische gegevens omtrent het eiland Flores. Jaarbock van het Mijnwezen in Ned. Ind. 39. 1910. Batavia 1912. Verhandel. p. 132—138, pl. X. — Overzicht van de geographisclie en geologische gegevens verkregen bij de Minbouwkundig-geologische verkenning van het eiland Flores in 1910 en 1911. Jaarboek van het Mynwezen 40. 1911. Batavia 1913. Verhdlg., p. 208—226. 4) This remark is, in so far as regards myself, entirely invented. The only thing ever wrilten by me about this subject runs as follows: “Ebenso schleier- “haft (namely, as the origin of the Muti Tanah) ist die Herkunft des Zinns, dem “eine gleiche Entstehung zugeschrieben wird. Es bedarf keiner eingehenden Ausein- “andersetzung, um darzuthun, dass Zinnerz durch brennendes Gras nicht reducirt “werden kann. Man hat auch noch niemals die geringste Spur von Zinnerz auf “Blores gefunden. Die uns zu Gesicht gekommenen Gegenstiinde aus Zinn hat “WEBER beschrieben. Sie sind siimmtlich bleihaltig.”” (Tydschr. K. Nederl. Aarde. Genootsch. (2) 8. 1891, p. 2830—231). It is exactly the same with P. G. Scumip- HAMER’s remark concerning the information of the... professors WICHMANN and Max Weper’, (J. c. p. 106). 5) ]. ¢., p. 226. 482 mountaineers possess tin ornaments, and 3°¢ tin has little value for them and iron and copper is valued much higher by them. Though in general the correctness of these hypotheses will be readily acknow- ledged, we cannot help remarking that they do not prove anything, for in the possession of the Rokkanese objects of another nature are found, the origin-of whieh is as littlke known, whilst they can by no possibility be constructed by them. Among these are e.g. the lens-shaped pieces of brass, ealled by the Endehnese “mas di Rokka” (gold of Rokka), and the dirty-red beads known in the Timor Ar- chipelago by the name of Muti Tanah or Muti Salah. These are made of artfully manufactured glass and certainly not originating from the Malay Archipelago’), but of these the same story is told as of the tin, ie. that they appear on the surface when the grass is burnt.’) - With regard to the “mas di Rokka” A. feunzer indicated already that it is an alioy of tin and copper.*) When I was in 1888 at Mbawa the mountaineers asked me a gold-piece “with the leaping horse’ (£ 1) for it. This “gold of Rokka’ can no more be originating from Flores, for a nation that stands so low, is not able to manu- facture such an alloy.’) With respeet to the so-called tin objects the same can be asserted. As early as 1884 it was known, that they consist in reality of an alloy of tin and lead, a fact which has not been taken into account, in the first place C. J. vAN ScHELLE did not do so, not even afierwards, when a piece of “tin” obtained during the campaign of 1890 appeared to consist of 59,8°/, tin and 40,2°/, lead. *®} Max Weper brought likewise into relief, that the bracelets bought by him in 1858 were composed of these two metals.") The fact communicated by him that the natives of East 1) This subject was treated very elaborately by G. P. Rourramr (“Waar kwamen de raadselachtige moetisalah’s (aggrikralen) in de Timor-groep oorspron- kelijk vandaan ?”’ Bijdr. v. de T. L. en Vk. (6) 6. ’s Gravenhage 1899, p. 409— 675). 2) J. E. Teysmann. Verslag eener botanische reis van Timor... Natuurk. Tyd- schrift van Ned. Ind. 34. Batavia 1874, p. 350. — S. Roos. lets over Endeh. Tijdschr. voor Ind. T. L, en Vk. 24. 1877, p. 501. ») Mineralogisches aus dem Ost Indischen Archipel. Tschermaks Mineralog. Mittheilg , Wien 1877, p. 3U6. ') With regard to copper, it is quile certain that at least since the middle of the 18th century it was imported into Flores, (J. C. M. RapemaAcHER. “Korte be- schrijving van het eiland Celebes en de cilanden Flores, Sumbawa, Lombok en Bali.” Verhandel. Batav. Genootsch. vy. K. en W. 4. Batavia 1786, p. 252.) 5) Koloniaal Verslag van 1891, p. 26. 6) “Mededeelinger over zijne reizen in Indié.”’ Tijdsch. K. Nederl. Aardr. Gen. (2) 7%. 1890, p. 457. — Ethnographische Notizen tiber Flores und (elebes. Intern. Archiy. f. Ethnographie, Suppl. 3. Leiden 1890, p. 15, 16. 483 Flores opened tins in order to work the solder into bracelets ete, made VAN ScsELLE remark that such an idea, with regard to the Rokkas, “must be rejected as utterly untenable’. Weber on the con- trary had positively asserted that this origin of the tin objects of the province of Rokka was unacceptable. The fact that among the constituents of the bracelets in question lead occurs, the import of which was in former times as little known as that of tin, would lead to the conclusion that this metal must likewise be originating from Flores itself. Leaving out of consideration the fact that lead-ore occurs only sporadically *), nobody will certainly suspect the natives of under- standing the art of reducing the metal from it. A boy of fourteen years who was taken prisoner in 1890 with the object of being able to interrogate him, rightly remarked “he “could not possibly give any information concerning the tin; the tin “that is in their possession, they have as pusaka from their ancestors’. *) If one should object that objects regarded as pusaka are as a rule higher valued, we may point out that for several years, the gold that is brought by Australian horse-dealers in the shape of sovereigns to Sumba, from where it has found its way to Flores is more to the taste of the natives. During the bad harvests which are by no means rare, they are moreover compelled to part with objects that are dear to them, in order to obtain food. Consequently we come to the conclusion that the metallic objeets in the Rokka territory are not originating from the island itself, but that they were imported in former times. Their origin is as unknown as that of the different metallic objects found with the natives of other islands. The last question that must be answered is, whether the geolo- gical condition of the island is of such a nature, that there is any prospect of being able to detect tin-ore — in whatever form it may be. The following summary may serve for this purpose. In Western Flores, the eastern frontier of which is situated between 1) Galena was found by J. J. PANNEKOEK VAN RHEDEN in small quantities in the neighbourhood of Lowo Sipi (Endeh) and in the penimsula of Batu Asa (Manggarai). J. P. FReyss supposed that the same mineral occurs near Rium and near Geliting on the north-coast, which is very unlikely. R. EverwisN mentioned lead from Mount “Himendiri in Western-Timor” (Jaarboek van het Mijnw. 1872. I, p. 261). The mountain is really called “Ilimandiri” and situated in Eastern Flores. The piece mentioned is an augite-andesite containing hematite, lead however is not present at all. 2) Java-Bode, Tuesday 8 July 1890, N°. 154. wo Ww Proceedings Royal Acad. Amsterdam. Vol. XVII. 484 120°53' E. on the north- and 120°47' E. on the south-coast, an orographical difference presents itself already between the northern and the southern part. Here very accidented grounds, steep moun- tains 2646 m. high, and deep valleys and ravines, yonder a more hilly region in which only few mountains reach a height of 1000 m. and more. This northern part is chiefly covered by a formation, to which J. J. Pannekork vAN Rugpen has given the name of Reo formation, and which consists of limestones — especially coral lime- stone — resting occasionally on eruptive rocks and sometimes enclosing volcanic products. Here and there they are covered with tuffas'). PANNEKOEK writes regarding the organic remains that are found: “A cursory investigation stated the presence of: Orbitoids, “Corals, fragments of Spatangus, Natiea, Corithium, Conus, Lima (Pla- “ojiostoma), Ctenostreon, Gervillia, Isocardia, Teredina’. A curious mixture indeed. It is to be hoped that this “cursory” examination may soon be followed by a more correct one. From the remark that the strata of the isle of Rindja, “seem to be younger, most “likely tertiary” we must deduce that he supposes the sediments of the Reo formation to be of a mesozoic age, which however cannot be the case. H. Zor.ineer has already drawn the attention to the similarity of these strata with regard to their petrographic character with those of the south-coast of Java (Besuki, Kediri)*). They have entirely the character of neogenic rocks, as appears already from the occurrence of Globigerina limestones *). PAaNNekorK however rightly makes distinction between these and the younger pleistocenic coral limestones, as they are found in the isle of Longos in the neighbourhood of Reo. On the bay of Reo they rest on andesite conglomerate. *) A continuation of the Reo formation is most likely still found as far as the Kolitang Bay (Soho Kolitang) 120°77' E. J. F. Horpr found eastward from the exteusive plain a low range 1) Overzicht van de geographische en geologische gegevens verkregen bij de Mynbouwkundig-geologische verkenning van het eiland Flores. Jaarboek van het Minwezen in Ned. Indié. 40. 1911. Batavia 1913. Verhandel. p. 217—218. ®) Verslag van eene reis naar Bima en Sumbawa .. . . Verhandel. Batay. Gen. y. K. en W. 27. Batavia 1850, p. 14. Remarkable is his annotation accord- ing to which at Badjo (meant is perhaps Padja) a day’s journey behind Bari a hot spring is found, forming a pond, on which a brownish mass floats, which hardens in the air and can be used for tarring proas. 8) J. W. Reraers describes likewise from Dangkawai 15 kilom. S. W. from Reo, a limestone containing foraminifera. (Jaarboek van het Mijnw. 24. 1895, Wet. ged., p. 135) 4) A. WicumaNN. Bericht tiber eine .. . . Reise nach dem Indischen Archipel. Tijdschr. K. Nederl. Aardr. Gen. (2) 8. 1891. p. 194. 485 of hills consisting of limestone, and in the plain itself a few isolated hills of limestone °*). Up to the present moment only younger tertiary and post-tertiary eruptive rocks were found in the entire southern half of Western Flores. In the utmost south-western part i.e. in the Madura Bay the Siboga Expedition collected in 1899 rocks that on more exact examin- ation proved to be augite-andesite. According to D. F. van Braam Morris Mount Sosa 1212 m. bigh farther westward 8°46’ S, 129°58’ E. must be a still active voleano’). By the voleano called by him Toda (5000 ft.) will most likely be meant Potjo Wai L740 m. high, the highest mountain of the province of Todo. Potjo Leo 2696 m. high was already called a voleano by J. P. Freyss *) and is still active according to Braam Morris. J. W. MergrsurG, who marched along its slopes in 1890, does not remark anything in this regard *) Potjo Lika (2212 m.) situated in the immediate neighbourhood to W.N.W. is, according to PANNekork’s map, voleanic, and the same can most likely be said of Potjo Rea (2006 m.) and Mata Wae (2077 m.) rising at a short distance. J. W. Reremrs has microscopically examined the rocks collected in this region by J. W. Mewreure.*) He mentions pyroxene-andesite from the Wai Renu near Dége, quartz-augite-andesite of the same place, quartz-hyperstene-andesite and hornblende-hy per- sthene-andesite from the Wai Leédé near Rute at the N.E. foot of Potjo Lika, hornblende-hypersthene-andesite from the Wai Soki, between Lidi and Todo, pyroxene-andesite from the Wai Madjo near Todo, hornblende-pyroxene and hornblende-hypersthene-andesite from the Wai Mau, a tributary of the Mése, 9,4 kilom. N. from Nanga Ramo. Toren Island 780 m. high (8°54’ §., 120°15,4’ E.) °) situated to the south of this place is most likely also of volcanic origin. According to PaNNEkork’s map the whole region situated between Nango Ramo and the Aimeéré Bay, the frontier of Western Flores is of a voleanie nature. It is wellknown, that Mount Komba (926 m.) 1) Verslag van de reis van den controleur Honpr naar de Noordkust van West« Flores, Tijdschr. v. Ind. T., L. en Vk. 36. Batavia. 1893, p. 292. 2) Nota van toelichting behoorende bij het contract gesloten met het landschap Bima. Tijdschr. v. Ind. T. L. en Vk. 36. 1893, p. 186. 8) Reizen in Manggarai en Lombok. Tijdschr. v. Ind. T. L. en Vk. 9. Batavia 1860, pp. 506 —507. 4) Dagboek van den controleur J. W. Merrsurea, gehouden gedurende zijne reis door het binnenland van Manggarai. Tijdschr. v. Ind. T. L. en Vk. 36. 1893, p. 290. 5) Mikroskopisch onderzoek van gesteenten uit Nederl. Oost-Indié. Jaarboek van het Mijnwezen 24. Amsterdam 1895, Wet. ged., p. 135. 6) Also called Pulu Ramo, Nusa Sigo, Gili Enta or Embuanga. 486 and Mount Lumu (663 m.) rising on the west-side of the mentioned bay over Sosi are extinct voleanoes. The expedition of 1890 had communicated regarding Central Flores that in the province of Toa, in the river-basin of the Nanga Koli, they had marched exclusively through a volcanic territory. In the upper-river-basin of this river, in the neighbourhood of Soa (about 8°40’ S., 121°2’ E.) — one of the repeatedly mentioned finding-places of tin-ore — Pannekork found at a height of = 400 m. a territory of horizontally stratified marls with interjacent light-yellow tufas containing impressions of leaves, molluscs, insects and fishes. He supposed these strata to be sediments, deposited in a fresh-water- basin and called it Soa formation '). More eastward, between Mautenda and Dondo on the North-coast another territory is situated whieh, according to PANNEKOEK’s map, is covered by sediments of the Reo formation. The southern half of Central Flores, on the contrary, contains most of the still active voleanoes of this island. To the East of the Aiméré Bay rises in the first place Inije Rije (Imé Rié) 2494 m. high, more known by the name of Gunung Rokka, which is in a solfatarie activity. Winiiam Brien saw it smoking for the first time on the 229d of August?) and Pannekork perceived on his visit in 1910 that the solfataras are situated on the east-side of the crater bottom *). The long ridge of the Langga Mountains seems to be, according to PANNEKORK, a Somma-edge of Mount Rokka. To the East of this mountain rises Watu Sipi 1466 m. and another mountain 1533 m. the name of which is unknown. Both are extinct volcanoes. In the North-east of the Rokka a group of voleanoes is found that are no longer active among others Kopo Lebo, Wolo Mere, about 2000 m. high, Pipodok, Wolo Lega, Lebi Saga, which were discovered during the military expedition of 1890 °). Inije Lika (Inié Like) 1600 m. high, hitherto entirely unknown, was discovered in 1910 in North Ngada and described by G. P. Rourranr °). 1) Eenige geologische gegevens omtrent het eiland Flores. Jaarboek van het Mijnwezen 39. 1910. Batavia 1912. Verhdl., p. 135. — Overzicht van de geogra- phische en geologische gegevens.... van het eiland Flores. Ibid. 40. 1911. Batavia 1913, p. 220—221. 2) A Voyage to the South Sea undertaken by Gommand of His Majesty. London 1792, p. 246. Dr. R. D. M. Verpeex kindly informs me that this is a mistake. Instead of Mount Rokka has to be put Mount Keo. 3) Eenige geologische gegevens. as quoted p. 135—136. 4) P. G. SCHMIDHAMER as quoted p. 389, 390, 393 and map. 5) De Inije Lika op de hoogvlakte van Ngada. Tijdschr. K. Ned. Aardr. Gen. (2) 27. 1910, p. 1233—1239, vide likewise J. J. PANNEKOEK VAN RHEDEN, Overzicht van de geographische en geologische gegevens. l.¢., p. 219, 223. 487 The heavy eruption, lasting only five hours, took place in 1905. About- Ambu Rombo 2147 m, high, also called Suri Laki, better known by the name of Gunung Keo, we do not know much more than that it has been for more than half a century in a situation of solfataric activity. According to PAnNnrKork') the solfataras are especially situated in the neighbourhood of the northern edge of the top’). As far as it is known only augite-andesite is found as rock on the coast. Ngaru Tangi (1537 m.) rising over the S. W. corner of the Endeh Bay is a voleanic ruin. In the territory of the Endeh Bay the western part of its north- coast, especially the environs of Nanga Pandan, was examined in 1910 by Jon. Exserr*). He wrote in his first communication that Central Flores had been “durchquert” *) by him and that he had found: gray wackes, diabase-tufas, melaphyre-breccias, quarzites, marls, which were perhaps{ of palaeozoic age. In his work published two years afterwards he does not mention these at all, neither are the above-named rocks found back in it, but quite different ones are indicated. Referring to the determinations of M. BrLowsky and G. Rack he says, that he has found on the Wawu Manu Balu as fundamental rock hypersthene-diorite-porphyrite, over it hornfels, which was succeeded by tufa-rock. On the steep declivities of Woro Weka in the valley of Oto Weka he perceived at the bottom augite-diorite over it hornfels and further quartz-sandstone. He surmised the existence of a contact of the plutonic rocks‘). In GrorG Rack’s deseription of the collection gathered by Enprrr (39 specimens in all) however the name of not a single one of the above-mentioned rocks occurs. On the contrary he describes from the river Manu Bala dacite and andesite, from Oto Weka and Langa Weka exclusively andesite!"). According to Ensert a gray limestone containing numerous Globigerina’s and a few Rotalia’s occurs near cape Ngaru Kua on the North-coast of the Endeh Bay ’). 1) J. J. PANNEKOEK VAN RuepEN. Kenige geologische gegevens. |. c., p. 136—137. — Overzicht van de geographische en geolog. gegevens... |. ¢., p. 220. ®) A. Wicumann. Bericht tiber eine... Reise nach dem Indischen Archipel. Tijdschr. K. Nederl. Aardr. Genootsch. (2) 8. 1891, p. 231. 8) B. Hagen. Bericht tber die von Dr. ELperr gefiihrte Sundaexpedition des Frankfurter Vereins fiir Geogr. und Stat. Petermanns Miltlg. 56. 1. 1910, p. 308. 4) A somewhat eupbemistic expression, if we consider that the direct distance between Nanga Pandan and Geni is only about 10 km. USGI ZO. 6) Petrographische Untersuchungen an Ergussgesteinen von Sumbawa und Flores. N. Jahrb. f. Min. Beil. Bd. 34. 1912, p. 73—82. ON MG (ce fon PADI 488 Also at Liana in the northern part of the province of Endeh PANNEKOEK found a lime stone rich in Foraminifera, in which moreover fragments of quartz, plagioclase and biotite were detected). From this it appears that the limestone is younger than the dacite. In the valley of Ndona, eastward from Ambugaga, I found a boulder of Globigerina- limestone. For the rest effusive rocks with their tufas and loose eruptive materials are prevalent in this region. The southern part of the peninsula of Endeh is formed by Mount Ta, usually called Gunung Api (6385 m.). The material from which it was formed is angite-andesite. For a long time it has been in a solfatarie activity. To the north of this mountain rises Pui or Gunung Medja only 394 m. high, which has retained a regular craterform’). In a northern direction Mount Kengo (514 m.) and Mount Wongo (723 m.) which Ensert regards as the two cupolas of one encircling mountain, are connected with the peninsula of Endeh*). Most likely the eruption of a mountain, situated behind Brai, in 1671, which P. J. Vurn mentions*) relates to Kengo, and not as I supposed formerly to Pui. To the West of the Ndona valley rise Geli Bara (1731 m.) and Geli Mutu (1494 m.), the latter of which is in a situation of solfatarie activity °). The pyroxene- and labrador-andesites originating from this territory were described by G. Rack’). I found in 1888 in the valley of Ndona numerous boulders of dacite, labrador-andesite, augite-andesite and on the deelivity of the mountain andesite. To the east of volcano Ndona Expert still mentions Nduri, which has a solfatara’). The island of Nusa Endeh situated in the Endeh Bay is likewise of a volcanic origin. In the eastern part of the island of Flores the limestone formations have become very scarce. The little information we have about it is limited to the hillrange in the W.N.W. of Sikka situated in the province of Liu on which, according to H. Ten Karr, the villages of Kiara (+ 275 m.),and Riipuang (+ 350 m.) are situated.*’) The rock collected by him is a Globigerina limestone. In the farthest 1) Overzicht van de geogr. en geolog. gegevens |. c¢., p. 219. 2) A. WIcHMANN l.c., p. 222. 8) l.c., p. 202. *) Het eiland Flores. Tijdschr. voor Nederl.-Indié. 1855. Il. p. 157. ®») J. J. PANNEKOEK vaN Ruepen. Eenige geolog. gegevens l.c., p. 157. — J. Expert. Die Sunda-Expedition. II. 1912, p. 202. 6) l.c., p. 78—82. D) lacsmpsecO2: *) Verslag eener reis in de Timorgroep en Polynesié. Tijdschr. K. Nederl. Aardr., Gen. (2) 11. 1894, p. 221, 489 Northeast occurs then limestone in the vicinity of Tanjung Bunga or Kopondai, the well-known Cape Flores, to which the island owes its name. At a distance of 300 m. eastward from the cape men- tioned, G. A. J. VAN DER SANDE discovered a grotto with stalactites. And at last, according to A.J. lL. Couvrnur, coral limestone is found to the North of Larantuka from Panté Lela to Panté Beli Beting, especially between the village of Labao and Ili Labao. The entire remaining part is covered with volcanic material the monotonousness of which is only interrupted by the numerous partly still active voleanoes. In the North westward from Maumeri rises the voleanic ruin of Kiman Buleng (1446 m.). Gunung Dobo or Iliang (900 m.) situated behind Geliting but nearer to the South- coast is on the contrary still active. Most known, though likewise not sufficiently examined, are the voleanoes situated on the East-coast of Flores. For times immemorial Ilimandiri (1570 m.) has not given any sign of activity. The rock of which it is composed is chiefly augite-andesite.*) Kabalelo (1075 m.) situated eastward is an old voleanic ruin. *) Westward from it Leworoh is situated where on the 16% of March 1881 an explosion-crater formed itself.*) The largest, highest and most active voleano however in this territory is Lobetobi, consisting of two cones Lakilaki 2170 m. high and Parampuan 2263 m. high. G. EF. Typrman perceived about 37 km. westward from Lobetobi a high voleanie cone; most likely Dara Woér is meant by it. *) As appears from the above, there is in Flores no room for praetertiary sediments and eruptive rocks. Repeatedly however the existence of such like rocks in the form of boulders was hinted at. Near the bay of Bari I found in 1888 quartz-porphyry, clay slate and quartzite.°) I may now add to this the communication that in the river Reo amphibole-granite and diabase occurs, the hornblende of which has changed into chlorite. More eastward in the territory 1) Ken dicnstreis benoorden Larantoeka (Oost-Flores). Tydschr. K. Ned. Aardr. Genootsch. (2) 25. 1908, p. 554. 2) A. |WicHMANN I. c., p. 159. — G. Rack. Beitriige zur Petrographie von Flores. Ceutralbl. f. Mineral, 1913, p.p. 134—139. — H. Méutu described from Okka, situated on the south-western extremity of Ilimandiri sanidine-trachite and Hauyn-andesite (N. Jahrb. f. Min. 1874, p.p. 694—697). The determination however was not correct. 3) J. P. vAN DER Stok. Uitbarstingen van vulkanen... gedurende het jaar 1881, Nat. Tidsch. Ned.-Ind. 42. 1882, p. 241. 4) Hydrographic Results of the Siboga Expedition, Siboga Expedition 3. Leiden 1903, p. 56. lca oo. 490 of the mouth of the Nanga Koli A. F. H. Heuscn collected in 1890 according to PANNEKOERK ') quartzite and greywakke(?). On the south- coast at Nanga Mbawa I found granite (read quartz-diorite) and gabbro*) and finally in the valley of the river Ndona quartz-diorite. None of these rocks were ever found as rock, they are con- sequently at least “auf tertidrer Lagerstatte’. They are the last remains of rockmasses that got into the conglomerates by washing from which they got afterwards free again. The oldest formations of Flores belong to the effusive rocks of the character of dacites, labrador-andesites and hornblende-andesites with their tufas, on which those of the limestones of the Reo-form- ation and those of the tuffas of the Soa formation follow. They were uncovered by subsequent elevation. Afterwards the island was over its entire length the scene of violent voleanic eruptions, from which the only partly known crater mountains proceeded. The material produced by them consists — as far as our knowledge reaches — exclusively of pyroxene-andesites belonging to the Pacific type of rocks. The younger coral limestones occurring only spora- dically have only been formed after the formation of the volcanoes. Von Scuenie’s postulation that the bottom “to the north of Mount Rokka is very rich in tin-ore” appears to have been not only vain but also very expensive. Mathematics. — “The theory of the combination of observations and the determination of the precision, illustrated by means of vectors.’ By Dr. M. J. van Uven. (Communicated by Prof. W. ” ’ IC APTEYN) (@ommunicated in the meeting of June 27, 1914). By L. von Scurutka*) and C. Ropricuez*) a method has been given of illustrating geometrically the theory of the combination of obser- vations by the method of least squares, namely by means of vector operations. RoprieurZ however chooses in the case of rigorous equations idition another way, whilst VON ScHRUTKA, who consistently 1) Overzicht der geographische en geologische gegevens I. c. p. 229. *) I. ce p. 229. 3) L. von ScHruTKA, Eine vektoranalytische Interpretation der Formeln der Ausgleichungsrechnung nach der Methode der klemsten Quadrate. Archiv der Mathematik und Physik. 3, Reihe, Bd. 21, (1913), p. 293. 4) C. Ropriauez, La compensacion de los Errores desde al punto de visto geo- metrico. Mexico, Soc. Cient. “Antonio Alzate’’, vol. 33 (1913—1914), p. 57. 491 operates with vectors, restricts himself to two variables and one rigorous equation of condition. It is our purpose not only to extend their method to the case of an arbitrary number (JV) of variables and an equally arbitrary number (») of conditions, but also to derive the wezght of the unknown quantities in the same way. I. There are given N quantities wv, 7, 2,... which are to be deter- mined from (approximate) equations of condition (equations of observation) : qe+tbhy +qze+...+m=0 Te epee On These equations have the weights g; resp., and so are equivalent to the equations aVg-t + bY g-y + aVg.2 +... +mVg=0 C= oss each of which has the weight unity. We now introduce ah aV 9 pee bY gi fe V9 me mi V Gi f Tea es ey ie A— miles], B= V [bz C= 2V [gras [gimi*] AAG: —=0,|-gi0a . By BUA gue, Ci C0 Yi; (/G;. 2 0: ay el Mi oi. [| | denoting summation over 7 from 1 to n. So the equations of observation run in the form A;+ B+ ¢C;+...M=0 il Ieee) We now consider A;, B;, C;,... 4; as the components of the vectors WU, 3, €,..©, resolved parallel to the rectangular coordinate axes of an n-dimensional space. Thus the tensors are 4, B,C... J/, @;, (Fi, Y¥i,++- ui representing the direction cosines. The set of m equations of observation may now be condensed in the single vector-equation YL SLC +...4m—0, which expresses, that the vectors 2, %,€,...9¢ must form a closed polygon. The coefticients a;, ;,¢;,... and the weights g; being given, the unit vectors a,6,c,... of the vectors U,%,&,... are determi- nate. So the vector-equation requires that 2% may be resolved in the N directions a,6,¢,..., in other words: that lies in the V-dimen- sional space Ry, determined by the vectors a,6,¢,... and called the space of the variables (or unknown quantities). In consequence of the errors of observation this condition is not ful- filled. The most probable corrected value of M is the projection of ® on the space Ry of the variables. 492 Denoting the projecting vector by 8 (tensor A, direction cosines x;, components A;) we have really U+B+E C+... FM=HK. As & is perpendicular to U, 3, 6,..., we have Q,k)=0, (8, K=O, C6 R=, ete or GLa => (o: 2 10; ly7iAG] =, ete: or because R=A4+ B+ C4...4+ M4=qG4A4+ 8:8 +7C04+...4+ mM, [a7] A+ [afi] B+ faiyi]C+...4+ [a Mi] =0, [Pia] A+ [@?7] B-+ [Fix] C+...+ [FM] =, ya] At [yi fi] B+ [yi?] C+...+ [yd] =0, By multiplying these equations by V[giai?], V[gibi?|, V[ gic’), . resp., We obtain the ‘normal equations” : [gia] @ + [ocai bi] y + [gcaicz] s+... + [giaim:] = 0, [gbiaila + [oib?*)])y + [gibi] 2 +... + [oibimi] = 0, [giccai]a + [gcbily -+ [gie?]e +...+ [gicim:] =9, II. After these developments which also are given by VON ScHRUTKA and Ropricurz we proceed to determine the weights of the variables. For this we notice that all the quantities J/; have the weight 1, and therefore have an equal mean error ¢. From this ensues, that the projection of 2X in any direction has the same mean error é. We have to investigate the influence on % due to the variation of M, if the other variables B,€,... do not undergo that influence. A variation of % which does not displace the foot on Ay of the projecting vector &, does not act upon any vector 4, 3, ©... So we have only to do with a variation of the projection ®’ of Mon Ry. In order to leave the vectors 3, &,... intact, the foot is to be moved in a direction $§ perpendicular to 3, &,..., and, because it lies in Ry, also perpendicular to 8. Denoting by 6; the direction cosines of 8, we may put the equation (4, 8) + (Mm, 8) = 0, obtained by multiplying the equation of observation scalarly with 8, in the form A [ajo; |] = — MU, M, designating the projection of MN on 8. As M, has the mean error ¢, the mean error ¢4 of A equals 493 é é4 = = [ao;|? whence GA = la70; \7- The vector 8, lying in Ry, may be resolved in the directions a,%,¢,... Denoting its components in these directions by X,Y, Z,... we find B= Xo Picea cee or 6;= Xa;+- VP; 7; -+ -.-. Now, 8 being perpendicular to &, €,..., whence | /?; 6; |=0,| y; 6; |=0,.., we have ‘ — [o;? == xX [ai 6; | or 1 X = ——_.. [a; 6; From the equations [az03|(—= (256; — 05) (7:6; |= 078: xX 5] which may also be written [a*] X + [afi] Y + [aiyi] 7+ -..= [(Piei] X + [82] Y + [ivi] 7+ --= [ye:i]X + fifi] Y + 7) 2+--= or -[ai?] X? + [a; i] XY + [eiyi] XZ + .. —1=—0, [Pia;] X? + [7] XY + [Aixi] XZ + [vi aj] X? + [vi (7: | XY+ [yi] A Z+.t0=0, the first unknown quantity X? takes the value oes ae, [a o;]? = GA The reciprocal value of the weight of A is therefore found to be the first unknown of the “modified normal equations”. Putting further X=EY[gia7], Y=Hyv[gib7], 2Z=—SV [gic], --- the modified normal equations pass into [giai?] §* + [giaibi] Sy + [giaics]§5+..—1=—0, [gi b; a; | 5? + [gi bf] Sy + [gi bic) 65+..+0=0, [gicra: |] §? + [giccdi] y+ [gie?] 66+ ..+90=—90, 494 Now, from A=xV|g;a;7] ensues €4= &/ [gia], hence een eee eat ig es Ca | les is [qia;? | Si [gi ai” | ee which is the well-known theorem on the weights of the variables. Example: 3 equations of observation with 2 variables. M The unit-vectors a and 6 determine a plan &,. The extremity J/ of —M=OM mM is projected on this plane in the point A M’. OM’ is resolved parallel to a and 6 : .y into the components OA=% and OB=%, In the plane A, (4,3) the vector 8 is M aS "erected perpendicular to 3. On this vector A A OM—=-—M® and OA=Y have the same Fig. i. projection OA,—= M,. This segment J/, has the mean error €; the variable A, i.e. the segment OA there- ; € fore has the mean error &4 = PETE III. We now suppose that besides the n approaimate equations of condition (equations of observation) » rigorous equations of con- dition are given, viz.: An pie + bn+ jy Sip Gaeta oo ge Og =D (RM con D) For the sake of regularity in the notation, we will also provide these equations with factors g,4; (which afterwards disappear from the calculation). Thus we really operate with Ant jV Int j-% + ont GV In45-Y Font gV Int y-2 feet Wnt 5 V Jn+j—0(J=1)-0)- Agreeing, that eal now means a summation over 7 from 1 to n+», we may, retaining the notation used above, consider 2, 3, @,..., M as vectors in a space of m+ v dimensions. The vector-equation YB ie 22 Wt 0 is again not fulfilled on account of the errors of observation. The last r component-equations (2 + 1)...(-+ ») however hold exactly this time. Putting again Y4+HLC+. .+mRM=—K the » projections An4i,.. Any, of # must be zero, whence tn4+; = 0 (j= 1,..>). 495 So the vector ® is perpendicular to the space R, ‘of condition” determined by the coordinate-axes 7,4; and therefore cannot generally be any longer assumed to be perpendicular to the space Ry (2, 3,6...) of the variables. # lies in the n-dimensional space Pn ap4j= M4; (j=1,.v), which is parallel to the space R, “of observation” determined by the axes a, (h=1, .. 7). The parallel-space f', cuts the space Ry of the variables in a linear space of NV + 2—(n-+-r) = N—»y dimensions, which we shall denote by e'y_,. This latter is parallel to the space @y_, of inter- section of the space /, of observation with the space Ry. We now project the extremity of M lying in R', in this space on the space e'y_, of intersection. The projecting vector will now be the ‘correction-vector” §. Translating & to the origin into the vector OP, OP wiil be per- pendicular to the space gy—, common to Ry and R,. Next we construct the normal space of @y—, which passes through the origin O. This space has n—-- vy —(N—v)=n-+ 2r»—WN dimens- ions. It contains the space &, of condition (as normal space of &,), further the line OP, and also the normal space of n+ »— N dimensions which can be drawn from P perpendicular to Ry. This latter space therefore lies together with #&, in a space of n-+2r— N dimensions and thus cuts #, in a space of (n-+r—N) + + » — (n+2r—N) =O dimensions, consequently in a point. As for this point Q, it thus lies both in A, and in the normal space drawn from P perpendicular to Ay, from which among other things follows, that PQ makes right angles with each line of Ry, more particularly with the vectors W,%,@,... So, projecting OP and OQ on 4, these projections are equal. The same holds for the projections un 2), Crook Representing OQ by the vector St'(K', x;', K;'), we have, as St lies in R, Ky! = 0 and x;' = 0. (A=1,...n) From Get) (I) (St) i ( Da (ts i — (RO), follows EG [oe nee Nl = RG [estrella see (sil KG [ote Sigil 2 [see |i Ee [ee Vg] 5 «2 AS: tpi Oh tory sa. the sum [x;e;| is only to be ex- 2 tended from 1 to n; hence [x;@; |] = S x,¢, = [*naq}'; and since 1 z, =0 for h=1,..n, the sum [x,'@;]| is to be extended from n--1 496 v to n+», so that [x;'a; | Sh On — [%n4j'en4j |" Here and in 1 7! what follows [;|' will denote a sum over h from 1 to n, and [n4; |" a sum over 7 from 1 to ». We may therefore write [e@,Ky)' = [an+; K45]", or, because Ki — Ae Be Oe ae ee yiC +... + Mi, [en?)'A + [enPi]'B +- Leaya]'C + .. + [andG]' = [en4jKn4j]"s [Pren}'A + [Fr B + ([Pryi]'C + + (PM! = [2n4j Kn, [ynceal'A + [vaFil'B+ [yO + + [vaMi]! = [vn jKn4j7': Putting Cn jpg Pn j=PP's Prt j= Ty's + Kny'=— Qi Mn4j—=MG, mn j= mj), we have fan?) A = enh Be lanyniGeonen [en Ma] fe [a;'Q;]" == (I) [PrenJA + [2VVB + [Prvi]'C + -. + [PaMal + [7;'Q;]"=0, Lyneny'A + [ynPalB+ [yO +... + LyaMal' + [77 Q)"=09, Introducing aj V [gi a?) PV [9 627] S77 a ae = er a V Inj , V oni i'V [oie] V Int) we obtain, after multiplying successively by Vigia;*], V(gib.7), Vigier), = Lonan?)'@ +- Lonanba]'y + [onanen]'e + -- + Cgnanmal! + [ay'g;]" = 0, Lonbranl'e + Landa? ly + Lonbrenl’e +--+ [gabama]' + [b;'q;]" = 0, Lonenan)'e + Loneabay'y + L[gncn*}'2 ++. + [gncnmal' + [e;'q/]" = 0, ’ Qj = On 5 = Ul Cj = 4 yj = 19 9 = QV Ont; N equations, which together with the » conditions aja + by + c'z2+.. + mj =0 serve to determine the N variables «, y,2z,... and the » auxiliary quantities g;. IV. In order to determine the weights of z,y,z,..., i.e. of A, B,C,..., we must examine the influence undergone by % from a variation of MN, the vectors 3, &,.. remaining unaltered. A variation of ® only acts upon %, 3, €,.. when the foot of & on the space 9'y_, of intersection moves. If the foot is fixed, #* may freely 49 ~) move in the space S, common to the normal space of @!y_, (of n+ 2» —N dimensions) and the space 7’; parallel to 2. The space S obviously has (n--2r—N ) + n —(n-+v) =n + v— N dimensions. A component of M in this space has no effect on the vectors U%, 3, ,... A com- ponent of M® will only have any effect on 2, B,&,..., when it lies in the normal space S’w of SS, which has n + »— (n4+-r—N)= N dimensions. By translating this normal space S'y to O, it contains both R, and oy_, (intersection of Ry and R,). The variation of ® will exclusively influence %, when the com- ponent of M undergoing this variation is perpendicular to B,€,... These considerations lead to the result that we want that direction 8, which lies in S’y and is perpendicular to %,@,... The vectors ¥, ©... determine together a space of N—-1 dimensions. The vector 8 must lie in the normal space (of mn -- »— N+ 1 dimensions) of the space (8, &,...). This normal space cuts S’y in a space of (n+ v— N+ 1)+ N—(n+ vr) =—1 dimension, hence ina straight line. So there is always one and only one line 8 fulfilling the imposed conditions. Since 8 lies in S’y, i.e. in the space joining R, with oy_., the projection t of 8 on 2, will fall into ev_,. Now we have for the direction cosines 1; of the projection f of gon R,: On h= Sere aae V [on] As t, being a line of ey_,, also lies in the space Ay and therefore may be resolved in the directions %, %, &,..., we have (SS he OME (paar) ty, = Po, + Q2, + Ryn +. (= 1,---n) ie QP Ryn 0. (7 = 1,..0) Putting PVG OY fora) 0 *s, = Ay for-|- = hi. .<. we obtain : wP' + fQ+yR +... =i (ie, an) nt jP! + Pn4jQ + yn Rh +... = 0, Gi lb) and, 8 being perpendicular to %, &...., 27Ga| == 0%, Ree]| == enc (ops) Stk In this way we have collected n +» + N equations to determine the n+» unknown quantities o, and the NV unknown quantities Eko OE i pers Ve S’y being perpendicular to &, $ is also perpendicular to ®. By multiplying the equation 498 Y1 $416 +4..4M=—=K sealarly by 8, it reduces to (a, 8) + (M, 8) =0 or A [ajo;] = — In order to determine the mean error of J/,, we remark that of all the lines through O in Ry t is that which makes the smallest angle with 8. The error of J/, therefore depends for the most part on the error in the components JZ, of M in the direction t. We may consequently write m. e. of M, =m. e. of Mi X cos (8, t) = € cos (8, f) or zs ae : €, =e [oi] =e | on. —— | = ev [o,']', ean) | : se | V [077] hence &s V [o,7]' = = [aioi] [aio;] Since Ls Oh aq ; M, =; lo;r:) = [AG xa. lor] = Ei sta | -V [on?]' = [Dfion]', V [on we have AYE m6, t 7 _ She . My, | ioi| [ aio; | or, putting Oh ——- = Dh, [ aio; | Le: A=— [paMil. 1 4° [ on? | : Ss ety OA & [ajoi]? Introducing f' (Qh PI Ontj Xa eS BS Se ee [aio] [aioi] ail Baty [aves] ” ) we arrive at aX | PY 3 yiZ es. = Ph (AS i1,...0) @tn = ;X + Pn+j¥ + yntjZ+--=0 (ji 15 =-P) lapl=1 , (Cal=0 .\ irpl— 0. From these 2 -—+ » + V equations we ean solve the 2+» unknown quantities p; @—=1...2-+ yr) and the NV auxiliary quantities X, Y,Z.... Il The quantity —-—J|p,°}' in question is also found as follows GA 499 1 ‘ . ; = =p?) =[pilenX+(21V +724...) =X [preeny+¥ [pr Pn\+Z[piyil'+-- " = X— NX [pnp jang yl" — VY (pot yiFr45)" — Z [patra]! = X— [png lang jg X + Bn V + ny Z +o)! =X Returning to the original variables x,y,2,..., we derive from A Ss —— Vigia*] tirstly &A4 & = ——— V [aai"| and ee Vall qa eee loner |e Further, putting V laa; | Vi[gai*] Li ky Saas oe Pr+j = Ken-tj Se Von V Inj X= § iovas* |; Ye) [loons ZAG Chall stelle = the n +--+ NV equations pass into L F ky age ibpap S cyS 2... = =, (6 == Ne oe nia) = ah Ont76 + Open tentgs +... = 01, Gly een) fark] = 1, [br k; | = 0, [feathered == O ener, whence Example: 2 equations of observation with 2 variables and 1 condition. The unit-vectors a and 6 determine a plane /?,(NV=2), the plane of the variables. This plane euts the plane of observation R,(m=2) in the line ev, N--»=1), which thus coincides with the line t. The line OP is drawn in the plane &, perpendicular to on, (0. Through the extremity J/ of the vector M a line is drawn parallel to OP; this line euts the plane Ry of the variables in 17’. The veetor JIM’ —//— PO is the correction-vector 8. OJ’ is resolved in the directions a and 6 into the components OA = %and OL=, The lengths of these lines represent the most probable values of the variables A and ZL. The line PQ is perpendicular to the plane ty and meets the normal /, (line of condition), erected in O on /2,, in the point Q, The vector OQ is ealled St’. 99 vv Proceedings Royal Acad. Amsterdam. Vol. XVII. Fig. 2. erected in O perpendicular to ¥, interseets S'y in the line 8, which therefore is perpendicular to 3 and S&. So A and J/ are projected on § in the same point Ag. The normal plane A As VW of g cuts t in a point 7. the distance of which to QO amounts to J/, (with mean error ¢). The mean error e, of A, thus has the value &; = «cos (8,t), and that of A the value Es cos (8, t) a cas (8,0) i: cos (8,a) V. The errors (residuals) of M,, M,,.. Mf, are K,, K,,.. Ky resp. The sum of their squares is [Aj?| = A®. For the ease that no equations of condition are given, ® must be perpendicular to /y. So S& may dispose of a space of »—NV dimen- sions (the normal space of /?y). Hence ® has 2—N components, all with the same mean value ¢. Consequently K? = (n—N) X & hence [Ai] S== -——., n—N In case p conditions are imposed, & may dispose of the space S of n+xr— N dimensions. Consequently ® now has n+ »— NV components, all with a mean value ¢. In this case we have therefore cee L LGA ae n+ v—N- 501 Physics. — “On the measurement of very low temperatures. XXIV. The hydrogen and helium thermometers of constant volume, down to the freezing-point of hydrogen compared with each other, and with the platinum-resistance thermometer. By Prof. H. KAmMertinGH Onnes and G. Horst. Communication N°. 1444 from the Physical Laboratory at Leiden. (Communicated in the meeting of May 30, 1914). § 1. Introduction. The measurements which this paper deals with bring the investigations undertaken in Leiden for the purpose of establishing the seale of the absolute temperatures as far down as the freezing point of hydrogen, to a conclusion, in so far that a direct comparison has now been made between the helium and hydrogen scales, by measurements with a differential thermometer, which had the object to test the corrections to the absolute seale of temperatures below 0° C., obtained separately for the helium seale (in XIX of this series) and the hydrogen seale (partially given in XVIII of this series ')). For the place which the mutual control of these corrections occupies in the more general investigation of the measurement of low temperatures which is being carried out in Leiden, we refer to § 6 Suppl. N°. 34a. The test could be extended as far as the freezing point of hydrogen, after the compressibility of hydrogen vapour had been determined by KAmERLINGH ONNEs and pe Haas, Comm. N°. 127¢c. June 1912) *). Our comparison of the helium seale with the hydrogen seale*) by means of the differential thermometer to which was added a new calibration of the Leiden standard platinum thermometer /7¢;' (formerly Pt,) shows that a very satisfactory agreement has been attained in the temperature determinations. 1) Compare also H. KaAMeRLINGH OnNes, CG. Braak and J, Guay, Comm. N°, 101@. (Nov. 1907) § 1 under 40. { *) In this Comm. a difference was discussed which existed between the tempe- rature delermination with a hydrogen thermometer according to the resistance thermometer Ply',-which was calibrated by means of it and the temperature deter- mination by extrapolation of the isotherms. According to caleulations by Dr. Kersom, suggested by SACKuR’s interesting‘ investigation, this deviation might be connected with the theory of quanta (Gomp. Suppl. N°. 30 and N® 34a § 11). 3) The comparison of the hydrogen and helium thermometers by Travers, Senver and Jaquerop, Phil. Trans. A 200 (1903), p. 105, has been discussed in Gomm. N° 102, In general their results are in good agreement with our measurements, 3o* S02 § 2. Apparatus. Two identical thermometers of Jena glass GUL, such as had been formerly used by H. Kammrirmcn Onnes and C. 3RAAK, Were connected to one manometer. The arrangement was otherwise exactly the same as that used before. The standardmeter was divided into '/, m.m. and allowed a direct estimation of '/;, m.m. This gave a considerable saving of time, as it made the use of the measuring eye-piece of the cathetometer unnecessary. The amount of gas in the capillary was measured by an auxiliary capillary of much larger section, as described by Crapputs. Besides the two thermometer bulbs, the cryostat contained the platinum resistance thermometer /’;) and a large pump, which provided for a good circulation of the liquid. The hydrogen and the helium were purified by distillation, and were both free from other gases. § 3. Calculations. The temperature for each of the thermometers forming the differential thermometer was calculated from the formula given in Comm. N°. 95e, but with a few alterations. The expansion of the glass f(t) of the bulb was not calculated from the quadratic formula given there, but taken from a graphic representation in whieh the curve was drawn through the points experimentally deter- mined and extrapolated by means of the expansion for a different kind of glass as determined by Cu. Linpemann. The influence of the different temperature function for the expansion of the glass is about ?/,,,° at hydrogen temperatures, at all other temperatures it is negligible. Moreover the volume was divided into three parts. a. The bulb at the temperature ¢ of the bath. >. The capillary in which the mean density of the gas was determined, by means of the auxiliary capillary: the mean density is proportional to ss he L being the pressure in the auxiliary capillary at 0°, 4 the measured pressure. c. The steel capillary and the volume about the point, the temperature of which is the same as that of the room. If we divide all the members of the above mentioned equation by the volume of the bulb it becomes IT i 3 Wear h, ue dvo 273 —_ |: tO hg tga Oo ayer ae a= h + ath l+at 273 1+ at). : The provisional temperature, which is needed for the calculation of the various corrections, was calculated from the resistance of Pt’. 508 i, ; Even move this temperature with sufficient accuracy. The zero- 0 pressure for the hydrogen thermometer was H/4, = 1191 m.m.'), for the helium thermometer //, = 1124 m.m. Circumstances unnecessary to be mentioned here, had prevented these pressures from being made more equal. A new set of determinations in which this will be attended to is planned. The pressure coefficient of hydrogen at the above mentioned pressure was taken at 0.0036625 ; for helium at 0.00386614, the value derived by KaAmertincH Onnes *) from the isothermals at O° C. and 100° C. If we ecaleulate with the pressure coefficient 0.0036617 deduced from the isothermals of 20° C. and 100°C, we find, after the introduction of the necessary corrections, almost the same temperature on the absolute scale. § 4. Arrangement for the resistance measurement. In order to measure and to compare resistance thermometers two identical differ- ential galvanometer circuits were fitted up according to KoHLRauscn’s method. Both galvanometers can be read from one place, so that nearly simultaneous measurements can be made. This removes all irregularity in the temperature of the bath in the comparison of resistance thermometers. Two moving coil differential galvanometers from Hartmann and Bracn were used. With an additional resistance of + 1000 2 in each of the coils these are practically aperiodic in the measurement of resistances less than 180 2, as with all our other thermometers. The sensitivity is sufficient to measure ——-— 2 100000 with a current of + 5 milliamperes, while the condition of propor- tionality between deflection and current-strength is very well fulfilled. Test-measurements have shown, that with this arrangement resist- ances of about 100 2, such as our thermometers have at ordinary 1 temperature, can be compared to TGuGE without any difficulty. Our 1) At these pressures even at the melting point of hydrogen no attent.on need be paid to the thermo-molecular pressure according to KNUDsreN (Comp. Suppl. NY, 34 § 7 and a Comm. by H. KamertinGH OnneEs and 8. WEBER which is shortly to be expected, on the determination of the temperatures which can be obtained with liquid helium). 2) H. Kamertincu Onnes. Comm. No. 1020. The value is here increased by O0.0000001, in consideration of the value 273.09 since assumed for Too ¢, Gomp. H. Kamertinex Oyves und W. HL. Keesom. Die Zustandsgleichung. Math.Enz. V 10, Suppl. No, 23) Einheilen c, and § 820. 504 experience with moving coil differential galvanometers, for this purpose at any rate is very favourable '). In the manner described we attained a much greater rapidity of measurement than was possible by the method described in the previous papers of this series, and this in its turn increases the accuracy. We must also refer to our experience with thermometers in which the wire was sealed to the glass (Comm. N°. 95) § 1). For tempe- ratures above that of liquid air they are not unsuitable, although even here they are less constant than those with a free thread. After immersion in liquid hydrogen their resistance was found to have increased by about one tenth of an Ohm. Each further immers- ion in hydrogen carried with it a permanent change of resistance, so that we replaced these thermometers by other ones with free threads wound on porcelain tubes with a double screw thread baked in. After a thermal treatment, consisting in several immersions in liquid hydrogen followed by moderate heating, these became satis- factorily constant. § 5. Results. In the following table the results of our researches are found. The two first columns contain the hydrogen and helium temperatures calculated from the formula given above. Column 3 and + contain the corrected temperatures on the absolute scale deduced from the hydrogen and from the helium thermometer, column 5 contains the resistance of the platinum thermometer P¢/. The agreement is on the whole very satisfactory. We have already mentioned that with thermometers of the kind described an accuracy of about */,,° might be expected. Our meas- urements show this to be the case; only in a few points larger deviations occur. These can readily be explained by a small defect which will be avoided when we repeat the experiments, namely that the eryostat which had to be used was not quite symmetrically built. When both auxiliary capillaries worked properly this was not of much consequence. But (except fortunately in the determina- tions most important for us viz. at the hydrogen-temperatures) the helium capillary got out of order, so that the distribution of the temperature of the stem of the helium thermometer had to be deduced from the observations with the hydrogen capillary. This cireumstance has the greatest influence at temperatures at which the methyl chloride and the oxygen evaporated under reduced pressure, and it is exactly there that the greatest deviations occur. 1) Compare JarGer, Zeitschr. f. Instrumentenkunde 1904. or S or TABLE I. fee | fete sO ee 9 tHe W pyr 0 | | 135.450 fal eesrea: |); = 23.96) |) = 23706 = 23, 94 | 122.613 | 2 43.09 | 43.07 3.00 | 4g.07 | 112.278 3 qps0. | 61.40 | 61.50 61.49 | 102.280 4 79.57 79.51 79.57 79.51 | 92.422 | 5 102.72 102.69 102.70 102.69 | 79.674 | 6 113.58 | 113.55 113.56 113.55 | 73.629 | 7 | 130.46 | 130.41 130.43 130.41 64.189 8 | 182.88 | 182.81 182.82 182.79 34.180 | 9 | 186.79 186.70 136.73 186.68 | 31.904 10 | 195.24 | 195.15 195.18 195.13 26.988 11 | 204.79 | 204.69 204.71 | 204.67 | 21.491 12 212.61 212.52 212.52 | 212.50 | 17.097 13 | 216.25 | 216.15 216.16 | 216.13 15.119 14 | 252.80 | 252.68 252.66 | 252.64 | 1.924 15 | 256.23 | 256.10 256.08 256.06 | 1.601 16 | 258.56 | 258.41 258.39 258.37 1.453 17 252.80 | 252.66 1.925 1S 253.78 253.64 | 1.819 19 255.20 | 255.05 1.685 20 257.22 257.05 1.531 The readings of P/ allow a comparison with the measurements of 1906—1907. WW In fig. 1 the deviations from the linear formula ¢/—= — 248 + 245 ae 0 are represented for all three calibrations, at temperatures above —-217°C. The circles refer to the calibration of 19138, the triangles to 1907 and the squares to 1906. For the calculation of temperatures in this field the above formula with the deviation curve belonging to it has been recently used in the Leiden researches, 506 2s Riess The differences between the calibrations of 1913 and 1907 are less than */,,‘¢ of a degree throughout. The fact that the differences with the first calibration (4906) are more considerable must un- doubtedly be attributed to the mechanical treatment of the wire: after the first calibration the wire broke, and had to be re-wound. It must be ascribed to chance, that the deviations are so small just at the points of the second calibration. § 6. The jield of utility of the platinum resistance thermometer at low temperatures. Resistance thermometers for other fields of tem- peratures. The curve in fig. 1 shows at onee the peculiar behaviour of platinum below — 200°. At this temperature a change of direction in the line which gives the resistance as a function of the temperature is sharply marked. In fig. 2 the deviations from the formula given above in the oxygen field are once more represented (circles) and also those for the thermo- meters (Pt; (squares) and /, (triangles), which were also directly compared with the hydrogen-ihermometer by Dr. C. DorsMan and us. It is clear from the curves that we have to deal with a specific peculiarity of platinum, which Fig. 2. makes it very unsuitable to be used as a thermometer in this field, as accurate interpolations ave im- possible. For this reason in the field of temperatures below —200°C., 507 a gold thermometer is preferable to a platinum one, as has already been pointed out by Kamertincn Onnes and Chay '). At hydrogen temperatures both platinum and gold are no longer approximately linear. Here and at helium temperatures manganine and constantin proved to be nearly linear and fit for resistance thermometers. Concerning these we refer to a future comm. dealing with resistance measurements in particular for the determination of the specific heat of mercury at helium temperatures. § 7. Comparison of our thermometer Pty with other platinum resistance thermometers. Comparing our measurements with those of F. Hrnnina *) formulae of the form: aN aN ; AR = M(R—1) - N(R—1)? and e' =— M=—— (11000) — 1. i : were used. This was done because there were objections to a direct determination of the temperature coefficient by measuring the resistance of Pfr at O° C. and 100° C. which since the first calibration bad never been brought to a temperature above the ordinary. We found W W —— = — We W, t (K.O. and H.) (Hennine) 10° A R Tel = WR INS 0.90523 0.90449 74 0.09551 43.09 0.82895 0.82775 118 0.17225 61.50 0.75511 0.75340 alfa 0.24660 79.57 0.68233 0.67989 237 0.32011 102.72 0.58822 0.58492 330 0.41508 113.58 0.54559 0.54007 do2 0.45995 150.46 0.47389 0.46986 403 0.55014 182.88 0.25254 0.24686 548 0.75314 186.79 0.23554 0.22998 556 0.77002 These numbers give: J/ = — 0.0078758 N = — 0.0007605. And further ¢ = — 0.30.10-° 100e’ = 0.38821 From the results it appears that our platinum thermometer, as regards its constants, lies between the platinum thermometers N°. 1 and N°. 7 used by Henning in his investigation. This was to be expected, as these thermometers, like ours, were obtained from Heranus, N°. 1 and Pr being of earlier date. The difference with the values calculated by Henninc is caused by the fact that his caleulation was based on our calibration of 1906, which differs from our present one and that of 1907 (Comp. § 5). 1) Comm. N°. 95, Used also by Grommenin, Comm. N°. 140u. *) Ann, der Phys. 4te Folge Bd. 40, 1913. 508 Physics. -— “On the electrical resistance of pure metals ete. 1X. The resistance of mercury, tin, cadmium, constantin, and manganin down to temperatures, obtainable with liquid hydrogen and with liquid heliwn at its boiling point.’ By Prof. H. KAMERLINGH OnnEs and G. Horst. Comm, N°. 142a from the physical Laboratory at Leiden. (Communicated by Prof. H. KAMERLINGH ONNES). (Communicated in the meeting of June 27, 1914). § 1. The resistance of wires of solid mercury. Several mercury resistances were compared with the platinum resistance thermometer /7/ of the laboratory, first in liquid oxygen, | r Wobs. W cate, AW | < 4.19 | supra- | conductor | 4.19 0.0560 | 0479 | 0,421 427 | 00600 |. 0489 ° | 0.429 4.33 0.0636 | 0.496 0.43 4.37 0.0656 | 0500 | 0.434 | 14.57 0.9390 1.667" |) 70,788 | 15.78 1.069. | 4,806. |" 0787 hn Eizo 1.298 2.047 ||P o no 20.39 1563. «S| Ss 2333Ss|CSs.770 | 80.92 8.086 9.261 1.175 90.13 9.088 10.316 1,228 | 116.52 ~ | -2/000,) | * 18.337 9 4).7 seaaan | 12281 | 12604 | 14056 | 1.962 132.72. © | 13800 ~ "|- “15490 1.390 | 141.83 | 14.855 | 16.233 | 1.278 154.22 16.354 | 17.651 1,297 165.80 | 17,806 | 18976 | 1.170 e402) | “anata en ieies 0.853 21869 | 24716 | — 25.029 | -O3I8 233,53 | 26.694 | 26:731. |. 0.037 234.16 26,800 26.800 =| 0.000 509 then at a number of other temperatures, with the differential-galvano- meter according to Konnravscu’s method. The result of these determinations was as shown in the table (7 = temperature on the Ketvin scale, with Zov¢, = 273°.09) In the third column are given the values, which would have been obtained. if the resistance diminished linearly from the melting point down to the absolute zero. : seen We tk sae Weatc. = — Wy, = —— 26.800 = 0.11445 7. ie 234.16 ts Column + gives the deviations w : S ool of the real values of the resistance us | 4 | | from those, calculated by means os 5 , 3 1 ° | of the linear formula. These devia- ra 4 - tions are also plotted in the figure. | | . : The relation between electrical msg +— : resistance and temperature seems to be of a very complicated ctl | character. aa | 3 § 2. Direct determination of the change im resistance at the melting- F yebeorse ih \ | point. ’ 2 1 9 Ee) 9 : é A AE aarp Of two resistances, which were Fig. 1. frozen without auxiliary bath, the change in resistance in melting was determined directly. The first consisted of a narrow capillary filled with mercury, section + 0,0015 mm’. At — 49°.88 the resistance was 25.095 2, immediately above the melting point 115.0 2, a eh Wa the ratio —“ = 4.66. Wsol The second capillary had a section of 0.48 mm’. With this resis- tance the ratio 4.50 was found. As a preliminary value of the melting point — 38°.93 C. was found.*) § 3. Indirect determination of the change in resistance at the melting point. During the numerous determinations of mercury resistances in liquid helium (Comm. N°. 133), we always measured the resistance at ordinary temperature too. By means of the resistances of solid mercury of 1) Our measurements date of 1912. In the meantime was published the paper of F. Henning Ann, d. Ph. (4) 43 p. 282, 1914 who finds —38°.89 C, 5LO § 1 and of the well-known behaviour of liquid mercury, we calculated lig Wsol As in these experiments the mercury resistance was suspended in in each case the ratio a vacuum-vessel cooled from the outside, the freezing took place very slowly. We found: 23 May 1914 4.40 a0) as - 4.63 WA (OX 3s 4.41 4.54 12 Jan. 1912 4.30 wso 9.06 wys0 7? Bebrs 4.69 4.19 eed; % 4.30 14 June ,, 4.37 4.90 As probably the highest figure thus obtained comes nearest to the true value of the ratio, we will be not far from the truth, if we assume the number 5 for the mean ratio. This result has also been found by Bavrruszaitis'), who obtained 4.90 as highest value in his melting-experiments. It is remarkable, that the ratio of the change with temperature of solid and liquid mercury is also about 5; the increase of resistance per degree remains thus fairly constant in melting. § 4. Some determinations of the change in resistance with the temperature of metals and alloys. a. Object of the experiments. We made a series of determinations, mainly for orientation, about the change of resistance of different metal wires down to helium-temperatures. The purpose of those determinations was to find a metal or an alloy, which could be used asa resistance thermometer down to the lowest helium temperatures. The results of these measurements are plotted in figure 2. Of special interest is the behaviour of manganin and constantin. While with copper, tin, iron and cadmium no further change of resistance could be established in the region of the lowest temperatures, it appeared, that the resistance of manganin diminished considerably and in a linear way with the temperature, from the lowest oxygen temperatures down to the region of the helium temperatures. So that wires of manganin might be 1) A. Barrruszastis, Cracovie Bull. Acad. Nov. 1912. used equally well as wires of constantin (the suitability of which was shown on a former occasion), as resistance thermometer in this region of temperatures. bh. Pure cadmium and pure tin. Pure cadmium (KAHLBAUM) was east in a glass tube like mercury. From the tin (KaHLBAUM) a thin wire was cut on the lathe. t Resistance t : Resistance | of tin | of SAE | 16.5 | 271.1030 16.6 | 76.7 10-30 --183.2 | 66.2 | —183.2 209 | —201.4 | 46.9 —201.2 | 15.7 2529 | 2.99 | —252.9 | 1.45 —258.3 | 1.18 | —258.3 | 0.58 —268.9 | 0.132 — 268.9 | 0,032 ec. Copper and iron. The eopper wire was made of commercial electrolytic copper’). The iron was from Sweden (Kolswa II). It 1) W. MEISSNER (Verh. D. Phys. Ges. (16), 262, 1914) used much purer copper. In his determinations the resistance at the boiling point of liquid hydrogen was only 0.26 °/9 of the resistance at O° C. had already been used by Dr. B. Buckman for measurements con- cerning the influence of the magnetic field on the resistance. | : W copper Wiron — 183.7 34.5 3.90 — 201.7 24.7 3.05 — 253.5 10.5 2.04 — 269.5 10.0 2.00 — 272.0 10.0 2.00 The resistance approaches here to a definite limiting value, in the same way as this has already been found for other not quite pure metals (Comm. N°. 119). d. Constantin and manganin. The temperature coefticient of con- stantin which is extremely small even down to oxygen temperatures, increases considerably in the region of the hydrogen temperatures, so that constantin wires are suitable thermometers in this region and especially in the region of helium temperatures. . = | | | | r Weonstantin Teale. r- Teale. | aie Aer | 90.75 145.680 | 65.18 144.320 | 20.36 | 138,259 20.36 0.00 | 18.985 | 137.988 | 19.00 | —001 | 17.33 | 137.662 17.37 | —0.04 | 15.83 | 137.3555 15.83 0,00 | 14.32 137.050 14.30 0,02 yy cale ave the values calculated by means of a linear formula of the form t=a-+ bu through the points at 20°36 and 15°.88. The deviation does not amount to more than 0°.04 and shows thus the suitability of eon- stantin wires as thermometers in the hydrogen region, where the platinnm-thermometer would require complicated calibrations (comp. Comm. N°. 142c). | 4 | W manganin | 465C| 124.20 —183.0 119.35 —201.7 117.90 —253.3 | 113.42 —258.0 | 112.91 =I G00e met O2 Sie es Ghul e. Gold. With a view to measurements -of specific heats, which will be published before long and to investigate the suitability of the ‘gold-thermometer in the region of oxygen- and hydrogen-temperatures, we determined the resistance of a gold wire at a great number of temperatures in those regions.') The result shows, that in the region of the reduced-oxygen temperatures (mainly below — 200° C.) the gold thermometer does not give rise to the difficulties, which make the platinum thermometer nearly worthless in that region (Comm. N°. 141@ § 6 and tig. 2). | T Resistance | of gold 1418K 0.2910 15.83 0.3037 17.30 0.3190 19,00 0.3412 | 20,35 0.3621 | 65.18 | 2.2901 | | 72.58 | 26763 | 83.31 3.2312 87,99 3.4710 90.75 3.6110 1) Calibrations of other gold wires will be given in the paper by W. H. Kersom and H. KAMpRLINGH ONNes on specific heats Comm, N°. 143, 514 Physics. “Further experiments with liquid helium. L. The persistence of currents without electro-motive force in supra-conducting circuits.’ (Continuation of J). By Prof. H. Kamerinen OnnEs. Communication N°. 1416 from the Physical Laboratory at Leiden. (Communicated in the meeting of June 27, 1914). § 9. The preservation af an electro-hinetic momentum. All the phenomena that were dealt with in the preceding sections (J) *) showing the persistence of the magnetic moment of the coil, without the acticn of an electro-motive force, agree with what was deduced on the supposition that a enrrent flows through the coil of the value calculated, and which diminishes according to the time- of relaxation calculated. At the same time, it was desirable to have a conelusive proof that the magnetic moment of the coil is really caused by a current. We should then be able to prove conversely by the continuation of the moment, that the time of relaxation of the current is very long, and a value, or otherwise an upper limit could) be given for the micro-residual-resistance of the conduetor in which this current flows. I got this proof in the following manner. On either side of the place, where the ends of the windings of the coil are sealed together and close to it, two wires b, b (see fio. 2 and 1) were fixed which lead to a ballistic galvanometer. Between these points of attachment the current can be cut through under helium, by pulling up by a thread a bronze loop provided on the inside with a knife edge at m (see figs 3 and 1. Figs 1 and 2 give 1) Disregarding the existence of threshold-values of current and field and consi- dering that, below these, supra-conductors add up algebraically without appreciable loss the inductional impulses which act on them in the course of time, two points of view may be very simply contrasted in connection with the experiments so far described on the production of currents persisting for a long lime. The first is analogous to that taken up in Weser’s explanation of diamagnetism. In this case we deal with supra-conducting circuits which are currentless outside the magnetic field. By bringing these into a field currents may be oblained which persist as long as the field remains unchanged. But when the field disappears the circuits become again free of current. In this manner a good imitation is obtained of diagmagnetic polarisation. The other point of view may be called the antilo- gon of that of Weser. We provide in a magnetic field’ supra-condueting cireuils which are free of current. When these circuits are brought outside the field, they show a current persisting for a long time. Outside the field they imitate permanent magnets. It, must, however, not be lost sight of, that. this imitation is in so far incomplete, as when the circuits are brought back into the field, they return to the currentless condition. S18 a combined view of the experiments of sees tions 9 and 11). The thread runs through a 2 Sk eee mee 4 tube, the lower part of which is of glass and can be moved by means of a rubber-tubing calles attachment at the top of the apparatus (fig. 1). The coil was cooled to 2°.4 K. in a field of 200 gauss by helium evaporating under reduced pressure. The current was again produced through induction by removing the field. When the compass needle with the com- pensation-coils was arranged, as before, beside the cryostat, a moment corresponding to a current of 0.36 amp. was registered. The observation was continued for an hour, in which the diminution of the current in 45 minutes was within the limits of probable error of the measurement (2°/,); after this the circuit of the coil was cut through. The (| needle of the compass fell back to a deviation | that corresponded to a current of 0.05 amp. in the coil. The ballistic galvanometer (with a negligible self-induction and with 2000 2 in Fig. Fig the circuit) showed an electro-kiretic momentum 2. 3. Lj of 300000, from which follows with L—10', that a current of about 0.8 amp. flowed in the coil. The remaining moment is again the same fraction of the principal effect as was observed previously, it was extinguished as soon as the coil was pulled up above the liquid helium. The experiment proves conclusively, that a current does really flow through the coil. § 10. Further consideration of the momentum produced in the coil, when the circuit is not closed. Persisting Foucauiy-currents. In the previous experiments the question arose in how far magnetic properties of the frame of the coil, which developed at the lowest temperatures had an influence, and whether a part of the moment that remained, when the coil, without the ends being connected, was cooled and exposed to the field, was due to windings which were short-circuited. For this purpose first of all a tube of brass, exactly like that used as the frame of the coil, was cooled in the field. It showed no residual magnetism. To get further light on possible short-cireuits in the coil Phx, after it had been shown that cooling in liquid air did not alter ot Proceedings Rayal Acad. Amsterdam. Vol. XVII. 51 iis moment, a new coil of 650 turns was wound, in which the possibility of short-cireuiting was excluded by insulation of the windings by picein ani paper. It is true that the magnetic properties of these materials are not known, but from the extinction immediately above the boiling-point of helium of persisting current which was found in the course of the experiments it is almost certain, that the phenomena are entirely due to the lead. It was ascertained that this coil was superconductive, which was a welcome result also for the reason that the wire had been manufactured by compression, and this process gives a much better guarantee of getting the same product again by using the same method, and therefore of obtaining beforehand the certainty of the wires prepared in this way being supra-conducting. In making the experiment with 200 gauss at 2°.4 K. a residual effect of the same order as with Pbx7;; was found, but smaller. The principal current was 0.5 and the residual current 0.020 Amp. It becomes probable, when these figures are compared with those found with Pbx,7,, that in the latter there really is some short-cireuiting, but there is also apart from the effect due to the short-circuited windings a moment caused by the lead. It seems as if in the mean time this may be attributed to circular currents in the lead of the wire, which are possible owing to the wire having a certain thickness. We must distinguish in the wire between an inside which is turned towards the axis of the coil, and an outside. In the wire, even when the circuit is opened, a current arises, in which the electricity passes along the whele length of the windings on the outside of the wire (that is not closed in itself), in order to turn round at the one end of the wire and go back along the internal side. With induction in the closed cireuit this current is superposed upon the mean electric movement in the cireulating current, so that in the wire there is say a stronger current on the outside, and a weaker on the inside. If by means of a galvanic cell a current is sent through the wire, the same phenomenon arises through the action of the field of the current itself. We are here evidently dealing with persisting Foucaun- currents '). § 11. A supraconducting key. In the experiments so far de- seribed the supra-conducting closing of the conductor tested for supra- conductivity was obtained by melting the two ends together. Now 1) Several of the well known experiments by Exinu Tuomson with alternating eurrents could also be made with parallel currents and supra-conducling experi- mental objects. 517 that these experiments had proved that a current generated in a circuit which is supra-conducting over its whole length, continues without electro-motive force, we could investigate in how far an electric contact interposed in an otherwise supra-conducting circuit, measured by the amount of conductivity of supra-conductors, might be considered as having no resistance. The immediate cause of this investigation was a suggestion made by my colleague Kunnnn, whether the current the relaxation period of which was to be studied, might not be obtained in the coil by short-cireuiting. I thought then, that the transitional resistance in a contact to be manipulated under liquid helinm could hardly be made small enough for this purpose. The transitional resistance of a stop- contact treated with all due care at ordinary temperature is not likely to be less than 0,0001 2, which is still 100,000 C.G.S. while the micro-resistance of the coil itself is only 37. It has now been found, however, that transitional resistances such as we are con- sidering can become very small at low temperatures. A quite moderate pressure, between two pieces of lead appeared to be sufficient for the purpose. The arrangement is shown in Fig. 2. The small lead plate p, provided with three small cones direeted upwards and connected with the coil through a spirally-wound part of the lead wire which acted as a spring, is attached to a thin rod (partly formed of wood) and was pressed against the block soldered to the glass tube by serewing up the rod, the force being accurately regulated by means of a spring (see top of fig. 1). The tube is provided with a number of side-openings to prevent the very much intensified heat convec- {ion (caused by resonance phenomena) which occurs in tubes closed at the top when the bottom is at a very low temperature, and which would lead to excessive evaporation of the helium. Ry means of this simple key we were enabled to arrange the following experiment. To each extremity of the windings of the coil two wires were attached (fig. 1 and 2). By means of the one pair ac a current can be sent through the coil. The other pair 6 can be con- nected toa ballistic galvanometer. Moreover the two ends are connected to the two parts of the supra-conducting key. With the key and the galvanometer open, a current is sent through the cooled coil, in the neighbourhood of which the compass-needle has been mounted. The coil is then closed in itself, which gives no change in the deviation of the needle. One ean then convince oneself as long as one likes, that the side-current, which in ordinary cases is imme- diately extinguished, remains unaltered in the supra-conductor; the galvanometer connection is then closed, which also brings no change 34% S18 in the current, and if thereupon the current connection is opened this is accompanied by a throw of the ballistie galvanometer in the circuit of which the current is instantly extinguished and by a return of the needle of the compass into the position which it would also take up, if the current in the closed coil had been generated by a magnetic field equal to that of the current itself. The continuation of the movements in Maxwenr’s mechanism, when it has a supra- conductor as carrier, is demonstrated by this experiment with equal clearness and simplicity. § 12. Combination of parallel currents into one of greater strength. In trying to make the same experiments with mereury that we have made with lead, it will be necessary in so far to change the experiment, that one winding will be sufficient. This might be got by. freezing mereury in a capillary tube returming in itself with an expansion head (like our other U-shaped mereury resistances). The chief questions then are 1) if with a conductor of as large a section (keeping for the present to the circular form) as would be necessary, with a view to the threshold value of current density, in order to get an action comparable to that with the lead coil, the threshold value of current density — of which as in N°. 183 if is assumed that it is determined principally by the current density —— does not undergo a considerable diminution in consequence of the larger section, as some considerations in N°. 183 would make us fear, and 2) if we ean reckon with the microresidual resistance as an ordinary resist- ance even for such a completely different section as that for whieh it has been determined. An inducement to try the experiment imme- diately with a lead ring*) was a remark by my colleague Enreneest, 1) f am glad to mention here that Mr. J. J. Taupin Caasor of Degerloch (Wiirttemberg) shortly after my paper on the disappearance of resistance in mer- cury and, as I found afterwards, only acquainted with my result, that the resist- ance of gold and platinum in an absolutely pure condition would probably disappear allogether at extremely low temperatures, communicated to me a number of suggest- ions regarding the condition into which meta!s pass below this temperature and which he would like to be considered as a distinct “fifth” state of aggregation. Amongst these suggestions was the following: “if a ring (of gold) is brought to the condition of absolutely no resistance (in helium), an impulse (viz. by im- duction) will be sufficient to produce a permanent current, which will make the ring into a magnetic shell, as long as the temperature of the metal remains below a certain critical value”. By critical value was meant — nol the vanishing point as discovered afterwards — but the temperature characteristic of each metal at which, according to my earlier views, the resistance of the pure metal would become zero independently of the current-strength. The idea, however, underlying this speculation — which was further developed by supposing the cooled ring to 519 that the experiment could be made equally well with the windings “parallel” as it had been made with the windings in “series”. A calculation (by estimation and further proceeding in the same way as with the coil) about the experiment with a lead ring of an internal radius of 1.2 em. of a thickness of 0.38 em. and of a width of 0.35 em. and assuming that the threshold value found for the thin lead wire would also hold for the thick ring, showed me, that it might sueceed very well.’ This proved to be the case. The current of 320 amp. that was registered in the ring remained constant for half-an-hour to 1°/,, hence the current density of 50 was in this experiment not much smaller than it had been in one of the experiments with the coil of lead wire, viz. 49. This may for the present be regarded as a confirm- ation of the supposition that the thresbold value of current strength of a conductor is mainly a threshold value of current density for the material of the conductor. be subjected to a magnetic field which was to be removed afterwards — was also applied in my experiments for the purpose of obtaining persisting currents in supra- conductors, and in the above last experiment actually with a ring as the conduet- ing circuit. At the time I was so much occupied with the investigation of the peculiar laws of electric conduction in mercury below the vanishing-point and of the degree to which currents miglit be realised in resistanceless circuits without electromotive force, that I had not yet attacked or was able to fully go into the problems relating to currents to be generated in closed supra-conductors by induction (amongst which proklems that of the imitation of diamagnetic polarisation was an obvious one). Still Mr. Taupin Cuazor’s letter was the cause of my coming even then to the conclusion, that in order to be able to obtain persisting currents outside the magnetic field by induction, an artifice based on the peculiarity of supra conductors was required. As such I then found, that the cooling which is to make the conductor supra-conducting is not applied, until the conductor is in the field which is to be used for the induction. Afterwards it was found, that by utilizing the knowledge of the threshold values of current and field circumstances may be realized, in which a permanent current may be obtained outside the field by induction on a circuit which has been made supraconducling by cooling before the field is applied. 520 Physics. — ‘“/urther experiments with liquid helium N. Waut-effect and the change of resistance in a maynetic field. X. Measure- ments on cadmium, graphite, gold, silver, bismuth, lead, tin and nickel, at hydrogen- and helium-temperatures. By Prot. H. Kamerrtincn Onnes and K. Hor. (Communication N°. 1424 from the Physical Laboratory at Leiden.) (Communicated in the meeting of June 27, 1914). § 1. Method. The method was the same as that used in the measurements of this series by H. Kamernincn Onnes and BuckMANN ‘ef. Comm. N°. 129a and others). The notation is also the same as in the previous papers. As regards the HA.t-effect, we used both the method in which a galvanometer-deflection caused by the effect’ is read and the compensation-method, in view of the fact, that the latter, althongh in general to be preferred, as it allows the elimination of various disturbances, is very troublesome, when small effects have to be measured. The differential-galvanometer used was of the Kervin-pattern with a volt-sensibility of 5 >¥ 10-8 ; it was iron: shielded and was mounted according to Jurius. As to the resistance measure- ments these were partly performed in immediate connection with the determination of the Haxt-effect, in which case the resistance of the plate used for this purpose was at the same time measured, partly (by means of the compensation-apparatus) with wires which were wound on thin sheets of mica and could be placed either at right angles to the field or parallel to it, the latter specially with a view to investigating the considerable difference between the trans- verse and the longitudinal effect, which difference develops specially at helinm-temperatures. § 2. Sismuth. In accordance with frequent practice (e.g. by KAMERLINGH ONNES and BrckKMANN) we used this substance in the form of pressed plates. The peculiarities in the resistance observed by Srrewntz with conductors of compressed powder — although occurring also in our plates at higher temperatures were not observable, when the plates were cooled below 0° C. The plates which served for our investigation were pressed in a steel mould and heated to about 200°C. in an electric furnace. When made in this way the granular structure was still clearly observable with a magnifying glass. The plate ip; was made without special precautions; with plate iyz, the metallic powder 521 was specially dried before moulding it. Diy; gave an abnormally high temperature-coefficient at higher temperatures and even after 36 hours’ heating had not yet attained a constant resistance. The metastable condition which according to Professor E. Conrn is peculiar of most metals as mixtures of different modifications manifested itself also in our experiments. The plates after being heated in the electric furnace to 60° or 100° C. showed some dif- ference as regards resistance and Hatt-effect after cooling, with the further peculiarity, that this change fook place, although no change in the specific gravity affecting the second decimal place could be established. The results are contained in tables I and II. TABLE I. ; | Biy,- | H —R Resistance —R | Resistance | } | | | T=2899° K | T=20°5 K | | 2400 Gauss | 7.71 | 2.5°10-3 Serato 2420, 42.13 4800, 6.68 Is 22385958 i200); 4 6.02 35.44 | | 9650, | 5.37 | 3862 | | | if 11800, | 29.76 | 1.1°10-3 | | 12000, 4.65 | 3.1°10-3 QO) | TABLE Il. Biyyy H —R Resistance —R Resistance | T=289° K T=20 K 2420 Gauss 10.57 2.4.10-3 80.03 3.10—-4 4800, 9.48 | 78.31 1200'= 5 8.11 | 75.15 9650, 7.26 72.51 | 12000, 6.28 3.2.10-3 | 70.82 | 1.6.10-3 522 § 3. Hant-effect in graphite. The great change in the properties of graphite through even small admixtures appears clearly from the fact, that with different kinds of graphite the temperature-coefficient of the resistance may even differ in sign. The material we started from in our experiments was fine graphite- powder, such as is used in electro-plating; the powder was first treated with acids and alkali and carefully dried; the forming of the plate was again carried out in a steel mould. The electrodes which gave some difficulty at first were finally contrived in the following manner: the powder was provisionaily moulded to a plate under comparatively low pressure, the stamp was then lifted off and six small pellets of solder were laid on the plate, after which a high pressure was applied. By trial we succeeded finally in obtaining suitable plates of */; mm. thickness with six point-electrodes of about ‘/, mm. diameter, penetrating through the whole thickness of the plate. The influence of insufficient drying of the powder was very marked; such plates, as did not come up to standard as regards drying, did not reach their final resistance until the current had gone through for 6 seconds. The following table contains the results. It may be specially noted that the ftemperature-coefficient is positive and that the Hats-effect falls strongly from 20° K. to 14° K. TABLE III. Graphite. H 290° K 20°.5 K 14°.5 K aes ee +R: +R: +R: | 4800 Gauss | 0.68 3.4 1.42 6000, 0.68 4200: te 3.39 8400, 0.68 1.52 96005 aa 2.81 11800, 0.74 2.22 1.52 § 4. The Haut-ejject in cadmium. Two eireular rolled-out Cadmium- plates of 1 em. diameter were experimented on, The results are found in the following table. TABLE IV. | Cadmium. | areas | eae | : | | H | 2O0OT Ke se 20e owke | 149.5 K | + R: \Neeeesce | +R: | 3000 Gauss | 13.1104 | 2600 ye 4.6.10—4 | 4800 ot, tt e202 OSA eens Oe 6000, 6.3.10—4 | 7200 + 20.6.10—4 | 23.4.10—4 | 3400) 5.9.10-4 | 9600 : 19.6.10—4 | 22.3:10—4 | | 11800 " LWie6.1054> | 191105255) | 12000 4, | 5.5.10-4 | | § 5. The Haut-ejiect at helium-temperatures. The method was the same as in the previous measurements. To check the results, measure- ments were made both with the compensation-apparatus and with the differential-galvanometer. Five different plates were experimented upon in the helium-bath. These were chosen so, that they could be regarded as representatives of metals for which the Hat-effect is of a different type. Each set of six wires from the six electrodes of one plate was completely separated from the other sets in the cryostat. The following plates were investigated. 1. A tin and a lead plate: both metals are supra-condueting at extremely low temperatures. Lead remains supra-conducting up toa considerable threshold-value of current. It may be added that both are diamagnetic: as pe Haas has shown, the diamagnetic properties are of great importance for the Ha.u-effect. At hydrogen-temperatures the Hatu-effect is still so small, that it escapes observation. It was found that at 4°.25 K. both with tin and lead the effect can be very well measured, when the field is so high, that ordinary resistance is generated in the metals. As long as the field is low enough for the metal to remain supra-condueting, the Haut-effect, like the ordinary resistance, disappears. 2. A silver plate, as representative of the group of metals for which at the ordinary temperature the Haz1-coefficient is of the 524 TABLE V. Measurements in Helium. H R | 1. Sr (tin) | Lane acs KK | 11300 Gauss + 2.6.10—5 Owe COn + 9.8.10—5 2. Pb (lead) A. AZO 300 Gauss < 6.10-5 1000, < 2.10-5 5000, -+ 0.8.10—4 11300, + 1,8.10-4 BIO OR 300 Gauss < 6.10-5 11300 Si, + 1.3.10—-4 3. Ag (silver) a. T={4925 K 11300 Gauss 16.10—4 b. T=2°S K 13000. 16.10—4 4. Ni (nickel) a. T= 4925 K 1300 < 5.105 11300 <— Wet0=5 Ox i= 228K 11300 <<) OSs 5. Bi TANK | 1000 Gauss | 86.3 5000, in = | 84.2 11300, 85.7 order of magnitude 10—4; silver is diamagnetic and does not become supra-conducting at helium-temperatures. As appears from the table, it was found that with silver also the Hati-effect increases, when the temperature falls to 4.925 K. At still lower temperature it does not show any further change, no more than the resistance without a field. 3. A bismuth-plate B/y7,;, moulded from electrolytic bismuth- powder. Bismuth has a very high Hant-effect at hydrogen-temperatures and the change from 20° K. to 14° K. is still very small. It is the strongest diamagnetic metal. The table shows that below 14o K. there is not much further change in the Haut-effect. From 71 at 20° K. & rises only to 85 at 4°.25 K. 4. A nickel plate as representative of the ferro-magnetic metals. With nickel at higner temperatures the Hatt-effect shows a tendency to saturation owing to the magnetisation of the metal (Comm. No. 129, 130, 132). At hydrogen-temperatures the effect is still easily measu- rable; at helium-temperatures it disappears, although the resistance of the plate is still considerable. Probably this is connected with the fact, that notwithstanding the already fairly considerable field the magnetisation of the nickel is still very small. The results are collected im table V. (zie p. 577). § 6. Change of the resistance in the magnetic field. It was found, that specially at helium-temperatures this change is very con- siderable, but that at 20° K. also it is still quite well measurable. In general there is a difference between the longitudinal and the trans- verse effects, which begins to show itself especially clearly at helium- temperatures. We shall give our results in the form of curves (figs. 1 to 6) on which the numerical values may also be read with sufficient accuracy by using the scale-values indicated in the figures. So far thé meas- 28. co T i if [ieee (a 3 T Bea 29% + ———_-|—_ ee ee = =a | a eo = — A | fore os eee eae { = a 4 |} =e ie a | | 191.1 ad lie 245 = = == =k a 2000 yoo. dan C000 10000, moo (yams. 526 urements both at hydrogen- and helium-temperatures have not gone beyond 12000 Gauss. They will afterwards be further extended to higher field-strengths especially at hydrogen-temperatures. 40S 127 "7 Figs. 1 and 2 contain the results for the resistance of lead and tin in a magnetic field. The difference between the longitudinal and - > , . aot7s syiolizitce Caio viv 1091. 1 Sa eral! aoz23s. }— oO £000 4000 do0a. e000 10000 12000 > Gauss Fig. 3. transverse effects was not more than the errors of the measurements. The abscissa gives the ratio of the resistance to that at 0° C. 2 Goss ] T | > . pian aos} 4 MNeoistance Mla tisrii ya 00381 aos4 }— ° yamss 527 Fic. 3 and 4 represent the longitudinal and transverse effects o | to) for cadmium and for platinum. The abscissae give directly the resistance in Ohms. as a Ja toa 190 100 t30 300 Dt Fie. 5 and 6 show the results for graphite, Fig. 5 the dependence of the resistance on ihe temperature, fig. 6 the dependence on the magnetic field. We have further made measurements on the resistance of a Bicgane | 1 ak el cy wat pbite. = ieee e000 wove. 1x00 a) Fig. 6. pice plate of not-purified graphite. These are not concluded, however, and will be published later together with measurements on polarisa- tion-phenomena which may possibly show themselves with pressed graphite. 598 Physics. — “Measurements on the capillarity of Viquid hydrogen”. By H. Kamerninch Onnes and H. A. Kuypers. (Communication N*. 142d from the physical laboratory at Leyden). (Communicated in the meeting of June 27, 1914). For the determination of the capillary constant of liquid hydrogen in contact with ifs saturated vapour the method of capillary rise was used. The apparatus are in the main arranged in the manner as used for other liquid gases in Comm. N°. 18. On plate IA of Comm. N°. 107a@ may be seen that part of the apparatus which serves to condense the gas in the wide experimental tube (fig. 1), inside which is the eapil- lary ; for this purpose the tube of fig. 1 is sealed — - Sty. in at g,. The radii of the sections of the tubes were found by calibration with mercury as follows : radius of the capillary inside 7 = 0.3316 em 3 Sere, 3 outside 7, = 0.0801 em ¥ » >», surrounding tube inside = 0.554 em Measurement of the capillary rise. The reading of the ascension gave some trouble as it had to be made threugh a number of glass vessels and baths. The rise was measured with a eathetometer ; to test the accuracy of the readings they were taken one {ime on a millimetrescale which had been etched Fig. 1. on the capillary and another time directly on the scale of the cathetometer. When it was found, that there was no difference between the heights obtained in the two ways, they were afterwards only measured by means of the scale of the catheto- ineter, because, when the eryostat was filled with the different liquid gases, the divisions on the capillary were difficult to distinguish owing to the rising gas-bubbles in the liquids. Temperature. The temperature was deduced from the pressure of the vapour in the hydrogen-bath using the vapour-pressure curve (H. Kamerninco Oxnes and W. H. Kersom, Comm. N°. 137d. table on page 41). Observations. The heights measured and the corresponding tem- peratures of the hydrogen are contained in the following table, 529 Repeated measurements show, that the accuracy of the reading of the rise may be estimated at 0.002. TABLE I. | Temperature in | Rise KELVIN-degrees | in cms, [is A See See 20.40 | 1.616 18.70 1.794 17.99 1.869 16.16 | 2.064 14.78 | 2.209 The observed heights (4) have to be corrected for the curvature of the surfaces by means of the following formulae : (1) the correction . ib s . . for the meniscus in the narrow tube is a ‘). (2) the correction for the ring-shaped meniscus is (according to VerscHarreiT Comm, N*. 18). : ipa 2 w=(1 -f ar (k =. > (R—?,) For this correction the height of the ring-shaped meniscus, as the minor axis of the elliptical section with a meridian plane, is required to be known. With the illumination used this height could not be measured accurately. Afterwards for further correction we hope to be able to determine its value by special measurements: in the mean time the section was assumed to be circular with sufficient approximation. The corrected values are given in column 6 of table II. When the capillary rise is plotted as a function of the temperature — fig, 2 —, a straight line is obtained. The constants determined from this line give the formula H= — 0.1124 7 + 40.44. This formula gives H=0 for T'y7=0 extray. = 35.98 K. Assuming the critical temperature to be 7), —= 31.11 1 (mean of 1) Laptace, Méc. Cél. Tome X, Supp. § 5, Paris 1805. id. , Oeuvres Tome IV, p. 415, Paris 1845. Attan Ferguson, Phil. Mag., p. 128, (6) 28, 1914. 530 oie 24 aS 35 | \ R 2.2 - x NN \ \ 29 XS : ® 19 < Ht 1,8 7 1 he J I = ‘ 1S 6 ” 8 19 £0 % - Fig. 2. Drwar, Oszewski and BuLir)') it is seen, that the formula, as was to be expected, does not hold up to the critical temperature and that the curve which gives the dependence of // on the temperature has its concave side towards the temperature-axis. The difference T'H=0extvap.— 7, for hydrogen amounts to T 77=0 extrap. — Lito eOits If Vry—oextrap. — 77. is divided by the critical temperature the I 4 | 3.87 positive value = 0.125 is obtained. For methyl-chloride*) and ethylether*) similar values are obtained *). Surface-tension. From the capillary rise the surface-tension yw, is found by means of the following formula : 2, 1 1 i NET vr (- — az) (tig. a! Ovap.) ANGE R =n The densities for liquid hydrogen are taken from the observations by H. Kamerninca Onnes and C. A. Crommetry (Comm. No. 137). 1) F, Burnie. Physik. Zeitschr. p. 860, XIV, 1913. *) According to measurements by J. VeRSCHAFFELT; comp. A. v. ELDIK, Comm. N°. 39, p. 14. 3) E. C. pE Vries, Comm. N°, 6. 4) The corresponding figures (deduced, however, from not-corresponding tem- perature ranges) are 9.038 and 0.017 respectively. 531 For the calculation of the vapour-densities use is made of the second virial coefficient, as deduced from the measurements by H. KamErLiIncH Onnes and W. J. pe Haas (Comm. No. 127c). | | { { | | 7 = 3332 3 2 dD — eet SS eS) = l SS. S25) Oi S2' Sk 1S | & St WRehit hatte peices West) panel eae taal ate > rec ae @& |@&a 8 BER B® 6 & = = Ss OF ITD COR Sn ecg i i ie = QIN EN AW I a con cd oe eal o | S || 10 16 0 “a oa yen Cy SG Nil er eS) | lmaeterenatrenentroy “al hse alse 1 . || eres AS | © o : Gere eel Gel oh ev Tse) Kat) &. Seo) St ON TO Os IO ze S wT oO = = im 10 4 CO = O) 00) Oecd Pe SE oH o SS 1S) Qs ies)! Wo o aa 4 LeSieg USaS ly ile Lah lah sal Soe — oa oS | faa) = —— < | 19 [= — Cy oy OT = Ste NO AOy a SHC cor =) (00) ee Wi eS ES ey SS Gai Ge) om NNON NN i ov o | <= ro IN A tts et C= = Sn | eens Us CCR CON SHE IOI COMO) a QA | a Se Se Se ea BSB Se 23) 3 S i>} SQ | | — Ore | So | met |S) ba ee ee 2 MS) Ss SS SSS SS m 3 2 oO a oS ie] CO Tos oy sta a = =- = = &® © & DB S OO OR) 00 OS a ic | J= ae we ae =z nna | 4 | Qa, Ol any: 19 & io ee OC &) © ey ce) 3 {Vibe Seay ites Sines eee = =) te fey ee) Te ke N A AN Hee me Oe With these data the values of yw, in table II are calculated. Under O—C are given the differences between w, ops, and values of yp, caleu- lated from vAN per Waats’ formula w= A(1—p2 where Proceedings Royal Acad. Amsterdam. Vol. XVII. 532 A = 5.792 B= 0.9885 From the value found for B it appears, that y, as a function of T is nearly a straight line. The constant in Eérvés’ formula for hydrogen deviates considerably from the value 2.12, found by Ramsay and Surrips ') as the average for a number of normal substances. In Table ITI the values of ps for a few of these substances, together with those for some liquid gases, are collected. As observed by KameriincH Onnes and Krgsom (note 3881 Suppl. No. 23), normal substances form a series in this respect, on the whole progressing with the critical temperature (although with deviations which may be ascribed to particularities in the law of molecular attraction, e.g. with oxygen). TABLE Ill. | Ethylether ) Pi ey Benzene 2) 2.1043 | Argon 3) 2.020 | Nitrogen 3) 2.002 | | | | Carb.monoxide3) 1.996 | Oxygen 3) | 1.917 _ Hydrogen | 1.464 A calculation of the constant 4’ in Ersrer’s formula ‘*) dw, 2 ip — LF jos Sk Api RL i(« dT ) "Tig. I Oe AAG for hydrogen gives 7.34 < 107 The fact, that hydrogen appears to have a considerably higher value of 4’ than that calculated by Erystrein for benzene, might, in view of the theory underlying the formula, indicate, that the radius of molecular action is larger for hydrogen molecules than for sub- stances like benzene. \) J. chem. Soc. 63 (1893); ZS. f. physik. Chem. 12 (1893). *) Ramsay and Surexps ZS. f. physik. Chem. 12 (1893), 15 (1894). 8) Baty and Donnan, Journ. chem. soe. 81 (1902). 4) A. Etnstern, Ann, d. Phys. 4. 34, 1911. 533 Chemistry. — “The system: copper sulphate, copper chlorid, potas- sium sulphate, potassium chlorid and water at 30°”. By Prof. F. A. H. Scurememakers and Miss W. C. bE Baar. 1. Introduction. In previous communications ') we have discussed the quaternary systems: Cu SO, — Cu Cl, — (NH,), SO, — NH, Cl — water and CuSO, — CuCl, — Na, SO, —NaCl — water Now we shall discuss the system Cu SO, — Cu Cl, — K, SO, — KCl — water, which we have examined at 30°. As solid substances occur at 30°: the anhydrie salts: K,SO, and KCl, the hydrates: CuSO,.5H,O and CuCl, . 2H,0, the doublesalts: CuSO,.K,SO,.6H,O and CuCl, : 2KCI. 20,0. Further a peculiar salt exists with the composition : Cus@, kK Cl or K. sO, Ca Cl, with or without one molecule H,O, while sometimes as metastable solid phase a salt with the composition : 2CuSO, . 3K,Cl, . H,O has occurred. In fig. 1 the equilibria occurring at 30° are represented schematic- G. SO, 222 (1911) and Zeitschr. fiir Phys. Chemie 69, 557, (1909). 35* 5384 ally, the sides of the quadrangle have been omitted, only a part of the diagonals with their point of intersection W is drawn. Fig. 1 is not the representation in space of the equilibria, but thew pro- jection on the quadrangle. Before discussing the quaternary equili- brium, we will first consider the four ternary equilibria. 2. The ternary equilibria. a. The system K,SO,— KCl— H,O. Only K,SO, and KCl occur as solid phases; in fig. 1 the satura- tioneurve of K,SO, is represented by Ag and that of KCl by /g. Consequently point ’ represents the solubility of K,SO,, point / the solubility of KCl in water; point g is the solution, saturated with the two salts. b. The system CuSO, — K,SO,— H,0. This system was examined already formerly *); as solid phases occur K,SO,, CuSO,.5H,O0 and the doublesalt CuSO,.K,SO,.6H,0. The isotherms of 80° and 40° are determined experimentally ; that of 30° is represented schematically in the figure. The saturation- curve of K,SO, has been represented by /z, that of CuSO, .5H,O by ak and that of the doublesalt by 47. When we represent this doublesalt in tig. 1 by the point D,.,., then the line WD,.,., intersects the curve 7k in a point 7. The doublesalt is, therefore, soluble in water without decomposition; its solution saturated at 30° is repre- sented by 7. The following is still of importance for the investigation of the quaternary system. When we heat an aqueous solution of K,SO, + CuSO, above 50°, a light green salt is separated from the solution. Mrrrpure found for the composition of this salt: 4CuO . K,O .. 450, . 30,0, while Brunner’), who examined first this basical salt has found four molecules instead of 38 molecules H,O. c. The system CuSO, — CuCl, — A, 0. Also. this system was investigated formerly *), as solid sub- stances occur: CuSO,.5H,O and CuCl, .2H,O. In fig. 1 ab represents the saturationcurve of CuSO,.5H,O and cb that of CuCl, . 2H,0. d. The system CuCl,— KCl — H,O. In this system of which the invariant (P) equilibria were 1) P. A. MeerpurG. Gedenkboek J. M. vAN BEMMELEN, 356 (1910). 2) BRuNNER. Pogg. Ann. 15 476 (1829). 3) F. A. H. ScHREINEMAKERS. These Communications l.c. and Zeilschr. Phys. Chem. 69 557 (1909). 5385 examined’ formerly ') oceur as solid phases: KCl, CuCl, . 2H,0, CuCl, . 2KCl.2H,0 and CuCl, . KCl. This last salt, however, occurs only above 57°, so that, at 30°: KCl,CuCl,.2H,O and CuCl,. 2KCl.2H,O only occur as solid phases. The isotherm of 30° is represented schematically in fig. 1; fe is the saturationcurve of KCI, cd that of CuCl, .2H,O and ed that of CuCl, .2KCl.2H,O. When we represent in fig. 1 this doublesalt by D,.,.,, then the line WD,.,., does not intersect curve ed, but curve fe. This doublesalt is, therefore, at 30° not soluble in water without decomposition, but it is decomposed with separation of KCl. This isotherm of 30° was determined already formerly *); we have also still determined some points. 3. The quaternary system. At first sight we may think that the examined system is built up by five components; as, however, between four of these substances, the reaction : Cul, > Ke SOp a KCl CusOes = 2 D oecurs, this is not the case. In view of the above-mentioned double-decomposition (1) we shall represent the equilibria with the aid of a quadrilateral pyramid, the base of which is a quadrangle. The four anglepoints of this qua- drangle indicate the four substances: CuSO,, CuCl,, K,SO, and K,Cl, and in this way that the two substances, which are in reaction (1) at the same side of the reaction-sign, are united by a diagonal of the quadrangle. Perpendicular above the point of intersection W_ of the diagonals, is situated the top of the pyramid, which represents the water. At the examination of this quaternary system we have always remained below the temperature, at which the basical salt 4Cu0. K,O. 450,. 3H,0 is separated. If this had not been the case, the reaction : 4CuSO, + K, S50, + 4H,0 2 4Cu0. K,0. 480,. 3H,0 + H,SO,. (2) would have occurred. We should then have had to examine a quinary system, in which reactions (1) and (2) occur. As the quaternary solutions saturated with a solid substance, are represented by a surface in the space, viz. the saturationsurface, we have seven saturationsurfaces. We find their projections in fig. 1 ; 1) W. Meyeruorrer. Zeilschrift fiir Phys- Chem. 0 336 (1889) 5 97 (1890). 2) H. Frutppo; not yet published. 536 from this it is apparent that six of these surfaces are side-surfaces and that one is a middle-surface. aklm6 is the saturationsurface of the CuSO,. 5H,0 ClO eee > 5 CU CIE ALG adnoe. ae i 5 on POW). 2KCII2AE® eopg ie AH ace 50 2 KCl GG Cl es 4 Sy Ke SO, iqlk » £ Re op OW SO KE ISO) .(Blal-(O, pqlimno,, 5, 3 Rae es 58) In order to get a better view, in the figure is indicated on each satura- tionsurface the solid substance, with which the solutions are saturated. For the sake of abbreviation we bave called Cu SO,. 5H,0 = Cu,, Cu Cl,. 2H,0 = Cu,, Ca Ch. 2KCI. 2H;0 = D..,., and CuSO; Kes@2 GHEO Dg : The middle-surface pq /mo is the saturationsurface of a salt, which we have represented by J. In order to find the composition of this salt we have applied the rest-method, viz. the analysis of the solution and the corresponding rest. From numerous definitions it follows that this salt has the composition : CwsO Kk Ce Ke son CalCit— Ds or CuSO,. K; Cl, 8,0 =K,S0,1Ca Cle HO ae Some determinations pointed viz. to D,, others to Dx, again others to a mixture of D, and Dx, so that in the region pqim no (tig. 1) perhaps the two salts D, and Dx occur. The probability that more than one solid salt occurs in this region, is enhanced by the following observations. In some eases the solid substance was precipitated after shaking (which lasted sometimes a month or longer) within some hours as a greenish powder, in other cases there was formed a greenish or blue-greenish paste, which after days did not yet settle, but stuek to the sides of the shake- bottle. In the first case we could easily remove a large part of the mother-substance by suction, in the latter case this appeared practi- cally impossible. From all this it is. apparent that in the saturation- surface (fig. 1) indicated by D different salts may occur, two of which have the composition D, and Dx. [t follows, however, from the position of the solutions saturated with D, or Dx in the region of fig. 1 indicated by D, that one of these salis must be metastable with respect to the other, perhaps they are both metastable with respect to a third, which we have however not found in onr investigation. 537 In order to get the solutions of the saturationsurface D saturated with solid salt, we put together the substances in such ratios that the solid substance must be formed in one case from Cu SO, .5H,O + KCl, in the other from Cu Cl,. 2H,0 + K, 50,. In both instances now D, then Dx was formed. In some cases also occurred as solid phase a double salt of the composition : 2Cu SO,. 3K, Cl,. H,0 =D, Later, however, we did not succeed again in getting this salt, but D, or Dx, appeared instead. The salt D, will therefore, very probably exist in a metastable condition only. On account of the uncertainty with respect to the substance D, we will further describe the equilibria as if in the region p q/in no occurs only one solid substance D. When in this region more solid phases may occur in stable condition, then the necessary changes in this region will have to be inserted. The intersectinglines of the saturationsurfaces represent the quater- nary solutions, which are saturated with two solid substances, con- sequently the quaternary saturationlines. The limit-lines of the saturationsurfaces on the side-planes of the pyramid form the ternary saturationcurves of the four ternary systems, which have already been discussed previously. The quaternary saturationcurves are the following : gp the saturationline of K, SO, + KCI COR ss a 9 it, SO, ce Dyas, eles paous » Sa Dic. bm ,5 3 » Cu, + Cu, dn the saturationline of Cu, + D,.,., BIO) os i iy KOh = Ding OU + +5 5 K,SO,4+ D Gl ne ‘5 5 D4 ieee is 7 Cle oe 3 » Cuy +D WiOw 5 x oe Diet sD OP os be + ACE tp The first six saturationlines are side-curves; each of these has an end on one of the side-planes of the pyramid. The last six satura- tionlines are middle-curves; each of these has its two ends within the pyramid. 538 The points of intersection of the saturationsurfaces represent the quaternary solutions, which are saturated with three solid substances consequently the quaternary saturationpoints. In each of these points three quaternary saturationcurves come together. In the ternary saturationpoints, which we already discussed previously, two ternary and one quaternary saturationcurve come together. The quaternary saturationpoints are the following: p saturated with K,SO,-+ KCl + D q - » K,SO,+D,.,..> D l 7 » Cu, © = Dew dD m 3 3. (Cu; ) =eiCiss ap n 5 5 Olu. + D,.,., + D Onan ICH SE Ds 25 1D As it is easy to see from fig. 1, in presence of solution can exist: | K, SO, by the side of: KCl or Dor D,.,., but not by the side of: Cu, or Cu, or D KCl by the side of: K, SO, or D or D,.,.,. but not by the side of: D,.,., or Cu, or Cu, ig-, Dy the side of: KCl or D or Cu, but not by the side of: K,SO, or D,.,., or Cu,. Cu, by the side of: Cu, or D or D,.., but not by the side of: KCl or K, SO, or D Cu, by the side of: Cu; or Dior D;.., but not by the side of: K, SO, or KCI or D D,.,., by the side of: Cu, or D or K,SO, but not by the side of: KCl or D,.,., or Cu, D by the side of all other substances. HOE Wy | D TSS 12353 Different conclusions can be made from the figure. Let us con- sider the behaviour of the salt D with respect to water. When D is the salt D,, it is indicated in the spacial represent- ation by the point of intersection W of the diagonals (fig. 1). When, however, D is the salt Dx, which contains water, it is situated in the spacial representation on the line, which unites the top of the pyramid with the point of intersection of the diagonals. Let us assume that D—=D,z and let us call T the top of the pyramid, so that point T represents the water. As the line D,T does not inter- sect the saturation-surface of D,, Da is not soluble in water without decomposition. The line D,T intersects, however, the saturation- surface zklq of D,.,.,, so that the salt D, = Cu'SO,. K, Cl, = K, SO,. Cu Cl, is decomposed by water, while D,.,., = Cu SO,. K, SO,.6H,O is separated. From this we see that we can not wash out the salt 539 D, with water to free it from its mother-substance, as this will lead to decomposition. When we wish to examine accurately what will take place when we bring together D, and water, we must consider which spaces of the pyramid are intersected by the line D,T. From this amongst others the following is apparent. When we add D, to water, then firstly unsaturated solutions arise, which are represented in fig. 1 by the point W. (In this it is to be considered that fig. 1 is the projection of the spacial representation and that point W is the projection of the line D,T). , With further addition of D, the solution W arises, which can be saturated with D,.,., (this D,.,.,. however, is not yet present as solid phase) consequently the solution W of the saturationsurface zq//-. With further addition of Dz now D,.,., is separated and the solution traces in fig. 1 the straight line Ws, this straight line is the projection of a curve situated on the saturationsurface 7q/k. When we add so much D, that the solution attains the point s, then, further addition of D, will no more change the solution and there is formed: D,.,., + Da + solution s. When we wish to examine what will take place when we bring together in variable quantities K,SO0,,CuCl, and water, then we must intersect the spacial representation by the plane K,5O,—CuCl,—T. When we bring together KCl— CuSO, and water in variable quantities we must draw the plane K, Cl, — CuSO, — T. As the manner, in which these sections with the saturationsurfaces, saturationlines and the different spaces can be obtained, was already discussed previously *), we will not apply this method now. In tables If and III we find indicated the compositions of several solutions; we have deduced with the aid of the restmethod graphically the solid phases with which these solutions are saturated. In table II the compositions are expressed in percentages by weight ; of the four salts Cu SO,,Cu Cl,, K,SO, and K, Ci,; only three at the same time are given. This is sufficient also because, if we wish to express the composition also in the fourth salt, it may be done in infinitely many ways with the aid of the reaction-equation Cu SO, + K, Cl, 2 K, SO, + Cu Cl, For this the quantities of the substances which take part in the reaction must be expressed in quantities by weight. 1) k. A. H. Scoremnemakers. Zeitschr. f. Phys. Chem. 66 699 (1909). 540 ACE ese. The ternary system K, SO, — KCl — H2O at 30°. Composition of the solutions in proc. by weight | in molproc. | Point Sie Solid phase. K,SO, | KCl H20 | K,SO4 | KeCh | H,0 epee 0. Wests i a-33 0 | 98.67 K»SO, 2.55 | 17.45 | 80.0 | 0.32 | 2.56 | 97.12 ” ge |e 4209.) 26.20.) 72.7. |, OMS: |) 4516 *) $95.69 K,SO, + KCl oe 0 222. 72.78 Oi 432 95.68 KCl. ABLE Il The quaternary system Cu SO, — Cu Cl, — Kz SO, — K,Clz — H20 at 302. Composition of the solutions in procents by weight. Point CuSO, | CuCl, | Kp SO, | KCl K | 20.60 On ali 3%61 0 | 75.79 | Cie ee 14.60 5 23a seus 0 76.44 | . Ex | 10.02 | 10.74 | 4.56 0 | 74.68 | i 7 1.70 | 24.48 | 6.92 0 | 66.90 | i 1 | 7.43 | 23.75 | “0 6.26 | 62.56 | Cue Dig gen i 1.63 0. | 12.01 | 0 | 65.36.| | Kiso -=DRe 1.63 oll ave | 2.98 | 86.26 A 1.2] 0 6.76 | 6.01 | 85.51 7 Es | o | 213 | 5.74 | 9.84 | 82.29 : % 0 5.05 | 3.82) |) Gl6s02) |) 75.11 . 2.96 | 6.07 | o | at.e6 | 69.11 . q 2.97 | 6.68 0 | 21.97 | 68.38 | K,SO4+-Dj..6--D g 0 o | 1.09 | 26.20 | 72.71 | kj S0,4+KC ae | 1.75 4.80 | 0 | 25.32 | 68.13 5 “>. [acest “6-86 | 24.68 | 66.70 | Ky SO,-+ KCl-+ D | | 541 TABLE Ir The quaternary system: Cu SO,— Cu Clz — K, SO4 — KoCl, — H,,0 at 30°. Composition of the solutions in procents by weight. Point | CuSO, | Cu Cl. | Ky SO, | K Cl | H,0 | Solid phase. p 2.06 | 6.56 | 0 24.68 | 66.70 | k_)SO,+KC1-+D g_ | 234 | 61 | 0 23.32 | 67.60 | K,S0,-+D Girl) /2-6f || "63 |. <0 22.17 | 68.59 | r q | 2.97 | 6.68 | 0 21.97 | 68.38 KSOn= Dire eD q 2.97 | 6.68 | 0 21.97 | 68.38 KeSOreEDaeeD 2.04 | 7.86 | 0 17.03 | 68.92 Be [esate 111.00 On Slt. ste set - Ee | 4:08 | 17.31 0 | 11.81 | 66.79 re = || vaces | 20:80 0 9.44 | 65.41 7 | 7.53 | 23.31 0 6.63 | 62.53 | : l 7.43 | 23.75 oO Weeo5 loose | Cue Die ED p | 2.06 | 6.56 0 24.68 | 66.70 KeSO0, = KID | i.54 | 9.22 0 23.64 | 65.60 KCI-+-D | 1.34 10.86 0 93.11 | 64.69 i g | 1.30 | 11.29 =O 22.80 64.11 S™ | 0.80 | 16.95 0 21.28 | 60.97 | i 0.75 | 17.51 | 0 | 21.35 | 60.39 | 2 0.72 | 18.56 0 21.37 | 59.35 0 0.56 | 21.43 | 0 | 20.47 | 57.54 KiCHED Dim | | Sar: 21.62 | 0 | 20.86 | 57.52 Keele oD pss o 0.56 | 21.43 er | 20.47 | 57.54 | KCl+D+Dh.2 | | oo O-scre| 21.48 0 20.47 | 57.54 | KCIED+Dio0 | 0.59 | 26.09 0 16.83 | 56.49 | Dee Diss a 0.63 | 29.41 | 0 | 15.01 | 54.95 | ' S | 0.71 | 32.60 0 13.10 | 53.59 r 0.70 | 37.61 0 10.62 | 51.07 | , n 0.4 | 424 | o | 7.86 | 48.75 | €u+-D+Dio | | | | TABLE Il The quaternary system: Cu SOy— Cu Cl) — Ky SOs — Ky Cl, — HO at 30°. SS Composition of the solutions in procents by weight. Point | Cu SO, | CuCl, | K,SO, | KCI H,O | Solid phase. n 0.94 | 42.45 0 | 7.86 | 48.75 Cu, +D +Dj29 ™ | d 0 | 43.1 ou 84 48.5 | Ci, Dien n 0.94 | 42.45 | 0 | 7.86 | 48.75 Cu, De apeee zs | “1.59 | 42.30 | 0 4) 52884] 50Ke3 Cu, -+D oe $.46.1\ 40.95 0s 0). lee anade | ates Cu; “Gus aR) | | m 3.46 | 40.95 | 0 | 4.34 | 51.25 | Cu, 42 Cu; D b Deal LOR Ou) | SOU mlunstes4 Cu, + Cus 3.46 | 40.95 | 0 | 24.34 | {51225 Cus ens , 4.15 | 36.69 | 0 4.79 | 54.37 Cuca ae | 4.48 | 34.33 0 | 5.14 | 56.05 . = 5.48 | 29.55 0 5.74 | 59.23 Phe) eas | 23.75 0 6.26 | 62.56 Cus 4 Dia | 4.90 | 24.49 0 7.64 | 62.97 | 2.88 | 10.71 0 18.57 | 67.84 2.29 | 10.44 0 90.12 | 73.15 2.15 | 10.83 | 0 19.97 | 67.05 | : outs | Giles 0 19.60 | 65.89 . teoeelp Cli be 21.24 | 66.00 E 1-31 4/16 267. lg ane 18.54 | 63.48 E 1.31 | 16.57 | 0 18.68 | 63.44 e 0.89 | 23.19 0 16.38 | 59.54 A 854 |e23.15° 4/10 16.25 | 59.17 0.669 |) =2160i-aO 15.92 | 61.62 |) 91:03 | ie2me0 0 13.70 | 58.17 | oc | 32.57 0 12.43 | 54.23 | | 2.03 | 27.75 | a) 9.93 | 60.29 | | 4.47 | 39.14 0 7.17 | 52.25 | 6.06 | 19.84 | 0 7.75 66.35 | Saturation surface Dj.;.g \ i 543 TA BIE, Ul The quaternary system: Cu SO4— Cu Cl, — Ky SO, — Ky Cl, — H; O at 30°. Ions Cu, Ky, SO, and Cl, and Mol. H,O in a quantity of solution which contains 100 Mol. in all. Point Cu K, SOF) Cl; H,O | Solid phase. | K 2.96 | 0.48 | 3.44 | 6 96.56 . Gis -eDire 2.97 | 0.49 | 2.51 | 0.89 | 96.54 | i a 3.34 | 0.61 2.10 1.85 | 96.05 $ : 4.88 1.01 1.28 | 4.61 | 94.11 . l 5.98 112 1.25 | 5.85 | 92.90 Gust Dia oD oe A So DS i Oe | er ace 0 Ognash ly | a KaSOh Dit 0.21 1.49 1.29 | 0.41 | 98.30 ‘ 0.22 1.64 1.03 | 0.83 | 98.14 é Ex 0.34 Dai GE70) lee Te toe |cO7-55 > > 0.86 | 2.98 | 0.51 3.33 | 96.16 < 1.58 | 3.62 | 0.46 | 4.74 | 94.80 ¢ q 1.70 | 3.68 | 0.46 | 4.92 | 94.62 Ke SO; oD ig Oh Te) 4-31 Pros 15) |b 4516)" | 95.69 K SO,-+ K Cl 58 1.17 | 4.25 | 0.28 | 5.14 | 94.58 | p . 1.56 | 4.21 0.33 | 5.44 | 94.23 K, SO,-+K Cl+D p 1.56 | 4.21 0.33 | 5.44 | 94.23 K,SO,+KCl+D wi 1.63 3.94 | 0.37 | 5.20 | 94.43 | K,SOn-D Sie 1.64 | 3.70 | 0.41 | 4.93 | 94.66 | i q 1.70 | 3.68 | 0.46 | 4.92 | 94.62 | K,S0y+-D+4 Dis q (710i? 3.68 a fe O:46.4|-4 14.92 \)eod G2 Lh KG SO," DAL Dit, 1.92 3.51 | 0.46 4.97 94.57 DitesaD 2.52 2.89 0.49 | 4.92 | 94.59 A aa 3.92 2501s.) 0.64 |- | (5.29 94.07 . = 4.68 1.63 | 0.78 | 5.53 | 93.69 r 5.90°| 1.19 | 1.26 | 5.83.| 92.91 ‘ l 5.98 1.12 | 1.25 | 5.85 | 92.90 Gite Dates D kK 544 TABLE Ill. The quaternary system: Cu SO,— Cu Clp — Kz SOy — K, Cl, — H, O at 30°. Ions Cu, Kg SO, and Cl, and Mol. H;O in a quantity of solution which contains 100 Mol. in all. Point Cu kK, SO, Cl, HO Solid phase. p 1.56 | 4.21 | 0.93 | 5.44 | 94.23 K, SO4-+-KCI-+D 2.02 MF acs | 0.25 | 5.85 | 93.89 KCI--ED 2.33 | 4.04 | 0.22 | 6.15 | 93.63 a a 2.40 | 3.99 | 0.21 6.18 | 93.61 - S™ | 3.58 | 3.90 | o14 | 7.98 | 92.92 2 3.72 |.3.95 )|2 0.18 | 7.54 1) 92.33 3.98:| 4.00 | 0.12 | 7.86 | 92.02 55 o 4.66 | 3.93 | 0.10 | 8.49 | 91.41 K Cl-E D+ Dies e 4.58 | 3.93 | o | ssi | 149 KGEsDies 0 4.66 | 3.93 | 0.10 | 8.49 | 91.41 K Cla= Dis ee D o 4.66 | 3.93 | 0.10 | 8.49 | 91.41 K Cl DyaaeeD 5.74 | 3.27 | 0.11 | 8.90 | 90.99 DaeDies 2 6.60 | 2.98 | 0.12 | 9.46 | 90.42 . Or 7.46 | 2.66 | 0.13 | 9.99 | 89.88 f 8.91 2.23 | 0.14 | 11.00 | 88.86 Z n 10.44 1.71 0.19 | 11.96 | 87.85 Cu Dag n 10.44 | 1.71 0.19 | 11.96 | 87.85 Ci; 4D sa 50 d 10.44 | 1.84 0 | 12.28 | 87.72 Cug- Diss n 10.44 | eel 0.19 | 11.96 | 87.85 Cig Dj oa as 10.30 | 1.25 0.32 | 11.23 | 88.45 Cu, + D Su eao.19, ora 0.68 | 10.42 | 88.90 Cu,+Cu; + D m 10.19 0.91 | 0.68 | 10.42 | 88.90 Ca, Gin b 10.03 | 0 0.54 | 9.49 89.97 Cu, + Cus 545 TABLE Ill. The quaternary system: Cu SO4— Cu Cl, — K, SO, — K, Cl, — Hy O at 30°. Ions Cu, K, SO, and Cl, and Mol. H, O in a quantity of solution which contains 100 Mol. in all. Poittty ee Cua) KG | SO, ch | H,O Solid phase. | " | : m 10.19 0.91 | 0.68 | 10.42 | 88.90 Guy |: Cu, 4 D 8.93 | 0.94 | 0.78 | 9.09 | 90.13 Cup-+D 8.27 1.01 | 0.82 | 8.46 | 90.72 | fr | 7.10 1.07 | 0.96 7.21 | 91.83 | é l 5.98 1612 | 1.25 5.85 | 92.90 | Cus-++Dy1.6-+D | 5.67 1.36 | 0.82 21 | 92.97 2.38 | 3.39 | 0.34 43 | 94.23 2.49 | 3.34 | 0.34 49 | 94.17 A 2.38 | 3.65 | 0.28 75 | 93.97 | 2 3.50 | 3.29 | 0.22 | 6.57 | 93.21 i 3.48 | 3.32 | 0.22 | 6.58 | 93.20 2 4.96 | 3.06 | 0.16 | 7:86 | 91.98 3 5.09 3.05 0.15 7.99 | 91.86 4.73 less | 0.97 5.09 93.94 Saturation surface Dy.;.¢. In table III the compositions are indicated in the number of ions Cu, K,, SO, and Cl, and molecules H,O, which are present in a quantity of solution, which contains in all 100 molecules. When a solution contains a ions Cu, 4 ions K,, c ions SO,, d ions Cl, and w molecules of water, then is consequently atb=c+d-ndwt+a+t+b=w+ce+d=100. Leiden. Anorg. Lab. Chem. 546 Chemistry. — “The catalyse”. By Prof. J. Bousexen. (Communi- cated by Prof. A. F. HoLieman). (Communicated in the meeting of June 27, 1914). 1. It appears to me that, a summary having been given from various quarters on catalytic phenomena, the time has arrived to show briefly how the development of my ideas on this subject has advanced and how the insight thus gained has been supported by a deduction of one of my students. I do this in the first place because in that historical account the eradual elucidation of the phenomena is exposed, but also because I imagine that a point has now been reached where the co-operation of many is necessary in order to assist in completing the edifice of the catalysis. 2. When working at my dissertation (1895—1897), when a large number of fatty-aromatic ketones was prepared according to the reaction of Frinper and Crarts, it struck me that when to a cooled mixture of acid chloride and benzene finely powdered aluminium chloride was added, this certainly dissolved rapidly, but that an evolution of hydrogen chloride only took place slowly on warming’). As aluminium chloride did not perceptibly dissolve in benzene, I was then convinced that not the benzene but the acid chloride might be the point of attack of the catalyst. This question was afterwards taken up by me and solved in so far that the synthesis of the aromatic ketones could be divided into two stages: (a) The catalyst combines with the acid chloride: (b) this compound is attacked by the aromatic hydrocarbon (Rec. 19 19 (1900) 20 102 (1901). Although the course of the reaction was indicated therewith, I was soon aware, however, that the catalytic action of aluminium chloride remained in complete obscurity *). In this I was corroborated by the observation that chloroform and benzyl chloride suffered the reaction with benzene still far better and more vigorously, whilst these substances did not combine 1) Afterwards | modified the preparation by taking the AICls in excess and then adding drop by drop the mixture of acid chloride and benzene, because the reaction then proceeded very regularly. By the research of OLIviER (Dissertation, Delft 1912) it has been shown that the cause of this favourable result must be attributed to the presence of free AIClg (see later). 2) PERRIER who had noticed this reaction course previously (Thése, Caen 1893) was of opinion that this explained the catalylic action of aluminium chloride. 547 with aluminium chloride and the quantities of the catalyst necessary for the reaction were much less than in the synthesis of the ketones. (Ree. 22, 301 (1903)). When it appeared that nitrobenzyl chloride, which does unite with AICI,, was also attacked much less rapidly than benzyl chloride, and further that the very reactive anisol, which also forms a molecular compound with AICI,, did so readily, the facts were such that | ventured the thesis that the formation of compounds between the catalyst and the activated did not react ad a// with CCl,, whereas benzene substance had nothing to do with the actual catalytic action (Ree. 23,104 (1904)) and that, when the catalyst does not unite with one of the substances present in the reaction, we are dealing with catalytic action in its purest form (Rec. 24, 10 (1905)). Thus by means of the inductive method, | came to the conclusion that the formation of a compound with the catalyst did not give an explanation of the catalytic action as such, and that with this the theory of the intermediate products exploded. 2. I have also tried to demonstrate subsequently by means of the deductive method that the formation of a compound of substance and catalyst must necessarily lead to a partial paralysis of the latter (Proc. 1907 p. 613; 1909 p. 418). Hence, if we wished to arrive at a satisfactory explanation this had to be looked for in what happened before there is any question of a compound between catalyst and substance. When the catalyst draws near to the activated substance a phenomenon ought to take place partaking more of a disruption or a dislocation than of a union (Gedenkboek vAN BeMMELEN p. 386, Rec. 29, 87 (1910)),. I have then demonstrated (Proc. 1909 p. 419; also Rec. 32, 1 (1913); Chem. Weekbl. 7, 121 (1910); Rec. 29, 86 (1910)) that a catalyst like AICi, exerts indeed a dissociating influence on the chlorides which it activates; chloral was resolved into CO, HCl and ©,Cl,; trimethylacethyl chloride into carbon-monoxide, HCl, and isobutene, ete. But here it transpired also that even now the explanation was not given, because the action had been too violent; instead of the to be expected condensation products with benzene there were obtained in similar cases, either the decomposition products or the condensation products of these molecule residues with benzene. Thus, from SO,Cl, and the benzene hydrocarbons were generated relatively very small quantities of sulphones compared to large quantities of sulphinie acid and chlorine derivatives; owing to too great an aciivily 36 Proceedings Royal Acad. Amsterdam. Vol. XVII. 548 the catalyst had disrupted the SO,Cl, into SO, and Cl, which were now subsequently influenced catalytically (Rec. 30, 381 (1911)). The catalytic action proper can, therefore, be no union, because in that compound the catalyst is paralysed; it also cannot be a dissociation because the substance is then too much attacked, hence, it must be an intermediary influence. I have called the latter a dislocation or disruption (Ree 80, 88 (1911) dating from Sept. 1909) in order to demonstrate that there certainly does exist an influence, but that this should effeet neither union or dissoeiation if it is to be considered as a purely catalytic one. In order to more sharply confirm experimentally this result obtained, the transformation of chloral into metachloral under the influence of diverse catalysts was submitted to a closer investigation. *) This system was chosen because it had been shown that: 1st it is an equilibrium between two substances, therefore a very simple ease because we are only dealing with the transformation of one substance into another one. 2nd this equilibrium is situated in a readily attainable temperature- zone, whereas the properties of monomeride and polymeride differ rather strongly, so that the specific influence of the catalyst may come perceptibly to the fore. 394 That the monomeride itself is a supercharged molecule, so that it was to be expected that the action of the catalyst would be a pronounced one. In fact it could now be demonstrated that the equilibrium was attained rapidly only then when the activator was present in small quantities and had not perceptibly united with one of the modifications. If the catalyst (pyridine) was retained (absorbed) in the colloidal polymeride the equilibrium set in, but in the hquid phase of the monomeride the reaction ceased. If the catalyst combined with one of the components (the mono- meride) the equilibrium was shifted in the direction of that component. If, finally, the action of the activator was stronger still, the split- ting products were obtained only. About the same time, S. C. J. Outvier (Diss. Delft 1913, Proe. 1912 and R 88, 91 (1914) had finished a dynamic research on the action of bromobenzenesulphochloride on some benzene-hydrocarbons under the influence of aluininium chloride. Whereas the researches had been as yet of a qualitative character it could now also be demonstrated quantitatively that the retention 1) KR 32, 112 (1913). 549 of the eatalyst in the sulpho-chloride or in the sulphone caused a partial paralysis, as the reaction proceeded much more rapidly the moment a small quantity of the catalyst in the solution was present in the free state. Also, could it be deduced sharply from the progress of the reaction (Proe. 1913 p. 1069) that this could be explained satisfactorily only then when the activating action was sought in) what happened between benzene on one side and chloride + catalyst on the other side before they had undergone chemical transformation. Hence, it was proved experimentally also here that the most important stage of the catalysis is that which takes place before the union. 3. If we now consider what can be the significance of the removal of the catalysis to the pre-stage of the reaction, it should be remembered that in view of Ostwatop’s definition a catalyst should be a substance unchanged in quantity and quality after the reaction. Guided by this definition we may during the reaction assume all kinds of material and energetic changes if only the condition is satisfied that the catalyst remains unmodified before the beginning and after the end of the reaction. If now, however, we look for a further explanation, that is to say, penetrate further into the mechanism of a reaction, we notice that somewhere during the reaction a catalyst can no longer satisfy that definition. Hence, a catalyst can never remain unchanged during the entire course of the reaction; an ideal catalyst exists no more than an ideal gas or an ideal dilute solution, but for all that we have been able to make excellent use of the notion. Now, a substance will approach this ideal condition all the more, the smaller the material or energetic displacements will be and it is plain without any further evidence, that similar very small changes will just take place on the approach of the catalyst to the bonds to be activated. When there the action ceases, we can understand that these shiftings may be so small that they elude observation (so that for instance, apparently a same equilibrium is reached under the influence of diverse catalysts, which in reality cannot be the case.) 4. If now we want to get a concrete conception of these exceed- ingly small actions, which in the catalysis are both satisfactory and authoritative, we may consult the modern views on our atomic. world. 36 550 It is supposed that the atoms consist of (or at least are populated by) electrons and that they hold together by means of force regions between these corpuscles; the catalytic action may then be deseribed as a change of these force regions on the approach of the catalyst. If this is so, we have in the pure photocatalysis the simplest catalytic actions and the study of these phenomena will no doubt much deepen our insights. *) On penetrating further into the phenomena in general we are obliged to resolve the substance into steadily decreasing units and the same has happened with the special phenomena called catalytic; here it will just be shown that what takes place in the atoms will be of preponderating importance. But just as we have not been able to find the ideal catalyst among the atoms, we cannot expect to meet it among the electro-magnetic equilibria-perturbations, only the limit of our insight in the catalytic phenomena has advanced a step. Il. 1. During this mainiy inductive development of my ideas my pupil H. J. Prtxs had found a synthesis of chloropropane derivatives and I advised him to couple this experimental subject with a survey of the different cases in the reaction of FrispeL and Crarts. *) With this, however, he did not content himself, but starting from the “Principle of Reciprocity” he has endeavoured to furnish an explanation of the catalytic phenomena in general, with the reaction of Friepet and Crarrs as a special case. The result of this is given in his dissertation (“Bijdrage tot de kennis der katalyse’, Delft 1912) and supplemented with a few subsequent articles (Journ. f. pr. Chem. N. F. 89, 425 (1914); Chem. Weekbl. 11, 474 (1914). In order to reproduce Prins’s intention in the simplest possible manner, | will quote a few parts of his deduction, taking the liberty to omit the, in my opinion, non-essential matter. 1) The simplest case is the photocatalytic change of a monatomic element. 2) The reaction of FR. and Cr. offers us already a great diversity of catalytic reactions, because AICI; can form all kinds of compounds. Only in such cases where it unites neither with the initial products nor with the end product, or attacks this secondarily do we approach a case ef pure catalysis. The number of these cases is very small, the chlorination of benzene is a very appropriate example thereof; here the quantity of the catalyst is minimal indeed (see further) The axioms which are more particularly applicable to the cata- lysis are: “When... the one exerts an influence on the other, this latter... is changed by the first... “If in the calculation of one of these the change may be neglected we may speak of a one-sided influencing, which, however, as such... may not be considered one-sidedly (dissertation p. 4—5). and subsequently : “If we consider the possible relation of two substances (whether element or compound) three stages are to be distinguished therein’. “J. The stage of the relative inertness. In this stadium even the catalytic influence is imperceptible, whilst there is no question of a chemical compound. “2. The catalytic stage’) in which occurs also the mutual acti- vation. In this stage the catalytic actions are enacted. “3. The reaction stage in which appears an intra- or extra- molecular reaction”. The catalytic stage forms the bridge between the inertness and the chemical compound. In each chemical reaction all three stages are gone through. By varying the conditions we can, however, cause the influencing to be confined to the second stage’. (Chem. Weekbl. 11, 475, also Journ. f. pr. Chem. N. F. 89, 448 (1913). 2. Prins starts from the general thesis that on interaction, there takes place a change in two conditions, which will be least powerful the moment it begins to reveal itself. This stage lies, chemically speaking, in the dissociation region where the free energy of the entire system approaches to zero and is called by Prins the catalytic stage. In this catalytic stage there is really no question of a catalyst in the sense of OstwaLp; we are dealing with a change of condition : AZB which taken by itself can take place more or less rapidly. Being in the catalytic stage does not at all imply, in my opinion, that the changes must take place rapidly; this depends on the nature of the change (chemically speaking on the nature of the atoms or atomic groups which in the transformation play a role in the first place). If, for convenience sake, we call A and B two molecules. one of these molecules, in a reaction in which the other one (with its 1) In order to prevent confusion it would be better to speak of the activating stage. (PRINS also points out that the word “activator”? expresses his ideas better than catalyst). 552 specific atomic group) occurs as a component, will be a catalyst in the sense of OsTWALp. BSC A—>D N N A B The above symbols represent this explanation from which we gather that the change of the’free energy in so far as it concerns the catalyst approaches in the pure catalysis to zero and wherewith we also wish to express that the catalyst is in faet more a change of condition than a substance. , In the positive catalytic action the equilibrinm A <> Bb will set in much more rapidly than the reaction B—+C or A—D and thus cause or accelerate the same. Hence an ideal catalyst, according to this deduction and in connexion with OstwWatp’s definition, is a substance which undergoes with one of the to be activated substances (or bonds) such reciprocal action that in the latter system the thermodynamic potential and chemical resistance simultaneously approach to zero. As it concerns here particularly the bond that is being activated, the other moleeule wili also be more or less influenced; this we notice immediately when we remember that intramolecular displace- ments come under the same point of view. Hence, we will obtaim the maximal catalytic action when, with the catalyst (for instance Bb) we approach as closely as possible the catalytic stage in regard to A as well as D. The chlorination of benzene again presents us with a suitable meaning example to elucidate the intention of this thesis. Both chlorine and benzene are in regard to AICI, in the catalytic stage; they are both rendered active without forming a compound. As soon as we replace benzene by nitrobenzene the action ceases at the ordinary temperature because A/C/, forms a solid combination with nitrobenzene so that these two are, in regard to each other, not in the catalytic stage and because AICI, cannot any longer activate the chlorine simultaneously. At a higher temperature the chlorination starts; we may assume that the system A/C7,NO,C,H, is then again approaching the catalytic stage. It is, however, self-evident that a case like the chlorination of benzene is rarely met with; as presumably somewhat similar cases I mention: all ionreactions in aqueous solutions; the union of hydrogen and oxygen and the decomposition of hydrogen peroxide on or in platinum; the transformation: aldehyde = paraldehyde under the influence of sulphuric acid ete. Much more frequent will be the cases. such as in the chlorination of nitrobenzene, where the catalyst is found, in regard to one of the substances, a good long way over this most favourable stage ; in that case it will have united with one of the components to a more or less firm compound. The sulphone formation from bromosulphone-chloride and benzene under co-operation of A/C7, is an illustrative instance hereof: The A/C/, is combined with the sulphone-chloride and is, therefore, in regard to the chloride, already far removed from the catalytic stage, at 25° it is however not completely paralysed, as according to the course of the reaction it is still capable of activating the second molecule (benzene). The sulphone formed now also unites with A/C/, and now it appears also from the course of the reaction that it keeps on activ- ating the benzene, but is, however, no longer capable of influencing the sulfone-chloride, for an excess of the latter exerts no influence on the reaction velocity. (Otivirr and Borseken, Proc. 1913 1. ¢.). From this case it is shown how complicated this reaction may become when in the reaction mixture different substances are present which paralyse the catalyst more or less, and that only a clear conception of the catalysis enables us to interpret the observations satisfactorily. Represented symbolically, we thus have here (when we assume that the HC/(D) does not interfere, which has also been proved by OLIVIER) : Rese Bees Cee 1) ae ae So The A/C/, united to C (the sulphone) can no longer reach A (the sulphonechloride), only the A/CZ, united to A itself can still activate the S-C7 bond, but much less so than free A/C/,; only the benzene (B) is still attainable for the A/C/,. I want to observe here that the paralysis starts here, presumably, from the SO,-group, because this occurs in the sulphonechloride as well as in the sulphone. These are just the cases, wherein the catalyst is united with one of the starting products, but is not entirely paralysed thereby, which have originated the theory of the intermediate products. By removing wilfully from the most favourable catalytic stage 554 (for instance by lowering the temperature) similar coumpounds have often been met with and if was imagined that the explanation of the catalytic phenomena had thus been found. Now, however, it is evident that the explanation is not given by the formation of these compounds, but should be found before the formation and that the best catalysts will be those whose dissociation equilibrium extends over as large as possible a region of tempera- ture and pressure, without any compounds being formed. 3. In this manner, ascending by the inductive method from the special case of the reaction of Friepen and Crarrs (BorseKEN) and descending by the deductive method from the general principle of reciprocity (H. J. Prins), we have come to the conclusion that the catalytic action is situated in the pre-stage of the chemical wnton, It is evident that with this result no explanation has been found in the sense that now everything is completely elucidated. Yet, in my opinion, owing to the sharper definition of the con- ceptions the whole field is easier to survey (Prins le.) and the special cases are more readily understood, also a fundament has been given on which we can pursue our researches with a greater certainly. These in view of the further elucidation will have to move in two directions. Ist. It must be ascertained, as has been already done in some cases (L¢.), in how far the change in velocity is connected with the shifting of the catalyst and activated bonds in the dissociation region. With this may be coupled systematic researches as to the most suitable catalysts for specified reactions, (for instance on metals which are in a rapidly setting in dissociation-equilibrium simultaneously with N, and H, at a low temperature in view of the ammonia synthesis; or on carbonates which in view of the ketone synthesis from acids according to Sapatier and SeENDERENS must, at about 300°, be with those acids in the same favourable conditions). 2ed, Those catalytic actions must be investigated where very sraall evergy shiftings are concerned; to this appertain in the first place the photocatalytic phenomena. The first series of researches are of a more direct practical result; the second series, on the other hand, are of a more penetrating nature, the object being to attack the catalytic phenomena in their last recess. Delft, June 1914. ayaa) Chemistry. — ‘Researches on the Temperature-coefficients of the Sree Surface-energy of Liquids between — 80° and 1650° C.: VIL. The specific surface-energy of the molten Halogenides of the Alcali-metals.” By Prof. Dr. F. M. Janerr. (Communicated by Prof. HaGa). § 1. Notwithstanding the original intention to publish the results of the measurements concerning the temperature-coefticients of the free surface-energy of molten salts at the same time as the deter- minations of the specific gravities of the investigated salts at different temperatures, and in this way to give completely all data, necessary for the calculation of the temperature-coefficients of their molecular surface-energy, — it seemed desirable on account of the present precarious conditions, to resolve already now on the publication of the results hitherto obtained, and relating to the change of the specific surface-energies of {hose salts with the temperature of observation. The present uncertainty about the moment, when the now stopped experiments, necessary for the determination of the specific weights, again may be resumed in future, makes it perhaps desirable to publish already now the available data of the free surface-energy of some forty salts, and to draw the attention on this occasion to some general conclusions, relating to these measurements. § 2. In this connection it is perhaps of interest to mention here also some details concerning our original tentatives, to reach the proposed aim by means of the method of capillar ascension-measure- ments, — notwithstanding the fact, that these experiments finally had to be given up because of reasons already formerly explained '); these details doubtlessly can be of use for later investigations to be made in this direction. Originally the investigated salt was introduced into wide tubes of heavily fusible /ena-glass, provided with rounded bottoms ; the tubes were heated in a bath of a molten mixture of potassium-, and sodium- nitrate, either by means of gas, or better by electrical current. The salt- mixture was filled into an iron cylinder, outwardly lined with thick asbestos ; its wall was provided with two diametrically opposed, narrow windows, which were closed by glassplates, fastened by means of asbestos-covered iron-frames. Through these planeparallel 1) F. M. JAr@rr, These Proc. Comm. I. (1914). 556 windows the desired observations were executed by means of a telescope; the beight of ascension in the capillary tubes was read upon a perpendicularly divided seale. The liquid salt in the surround- ing bath was continually stirred; an arrangement was made to prevent as much as possible the annoying currents of hot air cireu- lating before the windows. In all these experiments it was stated very soon, that the investi- gated salts, when melted in the glass-tubes and on cooling again solidifying therein, made the tubes in most cases crack ; or at least they appeared on renewed heating to get soon unsuitable and badly damaged, thus a substitution of the tubes by new ones being necessary after each experiment. After many attempts, the tubes were arranged finally in the fol- lowing way, to prevent this effect. AB (fig. 1) is a tube of Jena heavily fusible glass, which has a conieal nar- rowing at a, and a sideway tube e with stopeock d; the wider tube ean be closed at its upper end by means of a stopper h, provided with the stopcock C. Just above the round bottom of the tube 5, a small plati- num crucible 7’ of about 1 cem. volume, hangs between three strong horizontal platinum-wires ; they are either melted into the glasswall of the tube, or they can be fixed to a platinum-ring, supported by three elevations in the wall of the tube. If in the last mentioned ease the tube 6 at the same time is arranged in such a way, that e.g. just below e the two parts of it can be put together by means of a ground col- lar, it will thus be possible eventu- ally to take the platinum-ring easily from the tube, and to restore it again after thoroughly cleaning the different parts of the apparatus. In every case the platinum-crucible 7’ needs to be fixed into the tube as centrally as possible. The narrowing at a is ground 557 conically ; the piece 4 (also conically shaped, ground and enlarged) of the heavily fusible, capillary glass-tube, can just be fixed into it; the capillary tube thus has the form represented in fig. 1, and it is cut to such a length, that it can be easily caught with a pincette from above through the hole 4, while at its other end it reaches just to a little above the bottom of 7, if 6 is caught by the collar a. The enlarged part of is provided at its outward side with two very fine, vertical canals, which thus have the function of capillary connections between the spaces A and JA. By means of a funnel with a broad and long stem, the erucible T is now filled with a sufficient quantity of the finely pulverised and dry salt; then AZ is put into the bath, and as soon as the salt in 7’ is molten, the carefully cleaned capillary tube is lowered very slowly into the apparatus, until 6 is lying just in the collar a; immediately the liquid begins to rise then into the capillary tube. Then both stopeocks C and d are closed, after the tube being put in such a_ position, that the capillary tube will be just vertical ; this may be easily controlled by means of a plummet. If now the air is eliminated from A through C, it will appear easily to let the liquid rise into the capillary tube, because the settlement of the pressure-differences in A and B will oceur only very slowly by the narrow canals in 4; in this way one can try to wet the walls of the tube by the liquid salt, and to eliminate the air-bubbles even- tually inelosed. A superfluous rising into the capillary tube can be stopped at any moment by means of the stopcock d. Reversely, by sucking at d, it will be possible, if necessary, to introduce air into the molten salt through the capillary tube, or to remove the liquid from it; also it is possible to substitute the air in AB by a neutral atmosphere, e.g. by nitrogen or another gas, if desired. The experi- ment being finished, the capillary tube 6 is removed first; the salt will afterwards solidify in 7 without causing the cracking of the olass-tube. In such a way several experiments can be made by means of a single apparatus. § 3. Although this method of operating can be recommended in such cases as in principle a very suitable one, the experimental difficulties however appeared to be of a rather appreciable magnitude. One of the chief difficulties was the elimination of the very small air-bubbles from the liquid in the capillary tube, which appeared to be transported into it, whenever the liquid begins to rise into the narrow tube. Notwithstanding all care, this could not be completely prevented, and the column of liquid then appears as if broken into 558 a great number of pieces. It is extremely difficult, again to eliminate such transported air-bubbles, even in repeating the above mentioned way of rising and falling of the liquid in the capillary tube for a number of times. Almost quite impossible is the elimination of the air, if the wall of the tube moreover is attacked by the molten salt, — this wall becoming more or less rough by it: the air-bubbles will then persist in sticking to the narrow canal. Moreover the microscopical control of the glass-tubes proved doubtlessly that the walls of it were attacked by the molten salt almost always seriously te a more or less extent; this faet, in con- nection with the just mentioned difficulties caused by the not removable air-bubbles and the impossibility to determine sufficiently the exact situation of the surface of the liquid in 7’, were the chief . causes why these tentatives finally had to be stopped. In some cases, e.g. in that of sodiumehromate, we could obtain rather reliable data ; but e.g. with lithiumsalts, which will always attack the glass in a high degree, and just so in the case of silvernitrate, only very un- trustworthy numbers could be obtained. It appeared moreover to be very difficult, to keep the temperature constant along the full length of the capillary tube; this can soon be controlled by means of a set of very small thermometers, placed within Z at several distances from the bottom. § 4. After this experience we thought it adviceable to abandon the said method completely. All numbers here given therefore are collected after the method formerly described by us in detail’); they relate to the purest salts. For the details of these experiments the reader is referred to Comm. I of this series. § 5. Measurements of molten Alcali-halogenides. This series includes the following salts: The Flwordes and Chlorides of Lithium, Sodium, Potassium, Rubidium and Caestum, and the Bromides and Lodides of Sodium, Potassium, Rubidium and Cuestium. The preparation of the anhydrous bromide and iodide of lithium gave hitherto no good results, because of the hydrolysis caused by heating the crystallized, hydrated salts. 1) F. M. Jaraer, loco cit. 335—348. Lithiumfluoride: LiF. Maximum Pressure Surface-tension Bere = = = z in Erg. : in mm. mer- ‘ , pro cm». cury of 0° C. in Dynes 868.5 7.098 9463 249.5 897.6 7.021 9360 248.0 944 6.890 9186 242.3 984.6 6.770 9026 238.3 1029.4 6.634 8844 233.5 1065 6.525 8699 229.8 1116.5 6.323 8430 222.7 1155.5 6.170 8226 217.4 1208 5.976 71967 210.6 1270 5.700 7599 201.1 Molecular weight: 25.99. Radius of the Capillary tube :0.05240 em: at 19° €: Depth: 0.1 mm. The salt melts at 840° C.; at 1150° it evaporates already rather rapidly, and above 1270° so fast, as to make measurements useless. The vapours show alkaline reaction. Il. Lithiumchloride: LiCl. } | Maximum Pressure ie | Surface-tension henperetire | hau Se hes 32 % in Erg. | in mm. mer- ; pro cme. | cury of oo c. | Dynes | — — al oe = = 611 | 3.928 5237 137.8 640 | 3.859 5145 135.4 680 3.786 5047 132.9 734.5 3.668 4890 128.8 775.5 3.580 4713 125.8 813.7 3.504 4672 123.2 860.1 3.410 4546 119.9 914.8 3.300 4400 116.1 967.8 3.199 4265 112.6 1021.9 | 3.082 4109 108.5 1074.6 2.976 3968 104.8 Molecular weight: 42.45. Radius of the Capillary tube: 0.05240 The salt melts at 608° C.; at 960 Gin: ath192 G. Depth: 0.1 mm. it begins to evaporate read- ily, and above 1080° so fast, that exact measurements become almost impossibie. The sublimed salt has a feeble alkaline reaction. | Ill. Sodiumfluoride: NaF. | Maximum Pressure . Surface-tension elas Ee 7 pl" eet eel z% in Erg. : in mm. mer- : pro cm?. cury of 0° C. in Dynes. fo} 1010 5.685 71579 199.5 1052.8 | 5.570 7426 195.5 1097 5.445 7259 191.2 1146.7 5.290 | 7053 185.8 1189 5.136 6847 180.5 1234 5.019 6691 176.4 1263.2 4.922 | 6562 173.1 1313 4.761 6347 167.5 1357.3 4.628 | 6170 | 162.9 1405.3 4.480 | 5973 157.8 1456.4 4.330 | 5773 152.5 1497 4.220 5626 148.7 1546 4.070 | 5426 143.5 Molecular weight: 42.0. Radius of the Capillary tube: 0.05223 cm. Depth: 0.1 mm. The salt melts at 990° C. At 1360° C. appreciable vaporisation sets in; at 1450° C. this occurs very rapidly. IV. Sodiumchloride: NaCl. Maximum Pressure 7 : Temperature << _ = ere eee es Surface-tensiony ee in mm. mer pro em? In 5 P= . | + euny, of, ONG: in Dynes. | 802.6 3.580 4772.9 113.8 810.5 | 3.572 4162.2 113.5 820.8 | SE5O2 4735.5 112.9 832 3.520 4692.9 111.9 859 3.457 4608.9 | 109.9 883.2 } 3.401 4534.3 108.2 907.5 3.345 4459.7 106.4 930.6 3.285 4379.7 104.5 960.5 3.227 4302.3 | 102.7 1999.5 Deloe 4175.6 | 99.7 037 3.047 4062.3 97.0 1080 2.951 3934.3 94.0 1122.3 2.864 3818.3 91.3 1171.8 2.761 3681.0 88.0 | | Molecular weight: 58.46. Radius of the Capillary tube: 0.04736 cm. at 18° C. Depth: 0.1 mm. The pure salt melts at 801° C.; at 1080° it begins to evaporate already rapidly, at 1150° C. very rapidly. Between 801° and 859° C. the coefficient of ~ seems to be about 0.57 Erg., and to increase with rise of temperature. The mass shows in water afterwards a | strong alkaline reaction. | 561 V. Sodiumbromide: NaBr. | : z Sees | Maximum Pressure | | Surface-tension | | | Temperaiure = | zi Erg. | | in mm. mer- : * | | cury of 0° C. oe eMeS | | | “De | 760.9 3.011 4015 105.8 809.5 2.928 3904 102.9 851.9 2.834 3778 99.6 896.8 2.737 3649 96.2 941.5 2.640 3520 92.9 984.5 2.556 3408 90.0 1029.4 2.449 3265 86.2 1073.5 2.384 3178 84.0 1116 2 302 3069 81.1 1165.7 2.214 2952 78.0 | Molecular weight: 102.92. Radius of the Capillar tube: 0.05240 | cm. at 19° C. | Depth: 0.1 mm. The salt melts at 768° C.; it begins readily to evaporate at 10002 C., and free bromine can be observed then. The sublimed salt possesses alkaline reaction. VI. Sodium-iodide: NaJ. Maximum Pressure Surface-tension ee sraneme|t fain Ere : : " é pro cm2, eirynet oie in Dynes | | 705.5 2.438 | 3250 85.6 746 2.388 | 3184 83.9 815.5 2.291 | 3054 80.5 860.7 2.209 | 2945 17.6 Molecular weight: 149.92. Radius of the Capillary tube : 0.05240 cm. at 19° C. Depth: 0.1 mm. The salt, which melts at about 660° C, evaporates soon to a high degree, and free iodine is observed. The sublimed salt reacts somewhat alkaline. 562 VII. Potassiumfluoride: KF. | Maximum Pressure y | Surface-tension Tene |= ee in mm. mer- | pro cm¢. cury of 0 C. in Dynes 912.7 4.123 | 5497 138.4 961.5 4.024 | 5365 135.2 1015 3.898 | 5197 131.0 1062 3.790 5053 127.4 1097 3 701 4934 124.5 1146.5 3.564 4752 119.9 1185 3.450 4600 116.1 1234 3.336 4448 PLES 1275 3.225 4300 108.6 1310 3.116 4154 104.9 Molecular weight: 58.1. | Radius of the Capillary tube: 0.05002 em. at 18° C. Depth: 0.1 mm. The salt melts at 860° C. At 1140° C. it begins to evaporate distinctly, at 1180° C. this goes on already rapidiy, while acid vapours are set free. VIII. Potassiumchloride: KCl. Maximum Pressure Temperature es eee ee eee meetin in ° C. in mm, mer- = : a cury of 0° C. | in Dynes. pro cm*, 799.5 | 3.015 4019 95.8 827.1 2.957 3942 94.0 861.5 2.873 3830 91.3 885.1 2.819 3758 89.7 908.5 2.768 3690 88.0 941 2.697 | 3595 85.8 986 2.582 | 3442 | 82.2 4 1029 | 2.484 | 3311 | 79.1 1054 | 2.425 3233 | dee 1087.5 | 2.361 3147 | Tei? 1103.6 | 2.313 | 3083 IBIS 1125 PPA 3033 72.5 1167 2.182 2909 69.6 Molecular weight: 74.56. Radius of the Capillary tube: 0.04736 cm. atgloanG, Depth: 0.1 mm. The compound solidifies after heating above its meltingpoint during 4 hours, at 768° C. It evaporates at 980° already appreci- | ably, at 1160 very rapidly. The vapours are acid, while the soli- dified mass shows in water alkaline reaction. The valves of the maximum pressure appear to decrease gradually, as a result of | | continuous heating of the molten mass above 1100? C. t 563 IX. Potassiumbromide: KBr. | Maximum Pressure | Temperature | . 7 SUP AES et sion | in® C. ha Gaia in ; - ‘ p 5 ane 0G. in Dynes 775° 2.702 3602 85.7 798 2.642 3522 83.8 826 2.585 3446 | 82.0 859 2.504 3338 719.5 886.5 2.450 3266 71.8 920 2.376 3167 715.4 Molecular weight: 119.02. Radius of the Capillary tube: 0.04728 cm. at 15? C. Depth: 0.1 mm. The salt melts at 734° C. At 825° C. already a decomposition under liberation of hydrobromic acid and bromine is observed; | at 940° C. the salt evaporates so rapidly and decomposes to such a degree, that further determinations seem to be useless. X Potassium-iodide: KJ. Maximum Pressure H Surface-tension Homperstace = a7 Ha Erg. ? in mm. mer- : pro cm*. cury of 0°? C. in Dynes ceils 2.372 3162 15.2 764 2.274 3031 Teal 812 2.183 2910 69.2 866 2.106 2807 66.8 873 2.097 2795 66.5 Molecular weight: 165.96. Radius of the Capillary tube: 0.04728 Chiat 15S; Depth: 0.1 mm. The salt melts at 681.95 C. At 750° C. already it begins to evaporate very appreciably, while iodine is set free. For again higher temperatures the determinations can hardly have any essential significance. 37 Proceedings Royal Acad; Amsterdam. Vol. XVII. 564 XI. } Rubidiumfluoride: RdbF. Maximum Pressure 7 Temperature ——— 2s Surface-tension | | | | | : : z in Erg. ° | by | ee | in mm. mer- | a anees | pro cm? | | cury of 0° (G, | ye | = = = : —— 1 — a ——— | 802.6 3.630 4839 ee | 847.2 3.461 4614 121.3 | 886.8 oroel 4436 116.7 | 936 3.220 4293 | 113.0 985.6 3.102 4136 108.9 1036.7 2.997 | 3996 105.2 1085.4 | 2.910 3879 102.2 Molecular weight: 104.45. Radius of the Capillary tube: 0.05223 cm. at 19° C. Depth: 0.1 mm. The salt melts at 765° C. At 1000° C. it begins already to evaporate in an appreciable degree. XL. Rubidiumchloride : RbC/. Maximum Pressure H ae é cs urface-tension Teepe rate . = ee apeaniienes | : in mm. mer- . | pro cm?. cury of 0? C. in Dynes | o 750 PAs BY 3642 95.7 769.7 2.689 3585 94.2 828.2 2.540 3386 89.0 880 2.410 3213 84.5 922.7 ZEB 3084 81.1 933 2.278 3037 719.9 961.5 2.205 2940 Tiles 994 2.130 2840 74.7 1036.6 2.030 2706 | es 1088.5 1.900 2533 66.7 1150 1.749 2332 61.4 Molecular weight: 120.91. Radius of the Capillary tube: 0.05223 cm. at 19° C. Depth: 0.1 mm. The salt melts at 720° C.; at 950° C. it begins to sublime already distinctly. Analysis gave: 29.25%, Cl and 70.75%, Rb, proving satisfactorily the purity of the salt. | 565 XIII. Rubidiumbromide: Rb£Er. Maximum Pressure S : urface-tension Peenealane wees cin Erg. in mm. mer- . pro cm’. cury of 0° C. zy Dynes | ————————————————— ———— ——— SSS = =—™ —= 729.2 2,504 3338 87.7 7719 2.401 3201 84.1 831 2.301 3068 80.7 884.3 2.200 2933 ile’ 943.5 2.084 2718 (Breil 985.7 2.000 2666 70.2 | 1041 1.900 2533 66.7 1121 1.724 | 2298 60.6 | | Molecular weight: 165.37. em. at 19°? C. Depth : 0.1 mm. Radius of the Capillary tube : 0.05223 The salt melts at about 685° C.; at 940° C. already it begins to subli- me, while bromine and hydrobromic acid distinctly are observed too. XIV. Rubidium-lodide: RbJ. Maximum Pressure 1 Surface-tension ee a Bee. ‘ in mm. mer- é : pro cm”, cury of 0° C. in Dynes, | | is} | 673.4 2.268 | 3024 79.4 721.8 2.165 2886 15.8 771.5 2.061 2748 PAE 822 1.956 2607 68.5 | 869 1.857 2476 65.1 918 Nalos 2344 61.6 968 1.663 | 2217 58.3 1016 1.578 | 2104 55.4 | Molecular weight: 212.37. Radius of the Capillary tube : 0.05223 em. at 19° C. Depth: 0.1 mm. The salt melts at 642° C. At 900° C. evaporation happens already distinctly; at 1000? C. it is so fast, that the measure- ments are influenced by it in a most troublesome way, the values of H seeming to be increased by the heavy vapours. 566 XV. Caesiumfluoride: CsF. | Maximum Pressure H é urface-tension femperaiue | ai Erg. ; in mm. mer- : pro cm? | cury of 0? C. in Dynes , | ° i | | 722.5 3.116 4154 104.5 768.7 3.011 4014 101.0 825.6 2.872 | 3829 96.4 877.3 2.748 3664 92.3 929.7 | 2.624 3498 | 88.1 985 2.510 | 3346 84.3 1042 2.418 | 3224 81.3 1100 2.346 3128 78.9 | | Molecular weight: 151.81. Radius of the Capillary tube: 0.05002 cm. at 18° C. Depth: 0.1 mm. The salt melts at 692° C. At 990° C. it begins to evaporate distmcetly. XVI. Caesiumchloride: CsCl. | Maximum Pressure H ; | Temperature Suriace tension | aa | ee | in mm, OC. | in Dynes |= : — | | 663.7 2.660 | 3546 | 89.2 717 2.560 3413 85.9 7711 2.440 3253 81.9 829.6 2.315 3086 | dilotl 881 | 2.193 2924 Sea 934.2 2.075 2766 69.7 979 | 1.975 2633 66.4 1034.7 | 1.833 | 2444 61.6 1080 1.673 2230 56.3 | | Molecular weight: 168.27. Radius of the Capillary tube: 0.05002 cm. at 18° C. Depth: 0.1 mm. The salt melts at 632? C. At 925° C. it begins to sublime; at 1000° C. the evaporation occurs already very rapidly. XVII. Caesiumbromide: CsBr. | Maximum Pressure H erate ea urface-tension meuTuevalure | - | - z in Erg. : | in mm, mer- % | pro cm2, + cury of 0° C. in) Dynes | i S.. | a A ee ; | 657.7 2.439 | 3252 81.8 693.6 2.351 | 3134 | 718.9 7152.5 2.231 2974 14.9 807.5 2.132 | 2842 71.6 858.3 2.040 | 2720 | 68.5 915.8 1.950 | 2600 65.5 970.6 1.865 | 2486 62.7 Molecular weight: 212.73. Radius of the Capillary tube: 0.05002 cm. at 18° C. Depth: 0.1 mm. The salt melts at 631° C. At 900° C. it evaporates already very rapidly, making the measurements very difficult. XVIII. Caesium-lodide: CsJ. Maximum Pressure Temperature e purlacetension bl OG, : ara ae mm. - : mG cury of 0? c, | itt Dynes 653.6 2178 | 2904 | 73.1 713 2.050 2733 68.8 768 .2 1.955 | 2606 65.7 821.4 1.860 | 2480 | 62.5 879 1.762 | 2349 59.2 926 1.684 | 2245 56.6 980 1.600 2134 53.8 1030 1.520 | 2026 tl Molecular weight: 259.73. Radius of the Capillary tube : 0.05002 emi aulsouG: Depth: 0.1 mm. The salt melts at 620° C. It begins to sublime appreciably at 825° C. 568 § 6. The temperature-cocjicients of the specific surface-energy of the molten alcali-halogenides. During these measurements, it became clear, that the shape of the curves, which illustrated the dependence of % and ¢, was in most cases much nearer to that of straight lines, than was the ease with most of the hitherto investigated organic liquids. However it must be remarked, that notwithstanding this, also in the case of molten salts, the y-curves could evidently belong to every one of the three formerly discerned possible types, while in the case of occurring dissociation a more rapid bending towards the temperature- axis could be stated, just as in the analogous cases formerly studied. Because of the much greater values of the maximum-pressures however in the here studied cases, those deviations from straight lines come much less to the foreground. As a consequence, in thirty cases of the about forty investigated salts, the dependence of y and ¢ could be expressed with sufficient accuracy by dimear expressions ; for the remaining cases a quadratic expression in ¢ with three con- stants appeared to be adapted to this purpose to a really sufficient degree. If ¢, is the meltingpoint of the salt, then x, above this melting- point, can be calculated from an equation of the form: A%=a—b(t—t)+ct—t,)’, in whieh «@ corresponds to the value of y, at the meltingpoint. In the following table the corresponding values of ¢,, a, 6 and ¢ for every one of the investigated halogenides are resumed : Formula of ates | | the Salt. fs in°C. | i | b | e | LiF s40 | 255.2 | 0.126 | 0 | Licl 608 140.2 | 0.076 0 NaF 990 201.6 | 0.106 0 NaCl 801 114.1 0.071 0 NaBr 768 106.5 0.069 0 NaJ 660 88.2 0.053 0 KF 858 143.2 | 0.087 0 Kel 780 97.4 0.072 0 KBr 7134 88.8 0.070 0 KJ 681 78.3 0.064 0 RbF 765 132.0 0.131 0.00012 R6éCl 720 98.3 | 0.086 0 | RobBr 685 90.7 | 0.069 | -0 | RbJ . 642 80.3 0.065 0 | CsF 692 107.1 0.088 0.00004 CsCl 646 91.3 0.077 0 | CsBr 631 83.6 0.063 0 CsJ | 620 91.6 0.056 0 569 Specific Surface-Energy in Erg pro cm?. 760 rere 700" 750" 800° 850" YOU" 950° 100 190 TU 150 10 Ti Ta TW Ta Tere —‘emperature Fig, 2: Specific Surface-Energy in Erg. pro cm2. 600° 650 100" 750 800" 850" 900° 950° 0w W050 morse 7200" +“ Temperature Fig. 3. Specific Surface-Energy in Erg pro cm2. 650° 700° 750° 800°850°900' 950" 000°1050 100 1150°/200° Temperature Fig. 4. Specific Surface-Energy in Erg pro cm2. 650° 100° 150° 800° 850° 900° 950" wer ese”—S heMperature Fig. 5. § 7. From these data it can be deduced in the first place, that in general the temperature-coefficients of the specific surface-energy x of these salts appear to be smadler than for most organic liquids. While in the last mentioned cases these values are oscillating between 0.09 and 0.18, —as the following instances may prove once more: Acetic acid: 0.118. | Guajacol : (OISEL, Benzene: 0.136. Resorcine- Dimethylether : 0.105. Diethylmalonate: 0.102 Hydroquinone Dimethylether: 0.109. Anisol: 0.114. Pyridine : 0.125. Phenetol: 0.102. a-Picoline: 0.128. Anethol: 0.094. Chinoline : 0.104. — the values of 06 for these salts are situated between 0,05 and 0,09, being thus about of the order of magnitude of the coefficient for e.g. ethylalcohol: 0,086. Only in the case of some fluorides some numbers for 6 were found, corresponding in some degree with those for organic liquids. (if : 0,126; RbF : 0,181; NaF : 0,106). If attention is drawn to the much higher temperatures of observation in the case of molten salts in comparison with those of the organie liquids, it will be hardly permitted to conelude to a principal differ- ence in this respect. in the behaviour of both classes of liquids; on the other side however just with respect to these much higher 571 temperatures, the enormously high absolute values of % with these salts, which may occasionally be more than three times that of water, must be considered as very remarkable. In connection with the data given above, we can moreover generally conclude: 1. The temperature-coefficient 6 of the specific surface-energy decreases continually in the case of the four halogenides of the same alcali-metal, with increasing atomic weight of the halogen-atom. This rule holds evidently quite accurately in all the cases here considered. As to the absolute values of y of these salts, attention can more- over be drawn to the following general rules: 2. At the same temperature t, the values x for the same halogenide of all alcali-metals, will decrease gradually with increasing atomic weight of the alcali-metal. 3. At the same temperature ¢ the values 4, will gradually. decrease in the case of the four halogenides of the same alcali-metal, with increas- ing atomic weight of the halogen-atom. These relations however do not possess a simple additive character. Generally speaking, the Z-compounds appear to deviate more from those of the other aleali-metals, than these from each other; the A-, Rdb-, and Cs-compounds approach each other more, than each of these elements do the corresponding Na-compounds, while in the series of the first mentioned three alcalimetals, the compounds of K and Rb appear to have the nearest analogies to each other, Probably the liquid lithium-salts imay possess a higher degree of molecular complexity, than the salts of the other aleali-metals. Groningen, Augustus 1914. Laboratory for Inorganic and Physical Chemistry of the University. Chemistry. — ‘Researches on the Temperature-coefficienis of the free Surface-energy of Liquids at Temperatures between — 80° and 1650° C. VIII. The Specific Surface-energy of some Salts of the Alcali-metals.” By Prof. Dr. F. M. Janenr. (Communicated by Prof. H. Haga). § 1. As a sequel to the data published in the foregoing com- munication, which related to the /alogenides of the aleali-metals, the results of the measurements made with a number of salts of the alcali-metals, which belong to some other series, are communicated in the following pages. These measurements include the following objects : 572 The Sulphates of Lithium, Sodium, Potassium, Rubidium and Caesium; the Nitrates of Lithium, Sodium, Potassium, Rubidium and Caesium; the Metaborates of Lithium, Sodium and Potassium; and the Molybdates, Tungstates and Metaphosphates of Sodium and Potassium. With the exception of rubidiumsulfate, which evidently contained some potassiumsulfate, all salts were chemically pure; the sulfates, molybdates and tungstates were those commonly used in this laboratory for the calibration of the thermoelements, and just the same was the ease with lithiummetaborate. For the method and practice of the measurements etc., we can refer to the foregoing communication. § 2. I. | | Lithiumsulphate: Li.SO,. Maximum Pressure 11 Temperature ¢ es ae ee | Suc eee inne G: ae : : pro cm?.: E cro Oc. | in Dynes | ie} | 860 | 6.361 8481 223.8 873.5 6.342 8455 223.1 897 6.303 8403 | 221.8 923 6.256 8341 220.2 962.5 6.169 | 8224 | 217.4 976.8 6.146 8194 216.4 1001.2 6.099 8132 214.8 1038.5 6.027 8035 | 212.3 1057 5.987 7982 211.0 | 1074 5.953 7936 209.8 1089.5 | 5.923 | 7897 | 208.8 1112 5.879 7838 | 207.3 } 1156.5 | 5.791 7720 | 204.2 | 1167.5 | 5.766 7687 203.4 | 1183.5 eye TET 7649 202.4 1192.2 | 5.718 7624 | 201.8 1214 5.675 7566 | 200.3 cm. at 16° Depth: 0.1 mm. The meltingpoint is 852° C.; the salt appears to be stable up | oe | Molecular weight: 109.94. Radius of ane Capillary tube 0.05240 | | to rather high temperatures. | 573 Il. Sodiumsulphate: Na,SO,. Maximum Pressure . Sui face-tension petupera ure laa: yin Erg. | : in mm. mer- é procm’. | cury of 0°C. ie Dyes | 900. 6.285 8379 194.8 | 945 6.247 8329 | 189.3 990 6.209 8278 188.2 | 1032 6.149 81¢8 186.5 1077 6.088 8116 184.7 Molecular weight: 142.07. Radius of the Capillary tube: 0.04512 Ciipeat, 1628: Depth: 0.1 mm. The salt melted at 884° C. The molten mass, if brought into | water, Shows an alkaline reaction, if the temperature of the | molten salt has been above 1100° C. ll. Potassiumsulphate: K,SO,. | Maximum Pressure ae Abiea | | Surface-tension Hemps! Ae | in Erg | in mm. mer- : . cury of 0° C. in Dynes fe) 1070.2 4.080 5439 143.7 1103 4.048 5397 | 142.6 1145 3.989 5318 | 140.6 1199 | 3.878 5171 | 136.7 1247 3.762 | 5016 132.7 1305.5 | 3.651 4868 128.8 1347 3.578 4770 126.2 ile 7fil ets) | 3.529 4705 124.6 1400 3.468 4623 122.4 1439.5 3.393 4523 119.8 1462.5 3.344 4458 118.1 1490.4 3.286 | 4381 116.1 1530.3 | 3.228 | 4304 114.1 1586 | 3.130 | 4173 110.7 1656 3.020 4026 106.8 Molecular weight: 174.27. Radius of the Capillary tube: 0.05240 cm. at 19° C. Depth: 0.1 mm. The salt melts at 1074° C., and does not dissociate appreciably up to 1550° C. Temperature Rubidiumsulphate: Rb,S0,. IV. Maximum Pressure 1 Surface-tension in ° a x in Erg. in mm. mer- : pro cm*. cury of 0° C. in Dynes | ° 1086 3.760 5013 132.5 1112 3.681 4907 | 129.7 1144.7 3.611 4814 ies 1195 3.520 4693 | 124.2 1234.5 3.452 4602 | 121.8 1289 3.368 4490 | 118.9 1343.8 3.286 4381 116.0 1396.8 3.223 4297 113.8 1414.6 3.200 4267 | 113.1 1482 3.138 4183 110.9 1545 3.079 4105 108.9 Molecular weight: 266.97. Radius of the Capillary tube: 0.0524 cm. at 18° C. Depht: 0.1 mm. The salt melts at 1055° C. At about 1400° C. it begins to evaporate somewhat faster, and sublimes against the colder parts of the apparatus. It appears to contain some KjSQ4; analysis gave: 37,45 % SO, and 62,56 % Rb, instead of 36 %, SO, and 64°, Rb. V. Caesiumsulphate: Cs,SQ,. Temperature Maximum Pressure H Surface-tension insos. i L : ro cm? } Segoe oe | cangoaces, 910g fo} 1036 3.170 4226 111.3 1063 3.080 4106 108.2 1105 2.988 3984 105.0 1165 2.869 3825 100.8 1221 2.764 3685 97.3 1274.5 2.691 3588 94.7 1331.4 2.607 3476 91.7 1372 2.552 3402 89.8 1423 2.482 3309 87.4 1470 2.427 3236 85.5 1530 2.354 3138 83.0 Molecular weight: 361.69. Radius of the Capillary tube: 0.05223 cm. at 18° C. Depth: 0.1 mm. The salt melts at ca. 1015° C. At 1325° C. it begins to evaporate in an appreciable degree; at 1440° C. very rapidly, and at nigher temperatures it sublimes in a rather troublesome way. Specific Surface-Energy in Erg. pro cm?. 850° 900° 950° 100° 050° 102° 1507 200° 12501300 1950 14001950 1500 15307600 7650 770" +~Temperature Fig. 1. VI. Lithiumnitrate: L7NO3. | | | Maximum Pressure : Temperature ers So ee Sunlace tension Dasccetee | 0 Er in mm. mer- | : *. cury of 0° C. in Dynes | | 358.5. | 3.334 | 4445 | 111.5 | 403 3.260 4347 109.1 418.2 3.240 4320 | 108.4 445.3 3.169 4225 106.0 492.5 3.069 4092 102.3 | 555.3 2.956 | 3941 99.0 | 609.4 2.872 3829 96.2 Molecular weight; 68.95. Radius of the Capillary tube : 0.05002 cm, at 18? C. Depth: 0.1 mm. The salt melts at 254° C. to a very thin liquid. The values of y are evidently szmadler than in the case of the sodium nitrate. At 600° C. already a decomposition, with oxygen and nitrous vapours setting free, can be stated. VIL. Sodiumnitrate: NaNO3. = = As “a Maximum Pressure H ; Temperature pe ss —— a See ingonG: is j in mm. mer- |

eG EJs ea ee : in mm. mer- . | pro cm’, Guryioh Onn) as Dynes | — ~~ — | — — 380. | 3.300 4400 110.4 436 3.168 | 4223 106.0 480.1 3.073 4097 102.8 534.3 | 2.942 3923 98.5 578 | 2.841 3788 95.2 628 | PS 7E%) 3646 91.6 675.4 | 2.623 | 3497 87.9 (PANG 2.506 3341 | 84.0 771.6 2.391 3188 80.2 Molecular weight: 101.11. Radius of the Capillary tube 0.05002 cm. at 18° C. Depth: 0.1 mm. The salt melts at 339° C. At 760° C. already a decomposition, ana- logous to that observed in the case of the sodiumsalt, can be stated. IX, | Rubidiumnitrate: RbNO3. | ane ee a PAs Maximum Pressure H : Temperature | __ ao ee ah Le aia TEE : ; es in mm. mer- | Carre pro cm?. cury of 0? C. | Meals | 326.5 | 3.215 | 4286 107.5 376 3.110 | 4146 104.0 428 2.982 3976 | 99.8 480 | 2.871 3828 96.1 oes 2.763 3684 | 92 8 578 2.653 | 3537 | 88. | 625 | 2.556 | 3408 | 85.6 | 676.2 2.429 | 3238 | 81.4 | 726.2 2.316 | 3088 | riley | | Molecular weight: 147.46. Radius of the Capillary tube: 0.05002 cm. at 18° C. Depth: 0.1 mm. The salt melts at 304° C. At 650° C. it begins to decompose, setting free oxygen and nitrous vapours. X. Caesiumnitrate: CsNO3. | | Maximum Pressure H Temperature ¥ Surface-tension id gs z in Erg. | NOUS | se rae ite 3 pro cm?. | | cury of 0° C. in Dynes | | ° | | 425.5 2.743 3657 91.8 459.7 2.636 | 3514 | 88.2 5il 2.500 3333 83.7 576.5 2.366 3154 | 79.2 602 2.277 | 3036 76.3 686.4 | 2.162 2882 1a Molecular weight: 194.82. Radius of the Capillary tube: 0.05002 cm. at 18’ C. Depth: 0.1 mm. The salt melts at 414° C.; just as in the case of the solubi- lities, also in the situation of the meltingpoints of K-. Rb-, and Cs-nitrates an evident irregularity can be stated. At 600° C. already the molten salt begins to decompose. or cot hy (eo oF) Specific Surface-Energy in Erg pro cm?. = Temperature Fig. 2. XI. Lithium-Metaborate: LiBO,. Maximum Pressure H Temperature |—— s Surtace-lensiea ree (Cx ae a ae in mm. mer- . : cury of 0° C. in Dyes fo} 879.2 7.442 9922 261.8 922 7.379 9838 259.7 967.5 7.279 9704 256.2 1011.5 7.190 9586 253.1 1054.5 7.108 9476 250.3 1097.3 7.034 9378 247.7 1149.7 6.912 9215 243.6 1198 6.800 9066 239.7 1249 6.638 | 8850 234.2 1309.3 6.399 | 8531 225.8 1355 6.252 8335 220.7 1408 6.022 | 8029 Zen 1457 5.750 | 7666 203.1 1520 5.445 7260 192.4 Molecular weight: 49.99. Radius of the Capillary tube: 0.05240 cm. at 19° C. Depth: 0.1 mm. The salt melts at 845° C. At 1200° C. it begins to evaporate appreciably; the vapours show alkaline reaction (LZ0). At 1300° C. the volatilisation of the £/,0 occurs already rather rapidly; the y-¢- curve descends by this dissociation far more rapidly, than in the beginning. Sodiummetaborate: NaBOs. | | Maximum Pressure 1 | | Surface-tension Be | an Erg. in mm. mer- | ; pro cm. | cury of 0° C. | in) Dynes 1015.6 5.762 1682 193.7 1051.9 5.599 7465 188.3 1096.5 | 5.378 1170 180.9 | 1140 | 5.190 6919 174.7 | 1192.2 4.933 6577 166.1 1234 4.700 6266 159.7 1276.5 4.476 5967 150.8 1323.3 4.239 5651 142.9 1372 4.006 5341 135.1 1441 3.740 4986 126.2 Molecular weight: 66.0. Radius of the Capillary tube: 0.05002 cm. at 18° C. Depth: 0.01 mm. The salt melts at ca. 965° C. At 1230? C.it begins toevaporate | distinctly; at 1350° the evaporation goes on rapidly. XIII. Potassiummetaborate: KBQ,. 3829 | 96.6 Maximum Pressure 7 Surface-tension Temperature -| yin Erg. | i x Bll : pro cm?, | cury of 0° C. oes Dynes | va 3i ae i 992 | Bere) | | 4901 | 123.5 1036 | 3.341 | 4454 112.3 | 1091 | 3.062 | 4083 103.0 1142 | 2.872 | Molecular weight: 82.1. Radius of the Capillary tube: 0.05002 cm. at 18°? C. Depth: 0.1—0.3 mm. The salt melts at about 946° C. The measurements were diffi- cult by the great volatility and high viscosity of the substance. The obtained values cannot be considered therefore as being highly accurate. wo (06) Proceedings Royal Acad. Amsterdam, Vol. XVII. Specific Surface-Energy in Erg pro cm?, SCO* 830° CO* 950° 1000" 1050" T100° 7150" L200° T250°7500 FEO°F400" 450° F300 950 16000" Temperatu re Fig. 3. XIV. Sodiummolybdate: Na.MoO,. | Maximum Pressure | , Temperature | es SUrTaCe ener fav SG 1m oto: pty In mm, mer- - 50 cury of 0° C. in Dynes 698.5 6.091 | 8122 | 214.0 728.5 5.975 | 7967 | 210.0 751 5.921 | 7893 208.1 7771 5.828 7170 204.9 818.8 Heol 7675 202.4 858.5 5.657 71542 199.0 903.8 5.552 7401 195.4 948 5.436 7247 191.4 989.5 5.330 7106 187.7 1035 5.224 6966 184.1 1078.5 5.141 6854 181.2 1121.5 5.070 6760 178.8 | MARKO 4,998 6654 176.1 1212 4.947 6595 174.6 Molecular weight: 206. Radius of the Capillary tube; 0.05240 cm. Depth: 0.1 mm. The salt melts at 687° C. to a colourless liquid. 581 XV. | Temperature Potassium-Molybdate: K,Mo0,. Maximum Pressure | | Surface-tension | x in Erg. in ° C | inmm. mer- |, | 3 | Giinys of 0°57 mene Dyn | LW Ate fe} 930.6 4.310 | 5746 150.5 977 | 4.218 | 5626 147.3 1021 4.158 5543 145.2 1105 4.021 5360 140.7 1143 | 3.960 5280 138.6 1189.3 | 3.868 5156 135.5 1273 3.714 4950 130.0 1286 | 3.676 4900 128.8 1356 I) Bevesss Mel ci 123.6 1438 3.364 4483 118.0 1452.8 3.330 4440 116.9 1522.3 3.205 4273 112.5 Molecular weight: 238.2. Radius of the Capillary tube: 0.05240 | cm, at 18° C. | Depth: 0.1 mm. The salt melts at 919° C.; at 1400°C. it begins to decompose very slowly. XVI. Sodiumtungstate: Na,Wo0,. : = | Remmperatiire Maximum Pressure | Surface-tension corr. on i = 5 | pee | ray, | atm mers | in Dynes | > proemé | = 710 Budg2m | 7909 | 993.3.) || 719.5 5.909 | 7878 | 202.6 741 5.863 7817 201.0 788 5.718 7103 198.2 834 5.686 7580 195.2 879 5.579 7438 191.5 932 eS ii 7355 189.5 985.3 5.364 7151 184.2 1038.5 5.280 7040 181.4 1080.5 5.186 6913 178.3 1133 5.073 6762 174.6 1181.4 5.010 6679 172.4 1231.5 4.880 6506 168.0 1281.8 4.755 6339 163.8 1331.5 4.663 6217 160.6 1390.5 4.494 5991 155.0 1450 4.405 5872 152.0 1516.5 4.265 5686 147.3 1559 4.171 5560 144.0 1595 4.129 5508 142.6 Molecular weight: Radius of the Capillary tube: 0.05113 cm. at 16° C. Depth: 0.1 mm. The colourless, perfectly anhydrous salt melts at 694° C toa very clear, somewhat viscous liquid, which however at higher temperatures soon becomes much thinner. 38* 582 XVII. Potassiumtungstate: K,W0,. Maximum Pressure ina : Temperature Suriac ees in CG: ? pro! ree in mm. mer- ‘ . cury of 0° C. in Dynes 925 4.611 6147 161.0 969 4.410 5879 154.1 1012.5 4.305 5739 150.2 1051.5 4.173 5563 145.9 1097 | 4.056 5409 141.9 1138.8 | 3.943 5257 138.0 1183.2 3.832 5109 134.1 1230 3.720 4960 130.3 1284 3.558 4744 124.6 1322.4 | 3.449 4598 120.9 1366.5 3.379 4505 118.4 | 1408.5 | 3.259 4345 114.3 | 1458.2 3.135 4180 110.0 | 1489 3.076 4101 107.9 | 1520.3 3.010 4013 105.6 Molecular weight: 326.2. Radius of the Capillary tube: 0.05201 cm. at 17° C. Depth: 0.1—0.2 mm. The meltingpoint of the salt is 921° C.; even at 1500° C. the compound does not sublime appreciably. — —————e Specific Surface-Energy in Erg. pro cm?. 700 650° 700" 750" 800° 850° YOO" 950" 10001050 M0 H50° 1200 1250" 100° 13501460 14301500 19501000" Tempe- rature Fig. 4, 583 XVIII. Sodium-Metaphosphate: NaP03. Maximum Pressure Temperature _ | Surface-tension in °C. | ASE in mm. mer- : pro cm-. cury, of 02a: in Dynes 827 5.730 7639 197.5 871.4 5.648 7538 194.8 927 52553 7403 191.6 1014 5.406 ALO2S | 186.7 1098.5 5.254 7004 181.6 1181 5.109 6811 176.6 1264.5 4.939 6584, 170.9 1317 4.814 6418 | 166.7 1434 4.511 6014 | 156.2 1516.5 4.254 5671 147.5 Molecular weight: 102.04. Radius of the Capillary tube: 0.05140 cme ablboaG: Depth: 0.1 mm. The salt melts at about 620° C. At 1200° C. it begins to eva- porate considerably, and sublimes readily at higher temperatures. XIX. Potassium-Metaphosphate: KP0O,. Maximum Pressure Surface-tension Tonperfute At nee cae =) EE = x in Erg. , in mm. mer- ; pro cm?. cury of 0? GC in Dynes fe} 897 4.506 6007 155.5 942 4.395 5860 151.8 995.7 4.346 5793 149.0 1036 4.233 5643 146.1 1082 4.137 5515 143.0 1120 4.060 5413 140.3 1167 | 3.957 5275 136.8 1205.2 3.859 5145 133.5 1250 3.842 5122 130.2 1288 3.650 4866 126.3 1344.5 3.538 4717 122.5 1372 3.422 4562 118.5 1412.5 3.310 4413 114.7 1496.5 3.043 4057 105.5 1536 2.894 3858 | 100.3 Molecular weight: 118. Radius of the Capillary tube: 0.05140 cm. Depth: 0.1 mm. The salt melts at about 820° C.; it begins to evaporate readily | at 1400° C,, and sublimes fast at higher temperatures, 584 § 8. The Temperature-coefficients of the Specific Surface-energy In connection with what was said in the foregoing communication about the calculation of xy, at any arbitrary temperature ¢, lying above the meltingpoint ¢, of the salt investigated, we only need to resume here the corresponding values of ¢,, a, 6, and ¢, for each salt: l | Formula of | eal entree eee | GPa Oe c | Remarks. | - Tasso, 852° 224.4 | 0.067 0 | NaoSO4 884 196.3 0.140 0.00042 KySO, 1074 144.5 0.066 0 | RboSO4 1055 135.0 | 0.087 0.00007 | CsySO4 | 1015 113.1 | 0.087 0.00006 LiNO3 254 118.4 | 0.063 0 | NaNO; | 312 120.7 | 0.063 0 KNO3 339 112.9 | 0.075 0 | RbNO; 304 109.4 | 0.075 | 0 CsNO3 | 414 92:0 | 0.084 0 | LiBO, 845 264.8 0.082 0 Decomposes above 1320° C. NaBO, 965 201.6 0.159 0 | KBO, 946 136.6 0.310 0.00053 Na,Mo0, 687 215.1 0.121 0.00009 Ky Mo0, 919 152.5 0.066 0 Na, WO, 694 204.4 0.068 0 KiWO, 921 158.2 0.083 0 NaPoO; 620 209.5 | 0.059 0 Only up to 1275° C.; then the curve KPO3 820 161.2 0.069 0 bends more ra- pidly to the tem- perature-axis. In connection with the general rules, given in § 7 of the foregoing communication, we can make the following remarks with respect to the data given above. Although in these cases also, the value of yx, at the same tempe- rature ¢ appears gradually to decrease with increasing atomic weights of the aleali-metals, whose corresponding salts are investigated, we see that in the series of the nitrates, the lithiumsalt represents an exception to this rule, because its y-t-curve lies under that of the sodiumnitrate. It is of interest, that just in this series of the aleali- nitrates also other deviations of the normal arrangement are found: so with respect to the solubilities and the meltingpoints. About the relative or absolute values of the temperature-coefficient 4, nothing of general application can be put to the fore: evidently no simple relations will be found here, where the structure of the salts is already more complicated than in the case of the halogenides of the alcali-metals. : Lab. for Inorg. and Physical Groningen, August 1914. : J J 5 a : ze Chemistry of the University. or Bd Chemistry. — “A crystaliized compound of isoprene with sulphur diowide’. By Mr. G. pé Brui. (Communicated by Prof. P. van ’ ROMBURGH). (Communicated in the meeting of June 27, 1914). As is known from the patent literature’) unsaturated hydrocarbons with conjugated double bonds combine in different circumstances with sulphurous acid. Thus, crude isoprene on shaking with an aqueous solution of that acid yields a compound separating in the form of white flakes. When I mixed isoprene, prepared according to Harrigs’s method *) (from ecarvene) and which had been purified by fractionation, the fraction from 384° to 38° being collected separately, with an equal volume of liquefied sulphur dioxide and left this mixture ina sealed tube at the temperature of the room, I obtained after one or two days a considerable quantity of a crystallized product. As a rule the mixture soon turns brown, but sometimes it remains colourless. Beside the erystals is always formed a viscous, white mass which on drying gets hard and brittle. In some experiments no crystals were deposited, but on pouring the contents of these tubes into a small flask it instantly solidified owing to the formation of a large number of crystals. The crystalline product may be readily recrystallized from ether. By repeating this operation a few times a pure, white product is obtained melting without decomposition at 62°.5, Presence of moisture is not necessary for the formation of the crystals, anyhow exactly the same result was obtained with tubes filled with sulphur dioxide dried over sulphuric acid, and dry isoprene. The analysis gave the following results : 0.2016 grm. of the substance (burnt in a close tube with lead chromate) gave: 0.3384 grm. CO, and 0.1107 grm. H,O 0.1612 gm. of the substance gave 0.2814 grm. BaSo, OE iObmGs pa ah 233 3 3» O:3156" 5 59 Found: 45.77 °/,C.6.10°/, H. I. 23.97 °/, 8. Il. 24.35 °/, S. Theory for C,H,SO,: 45.46 °/, C. 6.06 °/, H. 24.29 °/, 5. Determination of the molecular weight by means of the lowering of the freezing point ih benzene: O5491 grm. of substance in 23.806 germs. of benzene gave a lowering of 0°.835. Molecular weight found: 138. 1) D. Par. B. 59862, kl. 120, Gr. 2, 18 Aug. 1910. 2) Ann. 383, 228 (1911). 586 Calculated for C,H,SO, : 132. Hence, the crystallized compound is formed from one mol. of isoprene and one mol. of SO,,. The substance is soluble in water. The aqueous solution has a neutral reaction. If a solution of the compound in carbon tetrachloride or ether is shaken with a solution of bromine in the same solvent, the colour of the bromine is not discharged; bromine water, however, is eradualiy decolourised. With dilute alkaline potassium permanganate a reduction sets in at once. As to the structure of this compound I do not as yet venture to pronounce an opinion. In connexion with Tnieve’s theory the occurrence of a compound of the formula CH, — C|CH,| = CH — CH, | SO, | would not be improbable. Utrecht. Org. Chem. Lab. University. Geophysics. — “7Vhe treatment of frequencies of directed quantities’. By Dr. J. P. vAN DER STOK. (Communicated in the meeting of June 27, 1914). 1. The frequency-curves of barometric heights, atmospheric temperatures and other meteorological quantities assume different and peculiar forms, which can be considered as climatological charac- teristics and, as the number of available data increases, it is desirable to subject these curves to such a treatment that these characteristic peculiarities are represented by climatological constants. If we choose for this purpose the development in series-form, the first question is, what treatment is to be chosen for each special case, in conformity with the distinctive features of the quantities under consideration and the limits between which they are com- prised. The purpose of this investigation is to inquire, what form is to be chosen for frequencies of wind-velocities independent of direction, and of direction without regard to velocity. Furthermore, to state in how far the observed series of quantities may be regarded as normal- or standard-values, and the problem may be stated also in this way: what is the best form for frequencies of directed quantities assuming the form of linear quantities, and further, how to integrate the expression 587 hh' : : eS(h.9) RdRdO Ed toe ere (Lt) J (R.A) =? [BR sin (9@—B) — a}? + h? [R cos (AQ—Bf) — 6}? i.e. the standard-value of directed quantities, on the one hand with respect to @ between the limits 2a and zero, on the other hand with respect to R between the limits o and zero. Both problems were treated in previous communications ')”), but it may appear from the following that now a more principal, and therefore more complete, solution can be obtained than seemed possible a few years hence. 2. If we wish to develop a function of one variable in an infinite series of polynomia n= [2 (a) =A, G;, . n=0 Opa =F aaat a a2 . . ans the quantities a@ can be determined so that — as in the Fourimr- series — for the assumed limits, @ and 6 if Dh thd = 0 for all values of m different from 7. The constants A, are then given by the equation : A, (. daz =(rio U, da. The values of the constants a@ are defermined by the n equations : af [o dz = 0, fe Pale = 0G +. | OE iS ey (2) x every integral being taken between the assumed limits. By partial integration we have: 1) The treatment of wind-observations. Proc. Sci. Kon. Akad. v. Wet. IX, (684—699). 2) On the Analysis of Frequency-curves according to a general method, Proc. Sci. K. Akad. Wet. X, (799-817). 588 x . | UR Gi —— ais 0 e x x | U, « dx = a P,— Ff > =u. da 0 0 x x {v. ui dz =x ~,—22 9, + Ys Ps = |. dx, ete. ‘ 0 0 By (2) it follows from these equations that the imposed conditions are fulfilled when, in the development | Un at de = x" —p,—n 1 —p,...(—1)—1 n(n—1) 20 (—1)rn! nts (8) v0 a y, be given such a value that this function, as also its (2—1) first differential-quotients, become zero for «= and «= «and that then = Apy si ; U,, =a and fee et (=) ain cae remem Cs) aun 8 B This simple method of determining the terms of the required series was indicated in 1833 by Murpny as a new method of coming to zonal harmonies ; in THomson and Tait’s “Natural Philosophy” it is mentioned in article 782. The method, however, is by no means restricted to the calculation of zonal harmonics but can easily be generalized and applied to other circumstances than those mentioned above. Instead of a complete polynomium we can also consider separately even and uneven polynomia; polynomia multiplied by an exponential factor as e-” or e-* may be used, and instead of dz we can take vdv (plane) or a*dzv (space) as the element of integration, whereas for v also quantities of another kind, e.g. siz @, may be substituted. 3. If the limits are + 1 and —4J, it is rational to put: Pn = C (a? — 1)" UF = (6 (z* — 1) C’ being an arbitrary constant. Putting 589 nl C= (2n)! U;, becomes ee ee eae eee oth. (S) 2(2n—1) 2 4.(2n—1)(2n—3) the well known form (but for a constant factor) of the zonal har- monie funetion and, a to (4): 41 eae nin! Qr+1(n!)! OR nS - -- 1)" dx ———— (2n)L J — n+ 12 ny! —l ; 1 . in ; ‘ : utine; = Bees find, if by P, the commonly used form of an! zonal harmonies is denoted, D»\! = _(2n)- U, LY tere nt 22 nInt from which 4 vad 9, TER Oh = = 5 2n+-1 —1l If the limits are + © and — o it is rational to choose for , dn Oy == (C7 lth, == (GF =. OH Pn n dian Putting C (1) aa an U,, assumes the form : | n(n — 1) 2 n(n—1) Yun —2 Yn a) G=ee|| gt — = qn—2 4 ant - 4 ral - CSG. (Oe = ami 219) ye ) eisai siete =— SH nm uneven ( a! (6) In—1 | 9 , Sie a ave genoo’ ( ) (m even) On ! = 2, or and, by (4): + x +a ~ 1? ! U2d nt 2 n: Vy 0h) = er dx = — uw. n On an -— o 0 The series (6), proposed by Bruns ') and CHARitpR *), is in mathe: maties known as Hermirn’s function and might, if applied to analysis of frequencies, be called the gv, function, as proposed by Bruns. It is the most appropriate form for quantities as atmospheric and watertemperatures, barometric heights ete., moving between un- certain limits, and also for wind-observations if generalized for application to functions of two variaoles. In either of the cases considered above the terms of even and uneven power are separated automatically because ae, +o | v+1 dx = 0 and fo e—? dv =0. hese 1 = If, however, the limits are 1 and O or w and O, then such a separation does not take place and we must either maintain the complete polynomium or consider both eases separately. 4. Considering the even polynomia separately for the limits 1 and 0, every polynomium U2, contains only » constants and the development (5) takes the form: x | U2, 02” da = a2" —~, — An a2 ~, + 2? n(n—1) a4 —|, — (7) 0 (— 1)! 22-1 hn (n—1) ... 2 @? Gn (— 1)" 2”. nl Gna where x eb rt = { Wey (ihe “GPS =) P, td@... Prt = | Pn vda 0 0 0 az ze | Us, da =(— 1) 2”. ut Pn wdea . 0 0 Putting lez, A=-— — Xv da ) Wahrscheinlichkeitsrechnting tind Kollektivmasslehre. 1906. 2) Researches ints the theory of Probability. (Comm. from the Astron. Obsery, Lund.). 1906, we find Wa Nar WA or eM seun renee ag 4c. | ((9) whereas for g,, as the simplest expression, we must take: Pn = Ca?! (2? — 1)”. Assigning to C the value: 1 (4n—1)(4n—3)... 2n +1) the zonal harmonic function, as given in (5), is again found also for the limits 1 and 0. In the case of uneven polynomia Uentt = C Ar amH(e? —1ye.. 2. . 2, (9) which for 1 (4n-+1) (4n—1). . ,(2n+8) again leads to the expression (5). ai s 1 Giving C' the value Bape obtain from (8) as well as from (9 - a"! the zonal harmonic function in the form as commonly used. No more as for the limits 1 and 0, the development (7) for the limits a and O leads to new expressions; we have to put Pr C a7 e—2 for even as well as for uneven functions, and by the formulae — Aye 1 H i — = 5 ee : (A = 2)n gen+ti ] on an" az (—1)" } o x (10) Uon4+1 = Sonik ene? (A — 2) aen+1 | we find the same expression as in § 3 for @, of formula (6), but by an abridged calculation. 5. The problem, which form of development is the fittest for frequencies of a quantity which assumes the form of a function of one variable, moving between the limits 1 and O or w and 0, but, as a matter of fact, must be considered as a function of two vari- ables, is not solved satisfactorily in § 5, at least if we are not satisfied by a merely formal representation. A graphical representation of such a function is given by the distribution of points in a plane about a given origin, ihe element of integration is then, not dz, but 27RdR and the question must be put as follows; to find a polynomium such that 592 | U, Um RAR = 0 for all values of m different from 2. The development by partial integration then becomes: | Us R2+1 dx = R2 —~,—2n R2n—2 —E, + 2?n(n—-1) R24 y, -(11) v (Ds Ein (nD) erect yeep where gy, =] Uakdk, 9p, = 19,kdR etc. if U%»,R dR = (—1) n! fotar. If the limits are 1 and 0, then we have to put: Gn = CR (R?—1)r and so that U2, = CAn R2n (R?—1)". 1 Putting C= — we tind for the polynomium : AL ” a (2n)! 2n—1)!/ Oo», — R2n nC, ( : ) nt (n—1)! 2n—2)) * (n—2)! R2n—-2 + ny Vititmes go Cie, —— (112) where "C, denotes the p'" binomium-coefficient of the x" power, further : 1 1 1 . . . l | U5, RAR = 2” (2)’f RdR=(2n)/ | R241 (F?—1)"dR= = 0 1) 0 nin! 2n+1- This new function may be considered as a zonal harmonic general- ized for the case of directed quantities and might be applied e.g. to the distribution of hits on a target. The analogy of (12) with the zonal harmonic function becomes 2n—1)! conspicuous if the latter (5), by multiplication by ae be m—1). given the form: 2n—1)! ; —2! 7, (2n—4)! Ge ak i wy an : : ge gn? oa Aen a) yi 4 selice (n—1)! 2 (n—2)! 2 (n—4)! The expression (12) satisfies the differential equation: Vay R + 4n(n 4-1) RU, =0. 2n aus ee BE) ee ok 593 For uneven polynomia ¢, has to be given the same value as (9) and then again the common zonal harmonie would result. As, however, the quantities under consideration are essentially positive, uneven functions ean be left out of consideration. If the limits are o and O, then the same reasoning holds; it is then rational to put: Gn CR tems Don = CA” BR e-RU'5n = C (A— 2)" RE Putting (—1y On a C= the polynomium assumes the form: TR 3 Den—? n*(n—1)? je. F , Von = R2" — n? R2N—2 + an Ren—4 — ,..(—-1)"n! . (18a) and ce oo Y ! fo RdR = 2”. utfir hak ae : 0 0 S . In analogy with (12) the polynomium, by putting liye Ga eal 2"n! may be written also: Rn R2n—2 R2n—4 es Sa ES yee oes iC had as ° 2), Seamer Ga ne This new function (13) seems to be the proper form of development in the case of directed quantities as wind-velocities, disregarding direction; it satisfies the diff. equations : aS oe poe = a? Usn i dk? R -f- An RUt>, = 0 dk In applyine this development, a simplification may be obtained pplymsg j by a change of seale-value: writing 7R for R and putting v to) to) c + (2R?- a a 4+ 4(n 41) RU» = 0 the second term with the coefficient A, will disappear as U', = (R?—1). Here J/° denotes the moment of the second order of the given frequency-series, 594 6. In the same manner as in §5 in the case of a directed quantity in a plane, the development appropriate for quantities in space may be found, e.g. for distances of stars, disregarding direction. The element of integration is then 47#?dR, and the development (11) holds good if in the left member A?"+! is written instead of 22” and, at the same time for ¢@, 7 = {0 Rdk 0 so that C Cr — R An Pn and fr = C R2n+1 e—R’, Vv Putting ,_ (|) Co Qn U7. becomes : n aon 1 n on 1 on—1 U' ne? Up —=R™ -C, =e R220, a ) R24 . (14 py CRED! es) aly) 22m! and | U*on F2dR = (—1)r. 2”. nt firn RdR = (—1)" 2°—1 nln! 0 0 e In applying this development a simplification may be obtained by writing HR for A and putting: Z 3 HT =o’ then A, = 0, because Uo = 3), 7. Although we may expect @ priort that the Fourier-series is the most appropriate form of development for frequencies of directions (disregarding velocity), it seems desirable in connection with the foregoing to show that, following the same method, we, in fact, come to this result. If 5G SU Ct evel las then we may distinguish four different types of functions, namely : Jes F,= U sinacos a F< Uscotae (en ie Usina 595 For F, the development holds good: ~. [ese ada = gp, sin” a — 2n x, sin?” a 4 (Ca) 5 2n2 — IN 2o (= V)hor nN where ie 9) _ an} » 2 i | Uda j= | Y, sinacosada ete. vu a Therefore, putting 1 d ———————— sin a cos a da 2m! Ga = Cosme" a cose" a and) (Ci (2n)! . . . . T we find for the limits = and OQ: 27. n! pe sin a cos a A” Gy, = cos 2na. (2n)! In the same manner: c 2° nn! car ; : Fy — — A™1 sin"-1 @ cos?"—1 a = sin 2nea (2n—1)! 2". n! i sin at A” sin2”—! @ ¢0s2"+1 « = cos (2n + loa (2n)! 2" .n! th @n)! cos a A” sin?'+1 @ cos?”—1 @ = sin (2n + l)a. an 8. The solution of the second problem, as formulated in § 1, can be simplified by putting @6—PB=~y in form. (1), ie. by counting the angular values not, as usual, from the North-direction, but from NpE; this has, of course, no influence on the sums of the velocities. It is, however, unfeasible to apply a similar correction for the components a and 6 of the resulting wind, and the problem to be solved comes to the development in series-form of the expression : hh as ef g—la—a)>—h'(y —b)2 Fi cos G6 = y FL Risin O =a. It appears from the first of the communications cited in § 1 that, in following the usual method of developing, difficulties are ex- perienced which practically are unsurmountable. In the second com- munication however, it wes shown that the development (6) may be extended to the case of two variables 2 and y, and that such a function ean be developed in a series of polynomia of the form: 39 Proceedings Royal Acad, Amsterdam. Vol. XVIL. 596 F(«,y)=e—°-1"| Aoo U,+-A1.0U1+A0.1 Vit-A2.0U2+A11 Ui VitAoe Vo+et>. ](15) where |’ represents the same funetion of (7) as U of (x) in form. (6). The coefficients A are then determined by the expression: Aa =ef fri ty) UnVm dedy = & Sam —o— © n\m!\ 2m+n xv and y, Rsin@ and Rcos 6, then, by Substituting again for to @, all uneven polynomia vanish and, integration with respect because sin Qn)! in?" a i hie ( nyt cos?” a 227 n'In! 0 we find Ue Vom d@ —- an - (2n)! ! (2m)! ie . »--H? 2 (HR) pe — x, cet 22(n-+4m) n!m! (m+n)! ! 0 (17) (HR 2(m—-n—1 ) HR)2(m-+n—2) = mn ATES ) os --m-fn C, Ce y = (ie, (m+n—1)! “(m+n—2) i.e. the same expression as 13°, found in a different way. As to the determination of the A coefficients, it is expedient to first the case that a and 6 are equal to zero. consider It is then easily found that (2n)! (2n)! Smo= 5,1 At ET? —— 7 fe On ae and similarly for the V funetion (2m)! (2m) ! on= M" H? — */,)2 = Suze am. m! re /s) 2m .m! il Mt = — M? = —— 2h? 2h? The arbitrary constant H now can be given such a value that P or Q=0; putting P=O, then H=A, and in the development only the V funetions remain. If a and 6 are different from zero, then it appears that (for P=0) S,=Q4 10 r|s S,=3 QV 4+ 6hd7Q + hid! 15 Q® + 45 h2b7Q? + 15 A4b'Q + Ab! ie) & or, generally : 597 : (2m)! F _b2Qn—i Son = f2n q2n at Qu 1 m( ES Adie aril m! Qm ; 1 8 Awe hi bs (Qn—? : f2m §2m |\ - (18) m rei, = =p ee —— kg 8 1 .3...(2m—1) Although, therefore, in this case the U functions do not altogether vanish, still the form remains the same as in (132) and (13’) because, as appears from (17), the polynomium has the same value for all terms where n+ m has the same value so that e.g. the terms with A40 Ayo and Ao4 can be taken together. In order to investigate in how far a given collection of wind- observations may be considered as a collection of two independent quantities depending on chance, we have, therefore, in the first place to ecaleulate the constants a, 4,8, hand’ from the set of observations. In the second place the development (184) has to be applied to the frequency-series of the wind-velocities, thereby taking for H either 2 or h’ so that the term J, remains. A comparison between the A constants calculated in this way with those determined according to (18) then gives an answer to the question. 9. By writing in (15) AR sin 6 and hRcos 6 for x and y, multi plying by RdR and integrating with respect to RA between the limits 0 and zero, we obtain a development representing the fre- quencies of the directions independent of velocity. The even terms Uy, and Vo,, or the product Vo, U2, then give rise to a series of terms of the type /, (§ 7) all of which have the factor cos 2ne in common. The even terms Us,41 Vo,41, produced by the product of two uneven terms have sim @ cosa as a common factor and give rise td terms with sin 2na, according to the functions /’, in § 7. The uneven terms, analogous to /’, and /’,, assume a simpler form, namely : Uont1 = Ksmacos*"a and Von41 = K cos a sin” a and therefore give rise to terms with sé (2n-++1) «and cos (2n-+-1) e, whereas all non-periodic terms vanish, except in the first term with A,. A comparison with the Fourter-series thus produced and calculated on the base of the five wind-constants with the Foukrer-series as directly deduced from the observations of direction-frequencies, then again gives an answer to the question. 39* 598 Physics. — “Some remarks on the values of the critical quantities in case of association.” By Dr. J. J. van Laar. (Communi- cated by Prof. H. A. Lorentz). (Communicated in the meeting of May 30, 1914). 1. Though this subject was treated already very fully by me ina paper in the Arch. Tryier') in 1908; and use was made afterwards (in 1909) of the contents of this paper in my Treatises on the Solid State *) — I wish to make a few remarks induced by a paper by Prof. van per Waats in These Proceedings of April 1914 (p. 1076 et seq.) which may contribute to the removal of the pretty large difference found by him (p. 1081) for the volume value of CH, for methyl- aleohol (2,12) and for ethylaleohol (2,76). Van per Waats makes namely use of values of vz, RT, and pz, of which he states (on p. 1078) that they would be exact by approxi- mation. But it has appeared from the investigation made by me in 1908 that the “linear” dependence of the quantities RZ), and s of the association factor 2: (1 + 8) cannot be assumed even by approxi- mation. Not only does this hold when (as v. p. W. assumes) the volume of the molecules does not undergo any change on association ; when in other words A/ = — */, 6, + 6, = 0 — but the deviation in question presents itself to a much greater degree, when Ad is not = 0, as is certainly the case for water *) and the alcohols. In the cited TryLer article I started from the equation ——) J 2 in which @ represents the degree of dissociation of the double mole- cules, so that to the original '/, double molecule are found '/, (1 — 3 double molecules and */, . 23 = @ single molecules, together ‘/, (1 + 8) molecules. 1) Arch. Teyier (2) T. XI, Troisiéme partie (1908): Théorie .générale de l’asso- ciation de molécules semblables et de Ja combinaison de molécules différentes. (p. 1—96). 2) These Proc. of April 22, June 25, Aug. 31 1909; Nov. 24, 1910; Jan. 26 and June 23, 1911; resp. p. 765, 26, 120, 138, 454, 656 and 84. (See especially the third paper, p. 127—130). 3) Already in 1899 I think I showed that the phenomenon of maximum density at 4° C. can be explained in a very simple way by the assumption of a negative value of ab, so that a double molecule would have a larger volume than two single molecules. [Zeitschr. f. physik. Ch. 31 (Jubelband fiir van ‘t Horr)], Doe The quantity @ appeared to have been left unchanged by the association, viz. =a, — the value for the case that all the molecules are single — everything referring to a single *) molecular quantity (e.g. 18 Gr. of H,O, 46 Gr. of C,H,O, ete.). For we have evidently (the index 2 now refers, in distinction with my Trytur article to the double molecules, the index 1 to the single molecules) : 1—p\? Je! AD 2B 7 a=|(— >-]% +2 - aa fh an ies = a c) - a, and a, = 4a,, so that we get: =] z = 5 R e | b a=(1 — @fa, +21 B) Ba, + B?a,=a 1° Further : 1—p 23 f ps =, BSS OS , SS a or ='/,6,+ 8(—‘°*/, 6, + 6,)="/, 6, + B Abd. The equation of state used by van pur Waats (p. 1078) is identical with ours, as VAN bDeR WaAAIS starts from 1 —.2 single molecules and 2 double molecules, together 1 mol., while we started from single molecules and (1— 3): 2 double molecules, together */, (1 + 6) molecules. Accordingly we left the quantity of substance (viz. a single molecular quantity, e.g. 18 gr. of water ete.) constant, and varied the number of mo/ecules on association from 1 to '/, (1 + 8) — and van ppER Waars left the number of molecules constant = 1, while he increased quantity of the substance from 1 to 1+ 2. If this is borne in mind, van per Waats’s v: (1 + 2) now passes into v' (now just as with us referring to a single molecular quantity of substance), and we get : RT :(l+e) a, P — (i ene Gaens? v—b, v in which therefore 1:(1-++x) is identical with our (1 + 8): 2, v’ with our v, VAN DER WaAAtLs putting 4/—0, and therefore identi- fying b with 6,. 2. As (, the degree of dissociation of the double molecules, is a function of v, the dependence of the quantity @ on v will have to be taken into aecount in order to find the values of the critical 1) In the cited Tryter article | made everything refer to a dowble molecular quantity, but I think it more practical to continue to make the different quantities refer to a single molecular quantity. Hence all the quantities have now been divided by 2, resp. 4. 600 3 ; f ; Op ) quantities in the determination of = = 0 and = = 0. The ealcula- v v tions relating to this are pretty laborious, and were carried out in a separate chapter (§ 5 p. 25—34) in the cited Tkyuer article (ef. also the above cited paper in These Proc. of Aug. 31, 1909, p. 127—130). We refer to this article, and give here only the results of the caleula- tions — again making everything have reference to a single mole- cular quantity. For vz was found: 2 mm BE APES 3m? — Qn’ (2) in which m=1 + */,8(1—8) (1+9)* a m=1 +4 */,8(1—8) (1+-y) + */8 1—8) 1884) (1+) w hile Ab PU) eae Peer ss (5) (p. 26 and 29 loc. cit.). When Ab=0 and so also gy =O, as VAN DER WAALS assumes, even then remains: m=1 + */,8(1—8) =(1+8) (1 —*/,8) 3 1/ £ 2 2 9 a(’ (3°) m— 1 4-9/6 (18) +) op) (hep) (an hea through which for vz, with 3m*—2n = (1+ 8)? (1—’/,8), is found: (ear "90 2a VI oN Tas (2°) In this the factor 3 must of course be replaced by a smaller one (e.g. 2,1), when & is a function of v, and varies between 6, and 6,, when v varies from o to 2%. With regard to the factor of 3b; —— which according to VAN DER Waats (referring namely to a single molecular quantity and not to a 1+ times larger quantity) would remain constant = 1 (at least by approximation) — we see immediately that this factor can differ pretty considerably from unity. For @=0 (only double molecules) and 3=1 (only single molecules) the factor is properly = 1, but for B= 7/, it has the minimum value */,. And this deviation, which al- ready amounts to 11 °/,, is still more pronounced when Ad is not =O, but has e.g. a negative value. For RT; we have found (p. 31 loc. cit.), again referring to a single molecular quantity : 601 8 a, 2 n*(dm? —2n) 27 by i= 8 m® RI, = teen c08 (5) which with 44 =O passes into 8 2 1+ 8)(1—°/,6 + */,8°)? 1—*/,8 ee ale ( +B) ( /sf an me /4P) (52) Nate ase (1—?/,8) A 8 If 8=1 (single molecules), then RZ, duly becomes = 1 8 but for 8=0O (double molecules) RZ; becomes = 2 Xap But it is again immediately seen that 7), certainly does not linearly change with 2:(1-+8), ie. with van per Waats’s 1-2, as the latter assumes on p. 1078 of his treatise. For the remaining factor is indeed again =1 for 8=O and B11, but it is 3456; 3125 = 1,106 for p= */,; = 1445: 1296 = =e tor P= */,; and 1125 ; 1024-— 1099) for 6 = 7/,. The deviation can therefore again amount to 9°/,, in comparison with 11°/, for vz, but in opposite direction. This deviation too is more pronounced, when 4é differs from 0. With regard to the value of pz, at last, we find: I a (8m? —2n)? (4n —3m) — » Oe OOM Ok 0 6 Pk 27 6; a m? (9) passing into 1k @ (1—*/,3)? (1+ 8—8p* + °/,8°) ‘ Pk = 55755 X — Pace (GO 27 6, (1—’/,8) when Ab=0. For 4n—3m = (1+) (1+8—36"+"/,6"). 1 The factor of aia duly has the value 1 both for 8 =O and a 1 pies but becomes == 4617 3 3125 — 1477 for §='/;; = 379: oto — e430 fon) p 7/2; and —— 189. 128: — 76) for p=". Accordingly the deviation from unity is very considerable — for B='/, more than 54°/,. Hence there is no longer any question of an approximate equality to as VAN DER Waals supposes he a a7 8” may assume. (p. 1078 l.c.). And this amount can still increase for Ab not = 0. 1) If it is taken into account that a = !/,d, b) =1/, by, RTk becomes as it ; a . A : always did = 5? in which a and b, now refer to a double molecular quantity. 2 8 27 602 It is therefore self-evident that when the quantities s= RT}: peor and 7: pz are caleulated, which occur in vAN Der WaAALs’s consi- derations, no linear dependence on 2:(1-+ 8), resp. 1 -+ x is to be expected there either. 3. Now Ri wee ae ni? = ee re Pevk & 14+ 8° mn? (4n—3m) is found for the quantity s, passing (with Ab = 0) into 8 2 \ (WIS ai Bom B*)* (7 ) = — — < = a a 3 1p (=, eb = see) For 8=1 (all simple molecules) s becomes = s, = °/, (or =3,77, § when 6 varies with v), and for 8=O (all double molecules) s becomes = °/, <2, hence twice the value. But here too we remain very far from linear dependence. For @='*/,; we find namely for the last factor in (7a) the value 384 :475 — 0,808; for B='/, the value 280: 360 = 0,803; and for 8=7?/, the value 375: 448 = 0,837. Hence a difference of about DO Aeon irae On account of the importance of the accurate knowledge of the value of the quantity s for associating substances, I have calculated the following table. 2 S B ae = ee Factor | ite X factor = S 0 2 haga | 2 0.1 1.818 | 0.903 1.642 0.2 1.667 | 0.847 1.412 0.3 | 1.5388 | 0.815 1.253 0.35} 1.481 | 0.805 1.192 o4 | 17420 | orent | 1.145 0.5 | 1.333 0.803 1.071 0.6 | 1.250 0.820 1.025 0.7 1.176 | 0.849 0.998 Oh |) Meili | 0.890 | 0.989 (min) 9 | 1.058 0.945 | 0.995 als 7a leit 1 603 Instead of a regular linear deerease with 2: (1)+ 8), 1.e. with 1+ 2, values are even seen to appear <4 in the neighbourhood of B=1 (all the molecules single), with a minzmum at about B= 0,8 (accurately at 80,8015), and a horizontal final direction, Le. d (ss is) =° On increasing association (3 from 1 to 0), s will therefore first become somewhat smaller than s, (= 3,77 for “ordinary” substances), and then (from @ = 0,7) s:.s, will become greater than 1, and increase to 2 for =O, when the association to double molecules is perfect. A straight line for s:s, (as VAN DER Waats thinks) therefore replaced by a line that is pretty considerably curved downward between the values 2 and 1 with a minimum close to 1, so that s:s, at first decreases there instead of increasing. What consequences this behaviour will have with respect to the degree of assvcuttion B, caleulated from the value found for s for methylalcohol, viz. 4,52, may appear from what follows. As s:s, == 4,52: 3,77 =1,2, we should find about S=0,67 or v=0,2 for B, according to the second column of the above table, when we were led by a supposed linear dependence. But when we also take account of the “factor” by the side of 2: (1+), we find about B= 0,35 or c=0,5 from the last column for the value for 8 answering to the ratio s:s, = 1,2. A difference, in fact, too large to be neglected. Instead of 0,8 single molecules to 0,2 double molecules, as vAN DER WaAats would find with his linear dependence, we find more accurately 0,5 single molecules to 0,5 double ones. The relation x: (1—a) has become 1 instead of 4. 4. The second quantity which plays a part in the cited paper by vAN DER Waats, is the quantity 7%: pe, which may be put propor- tional to the molecule size for non-associating substances. We now find for it: Lee 8 2 (1-8) U—*/,8+ */.8°)° —— oak (Sa) ap IP BL S83) (Sais oS) which with 46 =O passes into IL ip 8 2 n* == by. = pth Lees go) BAe) Dk - Ri 1+. s (3m?—2n) (4n—3m) We shall not discuss the course of this again, but solve from this 604 Q 5 the required value of = Ok: By means of (7) and (8) we find easily : ay 8 Tienes 3m?—2n 6) = — b = : ran. eee 5. ((Y) R : ie *) x m?* @) or when Ab=0O: 8 Ty 1—'/.8 6b) = — 6. = : A ¥ ye ee Qa One & Shae ue When therefore the value of 8 has been found from (7) and (7a), it can be substituted in (9) or (9a), and 8/p 6, is known. According to van per Waaus, (0) would be = 6,52 : 1,2 = 5,43 for methylaleohol, whereas (for A= 0) the more accurate value with 8= 0,35 (see above) would amount to 5,43 1,084 = 5,89. This value is still larger than that found by van per Waats, and would yield 7,55 5,89 = 1,66 for CH,, instead of 2,12. And when 4)=0 is assumed, the accurate value of (4) will be larger than ihe approximate one for every value of 8, because 1 — */, is always SS (eee ae It is, however, easy to see that when not (7a) and (9a) are used for the calculation resp. of 6 and (6), a value <1, e.g. 0,88 can very well be found for the factor (8m*— 2n):m? in (9), through which 5,48 would diminish to 4,78, so that 7,55 — 4,78 = 2,77 would be found for CH,, in good harmony with the value found for ethylaleohol. Now (8m? — 2n):m? becomes < 1, when ‘ > ye Or) m2 fh (ie) (loa) (aaa must be, i. e. BULB) CL Pee) On Bie pa — 7, namely = about 8,6 (ef. Kurnen, Die Zustandsgleichung, p. 142, where the value 3,75 >< 2,30 is given), the factor of /, would have to be about J,2 instead of 0,84; i.e. Ab not =0, and again negative or also the value of g (see the full formula in Tryner, p. 42) would moreover have to be different ik — Te x ’ from 0, and that positive. Fontunivent sur Clarens, May 1, 1914. Physics. — “On apparent thermodynamic discontinuities, im connection with the value of the quantity b for infinitely large volume.” By Dr. J. J. van Laar. (Communicated by Prof. H. A. Lorgntz). (Communicated in the meeting of June 27, 1914). 1. One of the principal results of the foregoing series of commu- nications ') has been this (cf. particularly II p. 926 and IV p. 464), that the quantity b,, i.e. the value of for infinitely large volume (hence in the ideal gas state) cannot possibly be = 4m as the classical kinetic theory gives for it. With decreasing temperature }, approaches namely more and more to &,. If in the ideal gas state 6, were —4m, 6b, would have to be =4m also at very low temperature (this kinetic result holds namely independent of the temperature), while in the condensed liquid state with cubic arrangement e.g. of the molecules, supposed to be spherical, 6, would be about = 2m’, in which m’ is either equal to or smaller than m, so that then b, cannot possibly become = /,. 1) These Proc. of March 26, April 23, May 29 and Sept. 26, 1914 (to be cited as I—IY). 607 And yet, everything seems to point to this that actually a// sub- stances at sufficiently low temperature approach to the type of the mon-atomice substances with exceedingly low critical temperature, at which the quantity 6 remains almost unchanged on diminution of the volume from o to v,. Instructive are in this respect the tables in I, p. 819 and III p. 1052, and also Porncaré’s and Kameruncu Onnes’s remarks in the discussion of Nernst’s Report (Conseil Sotvay German edition, p. 241 at the bottom to 242), where it was pointed out that at very low temperature also the molecular heats of air and hydrogen would probably approach to those of monatomic gases. The above contradiction is now immediately removed by the assumption that in the rarefied gas state 6 is not = 4m, but simply =m (the real volume of the molecules, at most enlarged by a certain sphere of influence), while also in the condensed liquid state 5, is =m’, (m’ as a function of v and 7 (of whatever nature this variability may be) — have yet come 608 the so-called quasi change, which would be caused by the diminution of the old factor 4 to about 2 in consequence of the partial over- lapping of the ‘‘distance spheres’. We namely assume that the volume available for the calculation of the pressure is immediately found by subtracting the volume of the molecules m from the total volume 2, always assuming that the kinetic energy of the moving molecules and molecule groups, with the permanent gradual interchange of the energy during the collisions, is continuously absorbed by the surrounding medium (see I p. 809, and IV, p. 464 at the bottom), and is finally after subtraction of the internal molecular pressure observed as ‘‘external pressure” It will be asked what part the so-called association or quasi-asso- | ciation plays in these considerations. Before answering this question I will first state clearly my opinion about the difference between association and quasi-association, which I hold in connection with the following considerations. We may briefly express this difference in the following way. Real association is quite individual and has a permanent character ; it quite depends on the chemical nature of the molecules (whether there are e.g. still free valencies or minor valencies present ete.). Water, alcohol, acetic acid are associating substances — _ ether, benzene, chlorobenzene ete. are non-associated substances. Quasi-association on the other hand in consequence of the action of the molecular forces, when two molecules get into each other's neighbourhood, and which gives rise to the formation of temporary “molecule aggregations’, ts entirely the same for all substances in corresponding states, and of transient, albeit stationary nature. This last form of association, which has been particularly studied by van per Waats, is competent to explain why with the ordinary kinetie view (which, when a// the active factors are taken into con- sideration, must also lead to the truth) not 6, = 4mis found but less. The theory which — evading the separate consideration of the moving under the notice of many, may appear again from an article by A. Wout in the Z. f. ph. Ch. 87, p. 1—39. This author thinks he can set everything right by an equation of state of the wholly unjustifiable form RT a c in which a, b, and c are constants. That it is also possible to arrive among others at the accurate values of the critical data by putting 6 variable with v in the ordinary equation of state, does not seem to have occurred to him. Also von Jiipryer’s many articles convey an impression of his not being at all in touch with the new investigations in this department. 609 molecules, of their collisions and their temporary aggregations — goes straight to its goal by imagining (see above) all the energy absorbed in the surrounding medium, makes it further acceptable that 4m would after all have to become simply m. But that the theory of the quasi-association can only be of any use in the rarefied gas state, in conjunction with the theory of the colliding molecules, and that the medium theory can be left aside — though there always remain constants undetermined (viz. the associ- ation constants), as we shall immediately see; and that this theory entirely fails for more condensed states — this is immediately to be seen. For if one would apply the quasi-association theory to liquids, the number of molecules associated to one molecule would theoretically continually increase, so that finally — in the limiting state — the whole liquid mass would have to be considered as one single asso- ciated giant molecule, for which the equation of state of the substance would then lose all its significance, as this is based on the joint action of an exceedingly large number of molecules, and not on a single molecule. What for larger volume can therefore be taken as the equation of state of the whole mass of the substance, would now have passed to the equation of state of a single giant molecule. But in this the separate moleeules can again be taken as unities (real association excluded of course) in consequence of the very slight mutual distances (just as for a solid substance), and the equation of state resulting from this will have analogous meaning as the original one, which holds for the gas state. Only we shall then have to take into account the continual change of the number of degrees of freedom. The theory of quasi-association, applied to condensed states, would therefore lead to great contradictions. While the molecules practi- cally behave as single ones, the said theory would lead to an infinite complexity in one giant molecule, with abolition of the original equation of state. While van per Waats, therefore, thought he could chiefly explain the deviations of the liquid state with respect to the ideal equation of state by the association theory, we see that exactly in this state this theory would lead to contradictions. It may only be applied in the rarefied gas state, though just there it is not necessary as an explanation of the deviations from the equation of state meant by vAN DER Waats, which would make their appearance not before the liquid state, but which as we saw in the foregoing articles cau be explained also without the assumption of quasi association. It is indeed necessary, however, as we shall see presently, to explain that then 47 can become m. 610 That with respect to the 4-values just liquids behave entirely according to the ordinary theory with 6= f(v,7) — without quasi association being taken into account — has appeared in my recent caleulations with respect to Argon. In 1V p. 458 we saw namely that the liquid values of 6 behave entirely according to the relation b= (v) derived by me (if namely 6, = 6,: vz is only raised from the value 0,286 obtained by extrapolation to 0,305). That the vapour values of 6 exhibit deviations, and even become impossible, is to be ascribed to the way of determination of the* vapour volumes at lower temperatures — since it is no longer by direet observation, but by application of the law of Boyin, which is not yet quite valid then, as I have shown in IV p. 457. 3. Let us now proceed to examine the influence of the quasi association in the very rarefied gas state, by which it will be proved that the kinetic result 6, = 4m can no longer be maintained. Abbreviated derivation. If in first approximation (this is permissible for great v) we put the quantity 6 independent of the state of (quasi) association (the quantity @ is always independent of it), the equation of state for great v is: po— 6) (ee) ee eee ee (C08) when a fraction a of one single molecule associates to double mole- cules, so that there will be 1—a single and */, double molecules, together 1—'/, a. With very large volume the numbers of triple, quadruple ete. molecules can namely be neglected with respect to that of the double molecules. In this « is given by an equation of the form (see for a justi- fication of this and of some other assumptions the Appendix) Ci (1 — x)? CL SS Ss SS _ ‘ cr 1 ,v(1—’/,@) p as the concentration c, of the single molecules = 1—«) : (1—’/,«), and that of the double molecules c, = */,«:(1—*/,2). In this it is supposed that also the specific heat does not undergo any change in the quasi association, and that moreover the energy change may be put = 0. In the ideal gas state we have 7’: p= (v—6): R(A—"/,2), according to (1), so that we can also write: (l—a)? 7 e@ or also, as a will always be exceedingly slight with large volume, C ; =F (v—)), and 7» may be written for v—b: If we put: pv - b') = RT, in which 6’ is the value of 6 which would be found by leaving the quasi association out of account — so the real value therefore in the usual sense —, then by comparison with (1) follows: v—b b b v— = —=v( 1 — —}(l +2/,e) =vj 1——+ 1,2], 1-—'/,a v v ; sO v—b =v— 64+ 0.'/, 2, thus CTU Os ia) ee se og oe ee (3) According to (2), however, v.'/,«®= R: C, when v approaches to o and wv to O, so that we finally get; y=! R » = b — C he a eo te a (2) in whieh 64m according to the kinetic theory of the perfectly elastic collisions of the molecules, supposed to be spherical. And as C’ — the association constant — will always possess a jinite value, for else there would not be quasi association, we have always: v< b, 1. @. b'< 4m (q.e.d.). At the head of our paper we spoke of “apparent” thermodynamic discontinuities, and mean by this what follows. If there were no quasi association at all, i.e. if the association constant C’ were absolutely = 0, so that there could not exist quasi association at any volume, however small — then 6’ = 6 = 4mm. But as soon as there exists quasi association ((C’ finite), however slight it may be (according to (2) =O for v=o), immediately 6 (= 4m) is diminished by the finite quantity R: C, as v X */,7= » XO is always finite, so that 6’ becomes < 4m. There is therefore discontinuity — for at an association state = 0 for v=o, b’ can have the value 4m, and also possess all the values <(4m. But this is only apparent, because the diminution of 4m depends continuously on the value of the dissociation constant C, which can vary from O to any finite value. Now Cis not known, and this quantity, which depends on the entropy constants, could only be determined by statistical-mechanical way, when we knew ail the circumstances accurately and could take them into account, which determine the quasi association. In 40 Proceedings Royal Acad. Amsterdam, Vol. XVIL. 612 default of this knowledge we can therefore only say that probably 2 ia C will be such that 6’ = 4m — 7 will become about 6’=m,, in which m,, represents the volume of the molecules with their immediate sphere of influence (see § 1) — in harmony with the theory of the absorption of energy and transmission through the intermolecular medium (ef. also § 1). If an analogous image is wanted: the old ballistic theory of the rectilinear motion of the colliding molecules is in the same relation to the modified theory, “in which the temporary mutual influencing of the molecules is considered which will take place at every impact, or (what comes to the same thing) to the medium theory — as the consideration of the effect of a ray of light, after it has passed through a narrow aperture without taking the inflection into account, so that only that part of the space behind the aperture would be affected by the light which is in the direction of the ray — is in relation to the complete consideration of the light- effeet with observance of the diffraction, in which therefore the whole space behind the aperture is affected by the light, and of which it is possible to determine the distribution of the intensity. Appendia. Complete derivation’) of (A). If a fraction x, of 1 mol. is temporarily joined to double molecules, a fraction v, to triple molecules etc., we have therefore: n,—1—2#,—2,... single mol. ; ,=%*/,2, double mol; n, ='/, «, triple mol.; ete. If further generally : b=n,b, +n,b, + 7,6, +.., then = (1 —a, — 2, — 222) 0; Ey OF, Oe ee or OD me (Des ig) eg Onan) ere In this 6, —*/,6,= A, 6 represents the change of +, always when a half double molecule dissociates to a single molecule; 6, —*/, 6, = A,b the change of 6, when one third triple molecule dissociates to a single mol.; ete., so that we can also write: b= b, — 2x, 4,b—a2x, A,b — ete. ee to (a That a does not change in consequence of the association, is known. For three kinds of molecules e.g. holds namely : 1) Already derived by me in 1908, but never published. 613 @=n,?a, + na, + n,’a, + 2n,n,a,, + 2n,n,a,, + 2n,n,a,, ; meawnich @, = 40. , a; = 90. 0, — 20. — 3d, and @,; = 6a;, so that we get: a=—n,?a, + 4n,?a, + 9n,?a, + 4nyn,a, + 6n,n,a, + 12n,n,a, = (n, 4+ 2n, + 3n,)?u, =a, , as n, + 2n, + 3n, = (1 —2,—a,)+2a,+2,=1 We may therefore write: (» a 5) (CES bao REE. erties arr () v in which 6 is given by («), and (see above) C= =n =) Sy —— ol Giese a vaso to 64) The following equations hold for the dissociation equilibrium of ihe double, triple ete. molecules resp. (cf my alveady frequently cited Teyler paper 1908: Théorie générale de association ete., p. 5, and also These Proc. of June 23, 1911 (Solid State VII), for- mula (28)): (l—a,—a,—...)? C 2 tt 5—%/RT ete eee RY - pe Tas ee = ere 3 e/ a pte re ees MO Gea ea Ge ee role? Wi a (p+4/o)? or taking the equation of state (@) into account : Bee ee By (1 Uyg— Lye ) a C, Th oe b/ RT e— 9. 2Agb : (e—b) (y— ) af ic R beep NN 7 papers tea) (L—#,—#,—-. ) wee 2778 6 —WRT ¢ - 9. 3Agb : (v—b) (y —)? 1 a 78 is Ws, vv . . . . ry . . . > . . . i . ry . . . in which C,, C,, ete. are the dissociation constants resp. of the double, triple ete. molecules; y,, y,, ete. the changes of the specific heat in the dissociation, divided by R, viz. y, = (2k,—A,): R, Y, = (38h4,—A4,): R, ete.; 9,, qs, ete. the heats of dissociation (energy changes) 2(¢,))—(e2)o, 3(€,)> —(@,),, ete.; Ab, Ad, ete. the variations of 6 already introduced above, which must now resp. be multiplied by 2, 3, ete., the above equations referring to n-fold molecular quantities, and not to a single quantity. The first member contains the relations of the molecular concen- trations, viz. 40* é* (n,:2n,)? 2,7 (1—#,—a,—...)? = = 7 Tt i ce Dn Oe nO ile 's (2) e,* _ (n,: &n,)? De (l—#,—2#,—...)* == ry ? cn Mae eaHey role Vion ald ete. (for Yn, has namely been put 0). For the dissociation constants C,, C,, ete. holds: log C, = — ¥. + Ay + (log R — 1), log C, = —y, + 4, + 2 (log R— 1), etc., in which A,y, 4,7, ete. represent the variations of the entropy constant, divided by A, viz. A,yj=(2(,),—(m;),): 4 Ap = = (3 (,), — (1,).): KR, ete. If we now put all the quantities y and g=0, which is allowed for quasi association (otherwise we only think the terms referriny io it included in the dissociation constants, e. g., CT? ¢ t/RI= = C,’, ete.), then for large volumes, where «,, 2, ete. will be slight: : S C, e— 4 2dgb :(v—b) (y—b) ie vy Kh 1 y; _— A e—4.3A3b : (v—b)(y — B)? ne - or as also Ab: (v—bd), A,b: (~—), ete. will be very small for large v, and v may be written for v — b: . R 1 ma “itr m ee C, ai CLC) er mae of which the first equation is identical with (2) of § 3. We further see, what we have already immediately put in our abbreviated derivation, that really for very large volume .,,.7,, ete. may be neglected by the side of «,, and that therefore the consider- ation of the dowble molecules suffices with disregard of the numbers of triple and multiple molecules. If we now again compare the equation (3) with (p+-¢/,2\v—bJ=RT (the latter therefore without taking quasi association into account), then (see also (@) and (y)): v—b = y—b,4+2,4,b+2,A,6 +... 6 1—*/,7, — ?/,0,—-- hence with neglect of z, ete. by the side of w,: v—b,—wx,A,b b, 4b ; v — = ——. ——— ore + fre . ; z —. SR or 615 7) l b! = »—b,--2, 4,6 + v.*/ ob In this the infinitesimal quantity ,4,b (also when A4,/ is finite) may be neglected by the side of 6, and the also finite quantity Ho /s2,, and we get: OO Ue eae, identical with (3) of § 3. For v.'/,2, the value R: C. , follows then again from (), and the conclusions are further as in the cited paragraph. Fontanivent sur Clarens. Chemistry. “Ourrent Potentials of Electrolyte solutions’. By Dr. H. R. Kruyr. (Communicated by Prof. Ernst Coney). (Communicated in the meeling of June 27, 1914). 1. For a proper understanding of the reciprocal action between electrolytes and colloids the knowledge of the capillary-electrie phenomena is indispensable’). Researches on the influence of the electrolyte ‘concentration in these phenomena have indeed been earried out of late years; Pwrrin*) and Enissarorr *) studied the electric endosmose of electrolyte solutions, Burron *) determined the influence of electrolytes in various concentrations on the cataphoresis whilst there already exists a vast material on the capillary-electro- meter and the dropping electrode’). The recent investigations were, therefore, chiefly concerned with the measurement of the phenomena of motion in consequence of a supplied electric tension ; the reverse phenomenon, however, namely the occurrence of an electric tension in consequence of a moving electrolyte solution has been but little studied "). The former investigations on these current potentials (generally, though less accurately, called “Str6mungsstréme”) are restricted to pure water. True, Crwonson’) states that electrolyte solutions cannot produce current potentials, but from the quoted treatises of Gourk pe ViILLEMONTEL *) it appears that the latter only 1) For full details of this problem see H. #RmUNDLICH, Kapillarchemie, Leipzig 1909 in very condensed form H. R. Kruyz, Aanteekeningen Prov. Utr. Gen. 3 June 1913 p. 9 and Chem. Weekbl. 10, 524 (1915). 2) Journal de Chimie physique 2. 601 (1904). 5), Z. f{. physik. Chem. 79, 385 (1912). ), Phil. Mag. [6] 11, 425; 12, 472 (1905) and 17, 583 (1909). 5) Detailed literature statements in Cuwo.son, Lehrbuch der Physik IV 1. 6) The most important investigations of recent times are those of CAMBRON and Orrrincrr, Phil. Mag. [6] 18, 586 (1909); GrumBacH, Ann. de chim. et de phys. [8] 24, 433 (1911) and Ruiry, ibidem [8] 30, 1 (1918). 7) |. ce. note 5. 8) Journ. de phys. [3] 6, 59 (1897). 616 investigated solutions of CuSO,, ZnSO, and NiSO, in the concentra- tion of 10 grams per litre. Because current potential and electro- endosmose are so to say each other’s reflected image *), one may rather expect that the electrolyte concentration will make itself felt in a similar manner in regard to those two phenomena. As Euissarorr (I. ¢.) found that even exceedingly feeble electro- lyte concentrations strongly diminish or suspend the electro- endosmotic transport, we can only assume from the negative result of Gourté pe Vitiemontée that in the concentrated solutions used by him the potential is already lowered to about zero. Rufty’s result *) have also confirmed this conclusion. Grumpacn *), who investigated the influence of non-electrolytes on the current potential, has not used pure water as comparison liquid but a KCl-solution of the concentration 1 millimol. per litre and in this manner obtained positiv results. In the investigation here described I have made use in many respects of the experimental methods mentioned in GruMBACH’s paper. 9, KEM Yi); CL A i —— SS SSP 5 & A Bee, EI el OW, We) QO oO f aR & Q oO =| iB; Fig. 1. *) Vel. SaxEn, Wied. Ann. 47, 16 (1892). =) JE Os ) I ee Vv I I 3 617 2. Apparatus. In tig. 1 the apparatus used is represented schematically. The liquid serving in the experiment runs from flask F into flask F, through a doubly bent glass tube Aap, which is partly drawn to a capillary. Into the three-necked Wouter flask /,, which is closed by means of rubber stoppers with copper wire ligature, arrives also (1) a tube @ through which air can be pressed and (2) an electrode #,. In the other flask /’, is found an electrode &, and a thermometer 7. The electrodes are Ag-AgCl electrodes. A silver wire is fixed into a glass capillary by means of CaiLLrret- wax, The protruding end is electrolytically covered with AgCl according to the indications given by JAHN *). A constant pressure above the liquid in flask /’, is obtained as follows: by means of a cycle foot-pump mereury can be pressed from the reservoir /, into R,; the pressure thereby generated is read off on the open mercury manometer. As owing to the transferring of the liquid from /, to /', the pressure would diminish a little during the experiment, it is kept constant by means of the arrangement CD by turning the handle C. The measurement of the potential differences between the electrodes E, and E, was carried out by the compensation method of Pogary- porFr-pu Bots Reymonp. A galvanometer could not be used as a zero instrument because the strength of the current passing through the instrument is exceedingly small in consequence of the enormous resistance in the battery /F,. Hence, a capillary electrometer (KEM in fig. 1) was used, which was fixed to the object table of an ordinary microscope; the axis of the microscope was, of course, placed horizontally. The readings were made using of an ocular- micrometer, objective 4c (Reicnert) and Huyeens ocular 1. The following serves to further explain the figure. S, is a key for cutting off the short circuit of the capillary electrometer; A in- diecates that this is connected with the earth. As working element are used one or more accumulators Acc whose tension was determ- ined by comparison with a Weston standard-cell, which was placed in a thermostat at 25° (WNE). By O the different current inter- rupters are indicated; by O, the electrodes #, and £, can be brought into short circuit, which was always done during the time that no observations were made. By Q, the current of the working cell is twitched in; QO, annables to introduce at will one, two or four accumulators as a compensation battery. QO, renders it possible to take up in the circuit either the standard cell or the battery 1, /’,. 1) Zeitschrift f. physik. Chem. 38, special page 556 (1900). 618 In order to protect the Ag-AgCl-electrodes from the light, the flasks /’, and /, are externally coated with a film of red gelatin obtained by inserting them in a solution of gelatin to which a little eosine had been added and which had just started to gelatinise. Moreover, they were always protected from direct daylight. 3. Method and preliminary experiments. The measurements were made a few minutes after the pressure had set in. A number of measurements at different pressures were always made. When between {wo measurements the liquid had to be pressed back from flask /, to flask 7’, (for which at @ the connection with the pressure arrange- ment could be broken off and an oil suction pump attached), no measurements were executed at suction pressure. From Grumpacn’s experiments we notice that the value of the current potentials varies a little during the first days after the con- struction of a battery /,F,. 1 repeated one of his observations, also with the object of comparing the results obtained with his and my own apparatus. Table I contains the results of a series of measurements carried TABLE I. p iE E P| ae ae em mercury) millivolts P cm mercury , millivolts | P 11 March = t= 14° | 622 | 253 4.1 61.2 271 4.4 SIe | 218 4.3 86.4 367 4.2 average 41 54.8 236 4.3 yj Mes March Le OS 70.8 315 4.4 82.2 310 | 3.8 average 4.3 85.2 323 | 3.8 12 March 1 1 ele 22 280 3.9 43.2 201 tel “eos | |) 1236 ll ene 57.2 240 4.2 average 3.9 68.1 | 280 41 16 March = t= 14° average 4.2 | 86.2 | 341 | 4.0 13 March = t= 14° 70.2 | 284 | 4.0 85.2 | 350 4.1 58.8 240 | 4.1 73.2 | 302 | 41 | average 4.0 619 out with a solution of the concentration 1 m. Mol. AC/ per Liter. The battery was filled March 11'". P indicates the pressure, E the current potentials. From this we notice that the apparatus acted splendidly. The potential per em. mercury pressure has each day a constant value, but varies the first two days. On the third day the terminal value is attained. 4. Ieasurements. In this paper a series of measurements is com- municated, the object of which was to ascertain the influence of some solutions which differed in the valency of the cation. Therefore solutions’ of the chlorides of A’, Ba’, and Al" were used. As solvent was always used so-called “conductivity water”. The very dilute solutions were made by diluting a standard solution. Ali measures used in this investigation were carefully calibrated or recalibrated. In order to shorten the time of these tedious measurements they were all executed 20 hours after filling the cell. True, the constant terminal value is then not yet attained, but the difference is comparatively small and the error introduced is the same in all measurements. Moreover, the inaccuracy caused thereby is without influence on the tendency of the conclusions presently to be drawn, in itself a good reason for proceeding to this measure of enormous time saving. Moreover, several sets of flasks were used, in such a manner however that, for instance, all the ACZ/ solutions were measured in the same set. Finally, the sets were compared mutually in which the solution of 100 a J/o/. (micromol ='/,,,, millimol) A C7 p. L. served as comparison liquid. With both apparatus was found exactly the same value for the potential per unit of pressure. In the subjoined tables, the concentrations in the first column are given in « mols. p. L.; in the second column is found the current potential #7 in millivolts per unit of pressure (ecm. of mercury) under which the liquid was forced over. This value is always the mean of two ov more measurements whose differences were of the order of those in Table | (generally much less than those). When in the tables no sign is indicated at the potential value, the condition (as with pure water) is such that the electrode E, in fig. 1 is negative. In the A/C/, solutions a change of poles took place, hence the potentials following are indicated by ++. The results of the tables If to [V are represented graphically in fig. 2. Fig. 3 also gives the curve for A/C/, on a larger scale. -300 -300 200 —200 = 100 —100 a 100 200 300 400 500 10 conc. Mol p.Li. conc. 4 Mol p.L, +100 J Fig. 2. Fig. 3. TABLE II TABLE III | KCI | BaCh | = | | Cone. | | Conc. in yMol | Bi | in #Mol Pa | P P Dale | Puls | = = : —| a 0 about 350 | 10 139 50 102 | | 25 79 100 | 51 | 50 44 250 | 23 | | 100 25 | 500 | 12 | 200 9 1000 | 4 | 1000 1 40000 no exchange of poles 621 TABLE IV | AICI, | be | | Conc. | | in »Mol = | p. L | 0 about 350 | 0.5 52 1 | + #2 2 le se | 3 + 129 | | 4 Le == 100 | | 10 Hee ease | | 100 Ib eectaves 500 ah 4A | 5. On considering these results we notice, of course, first of all the great influence of the valency of the cation; as this gets higher the capillary gets more strongly discharged at an equal concentration. This had also been observed by Enissarorr when measuring the electric endosmose and may be noticed with Risry from his experiments with uni- and bivalent ions. The latter has observed a change of poles only onee, namely with copper nitrate and that only at a high concen- tration’). In the case of A/C/, about 0.8 uw mol. or about O.1 mg. per liter appears to be sufficient to lower the current potential from about 350 mV. to zero. It seems remarkable that this charge reversal does not take place with AaC/, (see Table II) neither with ZnSO, or CuSO, (Rifty) nor with substances with a univalent cation. Still more striking is the fact that according to Exissarorr, the electro-endosmotic transport requires, in a glass capillary, 100 micro- mols of Al: to be reduced to 0 without a reversal occurring, whereas the same investigator, although attaining the zero point, with a quartz capillary, at about the same concentration as required in our research {he found 1.6 @ mol. $ Al, (SO,),| could not even then notice a reversal of the transport direction. This creates the impression that 1) The exact concentration cannot be made out from his experiments. In any case, however, it lies above 900 « mol p. L. 622 in that research secondary influences come to the fore; perhaps the powerful electric field in which the measurements are executed is not without influence on the capillary itself. Only the quadrivalent Th-ion was capable of causing a charge reversal. The results obtained here are in harmony with the general theore- tical points of view. The electric double layer in the capillary, in the case of pure water consists of 'OH-ions at the side of the glass wall and ‘H-ions at the side of the liquid in consequence of the selective ion adsorption of the glass wall which always adsorbs the ‘OH-ion more strongly. From the electrolyte solutions the cations are absorbed more eagerly than the anions so that the charge gets lowered. If this adsorption for KCI, BaCl, and AICI, is such that solutions of the same molecular concentration are absorbed about equally, it is conceivable that the three times more active Al-:-ion requires a much lesser concentration than the K'-ion in order to attain an equal potential reduction. If once the capillary is charged reversely the adsorption of the Cl-ion, which carries a charge now opposite to that of the capillary, seems to predominate. The positive charge now soon attains (at 3 j mol.) a maximum value, and than decreases, but only slowly, because the discharging ion is univalent here. In agreement with the theory are also the resalis of Ruiry '), for instance that the salt of a heavy metal has a stronger discharging action than that of a lighter one (Cu and Zn, at least in the small concentrations). A cation of a heavy metal is known to be adsorbed more strongly than that of a light one.*) Moreover, the behaviour in the case of CuSO, and of Cu(NO,), is in agreement with investigations as to the adsorbability of those salts *). The influence of the anions is also observable in Rusry’s results and appears to have an effect corresponding with that in the ease of AICI, just described. The question whether the organic cations also behave according to the theoretical expectations is being considered. Several other solutions of electrolytes in water as well as in mixed solvents *) will be investigated. Utrecht, June 1914. van ‘ Horr-Laboratory. MHL @ 2) Morawitz, Koll. Beih. 1, 301 (1910). 5) Freunpuicu and Scuucui, Z. f. physik. Ghem. 85, 641 (1913). *) Of these have also already been measured a few series in connexion with the researches of Kruyr and van Dury, Koll. Beih. 5, 269 (1914). 623 Chemistry. — “Electric charge and limit value of Colloids’. By Dr. H. R. Kruyr. (Communicated by Prof. Ernst Coney). (Communicated in the meeting of June 27, 1914). 1. The present conception as to the relative stability of the sus- pensoid system and the way in which it may be suspended has been developed according to the following train of thoughts. Harpy *) and afterwards burton *) have undoubtedly established the fact that this relative stability falls and stands with the electric charge of the suspended particle. Indeed, the permanently suspended particle that exhibits a vivid Brown’s motion, has a cataphoretic oF : Volt—. re mobility of the order 2—4 uw per second and per eM. ;if by addition e.M. of an electrolyte one diminishes the relative stability, this velocity also decreases and therefore, the electric charge of the particle has evidently decreased also. The ‘iso-electric’” point, where that charge seems to have become zero, coincides with the moment of the small- est stability. Since the research of Wuitney and Ossr *) we know moreover, that with the repeal of the stability (the coagulation) is coupled a combination of the coagulating ion with the particles, and by Freunpiicu’s *) researches we arrived at the knowledge that these phenomena are described quantitatively by the equation of the adsorption-isotherm. From these elements is built up the theory that the particle owes its charge to the selective ion-absorption in its boundary layer and loses it by tke selective adsorption of the oppositely charged ion of the coagulating electrolyte. As specific properties of the adsorbent are usually of but very subordinate influence on the order of the charac- terizing quantities in the adsorption, the action of diverse electro- lytes on all capillary-electric phenomena ought to exhibit the same order, which the researches as to the electro-endosmotic phenomena compared with those of the coagulation of colloids have indeed confirmed. It now occurs to me that the researches on the current potentials, particularly those which have been communicated in the preceding paper, are capable of furnishing us not only with a new proof of that equality of order, but also demonstrate that the influence which 1) Z. f. physik. Chem. 33, 385 (1900). 2) Phil. Mag. [6] 11, 425; 12, 472 (1906) and 17, 582 (1909). 8) Z. f. physik. Chem. 39, 630 (1902), ) Zeitschr. f. physik. Chem. 73, 385 (1910) and 85, 641 (1913), 624 electrolytes exert on the charge of a glass capillary is quantitatively the same as that exerted on the colloidal particle during the coagulation. 2. As regards the order of the ion-actions, it has been pointed out in the previous paper that the ions discharge more strongly, when their valency is higher and that the heavy metals exert more influence than the light ones of equal valency. It is well-known that the limit values for the coagulation of suspensoids just exhibit the same peculiarities. 3. In order to make a quantitative comparison it should be first observed that the limit values for KCl and BaCl, in the same sol. are generally in the proportion of about 60: 1. In contact with either of these solutions the charge of the particle thus gets equally diminished. We may, therefore also expect that the charge of a glass capillary will be lowered by a solution of KCI to the same extent as by the sixty times weaker BaCl, solution. Hence, when from the tables 1 the preceding paper we calculate the charge in concen- trations of KCl and BaCl, in the said proportion, those should be equal if the idea as to the limit value just revealed is a correct one. The caleulation of the charge is possible according to the theory developed by Hetmno.rz'). The current potential is sequel to the electric double layer formed at the wall of the capillary and is related to the electric moment J/ as follows. w f= WP 6 S|) Sea y) in which w represents the specific resistance and 1 the constant of the internal friction whilst P represents the pressure employed. For comparison purposes we can consider the electric moment of the double layer just as well as the charge ¢ per unit of section, as it is in inverse proportion therewith. We write equation (1): If now we indicate the quantities relating to a BaCl,- solution with the index /, those relating to the 60 times more concentrated solution of KCl with the index /, then on the strength of the above considerations we must get EN Mb ef ie al wy \PJe wx (! Wied. Am. 7, 337 (1879). 625 As we only have in view very dilute solutions, we may put Hy = 7 (namely = yu,0). From this follows or in words: the relation of the current potentials of two electrolyte solutions whose concentrations are related as in the limit values of colloids are inversely proportional to the specific resistances of those solutions. Meanwhile attention should be called to the fact that by limit values in this connexion we must not understand the concentration y of the electrolyte added. From this a part is withdrawn by adsorption and hence, to the setting in end-condition appertains a lower concentration, which we will call x. In the experiments as to the current potentials we may probably identify the total con- centrations with the equilibrium concentrations as the adsorbing surface (the glass walls) is so small: only in the ease of the exceedingly weak AICI, solutions a doubt may arise. But in the colloid systems that difference may not be neglected. These y-values themselves Fig. 1.1) ae 1) In Fig. 1 on the axis of coordinates should be read in stead of mm m 626 have been determined only for As,S,') and HgS, *) and for electro- lytes not used here. The proportions are : With As,S, XNH,Cl : XUO(NO;). —= 82 » Hg,S ~xNH.Cl: XBaB, = 29. The proportion chosen 60:1 is, therefore, a rough approximation, but a comparison with y-values of other sols (P¢, Aw ete.) renders it probable that it represents the average. The relations between charge, adsorption and limit value are elucidated schematically in the above figure. In the upper half of the figure is drawn the charge ¢ of the capillary in dependence on the concentration of the traversing liquid, so that J, I], and III stand for uni-, di- and trivalent cations respectively. In the lower half is given, with the same concentration axis, the correlated adsorption of the electrolyte as a downward directed ordinate. If now y,, ¥%, and y, indicate the relation of the limit values for uni-, di- and trivalent cations, respectively the correlated downward directed ordinates must sbow the proportion 1:13 :3 and the upward directed ones equal values. 4. For verification of this relation appeared suitable : (a) 10 uMol BaCl, — 600 uMol KCI. 6) 25 uMol BaCl, — 1500 «Mol KCL. It would not do to simply take the specific conductivity powers as being proportional to the concentrations because in the so strongly diluted BaCl, solutions the conductivity power of water could not be neglected. Hence, I have made a direct measurement of the relation of the specific resistances by fillmge m1 Wuwatstonn’s bridge a vessel of arbitrary but fixed capacity with the liquids used. The relation of these resistances was in the pair (@) o, 4680 — = —_—_=—19 wk 247 and in the pair (¢) oy 20 70n wr 99.9 K , The values of P are obtained from the research communicated in the preceding paper. !) Freunpuicu, Zeitschr. f. physik. Chem. 73, 385 (1910). *) Freunpiicu en Scuucut, ibidem 85, 641 (1913). 627 As the relation of the potentials for (a) we obtain +4* or 14; as the relation of the resistances: 19. From the combination (4) we obtain for the potentials = cr 26, for the resistance 28. This agreement undoubtedly tells much in favour of the above mentioned theory. With concentrations somewhat larger than 60 the agreement might be better still. 5. The material of Rifry') is only once suitable for testing the relation (2). For so far his measurements have been executed with solutions of salts other than chlorides his measuring electrodes were non- reversable ones and his results are therefore useless for quantitative verification. | have only been able to find one combination of chlorides where concentrations have been measured which are com- parable with limit values: they are KCl and HCl. For As,S,-sol these limit values have been determined to 50 and 31 mMol p. L. respectively °*). Now from his experiments Rifry has calculated the potential at the capillary wall in certain units for 0.01 n. KCl as 3.1. We can use this figure again for comparison purposes at it is directly propor- tional to the charge. In the case of HC] he determined for 0.005 7 : 3.39, for O.OLO 7 : 2.8, For the comparison with 0.01 2 HCl we must know the potential at the concentration #4 x 0.01 = 0.0062. This, | have interpolated by assuming that the logarithms of the potentials are directly propor- tional to those of the concentrations, after I had first convinced myself that this interpolation") formula was quite satisfactory in the longer series stated in Rigrys paper. We then find 3.2 which is again a splendid agreement. 6. Quantitative comparisons with the trivalent cation are difficult to draw, because the y-values thereof are either not known or uncer- tain. From the treatises cited on p. 648 we, however, get the impression that the z-values diverge very little from zero, as is also expected from Table IV of the preceding communication, because a complete discharge takes place already at a concentration of 0.8 u mol. 7. A no less striking parallelism between charge and limit value 1) Ann. de chim. et de phys. [8], 30, 1 (1913). 2) Frevuxpuicu, Kapillarchemie (Leipzig 1909) Table 81. True, those are 7- and not y-values, but with these univalent ions, this cannot have any serious influence, 8) To this formula should only be attached the significance of an interpolation formula, 41 Proceedmes Royal Acad. Amsterdam. Vol, X VII 628 is furnished by the shape of the curve found for the current potential with AICI, solutions. This line is absolutely connected with the so-called irregular series. From what is stated in § 3 in connection with Table 1V (fig. 3, respectively) of the preceding paper it follows that the concentration at which the battery- shows an exchange of poles, is also that of the zero-charge of the capillary, whilst its positive charge goes up to about 3a mol. and thence lowers without however reaching zero again. An AICI, solution will consequently have first a discharging and therefore a coagulating effect on a negative sol. ; at higher concen- trations it will render it a positive sol and only at a much higher concentration it will again reverse the charge and cause coagulation. But therewith are described exactly the phenomena which, for instance, have been observed by Buxton and Taneur'), when they coagulated mastix with AICI, and indigo or Pt with FeCl,. The lower non- coalescent, the lower coalescent zone, the upper non- and coalescent zones, they can so to say be read off from the figures of the preceding communication. One is accustomed to attribute the phenomenon of the irregular series tO a special action of the hydrolytically resolved hydroxides of the coagulating ion. In connection with the preceding arises a doubt whether to Al(OH), ought really to be attributed a preponderating significance. For it does not seem probable that the AICI, which is present in such a small concentration, can cause a reversal of charge in the capillary. Much more acceptable seems the following idea. A strongly discharging cation unloads the capillary at such a small concentration that the small anion-concentration cannot prevent a complete reversal of charge. Of this the anion-concentrations are capable in the case of Ba and K- because there the charge gets nearer the zero value only at so much larger concentrations. Hence, the afterzone phenomenon will occur, as soon as the dis- charge by the cation is already very large at small concentrations— and is favoured by a feeble action of the anions. This strongly dis- charging action of the cation may arise from its higher valency or from its strong adsorbability. The fact that irregular series were observed, for instance, also with strychnine nitrate, new fuchsin, brilliant-green, auramine and_ silver nitrate *) is quite in harmony with this argument. For here we are dealing with strongly adsorb- able cations and because they are univalent the equivalent anion 1) Z. f. physik. Chem. 57, 64 (1907. *) FREUNDLICH, I. ©. 629 concentration present is still proportionately three times less than with AICI,. A start has already been made with investigations to get a proper insight, particularly in this question of the irregular series. 8. Finally it should be pointed out that the previous considera- tions also give an explanation of the fact often stated by us that in the ease of Al-salis we can determine the limit value much more accurately than with salts of uni- or bivalent metals. Two tubes with As,S, sol. which contain Al in concentrations situated 1°/, above and below the limit value, respectively exhibit after shaking a quite clear and a turbid fluid respectively. In the case of bivalent cations we must, so as to make quite sure, take the difference somewhat Jarger and very much so for a univalent ion. It is self-evident ae de that the cause lies in the fact that ae charge, ¢ concentration of coalescing ion) for Al is > for Ba and this again > for K-. Utrecht. June 1914. van ‘Tt Horr- Laboratory. {November 7, 1914). KONINKLIJKE AKADEMIE VAN WETENSCHAPPEN TE AMSTERDAM. PROCEEDINGS OF THE MEETING of Saturday October 31, 1914. Vou. XVII. Doce President: Prof. H. A. Lorentz. Secretary: Prof. P. Zeeman. (Translated from: Verslag van de gewone vergadering der Wis- en Natuurkundige Afdeeling van Zaterdag 3i October 1914, Dl. XXIID). ChE) ANF ah ao IN ae SS). G. van Rignsperk: “Jn the nerve-distribution in the trunk-dermatoma.” (Communicated by Prof. C. WinkixrR), p. 632. Ernst Couen and W,. D. Herperman: “The Allotropy of Cadmium” IV. p. 638. Ernst Conen and W. D. Herperman: “The Allotropy of Zine.” III, p. 641. Ernst Conen and J. C. van pen Bosco: “The Allotropy of Antimony”, I. p. 645. A. P. N. Francuimonr and H. J. Backer: “The Coloration of some derivatives of Pi- erylmethylamide with alkalies”. p. 647. A. P. N. Francutmonr and H. J. Backer: ‘“z-Sulpho-propionic acid and its resolution into optically active isomerides”’, p. 653. Miss H. J. Former: “A new electrometer, specially arranged for radio-active investigations.” Part I. (Communicated by Prof. H.-Iaca), p: 659. A. Suits: “The metastable continuation of the mixed crystal series of pseudo-components in connection with the phenomenon allotropy”. If. (Communicated by Prof. J. D. yan pER WaAats). p. 672. % A. Smits and S$. C. Boxnorst: “On the vapour pressure lines of the system phosphorus”. IT. (Communicated by Prof. J. D. van pER WaAALs), p. 678, A. Suits and A. H. W. Aten: “The application of the theory of allotropy to electro-motive equilibria.” III. (Communicated by Prof. J. D. van per Waats). p. 680. ¥. E. C. Scurrrer: “On gas equilibria, and a test of Prof. van per Waats Jr.’s formula”, I. (Communicated by Prof. J. D. vAN per WaAAts), p. 695. W. Reivers: “Equilibria in the system Pb—S—O; the roasting reaction process”. (Commu- nicated by Prof. S. HooGrwerre), p. 703. Proceedings Royal Acad. Amsterdam, Vol. XVIL. 632 Physiology. — “On the nerve-distribution in the trunk-dermatoma’. By Prof. G. van Ruyperk. (Communicated by Prof. C. WINKLER). (Communicated in the meeting of September 26, 1914). We know as a result from the researches on the segmental skin- innervation, made after the method of the so called “remaining aesthesia’”’, first introduced by Snerrincton, that from a definite zone on the skin (the dermatoma or root-area) stimuli may reach the spinal cord along each separate dorsal root of the spinal cord. Such investigations, however, do not teach us anything about the manner in which the sensibility in each of these root-areas is provided for by the peripherical cutaneous nerves. A few experi- ments made on dogs have enabled me _ presently to offer the following conclusions concerning exclusively the dermatomata of the trunk. In a dissertation by O. NAnricn’), written under the direction of ELLENBERGER, the nerves providing the skin of the dog are described with elegant accuracy. It is shown therein, that the skin of the Fig. 1. Cutaneous nerves of the dog, according to NAuricu. —0O1 = Th. 1, first thoracic nerve, dorsal branch. rl = first thoracic nerve, lateral branch. rl = Th. 3, third thoracic nerve, ventral branch, ul = L. 1, first lumbar nerve, dorsal branch, q =nerve of the large subcutaneous muscle. 1) O. N&uricw. Die Gefiihlshezirke und die motorischen Punkte des Hundes, Ein Beitrag zur vergl. Anatomie und Physiologie. Inaug. Diss. Ziirich 1907. 633 trunk is innervated by means of the perforating branches of the intercostal and lumbar nerves. If Th. 3 is taken to be the most cranial and L. 4 to be the most caudal nerve of the trunk, it will be found that from Th. 3 to Th. 7 each nerve-root is sending three perforating branches to the skin: a dorsal, a lateral, and a ventral branch. The dorsal nerve- trunk generally supplies two main branches: a medio-dorsal and a dorso-lateral one. The lateral nerve invariably supplies two branches : a latero-dorsal and a latero-ventral branch. The ventral nerve-trunk usually consists of one main trunk, which may be said to be medio- ventral. From Th. 8 to L. 4 the medio-ventral branches are wanting: their place is taken by the latero-ventral ones. The different points, where the dorsal, lateral, and ventral nerves enter into the skin, may be interconnected by lines. This having been done, it becomes evident that the dorsal branches, going in a cranial-caudalward direction, perforate the fascia continually at a greater distance from the mid-dorsal line, whilst the lateral trunks on the contrary come forth more dorsalward. A correct insight into the relations of these nerves is offered by Fig. 1. From Fig. 2 it may be seen moreover, that the skin of the trunk can be divided, according to a superficial scheme, into three zones as regards its peripherical nerves: a dorsal, a lateral, and a ventral zone. rt dyrsales dM yok Framt laterales dda tntercostalest > . cum M pectoralts dorsaltsve } Ss Ash > Ss J Q nn S & JA & ast! > =~ ~ Netut hunger pest W axill) B . cul cruris _ anterior, Se Fig. 2 Extension-zones of the dorsal, lateral, and ventral nerve-branches of the skin of dogs, according to NAuricu. I. The first question I now put to myself was the following: are the perforating dorsal, lateral, and ventral trunks, which belong when 42* 634 prepared macroscopically, to one intercostal resp. to one lumbar nerve, unisegmental or pluri-segmental nerve-canals. For whilst it is admitted almost generally that the intercostal nerves are uniseg- mental courses, Ersier') believes “he has sufficient grounds for stating that delicate nerve-plexus, situated on the inside of the ribs always connect two intercostal nerves. This being so, an interchange would oceur here between nerve-fibres of a different segmental origin. Concerning the nerve-distribution of the root-areas, this question may be formulated as follows: Do the nerve-fibres of each separate dorsal root of the spinal cord reach the skin-area belonging to that root along one single dorsal lateral or ventral perforating nerve- trunk, or along several ones? In order to solve this question, I made the following experiment. After the afore mentioned method of Samrrinctron, the dorsal (and ventral) spinal nerve root of a segment on one side of the spinal cord of some dogs was “isolated”, usually between three cranial and as many caudal roots, which were cut through extradural. This being done, the isolated root-area, corresponding to the isolated root, was demareated against the two insensible zones, corresponding to the sectioned roots. Situation, form and extension of the sensible root- area once being well defined, the skin was entirely cleft both in the cranial and in the caudal insensible zone by a slit passing from the mid-dorsal to the mid-ventral line. This of course could be done without narcosis. Immediately after this, a search was made for the perforating skin-nerves, and at least three successive ones of these in cranio-caudal direction, in the dorsal, lateral, and ventral skin-area, were prepared free, as much as possible avoiding any lesion of them. Next to this, by means of the induction-current, these nerves were stimulated to ascertain whether they conducted painstimuli. Invariably the result was, that for each skin-area such was only the case with these branches that belonged to one point of entrance. lrritation of the other branches, even with the strongest induction currents (the bobbin being entirely pushed in), never produced any symptom of pain, if slippings of the current were avoided. This result was wholly confirmed by a contra-experiment. If, after careful determination of the dorsal, lateral and eventually ventral branches, which were conductors of pain-stimuli, these branches were cut through, the sensibility in the isolated root-area proved to be destroyed entirely and irrevocably. 1) P. Etster. Ueber die Ursachen der Gefleclitbildung an den peripheren Nerven. Verh. d Anatom. Gesellsch a. d. 16e Vers. in Halle. 1902. S. 200. 635 Thus it results that the trunk-skin of the dog forwards its stimuli, destined for a definite segment of the spinal cord, only by means of one set of peripherical skin-nerves. This means that in those nerves only fibres belonging to one posterior root have their course, and that consequently the perforating skin-branches are segmental nerve-canals. II. A second question, necessarily presenting itself, is the following one: what separate portion within the dermatoma is innervated by either the dorsal or the lateral (ventral) peripherical branches ? To investigate this, the above-mentioned method was partially repeated once more. With dogs, where a nerve-root had been isolated, the peripherical branches entertaining its sensibility were sought for and prepared free. After this the conduction was successively interrupted, either provisorily or lastingly, in one or more of these branches. To obtain a lasting interruption of the conduction, the branch was cut through. For a provisory interruption the branch was enfolded by a piece of cottonwool, drenched in a 5°/, solution of stovaine. The conduction .once interrupted, the root-area was tested to ascertain whether a portion of it had become insensible, and if so the confines of the insensible area found in this manner were determinated. Fig. 3. On a dog a root-area (Th. 10) has been isolated between two insensible zones. After this, three cutaneous branches belonging to the dorsal perforating nerve-trunk, are successively cut through. The dotted portion of the root-area then becomes successively insensible, until finally the whole of its dorsal part has lost sensibility. a. Interruption of the conduction in the joint dorsal cutaneous branches. 636 After this operation the entire dorsal portion of the isolated dermatoma was found to have lost sensibility. To make the ventral demarcation of the area that has been made insensible in this way rightly understood, I may add the following: For a long time I had been struck by the fact that after a carefully performed root-isolation, the demarcation-lines of the isolated root-areas showed at a definite point a distinct bent. The origin of this bent is, that at some distance from the mid-dorsal line of the body, both the cranial and the caudal demarcation lines of the root-area, change their direction somewhat cranialward. In the cranial demarcationline this bent is always found a little more dorsalward than in the caudal demareationline. Now it is remarkable, that the ventral limit of the insensible zone, originated by the sectioning of the dorsal nerve- branches, is invariably found to be a straight line, connecting the cranial with the caudal limit just above this bent. This line therefore goes in a cranio-caudal direction. At the same time however it deviates slightly in a dorso-ventral direction. Consequently the latero-ventral nerves supply within the root-area the innervation of a zone extending to a point somewhat above the alleged bent in its demarcation-lines. 6. If the conduction is interrupted in the joint latero-ventral branches, the entire ventral portion of the root-area becomes insensible. Fig. 4. The same as in ig. 3, only for branches of the Jatero- ventral trunk. (The isolated root-area is probably in the main Th. 12. Its closer definition was neglected in the necropy.) If we compare the demarcationline found in this way, with that found after interrupting the conduction in the dorsal branches, it becomes evident that the ventral boundary of the dorsal area does not coincide exactly with the dorsal boundary of the ventral area, but that a reciprocal overlapping occurs, although it be only a slight one. It is shown thereby that the bent, found in the demar- cationline of the root-area, is situated exactly at the point where the dorsal and latero-ventral portions of the dermatoma meet. The cranial direction of this bent indicates that the latero-ventral portion must be lying somewhat more cranialward than the dorsal one. This fact has been stated previously by Bok"), when he found in 1897 a “discrepancy” of the dorsal and ventral dermatoma-areas on the human trunk. In the experimentally defined dermatoma this discre- pancy finds its expression in the alleged ‘bent’. Similar conditions have been observed clinically by Eicuuorst’), after transversal lesions of the spinal cord in the trunk-area. ce. Interruption of the conduction in separate minor branches of the dorsal and Jatero-ventral nerves. The conduction may be interrupted in the separate minor branches of the perforating nerves as well in the dorsal as in the latero-ventral portion of the root-area. When this operation has been performed it becomes evident, as long as only the larger branches were subjected to it, that each of these supplies the innervation of a small zone, extending equally into the cranial and into the caudal boundary of the root-area, and for the rest demarcated by lines going in a cranio-caudal direction. The whole root-area therefore is divided into a series of small areas, lying alongside of one another in dorso-ventral direction. The skin-area of the medio-dorsal branch adjoins the mid-dorsal line, the dorso-lateral branch on the other hand extends over an area, adjacent to the lateral portion of the dermatoma, more ventralward than that of the medio-dorsal branch. A similar ordination is found likewise to exist for all skin-areas corresponding to the various latero-ventral branches. Whenever very thin branches are cut through, either no insensi- bility ensues, or else an irregularly insensible spot is found some- where within the root-area. From the fact that in many cases, after the sectioning of such small branches, no insensibility is found, we may conclude that the areas of extension of the separate branches of the cutaneous nerves must overlap one another to a certain degree. I have not been able however to determine the extension of these overlappings. 1) L. Bouk, A few data from the segmental anatomy of the human body. Ned. Tijdschrift v. Geneeskunde. 1897. I p. 982—995, and 1897. II. p. 865—379. (Compare especially p. 366 et seq.). 2) H. ErcHaorsr, Verbreitungsweise der Hautnerven beim Menschen. Zeitschr. f. Klin. Medicin. Bd. XIV. S. 519. Berlin 1888. 638 Ill. Finally my attention was given to the nerve of the subcutaneous muscle. NAnricn') testifies that by irritation of this nerve, in addition to contraction of the cutaneous muscle, also pain-symptoms are brought forth, whilst after the sectioning of this nerve, the sensibility of the skin had diminished. I have not been able to verify this latter fact. It is not to be doubted moreover that e.q. an isolated root-area, if either the isolated root or the peripherical branches have been cut through, becomes entirely and completely insensible, whilst the nerve of the cutaneous muscle remains intact. It is therefore probable that this nerve does not contribute to the sensibility of the skin. Nevertheless I can confirm the statement of NAurica, that after its having been cut through, irritation of the central end proves painful. It may be that the muscular sensibility plays a part in producing these symp- toms of pain. Chemistry. — “The Allotrepy of Cadmium.” 1V. By Prof. Ernst Courn and W. D. Her.peErMAn. (Communicated in the meeting of September 26, 1914). The electromotive behaviour of Cadmium. LI. 1. Up to the present we have only directed attention to the electromotive behaviour of @- and y-cadmium; the 8-modification has not been mentioned hitherto. It will be treated in the following lines. 2. It may be remembered that a number of cells constructed according to the scheme: Cd Guinea | Cd-amalgam electrolytically : fee 12.5 percent cenosied cadmium sulphate | py een had an E.M.F. of 0.050 Volt at 25°.0, whilst the E.M.F. of others was only 0.047 Volt at the same temperature. (The cells were reproducible within 0.5 millivolt). 3. Now we were struck by the fact that when constructing a large nuniber of these cells we often got cells which had an E.M.F. of 0.048 Volt at 25°.0. The E.M.F. of cells which originally had an E.M.F. of 0.050 Volt at 25°.0, spontaneously decreased till the value 0,048 Volt was reached. After this their E.M.F. remained constant. 4. The conclusion was plain that the cells giving 0.048 Volt might 1) L. c. p. 95—96, 639 contain /-cadmium, those giving 0.047 Volt ecadmium, whilst those giving 0.050 Volt have y-cadmium as a negative electrode. 5. If this were really the case, it would be possible to construct a transition cell by combining a cell with a@-cadmium with one containing B-cadmium,; the E.M.F. of this combination would be zero at the transition temperature of the change v-cadmium 2 p-cadmium. 6. However it is impossible to carry out an exact determination of the transition point in this way, as the E.M.F. of the combination is (at 25°.0) only (0.048—0.047) = 0.001 Volt and the reproducibility of each of the cells is only 0.5 millivolt. 7. In order to ascertain if the E.M.F. of the B-cells has a real significance, experiinents may be carried out on the following lines: At temperatures above the transition point of the change «-cad- mium 2 #-cadmium (which we found in the neighbourhood of 60° by dilatometriec measurements) the E.M.F. of a@-cells must be higher than that of p-cells. After cooling the cells below the transition point mentioned, the contrary will occur. 8. Our experiments in this direction were carried out in the following way: We constructed a large number of Hurnrr cells’); one of these, the E.M.F. of which had been originally 0.050 Volt at 25°.0, had an E.M.F. of 0.047 Volt (at 25°.0) after having been kept for 4 weeks at 47°.5. After this time it remained constant. We combined this cell (N°. 7) with another one (N°. 22) the E.M.F. of which was 0.048 Volt at 25°.0. The two cells AB (N°. 7) and CD (N°. 22) were connected by a siphon H, which contained the same solution of cadmium sulphate as was present in the cells. (Fig. 1). The lateral tube E of the siphon was closed by a rubber tube F, in which was put a glass rod G. The little apparatus was brought into a Fig. 1. thermostat which could be kept at will at 25°.0 or 64°.5. 9. We measured the E.M.F. between the cadmium which had been electrolytically deposited on the platinum spirals A and C 1) Proceedings 17, 122 (1914), 640 against the common amalgam electrode B. (12.5°/, by weight). It is absolutely necessary to use a common electrode as the cadmium amalgam of 12.5 percent by weight does not form a heterogeneous system at 64°.5; its E.M.F. is then a function of its composition. The use of the #vo amalgam electrodes B and D might give rise to serious mistakes, if there were only small differences in their com- position. The absolute E.M.F. of our amalgam electrode against cadmium in A and C does not play any role in our measurements. 10. The determinations of E.M.F. were carried out by the Poe- GENDORFF compensation method. The resistances used, had been checked by the Physikalisch-Technische Reichsanstalt at Charlottenburg— Berlin. The same was the case with the thermometers used. Our two standard elements (WesToN) were put into a thermostat which was kept at 25°.0. We used as a zero instrument a Deprez-D’ ARSONVAL galvanometer, which was mounted on a vibration-free suspension (Junius). The readings were made by means of a telescope and scale; 0.02 millivolt could easily be measured. The determinations were continued during several days, until the E.M.F. of the cells had become constant. Our table I shows the results. GAs elves ale Temperature 25°.0. E.M.F. Cell 7 0.04741 Volt Cell 22 0.04815 _,, Temperature 64°.5 Cell 7 0.04029 Volt. Cell 22 0.03979 __,, After having brought the cells to 25°.0, we found: Celli 0.04741 Volt. Cell 22 0.04806 __,, The table shows that at 64°.5 there has taken place an inversion of the poles and that the cells regain their original E.M.F. at 25°.0. A second experiment with two cells (n°. 4 and 8) newly con- structed, gave the following results: 641 AM Nasa a8 JN Temperature 25°.0, E.K. Cell 8 0.04757 Volt Cell 4 0.04839 _,, Temperature 64°.5. Cell 8 0.04737 Volt Cell 4 0.04633 _,, After having brought the cells to 25°.0, we found: Cell 8 0.04776 Volt Cell 4 0.04789, . 11. From table II it may be seen that we are here at the limit of measurement obtainable in working with cells of so small an E.M.F. the reproducibility of which is 0.5 Millivolt. 12. From the inversion of poles which has been observed, we may conclude that the value 0.048 Volt at 25°.0 really has signi- licance and is to be attributed to the presence of $-cadmium. 13. As to the bearing of the existence of different modifications of cadmium on the E.M.F. of the standard cell of Weston, we refer to our paper “On the Thermodynamics of standard cells” (sixth communication), published some months ago '). Utrecht, September 1914. van “Tt Horr- Laboratory. Chemistry. — “The Allotropy of Zinc.” I. By Prof. Ernst Couen and W. D. HeLperMan. (Communicated in the meeting of September 26, 1914). 1. In our first communication on the allotropy of zine’), we summarized the earlier literature on this subject as follows: as long as half a century ago various investigators tried to solve the problem whether zine might be capable of existing in different allotropic modifications. As late as 1890 Le Cratetimr proved that this metal does really show a transition point in the neighbourhood of 350°. Monkemerer found this point at 321°, Brnepicks at 330° (melting point of pure zine 419.°4) whilst the measurements of Max Werner i 1) Chemisch Weekblad 11, 740 (1914). This paper will be published before long in the Zeitschr. f. physik. Chemie. 2) Proceedings 16, 565 (1913). 642 (who found 800°), published some weeks ago, agree sufficiently with those of Le Cuarruimr. We shall discuss in a subsequent paper the differences which exist amongst the results of the investigators mentioned above. Whilst Brenepicks mentions a second transition point (at 170°), Max Werner was unable to find this point. The question as to whether it really exists or not, may be left open for the moment. 2. Since writing the above we became acquainted with the paper of Le Verrier’), which has been summarized by one of us’). Le Verrter found that the specific heat of zine varies greatly between 100 and 140° and that there oceurs an absorption of heat within this interval of temperature of O—8 calories. This result indicates that there exists here a transition point. Mr. G. pe Bruin is carrying out a systematic investigation in this direction. 3. Brnepicks and RaGnar Arpt have recently published *) a new investigation of this subject. In his first paper BrnEpicks pointed out that ‘‘beziiglich der Frage, ob die fiir das Zine. puriss. Merck (garantiert frei von Kisen und Arsen in Staben) gefundenen Angaben auch fiir das absolut reine Metall gelten, bedarf es ebenfalls weiterer Versuche”’. That there was no reason to suppose that this sample contained impurities may be coneluded from the authors’ words: “Jedoch ist es im Hinblick auf die Wichtigkeit der Reinheit dieses Produktes fiir seine Verwendung fiir analytische Zwecke sehr wahrscheinlich, dass die Menge von Fremdkérpern zu vernachlassigen ist’. 4. However Brnepicks writes in his most recent paper: “Es ist deshalb hier eine Revision der einschlagigen Verhaltnisse vorgenomen worden, die zu ziemlich unerwarteten Ergebnissen gefiihrt hat. Namlich, dass iiberhaupt keine Allotropiebeweise fiir Zink z. Z. vorliegen”. He adds: “ Abgesehen wird dabei zuniachst von derjenigen Andeutung von Allotropie, die neuerdings von EK. Courn und W. D. HeLpEermMan durch spez. Gewichtsbestimmungen gefunden wurde”. We shall revert to this point later. 5. The method followed by Brnepicks and Arpi to discover possible transition points was the same as used formerly by BEnepicks, viz. the determination of the electrical conductivity of the metal at different temperatures. Whilst he found in his first determinations (working with zine. puriss. Merck) transition points at 170° and 330° respectively, he was not able to find them when he used ‘Zine KaHLBaum”’ which i) C. R. 114, 907 (1892). 2) Ernst Conen, Proceedings 17, 200 (1914). 5) Zeitschr. f. anorg. Chemie 88, 237 (1914). 643 only contained 0,0047°/, of Cd., 0,0033°/, of Pb., 0,00045°/, Ke,Cu). But working with the same material to which 0.52 per cent by weight of Cd, resp. 0,5 per cent of Pb. or 0,5 per cent of Cd--0,5 per cent of Pb had been added, he found several transition points which grosso modo agreed with those found formerly by Brnapicks a.o. On account of these results Benrpicks and Arvr conclude that the transition points found by Brnepicks in his first investigation are to be attributed to impurities in the metal used and that zine which is pure does nof show transition points. 6. In the first place it may be pointed out that the curves which form the basis of the authors’ conclusions, are so roughly defined, that it is almost impossible to conclude anything from them. For example, from a consideration of the curve 2 in Fig. 2 (which refers to pure zinc), one might arrive at the conclusion that a break ') exists at 150°. 7. However, a more serious objection to the method followed, may be pointed out. Our recent investigations on the allotropy of metals have shown that the changes in these substances take place very slowly even at high temperatures. These retardations can only be removed by special means (inoculating in contact with an electro- lyte, repeated changes of temperature etc.). We may call to mind the fact that we were able to heat cadmium 95 degrees above one of its transition points without any changes occurring. It will be necessary to give special attention in future to these phenomena, which play also a role in ‘thermal analysis” and which may falsify its results. Benepicks and Arpr did not make any provision to eliminate these phenomena. On account of what we know now about these hyste- resis phenomena it was to be expected that any transition point, if it really existed, would only be found under favourable circumstances, or by a systematic elimination of the retardations mentioned above. 8. Moreover it may be pointed out that Benepicks and Arpt made the supposition “dass die betreffenden Metalle nicht geniigend rein waren” (viz. the zinc. puriss. Merck, used by Brnepicks in his first investigations and by Le Caaretier among others). We think that the opinion put forward by Brnepicks in his first paper (see above § 3) “dass die Menge von Fremdk6rpern zu vernachlassigen ist’’, is the just one. As we were told by Messrs. Merck at Darmstadt their ‘Zinc. puriss. Merck (garantiert frei von Hisen und Arsen in Stiben)” contains only small traces of cadmium. We carried out an analysis of this material ‘) Whether this point really exists or not may be left open for the moment. 644 following the method described by Myzius?). In 100 gr. of this metal we could only detect small traces of cadmium (lead and iron). We think that the explanation of B. and A. which is based on the presence of large amounts of impurities falls to the ground. 9. That it is not the presence of foreign substances which give rise. to the strongly marked change of the mechanical properties of zine at higher temperatures (which fact has been the starting point of Brnepicks’ investigations) is evident from the fact, that this change may also be observed in the purest zine (Zink ‘Kahlbaum”, comp. § 5). We bave been able to confirm this result repeatedly ourselves. 10. Finally some remarks, made in a note by Bengpicks and ArpI may be considered here. In the first place they believe, on account of an investigation con- cerning the quenching velocities of metals, carried out by BENEDICKs *), that “eine besonders grosse Abkiihlungsgeschwindigkeit nicht zu erzielen ist” when the method is followed which we used. (1 kilo of zine was chilled in a mixture of solid carbid dioxide and alcohol). It may be pointed out that the velocity we used has been greatly exag- gerated; we got the same results by using water or air of room tempe- rature. We also carried out some experiments with carbon dioxide and aleo hol in order to vary the external conditions of our experiments as much as possible. In our researches on the allotropy of copper and cadmium we also used water or air as a cooling medium. 14. Secondly Benwpicks and Arpr raise the question as to whether there has not taken place an ‘Auflockerung der Oberflache” of our preparations when we washed them with dilute hydrochloric acid. By this operation a change of density might have occurred. They have however overlooked two facts: in the first place the recent investigations of JouHnsron and Apams*), which prove that the density of any substance is independent of its state of division. Moreover they have not taken into account the results of our inves- tigations on cadmium‘), where the same difficulties would have occurred. The reproducibility and reversibility of the phenomena prove that the disturbances, mentioned by BrNepicks and Arpi really do not occur. We hope to report shortly on the real transition points of zine. Utrecht, September 1914. van “t Horr-Laboratory. 1) Zeitschr. f. anorg. Chemie 9, 144 (1895); Myxius, ibid. 74, 407 (1912). 2) Journ. of the Iron and Steel Institute 77, 153 (1908). 3) Journ. Americ. Chem. Soc. 34, 563 (1912). 4) Proceedings 16, 485 (1913). 645 Chemistry. — “The Allotropy of Antimony.” I. By Prof. Erxst Conen and J. C. van pen Boscn. (Communicated in the meeting of September 26, 1914). 1. The following modifications of this metal were known hitherto: a. The so called metallic antimony, a bluish-white solid with metallic lustre. It is very brittle at ordinary temperatures and is said to crystallize in the hexagonal system. Only this modification is found in nature. 6. Black antimony. This form has been prepared by Stock and Siebert’) in three different ways, the best method being by rapid cooling of the vapour of ordinary metallic antimony. This black modification is converted by heating into metallic antimony. Its colour and density change slowly at 100°; at 400° the conversion occurs instantly. This form seems to be metastable at ordinary temperatures. c. Yellow antimony was first prepared by Stock and Gu?TTMANN *) in the year 1904, by the interaction of antimony hydride (at —90°) with air, oxygen or chlorine. Even at — 50° this form is meta- stabie: it is converted by heating into the black modification. d. Explosive Antimony. Ernst Conrn, Rinckr, StRENGgRs, and Cotuins*) proved that the explosion which occurs when this body is pounded, pressed or scraped, is to be attributed to the transformation of an allotropic form called by them 3-antimony, into the ordinary modification (metallic antimony ; ¢-antimony). Hitherto no investigation of the connexion between these different forms has been carried out as it is very difficult to procure sufficiently large quantities of them. 2. The investigations described below deal with the question whether the metal known hitherto as “metallic antimony” is to be considered at ordinary temperatures and pressures as a metastable system, as is the case with the metals we have already investigated. Our experiments will prove that this is really the case. 3. A kilogram of antimony (KaniBaum — Berlin) which contained some hundredths of a percent of impurity, was melted and poured into a cylinder of asbestos paper, which was surrounded by a mixture of aleobol and solid carbon dioxide. The chilled metal so obtained was used in all experiments. 4. It was powdered in a mortar. We determined its density at 25°.0 using two pycnometers as described by JoHNnsron and Apams‘), 1) Ber. d. d. chem. Ges. 38, 3837 (1906). 2) Ber. d. d. chem. Ges. 37, 885 (1904). 8) Zeitschr. f. physik. Chemie 47, 1 (1904); 50, 292 (1904); 52, 129 (1905). 4) Journ. Am. Chem. Soc. 34, 563 (1912). 646 The difference between any two of these determinations never exceeded three units in the third decimal place. Our thermometers had been compared with a standard of the Phys. Techn. Reichanstalt at Charlottenburg — Berlin. We used toluene as the liquid in the pyenometer; its density had KO fe a0. ad been determined in four experiments to be d =e, 0.8603. Two different parts (A) and (/) of our material gave the values 25°.0 6.6900 (A) and 4° 6.6897 (£). 5. The samples (A) and (2) were now heated separately during 4 x 24 hours in an aqueous solution of potassium chloride (10 gr. KCI on 100 er. of water), using a reflux condenser, the boiling point of the solution being 102°.5. The metal was then washed with dilute hydrochloric acid, water, aleohol and ether, and dried iz vacuo over sulphuric acid. Its density was now 25°.0 6.6744 (A) 4° 6.6803 (E); Consequently the density has decreased by 13 units in the third ad. decimal place. 6. After having heated (A) and (/) for a second time (6 x 24 hours) in the boiling solution, we found: 25°.0 6.6784 and 6.6765 (A) “4° «6.6789 and 6.6778 (E). The density had undergone no further change. 7. The experiments described in §§ 4—6 show that the antimony after chilling is present in a form which changes at 100° with a measurable velocity. In order to investigate if there exists here a transition tempera- ture as in the case of the other metals which we have hitherto studied, we carried out some dilatometric measurements, using the electric thermostat which we described formerly. *) 8. The material which was put into the dilatometer consisted of small pieces of the metal mixed up with fine powder and a part of the metal from the pyenometers. (500 grams). The paraffin oil used had been heated for some time at 200° in contact with finely divided antimony. There was no evolution of gasbubbles. 9. At temperatures below 119° there occurred no change of the meniscus at the jirst heating (the bore of the capillary tube was 1) Zeitschr. f, physik. Chemie 87, 409 (1914). 647 1 mm.), not even when the heating was continued for 48 hours. On the contrary, the dilatometer having been kept at 15° during a month, the change was: At 101°.8 in 2 hours, + 74 mm.; ie. + 37 mm. per hour a OO ORR Te Ar so> = 20, oe ells A Re ac NOON el 5 BO Pre ala ha ae, From these data one might conclude that there exists a transition point in the neighbourhood of 101° which is in perfect agreement with our density determinations (§ 4—6). 10. Guided by the experience gained in the case of cadmium and copper‘), we now earried out some experiments with antimony whose previous thermal history had been changed between wide limits. After having kept the dilatometer for 50 minutes at.150°, the meniscus fell during a certain time at the constant temperature of 96°.0; after this it became stationary and then began to rise. From these observations one would conclude that there is a transition point below 96°.0 and that, in consequence of the heating at 150°, the transition temperature had thus been lowered. This experiment proves, that at 96°.0 there are present at the same time more than two modifications. 11. The dilatometer was now kept at 225° for 12 hours. After this there occurred at 94°.6 (at constant temperature) a marked fall in the oil level (569 mm. within 48 hours), while in the experiment described in § 10 there took place a rise of the meniscus at the same temperature. 12. The phenomena deseribed above show that meta/lic antimony, such as we have known it hitherto, is also a metastable system which consists of more than two allotropic forms. We hope shortly to report on the modifications which play a role here. Utrecht, April 1914. van ‘t Horr-Laboratory. Chemistry. — “Vhe Coloration of some derivatives of Picrylne- thylamide with alkalies’. By Prof. A. P. N. Francumonr and H. J. Backrr. (Communicated in the meeting of September 26, 1914). In a previous communication (Fee. trav. chim. 1913, 82, 325 ; Abstr. Chem. Soc. 1914, ii, 84) we described the spectrographie investigation of the coloration which picrylalkylnitramines undergo by alkalies. It was shown, that the absorption spectrum of picrylmethylnitraimine C,H, (NO,), N Me(NO,) after addition of alkali gets a certain ana- 1) Proceedings 17, 54, 60 (1914). 43 Proceedings Royal Acad. Amsterdam. Vol. XVII. 648 logy with that of picrylmethylamide C,H, (NO,), NHMe, and that the latter spectrum is not much changed by alkali. We then concluded, that the coloration of picrylalkyInitramines with alkalies had a similar cause as the colour of nitranilines (wid. Francumont, Rec. trav. chim. 1910, 29, 298, 313), which is ascribed by Hanrzscu (Ler. 1910, 48, 1669) to an action between the nitro and amino groups attached to the benzene nucleus. The coloration of the nitramines would thus be produced by nitro groups of the nucleus reacting with the base, the nitro group attached to nitrogen playing only a secondary part. In order to test this hypothesis, we have now examined several derivatives of picrylmethylamide, compounds of the formula Pier. N Me X?). For X we have chosen the nitroso group, the organic . acyl groups COCH,, CO,Me, CO,,Et and finally the phenyl group as example of a negative group being no acylgroup. The compounds investigated were thus picrylmethyInitrosamine Picr. N Me(NO), pieryl- methylacetamide Picr. NMe(COCH,), methylpicrylmethylaminoformiate Picr. N Me (CO,Me) and the ethylester Picr. NMe (CO, Et), and picryl- phenylmethylamide Pier. NMe Ph. In the first place it should be observed that, like the nitrogroup, also the acyl groups NO, COCH,, CO,Me, CO,Et strongly diminish the colour of the picrylmethylamide. Compared with this deeply yellow coloured amide, the nitramine, nitrosamine, acetyl derivative and both the urethanes are only palish yellow. These differences are clearly shown by the absorption curves. Both the absorption bands of pierylmethylamide at = 2390 and 2875 (see curve 15) disappear wholly; the acyl derivatives give for the concentrations examined, only a continuous absorption in the ultra- violet (curves 3, 5, 8, 10), just as it was found for the nitramine (Rec. trav. chim. 1913, 32, 332). It must be admitted, that the presence of acyl groups in the aminogroup of picrylmethylamide so strongly diminishes the basie properties of this group, that it loses the power to act with a nitro- group, and thus to produce colour. If this hypothesis is correct, it must be possible to prevent this reaction also by addition of a strong acid combining witlr the amine group. Indeed, picrylmethylamide dissolves perfectly colourless in strong 1) In this paper Pier. means the group 2, 4, 6-trinitrophenyl. 649 sulphurie acid. The absorption bands disappear wholly from the spec- trum, and only a modest continuous absorption in the ultraviolet remains (compare curves 14 and 15). For a concentration of 0.0002 gram- molecules per litre and an absorbing layer of 100 m.m. the beginning il of the absorption is repelled by the sulphuric acid from — 2150 to 3400. This decoloration of picrylmethylamide by sulphuric acid is just the reverse of the coloration of the nitramine with alkali. In the first case the nitro groups of the nucleus are deprived of the opportunity to combine with a basic group, in the latter case this opportunity is on the contrary given. The reaction with alkalies seems to be the same for the acylderi- vatives now investigated as for the pierylalkylnitramines, the only difference being that they want a little more alkali for the red mY coloration. Formerly we found (Rec. trav. chim. 1918, 32, 332), that a solution of picrylmethylnitramine containing an excess of 1 alkali gives two bands at A 1975 and 2350. At nearly the same places two bands are shown by the alkaline solutions of the acetyl derivative (curve 6) and the urethanes (9 and 11), though one of the bands is only represented by a flat part of the absorption curve. The anomalous curve given by the nitrosamine with alkali (4) will be discussed separately. Pierylphenylmethylamide, the last derivative of picrylmethylamide we examined, exists in two forms of the same dark red colour but of different melting points, 108 and 129°. Hanrzscu (Ber. 1910, 98, 1651) calls the two forms homochromo isomerides, whilst BitMANn (Ber. 1911, 44, 827) regards them as polymorphous forms. As Hawnrzscu has already observed, the spectra of the two forms are completely eqaal (curve 12). It was now found, that the «and 8 forms in presence of alkalies also behave in the same way (curve 13), so that the two forms when dissolved seem to be wholly identical. The broad absorption band of the amide at 2350 becomes by addition of alkali a little deeper and is somewhat displaced to larger wave- lengths. At the same time it undergoes a division into a flat part at 2070 and a feeble band at 2400. This agrees with the behaviour of the other compounds with bases. Finally we have examined the coloration of 1,3,5-trinitrobenzene with alkali, since here only the nitrogroups of the nucleus can act with the base. Whilst trinitrobenzene only absorbs continuously (curve 1), addition 43% 650 of alkali produces a broad band from 2040 to 2300 (curve 2). Its centre is at about the same place as the centre of the two bands, which show the picrylmethylamide derivates in presence of alkalies. In the previous publication (l.c.) we mentioned a remarkable decomposition of the alkaline solution of picrylmethylnitramine. After a day it gave the spectrum of potassium picrate, being hydrolysed in this way: Pier. N Me NO, — Picr. OH + Me NH NO,. An analogous decomposition takes place, though more slowly, with the acetyl derivative and the two urethanes. In a few days the spec- trum of their alkaline solutions is perfectly the same as that shown by potassium picrate (curve 7). With picrylmethylnitrosamine this decomposition proceeds very quickly, much more rapidly than with the nitramine. During the few minutes required for the spectrographic examination its alkaline solution is already partly decomposed. ; The anomalous absorption curve (4) is apparantly due to a super- position of the spectrum of the potassium compound of the nitro- samine with that of potassium picrate. From the three bands shown 1 : 2 by this curve at A 2000, 2400 and 2900 the latter is undoubtedly caused by the presence of potassium picrate, which gives a band at about 2880. In the spectrum of the potassium compound of the nitro- samine there may be expected two bands at about 2000 and 2350, in analogy to the observations made with the other derivatives of picrylmethylamide. The former band is indeed present, whilst the second band, likely with assistance of the flat band shown by potassium picrate at 2500, is transferred to 2400. Two hours after its preparation, the alkaline solution of the nitrosamine was again examined; it then showed the pure spectrum of potassium picrate curve 7). The results of this investigation may be expressed as follows. The coloration of picrylmethylnitramine by alkali has the same cause as the coloration of other derivatives of picrylmethylamide by this reagent. For the nitramine, the acetyl-, carboxymethyl- and carboxyethyl- derivatives, which altogether only have continuous absorption for ultraviolet rays, show two bands at about 2000 and 2350 after addition of alkali. Picrylphenylmethylamide has already of itself an absorption band, which, however, by alkali is divided into two parts at 2070 and 2400. Logarithms of the thickness of the layers in mm. of 0.0002 normal solutions. Fig. I. 651 16 18-2000) 22) 5524-26) 28-3000) 32, 34 36-38 4000 42 Reciprocal wavelengths. 1. 1,3,5-Trinitrobenzene. 2. id. + KOH. 3. Picrylmethylnitrosamine. 4. id. + KOH. 5. Pierylmethylacetamide. 6. id. -+-KOH. 7. Picric acid + KOH, 8. Methyl picrylmethylaminoformiate. 9. id. -- KOH. 10. Ethyl picryl- methylaminoformiate. 11. id. + KOH. Logarithms of the thickness of the layers in mm. of 0.0002 normal solutions. Vig. = 1 Bane el etl ge ic i Pee ere ee ae Heyl 2 AZ Bee A Zoe eS Za eee 16 If. 18 2000 22 24 26 28 3000 32 34 36 38 4000 42 Reciprocal wavelengths. 12. Picrylphenyimethylamide (z & @). 13. id. +- KOH. 14. Picrylmethyl- amide in sulphuric acid. 15, Pierylmethylamide, 653 The nitrogroup attached to the nitrogen atom of the nitramine is evidently not essential for the reaction. Further, the spectrum of trinitrobenzene with alkali, though much differing from that of the other alkaline solutions, has yet its absorption 1 in about the same part (> 18002500 ) We may thus conclude, that in all these cases the coloration is produced by a reaction of the base with one or more nitrogroups of the nucleus. Finally it bas been shown, that the presence of a strong acid, as well as the introduction of acyl radicals, completely expels the absorp- tion bands of picrylmethylamide. Cheniistry. — ‘“a-Sulpho-propionic acid and its resolution into optically active isomerides’. By Prof. A. P. N. Francuimont and Dr. H. J. Backrr. (Communicated in the meeting of September 26, 1914). Already in 1902 a great number of diverse chemical and bioche- mical methods were tried by the first of us to separate the e-sul- phopropionic acid CH,(SO,H)CHCO,H prepared by him ') from pro- pionie anhydride and sulphuric acid, into the two optical isomerides that one might expect according to theory. Not a single one, however, had given the desired result, although sometimes strychnine salts with a different rotating power were obtained, but after their conversion into ammonium salts these always appeared to be inactive. As Swarts *) had stated that he certainly had obtained from fluorochlorobromoacetic acid strychnine salts with varying rotating power, but had not succeeded in isolating the optically active acids. and as also Poncuer*), who tried to effect a separation of bromo- chloromethanesulphonie acid by means of cinchonine, only obtained rotating ammonium and barium salts, but no acids, it appeared as if with such simple acids the tendency to form racemic mixtures or compounds was very great and likewise the velocity of conver- sion. This was provisionally also assumed in the case of «-sulpho- propionic acid (methylsulphoacetic acid) and the experiments were discontinued in consequence. Still with lactic acid (methyloxyacetic acid) Purpim and Watknr *) MD) TRE, Cl abe, Cla, Gls WAS Zo joo Ad (akststs)\ 2) Bull. Ac. Belg. (3) 31. p. 25 (1896). 3) Bull. Soe. ch. (3) 27. p. 438 (1903). 4) J. ch. Soc. 61. p. 754 (1892). and with ebromopropionic acid (methylbromoacetic acid) RaMBERG *) had obtained decided results, but on the other hand, Por and Reap *) did not sueceed in resolving the chlorosulphoacetie acid. The question now arose whether perhaps the sulphogroup created the difficulty, i.e. causes the rapid racemisation. This became less probable after Pope and Reap *) had succeeded in splitting the chloroiodomethanesulphonie acid and had found that the optically active acids thus obtained were not so readily transformed into the racemie mixture. Hence, the investigation of sulphopropionie acid was at once again taken in hand. Both ehlorosulphoacetic acid and methylsulphoacetic acid (¢-sulpho- propionic acid) are dibasic and thus can form acid salts. Moreover, ihe two groups that cause the acid reaction, have a different com- position, the one being a carboxyl- and the other a sulphoxyl-group, and of different strengtb, so that as the sulphoxyl is stronger acid, salts will presumably contain the carboxyl-group in the free and the sulphoxyl-group in the combined state. Whereas, previously; chiefly the neutral and mixed metallic salts and ihe neutral strychnine salt had been experimented with, the acid strychnine salt was now employed and the desired result was obtained at once. a-Sulphopropionic acid itself was hitherto only known as a viscous syrup, whilst sulphoacetic acid had been obtained in crystals; therefore we have tried also to obtain «-sulphopropionie acid in a crystallized condition. A dilute solution of the acid prepared by decomposition of the barium salt with the theoretical quantity of sulphuric acid was concentrated by partial freezing and draining by suction. The strong solution was placed in vacuo first over sulphuric acid and then over P,O,. The viscous residue was kept for a day in an ice safe at about 0°, when gradually large crystals were formed. The acid thus obtained contains one mol. of water and is exceedingly hygro- scopic. In order to determine its melting point a little apparatus was constructed, consisting of two tubes communicating with a transverse tube, one of which contained P,O, and the other the «-sulphopropionie acid. After the apparatus had been evacuated and sealed, it was allowed to stand for a few days. The m.p. of the a-sulphopropionie acid was then found to be 100°.5, therefore, higher than that of sulphoacetie acid, which is stated to be 84°—86°. ~ 1) Ber. d. D ch. G. 33. p. 3354 (1900). 2) J. ch. Soc. 93. p. 795 (1908). 3) J. ch. Soc, 105. p. 811 (1914). 655 An acid strychnine salt was obtained by evaporating an aqueous solution of the acid with the equimolecular quantity of strychnine on a steam-bath until crystallisation set in. The large erystals that had separated were purified by repeated crystallisation from water ; their composition then was C,H,O,5 + C,,H,,O,N, + H,O. They, however, proved to be not the acid strychnine salt of the inactive (racemic) c- ulphopropionie acid, but of the dextrorotatory acid. On heating, they are decomposed at about 250° with evolution of gas and formation of a brown liquid. As in the case of all other compounds described here, the rotating power was determined in aqueous solution with sodium light at 20°. By concentration c is meant the number of grams of anhydrous active substance per 100 ce. solution. The specific rotation [e] is likewise calculated on the anhydrous substance. The molecular rotation has, of course, the same value for the anhydrous and the hydrated crystalline substance. For the acid strychnine salt was found at c = 1.938, any == — (Sine [41] = — TIA By way of comparing, strychnine hydrochloride was also investiga- ted and at c=1.297 was found: [a]= —- 30°.2 and | M]—-— 112°’). The acid strychnine salt of @-sulphopropionic acid investigated is therefore, presumably that of the dextrorotatory acid. In order to obtain this acid, the acid strychnine salt was first decomposed with the theoretical quantity of barium hydroxide *). After complete separation of the strychnine by extracting the drained off liquid with chloroform, the neutral barium salt was precipitated by addition of alcohol. This salt is dwevorotatory. For c=1.764 was found [«]=—4°.96 and [J |= —14°.4. From this salt the active a-sulphopropionic acid was liberated by 3 1) This value agrees fairly well with the constant |J2]—— 114° found by Porr and Reap for a somewhat different concentration. J. Chem. Soc. 105, p. 820 (1914). 2) The acid strychnine g-sulphopropionate can be titrated with baryta water and a suitable indicator such as methyl-red which is sensitive to feeble bases. It may also be titrated with litmus to violet-blue. If however, phenolphthalein is used which is but little sensitive to weak bases such as strychnine, the colour does not appear until also the second acid group combined to the strychnine has been neutralised by the inorganic base. As the change in colour is fairly sharp, both with methyl- red and phenolphihalein, the titration forms an interesting application of the theory of indicators. Still more remarkable becomes the experiment, when both indicators are used simultaneously. The methyl-red passes into yellow after addition of a semi-molecule of barium hydroxide, the phenolphthalein then being still colourless; so soon, however, one mol. bas been added, the violet colour of the phenolphithalein salt appears, unaffected by the pale yellow colour of the methyl-red, 656 the theoretical quantity of sulphurie acid and its rotatory power was then determined. For c=0.645 was found [¢]=-+ 31°.6 and [7 ]=- 48°.7. In another preparation was found for ¢=1.85, [@]=- 32°.0 and [J] = + 49°.2. Therefore, it is the dextrorotatory acid, whose neutral barium salt is laevorotatory. It was now tried to obtain also this dextrorotatory acid in the solid condition. The solution was, therefore, concentrated in vacuo first over sulphuric acid and then over P,O,. The viscous mass did not erystallize on cooling, but did so slowly after a trace of the racemic compound had been introduced. The crystals are exceedingly hygroscopic, melt between 81° and 82° and contain one mol. of water. As the neutral barium salt of the dextro a-sulphopropionic acid rotates in the opposite direction of the free acid, it became of importance to investigate also the acid salt. For this was found at c=0.776 [a] = + 18°.0 and [Af] = -+ 79°.8 or =2 X 39°.9%). The acid potassium salt gave at c= 0.516 the valnes: [eo] = + 23°.8. [MM] = 4+ 45°.7. The acid metallic salts of dextro a-sulphopropionic acid are, there- fore, dextrorotatory like the acid itself. The racemisation of dextro e-sulphopropionic acid and its salts was also tried. The aqueous solution, at c= 0.645, when heated for six hours at 100°, suffered no appreciable racemisation, the rotation remaining unchanged. A solution of the barium salt at ¢ = 1.28 after being heated for eight hours at 150° was racemised to the extent of 80°/,. A solution of the potassium salt at ¢ = 0.64, which also contained 2°/, of free potassium hydroxide, was completely racemised after being heated for eight hours at 180°. An excess of free base thus seems to accelerate the racemisation *), although also the temperature, the 1) As the molecule of the acid barium salt contains two groups of the sulpho- propionic acid, it may for the sake of comparison with the other rotations be written more conveniently [IJ] = 2X 39°.9. *) This would agree with the rule given by Rorue Ber. d. D. ch. G. 46. p. 845, (1914), that active carboxylic acids, the z-carbon atom of which is asymmetric and carries a hydrogen atom, are readily racemised under the influence of alkalies. He tries to explain this by assuming that, owing to the base, enol formation takes place in the molecule, thus causing the asymmetric carbon atom to disappear temporarily. 657 concentration and the duration of the reaction may exert an influence. In the motherliquor, from which the acid strychnine salt of the dextro-acid had deposited, there should still be present that of the laevo-acid, this being more soluble. On addition of acetone a preci- pitate was obtained which could be recrystallized from absolute alcohol. Of course, it still contains a trifle of the less soluble salt of the antipode, but yet in one of the preparations it was obtained in a fairly pure condition. For the rotating power at c= 1.658 was found [a] = — 27°.7 and {J/]=-— 135°. The concentration does not seem to exert a great influence on the specific rotation, for, at e=8.424 was found [a] = — 27°.4 and [M| = — 134°. From this acid strychnine salt of the acid the neutral ammonium salt was prepared. This gave for c=3.113 the values [a|=-+ 7°.9 and {J/|—-+ 14°.8. The neutral ammonium salt of the /acid is therefore, dextrorotatory. If to a solution of the ammonium salt is slowly added dilute sulphurie acid, the dextrorotation diminishes, becomes zero and then changes to a laevorotation, which finally remains constant, as soon as all the erganie acid has been liberated. The rotation for the acid, at c= 2.449, amounted to [@] = — 29°.8 and [MM] = — 45°.8. Although we have not prepared the /-a-sulphopropionie acid in a pure and solid condition, it appears from the experiments in quite a d-acid l-acid 20 20 20 20 l4Ip | Mp [Ip IM]p z-sulphopropionic acid C3H,O;S | + 32? | - 49.2 — 29.8 | =e | acid potassium salt C;H;0;SK | + 23.8 | + 45.7 | | acid barium salt (C3H;0;S),Ba | -- 18.0 | + 79.8 | acid strychnine salt leeueoes | neutral ammonium salt C3H,O;S(NH4), si Oneal 1428 neutral barium salt C;HjO;SBa| — 4.96 | — 14.4 | 658 satisfactory manner that a resolution has been effected of the racemic a-sulphopropionic acid. The specific and molecular rotations of the compounds investigated are united in the subjoined table. It should, however, be remarked that the values of the acid and its derivatives are less trustworthy because the acid has not been quite pure. It deserves notice that the molecular rotation of the @-sulphopropionic acid (49°.2) is certainly somewhat stronger than that of the «-bromo- propionie acid *) (44°.4) although the bromine atom (80) differs but little in weight from the sulpho-group (81); still this may perhaps support the view that the weight of the group influences the rotatory power. If for instance, we compare with the rotation of a-ethylpropionic acid?) (18°.2) we notice that both the rotation and the weight of the group (29) are less. More interesting seems the fact that the rotation of the neutral metallic salts is much less than, and of an opposite sign to that of the acid metallic salts and the acids themselves, particularly in connexion with what has been stated at the commencement, namely that it concerns here a dibasic acid with two groups of different ionisibility which cause the acid functions. Although the phenomenon that salts of optically active acids possess a rotatory power contrary to that of the acids themselves was observed previously, for instance with lactic and glyceric acids, the example now found seems a more simple one, because there are not present any groups that can react on each other, and because it may be called highly improbable that in the circumstances stated the carboxyl- and the sulphoxyl-group should react on each other. Consequently, the rotation will, probably, be less dependent on concentration, temperature, age of solution ete. In conclusion, it may be remarked that the laevorotation of the acid strychnine salt of the d-e-sulphopropionic acid as compared with that of strychnine hydrochloride, amounts to about as much Jess as the dextrorotation of the acid metallic salts. +) RamBerG. Liebig’s Ann. 370. p. 234 (1909) gives[z] = 29°.0, whence [M] = 44°.4. 2) Scutirz & Marckwatp. Ber. d. D. ch. G. 29. p. 59 (1896) [z] = 179.85, hence [J] = 18.2. Physics. - - “A new electrometer, specially arranged for radio-active L Oe investigations’. Part I. By Miss H. J. Foumpr. (Communicated by Prof. H. Haga). (Communicated in the meeting of May 30, 1914). Introduction. In trying to find an accurate method for measurements of the natural ionisation of air in closed vessels, radio-active radiation of the elements, ete., researches in which very small ionisation currents are to be measured, it seemed to me that the need is felt of an electrometer, which, besides possessing a great sensibility of charge, will also be able to measure very minute currents with accwracy. As to the mentioned conditions, the latter is fulfilled by C.T. R. Witson’s electroscope (the gold-leaf type), which owes this favour- able quality to the very simplicity of the system; this namely renders it possible to bring about the ionisation which is to be measured, in the air contained in the apparatus itself, to avoid connecting wires, together with electrostatic and other influences, the disturbance caused by insulators being confined to that of a single one. In my opinion this is the reason that this electroscope is generally preferred for various measurements requiring great accuracy to say a sensitive DoEzALek electrometer, which lacks these advantages, -notwithstand- ing the fact of a much greater sensibility of charge of the latter ; in consequence of this sudden changes in the natural ionisation of air in closed vessels, for instance, the existence of which is accepted by many investigators, cannot manifest themselves clearly when the electroscope is used; moreover measurements of small currents will take much time. This has led me to construct an electrometer, the principle and the method of working of which I shall discuss in what follows, and which in my opinion ean supply the mentioned need. It appeared from the results obtained, that with this apparatus currents can be measured both very accurately and very sensitively; accordingly it seems to me, that for these reasons the apparatus may be very suitable for various radioactive researches requiring the above mentioned qualities, as was also corroborated by experience. Description of the principle of the apparatus. In the figure a schematic representation of the arrangement is given’); the apparatus consists of: 1) An accurate description of the apparatus will follow in a 2nd communication, 660 two separate spaces, viz. the measuring space c: a flat brass cylinder, and the ionisation space J: a brass cylinder of volume 1 litre; the two cylinders are insulated from each other by ebonite. In the measuring space is the metal needle 6, supported in the middle by a second metal needle d, insulated by amber; 6 + d together form the conductor, which is charged by the ionisation current. In ¢ is also found the very thin aluminium strip a, which a few mm. above / is fastened to a thin metal rod with mirror, suspended on a Wollaston wire, which is fastened to a torsion head insulated by means of ebonite. Through a perforation in the amber and in the ebonite a rod / can be brought in contact with the needle d. In this way a, 6-+d, ¢, and f, can therefore be separately brought in a conductive connection with a storage battery or with earth ; e rests on a bottom plate, to which legs are fastened which support the apparatus. The charging of the apparatus before use. In what follows we shall examine from the course of the lines of foree, what state arises in the space c, and how this takes place, when the system is charged: the lower cylinder f is of no account as regards this, as it does not belong to the measuring system proper. The method of charging is founded on this that the two needles a and b, which with untwisted position of a form an angle, let us say of 30°, will sé// have this position with respect to each other, when the system is in the charged state, in which latter case, however, lines of force run between the different conductors. We begin to charge a to a constant potential, e.g. to, + 20 volts, keeping 6 and c still at potential O volt. If for the sake of simplicity we first imagine the state as it would be without the presence of 6, the course of the lines of foree would be as follows: lines of force would start from a, and end upon the bottom, the walls, . 661 and the lid of c; in consequence, however, of the unequal distance from a to those different parts of c, the potential gradient per unit of length or the electric force, as also the density of the lines of force, or the value of the tensions directed along the lines of force in the space round @ would be of very unequal value ; how great, however, the variation in different directions might be, yet there would be complete symmetry in the course of the lines of force with respect to the vertical plane in which the needle itself is situated. The presence of /, however, disturbs this symmetry in the following way : 1. The lines of force starting from @ in the direction of ) will no longer end on c¢, but on 4; besides, on account of their diminished length, therefore on account of the increased electric force, they become there denser than before. 2. There will be inflection of lines of force ; some lines of force, viz. those which, when not subjected to the influence of 6, would run beside 6 from a to c, will pass into lines of force from a to } under the influence of 0. This disturbance caused by 6 will give rise to the formation of a resulting electrostatic couple, acting on those halves of the side faces of a, which are directed to the side of the acute angle between a and 6, so that consequently @ is deflected to the side of 6, and the angle between a and / will become such that the formed torsion couple of the suspension wire will be in equilibrium with the electrostatic directive couple. In order to make @ return to the untwisted position, ¢ is charged to a negative potential, which brings about the desired change; for 1. then the density of the lines of force between a and ¢ will increase, which causes a slighter variation of lines of force on those halves of the sides of @ which are directed to the side of the acute angle between a and 0 ; 2. some lines of force between a and ¢/ will deflect and become lines of force between a and c. In case of a sufficient negative potential of c¢ the above mentioned electrostatic resulting couple will be annihilated through this change. The course of the lines of force has now become more symmetrical (of course not quite), while @ returns to the untwisted position. In this way e.g. a state of charge is realized for a= - 20 V., H=O V, == 3 For the sake of simplicity a whole number was taken for the potential of c. the consequence of which is, that in the final state the needle is only approximately in the untwisted position. 662 Measuring method of ionisation currents. A quantity of vadio-active substance is placed on the bottom of the ionisation cylinder /; the system is charged to the state : + 20 V., O V., —3 V.; f is then brought to a potential value, dependent on the strength of current to be measured. While a, c, and / maintain their potential values, 6 is insulated by breaking the contact with /; the ions formed, let us say the positive ones, will then charge 6 to a constantly increasing potential, with the consequence that the number of lines of foree between a and 4 will decrease, and a couple will be formed, which will cause the needles to slowly recede from each other, and that the quickeras the current is the stronger (to return later on to particulars of the motion). Consideration. It will be seen from the arrangement of the electrometer, how the before mentioned advantages of the Witson-electroscope are. realized in it; in the space / namely the ionisation current is directly carried to the needle 4+ d, this needle being perfectly insulated by a single piece of amber. The separation of ionisation space and measuring space has, moreover, this advantage that the measuring system is not contaminated with radio-active impurities, while the ionisation space and the rod d, which can be removed, as regards the part that lies in 7, can be easily cleaned. As to the measuring system proper, the principle of it differs from that of the quadrant electrometer; it has been thus chosen on purpose that the lines of foree formed by the ionisation current contribute as much as possible and as favourably as possible to the movement of the needle a. This is not the case in the quadrant electrometer; there namely the movement is caused by the lines of force which run between the quadrants and the rims of the needle, whereas the vertical lines of force between needle and quadrants do not contribute anything to the moving couple. In my opinion it would not be possible to modify the quadrant electrometer in such a way that, while maintaining the principle of the quadrants, many lines of force are not retained at the same time which in a measurement either give no movement, or will even counteract the movement. The latter might be possible, if the flat needle should be replaced by a horizontal wire, in which way a large horizontal surface is, indeed, avoided, but on the other hand the formed lines of force would act on the two sides of the needle, when the latter is rotated. The advantage of the described apparatus 663 lies in this that the lines of foree between a and 6, which ave subjected to a change on ionisation, will mostly arise on one side of the vertical strip. This removes the last mentioned drawback, a large injurious horizontal surface also being avoided. I think that with this apparatus I have obtained a sensibility of charge, greater than is possible with a DorezainK-electrometer, the same thickness of wire given. The realization of a greater sensibility of charge. -The sensibility of the apparatus appeared to be capable of great variation, the suspension wire being left unaltered, and that by varying the state of charge, whereas, for the rest, the method of charging and measuring remains the same. To make the system more sensitive, a is not charged to + 20 V, but say to +32 V, after which a negative potential value is imparted to ¢ such that a has turned back to an almost untwisted position. The potential of e will also be more strongly negative, of course, for this state than for the state (+ 20.0, e.g. (+ 32,0, —6) V. In order to understand what causes this modification of charge to bring about greater sensibility of charge, we must examine in the apparatus 1. the variation of the potential sensibility. 2. the variation of the value of the capacity; for these two factors together determine the sensibility of charge. 1. The former is to be found from the curves I, in which examples of some states of charge are given; to investigate the potential 3) V; the state of charge will then become z S & 50 — Ss o S o = a 25 2. fe Q 0 ry) 30 Votts 20 Fig. 1. 44 Proceedings Royal Acad. Amsterdam, Vol. XVII. 664 sensibility & was increased every time by 2 Volts in potential for every state separately. The state, as indicated over every curve, always represents the initial state. All the measurements following here were made with a provisional apparatus; the suspen- sion consisted of a Wortaston wire 7m thick, and 97 mm. long. (Seale distance 1.5 m.). From these curves appears the greater potential sensibility of the system for greater potential difference between a and 6; for the state (+ 32.0, —6) V e.g. a displacement of almost 700 mm. was fuund for 2 V potential increase of 4; for (+8.0, —2) V it amounted to +500 mm. for 20 Volts. The state (+382.0,—6) V does not represent the most sensitive state that could be obtained. I think the cause of this greater potential sensibility is the following : When a recedes from / in consequence of a potential increase of 4, which is brought about by increase of charge of 6, the negative induced charge on 6 will diminish in consequence of this motion, or rather the potential value of 6 will be diminished ; for a positively charged body (a) recedes from 6. The greater the potential difference is between a and #, the greater will be the potential diminution in question for a definite angle; in other words the potential diminution of 6 required for a receding of a over a definite angle will be the less, i. e. the potential sensibility will be the greater. Besides the said change of the induced charge at the same time increases the angular displacement, which is another reason for greater potential sensibility. 2. It follows from the foregoing, that greater potential sensibility obtained in this way, must be attended by an increasing capacity ; for when through a definite addition of charge to 4 in a state with greater potential difference between a and + a slighter potential increase will set in in consequence of the motion of a, this will imply a greater capacity of 4. Capacity measurements (method Harms, Phys. Zs. 1904) give the same result; the capacity in the state (+ 8,0—2) V amounted namely to 5,2 e.s. units; that in the state (+ 20,0—3) V 6,0 es. units. Both values are the mean from a great many determinations. What is the reason why, in spite of this increase of capacity, the increase of potential sensibility more than counterbalances it, will appear from the application of the following consideration of the capacity. Though for an electrometer the sensibility of charge is in direct ratio to the potential sensibility, and at the same time in inverse ratio 665 to the value of the capacity, it does by no means follow from this that the sensibility of charge will be greatest for a capacity as small as possible, and a potential sensibility as great as possible; for the latter quantities are not independent of each other, as appears clearly among others in what was said under 2. therefore I cannot entirely concur with Lasorpk’s statement, in his: ‘‘Methodes de mesure, employées en radioactivité, page 66”, where he says: “l'appareil le plus sensible aura une grande sensibilité aux Volts et une faible capacité”; in this statement the above mentioned relation is namely not taken into account. Thus in consequence of the existing mutual dependence of capacity and potential sensibility it will be possible — and it will be shown here that this really applies to the discussed electrometer —_ that it will be favourable for the sensibility of charge, to take the capacity not as slight as possible, when namely an accompanying increasing potential sensibility more than compensates the disadvantage of this procedure. That this case presents itself in the described apparatus may be shown by first examiming of what the capacity of the apparatus, i.e. of the needle 6-++-d really consists. This capacity consists of : capacity of the part 6, which refers to arising or vanishing lines of force leading to a or c, and capacity of d. Now | would distinguish in this capacity between: a. useful capacity, by which I mean capacity which has an influence on the motion of a; b. injurious capacity which lacks this influence, and which is really a disadvantage here, because it binds charge of the ionisation current without making it demonstrable. Of the above mentioned capacity only that corresponding to the lines of foree between a and d is certainly almost entirely useful capacity (see below); the rest is injurious. And in this lies the cause why the state with greater potential difference between a and 6, though attended with greater capacity, can yet mean greater sensibility of charge; for this increase of capacity concerns here the capacity of 4 with respect to a; this is increased, (according to 2) hence the useful capacity of 6 is increased; the greater now the ratio of useful to injurious capacity is, the greater the sensibility of charge. For the rest, as regards the value of the injurious capacity in the apparatus, the following remarks may be made: 1. The injurious capacity of d with respect to / will not be of great influence, since the distance to / is great. 44% 666 2. So far the lines of force starting from the lower rim of a, or from the back of a, ending on 6, were not taken into account; they represent injurious capacity. This influence will make itself slightly felt in the middle of the needle, but will nave little effect there on the motion. 3. It is difficult to say anything definite about the value of the injurious capacity of b with respect to ce. At any rate it will also appear from what follows, how for very sensitive states the total influence of the injurious capacity may almost be disregarded. In the case of the quadrant-electrometer, on the other hand, the injurious capacity is that of large surfaces with respect to a metal needle lying close by. Before confirming what has been said above about this increased sensibility of charge for greater potential differences between a and b by the communication of some experimental results, a few par- ticulars may be added abont the mode of motion of the needle during the current measurement. Mode of motion of the needle during the current measurement : When the needle 4 is charged starting from potential 0 V_ by means of an ionisation current, when therefore the potential difference between a and / decreases, a will begin to move away from 4; consequently a motion of the scale division under the crosswire will take place through the reflection of the mirror, which, however, will not be uniform. For the different positions occupied by a both the potential sensibility and the value of the capacity of 6 will be different; for the smaller the angle with b, the greater is the potential sensibility, as well as the capacity. The causes are the following: 1. With a smaller angle the distance between qa and / is smaller and therefore the diminution of the induced charge for a definite change of angle greater. 2) With a smaller angle the potential difference itself is also greater, and this again causes a greater decrease of induced charge for a definite angle. For both reasons greater potential sensibility, but at the same time greater capacity is to be expected at a smaller angle, but here too for the same reason as for conditions of charge with greater potential difference between a and 6, the result will be a greater sensibility of charge In agreement with this the curves I show, how for every state of charge the potential sensibility decreases with greater angle between a and b, Capacity determinations gave the further result that the capacity amounted to 5.75 e.s. units for the state (+ 20,0—3) measured from an angular displacement (recession), corresponding to 550 mm. seale displacement, whereas it gave the value 6 e. s. units, when this dis- placement only extended over 250 mm. Measurement of the current. With the different above mentioned states of charge ionisation currents were measured, obtained with two different very slight quantities of polonium, which were placed in a dish on the bottom of f; the larger quantity is called A, the smaller 4. The velocity with which the scale moved under the cress wire was determined, and then the intensities of current were derived in absolute measure from this by means of the knowledge of the capacities and potential sensibilities holding for some of the states of charge. The curves IL. represent the result of the measurements for the quantity A; it appears from this, that in accordance with expecta- tion the sensibility of charge increases for states with greater potential difference between a and (; at the same time this confirms what 60 p a 40 Sensibility of charge Displacement in cm. ts) o aco seconds 400 Fig. 2. was discussed before, that namely the sensibility of charge for one and the same state is greatest, when @ is nearest 0. From the experiment in itself the ratio of the current intensities of the two quantities of polonium could already be derived, and that even for each state of charge taken by itself. It will namely be equal to the ratio of the times required by a to pass through the same angle for the quantity 4 and for B. This ratio, which would have to yield the same value for every state of charge, amounted successively to 2.5, 2.7, 2.7, mean 2.6. According to the above it was now possible at the same time by means of the measured capacities and the known potential sen- 668 sibilities to determine the currents for A and B in amperes, from CX V-inerease per sec. . : the formula : 44 == = in which C represents SS) S< AKOee the capacity of the needle / +d. As mean values from the values for the 3 most insensitive states we thus obtained : 14 = 1.3 X 10-8 (quantity B) 24 Ore >< 10718 ( 5p A) Limits of sensitiwity of the apparatus. Besides being dependent on the state of charge of the system, the sensibility of charge can also be modified by varying the thickness of the suspension wire and the angle between the needles. It was now of interest to ascertain how far the influence of a change of the state of charge in this respect could extend, how far in other words the apparatus might gain, resp. lose sensibility of charge by a constantly increasing or diminishing potential difference between a@ and 6. Experiment showed, that there are limits on either side, at which the apparatus presents a very peculiar character ; this will successively be examined for a smallest sensibility, and then for a greatest sensibility. a, Limit of smallest sensibility. Though for the just mentioned state of charge (-+ 8, 0, + 2) V the phenomena were similar to those for the other states of charge, yet the limit of sensibility appeared to be close in the neighbourhood, viz. at the state: (+ 4,0,0) V; this will most clearly appear from the experiment in which the potential sensibility was examined by | [ te aie 0 5 7 =T = \ | IL Behaviour of the most insensitive state Sg ° 6 =e = = = 5 7 g XN ee nN a 5 ic at S = al SNe 21 eae 0 36 Volls 32 669 the regular increase of the potential value of 4. It appears from curve III how, in contradistinection with the other states, @ first recedes from 6, and then approaches 6 again. The explanation of this deviation from the ordinary phenomena is very obvious; for the potential value of a being low, 6 will soon rise above this value in potential value, and this more and more; hence the diminution in lines of force between a and 6 first con- tinues, till the potential value of 6 has risen to +-4V; then lines of force arise again between a and 6, whose number increases with the rise of the potential of 4, so that finally the needles will, instead of receding, approach each other. In accordance with expectation it appeared from the experiment for the current measurement that the needle first receded from 4, stopped, and then approached 0. This state of charge appeared, therefore, to be unsuitable for the current measurement, of course under for the rest entirely definite circumstances of thickness of wire, height, and angle of the needles. b. Limit of greatest sensibility. In the following examples of states of charge illustrating this case a certain difference with the foregoing ones may be observed; for the rest this modification was taken voluntarily; 6 is here namely in the initial state already at positive potential, while the potential value was /owered during the measurement, in other words in contrast with the preceding cases a approached to 4 through increase of the lines of force between a and 6. In the following examples the potential decrease for 4 amounts every time to 2V, and it is always stated how much then the deviation is for a, expressed in mm. of scale displacement. A) state (+ 80, +60, +60,) V.| (2) state (+80, +40, + 36,) V. GED Se Vi S2smm: b +838 V. 130 mm. ss q 513 , 6) 55 + 36 af Oe apo“ 71) 4 | » +24 ,, theneedle A SEPIA aE ae | turns. ie state) (meet) ees (3) state (+80, + 30,+26,) V.| (4) state (+ 80, +10, +4,) V. iy arts) Wo Oils | b +8 V. theneedle >» 26 5, theneedle | turns. turns. (5) state (+ 120, + 40,+ 32) V.| (6) state (+ 120, +10, +2) V. 6 + 388 V. the needle 6 + 8 V. the needle turns. | turns, The phenomenon that occurred now was the following: when e.g. in the 3 state 6 was charged to + 26 V, after having first been brought to -+- 28 V, we did not once more observe a deviation which amounted. to somewhat more than that for the change of the potential value of 6 from -+ 30 V to + 28 V (since the sensibility at smaller angle zncreases), but a passed over so great an angle that the whole scale disappeared from the field, and a assumed almost a position parallel to 6: the needle turned suddenly. In state 4 this phenomenon occurred immediately at the first potential decrease of b with 2 V, and the sume applies to the 5 and 6" states, whereas in contradistinetion with this the first state exhibited stable states throughout the scale for definite potential values of 0. The experiment seemed therefore to point to the existence of an . unstable state of equilibrium of a, which gradually shifted to an increasing angle with 6 as the state of charge became more sensitive. To ascertain, whether this displacement was a gradual one, the inrning point was approximated as nearly as possible for every state separately; this was done by diminishing ® in potential value not by 2 Volts every time, but only by parts of 1 Volt. The result of this was that, as had been expected, the 2"¢ and 38'¢ states were still realisable throughout the scale, the 4", 5, 6 states on the other hand only partially, but again in such a way that the said unstable state of equilibrium, hence the turning point, occurred at a greater angle, as the state of charge was more sensitive. When after the turning a had reached its new state of equilibrium, it was not possible to make a return to its position through a slight potential increase of 4, which, considered in itself, would give rise to a state of charge with a stable equilibrium ozéside the region of turning. This too pointed to the existence of an unstable equilibrium. The explanation of the existence of such an unstable equilibrium at the point of turning seems to me the following : In what precedes the change was already discussed of the induced charge on 6, in consequence of an angular displacement of a; we saw how this change takes place for a definite angular displacement to a greater degree, the greater the potential difference is between a and 4, and the smaller the angle is between the needles. Taking this into consideration we may ask what will take place when e.g. the state (+ 83, + 30, + 26,)V is realized, and when the negative charge is continually supplied to 6. In this the ratio of useful to injurious capacity will namely con- tinually change for the before-mentioned reasons; it will become continually greater; at a definite angle the influence of this injurious capacity can even ‘all but vanish. This circumstance can also be expressed thus, that then even a supply of negative charge will no longer make the potential of 4 go down, because the approach of a to 6 brought about by this supply just compensates the expected potential decrease. The angle, for whic) this consideration holds, will still be found outside the region of turning and may be realized by means of a storage battery. If more and more negative charge is added at this angle to 4, e.g. through an ionisation current, the potential value of 6 will even continually rise in consequence of the preponderating influence of the approach of a to 6. Finally the state becomes this, and it is then that the turning takes place, that for a further approach of a toda supply of charge to / is not even required any longer. For the mere induced charge on 6 called forth by the approach will be more than sufficient to give rise to an electrostatic couple, which can be in equilibrium with the formed torsion couple. That, however, in case of such a turning the parallel state is not entirely reached, which was already pointed out, may be accounted for in this way that the lines of force between a and 6 at decreas- ing angle will also act on the back of a in appreciable quantity, and this more and more as the angle becomes smaller, so that through this circumstance the electrostatic couple, which tends to make the angle between a and 6 smaller, is counteracted. It will follow from this, that after the turning, the two needles will always continue to form a (generally small) angle with each other. It follows therefore from this explanation of the angle of turning, as was already pointed out on p. 47, that, when the measure- ment is made in the neighbourhood of this angle, the capacity which must then be taken into account, will chiefly consist of useful capacity, by which the sensitivity of the state is to be explained. In conclusion a single example of a measurement of air-ionisation and of Rubidium-ionisation. In thcse measurements the needle a@ was brought to potential zero ; the state of charge was: 0 V., — 26 V., — 32 V. The ionisation space contained only air; volume 1 litre; the number of seconds successively found for the passage through 10 mm. WAS Low dewolemont Ooq Hae Then a quantity of Rubidium salt was placed in a dish with an area of.50 em’, on the bottom of /; it was found that successively : 9, 10, 10, 11 seconds were required for the passage of 20 mm. In this case 7 was at + 80 V. Physical Laboratory of the University at Groningen. 672 Chemistry. — “The metastable continuation of the mixed crystal series of pseudo-components in connection with the phenomenon allotropy”. Il. By Prof. A. Smits. (Communicated by Prof. J. D. vAN DER Waals). (Communicated in the meeting of Sept. 26, 1914). In the first communication on this subject ') different possible continuations of the mixed crystal series in the metastable region have been discussed, in which chiefly the mixed crystal phases coexisting with liquid were considered. The metastable continuation of the coexistence of two mixed crystal phases was only mentioned in a single case, where namely continuity of the mixed erystal phases in the metastable region was supposed. It is now, however, the question what can be said of this coexistence for the case that the said continuity does not exist. We consider, therefore, one of the figures from 7 to 12 inclusive from the previous communication, and ask what can be predicted about the metastable continuation of the lines p and m. On the whole a transgression of the melting temperature without melting setting in, or in otber words supersolidification, is considered possible also on slow rise of temperature. The continuity discussed by Vax per Waats between the sublimation line a 6 and the melting point line 4c of a single sub- stance, see fig. 1, starts from this supposition; we shall, there- fore, also here have to take the possibility into account that the melting fails to appear at the eutectic temperature, and_ that the coexistence continues to exist between the two mixed crystal phases. It is, however, the ques- tion whether this possibility is limited. It follows from the con- tinuity between the sublimation line and the melting-point line considered by vAN DER WAALS that such a limit has been assumed for the coexistence between solid + vapour and solid + liquid. 1) These Proc. XVI p. 1167, 673 Above the temperature of the higher cusp e, and below the pressure of the lower cusp d, the solid substance can no longer exist by the side of the gas resp. liquid. For our purpose the cusp c is the most important, for this point expresses that there exists a limit for the coexistence solid + gas, which implies that the orientated condition of the molecules in the solid substance coexisting with its vapour cannot exist any longer at a definite temperature, in consequence of the increasing molecular motion. If this holds for the solid substance in coexistence with vapour, there must also be a limit of existence for the solid substance without vapour, and as the contact with the vapour will diminish the stability of the solid state in consequence of the molecular attraction between the molecules in the solid phase and those in the gas phase, we may expect that the limit of existence of the solid substance without vapour will lie at a higher temperature. This temperature limit of existence will vary with the pressure, and thus we shall be able to draw a line wv in the P7-figure indicating the limit of existence of the solid substance. For a binary system this holds of course, for both the components. When, therefore, we pass from the triple point of the components to the quadruple point, we get something similar. As Dr. Scurrrmr has demonstrated ’) and as is expressed in Fig. 2, the lines for Sat Se+ G, Sit Spg+ L merge continuously into each other also by means of a ridge with two cusps and an unstable inter- 1) These Proc, XIII p. 158, 674 mediate portion, and here a line pg can be given for the limit of coexistence of S4+ Sg, because either S4 or Sp has reached its limit of coexistence there, which makes it impossible for the said coexistence to occur any longer. It follows therefore from this that the lines p and m extend metastable to a definite temperature above the eutectic one. Transition from monolropy ¢o enantiotropy. As is known it often happens that a substance under the vapour pressure presents the phenomenon of monotropy, whereas under higher pressure enantiotropy takes place, as has e.g. been indicated in the P7Z-figure 3. The theory of allotropy again enables us to get a clear insight into the signification of this phenomenon. Suppose the 7. X-figure 4 to hold for a pressure above the triple point O, and below the triple point O,, then according to the said theory the conclusion may be drawn from the fact that at higher temperature enantiotropy occurs, that the situation of the internal equilibrium with respect to the pseudo system is dependent on the pressure. For only in this case e.g. the situation of the line for the internal equilibrium in the liquid with respect to the pseudo system will shift with the pressure, and if this displacement is such that the point /, moves downward with respect to the pseudo binary T,X-figure, /, will coincide with c, S, with d and S, with e at a given pressure, or in other words under this pressure two solid modifications of the unary system will be in equilibrium with each other and with their melt at a definite temperature (triple point temperature). At this temperature the two modifications have therefore the same melting-point pressure, so that this temperature can also be ealled a transition temperature under the melting-point pressure. If we raise the pressure still more, we get a 7\r-figure as given in Fig. 5, from which it appears that whereas the direction of the lines for the internal equilibrium in the solid phase excluded: the appearance of a stable point of transition at lower pressure, it must now at higher pressure neces- ¢ sarily lead to a transition point. We see further that the solid phase which appears at the stable point of solidification now lies on that mixed erystal line on which the solid phase of the metastable melting equilibrium lay before, and vice versa, so that the form of erystallisation of the solid phase at the stable point of solidification will now be equal to that in which the metastable phase showed itself at a pressure be/ow the transi-’ tion pressure. On further increase of pressure EE ea & the puints /, and s, move still Fig. 5. more to the left, and the transi- tion equilibrium gets deeper and deeper below the equilibrium of melting. The P, 7-projections of the points s, and /,, at different pressures will form the stable melting-point line, that of the point s, and /, the metastable one, whereas those of the points s’,, s', form the transition line as indicated in fig. 3. It therefore appears from the foregoing that the transition from 676 monotropy into enantiotropy can be explained in a simple way by means of the theory of allotropy. Now the question rises where the transition line eo, starts from. A possibility has been given in fig. 3, from which follows that the transition line starts in a metastable point of transition under the vapour pressure O,. This is the view to which lead Ostwatp’s *) and Scuaum’s*) assumptions on the existence of a metastable point of transition under vapour pressure*). Now it is the question whether this is the only possibility. It has been pointed out just now that the metastable coexistence is confined between the two mixed erystal series md and pe (see Fig. 4), and as the metastable point of transition arises by intersection of the internal equilibrium line of the solid phases with the above mentioned mixed crystal lines, it is clear that it may happen that this intersection does e.g. noé exist under the vapour pressure. If in such a ease enantiotropy does oecur at higher pressure, the transition line will proceed in a metastable way up to that pressure and that temperature at which for the first time an intersection between binary mixed crystal lines and internal equilibrium lines takes place, and there the transition line will then suddenly terminate in a point that indicates the limit of existence of the coexistence between two solid phases which are in internal equilibrium, as fig. 6 shows. Now it is clear that the main cause of the transition from monotropy to enantio- tropy can jind its origin exclusively in this that the situation of the pseudo figure varies more greatly with the pressure than that of the unary figure, but in by far the most cases, namely there where the pseudo components Fig. 6. are different in molecular sizes, the situation of the pseudo figure will vary less with the 1) Z. f. phys. Chem. 22, 313 (1897). 2) Lieb. Ann. 300, 215. *) Cf also Bakuuis Roozesoom, “Die Heterogenen Gleichgewichte” I, 187. 677 pressure than that of the internal equilibrium, and the phenomenon discussed here will have to be attributed to this superposition. In conclusion it may be pointed out that other particularities may still present themselves, when the internal equilibrium line of the liquid phase under the vapour pressure lies so much on one side that there exists no meta- stable melting point under this pressure. If we now think that this case occurs, and that the internal equili- brium line for the liquid phase under the vapour pressure lies greatly on one side towards the right, and that this line moves towards the left on increase of pressure, we get what follows: The phenomenon Fig. 7. of phase allotropy’) is wanting under the vapour pressure, monotropy can however, occur at higher pressure. The metastable melting-point line will start at the absolute zero e.g. in the case of fig. 10 of the preceding communication *), and run further as represented in fig. 7. If on the other hand we have to do with the ease of fig. 12 of Fig. 8. 1) For the occurrence of a substance in two or more similar phases the word phase allotropy might be used, while the occurrence of a substance in different kinds of molecules, for which I before introduced the name homogeneous allotropy, might be designated by molecular allotropy. 2) loc. cit. ihe preceding communication, a P7-figure is possible as fig. 8 shows. These considerations open our eyes to the possibility that enantiotropy occurs under higher pressure, notwithstanding the phenomenon of monotropy is not found wader the vapour pressure, Amsterdam, June 25, 1914. Anorg. Chem. Laboratory of the University. Chemistry. — “On the vapour pressure lines of the system phosphorus.” (Ul. By Prof. A. Smits and 8. C. Boksorst. (Communicated by Prof. J. D. van per Waats). (Communicated in the meeting of Sept. 26, 1914). The continued investigation of the phosphorus purposed to decide with certainty whether the red and the violet phosphorus must be regarded as two different modifications exhibiting the phenomenon of enantiotropy, as seemed to follow from Jonipors’') researches and also from our first investigations. Confining ourselves te the communication of the result we can state with certainty that the supposed point of transition between red and violet phosphorus does uot exist, and that only one solid stable modification of the phosphorus has been found, which is violet in coarser crystalline state, but red in a more finely divided state. The vapour tensions of different phosphorus preparations approach to amounts which form one continuous vapour pressure line, when the heating is long continued. An apparent discontinuity may arise under definite circumstances in consequence of too rapid heating. If namely, the preparation at lower temperature contains too much of the more volatile pseudo- component, too high vapour pressures are observed at these lower temperatures, in consequence of the not setting in of the internal equilibrium. In the neighbourhood of 450°, however, the setting in of the internal equilibrium becomes appreciable, and this transformation being attended with a diminution of the vapour pressure, the vapour pressure line will present a course that reminds of a discontinuity. When we worked very slowly and started from states which could only differ little from internal equilibrium states, any discontinuity had, however, disappeared. At the same time this investigation furnished a fine confirmation 1) CG. R. 149, 287 (1909) and 151, 382 (1910). 679 20 10 he 300° 350° 400° 450° 500° 550° 600° Vapour pressure line red phosphorus determined by means of the glass spring indicator, — = —_ — SS | Vapour pres- ; Vapour pres- | Temperature | Sarena atin | Temperature "sure in atm. (e) (eo) | 300 0.05 480 5.0 | 325 0.1 490 6.25 | 350 0.2 500 esl | 375 0.4 510 9.4 400 0.7 520 2 410 0.9 530 PiS32 420 15 540 15.65 430 1.55 550 18.75 440 1.90 560 22.95 450 2.45 570 28.6 | 460 3.15 580 35.6 470 4.0 589.5 43.1 Triple point 45 Proceedings Royal Acad. Amsterdam. Vol. XVII. 680 of the theory of allotropy, as it necessarily led to the conclusion that the stable red or violet modification is really complex, and consists at least of two components, which greatly differ in volatility. As the denomination ved phosphorus is universally known, we will also apply this term to the stable modification, though, as was said before, this modification is violet in coarser crystalline state. The adjoined figure represents the vapour pressure line, as it has been found by us after laborious study, and the table gives the vapour pressures at different temperatures, as they can be read from the vapour pressure line. In a following communication this investigation will be treated more fully. Amsterdam, Sept. 25, 1914. Anorg. Chem. Laboratory of the University. Chemistry. — “The application of the theory of allotropy to electro- motive equilibria.” IL. By Prof. A. Smits and Dr. A. H. W. Atrrn. (Communicated by Prof. J. D. van DER WaAats). (Communicated in the meeting of Sept. 26, 1914). Introduction. The application of the theory of allotropy to metals necessarily led to the assumption that every metal that exhibits the phenomenon of phase allotropy, must contain different kinds of ions. As was already mentioned before, these kinds of ions can 1. differ in com- position, the electric charge per atom being the same; 2. differ in valence with the same composition, and 3. differ in composition and charge per atom. On extension of the said theory to the electromotive equilibria it was now demonstrated 1. that the unary electromotive equilibrium finds its place in a Aw figure of a pseudo system, 2. what can be the relation between the unary and the pseudo-binary system, and 3. what phenomena will have to appear when in case of electrolytic solution resp. separation of metals the internal equilibrium is noticeably disturbed. The phenomena of anodic and cathodic polarisation appeared by this in a new light and the passivity of metals revealed itself as a disturbance of the internal equilibrium in the metal surface in the direction of the noblest kind of ions’), which view seemed already to be confirmed by a preliminary investigation *). Thus we had arrived at the region of the passivity of metals, and !) These Proc. XVI p. 699. *) These Proc. XVII p. 37. 681 it became desirable to get acquainted with the immensely extensive literature on this phenomenon. The most important hypotheses that have been proposed as an explanation of this phenomenon, and which have been collected by FREDENHAGEN ') in an interesting summary, are the following: 1. The oxide theory of Farapay, who assumes that passive metals are covered by a coat of oxide *). 2. KriGer FINKELSTEIN’s *) valence theory which slightly modified is also adopted by Métrer‘). In this it is assumed that the passivity consists in a change of the proportion between the components of different valence. 3. Le Buianc’s velocity theory *), which supposes the phenomena of passivity to be due to the slight velocity with which the formation of metal ions would take place. 4. The velocity theory of FREDENHAGEN °), MutHmMann, and FRAUvEN- BERGER’), who start from the supposition that the passivity is caused by the slight reaction velocity between the anodically separated oxygen and the passifiable metal, which causes oxygen charges or solutions of oxygen in metal to originate. 5. The theory of Grave‘), who assumes a retarded heterogeneous equilibrium metal-electrolyte which is under catalytic influences. If we now consider the passivity which has arisen by an electrolytic way, it seems to us that too little attention has been paid to the primary character of the phenomenon. First of all we should inquire to what it is owing that in case of anodic polarisation of base metals the potential difference is modified in such a way that the tension of separation for the O, is reached, and we should also question why in case of cathodic polarisation of base metals the potential difference changes in such a way that the tension of separation for the H, is reached. 1) Z. f. phys. Chem. 63, 1 (1908). ®) Farapay has not expressed himself so positively as is generally thought. In a letter to R. Taytor Farapay writes explicitly [Phil Mag X 175. Jan. 2! (1837)]: “IT have said (Phil. Mag. IX. 61 1837) that my impression is, that the surface of the metal is oxidized, or else, that the superficial particles of the metal are in such a relation to the oxygen of the electrolyte as to be equivalent to an oxidation, meaning by that not an actual oxidation but a relation... 8) Z. f. phys. Chem. 39, 104, (1902). ) Renee re » 48, 577, (1904). Z. f. Electr. Chem. 11, 755, 8238, (1905) 5) Chem. News 109, 63 (1914). 6) Z. f. phys. chem. 48, 1 (1903). 7) Sitzber. K. Bayr. Akad. 34, 201 (1904). 8) Z f. phys. Chem. 77, 513 (1911). 45* 682 These phenomena being only observed above a certain current density, it is clear that we have to do here with a disturbance which makes its appearance when the electric current is passed through with too great velocity. We have, therefore, to do here with a question of velocity, and as an explanation of the primary character of the passivity pheno- menon Farapay’s oxide theory is to be rejected from the beginning. With regard to Grave's theory we may remark that it seemed very improbable already at a cursory examination, Nernst has namely demonstrated that in the phenomenon of solution equilibrium of saturation always prevails in the boundary layer solid-liquid. In connection with this we may, therefore, expect that this continues to hold for the phenomenon of solution by an electrolytic way. There is no reason at all to make an exception here. With regard to the second theory it should be observed that the valence hypothesis, on which it is founded, is implied in the con- clusions to which the application to metals of the theory of allotropy leads. This theory generally concludes, namely, as was already said before, to the existence of different kinds of ions in the metal phases and points out that one of the possibilities is this that the metal ions with the same composition only differ in valence. The application of the theory of allotropy to the heterogeneous electrolytic equilibria has further shown that when the metal phase is complex, apart from the nature of the difference between the ions, the anodie and cathodie polarisation, and also the passivity of metals can be explained. Diametrically opposed to this theory are the theories 3, 4 and 5, and it is now clear what will have to be decided. By an experimental way we must try to get an answer to the question as to whether the phenomenon polarisation and’ passivity resides in the boundary surface between metal and electrolyte, as the theories 3, 4 and 5 suppose, or in the metal surface itself, as the theory of allotropy has rendered probable. For this purpose the investigation about the complexity is the obvious way. When experiment has proved the complexity, we can try to find out whether it possesses metal ions of different valence. Experimental part. 1. To examine whether or no the phenomenon of polarisation and that of passivity resides in the metal surface, it seemed to us the simplest course to attack the metal surface by means of chemical reagents, and to see if it has changed its properties in consequence 683 of this. If a metal really contains different kinds of ions they will, as was stated before, differ in reactive power; hence an attack may result in a change of the concentration in the metal surface, in the sense of enobling. It is, however, to be seen beforehand that the investigation in this direction will be successful only when the in- ternal equilibrium in the metal surface in contact with the electro- lyte is established slowly enough. If this equilibrium is established with very great velocity, no disturbance will of course, take place, even though the ion-kinds differ greatly in reactivity. It appeared in our previous investigation about polarisation that the metals Ag, Ca, Pb are exceedingly little polarisable, from which we inferred that these metals quickly assume internal equilibrium. Hence the etching of these metals promised little success. Quite in agreement with our anticipations it appeared that the potential dif- ference metal- */,, norm. salt solution was not to be changed for these metals by previous etching. To examine this the electrode of the metal that was to be investi- gated, fastened to a platinum thread was etched with acid, and then quickly rinsed with water. Then this electrode was immerged in a ‘/,, norm. salt solution, and made to rotate, after which the potential with respect to a ‘/,, N. calomel-electrode was measured as quickly as possible. When the above mentioned metals according to our anticipations had yielded a negative result, the metals Co, Ni, Cr, and Fe were examined with the following result: | Metal | Potential rise through etching | by HCl 0,108 V Co | 5 abSoy 0,109 ,, | » HNO; 0,107 ,, by HCl 0,04 V Ni » HNO; 0,10 5, » Br-water 0,00 ,, by HNO; 1,00 V Gr , Br-water 0,60 ,, Fe by HNO3 above 1,00 V 684 It follows from this table that these metals about which it was derived from the phenomenon of polarisation that they assume their internal equilibrium much more slowly than Ag ete. really become nobler when etched with acid, as was expected. This temporary change of the potential difference in the sense noble must find its origin in a change in the metal surface, and so it is perfectly clear that theories 3,4, cannot be of any use here. At the same time they throw a peculiar light on Grave’s theory. Grave thinks that the heterogeneous equilibrium metal-electrolyte can be easily retarded, but that the hydrogen exerts a positively catalytic influence on the heterogeneous equilibrium. According to him iron would become passive by extraction of the dissolved hydrogen, which would take place on anodic polarisation. Now specially in ion-state hydrogen is certainly a catalyst for the transition passive — active, but it is quite unpermissible to derive from this that hydrogen catalyses the heterogeneous equilibrium. It is of importance to state emphatically that according to Gravr’s theory it could by no means be expected that an enobling of the metal surface would be brought about when it was etched with HCl or H,SO,, in which the metal can absorb hydrogen. We have to do here with a pheno- menon that cannot be counteracted by the positively catalytic influence of the hydrogen on the internal transformations in the metal surface. Further we made the following in our opinion very important experiment with iron. An iron electrode forged to a platinum wire was made passive one time through anodic polarisation, another time through immersion in strong nitrie acid. Both times the potential of these passive states of the iron electrode immerged in */,, N.FeSO, solution, was measured with respect to */,, norm. calomel, in which the following appeared. The potential difference of the passive iron, both after anodic polarisation and after etching with strong HNO, at first decreases pretty rapidly, then remains constant for a time, and then descends again rapidly. We now compared the temporarily constant potential differ- ence of the quickly rotating electrode in the two cases, and then found what follows: Tension of the constant part of OSEEN OIE the potential of passive iron Passivity arisen by anodic polari- -+0,20 V with respect to 1);9 Norm. sation Calomel electrode Passivity arisen on attack of -+-0,205 V with respect to*!/;9 Norm, strong HNO; Calomel electrode 685 From this experiment the important conclusion could, therefore, be drawn that the two passive states are the same. At the end of this series of experiments we may finally already conclude that from the fact that where anodic enobling was observed, also ore enobling could be demonstrated, follows that the two phenomena must be explained from one and the same point of view, as the theory of allotropy makes possible. 2. As the course followed bade fair to lead to success, we have changed our mode of procedure so that we could expect still greater effects. Our purpose was now to attack the metals while they were im- merged in the salt-solutions, and measure the potential with respect to the calomel-electrodes at the same time. Very effective in this respect is bromic water, with which in some cases enormous effects were obtained, and a catalytic influence was also discovered of Br-ions for Ni. Nickel. The first experiment was made with a screwshaped Ni-electrode, which was kept in rapidly rotatory mction by a motor, and served therefore at the same time as stirrer. The result was as follows. Ni-electrode in 100 cm$ '/,;g N. Ni(NO3)9-Solution. | | Potential of the Ni-electrode with Observations | respect to !/;) Norm.Calomel-electrode Initial value + 0,15 V with one drop of Br-water + 0,44 , pO GrOps!) iy, -) + 0,51 , 5 7 * + 0,64 ,, eel is 7 7 + 0,67 , 5 8 ene 5 3 + 0,80 , Now a pretty abrupt descent of the potential set in. | After 4 minutes the potential is constant + 0,42 V At last 2 drops of pure Br. are ) added i) qr URE 686 It follows from this table in the first place that addition of bromic water makes the potential of the nickel rise at first by about 0,65 Volt. Then a maximum is reached, after which a considerable decrease takes place. We further see that when after the potential did not change any more, the bromic concentration was raised to saturation by the addition of three drops of bromine, the potential of the Ni changed only exceedingly little. This very remarbable result’) led us to suspect that the disturb- ance of the internal equilibrium caused by the action of the bromine, is catalytically influenced by Br’-ions which had arisen when the metal was etched. With certain Br’-ion-concentration the positive cata- lytic action of the Br’-ions is so great that it can just compensate the disturbing action of the bromine, and the br’-ion-concentration increasing - continually, a considerable decrease will then have to set in. If now the bromine concentration is increased considerably, both the disturb- ing action and the catalytic action is greatly increased, after which ihe condition can become pretty well stationary, and addition of more bromine has litthke or no influence. To test this supposition the potential of the Ni was first carried up by bromine water, and then KBr was added with the following result : Ni-electrode in 100 cm3 !/;9 Norm. Ni(NO3)2-solution. | Potential of the Ni-electrode with Observations | respectto !);9 Norm. Calomel-electrode Initial state | + 0,07 V With 5 drops of Br-water + 0,52 ,, Bo OMe eke H + 0,64 , » 2 cm? N.KBr solution + 0,24 ,, » 2 drops of pure Br + 0,35) ,, After this a slight decrease takes slowly place. We see from this that addition of KBr made the potential of Ni really decrease greatly, but then it was necessary in order to get more certainty about the signification of the phenomenon to examine in how far Ni behaved here as a Bromine electrode. ‘) The same result was oblained with a Ni-electrode glowed in vacuo, from which follows that possibly dissolved hydrogen exerts no influence on the pheno- menon. 687 For this purpose besides a Ni-electrode, also a_ Pt-electrode covered with Pt-black was placed in the same Ni-nitrate-solution, and then after addition of Br-water the potential of the Ni- and of the Bromine-electrode was determined. Then the following was found : Ni and Pt-electrodes immerged in 100 cm3 N. Ni (NO3)9-solution. 7 oe Potential of the Br-elec- | Potential of the Ni-elec- Observations | trode with respect to | trode with respect to igN. Calomel electrode 119 N. Calomel electrode Initial value (Key ES | == 0105) Vane | 5 €0,60V, > 085 v With 10 drops of Br-water + 0,27 , | + 0,82',, = ost | S002 ” 1 cms Ue ae 8) | ile 0,58 ” | =F 0,84 ” | > 004. | SSH a Sp ” ” = 0,62 , | + 0)83) ;, >—0,16 , > — 0,04 , » 1, N.KBr-solution | + 0,46 ,, + 0,79 , 005i 101040" ” 4 n »” ” aly 0,41 ” ar 0,75 ” | SSG | SSO. 9 es »Na-thiosulphate| — 0,43 , i == 0,04; | Of an unassailable metal which behaves as bromine electrode it may be expected according to the formula : V Cai, Vinet. — Veo. = A=A, + 9,058 log’? ———= C By! that the addition of the first small quantity of bromine will give rise to a considerable increase of the potential difference, while a subsequent increase of the bromine concentration must exercise a much smaller influence. Our bromine electrode very clearly exhibited this behaviour ; the first 10 drops of brominewater made the potential rise 0,85 Volt, whereas the subsequent addition of 1 em* resp. 3 em* of bromine water no longer practically changed the potential. Increase of the br’-ion-concentration must lower the potential differ- ence of the bromine electrodes again, and this too was observed. By the addition of 1 cm’® of N.KBr-solution the potential fell 0.04 Volt. That this lowering is not greater is owing to this that during the action of Bromine on nickel bromine ions had already been formed. In conelusion we removed all the bromine by addition of Na- 1) This negative value must be attributed to the catalytic influence exerted by KBr in the preceding experiment. 688 thiosulphate, and then the potential fell to — 0,04 V., which was about the initial value. If we now compare the behaviour of the Ni-electrode with this behaviour, we notice that the addition of the fist quantity of bromine has a smaller influence than for the bromine- electrode, and that the addition of more bromine has a much greater influence here than for the bromine-electrode. While the potential of the bromine electrode no longer changes on further addition of Bromine up to 3 em*., it increased for the nickel-electrode by an amount of 0,384 V., so that the total rise amounted to 0,95 V. And we see further that while the addition of KBr brought about a decrease of only 0,04 V. for the bromine-electrode, it came to four times the amount, viz. to 0,16 V. for the nickel-electrode. All this suggests that the nickel-electrode does not behave at all as a bromine-electrode in the experiments mentioned here, which is, indeed, not astonishing, as the br pretty strongly attacks the Ni-electrode. It is, therefore, clear that we have to do here with a very parti- cular behaviour of the metal itself, and that the explanation, as was already surmised, must be this that during the action of bromine on nickel a disturbance of the internal equilibrium takes place in the meta! surface, in the nobler sense, and that this disturbance is counteracted by addition of Br-ions, from which follows that bromine ions execute a positively catalytic action. The result is that we have observed bere a great disturbance of the internal equilibrium in the metal surface caused by chemical action, which proceeds continuously, in the same direction as was found in case of anodic polarisation. The electrolytical solution of metals is, however, very certainly the most efficient means to disturb the internal equilibrium in the metal, and thus in this way an anodic polarisation of 1,88 V. was observed for Ni, which after the current had been broken off still amounted to 0,95 V., a value which is in fairly good agreement with that found now. The disturbance brought about by Br during the rinsing of the electrode with water being again neutralized, the previous etching experiments with Br had a negative result. Chromium. Of all the metals which we have investigated up to now, chro- mium is nearest akin to Ni. The following table represents the result obtained when bromine was added to a rotating chromiumelectrode immerged in a ‘/,, N.CrCl,-solution. 689 Cr-electrode in 100 cm3 1/;9 norm. CrCl,-solution. Potential of the Cr-electrode with Observations | respect to !/;9 norm. Calomelelectrode Initial state with active chromium!) | — 0,26 V with 3 drops of Br-water — 0,08 ,, then slowly descends to —- 0,24 V with 1 cm3 of Br-water + 0,62 , rises in a few minutes to -++ 0,79 V with 2 cm3 of Br-water + 0,79 , with | cms of N. KBr solution + 0,78 , Then the preceding experiment was repeated with a solution of Cr(NO,), with the following result : Potential of the Cr-electrode with Observations respect to '/;) Norm. Calomelelectrode Initial state — 0,35 V with 9 drops of Br-water + 0,73 ,, » 1 cm of N. KBr-solution + 0,74 , In the first place we see from this that the chromium elecirode undergoes an exceedingly strong enobling, in which the metal beco- mes passive, as could be demonstrated. By 1 cm’. of bromine water the potential rises more than 1 Volt. Further we see that addition of KBr has no influence on the Cr-potential, which proves both that chromium does not behave here as bromine electrode, and that Br'-ions do not exert a catalytic influence on the setting in of the metal equilibrium. The metals Co, Al gave a smaller rise of the potential when attacked by Bromine. We shall revert to this behaviour later on. 1) The commercial chromium is passive, and can as Hrrrorr states, be activated by heating with strong HCl, Z. f. phys. Chem, 25, 729 (1898) and 30, 481 (1889), 690 Tron. The metal iron yielded a remarkable result. The potential of a rotating iron electrode immerged in 100 em*. of '/,, NFeCl’, could be ajjected neither by addition of bromine up to saturation, nor by addition of a solution of N.KBr. This remarkable result must be explained in the following way. As we. shall soon see, iron is strongly attacked by a solution of FeCl,, and when acted on in this way iron becomes nobler. Now Br. also attacks iron pretty strongly, and this attack would undoubt- edly also lead to an enobling of the iron surface. Evidently, how- ever, the disturbance called forth on attack by Br, is slighter than that caused by FeCl,, on account of which the addition of Br could. of course have no influence in the just mentioned experiment. What is further most convineingly proved here is this that the iron abso- Jutely cannot behave as bromine electrode in consequence of the attack. This is quite in accordance with what has now been found by us, that namely an enobling of the potential of a metal-electrode caused by addition of bromine, must be attributed to a disturbance of the internal metal equilibrium, at least when the metal is attacked by bromine. Chlorine acting more strongly on iron than bromine, it was expected that when the former experiment was repeated with chlo- rine instead of with bromine, a marked rise of the iron potential would be found. As the following table shows, this was actually the case. Fe-electrode in 100 cm3 of N.FeCl3-solution. a ST Potential of the Fe-electrode with | respectto !/;9 Norm. Calomel electrode Observations Fe in Norm. FeCl3-solution — 0,292 V > 0,108 V In a current of chlorine. — 0,184 , We may be sure that the iron which is strongly attacked by chlorine, cannot have behaved here as chlorine electrode, and that this experiment therefore proves that we have succeeded also for iron in disturbing the internal equilibrium in the surface. Another phenomenon which is in perfect harmony with this view, and which had already been observed by FINKELSTEIN *), is the elec- 1) Z. f. phys. Chem. 39, 91 (1901). phy 691 tromotive behaviour of iron with respect to solutions containing a varying ferro- and ferri-ion content, as appears from the following table. ferrosalt Fe-electrode in solutions with varying ratio RSRGISEIE: | Potential of the Fe-electrode with Obseqvation | respect to 1/19 of N. Calomel electrode Fe-electrode in 1 N. Ferrosulphate | — 0,622 V » YN. Ferro + 14N. Ferrisalt — 0,400 ,, in 1 N. Ferrisulphate | — 0,292 ,, As was said in the introduction, the complexity must first be proved, and then we may try and decide whether the ions differ in valence. The theory of allotropy already considered the anodic polarisation phenomenon of iron a clear experimental proof, and now the attack experiments have furnished in our opinion the first irrefutable proof. And now that this stage is reached the electromotive behaviour of iron with respect to solutions with varying ferro- and ferri-ion content appears in a new light. Now that we namely know that iron must contain different metal ions, it was natural to try it the observed phenomena may be accounted for from the new point of view on the assump- tion that iron contains ions_ of different valence. And_ really, for so far as we can now sur- vey the region of the observa- tions, this attempt is entirely successful. ‘. If we construct a A,wx tigure for the system Fe-electrolyte in the way as was already indi- eated by one of us, the con- nection between the pseudo-bi- nary and the unary system drawn in fig. 1 harmonizes well with the experimental facts. The stable unary electromotive two-phase equilibrium is indicated 692 by the solution / and the solid phase S. This solid phase, therefore, contains very much of the less noble pseudo component a. The metastable unary electromotive two-phase equilibrium is indicated by the solution ZL’ and the solid phase S’, As was set forth before, on anodic polarisation the metal phase S will move down along Sd, hence become nobler, whereas the metal surface will move upward along Sa on cathodic polarisation, hence become less noble. The stable unary electromotive equilibrium requires an electrolyte which contains only exceedingly few ferri-ions (?) by the side of the ferro-ions («). When iron is immerged in a solution of ferri- chloride, the system tends to assume unary electromotive equilibrium, in which we may assume the metal phase to send ferro-ions into solution, whereas ferri-ions are deposited from the solution on the metal. As follows from the A, v-figure, a solution containing many ferri- ions could only be in pseudo-electromotive equilibrium with the iron for much less negative potential of the iron. Hence there will be a tendency to make the electrolyte richer in ferro-ions, and the metal in ferri-ions, but until the unary equilibrium concentration has been reached, the iron potential will possess a too small negative value, as was also observed. It is further to be seen that the negative value of the iron poten- tial will have to increase in a solution of ferro-sulphate, when during the measurement the ferri-ions are precipitated as much as possible. This follows, indeed, from the following table. Initial potential of Fe in }/;g N. FeSO4-solution ') = — 0,538 V Potential - idem . with a little NH,CNS =—0,578,, ” ” idem Uy Ue oy HPO, = — 0,569 ” = . idem » » » NH,oxalate=—0,555,, The removal of the ferri-ions makes the iron clearly baser. It is here the place to point out that in the just mentioned etching experiments with chlorine, this substance has only indirectly caused etching. It is namely very well possible that the action of the chlorine has consisted in this that the ferro-ion emitted by the iron is immediately converted into the ferri-ion, in consequence of which the electrolyte remains as far as_ possible from the concentration of the unary electromotive equilibrium, and that this gives to the electrolyte its maximum etching action with respect to the iron electrode. 1) This solution contained traces of ferri salt. 693 In this case the chlorine would, therefore, indirectly bring about an inerease of the disturbance of the internal equilibrium. What is not improbable for iron, may also be true for nickel in the experi- ment with bromine, when namely the nickel possesses ions of different valence, but this cannot yet be stated with certainty. Besides this figure accounts for the discontinuous course of the potential, when passive iron immerged in an iron-salt solution, passes into the active form. Iron which has passed into the passive state by anodic polarisation or by attack with strong HNO,, is greatly enobled superficially, and the potential possesses even a positive value. The concentration of the surface of passive iron, therefore, corresponds to a point on the line eb, and that below the line A= 0. When this passive iron is immerged in a solution of ferro-sulphate, transformations will take place, in consequence of which the unary electromotive equilibrium is approached, and while the potential is falling, the metal surface moves upward along /e, till it has arrived in e. Here a second metal phase must occur, viz. d, and as long as the two metal phases occur side by side, the potential of the metal remains constant. The phase e must be entirely converted to d, and when this has taken place, the potential descends further, till the unary electromotive equilibrium has been reached, and the metal phase has been superficially transformed into S. This is exactly the behaviour that has been observed by many others and also by us. According to our measurements the three- phase equilibrium cde must lie at + 0,20 V. with respect to */,, N. calomel electrode. The place of the dotted line 4 =O is therefore not correct here; it must be thought between ZS and cde. We too found that the transition passive-active is accelerated by H-ions, and we are therefore obliged to assume that hydrogen is an accelerator for the internal transformations in the metal, as are also the ions of the halogens. On treatment with strong HNO, and on anodie polarisation the hydrogen is superficially removed, and this greatly promotes the internal transformation, so that the strongly metastable state which we call passive iron, is observed for some time. Through the diffusion of the hydrogen from within towards the surface the passive iron, no longer subjected to the action of strong HNO, or anodic polarisation, will soon again return to the active form. Summarizing we come to the following conclusion. 1. Farapay’s oxide theory, which seemed already sufficiently refuted by others, cannot give an explanation of the origin of the 694 passivity. If a metal is once passive, it can undoubtedly be covered by an oxide coat on anodic polarisation, but the formation of this coat is a secondary phenomenon. Leaving apart whether on anodic polarisation oxygen charges give rise to a certain rise of the potential, it should be borne in mind that it is exactly the origin of these gas charges that is to be explained. Only when the metal during the passage of the current undergoes. a rise of the potential and the tension of generation of the O, is reached, these gas charges can arise, and so a theory which purposes to explain the phenomenon of passivity, will have to account for this potential rise. lt follows from this that the theories of FrepkENHacen, MutrHMANN, FRAUENBERGER and others leave the essential part of the passivity phenomenon an open question. 3. Our experiments have proved that the phenomenon of passivity resides in the metal itself, and that though this phenomenon is decidedly a phenomenon of retardation, this retardation is not a retardation of the ion hydratation in the electrolyte, as Le Brane thinks, but a retardation of the ion transformations in the metal- surface. 4. It is perfectly true, as Grave states, that hydrogen accelerates the setting in of the electromotive equilibrium. That the hydrogen would accelerate the setting in of the heterogeneous equilibrium metal- electrolyte, 1s an untenable supposition. The hydrogen accelerates the establishment of the homogeneous internal equilibrium, but has often appeared to be inadequate to neutralize the disturbance of the equilibrium brought about by etching. 5. With regard to Finkeisrein’s (Kriienr’s) view it might be said to be impled in the new conceptions to which the theory of allo- tropy has led, but that the said observers, not understanding the deeper signification and the drift of their assumption, were not able to embody tneir view in a theory. 6. W. J. Miier’s views, which are only distinguished from those of FINKELSTEIN (KriGER) by the assumption that the states of different valence formed different phases, are theoretically incorrect, and have therefore not led to any result either. 7. The trustworthy experimental data about passivity mentioned in the literature, just as the new results in this department described here, can all be easily explained by the application of the theory of allotropy to the electromotive equilibria. Anorg. Chem. Lab. of the University. Amsterdam, Sept. 25, 1914. 695 Chemistry. — “On gas equilibria, and a test of Prot. van pnt Waats Jros formula.” I. By Dr. F. E. C. Scoerrer. (Communi- eated by Prof. J. D. vAN per Waats). (Communicated in the meeting of Sept. 26, 1914). 1. Introduction. It may be supposed as known that the situation of the equilibrium of a gas reaction at a definite temperature.can be caleulated, when at that temperature we know the energy of reaction and the variation in entropy free from concentration for molecular conversion according to the chemical equation of reaction. Both quantities are algebraic sums of the energies and entropies of the reacting gases separately, in which the terms referring to substances of different members of the equation of reaction have opposite signs. Energy and entropy of a gas free from concentration are pure functions of the tempe- rature ; in the expression for the “equilibrium constant” as funetion of the temperature the transformation energy and the change in entropy free from concentration at one definite temperature and the tem- perature coefficients of both occur as constants. The transformation energy of a great number of reactions may be directly derived from BertHeLor and THomsen’s tables; the temperature coefficients are in simple relation with the specific heats, and for this a great number of data are found in the literature; the transformation entropy, how- ever, is generally not determined directly, but from the chemical equilibria by the aid of the above expression. If one purposes to calculate the chemical equilibria from caloric data, one will have to apply instead of the said mode of calculation of the transformation entropy either direct determinations, or another mode of calculation, in which exclusively quantities of the gases separately are used. The determination of electromotive forces of gas cells might be counted among the direct measurements ; for the tem- perature coefficient of the electromotive force is a measure for the transformation entropy. But this method cannot be applied for a great number of reactions e.g. for dissociations in molecules or atoms of the same kind. Hence the calculation of chemical equilibria will succeed only when we have a method at our disposal to calculate the entropies of the gases separately or the algebraic sum of the entropies of a gas equi- librium from the constants of the substances. The thermodynamic entropy of a gas is a quantity, which through its definition is determined except for a constant, and it is therefore 46 Proceedings Royal Acad. Amsterdam. Vol. XVII. 696 clear that the above mentioned calculations of the entropy of the gases separately have only sense for another definition of entropy. If the entropy is defined as a function of the probability of the con- dition, it is possible to find a definite value for this entropy ; but this value will vary with different meaning of the “probability”. Thus the expressions derived by Kerrsom'), TreTropr *), and Sackur *) for the entropy of gases present differences which are the consequence of different definitions of probability. These differences only oceur in the constant part; if these differences cancelled each other in the algebraic sum, a test by the equilibrium determinations could not give a decision about the correctness of the entropy values. When, however, the algebraic sum of the entropies according to SACKUR and Trrropr are drawn up, it appears that these differences continue to exist also in the algebraic sums, and it must therefore be possible from experimental determinations at least if the accuracy is great enough to get a decision which expression is correct. While these calculations yield a value for the entropy of the gases separately, Prof. vaAN per Waats Jr. has derived an expression for the “equilibrium constant” of gas reactions, from which the algebraic sum of the entropies can be easily derived; the entropy of the gases separately is again determined here with the exception of a constant. Besides this expression tries to take the variability of the specifie heat with the temperature into account‘). I intend to test this formula and the above mentioned expressions of Sackur and Trrropr by a unmber of data from the chemical literature. 2. The expressions for the entropy of gases. For monatomic gases Kersom, Sackur, and Trrropr give the value for the entropy free from concentration (eventually after recaleula- tion) successively by the following expressions: 3 3 5 3 he 5 Rlrn T + 3 Rin R - : RinN+ 5 Rinm—3Rinh + C, . (1) . : . : s a in which C, represents according to KeEsom R /n a+ R{ 4-+ in ale A : 3 3 according to SACKUR 5 Rin 2a + R, and according to Trrropr 1) Keesom. These Proc. XVI, p. 227, 669, XVII, p. 20. 2) Terrope. Ann. de Phys. (4) 38. 434. 39. 255, (1912). 8) Saokur. Ann. d. Phys, (4) 86. 958, (1911); 40. 67, 87, (1913). 4) These Proc. XVI p. 1082. 697 3 5 ~f In 20 + ai R.*) This value of ©, amounts successively to 3,567 R, _ — 4,257 R and 5,257 R. The values given by Sackur and Trerropr for di-atomic gases, are: Hy = —Rln T41—RinR——Rin N+ -Rlnm — “ “ ray 2 9 7 —5Rmh+RnM+—Rm2+—Rinx+C,, . . (2) a x o in which C, according to Sackur amounts to R, according to ( Trrrope to > R. We get for a tri-atomic gas: 3 Ay=\= 8 RaT+3RnmR—4RinN + 5 kRinm — 1 —§ Rink + = Rin M,M,M,+-6Rn2+5Rna+ C,, . - (8) in which C, amounts to 3 R according to Sackur, to 4 R according to Trrrope. Besides the known values NV and h, the moments of inertia of the molecules occur therefore in these expressions. For the di-atomie molecules J/ is the moment of inertia of the dumbbell shaped mole- cule with respect to an axis through the centre of gravity, normal to the bar of the dumbbell; for the tri-atomie molecules J7/,,./, and M, are the three chief moments of inertia, which accordingly depend on the relative position of the three atoms in the molecule. For equilibria in which only mon- or di-atomic molecules parti- cipate, the moments of inertia of the di-atomie particles therefore occur, which can be approximately calculated from the different determinations of the mean molecule radius. For a_ test of the formulae by equilibria of tri-atomic molecules, however, a hypothesis concerning the relative situation of the atoms is indispensable, which is more or less arbitrary, and can make the test less convincing, 3. The equilibrium ABZ A+ B. For the simplest gas equilibrium ABZA-+ 4, in which the atoms A and #& ean be of the same or of different kinds, we 1) In the expressions of Trrrope |.c. the terms with 2 are omitted, which seems justified. 46% 698 find for the algebraic sum of the entropies free from concentration making use of the expressions of § 2: nH, —1 = 2 (=i) monate = (=) aiat. — MAMNB —— Rinh — m4+mBp l 1 3 3 =>5 Rin Li RinR—~ RinN +— Rln 3 1 a Rin2 == Rinx—-RinM+C,, (’, amounts to '/, R when Sackur’s values are used, to */, R when Terrope’s values are used. Sackur and Terrope’s calculations are based on the following assumptions for the specific heats: in which C 3 Comonat: = 2 es ts Cy diat. —= ry RR. The value of the transformation energy in its dependence on the temperature is therefore given by: ys}, SP Oia Soy fades In this expression and the following the molecular values 2 of the substances of the second member of the chemical reaction equa- tion are. always taken positive, those of the first member negative. Inserting these values into the expression for A., we find: RT In Kp = — YnET=0 — */, RT + T2nH,= — RT, in which 27/7, is represented by the above derived expressions. We can transform this expression as follows: nk T= 1 nike melee +—mT—inmM+InC,, . . . (4) RT 2 in which InC ai (jo OND +- ue Ink — E m2ax+C,; (4a) £ 2 m4 + mB 2 2 é C, amounting to —1 according to Sackur’s expressions, to 0 according o TETRODE. 4. In the fifth communication on the law of partition of energy Prof. van pyr Waats Jr. derives the following equation for the dissociation equilibrium of a di-atomic molecule: &,—€& — — oi as 0 (aa i. ies Mee er ro) MA imp a 2 on. Gata Ce €, — &, here represents the transformation energy at the absolute zero for one particle; n, and n, represent the number of split and unsplit molecules per volume unity; hence we get: ny 699 cae SnET—0 * SnET—o K ie Onan Nii Re a Sia Equation (5) can, therefore be written in the following form: vh 1 — — + = In T—In MpIn(1—e ) +imC,, . (6) SnET=0 nk, = —— n RT in which is 3 MAMP $ 1 1 : nC, = — ln ————__ -— In2Nh + —Ink — —In2x . . (6a) f 2 ma+mp - 2 2 Equation (6) differs from equation (4) in this that in (6) the term with » oeeurs, which takes a vibration of the two atoms in the molecule into account; equation (6a) quite agrees with (4a), if in the latter Trrropr’s value is substituted; Sackur’s value yields a unity difference. 5. The equilibrium J,Z 2J. In the chemical literature a series of acenrate observations occur of Starck and Bopenstein'); the dissociation constant of iodium is given by them in concentrations, i.e. gram molecules per litre. The equations (4) and (4a), resp. (6) and (6a) yield for their disso- ciation constant : vh > E; —— 1 = SS x ie Kigy a +5 In T—In M + E (: es )| Vin C. @ in which log C, = log C, + 3 (according to Trrrope and v. p. Waazs Jr.); log C, = log C, + 2,566 (according to Sackur). Making use of the values: V = 6.85 107°. (Prrrin), £ = 1.2110—'6, 127 h=5.8810—-2’, m4 =mz = ———., we find: 6.85 1023 log C, = — 36.313 (according to TerropE and van DER Waats Jr) — 36.747 (according to Sackur) . . . . . . . (Va) In equation (7) there occur iwo (resp. three) quantities, which can be caleulated from the observations: +n Hypo, M (and »). As the term with » can only have slight influence on the result, we write equation (7) as follows: vh SS SS Sa ere pa ae thy TM Toa tora EE | 9.303RkRT ' 2 ee oale oa 9 — 36.313 (resp. — 36.747) . . (8) Let us now assume that 4 remains below 20u, which seems justified 1) Zeitschr. f. Elektrochem. 16, 961 (1910). 700 in virtue of the observations of the absorption lines and their influence on the specific heats of other gases (see among others BsmnrruM); we then find as extremes for the term with pv: 3.104. 4.86.10—U cero and log (1— 207 ) Starck and Bopenstein’s observations now yield the following table for the terms of 8: TABLE I. Second member of 8 t(Cels)| T Kg 108) log Kg p | term);—90,,) Y2log T| ——_—__—___—_ Bc! Sa 4=0 |4=202 | 800 | 1073 | 0.129 | 0.111- 4] 0.693-1 | 1.515 | — 30.909 | — 31.216 900 | 1173 | 0.492 | 0.692—4 | 0.665—1 | 1.535 | — 31.470 | — 31.805 1000 | 1273 | 1.58 | 0.199-3] 0.630-1 | 1.552 | — 31.960 | — 32.321 | | | 1100 | 1373 | 4.36 | 0.6393) 0.615—1 | 1.569 | — 32.383 | — 32.768 1200 | 1473 | 10.2 | 0.009-2| 0.5911 | 1.584 | 32.738 | — 33.147 Van per Waats’s equation for 2—=0O and Terrropr’s entropy expressions yield, therefore, the values of the seventh column of the above table; Sackur’s values always yield 0,4343 less; Van DER WAALS’S equation with 2= 204 yields the values of the eighth column. If we now write equation 8 in the form: =n Eir— 1) + T log Me IEE 2. 4) ON ree (9) 2.303R° we find: TABLE II. ATC ATC, | ATC. y 9 ‘ 9 : ao) v ( Al ee es ( AT Je ON ( a7 ja 1073 — 33166 ==336310) | — 33494 ery | = 19 | = TS8 al 1173 — 36915 371493 | — 37308 37-7 | .88.15 | Hea Saad 1273 — 40685 — 41238 | | — 41145 STS = 38.2 | | =ege55 1373 — 44462 — 45058 | | — 44990 | — 37.6 | | — 38.0 | | —asaee 1473 eeAS 22 20a — 48862 | — 48824 mean — 37.6 | mean-38.05, | mean—38.3 | | | | 701 ry It will be clear that the values of ———* represent the values for Al log M ecaleulated from equation (9). Therefore the value of J becomes 10-876 according to Trrropr, 10-359 according to Sackur, 10-86 according to Van per Waats for 2=0, 10-33 for 2= 204. It is clear from the calculation that the variation of 2 from zero to 20m does not cause a change in the order of magnitude of J/, that therefore the fact that the frequency is unknown yet renders the rough calculation of W possible, and that reversely the frequency cannot be calculated but from exceedingly accurate observations. With the measurements available at present this is not yet possible, as appears from table 2. If the iodine molecule is represented by two spheres, the masses of which are thought concentrated in the centres, and if the distance from the centres is d, the moment of inertia with respect to an axis through the centre of gravity and normal to the molecule axis is a 2m i) . From this follows for the limits of d: 10—276, resp. 10-883 — 2 sees a d—=170:10—* resp: 7 10=9 (10) : ~ 6.85 1023.4 a value which as far as the order of magnitude is concerned is in satisfactory concordance with the diameter calculations according to other methods. 6. Sackur and Trrrope’s entropy expressions which were used in the preceding paragraph are founded on the assumption that the specific heats of the gases are independent of the temperature; the test of these formulae can therefore only be a rough one.') In the expression proposed by Van per WaAats, the variability of the specific heats is, however, taken into account. According to this expression the transformation energy for the iodine dissociation is represented by : < = aes Nvh SnE = SnE y=) + °/, RI eee (11) ekT —] Hence the algebraic sum of the specific heats becomes : hy dSnE 1 hv\? kT === fh — Sh = ——— dT 2 \) A number of calculations of chemical equilibria carried out by the aid of his formula are found in Sackur. Ann, d. Phys. (4) 40. 87 (1918), 702 The specific heat of the two iodine atoms is 3 FR, that of the iodine molecule therefore 5 , : ‘hy \? ekT ~ HER (ae eee li. Ti, eae The real specific heat of iodine at 300° C. is according to STRECKER 8.58 — 1.985 = 6.545. If this expression is substituted for (12), the equation is satisfied for 2 — cir. 15. If we use this value for equa- tion (8), we get in analogy with tables 1 and 2: TABLE III. Second member | TC t(Cels) (v-term), 15, of 8 (709); 15, (e ~a" | Aa jell d=15e4 800 } On7s led — 33406 | — 38.01 900 e051 5 BTN — 37207 | | == 1SRED5 1000 OWS |) . = Baeep — 41032 | ; | — 38.35 1100 0.705—1 — 32.678 — 44867 — 38.21 1200 0.684—1 — 33.054 — 48688 | mean — 38.20 This value yields for the atomic distance: d= 0.82 10-8 cm. If this value is compared with that for the mean molecule radius, which has been determined in three different ways, it appears that the value for the atomie distance as it is found above, is smaller than the mean molecule radius. We must derive from this that the atom centra in the iodine molecule lie closer together. Remark- able is the agreement of the found d-value with that of the atom distances, which were calculated by Manprrstoor from the width TABLE IV. Gas Radius of Inertia 108 (o@) 0.566 HCl 0.22 HBr 0.165 Jy 0.41 of the infra-red bands for three gases '). This agreement appears from the foregoing table, in which the values of the three first mentioned gases are derived from MAnprERsLoor. I hope soon to come back to the application of the used expres- sions to some other equilibria. Postscript. During the correction of the proofs a treatise by QO. Stern in the Annalen der Physik of June came under my notice, in which an expression is derived which shows close resemblance with that of Prof. van per Waats. Application on the iodine equilibrium can also here lead to a small moment of inertia, which is however considered improbable by Stern. Amsterdam, Sept. 1914. Anorg. Chem. Laboratory of the University. Chemistry. — “Equilibria in the system Pb—S—O, the roasting reaction process’. By Prof. W. Reinpers. (Communicated by Prof. 5. Hoocrwerrr). (Communicated in the meeting of Sept. 26, 1914). Introduction. 1. The manufacture of galena into metallic lead is mostly carried out in this manner that the sulphide is first partially roasted and the mass then again strongly heated with unchanged or freshly added lead sulphide out of contact with air. Lead is then formed with evolution of SO,. The reactions that take place in this process known under the name of “Rostreactionsarbeit” are generally given in the text-books as follows: PbS + 20, = PbsO, 2 PbS + 30, = 2 PbO + 2 SO, and then: PbS + PbSO, = 2Pb + 2 SO, PbS + 2 PbO = 3 Pb + SO, 1) Manperstoor. Thesis for the Doctorate. Utrecht. 1914. 704 For a proper insight into this process and to answer the question whether these reactions actually do take place it is necessary to study the equilibria between the different phases that may be formed therein. After various older researches among which deserve to be men- tioned those of H. C. Jenkins and E. H. Smita *), a systematic research as to these equilibria was carried out some years ago by R. Scnenck and W. Rasspacn *). They determined the equilibrium pressure of the sulphur dioxide evolved when three of the four phases PbS, PbSO,, PbO and Pb are heated together in an evacuated tube at 550° to 900°. The conelusions which they drew from these measurements as to the nature of the equilibria occurring therein could, however, not - be correct in many respects. Their idea has in fact been consider- ably modified in various. subsequent publications thereon *). But even the last concluding articles still contain many contradictions so that it is not plain what equilibria they have actually determined and which phases are stable in the presence of each other. In the following will, therefore, be discussed (1) the different equilibria imaginable in this system and (2) the results will be communicated of researches which in consequence thereof have been carried out conjointly with Dr. F. Gouprisan. 2. The equilibria between Pb and the compounds PbO, PbS, PbSO, and SO, may be considered as those in a system of three components, namely Pb, O, and S$. The isotherm for the equilibria between the different phases can, then, be indicated by a triangle with these components as apexes. (See fig. 1), Let us now first suppose that a. only the phases Pb, PbS, PbSO,, PbO and SO, are possible 4. the gaseous phase is pure SO, and the lead phase pure lead. In the last supposition we therefore neglect the small amount of PbS in the vapour and the solubility of PbS in molten lead; in the first supposition no notice is ‘taken of the basic sulphates which according to the later researches of Scuenck and RassBacH *) occur as intermediate phases between PbSO, and PbO. 1) Journ. Chem. Soe. 71, 666 (1897). 2) Ber. d. d. chem. Ges. 40, 2185 (1907). Metallurgie 4, 455, (1907). 5) Ber. d. d. chem. Ges. 40, 2947 (1907); 41, 2917 (1908). R, ScHenck, Physi- kalische Chemie der Metalle. 4) Ber. d. d, chem. Ges. 41, 2917, (1908). 705 Ss We shall see later how the deduced equilibria are being mo- dified when we drop these sim- plifications. sy 3. Let us imagine PbS heated at constant temperature between 600° and 800° in an enclosed space wherein a limited quan- o lity of oxygen is forced. PbS 30 is then partly converted into Fig. 1. PbSO,. The two phases will be capable of existing in the presence of each S0, Pb other and in an unchanged condition at a series of temperatures and pressures, If on lowering the pressure this falls below a certain limit, one of the two following reactions will take place PhS PhsOs == 2 Ppa Oo SONY ae, ty or PbS + 3PpS0,=4Pb0 +480, .... 2) In both cases there are formed in addition to the two existing solid phases two new phases, namely fused Pb and SO,-gas, or solid PbO and SO,-gas. Hence, between these four phases a monovariant equilibrium will set in, which, at a constant temperature, is possible only at one special pressure. This will be p, or p,. Only in a very special case, namely with an eventual transition point where the five phases PbS, PbSO,, PbO, Pb, and SO, might coexist, p, and p, are equal. As a rule, however, they are not and in consequence only one of the two monovariant equilibria can be stable. For if p, > p, the reaction (1), in the presence of the five phases, will take place from the left to the right and the SO, formed act on PbO according to equation (2) in the direction <—. Hence, the two reactions together result in the following conversion: 2PbS-+2PbSO, —4Pb +480, 4S0, +4Pb0 =3PbSO, + PbS Pee eEyOMenaep erasO,. ©... 26 This transformation takes place until one of the phases of the first member of the equation is used up, whilst the other with Pb 706 and PbSO, is left. PbS and PbO are, therefore, not capable of existing side by side of each other. If, conversely p, < p, the different reactions take place in the opposite sense and Pb and PbSO, recede from each other. Hence, of the phase pairs Pb + PbSO, and PbS + PbO only one can be stable, the other forms a metastable equilibrium. Here we have a case quite similar to that occurring with reci- procal salt pairs where also only one of the two pairs can be stable. 4. Let us now also consider the two other monovariant equilibria which may be assumed to exist with SO,-vapour and which are indicated by the equations 2 PbO + PbS 223.Pb 4: S0) =. ee Pb ++ PbSO,=2 PhO'4- SO, ee In the case p, >> p,, it follows at once from the incompatibility of the phases PbS and PbO that the equilibrium (4) can be stable, but not equilibrium (3). Moreover, we then must have p, > p, for otherwise after the reaction (1) in the direction — might follow the reaction (3) in the direction < which reactions might jointly cause the conversion (5) in the direction <—, which is in conflict with the premiss. Finally we shall have p, followed by (4) in the direction <—, namely: PbS +3 PbSO,—4 PbO + 480, 480,-+8PbO = 4 Pbh+ 4 Ppso, PbS + 4 PbO =4Pb-+ PbSO, Hence, we get this result: If Pb + PbSO, forms the stable phase pair, then only the mono variant equilibria (1) and (4) are stable and p, > p, > p2 > Ps: If PLO + PbS form the stable phase pair, all the reactions occur in the opposite sense and only the monovariant equilibria (2) and (3) are stable, whereas then p, > p. > pi > Ps- 5. Starting from the mixture of PbS and PbSO, (for instance a in fig. 1) we will, on withdrawal of SO, travel either through the monovariant equilibria (1) and (4) (region PbS, PbSO,, Pb and region PbSO,, Pb, PbO of Fig. 1) or the equilibria (2) and (3) (region 707 PbS, PbSO,, PbO and region PbS, PbO, Pb) to finally retain the equilibrium Pb-—+ PbS or Pb-+ PbO after eliminating the SO, as much as possible. Hence, the reactions (1) and (3), which are generally quoted as taking place in the roasting reaction process cannot possibly indicate both stable equilibria. Of the p-T-lines which Scnenck and RossBacn determined by addi- tion of “PbSO,, PbS and Pb and of PbS, PbO and Pb one at least must, therefore, indicate an instable equilibrium or an equilibrium between phases other than those which were brought together in the reaction tube. We will see later that both equilibria are metastable and that the pressure lines recorded by them relate to the equilibrium between , other phases. 6. The supposition made in (2) sub @ is not correct. Between PbSO, and PbO there still arrive three basic salts as intermediate phases, namely PbO.PbSO, , (PbO), PbSO, and (PbO), PbSO,. The first of these can be in equilibrium with PbdSO,. The four monovariant equilibria mentioned in (3) now become: Bhs a eEsOr= UPHELD SOS 9 coin. se ot PbS -—- 7 PbSO, = 4 PbO. PbSO, + 4S0,. . . . (2) DsPhO PESO: AaPbSi= FED 51805 7-2) Sh 6) Pb! sPusOr== 2 ibb@:.PbSO, SO, =." 08! sa and the alternative found must read: either Pb + PbSO, stable and then p, >p, >p, > p, and only (1) and (2) stable, or PbS + PbO. PbSO, stable and then p, << p, << py 95 (PbO), PbSO, ++ Pb a Hild ares = 57 DO == Pb: Hence, at the temperatures and pressures of region /’ all the sulphur will have been expelled from the roasting material. 20. By substituting the values found in table 1 first series in Q 4,571 T thus obtained in pairs, Q, was caleulated for the reaction: PbS + 7 PbSO, = 4 PbO. PbSO, + 450, + 4Q, the equation log p= — + C and combining the equations 718 and as mean value was found — 38390 cals. Applying the same principle to the p-Z-values of table 2 we found as the mean value for Q, in the reaction: 3 PbS + 2 PbO.PbSO, = 7 Pb + 5S0, + 5 Q, -— 54324 cal. In order to check these, figures we eliminate the unknown heat of formation of the basis sulphate from these equations: PbS + 7 PbSO, = 4 PbO . PbSO, + 450, — 4 X 38390 cal. 6 PbS+ 4 PbO. PbSO, = 14 Pb+ 1080, —10 X 543824 cal. 7 PbS + 7 PbSO, = 14 Pb +1480, —696800cal. PbS + PbSO, = 2 Pb + 250, — 99548 eal. From the molecular heats ') PbSO, = 216210 cal. PbS= 18420 ,, SO, = 71080 %; the calculation for the above reaction at 20° gives — 92470 eal. The agreement is tolerable. Delft. Inorg. and phys. chem. Laboratory Technical University. 1) LANDOLT. Bornstein, Phys. Chem. Tabelle 1912, 870 and 853. (November 27, 1914). KONINKLUKE AKADEMIE VAN WETENSCHAPPEN TE AMSTERDAM. PROCEEDINGS OF THE MEETING of Saturday November 28, 1914. Vou. XVII. ye So President: Prof. H. A. Lorentz. Secretary: Prof. P. Zeman. (Translated from: Verslag van de gewone vergadering der Wis- en Natuurkundige Afdeeling van Zaterdag 28 November 1914, Dl. XXIII). SL OENE EEE eN a Se G. J. Exvias: “On the structure of the absorption lines Dy and D,”. (Communicated by Prof. H. Lorentz), p. 720. , G. J. Exvias: “On the lowering of the freezing point in consequence of an elastic deformation.} (Communicated by Prof. H. A. Lorentz), p. 732. : G. J. Exias: “The effect of magnetisation of the electrodes on the electromotive force.” (Communicated by Prof. H. A, Lorentz), p. 745. 1 H. Kameruinen Onnes and G. Ilorsr: “Further experiments with liquid helium. M. Prelimi- nary determination of the specific heat and of the thermal conductivity of mercury at temperatures obtainable with liquid helium, besides some measurements of thermoelectric forces and resistances for the purpose of these investigations”. p. 760. F, A. H. Scurememaxers: “Equilibria in ternary systems” XVII, p. 767. | F, A. H. Scarememakers and Miss W. C. pe Baar: “On the quaternary system : KC]l— CuCl,—BaCl,—H,0”, p. 781. T.. S. Ornstems: “On the theory of the string galvanometer of EryrHoven”. (Communicated * by Prof. H. A. Lorentz), p. 784. L. S. Ornstern and F. Zernike: “Accidental deviations of density and opalescénce at the critical point of a single substance”. (Communicated by Prof. H. A. Lorentz), p. 793. A. A. Hismays VAN ven Beren and J. J. pk 1a Fontare Scururrer: ‘The identification of traces of bilirubin in albuminons fluids” (Communicated by Prof. H. J. Hampurcrer); p. 807. (With one plate). M. W. Bewerinck : “Gummosis in the fruit of the Almond and the Peachalmond asa process of normal life”, p. 810. Ernst Conen and W. D. Hetperman: “The allotropy of Lead” I. p. 822. (With one plate). J. C. Kivyver: On an integral formala of Strerrses”, p. 829. F. E. C. Scurerer: “On unmixing in a binary system for which the three-phase pressure is greater than the sum of the vapour tension; of the two components”. (Communicated by Prof, J. D. van per WAAts), p. 834. Mrs. T. Enrenrest-Aranasssewa: “Contribution to the theory of corresponding states”, (Communicated by Prof. H. A. Lorentz), p. 840. A. FB. Hotreman: “The nitration of the mixed dihalogen benzenes”, p. 846. J. Borsexen and W. D. Conrn: “The reduction of aromatic ketones. III. Contribution to the knowledge of the photochemical phenomena” (Communicated by Prof. A. F. Hoiirs- MAN), p. 849. YP, Enrenrest and H. Kamertincu Onyes: “Simplified deduction of the formula from the theory! of combinations which PLANcK usvs as the basis of his radiation-theory, p. 870. 48 Proceedings Royal Acad. Amsterdam, Vol. XVII. ; 720 Physics. — “On the structure of the absorption lines D, and D,”. By Dr. G. J. En1as. (Communicated by Prof. H. A. Lorentz). (Communicated in the meeting of April 24, 1914). Some time ago Prof. H. A. Lorentz drew my attention to the results of an investigation by Miss G. v. Usiscu'). From phenomena observed by the writer during the investigation of the polarisation state of light emitted by a sodium flame in a magnetic field after it had passed through a tube filled with absorbing sodium vapour, she infers that the wave length for which the absorption of the vapour is a maximum, depends on its temperature, and in such a way too that on rise of temperature a displacement towards the red takes place. The amount of this at 270° would be about 0.17 A.U. with respect to the emission line. If seemed worth while to ascertain this result by direct observation. During the summer months of last year Dr. W. J. pk Haas and myself occupied ourselves with this question. At first we intended to use an échelon-spectroscope for these researches, observe by the aid of this the spectrum of a monochromatic source of light, and then superpose the absorption lines of sodium vapour on this. This vapour was in an iron tube, closed on both ends by plates of selected plate glass, and provided with water cooling; in the middle the tube, which contained there a vessel of metallic sodium, could be heated. Such tubes were used by R. W. Woop for the investigation of fluorescence of sodium vapour. First a blow- flame served as monochromatic source of light, which was blown by means of air in which a very finely divided solution (mist) of soda was suspended. Afterwards the flame of a Méker-burner was preferred, burning in an atmosphere in which a mist of soda was also suspended. This was reached by placing the flame inside an iron exit tube, at the bottom of which a reservoir was attached, which was in communication with the air, and into which the soda-mist was blown by means of an aspirator. This method appeared very efficient to obtain a sodium flame of constant intensity, which is moreover easy to regulate. : The lines obtained by means of this source of light, were too broad for the investigation with the échelon-spectroscope when the intensity of the light was sufficient for the observation, the self- reversal moreover being very troublesome then. If on the other hand, the light intensity was diminished till the lines were narrow enough, the intensity was again too slight for the observation. 1) G. y. Usiscu. Inaug. Diss. Strassburg. 1911. Aun. d. Phys, 35. p. 790; 1911, 724 We have therefore then tried to see the phenomenon directly by means of the spectrometer, which served for provisional dispersion in the experiments with the échelon spectroscope. We were of opinion that, the dissolving power of the prism system amounting to 60.000, it must be possible to observe in this way a displacement of the above given amount. Nothing was to be detected of this, however. It is true that the at first narrow absorption line (which _ has originated by self-reversal in the sodium flame) widened considerably on the heating of the Woop tube up to about half the distance of the two D-lines, but a displacement could not be perceived. On account of Dr. pe Haas’ return to Berlin we had to stop our joint observations at this point, and I continued the research alone. First I tried to obtain comparatively narrow emission lines, which should be intensive enough to superpose the absorption lines on them in the investigation with the echelon spectroscope by eleetric discharges in a heated evacuated Woop tube with sodium. This, however, appeared impossible, the width remained considerable, and the self-reversal troublesome. Then I took another course, and used an arclamp as source of light. To obtain monochromatic light I used the above mentioned spectrometer as monochromator, diminishing the widths of the slits so that the issuing light comprised a range of only about 0,5 A.U., for some observations 0,4 A.U. In this case the adjacent spectra will overlap only for a small part, as the distance between two successive orders amounts to 0,39 A.U. The dissolving power of .the échelon spectroscope, which consists of 80 plates of 14,45 m.m., amounts to 450.000 *) for D-light. The absorption lines of the are of light, which are caused by the sodium vapour present in it, appear, observed in this way, to be double. Both for D, and for D, there are two maxima of absorp- tion, which are somewhat sharper for D, than for D,, and the distance of which is smaller for ), than for D, under for the rest the same circumstances. These distances are, however, variable. The lamp burning normally, the distance generally amounted to 0.053 A.U. for D,, to 0.078 A.U. for D, for a point lying in the middle of the are, when Sitrmens’ S A-carbons were used. It sometimes occurred, however, for a certain pair of carbons that the distance was much smaller, down to half the value; sometimes too that it was much larger, up to almost double the said amount. When new 1) The results of the observations made about the components of the mereury lines by the aid of Uns échelon spectroscope, were in agreement with those of most of the other observers. 48* 722 earbons are set burning, the distance is also much larger than the normal one, When the are hisses, the reverse takes place: the lines erow fainter, and the distance grows smaller, in case of very decided hissing they can even become entirely invisible. Also in different places of the are the distance is different, for the negative carbon the distance is much larger — about twice as large as a rule — than for the positive carbon. Between the two absorption maxima lies also a region of absorption, which on the whole is of only little greater intensity than the maxima of absorption. Now and then it makes the impression that there are still more feeble maxima of absorption in this region; I have, however, not been able to ascertain this with perfect certainty. I could artificially modify the aspect of the absorption lines very considerably by blowing a little soda mist into the are by means of a tube placed parallel to the positive carbon, which lies horizontal ; in order not to disturb the equilibrium of the are the blown in air current had to be only very weak, while the quantity of sodium could be modified by varying the concentration of the sodium solution. It then appeared that always when soda was blown into the are the distance of the components of the two D-lines increased, these becoming vaguer at the same time. The greater the quantity was of the soda that was blown in, the further the components were split up, and the less sharp they became. This splitting up could even reach an amount of about 0,3 A. U., in which case they were, however, very vague. The splitting was always perfectly symmetrical with respect to the original double absorption line. The maxima of absorption were — for so far as perceptible — of equal intensity, the sharpness of the two components also seeming pretty well equal. | have not undertaken further quantitative measurements about this, since if would have been impossible to determine the quantity of sodium in the are, even when the velocity of supply was known; at most this quantity could be very roughly estimated ; nor was the phenomenon perfectly constant. Similar phenomena, still less constant, however, were observed when carbons were used which were soaked in a diluted solution of soda. When the Woop tube is placed in the way of the rays of light so that it follows the spectrometer, which cuts a small portion out of the spectrum, so e.g. between object glass and eye-glass of the reading glass, the absorption lines of the sodium vapour appear also to be double, in which the distance of the components increases as the temperature rises. At the same time, however, distinct phenomena of anomalous dispersion are perceptible, as soon as the heating of 723 the tube takes place in a somewhat unsymmetrical way. For this reason, and at the same time on account of the large differences of temperature which must necessarily exist in the Woop tube, at which there can be no question of saturate vapour, I did not under- take quantitative measurements. Finally in order to be able to carry out measurements which should be liable to interpretation, | have generated the sodium vapour in a vertical glass tube, which was first provided with some pieces of. sodium, then evacuated down to about O.OOL m.m. of mercury, and sealed to. This tube was uniformly heated all over its length by an electrical way, so that the temperature may be assumed to be the same at all places, and accordingly the sodium vapour to be saturate. In the enclosure there were made two apertures, through which the light fell in horizontal direction. As the glass gradually clouded somewhat at these places, | later on applied side tubes which were also electrically heated, while a wider glass tube was also used. The bore of the tube, with which | carried out my final measurements, amounted to 28 mm. For a reason to be stated later, this tube was placed between object glass and eyeglass of the reading glass. Of course the image suffered by this, but nevertheless it was possible to measure the distances of the components. The pbenomena which I observed in this way were qualitatively in perfect harmony with what I had seen by means of Woop’s tube. and during the blowing in of the soda mist into the are. On vise of temperature the distance of the components increases, while they become less sharp at the same time. Up to almost 300° the distance can be very well measured, the vesults of these measurements have been represented in the curves D, and PD,. At higher temperature the width is too large to be investigated by means of the échelon spectroscope, the phenomenon becoming very vague then, so that the absorption maxima are clearly perceptible on slight magnitication only, the light intensity is only little greater then between the absorption maxima than in the maxima themselves. The greatest width measu- red amounts to about 0,21 A.U., as is visible from the figure. The resolution is always greater for D, than for D,; the curves indicating the course in the two cases run perfectly parallel. On the whole the components of D, are somewhat sharper than those of D,; of D, the component lying to the side of the red is the stronger and sharper, of D,, that which lies to the side of the violet. I think I have been able to observe with pretty great certainty that the two components of D, are each double, so that the absorption region would be bounded here by two absorption maxima on either 724 0.05 ° 200° 250 side, which can be distinguished from each other with difficulty. I have not been able to observe anything similar for D,, there the - absorption maxima seemed single to me. At 274° I found about 0.035 A.U. for the distance of the two absorption maxima, of which each component of D, consists, at 290° about 0,045 A.U. The dis: - tances of the components of YD, indicated in the figure refer to the extreme components. The region lying between the absorption maxima ~ situated on either side is on the whole of uniform intensity, whieh, . chiefly at tbe higher temperatures, is but very little greater than , that of the absorption maxima. Whether there are still more faint maxima in this region, I have not been able to observe with certainty, though | now and then got the impression that such was, indeed, the case, 725 In the figure IT have also indicated the mean amount of the width of the region of the are absorption by means of short dotted lines. Further the curve indicated by p denotes the vapour tension of the sodium vapour for the temperature in question. The scale of the ordinates on the right hand side of the figure refers to this curve. For the determination of this curve I made use of KRONER’S ') research on the vapour tension of alkalimetals ; for this it was necessary to extrapolate the values found by Kroner, for which purpose I used Graitz’s”) formula, which is formed from Dupré-Herrz’s *) formula based on that of CLapnyron by assuming the validity of Van pmr Waats’s law for the vapour instead of that of Borne-Gay Lussac. Grairz’s formula ap n p-e T — kT—™e GE containing four constants, | had to assume four points of the vapour tension curve. | took three points for them, which had been directly determined for sodium by Kronur, viz. 7= 693, p=2.00 ; T= 733, p = 420; T= 773, p= 8.64 (temperatures in absolute scale, pres- sures in m.m. of mercury). I derived the fourth point, availing myself of Ramsay and Youne’s rule, from Kronur’s determinations for pot- assium and found for it 7’= 589, p=0.11. I found from this for the constants using Brice’s logarithms, «@ = 28.877, log k = 164.88, m = 48.748, n = 18148. By the aid of these constants I calculated the values of p given in the figure. One might be inclined to ascribe the observed phenomena to ano- malous dispersion ; the observed dark lines would then be no absorp- tion lines proper, but “dispersion lines”. If this were actually the ease, tie light of the considered wave length would only have changed its direction, without having undergone absorption. As to the absorption lines in the light are, taking the comparatively small value of the anomalous dispersion at the densities in question into consideration, the point of intersection of the rays of light coming from the are with the plane of the spectrometer slit could never be far distant from the crater image. When this image is moved over the plane of the slit we should therefore have to see light lines in some positions instead of dark ones. As I have never observed anything like this, not when I placed the are lamp in other positions 1) A. Kroner. Ann. der Phys. 40. p. 438. 1913. 2) Grirz. Zeitschr. f. Math. u. Phys. 49 p. 289. 1903. 8) Herrz Wied. Ann. 17. p. 177. 1882. Dupré. Théorie mécanique de la chaleur. p. 69. Paris 1862. 726 either, so that the direction of the issuing beam of light with respect io the light are was a quite different one, I think I may conclude that the are lines are not to be attributed to anomalous dispersion. Nor can for analogous reasons this be the ease with the lines which were observed after the light’ had passed through sodium vapour in a uniformly heated glass tube. Here too light lines would have to be observed at some distance from the dark ones, of which there was however, no question. On the other hand — as I already remarked just now — when the unsymmetrically heated Woop tube was used, I saw a sharp light line by the side of the dark region, which latter became blacker then at the same time; in fact besides the absorbed light, also the anomalously dispersed light has vanished from this region. Everything considered I am therefore of opinion that anomalous dispersion has had no influence on my final results. I will mention here another phenomenon, which at first made its influence felt in a peculiar way. In my first experiments I had placed the glass tubes in which the sodium vapour was generated, before the entrance slit of the spectrometer, so that the whole beam of white light passed through it. The measurements which I then made of the distances of the components for different tubes, which were distinguished by the thickness of the radiated layer of vapour, were not in harmony; at the same temperature the distance of the components was found larger as the radiated layer was thicker. This peculiar phenomenon must undoubtedly be a consequence of the presence of fluorescence light, which the sodium emits under the influence of the incident white light. According to Woop’s researches!) it is just the two D-lines which are very prominent in the fluorescence light. This light will be the stronger as the traversed layer is thicker. In this way it is explicable that the absorption spectrum can be subjected to a modification which will become greater with increasing thickness of layer. When, however, the distance of the absorption maxima increases in consequence of the superposition of the fluorescence light over the absorption spectrum, which is greatly the case at higher tempe- ratures (see the curves (D,)' and (D,)'), it is easy to see that the maximum, resp. the maxima, of the fluorescence light must be situated between the absorption maxima so that the curve representing the intensity of the fluorescence light, exhibits a rise at the place of the absorption maxima, when we move to a point lying halfway 1) R. W. Woop. Phys. Opt. p. 444; 1905, 727 between the two absorption maxima, If the absorption maxima coincided with maxima of fluorescence, the former wouid either not shift their places, or they would split up. Hence we arrive at the conclusion that at temperatures above about 260° the maxima of absorption do not coincide with maxima of fluorescence, but that the latter maxima, resp. maximum, lie between the maxima of absorption, I have indicated two curves in the figure for which the influence of the fluorescence light is visible, the curves (),)' and (D,)'. They represent the distance of the components of D, and D, fora radiated thickness of layer of 40 m.m., in which the tube of sodium vapour was placed before the entrance slit of the spectrometer: the distance from the tube to the sht was about 10 em., the opening of the incident beam being about L : 10. Under these circumstances it was also possible to observe the fluorescence light by means of a spectroscope. If the tube with sodium vapour was placed between object glass and eye glass of the reading glass, the fluorescence can only be brought about by the light that belongs to the narrow spectral range, issuing from the spectrometer, instead of through the undivided white light. It is easy to see that the part of the fluorescence light, which in this case is already very faint, the part that finally reaches the retina, will have to be exceedingly small in comparison with the observed light; the influence of the fluorescence light will, therefore, have to be imperceptible then. I have actually convinced myself that when the tube with vapour is placed between object glass and eye glass of the reading glass the distance of the absorption maxima is independent of the thickness of layer traversed by the rays. For this purpose I compared a tube of 50 m.m. bore with the tube of 28 m.m. used for the measurements ; in these two cases the distance of the components was the same at the same temperature. I think myself justified in drawing the conclusion from all that has been observed that the distance of the absorption maxima of the sodium limes is closely connected with the density of the vapour, and that in this way that the splitting up increases with increasing density. That what has been observed is chiefly an effect of density, aud not in the first place a temperature effect, is supported by the fact that the influence of the soda mist blown into the are is for the greater part the same as that of absorbing sodium vapour of much lower temperature. The temperature at which the absorption in the are takes place, will namely undoubtedly be much higher than that of the vapour in the glass tube. On the other hand the phenomenon in the are is dependent in a high degree on the quantity of soda, the temperature varying very little as long as the equilibrium in the light are is not disturbed. In my opinion besides the density also the temperature can have influence, though the latter will be slight. If the are lines were exclusively dependent on the density of the vapour in the are, the horizontal dotted lines in the figure would have to cut the curves for D, and D, in points for which the abscissae are equal. As this seems to be almost the case, the influence of the temperature cannot be very large. Also with regard to the degree of the absorption —- so the value of the absorption index —, there can very well be difference between higher and lower temperatures; I have, however, not examined this. And at last, the absorption lines of low temperature are somewhat sharper than those in the light are. Returning to what Miss v. Usiscu derived from her experiments, viz. a displacement of the absorption maxima of sodium vapour on change of temperature, we may question whether this result can be brought into connection with the observations described just now. In the experiments under consideration the main point was the absorption to which the components of the two magnetically split sodium lines (briefly called ZeEMAN-components) were subjected in the Woop tube filled with sodium vapour. The measurements were made of the relative intensities of the differently polarized beams of light both normal to the lines of force of the magnetic field (transversal), and in the direction of the lines of force (longitudinal) (in the transversal observations the beams polarized parallel to and normal to the lines of force, in the longi- tudinal observations both the circularly polarized ones.) These beams of light were emitted by a sodium flame which was placed between the poles of a magnet: the undispersed sodium light was subjected to absorption in a Woop tube. This tube was every time heated to a definite temperature, and the temperature being kept constant, the magnetic field was varied till the difference of the intensities of the differently polarized beams of light was a maximum; this measurement took place by rotation of a glass plate, which served as a compensator. For every temperature of the Woop tube the field was determined, in which the difference of the intensities became a maximum. Miss v. Usisch makes the supposition that this difference will be a maximum when one ZeeMAN-component coincides with the maximum of absorption, and the other is not absorbed at all. By the aid of this the writer deduces that at 270° the displacement of the 729 ° sodium lines would amount to 0.47 A.U.; im this ease the differe2&e of the intensities was therefore a maximum at a distance of the ZEEMAN-components or on an average 0.34 AU. Now on closer consideration it is clear that the correct interpreta- tion of Miss v. Usiscn’s observations would be very intricate, and many more data would have to be available for it. In the first place we should have to know the correct distances and intensities of the Zenman-components, before they undergo absorption in the Woop tube; further the accurate course of the curve that denotes the connection between the intensity of the lhght transmitted in this tube with the wave length, should be known. The absorption maxima of sodium vapour not being sharply defined lines, much will depend on the intensity and sharpness of these maxima; this is the more obvious when it is borne in mind that the real maxi- mum difference of intensity observed by Miss v. Usiscn, constitutes only a few percentages of the whole amount. With so small a difference we should be sooner inclined to assume a difference in absorption to that amount than as the author does, suppose that one ZeEMAN-component is not weakened at all, the other only a few percentages in the case of a thickness of layer which is at any rate pretty considerable. It is easy to imagine cases in which the absorption maxima are of equal intensity, but difference of intensity of the ZeeMAN-components is a maximum, when they lie outside the absorption maxima. Everything considered the amount given by the author can only represent the distance of the absorption maxima as far as the order of magnitude is concerned; accordingly I do not think that the result of my observations (distance of the absorption maxima of about 0.15 A.U. at 270°) is in contradiction with that of Miss v. Uniscu. Besides it is possible that the temperature has not been given perfectly accurately. In this respect a Woop tube presents more sources of errors than the uniformly heated tube which I used. Moreover the difference need. not be very great, taking the very rapid inerease of the resolution in the neighbourhood of 300° into consideration. When seeking an explanation of the observed phenomena now that it has appeared that in the first place there is here question of a density effect, we are naturally led to look for a connection with the widening of spectrum lines in general, and with the explanation which Stark has given for it, which comes to this that this widening 730 would be the consequence of electrical resolutions of the spectrum lines. It is easy to understand that the greater the density of an (emitting or absorbing) gas, the more frequently it will oecur that the vibrating electron systems are in the neighbourhood of electric- ally charged systems, and will therefore perform their vibrations under the influence of the electric field of these charged systems ; hence the spectrum lines brought about by these vibrations will be the more perceptible by the side of those which arise from systems whieh do not vibrate in an electrical field. In this way we shall be able to obtain a great number of lines, which all being superposed, can make the impression of a broad band. It is very well possible that definite groups of these vibrations can be predominant which will give rise to the appearance of maxima of absorption (resp. emission). If we wanted to give further particulars about this, it would be necessary to enter into an examination of the mechanism of the phenomena *). As to the order of magnitude of the above described phenomena, it is indeed interesting to compare it with the order of magnitude of the electrical resolutions as Stark has observed them. When we assume that a vibrating system is placed in an electrical field origi- nating from an electrical elementary charge at such a distance as the mean distance of the atoms in saturate sodium vapour of about 280° amounts to, the resolution of the D-lines, when taken as an electrical resolution, would at this temperature agree as far as ihe order of magnitude is concerned — with the resolutions whieh Srark found in this part of the spectrum, always on the supposition of a linear course of the electrical resolution with the intensity of the field. Above 260° the observed resolution increases pretty accurately with the power ?/, of the density, the increase being slower at the lower temperatures ; therefore what was observed just now about the order of magnitude of the resolution at 280° cannot possibly be of general validity, as this would require an increase not with the power */,, but with the power */, of the density. I also observed the D-lines in the solar spectrum, which also exhibited two components each. On the whole the phenomenon was in accordance with what is observed for saturate sodium vapour of about 270°. The distance of the components was about 0.15 Nae 1) Even without thinking of electrical resolutions, | pronounced the opinion already before that the “own period” of a vibrating system might vary as it was under the influence of neighbouring systems, and that widenings of spectrum lines might be the consequence of this. Cf, G. J. Extras, Diss. Utrechit; p. 146 et seq. 731 I did not however carry out accurate measurements about this. They further seemed to me slightly less sharp than those whieh were observed for sodium vapour of low temperature, though this difference Was not very conspicuous. If the resolution were really only little dependent on the temperature and possible other factors, we might draw the conclusion from this that the density of the sodium vapour in the chromosphere of the sun is as great as that of saturate sodium vapour of about 270°. I further made some observations on the emission lines of sodium vapour. For this purpose I used a glass discharge tube which con- tained some sodium, and which was heated to 200° or 200°. It then appeared that. the emission lines, both D, and D,, were double, and that the distance of the two light lines increased with increasing temperature. It is not impossible that self-reversal plays a part in this; it was, however, peculiar in this that chiefly for D,, the two light lines on either side of the dark core differed in intensity, which would not have to be the case for self-reversal. With regard to the emission lines D, and D, Micnetson ') has pronounced the opinion that they would each consist of four com- ponents, {wo intenser ones, and two very faint ones, the distance of the intenser ones amounting to about 0.15 A.U. Fapry and Pxror’) are, however, of opinion, that reversal phenomena would play the principal part in this. In conclusion I will still state that already a long time ago I observed for the emission lines of copper when this is in the light are, resolutions of entirely the same order of magnitude as those which I have now described for the absorption lines D, and D, of the sodium, also with the aid of the échelon spectroscope. I then observed with a pretty high degree of certainty that these resolutions were greater as the density of the copper in the are increased. I could not carry out measurements about this, however, as the amount of the resolution was very variable, and besides I had no means to determine the density of the copper in the are. Haarlem, February-April 1914. Physical Laboratory of ‘“Tryier’s Stichting.” 1) A. A. MicHELson and E. W. Moriey. Amer. J. (3) 34. p. 427; 1887. Phil. Mag. (5) 24 p. 463. 1887. A. A. Micnetson. Rep. Brit. Ass. 1892 p. 170. Phil. Mag. (5) 34 p. 280. 1802. 2) Gu. Fasry and A. Piror. CG. R. 180 p. 653. 1900. Physics. -— ‘On the lowering of the freezing point in consequence of an elastic deformation.” By Dr. G. J. Extas. (Communicated by Prof. H. A. Lorenz). (Communicated in the meeting of May 30, 1914). A number of years ago E. Riecky ') derived from thermodynamic considerations that a solid body subjected te forces which bring about an extension or Compression, will in general exhibit a lowering of the freezing point, also at those places of the surface where no deformative forces are directly active. This case may be extended to that of an arbitrarily deformed body. J. Let the free energy per unity of mass be w, and the density @, then the total free energy of a certain system will amount to v= [ewe eer mol cme 0 (Il) in whieh the integration must be extended over all the material elements 9.dt. Further we make no suppositions at all on the state of the system. Let us suppose the system to undergo an infinitely small deform- ation at constant temperature. We can always assume this deform- ation to consist of the infinitely small dilatations «,, y,, 2:, and the distortions y-, 2,2), for whieh the well-known relations hold: 0g uy 17205 oa) i ars One mnOS 0s § &: Ox ena 2) i oa aaa Pea eee a Taee ek IS, when §,,§ denote the infinitely small displacements of the points of the system. In consequence of this deformation the free energy of the material element odr will increase by the amount Ow Ow 0 ow Ow Ow o dt & &y, + ue Yy + wid Ze+ oe yz + - zs fe + eM vy) > (63) Oar, On the other hand work has been done by the external forces. When the components of the joint volume forees which act on the 1) E. Riecke, Wied, Ann. 54 p. 731. 1895, 733 material element odrt are @ Ndr, 9 Vdr, and er, and the components of the joint external tensions which act on the surface elements do of the surface that bounds the system: p.do, p,de, and p.do, the total work of the external forces, the displacements being §, 9, ¢ will amount to JA = | o (X§ + Ya + 26) dr + | (px S + Pyy + pz) do (4) Now when the temperature is constant Ovi — 0 Ame gua 5 o o ee (6) holds generally as condition of equilibrium. Hence we derive from (3), (4), and (5): ~ /fdw ; Ow Ow Ow Ou Op > ty -- Y= = Oe als es WE | Se ed nS Ly fe sae Rae Oly Ty 0z- 1 Oy J 022 du, r) . 7 » (6) = fe (X§ + Yo + 26) dr +f (pis + Pyy + p2S) do \ . — Making use of the relations (2) we get from this after partial integration : aT We b dw 2 Ow f il E — cos (Nie) + a cos (Ny) + - cos (Nz) | + 7) vy vz 0 Ou 0 + 4 be cos (Na) + a cos (Ny) + = cos (Nz) | + +6 an s (Nz) = cos (Ny) + cos (Nz) |. o do — ey 0z- | Ow ) ’ ) \o a Tea eo ee ee S iipen: ~ 02x, » Ox, > 0x2) } ° Our (7) - (|e) ep ee Te, a ie Oa Oy Oz Boe E Ou 0 ) 1D) dus 5) 0 * 0 a | \o o ot dlo ay zt - OYy ts ME | Lg A 3 Oz, J = 2 Ozy Oa Oz ee | Ow a Oy a r ost ae rae dt =foxs + Yy +Z8)dr +f + pyy + pz$) do | The quantities §, 1, and ¢ for the different points of the system being quite independent of each other, we obtain from (7) the relations; 734 yr — ae ‘0s (Nix) - a) 2 _ Ny pi) 10s (Nz | al Px 0 Ves a ( ‘ ) + ary s (i y) + yaa Ss (: 2) == () Oxp Ow Ow Dy — 0 yoy cos (Na) 4- 2d cos (Ny) + ae cos (| =I) (8) : 1Oy» Oy Oyz Oy 0 p ow f ». -- 0 \—— cos (Ne) - — cos (Ny) -- — cos (Nz)) =0 % pee |ge em (Ne) + Gr em (NE Gee ON | 0 Ow a) ow uM. Nilaeeat : ) (c =) ¢ (¢ in 0 (¢ =| ae Sees nee ei ‘ Ow Ow Oxp 68) (2) | a OY x U Se WEA ae \ . 0 5 ) ae On : Oy + Zz are dy dy dup e Y (3) ; : (e3) ‘ (e5) ee ib Sar | iy Oe ae If we now introduce the internal tensions Vz, Yy, Ze Y=, Zr, My; usual in the theory of elasticity, then hold for the components of these tensions on an element of the surface: tye ole ee ¥ v= Y,eos (Nx) -+ Yycos(Ny) + Y= eos(Nz) i .. (10) ZN = Z, cos (Nx) + 4, cos(Ny) + Zz (cos (Nz) Further in ease of equilibrium : pz + Xv=0 pik Yn ==0 2+ Zn =0. From (8), (10), and (411) Follower ow Ow Ow Le = —_ a Wf, — Sie Z: = — Pees y Q dy, 2 Oz, | F a ‘eae Me — Ly = —@ ui Lx = XxX: — ae Xy = Vx ae oo | A Oy: 2x ay | The relations (12) introduced into (9) now yield the equations ya Ok, Oy 0%: Ow Oy Oz ig Oy Oi. —— = -f es Ow Oy Oz ae 0Z, d0Z, , 024, y (13) REL re Pale: the known conditions of equilibrium for a deformed system, 735 2. If we now consider a material element which ean be arbi- trarily deformed, we can subject its state to an infinitely small variation. With respect to the deformation this. variation. will be determined by six mutually independent quantities, three dilatations, which determine the change of volume, and three, which determine the change of form. Hence speaking thermodynamieally, the Variation of state of this element (which need not necessarily be infinitely small, provided it is to be considered as homogeneously deformed) is determined besides by the temperature, by six mutually independ- ent quantities. It now follows from (3) and (12) that for a virtual isothermal variation of siaie the following equation will hold for the unity of mass 1 E r r Yr : z oa dy = — 33 (Xcae + Vy Yyt Beez + Veyst+ Zpza+Xyty) .. (14) U - If we now start from the unity of volume, and eall the free enerey of it yr, the following form holds for it dy! = — (Anez Vy Yy eee Vaya t Duta + Xyity).-, < ~ (15) (In this it should be borne in mind. that after the variation the volume will in general be no longer equal to unity). Now : ow ue) holds generally for the free energy on change of temperature, when in the expression for the external work with an infinitely small variation no -term with JZ’ occurs as factor. Hence: STMT e Aiton ie Yaya ete. coe (GU) ae diy - (Xawx-+ Yyyy+ 2222+ Veyz4+ 2x2 + Xyxy) — dT. (17) holds. for virtual variations of state, in which also the temperature can undergo a change. When we start, from unity..of volame, we have dp! = — (Kyte Vy yyjt 4222 is Yeyz+Zyz¢ Xyhy) —7dT. (18) where 7 represents. the entropy of the unity. of volume. 3. Let us now consider a system consisting of two phases, a liquid and a solid state. We assume the system to be at rest. Let it further as a whole be subjected to the hydrostatic pressure p, while arbitrary deformative forces can be active on the surface’ of the solid phase, with the exception of that part that is in contact with the liquid phase; we exclude volume forces. Consequently the same 49 Proceedings Royal Acad. Amsterdam, Vol. XVIL. 736 hydrostatic pressure will prevail everywhere in the liquid. We direct our attention to a part of the system that contains a portion of the boundary plane between the solid and the liquid phase. We assume the surface that bounds the considered part of the system, for so far as it falls inside the solid phase, to be invariable of position, whereas we can subject it to variations of form for so far as it falls inside the liquid phase. On this latter part acts then everywhere the vertically directed hydrostatic pressure p. We take the part of the solid phase that falls inside the considered part of the system, as homogeneously deformed. Let the considered part of the system contain m, unities of mass of the solid phase, m, unities of mass of the liquid phase. The direction of the normal to the boundary plane, which points from the solid towards the liquid phase, may be called J. For the part of the system in question are the free energy, the mass, and the volume resp. : y=m, p, + m, fp, | M=m, + m, \ erreprerme ime ge (1149) V = my», + mv, when v, and v, represent resp. the volume of the unity of mass of the solid and the liquid phase. We now subject this part of the system to a virtual change. For this purpose we make a small quantity of one phase pass into the other at constant temperature. This will be attended with a change of the total volume of the considered part of the system. In virtue of the suppositions made above this change of volume can only take place through the change of position of that part of the surface bounding the considered part of the system, which lies in the liquid phase. For the rest the state of the liquid phase will not change. In order to keep also the solid phase in the same state, to leave the quantities determining the deformation unchanged, it will be necessary, to make the tensions of the part of the boundary surface of the considered part of the system lying inside the solid phase undergo intinitesimal variations. Since this part of the boundary surface remains unchanged, no work will be required for this. The only quantity of external work that we have to take into account, will be that which is attended with the change of the part of the boundary surface lying inside the liquid phase. When dm, and dm, represent the changes of the quantities of the two phases, then on account of (19), we shall have: 737 dw = yw, dm, -+ w, dm, 0= dm, + dm, ee ees (0) SV =v,dm, + v,dm, th connection with the above considerations the work done by external forces amounts to: dA = — pdbV = — p(v,dm, + v,dm,) . . . . (21) If we now apply the condition of equilibrium (5), we obtain, making use of (20) and (21), Sat Peewee | Daten Pe els ve veh Jone ee (((2id) This equation represents the condition of equilibrium for the two phases in the case considered here. 4. Let us now imagine that the system consisting of the two phases undergoes a real, infinitesimal change. The condition of equilibrium (22) will then retain its validity. It is clear that it will give us then a connection between the differentials of the variables. As variables determining the state, we choose for the solid phase the dilatations and distortions wz, v/y, Zz, yz, 2x, vy, besides the tempera- ture 7, for the liquid phase the volume v and the temperature 7. We ascribe the value zero to the variables xy, 7, 22, yz, 2x, and 2, in the state from which we start (which, however, need not be without tension). In order to be able to distinguish the difference between an eventually ultimately reached final condition (which need not differ infinitely little from the initial condition in mathematical sense) and the initial condition from an actually infinitely small change of condition, we shall ee the latter by dz,, dyy, dzz, dyz, dzz, day instead of by ®xy Yys 22) Yxx Fx» Ly, Which we shall use for the final condition that is eventually to be reached. This does not alter the fact that the latter’ quantities are always treated as if they were infinitely small. Proceeding in this way we obtain by differentiation from (22): dw, dy, dup, cm Oy, dT dity yt — dzz d bs poelle or any pele sag. Urayee eg (23) Ow, Ow, i 4+ ain ty + pdv, + 0,dp = T OT te es dv, + pdv, + v,dp a . ia : eH & In this ; dx, denotes the increase of the free energy y,, when or the initial state undergoes a dilatation diz ete., just at this was the ease in (3) and the following formulae. Now according to the theory of elasticity we have: 49%* 738 1 (y= ——— (Wa saeiy se Wa) os os 8 ¢ (24) Syl while further the well known relations: Ow, Ow, be aT tia eae ne hold for the liquid phase. On introduction of (12), (24), and (25) we get from (23). a ae SEN ats | (2],—4,) dT = ip( a >) ar [(Xa—p) dv ++ | 0. 1 Q, (26) Se (Yy —p) dyy IF (2. —p) dzz + Y.dy: =e Zz x aI X dey] We can now put: r Ll Uh = ’ (27) T -In this we ean call the “heat of melting” 7, by which that quantity of heat is to be understood which must be added to convert the unity of mass from the solid to the liquid phase, without the con- dition of the two phases changing for the rest. We then get: abe iy ibe ck Ths aT = —|-— —— |} dp + —— [(.— >) dz, --(%—p) aay TIO (28) + (4:—p) dzz + VYzdy. + 4,dzz + X,da,| When the only deformative force is the hydrostatic pressure, we get the known formula of Tuomson and Crausius, since then the following equations generally hold: Xx — p=0 iy —p=0 Z.—p=0 | N2 Sy 29 Y.=0 Z,—=0 x Oe ee) Tefal 1 dT = — (= ~ da ere (3X0) 7 \Os 01 If on the other hand dp = 0, we get: dT = —— [(X.—p) dre + (Yy—p) dy + (Zp) dee + | Pre Or (31) + Y.dy. + Z,dz, + X,dxy| | Since the form between square brackets, provided with the negative sign, represents the work performed in the deformative forces, with the exception of the pressure p, a deformation will bring about a lowering of the freezing point, when this work is positive. 5. We shall now assume that the initial state (for which we put Vay Yyy Zz Yzs 22, ty. EQual to zero) is to be considered as without 739 tension. In this case (81) will also be applicable; we may then, however, replace 7 and e, by 7, and o9,,, in which 7, denotes the heat of melting, and o0,, the density of the solid phase in the tension- less state; then we have Tt dT = —— [(Xs—p) dts + (Yy—p) dyy + (Z—p) de. +| PP 10 ro + Y.dyz + Zdzz + X,day] If we disregard quantities of the second order, which we are allowed to do when we consider the dilatations and distortions as infinitely small, we can integrate (32), placing 7, r,, and @,, outside the integral sign. We then get for the lowering of the freezing point in the state determined by @z, Wy. Zz, Yes Za Vy, vy T PQ r0 Uz «ae f (eo ie ae eae AL = 0 (33) Y.dyz =F Z,dzz + X,da| The heat of melting in the state determined by 2,, yy, 2:. Ys, Zr, dy will differ- from that in the tensionless state by an amount that is of the same order as the dilatations and distortions themselves. For an infinitely small change follows for the change of the free energy from (14): 1 dy = — — (Xzdxx + Yydyy + Z.dzz + Y.dyz + Zydzz + X,day) o 7 : Hence the difference in free energy between the deformative and the tensionless state amounts to: HAS exo IES Do all sh = =! — [Xzdxy 4+ Yydyy + Zdzz + V.dyz + Zrdzz + X,da,]. 0 ye, 0 For the difference in entropy between these states follows then from (16) y Te ceo Pick 0 28 Ay = at [Xzdaz + Vydy, + Z.dzz + Yzdy: + Zrdzez + X,de,]. (sae From (27) follows then for the difference in heat of melting: ditty Cis Eno 6) fll Ar = — T— {= [Xida,z-++ VY dy,4 Zdzz+ Y.dyz+ Zyde,+ Xydx,| (34) or Q k : 0 740 This will also apply to the case that the initial state is not tensionless; only (384) does not represent then the difference in melting heat between the state v,...yz... and the tensionless state, but the difference between the state a,...y:z... and the initial state, which is not tensionless in this case. 6. Let us now suppose that forees act on the surface of the solid phase which are exerted by solid bodies which rest on the solid phase, and in consequence of the presence of which the sur- face of the phase is not in contact with the liquid phase. We can then imagine that a small part of the solid phase that is in contact with the solid bodies which exert forces, is converted to the liquid state, without the solid bodies changing their places. For this case we can again draw up the condition of equilibrium. We take the boundary plane of the solid phase as X Y-plane, and suppose that the Z-axis is the normal to this plane which is directed from the solid to the liquid phase. For the total free energy, the mass, and the volume the following relations hold in this case: Y—m, yp, +m, wp, M=m, +m, Mier. tc. « (23); V=m,v, + m, », Let now an infinitely small quantity of the solid phase be con- verted to the liquid phase, then: JE = mdw, + w,dm, + mdi, + ,dm, . . . (36) During the conversion the volumes v, and v, will have to change, as the total volume remains constant, as we supposed. The considered change being a virtual change, we may assume that as far as the solid phase is concerned, this change is brought about by variation of z- alone. Then we get: Ow, OU —— 20220 3 os 9 5) Further : ge Ou, ; ae Cae carrag Nes SCCM IEON IO 5 1 ici « ((ic\) By introduction of (87) and (88) into (86) we get: he Op, dw, OF =m, au diz 3M; Fatt dv, + dm, + w,dm, . . (39) Just as before (see above under 3) the tensions at the surface that bounds tne considered part of the system will have to vary now too. We supposed, however, that this surface does not change its 741 position, so that no work will be done by external forces. The condition of equilibrium is now: Oui Qe eters tae e.g | (A) We must use here the double sign seeing that there is only a conversion possible in one direction. The sign = will hold for the boundary equilibrium, i.e. the equilibrium at which a transition from the solid to the liquid phase will just be possible. Now the equations (35) give further ve dm, + dm, = 0 : 41 m, dv, + v,dm, + m,dv, + v,dm, = 0 ( y in addition we have 1 OSS = Uae on 0 ro (IBF Qe; An : If we limit ourselves to the boundary equilibrium we get from (12), (85). (89), (40), (41) and (42) making use of the equation Z, — p= 0*. i faliQet os? Soi Wit Pepe tpl, «= = |S 5 lee) Hence we get the same relation as condition of equilibrium between solid and liquid phase as we had for the case that the two phases were in contact. Therefore the conclusions about the lowering of the freezing point will also be the same. Of course as pressure on the solid phase must then be taken into account the hydrostatic pressure, to which must be added that which is exerted by the solid bodies which are on the solid phase. 7. We shall now consider more closely the amount of the lowering of the freezing point, in which we shall make use of the expres- sion (32). To caleulate this amount it is necessary to know the relation between the quantities x... y:...andthe tensions X,... Y.... In the most general case, the quantities 2... y:... being considered as infinitely small quantities, we shall be allowed to assume a linear relation of the form: Xx S Oy, @e + Oy gYy F Oy ,%z FO Yo Ah Gyytz + yy ity : me ae a : : (45) Ve yy + Oy yy + Gy,22 + Oy Ye FOyee Qo hy in which Pia Ge fe Ss ee (AG) will generally hold, because the tensions X,... ¥.... according to (8) may be considered as the partial differential quotients of the free 742 energy per unity of volume taken with the negative sign. Further the coeflicients «@ must be considered as functions of the temperature. To this most general case, in which the number of coetficients amounts io 21, answers a crystal of the lowest symmetry. This leads, of course, to very intricate calculations. ‘ We prefer, therefore, to consider the simplest case, viz. an isotropous body. For this holds, if we use the prevalent notation ’). — ale lee is BX (vx a Yy + z 2) (47) Seas ae ity, : from which equations can be derived ; sear six z gr YA ot Se eke ae Sa C2 + y »|| Y,=— —YV, K In this the relation : 136; a es “7420 ae exists between the coefticients AK and @ on one side and the elasticity coefficient / on the other side. - Let us now consider a circular cylinder, the axis of which coin- cides with the Z-axis. Let one end be rigidly fastened, while forees resp. couples act on the other. Let the length in the direction of the Z-axis be /, and the radius of the cylinder &. The conditions of this problem may be satisfied by putting oo Xp == xy == () Y,—=09 merely seni, 11,1 (240)! If P,, Py, P; ave the components of the force, Qe, Q,, Q, the com- ponents of the couple acting on the end plane, then for the other tensions hold the expressions : jen Mer Walsr aie hayes AP oe ease eave Tips = a | © 1 2 Sere han, ner wee hie ae aa Sa = 3s sy * PP. 86) (R2—2x)—y? - P, 1446 5 Px (8 +89) ( eee ay EM aR* | 2k 1436 Ri1430° age 2Q..%@ b, 1446 P, (8+ 84) ( (R?—y* ice =i “" @R! 2R1+30 oa peat 538 Further : _ 3) Cf. among others G, Kircurorr, Vorlesungen tiber Mechanik, 143 ip 0 ape ea ez - 126 E1260 See Ie re (52) 21430 E1+26 Fico eile Ys We shall now discuss some special cases. 1. Compression resp. extension. In this only P:=£0 is put, from which follows : La Pe Ne SS) aR? (in this the liquid pressure p is neglected). Then the lowering of the freezing point is it AT =— [ete 7,0 oso Making use of (52) and carrying out the integration, we get : tee si OF 7.0, 2h AT = — which formula is in perfect concordance with Rinckw’s. *) We apply this to ice, which we shall treat as an isotropous substance. RieckE assumes 0,7 ke. for the drawing-solidity of ice per mm’, and calculates with this O°.017 for AT. As for most substances the _pressing-solidity is considerably greater than the drawing-solidity, this diminution can probably be made larger in the case of compression, so that it can be measured comparatively easily and with suitable apparatus even the just mentioned lowering of the freezing point would also be liable to be measured. 2. Sagging. In this case we only assume that P,==0. When we consider a point for which «= Rk, y = 0, then it follows from the formulae that : Py 1420 i) =) Ve é ah? 1+-30 The lowering of the freezing point of the considered point is: 1) E. Rirexeg, loc. cit. p. 7386 form. (20), 744 Making use of (52) we get after integration : T +30 Y# TRo, 15208 Sa (i In order to obtain a limiting value for Y., we make use of the results of an investigation by Hess’) on. the sagging of ice erystals. He charged a crystal 2.9 em long, 1.0 em broad, and 1,2 em thick at its end with a weight of 5000 grams, without rupture taking place. Let us assume by approximation that an ice cylinder of a diameter of 1 em could bear the same load. We can then derive a limiting value of VY. from (54). If we introduce this into (52), we find finally, assuming that 0 = 3, which is about correct for a great many substances, — 1.19 x 10-4 — degree for AZ, which quantity is probably not lable to measure- ment. That this quantity is so small, is the consequence of the sinall value of the maximum tangential tensions which ice can bear. We considered the point on the circumference for which «= R, y=0. If on the other hand we take the point for which w= 0, y= Rk, we get the formulae 4l Yin = ak? Py Mos Wa =O, If as before, we again assume that an ice cylinder of a diameter of 1 em. can bear a load of 5000 grams at its end, we find for Z, a value which appears to be greater than the value assumed ‘by Riecke. If we calculate the lowering of the freezing point by means , of this, we find 4 7’—= — 0°.081, an amount that can be easily measured. We see at the same time that the lowering of the freezing point has different values at different points of the surface; a state of equilibrium is therefore impossible. The rod of ice will diminish on the upper surface and on the lower surface, and that much more quickly than on the sides, which will also diminish a little. Further this diminution will increase towards the end where the rod is loaded. 3. Torsion. In this case only Q-—|—0. From the formulae (51) follows then for the point 2=0, y= & 2Q. Viet) x, = — 3 aR Taking the small amount of the tangential tensions which ice can 1) H. Hess Ann. d. Phys. 8 p. 405, 1902, 745 bear into consideration, the lowering of the freezing point will again become very small in this case. Since the tangential tension all along the cylinder surface has the same value, equilibrium with the sur- rounding liquid will now be possible. Haarlem, May 1914 Physical Laboratory of “Tryier’s Stichting’. Physics. — “The effect of magnetisation of the electrodes on the electromotive force.’ By Dr, G. J. Er1as. (Communicated by Prof. H. A. Lorentz). (Communicated in the meeting of June 27, 1914). 1. The question in how far magnetisation of the electrodes is of influence on the electromotive force in a circuit in which there are electrolytes, has already often been examined, without it being possible to derive a definite answer to this question from the results of these researches. Thus Gross') found no definite direction of the current in concentrated solutions of ferro salts, while in concentrated solutions of ferri salts the magnetized electrode (both electrodes consisted of iron) became the anode. ANDREWS”) arrived at the same result working with strong acids as electrolytes. NicHois and FRANKLIN *) obtained results which were in concordance with those of Gross and ANbDREWs, in case a pole of a magnetized iron rod came in contact with the electrolyte, which consisted of a solution of chromic acid. In this case the electromotive force greatly increased with the magnetisation, and reached the value of about 68 millivolts in a field of 20000 Gauss. If on the other hand the neutral region of the magnetized rod was in contact with the electrolyte, the sense of the electromotive force was opposite. Row1nanp and Bru‘) found that the magnetized electrode became cathode when acids that attacked the iron, were used as electrolytes. Squirr*), who took nitric acid as electrolyte, came to the same result. The maximum electromotive force amounted to 36 millivolts, in a field of 10000 1) Tu. Gross. Sitz. Ber. d. kais. Ak. d. Wiss. 92. Dec. 1885. 2) ANDREWS. Proc. Roy. Soc. 42 p. 459, 1887; 44 p. 152, 1888. 8) E. L. Nicpots and W. 8. Franxur, Am. Journ. of Science 31 p. 272. 1886; 34 p. 419, 1887; 35 p. 290, 1888. 4) H. A. Rownanp and L. Bextu. Am, Journ. of Science. 86 p. 39, 1888. 5) G. O. Squmer. Am. Journ. of Science. 45 p. 443, 1893, 746 Gauss; on further strengthening of the field this amount did not change. Also Hurmucrsct *) found the electromotive force in the same -sense, when diluted acetic acid or oxalic acid was used as electro- lyte. In a field of 7300 Gauss the electromotive force amounted to 14 millivolts. Finally Bucanrer*) has occupied himself with this question. His result is in so far entirely negative that he finds no electromotive force which would reach the value of 10~-° Volts for neutral solutions of ferro salts in the case of magnetisation of the electrode in a field of 1200 Gauss. He further pronounces the opinion that the electromotive forces found by Rownanp are caused by mechanical disturbances of the equilibrium (‘‘Erschiitterungen’’), which would be the consequence of the origin of the magnetic field. Then Bucuerrr compares Hurmucescu’s results with what has been theoreti- cally derived by Dunem*), and coneludes that no concordance exists between them. Dune arrives at the formula: /ERY 7 i ad .% (1) in which / represents the magnetisation of the electrode, 2 the electro- chemical equivalent of the iron, x the susceptibility, and d@ the density, the electromotive force / being taken positive, when the magnetized electrode is cathode. When we eliminate H;, /, and # by the aid of the relations: B= H;+ 421 33 he Jal Th03 5156 we get instead of (1) R ioe Al i S| (2 t= Gada hi co, It has appeared to me that in consequence of an inaccurate expres- sion for the energy of a magnetic field, this value of / is about fe times too small, so that we may write by approximation because has a large value: f IB oh: P=. which expression, however, only holds when the electrolyte is a neutral iron solution. When the experiment is arranged in such a way that 5 may be put equal to the external intensity of the field H7, we see from (3) 1) Hurmucescu. Eclair. Electr. Nr. 6 and 7, 1895. 2) A. H. Bucnerer. Wied. Ann. 58 p. 564, 1896 ; 59 p. 735, 1896 ; 61 p. 807, 1897. 5) P. Duuem. Ann. de la Fac. des Sciences de Toulouse, 1888—89. Wied. Ann, Beibl. 13 p. 101, 1889. ; 747 that the electromotive force would have to increase with the square of the intensity of the field. On introduction of the values for iron 7 == 29 So INS Gees d=7.9 we get for H = 10000 Gauss ESOS = 2 Wot In Bucnerer’s experiment the intensity of the field was 1200, if the induction 4 bad had the same value, the electromotive force would have been 2.4 x 10—* Volts. As this amount is much less than the smallest value whieh Bocnerer could measure (10~° Volts), its negative result cannet be considered in conflict with the theoretical resuit. The results of the other investigators, who worked with acids as electrolytes, ave not at all in agreement with formula (3), in fact they could hardly be so, as (8) rests on the supposition of a neutral iron solution. As the case that the electroiyte is a dilute solution of the metal of electrodes, which is assumed to be equal for the two electrodes, is the only one that is liable to exact thermodynamic treatment, | have calculated the value of the potential difference for this case in what follows. Further I have communicated the results of experiments made on this subject. 2. Let us now consider‘) an arbitrary system in which also electric currents and magnetic fields can be present. As variables in this system we choose the temperature 7, further a number of geometrical quantities «,,«@,..., and finally the magnetic induction %; when the last quantity is known everywhere, then, besides the magnetic field. the electrical current is also determined everywhere. The external forces exerted by the system, are the components of force A,, A,... corresponding to the geometrical quantities, besides the external electromotive forces &,. In order to be justified in leaving JouLr’s heat out of consideration we shall assume that the conductors, for so far as a current passes through them, possess no resistance. We shall further assume that the system loses no energy by electro- motive radiation and we exclude currents of displacement. If the .system undergoes an infinitely small virtual variation, we first inquire into the work performed by the system on its surround- ings. If .the variations of the geometrical quantifies are d« the corresponding work can be expressed by ny Olersa op 1) The train of reasoning on which the general method of treatment followed here is based, was suggested to me by Prof. Dr. H. A. Lorenvz, for which | will express here my heartfelt thanks. 748 a A da, Apdo Dom tiete G Oe Further the external electromotive forces will perform work per unity of time equal to dW, Ca ——— = | (©, €) .dr dt in which © denotes the electrical current. The work done by the system amounts, therefore, per unity of time to: dW, =—{(€.§), dr. For this we may write: dW, — fe + €,, @) dr +{G €) dr, in which € denotes the electrical force. Now in the conductors ¢ — o(€ +- &,). From the supposition that in the conductors 6 will be infinitely large, follows that here € + €, must be = 0, whereas outside the x : F dw* conductors © =0. Hence the first term in the expression for disappears. When we make use of the expression : $ =ccurl f°) we get after partial integration dW, r= fe curl ©). dr4- oft. ely. de. The second term disappears on account of the supposition that no energy leaves the system through radiation. We finally get then by the aid of the relation: Pagers ee Ot dW. 0d = — Jagp——= lo @ at, wah re a Ot ) a If the variation of 8 in the time dt is JB, we get: BW, = — {(9, 4%). dr, wt. ae The total work performed by the system now amounts to the sum of (4) and (5), 1) Here Lorentz's system of unities is used. y 749 SW = Ada, + A,da,4+ .. —[o 1 GR5))in Che oF oo (3) If we now introduce the free energy of the system, the following well known relation holds for it w= E—-T.H when E represents the internal energy, H the entropy. For au infinitely small variaton we get from this: JW = dE—T . dSH—H. dT. Further T.dH= dQ=dE + dW, in which dQ is the quantity of heat added to the system. Making use of (6) we get from this: dW — Ada, —A,da,.... + [ (9,08) de— a Let in a certain initial state, in which the variables a,,a,.. have the values «,,, @,,-- energy ¥,. In the magnetic state, in which & will have a certain value everywhere, and the temperature and another quantity, e.g. the external pressure have remained constant, the geometrical variables will assume other values, which we shall denote by a,, @, .. We can now make this transition take place in two steps. We first give the geometrical variables the values «,,a,, 8 remaining = 0; hence the free energy will increase by an amount A, W% Further, while a,,@,... remains unchanged, we can bring the magnetic induction B from zero to the final value; then the free energy will inerease by Ay. In this way the final state is reached, in which the free energy will be: ; v= UW+ A w+ Aut . . . . ’ . (8) Then according to (7) the following equation will hold: by t= f [19 AB) de 5 3 SG oe ee (M)] 3. Let us now return to the above discussed case, in which two electrodes of the same metal are placed in the dilute solution of a salt of this metal. The concentration of the solution can be different at different places. We think the circuit closed by means of a wire connecting the two electrodes. Let one electrode be in a magnetic field, in consequence of which it is magnetized. We think the magnetic field excited by an electromagnet, the leads of which possess no resistance, .. © being = 0, the system have the free 750: In the second eireuit in which the electrolyte is found, we think inserted an electromotive force -— /, which is in equilibrium with the electromotive force /’ existing eventually in consequence of the presence of the magnetic field; we shall assume that sense of circuit which is directed inside the electrolyte towards the magnetised electrode, to be positive. We shall assume also the resistance of this second circuit to be zero. We shall subject this whole system to an infinitesimal variation. Let this variation consist’ in the passage of an infinitely small quantity of electricity e through the second circuit, and that in that sense that is directed inside the electrolyte towards the magnetized electrode. We shall moreover ‘assume that in this variation the magnetic induction remains unchanged. in all the points of the’ system. We shall further assume that the surface that bounds the second circuit, does not change its position. In the first place we shall consider the work of the external forces. These forces consist of: 1. the electromotive forces in the first cireuit (that of the electromagnet); 2. the electromotive force — FF in the second circuit; 3. the external pressure p. As we have supposed % to remain constant in all the points of the system, the [dwt Which represents the flux of B through the first cireuit will not change either. It follows from this that no electromotive force is. active in this circuit, so that the work of this force is zero, The, electromotive foree —# in the second cirenit will perform. work. equal to —.e, when a quantity of electricity e passes. The whole volume of the second circuit being supposed constant, the work of the external pressure will amount to zero. value of In all the work performed by the system is therefore OW = Ee. ss Let us then consider the change of the free energy of the system. For this purpose we shall examine what are the consequences of the passage of the quantity of electricity e through the electrolyte in the direction of the non-magnetized electrode towards the mag- netized one. We shall eall the former the anode, the latter the cathode. 7 If w and v represent the absolute values of the velocities of cation. 751 and anion in the solution, then n= is the quantity which v Hirrorr has called “Ueberfiihrungszahl” of the cation. Of a current i the part n.t is carried by the cation, the part (1—n).i by the anion. So the number of gram equivalents of the cation in the unity of volume will increase per unity of time by : L is . ee ec) = aay as div.i—0 is; represents the charge of a univalent gram ion. In the same way the number of gram equivalents of the anion will increase by the same amount per unity of time, so that the solution will remain neutral. If / is the valency of the molecule, and m the molecular weight, the mass of the salt will increase per unity of time by an amount: GO 5, = (i, 7). If the quantity of electricity e, passes through the unity of surface, and if i, represents the unity vector in the direction t, the increment is: m.eé dy = —— (I,, yn) - Sh cies, ives bas) Migs (GL) k.g In the volume elements which lie on the surface, the increment of the mass of salt will be per unity of surface : Re eo gee tk ke AN when NV is the direction of the normal directed inward. The total quantity of salt inside the solution will now increase by an amount: fo + fara] fo Cooma + fet. nda] =o S ease) 8 7 When we apply Gauss’s theorem and make use of the equation divi = 0. The quantity of salt, therefore, does not change. The only change consists in this that the concentration in the different volume elements is modified, and that a quantity of elec- tricity e dissolved at the anode, has deposited at the cathode. We shall examine what change the total free energy of the system has undergone in consequence of what has taken place in the electrolyte. Above we found the expression (8) for the free energy, (9) holding for the “magnetic”? part of it. We further chose the variation so that the magnetic induction did not undergo any change. In the first place we must now take into account that at 50 Proceedings Royal Acad Amsterdam. Vol. XVII. (52 the anode a certain volume of iron has been replaced by the solution, whereas at the eathode the solution has been replaced by iron. The Gy . . volume of iron —.—.— will correspond to the quantity of elee- ( Fy 3 tricity e, when a denotes the atomic weight, 4, the valeney of the atom, « the density of the iron. If we assume that at the anode no magnetic field is present, the substitution of iron solution for iron will not bring about any modification in the magnetic part of the free energy. At the cathode, however, this substitution will give rise to a change in the expression (9), which, when «, represents the permeability of the iron solution, uw that of the iron, amounts to: b b ! a.e ES 183 Jd (AyweY)= a he ee ea Bi ae cee . . (13) 0 when B means the absolute value of 3 and B this value at the - eathode. When we speak of “at the cathode” or “at the anode”, we mean by this that we must take the value of the considered quantity at a plane that is at a very small distance from the cathode resp. anode, this to evade the difficulties which the phe- nomena taking place in the boundary layer might cause; we shall examine this question more closely further on. On account of the smallness of the considered volume we may assume that the value of £B is the same everywhere inside the volume. If we put u, = 1+ 4x,, in which «,, the susceptibility per unity of volume, is to be considered as a small quantity, we get about : B > x a.é B _ B d(AyW)=— |= (1 dare, — [58 aes 0 when x 0 represents the susceptibility at the cathode. If we assume 1 u to be very great for iron, so that — is to be neglected with respect Uu to unity, and if we replace B by H, the absolute value of the inten- sity of the tield in air at the cathode, we get: 6 (4uY)=—s7— — (1—Az'x,) (2 1 eee Instead of (13), using the relation : 1 B(1——)=4e4, u in which / is the absolute value of the magnetisation we may further write : 753 B Age ath ee = J, (Au ¥)= - ———.]fCU—T,)dB. . . . . (16) Dak neon 0 We must further take the changes of concentration in the different elements of the electrolyte into account. If we introduce the concen- tration ¢ as the number of grammolecules of the dissolved substance per unity of mass of the solution, this is modified by the passage of the quantity of electricity e. If the density of the electrolyte is @, then the variation of density, when the volume remains unchanged, will amount to: QOS U0 6 6 56 0 neyo A(hM)) in which dy is given by (11) and (12). By means of this we find easily for the change of concentration : 1—me Jc = 0p Set i ee ee oe 8, (LS) mm. 0) Now for dilute solutions very nearly : YR Ole Cee Wien ail gts reassess (LO) holds, in which x is the so-called absolute specific susceptibility per unity of volume; which is considered as independent of @*). We get from this by the aid of (17) and (18): Ota ODr. This then gives, as x, must be considered as small : B | f) dB = — 2a By dv. 0 When we multiply this expression by the volume element dr, theti introduce the value of dy from (11) and (12), and integrate witli respect to the whole volume of the solution, we get: f 2ay.m ‘ PITTA TIN {ise J, (AuW) = — - TA (Be liu gn) = | [ae och iy t do. V Ss If we assume n to be constant, which is permissible, on account of the relative smallness of this term, if we suppose further that at the anode B=O, at the cathode in air B=—H, we get: 2TmM.y.en — J, (Au ¥)= Taree! Alo Hee oe (20) 1) Relation (19) holds of course only as long as the specific magnetic properties are independent of the concentration. 50" ~I ox rss as for the cathode holds : — forty dome. 4. We must further consider the change of the “non-magnetic” part of the free energy; as we saw above the values must be assigned to the variables which they will have in the magnetic field. The only change which is involved in this, is the change of con- centration of the solution. If the free energy of the unity of mass of this is w, then that of the volume of solution @ of density @ is d¥Y, =0.o0.e, when ¥*, is the free energy of the solution. When we make use of (17) and (18), and further of the relation : ow === — oe eee (te ae P (21) which follows from (7), the variation of this will amount to: : 7 Ow 1—me dd, = dv ly + P + =| BD 5 (2:2) Q 0c m For the free energy of the unity of mass of the solution we shall use the well-known equation : w=w, tact per+... .+ RVelogc,. . . . (28) in which yw, means the free energy for c= 0. In this we must give to the variables c and v the values which they possess in the magnetic field in the state of equilibrium. On the other hand we can, however, also imagine that different concentrations can permanently exist in the different volume elements of the solution, in such a way that no change can be brought about in this by the magnetic field. Thus we shall obtain the potential difference between the electrodes on arbitrary distribution of the concentration. The supposition made is a fiction; the more so as we have assumed also the resistance equal to zero; in general the velocity of diffusion will namely increase as the resistance decreases, with which permanent concentration differences are in contradiction. This supposition, however, must always be made for such problems, in order to be able to apply the laws of the reversible processes ; hence we also make them here. With the aid of (22) we get from (21) E p RI a dd ¥, = dv | w, +— + — (1 + loge) — RTc + — | .w. 0 m m When we use here the expressions (11) and (12), and integrate 755 over the whole volume of the solution, we get: 7 m : RI Cie = fe . (i, ’ vn) : EB — =. == (1 ai log oj hie ar =| . at m m kg . m jo. aya Fa a + = | é.in,.2.| wp, +— + —(1 + loge) — RTc-+ —1|.do. hg 0 m m & a When we take n again as constant, we get: mM. e@ 1 1 Iiedhe a — =.—1%, —wW,, t$pl— — — | + —log—— RT (c,— of k Eas OE, Qs, ue C5 = when we denote the quantities referring to the anode by the index 1, those referring to the cathode by the index 2. We may further write: bos = Won + (2) or, because OW, jiiwase 1 1 Woo =U. + P{ ———}- Q, 02 There remains finally mn 1 : US ret Rt | To? =e —0)| | joy cue (24) e ‘§ m Cy From the well known theorem for the free energy : dv 4+ 6¢w—0 we get with the aid of (10), (16), (20), and (24): B \ pee. PO ot) | ji — (1—T,) dB — - oaks d kg 0 Ww a. 1 C -— . RT .| —log — — (¢,—e,) kg E Os | in which 4 is the electrochemical equivalent of iron. Hence the potential difference consists of two parts, viz. oue part (the first two terms), which depends on ‘the magnetic field, and a second part, which depends on the concentrations at the electrodes. The second term of the first part will increase proportional to the second power of the external intensity of the field, the first term, too, in case of small intensities of the field, where we may replace (16) by (15); at great intensities of the field, however, / will reach 756 the value of saturation, so that this term — which far exceeds the other “magnetie’? term — will increase only about linearly with the external intensity of the field. The sense of the electromotive force determined by the first term is directed inside the solution from the non-magnetized towards the magnetized electrode. The second part of the expression becomes equal to zero for c, =e, ; with neglect of the contraction which the solution undergoes on concentration, this expression agrees with the potential difference - calculated by Hertmno1tz'), between two electrodes which are in solutions of different concentrations. If we assume c,—c,, and neglect the terms which depend on the suseeptibility of the solution, the following form holds for not foo great intensities of the field (in which « is still to be considered as very great) i phe (26) 2d If we use electromagnetic unities, this becomes: SF aah 7 Smad’ which agrees with (38). In order to simplify our considerations we have disregarded the transition layers between iron and electrolyte; in them phenomena will namely take place which cannot be examined in detail. It now remains to prove that in the caleulation of the free energy the in- fluence of these transition layers may be neglected. For this purpose it is necessary to assume that the thickness of the transition layers is of the order of magnitude 7, when / represents so small a quantity that we may assume that inside the thickness / the liquid is in equilibrium with the electrode. We shall further assume the limits of these transition layers on one side inside the iron, on the other side inside the solution. Let the quantity of electricity e, which we have passed through the solution, be of the order of magnitude §; the same thing will be the case with the thickness of the iron layer, which has dissolved at the anode, deposited at the cathode. This iron layer may be infinitely thin with respect to the thickness of the transition layer, and entirely fall within it- We have already taken into account the change of the “magnetic part” of the freé energy, which is the consequence of the displacement of the iron and the dissolved substance. Now we have still to take into account the change of the state of the transition layers, which 1) H. Hetmunoirz. Wied. Ann. 3 p. 201, 1878, Miel TOM is the consequence of the conveyance of iron and dissolved substance. The quantity of dissolved substance supplied resp. extracted in the transition layers is of the order £, just as the quantity of electricity e. As the volume of the transition layers is of the order of magnitude /, the change of state inside these layer will be of the order 7 Now there was equilibrium in the transition layers before the variation; hence a variation of the free energy per unity of mass 2 of the order of magnitude (=) will correspond to a change of state § ; ae of the order 5 (the external work is zero). The variation of the total free energy of the transition layers will therefore be of the Yeo s am order qe Thence we see that this variation may be neglected with respect to the other variations of the free energy, which are of the order §. 5. We shall now still examine what will be the equilibrium concentration in the magnetic field, i. e. that concentration which will finally exist after the diffusion has been active between the different volume elements. For this purpose we consider an infini- tesimal variation of the total free energy YW of the system. We choose this so that all the parts of the system, with the exception of the solution, remain unvaried ; moreover we leave the magnetic induction 3 unvaried. We can, therefore, restrict ourselves to the variation of ¥Y, the free energy of the solution in the magnetic state. For this free energy holds the expression according to (8) and (9): Ue = || le w+ | 13) 25 |r, when we use the expression (23) for w. As the susceptibility may be considered as small, we may put Ore ail € a Jew 4G O—daay) [ae co 5 of 6 (8H) We shall now let the variation consist in a change of the con- centration, accompanied with a change of the specifie volume ; in this we leave the volume of every volume element unvaried, so that the external work is equal to zero. We get the relation between concentration variation and volume variation by eliminating dg from (17) and (18), by which we get: 6c = 10 fo a ee eed mo Now we get from (27), keeping in view that 6 remains unchanged: Je, = fle .dy+w . do —20 B* dx, | dr. Making use of (19), (21), and (28) we get from this, when we apply the thesis of the free energy : OI; 1—mc 0 [ [e+ e+ Pane y|.0e.dr =o Sie de @ m Further exists the relation : fe seh SUE the total mass, from which follows : [a Ton 0: — 0 s ue w+ Tactics ~ —2nxB* .y¥ = const. . .’ ee) c me The formula follows from i two relations as condition of equilibrium for the solution in the magnetic field. For this we may put, just as above in the expressions (22) P RI a a “ hy + — + —— (1 + logo) — RT¢ + — — 2B. = const, m m ry from whieh follows, because at the anode B =0, at the cathode B=A, just as above for (24): RT ; — log? — RT (c,—c,) = 2ay. 7). . « + G0) Mm Cy K 5), we get for the potential differ- ence in the state of equilibrium, at which also the solution is in equilibrium When we introduce this into (2 B Ae = (I=1) dB.) 2 ne € 0 6. In order to test the obtained result by observation, IT madea number of experiments, in the first place with iron. The iron used for this was electrolytic iron, which Prof. Franz Fiscumr at 1) With ee of the contraction which the solution undergoes, this result is in accordance with the result derived by Vorar (Gétt, Nachr. Math. phys. KI, 1910 p. 545), 759 Charlottenburg kindly procured me. The magnetized electrode con- sisted of a circular plate, which was of the same size as the pole plane of the electromagnet, and was rigidly fastened to it, a glass plate serving as isolation. The other electrode was outside the field. The concentration of the used solution of ferrosulphate was generally 5°/,. The results obtained with this may be summarized as follows. On excitation of the magnetic field I always obtained a current in the sense as the theory requires. The extent of the obtained effect differed, however, greatly from the theoretical value ; the measured potential differences were, namely, between the strengths of the field O and about 20.000 Gauss 10 or 20 times as great as the for- mula would require. At first the course was about proportional to the second power of the strength of the field, the effect reaching a value of 6.38 « 10-4 Volts at about 16000 Gauss, which did not change on further strengthening of the field. If the used solutions were neutral, the effect remained pretty well constant after excita- tion of the field. On the other hand for acid solutions (which con- tained only very little free acid) a diminution and a reversal of the effect soon took place, till a value was reached, about ten times as great as the first effect after the excitation of the field. It is remark- able that Rowrnanp and Beni also always found such a reversal, whereas Squimr found that above a certain strength of field the effect no longer increased, which is in agreement with what I observed. Another phenomenon that I regularly observed was the increase of the resistance of the solution as it was longer in the tube. At last this resistance can reach a value of some hundreds of thousands of ohms. Besides I made experiments with nickel. The electrodes were of so-called “Rein nickel” from the firm Kanrsaum; as electrolyte generally a 5°/, solution of nickel sulphate was used. No effect, however, was observed with certainty, so long as the solution was neutral. Probably there was an effect in the sense required by the theory, but about five times smaller than for iron, which would therefore harmonize better with the theory. It was, however, impos- sible to obtain certainty in this respect, as the resistance of the solution soon became exceedingly great, even up to more than 10° 2; moreover the zero position was very variable, much more so than was the case for iron, It is peculiar that the large resistance only consisted for very small electromotive forces; if on the other hand the latter was a few volts, the resistance became only a few thousands of ohms. For solutions of nickel sulphate greatly acidified with sulphurie acid no other effect was found than in neutral solutions ; there was no question of a reversal here, 760 Physics. — “Further experiments with liquid helium M. Prelimi- nary determination of the specific heat and of the thermal conductivity of mercury at temperatures obtainable with liquid helium, besides some measurements of thermoelectric forces and resistances for the purpose of these investigations’. By H. KamernincH Onnes and G. Houst. Communication N°. 142¢ from the Physical Laboratory at Leiden. (Communicated in the meeting of June 27, 1914). § 1. /ntroduction. Measurements of the specific heat and of the thermal conductivity of mercury were considered to be of special importance with a view to the discontinuity, found at 4°.19 K. in the galvanic resistance of this metal. The preliminary results have been already mentioned in Comm. N°. 133, for the measurements were carried out as early as June 1912. We wished to repeat the experi- ments, which we considered only as a first reconnoitring in this region, because our opinion was, that, by some improvements in the experiments, the accuracy of the results could be considerably increased. Special circumstances frustrated this, and now, as there seems to be no prospect of a repetition for the present, we com- municate the details of our investigation. § 2. Thermoelectric forces. The first difficulty in these deter- minations was the choice of a suitable thermometer. The measure- ments already performed about the resistance of platinum, gold and mercury did not give much hope, that there would be among the metals a suitable material for resistance thermometers. We have therefore investigated a series of thermoelements. The gold-silver couple, a suitable thermometer at hydrogen temperatures *), showed down to the higher helium temperatures a fairly large thermoelectric power, at the lower helium temperatures, however, the thermoelectric power diminishes rapidly, so that this couple did not satisfy the requirements. Moreover, this couple was not at all free from disturbing electromotive forces, which appeared at places of great fall of tem- perature in the cryostat. Nearly all other elements were subject to the same fault. But apart from this, none of the combinations was suitable. Notwithstanding, we communicate the results of our determinations, because they show clearly that according to the theoretical investi- gations of Nernst and Kersom*), the thermoelectric power of all 1) Compare H. Kameruingu Onnes and J. Cray, Comm, N°. 1070. 2) W. Nernst, Theor. Chem. 7e Aufl. 1913 p. 753. Berl. Sitz. Ber. 11 Dez. 1913 p. 972. W. H. Kessom, Leiden. Gomm. Suppl. N°. 30) (Proceedings May 1913), 761 couples investigated approaches to zero at heliumtemperatures. The different wires were measured against copper. After a preliminary research, which included also the determination of the thermo- 0, 107 +1309 2° = 499! ~400 ~ $00 — 600 {00 Fig. 1. electric forces of nickel and of six gold-silver alloys, the following combinations were selected as most promising for investigations in liquid helium. Thermoelectric forces against copper. : | i Ag Au | Au, | Pt Pb Fe | Const. | VIA} | SS SaaS SS SS a paige = ie, — ——— = = 7 81° K.| —28 S78) | S257) —298 | —457 | --1293 | —5320 | — 432 {en ate ae He 20° —28 | —282 | —326 —68 | —553 | +1319 | —6280 | —819 | 4°26 —21 | —375 | —328 —58 —559 | +1309 | —6630 | —990 | | ‘¢ eg wulbas 3°20 aed — 383 — —59 | — +1309 | —6630 | — 1002 — : 7 4 Li se aE = | | 2096 == Sone eS = = _ =) Si 1004 “1 Aw with 0,476 weight °/) Ag. Figure 1 shows thew thermoelectric forces against copper, at the absolute temperature 7’, given in the first column of the table. The temperature of the second juncture was 16° C. § 3. Change of the resistance of alloys with temperature. As it appeared impossible to find a suitable thermo-couple, our attention was drawn to the change of resistance of constantin, which had already been measured at hydrogen temperatures by KamprLINGH Onnes and Cray. This alloy shows bere a considerable decrease of resistance at decreasing temperature; it was, therefore, probable that constantin could be suitably used as a resistance thermometer at helium temperatures. Experiments have shown that this was in fact the case. Later measurements (see comm. N°’. 142a § 4) proved that also. manganin, whose resistance begins to diminish at decreasing temperature and which has at oxygen temperatures a considerable smaller resistance than at ordinary temperatures, is fit for tempera- ture measurements in liquid helium. § 4. Specific heat of mercury. a. Experimental arrangements. The method, used in the determination of the specifie heat, agrees most with the one used by Nernst in his investigations about the specific heat. A little block of solid mercury hung freely in a high vacuum and was heated electrically. The increase of temperature was determined by means of a constantin resistance thermometer. To obtain the little block of mercury the liquid metal (comp. fig. 2 with magnified fig. of details) was poured into the vessel C through a capillary, provided with a funnel, which could be introduced through m. First C was in the same way supplied by means of a funnel with a small quantity of pure pentane, which, at the intro- duction of the mercury, remains as a thin layer between the glass and the mercury. A little hollow steel cylinder (thickness of the wall '/,, m.m.), which contained the heating wire — a constantin wire, insulated with silk and covered with a thin layer of celluloid to avoid all electrical contact with the mercury — was immersed in the mercury. Round this cylinder a second constantin wire was wrapped, which was to be used as a thermometer. The little cy- linder was, by means of silk wires (stiffened by celluloid) fixed to a little glass rod, which could be moved up and down through the tube 4, and which was centred by constrictions in this tube. This glass rod was connected to a silk wire, which could be screwed up and down by turning the handle A. Now the mereury was frozen by cooling down to the temperature of liquid air, The Fig. 2. possible, that the results are accurate to about 10 HRs The thermat capacity of the hollow steel cylinder with the thermo- meter and the heating wires was determined afterwards by a separate 763 Sen Fig. 3. thin layer of pentane, which is spread over the glass, acts as a viscous lubricant at this temperature and prevents the sticking of the mercury to the wall in freezing. After having been frozen, the little block ofsolid mercury was screwed up by means of the handle K and the temperature was increased to about — 50° C. Thereupon a high vacuum was established by means of a GAEDE mercury pump and the pentane was distilled off into a tube, immersed in liquid air. During the experiments the heat insulation of the block appeared to be so good, that the tem- perature remained many degrees above that of liquid helium, al- though it was let down against the glass wall. Therefore a little gas had to be admitted in order to eool the block. This manipula- tion sueceeded perfectly, but the gas could not be removed quickly enough in the short time available for the experiments. The loss of heat of the mercury was thus very considerable (decrease of the temperature difference to half of the original value in about JOO seconds) and therefore the cor- rection, to be applied to the in- crease of temperature while heat- ing, remains the greatest source of uncertainty. Nevertheless it seems experiment, Fig. 3 shows the apparatus used for this purpose. b. Results. Measurement at the boiling point of helium. The quantity of heat supplied to the mercury amounted to 1,10 cal., the increase of "64 temperature, corrected for the loss of heat during the period of heating, was 2,22 degrees K. whilst the quantity of heat, necessary to heat the little steel cylinder with the thermometers 2,22 degrees, amounted to O.11 cal. (result of a separate experiment). Control experiments showed that the heating wire (used as a thermometer). and the thermometer wire outside the steel cylinder had the same temperature. The mass of the mercury was 314 erammes, so that 0,00142 cal./degree K. was obtained for the mean specific heat between 4°,26 K. and 6°,48 K. The relation of GRUNEISEN ') = = c, would”) have given ¢,=0.0087, for 4°.27 K. Measurement at 3°.5 K. Afterwards the experiment was repeated at the temperature of liquid helium, boiling under a pressure of 6 em. of mereury ; 0.000534 cal./degree K. was found for the mean specific heat between 2°93 K. and 3°97 K. Assuming this mean value of the specifie heat, we shall calculate now the value of this quantity for a definite temperature according to Desue’s formula, which holds for our very low temperatures c= C.T?, so that the mean specific heat between two temperatures 7’, and [aS ee Uh 0) GSI) We obtain from the two experiments C= 0.0000088 and 0.0000127 respectively. The agreement is not satisfactory; although, taking into account that the absolute temperature occurs in the formula in the 4" power, and that therefore small deviations in 7’ involve very large ones in (, we may safely conclude from our experiments, that, ith respect to the specific heat, nothing peculiar happens at the point of discontinuity, and that we may content ourselves with a preliminary mean value C= 0.0000110, when we assume for the moment that the specific heat does not show any discontinuity at all. We have then == Cit — 1010 0.000 0e* or for a gramme-molecule c= 0.00220 T?. For the characteristic constant 6, introduced by Drsue we find 1) KE. Griersen, Verh. d. Deutschen Phys. Ges. 1913 p. 186. *) Compare KamertincH Onnes and Hotsr, Leiden Comm. N°, 142a@ Proceed. June 1914. with c, = 5.96 and 13 3 C= 0:00220 7 2 = 77-988 —— ce = 464 — ge “ C= 60: As a matter of fact, the specific heat has been determined here at constant pressure and not at constant volume. In the foregoing calculation, the difference of the specific heats ¢, and ¢,, given by Gy 6, — Aca has been neglected. Indeed, A is about 7,2.10—° and c, and T ave both small. Using Desur’s formula, we can compare our results with those of Potuitzer'’ at somewhat higher temperatures. For this purpose we calculate a value of 6 agreeing as well as possible c with Poniirzer’s figures of —, we find then 110. In fig. 4 c, is c “ plotted as a function of 7’ according to Drie; the values, deter- mined experimentally, are indicated by circles. The accordance at helium temperatures is bad, as could be_ expected in consequence of the difference between the value of @ used in the calculation, and the one deduced from our experiments. b= are = ta if C, © EC = Se cast eae a7 A all | Qs d IAS | fe) o LO = fe] RV ae Cv SQ JOO dso Fig. 4. 1) See F. Poxtirzer. Zeitschr. f. Elektrochem. 1911. p. 5. 766 Meanwhile we remark, that in Po.iitzer’s experiments too a distinet deviation from Drsiwn’s curve is to be noticed, in the sense of a decrease of @ (about 115—162) with decreasing temperature, which would be, according to our experiments, very considerable down to helium temperatures ; further that, according to LinprMann’s formula and by comparison with lead (88), 661 is to be expected for mercury. § 5. The thermal conductivity. The thermal conductivity was determined by means of the appa- ratus, represented in figure 5. A U-shaped tube, with double walls, and closed at ene end, was provided . NG with mereury. The closed branch contained Shaan a constantin wire S, insulated by means of celluloid, which made contact with the a mercury at the free end. This wire’ was 5 used as a heating wire. The current return- ein ed through the mereury itself by means of a wire, in contact with the mercury at M8 the open end of the tube. The fall of tem- perature was measured with 38 constantin thermometers 7’, 7, and 7’, consisting of wire of '/,, mm. thickness, wrapped around a small glass tube. The experimental arrangement is further ex- plained by the diagrammatic figure. All wires were connected to each other by two wires, insulated by thin layers of celluloid and further running free through the liquid helium. In consequence of a wrong manipulation during the preparation, the tube had lost a little mercury, so that only the two lower thermometer wires could be used. The heat developed in the heating wire and the difference in temperature thus produced were measured at two different temperatures, the one above and the other one below the point of discontinuity in the electrical resistance. The section of the cylinder of solid mercury amounted to 0.47 em’, the distance of the thermometers to 5,0 em. At the boiling point of helium the supplied energy was 0,633 watt/sec., the difference in temperature produced 0.58; at 3°7 K 0,0365 watt sec. and 0,23. From this we find for the mean thermal conductivity between 4°.5 K and 5°,1 K. £=0.27 cal/em. sec. and between 3°.7 K and 3.9 K: £=040 cal/em. sec. The thing, which immediately strikes us, is that there is here no 767 distinet discontinuity as was found at 4°.19 K in the electrical con- ductivity, although the thermal conductivity becomes much larger, when the temperature decreases. As there do not exist direet deter- minations for solid mercury, we only can make a rough estimation with the aid of Wirpemann and Franz's law. At the melting point, the electrical conductivity of liquid mercury amounts to 1.10. 10° em. 2~'and of solid mercury to about five times as much, thus to 5.50. 10* em—! 2~!. From this we find by comparison e.g. with lead about 0.075 for the thermal conductivity. The values here obtained in liquid helium are 3.5 and 5.5 times as large. Chemistry. “Hqwilibrie in ternary systems’. XVII. By Prof. SCHREINEMAKERS. (Communicated in the meeting of Oct. 31, 1914). Now we will consider the case, mentioned sub 3 (XVI), viz: the solid substance is a binary compound of a_volatile- and a non-volatile component. A similar case occurs for instance in the system Na,SO, + water + alcohol, when the solid phase is Na,SO,. 10H,O,; or in the system FeCl, + HCI + H,O, when the solid phase is one of the hydrates of ferric chloride, for instance Fe,Cl, .12 H,0. For fixing the ideas we shall assume that of the three compo- nents A, B, and C (fig. 1) only A and C' are volatile, so that all ‘fapours consist either of A or of C or of A+ C. In fig. 1 CAde represents a heterogeneous region L—G; ed is the liquid eurve, CA the corresponding straight vapour-line. The liquid d, therefore, can be in equilibrium with the vapour A, the liquid e with the vapour C' and each liquid of curve ed with a definite Vapour of AC. Previously (XVI) we have seen that this heterogeneous region L—G can arise in different ways on decrease of pressure, viz. either in one of the angiepoints A and ( or in a point of AC; also two heterogeneous regions may occur, the one in A and the other in C, which come together on further decrease of pressure somewhere in a point of AC. In fig. 1 we may imagine that the region L—G has arisen in these different ways; curve ed may of course also turn its convex side towards AC. Besides this heterogeneous region 1—G' we also find, in fig. 1 the saturationcurve under constant pressure of the binary : dk Proceedings Royal Acad. Amsterdam, Vol. XVII. 768 substance /’, represented by pg [we leave the curve rs, drawn in the figure out of consideration for the present]. A Fig. 1. In the same way as we have acted in the general case | fig. 11 (1) | or in the peeuliar case (XI), we may deduce also now the different diagrams. T< Ty. At first we take a temperature 7’ lower than the minimummeltingpoint 7’ of the binary compound /. Now we tind a diagram just as fig. 2 for the saturationcurve under its own vapour- pressure of / and the corresponding straight vapour-line. In_ this figure, in which the component-triangle is only partly drawn, Agn is the saturationcurve under its own vapourpressure; we find the corresponding straight vapour line Cy, on side CA. When we assume, as is supposed at the deduction of fig. 2, that neither a point of maximum-pressure, nor a point of minimum- pressure occurs, the pressure increases from m towards h; conse- quently it is lowest in n and highest in 4, without being, however, a minimum in 2 or a maximum in hk. It follows from the deduction that the sides solid-gas and_ solid-liquid of the threephasetriangles must be situated with respect to one another and to the side CB just as is drawn in fig. 2. It is apparent from the figure that the binary liquids 1 and 7 ean be in equilibrium with the unary vapour C' and that the ternary liquids a, c and #4 ean be in equilibrium with the binary vapours a,, c, and #,. It is apparent that somewhere between the liquids c 1 and 4 a liquid g must be situated, the corresponding vapour g, of which represents the extreme point of the straight vapour line Cg,. When a liquid follows curve /n, first from / towards g¢ and after- wards from g towards n, the corresponding vapour g, follows conse- 769 quently first Cy, from C towards g, and afterwards again this same line, but in opposite direction, consequently from g, towards C. Fig. 2. Kach vapour of this straight vapour line Cy, can, therefore, be in equilibrium with two different liquids, the one of branch hy and the other of branch gn. We may express this also in the following way: when we have an ‘equilibrium /’-+- Z + G, then there exists under another pressure, also an equilibrium + 7,+.G,, in which Z and ZL, have a different composition; G and G,, however, have the same composition. It is apparent from the deduction of fig. 2 that in curve jn also a point of maximumpressure can occur. This case is drawn in fig. 3; in represents again the saturationcurve under its own vapourpressure and Cy, represents the corresponding straight vapourline; M7 is the point of maximumpressure, J/, the corresponding vapour. The points M,, M, and F must of course be situated on a straight line. While under the pressure Pj; there occurs only one equilibrium, viz. f+ Lip+ Gau,, under each pressure, somewhat lower than P\, there exist two equilibria, for instance + L, + Gi, and F+ L,+ G.,.; we can imagine these to be represented by the threephasetriangles Maa, and /cc,, when we imagine both triangles in the vicinity of the line #//,. It follows from the deduction of the diagram that both these triangles turn their sides solid-gas towards one another, consequently also towards the line /J/M,. Suppose, we want the curves ed and pg to move in fig. 1 with respect to one another in such a way that a point of minimum- pressure occurs on the satnrationcurve under its own vapourpressure, 51* 770 then we see that this is impossible. Yet we can imagine a saturation- eurve with a point of maximum- and a point of minimumpressure. When we trace curve /n starting from n, we arrive first in the pot of maximura- afterwards in the point of minimumpressure. We will refer to this later. Tp < T. Now we take a temperature 7’a little above the minimum meltingpoint 7p of the solid substance /#. Then we must distinguish two cases, according as the solid substance expands or contracts on melting. We take the first case only. Then we find a diagram like fig. 4 (XI); herein, however, the same as in figs. 2 and 3, we must imagine that the vapourcurve han, is replaced by a straight vapourline Cg, on side CA. We will refer later to the possibility of the occurrence of a point of maximum- and a point of minimumpressure. We can, however, also get curves of a form as curve /nand the curves situated inside this in fig. 6 (XI); these curves show as well a point of maximum- as a point of minimumpressure, When we draw the saturationcurves under their own vapour- pressure for different temperatures, we can distinguish two prineipal types; we can imagine those to be represented by figs. 5 (AI) and 6 (XD. At temperatures below 7'p these curves are circumphased, above Z'p they are exphased. In tig. 5 (XI) they disappear in a point H on side BC, in tig. 6 (XI) in a point A within the triangle. The corresponding straight vapourlines disappear in fig. 5 (XI) at 7 in the point C; in figure 6 (XI) they disappear at 7 in a point R,, the intersecting point of the line /’R with the side CA. 771 Now we will consider some points more in detail. In order to get the conditions of equilibrium for the system #’+- 4 + G, when Fis a binary compound of 6 and C and when the vapour consists only of A and C. we must equate «=O and y,=0. The conditions (1) (II) pass then into: Z OZ Ew Mite he Cig ge ae az az, | : 0%, | 02 _, Ow ae, | ) ae” og, tb Sanur = Now we put: b= Was ikititird pnol A SG Je iii lon 5 2 (P) Hence the conditions (1) pass into: OU 0U «—+(y — 8)—+ RTe—U+S5=0... . (8) Ow 7 Oy aU. oo #,—— —6— + RTx, —U,+5=>0... . (4) Ow, Oy 0U aU, ? — + RT logx =——+ RT loge, . . . . . (5) Ow Ox ; 1 When we keep the temperature constant, we may deduce from (5): [er + (y — B)s + RT) dz + [as + (y—A)t]dy=AdP . (6) (3) E — ps + “ rr | dx + [#,s — Bt]dy =(A+ C)dP. . (7) RL RT OV OV r + —— | da + sdy — (» + —— | dz, =({| —— — ]dP . (8) 2 2X, Ox, Ow i Here we must equate of course in A and C a=O and y, = 0. In order to let the pressure be a maximum or a minimum, dP must be = 0. From (6) and (7) it follows that then must be satisfied : ip [o) a= Gann) ==, ato ogo co oe A) This means that the point of maximum- or of minimumpressure M (x,y) and the corresponding vapourpoint J/, (v,y,) are situated with / on a straight line (fig. 3). In order to examine the change of pressure along a satuyration- curve under its own vapourpressure in its ends / and n (figs. 2 and 3) we equate in (6) and (7) e=0 and a, =U. Then we find: OV [(y—B) s + RT] de + (y—p) tdy = | v- v + (B—y) F | dP (10) OY ae “ OV — ps + — RT | dx — ptdy =| V, —v + 8 a CLE es (Lal) : y 772 The ratio v,:2 has a definite value herein, as it follows from (5). When we eliminate dy from (10) and (11), then we find: [2+ a | era =[3V + (y—B) V, — yx] dP. . (12) The quantities in the coefficient of dP relate all to the binary equilibrium # + £-+ G. When we eall AV, the change of volume, when between the three phases of this binary equilibrium a reaction takes place, at which the unity of quantity of vapour arises, then is: (y—B) AV, = BV + (y—8) VV, — yo «.. « «= (18) Consequently we may write for (12): pe SA ela 14 Ni — aura Ame mere es. 5, (124) Now we introduce again, as in (XI) the perspective concentrations of the substance A in liquid and gas; it is evident that the per- spective concentration S, is equal to the real concentration «, of A in the vapour; we find for the perspective concentration of A in the liquid: fa a p—y so that we can write for (14): . dP ie S\ RL é = —/{ 1 — — |—— .w sz 2 (th) aa ) c—0 x x, Ay : When the vapour contains the three components, then. as we have seen previously (14) (XI) is true; when we replace herein S, by 2,, this passes into (16). It follows from (16) that the sign of the change of pressure in the ends / and n of a saturationcurve under its own vapourpressure, depends on the sign of AV,. Now AV, is almost always positive for the binary equilibrium PLELG and it is only negative between the points / and H'|fig. 5 (XI) and fig. 6 (X1)]. Consequently AV, is positive in the points 4 and m of figs. 2 and 3, also in the point h of fig. 5 (XI) and 6(X1I); AV, is negative in the point n of the two last figures. Further it follows that the sign of the change of pressure is not determined by the ratio «,:a (the partition of the third substance between gas and liquid) but by the ratio S: a, (the perspective partition of the third substance between gas and liquid). Let us take now a liquid of the saturationcurve under its own vapourpressure in the vicinity of the point / of fig. 2, for this we imagine triangle Maa, in the vicinity of the side LC. From the position of Fa and Fa, with respect to one another, follows 773 S>z2x,. As AV, is positive in fh, it follows from (16) that the pressure must decrease on addition of a third substance. We see that this is in accordance with the direction of the arrow in the vicinity of h. In the vicinity of point / of fig. 3 is a, > S as follows from the position of triangle Kaa,. As AV, is positive, it follows from (16) that the pressure must increase on addition of a third substance. This is in accordance with the direction of the arrow in the vicinity of fh. In the vicinity of point n of the figs. 2 and 3 S is negative (we imagine for instance in fig. 2 triangle /6/, in the vicinity of side BC); as AV, is positive, it follows from (16) that in both figures the pressure must increase, starting from n. Consequently we find: in a terminatingpoint of a saturationcurve under its Own vapourpressure, situated between Cand H, the pressure decreases on addition of a third substance, when the threephase- triangle turns its side solid-gas towards LC (fig. 2) and the pressure increases when the threephasetriangle turns its side solid-liquid towards BC. As, therefore, at temperatures lower than 7'p (figs. 2 and 8) the pressure always increases, starting from 7, and increases or decreases starting from /, we find the following. When we trace curve nh, the pressure increases continually starting from » towards / (fig. 2), or we come starting from 7 first in a point of maximumpressure, after which the pressure decreases as far as in / (fig. 3) or we come, starting from 7 first in a point of maximum- and afterwards in a point of minimumpressure, after which the pressure increases up to /. As in point / of fig. 5 (XD the pressure decreases starting from h, consequent it is assumed here, that the threephasetriangle furns its ‘side solid-gas towards BC. (Cf. fig. 2 and fig.4 (XI); in this Jast figure we imagine however curve /,n, on side CA). In the point h of fig. 6 (XI) is assumed that the threephasetriangle turns its side solid-liquid towards BC. Let us consider now the terminatingpoint 7 of the saturationcurve in fig. 5 (XI) and fig. 6 (XI). As n is situated between F and H, AV, is negative, when the threephasetriangle turns its side solid- gas towards BC, then is S>.2, and it follows from (16) that the pressure increases on addition of a third substance. We then have the case of fig. 5 (XI). When, however, the threephasetriangle turns its side solid-liquid towards LC, then S<.w, and it follows from (16) that the pressure decreases on addition of a third substance, We then have the case represented in fig. 6 (XI). 774 When we consider the saturationcurve going through the point F in fig. 5 (XI) and fig. 6 (XI), then for this point y=, conse- quently, according to (15) S=o. From (13) follows also AV,= @. Therefore we take (12); from this follows for y= 8 dP th 17) de tar eee Ge ee ( As fig. 5 (XI) and fig. 6 (XT) are drawn for V > v, the pressure must increase starting from / along the saturationcurve going through F. As the pressure increases starting from /’ along the saturation- curves under their own vapourpressure of fig. 6 (XI) and decreases starting from a point , situated in the vicinity of H, somewhere between /’ and n must consequently be situated a point, starting from which the pressure neither increases nor decreases. This point is, therefore, the point of maximum- or of minimumpressure of a saturationcurve, and is not situated within the componenttriangle, but accidentally it falls on side LC. It follows from the figure that this point is a point of minimumpressure; we shall call this the point m. The limiteurve (viz. the geometrical position of the points of maximum- and minimumpressure) goes consequently through the points m and R&R; it represents from m to & points of minimum- pressure; starting from / further within the triangle, it represents points of maximumpressure. This latter branch can end anywhere between /7 and C' on side BC. The terminatingpoint of a limiteurve on side SC’ can be situated between “and C, but cannot be situated between /’and B. A similar terminatingpoint is viz. a point of maximum- ora point of minimum- pressure of the saturationcurve, going through this point. Consequently in this poimt along this saturationcurve dP=0O,; from (16) it follows that then must be satisfied : S=2,. or, Pe - (y—S) ac, 0, eee eremea (l) Herein w and «, are infinitely small; their limit-ratio is determined by (5). As 2 and a, are both positive, it follows from (18): y < ~. The terminatingpoint of a limiteurve must, therefore, be situated between /’ and C' (fig. 6) and it cannot be: situated between / and B. In accordance with this we found above that one of the ends of the limiteurve is situated in fig. 6 (XI) between n and PF, Now we must still consider the case mentioned sub 4«(XIV), viz. that the solid substance is one of the components. A similar case 775 occurs for instance in the systems: 7+ water + aleohol, wherein Z represents an anhydrie single, salt, which is not-volatile. For fixing the ideas we assume that B is the component, which is not-volatile (fig. 1), so that A and C'represent the volatile components. Now we imagine in. fig. 1 curve pq to be omitted, so that the curves ed and rs rest only, ed is the liquideurve of the region L —G, rs is the saturationcurve under a constant pressure of the substance B. We can, in order to obtain the different diagrams, act in the same way as we did before in the general case, or as in communication XI. For this we consider the movement of the curves ed and rs with respect to one another on decrease of pressure. As we assume that A is not volatile, these considerations are not true, therefore, for points situated in the vicinity of B. Equilibria situated in the immediate vicinity of B have viz. also always the substance 4 in their vapour, so that the considerations of com- munication XIII apply to these. When we decrease the pressure, the liquideurve ed (fig. 1) shifts further into the triangle towards the point 4, so that under a definite pressure the curves ed and rs meet one another. Now we distinguish three cases. 1. We assume that the curves ed and 7s meet one another first in a point on one of the sides of the triangle; when this takes place on side BC, then consequently the points e and 7 coincide in fig. 1, while the two curves have no other point in common further. On further decrease of P, this intersecting point shifts within the triangle and it disappears at last on the side A, when in fig. 1 the points s and d coincide. Curve ed is situated then inside the sector Brs and curve 7s inside the region CedA. . From this follows that the saturationcurve of B under its own vapourpressure can be represented by curve habn in fig. 4, in which the arrows indicate the direction, in which the vapourpressure increases. The corresponding vapourcurve is the side CA; the liquid / viz. is in equilibrium with the vapour C, liquid n with the vapour A and with each liquid (a and 6) of in a definite vapour (a, and 6,) of CA is in equilibrium. It follows from the deduction that the threepbase- triangles (Bua,, bbb,) turn their sides solid-gas towards the point / and their sides solid-liquid towards the point 7. This fig. 4 is a peculiar case of fig. 2 (XIII); when we suppose viz. that the substance 6 does not occur in the vapour, curve h,a@,b,7, of fig. 2 (XIII) must coincide with the side CA of the triangle and fig. 4 arises, 2. Now we assume again that the curves ed and rs (fig. 1) meet one another first in a point of the side BC; this point of inter- section shifts then on further decrease of P into the triangle. Under a definite pressure we want a second point of intersection to be formed by the coincidence of d and s (fig. 1). The two points of B \ C44 doe Fig. 5. intersection approach one another on further decrease of pressure, in order to coincide at last in a point m. It is evident that m is a point of minimumpressure of the saturationcurve under its own vapourpressure; if is represented in fig. 5 by curve wambv, the corresponding vapourcurve is the side Cd. It is evident that the vapour m,, which can be in equilibrium with the liquid m, is situated on the line Am. 3. We can assume also that the curves ed and rs (fig. 1) meet on decrease of pressure first in a point J/, which is situated within the triangle. On further decrease of pressure then two points of Tae intersection arise; the one disappears on BC by the coincidence of e and 7, the other on LA by the coincidence of d and s (fig. 1). It is evident that J/ is then the point of maximum-pressure of the saturationcurve of 6 under its own vapourpressure, the corresponding vapourpoint J/, is situated of course on the line JZ. One can understand the occurring diagram with the aid of fig. 5 ; herein we have to give an opposite direction to the arrows and we have to replace the points of minimumpressure m and m, by the points of maximumpressure Jf and J/,; further the triangles Baa, and bbb, are to be drawn, in such a way that they turn their sides solid—gas towards the line BILM,. We shall consider some points in another way now. In order to find the conditions of equilibrium for the equilibrium 6 -+ LZ + G, when the vapour consists of A and C only, we equate in the relations (1)—(8) @=1; in the general values of A and C (II) we put c= 0, B=1 and y, = 0. The condition for the occurrence of a pot of maximum- or of minimumpressure (d= 0) becomes then : = (=) a 2 co 6) oso, 5 (LO) »lhis relation also follows from (9), when we put B=41. This means: the pot of maximum. or of minimumpressure of the saturation- curve of £6 under its own vapourpressure and the corresponding vapourpoint are situated with point B on a straight line (fig. 5). In order to determine the change of pressure along a saturation- curve under its Own vapourpressure in its ends on the sides bC and BA (figs. 4 and 5) we put in (16) B=1. We then find dP ie ISIN\. tase ee sia ae sh Ae es E00) dz ]y—0 au Goad (AWS In this S and AV, are determined by (13) and (15), when we put herein 3=1. Consequently S is always positive. When we apply (20) to the figures (4) and (5), then we see that the change of pressure is in accordance with the position of the sides solid-gas and solid-liquid of the threephasetriangles. Now we have treated the case that either the binary compound J (figs. 2 and 3) or the component / (figs. 4 and 5) occurs as solid phase. When /’ and #4 occur both as solid phases, then the two saturationcurves under their own vapourpressure can either intersect one another or not. We only consider the case, drawn in fig. 6, that the two curves intersect one another in a point; the vapour, being in equilibrium with the liquid s, is represented by s, (s, or s,). A similar case may occur for instance in the system Na,SO, + water + alcohol, then curve cs is the saturationcurve under its own 778 vapourpressure of Na,SO,.10H,O (/’), sa the saturationcurve of the anhydriec Na,SO, (3). Then there exists a series of solutions, saturated under their own vapourpressure with Na,SO,.10H,O (curve cs) and one series saturated with Na,SO, (curve sa); the equilibrium Na,SO, . 10 H,O + Na,SO, + L;-++ G, occurs only under a definite pressure P,. The solution ZL, has then a detinite Composition s and the vapour, which consists only of water and alcohol has a definite composition s,. In the binary system Na,SO, + water, the equilibrium Na,SO, . 10 H,O + Na,SO, -+ vapour exists only under one definite pressure; we shall eall this pressure P,. In the ternary system Na,SO, + water + aleohol the equilibrium Na,SO, . 10 H,O+Na,SO,+-L.-++G, exists also _ only under a definite vapourpressure P.. This pressure P. is influenced A Fig. 6. by the watervapour and the alcohol-vapour together; now we may show that the partialpressure of the watervapour herein is also equal tio P, and that the pressure of the alcohol vapour is consequently P,— P,. In order to show this, we consider the general case that in the system A+ B+ C (figs. 1—6) the substances A and C are volatile and that a compound /° of 6 and C occurs. The binary equilibrium 5 -+ /-+ G,, wherein the vapour consists of C only, occurs under a single pressure P, only. The ternary equilibrium 6-+ /’+ G, wherein consequently the vapour consists of A and C, can occur at a whole series of vapour- pressures. When we represent the § of 45 and / by § and &,, then the condition of equilibrium is true: Z, 5 —e=0—A) (4 — nie): Serer.) vars) Hence follows: j OAT on nh Oe v, — bv — (1 — p){ V, — 2, e dP+ (1—§8)a,r,de#,=0. (22) eB When we assume that the gas-laws hold for the vapour G, then: Ok eee RT — SU 20) 3 SSS Oar, a,(1—2,) From (22) now follows: (23) l=6 [(d —8) V, =», + Bo] dP= — tH) donee ee (24) 1 The coefficient of ¢@P represents the change of volume when 1 Mol. F is decomposed into 3 Mol 6-+ (1 — g) quantities of G; this is very nearly (1— 8) V’,. As at the same time PV, = RT, we can write for (24); (Al = op) CUP Sse 5 5 9 Go 6 o 4 ira) From this follows: i 0 oR ear MEPS we eet an (26) When we call the partial pressures of A and C in the vapour )4 and Pc, then Pg=2,P and Pe=(1—a2,)P; from (26) now follows : Pea ands PG == Py) a2) ater 0 l—2, A This means that in the ternary equilibrium 5+ /-+-G the partial pressure Po of the substance C is equal to the vapourpressure of the binary equilibrium 6+ #' + G,. When we bear in mind now that in a system the pressure and the composition of the vapour do not change, when we add to this system stili a liquid, which is in equilibrium with all phases of this system, then follows: In the ternary equilibria B+ F+G and 6+ F+ L,+ G, the partialpressure of the substance C in the vapour is equal to the vapourpressure of the binary equilibrium 4+ + G,. The first equilibrium (viz. 5+ /’+ G) exists at a whole series of pressures; both the others oecur under a definite pressure only. The binary equilibrium Na,SO .10H,O + Na,SO, + watervapour has at 25° a vapourpressure of 18.1 m.m. when we add alcohol, then, when the gas laws hold in the vapour, in the equilibriam Na,SO,.10H,O + Na,SO, + G and Na,SO,.10H,O + Na,SO, + L+G the partialpressure of the watervapour will also be equal to 18.1 m.m. Now we will put the question, whether we can also deduce some- 780 thing abont the change of pressure starting from s along the curves sa and sc (fig. 6). In communication V we have deduced the following rule. When the equilibrium solid + Z ean be converted with increase of volume into solid + L’ + G’ (in which ZL’ differs extremely little from £) then of a threephasetriangle solid—liquid—gas the side solid—liquid turns on increase of pressure towards the vapourpoint and it turns away from the vapourpoint on decrease of pressure. When we assume now that s (fig. 6) is not situated in the vicinity of B or F (the equilibrium 5-+ L and + LF converts itself into B+ L’+ G6’ and &+ L’+G" with increase of volume) we can apply the above-mentioned rule. We distinguish now according as the vapour is represented by s,,s, or s,, three cases. 1. The vapour is represented by s,. First we consider the threephasetriangle /’ss,. When the side Fs turns towards c, then consequently it turns towards its vapourpoint s,; the vapourpressure increases, therefore, starting from s along ‘sc towards ec, Let us consider now the threephasetriangle Lss,. When the side Ls turns towards a, if turns, therefore, away from its vapourpoint s,; consequently the vapourpressure decreases starting from s along sa towards a. : Consequently we find that the vapourpressure starting from s increases along sc and that it decreases along sa. It is evident that this is only true for points in the vicinity of s; the occurrence at a greater distance of s of a point of maximumpressure on sc and a point of minimumpressure on sa, is viz. not excluded. 2. The vapour is represented by s,. It follows from a consideration of the threephasetriangles /ss, and ss, that the vapourpressure starting from s increases as well along sc as along sa. 3. The vapour is represented by s,. It follows from a consideration of threephasetriangles #’ss, and Bss, that the vapourpressure starting from s decreases along sce and increases along sa. We can obtain the previous results also in the following way. Between the four phases of the equilibrium 6+ #’+ L, + vapour or s,) a phasereaction occurs on change of volume. We choose this reaction in such a direction that vapour is formed, we call the (Si, Sq change of volume AV. The point s (fig. 6) is a point of the quadruplecurve B-+ #+ +L+G; AV is positive for each point of this curve. When, however, a point of maximumtemperature /7 occurs on this curve, 781 then AV is negative between this point /7 and the terminatingpoint of the curve on side BC. It is apparent from the position of the curves sc and sa (fig. 6) that point s is chosen on that part of the quadruplecurve, where AJ is positive. We distinguish now again the same three cases as above. 1st. The vapour is represented by s,. It is apparent from the position of the points 7’, B,s and s, with respect to one another that the fourphase-reaction : Nee GV. S0) F+ L4G (Curve sc) B+ L+ G (Curve sa) FH+B+L FI+B+G takes place; it proceeds from left to right with inerease of volume Hence it follows that the equilibria written at the right of tbe vertical line occur under lower pressures, the equilibria at the left occur under higher pressures. In accordance with the above we find, therefore, that starting from s (fig. 6) the pressure increases along se (equilibrium + 1+ G) and decreases along sa (equilibrium B+L+ GQ). 2°¢ and 3". Also in these cases we find agreement with the previous considerations. When a point of maximumtemperature H occurs on the quadruple- curve b+ F+ 2+ G, then two points of intersection s occur at temperatures a little below 77. When we consider now a point of intersection s between // and the terminatingpoint of the qua- druplecurve on side AC, then ATV’ is negative. This involves that above in 1st—3'4 increase of P is replaced by decrease of P and reversally. We find also the same when we consider the threephase- triangles solid-liquid-vapour. To be continued.) Chemistry. — “On the quaternary system: KCI—CuCt,— Ba Cl,—H, 0.” sy Prof. Scurememakers and Miss W. ©. pr Baar. (Communicated in the meeting of October 31, 1914). In a previous communication’) we have already discussed the equilibria occurring in this system at 40° and at 60°; the results of the analysis on which these considerations are based, we have hitherto not yet communicated. Now we will communicate the results of the analysis; all the points, curves ete. quoted in this communication apply to the two figures of the previous communication (1. c¢.). We want to draw the attention to the fact that fig. 1 represents the equilibria at 40° and tig. 2 the equilibria at 60°. 1) These Communications (1912) 326. 782 vACE eae Composition of the solutions in percentages by weight at 40° (fig. 1. I.c.). Point KCl BaClo | CuCl, H,O | Solid phases a 0 0 44.67 | 55.33 Cu Cly.2H,0 b 0 3.72 | 42.72 | 53.56 | BaCl.2H,O-+CuCl.2H,0 c 0 28.98 0 11.02 |) Ba Cl. Hp O d | 23.98 | 9.15 0 66.87 BaCl).2H,0+KCI e | 28.63 Deg Og, [eres KCI f | 21.53 0 | 22.85 | 55.62 Keeper gz | 9.79 0 | 43.83 | 46.38 CuCl, 2H; 0- Des b 0 3.72 | 42.72 | 53.56 | BaCl,.2H,O +CuCl,.2H,0 es 5.52 | 3.39 | 42.35 | 48.74 : “pn | 9.88 | 2.99 | 42.07 | 45.06 | BaClh.2H,O4- CuCl. 2H0°-D gs di VW/23508s)) V94s lao 66.87 Ba Cl,. 2H» O + KCl 2 | 21.46 | 8.90 | 8.44 | 61.20 ? >| 20.61 | 7.63 | 14.31 | 57.45 | ; i | 20.61 | -5:40 | 20.47 | 53.52 | BaCh.2Hs0--KCI--Dioo f | 21.53 0 22.85 | 55.62 Ke eD ee a 21.31 | 2.59 | 22.06 | 54.04 f eel 20K | 5.40 | 20.47 | 53.52 BaCly.2H:0 + KCl + Dy.20. pel Sods h 43.83 | 46.38 CuCl, .2H:0 + Dy.o» aa 9.94 | 1.46 | 43.22 | 45.38 : oh 9.88 | 2.99 | 42.07 | 45.06 | CuCl. 2H,O + BaCl.2H,0+ Dhow i | 20.61 | 5.40 | 20.47 | 53.52 BaCly. 2H,0 + KCI+ Dig. 2 | 16.44 | 4.72 | 27.22 | 51.62 Ba Cly 2H,0 + Dy.o.0- G” | q1.44 [93.65 | aales | 0.55 : h 9.88 | 2.99 | 42.07 | 45.06 | CuCl,.2H,O + BaCly. 2H.0 + Dj.» TABE ES IE 4 ¢3 - Composition of the solutions in percentages by weight at 60° (fig. 2 1.c.). Point) KCI | BaCl, CuCl, H.,0 Solid phases a OS... if eo 41.42 | 52.58 CuCly . 2H,0 b 0 6.87 | 43.57 | 49.56 CuCl, . 2H,O ++ BaCly . 2H,0 pe aaa Bi 0 68.3 BaCly . 2H,0 @ | 23.09, | 14.83: | 0 62.08 BaCly . 2H,0 + KCl aa 32 0 0 68.8 KCI | | if 26.12 0 26.57 | 47.31 Kele= Dis @ | 17:13 | 43.45 | 39.42 Dioce Dia k | 13.67 0 46.40 | 39.93 CuCl, .2H,O0 + Dy. S | b o | 6.87 | 43.57 | 49.56 CuCl, . 2H.0 + BaCl, .2H,O v | ES | 6.32 | 5.99 | 43.68 | 44.01 : O \ l 12.45 4.93 44,09 | 38.53 | CuCl.2H,O-+BaCl.2H.O+D,, d | 23.09 | 14.83 0 62.08 | BaCl,.2H,O+ KCl ~* Bos ES | 23.15 | 10.01 | 12.01 | 54.83 | O i | 23.78 | 5.97 | 24.61 | 45.64 BaCl, .2H,O + KCl + Dj.2.0 FA e26u 1b ee 6 26.57 | 47.31 KEleD os 2 Ew | 24.53 3.32 | 25.46 | 46.69 E a | i | 23.78 | 5.97 | 24.61 | 45.64 KCI + BaCly . 2H,0 + Dj.0. medidas |) 0 43.45 | 30.42 Dios Dix vu ES, | 16.50 | 2.51 | 42.20 | 38.79 : O h | 15.75 | 4.75 | 40.84 | 38.66 BaCly.2H,0 + Dyno + Din bee See) ree EE ee k | 18.67 0 46.40 | 39.93 Cue wZHO sa Dig vu Em | 13.04 | 2.52 | 45.24 | 39.20 i O 1 | 12.45 | 4.93 | 44.09 | 38.53 | CuCl,.2H,O+ BaCly.2H,O+ D,, i | 23.78 | 5.97 | 24.61 | 45.64 KCI + BaCly. 2H,O + Dy.o. [-P) ES | 19.53 | 5.40 | 32.37 | 42.70 | BaCl, . 2H,O + D 1.0.5 O | h | 15.75 | 4.75 | 40.84 | 38.66 BaCl, .2H,O + D, 90+ Diy h Msierey |) eis 40.84 38.66 BaGly. 2H30 -— Dj.o.0-F Dj. {Ac 760i) 483 s\) APES) [88526 BaCly.2H,O + D:., 1 | 12.45 | 4.93 | 44.09 | 38.53 | CuCl. 2H,O+ BaCl,.2H.O+D,4 52 Vroceedings Royal Acad. Amsterdam, Vol, XVII. 784 Physics. — “On the theory of the string galvanometer of KINtTHOVEN.” By Dr. L.S. Ornstein, (Communicated by Prof. H. A. Lorentz.) (Communicated in the meeting of September 26, 1914). § 1. Mr. A. C. Crenore has developed some considerations in the Phil. Mag. of Aug. 1914°), on the motion of the string galvano- meter, which cause me to make some remarks on this subject. For a string, immersed in a magnetic field 7, and carrying a current of the strength -/, the differential equation for the elongation in the motion of the string is O*y a Oy ah | JER] (1) — +x%x— = a — + — a6 Or? ot Ox” 0 in which x is the constant damping factor, a? = —, 7, is the tension g and 0 is the density. The direction of the stretched string has been chosen as the a-axis. For «=O and «=/ the string is fixed, so y =. In deducing the equation the ponderomotive force is supposed to be continually parellel to the elongation y, which is only approxi- mately true, since the force is at every moment perpendicular to the elements of the string (perpendicular to / and //); but if y may be taken small, then the equation (1) is valid. The approxi- mation causes a parabola to be found for the state of equilibrium with constant H and ./, instead of the are of a cirele, as it ought to be; however, the parabola is identical with a circle to the degree of approximation used. Dr. Crrnork now observes, that the equation (1) may be treated after the method of normal codrdinates by putting DD OZ OREN Seo os of IS), Besides the equation 1, he deduces a set of equations, the “circuit equations’, which give a second relation between gy; and J (from (1) there originates in the well-known way an equation for every coordinate y,). The obtained solutions will be independent, when the cireuit equation is true, and again their sum is a solution of the problem. However, from the deduction of the circuit equation it cannot well be seen whether this is the ease, since not entirely exact energetic considerations underlie this deduction. Now supposing the string to be linked in a cireuit with resistance /, and self-induction L, the circuit-equation may be easily found by applying MaxweEt.t’s 1) Theory of the String Galvanometer of EinrHoven. Phil. Mag. Vol. 28, 1914, p. 207. 785 induction-equation. For in consequence of the motion of the string in the magnetic field the number of lines of force passing through the circuit changes to an amount proportional to Expressed in the units used by Dr. Crenore, the induction-equation now takes the form: l dJ “Oy } ij EI eal Aah eee 8 oo dt Ot 0 where /# is an external electromotive force acting on the circuit. § 2. The problem of finding the vibrations governed by the equations (1), (3) and the condition y=O for c=O and «=/, can be easily solved. First, let E be O, and so the question of free (damped) vibrations may be put. Suppose that y = —p er J = Feat where y is a function of 2and / is a constant. Then the equations change into 9 — wf + iwxg — a Oe eee 0a? fe) l 0= R14 Liwl + ‘He | gd. 0 Hence l Oy iw @? — iwe*) 4 a = pda. ( NP or dx? o(R+ Liw) ¢ 0 : 4 . : ; FH’iw Putting w* — 7x in the first member n* and Ae =p we have 3 l 2 Ge n° p+ a? =s pdx. ie f p 0 This equation may be satisfied by n nt : p=Acs—x+ Bsn—2 + C a a provided that or bo Eo TS6 “a nl a nl : n? C=p Asin— + — Bl 1—cos—]+ Cl). . (4) n a dv a whereas, because of the boundary conditions, we must have A+. C= nl _ nl f A cos— + Bsin— + C=0. ai a This gives for the frequency the transcendental equation nl? 1 — cos - a nlooa a np | — = en — = = l n a n _ nl sin — a or een _ nl a nl n* sin — == || Ls — — 1 —cos : a a 7 a From this it appears immediately that we must have _ nl E Ti PC AE ta! oS (5) 2a or ¥ nl nl 20) een ; Ww” COS = p l COS = sin . . . . . (6) 2a 2a n 2a (5) can be satisfied by nl Sica (7) 2a or, hence . 2k ra \* pA all : As is immediately to be seen, these are the damped vibrations of even order, which the string can perform in the absence of the enrrent. It is evident that the presence of current and field have no influence on the vibrations of even order. [f the resistance is infinitely great, the constant p in the equation (6) is zero. In this case the equations can be satisfied by m= 0, or w =0, i.e. the string is at rest; and further by nl cos — = 0. 2a Hence nl oy 1 4g 8 Qa — (2 tL + ) 2 . . . . . . . . ( ) or 787 ae (a) w* — iwx = | — es) The frequencies arrived at are those of odd order, altered by current and field. For large values of R an approximate value of : : : Ge eas 4) n can easily be expressed in the form ny + je From (6) follows N; =n; + Has aes i ag Oe Ohne ane s being an odd number, 7 being taken zero, while for w and n, their values for A=o must be put. Taking x= 0, i.e. neglecting the air-damping in comparison with the electrical damping, we find sa 4H*il Cys 22 Le 9 3 l Ro s°x* (9) In the solution, therefore, there is a damping factor of the form 4H] —= t e Res*x? The influence of the damping is the less, the greater the value of s is. This is directly evident, for if s is great, the string vibrates in a great number of parts with opposite motion. The electromotive force generated by those parts therefore is annulled. In case # is small, the roots of the equation (6) are those of the transcendental equation nl 2a nl lcos—= — = sin = (() 2a n 2a or 2a nl i) eal Lin, Se ee pa Sa CMa (10) *) ; nl . Xe ee The quantity >— approaches to odd multiples of —. For small values of A an approximate form n,--a@R can be easily indicated. Taking again L—0O and x =—0, we find 2a Ko . PEP * where 7, is an arbitrary root of (10). In case the resistance is small, Oe Se all vibrations suffer the same damping. For @ we find _ nl _ n(l—a) _ ne sin — — sin — — sin — 2 a a —— — ie P _ nl sin — a 1) Compare for instance Riemann-Weser, Partielle-Differential Gleichungen, II, p. 129. hence for inl _ n(l—e) _ ne sin — — sin — sin — . oy de a a 1 Se Reo on (filthy) 7 _ nl sin — a The real and imaginary part of this expression satisfy the equations and the boundary conditions. A sum of solutions for different values . oc : : dy ’ ‘ of @ satisfies the equation. If y and “ate given for {= 0, we can : dt with the aid of the given functions find the solution. The found proper functions are not orthogonal, but by an appropriate linear substitution orthogonal functions can be obtained. If y is known, I can be calculated from (3). § 3. It is useful to work out the problem. Using the assumption (2) of Crenork, we obtain for gs, the following set of equations (taking & and / zero): = AHS Pot ns’ Ps = SM Sal) oe (5) 0) and 21H _ Qs RB se Uv s where SITA n= e 3 l Here s is an odd number; for even values the second member of (12) is zero, and the even vibrations are therefore unchanged. Now putting Ps = ay ett ‘ Ji wlagioln and AHI 1 2 2? 8XO Ns? —W i we find 21 Hiw st Lh, a 8 RE A The frequency-equation therefore is 81 Tio _ ] é - = SS Me 5 on so (Ga) On, ~~ (n;?—o’) a R+ This trequency-equation has the same roots as equation (6), which if x and / have been taken O, takes the form wl ie ( wl 2a , =) @ cos — = cos — — — sin — }. 2a Ro 2a lw 2a The identity of these frequency-equations can be easily shown. Sl H? . ; : Put i=h, then (6a) takes the form i} a al Siete Ns W 1s hy = Se Ee — 0 nS a? 8? (ns? —w’) x? The sum of inverse squares of odd numbers is 3 Further, Oo : Ey dat i : , ————; therefore the first member amounts to c k ase a 1 1——+ 8— & == (0), i) Pa n—w* For tg z we have 22 eo es a 2 tg er? a a te ey ay where s is again an odd number, therefore we obtain k 2a ol 1——-+ —kig—=0 ..... .« (14) oOo wil 2a The equation (6) takes the form wl k 2a ol @ cos 1— — + ——ktg —— eee en-au (ko) 2 a leo? 2a The equations (14) and (15) have the same roots, for the vectors wl ‘ = wo and cos = do not contribute roots to (15). atl Having found the roots of (14), we can determine y. Each root STL yields a Fourter series. In the case that (=o), sin must be é combined with one frequency only. For our case we have a A, iw,t , sTx y = >, >, ——— -e sin $ 2 2 s (ns?—w+’) 1 Sa A, 1 xt = sin =R e co o oe re UG) ‘ ; ; s l ns —W, The Fourier series which is the vector of A Dae must be equal to the function whieh in § 2 appears as the vector of the same exponential. This can be shown by direct development. It is apparent that by a given frequency all the original normal coordinates are 790 § et into motion. For very great and very small values of R, the constants A in the expression (16) can easily be determined. ~. We can also use (9) and (11). Let us write (41) in the form y = emt : nl cos 2a and let us introduce the value of 2 from (9), we then find 4HT?] nt — —— t > 8 Nagas Ng TR nse —T Ros* a 1 — cos — i— sin — a as a 2H tse where d, = ————. Separating the real and imaginary parts, we find Rus aC: : : 4 FT? Sp aaa, 7 Re Regs tae Bs dé, Nett Nk — | 1 — cos — } cos ny t + sin sin nst | As i a a J, M8 , 5 Pe ap | = 1 — cos — ] sinnst — sin COS Net R a a J. gv st ( — cos ms ‘) As —sin ae B.| v a a : dy Nyt J. Nk 4 f*] ee) | = SS HS Ag —{ 1 — cos B, = Bene @) oa sre Be a = ( a a ) z Ras*ng 7 l l ae % swe “y Sma Putting fr sin dx =a, and _ dz = bs we have e e 4 0 0 and ree l (eae SS = SE R 2 l eam 2n5 SUB 4H] B ae As ——~ «at Os Ds San : 2 R i Ros*ns 2 ; ngl ; For R=o we get b= — Fei Ss Therefore B.—— = bs 2 and A, = —a,. Putting Ns A 2 Ee ts a Os == Ns R ) Bs (= — fit = iy if R t9L we have () = ial = capes i Bs Ri Ns 2k ls 8H*b, 0) SS SS SS SS i OS R IR Res*ns These series are convergent, if the conditions for the ordinary Fourtmr.series are fulfilled. We can therefore calculate a, and P, with the help of the given formulae. § 4. In the case # is a given function of the time, our equation can also easily be solved. a. First if / is constant, we have 07y Oy O°, AJ A Ge ae ai 7 l B=RJ+ | y de. 0 The current / and y ean be divided into two parts, the one depending on ¢, the other not; we indicate those parts by the indices 1 and 2. For the first part we have ~ has another value for the surrounding elements, than if », = 0. Be in the element at xyz Dive SSO DOr ed a bd B 0 0 o (4) and let us try “to determine the function g, the function / being given. Now take the mean of formula (3), a fixed value », being ascribed to yp in a certain element dv, dy, dz,. In w, y, z, according to (4) Veyz = g(&@—2,, y—y,, 2—Z,, v, dv,dy,dz,). ». - . (0) For the first member we therefore get Ht, Ys 2, v,de,dy,dz,) as jf and g do not depend on the direction of the line joining the . elements. In the integral, (5) cannot be applied to the element dx, dy, dz,; owever, this element gives Di Fi (@anyan ey) cn ay az. Further taking g (0,0,0) zero, as it may arbitrarily be chosen, we get 4 G(@ 454 132,50, 42, dy, dz,) = [ foe#rane-sumdondin de) fey? dadydz-4- e/fe —o = Dif (#141921) dx, dy,dz,. This is true for all values of », dz, dy, dz,, hence g must contain this quantity as a factor, and we obtain ae G(@ 454192) =| foe, Y— Yrs © —2) f (wyz) dadydz = flz,,4,-2,) —o Now put e«—a,=6& y—y, =, z—2z,=5, and omit the index, then for g we get the integral equation +a a5y/,2) a [Jr +§, yt, e+) o(Sy6) d&dyd> = f(xyc). . (6) For g we have Dayz = 9(ey2) Dis ss 5 oe ee from which it appears immediately that Daye v= y(ayz) v,? Cer oS 5 ((e) continuous. The integral-formulae obtained in this way are easier to deal with mathematically, and besides the integral equation (6) has been solved, this being not so easily found from the analogous sum-formula. 797 Now let us consider more closely the coefficient of g in (8). Let a molecules be present in the unit of volume, then the mean number of molecules in dv is equal to adv. If we take dv very small, there may be no or one molecule in it. The chance for one molecule l is, therefore, adv; for none 1 — adv. In the first case » = Ey a, av in the latter it is — «a, thus z a . D> = — — ar du or Baye ee eS, Ue ete tee ee (9) Introducing this into (8), we find for the two elements «,y-2, and UY Ze pv. = a — Vey Ys— Yry 25—2r) : . : . : (10) This result can be used to indicate the values of (W—NV)? = A N? for any volume. We have JIN = fra AN? = foe dv, dv- +{{ rv. da, dy; dz, dz- dy~ dz- VV VV from which applying (9) and (10) AN? =aV-+a g (@s— 2x, Ys —Yry 22 —2z) daz dys dz, dz, dy- dz. VV This holds for every size and form of V. Elaborating it for a cube with side / the dependence on |’ is seen more clearly. Putting Lf — kt, = 6, Yo — Yr =, 2% — 2 = $, and integrating only for $45 positive, by which '/, of the integral in question is found then, we get U az l Li AN* = N+ 80f {fotsnt) | { (ae dye de 000 gus Ee ee so | (PP ($4445) + lGyt+ 8+ 55) — Sud) g ds dy db. 000 79S é +] Jay) AN? ap “rr 2 = | g (ayz) dedydz — 3 {ff — gq dadydz N a/e/e aes e/eu l = oe ®, +1 ane even “77 |a°| 3) — gda dy dz — —_q dx dy dz. arg) ney Every integral in this formula is always smaller than the prece- ding one. If / is large with respect to the distance for which g has an appreciable value, there remains only the first integral. For any great volume we have > = = 1+ oda dyidz ~~ =) aes) 3. In trying to determine the function / by means of statistical mechanics, we meet with difficulties. Still something may be found about the quantities v.»- by applying the statistie-mechanieal method to our problem. Indeed statistical mechanics permit to introduce a mutual action of the elements of volume. We will avail ourselves of a canonical ensemble. We suppose the moleeules to be spherical and rigid, and to attract each other for distances which are great with respeet to their size. Elements small with respect to the sphere of attraction therefore may still contain a great number of molecules. But now we drop the supposition of the sphere of attraction being homogeneously filled for all systems (or at least for by far the greater part of them) *). In calculating the number of the various distributions, we must, for the potential energy of attraction, take into account the mutual action of the elements; whereas, in calculating the exclusion of definite contigurations of centres, we may neglect the fact that there is some correlation on the borders of the elements. For the dimensions of the elements have been supposed large with respect to the molecular diameter. The mutual potential energy of the » +7 molecules contained in an element dv, will be represented by in this formula » represents the number of molecules contained in the volume dy for the most frequent system. In this system the distribution is homogeneous. ) Cf OrwsSTEIN, Toepassing der Statistische mechanica van Gipss op molekulair- theorelische vraagstukken. Diss. Leiden 1908, p. 43 and p. 110. 799 Of course, the potential energies will not strictly be the same for different configurations within the elements, but we shall neglect this complication. Further we will represent the mutual potential energy for the two elements o and 9 by == (Oa a) (Bhat T2) Pos does: xt Hi all elements of volume being put equal. For the total potential energy we find, in this way l ey aT Sines ee oa +- %) &_(Y + To) cr. For the frequency §¢ of a system with the given distribution of molecules we find les 2 » nf ——— Selves) Sp Wr) os F(—— — Or dV) Ee «(o, dV y IT p2Odv ‘ (v1, Ww-tr, Hie Here w is the function defined in the quoted dissertation on p. 48. Supposing & & py and developing, we get, 1 1 Ila) 1 Loy ! — na Pee § (— a gee si et S—C wr a-” e Y vp da da Odv The number of molecules per unit of volume represented there by n, has been put @ in this paper. The function @ and the faculties are developed in the same way as in the quoted dissertation. The double sum in the exponent gives the forms +.» u1-y7.,and +12 ry... These forms are identical, as they consist of the same terms differ- ently arranged, further 2y., is the same for all molecules and Yt. = 0, consequently both sums vanish. The constant C' contains the factor / Tew/O do not depend on the volume by summing up (12) over all possible along with quantities which values of < (and taking into account that +r; =O) we get JN, the total number of systems in the ensemble. So we find ) 2 — Y all ae 3S ¢ oc e O— _—_ wy Vn 929 4 VA the quantity A being the discriminant of the quadratic form in the exponent. When we write 2,9,; =a, we find for the pressure p= — — 53 Proceedings Royal Acad. Amsterdam. Vol. XVII. 800 9 Den dlgw aw SS SP i SS 7) J dy A—s being very small with respect to the other factors, we may 20. V? neglect its influence in w?'). The equation of state has the same form as vAN perk WaAALs’ equation. However, the correlation is sensible in the accidental deviation; for it changes the value of 17; and rt, which vanish if the correlation is neglected, obtain values deviating from zero. Denoting by A. and by 4,. the minors of the discriminant, we have = = (k—1) “ 7,02 = — (k—1) ’) A where J is the number of elements into which the volume is divided. as if Res tea Oe) E rhe condition &4 =O is equivalent to the condition = 0; For au if we write down the determinant in some arrangement, and if we add all rows to the first row, we get a determinant of which all terms of the first row have the form l ld .dlgw 1 | a = Y yp da da Odv NPs: Strictly speaking, this is not true for some terms at the end of the row, but as we have neglected the action on the borders, we may neglect this fact too. In reality our considerations are only true for an infini- tely great volume, where this difficulty disappears, as A is then an infinite determinant. Now if De eee — U = i= yp Y da Odv oe then Ay—10) OrmitAv=="() d _dfw a ——a ~—+ —-a=0 da da (0) i ; _, dp which therefore agrees with 5 = (i), dv 1) Cf Le p. 129. 2) Cf. Ornsvery, Accidental deviations in mixtures. These Proceedings 15, p. D4, (1912). 801 The quantities rr, ete. here found are related to those mentioned above. And though a statistical deduction of the function / enter- ing into details’ may lead to difficulties, yet it is clear that statistical mechanics yield a correlation analogous to that expressed in g. If we should wish to continue the deduction of the conditions of the critical point, we should have to use higher powers of r,, which can be done without difficulty; we then find for the second condition ee) de? If we drop the supposition that the sphere of attraction is large, we can use the function %, defined in the quoted dissertation. In order to take into account the correlation, we must suppose the integrals é Gh Pon oc dan Tt, w (n,) 1 r — &/0 defining %, to depend on nz for the element in question and also on the numbers of molecules in the surrounding elements. Therefore, in general, the numbers of molecules of all elements will appear in : O9n, 9n, , but the influence of distant elements is so small that —— Ne ‘an be put zero. By considerations analogous to those used in the quoted disserta- tion, we can show that %(n,) has the form Ny Nx V, (@ dy Dy, Dy) in which n,n, denote the densities (molecular), in the elements with which V, is in mutual action. The values of all n, are equal for the most frequent system. Now we find for ¢ Ga nia (uns ny Ms ts eae where P is a quadratic form in the deviations for the various elements, containing squares as well as double products. The form might be easily indicated, but we will omit it, as it is only our purpose to show how in general the statistic-mechanical considera- tions, changed in the sense of a correlation of elements of volume, lead to formulae analogous to those given in § 2. Here too the mean square of deviation and the means of double products are represented by quotients of minors of the discriminant of P and eeu : the “Freee : this quantity itself. Here too for : =0( the discriminant vanishes. av 53% 802 4. The above considerations can be applied in ealeulating the critical opaleseence. For that purpose we use the simple method indicated by Lorentz"), whieh consists in superposing the light- vectors caused by the intluenee of every individual molecule in a point at great distance. Consider in the substance through which a beam of light passes, a volume J” great with respect to the wave-length, and take a distant point P, the direction |7P forming an angle gy with the incident Tay. All molecules lying in one plane perpendicular to the line which Take therefore a system of axes with the Z-axis parallel to this line, then the con- bisects the angle y, will cause equal phase in 7. tribution of one molecule will be 9 _ Qa B sin — (ct + 22 cost gp) ud where p. depends only on the kind of molecules, on 4 and on the distance |’P, w being the index of refraction. The number of molecules in dv dy dz amounts to (a + v) dex dy dz. The total light-vector in P? thus becomes 2 fe +r) sin = Ae +22 cos bq) da dy dz. : and the intensity pile » re _ 2a Bp? ell [J a-+ p;) (a +-v-) sin — (ct4-22, cos } gp) ud ) are on sin \- ~ sS ~— dx; - dz, dv. dy- dz-. Integrating with resp. to /, we get . 4n } - ae: # {fie -a(v,+ py.) -| v.»-! cos a (2,—<-) cos 8 y } da, dy,dz,da,dy-dz.. uA VV The-mean value of this must be caleulated. The term with », +- v- vanishes, and that with a? yields no contribution proportional to V. We introduce the value of »,»- from formula (10), and for c=t from form. (9). This gives 1) H. A. Lorentz, On the scattering of light by molecules, These Proceedings 13 p. 92 (1910). 803 — ap : ay ie ) = ( =v ) i ] i = Yes Wr, a Yrs So ez SNe Sr) diigo + MY = ali av -{- Ee [fo (Ws Ury Y UE cos 0 7] VV For a great volume one integration over VV can be performed (compare the deduction of formula (41)); further we put aV=N . Ax and for the sake of brevity —cos}gy=C, then we get {ur Ps 1 — ws ye ue Als J feos Cz (#, y, 2) dadydz 5 oie 4(t8)) The integral appearing here will be represented by G,, that of formula (11) by G. It will be seen that the deductions criticised in § 1 yield an opalescence proportional to v*,a quantity which accord- ing to the above is proportional to i + G, whereas the opalescence is proportional to 1+ G. With the aid of the integral-equation (6) we can express G and (, in the corresponding integrals of the funetion f. which we will indicate by / and F.. Integrating (6) with ah to xyz eat —o to + om, we find = [J fo wyz) da ty de (fos smi ffi + §,y +-3),2 +$) dudyde= de ne {ffi ‘(ayz) dndydz or i ean At eh od 1—F Multiplying (6) by cos Cz and again integrating, we get pa as al G. — SL (S75) azine f fosc (2+$) cos CO4- sin C (z +8) sin CS ——@ F(@+§, y+n, 248) dedydz = F,. The integral with the sines disappears because / and g are even functions; we find F. (a ek ie |) 1— Ff, In order to apply the results obtained and to test them experi- mentally, one might try to deduce f from molecular theory. This would at best be possible under very simplifying suppositions and S04 even then only an approximation can be obtained. Therefore we will take another way. As remarked in § 1, the exact value of x? for very great volumes was already known. In our notation we have =) TEP ae ; cio aN dp yeas dv where .V is the number of AvoGrapo, v the molecular volume. According to formula (4) we have In the critical point = 1. ') The formula of opalescence first arrived at by Kresom and Ensrern 1) There appears to exist a closer correspondence between the given statistic- mechanical method and the method using general considerations of probability, than perhaps might be expected. The elements of the discriminant (which is an infinite determinant in the former) agree with the function f in the latter. The former finds from this the value of ¥- vz as the quotient of a minor with that discriminant, the latter deduces this value from an integral-equation. In the critical point the discriminant vanishes, corresponding to this the FrepHotm determinant of the integral-equation is likewise zero. Thal this is the case when /’=1, appears by more closely studying the equation a (Sys) — i fo (S76) f (@-+8, y+, -+$) d§dnd§ = 0 which only permits appropriate solutions if 1= >, (i e. this is the only proper I value). For /=1 this is therefore the case with the equation (6) without second member. From the formula (15) it will be seen that form. (6) can be solved by aFourtER integral. Putting +a l| {eo ma cos ny cos lz f (wyz) dadydz = —p (m, n, 1) afte —o we have ‘ +a 1 “CC pm, n, 2) g (ayz) = ———— cos mw cos ny cos lz dmdndl. 82° JIT 1—e(m, n, 1) wo 805 (#) ee | = Top, 22°V RIT dv Ope ie Aioast eee berate. 5s 2, (16) BE DPR Pa in which represent PD distance of observation mw index of refraction, y angle of electric force in ineident light with direction of observation, will likewise be found by using in (13) the value found for instead of #.. The exact formula then will result by multiplying by 2 2) * f(ayz) dedydz. bass | yy || ro} Q 23 Representing this integral by « and introducing the value of C, we get 7 7 2 é % F— F.= 4n’ (1 + cose) { —}). te The formula of opalescence then will be: Top. ID Iss dv = = BS aed enol KC) i dp RI El\a — — + 4n*? — (1 + cos) dv vy a2 In the critical point itself it therefore is 1 2 ONS ae ere w Lop. J dv —— eG eee lee age Oe) IT Dt Ne (t + cos) The greater exactness of form. (17) as compared with (16) is 5 confirmed by the measurements of one of us (Z.). According to these measurements, which however bear upon a mixture of liquids the 1) According to this formula the proportionality of the opalescence to d~4, which holds for higher temperatures, changes continuously in the immediate neigbourhood of the critical point, into proportionality with %—2. This rea/ “getting whiter” of the opalescence should not be confused with the appurent changing of colour which is always observed much farther from the eritical point. The latter indeed is only a result of the method of observation, as is clearly proved by the measurements of one of us (cf. ZuRNIKE thesis). 806 reciprocal value of a quantity proportional to the opalescence changes linearly witb the difference of temperature 7’—7;, but by extrapolation does “not vanish for 27. “but for 777 — 10.0125 aWihen therefore for this value of 7—TZ;, the denominator of (17) is equal to zero, we can find from this, using VAN DER Waats’ equation, an estimation for ¢/,. The calculation yields : € A » = = 00,0022 or ¢ = 1,2.10—* em. The quantity «is a measure for the size of the sphere of attraction. For +x 1 — Affe T (eyz) dadydz o - (go distance to origin) whereas in the critical point of { F (wyz) da dy dz=1. ve} If f were constant within a sphere with radius R, then «* would be */, R?, and the above estimation would give el Omercits SUMMARY. 1. The known formulae of critical opalescence give an infinite value at the critical point. Efforts to escape from this difficulty have furnished formulae for the deviations of density with a dependence upon the volume, at variance with the assumed mutual independence of the elements of volume. 2. In order, to obtain formulae applicable in the critical point, it is found necessary to take into account the mutual influence of the elements of volume, it being shown that near the critical point this influence is sensible for distances large in comparison with the radius of the sphere of attraction. 3. Two functions are introduced, one relating to the direct inter- action of molecules, the other to the mutual influence of two elements of volume. An integral equation gives the relation between the two functions. 4. Corrected values are found for the mean deviations, and in the formula of opalescence a correction is introduced. The latter depends upon the sphere of attraction which can thus be calculated from observations. 5. Further it is shown that the same results may be arrived at by taking into account the mutual influence of the elements of volume in the deductions of statistical mechanics, Groningen, Sept. 1914. A. A HIJMANS VAN DEN BERGH and J. J. DE LA FONTAINE SCHLUITER. ,, The identification of traces of bilirubin in albuminous fluids.” Bilirubin from human ascites fluid 3ilirubin from human ascites fluid (Aether-method) (Chloroform-method) Proceedings Roval Acad. Amsterdam, Vol. XVII. 807 Physiology. -- “Zhe identification of traces of bilirubin in albu- minous fluids.” By Prof. A. A. Hismans vaAN bEN BrrGu and J. J. pe ua Fontaine Scuiurrer. (Communicated by Prof. H. J. Hampureer). Several investigators have tried to demonstrate the presence of slight quantities of bilirubin in albuminous substances, for instance in normal human bloodserum. Most of them did this by adding various oxidizing substances, either directly to the serum or to an alcoholic extract of the latter. The first oxidation-stages of bilirubin having a green or a blue colour, the presence of bilirubin was regarded as established if an addition of these oxidizing substances eave rise to a green or a blue colour (OpeRMAER and Popper, STEIGER, Gitpert') and others). AvucnHé*) employed a much more reliable method based on the fact that bilirubin, in alkalic solution in the presence of oxide of zine, is changed, by careful oxidation with iodine, into a substance with a characteristic spectrum. This reaction had already been deseribed by Sroxvis, but Avcné, who mentions Sroxvis’ work, owns the merit of having stated accurately the con- ditions required if the reaction is to take place with absolute cer- tainty, so that it may be used to demonstrate the presence of bilirubin. Undoubtedly the reaction of Sroxvis-AucHE can be used with success. Only the spectrum-line is very slight in the case of the small amounts of bilirubin dealt with in this treatise: if the presence of bilirubin is to be demonstrated in normal human serum by means of this method, the layer of fluid intended for spectroscopic investigation is to have a thickness of ten centimetres. And even then the result is not always a positive one. For quantitative determinations this method cannot be used. Bieri extracted the serum at once with chloroform and carried out his reactions with this *). The reaction of Enrucn has supplied us with an excellent means of tracing bilirubin in bloodserum and other albuminous fluids and of determining it quantitatively ‘). The characteristic difference in colour between av alkaline and an acid medium increases its relia- bility, whilst the reaction is an extremely sensitive one. It must, 1) OBerMAWER u. Pepper. Wiener Klin. Wochenschr. 1908. Sreicer. Dissert. Ztirich 1911. Gitpert. See for his werks the bibliography in: Clinique médicale 1910/1911. 2) Aucueé. Compt. rend. Acad. d. Sciences 108. 3) Bieri. Folia Haematolog. 1906 ILI. 189. ') Hismans van pEN Berg and Snapper. Deutsch. Arch, f. klin. Med. 1913, 808 however, be admitted that neither this nor any other colour-reaction enables us to identify the presence of bilirubin with absolute certainty. The possibility of other substances contained in the serum giving the same reaction with the diazo-body may be esteemed less probable, it cannot with absolute certainty be denied. As far as we know it has hitherto been found impossible to isolate bilirnbin from normal human serum, which would have afforded an incontestable proof of its presence. HAMMERSTEN has attempted it’). But though in a great majority of cases he obtained fine bilirubin-erystals from horse-serum, he never succeeded in ob- taining them from normal human serum. From the terms used in the latest edition of his Handbook of Physiological Chemistry we eather that this investigator is not quite convinced yet of the presence of biluribin in normal human serum. With a view to researches on anhepatic bilirubin-formation we needed a method which would enable us to identify with absolute certainty the presence of small quantities of bilirubin in bloodserum, exsudates and transsudates, if possible by obtaining the pigment in the form of erystals. After some experiments we have succeeded in this, starting from the property of bilirubin — which we have not found mentioned anywhere — of dissolving readily in acetone. To 10 em*. of bloodserum 20 em’. of pure colourless acetone are added. An albumen precipitate is formed, which is centrifugalized. The fluid at the top, coloured more or less intensely yellow, contains all the bilirubin and only traces of albumen. This liquid is evaporated in vacuo at the ordinary laboratory temperature. If one has a good vacuum-pump at one’s disposal the liquid soon begins to boil; after some minutes the acetone is evaporated. A watery fluid remains in which, besides other serum-substances, all the bili- rubin is dissolved. Then the fluid is shaken 2 times or more with aether to remove the fatty bodies as much as possible. These pass into the aether which is pipetted. The last traces of aether are removed in vacuo. The aether may of course also be removed by means of a separatory. Then a certain amount of chloro- form e.g. 2 em*. are added, the fluid is slightly acidified with HCl and shaken. The bilirubin then passes into the chloroform. By centri- fugalization the watery fluid can easily be separated from the chloro- form. The chloroform is washed thoroughly with water to get rid of all the hydrochloric acid and centrifugalized onve more, the water being removed by means of a separatory or by pipetting. Traces of water, however, remain mixed with the chloroform, which sometimes renders ; 1) Hanmarsren, Maly’s Jahresber. 1878 Il. 119. 809 the fluid slightly troubled. These traces of water are removed by shaking with glowed sulphate of sodium. The latter is removed by filtration. The result is a very pure solution of the yellow pigment in chloroform (solution A). It may be easily proved that this yellow pigment is bilirubin. 1. If the chloroform solution is shaken with diluted KOH or NaOH the pigment passes into the latter, while the chloroform loses its colour (solution £). 2. If now some acid is added till the fluid reacts distinctly as an acid, then the fluid at the top loses its colour, the pigment passing into the chloroform at the bottom. 3. If to the alkaline solution (see sub 1) HNO, containing some HNO, is added, the result is the well-known colour-play of the reaction of GMELIN. 4. If a slight quantity of a diluted iodine-solution in alcohol (1: 100) is carefully poured on to the alkaline solution, a blue ring is formed. 5. If to the alkaline solution first an equal volume of alcohol is added, and then +} of the original volume of the diazo-mixture ot Enriuicu, a red colour is the result. An addition of a few drops of concentrated HCl changes the red colour into blue. _All these reactions together, prove conclusively that the pigment obtained in the above way is indeed bilirubin. Crystals of bilirubin can be easily obtained from the pure chloro- form-solution (sol. A) in the following manner. The latter is poured ont into a wateh-glass which is covered with another watch-glass and placed in the ice-safe. The chloroform evaporates slowly and on the watch-glass the microscopically visible, pretty, yellow bilirubin- crystals are left. When HNO, containing HNO, is added, these crystals present under the microscope the reaction of Gmrnin. We can also dissolve the yellow crystals again in some solvent (chloroform, dil. NaOH ete.) and carry out the above-mentioned reaction with them. If one has no good vacuum-pump at one’s disposal the method ean also be applied with the following modification suggested by Dr. SNAPPER. 10 em* of bloodserum are precipitated with 20 em* of acetone. The albumen-precipitate is centrifugalized. To the pipetted upper- fluid some drops of water are added; then this fluid is washed carefully with aether a few times, to remove the fatty substances as much as possible. These volumes of aether are removed with the pipette every time. Then some drops of ice-vinegar and 1 em* 810 of aether are added to the fluid. All the bilirubin passes into the mixture of ice-vinegar and aether, which separates entirely from the fluid underneath. If this yellow-coloured aether is pipetted and placed in an ice-safe in a loosely covered watch-glass, we likewise observe that crystals are formed. The accompanying ~ picture is a micro-photograph of bilirubin crystals which we obtained from the ascites-fluid of a heart-patient, and from normal human serum. Attempts to produce bilirubin-crystals by the above-mentioned method from the intensely yellow-coloured serum of two icterus- patients, led to a remarkable experience. If namely we placed the chloroform-solution which, as appeared from various reactions, con- tained much bilirubin, in the ice-safe, for the purpose of a slow evaporation, the yellow colour at a certain moment when, owing to the evaporation of the solvent the concentration had reached a certain value, suddenly passed over into a green one, evidently by a change of the bilirubin into biliverdin. The same phenomenon occurred when we evaporated the chloroform-solution in vacuo. It must be distinctly understood that this occurred only with the solution obtained from the serum of patients suffering from obstructive jaundice. We cannot give an explanation of this phenomenon. Most likely the icterus-serum contains substances promoting the oxidation of bilirubin into biliverdin. Botany. — “Gummosis in the fruit of the Almond and the Peachal- mond as a ‘process of normal life.” By Prof. M. W. BrisErinck. (Communicated in the meeting of September 26, 1914). [t has hitherto been generally accepted that the formation of gum in the branches of the Amygdalaceae always is a process of patho- logical nature. I have found that this opinion is erroneous, and that gummosis occurs normally in the fruits of the Almond (Amygdalus communis) and the Peachalmond ( Amygdalus amygdalo-persica ) DunameL Dumoncrav. *) 1) In some Dutch nurseries the peachalmond is simply called *Almondtree”. The difference is in fact very slight as it consists only in the drying up of the almond fruit before the epicarp opens, and the position of the flowers in pairs, whereas the fruit of the peachalmond remains fleshy even at the dehiscence, and its flowers are mostly single. Between leaves, flowers and branches no con- stant differences are found. GRENIER et GopRon (Flore de France T, 1, Pag. 512, 1848) call the peach- S11 Contrary to what might be expected the phenomenon is the more obvious as the trees are better fed and more vigorous. In specimens on sandy grounds it can only be observed with the microscope. As gummosis is the effect of a wound stimulus, if is of import- ance that this process also takes place in the normal development of the healthy plant. The subject is moreover of practical interest. All the chief facts relating to gum formation can almost unchanged be apphed to the production of gums in general, of gum resins, and of resins, among which are substances of great medical and technical value. As the study of the influence of parasitism has made it possible to produce gum, and no doubt many of the other sub- stances mentioned, in a more rational way than has been done till now, a short review of the whole subject seems not superfluous. Wound stimulus as cause of gummosis. Poisoning, and parasitism also causes of this stimulus. Gummosis in the Amygdalaceae is a process of cytolysis, whereby young cells, freshly sprung from cambium or procambium, and sometimes also young parenchyma, are more or less completely dissolved ‘and converted into canals or intercellular spaces, filled with gum. In dissolved parenchymatous tissues usually remains of not wholly disappeared cell walls are found; the gum of the phloem bundles is more homogeneous, but always the microsomes of the dissolved protoplasm are found. The nitrogen of the gum springs from the dissolved protoplasm. Formerly we proved’) that by such different causes as poisoning, parasitism and mechanical wounding gummosis may be experimentally almond Amygdalus communis var. amygdalo-persica. At present the name Amygdalus persicoides (Koon, SERINGE, ZABEL) is also used, as in the Hortus of the University of Leiden. The opinion that it is a hybrid is not sufficiently founded. When grown from seed the tree seems constant (see Mreter’s Conver- sationslexikon, Articles “Mandel’’ Bd. 11, p. 853 and “Pfirsich” Bd. 13, p. 782, 1896) and identic with the “English almond”, of which Darwin reproduces a stone (Domestication, 2nd Ed., Vol. 1, p. 858, 1875). The fruit is fleshy and bursts open, the kernel is edible, not bitter. At Delft sowing experiments have been going on a long time already, but under unfavourable circumstances. The root cannot resist the winter temperature of the soil, hence, grafting on the plumtree is required. 1) M. W. Bevertnck et A. Rant. Excitation par traumatisme et parasitisme, et écoulement gommeux chez les Amygdalées. Archives Néerlandaises, Sér. 2, T. Il, Pag. 184, 1905. — Centralblatt f. Bakteriologie, 2te Abt., Bd. 15, Pag. 366, 1905. — A. Rant: De Gummosis der Amygdalaceae. Disserltatie Amsterdam, Bussy, 1906. provoked in many Amygdalaceae, as almond, peachalmond, apricot, peach, plum, cherry, and bird’s cherry. But these three groups of causes may all be considered from one single point of view, by accepting that gummosis is always the effect of a wound sumulus, proceeding from the slowly dying cells, which are found as well in every wound, as at poisoning and parasitism. These dying cells may change into gum themselves, but besides, exert their influence on cambium tissues to distances of some centimeters. This distance-influence is the principal effect of the wound stimulus. But poisoning by sublimate or oxalic acid, introduced under the bark, can as well excite gummosis as an incision or a wound by burning or pricking. Neither the dead cells nor the poison are the active factors here; the stimulus proceeds from the slowly extinguishing cells, so that gummosis is essentially a necrobiotic process. Probably the dying cells, after the death of the protoplasm, give off an enzyme or enzyme-like substance, a lysine, fixed during active life, but, which being freed by necrobiosis and absorbed by the young division produets of the cambium causes their cytolysis. This reminds of the eytolysimes of the animal body, originating when foreign cells are introduced, which liquefy the corresponding cells, for example the haemolysines which dissolve the red blood-cells. Furthermore of the bacteriolysines and of cytase, the enzyme of celiulose. If the hypothesis of the existence of a “gumlysine” is right, — and I think it is, — this substance must be of a very labile nature, for when bark wounds are infected with gum, quite free from germs of parasites, no more abundant gummosis is observed than at mechanical wounding only. But a difference, however slight, will certainly exist. Gummosis produced by wound stimulus. The influence of this cause is best studied in the following experiment. A deep wound, penetrating into the cambium of a branch of almond or peach, commonly soon heals completely, but it may be that gum flows from the wound. This is the case when the trees are in sap, thus in February or March at temperatures above 20° C. and below 33° C. The experiment succeeds best with cut branches in the laboratory. When the wounds are made in the open air in that season no gummosis ensues, the temperature then being too low.) In 1) If the wounds are infected with Corynewm, an extremely copious gum production follows in spring, as the parasite then finds abundant food in the branches. There is, however, no season when wounds, infected with Corynewm, do not sooner or later yield gum. 813 summer the cambium of the still longitudinally growing part of young green branches may be caused to form gum by punctures or incisions, but these wounds heal quickly, except when ‘kept open” by Coryneum or other parasites. As to thicker branches, wounded in spring, the microscope shows the following. Around the wound a great number of gum canals are formed in the cambium, about parallel with the axis of the branch, some centi- meters long, which become the thinner and shorter as they are more remote from the wound. The canals are separated by the medullary rays, which are with more difficulty converted into gum than the phloeoterma. All the gum canals together form a kind of net- work, whose meshes are filled by the medullary rays. The whole network has the shape of an ellipse, the “gum ellipse’, the wound lies in the lower focus towards the base of the branch. The stimulus extends over the ellipse, evidently farthest in the direction of the branch, less far towards the base and sideways. So it may also be said that the wound stimulus extends farthest opposite to the “de- scending” current of nutrient inatter, following the phloem bundles, or along with the “ascending” water-current, following the wood. Evidently the gum canals are more easily formed in the better fed ceils above the wound than in those beneath it, where the nutrition must be worse. This is especially obvious in ringed branches. Wounds in the cambinm, directly above the ring produce much more gum than those immediately below. ’) Under ordinary circumstances the branches, after simple mechanical wounding, are soon completely healed, and if the cambium at the outside of the gum canals then again begins to produce normal secondary wood, the gum canals may later be found back in the wood itself.*) Evidently the healing takes place as soon as the stimulus ceases, and so it is not strange that when it continues by poisons or parasitism the gum production also continues. 1) The nature of the power, by which the food transmitting, ‘“descending” sap current moves through the phloem bundles, is not known, It is thus not impossible, that if the cause of gummosis is of a material nature, a lysine, moving through the tissues, it is able to run in opposition to the ‘descending’ current. I think, however, that the extension of the stimulus does not go along the phloem but along the xylem bundles and the young wood, with the “ascending” sap. 2) [ have never seen distinct gum canals in the secondary wood, but according to the descriptions they occur eventually. sl4 Parasitism as cause of guinmosis. The connection between wounding and parasitism. Wounds in peach branches treated with poisonous substances, such as sublimate, produce gum much longer and more copiously than the like wounds without sublimate. Other poisons have quite the ‘same effect. Now it is clear that the direct intluence of para- sitism on the organism must be sought in the action of some poisonous substance. Hence it seems ceriain that what these three causes have in common, namely necrobiose, or the slowly dying of the cells surrounding the dead ones, is the base of gummosis, and that parasitism, where necrobiose lasts as it were endlessly, must be the most powerful instigator of the process. That this simple view of the question has not yet taken root in science is proved by the most recent treatise on our subject by Mikoscu,') illustrated) with beautiful anatomical figures. After the publication of Dr. A. Rant and myself of 1905, he described the relation of mechanical wounding to gummosis. But he did not think of poisoning experiments, nor has he any belief in the influence of parasitism on gum formation. Wisner, in his recently published paper on gums in the new edition of his ‘“Rohstoffe des Pflanzen reichs’, is also of the same opinion as Mixoson. For my. object a short discussion of a few examples of parasitism will suffice. The little caterpillar Grapholitha weberiana makes borings into the bark of plum and apricot, and if the outermost corklayer is removed by shaving it off, the butterfly finds so many fit places for deposing its eggs, that the larvae creep in by hundreds and make new borings from which later the gum flows out. These holes are coated with a layer of slowly dying cells, whence the stimulus extends, which produces the gum canals in the contiguous “cambium”. By cambium I simply understand the not yet differentiated division products, “young wood” and young phloeoterma. The necrobiotic cells, clothing the continually extending holes in the bark, and the great numbers of new individuals of the caterpillars, make the gum production a chronical process. To explain the formation of the enormous quantities of gum produced in this way, it seems only necessary to think of mechanical wounding and not of any special excretion from the animal. But it must be noted that the space, where the caterpillar lives during its 1) Untersuchungen tiber die Entstehung des Kirschgummi. Sitzungsber. d. Kais. Akad. d. Wiss. in Wien. Mathem. naturw. Klasse. Bd. 115, Abt. 1. Pag. 912, 1906. S15 erowth, namely a vertical narrow canal in the inherbark, very near to the cambium, could not possibly be imitated artificially. a Fig. 1. (Natural size). Gum producing peachalmond in September, whose summit is cut off; the gum from the gum canals is afler drying, swollen by moistening with cold water. Much more common and interesting than the animal parasites are the gum producing Fungi of the Amygdalaceae, five of which are found in our country.') The commonest and most vigorous is Cor- 1) Coryneum beyerinckii OupEMANS, Cytospora leucosioma Prrsoon, Monilia cinerea BonorDEN, Monilia fructigena BoNnoRDEN and Botrytis cinerea PERSOON (see Rant, l.c. p. 88). German authors also mention bacteria as instigators of cummosis, | never found them. a4 Proceedings Royal Acad. Amsterdam. Vol. XVII. SI6 yneum bejerinckii Ouvemans (Clasterosporium carpophilum Apgru.).") Pure cultures of Corynewn in bark wounds of almond, peachal- mond, peach, cherry, plum, bird’s cherry, sloe, virginian plum, develop with remarkable quickness and soon make the bark die off, evidently in consequence of the secretion of a poison. Around the dead cells ihe necrobiotie are found from which the stimulus issues, which, penetrating into the cambfum .in the usual way, forms gum canals in the young wood. Many mycelial threads of the parasite itself are then cytolised and converted into gum. I think this facet remarkable and a strong argument for the material nature of the stimulus. Undamaged branches are with difficulty infected by the parasite, but it is easy, even by very slight wounds and artificial infection, if — only the wounds be numerons, to obtain great quantities of gum. This circumstance explains why nursery men dread wounds in the trunks and branches of stone-fruit trees. In the green shoots, especially of the peach, the formation of anthocyan is observed in’ the enfeebled tissue around the wounds infected with Corynewim when exposed to sunlight. *) The supposition that secretion products of the parasitic caterpillar or the Fungus could be the direct cause of the stimulus, is contrary to the positively existing relation between mechanical wounding and o1UNMOSIS. Gum canals in the fruitilesh of almond and peachalnond. To the preceding facts, long since stated, I wish to add the following. Already in my first paper of 1883 I called attention to the cireum- 1) BetERINCK, Onderzoekingen over de besmettelykheid der gomziekte bi planten. Versl. d. Akad. v. Wetensch. Amsterdam, 1883. — Contagiosité de la maladie de gomme chez les plantes. Archives Néerlandaises, 1é Sér., T. 19, Pag. 1, 1886, — Cc. A. J. A. OupEMANS, Hedwigia, 1883, N°. 8. — Saccarpo, Sylloge Fungorum, Vol. 3, Pag. 774, 1884. — AprERHOoLD, Ueber Clasterosporium carpophilwm (LEy.) ADERH. und dessen Beziéhung zum Gummifluss des Steinobstes. Arbeiten der Biolog. Abt. am Gesundheitsamte zu Berlin. Bd. 2, Pag. 515, 1902. ADERHOLD has experimented with pure cultures of Corynewm, which | had made and sent him. He himself has not executed any isolations of gum parasites. His determination as Clasterosporium amygdalearum (L&y.) is thus founded on the imperfect de- scriptions from the older mycological literature, in which OupEMANS was no doubt better at home than he. Like Linpau [ reckon Clasterosporiwm to another family than Coryneum. 2) The apperance of anthocyan in the light is commonly a token of diminished vitality and often a consequence of necrobiose in the adjoining cells. Hence, wounds, poisons and parasitism cause anthoeyan production in the most different plants. 817 stance, that in the fruit-flesh of the peachalmond, and as I may add now, also in that of the almond itself, there is a system of gum canals, precisely corresponding to that of the vaseular bundles. Of these the phloem bundles are converted into gum canals by cytolysis, either entirely or with the exception of the outer protophloem ; the gum canal (gp Fig. 2 and 3) thus, is always immediately contiguous to the woody bundle 2d. Fig. 2 (38). Gum canals in the transverse section of the fruit-flesh of a peachalmond : ha. hairs on epidermis ; 20 dermoidal tissue; bp chlorophyll-parenchyma; #/ xylem bund- les; ph phloem bundles; gp gum canals sprung from phloem bundles. Fig. 2 and 3 are reproductions from my above mentioned treatises of 1883 and 1886. The presence of gum in the canals of the fruit is easily shown. In August or September the summit of a peachalmond fruit is cut off and the fruit, or the branch with the fruit, is placed in water. After some moments all over the section droplets of gum are seen evidently issuing from the vascular bundles. As these bundles are distributed through the fruit-flesh, running longitudinally and transversely, and are partly reticulated, the number of droplets is very great and they are of different size. In particular near the stone they are big. If in August the gum is allowed to flow out in cold water it dissolves completely or nearly so. In September the dissolving is nO more complete. By drying the gum, its solubility in cold water gets almost lost, but it continues in hot water. From lateral incisions also much gum flows out. In Fig. 1 the drops are represented after drying, followed by swelling up in cold water. Although this gum does not only consist of dissolved wall material 54* $18 but also of cell contents, the microscope can only detect fine granules, evidently corresponding to the microsomes of the protoplasm, which are not dissolved during the eytolysis [ could) not find back the cell nuclei in the gum, but in the cells of the not yet cytolised phloem bundles, they are neither perceptible. As under normal cir- cumstances the gum does not flow out, ifs volume must be about as great as that of the phloem bundles which are cytolised. It is, however, certain that the capability of the gum to swell up by imbibition is much greater than that of the cell-tissue which gave rise to its formation. It seems thus certain that imbibition with Nie Fig. 3 (360). Gum eanal with surrounding ; gp gum; x/ xylum bundles, unchanged; ph non- dissolved cells of the phloem bundles; cd thread- shaped cells in a gum canal, originating from the phloem bundles. sufficient access of water must lead to a perceptible pressure and also. some thickening of the fruit-wall. This must promote the opening of the fruit as well as the remarkable detaching of the stone, although the required mechanical power for these processes must, no doubt, chiefly be the tension of the tissue of the paren- chyma of the fruit-wall existing independently of the gummosis. Finally the stone is found quite loose within the fleshy shell, which mostly opens like a bivalvate mollusk, but sometimes shows three or four fractures. The vascular bundles, which pass from the fruit- flesh into the stone, are thereby torn off clear from the stone. At the base the separation seems provided for by an intercepting layer, as at the fall of leaves. 819 The portion of the phloem bundles within the stone of the peachal- mond is never converted into gum; in the almond itself such gum is found in rare cases inside the shell. Wound gun in the fruit-wall as a consequence of mechanical stress of the tissue. Gumming almonds. In many cases real wound gum is found in the fruits of the almond and the peachalmond, not proceeding from the gum canals but from fractures in the parenchyma of the fruit-flesh. Its origin must undoubtedly be sought in the tension or stress of the tissue, which causes the opening of the fruit. An additional circumstance, however, is required, namely a loss of vital strength, by which the regenerative power of the tissue that coats the fracture is annihilated. The therefrom resulting incapability of regeneration is associated with the ripening of the fruit in a way not yet explained and should rather be attributed to superfluous than to poor nutrition. Parasitism is wholly absent in the production of wound gum from the parenchyma of the fruit. The fracture is mostly at the side where the two edges of the carpels are grown together and the fruit later opens. Not seldom in this case is wound gum seen to flow spontaneously from the base of the fruit along the short peduncle. In other cases the wound is at the side of the middle nerve of the carpel. Always the edges of the fracture are coated with cells in a condition of necrobiose, which is evident by their quickly colouring brown at the air, which normal living cells do not. These necrobiotic cells and the adjoining tissue produce gum. With the microscope not quite dissolved cell- walls may be found in the gum, showing that the cells were about full-grown when the process began. In common almonds gum is sometimes found within the hard shell,') and eventually part of the kernel itself is then also changed into real wound gum with still recognisable remains of the cell- wall. In such almonds the phloem of the vascular bundles, whieh run through the stone to the funiculus, is always changed into a eum canal, so that the gum can reach the surface of the young seed. If we suppose that gummosis originates by the action of a cytolvsine, if seems very well possible, that the lysine which has flowed inward together with the ‘canal gum’, is able to attack the developing 1) The small quantity of gum found, especially in “hard almonds”, at the surface of the shell, proceeds from the gum canals of the fruitflesh. The sugar Jayer which covers the shell of the ‘soft’ species is dextrose. 820 seed and is yet too labile to be demonstrated by infection of bark wounds with gum. Experiments in this direction may perhaps be effected with the peachalmond. Wound stimulus as factor of development. Formerly I thought that the presence of gum canals in the fruits was accidental and should be explained by parasitism, although I could not find any parasites. In later years, with better knowledge, 1 again examined the gum canals in the peachalmond and their surroundings repeatedly. Never did I find a fruit without them, but they were not equally developed in different trees from different gardens. In specimens of sandy grounds they can sometimes only be found with the microscope. Neither mucroscopically nor by experiments has it been possible to detect gum parasites. This makes it quite certain that in the formation of gum eanals parasitism is excluded. *) The great ease wherewith mechanical tension causes wounds in the fruit-flesh of the peachalmond, gives rise to the supposition, that the normal gum canals may be the product of some hidden wound stimulus. If this supposition is true, ave cannot think of wounding in the common sense of the word. When the flowers fall off, a ring-shaped wound forms around the base of the young fruit, but this is a normal process, taking place in an_ intercepting layer and soon followed by complete healing. In the flowers of peach, plum, apricot, cherry, we observe the same without any formation of gum canals in the fruit-flesh. Moreover, although the peculiar structure of the layer between the woody peduncle and the stone, along which the ripe fruit detaches, reminds of rent tissue, no gum is formed at that spot and the layer also exists in the other stone-fruits, where no gum canals occur. So long as nothing else has been proved it must therefore be accepted that in the phloem bundles of the fruit of the peachalmond, where cytolysis takes place, the same factor of development is active as that, which gives rise to the pathological gum canals in the cambium of the branches. This leads to the conclusion, that the wound stimulus belongs to the normal factors of development of this fruit, although nothing is seen of external wounds. When considering, that the phloem bundles are built up of extremely thin and _ soft-walled cells, ') The supposition, sometimes met with in literature that the gum of the Amyg- dalaceae should consist of bacterial slime is quite erroneous. That parasitic bacteria eventually occur as gum parasites, as is stated by some authors, I do not think impossible, although till now I only found caterpillars and Fungi as active agents, 821 it is conceivable, that by great tension of the tissue in the surrounding parenchyma, they undergo strain and pressure causing mechanical rupture and necrobiose, centre and prey of the wound stimulus being the phloem bundles themselves. This conception is in accordance with the fact that the gum canals are broad in the fruits of well-fed trees on rich grounds, which have a hard and solid flesh, wherein stress and strain are certainly very great. Only here and there remains of the protophloem along the gum canals are still to be found in sueh fruits. But in the softer fruits of sandy soils, along the much narrower gum canals not only the protophloem is still present, but also stripes of the secondary phloem. Summarising we come to the following conclusions. Mechanical wounds in growing tissues of Amygdalaceae will some- times heal directly, sometimes after previous gummosis. The chief tissue, which is transformed into gum is the young secondary wood newly sprung from the cambium and not yet differentiated. By the wound stimulus a network of gum canals is formed around the wound. In thick branches, with a bark wound, this network has an elliptical circumference, the wound being in the lower focus of the ellipse, If the stimulus is removed by the cure of the wound, the cam- bium again continues to produce normal secondary wood, so that afterwards the gum canals may be found in the wood itself. If the stimulus continues the gum formation also becomes lasting. The stimulus issues from the cells that die slowly by wounding, poisoning or parasitism. Probably a cytolysine flows from these cells into the young wood or the procambium; these bind the lysine and liquefy to gum. Hence, gummosis is caused by necrobiose. Young medullary rays and phloembundles are with move difficulty converted into gum than the young secondary wood. But in the fruit-flesh of the almond and the peachalmond it is the phloem which changes into gum. The protophloem of the bundles often remains unchanged. Although gummosis in these fruits belongs to their normal develop- ment, a wound stimulus is nevertheless active. This stimulus springs from the strong tension in the parenchyma of the fruit-wall, which gives rise to tearing, necrobiose and gum formation in the delicate tissue of the phloem bundles. Consequently the wound stimulus is here a normal factor of development. It might also be said that the almond and the peachalmond are pathological species, but thereby nothing would be explained, 822 Chemistry. — “The allotropy of Lead.’ I. By Prof. Ernst Conen and W. D. Hinprrman. (Communicated in the meeting of Oct. 31, 1914.) 1. Indications concerning the existence of allotropic forms of lead are found not only in the earlier chemical literature. Fourteen years ago Ernst Cowen’) pointed out in his studies on tin a clause in Piorarcr’s (50—120 A.D.) Symposiaca (VI, 8) in which allusion is made *) to the fact that lead is sometimes disintegrated spontaneously at low temperatures. This clause runs as follows: ‘No, the craving for food is not caused by the cold, but in the body something takes place similar to that which happens with metals in a very strong winter. There it is seen that cooling not only causes congealing, but also melting, for in strong winters CKOvEL o2(3dov (pieces of lead) occasionally melt away, consequently something similar may be supposed to take place in the intestinal process, elec... .” Moreover THESOPHRAST (390—286 B.C.) mentions such phenomena in his book aeQi AVQdS: “xatTitEQoY yo uci zat WoAUBdoy Ydy TaxFvae tv TO IIcvt adyou xa yEmoOrog drtog veavizot, yadxov dé Oayiva.” (It is told that tin and Jead melted sometimes in the Pontos when it was very cold in a strong winter, and that copper was disintegrated. 2. Samre-Ciaire DevitLe*) stated that the density of lead is a function of its previous thermal history. He gives the following figures (water at 4° — 1; Temp. ?) After quick cooling of molten lead 11.363. er slow - * A ellen nae In a second experiment he found: Density of lead electrolytically deposited 11.542. After melting and rapid cooling 11.225. About the value 11.542 he says: “Mais telle est la rapidité avec laquelle se carbonate a l’air ce plomb extréme- ment diviseé, quil a fallu le transformer en sulfate pour en déduire ensuite le poids de la matiére employée. Cette complication introduil-elle quelque incertitude sur le premier nombre, ou ne doit on pas plutot ladmettre comme représentant la densité de ce plomb parfaitement cristallisé ?” 3. These values as well as others given in earlier literature have to be aecepted with reserve as generally no data are given about 1) Proceedings of the meeting of Jan. 26, 1901, p. 469. Zeitschr. f. physik. Chemie 36, 513 (1901). *) PLurarcut Chaeronensis varia scripta quae moralia vulgo yocantur. Lipsiae, ex officina Car. Tauchnitii 1820, Tomus IV, 339, 5) ©. R. 40, 769 (1855), Prof. ERNST COHEN and W. D. HELDERMAN, ,,The Allotropy of Lead I”. (Natural size). Proceedings Royal Acad. Amsterdam, Vol. XVII. 823 the purity of the material experimented on and as there often exists some uncertainty concerning the method whereby the density has been determined. 4. Kanipaum, Rotn and Siepier') found the density of a pure 91° specimen of lead prepared by distillation in vacuo to be do 11.541. 5. The values given by different authors for the specific heat of lead vary within wide limits, as may be seen from the table given in Arneae’s Handbuch der anorganischen Chemie.*) Moreover it may be called to mind that Le Verrier’) stated, that the specific heat of lead is a function of its previous thermal history. 6. The facts mentioned above as well as the investigations of Storpa, *) and those of Orro LEHMANN *) render a new investigation of the subject very desirable. ‘ 7. A year ago we carried out some experiments in this direction. As the results were negative we experimented with other metals, which yielded a more favourable result. Since a fresh investigation on lead has given positive results, as will be proved below, we give here also a short description of our earlier experiments, which taken together with the new experiments furnish a confirmation of the results obtained by us in the case of other metals (bismuth, cad- mium, copper, zinc, antimony). 8. Our experiments have been carried out with lead which contained only 0.001 per cent of copper and 0.0006 per cent of iron (Blei-‘‘KaaLBAUM’-Berlin). °) The metal was turned into shavings on a lathe and washed with dilute nitric acid, water, alcohol and ether. After this it was dried in vacuo over sulphuric acid. 9. The density of this material was found to be 0 P= de, 116398; b. 11.330, _ We put the, metal into an aqueous solution of PbCl, and kept it for 48 hours at 100°. After washing and drying it, we found: 1) Zeitschr. f anorg. Chemie 29, 177 (1902). 2) Bd. 3, 2te Abteilung, p. 633 (Leipzig 1909). 3) Comp. Ernst Couen, Proceedings 17, 200 (1914). 4) Journ. f. prakt. Chemie 94, 113 (1865); 96, 178 (1865). 5) Zeitschrift f. Kristallographie und Mineralogie 17, 274 (1890). Ernst CoHen and Karsusr Inovyi, Zeitschr. f. physik. Chemie 74, 202 (1910), 6) Mytius, Zeitschr. f. anorg. Chemie 74, 407 (1912), 824 d aa G5 1aES 297 d. 11.328, Another part of the original material was melted and chilled in a mixture of alcohol and solid carbon dioxide. The determination of the density gave the following result : 25° ioe e. 11.330, fF: dio33; 10. As our determinations had been carried out with an accuracy of 3 or 4 units in the third decimal place, it is evident from the experiments described above that we had not been able to detect. any transformation in the lead experimented with. 11. However, some months ago Mr. Hans Heuer at Leipzie was kind enough to call our attention to some phenomena which he described in the letter which follows : “Gelegentlich eines Vorlesungsyersuches, der einen sogenannten ‘Bleibaum” zur Darstellung bringen sollte, bereitete ich eine Lésung von 400 gr. Bleiazetat in 1000 ec. Wasser unter Zusatz von 100 ce. Salpetersiiure (spez. Gew. 1.16), die als Elektrolyt bei der Bleiabscheidung diente. Als Elektroden dienten bei dem Versuch Stiicke aus reinem Blei. Diese -Bleistiicke bliehen nach der Elektrolyse etwa 3 Wochen in der Lésung stehen. Als ich sie alsdann herausnehmen wollte, bemerkte ich, dass sie ihre weiche, dehnbare Beschatfenheit véllig verloren hatten und eine spréde, bréckelnde Masse geworden waren. Der Gedanke, es hier mit einer stabilen Modifikation zu tun zu haben, erschien mir um so wahrscheinlicher, als das spréde Blei ganz dem grauen Zinn gleicht, beide Metalle zu der gleichen Gruppe des periodischen Systems gehéren und Metastabilitét unserer Metalle nach Ihren Forschungen nichts Befremdliches mehr ist. Kurze Zeit darauf brachte mir ein Kollege ein Bleikabel, das an verschiedenen Stellen eine weisse pulvrige Beschaffenheit zeigte von ganz ahnlicher Art, wie ich sie an den vorhergenannten Bleistiicken beschrieb. Wir machten darauf den Ver- such reine Bleistiicke unter konzentrierle Salpetersiiure zu bringen und sie mit ein wenig unseres spréden Bleies zu impfen. Der Erfolg blieb nicht aus: nach wenigen Tagen hatten sich betrachtliche Teile der Bleistiicke zu der bréckligen Modifikation verwandelt.” Mr. Hetiwr kindly invited us to continue these investigations ; repeating his experiments with our pure lead we were able to corro- borate his statements. 12. The lead was melted, chilled in water and cut into small blocks (8,5 & 2 x 0,5 em.). We put them into glass dishes which were filled up with the solution mentioned by Henier. The dishes were covered with glass plates. The temperature of the solution was 15°—20°. The addition of some nitrie acid has the effect that the surface of the metal remains bright during the experiment, In this way the electrolyte is in constant contact with the metal and the inoculation which occurs can go on undisturbed. The photographic reproductions (natural size) which accompany this paper illustrate the development of the phenomenon. Fig. 1 shows a plate of pure lead in its original condition. Fig. 2 represents the plates after having been in contaet with the solution for some days; there are to be seen deep cracks, which show that the material has shrunk locally. In consequence of this an increase of the density was to be expected which was proved by means of the pyenometer (comp. § 19). Fig. 3 shows the plates after three weeks in the same conditions: the metal has been disintegrated. Repeating the experiment with 15 or 20 blocks we got in all cases the same results. 13. We shall prove below that the phenomenon is not a chemical one; the following experiment may give already an indication in this direction. One of the blocks (+= 40 grams) was put into a cali- brated tube which had been filled up with the solution mentioned. This tube stood in a small dish containing the same solution. After three weeks no evolution of gas had occurred, either at room tem- perature or at higher temperatures. 14. After this the phenomena described above were investigated by means of both the pyenometer and the dilatometer. A. Measurements with the Pycnometer. 15. We exclusively used the instrument (Fig. 4) described by Apams and Jounston'), following the indications given by the authors. Moreover we took the precaution of dipping the pycnometer into water before weighing (empty) and wiping the water off with a dry cloth. If this is omitted a slight error occurs. as the surface of the pyenometer is then not in the same condition as at the sub- sequent weighings, after it has stood in a (water) thermostat. All determinations were carried out in duplicate with two pycnometers (C and D) which contained = 25 cem. 16. Our investigations on bismuth, cadmium ete. had shown that the pyenometer measurements have to be carried out with special care. The volume changes which accompany the transformation of the 1) Journ. Americ. Chem. Soc. 34, 563 (1912). 826 different modifications are, it is true, not inconsiderable, but they may be partially compensated in consequence of the simultaneous presence of different forms. In order to detect the remaining volume changes, very accurate determinations of the density must be made. We shall see below that special precautions must also be taken with lead. Evidently it is to be aseribed to such compensations that these phenomena have escaped the attention of earlier authors. 17. We used toluene as a liquid in the pycnometer. Its density was found to be: 9KO d —~ 0.86013 by means of the pyenometer C. 4° . . 0.86013 nimi 8 D. The quantity of lead used for each determination was 40—-60 grams. The thermometers (divided into 0.05 degrees) had been checked against a standard of the Phys. Techn. Reichsanstalt at Charlotten- burg-Berlin. The weighings were carried out on a Bunex-balance with telescope. The weights had been checked by the method deseribed by TH. W. Ricuarps '). 18. In the first place we determined (at 25°.0) the density ot the lead immediately after its preparation for the experiments. It was melted, chilled in water and filed to powder. It was then treated with a magnet in order to remove traces of iron from the file. We washed the powder with dilute nitric acid, water, alcohol and ether, and dried it in vacuo over sulphuric acid. Its density was now: gro av d 7 11.325, (Pycnometer C). The metal was then washed and dried again in the same way ; ORO d =e 11.322, (Pyenometer D). After treating again in this way we 9FO a0 found d ie 11.324, (Pycnometer D). 19. We brought the metal into the solution of the acetate (temp. 15°). After standing for 3 weeks the material was washed and 95° dried. Its density was now d io 11.340, (Pycnometer C) 11.3842, (Pvenometer JD). 1) Zeitschr. f. physik, Chemie 33, 605 (1900), 827 The figures show that there has occurred at 15° an increase of 17 units in the third decimal place. 20. We put the metal again into the solution which was kept at 50° (in a thermostat) for 120 hours. We found after washing and drying [> ral e} d = 11.313, (Pyenometer C 11.312, (Pycnometer D). The density had decreased 28 units in the third decimal place. 21. The experiment was repeated again, this time at 25°.0 (in a thermostat) for 144 hours. 9ro We found: ie 11.327, (Pycnometer C) 11.3829, (Pycnometer D). An tinerease of 15 units in the third decimal place had occurred. 22. Our table I contains the results of these determinations: AT IN 18} VG EE 252. d 40 Without any previous treatment | 11.324 After treatment at 15° 11.341 s rf ee |} 11.3i3 | ” » n 25° | 11.328 B. Measurements with the dilatometer. 23. This investigation was carried out in the same way as has been described in the case of cadmium *). Some kilograms of lead were melted in a spoon and poured out into an iron form. The metal cooled in contact with the air. After filing it we treated it with a magnet and put it into the solution of the acetate. Here it remained (at 15°) for 15 X 24 hours. After this it was washed and dried in the way described above. We used + 600 grams in the dilatometer. (Bore of the capillary tube 1 mm.). 1) Proceedings 16, 485 (1913); Zeitschr. f. physik. Chemie 87, 409 (1914), 828 At 50°.8 the decrease of the level was 700 mm. (34 hours). 5 74°.4 5p rise 9 % . ” 275 oo) ( DH ” Ns Whilst the first preparation (§ 20) had shown at 50° a decrease of density, we now find an imerease. From this result we may conclude that there are more than two allotropic forms simultane- ously present. 24. Special attention may be paid to a phenomenon which we observed with all our preparations and which stands in close con- nexion with the fact that lead as it has been known up to the present, forms a metastable system containing simultaneously several allotropic modifications of this metal. It is generally known that when a bar of any metal which is more electro-negative (resp. electro-positive) than lead is suspended in a solution of a lead salt, the lead is thrown out of solution and a lead tree is formed. We found that the same phenomenon occurred when our pure lead was placed in the solution mentioned above or in a (neutral) solution of lead nitrate (30 grams of nitrate, 70 grams of water). Both at room temperature or at higher temperatures (50°) a lead tree was formed in a few days. 25. We are in the case of lead in specially favourable cireum- stances for the observation of this phenomenon. The galvanic current which is generated between the stable and metastable modification decomposes the solution. The metal which is electrolytically deposited *), shows in this case a characteristic form (lead tree) so that the phenomenon is very striking *). 26. We hope to report shortly on the different pure modifications of lead and their limits of stability. Utrecht, October 1914. van 't Horr- Laboratory. 1) That the phenomenon is not to be attributed to the presence of iron (0.0006 per cent) or copper (0.001 per cent) is proved by the investigations of OBERBECK {Wied Ann. 31, 337 (1887)] and by those of KénIGSBERGHR and MiLueER [Physik. Zeitschr. 6, 847 and 842 (1905). 2) We also carried out an experiment with tin: white and grey tin were putin contact in a solution of SnCl, (Temp. 15°). After some time a great many beautiful crystals of white tin were deposited by electrolysis upon the white metal. (Comp. Ernst CoHen and E. Gonpscumipt, Zeilschr. fiir physik. Chemie 50, 225 (1905)]. 829 Mathematics. — “On an integral formula of Stiuises.” By Prof. J. C. Kivuyver. (Communicated in the meeting October 31, 1914). In the Proceedings, and Communications, Physical Section, series 3, 2, 1886, p. 210, Stivites treats of definite integrals, referring to the function Y= == ‘ 1—y4 NI. In this function @ stands for a positive odd integer without qua- h a dratic factors, and ( ) represents LEGuNDRE’s symbol with the ex- tension given to it by Jacopt. nile As poles of the function f(y) only the points y=e* are to be taken into consideration, and for the residue, belonging to such a pole, one finds From the well-known fundamental equation ey ae > é a —7 2 sa Va h=1 a Qik it follows, that a pole is only to be found in those points y= e-¢ in whieh & is prime to a. Consequently y= 1 is not a pole of the function, and we have, 1 '=a—1 /), hy) == Gz a h=1 a from which it follows that —«af(1) is equal to’the sum of the : h numbers smaller than «, for which @E- (residues), diminished a . . 4 : be With the sum of the numbers smaller than a, for which ( i — 1 Ka, is (non-residues). In the paper quoted, Stipirsjus considers the definite integrals a <3) ee , tate: has. ata J (e—) sin da and aI f (e—*) cos dx, é 2a 7 2m 0 0 830 and he calculates the value of the first integral for the case a= 4w + 1, the value of the second integral for the case a = 4w — 1. . In the following I give a shorter deduction for these results. I suppose that the two positive, otherwise arbitrary numbers 3 and y have a for product, that ¢ is a positive parameter and now consider the integral pa file )aneas, In order to valeulate this integral, it is not necessary, as STIELTJES does, to fall back on an integral formula treated by Lecrnpre and by Aber. It need. only be observed that in the upper half of the complex v-plane for inereasing values of |.) the modulus of the integrand approaches sufficiently rapidly to zero, to permit us to equate the integral / to the sam of the residues in this upper half plane, multiplied by 222. Qnx The poles of the integrand are the poles of Fle 8 ie that is to E ki say the points z= —(#= 0,1, 2,:..), where & is prime to a. The ” ‘ residue of such a pole is 1 h=a=1 AN * | 5 LN ea é / SS ) ¢ | ( = a 2 ) Va = || Uo 2ay Swe any a hence a—| bey ees 7 _ 2akt a 1\2 a al eG, Pe i 2 ) > Ge v = 2 es 2 me a Y Nae Y We ought to distinguish now between the two cases a= 4w-+ 1 and a = 4w — 1. For a= 4w-+1 we have is wey seals (a= ie) =-+ ( =) and consequently / C B ) =—f fe B ) ; a a so that it follows from the result found for J, that 5 (ae /2 mee mc oe ree ee r). (c=40 - 1) ee) wv 2 0 On the other hand for a= 4w—-1 h =) == = .) ——— (=) and consequently / (« i ) = +s(4 i ) : a a so that in this case it may be concluded from the integral formula that 272 2rt a ; 2 {ole ip ) cos 2zta da =} ye = if (« 7 ; oe (@ — 4A es (OL) wy Y 0 nh | As may be proved the equation (II) remains true if we suppose ¢=0, and if the expansion in series 2r2 2rmx : ee 10 “m ss PEALE B = 2 — | |e B ' M11 Nea is made use of, we get in this exceptional case m =e m\ 1 ae rd ha 1 fe) Ss -}|—= — f(1) = — > ( h. (a= 4w — 1) ee MO Ya aya j= a The results found by Stipitses have been derived with this, the equations (1) and (I]) may now, however, be used, to find other results less known in the theory of numbers. For real values of « the function / (e~**) has the property of approach- ing rapidly to zero for positive and negative values of x of increasing modulus. This leads. to the conclusion that Fourimr’s general sum- mation-formula is $x n=+an a n= 43 => F(§+n) =| F(y)dy +2 XS | F'(y) cos 2arn (y—&) dy 1i—— © no as a may be applied, if we write (a) 7 aa £1 Distinguishing again the eases a=4v+1 and a=4w—1, the Se and if we suppose 0< value of the integrals in the right-hand member may be determined by means of the equations (I) and (Il). It should be taken into consideration in the summations in the left-hand member, that / (¢-*) changes ifs sign together with « or not, according as @ is equal to dw +1 or to 4 — 1. In this way the two following general equations are derived from the summation formula. One sa 2n(n--5) 2rn(n—é) Y oF pt) n= ES ze SS Ee, ih (« B ) 5H i(- le ) ==) (- 8 ) = ] i) | : p n= Zan | he fae = sin sani (« 7 ) , (a= 4w + 1) 7 n=!) Proceedings Royal Acad. Amsterdam. Vol. XVII. 832 p oa eee , _ onln-ts) ys 2n(n—F) \ ! (’ i ) = i(< : ) : I (« : ) | = ] =| (IV ) 7u=—= ; ae Q7n as} t ray HED) SS cos Bank « 7 )| te Y n=l If in both members of these equations the functions / are expanded into series, the summations indicated are to be executed still further. 1 shall, however, perform these reductions only for special values of the parameter §, in consequence of which the general results are simplitied. In the equation (IID) I substitute therefore §= 4, at the same time L replace 3 by g and accordingly y by 2y. I further write us T Be =f, Cin OKe The numbers g and g’ are then positive and smaller than 1; they satisfy the relation ! m* log qex log ns a but are for the rest arbitrary. In this way the equation (III) passes into re 3B n= 2S) (—1)" F (q+) — > (—1)" F(t), n=O of n—0 and if the functions / are expanded into series, we shall find | ; 1 ne (“) qn rs | i ] ven (=) q” a oO” — ——<—<——— og a aid = = ToD a= w+l (V “ qG m=1 a) 14-92" i rj} 3d Qh ( ) ) In the equation (IV) I substitute $—=0O. We have then in the first place : no i /B é 1S As 70) +2= Fq) =)" a) +25 70%, rm y N= and if again use is made of the expansion into series of the functions J we tind Vig | soya (2) 2. qd a y) = gFuc /, 1 Z LUE IL g2m / =! log ar) vay +23 ee ' (a = 4w—1) . (VI) qd m=1 \@ —q'2m The equations (V) and (VI) completely symmetrical with regard to y and gy’ are again conspicuous for the remarkable properties of 833 ; m : Ae, the arithmetical symbol ( For the rest they show some similarity ct with f formulae in the theory of the functions, and point to a ‘ ’ z 1 certain connection between the functions & (« a) and or " { Y So it may be observed, that, from the equation F ae A v, U, 4 1 re it) B mn gq” Fe (ea See Se a p p —_= 4 = —— ¢os 22 mv a t m1 l--qm Dv, Osho p a la @ fe: ment rn ap Or 0, <7 vo, (Nee = = SS a 4 B B h=1 r oe a e h 7 1 i iN US ig . (| B VA vd, 0, | v, (0, | ve = i { — = \@ ae (a = 4w + 1) ( 3) remains unchanged, if 3 is replaced by y In a similar way we conclude from (3) N v, — 1 B m=o tA CA = (ple - otunm + 4a S ——— sin 2x mv U m=1 [—gen « (Pas = B for the case a= 4w —1 to 7 ( | —=7— }) os a? We m= e6 27 Le Banded Oot BOSH feat (a 1 PUVA) san Ye? a I= a ae m1 We can prove now, that h=v—1 h ath >> ia 2Va Ff (1) h=1 a consequently it ensues from the aneaede (VJ), that the expression 5 ic -) 1 t=a—1 Sh ale a — 2 4 eS (a = 4w — 1) Vl jot NG € ,) a ee p holds its value, if 8 is changed into y on or * Physics. — “On unmiving in a binary system for which the three- phase pressure is greater than the sum of the vapour tensions of the two components.” By Dr. F. E. C. Scuerrrr. (Commu- nicated by Prof. J. D. van per WaAats). (Communicated in the meeting of Sept. 26, 1914). l.-In my investigation on the system hexane-water the remarkable phenomenon presented itself that the three-phase tension of the two liquid layers by the side of gas appeared to be greater than the sum of the vapour tensions of pure hexane and pure water‘). When the tensions of the pure substances at a definite temperature are denoted by P, and P,, the three-phase presstwe by /, then for temperatures which are not too far from the critical end-point | cae eee el a If we could speak of ‘partial pressures” for such an equilibrium, this result would be impossible. A proof of this is found in VAN DER Waats--Konnstamm’s “Thermodynamik’, which however is only valid when the gas-laws*) hold for the saturate vapours. When the vas-laws do not hold for the gas phases, in other words if the gases possess surface layers, the proof is not valid, and the statement that the three-phase pressure must always be smaller than the sum of the vapour tensions of the components, holds therefore only for rarefied saturate vapours. In my paper on the system hexane-water I have shown that the contradiction with the second law of thermodynamics, which at first sight may be supposed to exist in the observed phenomenon, is only an apparent one. We might, namely, be inclined to reason as follows: If the three-phase mixture possesses such a high pressnre, the pressure exerted by the water and hexane molecules, or at least that of one of them will have to be greater than the pressure of water vapour, resp. hexane vapour over the pure components. If we therefore bring the three-phase mixture by means of a semi-permeable membrane into contact with pure hexane and with pure water under their own vapour pressure, bexane or water will pass through the semi-permeable membranes from the three-phase mixture towards the pure liquid. We should then get splitting up of the three-phase mixture, whereas just on the contrary the so high three-phase pressure sets in of its own accord from pure water and pure hexane. This is in conflict with the second law of thermodynamics. 1) These Proc. 16. 404. (1913). 2) Thermodynamik. Il. S. 476. 835 I have shown in the cited paper that the conclusion that the three-phase mixture will expel water through a membrane permeable to water, is really correct, and that probably mutatis mutandis the opposite thing will apply to hexane. The error in the above reasoning lies therefore only in the very last conclusion. I have pointed out loc. cit. that it is, indeed, possible that two liquids, each under its own vapour pressure, mix to a three-phase mixture that possesses the property to get unmixed again into the pure components through semi-permeable membranes; that this is not in contradiction with the second law of thermodynamics, but that on the contrary this phenomenon will be frequently met with in my opinion, also for systems which do not present the special behaviour mentioned at the head of this paper. Thus solutions of gases which are but sparingly soluble in water will certainly expel water, when they are osmotic- ally brought in contact with pure water of the saturate tension. The observed phenomenon is therefore not in conflict with our theoretical considerations. 2. To get an answer to the question whether the system hexane- water presents an exceptional behaviour in the appearance of a three-phase pressure which is greater than the sum of the vapour tensions of the components, I have investigated a number of other systems in the hope of findiug the remarkable phenomenon there too. First of all I have chosen the system pentane-water. The pentane which I had at my disposal, was however KaAHLBAUM’s ‘normal pentane’, which is no pure normal pentane, but a mixture of normal and isopentane, which can only be separated with great loss of substance and time, as the boiling-points of the. two substances lie near room-temperature, and differ only little (slightly more than 8 degrees). This slight difference of boiling-point involves that the pentane mixture behaves pretty well as a pure simple substance; the isothermal pressure ranges for condensation are slight. I have therefore given up the separation of the two pentanes, and compared the vapour tensions of the pentane mixture and of pure water with the three-phase tension of a pentane-water mixture. It is clear that both the pentane mixture and the three-phase mixture must possess a tension dependent on the volume at constant temperature, but also the three-phase tension appeared to be only little dependent on the volume. To execute this comparison of the pressures as exactly as possible I have determined the pressures for final condensation and for about equal volumes of gas and liquids both of the pentane mixture and of the three-phase mixture. 836 TABLE I. a i = al | | Pentane mixture. | Pressure (atm.) Tem | =i a | | -, | perature. Erle : | V, =V condensation L G | 51S) es M65 | | | 151.9 | 17.8 | 161.1 20.6 | | 161.45 20.8 | 169.95 Pele | 170.1 | 23.7 180.1 21.6 | 180.3 27.8 \\ =a) | 190.25 32.15 | | | | i 400.30" i sS205).5 ul | 193.3 | 9) 33:6 TABLE II. Threephase mixture. Pressure (atm.) Tem- 2 a perature. Ende Vi Va condensation| 4 G 150.15 22.45 150.7 22.7 160.6 27.25 160.7 27.35 166.5 30.3 170.25 32),55 170.35 32.65 180.3 39.0 180.5 3925 | 187.1 44.1 When the values of pressure and temperature indicated in the above tables are graphically represented, it appears that the line for the end-condensation coincides fairly well with that which holds for equal liquid and vapour volume both for the pentane mixture and for the three-phase mixture: the difference is nearly everywhere smaller than O.1° atmosphere, and is therefore of about the same value as the errors of observations. When the pressure values are read for definite temperatures from the graphical representation, the values of table 3 are found. IWAVBsL ET | oe Three-phase | Pentane | ; Temperature | pressure pressure Waterpressure | Difference — _— — —_—____—_- —_ ————_——— | ————— — — == 150 22.4 7s} 4.7 0.4 160 27.0 20.3 6.05 0.65 170 32.4 23.7 7.8 0.9 180 38.8 27.6 9.8 1.4 187.1 44.1 30.7 11.6 1.8 The values for the vapour tension of water lave not been derived from earlier observations, but determined by myself to prevent an eventual deviation of the thermometer from vitiating the comparison. All the observations have been carried out with a normal thermo- meter, and with an Anschiitzthermometer verified by the boiling point of pure aniline. We draw the conclusion from the last column of table 3 that the three-phase tension is again greater than the sum of the vapour tensions of the pentane mixture and of pure water. The difference appears again to. be greatest at the critical endpoint —— in all thie tables the critical values are printed in bold type —; with decrease of temperature the difference decreases rapidly, and according to the theory it must reverse its sign at temperatures where the saturate vapours follow the gas laws. The above described example shows therefore again a case of very high three-phase pressure. Though these experiments would have to be repeated with the pure substances to get perfect certainty about the behaviour of the binary systems, the conclusion that the pentanes and hexane behave analogously with respect to water, seems yet sufficiently certain to me. Also the relative situation of the critical end point with respect to the critical points of the com- ponents is the same as for the hexane-water mixtures. Finally I will still point out that the above only proves that there exists a pentane-water mixture that possesses the repeatedly men- tioned remarkable property, and this suffices also for my purpose ; other proportions of pentane mixture and water will probably give rise to some change in the three-phase tensions because the pentane mixture is not a simple substance; for the solubilities of the two pentanes in water will probably not be in the same proportion as the quantities of the pentanes in the pentane mixture; the difference in the fifth column can therefore undergo some modification for another ratio of the two “components”. § 3. The experiments of § 2 confirming my supposition that the abnormal value of the three-phase pressure would be a phenomenon of frequent occurrence, | thought I had a great chance to find the same peculiarity also for other binary systems. I have therefore looked for binary systems of which it was known that for low temperatures the threephase pressure lies higher than the vapour tensions of the pure components separately and is about equal to the sum. Dr. Bicuner drew my attention to the systems carbon tetrachloride-water and benzene-water, which possess three-phase 838 tensions according to Rrexavir, which deviate little from the sum of the vapour tensions of the pure substances. ReGNauLT even asserted that the tension of carbon tetrachloride-water mixtures is somewhat higher than the sum, and thought he had to ascribe this to slight contaminations; GerNpz has shown later that the three-phase tension is really slightly smaller than the sum of the vapour tensions, which is therefore in harmony with the theory. I have now tried to inves- tigate the two systems at higher pressure; I have, however, not succeeded in doing so with the system carbontetrachloride-water, as the components act on each other at higher temperatures. The inves- tigation is possible for the system benzene-water, and also this system appeared really to furnish an example of the remarkable phenomenon. Benzene free from thiophene (negative isatine reaction) was distilled from phosphorus pentoxide; the boiling point under normal pressure was 80°.2, and was therefore in perfect concordance with the value given by Youne. The vapour tension line of this benzene was deter- mined, and then the three-phase tensions of a benzene-water mixture were measured and compared with the vapour pressure line of water, which was also determined by the aid of the same thermometers. To avoid corrections I have measured the three pressure values TAB ie AV: Temperature | Bo | Waterpressure | re | Difference 0 150.0 10.6 | 4.7 5.9 0 160.0 13.2 | 6.05 Tht 0.05 170.0 16.4 | 71.8 8.5 0. 180.0 20.1 | 9.8 10.2 0.1 190.0 24.6 12.35 12.15 0.1 200.0 29.8 15.3 [OS aks 0.2 210.0 | 35.9 | 18.75 | 16.7 0.45 220.0 | 42.9 | 22.8 19.45 0.65 230.0 50.9 | 27.5 22.5 0.9 2AO ele Ne e602355 9/0 8330 25.95 1.4 250.2 | 70.65 | 39.1 | 29.55 | 2.0 260.1 82.15 | 46.1 | 33.7 | 2:35 967.82 dul ok ode7 ‘cale.(52.4) ‘cale.(37.35) 2.95 268.2 | = 52.6 37.5 — | = 839 always at the same temperatures; if a slight error should occur in the absolute value of the given temperatures, this has no influence on the pressure differences. The thermometers which I used in this investigation, have been tested by a resistance thermometer, the resistance of which was determined for boiling water, naphthaline, benzophenon, and sulphur. The obtained results are given in table 4, the pressures are given in atmospheres. It appears from the last column of table 4 that the difference at 150° to 200° is only slightly greater than the errors of observation, that the three-phase tension becomes appreciably greater than the sum of the vapour tensions at 210°, and that this difference rapidly increases with ascending temperature. 4. When we combine the results of the system hexane-water and those of § 2 and 3, it appears that in the three systems the three-phase tension is always greater than the sum of the vapour tensions of the components in the neighbourhood of the critical endpoint. Moreover these three systems present the same shape of the plaitpointline in the 7-x-projection; the upper critical endpoint always lies lower than the critical points of the two components ; the plaitpoint line presents therefore a minimum temperature in the T-x-projection (homogeneous double plaitpoint). Though in my opinion it is probable that the systems will behave perfectly analogously, a furtber investigation would have to decide whether for all this homogeneous double plaitpoint lies in the metastable region; | have shown this for the system hexane-water in my cited paper. It is remarkable that in the system ether-water the homogeneous double plaitpoint appears in the immediate neighbourhood of the ether axis or would perhaps lie outside the figure, so that the eritical endpoint in contrast with the above discussed systems lies between the critical points of the components. In this system the said peculiarity does vot occur. Accordingly I think I have to conclude that the systems which present critical endpoints which lie lower than the critical temperatures of the two components possess three-phase pressures which are higher at high temperatures than the sum of the vapour tensions of the pure substances, whereas the opposite is the case for systems for which the critical endpoint lies between the critical temperatures of the components. Perhaps this conclusion may contribute to account for this remarkable phenomenon. Anorg. Chem. Laboratory of the June 25, 1914. Ae : : University of Amsterdam. 840 Physics. — “Contribution to the theory of corresponding states.” By Mrs. T. Exrunrest-Aranassyewa. D. Se. (Communicated by Prof. H. A. Lorentz). (Communicated in the meeting of September 26, 1914), § 1. Mestin') has tried to demonstrate that every equation of state which contains the same number of material constants as variables, is to be reduced to a universal shape (.e. to sucha form that no parameters occur any more which vary with the substance), if the variables are replaced by their relations to suitable special values, which may be designated as “corresponding” for different substances. On closer investigation it appears, however, that the equality of the number of the parameters and that of the variables is neither necessary nor sufficient for the existence of corresponding states. A method will be given here to decide whether a given equation allows the existence of corresponding states. This method furnishes at the same time the possibility to calculate the eventually corre- sponding values of the variables for different substances. § 2. In the first place we shall define the term ‘corresponding states” in a somewhat more general form. Let an equation be given between a system of nm variables: 7,,.v,,...%, and a number m of such parameters: C\, C,,...C, that they can vary with change of definite circumstances (for evample of the substance). Let an arbitrary system of special values: 2,',2,',...2,' (we shall briefly denote it by a) of the variables 2; be known, which satisfies this equation for definite special values C;' of the parameters C;. Let us introduce the following new variables: a, vs &y R= RS Se = = 2, vy an ee (ik All the constants S; of the thus transformed equation ean be calenlated as functions of the former constant coefficients, of the values Cy) and of the values 2,/. When the parameters C; assume other special values C;", other systems of special values of the variables will satisfy the original equation. The case may occur that there is among them such a system of values : }) Mestin: Sur lVéquation de vAN DER WAALS et la démonstration du théoréme des élats correspondants C.R. 1898, p. 180. S41 " . PL roy ht Uy Uy 02+ Uy that on the substitution of for vi, the constants of the transformed equation assume exactly the same numerical values S; as in the first case. We call such values Na ae Vat ald: thie state defined by the values 2;", correspondent to that defined by the ! a .t, correspondent to the values x,', x, 1? M1 9 Ug yee values a; (or corresponding to it). The form to which the given equation is reduced in this case XL vi by the substitution y; = —, resp. yi= — will be indicated by the Xi vi word universal. § 3. When for the system a; the system 2; corresponding to it has been given, the system aj" can be easily caleulated, which cor- responds with every other system 2’ of ; values, which satisfies the equation in the first case, by the aid of the following equations: Indeed the values 2;' resp. v;" satisfy the original equation, when the parameters C; assume in it the values (;' resp. Ci". When now the substitution ABS P ee ee ke ee 28) =f vi has been earried out, the constants S; which we have calculated, assume other values, e.g. S41, and we must now find the values 2", oD it) which keep the quantities Sj, invariant on substitution of Gy tom Ge when the substitution : hy i Geet ies) oo Gaetan ca) LY is carried out. The values x;', however, satisfying the given equation, ; Qe ya =, ly satisfy the transformed equation. The constants of the transformed equation do not change, when ll 9 f av; Vi " ! Ly Li) is substituted for Yar: 842 The fraction: " t 2; wey wi" wit! belongs therefore to the corresponding values ;", hence wv’ corre- sponds to ay". Hence it is proved that im the case of a system of values corre- sponding to a system of solutions, there also enists a system corre- sponding to every other system of solutions (when C;’ have been replaced by C;"). § 4. To find a system «;", if the system x,’ has been given, we take into account every product of powers of the variables: [OR (OES og 0 F Bain. <0 which appears as separate argument in the given equation. We shall therefore write the given equation as follows: @(K,P,, K,P,,..:: KePpj Ly Dy. 0. ti) = 0 K; and LZ; are constants with relation to 2;, Z; are those constants which do not oceur as factor of Pi, but in any other way. Among the A; and Z£; are therefore also included the variable parameters (for their funetions). Let us put that the constants A;, 4; in the first, resp. second case have the special values: K;', 0’, resp. Ky", 1," (those among them which are independent of C;, have the same values in both cases); they are to be considered as given. We can write every variable also in the following way : CS ge —— ie Yi- (05 If we put them in this form in the equation (7), it assumes the following form: D(Qi Pina. 2 Qe Lay) oe) 0 (8) in which Q) Kp! vo: ee Pg JOA gp (002 aon Pee (10) P:(y) = y ol yt? Wane yn tin Se (11) Now it is evidently the question to find such values z;" that when Ci' is replaced by Ci" and «2;' by @;", all the constants Q; and ZL; — eventually with the exception of one factor, by which all the terms of the equation can be divided — assume the same values. 843 When we carry out this division — let the factor in question be FR (it can be both one of the Q, and one of the Z;) in all A+/—1 constants remain, which can have four different forms: ee : lca The required 2;" must now satisfy the following equations: Q = &" Siena RR eae ee) L;' L;" Ses ae and besides the following equations must hold: Eko a eee titantron att). TLS) The number of equations (12), in which 2;" occurs, is quite independent of the number of mm of the variable parameters C;. When all equations (13) are satisfied, and all those among the equations (12) which do not contain a;", the three following cases can occur. 1. Equations (12) are in conflict with each other (a group of s of the sought values is defined by more than s independent equations. 2. They have one, or a finite number of systems of solutions. (It is required, though not sufficient for this that the number of independent equations in which 2;" occurs, is equal to xn. Hence m must not be greater than 7). Which of the systems of solutions corresponds with the given system ;', has to be decided by a further investigation in every separate case. This is the case in which we have corresponding states. / 3. They have an infinite number of systems of solutions. (It is required for this that m is greater than the number of the equations that are mutually independent). In this case we may speak of corre- sponding states for the same conditions (e.g. for the same substance). § 5. We shall now examine how Mesuin has come to another conclusion. Mersin starts from the conviction that all the constants of an equation are independent of the choice of the unities, when every variable in the equation bas been divided by a special value of it. This is perfectly correct. It is also true, as we have seen, that every equation can be reduced to a form as meant here. It is however not true that those constants that do not change throuyh exchange of the unities, would also have to be unive. sal. S44 Mrstin seems to be not quite free from a confusion, which is indeed pretty widely spread: between the change of a number occurring in an equation through change of unities, (“formal” change) and its change through transition to other conditions (to other specimens of the quantities which are measured by this number) (‘“‘material” change). In connection with this the assertion that in case of an equal number of variables and parameters the latter can always be com- pletely expressed in the former, is to be rejected. § 6. We shall illustrate what we have discussed by examples, which though fictitious, are as simple as possible. Their claim to physical signification, can indeed always be vindicated in this way that they are interpreted as equations for the geometric shape of some physical system. 1. y=ar’+ea+t+d QS23,. i=): a. Introduction of special values of the variables y BNE a Yo == ax,” rs ap vo =F b 0 Yo ey ‘ 6. Division by @,=¥,: y Dal ac a ae b Foes (joe =) |) fe SS Sh Yo Yo vy Yo Xo Yo c. Determination of the numerical values of the special values of the variables satisfying the equation and of the coefficients : 1 i ; ie—=10 a ax,” 1 Yo ab L, 1 Yo ab b 3S) Ile J) d. Determination of the system of corresponding values : ign l — — 2 ! Yo. ab Y= ae. 1 , b! = — — i yo! ab H ab b i Hep. capley 1 ale Me ath? ab’ 845 from which would follow that a'b'! = ab, whieh would be possible. only when we have really but one independent parameter. It follows, however, from the thesis of § 3 that if for one system of solutions there is not to be found a corresponding one, there does not exist one for any other system of solutions. Hence the given equation cannot be reduced to a universal form. 2. y=au? + abe + Db? (oh 2n rt 2) D BENE a i a Yo — =@e, + abe, — + b? Yo a oe b yo wef“ aby,c 6 ae aio ve Yo Y 0 a 0 Yo a 0 Yo ‘ —b t ys? : “= — a Gnas ae b? —— = | c i) = i : = = | Yo Yo Yo ' ! b d ye — 02 Co a 3. y Save? +e (rol) D az \* a a Uy = = Ge || I) Sa ae Yo x4 & 5, y vei ain (Z i ae eh Yo Yo vo Yoo 1 2 C. e, = H y= a a dine 1 ip. I =- ; —-=- Y «4 Yo 2 1 9 d i ; y= ; — : a a a 41). pu=A+t BIT CT? (35, 12 3) Pp v En ah bs 5 pp 2 a. Po% —— =A -f Blo TCL, r Poo 0 0 Gmp Diplo! ct A Al: BSB as Cie = OT. B : C As 7 independent of Cc T,*, the two last comparisons are contra- dictory, so that even if A= A’, we should not have corresponding states. Leiden, August 1914. 1) This example fails in the Dutch text. 846 Chemistry. -— “The nitration of the mixed dihalogen benzenes”’. By Prof. A. F. Honieman. (Communicated in the meeting of Oct. 31, 1914). When in benzene are present two substituents and a_ third is introduced, the substitution velocity caused by the two groups already present is unequal. From the data given in the literature it may be deduced that those velocities for the substituents poimting to the p-o-positions decrease in the subjoined order: OH > NH, > halogens > CH,. The question now arose how to express those velocities also in figures. Dr. Wipavut has done this for chlorine and methyl by determining - in what proportion the isomerides are formed in the nitration of o-chlorotoluene. In this compound the positions 4 and 6 are occupied, under the influence of methyl, by a nitro-group, the positions 3 and OU, 5 under the influence of chlorine. If now we determine Ns the proportion in which the mononitro-chlorotoluenes 4 —-+ 6 L ; are present in regard to the isomerides 3+ 5 in the N nitration product, this is then also the proportion of the substitution velocities caused by methyl and chlorine, because they can exert their action in this o-chlorotoluene independently of each other; for the positions which are substituted under the influence of methyl are different from those that ave substituted under the influence of chlorine. For this proportion was found CH, : Cl=1: 1.475. Dr. vAN pen AruND had previously determined the proportion in which the nitro-p-chlorotoluenes are formed in the nitration of p-chloro- toluene. If now, with the above mentioned ratio, we calculate the relative quantities, those calculated figures appear to agree approxi- mately with the observed ones. These researches, carried out in my laboratory, have now been continued, partly by Dr. Hrinkken, so as to determine also the ratios of the halogens. The method followed previously for the quantitative determination of the isomerides, namely by means of the solidification curves, could, however, not be applied here as the two nitro-p- chlorobromobenzenes give a continuous series of mixed crystals and because it was to be expected, on account of the fact that the properties of the nitrodihalogen benzenes present a strong mutual resemblance, that this would oceur in other cases also. Hence, for the quantitative determination of the isomerides present in the nitration mixtures, we made use of the property that a halogen in nitrohalogen benzenes is taken from the nucleus by Na-methoxide S47 only then when it is placed in the ortho- or the paraposition in regard to a yee Of the isomerides aes Ds Br ie iy Ome ne | Iv oe 3r NOs val I, IV and VI only chlorine, of If, IIL and V only bromine will be replaced by OCH,. Hence, if we determine the proportion in which chlorine and bromine are split off from the nitration product of p-chlovobromobenzene and trom that of o-chlorobromobenzene, we get at once the proportion wherein in the first nitration product I and II are present in the second one IV + VI on one side, UI + V on the other side. This method has also the considerable advantage that all the isomerides for the construction of the fusion lines now need not be prepared individually and that in the nitration products the various isomerides need not be separated; this latter attempt in particular would, presumably, have failed owing to insuperable obstacles. The results obtained are as follows Nitrationproduct of p-chlorobromobenzene contains 45,.2°/, of the Cl JNNOz compound | ; and 54.8°/, of the isomeride 1, 3, 4. NZ Br Cl cl Br NO, Bi Nutr. product of o-chlorobenzené consists of 55.5°/, of + NO, T\ ne th | ; orin molecular proportion 1 :0.80, Ye NON The substitution velocity caused by chlorine and bromine when and of 44.5°/, of present together in the benzene nucleus is therefore as 1: 0.80. When caleulating this proportion from the composition of the nitration product of p-chlorobromobenzene it must be remembered that in the nitration of chlorobenzene there is formed 30.1° , of the o-compound, but in that of the bromobenzene 38.3°/, of the same. If we eall wv the ratio of the velocities caused by chlorine and bromine we have 30.1 : 38.382 = 45.2 : 54.8, ob Proceediugs Royal Acad. Amsterdam. Vol. XVIL S45 from which «= 0.96. Hence, the result is here Cl: Br = 1: 0.96, The mean result of these two experimental series is therefore: Cle Br sAOrSse: The nitration of p-chloroiodobenzene caused the separation of large quantities of iodine with formation of p-chloronitrobenzene. Hence, for my purpose it was unsuitable. In the nitration of o-ch/oroiodobenzene, there was also some separation of iodine, but the formation of o-chlovonitrobenzene did not amount fo more than about 3°/,. When determining the proportion in which Cl and I were separated from the nitration product by NaOCH, a correction for this must therefore, be applied. For the velocity ratio Cl: 1 was thus found the mean value of 1:41.84. It now became interesting to also investigate the nitration product of o-bromoiodo benzene quantitatively as to its components. For, as Cl: Br was found —1:0:80 and Cl:1=1:1.84, Br:] should be = 1: 2.80, if indeed the two halogens present, aet quite indepen- dently of each other. Also in this nitration a little separation of iodine took place; the content of o-bromonitrobenzene in the nitration product was in this case 4.4°/,. Applying a correction for this the mean ratio Br: 1} 1:1.75 was found, which rather differs from the calculated figure. If, however, we caleulate the percentages of the isomerides with the ratios 1.75 and 2.380 the theoretical value gives 69.7°/, of the isomerides Br, 1, NO, = 1, 2,3 +1, 2,5, and the experimental value 63.6°/, which may be considered as a sufficient approximation 0 if we bear in mind the difficulties of these quantitative determinations. The conclusions from the above are obvious. Since it has appeared that two substituents simultaneously present in ortho- and in parapositions do not sensibly interfere with their respective actions in regard to a third entering group, we shall be able to calculate from the figures now found with sufficient probability in What proportion are formed the isomerides of other compounds, for instance in the nitration of o- and of p-bromotoluene. The above mentioned order of the substituents towards the decreasing substitution velocity caused by the same now becomes : OH > NH, >I >Cl> Br > CH,. Hence, the ratio OH: NH, and NH,:1 still remains to be deters mined. As, however, in the nitration of the iodoanilines great diffi- culties may be expected, A. F. H. Losry pr Bruyn has taken in hand a quantitative research of the nitration of o- and p-chloro- aniline in the above direction. As a preliminary result of his experi- 849 ments it may be mentioned that the ratio Cl: NH, is very large. The above velocity series must, therefore, be resolved into two parts: OH and NH, which cause a great substitution velocity and which are presumably of the same order of magnitude; on the other side the halogens and CH, with a lesser velocity, also of the sanie order of magnitude. A more detailed deseription of the above experiments will be published in the Recueil. Oct. 714. Org. Chem. Lab. University Amsterdam. Physics. — “The reduction of aromatic ketones. U1. Contribution to the knowledye of the photochemical phenomena.” By Prof. J. BorseKen and Mv. W. D. Congnx. (Communicated by Prof. A. F. Honinman). (Communicated in the meeting of October 31, 1914). I. The reduction of the aromatic ketones in a perfectly neutral medium. In our former communications?) we have shown that the reduction of the aromatic ketones does not proceed any further than to pinacone, which is presumably formed from the primary generated half pina- cone molecule by vapid polymerisation. The fact that in an alkaline medium hydrol is always obtained, must be attributed to the rapid transformation of the pinacone, under the influence of the hydroxyl- ions, into an equimolecular mixture of hydrol and ketone, the latter of which can be again reduced to pinacone. This explanation was confirmed by the study of the reduction of ketones by means of aluminium amalgam. Here is formed a mixture of pinacone and hydrol; the proportion in which these two substances are formed differs from ketone to ketone and now it appeared that the quantities of hydrol ran strietly parallel to the velocities with which the diverse pinacones are con- verted into a mixture of ketone and hydro! under the influence ef sodium ethoxide. Hence, aluminium amalgam in 80°/, alcohol may by no means be considered as a neutral reducing agent. The only modus operandi that gives the necessary guarantee that complete neutrality would prevail during and after the reduction is the action of the aromatic ketone on an alcohol under the cooperation of sunlight. The original intention of this part of the research, 1) Proc. XVI. p. 91 and 962 (1913). 56* $50 namely the tracing of the progressive change of the reduction, was soon attained by applying this method. A series of ketones dissolved in a great variety of alcohols and a few other substances, was exposed to sunlight (or to the light of the quartz-lamp); dn all cases where reduction set in, not a trace of hydrol was obtamed. The ketone was usually quantitatively converted into pinacone ; occasionally, namely with benzylaleohol and a prolonged exposure to sunlight a combination of the half pinacone molecule with a eroup of the benzylaleohol, namely triphenylglycol was obtained as a by-produet. *). When to the aleohol some ethoxide was added hydrol was formed, as was to be fully expected. Hence, we arrive at the result that in the reduction of aromatic ketones the hydrogen unites exclusively with the oxygen. The experiments were carried ont as follows : Quantities of 5 grams of the ketone were dissolved in 50 ce of 2 alcohol rendered carefully anhydrous *) and exposed in sealed tubes of common glass to direct sunlight. The drying of the lower terms was performed by successively boiling with CaO, allowing to remain over metalli¢ calcium at O°, and distilling; the higher ones were purified by distillation and both were then immediately sealed into the tube together with the ketone. After exposure to the light for some time, during which the course of the reduction could be traced by noticing the deposition of the sparingly soluble pinacone, the tube was opened, the pinacone was filtered off, the filtrate distilled, the residue united with the pinacone and in the distillate the aldehyde or ketone was tested and in some cases determined quantitatively. The exact details will be published elsewhere by one of us, a few remarks may suffice here. First of all was investigated the behaviour of benzophenone in regard to methyl, ethyl, -propyl, sec.-propyl, cso-butyl, n-heptyl, sec.-oetyl and cetylalcohol. The latter only was not attacked, not 1) This had already been noticed by Cramrctan and Sitper (B. 36, 1577 (1903)) ; the formation thereof is moreover a confirmation of our conception that as the first reaction product the half pinacone molecule is formed. *) Water acts in this reaction in a remarkable manner as a powerful negative catalyst; in 80°, alcohol no reduction takes place after exposure for months, whereas in absolute alcohol in the same conditions, about two grams of pinacone are formed during ten hours’ action of sun-light. 851 even at higher temperatures ; the mixture however, was of a fairly strong yellow colour. The other alcohols reduced the benzophenone in some sunny spring days, with the exception of methylalcohol which required a much longer time. The research was then continued with allylalcohol, geraniol, cyclo- hexanol, benzylealeohol, phenylmethylaleohol, benzhydrol and cinna- mylaleohol. Of these, the saturated alcohols reduced rapidly and quantitatively ; the allylaleohol was attacked more slowly with form- ation of acraldehyde (even after two months’ exposure to light, the acraldehyde was unchanged, thus showing that the light alone does not exert a polymerising influence on this mobile substance). The geraniol was also oxidized very slowly, the cinnamylalcohol remained unaffected (we will refer to this behaviour later). A few tertiary alcohols were also investigated; if was expected that these would remain unaffected and indeed this was the case with the dimethyiethylearbinol after two months’ exposure; during that period, diaethylmethylearbinol had generated 0,38 gram of pina- cone; with methyl-di-nu-propylearbinol the separation of pinacone started after a few days and after two months 0.7 gram bad formed. From this we notice that when the chain becomes longer, the activity of the hydrogen of tertiary alcohols gets enhanced, which enables it, with the cooperation of sun-light, to attack an aromatic ketone; what gets formed from the alcohol has not been investigated by us. From observations of Ciawician and SiLBer') it is known that the hydrogen of some hydrocarbons, such as toluene, is already active enough to cause this reduction. We have been able to show that also the hydrogen of the cyclohevane is transferred to the ketone, on the other hand, hydrogen itself was not capable of acting. Besides benzophenone some other ketones — particularly those that. were previously subjected by us to the action of aluminium amalgam — were subsequently exposed in alcoholic solution to the light. Nothing but pinacone was ever obtained, but the phenomena occurring in these photo-reactions induced us to systematically repeat a large part of these purely qualitative observations in such a manner that on using a very simple modus operandi a relatively-quantitative result was still obtained. 1) B. 48, 1537 (1910), Il. The photo-reaction: ketone +- hydrogen'= pinacone. In order to obtain a relatively-quantitative result we could make use of a constant source of light and allow this to act on the differ- ent solutions under the same conditions; for this purpose a small 7 em. quartz-mercury lamp was at our disposal. Yet we have em- ployed this method but rarely, for instance in continuous dark weather, because on account of the unequal distribution of the light, at most two little tubes could be placed in front of the lamp in such a manner that it might be assumed that they existed under equal conditions. When it had been ascertained by us that the reduction took place quite as well in ordinary white glass as in quartz, from which it appeared that a very large part of the actinie rays was situated in the visible spectrum, the experiments intended for comparison were carried out as follows: A number of equally wide tubes of the same kind of glass and having walls of approximately the same thickness were filled with the same quantity of solution, and all placed at the same distance in front of a white screen, which was placed close to a large labora- tory window. In this manner it was attained that the quantity of light that fell in the same time on each solution was practically the same, and perfectly comparable results were thus obtained. s It speaks for itself that even then only the figures of a same experimental series were mutually comparable. *). A photo-reaction is distinguished from a reaction in the dark by two points. It is of a lower and frequently of the O order in regard to the substance which is being activated and the temperature coefficient is smail. *) As we found that the active light was situated in the visible spectrum and that the alcohols do not absorb visible rays, the ketones are in this reaction the sensitive substances, and so we could expect that the quantities of pinacone would be independent of the 1!) Also comp. O. Gross Z. phys. Gh. 37, 168 (1901) and E. GoupBere Z. phys. Ch. 41, 1 (1902). *) The first property is due to the activation occurring in the outer layer; from the sensitive substance only a limited number of molecules can be raised by the same quantity of light to the same degree of activily; even at a moderate dilution, the reaction becomes, on this account, indevendent of the concentraticn of the sensitive substance and therefore of the O order. This applies to slowly progress- ing veactions where the sensitive substance can be rapidly supplied by diffusion frora the dark interior to the light zone. ketone concentration (in regard to the sensitive substance a reaction of the O order). By selecting the alcohol itself as a solvent the change in con- centration thereof could be eliminated. (Table 1). In order to determine the order of the reaction in regard to the alcohol, benzene was chosen as being a general, non-absorbing and non-reducing solvent. (Table Ia) (Chronologically these last experiments were made after the position of the active light in the spectrum had been ascertained; we, however, state them here because they enabled us to give a complete image of the course of the reaction.) We notice that this reaction is indeed independent of the con- centration of the ketone, but not independent, however, of the con- centration of the aleohol. As the quantities thereof had been chosen in such a manner that they were amply sufficient even at the slightest concentration, it follows from the figures obtained that the velocity of the pinacone formation is proportional to the concentration of the alcohol. *) Thus we may represent the reaction by the kinetic equation : Mpinacone) = K L, [Alcoh.| dt With a constant light-quantity, the velocity of the pinacone forma- tion thus becomes proportional to the alcohol concentration; how many molecules of the ketone act simultaneously cannot be ascer- tained in this manner. As, however, pinacone and aldehyde are formed and as according to the above equation one molecule of alcohol is attacked simultaneously, the reaction scheme becomes : €,H,OH -— 2(C,H,),CO = C,H,0 + (C,H,),(CO), ?). In order to learn the temperature coefficient the ordinary tubes (16 mm. diameter) were enclosed and sealed into a second tube (244mm. internal diameter); the intervening space was filled with conductivity water and now two of these tubes were exposed to light as deseribed, one of them being kept at 25°— 28° and the other at 752—78°*). 1) Here we have assumed that the change in concentration of the alcohol during each of the four experiments was so slight that it could be regarded as being constant; this, of course, is not correct and we really ought to have taken each time a portion from larger apparatus. In that case, however, the experiments would become much more complicated, because the light-quantilty did not then remain constant during the experiment. Hence, we have rested content with the above modus operandi which is sufficiently accurate for our purpose. *) For a mixture of ketone and benzhydrole we have proved this reaction scheme yet in another manner (see next communication). , 5) Compare Rk. LutHeR and F. Weiaerv, Z. phys. Ch. 58, 400 (190d). 854 TASB EGE aE ee eri |e reson j-— —--——- = = — — = Ist Series 1 0.1 gr. benzophenone 0.09 gr. _; entirely converted 2 | OP ses ; O23, 3 | 050g "A 0.34, 4 OWS, , 0.36, 5 l— , 5 0:36) 2nd Series 1 1 gr. benzophenone 0.47 gr. 2 Aa 9 0.49 ,, he F 0.49 ,, \3rd Series| 1 0.1 gr.ochlorobenzophenone 0.09 gr. , 5 | 025 , : sone entirely converted 3 | 0.50 ,, 1 0.38, 1 | OSs, %) 0.39 ,, Bie |) ng - 0.39 ,, 6 2— ,, * 0.38 ,, ea iat ea oeoso.e Lan | ee 0.41 ,, ASB EVE. Ta: won | Gaveentiation/e] CRLOG in) | Gunster ore aes (CsH;)2CO per 25 ce. pig eS | 1 0.2527 gr. or 1 eq. 0.08 gr. 1 2 05054 ar wean arc ayy 0.18 ., 2.25 3 MOLOS ais ee 5 O36 4.50 4 PAWN" 55 gy 13 sp 0.66 ,, 8.25 5 © (pure alcohol) 0.69 ,, | 855 More accurate experiments were not considered necessary as we did not care for the absolute value, but only for the order of mag- nitude of the temperature coefficient. Adjacent to the jacketed tube was also suspended an ordinary tube to ascertain whether the presence of the jacket had any influence on the pinacone formation. The subjoined table II gives a survey of some series of experiments. From these results it follows that the method is sufficiently accurate for our purpose, the ketone reduction is indeed a_ photo-reaction with a small temperature coefficient; this still falls below the mean stated by PLornixkow') of 1,17 per 10°. TABLE Il. Time of exposure 2—3 days. a eee | K N° | Contents of inner tube 2 oes pinacone 4" | Ay a = = = ] =e ee = oe a —— =, Ist Series) | | \ 1 gee (CgH5)2 CO in 25 ce. alcohol | 25°—28° | 0.45 gr. | without jacket | | | | | 2 | SAS tends: with eee | 0.76 ,, | | {+ 50° | 1.06 3 Ns Re Nile eae —78° 02a 2nd Series) | | 1 |. - . « . without jacket | 25°—28° | 0.44 gr. | 2 1p 6-0 6 oo co WAU IECG: Fi ORK | | | 50° | 1.065 3 WeMlerva tee ch SO my Skis, | ale =18e 0.96 ,, | | a \3rd Series 1 Ips (CICgH4)3COin 25cc. alcohol | 25°—28? | 0.27 gr. | without jacket | Be cals ses 7 with jacket ne al 0.35, | |: a0 | 1.095 | Sea 7°—18" | 0.55 ,, | bs BL = 1 | || | | 4th Series | | 1 . . . . . Without jacket | 25°—28° | | 0.24 gr. | 2 | aeecee? Gel swithtjacket ij | 0.30 ,, | + 50° | | 1.10 | ue re eae Cas | | 0.50 ,, | : i, ao L 1) Jon. Prornikow. Photochemische Versuchstechnik. p. 273 (1912), 856 That the temperature coefficient for orthochlorobenzophenone is really somewhat higher than for benzophenone seems to us rather probable, but this can only be ascertained by more delicate measu- rements '). The independence of the concentration and the very small tempe- rature coefficient now enables us to continue following this very simple method in the quantitative investigation as to the influence of the ketone to be reduced as well as of the reducing alcohol. Influence of the alcohol. The aleohols, as described above, were carefully dried over calcium and, after distillation, poured at once into the tubes containing two grams of ketone. These were then sealed and exposed to the light. These tubes were suspended at such a distance that they could not interfere with each other. The subjoined table gives two series of experiments, the first series was exposed for three and the second one for six days: particularly during the first days it was sunny spring weather. What strikes us here in the first place is the agreement in the action of the aleohols 2—6; the secondary propyl alcohol gets oxidised somewhat more rapidly. the amyl alcohol a little more slowly. In the latter case a strong yellow coloration sets in. Very much smaller is the velocity of the pinacone formation in the case of methyl and allyl aleohol; as no interfering yellow coloration occurred here and as the conditions were moreover quite equal, this different behaviour must be attributed to the particular position these alcohols occupy. Although we cannot yet enter here into an explanation of the process, if is obvious that the reduction of benzophenone will proceed all the more readily when in the conversion of alcohol into aldehyde (or ketone) more energy is set free. The absolute extent of this energy is unknown to us, but still some thermic data point to the existence of a parallelism in the 1) The remarkably greater reduction velocity in the jacketed as compared with that in an ordinary tube, must be attributed to the larger quantity of light which, owing to refraction in the jacket filled with water, falls on the inner tube. In fact nothing could be noticed of this inner tube when the tube was entirely filled; it looked as if the alcoholic solution has the width of the outer tube. In harmony with this observation, it appears that the ratios of the velocities in the four series namely 76:45, 70:44, 35:27 and 30:24 do not greatly diverge and are about equal to the proportions of the sections of the outer and inner tube 24; 16. (Compare Lurner and Weicert |. c. p. 391). 857 TABLE Ill. lyst Nee 2 gr. benzophenone in 25 cc. panes Remarks 1 | methyl alcohol 0.29 gr 2 ethyl alcohol 0.84 ,, 3 | n-propyl alcohol (Oates) — sy | faint yellow | coloration 4 | sec. propyl alcohol | ORE | | | 5 n. butyl alcohol On84 55 I 6 _amylalcohol (Bp. 130 -133°), 0.75 _,, Sires yellows | 7 allyl alcohol Ok25) | : Ratio | ies Sees | | | i’: 1 ete: = es ee iV methyl alcoho! | 0.49 gr. | 1.69 | ea ethyl alcohol Vea ae | lhe wltgTA | | yellow coloration 3f | n. propyl alcohol alts} a ea not much | 1.75 | | | increased 4’ sec. propyl alcohol L605; 1.58 ; x ( yellow coloration) 6 amyl alcohol (a. ab.) 1.05: |; par acre | 1.40 I solr ea allyl alcohol Q:42e 6 1.68 velocity of the reduction and the extent of the difference of the molecular heat of combustion of aleohol and the correlated aldehyde (or ketone). The greater this difference the more energy will be represented by the hydrogen atoms playing a role in that transformation. As the heats of evaporation of the alcohols on one side and of the aldehydes on the other side do not sensibly differ and as all we require lere are a few figures for comparison, a correction for this may be omitted here. We then find for these differences (according to data from the tables of Lanpoir-B6rnstein-Rota). (See table IV.) The heat of combustion of acraldehyde is not known, neither that of formaldehyde. There is, however, a statement as to meta- formaldehyde: if from this one calculates the molecular combustion as if it were a monomeride, the difference amounts to 47 cal. As, however, this also includes the heat of polymerisation the difference is presumably considerably less than 47 calories, 858 TABLE IV. a = ees vee 3 = methyl alcohol—(meta)formaldehyde lwernss 47.0 cal. e = ethyl alcohol—aldehyde 47.075; 5 g n. propyl alcohol—propionaldehyde 505 0ieny g 5 sec. propy: alcohol—acetone SOs 2 r amyl alcohol (?)—valeraldehyde Ac O las The two series of experiments of table II] were started at the same moment, the first was investigated after three and the latter after six days; when the converted quantity of substance is proportional to the quantity of light and no secondary hindrances occur, the proportion of the quantities of pinacone at each of the numbers 1:1’, 2:2’ ete. must be the same; these ratios have been inserted in the last column of the second series. We notice that this ratio is indeed almost constant except in the ease of amy! alcohol, where a hindrance in the form of an increasing yellow coloration is distinctly observed. Influence of the ketone. The tubes were filled with solutions of one gram of ketone in 50 ce. of absolute ethyl alcohol. Two series were exposed simulta- neously to the action of the light; the first was investigated after three, the second after six days. Some pinacones remain very long in supersaturated solution, hence the alcohol was always distilled off and the residue shaken with 80°/, aleohol so as to remove all unconverted ketone The subjoined table V gives the results obtained and the ratios of the velocities with those of the benzopinacone formation as unit. Table VI gives a similar double series; most of the ketones investigated here were not attacked. Table VIL gives a survey of the results obtained in amyl alcohol as solvent and as reducing agent. 1st. The velocity of the pinacone formation, according to this survey, is greatly dependent on the nature and on the position of the substituent. As regards the nature, there is only one group (the methyl group on the two para-positions (N°. 7)) that appears to accelerate the reduction velocity somewhat, for the rest the substitution causes a decrease in velocity. This decrease is strongest when the substituting group isa phenyl 859 TA'BLE V. | Quantities of pimacone Ratio. | Ratio of the Re- No.| Name of the ketone SeriesI Series i Series I Series I | with tat obo In grams In millimols. (CoB CO as unit 1 | benzophenone 0.41 0.85 1.12 2.32 2.05 io 2 | 2 chlorobenzophenone 0.12 0.25 0.28 0.58 2.07 0.25 3 | 3 chlorobenzophenone 2 +0.10 - 0.23 — +0.1 (from II) '4 | 4 chlorobenzophenone 0.32 0.75 0.74 1.73 2.34 0.66 5 | 4 methoxybenzophenone 0.39 0.80 0.92 1.88 2.04 0.82 6 | 4 methylbenzophenone 0.41 0.86 1.04 2.18 2.09 0.93 7 | 44’ dimethylbenzophenone 0.48 0.95 (off)| 1.19 — a 1.06 8 | 4 bromobenzophenone 0.51 0.98 (off) 1.— _ — 0.90 9!) | 44’ dichlorobenzophenone 1% 0.73 — 1.45 =| 0.63 (from II) 10 | 2.2.4.4’ tetrachlorobenzoph. 0.22 0.47 0.34 | 0.72 7512 | 0.30 11 | 2 chloro 4’ methyl ne | 0.27 | 0.55 0.58 | 1.18 2.03 0.52 12!) | 4 chloro 4’ methyl " 0.19 | 0.70 0.41(2), 1.50 3.66(?), 0.64 (from II) | ABE Vie 13. benzophenone 0.85 0. og (oft 2ESO | _ — 1 14!) | 4 phenylbenzophenone To | _ | _ — 0 15 | phenyl-~-naphtylketone a2 | es = | bs ue 0 16 | phenyl-3- 5 _ _ De el es — 0 17 | 2 methylbenzophenone _ == re es ere _— 0 18 | 3 methylbenzophenone | 0.80 | 0,96 (off) 2.03 — = 0.89 19 | 2.4.2’.4’ tetramethyl ,, ae a = | — = 0 20 | fluorenone } — |e Tels — 0 te | TABLE VII. Amy! alcohol as solvent. 21 | benzophenone ) Osis 0.97 (off) 2.05 | -- 22 1 22 | 2 chlorobenzophenone | 0.22 | 0.33 | 0.51 0.76 1.49 | 0.25 23 | 4 chlorobenzophenone 0.65 0.96 1.49 | 2.20 1.48 | 0.72 24 | 4 methylbenzophenone 0.74 0.96 (off), Hash} |) — | 0.91 25 | phenyl «-naphthylketone | _ | _ | _ | — — | 0) ') These ketones had not entirely passed in solution in the alcohol. S60 vroup, because 4-phenylbenzophenone (14) and the two phenyl- naphthylketones (J5 and 16) are not reduced. Halogen atoms and methyl groups do diminish the single substitution, but (with one exception) do not prevent the same. Para substitution has the least influence, ortho the greatest; this, however does not apply to the chlorobenzophenones (3), so that we can hardly speak of a universal rule. The symmetry of the molecule seems to accelerate the velocity. Whereas the 4-methylbenzophenone has a smaller velocity than the benzophenone (5), the 4.4’-dimethylbenzophenone has a somewhat greater one. The fairly considerable decrease in velocity in the 4-chlorobenzophenone (4) is not continued in the 44’-dichlorobenzo- phenone (9). In connexion with the considerable decrease in the 2-chlorobenzophenone (2) that in the 2.2’.4.4’-tetrachlorobenzophenone (10) is unexpectedly high. A remarkable fact is the slight influence of the methyl group on the meta position (18) in regard to the great one of the chlorine atom (8). 2nd. Of more importance is the fact that the aleohol, the reducing agent, is of very secondary significance as regards the ratio of the reduction velocities; this is shown from the comparison of tables V and VII. The ratio of the velocities in ethyl and amyi alcohol is practically the same. We have completed these observations with a few on methyl and propyl! alcohol, selecting methy! aleohol because the velocities therein are generally much less, whereas o-chloro- benzophenone with benzophenone were compared as ketones, because the velocities in ethyl (and amyl) alcohol differ strongly. The subjoined table VIII gives a survey of the results. thyl ketone | § TABLE VIII. fi kee = eras We ee: Sol. C,H5;OH, |) Sol.C;H,,OH, | Sol. CHg OH, || Sol. nC3H;OH, Ist Series |; 3rd Series || 4th Series 5th Series | ~-— |. |X Quantity Quantity | | Quantity | Quantity | in Ratio in Ratio | in | Ratio in Ratio | m.mols. | m.mols, m.mols. | | m.mols. | Benzophenone|} 2.32 | 1.0 2.05) 91 ek Art |) “2.93. ad /2Chloro_,, 0.58 0.25) 0.51 (0.25 | 0.46 | 0.24 || 1.08 | 0.27 | | | (Ne . | 1.73 | 0.66 || 1.49 | | 0.72 | [4methyl | 2.18 | 0.93 1.88 | 0.91 | | ] | | phenyl «-naph- } 9 | eel 0 | | | 861 First of ali it follows from this constant ratio that the hefore is prominent in the photo-reaction, that this passes into a photo-active condition. Further, that the diverse ketones are activated in a perfectly analogous manner in such a way that either a number of molecules (the same for all ketones) become photo-active, which molecules then react with the alcohol with a velocity specific for the ketone; or, a number of molecules specific for each ketone becomes activated which, with a definite velocity which is independent of the ketone, dehydrogenises the alcohol. A choice from these alternatives can only be made by a further study of the photo-reaction. The active light of the ketone reduction. The first attempt to ascertain the position of the active light in the spectrum has been made by Cramician and Sinper'). They in- vestigated, for instance, the reduction of benzophenone and alcohol, employing two photo-filters. As a red photo-filter was used a cold saturated solution of fluo- rescein in alcohol (thickness of layer 15 mm.) which extinguishes all light to 0.510 @; by adding gentian-violet the absorption could be raised to 0.620 «. As a blue filter served a 10°/, solution of cobalt chloride in alcohol which transmits rays of a wavelength less than 0,480 uw; a ereen band at + 0,560 w and a red one at + 770u remain, however, unextinguished. They arrive at the result that all the reactions with which they were engaged, took place under the influence of blue light. We have used a larger number of photo-filters and carried out the research in jacketed tubes; the inner tubes were those which were used by us in the other experiments; the intervening space was 15 mm. Above the liquid in the jacket the outer tubes were covered with black lacquer, so that none but filtered light could penetrate into the inner tube. As photo-filters were selected : I. Red: aqueous solution of chrysoidin *). Pe Greeny:) ©; » 9, potassium dichromate + acid green B. extra. ?) Blue and violet. ILI. 10°/, aleoholic solution of CoCl,. IV. Cold saturated aqueous solution of erystal violet 5 B. O.?). VALS 2 » 5 » acid violet 4 B. N. ?). VI. Solution of iodine in CCl,. 1) B. 35, 3593 (1902) 2) Colouring matters from the “Gesellschaft f. chem. Ind. Basel’. 862 In agreement with that found by Cramiciay and Sitper for the red fluorescein filter we found that the filters I and Il which only red (690—598 we) or red and green (> 500 uy) absorbed all actinic rays. Also V, which besides red rays of about 700 ue still transmitted blue and violet > 483 nu, completely prevented the reduction in the inner tube. On the other hand an important reduction took place with the filters 11], 1V, and VI which transmitted rays to the extreme, visible violet + 400 ay. The series of experiments were conducted in this way that a set transmit of four jacketed tubes with photo-filters were exposed to sun-light for some days in front of the white screen: the results are contained in the subjoined table. TABLE Ix. : ee | Quantity | = 7 5 : ; i | Photo- of N>. | Ketone in the inner tube | filter | pinacone Remarks Poel ae ee cee eae oe list Series | 1 2 gr.benzophenone in 25 cc,C,H;OH I 0 | 2 | : Il 0 entirely 3 ie il 2 converted 4 We IV 0.67 | . 2nd Series) 5 | « 4 Ill 0.85 | From the com- | parison of the 6 Jab, 0 | figures for III | | and IV with the 7 ne i AL 0.48 controlling tube with conduct- (conduct- ivity water it Sma . (2. ivity 1.28 | appears that | ? water there always | | takes place a ail as : Shae partial absorpt- I3rd Series ion of the actinic rays; this, how- | 9 2 gr. o-chlorobenzophenone lll 0.33 ever, isrelatively — | small and is pro- 10 Vv 0 | bably based on a general ab- 11 VI 0.28 sorption, which | in a_spectros- (conduct. | copic investigat- \, 2 | . |. ivity 0.42 | ion was readily ri observed. eel 863 Now with this method we can only get a very rough determination of the position of the active region, still it appears that the active rays are presumably situated in the violet and have a wavelength smaller than + 480 uu. In order to see whether in the beginning of the ultraviolet active rays were still present, a small jacketed tube was constructed from quartz, the alcoholic benzophenone solution was put into the inner tube and in the jacket a cold saturated solution of nitrosodimethylaniline') which absorbs all visible violet and blue rays and transmits ultra-violet ones of 400—280 uu. Neither in sun-light, nor in front of the quartz lamp did any reduction set in; from this we could conclude that the active rays were not situated in the ultra violet, but in the visible spectrum < 480 and > 400 au. A fortunate incident now came to our aid when we were engaged in determining the correct position of the active light. We had noticed that the ketones were converted with compara- tively great rapidity into pinacones by means of the HerAvs quartz- mercury lamp. ‘ The mercury spectrum must thus contain a great quantity of the chemically active rays. This spectrum exhibits a very intensive blue line at 436—434 wu and two violet ones at 407,8 uu and 404.7 wu?), Photo-filter V completely removes the violet lines and leaves the blue ones unchanged; as this filter in sunlight as well as in front of the quartz lamp prevents all conversion of benzophenone as well as of o-chlorobenzophenone, and as we have noticed that the ultra- violet light of the lamp is inactive we may conclude that the active light for the photochemical reduction of the aromatic ketones is situated in the extreme end of the visible violet. The fact that the nature of the source of light has no principal influence on the reduction process is shown from the subjoined table, in which are given the ratios of the quantities of pinacone that are formed from diverse ketones when exposed either to sun-light or mercury-light. The exposure to mercury-light was carried out by placing a solution of 0.5 gram of ketone in 15 ce of ethyl alcohol at a distance of 5 em from and parallel to the quartz lamp and exposing these for 10 hours; hence, the quantity of light was approximately the same for all ketones. The close agreement of these ratios also renders it probable that 1) Compare PLornixow etc. p. 19. 2) Lenmann, Plays. Zeitschr. 11, 1039 (1910), Proceedings Roya! Acad. Amsterdam. Vol. XVII. 864 TMA E IE, 0G 3 | ene of pinacone a Semen Gaenaes of to Hg light pinacone on No. Name of the ketone | in m.mols. Gite ligtt with beng in grams benzopinacone pinacone as as unit unit 1 benzophenone 0.35 1 1 2 2 chlorobenzophenone 0.10 0.23 0.25 3 4 chlorobenzophenone 0.30 0.70 0.66 4 2 methylbenzophenone 0 0 0 5 4 methylbenzophenone 0.34 0.89 0.93 6 phenyl z-naphthylketone 0 0 0 7 fluorenone 0 0 0 the active rays are situated for the greater part at 407.8 and 404.7 wa *). The action of light on mixtures of ketones. The phenomena observed by us during the exposure to light of ketone mixtures in absolute alcohol divulged a very strong mutual influence. In order to better understand these observations, the following should precede: We have noticed that the chemically active light comprises a very limited part of the spectrum, yet, therein are rays of different frequency and intensity. A. We can now suppose that each of the ketones present wants its own active rays without absorbing rays intended for the other ketone; then — as the pinacone formation is independent of the concentration — there will have formed in the tube with the mixture the sum of the quantities of pinacone that are formed in the separate tubes under the same conditions. Those quantities within certain limits must also be independent of the proportion of the concentrations of the ketones in the tube containing the mixture. 1) Presumably, the action is in a high degree selective, as a layer of 3 dm 4°/, benzophenone in absolute alcohol certainly caused a very distinct fading of these two mercury lines, whereas nothing could be noticed of a curtailing or fading at the violet side of the are lamp spectrum through that same liquid layer. We attach, moreover, not much value to this subjective observation, for only an accurate spectrophotometric investigation of the absorption spectra of the ketones can properly delermine the connexion between absorption and chemical action. 865 b. As soon, however, as rays for the one ketone are also con- sumed by the other one, the quantity of pinacone will be less than the sum in question and, moreover, the proportions of concentrations will no longer be a matter of indifference. For in the layer where the photo-reaction takes place each molecule of the one ketone requires a part of the light-energy also wanted by the second ketone, so that the hindrance experienced by the latter will become greater when its relative concentration gets less. C. The extreme case would be that both ketones require just the same rays; we should then obtain a quantity of each of the ketones which in equimolecular concentration is equal to half the quantity that forms in the tube with the separate ketone (always supposing that no other obstacles occur). The phenomena recorded by us are now best understood from the supposition B; a ketone does require specific rays from its neighbour. Some of the observations approach to A, others to C, some even exceed this extreme case, showing that the action is more complicated than was at first supposed, as will appear from the subjoined tabulated survey. HAGE I ENeX | Ist | Solution of 2 gr. of o-chlorobenzo- ind50cc, Quantity /Series phenone and varying quantities of Aohal pinacone Remarks No. phenyl z-naphthylketone in gr. } | og nr | 1 |2 gr. o-Clbenzophenone pure 0.84 |S, ES | ; ; ae ae 62 * +-0.1 gr. phenyl z-naphthylketone 0.30 5 5305S | eoFag 5 3 - SOIR 5 , PO) ea eee aI) coy ee! vas 4 +0,50 , i 0 Sesgeco. ” s} » tr oor aS - 5 ” ail ” » ” 0 ve Sd%a ea c& oc ° ees iS = = fe 3 s A v = esezas zie As above o-Cl benzophenone and varying Quantit jopaccite s above o- one ¢ ary uantity) , spe pees quantities of o-methylbenzophenone pinacone Remarks | i = BAN RIN : | 1 | 2gr. o-Cl benzophenone pure Ose 2 a +-0.1 gr.o-CHg3benzophenone 0.36 || ees és + 0.25 Fe 0.30 As above | 4 | . + 0.50 ; 0.26 j | fect i + 1 ; | 0.15 866 We notice that when one of the ketones does not get reduced it exerts a very powerful retarding action on the reduction of the other. ketone. This action, particularly with phenyl-e-naphtylketone is much more important than we should expect even in the extreme case C; besides the elimination of the chemically active rays, the molecules of the naphtylketone must cause an impediment, which may, perhaps be put on a par with the obstruction caused by oxygen in the photo-halogenations. TABLE XII. ree ewes - p> 3 Seo ol ee Solutions of various ketones, which are | 5 oo Re SEs N : : [See o2w | oes] Remark reduced separately in 50 cc. solution. SSS Bae | sso ole m°S|ros | ° = ; moe eT be eee lll 3 ee ee WN) | | = cH 1 2gr. benzophenone Neel ite |p - Boe. | | =%27y2 2~|2 > + 2gr.0-Cl benzophenone | 2.31 | 4.16 5 Eta 2.37 3.8) efea Su ane > +1» > 2ST} | 3.46 8 M4 ot oe oLor 7 : = es = 2 2f | sige jan oo 1 | 2gr. benzophenone 166" || 1667) a E Bus g | : Qa, 2 |2> > +2gr.pClbenzophenone 2.18 9.19 | | S°5E 2.76 1.2: Saas 3 |2 > +1» > 1.69 \ 3.19 | fees os a 2 ; ee (S788 ze | 338e oO oO | ats a | eels 1 2gr. benzophenone . 0.85 0.85 —_ = 5 2 ae WS Sw Qu | 2s > + 2gr.pBrbenzophenone | 1.65 | 23.9 | |= ae iS 1.95 19.0 | w@E& 3 12> r iis ‘ 1.05 |) 11.4 || \oe 8 From Table XII it appears that, in the case when both ketones are reduced, we have demonstrated a considerably less impediment than in the case that one of them is not reduced. Still, there is always a negative influence, we obtain in all cases a quantity less than the sum of the quantities which we should have obtained, in separate tubes; we are always dealing with case B. In this we notice the smallest mutual hindrance in the mixture of benzophenone and o-chlorobenzophenone, yet we notice plainly that the impediment increases when one of the ketones is present in large excess (18tseries N’. 3) and that in such a case that present in the smallest amount is the most strongly impeded. Much more pronounced is the hindrance observed with mixtures of benzophenone and p. Cl- or p. Br-benzophenone; the sum of the pinacones remains here far below the calculated quantity. The halogen ketone has as a rule a stronger impeding action than benzophenone, for even in smaller quantities than the molecular ones (N°. 2 of the three series) the halogen pinacone in the mixture is predominant. Only with a considerable excess of benzophenone the halogen pinacone is repelled and mostly so in the cases where the greatest hindrance is present (compare N°. 3 of the three series). We thus find in rough traits what we could expect; there occur, however, particularly when one of the ketones is not reduced separately, such great hindrances that they cannot be satisfactorily TABLE XIill. | Quantity Contents inner tube | Contents outer tube : Quantity of eer | Pinacone |pinacone in the | N.|2 gr. benzophenone in| 50 cc. abs. alcoholic | Ps inner tube with | < ; ; | #38 Y the blank tube | 20 ce. abs. aluohol | solution of 4 grams: 2 ej aan tit | : wn —- = = = = == = = ~ Vv ,n°s 25 n } Te | alcohol (blank-exper.) | 0.64 — | 1.— 2 p CH; benzophenone 0.28 | 0.66 0.44 aes | oCl benzophenone | 0.18 0.19 0.28 | | 4 | phenylz naphthylketone trace 0 | trace =F —— 77 == 4 ro | Sis] N VU) a Hele| alcohol (blank-exper.) 1.05 - 1.— | | Hee o CH3 benzophenone | 0.50 0 0.48 3 ‘phenyl-naphthylketone) 0.28 0 0.27 4 fluorenone 0 0 0 | wi a ———_=. ci aoa = 73 aeig) 6 5) w) | | 1 | alcohol (blank-exper.) | 0.79 | — 1.— 2 p Brbenzophenone | 0.42) 1,18~ 0.54 3 p Cl benzophenone 0.38 | 0.83 0.47 | 4 benzophenone 0.29 | 0.93 0.37 868 explained in the above cited manner. There seems to be a connexion: here between the extent of the impediment and the non-appearance of the photo-reduction. Now, in order to eliminate the hindrance which might eventually take place owing to the mixing, the oft-quoted jacketed tubes were filled in such a manner that in the inner tube was alivays inserted a definite ketone and in the jacket diverse other ketones, The light then first traversed a + 2 mm. thick layer ofa ketone then to exert ifs action on the benzophenone; in this way we could form a better opinion as to the absorption of rays of light by the one ketone (in the jacket) which were needed for the other ketone (in the inner tube). There exists no doubt that a// ketones absorb actinic rays intended for the benzophenone; the degree of this absorption is certainly very different and specific. The ketones which were attacked in the jacket were, during the experiment, reduced in concentration, so that the conditions for the reducing of the benzophenone in the inner tube gradually became more favourable; this causes, however, that we can only consider as fairly comparable the experiments where no reduction takes place in the jacket. Hence, a few ketones have been placed in the jacket in benzene solution whilst in the inner tube was again present a solution of 2 grams of benzophenone in 20 ec. of absolute alcohol ; the following result was thus obtained: TVAVB EE exw. In the inner tube | In the jacket a Quantity of N°.! 2 gr. (CgsHs),CO | N/4 benzene solu- | pinacone in the | Remarks in 20cc. abs. ale. tion of itmer tube. 1 — (blank) Pa 134e 91%) 1/50 | | | | The benzene 2 | benzophenone | 0.45 | OFS4 ea | solutiontaniaer a i a | i jacket was al- 3 o-chloro | 0.53 0.40 | | Ways coloured | S42 ~ pale yellow | as | Pp 0.34 0.25 | which colour rae | : é again faded in | 5 p-methyl » 0.40 0.30 the dane It appears that several ketenes absorb rays of light which effeet the benzophenone activation, even when they are dissclved in benzene. The reversible yellow coloration of this benzene solution, however, tells us to be careful, for the activated ketone can form with benzene R69 a light-sereen, thus causing the absorption effect to be greater than when the ketone had been present in alcoholic solution. In each case a circumstance oecurs owing to which the phenomenon becomes more complicated, so that from these last experiments we may at most draw the conclusiun that rays of light are indeed always absorbed by the one ketone, which the other required for the oxidation of alcohols. The most powerful absorbing ketones appear mostly — but not always — to oxidise the alcohol slowly or not at all, so that we gain the impression that a liberal absorption does take place, but that the possibility of the setting in of a reaction and its velocity does not only depend on the aleohol, but in a great measure on the ketone. It speaks for itself that the experiments on this almost quite unexplored region can only bear a very provisional character ; still we believe we have attained, with very siinple means and methods, some results which will prove of importance for the insight into the photochemical reactions. For the moment, however, we wish to refrain from an attempt to explain the phenomena observed until more accurate spectrophoto- metric data are at our disposal. SUMMARY. I From aromatic ketones and alcohol are formed, in the light, exclusively pinacones; these latter are, therefore, the products to be first isolated in the reduction. Hydrols are, in the reduct- ion of the aromatic ketones, always formed secondarily (see Proc. XVI 91 and 962) either from the pinacones or from the primarily formed half pinacone molecules. II 1. The photo-reduction - of the ketone by alcohols was studied by exposing simultaneously to the light a set of tubes of equal dimensions and filled with equal quantities of liquid, thus causing the light-quantity (i.t) for each object of a serial experiment to be equal. 2. The velocity of the pinacone formation appeared to be inde- pendent of the concentration of the benzophenone and propor- tional to the concentration of the alcohol. Hence, it satisfied the equation : d pinacone —= KT. [alcohol and, therefore, the reaction scheme: dt 2 ketone + alcohol = pinacone + aldehyde, 870 3. The temperature coefficient was small: 1.06—1.11 for 10°. 4. The velocity of the pinacone formation is greatly dependent on the aleohol; for instance, the methyl aleohol and the allyl aleohol were oxidised much more slowly than other primary and secondary alcohols. 5. The velocity of the pinacone formation is greatly dependent on the ketone, the benzophenone is attacked rapidly, most of the ketones as yet examined less rapidly, many not at all. 6. The ratio of these velocities in different alcohols is constant. 7. The aetive light of the ketone reduction is sure to be situated in the spectrum between 400 and 480 «qe and very probably in, or adjacent to, the rays 404.7 and 407.8 of the mercury quartz lamp. 8. The ratio of the velocities of the pinacone formation in sun- light and in mercury light is the same. <2 When two ketones are present simultaneously one of them absorbs a part of the rays required by the other ketone; this also appears when the light passes through a solution of the one ketone and falls on that of the other. Particularly in the case of the powerfully absorbing ketones the hindrances are stronger than was to be expected. Delft, October 1914. Physics. — “Simplified deduction of the formula from the theory of combinations which PLanck uses as the basis of his radiation- theory.” By Prof. P. Eurenrest and Prof. H. Kammrtincu ONNEs. (Communicated in the meeting of Oct. 31, 1914). We refer to the expression , (N—1+4P)! oN ™ ae )! (4) ted PN—1)! which gives the number of ways in which .V monochromatic reso- nators f,, R,,... Ry may be distributed over the various degrees of energy, determined by the series of multiples 0, ¢, 2¢... of the unit energy ¢, when the resonators together must each time contain the given multiple Pe. Two methods of distribution will be called identical, and only then, when the first resonator in the one distri- bution is at the same grade of energy as the same resonator in the second and similarly the second, third,.... and the Vth resonator are each at the same energy-grades in the two distributions. Taking a special example, we shall introduce a symbol for the distribution. Let NV = 4, and ?=7. One of the possible distributions 871 is the following: resonator A, has reached the energy-grade 4e (R, contains the energy 4s), R, the grade 2s, R, the grade Oe (contains no energy), R, the grade «. Our symbol will, read from left to right, indicate the energy of R,, R,, R,. R, in the distribution chosen, and particularly express, that the total energy is 7s. For this case the symbol will be: (EES 0FHO00H] or also more simply : ceeeOreQOr]] With general values of .V and P the symbol will contain P? times the sign ¢ and (.V—1) times the sign O'). The question now is, how many diferent symbols for the distribution may be formed in the manner indicated above from the given number of ¢ and O? The answer is (N—1+4P)/ el ee ea) Proof: first considering the (M—1-+ P) elements ¢...2, 0...0 as so many distinguishable entities, they may be arranged in (NGA OP Re tytn ee na 2, different manners between the ends ][ [[. Next note, that each time (NMRA PROT em inl ee UR (3) of the combinations thus obtained give the same symbol for the distribution (and give the same energy-grade to each resonator), viz. all those combinations which are formed from each other by the permutation of the P elements ¢7*) or the (N—1) elements 0. The number of the different symbols for the distribution and that of the 1) We were led to the introduction of the (N—1) partitions between the NV resonators, in trying to find an explanation of the form (NV — 1)! in the denomi- nator of (A) (compare note 1 on page 872). Pranck proves, that the number of distributions must be equal to the number of al! ‘‘combinations with repetitions of N elements of class P” and fur the proof, that this number is given by the expression (A), he refers to the train of reasoning followed in treatises on com- binations for this particular case. In these treatises the expression (A) is arrived at by the aid of the device of “transition from nton-+-1”, and this method taken as a whole does not give an insight into the origin of the final expression. *) See appendix, 872 distributions themselves required is thus obtained by dividing (2) by (3) q. e.d.*). AGP AE BENG DFIEXe The contrast between Purncx’s hypothesis of the energy-qrades and Einstein's hypothesis of energy-quanta. The permutation of the elements ¢ is a purely formal device, just as the per- mutation of the elements 0 is. More than once the analogous, equally formal device used by PLANCK, viz. distribution of P energy-elements over N resonators, has by a misunderstanding been given a physical interpretation, which is absolutely in conflict with PLANCK’s radiation-formula and would lead to Wien’s radiation formula. As a matter of fact PLANCK’s energy-elements were in that case almost entirely identified with Ernstern’s light-quanta and accordingly it was said, that the difference . between PLANcK and Erysrein consists herein that the latter assumes the existence of mutually independent energy-quanta also in empty space, the former only in the interior of matter, in the resonators. The confusion which underlies this view has been more than once pointed out *). EINSTEIN really considers P similar quanta, existing independently of each other. He discusses for instance the case, that they distribute themselves irreversibly from a space of NV, cm’ over a larger space of Ng em® and -he finds using BoutzMan’s entropy-formula: S = klog W, that this produces a gain of entropy %): 2 N,\P S— s, = ley (2) pete So. (3) ai 1) It may be added, that the problem of the distribution of N resonators over the energy-grades corresponds to the following: On a rod, whose length is a mul- tiple Pe of a given length -, notches have been cut at distances ¢, 2e, ete. from one of the ends. At each of the notches, and only there, the rod may be broken, the separate pieces may subsequently be joined together in arbitrary numbers and in arbitrary order, the rods thus obtained not being distinguishable from each other otherwise than by a possible difference in length. The question is, in how many different manners (comp. Appendix) the rod may be divided and the pieces distri- buted over a given number of boxes, to be distinguished from each other as the Ist 2nd,.... Nth, when no box may contain more than one rod. If the boxes, which may be thought of as rectangular, are placed side by side in one line, they form together as it were an oblong drawer with (N—1) partitions, formed of two walls each, (comp. the above symbol in its first form, from which the second form was derived by abstracting from the fact, that each multiple of < forms one whole each time), and these double partitions may be imagined to be mutually exchanged, the boxes themselves remaining where they are. The possibility of this exchange is indicated by the form of the symbol chosen. As a further example corresponding to the symbol we may take a thread on which between P beads of the same kind, (N—1) beads of a different kind are strung, which divide the beads of the first kind in a Ist, 2nd... Nth group. *) P. Enrenrest, Ann. d. Phys. 36, 91, 1911, G. KrurKow, Physik. Zschr. 15, 133, 363, 1914. 3) A. Eysrern, Ann. d. Phys. 17, 132, 1905, Sie i.e. the same increase as in the analogous irreversible distribution of P similar, independent gas-molecules, for the number of ways in which P quanta may be distributed first over N,, then over Ny cells in space, are to each other in the ratio INERT tas 5. Cate oe ee (O) If with PLanek the object were to distribute P mutually independent elements « over N resonators, in passing from N, to Nz resonators the number of possible distributions would in this case also increase in the ratio (=) and correspondingly the entropy according to equition (z). We know, however, that PLANncK obtains the totally different formula (V,—1+4+ P)! Ned SI (N= 1)! P! (N= 1) P! (”) (which only coincides approximately with (@) for very large values of P) and a corresponding law of dependence of the entropy on N. This can be simply explained as follows: PLancKk does not deal with really mutuaily free quanta < , the resolution of the multiples of ¢ into separate elements <, which is essential in his method, and the introduction of these separate elements have to be taken “cum grano salis”; it is simply a formal device entirely analogous to our permut- ation of the elements = or O. The real object which is counted remains the number of all the different distributions of NV resonators over the energy-grades 0, ¢, 2, ... with a given total energy P:. If for instance P= 3, and N=2, Erysretn has to distinguish 23— 8 ways in which the three (similar) light-quanta A, B, C can be distributed over the space-cells 1, 2. ae B= €C Teleie mete 1 Hee tari eee i te eee Wet, 22 op Bagh See VIP 2p yet. 2 Vil 2a ae VII | 2-2 2 PiaNncK on the other hand must count the three eases II, Ill and V asasingle one, for all three express that resonator R, is at the grade 2, R, at<; similarly he has to reckon the cases IV, VI and VII as one; R, has here ¢ and R, Qe. Adding the two remaining cases I (A, contains 3¢, Ry Oe) and II (R, has Oz, Ry Be) one actually obtains (N--1--P)! (2—1+8)/ Wren C= 37 different distributions of the resonators R), R, over the energy-grades. We may summarize the above as follows ; Etysrrtn’s hypothesis leads necessarily to formula (z) for the entropy and thus necessarily to Wren’s radiation-formula, not PLANCK’s PLANCK’s formal device (distribution of P energy-elements < over N resonators) cannot be interpreted in the sense of Etysrern’s ligit-quanta. (December 24, 1914). Q Akademie van Wetenschappen, 57 Amsterdam. Afdeeling voor Ads de Wis- en Natuurkundige Werk Wetenschappen pu. dL Proceedings of the Section Physical & Of Sciences Applied Sci. PLEASE DO NOT REMOVE CARDS OR SLIPS FROM THIS POCKET UNIVERSITY OF TORONTO LIBRARY STORAGE ~ Y4s